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0000000000000000000000000000000000000000..333b3557004dbd833281d2df896c37434a233e6e --- /dev/null +++ b/2024/Image Neural Field Diffusion Models/e632bc2a-df53-472b-b65b-a754db96e990_content_list.json @@ -0,0 +1,1486 @@ +[ + { + "type": "text", + "text": "Image Neural Field Diffusion Models", + "text_level": 1, + "bbox": [ + 295, + 130, + 673, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yinbo Chen1 Oliver Wang2 Richard Zhang3 Eli Shechtman3 Xiaolong Wang1† Michael Gharbi3† \n1UC San Diego 2Google Research 3Adobe Research https://yinboc.github.io/infd/", + "bbox": [ + 94, + 178, + 897, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d01dd13a4fd2c6cc81f34591355204926361717891bf905458923916ea59d39.jpg", + "image_caption": [ + "FFHQ Resolution: $1024\\times 1024$" + ], + "image_footnote": [], + "bbox": [ + 80, + 243, + 344, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c182bbfc05caec26c2e2b1b3dbe62d348f0d7696890e72ec6664eeb3f6e051e9.jpg", + "image_caption": [ + "Mountains Resolution: $2048\\times 2048$", + "Figure 1. Generated samples from our image neural field diffusion models. We show photorealistic high-resolution image generation by rendering generated image neural fields at $2\\mathrm{K}$ resolution for single domain models (left and middle), as well as general text-to-image models (right), with an efficient diffusion process on latent representation at only $64 \\times 64$ resolution." + ], + "image_footnote": [], + "bbox": [ + 351, + 243, + 616, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/799944e1f2383423cd5b9a48854b66a8f88ad2496addbeb5fbe89275c21c4983.jpg", + "image_caption": [ + "\"A cute corgi sleeping on a book, 4k\" Resolution: $2048 \\times 2048$" + ], + "image_footnote": [], + "bbox": [ + 622, + 244, + 890, + 383 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 464, + 313, + 478 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse problems without extra training. However, most diffusion models learn the distribution of fixed-resolution images. We propose to learn the distribution of continuous images by training diffusion models on image neural fields, which can be rendered at any resolution, and show its advantages over fixed-resolution models. To achieve this, a key challenge is to obtain a latent space that represents photorealistic image neural fields. We propose a simple and effective method, inspired by several recent techniques but with key changes to make the image neural fields photorealistic. Our method can be used to convert existing latent diffusion autoencoders into image neural field autoencoders. We show that image neural field diffusion models can be trained using mixed-resolution image datasets, outperform fixed-resolution diffusion models followed by super-resolution models, and can solve inverse problems with conditions applied at different scales efficiently.", + "bbox": [ + 73, + 484, + 470, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 820, + 207, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models [16, 34, 50] have recently become attractive alternatives to GANs. These likelihood-based models", + "bbox": [ + 75, + 845, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "exhibit fewer artifacts, stable training, can model complex data distributions, do not suffer from mode collapse, and can solve inverse problems using the score function without extra training. Since diffusion typically requires many iterations at a fixed dimension, directly modeling the diffusion process in the pixel space [17, 40, 43] can be inefficient for high-resolution image synthesis. Latent diffusion models (LDMs) [41, 57] were proposed as a more efficient alternative. The key idea is to learn an autoencoder to map images to a latent representation from which the image can be decoded back, and train a diffusion model on the lower-dimensional latent representation. Despite their success, LDMs' latent space still represents images at fixed resolution (for example, 256 in LDM [41] and 512 in Stable Diffusion). To generate higher-resolution images (e.g., 2K), LDMs usually first generate a low-resolution image and up-sample it using a separate super-resolution model.", + "bbox": [ + 500, + 464, + 890, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we propose Image Neural Field Diffusion models (INFD). Our method is based on the latent diffusion framework, where we first learn a latent representation that represents an image neural field (which can be rendered at any resolution), then learn a diffusion model on this latent representation. A key challenge of our approach is to learn a latent space of photorealistic image neural fields where the diffusion model is applied. We propose a simple and effective method that can convert an existing autoencoder of latent diffusion models to a neural field autoencoder. We find that directly implementing an autoencoder with LIIF [8]", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal advising.", + "bbox": [ + 101, + 886, + 192, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8007", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "leads to blurred image details, and propose a Convolutional Local Image Function (CLIF), which can render the latent representation to photorealistic high-resolution images and the image content is consistent at different resolutions. Our neural field autoencoder is trained with L1 loss, perceptual loss [60], and GAN loss following LDM [41], and is supervised from multi-scale patches similar to AnyResGAN [6].", + "bbox": [ + 75, + 90, + 467, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We show that image neural field diffusion models have several key advantages over fixed-resolution diffusion models: (i) They can be built from mixed-resolution datasets without resizing images. The neural field decoder can render latent representation at any resolution and from patches, which can take supervision from ground-truth images at arbitrary high resolution without decoding the whole image. (ii) The same latent representation can be supervised with GAN loss from fixed-resolution patches at different scales, with the content consistency across scales, the multiscale supervision helps high-resolution generation even if all ground-truth images are at a fixed high resolution. (iii) It does not require an extra Super-Resolution (SR) model for high-resolution generation. Besides the advantage of simplicity, since diffusion-generated low-resolution images do not have high-resolution ground truth, separate SR models are typically trained on real images, while the domain gap between real and generated images could significantly harm the performance of the SR model. (iv) Image neural field diffusion models learn a resolution-agnostic image prior. Therefore, it can be used to solve inverse problems with a set of conditions defined at different scales efficiently.", + "bbox": [ + 75, + 198, + 468, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are:", + "bbox": [ + 96, + 530, + 364, + 542 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An image neural field autoencoder that can learn representations from mixed-resolution datasets and renders scale-consistent and photorealistic images.", + "- A method to build diffusion models on mixed-resolution datasets and synthesize high-resolution images without extra SR models. Image synthesis is up to 2K resolution with an efficient latent diffusion process at only $64 \\times 64$ resolution (see samples in Figure 1).", + "- A framework to solve inverse problems with conditions applied at different scales of the same image." + ], + "bbox": [ + 76, + 545, + 468, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 709, + 217, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Models. Diffusion models are first proposed by Sohl-Dickstein et. al. [50]. They were recently connected to score-based generative models [51-53] and have been greatly improved [16, 34] for architectures and other training details, achieving state-of-the-art results on both unconditional and conditional image synthesis [11, 17, 33, 42, 44]. Compared to prior GAN-based methods [14, 21, 22, 38, 62], diffusion models have shown nice properties such as stable training, not suffering from mode collapse, and can perform image-to-image translation [28, 29] or be used to solve inverse problems [54], even with an uncondi", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tional model. One of the main drawbacks of current diffusion models is slow inference speed, as it relies on iterative reverse diffusion steps. While this can be remedied with faster sampling methods [23, 27, 46], performing the diffusion process in the pixel space of high-resolution images remains computationally expensive.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is most closely related to latent diffusion models, which learn to map images to latent representation and train diffusion model on the latent space [41, 47, 57]. A key design in this direction is to choose the latent representation where the diffusion model is learned. Different from prior works that learn an autoencoder, where the latent representation corresponds to a fixed resolution image, we design a decoder and a renderer to learn a latent space that represents image neural fields. Since our latent space represents image neural fields, our autoencoder can learn a representation from high-resolution images in varied sizes with multi-scale patches, and can synthesize images at high resolution without relying on extra super-resolution models. Our method follows LDM [41], which trains in two stages.", + "bbox": [ + 496, + 183, + 892, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Fields for Image Synthesis. Neural field is also known as Implicit Neural Representations (INR), which represents signals as coordinate-based neural networks. It serves as a compact and powerful differentiable representation and achieves state-of-the-art results mainly for representing 3D shapes [9, 30, 36] and scenes [2, 5, 19, 31, 37, 45, 48]. Applications of neural fields for images are explored in early works [32, 55] and proposed for more applications such as image super-resolution [8] and image synthesis [1, 49]. Several recent works [6, 22] relax the pixel-independent assumption and perform convolutions on the coordinate map to render the output for image synthesis.", + "bbox": [ + 496, + 405, + 892, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The idea of using neural fields for training with any-resolution images is explored in LIIF [8] for autoencoding with an L1 loss, AnyResGAN [6] and ScaleParty [35] for GANs with adversarial loss. Our work aims at building the resolution-agnostic learning framework for diffusion models, which is a different model family of generative models.", + "bbox": [ + 496, + 587, + 890, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Super-Resolution. Image Super-Resolution [7, 12, 24, 26, 56, 58, 61] (SR) aims at upsampling a low-resolution image to higher resolution. Many recent works [8, 18, 25, 59] explore Arbitrary-Scale SR (ASSR) with a single network. While they are related to our method, the differences include: (i) Instead of learning an autoencoder and an extra SR model, our implementation can be viewed as making a bottleneck in a single ASSR model and training diffusion models on the bottleneck. (ii) Our decoder is decoding from latent space to RGB space while super-resolution is upsampling from RGB space to RGB space. (iii) Our input can potentially have any higher resolution information (e.g. crops from high resolution), we choose it as a fixed-low-resolution image for efficiency.", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8008", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d0804231f9cdc9222a74fe51d6aa149bd1784bb563dea899f6c64b3e7c3e5f12.jpg", + "image_caption": [ + "Figure 2. Method overview. Given a training image at an arbitrary resolution, we first downsample it to a fixed resolution and pass it into the encoder $E$ to get a latent representation $z$ . A decoder $D$ then takes $z$ as input and produces a feature map $\\phi$ that drives a neural field renderer $R$ , which can render images by querying with the appropriate grid of pixel coordinates $c$ and pixel sizes $s$ . The autoencoder is trained on crops from a randomly downsampled image ground truth, generating image crops at the corresponding coordinates. At test time, a diffusion model generates a latent representation $z$ , which is then decoded and used to render a high-resolution image." + ], + "image_footnote": [], + "bbox": [ + 176, + 95, + 794, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "IDM [13] uses a diffusion model for ASSR where the output is at a medium resolution.", + "bbox": [ + 76, + 357, + 470, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 398, + 215, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our algorithm builds on diffusion models and neural fields. We introduce the core concepts and notation below.", + "bbox": [ + 76, + 424, + 468, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models. Given a sample $x_0$ from a data distribution $q(x_0)$ , forward diffusion progressively destroys the information in $x_0$ in $T$ steps, $x_{t-1} \\mapsto x_t$ , each adding some small Gaussian noise. The process can be concisely rewritten as $x_t = \\sqrt{\\bar{\\alpha}_t} x_0 + \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon$ , where $\\epsilon \\sim \\mathcal{N}(0, I)$ , and $\\bar{\\alpha}_{0\\dots T-1}$ gradually decreases from 1 to 0. The final distribution is approximately normal, $q(x_T) \\sim \\mathcal{N}(0, I)$ . A diffusion model learns to reverse this diffusion process. Once trained, new samples can be generated by first sampling $x_T \\sim q(x_T)$ and reversing each step of the diffusion process using a learned transition probability $p_\\theta(x_{t-1}|x_t)$ , parameterized by a neural network. Many prior works on image generation are based on maximizing a reweighted variational lower-bound of $p_\\theta(x_0)$ , which is shown by [16] to lead to the following training objective:", + "bbox": [ + 75, + 459, + 468, + 685 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathbb {E} _ {x _ {0}, t, \\epsilon} \\left[ \\left| \\left| \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) - \\epsilon \\right| \\right| ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 690, + 468, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t$ is sampled in $\\{0,\\dots ,T - 1\\}$ , and $\\epsilon_{\\theta}$ is the network trained to reverse the diffusion process.", + "bbox": [ + 76, + 714, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Fields. Neural Fields represent a signal using a coordinate-based neural network. For example, a neural field can represent an image as a function $c = f(x; \\phi)$ , where $x \\in [-1, 1]^2$ are the spatial coordinates in the image domain, $c \\in \\mathbb{R}^3$ is the RGB color at the corresponding continuous coordinate, and $\\phi$ denotes the parameters of the neural field $f$ . Since $x$ can take continuous values, the RGB value can be decoded at arbitrary coordinates. Accordingly, an image neural field can be rendered at arbitrary resolution by sampling the corresponding pixel coordinates.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 354, + 589, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similar to LDM [41], our approach has two stages. First, we train an autoencoder that converts images to latent representations of 2D neural fields ( $\\S 4.1$ ), which can be rendered to images at any given resolution ( $\\S 4.2$ ). Second, we train a diffusion model to generate samples from this latent space ( $\\S 4.3$ ). Figure 2 illustrates our pipeline.", + "bbox": [ + 498, + 381, + 892, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Image Neural Field Autoencoder", + "text_level": 1, + "bbox": [ + 498, + 483, + 787, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the first stage, we seek to convert every image in our training set into a photorealistic image neural field. We do this by training an autoencoder, made of an encoder $E$ , a decoder $D$ , and a neural field renderer $R$ . The encoder maps an RGB input image $I$ to a latent code $z = E(I)$ , which is decoded by the decoder to a feature tensor $\\phi = D(z)$ used by the neural field renderer to produce the final image.", + "bbox": [ + 496, + 508, + 892, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Patch-wise decoding. For training efficiency, we want to avoid decoding the whole image, because the ground truth can be at a very high resolution. We take advantage of the coordinate-based decoding property of neural fields, to train with constant-size crops from mixed-resolution data, which is amenable to batching. Specifically, we crop a random patch $p_{GT}$ at a fixed $P \\times P$ resolution (the red box in Figure 2) from a randomly downsampled ground-truth. Since $p_{GT}$ is a fixed-size patch, downsampling the global ground truth lets the patch $p_{GT}$ cover regions at varying scales of the image. This provides supervision at multiple scales to the latent representation, from local details to global structure. We discuss this further in § 5.2. Let $c$ denote the coordinates of pixel centers in the patch within the image, and $s$ denote their pixel sizes relative to the whole ground-truth image. Our renderer $R$ takes as input the features $\\phi = D(z)$ decoded from the latent representation, and the coordinates and pixel sizes $c, s$ to synthesize an output patch $p = R(c, s; \\phi)$ .", + "bbox": [ + 496, + 622, + 893, + 910 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8009", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a6ba6cea5ae75798a4151e4360863d9518d89c29629bdd4b74b131b60f446033.jpg", + "image_caption": [ + "Figure 3. Convolutional Local Image Function (CLIF). Given a feature map $\\phi$ (yellow dots), for each query point $x$ (green dot), we fetch the nearest feature vector, along with the relative coordinates and the pixel size. The grid of query information is then passed into a convolutional network (right) that renders an RGB grid. Different than the pointwise function LIIF, CLIF has a higher generation capacity and is learned to be still scale-consistent." + ], + "image_footnote": [], + "bbox": [ + 122, + 89, + 424, + 191 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training objective. We compare the synthesized patch to the ground truth using a sum of an $L_{1}$ loss, a perceptual loss $\\mathcal{L}_{\\mathrm{perc}}$ [60], and an adversarial loss $\\mathcal{L}_{\\mathrm{GAN}}$ [14]. The discriminator is simultaneously trained to distinguish between the distributions of $p$ and $p_{GT}$ . Thus, we minimize the following objective to train $E$ , $D$ , and $R$ :", + "bbox": [ + 75, + 306, + 468, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {A E} = \\left\\| p - p _ {G T} \\right\\| _ {1} + \\mathcal {L} _ {\\text {p e r c}} (p, p _ {G T}) + \\mathcal {L} _ {\\mathrm {G A N}} (p). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 412, + 468, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our implementation follows the autoencoder architecture of LDM [41], with the same encoder and decoder (removed the last layer) architectures to facilitate comparisons. Since training images have arbitrary resolutions, we resample the encoder's input to a fixed resolution $256 \\times 256$ . Note that despite this downsampling, we still train against mixed-resolution references. The encoder and decoder are with a spatial downsampling/upsampling rate of 4 correspondingly, therefore the latent representation is in $64 \\times 64$ . A vector-quantization (VQ) layer is prepended to the first layer of the decoder to regularize the latent space. $\\phi$ is $256 \\times 256$ with 128 channels. We set patch size $P = 256$ .", + "bbox": [ + 75, + 441, + 472, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Neural Field Renderer", + "text_level": 1, + "bbox": [ + 76, + 635, + 287, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our renderer $R$ , shown in Figure 3, is a neural field coordinate-based decoder, which we dubbed Convolutional Local Image Function (CLIF). To decode an image patch with CLIF, each query point $c$ (green dot) fetches the spatially nearest feature vector from the feature map $\\phi$ (yellow dots). We concatenate the nearest feature vector with the query coordinates $c$ and pixel size $s$ , then process the grid of query information using a convolutional network to output an RGB image. Intuitively, the concatenated feature is the field information at a point. By changing the query coordinates and pixel sizes, we can decode images at any resolution. LIIF [8] decodes with similar information, but it uses a pointwise function. We found this limits LIIF's ability to produce realistic high-frequency details (see supplementary material). CLIF remedies this issue by exploiting more local feature context. Our CLIF renderer is learned to be", + "bbox": [ + 75, + 657, + 472, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "scale-consistent, i.e., details are consistent when decoding at different resolutions (see supplementary material).", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Latent diffusion", + "text_level": 1, + "bbox": [ + 500, + 131, + 660, + 145 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the autoencoder is trained, we map every image $I$ in the training dataset to its latent representation $z$ , and train a diffusion model by optimizing the DDPM [16] objective", + "bbox": [ + 498, + 154, + 893, + 200 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D M} = \\mathbb {E} _ {z \\sim E (I), t, \\epsilon} \\left[ \\left| \\left| \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} z + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) - \\epsilon \\right| \\right| ^ {2} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 210, + 890, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "using the distribution over $z$ induced by the encoder. After training, the encoder can be discarded. The diffusion model generates a latent representation $z$ , which is then decoded to $\\phi = D(z)$ and rendered at a resolution specified by the pixel coordinates $R(c,s;\\phi)$ as described next.", + "bbox": [ + 498, + 241, + 890, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Patchwise Image Generation", + "text_level": 1, + "bbox": [ + 500, + 327, + 756, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Despite being trained with small patches for efficiency, our method can generate high-resolution images. For this, we first generate a global feature map $\\phi$ from a sampled $z$ , then generate sub-tiles of a large image by querying the renderer at the corresponding coordinates, as described in § 4.2. To avoid discontinuities at tile boundaries, we expand the query region for each tile by a fixed padding size larger than CLIF's receptive field (8 in our experiments). We then crop the output tiles by the same amount and assemble the tiles into a seamless composite. Our renderer is fully convolutional, it can also generate the image at once, as long as memory is sufficient to hold intermediate buffers.", + "bbox": [ + 498, + 349, + 890, + 531 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 546, + 632, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate our method on several datasets and compare it to LDM [41] with super-resolution models (§ 5.1). Sections § 5.2 and § 5.3 presents model ablations. We show results in solving multi-scale inverse problems in § 5.5, and text-to-image generation in § 5.6.", + "bbox": [ + 498, + 571, + 890, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data. The FFHQ [20] used in LDM [41] contains 70K high-resolution images $(1024\\times 1024)$ and several baselines use it for comparison. When comparing to LDM, we follow their training and validation split: 60K images for training and 10K for validation. Since our method is flexible and not limited to a fixed-resolution dataset, we also follow a controlled setting in prior work [6], which constructs a varied-resolution dataset from FFHQ by constructing and merging three sets: (i) all images at 256 low-resolution; (ii) a subset of 5K samples in varied-resolution from 512 to 1024; (iii) a subset of 1K images at 1024 resolution. We denote this setting as FFHQ 6K-Mix. Besides FFHQ, we evaluate our method on the Mountains dataset [6], which contains a low-resolution subset, with about 500K samples around 1024 resolution, and a high-resolution subset, with about 9K images at resolutions beyond 2048. Figure 4 shows examples of our generated results on these datasets.", + "bbox": [ + 496, + 652, + 893, + 910 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8010", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e5766754da577df85022f2b9067b28810c9c6f25bff81783d5a882434e609088.jpg", + "image_caption": [ + "Figure 4. Generated samples from our method on FFHQ and Mountains dataset." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 893, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pFID metric. Standard FID evaluation first resize images to 299, which evaluates the global structure of images regardless of their original resolution, but is insufficient to measure the quality of details from high-resolution generators. Patch-FID [6] (pFID) addresses this limitation. It computes the FID between fixed-resolution patches cropped from arbitrary resolution ground-truth and generated images, thus evaluating local details in synthesized images.", + "bbox": [ + 75, + 446, + 468, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The original pFID reports the metric on random crops from images at varying resolutions. Since our practical focus is on high-resolution synthesis, we evaluate pFID between patches cropped from fixed-high-resolution images. To further disentangle the evaluation for image details at different scales, we separately report pFID for patches at different resolutions. $P / 1\\mathrm{K}$ will denote the FID between random crops at resolution $P$ from ground truth and synthesized images at resolution 1024. For example, pFID-256/1K evaluates the local details, pFID-1K/1K evaluates the global structure and is the same as standard FID applied to 1024-resolution images. We generate 50K samples to compute FID in most experiments. In some experiments, we use 5K samples if it suffices to observe the performance gap (specified after FID@ in Tables).", + "bbox": [ + 75, + 570, + 470, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Comparison to LDM", + "text_level": 1, + "bbox": [ + 76, + 814, + 274, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LDM [41] trains an autoencoder for images at $256 \\times 256$ resolution and learns a diffusion model on its latent space. For a fair comparison, we used the same encoder and decoder architectures as LDM. Our method only adds a lightweight", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CLIF renderer, which contains 2 convolution layers and 2 ResNet [15] blocks.", + "bbox": [ + 498, + 446, + 890, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Even though LDM's denoiser is fully convolutional and can generate high-resolution images simply by diffusing from a larger noise map, it is known that this approach generates repetitive patterns (e.g., distorted faces with duplicate features), we show examples in the supplementary material. As a result, we follow the standard approach to generate high-resolution images with LDM by running an independent super-resolution model on its output. We combine LDM with several recent state-of-the-art arbitrary-scale super-resolution methods: LIIF [8], ITSRN [59], LTE [25], which allow for inference at continuous upsampling scales, and Real-ESRGAN [58], a super-resolution model for a fixed upsampling scale that has state-of-the-art perceptual quality. We report qualitative results in Figure 5, and the pFID in Table 1 on FFHQ. As Real-ESRGAN shows the most competitive results, we also compare to it on Mountains dataset in Table 2.", + "bbox": [ + 496, + 484, + 892, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We find that for standard FID at 256 resolution (i.e. pFID 256/256), the image neural field diffusion model is competitive with the original LDM, which can only generate images at 256. Our retraining of LDM reaches a slightly worse FID than the officially reported scores, which we attribute to implementation differences and training variance. At all higher resolutions, our method outperforms LDM followed by super-resolution, which is consistent with our qualitative observation and suggests we achieve better image quality for high-resolution detail at different scales.", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8011", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cb12a73ef95595989ef118da020081747bac5c4685f9683b19a03042542020c5.jpg", + "image_caption": [ + "$\\mathrm{LDM} + \\mathrm{LIIF}$" + ], + "image_footnote": [], + "bbox": [ + 80, + 93, + 230, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0638ad6c7b2a2c8695e8e6edb91a48c5d8a79b9d76af42af721b9797fad1d502.jpg", + "image_caption": [ + "LDM + Real-ESRGAN" + ], + "image_footnote": [], + "bbox": [ + 253, + 93, + 405, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/40cd23083a74e3e54735eb05e573737129de8c85da10001c7cd847a344d7881f.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison with LDM followed by super-resolution on FFHQ. LIIF shows noise in details, while Real-ESRGAN tends to be smooth and results lack rich details. Our approach generates images with more realistic details." + ], + "image_footnote": [], + "bbox": [ + 410, + 93, + 560, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ae482dead9ef4fff3cc2b4b0db33b0667a5c73c826432a063e2168c05306085.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 584, + 93, + 733, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2a5366167c187ecf862aa2d6136bd3944f7405704c9673aff92ef262f9ed3006.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 93, + 888, + 210 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2d2b8e8f14e0fe1b5d3c6403229c3d679dd6340ed3e1743b02f20de657804845.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Model#ParamsCoordinate-based DecoderpFID@50K
256/256256/1K512/1K1K/1K
LDM [41]33.0M4.98---
LDM + LIIF [8]33.0M + 22.3M✓-56.6517.838.97
LDM + ITS RN-RDN [59]33.0M + 22.6M✓-51.7317.948.02
LDM + SwinIR-LTE [25]33.0M + 12.1M✓-52.6217.729.09
LDM + Real-ESRGAN [58]33.0M + 16.7M-18.3818.4616.04
LDM (our reimplementation)33.0M6.02---
INFD (ours)35.7M✓5.348.076.645.57
", + "bbox": [ + 109, + 273, + 859, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We hypothesize that the main issues for extra superresolution models are that: (i) LDM with an extra superresolution model can be viewed as first decoding the latent representation to RGB space, then upsample to another RGB space, where the first RGB space becomes a bottleneck that contains much less information than feature space; (ii) the artifacts generated by LDM, even inconspicuous, can cause a domain shift to the input of the superresolution models, which could significantly degrade their performance. The super-resolution models can not be directly trained to upsample the generated low-resolution images since no paired high-resolution ground truth is available. In our method, the domain shift from real to generated samples happens in the latent space (with VQ or KL regularization). We hypothesize that latent space is much more robust than RGB space to the domain shift. We observe that when replacing the latent space with RGB space, the generated images become overly smooth similar to LDM with Real-ESRGAN super-resolution, which is consistent with our hypothesis (see supplementary material).", + "bbox": [ + 75, + 489, + 468, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Effect of scale-varied training", + "text_level": 1, + "bbox": [ + 76, + 801, + 341, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Randomly downsampling the global image before extracting fixed-resolution training patches would make patches cover all scales. With the scale consistency of CLIF, an image neural field is supervised to be realistic in all scales via the perceptual and GAN losses. We conduct an ablation on", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/aa2375196e19b9cdfbcb69d434ac437ea216a567c7c3417ca6f0d66ccafa5c0a.jpg", + "table_caption": [ + "Table 1. Comparison to Latent Diffusion Model (LDM) with super-resolution models for high-resolution image synthesis on FFHQ dataset. #Params counts for the decoder, and the renderer or super-resolution model if it exists, which are used in image generation." + ], + "table_footnote": [], + "table_body": "
ModelpFID@50K
256/1K512/1K1K/1K
LDM + Real-ESRGAN [58]17.3615.1110.39
INFD (ours)7.536.845.13
", + "bbox": [ + 506, + 486, + 883, + 564 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison to Latent Diffusion Model (LDM) with super-resolution models on Mountains dataset.", + "bbox": [ + 498, + 574, + 890, + 602 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FFHQ to evaluate the impact of this random downsampling strategy. Specifically, we disable it during training, keeping all ground-truth images at 1024 resolution. The results are shown in Table 3. Without random downsampling, the pFID is worse especially for $512/1\\mathrm{K}$ and $1\\mathrm{K}/1\\mathrm{K}$ , suggesting that random downsampling of the ground truth improves quality, even if we only aim at generating images at 1024 high resolution, because it helps supervise every single image to be realistic at all scales. For Mountains dataset, we observe that there will be obvious artifacts without random downsampling (see supplementary material). This contrasts with the observation in LIIF [8], which found that random downsampling hurts performance at a fixed highest scale when it is only using an L1 loss.", + "bbox": [ + 496, + 611, + 892, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Training with limited high-resolution images", + "text_level": 1, + "bbox": [ + 498, + 832, + 877, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While previous experiments use high-resolution training images, a key advantage of our method is that it can learn from mixed-resolution datasets and still generate", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8012", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/58d766aabc36b00ffc14dcb968413992e893f559e46d14740f4f00bc7bac2015.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DownsamplepFID@50K
256/1K512/1K1K/1K
Fix 10248.196.826.04
256–10248.076.645.57
Δ0.120.180.47
", + "bbox": [ + 125, + 88, + 416, + 186 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/407600f70a46a24d75582f3ece3bef9e23b351692a3bb15046e796641b6664a6.jpg", + "table_caption": [ + "Table 3. FFHQ dataset. Random downsampling during training improves image generation quality even for fixed high resolution." + ], + "table_footnote": [], + "table_body": "
DatapFID@50K
256/1K512/1K1K/1K
All HR8.076.645.57
6K-Mix16.2710.811.3
6K-Mix, bal.12.417.746.9
", + "bbox": [ + 127, + 222, + 415, + 319 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. FFHQ dataset. Our method can learn from mixed-resolution images with a limited number of full-resolution images.", + "bbox": [ + 76, + 325, + 467, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "high-resolution outputs, even when the number of high-resolution images is limited. We quantify this in Table 4 using FFHQ 6K-Mix, where most images are at low resolution 256, 5K images are at 512-1024, and 1K images are at 1024. Training with the mixed-resolution dataset as-is (also with random downsampling) already yields a model that performs decently at 1024, but with worse details than the model trained with all images at 1024. We suspect that the model is optimized for too few steps using images at 1024, since the number of high-resolution images is small and they go through random downsampling. We balance the training resolution by sampling images from the $5\\mathrm{K}+$ 1K high-resolution subset with a probability of 0.5. This largely closes the performance gap (6K-Mix, bal.) with the model train on high-resolution images only.", + "bbox": [ + 75, + 368, + 468, + 594 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Image generation beyond 1024", + "text_level": 1, + "bbox": [ + 76, + 603, + 348, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We explore going beyond the 1024 resolution and train our model on a collected dataset of faces at varied resolutions between 1024 to 2048, and on Mountains dataset including a higher-resolution subset (a generated sample is shown in Figure 1). We observe that our method can be effectively applied to resolutions up to $2\\mathrm{K}$ . More samples and details are in the supplementary material.", + "bbox": [ + 75, + 626, + 467, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Inverse problems with conditions at any scale", + "text_level": 1, + "bbox": [ + 76, + 741, + 460, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method builds a diffusion model on a latent space that represents image neural fields. A key property of image neural fields is that they can be efficiently rendered for any sub-region at any given resolution without decoding the whole image at full resolution. With the image prior learned by diffusion models, it enables efficiently solving inverse problems where conditions can be defined on any scale of the image based on coordinates. We take zero-shot any-scale layout-to-image generation as an example. It uses", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a265c2fa2958547b89f377113bb0457cc15a30fe13ee9f22ec712a88c02bb673.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/105169e3999789e502224981fa172c5d8e7eaeff54966a1acf816472549a86e9.jpg", + "image_caption": [ + "Figure 6. Solving inverse problems with multi-scale conditions per image. We can solve for an image that satisfies multiscale conditions, defined as square regions and a text prompt (left). For this, we decode the corresponding region and pass it to a pre-trained CLIP [39] model operating at fixed-resolution $(224 \\times 224)$ , and maximize the CLIP similarity to the corresponding text prompt. This enables layout-to-image generation without extra training. We show generated solutions on the right." + ], + "image_footnote": [], + "bbox": [ + 501, + 166, + 890, + 241 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CLIP [39] similarity as the constraint for image generation with semantic bounding boxes at arbitrary scales.", + "bbox": [ + 498, + 369, + 890, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, we take a pre-trained CLIP model, which takes $224 \\times 224$ fixed-resolution images as inputs. Given a layout and our image neural field diffusion model (unconditional), in each diffusion step, let $z$ denote the current denoised latent representation, for each semantic bounding box $i$ in the input layout we render $z$ for the corresponding sub-region to a patch at the resolution $224 \\times 224$ , i.e. patch $p_i = R \\circ D(z; c_i, s_i)$ , with our decoder $D$ and renderer $R$ , where $c_i, s_i$ denote the coordinates and scale of a $224 \\times 224$ pixel grid of bounding box $i$ . The clip similarity loss $l_i = \\mathrm{CLIP}(p_i, T_i)$ is computed between patch $p_i$ and the given text $T_i$ . The gradients $\\frac{\\partial l_i}{\\partial z}$ are back-propagated and then used to modify the diffusion score for each diffusion step. We follow the techniques in DPS [10] as the inverse problem solver. Figure 6 shows the results of using our mountains model (2K resolution). Note that without image neural field diffusion models, a fixed-resolution diffusion model needs to decode the whole region at full resolution (e.g. $1000 \\times 1000$ \"cloud\" region in a $2048 \\times 2048$ canvas) before passing it as $224 \\times 224$ input to CLIP, which would have very intensive computation and memory cost.", + "bbox": [ + 496, + 400, + 892, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.6. Qualitative results for text to image generation", + "text_level": 1, + "bbox": [ + 500, + 726, + 890, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We explore a preliminary application of our method for text-to-image generation by finetuning a pre-trained Stable Diffusion model [41]. Because of the high computational cost of training Stable Diffusion, we freeze the encoder and only finetune the decoder from publicly available pre-trained weights on a high-resolution subset of LAION-5B, which contains samples at resolutions higher than 2K. Our renderer has the same architecture as in previous experiments and is jointly trained from scratch. We show some qualitative samples from our fine-tuned model and compare them", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8013", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/34e0bff27fd91c29311ea11d249327f4224d73dd633d54da80d82f2f2302375f.jpg", + "image_caption": [ + "Figure 7. Samples of our method finetuned from Stable Diffusion (LDM) compared to Stable Diffusion with an extra super-resolution model. Our approach yields finer, high-frequency textures." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 352, + 337 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1d181db617c5e6392998a819d0ad2db1f7bdcba43f03591d4dab2ebbc33147a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 85, + 614, + 335 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ee136a3c6feaf2e1981cc24f5d7c05785c60c8998fd98f4614f5211d183981f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 85, + 875, + 337 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to upsampling the Stable Diffusion's $512 \\times 512$ output using Real-ESRGAN in Figure 7. We observe that the comparison is similar to the experiments on FFHQ and Mountains: our method generates more details than the Real-ESRGAN applied to Stable Diffusion's outputs. More samples and details are in the supplementary material.", + "bbox": [ + 75, + 387, + 468, + 478 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 491, + 191, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison to GANs with any-resolution learning. In this work, we propose a method to build diffusion models on a resolution-agnostic space and show its applications. The any-resolution learning framework has also been developed for different generative model families in prior works, for example, AnyresGAN [6]. We observe that the comparison between image neural field diffusion models and AnyresGAN matches the comparison between typical fixed-resolution diffusion models and GANs. A detailed comparison is in the supplementary material. In summary, we observe that GANs are still state-of-the-art on FID value (which is not always consistent with image quality [3, 4]) for the single-class generation, while image neural field diffusion model has better visual quality and diversity than AnyRes-GAN. Image neural field diffusion models are also free of the artifacts that commonly affect AnyRes-GAN's outputs, such as black dots and grid-like patterns. Finally, image neural field diffusion models can be directly applied for text-to-image synthesis, which remains a challenge for any-resolution GANs. Solving inverse problems based on the score functions of diffusion models is also not yet available in GANs.", + "bbox": [ + 75, + 516, + 470, + 848 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our current method assumes that the training data are scale-consistent, i.e., low-resolution images follow the same distribution as downsampled high-resolution", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "images (see supplementary material). This assumption is violated by datasets that contain a low-resolution subset with noisy, compressed images, and a high-resolution subset with clean images (e.g., Birds, Churches datasets [6]).", + "bbox": [ + 496, + 387, + 890, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Due to limited resources, our text-to-image synthesis model only fine-tunes an existing Stable Diffusion checkpoint on a small subset of the LAION dataset containing high-resolution images. This causes two issues. First, the training set of the pre-trained model includes noisy images, but our high-resolution fine-tuning dataset only contains clean images; this violates our scale consistency assumption. As a result, we found that our model requires extra prompts such as \"4k\" to generate detailed high-resolution images. Second, our fine-tuning LAION subset does not cover all possible object categories, so our model may not perform optimally on some out-of-distribution objects. Training from scratch on the full LAION dataset might resolve these limitations. Researching efficient any-resolution encoders is also a promising avenue for future work.", + "bbox": [ + 496, + 448, + 892, + 675 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 684, + 617, + 699 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed image neural field diffusion models, the diffusion models on a resolution-agnostic latent space, and demonstrated its advantages over fixed-resolution models. We presented a simple yet effective framework as an implementation, which can be easily applied to convert from an existing latent diffusion model. Our method can build diffusion models from mixed-resolution datasets, achieving high-resolution synthesis without extra super-resolution models. The resolution-agnostic image prior learned by the diffusion model also enables solving inverse problems with conditions applied at different scales of the same image.", + "bbox": [ + 496, + 703, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported, in part, by NSF CAREER Award IIS-2240014, and the CISCO Faculty Award.", + "bbox": [ + 500, + 871, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8014", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ivan Anokhin, Kirill Demochkin, Taras Khakhulin, Gleb Sterkin, Victor Lempitsky, and Denis Korzhenkov. Image generators with conditionally-independent pixel synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14278-14287, 2021. 2", + "[2] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 2" + ], + "bbox": [ + 78, + 92, + 468, + 655 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "8017", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Image Neural Field Diffusion Models/e632bc2a-df53-472b-b65b-a754db96e990_model.json b/2024/Image Neural Field Diffusion Models/e632bc2a-df53-472b-b65b-a754db96e990_model.json new file mode 100644 index 0000000000000000000000000000000000000000..051cc5c2c3d19a23cbc3a862e1ff7c08d40238df --- /dev/null +++ b/2024/Image Neural Field Diffusion Models/e632bc2a-df53-472b-b65b-a754db96e990_model.json @@ -0,0 +1,2235 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.297, + 0.131, + 0.674, + 0.153 + ], + "angle": 0, + "content": "Image Neural Field Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.179, + 0.898, + 0.24 + ], + "angle": 0, + "content": "Yinbo Chen1 Oliver Wang2 Richard Zhang3 Eli Shechtman3 Xiaolong Wang1† Michael Gharbi3† \n1UC San Diego 2Google Research 3Adobe Research https://yinboc.github.io/infd/" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.244, + 0.346, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.387, + 0.282, + 0.412 + ], + "angle": 0, + "content": "FFHQ Resolution: \\(1024\\times 1024\\)" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.244, + 0.617, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.416, + 0.388, + 0.553, + 0.412 + ], + "angle": 0, + "content": "Mountains Resolution: \\(2048\\times 2048\\)" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.245, + 0.891, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.65, + 0.387, + 0.867, + 0.412 + ], + "angle": 0, + "content": "\"A cute corgi sleeping on a book, 4k\" Resolution: \\(2048 \\times 2048\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.418, + 0.893, + 0.46 + ], + "angle": 0, + "content": "Figure 1. Generated samples from our image neural field diffusion models. We show photorealistic high-resolution image generation by rendering generated image neural fields at \\(2\\mathrm{K}\\) resolution for single domain models (left and middle), as well as general text-to-image models (right), with an efficient diffusion process on latent representation at only \\(64 \\times 64\\) resolution." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.465, + 0.314, + 0.479 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.486, + 0.471, + 0.804 + ], + "angle": 0, + "content": "Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse problems without extra training. However, most diffusion models learn the distribution of fixed-resolution images. We propose to learn the distribution of continuous images by training diffusion models on image neural fields, which can be rendered at any resolution, and show its advantages over fixed-resolution models. To achieve this, a key challenge is to obtain a latent space that represents photorealistic image neural fields. We propose a simple and effective method, inspired by several recent techniques but with key changes to make the image neural fields photorealistic. Our method can be used to convert existing latent diffusion autoencoders into image neural field autoencoders. We show that image neural field diffusion models can be trained using mixed-resolution image datasets, outperform fixed-resolution diffusion models followed by super-resolution models, and can solve inverse problems with conditions applied at different scales efficiently." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.821, + 0.208, + 0.836 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.847, + 0.469, + 0.876 + ], + "angle": 0, + "content": "Diffusion models [16, 34, 50] have recently become attractive alternatives to GANs. These likelihood-based models" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.465, + 0.892, + 0.722 + ], + "angle": 0, + "content": "exhibit fewer artifacts, stable training, can model complex data distributions, do not suffer from mode collapse, and can solve inverse problems using the score function without extra training. Since diffusion typically requires many iterations at a fixed dimension, directly modeling the diffusion process in the pixel space [17, 40, 43] can be inefficient for high-resolution image synthesis. Latent diffusion models (LDMs) [41, 57] were proposed as a more efficient alternative. The key idea is to learn an autoencoder to map images to a latent representation from which the image can be decoded back, and train a diffusion model on the lower-dimensional latent representation. Despite their success, LDMs' latent space still represents images at fixed resolution (for example, 256 in LDM [41] and 512 in Stable Diffusion). To generate higher-resolution images (e.g., 2K), LDMs usually first generate a low-resolution image and up-sample it using a separate super-resolution model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In this work, we propose Image Neural Field Diffusion models (INFD). Our method is based on the latent diffusion framework, where we first learn a latent representation that represents an image neural field (which can be rendered at any resolution), then learn a diffusion model on this latent representation. A key challenge of our approach is to learn a latent space of photorealistic image neural fields where the diffusion model is applied. We propose a simple and effective method that can convert an existing autoencoder of latent diffusion models to a neural field autoencoder. We find that directly implementing an autoencoder with LIIF [8]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.887, + 0.193, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal advising." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8007" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.198 + ], + "angle": 0, + "content": "leads to blurred image details, and propose a Convolutional Local Image Function (CLIF), which can render the latent representation to photorealistic high-resolution images and the image content is consistent at different resolutions. Our neural field autoencoder is trained with L1 loss, perceptual loss [60], and GAN loss following LDM [41], and is supervised from multi-scale patches similar to AnyResGAN [6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.47, + 0.529 + ], + "angle": 0, + "content": "We show that image neural field diffusion models have several key advantages over fixed-resolution diffusion models: (i) They can be built from mixed-resolution datasets without resizing images. The neural field decoder can render latent representation at any resolution and from patches, which can take supervision from ground-truth images at arbitrary high resolution without decoding the whole image. (ii) The same latent representation can be supervised with GAN loss from fixed-resolution patches at different scales, with the content consistency across scales, the multiscale supervision helps high-resolution generation even if all ground-truth images are at a fixed high resolution. (iii) It does not require an extra Super-Resolution (SR) model for high-resolution generation. Besides the advantage of simplicity, since diffusion-generated low-resolution images do not have high-resolution ground truth, separate SR models are typically trained on real images, while the domain gap between real and generated images could significantly harm the performance of the SR model. (iv) Image neural field diffusion models learn a resolution-agnostic image prior. Therefore, it can be used to solve inverse problems with a set of conditions defined at different scales efficiently." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.531, + 0.365, + 0.544 + ], + "angle": 0, + "content": "In summary, our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.546, + 0.469, + 0.589 + ], + "angle": 0, + "content": "- An image neural field autoencoder that can learn representations from mixed-resolution datasets and renders scale-consistent and photorealistic images." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.59, + 0.469, + 0.664 + ], + "angle": 0, + "content": "- A method to build diffusion models on mixed-resolution datasets and synthesize high-resolution images without extra SR models. Image synthesis is up to 2K resolution with an efficient latent diffusion process at only \\(64 \\times 64\\) resolution (see samples in Figure 1)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.666, + 0.468, + 0.695 + ], + "angle": 0, + "content": "- A framework to solve inverse problems with conditions applied at different scales of the same image." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.546, + 0.469, + 0.695 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.218, + 0.725 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Diffusion Models. Diffusion models are first proposed by Sohl-Dickstein et. al. [50]. They were recently connected to score-based generative models [51-53] and have been greatly improved [16, 34] for architectures and other training details, achieving state-of-the-art results on both unconditional and conditional image synthesis [11, 17, 33, 42, 44]. Compared to prior GAN-based methods [14, 21, 22, 38, 62], diffusion models have shown nice properties such as stable training, not suffering from mode collapse, and can perform image-to-image translation [28, 29] or be used to solve inverse problems [54], even with an uncondi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "tional model. One of the main drawbacks of current diffusion models is slow inference speed, as it relies on iterative reverse diffusion steps. While this can be remedied with faster sampling methods [23, 27, 46], performing the diffusion process in the pixel space of high-resolution images remains computationally expensive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.184, + 0.893, + 0.395 + ], + "angle": 0, + "content": "Our work is most closely related to latent diffusion models, which learn to map images to latent representation and train diffusion model on the latent space [41, 47, 57]. A key design in this direction is to choose the latent representation where the diffusion model is learned. Different from prior works that learn an autoencoder, where the latent representation corresponds to a fixed resolution image, we design a decoder and a renderer to learn a latent space that represents image neural fields. Since our latent space represents image neural fields, our autoencoder can learn a representation from high-resolution images in varied sizes with multi-scale patches, and can synthesize images at high resolution without relying on extra super-resolution models. Our method follows LDM [41], which trains in two stages." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.893, + 0.587 + ], + "angle": 0, + "content": "Neural Fields for Image Synthesis. Neural field is also known as Implicit Neural Representations (INR), which represents signals as coordinate-based neural networks. It serves as a compact and powerful differentiable representation and achieves state-of-the-art results mainly for representing 3D shapes [9, 30, 36] and scenes [2, 5, 19, 31, 37, 45, 48]. Applications of neural fields for images are explored in early works [32, 55] and proposed for more applications such as image super-resolution [8] and image synthesis [1, 49]. Several recent works [6, 22] relax the pixel-independent assumption and perform convolutions on the coordinate map to render the output for image synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.892, + 0.678 + ], + "angle": 0, + "content": "The idea of using neural fields for training with any-resolution images is explored in LIIF [8] for autoencoding with an L1 loss, AnyResGAN [6] and ScaleParty [35] for GANs with adversarial loss. Our work aims at building the resolution-agnostic learning framework for diffusion models, which is a different model family of generative models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Image Super-Resolution. Image Super-Resolution [7, 12, 24, 26, 56, 58, 61] (SR) aims at upsampling a low-resolution image to higher resolution. Many recent works [8, 18, 25, 59] explore Arbitrary-Scale SR (ASSR) with a single network. While they are related to our method, the differences include: (i) Instead of learning an autoencoder and an extra SR model, our implementation can be viewed as making a bottleneck in a single ASSR model and training diffusion models on the bottleneck. (ii) Our decoder is decoding from latent space to RGB space while super-resolution is upsampling from RGB space to RGB space. (iii) Our input can potentially have any higher resolution information (e.g. crops from high resolution), we choose it as a fixed-low-resolution image for efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8008" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.178, + 0.096, + 0.795, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.274, + 0.895, + 0.346 + ], + "angle": 0, + "content": "Figure 2. Method overview. Given a training image at an arbitrary resolution, we first downsample it to a fixed resolution and pass it into the encoder \\( E \\) to get a latent representation \\( z \\). A decoder \\( D \\) then takes \\( z \\) as input and produces a feature map \\( \\phi \\) that drives a neural field renderer \\( R \\), which can render images by querying with the appropriate grid of pixel coordinates \\( c \\) and pixel sizes \\( s \\). The autoencoder is trained on crops from a randomly downsampled image ground truth, generating image crops at the corresponding coordinates. At test time, a diffusion model generates a latent representation \\( z \\), which is then decoded and used to render a high-resolution image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.358, + 0.471, + 0.389 + ], + "angle": 0, + "content": "IDM [13] uses a diffusion model for ASSR where the output is at a medium resolution." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.399, + 0.216, + 0.415 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.425, + 0.469, + 0.455 + ], + "angle": 0, + "content": "Our algorithm builds on diffusion models and neural fields. We introduce the core concepts and notation below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.686 + ], + "angle": 0, + "content": "Diffusion Models. Given a sample \\( x_0 \\) from a data distribution \\( q(x_0) \\), forward diffusion progressively destroys the information in \\( x_0 \\) in \\( T \\) steps, \\( x_{t-1} \\mapsto x_t \\), each adding some small Gaussian noise. The process can be concisely rewritten as \\( x_t = \\sqrt{\\bar{\\alpha}_t} x_0 + \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon \\), where \\( \\epsilon \\sim \\mathcal{N}(0, I) \\), and \\( \\bar{\\alpha}_{0\\dots T-1} \\) gradually decreases from 1 to 0. The final distribution is approximately normal, \\( q(x_T) \\sim \\mathcal{N}(0, I) \\). A diffusion model learns to reverse this diffusion process. Once trained, new samples can be generated by first sampling \\( x_T \\sim q(x_T) \\) and reversing each step of the diffusion process using a learned transition probability \\( p_\\theta(x_{t-1}|x_t) \\), parameterized by a neural network. Many prior works on image generation are based on maximizing a reweighted variational lower-bound of \\( p_\\theta(x_0) \\), which is shown by [16] to lead to the following training objective:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.691, + 0.47, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathbb {E} _ {x _ {0}, t, \\epsilon} \\left[ \\left| \\left| \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) - \\epsilon \\right| \\right| ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.47, + 0.746 + ], + "angle": 0, + "content": "where \\(t\\) is sampled in \\(\\{0,\\dots ,T - 1\\}\\), and \\(\\epsilon_{\\theta}\\) is the network trained to reverse the diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Neural Fields. Neural Fields represent a signal using a coordinate-based neural network. For example, a neural field can represent an image as a function \\( c = f(x; \\phi) \\), where \\( x \\in [-1, 1]^2 \\) are the spatial coordinates in the image domain, \\( c \\in \\mathbb{R}^3 \\) is the RGB color at the corresponding continuous coordinate, and \\( \\phi \\) denotes the parameters of the neural field \\( f \\). Since \\( x \\) can take continuous values, the RGB value can be decoded at arbitrary coordinates. Accordingly, an image neural field can be rendered at arbitrary resolution by sampling the corresponding pixel coordinates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.591, + 0.372 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.893, + 0.473 + ], + "angle": 0, + "content": "Similar to LDM [41], our approach has two stages. First, we train an autoencoder that converts images to latent representations of 2D neural fields (\\(\\S 4.1\\)), which can be rendered to images at any given resolution (\\(\\S 4.2\\)). Second, we train a diffusion model to generate samples from this latent space (\\(\\S 4.3\\)). Figure 2 illustrates our pipeline." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.484, + 0.788, + 0.501 + ], + "angle": 0, + "content": "4.1. Image Neural Field Autoencoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.893, + 0.614 + ], + "angle": 0, + "content": "In the first stage, we seek to convert every image in our training set into a photorealistic image neural field. We do this by training an autoencoder, made of an encoder \\( E \\), a decoder \\( D \\), and a neural field renderer \\( R \\). The encoder maps an RGB input image \\( I \\) to a latent code \\( z = E(I) \\), which is decoded by the decoder to a feature tensor \\( \\phi = D(z) \\) used by the neural field renderer to produce the final image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.895, + 0.911 + ], + "angle": 0, + "content": "Patch-wise decoding. For training efficiency, we want to avoid decoding the whole image, because the ground truth can be at a very high resolution. We take advantage of the coordinate-based decoding property of neural fields, to train with constant-size crops from mixed-resolution data, which is amenable to batching. Specifically, we crop a random patch \\( p_{GT} \\) at a fixed \\( P \\times P \\) resolution (the red box in Figure 2) from a randomly downsampled ground-truth. Since \\( p_{GT} \\) is a fixed-size patch, downsampling the global ground truth lets the patch \\( p_{GT} \\) cover regions at varying scales of the image. This provides supervision at multiple scales to the latent representation, from local details to global structure. We discuss this further in § 5.2. Let \\( c \\) denote the coordinates of pixel centers in the patch within the image, and \\( s \\) denote their pixel sizes relative to the whole ground-truth image. Our renderer \\( R \\) takes as input the features \\( \\phi = D(z) \\) decoded from the latent representation, and the coordinates and pixel sizes \\( c, s \\) to synthesize an output patch \\( p = R(c, s; \\phi) \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8009" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.124, + 0.09, + 0.426, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.195, + 0.473, + 0.295 + ], + "angle": 0, + "content": "Figure 3. Convolutional Local Image Function (CLIF). Given a feature map \\(\\phi\\) (yellow dots), for each query point \\(x\\) (green dot), we fetch the nearest feature vector, along with the relative coordinates and the pixel size. The grid of query information is then passed into a convolutional network (right) that renders an RGB grid. Different than the pointwise function LIIF, CLIF has a higher generation capacity and is learned to be still scale-consistent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.47, + 0.4 + ], + "angle": 0, + "content": "Training objective. We compare the synthesized patch to the ground truth using a sum of an \\( L_{1} \\) loss, a perceptual loss \\( \\mathcal{L}_{\\mathrm{perc}} \\) [60], and an adversarial loss \\( \\mathcal{L}_{\\mathrm{GAN}} \\) [14]. The discriminator is simultaneously trained to distinguish between the distributions of \\( p \\) and \\( p_{GT} \\). Thus, we minimize the following objective to train \\( E \\), \\( D \\), and \\( R \\):" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.413, + 0.47, + 0.43 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {A E} = \\left\\| p - p _ {G T} \\right\\| _ {1} + \\mathcal {L} _ {\\text {p e r c}} (p, p _ {G T}) + \\mathcal {L} _ {\\mathrm {G A N}} (p). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.473, + 0.625 + ], + "angle": 0, + "content": "Our implementation follows the autoencoder architecture of LDM [41], with the same encoder and decoder (removed the last layer) architectures to facilitate comparisons. Since training images have arbitrary resolutions, we resample the encoder's input to a fixed resolution \\(256 \\times 256\\). Note that despite this downsampling, we still train against mixed-resolution references. The encoder and decoder are with a spatial downsampling/upsampling rate of 4 correspondingly, therefore the latent representation is in \\(64 \\times 64\\). A vector-quantization (VQ) layer is prepended to the first layer of the decoder to regularize the latent space. \\(\\phi\\) is \\(256 \\times 256\\) with 128 channels. We set patch size \\(P = 256\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.288, + 0.65 + ], + "angle": 0, + "content": "4.2. Neural Field Renderer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Our renderer \\( R \\), shown in Figure 3, is a neural field coordinate-based decoder, which we dubbed Convolutional Local Image Function (CLIF). To decode an image patch with CLIF, each query point \\( c \\) (green dot) fetches the spatially nearest feature vector from the feature map \\( \\phi \\) (yellow dots). We concatenate the nearest feature vector with the query coordinates \\( c \\) and pixel size \\( s \\), then process the grid of query information using a convolutional network to output an RGB image. Intuitively, the concatenated feature is the field information at a point. By changing the query coordinates and pixel sizes, we can decode images at any resolution. LIIF [8] decodes with similar information, but it uses a pointwise function. We found this limits LIIF's ability to produce realistic high-frequency details (see supplementary material). CLIF remedies this issue by exploiting more local feature context. Our CLIF renderer is learned to be" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "scale-consistent, i.e., details are consistent when decoding at different resolutions (see supplementary material)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.132, + 0.661, + 0.146 + ], + "angle": 0, + "content": "4.3. Latent diffusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.155, + 0.894, + 0.201 + ], + "angle": 0, + "content": "Once the autoencoder is trained, we map every image \\(I\\) in the training dataset to its latent representation \\(z\\), and train a diffusion model by optimizing the DDPM [16] objective" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.212, + 0.892, + 0.231 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D M} = \\mathbb {E} _ {z \\sim E (I), t, \\epsilon} \\left[ \\left| \\left| \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} z + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) - \\epsilon \\right| \\right| ^ {2} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.242, + 0.892, + 0.318 + ], + "angle": 0, + "content": "using the distribution over \\(z\\) induced by the encoder. After training, the encoder can be discarded. The diffusion model generates a latent representation \\(z\\), which is then decoded to \\(\\phi = D(z)\\) and rendered at a resolution specified by the pixel coordinates \\(R(c,s;\\phi)\\) as described next." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.328, + 0.757, + 0.344 + ], + "angle": 0, + "content": "4.4. Patchwise Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.351, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Despite being trained with small patches for efficiency, our method can generate high-resolution images. For this, we first generate a global feature map \\(\\phi\\) from a sampled \\(z\\), then generate sub-tiles of a large image by querying the renderer at the corresponding coordinates, as described in § 4.2. To avoid discontinuities at tile boundaries, we expand the query region for each tile by a fixed padding size larger than CLIF's receptive field (8 in our experiments). We then crop the output tiles by the same amount and assemble the tiles into a seamless composite. Our renderer is fully convolutional, it can also generate the image at once, as long as memory is sufficient to hold intermediate buffers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.547, + 0.633, + 0.563 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.572, + 0.892, + 0.648 + ], + "angle": 0, + "content": "We evaluate our method on several datasets and compare it to LDM [41] with super-resolution models (§ 5.1). Sections § 5.2 and § 5.3 presents model ablations. We show results in solving multi-scale inverse problems in § 5.5, and text-to-image generation in § 5.6." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.895, + 0.911 + ], + "angle": 0, + "content": "Data. The FFHQ [20] used in LDM [41] contains 70K high-resolution images \\((1024\\times 1024)\\) and several baselines use it for comparison. When comparing to LDM, we follow their training and validation split: 60K images for training and 10K for validation. Since our method is flexible and not limited to a fixed-resolution dataset, we also follow a controlled setting in prior work [6], which constructs a varied-resolution dataset from FFHQ by constructing and merging three sets: (i) all images at 256 low-resolution; (ii) a subset of 5K samples in varied-resolution from 512 to 1024; (iii) a subset of 1K images at 1024 resolution. We denote this setting as FFHQ 6K-Mix. Besides FFHQ, we evaluate our method on the Mountains dataset [6], which contains a low-resolution subset, with about 500K samples around 1024 resolution, and a high-resolution subset, with about 9K images at resolutions beyond 2048. Figure 4 shows examples of our generated results on these datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8010" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.894, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.247, + 0.42, + 0.724, + 0.435 + ], + "angle": 0, + "content": "Figure 4. Generated samples from our method on FFHQ and Mountains dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.57 + ], + "angle": 0, + "content": "pFID metric. Standard FID evaluation first resize images to 299, which evaluates the global structure of images regardless of their original resolution, but is insufficient to measure the quality of details from high-resolution generators. Patch-FID [6] (pFID) addresses this limitation. It computes the FID between fixed-resolution patches cropped from arbitrary resolution ground-truth and generated images, thus evaluating local details in synthesized images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.471, + 0.799 + ], + "angle": 0, + "content": "The original pFID reports the metric on random crops from images at varying resolutions. Since our practical focus is on high-resolution synthesis, we evaluate pFID between patches cropped from fixed-high-resolution images. To further disentangle the evaluation for image details at different scales, we separately report pFID for patches at different resolutions. \\( P / 1\\mathrm{K} \\) will denote the FID between random crops at resolution \\( P \\) from ground truth and synthesized images at resolution 1024. For example, pFID-256/1K evaluates the local details, pFID-1K/1K evaluates the global structure and is the same as standard FID applied to 1024-resolution images. We generate 50K samples to compute FID in most experiments. In some experiments, we use 5K samples if it suffices to observe the performance gap (specified after FID@ in Tables)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.276, + 0.831 + ], + "angle": 0, + "content": "5.1. Comparison to LDM" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "LDM [41] trains an autoencoder for images at \\(256 \\times 256\\) resolution and learns a diffusion model on its latent space. For a fair comparison, we used the same encoder and decoder architectures as LDM. Our method only adds a lightweight" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.448, + 0.892, + 0.478 + ], + "angle": 0, + "content": "CLIF renderer, which contains 2 convolution layers and 2 ResNet [15] blocks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.893, + 0.742 + ], + "angle": 0, + "content": "Even though LDM's denoiser is fully convolutional and can generate high-resolution images simply by diffusing from a larger noise map, it is known that this approach generates repetitive patterns (e.g., distorted faces with duplicate features), we show examples in the supplementary material. As a result, we follow the standard approach to generate high-resolution images with LDM by running an independent super-resolution model on its output. We combine LDM with several recent state-of-the-art arbitrary-scale super-resolution methods: LIIF [8], ITSRN [59], LTE [25], which allow for inference at continuous upsampling scales, and Real-ESRGAN [58], a super-resolution model for a fixed upsampling scale that has state-of-the-art perceptual quality. We report qualitative results in Figure 5, and the pFID in Table 1 on FFHQ. As Real-ESRGAN shows the most competitive results, we also compare to it on Mountains dataset in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We find that for standard FID at 256 resolution (i.e. pFID 256/256), the image neural field diffusion model is competitive with the original LDM, which can only generate images at 256. Our retraining of LDM reaches a slightly worse FID than the officially reported scores, which we attribute to implementation differences and training variance. At all higher resolutions, our method outperforms LDM followed by super-resolution, which is consistent with our qualitative observation and suggests we achieve better image quality for high-resolution detail at different scales." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8011" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.094, + 0.231, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.118, + 0.215, + 0.193, + 0.225 + ], + "angle": 0, + "content": "\\(\\mathrm{LDM} + \\mathrm{LIIF}\\)" + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.094, + 0.406, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.342, + 0.215, + 0.478, + 0.225 + ], + "angle": 0, + "content": "LDM + Real-ESRGAN" + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.094, + 0.561, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.585, + 0.094, + 0.735, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.094, + 0.89, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.726, + 0.215, + 0.756, + 0.225 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.233, + 0.894, + 0.262 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison with LDM followed by super-resolution on FFHQ. LIIF shows noise in details, while Real-ESRGAN tends to be smooth and results lack rich details. Our approach generates images with more realistic details." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.275, + 0.861, + 0.435 + ], + "angle": 0, + "content": "
Model#ParamsCoordinate-based DecoderpFID@50K
256/256256/1K512/1K1K/1K
LDM [41]33.0M4.98---
LDM + LIIF [8]33.0M + 22.3M✓-56.6517.838.97
LDM + ITS RN-RDN [59]33.0M + 22.6M✓-51.7317.948.02
LDM + SwinIR-LTE [25]33.0M + 12.1M✓-52.6217.729.09
LDM + Real-ESRGAN [58]33.0M + 16.7M-18.3818.4616.04
LDM (our reimplementation)33.0M6.02---
INFD (ours)35.7M✓5.348.076.645.57
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.446, + 0.893, + 0.474 + ], + "angle": 0, + "content": "Table 1. Comparison to Latent Diffusion Model (LDM) with super-resolution models for high-resolution image synthesis on FFHQ dataset. #Params counts for the decoder, and the renderer or super-resolution model if it exists, which are used in image generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.792 + ], + "angle": 0, + "content": "We hypothesize that the main issues for extra superresolution models are that: (i) LDM with an extra superresolution model can be viewed as first decoding the latent representation to RGB space, then upsample to another RGB space, where the first RGB space becomes a bottleneck that contains much less information than feature space; (ii) the artifacts generated by LDM, even inconspicuous, can cause a domain shift to the input of the superresolution models, which could significantly degrade their performance. The super-resolution models can not be directly trained to upsample the generated low-resolution images since no paired high-resolution ground truth is available. In our method, the domain shift from real to generated samples happens in the latent space (with VQ or KL regularization). We hypothesize that latent space is much more robust than RGB space to the domain shift. We observe that when replacing the latent space with RGB space, the generated images become overly smooth similar to LDM with Real-ESRGAN super-resolution, which is consistent with our hypothesis (see supplementary material)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.342, + 0.818 + ], + "angle": 0, + "content": "5.2. Effect of scale-varied training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Randomly downsampling the global image before extracting fixed-resolution training patches would make patches cover all scales. With the scale consistency of CLIF, an image neural field is supervised to be realistic in all scales via the perceptual and GAN losses. We conduct an ablation on" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.487, + 0.885, + 0.565 + ], + "angle": 0, + "content": "
ModelpFID@50K
256/1K512/1K1K/1K
LDM + Real-ESRGAN [58]17.3615.1110.39
INFD (ours)7.536.845.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.575, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Table 2. Comparison to Latent Diffusion Model (LDM) with super-resolution models on Mountains dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.893, + 0.824 + ], + "angle": 0, + "content": "FFHQ to evaluate the impact of this random downsampling strategy. Specifically, we disable it during training, keeping all ground-truth images at 1024 resolution. The results are shown in Table 3. Without random downsampling, the pFID is worse especially for \\(512/1\\mathrm{K}\\) and \\(1\\mathrm{K}/1\\mathrm{K}\\), suggesting that random downsampling of the ground truth improves quality, even if we only aim at generating images at 1024 high resolution, because it helps supervise every single image to be realistic at all scales. For Mountains dataset, we observe that there will be obvious artifacts without random downsampling (see supplementary material). This contrasts with the observation in LIIF [8], which found that random downsampling hurts performance at a fixed highest scale when it is only using an L1 loss." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.833, + 0.878, + 0.849 + ], + "angle": 0, + "content": "5.3. Training with limited high-resolution images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "While previous experiments use high-resolution training images, a key advantage of our method is that it can learn from mixed-resolution datasets and still generate" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8012" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.127, + 0.089, + 0.418, + 0.187 + ], + "angle": 0, + "content": "
DownsamplepFID@50K
256/1K512/1K1K/1K
Fix 10248.196.826.04
256–10248.076.645.57
Δ0.120.180.47
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.192, + 0.468, + 0.22 + ], + "angle": 0, + "content": "Table 3. FFHQ dataset. Random downsampling during training improves image generation quality even for fixed high resolution." + }, + { + "type": "table", + "bbox": [ + 0.129, + 0.223, + 0.416, + 0.32 + ], + "angle": 0, + "content": "
DatapFID@50K
256/1K512/1K1K/1K
All HR8.076.645.57
6K-Mix16.2710.811.3
6K-Mix, bal.12.417.746.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.326, + 0.468, + 0.354 + ], + "angle": 0, + "content": "Table 4. FFHQ dataset. Our method can learn from mixed-resolution images with a limited number of full-resolution images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.595 + ], + "angle": 0, + "content": "high-resolution outputs, even when the number of high-resolution images is limited. We quantify this in Table 4 using FFHQ 6K-Mix, where most images are at low resolution 256, 5K images are at 512-1024, and 1K images are at 1024. Training with the mixed-resolution dataset as-is (also with random downsampling) already yields a model that performs decently at 1024, but with worse details than the model trained with all images at 1024. We suspect that the model is optimized for too few steps using images at 1024, since the number of high-resolution images is small and they go through random downsampling. We balance the training resolution by sampling images from the \\(5\\mathrm{K}+\\) 1K high-resolution subset with a probability of 0.5. This largely closes the performance gap (6K-Mix, bal.) with the model train on high-resolution images only." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.349, + 0.62 + ], + "angle": 0, + "content": "5.4. Image generation beyond 1024" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.468, + 0.732 + ], + "angle": 0, + "content": "We explore going beyond the 1024 resolution and train our model on a collected dataset of faces at varied resolutions between 1024 to 2048, and on Mountains dataset including a higher-resolution subset (a generated sample is shown in Figure 1). We observe that our method can be effectively applied to resolutions up to \\(2\\mathrm{K}\\). More samples and details are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.462, + 0.759 + ], + "angle": 0, + "content": "5.5. Inverse problems with conditions at any scale" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Our method builds a diffusion model on a latent space that represents image neural fields. A key property of image neural fields is that they can be efficiently rendered for any sub-region at any given resolution without decoding the whole image at full resolution. With the image prior learned by diffusion models, it enables efficiently solving inverse problems where conditions can be defined on any scale of the image based on coordinates. We take zero-shot any-scale layout-to-image generation as an example. It uses" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.167, + 0.892, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.246, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Figure 6. Solving inverse problems with multi-scale conditions per image. We can solve for an image that satisfies multiscale conditions, defined as square regions and a text prompt (left). For this, we decode the corresponding region and pass it to a pre-trained CLIP [39] model operating at fixed-resolution \\((224 \\times 224)\\), and maximize the CLIP similarity to the corresponding text prompt. This enables layout-to-image generation without extra training. We show generated solutions on the right." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.371, + 0.891, + 0.4 + ], + "angle": 0, + "content": "CLIP [39] similarity as the constraint for image generation with semantic bounding boxes at arbitrary scales." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.893, + 0.718 + ], + "angle": 0, + "content": "Specifically, we take a pre-trained CLIP model, which takes \\(224 \\times 224\\) fixed-resolution images as inputs. Given a layout and our image neural field diffusion model (unconditional), in each diffusion step, let \\(z\\) denote the current denoised latent representation, for each semantic bounding box \\(i\\) in the input layout we render \\(z\\) for the corresponding sub-region to a patch at the resolution \\(224 \\times 224\\), i.e. patch \\(p_i = R \\circ D(z; c_i, s_i)\\), with our decoder \\(D\\) and renderer \\(R\\), where \\(c_i, s_i\\) denote the coordinates and scale of a \\(224 \\times 224\\) pixel grid of bounding box \\(i\\). The clip similarity loss \\(l_i = \\mathrm{CLIP}(p_i, T_i)\\) is computed between patch \\(p_i\\) and the given text \\(T_i\\). The gradients \\(\\frac{\\partial l_i}{\\partial z}\\) are back-propagated and then used to modify the diffusion score for each diffusion step. We follow the techniques in DPS [10] as the inverse problem solver. Figure 6 shows the results of using our mountains model (2K resolution). Note that without image neural field diffusion models, a fixed-resolution diffusion model needs to decode the whole region at full resolution (e.g. \\(1000 \\times 1000\\) \"cloud\" region in a \\(2048 \\times 2048\\) canvas) before passing it as \\(224 \\times 224\\) input to CLIP, which would have very intensive computation and memory cost." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.891, + 0.743 + ], + "angle": 0, + "content": "5.6. Qualitative results for text to image generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We explore a preliminary application of our method for text-to-image generation by finetuning a pre-trained Stable Diffusion model [41]. Because of the high computational cost of training Stable Diffusion, we freeze the encoder and only finetune the decoder from publicly available pre-trained weights on a high-resolution subset of LAION-5B, which contains samples at resolutions higher than 2K. Our renderer has the same architecture as in previous experiments and is jointly trained from scratch. We show some qualitative samples from our fine-tuned model and compare them" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8013" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.353, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.087, + 0.615, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.087, + 0.876, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.892, + 0.374 + ], + "angle": 0, + "content": "Figure 7. Samples of our method finetuned from Stable Diffusion (LDM) compared to Stable Diffusion with an extra super-resolution model. Our approach yields finer, high-frequency textures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.47, + 0.479 + ], + "angle": 0, + "content": "to upsampling the Stable Diffusion's \\(512 \\times 512\\) output using Real-ESRGAN in Figure 7. We observe that the comparison is similar to the experiments on FFHQ and Mountains: our method generates more details than the Real-ESRGAN applied to Stable Diffusion's outputs. More samples and details are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.492, + 0.192, + 0.508 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.471, + 0.849 + ], + "angle": 0, + "content": "Comparison to GANs with any-resolution learning. In this work, we propose a method to build diffusion models on a resolution-agnostic space and show its applications. The any-resolution learning framework has also been developed for different generative model families in prior works, for example, AnyresGAN [6]. We observe that the comparison between image neural field diffusion models and AnyresGAN matches the comparison between typical fixed-resolution diffusion models and GANs. A detailed comparison is in the supplementary material. In summary, we observe that GANs are still state-of-the-art on FID value (which is not always consistent with image quality [3, 4]) for the single-class generation, while image neural field diffusion model has better visual quality and diversity than AnyRes-GAN. Image neural field diffusion models are also free of the artifacts that commonly affect AnyRes-GAN's outputs, such as black dots and grid-like patterns. Finally, image neural field diffusion models can be directly applied for text-to-image synthesis, which remains a challenge for any-resolution GANs. Solving inverse problems based on the score functions of diffusion models is also not yet available in GANs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Limitations. Our current method assumes that the training data are scale-consistent, i.e., low-resolution images follow the same distribution as downsampled high-resolution" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.448 + ], + "angle": 0, + "content": "images (see supplementary material). This assumption is violated by datasets that contain a low-resolution subset with noisy, compressed images, and a high-resolution subset with clean images (e.g., Birds, Churches datasets [6])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.893, + 0.676 + ], + "angle": 0, + "content": "Due to limited resources, our text-to-image synthesis model only fine-tunes an existing Stable Diffusion checkpoint on a small subset of the LAION dataset containing high-resolution images. This causes two issues. First, the training set of the pre-trained model includes noisy images, but our high-resolution fine-tuning dataset only contains clean images; this violates our scale consistency assumption. As a result, we found that our model requires extra prompts such as \"4k\" to generate detailed high-resolution images. Second, our fine-tuning LAION subset does not cover all possible object categories, so our model may not perform optimally on some out-of-distribution objects. Training from scratch on the full LAION dataset might resolve these limitations. Researching efficient any-resolution encoders is also a promising avenue for future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.685, + 0.619, + 0.7 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.87 + ], + "angle": 0, + "content": "We proposed image neural field diffusion models, the diffusion models on a resolution-agnostic latent space, and demonstrated its advantages over fixed-resolution models. We presented a simple yet effective framework as an implementation, which can be easily applied to convert from an existing latent diffusion model. Our method can build diffusion models from mixed-resolution datasets, achieving high-resolution synthesis without extra super-resolution models. The resolution-agnostic image prior learned by the diffusion model also enables solving inverse problems with conditions applied at different scales of the same image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.872, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported, in part, by NSF CAREER Award IIS-2240014, and the CISCO Faculty Award." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8014" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Ivan Anokhin, Kirill Demochkin, Taras Khakhulin, Gleb Sterkin, Victor Lempitsky, and Denis Korzhenkov. Image generators with conditionally-independent pixel synthesis. 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Generated samples from our image neural field diffusion models. We show photorealistic high-resolution image generation by rendering generated image neural fields at $2\mathrm{K}$ resolution for single domain models (left and middle), as well as general text-to-image models (right), with an efficient diffusion process on latent representation at only $64 \times 64$ resolution. + +![](images/799944e1f2383423cd5b9a48854b66a8f88ad2496addbeb5fbe89275c21c4983.jpg) +"A cute corgi sleeping on a book, 4k" Resolution: $2048 \times 2048$ + +# Abstract + +Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse problems without extra training. However, most diffusion models learn the distribution of fixed-resolution images. We propose to learn the distribution of continuous images by training diffusion models on image neural fields, which can be rendered at any resolution, and show its advantages over fixed-resolution models. To achieve this, a key challenge is to obtain a latent space that represents photorealistic image neural fields. We propose a simple and effective method, inspired by several recent techniques but with key changes to make the image neural fields photorealistic. Our method can be used to convert existing latent diffusion autoencoders into image neural field autoencoders. We show that image neural field diffusion models can be trained using mixed-resolution image datasets, outperform fixed-resolution diffusion models followed by super-resolution models, and can solve inverse problems with conditions applied at different scales efficiently. + +# 1. Introduction + +Diffusion models [16, 34, 50] have recently become attractive alternatives to GANs. These likelihood-based models + +exhibit fewer artifacts, stable training, can model complex data distributions, do not suffer from mode collapse, and can solve inverse problems using the score function without extra training. Since diffusion typically requires many iterations at a fixed dimension, directly modeling the diffusion process in the pixel space [17, 40, 43] can be inefficient for high-resolution image synthesis. Latent diffusion models (LDMs) [41, 57] were proposed as a more efficient alternative. The key idea is to learn an autoencoder to map images to a latent representation from which the image can be decoded back, and train a diffusion model on the lower-dimensional latent representation. Despite their success, LDMs' latent space still represents images at fixed resolution (for example, 256 in LDM [41] and 512 in Stable Diffusion). To generate higher-resolution images (e.g., 2K), LDMs usually first generate a low-resolution image and up-sample it using a separate super-resolution model. + +In this work, we propose Image Neural Field Diffusion models (INFD). Our method is based on the latent diffusion framework, where we first learn a latent representation that represents an image neural field (which can be rendered at any resolution), then learn a diffusion model on this latent representation. A key challenge of our approach is to learn a latent space of photorealistic image neural fields where the diffusion model is applied. We propose a simple and effective method that can convert an existing autoencoder of latent diffusion models to a neural field autoencoder. We find that directly implementing an autoencoder with LIIF [8] + +leads to blurred image details, and propose a Convolutional Local Image Function (CLIF), which can render the latent representation to photorealistic high-resolution images and the image content is consistent at different resolutions. Our neural field autoencoder is trained with L1 loss, perceptual loss [60], and GAN loss following LDM [41], and is supervised from multi-scale patches similar to AnyResGAN [6]. + +We show that image neural field diffusion models have several key advantages over fixed-resolution diffusion models: (i) They can be built from mixed-resolution datasets without resizing images. The neural field decoder can render latent representation at any resolution and from patches, which can take supervision from ground-truth images at arbitrary high resolution without decoding the whole image. (ii) The same latent representation can be supervised with GAN loss from fixed-resolution patches at different scales, with the content consistency across scales, the multiscale supervision helps high-resolution generation even if all ground-truth images are at a fixed high resolution. (iii) It does not require an extra Super-Resolution (SR) model for high-resolution generation. Besides the advantage of simplicity, since diffusion-generated low-resolution images do not have high-resolution ground truth, separate SR models are typically trained on real images, while the domain gap between real and generated images could significantly harm the performance of the SR model. (iv) Image neural field diffusion models learn a resolution-agnostic image prior. Therefore, it can be used to solve inverse problems with a set of conditions defined at different scales efficiently. + +In summary, our main contributions are: + +- An image neural field autoencoder that can learn representations from mixed-resolution datasets and renders scale-consistent and photorealistic images. +- A method to build diffusion models on mixed-resolution datasets and synthesize high-resolution images without extra SR models. Image synthesis is up to 2K resolution with an efficient latent diffusion process at only $64 \times 64$ resolution (see samples in Figure 1). +- A framework to solve inverse problems with conditions applied at different scales of the same image. + +# 2. Related Work + +Diffusion Models. Diffusion models are first proposed by Sohl-Dickstein et. al. [50]. They were recently connected to score-based generative models [51-53] and have been greatly improved [16, 34] for architectures and other training details, achieving state-of-the-art results on both unconditional and conditional image synthesis [11, 17, 33, 42, 44]. Compared to prior GAN-based methods [14, 21, 22, 38, 62], diffusion models have shown nice properties such as stable training, not suffering from mode collapse, and can perform image-to-image translation [28, 29] or be used to solve inverse problems [54], even with an uncondi + +tional model. One of the main drawbacks of current diffusion models is slow inference speed, as it relies on iterative reverse diffusion steps. While this can be remedied with faster sampling methods [23, 27, 46], performing the diffusion process in the pixel space of high-resolution images remains computationally expensive. + +Our work is most closely related to latent diffusion models, which learn to map images to latent representation and train diffusion model on the latent space [41, 47, 57]. A key design in this direction is to choose the latent representation where the diffusion model is learned. Different from prior works that learn an autoencoder, where the latent representation corresponds to a fixed resolution image, we design a decoder and a renderer to learn a latent space that represents image neural fields. Since our latent space represents image neural fields, our autoencoder can learn a representation from high-resolution images in varied sizes with multi-scale patches, and can synthesize images at high resolution without relying on extra super-resolution models. Our method follows LDM [41], which trains in two stages. + +Neural Fields for Image Synthesis. Neural field is also known as Implicit Neural Representations (INR), which represents signals as coordinate-based neural networks. It serves as a compact and powerful differentiable representation and achieves state-of-the-art results mainly for representing 3D shapes [9, 30, 36] and scenes [2, 5, 19, 31, 37, 45, 48]. Applications of neural fields for images are explored in early works [32, 55] and proposed for more applications such as image super-resolution [8] and image synthesis [1, 49]. Several recent works [6, 22] relax the pixel-independent assumption and perform convolutions on the coordinate map to render the output for image synthesis. + +The idea of using neural fields for training with any-resolution images is explored in LIIF [8] for autoencoding with an L1 loss, AnyResGAN [6] and ScaleParty [35] for GANs with adversarial loss. Our work aims at building the resolution-agnostic learning framework for diffusion models, which is a different model family of generative models. + +Image Super-Resolution. Image Super-Resolution [7, 12, 24, 26, 56, 58, 61] (SR) aims at upsampling a low-resolution image to higher resolution. Many recent works [8, 18, 25, 59] explore Arbitrary-Scale SR (ASSR) with a single network. While they are related to our method, the differences include: (i) Instead of learning an autoencoder and an extra SR model, our implementation can be viewed as making a bottleneck in a single ASSR model and training diffusion models on the bottleneck. (ii) Our decoder is decoding from latent space to RGB space while super-resolution is upsampling from RGB space to RGB space. (iii) Our input can potentially have any higher resolution information (e.g. crops from high resolution), we choose it as a fixed-low-resolution image for efficiency. + +![](images/d0804231f9cdc9222a74fe51d6aa149bd1784bb563dea899f6c64b3e7c3e5f12.jpg) +Figure 2. Method overview. Given a training image at an arbitrary resolution, we first downsample it to a fixed resolution and pass it into the encoder $E$ to get a latent representation $z$ . A decoder $D$ then takes $z$ as input and produces a feature map $\phi$ that drives a neural field renderer $R$ , which can render images by querying with the appropriate grid of pixel coordinates $c$ and pixel sizes $s$ . The autoencoder is trained on crops from a randomly downsampled image ground truth, generating image crops at the corresponding coordinates. At test time, a diffusion model generates a latent representation $z$ , which is then decoded and used to render a high-resolution image. + +IDM [13] uses a diffusion model for ASSR where the output is at a medium resolution. + +# 3. Preliminaries + +Our algorithm builds on diffusion models and neural fields. We introduce the core concepts and notation below. + +Diffusion Models. Given a sample $x_0$ from a data distribution $q(x_0)$ , forward diffusion progressively destroys the information in $x_0$ in $T$ steps, $x_{t-1} \mapsto x_t$ , each adding some small Gaussian noise. The process can be concisely rewritten as $x_t = \sqrt{\bar{\alpha}_t} x_0 + \sqrt{1 - \bar{\alpha}_t} \epsilon$ , where $\epsilon \sim \mathcal{N}(0, I)$ , and $\bar{\alpha}_{0\dots T-1}$ gradually decreases from 1 to 0. The final distribution is approximately normal, $q(x_T) \sim \mathcal{N}(0, I)$ . A diffusion model learns to reverse this diffusion process. Once trained, new samples can be generated by first sampling $x_T \sim q(x_T)$ and reversing each step of the diffusion process using a learned transition probability $p_\theta(x_{t-1}|x_t)$ , parameterized by a neural network. Many prior works on image generation are based on maximizing a reweighted variational lower-bound of $p_\theta(x_0)$ , which is shown by [16] to lead to the following training objective: + +$$ +\mathcal {L} = \mathbb {E} _ {x _ {0}, t, \epsilon} \left[ \left| \left| \epsilon_ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t\right) - \epsilon \right| \right| ^ {2} \right], \tag {1} +$$ + +where $t$ is sampled in $\{0,\dots ,T - 1\}$ , and $\epsilon_{\theta}$ is the network trained to reverse the diffusion process. + +Neural Fields. Neural Fields represent a signal using a coordinate-based neural network. For example, a neural field can represent an image as a function $c = f(x; \phi)$ , where $x \in [-1, 1]^2$ are the spatial coordinates in the image domain, $c \in \mathbb{R}^3$ is the RGB color at the corresponding continuous coordinate, and $\phi$ denotes the parameters of the neural field $f$ . Since $x$ can take continuous values, the RGB value can be decoded at arbitrary coordinates. Accordingly, an image neural field can be rendered at arbitrary resolution by sampling the corresponding pixel coordinates. + +# 4. Method + +Similar to LDM [41], our approach has two stages. First, we train an autoencoder that converts images to latent representations of 2D neural fields ( $\S 4.1$ ), which can be rendered to images at any given resolution ( $\S 4.2$ ). Second, we train a diffusion model to generate samples from this latent space ( $\S 4.3$ ). Figure 2 illustrates our pipeline. + +# 4.1. Image Neural Field Autoencoder + +In the first stage, we seek to convert every image in our training set into a photorealistic image neural field. We do this by training an autoencoder, made of an encoder $E$ , a decoder $D$ , and a neural field renderer $R$ . The encoder maps an RGB input image $I$ to a latent code $z = E(I)$ , which is decoded by the decoder to a feature tensor $\phi = D(z)$ used by the neural field renderer to produce the final image. + +Patch-wise decoding. For training efficiency, we want to avoid decoding the whole image, because the ground truth can be at a very high resolution. We take advantage of the coordinate-based decoding property of neural fields, to train with constant-size crops from mixed-resolution data, which is amenable to batching. Specifically, we crop a random patch $p_{GT}$ at a fixed $P \times P$ resolution (the red box in Figure 2) from a randomly downsampled ground-truth. Since $p_{GT}$ is a fixed-size patch, downsampling the global ground truth lets the patch $p_{GT}$ cover regions at varying scales of the image. This provides supervision at multiple scales to the latent representation, from local details to global structure. We discuss this further in § 5.2. Let $c$ denote the coordinates of pixel centers in the patch within the image, and $s$ denote their pixel sizes relative to the whole ground-truth image. Our renderer $R$ takes as input the features $\phi = D(z)$ decoded from the latent representation, and the coordinates and pixel sizes $c, s$ to synthesize an output patch $p = R(c, s; \phi)$ . + +![](images/a6ba6cea5ae75798a4151e4360863d9518d89c29629bdd4b74b131b60f446033.jpg) +Figure 3. Convolutional Local Image Function (CLIF). Given a feature map $\phi$ (yellow dots), for each query point $x$ (green dot), we fetch the nearest feature vector, along with the relative coordinates and the pixel size. The grid of query information is then passed into a convolutional network (right) that renders an RGB grid. Different than the pointwise function LIIF, CLIF has a higher generation capacity and is learned to be still scale-consistent. + +Training objective. We compare the synthesized patch to the ground truth using a sum of an $L_{1}$ loss, a perceptual loss $\mathcal{L}_{\mathrm{perc}}$ [60], and an adversarial loss $\mathcal{L}_{\mathrm{GAN}}$ [14]. The discriminator is simultaneously trained to distinguish between the distributions of $p$ and $p_{GT}$ . Thus, we minimize the following objective to train $E$ , $D$ , and $R$ : + +$$ +\mathcal {L} _ {A E} = \left\| p - p _ {G T} \right\| _ {1} + \mathcal {L} _ {\text {p e r c}} (p, p _ {G T}) + \mathcal {L} _ {\mathrm {G A N}} (p). \tag {2} +$$ + +Our implementation follows the autoencoder architecture of LDM [41], with the same encoder and decoder (removed the last layer) architectures to facilitate comparisons. Since training images have arbitrary resolutions, we resample the encoder's input to a fixed resolution $256 \times 256$ . Note that despite this downsampling, we still train against mixed-resolution references. The encoder and decoder are with a spatial downsampling/upsampling rate of 4 correspondingly, therefore the latent representation is in $64 \times 64$ . A vector-quantization (VQ) layer is prepended to the first layer of the decoder to regularize the latent space. $\phi$ is $256 \times 256$ with 128 channels. We set patch size $P = 256$ . + +# 4.2. Neural Field Renderer + +Our renderer $R$ , shown in Figure 3, is a neural field coordinate-based decoder, which we dubbed Convolutional Local Image Function (CLIF). To decode an image patch with CLIF, each query point $c$ (green dot) fetches the spatially nearest feature vector from the feature map $\phi$ (yellow dots). We concatenate the nearest feature vector with the query coordinates $c$ and pixel size $s$ , then process the grid of query information using a convolutional network to output an RGB image. Intuitively, the concatenated feature is the field information at a point. By changing the query coordinates and pixel sizes, we can decode images at any resolution. LIIF [8] decodes with similar information, but it uses a pointwise function. We found this limits LIIF's ability to produce realistic high-frequency details (see supplementary material). CLIF remedies this issue by exploiting more local feature context. Our CLIF renderer is learned to be + +scale-consistent, i.e., details are consistent when decoding at different resolutions (see supplementary material). + +# 4.3. Latent diffusion + +Once the autoencoder is trained, we map every image $I$ in the training dataset to its latent representation $z$ , and train a diffusion model by optimizing the DDPM [16] objective + +$$ +\mathcal {L} _ {D M} = \mathbb {E} _ {z \sim E (I), t, \epsilon} \left[ \left| \left| \epsilon_ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} z + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t\right) - \epsilon \right| \right| ^ {2} \right], \tag {3} +$$ + +using the distribution over $z$ induced by the encoder. After training, the encoder can be discarded. The diffusion model generates a latent representation $z$ , which is then decoded to $\phi = D(z)$ and rendered at a resolution specified by the pixel coordinates $R(c,s;\phi)$ as described next. + +# 4.4. Patchwise Image Generation + +Despite being trained with small patches for efficiency, our method can generate high-resolution images. For this, we first generate a global feature map $\phi$ from a sampled $z$ , then generate sub-tiles of a large image by querying the renderer at the corresponding coordinates, as described in § 4.2. To avoid discontinuities at tile boundaries, we expand the query region for each tile by a fixed padding size larger than CLIF's receptive field (8 in our experiments). We then crop the output tiles by the same amount and assemble the tiles into a seamless composite. Our renderer is fully convolutional, it can also generate the image at once, as long as memory is sufficient to hold intermediate buffers. + +# 5. Experiments + +We evaluate our method on several datasets and compare it to LDM [41] with super-resolution models (§ 5.1). Sections § 5.2 and § 5.3 presents model ablations. We show results in solving multi-scale inverse problems in § 5.5, and text-to-image generation in § 5.6. + +Data. The FFHQ [20] used in LDM [41] contains 70K high-resolution images $(1024\times 1024)$ and several baselines use it for comparison. When comparing to LDM, we follow their training and validation split: 60K images for training and 10K for validation. Since our method is flexible and not limited to a fixed-resolution dataset, we also follow a controlled setting in prior work [6], which constructs a varied-resolution dataset from FFHQ by constructing and merging three sets: (i) all images at 256 low-resolution; (ii) a subset of 5K samples in varied-resolution from 512 to 1024; (iii) a subset of 1K images at 1024 resolution. We denote this setting as FFHQ 6K-Mix. Besides FFHQ, we evaluate our method on the Mountains dataset [6], which contains a low-resolution subset, with about 500K samples around 1024 resolution, and a high-resolution subset, with about 9K images at resolutions beyond 2048. Figure 4 shows examples of our generated results on these datasets. + +![](images/e5766754da577df85022f2b9067b28810c9c6f25bff81783d5a882434e609088.jpg) +Figure 4. Generated samples from our method on FFHQ and Mountains dataset. + +pFID metric. Standard FID evaluation first resize images to 299, which evaluates the global structure of images regardless of their original resolution, but is insufficient to measure the quality of details from high-resolution generators. Patch-FID [6] (pFID) addresses this limitation. It computes the FID between fixed-resolution patches cropped from arbitrary resolution ground-truth and generated images, thus evaluating local details in synthesized images. + +The original pFID reports the metric on random crops from images at varying resolutions. Since our practical focus is on high-resolution synthesis, we evaluate pFID between patches cropped from fixed-high-resolution images. To further disentangle the evaluation for image details at different scales, we separately report pFID for patches at different resolutions. $P / 1\mathrm{K}$ will denote the FID between random crops at resolution $P$ from ground truth and synthesized images at resolution 1024. For example, pFID-256/1K evaluates the local details, pFID-1K/1K evaluates the global structure and is the same as standard FID applied to 1024-resolution images. We generate 50K samples to compute FID in most experiments. In some experiments, we use 5K samples if it suffices to observe the performance gap (specified after FID@ in Tables). + +# 5.1. Comparison to LDM + +LDM [41] trains an autoencoder for images at $256 \times 256$ resolution and learns a diffusion model on its latent space. For a fair comparison, we used the same encoder and decoder architectures as LDM. Our method only adds a lightweight + +CLIF renderer, which contains 2 convolution layers and 2 ResNet [15] blocks. + +Even though LDM's denoiser is fully convolutional and can generate high-resolution images simply by diffusing from a larger noise map, it is known that this approach generates repetitive patterns (e.g., distorted faces with duplicate features), we show examples in the supplementary material. As a result, we follow the standard approach to generate high-resolution images with LDM by running an independent super-resolution model on its output. We combine LDM with several recent state-of-the-art arbitrary-scale super-resolution methods: LIIF [8], ITSRN [59], LTE [25], which allow for inference at continuous upsampling scales, and Real-ESRGAN [58], a super-resolution model for a fixed upsampling scale that has state-of-the-art perceptual quality. We report qualitative results in Figure 5, and the pFID in Table 1 on FFHQ. As Real-ESRGAN shows the most competitive results, we also compare to it on Mountains dataset in Table 2. + +We find that for standard FID at 256 resolution (i.e. pFID 256/256), the image neural field diffusion model is competitive with the original LDM, which can only generate images at 256. Our retraining of LDM reaches a slightly worse FID than the officially reported scores, which we attribute to implementation differences and training variance. At all higher resolutions, our method outperforms LDM followed by super-resolution, which is consistent with our qualitative observation and suggests we achieve better image quality for high-resolution detail at different scales. + +![](images/cb12a73ef95595989ef118da020081747bac5c4685f9683b19a03042542020c5.jpg) +$\mathrm{LDM} + \mathrm{LIIF}$ + +![](images/0638ad6c7b2a2c8695e8e6edb91a48c5d8a79b9d76af42af721b9797fad1d502.jpg) +LDM + Real-ESRGAN + +![](images/40cd23083a74e3e54735eb05e573737129de8c85da10001c7cd847a344d7881f.jpg) +Figure 5. Qualitative comparison with LDM followed by super-resolution on FFHQ. LIIF shows noise in details, while Real-ESRGAN tends to be smooth and results lack rich details. Our approach generates images with more realistic details. + +![](images/3ae482dead9ef4fff3cc2b4b0db33b0667a5c73c826432a063e2168c05306085.jpg) +Ours + +![](images/2a5366167c187ecf862aa2d6136bd3944f7405704c9673aff92ef262f9ed3006.jpg) + +
Model#ParamsCoordinate-based DecoderpFID@50K
256/256256/1K512/1K1K/1K
LDM [41]33.0M4.98---
LDM + LIIF [8]33.0M + 22.3M✓-56.6517.838.97
LDM + ITS RN-RDN [59]33.0M + 22.6M✓-51.7317.948.02
LDM + SwinIR-LTE [25]33.0M + 12.1M✓-52.6217.729.09
LDM + Real-ESRGAN [58]33.0M + 16.7M-18.3818.4616.04
LDM (our reimplementation)33.0M6.02---
INFD (ours)35.7M✓5.348.076.645.57
+ +We hypothesize that the main issues for extra superresolution models are that: (i) LDM with an extra superresolution model can be viewed as first decoding the latent representation to RGB space, then upsample to another RGB space, where the first RGB space becomes a bottleneck that contains much less information than feature space; (ii) the artifacts generated by LDM, even inconspicuous, can cause a domain shift to the input of the superresolution models, which could significantly degrade their performance. The super-resolution models can not be directly trained to upsample the generated low-resolution images since no paired high-resolution ground truth is available. In our method, the domain shift from real to generated samples happens in the latent space (with VQ or KL regularization). We hypothesize that latent space is much more robust than RGB space to the domain shift. We observe that when replacing the latent space with RGB space, the generated images become overly smooth similar to LDM with Real-ESRGAN super-resolution, which is consistent with our hypothesis (see supplementary material). + +# 5.2. Effect of scale-varied training + +Randomly downsampling the global image before extracting fixed-resolution training patches would make patches cover all scales. With the scale consistency of CLIF, an image neural field is supervised to be realistic in all scales via the perceptual and GAN losses. We conduct an ablation on + +Table 1. Comparison to Latent Diffusion Model (LDM) with super-resolution models for high-resolution image synthesis on FFHQ dataset. #Params counts for the decoder, and the renderer or super-resolution model if it exists, which are used in image generation. + +
ModelpFID@50K
256/1K512/1K1K/1K
LDM + Real-ESRGAN [58]17.3615.1110.39
INFD (ours)7.536.845.13
+ +Table 2. Comparison to Latent Diffusion Model (LDM) with super-resolution models on Mountains dataset. + +FFHQ to evaluate the impact of this random downsampling strategy. Specifically, we disable it during training, keeping all ground-truth images at 1024 resolution. The results are shown in Table 3. Without random downsampling, the pFID is worse especially for $512/1\mathrm{K}$ and $1\mathrm{K}/1\mathrm{K}$ , suggesting that random downsampling of the ground truth improves quality, even if we only aim at generating images at 1024 high resolution, because it helps supervise every single image to be realistic at all scales. For Mountains dataset, we observe that there will be obvious artifacts without random downsampling (see supplementary material). This contrasts with the observation in LIIF [8], which found that random downsampling hurts performance at a fixed highest scale when it is only using an L1 loss. + +# 5.3. Training with limited high-resolution images + +While previous experiments use high-resolution training images, a key advantage of our method is that it can learn from mixed-resolution datasets and still generate + +
DownsamplepFID@50K
256/1K512/1K1K/1K
Fix 10248.196.826.04
256–10248.076.645.57
Δ0.120.180.47
+ +Table 3. FFHQ dataset. Random downsampling during training improves image generation quality even for fixed high resolution. + +
DatapFID@50K
256/1K512/1K1K/1K
All HR8.076.645.57
6K-Mix16.2710.811.3
6K-Mix, bal.12.417.746.9
+ +Table 4. FFHQ dataset. Our method can learn from mixed-resolution images with a limited number of full-resolution images. + +high-resolution outputs, even when the number of high-resolution images is limited. We quantify this in Table 4 using FFHQ 6K-Mix, where most images are at low resolution 256, 5K images are at 512-1024, and 1K images are at 1024. Training with the mixed-resolution dataset as-is (also with random downsampling) already yields a model that performs decently at 1024, but with worse details than the model trained with all images at 1024. We suspect that the model is optimized for too few steps using images at 1024, since the number of high-resolution images is small and they go through random downsampling. We balance the training resolution by sampling images from the $5\mathrm{K}+$ 1K high-resolution subset with a probability of 0.5. This largely closes the performance gap (6K-Mix, bal.) with the model train on high-resolution images only. + +# 5.4. Image generation beyond 1024 + +We explore going beyond the 1024 resolution and train our model on a collected dataset of faces at varied resolutions between 1024 to 2048, and on Mountains dataset including a higher-resolution subset (a generated sample is shown in Figure 1). We observe that our method can be effectively applied to resolutions up to $2\mathrm{K}$ . More samples and details are in the supplementary material. + +# 5.5. Inverse problems with conditions at any scale + +Our method builds a diffusion model on a latent space that represents image neural fields. A key property of image neural fields is that they can be efficiently rendered for any sub-region at any given resolution without decoding the whole image at full resolution. With the image prior learned by diffusion models, it enables efficiently solving inverse problems where conditions can be defined on any scale of the image based on coordinates. We take zero-shot any-scale layout-to-image generation as an example. It uses + +![](images/a265c2fa2958547b89f377113bb0457cc15a30fe13ee9f22ec712a88c02bb673.jpg) + +![](images/105169e3999789e502224981fa172c5d8e7eaeff54966a1acf816472549a86e9.jpg) +Figure 6. Solving inverse problems with multi-scale conditions per image. We can solve for an image that satisfies multiscale conditions, defined as square regions and a text prompt (left). For this, we decode the corresponding region and pass it to a pre-trained CLIP [39] model operating at fixed-resolution $(224 \times 224)$ , and maximize the CLIP similarity to the corresponding text prompt. This enables layout-to-image generation without extra training. We show generated solutions on the right. + +CLIP [39] similarity as the constraint for image generation with semantic bounding boxes at arbitrary scales. + +Specifically, we take a pre-trained CLIP model, which takes $224 \times 224$ fixed-resolution images as inputs. Given a layout and our image neural field diffusion model (unconditional), in each diffusion step, let $z$ denote the current denoised latent representation, for each semantic bounding box $i$ in the input layout we render $z$ for the corresponding sub-region to a patch at the resolution $224 \times 224$ , i.e. patch $p_i = R \circ D(z; c_i, s_i)$ , with our decoder $D$ and renderer $R$ , where $c_i, s_i$ denote the coordinates and scale of a $224 \times 224$ pixel grid of bounding box $i$ . The clip similarity loss $l_i = \mathrm{CLIP}(p_i, T_i)$ is computed between patch $p_i$ and the given text $T_i$ . The gradients $\frac{\partial l_i}{\partial z}$ are back-propagated and then used to modify the diffusion score for each diffusion step. We follow the techniques in DPS [10] as the inverse problem solver. Figure 6 shows the results of using our mountains model (2K resolution). Note that without image neural field diffusion models, a fixed-resolution diffusion model needs to decode the whole region at full resolution (e.g. $1000 \times 1000$ "cloud" region in a $2048 \times 2048$ canvas) before passing it as $224 \times 224$ input to CLIP, which would have very intensive computation and memory cost. + +# 5.6. Qualitative results for text to image generation + +We explore a preliminary application of our method for text-to-image generation by finetuning a pre-trained Stable Diffusion model [41]. Because of the high computational cost of training Stable Diffusion, we freeze the encoder and only finetune the decoder from publicly available pre-trained weights on a high-resolution subset of LAION-5B, which contains samples at resolutions higher than 2K. Our renderer has the same architecture as in previous experiments and is jointly trained from scratch. We show some qualitative samples from our fine-tuned model and compare them + +![](images/34e0bff27fd91c29311ea11d249327f4224d73dd633d54da80d82f2f2302375f.jpg) +Figure 7. Samples of our method finetuned from Stable Diffusion (LDM) compared to Stable Diffusion with an extra super-resolution model. Our approach yields finer, high-frequency textures. + +![](images/1d181db617c5e6392998a819d0ad2db1f7bdcba43f03591d4dab2ebbc33147a7.jpg) + +![](images/8ee136a3c6feaf2e1981cc24f5d7c05785c60c8998fd98f4614f5211d183981f.jpg) + +to upsampling the Stable Diffusion's $512 \times 512$ output using Real-ESRGAN in Figure 7. We observe that the comparison is similar to the experiments on FFHQ and Mountains: our method generates more details than the Real-ESRGAN applied to Stable Diffusion's outputs. More samples and details are in the supplementary material. + +# 6. Discussion + +Comparison to GANs with any-resolution learning. In this work, we propose a method to build diffusion models on a resolution-agnostic space and show its applications. The any-resolution learning framework has also been developed for different generative model families in prior works, for example, AnyresGAN [6]. We observe that the comparison between image neural field diffusion models and AnyresGAN matches the comparison between typical fixed-resolution diffusion models and GANs. A detailed comparison is in the supplementary material. In summary, we observe that GANs are still state-of-the-art on FID value (which is not always consistent with image quality [3, 4]) for the single-class generation, while image neural field diffusion model has better visual quality and diversity than AnyRes-GAN. Image neural field diffusion models are also free of the artifacts that commonly affect AnyRes-GAN's outputs, such as black dots and grid-like patterns. Finally, image neural field diffusion models can be directly applied for text-to-image synthesis, which remains a challenge for any-resolution GANs. Solving inverse problems based on the score functions of diffusion models is also not yet available in GANs. + +Limitations. Our current method assumes that the training data are scale-consistent, i.e., low-resolution images follow the same distribution as downsampled high-resolution + +images (see supplementary material). This assumption is violated by datasets that contain a low-resolution subset with noisy, compressed images, and a high-resolution subset with clean images (e.g., Birds, Churches datasets [6]). + +Due to limited resources, our text-to-image synthesis model only fine-tunes an existing Stable Diffusion checkpoint on a small subset of the LAION dataset containing high-resolution images. This causes two issues. First, the training set of the pre-trained model includes noisy images, but our high-resolution fine-tuning dataset only contains clean images; this violates our scale consistency assumption. As a result, we found that our model requires extra prompts such as "4k" to generate detailed high-resolution images. Second, our fine-tuning LAION subset does not cover all possible object categories, so our model may not perform optimally on some out-of-distribution objects. Training from scratch on the full LAION dataset might resolve these limitations. Researching efficient any-resolution encoders is also a promising avenue for future work. + +# 7. Conclusion + +We proposed image neural field diffusion models, the diffusion models on a resolution-agnostic latent space, and demonstrated its advantages over fixed-resolution models. We presented a simple yet effective framework as an implementation, which can be easily applied to convert from an existing latent diffusion model. 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In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 2 \ No newline at end of file diff --git a/2024/Image Neural Field Diffusion Models/images.zip b/2024/Image Neural Field Diffusion Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..9d6f0d423836b7269d51420e314f422f333b92cb --- /dev/null +++ b/2024/Image Neural Field Diffusion Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:acd8bb12673e672dc72e32ae704a61c0f5a144a3b5d8a18b8348660be8828a74 +size 585078 diff --git a/2024/Image Neural Field Diffusion Models/layout.json b/2024/Image Neural Field Diffusion Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..dff35e3832d0a0def03a55ae5b7e1f90c5ef766a --- /dev/null +++ b/2024/Image Neural Field Diffusion Models/layout.json @@ -0,0 +1,9093 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 181, + 103, + 412, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 103, + 412, + 121 + ], + "spans": [ + { + "bbox": [ + 181, + 103, + 412, + 121 + ], + "type": "text", + "content": "Image Neural Field Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 141, + 549, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 141, + 549, + 190 + ], + "spans": [ + { + "bbox": [ + 58, + 141, + 549, + 190 + ], + "type": "text", + "content": "Yinbo Chen1 Oliver Wang2 Richard Zhang3 Eli Shechtman3 Xiaolong Wang1† Michael Gharbi3† \n1UC San Diego 2Google Research 3Adobe Research https://yinboc.github.io/infd/" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 49, + 193, + 211, + 304 + ], + "blocks": [ + { + "bbox": [ + 49, + 193, + 211, + 304 + ], + "lines": [ + { + "bbox": [ + 49, + 193, + 211, + 304 + ], + "spans": [ + { + "bbox": [ + 49, + 193, + 211, + 304 + ], + "type": "image", + "image_path": "8d01dd13a4fd2c6cc81f34591355204926361717891bf905458923916ea59d39.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 87, + 306, + 172, + 326 + ], + "lines": [ + { + "bbox": [ + 87, + 306, + 172, + 326 + ], + "spans": [ + { + "bbox": [ + 87, + 306, + 172, + 326 + ], + "type": "text", + "content": "FFHQ Resolution: " + }, + { + "bbox": [ + 87, + 306, + 172, + 326 + ], + "type": "inline_equation", + "content": "1024\\times 1024" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 215, + 193, + 377, + 304 + ], + "blocks": [ + { + "bbox": [ + 215, + 193, + 377, + 304 + ], + "lines": [ + { + "bbox": [ + 215, + 193, + 377, + 304 + ], + "spans": [ + { + "bbox": [ + 215, + 193, + 377, + 304 + ], + "type": "image", + "image_path": "c182bbfc05caec26c2e2b1b3dbe62d348f0d7696890e72ec6664eeb3f6e051e9.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 254, + 307, + 338, + 326 + ], + "lines": [ + { + "bbox": [ + 254, + 307, + 338, + 326 + ], + "spans": [ + { + "bbox": [ + 254, + 307, + 338, + 326 + ], + "type": "text", + "content": "Mountains Resolution: " + }, + { + "bbox": [ + 254, + 307, + 338, + 326 + ], + "type": "inline_equation", + "content": "2048\\times 2048" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 331, + 546, + 364 + ], + "lines": [ + { + "bbox": [ + 45, + 331, + 546, + 364 + ], + "spans": [ + { + "bbox": [ + 45, + 331, + 546, + 364 + ], + "type": "text", + "content": "Figure 1. 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However, most diffusion models learn the distribution of fixed-resolution images. We propose to learn the distribution of continuous images by training diffusion models on image neural fields, which can be rendered at any resolution, and show its advantages over fixed-resolution models. To achieve this, a key challenge is to obtain a latent space that represents photorealistic image neural fields. We propose a simple and effective method, inspired by several recent techniques but with key changes to make the image neural fields photorealistic. Our method can be used to convert existing latent diffusion autoencoders into image neural field autoencoders. We show that image neural field diffusion models can be trained using mixed-resolution image datasets, outperform fixed-resolution diffusion models followed by super-resolution models, and can solve inverse problems with conditions applied at different scales efficiently." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 650, + 127, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 650, + 127, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 650, + 127, + 662 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 670, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 670, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 670, + 287, + 693 + ], + "type": "text", + "content": "Diffusion models [16, 34, 50] have recently become attractive alternatives to GANs. These likelihood-based models" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 368, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 368, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 306, + 368, + 545, + 571 + ], + "type": "text", + "content": "exhibit fewer artifacts, stable training, can model complex data distributions, do not suffer from mode collapse, and can solve inverse problems using the score function without extra training. Since diffusion typically requires many iterations at a fixed dimension, directly modeling the diffusion process in the pixel space [17, 40, 43] can be inefficient for high-resolution image synthesis. Latent diffusion models (LDMs) [41, 57] were proposed as a more efficient alternative. The key idea is to learn an autoencoder to map images to a latent representation from which the image can be decoded back, and train a diffusion model on the lower-dimensional latent representation. Despite their success, LDMs' latent space still represents images at fixed resolution (for example, 256 in LDM [41] and 512 in Stable Diffusion). To generate higher-resolution images (e.g., 2K), LDMs usually first generate a low-resolution image and up-sample it using a separate super-resolution model." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "In this work, we propose Image Neural Field Diffusion models (INFD). Our method is based on the latent diffusion framework, where we first learn a latent representation that represents an image neural field (which can be rendered at any resolution), then learn a diffusion model on this latent representation. A key challenge of our approach is to learn a latent space of photorealistic image neural fields where the diffusion model is applied. We propose a simple and effective method that can convert an existing autoencoder of latent diffusion models to a neural field autoencoder. We find that directly implementing an autoencoder with LIIF [8]" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 702, + 118, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 702, + 118, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 702, + 118, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 62, + 702, + 118, + 712 + ], + "type": "text", + "content": " Equal advising." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8007" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "content": "leads to blurred image details, and propose a Convolutional Local Image Function (CLIF), which can render the latent representation to photorealistic high-resolution images and the image content is consistent at different resolutions. Our neural field autoencoder is trained with L1 loss, perceptual loss [60], and GAN loss following LDM [41], and is supervised from multi-scale patches similar to AnyResGAN [6]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 287, + 418 + ], + "type": "text", + "content": "We show that image neural field diffusion models have several key advantages over fixed-resolution diffusion models: (i) They can be built from mixed-resolution datasets without resizing images. The neural field decoder can render latent representation at any resolution and from patches, which can take supervision from ground-truth images at arbitrary high resolution without decoding the whole image. (ii) The same latent representation can be supervised with GAN loss from fixed-resolution patches at different scales, with the content consistency across scales, the multiscale supervision helps high-resolution generation even if all ground-truth images are at a fixed high resolution. (iii) It does not require an extra Super-Resolution (SR) model for high-resolution generation. Besides the advantage of simplicity, since diffusion-generated low-resolution images do not have high-resolution ground truth, separate SR models are typically trained on real images, while the domain gap between real and generated images could significantly harm the performance of the SR model. (iv) Image neural field diffusion models learn a resolution-agnostic image prior. Therefore, it can be used to solve inverse problems with a set of conditions defined at different scales efficiently." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 420, + 223, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 420, + 223, + 430 + ], + "spans": [ + { + "bbox": [ + 59, + 420, + 223, + 430 + ], + "type": "text", + "content": "In summary, our main contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 432, + 287, + 550 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 432, + 287, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 466 + ], + "type": "text", + "content": "- An image neural field autoencoder that can learn representations from mixed-resolution datasets and renders scale-consistent and photorealistic images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 467, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 287, + 525 + ], + "type": "text", + "content": "- A method to build diffusion models on mixed-resolution datasets and synthesize high-resolution images without extra SR models. Image synthesis is up to 2K resolution with an efficient latent diffusion process at only " + }, + { + "bbox": [ + 47, + 467, + 287, + 525 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 47, + 467, + 287, + 525 + ], + "type": "text", + "content": " resolution (see samples in Figure 1)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 527, + 286, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 286, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 286, + 550 + ], + "type": "text", + "content": "- A framework to solve inverse problems with conditions applied at different scales of the same image." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 562, + 133, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 133, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 133, + 574 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Diffusion Models. Diffusion models are first proposed by Sohl-Dickstein et. al. [50]. They were recently connected to score-based generative models [51-53] and have been greatly improved [16, 34] for architectures and other training details, achieving state-of-the-art results on both unconditional and conditional image synthesis [11, 17, 33, 42, 44]. Compared to prior GAN-based methods [14, 21, 22, 38, 62], diffusion models have shown nice properties such as stable training, not suffering from mode collapse, and can perform image-to-image translation [28, 29] or be used to solve inverse problems [54], even with an uncondi" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "tional model. One of the main drawbacks of current diffusion models is slow inference speed, as it relies on iterative reverse diffusion steps. While this can be remedied with faster sampling methods [23, 27, 46], performing the diffusion process in the pixel space of high-resolution images remains computationally expensive." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 145, + 546, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 145, + 546, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 145, + 546, + 312 + ], + "type": "text", + "content": "Our work is most closely related to latent diffusion models, which learn to map images to latent representation and train diffusion model on the latent space [41, 47, 57]. A key design in this direction is to choose the latent representation where the diffusion model is learned. Different from prior works that learn an autoencoder, where the latent representation corresponds to a fixed resolution image, we design a decoder and a renderer to learn a latent space that represents image neural fields. Since our latent space represents image neural fields, our autoencoder can learn a representation from high-resolution images in varied sizes with multi-scale patches, and can synthesize images at high resolution without relying on extra super-resolution models. Our method follows LDM [41], which trains in two stages." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 321, + 546, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 546, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 546, + 464 + ], + "type": "text", + "content": "Neural Fields for Image Synthesis. Neural field is also known as Implicit Neural Representations (INR), which represents signals as coordinate-based neural networks. It serves as a compact and powerful differentiable representation and achieves state-of-the-art results mainly for representing 3D shapes [9, 30, 36] and scenes [2, 5, 19, 31, 37, 45, 48]. Applications of neural fields for images are explored in early works [32, 55] and proposed for more applications such as image super-resolution [8] and image synthesis [1, 49]. Several recent works [6, 22] relax the pixel-independent assumption and perform convolutions on the coordinate map to render the output for image synthesis." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 465, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 536 + ], + "type": "text", + "content": "The idea of using neural fields for training with any-resolution images is explored in LIIF [8] for autoencoding with an L1 loss, AnyResGAN [6] and ScaleParty [35] for GANs with adversarial loss. Our work aims at building the resolution-agnostic learning framework for diffusion models, which is a different model family of generative models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Image Super-Resolution. Image Super-Resolution [7, 12, 24, 26, 56, 58, 61] (SR) aims at upsampling a low-resolution image to higher resolution. Many recent works [8, 18, 25, 59] explore Arbitrary-Scale SR (ASSR) with a single network. While they are related to our method, the differences include: (i) Instead of learning an autoencoder and an extra SR model, our implementation can be viewed as making a bottleneck in a single ASSR model and training diffusion models on the bottleneck. (ii) Our decoder is decoding from latent space to RGB space while super-resolution is upsampling from RGB space to RGB space. (iii) Our input can potentially have any higher resolution information (e.g. crops from high resolution), we choose it as a fixed-low-resolution image for efficiency." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8008" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 76, + 486, + 213 + ], + "blocks": [ + { + "bbox": [ + 108, + 76, + 486, + 213 + ], + "lines": [ + { + "bbox": [ + 108, + 76, + 486, + 213 + ], + "spans": [ + { + "bbox": [ + 108, + 76, + 486, + 213 + ], + "type": "image", + "image_path": "d0804231f9cdc9222a74fe51d6aa149bd1784bb563dea899f6c64b3e7c3e5f12.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": "Figure 2. Method overview. Given a training image at an arbitrary resolution, we first downsample it to a fixed resolution and pass it into the encoder " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": " to get a latent representation " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": ". A decoder " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": " then takes " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": " as input and produces a feature map " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": " that drives a neural field renderer " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": ", which can render images by querying with the appropriate grid of pixel coordinates " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": " and pixel sizes " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": ". The autoencoder is trained on crops from a randomly downsampled image ground truth, generating image crops at the corresponding coordinates. At test time, a diffusion model generates a latent representation " + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 217, + 547, + 274 + ], + "type": "text", + "content": ", which is then decoded and used to render a high-resolution image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 283, + 288, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 283, + 288, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 283, + 288, + 308 + ], + "type": "text", + "content": "IDM [13] uses a diffusion model for ASSR where the output is at a medium resolution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 132, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 132, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 132, + 328 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 336, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 287, + 360 + ], + "type": "text", + "content": "Our algorithm builds on diffusion models and neural fields. We introduce the core concepts and notation below." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": "Diffusion Models. Given a sample " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": " from a data distribution " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ", forward diffusion progressively destroys the information in " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": " steps, " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "x_{t-1} \\mapsto x_t" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ", each adding some small Gaussian noise. The process can be concisely rewritten as " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "x_t = \\sqrt{\\bar{\\alpha}_t} x_0 + \\sqrt{1 - \\bar{\\alpha}_t} \\epsilon" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{0\\dots T-1}" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": " gradually decreases from 1 to 0. The final distribution is approximately normal, " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "q(x_T) \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ". A diffusion model learns to reverse this diffusion process. Once trained, new samples can be generated by first sampling " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "x_T \\sim q(x_T)" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": " and reversing each step of the diffusion process using a learned transition probability " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "p_\\theta(x_{t-1}|x_t)" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ", parameterized by a neural network. Many prior works on image generation are based on maximizing a reweighted variational lower-bound of " + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "inline_equation", + "content": "p_\\theta(x_0)" + }, + { + "bbox": [ + 46, + 364, + 287, + 543 + ], + "type": "text", + "content": ", which is shown by [16] to lead to the following training objective:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 547, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 547, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 63, + 547, + 287, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathbb {E} _ {x _ {0}, t, \\epsilon} \\left[ \\left| \\left| \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) - \\epsilon \\right| \\right| ^ {2} \\right], \\tag {1}", + "image_path": "1196506de0e37b39e07a4875a7aeed7f82dbe1ef119b7e7a8486bb3fc946b007.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "text", + "content": " is sampled in " + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\{0,\\dots ,T - 1\\}" + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 47, + 566, + 287, + 590 + ], + "type": "text", + "content": " is the network trained to reverse the diffusion process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Neural Fields. Neural Fields represent a signal using a coordinate-based neural network. For example, a neural field can represent an image as a function " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "c = f(x; \\phi)" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "x \\in [-1, 1]^2" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " are the spatial coordinates in the image domain, " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " is the RGB color at the corresponding continuous coordinate, and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " denotes the parameters of the neural field " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " can take continuous values, the RGB value can be decoded at arbitrary coordinates. Accordingly, an image neural field can be rendered at arbitrary resolution by sampling the corresponding pixel coordinates." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 281, + 361, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 361, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 361, + 294 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "text", + "content": "Similar to LDM [41], our approach has two stages. First, we train an autoencoder that converts images to latent representations of 2D neural fields (" + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "inline_equation", + "content": "\\S 4.1" + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "text", + "content": "), which can be rendered to images at any given resolution (" + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "inline_equation", + "content": "\\S 4.2" + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "text", + "content": "). Second, we train a diffusion model to generate samples from this latent space (" + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "inline_equation", + "content": "\\S 4.3" + }, + { + "bbox": [ + 305, + 302, + 546, + 374 + ], + "type": "text", + "content": "). Figure 2 illustrates our pipeline." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 383, + 482, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 482, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 482, + 396 + ], + "type": "text", + "content": "4.1. Image Neural Field Autoencoder" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": "In the first stage, we seek to convert every image in our training set into a photorealistic image neural field. We do this by training an autoencoder, made of an encoder " + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": ", a decoder " + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": ", and a neural field renderer " + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": ". The encoder maps an RGB input image " + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": " to a latent code " + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "inline_equation", + "content": "z = E(I)" + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": ", which is decoded by the decoder to a feature tensor " + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\phi = D(z)" + }, + { + "bbox": [ + 304, + 403, + 546, + 486 + ], + "type": "text", + "content": " used by the neural field renderer to produce the final image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": "Patch-wise decoding. For training efficiency, we want to avoid decoding the whole image, because the ground truth can be at a very high resolution. We take advantage of the coordinate-based decoding property of neural fields, to train with constant-size crops from mixed-resolution data, which is amenable to batching. Specifically, we crop a random patch " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "p_{GT}" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " at a fixed " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "P \\times P" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " resolution (the red box in Figure 2) from a randomly downsampled ground-truth. Since " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "p_{GT}" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " is a fixed-size patch, downsampling the global ground truth lets the patch " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "p_{GT}" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " cover regions at varying scales of the image. This provides supervision at multiple scales to the latent representation, from local details to global structure. We discuss this further in § 5.2. Let " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " denote the coordinates of pixel centers in the patch within the image, and " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " denote their pixel sizes relative to the whole ground-truth image. Our renderer " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " takes as input the features " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "\\phi = D(z)" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " decoded from the latent representation, and the coordinates and pixel sizes " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "c, s" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": " to synthesize an output patch " + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "inline_equation", + "content": "p = R(c, s; \\phi)" + }, + { + "bbox": [ + 304, + 493, + 547, + 721 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8009" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 71, + 260, + 152 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 260, + 152 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 260, + 152 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 260, + 152 + ], + "type": "image", + "image_path": "a6ba6cea5ae75798a4151e4360863d9518d89c29629bdd4b74b131b60f446033.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "lines": [ + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "spans": [ + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "type": "text", + "content": "Figure 3. Convolutional Local Image Function (CLIF). Given a feature map " + }, + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "type": "text", + "content": " (yellow dots), for each query point " + }, + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 154, + 289, + 233 + ], + "type": "text", + "content": " (green dot), we fetch the nearest feature vector, along with the relative coordinates and the pixel size. The grid of query information is then passed into a convolutional network (right) that renders an RGB grid. Different than the pointwise function LIIF, CLIF has a higher generation capacity and is learned to be still scale-consistent." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": "Training objective. We compare the synthesized patch to the ground truth using a sum of an " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " loss, a perceptual loss " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{perc}}" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " [60], and an adversarial loss " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{GAN}}" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " [14]. The discriminator is simultaneously trained to distinguish between the distributions of " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "p_{GT}" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": ". Thus, we minimize the following objective to train " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 327, + 287, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 327, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 59, + 327, + 287, + 340 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {A E} = \\left\\| p - p _ {G T} \\right\\| _ {1} + \\mathcal {L} _ {\\text {p e r c}} (p, p _ {G T}) + \\mathcal {L} _ {\\mathrm {G A N}} (p). \\tag {2}", + "image_path": "4296e931416d6e84b14cce7c634d30c74edc700b84f2a24da3e2910d7895162c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": "Our implementation follows the autoencoder architecture of LDM [41], with the same encoder and decoder (removed the last layer) architectures to facilitate comparisons. Since training images have arbitrary resolutions, we resample the encoder's input to a fixed resolution " + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": ". Note that despite this downsampling, we still train against mixed-resolution references. The encoder and decoder are with a spatial downsampling/upsampling rate of 4 correspondingly, therefore the latent representation is in " + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": ". A vector-quantization (VQ) layer is prepended to the first layer of the decoder to regularize the latent space. " + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": " with 128 channels. We set patch size " + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 503, + 176, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 176, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 176, + 514 + ], + "type": "text", + "content": "4.2. Neural Field Renderer" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "content": "Our renderer " + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "content": ", shown in Figure 3, is a neural field coordinate-based decoder, which we dubbed Convolutional Local Image Function (CLIF). To decode an image patch with CLIF, each query point " + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "content": " (green dot) fetches the spatially nearest feature vector from the feature map " + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "content": " (yellow dots). We concatenate the nearest feature vector with the query coordinates " + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "content": " and pixel size " + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 521, + 289, + 713 + ], + "type": "text", + "content": ", then process the grid of query information using a convolutional network to output an RGB image. Intuitively, the concatenated feature is the field information at a point. By changing the query coordinates and pixel sizes, we can decode images at any resolution. LIIF [8] decodes with similar information, but it uses a pointwise function. We found this limits LIIF's ability to produce realistic high-frequency details (see supplementary material). CLIF remedies this issue by exploiting more local feature context. Our CLIF renderer is learned to be" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "scale-consistent, i.e., details are consistent when decoding at different resolutions (see supplementary material)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 104, + 404, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 104, + 404, + 115 + ], + "spans": [ + { + "bbox": [ + 306, + 104, + 404, + 115 + ], + "type": "text", + "content": "4.3. Latent diffusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "spans": [ + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "content": "Once the autoencoder is trained, we map every image " + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "content": " in the training dataset to its latent representation " + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "content": ", and train a diffusion model by optimizing the DDPM [16] objective" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 167, + 545, + 182 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 167, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 310, + 167, + 545, + 182 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D M} = \\mathbb {E} _ {z \\sim E (I), t, \\epsilon} \\left[ \\left| \\left| \\epsilon_ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} z + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t\\right) - \\epsilon \\right| \\right| ^ {2} \\right], \\tag {3}", + "image_path": "cd24245d8780269a773637801d7a9be6c5beeef7fcf69b9714ea9eef199191c4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": "using the distribution over " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": " induced by the encoder. After training, the encoder can be discarded. The diffusion model generates a latent representation " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": ", which is then decoded to " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "\\phi = D(z)" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": " and rendered at a resolution specified by the pixel coordinates " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "R(c,s;\\phi)" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": " as described next." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 259, + 463, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 259, + 463, + 272 + ], + "spans": [ + { + "bbox": [ + 306, + 259, + 463, + 272 + ], + "type": "text", + "content": "4.4. Patchwise Image Generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "type": "text", + "content": "Despite being trained with small patches for efficiency, our method can generate high-resolution images. For this, we first generate a global feature map " + }, + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "type": "text", + "content": " from a sampled " + }, + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 277, + 545, + 421 + ], + "type": "text", + "content": ", then generate sub-tiles of a large image by querying the renderer at the corresponding coordinates, as described in § 4.2. To avoid discontinuities at tile boundaries, we expand the query region for each tile by a fixed padding size larger than CLIF's receptive field (8 in our experiments). We then crop the output tiles by the same amount and assemble the tiles into a seamless composite. Our renderer is fully convolutional, it can also generate the image at once, as long as memory is sufficient to hold intermediate buffers." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 433, + 387, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 387, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 387, + 445 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 453, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 513 + ], + "type": "text", + "content": "We evaluate our method on several datasets and compare it to LDM [41] with super-resolution models (§ 5.1). Sections § 5.2 and § 5.3 presents model ablations. We show results in solving multi-scale inverse problems in § 5.5, and text-to-image generation in § 5.6." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 517, + 547, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 721 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 721 + ], + "type": "text", + "content": "Data. The FFHQ [20] used in LDM [41] contains 70K high-resolution images " + }, + { + "bbox": [ + 304, + 517, + 547, + 721 + ], + "type": "inline_equation", + "content": "(1024\\times 1024)" + }, + { + "bbox": [ + 304, + 517, + 547, + 721 + ], + "type": "text", + "content": " and several baselines use it for comparison. When comparing to LDM, we follow their training and validation split: 60K images for training and 10K for validation. Since our method is flexible and not limited to a fixed-resolution dataset, we also follow a controlled setting in prior work [6], which constructs a varied-resolution dataset from FFHQ by constructing and merging three sets: (i) all images at 256 low-resolution; (ii) a subset of 5K samples in varied-resolution from 512 to 1024; (iii) a subset of 1K images at 1024 resolution. We denote this setting as FFHQ 6K-Mix. Besides FFHQ, we evaluate our method on the Mountains dataset [6], which contains a low-resolution subset, with about 500K samples around 1024 resolution, and a high-resolution subset, with about 9K images at resolutions beyond 2048. Figure 4 shows examples of our generated results on these datasets." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8010" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 547, + 330 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 547, + 330 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 547, + 330 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 547, + 330 + ], + "type": "image", + "image_path": "e5766754da577df85022f2b9067b28810c9c6f25bff81783d5a882434e609088.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 151, + 332, + 443, + 344 + ], + "lines": [ + { + "bbox": [ + 151, + 332, + 443, + 344 + ], + "spans": [ + { + "bbox": [ + 151, + 332, + 443, + 344 + ], + "type": "text", + "content": "Figure 4. Generated samples from our method on FFHQ and Mountains dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 354, + 287, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 451 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 451 + ], + "type": "text", + "content": "pFID metric. Standard FID evaluation first resize images to 299, which evaluates the global structure of images regardless of their original resolution, but is insufficient to measure the quality of details from high-resolution generators. Patch-FID [6] (pFID) addresses this limitation. It computes the FID between fixed-resolution patches cropped from arbitrary resolution ground-truth and generated images, thus evaluating local details in synthesized images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "type": "text", + "content": "The original pFID reports the metric on random crops from images at varying resolutions. Since our practical focus is on high-resolution synthesis, we evaluate pFID between patches cropped from fixed-high-resolution images. To further disentangle the evaluation for image details at different scales, we separately report pFID for patches at different resolutions. " + }, + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "type": "inline_equation", + "content": "P / 1\\mathrm{K}" + }, + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "type": "text", + "content": " will denote the FID between random crops at resolution " + }, + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 452, + 288, + 632 + ], + "type": "text", + "content": " from ground truth and synthesized images at resolution 1024. For example, pFID-256/1K evaluates the local details, pFID-1K/1K evaluates the global structure and is the same as standard FID applied to 1024-resolution images. We generate 50K samples to compute FID in most experiments. In some experiments, we use 5K samples if it suffices to observe the performance gap (specified after FID@ in Tables)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 645, + 168, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 168, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 168, + 658 + ], + "type": "text", + "content": "5.1. Comparison to LDM" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "LDM [41] trains an autoencoder for images at " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " resolution and learns a diffusion model on its latent space. For a fair comparison, we used the same encoder and decoder architectures as LDM. Our method only adds a lightweight" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 354, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 354, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 545, + 378 + ], + "type": "text", + "content": "CLIF renderer, which contains 2 convolution layers and 2 ResNet [15] blocks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 384, + 546, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 546, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 546, + 587 + ], + "type": "text", + "content": "Even though LDM's denoiser is fully convolutional and can generate high-resolution images simply by diffusing from a larger noise map, it is known that this approach generates repetitive patterns (e.g., distorted faces with duplicate features), we show examples in the supplementary material. As a result, we follow the standard approach to generate high-resolution images with LDM by running an independent super-resolution model on its output. We combine LDM with several recent state-of-the-art arbitrary-scale super-resolution methods: LIIF [8], ITSRN [59], LTE [25], which allow for inference at continuous upsampling scales, and Real-ESRGAN [58], a super-resolution model for a fixed upsampling scale that has state-of-the-art perceptual quality. We report qualitative results in Figure 5, and the pFID in Table 1 on FFHQ. As Real-ESRGAN shows the most competitive results, we also compare to it on Mountains dataset in Table 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "We find that for standard FID at 256 resolution (i.e. pFID 256/256), the image neural field diffusion model is competitive with the original LDM, which can only generate images at 256. Our retraining of LDM reaches a slightly worse FID than the officially reported scores, which we attribute to implementation differences and training variance. At all higher resolutions, our method outperforms LDM followed by super-resolution, which is consistent with our qualitative observation and suggests we achieve better image quality for high-resolution detail at different scales." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "8011" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 74, + 141, + 167 + ], + "blocks": [ + { + "bbox": [ + 49, + 74, + 141, + 167 + ], + "lines": [ + { + "bbox": [ + 49, + 74, + 141, + 167 + ], + "spans": [ + { + "bbox": [ + 49, + 74, + 141, + 167 + ], + "type": "image", + "image_path": "cb12a73ef95595989ef118da020081747bac5c4685f9683b19a03042542020c5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 170, + 118, + 178 + ], + "lines": [ + { + "bbox": [ + 72, + 170, + 118, + 178 + ], + "spans": [ + { + "bbox": [ + 72, + 170, + 118, + 178 + ], + "type": "inline_equation", + "content": "\\mathrm{LDM} + \\mathrm{LIIF}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 155, + 74, + 248, + 167 + ], + "blocks": [ + { + "bbox": [ + 155, + 74, + 248, + 167 + ], + "lines": [ + { + "bbox": [ + 155, + 74, + 248, + 167 + ], + "spans": [ + { + "bbox": [ + 155, + 74, + 248, + 167 + ], + "type": "image", + "image_path": "0638ad6c7b2a2c8695e8e6edb91a48c5d8a79b9d76af42af721b9797fad1d502.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 209, + 170, + 292, + 178 + ], + "lines": [ + { + "bbox": [ + 209, + 170, + 292, + 178 + ], + "spans": [ + { + "bbox": [ + 209, + 170, + 292, + 178 + ], + "type": "text", + "content": "LDM + Real-ESRGAN" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 251, + 74, + 343, + 167 + ], + "blocks": [ + { + "bbox": [ + 251, + 74, + 343, + 167 + ], + "lines": [ + { + "bbox": [ + 251, + 74, + 343, + 167 + ], + "spans": [ + { + "bbox": [ + 251, + 74, + 343, + 167 + ], + "type": "image", + "image_path": "40cd23083a74e3e54735eb05e573737129de8c85da10001c7cd847a344d7881f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 184, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 46, + 184, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 547, + 207 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison with LDM followed by super-resolution on FFHQ. LIIF shows noise in details, while Real-ESRGAN tends to be smooth and results lack rich details. Our approach generates images with more realistic details." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 358, + 74, + 449, + 167 + ], + "blocks": [ + { + "bbox": [ + 358, + 74, + 449, + 167 + ], + "lines": [ + { + "bbox": [ + 358, + 74, + 449, + 167 + ], + "spans": [ + { + "bbox": [ + 358, + 74, + 449, + 167 + ], + "type": "image", + "image_path": "3ae482dead9ef4fff3cc2b4b0db33b0667a5c73c826432a063e2168c05306085.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 444, + 170, + 462, + 178 + ], + "lines": [ + { + "bbox": [ + 444, + 170, + 462, + 178 + ], + "spans": [ + { + "bbox": [ + 444, + 170, + 462, + 178 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 452, + 74, + 544, + 167 + ], + "blocks": [ + { + "bbox": [ + 452, + 74, + 544, + 167 + ], + "lines": [ + { + "bbox": [ + 452, + 74, + 544, + 167 + ], + "spans": [ + { + "bbox": [ + 452, + 74, + 544, + 167 + ], + "type": "image", + "image_path": "2a5366167c187ecf862aa2d6136bd3944f7405704c9673aff92ef262f9ed3006.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 67, + 217, + 526, + 344 + ], + "blocks": [ + { + "bbox": [ + 67, + 217, + 526, + 344 + ], + "lines": [ + { + "bbox": [ + 67, + 217, + 526, + 344 + ], + "spans": [ + { + "bbox": [ + 67, + 217, + 526, + 344 + ], + "type": "table", + "html": "
Model#ParamsCoordinate-based DecoderpFID@50K
256/256256/1K512/1K1K/1K
LDM [41]33.0M4.98---
LDM + LIIF [8]33.0M + 22.3M✓-56.6517.838.97
LDM + ITS RN-RDN [59]33.0M + 22.6M✓-51.7317.948.02
LDM + SwinIR-LTE [25]33.0M + 12.1M✓-52.6217.729.09
LDM + Real-ESRGAN [58]33.0M + 16.7M-18.3818.4616.04
LDM (our reimplementation)33.0M6.02---
INFD (ours)35.7M✓5.348.076.645.57
", + "image_path": "2d2b8e8f14e0fe1b5d3c6403229c3d679dd6340ed3e1743b02f20de657804845.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 388, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 627 + ], + "type": "text", + "content": "We hypothesize that the main issues for extra superresolution models are that: (i) LDM with an extra superresolution model can be viewed as first decoding the latent representation to RGB space, then upsample to another RGB space, where the first RGB space becomes a bottleneck that contains much less information than feature space; (ii) the artifacts generated by LDM, even inconspicuous, can cause a domain shift to the input of the superresolution models, which could significantly degrade their performance. The super-resolution models can not be directly trained to upsample the generated low-resolution images since no paired high-resolution ground truth is available. In our method, the domain shift from real to generated samples happens in the latent space (with VQ or KL regularization). We hypothesize that latent space is much more robust than RGB space to the domain shift. We observe that when replacing the latent space with RGB space, the generated images become overly smooth similar to LDM with Real-ESRGAN super-resolution, which is consistent with our hypothesis (see supplementary material)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "type": "text", + "content": "5.2. Effect of scale-varied training" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Randomly downsampling the global image before extracting fixed-resolution training patches would make patches cover all scales. With the scale consistency of CLIF, an image neural field is supervised to be realistic in all scales via the perceptual and GAN losses. We conduct an ablation on" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 310, + 385, + 541, + 447 + ], + "blocks": [ + { + "bbox": [ + 46, + 353, + 546, + 375 + ], + "lines": [ + { + "bbox": [ + 46, + 353, + 546, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 546, + 375 + ], + "type": "text", + "content": "Table 1. Comparison to Latent Diffusion Model (LDM) with super-resolution models for high-resolution image synthesis on FFHQ dataset. #Params counts for the decoder, and the renderer or super-resolution model if it exists, which are used in image generation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 385, + 541, + 447 + ], + "lines": [ + { + "bbox": [ + 310, + 385, + 541, + 447 + ], + "spans": [ + { + "bbox": [ + 310, + 385, + 541, + 447 + ], + "type": "table", + "html": "
ModelpFID@50K
256/1K512/1K1K/1K
LDM + Real-ESRGAN [58]17.3615.1110.39
INFD (ours)7.536.845.13
", + "image_path": "aa2375196e19b9cdfbcb69d434ac437ea216a567c7c3417ca6f0d66ccafa5c0a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 455, + 545, + 477 + ], + "lines": [ + { + "bbox": [ + 305, + 455, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 545, + 477 + ], + "type": "text", + "content": "Table 2. Comparison to Latent Diffusion Model (LDM) with super-resolution models on Mountains dataset." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "type": "text", + "content": "FFHQ to evaluate the impact of this random downsampling strategy. Specifically, we disable it during training, keeping all ground-truth images at 1024 resolution. The results are shown in Table 3. Without random downsampling, the pFID is worse especially for " + }, + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "type": "inline_equation", + "content": "512/1\\mathrm{K}" + }, + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "type": "inline_equation", + "content": "1\\mathrm{K}/1\\mathrm{K}" + }, + { + "bbox": [ + 304, + 484, + 546, + 652 + ], + "type": "text", + "content": ", suggesting that random downsampling of the ground truth improves quality, even if we only aim at generating images at 1024 high resolution, because it helps supervise every single image to be realistic at all scales. For Mountains dataset, we observe that there will be obvious artifacts without random downsampling (see supplementary material). This contrasts with the observation in LIIF [8], which found that random downsampling hurts performance at a fixed highest scale when it is only using an L1 loss." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 659, + 537, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 659, + 537, + 672 + ], + "spans": [ + { + "bbox": [ + 305, + 659, + 537, + 672 + ], + "type": "text", + "content": "5.3. Training with limited high-resolution images" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "While previous experiments use high-resolution training images, a key advantage of our method is that it can learn from mixed-resolution datasets and still generate" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8012" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 70, + 255, + 148 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 255, + 148 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 255, + 148 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 255, + 148 + ], + "type": "table", + "html": "
DownsamplepFID@50K
256/1K512/1K1K/1K
Fix 10248.196.826.04
256–10248.076.645.57
Δ0.120.180.47
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DatapFID@50K
256/1K512/1K1K/1K
All HR8.076.645.57
6K-Mix16.2710.811.3
6K-Mix, bal.12.417.746.9
", + "image_path": "407600f70a46a24d75582f3ece3bef9e23b351692a3bb15046e796641b6664a6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 258, + 286, + 280 + ], + "lines": [ + { + "bbox": [ + 47, + 258, + 286, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 286, + 280 + ], + "type": "text", + "content": "Table 4. FFHQ dataset. Our method can learn from mixed-resolution images with a limited number of full-resolution images." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 292, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 471 + ], + "type": "text", + "content": "high-resolution outputs, even when the number of high-resolution images is limited. We quantify this in Table 4 using FFHQ 6K-Mix, where most images are at low resolution 256, 5K images are at 512-1024, and 1K images are at 1024. Training with the mixed-resolution dataset as-is (also with random downsampling) already yields a model that performs decently at 1024, but with worse details than the model trained with all images at 1024. We suspect that the model is optimized for too few steps using images at 1024, since the number of high-resolution images is small and they go through random downsampling. We balance the training resolution by sampling images from the " + }, + { + "bbox": [ + 46, + 292, + 287, + 471 + ], + "type": "inline_equation", + "content": "5\\mathrm{K}+" + }, + { + "bbox": [ + 46, + 292, + 287, + 471 + ], + "type": "text", + "content": " 1K high-resolution subset with a probability of 0.5. This largely closes the performance gap (6K-Mix, bal.) with the model train on high-resolution images only." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 478, + 213, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 213, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 213, + 491 + ], + "type": "text", + "content": "5.4. Image generation beyond 1024" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 496, + 286, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 286, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 286, + 579 + ], + "type": "text", + "content": "We explore going beyond the 1024 resolution and train our model on a collected dataset of faces at varied resolutions between 1024 to 2048, and on Mountains dataset including a higher-resolution subset (a generated sample is shown in Figure 1). We observe that our method can be effectively applied to resolutions up to " + }, + { + "bbox": [ + 46, + 496, + 286, + 579 + ], + "type": "inline_equation", + "content": "2\\mathrm{K}" + }, + { + "bbox": [ + 46, + 496, + 286, + 579 + ], + "type": "text", + "content": ". More samples and details are in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 282, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 282, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 282, + 601 + ], + "type": "text", + "content": "5.5. Inverse problems with conditions at any scale" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Our method builds a diffusion model on a latent space that represents image neural fields. A key property of image neural fields is that they can be efficiently rendered for any sub-region at any given resolution without decoding the whole image at full resolution. With the image prior learned by diffusion models, it enables efficiently solving inverse problems where conditions can be defined on any scale of the image based on coordinates. We take zero-shot any-scale layout-to-image generation as an example. It uses" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 131 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 131 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 131 + ], + "type": "image", + "image_path": "a265c2fa2958547b89f377113bb0457cc15a30fe13ee9f22ec712a88c02bb673.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 132, + 545, + 191 + ], + "blocks": [ + { + "bbox": [ + 307, + 132, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 307, + 132, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 307, + 132, + 545, + 191 + ], + "type": "image", + "image_path": "105169e3999789e502224981fa172c5d8e7eaeff54966a1acf816472549a86e9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 194, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 305, + 194, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 194, + 545, + 282 + ], + "type": "text", + "content": "Figure 6. Solving inverse problems with multi-scale conditions per image. We can solve for an image that satisfies multiscale conditions, defined as square regions and a text prompt (left). For this, we decode the corresponding region and pass it to a pre-trained CLIP [39] model operating at fixed-resolution " + }, + { + "bbox": [ + 305, + 194, + 545, + 282 + ], + "type": "inline_equation", + "content": "(224 \\times 224)" + }, + { + "bbox": [ + 305, + 194, + 545, + 282 + ], + "type": "text", + "content": ", and maximize the CLIP similarity to the corresponding text prompt. This enables layout-to-image generation without extra training. We show generated solutions on the right." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 293, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 316 + ], + "type": "text", + "content": "CLIP [39] similarity as the constraint for image generation with semantic bounding boxes at arbitrary scales." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": "Specifically, we take a pre-trained CLIP model, which takes " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " fixed-resolution images as inputs. Given a layout and our image neural field diffusion model (unconditional), in each diffusion step, let " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " denote the current denoised latent representation, for each semantic bounding box " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " in the input layout we render " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " for the corresponding sub-region to a patch at the resolution " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": ", i.e. patch " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "p_i = R \\circ D(z; c_i, s_i)" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": ", with our decoder " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " and renderer " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "c_i, s_i" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " denote the coordinates and scale of a " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " pixel grid of bounding box " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": ". The clip similarity loss " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "l_i = \\mathrm{CLIP}(p_i, T_i)" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " is computed between patch " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " and the given text " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "T_i" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": ". The gradients " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\frac{\\partial l_i}{\\partial z}" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " are back-propagated and then used to modify the diffusion score for each diffusion step. We follow the techniques in DPS [10] as the inverse problem solver. Figure 6 shows the results of using our mountains model (2K resolution). Note that without image neural field diffusion models, a fixed-resolution diffusion model needs to decode the whole region at full resolution (e.g. " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "1000 \\times 1000" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " \"cloud\" region in a " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "2048 \\times 2048" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " canvas) before passing it as " + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 317, + 546, + 568 + ], + "type": "text", + "content": " input to CLIP, which would have very intensive computation and memory cost." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 575, + 545, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 545, + 588 + ], + "type": "text", + "content": "5.6. Qualitative results for text to image generation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We explore a preliminary application of our method for text-to-image generation by finetuning a pre-trained Stable Diffusion model [41]. Because of the high computational cost of training Stable Diffusion, we freeze the encoder and only finetune the decoder from publicly available pre-trained weights on a high-resolution subset of LAION-5B, which contains samples at resolutions higher than 2K. Our renderer has the same architecture as in previous experiments and is jointly trained from scratch. We show some qualitative samples from our fine-tuned model and compare them" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8013" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 216, + 267 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 216, + 267 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 216, + 267 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 216, + 267 + ], + "type": "image", + "image_path": "34e0bff27fd91c29311ea11d249327f4224d73dd633d54da80d82f2f2302375f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 273, + 545, + 296 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 545, + 296 + ], + "type": "text", + "content": "Figure 7. Samples of our method finetuned from Stable Diffusion (LDM) compared to Stable Diffusion with an extra super-resolution model. Our approach yields finer, high-frequency textures." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 228, + 68, + 376, + 266 + ], + "blocks": [ + { + "bbox": [ + 228, + 68, + 376, + 266 + ], + "lines": [ + { + "bbox": [ + 228, + 68, + 376, + 266 + ], + "spans": [ + { + "bbox": [ + 228, + 68, + 376, + 266 + ], + "type": "image", + "image_path": "1d181db617c5e6392998a819d0ad2db1f7bdcba43f03591d4dab2ebbc33147a7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 388, + 68, + 536, + 267 + ], + "blocks": [ + { + "bbox": [ + 388, + 68, + 536, + 267 + ], + "lines": [ + { + "bbox": [ + 388, + 68, + 536, + 267 + ], + "spans": [ + { + "bbox": [ + 388, + 68, + 536, + 267 + ], + "type": "image", + "image_path": "8ee136a3c6feaf2e1981cc24f5d7c05785c60c8998fd98f4614f5211d183981f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 307, + 287, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 287, + 379 + ], + "type": "text", + "content": "to upsampling the Stable Diffusion's " + }, + { + "bbox": [ + 46, + 307, + 287, + 379 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 307, + 287, + 379 + ], + "type": "text", + "content": " output using Real-ESRGAN in Figure 7. We observe that the comparison is similar to the experiments on FFHQ and Mountains: our method generates more details than the Real-ESRGAN applied to Stable Diffusion's outputs. More samples and details are in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 389, + 117, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 117, + 402 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 117, + 402 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 409, + 288, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 288, + 672 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 288, + 672 + ], + "type": "text", + "content": "Comparison to GANs with any-resolution learning. In this work, we propose a method to build diffusion models on a resolution-agnostic space and show its applications. The any-resolution learning framework has also been developed for different generative model families in prior works, for example, AnyresGAN [6]. We observe that the comparison between image neural field diffusion models and AnyresGAN matches the comparison between typical fixed-resolution diffusion models and GANs. A detailed comparison is in the supplementary material. In summary, we observe that GANs are still state-of-the-art on FID value (which is not always consistent with image quality [3, 4]) for the single-class generation, while image neural field diffusion model has better visual quality and diversity than AnyRes-GAN. Image neural field diffusion models are also free of the artifacts that commonly affect AnyRes-GAN's outputs, such as black dots and grid-like patterns. Finally, image neural field diffusion models can be directly applied for text-to-image synthesis, which remains a challenge for any-resolution GANs. Solving inverse problems based on the score functions of diffusion models is also not yet available in GANs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Limitations. Our current method assumes that the training data are scale-consistent, i.e., low-resolution images follow the same distribution as downsampled high-resolution" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 307, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 354 + ], + "type": "text", + "content": "images (see supplementary material). This assumption is violated by datasets that contain a low-resolution subset with noisy, compressed images, and a high-resolution subset with clean images (e.g., Birds, Churches datasets [6])." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 355, + 546, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 546, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 546, + 535 + ], + "type": "text", + "content": "Due to limited resources, our text-to-image synthesis model only fine-tunes an existing Stable Diffusion checkpoint on a small subset of the LAION dataset containing high-resolution images. This causes two issues. First, the training set of the pre-trained model includes noisy images, but our high-resolution fine-tuning dataset only contains clean images; this violates our scale consistency assumption. As a result, we found that our model requires extra prompts such as \"4k\" to generate detailed high-resolution images. Second, our fine-tuning LAION subset does not cover all possible object categories, so our model may not perform optimally on some out-of-distribution objects. Training from scratch on the full LAION dataset might resolve these limitations. Researching efficient any-resolution encoders is also a promising avenue for future work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 542, + 378, + 554 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 542, + 378, + 554 + ], + "spans": [ + { + "bbox": [ + 306, + 542, + 378, + 554 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": "We proposed image neural field diffusion models, the diffusion models on a resolution-agnostic latent space, and demonstrated its advantages over fixed-resolution models. We presented a simple yet effective framework as an implementation, which can be easily applied to convert from an existing latent diffusion model. Our method can build diffusion models from mixed-resolution datasets, achieving high-resolution synthesis without extra super-resolution models. The resolution-agnostic image prior learned by the diffusion model also enables solving inverse problems with conditions applied at different scales of the same image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported, in part, by NSF CAREER Award IIS-2240014, and the CISCO Faculty Award." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8014" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Ivan Anokhin, Kirill Demochkin, Taras Khakhulin, Gleb Sterkin, Victor Lempitsky, and Denis Korzhenkov. 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CNNs and window-attention methods are two major categories of canonical SR models. However, these measures are rigid: in both operations, each pixel gathers the same number of neighboring pixels, hindering their effectiveness in SR tasks. Alternatively, we leverage the flexibility of graphs and propose the Image Processing GNN (IPG) model to break the rigidity that dominates previous SR methods. Firstly, SR is unbalanced in that most reconstruction efforts are concentrated to a small proportion of detail-rich image parts. Hence, we leverage degree flexibility by assigning higher node degrees to detail-rich image nodes. Then in order to construct graphs for SR-effective aggregation, we treat images as pixel node sets rather than patch nodes. Lastly, we hold that both local and global information are crucial for SR performance. In the hope of gathering pixel information from both local and global scales efficiently via flexible graphs, we search node connections within nearby regions to construct local graphs; and find connections within a strided sampling space of the whole image for global graphs. The flexibility of graphs boosts the SR performance of the IPG model. Experiment results on various datasets demonstrate that the proposed IPG outperforms State-of-the-Art baselines. Codes are available at this link.", + "bbox": [ + 76, + 301, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 710, + 209, + 726 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ill-posed task of Super-Resolution (SR) constructs high-resolution images from low-resolution ones. SR works typically apply Deep Neural Network (DNN) knowledge learned from High-Resolution training images to construct missing details in low-resolution inputs. Existing DNN variants for classical SR tasks include CNNs [16, 24, 50] and Transformers [5, 6, 23]. These measures have proved effective in creating High-Resolution images, and are used in real-world applications like medical imaging [10], re", + "bbox": [ + 75, + 737, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f9407516bdd427c1a3c11dbadaf6e5aa92cbd90cb1768401cbaffe4567f98ae0.jpg", + "image_caption": [ + "Convolution" + ], + "image_footnote": [], + "bbox": [ + 513, + 273, + 591, + 329 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a03f148d486c349d3323fff93d6b557020a86faeda9a440811e623d3f01c72c3.jpg", + "image_caption": [ + "Self-Attention" + ], + "image_footnote": [], + "bbox": [ + 606, + 282, + 663, + 324 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/78d907fceb672e0d8f08851975c8600138aced3d9c0abf480897703bce2e01ed.jpg", + "image_caption": [ + "KNN Graph" + ], + "image_footnote": [], + "bbox": [ + 679, + 273, + 766, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/86263c14de8ea65088d6d0913ce3ad7e50fdd407c248f70a63a90e06f86c3571.jpg", + "image_caption": [ + "Ours", + "Figure 1. Convolution (left), Self-Attention (middle-left), KNN Graph Aggregation (middle-right), and Graph Aggregation in IPG (right). Compared with other methods, IPG graph aggregation considers the unbalanced nature of SR: detail-rich, high-frequency image nodes (red) have higher node degrees; while flat, low-frequency image nodes (blue) require fewer aggregations." + ], + "image_footnote": [], + "bbox": [ + 789, + 267, + 890, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mote sensing [15], et cetera.", + "bbox": [ + 500, + 455, + 689, + 470 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite various measures, it is taken for granted that mainstream SR models treat all pixels in a fairly rigid manner. For instance, as shown in Figure 1, in convolution layers of the CNN-based SR model VDSR [16], the same convolution kernel scans through all pixels of feature maps, i.e. each pixel is rigidly designated to communicate with its nearest neighbors; in the Transformer-based model SwinIR [23], all pixels are assigned to equal-sized attention grids for self-attention operations. In both examples, each pixel aggregates information from a fixed number of pixels within a neighborhood of fixed size.", + "bbox": [ + 496, + 473, + 892, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Efforts have been made to overcome the rigidity of convolution and window-attention operations. For example, some recent SR research tries to enhance SR models by enlarging self-attention grids [5, 46] and designing striped global attention windows [6, 22]. But these improvements also introduce a large computation burden. Some other works [12, 26, 52] leverage the flexibility of graphs and propose graph-based methods. With content-based graphs constructed from patch nodes, each image patch could aggregate top- $k$ relevant but distant parts beyond hard local boundaries in convolution and window-attention.", + "bbox": [ + 496, + 641, + 893, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, these graph measures have limited flexibility because the lopsided nature of SR is overlooked. In SR tasks, only a small proportion of high-frequency pixels require hard reconstruction efforts; the majority of pixels are located in flat, low-frequency regions and thus almost left intact [9]. In response to the imbalance, SR methods should", + "bbox": [ + 496, + 809, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24108", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ideally pay more attention to detail-rich regions and care less about flat, detail-poor image parts. However, existing $k$ -Nearest-Neighbor graph-based methods treat all image nodes equally. In other words, all nodes share the same pre-set degree $k$ and the unbalanced nature of SR is not considered. In fact, as we inspect canonical operation paradigms in SR from a graph perspective, we found that degree-equivalence rigidity also manifests in convolution and window-attention: in these paradigms, each pixel on the image aggregates the same number of pixels regardless of image content, and thus, sharing \"equal degrees\" in graph terms. Equal node degrees that are rigidly assigned to nodes or pixels mismatch their unequal reconstruction demands in SR, thus impacting SR performance.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Trying to break rigidity, we propose the graph-based Image Processing Graph Neural Networks (IPG) model for SR that taps the flexibility potential of graphs. Firstly, to break the degree-equivalence rigidity of convolution, window-attention, and $k$ -Nearest-Neighbor (KNN) graphs, we leverage degree flexibility by proposing a novel degree-variant graph solution based on the unbalanced nature of SR. Specifically, a detail-aware metric is designed to measure the importance of image nodes where larger degrees are assigned to high-frequency nodes. Then, different from graph-based model counterparts, IPG adopts pixels rather than patches as image graph nodes to avoid misalignment issues due to patch rigidity. Finally, in the interest of having both local and global perception without sacrificing efficiency due to large pixel-level search space, we resort to local and global node sampling strategies. In this way, graphs are established efficiently from small pixel subsets and could either focus on local information for detail reconstruction, or span over the whole image for spatially distant but crucial features. With the measures mentioned above, IPG could fully exert graph flexibilities and achieve outstanding performances on SR tasks.", + "bbox": [ + 75, + 301, + 472, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 648, + 218, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent SR Methods. In canonical approaches to SuperResolution, manifold previous works phrase SR as a regression problem and is proved effective via applications of CNN models [16, 24, 50, 51]. In these works, a crafted CNN model is applied to the LR image to render it into HR. Since the introduction of Transformers to vision [8], manifold works integrate the self-attention mechanism in Transformers into SR models [4-7, 23, 47, 53]. SwinIR [23] borrows shifted window-attention to SR and demonstrates good performance. Latest SR models include using striped attention windows [6, 22], channel attention [5, 22, 40], permuted attention [53], et cetera.", + "bbox": [ + 75, + 672, + 468, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the fact that manifold SR works follow similar convolution or window-attention methodologies, their SR performance is still confined to the rigidity of ordinary vi", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sion models, i.e. fixed paradigms for aggregating neighboring pixels and neglecting the unbalanced reconstruction demand among pixels in SR. Hence, we resort to graphs as a flexible way to aggregate information in order to break these sorts of rigidity.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graphs for Vision. Graphs have been widely applied to vision tasks, including point cloud segmentation [17, 41], human action recognition [42], and image classification [12, 32]. Some previous low-level vision works also view images as graphs. Most works leverage graph to aggregate non-local information, either intra-scale [2, 18, 21, 35, 38] or cross-scale [26, 52]. Other low-level vision works on graphs include cross-layer [27] or inter-image information aggregation [37]. Among these works, edge-conditioned aggregation from neighboring nodes is mostly preferred.", + "bbox": [ + 496, + 167, + 892, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In terms of graph construction from images, a majority of works use $k$ -nearest neighbors [18, 21, 26, 35, 38, 52]. Since all image nodes share the same degree, KNN graphs are not flexible enough; and the unbalanced nature of image nodes in low-level vision tasks is neglected as well. Besides, most graph works regard patches as image nodes [18, 21, 26, 35, 52], disregarding potential patch misalignment issues in low-level vision. As for the scale of graphs, some works [21, 26, 52] search in a global scale to construct graphs; other works [38, 39] construct graphs from a local box. Graphs in these works are not flexible enough in that they fail to take care of both local and global aspects.", + "bbox": [ + 496, + 319, + 893, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 517, + 591, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Rigidity of Previous SR Methods", + "text_level": 1, + "bbox": [ + 500, + 542, + 785, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Convolution [16, 24, 50] and window-attention [5, 6, 23] are two major pathways for SR model designs. Despite popular usages in SR, these measures are not flexible; their deep-rooted rigidity could hinder SR performance. In one convolution operation, each outputted pixel gathers information within a tiny kernel-sized window; each pixel only has access to its neighboring pixels. For instance, in a standard $3 \\times 3$ convolution, the perception field of a single pixel is confined to a tiny $3 \\times 3$ box. All pixels on the image collect information from 8 respective neighbors and themselves. The similar rigidity goes for window attention: though larger window sizes (compared to convolution) are usually adopted, the perception field of window attention is still confined within hard window boundaries. In a $8 \\times 8$ window-attention scenario, all pixels gather 64 pixels within the window where they belong.", + "bbox": [ + 496, + 566, + 890, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, beyond rigidity in convolution and window-attention, some works think out of the box and adopt graphs in SR models. Unlike convolution and window-attention where information aggregation is bounded to boxes, these graph-based works are more spatially flexible: each node could aggregate information from its favorite top- $k$ nodes", + "bbox": [ + 496, + 809, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24109", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with loose spatial constraints. In this sense, graph aggregation is not limited to preset rigid patterns; it is more dynamic and scalable compared to convolution and window-attention counterparts.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, though previous graph-based methods break through hard aggregation boundaries, we hold that the flexibility of graphs is not fully exploited in SR tasks. First and foremost, as shown in Figure 1, all previous methodologies (either graph-based, convolution-based, or window-attention-based) are degree-rigid. SR reconstruction demand is unbalanced among different image parts. But in previous methods, all pixels or nodes on the image are aggregating the same number of pixels or nodes; i.e. in graph terms, they share the same aggregation degree. Secondly, previous graph-based works are patch-rigid. Though patches are usually regarded as image nodes, patch aggregation usually requires rigid pixel-wise alignment. Possible misalignment of low-level features in patches makes SR models perform worse. Thirdly, previous graph-based works rigidly use graphs on either global or local scales, but information at both scales is potentially important for SR reconstruction. These rigid aspects are hindering the performance of SR models.", + "bbox": [ + 75, + 152, + 472, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Graph Construction", + "text_level": 1, + "bbox": [ + 76, + 449, + 269, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To break these rigidities, we construct degree-flexible pixel graphs at local and global scales in the IPG model. In this manner, we could fully exploit the flexibility of graphs and achieve outstanding performance in SR tasks.", + "bbox": [ + 75, + 472, + 468, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Degree Flexibility. Firstly, we try to figure out a degree-flexible graph solution based on the unique \"unbalanced property\" of SR tasks. SR reconstruction of images features imbalance. As Gou et al. [9] put it, SR is a long-tailed problem where only a small proportion of high-frequency pixels need to be reconstructed; the rest of the image parts need minimal restoration only. However, Gou et al. [9] tries to address the issue by designing training losses rather than rethinking it from the aspect of model designs. In the lopsided SR problem, it is a long-neglected aspect that treating all pixels or parts on the image equivalently is unsuitable and inefficient.", + "bbox": [ + 75, + 532, + 468, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To this end, we opt to assign various node degrees to pixels based on a detail-rich indicator that marks pixels needing more reconstruction efforts. Then we design the detail-rich indicator as follows: given feature map $F \\in \\mathbb{R}^{H \\times W \\times C}$ and downsampling ratio $s$ , the detail-rich indicator metric per pixel $D_F \\in \\mathbb{R}^{H \\times W}$ is designated as the absolute difference between the bilinearly downsampled and upsampled feature map and the feature map itself:", + "bbox": [ + 75, + 714, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nD _ {F} := \\sum_ {C} | F - F _ {\\downarrow s \\uparrow s} |, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 848, + 468, + 878 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $s$ is taken as 2 to avoid severe information loss. We", + "bbox": [ + 76, + 885, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are aware that some explainable SR works [11, 43] propose metrics to measure the importance of a certain part in the output. However, these measures are gradient-based, which requires costly backward passes. In comparison, the proposed metric $D_F$ is operation cheap in that it only requires bilinear interpolation twice. We also provide FLOPs statistics in the Appendix.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/463e47e7bd2a8b7d799ab62add45771562c7dcf21c6c68a1528a5b18abec70be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 210, + 627, + 292 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fec15f367ba9b91678acc6325cf0fb2ad52985f213cf32f3440dc3264191caf8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 643, + 210, + 750, + 291 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8aa71af9f51d10f89a4b7e2940acca9397a8c565ab72361d88018522bf32ad83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 210, + 867, + 291 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dc9a4901359db228b540609b3e68d516bdc0a10b8557c3f3df625ce5d228d07e.jpg", + "image_caption": [ + "Figure 2. Visualization of the detail-rich indicator $D_F$ in IPG. Original image (left); $D_F$ of the shallowest block (middle); $D_F$ of the deepest block (right). $D_F$ could effectively reflect detail-rich parts on the image." + ], + "image_footnote": [], + "bbox": [ + 522, + 306, + 627, + 386 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ba07e71de4be529142d8edde203d378812cdc27a87cd935eec2f451935500efd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 643, + 306, + 750, + 386 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b4a96cd5f0bafdfdabf64e846f7b31234aa2d122d51179bd23edf5cb3125b809.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 306, + 867, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall degree budgets are assigned to each pixels based on $D_F$ . The degree for a pixel node $v \\in F$ on the feature map is in proportion to its corresponding pixel value at $D_F$ :", + "bbox": [ + 496, + 473, + 890, + 532 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\deg (v) \\propto D _ {F} (v). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 547, + 890, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The detail-rich indicator $D_F$ in different MGB blocks is visualized. From Figure 2, it can be seen that detail-rich parts are responsive: margins and corners have high $D_F$ while flat color blocks are low in $D_F$ . The visualization reveals that the proposed $D_F$ could effectively reflect high-frequency parts on the image throughout layers.", + "bbox": [ + 496, + 568, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pixel Node Flexibility. Then we are faced with the formulation of vertices in image graphs. In previous graph-based vision works [21, 26, 36, 52], graph nodes are typically set as image patches. During graph aggregation, patches are weighted-summed in a pixel-wise manner. However, the forcible element-wise alignment of pixels during aggregation is unsuitable for SR tasks where feature maps have rich low-level features. Object shift and rotation within low-level patches are two major issues causing patch misalignment. As for object shift, locations of objects within patches could vary; location-misaligned patch objects introduce noises. Object rotation is another faulty aspect of patch aggregation. The orientation of patches is disregarded due to rigid rectangular patch shapes during patch alignment.", + "bbox": [ + 496, + 659, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To avoid the above problems during node aggregation, we hold that finer-grained pixel nodes are better solutions", + "bbox": [ + 500, + 871, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24110", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5e5e9c01f0040e16728651be5036daff69339ac10a3c575956f2ea7702ea459c.jpg", + "image_caption": [ + "Figure 3. The architectures of IPG, Multiscale Graph-aggregation Blocks (MGB), and Graph Aggregation Layers (GAL). Each IPG consists of $M$ MGB blocks, and each MGB has $G$ GAL layers. Local and global graphs are distributed to GALs alternatively within MGB." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in the low-level vision scenario. Pixel graphs are more flexible: each pixel node could directly find its relevant pixels in aggregation, therefore avoiding pixel misalignment.", + "bbox": [ + 75, + 311, + 468, + 358 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, we admit that compared to pixel graphs, patch graphs could potentially have larger perception fields and are easier to construct due to a smaller number of nodes in total, which means a smaller search space for edge connections. Hence, we need an efficient way to construct a flexible and effective pixel graph.", + "bbox": [ + 75, + 359, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Space Flexibility. Then we develop the space flexibility of IPG graphs via an efficient search of pixel node connections both locally and globally. We propose that both local and global information are crucial for SR reconstruction: while lossy image parts could rebuild themselves from local neighborhoods, they could also learn from distant but similar features for refinement.", + "bbox": [ + 75, + 454, + 468, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing graph-based methods have demonstrated some sort of space flexibility. As shown in Figure 1, compared to convolution and window attention options where a pixel always attends to a fixed neighboring region, graph aggregation could flexibly focus on crucial image parts regardless of space limits. However, existing graph-based works are not spatially flexible enough as they fail to consider both local and global aspects.", + "bbox": [ + 75, + 561, + 468, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In fact, computation considerations are the major concern of a comprehensive connection search. It is costly to construct global graphs by searching through all image nodes. As a remedy, strided sampling is always adopted [21, 26, 52]. But consequently, local regions are neglected. The choice of pixels as graph nodes makes graph construction even more challenging, because node spaces are enlarged further and it is hardly impractical to search through all pixels for graph construction.", + "bbox": [ + 75, + 686, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the sake of efficiency, and to gather local-level surrounding features and global-level distant features contributive to detail reconstruction in SR tasks, we use two types of sampling to aggregate both local and global information, shown in Figure 4. For local sampling, the neighborhood", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "surrounding a certain node is chosen as a local-scale search space on which a graph is established; for global sampling, sampled nodes span over the image in a dilated pattern.", + "bbox": [ + 498, + 311, + 890, + 359 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ef3ba82d44582151f347c7a186ff6a1dbf68270487ec97e20f541f97788e68a2.jpg", + "image_caption": [ + "Figure 4. An illustration of sampling strategies. The original image with the highlighted image node (left), local sampling (middle), and global sampling (right) are demonstrated. In this way, image graphs could flexibly gather both local and global information in an efficient manner." + ], + "image_footnote": [], + "bbox": [ + 511, + 378, + 629, + 470 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8ef6bd8f289fb2a6ea95e177e751ccaf33fd1138c46400eec4895678ee56d43f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 378, + 756, + 470 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6d9f9ac110afed8545f74672707bebf4a14b3d5d6ecc22eff944ac5be8d08e15.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 378, + 880, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the proposed IPG SR model, both sampling methods are performed in order to construct local and global-scale graphs. For each pixel node, its node connections are searched within the sampling space. In this way, we achieve spatial flexibility in a cost-efficient fashion.", + "bbox": [ + 498, + 577, + 890, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Graph Aggregation", + "text_level": 1, + "bbox": [ + 500, + 665, + 687, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now that flexible graphs are constructed, graph aggregation is performed such that each node can communicate with its connected neighbors and use their information for self-refinement in SR. In vision applications of graphs, aggregation in max-pooling [12, 28] or edge-conditioned [21, 26, 36] forms are mostly preferred. We tend to adopt edge-conditioned aggregation [36], as max-pooling could result in significant loss of information from neighboring pixels that are crucial for low-level vision. Since pixel reconstruction in SR heavily relies on abundant neighboring information, edge-conditioned aggregation is adopted as it cares about pixel inter-relations and maintains more neighboring information for effective reconstruction. The edge-conditioned aggregation [21, 26, 36, 52] is mathematically", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24111", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "formulated as follows: at the $k^{th}$ layer in IPG, given node feature $\\mathbf{h}^{k - 1}$ as input, neighboring node set $\\mathcal{N}(v)$ , the node $v$ output $\\mathbf{h}_v^k$ is calculated as:", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {v} ^ {k} = \\frac {1}{C ^ {k}} \\sum_ {u \\in N (v)} \\exp \\left(f ^ {k} (u, v)\\right) \\mathbf {h} _ {u} ^ {k - 1}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 148, + 468, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f^k: \\mathbb{R}^d \\times \\mathbb{R}^d \\to \\mathbb{R}$ is a parameterized function that measures the correlation between node pair $(u, v)$ ; $C^k := \\sum_{u \\in N(v)} \\exp(f^k(u, v))$ is a normalizing constant. In our case, cosine similarity is adopted as the correlation metric.", + "bbox": [ + 76, + 196, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Despite the flexibility of graph aggregation, we are concerned that the spatial information is damaged in the process of graph aggregation: since all nodes are treated equally, the model will grasp little knowledge about node position. Hence, inspired by Liu et al. [25, 29], we add relative position encoding to node features before aggregation to enhance position information.", + "bbox": [ + 75, + 258, + 468, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Model Architecture", + "text_level": 1, + "bbox": [ + 76, + 376, + 264, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed graph construction and graph aggregation mechanisms are then merged into the effective MetaFormer architecture as the IPG model. The detailed structure of IPG is shown in Figure 3.", + "bbox": [ + 75, + 400, + 468, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The IPG Architecture. The general architecture of IPG follows mainstream SR models [5-7, 23, 53]. As an LR image is inputted into the model, it is first passed to a Conv Layer to extract shallow features. Then the features are passed through a series of Multiscale Graph-aggregation Blocks (MGB) for effective deep feature extraction with the aid of flexible graphs. Each MGB consists of a stack of Graph Aggregation Layers (GAL) where graph aggregation on both local and global scales is performed. Finally, the image is spatially reconstructed via a pixel-shuffle upsampler.", + "bbox": [ + 75, + 460, + 468, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MGB Blocks. Multiscale Graph-aggregation Blocks (MGB) gather both local and global-scale information for effective image SR reconstruction. Both local and global pixel graphs are calculated per block based on block inputs. Block-wise graph calculations enable regular graph updates throughout the model. The construction steps are detailed in Section 3.2, where local and global sampling is performed respectively for local or global graph construction. The two types of graphs (local/global) are then distributed to GALs throughout the block for aggregation operations. Local and global graphs are distributed in a sequentially alternative manner to ensure that both local and global-scale information are sufficiently aggregated.", + "bbox": [ + 75, + 628, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GAL Layers. The design of Graph Aggregation Layers (GAL) follows the general MetaFormer-like structure [44]. Graphers that are responsible for graph aggregation (as introduced in Section 3.3) are used as token mixers. Grapher gathers local or global information based on the type", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of graph it receives. Following [5, 22, 53], we leverage efficient Channel Attention (CA) modules and ConvFFN blocks to aid the SR performance of our model.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 150, + 633, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Setting", + "text_level": 1, + "bbox": [ + 498, + 174, + 686, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt the general training setting of recent SR works [5, 6, 23] for fair comparison. We use DIV2K+Flickr2K (DF2K) as the training set (DIV2K for lightweight models). Cropped patches of size $64 \\times 64$ are sent into the model. Training data is augmented by random flipping and random rotation of degrees [0,90,180,270]. Our model is trained for 500K iterations using the Adam Optimizer $(\\beta_{1} = 0.9, \\beta_{2} = 0.99)$ at a learning rate of $2e - 4$ . The training input size is set at $64 \\times 64$ . MultistepLR is adopted where the learning rate is halved at iterations [250000, 400000, 450000, 475000]. Batchsize is set as 32.", + "bbox": [ + 496, + 198, + 890, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Super-Resolution Performance", + "text_level": 1, + "bbox": [ + 500, + 375, + 772, + 390 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dac100cdcab2d127ae1cdf7e27ba9034584d234c2801b9563b8b12571c34c56f.jpg", + "image_caption": [ + "Figure 5. Comparison of the proposed IPG-S and IPG with SR baselines in FLOPs and performance. Urban $100 \\times 4$ in PSNR is reported. Thanks to the flexibility of graphs, IPG could outperform other SR models by $>0.1\\mathrm{dB}$ at similar FLOPs. Notably, FLOPs only reflect theoretical computation costs instead of actual inference speed." + ], + "image_footnote": [], + "bbox": [ + 529, + 412, + 856, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare the performance of our model with various SR baselines in Table 1 on Set5 [3], Set14 [45], BSDS100 [33], Urban100 [13], and Manga109 [34] benchmarks. The chosen baselines are as follows: IGN [52] is a patch-graph-based SR method; ELAN [49], IPT [4], SwinIR [23], CAT-A [6], ART [47], GRL-B [22], and HAT [5] are transformer-based methods. Performance of $\\mathrm{SR}\\times 2$ $x3$ $x4$ models are measured by PSNR and SSIM. \" $^+$ \" marks stand for baselines with self-ensemble strategies, which boosts SR performance further. IPG could outcompete other models by large margins. In particular, IPG reaches 28.13dB of PSNR on the Urban $100\\times 4$ task, exceeding existing SOTA by more than 0.1dB with standard training setting. IPG has an outstanding performance in the PSNR versus theoretical FLOPs plot, shown in Figure 5. But notably, IPG runs slower than previous methods for", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24112", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f56c63d47241cb6e935c98016f68583194799cb92cc8ba29b3f208616ad5dfa6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
SR×2IGNN [52]38.240.961334.070.921732.410.902533.230.938339.350.9786
ELAN [49]38.360.962034.200.922832.450.903033.440.939139.620.9793
IPT [4]38.37N/A34.43N/A32.48N/A33.76N/AN/AN/A
SwinIR [23]38.420.962334.460.925032.530.904133.810.942739.920.9797
EDT [20]38.450.962434.570.925832.520.904133.800.942539.930.9800
CAT-A [6]38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [47]38.560.962934.590.926732.580.904834.300.945240.240.9808
GRL-B* [22]38.480.962734.640.926532.550.904533.970.943740.060.9804
HAT* [5]38.610.963034.770.926632.610.905334.450.946540.230.9806
IPG (Ours)38.610.963234.730.927032.600.905234.480.946440.240.9810
IPG+ (Ours)38.650.963334.870.927432.620.905334.540.946840.320.9811
SR×3IGNN [52]34.720.929830.660.848429.310.810529.030.869634.390.9496
ELAN [49]34.900.931330.800.850429.380.812429.320.874534.730.9517
IPT [4]34.81N/A30.85N/A29.38N/A29.49N/AN/AN/A
SwinIR [23]34.970.931830.930.853429.460.814529.750.882635.120.9537
EDT [20]34.970.931630.890.852729.440.814229.720.881435.130.9534
CAT-A [6]35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [47]35.070.932531.020.854129.510.815930.100.887135.390.9548
GRL-B* [22]35.050.932331.000.854329.490.815329.830.883735.240.9541
HAT [5]35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG (Ours)35.100.933231.100.855429.530.816830.360.890135.530.9554
IPG+ (Ours)35.190.933531.140.855829.570.817130.480.891135.650.9558
SR×4IGNN [52]32.570.899828.850.789127.770.743426.840.809031.280.9182
ELAN [49]32.750.902228.960.791427.830.745927.130.816731.680.9226
IPT [4]32.64N/A29.01N/A27.82N/A27.26N/AN/AN/A
SwinIR [23]32.920.904429.090.795027.920.748927.450.825432.030.9260
EDT [20]32.820.903129.090.793927.910.748327.460.824632.030.9254
CAT-A [6]33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [47]33.040.905129.160.795827.970.751027.770.832132.310.9283
GRL-B* [22]32.900.903929.140.795627.960.749727.530.827632.190.9266
HAT [5]33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG (Ours)33.150.906229.240.797327.990.751928.130.839232.530.9300
IPG+ (Ours)33.230.906429.300.797928.040.752528.220.840732.720.9310
", + "bbox": [ + 112, + 88, + 854, + 478 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lack of hardware support; IPG costs slightly advantageous peak memory. Apart from the quantitative comparison in PSNR/SSIM metrics, we also provide visual results of difficult details reconstructed by IPG. As shown in Figure 6, the proposed IPG model is compared against recent top-tier SR baselines on the $\\mathrm{SR} \\times 4$ task. Our IPG model could visually outcompete other methods.", + "bbox": [ + 75, + 523, + 468, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Lightweight SR", + "text_level": 1, + "bbox": [ + 76, + 657, + 233, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also provide some lightweight variants of IPG. While the architecture of IPG-S and IPG-Tiny remains the same as the base version, their depth and dimension width are significantly reduced for computation-constrained applications. Variant config details are in the Appendix. We choose canonical SR baselines including CARN [1], IMDN [14], LAPAR-A [19], LatticeNet [31], and ESRT [30]; other baselines have MetaFormer architectures, including SwinIR-light [23], ELAN [48], SwinIRNG [53], and SRFormer-light [53]. IPG could outcompete SR baselines that share similar MetaFormer [44] architectures at similar computation costs. Specifically, IPG-Tiny could achieve more than 0.1dB of PSNR improvement on Urban100 compared with other lightweight baselines.", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 522, + 653, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pixel Nodes vs. Patch Nodes. As claimed in Section 3.2, patches as image graph nodes may suffer in cases like object shift and object rotation. The forcible element-wise alignment of patch pixels could hinder SR performance to a great extent. In order to investigate the negative impact of patch nodes, we provide a patched version of IPG as follows: rather than using pixel nodes, we use $2 \\times 2$ -sized patches as nodes in this patched variant. Other model settings are kept unchanged for fair comparison, including model depths, feature dimensions, MLP ratios, and sampling region size. However, we are aware that the computation costs of patch node aggregation could be different compared to pixel nodes. Hence, we tune the number of aggregation times for the patched variant, to make sure that aggregation of patch nodes has a similar cost as pixel node aggregation. The ablation results are shown in Table 2.", + "bbox": [ + 496, + 547, + 890, + 789 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/33e436109092b6797756af634738aaaf98217d9af7c5ad9ac9675068964de050.jpg", + "table_caption": [ + "Table 1. Comparison of IPG with recent SR methods. Methods with ${}^{* * * }$ are replicated with standard setting, detailed in the Appendix; items with \"+\" stands for self-ensemble strategies." + ], + "table_footnote": [], + "table_body": "
Set5Set14Urban100
2 × 2-Patched IPG33.0129.1827.81
Pixel IPG33.1529.2428.13
", + "bbox": [ + 547, + 797, + 844, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison of pixel-node graphs against patch-node graphs in IPG. $\\mathrm{SR} \\times 4$ results are reported.", + "bbox": [ + 498, + 851, + 890, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Figure 7, we also provide a vision comparison be", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24113", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e423b99a88d4395079e472e078db41692da4b147e7571d9a1cbd32dad57099df.jpg", + "image_caption": [ + "Urban100: img_024 $(\\times 4)$" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 261, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9a5b44565e2bf03b45b0bdadeeece04c8c8779819d0282266ee47bcea278b34f.jpg", + "image_caption": [ + "HQ" + ], + "image_footnote": [], + "bbox": [ + 263, + 90, + 382, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a49435cd09d1f42fc074597edbbf71ca2a9c64051ef49b23507ee0b47549de9.jpg", + "image_caption": [ + "Bicubic" + ], + "image_footnote": [], + "bbox": [ + 387, + 90, + 506, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6507bd257bff0a48bc97ab6c771c020eec17c5d3a883d26409e2fec992dd9bbe.jpg", + "image_caption": [ + "IGNN [52]" + ], + "image_footnote": [], + "bbox": [ + 511, + 90, + 630, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ccace8dbf49145ef23190a23e3a993e53b84dcb733dbb0f9e1c30f359d6cd6fc.jpg", + "image_caption": [ + "IPT [4]" + ], + "image_footnote": [], + "bbox": [ + 637, + 90, + 754, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/57df80500b52a45157136abd23b6faeef81804b74727cb69fa64aef9b1a442dc.jpg", + "image_caption": [ + "SwinIR [23]" + ], + "image_footnote": [], + "bbox": [ + 761, + 90, + 880, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d52cd349c1827161413339d4c0930068ee6e6a866aeef0fa454cf8bd58a95c5.jpg", + "image_caption": [ + "Urban100: img_092 $(\\times 4)$" + ], + "image_footnote": [], + "bbox": [ + 81, + 210, + 259, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bb7795dd489aeb8744cc3d605a46212c29b0c192b6e188377f154183c8abb01f.jpg", + "image_caption": [ + "GRL-B [22]" + ], + "image_footnote": [], + "bbox": [ + 263, + 152, + 382, + 198 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03b8ffaf4356ff53afb8da73402b99998a3e655e1625b2d23906be1d64eb7e0e.jpg", + "image_caption": [ + "ART [47]" + ], + "image_footnote": [], + "bbox": [ + 387, + 152, + 506, + 198 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6fc624216f7ef5627569994aaee331809014dde2ebc90964077c58c3341ac3ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 152, + 630, + 198 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": 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"image_caption": [ + "CAT-A [6]" + ], + "image_footnote": [], + "bbox": [ + 511, + 212, + 630, + 260 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e914ab0e0e7633bc2a9a68611602ff23c940c3a4f4c347a8a53ef9ab000884e.jpg", + "image_caption": [ + "HAT [5]" + ], + "image_footnote": [], + "bbox": [ + 637, + 212, + 754, + 260 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ba28388a6e8233e4483b6626485aee07ba077ca999f9d8204adce66fca449e8.jpg", + "image_caption": [ + "IPG (ours)" + ], + "image_footnote": [], + "bbox": [ + 761, + 212, + 880, + 260 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/66307db540dc5bf01795c64df7cbae1795af06a62dbf85c1a4c194ae16647e8a.jpg", + "image_caption": [ + "HQ" + ], + "image_footnote": [], + "bbox": [ + 263, + 273, + 382, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1206732d88892f1d653b8e0fa7b5d5bcdd1fc12e716f879915dea6e0aaf0550d.jpg", + "image_caption": [ + "Bicubic" + ], + "image_footnote": [], + "bbox": [ + 387, + 273, + 506, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b270bd15c276689678ef7093711109198701979faf15d874d7194ac8034b13da.jpg", + "image_caption": [ + "IGNN [52]" + ], + "image_footnote": [], + "bbox": [ + 511, + 273, + 630, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c6df0431fd291fceffa905f131787268ff8e3bd3c4ff38f49cb8535c0e5a7b9d.jpg", + "image_caption": [ + "IPT [4]" + ], + "image_footnote": [], + "bbox": [ + 637, + 273, + 754, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cdc3a24892103f2dec4f391aa941c26138fdeba35bb87b928bd5feac3219728a.jpg", + "image_caption": [ + "SwinIR [23]" + ], + "image_footnote": [], + "bbox": [ + 761, + 273, + 880, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc8d61ed7726976b98ae186507e7a607e6f35ebd3dc86541714cb0cced8e3d91.jpg", + "image_caption": [ + "Urban100: img_098 $(\\times 4)$" + ], + "image_footnote": [], + "bbox": [ + 83, + 334, + 258, + 426 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86f4141ebfadeead72bd9f3b39f2a1a4f6851fdeefbf1edd045c3693543964a2.jpg", + "image_caption": [ + "GRL-B [22]" + ], + "image_footnote": [], + "bbox": [ + 263, + 334, + 382, + 382 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/32930b21ba11d78702215a21eb64e36e3de43cc0146116c659539a448f569bc9.jpg", + "image_caption": [ + "ART [47]" + ], + "image_footnote": [], + "bbox": [ + 387, + 334, + 506, + 382 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a3f183fddd6ff7d90c56bf6dff044452b7a0abe431b1c2223d7961ae49df2ee.jpg", + "image_caption": [ + "CAT-A [6]" + ], + "image_footnote": [], + "bbox": [ + 511, + 334, + 630, + 382 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b58ebd049c8dde172c71970237a6c10b1b48a6a8792a57ed746561ea45c5e52d.jpg", + "image_caption": [ + "HAT [5]" + ], + "image_footnote": [], + "bbox": [ + 637, + 334, + 754, + 382 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35365fa6fa8d7343fd2aabc163394836fbf0014a7f020ed08bf6fb68ef50ee51.jpg", + "image_caption": [ + "IPG (ours)" + ], + "image_footnote": [], + "bbox": [ + 761, + 334, + 880, + 382 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27416372a15b0dc3c0dc721a7616a556d617e99d072aec9731eadba483f55947.jpg", + "image_caption": [ + "HQ", + "GRL-B [22]" + ], + "image_footnote": [], + "bbox": [ + 263, + 396, + 382, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/29e7a4701530ba5e40a9ac274cff5ea421d0d2c8aaebbe4475663134ac31b245.jpg", + "image_caption": [ + "Bicubic", + "ART [47]" + ], + "image_footnote": [], + "bbox": [ + 387, + 396, + 506, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d2534ccf66b6a7e0e2f8f3b9fa68eea09a7af3f56bdaaa59d18081cf00dfd4a.jpg", + "image_caption": [ + "IGNN [52]", + "CAT-A [6]" + ], + "image_footnote": [], + "bbox": [ + 511, + 396, + 630, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0a11a5c9fc2026e203ca475dfd9fa23b59780420d774550b2f2ea49154fbd8de.jpg", + "image_caption": [ + "IPT [4]", + "HAT [5]" + ], + "image_footnote": [], + "bbox": [ + 637, + 396, + 754, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03c6c96d2a17f555a2e2c6d65f80c6f65300b8c869316e5c96fca4e7d8e31cd6.jpg", + "image_caption": [ + "SwinIR [23]", + "IPG (ours)" + ], + "image_footnote": [], + "bbox": [ + 761, + 396, + 880, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e20f6b215f8088146c619fa3c580bffba9d4df5d432dbca5ef195197ab752b7.jpg", + "image_caption": [ + "Figure 6. Visual comparison of image SR $(\\times 4)$ with latest SR baselines in challenging cases.", + "Urban100: img_092 $(\\times 4)$" + ], + "image_footnote": [], + "bbox": [ + 81, + 489, + 250, + 580 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44d962f30743323d3d0fbd027b2d9e245333401461656105c1c1060384e694f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 254, + 489, + 359, + 532 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6205dcc14dc0b5c84b0c7f9e03ea726eea05b8f25a7633d1b2748c29d48ed8c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 366, + 489, + 470, + 532 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ac3fc8b2725e0d530420c1672ab44927b118edbf824857624355ad29cec89b77.jpg", + "image_caption": [ + "HQ", + "Patched IPG [6] $(2\\times 2)$", + "Figure 7. Visual comparison of patch-node graph methods over IPG that uses pixel node graphs." + ], + "image_footnote": [], + "bbox": [ + 254, + 546, + 359, + 588 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/211b3b66a974c7e8c8c07d5a15c2cecdf746c2592f580ada5f266c9636c68e20.jpg", + "image_caption": [ + "IGNN [52] $(3\\times 3)$", + "IPG [47]" + ], + "image_footnote": [], + "bbox": [ + 366, + 546, + 470, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tween IGNN [52] $(3 \\times 3$ patch), patched IPG $(2 \\times 2$ patch), and IPG (pixel graph). For the IGNN case that uses large patches as nodes, patch alignment is causing trouble: the model is puzzled about the texture orientations, so it makes mistakes during texture reconstruction by aligning pattern-similar but orientation-different patches. For patched IPG, misaligned orientation is causing issues as well: line textures are distorted. In contrast, pixel aggregation in IPG avoids misalignment and performs well.", + "bbox": [ + 75, + 640, + 468, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "KNN vs. Degree-flexible Graphs. In canonical graph", + "bbox": [ + 76, + 776, + 468, + 791 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7a70427701a187bceac58726df114fe78a5270333e77cd5c92e6c53e09e1dd04.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Set5Set14Urban100
KNN33.0929.1928.06
Degree-Flex33.1529.2428.13
", + "bbox": [ + 143, + 803, + 401, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison of degree-flexible graphs against plain KNN graphs in IPG. $\\mathrm{SR} \\times 4$ results are reported.", + "bbox": [ + 75, + 856, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "applications for vision tasks, $k$ -Nearest-Neighbor (KNN)", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "graphs are normally adopted for graph construction. However, KNN still suffers the degree rigidity, as all nodes are connected to a fixed number of neighboring nodes. To improve degree flexibility, we consider the unbalanced demand of pixels in SR tasks and propose a degree-flexible scheme of graph construction (introduced in Section 3.2). We compare KNN and the degree-flexible graph scheme in IPG under the same settings. According to Table 3, Degree-Flex could outcompete the KNN variant of IPG. Interestingly, our Degree-Flex graph could outcompete computation-heavy fully-connected graphs (see Appendix), further implying the effectiveness of our DegreeFlex graphs.", + "bbox": [ + 496, + 493, + 890, + 689 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Figure 8, we visually compare the connected regions of detail-poor and detail-rich pixels at the local scale. Detail-poor pixels are usually on flat, changeless parts of the image; these pixels require minimal node connection for reconstruction. On the contrary, detail-rich pixel nodes are usually on edges and corners, which are assigned higher node degrees and thus a larger region of perception. In this sense, the detail-rich indicator metric $D_{F}$ could endow IPG with degree flexibility.", + "bbox": [ + 496, + 696, + 890, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Local/Global Graphs. In the design of IPG, we aggregate information from both local and global scales based on local and global pixel node sampling. Though numerous SR works highlight the importance of either local or non-local", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24114", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ec1a9202ed5d7c117577cfc400d430753b732fb27c44c0d277a3bda860044363.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTraining DatasetParamsFLOPsSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
×2 SRCARN [1]DIV2K1592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [14]DIV2K694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [19]DF2K548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [31]DIV2K756K169.5G38.150.961033.780.919332.250.900532.430.9302N/AN/A
ESRT [30]DIV2K751K-38.030.960033.750.918432.250.900132.580.931839.120.9774
SwinIR-light [23]DIV2K910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [49]DIV2K621K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [7]DIV2K1181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
SRFormer-light [53]DIV2K853K236G38.230.961333.940.920932.360.901932.910.935339.280.9785
IPG-Tiny (Ours)DIV2K872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
×3 SRCARN [1]DIV2K1592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [14]DIV2K703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [19]DF2K594K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [31]DIV2K765K76.3G34.530.928130.390.842429.150.805928.330.8538N/AN/A
ESRT [30]DIV2K751K-34.420.926830.430.843329.150.806328.460.857433.950.9455
SwinIR-light [23]DIV2K918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [49]DIV2K629K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [7]DIV2K1190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
SRFormer-light [53]DIV2K861K105G34.670.929630.570.846929.260.809928.810.865534.190.9489
IPG-Tiny (Ours)DIV2K878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
×4 SRCARN [1]DIV2K1592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [14]DIV2K715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [19]DF2K659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [31]DIV2K777K43.6G32.300.896228.680.783027.620.736726.250.7873N/AN/A
ESRT [30]DIV2K751K-32.190.894728.690.783327.690.737926.390.796230.750.9100
SwinIR-light [23]DIV2K930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [49]DIV2K640K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [7]DIV2K1201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
SRFormer-light [53]DIV2K873K62.8G32.510.898828.820.787227.730.742226.670.803231.170.9165
IPG-Tiny (Ours)DIV2K887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
", + "bbox": [ + 89, + 88, + 877, + 438 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/14067148f7bd1232ab4c912c1a7ffaab4c40026c2569f2f3f7512ce2cf7a3c7e.jpg", + "image_caption": [ + "Figure 8. Visual demonstration of parts connected to a pixel node. Compared with detail-poor nodes (left), detail-rich nodes (right) requires a larger amount of aggregation due to difficulty in reconstruction." + ], + "image_footnote": [], + "bbox": [ + 88, + 488, + 454, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "aggregation, we demonstrate that both aspects are actually crucial for SR performance. As shown in Table 5, we perform experiments that uses local or global-scale graphs only under identical settings, and compare them with the original version of IPG. The optimal performance is reached when", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "both local and global aggregation are performed.", + "bbox": [ + 500, + 492, + 821, + 508 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e77499f199d3b08743997a3a0e44077e8155246e635dba971ece8a80349993bc.jpg", + "table_caption": [ + "Table 4. Comparison of IPG-Tiny with recent lightweight SR methods. Under comparable Params and FLOPs, IPG-Tiny could outcompete lightweight SR baselines." + ], + "table_footnote": [], + "table_body": "
Set5Set14Urban100
Local Only33.0829.1928.10
Global Only33.0429.1127.59
Local + Global33.1529.2428.13
", + "bbox": [ + 560, + 518, + 834, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablations of local and global graph usages on $\\mathrm{{SR}} \\times 4$ .", + "bbox": [ + 509, + 587, + 879, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 617, + 617, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Existing SR measures are rigid both in terms of space and degree. In order to break rigidity in SR, the paper proposes IPG – an SR model that fully leverages the flexibility of graphs. Firstly, we are aware that SR is a task where detail-rich image parts require lopsided reconstruction efforts. Hence, we designed a degree-varying scheme for graph construction rather than $k$ -nearest neighbors. Then we take pixels rather than patches for graph aggregation. To reach the maximum amount of spatial flexibility, nodes are sampled both on local and global scales. IPG reaches State-of-the-art performance compared with SR baselines.", + "bbox": [ + 496, + 642, + 890, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by the National Key R&D Program of China under Grant No.2022ZD0160300 and the National Natural Science Foundation of China under Grant No.62276007. We gratefully acknowledge the support of MindSpore, CANN and Ascend AI Processor used for this research.", + "bbox": [ + 496, + 809, + 892, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24115", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. Fast, accurate, and lightweight super-resolution with cascading residual network. 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Srformer: Permuted self-attention for single image super-resolution. arXiv preprint arXiv:2303.09735, 2023. 2, 5, 6, 8" + ], + "bbox": [ + 501, + 92, + 890, + 698 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24117", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/dacb6475-02d0-43fb-ade3-b56b50c0b0c7_model.json b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/dacb6475-02d0-43fb-ade3-b56b50c0b0c7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b11c3ac3cc55406d0f6a3bde703e95627e007a08 --- /dev/null +++ b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/dacb6475-02d0-43fb-ade3-b56b50c0b0c7_model.json @@ -0,0 +1,2937 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.168, + 0.131, + 0.804, + 0.154 + ], + "angle": 0, + "content": "Image Processing GNN: Breaking Rigidity in Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.181, + 0.719, + 0.2 + ], + "angle": 0, + "content": "Yuchuan Tian\\(^{1}\\), Hanting Chen\\(^{2}\\), Chao Xu\\(^{1}\\), Yunhe Wang\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.201, + 0.868, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\) National Key Lab of General AI, School of Intelligence Science and Technology, Peking University. \\(^{2}\\) Huawei Noah's Ark Lab." + }, + { + "type": "text", + "bbox": [ + 0.288, + 0.22, + 0.682, + 0.234 + ], + "angle": 0, + "content": "tianyc@stu.pku.edu.cn, yunhe.wang@huawei.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.474, + 0.681 + ], + "angle": 0, + "content": "Super-Resolution (SR) reconstructs high-resolution images from low-resolution ones. CNNs and window-attention methods are two major categories of canonical SR models. However, these measures are rigid: in both operations, each pixel gathers the same number of neighboring pixels, hindering their effectiveness in SR tasks. Alternatively, we leverage the flexibility of graphs and propose the Image Processing GNN (IPG) model to break the rigidity that dominates previous SR methods. Firstly, SR is unbalanced in that most reconstruction efforts are concentrated to a small proportion of detail-rich image parts. Hence, we leverage degree flexibility by assigning higher node degrees to detail-rich image nodes. Then in order to construct graphs for SR-effective aggregation, we treat images as pixel node sets rather than patch nodes. Lastly, we hold that both local and global information are crucial for SR performance. In the hope of gathering pixel information from both local and global scales efficiently via flexible graphs, we search node connections within nearby regions to construct local graphs; and find connections within a strided sampling space of the whole image for global graphs. The flexibility of graphs boosts the SR performance of the IPG model. Experiment results on various datasets demonstrate that the proposed IPG outperforms State-of-the-Art baselines. Codes are available at this link." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.712, + 0.21, + 0.727 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.47, + 0.875 + ], + "angle": 0, + "content": "The ill-posed task of Super-Resolution (SR) constructs high-resolution images from low-resolution ones. SR works typically apply Deep Neural Network (DNN) knowledge learned from High-Resolution training images to construct missing details in low-resolution inputs. Existing DNN variants for classical SR tasks include CNNs [16, 24, 50] and Transformers [5, 6, 23]. These measures have proved effective in creating High-Resolution images, and are used in real-world applications like medical imaging [10], re" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.274, + 0.593, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.334, + 0.583, + 0.344 + ], + "angle": 0, + "content": "Convolution" + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.283, + 0.665, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.603, + 0.333, + 0.674, + 0.344 + ], + "angle": 0, + "content": "Self-Attention" + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.274, + 0.767, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.697, + 0.333, + 0.758, + 0.344 + ], + "angle": 0, + "content": "KNN Graph" + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.268, + 0.891, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.822, + 0.333, + 0.848, + 0.343 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.356, + 0.893, + 0.44 + ], + "angle": 0, + "content": "Figure 1. Convolution (left), Self-Attention (middle-left), KNN Graph Aggregation (middle-right), and Graph Aggregation in IPG (right). Compared with other methods, IPG graph aggregation considers the unbalanced nature of SR: detail-rich, high-frequency image nodes (red) have higher node degrees; while flat, low-frequency image nodes (blue) require fewer aggregations." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.457, + 0.691, + 0.471 + ], + "angle": 0, + "content": "mote sensing [15], et cetera." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.893, + 0.639 + ], + "angle": 0, + "content": "Despite various measures, it is taken for granted that mainstream SR models treat all pixels in a fairly rigid manner. For instance, as shown in Figure 1, in convolution layers of the CNN-based SR model VDSR [16], the same convolution kernel scans through all pixels of feature maps, i.e. each pixel is rigidly designated to communicate with its nearest neighbors; in the Transformer-based model SwinIR [23], all pixels are assigned to equal-sized attention grids for self-attention operations. In both examples, each pixel aggregates information from a fixed number of pixels within a neighborhood of fixed size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.895, + 0.807 + ], + "angle": 0, + "content": "Efforts have been made to overcome the rigidity of convolution and window-attention operations. For example, some recent SR research tries to enhance SR models by enlarging self-attention grids [5, 46] and designing striped global attention windows [6, 22]. But these improvements also introduce a large computation burden. Some other works [12, 26, 52] leverage the flexibility of graphs and propose graph-based methods. With content-based graphs constructed from patch nodes, each image patch could aggregate top-\\(k\\) relevant but distant parts beyond hard local boundaries in convolution and window-attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.901 + ], + "angle": 0, + "content": "However, these graph measures have limited flexibility because the lopsided nature of SR is overlooked. In SR tasks, only a small proportion of high-frequency pixels require hard reconstruction efforts; the majority of pixels are located in flat, low-frequency regions and thus almost left intact [9]. In response to the imbalance, SR methods should" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24108" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "ideally pay more attention to detail-rich regions and care less about flat, detail-poor image parts. However, existing \\( k \\)-Nearest-Neighbor graph-based methods treat all image nodes equally. In other words, all nodes share the same pre-set degree \\( k \\) and the unbalanced nature of SR is not considered. In fact, as we inspect canonical operation paradigms in SR from a graph perspective, we found that degree-equivalence rigidity also manifests in convolution and window-attention: in these paradigms, each pixel on the image aggregates the same number of pixels regardless of image content, and thus, sharing \"equal degrees\" in graph terms. Equal node degrees that are rigidly assigned to nodes or pixels mismatch their unequal reconstruction demands in SR, thus impacting SR performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.635 + ], + "angle": 0, + "content": "Trying to break rigidity, we propose the graph-based Image Processing Graph Neural Networks (IPG) model for SR that taps the flexibility potential of graphs. Firstly, to break the degree-equivalence rigidity of convolution, window-attention, and \\( k \\)-Nearest-Neighbor (KNN) graphs, we leverage degree flexibility by proposing a novel degree-variant graph solution based on the unbalanced nature of SR. Specifically, a detail-aware metric is designed to measure the importance of image nodes where larger degrees are assigned to high-frequency nodes. Then, different from graph-based model counterparts, IPG adopts pixels rather than patches as image graph nodes to avoid misalignment issues due to patch rigidity. Finally, in the interest of having both local and global perception without sacrificing efficiency due to large pixel-level search space, we resort to local and global node sampling strategies. In this way, graphs are established efficiently from small pixel subsets and could either focus on local information for detail reconstruction, or span over the whole image for spatially distant but crucial features. With the measures mentioned above, IPG could fully exert graph flexibilities and achieve outstanding performances on SR tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.22, + 0.665 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Recent SR Methods. In canonical approaches to SuperResolution, manifold previous works phrase SR as a regression problem and is proved effective via applications of CNN models [16, 24, 50, 51]. In these works, a crafted CNN model is applied to the LR image to render it into HR. Since the introduction of Transformers to vision [8], manifold works integrate the self-attention mechanism in Transformers into SR models [4-7, 23, 47, 53]. SwinIR [23] borrows shifted window-attention to SR and demonstrates good performance. Latest SR models include using striped attention windows [6, 22], channel attention [5, 22, 40], permuted attention [53], et cetera." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Despite the fact that manifold SR works follow similar convolution or window-attention methodologies, their SR performance is still confined to the rigidity of ordinary vi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "sion models, i.e. fixed paradigms for aggregating neighboring pixels and neglecting the unbalanced reconstruction demand among pixels in SR. Hence, we resort to graphs as a flexible way to aggregate information in order to break these sorts of rigidity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.893, + 0.32 + ], + "angle": 0, + "content": "Graphs for Vision. Graphs have been widely applied to vision tasks, including point cloud segmentation [17, 41], human action recognition [42], and image classification [12, 32]. Some previous low-level vision works also view images as graphs. Most works leverage graph to aggregate non-local information, either intra-scale [2, 18, 21, 35, 38] or cross-scale [26, 52]. Other low-level vision works on graphs include cross-layer [27] or inter-image information aggregation [37]. Among these works, edge-conditioned aggregation from neighboring nodes is mostly preferred." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.895, + 0.502 + ], + "angle": 0, + "content": "In terms of graph construction from images, a majority of works use \\( k \\)-nearest neighbors [18, 21, 26, 35, 38, 52]. Since all image nodes share the same degree, KNN graphs are not flexible enough; and the unbalanced nature of image nodes in low-level vision tasks is neglected as well. Besides, most graph works regard patches as image nodes [18, 21, 26, 35, 52], disregarding potential patch misalignment issues in low-level vision. As for the scale of graphs, some works [21, 26, 52] search in a global scale to construct graphs; other works [38, 39] construct graphs from a local box. Graphs in these works are not flexible enough in that they fail to take care of both local and global aspects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.518, + 0.593, + 0.533 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.543, + 0.787, + 0.56 + ], + "angle": 0, + "content": "3.1. Rigidity of Previous SR Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Convolution [16, 24, 50] and window-attention [5, 6, 23] are two major pathways for SR model designs. Despite popular usages in SR, these measures are not flexible; their deep-rooted rigidity could hinder SR performance. In one convolution operation, each outputted pixel gathers information within a tiny kernel-sized window; each pixel only has access to its neighboring pixels. For instance, in a standard \\(3 \\times 3\\) convolution, the perception field of a single pixel is confined to a tiny \\(3 \\times 3\\) box. All pixels on the image collect information from 8 respective neighbors and themselves. The similar rigidity goes for window attention: though larger window sizes (compared to convolution) are usually adopted, the perception field of window attention is still confined within hard window boundaries. In a \\(8 \\times 8\\) window-attention scenario, all pixels gather 64 pixels within the window where they belong." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Therefore, beyond rigidity in convolution and window-attention, some works think out of the box and adopt graphs in SR models. Unlike convolution and window-attention where information aggregation is bounded to boxes, these graph-based works are more spatially flexible: each node could aggregate information from its favorite top-\\(k\\) nodes" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24109" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "with loose spatial constraints. In this sense, graph aggregation is not limited to preset rigid patterns; it is more dynamic and scalable compared to convolution and window-attention counterparts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.473, + 0.44 + ], + "angle": 0, + "content": "However, though previous graph-based methods break through hard aggregation boundaries, we hold that the flexibility of graphs is not fully exploited in SR tasks. First and foremost, as shown in Figure 1, all previous methodologies (either graph-based, convolution-based, or window-attention-based) are degree-rigid. SR reconstruction demand is unbalanced among different image parts. But in previous methods, all pixels or nodes on the image are aggregating the same number of pixels or nodes; i.e. in graph terms, they share the same aggregation degree. Secondly, previous graph-based works are patch-rigid. Though patches are usually regarded as image nodes, patch aggregation usually requires rigid pixel-wise alignment. Possible misalignment of low-level features in patches makes SR models perform worse. Thirdly, previous graph-based works rigidly use graphs on either global or local scales, but information at both scales is potentially important for SR reconstruction. These rigid aspects are hindering the performance of SR models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.45, + 0.271, + 0.466 + ], + "angle": 0, + "content": "3.2. Graph Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.533 + ], + "angle": 0, + "content": "To break these rigidities, we construct degree-flexible pixel graphs at local and global scales in the IPG model. In this manner, we could fully exploit the flexibility of graphs and achieve outstanding performance in SR tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Degree Flexibility. Firstly, we try to figure out a degree-flexible graph solution based on the unique \"unbalanced property\" of SR tasks. SR reconstruction of images features imbalance. As Gou et al. [9] put it, SR is a long-tailed problem where only a small proportion of high-frequency pixels need to be reconstructed; the rest of the image parts need minimal restoration only. However, Gou et al. [9] tries to address the issue by designing training losses rather than rethinking it from the aspect of model designs. In the lopsided SR problem, it is a long-neglected aspect that treating all pixels or parts on the image equivalently is unsuitable and inefficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.47, + 0.837 + ], + "angle": 0, + "content": "To this end, we opt to assign various node degrees to pixels based on a detail-rich indicator that marks pixels needing more reconstruction efforts. Then we design the detail-rich indicator as follows: given feature map \\( F \\in \\mathbb{R}^{H \\times W \\times C} \\) and downsampling ratio \\( s \\), the detail-rich indicator metric per pixel \\( D_F \\in \\mathbb{R}^{H \\times W} \\) is designated as the absolute difference between the bilinearly downsampled and upsampled feature map and the feature map itself:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.849, + 0.469, + 0.88 + ], + "angle": 0, + "content": "\\[\nD _ {F} := \\sum_ {C} | F - F _ {\\downarrow s \\uparrow s} |, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.9 + ], + "angle": 0, + "content": "where \\( s \\) is taken as 2 to avoid severe information loss. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "are aware that some explainable SR works [11, 43] propose metrics to measure the importance of a certain part in the output. However, these measures are gradient-based, which requires costly backward passes. In comparison, the proposed metric \\( D_F \\) is operation cheap in that it only requires bilinear interpolation twice. We also provide FLOPs statistics in the Appendix." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.211, + 0.629, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.212, + 0.75, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.212, + 0.869, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.307, + 0.629, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.307, + 0.75, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.307, + 0.869, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Figure 2. Visualization of the detail-rich indicator \\( D_F \\) in IPG. Original image (left); \\( D_F \\) of the shallowest block (middle); \\( D_F \\) of the deepest block (right). \\( D_F \\) could effectively reflect detail-rich parts on the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.533 + ], + "angle": 0, + "content": "The overall degree budgets are assigned to each pixels based on \\( D_F \\). The degree for a pixel node \\( v \\in F \\) on the feature map is in proportion to its corresponding pixel value at \\( D_F \\):" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.549, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\deg (v) \\propto D _ {F} (v). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.659 + ], + "angle": 0, + "content": "The detail-rich indicator \\( D_F \\) in different MGB blocks is visualized. From Figure 2, it can be seen that detail-rich parts are responsive: margins and corners have high \\( D_F \\) while flat color blocks are low in \\( D_F \\). The visualization reveals that the proposed \\( D_F \\) could effectively reflect high-frequency parts on the image throughout layers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Pixel Node Flexibility. Then we are faced with the formulation of vertices in image graphs. In previous graph-based vision works [21, 26, 36, 52], graph nodes are typically set as image patches. During graph aggregation, patches are weighted-summed in a pixel-wise manner. However, the forcible element-wise alignment of pixels during aggregation is unsuitable for SR tasks where feature maps have rich low-level features. Object shift and rotation within low-level patches are two major issues causing patch misalignment. As for object shift, locations of objects within patches could vary; location-misaligned patch objects introduce noises. Object rotation is another faulty aspect of patch aggregation. The orientation of patches is disregarded due to rigid rectangular patch shapes during patch alignment." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.872, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To avoid the above problems during node aggregation, we hold that finer-grained pixel nodes are better solutions" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24110" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.892, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.894, + 0.288 + ], + "angle": 0, + "content": "Figure 3. The architectures of IPG, Multiscale Graph-aggregation Blocks (MGB), and Graph Aggregation Layers (GAL). Each IPG consists of \\( M \\) MGB blocks, and each MGB has \\( G \\) GAL layers. Local and global graphs are distributed to GALs alternatively within MGB." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.47, + 0.359 + ], + "angle": 0, + "content": "in the low-level vision scenario. Pixel graphs are more flexible: each pixel node could directly find its relevant pixels in aggregation, therefore avoiding pixel misalignment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.452 + ], + "angle": 0, + "content": "However, we admit that compared to pixel graphs, patch graphs could potentially have larger perception fields and are easier to construct due to a smaller number of nodes in total, which means a smaller search space for edge connections. Hence, we need an efficient way to construct a flexible and effective pixel graph." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Space Flexibility. Then we develop the space flexibility of IPG graphs via an efficient search of pixel node connections both locally and globally. We propose that both local and global information are crucial for SR reconstruction: while lossy image parts could rebuild themselves from local neighborhoods, they could also learn from distant but similar features for refinement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Existing graph-based methods have demonstrated some sort of space flexibility. As shown in Figure 1, compared to convolution and window attention options where a pixel always attends to a fixed neighboring region, graph aggregation could flexibly focus on crucial image parts regardless of space limits. However, existing graph-based works are not spatially flexible enough as they fail to consider both local and global aspects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.822 + ], + "angle": 0, + "content": "In fact, computation considerations are the major concern of a comprehensive connection search. It is costly to construct global graphs by searching through all image nodes. As a remedy, strided sampling is always adopted [21, 26, 52]. But consequently, local regions are neglected. The choice of pixels as graph nodes makes graph construction even more challenging, because node spaces are enlarged further and it is hardly impractical to search through all pixels for graph construction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "For the sake of efficiency, and to gather local-level surrounding features and global-level distant features contributive to detail reconstruction in SR tasks, we use two types of sampling to aggregate both local and global information, shown in Figure 4. For local sampling, the neighborhood" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.313, + 0.892, + 0.36 + ], + "angle": 0, + "content": "surrounding a certain node is chosen as a local-scale search space on which a graph is established; for global sampling, sampled nodes span over the image in a dilated pattern." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.38, + 0.63, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.379, + 0.757, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.379, + 0.882, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.487, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Figure 4. An illustration of sampling strategies. The original image with the highlighted image node (left), local sampling (middle), and global sampling (right) are demonstrated. In this way, image graphs could flexibly gather both local and global information in an efficient manner." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.578, + 0.892, + 0.655 + ], + "angle": 0, + "content": "In the proposed IPG SR model, both sampling methods are performed in order to construct local and global-scale graphs. For each pixel node, its node connections are searched within the sampling space. In this way, we achieve spatial flexibility in a cost-efficient fashion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.688, + 0.683 + ], + "angle": 0, + "content": "3.3. Graph Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Now that flexible graphs are constructed, graph aggregation is performed such that each node can communicate with its connected neighbors and use their information for self-refinement in SR. In vision applications of graphs, aggregation in max-pooling [12, 28] or edge-conditioned [21, 26, 36] forms are mostly preferred. We tend to adopt edge-conditioned aggregation [36], as max-pooling could result in significant loss of information from neighboring pixels that are crucial for low-level vision. Since pixel reconstruction in SR heavily relies on abundant neighboring information, edge-conditioned aggregation is adopted as it cares about pixel inter-relations and maintains more neighboring information for effective reconstruction. The edge-conditioned aggregation [21, 26, 36, 52] is mathematically" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24111" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.138 + ], + "angle": 0, + "content": "formulated as follows: at the \\(k^{th}\\) layer in IPG, given node feature \\(\\mathbf{h}^{k - 1}\\) as input, neighboring node set \\(\\mathcal{N}(v)\\), the node \\(v\\) output \\(\\mathbf{h}_v^k\\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.15, + 0.47, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {v} ^ {k} = \\frac {1}{C ^ {k}} \\sum_ {u \\in N (v)} \\exp \\left(f ^ {k} (u, v)\\right) \\mathbf {h} _ {u} ^ {k - 1}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.197, + 0.469, + 0.259 + ], + "angle": 0, + "content": "where \\( f^k: \\mathbb{R}^d \\times \\mathbb{R}^d \\to \\mathbb{R} \\) is a parameterized function that measures the correlation between node pair \\( (u, v) \\); \\( C^k := \\sum_{u \\in N(v)} \\exp(f^k(u, v)) \\) is a normalizing constant. In our case, cosine similarity is adopted as the correlation metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.26, + 0.469, + 0.365 + ], + "angle": 0, + "content": "Despite the flexibility of graph aggregation, we are concerned that the spatial information is damaged in the process of graph aggregation: since all nodes are treated equally, the model will grasp little knowledge about node position. Hence, inspired by Liu et al. [25, 29], we add relative position encoding to node features before aggregation to enhance position information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.377, + 0.265, + 0.391 + ], + "angle": 0, + "content": "3.4. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.469, + 0.461 + ], + "angle": 0, + "content": "The proposed graph construction and graph aggregation mechanisms are then merged into the effective MetaFormer architecture as the IPG model. The detailed structure of IPG is shown in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.469, + 0.627 + ], + "angle": 0, + "content": "The IPG Architecture. The general architecture of IPG follows mainstream SR models [5-7, 23, 53]. As an LR image is inputted into the model, it is first passed to a Conv Layer to extract shallow features. Then the features are passed through a series of Multiscale Graph-aggregation Blocks (MGB) for effective deep feature extraction with the aid of flexible graphs. Each MGB consists of a stack of Graph Aggregation Layers (GAL) where graph aggregation on both local and global scales is performed. Finally, the image is spatially reconstructed via a pixel-shuffle upsampler." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.824 + ], + "angle": 0, + "content": "MGB Blocks. Multiscale Graph-aggregation Blocks (MGB) gather both local and global-scale information for effective image SR reconstruction. Both local and global pixel graphs are calculated per block based on block inputs. Block-wise graph calculations enable regular graph updates throughout the model. The construction steps are detailed in Section 3.2, where local and global sampling is performed respectively for local or global graph construction. The two types of graphs (local/global) are then distributed to GALs throughout the block for aggregation operations. Local and global graphs are distributed in a sequentially alternative manner to ensure that both local and global-scale information are sufficiently aggregated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.902 + ], + "angle": 0, + "content": "GAL Layers. The design of Graph Aggregation Layers (GAL) follows the general MetaFormer-like structure [44]. Graphers that are responsible for graph aggregation (as introduced in Section 3.3) are used as token mixers. Grapher gathers local or global information based on the type" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "of graph it receives. Following [5, 22, 53], we leverage efficient Channel Attention (CA) modules and ConvFFN blocks to aid the SR performance of our model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.151, + 0.634, + 0.168 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.175, + 0.687, + 0.192 + ], + "angle": 0, + "content": "4.1. Experiment Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.366 + ], + "angle": 0, + "content": "We adopt the general training setting of recent SR works [5, 6, 23] for fair comparison. We use DIV2K+Flickr2K (DF2K) as the training set (DIV2K for lightweight models). Cropped patches of size \\(64 \\times 64\\) are sent into the model. Training data is augmented by random flipping and random rotation of degrees [0,90,180,270]. Our model is trained for 500K iterations using the Adam Optimizer \\((\\beta_{1} = 0.9, \\beta_{2} = 0.99)\\) at a learning rate of \\(2e - 4\\). The training input size is set at \\(64 \\times 64\\). MultistepLR is adopted where the learning rate is halved at iterations [250000, 400000, 450000, 475000]. Batchsize is set as 32." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.375, + 0.774, + 0.391 + ], + "angle": 0, + "content": "4.2. Super-Resolution Performance" + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.414, + 0.857, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Figure 5. Comparison of the proposed IPG-S and IPG with SR baselines in FLOPs and performance. Urban \\(100 \\times 4\\) in PSNR is reported. Thanks to the flexibility of graphs, IPG could outperform other SR models by \\(>0.1\\mathrm{dB}\\) at similar FLOPs. Notably, FLOPs only reflect theoretical computation costs instead of actual inference speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We compare the performance of our model with various SR baselines in Table 1 on Set5 [3], Set14 [45], BSDS100 [33], Urban100 [13], and Manga109 [34] benchmarks. The chosen baselines are as follows: IGN [52] is a patch-graph-based SR method; ELAN [49], IPT [4], SwinIR [23], CAT-A [6], ART [47], GRL-B [22], and HAT [5] are transformer-based methods. Performance of \\(\\mathrm{SR}\\times 2\\) \\(x3\\) \\(x4\\) models are measured by PSNR and SSIM. \" \\(^+\\) \" marks stand for baselines with self-ensemble strategies, which boosts SR performance further. IPG could outcompete other models by large margins. In particular, IPG reaches 28.13dB of PSNR on the Urban \\(100\\times 4\\) task, exceeding existing SOTA by more than 0.1dB with standard training setting. IPG has an outstanding performance in the PSNR versus theoretical FLOPs plot, shown in Figure 5. But notably, IPG runs slower than previous methods for" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24112" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.113, + 0.089, + 0.855, + 0.479 + ], + "angle": 0, + "content": "
MethodSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
SR×2IGNN [52]38.240.961334.070.921732.410.902533.230.938339.350.9786
ELAN [49]38.360.962034.200.922832.450.903033.440.939139.620.9793
IPT [4]38.37N/A34.43N/A32.48N/A33.76N/AN/AN/A
SwinIR [23]38.420.962334.460.925032.530.904133.810.942739.920.9797
EDT [20]38.450.962434.570.925832.520.904133.800.942539.930.9800
CAT-A [6]38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [47]38.560.962934.590.926732.580.904834.300.945240.240.9808
GRL-B* [22]38.480.962734.640.926532.550.904533.970.943740.060.9804
HAT* [5]38.610.963034.770.926632.610.905334.450.946540.230.9806
IPG (Ours)38.610.963234.730.927032.600.905234.480.946440.240.9810
IPG+ (Ours)38.650.963334.870.927432.620.905334.540.946840.320.9811
SR×3IGNN [52]34.720.929830.660.848429.310.810529.030.869634.390.9496
ELAN [49]34.900.931330.800.850429.380.812429.320.874534.730.9517
IPT [4]34.81N/A30.85N/A29.38N/A29.49N/AN/AN/A
SwinIR [23]34.970.931830.930.853429.460.814529.750.882635.120.9537
EDT [20]34.970.931630.890.852729.440.814229.720.881435.130.9534
CAT-A [6]35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [47]35.070.932531.020.854129.510.815930.100.887135.390.9548
GRL-B* [22]35.050.932331.000.854329.490.815329.830.883735.240.9541
HAT [5]35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG (Ours)35.100.933231.100.855429.530.816830.360.890135.530.9554
IPG+ (Ours)35.190.933531.140.855829.570.817130.480.891135.650.9558
SR×4IGNN [52]32.570.899828.850.789127.770.743426.840.809031.280.9182
ELAN [49]32.750.902228.960.791427.830.745927.130.816731.680.9226
IPT [4]32.64N/A29.01N/A27.82N/A27.26N/AN/AN/A
SwinIR [23]32.920.904429.090.795027.920.748927.450.825432.030.9260
EDT [20]32.820.903129.090.793927.910.748327.460.824632.030.9254
CAT-A [6]33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [47]33.040.905129.160.795827.970.751027.770.832132.310.9283
GRL-B* [22]32.900.903929.140.795627.960.749727.530.827632.190.9266
HAT [5]33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG (Ours)33.150.906229.240.797327.990.751928.130.839232.530.9300
IPG+ (Ours)33.230.906429.300.797928.040.752528.220.840732.720.9310
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.483, + 0.891, + 0.511 + ], + "angle": 0, + "content": "Table 1. Comparison of IPG with recent SR methods. Methods with \\( {}^{* * * } \\) are replicated with standard setting, detailed in the Appendix; items with \"+\" stands for self-ensemble strategies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.629 + ], + "angle": 0, + "content": "lack of hardware support; IPG costs slightly advantageous peak memory. Apart from the quantitative comparison in PSNR/SSIM metrics, we also provide visual results of difficult details reconstructed by IPG. As shown in Figure 6, the proposed IPG model is compared against recent top-tier SR baselines on the \\(\\mathrm{SR} \\times 4\\) task. Our IPG model could visually outcompete other methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.659, + 0.235, + 0.675 + ], + "angle": 0, + "content": "4.3. Lightweight SR" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We also provide some lightweight variants of IPG. While the architecture of IPG-S and IPG-Tiny remains the same as the base version, their depth and dimension width are significantly reduced for computation-constrained applications. Variant config details are in the Appendix. We choose canonical SR baselines including CARN [1], IMDN [14], LAPAR-A [19], LatticeNet [31], and ESRT [30]; other baselines have MetaFormer architectures, including SwinIR-light [23], ELAN [48], SwinIRNG [53], and SRFormer-light [53]. IPG could outcompete SR baselines that share similar MetaFormer [44] architectures at similar computation costs. Specifically, IPG-Tiny could achieve more than 0.1dB of PSNR improvement on Urban100 compared with other lightweight baselines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.523, + 0.655, + 0.539 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.79 + ], + "angle": 0, + "content": "Pixel Nodes vs. Patch Nodes. As claimed in Section 3.2, patches as image graph nodes may suffer in cases like object shift and object rotation. The forcible element-wise alignment of patch pixels could hinder SR performance to a great extent. In order to investigate the negative impact of patch nodes, we provide a patched version of IPG as follows: rather than using pixel nodes, we use \\(2 \\times 2\\)-sized patches as nodes in this patched variant. Other model settings are kept unchanged for fair comparison, including model depths, feature dimensions, MLP ratios, and sampling region size. However, we are aware that the computation costs of patch node aggregation could be different compared to pixel nodes. Hence, we tune the number of aggregation times for the patched variant, to make sure that aggregation of patch nodes has a similar cost as pixel node aggregation. The ablation results are shown in Table 2." + }, + { + "type": "table", + "bbox": [ + 0.549, + 0.799, + 0.845, + 0.851 + ], + "angle": 0, + "content": "
Set5Set14Urban100
2 × 2-Patched IPG33.0129.1827.81
Pixel IPG33.1529.2428.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.852, + 0.892, + 0.88 + ], + "angle": 0, + "content": "Table 2. Comparison of pixel-node graphs against patch-node graphs in IPG. \\(\\mathrm{SR} \\times 4\\) results are reported." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In Figure 7, we also provide a vision comparison be" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24113" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.089, + 0.262, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.194, + 0.233, + 0.205 + ], + "angle": 0, + "content": "Urban100: img_024 \\((\\times 4)\\)" + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.091, + 0.383, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.141, + 0.333, + 0.151 + ], + "angle": 0, + "content": "HQ" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.091, + 0.507, + 0.138 + ], + "angle": 0, + 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"image_caption", + "bbox": [ + 0.112, + 0.307, + 0.232, + 0.318 + ], + "angle": 0, + "content": "Urban100: img_092 \\((\\times 4)\\)" + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.153, + 0.383, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.294, + 0.202, + 0.352, + 0.212 + ], + "angle": 0, + "content": "GRL-B [22]" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.153, + 0.507, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.425, + 0.202, + 0.471, + 0.212 + ], + "angle": 0, + "content": "ART [47]" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.153, + 0.631, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.202, + 0.597, + 0.212 + ], + "angle": 0, + "content": "CAT-A [6]" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.153, + 0.756, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.202, + 0.716, + 0.213 + ], + "angle": 0, + "content": "HAT [5]" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.153, + 0.881, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.202, + 0.846, + 0.212 + ], + "angle": 0, + "content": "IPG (ours)" + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.213, + 0.383, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.264, + 0.332, + 0.273 + ], + "angle": 0, + "content": "HQ" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.213, + 0.507, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.429, + 0.264, + 0.467, + 0.273 + ], + "angle": 0, + "content": "Bicubic" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.213, + 0.631, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.264, + 0.598, + 0.273 + ], + "angle": 0, + "content": "IGNN [52]" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.213, + 0.756, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.264, + 0.715, + 0.274 + ], + "angle": 0, + "content": "IPT [4]" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.213, + 0.881, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.264, + 0.85, + 0.273 + ], + "angle": 0, + "content": "SwinIR [23]" + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.274, + 0.383, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.294, + 0.325, + 0.352, + 0.335 + ], + "angle": 0, + "content": "GRL-B [22]" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.274, + 0.507, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.425, + 0.325, + 0.471, + 0.335 + ], + "angle": 0, + "content": "ART [47]" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.274, + 0.631, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.325, + 0.598, + 0.335 + ], + "angle": 0, + "content": "CAT-A [6]" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.274, + 0.756, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.325, + 0.717, + 0.335 + ], + "angle": 0, + "content": "HAT [5]" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.274, + 0.881, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.325, + 0.846, + 0.335 + ], + "angle": 0, + "content": "IPG (ours)" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.335, + 0.259, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.429, + 0.232, + 0.439 + ], + "angle": 0, + "content": "Urban100: img_098 \\((\\times 4)\\)" + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.335, + 0.383, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.387, + 0.333, + 0.396 + ], + "angle": 0, + "content": "HQ" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.335, + 0.507, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.429, + 0.387, + 0.466, + 0.396 + ], + "angle": 0, + "content": "Bicubic" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.335, + 0.631, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.387, + 0.598, + 0.396 + ], + "angle": 0, + "content": "IGNN [52]" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.335, + 0.756, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.387, + 0.714, + 0.396 + ], + "angle": 0, + "content": "IPT [4]" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.335, + 0.881, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.387, + 0.851, + 0.396 + ], + "angle": 0, + "content": "SwinIR [23]" + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.397, + 0.383, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.294, + 0.448, + 0.352, + 0.459 + ], + "angle": 0, + "content": "GRL-B [22]" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.397, + 0.507, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.425, + 0.448, + 0.471, + 0.459 + ], + "angle": 0, + "content": "ART [47]" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.397, + 0.631, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.448, + 0.598, + 0.459 + ], + "angle": 0, + "content": "CAT-A [6]" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.397, + 0.756, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.448, + 0.716, + 0.459 + ], + "angle": 0, + "content": "HAT [5]" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.397, + 0.881, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.448, + 0.846, + 0.458 + ], + "angle": 0, + "content": "IPG (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.21, + 0.463, + 0.758, + 0.478 + ], + "angle": 0, + "content": "Figure 6. Visual comparison of image SR \\((\\times 4)\\) with latest SR baselines in challenging cases." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.491, + 0.25, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.583, + 0.227, + 0.593 + ], + "angle": 0, + "content": "Urban100: img_092 \\((\\times 4)\\)" + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.491, + 0.361, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.537, + 0.318, + 0.546 + ], + "angle": 0, + "content": "HQ" + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.491, + 0.472, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.537, + 0.463, + 0.546 + ], + "angle": 0, + "content": "IGNN [52] \\((3\\times 3)\\)" + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.547, + 0.361, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.592, + 0.364, + 0.602 + ], + "angle": 0, + "content": "Patched IPG [6] \\((2\\times 2)\\)" + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.547, + 0.472, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.398, + 0.592, + 0.44, + 0.602 + ], + "angle": 0, + "content": "IPG [47]" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.602, + 0.469, + 0.63 + ], + "angle": 0, + "content": "Figure 7. Visual comparison of patch-node graph methods over IPG that uses pixel node graphs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.469, + 0.776 + ], + "angle": 0, + "content": "tween IGNN [52] \\((3 \\times 3\\) patch), patched IPG \\((2 \\times 2\\) patch), and IPG (pixel graph). For the IGNN case that uses large patches as nodes, patch alignment is causing trouble: the model is puzzled about the texture orientations, so it makes mistakes during texture reconstruction by aligning pattern-similar but orientation-different patches. For patched IPG, misaligned orientation is causing issues as well: line textures are distorted. In contrast, pixel aggregation in IPG avoids misalignment and performs well." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.777, + 0.469, + 0.792 + ], + "angle": 0, + "content": "KNN vs. Degree-flexible Graphs. In canonical graph" + }, + { + "type": "table", + "bbox": [ + 0.145, + 0.804, + 0.403, + 0.856 + ], + "angle": 0, + "content": "
Set5Set14Urban100
KNN33.0929.1928.06
Degree-Flex33.1529.2428.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.857, + 0.469, + 0.884 + ], + "angle": 0, + "content": "Table 3. Comparison of degree-flexible graphs against plain KNN graphs in IPG. \\(\\mathrm{SR} \\times 4\\) results are reported." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "applications for vision tasks, \\(k\\)-Nearest-Neighbor (KNN)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.69 + ], + "angle": 0, + "content": "graphs are normally adopted for graph construction. However, KNN still suffers the degree rigidity, as all nodes are connected to a fixed number of neighboring nodes. To improve degree flexibility, we consider the unbalanced demand of pixels in SR tasks and propose a degree-flexible scheme of graph construction (introduced in Section 3.2). We compare KNN and the degree-flexible graph scheme in IPG under the same settings. According to Table 3, Degree-Flex could outcompete the KNN variant of IPG. Interestingly, our Degree-Flex graph could outcompete computation-heavy fully-connected graphs (see Appendix), further implying the effectiveness of our DegreeFlex graphs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.698, + 0.892, + 0.834 + ], + "angle": 0, + "content": "As shown in Figure 8, we visually compare the connected regions of detail-poor and detail-rich pixels at the local scale. Detail-poor pixels are usually on flat, changeless parts of the image; these pixels require minimal node connection for reconstruction. On the contrary, detail-rich pixel nodes are usually on edges and corners, which are assigned higher node degrees and thus a larger region of perception. In this sense, the detail-rich indicator metric \\( D_{F} \\) could endow IPG with degree flexibility." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Local/Global Graphs. In the design of IPG, we aggregate information from both local and global scales based on local and global pixel node sampling. Though numerous SR works highlight the importance of either local or non-local" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24114" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.878, + 0.439 + ], + "angle": 0, + "content": "
MethodTraining DatasetParamsFLOPsSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
×2 SRCARN [1]DIV2K1592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [14]DIV2K694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [19]DF2K548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [31]DIV2K756K169.5G38.150.961033.780.919332.250.900532.430.9302N/AN/A
ESRT [30]DIV2K751K-38.030.960033.750.918432.250.900132.580.931839.120.9774
SwinIR-light [23]DIV2K910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [49]DIV2K621K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [7]DIV2K1181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
SRFormer-light [53]DIV2K853K236G38.230.961333.940.920932.360.901932.910.935339.280.9785
IPG-Tiny (Ours)DIV2K872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
×3 SRCARN [1]DIV2K1592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [14]DIV2K703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [19]DF2K594K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [31]DIV2K765K76.3G34.530.928130.390.842429.150.805928.330.8538N/AN/A
ESRT [30]DIV2K751K-34.420.926830.430.843329.150.806328.460.857433.950.9455
SwinIR-light [23]DIV2K918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [49]DIV2K629K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [7]DIV2K1190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
SRFormer-light [53]DIV2K861K105G34.670.929630.570.846929.260.809928.810.865534.190.9489
IPG-Tiny (Ours)DIV2K878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
×4 SRCARN [1]DIV2K1592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [14]DIV2K715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [19]DF2K659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [31]DIV2K777K43.6G32.300.896228.680.783027.620.736726.250.7873N/AN/A
ESRT [30]DIV2K751K-32.190.894728.690.783327.690.737926.390.796230.750.9100
SwinIR-light [23]DIV2K930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [49]DIV2K640K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [7]DIV2K1201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
SRFormer-light [53]DIV2K873K62.8G32.510.898828.820.787227.730.742226.670.803231.170.9165
IPG-Tiny (Ours)DIV2K887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.444, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Table 4. Comparison of IPG-Tiny with recent lightweight SR methods. Under comparable Params and FLOPs, IPG-Tiny could outcompete lightweight SR baselines." + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.489, + 0.455, + 0.752 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.811 + ], + "angle": 0, + "content": "Figure 8. Visual demonstration of parts connected to a pixel node. Compared with detail-poor nodes (left), detail-rich nodes (right) requires a larger amount of aggregation due to difficulty in reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "aggregation, we demonstrate that both aspects are actually crucial for SR performance. As shown in Table 5, we perform experiments that uses local or global-scale graphs only under identical settings, and compare them with the original version of IPG. The optimal performance is reached when" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.493, + 0.822, + 0.509 + ], + "angle": 0, + "content": "both local and global aggregation are performed." + }, + { + "type": "table", + "bbox": [ + 0.561, + 0.52, + 0.835, + 0.584 + ], + "angle": 0, + "content": "
Set5Set14Urban100
Local Only33.0829.1928.10
Global Only33.0429.1127.59
Local + Global33.1529.2428.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.511, + 0.588, + 0.88, + 0.603 + ], + "angle": 0, + "content": "Table 5. Ablations of local and global graph usages on \\( \\mathrm{{SR}} \\times 4 \\) ." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.619, + 0.634 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Existing SR measures are rigid both in terms of space and degree. In order to break rigidity in SR, the paper proposes IPG – an SR model that fully leverages the flexibility of graphs. Firstly, we are aware that SR is a task where detail-rich image parts require lopsided reconstruction efforts. Hence, we designed a degree-varying scheme for graph construction rather than \\( k \\)-nearest neighbors. Then we take pixels rather than patches for graph aggregation. To reach the maximum amount of spatial flexibility, nodes are sampled both on local and global scales. IPG reaches State-of-the-art performance compared with SR baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.893, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by the National Key R&D Program of China under Grant No.2022ZD0160300 and the National Natural Science Foundation of China under Grant No.62276007. We gratefully acknowledge the support of MindSpore, CANN and Ascend AI Processor used for this research." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "24115" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. 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Srformer: Permuted self-attention for single image super-resolution. arXiv preprint arXiv:2303.09735, 2023. 2, 5, 6, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24117" + } + ] +] \ No newline at end of file diff --git a/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/dacb6475-02d0-43fb-ade3-b56b50c0b0c7_origin.pdf b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/dacb6475-02d0-43fb-ade3-b56b50c0b0c7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0c89ec29817ca439c683f4629e8049ae738dc751 --- /dev/null +++ b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/dacb6475-02d0-43fb-ade3-b56b50c0b0c7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9ab9a3de434d487342e0444de16f26fd5988709754e0911113d187d101dc034a +size 9165006 diff --git a/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/full.md b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..64a5eb082f00d934378421d207c68b214d94abd6 --- /dev/null +++ b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/full.md @@ -0,0 +1,402 @@ +# Image Processing GNN: Breaking Rigidity in Super-Resolution + +Yuchuan Tian $^{1}$ , Hanting Chen $^{2}$ , Chao Xu $^{1}$ , Yunhe Wang $^{2*}$ + +$^{1}$ National Key Lab of General AI, School of Intelligence Science and Technology, Peking University. $^{2}$ Huawei Noah's Ark Lab. + +tianyc@stu.pku.edu.cn, yunhe.wang@huawei.com + +# Abstract + +Super-Resolution (SR) reconstructs high-resolution images from low-resolution ones. CNNs and window-attention methods are two major categories of canonical SR models. However, these measures are rigid: in both operations, each pixel gathers the same number of neighboring pixels, hindering their effectiveness in SR tasks. Alternatively, we leverage the flexibility of graphs and propose the Image Processing GNN (IPG) model to break the rigidity that dominates previous SR methods. Firstly, SR is unbalanced in that most reconstruction efforts are concentrated to a small proportion of detail-rich image parts. Hence, we leverage degree flexibility by assigning higher node degrees to detail-rich image nodes. Then in order to construct graphs for SR-effective aggregation, we treat images as pixel node sets rather than patch nodes. Lastly, we hold that both local and global information are crucial for SR performance. In the hope of gathering pixel information from both local and global scales efficiently via flexible graphs, we search node connections within nearby regions to construct local graphs; and find connections within a strided sampling space of the whole image for global graphs. The flexibility of graphs boosts the SR performance of the IPG model. Experiment results on various datasets demonstrate that the proposed IPG outperforms State-of-the-Art baselines. Codes are available at this link. + +# 1. Introduction + +The ill-posed task of Super-Resolution (SR) constructs high-resolution images from low-resolution ones. SR works typically apply Deep Neural Network (DNN) knowledge learned from High-Resolution training images to construct missing details in low-resolution inputs. Existing DNN variants for classical SR tasks include CNNs [16, 24, 50] and Transformers [5, 6, 23]. These measures have proved effective in creating High-Resolution images, and are used in real-world applications like medical imaging [10], re + +![](images/f9407516bdd427c1a3c11dbadaf6e5aa92cbd90cb1768401cbaffe4567f98ae0.jpg) +Convolution + +![](images/a03f148d486c349d3323fff93d6b557020a86faeda9a440811e623d3f01c72c3.jpg) +Self-Attention + +![](images/78d907fceb672e0d8f08851975c8600138aced3d9c0abf480897703bce2e01ed.jpg) +KNN Graph + +![](images/86263c14de8ea65088d6d0913ce3ad7e50fdd407c248f70a63a90e06f86c3571.jpg) +Ours +Figure 1. Convolution (left), Self-Attention (middle-left), KNN Graph Aggregation (middle-right), and Graph Aggregation in IPG (right). Compared with other methods, IPG graph aggregation considers the unbalanced nature of SR: detail-rich, high-frequency image nodes (red) have higher node degrees; while flat, low-frequency image nodes (blue) require fewer aggregations. + +mote sensing [15], et cetera. + +Despite various measures, it is taken for granted that mainstream SR models treat all pixels in a fairly rigid manner. For instance, as shown in Figure 1, in convolution layers of the CNN-based SR model VDSR [16], the same convolution kernel scans through all pixels of feature maps, i.e. each pixel is rigidly designated to communicate with its nearest neighbors; in the Transformer-based model SwinIR [23], all pixels are assigned to equal-sized attention grids for self-attention operations. In both examples, each pixel aggregates information from a fixed number of pixels within a neighborhood of fixed size. + +Efforts have been made to overcome the rigidity of convolution and window-attention operations. For example, some recent SR research tries to enhance SR models by enlarging self-attention grids [5, 46] and designing striped global attention windows [6, 22]. But these improvements also introduce a large computation burden. Some other works [12, 26, 52] leverage the flexibility of graphs and propose graph-based methods. With content-based graphs constructed from patch nodes, each image patch could aggregate top- $k$ relevant but distant parts beyond hard local boundaries in convolution and window-attention. + +However, these graph measures have limited flexibility because the lopsided nature of SR is overlooked. In SR tasks, only a small proportion of high-frequency pixels require hard reconstruction efforts; the majority of pixels are located in flat, low-frequency regions and thus almost left intact [9]. In response to the imbalance, SR methods should + +ideally pay more attention to detail-rich regions and care less about flat, detail-poor image parts. However, existing $k$ -Nearest-Neighbor graph-based methods treat all image nodes equally. In other words, all nodes share the same pre-set degree $k$ and the unbalanced nature of SR is not considered. In fact, as we inspect canonical operation paradigms in SR from a graph perspective, we found that degree-equivalence rigidity also manifests in convolution and window-attention: in these paradigms, each pixel on the image aggregates the same number of pixels regardless of image content, and thus, sharing "equal degrees" in graph terms. Equal node degrees that are rigidly assigned to nodes or pixels mismatch their unequal reconstruction demands in SR, thus impacting SR performance. + +Trying to break rigidity, we propose the graph-based Image Processing Graph Neural Networks (IPG) model for SR that taps the flexibility potential of graphs. Firstly, to break the degree-equivalence rigidity of convolution, window-attention, and $k$ -Nearest-Neighbor (KNN) graphs, we leverage degree flexibility by proposing a novel degree-variant graph solution based on the unbalanced nature of SR. Specifically, a detail-aware metric is designed to measure the importance of image nodes where larger degrees are assigned to high-frequency nodes. Then, different from graph-based model counterparts, IPG adopts pixels rather than patches as image graph nodes to avoid misalignment issues due to patch rigidity. Finally, in the interest of having both local and global perception without sacrificing efficiency due to large pixel-level search space, we resort to local and global node sampling strategies. In this way, graphs are established efficiently from small pixel subsets and could either focus on local information for detail reconstruction, or span over the whole image for spatially distant but crucial features. With the measures mentioned above, IPG could fully exert graph flexibilities and achieve outstanding performances on SR tasks. + +# 2. Related Work + +Recent SR Methods. In canonical approaches to SuperResolution, manifold previous works phrase SR as a regression problem and is proved effective via applications of CNN models [16, 24, 50, 51]. In these works, a crafted CNN model is applied to the LR image to render it into HR. Since the introduction of Transformers to vision [8], manifold works integrate the self-attention mechanism in Transformers into SR models [4-7, 23, 47, 53]. SwinIR [23] borrows shifted window-attention to SR and demonstrates good performance. Latest SR models include using striped attention windows [6, 22], channel attention [5, 22, 40], permuted attention [53], et cetera. + +Despite the fact that manifold SR works follow similar convolution or window-attention methodologies, their SR performance is still confined to the rigidity of ordinary vi + +sion models, i.e. fixed paradigms for aggregating neighboring pixels and neglecting the unbalanced reconstruction demand among pixels in SR. Hence, we resort to graphs as a flexible way to aggregate information in order to break these sorts of rigidity. + +Graphs for Vision. Graphs have been widely applied to vision tasks, including point cloud segmentation [17, 41], human action recognition [42], and image classification [12, 32]. Some previous low-level vision works also view images as graphs. Most works leverage graph to aggregate non-local information, either intra-scale [2, 18, 21, 35, 38] or cross-scale [26, 52]. Other low-level vision works on graphs include cross-layer [27] or inter-image information aggregation [37]. Among these works, edge-conditioned aggregation from neighboring nodes is mostly preferred. + +In terms of graph construction from images, a majority of works use $k$ -nearest neighbors [18, 21, 26, 35, 38, 52]. Since all image nodes share the same degree, KNN graphs are not flexible enough; and the unbalanced nature of image nodes in low-level vision tasks is neglected as well. Besides, most graph works regard patches as image nodes [18, 21, 26, 35, 52], disregarding potential patch misalignment issues in low-level vision. As for the scale of graphs, some works [21, 26, 52] search in a global scale to construct graphs; other works [38, 39] construct graphs from a local box. Graphs in these works are not flexible enough in that they fail to take care of both local and global aspects. + +# 3. Method + +# 3.1. Rigidity of Previous SR Methods + +Convolution [16, 24, 50] and window-attention [5, 6, 23] are two major pathways for SR model designs. Despite popular usages in SR, these measures are not flexible; their deep-rooted rigidity could hinder SR performance. In one convolution operation, each outputted pixel gathers information within a tiny kernel-sized window; each pixel only has access to its neighboring pixels. For instance, in a standard $3 \times 3$ convolution, the perception field of a single pixel is confined to a tiny $3 \times 3$ box. All pixels on the image collect information from 8 respective neighbors and themselves. The similar rigidity goes for window attention: though larger window sizes (compared to convolution) are usually adopted, the perception field of window attention is still confined within hard window boundaries. In a $8 \times 8$ window-attention scenario, all pixels gather 64 pixels within the window where they belong. + +Therefore, beyond rigidity in convolution and window-attention, some works think out of the box and adopt graphs in SR models. Unlike convolution and window-attention where information aggregation is bounded to boxes, these graph-based works are more spatially flexible: each node could aggregate information from its favorite top- $k$ nodes + +with loose spatial constraints. In this sense, graph aggregation is not limited to preset rigid patterns; it is more dynamic and scalable compared to convolution and window-attention counterparts. + +However, though previous graph-based methods break through hard aggregation boundaries, we hold that the flexibility of graphs is not fully exploited in SR tasks. First and foremost, as shown in Figure 1, all previous methodologies (either graph-based, convolution-based, or window-attention-based) are degree-rigid. SR reconstruction demand is unbalanced among different image parts. But in previous methods, all pixels or nodes on the image are aggregating the same number of pixels or nodes; i.e. in graph terms, they share the same aggregation degree. Secondly, previous graph-based works are patch-rigid. Though patches are usually regarded as image nodes, patch aggregation usually requires rigid pixel-wise alignment. Possible misalignment of low-level features in patches makes SR models perform worse. Thirdly, previous graph-based works rigidly use graphs on either global or local scales, but information at both scales is potentially important for SR reconstruction. These rigid aspects are hindering the performance of SR models. + +# 3.2. Graph Construction + +To break these rigidities, we construct degree-flexible pixel graphs at local and global scales in the IPG model. In this manner, we could fully exploit the flexibility of graphs and achieve outstanding performance in SR tasks. + +Degree Flexibility. Firstly, we try to figure out a degree-flexible graph solution based on the unique "unbalanced property" of SR tasks. SR reconstruction of images features imbalance. As Gou et al. [9] put it, SR is a long-tailed problem where only a small proportion of high-frequency pixels need to be reconstructed; the rest of the image parts need minimal restoration only. However, Gou et al. [9] tries to address the issue by designing training losses rather than rethinking it from the aspect of model designs. In the lopsided SR problem, it is a long-neglected aspect that treating all pixels or parts on the image equivalently is unsuitable and inefficient. + +To this end, we opt to assign various node degrees to pixels based on a detail-rich indicator that marks pixels needing more reconstruction efforts. Then we design the detail-rich indicator as follows: given feature map $F \in \mathbb{R}^{H \times W \times C}$ and downsampling ratio $s$ , the detail-rich indicator metric per pixel $D_F \in \mathbb{R}^{H \times W}$ is designated as the absolute difference between the bilinearly downsampled and upsampled feature map and the feature map itself: + +$$ +D _ {F} := \sum_ {C} | F - F _ {\downarrow s \uparrow s} |, \tag {1} +$$ + +where $s$ is taken as 2 to avoid severe information loss. We + +are aware that some explainable SR works [11, 43] propose metrics to measure the importance of a certain part in the output. However, these measures are gradient-based, which requires costly backward passes. In comparison, the proposed metric $D_F$ is operation cheap in that it only requires bilinear interpolation twice. We also provide FLOPs statistics in the Appendix. + +![](images/463e47e7bd2a8b7d799ab62add45771562c7dcf21c6c68a1528a5b18abec70be.jpg) + +![](images/fec15f367ba9b91678acc6325cf0fb2ad52985f213cf32f3440dc3264191caf8.jpg) + +![](images/8aa71af9f51d10f89a4b7e2940acca9397a8c565ab72361d88018522bf32ad83.jpg) + +![](images/dc9a4901359db228b540609b3e68d516bdc0a10b8557c3f3df625ce5d228d07e.jpg) +Figure 2. Visualization of the detail-rich indicator $D_F$ in IPG. Original image (left); $D_F$ of the shallowest block (middle); $D_F$ of the deepest block (right). $D_F$ could effectively reflect detail-rich parts on the image. + +![](images/ba07e71de4be529142d8edde203d378812cdc27a87cd935eec2f451935500efd.jpg) + +![](images/b4a96cd5f0bafdfdabf64e846f7b31234aa2d122d51179bd23edf5cb3125b809.jpg) + +The overall degree budgets are assigned to each pixels based on $D_F$ . The degree for a pixel node $v \in F$ on the feature map is in proportion to its corresponding pixel value at $D_F$ : + +$$ +\deg (v) \propto D _ {F} (v). \tag {2} +$$ + +The detail-rich indicator $D_F$ in different MGB blocks is visualized. From Figure 2, it can be seen that detail-rich parts are responsive: margins and corners have high $D_F$ while flat color blocks are low in $D_F$ . The visualization reveals that the proposed $D_F$ could effectively reflect high-frequency parts on the image throughout layers. + +Pixel Node Flexibility. Then we are faced with the formulation of vertices in image graphs. In previous graph-based vision works [21, 26, 36, 52], graph nodes are typically set as image patches. During graph aggregation, patches are weighted-summed in a pixel-wise manner. However, the forcible element-wise alignment of pixels during aggregation is unsuitable for SR tasks where feature maps have rich low-level features. Object shift and rotation within low-level patches are two major issues causing patch misalignment. As for object shift, locations of objects within patches could vary; location-misaligned patch objects introduce noises. Object rotation is another faulty aspect of patch aggregation. The orientation of patches is disregarded due to rigid rectangular patch shapes during patch alignment. + +To avoid the above problems during node aggregation, we hold that finer-grained pixel nodes are better solutions + +![](images/5e5e9c01f0040e16728651be5036daff69339ac10a3c575956f2ea7702ea459c.jpg) +Figure 3. The architectures of IPG, Multiscale Graph-aggregation Blocks (MGB), and Graph Aggregation Layers (GAL). Each IPG consists of $M$ MGB blocks, and each MGB has $G$ GAL layers. Local and global graphs are distributed to GALs alternatively within MGB. + +in the low-level vision scenario. Pixel graphs are more flexible: each pixel node could directly find its relevant pixels in aggregation, therefore avoiding pixel misalignment. + +However, we admit that compared to pixel graphs, patch graphs could potentially have larger perception fields and are easier to construct due to a smaller number of nodes in total, which means a smaller search space for edge connections. Hence, we need an efficient way to construct a flexible and effective pixel graph. + +Space Flexibility. Then we develop the space flexibility of IPG graphs via an efficient search of pixel node connections both locally and globally. We propose that both local and global information are crucial for SR reconstruction: while lossy image parts could rebuild themselves from local neighborhoods, they could also learn from distant but similar features for refinement. + +Existing graph-based methods have demonstrated some sort of space flexibility. As shown in Figure 1, compared to convolution and window attention options where a pixel always attends to a fixed neighboring region, graph aggregation could flexibly focus on crucial image parts regardless of space limits. However, existing graph-based works are not spatially flexible enough as they fail to consider both local and global aspects. + +In fact, computation considerations are the major concern of a comprehensive connection search. It is costly to construct global graphs by searching through all image nodes. As a remedy, strided sampling is always adopted [21, 26, 52]. But consequently, local regions are neglected. The choice of pixels as graph nodes makes graph construction even more challenging, because node spaces are enlarged further and it is hardly impractical to search through all pixels for graph construction. + +For the sake of efficiency, and to gather local-level surrounding features and global-level distant features contributive to detail reconstruction in SR tasks, we use two types of sampling to aggregate both local and global information, shown in Figure 4. For local sampling, the neighborhood + +surrounding a certain node is chosen as a local-scale search space on which a graph is established; for global sampling, sampled nodes span over the image in a dilated pattern. + +![](images/ef3ba82d44582151f347c7a186ff6a1dbf68270487ec97e20f541f97788e68a2.jpg) +Figure 4. An illustration of sampling strategies. The original image with the highlighted image node (left), local sampling (middle), and global sampling (right) are demonstrated. In this way, image graphs could flexibly gather both local and global information in an efficient manner. + +![](images/8ef6bd8f289fb2a6ea95e177e751ccaf33fd1138c46400eec4895678ee56d43f.jpg) + +![](images/6d9f9ac110afed8545f74672707bebf4a14b3d5d6ecc22eff944ac5be8d08e15.jpg) + +In the proposed IPG SR model, both sampling methods are performed in order to construct local and global-scale graphs. For each pixel node, its node connections are searched within the sampling space. In this way, we achieve spatial flexibility in a cost-efficient fashion. + +# 3.3. Graph Aggregation + +Now that flexible graphs are constructed, graph aggregation is performed such that each node can communicate with its connected neighbors and use their information for self-refinement in SR. In vision applications of graphs, aggregation in max-pooling [12, 28] or edge-conditioned [21, 26, 36] forms are mostly preferred. We tend to adopt edge-conditioned aggregation [36], as max-pooling could result in significant loss of information from neighboring pixels that are crucial for low-level vision. Since pixel reconstruction in SR heavily relies on abundant neighboring information, edge-conditioned aggregation is adopted as it cares about pixel inter-relations and maintains more neighboring information for effective reconstruction. The edge-conditioned aggregation [21, 26, 36, 52] is mathematically + +formulated as follows: at the $k^{th}$ layer in IPG, given node feature $\mathbf{h}^{k - 1}$ as input, neighboring node set $\mathcal{N}(v)$ , the node $v$ output $\mathbf{h}_v^k$ is calculated as: + +$$ +\mathbf {h} _ {v} ^ {k} = \frac {1}{C ^ {k}} \sum_ {u \in N (v)} \exp \left(f ^ {k} (u, v)\right) \mathbf {h} _ {u} ^ {k - 1}, \tag {3} +$$ + +where $f^k: \mathbb{R}^d \times \mathbb{R}^d \to \mathbb{R}$ is a parameterized function that measures the correlation between node pair $(u, v)$ ; $C^k := \sum_{u \in N(v)} \exp(f^k(u, v))$ is a normalizing constant. In our case, cosine similarity is adopted as the correlation metric. + +Despite the flexibility of graph aggregation, we are concerned that the spatial information is damaged in the process of graph aggregation: since all nodes are treated equally, the model will grasp little knowledge about node position. Hence, inspired by Liu et al. [25, 29], we add relative position encoding to node features before aggregation to enhance position information. + +# 3.4. Model Architecture + +The proposed graph construction and graph aggregation mechanisms are then merged into the effective MetaFormer architecture as the IPG model. The detailed structure of IPG is shown in Figure 3. + +The IPG Architecture. The general architecture of IPG follows mainstream SR models [5-7, 23, 53]. As an LR image is inputted into the model, it is first passed to a Conv Layer to extract shallow features. Then the features are passed through a series of Multiscale Graph-aggregation Blocks (MGB) for effective deep feature extraction with the aid of flexible graphs. Each MGB consists of a stack of Graph Aggregation Layers (GAL) where graph aggregation on both local and global scales is performed. Finally, the image is spatially reconstructed via a pixel-shuffle upsampler. + +MGB Blocks. Multiscale Graph-aggregation Blocks (MGB) gather both local and global-scale information for effective image SR reconstruction. Both local and global pixel graphs are calculated per block based on block inputs. Block-wise graph calculations enable regular graph updates throughout the model. The construction steps are detailed in Section 3.2, where local and global sampling is performed respectively for local or global graph construction. The two types of graphs (local/global) are then distributed to GALs throughout the block for aggregation operations. Local and global graphs are distributed in a sequentially alternative manner to ensure that both local and global-scale information are sufficiently aggregated. + +GAL Layers. The design of Graph Aggregation Layers (GAL) follows the general MetaFormer-like structure [44]. Graphers that are responsible for graph aggregation (as introduced in Section 3.3) are used as token mixers. Grapher gathers local or global information based on the type + +of graph it receives. Following [5, 22, 53], we leverage efficient Channel Attention (CA) modules and ConvFFN blocks to aid the SR performance of our model. + +# 4. Experiments + +# 4.1. Experiment Setting + +We adopt the general training setting of recent SR works [5, 6, 23] for fair comparison. We use DIV2K+Flickr2K (DF2K) as the training set (DIV2K for lightweight models). Cropped patches of size $64 \times 64$ are sent into the model. Training data is augmented by random flipping and random rotation of degrees [0,90,180,270]. Our model is trained for 500K iterations using the Adam Optimizer $(\beta_{1} = 0.9, \beta_{2} = 0.99)$ at a learning rate of $2e - 4$ . The training input size is set at $64 \times 64$ . MultistepLR is adopted where the learning rate is halved at iterations [250000, 400000, 450000, 475000]. Batchsize is set as 32. + +# 4.2. Super-Resolution Performance + +![](images/dac100cdcab2d127ae1cdf7e27ba9034584d234c2801b9563b8b12571c34c56f.jpg) +Figure 5. Comparison of the proposed IPG-S and IPG with SR baselines in FLOPs and performance. Urban $100 \times 4$ in PSNR is reported. Thanks to the flexibility of graphs, IPG could outperform other SR models by $>0.1\mathrm{dB}$ at similar FLOPs. Notably, FLOPs only reflect theoretical computation costs instead of actual inference speed. + +We compare the performance of our model with various SR baselines in Table 1 on Set5 [3], Set14 [45], BSDS100 [33], Urban100 [13], and Manga109 [34] benchmarks. The chosen baselines are as follows: IGN [52] is a patch-graph-based SR method; ELAN [49], IPT [4], SwinIR [23], CAT-A [6], ART [47], GRL-B [22], and HAT [5] are transformer-based methods. Performance of $\mathrm{SR}\times 2$ $x3$ $x4$ models are measured by PSNR and SSIM. " $^+$ " marks stand for baselines with self-ensemble strategies, which boosts SR performance further. IPG could outcompete other models by large margins. In particular, IPG reaches 28.13dB of PSNR on the Urban $100\times 4$ task, exceeding existing SOTA by more than 0.1dB with standard training setting. IPG has an outstanding performance in the PSNR versus theoretical FLOPs plot, shown in Figure 5. But notably, IPG runs slower than previous methods for + +
MethodSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
SR×2IGNN [52]38.240.961334.070.921732.410.902533.230.938339.350.9786
ELAN [49]38.360.962034.200.922832.450.903033.440.939139.620.9793
IPT [4]38.37N/A34.43N/A32.48N/A33.76N/AN/AN/A
SwinIR [23]38.420.962334.460.925032.530.904133.810.942739.920.9797
EDT [20]38.450.962434.570.925832.520.904133.800.942539.930.9800
CAT-A [6]38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [47]38.560.962934.590.926732.580.904834.300.945240.240.9808
GRL-B* [22]38.480.962734.640.926532.550.904533.970.943740.060.9804
HAT* [5]38.610.963034.770.926632.610.905334.450.946540.230.9806
IPG (Ours)38.610.963234.730.927032.600.905234.480.946440.240.9810
IPG+ (Ours)38.650.963334.870.927432.620.905334.540.946840.320.9811
SR×3IGNN [52]34.720.929830.660.848429.310.810529.030.869634.390.9496
ELAN [49]34.900.931330.800.850429.380.812429.320.874534.730.9517
IPT [4]34.81N/A30.85N/A29.38N/A29.49N/AN/AN/A
SwinIR [23]34.970.931830.930.853429.460.814529.750.882635.120.9537
EDT [20]34.970.931630.890.852729.440.814229.720.881435.130.9534
CAT-A [6]35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [47]35.070.932531.020.854129.510.815930.100.887135.390.9548
GRL-B* [22]35.050.932331.000.854329.490.815329.830.883735.240.9541
HAT [5]35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG (Ours)35.100.933231.100.855429.530.816830.360.890135.530.9554
IPG+ (Ours)35.190.933531.140.855829.570.817130.480.891135.650.9558
SR×4IGNN [52]32.570.899828.850.789127.770.743426.840.809031.280.9182
ELAN [49]32.750.902228.960.791427.830.745927.130.816731.680.9226
IPT [4]32.64N/A29.01N/A27.82N/A27.26N/AN/AN/A
SwinIR [23]32.920.904429.090.795027.920.748927.450.825432.030.9260
EDT [20]32.820.903129.090.793927.910.748327.460.824632.030.9254
CAT-A [6]33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [47]33.040.905129.160.795827.970.751027.770.832132.310.9283
GRL-B* [22]32.900.903929.140.795627.960.749727.530.827632.190.9266
HAT [5]33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG (Ours)33.150.906229.240.797327.990.751928.130.839232.530.9300
IPG+ (Ours)33.230.906429.300.797928.040.752528.220.840732.720.9310
+ +lack of hardware support; IPG costs slightly advantageous peak memory. Apart from the quantitative comparison in PSNR/SSIM metrics, we also provide visual results of difficult details reconstructed by IPG. As shown in Figure 6, the proposed IPG model is compared against recent top-tier SR baselines on the $\mathrm{SR} \times 4$ task. Our IPG model could visually outcompete other methods. + +# 4.3. Lightweight SR + +We also provide some lightweight variants of IPG. While the architecture of IPG-S and IPG-Tiny remains the same as the base version, their depth and dimension width are significantly reduced for computation-constrained applications. Variant config details are in the Appendix. We choose canonical SR baselines including CARN [1], IMDN [14], LAPAR-A [19], LatticeNet [31], and ESRT [30]; other baselines have MetaFormer architectures, including SwinIR-light [23], ELAN [48], SwinIRNG [53], and SRFormer-light [53]. IPG could outcompete SR baselines that share similar MetaFormer [44] architectures at similar computation costs. Specifically, IPG-Tiny could achieve more than 0.1dB of PSNR improvement on Urban100 compared with other lightweight baselines. + +# 4.4. Ablation Study + +Pixel Nodes vs. Patch Nodes. As claimed in Section 3.2, patches as image graph nodes may suffer in cases like object shift and object rotation. The forcible element-wise alignment of patch pixels could hinder SR performance to a great extent. In order to investigate the negative impact of patch nodes, we provide a patched version of IPG as follows: rather than using pixel nodes, we use $2 \times 2$ -sized patches as nodes in this patched variant. Other model settings are kept unchanged for fair comparison, including model depths, feature dimensions, MLP ratios, and sampling region size. However, we are aware that the computation costs of patch node aggregation could be different compared to pixel nodes. Hence, we tune the number of aggregation times for the patched variant, to make sure that aggregation of patch nodes has a similar cost as pixel node aggregation. The ablation results are shown in Table 2. + +Table 1. Comparison of IPG with recent SR methods. Methods with ${}^{* * * }$ are replicated with standard setting, detailed in the Appendix; items with "+" stands for self-ensemble strategies. + +
Set5Set14Urban100
2 × 2-Patched IPG33.0129.1827.81
Pixel IPG33.1529.2428.13
+ +Table 2. Comparison of pixel-node graphs against patch-node graphs in IPG. $\mathrm{SR} \times 4$ results are reported. + +In Figure 7, we also provide a vision comparison be + +![](images/e423b99a88d4395079e472e078db41692da4b147e7571d9a1cbd32dad57099df.jpg) +Urban100: img_024 $(\times 4)$ + +![](images/9a5b44565e2bf03b45b0bdadeeece04c8c8779819d0282266ee47bcea278b34f.jpg) +HQ + +![](images/8a49435cd09d1f42fc074597edbbf71ca2a9c64051ef49b23507ee0b47549de9.jpg) +Bicubic + +![](images/6507bd257bff0a48bc97ab6c771c020eec17c5d3a883d26409e2fec992dd9bbe.jpg) +IGNN [52] + +![](images/ccace8dbf49145ef23190a23e3a993e53b84dcb733dbb0f9e1c30f359d6cd6fc.jpg) +IPT [4] + +![](images/57df80500b52a45157136abd23b6faeef81804b74727cb69fa64aef9b1a442dc.jpg) +SwinIR [23] + +![](images/7d52cd349c1827161413339d4c0930068ee6e6a866aeef0fa454cf8bd58a95c5.jpg) +Urban100: img_092 $(\times 4)$ + +![](images/bb7795dd489aeb8744cc3d605a46212c29b0c192b6e188377f154183c8abb01f.jpg) +GRL-B [22] + +![](images/03b8ffaf4356ff53afb8da73402b99998a3e655e1625b2d23906be1d64eb7e0e.jpg) +ART [47] + +![](images/6fc624216f7ef5627569994aaee331809014dde2ebc90964077c58c3341ac3ac.jpg) + +![](images/c0e34f43efb8b02bb480c421b136c6251750eb49913c0f6adc5f50019440015a.jpg) + +![](images/7df4021fe428321bc856ae03c6d55e0f553826f1623b429f97990c474ffa80fc.jpg) + +![](images/bfe5360b2ef48bbc560bcd08cd0a9e1a5c8f2a5182044153b4b12d4af5ed4852.jpg) + +![](images/436e154461cb688675b36fdb084f6f66d3f945bf3ab8be4d71d30c7fc6b720c5.jpg) + +![](images/c94dcdeb817cb72866c6dfb52903c532bf738c004dba2bdfe6fc680a1d2c8fbb.jpg) +CAT-A [6] + +![](images/8e914ab0e0e7633bc2a9a68611602ff23c940c3a4f4c347a8a53ef9ab000884e.jpg) +HAT [5] + +![](images/2ba28388a6e8233e4483b6626485aee07ba077ca999f9d8204adce66fca449e8.jpg) +IPG (ours) + +![](images/66307db540dc5bf01795c64df7cbae1795af06a62dbf85c1a4c194ae16647e8a.jpg) +HQ + +![](images/1206732d88892f1d653b8e0fa7b5d5bcdd1fc12e716f879915dea6e0aaf0550d.jpg) +Bicubic + +![](images/b270bd15c276689678ef7093711109198701979faf15d874d7194ac8034b13da.jpg) +IGNN [52] + +![](images/c6df0431fd291fceffa905f131787268ff8e3bd3c4ff38f49cb8535c0e5a7b9d.jpg) +IPT [4] + +![](images/cdc3a24892103f2dec4f391aa941c26138fdeba35bb87b928bd5feac3219728a.jpg) +SwinIR [23] + +![](images/bc8d61ed7726976b98ae186507e7a607e6f35ebd3dc86541714cb0cced8e3d91.jpg) +Urban100: img_098 $(\times 4)$ + +![](images/86f4141ebfadeead72bd9f3b39f2a1a4f6851fdeefbf1edd045c3693543964a2.jpg) +GRL-B [22] + +![](images/32930b21ba11d78702215a21eb64e36e3de43cc0146116c659539a448f569bc9.jpg) +ART [47] + +![](images/5a3f183fddd6ff7d90c56bf6dff044452b7a0abe431b1c2223d7961ae49df2ee.jpg) +CAT-A [6] + +![](images/b58ebd049c8dde172c71970237a6c10b1b48a6a8792a57ed746561ea45c5e52d.jpg) +HAT [5] + +![](images/35365fa6fa8d7343fd2aabc163394836fbf0014a7f020ed08bf6fb68ef50ee51.jpg) +IPG (ours) + +![](images/27416372a15b0dc3c0dc721a7616a556d617e99d072aec9731eadba483f55947.jpg) +HQ +GRL-B [22] + +![](images/29e7a4701530ba5e40a9ac274cff5ea421d0d2c8aaebbe4475663134ac31b245.jpg) +Bicubic +ART [47] + +![](images/4d2534ccf66b6a7e0e2f8f3b9fa68eea09a7af3f56bdaaa59d18081cf00dfd4a.jpg) +IGNN [52] +CAT-A [6] + +![](images/0a11a5c9fc2026e203ca475dfd9fa23b59780420d774550b2f2ea49154fbd8de.jpg) +IPT [4] +HAT [5] + +![](images/03c6c96d2a17f555a2e2c6d65f80c6f65300b8c869316e5c96fca4e7d8e31cd6.jpg) +SwinIR [23] +IPG (ours) + +![](images/7e20f6b215f8088146c619fa3c580bffba9d4df5d432dbca5ef195197ab752b7.jpg) +Figure 6. Visual comparison of image SR $(\times 4)$ with latest SR baselines in challenging cases. +Urban100: img_092 $(\times 4)$ + +![](images/44d962f30743323d3d0fbd027b2d9e245333401461656105c1c1060384e694f1.jpg) + +![](images/6205dcc14dc0b5c84b0c7f9e03ea726eea05b8f25a7633d1b2748c29d48ed8c0.jpg) + +![](images/ac3fc8b2725e0d530420c1672ab44927b118edbf824857624355ad29cec89b77.jpg) +HQ +Patched IPG [6] $(2\times 2)$ +Figure 7. Visual comparison of patch-node graph methods over IPG that uses pixel node graphs. + +![](images/211b3b66a974c7e8c8c07d5a15c2cecdf746c2592f580ada5f266c9636c68e20.jpg) +IGNN [52] $(3\times 3)$ +IPG [47] + +tween IGNN [52] $(3 \times 3$ patch), patched IPG $(2 \times 2$ patch), and IPG (pixel graph). For the IGNN case that uses large patches as nodes, patch alignment is causing trouble: the model is puzzled about the texture orientations, so it makes mistakes during texture reconstruction by aligning pattern-similar but orientation-different patches. For patched IPG, misaligned orientation is causing issues as well: line textures are distorted. In contrast, pixel aggregation in IPG avoids misalignment and performs well. + +KNN vs. Degree-flexible Graphs. In canonical graph + +
Set5Set14Urban100
KNN33.0929.1928.06
Degree-Flex33.1529.2428.13
+ +Table 3. Comparison of degree-flexible graphs against plain KNN graphs in IPG. $\mathrm{SR} \times 4$ results are reported. + +applications for vision tasks, $k$ -Nearest-Neighbor (KNN) + +graphs are normally adopted for graph construction. However, KNN still suffers the degree rigidity, as all nodes are connected to a fixed number of neighboring nodes. To improve degree flexibility, we consider the unbalanced demand of pixels in SR tasks and propose a degree-flexible scheme of graph construction (introduced in Section 3.2). We compare KNN and the degree-flexible graph scheme in IPG under the same settings. According to Table 3, Degree-Flex could outcompete the KNN variant of IPG. Interestingly, our Degree-Flex graph could outcompete computation-heavy fully-connected graphs (see Appendix), further implying the effectiveness of our DegreeFlex graphs. + +As shown in Figure 8, we visually compare the connected regions of detail-poor and detail-rich pixels at the local scale. Detail-poor pixels are usually on flat, changeless parts of the image; these pixels require minimal node connection for reconstruction. On the contrary, detail-rich pixel nodes are usually on edges and corners, which are assigned higher node degrees and thus a larger region of perception. In this sense, the detail-rich indicator metric $D_{F}$ could endow IPG with degree flexibility. + +Local/Global Graphs. In the design of IPG, we aggregate information from both local and global scales based on local and global pixel node sampling. Though numerous SR works highlight the importance of either local or non-local + +
MethodTraining DatasetParamsFLOPsSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
×2 SRCARN [1]DIV2K1592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [14]DIV2K694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [19]DF2K548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [31]DIV2K756K169.5G38.150.961033.780.919332.250.900532.430.9302N/AN/A
ESRT [30]DIV2K751K-38.030.960033.750.918432.250.900132.580.931839.120.9774
SwinIR-light [23]DIV2K910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [49]DIV2K621K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [7]DIV2K1181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
SRFormer-light [53]DIV2K853K236G38.230.961333.940.920932.360.901932.910.935339.280.9785
IPG-Tiny (Ours)DIV2K872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
×3 SRCARN [1]DIV2K1592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [14]DIV2K703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [19]DF2K594K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [31]DIV2K765K76.3G34.530.928130.390.842429.150.805928.330.8538N/AN/A
ESRT [30]DIV2K751K-34.420.926830.430.843329.150.806328.460.857433.950.9455
SwinIR-light [23]DIV2K918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [49]DIV2K629K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [7]DIV2K1190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
SRFormer-light [53]DIV2K861K105G34.670.929630.570.846929.260.809928.810.865534.190.9489
IPG-Tiny (Ours)DIV2K878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
×4 SRCARN [1]DIV2K1592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [14]DIV2K715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [19]DF2K659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [31]DIV2K777K43.6G32.300.896228.680.783027.620.736726.250.7873N/AN/A
ESRT [30]DIV2K751K-32.190.894728.690.783327.690.737926.390.796230.750.9100
SwinIR-light [23]DIV2K930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [49]DIV2K640K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [7]DIV2K1201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
SRFormer-light [53]DIV2K873K62.8G32.510.898828.820.787227.730.742226.670.803231.170.9165
IPG-Tiny (Ours)DIV2K887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
+ +![](images/14067148f7bd1232ab4c912c1a7ffaab4c40026c2569f2f3f7512ce2cf7a3c7e.jpg) +Figure 8. Visual demonstration of parts connected to a pixel node. Compared with detail-poor nodes (left), detail-rich nodes (right) requires a larger amount of aggregation due to difficulty in reconstruction. + +aggregation, we demonstrate that both aspects are actually crucial for SR performance. As shown in Table 5, we perform experiments that uses local or global-scale graphs only under identical settings, and compare them with the original version of IPG. The optimal performance is reached when + +both local and global aggregation are performed. + +Table 4. Comparison of IPG-Tiny with recent lightweight SR methods. Under comparable Params and FLOPs, IPG-Tiny could outcompete lightweight SR baselines. + +
Set5Set14Urban100
Local Only33.0829.1928.10
Global Only33.0429.1127.59
Local + Global33.1529.2428.13
+ +Table 5. Ablations of local and global graph usages on $\mathrm{{SR}} \times 4$ . + +# 5. Conclusion + +Existing SR measures are rigid both in terms of space and degree. In order to break rigidity in SR, the paper proposes IPG – an SR model that fully leverages the flexibility of graphs. Firstly, we are aware that SR is a task where detail-rich image parts require lopsided reconstruction efforts. Hence, we designed a degree-varying scheme for graph construction rather than $k$ -nearest neighbors. Then we take pixels rather than patches for graph aggregation. To reach the maximum amount of spatial flexibility, nodes are sampled both on local and global scales. IPG reaches State-of-the-art performance compared with SR baselines. + +Acknowledgement. This work is supported by the National Key R&D Program of China under Grant No.2022ZD0160300 and the National Natural Science Foundation of China under Grant No.62276007. 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Srformer: Permuted self-attention for single image super-resolution. arXiv preprint arXiv:2303.09735, 2023. 2, 5, 6, 8 \ No newline at end of file diff --git a/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/images.zip b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8e8af2e809c79a3b14ddf4eec003393e540c146e --- /dev/null +++ b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3265ce77c09c804ba0724bba56f363873dafd0e6c976a063d4a9a2237f549924 +size 1114456 diff --git a/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/layout.json b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6281162c5e44ab28ce38499cad2a6324d75f343f --- /dev/null +++ b/2024/Image Processing GNN_ Breaking Rigidity in Super-Resolution/layout.json @@ -0,0 +1,10801 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 102, + 103, + 492, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 103, + 492, + 121 + ], + "spans": [ + { + "bbox": [ + 102, + 103, + 492, + 121 + ], + "type": "text", + "content": "Image Processing GNN: Breaking Rigidity in Super-Resolution" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "spans": [ + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "text", + "content": "Yuchuan Tian" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "text", + "content": ", Hanting Chen" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "text", + "content": ", Chao Xu" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "text", + "content": ", Yunhe Wang" + }, + { + "bbox": [ + 157, + 143, + 440, + 158 + ], + "type": "inline_equation", + "content": "^{2*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 159, + 531, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 159, + 531, + 171 + ], + "spans": [ + { + "bbox": [ + 62, + 159, + 531, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 62, + 159, + 531, + 171 + ], + "type": "text", + "content": " National Key Lab of General AI, School of Intelligence Science and Technology, Peking University. 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CNNs and window-attention methods are two major categories of canonical SR models. However, these measures are rigid: in both operations, each pixel gathers the same number of neighboring pixels, hindering their effectiveness in SR tasks. Alternatively, we leverage the flexibility of graphs and propose the Image Processing GNN (IPG) model to break the rigidity that dominates previous SR methods. Firstly, SR is unbalanced in that most reconstruction efforts are concentrated to a small proportion of detail-rich image parts. Hence, we leverage degree flexibility by assigning higher node degrees to detail-rich image nodes. Then in order to construct graphs for SR-effective aggregation, we treat images as pixel node sets rather than patch nodes. Lastly, we hold that both local and global information are crucial for SR performance. In the hope of gathering pixel information from both local and global scales efficiently via flexible graphs, we search node connections within nearby regions to construct local graphs; and find connections within a strided sampling space of the whole image for global graphs. The flexibility of graphs boosts the SR performance of the IPG model. Experiment results on various datasets demonstrate that the proposed IPG outperforms State-of-the-Art baselines. Codes are available at this link." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 563, + 128, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 128, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 128, + 575 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 584, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 584, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 287, + 693 + ], + "type": "text", + "content": "The ill-posed task of Super-Resolution (SR) constructs high-resolution images from low-resolution ones. SR works typically apply Deep Neural Network (DNN) knowledge learned from High-Resolution training images to construct missing details in low-resolution inputs. Existing DNN variants for classical SR tasks include CNNs [16, 24, 50] and Transformers [5, 6, 23]. 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Convolution (left), Self-Attention (middle-left), KNN Graph Aggregation (middle-right), and Graph Aggregation in IPG (right). Compared with other methods, IPG graph aggregation considers the unbalanced nature of SR: detail-rich, high-frequency image nodes (red) have higher node degrees; while flat, low-frequency image nodes (blue) require fewer aggregations." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 361, + 422, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 422, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 422, + 373 + ], + "type": "text", + "content": "mote sensing [15], et cetera." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 375, + 546, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 546, + 506 + ], + "type": "text", + "content": "Despite various measures, it is taken for granted that mainstream SR models treat all pixels in a fairly rigid manner. For instance, as shown in Figure 1, in convolution layers of the CNN-based SR model VDSR [16], the same convolution kernel scans through all pixels of feature maps, i.e. each pixel is rigidly designated to communicate with its nearest neighbors; in the Transformer-based model SwinIR [23], all pixels are assigned to equal-sized attention grids for self-attention operations. In both examples, each pixel aggregates information from a fixed number of pixels within a neighborhood of fixed size." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 508, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 639 + ], + "type": "text", + "content": "Efforts have been made to overcome the rigidity of convolution and window-attention operations. For example, some recent SR research tries to enhance SR models by enlarging self-attention grids [5, 46] and designing striped global attention windows [6, 22]. But these improvements also introduce a large computation burden. Some other works [12, 26, 52] leverage the flexibility of graphs and propose graph-based methods. With content-based graphs constructed from patch nodes, each image patch could aggregate top-" + }, + { + "bbox": [ + 304, + 508, + 547, + 639 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 508, + 547, + 639 + ], + "type": "text", + "content": " relevant but distant parts beyond hard local boundaries in convolution and window-attention." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": "However, these graph measures have limited flexibility because the lopsided nature of SR is overlooked. In SR tasks, only a small proportion of high-frequency pixels require hard reconstruction efforts; the majority of pixels are located in flat, low-frequency regions and thus almost left intact [9]. In response to the imbalance, SR methods should" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24108" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "ideally pay more attention to detail-rich regions and care less about flat, detail-poor image parts. However, existing " + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "-Nearest-Neighbor graph-based methods treat all image nodes equally. In other words, all nodes share the same pre-set degree " + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": " and the unbalanced nature of SR is not considered. In fact, as we inspect canonical operation paradigms in SR from a graph perspective, we found that degree-equivalence rigidity also manifests in convolution and window-attention: in these paradigms, each pixel on the image aggregates the same number of pixels regardless of image content, and thus, sharing \"equal degrees\" in graph terms. Equal node degrees that are rigidly assigned to nodes or pixels mismatch their unequal reconstruction demands in SR, thus impacting SR performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 502 + ], + "type": "text", + "content": "Trying to break rigidity, we propose the graph-based Image Processing Graph Neural Networks (IPG) model for SR that taps the flexibility potential of graphs. Firstly, to break the degree-equivalence rigidity of convolution, window-attention, and " + }, + { + "bbox": [ + 46, + 239, + 289, + 502 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 239, + 289, + 502 + ], + "type": "text", + "content": "-Nearest-Neighbor (KNN) graphs, we leverage degree flexibility by proposing a novel degree-variant graph solution based on the unbalanced nature of SR. Specifically, a detail-aware metric is designed to measure the importance of image nodes where larger degrees are assigned to high-frequency nodes. Then, different from graph-based model counterparts, IPG adopts pixels rather than patches as image graph nodes to avoid misalignment issues due to patch rigidity. Finally, in the interest of having both local and global perception without sacrificing efficiency due to large pixel-level search space, we resort to local and global node sampling strategies. In this way, graphs are established efficiently from small pixel subsets and could either focus on local information for detail reconstruction, or span over the whole image for spatially distant but crucial features. With the measures mentioned above, IPG could fully exert graph flexibilities and achieve outstanding performances on SR tasks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 514, + 134, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 134, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 134, + 526 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": "Recent SR Methods. In canonical approaches to SuperResolution, manifold previous works phrase SR as a regression problem and is proved effective via applications of CNN models [16, 24, 50, 51]. In these works, a crafted CNN model is applied to the LR image to render it into HR. Since the introduction of Transformers to vision [8], manifold works integrate the self-attention mechanism in Transformers into SR models [4-7, 23, 47, 53]. SwinIR [23] borrows shifted window-attention to SR and demonstrates good performance. Latest SR models include using striped attention windows [6, 22], channel attention [5, 22, 40], permuted attention [53], et cetera." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Despite the fact that manifold SR works follow similar convolution or window-attention methodologies, their SR performance is still confined to the rigidity of ordinary vi" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "sion models, i.e. fixed paradigms for aggregating neighboring pixels and neglecting the unbalanced reconstruction demand among pixels in SR. Hence, we resort to graphs as a flexible way to aggregate information in order to break these sorts of rigidity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 133, + 546, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 546, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 546, + 253 + ], + "type": "text", + "content": "Graphs for Vision. Graphs have been widely applied to vision tasks, including point cloud segmentation [17, 41], human action recognition [42], and image classification [12, 32]. Some previous low-level vision works also view images as graphs. Most works leverage graph to aggregate non-local information, either intra-scale [2, 18, 21, 35, 38] or cross-scale [26, 52]. Other low-level vision works on graphs include cross-layer [27] or inter-image information aggregation [37]. Among these works, edge-conditioned aggregation from neighboring nodes is mostly preferred." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 253, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 547, + 397 + ], + "type": "text", + "content": "In terms of graph construction from images, a majority of works use " + }, + { + "bbox": [ + 304, + 253, + 547, + 397 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 253, + 547, + 397 + ], + "type": "text", + "content": "-nearest neighbors [18, 21, 26, 35, 38, 52]. Since all image nodes share the same degree, KNN graphs are not flexible enough; and the unbalanced nature of image nodes in low-level vision tasks is neglected as well. Besides, most graph works regard patches as image nodes [18, 21, 26, 35, 52], disregarding potential patch misalignment issues in low-level vision. As for the scale of graphs, some works [21, 26, 52] search in a global scale to construct graphs; other works [38, 39] construct graphs from a local box. Graphs in these works are not flexible enough in that they fail to take care of both local and global aspects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 410, + 362, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 410, + 362, + 422 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 362, + 422 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 430, + 481, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 481, + 443 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 481, + 443 + ], + "type": "text", + "content": "3.1. Rigidity of Previous SR Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": "Convolution [16, 24, 50] and window-attention [5, 6, 23] are two major pathways for SR model designs. Despite popular usages in SR, these measures are not flexible; their deep-rooted rigidity could hinder SR performance. In one convolution operation, each outputted pixel gathers information within a tiny kernel-sized window; each pixel only has access to its neighboring pixels. For instance, in a standard " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": " convolution, the perception field of a single pixel is confined to a tiny " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": " box. All pixels on the image collect information from 8 respective neighbors and themselves. The similar rigidity goes for window attention: though larger window sizes (compared to convolution) are usually adopted, the perception field of window attention is still confined within hard window boundaries. In a " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": " window-attention scenario, all pixels gather 64 pixels within the window where they belong." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": "Therefore, beyond rigidity in convolution and window-attention, some works think out of the box and adopt graphs in SR models. Unlike convolution and window-attention where information aggregation is bounded to boxes, these graph-based works are more spatially flexible: each node could aggregate information from its favorite top-" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " nodes" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24109" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "with loose spatial constraints. In this sense, graph aggregation is not limited to preset rigid patterns; it is more dynamic and scalable compared to convolution and window-attention counterparts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 289, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 289, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 289, + 348 + ], + "type": "text", + "content": "However, though previous graph-based methods break through hard aggregation boundaries, we hold that the flexibility of graphs is not fully exploited in SR tasks. First and foremost, as shown in Figure 1, all previous methodologies (either graph-based, convolution-based, or window-attention-based) are degree-rigid. SR reconstruction demand is unbalanced among different image parts. But in previous methods, all pixels or nodes on the image are aggregating the same number of pixels or nodes; i.e. in graph terms, they share the same aggregation degree. Secondly, previous graph-based works are patch-rigid. Though patches are usually regarded as image nodes, patch aggregation usually requires rigid pixel-wise alignment. Possible misalignment of low-level features in patches makes SR models perform worse. Thirdly, previous graph-based works rigidly use graphs on either global or local scales, but information at both scales is potentially important for SR reconstruction. These rigid aspects are hindering the performance of SR models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 356, + 165, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 165, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 165, + 369 + ], + "type": "text", + "content": "3.2. Graph Construction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 374, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 422 + ], + "type": "text", + "content": "To break these rigidities, we construct degree-flexible pixel graphs at local and global scales in the IPG model. In this manner, we could fully exploit the flexibility of graphs and achieve outstanding performance in SR tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 422, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 564 + ], + "type": "text", + "content": "Degree Flexibility. Firstly, we try to figure out a degree-flexible graph solution based on the unique \"unbalanced property\" of SR tasks. SR reconstruction of images features imbalance. As Gou et al. [9] put it, SR is a long-tailed problem where only a small proportion of high-frequency pixels need to be reconstructed; the rest of the image parts need minimal restoration only. However, Gou et al. [9] tries to address the issue by designing training losses rather than rethinking it from the aspect of model designs. In the lopsided SR problem, it is a long-neglected aspect that treating all pixels or parts on the image equivalently is unsuitable and inefficient." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": "To this end, we opt to assign various node degrees to pixels based on a detail-rich indicator that marks pixels needing more reconstruction efforts. Then we design the detail-rich indicator as follows: given feature map " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " and downsampling ratio " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": ", the detail-rich indicator metric per pixel " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "D_F \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " is designated as the absolute difference between the bilinearly downsampled and upsampled feature map and the feature map itself:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 672, + 287, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 116, + 672, + 287, + 696 + ], + "type": "interline_equation", + "content": "D _ {F} := \\sum_ {C} | F - F _ {\\downarrow s \\uparrow s} |, \\tag {1}", + "image_path": "3e6c7432c257c39d85cb0dba0f99d92ec201d4553cab21c28e0f1b9d58e8b1fb.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "type": "text", + "content": " is taken as 2 to avoid severe information loss. We" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "are aware that some explainable SR works [11, 43] propose metrics to measure the importance of a certain part in the output. However, these measures are gradient-based, which requires costly backward passes. In comparison, the proposed metric " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " is operation cheap in that it only requires bilinear interpolation twice. We also provide FLOPs statistics in the Appendix." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 320, + 167, + 384, + 232 + ], + "blocks": [ + { + "bbox": [ + 320, + 167, + 384, + 232 + ], + "lines": [ + { + "bbox": [ + 320, + 167, + 384, + 232 + ], + "spans": [ + { + "bbox": [ + 320, + 167, + 384, + 232 + ], + "type": "image", + "image_path": "463e47e7bd2a8b7d799ab62add45771562c7dcf21c6c68a1528a5b18abec70be.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 394, + 167, + 459, + 231 + ], + "blocks": [ + { + "bbox": [ + 394, + 167, + 459, + 231 + ], + "lines": [ + { + "bbox": [ + 394, + 167, + 459, + 231 + ], + "spans": [ + { + "bbox": [ + 394, + 167, + 459, + 231 + ], + "type": "image", + "image_path": "fec15f367ba9b91678acc6325cf0fb2ad52985f213cf32f3440dc3264191caf8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 468, + 167, + 531, + 231 + ], + "blocks": [ + { + "bbox": [ + 468, + 167, + 531, + 231 + ], + "lines": [ + { + "bbox": [ + 468, + 167, + 531, + 231 + ], + "spans": [ + { + "bbox": [ + 468, + 167, + 531, + 231 + ], + "type": "image", + "image_path": "8aa71af9f51d10f89a4b7e2940acca9397a8c565ab72361d88018522bf32ad83.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 320, + 243, + 384, + 306 + ], + "blocks": [ + { + "bbox": [ + 320, + 243, + 384, + 306 + ], + "lines": [ + { + "bbox": [ + 320, + 243, + 384, + 306 + ], + "spans": [ + { + "bbox": [ + 320, + 243, + 384, + 306 + ], + "type": "image", + "image_path": "dc9a4901359db228b540609b3e68d516bdc0a10b8557c3f3df625ce5d228d07e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "text", + "content": "Figure 2. Visualization of the detail-rich indicator " + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "text", + "content": " in IPG. Original image (left); " + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "text", + "content": " of the shallowest block (middle); " + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "text", + "content": " of the deepest block (right). " + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 316, + 545, + 361 + ], + "type": "text", + "content": " could effectively reflect detail-rich parts on the image." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 394, + 243, + 459, + 306 + ], + "blocks": [ + { + "bbox": [ + 394, + 243, + 459, + 306 + ], + "lines": [ + { + "bbox": [ + 394, + 243, + 459, + 306 + ], + "spans": [ + { + "bbox": [ + 394, + 243, + 459, + 306 + ], + "type": "image", + "image_path": "ba07e71de4be529142d8edde203d378812cdc27a87cd935eec2f451935500efd.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 468, + 243, + 531, + 306 + ], + "blocks": [ + { + "bbox": [ + 468, + 243, + 531, + 306 + ], + "lines": [ + { + "bbox": [ + 468, + 243, + 531, + 306 + ], + "spans": [ + { + "bbox": [ + 468, + 243, + 531, + 306 + ], + "type": "image", + "image_path": "b4a96cd5f0bafdfdabf64e846f7b31234aa2d122d51179bd23edf5cb3125b809.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "text", + "content": "The overall degree budgets are assigned to each pixels based on " + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "text", + "content": ". The degree for a pixel node " + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "inline_equation", + "content": "v \\in F" + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "text", + "content": " on the feature map is in proportion to its corresponding pixel value at " + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 375, + 545, + 422 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 385, + 434, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 434, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 385, + 434, + 545, + 447 + ], + "type": "interline_equation", + "content": "\\deg (v) \\propto D _ {F} (v). \\tag {2}", + "image_path": "5a5b1441b4cc87c2044e47a6be284f72519ea9b47f3de5d94adc84fd9f1f3268.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": "The detail-rich indicator " + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": " in different MGB blocks is visualized. From Figure 2, it can be seen that detail-rich parts are responsive: margins and corners have high " + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": " while flat color blocks are low in " + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": ". The visualization reveals that the proposed " + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": " could effectively reflect high-frequency parts on the image throughout layers." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 522, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 689 + ], + "type": "text", + "content": "Pixel Node Flexibility. Then we are faced with the formulation of vertices in image graphs. In previous graph-based vision works [21, 26, 36, 52], graph nodes are typically set as image patches. During graph aggregation, patches are weighted-summed in a pixel-wise manner. However, the forcible element-wise alignment of pixels during aggregation is unsuitable for SR tasks where feature maps have rich low-level features. Object shift and rotation within low-level patches are two major issues causing patch misalignment. As for object shift, locations of objects within patches could vary; location-misaligned patch objects introduce noises. Object rotation is another faulty aspect of patch aggregation. The orientation of patches is disregarded due to rigid rectangular patch shapes during patch alignment." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "type": "text", + "content": "To avoid the above problems during node aggregation, we hold that finer-grained pixel nodes are better solutions" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24110" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 198 + ], + "type": "image", + "image_path": "5e5e9c01f0040e16728651be5036daff69339ac10a3c575956f2ea7702ea459c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "type": "text", + "content": "Figure 3. The architectures of IPG, Multiscale Graph-aggregation Blocks (MGB), and Graph Aggregation Layers (GAL). Each IPG consists of " + }, + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "type": "text", + "content": " MGB blocks, and each MGB has " + }, + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 204, + 547, + 228 + ], + "type": "text", + "content": " GAL layers. Local and global graphs are distributed to GALs alternatively within MGB." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 247, + 287, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 284 + ], + "type": "text", + "content": "in the low-level vision scenario. Pixel graphs are more flexible: each pixel node could directly find its relevant pixels in aggregation, therefore avoiding pixel misalignment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": "However, we admit that compared to pixel graphs, patch graphs could potentially have larger perception fields and are easier to construct due to a smaller number of nodes in total, which means a smaller search space for edge connections. Hence, we need an efficient way to construct a flexible and effective pixel graph." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 360, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 443 + ], + "type": "text", + "content": "Space Flexibility. Then we develop the space flexibility of IPG graphs via an efficient search of pixel node connections both locally and globally. We propose that both local and global information are crucial for SR reconstruction: while lossy image parts could rebuild themselves from local neighborhoods, they could also learn from distant but similar features for refinement." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 445, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 541 + ], + "type": "text", + "content": "Existing graph-based methods have demonstrated some sort of space flexibility. As shown in Figure 1, compared to convolution and window attention options where a pixel always attends to a fixed neighboring region, graph aggregation could flexibly focus on crucial image parts regardless of space limits. However, existing graph-based works are not spatially flexible enough as they fail to consider both local and global aspects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 651 + ], + "type": "text", + "content": "In fact, computation considerations are the major concern of a comprehensive connection search. It is costly to construct global graphs by searching through all image nodes. As a remedy, strided sampling is always adopted [21, 26, 52]. But consequently, local regions are neglected. The choice of pixels as graph nodes makes graph construction even more challenging, because node spaces are enlarged further and it is hardly impractical to search through all pixels for graph construction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "For the sake of efficiency, and to gather local-level surrounding features and global-level distant features contributive to detail reconstruction in SR tasks, we use two types of sampling to aggregate both local and global information, shown in Figure 4. For local sampling, the neighborhood" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 247, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 545, + 285 + ], + "type": "text", + "content": "surrounding a certain node is chosen as a local-scale search space on which a graph is established; for global sampling, sampled nodes span over the image in a dilated pattern." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 313, + 300, + 385, + 373 + ], + "blocks": [ + { + "bbox": [ + 313, + 300, + 385, + 373 + ], + "lines": [ + { + "bbox": [ + 313, + 300, + 385, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 385, + 373 + ], + "type": "image", + "image_path": "ef3ba82d44582151f347c7a186ff6a1dbf68270487ec97e20f541f97788e68a2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 385, + 545, + 440 + ], + "lines": [ + { + "bbox": [ + 305, + 385, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 545, + 440 + ], + "type": "text", + "content": "Figure 4. An illustration of sampling strategies. The original image with the highlighted image node (left), local sampling (middle), and global sampling (right) are demonstrated. In this way, image graphs could flexibly gather both local and global information in an efficient manner." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 391, + 300, + 463, + 373 + ], + "blocks": [ + { + "bbox": [ + 391, + 300, + 463, + 373 + ], + "lines": [ + { + "bbox": [ + 391, + 300, + 463, + 373 + ], + "spans": [ + { + "bbox": [ + 391, + 300, + 463, + 373 + ], + "type": "image", + "image_path": "8ef6bd8f289fb2a6ea95e177e751ccaf33fd1138c46400eec4895678ee56d43f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 466, + 300, + 539, + 373 + ], + "blocks": [ + { + "bbox": [ + 466, + 300, + 539, + 373 + ], + "lines": [ + { + "bbox": [ + 466, + 300, + 539, + 373 + ], + "spans": [ + { + "bbox": [ + 466, + 300, + 539, + 373 + ], + "type": "image", + "image_path": "6d9f9ac110afed8545f74672707bebf4a14b3d5d6ecc22eff944ac5be8d08e15.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 457, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 518 + ], + "type": "text", + "content": "In the proposed IPG SR model, both sampling methods are performed in order to construct local and global-scale graphs. For each pixel node, its node connections are searched within the sampling space. In this way, we achieve spatial flexibility in a cost-efficient fashion." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 527, + 421, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 421, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 421, + 540 + ], + "type": "text", + "content": "3.3. Graph Aggregation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Now that flexible graphs are constructed, graph aggregation is performed such that each node can communicate with its connected neighbors and use their information for self-refinement in SR. In vision applications of graphs, aggregation in max-pooling [12, 28] or edge-conditioned [21, 26, 36] forms are mostly preferred. We tend to adopt edge-conditioned aggregation [36], as max-pooling could result in significant loss of information from neighboring pixels that are crucial for low-level vision. Since pixel reconstruction in SR heavily relies on abundant neighboring information, edge-conditioned aggregation is adopted as it cares about pixel inter-relations and maintains more neighboring information for effective reconstruction. The edge-conditioned aggregation [21, 26, 36, 52] is mathematically" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24111" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "formulated as follows: at the " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " layer in IPG, given node feature " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{h}^{k - 1}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " as input, neighboring node set " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(v)" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": ", the node " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " output " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_v^k" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 118, + 287, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 118, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 85, + 118, + 287, + 148 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {v} ^ {k} = \\frac {1}{C ^ {k}} \\sum_ {u \\in N (v)} \\exp \\left(f ^ {k} (u, v)\\right) \\mathbf {h} _ {u} ^ {k - 1}, \\tag {3}", + "image_path": "67510ac6ce131ad648bd341b245f20e7de3cf44ae5919ff53886bee9e9ac1097.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "f^k: \\mathbb{R}^d \\times \\mathbb{R}^d \\to \\mathbb{R}" + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "text", + "content": " is a parameterized function that measures the correlation between node pair " + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "(u, v)" + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "C^k := \\sum_{u \\in N(v)} \\exp(f^k(u, v))" + }, + { + "bbox": [ + 47, + 156, + 287, + 205 + ], + "type": "text", + "content": " is a normalizing constant. In our case, cosine similarity is adopted as the correlation metric." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 205, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 289 + ], + "type": "text", + "content": "Despite the flexibility of graph aggregation, we are concerned that the spatial information is damaged in the process of graph aggregation: since all nodes are treated equally, the model will grasp little knowledge about node position. Hence, inspired by Liu et al. [25, 29], we add relative position encoding to node features before aggregation to enhance position information." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 298, + 162, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 162, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 162, + 309 + ], + "type": "text", + "content": "3.4. Model Architecture" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 317, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 365 + ], + "type": "text", + "content": "The proposed graph construction and graph aggregation mechanisms are then merged into the effective MetaFormer architecture as the IPG model. The detailed structure of IPG is shown in Figure 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 365, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 496 + ], + "type": "text", + "content": "The IPG Architecture. The general architecture of IPG follows mainstream SR models [5-7, 23, 53]. As an LR image is inputted into the model, it is first passed to a Conv Layer to extract shallow features. Then the features are passed through a series of Multiscale Graph-aggregation Blocks (MGB) for effective deep feature extraction with the aid of flexible graphs. Each MGB consists of a stack of Graph Aggregation Layers (GAL) where graph aggregation on both local and global scales is performed. Finally, the image is spatially reconstructed via a pixel-shuffle upsampler." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 652 + ], + "type": "text", + "content": "MGB Blocks. Multiscale Graph-aggregation Blocks (MGB) gather both local and global-scale information for effective image SR reconstruction. Both local and global pixel graphs are calculated per block based on block inputs. Block-wise graph calculations enable regular graph updates throughout the model. The construction steps are detailed in Section 3.2, where local and global sampling is performed respectively for local or global graph construction. The two types of graphs (local/global) are then distributed to GALs throughout the block for aggregation operations. Local and global graphs are distributed in a sequentially alternative manner to ensure that both local and global-scale information are sufficiently aggregated." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "GAL Layers. The design of Graph Aggregation Layers (GAL) follows the general MetaFormer-like structure [44]. Graphers that are responsible for graph aggregation (as introduced in Section 3.3) are used as token mixers. Grapher gathers local or global information based on the type" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "of graph it receives. Following [5, 22, 53], we leverage efficient Channel Attention (CA) modules and ConvFFN blocks to aid the SR performance of our model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 119, + 388, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 119, + 388, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 119, + 388, + 133 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 138, + 420, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 138, + 420, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 138, + 420, + 152 + ], + "type": "text", + "content": "4.1. Experiment Setting" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "text", + "content": "We adopt the general training setting of recent SR works [5, 6, 23] for fair comparison. We use DIV2K+Flickr2K (DF2K) as the training set (DIV2K for lightweight models). Cropped patches of size " + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "text", + "content": " are sent into the model. Training data is augmented by random flipping and random rotation of degrees [0,90,180,270]. Our model is trained for 500K iterations using the Adam Optimizer " + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "inline_equation", + "content": "(\\beta_{1} = 0.9, \\beta_{2} = 0.99)" + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "text", + "content": " at a learning rate of " + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "inline_equation", + "content": "2e - 4" + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "text", + "content": ". The training input size is set at " + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 157, + 545, + 289 + ], + "type": "text", + "content": ". MultistepLR is adopted where the learning rate is halved at iterations [250000, 400000, 450000, 475000]. Batchsize is set as 32." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 297, + 473, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 297, + 473, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 297, + 473, + 309 + ], + "type": "text", + "content": "4.2. Super-Resolution Performance" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 324, + 327, + 524, + 449 + ], + "blocks": [ + { + "bbox": [ + 324, + 327, + 524, + 449 + ], + "lines": [ + { + "bbox": [ + 324, + 327, + 524, + 449 + ], + "spans": [ + { + "bbox": [ + 324, + 327, + 524, + 449 + ], + "type": "image", + "image_path": "dac100cdcab2d127ae1cdf7e27ba9034584d234c2801b9563b8b12571c34c56f.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "type": "text", + "content": "Figure 5. Comparison of the proposed IPG-S and IPG with SR baselines in FLOPs and performance. Urban " + }, + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "type": "inline_equation", + "content": "100 \\times 4" + }, + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "type": "text", + "content": " in PSNR is reported. Thanks to the flexibility of graphs, IPG could outperform other SR models by " + }, + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "type": "inline_equation", + "content": ">0.1\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 453, + 545, + 520 + ], + "type": "text", + "content": " at similar FLOPs. Notably, FLOPs only reflect theoretical computation costs instead of actual inference speed." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "We compare the performance of our model with various SR baselines in Table 1 on Set5 [3], Set14 [45], BSDS100 [33], Urban100 [13], and Manga109 [34] benchmarks. The chosen baselines are as follows: IGN [52] is a patch-graph-based SR method; ELAN [49], IPT [4], SwinIR [23], CAT-A [6], ART [47], GRL-B [22], and HAT [5] are transformer-based methods. Performance of " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{SR}\\times 2" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "x3" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "x4" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " models are measured by PSNR and SSIM. \" " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " \" marks stand for baselines with self-ensemble strategies, which boosts SR performance further. IPG could outcompete other models by large margins. In particular, IPG reaches 28.13dB of PSNR on the Urban " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "100\\times 4" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " task, exceeding existing SOTA by more than 0.1dB with standard training setting. IPG has an outstanding performance in the PSNR versus theoretical FLOPs plot, shown in Figure 5. But notably, IPG runs slower than previous methods for" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24112" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 523, + 379 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 523, + 379 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 523, + 379 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 523, + 379 + ], + "type": "table", + "html": "
MethodSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
SR×2IGNN [52]38.240.961334.070.921732.410.902533.230.938339.350.9786
ELAN [49]38.360.962034.200.922832.450.903033.440.939139.620.9793
IPT [4]38.37N/A34.43N/A32.48N/A33.76N/AN/AN/A
SwinIR [23]38.420.962334.460.925032.530.904133.810.942739.920.9797
EDT [20]38.450.962434.570.925832.520.904133.800.942539.930.9800
CAT-A [6]38.510.962634.780.926532.590.904734.260.944040.100.9805
ART [47]38.560.962934.590.926732.580.904834.300.945240.240.9808
GRL-B* [22]38.480.962734.640.926532.550.904533.970.943740.060.9804
HAT* [5]38.610.963034.770.926632.610.905334.450.946540.230.9806
IPG (Ours)38.610.963234.730.927032.600.905234.480.946440.240.9810
IPG+ (Ours)38.650.963334.870.927432.620.905334.540.946840.320.9811
SR×3IGNN [52]34.720.929830.660.848429.310.810529.030.869634.390.9496
ELAN [49]34.900.931330.800.850429.380.812429.320.874534.730.9517
IPT [4]34.81N/A30.85N/A29.38N/A29.49N/AN/AN/A
SwinIR [23]34.970.931830.930.853429.460.814529.750.882635.120.9537
EDT [20]34.970.931630.890.852729.440.814229.720.881435.130.9534
CAT-A [6]35.060.932631.040.853829.520.816030.120.886235.380.9546
ART [47]35.070.932531.020.854129.510.815930.100.887135.390.9548
GRL-B* [22]35.050.932331.000.854329.490.815329.830.883735.240.9541
HAT [5]35.070.932931.080.855529.540.816730.230.889635.530.9552
IPG (Ours)35.100.933231.100.855429.530.816830.360.890135.530.9554
IPG+ (Ours)35.190.933531.140.855829.570.817130.480.891135.650.9558
SR×4IGNN [52]32.570.899828.850.789127.770.743426.840.809031.280.9182
ELAN [49]32.750.902228.960.791427.830.745927.130.816731.680.9226
IPT [4]32.64N/A29.01N/A27.82N/A27.26N/AN/AN/A
SwinIR [23]32.920.904429.090.795027.920.748927.450.825432.030.9260
EDT [20]32.820.903129.090.793927.910.748327.460.824632.030.9254
CAT-A [6]33.080.905229.180.796027.990.751027.890.833932.390.9285
ART [47]33.040.905129.160.795827.970.751027.770.832132.310.9283
GRL-B* [22]32.900.903929.140.795627.960.749727.530.827632.190.9266
HAT [5]33.040.905629.230.797328.000.751727.970.836832.480.9292
IPG (Ours)33.150.906229.240.797327.990.751928.130.839232.530.9300
IPG+ (Ours)33.230.906429.300.797928.040.752528.220.840732.720.9310
", + "image_path": "f56c63d47241cb6e935c98016f68583194799cb92cc8ba29b3f208616ad5dfa6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 415, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 498 + ], + "type": "text", + "content": "lack of hardware support; IPG costs slightly advantageous peak memory. Apart from the quantitative comparison in PSNR/SSIM metrics, we also provide visual results of difficult details reconstructed by IPG. As shown in Figure 6, the proposed IPG model is compared against recent top-tier SR baselines on the " + }, + { + "bbox": [ + 46, + 415, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathrm{SR} \\times 4" + }, + { + "bbox": [ + 46, + 415, + 287, + 498 + ], + "type": "text", + "content": " task. Our IPG model could visually outcompete other methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 521, + 143, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 143, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 143, + 534 + ], + "type": "text", + "content": "4.3. Lightweight SR" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "We also provide some lightweight variants of IPG. While the architecture of IPG-S and IPG-Tiny remains the same as the base version, their depth and dimension width are significantly reduced for computation-constrained applications. Variant config details are in the Appendix. We choose canonical SR baselines including CARN [1], IMDN [14], LAPAR-A [19], LatticeNet [31], and ESRT [30]; other baselines have MetaFormer architectures, including SwinIR-light [23], ELAN [48], SwinIRNG [53], and SRFormer-light [53]. IPG could outcompete SR baselines that share similar MetaFormer [44] architectures at similar computation costs. Specifically, IPG-Tiny could achieve more than 0.1dB of PSNR improvement on Urban100 compared with other lightweight baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 414, + 400, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 414, + 400, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 414, + 400, + 426 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 434, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 625 + ], + "type": "text", + "content": "Pixel Nodes vs. Patch Nodes. As claimed in Section 3.2, patches as image graph nodes may suffer in cases like object shift and object rotation. The forcible element-wise alignment of patch pixels could hinder SR performance to a great extent. In order to investigate the negative impact of patch nodes, we provide a patched version of IPG as follows: rather than using pixel nodes, we use " + }, + { + "bbox": [ + 304, + 434, + 545, + 625 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 304, + 434, + 545, + 625 + ], + "type": "text", + "content": "-sized patches as nodes in this patched variant. Other model settings are kept unchanged for fair comparison, including model depths, feature dimensions, MLP ratios, and sampling region size. However, we are aware that the computation costs of patch node aggregation could be different compared to pixel nodes. Hence, we tune the number of aggregation times for the patched variant, to make sure that aggregation of patch nodes has a similar cost as pixel node aggregation. The ablation results are shown in Table 2." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 335, + 632, + 517, + 673 + ], + "blocks": [ + { + "bbox": [ + 46, + 382, + 545, + 404 + ], + "lines": [ + { + "bbox": [ + 46, + 382, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 545, + 404 + ], + "type": "text", + "content": "Table 1. Comparison of IPG with recent SR methods. Methods with " + }, + { + "bbox": [ + 46, + 382, + 545, + 404 + ], + "type": "inline_equation", + "content": "{}^{* * * }" + }, + { + "bbox": [ + 46, + 382, + 545, + 404 + ], + "type": "text", + "content": " are replicated with standard setting, detailed in the Appendix; items with \"+\" stands for self-ensemble strategies." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 335, + 632, + 517, + 673 + ], + "lines": [ + { + "bbox": [ + 335, + 632, + 517, + 673 + ], + "spans": [ + { + "bbox": [ + 335, + 632, + 517, + 673 + ], + "type": "table", + "html": "
Set5Set14Urban100
2 × 2-Patched IPG33.0129.1827.81
Pixel IPG33.1529.2428.13
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Visual comparison of image SR " + }, + { + "bbox": [ + 128, + 366, + 463, + 378 + ], + "type": "inline_equation", + "content": "(\\times 4)" + }, + { + "bbox": [ + 128, + 366, + 463, + 378 + ], + "type": "text", + "content": " with latest SR baselines in challenging cases." + } + ] + } + ], + "index": 66, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 388, + 153, + 460 + ], + "lines": [ + { + "bbox": [ + 50, + 388, + 153, + 460 + ], + "spans": [ + { + "bbox": [ + 50, + 388, + 153, + 460 + ], + "type": "image", + "image_path": "7e20f6b215f8088146c619fa3c580bffba9d4df5d432dbca5ef195197ab752b7.jpg" + } + ] + } + ], + "index": 67, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 461, + 138, + 469 + ], + "lines": [ + { + "bbox": [ + 64, + 461, + 138, + 469 + ], + "spans": [ + { + "bbox": [ + 64, + 461, + 138, + 469 + ], + "type": "text", + "content": "Urban100: img_092 " + }, + { + "bbox": [ + 64, + 461, + 138, + 469 + ], + "type": "inline_equation", + "content": "(\\times 4)" + } + ] + } + ], + "index": 68, + "angle": 0, + "type": "image_caption" + } + ], + "index": 67 + }, + { + "type": "image", + "bbox": [ + 156, + 388, + 220, + 422 + ], + "blocks": [ + { + "bbox": [ + 156, + 388, + 220, + 422 + ], + "lines": [ + { + "bbox": [ + 156, + 388, + 220, + 422 + ], + "spans": [ + { + "bbox": [ + 156, + 388, + 220, + 422 + ], + "type": "image", + "image_path": "44d962f30743323d3d0fbd027b2d9e245333401461656105c1c1060384e694f1.jpg" + } + ] + } + ], + "index": 69, + "angle": 0, + "type": "image_body" + } + ], + "index": 69 + }, + { + "type": "image", + "bbox": [ + 224, + 388, + 288, + 422 + ], + "blocks": [ + { + "bbox": [ + 224, + 388, + 288, + 422 + ], + "lines": [ + { + "bbox": [ + 224, + 388, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 224, + 388, + 288, + 422 + ], + "type": "image", + "image_path": "6205dcc14dc0b5c84b0c7f9e03ea726eea05b8f25a7633d1b2748c29d48ed8c0.jpg" + } + ] + } + ], + "index": 71, + "angle": 0, + "type": "image_body" + } + ], + "index": 71 + }, + { + "type": "image", + "bbox": [ + 156, + 433, + 220, + 466 + ], + "blocks": [ + { + "bbox": [ + 182, + 425, + 194, + 432 + ], + "lines": [ + { + "bbox": [ + 182, + 425, + 194, + 432 + ], + "spans": [ + { + "bbox": [ + 182, + 425, + 194, + 432 + ], + "type": "text", + "content": "HQ" + } + ] + } + ], + "index": 70, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 156, + 433, + 220, + 466 + ], + "lines": [ + { + "bbox": [ + 156, + 433, + 220, + 466 + ], + "spans": [ + { + "bbox": [ + 156, + 433, + 220, + 466 + ], + "type": "image", + "image_path": "ac3fc8b2725e0d530420c1672ab44927b118edbf824857624355ad29cec89b77.jpg" + } + ] + } + ], + "index": 73, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 468, + 222, + 476 + ], + "lines": [ + { + "bbox": [ + 154, + 468, + 222, + 476 + ], + "spans": [ + { + "bbox": [ + 154, + 468, + 222, + 476 + ], + "type": "text", + "content": "Patched IPG [6] " + }, + { + "bbox": [ + 154, + 468, + 222, + 476 + ], + "type": "inline_equation", + "content": "(2\\times 2)" + } + ] + } + ], + "index": 74, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 476, + 287, + 498 + ], + "lines": [ + { + "bbox": [ + 47, + 476, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 287, + 498 + ], + "type": "text", + "content": "Figure 7. Visual comparison of patch-node graph methods over IPG that uses pixel node graphs." + } + ] + } + ], + "index": 77, + "angle": 0, + "type": "image_caption" + } + ], + "index": 73 + }, + { + "type": "image", + "bbox": [ + 224, + 433, + 288, + 466 + ], + "blocks": [ + { + "bbox": [ + 229, + 425, + 283, + 432 + ], + "lines": [ + { + "bbox": [ + 229, + 425, + 283, + 432 + ], + "spans": [ + { + "bbox": [ + 229, + 425, + 283, + 432 + ], + "type": "text", + "content": "IGNN [52] " + }, + { + "bbox": [ + 229, + 425, + 283, + 432 + ], + "type": "inline_equation", + "content": "(3\\times 3)" + } + ] + } + ], + "index": 72, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 224, + 433, + 288, + 466 + ], + "lines": [ + { + "bbox": [ + 224, + 433, + 288, + 466 + ], + "spans": [ + { + "bbox": [ + 224, + 433, + 288, + 466 + ], + "type": "image", + "image_path": "211b3b66a974c7e8c8c07d5a15c2cecdf746c2592f580ada5f266c9636c68e20.jpg" + } + ] + } + ], + "index": 75, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 243, + 468, + 269, + 476 + ], + "lines": [ + { + "bbox": [ + 243, + 468, + 269, + 476 + ], + "spans": [ + { + "bbox": [ + 243, + 468, + 269, + 476 + ], + "type": "text", + "content": "IPG [47]" + } + ] + } + ], + "index": 76, + "angle": 0, + "type": "image_caption" + } + ], + "index": 75 + }, + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "text", + "content": "tween IGNN [52] " + }, + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "inline_equation", + "content": "(3 \\times 3" + }, + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "text", + "content": " patch), patched IPG " + }, + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "inline_equation", + "content": "(2 \\times 2" + }, + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "text", + "content": " patch), and IPG (pixel graph). For the IGNN case that uses large patches as nodes, patch alignment is causing trouble: the model is puzzled about the texture orientations, so it makes mistakes during texture reconstruction by aligning pattern-similar but orientation-different patches. For patched IPG, misaligned orientation is causing issues as well: line textures are distorted. In contrast, pixel aggregation in IPG avoids misalignment and performs well." + } + ] + } + ], + "index": 78 + }, + { + "bbox": [ + 47, + 615, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 615, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 47, + 615, + 287, + 627 + ], + "type": "text", + "content": "KNN vs. Degree-flexible Graphs. In canonical graph" + } + ] + } + ], + "index": 79 + }, + { + "type": "table", + "bbox": [ + 88, + 636, + 246, + 677 + ], + "blocks": [ + { + "bbox": [ + 88, + 636, + 246, + 677 + ], + "lines": [ + { + "bbox": [ + 88, + 636, + 246, + 677 + ], + "spans": [ + { + "bbox": [ + 88, + 636, + 246, + 677 + ], + "type": "table", + "html": "
Set5Set14Urban100
KNN33.0929.1928.06
Degree-Flex33.1529.2428.13
", + "image_path": "7a70427701a187bceac58726df114fe78a5270333e77cd5c92e6c53e09e1dd04.jpg" + } + ] + } + ], + "index": 80, + "angle": 0, + "type": "table_body" + } + ], + "index": 80 + }, + { + "bbox": [ + 46, + 678, + 287, + 700 + ], + "lines": [ + { + "bbox": [ + 46, + 678, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 678, + 287, + 700 + ], + "type": "text", + "content": "Table 3. Comparison of degree-flexible graphs against plain KNN graphs in IPG. " + }, + { + "bbox": [ + 46, + 678, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{SR} \\times 4" + }, + { + "bbox": [ + 46, + 678, + 287, + 700 + ], + "type": "text", + "content": " results are reported." + } + ] + } + ], + "index": 81, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "applications for vision tasks, " + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "-Nearest-Neighbor (KNN)" + } + ] + } + ], + "index": 82 + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": "graphs are normally adopted for graph construction. However, KNN still suffers the degree rigidity, as all nodes are connected to a fixed number of neighboring nodes. To improve degree flexibility, we consider the unbalanced demand of pixels in SR tasks and propose a degree-flexible scheme of graph construction (introduced in Section 3.2). We compare KNN and the degree-flexible graph scheme in IPG under the same settings. According to Table 3, Degree-Flex could outcompete the KNN variant of IPG. Interestingly, our Degree-Flex graph could outcompete computation-heavy fully-connected graphs (see Appendix), further implying the effectiveness of our DegreeFlex graphs." + } + ] + } + ], + "index": 83 + }, + { + "bbox": [ + 304, + 552, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 660 + ], + "type": "text", + "content": "As shown in Figure 8, we visually compare the connected regions of detail-poor and detail-rich pixels at the local scale. Detail-poor pixels are usually on flat, changeless parts of the image; these pixels require minimal node connection for reconstruction. On the contrary, detail-rich pixel nodes are usually on edges and corners, which are assigned higher node degrees and thus a larger region of perception. In this sense, the detail-rich indicator metric " + }, + { + "bbox": [ + 304, + 552, + 545, + 660 + ], + "type": "inline_equation", + "content": "D_{F}" + }, + { + "bbox": [ + 304, + 552, + 545, + 660 + ], + "type": "text", + "content": " could endow IPG with degree flexibility." + } + ] + } + ], + "index": 84 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Local/Global Graphs. In the design of IPG, we aggregate information from both local and global scales based on local and global pixel node sampling. Though numerous SR works highlight the importance of either local or non-local" + } + ] + } + ], + "index": 85 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24114" + } + ] + } + ], + "index": 86 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 537, + 347 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 537, + 347 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 537, + 347 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 537, + 347 + ], + "type": "table", + "html": "
MethodTraining DatasetParamsFLOPsSET5 [3]SET14 [45]B100 [33]Urban100 [13]Manga109 [34]
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
×2 SRCARN [1]DIV2K1592K222.8G37.760.959033.520.916632.090.897831.920.925638.360.9765
IMDN [14]DIV2K694K158.8G38.000.960533.630.917732.190.899632.170.928338.880.9774
LAPAR-A [19]DF2K548K171G38.010.960533.620.918332.190.899932.100.928338.670.9772
LatticeNet [31]DIV2K756K169.5G38.150.961033.780.919332.250.900532.430.9302N/AN/A
ESRT [30]DIV2K751K-38.030.960033.750.918432.250.900132.580.931839.120.9774
SwinIR-light [23]DIV2K910K244G38.140.961133.860.920632.310.901232.760.934039.120.9783
ELAN [49]DIV2K621K203G38.170.961133.940.920732.300.901232.760.934039.110.9782
SwinIR-NG [7]DIV2K1181K274.1G38.170.961233.940.920532.310.901332.780.934039.200.9781
SRFormer-light [53]DIV2K853K236G38.230.961333.940.920932.360.901932.910.935339.280.9785
IPG-Tiny (Ours)DIV2K872K245.2G38.270.961634.240.923632.350.901833.040.935939.310.9786
×3 SRCARN [1]DIV2K1592K118.8G34.290.925530.290.840729.060.803428.060.849333.500.9440
IMDN [14]DIV2K703K71.5G34.360.927030.320.841729.090.804628.170.851933.610.9445
LAPAR-A [19]DF2K594K114G34.360.926730.340.842129.110.805428.150.852333.510.9441
LatticeNet [31]DIV2K765K76.3G34.530.928130.390.842429.150.805928.330.8538N/AN/A
ESRT [30]DIV2K751K-34.420.926830.430.843329.150.806328.460.857433.950.9455
SwinIR-light [23]DIV2K918K111G34.620.928930.540.846329.200.808228.660.862433.980.9478
ELAN [49]DIV2K629K90.1G34.610.928830.550.846329.210.808128.690.862434.000.9478
SwinIR-NG [7]DIV2K1190K114.1G34.640.929330.580.847129.240.809028.750.863934.220.9488
SRFormer-light [53]DIV2K861K105G34.670.929630.570.846929.260.809928.810.865534.190.9489
IPG-Tiny (Ours)DIV2K878K109.0G34.640.929230.610.847029.260.809728.930.866634.300.9493
×4 SRCARN [1]DIV2K1592K90.9G32.130.893728.600.780627.580.734926.070.783730.470.9084
IMDN [14]DIV2K715K40.9G32.210.894828.580.781127.560.735326.040.783830.450.9075
LAPAR-A [19]DF2K659K94G32.150.894428.610.781827.610.736626.140.787130.420.9074
LatticeNet [31]DIV2K777K43.6G32.300.896228.680.783027.620.736726.250.7873N/AN/A
ESRT [30]DIV2K751K-32.190.894728.690.783327.690.737926.390.796230.750.9100
SwinIR-light [23]DIV2K930K63.6G32.440.897628.770.785827.690.740626.470.798030.920.9151
ELAN [49]DIV2K640K54.1G32.430.897528.780.785827.690.740626.540.798230.920.9150
SwinIR-NG [7]DIV2K1201K63.0G32.440.898028.830.787027.730.741826.610.801031.090.9161
SRFormer-light [53]DIV2K873K62.8G32.510.898828.820.787227.730.742226.670.803231.170.9165
IPG-Tiny (Ours)DIV2K887K61.3G32.510.898728.850.787327.730.741826.780.805031.220.9176
", + "image_path": "ec1a9202ed5d7c117577cfc400d430753b732fb27c44c0d277a3bda860044363.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 54, + 387, + 278, + 595 + ], + "blocks": [ + { + "bbox": [ + 54, + 387, + 278, + 595 + ], + "lines": [ + { + "bbox": [ + 54, + 387, + 278, + 595 + ], + "spans": [ + { + "bbox": [ + 54, + 387, + 278, + 595 + ], + "type": "image", + "image_path": "14067148f7bd1232ab4c912c1a7ffaab4c40026c2569f2f3f7512ce2cf7a3c7e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 598, + 287, + 642 + ], + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 642 + ], + "type": "text", + "content": "Figure 8. Visual demonstration of parts connected to a pixel node. Compared with detail-poor nodes (left), detail-rich nodes (right) requires a larger amount of aggregation due to difficulty in reconstruction." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "aggregation, we demonstrate that both aspects are actually crucial for SR performance. As shown in Table 5, we perform experiments that uses local or global-scale graphs only under identical settings, and compare them with the original version of IPG. The optimal performance is reached when" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 390, + 503, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 503, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 503, + 403 + ], + "type": "text", + "content": "both local and global aggregation are performed." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 343, + 411, + 511, + 462 + ], + "blocks": [ + { + "bbox": [ + 47, + 351, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 47, + 351, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 545, + 373 + ], + "type": "text", + "content": "Table 4. Comparison of IPG-Tiny with recent lightweight SR methods. Under comparable Params and FLOPs, IPG-Tiny could outcompete lightweight SR baselines." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 343, + 411, + 511, + 462 + ], + "lines": [ + { + "bbox": [ + 343, + 411, + 511, + 462 + ], + "spans": [ + { + "bbox": [ + 343, + 411, + 511, + 462 + ], + "type": "table", + "html": "
Set5Set14Urban100
Local Only33.0829.1928.10
Global Only33.0429.1127.59
Local + Global33.1529.2428.13
", + "image_path": "e77499f199d3b08743997a3a0e44077e8155246e635dba971ece8a80349993bc.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 312, + 465, + 538, + 477 + ], + "lines": [ + { + "bbox": [ + 312, + 465, + 538, + 477 + ], + "spans": [ + { + "bbox": [ + 312, + 465, + 538, + 477 + ], + "type": "text", + "content": "Table 5. Ablations of local and global graph usages on " + }, + { + "bbox": [ + 312, + 465, + 538, + 477 + ], + "type": "inline_equation", + "content": "\\mathrm{{SR}} \\times 4" + }, + { + "bbox": [ + 312, + 465, + 538, + 477 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 489, + 378, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 378, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 378, + 502 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 509, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 640 + ], + "type": "text", + "content": "Existing SR measures are rigid both in terms of space and degree. In order to break rigidity in SR, the paper proposes IPG – an SR model that fully leverages the flexibility of graphs. Firstly, we are aware that SR is a task where detail-rich image parts require lopsided reconstruction efforts. Hence, we designed a degree-varying scheme for graph construction rather than " + }, + { + "bbox": [ + 304, + 509, + 545, + 640 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 509, + 545, + 640 + ], + "type": "text", + "content": "-nearest neighbors. Then we take pixels rather than patches for graph aggregation. To reach the maximum amount of spatial flexibility, nodes are sampled both on local and global scales. IPG reaches State-of-the-art performance compared with SR baselines." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 546, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work is supported by the National Key R&D Program of China under Grant No.2022ZD0160300 and the National Natural Science Foundation of China under Grant No.62276007. We gratefully acknowledge the support of MindSpore, CANN and Ascend AI Processor used for this research." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "24115" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Namhyuk Ahn, Byungkon Kang, and Kyung-Ah Sohn. 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Srformer: Permuted self-attention for single image super-resolution. arXiv preprint arXiv:2303.09735, 2023. 2, 5, 6, 8" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24117" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/aad8aa4f-e5bd-4107-bdf3-47998cec58ac_content_list.json b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/aad8aa4f-e5bd-4107-bdf3-47998cec58ac_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9443b681b423b7e5ccc8f33559d47db205061644 --- /dev/null +++ b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/aad8aa4f-e5bd-4107-bdf3-47998cec58ac_content_list.json @@ -0,0 +1,1963 @@ +[ + { + "type": "text", + "text": "Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance", + "text_level": 1, + "bbox": [ + 153, + 130, + 818, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tomer Garber \nOpen University of Israel \ntomergarber@gmail.com", + "bbox": [ + 248, + 204, + 450, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tom Tirer Bar-Ilan University, Israel tirer.tom@gmail.com", + "bbox": [ + 513, + 204, + 720, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a \"task-specific\" network for each observation model is to use pretrained deep denoisers for imposing only the signal's prior within iterative algorithms, without additional training. Recently, a sampling-based variant of this approach has become popular with the rise of diffusion/score-based generative models. Using denoisers for general purpose restoration requires guiding the iterations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on backprojection (BP) has been shown to be a promising strategy (used recently also under the names \"pseudoinverse\" or \"range/null-space\" guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., it does not require SVD or a large number of iterations). We use it within both an optimization scheme and a sampling-based scheme, and demonstrate its advantages over existing methods for image deblurring and super-resolution.", + "bbox": [ + 76, + 327, + 473, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 742, + 209, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image restoration problems appear in a wide range of applications, where the goal is to recover a high-quality image $\\mathbf{x}^{*}\\in \\mathbb{R}^{n}$ from its degraded version $\\mathbf{y}\\in \\mathbb{R}^{m}$ , which can be noisy, blurry, low-resolution, etc. In many problems, the relation between $\\mathbf{y}$ and $\\mathbf{x}^{*}$ can be expressed using a linear observation model", + "bbox": [ + 75, + 770, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = \\mathbf {A} \\mathbf {x} ^ {*} + \\mathbf {e} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 222, + 881, + 468, + 896 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5ce14a486cb8359dd8fa668af08d73b9231f3951f36c8477899229bda3a8fa30.jpg", + "image_caption": [ + "Figure 1. Motion deblurring with noise level 0.05. From top to bottom and left to right: original, observation, DPS [6], DiffPIR [45] and our DDPG." + ], + "image_footnote": [], + "bbox": [ + 506, + 290, + 890, + 486 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "where $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$ is a measurement operator with $m \\leq n$ , and $\\mathbf{e} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_e^2 \\mathbf{I}_m)$ is an additive white Gaussian noise. For example, in the denoising task $\\mathbf{A}$ is the identity matrix $\\mathbf{I}_n$ ; in the deblurring task $\\mathbf{A}$ is a blur operator; and in the super-resolution task $\\mathbf{A}$ is a composition of sub-sampling and (anti-aliasing) filtering. Image restoration problems are ill-posed: just looking for $\\mathbf{x} \\in \\mathbb{R}^n$ that fits $\\mathbf{y}$ based on the observation model does not suffice for a successful recovery. Thus, it is required to utilize prior knowledge on the nature of $\\mathbf{x}^*$ .", + "bbox": [ + 496, + 566, + 890, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nowadays, it has become common to address these problems by exhaustively training a different deep neural network (DNN) for each predefined observation model in a supervised manner. Namely, using (1) to generate training pairs $\\{\\mathbf{y}_i,\\mathbf{x}_i^*\\}$ and training a DNN to invert the map [8, 18, 34, 43]. However, these \"task-specific\" DNNs suffer from a huge performance drop when the observations at test-time mismatch (even slightly) the assumptions made in training [1, 28, 37], which limits their applicability in many practical cases.", + "bbox": [ + 496, + 719, + 892, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An alternative approach is to use pretrained DNNs that impose only the signal prior, while the agreement with the", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25245", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "observations is being handled at test-time in a \"zero-shot\" manner. A successful choice of such pretrained DNNs are Gaussian denoisers, as was initially demonstrated in different \"plug-and-play\" (PnP) and \"regularization by denoising\" (RED) iterative schemes [25, 36, 40, 44]. The rise of score-based generative modeling [13, 31] — typically referred to as denoising diffusion models (DDMs) — whose inference/sampling \"reversed\" flows are based on iteratively injecting Gaussian noise and denoising, has further increased the popularity of using iterative denoising for general purpose restoration. In particular, operations that promote data-fidelity, similar to those used in PnP/RED, have been used within the diffusion models' iterative sampling schemes to guide the iterations towards an image that not only looks natural but also agrees with the observations [2, 5, 6, 16, 21, 30, 32, 41, 45].", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Combining iterative denoising with guidance that is based on back-projection (BP) of intermediate estimates on the subspace $\\{\\mathbf{x}:\\mathbf{A}\\mathbf{x} = \\mathbf{y}\\}$ (more details in Section 2) was originally proposed in [36] (in the context of PnP), and has been shown to be a promising strategy in both the PnP and the DDM literature [5, 11, 19, 26, 27, 30, 37, 41, 46]. In the context of diffusion models it has been rediscovered under the names \"pseudoinverse\" [30] or \"range/null-space\" [41] guidance. However, in cases where $\\mathbf{A}$ has low singular values (e.g., in image deblurring and super-resolution), the presence of noise in the observations $\\mathbf{y}$ hinders the application of this approach: careful regularization is required and the performance gains tend to decrease.", + "bbox": [ + 75, + 335, + 472, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contribution. In this paper, we identify the BP step as a preconditioned version of a least squares (LS) gradient step. This inspires us to propose an iteration-dependent preconditioned guidance approach that essentially traverses from the BP step to the LS gradient step along the restoration scheme. Thus, it enjoys benefits of BP step [38, 39], such as stronger consistency with y and accelerated convergence in early iterations, and the better robustness to noise of LS as the scheme approaches its end. The specific trajectory that we devise in this paper is also more simple and efficient to implement than other potential alternatives for BP, which either require having full knowledge on the SVD of A [16], or many neural function evaluations (NFEs) [6].", + "bbox": [ + 75, + 535, + 472, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We present formal mathematical motivation for our guidance technique and use it within both a PnP-based scheme and its DDM sampling-based counterpart that we design. We examine the proposed approach for image deblurring and super-resolution on the CelebA-HQ and ImageNet datasets, where we exploit the powerful denoisers of DDMs [7, 20], and demonstrate its advantages over existing methods. In particular, our sampling-based reconstruction approach is flexible to the observation model, computationally convenient, and displays a good combination of perceptual quality and accuracy.", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Related Work", + "text_level": 1, + "bbox": [ + 498, + 89, + 787, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. PnP Denoisers and Back-Projections", + "text_level": 1, + "bbox": [ + 500, + 114, + 816, + 131 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditionally, estimating $\\mathbf{x}^*$ from its measurements (1) has been tackled by minimizing an explicit objective function", + "bbox": [ + 498, + 137, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nL (\\mathbf {x}) = \\ell (\\mathbf {x}; \\mathbf {y}) + s (\\mathbf {x}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 179, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which is composed of a data-fidelity term $\\ell (\\mathbf{x};\\mathbf{y})$ and a signal prior term $s(\\mathbf{x})$ . The PnP concept [40] suggests applying a proximal algorithm to (2), where the proximal mapping associated with the prior function $s(\\cdot)$ , i.e., $\\mathrm{prox}_s(\\mathbf{x})\\coloneqq \\mathrm{argmin}_{\\mathbf{z}}\\frac{1}{2}\\| \\mathbf{z} - \\mathbf{x}\\|_2^2 +s(\\mathbf{z})$ [22], is replaced with an off-the-shelf Gaussian denoiser $\\mathcal{D}(\\cdot ;\\sigma_t)$ ( $\\sigma_{t}$ denotes the denoiser's noise level) that need not be associated with an explicit prior function (e.g., a pretrained DNN). A vast amount of literature has been dedicated to designing and analyzing PnP algorithms [4, 14, 24, 25, 35, 36, 40, 44].", + "bbox": [ + 496, + 207, + 890, + 368 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A popular PnP scheme based on the proximal-gradient method (PGM) is given by:", + "bbox": [ + 498, + 369, + 890, + 398 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {0 \\mid t} = \\mathcal {D} \\left(\\mathbf {x} _ {t}; \\sigma_ {t}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 411, + 890, + 426 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\nabla_ {\\mathbf {x}} \\ell (\\mathbf {x} _ {0 | t}; \\mathbf {y}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 430, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $t = T, T - 1, \\ldots, 1$ is the iteration index (decreases over time, to match the notation in diffusion/score-based models), $\\mu_t$ is a step-size, and $\\sigma_T > \\ldots > \\sigma_1$ is a predefined decreasing set of noise levels. The scheme is initialized with some $\\mathbf{x}_T$ and the final estimate is given by $\\mathbf{x}_{0|1}$ .", + "bbox": [ + 496, + 455, + 890, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A typical choice of data-fidelity term is the LS objective", + "bbox": [ + 517, + 532, + 890, + 547 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {L S} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\| \\mathbf {A x} - \\mathbf {y} \\| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 558, + 890, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for which the gradient step in (4) is given by", + "bbox": [ + 500, + 595, + 795, + 612 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 622, + 890, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Note though that PnP methods based on LS gradient steps tend to require many iterations [25, 39]. The IDBP method [36] suggests that the data-fidelity guidance, which follows the denoising operation, will be the back-projection (BP) of $\\mathbf{x}_{0|t}$ onto the affine subspace $\\{\\mathbf{x}:\\mathbf{A}\\mathbf{x} = \\mathbf{y}\\}$ :", + "bbox": [ + 496, + 651, + 890, + 727 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {t - 1} = \\operatorname {a r g m i n} _ {\\mathbf {x}} \\| \\mathbf {x} - \\mathbf {x} _ {0 | t} \\| _ {2} \\text {s . t .} \\mathbf {A x} = \\mathbf {y} (7) \\\\ = \\mathbf {A} ^ {\\dagger} \\mathbf {y} + \\left(\\mathbf {I} _ {n} - \\mathbf {A} ^ {\\dagger} \\mathbf {A}\\right) \\mathbf {x} _ {0 | t} (8) \\\\ = \\mathbf {x} _ {0 | t} - \\mathbf {A} ^ {\\dagger} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}), (9) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 738, + 890, + 796 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbf{A}^{\\dagger}$ denotes the pseudoinverse of $\\mathbf{A}$ .", + "bbox": [ + 500, + 809, + 784, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "When $\\mathbf{A}$ has near-zero singular values, it has been shown to be beneficial to replace $\\mathbf{A}^{\\dagger} = \\mathbf{A}^{T}(\\mathbf{A}\\mathbf{A}^{T})^{\\dagger}$ with a regularized version $\\mathbf{A}^T (\\mathbf{A}\\mathbf{A}^T +\\eta \\mathbf{I}_m)^{-1}$ , where $\\eta >0$ is the regularization hyperparameter [36, 37]. Importantly, note that there are popular tasks where the pseudoinverse can be", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25246", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "implemented efficiently (e.g., see the supplementary material for FFT based implementations of this operation for deblurring and super-resolution). And, in general, full rank $\\mathbf{A}\\mathbf{A}^T$ (and $\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m$ otherwise) can be typically \"inverted\" using few conjugate gradient iterations [12], which only require applying $\\mathbf{A}$ and $\\mathbf{A}^T$ and bypass the need of matrix inversion or SVD.", + "bbox": [ + 75, + 90, + 468, + 195 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As pointed out in [38, 39], (9) is equivalent to a gradient step (4) with step-size $\\mu_t = 1$ and a special choice of $\\ell(\\mathbf{x};\\mathbf{y})$ , which they dubbed as the \"BP term\":", + "bbox": [ + 76, + 196, + 470, + 242 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {B P} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\| \\left(\\mathbf {A} \\mathbf {A} ^ {T}\\right) ^ {- 1 / 2} (\\mathbf {A x} - \\mathbf {y}) \\| _ {2} ^ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 252, + 468, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These works have analyzed, both empirically and theoretically, the effects of using BP steps (9) rather than LS steps (6) in inverse problems. They show provable faster convergence benefits (less iterations) and, in the low-noise regime, also MSE benefits. However, it is also shown that in the presence of observation noise and $\\mathbf{A}$ with small singular values, we have that $\\mathbf{A}^{\\dagger}\\mathbf{y}$ amplifies the noise. Thus a strong regularization $\\eta$ is needed which hinders the advantages.", + "bbox": [ + 75, + 289, + 468, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Restoration via Guidance of DDMs", + "text_level": 1, + "bbox": [ + 76, + 419, + 382, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pretrained diffusion/score-based generative models [13, 31, 33] have been shown to be a powerful signal prior for image restoration. These generative models are based on training a network that approximates the score function $\\nabla_{\\mathbf{x}_t}\\log p_t(\\mathbf{x}_t)$ , where $p_t$ denotes the distribution of $\\mathbf{x}_t$ , a Gaussian noisy version of the data $\\mathbf{x}_0\\sim p_0$ with noise level indexed by $t\\in [0,T]$ . For $\\mathbf{x}_t = \\mathbf{x}_0 + \\epsilon_t$ with $\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\sigma_t^2\\mathbf{I}_n)$ , by Tweedie's formula $-\\sigma_t^2\\nabla_{\\mathbf{x}_t}\\log p_t(\\mathbf{x}_t) = \\mathbf{x}_t - \\mathbb{E}[\\mathbf{x}_0|\\mathbf{x}_t] = \\mathbb{E}[\\epsilon_t|\\mathbf{x}_t]$ [9]. Therefore, these approaches essentially attempt to learn the MMSE Gaussian denoiser or, equivalently, noise estimation. After training, the sampling schemes are based on random Gaussian initialization and alternatively denoising and injection of Gaussian noise with a decreasing noise level.", + "bbox": [ + 75, + 441, + 468, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For concreteness, let us focus on the popular DDPM formulation [13]. In DDPM, $\\mathbf{x}_t$ is generated from a data point $\\mathbf{x}_0$ by the \"forward flow\":", + "bbox": [ + 75, + 654, + 468, + 699 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 709, + 468, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)$ and $\\{\\beta_t\\}_{t = 1}^T$ is a predetermined \"noise schedule\" obeying $0 < \\beta_{1} < \\dots < \\beta_{T}\\leq 1$ . By properties of Gaussians, $\\mathbf{x}_t$ can be directly generated from $\\mathbf{x}_0$ by", + "bbox": [ + 75, + 739, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 796, + 468, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which includes noise variance $1 - \\bar{\\alpha}_{t}$ and signal scale factor $\\sqrt{\\bar{\\alpha}_t}$ , where $\\bar{\\alpha}_t = \\Pi_{s=1}^t\\alpha_s$ and $\\alpha_t = 1 - \\beta_t$ . In training time, a U-net DNN $\\epsilon_{\\theta}(\\cdot ; t)$ is trained to predict the noise $\\epsilon$ given $\\mathbf{x}_t$ by minimizing an MSE loss. In DDPM's inference time, starting from a random $\\mathbf{x}_T \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}_n)$ , one step of", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the \"reverse flow\" that is used for generating a sample from $p_0$ is given by", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t)\\right) + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 130, + 890, + 164 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{t}$ is drawn from $\\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)$ .", + "bbox": [ + 498, + 172, + 725, + 188 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A faster generation scheme, denoted DDIM [29], is based on diverging from the Markovian guideline of DDPM. In DDIM, the step (13) is replaced with", + "bbox": [ + 498, + 188, + 890, + 234 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} \\mathbf {x} _ {0 | t} + \\hat {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t) + \\tilde {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {t}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 244, + 890, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)$ and", + "bbox": [ + 500, + 270, + 673, + 286 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {t} = \\sqrt {1 - \\bar {\\alpha} _ {t - 1} - \\tilde {\\sigma} _ {t} ^ {2}}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 296, + 890, + 321 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {0 \\mid t} = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} \\left(\\mathbf {x} _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t)\\right). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 324, + 890, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The hyperparameter $\\tilde{\\sigma}_t$ allows trading between the levels of two noise terms: the estimated noise $\\epsilon_{\\theta}(\\mathbf{x}_t;t)$ and a pure stochastic noise $\\epsilon_t$ . Moreover, $\\mathbf{x}_{0|t}$ in (16) is an estimate of $\\mathbf{x}_0$ given $\\mathbf{x}_t$ , which is essentially performing Gaussian denoising: $\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}}\\mathcal{D}(\\mathbf{x}_t;\\sigma_t = \\sqrt{1 - \\bar{\\alpha}_t})$ , as implied by (12).", + "bbox": [ + 498, + 363, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Many of the methods that use DDMs as priors for image restoration [16, 30, 41, 45] are based on the DDIM scheme [29]. Yet, in order that the sampling scheme will produce an image that is not only perceptually pleasing but also agrees with the measurements $\\mathbf{y}$ and the observation model (1) it is required to equip the iterations with some data-fidelity guidance. This guidance is typically based on the gradient of a data-fidelity term $\\ell (\\mathbf{x};\\mathbf{y})$ . In other words, the iterations (14) are modified into", + "bbox": [ + 498, + 465, + 890, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} \\mathbf {x} _ {0 | t} - \\mu_ {t} \\nabla_ {\\mathbf {x}} \\ell \\left(\\mathbf {x} _ {0 | t}; \\mathbf {y}\\right) + \\hat {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {x} _ {t}; t\\right) + \\tilde {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {t}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 613, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu_t$ is the guidance scaling factor.", + "bbox": [ + 500, + 643, + 761, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note the similarity between the PnP restoration (3)-(4) and the DDM restoration (16)-(17). Namely, ignoring the scaling of the signal by $\\{\\bar{\\alpha}_t\\}$ , the main difference is the noise injection, composed of the estimated noise $\\epsilon_{\\theta}$ and the random noise $\\epsilon_t$ . The similarity of DDMs schemes to previous iterative denoising methods is further seen by the formulation of [15], which decouples the diffusion \"forward\" flows, used for training the denoisers, from the \"reverse\" inference flows. More discussion on such connections can be found in a recent review paper [10].", + "bbox": [ + 496, + 659, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For example, the DDM restoration method in [6], dubbed DPS, where the guidance is based on the gradient of the LS term, resembles (6) with noise injection. Interestingly, just like its PnP counterpart, it requires a very large number of iterations (and thus many NFEs). Alternatively, by using BP guidance in (17) — equivalently, when injecting noise", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25247", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to step (9) in IDBP — one gets the recent DDNM method [41] (which is also similar to the method in [30]). However, note that the DDNM paper focuses on noiseless settings and has difficulties in noisy settings (in Section 4 we state its technical limitation), which is aligned with the sensitivity of BP guidance to noise in $\\mathbf{y}$ , as mentioned above.", + "bbox": [ + 75, + 90, + 467, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At this point, we would also like to mention the DDRM method [16], which resembles the BP approach as it generates \"spectral space\" measurements $\\bar{\\mathbf{y}}$ in a way similar to applying $\\mathbf{A}^{\\dagger}$ on $\\mathbf{y}$ . Yet, it is more robust to observation noise as it requires access to the full SVD of $\\mathbf{A}$ , which allows it to mitigate noise amplification per singular component in each iteration. In this paper we aim to devise an approach that does not require computing and storing the SVD of $\\mathbf{A}$ , which is impractical is most cases.", + "bbox": [ + 75, + 181, + 467, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we note that the way we construct a sampling scheme from a deterministic algorithm shares similarity with the recent method DIfPIR [45]. However, while [45] uses an existing PnP baseline, here we propose a novel core reconstruction method. Also, empirically our new sampling scheme demonstrates better accuracy than DiffPIR (evaluated by PSNR) without compromising on perceptual quality (evaluated by LPIPS).", + "bbox": [ + 75, + 316, + 467, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 450, + 287, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we present our image restoration method that is more robust to observation noise than methods that use only back-projections while still having low computational complexity and clear benefits over methods that are based only on plain LS based guidance. To this end, we present a novel core guidance approach, equip it with formal theoretical motivation, and utilize it to devise a new sampling-based reconstruction scheme.", + "bbox": [ + 75, + 477, + 467, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "All the claims in this section are proved in the supplementary material.", + "bbox": [ + 75, + 598, + 467, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Core approach", + "text_level": 1, + "bbox": [ + 76, + 638, + 227, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The idea for our approach comes from identifying (9) as a specific instance of the formula", + "bbox": [ + 75, + 661, + 467, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} \\mathbf {W} (\\mathbf {A x} _ {0 | t} - \\mathbf {y}) \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 702, + 467, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T)^{-1}$ (assuming full rank $\\mathbf{A}$ ) and $\\mu_t = 1$ . The plain LS step (6) is obviously also an instance of this expression with $\\mathbf{W} = \\mathbf{I}_m$ .", + "bbox": [ + 75, + 732, + 467, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recall traditional preconditioning in optimization [23]: The optimization of an objective, e.g., $L: \\mathbb{R}^n \\to \\mathbb{R}$ in (2), is based on gradient-based optimizers where the full gradient $\\nabla L(\\mathbf{x})$ is multiplied by a (symmetric) positive definite matrix $\\mathbf{P} \\in \\mathbb{R}^{n \\times n}$ . Such practice does not affect the problem's minimizers (since $\\mathbf{P} \\nabla L(\\mathbf{x}) = \\mathbf{0} \\iff \\nabla L(\\mathbf{x}) = \\mathbf{0}$ due to the invertibility of $\\mathbf{P}$ ), and its goal is to ease the optimization landscape, characterized by the condition number", + "bbox": [ + 75, + 779, + 467, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of the effective Hessian $\\mathbf{P}^{1 / 2}\\nabla^2 L(\\mathbf{x})\\mathbf{P}^{1 / 2}$ . In (18), however, $\\mathbf{W}\\in \\mathbb{R}^{m\\times m}$ does not directly affect the signal's prior and for general $\\mathbf{W}$ we may not have $\\mathbf{A}^T\\mathbf{W}(\\mathbf{A}\\mathbf{x} - \\mathbf{y}) = \\mathbf{0}\\iff \\nabla \\ell_{LS}(\\mathbf{x}) = \\mathbf{A}^T (\\mathbf{A}\\mathbf{x} - \\mathbf{y}) = \\mathbf{0}$ .", + "bbox": [ + 496, + 89, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Nevertheless, we have the following claims.", + "bbox": [ + 517, + 152, + 808, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Claim 3.1. Let $\\mathbf{A} \\in \\mathbb{A}^{m \\times n}$ with $m \\leq n$ and $\\operatorname{rank}(\\mathbf{A}) = m$ . Let $\\mathbf{W} \\in \\mathbb{R}^{m \\times m}$ such that $\\operatorname{rank}(\\mathbf{A}^T \\mathbf{W}) = m$ . Then,", + "bbox": [ + 496, + 174, + 890, + 205 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} ^ {T} \\mathbf {W} (\\mathbf {A x} - \\mathbf {y}) = \\mathbf {0} \\iff \\mathbf {A} ^ {T} (\\mathbf {A x} - \\mathbf {y}) = \\mathbf {0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 214, + 854, + 232 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Claim 3.2. Let $\\mathbf{A} \\in \\mathbb{A}^{m \\times n}$ with $m \\leq n$ . Let $\\mathbf{W} \\in \\mathbb{R}^{m \\times m}$ be a positive definite matrix that shares eigenbasis with $\\mathbf{A A}^T$ . Then, there exists a positive definite $\\mathbf{P} \\in \\mathbb{R}^{n \\times n}$ such that", + "bbox": [ + 496, + 242, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} ^ {T} \\mathbf {W} \\mathbf {A} = \\mathbf {P} ^ {1 / 2} \\mathbf {A} ^ {T} \\mathbf {A} \\mathbf {P} ^ {1 / 2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 300, + 790, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, if $\\mathbf{A}$ is full rank, then any $\\mathbf{W}$ for which $\\mathbf{A}^T\\mathbf{W}$ is full rank (e.g., $\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T)^{-1}$ ) can be interpreted as a preconditioner of $\\nabla \\ell_{LS}$ (rather than of the full objective that may include additional terms). Alternatively, even if $\\mathbf{A}$ is not full rank, but $\\mathbf{W}$ shares eigenbasis with $\\mathbf{A}\\mathbf{A}^T$ (e.g., $\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m)^{-1}$ ), we allow ourselves to refer to $\\mathbf{W}$ as a preconditioner of $\\nabla \\ell_{LS}$ since it has the same effect on the effective Hessian, $\\mathbf{P}^{1/2}\\nabla^2\\ell_{LS}(\\mathbf{x})\\mathbf{P}^{1/2}$ , as a traditional preconditioner $\\mathbf{P}$ .", + "bbox": [ + 496, + 327, + 890, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by this, in lieu of (4) we propose a data-fidelity guidance based on iteration-dependent preconditioner:", + "bbox": [ + 496, + 463, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} \\mathbf {W} _ {t} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}) \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 503, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with a \"smooth\" discretization of the path of symmetric preconditioners $\\{\\mathbf{W}_t\\}$ — invertible with eigenbasis shared with $\\mathbf{A}\\mathbf{A}^T$ — that starts roughly at $\\mathbf{W}_T \\propto (\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m)^{-1}$ and ends roughly at $\\mathbf{W}_0 \\propto \\mathbf{I}_m$ .", + "bbox": [ + 496, + 530, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In words, the proposed guidance is based on gently traversing from the (regularized) BP step to the LS step along the restoration scheme. Thus, it enjoys benefits of BP steps (stronger consistency with $\\mathbf{y}$ , accelerated convergence, etc.) in early iterations and the better robustness to noise of LS steps as the scheme approaches its end.", + "bbox": [ + 496, + 590, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Potentially, a sequence of preconditioners $\\{\\mathbf{W}_t\\}$ might be learned in a data-driven manner under some optimality criterion. Yet, this is expected to come at the price of losing their generality to arbitrary data. Thus, here we propose an engineered, but simple and effective, update rule of $\\mathbf{W}_t$ that, as we will show empirically, already demonstrates the usefulness of our new concept. Specifically, the rule that we propose is given by the following convex combination:", + "bbox": [ + 496, + 681, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} _ {t} = (1 - \\delta_ {t}) \\left(\\mathbf {A} \\mathbf {A} ^ {T} + \\eta \\mathbf {I} _ {m}\\right) ^ {- 1} + \\delta_ {t} c \\mathbf {I} _ {m} \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 811, + 890, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $0 \\leq \\delta_T < \\ldots < \\delta_0 \\leq 1$ is a predefined sequence, and $c$ is a positive scalar that balances the two terms.", + "bbox": [ + 496, + 839, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In general, the main motivation for (20) is that it both obeys the previously stated conditions and also yields a", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25248", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "data-fidelity guidance that is very simple to implement. Indeed, plugging (20) in (19) yields", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\left((1 - \\delta_ {t}) \\mathbf {g} _ {B P} (\\mathbf {x} _ {0 | t}) + \\delta_ {t} \\mathbf {g} _ {L S} (\\mathbf {x} _ {0 | t})\\right), \\\\ =: \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {g} _ {\\delta_ {t}} \\left(\\mathbf {x} _ {0 | t}\\right) \\tag {21} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 132, + 468, + 169 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 181, + 122, + 194 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {g} _ {B P} \\left(\\mathbf {x} _ {0 | t}\\right) = \\mathbf {A} ^ {T} \\left(\\mathbf {A} \\mathbf {A} ^ {T} + \\eta \\mathbf {I} _ {m}\\right) ^ {- 1} \\left(\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}\\right), \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 205, + 468, + 224 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {g} _ {L S} \\left(\\mathbf {x} _ {0 | t}\\right) = c \\mathbf {A} ^ {T} \\left(\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}\\right), \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 227, + 468, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "can be computed efficiently for a wide range of observation models.", + "bbox": [ + 76, + 257, + 468, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Section 3.4 we will discuss practical implementations details for simple hyperparameter tuning (e.g., a simple way to tune $\\{\\delta_t\\}$ ). As for setting $c$ , observe that (19) is essentially a gradient step (at $\\mathbf{x}_{0|t}$ ) of the weighted least squares (WLS) data-fidelity term:", + "bbox": [ + 76, + 287, + 468, + 363 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {W L S, t} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\left\\| \\mathbf {W} _ {t} ^ {1 / 2} (\\mathbf {A x} - \\mathbf {y}) \\right\\| _ {2} ^ {2}, \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 375, + 468, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for which we have the following property.", + "bbox": [ + 76, + 412, + 354, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Claim 3.3. Denote by $\\lambda_{1}$ the largest singular value of $\\mathbf{A}$ . Let $c \\leq 1 / \\lambda_1^2$ . Then, the update (21) with $\\mu_t = 1$ ensures reduction in (24).", + "bbox": [ + 76, + 438, + 468, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Many popular degradation models obey $\\lambda_1 \\lesssim 1$ (e.g., in deblurring $\\lambda_1 = 1$ and in super-resolution $\\lambda_1$ is moderately lower than 1). Thus, following the claim, unless stated otherwise, we use $c = 1$ and $\\mu_t = 1$ .", + "bbox": [ + 76, + 494, + 468, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To conclude this subsection, the core of the proposed algorithm is based on iteratively computing (3) and (21). Without noise injection, this is essentially a novel PnP scheme, which we call Iterative Denoising and Preconditioned Guidance (IDPG). As we will empirically show in Section 4, while this method has good PSNR performance, turning it into a DDM-based sampling scheme leads to better recoveries, especially in terms of perceptual quality. Before presenting the sampling scheme in Section 3.3, let us provide some theoretical motivation for our preconditioned guidance approach.", + "bbox": [ + 75, + 555, + 468, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Theory", + "text_level": 1, + "bbox": [ + 76, + 731, + 169, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let us state some mathematical claims that motivate the core guidance approach. In this subsection we consider a simplified setting of having a fixed $0 < \\delta < 1$ , i.e., a fixed WLS data-fidelity term (24) with $\\mathbf{W}$ given as in (20) but with $\\delta_t = \\delta$ . We examine the effects of this WLS, compared to LS and BP fidelity terms, on an estimator of $\\mathbf{x}^*$ , denoted by $\\hat{\\mathbf{x}}$ , which is obtained by minimizing (2) with Tikhonov prior $s(\\mathbf{x}) = \\frac{\\beta}{2} \\| \\mathbf{Dx} \\|_2^2$ , where $\\beta > 0$ and $\\mathbf{D}^T \\mathbf{D}$ is invertible, so, the estimator $\\hat{\\mathbf{x}}$ per data-fidelity term is unique.", + "bbox": [ + 75, + 753, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The MSE of $\\hat{\\mathbf{x}}$ (conditioned on $\\mathbf{x}^*$ , averaged over the noise e) can be decomposed into two terms: squared bias, $b^{2}$ (independent of e), and variance, $v$ (depends on $\\sigma_e^2$ ), given by", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nb ^ {2} := \\left\\| \\mathbb {E} \\left[ \\hat {\\mathbf {x}} \\mid \\mathbf {x} ^ {*} \\right] - \\mathbf {x} ^ {*} \\right\\| _ {2} ^ {2}, \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 143, + 890, + 160 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv := \\operatorname {T r} \\left(\\operatorname {V a r} \\left(\\hat {\\mathbf {x}} \\mid \\mathbf {x} ^ {*}\\right)\\right). \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 162, + 890, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The motivation for analyzing this setting (even though in the proposed core procedure (3) & (21), we modify $\\delta_t$ along the iterations and do not attempt to reach a minimizer per $\\delta_t$ ) is that insights on gains in bias and variance at the minimizer level hint that similar effects are possible even with limited optimizer iterations per $\\delta_t$ . Also, in [38], it was shown that insights gained for Tikhonov prior generalize empirically to more complex priors. Specifically, they showed that BP typically leads to smaller bias but higher variance than LS. In what follows, the intuition that $0 < \\delta < 1$ enables trading bias and variance is made formal.", + "bbox": [ + 496, + 186, + 890, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 3.4. Consider the observation model (1) and estimating $\\mathbf{x}^*$ via minimization of (2) with $s(\\mathbf{x}) = \\frac{\\beta}{2}\\|\\mathbf{D}\\mathbf{x}\\|_2^2$ .", + "bbox": [ + 498, + 375, + 890, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assume that: (a) $\\mathbf{A}^T\\mathbf{A}$ and $\\mathbf{D}^T\\mathbf{D} \\succ 0$ share eigenbasis; (b) the singulars value of $\\mathbf{A}$ are in $(0,1]$ , and not all equal (common case); (c) $\\eta = 0$ and $c = 1$ . Then, $b_{BP} < b_{WLS} < b_{LS}$ , and $v_{LS} < v_{WLS} < v_{BP}$ .", + "bbox": [ + 498, + 416, + 890, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that the margins in the theorem's inequalities depend on where $\\delta$ is located in $(0,1)$ (e.g., $v_{\\mathrm{WLS}} \\to v_{\\mathrm{LS}}$ for $\\delta \\to 1$ ). This further motivates having a set $\\{\\delta_t\\}$ instead of a fixed $\\delta$ in (20) to gain flexibility in handling the error's bias/variance.", + "bbox": [ + 496, + 484, + 890, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As for the convergence rates of first-order optimization algorithms (which affect the number of NFEs with practical DNN-based priors), recall that it can typically be characterized by the condition number, $\\kappa(\\cdot)$ , of the problem's Hessian, which equals the ratio between the largest and smallest eigenvalues of the Hessian — the lower the better. Note, though, that for $m < n$ , the Hessian of each of the three data-fidelity terms (LS, BP, WLS) is rank-deficient due to the ill-posedness of the observation model. Nevertheless, we have the following property on the component of their Hessian in the row-range of $\\mathbf{A}$ (a subspace in $\\mathbb{R}^n$ ).", + "bbox": [ + 496, + 560, + 890, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Claim 3.5. Assume that $\\mathrm{rank}(\\mathbf{A}) = m$ , the singular values of $\\mathbf{A}$ are not all equal, $\\eta = 0$ , and denote by $\\mathbf{V} \\in \\mathbb{R}^{n \\times m}$ an orthonormal basis for the row-range of $\\mathbf{A}$ . We have that", + "bbox": [ + 496, + 732, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {B P} \\mathbf {V}) < \\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {W L S} \\mathbf {V}) < \\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {L S} \\mathbf {V}).\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 784, + 893, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Namely, the flexibility in $\\delta$ allows accelerating the reconstruction procedure compared to using only a LS based guidance. Leveraging this result to establish ranking claims for specific algorithms may follow the approaches of [39] (based on constraints on the null space of $\\mathbf{A}$ that are implicitly imposed by the signal prior term).", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25249", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Denoising Diffusion with iterative Preconditioned Guidance (DDPG)" + ], + "code_body": "Require: $\\epsilon_{\\theta}(\\cdot ,t)$ (noise estimator), $T,\\mathbf{y},\\mathbf{A},\\{\\bar{\\alpha}_t\\} ,\\{\\mu_t\\} ,c,$ $\\eta ,\\gamma ,\\zeta$ 1: if $\\sigma_e > 0$ then 2: $\\delta_t = \\bar{\\alpha}_t^\\gamma$ and $w_{t} = \\delta_{t}$ 3: else 4: $\\delta_t = 0$ and $w_{t} = 1$ 5: end if 6: Initialize $\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)$ 7: for $t$ from $T$ to 1 do 8: $\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}}\\left(\\mathbf{x}_t - \\sqrt{1 - \\bar{\\alpha}_t}\\epsilon_\\theta (\\mathbf{x}_t,t)\\right)$ 9: $\\mathbf{g}_{BP} = \\mathbf{A}^T (\\mathbf{A}\\mathbf{A}^T +\\eta \\mathbf{I}_m)^{-1}(\\mathbf{A}\\mathbf{x}_{0|t} - \\mathbf{y})$ 10: $\\mathbf{g}_{LS} = c\\mathbf{A}^T (\\mathbf{A}\\mathbf{x}_{0|t} - \\mathbf{y})$ 11: $\\tilde{\\mathbf{x}}_{t - 1} = \\mathbf{x}_{0|t} - \\mu_t((1 - \\delta_t)\\mathbf{g}_{BP} + \\delta_t\\mathbf{g}_{LS})$ 12: $\\hat{\\epsilon}_t = \\frac{1}{\\sqrt{1 - \\bar{\\alpha}_t}} (\\mathbf{x}_t - \\sqrt{\\bar{\\alpha}_t}\\tilde{\\mathbf{x}}_{t - 1})$ 13: $\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)$ 14: $\\mathbf{x}_{t - 1} =$ 15: $\\sqrt{\\bar{\\alpha}_{t - 1}}\\tilde{\\mathbf{x}}_{t - 1} + \\sqrt{1 - \\bar{\\alpha}_{t - 1}}\\left(w_t\\sqrt{1 - \\zeta}\\hat{\\epsilon}_t + \\sqrt{\\zeta}\\epsilon_t\\right)$ 16: end for 17: return ${\\bf x}_0$", + "bbox": [ + 76, + 123, + 468, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Sampling scheme", + "text_level": 1, + "bbox": [ + 76, + 479, + 246, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As previously mentioned, in this subsection we turn IDPG (alternating (3) and (21)) into a DDM-based sampling scheme that empirically leads to better recoveries, especially in terms of perceptual quality. Injecting noise to the estimate in a certain iteration leads to an image that better matches the data on which the denoiser has been trained. Intuitively, this should improve the denoiser's performance and also allow it to mitigate error propagation along the iterations, by masking artifacts with noise that will be removed. Accordingly, it allows using a smaller value of the regularization parameter $\\eta$ when handling noisy $\\mathbf{y}$ , which yields results with sharper details.", + "bbox": [ + 75, + 505, + 468, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The sampling scheme that we propose is based on modification of the DDIM guided scheme, stated in (17). Namely, $\\mathbf{x}_{0|t}$ is computed using a DDM's noise estimator as in (16) and the novel guidance $\\mathbf{g}_{\\delta_t}$ is being used in lieu of the abstract gradient $\\nabla_{\\mathbf{x}}\\ell$ . However, we propose several important modifications of the additive noise terms $\\hat{\\sigma}_t\\epsilon_\\theta (\\mathbf{x}_t;t) + \\tilde{\\sigma}_t\\epsilon_t$ that appear in (17).", + "bbox": [ + 75, + 686, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The first modification is inspired by [45]. Note that, contrary to the unconditional image generation task, the data-fidelity guidance can significantly modify the estimated signal $\\tilde{\\mathbf{x}}_{t - 1}\\coloneqq \\mathbf{x}_{0|t} - \\mu_t\\mathbf{g}_{\\delta_t}$ compared to $\\mathbf{x}_{0|t}$ . Therefore, the effective predicted noise can be significantly different than $\\epsilon_{\\theta}(\\mathbf{x}_t;t)$ . Accordingly, based on the relation between $\\epsilon_{\\theta}(\\mathbf{x}_t;t)$ and $\\mathbf{x}_{0|t}$ in (16), the effective predicted noise takes", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the form of", + "bbox": [ + 500, + 90, + 578, + 104 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {\\epsilon}} _ {t} = \\frac {1}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\left(\\mathbf {x} _ {t} - \\sqrt {\\bar {\\alpha} _ {t}} \\tilde {\\mathbf {x}} _ {t - 1}\\right), \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 114, + 890, + 147 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and we use it instead of $\\epsilon_{\\theta}(\\mathbf{x}_t;t)$ for generating $\\mathbf{x}_{t - 1}$", + "bbox": [ + 498, + 159, + 854, + 174 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similarly to this prior work, we also simplify the way of trading between the (effective) estimated noise and the stochastic noise. Instead of time-dependent noise level $\\tilde{\\sigma}_t$ which affects $\\hat{\\sigma}_t = \\sqrt{1 - \\bar{\\alpha}_{t-1} - \\tilde{\\sigma}_t^2}$ in a complicated way, we balance between the levels of $\\hat{\\epsilon}_t$ and $\\epsilon_t$ using the simple to tune weight $\\sqrt{1 - \\zeta}$ and $\\sqrt{\\zeta}$ , respectively, with a single hyperparameter $\\zeta \\in [0,1]$ .", + "bbox": [ + 496, + 175, + 890, + 289 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our key novel modification is the following. In the case of observation noise (i.e., $\\sigma_{e} > 0$ ), the effective predicted noise $\\hat{\\epsilon}_{t}$ may not be useful in iterations where the overall guidance $\\mathbf{g}_{\\delta_t}$ is dominated by $\\mathbf{g}_{BP}$ , due to the sensitivity to noise of the BP guidance. Therefore, we scale it by $\\delta_{t}$ — the weight that is given to $\\mathbf{g}_{LS}$ , which is more robust to observation noise.", + "bbox": [ + 496, + 289, + 890, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We remark that our sampling scheme transfers smoothly to the noiseless case, where one can simply use pure BP guidance – or equivalently $\\delta_t = 0$ : it is only required to omit the last modification (i.e., avoid attenuating the noise injection by $\\delta_t$ ). As will be shown empirically, this scheme performs on par with BP-based DDM methods that are specifically devised for noiseless observations, and outperforms other methods.", + "bbox": [ + 496, + 396, + 890, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The resulted DDM-based sampling algorithm, that we name Denoising Diffusion with iterative Preconditioned Guidance (DDPG), is summarized in Algorithm 1. The algorithm includes a simple way to set $\\{\\delta_t\\}$ that is explained in the next subsection.", + "bbox": [ + 496, + 517, + 890, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 604, + 714, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the experimental section, we wish to test the approach (both DDPG and its core version IDPG) with powerful DDM's denoisers trained and used in [7, 20]. These models are based on DDPM formulation [13, 29], that we use to reduce the hyperparameter tuning effort in all our examined tasks, and in particular setting $\\{\\delta_t\\}$ for noisy observations. (Recall that in the noiseless case, we simply set $\\delta_t = 0$ ).", + "bbox": [ + 496, + 628, + 890, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As presented in Section 2, in DDPM there are the parameters $\\{\\bar{\\alpha}_t\\}$ , which are determined by the hyperparameters $\\{\\beta_t\\}$ , and determine many other parameters (e.g., the model's noise levels $\\{\\sigma_t\\}$ ). These $\\{\\bar{\\alpha}_t\\}$ obey $0_+ \\approx \\bar{\\alpha}_T < \\ldots < \\bar{\\alpha}_0 = 1$ . We do not change $\\{\\beta_t\\}$ and $\\{\\bar{\\alpha}_t\\}$ at all compared to previous methods that we compare with [16, 41]. In fact, we use $\\{\\bar{\\alpha}_t\\}$ to set $\\delta_t = \\bar{\\alpha}_t^\\gamma$ with a single positive scalar hyperparameter $\\gamma$ . This ensures that as $t$ decreases, $\\{\\delta_t\\}$ is monotonically increasing from 0 to 1 in rate that can be controlled by $\\gamma$ . Observe that smaller $\\gamma$ yields higher intermediate $\\bar{\\alpha}_t^\\gamma$ and thus a larger portion of $\\{\\mathbf{W}_t\\}$ closer to", + "bbox": [ + 496, + 734, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25250", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "identity matrix — or, equivalently, \"faster\" progress from BP to LS. This is beneficial for larger observation noise $\\sigma_{e}$ .", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To conclude, when using $c = 1$ and $\\mu_t = 1$ , applying our approach requires tuning only $\\eta, \\gamma$ and $\\zeta$ (for DDPG). Note that, potentially, tuning more hyperparameters for our method can further boost its results.", + "bbox": [ + 75, + 122, + 468, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 200, + 209, + 217 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we examine the performance of our approach. We start with examining our core guidance, as reflected in IDPG, compared to its extreme cases: deterministic methods with pure BP and LS based guidance. Then, we compare both IDPG and DDPG to existing methods: DDRM [16], DPS [6], DDNM [41], and DiffPIR [45]. We consider the CelebA-HQ 1K and ImageNet 1K test sets, where for fair comparison all the methods use the same pretrained DDM's denoisers: the model from [20] trained on CelebA-HQ and the (unconditional) model from [7] trained on ImageNet. We use $T = 100$ iterations for each of the methods as in [41]. An exception is DPS, which requires $T = 1000$ iterations with much larger per-iteration complexity, making it extremely slow compared to others. All the methods are initialized with the same random $\\mathbf{x}_T$ .", + "bbox": [ + 75, + 226, + 468, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We consider image deblurring and super-resolution tasks that have been widely examined in the previous works, and for each method we use the hyperparameter settings suggested by its authors. The settings for our methods are stated in the supplementary material. Specifically, we consider super-resolution with bicubic downsampling and scale factor 4 and deblurring with Gaussian kernel as, e.g., in [16, 41]. However, we also examine challenging noisy deblurring with random motion kernels, as in [45]. This is an example for a common task that cannot be handled by DDRM [16], which is limited to separable kernels for which the SVD of $\\mathbf{A}$ can be efficiently computed and stored. This task cannot be addressed also by DDNM [41], which fails to tackle noisy observations. We examine the noisy cases also in the two aforementioned tasks.", + "bbox": [ + 75, + 454, + 468, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the supplementary material, we demonstrate the advantages of our approach over recent task-specific DNNs, as well as its superior performance also with lower noise level than demonstrated here. In addition, we report there the impressive performance of our approach for sparse-view computed tomography (another task where computing the SVD of $\\mathbf{A}$ is infeasible).", + "bbox": [ + 75, + 681, + 468, + 787 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/02482149ac67ddac4255b19f4944597a51ef1492c32e837d7049fe7186ed715e.jpg", + "table_caption": [ + "Table 1. Data-fidelity guidance ablation: super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K." + ], + "table_footnote": [], + "table_body": "
TaskPGM-LSIDBPIDPG (ours)
Bicub. SRx4 σe=032.40 / 0.12732.66 / 0.11132.66 / 0.111
Bicub. SRx4 σe=0.0528.91 / 0.20928.95 / 0.22929.89 / 0.155
Gauss. Deb. σe=032.25 / 0.14145.58 / 0.00245.58 / 0.002
Gauss. Deb. σe=0.0528.61 / 0.19130.55 / 0.15031.08 / 0.150
Gauss. Deb. σe=0.127.89 / 0.23928.29 / 0.22629.28 / 0.146
", + "bbox": [ + 511, + 128, + 880, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7b93fc4180e7ccd6cc5c954c8ff73b3b4382afe12f5e43c4e3dd578ce7824182.jpg", + "image_caption": [ + "Figure 2. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our DDPG. Bottom row, from left to right: PGM-LS, IDBP, and our IDPG (baseline for DDPG)." + ], + "image_footnote": [], + "bbox": [ + 542, + 228, + 844, + 381 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Examining the core approach", + "text_level": 1, + "bbox": [ + 500, + 467, + 761, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As the main contribution of our paper is the novel guidance approach that smoothly traverses from BP to LS guidance, we start with examining our baseline IDPG method (alternating (3) and (21)) with IDBP [36] ( $\\delta_t = 0$ ) and a method with LS based updates ( $\\delta_t = 1$ ), denoted here by PGM-LS (a common PnP scheme [14]). This comparison essentially provides an ablation study for our core approach.", + "bbox": [ + 498, + 489, + 890, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results for bicubic super-resolution and Gaussian deblurring with various and without noise for the CelebA-HQ 1K test set are presented in Table 1. They show that IDPG consistently outperforms IDBP and PGM-LS. Figure 2 displays qualitative results, showing that IDPG has less artifacts than IDBP and finer details than PGM-LS. Yet, while IDPG provides high PSNR values its perceptual quality can be improved by using the sampling-based DDPG, as shown in this figure.", + "bbox": [ + 498, + 595, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison with other methods", + "text_level": 1, + "bbox": [ + 500, + 741, + 784, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We turn to compare the proposed approach to DDRM, DPS, DDNM and DiffPIR. We consider all deblurring and superresolution tasks that have been described above with various noise levels. The results for the CelebA-HQ 1K test set and the ImageNet 1K test set are presented in Table 2 and Table 3, respectively. We present qualitative results for motion deblurring, Gaussian deblurring and super-resolution in Figures 1, 3 and 4, respectively. More results appear in the supplementary material.", + "bbox": [ + 498, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1Using the same hardware, DPS takes a dozen minutes per image compared to a couple of seconds of the other methods, and limiting it to 100 iterations fails to produce meaningful recoveries.", + "bbox": [ + 75, + 801, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2Note that DDMN is tailored for $\\sigma_{e} = 0$ . We remark that DDNM+ that was proposed in [41] for handling noisy $\\mathbf{y}$ (via SVD) seems to be heavily tied to a specific downsampling task (without bicubic kernel) and does not support the considered tasks, as shown in the supplementary material. Our efforts to adapt it failed.", + "bbox": [ + 75, + 838, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25251", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6777dbc256aa1ffbaf3114556db76a7e24f571836e9feb81929fe6ee715d72df.jpg", + "table_caption": [ + "Table 2. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text)." + ], + "table_footnote": [], + "table_body": "
Task\\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=031.64 / 0.05429.39 / 0.06530.26 / 0.05131.64 / 0.04832.66 / 0.11131.60 / 0.052
Bicub. SRx4 σe=0.0529.26 / 0.09027.49 / 0.08627.44 / 0.085N/A29.89 / 0.15529.39 / 0.105
Gauss. Deb. σe=042.49 / 0.00631.25 / 0.05532.97 / 0.04145.56 / 0.00245.58 / 0.00245.46 / 0.002
Gauss. Deb. σe=0.0530.53 / 0.07427.75 / 0.08428.89 / 0.074N/A31.08 / 0.15030.41 / 0.068
Gauss. Deb. σe=0.128.79 / 0.08826.67 / 0.09727.59 / 0.083N/A29.28 / 0.14629.18 / 0.080
Motion Deb. σe=0.05N/A19.63 / 0.22727.96 / 0.102N/A29.73 / 0.13429.02 / 0.082
Motion Deb. σe=0.1N/A19.64 / 0.23126.23 / 0.132N/A27.86 / 0.16627.74 / 0.099
", + "bbox": [ + 165, + 125, + 802, + 244 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ee825a19a5428d3cea2948c02c7a66123f9cbd2dda2582a19767b48c63cd7187.jpg", + "table_caption": [ + "Table 3. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on Imagenet 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text)." + ], + "table_footnote": [], + "table_body": "
Task\\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=027.38 / 0.27025.56 / 0.23626.99 / 0.22527.45 / 0.24527.20 / 0.32627.41 / 0.255
Bicub. SRx4 σe=0.0525.54 / 0.33324.05 / 0.27124.65 / 0.318N/A25.51 / 0.41125.55 / 0.354
Gauss. Deb. σe=040.53 / 0.00825.54 / 0.25930.54 / 0.08243.64 / 0.00344.02 / 0.00244.21 / 0.002
Gauss. Deb. σe=0.0527.71 / 0.24323.59 / 0.29426.64 / 0.240N/A27.47 / 0.31327.73 / 0.205
Motion Deb. σe=0.05N/A17.52 / 0.46825.34 / 0.284N/A26.02 / 0.35425.94 / 0.249
", + "bbox": [ + 165, + 294, + 802, + 386 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Examining the results, observe that, indeed, the sampling-based version of our approach (DDPG) consistently leads to better perceptual quality, both visually and as measured by LPIPS. Interestingly, while there is an inherent tradeoff between accuracy and perceptual quality [3], the PSNR reduction in DDPG compared to IDPG is rather moderate (and in some case DDPG even has slightly better PSNR than IDPG). One can observe that our approach typically outperforms other approaches in deblurring and is competitive in super-resolution.", + "bbox": [ + 75, + 407, + 468, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Importantly, note that the only reference methods that are as flexible as our approach to the observation model are DPS, which is very slow, and DiffPIR. However, their PSNR is significantly lower than the PSNR of our DDPG. Recall that in many critical applications (e.g., medical imaging), accuracy, as measured by the classical PSNR metric, is extremely important.", + "bbox": [ + 75, + 559, + 470, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 679, + 194, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a framework for solving linear inverse problems with DNN denoisers/diffusers, which uses a novel preconditioned data-fidelity guidance approach, based on traversing from back-projection steps to least squares steps, exploiting the advantages of each. We used the new approach with a computationally convenient trajectory within a \"plug-and-play\" optimization scheme and its DDM sampling-based counterpart, which we devised. The performance advantages of the new technique were shown in various deblurring and super-resolution settings, with and without observation noise. (See the supplementary material for computed tomography experiments as well). As a direction for future research, one can try to learn the precondi", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ada4cc2aa5a7892b2a4aa1bc82e242f4ebe0865bcac01bca1aa108823abb08e.jpg", + "image_caption": [ + "Figure 3. Gaussian deblurring with noise level 0.05. Top row, from left to right: original, observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DPS, DiffPIR, and our DDPG." + ], + "image_footnote": [], + "bbox": [ + 542, + 405, + 846, + 558 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c97fafc1798925cfd8d8183953345bbcdc82d25c5b03f794fd3dee01777496e1.jpg", + "image_caption": [ + "Figure 4. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DDRM, DiffPIR, and our DDPG." + ], + "image_footnote": [], + "bbox": [ + 542, + 627, + 846, + 780 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tioners $\\{\\mathbf{W}_t\\}$ instead of designing them.", + "bbox": [ + 500, + 851, + 769, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. The work is partially supported by ISF grant no. 1940/23.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25252", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shady Abu Hussein, Tom Tirer, and Raja Giryes. Correction filter for single image super-resolution: Robustifying off-the-shelf deep super-resolvers. 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In" + ], + "bbox": [ + 78, + 90, + 468, + 901 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3929-3938, 2017. 2", + "[45] Yuanzhi Zhu, Kai Zhang, Jingyun Liang, Jiezhang Cao, Bihan Wen, Radu Timofte, and Luc Van Gool. Denoising diffusion models for plug-and-play image restoration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1219-1229, 2023. 1, 2, 3, 4, 6, 7, 15, 16", + "[46] Jenny Zukerman, Tom Tirer, and Raja Giryes. Bp-dip: A backprojection based deep image prior. In 2020 28th European Signal Processing Conference (EUSIPCO), pages 675-679, 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 260 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "25254", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/aad8aa4f-e5bd-4107-bdf3-47998cec58ac_model.json b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/aad8aa4f-e5bd-4107-bdf3-47998cec58ac_model.json new file mode 100644 index 0000000000000000000000000000000000000000..48dd1469b8971958330444028b1a577c015b99ad --- /dev/null +++ b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/aad8aa4f-e5bd-4107-bdf3-47998cec58ac_model.json @@ -0,0 +1,2475 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.155, + 0.131, + 0.819, + 0.175 + ], + "angle": 0, + "content": "Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance" + }, + { + "type": "text", + "bbox": [ + 0.249, + 0.205, + 0.452, + 0.257 + ], + "angle": 0, + "content": "Tomer Garber \nOpen University of Israel \ntomergarber@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.205, + 0.722, + 0.257 + ], + "angle": 0, + "content": "Tom Tirer Bar-Ilan University, Israel tirer.tom@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.328, + 0.474, + 0.706 + ], + "angle": 0, + "content": "Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a \"task-specific\" network for each observation model is to use pretrained deep denoisers for imposing only the signal's prior within iterative algorithms, without additional training. Recently, a sampling-based variant of this approach has become popular with the rise of diffusion/score-based generative models. Using denoisers for general purpose restoration requires guiding the iterations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on backprojection (BP) has been shown to be a promising strategy (used recently also under the names \"pseudoinverse\" or \"range/null-space\" guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., it does not require SVD or a large number of iterations). We use it within both an optimization scheme and a sampling-based scheme, and demonstrate its advantages over existing methods for image deblurring and super-resolution." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.21, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.47, + 0.862 + ], + "angle": 0, + "content": "Image restoration problems appear in a wide range of applications, where the goal is to recover a high-quality image \\(\\mathbf{x}^{*}\\in \\mathbb{R}^{n}\\) from its degraded version \\(\\mathbf{y}\\in \\mathbb{R}^{m}\\), which can be noisy, blurry, low-resolution, etc. In many problems, the relation between \\(\\mathbf{y}\\) and \\(\\mathbf{x}^{*}\\) can be expressed using a linear observation model" + }, + { + "type": "equation", + "bbox": [ + 0.223, + 0.882, + 0.47, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = \\mathbf {A} \\mathbf {x} ^ {*} + \\mathbf {e} \\tag {1}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.291, + 0.891, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.498, + 0.894, + 0.541 + ], + "angle": 0, + "content": "Figure 1. Motion deblurring with noise level 0.05. From top to bottom and left to right: original, observation, DPS [6], DiffPIR [45] and our DDPG." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.718 + ], + "angle": 0, + "content": "where \\(\\mathbf{A} \\in \\mathbb{R}^{m \\times n}\\) is a measurement operator with \\(m \\leq n\\), and \\(\\mathbf{e} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_e^2 \\mathbf{I}_m)\\) is an additive white Gaussian noise. For example, in the denoising task \\(\\mathbf{A}\\) is the identity matrix \\(\\mathbf{I}_n\\); in the deblurring task \\(\\mathbf{A}\\) is a blur operator; and in the super-resolution task \\(\\mathbf{A}\\) is a composition of sub-sampling and (anti-aliasing) filtering. Image restoration problems are ill-posed: just looking for \\(\\mathbf{x} \\in \\mathbb{R}^n\\) that fits \\(\\mathbf{y}\\) based on the observation model does not suffice for a successful recovery. Thus, it is required to utilize prior knowledge on the nature of \\(\\mathbf{x}^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Nowadays, it has become common to address these problems by exhaustively training a different deep neural network (DNN) for each predefined observation model in a supervised manner. Namely, using (1) to generate training pairs \\(\\{\\mathbf{y}_i,\\mathbf{x}_i^*\\}\\) and training a DNN to invert the map [8, 18, 34, 43]. However, these \"task-specific\" DNNs suffer from a huge performance drop when the observations at test-time mismatch (even slightly) the assumptions made in training [1, 28, 37], which limits their applicability in many practical cases." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "An alternative approach is to use pretrained DNNs that impose only the signal prior, while the agreement with the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25245" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.333 + ], + "angle": 0, + "content": "observations is being handled at test-time in a \"zero-shot\" manner. A successful choice of such pretrained DNNs are Gaussian denoisers, as was initially demonstrated in different \"plug-and-play\" (PnP) and \"regularization by denoising\" (RED) iterative schemes [25, 36, 40, 44]. The rise of score-based generative modeling [13, 31] — typically referred to as denoising diffusion models (DDMs) — whose inference/sampling \"reversed\" flows are based on iteratively injecting Gaussian noise and denoising, has further increased the popularity of using iterative denoising for general purpose restoration. In particular, operations that promote data-fidelity, similar to those used in PnP/RED, have been used within the diffusion models' iterative sampling schemes to guide the iterations towards an image that not only looks natural but also agrees with the observations [2, 5, 6, 16, 21, 30, 32, 41, 45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.473, + 0.533 + ], + "angle": 0, + "content": "Combining iterative denoising with guidance that is based on back-projection (BP) of intermediate estimates on the subspace \\(\\{\\mathbf{x}:\\mathbf{A}\\mathbf{x} = \\mathbf{y}\\}\\) (more details in Section 2) was originally proposed in [36] (in the context of PnP), and has been shown to be a promising strategy in both the PnP and the DDM literature [5, 11, 19, 26, 27, 30, 37, 41, 46]. In the context of diffusion models it has been rediscovered under the names \"pseudoinverse\" [30] or \"range/null-space\" [41] guidance. However, in cases where \\(\\mathbf{A}\\) has low singular values (e.g., in image deblurring and super-resolution), the presence of noise in the observations \\(\\mathbf{y}\\) hinders the application of this approach: careful regularization is required and the performance gains tend to decrease." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.473, + 0.734 + ], + "angle": 0, + "content": "Contribution. In this paper, we identify the BP step as a preconditioned version of a least squares (LS) gradient step. This inspires us to propose an iteration-dependent preconditioned guidance approach that essentially traverses from the BP step to the LS gradient step along the restoration scheme. Thus, it enjoys benefits of BP step [38, 39], such as stronger consistency with y and accelerated convergence in early iterations, and the better robustness to noise of LS as the scheme approaches its end. The specific trajectory that we devise in this paper is also more simple and efficient to implement than other potential alternatives for BP, which either require having full knowledge on the SVD of A [16], or many neural function evaluations (NFEs) [6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We present formal mathematical motivation for our guidance technique and use it within both a PnP-based scheme and its DDM sampling-based counterpart that we design. We examine the proposed approach for image deblurring and super-resolution on the CelebA-HQ and ImageNet datasets, where we exploit the powerful denoisers of DDMs [7, 20], and demonstrate its advantages over existing methods. In particular, our sampling-based reconstruction approach is flexible to the observation model, computationally convenient, and displays a good combination of perceptual quality and accuracy." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.09, + 0.789, + 0.108 + ], + "angle": 0, + "content": "2. Background and Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.818, + 0.132 + ], + "angle": 0, + "content": "2.1. PnP Denoisers and Back-Projections" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.138, + 0.892, + 0.169 + ], + "angle": 0, + "content": "Traditionally, estimating \\(\\mathbf{x}^*\\) from its measurements (1) has been tackled by minimizing an explicit objective function" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.18, + 0.892, + 0.198 + ], + "angle": 0, + "content": "\\[\nL (\\mathbf {x}) = \\ell (\\mathbf {x}; \\mathbf {y}) + s (\\mathbf {x}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.208, + 0.892, + 0.369 + ], + "angle": 0, + "content": "which is composed of a data-fidelity term \\(\\ell (\\mathbf{x};\\mathbf{y})\\) and a signal prior term \\(s(\\mathbf{x})\\). The PnP concept [40] suggests applying a proximal algorithm to (2), where the proximal mapping associated with the prior function \\(s(\\cdot)\\), i.e., \\(\\mathrm{prox}_s(\\mathbf{x})\\coloneqq \\mathrm{argmin}_{\\mathbf{z}}\\frac{1}{2}\\| \\mathbf{z} - \\mathbf{x}\\|_2^2 +s(\\mathbf{z})\\) [22], is replaced with an off-the-shelf Gaussian denoiser \\(\\mathcal{D}(\\cdot ;\\sigma_t)\\) (\\(\\sigma_{t}\\) denotes the denoiser's noise level) that need not be associated with an explicit prior function (e.g., a pretrained DNN). A vast amount of literature has been dedicated to designing and analyzing PnP algorithms [4, 14, 24, 25, 35, 36, 40, 44]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.37, + 0.892, + 0.4 + ], + "angle": 0, + "content": "A popular PnP scheme based on the proximal-gradient method (PGM) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.412, + 0.891, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {0 \\mid t} = \\mathcal {D} \\left(\\mathbf {x} _ {t}; \\sigma_ {t}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.431, + 0.892, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\nabla_ {\\mathbf {x}} \\ell (\\mathbf {x} _ {0 | t}; \\mathbf {y}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.534 + ], + "angle": 0, + "content": "where \\( t = T, T - 1, \\ldots, 1 \\) is the iteration index (decreases over time, to match the notation in diffusion/score-based models), \\( \\mu_t \\) is a step-size, and \\( \\sigma_T > \\ldots > \\sigma_1 \\) is a predefined decreasing set of noise levels. The scheme is initialized with some \\( \\mathbf{x}_T \\) and the final estimate is given by \\( \\mathbf{x}_{0|1} \\)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.534, + 0.892, + 0.549 + ], + "angle": 0, + "content": "A typical choice of data-fidelity term is the LS objective" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.559, + 0.892, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\ell_ {L S} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\| \\mathbf {A x} - \\mathbf {y} \\| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.597, + 0.797, + 0.613 + ], + "angle": 0, + "content": "for which the gradient step in (4) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.623, + 0.892, + 0.641 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Note though that PnP methods based on LS gradient steps tend to require many iterations [25, 39]. The IDBP method [36] suggests that the data-fidelity guidance, which follows the denoising operation, will be the back-projection (BP) of \\(\\mathbf{x}_{0|t}\\) onto the affine subspace \\(\\{\\mathbf{x}:\\mathbf{A}\\mathbf{x} = \\mathbf{y}\\}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.739, + 0.892, + 0.797 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {t - 1} = \\operatorname {a r g m i n} _ {\\mathbf {x}} \\| \\mathbf {x} - \\mathbf {x} _ {0 | t} \\| _ {2} \\text {s . t .} \\mathbf {A x} = \\mathbf {y} (7) \\\\ = \\mathbf {A} ^ {\\dagger} \\mathbf {y} + \\left(\\mathbf {I} _ {n} - \\mathbf {A} ^ {\\dagger} \\mathbf {A}\\right) \\mathbf {x} _ {0 | t} (8) \\\\ = \\mathbf {x} _ {0 | t} - \\mathbf {A} ^ {\\dagger} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}), (9) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.81, + 0.785, + 0.825 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}^{\\dagger}\\) denotes the pseudoinverse of \\(\\mathbf{A}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "When \\(\\mathbf{A}\\) has near-zero singular values, it has been shown to be beneficial to replace \\(\\mathbf{A}^{\\dagger} = \\mathbf{A}^{T}(\\mathbf{A}\\mathbf{A}^{T})^{\\dagger}\\) with a regularized version \\(\\mathbf{A}^T (\\mathbf{A}\\mathbf{A}^T +\\eta \\mathbf{I}_m)^{-1}\\), where \\(\\eta >0\\) is the regularization hyperparameter [36, 37]. Importantly, note that there are popular tasks where the pseudoinverse can be" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25246" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.196 + ], + "angle": 0, + "content": "implemented efficiently (e.g., see the supplementary material for FFT based implementations of this operation for deblurring and super-resolution). And, in general, full rank \\(\\mathbf{A}\\mathbf{A}^T\\) (and \\(\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m\\) otherwise) can be typically \"inverted\" using few conjugate gradient iterations [12], which only require applying \\(\\mathbf{A}\\) and \\(\\mathbf{A}^T\\) and bypass the need of matrix inversion or SVD." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.197, + 0.471, + 0.243 + ], + "angle": 0, + "content": "As pointed out in [38, 39], (9) is equivalent to a gradient step (4) with step-size \\(\\mu_t = 1\\) and a special choice of \\(\\ell(\\mathbf{x};\\mathbf{y})\\), which they dubbed as the \"BP term\":" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.253, + 0.47, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\ell_ {B P} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\| \\left(\\mathbf {A} \\mathbf {A} ^ {T}\\right) ^ {- 1 / 2} (\\mathbf {A x} - \\mathbf {y}) \\| _ {2} ^ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.47, + 0.412 + ], + "angle": 0, + "content": "These works have analyzed, both empirically and theoretically, the effects of using BP steps (9) rather than LS steps (6) in inverse problems. They show provable faster convergence benefits (less iterations) and, in the low-noise regime, also MSE benefits. However, it is also shown that in the presence of observation noise and \\(\\mathbf{A}\\) with small singular values, we have that \\(\\mathbf{A}^{\\dagger}\\mathbf{y}\\) amplifies the noise. Thus a strong regularization \\(\\eta\\) is needed which hinders the advantages." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.42, + 0.383, + 0.435 + ], + "angle": 0, + "content": "2.2. Restoration via Guidance of DDMs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.653 + ], + "angle": 0, + "content": "Pretrained diffusion/score-based generative models [13, 31, 33] have been shown to be a powerful signal prior for image restoration. These generative models are based on training a network that approximates the score function \\(\\nabla_{\\mathbf{x}_t}\\log p_t(\\mathbf{x}_t)\\), where \\(p_t\\) denotes the distribution of \\(\\mathbf{x}_t\\), a Gaussian noisy version of the data \\(\\mathbf{x}_0\\sim p_0\\) with noise level indexed by \\(t\\in [0,T]\\). For \\(\\mathbf{x}_t = \\mathbf{x}_0 + \\epsilon_t\\) with \\(\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\sigma_t^2\\mathbf{I}_n)\\), by Tweedie's formula \\(-\\sigma_t^2\\nabla_{\\mathbf{x}_t}\\log p_t(\\mathbf{x}_t) = \\mathbf{x}_t - \\mathbb{E}[\\mathbf{x}_0|\\mathbf{x}_t] = \\mathbb{E}[\\epsilon_t|\\mathbf{x}_t]\\) [9]. Therefore, these approaches essentially attempt to learn the MMSE Gaussian denoiser or, equivalently, noise estimation. After training, the sampling schemes are based on random Gaussian initialization and alternatively denoising and injection of Gaussian noise with a decreasing noise level." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.7 + ], + "angle": 0, + "content": "For concreteness, let us focus on the popular DDPM formulation [13]. In DDPM, \\(\\mathbf{x}_t\\) is generated from a data point \\(\\mathbf{x}_0\\) by the \"forward flow\":" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.71, + 0.469, + 0.73 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.469, + 0.788 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)\\) and \\(\\{\\beta_t\\}_{t = 1}^T\\) is a predetermined \"noise schedule\" obeying \\(0 < \\beta_{1} < \\dots < \\beta_{T}\\leq 1\\). By properties of Gaussians, \\(\\mathbf{x}_t\\) can be directly generated from \\(\\mathbf{x}_0\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.797, + 0.469, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "which includes noise variance \\(1 - \\bar{\\alpha}_{t}\\) and signal scale factor \\(\\sqrt{\\bar{\\alpha}_t}\\), where \\(\\bar{\\alpha}_t = \\Pi_{s=1}^t\\alpha_s\\) and \\(\\alpha_t = 1 - \\beta_t\\). In training time, a U-net DNN \\(\\epsilon_{\\theta}(\\cdot ; t)\\) is trained to predict the noise \\(\\epsilon\\) given \\(\\mathbf{x}_t\\) by minimizing an MSE loss. In DDPM's inference time, starting from a random \\(\\mathbf{x}_T \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}_n)\\), one step of" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "the \"reverse flow\" that is used for generating a sample from \\( p_0 \\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.131, + 0.892, + 0.165 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t)\\right) + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.174, + 0.726, + 0.189 + ], + "angle": 0, + "content": "where \\(\\epsilon_{t}\\) is drawn from \\(\\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.189, + 0.892, + 0.235 + ], + "angle": 0, + "content": "A faster generation scheme, denoted DDIM [29], is based on diverging from the Markovian guideline of DDPM. In DDIM, the step (13) is replaced with" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.245, + 0.892, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} \\mathbf {x} _ {0 | t} + \\hat {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t) + \\tilde {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {t}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.271, + 0.674, + 0.287 + ], + "angle": 0, + "content": "where \\(\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)\\) and" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.297, + 0.892, + 0.322 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {t} = \\sqrt {1 - \\bar {\\alpha} _ {t - 1} - \\tilde {\\sigma} _ {t} ^ {2}}, \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.325, + 0.892, + 0.357 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {0 \\mid t} = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} \\left(\\mathbf {x} _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t)\\right). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.364, + 0.892, + 0.466 + ], + "angle": 0, + "content": "The hyperparameter \\(\\tilde{\\sigma}_t\\) allows trading between the levels of two noise terms: the estimated noise \\(\\epsilon_{\\theta}(\\mathbf{x}_t;t)\\) and a pure stochastic noise \\(\\epsilon_t\\). Moreover, \\(\\mathbf{x}_{0|t}\\) in (16) is an estimate of \\(\\mathbf{x}_0\\) given \\(\\mathbf{x}_t\\), which is essentially performing Gaussian denoising: \\(\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}}\\mathcal{D}(\\mathbf{x}_t;\\sigma_t = \\sqrt{1 - \\bar{\\alpha}_t})\\), as implied by (12)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Many of the methods that use DDMs as priors for image restoration [16, 30, 41, 45] are based on the DDIM scheme [29]. Yet, in order that the sampling scheme will produce an image that is not only perceptually pleasing but also agrees with the measurements \\(\\mathbf{y}\\) and the observation model (1) it is required to equip the iterations with some data-fidelity guidance. This guidance is typically based on the gradient of a data-fidelity term \\(\\ell (\\mathbf{x};\\mathbf{y})\\). In other words, the iterations (14) are modified into" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.614, + 0.892, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} \\mathbf {x} _ {0 | t} - \\mu_ {t} \\nabla_ {\\mathbf {x}} \\ell \\left(\\mathbf {x} _ {0 | t}; \\mathbf {y}\\right) + \\hat {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {x} _ {t}; t\\right) + \\tilde {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {t}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.645, + 0.762, + 0.659 + ], + "angle": 0, + "content": "where \\(\\mu_t\\) is the guidance scaling factor." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Note the similarity between the PnP restoration (3)-(4) and the DDM restoration (16)-(17). Namely, ignoring the scaling of the signal by \\(\\{\\bar{\\alpha}_t\\}\\), the main difference is the noise injection, composed of the estimated noise \\(\\epsilon_{\\theta}\\) and the random noise \\(\\epsilon_t\\). The similarity of DDMs schemes to previous iterative denoising methods is further seen by the formulation of [15], which decouples the diffusion \"forward\" flows, used for training the denoisers, from the \"reverse\" inference flows. More discussion on such connections can be found in a recent review paper [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For example, the DDM restoration method in [6], dubbed DPS, where the guidance is based on the gradient of the LS term, resembles (6) with noise injection. Interestingly, just like its PnP counterpart, it requires a very large number of iterations (and thus many NFEs). Alternatively, by using BP guidance in (17) — equivalently, when injecting noise" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25247" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.468, + 0.182 + ], + "angle": 0, + "content": "to step (9) in IDBP — one gets the recent DDNM method [41] (which is also similar to the method in [30]). However, note that the DDNM paper focuses on noiseless settings and has difficulties in noisy settings (in Section 4 we state its technical limitation), which is aligned with the sensitivity of BP guidance to noise in \\(\\mathbf{y}\\), as mentioned above." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.182, + 0.468, + 0.317 + ], + "angle": 0, + "content": "At this point, we would also like to mention the DDRM method [16], which resembles the BP approach as it generates \"spectral space\" measurements \\(\\bar{\\mathbf{y}}\\) in a way similar to applying \\(\\mathbf{A}^{\\dagger}\\) on \\(\\mathbf{y}\\). Yet, it is more robust to observation noise as it requires access to the full SVD of \\(\\mathbf{A}\\), which allows it to mitigate noise amplification per singular component in each iteration. In this paper we aim to devise an approach that does not require computing and storing the SVD of \\(\\mathbf{A}\\), which is impractical is most cases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.468, + 0.439 + ], + "angle": 0, + "content": "Finally, we note that the way we construct a sampling scheme from a deterministic algorithm shares similarity with the recent method DIfPIR [45]. However, while [45] uses an existing PnP baseline, here we propose a novel core reconstruction method. Also, empirically our new sampling scheme demonstrates better accuracy than DiffPIR (evaluated by PSNR) without compromising on perceptual quality (evaluated by LPIPS)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.452, + 0.288, + 0.469 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.468, + 0.597 + ], + "angle": 0, + "content": "In this section, we present our image restoration method that is more robust to observation noise than methods that use only back-projections while still having low computational complexity and clear benefits over methods that are based only on plain LS based guidance. To this end, we present a novel core guidance approach, equip it with formal theoretical motivation, and utilize it to devise a new sampling-based reconstruction scheme." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.468, + 0.629 + ], + "angle": 0, + "content": "All the claims in this section are proved in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.639, + 0.228, + 0.655 + ], + "angle": 0, + "content": "3.1. Core approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.468, + 0.692 + ], + "angle": 0, + "content": "The idea for our approach comes from identifying (9) as a specific instance of the formula" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.703, + 0.468, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} \\mathbf {W} (\\mathbf {A x} _ {0 | t} - \\mathbf {y}) \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.468, + 0.779 + ], + "angle": 0, + "content": "with \\(\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T)^{-1}\\) (assuming full rank \\(\\mathbf{A}\\)) and \\(\\mu_t = 1\\). The plain LS step (6) is obviously also an instance of this expression with \\(\\mathbf{W} = \\mathbf{I}_m\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Recall traditional preconditioning in optimization [23]: The optimization of an objective, e.g., \\( L: \\mathbb{R}^n \\to \\mathbb{R} \\) in (2), is based on gradient-based optimizers where the full gradient \\( \\nabla L(\\mathbf{x}) \\) is multiplied by a (symmetric) positive definite matrix \\( \\mathbf{P} \\in \\mathbb{R}^{n \\times n} \\). Such practice does not affect the problem's minimizers (since \\( \\mathbf{P} \\nabla L(\\mathbf{x}) = \\mathbf{0} \\iff \\nabla L(\\mathbf{x}) = \\mathbf{0} \\) due to the invertibility of \\( \\mathbf{P} \\)), and its goal is to ease the optimization landscape, characterized by the condition number" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.152 + ], + "angle": 0, + "content": "of the effective Hessian \\(\\mathbf{P}^{1 / 2}\\nabla^2 L(\\mathbf{x})\\mathbf{P}^{1 / 2}\\). In (18), however, \\(\\mathbf{W}\\in \\mathbb{R}^{m\\times m}\\) does not directly affect the signal's prior and for general \\(\\mathbf{W}\\) we may not have \\(\\mathbf{A}^T\\mathbf{W}(\\mathbf{A}\\mathbf{x} - \\mathbf{y}) = \\mathbf{0}\\iff \\nabla \\ell_{LS}(\\mathbf{x}) = \\mathbf{A}^T (\\mathbf{A}\\mathbf{x} - \\mathbf{y}) = \\mathbf{0}\\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.153, + 0.81, + 0.167 + ], + "angle": 0, + "content": "Nevertheless, we have the following claims." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.175, + 0.892, + 0.206 + ], + "angle": 0, + "content": "Claim 3.1. Let \\(\\mathbf{A} \\in \\mathbb{A}^{m \\times n}\\) with \\(m \\leq n\\) and \\(\\operatorname{rank}(\\mathbf{A}) = m\\). Let \\(\\mathbf{W} \\in \\mathbb{R}^{m \\times m}\\) such that \\(\\operatorname{rank}(\\mathbf{A}^T \\mathbf{W}) = m\\). Then," + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.215, + 0.855, + 0.233 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} ^ {T} \\mathbf {W} (\\mathbf {A x} - \\mathbf {y}) = \\mathbf {0} \\iff \\mathbf {A} ^ {T} (\\mathbf {A x} - \\mathbf {y}) = \\mathbf {0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.302 + ], + "angle": 0, + "content": "Claim 3.2. Let \\(\\mathbf{A} \\in \\mathbb{A}^{m \\times n}\\) with \\(m \\leq n\\). Let \\(\\mathbf{W} \\in \\mathbb{R}^{m \\times m}\\) be a positive definite matrix that shares eigenbasis with \\(\\mathbf{A A}^T\\). Then, there exists a positive definite \\(\\mathbf{P} \\in \\mathbb{R}^{n \\times n}\\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.301, + 0.791, + 0.318 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} ^ {T} \\mathbf {W} \\mathbf {A} = \\mathbf {P} ^ {1 / 2} \\mathbf {A} ^ {T} \\mathbf {A} \\mathbf {P} ^ {1 / 2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Therefore, if \\(\\mathbf{A}\\) is full rank, then any \\(\\mathbf{W}\\) for which \\(\\mathbf{A}^T\\mathbf{W}\\) is full rank (e.g., \\(\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T)^{-1}\\)) can be interpreted as a preconditioner of \\(\\nabla \\ell_{LS}\\) (rather than of the full objective that may include additional terms). Alternatively, even if \\(\\mathbf{A}\\) is not full rank, but \\(\\mathbf{W}\\) shares eigenbasis with \\(\\mathbf{A}\\mathbf{A}^T\\) (e.g., \\(\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m)^{-1}\\)), we allow ourselves to refer to \\(\\mathbf{W}\\) as a preconditioner of \\(\\nabla \\ell_{LS}\\) since it has the same effect on the effective Hessian, \\(\\mathbf{P}^{1/2}\\nabla^2\\ell_{LS}(\\mathbf{x})\\mathbf{P}^{1/2}\\), as a traditional preconditioner \\(\\mathbf{P}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.891, + 0.495 + ], + "angle": 0, + "content": "Inspired by this, in lieu of (4) we propose a data-fidelity guidance based on iteration-dependent preconditioner:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.504, + 0.891, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} \\mathbf {W} _ {t} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}) \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.592 + ], + "angle": 0, + "content": "with a \"smooth\" discretization of the path of symmetric preconditioners \\(\\{\\mathbf{W}_t\\}\\) — invertible with eigenbasis shared with \\(\\mathbf{A}\\mathbf{A}^T\\) — that starts roughly at \\(\\mathbf{W}_T \\propto (\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m)^{-1}\\) and ends roughly at \\(\\mathbf{W}_0 \\propto \\mathbf{I}_m\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.682 + ], + "angle": 0, + "content": "In words, the proposed guidance is based on gently traversing from the (regularized) BP step to the LS step along the restoration scheme. Thus, it enjoys benefits of BP steps (stronger consistency with \\(\\mathbf{y}\\), accelerated convergence, etc.) in early iterations and the better robustness to noise of LS steps as the scheme approaches its end." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Potentially, a sequence of preconditioners \\(\\{\\mathbf{W}_t\\}\\) might be learned in a data-driven manner under some optimality criterion. Yet, this is expected to come at the price of losing their generality to arbitrary data. Thus, here we propose an engineered, but simple and effective, update rule of \\(\\mathbf{W}_t\\) that, as we will show empirically, already demonstrates the usefulness of our new concept. Specifically, the rule that we propose is given by the following convex combination:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.812, + 0.891, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} _ {t} = (1 - \\delta_ {t}) \\left(\\mathbf {A} \\mathbf {A} ^ {T} + \\eta \\mathbf {I} _ {m}\\right) ^ {- 1} + \\delta_ {t} c \\mathbf {I} _ {m} \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.891, + 0.87 + ], + "angle": 0, + "content": "where \\(0 \\leq \\delta_T < \\ldots < \\delta_0 \\leq 1\\) is a predefined sequence, and \\(c\\) is a positive scalar that balances the two terms." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In general, the main motivation for (20) is that it both obeys the previously stated conditions and also yields a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25248" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "data-fidelity guidance that is very simple to implement. Indeed, plugging (20) in (19) yields" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.133, + 0.469, + 0.17 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\left((1 - \\delta_ {t}) \\mathbf {g} _ {B P} (\\mathbf {x} _ {0 | t}) + \\delta_ {t} \\mathbf {g} _ {L S} (\\mathbf {x} _ {0 | t})\\right), \\\\ =: \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {g} _ {\\delta_ {t}} \\left(\\mathbf {x} _ {0 | t}\\right) \\tag {21} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.183, + 0.124, + 0.195 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.207, + 0.469, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\mathbf {g} _ {B P} \\left(\\mathbf {x} _ {0 | t}\\right) = \\mathbf {A} ^ {T} \\left(\\mathbf {A} \\mathbf {A} ^ {T} + \\eta \\mathbf {I} _ {m}\\right) ^ {- 1} \\left(\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}\\right), \\tag {22}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.228, + 0.469, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\mathbf {g} _ {L S} \\left(\\mathbf {x} _ {0 | t}\\right) = c \\mathbf {A} ^ {T} \\left(\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}\\right), \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.258, + 0.469, + 0.287 + ], + "angle": 0, + "content": "can be computed efficiently for a wide range of observation models." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.289, + 0.469, + 0.364 + ], + "angle": 0, + "content": "In Section 3.4 we will discuss practical implementations details for simple hyperparameter tuning (e.g., a simple way to tune \\(\\{\\delta_t\\}\\)). As for setting \\(c\\), observe that (19) is essentially a gradient step (at \\(\\mathbf{x}_{0|t}\\)) of the weighted least squares (WLS) data-fidelity term:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.375, + 0.469, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\ell_ {W L S, t} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\left\\| \\mathbf {W} _ {t} ^ {1 / 2} (\\mathbf {A x} - \\mathbf {y}) \\right\\| _ {2} ^ {2}, \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.414, + 0.356, + 0.43 + ], + "angle": 0, + "content": "for which we have the following property." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.439, + 0.469, + 0.484 + ], + "angle": 0, + "content": "Claim 3.3. Denote by \\(\\lambda_{1}\\) the largest singular value of \\(\\mathbf{A}\\). Let \\(c \\leq 1 / \\lambda_1^2\\). Then, the update (21) with \\(\\mu_t = 1\\) ensures reduction in (24)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.495, + 0.469, + 0.556 + ], + "angle": 0, + "content": "Many popular degradation models obey \\(\\lambda_1 \\lesssim 1\\) (e.g., in deblurring \\(\\lambda_1 = 1\\) and in super-resolution \\(\\lambda_1\\) is moderately lower than 1). Thus, following the claim, unless stated otherwise, we use \\(c = 1\\) and \\(\\mu_t = 1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.469, + 0.723 + ], + "angle": 0, + "content": "To conclude this subsection, the core of the proposed algorithm is based on iteratively computing (3) and (21). Without noise injection, this is essentially a novel PnP scheme, which we call Iterative Denoising and Preconditioned Guidance (IDPG). As we will empirically show in Section 4, while this method has good PSNR performance, turning it into a DDM-based sampling scheme leads to better recoveries, especially in terms of perceptual quality. Before presenting the sampling scheme in Section 3.3, let us provide some theoretical motivation for our preconditioned guidance approach." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.732, + 0.171, + 0.748 + ], + "angle": 0, + "content": "3.2. Theory" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Let us state some mathematical claims that motivate the core guidance approach. In this subsection we consider a simplified setting of having a fixed \\(0 < \\delta < 1\\), i.e., a fixed WLS data-fidelity term (24) with \\(\\mathbf{W}\\) given as in (20) but with \\(\\delta_t = \\delta\\). We examine the effects of this WLS, compared to LS and BP fidelity terms, on an estimator of \\(\\mathbf{x}^*\\), denoted by \\(\\hat{\\mathbf{x}}\\), which is obtained by minimizing (2) with Tikhonov prior \\(s(\\mathbf{x}) = \\frac{\\beta}{2} \\| \\mathbf{Dx} \\|_2^2\\), where \\(\\beta > 0\\) and \\(\\mathbf{D}^T \\mathbf{D}\\) is invertible, so, the estimator \\(\\hat{\\mathbf{x}}\\) per data-fidelity term is unique." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "The MSE of \\(\\hat{\\mathbf{x}}\\) (conditioned on \\(\\mathbf{x}^*\\), averaged over the noise e) can be decomposed into two terms: squared bias, \\(b^{2}\\) (independent of e), and variance, \\(v\\) (depends on \\(\\sigma_e^2\\)), given by" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.144, + 0.891, + 0.161 + ], + "angle": 0, + "content": "\\[\nb ^ {2} := \\left\\| \\mathbb {E} \\left[ \\hat {\\mathbf {x}} \\mid \\mathbf {x} ^ {*} \\right] - \\mathbf {x} ^ {*} \\right\\| _ {2} ^ {2}, \\tag {25}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.164, + 0.891, + 0.18 + ], + "angle": 0, + "content": "\\[\nv := \\operatorname {T r} \\left(\\operatorname {V a r} \\left(\\hat {\\mathbf {x}} \\mid \\mathbf {x} ^ {*}\\right)\\right). \\tag {26}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.187, + 0.892, + 0.368 + ], + "angle": 0, + "content": "The motivation for analyzing this setting (even though in the proposed core procedure (3) & (21), we modify \\(\\delta_t\\) along the iterations and do not attempt to reach a minimizer per \\(\\delta_t\\)) is that insights on gains in bias and variance at the minimizer level hint that similar effects are possible even with limited optimizer iterations per \\(\\delta_t\\). Also, in [38], it was shown that insights gained for Tikhonov prior generalize empirically to more complex priors. Specifically, they showed that BP typically leads to smaller bias but higher variance than LS. In what follows, the intuition that \\(0 < \\delta < 1\\) enables trading bias and variance is made formal." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.376, + 0.892, + 0.417 + ], + "angle": 0, + "content": "Theorem 3.4. Consider the observation model (1) and estimating \\(\\mathbf{x}^*\\) via minimization of (2) with \\(s(\\mathbf{x}) = \\frac{\\beta}{2}\\|\\mathbf{D}\\mathbf{x}\\|_2^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.417, + 0.892, + 0.479 + ], + "angle": 0, + "content": "Assume that: (a) \\(\\mathbf{A}^T\\mathbf{A}\\) and \\(\\mathbf{D}^T\\mathbf{D} \\succ 0\\) share eigenbasis; (b) the singulars value of \\(\\mathbf{A}\\) are in \\((0,1]\\), and not all equal (common case); (c) \\(\\eta = 0\\) and \\(c = 1\\). Then, \\(b_{BP} < b_{WLS} < b_{LS}\\), and \\(v_{LS} < v_{WLS} < v_{BP}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.559 + ], + "angle": 0, + "content": "Note that the margins in the theorem's inequalities depend on where \\(\\delta\\) is located in \\((0,1)\\) (e.g., \\(v_{\\mathrm{WLS}} \\to v_{\\mathrm{LS}}\\) for \\(\\delta \\to 1\\)). This further motivates having a set \\(\\{\\delta_t\\}\\) instead of a fixed \\(\\delta\\) in (20) to gain flexibility in handling the error's bias/variance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.727 + ], + "angle": 0, + "content": "As for the convergence rates of first-order optimization algorithms (which affect the number of NFEs with practical DNN-based priors), recall that it can typically be characterized by the condition number, \\(\\kappa(\\cdot)\\), of the problem's Hessian, which equals the ratio between the largest and smallest eigenvalues of the Hessian — the lower the better. Note, though, that for \\(m < n\\), the Hessian of each of the three data-fidelity terms (LS, BP, WLS) is rank-deficient due to the ill-posedness of the observation model. Nevertheless, we have the following property on the component of their Hessian in the row-range of \\(\\mathbf{A}\\) (a subspace in \\(\\mathbb{R}^n\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Claim 3.5. Assume that \\(\\mathrm{rank}(\\mathbf{A}) = m\\), the singular values of \\(\\mathbf{A}\\) are not all equal, \\(\\eta = 0\\), and denote by \\(\\mathbf{V} \\in \\mathbb{R}^{n \\times m}\\) an orthonormal basis for the row-range of \\(\\mathbf{A}\\). We have that" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.785, + 0.894, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {B P} \\mathbf {V}) < \\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {W L S} \\mathbf {V}) < \\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {L S} \\mathbf {V}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Namely, the flexibility in \\(\\delta\\) allows accelerating the reconstruction procedure compared to using only a LS based guidance. Leveraging this result to establish ranking claims for specific algorithms may follow the approaches of [39] (based on constraints on the null space of \\(\\mathbf{A}\\) that are implicitly imposed by the signal prior term)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25249" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.078, + 0.091, + 0.47, + 0.121 + ], + "angle": 0, + "content": "Algorithm 1 Denoising Diffusion with iterative Preconditioned Guidance (DDPG)" + }, + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.124, + 0.47, + 0.449 + ], + "angle": 0, + "content": "Require: \\(\\epsilon_{\\theta}(\\cdot ,t)\\) (noise estimator), \\(T,\\mathbf{y},\\mathbf{A},\\{\\bar{\\alpha}_t\\} ,\\{\\mu_t\\} ,c,\\) \\(\\eta ,\\gamma ,\\zeta\\) 1: if \\(\\sigma_e > 0\\) then 2: \\(\\delta_t = \\bar{\\alpha}_t^\\gamma\\) and \\(w_{t} = \\delta_{t}\\) 3: else 4: \\(\\delta_t = 0\\) and \\(w_{t} = 1\\) 5: end if 6: Initialize \\(\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)\\) 7: for \\(t\\) from \\(T\\) to 1 do 8: \\(\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}}\\left(\\mathbf{x}_t - \\sqrt{1 - \\bar{\\alpha}_t}\\epsilon_\\theta (\\mathbf{x}_t,t)\\right)\\) 9: \\(\\mathbf{g}_{BP} = \\mathbf{A}^T (\\mathbf{A}\\mathbf{A}^T +\\eta \\mathbf{I}_m)^{-1}(\\mathbf{A}\\mathbf{x}_{0|t} - \\mathbf{y})\\) 10: \\(\\mathbf{g}_{LS} = c\\mathbf{A}^T (\\mathbf{A}\\mathbf{x}_{0|t} - \\mathbf{y})\\) 11: \\(\\tilde{\\mathbf{x}}_{t - 1} = \\mathbf{x}_{0|t} - \\mu_t((1 - \\delta_t)\\mathbf{g}_{BP} + \\delta_t\\mathbf{g}_{LS})\\) 12: \\(\\hat{\\epsilon}_t = \\frac{1}{\\sqrt{1 - \\bar{\\alpha}_t}} (\\mathbf{x}_t - \\sqrt{\\bar{\\alpha}_t}\\tilde{\\mathbf{x}}_{t - 1})\\) 13: \\(\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)\\) 14: \\(\\mathbf{x}_{t - 1} =\\) 15: \\(\\sqrt{\\bar{\\alpha}_{t - 1}}\\tilde{\\mathbf{x}}_{t - 1} + \\sqrt{1 - \\bar{\\alpha}_{t - 1}}\\left(w_t\\sqrt{1 - \\zeta}\\hat{\\epsilon}_t + \\sqrt{\\zeta}\\epsilon_t\\right)\\) 16: end for 17: return \\({\\bf x}_0\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.481, + 0.248, + 0.497 + ], + "angle": 0, + "content": "3.3. Sampling scheme" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.686 + ], + "angle": 0, + "content": "As previously mentioned, in this subsection we turn IDPG (alternating (3) and (21)) into a DDM-based sampling scheme that empirically leads to better recoveries, especially in terms of perceptual quality. Injecting noise to the estimate in a certain iteration leads to an image that better matches the data on which the denoiser has been trained. Intuitively, this should improve the denoiser's performance and also allow it to mitigate error propagation along the iterations, by masking artifacts with noise that will be removed. Accordingly, it allows using a smaller value of the regularization parameter \\(\\eta\\) when handling noisy \\(\\mathbf{y}\\), which yields results with sharper details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.794 + ], + "angle": 0, + "content": "The sampling scheme that we propose is based on modification of the DDIM guided scheme, stated in (17). Namely, \\(\\mathbf{x}_{0|t}\\) is computed using a DDM's noise estimator as in (16) and the novel guidance \\(\\mathbf{g}_{\\delta_t}\\) is being used in lieu of the abstract gradient \\(\\nabla_{\\mathbf{x}}\\ell\\). However, we propose several important modifications of the additive noise terms \\(\\hat{\\sigma}_t\\epsilon_\\theta (\\mathbf{x}_t;t) + \\tilde{\\sigma}_t\\epsilon_t\\) that appear in (17)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.902 + ], + "angle": 0, + "content": "The first modification is inspired by [45]. Note that, contrary to the unconditional image generation task, the data-fidelity guidance can significantly modify the estimated signal \\(\\tilde{\\mathbf{x}}_{t - 1}\\coloneqq \\mathbf{x}_{0|t} - \\mu_t\\mathbf{g}_{\\delta_t}\\) compared to \\(\\mathbf{x}_{0|t}\\). Therefore, the effective predicted noise can be significantly different than \\(\\epsilon_{\\theta}(\\mathbf{x}_t;t)\\). Accordingly, based on the relation between \\(\\epsilon_{\\theta}(\\mathbf{x}_t;t)\\) and \\(\\mathbf{x}_{0|t}\\) in (16), the effective predicted noise takes" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.58, + 0.106 + ], + "angle": 0, + "content": "the form of" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.115, + 0.892, + 0.148 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {\\epsilon}} _ {t} = \\frac {1}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\left(\\mathbf {x} _ {t} - \\sqrt {\\bar {\\alpha} _ {t}} \\tilde {\\mathbf {x}} _ {t - 1}\\right), \\tag {27}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.16, + 0.856, + 0.175 + ], + "angle": 0, + "content": "and we use it instead of \\(\\epsilon_{\\theta}(\\mathbf{x}_t;t)\\) for generating \\(\\mathbf{x}_{t - 1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.176, + 0.892, + 0.29 + ], + "angle": 0, + "content": "Similarly to this prior work, we also simplify the way of trading between the (effective) estimated noise and the stochastic noise. Instead of time-dependent noise level \\(\\tilde{\\sigma}_t\\) which affects \\(\\hat{\\sigma}_t = \\sqrt{1 - \\bar{\\alpha}_{t-1} - \\tilde{\\sigma}_t^2}\\) in a complicated way, we balance between the levels of \\(\\hat{\\epsilon}_t\\) and \\(\\epsilon_t\\) using the simple to tune weight \\(\\sqrt{1 - \\zeta}\\) and \\(\\sqrt{\\zeta}\\), respectively, with a single hyperparameter \\(\\zeta \\in [0,1]\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.395 + ], + "angle": 0, + "content": "Our key novel modification is the following. In the case of observation noise (i.e., \\(\\sigma_{e} > 0\\)), the effective predicted noise \\(\\hat{\\epsilon}_{t}\\) may not be useful in iterations where the overall guidance \\(\\mathbf{g}_{\\delta_t}\\) is dominated by \\(\\mathbf{g}_{BP}\\), due to the sensitivity to noise of the BP guidance. Therefore, we scale it by \\(\\delta_{t}\\) — the weight that is given to \\(\\mathbf{g}_{LS}\\), which is more robust to observation noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.517 + ], + "angle": 0, + "content": "We remark that our sampling scheme transfers smoothly to the noiseless case, where one can simply use pure BP guidance – or equivalently \\(\\delta_t = 0\\): it is only required to omit the last modification (i.e., avoid attenuating the noise injection by \\(\\delta_t\\)). As will be shown empirically, this scheme performs on par with BP-based DDM methods that are specifically devised for noiseless observations, and outperforms other methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.593 + ], + "angle": 0, + "content": "The resulted DDM-based sampling algorithm, that we name Denoising Diffusion with iterative Preconditioned Guidance (DDPG), is summarized in Algorithm 1. The algorithm includes a simple way to set \\(\\{\\delta_t\\}\\) that is explained in the next subsection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.715, + 0.621 + ], + "angle": 0, + "content": "3.4. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.734 + ], + "angle": 0, + "content": "In the experimental section, we wish to test the approach (both DDPG and its core version IDPG) with powerful DDM's denoisers trained and used in [7, 20]. These models are based on DDPM formulation [13, 29], that we use to reduce the hyperparameter tuning effort in all our examined tasks, and in particular setting \\(\\{\\delta_t\\}\\) for noisy observations. (Recall that in the noiseless case, we simply set \\(\\delta_t = 0\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As presented in Section 2, in DDPM there are the parameters \\(\\{\\bar{\\alpha}_t\\}\\), which are determined by the hyperparameters \\(\\{\\beta_t\\}\\), and determine many other parameters (e.g., the model's noise levels \\(\\{\\sigma_t\\}\\)). These \\(\\{\\bar{\\alpha}_t\\}\\) obey \\(0_+ \\approx \\bar{\\alpha}_T < \\ldots < \\bar{\\alpha}_0 = 1\\). We do not change \\(\\{\\beta_t\\}\\) and \\(\\{\\bar{\\alpha}_t\\}\\) at all compared to previous methods that we compare with [16, 41]. In fact, we use \\(\\{\\bar{\\alpha}_t\\}\\) to set \\(\\delta_t = \\bar{\\alpha}_t^\\gamma\\) with a single positive scalar hyperparameter \\(\\gamma\\). This ensures that as \\(t\\) decreases, \\(\\{\\delta_t\\}\\) is monotonically increasing from 0 to 1 in rate that can be controlled by \\(\\gamma\\). Observe that smaller \\(\\gamma\\) yields higher intermediate \\(\\bar{\\alpha}_t^\\gamma\\) and thus a larger portion of \\(\\{\\mathbf{W}_t\\}\\) closer to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "25250" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "identity matrix — or, equivalently, \"faster\" progress from BP to LS. This is beneficial for larger observation noise \\(\\sigma_{e}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.123, + 0.47, + 0.182 + ], + "angle": 0, + "content": "To conclude, when using \\( c = 1 \\) and \\( \\mu_t = 1 \\), applying our approach requires tuning only \\( \\eta, \\gamma \\) and \\( \\zeta \\) (for DDPG). Note that, potentially, tuning more hyperparameters for our method can further boost its results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.201, + 0.21, + 0.218 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.227, + 0.47, + 0.452 + ], + "angle": 0, + "content": "In this section, we examine the performance of our approach. We start with examining our core guidance, as reflected in IDPG, compared to its extreme cases: deterministic methods with pure BP and LS based guidance. Then, we compare both IDPG and DDPG to existing methods: DDRM [16], DPS [6], DDNM [41], and DiffPIR [45]. We consider the CelebA-HQ 1K and ImageNet 1K test sets, where for fair comparison all the methods use the same pretrained DDM's denoisers: the model from [20] trained on CelebA-HQ and the (unconditional) model from [7] trained on ImageNet. We use \\( T = 100 \\) iterations for each of the methods as in [41]. An exception is DPS, which requires \\( T = 1000 \\) iterations with much larger per-iteration complexity, making it extremely slow compared to others. All the methods are initialized with the same random \\( \\mathbf{x}_T \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.68 + ], + "angle": 0, + "content": "We consider image deblurring and super-resolution tasks that have been widely examined in the previous works, and for each method we use the hyperparameter settings suggested by its authors. The settings for our methods are stated in the supplementary material. Specifically, we consider super-resolution with bicubic downsampling and scale factor 4 and deblurring with Gaussian kernel as, e.g., in [16, 41]. However, we also examine challenging noisy deblurring with random motion kernels, as in [45]. This is an example for a common task that cannot be handled by DDRM [16], which is limited to separable kernels for which the SVD of \\(\\mathbf{A}\\) can be efficiently computed and stored. This task cannot be addressed also by DDNM [41], which fails to tackle noisy observations. We examine the noisy cases also in the two aforementioned tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.469, + 0.788 + ], + "angle": 0, + "content": "In the supplementary material, we demonstrate the advantages of our approach over recent task-specific DNNs, as well as its superior performance also with lower noise level than demonstrated here. In addition, we report there the impressive performance of our approach for sparse-view computed tomography (another task where computing the SVD of \\(\\mathbf{A}\\) is infeasible)." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Data-fidelity guidance ablation: super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.129, + 0.882, + 0.217 + ], + "angle": 0, + "content": "
TaskPGM-LSIDBPIDPG (ours)
Bicub. SRx4 σe=032.40 / 0.12732.66 / 0.11132.66 / 0.111
Bicub. SRx4 σe=0.0528.91 / 0.20928.95 / 0.22929.89 / 0.155
Gauss. Deb. σe=032.25 / 0.14145.58 / 0.00245.58 / 0.002
Gauss. Deb. σe=0.0528.61 / 0.19130.55 / 0.15031.08 / 0.150
Gauss. Deb. σe=0.127.89 / 0.23928.29 / 0.22629.28 / 0.146
" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.229, + 0.845, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.389, + 0.892, + 0.444 + ], + "angle": 0, + "content": "Figure 2. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our DDPG. Bottom row, from left to right: PGM-LS, IDBP, and our IDPG (baseline for DDPG)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.763, + 0.484 + ], + "angle": 0, + "content": "4.1. Examining the core approach" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.491, + 0.892, + 0.596 + ], + "angle": 0, + "content": "As the main contribution of our paper is the novel guidance approach that smoothly traverses from BP to LS guidance, we start with examining our baseline IDPG method (alternating (3) and (21)) with IDBP [36] (\\(\\delta_t = 0\\)) and a method with LS based updates (\\(\\delta_t = 1\\)), denoted here by PGM-LS (a common PnP scheme [14]). This comparison essentially provides an ablation study for our core approach." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.597, + 0.892, + 0.732 + ], + "angle": 0, + "content": "The results for bicubic super-resolution and Gaussian deblurring with various and without noise for the CelebA-HQ 1K test set are presented in Table 1. They show that IDPG consistently outperforms IDBP and PGM-LS. Figure 2 displays qualitative results, showing that IDPG has less artifacts than IDBP and finer details than PGM-LS. Yet, while IDPG provides high PSNR values its perceptual quality can be improved by using the sampling-based DDPG, as shown in this figure." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.785, + 0.758 + ], + "angle": 0, + "content": "4.2. Comparison with other methods" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We turn to compare the proposed approach to DDRM, DPS, DDNM and DiffPIR. We consider all deblurring and superresolution tasks that have been described above with various noise levels. The results for the CelebA-HQ 1K test set and the ImageNet 1K test set are presented in Table 2 and Table 3, respectively. We present qualitative results for motion deblurring, Gaussian deblurring and super-resolution in Figures 1, 3 and 4, respectively. More results appear in the supplementary material." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.803, + 0.469, + 0.839 + ], + "angle": 0, + "content": "1Using the same hardware, DPS takes a dozen minutes per image compared to a couple of seconds of the other methods, and limiting it to 100 iterations fails to produce meaningful recoveries." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.839, + 0.469, + 0.9 + ], + "angle": 0, + "content": "2Note that DDMN is tailored for \\(\\sigma_{e} = 0\\). We remark that DDNM+ that was proposed in [41] for handling noisy \\(\\mathbf{y}\\) (via SVD) seems to be heavily tied to a specific downsampling task (without bicubic kernel) and does not support the considered tasks, as shown in the supplementary material. Our efforts to adapt it failed." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.803, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25251" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 2. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text)." + }, + { + "type": "table", + "bbox": [ + 0.166, + 0.125, + 0.803, + 0.246 + ], + "angle": 0, + "content": "
Task\\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=031.64 / 0.05429.39 / 0.06530.26 / 0.05131.64 / 0.04832.66 / 0.11131.60 / 0.052
Bicub. SRx4 σe=0.0529.26 / 0.09027.49 / 0.08627.44 / 0.085N/A29.89 / 0.15529.39 / 0.105
Gauss. Deb. σe=042.49 / 0.00631.25 / 0.05532.97 / 0.04145.56 / 0.00245.58 / 0.00245.46 / 0.002
Gauss. Deb. σe=0.0530.53 / 0.07427.75 / 0.08428.89 / 0.074N/A31.08 / 0.15030.41 / 0.068
Gauss. Deb. σe=0.128.79 / 0.08826.67 / 0.09727.59 / 0.083N/A29.28 / 0.14629.18 / 0.080
Motion Deb. σe=0.05N/A19.63 / 0.22727.96 / 0.102N/A29.73 / 0.13429.02 / 0.082
Motion Deb. σe=0.1N/A19.64 / 0.23126.23 / 0.132N/A27.86 / 0.16627.74 / 0.099
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.258, + 0.893, + 0.288 + ], + "angle": 0, + "content": "Table 3. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on Imagenet 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text)." + }, + { + "type": "table", + "bbox": [ + 0.166, + 0.295, + 0.803, + 0.387 + ], + "angle": 0, + "content": "
Task\\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=027.38 / 0.27025.56 / 0.23626.99 / 0.22527.45 / 0.24527.20 / 0.32627.41 / 0.255
Bicub. SRx4 σe=0.0525.54 / 0.33324.05 / 0.27124.65 / 0.318N/A25.51 / 0.41125.55 / 0.354
Gauss. Deb. σe=040.53 / 0.00825.54 / 0.25930.54 / 0.08243.64 / 0.00344.02 / 0.00244.21 / 0.002
Gauss. Deb. σe=0.0527.71 / 0.24323.59 / 0.29426.64 / 0.240N/A27.47 / 0.31327.73 / 0.205
Motion Deb. σe=0.05N/A17.52 / 0.46825.34 / 0.284N/A26.02 / 0.35425.94 / 0.249
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Examining the results, observe that, indeed, the sampling-based version of our approach (DDPG) consistently leads to better perceptual quality, both visually and as measured by LPIPS. Interestingly, while there is an inherent tradeoff between accuracy and perceptual quality [3], the PSNR reduction in DDPG compared to IDPG is rather moderate (and in some case DDPG even has slightly better PSNR than IDPG). One can observe that our approach typically outperforms other approaches in deblurring and is competitive in super-resolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.471, + 0.665 + ], + "angle": 0, + "content": "Importantly, note that the only reference methods that are as flexible as our approach to the observation model are DPS, which is very slow, and DiffPIR. However, their PSNR is significantly lower than the PSNR of our DDPG. Recall that in many critical applications (e.g., medical imaging), accuracy, as measured by the classical PSNR metric, is extremely important." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.196, + 0.695 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we presented a framework for solving linear inverse problems with DNN denoisers/diffusers, which uses a novel preconditioned data-fidelity guidance approach, based on traversing from back-projection steps to least squares steps, exploiting the advantages of each. We used the new approach with a computationally convenient trajectory within a \"plug-and-play\" optimization scheme and its DDM sampling-based counterpart, which we devised. The performance advantages of the new technique were shown in various deblurring and super-resolution settings, with and without observation noise. (See the supplementary material for computed tomography experiments as well). As a direction for future research, one can try to learn the precondi" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.406, + 0.847, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.562, + 0.892, + 0.618 + ], + "angle": 0, + "content": "Figure 3. Gaussian deblurring with noise level 0.05. Top row, from left to right: original, observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DPS, DiffPIR, and our DDPG." + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.628, + 0.847, + 0.781 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.784, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Figure 4. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DDRM, DiffPIR, and our DDPG." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.852, + 0.771, + 0.868 + ], + "angle": 0, + "content": "tioners \\(\\{\\mathbf{W}_t\\}\\) instead of designing them." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgment. The work is partially supported by ISF grant no. 1940/23." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25252" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Shady Abu Hussein, Tom Tirer, and Raja Giryes. Correction filter for single image super-resolution: Robustifying off-the-shelf deep super-resolvers. 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An alternative for training a "task-specific" network for each observation model is to use pretrained deep denoisers for imposing only the signal's prior within iterative algorithms, without additional training. Recently, a sampling-based variant of this approach has become popular with the rise of diffusion/score-based generative models. Using denoisers for general purpose restoration requires guiding the iterations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on backprojection (BP) has been shown to be a promising strategy (used recently also under the names "pseudoinverse" or "range/null-space" guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., it does not require SVD or a large number of iterations). We use it within both an optimization scheme and a sampling-based scheme, and demonstrate its advantages over existing methods for image deblurring and super-resolution. + +# 1. Introduction + +Image restoration problems appear in a wide range of applications, where the goal is to recover a high-quality image $\mathbf{x}^{*}\in \mathbb{R}^{n}$ from its degraded version $\mathbf{y}\in \mathbb{R}^{m}$ , which can be noisy, blurry, low-resolution, etc. In many problems, the relation between $\mathbf{y}$ and $\mathbf{x}^{*}$ can be expressed using a linear observation model + +$$ +\mathbf {y} = \mathbf {A} \mathbf {x} ^ {*} + \mathbf {e} \tag {1} +$$ + +![](images/5ce14a486cb8359dd8fa668af08d73b9231f3951f36c8477899229bda3a8fa30.jpg) +Figure 1. Motion deblurring with noise level 0.05. From top to bottom and left to right: original, observation, DPS [6], DiffPIR [45] and our DDPG. + +where $\mathbf{A} \in \mathbb{R}^{m \times n}$ is a measurement operator with $m \leq n$ , and $\mathbf{e} \sim \mathcal{N}(\mathbf{0}, \sigma_e^2 \mathbf{I}_m)$ is an additive white Gaussian noise. For example, in the denoising task $\mathbf{A}$ is the identity matrix $\mathbf{I}_n$ ; in the deblurring task $\mathbf{A}$ is a blur operator; and in the super-resolution task $\mathbf{A}$ is a composition of sub-sampling and (anti-aliasing) filtering. Image restoration problems are ill-posed: just looking for $\mathbf{x} \in \mathbb{R}^n$ that fits $\mathbf{y}$ based on the observation model does not suffice for a successful recovery. Thus, it is required to utilize prior knowledge on the nature of $\mathbf{x}^*$ . + +Nowadays, it has become common to address these problems by exhaustively training a different deep neural network (DNN) for each predefined observation model in a supervised manner. Namely, using (1) to generate training pairs $\{\mathbf{y}_i,\mathbf{x}_i^*\}$ and training a DNN to invert the map [8, 18, 34, 43]. However, these "task-specific" DNNs suffer from a huge performance drop when the observations at test-time mismatch (even slightly) the assumptions made in training [1, 28, 37], which limits their applicability in many practical cases. + +An alternative approach is to use pretrained DNNs that impose only the signal prior, while the agreement with the + +observations is being handled at test-time in a "zero-shot" manner. A successful choice of such pretrained DNNs are Gaussian denoisers, as was initially demonstrated in different "plug-and-play" (PnP) and "regularization by denoising" (RED) iterative schemes [25, 36, 40, 44]. The rise of score-based generative modeling [13, 31] — typically referred to as denoising diffusion models (DDMs) — whose inference/sampling "reversed" flows are based on iteratively injecting Gaussian noise and denoising, has further increased the popularity of using iterative denoising for general purpose restoration. In particular, operations that promote data-fidelity, similar to those used in PnP/RED, have been used within the diffusion models' iterative sampling schemes to guide the iterations towards an image that not only looks natural but also agrees with the observations [2, 5, 6, 16, 21, 30, 32, 41, 45]. + +Combining iterative denoising with guidance that is based on back-projection (BP) of intermediate estimates on the subspace $\{\mathbf{x}:\mathbf{A}\mathbf{x} = \mathbf{y}\}$ (more details in Section 2) was originally proposed in [36] (in the context of PnP), and has been shown to be a promising strategy in both the PnP and the DDM literature [5, 11, 19, 26, 27, 30, 37, 41, 46]. In the context of diffusion models it has been rediscovered under the names "pseudoinverse" [30] or "range/null-space" [41] guidance. However, in cases where $\mathbf{A}$ has low singular values (e.g., in image deblurring and super-resolution), the presence of noise in the observations $\mathbf{y}$ hinders the application of this approach: careful regularization is required and the performance gains tend to decrease. + +Contribution. In this paper, we identify the BP step as a preconditioned version of a least squares (LS) gradient step. This inspires us to propose an iteration-dependent preconditioned guidance approach that essentially traverses from the BP step to the LS gradient step along the restoration scheme. Thus, it enjoys benefits of BP step [38, 39], such as stronger consistency with y and accelerated convergence in early iterations, and the better robustness to noise of LS as the scheme approaches its end. The specific trajectory that we devise in this paper is also more simple and efficient to implement than other potential alternatives for BP, which either require having full knowledge on the SVD of A [16], or many neural function evaluations (NFEs) [6]. + +We present formal mathematical motivation for our guidance technique and use it within both a PnP-based scheme and its DDM sampling-based counterpart that we design. We examine the proposed approach for image deblurring and super-resolution on the CelebA-HQ and ImageNet datasets, where we exploit the powerful denoisers of DDMs [7, 20], and demonstrate its advantages over existing methods. In particular, our sampling-based reconstruction approach is flexible to the observation model, computationally convenient, and displays a good combination of perceptual quality and accuracy. + +# 2. Background and Related Work + +# 2.1. PnP Denoisers and Back-Projections + +Traditionally, estimating $\mathbf{x}^*$ from its measurements (1) has been tackled by minimizing an explicit objective function + +$$ +L (\mathbf {x}) = \ell (\mathbf {x}; \mathbf {y}) + s (\mathbf {x}), \tag {2} +$$ + +which is composed of a data-fidelity term $\ell (\mathbf{x};\mathbf{y})$ and a signal prior term $s(\mathbf{x})$ . The PnP concept [40] suggests applying a proximal algorithm to (2), where the proximal mapping associated with the prior function $s(\cdot)$ , i.e., $\mathrm{prox}_s(\mathbf{x})\coloneqq \mathrm{argmin}_{\mathbf{z}}\frac{1}{2}\| \mathbf{z} - \mathbf{x}\|_2^2 +s(\mathbf{z})$ [22], is replaced with an off-the-shelf Gaussian denoiser $\mathcal{D}(\cdot ;\sigma_t)$ ( $\sigma_{t}$ denotes the denoiser's noise level) that need not be associated with an explicit prior function (e.g., a pretrained DNN). A vast amount of literature has been dedicated to designing and analyzing PnP algorithms [4, 14, 24, 25, 35, 36, 40, 44]. + +A popular PnP scheme based on the proximal-gradient method (PGM) is given by: + +$$ +\mathbf {x} _ {0 \mid t} = \mathcal {D} \left(\mathbf {x} _ {t}; \sigma_ {t}\right), \tag {3} +$$ + +$$ +\mathbf {x} _ {t - 1} = \mathbf {x} _ {0 | t} - \mu_ {t} \nabla_ {\mathbf {x}} \ell (\mathbf {x} _ {0 | t}; \mathbf {y}), \tag {4} +$$ + +where $t = T, T - 1, \ldots, 1$ is the iteration index (decreases over time, to match the notation in diffusion/score-based models), $\mu_t$ is a step-size, and $\sigma_T > \ldots > \sigma_1$ is a predefined decreasing set of noise levels. The scheme is initialized with some $\mathbf{x}_T$ and the final estimate is given by $\mathbf{x}_{0|1}$ . + +A typical choice of data-fidelity term is the LS objective + +$$ +\ell_ {L S} (\mathbf {x}; \mathbf {y}) = \frac {1}{2} \| \mathbf {A x} - \mathbf {y} \| _ {2} ^ {2}, \tag {5} +$$ + +for which the gradient step in (4) is given by + +$$ +\mathbf {x} _ {t - 1} = \mathbf {x} _ {0 | t} - \mu_ {t} \mathbf {A} ^ {T} (\mathbf {A} \mathbf {x} _ {0 | t} - \mathbf {y}). \tag {6} +$$ + +Note though that PnP methods based on LS gradient steps tend to require many iterations [25, 39]. The IDBP method [36] suggests that the data-fidelity guidance, which follows the denoising operation, will be the back-projection (BP) of $\mathbf{x}_{0|t}$ onto the affine subspace $\{\mathbf{x}:\mathbf{A}\mathbf{x} = \mathbf{y}\}$ : + +$$ +\begin{array}{l} \mathbf {x} _ {t - 1} = \operatorname {a r g m i n} _ {\mathbf {x}} \| \mathbf {x} - \mathbf {x} _ {0 | t} \| _ {2} \text {s . t .} \mathbf {A x} = \mathbf {y} (7) \\ = \mathbf {A} ^ {\dagger} \mathbf {y} + \left(\mathbf {I} _ {n} - \mathbf {A} ^ {\dagger} \mathbf {A}\right) \mathbf {x} _ {0 | t} (8) \\ = \mathbf {x} _ {0 | t} - \mathbf {A} ^ {\dagger} (\mathbf {A} \mathbf {x} _ {0 | t} - \mathbf {y}), (9) \\ \end{array} +$$ + +where $\mathbf{A}^{\dagger}$ denotes the pseudoinverse of $\mathbf{A}$ . + +When $\mathbf{A}$ has near-zero singular values, it has been shown to be beneficial to replace $\mathbf{A}^{\dagger} = \mathbf{A}^{T}(\mathbf{A}\mathbf{A}^{T})^{\dagger}$ with a regularized version $\mathbf{A}^T (\mathbf{A}\mathbf{A}^T +\eta \mathbf{I}_m)^{-1}$ , where $\eta >0$ is the regularization hyperparameter [36, 37]. Importantly, note that there are popular tasks where the pseudoinverse can be + +implemented efficiently (e.g., see the supplementary material for FFT based implementations of this operation for deblurring and super-resolution). And, in general, full rank $\mathbf{A}\mathbf{A}^T$ (and $\mathbf{A}\mathbf{A}^T + \eta \mathbf{I}_m$ otherwise) can be typically "inverted" using few conjugate gradient iterations [12], which only require applying $\mathbf{A}$ and $\mathbf{A}^T$ and bypass the need of matrix inversion or SVD. + +As pointed out in [38, 39], (9) is equivalent to a gradient step (4) with step-size $\mu_t = 1$ and a special choice of $\ell(\mathbf{x};\mathbf{y})$ , which they dubbed as the "BP term": + +$$ +\ell_ {B P} (\mathbf {x}; \mathbf {y}) = \frac {1}{2} \| \left(\mathbf {A} \mathbf {A} ^ {T}\right) ^ {- 1 / 2} (\mathbf {A x} - \mathbf {y}) \| _ {2} ^ {2}. \tag {10} +$$ + +These works have analyzed, both empirically and theoretically, the effects of using BP steps (9) rather than LS steps (6) in inverse problems. They show provable faster convergence benefits (less iterations) and, in the low-noise regime, also MSE benefits. However, it is also shown that in the presence of observation noise and $\mathbf{A}$ with small singular values, we have that $\mathbf{A}^{\dagger}\mathbf{y}$ amplifies the noise. Thus a strong regularization $\eta$ is needed which hinders the advantages. + +# 2.2. Restoration via Guidance of DDMs + +Pretrained diffusion/score-based generative models [13, 31, 33] have been shown to be a powerful signal prior for image restoration. These generative models are based on training a network that approximates the score function $\nabla_{\mathbf{x}_t}\log p_t(\mathbf{x}_t)$ , where $p_t$ denotes the distribution of $\mathbf{x}_t$ , a Gaussian noisy version of the data $\mathbf{x}_0\sim p_0$ with noise level indexed by $t\in [0,T]$ . For $\mathbf{x}_t = \mathbf{x}_0 + \epsilon_t$ with $\epsilon_t\sim \mathcal{N}(\mathbf{0},\sigma_t^2\mathbf{I}_n)$ , by Tweedie's formula $-\sigma_t^2\nabla_{\mathbf{x}_t}\log p_t(\mathbf{x}_t) = \mathbf{x}_t - \mathbb{E}[\mathbf{x}_0|\mathbf{x}_t] = \mathbb{E}[\epsilon_t|\mathbf{x}_t]$ [9]. Therefore, these approaches essentially attempt to learn the MMSE Gaussian denoiser or, equivalently, noise estimation. After training, the sampling schemes are based on random Gaussian initialization and alternatively denoising and injection of Gaussian noise with a decreasing noise level. + +For concreteness, let us focus on the popular DDPM formulation [13]. In DDPM, $\mathbf{x}_t$ is generated from a data point $\mathbf{x}_0$ by the "forward flow": + +$$ +\mathbf {x} _ {t} = \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1} + \sqrt {\beta_ {t}} \boldsymbol {\epsilon}, \tag {11} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I}_n)$ and $\{\beta_t\}_{t = 1}^T$ is a predetermined "noise schedule" obeying $0 < \beta_{1} < \dots < \beta_{T}\leq 1$ . By properties of Gaussians, $\mathbf{x}_t$ can be directly generated from $\mathbf{x}_0$ by + +$$ +\mathbf {x} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon}, \tag {12} +$$ + +which includes noise variance $1 - \bar{\alpha}_{t}$ and signal scale factor $\sqrt{\bar{\alpha}_t}$ , where $\bar{\alpha}_t = \Pi_{s=1}^t\alpha_s$ and $\alpha_t = 1 - \beta_t$ . In training time, a U-net DNN $\epsilon_{\theta}(\cdot ; t)$ is trained to predict the noise $\epsilon$ given $\mathbf{x}_t$ by minimizing an MSE loss. In DDPM's inference time, starting from a random $\mathbf{x}_T \sim \mathcal{N}(\mathbf{0}, \mathbf{I}_n)$ , one step of + +the "reverse flow" that is used for generating a sample from $p_0$ is given by + +$$ +\mathbf {x} _ {t - 1} = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} _ {\theta} (\mathbf {x} _ {t}; t)\right) + \sqrt {\beta_ {t}} \boldsymbol {\epsilon} _ {t}, \tag {13} +$$ + +where $\epsilon_{t}$ is drawn from $\mathcal{N}(\mathbf{0},\mathbf{I}_n)$ . + +A faster generation scheme, denoted DDIM [29], is based on diverging from the Markovian guideline of DDPM. In DDIM, the step (13) is replaced with + +$$ +\mathbf {x} _ {t - 1} = \sqrt {\bar {\alpha} _ {t - 1}} \mathbf {x} _ {0 | t} + \hat {\sigma} _ {t} \boldsymbol {\epsilon} _ {\theta} (\mathbf {x} _ {t}; t) + \tilde {\sigma} _ {t} \boldsymbol {\epsilon} _ {t}, \tag {14} +$$ + +where $\epsilon_t\sim \mathcal{N}(\mathbf{0},\mathbf{I}_n)$ and + +$$ +\hat {\sigma} _ {t} = \sqrt {1 - \bar {\alpha} _ {t - 1} - \tilde {\sigma} _ {t} ^ {2}}, \tag {15} +$$ + +$$ +\mathbf {x} _ {0 \mid t} = \frac {1}{\sqrt {\bar {\alpha} _ {t}}} \left(\mathbf {x} _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon} _ {\theta} (\mathbf {x} _ {t}; t)\right). \tag {16} +$$ + +The hyperparameter $\tilde{\sigma}_t$ allows trading between the levels of two noise terms: the estimated noise $\epsilon_{\theta}(\mathbf{x}_t;t)$ and a pure stochastic noise $\epsilon_t$ . Moreover, $\mathbf{x}_{0|t}$ in (16) is an estimate of $\mathbf{x}_0$ given $\mathbf{x}_t$ , which is essentially performing Gaussian denoising: $\mathbf{x}_{0|t} = \frac{1}{\sqrt{\bar{\alpha}_t}}\mathcal{D}(\mathbf{x}_t;\sigma_t = \sqrt{1 - \bar{\alpha}_t})$ , as implied by (12). + +Many of the methods that use DDMs as priors for image restoration [16, 30, 41, 45] are based on the DDIM scheme [29]. Yet, in order that the sampling scheme will produce an image that is not only perceptually pleasing but also agrees with the measurements $\mathbf{y}$ and the observation model (1) it is required to equip the iterations with some data-fidelity guidance. This guidance is typically based on the gradient of a data-fidelity term $\ell (\mathbf{x};\mathbf{y})$ . In other words, the iterations (14) are modified into + +$$ +\mathbf {x} _ {t - 1} = \sqrt {\bar {\alpha} _ {t - 1}} \mathbf {x} _ {0 | t} - \mu_ {t} \nabla_ {\mathbf {x}} \ell \left(\mathbf {x} _ {0 | t}; \mathbf {y}\right) + \hat {\sigma} _ {t} \boldsymbol {\epsilon} _ {\theta} \left(\mathbf {x} _ {t}; t\right) + \tilde {\sigma} _ {t} \boldsymbol {\epsilon} _ {t}, \tag {17} +$$ + +where $\mu_t$ is the guidance scaling factor. + +Note the similarity between the PnP restoration (3)-(4) and the DDM restoration (16)-(17). Namely, ignoring the scaling of the signal by $\{\bar{\alpha}_t\}$ , the main difference is the noise injection, composed of the estimated noise $\epsilon_{\theta}$ and the random noise $\epsilon_t$ . The similarity of DDMs schemes to previous iterative denoising methods is further seen by the formulation of [15], which decouples the diffusion "forward" flows, used for training the denoisers, from the "reverse" inference flows. More discussion on such connections can be found in a recent review paper [10]. + +For example, the DDM restoration method in [6], dubbed DPS, where the guidance is based on the gradient of the LS term, resembles (6) with noise injection. Interestingly, just like its PnP counterpart, it requires a very large number of iterations (and thus many NFEs). Alternatively, by using BP guidance in (17) — equivalently, when injecting noise + +to step (9) in IDBP — one gets the recent DDNM method [41] (which is also similar to the method in [30]). However, note that the DDNM paper focuses on noiseless settings and has difficulties in noisy settings (in Section 4 we state its technical limitation), which is aligned with the sensitivity of BP guidance to noise in $\mathbf{y}$ , as mentioned above. + +At this point, we would also like to mention the DDRM method [16], which resembles the BP approach as it generates "spectral space" measurements $\bar{\mathbf{y}}$ in a way similar to applying $\mathbf{A}^{\dagger}$ on $\mathbf{y}$ . Yet, it is more robust to observation noise as it requires access to the full SVD of $\mathbf{A}$ , which allows it to mitigate noise amplification per singular component in each iteration. In this paper we aim to devise an approach that does not require computing and storing the SVD of $\mathbf{A}$ , which is impractical is most cases. + +Finally, we note that the way we construct a sampling scheme from a deterministic algorithm shares similarity with the recent method DIfPIR [45]. However, while [45] uses an existing PnP baseline, here we propose a novel core reconstruction method. Also, empirically our new sampling scheme demonstrates better accuracy than DiffPIR (evaluated by PSNR) without compromising on perceptual quality (evaluated by LPIPS). + +# 3. The Proposed Method + +In this section, we present our image restoration method that is more robust to observation noise than methods that use only back-projections while still having low computational complexity and clear benefits over methods that are based only on plain LS based guidance. To this end, we present a novel core guidance approach, equip it with formal theoretical motivation, and utilize it to devise a new sampling-based reconstruction scheme. + +All the claims in this section are proved in the supplementary material. + +# 3.1. Core approach + +The idea for our approach comes from identifying (9) as a specific instance of the formula + +$$ +\mathbf {x} _ {t - 1} = \mathbf {x} _ {0 | t} - \mu_ {t} \mathbf {A} ^ {T} \mathbf {W} (\mathbf {A x} _ {0 | t} - \mathbf {y}) \tag {18} +$$ + +with $\mathbf{W} = (\mathbf{A}\mathbf{A}^T)^{-1}$ (assuming full rank $\mathbf{A}$ ) and $\mu_t = 1$ . The plain LS step (6) is obviously also an instance of this expression with $\mathbf{W} = \mathbf{I}_m$ . + +Recall traditional preconditioning in optimization [23]: The optimization of an objective, e.g., $L: \mathbb{R}^n \to \mathbb{R}$ in (2), is based on gradient-based optimizers where the full gradient $\nabla L(\mathbf{x})$ is multiplied by a (symmetric) positive definite matrix $\mathbf{P} \in \mathbb{R}^{n \times n}$ . Such practice does not affect the problem's minimizers (since $\mathbf{P} \nabla L(\mathbf{x}) = \mathbf{0} \iff \nabla L(\mathbf{x}) = \mathbf{0}$ due to the invertibility of $\mathbf{P}$ ), and its goal is to ease the optimization landscape, characterized by the condition number + +of the effective Hessian $\mathbf{P}^{1 / 2}\nabla^2 L(\mathbf{x})\mathbf{P}^{1 / 2}$ . In (18), however, $\mathbf{W}\in \mathbb{R}^{m\times m}$ does not directly affect the signal's prior and for general $\mathbf{W}$ we may not have $\mathbf{A}^T\mathbf{W}(\mathbf{A}\mathbf{x} - \mathbf{y}) = \mathbf{0}\iff \nabla \ell_{LS}(\mathbf{x}) = \mathbf{A}^T (\mathbf{A}\mathbf{x} - \mathbf{y}) = \mathbf{0}$ . + +Nevertheless, we have the following claims. + +Claim 3.1. Let $\mathbf{A} \in \mathbb{A}^{m \times n}$ with $m \leq n$ and $\operatorname{rank}(\mathbf{A}) = m$ . Let $\mathbf{W} \in \mathbb{R}^{m \times m}$ such that $\operatorname{rank}(\mathbf{A}^T \mathbf{W}) = m$ . Then, + +$$ +\mathbf {A} ^ {T} \mathbf {W} (\mathbf {A x} - \mathbf {y}) = \mathbf {0} \iff \mathbf {A} ^ {T} (\mathbf {A x} - \mathbf {y}) = \mathbf {0}. +$$ + +Claim 3.2. Let $\mathbf{A} \in \mathbb{A}^{m \times n}$ with $m \leq n$ . Let $\mathbf{W} \in \mathbb{R}^{m \times m}$ be a positive definite matrix that shares eigenbasis with $\mathbf{A A}^T$ . Then, there exists a positive definite $\mathbf{P} \in \mathbb{R}^{n \times n}$ such that + +$$ +\mathbf {A} ^ {T} \mathbf {W} \mathbf {A} = \mathbf {P} ^ {1 / 2} \mathbf {A} ^ {T} \mathbf {A} \mathbf {P} ^ {1 / 2}. +$$ + +Therefore, if $\mathbf{A}$ is full rank, then any $\mathbf{W}$ for which $\mathbf{A}^T\mathbf{W}$ is full rank (e.g., $\mathbf{W} = (\mathbf{A}\mathbf{A}^T)^{-1}$ ) can be interpreted as a preconditioner of $\nabla \ell_{LS}$ (rather than of the full objective that may include additional terms). Alternatively, even if $\mathbf{A}$ is not full rank, but $\mathbf{W}$ shares eigenbasis with $\mathbf{A}\mathbf{A}^T$ (e.g., $\mathbf{W} = (\mathbf{A}\mathbf{A}^T + \eta \mathbf{I}_m)^{-1}$ ), we allow ourselves to refer to $\mathbf{W}$ as a preconditioner of $\nabla \ell_{LS}$ since it has the same effect on the effective Hessian, $\mathbf{P}^{1/2}\nabla^2\ell_{LS}(\mathbf{x})\mathbf{P}^{1/2}$ , as a traditional preconditioner $\mathbf{P}$ . + +Inspired by this, in lieu of (4) we propose a data-fidelity guidance based on iteration-dependent preconditioner: + +$$ +\mathbf {x} _ {t - 1} = \mathbf {x} _ {0 | t} - \mu_ {t} \mathbf {A} ^ {T} \mathbf {W} _ {t} (\mathbf {A} \mathbf {x} _ {0 | t} - \mathbf {y}) \tag {19} +$$ + +with a "smooth" discretization of the path of symmetric preconditioners $\{\mathbf{W}_t\}$ — invertible with eigenbasis shared with $\mathbf{A}\mathbf{A}^T$ — that starts roughly at $\mathbf{W}_T \propto (\mathbf{A}\mathbf{A}^T + \eta \mathbf{I}_m)^{-1}$ and ends roughly at $\mathbf{W}_0 \propto \mathbf{I}_m$ . + +In words, the proposed guidance is based on gently traversing from the (regularized) BP step to the LS step along the restoration scheme. Thus, it enjoys benefits of BP steps (stronger consistency with $\mathbf{y}$ , accelerated convergence, etc.) in early iterations and the better robustness to noise of LS steps as the scheme approaches its end. + +Potentially, a sequence of preconditioners $\{\mathbf{W}_t\}$ might be learned in a data-driven manner under some optimality criterion. Yet, this is expected to come at the price of losing their generality to arbitrary data. Thus, here we propose an engineered, but simple and effective, update rule of $\mathbf{W}_t$ that, as we will show empirically, already demonstrates the usefulness of our new concept. Specifically, the rule that we propose is given by the following convex combination: + +$$ +\mathbf {W} _ {t} = (1 - \delta_ {t}) \left(\mathbf {A} \mathbf {A} ^ {T} + \eta \mathbf {I} _ {m}\right) ^ {- 1} + \delta_ {t} c \mathbf {I} _ {m} \tag {20} +$$ + +where $0 \leq \delta_T < \ldots < \delta_0 \leq 1$ is a predefined sequence, and $c$ is a positive scalar that balances the two terms. + +In general, the main motivation for (20) is that it both obeys the previously stated conditions and also yields a + +data-fidelity guidance that is very simple to implement. Indeed, plugging (20) in (19) yields + +$$ +\begin{array}{l} \mathbf {x} _ {t - 1} = \mathbf {x} _ {0 | t} - \mu_ {t} \left((1 - \delta_ {t}) \mathbf {g} _ {B P} (\mathbf {x} _ {0 | t}) + \delta_ {t} \mathbf {g} _ {L S} (\mathbf {x} _ {0 | t})\right), \\ =: \mathbf {x} _ {0 | t} - \mu_ {t} \mathbf {g} _ {\delta_ {t}} \left(\mathbf {x} _ {0 | t}\right) \tag {21} \\ \end{array} +$$ + +where + +$$ +\mathbf {g} _ {B P} \left(\mathbf {x} _ {0 | t}\right) = \mathbf {A} ^ {T} \left(\mathbf {A} \mathbf {A} ^ {T} + \eta \mathbf {I} _ {m}\right) ^ {- 1} \left(\mathbf {A} \mathbf {x} _ {0 | t} - \mathbf {y}\right), \tag {22} +$$ + +$$ +\mathbf {g} _ {L S} \left(\mathbf {x} _ {0 | t}\right) = c \mathbf {A} ^ {T} \left(\mathbf {A} \mathbf {x} _ {0 | t} - \mathbf {y}\right), \tag {23} +$$ + +can be computed efficiently for a wide range of observation models. + +In Section 3.4 we will discuss practical implementations details for simple hyperparameter tuning (e.g., a simple way to tune $\{\delta_t\}$ ). As for setting $c$ , observe that (19) is essentially a gradient step (at $\mathbf{x}_{0|t}$ ) of the weighted least squares (WLS) data-fidelity term: + +$$ +\ell_ {W L S, t} (\mathbf {x}; \mathbf {y}) = \frac {1}{2} \left\| \mathbf {W} _ {t} ^ {1 / 2} (\mathbf {A x} - \mathbf {y}) \right\| _ {2} ^ {2}, \tag {24} +$$ + +for which we have the following property. + +Claim 3.3. Denote by $\lambda_{1}$ the largest singular value of $\mathbf{A}$ . Let $c \leq 1 / \lambda_1^2$ . Then, the update (21) with $\mu_t = 1$ ensures reduction in (24). + +Many popular degradation models obey $\lambda_1 \lesssim 1$ (e.g., in deblurring $\lambda_1 = 1$ and in super-resolution $\lambda_1$ is moderately lower than 1). Thus, following the claim, unless stated otherwise, we use $c = 1$ and $\mu_t = 1$ . + +To conclude this subsection, the core of the proposed algorithm is based on iteratively computing (3) and (21). Without noise injection, this is essentially a novel PnP scheme, which we call Iterative Denoising and Preconditioned Guidance (IDPG). As we will empirically show in Section 4, while this method has good PSNR performance, turning it into a DDM-based sampling scheme leads to better recoveries, especially in terms of perceptual quality. Before presenting the sampling scheme in Section 3.3, let us provide some theoretical motivation for our preconditioned guidance approach. + +# 3.2. Theory + +Let us state some mathematical claims that motivate the core guidance approach. In this subsection we consider a simplified setting of having a fixed $0 < \delta < 1$ , i.e., a fixed WLS data-fidelity term (24) with $\mathbf{W}$ given as in (20) but with $\delta_t = \delta$ . We examine the effects of this WLS, compared to LS and BP fidelity terms, on an estimator of $\mathbf{x}^*$ , denoted by $\hat{\mathbf{x}}$ , which is obtained by minimizing (2) with Tikhonov prior $s(\mathbf{x}) = \frac{\beta}{2} \| \mathbf{Dx} \|_2^2$ , where $\beta > 0$ and $\mathbf{D}^T \mathbf{D}$ is invertible, so, the estimator $\hat{\mathbf{x}}$ per data-fidelity term is unique. + +The MSE of $\hat{\mathbf{x}}$ (conditioned on $\mathbf{x}^*$ , averaged over the noise e) can be decomposed into two terms: squared bias, $b^{2}$ (independent of e), and variance, $v$ (depends on $\sigma_e^2$ ), given by + +$$ +b ^ {2} := \left\| \mathbb {E} \left[ \hat {\mathbf {x}} \mid \mathbf {x} ^ {*} \right] - \mathbf {x} ^ {*} \right\| _ {2} ^ {2}, \tag {25} +$$ + +$$ +v := \operatorname {T r} \left(\operatorname {V a r} \left(\hat {\mathbf {x}} \mid \mathbf {x} ^ {*}\right)\right). \tag {26} +$$ + +The motivation for analyzing this setting (even though in the proposed core procedure (3) & (21), we modify $\delta_t$ along the iterations and do not attempt to reach a minimizer per $\delta_t$ ) is that insights on gains in bias and variance at the minimizer level hint that similar effects are possible even with limited optimizer iterations per $\delta_t$ . Also, in [38], it was shown that insights gained for Tikhonov prior generalize empirically to more complex priors. Specifically, they showed that BP typically leads to smaller bias but higher variance than LS. In what follows, the intuition that $0 < \delta < 1$ enables trading bias and variance is made formal. + +Theorem 3.4. Consider the observation model (1) and estimating $\mathbf{x}^*$ via minimization of (2) with $s(\mathbf{x}) = \frac{\beta}{2}\|\mathbf{D}\mathbf{x}\|_2^2$ . + +Assume that: (a) $\mathbf{A}^T\mathbf{A}$ and $\mathbf{D}^T\mathbf{D} \succ 0$ share eigenbasis; (b) the singulars value of $\mathbf{A}$ are in $(0,1]$ , and not all equal (common case); (c) $\eta = 0$ and $c = 1$ . Then, $b_{BP} < b_{WLS} < b_{LS}$ , and $v_{LS} < v_{WLS} < v_{BP}$ . + +Note that the margins in the theorem's inequalities depend on where $\delta$ is located in $(0,1)$ (e.g., $v_{\mathrm{WLS}} \to v_{\mathrm{LS}}$ for $\delta \to 1$ ). This further motivates having a set $\{\delta_t\}$ instead of a fixed $\delta$ in (20) to gain flexibility in handling the error's bias/variance. + +As for the convergence rates of first-order optimization algorithms (which affect the number of NFEs with practical DNN-based priors), recall that it can typically be characterized by the condition number, $\kappa(\cdot)$ , of the problem's Hessian, which equals the ratio between the largest and smallest eigenvalues of the Hessian — the lower the better. Note, though, that for $m < n$ , the Hessian of each of the three data-fidelity terms (LS, BP, WLS) is rank-deficient due to the ill-posedness of the observation model. Nevertheless, we have the following property on the component of their Hessian in the row-range of $\mathbf{A}$ (a subspace in $\mathbb{R}^n$ ). + +Claim 3.5. Assume that $\mathrm{rank}(\mathbf{A}) = m$ , the singular values of $\mathbf{A}$ are not all equal, $\eta = 0$ , and denote by $\mathbf{V} \in \mathbb{R}^{n \times m}$ an orthonormal basis for the row-range of $\mathbf{A}$ . We have that + +$$ +\kappa (\mathbf {V} ^ {T} \nabla_ {\mathbf {x}} ^ {2} \ell_ {B P} \mathbf {V}) < \kappa (\mathbf {V} ^ {T} \nabla_ {\mathbf {x}} ^ {2} \ell_ {W L S} \mathbf {V}) < \kappa (\mathbf {V} ^ {T} \nabla_ {\mathbf {x}} ^ {2} \ell_ {L S} \mathbf {V}). +$$ + +Namely, the flexibility in $\delta$ allows accelerating the reconstruction procedure compared to using only a LS based guidance. Leveraging this result to establish ranking claims for specific algorithms may follow the approaches of [39] (based on constraints on the null space of $\mathbf{A}$ that are implicitly imposed by the signal prior term). + +Algorithm 1 Denoising Diffusion with iterative Preconditioned Guidance (DDPG) +Require: $\epsilon_{\theta}(\cdot ,t)$ (noise estimator), $T,\mathbf{y},\mathbf{A},\{\bar{\alpha}_t\} ,\{\mu_t\} ,c,$ $\eta ,\gamma ,\zeta$ 1: if $\sigma_e > 0$ then 2: $\delta_t = \bar{\alpha}_t^\gamma$ and $w_{t} = \delta_{t}$ 3: else 4: $\delta_t = 0$ and $w_{t} = 1$ 5: end if 6: Initialize $\mathbf{x}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I}_n)$ 7: for $t$ from $T$ to 1 do 8: $\mathbf{x}_{0|t} = \frac{1}{\sqrt{\bar{\alpha}_t}}\left(\mathbf{x}_t - \sqrt{1 - \bar{\alpha}_t}\epsilon_\theta (\mathbf{x}_t,t)\right)$ 9: $\mathbf{g}_{BP} = \mathbf{A}^T (\mathbf{A}\mathbf{A}^T +\eta \mathbf{I}_m)^{-1}(\mathbf{A}\mathbf{x}_{0|t} - \mathbf{y})$ 10: $\mathbf{g}_{LS} = c\mathbf{A}^T (\mathbf{A}\mathbf{x}_{0|t} - \mathbf{y})$ 11: $\tilde{\mathbf{x}}_{t - 1} = \mathbf{x}_{0|t} - \mu_t((1 - \delta_t)\mathbf{g}_{BP} + \delta_t\mathbf{g}_{LS})$ 12: $\hat{\epsilon}_t = \frac{1}{\sqrt{1 - \bar{\alpha}_t}} (\mathbf{x}_t - \sqrt{\bar{\alpha}_t}\tilde{\mathbf{x}}_{t - 1})$ 13: $\epsilon_t\sim \mathcal{N}(\mathbf{0},\mathbf{I}_n)$ 14: $\mathbf{x}_{t - 1} =$ 15: $\sqrt{\bar{\alpha}_{t - 1}}\tilde{\mathbf{x}}_{t - 1} + \sqrt{1 - \bar{\alpha}_{t - 1}}\left(w_t\sqrt{1 - \zeta}\hat{\epsilon}_t + \sqrt{\zeta}\epsilon_t\right)$ 16: end for 17: return ${\bf x}_0$ + +# 3.3. Sampling scheme + +As previously mentioned, in this subsection we turn IDPG (alternating (3) and (21)) into a DDM-based sampling scheme that empirically leads to better recoveries, especially in terms of perceptual quality. Injecting noise to the estimate in a certain iteration leads to an image that better matches the data on which the denoiser has been trained. Intuitively, this should improve the denoiser's performance and also allow it to mitigate error propagation along the iterations, by masking artifacts with noise that will be removed. Accordingly, it allows using a smaller value of the regularization parameter $\eta$ when handling noisy $\mathbf{y}$ , which yields results with sharper details. + +The sampling scheme that we propose is based on modification of the DDIM guided scheme, stated in (17). Namely, $\mathbf{x}_{0|t}$ is computed using a DDM's noise estimator as in (16) and the novel guidance $\mathbf{g}_{\delta_t}$ is being used in lieu of the abstract gradient $\nabla_{\mathbf{x}}\ell$ . However, we propose several important modifications of the additive noise terms $\hat{\sigma}_t\epsilon_\theta (\mathbf{x}_t;t) + \tilde{\sigma}_t\epsilon_t$ that appear in (17). + +The first modification is inspired by [45]. Note that, contrary to the unconditional image generation task, the data-fidelity guidance can significantly modify the estimated signal $\tilde{\mathbf{x}}_{t - 1}\coloneqq \mathbf{x}_{0|t} - \mu_t\mathbf{g}_{\delta_t}$ compared to $\mathbf{x}_{0|t}$ . Therefore, the effective predicted noise can be significantly different than $\epsilon_{\theta}(\mathbf{x}_t;t)$ . Accordingly, based on the relation between $\epsilon_{\theta}(\mathbf{x}_t;t)$ and $\mathbf{x}_{0|t}$ in (16), the effective predicted noise takes + +the form of + +$$ +\hat {\boldsymbol {\epsilon}} _ {t} = \frac {1}{\sqrt {1 - \bar {\alpha} _ {t}}} \left(\mathbf {x} _ {t} - \sqrt {\bar {\alpha} _ {t}} \tilde {\mathbf {x}} _ {t - 1}\right), \tag {27} +$$ + +and we use it instead of $\epsilon_{\theta}(\mathbf{x}_t;t)$ for generating $\mathbf{x}_{t - 1}$ + +Similarly to this prior work, we also simplify the way of trading between the (effective) estimated noise and the stochastic noise. Instead of time-dependent noise level $\tilde{\sigma}_t$ which affects $\hat{\sigma}_t = \sqrt{1 - \bar{\alpha}_{t-1} - \tilde{\sigma}_t^2}$ in a complicated way, we balance between the levels of $\hat{\epsilon}_t$ and $\epsilon_t$ using the simple to tune weight $\sqrt{1 - \zeta}$ and $\sqrt{\zeta}$ , respectively, with a single hyperparameter $\zeta \in [0,1]$ . + +Our key novel modification is the following. In the case of observation noise (i.e., $\sigma_{e} > 0$ ), the effective predicted noise $\hat{\epsilon}_{t}$ may not be useful in iterations where the overall guidance $\mathbf{g}_{\delta_t}$ is dominated by $\mathbf{g}_{BP}$ , due to the sensitivity to noise of the BP guidance. Therefore, we scale it by $\delta_{t}$ — the weight that is given to $\mathbf{g}_{LS}$ , which is more robust to observation noise. + +We remark that our sampling scheme transfers smoothly to the noiseless case, where one can simply use pure BP guidance – or equivalently $\delta_t = 0$ : it is only required to omit the last modification (i.e., avoid attenuating the noise injection by $\delta_t$ ). As will be shown empirically, this scheme performs on par with BP-based DDM methods that are specifically devised for noiseless observations, and outperforms other methods. + +The resulted DDM-based sampling algorithm, that we name Denoising Diffusion with iterative Preconditioned Guidance (DDPG), is summarized in Algorithm 1. The algorithm includes a simple way to set $\{\delta_t\}$ that is explained in the next subsection. + +# 3.4. Implementation details + +In the experimental section, we wish to test the approach (both DDPG and its core version IDPG) with powerful DDM's denoisers trained and used in [7, 20]. These models are based on DDPM formulation [13, 29], that we use to reduce the hyperparameter tuning effort in all our examined tasks, and in particular setting $\{\delta_t\}$ for noisy observations. (Recall that in the noiseless case, we simply set $\delta_t = 0$ ). + +As presented in Section 2, in DDPM there are the parameters $\{\bar{\alpha}_t\}$ , which are determined by the hyperparameters $\{\beta_t\}$ , and determine many other parameters (e.g., the model's noise levels $\{\sigma_t\}$ ). These $\{\bar{\alpha}_t\}$ obey $0_+ \approx \bar{\alpha}_T < \ldots < \bar{\alpha}_0 = 1$ . We do not change $\{\beta_t\}$ and $\{\bar{\alpha}_t\}$ at all compared to previous methods that we compare with [16, 41]. In fact, we use $\{\bar{\alpha}_t\}$ to set $\delta_t = \bar{\alpha}_t^\gamma$ with a single positive scalar hyperparameter $\gamma$ . This ensures that as $t$ decreases, $\{\delta_t\}$ is monotonically increasing from 0 to 1 in rate that can be controlled by $\gamma$ . Observe that smaller $\gamma$ yields higher intermediate $\bar{\alpha}_t^\gamma$ and thus a larger portion of $\{\mathbf{W}_t\}$ closer to + +identity matrix — or, equivalently, "faster" progress from BP to LS. This is beneficial for larger observation noise $\sigma_{e}$ . + +To conclude, when using $c = 1$ and $\mu_t = 1$ , applying our approach requires tuning only $\eta, \gamma$ and $\zeta$ (for DDPG). Note that, potentially, tuning more hyperparameters for our method can further boost its results. + +# 4. Experiments + +In this section, we examine the performance of our approach. We start with examining our core guidance, as reflected in IDPG, compared to its extreme cases: deterministic methods with pure BP and LS based guidance. Then, we compare both IDPG and DDPG to existing methods: DDRM [16], DPS [6], DDNM [41], and DiffPIR [45]. We consider the CelebA-HQ 1K and ImageNet 1K test sets, where for fair comparison all the methods use the same pretrained DDM's denoisers: the model from [20] trained on CelebA-HQ and the (unconditional) model from [7] trained on ImageNet. We use $T = 100$ iterations for each of the methods as in [41]. An exception is DPS, which requires $T = 1000$ iterations with much larger per-iteration complexity, making it extremely slow compared to others. All the methods are initialized with the same random $\mathbf{x}_T$ . + +We consider image deblurring and super-resolution tasks that have been widely examined in the previous works, and for each method we use the hyperparameter settings suggested by its authors. The settings for our methods are stated in the supplementary material. Specifically, we consider super-resolution with bicubic downsampling and scale factor 4 and deblurring with Gaussian kernel as, e.g., in [16, 41]. However, we also examine challenging noisy deblurring with random motion kernels, as in [45]. This is an example for a common task that cannot be handled by DDRM [16], which is limited to separable kernels for which the SVD of $\mathbf{A}$ can be efficiently computed and stored. This task cannot be addressed also by DDNM [41], which fails to tackle noisy observations. We examine the noisy cases also in the two aforementioned tasks. + +In the supplementary material, we demonstrate the advantages of our approach over recent task-specific DNNs, as well as its superior performance also with lower noise level than demonstrated here. In addition, we report there the impressive performance of our approach for sparse-view computed tomography (another task where computing the SVD of $\mathbf{A}$ is infeasible). + +Table 1. Data-fidelity guidance ablation: super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K. + +
TaskPGM-LSIDBPIDPG (ours)
Bicub. SRx4 σe=032.40 / 0.12732.66 / 0.11132.66 / 0.111
Bicub. SRx4 σe=0.0528.91 / 0.20928.95 / 0.22929.89 / 0.155
Gauss. Deb. σe=032.25 / 0.14145.58 / 0.00245.58 / 0.002
Gauss. Deb. σe=0.0528.61 / 0.19130.55 / 0.15031.08 / 0.150
Gauss. Deb. σe=0.127.89 / 0.23928.29 / 0.22629.28 / 0.146
+ +![](images/7b93fc4180e7ccd6cc5c954c8ff73b3b4382afe12f5e43c4e3dd578ce7824182.jpg) +Figure 2. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our DDPG. Bottom row, from left to right: PGM-LS, IDBP, and our IDPG (baseline for DDPG). + +# 4.1. Examining the core approach + +As the main contribution of our paper is the novel guidance approach that smoothly traverses from BP to LS guidance, we start with examining our baseline IDPG method (alternating (3) and (21)) with IDBP [36] ( $\delta_t = 0$ ) and a method with LS based updates ( $\delta_t = 1$ ), denoted here by PGM-LS (a common PnP scheme [14]). This comparison essentially provides an ablation study for our core approach. + +The results for bicubic super-resolution and Gaussian deblurring with various and without noise for the CelebA-HQ 1K test set are presented in Table 1. They show that IDPG consistently outperforms IDBP and PGM-LS. Figure 2 displays qualitative results, showing that IDPG has less artifacts than IDBP and finer details than PGM-LS. Yet, while IDPG provides high PSNR values its perceptual quality can be improved by using the sampling-based DDPG, as shown in this figure. + +# 4.2. Comparison with other methods + +We turn to compare the proposed approach to DDRM, DPS, DDNM and DiffPIR. We consider all deblurring and superresolution tasks that have been described above with various noise levels. The results for the CelebA-HQ 1K test set and the ImageNet 1K test set are presented in Table 2 and Table 3, respectively. We present qualitative results for motion deblurring, Gaussian deblurring and super-resolution in Figures 1, 3 and 4, respectively. More results appear in the supplementary material. + +Table 2. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text). + +
Task\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=031.64 / 0.05429.39 / 0.06530.26 / 0.05131.64 / 0.04832.66 / 0.11131.60 / 0.052
Bicub. SRx4 σe=0.0529.26 / 0.09027.49 / 0.08627.44 / 0.085N/A29.89 / 0.15529.39 / 0.105
Gauss. Deb. σe=042.49 / 0.00631.25 / 0.05532.97 / 0.04145.56 / 0.00245.58 / 0.00245.46 / 0.002
Gauss. Deb. σe=0.0530.53 / 0.07427.75 / 0.08428.89 / 0.074N/A31.08 / 0.15030.41 / 0.068
Gauss. Deb. σe=0.128.79 / 0.08826.67 / 0.09727.59 / 0.083N/A29.28 / 0.14629.18 / 0.080
Motion Deb. σe=0.05N/A19.63 / 0.22727.96 / 0.102N/A29.73 / 0.13429.02 / 0.082
Motion Deb. σe=0.1N/A19.64 / 0.23126.23 / 0.132N/A27.86 / 0.16627.74 / 0.099
+ +Table 3. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on Imagenet 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text). + +
Task\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=027.38 / 0.27025.56 / 0.23626.99 / 0.22527.45 / 0.24527.20 / 0.32627.41 / 0.255
Bicub. SRx4 σe=0.0525.54 / 0.33324.05 / 0.27124.65 / 0.318N/A25.51 / 0.41125.55 / 0.354
Gauss. Deb. σe=040.53 / 0.00825.54 / 0.25930.54 / 0.08243.64 / 0.00344.02 / 0.00244.21 / 0.002
Gauss. Deb. σe=0.0527.71 / 0.24323.59 / 0.29426.64 / 0.240N/A27.47 / 0.31327.73 / 0.205
Motion Deb. σe=0.05N/A17.52 / 0.46825.34 / 0.284N/A26.02 / 0.35425.94 / 0.249
+ +Examining the results, observe that, indeed, the sampling-based version of our approach (DDPG) consistently leads to better perceptual quality, both visually and as measured by LPIPS. Interestingly, while there is an inherent tradeoff between accuracy and perceptual quality [3], the PSNR reduction in DDPG compared to IDPG is rather moderate (and in some case DDPG even has slightly better PSNR than IDPG). One can observe that our approach typically outperforms other approaches in deblurring and is competitive in super-resolution. + +Importantly, note that the only reference methods that are as flexible as our approach to the observation model are DPS, which is very slow, and DiffPIR. However, their PSNR is significantly lower than the PSNR of our DDPG. Recall that in many critical applications (e.g., medical imaging), accuracy, as measured by the classical PSNR metric, is extremely important. + +# 5. Conclusion + +In this paper, we presented a framework for solving linear inverse problems with DNN denoisers/diffusers, which uses a novel preconditioned data-fidelity guidance approach, based on traversing from back-projection steps to least squares steps, exploiting the advantages of each. We used the new approach with a computationally convenient trajectory within a "plug-and-play" optimization scheme and its DDM sampling-based counterpart, which we devised. The performance advantages of the new technique were shown in various deblurring and super-resolution settings, with and without observation noise. (See the supplementary material for computed tomography experiments as well). As a direction for future research, one can try to learn the precondi + +![](images/1ada4cc2aa5a7892b2a4aa1bc82e242f4ebe0865bcac01bca1aa108823abb08e.jpg) +Figure 3. Gaussian deblurring with noise level 0.05. Top row, from left to right: original, observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DPS, DiffPIR, and our DDPG. + +![](images/c97fafc1798925cfd8d8183953345bbcdc82d25c5b03f794fd3dee01777496e1.jpg) +Figure 4. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DDRM, DiffPIR, and our DDPG. + +tioners $\{\mathbf{W}_t\}$ instead of designing them. + +Acknowledgment. The work is partially supported by ISF grant no. 1940/23. + +# References + +[1] Shady Abu Hussein, Tom Tirer, and Raja Giryes. Correction filter for single image super-resolution: Robustifying off-the-shelf deep super-resolvers. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 1428-1437, 2020. 1 +[2] Shady Abu-Hussein, Tom Tirer, and Raja Giryes. Adir: Adaptive diffusion for image reconstruction. arXiv preprint arXiv:2212.03221, 2022. 2 +[3] Yochai Blau and Tomer Michaeli. The perception-distortion tradeoff. 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In 2020 28th European Signal Processing Conference (EUSIPCO), pages 675-679, 2021. 2 \ No newline at end of file diff --git a/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/images.zip b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..06bd7712577a80f1e3430dd09318d5c357b20ecf --- /dev/null +++ b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8e48a414e6670e5f652841e6e0a0a8a2291dfd9c22151b36e6a283c0637a7772 +size 405221 diff --git a/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/layout.json b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..34bed575e5f8c02b43a0dafb30d35f148f30dd59 --- /dev/null +++ b/2024/Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance/layout.json @@ -0,0 +1,13004 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 94, + 103, + 501, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 103, + 501, + 138 + ], + "spans": [ + { + "bbox": [ + 94, + 103, + 501, + 138 + ], + "type": "text", + "content": "Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 152, + 162, + 276, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 162, + 276, + 203 + ], + "spans": [ + { + "bbox": [ + 152, + 162, + 276, + 203 + ], + "type": "text", + "content": "Tomer Garber \nOpen University of Israel \ntomergarber@gmail.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 314, + 162, + 441, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 162, + 441, + 203 + ], + "spans": [ + { + "bbox": [ + 314, + 162, + 441, + 203 + ], + "type": "text", + "content": "Tom Tirer Bar-Ilan University, Israel tirer.tom@gmail.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 259, + 290, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 290, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 290, + 559 + ], + "type": "text", + "content": "Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a \"task-specific\" network for each observation model is to use pretrained deep denoisers for imposing only the signal's prior within iterative algorithms, without additional training. Recently, a sampling-based variant of this approach has become popular with the rise of diffusion/score-based generative models. Using denoisers for general purpose restoration requires guiding the iterations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on backprojection (BP) has been shown to be a promising strategy (used recently also under the names \"pseudoinverse\" or \"range/null-space\" guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., it does not require SVD or a large number of iterations). We use it within both an optimization scheme and a sampling-based scheme, and demonstrate its advantages over existing methods for image deblurring and super-resolution." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "text", + "content": "Image restoration problems appear in a wide range of applications, where the goal is to recover a high-quality image " + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{*}\\in \\mathbb{R}^{n}" + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "text", + "content": " from its degraded version " + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{y}\\in \\mathbb{R}^{m}" + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "text", + "content": ", which can be noisy, blurry, low-resolution, etc. In many problems, the relation between " + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{*}" + }, + { + "bbox": [ + 46, + 610, + 287, + 682 + ], + "type": "text", + "content": " can be expressed using a linear observation model" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 136, + 698, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 698, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 136, + 698, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = \\mathbf {A} \\mathbf {x} ^ {*} + \\mathbf {e} \\tag {1}", + "image_path": "7111ffcfa12978d58df415f12aeb0f96c263552f512612a58f277c94a178d292.jpg" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 230, + 545, + 385 + ], + "blocks": [ + { + "bbox": [ + 310, + 230, + 545, + 385 + ], + "lines": [ + { + "bbox": [ + 310, + 230, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 310, + 230, + 545, + 385 + ], + "type": "image", + "image_path": "5ce14a486cb8359dd8fa668af08d73b9231f3951f36c8477899229bda3a8fa30.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 394, + 547, + 428 + ], + "lines": [ + { + "bbox": [ + 305, + 394, + 547, + 428 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 547, + 428 + ], + "type": "text", + "content": "Figure 1. Motion deblurring with noise level 0.05. From top to bottom and left to right: original, observation, DPS [6], DiffPIR [45] and our DDPG." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{m \\times n}" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " is a measurement operator with " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "m \\leq n" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{e} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_e^2 \\mathbf{I}_m)" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " is an additive white Gaussian noise. For example, in the denoising task " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " is the identity matrix " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_n" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": "; in the deblurring task " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " is a blur operator; and in the super-resolution task " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " is a composition of sub-sampling and (anti-aliasing) filtering. Image restoration problems are ill-posed: just looking for " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " that fits " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": " based on the observation model does not suffice for a successful recovery. Thus, it is required to utilize prior knowledge on the nature of " + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "type": "text", + "content": "Nowadays, it has become common to address these problems by exhaustively training a different deep neural network (DNN) for each predefined observation model in a supervised manner. Namely, using (1) to generate training pairs " + }, + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{y}_i,\\mathbf{x}_i^*\\}" + }, + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "type": "text", + "content": " and training a DNN to invert the map [8, 18, 34, 43]. However, these \"task-specific\" DNNs suffer from a huge performance drop when the observations at test-time mismatch (even slightly) the assumptions made in training [1, 28, 37], which limits their applicability in many practical cases." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "An alternative approach is to use pretrained DNNs that impose only the signal prior, while the agreement with the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25245" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "observations is being handled at test-time in a \"zero-shot\" manner. A successful choice of such pretrained DNNs are Gaussian denoisers, as was initially demonstrated in different \"plug-and-play\" (PnP) and \"regularization by denoising\" (RED) iterative schemes [25, 36, 40, 44]. The rise of score-based generative modeling [13, 31] — typically referred to as denoising diffusion models (DDMs) — whose inference/sampling \"reversed\" flows are based on iteratively injecting Gaussian noise and denoising, has further increased the popularity of using iterative denoising for general purpose restoration. In particular, operations that promote data-fidelity, similar to those used in PnP/RED, have been used within the diffusion models' iterative sampling schemes to guide the iterations towards an image that not only looks natural but also agrees with the observations [2, 5, 6, 16, 21, 30, 32, 41, 45]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": "Combining iterative denoising with guidance that is based on back-projection (BP) of intermediate estimates on the subspace " + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}:\\mathbf{A}\\mathbf{x} = \\mathbf{y}\\}" + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": " (more details in Section 2) was originally proposed in [36] (in the context of PnP), and has been shown to be a promising strategy in both the PnP and the DDM literature [5, 11, 19, 26, 27, 30, 37, 41, 46]. In the context of diffusion models it has been rediscovered under the names \"pseudoinverse\" [30] or \"range/null-space\" [41] guidance. However, in cases where " + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": " has low singular values (e.g., in image deblurring and super-resolution), the presence of noise in the observations " + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": " hinders the application of this approach: careful regularization is required and the performance gains tend to decrease." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 424, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 289, + 581 + ], + "type": "text", + "content": "Contribution. In this paper, we identify the BP step as a preconditioned version of a least squares (LS) gradient step. This inspires us to propose an iteration-dependent preconditioned guidance approach that essentially traverses from the BP step to the LS gradient step along the restoration scheme. Thus, it enjoys benefits of BP step [38, 39], such as stronger consistency with y and accelerated convergence in early iterations, and the better robustness to noise of LS as the scheme approaches its end. The specific trajectory that we devise in this paper is also more simple and efficient to implement than other potential alternatives for BP, which either require having full knowledge on the SVD of A [16], or many neural function evaluations (NFEs) [6]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "We present formal mathematical motivation for our guidance technique and use it within both a PnP-based scheme and its DDM sampling-based counterpart that we design. We examine the proposed approach for image deblurring and super-resolution on the CelebA-HQ and ImageNet datasets, where we exploit the powerful denoisers of DDMs [7, 20], and demonstrate its advantages over existing methods. In particular, our sampling-based reconstruction approach is flexible to the observation model, computationally convenient, and displays a good combination of perceptual quality and accuracy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 71, + 482, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 482, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 482, + 85 + ], + "type": "text", + "content": "2. Background and Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 91, + 500, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 500, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 500, + 104 + ], + "type": "text", + "content": "2.1. PnP Denoisers and Back-Projections" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 109, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 109, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 109, + 545, + 133 + ], + "type": "text", + "content": "Traditionally, estimating " + }, + { + "bbox": [ + 305, + 109, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 305, + 109, + 545, + 133 + ], + "type": "text", + "content": " from its measurements (1) has been tackled by minimizing an explicit objective function" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 376, + 142, + 545, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 142, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 376, + 142, + 545, + 156 + ], + "type": "interline_equation", + "content": "L (\\mathbf {x}) = \\ell (\\mathbf {x}; \\mathbf {y}) + s (\\mathbf {x}), \\tag {2}", + "image_path": "f8245fba30249bbc501785ad8e382dab1ebd2d7c2dfc360a380a4bac44ddf621.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": "which is composed of a data-fidelity term " + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\ell (\\mathbf{x};\\mathbf{y})" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": " and a signal prior term " + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "inline_equation", + "content": "s(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": ". The PnP concept [40] suggests applying a proximal algorithm to (2), where the proximal mapping associated with the prior function " + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "inline_equation", + "content": "s(\\cdot)" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\mathrm{prox}_s(\\mathbf{x})\\coloneqq \\mathrm{argmin}_{\\mathbf{z}}\\frac{1}{2}\\| \\mathbf{z} - \\mathbf{x}\\|_2^2 +s(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": " [22], is replaced with an off-the-shelf Gaussian denoiser " + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot ;\\sigma_t)" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 304, + 164, + 545, + 292 + ], + "type": "text", + "content": " denotes the denoiser's noise level) that need not be associated with an explicit prior function (e.g., a pretrained DNN). A vast amount of literature has been dedicated to designing and analyzing PnP algorithms [4, 14, 24, 25, 35, 36, 40, 44]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 293, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 316 + ], + "type": "text", + "content": "A popular PnP scheme based on the proximal-gradient method (PGM) is given by:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 365, + 326, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 326, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 365, + 326, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {0 \\mid t} = \\mathcal {D} \\left(\\mathbf {x} _ {t}; \\sigma_ {t}\\right), \\tag {3}", + "image_path": "8a32721e50eeb7dbb7d9b08bc29e9c1a23d3b3a94db8489cfdae6232b6a7add5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 361, + 341, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 341, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 361, + 341, + 545, + 354 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\nabla_ {\\mathbf {x}} \\ell (\\mathbf {x} _ {0 | t}; \\mathbf {y}), \\tag {4}", + "image_path": "12aa428f1265d92c2474a5beee8a4519679c5edd0b98c617309c710ee91f1956.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "inline_equation", + "content": "t = T, T - 1, \\ldots, 1" + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "content": " is the iteration index (decreases over time, to match the notation in diffusion/score-based models), " + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mu_t" + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "content": " is a step-size, and " + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\sigma_T > \\ldots > \\sigma_1" + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "content": " is a predefined decreasing set of noise levels. The scheme is initialized with some " + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "content": " and the final estimate is given by " + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|1}" + }, + { + "bbox": [ + 304, + 361, + 545, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 422, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 422, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 545, + 434 + ], + "type": "text", + "content": "A typical choice of data-fidelity term is the LS objective" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 368, + 442, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 442, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 368, + 442, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\ell_ {L S} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\| \\mathbf {A x} - \\mathbf {y} \\| _ {2} ^ {2}, \\tag {5}", + "image_path": "a84da9d3562f61812a40f410bff2c9fabe8471b75db55e1b54c4f4a0fa31e726.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 472, + 487, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 487, + 485 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 487, + 485 + ], + "type": "text", + "content": "for which the gradient step in (4) is given by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 354, + 493, + 545, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 493, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 354, + 493, + 545, + 507 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}). \\tag {6}", + "image_path": "537451055f27cf7f5ad5067e114c56c6a1989dbf43b90bb827c01ecf62c1a4b7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "type": "text", + "content": "Note though that PnP methods based on LS gradient steps tend to require many iterations [25, 39]. The IDBP method [36] suggests that the data-fidelity guidance, which follows the denoising operation, will be the back-projection (BP) of " + }, + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t}" + }, + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "type": "text", + "content": " onto the affine subspace " + }, + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}:\\mathbf{A}\\mathbf{x} = \\mathbf{y}\\}" + }, + { + "bbox": [ + 304, + 516, + 545, + 576 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 335, + 585, + 545, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 585, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 335, + 585, + 545, + 631 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {x} _ {t - 1} = \\operatorname {a r g m i n} _ {\\mathbf {x}} \\| \\mathbf {x} - \\mathbf {x} _ {0 | t} \\| _ {2} \\text {s . t .} \\mathbf {A x} = \\mathbf {y} (7) \\\\ = \\mathbf {A} ^ {\\dagger} \\mathbf {y} + \\left(\\mathbf {I} _ {n} - \\mathbf {A} ^ {\\dagger} \\mathbf {A}\\right) \\mathbf {x} _ {0 | t} (8) \\\\ = \\mathbf {x} _ {0 | t} - \\mathbf {A} ^ {\\dagger} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}), (9) \\\\ \\end{array}", + "image_path": "7d188e0b3942a80c78d09a7f2605f680fc33a4c8dc391885a7294517f845006c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{\\dagger}" + }, + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "type": "text", + "content": " denotes the pseudoinverse of " + }, + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 306, + 641, + 480, + 653 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " has near-zero singular values, it has been shown to be beneficial to replace " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{\\dagger} = \\mathbf{A}^{T}(\\mathbf{A}\\mathbf{A}^{T})^{\\dagger}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " with a regularized version " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^T (\\mathbf{A}\\mathbf{A}^T +\\eta \\mathbf{I}_m)^{-1}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\eta >0" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " is the regularization hyperparameter [36, 37]. Importantly, note that there are popular tasks where the pseudoinverse can be" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25246" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": "implemented efficiently (e.g., see the supplementary material for FFT based implementations of this operation for deblurring and super-resolution). And, in general, full rank " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\mathbf{A}^T" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " (and " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " otherwise) can be typically \"inverted\" using few conjugate gradient iterations [12], which only require applying " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^T" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " and bypass the need of matrix inversion or SVD." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "type": "text", + "content": "As pointed out in [38, 39], (9) is equivalent to a gradient step (4) with step-size " + }, + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "type": "inline_equation", + "content": "\\mu_t = 1" + }, + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "type": "text", + "content": " and a special choice of " + }, + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "type": "inline_equation", + "content": "\\ell(\\mathbf{x};\\mathbf{y})" + }, + { + "bbox": [ + 47, + 156, + 288, + 192 + ], + "type": "text", + "content": ", which they dubbed as the \"BP term\":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 71, + 200, + 287, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 200, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 71, + 200, + 287, + 223 + ], + "type": "interline_equation", + "content": "\\ell_ {B P} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\| \\left(\\mathbf {A} \\mathbf {A} ^ {T}\\right) ^ {- 1 / 2} (\\mathbf {A x} - \\mathbf {y}) \\| _ {2} ^ {2}. \\tag {10}", + "image_path": "558c5beb066b3bd0d6a78ca3139f4ca1e5278f95711dd25a8972816bae96996e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "text", + "content": "These works have analyzed, both empirically and theoretically, the effects of using BP steps (9) rather than LS steps (6) in inverse problems. They show provable faster convergence benefits (less iterations) and, in the low-noise regime, also MSE benefits. However, it is also shown that in the presence of observation noise and " + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "text", + "content": " with small singular values, we have that " + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{\\dagger}\\mathbf{y}" + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "text", + "content": " amplifies the noise. Thus a strong regularization " + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 229, + 287, + 326 + ], + "type": "text", + "content": " is needed which hinders the advantages." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 332, + 234, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 234, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 234, + 344 + ], + "type": "text", + "content": "2.2. Restoration via Guidance of DDMs" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": "Pretrained diffusion/score-based generative models [13, 31, 33] have been shown to be a powerful signal prior for image restoration. These generative models are based on training a network that approximates the score function " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}_t}\\log p_t(\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": " denotes the distribution of " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": ", a Gaussian noisy version of the data " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0\\sim p_0" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": " with noise level indexed by " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "t\\in [0,T]" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t = \\mathbf{x}_0 + \\epsilon_t" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\sigma_t^2\\mathbf{I}_n)" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": ", by Tweedie's formula " + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "inline_equation", + "content": "-\\sigma_t^2\\nabla_{\\mathbf{x}_t}\\log p_t(\\mathbf{x}_t) = \\mathbf{x}_t - \\mathbb{E}[\\mathbf{x}_0|\\mathbf{x}_t] = \\mathbb{E}[\\epsilon_t|\\mathbf{x}_t]" + }, + { + "bbox": [ + 46, + 350, + 287, + 517 + ], + "type": "text", + "content": " [9]. Therefore, these approaches essentially attempt to learn the MMSE Gaussian denoiser or, equivalently, noise estimation. After training, the sampling schemes are based on random Gaussian initialization and alternatively denoising and injection of Gaussian noise with a decreasing noise level." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "type": "text", + "content": "For concreteness, let us focus on the popular DDPM formulation [13]. In DDPM, " + }, + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "type": "text", + "content": " is generated from a data point " + }, + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 518, + 287, + 554 + ], + "type": "text", + "content": " by the \"forward flow\":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 562, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 562, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 562, + 287, + 578 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon}, \\tag {11}", + "image_path": "45a9edb8f9924490d5bfbc21962a2371b70902223dc71719625ee1c69d66a5f3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)" + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\}_{t = 1}^T" + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "content": " is a predetermined \"noise schedule\" obeying " + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "inline_equation", + "content": "0 < \\beta_{1} < \\dots < \\beta_{T}\\leq 1" + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "content": ". By properties of Gaussians, " + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "content": " can be directly generated from " + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 586, + 287, + 624 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 111, + 631, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 631, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 111, + 631, + 287, + 645 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\tag {12}", + "image_path": "20a7658991bdcef25a5db84aa3f97ada8abb452c7e243eec2e0cd1253912e307.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "which includes noise variance " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "1 - \\bar{\\alpha}_{t}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and signal scale factor " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sqrt{\\bar{\\alpha}_t}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t = \\Pi_{s=1}^t\\alpha_s" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\alpha_t = 1 - \\beta_t" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ". In training time, a U-net DNN " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\cdot ; t)" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " is trained to predict the noise " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " by minimizing an MSE loss. In DDPM's inference time, starting from a random " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}_n)" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ", one step of" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "the \"reverse flow\" that is used for generating a sample from " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "p_0" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 311, + 103, + 545, + 130 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 103, + 545, + 130 + ], + "spans": [ + { + "bbox": [ + 311, + 103, + 545, + 130 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t)\\right) + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\tag {13}", + "image_path": "79b58d0cde59eedf8f891114e7e166a641dfa5a14337de02b11048db6f6ef870.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "spans": [ + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "type": "text", + "content": " is drawn from " + }, + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)" + }, + { + "bbox": [ + 305, + 137, + 444, + 149 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 149, + 545, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 149, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 305, + 149, + 545, + 186 + ], + "type": "text", + "content": "A faster generation scheme, denoted DDIM [29], is based on diverging from the Markovian guideline of DDPM. In DDIM, the step (13) is replaced with" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 194, + 545, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 194, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 340, + 194, + 545, + 208 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} \\mathbf {x} _ {0 | t} + \\hat {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t) + \\tilde {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {t}, \\tag {14}", + "image_path": "cb5faa4c8965ac3f467b5d0a4373f3f75acea28cb91e87d537d9ba856403ff68.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 214, + 412, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 214, + 412, + 227 + ], + "spans": [ + { + "bbox": [ + 306, + 214, + 412, + 227 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 214, + 412, + 227 + ], + "type": "inline_equation", + "content": "\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)" + }, + { + "bbox": [ + 306, + 214, + 412, + 227 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 351, + 235, + 545, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 235, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 351, + 235, + 545, + 255 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {t} = \\sqrt {1 - \\bar {\\alpha} _ {t - 1} - \\tilde {\\sigma} _ {t} ^ {2}}, \\tag {15}", + "image_path": "a4ff080e0c3bdb3df3a8f06fec4b2d79702887f9932ca85ee32cb93a840b8c9e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 345, + 257, + 545, + 282 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 257, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 345, + 257, + 545, + 282 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {0 \\mid t} = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} \\left(\\mathbf {x} _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {x} _ {t}; t)\\right). \\tag {16}", + "image_path": "10beaa86fb852218b7ce93481f11a6df151b171d1f1350cce91af469b72a2016.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": "The hyperparameter " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}_t" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": " allows trading between the levels of two noise terms: the estimated noise " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t;t)" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": " and a pure stochastic noise " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\epsilon_t" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": ". Moreover, " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t}" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": " in (16) is an estimate of " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": ", which is essentially performing Gaussian denoising: " + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}}\\mathcal{D}(\\mathbf{x}_t;\\sigma_t = \\sqrt{1 - \\bar{\\alpha}_t})" + }, + { + "bbox": [ + 305, + 288, + 545, + 369 + ], + "type": "text", + "content": ", as implied by (12)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "type": "text", + "content": "Many of the methods that use DDMs as priors for image restoration [16, 30, 41, 45] are based on the DDIM scheme [29]. Yet, in order that the sampling scheme will produce an image that is not only perceptually pleasing but also agrees with the measurements " + }, + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "type": "text", + "content": " and the observation model (1) it is required to equip the iterations with some data-fidelity guidance. This guidance is typically based on the gradient of a data-fidelity term " + }, + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\ell (\\mathbf{x};\\mathbf{y})" + }, + { + "bbox": [ + 305, + 369, + 545, + 477 + ], + "type": "text", + "content": ". In other words, the iterations (14) are modified into" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 486, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t - 1}} \\mathbf {x} _ {0 | t} - \\mu_ {t} \\nabla_ {\\mathbf {x}} \\ell \\left(\\mathbf {x} _ {0 | t}; \\mathbf {y}\\right) + \\hat {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {x} _ {t}; t\\right) + \\tilde {\\sigma} _ {t} \\boldsymbol {\\epsilon} _ {t}, \\tag {17}", + "image_path": "ffd512907ecc76308596c3c3eb81ca0626b2947a7692af04ba1fd90670566b6a.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 510, + 466, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 466, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 466, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 510, + 466, + 521 + ], + "type": "inline_equation", + "content": "\\mu_t" + }, + { + "bbox": [ + 306, + 510, + 466, + 521 + ], + "type": "text", + "content": " is the guidance scaling factor." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "text", + "content": "Note the similarity between the PnP restoration (3)-(4) and the DDM restoration (16)-(17). Namely, ignoring the scaling of the signal by " + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\{\\bar{\\alpha}_t\\}" + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "text", + "content": ", the main difference is the noise injection, composed of the estimated noise " + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "text", + "content": " and the random noise " + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\epsilon_t" + }, + { + "bbox": [ + 304, + 522, + 545, + 641 + ], + "type": "text", + "content": ". The similarity of DDMs schemes to previous iterative denoising methods is further seen by the formulation of [15], which decouples the diffusion \"forward\" flows, used for training the denoisers, from the \"reverse\" inference flows. More discussion on such connections can be found in a recent review paper [10]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "For example, the DDM restoration method in [6], dubbed DPS, where the guidance is based on the gradient of the LS term, resembles (6) with noise injection. Interestingly, just like its PnP counterpart, it requires a very large number of iterations (and thus many NFEs). Alternatively, by using BP guidance in (17) — equivalently, when injecting noise" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25247" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": "to step (9) in IDBP — one gets the recent DDNM method [41] (which is also similar to the method in [30]). However, note that the DDNM paper focuses on noiseless settings and has difficulties in noisy settings (in Section 4 we state its technical limitation), which is aligned with the sensitivity of BP guidance to noise in " + }, + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": ", as mentioned above." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": "At this point, we would also like to mention the DDRM method [16], which resembles the BP approach as it generates \"spectral space\" measurements " + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{y}}" + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": " in a way similar to applying " + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{\\dagger}" + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": ". Yet, it is more robust to observation noise as it requires access to the full SVD of " + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": ", which allows it to mitigate noise amplification per singular component in each iteration. In this paper we aim to devise an approach that does not require computing and storing the SVD of " + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": ", which is impractical is most cases." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 286, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 286, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 286, + 347 + ], + "type": "text", + "content": "Finally, we note that the way we construct a sampling scheme from a deterministic algorithm shares similarity with the recent method DIfPIR [45]. However, while [45] uses an existing PnP baseline, here we propose a novel core reconstruction method. Also, empirically our new sampling scheme demonstrates better accuracy than DiffPIR (evaluated by PSNR) without compromising on perceptual quality (evaluated by LPIPS)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 357, + 176, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 176, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 176, + 371 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 378, + 286, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 286, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 286, + 472 + ], + "type": "text", + "content": "In this section, we present our image restoration method that is more robust to observation noise than methods that use only back-projections while still having low computational complexity and clear benefits over methods that are based only on plain LS based guidance. To this end, we present a novel core guidance approach, equip it with formal theoretical motivation, and utilize it to devise a new sampling-based reconstruction scheme." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 286, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 286, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 286, + 498 + ], + "type": "text", + "content": "All the claims in this section are proved in the supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 506, + 139, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 139, + 518 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 139, + 518 + ], + "type": "text", + "content": "3.1. Core approach" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 524, + 286, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 286, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 286, + 548 + ], + "type": "text", + "content": "The idea for our approach comes from identifying (9) as a specific instance of the formula" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 90, + 556, + 286, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 556, + 286, + 571 + ], + "spans": [ + { + "bbox": [ + 90, + 556, + 286, + 571 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} \\mathbf {W} (\\mathbf {A x} _ {0 | t} - \\mathbf {y}) \\tag {18}", + "image_path": "afea531fc08e9d383513fc8adf905ce00eba69201197ae339cb1c5a7539e5e62.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T)^{-1}" + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "text", + "content": " (assuming full rank " + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\mu_t = 1" + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "text", + "content": ". The plain LS step (6) is obviously also an instance of this expression with " + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = \\mathbf{I}_m" + }, + { + "bbox": [ + 46, + 580, + 286, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": "Recall traditional preconditioning in optimization [23]: The optimization of an objective, e.g., " + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "inline_equation", + "content": "L: \\mathbb{R}^n \\to \\mathbb{R}" + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": " in (2), is based on gradient-based optimizers where the full gradient " + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\nabla L(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": " is multiplied by a (symmetric) positive definite matrix " + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": ". Such practice does not affect the problem's minimizers (since " + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\nabla L(\\mathbf{x}) = \\mathbf{0} \\iff \\nabla L(\\mathbf{x}) = \\mathbf{0}" + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": " due to the invertibility of " + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": "), and its goal is to ease the optimization landscape, characterized by the condition number" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "text", + "content": "of the effective Hessian " + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{1 / 2}\\nabla^2 L(\\mathbf{x})\\mathbf{P}^{1 / 2}" + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "text", + "content": ". In (18), however, " + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}\\in \\mathbb{R}^{m\\times m}" + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "text", + "content": " does not directly affect the signal's prior and for general " + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "text", + "content": " we may not have " + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^T\\mathbf{W}(\\mathbf{A}\\mathbf{x} - \\mathbf{y}) = \\mathbf{0}\\iff \\nabla \\ell_{LS}(\\mathbf{x}) = \\mathbf{A}^T (\\mathbf{A}\\mathbf{x} - \\mathbf{y}) = \\mathbf{0}" + }, + { + "bbox": [ + 304, + 71, + 545, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 121, + 495, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 121, + 495, + 132 + ], + "spans": [ + { + "bbox": [ + 317, + 121, + 495, + 132 + ], + "type": "text", + "content": "Nevertheless, we have the following claims." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "content": "Claim 3.1. Let " + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{A}^{m \\times n}" + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "m \\leq n" + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "\\operatorname{rank}(\\mathbf{A}) = m" + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{m \\times m}" + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "\\operatorname{rank}(\\mathbf{A}^T \\mathbf{W}) = m" + }, + { + "bbox": [ + 304, + 138, + 545, + 163 + ], + "type": "text", + "content": ". Then," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 327, + 170, + 523, + 184 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 170, + 523, + 184 + ], + "spans": [ + { + "bbox": [ + 327, + 170, + 523, + 184 + ], + "type": "interline_equation", + "content": "\\mathbf {A} ^ {T} \\mathbf {W} (\\mathbf {A x} - \\mathbf {y}) = \\mathbf {0} \\iff \\mathbf {A} ^ {T} (\\mathbf {A x} - \\mathbf {y}) = \\mathbf {0}.", + "image_path": "f2344811e078850f8222d986325a54ccbed782b0a6cfee60be1131ce68704a55.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": "Claim 3.2. Let " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{A}^{m \\times n}" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "m \\leq n" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{m \\times m}" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": " be a positive definite matrix that shares eigenbasis with " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathbf{A A}^T" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": ". Then, there exists a positive definite " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 367, + 238, + 484, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 238, + 484, + 251 + ], + "spans": [ + { + "bbox": [ + 367, + 238, + 484, + 251 + ], + "type": "interline_equation", + "content": "\\mathbf {A} ^ {T} \\mathbf {W} \\mathbf {A} = \\mathbf {P} ^ {1 / 2} \\mathbf {A} ^ {T} \\mathbf {A} \\mathbf {P} ^ {1 / 2}.", + "image_path": "20f80c2becc81ba9a249c22a450f4c0a2d25169ea5a9ff5355b8126f3fa6edbb.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": "Therefore, if " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " is full rank, then any " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " for which " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^T\\mathbf{W}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " is full rank (e.g., " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T)^{-1}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": ") can be interpreted as a preconditioner of " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\nabla \\ell_{LS}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " (rather than of the full objective that may include additional terms). Alternatively, even if " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " is not full rank, but " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " shares eigenbasis with " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\mathbf{A}^T" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " (e.g., " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = (\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m)^{-1}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": "), we allow ourselves to refer to " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " as a preconditioner of " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\nabla \\ell_{LS}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": " since it has the same effect on the effective Hessian, " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{1/2}\\nabla^2\\ell_{LS}(\\mathbf{x})\\mathbf{P}^{1/2}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": ", as a traditional preconditioner " + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 304, + 259, + 545, + 366 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 367, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 392 + ], + "type": "text", + "content": "Inspired by this, in lieu of (4) we propose a data-fidelity guidance based on iteration-dependent preconditioner:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 347, + 399, + 545, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 399, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 347, + 399, + 545, + 413 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {A} ^ {T} \\mathbf {W} _ {t} (\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}) \\tag {19}", + "image_path": "a8830f30c2f857d693ee34faea2be0d94207293c05ca6f3ac07a828290d02bac.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": "with a \"smooth\" discretization of the path of symmetric preconditioners " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{W}_t\\}" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": " — invertible with eigenbasis shared with " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\mathbf{A}^T" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": " — that starts roughly at " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_T \\propto (\\mathbf{A}\\mathbf{A}^T + \\eta \\mathbf{I}_m)^{-1}" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": " and ends roughly at " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_0 \\propto \\mathbf{I}_m" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 468, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 540 + ], + "type": "text", + "content": "In words, the proposed guidance is based on gently traversing from the (regularized) BP step to the LS step along the restoration scheme. Thus, it enjoys benefits of BP steps (stronger consistency with " + }, + { + "bbox": [ + 304, + 468, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 468, + 545, + 540 + ], + "type": "text", + "content": ", accelerated convergence, etc.) in early iterations and the better robustness to noise of LS steps as the scheme approaches its end." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "content": "Potentially, a sequence of preconditioners " + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{W}_t\\}" + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "content": " might be learned in a data-driven manner under some optimality criterion. Yet, this is expected to come at the price of losing their generality to arbitrary data. Thus, here we propose an engineered, but simple and effective, update rule of " + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t" + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "content": " that, as we will show empirically, already demonstrates the usefulness of our new concept. Specifically, the rule that we propose is given by the following convex combination:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 339, + 643, + 545, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 643, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 339, + 643, + 545, + 657 + ], + "type": "interline_equation", + "content": "\\mathbf {W} _ {t} = (1 - \\delta_ {t}) \\left(\\mathbf {A} \\mathbf {A} ^ {T} + \\eta \\mathbf {I} _ {m}\\right) ^ {- 1} + \\delta_ {t} c \\mathbf {I} _ {m} \\tag {20}", + "image_path": "180a529d8257af3ed6b83bd6f3f613289a9fe581114cdbfd21308f6d3299b059.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "inline_equation", + "content": "0 \\leq \\delta_T < \\ldots < \\delta_0 \\leq 1" + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "content": " is a predefined sequence, and " + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "content": " is a positive scalar that balances the two terms." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "In general, the main motivation for (20) is that it both obeys the previously stated conditions and also yields a" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25248" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "data-fidelity guidance that is very simple to implement. Indeed, plugging (20) in (19) yields" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 105, + 287, + 134 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 105, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 105, + 287, + 134 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {x} _ {t - 1} = \\mathbf {x} _ {0 | t} - \\mu_ {t} \\left((1 - \\delta_ {t}) \\mathbf {g} _ {B P} (\\mathbf {x} _ {0 | t}) + \\delta_ {t} \\mathbf {g} _ {L S} (\\mathbf {x} _ {0 | t})\\right), \\\\ =: \\mathbf {x} _ {0 | t} - \\mu_ {t} \\mathbf {g} _ {\\delta_ {t}} \\left(\\mathbf {x} _ {0 | t}\\right) \\tag {21} \\\\ \\end{array}", + "image_path": "f9a82fbce37209cf1419fde4972e4ae6cf31c606987019ff4b85be368ce40e35.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 144, + 75, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 75, + 154 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 75, + 154 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 163, + 287, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 163, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 59, + 163, + 287, + 178 + ], + "type": "interline_equation", + "content": "\\mathbf {g} _ {B P} \\left(\\mathbf {x} _ {0 | t}\\right) = \\mathbf {A} ^ {T} \\left(\\mathbf {A} \\mathbf {A} ^ {T} + \\eta \\mathbf {I} _ {m}\\right) ^ {- 1} \\left(\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}\\right), \\tag {22}", + "image_path": "e09b2d288b7beb3249617eddb42330f8494594606ca9dffa8cda949215a201e7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 180, + 287, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 180, + 287, + 196 + ], + "spans": [ + { + "bbox": [ + 62, + 180, + 287, + 196 + ], + "type": "interline_equation", + "content": "\\mathbf {g} _ {L S} \\left(\\mathbf {x} _ {0 | t}\\right) = c \\mathbf {A} ^ {T} \\left(\\mathbf {A} \\mathbf {x} _ {0 | t} - \\mathbf {y}\\right), \\tag {23}", + "image_path": "c0dc8fa51b55522cf0c6bd08a3f05a2e9339321a6849665326401ab196ad93d1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 204, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 204, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 287, + 227 + ], + "type": "text", + "content": "can be computed efficiently for a wide range of observation models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "text", + "content": "In Section 3.4 we will discuss practical implementations details for simple hyperparameter tuning (e.g., a simple way to tune " + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "inline_equation", + "content": "\\{\\delta_t\\}" + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "text", + "content": "). As for setting " + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "text", + "content": ", observe that (19) is essentially a gradient step (at " + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t}" + }, + { + "bbox": [ + 47, + 228, + 287, + 288 + ], + "type": "text", + "content": ") of the weighted least squares (WLS) data-fidelity term:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 297, + 287, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 297, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 86, + 297, + 287, + 320 + ], + "type": "interline_equation", + "content": "\\ell_ {W L S, t} (\\mathbf {x}; \\mathbf {y}) = \\frac {1}{2} \\left\\| \\mathbf {W} _ {t} ^ {1 / 2} (\\mathbf {A x} - \\mathbf {y}) \\right\\| _ {2} ^ {2}, \\tag {24}", + "image_path": "cc9fda85af22e1c8af4a80112659bdd4dbb1b607ae0308e253dad7f26327229e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 327, + 217, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 217, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 217, + 340 + ], + "type": "text", + "content": "for which we have the following property." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "text", + "content": "Claim 3.3. Denote by " + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "text", + "content": " the largest singular value of " + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "inline_equation", + "content": "c \\leq 1 / \\lambda_1^2" + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "text", + "content": ". Then, the update (21) with " + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\mu_t = 1" + }, + { + "bbox": [ + 47, + 347, + 287, + 383 + ], + "type": "text", + "content": " ensures reduction in (24)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "content": "Many popular degradation models obey " + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\lambda_1 \\lesssim 1" + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "content": " (e.g., in deblurring " + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 1" + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "content": " and in super-resolution " + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\lambda_1" + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "content": " is moderately lower than 1). Thus, following the claim, unless stated otherwise, we use " + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "inline_equation", + "content": "c = 1" + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mu_t = 1" + }, + { + "bbox": [ + 47, + 392, + 287, + 440 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 440, + 287, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 572 + ], + "type": "text", + "content": "To conclude this subsection, the core of the proposed algorithm is based on iteratively computing (3) and (21). Without noise injection, this is essentially a novel PnP scheme, which we call Iterative Denoising and Preconditioned Guidance (IDPG). As we will empirically show in Section 4, while this method has good PSNR performance, turning it into a DDM-based sampling scheme leads to better recoveries, especially in terms of perceptual quality. Before presenting the sampling scheme in Section 3.3, let us provide some theoretical motivation for our preconditioned guidance approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 579, + 104, + 592 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 104, + 592 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 104, + 592 + ], + "type": "text", + "content": "3.2. Theory" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": "Let us state some mathematical claims that motivate the core guidance approach. In this subsection we consider a simplified setting of having a fixed " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "0 < \\delta < 1" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": ", i.e., a fixed WLS data-fidelity term (24) with " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": " given as in (20) but with " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\delta_t = \\delta" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": ". We examine the effects of this WLS, compared to LS and BP fidelity terms, on an estimator of " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": ", which is obtained by minimizing (2) with Tikhonov prior " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "s(\\mathbf{x}) = \\frac{\\beta}{2} \\| \\mathbf{Dx} \\|_2^2" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta > 0" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{D}^T \\mathbf{D}" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": " is invertible, so, the estimator " + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 597, + 287, + 713 + ], + "type": "text", + "content": " per data-fidelity term is unique." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "The MSE of " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " (conditioned on " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", averaged over the noise e) can be decomposed into two terms: squared bias, " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "b^{2}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " (independent of e), and variance, " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " (depends on " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\sigma_e^2" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "), given by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 375, + 114, + 545, + 127 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 114, + 545, + 127 + ], + "spans": [ + { + "bbox": [ + 375, + 114, + 545, + 127 + ], + "type": "interline_equation", + "content": "b ^ {2} := \\left\\| \\mathbb {E} \\left[ \\hat {\\mathbf {x}} \\mid \\mathbf {x} ^ {*} \\right] - \\mathbf {x} ^ {*} \\right\\| _ {2} ^ {2}, \\tag {25}", + "image_path": "05a5b9b61f9c65ba4bdbdc52f501f28855da19f470e4744c02cc1f76b3b01f5a.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 380, + 129, + 545, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 129, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 380, + 129, + 545, + 142 + ], + "type": "interline_equation", + "content": "v := \\operatorname {T r} \\left(\\operatorname {V a r} \\left(\\hat {\\mathbf {x}} \\mid \\mathbf {x} ^ {*}\\right)\\right). \\tag {26}", + "image_path": "b410574a04dbce1223443e32f223c34b2c0fa5932a17c6199fe40d6430be5b8b.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "text", + "content": "The motivation for analyzing this setting (even though in the proposed core procedure (3) & (21), we modify " + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\delta_t" + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "text", + "content": " along the iterations and do not attempt to reach a minimizer per " + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\delta_t" + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "text", + "content": ") is that insights on gains in bias and variance at the minimizer level hint that similar effects are possible even with limited optimizer iterations per " + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\delta_t" + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "text", + "content": ". Also, in [38], it was shown that insights gained for Tikhonov prior generalize empirically to more complex priors. Specifically, they showed that BP typically leads to smaller bias but higher variance than LS. In what follows, the intuition that " + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "inline_equation", + "content": "0 < \\delta < 1" + }, + { + "bbox": [ + 304, + 148, + 545, + 291 + ], + "type": "text", + "content": " enables trading bias and variance is made formal." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "type": "text", + "content": "Theorem 3.4. Consider the observation model (1) and estimating " + }, + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "type": "text", + "content": " via minimization of (2) with " + }, + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "type": "inline_equation", + "content": "s(\\mathbf{x}) = \\frac{\\beta}{2}\\|\\mathbf{D}\\mathbf{x}\\|_2^2" + }, + { + "bbox": [ + 305, + 297, + 545, + 330 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": "Assume that: (a) " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^T\\mathbf{A}" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{D}^T\\mathbf{D} \\succ 0" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": " share eigenbasis; (b) the singulars value of " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": " are in " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "(0,1]" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": ", and not all equal (common case); (c) " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\eta = 0" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "c = 1" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "b_{BP} < b_{WLS} < b_{LS}" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "inline_equation", + "content": "v_{LS} < v_{WLS} < v_{BP}" + }, + { + "bbox": [ + 305, + 330, + 545, + 379 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": "Note that the margins in the theorem's inequalities depend on where " + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": " is located in " + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "inline_equation", + "content": "(0,1)" + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": " (e.g., " + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "inline_equation", + "content": "v_{\\mathrm{WLS}} \\to v_{\\mathrm{LS}}" + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\delta \\to 1" + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": "). This further motivates having a set " + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\{\\delta_t\\}" + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": " instead of a fixed " + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 384, + 545, + 442 + ], + "type": "text", + "content": " in (20) to gain flexibility in handling the error's bias/variance." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "content": "As for the convergence rates of first-order optimization algorithms (which affect the number of NFEs with practical DNN-based priors), recall that it can typically be characterized by the condition number, " + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\kappa(\\cdot)" + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "content": ", of the problem's Hessian, which equals the ratio between the largest and smallest eigenvalues of the Hessian — the lower the better. Note, though, that for " + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "inline_equation", + "content": "m < n" + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "content": ", the Hessian of each of the three data-fidelity terms (LS, BP, WLS) is rank-deficient due to the ill-posedness of the observation model. Nevertheless, we have the following property on the component of their Hessian in the row-range of " + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "content": " (a subspace in " + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": "Claim 3.5. Assume that " + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{rank}(\\mathbf{A}) = m" + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": ", the singular values of " + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": " are not all equal, " + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\eta = 0" + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": ", and denote by " + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{n \\times m}" + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": " an orthonormal basis for the row-range of " + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": ". We have that" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 621, + 547, + 636 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 547, + 636 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 547, + 636 + ], + "type": "interline_equation", + "content": "\\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {B P} \\mathbf {V}) < \\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {W L S} \\mathbf {V}) < \\kappa (\\mathbf {V} ^ {T} \\nabla_ {\\mathbf {x}} ^ {2} \\ell_ {L S} \\mathbf {V}).", + "image_path": "5fee902afe9002062361bba9b3117a80a7f422a61b2c19e62a70ea0aa977ce74.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Namely, the flexibility in " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " allows accelerating the reconstruction procedure compared to using only a LS based guidance. Leveraging this result to establish ranking claims for specific algorithms may follow the approaches of [39] (based on constraints on the null space of " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " that are implicitly imposed by the signal prior term)." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25249" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 98, + 287, + 355 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "Algorithm 1 Denoising Diffusion with iterative Preconditioned Guidance (DDPG)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "lines": [ + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\cdot ,t)" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " (noise estimator), " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "T,\\mathbf{y},\\mathbf{A},\\{\\bar{\\alpha}_t\\} ,\\{\\mu_t\\} ,c," + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\eta ,\\gamma ,\\zeta" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 1: if " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\sigma_e > 0" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " then 2: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\delta_t = \\bar{\\alpha}_t^\\gamma" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "w_{t} = \\delta_{t}" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 3: else 4: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\delta_t = 0" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "w_{t} = 1" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 5: end if 6: Initialize " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 7: for " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " to 1 do 8: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}}\\left(\\mathbf{x}_t - \\sqrt{1 - \\bar{\\alpha}_t}\\epsilon_\\theta (\\mathbf{x}_t,t)\\right)" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 9: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{BP} = \\mathbf{A}^T (\\mathbf{A}\\mathbf{A}^T +\\eta \\mathbf{I}_m)^{-1}(\\mathbf{A}\\mathbf{x}_{0|t} - \\mathbf{y})" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 10: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{LS} = c\\mathbf{A}^T (\\mathbf{A}\\mathbf{x}_{0|t} - \\mathbf{y})" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 11: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_{t - 1} = \\mathbf{x}_{0|t} - \\mu_t((1 - \\delta_t)\\mathbf{g}_{BP} + \\delta_t\\mathbf{g}_{LS})" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 12: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_t = \\frac{1}{\\sqrt{1 - \\bar{\\alpha}_t}} (\\mathbf{x}_t - \\sqrt{\\bar{\\alpha}_t}\\tilde{\\mathbf{x}}_{t - 1})" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 13: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}_n)" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 14: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t - 1} =" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 15: " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\sqrt{\\bar{\\alpha}_{t - 1}}\\tilde{\\mathbf{x}}_{t - 1} + \\sqrt{1 - \\bar{\\alpha}_{t - 1}}\\left(w_t\\sqrt{1 - \\zeta}\\hat{\\epsilon}_t + \\sqrt{\\zeta}\\epsilon_t\\right)" + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "text", + "content": " 16: end for 17: return " + }, + { + "bbox": [ + 47, + 98, + 287, + 355 + ], + "type": "inline_equation", + "content": "{\\bf x}_0" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 380, + 151, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 151, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 151, + 393 + ], + "type": "text", + "content": "3.3. Sampling scheme" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "type": "text", + "content": "As previously mentioned, in this subsection we turn IDPG (alternating (3) and (21)) into a DDM-based sampling scheme that empirically leads to better recoveries, especially in terms of perceptual quality. Injecting noise to the estimate in a certain iteration leads to an image that better matches the data on which the denoiser has been trained. Intuitively, this should improve the denoiser's performance and also allow it to mitigate error propagation along the iterations, by masking artifacts with noise that will be removed. Accordingly, it allows using a smaller value of the regularization parameter " + }, + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "type": "text", + "content": " when handling noisy " + }, + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 400, + 287, + 543 + ], + "type": "text", + "content": ", which yields results with sharper details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": "The sampling scheme that we propose is based on modification of the DDIM guided scheme, stated in (17). Namely, " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t}" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " is computed using a DDM's noise estimator as in (16) and the novel guidance " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\delta_t}" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " is being used in lieu of the abstract gradient " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}}\\ell" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": ". However, we propose several important modifications of the additive noise terms " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_t\\epsilon_\\theta (\\mathbf{x}_t;t) + \\tilde{\\sigma}_t\\epsilon_t" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " that appear in (17)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "The first modification is inspired by [45]. Note that, contrary to the unconditional image generation task, the data-fidelity guidance can significantly modify the estimated signal " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_{t - 1}\\coloneqq \\mathbf{x}_{0|t} - \\mu_t\\mathbf{g}_{\\delta_t}" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " compared to " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t}" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": ". Therefore, the effective predicted noise can be significantly different than " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t;t)" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": ". Accordingly, based on the relation between " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t;t)" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{0|t}" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " in (16), the effective predicted noise takes" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 354, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 354, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 354, + 83 + ], + "type": "text", + "content": "the form of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 358, + 91, + 545, + 117 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 91, + 545, + 117 + ], + "spans": [ + { + "bbox": [ + 358, + 91, + 545, + 117 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {\\epsilon}} _ {t} = \\frac {1}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\left(\\mathbf {x} _ {t} - \\sqrt {\\bar {\\alpha} _ {t}} \\tilde {\\mathbf {x}} _ {t - 1}\\right), \\tag {27}", + "image_path": "b2f1208efa534f027612d5e03c6e4bd51b48a9c7136c0df9ec630314b4fee74d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 126, + 523, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 126, + 523, + 138 + ], + "spans": [ + { + "bbox": [ + 305, + 126, + 523, + 138 + ], + "type": "text", + "content": "and we use it instead of " + }, + { + "bbox": [ + 305, + 126, + 523, + 138 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t;t)" + }, + { + "bbox": [ + 305, + 126, + 523, + 138 + ], + "type": "text", + "content": " for generating " + }, + { + "bbox": [ + 305, + 126, + 523, + 138 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t - 1}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": "Similarly to this prior work, we also simplify the way of trading between the (effective) estimated noise and the stochastic noise. Instead of time-dependent noise level " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}_t" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": " which affects " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_t = \\sqrt{1 - \\bar{\\alpha}_{t-1} - \\tilde{\\sigma}_t^2}" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": " in a complicated way, we balance between the levels of " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_t" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\epsilon_t" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": " using the simple to tune weight " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\sqrt{1 - \\zeta}" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\sqrt{\\zeta}" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": ", respectively, with a single hyperparameter " + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\zeta \\in [0,1]" + }, + { + "bbox": [ + 304, + 139, + 545, + 229 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": "Our key novel modification is the following. In the case of observation noise (i.e., " + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\sigma_{e} > 0" + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": "), the effective predicted noise " + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{t}" + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": " may not be useful in iterations where the overall guidance " + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\delta_t}" + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": " is dominated by " + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{BP}" + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": ", due to the sensitivity to noise of the BP guidance. Therefore, we scale it by " + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\delta_{t}" + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": " — the weight that is given to " + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{LS}" + }, + { + "bbox": [ + 304, + 229, + 545, + 312 + ], + "type": "text", + "content": ", which is more robust to observation noise." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "type": "text", + "content": "We remark that our sampling scheme transfers smoothly to the noiseless case, where one can simply use pure BP guidance – or equivalently " + }, + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "type": "inline_equation", + "content": "\\delta_t = 0" + }, + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "type": "text", + "content": ": it is only required to omit the last modification (i.e., avoid attenuating the noise injection by " + }, + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "type": "inline_equation", + "content": "\\delta_t" + }, + { + "bbox": [ + 304, + 314, + 545, + 409 + ], + "type": "text", + "content": "). As will be shown empirically, this scheme performs on par with BP-based DDM methods that are specifically devised for noiseless observations, and outperforms other methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 410, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 469 + ], + "type": "text", + "content": "The resulted DDM-based sampling algorithm, that we name Denoising Diffusion with iterative Preconditioned Guidance (DDPG), is summarized in Algorithm 1. The algorithm includes a simple way to set " + }, + { + "bbox": [ + 304, + 410, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\{\\delta_t\\}" + }, + { + "bbox": [ + 304, + 410, + 545, + 469 + ], + "type": "text", + "content": " that is explained in the next subsection." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 479, + 437, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 437, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 437, + 491 + ], + "type": "text", + "content": "3.4. Implementation details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "text", + "content": "In the experimental section, we wish to test the approach (both DDPG and its core version IDPG) with powerful DDM's denoisers trained and used in [7, 20]. These models are based on DDPM formulation [13, 29], that we use to reduce the hyperparameter tuning effort in all our examined tasks, and in particular setting " + }, + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\{\\delta_t\\}" + }, + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "text", + "content": " for noisy observations. (Recall that in the noiseless case, we simply set " + }, + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\delta_t = 0" + }, + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": "As presented in Section 2, in DDPM there are the parameters " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\bar{\\alpha}_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": ", which are determined by the hyperparameters " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": ", and determine many other parameters (e.g., the model's noise levels " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\sigma_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": "). These " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\bar{\\alpha}_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " obey " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "0_+ \\approx \\bar{\\alpha}_T < \\ldots < \\bar{\\alpha}_0 = 1" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": ". We do not change " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\bar{\\alpha}_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " at all compared to previous methods that we compare with [16, 41]. In fact, we use " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\bar{\\alpha}_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " to set " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\delta_t = \\bar{\\alpha}_t^\\gamma" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " with a single positive scalar hyperparameter " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": ". This ensures that as " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " decreases, " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\delta_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " is monotonically increasing from 0 to 1 in rate that can be controlled by " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": ". Observe that smaller " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " yields higher intermediate " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t^\\gamma" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " and thus a larger portion of " + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{W}_t\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": " closer to" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25250" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "identity matrix — or, equivalently, \"faster\" progress from BP to LS. This is beneficial for larger observation noise " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\sigma_{e}" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "text", + "content": "To conclude, when using " + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "inline_equation", + "content": "c = 1" + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\mu_t = 1" + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "text", + "content": ", applying our approach requires tuning only " + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\eta, \\gamma" + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 46, + 97, + 287, + 144 + ], + "type": "text", + "content": " (for DDPG). Note that, potentially, tuning more hyperparameters for our method can further boost its results." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 159, + 128, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 159, + 128, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 128, + 172 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "text", + "content": "In this section, we examine the performance of our approach. We start with examining our core guidance, as reflected in IDPG, compared to its extreme cases: deterministic methods with pure BP and LS based guidance. Then, we compare both IDPG and DDPG to existing methods: DDRM [16], DPS [6], DDNM [41], and DiffPIR [45]. We consider the CelebA-HQ 1K and ImageNet 1K test sets, where for fair comparison all the methods use the same pretrained DDM's denoisers: the model from [20] trained on CelebA-HQ and the (unconditional) model from [7] trained on ImageNet. We use " + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "text", + "content": " iterations for each of the methods as in [41]. An exception is DPS, which requires " + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "text", + "content": " iterations with much larger per-iteration complexity, making it extremely slow compared to others. All the methods are initialized with the same random " + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 46, + 179, + 287, + 357 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 360, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 538 + ], + "type": "text", + "content": "We consider image deblurring and super-resolution tasks that have been widely examined in the previous works, and for each method we use the hyperparameter settings suggested by its authors. The settings for our methods are stated in the supplementary material. Specifically, we consider super-resolution with bicubic downsampling and scale factor 4 and deblurring with Gaussian kernel as, e.g., in [16, 41]. However, we also examine challenging noisy deblurring with random motion kernels, as in [45]. This is an example for a common task that cannot be handled by DDRM [16], which is limited to separable kernels for which the SVD of " + }, + { + "bbox": [ + 46, + 360, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 360, + 287, + 538 + ], + "type": "text", + "content": " can be efficiently computed and stored. This task cannot be addressed also by DDNM [41], which fails to tackle noisy observations. We examine the noisy cases also in the two aforementioned tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": "In the supplementary material, we demonstrate the advantages of our approach over recent task-specific DNNs, as well as its superior performance also with lower noise level than demonstrated here. In addition, we report there the impressive performance of our approach for sparse-view computed tomography (another task where computing the SVD of " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " is infeasible)." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 313, + 102, + 539, + 171 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 93 + ], + "type": "text", + "content": "Table 1. Data-fidelity guidance ablation: super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 102, + 539, + 171 + ], + "lines": [ + { + "bbox": [ + 313, + 102, + 539, + 171 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 539, + 171 + ], + "type": "table", + "html": "
TaskPGM-LSIDBPIDPG (ours)
Bicub. SRx4 σe=032.40 / 0.12732.66 / 0.11132.66 / 0.111
Bicub. SRx4 σe=0.0528.91 / 0.20928.95 / 0.22929.89 / 0.155
Gauss. Deb. σe=032.25 / 0.14145.58 / 0.00245.58 / 0.002
Gauss. Deb. σe=0.0528.61 / 0.19130.55 / 0.15031.08 / 0.150
Gauss. Deb. σe=0.127.89 / 0.23928.29 / 0.22629.28 / 0.146
", + "image_path": "02482149ac67ddac4255b19f4944597a51ef1492c32e837d7049fe7186ed715e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 332, + 181, + 517, + 302 + ], + "blocks": [ + { + "bbox": [ + 332, + 181, + 517, + 302 + ], + "lines": [ + { + "bbox": [ + 332, + 181, + 517, + 302 + ], + "spans": [ + { + "bbox": [ + 332, + 181, + 517, + 302 + ], + "type": "image", + "image_path": "7b93fc4180e7ccd6cc5c954c8ff73b3b4382afe12f5e43c4e3dd578ce7824182.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 308, + 545, + 351 + ], + "lines": [ + { + "bbox": [ + 305, + 308, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 545, + 351 + ], + "type": "text", + "content": "Figure 2. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our DDPG. Bottom row, from left to right: PGM-LS, IDBP, and our IDPG (baseline for DDPG)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 370, + 466, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 466, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 466, + 383 + ], + "type": "text", + "content": "4.1. Examining the core approach" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "type": "text", + "content": "As the main contribution of our paper is the novel guidance approach that smoothly traverses from BP to LS guidance, we start with examining our baseline IDPG method (alternating (3) and (21)) with IDBP [36] (" + }, + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\delta_t = 0" + }, + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "type": "text", + "content": ") and a method with LS based updates (" + }, + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\delta_t = 1" + }, + { + "bbox": [ + 305, + 388, + 545, + 472 + ], + "type": "text", + "content": "), denoted here by PGM-LS (a common PnP scheme [14]). This comparison essentially provides an ablation study for our core approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 472, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 579 + ], + "type": "text", + "content": "The results for bicubic super-resolution and Gaussian deblurring with various and without noise for the CelebA-HQ 1K test set are presented in Table 1. They show that IDPG consistently outperforms IDBP and PGM-LS. Figure 2 displays qualitative results, showing that IDPG has less artifacts than IDBP and finer details than PGM-LS. Yet, while IDPG provides high PSNR values its perceptual quality can be improved by using the sampling-based DDPG, as shown in this figure." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 587, + 480, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 480, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 480, + 600 + ], + "type": "text", + "content": "4.2. Comparison with other methods" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 605, + 545, + 713 + ], + "type": "text", + "content": "We turn to compare the proposed approach to DDRM, DPS, DDNM and DiffPIR. We consider all deblurring and superresolution tasks that have been described above with various noise levels. The results for the CelebA-HQ 1K test set and the ImageNet 1K test set are presented in Table 2 and Table 3, respectively. We present qualitative results for motion deblurring, Gaussian deblurring and super-resolution in Figures 1, 3 and 4, respectively. More results appear in the supplementary material." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 635, + 287, + 664 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 664 + ], + "type": "text", + "content": "1Using the same hardware, DPS takes a dozen minutes per image compared to a couple of seconds of the other methods, and limiting it to 100 iterations fails to produce meaningful recoveries." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "type": "text", + "content": "2Note that DDMN is tailored for " + }, + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\sigma_{e} = 0" + }, + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "type": "text", + "content": ". We remark that DDNM+ that was proposed in [41] for handling noisy " + }, + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 664, + 287, + 712 + ], + "type": "text", + "content": " (via SVD) seems to be heavily tied to a specific downsampling task (without bicubic kernel) and does not support the considered tasks, as shown in the supplementary material. Our efforts to adapt it failed." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25251" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 101, + 99, + 491, + 194 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 2. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on CelebA-HQ 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 101, + 99, + 491, + 194 + ], + "lines": [ + { + "bbox": [ + 101, + 99, + 491, + 194 + ], + "spans": [ + { + "bbox": [ + 101, + 99, + 491, + 194 + ], + "type": "table", + "html": "
Task\\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=031.64 / 0.05429.39 / 0.06530.26 / 0.05131.64 / 0.04832.66 / 0.11131.60 / 0.052
Bicub. SRx4 σe=0.0529.26 / 0.09027.49 / 0.08627.44 / 0.085N/A29.89 / 0.15529.39 / 0.105
Gauss. Deb. σe=042.49 / 0.00631.25 / 0.05532.97 / 0.04145.56 / 0.00245.58 / 0.00245.46 / 0.002
Gauss. Deb. σe=0.0530.53 / 0.07427.75 / 0.08428.89 / 0.074N/A31.08 / 0.15030.41 / 0.068
Gauss. Deb. σe=0.128.79 / 0.08826.67 / 0.09727.59 / 0.083N/A29.28 / 0.14629.18 / 0.080
Motion Deb. σe=0.05N/A19.63 / 0.22727.96 / 0.102N/A29.73 / 0.13429.02 / 0.082
Motion Deb. σe=0.1N/A19.64 / 0.23126.23 / 0.132N/A27.86 / 0.16627.74 / 0.099
", + "image_path": "6777dbc256aa1ffbaf3114556db76a7e24f571836e9feb81929fe6ee715d72df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 101, + 233, + 491, + 306 + ], + "blocks": [ + { + "bbox": [ + 46, + 204, + 546, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 546, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 546, + 228 + ], + "type": "text", + "content": "Table 3. Super-resolution and deblurring PSNR [dB] (↑) and LPIPS (↓) results on Imagenet 1K. N/A marks applicability limitation of: (1) DDNM to noiseless settings and (2) DDRM to settings where the SVD is given and stored. (More details in the text)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 101, + 233, + 491, + 306 + ], + "lines": [ + { + "bbox": [ + 101, + 233, + 491, + 306 + ], + "spans": [ + { + "bbox": [ + 101, + 233, + 491, + 306 + ], + "type": "table", + "html": "
Task\\MethodDDRMDPS (1000 NFEs)DiffPIRDDNMIDPG (ours)DDPG (ours)
Bicub. SRx4 σe=027.38 / 0.27025.56 / 0.23626.99 / 0.22527.45 / 0.24527.20 / 0.32627.41 / 0.255
Bicub. SRx4 σe=0.0525.54 / 0.33324.05 / 0.27124.65 / 0.318N/A25.51 / 0.41125.55 / 0.354
Gauss. Deb. σe=040.53 / 0.00825.54 / 0.25930.54 / 0.08243.64 / 0.00344.02 / 0.00244.21 / 0.002
Gauss. Deb. σe=0.0527.71 / 0.24323.59 / 0.29426.64 / 0.240N/A27.47 / 0.31327.73 / 0.205
Motion Deb. σe=0.05N/A17.52 / 0.46825.34 / 0.284N/A26.02 / 0.35425.94 / 0.249
", + "image_path": "ee825a19a5428d3cea2948c02c7a66123f9cbd2dda2582a19767b48c63cd7187.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 323, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 443 + ], + "type": "text", + "content": "Examining the results, observe that, indeed, the sampling-based version of our approach (DDPG) consistently leads to better perceptual quality, both visually and as measured by LPIPS. Interestingly, while there is an inherent tradeoff between accuracy and perceptual quality [3], the PSNR reduction in DDPG compared to IDPG is rather moderate (and in some case DDPG even has slightly better PSNR than IDPG). One can observe that our approach typically outperforms other approaches in deblurring and is competitive in super-resolution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 443, + 288, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 288, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 288, + 526 + ], + "type": "text", + "content": "Importantly, note that the only reference methods that are as flexible as our approach to the observation model are DPS, which is very slow, and DiffPIR. However, their PSNR is significantly lower than the PSNR of our DDPG. Recall that in many critical applications (e.g., medical imaging), accuracy, as measured by the classical PSNR metric, is extremely important." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 538, + 119, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 119, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 119, + 550 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we presented a framework for solving linear inverse problems with DNN denoisers/diffusers, which uses a novel preconditioned data-fidelity guidance approach, based on traversing from back-projection steps to least squares steps, exploiting the advantages of each. We used the new approach with a computationally convenient trajectory within a \"plug-and-play\" optimization scheme and its DDM sampling-based counterpart, which we devised. The performance advantages of the new technique were shown in various deblurring and super-resolution settings, with and without observation noise. (See the supplementary material for computed tomography experiments as well). As a direction for future research, one can try to learn the precondi" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 332, + 321, + 518, + 442 + ], + "blocks": [ + { + "bbox": [ + 332, + 321, + 518, + 442 + ], + "lines": [ + { + "bbox": [ + 332, + 321, + 518, + 442 + ], + "spans": [ + { + "bbox": [ + 332, + 321, + 518, + 442 + ], + "type": "image", + "image_path": "1ada4cc2aa5a7892b2a4aa1bc82e242f4ebe0865bcac01bca1aa108823abb08e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 445, + 545, + 489 + ], + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 489 + ], + "type": "text", + "content": "Figure 3. Gaussian deblurring with noise level 0.05. Top row, from left to right: original, observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DPS, DiffPIR, and our DDPG." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 332, + 497, + 518, + 618 + ], + "blocks": [ + { + "bbox": [ + 332, + 497, + 518, + 618 + ], + "lines": [ + { + "bbox": [ + 332, + 497, + 518, + 618 + ], + "spans": [ + { + "bbox": [ + 332, + 497, + 518, + 618 + ], + "type": "image", + "image_path": "c97fafc1798925cfd8d8183953345bbcdc82d25c5b03f794fd3dee01777496e1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 620, + 545, + 664 + ], + "lines": [ + { + "bbox": [ + 305, + 620, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 305, + 620, + 545, + 664 + ], + "type": "text", + "content": "Figure 4. SRx4 with noise level 0.05. Top row, from left to right: original, upsampled observation, and our IDPG (baseline for DDPG). Bottom row, from left to right: DDRM, DiffPIR, and our DDPG." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 674, + 471, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 674, + 471, + 687 + ], + "spans": [ + { + "bbox": [ + 306, + 674, + 471, + 687 + ], + "type": "text", + "content": "tioners " + }, + { + "bbox": [ + 306, + 674, + 471, + 687 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{W}_t\\}" + }, + { + "bbox": [ + 306, + 674, + 471, + 687 + ], + "type": "text", + "content": " instead of designing them." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgment. The work is partially supported by ISF grant no. 1940/23." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25252" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Shady Abu Hussein, Tom Tirer, and Raja Giryes. 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Achieving precise control in image editing tasks can be challenging with standard 2D generative pipelines. Our Image Sculpting framework offers the ability to interact with 3D geometry starting with a single image. This enables users to perform detailed, quantifiable, and physically-plausible edits, including precise pose editing, rotation, translation, 3D composition, carving, and serial addition." + ], + "image_footnote": [], + "bbox": [ + 200, + 441, + 348, + 540 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e9e99dcdf62501ca01498a2c3060c65336c3a8469e392991af8e5330bbb75753.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 444, + 472, + 535 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/65f4720db23241e92e8f82a6afb5b0a4dd40445ea1a2a5d11dffab1de4be3cbc.jpg", + "image_caption": [ + "(b) Precise Rotation" + ], + "image_footnote": [], + "bbox": [ + 500, + 231, + 616, + 323 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f90c239fcea19043989a79455edde1170d82f384991fe8d1de95f108e6df6ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 229, + 769, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b489649a115fd131e3521c35815060346dd885754306ed7bdf3a7553a4fd3d47.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 231, + 890, + 323 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e284b5a9bccd4947324fe4538ef3a14e2de3f39de52abe80d9339e5e0457af30.jpg", + "image_caption": [ + "(d) Precise 3D Composition" + ], + "image_footnote": [], + "bbox": [ + 500, + 337, + 617, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e95e883e550f1dc0e5bbaa20645024de233bfae9cb824f7a5605169cca1aaeb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 335, + 769, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a309c22c2aca3c736843c1ce209b9933e94da0db985a01800b4f59e8d31ab57c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 337, + 890, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eb94857884369e8d422d73bfb644833eaad50c2a2a5c818b80b9471596df64fe.jpg", + "image_caption": [ + "(f) Serial Addition" + ], + "image_footnote": [], + "bbox": [ + 500, + 444, + 617, + 536 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7e072803cae094a5f787675955b6e87c1fa09b841fe70b702eda1ca12fe42883.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 439, + 769, + 542 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2f6ddb4608e1b0e51d8ec58636a51af06b247030df658b434e0a0f362282d920.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 445, + 890, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 613, + 313, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines.", + "bbox": [ + 75, + 640, + 470, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 613, + 630, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent developments in the field of image generative modeling [63, 66, 68, 89] have unlocked new potentials in creative content creation, offering unprecedented opportunities for the generation of diverse visual content by materializing ideas and concepts articulated through language prompts. However, the integration of these models into real-world content creation workflows still poses significant challenges. Among the most critical is the need for users to have detailed control over various aspects of generated objects, including their pose, shape, location, layout, and spatial compositions. The precision extends to quantifiable manipulations, such as rotating an object by a specific angle or making physically-realistic modifications, such as positioning a character in a way that conforms to basic anatomical and physical principles. Interestingly, such a quest for precision and controllability aligns closely with the core principles of computer graphics, which strive to generate pho", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Code and project page available at this https URL", + "bbox": [ + 109, + 886, + 374, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4241", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "torealistic images with artistic control.", + "bbox": [ + 76, + 90, + 331, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In virtual effects (VFX) and rendering pipelines, experts meticulously craft and edit every detail within a fully controllable 3D environment, striving for utmost realism. For decades, methods for accurately manipulating and rendering objects have been explored, leading to the development of numerous advanced techniques in 3D model acquisition, rigging, posing, lighting, texturing, and scene rendering. These methods form the bedrock of the modern computer graphics pipeline. However, it often requires custom hardware and software for (1) acquiring production-quality 3D models or designing them from scratch, (2) making these models possible to animate (rigging), (3) creating visually plausible animations (animation), (4) rendering back in the 2D world after applying material and setting up the lighting, and (5) compositing the resulting image with a background or other objects. This process often employs teams of artists and engineers for each one of these steps, as it requires substantial manual input using specialized tools (e.g. After Effects [2], Substance [4], and 3ds Max [29]).", + "bbox": [ + 76, + 109, + 468, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, AI-based image generation avoids all this manual work, requiring only a text prompt. Leveraging the power of human language and large datasets of curated content, transforming a text description into a visually striking image is more accessible than ever. Yet, when it comes to precise object manipulation, the current 2D-based generative approach faces inherent limitations due to the lack of a third dimension, leading to incomplete information, limited user interaction on a flat plane, and possible ambiguities. The gap in controllability with respect to image generation using computer graphics techniques is striking, and closing it is a major goal of our work.", + "bbox": [ + 76, + 398, + 468, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most interfaces for image editing frameworks rely on text-based instructions. For example, techniques such as Prompt-to-Prompt [26], Plug-and-Play [79], InstructPix2Pix [10], Imagic [36] and Object 3DIT [50] offer adaptable language control. However, achieving precise manipulation through these models remains a challenge. Straightforward manipulations such as \"changing a style to mimic Van Gogh\" are manageable. However, more specific instructions such as \"lift the object by $5\\mathrm{cm}$ and rotate it by 42 degrees.\" are less likely to be successful, as current generative models cannot fulfill such detailed requests through textual prompts alone. 2D-based interactive methods such as DragGAN [57], FreeDrag [42], and DragDiffusion [73] demonstrate the ability to alter part of an object through transitions in the latent space. Despite this, they have their limitations: 1) they can accomplish basic deformations, but the outcomes are not entirely predictable, often leading to results that do not align with the user's intentions; 2) these latent transformations operate within the 2D feature space, which inherently limits their ability to represent 3D transformations and handle occlusions accurately; 3) they lack", + "bbox": [ + 76, + 583, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "physics-awareness, which complicates incorporating external constraints, such as skeletal structures.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work draws inspiration from the computer graphics pipeline and ventures into a novel approach for 2D image-based object manipulation tasks. Our proposed Image Sculpting framework, which metaphorically suggests the flexible and precise sculpting of a 2D image in a 3D space, integrates three key components: (1) single-view 3D reconstruction, (2) manipulation of objects in 3D, and (3) a coarse-to-fine generative enhancement process. More specifically, 2D objects are converted into 3D models, granting users the ability to interact with and manipulate the 3D geometry directly, which allows for precision in editing. The manipulated objects are then seamlessly reincorporated into their original 2D contexts, maintaining visual coherence and fidelity. A critical hurdle in this process is the single-view 3D reconstruction method, a task that, despite rapid progress [27, 41, 43-46, 62, 71], often results in relatively low-fidelity, coarse geometric and texture representations. Unlike manually crafted 3D assets used for graphics, their rendered version is far from photo-realistic. Nonetheless, the extracted geometries are sufficient for interactive and precise control. To achieve high-quality final images, a separate enhancement procedure is necessary. In summary, our Image Sculpting pipeline has three key phases:", + "bbox": [ + 496, + 126, + 892, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Phase 1. For the 3D reconstruction phase, we employ a zero-shot single image reconstruction model (Zero-1-to-3 [44]), which has been trained on extensive datasets [17] of 3D objects.", + "bbox": [ + 498, + 478, + 890, + 539 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Phase 2. The deformation process utilizes established geometric processing tools, such as As-Rigid-As-Possible (ARAP) [78] and linear-based skinning [48], enabling interactive and precise manipulation of the 3D models.", + "bbox": [ + 498, + 542, + 890, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Phase 3. For the generative enhancement process, we develop a coarse-to-fine enhancement pipeline, using an feature injection approach [79]. Our method strikes a balance between maintaining the original texture of the object and the modified geometry, utilizing a pre-trained text-to-image diffusion model with additional controls.", + "bbox": [ + 496, + 608, + 890, + 699 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our Image Sculpting framework showcases an array of precise and quantifiable image editing capabilities. These include precise pose editing, rotation, translation, multiobject 3D composition, carving, and serial addition. This suite of functionalities demonstrates the versatility of our approach and its superiority in precision and control compared to existing image editing methods. Our method also outperforms various baselines in image quality, as confirmed by both qualitative and quantitative evaluations on the new SculptingBench benchmark. We believe that our method can foster new opportunities in merging the flexibility of generative models with the precise controllability inherent in traditional graphics pipelines.", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4242", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/981ed4f782e538a078d25c5cb4c1c5a5dd27d907a77e3e8213b15b6cbff8dd64.jpg", + "image_caption": [ + "(a) Space Deformations" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 330, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4744e0e4bfd4308dd7f0896ebb864a39c2d1a53dda64f9de04072c93a3739f49.jpg", + "image_caption": [ + "Figure 2. Illustration of three mesh deformation methods applied to a 3D model. In cage-based space deformation (a), the model is placed in a cage and deformed when the user moves the cage vertices [33]. As-Rigid-As-Possible (ARAP) [78] deformation (b) deforms the model when user-selected blue handle points are moved towards designated red target points. Linear blend skinning (c) maps the deformation of a skeleton to the model [32]. Following deformation, a diffusion rendering process can be added for controllable generation. Each mesh deformation technique offers a different balance of control, speed, and precision. Our framework can use any of these techniques." + ], + "image_footnote": [], + "bbox": [ + 331, + 114, + 411, + 181 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4e856113b9e7f8141204e284bc8d96f2f8e316b516ecf783119fa3732d846cc1.jpg", + "image_caption": [ + "(b) Shape-Aware Deformation" + ], + "image_footnote": [], + "bbox": [ + 424, + 114, + 493, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c8f6bcb77ef1c92c0f37db13c8737ad08793183f58d41ee1c16dcf96da370f50.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 114, + 570, + 178 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/57f9d0f900140dbfee6c6af912fe25891446f408e65666462502958ac06d5497.jpg", + "image_caption": [ + "(c) Linear Blend Skinning" + ], + "image_footnote": [], + "bbox": [ + 578, + 113, + 647, + 178 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4f31fb33fa4f44471f04715c44943da2809fee498f8dcc36035d7f8c77b4c34d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 113, + 727, + 176 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/12e9e69ae1fcc6dab9f2d45321d39aba6fbbac2a0c93e08145eca3d7a0fc57d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 113, + 800, + 176 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ff132d14983564200e0ab981e21c7a657f73bf3025837fa66f521bf34d4e05a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 114, + 875, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 295, + 218, + 310 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generative Image Editing In computer graphics, extensive research on interactive raster image editing exists, and we defer its detailed review to the next section. In computer vision, the advent of image generative models such as GANs [22, 34, 35] has expanded the scope of image editing to include style transfer [21], image-to-image translation [30, 91], latent manipulation [70, 84], and text-based manipulation [1, 58, 85]. Recently, capabilities in image editing have advanced significantly with the rise of diffusion models [18, 59, 66]. The leading systems [51, 56, 63, 68] allow users to generate image variations or use inpainting masks [54] to generate specific parts of scenes based on a text prompt. Other work explores enhancing pretrained diffusion models with text-guided editing capabilities [10, 26, 52, 79]. Yet, text-based editing has limitations in precisely controlling object shapes and positions. ControlNet [90] incorporates additional conditional inputs such as depth [64], poses [11], and edges [86] for controllable generation. For more intuitive interactions, DragGAN [57] enables users to drag control points on objects with GANs, and similar techniques have been adapted for diffusion models [42, 73]. However, these methods are mostly confined to 2D and face challenges in tasks requiring more complex, out-of-plane transformations. 3D-aware generative models such as EG3D [13] and StyleNeRF [23] have explored this direction. OBJECT-3DIT [50], a baseline in our paper, studied 3D-aware editing using language instructions. However, its effectiveness is somewhat constrained due to its training on a synthetic dataset.", + "bbox": [ + 75, + 323, + 472, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Single-View Reconstruction Single-view 3D reconstruction is a long-standing problem in computer vision [25]. While algorithmic advancements are important, the significance of training data has been increasingly recognized. Earlier efforts were geared towards training models [55, 76, 83, 88] using smaller, simplistic 3D datasets [14, 65]. Recent approaches [61, 80] have started to utilize density distillation from pre-trained 2D diffusion models trained on large-scale text-image datasets, lessening the reliance on 3D", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "data. Nonetheless, for improved view-consistency, the demand for high-quality 3D data is indispensable. The emergence of large-scale 3D datasets, such as Objaverse [16, 17], has spurred methods such as Zero-1-to-3 [44] to combine 2D score distillation with 3D data training. This has led to a surge in new models in this domain, noticeably enhancing reconstruction quality [43, 62, 72, 82]. Our work is also closely related to 3-Sweep [15] and 3D Object Manipulation [37]. These pioneering studies in graphics involve constructing a 3D model using edge information or retrieving an online repository for image editing. We now employ generative models to further enhance shape editing capabilities and user experience.", + "bbox": [ + 496, + 297, + 890, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Overview of 3D Shape Deformation", + "text_level": 1, + "bbox": [ + 500, + 494, + 821, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The deformation of 3D shapes has been extensively studied in the last four decades, with both traditional and data-driven methods being proposed and successfully used in robotics, graphics, and engineering. We review the main approaches and their usability within our framework.", + "bbox": [ + 496, + 520, + 890, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Space Deformations The older and still widely used approach is applying a volumetric warp function $f: R^3 \\to R^3$ to all points of a 3D domain [69]. This approach can be applied to explicit (triangular or polygonal meshes) or implicit representations. The map can be parametrized using splines on lattices [69], vertices on a cage [33], or neural fields [19]. A limitation of these approaches is that they are unaware of the object shape, making them more challenging to use on complex articulated objects [9].", + "bbox": [ + 496, + 597, + 890, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Shape-Aware Deformation Shape-aware deformations provide a set of controls linked to the objects' surface. In Computer-Aided-Design (CAD), a small set of control points define a smooth surface using spline patches [20]. Despite its flexibility and quality, extracting spline patches from 3D models or NeRFs is a challenging and open problem [7]. Partial differential equation (PDE)-based methods simulate the deformation of an object, representing it as a volumetric deformable solid [75] or as a thin rubber shell [78]. The forces guiding the deformation are applied by moving handles selected on a surface [8], making them in", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4243", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/040c556a52992d706ac8a0be927fa8e1b1e78db42ee77314c10b5f4fda460ae2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2f0348ecc5c168aaaad3e829b0b316fcee1d1c3fd2027a9a039169ea339b1538.jpg", + "image_caption": [ + "Figure 3. Overview of our Image Sculpting pipeline, $\\mathrm{DDIM}^+$ represents DDIM with the DreamBooth fine-tuned and depth controlled model. The process begins by converting the input image into a textured 3D model through a de-rendering process. This model is then prepared for interactive deformation by creating a skeleton and calculating skinning weights. The user can modify the skeleton to deform the model, resulting in an initial coarse image. To refine this edited image, we invert the coarse rendering $I_{c}$ into the noise $\\pmb{x}_T^c$ . We then inject self-attention maps $\\pmb{A}_{t}^{c}$ and feature maps $\\pmb{f}_{t}^{c}$ from the initial image's denoising process into the enhanced image denoising steps. This technique helps in preserving the geometry of the modified object while restoring the visual quality of the edited image." + ], + "image_footnote": [], + "bbox": [ + 83, + 232, + 893, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tutive to use and requiring minimal user interaction.", + "bbox": [ + 76, + 460, + 424, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Linear Blend Skinning The most popular deformation approach is linear blend skinning [32], which defines a space deformation function as a blended average of a set of affine transformations weighted by shape-aware scalar functions, often computed with methods based on solutions of PDEs on surfaces [31] or manually edited. This approach offers complete control and flexibility, as the affine transformation can be attached to points, vertexes of a cage, or segments in a skeleton [6].", + "bbox": [ + 75, + 479, + 470, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our approach We can use any of these algorithms to precisely control the shape deformation and, thus, the rendered image. We show an example of one representative method for each class in Fig. 2, and we leave as future work additional automation of this step.", + "bbox": [ + 75, + 621, + 468, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Methods", + "text_level": 1, + "bbox": [ + 76, + 720, + 174, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a single 2D image, our objective is to enable precise manipulation of the objects and their orientations in 3D space, before converting this back into a high-quality edited 2D image. To achieve this, we have developed a novel editing pipeline tailored for image sculpting (see Fig. 3) composed of three steps: (1) We initially convert the input image into a 3D model, (2) the 3D model is edited by deforming it in 3D space, and (3) we use a coarse-to-fine generative enhancement pipeline to turn the coarse rendering of the 3D model into a high-fidelity image.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. De-Rendering and Deformation", + "text_level": 1, + "bbox": [ + 500, + 460, + 779, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an image of an object, our goal is to perform 3D reconstruction to obtain its 3D model.", + "bbox": [ + 498, + 487, + 890, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image to NeRF With advancements in text-to-image foundation models [66] and the viewpoint-conditioned image translation model [44], our initial step involves segmenting the selected object from the input image using SAM [38]. Building upon this, we then train a NeRF using Score Distillation Sampling (SDS) [61].", + "bbox": [ + 498, + 523, + 890, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "NeRF to 3D Model We use the implementation in three-studio [24] to convert a NeRF volume into a mesh. This algorithm transforms the volume density into a signed distance function, extracts an isosurface [47], and parameterizes it [87] for texture mapping [74]. The texture is extracted by differentiable rendering [39].", + "bbox": [ + 498, + 619, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D Model Deformation After obtaining the 3D model, a user can manually construct a skeleton and interactively manipulate it by rotating the bones to achieve the target pose. The mesh deformation affects the vertex positions of the object but not the UV coordinates used for texture mapping; this procedure thus deforms the texture mapped on the object following its deformation.", + "bbox": [ + 496, + 715, + 890, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the resulting image quality depends on the 3D reconstruction's accuracy, which, in our case, is coarse and insufficient for the intended visual outcome (Fig. 3). Therefore, we rely on an image enhancement pipeline to convert the coarse rendering into a high-quality output.", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4244", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3e281a7734339f7c4829b3b10b1356bd69df3230ead7c634d4d6243cb23052b6.jpg", + "image_caption": [ + "Input Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 181, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/771454ec0a33ae9b0516cc84d7afc74421959d6097c87abb25f86f10e62b1106.jpg", + "image_caption": [ + "Coarse Rendering" + ], + "image_footnote": [], + "bbox": [ + 181, + 90, + 284, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d392e2bccf8e58bc3bebfdf2e8dca6fd16bd6ba49c0347b301b809d815c643dd.jpg", + "image_caption": [ + "DreamBooth [67]" + ], + "image_footnote": [], + "bbox": [ + 284, + 90, + 383, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f74b4c3bbb23d5823a53b2a83cb791a8eed08bfa65a88250ccc1154678a276f8.jpg", + "image_caption": [ + "SDEdit [49] $(t_0 = 0.4)$" + ], + "image_footnote": [], + "bbox": [ + 383, + 90, + 483, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d0409b4a164f25957f2d6dc1f9e749f8fb418bd934ae94bd154d10a37eaf7e77.jpg", + "image_caption": [ + "SDEdit [49] $(t_0 = 0.6)$" + ], + "image_footnote": [], + "bbox": [ + 483, + 90, + 584, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/06f79e740a20289932624a45d1833daa463360c508d95973d3af0bc1bcdf08ca.jpg", + "image_caption": [ + "Ours w/o Feature Injection" + ], + "image_footnote": [], + "bbox": [ + 584, + 90, + 684, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/11f240233e3a78cd04bd3cfe6b36e4ee5b93b5394124660671452cda6cbfdd63.jpg", + "image_caption": [ + "Ours w/o Depth Control" + ], + "image_footnote": [], + "bbox": [ + 684, + 90, + 785, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ea07bd25e775311b8bd686f178601fd1c2163c78b09dfb08fef4bd9b724e06be.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 785, + 90, + 890, + 246 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a67f3aba33e49f9ce2ab03791e72008ed7f9e9143e7503da8fa00903f12a7ff3.jpg", + "image_caption": [ + "Figure 4. Comparison of our final method with various baseline methods and ablations. Our approach effectively maintains the geometric information while ensuring the texture quality. In contrast, other methods typically preserve either the texture or the geometry, but not both.", + "Figure 5. Overview of the coarse-to-fine generative enhancement model architecture. The red module denotes the one-shot Dream-Booth [67], which requires tuning; the grey module is the SDXL Refiner [5], which is frozen in our experiments." + ], + "image_footnote": [], + "bbox": [ + 78, + 297, + 468, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Coarse-to-Fine Generative Enhancement", + "text_level": 1, + "bbox": [ + 76, + 483, + 426, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section focuses on blending a coarsely rendered image back to its original background. The aim is to restore textural details while keeping the edited geometry intact. Image restoration and enhancement are commonly approached as image-to-image translation tasks [81], leveraging the strong correlation between the source and target images. Our challenge, however, presents a unique scenario: despite overall similarities in appearance and texture between the input and desired output, the input object's geometry changes, sometimes significantly, after user editing.", + "bbox": [ + 75, + 507, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In exploring possible solutions, one approach is to use subject-driven personalization techniques like DreamBooth [67]. They aim to preserve key details from the input, but might compromise the edited geometry. Alternatively, image-to-image translation methods like SDEdit [49] can be used to preserve the edited geometry, but this might disturb the textural consistency with the original image. This dichotomy was clear in our preliminary study, as shown in Fig. 4. SDEdit can maintain the geometry, but it was unable to accurately replicate the textures. On the other hand, DreamBooth produced high-fidelity outputs, but struggled to preserve both the texture and geometry effectively.", + "bbox": [ + 75, + 659, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address the balance between preserving texture and geometry, our approach begins by \"personalizing\" a pretrained text-to-image diffusion model. To capture the object's key features, we fine-tune the diffusion model with", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DreamBooth on one input reference image. To maintain the geometry, we adapt a feature and attention injection technique [79], originally designed for semantic layout control. Furthermore, we incorporate depth data from the 3D model through ControlNet [90]. We find this integration crucial in minimizing uncertainties during the enhancement process.", + "bbox": [ + 496, + 297, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One-shot Dreambooth DreamBooth [67] fine-tunes a pre-trained diffusion model with a few images for subject-driven generation. The original DreamBooth paper [67] has shown its ability to leverage the semantic class priors to generate novel views of an object, given only a few frontal images of the subject. This aspect is particularly useful in our setting, since the coarse rendering we work with lacks explicit viewpoint information. In our application, we train DreamBooth using just a single example, which is the input image. Notably, this one-shot approach with DreamBooth also effectively captures the detailed texture, thereby filling in the textural gaps present in the coarse rendering.", + "bbox": [ + 496, + 393, + 892, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth Control We use depth ControlNet [90] to preserve the geometric information of user editing. The depth map is rendered directly from the deformed 3D model, bypassing the need for any monocular depth estimation. For the background region, we don't use the depth map. This depth map serves as a spatial control signal, guiding the geometry generation in the final edited images. However, relying solely on depth control is not sufficient – although it can preserve the geometry to some extent, it still struggles in local, more nuanced editing, such as capturing the specific shapes of a pumpkin's eyes or the bent legs of a chair (Fig. 4).", + "bbox": [ + 496, + 579, + 890, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature Injection To better preserve the geometry, we use feature injection. As demonstrated in Fig. 3, this step begins with DDIM inversion [77] (with the DreamBooth finetuned, depth controlled diffusion model) of the coarse rendering image to obtain the inverted latents. At each denoising step, we denoise the inverted latent of the coarse rendering along with the latent of the refined image, extracting their respective feature maps (from the residual blocks) and self-attention maps (from the transformer blocks). It has been shown in [79] that the feature maps carry semantic in", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4245", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f251783eafd51651092ebb1b272df74c53946e0426ace3ffe4bd6c131a0f5752.jpg", + "image_caption": [ + "Figure 6. A compilation of qualitative results from six image editing tasks. Additionally, we include additional examples (termed as 'Mixture' in the final row) to illustrate the versatile combination of these capabilities." + ], + "image_footnote": [], + "bbox": [ + 99, + 87, + 872, + 847 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4246", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5803c658df05b4788edb0ceaaf0c88f5c817a6bac22a458130b21fee6d0b15a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 90, + 467, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ec8684ee51f651643b1c2553c128a83e72a78b83e72bb626d850dc9f541f241.jpg", + "image_caption": [ + "Figure 7. Our blend-in process. At every denoising step, we mask the background areas and blend them with the unmasked regions from the denoised latent. This process helps maintain visual coherence and preserve the background.", + "Figure 8. Our blend-in process yields visually harmonious results. Top: Results from direct copy-pasting. Bottom: Our results." + ], + "image_footnote": [], + "bbox": [ + 101, + 250, + 444, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "formation, while the self-attention maps contain the geometry and layout of the generated images. By overriding the feature and self-attention maps during the enhanced image denoising steps with those from the coarser version, we ensure the geometry of the enhanced image can reflect those of the coarse rendering. The pseudo code for our generative enhancement is detailed in Appendix A. Note that our method differs from the original Plug-and-Play use cases: we use feature injection to preserve the geometry during the coarse-to-fine process rather than translating the image according to a new text prompt. We present the injection layer selection and the replacement schedule in Section 5.", + "bbox": [ + 75, + 474, + 468, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Background Blend-In To maintain the consistency of the background between the input and edited images, we first inpaint the area initially occupied by the object in the input image, thus obtaining an unobstructed background. However, another challenge arises in merging the edited object into this background smoothly. Merely copy-pasting it onto the background leads to an unrealistic visual effect, such as the improper water reflections over the fish and the absence of shadow casting from the truck (Fig. 8). To overcome this, as demonstrated in Fig. 7, our approach involves masking the background areas during the denoising steps to preserve their original background. This means we retain the unedited background by blending the unmasked (edited) regions from the denoising step with the masked (original) background. We use SDXL [60] as our pre-trained text-to-image model, which includes a refiner module by de", + "bbox": [ + 75, + 657, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6eba05c221ac6e83f6dca7878ed58d46d62e3e8723a5e7100f3a4703b21280a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 498, + 88, + 893, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2538e286f39754666dadb38696a0824160c8822d8a4c0204dd85cfaac086352f.jpg", + "image_caption": [ + "Figure 9. Comparisons with Object-3DIT [50] on object translation, rotation, and composition tasks." + ], + "image_footnote": [], + "bbox": [ + 501, + 311, + 893, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b8bc9bcb439d0425fa03338a0c950b26b24893330614478c12ad332b7d55b8b4.jpg", + "image_caption": [ + "Figure 10. Comparisons with DragDiffusion [73] and ControlNet [90] on pose editing. These techniques face difficulties in handling complex pose modifications.", + "Figure 11. Comparisons with InstructPix2Pix [10] and DALL-E 3 [56] on serial addition. These text-based editing methods fail to follow precise and quantifiable instructions." + ], + "image_footnote": [], + "bbox": [ + 500, + 544, + 890, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fault. We keep this module in our pipeline, as empirically it slightly enhances the results by reducing artifacts.", + "bbox": [ + 498, + 776, + 890, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 813, + 632, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental Setup We follow [24] to obtain the initial NeRF representation and to extract the textured 3D model. We use Instant-NGP [53] and a grid size of 256 for the 3D model extraction from NeRF. During the coarse-to-fine gen", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4247", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4ced16c09d08f77c1d3e83e6a894ef6312a81fe03379a1a7128d68cbd7f7de0b.jpg", + "image_caption": [ + "Figure 12. Ablation studies on feature injection layers. From left to right, progressively injecting more self-attention layers can result in increasingly improved alignment with user edits." + ], + "image_footnote": [], + "bbox": [ + 99, + 109, + 187, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Injecting more layers", + "bbox": [ + 464, + 93, + 593, + 106 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3125134acd0d1dac7bd232f3b7c5d47c21a3123d982ecb237cdbb143cef18098.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 200, + 107, + 880, + 256 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d1efd42f85c91ef16a97941e0db572f938fe781402ddafe886f95c32cf80b217.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsDINO↑D-RMSE↓
Original Coarse Rendering0.7580.00
SDEdit [49] (t0=0.4)0.7881.71
SDEdit [49] (t0=0.6)0.8002.12
Ours w/o Feature Injection0.8482.33
Ours w/o Depth Control0.8512.15
Ours0.8531.99
", + "bbox": [ + 78, + 299, + 468, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Ablation studies of the enhancement methods on SculptingBench. DINO score measures the textural details, and D-RMSE measures the geometric fidelity. Depth control and feature injection enhance texture quality while maintaining geometric fidelity.", + "bbox": [ + 75, + 422, + 468, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "erative enhancement process, for one-shot DreamBooth, we fine-tune the SDXL-1.0 [60] model using LoRA [28] for 800 steps with a learning rate of 1e-5. For feature injection stage, we utilize all the self-attention layers of the SDXL decoder and the first block of the SDXL's upsampling decoder. The SDXL refiner is applied after $t = 0.1T$ . For background inpainting, we use Adobe generative fill [3].", + "bbox": [ + 75, + 487, + 468, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results We showcase qualitative results in Fig. 6, covering six precise image editing tasks. Detailed descriptions of these tasks are presented in Appendix B. Qualitatively, our method combines the creative freedom of generative models with the precision of graphics pipelines to achieve precise, quantifiable, and physically plausible outcomes for object editing across a variety of scenarios.", + "bbox": [ + 75, + 595, + 468, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our approach introduces new editing features through precise 3D geometry control, a capability not present in existing methods. We compare our method with the state-of-the-art object editing techniques for a comprehensive analysis. In Fig. 9, we show that 3DIT [50], designed for 3D-aware editing via language instructions, faces limitations when applied to real, complex images, largely because its training is based on a synthetic dataset. In Fig. 10, we compare the pose editing ability with DragDiffusion [73] and ControlNet [90]. This comparison reveals that these methods encounter difficulties with complex pose manipulations because they are constrained to the 2D domain. Furthermore, in Fig. 11, we show how text-based editing methods", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "like InstructPix2Pix [10] and DALL-E 3 [56] struggle with precise and quantifiable instructions.", + "bbox": [ + 496, + 300, + 890, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Studies We create a new dataset *SculptingBench* to evaluate our new image editing capabilities. This dataset contains 28 images covering six categories: pose editing, rotation, translation, composition, carving, and serial addition (see Appendix C). We perform quantitative studies using different coarse-to-fine enhancement methods. To measure the visual similarity between the edited images and the original ones, particularly in terms of maintaining textural details through the editing process, we employ DINO score [67] as our metrics. This choice is motivated by the self-supervised training objective of DINO [12], which encourages distinction of unique features of a image. To evaluate the geometric fidelity of user edits after enhancement, we introduce a novel metric, $D$ -RMSE. This metric is specifically created to evaluate how well geometric information is retained after the enhancement procedure. $D$ -RMSE measures the discrepancies between the depth maps of the coarse renderings and their enhanced counterparts:", + "bbox": [ + 496, + 333, + 892, + 604 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {D} - \\mathrm {R M S E} = \\sqrt {\\mathbb {E} \\left[ \\left(\\mathrm {d e p t h} _ {\\text {c o a r s e}} - \\mathrm {d e p t h} _ {\\text {e n h a n c e d}}\\right) ^ {2} \\right]}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 612, + 846, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where depth_coarse, depth_enhanced denote the depth maps MiDaS [64] estimates, for the coarse rendering and the enhanced output image, respectively. In Table 1, we show that without any enhancement, the textural quality metrics (DINO score) are quite low. SDEdit effectively preserves the edited geometry with a low D-RMSE, yet the visual quality significantly deteriorates compared to the original image (see Fig. 4). Our method offers a more advantageous balance, significantly enhancing texture quality as demonstrated by higher DINO score, while preserving geometric consistency, evidenced by a low D-RMSE score. We observe that both feature injection and depth control contribute to enhanced geometric consistency and can lead to further improvement when used together. Additionally, we conduct an empirical study to explore the number of self-attention layers for injection. Fig. 12 shows that more layers improve alignment with user edits. We use all layers for injection.", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4248", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. CLIP2StyleGAN: Unsupervised extraction of StyleGAN edit directions. In SIGGRAPH, 2022. 3", + "[2] Adobe. Adobe After Effects. https://www.adobe.com/products/aftereffects.html, 2023.2", + "[3] Adobe. Adobe Firefly. https://www.adobe.com/sensei/generative-ai/firefly.html, 2023.8", + "[4] Adobe. Adobe Substance 3D. https://www.adobe.com/creativecommons/3d-ar.html, 2023.2", + "[5] Stability AI. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.131, + 0.828, + 0.154 + ], + "angle": 0, + "content": "Image Sculpting: Precise Object Editing with 3D Geometry Control" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.18, + 0.84, + 0.201 + ], + "angle": 0, + "content": "Jiraphon Yenphraphai\\(^{1}\\) Xichen Pan\\(^{1}\\) Sainan Liu\\(^{2}\\) Daniele Panozzo\\(^{1}\\) Saining Xie\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.332, + 0.209, + 0.64, + 0.228 + ], + "angle": 0, + "content": "\\(^{1}\\)New York University \\(^{2}\\)Intel Labs" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.232, + 0.198, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.325, + 0.189, + 0.335 + ], + "angle": 0, + "content": "(a) Precise Pose Editing" + }, + { + "type": "image", + "bbox": [ + 0.203, + 0.23, + 0.351, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.233, + 0.473, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.338, + 0.198, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.431, + 0.186, + 0.44 + ], + "angle": 0, + "content": "(c) Precise Translation" + }, + { + "type": "image", + "bbox": [ + 0.202, + 0.334, + 0.349, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.338, + 0.473, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.445, + 0.198, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.538, + 0.18, + 0.548 + ], + "angle": 0, + "content": "(e) Precise Carving" + }, + { + "type": "image", + "bbox": [ + 0.202, + 0.442, + 0.349, + 0.541 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.445, + 0.473, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.232, + 0.617, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.325, + 0.601, + 0.334 + ], + "angle": 0, + "content": "(b) Precise Rotation" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.23, + 0.77, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.774, + 0.232, + 0.892, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.338, + 0.618, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.501, + 0.431, + 0.617, + 0.44 + ], + "angle": 0, + "content": "(d) Precise 3D Composition" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.336, + 0.77, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.774, + 0.338, + 0.892, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.445, + 0.618, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.538, + 0.598, + 0.547 + ], + "angle": 0, + "content": "(f) Serial Addition" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.44, + 0.77, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.774, + 0.446, + 0.892, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.558, + 0.894, + 0.601 + ], + "angle": 0, + "content": "Figure 1. Achieving precise control in image editing tasks can be challenging with standard 2D generative pipelines. Our Image Sculpting framework offers the ability to interact with 3D geometry starting with a single image. This enables users to perform detailed, quantifiable, and physically-plausible edits, including precise pose editing, rotation, translation, 3D composition, carving, and serial addition." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.614, + 0.314, + 0.629 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.471, + 0.868 + ], + "angle": 0, + "content": "We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.614, + 0.631, + 0.629 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recent developments in the field of image generative modeling [63, 66, 68, 89] have unlocked new potentials in creative content creation, offering unprecedented opportunities for the generation of diverse visual content by materializing ideas and concepts articulated through language prompts. However, the integration of these models into real-world content creation workflows still poses significant challenges. Among the most critical is the need for users to have detailed control over various aspects of generated objects, including their pose, shape, location, layout, and spatial compositions. The precision extends to quantifiable manipulations, such as rotating an object by a specific angle or making physically-realistic modifications, such as positioning a character in a way that conforms to basic anatomical and physical principles. Interestingly, such a quest for precision and controllability aligns closely with the core principles of computer graphics, which strive to generate pho" + }, + { + "type": "page_footnote", + "bbox": [ + 0.11, + 0.887, + 0.375, + 0.9 + ], + "angle": 0, + "content": "Code and project page available at this https URL" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4241" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.332, + 0.106 + ], + "angle": 0, + "content": "torealistic images with artistic control." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.11, + 0.47, + 0.397 + ], + "angle": 0, + "content": "In virtual effects (VFX) and rendering pipelines, experts meticulously craft and edit every detail within a fully controllable 3D environment, striving for utmost realism. For decades, methods for accurately manipulating and rendering objects have been explored, leading to the development of numerous advanced techniques in 3D model acquisition, rigging, posing, lighting, texturing, and scene rendering. These methods form the bedrock of the modern computer graphics pipeline. However, it often requires custom hardware and software for (1) acquiring production-quality 3D models or designing them from scratch, (2) making these models possible to animate (rigging), (3) creating visually plausible animations (animation), (4) rendering back in the 2D world after applying material and setting up the lighting, and (5) compositing the resulting image with a background or other objects. This process often employs teams of artists and engineers for each one of these steps, as it requires substantial manual input using specialized tools (e.g. After Effects [2], Substance [4], and 3ds Max [29])." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.4, + 0.47, + 0.581 + ], + "angle": 0, + "content": "In contrast, AI-based image generation avoids all this manual work, requiring only a text prompt. Leveraging the power of human language and large datasets of curated content, transforming a text description into a visually striking image is more accessible than ever. Yet, when it comes to precise object manipulation, the current 2D-based generative approach faces inherent limitations due to the lack of a third dimension, leading to incomplete information, limited user interaction on a flat plane, and possible ambiguities. The gap in controllability with respect to image generation using computer graphics techniques is striking, and closing it is a major goal of our work." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.584, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Most interfaces for image editing frameworks rely on text-based instructions. For example, techniques such as Prompt-to-Prompt [26], Plug-and-Play [79], InstructPix2Pix [10], Imagic [36] and Object 3DIT [50] offer adaptable language control. However, achieving precise manipulation through these models remains a challenge. Straightforward manipulations such as \"changing a style to mimic Van Gogh\" are manageable. However, more specific instructions such as \"lift the object by \\(5\\mathrm{cm}\\) and rotate it by 42 degrees.\" are less likely to be successful, as current generative models cannot fulfill such detailed requests through textual prompts alone. 2D-based interactive methods such as DragGAN [57], FreeDrag [42], and DragDiffusion [73] demonstrate the ability to alter part of an object through transitions in the latent space. Despite this, they have their limitations: 1) they can accomplish basic deformations, but the outcomes are not entirely predictable, often leading to results that do not align with the user's intentions; 2) these latent transformations operate within the 2D feature space, which inherently limits their ability to represent 3D transformations and handle occlusions accurately; 3) they lack" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "physics-awareness, which complicates incorporating external constraints, such as skeletal structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.893, + 0.475 + ], + "angle": 0, + "content": "Our work draws inspiration from the computer graphics pipeline and ventures into a novel approach for 2D image-based object manipulation tasks. Our proposed Image Sculpting framework, which metaphorically suggests the flexible and precise sculpting of a 2D image in a 3D space, integrates three key components: (1) single-view 3D reconstruction, (2) manipulation of objects in 3D, and (3) a coarse-to-fine generative enhancement process. More specifically, 2D objects are converted into 3D models, granting users the ability to interact with and manipulate the 3D geometry directly, which allows for precision in editing. The manipulated objects are then seamlessly reincorporated into their original 2D contexts, maintaining visual coherence and fidelity. A critical hurdle in this process is the single-view 3D reconstruction method, a task that, despite rapid progress [27, 41, 43-46, 62, 71], often results in relatively low-fidelity, coarse geometric and texture representations. Unlike manually crafted 3D assets used for graphics, their rendered version is far from photo-realistic. Nonetheless, the extracted geometries are sufficient for interactive and precise control. To achieve high-quality final images, a separate enhancement procedure is necessary. In summary, our Image Sculpting pipeline has three key phases:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.54 + ], + "angle": 0, + "content": "Phase 1. For the 3D reconstruction phase, we employ a zero-shot single image reconstruction model (Zero-1-to-3 [44]), which has been trained on extensive datasets [17] of 3D objects." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.544, + 0.892, + 0.605 + ], + "angle": 0, + "content": "Phase 2. The deformation process utilizes established geometric processing tools, such as As-Rigid-As-Possible (ARAP) [78] and linear-based skinning [48], enabling interactive and precise manipulation of the 3D models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.7 + ], + "angle": 0, + "content": "Phase 3. For the generative enhancement process, we develop a coarse-to-fine enhancement pipeline, using an feature injection approach [79]. Our method strikes a balance between maintaining the original texture of the object and the modified geometry, utilizing a pre-trained text-to-image diffusion model with additional controls." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Our Image Sculpting framework showcases an array of precise and quantifiable image editing capabilities. These include precise pose editing, rotation, translation, multiobject 3D composition, carving, and serial addition. This suite of functionalities demonstrates the versatility of our approach and its superiority in precision and control compared to existing image editing methods. Our method also outperforms various baselines in image quality, as confirmed by both qualitative and quantitative evaluations on the new SculptingBench benchmark. We believe that our method can foster new opportunities in merging the flexibility of generative models with the precise controllability inherent in traditional graphics pipelines." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4242" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.331, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.187, + 0.194, + 0.314, + 0.206 + ], + "angle": 0, + "content": "(a) Space Deformations" + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.116, + 0.413, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.425, + 0.116, + 0.494, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.115, + 0.571, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.114, + 0.648, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.114, + 0.728, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.114, + 0.801, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.116, + 0.877, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.194, + 0.621, + 0.206 + ], + "angle": 0, + "content": "(b) Shape-Aware Deformation" + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.194, + 0.844, + 0.206 + ], + "angle": 0, + "content": "(c) Linear Blend Skinning" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.214, + 0.894, + 0.284 + ], + "angle": 0, + "content": "Figure 2. Illustration of three mesh deformation methods applied to a 3D model. In cage-based space deformation (a), the model is placed in a cage and deformed when the user moves the cage vertices [33]. As-Rigid-As-Possible (ARAP) [78] deformation (b) deforms the model when user-selected blue handle points are moved towards designated red target points. Linear blend skinning (c) maps the deformation of a skeleton to the model [32]. Following deformation, a diffusion rendering process can be added for controllable generation. Each mesh deformation technique offers a different balance of control, speed, and precision. Our framework can use any of these techniques." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.296, + 0.219, + 0.311 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.761 + ], + "angle": 0, + "content": "Generative Image Editing In computer graphics, extensive research on interactive raster image editing exists, and we defer its detailed review to the next section. In computer vision, the advent of image generative models such as GANs [22, 34, 35] has expanded the scope of image editing to include style transfer [21], image-to-image translation [30, 91], latent manipulation [70, 84], and text-based manipulation [1, 58, 85]. Recently, capabilities in image editing have advanced significantly with the rise of diffusion models [18, 59, 66]. The leading systems [51, 56, 63, 68] allow users to generate image variations or use inpainting masks [54] to generate specific parts of scenes based on a text prompt. Other work explores enhancing pretrained diffusion models with text-guided editing capabilities [10, 26, 52, 79]. Yet, text-based editing has limitations in precisely controlling object shapes and positions. ControlNet [90] incorporates additional conditional inputs such as depth [64], poses [11], and edges [86] for controllable generation. For more intuitive interactions, DragGAN [57] enables users to drag control points on objects with GANs, and similar techniques have been adapted for diffusion models [42, 73]. However, these methods are mostly confined to 2D and face challenges in tasks requiring more complex, out-of-plane transformations. 3D-aware generative models such as EG3D [13] and StyleNeRF [23] have explored this direction. OBJECT-3DIT [50], a baseline in our paper, studied 3D-aware editing using language instructions. However, its effectiveness is somewhat constrained due to its training on a synthetic dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Single-View Reconstruction Single-view 3D reconstruction is a long-standing problem in computer vision [25]. While algorithmic advancements are important, the significance of training data has been increasingly recognized. Earlier efforts were geared towards training models [55, 76, 83, 88] using smaller, simplistic 3D datasets [14, 65]. Recent approaches [61, 80] have started to utilize density distillation from pre-trained 2D diffusion models trained on large-scale text-image datasets, lessening the reliance on 3D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.298, + 0.892, + 0.493 + ], + "angle": 0, + "content": "data. Nonetheless, for improved view-consistency, the demand for high-quality 3D data is indispensable. The emergence of large-scale 3D datasets, such as Objaverse [16, 17], has spurred methods such as Zero-1-to-3 [44] to combine 2D score distillation with 3D data training. This has led to a surge in new models in this domain, noticeably enhancing reconstruction quality [43, 62, 72, 82]. Our work is also closely related to 3-Sweep [15] and 3D Object Manipulation [37]. These pioneering studies in graphics involve constructing a 3D model using edge information or retrieving an online repository for image editing. We now employ generative models to further enhance shape editing capabilities and user experience." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.496, + 0.822, + 0.512 + ], + "angle": 0, + "content": "3. Overview of 3D Shape Deformation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.596 + ], + "angle": 0, + "content": "The deformation of 3D shapes has been extensively studied in the last four decades, with both traditional and data-driven methods being proposed and successfully used in robotics, graphics, and engineering. We review the main approaches and their usability within our framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Space Deformations The older and still widely used approach is applying a volumetric warp function \\( f: R^3 \\to R^3 \\) to all points of a 3D domain [69]. This approach can be applied to explicit (triangular or polygonal meshes) or implicit representations. The map can be parametrized using splines on lattices [69], vertices on a cage [33], or neural fields [19]. A limitation of these approaches is that they are unaware of the object shape, making them more challenging to use on complex articulated objects [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Shape-Aware Deformation Shape-aware deformations provide a set of controls linked to the objects' surface. In Computer-Aided-Design (CAD), a small set of control points define a smooth surface using spline patches [20]. Despite its flexibility and quality, extracting spline patches from 3D models or NeRFs is a challenging and open problem [7]. Partial differential equation (PDE)-based methods simulate the deformation of an object, representing it as a volumetric deformable solid [75] or as a thin rubber shell [78]. The forces guiding the deformation are applied by moving handles selected on a surface [8], making them in" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4243" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.09, + 0.892, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.233, + 0.895, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.37, + 0.895, + 0.456 + ], + "angle": 0, + "content": "Figure 3. Overview of our Image Sculpting pipeline, \\(\\mathrm{DDIM}^+\\) represents DDIM with the DreamBooth fine-tuned and depth controlled model. The process begins by converting the input image into a textured 3D model through a de-rendering process. This model is then prepared for interactive deformation by creating a skeleton and calculating skinning weights. The user can modify the skeleton to deform the model, resulting in an initial coarse image. To refine this edited image, we invert the coarse rendering \\(I_{c}\\) into the noise \\(\\pmb{x}_T^c\\). We then inject self-attention maps \\(\\pmb{A}_{t}^{c}\\) and feature maps \\(\\pmb{f}_{t}^{c}\\) from the initial image's denoising process into the enhanced image denoising steps. This technique helps in preserving the geometry of the modified object while restoring the visual quality of the edited image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.462, + 0.426, + 0.478 + ], + "angle": 0, + "content": "tutive to use and requiring minimal user interaction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.471, + 0.618 + ], + "angle": 0, + "content": "Linear Blend Skinning The most popular deformation approach is linear blend skinning [32], which defines a space deformation function as a blended average of a set of affine transformations weighted by shape-aware scalar functions, often computed with methods based on solutions of PDEs on surfaces [31] or manually edited. This approach offers complete control and flexibility, as the affine transformation can be attached to points, vertexes of a cage, or segments in a skeleton [6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Our approach We can use any of these algorithms to precisely control the shape deformation and, thus, the rendered image. We show an example of one representative method for each class in Fig. 2, and we leave as future work additional automation of this step." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.721, + 0.176, + 0.737 + ], + "angle": 0, + "content": "4. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Given a single 2D image, our objective is to enable precise manipulation of the objects and their orientations in 3D space, before converting this back into a high-quality edited 2D image. To achieve this, we have developed a novel editing pipeline tailored for image sculpting (see Fig. 3) composed of three steps: (1) We initially convert the input image into a 3D model, (2) the 3D model is edited by deforming it in 3D space, and (3) we use a coarse-to-fine generative enhancement pipeline to turn the coarse rendering of the 3D model into a high-fidelity image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.462, + 0.78, + 0.478 + ], + "angle": 0, + "content": "4.1. De-Rendering and Deformation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.488, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Given an image of an object, our goal is to perform 3D reconstruction to obtain its 3D model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.524, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Image to NeRF With advancements in text-to-image foundation models [66] and the viewpoint-conditioned image translation model [44], our initial step involves segmenting the selected object from the input image using SAM [38]. Building upon this, we then train a NeRF using Score Distillation Sampling (SDS) [61]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.62, + 0.892, + 0.711 + ], + "angle": 0, + "content": "NeRF to 3D Model We use the implementation in three-studio [24] to convert a NeRF volume into a mesh. This algorithm transforms the volume density into a signed distance function, extracts an isosurface [47], and parameterizes it [87] for texture mapping [74]. The texture is extracted by differentiable rendering [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.822 + ], + "angle": 0, + "content": "3D Model Deformation After obtaining the 3D model, a user can manually construct a skeleton and interactively manipulate it by rotating the bones to achieve the target pose. The mesh deformation affects the vertex positions of the object but not the UV coordinates used for texture mapping; this procedure thus deforms the texture mapped on the object following its deformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "However, the resulting image quality depends on the 3D reconstruction's accuracy, which, in our case, is coarse and insufficient for the intended visual outcome (Fig. 3). Therefore, we rely on an image enhancement pipeline to convert the coarse rendering into a high-quality output." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4244" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.182, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.183, + 0.091, + 0.285, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.091, + 0.385, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.091, + 0.485, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.091, + 0.585, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.585, + 0.091, + 0.685, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.091, + 0.787, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.091, + 0.892, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.249, + 0.149, + 0.258 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.249, + 0.266, + 0.258 + ], + "angle": 0, + "content": "Coarse Rendering" + }, + { + "type": "image_caption", + "bbox": [ + 0.304, + 0.249, + 0.364, + 0.258 + ], + "angle": 0, + "content": "DreamBooth [67]" + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.249, + 0.481, + 0.258 + ], + "angle": 0, + "content": "SDEdit [49] \\((t_0 = 0.4)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.492, + 0.249, + 0.583, + 0.258 + ], + "angle": 0, + "content": "SDEdit [49] \\((t_0 = 0.6)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.249, + 0.684, + 0.258 + ], + "angle": 0, + "content": "Ours w/o Feature Injection" + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.249, + 0.782, + 0.258 + ], + "angle": 0, + "content": "Ours w/o Depth Control" + }, + { + "type": "image_caption", + "bbox": [ + 0.829, + 0.249, + 0.847, + 0.257 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Figure 4. Comparison of our final method with various baseline methods and ablations. Our approach effectively maintains the geometric information while ensuring the texture quality. In contrast, other methods typically preserve either the texture or the geometry, but not both." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.298, + 0.47, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.424, + 0.471, + 0.48 + ], + "angle": 0, + "content": "Figure 5. Overview of the coarse-to-fine generative enhancement model architecture. The red module denotes the one-shot Dream-Booth [67], which requires tuning; the grey module is the SDXL Refiner [5], which is frozen in our experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.484, + 0.428, + 0.499 + ], + "angle": 0, + "content": "4.2. Coarse-to-Fine Generative Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.658 + ], + "angle": 0, + "content": "This section focuses on blending a coarsely rendered image back to its original background. The aim is to restore textural details while keeping the edited geometry intact. Image restoration and enhancement are commonly approached as image-to-image translation tasks [81], leveraging the strong correlation between the source and target images. Our challenge, however, presents a unique scenario: despite overall similarities in appearance and texture between the input and desired output, the input object's geometry changes, sometimes significantly, after user editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.84 + ], + "angle": 0, + "content": "In exploring possible solutions, one approach is to use subject-driven personalization techniques like DreamBooth [67]. They aim to preserve key details from the input, but might compromise the edited geometry. Alternatively, image-to-image translation methods like SDEdit [49] can be used to preserve the edited geometry, but this might disturb the textural consistency with the original image. This dichotomy was clear in our preliminary study, as shown in Fig. 4. SDEdit can maintain the geometry, but it was unable to accurately replicate the textures. On the other hand, DreamBooth produced high-fidelity outputs, but struggled to preserve both the texture and geometry effectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To address the balance between preserving texture and geometry, our approach begins by \"personalizing\" a pretrained text-to-image diffusion model. To capture the object's key features, we fine-tune the diffusion model with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.39 + ], + "angle": 0, + "content": "DreamBooth on one input reference image. To maintain the geometry, we adapt a feature and attention injection technique [79], originally designed for semantic layout control. Furthermore, we incorporate depth data from the 3D model through ControlNet [90]. We find this integration crucial in minimizing uncertainties during the enhancement process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.893, + 0.576 + ], + "angle": 0, + "content": "One-shot Dreambooth DreamBooth [67] fine-tunes a pre-trained diffusion model with a few images for subject-driven generation. The original DreamBooth paper [67] has shown its ability to leverage the semantic class priors to generate novel views of an object, given only a few frontal images of the subject. This aspect is particularly useful in our setting, since the coarse rendering we work with lacks explicit viewpoint information. In our application, we train DreamBooth using just a single example, which is the input image. Notably, this one-shot approach with DreamBooth also effectively captures the detailed texture, thereby filling in the textural gaps present in the coarse rendering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.746 + ], + "angle": 0, + "content": "Depth Control We use depth ControlNet [90] to preserve the geometric information of user editing. The depth map is rendered directly from the deformed 3D model, bypassing the need for any monocular depth estimation. For the background region, we don't use the depth map. This depth map serves as a spatial control signal, guiding the geometry generation in the final edited images. However, relying solely on depth control is not sufficient – although it can preserve the geometry to some extent, it still struggles in local, more nuanced editing, such as capturing the specific shapes of a pumpkin's eyes or the bent legs of a chair (Fig. 4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Feature Injection To better preserve the geometry, we use feature injection. As demonstrated in Fig. 3, this step begins with DDIM inversion [77] (with the DreamBooth finetuned, depth controlled diffusion model) of the coarse rendering image to obtain the inverted latents. At each denoising step, we denoise the inverted latent of the coarse rendering along with the latent of the refined image, extracting their respective feature maps (from the residual blocks) and self-attention maps (from the transformer blocks). It has been shown in [79] that the feature maps carry semantic in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4245" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.088, + 0.874, + 0.848 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.855, + 0.892, + 0.883 + ], + "angle": 0, + "content": "Figure 6. A compilation of qualitative results from six image editing tasks. Additionally, we include additional examples (termed as 'Mixture' in the final row) to illustrate the versatile combination of these capabilities." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4246" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.092, + 0.468, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.191, + 0.471, + 0.248 + ], + "angle": 0, + "content": "Figure 7. Our blend-in process. At every denoising step, we mask the background areas and blend them with the unmasked regions from the denoised latent. This process helps maintain visual coherence and preserve the background." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.251, + 0.446, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.436, + 0.468, + 0.465 + ], + "angle": 0, + "content": "Figure 8. Our blend-in process yields visually harmonious results. Top: Results from direct copy-pasting. Bottom: Our results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.656 + ], + "angle": 0, + "content": "formation, while the self-attention maps contain the geometry and layout of the generated images. By overriding the feature and self-attention maps during the enhanced image denoising steps with those from the coarser version, we ensure the geometry of the enhanced image can reflect those of the coarse rendering. The pseudo code for our generative enhancement is detailed in Appendix A. Note that our method differs from the original Plug-and-Play use cases: we use feature injection to preserve the geometry during the coarse-to-fine process rather than translating the image according to a new text prompt. We present the injection layer selection and the replacement schedule in Section 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Background Blend-In To maintain the consistency of the background between the input and edited images, we first inpaint the area initially occupied by the object in the input image, thus obtaining an unobstructed background. However, another challenge arises in merging the edited object into this background smoothly. Merely copy-pasting it onto the background leads to an unrealistic visual effect, such as the improper water reflections over the fish and the absence of shadow casting from the truck (Fig. 8). To overcome this, as demonstrated in Fig. 7, our approach involves masking the background areas during the denoising steps to preserve their original background. This means we retain the unedited background by blending the unmasked (edited) regions from the denoising step with the masked (original) background. We use SDXL [60] as our pre-trained text-to-image model, which includes a refiner module by de" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.311 + ], + "angle": 0, + "content": "Figure 9. Comparisons with Object-3DIT [50] on object translation, rotation, and composition tasks." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.313, + 0.895, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.501, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Figure 10. Comparisons with DragDiffusion [73] and ControlNet [90] on pose editing. These techniques face difficulties in handling complex pose modifications." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.545, + 0.892, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.731, + 0.892, + 0.772 + ], + "angle": 0, + "content": "Figure 11. Comparisons with InstructPix2Pix [10] and DALL-E 3 [56] on serial addition. These text-based editing methods fail to follow precise and quantifiable instructions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.777, + 0.892, + 0.807 + ], + "angle": 0, + "content": "fault. We keep this module in our pipeline, as empirically it slightly enhances the results by reducing artifacts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.633, + 0.831 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Experimental Setup We follow [24] to obtain the initial NeRF representation and to extract the textured 3D model. We use Instant-NGP [53] and a grid size of 256 for the 3D model extraction from NeRF. During the coarse-to-fine gen" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4247" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.111, + 0.189, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.465, + 0.094, + 0.594, + 0.107 + ], + "angle": 0, + "content": "Injecting more layers" + }, + { + "type": "image", + "bbox": [ + 0.202, + 0.108, + 0.881, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.265, + 0.893, + 0.294 + ], + "angle": 0, + "content": "Figure 12. Ablation studies on feature injection layers. From left to right, progressively injecting more self-attention layers can result in increasingly improved alignment with user edits." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.3, + 0.47, + 0.419 + ], + "angle": 0, + "content": "
MethodsDINO↑D-RMSE↓
Original Coarse Rendering0.7580.00
SDEdit [49] (t0=0.4)0.7881.71
SDEdit [49] (t0=0.6)0.8002.12
Ours w/o Feature Injection0.8482.33
Ours w/o Depth Control0.8512.15
Ours0.8531.99
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.424, + 0.47, + 0.482 + ], + "angle": 0, + "content": "Table 1. Ablation studies of the enhancement methods on SculptingBench. DINO score measures the textural details, and D-RMSE measures the geometric fidelity. Depth control and feature injection enhance texture quality while maintaining geometric fidelity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.47, + 0.595 + ], + "angle": 0, + "content": "erative enhancement process, for one-shot DreamBooth, we fine-tune the SDXL-1.0 [60] model using LoRA [28] for 800 steps with a learning rate of 1e-5. For feature injection stage, we utilize all the self-attention layers of the SDXL decoder and the first block of the SDXL's upsampling decoder. The SDXL refiner is applied after \\( t = 0.1T \\). For background inpainting, we use Adobe generative fill [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.703 + ], + "angle": 0, + "content": "Qualitative Results We showcase qualitative results in Fig. 6, covering six precise image editing tasks. Detailed descriptions of these tasks are presented in Appendix B. Qualitatively, our method combines the creative freedom of generative models with the precision of graphics pipelines to achieve precise, quantifiable, and physically plausible outcomes for object editing across a variety of scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Our approach introduces new editing features through precise 3D geometry control, a capability not present in existing methods. We compare our method with the state-of-the-art object editing techniques for a comprehensive analysis. In Fig. 9, we show that 3DIT [50], designed for 3D-aware editing via language instructions, faces limitations when applied to real, complex images, largely because its training is based on a synthetic dataset. In Fig. 10, we compare the pose editing ability with DragDiffusion [73] and ControlNet [90]. This comparison reveals that these methods encounter difficulties with complex pose manipulations because they are constrained to the 2D domain. Furthermore, in Fig. 11, we show how text-based editing methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.892, + 0.331 + ], + "angle": 0, + "content": "like InstructPix2Pix [10] and DALL-E 3 [56] struggle with precise and quantifiable instructions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.893, + 0.606 + ], + "angle": 0, + "content": "Ablation Studies We create a new dataset *SculptingBench* to evaluate our new image editing capabilities. This dataset contains 28 images covering six categories: pose editing, rotation, translation, composition, carving, and serial addition (see Appendix C). We perform quantitative studies using different coarse-to-fine enhancement methods. To measure the visual similarity between the edited images and the original ones, particularly in terms of maintaining textural details through the editing process, we employ DINO score [67] as our metrics. This choice is motivated by the self-supervised training objective of DINO [12], which encourages distinction of unique features of a image. To evaluate the geometric fidelity of user edits after enhancement, we introduce a novel metric, \\(D\\)-RMSE. This metric is specifically created to evaluate how well geometric information is retained after the enhancement procedure. \\(D\\)-RMSE measures the discrepancies between the depth maps of the coarse renderings and their enhanced counterparts:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.613, + 0.848, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\mathrm {D} - \\mathrm {R M S E} = \\sqrt {\\mathbb {E} \\left[ \\left(\\mathrm {d e p t h} _ {\\text {c o a r s e}} - \\mathrm {d e p t h} _ {\\text {e n h a n c e d}}\\right) ^ {2} \\right]}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.901 + ], + "angle": 0, + "content": "where depth_coarse, depth_enhanced denote the depth maps MiDaS [64] estimates, for the coarse rendering and the enhanced output image, respectively. In Table 1, we show that without any enhancement, the textural quality metrics (DINO score) are quite low. SDEdit effectively preserves the edited geometry with a low D-RMSE, yet the visual quality significantly deteriorates compared to the original image (see Fig. 4). Our method offers a more advantageous balance, significantly enhancing texture quality as demonstrated by higher DINO score, while preserving geometric consistency, evidenced by a low D-RMSE score. We observe that both feature injection and depth control contribute to enhanced geometric consistency and can lead to further improvement when used together. Additionally, we conduct an empirical study to explore the number of self-attention layers for injection. Fig. 12 shows that more layers improve alignment with user edits. We use all layers for injection." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4248" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. CLIP2StyleGAN: Unsupervised extraction of StyleGAN edit directions. In SIGGRAPH, 2022. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.466, + 0.186 + ], + "angle": 0, + "content": "[2] Adobe. Adobe After Effects. https://www.adobe.com/products/aftereffects.html, 2023.2" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.188, + 0.468, + 0.215 + ], + "angle": 0, + "content": "[3] Adobe. 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Achieving precise control in image editing tasks can be challenging with standard 2D generative pipelines. Our Image Sculpting framework offers the ability to interact with 3D geometry starting with a single image. This enables users to perform detailed, quantifiable, and physically-plausible edits, including precise pose editing, rotation, translation, 3D composition, carving, and serial addition. + +![](images/e9e99dcdf62501ca01498a2c3060c65336c3a8469e392991af8e5330bbb75753.jpg) + +![](images/65f4720db23241e92e8f82a6afb5b0a4dd40445ea1a2a5d11dffab1de4be3cbc.jpg) +(b) Precise Rotation + +![](images/9f90c239fcea19043989a79455edde1170d82f384991fe8d1de95f108e6df6ac.jpg) + +![](images/b489649a115fd131e3521c35815060346dd885754306ed7bdf3a7553a4fd3d47.jpg) + +![](images/e284b5a9bccd4947324fe4538ef3a14e2de3f39de52abe80d9339e5e0457af30.jpg) +(d) Precise 3D Composition + +![](images/e95e883e550f1dc0e5bbaa20645024de233bfae9cb824f7a5605169cca1aaeb3.jpg) + +![](images/a309c22c2aca3c736843c1ce209b9933e94da0db985a01800b4f59e8d31ab57c.jpg) + +![](images/eb94857884369e8d422d73bfb644833eaad50c2a2a5c818b80b9471596df64fe.jpg) +(f) Serial Addition + +![](images/7e072803cae094a5f787675955b6e87c1fa09b841fe70b702eda1ca12fe42883.jpg) + +![](images/2f6ddb4608e1b0e51d8ec58636a51af06b247030df658b434e0a0f362282d920.jpg) + +# Abstract + +We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines. + +# 1. Introduction + +Recent developments in the field of image generative modeling [63, 66, 68, 89] have unlocked new potentials in creative content creation, offering unprecedented opportunities for the generation of diverse visual content by materializing ideas and concepts articulated through language prompts. However, the integration of these models into real-world content creation workflows still poses significant challenges. Among the most critical is the need for users to have detailed control over various aspects of generated objects, including their pose, shape, location, layout, and spatial compositions. The precision extends to quantifiable manipulations, such as rotating an object by a specific angle or making physically-realistic modifications, such as positioning a character in a way that conforms to basic anatomical and physical principles. Interestingly, such a quest for precision and controllability aligns closely with the core principles of computer graphics, which strive to generate pho + +torealistic images with artistic control. + +In virtual effects (VFX) and rendering pipelines, experts meticulously craft and edit every detail within a fully controllable 3D environment, striving for utmost realism. For decades, methods for accurately manipulating and rendering objects have been explored, leading to the development of numerous advanced techniques in 3D model acquisition, rigging, posing, lighting, texturing, and scene rendering. These methods form the bedrock of the modern computer graphics pipeline. However, it often requires custom hardware and software for (1) acquiring production-quality 3D models or designing them from scratch, (2) making these models possible to animate (rigging), (3) creating visually plausible animations (animation), (4) rendering back in the 2D world after applying material and setting up the lighting, and (5) compositing the resulting image with a background or other objects. This process often employs teams of artists and engineers for each one of these steps, as it requires substantial manual input using specialized tools (e.g. After Effects [2], Substance [4], and 3ds Max [29]). + +In contrast, AI-based image generation avoids all this manual work, requiring only a text prompt. Leveraging the power of human language and large datasets of curated content, transforming a text description into a visually striking image is more accessible than ever. Yet, when it comes to precise object manipulation, the current 2D-based generative approach faces inherent limitations due to the lack of a third dimension, leading to incomplete information, limited user interaction on a flat plane, and possible ambiguities. The gap in controllability with respect to image generation using computer graphics techniques is striking, and closing it is a major goal of our work. + +Most interfaces for image editing frameworks rely on text-based instructions. For example, techniques such as Prompt-to-Prompt [26], Plug-and-Play [79], InstructPix2Pix [10], Imagic [36] and Object 3DIT [50] offer adaptable language control. However, achieving precise manipulation through these models remains a challenge. Straightforward manipulations such as "changing a style to mimic Van Gogh" are manageable. However, more specific instructions such as "lift the object by $5\mathrm{cm}$ and rotate it by 42 degrees." are less likely to be successful, as current generative models cannot fulfill such detailed requests through textual prompts alone. 2D-based interactive methods such as DragGAN [57], FreeDrag [42], and DragDiffusion [73] demonstrate the ability to alter part of an object through transitions in the latent space. Despite this, they have their limitations: 1) they can accomplish basic deformations, but the outcomes are not entirely predictable, often leading to results that do not align with the user's intentions; 2) these latent transformations operate within the 2D feature space, which inherently limits their ability to represent 3D transformations and handle occlusions accurately; 3) they lack + +physics-awareness, which complicates incorporating external constraints, such as skeletal structures. + +Our work draws inspiration from the computer graphics pipeline and ventures into a novel approach for 2D image-based object manipulation tasks. Our proposed Image Sculpting framework, which metaphorically suggests the flexible and precise sculpting of a 2D image in a 3D space, integrates three key components: (1) single-view 3D reconstruction, (2) manipulation of objects in 3D, and (3) a coarse-to-fine generative enhancement process. More specifically, 2D objects are converted into 3D models, granting users the ability to interact with and manipulate the 3D geometry directly, which allows for precision in editing. The manipulated objects are then seamlessly reincorporated into their original 2D contexts, maintaining visual coherence and fidelity. A critical hurdle in this process is the single-view 3D reconstruction method, a task that, despite rapid progress [27, 41, 43-46, 62, 71], often results in relatively low-fidelity, coarse geometric and texture representations. Unlike manually crafted 3D assets used for graphics, their rendered version is far from photo-realistic. Nonetheless, the extracted geometries are sufficient for interactive and precise control. To achieve high-quality final images, a separate enhancement procedure is necessary. In summary, our Image Sculpting pipeline has three key phases: + +Phase 1. For the 3D reconstruction phase, we employ a zero-shot single image reconstruction model (Zero-1-to-3 [44]), which has been trained on extensive datasets [17] of 3D objects. + +Phase 2. The deformation process utilizes established geometric processing tools, such as As-Rigid-As-Possible (ARAP) [78] and linear-based skinning [48], enabling interactive and precise manipulation of the 3D models. + +Phase 3. For the generative enhancement process, we develop a coarse-to-fine enhancement pipeline, using an feature injection approach [79]. Our method strikes a balance between maintaining the original texture of the object and the modified geometry, utilizing a pre-trained text-to-image diffusion model with additional controls. + +Our Image Sculpting framework showcases an array of precise and quantifiable image editing capabilities. These include precise pose editing, rotation, translation, multiobject 3D composition, carving, and serial addition. This suite of functionalities demonstrates the versatility of our approach and its superiority in precision and control compared to existing image editing methods. Our method also outperforms various baselines in image quality, as confirmed by both qualitative and quantitative evaluations on the new SculptingBench benchmark. We believe that our method can foster new opportunities in merging the flexibility of generative models with the precise controllability inherent in traditional graphics pipelines. + +![](images/981ed4f782e538a078d25c5cb4c1c5a5dd27d907a77e3e8213b15b6cbff8dd64.jpg) +(a) Space Deformations + +![](images/4744e0e4bfd4308dd7f0896ebb864a39c2d1a53dda64f9de04072c93a3739f49.jpg) +Figure 2. Illustration of three mesh deformation methods applied to a 3D model. In cage-based space deformation (a), the model is placed in a cage and deformed when the user moves the cage vertices [33]. As-Rigid-As-Possible (ARAP) [78] deformation (b) deforms the model when user-selected blue handle points are moved towards designated red target points. Linear blend skinning (c) maps the deformation of a skeleton to the model [32]. Following deformation, a diffusion rendering process can be added for controllable generation. Each mesh deformation technique offers a different balance of control, speed, and precision. Our framework can use any of these techniques. + +![](images/4e856113b9e7f8141204e284bc8d96f2f8e316b516ecf783119fa3732d846cc1.jpg) +(b) Shape-Aware Deformation + +![](images/c8f6bcb77ef1c92c0f37db13c8737ad08793183f58d41ee1c16dcf96da370f50.jpg) + +![](images/57f9d0f900140dbfee6c6af912fe25891446f408e65666462502958ac06d5497.jpg) +(c) Linear Blend Skinning + +![](images/4f31fb33fa4f44471f04715c44943da2809fee498f8dcc36035d7f8c77b4c34d.jpg) + +![](images/12e9e69ae1fcc6dab9f2d45321d39aba6fbbac2a0c93e08145eca3d7a0fc57d1.jpg) + +![](images/ff132d14983564200e0ab981e21c7a657f73bf3025837fa66f521bf34d4e05a7.jpg) + +# 2. Related Work + +Generative Image Editing In computer graphics, extensive research on interactive raster image editing exists, and we defer its detailed review to the next section. In computer vision, the advent of image generative models such as GANs [22, 34, 35] has expanded the scope of image editing to include style transfer [21], image-to-image translation [30, 91], latent manipulation [70, 84], and text-based manipulation [1, 58, 85]. Recently, capabilities in image editing have advanced significantly with the rise of diffusion models [18, 59, 66]. The leading systems [51, 56, 63, 68] allow users to generate image variations or use inpainting masks [54] to generate specific parts of scenes based on a text prompt. Other work explores enhancing pretrained diffusion models with text-guided editing capabilities [10, 26, 52, 79]. Yet, text-based editing has limitations in precisely controlling object shapes and positions. ControlNet [90] incorporates additional conditional inputs such as depth [64], poses [11], and edges [86] for controllable generation. For more intuitive interactions, DragGAN [57] enables users to drag control points on objects with GANs, and similar techniques have been adapted for diffusion models [42, 73]. However, these methods are mostly confined to 2D and face challenges in tasks requiring more complex, out-of-plane transformations. 3D-aware generative models such as EG3D [13] and StyleNeRF [23] have explored this direction. OBJECT-3DIT [50], a baseline in our paper, studied 3D-aware editing using language instructions. However, its effectiveness is somewhat constrained due to its training on a synthetic dataset. + +Single-View Reconstruction Single-view 3D reconstruction is a long-standing problem in computer vision [25]. While algorithmic advancements are important, the significance of training data has been increasingly recognized. Earlier efforts were geared towards training models [55, 76, 83, 88] using smaller, simplistic 3D datasets [14, 65]. Recent approaches [61, 80] have started to utilize density distillation from pre-trained 2D diffusion models trained on large-scale text-image datasets, lessening the reliance on 3D + +data. Nonetheless, for improved view-consistency, the demand for high-quality 3D data is indispensable. The emergence of large-scale 3D datasets, such as Objaverse [16, 17], has spurred methods such as Zero-1-to-3 [44] to combine 2D score distillation with 3D data training. This has led to a surge in new models in this domain, noticeably enhancing reconstruction quality [43, 62, 72, 82]. Our work is also closely related to 3-Sweep [15] and 3D Object Manipulation [37]. These pioneering studies in graphics involve constructing a 3D model using edge information or retrieving an online repository for image editing. We now employ generative models to further enhance shape editing capabilities and user experience. + +# 3. Overview of 3D Shape Deformation + +The deformation of 3D shapes has been extensively studied in the last four decades, with both traditional and data-driven methods being proposed and successfully used in robotics, graphics, and engineering. We review the main approaches and their usability within our framework. + +Space Deformations The older and still widely used approach is applying a volumetric warp function $f: R^3 \to R^3$ to all points of a 3D domain [69]. This approach can be applied to explicit (triangular or polygonal meshes) or implicit representations. The map can be parametrized using splines on lattices [69], vertices on a cage [33], or neural fields [19]. A limitation of these approaches is that they are unaware of the object shape, making them more challenging to use on complex articulated objects [9]. + +Shape-Aware Deformation Shape-aware deformations provide a set of controls linked to the objects' surface. In Computer-Aided-Design (CAD), a small set of control points define a smooth surface using spline patches [20]. Despite its flexibility and quality, extracting spline patches from 3D models or NeRFs is a challenging and open problem [7]. Partial differential equation (PDE)-based methods simulate the deformation of an object, representing it as a volumetric deformable solid [75] or as a thin rubber shell [78]. The forces guiding the deformation are applied by moving handles selected on a surface [8], making them in + +![](images/040c556a52992d706ac8a0be927fa8e1b1e78db42ee77314c10b5f4fda460ae2.jpg) + +![](images/2f0348ecc5c168aaaad3e829b0b316fcee1d1c3fd2027a9a039169ea339b1538.jpg) +Figure 3. Overview of our Image Sculpting pipeline, $\mathrm{DDIM}^+$ represents DDIM with the DreamBooth fine-tuned and depth controlled model. The process begins by converting the input image into a textured 3D model through a de-rendering process. This model is then prepared for interactive deformation by creating a skeleton and calculating skinning weights. The user can modify the skeleton to deform the model, resulting in an initial coarse image. To refine this edited image, we invert the coarse rendering $I_{c}$ into the noise $\pmb{x}_T^c$ . We then inject self-attention maps $\pmb{A}_{t}^{c}$ and feature maps $\pmb{f}_{t}^{c}$ from the initial image's denoising process into the enhanced image denoising steps. This technique helps in preserving the geometry of the modified object while restoring the visual quality of the edited image. + +tutive to use and requiring minimal user interaction. + +Linear Blend Skinning The most popular deformation approach is linear blend skinning [32], which defines a space deformation function as a blended average of a set of affine transformations weighted by shape-aware scalar functions, often computed with methods based on solutions of PDEs on surfaces [31] or manually edited. This approach offers complete control and flexibility, as the affine transformation can be attached to points, vertexes of a cage, or segments in a skeleton [6]. + +Our approach We can use any of these algorithms to precisely control the shape deformation and, thus, the rendered image. We show an example of one representative method for each class in Fig. 2, and we leave as future work additional automation of this step. + +# 4. Methods + +Given a single 2D image, our objective is to enable precise manipulation of the objects and their orientations in 3D space, before converting this back into a high-quality edited 2D image. To achieve this, we have developed a novel editing pipeline tailored for image sculpting (see Fig. 3) composed of three steps: (1) We initially convert the input image into a 3D model, (2) the 3D model is edited by deforming it in 3D space, and (3) we use a coarse-to-fine generative enhancement pipeline to turn the coarse rendering of the 3D model into a high-fidelity image. + +# 4.1. De-Rendering and Deformation + +Given an image of an object, our goal is to perform 3D reconstruction to obtain its 3D model. + +Image to NeRF With advancements in text-to-image foundation models [66] and the viewpoint-conditioned image translation model [44], our initial step involves segmenting the selected object from the input image using SAM [38]. Building upon this, we then train a NeRF using Score Distillation Sampling (SDS) [61]. + +NeRF to 3D Model We use the implementation in three-studio [24] to convert a NeRF volume into a mesh. This algorithm transforms the volume density into a signed distance function, extracts an isosurface [47], and parameterizes it [87] for texture mapping [74]. The texture is extracted by differentiable rendering [39]. + +3D Model Deformation After obtaining the 3D model, a user can manually construct a skeleton and interactively manipulate it by rotating the bones to achieve the target pose. The mesh deformation affects the vertex positions of the object but not the UV coordinates used for texture mapping; this procedure thus deforms the texture mapped on the object following its deformation. + +However, the resulting image quality depends on the 3D reconstruction's accuracy, which, in our case, is coarse and insufficient for the intended visual outcome (Fig. 3). Therefore, we rely on an image enhancement pipeline to convert the coarse rendering into a high-quality output. + +![](images/3e281a7734339f7c4829b3b10b1356bd69df3230ead7c634d4d6243cb23052b6.jpg) +Input Image + +![](images/771454ec0a33ae9b0516cc84d7afc74421959d6097c87abb25f86f10e62b1106.jpg) +Coarse Rendering + +![](images/d392e2bccf8e58bc3bebfdf2e8dca6fd16bd6ba49c0347b301b809d815c643dd.jpg) +DreamBooth [67] + +![](images/f74b4c3bbb23d5823a53b2a83cb791a8eed08bfa65a88250ccc1154678a276f8.jpg) +SDEdit [49] $(t_0 = 0.4)$ + +![](images/d0409b4a164f25957f2d6dc1f9e749f8fb418bd934ae94bd154d10a37eaf7e77.jpg) +SDEdit [49] $(t_0 = 0.6)$ + +![](images/06f79e740a20289932624a45d1833daa463360c508d95973d3af0bc1bcdf08ca.jpg) +Ours w/o Feature Injection + +![](images/11f240233e3a78cd04bd3cfe6b36e4ee5b93b5394124660671452cda6cbfdd63.jpg) +Ours w/o Depth Control + +![](images/ea07bd25e775311b8bd686f178601fd1c2163c78b09dfb08fef4bd9b724e06be.jpg) +Ours + +![](images/a67f3aba33e49f9ce2ab03791e72008ed7f9e9143e7503da8fa00903f12a7ff3.jpg) +Figure 4. Comparison of our final method with various baseline methods and ablations. Our approach effectively maintains the geometric information while ensuring the texture quality. In contrast, other methods typically preserve either the texture or the geometry, but not both. +Figure 5. Overview of the coarse-to-fine generative enhancement model architecture. The red module denotes the one-shot Dream-Booth [67], which requires tuning; the grey module is the SDXL Refiner [5], which is frozen in our experiments. + +# 4.2. Coarse-to-Fine Generative Enhancement + +This section focuses on blending a coarsely rendered image back to its original background. The aim is to restore textural details while keeping the edited geometry intact. Image restoration and enhancement are commonly approached as image-to-image translation tasks [81], leveraging the strong correlation between the source and target images. Our challenge, however, presents a unique scenario: despite overall similarities in appearance and texture between the input and desired output, the input object's geometry changes, sometimes significantly, after user editing. + +In exploring possible solutions, one approach is to use subject-driven personalization techniques like DreamBooth [67]. They aim to preserve key details from the input, but might compromise the edited geometry. Alternatively, image-to-image translation methods like SDEdit [49] can be used to preserve the edited geometry, but this might disturb the textural consistency with the original image. This dichotomy was clear in our preliminary study, as shown in Fig. 4. SDEdit can maintain the geometry, but it was unable to accurately replicate the textures. On the other hand, DreamBooth produced high-fidelity outputs, but struggled to preserve both the texture and geometry effectively. + +To address the balance between preserving texture and geometry, our approach begins by "personalizing" a pretrained text-to-image diffusion model. To capture the object's key features, we fine-tune the diffusion model with + +DreamBooth on one input reference image. To maintain the geometry, we adapt a feature and attention injection technique [79], originally designed for semantic layout control. Furthermore, we incorporate depth data from the 3D model through ControlNet [90]. We find this integration crucial in minimizing uncertainties during the enhancement process. + +One-shot Dreambooth DreamBooth [67] fine-tunes a pre-trained diffusion model with a few images for subject-driven generation. The original DreamBooth paper [67] has shown its ability to leverage the semantic class priors to generate novel views of an object, given only a few frontal images of the subject. This aspect is particularly useful in our setting, since the coarse rendering we work with lacks explicit viewpoint information. In our application, we train DreamBooth using just a single example, which is the input image. Notably, this one-shot approach with DreamBooth also effectively captures the detailed texture, thereby filling in the textural gaps present in the coarse rendering. + +Depth Control We use depth ControlNet [90] to preserve the geometric information of user editing. The depth map is rendered directly from the deformed 3D model, bypassing the need for any monocular depth estimation. For the background region, we don't use the depth map. This depth map serves as a spatial control signal, guiding the geometry generation in the final edited images. However, relying solely on depth control is not sufficient – although it can preserve the geometry to some extent, it still struggles in local, more nuanced editing, such as capturing the specific shapes of a pumpkin's eyes or the bent legs of a chair (Fig. 4). + +Feature Injection To better preserve the geometry, we use feature injection. As demonstrated in Fig. 3, this step begins with DDIM inversion [77] (with the DreamBooth finetuned, depth controlled diffusion model) of the coarse rendering image to obtain the inverted latents. At each denoising step, we denoise the inverted latent of the coarse rendering along with the latent of the refined image, extracting their respective feature maps (from the residual blocks) and self-attention maps (from the transformer blocks). It has been shown in [79] that the feature maps carry semantic in + +![](images/f251783eafd51651092ebb1b272df74c53946e0426ace3ffe4bd6c131a0f5752.jpg) +Figure 6. A compilation of qualitative results from six image editing tasks. Additionally, we include additional examples (termed as 'Mixture' in the final row) to illustrate the versatile combination of these capabilities. + +![](images/5803c658df05b4788edb0ceaaf0c88f5c817a6bac22a458130b21fee6d0b15a0.jpg) + +![](images/5ec8684ee51f651643b1c2553c128a83e72a78b83e72bb626d850dc9f541f241.jpg) +Figure 7. Our blend-in process. At every denoising step, we mask the background areas and blend them with the unmasked regions from the denoised latent. This process helps maintain visual coherence and preserve the background. +Figure 8. Our blend-in process yields visually harmonious results. Top: Results from direct copy-pasting. Bottom: Our results. + +formation, while the self-attention maps contain the geometry and layout of the generated images. By overriding the feature and self-attention maps during the enhanced image denoising steps with those from the coarser version, we ensure the geometry of the enhanced image can reflect those of the coarse rendering. The pseudo code for our generative enhancement is detailed in Appendix A. Note that our method differs from the original Plug-and-Play use cases: we use feature injection to preserve the geometry during the coarse-to-fine process rather than translating the image according to a new text prompt. We present the injection layer selection and the replacement schedule in Section 5. + +Background Blend-In To maintain the consistency of the background between the input and edited images, we first inpaint the area initially occupied by the object in the input image, thus obtaining an unobstructed background. However, another challenge arises in merging the edited object into this background smoothly. Merely copy-pasting it onto the background leads to an unrealistic visual effect, such as the improper water reflections over the fish and the absence of shadow casting from the truck (Fig. 8). To overcome this, as demonstrated in Fig. 7, our approach involves masking the background areas during the denoising steps to preserve their original background. This means we retain the unedited background by blending the unmasked (edited) regions from the denoising step with the masked (original) background. We use SDXL [60] as our pre-trained text-to-image model, which includes a refiner module by de + +![](images/6eba05c221ac6e83f6dca7878ed58d46d62e3e8723a5e7100f3a4703b21280a6.jpg) + +![](images/2538e286f39754666dadb38696a0824160c8822d8a4c0204dd85cfaac086352f.jpg) +Figure 9. Comparisons with Object-3DIT [50] on object translation, rotation, and composition tasks. + +![](images/b8bc9bcb439d0425fa03338a0c950b26b24893330614478c12ad332b7d55b8b4.jpg) +Figure 10. Comparisons with DragDiffusion [73] and ControlNet [90] on pose editing. These techniques face difficulties in handling complex pose modifications. +Figure 11. Comparisons with InstructPix2Pix [10] and DALL-E 3 [56] on serial addition. These text-based editing methods fail to follow precise and quantifiable instructions. + +fault. We keep this module in our pipeline, as empirically it slightly enhances the results by reducing artifacts. + +# 5. Experiments + +Experimental Setup We follow [24] to obtain the initial NeRF representation and to extract the textured 3D model. We use Instant-NGP [53] and a grid size of 256 for the 3D model extraction from NeRF. During the coarse-to-fine gen + +![](images/4ced16c09d08f77c1d3e83e6a894ef6312a81fe03379a1a7128d68cbd7f7de0b.jpg) +Figure 12. Ablation studies on feature injection layers. From left to right, progressively injecting more self-attention layers can result in increasingly improved alignment with user edits. + +Injecting more layers + +![](images/3125134acd0d1dac7bd232f3b7c5d47c21a3123d982ecb237cdbb143cef18098.jpg) + +
MethodsDINO↑D-RMSE↓
Original Coarse Rendering0.7580.00
SDEdit [49] (t0=0.4)0.7881.71
SDEdit [49] (t0=0.6)0.8002.12
Ours w/o Feature Injection0.8482.33
Ours w/o Depth Control0.8512.15
Ours0.8531.99
+ +Table 1. Ablation studies of the enhancement methods on SculptingBench. DINO score measures the textural details, and D-RMSE measures the geometric fidelity. Depth control and feature injection enhance texture quality while maintaining geometric fidelity. + +erative enhancement process, for one-shot DreamBooth, we fine-tune the SDXL-1.0 [60] model using LoRA [28] for 800 steps with a learning rate of 1e-5. For feature injection stage, we utilize all the self-attention layers of the SDXL decoder and the first block of the SDXL's upsampling decoder. The SDXL refiner is applied after $t = 0.1T$ . For background inpainting, we use Adobe generative fill [3]. + +Qualitative Results We showcase qualitative results in Fig. 6, covering six precise image editing tasks. Detailed descriptions of these tasks are presented in Appendix B. Qualitatively, our method combines the creative freedom of generative models with the precision of graphics pipelines to achieve precise, quantifiable, and physically plausible outcomes for object editing across a variety of scenarios. + +Our approach introduces new editing features through precise 3D geometry control, a capability not present in existing methods. We compare our method with the state-of-the-art object editing techniques for a comprehensive analysis. In Fig. 9, we show that 3DIT [50], designed for 3D-aware editing via language instructions, faces limitations when applied to real, complex images, largely because its training is based on a synthetic dataset. In Fig. 10, we compare the pose editing ability with DragDiffusion [73] and ControlNet [90]. This comparison reveals that these methods encounter difficulties with complex pose manipulations because they are constrained to the 2D domain. Furthermore, in Fig. 11, we show how text-based editing methods + +like InstructPix2Pix [10] and DALL-E 3 [56] struggle with precise and quantifiable instructions. + +Ablation Studies We create a new dataset *SculptingBench* to evaluate our new image editing capabilities. This dataset contains 28 images covering six categories: pose editing, rotation, translation, composition, carving, and serial addition (see Appendix C). We perform quantitative studies using different coarse-to-fine enhancement methods. To measure the visual similarity between the edited images and the original ones, particularly in terms of maintaining textural details through the editing process, we employ DINO score [67] as our metrics. This choice is motivated by the self-supervised training objective of DINO [12], which encourages distinction of unique features of a image. To evaluate the geometric fidelity of user edits after enhancement, we introduce a novel metric, $D$ -RMSE. This metric is specifically created to evaluate how well geometric information is retained after the enhancement procedure. $D$ -RMSE measures the discrepancies between the depth maps of the coarse renderings and their enhanced counterparts: + +$$ +\mathrm {D} - \mathrm {R M S E} = \sqrt {\mathbb {E} \left[ \left(\mathrm {d e p t h} _ {\text {c o a r s e}} - \mathrm {d e p t h} _ {\text {e n h a n c e d}}\right) ^ {2} \right]} +$$ + +where depth_coarse, depth_enhanced denote the depth maps MiDaS [64] estimates, for the coarse rendering and the enhanced output image, respectively. In Table 1, we show that without any enhancement, the textural quality metrics (DINO score) are quite low. SDEdit effectively preserves the edited geometry with a low D-RMSE, yet the visual quality significantly deteriorates compared to the original image (see Fig. 4). Our method offers a more advantageous balance, significantly enhancing texture quality as demonstrated by higher DINO score, while preserving geometric consistency, evidenced by a low D-RMSE score. We observe that both feature injection and depth control contribute to enhanced geometric consistency and can lead to further improvement when used together. Additionally, we conduct an empirical study to explore the number of self-attention layers for injection. Fig. 12 shows that more layers improve alignment with user edits. We use all layers for injection. + +# References + +[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. CLIP2StyleGAN: Unsupervised extraction of StyleGAN edit directions. In SIGGRAPH, 2022. 3 +[2] Adobe. Adobe After Effects. https://www.adobe.com/products/aftereffects.html, 2023.2 +[3] Adobe. Adobe Firefly. https://www.adobe.com/sensei/generative-ai/firefly.html, 2023.8 +[4] Adobe. 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], + "index": 30 + }, + { + "bbox": [ + 46, + 507, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 288, + 687 + ], + "type": "text", + "content": "We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 307, + 486, + 386, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 486, + 386, + 498 + ], + "spans": [ + { + "bbox": [ + 307, + 486, + 386, + 498 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Recent developments in the field of image generative modeling [63, 66, 68, 89] have unlocked new potentials in creative content creation, offering unprecedented opportunities for the generation of diverse visual content by materializing ideas and concepts articulated through language prompts. However, the integration of these models into real-world content creation workflows still poses significant challenges. Among the most critical is the need for users to have detailed control over various aspects of generated objects, including their pose, shape, location, layout, and spatial compositions. The precision extends to quantifiable manipulations, such as rotating an object by a specific angle or making physically-realistic modifications, such as positioning a character in a way that conforms to basic anatomical and physical principles. Interestingly, such a quest for precision and controllability aligns closely with the core principles of computer graphics, which strive to generate pho" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 702, + 229, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 702, + 229, + 712 + ], + "spans": [ + { + "bbox": [ + 67, + 702, + 229, + 712 + ], + "type": "text", + "content": "Code and project page available at this https URL" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4241" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 203, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 203, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 203, + 83 + ], + "type": "text", + "content": "torealistic images with artistic control." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 87, + 287, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 87, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 287, + 314 + ], + "type": "text", + "content": "In virtual effects (VFX) and rendering pipelines, experts meticulously craft and edit every detail within a fully controllable 3D environment, striving for utmost realism. For decades, methods for accurately manipulating and rendering objects have been explored, leading to the development of numerous advanced techniques in 3D model acquisition, rigging, posing, lighting, texturing, and scene rendering. These methods form the bedrock of the modern computer graphics pipeline. However, it often requires custom hardware and software for (1) acquiring production-quality 3D models or designing them from scratch, (2) making these models possible to animate (rigging), (3) creating visually plausible animations (animation), (4) rendering back in the 2D world after applying material and setting up the lighting, and (5) compositing the resulting image with a background or other objects. This process often employs teams of artists and engineers for each one of these steps, as it requires substantial manual input using specialized tools (e.g. After Effects [2], Substance [4], and 3ds Max [29])." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 316, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 460 + ], + "type": "text", + "content": "In contrast, AI-based image generation avoids all this manual work, requiring only a text prompt. Leveraging the power of human language and large datasets of curated content, transforming a text description into a visually striking image is more accessible than ever. Yet, when it comes to precise object manipulation, the current 2D-based generative approach faces inherent limitations due to the lack of a third dimension, leading to incomplete information, limited user interaction on a flat plane, and possible ambiguities. The gap in controllability with respect to image generation using computer graphics techniques is striking, and closing it is a major goal of our work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 462, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 462, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 462, + 287, + 713 + ], + "type": "text", + "content": "Most interfaces for image editing frameworks rely on text-based instructions. For example, techniques such as Prompt-to-Prompt [26], Plug-and-Play [79], InstructPix2Pix [10], Imagic [36] and Object 3DIT [50] offer adaptable language control. However, achieving precise manipulation through these models remains a challenge. Straightforward manipulations such as \"changing a style to mimic Van Gogh\" are manageable. However, more specific instructions such as \"lift the object by " + }, + { + "bbox": [ + 47, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "5\\mathrm{cm}" + }, + { + "bbox": [ + 47, + 462, + 287, + 713 + ], + "type": "text", + "content": " and rotate it by 42 degrees.\" are less likely to be successful, as current generative models cannot fulfill such detailed requests through textual prompts alone. 2D-based interactive methods such as DragGAN [57], FreeDrag [42], and DragDiffusion [73] demonstrate the ability to alter part of an object through transitions in the latent space. Despite this, they have their limitations: 1) they can accomplish basic deformations, but the outcomes are not entirely predictable, often leading to results that do not align with the user's intentions; 2) these latent transformations operate within the 2D feature space, which inherently limits their ability to represent 3D transformations and handle occlusions accurately; 3) they lack" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "physics-awareness, which complicates incorporating external constraints, such as skeletal structures." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 100, + 546, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 100, + 546, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 100, + 546, + 376 + ], + "type": "text", + "content": "Our work draws inspiration from the computer graphics pipeline and ventures into a novel approach for 2D image-based object manipulation tasks. Our proposed Image Sculpting framework, which metaphorically suggests the flexible and precise sculpting of a 2D image in a 3D space, integrates three key components: (1) single-view 3D reconstruction, (2) manipulation of objects in 3D, and (3) a coarse-to-fine generative enhancement process. More specifically, 2D objects are converted into 3D models, granting users the ability to interact with and manipulate the 3D geometry directly, which allows for precision in editing. The manipulated objects are then seamlessly reincorporated into their original 2D contexts, maintaining visual coherence and fidelity. A critical hurdle in this process is the single-view 3D reconstruction method, a task that, despite rapid progress [27, 41, 43-46, 62, 71], often results in relatively low-fidelity, coarse geometric and texture representations. Unlike manually crafted 3D assets used for graphics, their rendered version is far from photo-realistic. Nonetheless, the extracted geometries are sufficient for interactive and precise control. To achieve high-quality final images, a separate enhancement procedure is necessary. In summary, our Image Sculpting pipeline has three key phases:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": "Phase 1. For the 3D reconstruction phase, we employ a zero-shot single image reconstruction model (Zero-1-to-3 [44]), which has been trained on extensive datasets [17] of 3D objects." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "content": "Phase 2. The deformation process utilizes established geometric processing tools, such as As-Rigid-As-Possible (ARAP) [78] and linear-based skinning [48], enabling interactive and precise manipulation of the 3D models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 482, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 554 + ], + "type": "text", + "content": "Phase 3. For the generative enhancement process, we develop a coarse-to-fine enhancement pipeline, using an feature injection approach [79]. Our method strikes a balance between maintaining the original texture of the object and the modified geometry, utilizing a pre-trained text-to-image diffusion model with additional controls." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "Our Image Sculpting framework showcases an array of precise and quantifiable image editing capabilities. These include precise pose editing, rotation, translation, multiobject 3D composition, carving, and serial addition. This suite of functionalities demonstrates the versatility of our approach and its superiority in precision and control compared to existing image editing methods. Our method also outperforms various baselines in image quality, as confirmed by both qualitative and quantitative evaluations on the new SculptingBench benchmark. We believe that our method can foster new opportunities in merging the flexibility of generative models with the precise controllability inherent in traditional graphics pipelines." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4242" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 202, + 151 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 202, + 151 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 202, + 151 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 202, + 151 + ], + "type": "image", + "image_path": "981ed4f782e538a078d25c5cb4c1c5a5dd27d907a77e3e8213b15b6cbff8dd64.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 114, + 153, + 192, + 163 + ], + "lines": [ + { + "bbox": [ + 114, + 153, + 192, + 163 + ], + "spans": [ + { + "bbox": [ + 114, + 153, + 192, + 163 + ], + "type": "text", + "content": "(a) Space Deformations" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 203, + 91, + 252, + 144 + ], + "blocks": [ + { + "bbox": [ + 203, + 91, + 252, + 144 + ], + "lines": [ + { + "bbox": [ + 203, + 91, + 252, + 144 + ], + "spans": [ + { + "bbox": [ + 203, + 91, + 252, + 144 + ], + "type": "image", + "image_path": "4744e0e4bfd4308dd7f0896ebb864a39c2d1a53dda64f9de04072c93a3739f49.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "type": "text", + "content": "Figure 2. Illustration of three mesh deformation methods applied to a 3D model. In cage-based space deformation (a), the model is placed in a cage and deformed when the user moves the cage vertices [33]. As-Rigid-As-Possible (ARAP) [78] deformation (b) deforms the model when user-selected blue handle points are moved towards designated red target points. Linear blend skinning (c) maps the deformation of a skeleton to the model [32]. Following deformation, a diffusion rendering process can be added for controllable generation. Each mesh deformation technique offers a different balance of control, speed, and precision. Our framework can use any of these techniques." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 260, + 91, + 302, + 142 + ], + "blocks": [ + { + "bbox": [ + 260, + 91, + 302, + 142 + ], + "lines": [ + { + "bbox": [ + 260, + 91, + 302, + 142 + ], + "spans": [ + { + "bbox": [ + 260, + 91, + 302, + 142 + ], + "type": "image", + "image_path": "4e856113b9e7f8141204e284bc8d96f2f8e316b516ecf783119fa3732d846cc1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 280, + 153, + 380, + 163 + ], + "lines": [ + { + "bbox": [ + 280, + 153, + 380, + 163 + ], + "spans": [ + { + "bbox": [ + 280, + 153, + 380, + 163 + ], + "type": "text", + "content": "(b) Shape-Aware Deformation" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 307, + 91, + 349, + 141 + ], + "blocks": [ + { + "bbox": [ + 307, + 91, + 349, + 141 + ], + "lines": [ + { + "bbox": [ + 307, + 91, + 349, + 141 + ], + "spans": [ + { + "bbox": [ + 307, + 91, + 349, + 141 + ], + "type": "image", + "image_path": "c8f6bcb77ef1c92c0f37db13c8737ad08793183f58d41ee1c16dcf96da370f50.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 354, + 90, + 396, + 141 + ], + "blocks": [ + { + "bbox": [ + 354, + 90, + 396, + 141 + ], + "lines": [ + { + "bbox": [ + 354, + 90, + 396, + 141 + ], + "spans": [ + { + "bbox": [ + 354, + 90, + 396, + 141 + ], + "type": "image", + "image_path": "57f9d0f900140dbfee6c6af912fe25891446f408e65666462502958ac06d5497.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 431, + 153, + 516, + 163 + ], + "lines": [ + { + "bbox": [ + 431, + 153, + 516, + 163 + ], + "spans": [ + { + "bbox": [ + 431, + 153, + 516, + 163 + ], + "type": "text", + "content": "(c) Linear Blend Skinning" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 402, + 90, + 445, + 140 + ], + "blocks": [ + { + "bbox": [ + 402, + 90, + 445, + 140 + ], + "lines": [ + { + "bbox": [ + 402, + 90, + 445, + 140 + ], + "spans": [ + { + "bbox": [ + 402, + 90, + 445, + 140 + ], + "type": "image", + "image_path": "4f31fb33fa4f44471f04715c44943da2809fee498f8dcc36035d7f8c77b4c34d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 449, + 90, + 490, + 140 + ], + "blocks": [ + { + "bbox": [ + 449, + 90, + 490, + 140 + ], + "lines": [ + { + "bbox": [ + 449, + 90, + 490, + 140 + ], + "spans": [ + { + "bbox": [ + 449, + 90, + 490, + 140 + ], + "type": "image", + "image_path": "12e9e69ae1fcc6dab9f2d45321d39aba6fbbac2a0c93e08145eca3d7a0fc57d1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 493, + 91, + 536, + 140 + ], + "blocks": [ + { + "bbox": [ + 493, + 91, + 536, + 140 + ], + "lines": [ + { + "bbox": [ + 493, + 91, + 536, + 140 + ], + "spans": [ + { + "bbox": [ + 493, + 91, + 536, + 140 + ], + "type": "image", + "image_path": "ff132d14983564200e0ab981e21c7a657f73bf3025837fa66f521bf34d4e05a7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 234, + 134, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 234, + 134, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 234, + 134, + 246 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 256, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 602 + ], + "type": "text", + "content": "Generative Image Editing In computer graphics, extensive research on interactive raster image editing exists, and we defer its detailed review to the next section. In computer vision, the advent of image generative models such as GANs [22, 34, 35] has expanded the scope of image editing to include style transfer [21], image-to-image translation [30, 91], latent manipulation [70, 84], and text-based manipulation [1, 58, 85]. Recently, capabilities in image editing have advanced significantly with the rise of diffusion models [18, 59, 66]. The leading systems [51, 56, 63, 68] allow users to generate image variations or use inpainting masks [54] to generate specific parts of scenes based on a text prompt. Other work explores enhancing pretrained diffusion models with text-guided editing capabilities [10, 26, 52, 79]. Yet, text-based editing has limitations in precisely controlling object shapes and positions. ControlNet [90] incorporates additional conditional inputs such as depth [64], poses [11], and edges [86] for controllable generation. For more intuitive interactions, DragGAN [57] enables users to drag control points on objects with GANs, and similar techniques have been adapted for diffusion models [42, 73]. However, these methods are mostly confined to 2D and face challenges in tasks requiring more complex, out-of-plane transformations. 3D-aware generative models such as EG3D [13] and StyleNeRF [23] have explored this direction. OBJECT-3DIT [50], a baseline in our paper, studied 3D-aware editing using language instructions. However, its effectiveness is somewhat constrained due to its training on a synthetic dataset." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Single-View Reconstruction Single-view 3D reconstruction is a long-standing problem in computer vision [25]. While algorithmic advancements are important, the significance of training data has been increasingly recognized. Earlier efforts were geared towards training models [55, 76, 83, 88] using smaller, simplistic 3D datasets [14, 65]. Recent approaches [61, 80] have started to utilize density distillation from pre-trained 2D diffusion models trained on large-scale text-image datasets, lessening the reliance on 3D" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 236, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 390 + ], + "type": "text", + "content": "data. Nonetheless, for improved view-consistency, the demand for high-quality 3D data is indispensable. The emergence of large-scale 3D datasets, such as Objaverse [16, 17], has spurred methods such as Zero-1-to-3 [44] to combine 2D score distillation with 3D data training. This has led to a surge in new models in this domain, noticeably enhancing reconstruction quality [43, 62, 72, 82]. Our work is also closely related to 3-Sweep [15] and 3D Object Manipulation [37]. These pioneering studies in graphics involve constructing a 3D model using edge information or retrieving an online repository for image editing. We now employ generative models to further enhance shape editing capabilities and user experience." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 392, + 503, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 503, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 503, + 405 + ], + "type": "text", + "content": "3. Overview of 3D Shape Deformation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "type": "text", + "content": "The deformation of 3D shapes has been extensively studied in the last four decades, with both traditional and data-driven methods being proposed and successfully used in robotics, graphics, and engineering. We review the main approaches and their usability within our framework." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "content": "Space Deformations The older and still widely used approach is applying a volumetric warp function " + }, + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "inline_equation", + "content": "f: R^3 \\to R^3" + }, + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "content": " to all points of a 3D domain [69]. This approach can be applied to explicit (triangular or polygonal meshes) or implicit representations. The map can be parametrized using splines on lattices [69], vertices on a cage [33], or neural fields [19]. A limitation of these approaches is that they are unaware of the object shape, making them more challenging to use on complex articulated objects [9]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Shape-Aware Deformation Shape-aware deformations provide a set of controls linked to the objects' surface. In Computer-Aided-Design (CAD), a small set of control points define a smooth surface using spline patches [20]. Despite its flexibility and quality, extracting spline patches from 3D models or NeRFs is a challenging and open problem [7]. Partial differential equation (PDE)-based methods simulate the deformation of an object, representing it as a volumetric deformable solid [75] or as a thin rubber shell [78]. The forces guiding the deformation are applied by moving handles selected on a surface [8], making them in" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4243" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 183 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 183 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 183 + ], + "type": "image", + "image_path": "040c556a52992d706ac8a0be927fa8e1b1e78db42ee77314c10b5f4fda460ae2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 184, + 547, + 286 + ], + "blocks": [ + { + "bbox": [ + 51, + 184, + 547, + 286 + ], + "lines": [ + { + "bbox": [ + 51, + 184, + 547, + 286 + ], + "spans": [ + { + "bbox": [ + 51, + 184, + 547, + 286 + ], + "type": "image", + "image_path": "2f0348ecc5c168aaaad3e829b0b316fcee1d1c3fd2027a9a039169ea339b1538.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "text", + "content": "Figure 3. Overview of our Image Sculpting pipeline, " + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\mathrm{DDIM}^+" + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "text", + "content": " represents DDIM with the DreamBooth fine-tuned and depth controlled model. The process begins by converting the input image into a textured 3D model through a de-rendering process. This model is then prepared for interactive deformation by creating a skeleton and calculating skinning weights. The user can modify the skeleton to deform the model, resulting in an initial coarse image. To refine this edited image, we invert the coarse rendering " + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "text", + "content": " into the noise " + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T^c" + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "text", + "content": ". We then inject self-attention maps " + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{A}_{t}^{c}" + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "text", + "content": " and feature maps " + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{f}_{t}^{c}" + }, + { + "bbox": [ + 46, + 293, + 547, + 361 + ], + "type": "text", + "content": " from the initial image's denoising process into the enhanced image denoising steps. This technique helps in preserving the geometry of the modified object while restoring the visual quality of the edited image." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 365, + 260, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 260, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 260, + 378 + ], + "type": "text", + "content": "tutive to use and requiring minimal user interaction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 288, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 288, + 489 + ], + "type": "text", + "content": "Linear Blend Skinning The most popular deformation approach is linear blend skinning [32], which defines a space deformation function as a blended average of a set of affine transformations weighted by shape-aware scalar functions, often computed with methods based on solutions of PDEs on surfaces [31] or manually edited. This approach offers complete control and flexibility, as the affine transformation can be attached to points, vertexes of a cage, or segments in a skeleton [6]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": "Our approach We can use any of these algorithms to precisely control the shape deformation and, thus, the rendered image. We show an example of one representative method for each class in Fig. 2, and we leave as future work additional automation of this step." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 571, + 107, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 107, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 107, + 583 + ], + "type": "text", + "content": "4. Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Given a single 2D image, our objective is to enable precise manipulation of the objects and their orientations in 3D space, before converting this back into a high-quality edited 2D image. To achieve this, we have developed a novel editing pipeline tailored for image sculpting (see Fig. 3) composed of three steps: (1) We initially convert the input image into a 3D model, (2) the 3D model is edited by deforming it in 3D space, and (3) we use a coarse-to-fine generative enhancement pipeline to turn the coarse rendering of the 3D model into a high-fidelity image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 365, + 477, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 477, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 477, + 378 + ], + "type": "text", + "content": "4.1. De-Rendering and Deformation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 386, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 386, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 545, + 410 + ], + "type": "text", + "content": "Given an image of an object, our goal is to perform 3D reconstruction to obtain its 3D model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "text", + "content": "Image to NeRF With advancements in text-to-image foundation models [66] and the viewpoint-conditioned image translation model [44], our initial step involves segmenting the selected object from the input image using SAM [38]. Building upon this, we then train a NeRF using Score Distillation Sampling (SDS) [61]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 491, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 563 + ], + "type": "text", + "content": "NeRF to 3D Model We use the implementation in three-studio [24] to convert a NeRF volume into a mesh. This algorithm transforms the volume density into a signed distance function, extracts an isosurface [47], and parameterizes it [87] for texture mapping [74]. The texture is extracted by differentiable rendering [39]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": "3D Model Deformation After obtaining the 3D model, a user can manually construct a skeleton and interactively manipulate it by rotating the bones to achieve the target pose. The mesh deformation affects the vertex positions of the object but not the UV coordinates used for texture mapping; this procedure thus deforms the texture mapped on the object following its deformation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "However, the resulting image quality depends on the 3D reconstruction's accuracy, which, in our case, is coarse and insufficient for the intended visual outcome (Fig. 3). Therefore, we rely on an image enhancement pipeline to convert the coarse rendering into a high-quality output." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4244" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 111, + 195 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 111, + 195 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 111, + 195 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 111, + 195 + ], + "type": "image", + "image_path": "3e281a7734339f7c4829b3b10b1356bd69df3230ead7c634d4d6243cb23052b6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 197, + 91, 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195 + ], + "type": "image", + "image_path": "f74b4c3bbb23d5823a53b2a83cb791a8eed08bfa65a88250ccc1154678a276f8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 239, + 197, + 294, + 204 + ], + "lines": [ + { + "bbox": [ + 239, + 197, + 294, + 204 + ], + "spans": [ + { + "bbox": [ + 239, + 197, + 294, + 204 + ], + "type": "text", + "content": "SDEdit [49] " + }, + { + "bbox": [ + 239, + 197, + 294, + 204 + ], + "type": "inline_equation", + "content": "(t_0 = 0.4)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 296, + 72, + 358, + 195 + ], + "blocks": [ + { + "bbox": [ + 296, + 72, + 358, + 195 + ], + "lines": [ + { + "bbox": [ + 296, + 72, + 358, + 195 + ], + "spans": [ + { + "bbox": [ + 296, + 72, + 358, + 195 + ], + "type": "image", + "image_path": "d0409b4a164f25957f2d6dc1f9e749f8fb418bd934ae94bd154d10a37eaf7e77.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 301, + 197, + 356, + 204 + ], + "lines": [ + { + "bbox": [ + 301, + 197, + 356, + 204 + ], + "spans": [ + { + "bbox": [ + 301, + 197, + 356, + 204 + ], + "type": "text", + "content": "SDEdit [49] " + }, + { + "bbox": [ + 301, + 197, + 356, + 204 + ], + "type": "inline_equation", + "content": "(t_0 = 0.6)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 358, + 72, + 419, + 195 + ], + "blocks": [ + { + "bbox": [ + 358, + 72, + 419, + 195 + ], + "lines": [ + { + "bbox": [ + 358, + 72, + 419, + 195 + ], + "spans": [ + { + "bbox": [ + 358, + 72, + 419, + 195 + ], + "type": "image", + "image_path": "06f79e740a20289932624a45d1833daa463360c508d95973d3af0bc1bcdf08ca.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 362, + 197, + 418, + 204 + ], + "lines": [ + { + "bbox": [ + 362, + 197, + 418, + 204 + ], + "spans": [ + { + "bbox": [ + 362, + 197, + 418, + 204 + ], + "type": "text", + "content": "Ours w/o Feature Injection" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 419, + 72, + 481, + 195 + ], + "blocks": [ + { + "bbox": [ + 419, + 72, + 481, + 195 + ], + "lines": [ + { + "bbox": [ + 419, + 72, + 481, + 195 + ], + "spans": [ + { + "bbox": [ + 419, + 72, + 481, + 195 + ], + "type": "image", + "image_path": "11f240233e3a78cd04bd3cfe6b36e4ee5b93b5394124660671452cda6cbfdd63.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 424, + 197, + 478, + 204 + ], + "lines": [ + { + "bbox": [ + 424, + 197, + 478, + 204 + ], + "spans": [ + { + "bbox": [ + 424, + 197, + 478, + 204 + ], + "type": "text", + "content": "Ours w/o Depth Control" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 481, + 72, + 545, + 195 + ], + "blocks": [ + { + "bbox": [ + 481, + 72, + 545, + 195 + ], + "lines": [ + { + "bbox": [ + 481, + 72, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 481, + 72, + 545, + 195 + ], + "type": "image", + "image_path": "ea07bd25e775311b8bd686f178601fd1c2163c78b09dfb08fef4bd9b724e06be.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 507, + 197, + 518, + 203 + ], + "lines": [ + { + "bbox": [ + 507, + 197, + 518, + 203 + ], + "spans": [ + { + "bbox": [ + 507, + 197, + 518, + 203 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 48, + 236, + 287, + 329 + ], + "blocks": [ + { + "bbox": [ + 46, + 208, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 545, + 232 + ], + "type": "text", + "content": "Figure 4. Comparison of our final method with various baseline methods and ablations. Our approach effectively maintains the geometric information while ensuring the texture quality. In contrast, other methods typically preserve either the texture or the geometry, but not both." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 236, + 287, + 329 + ], + "lines": [ + { + "bbox": [ + 48, + 236, + 287, + 329 + ], + "spans": [ + { + "bbox": [ + 48, + 236, + 287, + 329 + ], + "type": "image", + "image_path": "a67f3aba33e49f9ce2ab03791e72008ed7f9e9143e7503da8fa00903f12a7ff3.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 335, + 288, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 288, + 380 + ], + "type": "text", + "content": "Figure 5. Overview of the coarse-to-fine generative enhancement model architecture. The red module denotes the one-shot Dream-Booth [67], which requires tuning; the grey module is the SDXL Refiner [5], which is frozen in our experiments." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 383, + 261, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 261, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 261, + 395 + ], + "type": "text", + "content": "4.2. Coarse-to-Fine Generative Enhancement" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 402, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 521 + ], + "type": "text", + "content": "This section focuses on blending a coarsely rendered image back to its original background. The aim is to restore textural details while keeping the edited geometry intact. Image restoration and enhancement are commonly approached as image-to-image translation tasks [81], leveraging the strong correlation between the source and target images. Our challenge, however, presents a unique scenario: despite overall similarities in appearance and texture between the input and desired output, the input object's geometry changes, sometimes significantly, after user editing." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": "In exploring possible solutions, one approach is to use subject-driven personalization techniques like DreamBooth [67]. They aim to preserve key details from the input, but might compromise the edited geometry. Alternatively, image-to-image translation methods like SDEdit [49] can be used to preserve the edited geometry, but this might disturb the textural consistency with the original image. This dichotomy was clear in our preliminary study, as shown in Fig. 4. SDEdit can maintain the geometry, but it was unable to accurately replicate the textures. On the other hand, DreamBooth produced high-fidelity outputs, but struggled to preserve both the texture and geometry effectively." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "To address the balance between preserving texture and geometry, our approach begins by \"personalizing\" a pretrained text-to-image diffusion model. To capture the object's key features, we fine-tune the diffusion model with" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 236, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 308 + ], + "type": "text", + "content": "DreamBooth on one input reference image. To maintain the geometry, we adapt a feature and attention injection technique [79], originally designed for semantic layout control. Furthermore, we incorporate depth data from the 3D model through ControlNet [90]. We find this integration crucial in minimizing uncertainties during the enhancement process." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 312, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 546, + 456 + ], + "type": "text", + "content": "One-shot Dreambooth DreamBooth [67] fine-tunes a pre-trained diffusion model with a few images for subject-driven generation. The original DreamBooth paper [67] has shown its ability to leverage the semantic class priors to generate novel views of an object, given only a few frontal images of the subject. This aspect is particularly useful in our setting, since the coarse rendering we work with lacks explicit viewpoint information. In our application, we train DreamBooth using just a single example, which is the input image. Notably, this one-shot approach with DreamBooth also effectively captures the detailed texture, thereby filling in the textural gaps present in the coarse rendering." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "type": "text", + "content": "Depth Control We use depth ControlNet [90] to preserve the geometric information of user editing. The depth map is rendered directly from the deformed 3D model, bypassing the need for any monocular depth estimation. For the background region, we don't use the depth map. This depth map serves as a spatial control signal, guiding the geometry generation in the final edited images. However, relying solely on depth control is not sufficient – although it can preserve the geometry to some extent, it still struggles in local, more nuanced editing, such as capturing the specific shapes of a pumpkin's eyes or the bent legs of a chair (Fig. 4)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Feature Injection To better preserve the geometry, we use feature injection. As demonstrated in Fig. 3, this step begins with DDIM inversion [77] (with the DreamBooth finetuned, depth controlled diffusion model) of the coarse rendering image to obtain the inverted latents. At each denoising step, we denoise the inverted latent of the coarse rendering along with the latent of the refined image, extracting their respective feature maps (from the residual blocks) and self-attention maps (from the transformer blocks). It has been shown in [79] that the feature maps carry semantic in" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4245" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 69, + 534, + 671 + ], + "blocks": [ + { + "bbox": [ + 61, + 69, + 534, + 671 + ], + "lines": [ + { + "bbox": [ + 61, + 69, + 534, + 671 + ], + "spans": [ + { + "bbox": [ + 61, + 69, + 534, + 671 + ], + "type": "image", + "image_path": "f251783eafd51651092ebb1b272df74c53946e0426ace3ffe4bd6c131a0f5752.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 677, + 545, + 699 + ], + "lines": [ + { + "bbox": [ + 48, + 677, + 545, + 699 + ], + "spans": [ + { + "bbox": [ + 48, + 677, + 545, + 699 + ], + "type": "text", + "content": "Figure 6. A compilation of qualitative results from six image editing tasks. Additionally, we include additional examples (termed as 'Mixture' in the final row) to illustrate the versatile combination of these capabilities." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "4246" + } + ] + } + ], + "index": 2 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 72, + 286, + 144 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 144 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 144 + ], + "type": "image", + "image_path": "5803c658df05b4788edb0ceaaf0c88f5c817a6bac22a458130b21fee6d0b15a0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 62, + 198, + 272, + 339 + ], + "blocks": [ + { + "bbox": [ + 46, + 151, + 288, + 196 + ], + "lines": [ + { + "bbox": [ + 46, + 151, + 288, + 196 + ], + "spans": [ + { + "bbox": [ + 46, + 151, + 288, + 196 + ], + "type": "text", + "content": "Figure 7. Our blend-in process. At every denoising step, we mask the background areas and blend them with the unmasked regions from the denoised latent. This process helps maintain visual coherence and preserve the background." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 198, + 272, + 339 + ], + "lines": [ + { + "bbox": [ + 62, + 198, + 272, + 339 + ], + "spans": [ + { + "bbox": [ + 62, + 198, + 272, + 339 + ], + "type": "image", + "image_path": "5ec8684ee51f651643b1c2553c128a83e72a78b83e72bb626d850dc9f541f241.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 345, + 286, + 368 + ], + "lines": [ + { + "bbox": [ + 47, + 345, + 286, + 368 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 286, + 368 + ], + "type": "text", + "content": "Figure 8. Our blend-in process yields visually harmonious results. Top: Results from direct copy-pasting. Bottom: Our results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 376, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 519 + ], + "type": "text", + "content": "formation, while the self-attention maps contain the geometry and layout of the generated images. By overriding the feature and self-attention maps during the enhanced image denoising steps with those from the coarser version, we ensure the geometry of the enhanced image can reflect those of the coarse rendering. The pseudo code for our generative enhancement is detailed in Appendix A. Note that our method differs from the original Plug-and-Play use cases: we use feature injection to preserve the geometry during the coarse-to-fine process rather than translating the image according to a new text prompt. We present the injection layer selection and the replacement schedule in Section 5." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "text", + "content": "Background Blend-In To maintain the consistency of the background between the input and edited images, we first inpaint the area initially occupied by the object in the input image, thus obtaining an unobstructed background. However, another challenge arises in merging the edited object into this background smoothly. Merely copy-pasting it onto the background leads to an unrealistic visual effect, such as the improper water reflections over the fish and the absence of shadow casting from the truck (Fig. 8). To overcome this, as demonstrated in Fig. 7, our approach involves masking the background areas during the denoising steps to preserve their original background. This means we retain the unedited background by blending the unmasked (edited) regions from the denoising step with the masked (original) background. We use SDXL [60] as our pre-trained text-to-image model, which includes a refiner module by de" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 305, + 70, + 547, + 221 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 221 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 221 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 221 + ], + "type": "image", + "image_path": "6eba05c221ac6e83f6dca7878ed58d46d62e3e8723a5e7100f3a4703b21280a6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 247, + 547, + 393 + ], + "blocks": [ + { + "bbox": [ + 305, + 224, + 545, + 246 + ], + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 246 + ], + "type": "text", + "content": "Figure 9. Comparisons with Object-3DIT [50] on object translation, rotation, and composition tasks." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 247, + 547, + 393 + ], + "lines": [ + { + "bbox": [ + 307, + 247, + 547, + 393 + ], + "spans": [ + { + "bbox": [ + 307, + 247, + 547, + 393 + ], + "type": "image", + "image_path": "2538e286f39754666dadb38696a0824160c8822d8a4c0204dd85cfaac086352f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 306, + 431, + 545, + 577 + ], + "blocks": [ + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "lines": [ + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "type": "text", + "content": "Figure 10. Comparisons with DragDiffusion [73] and ControlNet [90] on pose editing. These techniques face difficulties in handling complex pose modifications." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 431, + 545, + 577 + ], + "lines": [ + { + "bbox": [ + 306, + 431, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 306, + 431, + 545, + 577 + ], + "type": "image", + "image_path": "b8bc9bcb439d0425fa03338a0c950b26b24893330614478c12ad332b7d55b8b4.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 578, + 545, + 611 + ], + "lines": [ + { + "bbox": [ + 305, + 578, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 305, + 578, + 545, + 611 + ], + "type": "text", + "content": "Figure 11. Comparisons with InstructPix2Pix [10] and DALL-E 3 [56] on serial addition. These text-based editing methods fail to follow precise and quantifiable instructions." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 615, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 615, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 615, + 545, + 639 + ], + "type": "text", + "content": "fault. We keep this module in our pipeline, as empirically it slightly enhances the results by reducing artifacts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 644, + 387, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 387, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 387, + 658 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Experimental Setup We follow [24] to obtain the initial NeRF representation and to extract the textured 3D model. We use Instant-NGP [53] and a grid size of 256 for the 3D model extraction from NeRF. During the coarse-to-fine gen" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4247" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 87, + 115, + 205 + ], + "blocks": [ + { + "bbox": [ + 61, + 87, + 115, + 205 + ], + "lines": [ + { + "bbox": [ + 61, + 87, + 115, + 205 + ], + "spans": [ + { + "bbox": [ + 61, + 87, + 115, + 205 + ], + "type": "image", + "image_path": "4ced16c09d08f77c1d3e83e6a894ef6312a81fe03379a1a7128d68cbd7f7de0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "type": "text", + "content": "Figure 12. Ablation studies on feature injection layers. From left to right, progressively injecting more self-attention layers can result in increasingly improved alignment with user edits." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 284, + 74, + 363, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 284, + 74, + 363, + 84 + ], + "spans": [ + { + "bbox": [ + 284, + 74, + 363, + 84 + ], + "type": "text", + "content": "Injecting more layers" + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 123, + 85, + 539, + 203 + ], + "blocks": [ + { + "bbox": [ + 123, + 85, + 539, + 203 + ], + "lines": [ + { + "bbox": [ + 123, + 85, + 539, + 203 + ], + "spans": [ + { + "bbox": [ + 123, + 85, + 539, + 203 + ], + "type": "image", + "image_path": "3125134acd0d1dac7bd232f3b7c5d47c21a3123d982ecb237cdbb143cef18098.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 237, + 287, + 331 + ], + "blocks": [ + { + "bbox": [ + 48, + 237, + 287, + 331 + ], + "lines": [ + { + "bbox": [ + 48, + 237, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 48, + 237, + 287, + 331 + ], + "type": "table", + "html": "
MethodsDINO↑D-RMSE↓
Original Coarse Rendering0.7580.00
SDEdit [49] (t0=0.4)0.7881.71
SDEdit [49] (t0=0.6)0.8002.12
Ours w/o Feature Injection0.8482.33
Ours w/o Depth Control0.8512.15
Ours0.8531.99
", + "image_path": "d1efd42f85c91ef16a97941e0db572f938fe781402ddafe886f95c32cf80b217.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 335, + 287, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 381 + ], + "type": "text", + "content": "Table 1. Ablation studies of the enhancement methods on SculptingBench. DINO score measures the textural details, and D-RMSE measures the geometric fidelity. Depth control and feature injection enhance texture quality while maintaining geometric fidelity." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 386, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 287, + 471 + ], + "type": "text", + "content": "erative enhancement process, for one-shot DreamBooth, we fine-tune the SDXL-1.0 [60] model using LoRA [28] for 800 steps with a learning rate of 1e-5. For feature injection stage, we utilize all the self-attention layers of the SDXL decoder and the first block of the SDXL's upsampling decoder. The SDXL refiner is applied after " + }, + { + "bbox": [ + 46, + 386, + 287, + 471 + ], + "type": "inline_equation", + "content": "t = 0.1T" + }, + { + "bbox": [ + 46, + 386, + 287, + 471 + ], + "type": "text", + "content": ". For background inpainting, we use Adobe generative fill [3]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "text", + "content": "Qualitative Results We showcase qualitative results in Fig. 6, covering six precise image editing tasks. Detailed descriptions of these tasks are presented in Appendix B. Qualitatively, our method combines the creative freedom of generative models with the precision of graphics pipelines to achieve precise, quantifiable, and physically plausible outcomes for object editing across a variety of scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Our approach introduces new editing features through precise 3D geometry control, a capability not present in existing methods. We compare our method with the state-of-the-art object editing techniques for a comprehensive analysis. In Fig. 9, we show that 3DIT [50], designed for 3D-aware editing via language instructions, faces limitations when applied to real, complex images, largely because its training is based on a synthetic dataset. In Fig. 10, we compare the pose editing ability with DragDiffusion [73] and ControlNet [90]. This comparison reveals that these methods encounter difficulties with complex pose manipulations because they are constrained to the 2D domain. Furthermore, in Fig. 11, we show how text-based editing methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 238, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 545, + 262 + ], + "type": "text", + "content": "like InstructPix2Pix [10] and DALL-E 3 [56] struggle with precise and quantifiable instructions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "type": "text", + "content": "Ablation Studies We create a new dataset *SculptingBench* to evaluate our new image editing capabilities. This dataset contains 28 images covering six categories: pose editing, rotation, translation, composition, carving, and serial addition (see Appendix C). We perform quantitative studies using different coarse-to-fine enhancement methods. To measure the visual similarity between the edited images and the original ones, particularly in terms of maintaining textural details through the editing process, we employ DINO score [67] as our metrics. This choice is motivated by the self-supervised training objective of DINO [12], which encourages distinction of unique features of a image. To evaluate the geometric fidelity of user edits after enhancement, we introduce a novel metric, " + }, + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "type": "text", + "content": "-RMSE. This metric is specifically created to evaluate how well geometric information is retained after the enhancement procedure. " + }, + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 264, + 546, + 479 + ], + "type": "text", + "content": "-RMSE measures the discrepancies between the depth maps of the coarse renderings and their enhanced counterparts:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 333, + 485, + 518, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 485, + 518, + 500 + ], + "spans": [ + { + "bbox": [ + 333, + 485, + 518, + 500 + ], + "type": "interline_equation", + "content": "\\mathrm {D} - \\mathrm {R M S E} = \\sqrt {\\mathbb {E} \\left[ \\left(\\mathrm {d e p t h} _ {\\text {c o a r s e}} - \\mathrm {d e p t h} _ {\\text {e n h a n c e d}}\\right) ^ {2} \\right]}", + "image_path": "115ce701d72e6b764d943336d3f2ea5e42ccd508389e64e823ebb5d5ab976ea1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "where depth_coarse, depth_enhanced denote the depth maps MiDaS [64] estimates, for the coarse rendering and the enhanced output image, respectively. In Table 1, we show that without any enhancement, the textural quality metrics (DINO score) are quite low. SDEdit effectively preserves the edited geometry with a low D-RMSE, yet the visual quality significantly deteriorates compared to the original image (see Fig. 4). Our method offers a more advantageous balance, significantly enhancing texture quality as demonstrated by higher DINO score, while preserving geometric consistency, evidenced by a low D-RMSE score. We observe that both feature injection and depth control contribute to enhanced geometric consistency and can lead to further improvement when used together. Additionally, we conduct an empirical study to explore the number of self-attention layers for injection. Fig. 12 shows that more layers improve alignment with user edits. We use all layers for injection." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4248" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. 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In ICCV, 2017. 3" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4251" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation/903a1b45-2229-4628-ac3b-aaa39b0c7384_content_list.json b/2024/Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation/903a1b45-2229-4628-ac3b-aaa39b0c7384_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5624627070fb832d94a10fc5ccdab61ad51bf5e7 --- /dev/null +++ b/2024/Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation/903a1b45-2229-4628-ac3b-aaa39b0c7384_content_list.json @@ -0,0 +1,1740 @@ +[ + { + "type": "text", + "text": "Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation", + "text_level": 1, + "bbox": [ + 107, + 130, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ji-Jia Wu1 Andy Chia-Hao Chang2 Chieh-Yu Chuang2 Chun-Pei Chen2 Yu-Lun Liu2 Min-Hung Chen3 Hou-Ning Hu4 Yung-Yu Chuang1 Yen-Yu Lin2", + "bbox": [ + 84, + 178, + 913, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ National Taiwan University $^{2}$ National Yang Ming Chiao Tung University $^{3}$ NVIDIA $^{4}$ MediaTek", + "bbox": [ + 205, + 237, + 794, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper addresses text-supervised semantic segmentation, aiming to learn a model capable of segmenting arbitrary visual concepts within images by using only image-text pairs without dense annotations. Existing methods have demonstrated that contrastive learning on image-text pairs effectively aligns visual segments with the meanings of texts. We notice that there is a discrepancy between text alignment and semantic segmentation: A text often consists of multiple semantic concepts, whereas semantic segmentation strives to create semantically homogeneous segments. To address this issue, we propose a novel framework, Image-Text Co-Decomposition (CoDe), where the paired image and text are jointly decomposed into a set of image regions and a set of word segments, respectively, and contrastive learning is developed to enforce region-word alignment. To work with a vision-language model, we present a prompt learning mechanism that derives an extra representation to highlight an image segment or a word segment of interest, with which more effective features can be extracted from that segment. Comprehensive experimental results demonstrate that our method performs favorably against existing text-supervised semantic segmentation methods on six benchmark datasets. The code is available at https://github.com/072jiajia/image-text-co-decomposition.", + "bbox": [ + 76, + 340, + 472, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 707, + 209, + 723 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation is essential to various applications [11, 15, 50] in computer vision but is hindered by several critical challenges. First, the expensive cost of acquiring pixel-level annotations limits the applicability of fully supervised semantic segmentation methods. Second, most existing methods [40, 43, 52] are developed to work on predefined categories and leave themselves inapplicable to rare or unseen concepts described by free-form text. To address these obstacles, a new research direction has emerged in vision-language models, referred to as text-supervised semantic segmentation [5, 28, 44-46, 49]. This task devel", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ops segmentation models capable of assigning labels across large vocabularies of concepts and supporting semantic segmentation model training without pixel-wise annotations.", + "bbox": [ + 496, + 310, + 890, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fig. 1 compares existing methods for text-supervised semantic segmentation by grouping their cross-domain alignment mechanisms into three categories, including image-text, region-text, and region-word alignment. Despite the differences, most of these methods compensate for the lack of pixel-wise annotations on broad semantic concepts by exploring abundant image-text pairs on the internet. The textual descriptions bring extensive knowledge across diverse categories. Thus, existing methods typically apply a vision-language model such as CLIP [34] to textual descriptions to acquire the semantic context of the corresponding images for segmentation model learning.", + "bbox": [ + 496, + 356, + 892, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The image-text alignment is widely adopted in the literature e.g. [28, 44, 45]. As depicted in Fig. 1a, methods of this group derive an image encoder and a text encoder by aligning them in a joint embedding space. They then use their proposed zero-shot transfer techniques to enable the two encoders to predict segmentation output. Despite the simplicity, they introduce unfavorable discrepancies between the training and testing phases since we aim to match the semantic features from the text to the corresponding image segments rather than the whole image during testing.", + "bbox": [ + 496, + 537, + 893, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To mitigate this issue, the region-text alignment is explored. As shown in Fig. 1b, methods of this group such as [5] utilize a pre-trained visual-language model to derive an additional image segmenter that discovers concepts described by the text. They enforce the consistency between the segmented region and the text but suffer from the discrepancy between the region-text alignment and semantic segmentation: A text may consist of multiple concepts, such as pub, night, and car in Fig. 1b, while semantic segmentation aims to identify regions of the same concept.", + "bbox": [ + 496, + 689, + 893, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the aforementioned issues in the image-text and region-text alignments, we propose a novel framework, Image-Text Co-Decomposition (CoDe), to achieve region-word alignment. As illustrated in Fig. 1c, we utilize a", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26794", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/533c862118c3b5d148049e3f67e9bc9ba30a274fc7591db532b7f739a96d4b31.jpg", + "image_caption": [ + "(a) image-text alignment" + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 267, + 189 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6292faa41fcb02c2b3e6d6839970cb3dbe6d219fcab2ab9571590d236ffeb3d4.jpg", + "image_caption": [ + "(b) region-text alignment", + "Figure 1. Existing methods perform text-supervised semantic segmentation by learning either (a) image-text alignment or (b) region-text alignment. This paper presents (c) region-word alignment via image-text co-decomposition, where the image and the text are decomposed into object regions and word segments, respectively, while contrastive learning is used to establish cross-modal correspondences between these image and word segments." + ], + "image_footnote": [], + "bbox": [ + 261, + 90, + 549, + 189 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6f50b2b6498792b54c3c9415caa28b4d4d0cd5d254d577327561475640bd2272.jpg", + "image_caption": [ + "(c) region-word alignment (ours)" + ], + "image_footnote": [], + "bbox": [ + 549, + 88, + 870, + 189 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "visual-language model to construct an image segmenter and a text segmenter: The former decomposes an image into image segments, while the latter decomposes a text into word segments. In addition, there exist one-to-one correspondence between image and word segments. This way, the discrepancy between training and testing is alleviated since each image segment is derived from a single concept given by the corresponding word segment.", + "bbox": [ + 75, + 282, + 468, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed CoDe framework comprises four components: an image segmenter, a text segmenter, a region-word alignment module, and a prompt learning module. We randomly select nouns in the text. For each selected noun e.g., \"car\", the image segmenter identifies the image segment that matches the noun, i.e., the region of the car, while the text segmenter discovers the corresponding word segment, i.e., \"red cars.\" The region-word alignment is developed to enforce the consensus between the image and word segments. To better work with a vision-language model, we present a prompt learning module to derive an extra representation, enabling more effective feature extraction.", + "bbox": [ + 75, + 404, + 468, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this work are as follows:", + "bbox": [ + 96, + 587, + 434, + 601 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a new framework, Image-Text Co-Decomposition (CoDe), to learn the region-word alignment for eliminating train-test and image-text discrepancies, facilitating text-supervised semantic segmentation.", + "- We propose a prompt learning method to address domain shift issues arising from blank areas during the highlighting process and enhance the alignment between highlighted regions and highlighted words.", + "- Our method effectively carries out zero-shot semantic segmentation and performs favorably against the state-of-the-art methods on six benchmark datasets." + ], + "bbox": [ + 76, + 604, + 468, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 787, + 225, + 804 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Open-Vocabulary Semantic Segmentation", + "text_level": 1, + "bbox": [ + 76, + 815, + 431, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Open-vocabulary semantic segmentation focuses on segmenting any concepts within images, even those unseen during training, based solely on textual descriptions. Its three important branches are discussed as follows:", + "bbox": [ + 75, + 840, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-supervised setting with mask-annotations. Methods of this group such as [16, 17, 24, 26, 31, 47] learn from dense annotations to produce high-quality segmentation masks, and then utilize image-text pairs and pre-trained vision-language models to extend the segmentation capability to a larger target vocabulary. Despite the remarkable results, these methods are hindered by their reliance on costly dense annotations, posing a challenge in cases where such annotations are difficult to obtain.", + "bbox": [ + 496, + 282, + 890, + 417 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Training-free methods. Another line of research e.g. [38, 41, 54] makes the most of large pre-trained models for open-vocabulary segmentation without training. MaskCLIP [54] introduces a modification to the final layer of the CLIP image encoder, yielding dense feature maps that could be employed as initial segmentation maps for further refinement. ReCo [38] constructs an image archive and makes use of retrieval and co-segmentation to identify co-occurrence regions among a specific category. Although these methods eliminate the process of training, the results exhibit significant room for improvement, which shows the need for additional supervision to accomplish this task.", + "bbox": [ + 496, + 421, + 890, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-supervised semantic segmentation. It strikes a balance between the two aforementioned branches. Methods of this group are discussed in detail in the following because our method belongs to this group.", + "bbox": [ + 496, + 606, + 890, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Text-Supervised Semantic Segmentation", + "text_level": 1, + "bbox": [ + 500, + 676, + 843, + 693 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-supervised semantic segmentation [4, 5, 28, 33, 36, 42, 44-46, 49] decomposes an image into semantic regions according to text descriptions. Unlike semi-supervised methods relying on a few images with mask annotations during training, methods of this group aim to learn semantic masks solely from text-based guidance. We roughly divide existing methods into two categories based on their cross-modal alignment between the image and text domains.", + "bbox": [ + 496, + 700, + 890, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image-text alignment. These methods train an image encoder alongside a text encoder to align pairs of image and text in a joint embedding space. They use zero-shot transfer to enable the encoders to produce segmentation results. GroupViT [45] introduces a bottom-up approach within", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26795", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformers, grouping image patches into regions and utilizing object semantics derived from texts to guide training. SimSeg [49] further introduces a pretraining method that densely aligns visual and language representations, enabling the trained image encoder to generate segmentation masks in a zero-shot manner.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Region-text alignment. Another line of research targets at aligning the embedding of a region, instead of the whole image, with text descriptions. For instance, TCL [5] learns to segment specific regions within an image while ensuring consistency between the segmented region and the original text. It enables the model to segment the relevant region described in the text.", + "bbox": [ + 75, + 200, + 468, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These methods for text-supervised semantic segmentation have shown that employing vision-language models and contrastive learning on image-text pairs enables aligning visual concepts with the meaning of the whole text. We notice that a text is usually a mix of multiple semantic concepts, but semantic segmentation aims to discover semantically homogeneous segments. To address this issue, inspired by the region-word matching techniques [8, 21, 22, 39] for cross-modal retrieval, we introduce image-text co-decomposition, where the image and the text are decomposed into image and word segments, respectively, and contrastive learning is adopted to enforce cross-modal consensus between these image and word segments. It turns out that image-text co-decomposition results in consistent performance gains on multiple benchmarks.", + "bbox": [ + 75, + 309, + 470, + 535 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Prompt Tuning for Vision-Language Models", + "text_level": 1, + "bbox": [ + 76, + 554, + 452, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Emerged from natural language processing [23, 25, 27], prompt tuning focuses on parameter-efficient adaptation of large pre-trained models to new tasks. In computer vision [20, 55-57], pioneering work such as CoOp [55, 56] incorporates learnable tokens into the CLIP text encoder, enhancing the classification task performance. Recent studies e.g. [12, 14, 35] leverage prompt tuning in the text modality for extending CLIP's capabilities to various applications such as detection and segmentation tasks. Notably, prompt learning methods are also applicable to the visual domain. VPT [19] employs prompt tuning in the visual modality by inserting learnable vectors into Vision Transformers. Further studies [18, 26] explore tuning methods that directly incorporate learnable prompts into the input image within the RGB domain to address downstream tasks.", + "bbox": [ + 75, + 580, + 468, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Drawing inspiration from the success of these methods, our method leverages the capabilities of prompt tuning on segment feature extraction in both the visual and text domains. Prompt learning is beneficial in this work when applying contrastive learning to the visual and textual features extracted by a vision-language model.", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 89, + 635, + 108 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first provide an overview of our method for image-text co-decomposition and define the notations in Sec. 3.1. Then, we specify the three major modules of our method, including 1) the image-text co-segmentation module in Sec. 3.2, 2) the region-word highlighting module in Sec. 3.3, and 3) the region-word alignment module in Sec. 3.4. These modules work harmoniously to address the region-word alignment for text-supervised semantic segmentation and enhance model performances. Finally, implementation details are given in Sec. 3.5.", + "bbox": [ + 496, + 116, + 890, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Method Overview", + "text_level": 1, + "bbox": [ + 498, + 282, + 671, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-text co-decomposition enables text-supervised segmenters to learn region-word consensus when segmenting an image $X^v$ with a paired text $X^t$ . Our method aims to jointly learn an image segmenter $F^v$ and a text segmenter $F^t$ with solely the supervision from a set of $K$ image-text pairs, $D = \\{X_k^v, X_k^t\\}_{k=1}^K$ , where no annotations are given. In addition, we optimize two learnable prompts, including a region prompt $P^v$ and a word prompt $P^t$ , to alleviate the unfavorable effect of blank embeddings caused by applying a vision-language model to masked images or texts for feature extraction.", + "bbox": [ + 496, + 308, + 890, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 illustrates the pipeline of our method, consisting of three modules, including the image-text co-segmentation, region-word highlighting, and region-word alignment modules. For an input image-text pair $(X^v, X^t)$ , we initiate the process by randomly selecting a noun $N$ , e.g., balloon in the figure, from the text $X^t$ using the noun selector [2]. This selected noun serves as a query. We take the query $N$ along with the image $X^v$ as input to the image segmenter $F^v$ to generate the region mask $M^v$ showing the estimated object region specified by the query. Similarly, a text segmenter $F^t$ takes the query $N$ and the text $X^t$ as input and estimates the word mask $M^t$ indicating the associated word segment.", + "bbox": [ + 496, + 476, + 892, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Subsequently, we apply the region mask $M^v$ to the image $X^v$ to crop the estimated object region. For the estimated background, i.e., the region outside the mask $M^v$ , we crop the corresponding region from the learned region prompt $P^v$ . The highlighted image $H^v$ is yielded by combining the cropped object and background regions. Similarly, the highlighted text $H^t$ is generated by combining the text $X^t$ inside the mask $M^t$ and the word prompt $P^t$ outside the mask $M^t$ . We extract features from the highlighted image and text by using the image encoder $E^v$ and the text encoder $E^t$ of CLIP [34], respectively. The procedure is repeated for each image-text pair and each selected noun. It follows that the region-word alignment is accomplished by contrastive learning [7]. Four loss functions, including $\\mathcal{L}_{\\mathrm{kg}}$ , $\\mathcal{L}_{\\mathrm{seg}}^v$ , $\\mathcal{L}_{\\mathrm{seg}}^t$ , and $\\mathcal{L}_{\\mathrm{hcl}}$ , are used for network optimization, and will be elaborated in the following.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26796", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a44ccf30a62c597ef517b469d555959d32ed3b45c15196a689b78f0799583e17.jpg", + "image_caption": [ + "Figure 2. Training pipeline of our method for image-text co-decomposition. Our method consists of three major modules, including (a) the image-text co-segmentation module where the image and text segmenters estimate the region and word masks according to a selected noun, respectively, (b) the region-word highlighting module where the estimated masks together with two learnable prompts produce the highlighted image and text, and (c) the region-word alignment module where contrastive learning is applied to the embedded object regions and word segments to accomplish region-word alignment." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 385, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cbf37813fb086eb30a52926767877fcecd44fe1167cf01a0f5279aee3b38a99b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 388, + 88, + 645, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4ed54001dd407076b0c2964f4486f0ad59940bdbd07b11a64c3f62968e437034.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 88, + 869, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Image-Text Co-Segmentation", + "text_level": 1, + "bbox": [ + 76, + 321, + 339, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The image-text co-segmentation module comprises a noun selector, an image segmenter, and a text segmenter, as shown in Fig. 2a. Taking an image-text pair $(X^v, X^t)$ as input, this module aims at jointly identifying an object region in image $X^v$ and its accompanying word segment in text $X^t$ according to a randomly selected noun.", + "bbox": [ + 75, + 344, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To begin with, we employ the noun selector [2], which takes the text $X^t$ as input and extracts a set of $J$ nouns, $\\{N_j\\}_{j=1}^J$ , in $X^t$ . For each noun $N_j$ , we carry out region mask generation, where the image segmenter $F^v$ predicts a region mask $M^v$ specifying the area in image $X^v$ relevant to noun $N_j$ . A similar task word mask generation is performed by the text segmenter $F^t$ , which seeks a word mask $M^t$ matching noun $N_j$ . The tasks of region and word mask generation are depicted as follows.", + "bbox": [ + 76, + 435, + 470, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Region mask generation. The image segmenter $F^v$ takes image $X^v$ and noun $N_j$ as input. It encodes the image into a pixel-wise embedding $\\mathbf{x}^v \\in \\mathbb{R}^{H \\times W \\times C}$ , where $H \\times W$ is the image resolution and $C$ is the channel dimension. We also compute the noun embedding $\\mathbf{n}_j \\in \\mathbb{R}^C$ for noun $N_j$ . The image segmenter generates a region mask $M^v \\in \\mathbb{R}^{H \\times W}$ by performing the dot product between the noun embedding $\\mathbf{n}_j$ and every location of the image embedding $\\mathbf{x}^v$ .", + "bbox": [ + 75, + 575, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we use the image segmentation model in [5] to serve as the image segmenter $F^v$ , and employ its corresponding loss, denoted by $\\mathcal{L}_{\\mathrm{seg}}^v$ here, to help derive the image segmenter. This loss considers segment regularization and contrastive learning that can be directly applied to the segmentation results along with the noun embedding. We use the KgCoOp method [48] to obtain the noun embedding $\\mathbf{n}_j$ , as it avoids the pitfalls of improper prompt selection. It appends learnable context tokens to the noun, forming pseudo-sentences for optimal prompt tuning. The noun embedding loss $\\mathcal{L}_{\\mathrm{kg}}$ [48] is included to improve the accuracy of these embeddings, i.e.,", + "bbox": [ + 75, + 696, + 470, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {k g}} = \\left| \\left| \\mathbf {n} _ {j} - \\mathbf {n} _ {j} ^ {\\prime} \\right| \\right| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the $\\mathbf{n}_j^{\\prime}\\in \\mathbb{R}^{C}$ represents the knowledge-guided noun embedding generated from hand-crafted prompts such as \"a photo of a $N_{j}$ \" using the text encoder.", + "bbox": [ + 498, + 321, + 890, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Word mask generation. The text segmenter $F^t$ takes the text $X^t$ and the noun $N_j$ as input. For text feature extraction, we consider the CLIP text encoder appended with two learnable multi-head attention layers. With the resultant feature extractor $\\tilde{E}^t$ , the word-wise features of text $X^t$ are obtained via $\\mathbf{x}^t = \\tilde{E}^t(X^t) \\in \\mathbb{R}^{L \\times C}$ , where $L$ is the text length, i.e., the number of word tokens. The word-specific logits $\\ell_j = [\\ell_{j,i}]_{i=1}^L \\in \\mathbb{R}^L$ for noun $N_j$ are computed via", + "bbox": [ + 498, + 375, + 892, + 496 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {j} = w \\cdot \\mathbf {x} ^ {t} \\mathbf {n} _ {j} + b, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 507, + 890, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w$ and $b$ are two learnable parameters, and $\\mathbf{n}_j\\in \\mathbb{R}^C$ is the noun embedding.", + "bbox": [ + 498, + 536, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since each word in text $X^t$ belongs to either one of the $J$ word segments associated with nouns $\\{N_j\\}_{j=1}^J$ or none of them, the word mask $M^t = [m_i^t]_{i=1}^L \\in \\mathbb{R}^L$ for noun $N_j$ is obtained by applying the softmax function over all the $J$ noun-associated segments, i.e.,", + "bbox": [ + 498, + 566, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nm _ {i} ^ {t} = \\frac {\\exp \\left(\\ell_ {j , i}\\right)}{1 + \\sum_ {j ^ {\\prime} = 1} ^ {J} \\exp \\left(\\ell_ {j ^ {\\prime} , i}\\right)}, \\text {f o r} 1 \\leq i \\leq L, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 655, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the additional 1 in the denominator is included for the case where word $i$ does not belong to any noun-associated segments. The word mask $M^t$ for noun $N_j$ is produced.", + "bbox": [ + 498, + 704, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to the softmax function defined in Eq. 3, we get the probabilities of word $i$ over $J + 1$ cases, namely belonging to one of the $J$ noun-associated segments or none of them. We compile a pseudo label vector $\\mathbf{p} = \\{p_i\\} \\in \\{0,1\\}^L$ , where $p_i$ takes value 1 if word $i$ belonging to the $j$ th noun-associated segment gets the highest probability, and 0 otherwise. We develop the text segmentation loss $\\mathcal{L}_{\\mathrm{seg}}^t$ , which is the cross-entropy loss on the word mask $M^t$ with respect to the pseudo label vector $\\mathbf{p}$ , and can help learn the text segmenter $F^t$ .", + "bbox": [ + 498, + 750, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26797", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Region-Word Highlighting", + "text_level": 1, + "bbox": [ + 76, + 90, + 318, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We present a prompt learning method to reliably extract features from an image region or a word segment using a vision-language model. Specifically, we propose a region-highlighting prompt learning method and a word-highlighting prompt learning method, as shown in Fig. 2b.", + "bbox": [ + 75, + 113, + 468, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Region highlighting prompt. When the region mask $M^v$ is directly applied to the image $X^v$ via $M^v * X^v$ , where $*$ denotes the element-wise multiplication operation, it makes specific regions of the image being zeroed out, resulting in what we refer to as blank areas. When a pre-trained vision-language model like CLIP is applied to these areas, the domain distribution may shift due to the introduction of zero tokens, which are unseen in natural images. To mitigate this issue, we introduce a region highlighting prompt, which is a learnable, universal image representation, denoted by $P^v$ . This representation is used alongside the original image in the process of feature extraction. The highlighted image is then obtained via", + "bbox": [ + 75, + 193, + 472, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH ^ {v} = X ^ {v} * M ^ {v} + P ^ {v} * \\left(1 - M ^ {v}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 398, + 468, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, the blank areas are filled with the corresponding areas of the region prompt $P^v$ alleviating the unfavorable effect of domain shift.", + "bbox": [ + 75, + 425, + 468, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Word highlighting prompt. A similar challenge arises in the text domain when applying the word mask $M^t$ to text $X^t$ . The resultant zero tokens in the masked part unintentionally carry meanings of specific words, leading to potential inaccuracies. To mitigate this issue, we introduce a word highlighting prompt, represented as a learnable, universal text representation $P^t$ . The highlighted text $H^t$ is obtained by", + "bbox": [ + 75, + 474, + 472, + 597 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH ^ {t} = X ^ {t} * M ^ {t} + P ^ {t} * (1 - M ^ {t}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 604, + 468, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the masked part is filled with content from $P^t$ , the risk of including unexpected text meanings is reduced.", + "bbox": [ + 75, + 632, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Region-Word Alignment", + "text_level": 1, + "bbox": [ + 76, + 670, + 303, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the following, we describe how our method achieves region-word alignment. Our objective is to optimize mutual evidence between the highlighted object regions and the highlighted word segments, as illustrated in Fig. 2c.", + "bbox": [ + 75, + 694, + 468, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrastive loss on highlighted region-word pairs. To achieve region-word alignment, we compute the highlighted region embedding $\\mathbf{e}^v$ and highlighted word segment embedding $\\mathbf{e}^t$ from the highlighted region-word pair by using the image and text encoders of CLIP by", + "bbox": [ + 75, + 758, + 468, + 835 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} ^ {v} = E ^ {v} \\left(H ^ {v}\\right) \\text {a n d} \\mathbf {e} ^ {t} = E ^ {t} \\left(H ^ {t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 843, + 468, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $E^v$ and $E^t$ are the CLIP image and text encoders, respectively.", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt batch optimization for model training. Each batch has several triplets, each of which is composed of an image, its paired text, and a randomly selected noun from the text. Each triplet yields a region embedding and a word embedding via Eq. 6. Suppose that there are $B$ triplets in this batch. We create a similarity matrix $S = [S_{i,j}] \\in \\mathbb{R}^{B \\times B}$ , where $S_{i,j}$ stores the cosine similarity between the $i$ th region embedding $\\mathbf{e}_i^v$ and the $j$ th word segment embedding $\\mathbf{e}_j^t$ . We adopt the symmetric version of InfoNCE loss to develop the highlighted region-word pair contrastive loss, which enhances the similarity of related region-word pairs while reducing it for unrelated pairs:", + "bbox": [ + 496, + 90, + 893, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {h c l}} = - \\frac {1}{2 B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp (S _ {i , i} / \\tau)}{\\sum_ {j = 1} ^ {B} \\exp (S _ {i , j} / \\tau)} \\\\ - \\frac {1}{2 B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(S _ {i , i} / \\tau\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(S _ {j , i} / \\tau\\right)}, \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 282, + 890, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is a learnable temperature. Notably, even though nouns may be selected multiple times across image-caption pairs, the corresponding highlighted regions $H^v$ and highlighted texts $H^t$ vary, ensuring the effectiveness of the InfoNCE loss in precise region-word alignment.", + "bbox": [ + 496, + 378, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss functions and optimization. In sum, the proposed network for image-text co-decomposition is optimized using a composite loss that combines the knowledge-guided, image segmentation, text segmentation, and highlighted region-word pair contrastive losses, defined as follows:", + "bbox": [ + 496, + 460, + 890, + 536 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {\\mathrm {k g}} \\mathcal {L} _ {\\mathrm {k g}} + \\lambda_ {\\mathrm {s e g}} ^ {v} \\mathcal {L} _ {\\mathrm {s e g}} ^ {v} + \\lambda_ {\\mathrm {s e g}} ^ {t} \\mathcal {L} _ {\\mathrm {s e g}} ^ {t} + \\lambda_ {\\mathrm {h c l}} \\mathcal {L} _ {\\mathrm {h c l}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 547, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 575, + 718, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilize NLTK's [2] part-of-speech tagging algorithm for noun selection. For image segmentation, we utilize TCL's image segmenter [5] to generate image masks, and we adopt the training loss in TCL, which relies solely on the image-capture pairs, to yield $\\mathcal{L}_{\\mathrm{seg}}^v$ . For text segmentation, we use a CLIP text encoder appended with two multi-head attention layers as the text segmenter $\\tilde{E}^t$ . Our model is trained on the CC3M and CC12M datasets. The resolution of input images is set to $224 \\times 224$ . For each forward pass of an image-text pair, we randomly select 2 nouns from the text. The loss weights are set as follows: $\\lambda_{\\mathrm{kg}} = 8.0$ , $\\lambda_{\\mathrm{seg}}^v = 1.0$ , $\\lambda_{\\mathrm{seg}}^t = 1.0$ , and $\\lambda_{\\mathrm{hcl}} = 0.5$ in the experiments. We train the model with a batch size of 64 on four NVIDIA 2080Ti GPUs and with a learning rate of $5 \\times *10^{-6}$ for a total of 50,000 iterations with 15,000 warmup steps and a cosine schedule. AdamW optimizer [29] is used with a weight decay of 0.05. To improve the quality of the predicted mask during the evaluation phase, we adopt the post-processing approach described in TCL [5], which uses pixel-adaptive mask refinement (PAMR) [1] for mask refinement.", + "bbox": [ + 496, + 598, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26798", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/76d36a6d378b3cfebecf403a8bf6711fda5c8f122a9fc7364e9aab573b97a0ab.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsPublicationDatasetVOCContextObjectStuffCityADEAvg.
GroupViT [45]CVPR 2022CC3M+CC12M+YFCC14M49.519.024.312.66.98.720.2
ViL-Seg [28]ECCV 2022CC12M37.318.918.1
ViewCo [36]ICLR 2023CC12M+YFCC14M52.423.023.5
OVSegmentor [46]CVPR 2023CC12M53.820.425.1
SimSeg [49]CVPR 2023CC3M+CC12M57.426.229.7
TCL [5]CVPR 2023CC3M+CC12M55.030.431.622.424.017.130.1
SegCLIP [30]ICML 2023CC3M + COCO52.624.726.5
CoCu [44]NeurIPS 2023CC3M+CC12M+YFCC14M51.423.622.715.222.112.324.6
PGSeg [51]NeurIPS 2023CC12M+RedCaps12M53.223.828.7
CoDe (Ours)CVPR 2024CC3M+CC12M57.730.532.323.928.917.731.8
", + "bbox": [ + 119, + 88, + 848, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Text-supervised semantic segmentation performance comparison in terms of mIoU. The proposed method is compared with nine SOTA methods on six popular semantic segmentation datasets: PASCAL VOC (VOC), PASCAL Context (Context), COCO-Object (Object), COCO-Stuff (Stuff), Cityscapes (City) and ADE20K (ADE). For each compared method, the dataset column lists its training datasets. Several methods used datasets in addition to CC3M and CC12M, such as YFCC14M, COCO and RedCaps12M. When applicable, we also provide an average mIoU across all six datasets. For each dataset, the best method is indicated by bold fonts, whereas the second best method is underlined.", + "bbox": [ + 75, + 270, + 890, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 368, + 209, + 385 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Settings", + "text_level": 1, + "bbox": [ + 76, + 393, + 366, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We utilize image-text datasets to train our proposed model and perform extensive experiments on six commonly used semantic segmentation benchmarks to validate our method.", + "bbox": [ + 75, + 416, + 468, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training datasets. We trained our model on two image-text datasets, Conceptual Captions 3M (CC3M) [37] and Conceptual 12M (CC12M) [6] containing 3M and 12M image-text pairs respectively. They have been widely adopted for training text-supervised semantic segmentation methods.", + "bbox": [ + 75, + 462, + 468, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation datasets. We used six zero-shot semantic segmentation benchmarks to validate the zero-shot transfer capability of our model on categories that were not specifically trained. As in previous work [5], the benchmarks can be categorized into two groups, with and without background classes. Benchmarks with a background generally label areas that do not belong to any predefined categories as \"background,\" which is usually removed by considering a probability threshold in text-supervised semantic segmentation. For this category, we use the validation split of the following datasets: PASCAL VOC 2012 [13], PASCAL Context [32], and COCO-Object [3]. They each contain 20, 59, and 80 foreground classes, respectively, with an additional background class. For the \"without background category,\" we evaluated our model with the validation split of COCO-Stuff [3], Cityscapes [10], and ADE20K [53] datasets. Each of them contains 171, 19, and 150 classes, respectively. In this category, all images are fully annotated, which is exceptionally challenging. Using datasets in this category, our model can be tested for its ability to recognize a variety of concepts. We employ mean intersection-over-union (mIoU) as our evaluation metric.", + "bbox": [ + 75, + 537, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For zero-shot semantic segmentation evaluation, we rely solely on the image segmenter. The image segmenter pro", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cesses the input image in conjunction with class names from each dataset to produce segmentation predictions. In accordance with the settings of prior work [5], we adopt the class names provided by the default version of MMSegmentation [9] and adhere to its post-processing methodology.", + "bbox": [ + 498, + 369, + 890, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative Comparisons", + "text_level": 1, + "bbox": [ + 498, + 458, + 738, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed method with nine text-supervised semantic segmentation methods on the six datasets. Tab. 1 reports the mIoU values. The numbers have been taken directly from the original papers. All methods were tested on the three datasets of the \"with background class,\" but only three methods (GroupViT [45], CoCu [44] and TCL [5]) were tested on the dataset of the \"without background class.\" For those three methods, we also report their average mIoU values across all six datasets. It is also worth noting that these methods use different combinations of training datasets, as indicated in the dataset column of Tab. 1.", + "bbox": [ + 496, + 482, + 890, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method achieves the best performance in all six datasets, while TCL [5] and SimSeg [49] are the runners-up. In terms of average mIoU, our method (CoDe) achieves 31.8 whereas TCL achieves 30.1, resulting in a $5.65\\%$ improvement. The result demonstrates the effectiveness of our image-text co-decomposition method in addressing the alignment-level train-test discrepancy that exists in previous methods by directly learning the region-word alignment.", + "bbox": [ + 496, + 650, + 890, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 498, + 784, + 684, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual comparison with existing methods. Fig. 3 visually compares the segmentation results of our methods and two runners-up, TCL [5] and SimSeg [49], on the PASCAL VOC, PASCAL Context, and COCO Object datasets.", + "bbox": [ + 496, + 808, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This figure illustrates the fundamental benefit of our approach, which involves the direct learning of region-word", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26799", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6f66e51aa0d46669848cdade8f6568f2ada089eca857ae7b78dcd568b0249c18.jpg", + "image_caption": [ + "Figure 3. Qualitative comparisons. The proposed method is compared with the two most competitive methods, TCL [5] and SimSeg [49], on PASCAL VOC, PASCAL Context, and COCO Object datasets. Our method provides more precise object boundaries and effectively localizes objects within images without misclassification, leading to more accurate segmentation." + ], + "image_footnote": [], + "bbox": [ + 122, + 84, + 370, + 354 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a25ec1e520bd082c5c504f40975173200a2c7cbc928bf93069bcfb9e7a8974b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 85, + 635, + 354 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/177a38e05c594c1facef112294a0b49d8f5db6ceb5d7c874126add69a0e0b391.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 85, + 848, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "alignments. Our model effectively establishes a strong connection between object regions and word segments, allowing a better understanding of how objects are represented in images. Through this enhanced understanding, both segmentation quality and localization capabilities can be improved. As a result, our method provides more accurate classification and more precise masks than other methods.", + "bbox": [ + 75, + 426, + 467, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The SimSeg[49] model, which learns from image-text alignments, occasionally assigns objects to the wrong classes. On the other hand, TCL [5], which is based on region-text alignment, produces coarser semantic masks. Accordingly, these observed limitations are most likely a result of the alignment-level discrepancy between the train and test, which may lead to suboptimal performance.", + "bbox": [ + 75, + 532, + 467, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of image-text co-segmentation results. Fig. 4 presents a visualization of the results obtained by our model. We denote regions and word segments associated with the different nouns in the corresponding colors. It demonstrates that our method effectively segments object regions within images based on various input nouns. It simultaneously segments corresponding word segments within the associated text, creating a harmonious alignment between the object region and the word segment.", + "bbox": [ + 75, + 657, + 467, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The region-word alignment plays a pivotal role in our approach, serving as a supervisory signal for the model. By taking advantage of this alignment, our model not only performs visual localization but also captures correlations within the language domain. It indicates that our trained model possesses a more comprehensive understanding of the segmentation task.", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2c29c18147bd0e13fb9d18506ed285e7aae1f9b412685c48ef642537c509149d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
C.W.R.VOCContextObjectStuffCityADEAvg.
54.427.632.722.525.016.629.8
✓56.229.232.923.327.517.031.0
✓✓56.129.332.623.629.017.331.3
✓✓✓57.730.532.323.928.917.731.8
", + "bbox": [ + 500, + 422, + 888, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Ablation study. The baseline model is augmented with the image-text co-decomposition method (C.), the word highlighting prompt (W.), and the region highlighting prompt (R.), one at a time. We report the mIoU values of the resultant models on the six datasets and their averages.", + "bbox": [ + 498, + 518, + 890, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 602, + 651, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Contributions of individual components. The ablation study in Tab. 2 assesses the contribution of the proposed components, including the image-text co-decomposition method, the word highlighting prompt, and the region highlighting prompt. Without the co-decomposition method, our baseline model only trains the image segmenter, resulting in an average mIoU of 29.8. Afterward, each proposed component is added to the baseline model one at a time to verify its contribution. As a result of adding the image-text co-decomposition module alone, the average mIoU has been increased to 31.0. It suggests that the image-text co-decomposition method can achieve region-word alignment and enhance localization capability. The model is further enhanced with the addition of word highlighting prompts and image highlighting prompts, resulting in further performance improvement. It demonstrates that the highlighting prompt learning method enhances feature extraction and strengthens alignment between regions and words.", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26800", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0513c558295e1493edd1a5041a3dac60172a1733ec763069ba8ecfe632c7c3d1.jpg", + "image_caption": [ + "this was her hair... it was beautiful, as you will see" + ], + "image_footnote": [], + "bbox": [ + 81, + 104, + 212, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/471594d8072a4a5b029bb566847616978450e70acc92fc7cc40a8ddb6865d838.jpg", + "image_caption": [ + "A black bear walks through dense vegetation." + ], + "image_footnote": [], + "bbox": [ + 215, + 104, + 348, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e9513cd3c604095064fa762cd88d5abfe7d1844143d627cea160349a2b2b9e93.jpg", + "image_caption": [ + "An old book lying open." + ], + "image_footnote": [], + "bbox": [ + 352, + 104, + 483, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e9fae17859652452c1009add2d0c3671f208d43421ef3c7ca0fa9fda3ea00116.jpg", + "image_caption": [ + "this was her hair... it wasbeautiful, as you will see" + ], + "image_footnote": [], + "bbox": [ + 81, + 208, + 212, + 308 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/822e096125363fdacd4af91f16b3f337db89c48bcb182b9d4af11d2b34c84f64.jpg", + "image_caption": [ + "An old book lying open.", + "Figure 4. Visualization of the results of our image-text co-decomposition method. The first two rows display text and images, representing input image-text pairs. In each text, nouns are underlined with different colors. Our method uses these nouns as queries for performing image-text co-decomposition. Using our image-text co-decomposition method, the last two rows depict the method's output, where regions and word segments associated with different nouns appear in corresponding colors." + ], + "image_footnote": [], + "bbox": [ + 215, + 208, + 348, + 310 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a8bf6621c20c4c6cf5c6fa10437e12e60f826182c5986dc952a4757b202eb8b1.jpg", + "image_caption": [ + "A black bear walks through dense vegetation." + ], + "image_footnote": [], + "bbox": [ + 352, + 208, + 483, + 310 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bb0ad4b007e5602c87647871c31498a3b964c1058fd3de67c06db9d3092ccfc3.jpg", + "image_caption": [ + "an ostrich egg laying on the grass" + ], + "image_footnote": [], + "bbox": [ + 488, + 104, + 617, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b37305c94b0f64812b02fd4fe4268bbd055adf6e496ef7403f51a12e92da8667.jpg", + "image_caption": [ + "an ostrich egg laying on the grass" + ], + "image_footnote": [], + "bbox": [ + 488, + 208, + 617, + 308 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e6f5f338a636b42a3672395123a3512288c17a2914761603f7eacf1930c88442.jpg", + "image_caption": [ + "2 large dogs posing on the beach at sunset" + ], + "image_footnote": [], + "bbox": [ + 622, + 104, + 753, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e90908288f76e5a6e4839efcdafb393c86be983a134243c382e61e5d1914ac2b.jpg", + "image_caption": [ + "2 large dogs posing on the beach at sunset" + ], + "image_footnote": [], + "bbox": [ + 622, + 208, + 753, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e2754902ada6522620528f5bd670bf2e34187a763ae718d694a3534f3574f74.jpg", + "image_caption": [ + "A girl's hand holding fresh white flowers" + ], + "image_footnote": [], + "bbox": [ + 756, + 104, + 888, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5c297821263d0e0929ef34990e4b25d6b1e84157025986225c1db690be9e655e.jpg", + "image_caption": [ + "A girl's hand holding fresh white flowers" + ], + "image_footnote": [], + "bbox": [ + 756, + 208, + 888, + 309 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/657d97dffdc2899593983766db06760233ae4b8258671d4f5ecaac4e6827c36d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
λhcl0.050.10.250.50.751.0
Avg.30.631.231.731.831.530.8
", + "bbox": [ + 135, + 426, + 406, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Sensitivity analysis on the hyperparameter $\\lambda_{\\mathrm{hcl}}$ . By varying $\\lambda_{\\mathrm{hcl}}$ , we examine the corresponding average mIoU values of all six datasets.", + "bbox": [ + 75, + 482, + 468, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyperparameter sensitivity analysis. Tab. 3 investigates the impact of the loss weight for the highlighted region-word pair contrastive loss, denoted as $\\lambda_{\\mathrm{hcl}}$ in Eq. (8). We observe that, when we apply the highlighted region-word pair contrastive loss in our training phase, the performance consistently outperforms our baseline model. The method is robust to the parameter to some degree as it achieves reasonable performance for a wide range of values. When $\\lambda_{\\mathrm{hcl}}$ is set to 0.5, our model achieves a peak score of 31.8. It is evident from these results that the image-text co-decomposition method is superior to the image-text decomposition method for achieving region-word alignment.", + "bbox": [ + 75, + 555, + 468, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of jointly decomposing text. We validate the effectiveness of decomposing text by assessing the performance enhancement achieved by generating word masks, as opposed to simply using extracted nouns. This experiment is conducted by modifying the calculation of $\\mathcal{L}_{\\mathrm{hcl}}$ . Instead of using word segment embeddings as mentioned in Sec. 3.4, we opt to compute the similarity matrix $S$ using region embeddings with the embeddings of individual nouns. The average mIoU across all benchmarks is", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$30.2\\%$ , which is below our method's $31.8\\%$ . This indicates the benefits of using word segments encompassing extra words associated with each noun. The contextual information encoded in these additional words can serve as valuable supervisory signals, thereby improving performance.", + "bbox": [ + 498, + 430, + 890, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 518, + 625, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose Image-Text Co-Decomposition (CoDe) to address cross-domain alignment discrepancies in the existing methods for text-supervised semantic segmentation. First, our method decomposes image-text pairs into corresponding regions and word segments to enforce the region-word alignment. CoDe, underpinned by contrastive learning, alleviates the train-test discrepancy by unifying image-text and region-text alignments to region-word alignment. Then, we introduce a region-highlighting prompt learning method to enhance feature extraction on masked images or texts for precise region-word alignment. Moreover, CoDe surpasses state-of-the-art methods in zero-shot semantic segmentation across six benchmark datasets. This novel approach opens new possibilities for research in vision-language models and their broader applications in computer vision.", + "bbox": [ + 496, + 544, + 890, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 784, + 679, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Science and Technology Council (NSTC) under grants 112-2221-E-A49-090-MY3, 111-2628-E-A49-025-MY3, 112-2634-F-002-005, 112-2634-F-002-006, and 110-2221-E-002-124-MY3, and NTU under grants 112L9009. This work was funded in part by MediaTek and NVIDIA.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26801", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nikita Araslanov and Stefan Roth. Single-stage semantic segmentation from image labels. In CVPR, 2020. 5", + "[2] Steven Bird, Ewan Klein, and Edward Loper. Natural language processing with Python: analyzing text with the natural language toolkit. 2009. 3, 4, 5", + "[3] Holger Caesar, Jasper Uijlings, and Vittorio Ferrari. Cocostuff: Thing and stuff classes in context. In CVPR, 2018. 6", + "[4] Kaixin Cai, Pengzhen Ren, Yi Zhu, Hang Xu, Jianzhuang Liu, Changlin Li, Guangrun Wang, and Xiaodan Liang. 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In ICCV, 2023. 3" + ], + "bbox": [ + 501, + 92, + 890, + 571 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "26803", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation/903a1b45-2229-4628-ac3b-aaa39b0c7384_model.json b/2024/Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation/903a1b45-2229-4628-ac3b-aaa39b0c7384_model.json new file mode 100644 index 0000000000000000000000000000000000000000..77d98138d9be94f36ba7422606e4ba353d37b4eb --- /dev/null +++ b/2024/Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation/903a1b45-2229-4628-ac3b-aaa39b0c7384_model.json @@ -0,0 +1,2453 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.109, + 0.131, + 0.862, + 0.154 + ], + "angle": 0, + "content": "Image-Text Co-Decomposition for Text-Supervised Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.179, + 0.914, + 0.221 + ], + "angle": 0, + "content": "Ji-Jia Wu1 Andy Chia-Hao Chang2 Chieh-Yu Chuang2 Chun-Pei Chen2 Yu-Lun Liu2 Min-Hung Chen3 Hou-Ning Hu4 Yung-Yu Chuang1 Yen-Yu Lin2" + }, + { + "type": "text", + "bbox": [ + 0.206, + 0.238, + 0.795, + 0.274 + ], + "angle": 0, + "content": "\\(^{1}\\)National Taiwan University \\(^{2}\\)National Yang Ming Chiao Tung University \\(^{3}\\)NVIDIA \\(^{4}\\)MediaTek" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.473, + 0.675 + ], + "angle": 0, + "content": "This paper addresses text-supervised semantic segmentation, aiming to learn a model capable of segmenting arbitrary visual concepts within images by using only image-text pairs without dense annotations. Existing methods have demonstrated that contrastive learning on image-text pairs effectively aligns visual segments with the meanings of texts. We notice that there is a discrepancy between text alignment and semantic segmentation: A text often consists of multiple semantic concepts, whereas semantic segmentation strives to create semantically homogeneous segments. To address this issue, we propose a novel framework, Image-Text Co-Decomposition (CoDe), where the paired image and text are jointly decomposed into a set of image regions and a set of word segments, respectively, and contrastive learning is developed to enforce region-word alignment. To work with a vision-language model, we present a prompt learning mechanism that derives an extra representation to highlight an image segment or a word segment of interest, with which more effective features can be extracted from that segment. Comprehensive experimental results demonstrate that our method performs favorably against existing text-supervised semantic segmentation methods on six benchmark datasets. The code is available at https://github.com/072jiajia/image-text-co-decomposition." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.708, + 0.21, + 0.724 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Semantic segmentation is essential to various applications [11, 15, 50] in computer vision but is hindered by several critical challenges. First, the expensive cost of acquiring pixel-level annotations limits the applicability of fully supervised semantic segmentation methods. Second, most existing methods [40, 43, 52] are developed to work on predefined categories and leave themselves inapplicable to rare or unseen concepts described by free-form text. To address these obstacles, a new research direction has emerged in vision-language models, referred to as text-supervised semantic segmentation [5, 28, 44-46, 49]. This task devel" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.892, + 0.356 + ], + "angle": 0, + "content": "ops segmentation models capable of assigning labels across large vocabularies of concepts and supporting semantic segmentation model training without pixel-wise annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.893, + 0.538 + ], + "angle": 0, + "content": "Fig. 1 compares existing methods for text-supervised semantic segmentation by grouping their cross-domain alignment mechanisms into three categories, including image-text, region-text, and region-word alignment. Despite the differences, most of these methods compensate for the lack of pixel-wise annotations on broad semantic concepts by exploring abundant image-text pairs on the internet. The textual descriptions bring extensive knowledge across diverse categories. Thus, existing methods typically apply a vision-language model such as CLIP [34] to textual descriptions to acquire the semantic context of the corresponding images for segmentation model learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.894, + 0.689 + ], + "angle": 0, + "content": "The image-text alignment is widely adopted in the literature e.g. [28, 44, 45]. As depicted in Fig. 1a, methods of this group derive an image encoder and a text encoder by aligning them in a joint embedding space. They then use their proposed zero-shot transfer techniques to enable the two encoders to predict segmentation output. Despite the simplicity, they introduce unfavorable discrepancies between the training and testing phases since we aim to match the semantic features from the text to the corresponding image segments rather than the whole image during testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.894, + 0.84 + ], + "angle": 0, + "content": "To mitigate this issue, the region-text alignment is explored. As shown in Fig. 1b, methods of this group such as [5] utilize a pre-trained visual-language model to derive an additional image segmenter that discovers concepts described by the text. They enforce the consistency between the segmented region and the text but suffer from the discrepancy between the region-text alignment and semantic segmentation: A text may consist of multiple concepts, such as pub, night, and car in Fig. 1b, while semantic segmentation aims to identify regions of the same concept." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To address the aforementioned issues in the image-text and region-text alignments, we propose a novel framework, Image-Text Co-Decomposition (CoDe), to achieve region-word alignment. As illustrated in Fig. 1c, we utilize a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26794" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.268, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.194, + 0.237, + 0.206 + ], + "angle": 0, + "content": "(a) image-text alignment" + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.091, + 0.55, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.36, + 0.194, + 0.491, + 0.207 + ], + "angle": 0, + "content": "(b) region-text alignment" + }, + { + "type": "image", + "bbox": [ + 0.55, + 0.089, + 0.872, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.194, + 0.796, + 0.207 + ], + "angle": 0, + "content": "(c) region-word alignment (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.214, + 0.894, + 0.27 + ], + "angle": 0, + "content": "Figure 1. Existing methods perform text-supervised semantic segmentation by learning either (a) image-text alignment or (b) region-text alignment. This paper presents (c) region-word alignment via image-text co-decomposition, where the image and the text are decomposed into object regions and word segments, respectively, while contrastive learning is used to establish cross-modal correspondences between these image and word segments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.47, + 0.404 + ], + "angle": 0, + "content": "visual-language model to construct an image segmenter and a text segmenter: The former decomposes an image into image segments, while the latter decomposes a text into word segments. In addition, there exist one-to-one correspondence between image and word segments. This way, the discrepancy between training and testing is alleviated since each image segment is derived from a single concept given by the corresponding word segment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.47, + 0.587 + ], + "angle": 0, + "content": "The proposed CoDe framework comprises four components: an image segmenter, a text segmenter, a region-word alignment module, and a prompt learning module. We randomly select nouns in the text. For each selected noun e.g., \"car\", the image segmenter identifies the image segment that matches the noun, i.e., the region of the car, while the text segmenter discovers the corresponding word segment, i.e., \"red cars.\" The region-word alignment is developed to enforce the consensus between the image and word segments. To better work with a vision-language model, we present a prompt learning module to derive an extra representation, enabling more effective feature extraction." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.588, + 0.435, + 0.602 + ], + "angle": 0, + "content": "The main contributions of this work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.605, + 0.469, + 0.666 + ], + "angle": 0, + "content": "- We propose a new framework, Image-Text Co-Decomposition (CoDe), to learn the region-word alignment for eliminating train-test and image-text discrepancies, facilitating text-supervised semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.666, + 0.469, + 0.725 + ], + "angle": 0, + "content": "- We propose a prompt learning method to address domain shift issues arising from blank areas during the highlighting process and enhance the alignment between highlighted regions and highlighted words." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.726, + 0.469, + 0.77 + ], + "angle": 0, + "content": "- Our method effectively carries out zero-shot semantic segmentation and performs favorably against the state-of-the-art methods on six benchmark datasets." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.605, + 0.469, + 0.77 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.789, + 0.227, + 0.805 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.816, + 0.433, + 0.832 + ], + "angle": 0, + "content": "2.1. Open-Vocabulary Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Open-vocabulary semantic segmentation focuses on segmenting any concepts within images, even those unseen during training, based solely on textual descriptions. Its three important branches are discussed as follows:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.418 + ], + "angle": 0, + "content": "Semi-supervised setting with mask-annotations. Methods of this group such as [16, 17, 24, 26, 31, 47] learn from dense annotations to produce high-quality segmentation masks, and then utilize image-text pairs and pre-trained vision-language models to extend the segmentation capability to a larger target vocabulary. Despite the remarkable results, these methods are hindered by their reliance on costly dense annotations, posing a challenge in cases where such annotations are difficult to obtain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.604 + ], + "angle": 0, + "content": "Training-free methods. Another line of research e.g. [38, 41, 54] makes the most of large pre-trained models for open-vocabulary segmentation without training. MaskCLIP [54] introduces a modification to the final layer of the CLIP image encoder, yielding dense feature maps that could be employed as initial segmentation maps for further refinement. ReCo [38] constructs an image archive and makes use of retrieval and co-segmentation to identify co-occurrence regions among a specific category. Although these methods eliminate the process of training, the results exhibit significant room for improvement, which shows the need for additional supervision to accomplish this task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.668 + ], + "angle": 0, + "content": "Text-supervised semantic segmentation. It strikes a balance between the two aforementioned branches. Methods of this group are discussed in detail in the following because our method belongs to this group." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.844, + 0.694 + ], + "angle": 0, + "content": "2.2. Text-Supervised Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Text-supervised semantic segmentation [4, 5, 28, 33, 36, 42, 44-46, 49] decomposes an image into semantic regions according to text descriptions. Unlike semi-supervised methods relying on a few images with mask annotations during training, methods of this group aim to learn semantic masks solely from text-based guidance. We roughly divide existing methods into two categories based on their cross-modal alignment between the image and text domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Image-text alignment. These methods train an image encoder alongside a text encoder to align pairs of image and text in a joint embedding space. They use zero-shot transfer to enable the encoders to produce segmentation results. GroupViT [45] introduces a bottom-up approach within" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26795" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "Transformers, grouping image patches into regions and utilizing object semantics derived from texts to guide training. SimSeg [49] further introduces a pretraining method that densely aligns visual and language representations, enabling the trained image encoder to generate segmentation masks in a zero-shot manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.201, + 0.47, + 0.306 + ], + "angle": 0, + "content": "Region-text alignment. Another line of research targets at aligning the embedding of a region, instead of the whole image, with text descriptions. For instance, TCL [5] learns to segment specific regions within an image while ensuring consistency between the segmented region and the original text. It enables the model to segment the relevant region described in the text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.471, + 0.536 + ], + "angle": 0, + "content": "These methods for text-supervised semantic segmentation have shown that employing vision-language models and contrastive learning on image-text pairs enables aligning visual concepts with the meaning of the whole text. We notice that a text is usually a mix of multiple semantic concepts, but semantic segmentation aims to discover semantically homogeneous segments. To address this issue, inspired by the region-word matching techniques [8, 21, 22, 39] for cross-modal retrieval, we introduce image-text co-decomposition, where the image and the text are decomposed into image and word segments, respectively, and contrastive learning is adopted to enforce cross-modal consensus between these image and word segments. It turns out that image-text co-decomposition results in consistent performance gains on multiple benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.555, + 0.453, + 0.571 + ], + "angle": 0, + "content": "2.3. Prompt Tuning for Vision-Language Models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Emerged from natural language processing [23, 25, 27], prompt tuning focuses on parameter-efficient adaptation of large pre-trained models to new tasks. In computer vision [20, 55-57], pioneering work such as CoOp [55, 56] incorporates learnable tokens into the CLIP text encoder, enhancing the classification task performance. Recent studies e.g. [12, 14, 35] leverage prompt tuning in the text modality for extending CLIP's capabilities to various applications such as detection and segmentation tasks. Notably, prompt learning methods are also applicable to the visual domain. VPT [19] employs prompt tuning in the visual modality by inserting learnable vectors into Vision Transformers. Further studies [18, 26] explore tuning methods that directly incorporate learnable prompts into the input image within the RGB domain to address downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Drawing inspiration from the success of these methods, our method leverages the capabilities of prompt tuning on segment feature extraction in both the visual and text domains. Prompt learning is beneficial in this work when applying contrastive learning to the visual and textual features extracted by a vision-language model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.636, + 0.109 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.892, + 0.269 + ], + "angle": 0, + "content": "In this section, we first provide an overview of our method for image-text co-decomposition and define the notations in Sec. 3.1. Then, we specify the three major modules of our method, including 1) the image-text co-segmentation module in Sec. 3.2, 2) the region-word highlighting module in Sec. 3.3, and 3) the region-word alignment module in Sec. 3.4. These modules work harmoniously to address the region-word alignment for text-supervised semantic segmentation and enhance model performances. Finally, implementation details are given in Sec. 3.5." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.283, + 0.673, + 0.299 + ], + "angle": 0, + "content": "3.1. Method Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.473 + ], + "angle": 0, + "content": "Image-text co-decomposition enables text-supervised segmenters to learn region-word consensus when segmenting an image \\( X^v \\) with a paired text \\( X^t \\). Our method aims to jointly learn an image segmenter \\( F^v \\) and a text segmenter \\( F^t \\) with solely the supervision from a set of \\( K \\) image-text pairs, \\( D = \\{X_k^v, X_k^t\\}_{k=1}^K \\), where no annotations are given. In addition, we optimize two learnable prompts, including a region prompt \\( P^v \\) and a word prompt \\( P^t \\), to alleviate the unfavorable effect of blank embeddings caused by applying a vision-language model to masked images or texts for feature extraction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.893, + 0.657 + ], + "angle": 0, + "content": "Fig. 2 illustrates the pipeline of our method, consisting of three modules, including the image-text co-segmentation, region-word highlighting, and region-word alignment modules. For an input image-text pair \\((X^v, X^t)\\), we initiate the process by randomly selecting a noun \\(N\\), e.g., balloon in the figure, from the text \\(X^t\\) using the noun selector [2]. This selected noun serves as a query. We take the query \\(N\\) along with the image \\(X^v\\) as input to the image segmenter \\(F^v\\) to generate the region mask \\(M^v\\) showing the estimated object region specified by the query. Similarly, a text segmenter \\(F^t\\) takes the query \\(N\\) and the text \\(X^t\\) as input and estimates the word mask \\(M^t\\) indicating the associated word segment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Subsequently, we apply the region mask \\( M^v \\) to the image \\( X^v \\) to crop the estimated object region. For the estimated background, i.e., the region outside the mask \\( M^v \\), we crop the corresponding region from the learned region prompt \\( P^v \\). The highlighted image \\( H^v \\) is yielded by combining the cropped object and background regions. Similarly, the highlighted text \\( H^t \\) is generated by combining the text \\( X^t \\) inside the mask \\( M^t \\) and the word prompt \\( P^t \\) outside the mask \\( M^t \\). We extract features from the highlighted image and text by using the image encoder \\( E^v \\) and the text encoder \\( E^t \\) of CLIP [34], respectively. The procedure is repeated for each image-text pair and each selected noun. It follows that the region-word alignment is accomplished by contrastive learning [7]. Four loss functions, including \\( \\mathcal{L}_{\\mathrm{kg}} \\), \\( \\mathcal{L}_{\\mathrm{seg}}^v \\), \\( \\mathcal{L}_{\\mathrm{seg}}^t \\), and \\( \\mathcal{L}_{\\mathrm{hcl}} \\), are used for network optimization, and will be elaborated in the following." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26796" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.387, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.39, + 0.089, + 0.647, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.089, + 0.87, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.237, + 0.895, + 0.307 + ], + "angle": 0, + "content": "Figure 2. Training pipeline of our method for image-text co-decomposition. Our method consists of three major modules, including (a) the image-text co-segmentation module where the image and text segmenters estimate the region and word masks according to a selected noun, respectively, (b) the region-word highlighting module where the estimated masks together with two learnable prompts produce the highlighted image and text, and (c) the region-word alignment module where contrastive learning is applied to the embedded object regions and word segments to accomplish region-word alignment." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.322, + 0.34, + 0.339 + ], + "angle": 0, + "content": "3.2. Image-Text Co-Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.435 + ], + "angle": 0, + "content": "The image-text co-segmentation module comprises a noun selector, an image segmenter, and a text segmenter, as shown in Fig. 2a. Taking an image-text pair \\((X^v, X^t)\\) as input, this module aims at jointly identifying an object region in image \\(X^v\\) and its accompanying word segment in text \\(X^t\\) according to a randomly selected noun." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.436, + 0.471, + 0.572 + ], + "angle": 0, + "content": "To begin with, we employ the noun selector [2], which takes the text \\( X^t \\) as input and extracts a set of \\( J \\) nouns, \\( \\{N_j\\}_{j=1}^J \\), in \\( X^t \\). For each noun \\( N_j \\), we carry out region mask generation, where the image segmenter \\( F^v \\) predicts a region mask \\( M^v \\) specifying the area in image \\( X^v \\) relevant to noun \\( N_j \\). A similar task word mask generation is performed by the text segmenter \\( F^t \\), which seeks a word mask \\( M^t \\) matching noun \\( N_j \\). The tasks of region and word mask generation are depicted as follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.697 + ], + "angle": 0, + "content": "Region mask generation. The image segmenter \\( F^v \\) takes image \\( X^v \\) and noun \\( N_j \\) as input. It encodes the image into a pixel-wise embedding \\( \\mathbf{x}^v \\in \\mathbb{R}^{H \\times W \\times C} \\), where \\( H \\times W \\) is the image resolution and \\( C \\) is the channel dimension. We also compute the noun embedding \\( \\mathbf{n}_j \\in \\mathbb{R}^C \\) for noun \\( N_j \\). The image segmenter generates a region mask \\( M^v \\in \\mathbb{R}^{H \\times W} \\) by performing the dot product between the noun embedding \\( \\mathbf{n}_j \\) and every location of the image embedding \\( \\mathbf{x}^v \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.471, + 0.877 + ], + "angle": 0, + "content": "In this work, we use the image segmentation model in [5] to serve as the image segmenter \\( F^v \\), and employ its corresponding loss, denoted by \\( \\mathcal{L}_{\\mathrm{seg}}^v \\) here, to help derive the image segmenter. This loss considers segment regularization and contrastive learning that can be directly applied to the segmentation results along with the noun embedding. We use the KgCoOp method [48] to obtain the noun embedding \\( \\mathbf{n}_j \\), as it avoids the pitfalls of improper prompt selection. It appends learnable context tokens to the noun, forming pseudo-sentences for optimal prompt tuning. The noun embedding loss \\( \\mathcal{L}_{\\mathrm{kg}} \\) [48] is included to improve the accuracy of these embeddings, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.884, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {k g}} = \\left| \\left| \\mathbf {n} _ {j} - \\mathbf {n} _ {j} ^ {\\prime} \\right| \\right| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.322, + 0.892, + 0.369 + ], + "angle": 0, + "content": "where the \\(\\mathbf{n}_j^{\\prime}\\in \\mathbb{R}^{C}\\) represents the knowledge-guided noun embedding generated from hand-crafted prompts such as \"a photo of a \\(N_{j}\\)\" using the text encoder." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.375, + 0.893, + 0.497 + ], + "angle": 0, + "content": "Word mask generation. The text segmenter \\( F^t \\) takes the text \\( X^t \\) and the noun \\( N_j \\) as input. For text feature extraction, we consider the CLIP text encoder appended with two learnable multi-head attention layers. With the resultant feature extractor \\( \\tilde{E}^t \\), the word-wise features of text \\( X^t \\) are obtained via \\( \\mathbf{x}^t = \\tilde{E}^t(X^t) \\in \\mathbb{R}^{L \\times C} \\), where \\( L \\) is the text length, i.e., the number of word tokens. The word-specific logits \\( \\ell_j = [\\ell_{j,i}]_{i=1}^L \\in \\mathbb{R}^L \\) for noun \\( N_j \\) are computed via" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.508, + 0.891, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\ell_ {j} = w \\cdot \\mathbf {x} ^ {t} \\mathbf {n} _ {j} + b, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.537, + 0.892, + 0.567 + ], + "angle": 0, + "content": "where \\(w\\) and \\(b\\) are two learnable parameters, and \\(\\mathbf{n}_j\\in \\mathbb{R}^C\\) is the noun embedding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.568, + 0.892, + 0.645 + ], + "angle": 0, + "content": "Since each word in text \\( X^t \\) belongs to either one of the \\( J \\) word segments associated with nouns \\( \\{N_j\\}_{j=1}^J \\) or none of them, the word mask \\( M^t = [m_i^t]_{i=1}^L \\in \\mathbb{R}^L \\) for noun \\( N_j \\) is obtained by applying the softmax function over all the \\( J \\) noun-associated segments, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.656, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\nm _ {i} ^ {t} = \\frac {\\exp \\left(\\ell_ {j , i}\\right)}{1 + \\sum_ {j ^ {\\prime} = 1} ^ {J} \\exp \\left(\\ell_ {j ^ {\\prime} , i}\\right)}, \\text {f o r} 1 \\leq i \\leq L, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.892, + 0.75 + ], + "angle": 0, + "content": "where the additional 1 in the denominator is included for the case where word \\( i \\) does not belong to any noun-associated segments. The word mask \\( M^t \\) for noun \\( N_j \\) is produced." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.751, + 0.893, + 0.901 + ], + "angle": 0, + "content": "According to the softmax function defined in Eq. 3, we get the probabilities of word \\(i\\) over \\(J + 1\\) cases, namely belonging to one of the \\(J\\) noun-associated segments or none of them. We compile a pseudo label vector \\(\\mathbf{p} = \\{p_i\\} \\in \\{0,1\\}^L\\), where \\(p_i\\) takes value 1 if word \\(i\\) belonging to the \\(j\\)th noun-associated segment gets the highest probability, and 0 otherwise. We develop the text segmentation loss \\(\\mathcal{L}_{\\mathrm{seg}}^t\\), which is the cross-entropy loss on the word mask \\(M^t\\) with respect to the pseudo label vector \\(\\mathbf{p}\\), and can help learn the text segmenter \\(F^t\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26797" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.32, + 0.108 + ], + "angle": 0, + "content": "3.3. Region-Word Highlighting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.19 + ], + "angle": 0, + "content": "We present a prompt learning method to reliably extract features from an image region or a word segment using a vision-language model. Specifically, we propose a region-highlighting prompt learning method and a word-highlighting prompt learning method, as shown in Fig. 2b." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.194, + 0.473, + 0.39 + ], + "angle": 0, + "content": "Region highlighting prompt. When the region mask \\( M^v \\) is directly applied to the image \\( X^v \\) via \\( M^v * X^v \\), where \\( * \\) denotes the element-wise multiplication operation, it makes specific regions of the image being zeroed out, resulting in what we refer to as blank areas. When a pre-trained vision-language model like CLIP is applied to these areas, the domain distribution may shift due to the introduction of zero tokens, which are unseen in natural images. To mitigate this issue, we introduce a region highlighting prompt, which is a learnable, universal image representation, denoted by \\( P^v \\). This representation is used alongside the original image in the process of feature extraction. The highlighted image is then obtained via" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.4, + 0.47, + 0.417 + ], + "angle": 0, + "content": "\\[\nH ^ {v} = X ^ {v} * M ^ {v} + P ^ {v} * \\left(1 - M ^ {v}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.47, + 0.471 + ], + "angle": 0, + "content": "In this way, the blank areas are filled with the corresponding areas of the region prompt \\( P^v \\) alleviating the unfavorable effect of domain shift." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.473, + 0.598 + ], + "angle": 0, + "content": "Word highlighting prompt. A similar challenge arises in the text domain when applying the word mask \\( M^t \\) to text \\( X^t \\). The resultant zero tokens in the masked part unintentionally carry meanings of specific words, leading to potential inaccuracies. To mitigate this issue, we introduce a word highlighting prompt, represented as a learnable, universal text representation \\( P^t \\). The highlighted text \\( H^t \\) is obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.606, + 0.47, + 0.623 + ], + "angle": 0, + "content": "\\[\nH ^ {t} = X ^ {t} * M ^ {t} + P ^ {t} * (1 - M ^ {t}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.664 + ], + "angle": 0, + "content": "Since the masked part is filled with content from \\( P^t \\), the risk of including unexpected text meanings is reduced." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.671, + 0.304, + 0.687 + ], + "angle": 0, + "content": "3.4. Region-Word Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.47, + 0.756 + ], + "angle": 0, + "content": "In the following, we describe how our method achieves region-word alignment. Our objective is to optimize mutual evidence between the highlighted object regions and the highlighted word segments, as illustrated in Fig. 2c." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.759, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Contrastive loss on highlighted region-word pairs. To achieve region-word alignment, we compute the highlighted region embedding \\(\\mathbf{e}^v\\) and highlighted word segment embedding \\(\\mathbf{e}^t\\) from the highlighted region-word pair by using the image and text encoders of CLIP by" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.844, + 0.469, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} ^ {v} = E ^ {v} \\left(H ^ {v}\\right) \\text {a n d} \\mathbf {e} ^ {t} = E ^ {t} \\left(H ^ {t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(E^v\\) and \\(E^t\\) are the CLIP image and text encoders, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.274 + ], + "angle": 0, + "content": "We adopt batch optimization for model training. Each batch has several triplets, each of which is composed of an image, its paired text, and a randomly selected noun from the text. Each triplet yields a region embedding and a word embedding via Eq. 6. Suppose that there are \\( B \\) triplets in this batch. We create a similarity matrix \\( S = [S_{i,j}] \\in \\mathbb{R}^{B \\times B} \\), where \\( S_{i,j} \\) stores the cosine similarity between the \\( i \\)th region embedding \\( \\mathbf{e}_i^v \\) and the \\( j \\)th word segment embedding \\( \\mathbf{e}_j^t \\). We adopt the symmetric version of InfoNCE loss to develop the highlighted region-word pair contrastive loss, which enhances the similarity of related region-word pairs while reducing it for unrelated pairs:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.284, + 0.892, + 0.372 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {h c l}} = - \\frac {1}{2 B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp (S _ {i , i} / \\tau)}{\\sum_ {j = 1} ^ {B} \\exp (S _ {i , j} / \\tau)} \\\\ - \\frac {1}{2 B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(S _ {i , i} / \\tau\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(S _ {j , i} / \\tau\\right)}, \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.457 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a learnable temperature. Notably, even though nouns may be selected multiple times across image-caption pairs, the corresponding highlighted regions \\(H^v\\) and highlighted texts \\(H^t\\) vary, ensuring the effectiveness of the InfoNCE loss in precise region-word alignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Loss functions and optimization. In sum, the proposed network for image-text co-decomposition is optimized using a composite loss that combines the knowledge-guided, image segmentation, text segmentation, and highlighted region-word pair contrastive losses, defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.548, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {\\mathrm {k g}} \\mathcal {L} _ {\\mathrm {k g}} + \\lambda_ {\\mathrm {s e g}} ^ {v} \\mathcal {L} _ {\\mathrm {s e g}} ^ {v} + \\lambda_ {\\mathrm {s e g}} ^ {t} \\mathcal {L} _ {\\mathrm {s e g}} ^ {t} + \\lambda_ {\\mathrm {h c l}} \\mathcal {L} _ {\\mathrm {h c l}}. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.719, + 0.592 + ], + "angle": 0, + "content": "3.5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We utilize NLTK's [2] part-of-speech tagging algorithm for noun selection. For image segmentation, we utilize TCL's image segmenter [5] to generate image masks, and we adopt the training loss in TCL, which relies solely on the image-capture pairs, to yield \\(\\mathcal{L}_{\\mathrm{seg}}^v\\). For text segmentation, we use a CLIP text encoder appended with two multi-head attention layers as the text segmenter \\(\\tilde{E}^t\\). Our model is trained on the CC3M and CC12M datasets. The resolution of input images is set to \\(224 \\times 224\\). For each forward pass of an image-text pair, we randomly select 2 nouns from the text. The loss weights are set as follows: \\(\\lambda_{\\mathrm{kg}} = 8.0\\), \\(\\lambda_{\\mathrm{seg}}^v = 1.0\\), \\(\\lambda_{\\mathrm{seg}}^t = 1.0\\), and \\(\\lambda_{\\mathrm{hcl}} = 0.5\\) in the experiments. We train the model with a batch size of 64 on four NVIDIA 2080Ti GPUs and with a learning rate of \\(5 \\times *10^{-6}\\) for a total of 50,000 iterations with 15,000 warmup steps and a cosine schedule. AdamW optimizer [29] is used with a weight decay of 0.05. To improve the quality of the predicted mask during the evaluation phase, we adopt the post-processing approach described in TCL [5], which uses pixel-adaptive mask refinement (PAMR) [1] for mask refinement." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26798" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.849, + 0.264 + ], + "angle": 0, + "content": "
MethodsPublicationDatasetVOCContextObjectStuffCityADEAvg.
GroupViT [45]CVPR 2022CC3M+CC12M+YFCC14M49.519.024.312.66.98.720.2
ViL-Seg [28]ECCV 2022CC12M37.318.918.1
ViewCo [36]ICLR 2023CC12M+YFCC14M52.423.023.5
OVSegmentor [46]CVPR 2023CC12M53.820.425.1
SimSeg [49]CVPR 2023CC3M+CC12M57.426.229.7
TCL [5]CVPR 2023CC3M+CC12M55.030.431.622.424.017.130.1
SegCLIP [30]ICML 2023CC3M + COCO52.624.726.5
CoCu [44]NeurIPS 2023CC3M+CC12M+YFCC14M51.423.622.715.222.112.324.6
PGSeg [51]NeurIPS 2023CC12M+RedCaps12M53.223.828.7
CoDe (Ours)CVPR 2024CC3M+CC12M57.730.532.323.928.917.731.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.271, + 0.892, + 0.354 + ], + "angle": 0, + "content": "Table 1. Text-supervised semantic segmentation performance comparison in terms of mIoU. The proposed method is compared with nine SOTA methods on six popular semantic segmentation datasets: PASCAL VOC (VOC), PASCAL Context (Context), COCO-Object (Object), COCO-Stuff (Stuff), Cityscapes (City) and ADE20K (ADE). For each compared method, the dataset column lists its training datasets. Several methods used datasets in addition to CC3M and CC12M, such as YFCC14M, COCO and RedCaps12M. When applicable, we also provide an average mIoU across all six datasets. For each dataset, the best method is indicated by bold fonts, whereas the second best method is underlined." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.369, + 0.21, + 0.386 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.394, + 0.367, + 0.41 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.469, + 0.462 + ], + "angle": 0, + "content": "We utilize image-text datasets to train our proposed model and perform extensive experiments on six commonly used semantic segmentation benchmarks to validate our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.469, + 0.538 + ], + "angle": 0, + "content": "Training datasets. We trained our model on two image-text datasets, Conceptual Captions 3M (CC3M) [37] and Conceptual 12M (CC12M) [6] containing 3M and 12M image-text pairs respectively. They have been widely adopted for training text-supervised semantic segmentation methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.469, + 0.869 + ], + "angle": 0, + "content": "Evaluation datasets. We used six zero-shot semantic segmentation benchmarks to validate the zero-shot transfer capability of our model on categories that were not specifically trained. As in previous work [5], the benchmarks can be categorized into two groups, with and without background classes. Benchmarks with a background generally label areas that do not belong to any predefined categories as \"background,\" which is usually removed by considering a probability threshold in text-supervised semantic segmentation. For this category, we use the validation split of the following datasets: PASCAL VOC 2012 [13], PASCAL Context [32], and COCO-Object [3]. They each contain 20, 59, and 80 foreground classes, respectively, with an additional background class. For the \"without background category,\" we evaluated our model with the validation split of COCO-Stuff [3], Cityscapes [10], and ADE20K [53] datasets. Each of them contains 171, 19, and 150 classes, respectively. In this category, all images are fully annotated, which is exceptionally challenging. Using datasets in this category, our model can be tested for its ability to recognize a variety of concepts. We employ mean intersection-over-union (mIoU) as our evaluation metric." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For zero-shot semantic segmentation evaluation, we rely solely on the image segmenter. The image segmenter pro" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.371, + 0.892, + 0.448 + ], + "angle": 0, + "content": "cesses the input image in conjunction with class names from each dataset to produce segmentation predictions. In accordance with the settings of prior work [5], we adopt the class names provided by the default version of MMSegmentation [9] and adhere to its post-processing methodology." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.459, + 0.74, + 0.475 + ], + "angle": 0, + "content": "4.2. Quantitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.649 + ], + "angle": 0, + "content": "We compare the proposed method with nine text-supervised semantic segmentation methods on the six datasets. Tab. 1 reports the mIoU values. The numbers have been taken directly from the original papers. All methods were tested on the three datasets of the \"with background class,\" but only three methods (GroupViT [45], CoCu [44] and TCL [5]) were tested on the dataset of the \"without background class.\" For those three methods, we also report their average mIoU values across all six datasets. It is also worth noting that these methods use different combinations of training datasets, as indicated in the dataset column of Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.772 + ], + "angle": 0, + "content": "Our method achieves the best performance in all six datasets, while TCL [5] and SimSeg [49] are the runners-up. In terms of average mIoU, our method (CoDe) achieves 31.8 whereas TCL achieves 30.1, resulting in a \\(5.65\\%\\) improvement. The result demonstrates the effectiveness of our image-text co-decomposition method in addressing the alignment-level train-test discrepancy that exists in previous methods by directly learning the region-word alignment." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.785, + 0.685, + 0.801 + ], + "angle": 0, + "content": "4.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Visual comparison with existing methods. Fig. 3 visually compares the segmentation results of our methods and two runners-up, TCL [5] and SimSeg [49], on the PASCAL VOC, PASCAL Context, and COCO Object datasets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This figure illustrates the fundamental benefit of our approach, which involves the direct learning of region-word" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26799" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.085, + 0.371, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.086, + 0.637, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.087, + 0.849, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparisons. The proposed method is compared with the two most competitive methods, TCL [5] and SimSeg [49], on PASCAL VOC, PASCAL Context, and COCO Object datasets. Our method provides more precise object boundaries and effectively localizes objects within images without misclassification, leading to more accurate segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.468, + 0.532 + ], + "angle": 0, + "content": "alignments. Our model effectively establishes a strong connection between object regions and word segments, allowing a better understanding of how objects are represented in images. Through this enhanced understanding, both segmentation quality and localization capabilities can be improved. As a result, our method provides more accurate classification and more precise masks than other methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.468, + 0.639 + ], + "angle": 0, + "content": "The SimSeg[49] model, which learns from image-text alignments, occasionally assigns objects to the wrong classes. On the other hand, TCL [5], which is based on region-text alignment, produces coarser semantic masks. Accordingly, these observed limitations are most likely a result of the alignment-level discrepancy between the train and test, which may lead to suboptimal performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.794 + ], + "angle": 0, + "content": "Visualization of image-text co-segmentation results. Fig. 4 presents a visualization of the results obtained by our model. We denote regions and word segments associated with the different nouns in the corresponding colors. It demonstrates that our method effectively segments object regions within images based on various input nouns. It simultaneously segments corresponding word segments within the associated text, creating a harmonious alignment between the object region and the word segment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The region-word alignment plays a pivotal role in our approach, serving as a supervisory signal for the model. By taking advantage of this alignment, our model not only performs visual localization but also captures correlations within the language domain. It indicates that our trained model possesses a more comprehensive understanding of the segmentation task." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.424, + 0.89, + 0.508 + ], + "angle": 0, + "content": "
C.W.R.VOCContextObjectStuffCityADEAvg.
54.427.632.722.525.016.629.8
✓56.229.232.923.327.517.031.0
✓✓56.129.332.623.629.017.331.3
✓✓✓57.730.532.323.928.917.731.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.519, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Table 2. Ablation study. The baseline model is augmented with the image-text co-decomposition method (C.), the word highlighting prompt (W.), and the region highlighting prompt (R.), one at a time. We report the mIoU values of the resultant models on the six datasets and their averages." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.652, + 0.618 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Contributions of individual components. The ablation study in Tab. 2 assesses the contribution of the proposed components, including the image-text co-decomposition method, the word highlighting prompt, and the region highlighting prompt. Without the co-decomposition method, our baseline model only trains the image segmenter, resulting in an average mIoU of 29.8. Afterward, each proposed component is added to the baseline model one at a time to verify its contribution. As a result of adding the image-text co-decomposition module alone, the average mIoU has been increased to 31.0. It suggests that the image-text co-decomposition method can achieve region-word alignment and enhance localization capability. The model is further enhanced with the addition of word highlighting prompts and image highlighting prompts, resulting in further performance improvement. It demonstrates that the highlighting prompt learning method enhances feature extraction and strengthens alignment between regions and words." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "26800" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.079, + 0.212, + 0.102 + ], + "angle": 0, + "content": "this was her hair... it was beautiful, as you will see" + }, + { + "type": "image_caption", + "bbox": [ + 0.226, + 0.086, + 0.339, + 0.097 + ], + "angle": 0, + "content": "An old book lying open." + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.079, + 0.483, + 0.103 + ], + "angle": 0, + "content": "A black bear walks through dense vegetation." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.105, + 0.213, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.105, + 0.349, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.105, + 0.485, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.08, + 0.603, + 0.103 + ], + "angle": 0, + "content": "an ostrich egg laying on the grass" + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.08, + 0.751, + 0.102 + ], + "angle": 0, + "content": "2 large dogs posing on the beach at sunset" + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.08, + 0.885, + 0.102 + ], + "angle": 0, + "content": "A girl's hand holding fresh white flowers" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.209, + 0.213, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.312, + 0.208, + 0.337 + ], + "angle": 0, + "content": "this was her hair... it wasbeautiful, as you will see" + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.209, + 0.349, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.227, + 0.319, + 0.337, + 0.332 + ], + "angle": 0, + "content": "An old book lying open." + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.209, + 0.484, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.313, + 0.483, + 0.337 + ], + "angle": 0, + "content": "A black bear walks through dense vegetation." + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.105, + 0.619, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.209, + 0.618, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.312, + 0.602, + 0.337 + ], + "angle": 0, + "content": "an ostrich egg laying on the grass" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.105, + 0.754, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.209, + 0.754, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.311, + 0.751, + 0.337 + ], + "angle": 0, + "content": "2 large dogs posing on the beach at sunset" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.105, + 0.89, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.209, + 0.89, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.311, + 0.885, + 0.337 + ], + "angle": 0, + "content": "A girl's hand holding fresh white flowers" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.894, + 0.409 + ], + "angle": 0, + "content": "Figure 4. Visualization of the results of our image-text co-decomposition method. The first two rows display text and images, representing input image-text pairs. In each text, nouns are underlined with different colors. Our method uses these nouns as queries for performing image-text co-decomposition. Using our image-text co-decomposition method, the last two rows depict the method's output, where regions and word segments associated with different nouns appear in corresponding colors." + }, + { + "type": "table", + "bbox": [ + 0.137, + 0.428, + 0.408, + 0.473 + ], + "angle": 0, + "content": "
λhcl0.050.10.250.50.751.0
Avg.30.631.231.731.831.530.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.483, + 0.47, + 0.525 + ], + "angle": 0, + "content": "Table 3. Sensitivity analysis on the hyperparameter \\( \\lambda_{\\mathrm{hcl}} \\). By varying \\( \\lambda_{\\mathrm{hcl}} \\), we examine the corresponding average mIoU values of all six datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Hyperparameter sensitivity analysis. Tab. 3 investigates the impact of the loss weight for the highlighted region-word pair contrastive loss, denoted as \\(\\lambda_{\\mathrm{hcl}}\\) in Eq. (8). We observe that, when we apply the highlighted region-word pair contrastive loss in our training phase, the performance consistently outperforms our baseline model. The method is robust to the parameter to some degree as it achieves reasonable performance for a wide range of values. When \\(\\lambda_{\\mathrm{hcl}}\\) is set to 0.5, our model achieves a peak score of 31.8. It is evident from these results that the image-text co-decomposition method is superior to the image-text decomposition method for achieving region-word alignment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of jointly decomposing text. We validate the effectiveness of decomposing text by assessing the performance enhancement achieved by generating word masks, as opposed to simply using extracted nouns. This experiment is conducted by modifying the calculation of \\(\\mathcal{L}_{\\mathrm{hcl}}\\). Instead of using word segment embeddings as mentioned in Sec. 3.4, we opt to compute the similarity matrix \\(S\\) using region embeddings with the embeddings of individual nouns. The average mIoU across all benchmarks is" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.892, + 0.507 + ], + "angle": 0, + "content": "\\(30.2\\%\\), which is below our method's \\(31.8\\%\\). This indicates the benefits of using word segments encompassing extra words associated with each noun. The contextual information encoded in these additional words can serve as valuable supervisory signals, thereby improving performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.627, + 0.536 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.772 + ], + "angle": 0, + "content": "We propose Image-Text Co-Decomposition (CoDe) to address cross-domain alignment discrepancies in the existing methods for text-supervised semantic segmentation. First, our method decomposes image-text pairs into corresponding regions and word segments to enforce the region-word alignment. CoDe, underpinned by contrastive learning, alleviates the train-test discrepancy by unifying image-text and region-text alignments to region-word alignment. Then, we introduce a region-highlighting prompt learning method to enhance feature extraction on masked images or texts for precise region-word alignment. Moreover, CoDe surpasses state-of-the-art methods in zero-shot semantic segmentation across six benchmark datasets. This novel approach opens new possibilities for research in vision-language models and their broader applications in computer vision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.681, + 0.803 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by the National Science and Technology Council (NSTC) under grants 112-2221-E-A49-090-MY3, 111-2628-E-A49-025-MY3, 112-2634-F-002-005, 112-2634-F-002-006, and 110-2221-E-002-124-MY3, and NTU under grants 112L9009. 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Existing methods have demonstrated that contrastive learning on image-text pairs effectively aligns visual segments with the meanings of texts. We notice that there is a discrepancy between text alignment and semantic segmentation: A text often consists of multiple semantic concepts, whereas semantic segmentation strives to create semantically homogeneous segments. To address this issue, we propose a novel framework, Image-Text Co-Decomposition (CoDe), where the paired image and text are jointly decomposed into a set of image regions and a set of word segments, respectively, and contrastive learning is developed to enforce region-word alignment. To work with a vision-language model, we present a prompt learning mechanism that derives an extra representation to highlight an image segment or a word segment of interest, with which more effective features can be extracted from that segment. Comprehensive experimental results demonstrate that our method performs favorably against existing text-supervised semantic segmentation methods on six benchmark datasets. The code is available at https://github.com/072jiajia/image-text-co-decomposition. + +# 1. Introduction + +Semantic segmentation is essential to various applications [11, 15, 50] in computer vision but is hindered by several critical challenges. First, the expensive cost of acquiring pixel-level annotations limits the applicability of fully supervised semantic segmentation methods. Second, most existing methods [40, 43, 52] are developed to work on predefined categories and leave themselves inapplicable to rare or unseen concepts described by free-form text. To address these obstacles, a new research direction has emerged in vision-language models, referred to as text-supervised semantic segmentation [5, 28, 44-46, 49]. This task devel + +ops segmentation models capable of assigning labels across large vocabularies of concepts and supporting semantic segmentation model training without pixel-wise annotations. + +Fig. 1 compares existing methods for text-supervised semantic segmentation by grouping their cross-domain alignment mechanisms into three categories, including image-text, region-text, and region-word alignment. Despite the differences, most of these methods compensate for the lack of pixel-wise annotations on broad semantic concepts by exploring abundant image-text pairs on the internet. The textual descriptions bring extensive knowledge across diverse categories. Thus, existing methods typically apply a vision-language model such as CLIP [34] to textual descriptions to acquire the semantic context of the corresponding images for segmentation model learning. + +The image-text alignment is widely adopted in the literature e.g. [28, 44, 45]. As depicted in Fig. 1a, methods of this group derive an image encoder and a text encoder by aligning them in a joint embedding space. They then use their proposed zero-shot transfer techniques to enable the two encoders to predict segmentation output. Despite the simplicity, they introduce unfavorable discrepancies between the training and testing phases since we aim to match the semantic features from the text to the corresponding image segments rather than the whole image during testing. + +To mitigate this issue, the region-text alignment is explored. As shown in Fig. 1b, methods of this group such as [5] utilize a pre-trained visual-language model to derive an additional image segmenter that discovers concepts described by the text. They enforce the consistency between the segmented region and the text but suffer from the discrepancy between the region-text alignment and semantic segmentation: A text may consist of multiple concepts, such as pub, night, and car in Fig. 1b, while semantic segmentation aims to identify regions of the same concept. + +To address the aforementioned issues in the image-text and region-text alignments, we propose a novel framework, Image-Text Co-Decomposition (CoDe), to achieve region-word alignment. As illustrated in Fig. 1c, we utilize a + +![](images/533c862118c3b5d148049e3f67e9bc9ba30a274fc7591db532b7f739a96d4b31.jpg) +(a) image-text alignment + +![](images/6292faa41fcb02c2b3e6d6839970cb3dbe6d219fcab2ab9571590d236ffeb3d4.jpg) +(b) region-text alignment +Figure 1. Existing methods perform text-supervised semantic segmentation by learning either (a) image-text alignment or (b) region-text alignment. This paper presents (c) region-word alignment via image-text co-decomposition, where the image and the text are decomposed into object regions and word segments, respectively, while contrastive learning is used to establish cross-modal correspondences between these image and word segments. + +![](images/6f50b2b6498792b54c3c9415caa28b4d4d0cd5d254d577327561475640bd2272.jpg) +(c) region-word alignment (ours) + +visual-language model to construct an image segmenter and a text segmenter: The former decomposes an image into image segments, while the latter decomposes a text into word segments. In addition, there exist one-to-one correspondence between image and word segments. This way, the discrepancy between training and testing is alleviated since each image segment is derived from a single concept given by the corresponding word segment. + +The proposed CoDe framework comprises four components: an image segmenter, a text segmenter, a region-word alignment module, and a prompt learning module. We randomly select nouns in the text. For each selected noun e.g., "car", the image segmenter identifies the image segment that matches the noun, i.e., the region of the car, while the text segmenter discovers the corresponding word segment, i.e., "red cars." The region-word alignment is developed to enforce the consensus between the image and word segments. To better work with a vision-language model, we present a prompt learning module to derive an extra representation, enabling more effective feature extraction. + +The main contributions of this work are as follows: + +- We propose a new framework, Image-Text Co-Decomposition (CoDe), to learn the region-word alignment for eliminating train-test and image-text discrepancies, facilitating text-supervised semantic segmentation. +- We propose a prompt learning method to address domain shift issues arising from blank areas during the highlighting process and enhance the alignment between highlighted regions and highlighted words. +- Our method effectively carries out zero-shot semantic segmentation and performs favorably against the state-of-the-art methods on six benchmark datasets. + +# 2. Related Works + +# 2.1. Open-Vocabulary Semantic Segmentation + +Open-vocabulary semantic segmentation focuses on segmenting any concepts within images, even those unseen during training, based solely on textual descriptions. Its three important branches are discussed as follows: + +Semi-supervised setting with mask-annotations. Methods of this group such as [16, 17, 24, 26, 31, 47] learn from dense annotations to produce high-quality segmentation masks, and then utilize image-text pairs and pre-trained vision-language models to extend the segmentation capability to a larger target vocabulary. Despite the remarkable results, these methods are hindered by their reliance on costly dense annotations, posing a challenge in cases where such annotations are difficult to obtain. + +Training-free methods. Another line of research e.g. [38, 41, 54] makes the most of large pre-trained models for open-vocabulary segmentation without training. MaskCLIP [54] introduces a modification to the final layer of the CLIP image encoder, yielding dense feature maps that could be employed as initial segmentation maps for further refinement. ReCo [38] constructs an image archive and makes use of retrieval and co-segmentation to identify co-occurrence regions among a specific category. Although these methods eliminate the process of training, the results exhibit significant room for improvement, which shows the need for additional supervision to accomplish this task. + +Text-supervised semantic segmentation. It strikes a balance between the two aforementioned branches. Methods of this group are discussed in detail in the following because our method belongs to this group. + +# 2.2. Text-Supervised Semantic Segmentation + +Text-supervised semantic segmentation [4, 5, 28, 33, 36, 42, 44-46, 49] decomposes an image into semantic regions according to text descriptions. Unlike semi-supervised methods relying on a few images with mask annotations during training, methods of this group aim to learn semantic masks solely from text-based guidance. We roughly divide existing methods into two categories based on their cross-modal alignment between the image and text domains. + +Image-text alignment. These methods train an image encoder alongside a text encoder to align pairs of image and text in a joint embedding space. They use zero-shot transfer to enable the encoders to produce segmentation results. GroupViT [45] introduces a bottom-up approach within + +Transformers, grouping image patches into regions and utilizing object semantics derived from texts to guide training. SimSeg [49] further introduces a pretraining method that densely aligns visual and language representations, enabling the trained image encoder to generate segmentation masks in a zero-shot manner. + +Region-text alignment. Another line of research targets at aligning the embedding of a region, instead of the whole image, with text descriptions. For instance, TCL [5] learns to segment specific regions within an image while ensuring consistency between the segmented region and the original text. It enables the model to segment the relevant region described in the text. + +These methods for text-supervised semantic segmentation have shown that employing vision-language models and contrastive learning on image-text pairs enables aligning visual concepts with the meaning of the whole text. We notice that a text is usually a mix of multiple semantic concepts, but semantic segmentation aims to discover semantically homogeneous segments. To address this issue, inspired by the region-word matching techniques [8, 21, 22, 39] for cross-modal retrieval, we introduce image-text co-decomposition, where the image and the text are decomposed into image and word segments, respectively, and contrastive learning is adopted to enforce cross-modal consensus between these image and word segments. It turns out that image-text co-decomposition results in consistent performance gains on multiple benchmarks. + +# 2.3. Prompt Tuning for Vision-Language Models + +Emerged from natural language processing [23, 25, 27], prompt tuning focuses on parameter-efficient adaptation of large pre-trained models to new tasks. In computer vision [20, 55-57], pioneering work such as CoOp [55, 56] incorporates learnable tokens into the CLIP text encoder, enhancing the classification task performance. Recent studies e.g. [12, 14, 35] leverage prompt tuning in the text modality for extending CLIP's capabilities to various applications such as detection and segmentation tasks. Notably, prompt learning methods are also applicable to the visual domain. VPT [19] employs prompt tuning in the visual modality by inserting learnable vectors into Vision Transformers. Further studies [18, 26] explore tuning methods that directly incorporate learnable prompts into the input image within the RGB domain to address downstream tasks. + +Drawing inspiration from the success of these methods, our method leverages the capabilities of prompt tuning on segment feature extraction in both the visual and text domains. Prompt learning is beneficial in this work when applying contrastive learning to the visual and textual features extracted by a vision-language model. + +# 3. Methodology + +In this section, we first provide an overview of our method for image-text co-decomposition and define the notations in Sec. 3.1. Then, we specify the three major modules of our method, including 1) the image-text co-segmentation module in Sec. 3.2, 2) the region-word highlighting module in Sec. 3.3, and 3) the region-word alignment module in Sec. 3.4. These modules work harmoniously to address the region-word alignment for text-supervised semantic segmentation and enhance model performances. Finally, implementation details are given in Sec. 3.5. + +# 3.1. Method Overview + +Image-text co-decomposition enables text-supervised segmenters to learn region-word consensus when segmenting an image $X^v$ with a paired text $X^t$ . Our method aims to jointly learn an image segmenter $F^v$ and a text segmenter $F^t$ with solely the supervision from a set of $K$ image-text pairs, $D = \{X_k^v, X_k^t\}_{k=1}^K$ , where no annotations are given. In addition, we optimize two learnable prompts, including a region prompt $P^v$ and a word prompt $P^t$ , to alleviate the unfavorable effect of blank embeddings caused by applying a vision-language model to masked images or texts for feature extraction. + +Fig. 2 illustrates the pipeline of our method, consisting of three modules, including the image-text co-segmentation, region-word highlighting, and region-word alignment modules. For an input image-text pair $(X^v, X^t)$ , we initiate the process by randomly selecting a noun $N$ , e.g., balloon in the figure, from the text $X^t$ using the noun selector [2]. This selected noun serves as a query. We take the query $N$ along with the image $X^v$ as input to the image segmenter $F^v$ to generate the region mask $M^v$ showing the estimated object region specified by the query. Similarly, a text segmenter $F^t$ takes the query $N$ and the text $X^t$ as input and estimates the word mask $M^t$ indicating the associated word segment. + +Subsequently, we apply the region mask $M^v$ to the image $X^v$ to crop the estimated object region. For the estimated background, i.e., the region outside the mask $M^v$ , we crop the corresponding region from the learned region prompt $P^v$ . The highlighted image $H^v$ is yielded by combining the cropped object and background regions. Similarly, the highlighted text $H^t$ is generated by combining the text $X^t$ inside the mask $M^t$ and the word prompt $P^t$ outside the mask $M^t$ . We extract features from the highlighted image and text by using the image encoder $E^v$ and the text encoder $E^t$ of CLIP [34], respectively. The procedure is repeated for each image-text pair and each selected noun. It follows that the region-word alignment is accomplished by contrastive learning [7]. Four loss functions, including $\mathcal{L}_{\mathrm{kg}}$ , $\mathcal{L}_{\mathrm{seg}}^v$ , $\mathcal{L}_{\mathrm{seg}}^t$ , and $\mathcal{L}_{\mathrm{hcl}}$ , are used for network optimization, and will be elaborated in the following. + +![](images/a44ccf30a62c597ef517b469d555959d32ed3b45c15196a689b78f0799583e17.jpg) +Figure 2. Training pipeline of our method for image-text co-decomposition. Our method consists of three major modules, including (a) the image-text co-segmentation module where the image and text segmenters estimate the region and word masks according to a selected noun, respectively, (b) the region-word highlighting module where the estimated masks together with two learnable prompts produce the highlighted image and text, and (c) the region-word alignment module where contrastive learning is applied to the embedded object regions and word segments to accomplish region-word alignment. + +![](images/cbf37813fb086eb30a52926767877fcecd44fe1167cf01a0f5279aee3b38a99b.jpg) + +![](images/4ed54001dd407076b0c2964f4486f0ad59940bdbd07b11a64c3f62968e437034.jpg) + +# 3.2. Image-Text Co-Segmentation + +The image-text co-segmentation module comprises a noun selector, an image segmenter, and a text segmenter, as shown in Fig. 2a. Taking an image-text pair $(X^v, X^t)$ as input, this module aims at jointly identifying an object region in image $X^v$ and its accompanying word segment in text $X^t$ according to a randomly selected noun. + +To begin with, we employ the noun selector [2], which takes the text $X^t$ as input and extracts a set of $J$ nouns, $\{N_j\}_{j=1}^J$ , in $X^t$ . For each noun $N_j$ , we carry out region mask generation, where the image segmenter $F^v$ predicts a region mask $M^v$ specifying the area in image $X^v$ relevant to noun $N_j$ . A similar task word mask generation is performed by the text segmenter $F^t$ , which seeks a word mask $M^t$ matching noun $N_j$ . The tasks of region and word mask generation are depicted as follows. + +Region mask generation. The image segmenter $F^v$ takes image $X^v$ and noun $N_j$ as input. It encodes the image into a pixel-wise embedding $\mathbf{x}^v \in \mathbb{R}^{H \times W \times C}$ , where $H \times W$ is the image resolution and $C$ is the channel dimension. We also compute the noun embedding $\mathbf{n}_j \in \mathbb{R}^C$ for noun $N_j$ . The image segmenter generates a region mask $M^v \in \mathbb{R}^{H \times W}$ by performing the dot product between the noun embedding $\mathbf{n}_j$ and every location of the image embedding $\mathbf{x}^v$ . + +In this work, we use the image segmentation model in [5] to serve as the image segmenter $F^v$ , and employ its corresponding loss, denoted by $\mathcal{L}_{\mathrm{seg}}^v$ here, to help derive the image segmenter. This loss considers segment regularization and contrastive learning that can be directly applied to the segmentation results along with the noun embedding. We use the KgCoOp method [48] to obtain the noun embedding $\mathbf{n}_j$ , as it avoids the pitfalls of improper prompt selection. It appends learnable context tokens to the noun, forming pseudo-sentences for optimal prompt tuning. The noun embedding loss $\mathcal{L}_{\mathrm{kg}}$ [48] is included to improve the accuracy of these embeddings, i.e., + +$$ +\mathcal {L} _ {\mathrm {k g}} = \left| \left| \mathbf {n} _ {j} - \mathbf {n} _ {j} ^ {\prime} \right| \right| _ {2} ^ {2}, \tag {1} +$$ + +where the $\mathbf{n}_j^{\prime}\in \mathbb{R}^{C}$ represents the knowledge-guided noun embedding generated from hand-crafted prompts such as "a photo of a $N_{j}$ " using the text encoder. + +Word mask generation. The text segmenter $F^t$ takes the text $X^t$ and the noun $N_j$ as input. For text feature extraction, we consider the CLIP text encoder appended with two learnable multi-head attention layers. With the resultant feature extractor $\tilde{E}^t$ , the word-wise features of text $X^t$ are obtained via $\mathbf{x}^t = \tilde{E}^t(X^t) \in \mathbb{R}^{L \times C}$ , where $L$ is the text length, i.e., the number of word tokens. The word-specific logits $\ell_j = [\ell_{j,i}]_{i=1}^L \in \mathbb{R}^L$ for noun $N_j$ are computed via + +$$ +\ell_ {j} = w \cdot \mathbf {x} ^ {t} \mathbf {n} _ {j} + b, \tag {2} +$$ + +where $w$ and $b$ are two learnable parameters, and $\mathbf{n}_j\in \mathbb{R}^C$ is the noun embedding. + +Since each word in text $X^t$ belongs to either one of the $J$ word segments associated with nouns $\{N_j\}_{j=1}^J$ or none of them, the word mask $M^t = [m_i^t]_{i=1}^L \in \mathbb{R}^L$ for noun $N_j$ is obtained by applying the softmax function over all the $J$ noun-associated segments, i.e., + +$$ +m _ {i} ^ {t} = \frac {\exp \left(\ell_ {j , i}\right)}{1 + \sum_ {j ^ {\prime} = 1} ^ {J} \exp \left(\ell_ {j ^ {\prime} , i}\right)}, \text {f o r} 1 \leq i \leq L, \tag {3} +$$ + +where the additional 1 in the denominator is included for the case where word $i$ does not belong to any noun-associated segments. The word mask $M^t$ for noun $N_j$ is produced. + +According to the softmax function defined in Eq. 3, we get the probabilities of word $i$ over $J + 1$ cases, namely belonging to one of the $J$ noun-associated segments or none of them. We compile a pseudo label vector $\mathbf{p} = \{p_i\} \in \{0,1\}^L$ , where $p_i$ takes value 1 if word $i$ belonging to the $j$ th noun-associated segment gets the highest probability, and 0 otherwise. We develop the text segmentation loss $\mathcal{L}_{\mathrm{seg}}^t$ , which is the cross-entropy loss on the word mask $M^t$ with respect to the pseudo label vector $\mathbf{p}$ , and can help learn the text segmenter $F^t$ . + +# 3.3. Region-Word Highlighting + +We present a prompt learning method to reliably extract features from an image region or a word segment using a vision-language model. Specifically, we propose a region-highlighting prompt learning method and a word-highlighting prompt learning method, as shown in Fig. 2b. + +Region highlighting prompt. When the region mask $M^v$ is directly applied to the image $X^v$ via $M^v * X^v$ , where $*$ denotes the element-wise multiplication operation, it makes specific regions of the image being zeroed out, resulting in what we refer to as blank areas. When a pre-trained vision-language model like CLIP is applied to these areas, the domain distribution may shift due to the introduction of zero tokens, which are unseen in natural images. To mitigate this issue, we introduce a region highlighting prompt, which is a learnable, universal image representation, denoted by $P^v$ . This representation is used alongside the original image in the process of feature extraction. The highlighted image is then obtained via + +$$ +H ^ {v} = X ^ {v} * M ^ {v} + P ^ {v} * \left(1 - M ^ {v}\right). \tag {4} +$$ + +In this way, the blank areas are filled with the corresponding areas of the region prompt $P^v$ alleviating the unfavorable effect of domain shift. + +Word highlighting prompt. A similar challenge arises in the text domain when applying the word mask $M^t$ to text $X^t$ . The resultant zero tokens in the masked part unintentionally carry meanings of specific words, leading to potential inaccuracies. To mitigate this issue, we introduce a word highlighting prompt, represented as a learnable, universal text representation $P^t$ . The highlighted text $H^t$ is obtained by + +$$ +H ^ {t} = X ^ {t} * M ^ {t} + P ^ {t} * (1 - M ^ {t}). \tag {5} +$$ + +Since the masked part is filled with content from $P^t$ , the risk of including unexpected text meanings is reduced. + +# 3.4. Region-Word Alignment + +In the following, we describe how our method achieves region-word alignment. Our objective is to optimize mutual evidence between the highlighted object regions and the highlighted word segments, as illustrated in Fig. 2c. + +Contrastive loss on highlighted region-word pairs. To achieve region-word alignment, we compute the highlighted region embedding $\mathbf{e}^v$ and highlighted word segment embedding $\mathbf{e}^t$ from the highlighted region-word pair by using the image and text encoders of CLIP by + +$$ +\mathbf {e} ^ {v} = E ^ {v} \left(H ^ {v}\right) \text {a n d} \mathbf {e} ^ {t} = E ^ {t} \left(H ^ {t}\right), \tag {6} +$$ + +where $E^v$ and $E^t$ are the CLIP image and text encoders, respectively. + +We adopt batch optimization for model training. Each batch has several triplets, each of which is composed of an image, its paired text, and a randomly selected noun from the text. Each triplet yields a region embedding and a word embedding via Eq. 6. Suppose that there are $B$ triplets in this batch. We create a similarity matrix $S = [S_{i,j}] \in \mathbb{R}^{B \times B}$ , where $S_{i,j}$ stores the cosine similarity between the $i$ th region embedding $\mathbf{e}_i^v$ and the $j$ th word segment embedding $\mathbf{e}_j^t$ . We adopt the symmetric version of InfoNCE loss to develop the highlighted region-word pair contrastive loss, which enhances the similarity of related region-word pairs while reducing it for unrelated pairs: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {h c l}} = - \frac {1}{2 B} \sum_ {i = 1} ^ {B} \log \frac {\exp (S _ {i , i} / \tau)}{\sum_ {j = 1} ^ {B} \exp (S _ {i , j} / \tau)} \\ - \frac {1}{2 B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(S _ {i , i} / \tau\right)}{\sum_ {j = 1} ^ {B} \exp \left(S _ {j , i} / \tau\right)}, \tag {7} \\ \end{array} +$$ + +where $\tau$ is a learnable temperature. Notably, even though nouns may be selected multiple times across image-caption pairs, the corresponding highlighted regions $H^v$ and highlighted texts $H^t$ vary, ensuring the effectiveness of the InfoNCE loss in precise region-word alignment. + +Loss functions and optimization. In sum, the proposed network for image-text co-decomposition is optimized using a composite loss that combines the knowledge-guided, image segmentation, text segmentation, and highlighted region-word pair contrastive losses, defined as follows: + +$$ +\mathcal {L} = \lambda_ {\mathrm {k g}} \mathcal {L} _ {\mathrm {k g}} + \lambda_ {\mathrm {s e g}} ^ {v} \mathcal {L} _ {\mathrm {s e g}} ^ {v} + \lambda_ {\mathrm {s e g}} ^ {t} \mathcal {L} _ {\mathrm {s e g}} ^ {t} + \lambda_ {\mathrm {h c l}} \mathcal {L} _ {\mathrm {h c l}}. \tag {8} +$$ + +# 3.5. Implementation Details + +We utilize NLTK's [2] part-of-speech tagging algorithm for noun selection. For image segmentation, we utilize TCL's image segmenter [5] to generate image masks, and we adopt the training loss in TCL, which relies solely on the image-capture pairs, to yield $\mathcal{L}_{\mathrm{seg}}^v$ . For text segmentation, we use a CLIP text encoder appended with two multi-head attention layers as the text segmenter $\tilde{E}^t$ . Our model is trained on the CC3M and CC12M datasets. The resolution of input images is set to $224 \times 224$ . For each forward pass of an image-text pair, we randomly select 2 nouns from the text. The loss weights are set as follows: $\lambda_{\mathrm{kg}} = 8.0$ , $\lambda_{\mathrm{seg}}^v = 1.0$ , $\lambda_{\mathrm{seg}}^t = 1.0$ , and $\lambda_{\mathrm{hcl}} = 0.5$ in the experiments. We train the model with a batch size of 64 on four NVIDIA 2080Ti GPUs and with a learning rate of $5 \times *10^{-6}$ for a total of 50,000 iterations with 15,000 warmup steps and a cosine schedule. AdamW optimizer [29] is used with a weight decay of 0.05. To improve the quality of the predicted mask during the evaluation phase, we adopt the post-processing approach described in TCL [5], which uses pixel-adaptive mask refinement (PAMR) [1] for mask refinement. + +
MethodsPublicationDatasetVOCContextObjectStuffCityADEAvg.
GroupViT [45]CVPR 2022CC3M+CC12M+YFCC14M49.519.024.312.66.98.720.2
ViL-Seg [28]ECCV 2022CC12M37.318.918.1
ViewCo [36]ICLR 2023CC12M+YFCC14M52.423.023.5
OVSegmentor [46]CVPR 2023CC12M53.820.425.1
SimSeg [49]CVPR 2023CC3M+CC12M57.426.229.7
TCL [5]CVPR 2023CC3M+CC12M55.030.431.622.424.017.130.1
SegCLIP [30]ICML 2023CC3M + COCO52.624.726.5
CoCu [44]NeurIPS 2023CC3M+CC12M+YFCC14M51.423.622.715.222.112.324.6
PGSeg [51]NeurIPS 2023CC12M+RedCaps12M53.223.828.7
CoDe (Ours)CVPR 2024CC3M+CC12M57.730.532.323.928.917.731.8
+ +Table 1. Text-supervised semantic segmentation performance comparison in terms of mIoU. The proposed method is compared with nine SOTA methods on six popular semantic segmentation datasets: PASCAL VOC (VOC), PASCAL Context (Context), COCO-Object (Object), COCO-Stuff (Stuff), Cityscapes (City) and ADE20K (ADE). For each compared method, the dataset column lists its training datasets. Several methods used datasets in addition to CC3M and CC12M, such as YFCC14M, COCO and RedCaps12M. When applicable, we also provide an average mIoU across all six datasets. For each dataset, the best method is indicated by bold fonts, whereas the second best method is underlined. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Settings + +We utilize image-text datasets to train our proposed model and perform extensive experiments on six commonly used semantic segmentation benchmarks to validate our method. + +Training datasets. We trained our model on two image-text datasets, Conceptual Captions 3M (CC3M) [37] and Conceptual 12M (CC12M) [6] containing 3M and 12M image-text pairs respectively. They have been widely adopted for training text-supervised semantic segmentation methods. + +Evaluation datasets. We used six zero-shot semantic segmentation benchmarks to validate the zero-shot transfer capability of our model on categories that were not specifically trained. As in previous work [5], the benchmarks can be categorized into two groups, with and without background classes. Benchmarks with a background generally label areas that do not belong to any predefined categories as "background," which is usually removed by considering a probability threshold in text-supervised semantic segmentation. For this category, we use the validation split of the following datasets: PASCAL VOC 2012 [13], PASCAL Context [32], and COCO-Object [3]. They each contain 20, 59, and 80 foreground classes, respectively, with an additional background class. For the "without background category," we evaluated our model with the validation split of COCO-Stuff [3], Cityscapes [10], and ADE20K [53] datasets. Each of them contains 171, 19, and 150 classes, respectively. In this category, all images are fully annotated, which is exceptionally challenging. Using datasets in this category, our model can be tested for its ability to recognize a variety of concepts. We employ mean intersection-over-union (mIoU) as our evaluation metric. + +For zero-shot semantic segmentation evaluation, we rely solely on the image segmenter. The image segmenter pro + +cesses the input image in conjunction with class names from each dataset to produce segmentation predictions. In accordance with the settings of prior work [5], we adopt the class names provided by the default version of MMSegmentation [9] and adhere to its post-processing methodology. + +# 4.2. Quantitative Comparisons + +We compare the proposed method with nine text-supervised semantic segmentation methods on the six datasets. Tab. 1 reports the mIoU values. The numbers have been taken directly from the original papers. All methods were tested on the three datasets of the "with background class," but only three methods (GroupViT [45], CoCu [44] and TCL [5]) were tested on the dataset of the "without background class." For those three methods, we also report their average mIoU values across all six datasets. It is also worth noting that these methods use different combinations of training datasets, as indicated in the dataset column of Tab. 1. + +Our method achieves the best performance in all six datasets, while TCL [5] and SimSeg [49] are the runners-up. In terms of average mIoU, our method (CoDe) achieves 31.8 whereas TCL achieves 30.1, resulting in a $5.65\%$ improvement. The result demonstrates the effectiveness of our image-text co-decomposition method in addressing the alignment-level train-test discrepancy that exists in previous methods by directly learning the region-word alignment. + +# 4.3. Qualitative Results + +Visual comparison with existing methods. Fig. 3 visually compares the segmentation results of our methods and two runners-up, TCL [5] and SimSeg [49], on the PASCAL VOC, PASCAL Context, and COCO Object datasets. + +This figure illustrates the fundamental benefit of our approach, which involves the direct learning of region-word + +![](images/6f66e51aa0d46669848cdade8f6568f2ada089eca857ae7b78dcd568b0249c18.jpg) +Figure 3. Qualitative comparisons. The proposed method is compared with the two most competitive methods, TCL [5] and SimSeg [49], on PASCAL VOC, PASCAL Context, and COCO Object datasets. Our method provides more precise object boundaries and effectively localizes objects within images without misclassification, leading to more accurate segmentation. + +![](images/a25ec1e520bd082c5c504f40975173200a2c7cbc928bf93069bcfb9e7a8974b2.jpg) + +![](images/177a38e05c594c1facef112294a0b49d8f5db6ceb5d7c874126add69a0e0b391.jpg) + +alignments. Our model effectively establishes a strong connection between object regions and word segments, allowing a better understanding of how objects are represented in images. Through this enhanced understanding, both segmentation quality and localization capabilities can be improved. As a result, our method provides more accurate classification and more precise masks than other methods. + +The SimSeg[49] model, which learns from image-text alignments, occasionally assigns objects to the wrong classes. On the other hand, TCL [5], which is based on region-text alignment, produces coarser semantic masks. Accordingly, these observed limitations are most likely a result of the alignment-level discrepancy between the train and test, which may lead to suboptimal performance. + +Visualization of image-text co-segmentation results. Fig. 4 presents a visualization of the results obtained by our model. We denote regions and word segments associated with the different nouns in the corresponding colors. It demonstrates that our method effectively segments object regions within images based on various input nouns. It simultaneously segments corresponding word segments within the associated text, creating a harmonious alignment between the object region and the word segment. + +The region-word alignment plays a pivotal role in our approach, serving as a supervisory signal for the model. By taking advantage of this alignment, our model not only performs visual localization but also captures correlations within the language domain. It indicates that our trained model possesses a more comprehensive understanding of the segmentation task. + +
C.W.R.VOCContextObjectStuffCityADEAvg.
54.427.632.722.525.016.629.8
✓56.229.232.923.327.517.031.0
✓✓56.129.332.623.629.017.331.3
✓✓✓57.730.532.323.928.917.731.8
+ +Table 2. Ablation study. The baseline model is augmented with the image-text co-decomposition method (C.), the word highlighting prompt (W.), and the region highlighting prompt (R.), one at a time. We report the mIoU values of the resultant models on the six datasets and their averages. + +# 4.4. Ablation Study + +Contributions of individual components. The ablation study in Tab. 2 assesses the contribution of the proposed components, including the image-text co-decomposition method, the word highlighting prompt, and the region highlighting prompt. Without the co-decomposition method, our baseline model only trains the image segmenter, resulting in an average mIoU of 29.8. Afterward, each proposed component is added to the baseline model one at a time to verify its contribution. As a result of adding the image-text co-decomposition module alone, the average mIoU has been increased to 31.0. It suggests that the image-text co-decomposition method can achieve region-word alignment and enhance localization capability. The model is further enhanced with the addition of word highlighting prompts and image highlighting prompts, resulting in further performance improvement. It demonstrates that the highlighting prompt learning method enhances feature extraction and strengthens alignment between regions and words. + +![](images/0513c558295e1493edd1a5041a3dac60172a1733ec763069ba8ecfe632c7c3d1.jpg) +this was her hair... it was beautiful, as you will see + +![](images/471594d8072a4a5b029bb566847616978450e70acc92fc7cc40a8ddb6865d838.jpg) +A black bear walks through dense vegetation. + +![](images/e9513cd3c604095064fa762cd88d5abfe7d1844143d627cea160349a2b2b9e93.jpg) +An old book lying open. + +![](images/e9fae17859652452c1009add2d0c3671f208d43421ef3c7ca0fa9fda3ea00116.jpg) +this was her hair... it wasbeautiful, as you will see + +![](images/822e096125363fdacd4af91f16b3f337db89c48bcb182b9d4af11d2b34c84f64.jpg) +An old book lying open. +Figure 4. Visualization of the results of our image-text co-decomposition method. The first two rows display text and images, representing input image-text pairs. In each text, nouns are underlined with different colors. Our method uses these nouns as queries for performing image-text co-decomposition. Using our image-text co-decomposition method, the last two rows depict the method's output, where regions and word segments associated with different nouns appear in corresponding colors. + +![](images/a8bf6621c20c4c6cf5c6fa10437e12e60f826182c5986dc952a4757b202eb8b1.jpg) +A black bear walks through dense vegetation. + +![](images/bb0ad4b007e5602c87647871c31498a3b964c1058fd3de67c06db9d3092ccfc3.jpg) +an ostrich egg laying on the grass + +![](images/b37305c94b0f64812b02fd4fe4268bbd055adf6e496ef7403f51a12e92da8667.jpg) +an ostrich egg laying on the grass + +![](images/e6f5f338a636b42a3672395123a3512288c17a2914761603f7eacf1930c88442.jpg) +2 large dogs posing on the beach at sunset + +![](images/e90908288f76e5a6e4839efcdafb393c86be983a134243c382e61e5d1914ac2b.jpg) +2 large dogs posing on the beach at sunset + +![](images/8e2754902ada6522620528f5bd670bf2e34187a763ae718d694a3534f3574f74.jpg) +A girl's hand holding fresh white flowers + +![](images/5c297821263d0e0929ef34990e4b25d6b1e84157025986225c1db690be9e655e.jpg) +A girl's hand holding fresh white flowers + +
λhcl0.050.10.250.50.751.0
Avg.30.631.231.731.831.530.8
+ +Table 3. Sensitivity analysis on the hyperparameter $\lambda_{\mathrm{hcl}}$ . By varying $\lambda_{\mathrm{hcl}}$ , we examine the corresponding average mIoU values of all six datasets. + +Hyperparameter sensitivity analysis. Tab. 3 investigates the impact of the loss weight for the highlighted region-word pair contrastive loss, denoted as $\lambda_{\mathrm{hcl}}$ in Eq. (8). We observe that, when we apply the highlighted region-word pair contrastive loss in our training phase, the performance consistently outperforms our baseline model. The method is robust to the parameter to some degree as it achieves reasonable performance for a wide range of values. When $\lambda_{\mathrm{hcl}}$ is set to 0.5, our model achieves a peak score of 31.8. It is evident from these results that the image-text co-decomposition method is superior to the image-text decomposition method for achieving region-word alignment. + +Effectiveness of jointly decomposing text. We validate the effectiveness of decomposing text by assessing the performance enhancement achieved by generating word masks, as opposed to simply using extracted nouns. This experiment is conducted by modifying the calculation of $\mathcal{L}_{\mathrm{hcl}}$ . Instead of using word segment embeddings as mentioned in Sec. 3.4, we opt to compute the similarity matrix $S$ using region embeddings with the embeddings of individual nouns. The average mIoU across all benchmarks is + +$30.2\%$ , which is below our method's $31.8\%$ . This indicates the benefits of using word segments encompassing extra words associated with each noun. The contextual information encoded in these additional words can serve as valuable supervisory signals, thereby improving performance. + +# 5. Conclusions + +We propose Image-Text Co-Decomposition (CoDe) to address cross-domain alignment discrepancies in the existing methods for text-supervised semantic segmentation. First, our method decomposes image-text pairs into corresponding regions and word segments to enforce the region-word alignment. CoDe, underpinned by contrastive learning, alleviates the train-test discrepancy by unifying image-text and region-text alignments to region-word alignment. Then, we introduce a region-highlighting prompt learning method to enhance feature extraction on masked images or texts for precise region-word alignment. Moreover, CoDe surpasses state-of-the-art methods in zero-shot semantic segmentation across six benchmark datasets. This novel approach opens new possibilities for research in vision-language models and their broader applications in computer vision. + +# 6. Acknowledgement + +This work was supported in part by the National Science and Technology Council (NSTC) under grants 112-2221-E-A49-090-MY3, 111-2628-E-A49-025-MY3, 112-2634-F-002-005, 112-2634-F-002-006, and 110-2221-E-002-124-MY3, and NTU under grants 112L9009. 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Existing methods have demonstrated that contrastive learning on image-text pairs effectively aligns visual segments with the meanings of texts. We notice that there is a discrepancy between text alignment and semantic segmentation: A text often consists of multiple semantic concepts, whereas semantic segmentation strives to create semantically homogeneous segments. To address this issue, we propose a novel framework, Image-Text Co-Decomposition (CoDe), where the paired image and text are jointly decomposed into a set of image regions and a set of word segments, respectively, and contrastive learning is developed to enforce region-word alignment. To work with a vision-language model, we present a prompt learning mechanism that derives an extra representation to highlight an image segment or a word segment of interest, with which more effective features can be extracted from that segment. Comprehensive experimental results demonstrate that our method performs favorably against existing text-supervised semantic segmentation methods on six benchmark datasets. The code is available at https://github.com/072jiajia/image-text-co-decomposition." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 560, + 128, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 128, + 573 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 128, + 573 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "Semantic segmentation is essential to various applications [11, 15, 50] in computer vision but is hindered by several critical challenges. First, the expensive cost of acquiring pixel-level annotations limits the applicability of fully supervised semantic segmentation methods. Second, most existing methods [40, 43, 52] are developed to work on predefined categories and leave themselves inapplicable to rare or unseen concepts described by free-form text. To address these obstacles, a new research direction has emerged in vision-language models, referred to as text-supervised semantic segmentation [5, 28, 44-46, 49]. This task devel" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "content": "ops segmentation models capable of assigning labels across large vocabularies of concepts and supporting semantic segmentation model training without pixel-wise annotations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 282, + 546, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 546, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 546, + 426 + ], + "type": "text", + "content": "Fig. 1 compares existing methods for text-supervised semantic segmentation by grouping their cross-domain alignment mechanisms into three categories, including image-text, region-text, and region-word alignment. Despite the differences, most of these methods compensate for the lack of pixel-wise annotations on broad semantic concepts by exploring abundant image-text pairs on the internet. The textual descriptions bring extensive knowledge across diverse categories. Thus, existing methods typically apply a vision-language model such as CLIP [34] to textual descriptions to acquire the semantic context of the corresponding images for segmentation model learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 545 + ], + "type": "text", + "content": "The image-text alignment is widely adopted in the literature e.g. [28, 44, 45]. As depicted in Fig. 1a, methods of this group derive an image encoder and a text encoder by aligning them in a joint embedding space. They then use their proposed zero-shot transfer techniques to enable the two encoders to predict segmentation output. Despite the simplicity, they introduce unfavorable discrepancies between the training and testing phases since we aim to match the semantic features from the text to the corresponding image segments rather than the whole image during testing." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 546, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 665 + ], + "type": "text", + "content": "To mitigate this issue, the region-text alignment is explored. As shown in Fig. 1b, methods of this group such as [5] utilize a pre-trained visual-language model to derive an additional image segmenter that discovers concepts described by the text. They enforce the consistency between the segmented region and the text but suffer from the discrepancy between the region-text alignment and semantic segmentation: A text may consist of multiple concepts, such as pub, night, and car in Fig. 1b, while semantic segmentation aims to identify regions of the same concept." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "To address the aforementioned issues in the image-text and region-text alignments, we propose a novel framework, Image-Text Co-Decomposition (CoDe), to achieve region-word alignment. As illustrated in Fig. 1c, we utilize a" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26794" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 164, + 150 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 164, + 150 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 164, + 150 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 164, + 150 + ], + "type": "image", + "image_path": "533c862118c3b5d148049e3f67e9bc9ba30a274fc7591db532b7f739a96d4b31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 153, + 145, + 163 + ], + "lines": [ + { + "bbox": [ + 66, + 153, + 145, + 163 + ], + "spans": [ + { + "bbox": [ + 66, + 153, + 145, + 163 + ], + "type": "text", + "content": "(a) image-text alignment" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 160, + 72, + 336, + 150 + ], + "blocks": [ + { + "bbox": [ + 160, + 72, + 336, + 150 + ], + "lines": [ + { + "bbox": [ + 160, + 72, + 336, + 150 + ], + "spans": [ + { + "bbox": [ + 160, + 72, + 336, + 150 + ], + "type": "image", + "image_path": "6292faa41fcb02c2b3e6d6839970cb3dbe6d219fcab2ab9571590d236ffeb3d4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 153, + 300, + 163 + ], + "lines": [ + { + "bbox": [ + 220, + 153, + 300, + 163 + ], + "spans": [ + { + "bbox": [ + 220, + 153, + 300, + 163 + ], + "type": "text", + "content": "(b) region-text alignment" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 169, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 169, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 547, + 213 + ], + "type": "text", + "content": "Figure 1. Existing methods perform text-supervised semantic segmentation by learning either (a) image-text alignment or (b) region-text alignment. This paper presents (c) region-word alignment via image-text co-decomposition, where the image and the text are decomposed into object regions and word segments, respectively, while contrastive learning is used to establish cross-modal correspondences between these image and word segments." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 336, + 70, + 533, + 150 + ], + "blocks": [ + { + "bbox": [ + 336, + 70, + 533, + 150 + ], + "lines": [ + { + "bbox": [ + 336, + 70, + 533, + 150 + ], + "spans": [ + { + "bbox": [ + 336, + 70, + 533, + 150 + ], + "type": "image", + "image_path": "6f50b2b6498792b54c3c9415caa28b4d4d0cd5d254d577327561475640bd2272.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 382, + 153, + 487, + 163 + ], + "lines": [ + { + "bbox": [ + 382, + 153, + 487, + 163 + ], + "spans": [ + { + "bbox": [ + 382, + 153, + 487, + 163 + ], + "type": "text", + "content": "(c) region-word alignment (ours)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 224, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 319 + ], + "type": "text", + "content": "visual-language model to construct an image segmenter and a text segmenter: The former decomposes an image into image segments, while the latter decomposes a text into word segments. In addition, there exist one-to-one correspondence between image and word segments. This way, the discrepancy between training and testing is alleviated since each image segment is derived from a single concept given by the corresponding word segment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 320, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 287, + 464 + ], + "type": "text", + "content": "The proposed CoDe framework comprises four components: an image segmenter, a text segmenter, a region-word alignment module, and a prompt learning module. We randomly select nouns in the text. For each selected noun e.g., \"car\", the image segmenter identifies the image segment that matches the noun, i.e., the region of the car, while the text segmenter discovers the corresponding word segment, i.e., \"red cars.\" The region-word alignment is developed to enforce the consensus between the image and word segments. To better work with a vision-language model, we present a prompt learning module to derive an extra representation, enabling more effective feature extraction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 465, + 266, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 465, + 266, + 476 + ], + "spans": [ + { + "bbox": [ + 59, + 465, + 266, + 476 + ], + "type": "text", + "content": "The main contributions of this work are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 479, + 287, + 609 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 47, + 479, + 287, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 287, + 527 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 287, + 527 + ], + "type": "text", + "content": "- We propose a new framework, Image-Text Co-Decomposition (CoDe), to learn the region-word alignment for eliminating train-test and image-text discrepancies, facilitating text-supervised semantic segmentation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 527, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 287, + 574 + ], + "type": "text", + "content": "- We propose a prompt learning method to address domain shift issues arising from blank areas during the highlighting process and enhance the alignment between highlighted regions and highlighted words." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 574, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 287, + 609 + ], + "type": "text", + "content": "- Our method effectively carries out zero-shot semantic segmentation and performs favorably against the state-of-the-art methods on six benchmark datasets." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 624, + 138, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 138, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 138, + 637 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 646, + 264, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 264, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 264, + 658 + ], + "type": "text", + "content": "2.1. Open-Vocabulary Semantic Segmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 712 + ], + "type": "text", + "content": "Open-vocabulary semantic segmentation focuses on segmenting any concepts within images, even those unseen during training, based solely on textual descriptions. Its three important branches are discussed as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 224, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 331 + ], + "type": "text", + "content": "Semi-supervised setting with mask-annotations. Methods of this group such as [16, 17, 24, 26, 31, 47] learn from dense annotations to produce high-quality segmentation masks, and then utilize image-text pairs and pre-trained vision-language models to extend the segmentation capability to a larger target vocabulary. Despite the remarkable results, these methods are hindered by their reliance on costly dense annotations, posing a challenge in cases where such annotations are difficult to obtain." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 334, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 478 + ], + "type": "text", + "content": "Training-free methods. Another line of research e.g. [38, 41, 54] makes the most of large pre-trained models for open-vocabulary segmentation without training. MaskCLIP [54] introduces a modification to the final layer of the CLIP image encoder, yielding dense feature maps that could be employed as initial segmentation maps for further refinement. ReCo [38] constructs an image archive and makes use of retrieval and co-segmentation to identify co-occurrence regions among a specific category. Although these methods eliminate the process of training, the results exhibit significant room for improvement, which shows the need for additional supervision to accomplish this task." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 480, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 545, + 529 + ], + "type": "text", + "content": "Text-supervised semantic segmentation. It strikes a balance between the two aforementioned branches. Methods of this group are discussed in detail in the following because our method belongs to this group." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 536, + 516, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 516, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 516, + 549 + ], + "type": "text", + "content": "2.2. Text-Supervised Semantic Segmentation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 555, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 651 + ], + "type": "text", + "content": "Text-supervised semantic segmentation [4, 5, 28, 33, 36, 42, 44-46, 49] decomposes an image into semantic regions according to text descriptions. Unlike semi-supervised methods relying on a few images with mask annotations during training, methods of this group aim to learn semantic masks solely from text-based guidance. We roughly divide existing methods into two categories based on their cross-modal alignment between the image and text domains." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Image-text alignment. These methods train an image encoder alongside a text encoder to align pairs of image and text in a joint embedding space. They use zero-shot transfer to enable the encoders to produce segmentation results. GroupViT [45] introduces a bottom-up approach within" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26795" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "Transformers, grouping image patches into regions and utilizing object semantics derived from texts to guide training. SimSeg [49] further introduces a pretraining method that densely aligns visual and language representations, enabling the trained image encoder to generate segmentation masks in a zero-shot manner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 159, + 287, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 287, + 242 + ], + "type": "text", + "content": "Region-text alignment. Another line of research targets at aligning the embedding of a region, instead of the whole image, with text descriptions. For instance, TCL [5] learns to segment specific regions within an image while ensuring consistency between the segmented region and the original text. It enables the model to segment the relevant region described in the text." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 245, + 288, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 288, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 288, + 424 + ], + "type": "text", + "content": "These methods for text-supervised semantic segmentation have shown that employing vision-language models and contrastive learning on image-text pairs enables aligning visual concepts with the meaning of the whole text. We notice that a text is usually a mix of multiple semantic concepts, but semantic segmentation aims to discover semantically homogeneous segments. To address this issue, inspired by the region-word matching techniques [8, 21, 22, 39] for cross-modal retrieval, we introduce image-text co-decomposition, where the image and the text are decomposed into image and word segments, respectively, and contrastive learning is adopted to enforce cross-modal consensus between these image and word segments. It turns out that image-text co-decomposition results in consistent performance gains on multiple benchmarks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 439, + 277, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 277, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 277, + 452 + ], + "type": "text", + "content": "2.3. Prompt Tuning for Vision-Language Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": "Emerged from natural language processing [23, 25, 27], prompt tuning focuses on parameter-efficient adaptation of large pre-trained models to new tasks. In computer vision [20, 55-57], pioneering work such as CoOp [55, 56] incorporates learnable tokens into the CLIP text encoder, enhancing the classification task performance. Recent studies e.g. [12, 14, 35] leverage prompt tuning in the text modality for extending CLIP's capabilities to various applications such as detection and segmentation tasks. Notably, prompt learning methods are also applicable to the visual domain. VPT [19] employs prompt tuning in the visual modality by inserting learnable vectors into Vision Transformers. Further studies [18, 26] explore tuning methods that directly incorporate learnable prompts into the input image within the RGB domain to address downstream tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Drawing inspiration from the success of these methods, our method leverages the capabilities of prompt tuning on segment feature extraction in both the visual and text domains. Prompt learning is beneficial in this work when applying contrastive learning to the visual and textual features extracted by a vision-language model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 71, + 389, + 86 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 389, + 86 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 389, + 86 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 92, + 545, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 545, + 213 + ], + "type": "text", + "content": "In this section, we first provide an overview of our method for image-text co-decomposition and define the notations in Sec. 3.1. Then, we specify the three major modules of our method, including 1) the image-text co-segmentation module in Sec. 3.2, 2) the region-word highlighting module in Sec. 3.3, and 3) the region-word alignment module in Sec. 3.4. These modules work harmoniously to address the region-word alignment for text-supervised semantic segmentation and enhance model performances. Finally, implementation details are given in Sec. 3.5." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 224, + 411, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 411, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 411, + 236 + ], + "type": "text", + "content": "3.1. Method Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": "Image-text co-decomposition enables text-supervised segmenters to learn region-word consensus when segmenting an image " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": " with a paired text " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": ". Our method aims to jointly learn an image segmenter " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "F^v" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": " and a text segmenter " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": " with solely the supervision from a set of " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": " image-text pairs, " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "D = \\{X_k^v, X_k^t\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": ", where no annotations are given. In addition, we optimize two learnable prompts, including a region prompt " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "P^v" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": " and a word prompt " + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "inline_equation", + "content": "P^t" + }, + { + "bbox": [ + 304, + 244, + 545, + 374 + ], + "type": "text", + "content": ", to alleviate the unfavorable effect of blank embeddings caused by applying a vision-language model to masked images or texts for feature extraction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": "Fig. 2 illustrates the pipeline of our method, consisting of three modules, including the image-text co-segmentation, region-word highlighting, and region-word alignment modules. For an input image-text pair " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "(X^v, X^t)" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": ", we initiate the process by randomly selecting a noun " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": ", e.g., balloon in the figure, from the text " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " using the noun selector [2]. This selected noun serves as a query. We take the query " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " along with the image " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " as input to the image segmenter " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "F^v" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " to generate the region mask " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "M^v" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " showing the estimated object region specified by the query. Similarly, a text segmenter " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " takes the query " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " and the text " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " as input and estimates the word mask " + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": " indicating the associated word segment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Subsequently, we apply the region mask " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "M^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " to the image " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " to crop the estimated object region. For the estimated background, i.e., the region outside the mask " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "M^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ", we crop the corresponding region from the learned region prompt " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "P^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". The highlighted image " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "H^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " is yielded by combining the cropped object and background regions. Similarly, the highlighted text " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "H^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " is generated by combining the text " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " inside the mask " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " and the word prompt " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "P^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " outside the mask " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". We extract features from the highlighted image and text by using the image encoder " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "E^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " and the text encoder " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "E^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " of CLIP [34], respectively. The procedure is repeated for each image-text pair and each selected noun. It follows that the region-word alignment is accomplished by contrastive learning [7]. Four loss functions, including " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kg}}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}^v" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}^t" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{hcl}}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ", are used for network optimization, and will be elaborated in the following." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26796" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 236, + 183 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 236, + 183 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 236, + 183 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 236, + 183 + ], + "type": "image", + "image_path": "a44ccf30a62c597ef517b469d555959d32ed3b45c15196a689b78f0799583e17.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 187, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 547, + 243 + ], + "type": "text", + "content": "Figure 2. Training pipeline of our method for image-text co-decomposition. Our method consists of three major modules, including (a) the image-text co-segmentation module where the image and text segmenters estimate the region and word masks according to a selected noun, respectively, (b) the region-word highlighting module where the estimated masks together with two learnable prompts produce the highlighted image and text, and (c) the region-word alignment module where contrastive learning is applied to the embedded object regions and word segments to accomplish region-word alignment." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 238, + 70, + 395, + 183 + ], + "blocks": [ + { + "bbox": [ + 238, + 70, + 395, + 183 + ], + "lines": [ + { + "bbox": [ + 238, + 70, + 395, + 183 + ], + "spans": [ + { + "bbox": [ + 238, + 70, + 395, + 183 + ], + "type": "image", + "image_path": "cbf37813fb086eb30a52926767877fcecd44fe1167cf01a0f5279aee3b38a99b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 395, + 70, + 532, + 183 + ], + "blocks": [ + { + "bbox": [ + 395, + 70, + 532, + 183 + ], + "lines": [ + { + "bbox": [ + 395, + 70, + 532, + 183 + ], + "spans": [ + { + "bbox": [ + 395, + 70, + 532, + 183 + ], + "type": "image", + "image_path": "4ed54001dd407076b0c2964f4486f0ad59940bdbd07b11a64c3f62968e437034.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 255, + 208, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 208, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 208, + 268 + ], + "type": "text", + "content": "3.2. Image-Text Co-Segmentation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "text", + "content": "The image-text co-segmentation module comprises a noun selector, an image segmenter, and a text segmenter, as shown in Fig. 2a. Taking an image-text pair " + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "inline_equation", + "content": "(X^v, X^t)" + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "text", + "content": " as input, this module aims at jointly identifying an object region in image " + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "text", + "content": " and its accompanying word segment in text " + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 46, + 273, + 287, + 344 + ], + "type": "text", + "content": " according to a randomly selected noun." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": "To begin with, we employ the noun selector [2], which takes the text " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": " as input and extracts a set of " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": " nouns, " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\{N_j\\}_{j=1}^J" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": ", in " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": ". For each noun " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": ", we carry out region mask generation, where the image segmenter " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "F^v" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": " predicts a region mask " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "M^v" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": " specifying the area in image " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": " relevant to noun " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": ". A similar task word mask generation is performed by the text segmenter " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": ", which seeks a word mask " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": " matching noun " + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 47, + 345, + 288, + 453 + ], + "type": "text", + "content": ". The tasks of region and word mask generation are depicted as follows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": "Region mask generation. The image segmenter " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "F^v" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " takes image " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " and noun " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " as input. It encodes the image into a pixel-wise embedding " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^v \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " is the image resolution and " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " is the channel dimension. We also compute the noun embedding " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_j \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " for noun " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": ". The image segmenter generates a region mask " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "M^v \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " by performing the dot product between the noun embedding " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_j" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " and every location of the image embedding " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^v" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "content": "In this work, we use the image segmentation model in [5] to serve as the image segmenter " + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "inline_equation", + "content": "F^v" + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "content": ", and employ its corresponding loss, denoted by " + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}^v" + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "content": " here, to help derive the image segmenter. This loss considers segment regularization and contrastive learning that can be directly applied to the segmentation results along with the noun embedding. We use the KgCoOp method [48] to obtain the noun embedding " + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_j" + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "content": ", as it avoids the pitfalls of improper prompt selection. It appends learnable context tokens to the noun, forming pseudo-sentences for optimal prompt tuning. The noun embedding loss " + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kg}}" + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "content": " [48] is included to improve the accuracy of these embeddings, i.e.," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 125, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 125, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {k g}} = \\left| \\left| \\mathbf {n} _ {j} - \\mathbf {n} _ {j} ^ {\\prime} \\right| \\right| _ {2} ^ {2}, \\tag {1}", + "image_path": "5f3139ad94c9d3eb4fc807d3bd9d6c217b71491f468f68d3d5f942af09d874b2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_j^{\\prime}\\in \\mathbb{R}^{C}" + }, + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "type": "text", + "content": " represents the knowledge-guided noun embedding generated from hand-crafted prompts such as \"a photo of a " + }, + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "type": "inline_equation", + "content": "N_{j}" + }, + { + "bbox": [ + 305, + 255, + 545, + 292 + ], + "type": "text", + "content": "\" using the text encoder." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": "Word mask generation. The text segmenter " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " takes the text " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " and the noun " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " as input. For text feature extraction, we consider the CLIP text encoder appended with two learnable multi-head attention layers. With the resultant feature extractor " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\tilde{E}^t" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": ", the word-wise features of text " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " are obtained via " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^t = \\tilde{E}^t(X^t) \\in \\mathbb{R}^{L \\times C}" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " is the text length, i.e., the number of word tokens. The word-specific logits " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\ell_j = [\\ell_{j,i}]_{i=1}^L \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " for noun " + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 305, + 297, + 546, + 393 + ], + "type": "text", + "content": " are computed via" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 386, + 402, + 545, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 402, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 386, + 402, + 545, + 416 + ], + "type": "interline_equation", + "content": "\\ell_ {j} = w \\cdot \\mathbf {x} ^ {t} \\mathbf {n} _ {j} + b, \\tag {2}", + "image_path": "af1941af0a3ce84ad38ded6cbda72968637c6e3293b4aedd2ed8958fca887610.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "text", + "content": " are two learnable parameters, and " + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_j\\in \\mathbb{R}^C" + }, + { + "bbox": [ + 305, + 425, + 545, + 449 + ], + "type": "text", + "content": " is the noun embedding." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": "Since each word in text " + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": " belongs to either one of the " + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": " word segments associated with nouns " + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\{N_j\\}_{j=1}^J" + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": " or none of them, the word mask " + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "inline_equation", + "content": "M^t = [m_i^t]_{i=1}^L \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": " for noun " + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": " is obtained by applying the softmax function over all the " + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 305, + 449, + 545, + 510 + ], + "type": "text", + "content": " noun-associated segments, i.e.," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 334, + 519, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 519, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 334, + 519, + 545, + 550 + ], + "type": "interline_equation", + "content": "m _ {i} ^ {t} = \\frac {\\exp \\left(\\ell_ {j , i}\\right)}{1 + \\sum_ {j ^ {\\prime} = 1} ^ {J} \\exp \\left(\\ell_ {j ^ {\\prime} , i}\\right)}, \\text {f o r} 1 \\leq i \\leq L, \\tag {3}", + "image_path": "492407cd9a04562062ed49c67f850e51c0231b73b51420940df6bd459a7010bd.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "text", + "content": "where the additional 1 in the denominator is included for the case where word " + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "text", + "content": " does not belong to any noun-associated segments. The word mask " + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "text", + "content": " for noun " + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "inline_equation", + "content": "N_j" + }, + { + "bbox": [ + 305, + 558, + 545, + 594 + ], + "type": "text", + "content": " is produced." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": "According to the softmax function defined in Eq. 3, we get the probabilities of word " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "J + 1" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": " cases, namely belonging to one of the " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": " noun-associated segments or none of them. We compile a pseudo label vector " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = \\{p_i\\} \\in \\{0,1\\}^L" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": " takes value 1 if word " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": " belonging to the " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": "th noun-associated segment gets the highest probability, and 0 otherwise. We develop the text segmentation loss " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}^t" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": ", which is the cross-entropy loss on the word mask " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": " with respect to the pseudo label vector " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": ", and can help learn the text segmenter " + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 305, + 594, + 546, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26797" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 195, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 195, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 195, + 85 + ], + "type": "text", + "content": "3.3. Region-Word Highlighting" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 150 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 150 + ], + "type": "text", + "content": "We present a prompt learning method to reliably extract features from an image region or a word segment using a vision-language model. Specifically, we propose a region-highlighting prompt learning method and a word-highlighting prompt learning method, as shown in Fig. 2b." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "content": "Region highlighting prompt. When the region mask " + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "inline_equation", + "content": "M^v" + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "content": " is directly applied to the image " + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "inline_equation", + "content": "X^v" + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "inline_equation", + "content": "M^v * X^v" + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "content": " denotes the element-wise multiplication operation, it makes specific regions of the image being zeroed out, resulting in what we refer to as blank areas. When a pre-trained vision-language model like CLIP is applied to these areas, the domain distribution may shift due to the introduction of zero tokens, which are unseen in natural images. To mitigate this issue, we introduce a region highlighting prompt, which is a learnable, universal image representation, denoted by " + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "inline_equation", + "content": "P^v" + }, + { + "bbox": [ + 46, + 153, + 289, + 308 + ], + "type": "text", + "content": ". This representation is used alongside the original image in the process of feature extraction. The highlighted image is then obtained via" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 316, + 287, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 316, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 94, + 316, + 287, + 330 + ], + "type": "interline_equation", + "content": "H ^ {v} = X ^ {v} * M ^ {v} + P ^ {v} * \\left(1 - M ^ {v}\\right). \\tag {4}", + "image_path": "5062f85293cba5334be5986e07e8563163e8fb50ed7c562ffec26384fcbd62a0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 337, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 287, + 373 + ], + "type": "text", + "content": "In this way, the blank areas are filled with the corresponding areas of the region prompt " + }, + { + "bbox": [ + 46, + 337, + 287, + 373 + ], + "type": "inline_equation", + "content": "P^v" + }, + { + "bbox": [ + 46, + 337, + 287, + 373 + ], + "type": "text", + "content": " alleviating the unfavorable effect of domain shift." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "text", + "content": "Word highlighting prompt. A similar challenge arises in the text domain when applying the word mask " + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "inline_equation", + "content": "M^t" + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "text", + "content": " to text " + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "inline_equation", + "content": "X^t" + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "text", + "content": ". The resultant zero tokens in the masked part unintentionally carry meanings of specific words, leading to potential inaccuracies. To mitigate this issue, we introduce a word highlighting prompt, represented as a learnable, universal text representation " + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "inline_equation", + "content": "P^t" + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "text", + "content": ". The highlighted text " + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "inline_equation", + "content": "H^t" + }, + { + "bbox": [ + 46, + 376, + 289, + 473 + ], + "type": "text", + "content": " is obtained by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 97, + 479, + 287, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 479, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 97, + 479, + 287, + 493 + ], + "type": "interline_equation", + "content": "H ^ {t} = X ^ {t} * M ^ {t} + P ^ {t} * (1 - M ^ {t}). \\tag {5}", + "image_path": "d82c228cba219f046218e67db402068c91fdf2b9fcb20d79b356a272308ee8b0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 501, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 525 + ], + "type": "text", + "content": "Since the masked part is filled with content from " + }, + { + "bbox": [ + 46, + 501, + 287, + 525 + ], + "type": "inline_equation", + "content": "P^t" + }, + { + "bbox": [ + 46, + 501, + 287, + 525 + ], + "type": "text", + "content": ", the risk of including unexpected text meanings is reduced." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 531, + 186, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 186, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 186, + 544 + ], + "type": "text", + "content": "3.4. Region-Word Alignment" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 550, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 598 + ], + "type": "text", + "content": "In the following, we describe how our method achieves region-word alignment. Our objective is to optimize mutual evidence between the highlighted object regions and the highlighted word segments, as illustrated in Fig. 2c." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": "Contrastive loss on highlighted region-word pairs. To achieve region-word alignment, we compute the highlighted region embedding " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{e}^v" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": " and highlighted word segment embedding " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{e}^t" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": " from the highlighted region-word pair by using the image and text encoders of CLIP by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 93, + 668, + 287, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 668, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 93, + 668, + 287, + 682 + ], + "type": "interline_equation", + "content": "\\mathbf {e} ^ {v} = E ^ {v} \\left(H ^ {v}\\right) \\text {a n d} \\mathbf {e} ^ {t} = E ^ {t} \\left(H ^ {t}\\right), \\tag {6}", + "image_path": "23a37cb7907204fbaaaf919accddda09db42871c73b2f78186313642702dfb04.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "E^v" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "E^t" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " are the CLIP image and text encoders, respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": "We adopt batch optimization for model training. Each batch has several triplets, each of which is composed of an image, its paired text, and a randomly selected noun from the text. Each triplet yields a region embedding and a word embedding via Eq. 6. Suppose that there are " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": " triplets in this batch. We create a similarity matrix " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "S = [S_{i,j}] \\in \\mathbb{R}^{B \\times B}" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "S_{i,j}" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": " stores the cosine similarity between the " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": "th region embedding " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i^v" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": "th word segment embedding " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_j^t" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": ". We adopt the symmetric version of InfoNCE loss to develop the highlighted region-word pair contrastive loss, which enhances the similarity of related region-word pairs while reducing it for unrelated pairs:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 340, + 224, + 545, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 224, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 340, + 224, + 545, + 294 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {h c l}} = - \\frac {1}{2 B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp (S _ {i , i} / \\tau)}{\\sum_ {j = 1} ^ {B} \\exp (S _ {i , j} / \\tau)} \\\\ - \\frac {1}{2 B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(S _ {i , i} / \\tau\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(S _ {j , i} / \\tau\\right)}, \\tag {7} \\\\ \\end{array}", + "image_path": "e9d0c4116de3b28ec40be74be00d98123dee12c2b859a7dfb476756ddbfbfb6e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "content": " is a learnable temperature. Notably, even though nouns may be selected multiple times across image-caption pairs, the corresponding highlighted regions " + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "inline_equation", + "content": "H^v" + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "content": " and highlighted texts " + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "inline_equation", + "content": "H^t" + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "content": " vary, ensuring the effectiveness of the InfoNCE loss in precise region-word alignment." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "content": "Loss functions and optimization. In sum, the proposed network for image-text co-decomposition is optimized using a composite loss that combines the knowledge-guided, image segmentation, text segmentation, and highlighted region-word pair contrastive losses, defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 333, + 434, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 434, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 333, + 434, + 545, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {\\mathrm {k g}} \\mathcal {L} _ {\\mathrm {k g}} + \\lambda_ {\\mathrm {s e g}} ^ {v} \\mathcal {L} _ {\\mathrm {s e g}} ^ {v} + \\lambda_ {\\mathrm {s e g}} ^ {t} \\mathcal {L} _ {\\mathrm {s e g}} ^ {t} + \\lambda_ {\\mathrm {h c l}} \\mathcal {L} _ {\\mathrm {h c l}}. \\tag {8}", + "image_path": "8121b286444c859e224be304b9e5098070dce79ea059d61a0f9308ae755e36ce.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 456, + 440, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 440, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 440, + 468 + ], + "type": "text", + "content": "3.5. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": "We utilize NLTK's [2] part-of-speech tagging algorithm for noun selection. For image segmentation, we utilize TCL's image segmenter [5] to generate image masks, and we adopt the training loss in TCL, which relies solely on the image-capture pairs, to yield " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}^v" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": ". For text segmentation, we use a CLIP text encoder appended with two multi-head attention layers as the text segmenter " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{E}^t" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": ". Our model is trained on the CC3M and CC12M datasets. The resolution of input images is set to " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": ". For each forward pass of an image-text pair, we randomly select 2 nouns from the text. The loss weights are set as follows: " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{kg}} = 8.0" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{seg}}^v = 1.0" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{seg}}^t = 1.0" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{hcl}} = 0.5" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": " in the experiments. We train the model with a batch size of 64 on four NVIDIA 2080Ti GPUs and with a learning rate of " + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "inline_equation", + "content": "5 \\times *10^{-6}" + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": " for a total of 50,000 iterations with 15,000 warmup steps and a cosine schedule. AdamW optimizer [29] is used with a weight decay of 0.05. To improve the quality of the predicted mask during the evaluation phase, we adopt the post-processing approach described in TCL [5], which uses pixel-adaptive mask refinement (PAMR) [1] for mask refinement." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26798" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 519, + 209 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 519, + 209 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 519, + 209 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 519, + 209 + ], + "type": "table", + "html": "
MethodsPublicationDatasetVOCContextObjectStuffCityADEAvg.
GroupViT [45]CVPR 2022CC3M+CC12M+YFCC14M49.519.024.312.66.98.720.2
ViL-Seg [28]ECCV 2022CC12M37.318.918.1
ViewCo [36]ICLR 2023CC12M+YFCC14M52.423.023.5
OVSegmentor [46]CVPR 2023CC12M53.820.425.1
SimSeg [49]CVPR 2023CC3M+CC12M57.426.229.7
TCL [5]CVPR 2023CC3M+CC12M55.030.431.622.424.017.130.1
SegCLIP [30]ICML 2023CC3M + COCO52.624.726.5
CoCu [44]NeurIPS 2023CC3M+CC12M+YFCC14M51.423.622.715.222.112.324.6
PGSeg [51]NeurIPS 2023CC12M+RedCaps12M53.223.828.7
CoDe (Ours)CVPR 2024CC3M+CC12M57.730.532.323.928.917.731.8
", + "image_path": "76d36a6d378b3cfebecf403a8bf6711fda5c8f122a9fc7364e9aab573b97a0ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 214, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 214, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 545, + 280 + ], + "type": "text", + "content": "Table 1. Text-supervised semantic segmentation performance comparison in terms of mIoU. The proposed method is compared with nine SOTA methods on six popular semantic segmentation datasets: PASCAL VOC (VOC), PASCAL Context (Context), COCO-Object (Object), COCO-Stuff (Stuff), Cityscapes (City) and ADE20K (ADE). For each compared method, the dataset column lists its training datasets. Several methods used datasets in addition to CC3M and CC12M, such as YFCC14M, COCO and RedCaps12M. When applicable, we also provide an average mIoU across all six datasets. For each dataset, the best method is indicated by bold fonts, whereas the second best method is underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 292, + 128, + 305 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 128, + 305 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 128, + 305 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 312, + 224, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 224, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 224, + 324 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 330, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 287, + 365 + ], + "type": "text", + "content": "We utilize image-text datasets to train our proposed model and perform extensive experiments on six commonly used semantic segmentation benchmarks to validate our method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 366, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 426 + ], + "type": "text", + "content": "Training datasets. We trained our model on two image-text datasets, Conceptual Captions 3M (CC3M) [37] and Conceptual 12M (CC12M) [6] containing 3M and 12M image-text pairs respectively. They have been widely adopted for training text-supervised semantic segmentation methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 688 + ], + "type": "text", + "content": "Evaluation datasets. We used six zero-shot semantic segmentation benchmarks to validate the zero-shot transfer capability of our model on categories that were not specifically trained. As in previous work [5], the benchmarks can be categorized into two groups, with and without background classes. Benchmarks with a background generally label areas that do not belong to any predefined categories as \"background,\" which is usually removed by considering a probability threshold in text-supervised semantic segmentation. For this category, we use the validation split of the following datasets: PASCAL VOC 2012 [13], PASCAL Context [32], and COCO-Object [3]. They each contain 20, 59, and 80 foreground classes, respectively, with an additional background class. For the \"without background category,\" we evaluated our model with the validation split of COCO-Stuff [3], Cityscapes [10], and ADE20K [53] datasets. Each of them contains 171, 19, and 150 classes, respectively. In this category, all images are fully annotated, which is exceptionally challenging. Using datasets in this category, our model can be tested for its ability to recognize a variety of concepts. We employ mean intersection-over-union (mIoU) as our evaluation metric." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "For zero-shot semantic segmentation evaluation, we rely solely on the image segmenter. The image segmenter pro" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 293, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 354 + ], + "type": "text", + "content": "cesses the input image in conjunction with class names from each dataset to produce segmentation predictions. In accordance with the settings of prior work [5], we adopt the class names provided by the default version of MMSegmentation [9] and adhere to its post-processing methodology." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 363, + 452, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 452, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 452, + 376 + ], + "type": "text", + "content": "4.2. Quantitative Comparisons" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 382, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 545, + 514 + ], + "type": "text", + "content": "We compare the proposed method with nine text-supervised semantic segmentation methods on the six datasets. Tab. 1 reports the mIoU values. The numbers have been taken directly from the original papers. All methods were tested on the three datasets of the \"with background class,\" but only three methods (GroupViT [45], CoCu [44] and TCL [5]) were tested on the dataset of the \"without background class.\" For those three methods, we also report their average mIoU values across all six datasets. It is also worth noting that these methods use different combinations of training datasets, as indicated in the dataset column of Tab. 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 515, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 611 + ], + "type": "text", + "content": "Our method achieves the best performance in all six datasets, while TCL [5] and SimSeg [49] are the runners-up. In terms of average mIoU, our method (CoDe) achieves 31.8 whereas TCL achieves 30.1, resulting in a " + }, + { + "bbox": [ + 304, + 515, + 545, + 611 + ], + "type": "inline_equation", + "content": "5.65\\%" + }, + { + "bbox": [ + 304, + 515, + 545, + 611 + ], + "type": "text", + "content": " improvement. The result demonstrates the effectiveness of our image-text co-decomposition method in addressing the alignment-level train-test discrepancy that exists in previous methods by directly learning the region-word alignment." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 621, + 419, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 621, + 419, + 634 + ], + "spans": [ + { + "bbox": [ + 305, + 621, + 419, + 634 + ], + "type": "text", + "content": "4.3. Qualitative Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "type": "text", + "content": "Visual comparison with existing methods. 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Qualitative comparisons. The proposed method is compared with the two most competitive methods, TCL [5] and SimSeg [49], on PASCAL VOC, PASCAL Context, and COCO Object datasets. 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Our model effectively establishes a strong connection between object regions and word segments, allowing a better understanding of how objects are represented in images. Through this enhanced understanding, both segmentation quality and localization capabilities can be improved. As a result, our method provides more accurate classification and more precise masks than other methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 422, + 286, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 286, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 286, + 506 + ], + "type": "text", + "content": "The SimSeg[49] model, which learns from image-text alignments, occasionally assigns objects to the wrong classes. On the other hand, TCL [5], which is based on region-text alignment, produces coarser semantic masks. Accordingly, these observed limitations are most likely a result of the alignment-level discrepancy between the train and test, which may lead to suboptimal performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 628 + ], + "type": "text", + "content": "Visualization of image-text co-segmentation results. Fig. 4 presents a visualization of the results obtained by our model. We denote regions and word segments associated with the different nouns in the corresponding colors. It demonstrates that our method effectively segments object regions within images based on various input nouns. It simultaneously segments corresponding word segments within the associated text, creating a harmonious alignment between the object region and the word segment." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "The region-word alignment plays a pivotal role in our approach, serving as a supervisory signal for the model. By taking advantage of this alignment, our model not only performs visual localization but also captures correlations within the language domain. 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Visualization of the results of our image-text co-decomposition method. The first two rows display text and images, representing input image-text pairs. In each text, nouns are underlined with different colors. Our method uses these nouns as queries for performing image-text co-decomposition. 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", + "image_path": "657d97dffdc2899593983766db06760233ae4b8258671d4f5ecaac4e6827c36d.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "lines": [ + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "type": "text", + "content": "Table 3. Sensitivity analysis on the hyperparameter " + }, + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{hcl}}" + }, + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "type": "text", + "content": ". By varying " + }, + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{hcl}}" + }, + { + "bbox": [ + 46, + 382, + 287, + 415 + ], + "type": "text", + "content": ", we examine the corresponding average mIoU values of all six datasets." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "type": "text", + "content": "Hyperparameter sensitivity analysis. Tab. 3 investigates the impact of the loss weight for the highlighted region-word pair contrastive loss, denoted as " + }, + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{hcl}}" + }, + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "type": "text", + "content": " in Eq. (8). We observe that, when we apply the highlighted region-word pair contrastive loss in our training phase, the performance consistently outperforms our baseline model. The method is robust to the parameter to some degree as it achieves reasonable performance for a wide range of values. When " + }, + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{hcl}}" + }, + { + "bbox": [ + 46, + 440, + 287, + 583 + ], + "type": "text", + "content": " is set to 0.5, our model achieves a peak score of 31.8. It is evident from these results that the image-text co-decomposition method is superior to the image-text decomposition method for achieving region-word alignment." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "Effectiveness of jointly decomposing text. We validate the effectiveness of decomposing text by assessing the performance enhancement achieved by generating word masks, as opposed to simply using extracted nouns. This experiment is conducted by modifying the calculation of " + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{hcl}}" + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": ". Instead of using word segment embeddings as mentioned in Sec. 3.4, we opt to compute the similarity matrix " + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": " using region embeddings with the embeddings of individual nouns. The average mIoU across all benchmarks is" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 341, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 341, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 545, + 401 + ], + "type": "inline_equation", + "content": "30.2\\%" + }, + { + "bbox": [ + 305, + 341, + 545, + 401 + ], + "type": "text", + "content": ", which is below our method's " + }, + { + "bbox": [ + 305, + 341, + 545, + 401 + ], + "type": "inline_equation", + "content": "31.8\\%" + }, + { + "bbox": [ + 305, + 341, + 545, + 401 + ], + "type": "text", + "content": ". This indicates the benefits of using word segments encompassing extra words associated with each noun. The contextual information encoded in these additional words can serve as valuable supervisory signals, thereby improving performance." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 411, + 383, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 383, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 383, + 424 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 431, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 545, + 611 + ], + "type": "text", + "content": "We propose Image-Text Co-Decomposition (CoDe) to address cross-domain alignment discrepancies in the existing methods for text-supervised semantic segmentation. First, our method decomposes image-text pairs into corresponding regions and word segments to enforce the region-word alignment. CoDe, underpinned by contrastive learning, alleviates the train-test discrepancy by unifying image-text and region-text alignments to region-word alignment. Then, we introduce a region-highlighting prompt learning method to enhance feature extraction on masked images or texts for precise region-word alignment. Moreover, CoDe surpasses state-of-the-art methods in zero-shot semantic segmentation across six benchmark datasets. This novel approach opens new possibilities for research in vision-language models and their broader applications in computer vision." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 621, + 416, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 416, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 416, + 635 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "This work was supported in part by the National Science and Technology Council (NSTC) under grants 112-2221-E-A49-090-MY3, 111-2628-E-A49-025-MY3, 112-2634-F-002-005, 112-2634-F-002-006, and 110-2221-E-002-124-MY3, and NTU under grants 112L9009. 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However, most previous best-performing methods, whether pixel grouping methods or region recognition methods, suffer from false matches between image features and category labels. We attribute this to the natural gap between the textual features and visual features. In this work, we rethink how to mitigate false matches from the perspective of image-to-image matching and propose a novel relation-aware intra-modal matching (RIM) framework for OVS based on visual foundation models. RIM achieves robust region classification by firstly constructing diverse image-modal reference features and then matching them with region features based on relation-aware ranking distribution. The proposed RIM enjoys several merits. First, the intra-modal reference features are better aligned, circumventing potential ambiguities that may arise in cross-modal matching. Second, the ranking-based matching process harnesses the structure information implicit in the inter-class relationships, making it more robust than comparing individually. Extensive experiments on three benchmarks demonstrate that RIM outperforms previous state-of-the-art methods by large margins, obtaining a lead of more than $10\\%$ in mIoU on PASCAL VOC benchmark.", + "bbox": [ + 75, + 340, + 473, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 733, + 209, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Aiming at allocating semantic labels to the corresponding pixels, semantic segmentation has achieved conspicuous achievements attributed to the development of large-scale datasets [11, 22, 25, 74] and elaborate algorithms [7, 8, 28]. However, the capabilities of conventional semantic segmentation models are restricted to predefined training categories, failing to recognize a broader spectrum of concepts, which", + "bbox": [ + 75, + 758, + 470, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f2e79793868010719c7713b6e8149a135c747d0c65c19ee376c922af75fc0557.jpg", + "image_caption": [ + "(a) Text-to-image Matching V.S. Image-to-image Matching" + ], + "image_footnote": [], + "bbox": [ + 511, + 321, + 888, + 416 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ebc9e6c42901228cc19c9e98a1d45d739ea920a89ca66140c54fd1ffae931f0c.jpg", + "image_caption": [ + "(b) Individual Matching V.S. Relation-aware Matching", + "Figure 1. Motivation of our method. (a) False matches tend to occur in cross-modal features. We establish well-aligned image-modal reference features thus transit the text-to-image matching to image-to-image matching. (b) Individual matching tends to suffer from disturbances. We propose a novel relation-aware matching strategy for more robust region classification." + ], + "image_footnote": [], + "bbox": [ + 514, + 428, + 888, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "poses a severe limitation for their practical applications. In pursuit of the human-like intelligence of unbounded and fine-grained scene understanding, open-vocabulary segmentation (OVS) [2, 67] has attracted increasing interest recently, which enables segmentation with an unrestricted vocabulary.", + "bbox": [ + 496, + 613, + 893, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "OVS is highly challenging as it requires not only grouping all pixels to corresponding visual concepts but also assigning each region the correct semantic label from a large vocabulary. Some early attempts [29, 64] optimize the pixel grouping process and the classification of visual concepts simultaneously by employing contrastive learning with image-text pairs. These methods inevitably yield masks of relatively low quality with only coarse supervision available. Another line of works [24, 67, 68] significantly dominate this field by modeling the OVS as a region recognition problem, which decouple OVS into two procedures, i.e. class-agnostic mask proposals prediction and mask class recognition. Though the mask proposals generation has been significantly improved with the assistance of pixel-level supervision and", + "bbox": [ + 496, + 689, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3952", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "elaborate segmenter architectures (e.g. Mask2Former [8]), the unsatisfactory region class recognition has emerged as the performance bottleneck of OVS [24]. We attribute this to the natural gap between the highly abstract and monotonous category textual features and the visual features that are more concrete and diverse.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most current OVS approaches achieve mask class recognition via cross-modal region-category alignment based on the pretrained vision-language models (e.g., CLIP [38]). Despite its exemplary generalization ability on downstream classification tasks, CLIP usually suffers from spatial relations ambiguity [66, 69] and co-occurring object confusion ascribed to the holistic pre-training objective. On the other side, also pre-trained on internet-scale data, Stable Diffusion [42] (SD) model has garnered growing research interest credited to the phenomenal power of synthesizing photorealistic images with diverse and plausible content conditioned on textual descriptions. Considering that features from the same modality inherently exhibit a higher degree of alignment compared to cross-modal features (as shown in Fig. 6), we ask the question: $\\mathbf{0}$ is it possible to transition the region classification in OVS from image-to-text matching to image-to-image matching using the SD model?", + "bbox": [ + 75, + 184, + 473, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Before tackling this issue, we first revisit the common practices in mask class recognition [24, 67], which involves matching visual concepts with a set of category reference features (e.g. category textual features from CLIP). Inspired by previous exploration [59, 60, 73] of the strong image-text correspondence exhibited by the SD model, we can establish better-aligned intra-modal category reference features as shown in Fig. 1 (a). The cross-attention maps in the conditional generation process could serve as exceptional tools to further refine the category features. Nonetheless, it is still non-trivial to map test region features to their corresponding category reference features precisely, as the intra-class diversity and disturbances from akin categories exhibit in practical scenarios potentially lead to mismatches. Previous methodologies process each category independently during the matching phase, overlooking the informative inter-class relationships, which implicitly integrate structured contextual information and effectively aid in disambiguation. Here another question arises: how to harness the structure information modeled in the inter-class relationship to facilitate more accurate matching?", + "bbox": [ + 75, + 444, + 473, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Driven by this question, we carefully design the relation-aware similarity measurement that incorporates the relations of the current region with some semantic relevant category agents. For a specified region feature within test image, a subset of category reference features that most akin to the region are selected to serve as category agents. The central idea is that we regard the category agent ranking as a stochastic event rather than a deterministic permutation. For example, in ranking, given the region feature specified by the", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mask proposal $m_{1}$ in Fig. 1 (a), its scores vary for different category agents, which can be taken as probabilities. The probability of being ranked first is 0.45 of the agent 'desk' and 0.35 of the agent 'chair'. The ranking permutation reflects the relevance of the corresponding categories w.r.t. the region feature. An agent-ranking probability distribution can be constructed by associating the probability with every rank permutation for both the region feature and all category reference features. Finally, as illustrated in Fig. 1 (b), we transform the similarity measurement from individual region-reference comparison to relation-aware agent-ranking distribution similarity.", + "bbox": [ + 496, + 90, + 893, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a training-free OVS framework RIM to achieve Relation-aware Intra-modal Matching based on visual foundation models that coherently addresses the questions 1-2. Specifically, we facilitate a synergistic collaboration between the SD model and SAM to generate category-specific reference features by prompting the Segment Anything Model [22] (SAM) with points selected from the cross-attention map within SD model. SAM is further adopted to provide mask proposals of the test images. Finally, we conduct the relation-aware matching based on ranking distribution in the robust all-purpose feature space of DINOv2 [35]. RIM ensembles expertise of different visual foundational models in a complementary manner, enhancing mask quality and region-category matching precision simultaneously. Moreover, the overall framework is training-free, substantially mitigating the risk of overfitting.", + "bbox": [ + 496, + 272, + 895, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be concluded as follows: (1) We reveal the problems of region feature classification in OVS and propose to construct well-aligned intra-modal reference features to circumvent ambiguities of cross-modal matching. (2) We design a relation-aware matching strategy based on ranking distribution, which captures structure information implicit in inter-class relationships and enables more robust matching. (3) We propose a training-free relation-aware intra-modal matching (RIM) network for OVS based on visual foundation models. Extensive experiments demonstrate that RIM remarkably surpasses previous state-of-the-art methods by a large margin.", + "bbox": [ + 496, + 513, + 895, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 709, + 640, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic Segmentation is a fundamental computer vision task with widespread applications in fields such as medical image processing [31, 37, 46, 48, 49, 58], video analysis [47, 51]. The pioneering FCN [28] has inspired a multitude of subsequent endeavors [6, 7, 43, 62, 72] centered around Convolutional Neural Networks (CNN). Beyond the CNN-based models, the triumph of the Vision Transformer (ViT) has spurred a succession of transformer-based segmentation models [30, 45, 63, 71], which have progressively evolved into a unified segmentation framework [8, 9] capable of addressing various segmentation tasks. Some alternative", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3953", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "settings, such as few-shot [23, 55-57], semi-supervised [23, 32, 33, 50], or weakly supervised [19, 54] segmentation, attempt to enhance the practicality of semantic segmentation techniques. Despite their success, these models are confined to predefined training categories or the specific foreground class, failing to recognize a broader spectrum of categories.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Open-vocabulary Semantic Segmentation aims to segment images with arbitrary categories described by texts. Some efforts [2, 29, 61, 65, 69] concentrated on developing a joint embedding space that bridges image pixels with class names or descriptions via learning objectives established from image-text pairs. For example, GroupViT [64] designed a hierarchical grouping transformer and learned the alignment between groups and text via contrastive loss. Another line of works [24, 66, 67] models OVS as a region recognition task by decoupling it into mask proposal generation and region classification, achieving notable progress attributed to advanced segmentation architectures [8] and pixel-level annotations [25, 74]. Large-scale vision-language pre-training models such as CLIP [38] and ALIGN [20] have been widely applied for OVS [15, 68, 70] which endows OVS model enhanced generalization. However, those pretraining models often encounter spatial confusion in dense prediction tasks [69], leading to recurring misclassification issues, which has emerged as a critical bottleneck in OVS.", + "bbox": [ + 75, + 181, + 473, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual foundation models is catching up with the research in natural language processing (NLP) [1, 10, 36] and have achieved conspicuous achievements across a wide range of visual tasks. For example, DINov2 [35] establishes an impressive all-purpose feature extractor via self-supervised learning at both the image and patch levels. Trained on over 1 billion masks, Segment Anything Model (SAM) [22] has demonstrated astonishing zero-shot class-agnostic segmentation performance. Diffusion models [18, 44] have propelled the advancement of a series of image-to-text generation systems such as DALL-E [39] and Stable Diffusion model [42]. A series of works [27, 60, 66] render visual foundation models as powerful out-of-the-box tools to handle downstream tasks. Though a single foundation model may have limited capacity in addressing complex visual tasks such as OVS, in this work, we demonstrate that integrating different foundation models leads to positive synergies.", + "bbox": [ + 75, + 470, + 473, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 744, + 169, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 76, + 770, + 259, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Open-vocabulary segmentation aims to segment any image against a new vocabulary of categories $\\mathbf{C}_{test}$ . Previous approaches typically involve training models on datasets annotated with image-level textual labels or pixel-level masks, with the category set $\\mathbf{C}_{train}$ . $\\mathbf{C}_{test}$ contains novel categories not exposed to the training process, i.e., $\\mathbf{C}_{train} \\neq \\mathbf{C}_{test}$ . Owing to the training-free nature of our method, it inher", + "bbox": [ + 75, + 795, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ently operates under a more challenging zero-shot setting wherein all test categories are considered novel.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Preliminary of Vision Foundation Models", + "text_level": 1, + "bbox": [ + 498, + 132, + 854, + 147 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stable-Diffusion model. Different from discriminative image-text models that model the class probability distribution $\\pmb{p}(\\pmb{c}|\\pmb{i})$ given the image, text-to-image stable diffusion model encode a text-conditional distribution of possible images $\\pmb{p}(\\pmb{i}|\\pmb{c})$ . This model demonstrates the prowess to synthesize high-fidelity images $\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}$ that closely align with the specified conditional text $\\mathcal{T}$ , all originating from a latent space defined by random Gaussian noise $\\mathbf{z} \\sim \\mathcal{N}(0,1)$ . Specifically, stable diffusion model consists of three components: a pre-trained variational autoencoder (VAE) [13] that encodes and decodes the image latent code, a text encoder for prompt embedding, and a time-conditional UNet [43] for the denoising of latent vectors. The visual-text interaction occurs in the cross-attention layers that are integral to the UNet structure for each denoising step. Target categories within synthesized images can be accurately localized based on class-discriminative cross-attention maps.", + "bbox": [ + 496, + 155, + 893, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Segment Anything Model. SAM comprises of three components: an image encoder $\\mathbf{Enc}_{\\mathbf{I}}$ , a prompt encoder $\\mathbf{Enc}_{\\mathbf{P}}$ , and fast mask decoder $\\mathbf{Dec}_{\\mathbf{M}}$ . $\\mathbf{Enc}_{\\mathbf{P}}$ takes as input the prompts of various optional forms such as points, boxes or coarse masks, and translates the prompts into feature tokens $\\mathbf{F}_{\\mathbf{P}}$ . Image feature tokens $\\mathbf{F}_{\\mathbf{I}}$ are also obtained from $\\mathbf{Enc}_{\\mathbf{I}}$ . A series of learnable mask tokens $\\mathbf{F}_{\\mathbf{M}}$ are introduced and concatenated with $\\mathbf{F}_{\\mathbf{P}}$ for diverse masks generation. Then the light weight $\\mathbf{Dec}_{\\mathbf{M}}$ integrates the $\\mathbf{F}_{\\mathbf{I}}$ and the concatenation of $\\mathbf{F}_{\\mathbf{P}}$ and $\\mathbf{F}_{\\mathbf{M}}$ to predict segmentation masks.", + "bbox": [ + 496, + 412, + 893, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DINOv2. Pretrained on a large quantity of curated data with image and patch level distributive self-supervised learning, DINOv2 [35] learns all-purpose visual features that work out of box on many tasks varying from image level, e.g., image classification and pixel level, e.g., semantic segmentation. Moreover, this all-purpose ViT model demonstrates impressive patch-matching ability, robustly capturing similar semantic intent across different objects and even distinct images [27].", + "bbox": [ + 496, + 564, + 893, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Overview", + "text_level": 1, + "bbox": [ + 500, + 710, + 609, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we propose a training-free OVS framework RIM based on visual foundation models. RIM tackles the challenging region classification in OVS from a novel image-to-image matching perspective via the following two procedures, i.e., 1) intra-modal reference features construction, and 2) relation-aware matching. We resort to the SD model [42] and the SAM [22] to establish category reference features in procedure 1). In procedure 2), we conduct ranking based matching between the reference features and the region features in the all-purpose DINOv2 feature space. The details are as follows.", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3954", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/46de0df1f835dd03df09d80de4143d16875f4d51df908b36635ef9b5dcf7b718.jpg", + "image_caption": [ + "Figure 2. Framework of our proposed Relation-aware Intra-modal Matching (RIM) Network. We first explore Stable Diffusion model and SAM to construct image-modal reference features, then we conduct relation-aware matching between region features and reference features based on ranking distribution. The matching is established in the all-purpose feature spaces of DINOv2." + ], + "image_footnote": [], + "bbox": [ + 99, + 95, + 869, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Intra-modal Reference Construction", + "text_level": 1, + "bbox": [ + 76, + 478, + 393, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast to the substantial gap between abstract, monotonous text features and the concrete, diverse image features, homogenous modality features naturally exhibit improved alignment characteristics as shown in Fig. 6. We resort to stable diffusion model to generate a handful of reference images $\\mathcal{I} = \\{\\mathbf{I}_1^c,\\mathbf{I}_2^c,\\dots ,\\mathbf{I}_K^c |\\mathbf{I}_k^c\\in \\mathbb{R}^{H\\times W\\times 3},c = 1,2,\\ldots ,C\\}$ for all $C$ candidate classes by simply prompting it with \"a photo of [category name]\". Together with the images, we also acquire the corresponding cross-attention maps for localizing the foreground targets. Specifically, for time step $t$ , the noisy image features $\\mathbf{F}_v\\in \\mathbb{R}^{h\\times w\\times c}$ are flattened and linearly projected into the queries $\\mathbf{Q}$ and the prompt features $\\mathbf{F}_p\\in \\mathbb{R}^{N\\times d}$ are respectively projected into the keys $\\mathbf{K}$ and values $\\mathbf{V}$ :", + "bbox": [ + 75, + 501, + 470, + 712 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {F} _ {v} \\mathbf {W} ^ {\\mathcal {Q}}, \\quad \\mathbf {K} = \\mathbf {F} _ {p} \\mathbf {W} ^ {\\mathcal {K}}, \\quad \\mathbf {V} = \\mathbf {F} _ {p} \\mathbf {W} ^ {\\mathcal {V}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 722, + 468, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Among which, $\\mathbf{W}^{\\mathcal{Q}}, \\mathbf{W}^{\\mathcal{K}}, \\mathbf{W}^{\\mathcal{V}}$ are linear projections. The cross-attention maps are calculated as:", + "bbox": [ + 76, + 751, + 468, + 782 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 792, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the $\\sqrt{d}$ is the scaling factor. Cross-attention maps $S_{n}^{l,t}$ of different text tokens from different layers of UNet can be obtained based on the Equ. 2 and $n,l,t$ are the index of text tokens, UNet layers and diffusion steps, respectively. To", + "bbox": [ + 75, + 838, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "obtain the cross-attention map corresponding to the category token for foreground mining, we follow [60] to aggregate normalized multi-time and multi-layer maps, formally,", + "bbox": [ + 498, + 479, + 890, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathcal {S}} _ {n} = \\frac {1}{L \\cdot T} \\sum_ {l \\in L, t \\in T} \\frac {\\mathcal {S} _ {n} ^ {l , t}}{\\operatorname* {m a x} \\left(\\mathcal {S} _ {n} ^ {l , t}\\right)}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 534, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where the $L$ and $T$ denote the total time steps and the number of UNet layers.", + "bbox": [ + 498, + 584, + 890, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The foreground area in the synthesized images should be further located to avoid the interference of the irrelevant background regions. However, simply binarizing the cross-attention maps by thresholding may fail to fully capture the target. We thus exploit SAM to generate target masks by sampling the prompt points within the binarized attention maps. The foreground masks $\\mathcal{M} = \\{\\mathbf{M}_1^c,\\mathbf{M}_2^c,\\dots,\\mathbf{M}_K^c |\\mathbf{M}_k^c\\in$ $\\mathbb{R}^{h\\times w},c = 1,2,\\ldots ,C\\}$ and corresponding images $\\mathcal{I}$ then serve as the class references.", + "bbox": [ + 496, + 614, + 893, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enhance the robustness of instance-level matching, we opt to construct class reference image features within the all-purpose feature space of DINOv2 [35] via mask average pooling (MAP). Specifically,", + "bbox": [ + 496, + 750, + 890, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {r e f} = \\left\\{\\mathbf {F} ^ {c} \\mid \\mathbf {F} ^ {c} = \\frac {1}{K} \\sum_ {k \\in K} \\mathbf {M A P} \\left(\\varphi \\left(\\mathbf {I} _ {k} ^ {c}\\right), \\zeta \\left(\\mathbf {M} _ {k} ^ {c}\\right)\\right) \\right\\} _ {c = 1} ^ {C} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 820, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the $\\varphi$ and $\\zeta$ denote the DINOv2 feature extractor (ViT) and the bilinear-interpolation resize function, respectively.", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3955", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $\\mathbf{F}^c\\in \\mathbb{R}^{1\\times D}$ represents the average of all synthesized foreground features. We also construct a background reference feature by averaging all the background features of synthesized images. Similarly, region features within the test image specified by mask proposals are obtained as:", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {t e s t} = \\left\\{\\mathbf {F} ^ {p} | \\mathbf {F} ^ {p} = \\mathbf {M A P} (\\varphi [ \\mathbf {I} _ {t e s t} ], \\zeta [ \\mathbf {M} ^ {p} ]) \\right\\} _ {p = 1} ^ {P}, \\quad (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 176, + 470, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "among which $\\mathbf{P}$ is the number of masks generated by SAM. By designing collaborative interactions among various visual foundational models, we establish well refined image-modal reference features thus shifts the paradigm of region classification in OVS from cross-modal matching to better-aligned intra-modal matching.", + "bbox": [ + 75, + 207, + 470, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Relation-aware Matching", + "text_level": 1, + "bbox": [ + 76, + 306, + 308, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The naive region classification strategy only selectively recruits the class reference feature with the highest similarity. However, independently taking each category exacerbates the risk of mismatches owing to the intra-class diversity and interference from similar categories. To further harness the structure information implicit in inter-class relationship for more effective matching, we select the top N reference features most similar to the region feature $\\mathbf{F}^p$ as category agents $\\mathbf{A}^p\\in \\mathbb{R}^{N\\times D}$ . We derive the scores of region-agent relation $s^p\\in \\mathbb{R}^{1\\times N}$ between the region feature $\\mathbf{F}^p$ and the category agents $\\mathbf{A}^p$ using cosine similarity:", + "bbox": [ + 75, + 330, + 468, + 498 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} ^ {p} = \\frac {\\mathbf {F} ^ {p} \\left(\\mathbf {A} ^ {p}\\right) ^ {\\mathsf {T}}}{\\| \\mathbf {F} ^ {p} \\| _ {2} \\cdot \\| \\mathbf {A} ^ {p} \\| _ {2}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 507, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The core idea is that we take the agent ranking as a random event rather than a deterministic permutation. This implies that each permutation of the category agents is present with a certain probability, as opposed to the exclusive existence of the permutation ordered from largest to smallest. The probability of one permutation $\\pi \\in \\mathcal{P}(|\\mathcal{P}| = N!)$ given s (we omit region index $p$ for brevity) can be calculated as:", + "bbox": [ + 75, + 551, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP (\\pi | \\mathbf {s}) = \\prod_ {k = 1} ^ {K} \\frac {\\mathbf {s} _ {\\pi (k)}}{\\sum_ {k ^ {\\prime} = k} ^ {K} \\mathbf {s} _ {\\pi \\left(k ^ {\\prime}\\right)}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 669, + 468, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "among which the $\\pi(k)$ denotes the $k^{th}$ class index of this permutation. For instance, assume that for a given region, the selected agents correspond to the categories \"sofa\", \"chair\", and \"bench\" respectively. One of the permutations of these three agents is $\\pi = (\\text{chair}, \\text{sofa}, \\text{bench})$ . We can derive the probability of $\\pi$ based on the region-agent relation s:", + "bbox": [ + 75, + 723, + 468, + 814 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP (\\pi | \\mathbf {s}) = \\frac {\\mathbf {s} (\\text {c h a i r})}{\\mathbf {s} (\\text {s o f a}) + \\mathbf {s} (\\text {b e n c h}) + \\mathbf {s} (\\text {c h a i r})} \\cdot \\frac {\\mathbf {s} (\\text {s o f a})}{\\mathbf {s} (\\text {s o f a}) + \\mathbf {s} (\\text {b e n c h})}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 825, + 491, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By associating the probabilities of all $|\\mathcal{P}|$ permutations, We convert the scores of individual region-agent relations into", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "class ranking probability distributions $P(\\pi \\in \\mathcal{P}|\\mathbf{s}^p) \\in \\mathbb{R}^{1 \\times |\\mathcal{P}|}$ , effectively modeling the inter-class relationship. Similarly, we compute the agent-ranking probability distributions for each category reference features on the same category agents, resulting in $P(\\pi \\in \\mathcal{P}|\\mathbf{s}^r) \\in \\mathbb{R}^{1 \\times |\\mathcal{P}|}$ , where $\\mathbf{s}^r$ is obtained through Equ. 6. The distribution of the region is compared against the distributions of all reference features via cosine similarity, enabling the determination of the classification result:", + "bbox": [ + 496, + 90, + 893, + 226 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc l s = \\underset {r = 1, 2, \\dots , C} {\\arg \\max } [ \\mathbf {c o s i n e} (P (\\pi \\in \\mathcal {P} | \\mathbf {s} ^ {p}), P (\\pi \\in \\mathcal {P} | \\mathbf {s} ^ {r})) ]. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 239, + 893, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further leverage the advantage of diversity in image-modal reference features, we construct a series of subcategory reference features by clustering the foreground prototypes (obtained by mask average pooling) of all synthesized images. The subcategory reference features are involved in the similarity computation instead of the holistic ones, and the final score of a category is obtained by summing up the similarities of all the corresponding subcategory reference features. The classification result is then obtained by:", + "bbox": [ + 496, + 279, + 893, + 415 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc l s = \\underset {r = 1, 2, \\dots , C} {\\arg \\max } \\left[ \\sum_ {t = 1} ^ {T} \\operatorname {c o s i n e} \\left(P \\left(\\pi \\in \\mathcal {P} \\mid \\mathbf {s} ^ {p}\\right), P \\left(\\pi \\in \\mathcal {P} \\mid \\mathbf {s} _ {t} ^ {r}\\right)\\right) \\right]. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 426, + 890, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the metric grounded in distributional similarity, instances of erroneous region classification can be effectively reduced as inter-class relationships are exploited to facilitate disambiguation.", + "bbox": [ + 496, + 481, + 890, + 541 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 556, + 632, + 573 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Evaluation Metric", + "text_level": 1, + "bbox": [ + 500, + 580, + 772, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our model on three commonly used benchmarks, namely, PASCAL VOC 2012 [14], PASCAL Context [34] and COCO Object [25], which have 20,59,80 foreground classes, respectively. We also consider an extra background class in all three datasets. Training sets of datasets are not needed as the proposed method is training-free. For a fair comparison with previous approaches, we directly evaluate our method on the validation sets of these datasets, including 1449, 5105, and 5000 images, respectively. We use the mean of class-wise intersection over union (mIoU) following the common practice to measure the performance.", + "bbox": [ + 496, + 604, + 890, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation of Visual Foundation Models", + "text_level": 1, + "bbox": [ + 498, + 771, + 883, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt the Stable Diffusion model v1.4 [42] to generate category-specific images of resolution $512 \\times 512$ for category reference feature construction. We employ DINOv2 [35] with a ViT-B [12] as the default image encoder for more discriminative matching. Specifically, the keys sequence of the last attention layer is reshaped as the feature map. SAM [22] with ViT-B is adopted as the segmenter. We collect $32 \\times 32$", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3956", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8e1ea4ec9d843ca71f6eea3e6ac5763f03fc510970fac644222df0b9272ed961.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodArchTraining datasetSupervisionZero-shot transferDownstream datasets
PASCAL VOCPASCAL ContextCOCO Object
DeiT [52]ViTIN-1Kclass label✘53.035.9-
MoCo [16]ViTIN-1Kself✘34.321.3-
DINO [3]ViTIN-1Kself✘39.120.4-
ViL-Seg [26]ViTCC12Mself+text✓33.615.9-
MaskCLIP [75]ViTLAIONtext + \\(CLIP_{\\mathrm{T}}\\)✓38.823.620.6
GroupViT [64]ViTCC12Mtext✓52.322.4-
ZeroSeg [5]ViTIN-1K\\(CLIP_{\\mathrm{V}}\\)✓40.820.420.2
TCL [4]ViTCC3M+CC12Mtext✓51.224.330.4
ViewCo [41]ViTCC12M+YFCCtext+self✓52.423.023.5
CLIPpy [40]ViTHQITP-134Mtext✓52.2-32.0
SegCLIP [29]ViTCC3M+COCOtext + \\(CLIP_{\\mathrm{T}}\\)✓52.624.726.5
OVSegmentor [65]ViTCC4Mself+text✓53.820.425.1
SimSeg [69]ViTCC3M+CC12Mtext✓57.426.229.7
DiffSeg [53]UNet+ViT✓60.127.537.9
OVDiff [21]UNetTraining-free✓67.130.134.8
OursUNet+ViT✓77.834.344.5
", + "bbox": [ + 99, + 88, + 870, + 328 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9adf5c9e0a19bc5ee8c0132ffb38df95f09d6a89091fae9d044cf089a6112acb.jpg", + "table_caption": [ + "Table 1. Comparison with existing methods. Models in the first three rows are finetuned on target datasets while the rest approaches perform zero-shot transfer. Bold fonts refer to the best results among the models which enable zero-shot transfer. With only image-text pairs available, our method significantly outperforms the existing approaches. More results please refer to Supplementary Material." + ], + "table_footnote": [], + "table_body": "
IRCRMmIOU
w/o fg-maskw/ fg-maskw/o subw/ sub
26.7
✓38.7
✓41.8
✓✓43.1
✓✓44.5
", + "bbox": [ + 81, + 377, + 468, + 489 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3ec3463ab2ba5e3dbc4a2950f73bc6bf2e75917acf57ddaf142b4c13ff7d9985.jpg", + "table_caption": [ + "Table 2. Ablation studies of the proposed RIM. We mainly verified the effectiveness of the image reference construction (IRC), and relation-aware matching (RM). Moreover, we also observe the effectiveness of foreground segmentation (fg-mask) of synthesized images and the subcategory reference features (sub)." + ], + "table_footnote": [], + "table_body": "
EncoderCLIP [38]SD [42]MAE [17]DINOv2
mIoU42.043.139.544.5
", + "bbox": [ + 81, + 580, + 468, + 623 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/079b8ded360ae5557f6e1a29be7cb677d7b78dc3c44e3458982ce842c986cf15.jpg", + "table_caption": [ + "Table 3. Comprison of different image feature extractors." + ], + "table_footnote": [], + "table_body": "
SegmenternoneMaskFormerSAM
mIoU42.076.777.8
", + "bbox": [ + 81, + 656, + 292, + 686 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/57b5b035fd684bbfc34b3ef769464508714197dc3f495af0b90d3ad8d63d402b.jpg", + "table_caption": [ + "Table 4. Comparison of mask proposal generators. \"none\" means direct pixel classification." + ], + "table_footnote": [], + "table_body": "
Selection of AgentsmIoU
Rand43.8
Top-N44.5
", + "bbox": [ + 310, + 650, + 467, + 693 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Comparison of category agents selection.", + "bbox": [ + 307, + 695, + 467, + 723 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "prompt points in a grid manner to generate mask proposals for the test images. To segment the foreground of synthesized reference images, We sample 5 prompt points within the binarized cross-attention map, where the binarization threshold is set to a relatively high value of 0.7 to prevent erroneous segmentation of background regions. The number of category agents is set to 4. More implementation details are provided in Supplementary materials.", + "bbox": [ + 75, + 780, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison to the state-of-the-arts", + "text_level": 1, + "bbox": [ + 498, + 377, + 805, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with approaches that have been trained with fully supervised finetuning transfer and zero-shot transfer. Besides, we also conduct performance comparisons with newly arising train-free approaches. Table 1 summarizes the results of the comparison.", + "bbox": [ + 496, + 400, + 893, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Firstly, we can observe that the proposed RIM significantly surpasses the non-zero-shot fully supervised segmentation baselines, i.e., DeiT [52], MoCo [16]. Furthermore, we compare with other zero-shot OVS approaches such as MaskCLIP [75], SegCLIP [29], and SimSeg [69], which also adopt the ViT backbones of visual foundation model, i.e., CLIP [38]. Our method also shows a clear lead. Specifically, we achieve $20.4\\%$ , $18.1\\%$ , $14.8\\%$ mIoU over the SimSeg [69] on three datasets, respectively. We posit that the primary cause is that CLIP is susceptible to ambiguities in spatial relations and confusion of co-occurring objects, a consequence stemming from its holistic training objective. Besides, RIM also demonstrates significant performance improvements over the most recently developed training-free methods based on visual foundation models, achieving $10.4\\%$ , $4.2\\%$ , and $6.6\\%$ mIoU gains, respectively. As shown in Fig. 3, we present a series of visualizations depicting segmentation outcomes across various datasets for a more intuitive observation.", + "bbox": [ + 496, + 476, + 895, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 771, + 653, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A series of ablation studies are conducted to thoroughly investigate the impact of each component of the proposed RIM. As shown in Table 2, we mainly implement our experiments on COCO Object [25] dataset, and the first row is our baseline, which follows a naive image-to-text matching for region classification. Specifically, we crop the test image along the bounding boxes corresponding to the mask proposals (gen-", + "bbox": [ + 496, + 794, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3957", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f7fefb3235c805360970ef272402c68249933a8242d075de54e7faee4c48c6e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 90, + 292, + 202 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/867fe7434e9d76eeb74203c4847698d61610b23396fcafe2494fce4678231a16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 90, + 467, + 202 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6fc90e8ae8c1d7cc4a54101fb45d14c65bd0dd3b73ff3493bf4e6f6caaabe777.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 467, + 90, + 653, + 202 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e8211fe90554a9045528e5d3debd1936eaa56cce72392e05c188a165f7ef007.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 90, + 859, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/268413f93dc76be9f6e559e053d34c5de64ad96b47938fc05c213b914702bce7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 203, + 246, + 318 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c6afc306f89e5c088196397d819373931d4ff5519966232559c23c72edc16f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 246, + 202, + 447, + 318 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0274cd0829002b6c82026b91658b2b79c7cfa384e0bb6507137eabb0b285841f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 449, + 202, + 658, + 318 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5755da2ad19877770e1da74ff0a478c87b6f775d0042f4053befce0de2fff56.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 202, + 859, + 318 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/014d7cac9ec6facc9f398e4242bb8c57bcf1c67eb5c245298b3d6a431bfe3b7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 319, + 292, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0a8eb40de9b828c4c549352604ec580fc7f4463f84a591cee2018e7d0473b23a.jpg", + "image_caption": [ + "Figure 3. Qualitative results of our method." + ], + "image_footnote": [], + "bbox": [ + 292, + 318, + 465, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5111f44e9523b66f45eaac5559e34dd1a5b36718be20e6f714cb7fc8c5db2d9c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 465, + 318, + 694, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08600b502d22f9042fdc3b46f1e382239c11b4459ab232c00de14bbd4bc1ca65.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 318, + 859, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "erated by SAM) and resize them to $224 \\times 224$ resolution. The background area of the cropped image is filled with zeros, and then CLIP [38] with ViT-B is exploited to perform image-to-text matching between the cropped image and category labels.", + "bbox": [ + 75, + 438, + 470, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study on intra-modal reference construction. To verify the effectiveness of intra-modal alignment, we first construct a naive image-to-image matching as the $2^{nd}$ row of Table 2. More concretely, DINOv2 features of all synthesized images of a category are condensed to a holistic reference feature via global average pooling. The matching process is simply implemented with cosine similarity. Despite its simplicity, this intra-modal matching exhibits a significant performance improvement, i.e., $12.0\\%$ in mIoU over the cross-modal matching based on CLIP. This improvement is anticipated as the holistic training objective of CLIP makes its prediction heavily reliant on contextual information. This reliance not only introduces spatial confusion but also leads to misclassification of frequently co-occurring objects, such as the sky and airplane. Attributed to the image generation capabilities of SD model and the robust high-level semantic feature extraction of DINOv2, an improved intra-modal alignment between region features and class reference features is achieved.", + "bbox": [ + 75, + 518, + 470, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Further performance improvements can be observed if we construct the category reference features with only foreground features as shown in the $3^{th}$ row of Table 2. We deem the main reason is that the background areas in synthetic images may contain information of other categories, which confuses the classification process. While in our im", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "plementation, more refined category reference features are constructed attributed to the spatial localization ability of the SD model embedded in the cross-attention map and the powerful segmentation capability of SAM, which effectively mitigates the influence of cluttered backgrounds. Despite utilizing merely cosine similarity for intra-modal matching, it has already achieved impressive performance, i.e., $44.5\\%$ mIoU on COCO Object dataset, which can be adopted as a strong baseline for further research.", + "bbox": [ + 496, + 438, + 893, + 573 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study on relation-aware matching. As described in Sec. 3.5, we propose to model the beneficial structure information contained in inter-class relationships via relation-aware matching. Compared to the naive approach that only considers only the cosine similarity between region features and each individual category reference feature, our proposed strategy achieves a sizeable gain, i.e., $1.3\\%$ in mIoU, as presented in the $3^{rd}$ and $4^{th}$ rows of Table 2. The results prove that the proposed similarity measurement based on ranking distribution facilitates effective disambiguation in the matching process, which brings a notable reduction in the misclassification of regions.", + "bbox": [ + 496, + 579, + 893, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "After integrating subcategory reference features into relation-aware matching, the performance further improved from $43.1\\%$ to $44.5\\%$ in mIoU, as shown in $5^{th}$ row of Table 2. This improvement can be attributed to the ability of the SD model to generate diverse image features, enabling our method to effectively handle intra-class diversity. Moreover, the scoring scheme in Equ. 10, akin to a voting mechanism, further enhances the robustness of the matching process. Furthermore, in Table 5, we demonstrate that reference features", + "bbox": [ + 496, + 765, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3958", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67f6c1aa8e6fad3bc328b12b66e6b7b5cea8e3560bf821f7d62eb37aa51bc79b.jpg", + "image_caption": [ + "Figure 4. Effectiveness of SAM based region-level matching. The SAM could well capture visual concepts within images." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 459, + 210 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d187ed82499ca9b19e671226db467d30b17222254de3c8755b6bbc19760f4ca.jpg", + "image_caption": [ + "Figure 5. Hyperparameter experiments on the number of subcategories and binarization threshold of cross-attention map." + ], + "image_footnote": [], + "bbox": [ + 78, + 243, + 272, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eefa186be170b0a3346d9cb77cfaa4d6df9e2bd4c82ab8bfed4bf056814955bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 243, + 460, + 339 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that share high similarities with region features are better candidates to serve as category agents.", + "bbox": [ + 76, + 382, + 468, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on DINOv2. To demonstrate the superiority of feature extraction using DINOv2, we conduct comparison experiments of CLIP [38], MAE [17], Stable Diffusion Unet (SD) [42], and DINOv2 as presented in Table 3. DINOv2 achieves the best performance attribute to effective pretraining based on image-level and patch-level discriminative self-supervised learning. While CLIP fails to match region-level features precisely, Stabel Diffusion UNet is constrained to some extent under the unconditional settings. MAE exhibits suboptimal performance in our setting due to its relatively limited high-level semantic modeling capability.", + "bbox": [ + 75, + 412, + 468, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on SAM. Our relation-aware matching operates at the region level, as SAM furnishes comprehensive mask proposals for the test images. To explore the effectiveness of SAM, on the PASCAL VOC dataset, we compare SAM with modified MaskFormer [9] pre-trained on the COCO-stuff dataset following [24]. We also construct a vanilla baseline that compares category reference features with pixel features of test images directly. As shown in Table 4, both segmenters outperform the baseline by a large margin. We deem the main reason is that the region-level matching is more robust than pixel-level one. As illustrated in Fig. 4, the pixel classification paradigm fails to capture all visual concepts within images. SAM slightly surpasses MaskFormer as SAM can generate higher-quality masks on novel classes, naturally more suitable for open-vocabulary tasks.", + "bbox": [ + 75, + 582, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Investigation of the intra-modal matching. In Fig. 6, we visualized the t-SNE plots of the region features alongside their corresponding text-modal reference features and image-modal reference features using the same image based on CLIP [38] and DINOv2 [35], respectively. It can be observed that in the all-purpose feature space of DINOv2, the", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3b2907540b3019077d7b15e83adeb4e514d523aa5c8ee2549cc18f4b8476af7c.jpg", + "image_caption": [ + "Figure 6. T-SNE visualization of features of different region, as well as corresponding intra-modal and cross-modal reference features." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 681, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f878055b0c74de40bbad91081d0931334fffb5a9a78b84f200de2f0c653b2822.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 89, + 880, + 229 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "region features of different categories are well-differentiated and align well with their corresponding reference features. However, in the case of CLIP, different region features not only exhibit notable overlap but also fail to align effectively with corresponding text-modal reference features. This difference substantiates the underlying rationale of our motivation, i.e., intra-modal matching.", + "bbox": [ + 496, + 277, + 893, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyperparameter Evaluations. Quantitative experiments are conducted to find a suitable number of subcategories used in relation-aware matching. As illustrated in Fig. 5 (a), the performance continues to grow until the number achieves 8, beyond which it starts to decline. It is reasonable as an appropriate number of subcategory references can model category diversity, but over-partitioning may lead to deviations from instance features. We then explore how the binarization threshold affects the performance in Fig. 5 (b). The model shows low sensitivity to threshold values owing to the capability of SAM, with a setting of 0.7 yields marginally better results.", + "bbox": [ + 496, + 388, + 890, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 595, + 617, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we presented a training-free Relation-aware Intra-modal Matching (RIM) framework to tackle the challenging open-vocabulary semantic segmentation. We construct better-aligned image-modal category reference features based on the Stable Diffusion model and SAM. Then a relation-aware matching strategy is employed for region classification. RIM not only achieves results significantly surpassing the state-of-the-art but also opens up new avenues for OVS from an image-to-image matching perspective.", + "bbox": [ + 496, + 625, + 893, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 787, + 678, + 804 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by the National Defense Basic Scientific Research Program of China (Grant JCKY2021130B016), National Nature Science Foundation of China (Grant 12150007), Youth Innovation Promotion Association CAS 2018166.", + "bbox": [ + 496, + 816, + 893, + 886 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3959", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.13, + 0.856, + 0.177 + ], + "angle": 0, + "content": "Image-to-Image Matching via Foundation Models: A New Perspective for Open-Vocabulary Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.203, + 0.245, + 0.222 + ], + "angle": 0, + "content": "Yuan Wang\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.28, + 0.203, + 0.362, + 0.221 + ], + "angle": 0, + "content": "Rui Sun\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.4, + 0.204, + 0.512, + 0.222 + ], + "angle": 0, + "content": "Naisong Luo" + }, + { + "type": "text", + "bbox": [ + 0.549, + 0.204, + 0.647, + 0.221 + ], + "angle": 0, + "content": "Yuwen Pan" + }, + { + "type": "text", + "bbox": [ + 0.684, + 0.204, + 0.831, + 0.222 + ], + "angle": 0, + "content": "Tianzhu Zhang\\(^{1,2\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.222, + 0.677, + 0.257 + ], + "angle": 0, + "content": "1University of Science and Technology of China 2Deep Space Exploration Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.26, + 0.794, + 0.275 + ], + "angle": 0, + "content": "{wy2016, issunrui, lns6, panyw}@mail.ustc.edu.cn, {tzzhang}@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.705 + ], + "angle": 0, + "content": "Open-vocabulary semantic segmentation (OVS) aims to segment images of arbitrary categories specified by class labels or captions. However, most previous best-performing methods, whether pixel grouping methods or region recognition methods, suffer from false matches between image features and category labels. We attribute this to the natural gap between the textual features and visual features. In this work, we rethink how to mitigate false matches from the perspective of image-to-image matching and propose a novel relation-aware intra-modal matching (RIM) framework for OVS based on visual foundation models. RIM achieves robust region classification by firstly constructing diverse image-modal reference features and then matching them with region features based on relation-aware ranking distribution. The proposed RIM enjoys several merits. First, the intra-modal reference features are better aligned, circumventing potential ambiguities that may arise in cross-modal matching. Second, the ranking-based matching process harnesses the structure information implicit in the inter-class relationships, making it more robust than comparing individually. Extensive experiments on three benchmarks demonstrate that RIM outperforms previous state-of-the-art methods by large margins, obtaining a lead of more than \\(10\\%\\) in mIoU on PASCAL VOC benchmark." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.734, + 0.21, + 0.749 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.759, + 0.471, + 0.866 + ], + "angle": 0, + "content": "Aiming at allocating semantic labels to the corresponding pixels, semantic segmentation has achieved conspicuous achievements attributed to the development of large-scale datasets [11, 22, 25, 74] and elaborate algorithms [7, 8, 28]. However, the capabilities of conventional semantic segmentation models are restricted to predefined training categories, failing to recognize a broader spectrum of concepts, which" + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.311, + 0.83, + 0.322 + ], + "angle": 0, + "content": "(a) Text-to-image Matching V.S. Image-to-image Matching" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.322, + 0.889, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.578, + 0.419, + 0.823, + 0.429 + ], + "angle": 0, + "content": "(b) Individual Matching V.S. Relation-aware Matching" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.429, + 0.889, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.529, + 0.895, + 0.612 + ], + "angle": 0, + "content": "Figure 1. Motivation of our method. (a) False matches tend to occur in cross-modal features. We establish well-aligned image-modal reference features thus transit the text-to-image matching to image-to-image matching. (b) Individual matching tends to suffer from disturbances. We propose a novel relation-aware matching strategy for more robust region classification." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.689 + ], + "angle": 0, + "content": "poses a severe limitation for their practical applications. In pursuit of the human-like intelligence of unbounded and fine-grained scene understanding, open-vocabulary segmentation (OVS) [2, 67] has attracted increasing interest recently, which enables segmentation with an unrestricted vocabulary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.896, + 0.902 + ], + "angle": 0, + "content": "OVS is highly challenging as it requires not only grouping all pixels to corresponding visual concepts but also assigning each region the correct semantic label from a large vocabulary. Some early attempts [29, 64] optimize the pixel grouping process and the classification of visual concepts simultaneously by employing contrastive learning with image-text pairs. These methods inevitably yield masks of relatively low quality with only coarse supervision available. Another line of works [24, 67, 68] significantly dominate this field by modeling the OVS as a region recognition problem, which decouple OVS into two procedures, i.e. class-agnostic mask proposals prediction and mask class recognition. Though the mask proposals generation has been significantly improved with the assistance of pixel-level supervision and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.204, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.22, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3952" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "elaborate segmenter architectures (e.g. Mask2Former [8]), the unsatisfactory region class recognition has emerged as the performance bottleneck of OVS [24]. We attribute this to the natural gap between the highly abstract and monotonous category textual features and the visual features that are more concrete and diverse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.474, + 0.442 + ], + "angle": 0, + "content": "Most current OVS approaches achieve mask class recognition via cross-modal region-category alignment based on the pretrained vision-language models (e.g., CLIP [38]). Despite its exemplary generalization ability on downstream classification tasks, CLIP usually suffers from spatial relations ambiguity [66, 69] and co-occurring object confusion ascribed to the holistic pre-training objective. On the other side, also pre-trained on internet-scale data, Stable Diffusion [42] (SD) model has garnered growing research interest credited to the phenomenal power of synthesizing photorealistic images with diverse and plausible content conditioned on textual descriptions. Considering that features from the same modality inherently exhibit a higher degree of alignment compared to cross-modal features (as shown in Fig. 6), we ask the question: \\(\\mathbf{0}\\) is it possible to transition the region classification in OVS from image-to-text matching to image-to-image matching using the SD model?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.474, + 0.763 + ], + "angle": 0, + "content": "Before tackling this issue, we first revisit the common practices in mask class recognition [24, 67], which involves matching visual concepts with a set of category reference features (e.g. category textual features from CLIP). Inspired by previous exploration [59, 60, 73] of the strong image-text correspondence exhibited by the SD model, we can establish better-aligned intra-modal category reference features as shown in Fig. 1 (a). The cross-attention maps in the conditional generation process could serve as exceptional tools to further refine the category features. Nonetheless, it is still non-trivial to map test region features to their corresponding category reference features precisely, as the intra-class diversity and disturbances from akin categories exhibit in practical scenarios potentially lead to mismatches. Previous methodologies process each category independently during the matching phase, overlooking the informative inter-class relationships, which implicitly integrate structured contextual information and effectively aid in disambiguation. Here another question arises: how to harness the structure information modeled in the inter-class relationship to facilitate more accurate matching?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Driven by this question, we carefully design the relation-aware similarity measurement that incorporates the relations of the current region with some semantic relevant category agents. For a specified region feature within test image, a subset of category reference features that most akin to the region are selected to serve as category agents. The central idea is that we regard the category agent ranking as a stochastic event rather than a deterministic permutation. For example, in ranking, given the region feature specified by the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.272 + ], + "angle": 0, + "content": "mask proposal \\( m_{1} \\) in Fig. 1 (a), its scores vary for different category agents, which can be taken as probabilities. The probability of being ranked first is 0.45 of the agent 'desk' and 0.35 of the agent 'chair'. The ranking permutation reflects the relevance of the corresponding categories w.r.t. the region feature. An agent-ranking probability distribution can be constructed by associating the probability with every rank permutation for both the region feature and all category reference features. Finally, as illustrated in Fig. 1 (b), we transform the similarity measurement from individual region-reference comparison to relation-aware agent-ranking distribution similarity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.897, + 0.514 + ], + "angle": 0, + "content": "In this paper, we present a training-free OVS framework RIM to achieve Relation-aware Intra-modal Matching based on visual foundation models that coherently addresses the questions 1-2. Specifically, we facilitate a synergistic collaboration between the SD model and SAM to generate category-specific reference features by prompting the Segment Anything Model [22] (SAM) with points selected from the cross-attention map within SD model. SAM is further adopted to provide mask proposals of the test images. Finally, we conduct the relation-aware matching based on ranking distribution in the robust all-purpose feature space of DINOv2 [35]. RIM ensembles expertise of different visual foundational models in a complementary manner, enhancing mask quality and region-category matching precision simultaneously. Moreover, the overall framework is training-free, substantially mitigating the risk of overfitting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.897, + 0.697 + ], + "angle": 0, + "content": "Our contributions can be concluded as follows: (1) We reveal the problems of region feature classification in OVS and propose to construct well-aligned intra-modal reference features to circumvent ambiguities of cross-modal matching. (2) We design a relation-aware matching strategy based on ranking distribution, which captures structure information implicit in inter-class relationships and enables more robust matching. (3) We propose a training-free relation-aware intra-modal matching (RIM) network for OVS based on visual foundation models. Extensive experiments demonstrate that RIM remarkably surpasses previous state-of-the-art methods by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.642, + 0.725 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Semantic Segmentation is a fundamental computer vision task with widespread applications in fields such as medical image processing [31, 37, 46, 48, 49, 58], video analysis [47, 51]. The pioneering FCN [28] has inspired a multitude of subsequent endeavors [6, 7, 43, 62, 72] centered around Convolutional Neural Networks (CNN). Beyond the CNN-based models, the triumph of the Vision Transformer (ViT) has spurred a succession of transformer-based segmentation models [30, 45, 63, 71], which have progressively evolved into a unified segmentation framework [8, 9] capable of addressing various segmentation tasks. Some alternative" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3953" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "settings, such as few-shot [23, 55-57], semi-supervised [23, 32, 33, 50], or weakly supervised [19, 54] segmentation, attempt to enhance the practicality of semantic segmentation techniques. Despite their success, these models are confined to predefined training categories or the specific foreground class, failing to recognize a broader spectrum of categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.474, + 0.47 + ], + "angle": 0, + "content": "Open-vocabulary Semantic Segmentation aims to segment images with arbitrary categories described by texts. Some efforts [2, 29, 61, 65, 69] concentrated on developing a joint embedding space that bridges image pixels with class names or descriptions via learning objectives established from image-text pairs. For example, GroupViT [64] designed a hierarchical grouping transformer and learned the alignment between groups and text via contrastive loss. Another line of works [24, 66, 67] models OVS as a region recognition task by decoupling it into mask proposal generation and region classification, achieving notable progress attributed to advanced segmentation architectures [8] and pixel-level annotations [25, 74]. Large-scale vision-language pre-training models such as CLIP [38] and ALIGN [20] have been widely applied for OVS [15, 68, 70] which endows OVS model enhanced generalization. However, those pretraining models often encounter spatial confusion in dense prediction tasks [69], leading to recurring misclassification issues, which has emerged as a critical bottleneck in OVS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.474, + 0.729 + ], + "angle": 0, + "content": "Visual foundation models is catching up with the research in natural language processing (NLP) [1, 10, 36] and have achieved conspicuous achievements across a wide range of visual tasks. For example, DINov2 [35] establishes an impressive all-purpose feature extractor via self-supervised learning at both the image and patch levels. Trained on over 1 billion masks, Segment Anything Model (SAM) [22] has demonstrated astonishing zero-shot class-agnostic segmentation performance. Diffusion models [18, 44] have propelled the advancement of a series of image-to-text generation systems such as DALL-E [39] and Stable Diffusion model [42]. A series of works [27, 60, 66] render visual foundation models as powerful out-of-the-box tools to handle downstream tasks. Though a single foundation model may have limited capacity in addressing complex visual tasks such as OVS, in this work, we demonstrate that integrating different foundation models leads to positive synergies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.745, + 0.17, + 0.76 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.26, + 0.785 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Open-vocabulary segmentation aims to segment any image against a new vocabulary of categories \\(\\mathbf{C}_{test}\\). Previous approaches typically involve training models on datasets annotated with image-level textual labels or pixel-level masks, with the category set \\(\\mathbf{C}_{train}\\). \\(\\mathbf{C}_{test}\\) contains novel categories not exposed to the training process, i.e., \\(\\mathbf{C}_{train} \\neq \\mathbf{C}_{test}\\). Owing to the training-free nature of our method, it inher" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "ently operates under a more challenging zero-shot setting wherein all test categories are considered novel." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.133, + 0.855, + 0.148 + ], + "angle": 0, + "content": "3.2. Preliminary of Vision Foundation Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.156, + 0.895, + 0.413 + ], + "angle": 0, + "content": "Stable-Diffusion model. Different from discriminative image-text models that model the class probability distribution \\( \\pmb{p}(\\pmb{c}|\\pmb{i}) \\) given the image, text-to-image stable diffusion model encode a text-conditional distribution of possible images \\( \\pmb{p}(\\pmb{i}|\\pmb{c}) \\). This model demonstrates the prowess to synthesize high-fidelity images \\( \\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3} \\) that closely align with the specified conditional text \\( \\mathcal{T} \\), all originating from a latent space defined by random Gaussian noise \\( \\mathbf{z} \\sim \\mathcal{N}(0,1) \\). Specifically, stable diffusion model consists of three components: a pre-trained variational autoencoder (VAE) [13] that encodes and decodes the image latent code, a text encoder for prompt embedding, and a time-conditional UNet [43] for the denoising of latent vectors. The visual-text interaction occurs in the cross-attention layers that are integral to the UNet structure for each denoising step. Target categories within synthesized images can be accurately localized based on class-discriminative cross-attention maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.895, + 0.565 + ], + "angle": 0, + "content": "Segment Anything Model. SAM comprises of three components: an image encoder \\(\\mathbf{Enc}_{\\mathbf{I}}\\), a prompt encoder \\(\\mathbf{Enc}_{\\mathbf{P}}\\), and fast mask decoder \\(\\mathbf{Dec}_{\\mathbf{M}}\\). \\(\\mathbf{Enc}_{\\mathbf{P}}\\) takes as input the prompts of various optional forms such as points, boxes or coarse masks, and translates the prompts into feature tokens \\(\\mathbf{F}_{\\mathbf{P}}\\). Image feature tokens \\(\\mathbf{F}_{\\mathbf{I}}\\) are also obtained from \\(\\mathbf{Enc}_{\\mathbf{I}}\\). A series of learnable mask tokens \\(\\mathbf{F}_{\\mathbf{M}}\\) are introduced and concatenated with \\(\\mathbf{F}_{\\mathbf{P}}\\) for diverse masks generation. Then the light weight \\(\\mathbf{Dec}_{\\mathbf{M}}\\) integrates the \\(\\mathbf{F}_{\\mathbf{I}}\\) and the concatenation of \\(\\mathbf{F}_{\\mathbf{P}}\\) and \\(\\mathbf{F}_{\\mathbf{M}}\\) to predict segmentation masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.894, + 0.701 + ], + "angle": 0, + "content": "DINOv2. Pretrained on a large quantity of curated data with image and patch level distributive self-supervised learning, DINOv2 [35] learns all-purpose visual features that work out of box on many tasks varying from image level, e.g., image classification and pixel level, e.g., semantic segmentation. Moreover, this all-purpose ViT model demonstrates impressive patch-matching ability, robustly capturing similar semantic intent across different objects and even distinct images [27]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.611, + 0.726 + ], + "angle": 0, + "content": "3.3. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 2, we propose a training-free OVS framework RIM based on visual foundation models. RIM tackles the challenging region classification in OVS from a novel image-to-image matching perspective via the following two procedures, i.e., 1) intra-modal reference features construction, and 2) relation-aware matching. We resort to the SD model [42] and the SAM [22] to establish category reference features in procedure 1). In procedure 2), we conduct ranking based matching between the reference features and the region features in the all-purpose DINOv2 feature space. The details are as follows." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3954" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.096, + 0.87, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.429, + 0.895, + 0.471 + ], + "angle": 0, + "content": "Figure 2. Framework of our proposed Relation-aware Intra-modal Matching (RIM) Network. We first explore Stable Diffusion model and SAM to construct image-modal reference features, then we conduct relation-aware matching between region features and reference features based on ranking distribution. The matching is established in the all-purpose feature spaces of DINOv2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.479, + 0.395, + 0.493 + ], + "angle": 0, + "content": "3.4. Intra-modal Reference Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.471, + 0.713 + ], + "angle": 0, + "content": "In contrast to the substantial gap between abstract, monotonous text features and the concrete, diverse image features, homogenous modality features naturally exhibit improved alignment characteristics as shown in Fig. 6. We resort to stable diffusion model to generate a handful of reference images \\(\\mathcal{I} = \\{\\mathbf{I}_1^c,\\mathbf{I}_2^c,\\dots ,\\mathbf{I}_K^c |\\mathbf{I}_k^c\\in \\mathbb{R}^{H\\times W\\times 3},c = 1,2,\\ldots ,C\\}\\) for all \\(C\\) candidate classes by simply prompting it with \"a photo of [category name]\". Together with the images, we also acquire the corresponding cross-attention maps for localizing the foreground targets. Specifically, for time step \\(t\\), the noisy image features \\(\\mathbf{F}_v\\in \\mathbb{R}^{h\\times w\\times c}\\) are flattened and linearly projected into the queries \\(\\mathbf{Q}\\) and the prompt features \\(\\mathbf{F}_p\\in \\mathbb{R}^{N\\times d}\\) are respectively projected into the keys \\(\\mathbf{K}\\) and values \\(\\mathbf{V}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.723, + 0.47, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {F} _ {v} \\mathbf {W} ^ {\\mathcal {Q}}, \\quad \\mathbf {K} = \\mathbf {F} _ {p} \\mathbf {W} ^ {\\mathcal {K}}, \\quad \\mathbf {V} = \\mathbf {F} _ {p} \\mathbf {W} ^ {\\mathcal {V}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.752, + 0.469, + 0.784 + ], + "angle": 0, + "content": "Among which, \\(\\mathbf{W}^{\\mathcal{Q}}, \\mathbf{W}^{\\mathcal{K}}, \\mathbf{W}^{\\mathcal{V}}\\) are linear projections. The cross-attention maps are calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.793, + 0.47, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.839, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where the \\(\\sqrt{d}\\) is the scaling factor. Cross-attention maps \\(S_{n}^{l,t}\\) of different text tokens from different layers of UNet can be obtained based on the Equ. 2 and \\(n,l,t\\) are the index of text tokens, UNet layers and diffusion steps, respectively. To" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.48, + 0.892, + 0.526 + ], + "angle": 0, + "content": "obtain the cross-attention map corresponding to the category token for foreground mining, we follow [60] to aggregate normalized multi-time and multi-layer maps, formally," + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.535, + 0.892, + 0.574 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathcal {S}} _ {n} = \\frac {1}{L \\cdot T} \\sum_ {l \\in L, t \\in T} \\frac {\\mathcal {S} _ {n} ^ {l , t}}{\\operatorname* {m a x} \\left(\\mathcal {S} _ {n} ^ {l , t}\\right)}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.585, + 0.892, + 0.615 + ], + "angle": 0, + "content": "Where the \\(L\\) and \\(T\\) denote the total time steps and the number of UNet layers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.895, + 0.75 + ], + "angle": 0, + "content": "The foreground area in the synthesized images should be further located to avoid the interference of the irrelevant background regions. However, simply binarizing the cross-attention maps by thresholding may fail to fully capture the target. We thus exploit SAM to generate target masks by sampling the prompt points within the binarized attention maps. The foreground masks \\(\\mathcal{M} = \\{\\mathbf{M}_1^c,\\mathbf{M}_2^c,\\dots,\\mathbf{M}_K^c |\\mathbf{M}_k^c\\in\\) \\(\\mathbb{R}^{h\\times w},c = 1,2,\\ldots ,C\\}\\) and corresponding images \\(\\mathcal{I}\\) then serve as the class references." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.813 + ], + "angle": 0, + "content": "To enhance the robustness of instance-level matching, we opt to construct class reference image features within the all-purpose feature space of DINOv2 [35] via mask average pooling (MAP). Specifically," + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.821, + 0.892, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {r e f} = \\left\\{\\mathbf {F} ^ {c} \\mid \\mathbf {F} ^ {c} = \\frac {1}{K} \\sum_ {k \\in K} \\mathbf {M A P} \\left(\\varphi \\left(\\mathbf {I} _ {k} ^ {c}\\right), \\zeta \\left(\\mathbf {M} _ {k} ^ {c}\\right)\\right) \\right\\} _ {c = 1} ^ {C} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "where the \\(\\varphi\\) and \\(\\zeta\\) denote the DINOv2 feature extractor (ViT) and the bilinear-interpolation resize function, respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3955" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.168 + ], + "angle": 0, + "content": "The \\(\\mathbf{F}^c\\in \\mathbb{R}^{1\\times D}\\) represents the average of all synthesized foreground features. We also construct a background reference feature by averaging all the background features of synthesized images. Similarly, region features within the test image specified by mask proposals are obtained as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.178, + 0.471, + 0.198 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {t e s t} = \\left\\{\\mathbf {F} ^ {p} | \\mathbf {F} ^ {p} = \\mathbf {M A P} (\\varphi [ \\mathbf {I} _ {t e s t} ], \\zeta [ \\mathbf {M} ^ {p} ]) \\right\\} _ {p = 1} ^ {P}, \\quad (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.208, + 0.471, + 0.299 + ], + "angle": 0, + "content": "among which \\(\\mathbf{P}\\) is the number of masks generated by SAM. By designing collaborative interactions among various visual foundational models, we establish well refined image-modal reference features thus shifts the paradigm of region classification in OVS from cross-modal matching to better-aligned intra-modal matching." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.308, + 0.31, + 0.325 + ], + "angle": 0, + "content": "3.5. Relation-aware Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.47, + 0.499 + ], + "angle": 0, + "content": "The naive region classification strategy only selectively recruits the class reference feature with the highest similarity. However, independently taking each category exacerbates the risk of mismatches owing to the intra-class diversity and interference from similar categories. To further harness the structure information implicit in inter-class relationship for more effective matching, we select the top N reference features most similar to the region feature \\(\\mathbf{F}^p\\) as category agents \\(\\mathbf{A}^p\\in \\mathbb{R}^{N\\times D}\\). We derive the scores of region-agent relation \\(s^p\\in \\mathbb{R}^{1\\times N}\\) between the region feature \\(\\mathbf{F}^p\\) and the category agents \\(\\mathbf{A}^p\\) using cosine similarity:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.508, + 0.47, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} ^ {p} = \\frac {\\mathbf {F} ^ {p} \\left(\\mathbf {A} ^ {p}\\right) ^ {\\mathsf {T}}}{\\| \\mathbf {F} ^ {p} \\| _ {2} \\cdot \\| \\mathbf {A} ^ {p} \\| _ {2}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.659 + ], + "angle": 0, + "content": "The core idea is that we take the agent ranking as a random event rather than a deterministic permutation. This implies that each permutation of the category agents is present with a certain probability, as opposed to the exclusive existence of the permutation ordered from largest to smallest. The probability of one permutation \\(\\pi \\in \\mathcal{P}(|\\mathcal{P}| = N!)\\) given s (we omit region index \\(p\\) for brevity) can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.67, + 0.47, + 0.711 + ], + "angle": 0, + "content": "\\[\nP (\\pi | \\mathbf {s}) = \\prod_ {k = 1} ^ {K} \\frac {\\mathbf {s} _ {\\pi (k)}}{\\sum_ {k ^ {\\prime} = k} ^ {K} \\mathbf {s} _ {\\pi \\left(k ^ {\\prime}\\right)}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.469, + 0.815 + ], + "angle": 0, + "content": "among which the \\(\\pi(k)\\) denotes the \\(k^{th}\\) class index of this permutation. For instance, assume that for a given region, the selected agents correspond to the categories \"sofa\", \"chair\", and \"bench\" respectively. One of the permutations of these three agents is \\(\\pi = (\\text{chair}, \\text{sofa}, \\text{bench})\\). We can derive the probability of \\(\\pi\\) based on the region-agent relation s:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.826, + 0.493, + 0.87 + ], + "angle": 0, + "content": "\\[\nP (\\pi | \\mathbf {s}) = \\frac {\\mathbf {s} (\\text {c h a i r})}{\\mathbf {s} (\\text {s o f a}) + \\mathbf {s} (\\text {b e n c h}) + \\mathbf {s} (\\text {c h a i r})} \\cdot \\frac {\\mathbf {s} (\\text {s o f a})}{\\mathbf {s} (\\text {s o f a}) + \\mathbf {s} (\\text {b e n c h})}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "By associating the probabilities of all \\(|\\mathcal{P}|\\) permutations, We convert the scores of individual region-agent relations into" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.227 + ], + "angle": 0, + "content": "class ranking probability distributions \\( P(\\pi \\in \\mathcal{P}|\\mathbf{s}^p) \\in \\mathbb{R}^{1 \\times |\\mathcal{P}|} \\), effectively modeling the inter-class relationship. Similarly, we compute the agent-ranking probability distributions for each category reference features on the same category agents, resulting in \\( P(\\pi \\in \\mathcal{P}|\\mathbf{s}^r) \\in \\mathbb{R}^{1 \\times |\\mathcal{P}|} \\), where \\( \\mathbf{s}^r \\) is obtained through Equ. 6. The distribution of the region is compared against the distributions of all reference features via cosine similarity, enabling the determination of the classification result:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.24, + 0.894, + 0.279 + ], + "angle": 0, + "content": "\\[\nc l s = \\underset {r = 1, 2, \\dots , C} {\\arg \\max } [ \\mathbf {c o s i n e} (P (\\pi \\in \\mathcal {P} | \\mathbf {s} ^ {p}), P (\\pi \\in \\mathcal {P} | \\mathbf {s} ^ {r})) ]. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.894, + 0.416 + ], + "angle": 0, + "content": "To further leverage the advantage of diversity in image-modal reference features, we construct a series of subcategory reference features by clustering the foreground prototypes (obtained by mask average pooling) of all synthesized images. The subcategory reference features are involved in the similarity computation instead of the holistic ones, and the final score of a category is obtained by summing up the similarities of all the corresponding subcategory reference features. The classification result is then obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.428, + 0.892, + 0.481 + ], + "angle": 0, + "content": "\\[\nc l s = \\underset {r = 1, 2, \\dots , C} {\\arg \\max } \\left[ \\sum_ {t = 1} ^ {T} \\operatorname {c o s i n e} \\left(P \\left(\\pi \\in \\mathcal {P} \\mid \\mathbf {s} ^ {p}\\right), P \\left(\\pi \\in \\mathcal {P} \\mid \\mathbf {s} _ {t} ^ {r}\\right)\\right) \\right]. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.892, + 0.542 + ], + "angle": 0, + "content": "Based on the metric grounded in distributional similarity, instances of erroneous region classification can be effectively reduced as inter-class relationships are exploited to facilitate disambiguation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.633, + 0.574 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.582, + 0.773, + 0.597 + ], + "angle": 0, + "content": "4.1. Dataset and Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.772 + ], + "angle": 0, + "content": "We evaluate our model on three commonly used benchmarks, namely, PASCAL VOC 2012 [14], PASCAL Context [34] and COCO Object [25], which have 20,59,80 foreground classes, respectively. We also consider an extra background class in all three datasets. Training sets of datasets are not needed as the proposed method is training-free. For a fair comparison with previous approaches, we directly evaluate our method on the validation sets of these datasets, including 1449, 5105, and 5000 images, respectively. We use the mean of class-wise intersection over union (mIoU) following the common practice to measure the performance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.885, + 0.788 + ], + "angle": 0, + "content": "4.2. Implementation of Visual Foundation Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We adopt the Stable Diffusion model v1.4 [42] to generate category-specific images of resolution \\(512 \\times 512\\) for category reference feature construction. We employ DINOv2 [35] with a ViT-B [12] as the default image encoder for more discriminative matching. Specifically, the keys sequence of the last attention layer is reshaped as the feature map. SAM [22] with ViT-B is adopted as the segmenter. We collect \\(32 \\times 32\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3956" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.872, + 0.329 + ], + "angle": 0, + "content": "
MethodArchTraining datasetSupervisionZero-shot transferDownstream datasets
PASCAL VOCPASCAL ContextCOCO Object
DeiT [52]ViTIN-1Kclass label✘53.035.9-
MoCo [16]ViTIN-1Kself✘34.321.3-
DINO [3]ViTIN-1Kself✘39.120.4-
ViL-Seg [26]ViTCC12Mself+text✓33.615.9-
MaskCLIP [75]ViTLAIONtext + \\(CLIP_{\\mathrm{T}}\\)✓38.823.620.6
GroupViT [64]ViTCC12Mtext✓52.322.4-
ZeroSeg [5]ViTIN-1K\\(CLIP_{\\mathrm{V}}\\)✓40.820.420.2
TCL [4]ViTCC3M+CC12Mtext✓51.224.330.4
ViewCo [41]ViTCC12M+YFCCtext+self✓52.423.023.5
CLIPpy [40]ViTHQITP-134Mtext✓52.2-32.0
SegCLIP [29]ViTCC3M+COCOtext + \\(CLIP_{\\mathrm{T}}\\)✓52.624.726.5
OVSegmentor [65]ViTCC4Mself+text✓53.820.425.1
SimSeg [69]ViTCC3M+CC12Mtext✓57.426.229.7
DiffSeg [53]UNet+ViT✓60.127.537.9
OVDiff [21]UNetTraining-free✓67.130.134.8
OursUNet+ViT✓77.834.344.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.331, + 0.895, + 0.375 + ], + "angle": 0, + "content": "Table 1. Comparison with existing methods. Models in the first three rows are finetuned on target datasets while the rest approaches perform zero-shot transfer. Bold fonts refer to the best results among the models which enable zero-shot transfer. With only image-text pairs available, our method significantly outperforms the existing approaches. More results please refer to Supplementary Material." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.378, + 0.47, + 0.491 + ], + "angle": 0, + "content": "
IRCRMmIOU
w/o fg-maskw/ fg-maskw/o subw/ sub
26.7
✓38.7
✓41.8
✓✓43.1
✓✓44.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.493, + 0.472, + 0.565 + ], + "angle": 0, + "content": "Table 2. Ablation studies of the proposed RIM. We mainly verified the effectiveness of the image reference construction (IRC), and relation-aware matching (RM). Moreover, we also observe the effectiveness of foreground segmentation (fg-mask) of synthesized images and the subcategory reference features (sub)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.581, + 0.47, + 0.624 + ], + "angle": 0, + "content": "
EncoderCLIP [38]SD [42]MAE [17]DINOv2
mIoU42.043.139.544.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.626, + 0.442, + 0.64 + ], + "angle": 0, + "content": "Table 3. Comprison of different image feature extractors." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.657, + 0.293, + 0.688 + ], + "angle": 0, + "content": "
SegmenternoneMaskFormerSAM
mIoU42.076.777.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.694, + 0.298, + 0.737 + ], + "angle": 0, + "content": "Table 4. Comparison of mask proposal generators. \"none\" means direct pixel classification." + }, + { + "type": "table", + "bbox": [ + 0.311, + 0.651, + 0.468, + 0.694 + ], + "angle": 0, + "content": "
Selection of AgentsmIoU
Rand43.8
Top-N44.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.308, + 0.696, + 0.468, + 0.724 + ], + "angle": 0, + "content": "Table 5. Comparison of category agents selection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.903 + ], + "angle": 0, + "content": "prompt points in a grid manner to generate mask proposals for the test images. To segment the foreground of synthesized reference images, We sample 5 prompt points within the binarized cross-attention map, where the binarization threshold is set to a relatively high value of 0.7 to prevent erroneous segmentation of background regions. The number of category agents is set to 4. More implementation details are provided in Supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.378, + 0.807, + 0.394 + ], + "angle": 0, + "content": "4.3. Comparison to the state-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.895, + 0.476 + ], + "angle": 0, + "content": "We compare our method with approaches that have been trained with fully supervised finetuning transfer and zero-shot transfer. Besides, we also conduct performance comparisons with newly arising train-free approaches. Table 1 summarizes the results of the comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.896, + 0.763 + ], + "angle": 0, + "content": "Firstly, we can observe that the proposed RIM significantly surpasses the non-zero-shot fully supervised segmentation baselines, i.e., DeiT [52], MoCo [16]. Furthermore, we compare with other zero-shot OVS approaches such as MaskCLIP [75], SegCLIP [29], and SimSeg [69], which also adopt the ViT backbones of visual foundation model, i.e., CLIP [38]. Our method also shows a clear lead. Specifically, we achieve \\(20.4\\%\\), \\(18.1\\%\\), \\(14.8\\%\\) mIoU over the SimSeg [69] on three datasets, respectively. We posit that the primary cause is that CLIP is susceptible to ambiguities in spatial relations and confusion of co-occurring objects, a consequence stemming from its holistic training objective. Besides, RIM also demonstrates significant performance improvements over the most recently developed training-free methods based on visual foundation models, achieving \\(10.4\\%\\), \\(4.2\\%\\), and \\(6.6\\%\\) mIoU gains, respectively. As shown in Fig. 3, we present a series of visualizations depicting segmentation outcomes across various datasets for a more intuitive observation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.655, + 0.789 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.897, + 0.903 + ], + "angle": 0, + "content": "A series of ablation studies are conducted to thoroughly investigate the impact of each component of the proposed RIM. As shown in Table 2, we mainly implement our experiments on COCO Object [25] dataset, and the first row is our baseline, which follows a naive image-to-text matching for region classification. Specifically, we crop the test image along the bounding boxes corresponding to the mask proposals (gen-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3957" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.091, + 0.293, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.091, + 0.468, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.468, + 0.091, + 0.655, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.091, + 0.861, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.204, + 0.247, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.203, + 0.449, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.45, + 0.203, + 0.66, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.203, + 0.861, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.32, + 0.293, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.319, + 0.466, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.466, + 0.319, + 0.696, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.319, + 0.861, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.42, + 0.615, + 0.433 + ], + "angle": 0, + "content": "Figure 3. Qualitative results of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.471, + 0.515 + ], + "angle": 0, + "content": "erated by SAM) and resize them to \\(224 \\times 224\\) resolution. The background area of the cropped image is filled with zeros, and then CLIP [38] with ViT-B is exploited to perform image-to-text matching between the cropped image and category labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.472, + 0.805 + ], + "angle": 0, + "content": "Ablation study on intra-modal reference construction. To verify the effectiveness of intra-modal alignment, we first construct a naive image-to-image matching as the \\(2^{nd}\\) row of Table 2. More concretely, DINOv2 features of all synthesized images of a category are condensed to a holistic reference feature via global average pooling. The matching process is simply implemented with cosine similarity. Despite its simplicity, this intra-modal matching exhibits a significant performance improvement, i.e., \\(12.0\\%\\) in mIoU over the cross-modal matching based on CLIP. This improvement is anticipated as the holistic training objective of CLIP makes its prediction heavily reliant on contextual information. This reliance not only introduces spatial confusion but also leads to misclassification of frequently co-occurring objects, such as the sky and airplane. Attributed to the image generation capabilities of SD model and the robust high-level semantic feature extraction of DINOv2, an improved intra-modal alignment between region features and class reference features is achieved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Further performance improvements can be observed if we construct the category reference features with only foreground features as shown in the \\(3^{th}\\) row of Table 2. We deem the main reason is that the background areas in synthetic images may contain information of other categories, which confuses the classification process. While in our im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.895, + 0.574 + ], + "angle": 0, + "content": "plementation, more refined category reference features are constructed attributed to the spatial localization ability of the SD model embedded in the cross-attention map and the powerful segmentation capability of SAM, which effectively mitigates the influence of cluttered backgrounds. Despite utilizing merely cosine similarity for intra-modal matching, it has already achieved impressive performance, i.e., \\(44.5\\%\\) mIoU on COCO Object dataset, which can be adopted as a strong baseline for further research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.761 + ], + "angle": 0, + "content": "Ablation study on relation-aware matching. As described in Sec. 3.5, we propose to model the beneficial structure information contained in inter-class relationships via relation-aware matching. Compared to the naive approach that only considers only the cosine similarity between region features and each individual category reference feature, our proposed strategy achieves a sizeable gain, i.e., \\(1.3\\%\\) in mIoU, as presented in the \\(3^{rd}\\) and \\(4^{th}\\) rows of Table 2. The results prove that the proposed similarity measurement based on ranking distribution facilitates effective disambiguation in the matching process, which brings a notable reduction in the misclassification of regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.901 + ], + "angle": 0, + "content": "After integrating subcategory reference features into relation-aware matching, the performance further improved from \\(43.1\\%\\) to \\(44.5\\%\\) in mIoU, as shown in \\(5^{th}\\) row of Table 2. This improvement can be attributed to the ability of the SD model to generate diverse image features, enabling our method to effectively handle intra-class diversity. Moreover, the scoring scheme in Equ. 10, akin to a voting mechanism, further enhances the robustness of the matching process. Furthermore, in Table 5, we demonstrate that reference features" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3958" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.46, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.214, + 0.468, + 0.24 + ], + "angle": 0, + "content": "Figure 4. Effectiveness of SAM based region-level matching. The SAM could well capture visual concepts within images." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.244, + 0.273, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.244, + 0.462, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.343, + 0.471, + 0.371 + ], + "angle": 0, + "content": "Figure 5. Hyperparameter experiments on the number of subcategories and binarization threshold of cross-attention map." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.383, + 0.469, + 0.413 + ], + "angle": 0, + "content": "that share high similarities with region features are better candidates to serve as category agents." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Ablation on DINOv2. To demonstrate the superiority of feature extraction using DINOv2, we conduct comparison experiments of CLIP [38], MAE [17], Stable Diffusion Unet (SD) [42], and DINOv2 as presented in Table 3. DINOv2 achieves the best performance attribute to effective pretraining based on image-level and patch-level discriminative self-supervised learning. While CLIP fails to match region-level features precisely, Stabel Diffusion UNet is constrained to some extent under the unconditional settings. MAE exhibits suboptimal performance in our setting due to its relatively limited high-level semantic modeling capability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Ablation on SAM. Our relation-aware matching operates at the region level, as SAM furnishes comprehensive mask proposals for the test images. To explore the effectiveness of SAM, on the PASCAL VOC dataset, we compare SAM with modified MaskFormer [9] pre-trained on the COCO-stuff dataset following [24]. We also construct a vanilla baseline that compares category reference features with pixel features of test images directly. As shown in Table 4, both segmenters outperform the baseline by a large margin. We deem the main reason is that the region-level matching is more robust than pixel-level one. As illustrated in Fig. 4, the pixel classification paradigm fails to capture all visual concepts within images. SAM slightly surpasses MaskFormer as SAM can generate higher-quality masks on novel classes, naturally more suitable for open-vocabulary tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Investigation of the intra-modal matching. In Fig. 6, we visualized the t-SNE plots of the region features alongside their corresponding text-modal reference features and image-modal reference features using the same image based on CLIP [38] and DINOv2 [35], respectively. It can be observed that in the all-purpose feature space of DINOv2, the" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.683, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.09, + 0.882, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.233, + 0.892, + 0.261 + ], + "angle": 0, + "content": "Figure 6. T-SNE visualization of features of different region, as well as corresponding intra-modal and cross-modal reference features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.279, + 0.895, + 0.384 + ], + "angle": 0, + "content": "region features of different categories are well-differentiated and align well with their corresponding reference features. However, in the case of CLIP, different region features not only exhibit notable overlap but also fail to align effectively with corresponding text-modal reference features. This difference substantiates the underlying rationale of our motivation, i.e., intra-modal matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.892, + 0.57 + ], + "angle": 0, + "content": "Hyperparameter Evaluations. Quantitative experiments are conducted to find a suitable number of subcategories used in relation-aware matching. As illustrated in Fig. 5 (a), the performance continues to grow until the number achieves 8, beyond which it starts to decline. It is reasonable as an appropriate number of subcategory references can model category diversity, but over-partitioning may lead to deviations from instance features. We then explore how the binarization threshold affects the performance in Fig. 5 (b). The model shows low sensitivity to threshold values owing to the capability of SAM, with a setting of 0.7 yields marginally better results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.596, + 0.619, + 0.612 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.895, + 0.763 + ], + "angle": 0, + "content": "In this work, we presented a training-free Relation-aware Intra-modal Matching (RIM) framework to tackle the challenging open-vocabulary semantic segmentation. We construct better-aligned image-modal category reference features based on the Stable Diffusion model and SAM. Then a relation-aware matching strategy is employed for region classification. RIM not only achieves results significantly surpassing the state-of-the-art but also opens up new avenues for OVS from an image-to-image matching perspective." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.789, + 0.679, + 0.805 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.895, + 0.887 + ], + "angle": 0, + "content": "This work was partially supported by the National Defense Basic Scientific Research Program of China (Grant JCKY2021130B016), National Nature Science Foundation of China (Grant 12150007), Youth Innovation Promotion Association CAS 2018166." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3959" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.471, + 0.185 + ], + "angle": 0, + "content": "[1] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. 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Springer, 2022. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.956 + ], + "angle": 0, + "content": "3963" + } + ] +] \ No newline at end of file diff --git a/2024/Image-to-Image Matching via Foundation Models_ A New Perspective for Open-Vocabulary Semantic Segmentation/bc2d94c7-b97d-48d5-b633-2ae9bb2d7d08_origin.pdf b/2024/Image-to-Image Matching via Foundation Models_ A New Perspective for Open-Vocabulary Semantic Segmentation/bc2d94c7-b97d-48d5-b633-2ae9bb2d7d08_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b47839d9cd13c7501dc6bd74956e2f5e10485629 --- /dev/null +++ b/2024/Image-to-Image Matching via Foundation Models_ A New Perspective for Open-Vocabulary Semantic Segmentation/bc2d94c7-b97d-48d5-b633-2ae9bb2d7d08_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4a2946f259744db37563231c6eebe656b8b664557fc3adebfe8b35eb091749c8 +size 2430206 diff --git a/2024/Image-to-Image Matching via Foundation Models_ A New Perspective for Open-Vocabulary Semantic Segmentation/full.md b/2024/Image-to-Image Matching via Foundation Models_ A New Perspective for Open-Vocabulary Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d5cd96b26a901aaa52c86addb3b35018c668f72c --- /dev/null +++ b/2024/Image-to-Image Matching via Foundation Models_ A New Perspective for Open-Vocabulary Semantic Segmentation/full.md @@ -0,0 +1,358 @@ +# Image-to-Image Matching via Foundation Models: A New Perspective for Open-Vocabulary Semantic Segmentation + +Yuan Wang $^{1*}$ + +Rui Sun $^{1*}$ + +Naisong Luo + +Yuwen Pan + +Tianzhu Zhang $^{1,2\dagger}$ + +1University of Science and Technology of China 2Deep Space Exploration Laboratory + +{wy2016, issunrui, lns6, panyw}@mail.ustc.edu.cn, {tzzhang}@ustc.edu.cn + +# Abstract + +Open-vocabulary semantic segmentation (OVS) aims to segment images of arbitrary categories specified by class labels or captions. However, most previous best-performing methods, whether pixel grouping methods or region recognition methods, suffer from false matches between image features and category labels. We attribute this to the natural gap between the textual features and visual features. In this work, we rethink how to mitigate false matches from the perspective of image-to-image matching and propose a novel relation-aware intra-modal matching (RIM) framework for OVS based on visual foundation models. RIM achieves robust region classification by firstly constructing diverse image-modal reference features and then matching them with region features based on relation-aware ranking distribution. The proposed RIM enjoys several merits. First, the intra-modal reference features are better aligned, circumventing potential ambiguities that may arise in cross-modal matching. Second, the ranking-based matching process harnesses the structure information implicit in the inter-class relationships, making it more robust than comparing individually. Extensive experiments on three benchmarks demonstrate that RIM outperforms previous state-of-the-art methods by large margins, obtaining a lead of more than $10\%$ in mIoU on PASCAL VOC benchmark. + +# 1. Introduction + +Aiming at allocating semantic labels to the corresponding pixels, semantic segmentation has achieved conspicuous achievements attributed to the development of large-scale datasets [11, 22, 25, 74] and elaborate algorithms [7, 8, 28]. However, the capabilities of conventional semantic segmentation models are restricted to predefined training categories, failing to recognize a broader spectrum of concepts, which + +![](images/f2e79793868010719c7713b6e8149a135c747d0c65c19ee376c922af75fc0557.jpg) +(a) Text-to-image Matching V.S. Image-to-image Matching + +![](images/ebc9e6c42901228cc19c9e98a1d45d739ea920a89ca66140c54fd1ffae931f0c.jpg) +(b) Individual Matching V.S. Relation-aware Matching +Figure 1. Motivation of our method. (a) False matches tend to occur in cross-modal features. We establish well-aligned image-modal reference features thus transit the text-to-image matching to image-to-image matching. (b) Individual matching tends to suffer from disturbances. We propose a novel relation-aware matching strategy for more robust region classification. + +poses a severe limitation for their practical applications. In pursuit of the human-like intelligence of unbounded and fine-grained scene understanding, open-vocabulary segmentation (OVS) [2, 67] has attracted increasing interest recently, which enables segmentation with an unrestricted vocabulary. + +OVS is highly challenging as it requires not only grouping all pixels to corresponding visual concepts but also assigning each region the correct semantic label from a large vocabulary. Some early attempts [29, 64] optimize the pixel grouping process and the classification of visual concepts simultaneously by employing contrastive learning with image-text pairs. These methods inevitably yield masks of relatively low quality with only coarse supervision available. Another line of works [24, 67, 68] significantly dominate this field by modeling the OVS as a region recognition problem, which decouple OVS into two procedures, i.e. class-agnostic mask proposals prediction and mask class recognition. Though the mask proposals generation has been significantly improved with the assistance of pixel-level supervision and + +elaborate segmenter architectures (e.g. Mask2Former [8]), the unsatisfactory region class recognition has emerged as the performance bottleneck of OVS [24]. We attribute this to the natural gap between the highly abstract and monotonous category textual features and the visual features that are more concrete and diverse. + +Most current OVS approaches achieve mask class recognition via cross-modal region-category alignment based on the pretrained vision-language models (e.g., CLIP [38]). Despite its exemplary generalization ability on downstream classification tasks, CLIP usually suffers from spatial relations ambiguity [66, 69] and co-occurring object confusion ascribed to the holistic pre-training objective. On the other side, also pre-trained on internet-scale data, Stable Diffusion [42] (SD) model has garnered growing research interest credited to the phenomenal power of synthesizing photorealistic images with diverse and plausible content conditioned on textual descriptions. Considering that features from the same modality inherently exhibit a higher degree of alignment compared to cross-modal features (as shown in Fig. 6), we ask the question: $\mathbf{0}$ is it possible to transition the region classification in OVS from image-to-text matching to image-to-image matching using the SD model? + +Before tackling this issue, we first revisit the common practices in mask class recognition [24, 67], which involves matching visual concepts with a set of category reference features (e.g. category textual features from CLIP). Inspired by previous exploration [59, 60, 73] of the strong image-text correspondence exhibited by the SD model, we can establish better-aligned intra-modal category reference features as shown in Fig. 1 (a). The cross-attention maps in the conditional generation process could serve as exceptional tools to further refine the category features. Nonetheless, it is still non-trivial to map test region features to their corresponding category reference features precisely, as the intra-class diversity and disturbances from akin categories exhibit in practical scenarios potentially lead to mismatches. Previous methodologies process each category independently during the matching phase, overlooking the informative inter-class relationships, which implicitly integrate structured contextual information and effectively aid in disambiguation. Here another question arises: how to harness the structure information modeled in the inter-class relationship to facilitate more accurate matching? + +Driven by this question, we carefully design the relation-aware similarity measurement that incorporates the relations of the current region with some semantic relevant category agents. For a specified region feature within test image, a subset of category reference features that most akin to the region are selected to serve as category agents. The central idea is that we regard the category agent ranking as a stochastic event rather than a deterministic permutation. For example, in ranking, given the region feature specified by the + +mask proposal $m_{1}$ in Fig. 1 (a), its scores vary for different category agents, which can be taken as probabilities. The probability of being ranked first is 0.45 of the agent 'desk' and 0.35 of the agent 'chair'. The ranking permutation reflects the relevance of the corresponding categories w.r.t. the region feature. An agent-ranking probability distribution can be constructed by associating the probability with every rank permutation for both the region feature and all category reference features. Finally, as illustrated in Fig. 1 (b), we transform the similarity measurement from individual region-reference comparison to relation-aware agent-ranking distribution similarity. + +In this paper, we present a training-free OVS framework RIM to achieve Relation-aware Intra-modal Matching based on visual foundation models that coherently addresses the questions 1-2. Specifically, we facilitate a synergistic collaboration between the SD model and SAM to generate category-specific reference features by prompting the Segment Anything Model [22] (SAM) with points selected from the cross-attention map within SD model. SAM is further adopted to provide mask proposals of the test images. Finally, we conduct the relation-aware matching based on ranking distribution in the robust all-purpose feature space of DINOv2 [35]. RIM ensembles expertise of different visual foundational models in a complementary manner, enhancing mask quality and region-category matching precision simultaneously. Moreover, the overall framework is training-free, substantially mitigating the risk of overfitting. + +Our contributions can be concluded as follows: (1) We reveal the problems of region feature classification in OVS and propose to construct well-aligned intra-modal reference features to circumvent ambiguities of cross-modal matching. (2) We design a relation-aware matching strategy based on ranking distribution, which captures structure information implicit in inter-class relationships and enables more robust matching. (3) We propose a training-free relation-aware intra-modal matching (RIM) network for OVS based on visual foundation models. Extensive experiments demonstrate that RIM remarkably surpasses previous state-of-the-art methods by a large margin. + +# 2. Related Work + +Semantic Segmentation is a fundamental computer vision task with widespread applications in fields such as medical image processing [31, 37, 46, 48, 49, 58], video analysis [47, 51]. The pioneering FCN [28] has inspired a multitude of subsequent endeavors [6, 7, 43, 62, 72] centered around Convolutional Neural Networks (CNN). Beyond the CNN-based models, the triumph of the Vision Transformer (ViT) has spurred a succession of transformer-based segmentation models [30, 45, 63, 71], which have progressively evolved into a unified segmentation framework [8, 9] capable of addressing various segmentation tasks. Some alternative + +settings, such as few-shot [23, 55-57], semi-supervised [23, 32, 33, 50], or weakly supervised [19, 54] segmentation, attempt to enhance the practicality of semantic segmentation techniques. Despite their success, these models are confined to predefined training categories or the specific foreground class, failing to recognize a broader spectrum of categories. + +Open-vocabulary Semantic Segmentation aims to segment images with arbitrary categories described by texts. Some efforts [2, 29, 61, 65, 69] concentrated on developing a joint embedding space that bridges image pixels with class names or descriptions via learning objectives established from image-text pairs. For example, GroupViT [64] designed a hierarchical grouping transformer and learned the alignment between groups and text via contrastive loss. Another line of works [24, 66, 67] models OVS as a region recognition task by decoupling it into mask proposal generation and region classification, achieving notable progress attributed to advanced segmentation architectures [8] and pixel-level annotations [25, 74]. Large-scale vision-language pre-training models such as CLIP [38] and ALIGN [20] have been widely applied for OVS [15, 68, 70] which endows OVS model enhanced generalization. However, those pretraining models often encounter spatial confusion in dense prediction tasks [69], leading to recurring misclassification issues, which has emerged as a critical bottleneck in OVS. + +Visual foundation models is catching up with the research in natural language processing (NLP) [1, 10, 36] and have achieved conspicuous achievements across a wide range of visual tasks. For example, DINov2 [35] establishes an impressive all-purpose feature extractor via self-supervised learning at both the image and patch levels. Trained on over 1 billion masks, Segment Anything Model (SAM) [22] has demonstrated astonishing zero-shot class-agnostic segmentation performance. Diffusion models [18, 44] have propelled the advancement of a series of image-to-text generation systems such as DALL-E [39] and Stable Diffusion model [42]. A series of works [27, 60, 66] render visual foundation models as powerful out-of-the-box tools to handle downstream tasks. Though a single foundation model may have limited capacity in addressing complex visual tasks such as OVS, in this work, we demonstrate that integrating different foundation models leads to positive synergies. + +# 3. Method + +# 3.1. Problem Definition + +Open-vocabulary segmentation aims to segment any image against a new vocabulary of categories $\mathbf{C}_{test}$ . Previous approaches typically involve training models on datasets annotated with image-level textual labels or pixel-level masks, with the category set $\mathbf{C}_{train}$ . $\mathbf{C}_{test}$ contains novel categories not exposed to the training process, i.e., $\mathbf{C}_{train} \neq \mathbf{C}_{test}$ . Owing to the training-free nature of our method, it inher + +ently operates under a more challenging zero-shot setting wherein all test categories are considered novel. + +# 3.2. Preliminary of Vision Foundation Models + +Stable-Diffusion model. Different from discriminative image-text models that model the class probability distribution $\pmb{p}(\pmb{c}|\pmb{i})$ given the image, text-to-image stable diffusion model encode a text-conditional distribution of possible images $\pmb{p}(\pmb{i}|\pmb{c})$ . This model demonstrates the prowess to synthesize high-fidelity images $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ that closely align with the specified conditional text $\mathcal{T}$ , all originating from a latent space defined by random Gaussian noise $\mathbf{z} \sim \mathcal{N}(0,1)$ . Specifically, stable diffusion model consists of three components: a pre-trained variational autoencoder (VAE) [13] that encodes and decodes the image latent code, a text encoder for prompt embedding, and a time-conditional UNet [43] for the denoising of latent vectors. The visual-text interaction occurs in the cross-attention layers that are integral to the UNet structure for each denoising step. Target categories within synthesized images can be accurately localized based on class-discriminative cross-attention maps. + +Segment Anything Model. SAM comprises of three components: an image encoder $\mathbf{Enc}_{\mathbf{I}}$ , a prompt encoder $\mathbf{Enc}_{\mathbf{P}}$ , and fast mask decoder $\mathbf{Dec}_{\mathbf{M}}$ . $\mathbf{Enc}_{\mathbf{P}}$ takes as input the prompts of various optional forms such as points, boxes or coarse masks, and translates the prompts into feature tokens $\mathbf{F}_{\mathbf{P}}$ . Image feature tokens $\mathbf{F}_{\mathbf{I}}$ are also obtained from $\mathbf{Enc}_{\mathbf{I}}$ . A series of learnable mask tokens $\mathbf{F}_{\mathbf{M}}$ are introduced and concatenated with $\mathbf{F}_{\mathbf{P}}$ for diverse masks generation. Then the light weight $\mathbf{Dec}_{\mathbf{M}}$ integrates the $\mathbf{F}_{\mathbf{I}}$ and the concatenation of $\mathbf{F}_{\mathbf{P}}$ and $\mathbf{F}_{\mathbf{M}}$ to predict segmentation masks. + +DINOv2. Pretrained on a large quantity of curated data with image and patch level distributive self-supervised learning, DINOv2 [35] learns all-purpose visual features that work out of box on many tasks varying from image level, e.g., image classification and pixel level, e.g., semantic segmentation. Moreover, this all-purpose ViT model demonstrates impressive patch-matching ability, robustly capturing similar semantic intent across different objects and even distinct images [27]. + +# 3.3. Overview + +As shown in Fig. 2, we propose a training-free OVS framework RIM based on visual foundation models. RIM tackles the challenging region classification in OVS from a novel image-to-image matching perspective via the following two procedures, i.e., 1) intra-modal reference features construction, and 2) relation-aware matching. We resort to the SD model [42] and the SAM [22] to establish category reference features in procedure 1). In procedure 2), we conduct ranking based matching between the reference features and the region features in the all-purpose DINOv2 feature space. The details are as follows. + +![](images/46de0df1f835dd03df09d80de4143d16875f4d51df908b36635ef9b5dcf7b718.jpg) +Figure 2. Framework of our proposed Relation-aware Intra-modal Matching (RIM) Network. We first explore Stable Diffusion model and SAM to construct image-modal reference features, then we conduct relation-aware matching between region features and reference features based on ranking distribution. The matching is established in the all-purpose feature spaces of DINOv2. + +# 3.4. Intra-modal Reference Construction + +In contrast to the substantial gap between abstract, monotonous text features and the concrete, diverse image features, homogenous modality features naturally exhibit improved alignment characteristics as shown in Fig. 6. We resort to stable diffusion model to generate a handful of reference images $\mathcal{I} = \{\mathbf{I}_1^c,\mathbf{I}_2^c,\dots ,\mathbf{I}_K^c |\mathbf{I}_k^c\in \mathbb{R}^{H\times W\times 3},c = 1,2,\ldots ,C\}$ for all $C$ candidate classes by simply prompting it with "a photo of [category name]". Together with the images, we also acquire the corresponding cross-attention maps for localizing the foreground targets. Specifically, for time step $t$ , the noisy image features $\mathbf{F}_v\in \mathbb{R}^{h\times w\times c}$ are flattened and linearly projected into the queries $\mathbf{Q}$ and the prompt features $\mathbf{F}_p\in \mathbb{R}^{N\times d}$ are respectively projected into the keys $\mathbf{K}$ and values $\mathbf{V}$ : + +$$ +\mathbf {Q} = \mathbf {F} _ {v} \mathbf {W} ^ {\mathcal {Q}}, \quad \mathbf {K} = \mathbf {F} _ {p} \mathbf {W} ^ {\mathcal {K}}, \quad \mathbf {V} = \mathbf {F} _ {p} \mathbf {W} ^ {\mathcal {V}}. \tag {1} +$$ + +Among which, $\mathbf{W}^{\mathcal{Q}}, \mathbf{W}^{\mathcal{K}}, \mathbf{W}^{\mathcal{V}}$ are linear projections. The cross-attention maps are calculated as: + +$$ +\mathcal {S} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q K} ^ {\top}}{\sqrt {d}}\right), \tag {2} +$$ + +where the $\sqrt{d}$ is the scaling factor. Cross-attention maps $S_{n}^{l,t}$ of different text tokens from different layers of UNet can be obtained based on the Equ. 2 and $n,l,t$ are the index of text tokens, UNet layers and diffusion steps, respectively. To + +obtain the cross-attention map corresponding to the category token for foreground mining, we follow [60] to aggregate normalized multi-time and multi-layer maps, formally, + +$$ +\bar {\mathcal {S}} _ {n} = \frac {1}{L \cdot T} \sum_ {l \in L, t \in T} \frac {\mathcal {S} _ {n} ^ {l , t}}{\operatorname* {m a x} \left(\mathcal {S} _ {n} ^ {l , t}\right)}, \tag {3} +$$ + +Where the $L$ and $T$ denote the total time steps and the number of UNet layers. + +The foreground area in the synthesized images should be further located to avoid the interference of the irrelevant background regions. However, simply binarizing the cross-attention maps by thresholding may fail to fully capture the target. We thus exploit SAM to generate target masks by sampling the prompt points within the binarized attention maps. The foreground masks $\mathcal{M} = \{\mathbf{M}_1^c,\mathbf{M}_2^c,\dots,\mathbf{M}_K^c |\mathbf{M}_k^c\in$ $\mathbb{R}^{h\times w},c = 1,2,\ldots ,C\}$ and corresponding images $\mathcal{I}$ then serve as the class references. + +To enhance the robustness of instance-level matching, we opt to construct class reference image features within the all-purpose feature space of DINOv2 [35] via mask average pooling (MAP). Specifically, + +$$ +\mathcal {F} _ {r e f} = \left\{\mathbf {F} ^ {c} \mid \mathbf {F} ^ {c} = \frac {1}{K} \sum_ {k \in K} \mathbf {M A P} \left(\varphi \left(\mathbf {I} _ {k} ^ {c}\right), \zeta \left(\mathbf {M} _ {k} ^ {c}\right)\right) \right\} _ {c = 1} ^ {C} \tag {4} +$$ + +where the $\varphi$ and $\zeta$ denote the DINOv2 feature extractor (ViT) and the bilinear-interpolation resize function, respectively. + +The $\mathbf{F}^c\in \mathbb{R}^{1\times D}$ represents the average of all synthesized foreground features. We also construct a background reference feature by averaging all the background features of synthesized images. Similarly, region features within the test image specified by mask proposals are obtained as: + +$$ +\mathcal {F} _ {t e s t} = \left\{\mathbf {F} ^ {p} | \mathbf {F} ^ {p} = \mathbf {M A P} (\varphi [ \mathbf {I} _ {t e s t} ], \zeta [ \mathbf {M} ^ {p} ]) \right\} _ {p = 1} ^ {P}, \quad (5) +$$ + +among which $\mathbf{P}$ is the number of masks generated by SAM. By designing collaborative interactions among various visual foundational models, we establish well refined image-modal reference features thus shifts the paradigm of region classification in OVS from cross-modal matching to better-aligned intra-modal matching. + +# 3.5. Relation-aware Matching + +The naive region classification strategy only selectively recruits the class reference feature with the highest similarity. However, independently taking each category exacerbates the risk of mismatches owing to the intra-class diversity and interference from similar categories. To further harness the structure information implicit in inter-class relationship for more effective matching, we select the top N reference features most similar to the region feature $\mathbf{F}^p$ as category agents $\mathbf{A}^p\in \mathbb{R}^{N\times D}$ . We derive the scores of region-agent relation $s^p\in \mathbb{R}^{1\times N}$ between the region feature $\mathbf{F}^p$ and the category agents $\mathbf{A}^p$ using cosine similarity: + +$$ +\mathbf {s} ^ {p} = \frac {\mathbf {F} ^ {p} \left(\mathbf {A} ^ {p}\right) ^ {\mathsf {T}}}{\| \mathbf {F} ^ {p} \| _ {2} \cdot \| \mathbf {A} ^ {p} \| _ {2}}. \tag {6} +$$ + +The core idea is that we take the agent ranking as a random event rather than a deterministic permutation. This implies that each permutation of the category agents is present with a certain probability, as opposed to the exclusive existence of the permutation ordered from largest to smallest. The probability of one permutation $\pi \in \mathcal{P}(|\mathcal{P}| = N!)$ given s (we omit region index $p$ for brevity) can be calculated as: + +$$ +P (\pi | \mathbf {s}) = \prod_ {k = 1} ^ {K} \frac {\mathbf {s} _ {\pi (k)}}{\sum_ {k ^ {\prime} = k} ^ {K} \mathbf {s} _ {\pi \left(k ^ {\prime}\right)}}, \tag {7} +$$ + +among which the $\pi(k)$ denotes the $k^{th}$ class index of this permutation. For instance, assume that for a given region, the selected agents correspond to the categories "sofa", "chair", and "bench" respectively. One of the permutations of these three agents is $\pi = (\text{chair}, \text{sofa}, \text{bench})$ . We can derive the probability of $\pi$ based on the region-agent relation s: + +$$ +P (\pi | \mathbf {s}) = \frac {\mathbf {s} (\text {c h a i r})}{\mathbf {s} (\text {s o f a}) + \mathbf {s} (\text {b e n c h}) + \mathbf {s} (\text {c h a i r})} \cdot \frac {\mathbf {s} (\text {s o f a})}{\mathbf {s} (\text {s o f a}) + \mathbf {s} (\text {b e n c h})}. \tag {8} +$$ + +By associating the probabilities of all $|\mathcal{P}|$ permutations, We convert the scores of individual region-agent relations into + +class ranking probability distributions $P(\pi \in \mathcal{P}|\mathbf{s}^p) \in \mathbb{R}^{1 \times |\mathcal{P}|}$ , effectively modeling the inter-class relationship. Similarly, we compute the agent-ranking probability distributions for each category reference features on the same category agents, resulting in $P(\pi \in \mathcal{P}|\mathbf{s}^r) \in \mathbb{R}^{1 \times |\mathcal{P}|}$ , where $\mathbf{s}^r$ is obtained through Equ. 6. The distribution of the region is compared against the distributions of all reference features via cosine similarity, enabling the determination of the classification result: + +$$ +c l s = \underset {r = 1, 2, \dots , C} {\arg \max } [ \mathbf {c o s i n e} (P (\pi \in \mathcal {P} | \mathbf {s} ^ {p}), P (\pi \in \mathcal {P} | \mathbf {s} ^ {r})) ]. \tag {9} +$$ + +To further leverage the advantage of diversity in image-modal reference features, we construct a series of subcategory reference features by clustering the foreground prototypes (obtained by mask average pooling) of all synthesized images. The subcategory reference features are involved in the similarity computation instead of the holistic ones, and the final score of a category is obtained by summing up the similarities of all the corresponding subcategory reference features. The classification result is then obtained by: + +$$ +c l s = \underset {r = 1, 2, \dots , C} {\arg \max } \left[ \sum_ {t = 1} ^ {T} \operatorname {c o s i n e} \left(P \left(\pi \in \mathcal {P} \mid \mathbf {s} ^ {p}\right), P \left(\pi \in \mathcal {P} \mid \mathbf {s} _ {t} ^ {r}\right)\right) \right]. \tag {10} +$$ + +Based on the metric grounded in distributional similarity, instances of erroneous region classification can be effectively reduced as inter-class relationships are exploited to facilitate disambiguation. + +# 4. Experiments + +# 4.1. Dataset and Evaluation Metric + +We evaluate our model on three commonly used benchmarks, namely, PASCAL VOC 2012 [14], PASCAL Context [34] and COCO Object [25], which have 20,59,80 foreground classes, respectively. We also consider an extra background class in all three datasets. Training sets of datasets are not needed as the proposed method is training-free. For a fair comparison with previous approaches, we directly evaluate our method on the validation sets of these datasets, including 1449, 5105, and 5000 images, respectively. We use the mean of class-wise intersection over union (mIoU) following the common practice to measure the performance. + +# 4.2. Implementation of Visual Foundation Models + +We adopt the Stable Diffusion model v1.4 [42] to generate category-specific images of resolution $512 \times 512$ for category reference feature construction. We employ DINOv2 [35] with a ViT-B [12] as the default image encoder for more discriminative matching. Specifically, the keys sequence of the last attention layer is reshaped as the feature map. SAM [22] with ViT-B is adopted as the segmenter. We collect $32 \times 32$ + +
MethodArchTraining datasetSupervisionZero-shot transferDownstream datasets
PASCAL VOCPASCAL ContextCOCO Object
DeiT [52]ViTIN-1Kclass label✘53.035.9-
MoCo [16]ViTIN-1Kself✘34.321.3-
DINO [3]ViTIN-1Kself✘39.120.4-
ViL-Seg [26]ViTCC12Mself+text✓33.615.9-
MaskCLIP [75]ViTLAIONtext + \(CLIP_{\mathrm{T}}\)✓38.823.620.6
GroupViT [64]ViTCC12Mtext✓52.322.4-
ZeroSeg [5]ViTIN-1K\(CLIP_{\mathrm{V}}\)✓40.820.420.2
TCL [4]ViTCC3M+CC12Mtext✓51.224.330.4
ViewCo [41]ViTCC12M+YFCCtext+self✓52.423.023.5
CLIPpy [40]ViTHQITP-134Mtext✓52.2-32.0
SegCLIP [29]ViTCC3M+COCOtext + \(CLIP_{\mathrm{T}}\)✓52.624.726.5
OVSegmentor [65]ViTCC4Mself+text✓53.820.425.1
SimSeg [69]ViTCC3M+CC12Mtext✓57.426.229.7
DiffSeg [53]UNet+ViT✓60.127.537.9
OVDiff [21]UNetTraining-free✓67.130.134.8
OursUNet+ViT✓77.834.344.5
+ +Table 1. Comparison with existing methods. Models in the first three rows are finetuned on target datasets while the rest approaches perform zero-shot transfer. Bold fonts refer to the best results among the models which enable zero-shot transfer. With only image-text pairs available, our method significantly outperforms the existing approaches. More results please refer to Supplementary Material. + +
IRCRMmIOU
w/o fg-maskw/ fg-maskw/o subw/ sub
26.7
✓38.7
✓41.8
✓✓43.1
✓✓44.5
+ +Table 2. Ablation studies of the proposed RIM. We mainly verified the effectiveness of the image reference construction (IRC), and relation-aware matching (RM). Moreover, we also observe the effectiveness of foreground segmentation (fg-mask) of synthesized images and the subcategory reference features (sub). + +
EncoderCLIP [38]SD [42]MAE [17]DINOv2
mIoU42.043.139.544.5
+ +Table 3. Comprison of different image feature extractors. + +
SegmenternoneMaskFormerSAM
mIoU42.076.777.8
+ +Table 4. Comparison of mask proposal generators. "none" means direct pixel classification. + +
Selection of AgentsmIoU
Rand43.8
Top-N44.5
+ +Table 5. Comparison of category agents selection. + +prompt points in a grid manner to generate mask proposals for the test images. To segment the foreground of synthesized reference images, We sample 5 prompt points within the binarized cross-attention map, where the binarization threshold is set to a relatively high value of 0.7 to prevent erroneous segmentation of background regions. The number of category agents is set to 4. More implementation details are provided in Supplementary materials. + +# 4.3. Comparison to the state-of-the-arts + +We compare our method with approaches that have been trained with fully supervised finetuning transfer and zero-shot transfer. Besides, we also conduct performance comparisons with newly arising train-free approaches. Table 1 summarizes the results of the comparison. + +Firstly, we can observe that the proposed RIM significantly surpasses the non-zero-shot fully supervised segmentation baselines, i.e., DeiT [52], MoCo [16]. Furthermore, we compare with other zero-shot OVS approaches such as MaskCLIP [75], SegCLIP [29], and SimSeg [69], which also adopt the ViT backbones of visual foundation model, i.e., CLIP [38]. Our method also shows a clear lead. Specifically, we achieve $20.4\%$ , $18.1\%$ , $14.8\%$ mIoU over the SimSeg [69] on three datasets, respectively. We posit that the primary cause is that CLIP is susceptible to ambiguities in spatial relations and confusion of co-occurring objects, a consequence stemming from its holistic training objective. Besides, RIM also demonstrates significant performance improvements over the most recently developed training-free methods based on visual foundation models, achieving $10.4\%$ , $4.2\%$ , and $6.6\%$ mIoU gains, respectively. As shown in Fig. 3, we present a series of visualizations depicting segmentation outcomes across various datasets for a more intuitive observation. + +# 4.4. Ablation Study + +A series of ablation studies are conducted to thoroughly investigate the impact of each component of the proposed RIM. As shown in Table 2, we mainly implement our experiments on COCO Object [25] dataset, and the first row is our baseline, which follows a naive image-to-text matching for region classification. Specifically, we crop the test image along the bounding boxes corresponding to the mask proposals (gen- + +![](images/f7fefb3235c805360970ef272402c68249933a8242d075de54e7faee4c48c6e0.jpg) + +![](images/867fe7434e9d76eeb74203c4847698d61610b23396fcafe2494fce4678231a16.jpg) + +![](images/6fc90e8ae8c1d7cc4a54101fb45d14c65bd0dd3b73ff3493bf4e6f6caaabe777.jpg) + +![](images/7e8211fe90554a9045528e5d3debd1936eaa56cce72392e05c188a165f7ef007.jpg) + +![](images/268413f93dc76be9f6e559e053d34c5de64ad96b47938fc05c213b914702bce7.jpg) + +![](images/5c6afc306f89e5c088196397d819373931d4ff5519966232559c23c72edc16f1.jpg) + +![](images/0274cd0829002b6c82026b91658b2b79c7cfa384e0bb6507137eabb0b285841f.jpg) + +![](images/a5755da2ad19877770e1da74ff0a478c87b6f775d0042f4053befce0de2fff56.jpg) + +![](images/014d7cac9ec6facc9f398e4242bb8c57bcf1c67eb5c245298b3d6a431bfe3b7b.jpg) + +![](images/0a8eb40de9b828c4c549352604ec580fc7f4463f84a591cee2018e7d0473b23a.jpg) +Figure 3. Qualitative results of our method. + +![](images/5111f44e9523b66f45eaac5559e34dd1a5b36718be20e6f714cb7fc8c5db2d9c.jpg) + +![](images/08600b502d22f9042fdc3b46f1e382239c11b4459ab232c00de14bbd4bc1ca65.jpg) + +erated by SAM) and resize them to $224 \times 224$ resolution. The background area of the cropped image is filled with zeros, and then CLIP [38] with ViT-B is exploited to perform image-to-text matching between the cropped image and category labels. + +Ablation study on intra-modal reference construction. To verify the effectiveness of intra-modal alignment, we first construct a naive image-to-image matching as the $2^{nd}$ row of Table 2. More concretely, DINOv2 features of all synthesized images of a category are condensed to a holistic reference feature via global average pooling. The matching process is simply implemented with cosine similarity. Despite its simplicity, this intra-modal matching exhibits a significant performance improvement, i.e., $12.0\%$ in mIoU over the cross-modal matching based on CLIP. This improvement is anticipated as the holistic training objective of CLIP makes its prediction heavily reliant on contextual information. This reliance not only introduces spatial confusion but also leads to misclassification of frequently co-occurring objects, such as the sky and airplane. Attributed to the image generation capabilities of SD model and the robust high-level semantic feature extraction of DINOv2, an improved intra-modal alignment between region features and class reference features is achieved. + +Further performance improvements can be observed if we construct the category reference features with only foreground features as shown in the $3^{th}$ row of Table 2. We deem the main reason is that the background areas in synthetic images may contain information of other categories, which confuses the classification process. While in our im + +plementation, more refined category reference features are constructed attributed to the spatial localization ability of the SD model embedded in the cross-attention map and the powerful segmentation capability of SAM, which effectively mitigates the influence of cluttered backgrounds. Despite utilizing merely cosine similarity for intra-modal matching, it has already achieved impressive performance, i.e., $44.5\%$ mIoU on COCO Object dataset, which can be adopted as a strong baseline for further research. + +Ablation study on relation-aware matching. As described in Sec. 3.5, we propose to model the beneficial structure information contained in inter-class relationships via relation-aware matching. Compared to the naive approach that only considers only the cosine similarity between region features and each individual category reference feature, our proposed strategy achieves a sizeable gain, i.e., $1.3\%$ in mIoU, as presented in the $3^{rd}$ and $4^{th}$ rows of Table 2. The results prove that the proposed similarity measurement based on ranking distribution facilitates effective disambiguation in the matching process, which brings a notable reduction in the misclassification of regions. + +After integrating subcategory reference features into relation-aware matching, the performance further improved from $43.1\%$ to $44.5\%$ in mIoU, as shown in $5^{th}$ row of Table 2. This improvement can be attributed to the ability of the SD model to generate diverse image features, enabling our method to effectively handle intra-class diversity. Moreover, the scoring scheme in Equ. 10, akin to a voting mechanism, further enhances the robustness of the matching process. Furthermore, in Table 5, we demonstrate that reference features + +![](images/67f6c1aa8e6fad3bc328b12b66e6b7b5cea8e3560bf821f7d62eb37aa51bc79b.jpg) +Figure 4. Effectiveness of SAM based region-level matching. The SAM could well capture visual concepts within images. + +![](images/3d187ed82499ca9b19e671226db467d30b17222254de3c8755b6bbc19760f4ca.jpg) +Figure 5. Hyperparameter experiments on the number of subcategories and binarization threshold of cross-attention map. + +![](images/eefa186be170b0a3346d9cb77cfaa4d6df9e2bd4c82ab8bfed4bf056814955bd.jpg) + +that share high similarities with region features are better candidates to serve as category agents. + +Ablation on DINOv2. To demonstrate the superiority of feature extraction using DINOv2, we conduct comparison experiments of CLIP [38], MAE [17], Stable Diffusion Unet (SD) [42], and DINOv2 as presented in Table 3. DINOv2 achieves the best performance attribute to effective pretraining based on image-level and patch-level discriminative self-supervised learning. While CLIP fails to match region-level features precisely, Stabel Diffusion UNet is constrained to some extent under the unconditional settings. MAE exhibits suboptimal performance in our setting due to its relatively limited high-level semantic modeling capability. + +Ablation on SAM. Our relation-aware matching operates at the region level, as SAM furnishes comprehensive mask proposals for the test images. To explore the effectiveness of SAM, on the PASCAL VOC dataset, we compare SAM with modified MaskFormer [9] pre-trained on the COCO-stuff dataset following [24]. We also construct a vanilla baseline that compares category reference features with pixel features of test images directly. As shown in Table 4, both segmenters outperform the baseline by a large margin. We deem the main reason is that the region-level matching is more robust than pixel-level one. As illustrated in Fig. 4, the pixel classification paradigm fails to capture all visual concepts within images. SAM slightly surpasses MaskFormer as SAM can generate higher-quality masks on novel classes, naturally more suitable for open-vocabulary tasks. + +Investigation of the intra-modal matching. In Fig. 6, we visualized the t-SNE plots of the region features alongside their corresponding text-modal reference features and image-modal reference features using the same image based on CLIP [38] and DINOv2 [35], respectively. It can be observed that in the all-purpose feature space of DINOv2, the + +![](images/3b2907540b3019077d7b15e83adeb4e514d523aa5c8ee2549cc18f4b8476af7c.jpg) +Figure 6. T-SNE visualization of features of different region, as well as corresponding intra-modal and cross-modal reference features. + +![](images/f878055b0c74de40bbad91081d0931334fffb5a9a78b84f200de2f0c653b2822.jpg) + +region features of different categories are well-differentiated and align well with their corresponding reference features. However, in the case of CLIP, different region features not only exhibit notable overlap but also fail to align effectively with corresponding text-modal reference features. This difference substantiates the underlying rationale of our motivation, i.e., intra-modal matching. + +Hyperparameter Evaluations. Quantitative experiments are conducted to find a suitable number of subcategories used in relation-aware matching. As illustrated in Fig. 5 (a), the performance continues to grow until the number achieves 8, beyond which it starts to decline. It is reasonable as an appropriate number of subcategory references can model category diversity, but over-partitioning may lead to deviations from instance features. We then explore how the binarization threshold affects the performance in Fig. 5 (b). The model shows low sensitivity to threshold values owing to the capability of SAM, with a setting of 0.7 yields marginally better results. + +# 5. Conclusion + +In this work, we presented a training-free Relation-aware Intra-modal Matching (RIM) framework to tackle the challenging open-vocabulary semantic segmentation. We construct better-aligned image-modal category reference features based on the Stable Diffusion model and SAM. Then a relation-aware matching strategy is employed for region classification. RIM not only achieves results significantly surpassing the state-of-the-art but also opens up new avenues for OVS from an image-to-image matching perspective. + +# 6. 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We propose a novel relation-aware matching strategy for more robust region classification." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 486, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 545 + ], + "type": "text", + "content": "poses a severe limitation for their practical applications. In pursuit of the human-like intelligence of unbounded and fine-grained scene understanding, open-vocabulary segmentation (OVS) [2, 67] has attracted increasing interest recently, which enables segmentation with an unrestricted vocabulary." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "type": "text", + "content": "OVS is highly challenging as it requires not only grouping all pixels to corresponding visual concepts but also assigning each region the correct semantic label from a large vocabulary. Some early attempts [29, 64] optimize the pixel grouping process and the classification of visual concepts simultaneously by employing contrastive learning with image-text pairs. These methods inevitably yield masks of relatively low quality with only coarse supervision available. Another line of works [24, 67, 68] significantly dominate this field by modeling the OVS as a region recognition problem, which decouple OVS into two procedures, i.e. class-agnostic mask proposals prediction and mask class recognition. Though the mask proposals generation has been significantly improved with the assistance of pixel-level supervision and" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3952" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "elaborate segmenter architectures (e.g. Mask2Former [8]), the unsatisfactory region class recognition has emerged as the performance bottleneck of OVS [24]. We attribute this to the natural gap between the highly abstract and monotonous category textual features and the visual features that are more concrete and diverse." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 290, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 290, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 290, + 350 + ], + "type": "text", + "content": "Most current OVS approaches achieve mask class recognition via cross-modal region-category alignment based on the pretrained vision-language models (e.g., CLIP [38]). Despite its exemplary generalization ability on downstream classification tasks, CLIP usually suffers from spatial relations ambiguity [66, 69] and co-occurring object confusion ascribed to the holistic pre-training objective. On the other side, also pre-trained on internet-scale data, Stable Diffusion [42] (SD) model has garnered growing research interest credited to the phenomenal power of synthesizing photorealistic images with diverse and plausible content conditioned on textual descriptions. Considering that features from the same modality inherently exhibit a higher degree of alignment compared to cross-modal features (as shown in Fig. 6), we ask the question: " + }, + { + "bbox": [ + 46, + 146, + 290, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{0}" + }, + { + "bbox": [ + 46, + 146, + 290, + 350 + ], + "type": "text", + "content": " is it possible to transition the region classification in OVS from image-to-text matching to image-to-image matching using the SD model?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 290, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 290, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 290, + 604 + ], + "type": "text", + "content": "Before tackling this issue, we first revisit the common practices in mask class recognition [24, 67], which involves matching visual concepts with a set of category reference features (e.g. category textual features from CLIP). Inspired by previous exploration [59, 60, 73] of the strong image-text correspondence exhibited by the SD model, we can establish better-aligned intra-modal category reference features as shown in Fig. 1 (a). The cross-attention maps in the conditional generation process could serve as exceptional tools to further refine the category features. Nonetheless, it is still non-trivial to map test region features to their corresponding category reference features precisely, as the intra-class diversity and disturbances from akin categories exhibit in practical scenarios potentially lead to mismatches. Previous methodologies process each category independently during the matching phase, overlooking the informative inter-class relationships, which implicitly integrate structured contextual information and effectively aid in disambiguation. Here another question arises: how to harness the structure information modeled in the inter-class relationship to facilitate more accurate matching?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Driven by this question, we carefully design the relation-aware similarity measurement that incorporates the relations of the current region with some semantic relevant category agents. For a specified region feature within test image, a subset of category reference features that most akin to the region are selected to serve as category agents. The central idea is that we regard the category agent ranking as a stochastic event rather than a deterministic permutation. For example, in ranking, given the region feature specified by the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": "mask proposal " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " in Fig. 1 (a), its scores vary for different category agents, which can be taken as probabilities. The probability of being ranked first is 0.45 of the agent 'desk' and 0.35 of the agent 'chair'. The ranking permutation reflects the relevance of the corresponding categories w.r.t. the region feature. An agent-ranking probability distribution can be constructed by associating the probability with every rank permutation for both the region feature and all category reference features. Finally, as illustrated in Fig. 1 (b), we transform the similarity measurement from individual region-reference comparison to relation-aware agent-ranking distribution similarity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 216, + 548, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 548, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 548, + 407 + ], + "type": "text", + "content": "In this paper, we present a training-free OVS framework RIM to achieve Relation-aware Intra-modal Matching based on visual foundation models that coherently addresses the questions 1-2. Specifically, we facilitate a synergistic collaboration between the SD model and SAM to generate category-specific reference features by prompting the Segment Anything Model [22] (SAM) with points selected from the cross-attention map within SD model. SAM is further adopted to provide mask proposals of the test images. Finally, we conduct the relation-aware matching based on ranking distribution in the robust all-purpose feature space of DINOv2 [35]. RIM ensembles expertise of different visual foundational models in a complementary manner, enhancing mask quality and region-category matching precision simultaneously. Moreover, the overall framework is training-free, substantially mitigating the risk of overfitting." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 407, + 548, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 548, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 548, + 552 + ], + "type": "text", + "content": "Our contributions can be concluded as follows: (1) We reveal the problems of region feature classification in OVS and propose to construct well-aligned intra-modal reference features to circumvent ambiguities of cross-modal matching. (2) We design a relation-aware matching strategy based on ranking distribution, which captures structure information implicit in inter-class relationships and enables more robust matching. (3) We propose a training-free relation-aware intra-modal matching (RIM) network for OVS based on visual foundation models. Extensive experiments demonstrate that RIM remarkably surpasses previous state-of-the-art methods by a large margin." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 562, + 392, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 392, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 392, + 574 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Semantic Segmentation is a fundamental computer vision task with widespread applications in fields such as medical image processing [31, 37, 46, 48, 49, 58], video analysis [47, 51]. The pioneering FCN [28] has inspired a multitude of subsequent endeavors [6, 7, 43, 62, 72] centered around Convolutional Neural Networks (CNN). Beyond the CNN-based models, the triumph of the Vision Transformer (ViT) has spurred a succession of transformer-based segmentation models [30, 45, 63, 71], which have progressively evolved into a unified segmentation framework [8, 9] capable of addressing various segmentation tasks. Some alternative" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3953" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "settings, such as few-shot [23, 55-57], semi-supervised [23, 32, 33, 50], or weakly supervised [19, 54] segmentation, attempt to enhance the practicality of semantic segmentation techniques. Despite their success, these models are confined to predefined training categories or the specific foreground class, failing to recognize a broader spectrum of categories." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 290, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 290, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 290, + 372 + ], + "type": "text", + "content": "Open-vocabulary Semantic Segmentation aims to segment images with arbitrary categories described by texts. Some efforts [2, 29, 61, 65, 69] concentrated on developing a joint embedding space that bridges image pixels with class names or descriptions via learning objectives established from image-text pairs. For example, GroupViT [64] designed a hierarchical grouping transformer and learned the alignment between groups and text via contrastive loss. Another line of works [24, 66, 67] models OVS as a region recognition task by decoupling it into mask proposal generation and region classification, achieving notable progress attributed to advanced segmentation architectures [8] and pixel-level annotations [25, 74]. Large-scale vision-language pre-training models such as CLIP [38] and ALIGN [20] have been widely applied for OVS [15, 68, 70] which endows OVS model enhanced generalization. However, those pretraining models often encounter spatial confusion in dense prediction tasks [69], leading to recurring misclassification issues, which has emerged as a critical bottleneck in OVS." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 373, + 290, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 290, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 290, + 577 + ], + "type": "text", + "content": "Visual foundation models is catching up with the research in natural language processing (NLP) [1, 10, 36] and have achieved conspicuous achievements across a wide range of visual tasks. For example, DINov2 [35] establishes an impressive all-purpose feature extractor via self-supervised learning at both the image and patch levels. Trained on over 1 billion masks, Segment Anything Model (SAM) [22] has demonstrated astonishing zero-shot class-agnostic segmentation performance. Diffusion models [18, 44] have propelled the advancement of a series of image-to-text generation systems such as DALL-E [39] and Stable Diffusion model [42]. A series of works [27, 60, 66] render visual foundation models as powerful out-of-the-box tools to handle downstream tasks. Though a single foundation model may have limited capacity in addressing complex visual tasks such as OVS, in this work, we demonstrate that integrating different foundation models leads to positive synergies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 590, + 104, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 104, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 104, + 601 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 610, + 159, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 159, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 159, + 621 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": "Open-vocabulary segmentation aims to segment any image against a new vocabulary of categories " + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{test}" + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": ". Previous approaches typically involve training models on datasets annotated with image-level textual labels or pixel-level masks, with the category set " + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{train}" + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{test}" + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": " contains novel categories not exposed to the training process, i.e., " + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{train} \\neq \\mathbf{C}_{test}" + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": ". Owing to the training-free nature of our method, it inher" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "ently operates under a more challenging zero-shot setting wherein all test categories are considered novel." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 105, + 523, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 105, + 523, + 117 + ], + "spans": [ + { + "bbox": [ + 305, + 105, + 523, + 117 + ], + "type": "text", + "content": "3.2. Preliminary of Vision Foundation Models" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "content": "Stable-Diffusion model. Different from discriminative image-text models that model the class probability distribution " + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\pmb{p}(\\pmb{c}|\\pmb{i})" + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "content": " given the image, text-to-image stable diffusion model encode a text-conditional distribution of possible images " + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\pmb{p}(\\pmb{i}|\\pmb{c})" + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "content": ". This model demonstrates the prowess to synthesize high-fidelity images " + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "content": " that closely align with the specified conditional text " + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "content": ", all originating from a latent space defined by random Gaussian noise " + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 304, + 123, + 547, + 327 + ], + "type": "text", + "content": ". Specifically, stable diffusion model consists of three components: a pre-trained variational autoencoder (VAE) [13] that encodes and decodes the image latent code, a text encoder for prompt embedding, and a time-conditional UNet [43] for the denoising of latent vectors. The visual-text interaction occurs in the cross-attention layers that are integral to the UNet structure for each denoising step. Target categories within synthesized images can be accurately localized based on class-discriminative cross-attention maps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": "Segment Anything Model. SAM comprises of three components: an image encoder " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{Enc}_{\\mathbf{I}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": ", a prompt encoder " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{Enc}_{\\mathbf{P}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": ", and fast mask decoder " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{Dec}_{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{Enc}_{\\mathbf{P}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " takes as input the prompts of various optional forms such as points, boxes or coarse masks, and translates the prompts into feature tokens " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{P}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": ". Image feature tokens " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{I}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " are also obtained from " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{Enc}_{\\mathbf{I}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": ". A series of learnable mask tokens " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " are introduced and concatenated with " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{P}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " for diverse masks generation. Then the light weight " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{Dec}_{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " integrates the " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{I}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " and the concatenation of " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{P}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": " to predict segmentation masks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 447, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 547, + 555 + ], + "type": "text", + "content": "DINOv2. Pretrained on a large quantity of curated data with image and patch level distributive self-supervised learning, DINOv2 [35] learns all-purpose visual features that work out of box on many tasks varying from image level, e.g., image classification and pixel level, e.g., semantic segmentation. Moreover, this all-purpose ViT model demonstrates impressive patch-matching ability, robustly capturing similar semantic intent across different objects and even distinct images [27]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 563, + 373, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 373, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 373, + 574 + ], + "type": "text", + "content": "3.3. Overview" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "As shown in Fig. 2, we propose a training-free OVS framework RIM based on visual foundation models. RIM tackles the challenging region classification in OVS from a novel image-to-image matching perspective via the following two procedures, i.e., 1) intra-modal reference features construction, and 2) relation-aware matching. We resort to the SD model [42] and the SAM [22] to establish category reference features in procedure 1). In procedure 2), we conduct ranking based matching between the reference features and the region features in the all-purpose DINOv2 feature space. The details are as follows." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3954" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 76, + 532, + 335 + ], + "blocks": [ + { + "bbox": [ + 61, + 76, + 532, + 335 + ], + "lines": [ + { + "bbox": [ + 61, + 76, + 532, + 335 + ], + "spans": [ + { + "bbox": [ + 61, + 76, + 532, + 335 + ], + "type": "image", + "image_path": "46de0df1f835dd03df09d80de4143d16875f4d51df908b36635ef9b5dcf7b718.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 339, + 547, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 339, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 547, + 373 + ], + "type": "text", + "content": "Figure 2. Framework of our proposed Relation-aware Intra-modal Matching (RIM) Network. We first explore Stable Diffusion model and SAM to construct image-modal reference features, then we conduct relation-aware matching between region features and reference features based on ranking distribution. The matching is established in the all-purpose feature spaces of DINOv2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 379, + 241, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 379, + 241, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 379, + 241, + 390 + ], + "type": "text", + "content": "3.4. Intra-modal Reference Construction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": "In contrast to the substantial gap between abstract, monotonous text features and the concrete, diverse image features, homogenous modality features naturally exhibit improved alignment characteristics as shown in Fig. 6. We resort to stable diffusion model to generate a handful of reference images " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{\\mathbf{I}_1^c,\\mathbf{I}_2^c,\\dots ,\\mathbf{I}_K^c |\\mathbf{I}_k^c\\in \\mathbb{R}^{H\\times W\\times 3},c = 1,2,\\ldots ,C\\}" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": " candidate classes by simply prompting it with \"a photo of [category name]\". Together with the images, we also acquire the corresponding cross-attention maps for localizing the foreground targets. Specifically, for time step " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": ", the noisy image features " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_v\\in \\mathbb{R}^{h\\times w\\times c}" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": " are flattened and linearly projected into the queries " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": " and the prompt features " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_p\\in \\mathbb{R}^{N\\times d}" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": " are respectively projected into the keys " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": " and values " + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 397, + 288, + 564 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 572, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 572, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 70, + 572, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {F} _ {v} \\mathbf {W} ^ {\\mathcal {Q}}, \\quad \\mathbf {K} = \\mathbf {F} _ {p} \\mathbf {W} ^ {\\mathcal {K}}, \\quad \\mathbf {V} = \\mathbf {F} _ {p} \\mathbf {W} ^ {\\mathcal {V}}. \\tag {1}", + "image_path": "b404eaa5617124b5cb4c288f0c1f520ae5b9380c52629420c33436b4c37b0020.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 595, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 287, + 620 + ], + "type": "text", + "content": "Among which, " + }, + { + "bbox": [ + 47, + 595, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathcal{Q}}, \\mathbf{W}^{\\mathcal{K}}, \\mathbf{W}^{\\mathcal{V}}" + }, + { + "bbox": [ + 47, + 595, + 287, + 620 + ], + "type": "text", + "content": " are linear projections. The cross-attention maps are calculated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 628, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 628, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 116, + 628, + 287, + 654 + ], + "type": "interline_equation", + "content": "\\mathcal {S} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right), \\tag {2}", + "image_path": "48086689029a37fd8a90bff85d0e01094ddc7ab6d43db8e3d78f494b44d4c7ff.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sqrt{d}" + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "text", + "content": " is the scaling factor. Cross-attention maps " + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "inline_equation", + "content": "S_{n}^{l,t}" + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "text", + "content": " of different text tokens from different layers of UNet can be obtained based on the Equ. 2 and " + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "inline_equation", + "content": "n,l,t" + }, + { + "bbox": [ + 46, + 664, + 288, + 714 + ], + "type": "text", + "content": " are the index of text tokens, UNet layers and diffusion steps, respectively. To" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 380, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 380, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 545, + 416 + ], + "type": "text", + "content": "obtain the cross-attention map corresponding to the category token for foreground mining, we follow [60] to aggregate normalized multi-time and multi-layer maps, formally," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 358, + 423, + 545, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 423, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 358, + 423, + 545, + 454 + ], + "type": "interline_equation", + "content": "\\bar {\\mathcal {S}} _ {n} = \\frac {1}{L \\cdot T} \\sum_ {l \\in L, t \\in T} \\frac {\\mathcal {S} _ {n} ^ {l , t}}{\\operatorname* {m a x} \\left(\\mathcal {S} _ {n} ^ {l , t}\\right)}, \\tag {3}", + "image_path": "3e4056560854facc159135ba39e9c82ebaa52929f102ff77420f7711995bf7e9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "type": "text", + "content": "Where the " + }, + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 463, + 545, + 487 + ], + "type": "text", + "content": " denote the total time steps and the number of UNet layers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "text", + "content": "The foreground area in the synthesized images should be further located to avoid the interference of the irrelevant background regions. However, simply binarizing the cross-attention maps by thresholding may fail to fully capture the target. We thus exploit SAM to generate target masks by sampling the prompt points within the binarized attention maps. The foreground masks " + }, + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{M} = \\{\\mathbf{M}_1^c,\\mathbf{M}_2^c,\\dots,\\mathbf{M}_K^c |\\mathbf{M}_k^c\\in" + }, + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{h\\times w},c = 1,2,\\ldots ,C\\}" + }, + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "text", + "content": " and corresponding images " + }, + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 487, + 547, + 594 + ], + "type": "text", + "content": " then serve as the class references." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 643 + ], + "type": "text", + "content": "To enhance the robustness of instance-level matching, we opt to construct class reference image features within the all-purpose feature space of DINOv2 [35] via mask average pooling (MAP). Specifically," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 650, + 545, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 650, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 313, + 650, + 545, + 689 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {r e f} = \\left\\{\\mathbf {F} ^ {c} \\mid \\mathbf {F} ^ {c} = \\frac {1}{K} \\sum_ {k \\in K} \\mathbf {M A P} \\left(\\varphi \\left(\\mathbf {I} _ {k} ^ {c}\\right), \\zeta \\left(\\mathbf {M} _ {k} ^ {c}\\right)\\right) \\right\\} _ {c = 1} ^ {C} \\tag {4}", + "image_path": "4d939ad46263c2ae2b427bdc19558d955a64da7229d31e18b5c924183595ca27.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": " denote the DINOv2 feature extractor (ViT) and the bilinear-interpolation resize function, respectively." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3955" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^c\\in \\mathbb{R}^{1\\times D}" + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": " represents the average of all synthesized foreground features. We also construct a background reference feature by averaging all the background features of synthesized images. Similarly, region features within the test image specified by mask proposals are obtained as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 140, + 288, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 140, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 61, + 140, + 288, + 156 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {t e s t} = \\left\\{\\mathbf {F} ^ {p} | \\mathbf {F} ^ {p} = \\mathbf {M A P} (\\varphi [ \\mathbf {I} _ {t e s t} ], \\zeta [ \\mathbf {M} ^ {p} ]) \\right\\} _ {p = 1} ^ {P}, \\quad (5)", + "image_path": "71ad25e58035e6d297d9525ad9ad56b7a7b61a9a64ec77cee73c6ccb8dabb90d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 164, + 288, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 164, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 288, + 236 + ], + "type": "text", + "content": "among which " + }, + { + "bbox": [ + 46, + 164, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 164, + 288, + 236 + ], + "type": "text", + "content": " is the number of masks generated by SAM. By designing collaborative interactions among various visual foundational models, we establish well refined image-modal reference features thus shifts the paradigm of region classification in OVS from cross-modal matching to better-aligned intra-modal matching." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 243, + 189, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 189, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 189, + 257 + ], + "type": "text", + "content": "3.5. Relation-aware Matching" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "content": "The naive region classification strategy only selectively recruits the class reference feature with the highest similarity. However, independently taking each category exacerbates the risk of mismatches owing to the intra-class diversity and interference from similar categories. To further harness the structure information implicit in inter-class relationship for more effective matching, we select the top N reference features most similar to the region feature " + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^p" + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "content": " as category agents " + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^p\\in \\mathbb{R}^{N\\times D}" + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "content": ". We derive the scores of region-agent relation " + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "inline_equation", + "content": "s^p\\in \\mathbb{R}^{1\\times N}" + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "content": " between the region feature " + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^p" + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "content": " and the category agents " + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^p" + }, + { + "bbox": [ + 46, + 262, + 287, + 395 + ], + "type": "text", + "content": " using cosine similarity:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 120, + 402, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 402, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 120, + 402, + 287, + 430 + ], + "type": "interline_equation", + "content": "\\mathbf {s} ^ {p} = \\frac {\\mathbf {F} ^ {p} \\left(\\mathbf {A} ^ {p}\\right) ^ {\\mathsf {T}}}{\\| \\mathbf {F} ^ {p} \\| _ {2} \\cdot \\| \\mathbf {A} ^ {p} \\| _ {2}}. \\tag {6}", + "image_path": "f867e026661523b71ff5c6cfe0d25215b31886b0ba6736caabeefbe185bed472.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "text", + "content": "The core idea is that we take the agent ranking as a random event rather than a deterministic permutation. This implies that each permutation of the category agents is present with a certain probability, as opposed to the exclusive existence of the permutation ordered from largest to smallest. The probability of one permutation " + }, + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\pi \\in \\mathcal{P}(|\\mathcal{P}| = N!)" + }, + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "text", + "content": " given s (we omit region index " + }, + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "text", + "content": " for brevity) can be calculated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 530, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 530, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 530, + 287, + 563 + ], + "type": "interline_equation", + "content": "P (\\pi | \\mathbf {s}) = \\prod_ {k = 1} ^ {K} \\frac {\\mathbf {s} _ {\\pi (k)}}{\\sum_ {k ^ {\\prime} = k} ^ {K} \\mathbf {s} _ {\\pi \\left(k ^ {\\prime}\\right)}}, \\tag {7}", + "image_path": "641d14866c9730d6a5c487100bd26b959a7bed636a551d1b595eddf9f2805cdf.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "text", + "content": "among which the " + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "inline_equation", + "content": "\\pi(k)" + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "text", + "content": " class index of this permutation. For instance, assume that for a given region, the selected agents correspond to the categories \"sofa\", \"chair\", and \"bench\" respectively. One of the permutations of these three agents is " + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "inline_equation", + "content": "\\pi = (\\text{chair}, \\text{sofa}, \\text{bench})" + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "text", + "content": ". We can derive the probability of " + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 573, + 287, + 645 + ], + "type": "text", + "content": " based on the region-agent relation s:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 654, + 301, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 301, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 301, + 689 + ], + "type": "interline_equation", + "content": "P (\\pi | \\mathbf {s}) = \\frac {\\mathbf {s} (\\text {c h a i r})}{\\mathbf {s} (\\text {s o f a}) + \\mathbf {s} (\\text {b e n c h}) + \\mathbf {s} (\\text {c h a i r})} \\cdot \\frac {\\mathbf {s} (\\text {s o f a})}{\\mathbf {s} (\\text {s o f a}) + \\mathbf {s} (\\text {b e n c h})}. \\tag {8}", + "image_path": "593f429dfc370f27fa8333055896a68e10b13ffed9ccc871366c7cf2e0e4dded.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "By associating the probabilities of all " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "|\\mathcal{P}|" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " permutations, We convert the scores of individual region-agent relations into" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": "class ranking probability distributions " + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "inline_equation", + "content": "P(\\pi \\in \\mathcal{P}|\\mathbf{s}^p) \\in \\mathbb{R}^{1 \\times |\\mathcal{P}|}" + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": ", effectively modeling the inter-class relationship. Similarly, we compute the agent-ranking probability distributions for each category reference features on the same category agents, resulting in " + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "inline_equation", + "content": "P(\\pi \\in \\mathcal{P}|\\mathbf{s}^r) \\in \\mathbb{R}^{1 \\times |\\mathcal{P}|}" + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{s}^r" + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": " is obtained through Equ. 6. The distribution of the region is compared against the distributions of all reference features via cosine similarity, enabling the determination of the classification result:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 190, + 547, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 190, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 547, + 220 + ], + "type": "interline_equation", + "content": "c l s = \\underset {r = 1, 2, \\dots , C} {\\arg \\max } [ \\mathbf {c o s i n e} (P (\\pi \\in \\mathcal {P} | \\mathbf {s} ^ {p}), P (\\pi \\in \\mathcal {P} | \\mathbf {s} ^ {r})) ]. \\tag {9}", + "image_path": "ab28fc151ea496b24fd37db61bf83288920a6c7fe276df88f28650328c95d2c8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 221, + 547, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 547, + 329 + ], + "type": "text", + "content": "To further leverage the advantage of diversity in image-modal reference features, we construct a series of subcategory reference features by clustering the foreground prototypes (obtained by mask average pooling) of all synthesized images. The subcategory reference features are involved in the similarity computation instead of the holistic ones, and the final score of a category is obtained by summing up the similarities of all the corresponding subcategory reference features. The classification result is then obtained by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 338, + 545, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 338, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 545, + 380 + ], + "type": "interline_equation", + "content": "c l s = \\underset {r = 1, 2, \\dots , C} {\\arg \\max } \\left[ \\sum_ {t = 1} ^ {T} \\operatorname {c o s i n e} \\left(P \\left(\\pi \\in \\mathcal {P} \\mid \\mathbf {s} ^ {p}\\right), P \\left(\\pi \\in \\mathcal {P} \\mid \\mathbf {s} _ {t} ^ {r}\\right)\\right) \\right]. \\tag {10}", + "image_path": "5cf27f1c7dc3c6397242780c29631090f6902a6356714251339518bc471ce0e2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 381, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 545, + 429 + ], + "type": "text", + "content": "Based on the metric grounded in distributional similarity, instances of erroneous region classification can be effectively reduced as inter-class relationships are exploited to facilitate disambiguation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 441, + 387, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 387, + 454 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 387, + 454 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 460, + 473, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 473, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 473, + 472 + ], + "type": "text", + "content": "4.1. Dataset and Evaluation Metric" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 479, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 611 + ], + "type": "text", + "content": "We evaluate our model on three commonly used benchmarks, namely, PASCAL VOC 2012 [14], PASCAL Context [34] and COCO Object [25], which have 20,59,80 foreground classes, respectively. We also consider an extra background class in all three datasets. Training sets of datasets are not needed as the proposed method is training-free. For a fair comparison with previous approaches, we directly evaluate our method on the validation sets of these datasets, including 1449, 5105, and 5000 images, respectively. We use the mean of class-wise intersection over union (mIoU) following the common practice to measure the performance." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 611, + 541, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 541, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 541, + 624 + ], + "type": "text", + "content": "4.2. Implementation of Visual Foundation Models" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "We adopt the Stable Diffusion model v1.4 [42] to generate category-specific images of resolution " + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": " for category reference feature construction. We employ DINOv2 [35] with a ViT-B [12] as the default image encoder for more discriminative matching. Specifically, the keys sequence of the last attention layer is reshaped as the feature map. SAM [22] with ViT-B is adopted as the segmenter. We collect " + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 32" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3956" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 533, + 260 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 533, + 260 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 533, + 260 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 533, + 260 + ], + "type": "table", + "html": "
MethodArchTraining datasetSupervisionZero-shot transferDownstream datasets
PASCAL VOCPASCAL ContextCOCO Object
DeiT [52]ViTIN-1Kclass label✘53.035.9-
MoCo [16]ViTIN-1Kself✘34.321.3-
DINO [3]ViTIN-1Kself✘39.120.4-
ViL-Seg [26]ViTCC12Mself+text✓33.615.9-
MaskCLIP [75]ViTLAIONtext + \\(CLIP_{\\mathrm{T}}\\)✓38.823.620.6
GroupViT [64]ViTCC12Mtext✓52.322.4-
ZeroSeg [5]ViTIN-1K\\(CLIP_{\\mathrm{V}}\\)✓40.820.420.2
TCL [4]ViTCC3M+CC12Mtext✓51.224.330.4
ViewCo [41]ViTCC12M+YFCCtext+self✓52.423.023.5
CLIPpy [40]ViTHQITP-134Mtext✓52.2-32.0
SegCLIP [29]ViTCC3M+COCOtext + \\(CLIP_{\\mathrm{T}}\\)✓52.624.726.5
OVSegmentor [65]ViTCC4Mself+text✓53.820.425.1
SimSeg [69]ViTCC3M+CC12Mtext✓57.426.229.7
DiffSeg [53]UNet+ViT✓60.127.537.9
OVDiff [21]UNetTraining-free✓67.130.134.8
OursUNet+ViT✓77.834.344.5
", + "image_path": "8e1ea4ec9d843ca71f6eea3e6ac5763f03fc510970fac644222df0b9272ed961.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 299, + 287, + 388 + ], + "blocks": [ + { + "bbox": [ + 46, + 262, + 547, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 547, + 297 + ], + "type": "text", + "content": "Table 1. Comparison with existing methods. Models in the first three rows are finetuned on target datasets while the rest approaches perform zero-shot transfer. Bold fonts refer to the best results among the models which enable zero-shot transfer. With only image-text pairs available, our method significantly outperforms the existing approaches. More results please refer to Supplementary Material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 299, + 287, + 388 + ], + "lines": [ + { + "bbox": [ + 50, + 299, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 50, + 299, + 287, + 388 + ], + "type": "table", + "html": "
IRCRMmIOU
w/o fg-maskw/ fg-maskw/o subw/ sub
26.7
✓38.7
✓41.8
✓✓43.1
✓✓44.5
", + "image_path": "9adf5c9e0a19bc5ee8c0132ffb38df95f09d6a89091fae9d044cf089a6112acb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 460, + 287, + 494 + ], + "blocks": [ + { + "bbox": [ + 46, + 390, + 288, + 447 + ], + "lines": [ + { + "bbox": [ + 46, + 390, + 288, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 288, + 447 + ], + "type": "text", + "content": "Table 2. Ablation studies of the proposed RIM. We mainly verified the effectiveness of the image reference construction (IRC), and relation-aware matching (RM). Moreover, we also observe the effectiveness of foreground segmentation (fg-mask) of synthesized images and the subcategory reference features (sub)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 460, + 287, + 494 + ], + "lines": [ + { + "bbox": [ + 50, + 460, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 50, + 460, + 287, + 494 + ], + "type": "table", + "html": "
EncoderCLIP [38]SD [42]MAE [17]DINOv2
mIoU42.043.139.544.5
", + "image_path": "3ec3463ab2ba5e3dbc4a2950f73bc6bf2e75917acf57ddaf142b4c13ff7d9985.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 520, + 179, + 544 + ], + "blocks": [ + { + "bbox": [ + 63, + 495, + 270, + 506 + ], + "lines": [ + { + "bbox": [ + 63, + 495, + 270, + 506 + ], + "spans": [ + { + "bbox": [ + 63, + 495, + 270, + 506 + ], + "type": "text", + "content": "Table 3. Comprison of different image feature extractors." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 520, + 179, + 544 + ], + "lines": [ + { + "bbox": [ + 50, + 520, + 179, + 544 + ], + "spans": [ + { + "bbox": [ + 50, + 520, + 179, + 544 + ], + "type": "table", + "html": "
SegmenternoneMaskFormerSAM
mIoU42.076.777.8
", + "image_path": "079b8ded360ae5557f6e1a29be7cb677d7b78dc3c44e3458982ce842c986cf15.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 190, + 515, + 286, + 549 + ], + "blocks": [ + { + "bbox": [ + 46, + 549, + 182, + 583 + ], + "lines": [ + { + "bbox": [ + 46, + 549, + 182, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 182, + 583 + ], + "type": "text", + "content": "Table 4. Comparison of mask proposal generators. \"none\" means direct pixel classification." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 190, + 515, + 286, + 549 + ], + "lines": [ + { + "bbox": [ + 190, + 515, + 286, + 549 + ], + "spans": [ + { + "bbox": [ + 190, + 515, + 286, + 549 + ], + "type": "table", + "html": "
Selection of AgentsmIoU
Rand43.8
Top-N44.5
", + "image_path": "57b5b035fd684bbfc34b3ef769464508714197dc3f495af0b90d3ad8d63d402b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 188, + 551, + 286, + 573 + ], + "lines": [ + { + "bbox": [ + 188, + 551, + 286, + 573 + ], + "spans": [ + { + "bbox": [ + 188, + 551, + 286, + 573 + ], + "type": "text", + "content": "Table 5. Comparison of category agents selection." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "type": "text", + "content": "prompt points in a grid manner to generate mask proposals for the test images. To segment the foreground of synthesized reference images, We sample 5 prompt points within the binarized cross-attention map, where the binarization threshold is set to a relatively high value of 0.7 to prevent erroneous segmentation of background regions. The number of category agents is set to 4. More implementation details are provided in Supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 299, + 493, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 493, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 493, + 312 + ], + "type": "text", + "content": "4.3. Comparison to the state-of-the-arts" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 317, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 547, + 376 + ], + "type": "text", + "content": "We compare our method with approaches that have been trained with fully supervised finetuning transfer and zero-shot transfer. Besides, we also conduct performance comparisons with newly arising train-free approaches. Table 1 summarizes the results of the comparison." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": "Firstly, we can observe that the proposed RIM significantly surpasses the non-zero-shot fully supervised segmentation baselines, i.e., DeiT [52], MoCo [16]. Furthermore, we compare with other zero-shot OVS approaches such as MaskCLIP [75], SegCLIP [29], and SimSeg [69], which also adopt the ViT backbones of visual foundation model, i.e., CLIP [38]. Our method also shows a clear lead. Specifically, we achieve " + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "inline_equation", + "content": "20.4\\%" + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "inline_equation", + "content": "18.1\\%" + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "inline_equation", + "content": "14.8\\%" + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": " mIoU over the SimSeg [69] on three datasets, respectively. We posit that the primary cause is that CLIP is susceptible to ambiguities in spatial relations and confusion of co-occurring objects, a consequence stemming from its holistic training objective. Besides, RIM also demonstrates significant performance improvements over the most recently developed training-free methods based on visual foundation models, achieving " + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "inline_equation", + "content": "10.4\\%" + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "inline_equation", + "content": "6.6\\%" + }, + { + "bbox": [ + 304, + 377, + 548, + 604 + ], + "type": "text", + "content": " mIoU gains, respectively. As shown in Fig. 3, we present a series of visualizations depicting segmentation outcomes across various datasets for a more intuitive observation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": "A series of ablation studies are conducted to thoroughly investigate the impact of each component of the proposed RIM. As shown in Table 2, we mainly implement our experiments on COCO Object [25] dataset, and the first row is our baseline, which follows a naive image-to-text matching for region classification. Specifically, we crop the test image along the bounding boxes corresponding to the mask proposals (gen-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3957" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 179, + 160 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 179, + 160 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 179, + 160 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 179, + 160 + ], + "type": "image", + "image_path": "f7fefb3235c805360970ef272402c68249933a8242d075de54e7faee4c48c6e0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": 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9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 216, + 332, + 376, + 342 + ], + "lines": [ + { + "bbox": [ + 216, + 332, + 376, + 342 + ], + "spans": [ + { + "bbox": [ + 216, + 332, + 376, + 342 + ], + "type": "text", + "content": "Figure 3. Qualitative results of our method." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 285, + 252, + 425, + 330 + ], + "blocks": [ + { + "bbox": [ + 285, + 252, + 425, + 330 + ], + "lines": [ + { + "bbox": [ + 285, + 252, + 425, + 330 + ], + "spans": [ + { + "bbox": [ + 285, + 252, + 425, + 330 + ], + "type": "image", + "image_path": "5111f44e9523b66f45eaac5559e34dd1a5b36718be20e6f714cb7fc8c5db2d9c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 425, + 252, + 526, + 330 + ], + "blocks": [ + { + "bbox": [ + 425, + 252, + 526, + 330 + ], + "lines": [ + { + "bbox": [ + 425, + 252, + 526, + 330 + ], + "spans": [ + { + "bbox": [ + 425, + 252, + 526, + 330 + ], + "type": "image", + "image_path": "08600b502d22f9042fdc3b46f1e382239c11b4459ab232c00de14bbd4bc1ca65.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 347, + 288, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 288, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 288, + 407 + ], + "type": "text", + "content": "erated by SAM) and resize them to " + }, + { + "bbox": [ + 46, + 347, + 288, + 407 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 347, + 288, + 407 + ], + "type": "text", + "content": " resolution. The background area of the cropped image is filled with zeros, and then CLIP [38] with ViT-B is exploited to perform image-to-text matching between the cropped image and category labels." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "type": "text", + "content": "Ablation study on intra-modal reference construction. To verify the effectiveness of intra-modal alignment, we first construct a naive image-to-image matching as the " + }, + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "type": "inline_equation", + "content": "2^{nd}" + }, + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "type": "text", + "content": " row of Table 2. More concretely, DINOv2 features of all synthesized images of a category are condensed to a holistic reference feature via global average pooling. The matching process is simply implemented with cosine similarity. Despite its simplicity, this intra-modal matching exhibits a significant performance improvement, i.e., " + }, + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "type": "inline_equation", + "content": "12.0\\%" + }, + { + "bbox": [ + 46, + 411, + 288, + 637 + ], + "type": "text", + "content": " in mIoU over the cross-modal matching based on CLIP. This improvement is anticipated as the holistic training objective of CLIP makes its prediction heavily reliant on contextual information. This reliance not only introduces spatial confusion but also leads to misclassification of frequently co-occurring objects, such as the sky and airplane. Attributed to the image generation capabilities of SD model and the robust high-level semantic feature extraction of DINOv2, an improved intra-modal alignment between region features and class reference features is achieved." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Further performance improvements can be observed if we construct the category reference features with only foreground features as shown in the " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "3^{th}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " row of Table 2. We deem the main reason is that the background areas in synthetic images may contain information of other categories, which confuses the classification process. While in our im" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 347, + 547, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 547, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 547, + 454 + ], + "type": "text", + "content": "plementation, more refined category reference features are constructed attributed to the spatial localization ability of the SD model embedded in the cross-attention map and the powerful segmentation capability of SAM, which effectively mitigates the influence of cluttered backgrounds. Despite utilizing merely cosine similarity for intra-modal matching, it has already achieved impressive performance, i.e., " + }, + { + "bbox": [ + 304, + 347, + 547, + 454 + ], + "type": "inline_equation", + "content": "44.5\\%" + }, + { + "bbox": [ + 304, + 347, + 547, + 454 + ], + "type": "text", + "content": " mIoU on COCO Object dataset, which can be adopted as a strong baseline for further research." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "text", + "content": "Ablation study on relation-aware matching. As described in Sec. 3.5, we propose to model the beneficial structure information contained in inter-class relationships via relation-aware matching. Compared to the naive approach that only considers only the cosine similarity between region features and each individual category reference feature, our proposed strategy achieves a sizeable gain, i.e., " + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "text", + "content": " in mIoU, as presented in the " + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 304, + 459, + 547, + 602 + ], + "type": "text", + "content": " rows of Table 2. The results prove that the proposed similarity measurement based on ranking distribution facilitates effective disambiguation in the matching process, which brings a notable reduction in the misclassification of regions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": "After integrating subcategory reference features into relation-aware matching, the performance further improved from " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "43.1\\%" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "44.5\\%" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " in mIoU, as shown in " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "5^{th}" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " row of Table 2. This improvement can be attributed to the ability of the SD model to generate diverse image features, enabling our method to effectively handle intra-class diversity. Moreover, the scoring scheme in Equ. 10, akin to a voting mechanism, further enhances the robustness of the matching process. Furthermore, in Table 5, we demonstrate that reference features" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3958" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 281, + 167 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 281, + 167 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 281, + 167 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 281, + 167 + ], + "type": "image", + "image_path": "67f6c1aa8e6fad3bc328b12b66e6b7b5cea8e3560bf821f7d62eb37aa51bc79b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 169, + 286, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 169, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 169, + 286, + 190 + ], + "type": "text", + "content": "Figure 4. Effectiveness of SAM based region-level matching. The SAM could well capture visual concepts within images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 193, + 167, + 269 + ], + "blocks": [ + { + "bbox": [ + 48, + 193, + 167, + 269 + ], + "lines": [ + { + "bbox": [ + 48, + 193, + 167, + 269 + ], + "spans": [ + { + "bbox": [ + 48, + 193, + 167, + 269 + ], + "type": "image", + "image_path": "3d187ed82499ca9b19e671226db467d30b17222254de3c8755b6bbc19760f4ca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 271, + 288, + 293 + ], + "lines": [ + { + "bbox": [ + 47, + 271, + 288, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 288, + 293 + ], + "type": "text", + "content": "Figure 5. Hyperparameter experiments on the number of subcategories and binarization threshold of cross-attention map." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 170, + 193, + 282, + 269 + ], + "blocks": [ + { + "bbox": [ + 170, + 193, + 282, + 269 + ], + "lines": [ + { + "bbox": [ + 170, + 193, + 282, + 269 + ], + "spans": [ + { + "bbox": [ + 170, + 193, + 282, + 269 + ], + "type": "image", + "image_path": "eefa186be170b0a3346d9cb77cfaa4d6df9e2bd4c82ab8bfed4bf056814955bd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 303, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 303, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 287, + 327 + ], + "type": "text", + "content": "that share high similarities with region features are better candidates to serve as category agents." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 327, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 460 + ], + "type": "text", + "content": "Ablation on DINOv2. To demonstrate the superiority of feature extraction using DINOv2, we conduct comparison experiments of CLIP [38], MAE [17], Stable Diffusion Unet (SD) [42], and DINOv2 as presented in Table 3. DINOv2 achieves the best performance attribute to effective pretraining based on image-level and patch-level discriminative self-supervised learning. While CLIP fails to match region-level features precisely, Stabel Diffusion UNet is constrained to some extent under the unconditional settings. MAE exhibits suboptimal performance in our setting due to its relatively limited high-level semantic modeling capability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 461, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 640 + ], + "type": "text", + "content": "Ablation on SAM. Our relation-aware matching operates at the region level, as SAM furnishes comprehensive mask proposals for the test images. To explore the effectiveness of SAM, on the PASCAL VOC dataset, we compare SAM with modified MaskFormer [9] pre-trained on the COCO-stuff dataset following [24]. We also construct a vanilla baseline that compares category reference features with pixel features of test images directly. As shown in Table 4, both segmenters outperform the baseline by a large margin. We deem the main reason is that the region-level matching is more robust than pixel-level one. As illustrated in Fig. 4, the pixel classification paradigm fails to capture all visual concepts within images. SAM slightly surpasses MaskFormer as SAM can generate higher-quality masks on novel classes, naturally more suitable for open-vocabulary tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Investigation of the intra-modal matching. In Fig. 6, we visualized the t-SNE plots of the region features alongside their corresponding text-modal reference features and image-modal reference features using the same image based on CLIP [38] and DINOv2 [35], respectively. It can be observed that in the all-purpose feature space of DINOv2, the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 417, + 182 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 417, + 182 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 417, + 182 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 417, + 182 + ], + "type": "image", + "image_path": "3b2907540b3019077d7b15e83adeb4e514d523aa5c8ee2549cc18f4b8476af7c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 184, + 545, + 206 + ], + "lines": [ + { + "bbox": [ + 306, + 184, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 306, + 184, + 545, + 206 + ], + "type": "text", + "content": "Figure 6. T-SNE visualization of features of different region, as well as corresponding intra-modal and cross-modal reference features." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 71, + 539, + 182 + ], + "blocks": [ + { + "bbox": [ + 427, + 71, + 539, + 182 + ], + "lines": [ + { + "bbox": [ + 427, + 71, + 539, + 182 + ], + "spans": [ + { + "bbox": [ + 427, + 71, + 539, + 182 + ], + "type": "image", + "image_path": "f878055b0c74de40bbad91081d0931334fffb5a9a78b84f200de2f0c653b2822.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 220, + 547, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 547, + 304 + ], + "type": "text", + "content": "region features of different categories are well-differentiated and align well with their corresponding reference features. However, in the case of CLIP, different region features not only exhibit notable overlap but also fail to align effectively with corresponding text-modal reference features. This difference substantiates the underlying rationale of our motivation, i.e., intra-modal matching." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 308, + 545, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 451 + ], + "type": "text", + "content": "Hyperparameter Evaluations. Quantitative experiments are conducted to find a suitable number of subcategories used in relation-aware matching. As illustrated in Fig. 5 (a), the performance continues to grow until the number achieves 8, beyond which it starts to decline. It is reasonable as an appropriate number of subcategory references can model category diversity, but over-partitioning may lead to deviations from instance features. We then explore how the binarization threshold affects the performance in Fig. 5 (b). The model shows low sensitivity to threshold values owing to the capability of SAM, with a setting of 0.7 yields marginally better results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 472, + 378, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 378, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 378, + 484 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 495, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 604 + ], + "type": "text", + "content": "In this work, we presented a training-free Relation-aware Intra-modal Matching (RIM) framework to tackle the challenging open-vocabulary semantic segmentation. We construct better-aligned image-modal category reference features based on the Stable Diffusion model and SAM. Then a relation-aware matching strategy is employed for region classification. RIM not only achieves results significantly surpassing the state-of-the-art but also opens up new avenues for OVS from an image-to-image matching perspective." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 624, + 415, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 415, + 637 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 415, + 637 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 647, + 547, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 547, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 547, + 702 + ], + "type": "text", + "content": "This work was partially supported by the National Defense Basic Scientific Research Program of China (Grant JCKY2021130B016), National Nature Science Foundation of China (Grant 12150007), Youth Innovation Promotion Association CAS 2018166." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3959" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 146 + ], + "type": "text", + "content": "[1] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. 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Unleashing text-to-image diffusion models for visual perception. arXiv preprint arXiv:2303.02153, 2023. 2" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 208, + 288, + 251 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 208, + 288, + 251 + ], + "spans": [ + { + "bbox": [ + 49, + 208, + 288, + 251 + ], + "type": "text", + "content": "[74] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. International Journal of Computer Vision, 127:302-321, 2019. 1, 3" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 253, + 287, + 285 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 253, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 49, + 253, + 287, + 285 + ], + "type": "text", + "content": "[75] Chong Zhou, Chen Change Loy, and Bo Dai. Extract free dense labels from clip. In European Conference on Computer Vision, pages 696-712. Springer, 2022. 6" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "3963" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/40bed3ab-f671-40b9-b3ce-7de57541124c_content_list.json b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/40bed3ab-f671-40b9-b3ce-7de57541124c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f6360d1a7b738aa9cf28dc8463bdbb0b87b8fc56 --- /dev/null +++ b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/40bed3ab-f671-40b9-b3ce-7de57541124c_content_list.json @@ -0,0 +1,1479 @@ +[ + { + "type": "text", + "text": "ImageNet-D: Benchmarking Neural Network Robustness on Diffusion Synthetic Object", + "text_level": 1, + "bbox": [ + 181, + 128, + 789, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chenshuang Zhang1 Fei Pan2 Junmo Kim1* In So Kweon1 Chengzhi Mao3,4* KAIST1, University of Michigan, Ann Arbor2, McGill University3, MILA4", + "bbox": [ + 143, + 202, + 828, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 313, + 289 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We establish rigorous benchmarks for visual perception robustness. Synthetic images such as ImageNet-C, ImageNet-9, and Stylized ImageNet provide specific type of evaluation over synthetic corruptions, backgrounds, and textures, yet those robustness benchmarks are restricted in specified variations and have low synthetic quality. In this work, we introduce generative model as a data source for synthesizing hard images that benchmark deep models' robustness. Leveraging diffusion models, we are able to generate images with more diversified backgrounds, textures, and materials than any prior work, where we term this benchmark as ImageNet-D. Experimental results show that ImageNet-D results in a significant accuracy drop to a range of vision models, from the standard ResNet visual classifier to the latest foundation models like CLIP and MiniGPT-4, significantly reducing their accuracy by up to $60\\%$ . Our work suggests that diffusion models can be an effective source to test vision models. The code and dataset are available at https://github.com/chenshuang-zhang/imagenet_d.", + "bbox": [ + 75, + 304, + 473, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 612, + 209, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural networks have achieved remarkable performance in tasks ranging from image classification [33, 34, 55] to visual question answering [10, 28, 31, 65]. These advances have inspired the application of neural networks in various fields, including security and safety-critical systems such as self-driving cars [27, 32, 42], malware detection [9, 43, 60] and robots [6, 7, 25]. Due to their wide adaptation, it is becoming increasingly important to identify the robustness of neural networks [30, 41] for safety reasons.", + "bbox": [ + 75, + 637, + 468, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To evaluate the robustness of neural networks, ObjectNet [3] collects real-world object images on controlled factors like background with human workers, which is time-consuming and labor-intensive. To scale up data collection, synthetic images are proposed as test images [15, 19, 58]. For example, ImageNet-C [19] introduces a set of low-level", + "bbox": [ + 75, + 773, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b6c359834f0d11be472e90b84048a8ed680ccad04e8c39960c371ebcefd3cde.jpg", + "image_caption": [ + "Tennis racket" + ], + "image_footnote": [], + "bbox": [ + 503, + 273, + 625, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7aaeb3bc5282b4fccfb1afd813b7a3d1e184d9c251aa79cc04ba23903cb74fa8.jpg", + "image_caption": [ + "Measuring cup" + ], + "image_footnote": [], + "bbox": [ + 633, + 273, + 754, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bf403728fe0a6b09d9d13fae02e33853f20e6d1e62e526655977d31a5b9dbd5e.jpg", + "image_caption": [ + "Mixing/salad bowl", + "Figure 1. Top predictions from CLIP (ViT-L/14) on ImageNet-D. We synthesize the images by changing their background, texture and material. The groundtruth for the images are plunger, spatula, and ladle in order, together with the background (badminton court), texture (freckled), and material (painted)." + ], + "image_footnote": [], + "bbox": [ + 764, + 273, + 887, + 369 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "common visual corruptions, such as gaussian noise and blur, to test models' robustness. ImageNet-9 [58] uses simple cutting and paste technique to create robustness benchmark on object background, yet the images are not realistic. Stylized-ImageNet [15] generates new images by altering the textures of ImageNet images, which cannot control the global factors like background.", + "bbox": [ + 496, + 474, + 892, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we introduce ImageNet-D, a synthetic test set generated by diffusion models for object recognition task. Capitalizing on the capability of pioneering Stable Diffusion models[48], we show that we can steer diffusion models with language to create realistic test images that cause vision models fail. Figure 1 shows three failure cases of CLIP model on our synthetic ImageNet-D dataset. Since we rely on language to create images, we can vary the high-level factors in the images in contrast to the local corruptions and texture in prior work, introducing addition factors that one can evaluate robustness on.", + "bbox": [ + 496, + 582, + 892, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enhance sample difficulty of our dataset, we selectively retain images that cause failures in multiple chosen vision models. Our results show that images triggering errors in chosen models can reliably transfer their challenging nature to other, previously untested models. This leads to a notable decrease in accuracy, even in state-of-the-art foundation models like MiniGPT-4 [65] and LLaVa [31], suggesting our dataset reveals common failures in vision models.", + "bbox": [ + 496, + 748, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visualizations demonstrate that Imagenet-D signifi-", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. Junmo Kim , Chengzhi Mao .", + "bbox": [ + 75, + 875, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21752", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/39a42d17fa53d4b1e3ac4bbd857e851a97692a311b6979de39fd2e4636270a2c.jpg", + "image_caption": [ + "Figure 2. Examples from ImageNet-9 [58], Stylized-ImageNet [15] and ImageNet-C [19] and our ImageNet-D. For the second row, we show images from ImageNet-D with different backgrounds, textures and materials orderly. Take the background for example (the two columns on the left), ImageNet-9 [58] generates new images by simply cutting and paste foreground and background from different images, leading to object deformation and dislocation. By contrast, ImageNet-D includes images with diverse backgrounds by diffusion generation, achieving superior visual fidelity." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 194 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cantly enhances image quality compared to previous synthetic robustness benchmarks, as evidenced in Figure 2. Imagenet-D serves as an effective tool for reducing the performance and assessing model robustness, including ResNet 101 (reducing $55.02\\%$ ), ViT-L/16 (reducing $59.40\\%$ ), CLIP (reducing $46.05\\%$ ), and transfer well to unforeseen large vision language models like LLaVa [31] (reducing $29.67\\%$ ), and MiniGPT-4 [65] (reducing $16.81\\%$ ). Our approach of utilizing generative models to evaluate model robustness is general, and shows significant potential for even greater effectiveness with future advancements in generative models.", + "bbox": [ + 75, + 375, + 467, + 553 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 570, + 212, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robustness of neural networks. Neural networks have evolved from CNN [16, 24], ViT [33, 55], to large foundation models [5, 12, 54]. Previous work has investigated neural networks robustness from multiple aspects, such as adversarial examples [35, 36, 38, 63, 64] and out-of-domain samples [17, 20, 22, 37]. Foundation models have shown greater robustness on out-of-distribution samples [45]. Robust explanation has also been investigated [31, 39, 65]. To systematically evaluate the robustness of deep models, test sets that cover different factors are urgently needed.", + "bbox": [ + 75, + 597, + 467, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dataset for benchmarking robustness. To evaluate neural network robustness, a branch of studies source images online, including ImageNet-A [23], Imagenet-R [22] and ImageNet-Sketch [57]. However, they are limited to images that exist on the web. ObjectNet [3] manually collects images with the help of 5982 workers, which is time-consuming and resource-intensive.", + "bbox": [ + 75, + 750, + 467, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the limitations of web images and reduce the cost of manual collection, synthetic images are proposed for robustness evaluation [15, 19, 58]. ImageNet-C [19]", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "benchmarks model robustness on low-level corruptions. ImageNet-9 [58] generates new images by combining foreground and background from different images, however, limited by poor image fidelity. Stylized-ImageNet [15] alters the textures of ImageNet images by AdaIN style transfer [26] or introducing texture-shape cue conflict, which cannot control other factors like backgrounds. In this work, we introduce a new test set ImageNet-D, which is generated by controlling diffusion models and includes novel images with diverse backgrounds, textures, and materials.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image generation. Diffusion models have achieved great success in various tasks including image generation [46, 49, 51, 62]. As a milestone work, Stable diffusion [48] enables high-fidelity image synthesis controlled by language. InstructPix2Pix [8] provides a more sophisticated control by editing a given image according to human instructions. In this paper, we build our pipeline with the standard Stable Diffusion model, yet our algorithm is compatible with other generative models that can be steered by language.", + "bbox": [ + 496, + 243, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Enhancing perception with diffusion images. Diffusion-generated images have been used for vision perception tasks. A branch of studies [1, 2, 53, 59] improves classification accuracy by using synthetic images as training data augmentation. DREAM-OOD [14] finds the outliers by decoding sampled latent embeddings to images. However, their method lacks specific control over image space, which is crucial for benchmarks like ImageNet-D. [40] identifies under-represented attribute pairs, while our study focuses on hard images with a single attribute. Unlike [29, 44, 56] that modify existing datasets, our work generates new images and mines the most challenging ones as the test set, achieving greater accuracy drop than [29, 44, 56].", + "bbox": [ + 496, + 380, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. ImageNet-D", + "text_level": 1, + "bbox": [ + 500, + 593, + 625, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first present how ImageNet-D is created in Section 3.1, followed by an overview of its statistics in Section 3.2.", + "bbox": [ + 496, + 619, + 888, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Dataset design", + "text_level": 1, + "bbox": [ + 500, + 662, + 645, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While neural networks excel in various applications, their robustness needs rigorous evaluation for safety. Traditional evaluations use existing test sets, including either natural [3, 23] or synthetic images [15, 19, 58]. Compared to manual image collection, collecting a synthetic test set is more efficient [15, 58]. However, the diversity of current synthetic test sets is limited due to their reliance on existing images for attribute extraction. These synthetic images are also not realistic, as shown in Figure 2. ImageNet-D is introduced to evaluate model robustness across various object and nuisance combinations, addressing these limitations.", + "bbox": [ + 496, + 686, + 890, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image generation by diffusion models. To construct ImageNet-D, diffusion models are used to create a vast image pool by combining all possible object and nuisances,", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21753", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0a37f76606b667979dcced3fb3bf263b586376fdb19a61988aff6af342e080f3.jpg", + "image_caption": [ + "Figure 3. The ImageNet-D test set. Each group of images is generated with the same object and nuisance, such as background, texture, and material. For each group of images, the ground truth label is color green, while the predicted categories by CLIP (ViT-L/14) on each image are in black. Leveraging diffusion models for image generation, we can create a test set with diverse combinations of objects and nuisances. For example, the top left corner shows a bench in the swimming pool background. Interestingly, CLIP (ViT-L/14) recognizes the bench in this image as swimming trunks." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 277 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/043abeda0e0a5cbb842e4106d795317796d3ed99dc2d8c2b39177720204a319c.jpg", + "image_caption": [ + "Figure 4. ImageNet-D creation framework. ImageNet-D is created by first combining various object categories and nuisances, including background, texture, and material. To make the test set challenging, we only keep the hard images from the large pool that commonly make multiple surrogate models fail to predict the correct object label. The test set is then refined through human verification to ensure the images are valid, single-class, and high-quality, making ImageNet-D suitable for evaluating the robustness of different neural networks." + ], + "image_footnote": [], + "bbox": [ + 78, + 372, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "enabling high-fidelity image generation based on user-defined text inputs. We use Stable Diffusion model[48] for image generation, while our approach is compatible with other generative models that can be steered by language. The image generation process is formulated as follows:", + "bbox": [ + 75, + 556, + 468, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\operatorname {Image}(C,N) = \\operatorname {Stable}\\operatorname {Diffusion}(\\operatorname {Prompt}(C,N))$ (1)", + "bbox": [ + 96, + 645, + 468, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $C$ and $N$ refer to the object category and nuisance, respectively. The nuisance $N$ includes background, material, and texture in this work. Table 1 presents an overview of nuisances and prompts to diffusion models. Using the backpack category as an example, we first generate images of backpacks with various backgrounds, materials, and textures (e.g., a backpack in a wheat field), offering a broader range of combinations than existing test sets. Each image is labeled with its prompt category $C$ as ground truth for classification. An image is viewed misclassified if the model's predicted label does not match the ground truth $C$ .", + "bbox": [ + 75, + 672, + 468, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After creating a large image pool with all object category and nuisance pairs, we evaluate CLIP (ViT-L/14) model on these images in Table 2. Experimental details are reported in Section 4.1. Table 2 shows that CLIP achieves high accu", + "bbox": [ + 75, + 840, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "racy on all the test sets, with an accuracy of around $94\\%$ on synthetic image pool. To create a challenging test set for robustness evaluation, we propose an efficient strategy to find the hard test samples from all generated images as follows.", + "bbox": [ + 496, + 556, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hard image mining with shared perception failures. Before introducing how to identify hard samples from synthetic image pool, we first define the concept of shared perception failure as follows.", + "bbox": [ + 496, + 619, + 890, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Shared failure: An image is a shared failure if it leads multiple models to predict object's label incorrectly.", + "bbox": [ + 496, + 681, + 890, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An ideal hard test set should include images that all tested models fail to identify. However, this is impractical due to the inaccessibility of future test models, termed target model. Instead, we construct the test set using shared failures of known surrogate models. If the failures of surrogate models lead to low accuracy in unknown models, the test set is deemed challenging. This is defined as transferable failure as follows:", + "bbox": [ + 496, + 714, + 890, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transferable failure: Shared failures of known surrogate models are transferable if they also result in low accuracy for unknown target models.", + "bbox": [ + 496, + 838, + 890, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To test if shared failures of surrogate models are trans", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21754", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/468597abd4c5fd5d5d58f38cb64d60d18174b9babb29c85e883868a3bb0b3887.jpg", + "table_caption": [ + "Table 1. Overview of nuisances and input prompts to diffusion models. During ImageNet-D construction, 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4] are used as nuisances. Images are generated by pairing each object with all nuisances in diffusion model prompts. This approach allows for efficient scaling of ImageNet-D with additional categories and nuisances." + ], + "table_footnote": [], + "table_body": "
NuisanceNuisance numberPrompt to diffusion modelsPrompt example
Background468A [category] in the [background]A backpack in the wheat field
Texture47A [texture] [category]A knitted backpack
Material32A [category] made of [material]A backpack made of leather
", + "bbox": [ + 81, + 142, + 893, + 223 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/448227842a4f320c346f4ba7cb21dfa92547a5a2f448e72b5849e2942e987c46.jpg", + "image_caption": [ + "Figure 5. Test accuracy of target models on shared failures of surrogate models. We adopt known surrogate models to identify their shared failure images as the test set, then evaluate a new target model on this test set. We show that the shared failures of surrogate models can also deceive a new target model, leading to low test accuracy. Increasing the number of surrogate models lowers the target models' test accuracy, suggesting a more difficult test set." + ], + "image_footnote": [], + "bbox": [ + 83, + 237, + 349, + 342 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4d2473964c5e54391d1822c2d1cd9b9f551fa5dd4043f019c8253b737ae706a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 237, + 617, + 340 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e216a0bf8f4856de0a890a70ede97a6f947b91d34e5b9805b32b9fa112c0ad19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 619, + 237, + 887, + 340 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/b95aafaae67b5fd43b3b278040f65e3611915024e1d62892e8c4a28f3ea3c74a.jpg", + "table_caption": [ + "Table 2. Test accuracy of CLIP (ViT-L/14) on the synthetic image pool by exhausting all the object category and nuisance combinations. We show that CLIP achieves high accuracy on the synthetic image pool. To create a challenging test set for robustness evaluation, we further mine the hard samples as the final test set." + ], + "table_footnote": [], + "table_body": "
Test SetImageNetObjectNetSynthetic image pool
BackgroundTextureMaterial
Acc (%)74.6466.9195.7994.0293.75
", + "bbox": [ + 81, + 517, + 470, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ferable for diffusion-generated images, we evaluate test sets created with shared failures from 1 to 8 surrogate models in Figure 5. We evaluate the accuracy of three target models that are not used during test set construction, including CLIP(ViT-B/16), LLaVa, and MiniGPT-4. Figure 5 shows that target model accuracy decreases as more surrogate models are used. The test sets are created with diverse backgrounds, while experiments for texture and material show the same trend. This trend demonstrates that failure images of multiple surrogate models can form a challenging test set for unseen new models. Notably, the accuracy decrease slows when the number of surrogate models exceeds four.", + "bbox": [ + 75, + 595, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Quality control by human-in-the-loop. The above process allows us to automatically find a challenging test set to unseen models. However, generative models can produce incorrect images not matching the prompt category. We resort to human annotation to ensure the ImageNet-D images are simultaneously valid, single-class, and high-quality. After first-round annotation by graduate students,", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we use Amazon Mechanical Turk [11, 22, 47] to evaluate labeling quality. We ask the workers to select the images that they can either recognize the main object or the main object can be used functionally as the ground truth category. Moreover, we design sentinels to ensure high-quality responses, including positive, negative and consistent sentinels. We report details of the labeling task in the appendix. A total of 679 qualified workers participated in 1540 labeling tasks, achieving an agreement of $91.09\\%$ . Figure 3 displays images from ImageNet-D, demonstrating high fidelity and diversity in object and nuisance pairs. We summarize the framework of creating ImageNet-D in Figure 4.", + "bbox": [ + 496, + 438, + 893, + 621 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dataset statistics", + "text_level": 1, + "bbox": [ + 500, + 628, + 666, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ImageNet-D includes 113 overlapping categories between ImageNet and ObjectNet, and 547 nuisances candidates from the Broden dataset [4](see Table 1), resulting in 4835 hard images featuring diverse backgrounds (3,764), textures (498), and materials (573). Our pipeline to create ImageNet-D is general and efficient, allowing easy addition of new categories and nuisances. ImageNet-D's category distribution exhibits a natural long-tail pattern, as shown in Figure 6. The sparse and non-uniform category-attribute distribution in Figure 7 shows the necessity of exhausting all category and nuisance pairs in test set creation.", + "bbox": [ + 496, + 651, + 893, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 830, + 633, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate various models on ImageNet-D benchmark. We find that ImageNet-D significantly decreases all models' accuracy by up to $60\\%$ . We then show whether prior", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21755", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d6e18835435ffd83f403e1c49c23c02fd37611e2d9d7536b5a33c768b93a3a96.jpg", + "image_caption": [ + "(a) Background" + ], + "image_footnote": [], + "bbox": [ + 116, + 88, + 359, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0ea4f2a91a74014ea9db46fc169a42010c5be7567ade0fcf566f79e27eedd5ab.jpg", + "image_caption": [ + "(b) Texture" + ], + "image_footnote": [], + "bbox": [ + 362, + 93, + 607, + 170 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6ae9074cb569c4e57555b719cbd10b6868158be3437923ecceae2c0a9a5e058f.jpg", + "image_caption": [ + "(c) Material" + ], + "image_footnote": [], + "bbox": [ + 611, + 89, + 854, + 175 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c715372289b6f2a9de8e5f8de739d558e01368e400b6011c576259c748f562b4.jpg", + "image_caption": [ + "Figure 6. Histogram of the image frequency per category in our test set, following a natural long-tail distribution.", + "(a) Background" + ], + "image_footnote": [], + "bbox": [ + 127, + 232, + 544, + 323 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6a849ac47dad30e3ed0f0fad0623ae1d555007446306455e24303fd6423f2cd3.jpg", + "image_caption": [ + "(b) Texture", + "(c) Material", + "Figure 7. Frequency of object category and nuisance pairs. Each dot indicates a pair, while the x-axis and y-axis indicate the nuisance and category, respectively. As shown in Table 1, we adopt 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4], leading to different widths of Figure (a) (b) (c). A darker color indicates more samples. The sparse and non-uniform distribution shows the necessity of exhausting all category and nuisance pairs in ImageNet-D creation." + ], + "image_footnote": [], + "bbox": [ + 563, + 233, + 843, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "advancements could improve ImageNet-D robustness, such as data augmentation. Lastly, we discuss ImageNet-D from various aspects, such as nearest neighbor retrieval.", + "bbox": [ + 75, + 436, + 468, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental setups", + "text_level": 1, + "bbox": [ + 76, + 494, + 271, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Test set construction setups. We use Stable Diffusion [48] to create ImageNet-D, and adopt the pretrained weight of version stable-diffusion-2-1 from Hugging Face. To find the hard images, we finalize ImageNet-D with shared failures of 4 surrogate models, including CLIP [45] (ViT-L/14, ViT-L/14-336px and ResNet50), and vision model (ResNet50 [16]). The candidate set of surrogate models in Figure 5 also includes CLIP (Resnet101,ViT-B/32) and vision model (ViT-L/16 [13] and VGG16 [52]).", + "bbox": [ + 75, + 520, + 468, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation of classification models. Robustness on ImageNet-D is measured by top-1 accuracy in object recognition, the ratio of correctly classified images to total images. We evaluate classification models with the open-source pretrained weights. For CLIP [45], we follow the original paper [45] to adopt A photo of a [category] as the text template. The zero-shot accuracy of CLIP is reported.", + "bbox": [ + 75, + 657, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation of visual question answering (VQA) models. We evaluate the accuracy of the state-of-the-art open-source VQA models on ImageNet-D, including LLaVa [31], and MiniGPT-4 [65]. Given an input image, VQA models output answers based on input text prompt. However, the textual output of VQA models is not limited to a certain template, thus may not include the category name in predefined category list of object recognition tasks. This makes it hard to assess the accuracy based on diverse answers.", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A common prompt that asks VQA models to recognize the object is: What is the main object in this image? To make VQA models choose from pre-defined category list, we ask VQA models as follows: What is the main object in this image? Choose from the following list: [GT category], [failure category]. GT category refers to the image's ground truth category. As for the failure category, we adopt the category that achieves the highest CLIP (ViT-L/14) confidence among all wrong categories. With this prompt, we find that both MiniGPT-4 and LLaVa can choose from provided category list in their output. If the model chooses ground truth category, this image is viewed to be correctly recognized. Therefore, we can compute the accuracy of VQA models.", + "bbox": [ + 496, + 436, + 890, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Robustness evaluation", + "text_level": 1, + "bbox": [ + 500, + 679, + 705, + 693 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative results. We evaluate ImageNet-D on 25 models, and plot test accuracy trend in Figure 8. The horizontal axis and vertical axis indicate the test accuracy on ImageNet and ImageNet-D, respectively. Figure 8 shows that as ImageNet accuracy increases, ImageNet-D accuracy also gets higher. ImageNet-D accuracy is much lower than ImageNet accuracy for all models, indicated by the lower distribution below the $y = x$ reference line. We report the accuracy of 14 models on different test sets in Table 3, and all models' accuracy in appendix. Table 3 shows that ImageNet-D achieves the lowest test accuracy for all models, except for the comparable result on Stylized-ImageNet for VQA models. Note that ImageNet-D achieves higher image fi", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21756", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f99cc870a3b288e1f9a36417eda7a8cef88a4838e65a7b31c20aba670ec60b66.jpg", + "image_caption": [ + "Figure 8. Model accuracy on ImageNet vs. ImageNet-D. Each data point corresponds to one tested model. The plots reveal that there is a significant accuracy drop from ImageNet to our new test set ImageNet-D. As the model's accuracy on ImageNet increases, the accuracy on ImageNet-D is also higher. These results show the effectiveness of ImageNet-D to evaluate the robustness of neural networks. We report the exact number of 14 models of this figure in Table 3, and the results for all models can be found in the appendix." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 349, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f6a6fa95452c152671a5da6580eeeedf9e6be34eef0ee8b81b0c0450c68a6eee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 89, + 617, + 212 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fd1474e73981c9852efa3b33e3084412038371890bcc0db56cd7f2abae5272c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 90, + 885, + 200 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cc824f82a9ca31804dfde038f72e01934ca9d3f57c7a9ccc07c0dbe2dbfc5477.jpg", + "table_caption": [ + "Table 3. Test accuracy of vision models and large foundation models (\\%). We show the test accuracy for the vision models and large foundation models (rows) on different test sets (columns). The numbers in green refer to the accuracy drop of ImageNet-D compared to ImageNet. For MiniGPT-4 and LLaVa, ImageNet-D reduces the accuracy by $16.81\\%$ and $29.67\\%$ compared to the ImageNet, respectively. Our results show that ImageNet-D is effective to evaluate the robustness of neural networks." + ], + "table_footnote": [], + "table_body": "
ModelArchitectureImageNetObjectNetImageNet-9StylizedImageNet-DImageNet-D Total
BackgroundTextureMaterial
Vision model (CNN)VGG1962.7727.1974.8416.259.8(-52.97)11.45(-51.32)12.39(-50.38)10.28(-52.49)
ResNet10167.6632.3481.8522.6612.38(-55.28)13.65(-54.01)13.44(-54.22)12.64(-55.02)
Densenet16166.9931.8684.9122.511.34(-55.65)14.06(-52.93)13.26(-53.73)11.85(-55.14)
Wideresnet10169.234.3782.1721.4810.55(-58.65)13.05(-56.15)12.04(-57.16)10.98(-58.22)
Vision model (ViT)ViT-B/3265.0227.5977.5142.346.64(-58.38)12.25(-52.77)13.79(-51.23)8.07(-56.95)
ViT-B/1672.1434.7982.4931.0210.49(-61.65)16.87(-55.27)17.63(-54.51)12.0(-60.14)
ViT-L/1668.6732.778.9129.387.68(-60.99)14.06(-54.61)15.53(-53.14)9.27(-59.40)
CLIPRN10162.4842.8983.0922.5821.47(-41.01)21.29(-41.19)25.83(-36.65)21.96(-40.52)
ViT-B/3264.0643.6779.5644.2218.73(-45.33)33.33(-30.73)30.37(-33.69)21.61(-42.45)
ViT-B/1667.9554.8785.1640.6220.64(-47.31)22.89(-45.06)29.32(-38.63)21.9(-46.05)
MiniGPT-4Vicuna 13B88.7777.5789.4669.8871.81(-16.96)72.48(-16.29)72.5(-16.27)71.96(-16.81)
LLaVaVicuna 13B79.3276.0290.8461.9452.89(-26.43)40.53(-38.79)36.28(-43.04)49.65(-29.67)
LLaVa-1.5Vicuna 13B89.0878.6693.8864.1473.31(-15.77)67.27(-21.81)67.08(-22.00)71.95(-17.13)
LLaVa-NeXTHermes-Yi-34B85.8377.5490.5257.9868.77(-17.06)46.67(-39.16)54.11(-31.72)64.76(-21.07)
", + "bbox": [ + 80, + 364, + 890, + 554 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "delyity than Stylized-ImageNet as shown in Figure 2. Although ObjectNet changes multiple attributes for each image, it still results in higher accuracy than ImageNet-D that specifies only one attribute per image. Compared to ImageNet, ImageNet-D yields a test accuracy drop of more than $16\\%$ for all models, including LLaVa (reducing $29.67\\%$ ) and MiniGPT-4 (reducing $16.81\\%$ ). Our ImageNet-D can also cause significant accuracy drop of the latest LLaVa-1.5 and LLaVa-NeXT. Although LLaVa-NeXT outperforms LLaVa-1.5 on benchmarks like MMMU [61], it achieves lower accuracy on ImageNet-D, demonstrating the uniqueness of ImageNet-D. For vision models, the accuracy drop is even close to $50\\%$ to $60\\%$ . The results in Figure 8 and Table 3 show the effectiveness of ImageNet-D in evaluating the robustness of neural networks.", + "bbox": [ + 75, + 580, + 470, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualization results. Figure 3 displays image examples from ImageNet-D, demonstrating high quality. Although humans can easily recognize the main object, CLIP (ViT-L/14) mistakenly classifies these images into a wrong category. Figure 9 shows conversations with MiniGPT-4 and LLaVa-1.5 on ImageNet-D images, indicating that", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MiniGPT-4 and LLaVa-1.5 can also fail to recognize the main object from ImageNet-D.", + "bbox": [ + 498, + 580, + 890, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Robustness improvement", + "text_level": 1, + "bbox": [ + 500, + 619, + 728, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data augmentation. Prior studies reveal that data augmentation is effective to improve model robustness, such as on ImageNet-C [19]. We evaluate data augmentation methods on ImageNet-D, including SIN [15], AugMix [21], ANT [50] and DeepAugment [22]. Table 4 shows the results with ResNet50 backbone for all methods. We report test accuracy for ImageNet and ImageNet-D, mean Corruption Error (mCE) for ImageNet-C following [19, 21, 22, 50]. Although these methods improve ImageNet-C robustness (lower mCE) than baseline model, Table 4 shows that their ImageNet-D robustness is comparable or even worse than baseline. This suggests that current benchmarks like ImageNet-C do not accurately represent real robustness of neural networks in our setting, making ImageNet-D a necessary benchmark for robustness evaluation.", + "bbox": [ + 496, + 643, + 890, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model architecture. We compare ImageNet-D robustness of different model architectures in Figure 11. When", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21757", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1367132a7d87fe71abc9f61f76359e0116174167616c39504921ecbeb0e24309.jpg", + "image_caption": [ + "(a)", + "Figure 9. Failure cases of MiniGPT-4 and LLaVa-1.5 from ImageNet-D. We ask MiniGPT-4 and LLaVa-1.5 for the category of the input image and the reason for their predictions. Figure (a) to (c) are images with different background, texture and material, respectively. Our results show that images from ImageNet-D can also make the state-of-the-art foundation models fail." + ], + "image_footnote": [], + "bbox": [ + 101, + 89, + 890, + 452 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/38ac05ad7e7f02df26e09a2b3ba34cd31641c32fab7936bd376ec2bb2ef5bead.jpg", + "table_caption": [ + "Table 4. Robustness of different augmentation methods. Despite superior ImageNet-C robustness, these methods fail to improve ImageNet-D robustness, demonstrating the uniqueness of ImageNet-D from ImageNet-C." + ], + "table_footnote": [], + "table_body": "
ModelImageNet (↑)ImageNet-C(mCE)(↓)ImageNet-D(↑)
Baseline65.8281.7410.22
SIN63.42(-2.40)78.45(-3.29)8.81(-1.41)
Augmix66.88(+1.06)74.7(-7.04)8.75(-1.47)
ANT65.95(+0.13)76.74(-5.00)10.09(-0.13)
DeepAugment66.54(+0.72)70.31(-11.43)9.37(-0.85)
", + "bbox": [ + 81, + 599, + 468, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we change the model from ViT to Swin Transformer [33] and ConvNeXt [34], the test accuracy on both ImageNet-D (Background) and ImageNet improve. However, the robustness on Texture and Material test set even decreases slightly. These results show the difficulty of improving ImageNet-D robustness by model architecture.", + "bbox": [ + 75, + 702, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pretraining with more data. Pretraining on a large data set is effective to improve model performance, such as ImageNet accuracy [18]. Figure 11 compares ConvNext, that is trained directly on ImageNet-1K, with ConvNext (Pretrained) which is first pretrained on ImageNet-22K. We find that ConvNext (Pretrained) achieves higher robustness than ConvNext on all three sets of ImageNet-D, especially for", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the Background set. These results show that pretraining on a large data set helps improve robustness on ImageNet-D.", + "bbox": [ + 498, + 534, + 890, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Further discussions", + "text_level": 1, + "bbox": [ + 500, + 574, + 686, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Can CLIP find the correct neighbors of ImageNet-D images? CLIP model [45] shows potential in nearest neighbor search tasks. With ImageNet-D images as query, we retrieve the most similar images from ImageNet to investigate whether CLIP can find correct neighbors, as shown in Figure 10. Take Background for example, retrieved images may either have a similar background to the query image (Figure 10(a)) or include the object that is related to the query image's background (Figure 10(b)). Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval.", + "bbox": [ + 496, + 598, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Can ImageNet-D match natural test sets in failure transferability? Section 3.1 defines transferable failure and finalize ImageNet-D with shared failures of surrogate models. We conduct the same experiment on ImageNet, introducing ImageNet (Failure) with the shared failure images of surrogate models. Table 5 show that ImageNet-D achieves similar accuracy to ImageNet (Failure), indicating that synthetic images can achieve similar failure transferability as natural images. In contrast to", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21758", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8388d0435fc58bc57c490c1e0111f81ccb7451d07f41451fd52ec9cbde5bdeca.jpg", + "image_caption": [ + "Figure 10. Visualizations of nearest neighbor images. We visualize the nearest neighbor images from ImageNet with ImageNet-D image as the query image. Instead of following the same object category as the query image, the nearest neighbor images either follow a similar background or follow another object category that is highly correlated with the background of query image. Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 885, + 210 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6923127a985bed378444bb9b8f2e36b729805c345b515aacdaac51474cb0c8c6.jpg", + "image_caption": [ + "Figure 11. Test accuracy of different architectures and training data. Each data point corresponds to one tested model. Apart from the ConvNeXt (Pretrained), all other models are trained on ImageNet-1K. The plots show that pretraining achieves higher robustness on all three subsets, while changing model architectures only improves on ImageNet-D (Background)." + ], + "image_footnote": [], + "bbox": [ + 81, + 286, + 352, + 406 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/607f368f4bca3411cccdc3f9f5c37c44c80ce6eabb302fca80fa4400c257fe40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 286, + 617, + 406 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cbef7ec2c1cbeaa6971fd23f2bf35d56ef0eecd6f697fd03418c4c3ba96d4060.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 619, + 286, + 885, + 406 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b63b73b95438d37d93e4df3d3048a33c4cb9c7da4071e8601c1bab2609479dfa.jpg", + "table_caption": [ + "Table 5. Results of failure transferability. We create ImageNet (Failure) with shared failures of surrogate models from original ImageNet, achieving comparable accuracy to ImageNet-D. These results show that our synthetic images achieve similar ability to natural images in finding the failures of new models." + ], + "table_footnote": [], + "table_body": "
ModelArchitectureImageNetImageNet (Failure)ImageNet-D
CLIPViT-B/1667.9511.0921.9
LLaVaVicuna 13B79.3241.4349.65
MiniGPT-4Vicuna 13B88.7765.2271.96
", + "bbox": [ + 81, + 569, + 468, + 625 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d2d716ca005fadfa33b66bca1f7ce065be9f039ec9566e8d931f929768d7c8fe.jpg", + "table_caption": [ + "Table 6. Test accuracy of models finetuned on synthetic data. We finetune a pretrained ResNet18 model on ImageNet-1K together with different extra training data. Training on synthetic images achieves highest robustness on both ImageNet-D and ObjectNet." + ], + "table_footnote": [], + "table_body": "
ModelExtra training dataImageNetObjectNetImageNet-D
A/55.6821.518.6
BImageNet59.78(+4.10)24.78(+3.27)10.4(+1.80)
CSynthetic-easy56.56(+0.88)26.12(+4.61)27.86(+19.26)
", + "bbox": [ + 81, + 709, + 468, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "natural datasets like ImageNet, ImageNet-D enjoys a lower cost in data collection and can be scaled efficiently.", + "bbox": [ + 75, + 792, + 468, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Training on diffusion-generated images. By contrast to shared failure images in ImageNet-D, we term generated images correctly classified by surrogate models as Synthetic-easy, and investigate their influence as training data. We finetune a pre-trained ResNet18 model on differ", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ent training sets in Table 6. Table 6 shows that training on Synthetic-easy significantly improves ImageNet-D robustness by $19.26\\%$ . Remarkably, model C outperforms model B in ObjectNet accuracy by $1.34\\%$ , indicating model C's superior generalization. These results imply that diffusion-generated images with diverse object and nuisance pairs could enhance model robustness as training samples.", + "bbox": [ + 496, + 489, + 890, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 609, + 617, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a test set ImageNet-D and establish a rigorous benchmark for visual perception robustness. Capitalizing the image generation ability of diffusion models, ImageNet-D includes images with diverse factors including background, texture and material. Experimental results show that ImageNet-D significantly decreases the accuracy of various models, including CLIP (reducing $46.05\\%$ ), LLaVa [31] (reducing $29.67\\%$ ), and MiniGPT-4 [65] (reducing $16.81\\%$ ), demonstrating the effectiveness in model evaluation. Our work makes a step forward in improving synthetic test sets, and will create more diverse and challenging test images as generative models improve.", + "bbox": [ + 496, + 635, + 890, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments: This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2022-0-00951, Development of Uncertainty-Aware Agents Learning by Asking Questions).", + "bbox": [ + 496, + 816, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21759", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shekoofeh Azizi, Simon Kornblith, Chitwan Sahara, Mohammad Norouzi, and David J. Fleet. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2, 5, 8", + "bbox": [ + 501, + 90, + 892, + 148 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21762", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/40bed3ab-f671-40b9-b3ce-7de57541124c_model.json b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/40bed3ab-f671-40b9-b3ce-7de57541124c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..be0cf3fc182ec7531b71b9b005d07833e45ab4b1 --- /dev/null +++ b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/40bed3ab-f671-40b9-b3ce-7de57541124c_model.json @@ -0,0 +1,2323 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.182, + 0.13, + 0.79, + 0.176 + ], + "angle": 0, + "content": "ImageNet-D: Benchmarking Neural Network Robustness on Diffusion Synthetic Object" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.203, + 0.83, + 0.24 + ], + "angle": 0, + "content": "Chenshuang Zhang1 Fei Pan2 Junmo Kim1* In So Kweon1 Chengzhi Mao3,4* KAIST1, University of Michigan, Ann Arbor2, McGill University3, MILA4" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.474, + 0.584 + ], + "angle": 0, + "content": "We establish rigorous benchmarks for visual perception robustness. Synthetic images such as ImageNet-C, ImageNet-9, and Stylized ImageNet provide specific type of evaluation over synthetic corruptions, backgrounds, and textures, yet those robustness benchmarks are restricted in specified variations and have low synthetic quality. In this work, we introduce generative model as a data source for synthesizing hard images that benchmark deep models' robustness. Leveraging diffusion models, we are able to generate images with more diversified backgrounds, textures, and materials than any prior work, where we term this benchmark as ImageNet-D. Experimental results show that ImageNet-D results in a significant accuracy drop to a range of vision models, from the standard ResNet visual classifier to the latest foundation models like CLIP and MiniGPT-4, significantly reducing their accuracy by up to \\(60\\%\\). Our work suggests that diffusion models can be an effective source to test vision models. The code and dataset are available at https://github.com/chenshuang-zhang/imagenet_d." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.613, + 0.21, + 0.629 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Neural networks have achieved remarkable performance in tasks ranging from image classification [33, 34, 55] to visual question answering [10, 28, 31, 65]. These advances have inspired the application of neural networks in various fields, including security and safety-critical systems such as self-driving cars [27, 32, 42], malware detection [9, 43, 60] and robots [6, 7, 25]. Due to their wide adaptation, it is becoming increasingly important to identify the robustness of neural networks [30, 41] for safety reasons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.775, + 0.47, + 0.866 + ], + "angle": 0, + "content": "To evaluate the robustness of neural networks, ObjectNet [3] collects real-world object images on controlled factors like background with human workers, which is time-consuming and labor-intensive. To scale up data collection, synthetic images are proposed as test images [15, 19, 58]. For example, ImageNet-C [19] introduces a set of low-level" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.275, + 0.627, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.372, + 0.605, + 0.383 + ], + "angle": 0, + "content": "Tennis racket" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.275, + 0.756, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.653, + 0.372, + 0.739, + 0.384 + ], + "angle": 0, + "content": "Measuring cup" + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.275, + 0.888, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.371, + 0.881, + 0.384 + ], + "angle": 0, + "content": "Mixing/salad bowl" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.395, + 0.893, + 0.466 + ], + "angle": 0, + "content": "Figure 1. Top predictions from CLIP (ViT-L/14) on ImageNet-D. We synthesize the images by changing their background, texture and material. The groundtruth for the images are plunger, spatula, and ladle in order, together with the background (badminton court), texture (freckled), and material (painted)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.893, + 0.583 + ], + "angle": 0, + "content": "common visual corruptions, such as gaussian noise and blur, to test models' robustness. ImageNet-9 [58] uses simple cutting and paste technique to create robustness benchmark on object background, yet the images are not realistic. Stylized-ImageNet [15] generates new images by altering the textures of ImageNet images, which cannot control the global factors like background." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.893, + 0.748 + ], + "angle": 0, + "content": "In this work, we introduce ImageNet-D, a synthetic test set generated by diffusion models for object recognition task. Capitalizing on the capability of pioneering Stable Diffusion models[48], we show that we can steer diffusion models with language to create realistic test images that cause vision models fail. Figure 1 shows three failure cases of CLIP model on our synthetic ImageNet-D dataset. Since we rely on language to create images, we can vary the high-level factors in the images in contrast to the local corruptions and texture in prior work, introducing addition factors that one can evaluate robustness on." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.895, + 0.884 + ], + "angle": 0, + "content": "To enhance sample difficulty of our dataset, we selectively retain images that cause failures in multiple chosen vision models. Our results show that images triggering errors in chosen models can reliably transfer their challenging nature to other, previously untested models. This leads to a notable decrease in accuracy, even in state-of-the-art foundation models like MiniGPT-4 [65] and LLaVa [31], suggesting our dataset reveals common failures in vision models." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Visualizations demonstrate that Imagenet-D signifi-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author. Junmo Kim , Chengzhi Mao ." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21752" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.207, + 0.47, + 0.346 + ], + "angle": 0, + "content": "Figure 2. Examples from ImageNet-9 [58], Stylized-ImageNet [15] and ImageNet-C [19] and our ImageNet-D. For the second row, we show images from ImageNet-D with different backgrounds, textures and materials orderly. Take the background for example (the two columns on the left), ImageNet-9 [58] generates new images by simply cutting and paste foreground and background from different images, leading to object deformation and dislocation. By contrast, ImageNet-D includes images with diverse backgrounds by diffusion generation, achieving superior visual fidelity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.468, + 0.554 + ], + "angle": 0, + "content": "cantly enhances image quality compared to previous synthetic robustness benchmarks, as evidenced in Figure 2. Imagenet-D serves as an effective tool for reducing the performance and assessing model robustness, including ResNet 101 (reducing \\(55.02\\%\\)), ViT-L/16 (reducing \\(59.40\\%\\)), CLIP (reducing \\(46.05\\%\\)), and transfer well to unforeseen large vision language models like LLaVa [31] (reducing \\(29.67\\%\\)), and MiniGPT-4 [65] (reducing \\(16.81\\%\\)). Our approach of utilizing generative models to evaluate model robustness is general, and shows significant potential for even greater effectiveness with future advancements in generative models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.571, + 0.214, + 0.587 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.468, + 0.748 + ], + "angle": 0, + "content": "Robustness of neural networks. Neural networks have evolved from CNN [16, 24], ViT [33, 55], to large foundation models [5, 12, 54]. Previous work has investigated neural networks robustness from multiple aspects, such as adversarial examples [35, 36, 38, 63, 64] and out-of-domain samples [17, 20, 22, 37]. Foundation models have shown greater robustness on out-of-distribution samples [45]. Robust explanation has also been investigated [31, 39, 65]. To systematically evaluate the robustness of deep models, test sets that cover different factors are urgently needed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.854 + ], + "angle": 0, + "content": "Dataset for benchmarking robustness. To evaluate neural network robustness, a branch of studies source images online, including ImageNet-A [23], Imagenet-R [22] and ImageNet-Sketch [57]. However, they are limited to images that exist on the web. ObjectNet [3] manually collects images with the help of 5982 workers, which is time-consuming and resource-intensive." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To overcome the limitations of web images and reduce the cost of manual collection, synthetic images are proposed for robustness evaluation [15, 19, 58]. ImageNet-C [19]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "benchmarks model robustness on low-level corruptions. ImageNet-9 [58] generates new images by combining foreground and background from different images, however, limited by poor image fidelity. Stylized-ImageNet [15] alters the textures of ImageNet images by AdaIN style transfer [26] or introducing texture-shape cue conflict, which cannot control other factors like backgrounds. In this work, we introduce a new test set ImageNet-D, which is generated by controlling diffusion models and includes novel images with diverse backgrounds, textures, and materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.38 + ], + "angle": 0, + "content": "Image generation. Diffusion models have achieved great success in various tasks including image generation [46, 49, 51, 62]. As a milestone work, Stable diffusion [48] enables high-fidelity image synthesis controlled by language. InstructPix2Pix [8] provides a more sophisticated control by editing a given image according to human instructions. In this paper, we build our pipeline with the standard Stable Diffusion model, yet our algorithm is compatible with other generative models that can be steered by language." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Enhancing perception with diffusion images. Diffusion-generated images have been used for vision perception tasks. A branch of studies [1, 2, 53, 59] improves classification accuracy by using synthetic images as training data augmentation. DREAM-OOD [14] finds the outliers by decoding sampled latent embeddings to images. However, their method lacks specific control over image space, which is crucial for benchmarks like ImageNet-D. [40] identifies under-represented attribute pairs, while our study focuses on hard images with a single attribute. Unlike [29, 44, 56] that modify existing datasets, our work generates new images and mines the most challenging ones as the test set, achieving greater accuracy drop than [29, 44, 56]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.594, + 0.627, + 0.611 + ], + "angle": 0, + "content": "3. ImageNet-D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.89, + 0.651 + ], + "angle": 0, + "content": "We first present how ImageNet-D is created in Section 3.1, followed by an overview of its statistics in Section 3.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.647, + 0.68 + ], + "angle": 0, + "content": "3.1. Dataset design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.854 + ], + "angle": 0, + "content": "While neural networks excel in various applications, their robustness needs rigorous evaluation for safety. Traditional evaluations use existing test sets, including either natural [3, 23] or synthetic images [15, 19, 58]. Compared to manual image collection, collecting a synthetic test set is more efficient [15, 58]. However, the diversity of current synthetic test sets is limited due to their reliance on existing images for attribute extraction. These synthetic images are also not realistic, as shown in Figure 2. ImageNet-D is introduced to evaluate model robustness across various object and nuisance combinations, addressing these limitations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Image generation by diffusion models. To construct ImageNet-D, diffusion models are used to create a vast image pool by combining all possible object and nuisances," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21753" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.893, + 0.359 + ], + "angle": 0, + "content": "Figure 3. The ImageNet-D test set. Each group of images is generated with the same object and nuisance, such as background, texture, and material. For each group of images, the ground truth label is color green, while the predicted categories by CLIP (ViT-L/14) on each image are in black. Leveraging diffusion models for image generation, we can create a test set with diverse combinations of objects and nuisances. For example, the top left corner shows a bench in the swimming pool background. Interestingly, CLIP (ViT-L/14) recognizes the bench in this image as swimming trunks." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.373, + 0.891, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.476, + 0.893, + 0.532 + ], + "angle": 0, + "content": "Figure 4. ImageNet-D creation framework. ImageNet-D is created by first combining various object categories and nuisances, including background, texture, and material. To make the test set challenging, we only keep the hard images from the large pool that commonly make multiple surrogate models fail to predict the correct object label. The test set is then refined through human verification to ensure the images are valid, single-class, and high-quality, making ImageNet-D suitable for evaluating the robustness of different neural networks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.47, + 0.635 + ], + "angle": 0, + "content": "enabling high-fidelity image generation based on user-defined text inputs. We use Stable Diffusion model[48] for image generation, while our approach is compatible with other generative models that can be steered by language. The image generation process is formulated as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.646, + 0.47, + 0.663 + ], + "angle": 0, + "content": "\\(\\operatorname {Image}(C,N) = \\operatorname {Stable}\\operatorname {Diffusion}(\\operatorname {Prompt}(C,N))\\) (1)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.84 + ], + "angle": 0, + "content": "where \\( C \\) and \\( N \\) refer to the object category and nuisance, respectively. The nuisance \\( N \\) includes background, material, and texture in this work. Table 1 presents an overview of nuisances and prompts to diffusion models. Using the backpack category as an example, we first generate images of backpacks with various backgrounds, materials, and textures (e.g., a backpack in a wheat field), offering a broader range of combinations than existing test sets. Each image is labeled with its prompt category \\( C \\) as ground truth for classification. An image is viewed misclassified if the model's predicted label does not match the ground truth \\( C \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.902 + ], + "angle": 0, + "content": "After creating a large image pool with all object category and nuisance pairs, we evaluate CLIP (ViT-L/14) model on these images in Table 2. Experimental details are reported in Section 4.1. Table 2 shows that CLIP achieves high accu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.62 + ], + "angle": 0, + "content": "racy on all the test sets, with an accuracy of around \\(94\\%\\) on synthetic image pool. To create a challenging test set for robustness evaluation, we propose an efficient strategy to find the hard test samples from all generated images as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Hard image mining with shared perception failures. Before introducing how to identify hard samples from synthetic image pool, we first define the concept of shared perception failure as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.714 + ], + "angle": 0, + "content": "Shared failure: An image is a shared failure if it leads multiple models to predict object's label incorrectly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.835 + ], + "angle": 0, + "content": "An ideal hard test set should include images that all tested models fail to identify. However, this is impractical due to the inaccessibility of future test models, termed target model. Instead, we construct the test set using shared failures of known surrogate models. If the failures of surrogate models lead to low accuracy in unknown models, the test set is deemed challenging. This is defined as transferable failure as follows:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.839, + 0.892, + 0.884 + ], + "angle": 0, + "content": "Transferable failure: Shared failures of known surrogate models are transferable if they also result in low accuracy for unknown target models." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To test if shared failures of surrogate models are trans" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21754" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.134 + ], + "angle": 0, + "content": "Table 1. Overview of nuisances and input prompts to diffusion models. During ImageNet-D construction, 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4] are used as nuisances. Images are generated by pairing each object with all nuisances in diffusion model prompts. This approach allows for efficient scaling of ImageNet-D with additional categories and nuisances." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.143, + 0.895, + 0.224 + ], + "angle": 0, + "content": "
NuisanceNuisance numberPrompt to diffusion modelsPrompt example
Background468A [category] in the [background]A backpack in the wheat field
Texture47A [texture] [category]A knitted backpack
Material32A [category] made of [material]A backpack made of leather
" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.238, + 0.351, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.238, + 0.619, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.238, + 0.888, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.897, + 0.414 + ], + "angle": 0, + "content": "Figure 5. Test accuracy of target models on shared failures of surrogate models. We adopt known surrogate models to identify their shared failure images as the test set, then evaluate a new target model on this test set. We show that the shared failures of surrogate models can also deceive a new target model, leading to low test accuracy. Increasing the number of surrogate models lowers the target models' test accuracy, suggesting a more difficult test set." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.437, + 0.473, + 0.509 + ], + "angle": 0, + "content": "Table 2. Test accuracy of CLIP (ViT-L/14) on the synthetic image pool by exhausting all the object category and nuisance combinations. We show that CLIP achieves high accuracy on the synthetic image pool. To create a challenging test set for robustness evaluation, we further mine the hard samples as the final test set." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.518, + 0.472, + 0.567 + ], + "angle": 0, + "content": "
Test SetImageNetObjectNetSynthetic image pool
BackgroundTextureMaterial
Acc (%)74.6466.9195.7994.0293.75
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.793 + ], + "angle": 0, + "content": "ferable for diffusion-generated images, we evaluate test sets created with shared failures from 1 to 8 surrogate models in Figure 5. We evaluate the accuracy of three target models that are not used during test set construction, including CLIP(ViT-B/16), LLaVa, and MiniGPT-4. Figure 5 shows that target model accuracy decreases as more surrogate models are used. The test sets are created with diverse backgrounds, while experiments for texture and material show the same trend. This trend demonstrates that failure images of multiple surrogate models can form a challenging test set for unseen new models. Notably, the accuracy decrease slows when the number of surrogate models exceeds four." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.904 + ], + "angle": 0, + "content": "Quality control by human-in-the-loop. The above process allows us to automatically find a challenging test set to unseen models. However, generative models can produce incorrect images not matching the prompt category. We resort to human annotation to ensure the ImageNet-D images are simultaneously valid, single-class, and high-quality. After first-round annotation by graduate students," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.895, + 0.622 + ], + "angle": 0, + "content": "we use Amazon Mechanical Turk [11, 22, 47] to evaluate labeling quality. We ask the workers to select the images that they can either recognize the main object or the main object can be used functionally as the ground truth category. Moreover, we design sentinels to ensure high-quality responses, including positive, negative and consistent sentinels. We report details of the labeling task in the appendix. A total of 679 qualified workers participated in 1540 labeling tasks, achieving an agreement of \\(91.09\\%\\). Figure 3 displays images from ImageNet-D, demonstrating high fidelity and diversity in object and nuisance pairs. We summarize the framework of creating ImageNet-D in Figure 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.629, + 0.667, + 0.644 + ], + "angle": 0, + "content": "3.2. Dataset statistics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.895, + 0.82 + ], + "angle": 0, + "content": "ImageNet-D includes 113 overlapping categories between ImageNet and ObjectNet, and 547 nuisances candidates from the Broden dataset [4](see Table 1), resulting in 4835 hard images featuring diverse backgrounds (3,764), textures (498), and materials (573). Our pipeline to create ImageNet-D is general and efficient, allowing easy addition of new categories and nuisances. ImageNet-D's category distribution exhibits a natural long-tail pattern, as shown in Figure 6. The sparse and non-uniform category-attribute distribution in Figure 7 shows the necessity of exhausting all category and nuisance pairs in test set creation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.634, + 0.848 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We evaluate various models on ImageNet-D benchmark. We find that ImageNet-D significantly decreases all models' accuracy by up to \\(60\\%\\). We then show whether prior" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21755" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.089, + 0.36, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.181, + 0.281, + 0.193 + ], + "angle": 0, + "content": "(a) Background" + }, + { + "type": "image", + "bbox": [ + 0.364, + 0.094, + 0.608, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.455, + 0.175, + 0.516, + 0.186 + ], + "angle": 0, + "content": "(b) Texture" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.09, + 0.855, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.7, + 0.181, + 0.765, + 0.193 + ], + "angle": 0, + "content": "(c) Material" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.205, + 0.819, + 0.22 + ], + "angle": 0, + "content": "Figure 6. Histogram of the image frequency per category in our test set, following a natural long-tail distribution." + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.233, + 0.545, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.331, + 0.331, + 0.414, + 0.343 + ], + "angle": 0, + "content": "(a) Background" + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.234, + 0.844, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.655, + 0.323, + 0.714, + 0.334 + ], + "angle": 0, + "content": "(b) Texture" + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.323, + 0.828, + 0.334 + ], + "angle": 0, + "content": "(c) Material" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.355, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Figure 7. Frequency of object category and nuisance pairs. Each dot indicates a pair, while the x-axis and y-axis indicate the nuisance and category, respectively. As shown in Table 1, we adopt 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4], leading to different widths of Figure (a) (b) (c). A darker color indicates more samples. The sparse and non-uniform distribution shows the necessity of exhausting all category and nuisance pairs in ImageNet-D creation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.47, + 0.482 + ], + "angle": 0, + "content": "advancements could improve ImageNet-D robustness, such as data augmentation. Lastly, we discuss ImageNet-D from various aspects, such as nearest neighbor retrieval." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.496, + 0.272, + 0.513 + ], + "angle": 0, + "content": "4.1. Experimental setups" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Test set construction setups. We use Stable Diffusion [48] to create ImageNet-D, and adopt the pretrained weight of version stable-diffusion-2-1 from Hugging Face. To find the hard images, we finalize ImageNet-D with shared failures of 4 surrogate models, including CLIP [45] (ViT-L/14, ViT-L/14-336px and ResNet50), and vision model (ResNet50 [16]). The candidate set of surrogate models in Figure 5 also includes CLIP (Resnet101,ViT-B/32) and vision model (ViT-L/16 [13] and VGG16 [52])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.764 + ], + "angle": 0, + "content": "Evaluation of classification models. Robustness on ImageNet-D is measured by top-1 accuracy in object recognition, the ratio of correctly classified images to total images. We evaluate classification models with the open-source pretrained weights. For CLIP [45], we follow the original paper [45] to adopt A photo of a [category] as the text template. The zero-shot accuracy of CLIP is reported." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Evaluation of visual question answering (VQA) models. We evaluate the accuracy of the state-of-the-art open-source VQA models on ImageNet-D, including LLaVa [31], and MiniGPT-4 [65]. Given an input image, VQA models output answers based on input text prompt. However, the textual output of VQA models is not limited to a certain template, thus may not include the category name in predefined category list of object recognition tasks. This makes it hard to assess the accuracy based on diverse answers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.892, + 0.664 + ], + "angle": 0, + "content": "A common prompt that asks VQA models to recognize the object is: What is the main object in this image? To make VQA models choose from pre-defined category list, we ask VQA models as follows: What is the main object in this image? Choose from the following list: [GT category], [failure category]. GT category refers to the image's ground truth category. As for the failure category, we adopt the category that achieves the highest CLIP (ViT-L/14) confidence among all wrong categories. With this prompt, we find that both MiniGPT-4 and LLaVa can choose from provided category list in their output. If the model chooses ground truth category, this image is viewed to be correctly recognized. Therefore, we can compute the accuracy of VQA models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.707, + 0.694 + ], + "angle": 0, + "content": "4.2. Robustness evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative results. We evaluate ImageNet-D on 25 models, and plot test accuracy trend in Figure 8. The horizontal axis and vertical axis indicate the test accuracy on ImageNet and ImageNet-D, respectively. Figure 8 shows that as ImageNet accuracy increases, ImageNet-D accuracy also gets higher. ImageNet-D accuracy is much lower than ImageNet accuracy for all models, indicated by the lower distribution below the \\( y = x \\) reference line. We report the accuracy of 14 models on different test sets in Table 3, and all models' accuracy in appendix. Table 3 shows that ImageNet-D achieves the lowest test accuracy for all models, except for the comparable result on Stylized-ImageNet for VQA models. Note that ImageNet-D achieves higher image fi" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21756" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.35, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.09, + 0.619, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.092, + 0.886, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.895, + 0.285 + ], + "angle": 0, + "content": "Figure 8. Model accuracy on ImageNet vs. ImageNet-D. Each data point corresponds to one tested model. The plots reveal that there is a significant accuracy drop from ImageNet to our new test set ImageNet-D. As the model's accuracy on ImageNet increases, the accuracy on ImageNet-D is also higher. These results show the effectiveness of ImageNet-D to evaluate the robustness of neural networks. We report the exact number of 14 models of this figure in Table 3, and the results for all models can be found in the appendix." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.298, + 0.895, + 0.355 + ], + "angle": 0, + "content": "Table 3. Test accuracy of vision models and large foundation models (\\%). We show the test accuracy for the vision models and large foundation models (rows) on different test sets (columns). The numbers in green refer to the accuracy drop of ImageNet-D compared to ImageNet. For MiniGPT-4 and LLaVa, ImageNet-D reduces the accuracy by \\(16.81\\%\\) and \\(29.67\\%\\) compared to the ImageNet, respectively. Our results show that ImageNet-D is effective to evaluate the robustness of neural networks." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.365, + 0.892, + 0.555 + ], + "angle": 0, + "content": "
ModelArchitectureImageNetObjectNetImageNet-9StylizedImageNet-DImageNet-D Total
BackgroundTextureMaterial
Vision model (CNN)VGG1962.7727.1974.8416.259.8(-52.97)11.45(-51.32)12.39(-50.38)10.28(-52.49)
ResNet10167.6632.3481.8522.6612.38(-55.28)13.65(-54.01)13.44(-54.22)12.64(-55.02)
Densenet16166.9931.8684.9122.511.34(-55.65)14.06(-52.93)13.26(-53.73)11.85(-55.14)
Wideresnet10169.234.3782.1721.4810.55(-58.65)13.05(-56.15)12.04(-57.16)10.98(-58.22)
Vision model (ViT)ViT-B/3265.0227.5977.5142.346.64(-58.38)12.25(-52.77)13.79(-51.23)8.07(-56.95)
ViT-B/1672.1434.7982.4931.0210.49(-61.65)16.87(-55.27)17.63(-54.51)12.0(-60.14)
ViT-L/1668.6732.778.9129.387.68(-60.99)14.06(-54.61)15.53(-53.14)9.27(-59.40)
CLIPRN10162.4842.8983.0922.5821.47(-41.01)21.29(-41.19)25.83(-36.65)21.96(-40.52)
ViT-B/3264.0643.6779.5644.2218.73(-45.33)33.33(-30.73)30.37(-33.69)21.61(-42.45)
ViT-B/1667.9554.8785.1640.6220.64(-47.31)22.89(-45.06)29.32(-38.63)21.9(-46.05)
MiniGPT-4Vicuna 13B88.7777.5789.4669.8871.81(-16.96)72.48(-16.29)72.5(-16.27)71.96(-16.81)
LLaVaVicuna 13B79.3276.0290.8461.9452.89(-26.43)40.53(-38.79)36.28(-43.04)49.65(-29.67)
LLaVa-1.5Vicuna 13B89.0878.6693.8864.1473.31(-15.77)67.27(-21.81)67.08(-22.00)71.95(-17.13)
LLaVa-NeXTHermes-Yi-34B85.8377.5490.5257.9868.77(-17.06)46.67(-39.16)54.11(-31.72)64.76(-21.07)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.471, + 0.806 + ], + "angle": 0, + "content": "delyity than Stylized-ImageNet as shown in Figure 2. Although ObjectNet changes multiple attributes for each image, it still results in higher accuracy than ImageNet-D that specifies only one attribute per image. Compared to ImageNet, ImageNet-D yields a test accuracy drop of more than \\(16\\%\\) for all models, including LLaVa (reducing \\(29.67\\%\\)) and MiniGPT-4 (reducing \\(16.81\\%\\)). Our ImageNet-D can also cause significant accuracy drop of the latest LLaVa-1.5 and LLaVa-NeXT. Although LLaVa-NeXT outperforms LLaVa-1.5 on benchmarks like MMMU [61], it achieves lower accuracy on ImageNet-D, demonstrating the uniqueness of ImageNet-D. For vision models, the accuracy drop is even close to \\(50\\%\\) to \\(60\\%\\). The results in Figure 8 and Table 3 show the effectiveness of ImageNet-D in evaluating the robustness of neural networks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Visualization results. Figure 3 displays image examples from ImageNet-D, demonstrating high quality. Although humans can easily recognize the main object, CLIP (ViT-L/14) mistakenly classifies these images into a wrong category. Figure 9 shows conversations with MiniGPT-4 and LLaVa-1.5 on ImageNet-D images, indicating that" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.892, + 0.611 + ], + "angle": 0, + "content": "MiniGPT-4 and LLaVa-1.5 can also fail to recognize the main object from ImageNet-D." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.73, + 0.637 + ], + "angle": 0, + "content": "4.3. Robustness improvement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Data augmentation. Prior studies reveal that data augmentation is effective to improve model robustness, such as on ImageNet-C [19]. We evaluate data augmentation methods on ImageNet-D, including SIN [15], AugMix [21], ANT [50] and DeepAugment [22]. Table 4 shows the results with ResNet50 backbone for all methods. We report test accuracy for ImageNet and ImageNet-D, mean Corruption Error (mCE) for ImageNet-C following [19, 21, 22, 50]. Although these methods improve ImageNet-C robustness (lower mCE) than baseline model, Table 4 shows that their ImageNet-D robustness is comparable or even worse than baseline. This suggests that current benchmarks like ImageNet-C do not accurately represent real robustness of neural networks in our setting, making ImageNet-D a necessary benchmark for robustness evaluation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Model architecture. We compare ImageNet-D robustness of different model architectures in Figure 11. When" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21757" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.159, + 0.099, + 0.175 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.09, + 0.892, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.466, + 0.893, + 0.509 + ], + "angle": 0, + "content": "Figure 9. Failure cases of MiniGPT-4 and LLaVa-1.5 from ImageNet-D. We ask MiniGPT-4 and LLaVa-1.5 for the category of the input image and the reason for their predictions. Figure (a) to (c) are images with different background, texture and material, respectively. Our results show that images from ImageNet-D can also make the state-of-the-art foundation models fail." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.533, + 0.471, + 0.589 + ], + "angle": 0, + "content": "Table 4. Robustness of different augmentation methods. Despite superior ImageNet-C robustness, these methods fail to improve ImageNet-D robustness, demonstrating the uniqueness of ImageNet-D from ImageNet-C." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.6, + 0.47, + 0.675 + ], + "angle": 0, + "content": "
ModelImageNet (↑)ImageNet-C(mCE)(↓)ImageNet-D(↑)
Baseline65.8281.7410.22
SIN63.42(-2.40)78.45(-3.29)8.81(-1.41)
Augmix66.88(+1.06)74.7(-7.04)8.75(-1.47)
ANT65.95(+0.13)76.74(-5.00)10.09(-0.13)
DeepAugment66.54(+0.72)70.31(-11.43)9.37(-0.85)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.793 + ], + "angle": 0, + "content": "we change the model from ViT to Swin Transformer [33] and ConvNeXt [34], the test accuracy on both ImageNet-D (Background) and ImageNet improve. However, the robustness on Texture and Material test set even decreases slightly. These results show the difficulty of improving ImageNet-D robustness by model architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Pretraining with more data. Pretraining on a large data set is effective to improve model performance, such as ImageNet accuracy [18]. Figure 11 compares ConvNext, that is trained directly on ImageNet-1K, with ConvNext (Pretrained) which is first pretrained on ImageNet-22K. We find that ConvNext (Pretrained) achieves higher robustness than ConvNext on all three sets of ImageNet-D, especially for" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.535, + 0.892, + 0.566 + ], + "angle": 0, + "content": "the Background set. These results show that pretraining on a large data set helps improve robustness on ImageNet-D." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.687, + 0.59 + ], + "angle": 0, + "content": "4.4. Further discussions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Can CLIP find the correct neighbors of ImageNet-D images? CLIP model [45] shows potential in nearest neighbor search tasks. With ImageNet-D images as query, we retrieve the most similar images from ImageNet to investigate whether CLIP can find correct neighbors, as shown in Figure 10. Take Background for example, retrieved images may either have a similar background to the query image (Figure 10(a)) or include the object that is related to the query image's background (Figure 10(b)). Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Can ImageNet-D match natural test sets in failure transferability? Section 3.1 defines transferable failure and finalize ImageNet-D with shared failures of surrogate models. We conduct the same experiment on ImageNet, introducing ImageNet (Failure) with the shared failure images of surrogate models. Table 5 show that ImageNet-D achieves similar accuracy to ImageNet (Failure), indicating that synthetic images can achieve similar failure transferability as natural images. In contrast to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21758" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.887, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.225, + 0.893, + 0.281 + ], + "angle": 0, + "content": "Figure 10. Visualizations of nearest neighbor images. We visualize the nearest neighbor images from ImageNet with ImageNet-D image as the query image. Instead of following the same object category as the query image, the nearest neighbor images either follow a similar background or follow another object category that is highly correlated with the background of query image. Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.287, + 0.353, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.287, + 0.619, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.287, + 0.886, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.422, + 0.893, + 0.465 + ], + "angle": 0, + "content": "Figure 11. Test accuracy of different architectures and training data. Each data point corresponds to one tested model. Apart from the ConvNeXt (Pretrained), all other models are trained on ImageNet-1K. The plots show that pretraining achieves higher robustness on all three subsets, while changing model architectures only improves on ImageNet-D (Background)." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.488, + 0.47, + 0.558 + ], + "angle": 0, + "content": "Table 5. Results of failure transferability. We create ImageNet (Failure) with shared failures of surrogate models from original ImageNet, achieving comparable accuracy to ImageNet-D. These results show that our synthetic images achieve similar ability to natural images in finding the failures of new models." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.57, + 0.469, + 0.626 + ], + "angle": 0, + "content": "
ModelArchitectureImageNetImageNet (Failure)ImageNet-D
CLIPViT-B/1667.9511.0921.9
LLaVaVicuna 13B79.3241.4349.65
MiniGPT-4Vicuna 13B88.7765.2271.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.7 + ], + "angle": 0, + "content": "Table 6. Test accuracy of models finetuned on synthetic data. We finetune a pretrained ResNet18 model on ImageNet-1K together with different extra training data. Training on synthetic images achieves highest robustness on both ImageNet-D and ObjectNet." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.71, + 0.469, + 0.763 + ], + "angle": 0, + "content": "
ModelExtra training dataImageNetObjectNetImageNet-D
A/55.6821.518.6
BImageNet59.78(+4.10)24.78(+3.27)10.4(+1.80)
CSynthetic-easy56.56(+0.88)26.12(+4.61)27.86(+19.26)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.469, + 0.823 + ], + "angle": 0, + "content": "natural datasets like ImageNet, ImageNet-D enjoys a lower cost in data collection and can be scaled efficiently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Training on diffusion-generated images. By contrast to shared failure images in ImageNet-D, we term generated images correctly classified by surrogate models as Synthetic-easy, and investigate their influence as training data. We finetune a pre-trained ResNet18 model on differ" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.892, + 0.598 + ], + "angle": 0, + "content": "ent training sets in Table 6. Table 6 shows that training on Synthetic-easy significantly improves ImageNet-D robustness by \\(19.26\\%\\). Remarkably, model C outperforms model B in ObjectNet accuracy by \\(1.34\\%\\), indicating model C's superior generalization. These results imply that diffusion-generated images with diverse object and nuisance pairs could enhance model robustness as training samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.619, + 0.627 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.817 + ], + "angle": 0, + "content": "In this paper, we introduce a test set ImageNet-D and establish a rigorous benchmark for visual perception robustness. Capitalizing the image generation ability of diffusion models, ImageNet-D includes images with diverse factors including background, texture and material. Experimental results show that ImageNet-D significantly decreases the accuracy of various models, including CLIP (reducing \\(46.05\\%\\)), LLaVa [31] (reducing \\(29.67\\%\\)), and MiniGPT-4 [65] (reducing \\(16.81\\%\\)), demonstrating the effectiveness in model evaluation. Our work makes a step forward in improving synthetic test sets, and will create more diverse and challenging test images as generative models improve." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.892, + 0.888 + ], + "angle": 0, + "content": "Acknowledgments: This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2022-0-00951, Development of Uncertainty-Aware Agents Learning by Asking Questions)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21759" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Shekoofeh Azizi, Simon Kornblith, Chitwan Sahara, Mohammad Norouzi, and David J. Fleet. 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Synthetic images such as ImageNet-C, ImageNet-9, and Stylized ImageNet provide specific type of evaluation over synthetic corruptions, backgrounds, and textures, yet those robustness benchmarks are restricted in specified variations and have low synthetic quality. In this work, we introduce generative model as a data source for synthesizing hard images that benchmark deep models' robustness. Leveraging diffusion models, we are able to generate images with more diversified backgrounds, textures, and materials than any prior work, where we term this benchmark as ImageNet-D. Experimental results show that ImageNet-D results in a significant accuracy drop to a range of vision models, from the standard ResNet visual classifier to the latest foundation models like CLIP and MiniGPT-4, significantly reducing their accuracy by up to $60\%$ . Our work suggests that diffusion models can be an effective source to test vision models. The code and dataset are available at https://github.com/chenshuang-zhang/imagenet_d. + +# 1. Introduction + +Neural networks have achieved remarkable performance in tasks ranging from image classification [33, 34, 55] to visual question answering [10, 28, 31, 65]. These advances have inspired the application of neural networks in various fields, including security and safety-critical systems such as self-driving cars [27, 32, 42], malware detection [9, 43, 60] and robots [6, 7, 25]. Due to their wide adaptation, it is becoming increasingly important to identify the robustness of neural networks [30, 41] for safety reasons. + +To evaluate the robustness of neural networks, ObjectNet [3] collects real-world object images on controlled factors like background with human workers, which is time-consuming and labor-intensive. To scale up data collection, synthetic images are proposed as test images [15, 19, 58]. For example, ImageNet-C [19] introduces a set of low-level + +![](images/0b6c359834f0d11be472e90b84048a8ed680ccad04e8c39960c371ebcefd3cde.jpg) +Tennis racket + +![](images/7aaeb3bc5282b4fccfb1afd813b7a3d1e184d9c251aa79cc04ba23903cb74fa8.jpg) +Measuring cup + +![](images/bf403728fe0a6b09d9d13fae02e33853f20e6d1e62e526655977d31a5b9dbd5e.jpg) +Mixing/salad bowl +Figure 1. Top predictions from CLIP (ViT-L/14) on ImageNet-D. We synthesize the images by changing their background, texture and material. The groundtruth for the images are plunger, spatula, and ladle in order, together with the background (badminton court), texture (freckled), and material (painted). + +common visual corruptions, such as gaussian noise and blur, to test models' robustness. ImageNet-9 [58] uses simple cutting and paste technique to create robustness benchmark on object background, yet the images are not realistic. Stylized-ImageNet [15] generates new images by altering the textures of ImageNet images, which cannot control the global factors like background. + +In this work, we introduce ImageNet-D, a synthetic test set generated by diffusion models for object recognition task. Capitalizing on the capability of pioneering Stable Diffusion models[48], we show that we can steer diffusion models with language to create realistic test images that cause vision models fail. Figure 1 shows three failure cases of CLIP model on our synthetic ImageNet-D dataset. Since we rely on language to create images, we can vary the high-level factors in the images in contrast to the local corruptions and texture in prior work, introducing addition factors that one can evaluate robustness on. + +To enhance sample difficulty of our dataset, we selectively retain images that cause failures in multiple chosen vision models. Our results show that images triggering errors in chosen models can reliably transfer their challenging nature to other, previously untested models. This leads to a notable decrease in accuracy, even in state-of-the-art foundation models like MiniGPT-4 [65] and LLaVa [31], suggesting our dataset reveals common failures in vision models. + +Visualizations demonstrate that Imagenet-D signifi- + +![](images/39a42d17fa53d4b1e3ac4bbd857e851a97692a311b6979de39fd2e4636270a2c.jpg) +Figure 2. Examples from ImageNet-9 [58], Stylized-ImageNet [15] and ImageNet-C [19] and our ImageNet-D. For the second row, we show images from ImageNet-D with different backgrounds, textures and materials orderly. Take the background for example (the two columns on the left), ImageNet-9 [58] generates new images by simply cutting and paste foreground and background from different images, leading to object deformation and dislocation. By contrast, ImageNet-D includes images with diverse backgrounds by diffusion generation, achieving superior visual fidelity. + +cantly enhances image quality compared to previous synthetic robustness benchmarks, as evidenced in Figure 2. Imagenet-D serves as an effective tool for reducing the performance and assessing model robustness, including ResNet 101 (reducing $55.02\%$ ), ViT-L/16 (reducing $59.40\%$ ), CLIP (reducing $46.05\%$ ), and transfer well to unforeseen large vision language models like LLaVa [31] (reducing $29.67\%$ ), and MiniGPT-4 [65] (reducing $16.81\%$ ). Our approach of utilizing generative models to evaluate model robustness is general, and shows significant potential for even greater effectiveness with future advancements in generative models. + +# 2. Related work + +Robustness of neural networks. Neural networks have evolved from CNN [16, 24], ViT [33, 55], to large foundation models [5, 12, 54]. Previous work has investigated neural networks robustness from multiple aspects, such as adversarial examples [35, 36, 38, 63, 64] and out-of-domain samples [17, 20, 22, 37]. Foundation models have shown greater robustness on out-of-distribution samples [45]. Robust explanation has also been investigated [31, 39, 65]. To systematically evaluate the robustness of deep models, test sets that cover different factors are urgently needed. + +Dataset for benchmarking robustness. To evaluate neural network robustness, a branch of studies source images online, including ImageNet-A [23], Imagenet-R [22] and ImageNet-Sketch [57]. However, they are limited to images that exist on the web. ObjectNet [3] manually collects images with the help of 5982 workers, which is time-consuming and resource-intensive. + +To overcome the limitations of web images and reduce the cost of manual collection, synthetic images are proposed for robustness evaluation [15, 19, 58]. ImageNet-C [19] + +benchmarks model robustness on low-level corruptions. ImageNet-9 [58] generates new images by combining foreground and background from different images, however, limited by poor image fidelity. Stylized-ImageNet [15] alters the textures of ImageNet images by AdaIN style transfer [26] or introducing texture-shape cue conflict, which cannot control other factors like backgrounds. In this work, we introduce a new test set ImageNet-D, which is generated by controlling diffusion models and includes novel images with diverse backgrounds, textures, and materials. + +Image generation. Diffusion models have achieved great success in various tasks including image generation [46, 49, 51, 62]. As a milestone work, Stable diffusion [48] enables high-fidelity image synthesis controlled by language. InstructPix2Pix [8] provides a more sophisticated control by editing a given image according to human instructions. In this paper, we build our pipeline with the standard Stable Diffusion model, yet our algorithm is compatible with other generative models that can be steered by language. + +Enhancing perception with diffusion images. Diffusion-generated images have been used for vision perception tasks. A branch of studies [1, 2, 53, 59] improves classification accuracy by using synthetic images as training data augmentation. DREAM-OOD [14] finds the outliers by decoding sampled latent embeddings to images. However, their method lacks specific control over image space, which is crucial for benchmarks like ImageNet-D. [40] identifies under-represented attribute pairs, while our study focuses on hard images with a single attribute. Unlike [29, 44, 56] that modify existing datasets, our work generates new images and mines the most challenging ones as the test set, achieving greater accuracy drop than [29, 44, 56]. + +# 3. ImageNet-D + +We first present how ImageNet-D is created in Section 3.1, followed by an overview of its statistics in Section 3.2. + +# 3.1. Dataset design + +While neural networks excel in various applications, their robustness needs rigorous evaluation for safety. Traditional evaluations use existing test sets, including either natural [3, 23] or synthetic images [15, 19, 58]. Compared to manual image collection, collecting a synthetic test set is more efficient [15, 58]. However, the diversity of current synthetic test sets is limited due to their reliance on existing images for attribute extraction. These synthetic images are also not realistic, as shown in Figure 2. ImageNet-D is introduced to evaluate model robustness across various object and nuisance combinations, addressing these limitations. + +Image generation by diffusion models. To construct ImageNet-D, diffusion models are used to create a vast image pool by combining all possible object and nuisances, + +![](images/0a37f76606b667979dcced3fb3bf263b586376fdb19a61988aff6af342e080f3.jpg) +Figure 3. The ImageNet-D test set. Each group of images is generated with the same object and nuisance, such as background, texture, and material. For each group of images, the ground truth label is color green, while the predicted categories by CLIP (ViT-L/14) on each image are in black. Leveraging diffusion models for image generation, we can create a test set with diverse combinations of objects and nuisances. For example, the top left corner shows a bench in the swimming pool background. Interestingly, CLIP (ViT-L/14) recognizes the bench in this image as swimming trunks. + +![](images/043abeda0e0a5cbb842e4106d795317796d3ed99dc2d8c2b39177720204a319c.jpg) +Figure 4. ImageNet-D creation framework. ImageNet-D is created by first combining various object categories and nuisances, including background, texture, and material. To make the test set challenging, we only keep the hard images from the large pool that commonly make multiple surrogate models fail to predict the correct object label. The test set is then refined through human verification to ensure the images are valid, single-class, and high-quality, making ImageNet-D suitable for evaluating the robustness of different neural networks. + +enabling high-fidelity image generation based on user-defined text inputs. We use Stable Diffusion model[48] for image generation, while our approach is compatible with other generative models that can be steered by language. The image generation process is formulated as follows: + +$\operatorname {Image}(C,N) = \operatorname {Stable}\operatorname {Diffusion}(\operatorname {Prompt}(C,N))$ (1) + +where $C$ and $N$ refer to the object category and nuisance, respectively. The nuisance $N$ includes background, material, and texture in this work. Table 1 presents an overview of nuisances and prompts to diffusion models. Using the backpack category as an example, we first generate images of backpacks with various backgrounds, materials, and textures (e.g., a backpack in a wheat field), offering a broader range of combinations than existing test sets. Each image is labeled with its prompt category $C$ as ground truth for classification. An image is viewed misclassified if the model's predicted label does not match the ground truth $C$ . + +After creating a large image pool with all object category and nuisance pairs, we evaluate CLIP (ViT-L/14) model on these images in Table 2. Experimental details are reported in Section 4.1. Table 2 shows that CLIP achieves high accu + +racy on all the test sets, with an accuracy of around $94\%$ on synthetic image pool. To create a challenging test set for robustness evaluation, we propose an efficient strategy to find the hard test samples from all generated images as follows. + +Hard image mining with shared perception failures. Before introducing how to identify hard samples from synthetic image pool, we first define the concept of shared perception failure as follows. + +Shared failure: An image is a shared failure if it leads multiple models to predict object's label incorrectly. + +An ideal hard test set should include images that all tested models fail to identify. However, this is impractical due to the inaccessibility of future test models, termed target model. Instead, we construct the test set using shared failures of known surrogate models. If the failures of surrogate models lead to low accuracy in unknown models, the test set is deemed challenging. This is defined as transferable failure as follows: + +Transferable failure: Shared failures of known surrogate models are transferable if they also result in low accuracy for unknown target models. + +To test if shared failures of surrogate models are trans + +Table 1. Overview of nuisances and input prompts to diffusion models. During ImageNet-D construction, 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4] are used as nuisances. Images are generated by pairing each object with all nuisances in diffusion model prompts. This approach allows for efficient scaling of ImageNet-D with additional categories and nuisances. + +
NuisanceNuisance numberPrompt to diffusion modelsPrompt example
Background468A [category] in the [background]A backpack in the wheat field
Texture47A [texture] [category]A knitted backpack
Material32A [category] made of [material]A backpack made of leather
+ +![](images/448227842a4f320c346f4ba7cb21dfa92547a5a2f448e72b5849e2942e987c46.jpg) +Figure 5. Test accuracy of target models on shared failures of surrogate models. We adopt known surrogate models to identify their shared failure images as the test set, then evaluate a new target model on this test set. We show that the shared failures of surrogate models can also deceive a new target model, leading to low test accuracy. Increasing the number of surrogate models lowers the target models' test accuracy, suggesting a more difficult test set. + +![](images/4d2473964c5e54391d1822c2d1cd9b9f551fa5dd4043f019c8253b737ae706a8.jpg) + +![](images/e216a0bf8f4856de0a890a70ede97a6f947b91d34e5b9805b32b9fa112c0ad19.jpg) + +Table 2. Test accuracy of CLIP (ViT-L/14) on the synthetic image pool by exhausting all the object category and nuisance combinations. We show that CLIP achieves high accuracy on the synthetic image pool. To create a challenging test set for robustness evaluation, we further mine the hard samples as the final test set. + +
Test SetImageNetObjectNetSynthetic image pool
BackgroundTextureMaterial
Acc (%)74.6466.9195.7994.0293.75
+ +ferable for diffusion-generated images, we evaluate test sets created with shared failures from 1 to 8 surrogate models in Figure 5. We evaluate the accuracy of three target models that are not used during test set construction, including CLIP(ViT-B/16), LLaVa, and MiniGPT-4. Figure 5 shows that target model accuracy decreases as more surrogate models are used. The test sets are created with diverse backgrounds, while experiments for texture and material show the same trend. This trend demonstrates that failure images of multiple surrogate models can form a challenging test set for unseen new models. Notably, the accuracy decrease slows when the number of surrogate models exceeds four. + +Quality control by human-in-the-loop. The above process allows us to automatically find a challenging test set to unseen models. However, generative models can produce incorrect images not matching the prompt category. We resort to human annotation to ensure the ImageNet-D images are simultaneously valid, single-class, and high-quality. After first-round annotation by graduate students, + +we use Amazon Mechanical Turk [11, 22, 47] to evaluate labeling quality. We ask the workers to select the images that they can either recognize the main object or the main object can be used functionally as the ground truth category. Moreover, we design sentinels to ensure high-quality responses, including positive, negative and consistent sentinels. We report details of the labeling task in the appendix. A total of 679 qualified workers participated in 1540 labeling tasks, achieving an agreement of $91.09\%$ . Figure 3 displays images from ImageNet-D, demonstrating high fidelity and diversity in object and nuisance pairs. We summarize the framework of creating ImageNet-D in Figure 4. + +# 3.2. Dataset statistics + +ImageNet-D includes 113 overlapping categories between ImageNet and ObjectNet, and 547 nuisances candidates from the Broden dataset [4](see Table 1), resulting in 4835 hard images featuring diverse backgrounds (3,764), textures (498), and materials (573). Our pipeline to create ImageNet-D is general and efficient, allowing easy addition of new categories and nuisances. ImageNet-D's category distribution exhibits a natural long-tail pattern, as shown in Figure 6. The sparse and non-uniform category-attribute distribution in Figure 7 shows the necessity of exhausting all category and nuisance pairs in test set creation. + +# 4. Experiments + +We evaluate various models on ImageNet-D benchmark. We find that ImageNet-D significantly decreases all models' accuracy by up to $60\%$ . We then show whether prior + +![](images/d6e18835435ffd83f403e1c49c23c02fd37611e2d9d7536b5a33c768b93a3a96.jpg) +(a) Background + +![](images/0ea4f2a91a74014ea9db46fc169a42010c5be7567ade0fcf566f79e27eedd5ab.jpg) +(b) Texture + +![](images/6ae9074cb569c4e57555b719cbd10b6868158be3437923ecceae2c0a9a5e058f.jpg) +(c) Material + +![](images/c715372289b6f2a9de8e5f8de739d558e01368e400b6011c576259c748f562b4.jpg) +Figure 6. Histogram of the image frequency per category in our test set, following a natural long-tail distribution. +(a) Background + +![](images/6a849ac47dad30e3ed0f0fad0623ae1d555007446306455e24303fd6423f2cd3.jpg) +(b) Texture +(c) Material +Figure 7. Frequency of object category and nuisance pairs. Each dot indicates a pair, while the x-axis and y-axis indicate the nuisance and category, respectively. As shown in Table 1, we adopt 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4], leading to different widths of Figure (a) (b) (c). A darker color indicates more samples. The sparse and non-uniform distribution shows the necessity of exhausting all category and nuisance pairs in ImageNet-D creation. + +advancements could improve ImageNet-D robustness, such as data augmentation. Lastly, we discuss ImageNet-D from various aspects, such as nearest neighbor retrieval. + +# 4.1. Experimental setups + +Test set construction setups. We use Stable Diffusion [48] to create ImageNet-D, and adopt the pretrained weight of version stable-diffusion-2-1 from Hugging Face. To find the hard images, we finalize ImageNet-D with shared failures of 4 surrogate models, including CLIP [45] (ViT-L/14, ViT-L/14-336px and ResNet50), and vision model (ResNet50 [16]). The candidate set of surrogate models in Figure 5 also includes CLIP (Resnet101,ViT-B/32) and vision model (ViT-L/16 [13] and VGG16 [52]). + +Evaluation of classification models. Robustness on ImageNet-D is measured by top-1 accuracy in object recognition, the ratio of correctly classified images to total images. We evaluate classification models with the open-source pretrained weights. For CLIP [45], we follow the original paper [45] to adopt A photo of a [category] as the text template. The zero-shot accuracy of CLIP is reported. + +Evaluation of visual question answering (VQA) models. We evaluate the accuracy of the state-of-the-art open-source VQA models on ImageNet-D, including LLaVa [31], and MiniGPT-4 [65]. Given an input image, VQA models output answers based on input text prompt. However, the textual output of VQA models is not limited to a certain template, thus may not include the category name in predefined category list of object recognition tasks. This makes it hard to assess the accuracy based on diverse answers. + +A common prompt that asks VQA models to recognize the object is: What is the main object in this image? To make VQA models choose from pre-defined category list, we ask VQA models as follows: What is the main object in this image? Choose from the following list: [GT category], [failure category]. GT category refers to the image's ground truth category. As for the failure category, we adopt the category that achieves the highest CLIP (ViT-L/14) confidence among all wrong categories. With this prompt, we find that both MiniGPT-4 and LLaVa can choose from provided category list in their output. If the model chooses ground truth category, this image is viewed to be correctly recognized. Therefore, we can compute the accuracy of VQA models. + +# 4.2. Robustness evaluation + +Quantitative results. We evaluate ImageNet-D on 25 models, and plot test accuracy trend in Figure 8. The horizontal axis and vertical axis indicate the test accuracy on ImageNet and ImageNet-D, respectively. Figure 8 shows that as ImageNet accuracy increases, ImageNet-D accuracy also gets higher. ImageNet-D accuracy is much lower than ImageNet accuracy for all models, indicated by the lower distribution below the $y = x$ reference line. We report the accuracy of 14 models on different test sets in Table 3, and all models' accuracy in appendix. Table 3 shows that ImageNet-D achieves the lowest test accuracy for all models, except for the comparable result on Stylized-ImageNet for VQA models. Note that ImageNet-D achieves higher image fi + +![](images/f99cc870a3b288e1f9a36417eda7a8cef88a4838e65a7b31c20aba670ec60b66.jpg) +Figure 8. Model accuracy on ImageNet vs. ImageNet-D. Each data point corresponds to one tested model. The plots reveal that there is a significant accuracy drop from ImageNet to our new test set ImageNet-D. As the model's accuracy on ImageNet increases, the accuracy on ImageNet-D is also higher. These results show the effectiveness of ImageNet-D to evaluate the robustness of neural networks. We report the exact number of 14 models of this figure in Table 3, and the results for all models can be found in the appendix. + +![](images/f6a6fa95452c152671a5da6580eeeedf9e6be34eef0ee8b81b0c0450c68a6eee.jpg) + +![](images/fd1474e73981c9852efa3b33e3084412038371890bcc0db56cd7f2abae5272c2.jpg) + +Table 3. Test accuracy of vision models and large foundation models (\%). We show the test accuracy for the vision models and large foundation models (rows) on different test sets (columns). The numbers in green refer to the accuracy drop of ImageNet-D compared to ImageNet. For MiniGPT-4 and LLaVa, ImageNet-D reduces the accuracy by $16.81\%$ and $29.67\%$ compared to the ImageNet, respectively. Our results show that ImageNet-D is effective to evaluate the robustness of neural networks. + +
ModelArchitectureImageNetObjectNetImageNet-9StylizedImageNet-DImageNet-D Total
BackgroundTextureMaterial
Vision model (CNN)VGG1962.7727.1974.8416.259.8(-52.97)11.45(-51.32)12.39(-50.38)10.28(-52.49)
ResNet10167.6632.3481.8522.6612.38(-55.28)13.65(-54.01)13.44(-54.22)12.64(-55.02)
Densenet16166.9931.8684.9122.511.34(-55.65)14.06(-52.93)13.26(-53.73)11.85(-55.14)
Wideresnet10169.234.3782.1721.4810.55(-58.65)13.05(-56.15)12.04(-57.16)10.98(-58.22)
Vision model (ViT)ViT-B/3265.0227.5977.5142.346.64(-58.38)12.25(-52.77)13.79(-51.23)8.07(-56.95)
ViT-B/1672.1434.7982.4931.0210.49(-61.65)16.87(-55.27)17.63(-54.51)12.0(-60.14)
ViT-L/1668.6732.778.9129.387.68(-60.99)14.06(-54.61)15.53(-53.14)9.27(-59.40)
CLIPRN10162.4842.8983.0922.5821.47(-41.01)21.29(-41.19)25.83(-36.65)21.96(-40.52)
ViT-B/3264.0643.6779.5644.2218.73(-45.33)33.33(-30.73)30.37(-33.69)21.61(-42.45)
ViT-B/1667.9554.8785.1640.6220.64(-47.31)22.89(-45.06)29.32(-38.63)21.9(-46.05)
MiniGPT-4Vicuna 13B88.7777.5789.4669.8871.81(-16.96)72.48(-16.29)72.5(-16.27)71.96(-16.81)
LLaVaVicuna 13B79.3276.0290.8461.9452.89(-26.43)40.53(-38.79)36.28(-43.04)49.65(-29.67)
LLaVa-1.5Vicuna 13B89.0878.6693.8864.1473.31(-15.77)67.27(-21.81)67.08(-22.00)71.95(-17.13)
LLaVa-NeXTHermes-Yi-34B85.8377.5490.5257.9868.77(-17.06)46.67(-39.16)54.11(-31.72)64.76(-21.07)
+ +delyity than Stylized-ImageNet as shown in Figure 2. Although ObjectNet changes multiple attributes for each image, it still results in higher accuracy than ImageNet-D that specifies only one attribute per image. Compared to ImageNet, ImageNet-D yields a test accuracy drop of more than $16\%$ for all models, including LLaVa (reducing $29.67\%$ ) and MiniGPT-4 (reducing $16.81\%$ ). Our ImageNet-D can also cause significant accuracy drop of the latest LLaVa-1.5 and LLaVa-NeXT. Although LLaVa-NeXT outperforms LLaVa-1.5 on benchmarks like MMMU [61], it achieves lower accuracy on ImageNet-D, demonstrating the uniqueness of ImageNet-D. For vision models, the accuracy drop is even close to $50\%$ to $60\%$ . The results in Figure 8 and Table 3 show the effectiveness of ImageNet-D in evaluating the robustness of neural networks. + +Visualization results. Figure 3 displays image examples from ImageNet-D, demonstrating high quality. Although humans can easily recognize the main object, CLIP (ViT-L/14) mistakenly classifies these images into a wrong category. Figure 9 shows conversations with MiniGPT-4 and LLaVa-1.5 on ImageNet-D images, indicating that + +MiniGPT-4 and LLaVa-1.5 can also fail to recognize the main object from ImageNet-D. + +# 4.3. Robustness improvement + +Data augmentation. Prior studies reveal that data augmentation is effective to improve model robustness, such as on ImageNet-C [19]. We evaluate data augmentation methods on ImageNet-D, including SIN [15], AugMix [21], ANT [50] and DeepAugment [22]. Table 4 shows the results with ResNet50 backbone for all methods. We report test accuracy for ImageNet and ImageNet-D, mean Corruption Error (mCE) for ImageNet-C following [19, 21, 22, 50]. Although these methods improve ImageNet-C robustness (lower mCE) than baseline model, Table 4 shows that their ImageNet-D robustness is comparable or even worse than baseline. This suggests that current benchmarks like ImageNet-C do not accurately represent real robustness of neural networks in our setting, making ImageNet-D a necessary benchmark for robustness evaluation. + +Model architecture. We compare ImageNet-D robustness of different model architectures in Figure 11. When + +![](images/1367132a7d87fe71abc9f61f76359e0116174167616c39504921ecbeb0e24309.jpg) +(a) +Figure 9. Failure cases of MiniGPT-4 and LLaVa-1.5 from ImageNet-D. We ask MiniGPT-4 and LLaVa-1.5 for the category of the input image and the reason for their predictions. Figure (a) to (c) are images with different background, texture and material, respectively. Our results show that images from ImageNet-D can also make the state-of-the-art foundation models fail. + +Table 4. Robustness of different augmentation methods. Despite superior ImageNet-C robustness, these methods fail to improve ImageNet-D robustness, demonstrating the uniqueness of ImageNet-D from ImageNet-C. + +
ModelImageNet (↑)ImageNet-C(mCE)(↓)ImageNet-D(↑)
Baseline65.8281.7410.22
SIN63.42(-2.40)78.45(-3.29)8.81(-1.41)
Augmix66.88(+1.06)74.7(-7.04)8.75(-1.47)
ANT65.95(+0.13)76.74(-5.00)10.09(-0.13)
DeepAugment66.54(+0.72)70.31(-11.43)9.37(-0.85)
+ +we change the model from ViT to Swin Transformer [33] and ConvNeXt [34], the test accuracy on both ImageNet-D (Background) and ImageNet improve. However, the robustness on Texture and Material test set even decreases slightly. These results show the difficulty of improving ImageNet-D robustness by model architecture. + +Pretraining with more data. Pretraining on a large data set is effective to improve model performance, such as ImageNet accuracy [18]. Figure 11 compares ConvNext, that is trained directly on ImageNet-1K, with ConvNext (Pretrained) which is first pretrained on ImageNet-22K. We find that ConvNext (Pretrained) achieves higher robustness than ConvNext on all three sets of ImageNet-D, especially for + +the Background set. These results show that pretraining on a large data set helps improve robustness on ImageNet-D. + +# 4.4. Further discussions + +Can CLIP find the correct neighbors of ImageNet-D images? CLIP model [45] shows potential in nearest neighbor search tasks. With ImageNet-D images as query, we retrieve the most similar images from ImageNet to investigate whether CLIP can find correct neighbors, as shown in Figure 10. Take Background for example, retrieved images may either have a similar background to the query image (Figure 10(a)) or include the object that is related to the query image's background (Figure 10(b)). Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval. + +Can ImageNet-D match natural test sets in failure transferability? Section 3.1 defines transferable failure and finalize ImageNet-D with shared failures of surrogate models. We conduct the same experiment on ImageNet, introducing ImageNet (Failure) with the shared failure images of surrogate models. Table 5 show that ImageNet-D achieves similar accuracy to ImageNet (Failure), indicating that synthetic images can achieve similar failure transferability as natural images. In contrast to + +![](images/8388d0435fc58bc57c490c1e0111f81ccb7451d07f41451fd52ec9cbde5bdeca.jpg) +Figure 10. Visualizations of nearest neighbor images. We visualize the nearest neighbor images from ImageNet with ImageNet-D image as the query image. Instead of following the same object category as the query image, the nearest neighbor images either follow a similar background or follow another object category that is highly correlated with the background of query image. Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval. + +![](images/6923127a985bed378444bb9b8f2e36b729805c345b515aacdaac51474cb0c8c6.jpg) +Figure 11. Test accuracy of different architectures and training data. Each data point corresponds to one tested model. Apart from the ConvNeXt (Pretrained), all other models are trained on ImageNet-1K. The plots show that pretraining achieves higher robustness on all three subsets, while changing model architectures only improves on ImageNet-D (Background). + +![](images/607f368f4bca3411cccdc3f9f5c37c44c80ce6eabb302fca80fa4400c257fe40.jpg) + +![](images/cbef7ec2c1cbeaa6971fd23f2bf35d56ef0eecd6f697fd03418c4c3ba96d4060.jpg) + +Table 5. Results of failure transferability. We create ImageNet (Failure) with shared failures of surrogate models from original ImageNet, achieving comparable accuracy to ImageNet-D. These results show that our synthetic images achieve similar ability to natural images in finding the failures of new models. + +
ModelArchitectureImageNetImageNet (Failure)ImageNet-D
CLIPViT-B/1667.9511.0921.9
LLaVaVicuna 13B79.3241.4349.65
MiniGPT-4Vicuna 13B88.7765.2271.96
+ +Table 6. Test accuracy of models finetuned on synthetic data. We finetune a pretrained ResNet18 model on ImageNet-1K together with different extra training data. Training on synthetic images achieves highest robustness on both ImageNet-D and ObjectNet. + +
ModelExtra training dataImageNetObjectNetImageNet-D
A/55.6821.518.6
BImageNet59.78(+4.10)24.78(+3.27)10.4(+1.80)
CSynthetic-easy56.56(+0.88)26.12(+4.61)27.86(+19.26)
+ +natural datasets like ImageNet, ImageNet-D enjoys a lower cost in data collection and can be scaled efficiently. + +Training on diffusion-generated images. By contrast to shared failure images in ImageNet-D, we term generated images correctly classified by surrogate models as Synthetic-easy, and investigate their influence as training data. We finetune a pre-trained ResNet18 model on differ + +ent training sets in Table 6. Table 6 shows that training on Synthetic-easy significantly improves ImageNet-D robustness by $19.26\%$ . Remarkably, model C outperforms model B in ObjectNet accuracy by $1.34\%$ , indicating model C's superior generalization. These results imply that diffusion-generated images with diverse object and nuisance pairs could enhance model robustness as training samples. + +# 5. Conclusion + +In this paper, we introduce a test set ImageNet-D and establish a rigorous benchmark for visual perception robustness. Capitalizing the image generation ability of diffusion models, ImageNet-D includes images with diverse factors including background, texture and material. Experimental results show that ImageNet-D significantly decreases the accuracy of various models, including CLIP (reducing $46.05\%$ ), LLaVa [31] (reducing $29.67\%$ ), and MiniGPT-4 [65] (reducing $16.81\%$ ), demonstrating the effectiveness in model evaluation. Our work makes a step forward in improving synthetic test sets, and will create more diverse and challenging test images as generative models improve. + +Acknowledgments: This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2022-0-00951, Development of Uncertainty-Aware Agents Learning by Asking Questions). + +# References + +[1] Shekoofeh Azizi, Simon Kornblith, Chitwan Sahara, Mohammad Norouzi, and David J. Fleet. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2, 5, 8 \ No newline at end of file diff --git a/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/images.zip b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..241d395b7f0d222a9f19ea4874e487faf6577533 --- /dev/null +++ b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b95529a2425006ae25f43b56bdb0595f0767cbdfd5af9fe9e066425edbeacbc4 +size 928418 diff --git a/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/layout.json b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..2b571c8d4d1c2585d8758727d4dfddaf44d7f902 --- /dev/null +++ b/2024/ImageNet-D_ Benchmarking Neural Network Robustness on Diffusion Synthetic Object/layout.json @@ -0,0 +1,7821 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 111, + 102, + 483, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 102, + 483, + 139 + ], + "spans": [ + { + "bbox": [ + 111, + 102, + 483, + 139 + ], + "type": "text", + "content": "ImageNet-D: Benchmarking Neural Network Robustness on Diffusion Synthetic Object" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 88, + 160, + 507, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 160, + 507, + 190 + ], + "spans": [ + { + "bbox": [ + 88, + 160, + 507, + 190 + ], + "type": "text", + "content": "Chenshuang Zhang1 Fei Pan2 Junmo Kim1* In So Kweon1 Chengzhi Mao3,4* KAIST1, University of Michigan, Ann Arbor2, McGill University3, MILA4" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 241, + 290, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 290, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 290, + 462 + ], + "type": "text", + "content": "We establish rigorous benchmarks for visual perception robustness. 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Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": "Neural networks have achieved remarkable performance in tasks ranging from image classification [33, 34, 55] to visual question answering [10, 28, 31, 65]. These advances have inspired the application of neural networks in various fields, including security and safety-critical systems such as self-driving cars [27, 32, 42], malware detection [9, 43, 60] and robots [6, 7, 25]. Due to their wide adaptation, it is becoming increasingly important to identify the robustness of neural networks [30, 41] for safety reasons." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 613, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 287, + 685 + ], + "type": "text", + "content": "To evaluate the robustness of neural networks, ObjectNet [3] collects real-world object images on controlled factors like background with human workers, which is time-consuming and labor-intensive. To scale up data collection, synthetic images are proposed as test images [15, 19, 58]. 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Top predictions from CLIP (ViT-L/14) on ImageNet-D. We synthesize the images by changing their background, texture and material. The groundtruth for the images are plunger, spatula, and ladle in order, together with the background (badminton court), texture (freckled), and material (painted)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 376, + 546, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 461 + ], + "type": "text", + "content": "common visual corruptions, such as gaussian noise and blur, to test models' robustness. ImageNet-9 [58] uses simple cutting and paste technique to create robustness benchmark on object background, yet the images are not realistic. Stylized-ImageNet [15] generates new images by altering the textures of ImageNet images, which cannot control the global factors like background." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 461, + 546, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 546, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 546, + 592 + ], + "type": "text", + "content": "In this work, we introduce ImageNet-D, a synthetic test set generated by diffusion models for object recognition task. Capitalizing on the capability of pioneering Stable Diffusion models[48], we show that we can steer diffusion models with language to create realistic test images that cause vision models fail. Figure 1 shows three failure cases of CLIP model on our synthetic ImageNet-D dataset. Since we rely on language to create images, we can vary the high-level factors in the images in contrast to the local corruptions and texture in prior work, introducing addition factors that one can evaluate robustness on." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 593, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 547, + 700 + ], + "type": "text", + "content": "To enhance sample difficulty of our dataset, we selectively retain images that cause failures in multiple chosen vision models. Our results show that images triggering errors in chosen models can reliably transfer their challenging nature to other, previously untested models. This leads to a notable decrease in accuracy, even in state-of-the-art foundation models like MiniGPT-4 [65] and LLaVa [31], suggesting our dataset reveals common failures in vision models." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Visualizations demonstrate that Imagenet-D signifi-" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 286, + 713 + ], + "type": "text", + "content": "*Corresponding author. Junmo Kim , Chengzhi Mao ." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21752" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 154 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 154 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 154 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 154 + ], + "type": "image", + "image_path": "39a42d17fa53d4b1e3ac4bbd857e851a97692a311b6979de39fd2e4636270a2c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 287, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 287, + 274 + ], + "type": "text", + "content": "Figure 2. Examples from ImageNet-9 [58], Stylized-ImageNet [15] and ImageNet-C [19] and our ImageNet-D. For the second row, we show images from ImageNet-D with different backgrounds, textures and materials orderly. Take the background for example (the two columns on the left), ImageNet-9 [58] generates new images by simply cutting and paste foreground and background from different images, leading to object deformation and dislocation. By contrast, ImageNet-D includes images with diverse backgrounds by diffusion generation, achieving superior visual fidelity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "content": "cantly enhances image quality compared to previous synthetic robustness benchmarks, as evidenced in Figure 2. Imagenet-D serves as an effective tool for reducing the performance and assessing model robustness, including ResNet 101 (reducing " + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "inline_equation", + "content": "55.02\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "content": "), ViT-L/16 (reducing " + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "inline_equation", + "content": "59.40\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "content": "), CLIP (reducing " + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "inline_equation", + "content": "46.05\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "content": "), and transfer well to unforeseen large vision language models like LLaVa [31] (reducing " + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "inline_equation", + "content": "29.67\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "content": "), and MiniGPT-4 [65] (reducing " + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "inline_equation", + "content": "16.81\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 438 + ], + "type": "text", + "content": "). Our approach of utilizing generative models to evaluate model robustness is general, and shows significant potential for even greater effectiveness with future advancements in generative models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 452, + 130, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 130, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 130, + 464 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 473, + 286, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 286, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 286, + 592 + ], + "type": "text", + "content": "Robustness of neural networks. Neural networks have evolved from CNN [16, 24], ViT [33, 55], to large foundation models [5, 12, 54]. Previous work has investigated neural networks robustness from multiple aspects, such as adversarial examples [35, 36, 38, 63, 64] and out-of-domain samples [17, 20, 22, 37]. Foundation models have shown greater robustness on out-of-distribution samples [45]. Robust explanation has also been investigated [31, 39, 65]. To systematically evaluate the robustness of deep models, test sets that cover different factors are urgently needed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 676 + ], + "type": "text", + "content": "Dataset for benchmarking robustness. To evaluate neural network robustness, a branch of studies source images online, including ImageNet-A [23], Imagenet-R [22] and ImageNet-Sketch [57]. However, they are limited to images that exist on the web. ObjectNet [3] manually collects images with the help of 5982 workers, which is time-consuming and resource-intensive." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "To overcome the limitations of web images and reduce the cost of manual collection, synthetic images are proposed for robustness evaluation [15, 19, 58]. ImageNet-C [19]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "benchmarks model robustness on low-level corruptions. ImageNet-9 [58] generates new images by combining foreground and background from different images, however, limited by poor image fidelity. Stylized-ImageNet [15] alters the textures of ImageNet images by AdaIN style transfer [26] or introducing texture-shape cue conflict, which cannot control other factors like backgrounds. In this work, we introduce a new test set ImageNet-D, which is generated by controlling diffusion models and includes novel images with diverse backgrounds, textures, and materials." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 193, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 300 + ], + "type": "text", + "content": "Image generation. Diffusion models have achieved great success in various tasks including image generation [46, 49, 51, 62]. As a milestone work, Stable diffusion [48] enables high-fidelity image synthesis controlled by language. InstructPix2Pix [8] provides a more sophisticated control by editing a given image according to human instructions. In this paper, we build our pipeline with the standard Stable Diffusion model, yet our algorithm is compatible with other generative models that can be steered by language." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 301, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 456 + ], + "type": "text", + "content": "Enhancing perception with diffusion images. Diffusion-generated images have been used for vision perception tasks. A branch of studies [1, 2, 53, 59] improves classification accuracy by using synthetic images as training data augmentation. DREAM-OOD [14] finds the outliers by decoding sampled latent embeddings to images. However, their method lacks specific control over image space, which is crucial for benchmarks like ImageNet-D. [40] identifies under-represented attribute pairs, while our study focuses on hard images with a single attribute. Unlike [29, 44, 56] that modify existing datasets, our work generates new images and mines the most challenging ones as the test set, achieving greater accuracy drop than [29, 44, 56]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 470, + 383, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 470, + 383, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 470, + 383, + 483 + ], + "type": "text", + "content": "3. ImageNet-D" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 491, + 544, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 544, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 544, + 515 + ], + "type": "text", + "content": "We first present how ImageNet-D is created in Section 3.1, followed by an overview of its statistics in Section 3.2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 525, + 395, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 395, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 395, + 538 + ], + "type": "text", + "content": "3.1. Dataset design" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 544, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 676 + ], + "type": "text", + "content": "While neural networks excel in various applications, their robustness needs rigorous evaluation for safety. Traditional evaluations use existing test sets, including either natural [3, 23] or synthetic images [15, 19, 58]. Compared to manual image collection, collecting a synthetic test set is more efficient [15, 58]. However, the diversity of current synthetic test sets is limited due to their reliance on existing images for attribute extraction. These synthetic images are also not realistic, as shown in Figure 2. ImageNet-D is introduced to evaluate model robustness across various object and nuisance combinations, addressing these limitations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Image generation by diffusion models. To construct ImageNet-D, diffusion models are used to create a vast image pool by combining all possible object and nuisances," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21753" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 220 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 220 + ], + "type": "image", + "image_path": "0a37f76606b667979dcced3fb3bf263b586376fdb19a61988aff6af342e080f3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 546, + 284 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 284 + ], + "type": "text", + "content": "Figure 3. The ImageNet-D test set. Each group of images is generated with the same object and nuisance, such as background, texture, and material. For each group of images, the ground truth label is color green, while the predicted categories by CLIP (ViT-L/14) on each image are in black. Leveraging diffusion models for image generation, we can create a test set with diverse combinations of objects and nuisances. For example, the top left corner shows a bench in the swimming pool background. Interestingly, CLIP (ViT-L/14) recognizes the bench in this image as swimming trunks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 295, + 545, + 369 + ], + "blocks": [ + { + "bbox": [ + 48, + 295, + 545, + 369 + ], + "lines": [ + { + "bbox": [ + 48, + 295, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 48, + 295, + 545, + 369 + ], + "type": "image", + "image_path": "043abeda0e0a5cbb842e4106d795317796d3ed99dc2d8c2b39177720204a319c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 376, + 546, + 421 + ], + "lines": [ + { + "bbox": [ + 46, + 376, + 546, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 546, + 421 + ], + "type": "text", + "content": "Figure 4. ImageNet-D creation framework. ImageNet-D is created by first combining various object categories and nuisances, including background, texture, and material. To make the test set challenging, we only keep the hard images from the large pool that commonly make multiple surrogate models fail to predict the correct object label. The test set is then refined through human verification to ensure the images are valid, single-class, and high-quality, making ImageNet-D suitable for evaluating the robustness of different neural networks." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "content": "enabling high-fidelity image generation based on user-defined text inputs. We use Stable Diffusion model[48] for image generation, while our approach is compatible with other generative models that can be steered by language. The image generation process is formulated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 511, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 511, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 59, + 511, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\operatorname {Image}(C,N) = \\operatorname {Stable}\\operatorname {Diffusion}(\\operatorname {Prompt}(C,N))" + }, + { + "bbox": [ + 59, + 511, + 287, + 525 + ], + "type": "text", + "content": " (1)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": " refer to the object category and nuisance, respectively. The nuisance " + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": " includes background, material, and texture in this work. Table 1 presents an overview of nuisances and prompts to diffusion models. Using the backpack category as an example, we first generate images of backpacks with various backgrounds, materials, and textures (e.g., a backpack in a wheat field), offering a broader range of combinations than existing test sets. Each image is labeled with its prompt category " + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": " as ground truth for classification. An image is viewed misclassified if the model's predicted label does not match the ground truth " + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "content": "After creating a large image pool with all object category and nuisance pairs, we evaluate CLIP (ViT-L/14) model on these images in Table 2. Experimental details are reported in Section 4.1. Table 2 shows that CLIP achieves high accu" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 441, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 491 + ], + "type": "text", + "content": "racy on all the test sets, with an accuracy of around " + }, + { + "bbox": [ + 304, + 441, + 545, + 491 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 304, + 441, + 545, + 491 + ], + "type": "text", + "content": " on synthetic image pool. To create a challenging test set for robustness evaluation, we propose an efficient strategy to find the hard test samples from all generated images as follows." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 491, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 539 + ], + "type": "text", + "content": "Hard image mining with shared perception failures. Before introducing how to identify hard samples from synthetic image pool, we first define the concept of shared perception failure as follows." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 540, + 545, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 565 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 565 + ], + "type": "text", + "content": "Shared failure: An image is a shared failure if it leads multiple models to predict object's label incorrectly." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 566, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 661 + ], + "type": "text", + "content": "An ideal hard test set should include images that all tested models fail to identify. However, this is impractical due to the inaccessibility of future test models, termed target model. Instead, we construct the test set using shared failures of known surrogate models. If the failures of surrogate models lead to low accuracy in unknown models, the test set is deemed challenging. This is defined as transferable failure as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 664, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 664, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 664, + 545, + 700 + ], + "type": "text", + "content": "Transferable failure: Shared failures of known surrogate models are transferable if they also result in low accuracy for unknown target models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "To test if shared failures of surrogate models are trans" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21754" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 113, + 547, + 177 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "text", + "content": "Table 1. Overview of nuisances and input prompts to diffusion models. During ImageNet-D construction, 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4] are used as nuisances. Images are generated by pairing each object with all nuisances in diffusion model prompts. This approach allows for efficient scaling of ImageNet-D with additional categories and nuisances." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 113, + 547, + 177 + ], + "lines": [ + { + "bbox": [ + 50, + 113, + 547, + 177 + ], + "spans": [ + { + "bbox": [ + 50, + 113, + 547, + 177 + ], + "type": "table", + "html": "
NuisanceNuisance numberPrompt to diffusion modelsPrompt example
Background468A [category] in the [background]A backpack in the wheat field
Texture47A [texture] [category]A knitted backpack
Material32A [category] made of [material]A backpack made of leather
", + "image_path": "468597abd4c5fd5d5d58f38cb64d60d18174b9babb29c85e883868a3bb0b3887.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 51, + 188, + 214, + 271 + ], + "blocks": [ + { + "bbox": [ + 51, + 188, + 214, + 271 + ], + "lines": [ + { + "bbox": [ + 51, + 188, + 214, + 271 + ], + "spans": [ + { + "bbox": [ + 51, + 188, + 214, + 271 + ], + "type": "image", + "image_path": "448227842a4f320c346f4ba7cb21dfa92547a5a2f448e72b5849e2942e987c46.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 548, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 548, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 548, + 327 + ], + "type": "text", + "content": "Figure 5. Test accuracy of target models on shared failures of surrogate models. We adopt known surrogate models to identify their shared failure images as the test set, then evaluate a new target model on this test set. We show that the shared failures of surrogate models can also deceive a new target model, leading to low test accuracy. Increasing the number of surrogate models lowers the target models' test accuracy, suggesting a more difficult test set." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 215, + 188, + 378, + 270 + ], + "blocks": [ + { + "bbox": [ + 215, + 188, + 378, + 270 + ], + "lines": [ + { + "bbox": [ + 215, + 188, + 378, + 270 + ], + "spans": [ + { + "bbox": [ + 215, + 188, + 378, + 270 + ], + "type": "image", + "image_path": "4d2473964c5e54391d1822c2d1cd9b9f551fa5dd4043f019c8253b737ae706a8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 379, + 188, + 543, + 270 + ], + "blocks": [ + { + "bbox": [ + 379, + 188, + 543, + 270 + ], + "lines": [ + { + "bbox": [ + 379, + 188, + 543, + 270 + ], + "spans": [ + { + "bbox": [ + 379, + 188, + 543, + 270 + ], + "type": "image", + "image_path": "e216a0bf8f4856de0a890a70ede97a6f947b91d34e5b9805b32b9fa112c0ad19.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 410, + 288, + 449 + ], + "blocks": [ + { + "bbox": [ + 46, + 346, + 289, + 403 + ], + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 403 + ], + "type": "text", + "content": "Table 2. Test accuracy of CLIP (ViT-L/14) on the synthetic image pool by exhausting all the object category and nuisance combinations. We show that CLIP achieves high accuracy on the synthetic image pool. To create a challenging test set for robustness evaluation, we further mine the hard samples as the final test set." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 410, + 288, + 449 + ], + "lines": [ + { + "bbox": [ + 50, + 410, + 288, + 449 + ], + "spans": [ + { + "bbox": [ + 50, + 410, + 288, + 449 + ], + "type": "table", + "html": "
Test SetImageNetObjectNetSynthetic image pool
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Acc (%)74.6466.9195.7994.0293.75
", + "image_path": "b95aafaae67b5fd43b3b278040f65e3611915024e1d62892e8c4a28f3ea3c74a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 472, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 628 + ], + "type": "text", + "content": "ferable for diffusion-generated images, we evaluate test sets created with shared failures from 1 to 8 surrogate models in Figure 5. We evaluate the accuracy of three target models that are not used during test set construction, including CLIP(ViT-B/16), LLaVa, and MiniGPT-4. Figure 5 shows that target model accuracy decreases as more surrogate models are used. The test sets are created with diverse backgrounds, while experiments for texture and material show the same trend. This trend demonstrates that failure images of multiple surrogate models can form a challenging test set for unseen new models. Notably, the accuracy decrease slows when the number of surrogate models exceeds four." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Quality control by human-in-the-loop. The above process allows us to automatically find a challenging test set to unseen models. However, generative models can produce incorrect images not matching the prompt category. We resort to human annotation to ensure the ImageNet-D images are simultaneously valid, single-class, and high-quality. After first-round annotation by graduate students," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 347, + 547, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 547, + 492 + ], + "type": "text", + "content": "we use Amazon Mechanical Turk [11, 22, 47] to evaluate labeling quality. We ask the workers to select the images that they can either recognize the main object or the main object can be used functionally as the ground truth category. Moreover, we design sentinels to ensure high-quality responses, including positive, negative and consistent sentinels. We report details of the labeling task in the appendix. A total of 679 qualified workers participated in 1540 labeling tasks, achieving an agreement of " + }, + { + "bbox": [ + 304, + 347, + 547, + 492 + ], + "type": "inline_equation", + "content": "91.09\\%" + }, + { + "bbox": [ + 304, + 347, + 547, + 492 + ], + "type": "text", + "content": ". Figure 3 displays images from ImageNet-D, demonstrating high fidelity and diversity in object and nuisance pairs. We summarize the framework of creating ImageNet-D in Figure 4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 498, + 408, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 408, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 408, + 510 + ], + "type": "text", + "content": "3.2. Dataset statistics" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 516, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 547, + 649 + ], + "type": "text", + "content": "ImageNet-D includes 113 overlapping categories between ImageNet and ObjectNet, and 547 nuisances candidates from the Broden dataset [4](see Table 1), resulting in 4835 hard images featuring diverse backgrounds (3,764), textures (498), and materials (573). Our pipeline to create ImageNet-D is general and efficient, allowing easy addition of new categories and nuisances. ImageNet-D's category distribution exhibits a natural long-tail pattern, as shown in Figure 6. The sparse and non-uniform category-attribute distribution in Figure 7 shows the necessity of exhausting all category and nuisance pairs in test set creation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "We evaluate various models on ImageNet-D benchmark. We find that ImageNet-D significantly decreases all models' accuracy by up to " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": ". We then show whether prior" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21755" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 70, + 220, + 140 + ], + "blocks": [ + { + "bbox": [ + 71, + 70, + 220, + 140 + ], + "lines": [ + { + "bbox": [ + 71, + 70, + 220, + 140 + ], + "spans": [ + { + "bbox": [ + 71, + 70, + 220, + 140 + ], + "type": "image", + "image_path": "d6e18835435ffd83f403e1c49c23c02fd37611e2d9d7536b5a33c768b93a3a96.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 120, + 143, + 171, + 152 + ], + "lines": [ + { + "bbox": [ + 120, + 143, + 171, + 152 + ], + "spans": [ + { + "bbox": [ + 120, + 143, + 171, + 152 + ], + "type": "text", + "content": "(a) Background" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 222, + 74, + 372, + 135 + ], + "blocks": [ + { + "bbox": [ + 222, + 74, + 372, + 135 + ], + "lines": [ + { + "bbox": [ + 222, + 74, + 372, + 135 + ], + "spans": [ + { + "bbox": [ + 222, + 74, + 372, + 135 + ], + "type": "image", + "image_path": "0ea4f2a91a74014ea9db46fc169a42010c5be7567ade0fcf566f79e27eedd5ab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 278, + 138, + 315, + 147 + ], + "lines": [ + { + "bbox": [ + 278, + 138, + 315, + 147 + ], + "spans": [ + { + "bbox": [ + 278, + 138, + 315, + 147 + ], + "type": "text", + "content": "(b) Texture" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 374, + 71, + 523, + 139 + ], + "blocks": [ + { + "bbox": [ + 374, + 71, + 523, + 139 + ], + "lines": [ + { + "bbox": [ + 374, + 71, + 523, + 139 + ], + "spans": [ + { + "bbox": [ + 374, + 71, + 523, + 139 + ], + "type": "image", + "image_path": "6ae9074cb569c4e57555b719cbd10b6868158be3437923ecceae2c0a9a5e058f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 428, + 143, + 468, + 152 + ], + "lines": [ + { + "bbox": [ + 428, + 143, + 468, + 152 + ], + "spans": [ + { + "bbox": [ + 428, + 143, + 468, + 152 + ], + "type": "text", + "content": "(c) Material" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 78, + 184, + 333, + 256 + ], + "blocks": [ + { + "bbox": [ + 91, + 162, + 501, + 174 + ], + "lines": [ + { + "bbox": [ + 91, + 162, + 501, + 174 + ], + "spans": [ + { + "bbox": [ + 91, + 162, + 501, + 174 + ], + "type": "text", + "content": "Figure 6. Histogram of the image frequency per category in our test set, following a natural long-tail distribution." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 78, + 184, + 333, + 256 + ], + "lines": [ + { + "bbox": [ + 78, + 184, + 333, + 256 + ], + "spans": [ + { + "bbox": [ + 78, + 184, + 333, + 256 + ], + "type": "image", + "image_path": "c715372289b6f2a9de8e5f8de739d558e01368e400b6011c576259c748f562b4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 202, + 262, + 253, + 271 + ], + "lines": [ + { + "bbox": [ + 202, + 262, + 253, + 271 + ], + "spans": [ + { + "bbox": [ + 202, + 262, + 253, + 271 + ], + "type": "text", + "content": "(a) Background" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 345, + 185, + 516, + 255 + ], + "blocks": [ + { + "bbox": [ + 345, + 185, + 516, + 255 + ], + "lines": [ + { + "bbox": [ + 345, + 185, + 516, + 255 + ], + "spans": [ + { + "bbox": [ + 345, + 185, + 516, + 255 + ], + "type": "image", + "image_path": "6a849ac47dad30e3ed0f0fad0623ae1d555007446306455e24303fd6423f2cd3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 255, + 436, + 264 + ], + "lines": [ + { + "bbox": [ + 400, + 255, + 436, + 264 + ], + "spans": [ + { + "bbox": [ + 400, + 255, + 436, + 264 + ], + "type": "text", + "content": "(b) Texture" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 468, + 255, + 506, + 264 + ], + "lines": [ + { + "bbox": [ + 468, + 255, + 506, + 264 + ], + "spans": [ + { + "bbox": [ + 468, + 255, + 506, + 264 + ], + "type": "text", + "content": "(c) Material" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 281, + 545, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 545, + 326 + ], + "type": "text", + "content": "Figure 7. Frequency of object category and nuisance pairs. Each dot indicates a pair, while the x-axis and y-axis indicate the nuisance and category, respectively. As shown in Table 1, we adopt 468 backgrounds, 47 textures, and 32 materials from the Broden dataset [4], leading to different widths of Figure (a) (b) (c). A darker color indicates more samples. The sparse and non-uniform distribution shows the necessity of exhausting all category and nuisance pairs in ImageNet-D creation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 346, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 381 + ], + "type": "text", + "content": "advancements could improve ImageNet-D robustness, such as data augmentation. Lastly, we discuss ImageNet-D from various aspects, such as nearest neighbor retrieval." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 392, + 166, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 166, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 166, + 406 + ], + "type": "text", + "content": "4.1. Experimental setups" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 412, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 519 + ], + "type": "text", + "content": "Test set construction setups. We use Stable Diffusion [48] to create ImageNet-D, and adopt the pretrained weight of version stable-diffusion-2-1 from Hugging Face. To find the hard images, we finalize ImageNet-D with shared failures of 4 surrogate models, including CLIP [45] (ViT-L/14, ViT-L/14-336px and ResNet50), and vision model (ResNet50 [16]). The candidate set of surrogate models in Figure 5 also includes CLIP (Resnet101,ViT-B/32) and vision model (ViT-L/16 [13] and VGG16 [52])." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": "Evaluation of classification models. Robustness on ImageNet-D is measured by top-1 accuracy in object recognition, the ratio of correctly classified images to total images. We evaluate classification models with the open-source pretrained weights. For CLIP [45], we follow the original paper [45] to adopt A photo of a [category] as the text template. The zero-shot accuracy of CLIP is reported." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Evaluation of visual question answering (VQA) models. We evaluate the accuracy of the state-of-the-art open-source VQA models on ImageNet-D, including LLaVa [31], and MiniGPT-4 [65]. Given an input image, VQA models output answers based on input text prompt. However, the textual output of VQA models is not limited to a certain template, thus may not include the category name in predefined category list of object recognition tasks. This makes it hard to assess the accuracy based on diverse answers." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 346, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 525 + ], + "type": "text", + "content": "A common prompt that asks VQA models to recognize the object is: What is the main object in this image? To make VQA models choose from pre-defined category list, we ask VQA models as follows: What is the main object in this image? Choose from the following list: [GT category], [failure category]. GT category refers to the image's ground truth category. As for the failure category, we adopt the category that achieves the highest CLIP (ViT-L/14) confidence among all wrong categories. With this prompt, we find that both MiniGPT-4 and LLaVa can choose from provided category list in their output. If the model chooses ground truth category, this image is viewed to be correctly recognized. Therefore, we can compute the accuracy of VQA models." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 538, + 432, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 432, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 432, + 549 + ], + "type": "text", + "content": "4.2. Robustness evaluation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Quantitative results. We evaluate ImageNet-D on 25 models, and plot test accuracy trend in Figure 8. The horizontal axis and vertical axis indicate the test accuracy on ImageNet and ImageNet-D, respectively. Figure 8 shows that as ImageNet accuracy increases, ImageNet-D accuracy also gets higher. ImageNet-D accuracy is much lower than ImageNet accuracy for all models, indicated by the lower distribution below the " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "y = x" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": " reference line. We report the accuracy of 14 models on different test sets in Table 3, and all models' accuracy in appendix. Table 3 shows that ImageNet-D achieves the lowest test accuracy for all models, except for the comparable result on Stylized-ImageNet for VQA models. Note that ImageNet-D achieves higher image fi" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21756" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 214, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 214, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 214, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 214, + 159 + ], + "type": "image", + "image_path": "f99cc870a3b288e1f9a36417eda7a8cef88a4838e65a7b31c20aba670ec60b66.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 547, + 225 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 547, + 225 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 547, + 225 + ], + "type": "text", + "content": "Figure 8. Model accuracy on ImageNet vs. ImageNet-D. Each data point corresponds to one tested model. The plots reveal that there is a significant accuracy drop from ImageNet to our new test set ImageNet-D. As the model's accuracy on ImageNet increases, the accuracy on ImageNet-D is also higher. These results show the effectiveness of ImageNet-D to evaluate the robustness of neural networks. We report the exact number of 14 models of this figure in Table 3, and the results for all models can be found in the appendix." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 71, + 378, + 168 + ], + "blocks": [ + { + "bbox": [ + 215, + 71, + 378, + 168 + ], + "lines": [ + { + "bbox": [ + 215, + 71, + 378, + 168 + ], + "spans": [ + { + "bbox": [ + 215, + 71, + 378, + 168 + ], + "type": "image", + "image_path": "f6a6fa95452c152671a5da6580eeeedf9e6be34eef0ee8b81b0c0450c68a6eee.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 380, + 72, + 542, + 159 + ], + "blocks": [ + { + "bbox": [ + 380, + 72, + 542, + 159 + ], + "lines": [ + { + "bbox": [ + 380, + 72, + 542, + 159 + ], + "spans": [ + { + "bbox": [ + 380, + 72, + 542, + 159 + ], + "type": "image", + "image_path": "fd1474e73981c9852efa3b33e3084412038371890bcc0db56cd7f2abae5272c2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 49, + 289, + 545, + 439 + ], + "blocks": [ + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": "Table 3. Test accuracy of vision models and large foundation models (\\%). We show the test accuracy for the vision models and large foundation models (rows) on different test sets (columns). The numbers in green refer to the accuracy drop of ImageNet-D compared to ImageNet. For MiniGPT-4 and LLaVa, ImageNet-D reduces the accuracy by " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "16.81\\%" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "29.67\\%" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": " compared to the ImageNet, respectively. Our results show that ImageNet-D is effective to evaluate the robustness of neural networks." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 289, + 545, + 439 + ], + "lines": [ + { + "bbox": [ + 49, + 289, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 49, + 289, + 545, + 439 + ], + "type": "table", + "html": "
ModelArchitectureImageNetObjectNetImageNet-9StylizedImageNet-DImageNet-D Total
BackgroundTextureMaterial
Vision model (CNN)VGG1962.7727.1974.8416.259.8(-52.97)11.45(-51.32)12.39(-50.38)10.28(-52.49)
ResNet10167.6632.3481.8522.6612.38(-55.28)13.65(-54.01)13.44(-54.22)12.64(-55.02)
Densenet16166.9931.8684.9122.511.34(-55.65)14.06(-52.93)13.26(-53.73)11.85(-55.14)
Wideresnet10169.234.3782.1721.4810.55(-58.65)13.05(-56.15)12.04(-57.16)10.98(-58.22)
Vision model (ViT)ViT-B/3265.0227.5977.5142.346.64(-58.38)12.25(-52.77)13.79(-51.23)8.07(-56.95)
ViT-B/1672.1434.7982.4931.0210.49(-61.65)16.87(-55.27)17.63(-54.51)12.0(-60.14)
ViT-L/1668.6732.778.9129.387.68(-60.99)14.06(-54.61)15.53(-53.14)9.27(-59.40)
CLIPRN10162.4842.8983.0922.5821.47(-41.01)21.29(-41.19)25.83(-36.65)21.96(-40.52)
ViT-B/3264.0643.6779.5644.2218.73(-45.33)33.33(-30.73)30.37(-33.69)21.61(-42.45)
ViT-B/1667.9554.8785.1640.6220.64(-47.31)22.89(-45.06)29.32(-38.63)21.9(-46.05)
MiniGPT-4Vicuna 13B88.7777.5789.4669.8871.81(-16.96)72.48(-16.29)72.5(-16.27)71.96(-16.81)
LLaVaVicuna 13B79.3276.0290.8461.9452.89(-26.43)40.53(-38.79)36.28(-43.04)49.65(-29.67)
LLaVa-1.5Vicuna 13B89.0878.6693.8864.1473.31(-15.77)67.27(-21.81)67.08(-22.00)71.95(-17.13)
LLaVa-NeXTHermes-Yi-34B85.8377.5490.5257.9868.77(-17.06)46.67(-39.16)54.11(-31.72)64.76(-21.07)
", + "image_path": "cc824f82a9ca31804dfde038f72e01934ca9d3f57c7a9ccc07c0dbe2dbfc5477.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "content": "delyity than Stylized-ImageNet as shown in Figure 2. Although ObjectNet changes multiple attributes for each image, it still results in higher accuracy than ImageNet-D that specifies only one attribute per image. Compared to ImageNet, ImageNet-D yields a test accuracy drop of more than " + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "inline_equation", + "content": "16\\%" + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "content": " for all models, including LLaVa (reducing " + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "inline_equation", + "content": "29.67\\%" + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "content": ") and MiniGPT-4 (reducing " + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "inline_equation", + "content": "16.81\\%" + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "content": "). Our ImageNet-D can also cause significant accuracy drop of the latest LLaVa-1.5 and LLaVa-NeXT. Although LLaVa-NeXT outperforms LLaVa-1.5 on benchmarks like MMMU [61], it achieves lower accuracy on ImageNet-D, demonstrating the uniqueness of ImageNet-D. For vision models, the accuracy drop is even close to " + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 46, + 460, + 288, + 638 + ], + "type": "text", + "content": ". The results in Figure 8 and Table 3 show the effectiveness of ImageNet-D in evaluating the robustness of neural networks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Visualization results. Figure 3 displays image examples from ImageNet-D, demonstrating high quality. Although humans can easily recognize the main object, CLIP (ViT-L/14) mistakenly classifies these images into a wrong category. Figure 9 shows conversations with MiniGPT-4 and LLaVa-1.5 on ImageNet-D images, indicating that" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "content": "MiniGPT-4 and LLaVa-1.5 can also fail to recognize the main object from ImageNet-D." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 491, + 446, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 446, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 446, + 504 + ], + "type": "text", + "content": "4.3. Robustness improvement" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 688 + ], + "type": "text", + "content": "Data augmentation. Prior studies reveal that data augmentation is effective to improve model robustness, such as on ImageNet-C [19]. We evaluate data augmentation methods on ImageNet-D, including SIN [15], AugMix [21], ANT [50] and DeepAugment [22]. Table 4 shows the results with ResNet50 backbone for all methods. We report test accuracy for ImageNet and ImageNet-D, mean Corruption Error (mCE) for ImageNet-C following [19, 21, 22, 50]. Although these methods improve ImageNet-C robustness (lower mCE) than baseline model, Table 4 shows that their ImageNet-D robustness is comparable or even worse than baseline. This suggests that current benchmarks like ImageNet-C do not accurately represent real robustness of neural networks in our setting, making ImageNet-D a necessary benchmark for robustness evaluation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Model architecture. We compare ImageNet-D robustness of different model architectures in Figure 11. When" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21757" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 71, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 49, + 125, + 60, + 138 + ], + "lines": [ + { + "bbox": [ + 49, + 125, + 60, + 138 + ], + "spans": [ + { + "bbox": [ + 49, + 125, + 60, + 138 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 71, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 62, + 71, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 62, + 71, + 545, + 358 + ], + "type": "image", + "image_path": "1367132a7d87fe71abc9f61f76359e0116174167616c39504921ecbeb0e24309.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 369, + 546, + 403 + ], + "lines": [ + { + "bbox": [ + 46, + 369, + 546, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 546, + 403 + ], + "type": "text", + "content": "Figure 9. Failure cases of MiniGPT-4 and LLaVa-1.5 from ImageNet-D. We ask MiniGPT-4 and LLaVa-1.5 for the category of the input image and the reason for their predictions. Figure (a) to (c) are images with different background, texture and material, respectively. Our results show that images from ImageNet-D can also make the state-of-the-art foundation models fail." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 475, + 287, + 534 + ], + "blocks": [ + { + "bbox": [ + 46, + 422, + 288, + 466 + ], + "lines": [ + { + "bbox": [ + 46, + 422, + 288, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 288, + 466 + ], + "type": "text", + "content": "Table 4. Robustness of different augmentation methods. Despite superior ImageNet-C robustness, these methods fail to improve ImageNet-D robustness, demonstrating the uniqueness of ImageNet-D from ImageNet-C." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 475, + 287, + 534 + ], + "lines": [ + { + "bbox": [ + 50, + 475, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 50, + 475, + 287, + 534 + ], + "type": "table", + "html": "
ModelImageNet (↑)ImageNet-C(mCE)(↓)ImageNet-D(↑)
Baseline65.8281.7410.22
SIN63.42(-2.40)78.45(-3.29)8.81(-1.41)
Augmix66.88(+1.06)74.7(-7.04)8.75(-1.47)
ANT65.95(+0.13)76.74(-5.00)10.09(-0.13)
DeepAugment66.54(+0.72)70.31(-11.43)9.37(-0.85)
", + "image_path": "38ac05ad7e7f02df26e09a2b3ba34cd31641c32fab7936bd376ec2bb2ef5bead.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": "we change the model from ViT to Swin Transformer [33] and ConvNeXt [34], the test accuracy on both ImageNet-D (Background) and ImageNet improve. However, the robustness on Texture and Material test set even decreases slightly. These results show the difficulty of improving ImageNet-D robustness by model architecture." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Pretraining with more data. Pretraining on a large data set is effective to improve model performance, such as ImageNet accuracy [18]. Figure 11 compares ConvNext, that is trained directly on ImageNet-1K, with ConvNext (Pretrained) which is first pretrained on ImageNet-22K. We find that ConvNext (Pretrained) achieves higher robustness than ConvNext on all three sets of ImageNet-D, especially for" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 423, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 423, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 423, + 545, + 448 + ], + "type": "text", + "content": "the Background set. These results show that pretraining on a large data set helps improve robustness on ImageNet-D." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 455, + 420, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 420, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 420, + 467 + ], + "type": "text", + "content": "4.4. Further discussions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": "Can CLIP find the correct neighbors of ImageNet-D images? CLIP model [45] shows potential in nearest neighbor search tasks. With ImageNet-D images as query, we retrieve the most similar images from ImageNet to investigate whether CLIP can find correct neighbors, as shown in Figure 10. Take Background for example, retrieved images may either have a similar background to the query image (Figure 10(a)) or include the object that is related to the query image's background (Figure 10(b)). Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Can ImageNet-D match natural test sets in failure transferability? Section 3.1 defines transferable failure and finalize ImageNet-D with shared failures of surrogate models. We conduct the same experiment on ImageNet, introducing ImageNet (Failure) with the shared failure images of surrogate models. Table 5 show that ImageNet-D achieves similar accuracy to ImageNet (Failure), indicating that synthetic images can achieve similar failure transferability as natural images. In contrast to" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21758" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 542, + 167 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 542, + 167 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 542, + 167 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 542, + 167 + ], + "type": "image", + "image_path": "8388d0435fc58bc57c490c1e0111f81ccb7451d07f41451fd52ec9cbde5bdeca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 178, + 546, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 546, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 546, + 222 + ], + "type": "text", + "content": "Figure 10. Visualizations of nearest neighbor images. We visualize the nearest neighbor images from ImageNet with ImageNet-D image as the query image. Instead of following the same object category as the query image, the nearest neighbor images either follow a similar background or follow another object category that is highly correlated with the background of query image. Our results show that ImageNet-D can find the failure cases of neural networks in nearest neighbor retrieval." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 227, + 216, + 322 + ], + "blocks": [ + { + "bbox": [ + 50, + 227, + 216, + 322 + ], + "lines": [ + { + "bbox": [ + 50, + 227, + 216, + 322 + ], + "spans": [ + { + "bbox": [ + 50, + 227, + 216, + 322 + ], + "type": "image", + "image_path": "6923127a985bed378444bb9b8f2e36b729805c345b515aacdaac51474cb0c8c6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 334, + 546, + 368 + ], + "lines": [ + { + "bbox": [ + 46, + 334, + 546, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 546, + 368 + ], + "type": "text", + "content": "Figure 11. Test accuracy of different architectures and training data. Each data point corresponds to one tested model. Apart from the ConvNeXt (Pretrained), all other models are trained on ImageNet-1K. The plots show that pretraining achieves higher robustness on all three subsets, while changing model architectures only improves on ImageNet-D (Background)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 216, + 227, + 378, + 322 + ], + "blocks": [ + { + "bbox": [ + 216, + 227, + 378, + 322 + ], + "lines": [ + { + "bbox": [ + 216, + 227, + 378, + 322 + ], + "spans": [ + { + "bbox": [ + 216, + 227, + 378, + 322 + ], + "type": "image", + "image_path": "607f368f4bca3411cccdc3f9f5c37c44c80ce6eabb302fca80fa4400c257fe40.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 379, + 227, + 542, + 322 + ], + "blocks": [ + { + "bbox": [ + 379, + 227, + 542, + 322 + ], + "lines": [ + { + "bbox": [ + 379, + 227, + 542, + 322 + ], + "spans": [ + { + "bbox": [ + 379, + 227, + 542, + 322 + ], + "type": "image", + "image_path": "cbef7ec2c1cbeaa6971fd23f2bf35d56ef0eecd6f697fd03418c4c3ba96d4060.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 451, + 287, + 495 + ], + "blocks": [ + { + "bbox": [ + 46, + 386, + 287, + 441 + ], + "lines": [ + { + "bbox": [ + 46, + 386, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 287, + 441 + ], + "type": "text", + "content": "Table 5. Results of failure transferability. We create ImageNet (Failure) with shared failures of surrogate models from original ImageNet, achieving comparable accuracy to ImageNet-D. These results show that our synthetic images achieve similar ability to natural images in finding the failures of new models." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 451, + 287, + 495 + ], + "lines": [ + { + "bbox": [ + 50, + 451, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 50, + 451, + 287, + 495 + ], + "type": "table", + "html": "
ModelArchitectureImageNetImageNet (Failure)ImageNet-D
CLIPViT-B/1667.9511.0921.9
LLaVaVicuna 13B79.3241.4349.65
MiniGPT-4Vicuna 13B88.7765.2271.96
", + "image_path": "b63b73b95438d37d93e4df3d3048a33c4cb9c7da4071e8601c1bab2609479dfa.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 50, + 562, + 287, + 604 + ], + "blocks": [ + { + "bbox": [ + 46, + 509, + 287, + 554 + ], + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 554 + ], + "type": "text", + "content": "Table 6. Test accuracy of models finetuned on synthetic data. We finetune a pretrained ResNet18 model on ImageNet-1K together with different extra training data. Training on synthetic images achieves highest robustness on both ImageNet-D and ObjectNet." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 562, + 287, + 604 + ], + "lines": [ + { + "bbox": [ + 50, + 562, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 50, + 562, + 287, + 604 + ], + "type": "table", + "html": "
ModelExtra training dataImageNetObjectNetImageNet-D
A/55.6821.518.6
BImageNet59.78(+4.10)24.78(+3.27)10.4(+1.80)
CSynthetic-easy56.56(+0.88)26.12(+4.61)27.86(+19.26)
", + "image_path": "d2d716ca005fadfa33b66bca1f7ce065be9f039ec9566e8d931f929768d7c8fe.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 628, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 651 + ], + "type": "text", + "content": "natural datasets like ImageNet, ImageNet-D enjoys a lower cost in data collection and can be scaled efficiently." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "Training on diffusion-generated images. By contrast to shared failure images in ImageNet-D, we term generated images correctly classified by surrogate models as Synthetic-easy, and investigate their influence as training data. We finetune a pre-trained ResNet18 model on differ" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "type": "text", + "content": "ent training sets in Table 6. Table 6 shows that training on Synthetic-easy significantly improves ImageNet-D robustness by " + }, + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "19.26\\%" + }, + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "type": "text", + "content": ". Remarkably, model C outperforms model B in ObjectNet accuracy by " + }, + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "1.34\\%" + }, + { + "bbox": [ + 304, + 388, + 545, + 473 + ], + "type": "text", + "content": ", indicating model C's superior generalization. These results imply that diffusion-generated images with diverse object and nuisance pairs could enhance model robustness as training samples." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 483, + 378, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 378, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 378, + 496 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "text", + "content": "In this paper, we introduce a test set ImageNet-D and establish a rigorous benchmark for visual perception robustness. Capitalizing the image generation ability of diffusion models, ImageNet-D includes images with diverse factors including background, texture and material. Experimental results show that ImageNet-D significantly decreases the accuracy of various models, including CLIP (reducing " + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "inline_equation", + "content": "46.05\\%" + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "text", + "content": "), LLaVa [31] (reducing " + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "inline_equation", + "content": "29.67\\%" + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "text", + "content": "), and MiniGPT-4 [65] (reducing " + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "inline_equation", + "content": "16.81\\%" + }, + { + "bbox": [ + 304, + 503, + 545, + 647 + ], + "type": "text", + "content": "), demonstrating the effectiveness in model evaluation. Our work makes a step forward in improving synthetic test sets, and will create more diverse and challenging test images as generative models improve." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 647, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 703 + ], + "type": "text", + "content": "Acknowledgments: This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2022-0-00951, Development of Uncertainty-Aware Agents Learning by Asking Questions)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21759" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Shekoofeh Azizi, Simon Kornblith, Chitwan Sahara, Mohammad Norouzi, and David J. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2, 5, 8" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21762" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_content_list.json b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a42854896f0600709def558518fa5a8c3169f90d --- /dev/null +++ b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_content_list.json @@ -0,0 +1,1385 @@ +[ + { + "type": "text", + "text": "Imagine Before Go: Self-Supervised Generative Map for Object Goal Navigation", + "text_level": 1, + "bbox": [ + 78, + 130, + 890, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sixian Zhang $^{1,2}$ , Xinyao Yu $^{1,2}$ , Xinhang Song $^{1,2}$ , Xiaohan Wang $^{1}$ , Shuqiang Jiang $^{1,2,3}$", + "bbox": [ + 145, + 179, + 821, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Key Lab of Intelligent Information Processing Laboratory of the Chinese Academy of Sciences (CAS), Institute of Computing Technology, Beijing, 2University of Chinese Academy of Sciences, Beijing", + "bbox": [ + 176, + 200, + 792, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3 Institute of Intelligent Computing Technology, Suzhou, CAS", + "bbox": [ + 297, + 234, + 669, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sixian.zhang, xinyao.yu, xinhang.song, xiaohan.wang}@vipl.ict.ac.cn, sqjiang@ict.ac.cn", + "bbox": [ + 99, + 253, + 867, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The Object Goal navigation (ObjectNav) task requires the agent to navigate to a specified target in an unseen environment. Since the environment layout is unknown, the agent needs to infer the unknown contextual objects from partially observations, thereby deducing the likely location of the target. Previous end-to-end RL methods capture contextual relationships through implicit representations while they lack notion of geometry. Alternatively, modular methods construct local maps for recording the observed geometric structure of unseen environment, however, lacking the reasoning of contextual relation limits the exploration efficiency. In this work, we propose the self-supervised generative map (SGM), a modular method that learns the explicit context relation via self-supervised learning. The SGM is trained to leverage both episodic observations and general knowledge to reconstruct the masked pixels of a cropped global map. During navigation, the agent maintains an incomplete local semantic map, meanwhile, the unknown regions of the local map are generated by the pretrained SGM. Based on the generated map, the agent sets the predicted location of the target as the goal and moves towards it. Experiments on Gibson, MP3D and HM3D show the effectiveness of our method. The code is available at https://github.com/sx-zhang/SGM.", + "bbox": [ + 76, + 335, + 473, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 724, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Navigating to specified targets [27, 44, 45, 55] is an essential capability for embodied AI systems to effectively manipulate and interact with real-world entities. Consequently, the visual object goal navigation (ObjectNav) task has recently gained widespread attention. In ObjectNav task, the agent is placed in an unseen and unmapped environment, and is tasked to navigate to an object of the user-specific category (e.g. couch) based on the visual observations. Since the environment is unseen, when the target is invisible, the agent needs to infer the likely location of the target. This", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9fd9a174456e73a104e3046a7ca9e51005c2151ddef1de001c4f63e7ba9f053b.jpg", + "image_caption": [ + "Figure 1. Agents employ SGM to 'imagine' details of unobserved regions during navigation. The SGM is trained in a self-supervised manner by predicting pixels in masked regions of sub-maps to capture contextual relations. The SGM leverages both episodic observations and general knowledge for map reconstruction." + ], + "image_footnote": [], + "bbox": [ + 506, + 303, + 885, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "requires the agent to learn and understand the contextual relationships between objects (e.g. couches typically appear with cushions and coffee tables), which enables it to deduce the target's location based on observed visual clues.", + "bbox": [ + 496, + 654, + 892, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To learn the contextual relations, end-to-end reinforcement learning (RL) methods embed pre-constructed object relation graph [52, 54, 59] into the end-to-end navigation models, or learn object associations directly via the RL [14, 15, 33]. These pre-learned priors are implicitly encoded within the policy. However, since the priors are episode-agnostic and lack geometric memory of current environment, the end-to-end RL methods exhibit limited generalization in unseen environments [32, 60]. Alternatively, modular methods [5-7] construct an explicit semantic local map, merging observed geometry and semantics of the unseen environment. The agent can disregard the observed", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16414", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "regions of the local map, where the target has not appeared, which simplifies the potential state space that needs to be explored. However, without learning the contextual object relation, the modular methods are still limited.", + "bbox": [ + 78, + 90, + 467, + 148 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, some methods [37, 56, 61] attempt to introduce priors of object contextual relationships into modular methods for predicting the long-term goal. They learn the contextual relation based on the local map by predicting the potential frontier nearest to the target [37], estimating the distance to the target [61], or directly anticipating the coordinate of the target [56]. However, individually learning the relations of targets with supervised learning may not be reliable, as the absolute position of targets may vary with different room layouts. In contrast, the joint associative relations among multiple objects are more reliable, e.g. chairs, tables, and cups are commonly found together, similarly, couches, cushions, and coffee tables often appear in conjunction. Therefore, we propose learning the joint contextual relations of the objects in a self-supervised manner: without any need for data collection and labeling as supervised learning, the model is trained to reconstruct the masked regions of a cropped global map based on its visible neighboring regions. This preparatory phase allows it to grasp not only individual object specifics (e.g. location and size) but also the patterns of its contextual companions (i.e. contextual object relation) and the surrounding environments (e.g. potential obstacle and free path). Then the trained model can 'imagine' unobserved regions during navigation to help agent deduce the target location.", + "bbox": [ + 80, + 156, + 467, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose self-supervised generative map (SGM) to scale up the coverage of the local map by generating the unobserved regions, as shown in Fig. 1. Specifically, given the global map of a training room, the global map is cropped into sub-maps with boxes of various scales, positions and angles, then uniformly resized to a fixed scale. Following the self-supervised learning settings of MAE [22], certain patches of the sub-maps are randomly masked. Our SGM is trained to predict the pixel values of the masked patches by leveraging both episodic observations and general knowledge. The episodic observations refer to the visible patches, which are encoded with a visual encoder, akin to many visual pre-training studies [8, 22]. However, contrary to image datasets, the quantity and diversity of training scenes for ObjectNav is notably limited. To enhance the generalization, general knowledge provided by Large Language Models (LLMs) is also considered. Visible patches are transformed into prompts for LLMs through a textual template, subsequently, LLMs (e.g. GPT-4 [34], ChatGLM [17]) predict the semantic contents of the masked patches in text. Furthermore, text predictions (general knowledge) and episodic observations merge via a cross-modality encoder. The decoder predicts the pixel values of the masked patches based on the encoded information. Episodic ob", + "bbox": [ + 80, + 539, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "servations and general knowledge are orthogonal and complementary, where episodic observations provide more geometric details, while general knowledge with rich semantic prior enhances the inference of contextual categories.", + "bbox": [ + 503, + 90, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "During navigation, the agent maintains a local semantic map that integrates observations of current unseen environment. Since the local map is incomplete, the trained SGM is employed to generate the unobserved regions of the local map. The local map is initially divided into non-overlapping patches. Then we propose a sample strategy that prioritizes the patches, which are informative or adjacent to unobserved regions. The selected patches are input into the SGM to predict the pixel values of the unknown regions. The agent selects the coordinates with the highest confidence of the target in the generated map as the long-term goal. The SGM continually generates the unknown regions based on updated local map until the target is found. We evaluate our SGM on photorealistic 3D environments of Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49]. The experimental results demonstrate the effectiveness of our SGM in generating unknown regions and assisting the agent in inferring the location of the target.", + "bbox": [ + 503, + 152, + 890, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 503, + 436, + 645, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ObjectGoal navigation. Existing visual object goal navigation can be categorized into: end-to-end methods and modular methods. The end-to-end methods learn to navigate by leveraging reinforcement learning (RL) [47, 58, 62] or imitation learning (IL) [38, 39]. Previous end-to-end RL methods attempt to learn object relation graph [14, 52, 54, 59], visual representation [24, 26, 33], historical states representation [16], auxiliary tasks [53] and data augmentation [10, 32] to enhance the navigation ability. To learn the contextual object relation for enhancing the deducing for target location, [52] constructs prior knowledge of object relations from external datasets [29], and [59] builds hierarchical object-to-zone graph. [14] proposes learning the object relations (i.e. the edges of predefined graph) by RL process. The learned contextual relations are implicitly encoded into the end-to-end model. However, lack of geometry memory and low sample efficiency of RL, the generalization of these methods in unseen environments remains limited. The modular methods [5-7] maintain a geometry semantic map for localization, memory and path planning. Recent modular methods [37, 56, 61] aim to address 'where to look?' subproblem (i.e. inferring the likely location of the target). These methods employ supervised learning to learn a target-related function. Based on a local map, they predict the nearest frontier to target [37], the minimal distance to target [61] or the absolute coordinates [56] of the target. Our SGM is also a modular method, while we learn joint contextual relations, i.e. the SGM predicts the unobserved regions, which contain both objects (not limited to", + "bbox": [ + 503, + 463, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16415", + "bbox": [ + 480, + 946, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "target) and environments with self-supervised learning.", + "bbox": [ + 76, + 90, + 441, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Several recent works attempt to predict the unobserved regions. [36] proposes to anticipate occupancy for point goal navigation. [19] takes a further step by adding the semantic prediction via two-stage segmentation models. [28] also predicts the unobserved semantic map, while implicitly encoding it into an RL-based policy. All of these works [19, 28, 36] only predict unobserved regions of a top-down map projected from the egocentric RGB-D view at a single timestamp. However, our SGM has a wider prediction scope as it predicts based on a broader local map, which integrates all historical observations. Additionally, it is worth to highlight that our SGM is trained through self-supervised learning, which avoids the tedious data collection and annotation of imitation and supervised learning.", + "bbox": [ + 75, + 107, + 468, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-supervised learning. Reconstructing signals from masked inputs has been validated as an effective self-supervised learning within the communities of NLP [2, 12, 35], CV [1, 13, 22], and multimodal pretraining [43]. We adopt the settings of Masked Autoencoders (MAE) [22] to train our SGM, which has demonstrated its robust capacity for learning contextual associations in many visual tasks [8, 18, 51]. Recently, there are few self-supervised works for goal-oriented navigation tasks. [20] proposes a distance estimator from passive videos through self-supervised learning for image goal navigation. Our SGM is proposed for ObjectNav task, which learns the contextual object relation by self-supervised learning, thereby generating the map of unobserved regions during navigation.", + "bbox": [ + 75, + 319, + 470, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 547, + 184, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Definition", + "text_level": 1, + "bbox": [ + 76, + 573, + 230, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The ObjectNav task is defined as: the agent is required to navigate to an instance of a specified object category (e.g. potted plant) in an unseen environment. The agent is placed at a random location at the start of an episode. At each timestamp $t$ , the agent receives egocentric RGB-D observations $s_t$ , target object $o$ and senor pose $(x_t, y_t, \\theta_t)$ , where $x_t, y_t$ and $\\theta_t$ denote coordinates and orientation of the agent. The agent executes a discrete action, where the action space consists of move_forward, turn_left, turn_right and stop. The agent autonomously executes the action stop when it determines to complete the task. A successful episode is denoted as that, within certain number of steps, the agent stops at a position where the distance to the target is less than a threshold (e.g. 1m) and the target is visible in the egocentric observation.", + "bbox": [ + 75, + 597, + 468, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is constructed based on the modular ObjectNav architecture. The modular methods typically build an accumulating semantic map during navigation [5] based on the RGB-D observations, sensor poses and segmentation models [21, 23]. The semantic map $m_{t} \\in \\mathbb{R}^{(N_{o} + N_{s}) \\times H \\times W}$", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b6bc36ee6b52319d4f142ce17e305bac36ba0270cd2c4956d19e2cb7a12fc619.jpg", + "image_caption": [ + "Figure 2. Self-supervised training of SGM. 'Self', 'Cross' and 'FF' denotes self-attention, cross-attention and feed-forward layers, respectively. The SGM is trained to predict the pixel value of the masked patches by utilizing episodic observations and the general knowledge from LLMs. Examples of responses from LLMs are detailed in the supplements." + ], + "image_footnote": [], + "bbox": [ + 511, + 89, + 883, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "utilizes multiple channels to represent different classes, where $N_{o}$ denotes the number occupancy classes including occupied and free, $N_{s}$ is the number of object classes and $H, W$ are the map size. The semantic map aggregates the observed object layout of the unseen environment from 0 to $t$ . However, since the semantic map is obtained only by partial observations of the entire environment, it is only a subset (i.e. local map) of the global map. Therefore, when the target is invisible, the agent needs to estimate its unobserved surroundings based on the learned context relation of the objects to infer the likely location of the target.", + "bbox": [ + 498, + 412, + 893, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Self-supervised Generative Map", + "text_level": 1, + "bbox": [ + 500, + 589, + 782, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To predict the potential position of the target, the contextual relations between objects can be used to generate the unseen regions of local maps. In particular, we propose the self-supervised generative map (SGM) to learn the context relations of both objects and environments (e.g. obstacle and free path) with the self-supervised setting of MAE [22].", + "bbox": [ + 496, + 612, + 890, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 1, given a global map of a training room, we first crop and sample a number of sub-maps from it using several boxes in various scales, positions and angles. Then the sub-maps are resized to a fixed scale and divided into non-overlapping patches. These patches are sampled without replacement by a uniform distribution strategy. The selected patches serve as the visible patches $m_{s}$ , while the remaining patches $m_{u}$ are masked.", + "bbox": [ + 496, + 704, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To learn the contextual relation, the SGM $P(m_u|m_s)$ is trained in a self-supervised manner by reconstructing the masked patches $m_{u}$ based on their visible neighboring patches $m_{s}$ . As shown in Fig. 2, the proposed SGM reconstructs the masked patches by leveraging the following", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16416", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "two aspects of information: 1) episodic observations, and 2) general knowledge from large language models (LLMs).", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Episodic observations. The visible patches are embedded with a linear projection and added with positional embeddings, and then processed with the visual encoder $E_{v}$ . The visual encoder is implemented by several Transformer blocks of ViT [13], consisting of self-attention and feedforward layers. Then the episodic observations are embedded as $E_{v}(m_{s}) = f_{v} \\in \\mathbb{R}^{n_{v} \\times n_{d}}$ , where $n_{v}$ is the number of visible patches and $n_{d}$ is the feature dimension. Following [22], the encoder only operates the visible patches, rather than all patches. Therefore, when the ratio of visible patches is small (e.g. 25%), the encoder consumes minimal computing and memory resources.", + "bbox": [ + 75, + 121, + 467, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "General knowledge. Due to limited training environments, the quantity and diversity of available global maps for training is considerably less than that of image datasets [11, 29]. As a result, models trained merely on visual clues are prone to overfitting to the limited training environments, leading to poor generalization to unseen environments [32]. Currently, the LLMs demonstrate strong reasoning abilities on many complex tasks [3]. In our work, we employ the LLMs (e.g. GPT-4 [34], ChatGLM [17]) to provide general knowledge for reasoning the contextual relation and predicting the probable objects, thereby enhancing generalization for unseen environments.", + "bbox": [ + 75, + 301, + 467, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For all visible patches, an object category is considered as observed if there is a pixel with the value of 1 existing in the corresponding channel. Then we fill in the observed categories into a fixed sentence template to generate the text prompt for LLMs. For instance, when couches and chairs are observed, the generated prompt is 'In an indoor environment, if couches and chairs are observed, what other objects might be around them? Answer in one sentence.' The LLMs receive the text prompt and predict the probable neighboring categories around the observed categories. The predictions $L(m_{s})$ of LLMs are further processed by Tokenizer and embedded with pre-trained RoBERTa [30] by $E_{L}(L(m_{s})) = f_{l}\\in \\mathbb{R}^{n_{l}\\times n_{d}}$ , where $n_l$ is the token number. Since LLMs are trained on massive data, the prediction $f_{l}$ can be regarded as an episode-agnostic, general knowledge. General knowledge $f_{l}$ provides a wealth of semantic priors, which is orthogonal and complementary to episodic observation $f_{v}$ that captures geometric details.", + "bbox": [ + 75, + 483, + 467, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fusion and anticipation. We utilize the cross-modality encoder of LXMERT [42] to fuse $f_{v}$ and $f_{l}$ , which consists of cross-attention, self-attention and feed-forward layers. The cross-attention layers are used to fuse the information between $f_{v}$ and $f_{l}$ , which is formally given by", + "bbox": [ + 75, + 755, + 467, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC r o s s A t t n \\left(f _ {v}, f _ {l}\\right) = \\sigma \\left(\\frac {f _ {v} W _ {q} \\left(f _ {l} W _ {k}\\right) ^ {T}}{\\sqrt {n _ {d}}}\\right) f _ {l} W _ {v} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 837, + 467, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma$ is the Softmax activation function, and $W_{*} \\in$", + "bbox": [ + 76, + 885, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{n_d\\times n_d}$ are learned parameters and biases are omitted. The output of the cross-modality encoder serves as the final embedding for all visible patches.", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The decoder takes full patches (i.e. encoded visible patches and masked patches) as the inputs, where the masked patches are initialized to the learnable vectors of the same size as the encoded visible patches. All patches are added with positional embeddings that represent their spatial locations. The decoder is also implemented by a series of Transformer blocks.", + "bbox": [ + 496, + 136, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training. The SGM is trained to predict the pixel value of the masked patches. Given the prediction $m_{u}$ , the training objective for all classes (i.e. occupancy and object classes) is given by", + "bbox": [ + 496, + 242, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {B C E} = \\frac {1}{n _ {u}} \\sum_ {i = 0} ^ {n _ {u}} B C E \\left(m _ {u} (i), \\hat {m} _ {u} (i)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 311, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $BCE$ denotes the pixel-wise binary cross entropy loss and $n_u$ is the number of masked patches. $m_u(i) \\in \\mathbb{R}^{(N_o + N_s) \\times \\delta \\times \\delta}$ represents one of the predicted patches, where $\\delta$ is the size of a patch. $\\hat{m}_u(i)$ is the ground-truth of the masked patches, and each pixel of $\\hat{m}_u(i)$ is a binary value. Additionally, to enhance the accuracy of predicting the position and size of objects, an IoU loss is added specifically for the object classes", + "bbox": [ + 496, + 358, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {I o U} = \\frac {1}{n _ {u}} \\sum_ {i = 0} ^ {n _ {u}} I o U \\left(m _ {u} (i, N ^ {s}), \\hat {m} _ {u} (i, N ^ {s})\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 488, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $IoU$ denotes the category-level pixel-wise intersection over union loss, and $m_u(i,N^s) \\in \\mathbb{R}^{N_s \\times \\delta \\times \\delta}$ only contains the object classes. We add up all the losses to train our SGM. The overall training objective is $L = L_{BCE} + \\lambda L_{IoU}$ , where $\\lambda$ denotes the loss weights. The advantages of our SGM are as following: 1) Data collection. The self-supervised training eliminates the requirement for target-oriented annotations or supervision from simulators. SGM requires only training with cropped and randomly masked global maps. 2) Scalability. SGM is compatible with various LLMs, allowing for concurrent improvements in our method as LLMs advance.", + "bbox": [ + 496, + 536, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. ObjectNav with SGM", + "text_level": 1, + "bbox": [ + 500, + 724, + 700, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The trained SGM is capable of generating unobserved regions based on their visible surroundings, which is utilized to help agent deduce the unobserved regions of the local maps during navigation.", + "bbox": [ + 496, + 750, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unobserved regions generation. At each timestamp $t$ during navigation, the agent constructs a local semantic map $m_t$ (as introduced in Sec. 3.1), and each channel of $m_t$ contains binary-valued pixels. The local semantic map includes numerous unobserved regions as shown in Fig. 3, where the pixel values of these regions are 0 across all channels.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16417", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the local semantic map $m_{t}$ of time $t$ , we first crop a sub-region of $m_{t}$ , where the size of this region is $\\epsilon$ times that of the smallest fitting square box around the known regions of $m_{t}$ as shown in Fig. 3. The $\\epsilon$ (e.g. $\\epsilon = 140\\%$ is decided via validation experiments) represents a scaled-up factor with a minimum value of $100\\%$ . The cropped region is resized to a fixed scale $m_{t}^{\\prime} \\in \\mathbb{R}^{(N_{o} + N_{s}) \\times L \\times L}$ (e.g. $L = 224$ for ViT-Base) and divided into non-overlapping patches. The size of each patch is $\\delta$ . To eliminate noise and reduce computational complexity, we select a subset of patches to serve as the input of the SGM. The sampling strategy prioritizes the patches, which are 1) informative and 2) adjacent to unobserved regions.", + "bbox": [ + 76, + 90, + 472, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To construct the sampling strategy, we calculate the average pixel value in each patch by $W = \\text{Avgpool}(m_t')$ , where $W \\in \\mathbb{R}^{\\frac{L}{\\delta} \\times \\frac{L}{\\delta}}$ , and Avgpool represents the average pooling in each patch for all channels. For each element $w_i \\in W$ , the higher value indicates that the corresponding patch is more informative, i.e., there are more observed object classes or larger observed regions in this patch. Furthermore, we leverage the Laplacian kernel $K$ as a gradient operator (i.e., edge detector), to operate the $W$ by $V = \\text{Conv}(W, K)$ , where $V \\in \\mathbb{R}^{\\frac{L}{\\delta} \\times \\frac{L}{\\delta}}$ and Conv denotes the convolution operation. The higher value of $v_i \\in V$ demonstrates that the corresponding patch is more likely to be adjacent to the unobserved regions.", + "bbox": [ + 75, + 287, + 472, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The $W$ and $V$ are further processed by flattening and Softmax operations for probability normalization. Then the sampling probability $P$ of each patch is defined as", + "bbox": [ + 76, + 484, + 470, + 531 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP = \\alpha \\bar {W} + (1 - \\alpha) \\bar {V} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 540, + 468, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{W}$ and $\\bar{V}$ denote the normalized $W$ and $V$ , respectively, and $\\alpha$ is a trade-off weight. We employ a multinomial distribution for sampling patches. Specifically, given a set of patches $m_t' = \\{m_t'(1), m_t'(2), \\ldots, m_t'(n_p)\\}$ ( $n_p = \\left(\\frac{L}{\\delta}\\right)^2$ ), and their associated probabilities $P = \\{p_1, p_2, \\ldots, p_{n_p}\\}$ . The patches are sampled without replacement according to $m_t'(i) \\sim \\text{Multinomial}(n, P)$ . The number of sampled patches $n$ constitutes only a small fraction (e.g. $30\\%$ ) of the total.", + "bbox": [ + 76, + 566, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on this strategy, sampled patches are fed into the SGM to predict unobserved regions. The predicted values are continuous, which reflect the confidence in its prediction. Furthermore, the raw prediction of SGM is enhanced by adding the actual local semantic map to form the final generated map, where if a coordinate has already been observed (having values in semantic map), its predicted value is replaced with the confirmed observed value. During ObjectNav task, the agent identifies the pixel with the highest confidence in the target's channel of the generated semantic map. Then the coordinates of this pixel are set as the long-term goal $g_{t}$ . Additionally, limited observation (e.g. no available contextual object is observed) may result in", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f0dac37d0d55f16e93ddd4876ca967a20a8bcf5c07b259f25460634c96b6e48c.jpg", + "image_caption": [ + "Figure 3. During navigation, the agent builds a local semantic map $m_t$ and crops it to $m_t'$ . The patches of $m_t'$ are sampled by multinomial distribution with probability $P$ . The SGM generates the unobserved regions based on selected $n$ patches. The long-term goal is determined by the generated map and the target." + ], + "image_footnote": [], + "bbox": [ + 511, + 88, + 883, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "unreliable prediction of the target (i.e. the confidence of the predicted semantic map is low). Therefore, we adopt the exploration strategy [31, 50] at the beginning of navigation until the prediction confidence of the target exceeds a certain threshold.", + "bbox": [ + 496, + 436, + 893, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Navigation policy. Once the long-term goal is identified, the agent simply needs to navigate from its current location $(x_{t},y_{t})$ to the long-term goal $g_{t}$ . Following previous works [5, 37], the local policy is implemented by the Fast Marching Method [41], which calculates the shortest path from current location to the long-term goal based on the occupancy channels of the generated map. Then the local policy calculates deterministic actions for the agent based on its step distance and the shortest path. At each times- tamp, the local policy will re-plan the actions for the agent according to the updated semantic map.", + "bbox": [ + 496, + 513, + 893, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 698, + 633, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 724, + 689, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We evaluate our SGM on standard ObjectNav datasets, including Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49] dataset.", + "bbox": [ + 496, + 748, + 890, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For Gibson and MP3D, we follow the setup of [37, 57], we we utilize 25 train /5 val scenes from the Gibson tiny split and choose 6 goal categories with 1,000 val episodes for Gibson. For MP3D, we employ 56 train / 11 val scenes, 21 goal categories and 2,195 episodes for validation. For HM3D, our setup is consistent with [9], where we choose 80 train / 20 val scenes, 6 goal categories and 2,000 valida", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16418", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/22acd425de35e67dfe8df2ef0a0c86604e212759bdf36fa82cddcbd3cbccb456.jpg", + "table_caption": [ + "Table 1. Comparisons of different map generation variants in the Gibson (val). R/C means the training map is masked by random (R) or connected (C) strategy. The connected masking strategy requires that retained patches must be adjacent to each other (remaining patches are akin to a local map), which is similar to [19, 28] that learn contextual relations by completing the local map. For LLMs, we compare GPT-4 [34] and ChatGLM [17]." + ], + "table_footnote": [], + "table_body": "
IDModelMaskLLMMap GenerationNavigation
IoU(%)Recall(%)SR(%)SPL(%)DTS(m)
I 1UNet--19.2847.3667.537.81.76
2ViT-LC-24.1859.4273.839.51.45
3ViT-LR-26.8579.0574.239.61.49
4ViT-BC-22.3155.5073.139.31.53
5ViT-BR-25.4579.2374.139.51.48
6ViT-BCGPT-432.0672.3476.843.41.27
7ViT-BRGPT-439.4787.3377.443.81.15
8ViT-BCChatGLM30.8780.6777.043.51.31
9ViT-BRChatGLM31.7391.6878.044.01.11
", + "bbox": [ + 78, + 191, + 468, + 385 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion episodes. The goal categories adopted by these three datasets are listed in supplements.", + "bbox": [ + 75, + 398, + 468, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. For evaluating the navigation performance, we adopt three standard metrics following [5, 37, 56]: 1) SR: the ratio of success episodes. 2) SPL: the success rate weighted by the path length, which measures the efficiency of the path length. 3) DTS: the distance to the goal at the end of the episode.", + "bbox": [ + 75, + 430, + 468, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To assess the quality of map predictions, we employ the following two metrics: 1) IoU: the pixel intersection over union for all channels (both occupancy and object). 2) Recall: the proportion of true positive predicted object categories over the total number of ground-truth categories.", + "bbox": [ + 75, + 521, + 468, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. For the self-supervised training of SGM, we sample 400,000 train /1,000 val sub-maps for training and validation in each dataset. We implement the SGM based on ViT-base/16, where the visual encoder, cross-modality encoder and decoder are respectively composed of 8, 4 and 2 Transformer blocks. The training mask ratio is set to $75\\%$ , the input size $L = 224$ , and patch size $\\delta = 16$ . We use the Adam optimizer [25] with a base learning rate of 0.00015. The warmup epoch is linearly scaled when the training epoch increases to 40. After warmup epochs, the learning rate is decayed by a factor of 0.05. The loss weights $\\lambda = 0.2$ .", + "bbox": [ + 75, + 598, + 468, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For ObjectNav task, since constructing local semantic map requires the semantic segmentation model, we adopt publicly available Mask-RCNN [21] from [37] for Gibson, RedNet [23] from [37] for MP3D, and Mask-RCNN [21] from [56] for HM3D. The scaled-up factor $\\epsilon = 140\\%$ , the number of selected patches $n = 59$ , and sample weights $\\alpha = 0.5$ . The experiments for these hyper-parameters are detailed in supplements. The turn angle is set to 30 degrees,", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3b448eed6905672d37daa9586ecece5b821bdc582b4f662966ff145c16c5946e.jpg", + "image_caption": [ + "Figure 4. Map reconstruction results. The 'w/ EO' means only using episodic observations in reconstruction, while 'w/ EO and GK' denotes leveraging both episodic observations and LLMs (ChatGLM). General knowledge enables the model to predict the completely unobserved contextual objects (see the regions highlighted by red circles). These sub-maps sourced from the val rooms of Gibson are unseen during training." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 887, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and the step distance of move_forward is $25\\mathrm{cm}$", + "bbox": [ + 500, + 369, + 834, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Results", + "text_level": 1, + "bbox": [ + 500, + 393, + 679, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons with previous map completion methods. Prior methods [19, 28] train a UNet [40] to directly predict unobserved regions based on the top-down map of a single timestamp. This comparison is to determine whether using UNet or learning contextual relations directly from the local map is more effective than our SGM (utilizing ViT and learning with randomly masked sub-maps). As shown in Tab. 1, we compare these two variants under identical training epochs and datasets. The UNet variant underperforms others in both map generation and navigation. In learning contextual relations, the random masking strategy (SGM) outperforms connected masking strategy [19, 28]. We infer that since visible patches are closely clustered in the connected masking strategy, the context of patches distant from the visible ones is completely absent, leading to difficulties for model in capturing the context relations of these patches during training. The results demonstrate that our SGM is more effective in capturing contextual relationships and assisting the navigation.", + "bbox": [ + 496, + 417, + 890, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model complexity. We compare the impact of more complex models on map generation and navigation. As indicated by the row II in Tab. 1, the more complex model (i.e. ViT Large) only yields a marginal performance improvement. Hence, we conjecture that the ViT Base model is sufficiently capable for the task. Consequently, our SGM is ultimately implemented based on the ViT Base model.", + "bbox": [ + 496, + 704, + 890, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Impact of LLMs. Our SGM not only leverages episodic observations but also incorporates general knowledge obtained from LLMs for prediction. Compared to rows II and III in Tab. 1, there is a significant improvement on the recall metric, which suggests that LLMs can substantially bolster the prediction of object categories. As shown", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16419", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8553ee42d187b371e0a505e69da743016e4735fc9c85bef7f9fe8727ecc20848.jpg", + "image_caption": [ + "Figure 5. Navigation episode with SGM in Gibson (val). The top row displays the agent's RGB view and local semantic map, including the trajectory and long-term goal (indicated by the deep blue dot). The bottom row shows the generated map by SGM. At about $30\\%$ of the navigation process (i.e. $t = 20$ ), the generated map accurately predicts the target's location even though the target has not yet been observed. Besides, SGM not only precisely predicts the target (couch), but also its contextual objects (e.g. potted plant)." + ], + "image_footnote": [], + "bbox": [ + 84, + 97, + 885, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3c1b74e8a5838876325b21c5ec73a473f51470c339a0e539bc31977d5d6400e9.jpg", + "image_caption": [ + "Figure 6. More generated maps during navigation. As shown by the circled objects, the generated map accurately anticipates the location of unobserved objects." + ], + "image_footnote": [], + "bbox": [ + 89, + 309, + 457, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in the Fig. 4, the model with solely episodic observations is capable of completing the contours of partially observed objects, while it struggles to predict entirely unobserved categories. However, the general knowledge from LLMs provides rich semantic contextual priors, enables the model to predict the context objects that are completely unobserved (e.g. the chairs in the first row, and the potted plants and sinks in the second row). Additionally, we compare two LLMs: GPT-4 [34] and ChatGLM [17]. The results show that the choice of LLMs has minimal impact on performance. Moreover, as ChatGLM is publicly available, thus, we employ it to provide general knowledge. To improve inference speed, we extract all possible combinations of goal categories to pre-generate the prompt and obtain responses by using LLMs. The SGM directly leverages pre-extracted", + "bbox": [ + 75, + 674, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0bedc864aee964f11a8db6772b8e5a3d6e5cb7ef959bcfa56a6dc0ece34cfab1.jpg", + "table_caption": [ + "Table 2. Ablation study of different components. GT means the long-term goal is set to the ground truth location of the target. 'EO' denotes the episodic observation, 'GK' represents the general knowledge and 'Explr' means using exploration strategy at the beginning of navigation." + ], + "table_footnote": [], + "table_body": "
IDModulesGibsonMP3D
GTEOGKExplrSR(%)SPL(%)DTS(m)SR(%)SPL(%)
I 21✓91.772.30.38--
2✓71.540.81.4631.912.2
3✓✓74.441.31.4934.713.2
II 64✓65.137.91.7625.911.6
5✓✓74.139.51.4833.011.8
6✓✓78.044.01.1137.614.7
", + "bbox": [ + 509, + 385, + 879, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "responses for prediction during both training and testing.", + "bbox": [ + 498, + 535, + 874, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of navigating with SGM. We further visualize the generated maps of SGM during the navigation, as shown in Fig. 5 and 6, noting that the scenes are unseen. As Fig. 5 illustrated, at the beginning of navigation $(t = 0)$ , the generated image offers limited additional information due to minimal observations. However, as more of the scene becomes observed, by $t = 20$ (only about $30\\%$ of the entire navigation), SGM successfully predicts the location of the target (couch) even though it has not yet been observed. Then, SGM continues to guide the agent by determining the long-term goal based on the generated map. Moreover, it is notable that SGM not only accurately locates the target but also anticipates its context objects (e.g. potted plant). Fig. 6 provides additional generated results, which is evident that the generated maps correctly estimate the approximate locations of objects and their context, while there is still a deviation in their absolute positions. However, we consider this deviation to be tolerable, as even humans cannot precisely locate unseen objects in unseen scenes. These two visualizations indicate that our SGM effectively scales up limited local maps by generating the unobserved regions, thereby guiding the agent to infer the target's location.", + "bbox": [ + 496, + 551, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablations study. As shown in row I of Tab. 2, the agent", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "□blank□floor wall □chair □couch □potted plant □bed □toilet □tv □oven □dining table □sink □refrigerator □book □clock □vase □cup □bottle", + "bbox": [ + 217, + 89, + 754, + 98 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16420", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/804f05992ca774ab9e94350c3d3af05073467191f45d8d74d23305cc91c3c1c8.jpg", + "table_caption": [ + "Table 3. Comparisons with the related works in Gibson and MP3D val. Note that THDA [32] and Habitat-Web [38] use additional data for training, while Red-Rabbit [53] utilizes auxiliary tasks to train the agent. For SemExp [5], L2M [19] and Stubborn [31], we report results from [57]. * denotes our implementation." + ], + "table_footnote": [], + "table_body": "
IDMethodGibsonMP3D
SR(%)SPL(%)DTS(m)SR(%)SPL(%)DTS(m)
1Random0.40.43.890.50.58.05
2DD-PPO [46]15.010.73.248.01.86.94
3Red-Rabbit [53]---34.67.9-
4THDA [32]---28.411.05.62
I5SSCNav* [28]---27.111.25.71
6EmbCLIP* [24]68.139.51.1529.210.15.42
7Habitat-Web [38]---35.410.2-
8ENTL [26]---17.05.0-
9FBE [50]48.528.92.5629.510.65.00
10ANS [7]67.134.91.6621.29.46.31
11SemExp [5]71.139.61.3928.310.96.06
II12PONI [37]73.641.01.2527.812.05.63
13L2M [19]---32.111.05.12
14Stubborn [31]---31.213.55.01
153D-aware [57]74.542.11.1634.014.64.78
16SGM (Ours)78.044.01.1137.714.74.93
", + "bbox": [ + 78, + 164, + 470, + 444 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "only relying on SGM has already achieved comparable performance to some supervised methods [5, 37]. Furthermore, the row II of Tab. 2 indicates that introducing an exploration strategy in the early stages of navigation is effective, which prevents misguidance by low-confidence predictions resulted from limited observations. Our exploration strategy utilizes the area potential function from [37], which calculates the nearest frontier as the long-term goal. In contrast to the computation-based FBE [50], the area potential function learns to predict potential frontiers through supervised training. The ablation studies demonstrate the effectiveness of each component in our method.", + "bbox": [ + 75, + 459, + 468, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparisons with the related works. Since there is no existing self-supervised work for ObjectNav task, our comparison is limited to previous supervised methods. We consider the following baselines: the end-to-end RL methods [9, 24, 26, 28, 32, 46, 53], the imitation learning method [38], and modular methods [5, 6, 19, 31, 37, 50, 56, 57] Note that, some works leverage additional data [10, 32, 38] or auxiliary task [9, 53] to improve the performance. Thus, it is challenging to compare all the methods in an equitable manner. Consequently, our focus is specifically on the most relevant baselines: SemExp [5], PONI [37], L2M [19], SSCNav [28], PEANUT [56], where PONI and PEANUT integrate goal-related function trained by supervised learning into SemExp, while L2M and SSCNav enhance navigation performance by learning to complete egocentric top-down map of single timestamp. They are also trained with supervised learning, while are limited to consider only single-", + "bbox": [ + 75, + 643, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d1bc8e6bfb62abf3944f07f269de4746d61ed242096cd746b37a6f3392cab702.jpg", + "table_caption": [ + "Table 4. Comparisons with the related works in HM3D val. * denotes our implementation." + ], + "table_footnote": [], + "table_body": "
IDMethodHM3D
SR(%)SPL(%)
1DD-PPO [46]27.914.2
2Habitat-Web [38]57.623.8
3RIM [9]57.827.2
4PEANUT* [56]59.130.3
5SGM (Ours)60.230.8
", + "bbox": [ + 550, + 123, + 839, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "frame observations. In contrast, our SGM predicts the unobserved regions for the broader local map, which incorporates full observations from time 0 to t. Notably, PEANUT [56] initially reports results on MP3D and HM3D, however, they only release their code for HM3D. Therefore, we only compare with [56] on HM3D with re-implementation results in our setup. Besides, L2M and SSCNav are evaluated with their self-made validation data. Thus, for comparing their results, we report our own implementations or adopt re-implementation results from other work [57] with experimental settings that align with ours.", + "bbox": [ + 496, + 248, + 890, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our SGM with the related works on the validation set of Gibson, MP3D and HM3D datasets, as shown in Tab. 3 and 4. Despite our SGM being self-supervised, it achieves comparable performance with existing supervised methods across all metrics on these datasets. Particularly on the Gibson dataset, compared to the current state-of-the-art [57], our SGM outperforms 3D-aware [57] by $3.5\\%$ , $1.9\\%$ , and $-0.05\\mathrm{m}$ in SR, SPL and DTS metrics, respectively. Note that lower value on DTS indicates better performance.", + "bbox": [ + 496, + 415, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 568, + 627, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present the Self-supervised Generative Map (SGM) for the object goal navigation task. Our SGM captures contextual relationships of both objects and environments through self-supervised training. SGM utilizes two distinct yet complementary information for prediction: episodic observations and general knowledge from Large Language Models (LLMs), where episodic observations provide geometric details, and general knowledge offers semantic priors. During navigation, the local semantic map maintained by agent is sampled by proposed sampling strategy to select informative patches. Then the selected patches are fed into SGM to generate the unobserved regions. The generated map helps agent infer the likely location of the target. The experimental results indicate that despite being a self-supervised method, our SGM achieves comparable performance to previous supervised methods.", + "bbox": [ + 496, + 594, + 890, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U23B2012, in part by Beijing Natural Science Foundation under Grant JQ22012, Z190020.", + "bbox": [ + 498, + 844, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16421", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. Beit: BERT pre-training of image transformers. 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In 2017 IEEE International Conference on" + ], + "bbox": [ + 501, + 92, + 890, + 901 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16424", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + }, + { + "type": "header", + "text": "Robotics and Automation, ICRA 2017, Singapore, Singapore, May 29 - June 3, 2017, pages 3357-3364, 2017. 2", + "bbox": [ + 109, + 90, + 468, + 119 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "16425", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_model.json b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_model.json new file mode 100644 index 0000000000000000000000000000000000000000..609b3e98e34ede50f435367fed330778acba07ab --- /dev/null +++ b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_model.json @@ -0,0 +1,2116 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.131, + 0.892, + 0.155 + ], + "angle": 0, + "content": "Imagine Before Go: Self-Supervised Generative Map for Object Goal Navigation" + }, + { + "type": "text", + "bbox": [ + 0.147, + 0.18, + 0.823, + 0.2 + ], + "angle": 0, + "content": "Sixian Zhang\\(^{1,2}\\), Xinyao Yu\\(^{1,2}\\), Xinhang Song\\(^{1,2}\\), Xiaohan Wang\\(^{1}\\), Shuqiang Jiang\\(^{1,2,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.177, + 0.201, + 0.794, + 0.234 + ], + "angle": 0, + "content": "1Key Lab of Intelligent Information Processing Laboratory of the Chinese Academy of Sciences (CAS), Institute of Computing Technology, Beijing, 2University of Chinese Academy of Sciences, Beijing" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.236, + 0.671, + 0.251 + ], + "angle": 0, + "content": "3 Institute of Intelligent Computing Technology, Suzhou, CAS" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.255, + 0.868, + 0.27 + ], + "angle": 0, + "content": "{sixian.zhang, xinyao.yu, xinhang.song, xiaohan.wang}@vipl.ict.ac.cn, sqjiang@ict.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.336, + 0.474, + 0.699 + ], + "angle": 0, + "content": "The Object Goal navigation (ObjectNav) task requires the agent to navigate to a specified target in an unseen environment. Since the environment layout is unknown, the agent needs to infer the unknown contextual objects from partially observations, thereby deducing the likely location of the target. Previous end-to-end RL methods capture contextual relationships through implicit representations while they lack notion of geometry. Alternatively, modular methods construct local maps for recording the observed geometric structure of unseen environment, however, lacking the reasoning of contextual relation limits the exploration efficiency. In this work, we propose the self-supervised generative map (SGM), a modular method that learns the explicit context relation via self-supervised learning. The SGM is trained to leverage both episodic observations and general knowledge to reconstruct the masked pixels of a cropped global map. During navigation, the agent maintains an incomplete local semantic map, meanwhile, the unknown regions of the local map are generated by the pretrained SGM. Based on the generated map, the agent sets the predicted location of the target as the goal and moves towards it. Experiments on Gibson, MP3D and HM3D show the effectiveness of our method. The code is available at https://github.com/sx-zhang/SGM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.725, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Navigating to specified targets [27, 44, 45, 55] is an essential capability for embodied AI systems to effectively manipulate and interact with real-world entities. Consequently, the visual object goal navigation (ObjectNav) task has recently gained widespread attention. In ObjectNav task, the agent is placed in an unseen and unmapped environment, and is tasked to navigate to an object of the user-specific category (e.g. couch) based on the visual observations. Since the environment is unseen, when the target is invisible, the agent needs to infer the likely location of the target. This" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.304, + 0.887, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.562, + 0.894, + 0.632 + ], + "angle": 0, + "content": "Figure 1. Agents employ SGM to 'imagine' details of unobserved regions during navigation. The SGM is trained in a self-supervised manner by predicting pixels in masked regions of sub-maps to capture contextual relations. The SGM leverages both episodic observations and general knowledge for map reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.893, + 0.716 + ], + "angle": 0, + "content": "requires the agent to learn and understand the contextual relationships between objects (e.g. couches typically appear with cushions and coffee tables), which enables it to deduce the target's location based on observed visual clues." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To learn the contextual relations, end-to-end reinforcement learning (RL) methods embed pre-constructed object relation graph [52, 54, 59] into the end-to-end navigation models, or learn object associations directly via the RL [14, 15, 33]. These pre-learned priors are implicitly encoded within the policy. However, since the priors are episode-agnostic and lack geometric memory of current environment, the end-to-end RL methods exhibit limited generalization in unseen environments [32, 60]. Alternatively, modular methods [5-7] construct an explicit semantic local map, merging observed geometry and semantics of the unseen environment. The agent can disregard the observed" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16414" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.15 + ], + "angle": 0, + "content": "regions of the local map, where the target has not appeared, which simplifies the potential state space that needs to be explored. However, without learning the contextual object relation, the modular methods are still limited." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.157, + 0.468, + 0.534 + ], + "angle": 0, + "content": "Recently, some methods [37, 56, 61] attempt to introduce priors of object contextual relationships into modular methods for predicting the long-term goal. They learn the contextual relation based on the local map by predicting the potential frontier nearest to the target [37], estimating the distance to the target [61], or directly anticipating the coordinate of the target [56]. However, individually learning the relations of targets with supervised learning may not be reliable, as the absolute position of targets may vary with different room layouts. In contrast, the joint associative relations among multiple objects are more reliable, e.g. chairs, tables, and cups are commonly found together, similarly, couches, cushions, and coffee tables often appear in conjunction. Therefore, we propose learning the joint contextual relations of the objects in a self-supervised manner: without any need for data collection and labeling as supervised learning, the model is trained to reconstruct the masked regions of a cropped global map based on its visible neighboring regions. This preparatory phase allows it to grasp not only individual object specifics (e.g. location and size) but also the patterns of its contextual companions (i.e. contextual object relation) and the surrounding environments (e.g. potential obstacle and free path). Then the trained model can 'imagine' unobserved regions during navigation to help agent deduce the target location." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.54, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In this paper, we propose self-supervised generative map (SGM) to scale up the coverage of the local map by generating the unobserved regions, as shown in Fig. 1. Specifically, given the global map of a training room, the global map is cropped into sub-maps with boxes of various scales, positions and angles, then uniformly resized to a fixed scale. Following the self-supervised learning settings of MAE [22], certain patches of the sub-maps are randomly masked. Our SGM is trained to predict the pixel values of the masked patches by leveraging both episodic observations and general knowledge. The episodic observations refer to the visible patches, which are encoded with a visual encoder, akin to many visual pre-training studies [8, 22]. However, contrary to image datasets, the quantity and diversity of training scenes for ObjectNav is notably limited. To enhance the generalization, general knowledge provided by Large Language Models (LLMs) is also considered. Visible patches are transformed into prompts for LLMs through a textual template, subsequently, LLMs (e.g. GPT-4 [34], ChatGLM [17]) predict the semantic contents of the masked patches in text. Furthermore, text predictions (general knowledge) and episodic observations merge via a cross-modality encoder. The decoder predicts the pixel values of the masked patches based on the encoded information. Episodic ob" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.891, + 0.151 + ], + "angle": 0, + "content": "servations and general knowledge are orthogonal and complementary, where episodic observations provide more geometric details, while general knowledge with rich semantic prior enhances the inference of contextual categories." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.153, + 0.891, + 0.424 + ], + "angle": 0, + "content": "During navigation, the agent maintains a local semantic map that integrates observations of current unseen environment. Since the local map is incomplete, the trained SGM is employed to generate the unobserved regions of the local map. The local map is initially divided into non-overlapping patches. Then we propose a sample strategy that prioritizes the patches, which are informative or adjacent to unobserved regions. The selected patches are input into the SGM to predict the pixel values of the unknown regions. The agent selects the coordinates with the highest confidence of the target in the generated map as the long-term goal. The SGM continually generates the unknown regions based on updated local map until the target is found. We evaluate our SGM on photorealistic 3D environments of Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49]. The experimental results demonstrate the effectiveness of our SGM in generating unknown regions and assisting the agent in inferring the location of the target." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.438, + 0.647, + 0.453 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.464, + 0.891, + 0.899 + ], + "angle": 0, + "content": "ObjectGoal navigation. Existing visual object goal navigation can be categorized into: end-to-end methods and modular methods. The end-to-end methods learn to navigate by leveraging reinforcement learning (RL) [47, 58, 62] or imitation learning (IL) [38, 39]. Previous end-to-end RL methods attempt to learn object relation graph [14, 52, 54, 59], visual representation [24, 26, 33], historical states representation [16], auxiliary tasks [53] and data augmentation [10, 32] to enhance the navigation ability. To learn the contextual object relation for enhancing the deducing for target location, [52] constructs prior knowledge of object relations from external datasets [29], and [59] builds hierarchical object-to-zone graph. [14] proposes learning the object relations (i.e. the edges of predefined graph) by RL process. The learned contextual relations are implicitly encoded into the end-to-end model. However, lack of geometry memory and low sample efficiency of RL, the generalization of these methods in unseen environments remains limited. The modular methods [5-7] maintain a geometry semantic map for localization, memory and path planning. Recent modular methods [37, 56, 61] aim to address 'where to look?' subproblem (i.e. inferring the likely location of the target). These methods employ supervised learning to learn a target-related function. Based on a local map, they predict the nearest frontier to target [37], the minimal distance to target [61] or the absolute coordinates [56] of the target. Our SGM is also a modular method, while we learn joint contextual relations, i.e. the SGM predicts the unobserved regions, which contain both objects (not limited to" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16415" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.442, + 0.107 + ], + "angle": 0, + "content": "target) and environments with self-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.47, + 0.319 + ], + "angle": 0, + "content": "Several recent works attempt to predict the unobserved regions. [36] proposes to anticipate occupancy for point goal navigation. [19] takes a further step by adding the semantic prediction via two-stage segmentation models. [28] also predicts the unobserved semantic map, while implicitly encoding it into an RL-based policy. All of these works [19, 28, 36] only predict unobserved regions of a top-down map projected from the egocentric RGB-D view at a single timestamp. However, our SGM has a wider prediction scope as it predicts based on a broader local map, which integrates all historical observations. Additionally, it is worth to highlight that our SGM is trained through self-supervised learning, which avoids the tedious data collection and annotation of imitation and supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.532 + ], + "angle": 0, + "content": "Self-supervised learning. Reconstructing signals from masked inputs has been validated as an effective self-supervised learning within the communities of NLP [2, 12, 35], CV [1, 13, 22], and multimodal pretraining [43]. We adopt the settings of Masked Autoencoders (MAE) [22] to train our SGM, which has demonstrated its robust capacity for learning contextual associations in many visual tasks [8, 18, 51]. Recently, there are few self-supervised works for goal-oriented navigation tasks. [20] proposes a distance estimator from passive videos through self-supervised learning for image goal navigation. Our SGM is proposed for ObjectNav task, which learns the contextual object relation by self-supervised learning, thereby generating the map of unobserved regions during navigation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.548, + 0.185, + 0.565 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.231, + 0.589 + ], + "angle": 0, + "content": "3.1. Task Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.824 + ], + "angle": 0, + "content": "The ObjectNav task is defined as: the agent is required to navigate to an instance of a specified object category (e.g. potted plant) in an unseen environment. The agent is placed at a random location at the start of an episode. At each timestamp \\( t \\), the agent receives egocentric RGB-D observations \\( s_t \\), target object \\( o \\) and senor pose \\( (x_t, y_t, \\theta_t) \\), where \\( x_t, y_t \\) and \\( \\theta_t \\) denote coordinates and orientation of the agent. The agent executes a discrete action, where the action space consists of move_forward, turn_left, turn_right and stop. The agent autonomously executes the action stop when it determines to complete the task. A successful episode is denoted as that, within certain number of steps, the agent stops at a position where the distance to the target is less than a threshold (e.g. 1m) and the target is visible in the egocentric observation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Our method is constructed based on the modular ObjectNav architecture. The modular methods typically build an accumulating semantic map during navigation [5] based on the RGB-D observations, sensor poses and segmentation models [21, 23]. The semantic map \\( m_{t} \\in \\mathbb{R}^{(N_{o} + N_{s}) \\times H \\times W} \\)" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.09, + 0.885, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.316, + 0.895, + 0.4 + ], + "angle": 0, + "content": "Figure 2. Self-supervised training of SGM. 'Self', 'Cross' and 'FF' denotes self-attention, cross-attention and feed-forward layers, respectively. The SGM is trained to predict the pixel value of the masked patches by utilizing episodic observations and the general knowledge from LLMs. Examples of responses from LLMs are detailed in the supplements." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.413, + 0.895, + 0.581 + ], + "angle": 0, + "content": "utilizes multiple channels to represent different classes, where \\( N_{o} \\) denotes the number occupancy classes including occupied and free, \\( N_{s} \\) is the number of object classes and \\( H, W \\) are the map size. The semantic map aggregates the observed object layout of the unseen environment from 0 to \\( t \\). However, since the semantic map is obtained only by partial observations of the entire environment, it is only a subset (i.e. local map) of the global map. Therefore, when the target is invisible, the agent needs to estimate its unobserved surroundings based on the learned context relation of the objects to infer the likely location of the target." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.783, + 0.607 + ], + "angle": 0, + "content": "3.2. Self-supervised Generative Map" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.704 + ], + "angle": 0, + "content": "To predict the potential position of the target, the contextual relations between objects can be used to generate the unseen regions of local maps. In particular, we propose the self-supervised generative map (SGM) to learn the context relations of both objects and environments (e.g. obstacle and free path) with the self-supervised setting of MAE [22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.825 + ], + "angle": 0, + "content": "As shown in Fig. 1, given a global map of a training room, we first crop and sample a number of sub-maps from it using several boxes in various scales, positions and angles. Then the sub-maps are resized to a fixed scale and divided into non-overlapping patches. These patches are sampled without replacement by a uniform distribution strategy. The selected patches serve as the visible patches \\( m_{s} \\), while the remaining patches \\( m_{u} \\) are masked." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To learn the contextual relation, the SGM \\( P(m_u|m_s) \\) is trained in a self-supervised manner by reconstructing the masked patches \\( m_{u} \\) based on their visible neighboring patches \\( m_{s} \\). As shown in Fig. 2, the proposed SGM reconstructs the masked patches by leveraging the following" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16416" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "two aspects of information: 1) episodic observations, and 2) general knowledge from large language models (LLMs)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.302 + ], + "angle": 0, + "content": "Episodic observations. The visible patches are embedded with a linear projection and added with positional embeddings, and then processed with the visual encoder \\( E_{v} \\). The visual encoder is implemented by several Transformer blocks of ViT [13], consisting of self-attention and feedforward layers. Then the episodic observations are embedded as \\( E_{v}(m_{s}) = f_{v} \\in \\mathbb{R}^{n_{v} \\times n_{d}} \\), where \\( n_{v} \\) is the number of visible patches and \\( n_{d} \\) is the feature dimension. Following [22], the encoder only operates the visible patches, rather than all patches. Therefore, when the ratio of visible patches is small (e.g. 25%), the encoder consumes minimal computing and memory resources." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.483 + ], + "angle": 0, + "content": "General knowledge. Due to limited training environments, the quantity and diversity of available global maps for training is considerably less than that of image datasets [11, 29]. As a result, models trained merely on visual clues are prone to overfitting to the limited training environments, leading to poor generalization to unseen environments [32]. Currently, the LLMs demonstrate strong reasoning abilities on many complex tasks [3]. In our work, we employ the LLMs (e.g. GPT-4 [34], ChatGLM [17]) to provide general knowledge for reasoning the contextual relation and predicting the probable objects, thereby enhancing generalization for unseen environments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.468, + 0.756 + ], + "angle": 0, + "content": "For all visible patches, an object category is considered as observed if there is a pixel with the value of 1 existing in the corresponding channel. Then we fill in the observed categories into a fixed sentence template to generate the text prompt for LLMs. For instance, when couches and chairs are observed, the generated prompt is 'In an indoor environment, if couches and chairs are observed, what other objects might be around them? Answer in one sentence.' The LLMs receive the text prompt and predict the probable neighboring categories around the observed categories. The predictions \\(L(m_{s})\\) of LLMs are further processed by Tokenizer and embedded with pre-trained RoBERTa [30] by \\(E_{L}(L(m_{s})) = f_{l}\\in \\mathbb{R}^{n_{l}\\times n_{d}}\\), where \\(n_l\\) is the token number. Since LLMs are trained on massive data, the prediction \\(f_{l}\\) can be regarded as an episode-agnostic, general knowledge. General knowledge \\(f_{l}\\) provides a wealth of semantic priors, which is orthogonal and complementary to episodic observation \\(f_{v}\\) that captures geometric details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.468, + 0.832 + ], + "angle": 0, + "content": "Fusion and anticipation. We utilize the cross-modality encoder of LXMERT [42] to fuse \\( f_{v} \\) and \\( f_{l} \\), which consists of cross-attention, self-attention and feed-forward layers. The cross-attention layers are used to fuse the information between \\( f_{v} \\) and \\( f_{l} \\), which is formally given by" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.838, + 0.468, + 0.88 + ], + "angle": 0, + "content": "\\[\nC r o s s A t t n \\left(f _ {v}, f _ {l}\\right) = \\sigma \\left(\\frac {f _ {v} W _ {q} \\left(f _ {l} W _ {k}\\right) ^ {T}}{\\sqrt {n _ {d}}}\\right) f _ {l} W _ {v} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is the Softmax activation function, and \\(W_{*} \\in\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.891, + 0.136 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{n_d\\times n_d}\\) are learned parameters and biases are omitted. The output of the cross-modality encoder serves as the final embedding for all visible patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.241 + ], + "angle": 0, + "content": "The decoder takes full patches (i.e. encoded visible patches and masked patches) as the inputs, where the masked patches are initialized to the learnable vectors of the same size as the encoded visible patches. All patches are added with positional embeddings that represent their spatial locations. The decoder is also implemented by a series of Transformer blocks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Training. The SGM is trained to predict the pixel value of the masked patches. Given the prediction \\( m_{u} \\), the training objective for all classes (i.e. occupancy and object classes) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.312, + 0.892, + 0.351 + ], + "angle": 0, + "content": "\\[\nL _ {B C E} = \\frac {1}{n _ {u}} \\sum_ {i = 0} ^ {n _ {u}} B C E \\left(m _ {u} (i), \\hat {m} _ {u} (i)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.481 + ], + "angle": 0, + "content": "where \\( BCE \\) denotes the pixel-wise binary cross entropy loss and \\( n_u \\) is the number of masked patches. \\( m_u(i) \\in \\mathbb{R}^{(N_o + N_s) \\times \\delta \\times \\delta} \\) represents one of the predicted patches, where \\( \\delta \\) is the size of a patch. \\( \\hat{m}_u(i) \\) is the ground-truth of the masked patches, and each pixel of \\( \\hat{m}_u(i) \\) is a binary value. Additionally, to enhance the accuracy of predicting the position and size of objects, an IoU loss is added specifically for the object classes" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.489, + 0.891, + 0.529 + ], + "angle": 0, + "content": "\\[\nL _ {I o U} = \\frac {1}{n _ {u}} \\sum_ {i = 0} ^ {n _ {u}} I o U \\left(m _ {u} (i, N ^ {s}), \\hat {m} _ {u} (i, N ^ {s})\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.718 + ], + "angle": 0, + "content": "where \\( IoU \\) denotes the category-level pixel-wise intersection over union loss, and \\( m_u(i,N^s) \\in \\mathbb{R}^{N_s \\times \\delta \\times \\delta} \\) only contains the object classes. We add up all the losses to train our SGM. The overall training objective is \\( L = L_{BCE} + \\lambda L_{IoU} \\), where \\( \\lambda \\) denotes the loss weights. The advantages of our SGM are as following: 1) Data collection. The self-supervised training eliminates the requirement for target-oriented annotations or supervision from simulators. SGM requires only training with cropped and randomly masked global maps. 2) Scalability. SGM is compatible with various LLMs, allowing for concurrent improvements in our method as LLMs advance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.702, + 0.743 + ], + "angle": 0, + "content": "3.3. ObjectNav with SGM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.81 + ], + "angle": 0, + "content": "The trained SGM is capable of generating unobserved regions based on their visible surroundings, which is utilized to help agent deduce the unobserved regions of the local maps during navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Unobserved regions generation. At each timestamp \\( t \\) during navigation, the agent constructs a local semantic map \\( m_t \\) (as introduced in Sec. 3.1), and each channel of \\( m_t \\) contains binary-valued pixels. The local semantic map includes numerous unobserved regions as shown in Fig. 3, where the pixel values of these regions are 0 across all channels." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16417" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.287 + ], + "angle": 0, + "content": "Given the local semantic map \\( m_{t} \\) of time \\( t \\), we first crop a sub-region of \\( m_{t} \\), where the size of this region is \\( \\epsilon \\) times that of the smallest fitting square box around the known regions of \\( m_{t} \\) as shown in Fig. 3. The \\( \\epsilon \\) (e.g. \\( \\epsilon = 140\\% \\) is decided via validation experiments) represents a scaled-up factor with a minimum value of \\( 100\\% \\). The cropped region is resized to a fixed scale \\( m_{t}^{\\prime} \\in \\mathbb{R}^{(N_{o} + N_{s}) \\times L \\times L} \\) (e.g. \\( L = 224 \\) for ViT-Base) and divided into non-overlapping patches. The size of each patch is \\( \\delta \\). To eliminate noise and reduce computational complexity, we select a subset of patches to serve as the input of the SGM. The sampling strategy prioritizes the patches, which are 1) informative and 2) adjacent to unobserved regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.486 + ], + "angle": 0, + "content": "To construct the sampling strategy, we calculate the average pixel value in each patch by \\( W = \\text{Avgpool}(m_t') \\), where \\( W \\in \\mathbb{R}^{\\frac{L}{\\delta} \\times \\frac{L}{\\delta}} \\), and Avgpool represents the average pooling in each patch for all channels. For each element \\( w_i \\in W \\), the higher value indicates that the corresponding patch is more informative, i.e., there are more observed object classes or larger observed regions in this patch. Furthermore, we leverage the Laplacian kernel \\( K \\) as a gradient operator (i.e., edge detector), to operate the \\( W \\) by \\( V = \\text{Conv}(W, K) \\), where \\( V \\in \\mathbb{R}^{\\frac{L}{\\delta} \\times \\frac{L}{\\delta}} \\) and Conv denotes the convolution operation. The higher value of \\( v_i \\in V \\) demonstrates that the corresponding patch is more likely to be adjacent to the unobserved regions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.486, + 0.471, + 0.532 + ], + "angle": 0, + "content": "The \\(W\\) and \\(V\\) are further processed by flattening and Softmax operations for probability normalization. Then the sampling probability \\(P\\) of each patch is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.541, + 0.47, + 0.559 + ], + "angle": 0, + "content": "\\[\nP = \\alpha \\bar {W} + (1 - \\alpha) \\bar {V} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.568, + 0.47, + 0.704 + ], + "angle": 0, + "content": "where \\(\\bar{W}\\) and \\(\\bar{V}\\) denote the normalized \\(W\\) and \\(V\\), respectively, and \\(\\alpha\\) is a trade-off weight. We employ a multinomial distribution for sampling patches. Specifically, given a set of patches \\(m_t' = \\{m_t'(1), m_t'(2), \\ldots, m_t'(n_p)\\}\\) (\\(n_p = \\left(\\frac{L}{\\delta}\\right)^2\\)), and their associated probabilities \\(P = \\{p_1, p_2, \\ldots, p_{n_p}\\}\\). The patches are sampled without replacement according to \\(m_t'(i) \\sim \\text{Multinomial}(n, P)\\). The number of sampled patches \\(n\\) constitutes only a small fraction (e.g. \\(30\\%\\)) of the total." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Based on this strategy, sampled patches are fed into the SGM to predict unobserved regions. The predicted values are continuous, which reflect the confidence in its prediction. Furthermore, the raw prediction of SGM is enhanced by adding the actual local semantic map to form the final generated map, where if a coordinate has already been observed (having values in semantic map), its predicted value is replaced with the confirmed observed value. During ObjectNav task, the agent identifies the pixel with the highest confidence in the target's channel of the generated semantic map. Then the coordinates of this pixel are set as the long-term goal \\( g_{t} \\). Additionally, limited observation (e.g. no available contextual object is observed) may result in" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.089, + 0.885, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.352, + 0.895, + 0.423 + ], + "angle": 0, + "content": "Figure 3. During navigation, the agent builds a local semantic map \\( m_t \\) and crops it to \\( m_t' \\). The patches of \\( m_t' \\) are sampled by multinomial distribution with probability \\( P \\). The SGM generates the unobserved regions based on selected \\( n \\) patches. The long-term goal is determined by the generated map and the target." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.895, + 0.514 + ], + "angle": 0, + "content": "unreliable prediction of the target (i.e. the confidence of the predicted semantic map is low). Therefore, we adopt the exploration strategy [31, 50] at the beginning of navigation until the prediction confidence of the target exceeds a certain threshold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.895, + 0.683 + ], + "angle": 0, + "content": "Navigation policy. Once the long-term goal is identified, the agent simply needs to navigate from its current location \\((x_{t},y_{t})\\) to the long-term goal \\(g_{t}\\). Following previous works [5, 37], the local policy is implemented by the Fast Marching Method [41], which calculates the shortest path from current location to the long-term goal based on the occupancy channels of the generated map. Then the local policy calculates deterministic actions for the agent based on its step distance and the shortest path. At each times- tamp, the local policy will re-plan the actions for the agent according to the updated semantic map." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.699, + 0.634, + 0.716 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.691, + 0.741 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Dataset. We evaluate our SGM on standard ObjectNav datasets, including Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49] dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "For Gibson and MP3D, we follow the setup of [37, 57], we we utilize 25 train /5 val scenes from the Gibson tiny split and choose 6 goal categories with 1,000 val episodes for Gibson. For MP3D, we employ 56 train / 11 val scenes, 21 goal categories and 2,195 episodes for validation. For HM3D, our setup is consistent with [9], where we choose 80 train / 20 val scenes, 6 goal categories and 2,000 valida" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16418" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.188 + ], + "angle": 0, + "content": "Table 1. Comparisons of different map generation variants in the Gibson (val). R/C means the training map is masked by random (R) or connected (C) strategy. The connected masking strategy requires that retained patches must be adjacent to each other (remaining patches are akin to a local map), which is similar to [19, 28] that learn contextual relations by completing the local map. For LLMs, we compare GPT-4 [34] and ChatGLM [17]." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.193, + 0.47, + 0.386 + ], + "angle": 0, + "content": "
IDModelMaskLLMMap GenerationNavigation
IoU(%)Recall(%)SR(%)SPL(%)DTS(m)
I 1UNet--19.2847.3667.537.81.76
2ViT-LC-24.1859.4273.839.51.45
3ViT-LR-26.8579.0574.239.61.49
4ViT-BC-22.3155.5073.139.31.53
5ViT-BR-25.4579.2374.139.51.48
6ViT-BCGPT-432.0672.3476.843.41.27
7ViT-BRGPT-439.4787.3377.443.81.15
8ViT-BCChatGLM30.8780.6777.043.51.31
9ViT-BRChatGLM31.7391.6878.044.01.11
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.43 + ], + "angle": 0, + "content": "tion episodes. The goal categories adopted by these three datasets are listed in supplements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.521 + ], + "angle": 0, + "content": "Evaluation metrics. For evaluating the navigation performance, we adopt three standard metrics following [5, 37, 56]: 1) SR: the ratio of success episodes. 2) SPL: the success rate weighted by the path length, which measures the efficiency of the path length. 3) DTS: the distance to the goal at the end of the episode." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.599 + ], + "angle": 0, + "content": "To assess the quality of map predictions, we employ the following two metrics: 1) IoU: the pixel intersection over union for all channels (both occupancy and object). 2) Recall: the proportion of true positive predicted object categories over the total number of ground-truth categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Implementation details. For the self-supervised training of SGM, we sample 400,000 train /1,000 val sub-maps for training and validation in each dataset. We implement the SGM based on ViT-base/16, where the visual encoder, cross-modality encoder and decoder are respectively composed of 8, 4 and 2 Transformer blocks. The training mask ratio is set to \\(75\\%\\), the input size \\(L = 224\\), and patch size \\(\\delta = 16\\). We use the Adam optimizer [25] with a base learning rate of 0.00015. The warmup epoch is linearly scaled when the training epoch increases to 40. After warmup epochs, the learning rate is decayed by a factor of 0.05. The loss weights \\(\\lambda = 0.2\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.904 + ], + "angle": 0, + "content": "For ObjectNav task, since constructing local semantic map requires the semantic segmentation model, we adopt publicly available Mask-RCNN [21] from [37] for Gibson, RedNet [23] from [37] for MP3D, and Mask-RCNN [21] from [56] for HM3D. The scaled-up factor \\(\\epsilon = 140\\%\\), the number of selected patches \\(n = 59\\), and sample weights \\(\\alpha = 0.5\\). The experiments for these hyper-parameters are detailed in supplements. The turn angle is set to 30 degrees," + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.888, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.259, + 0.895, + 0.357 + ], + "angle": 0, + "content": "Figure 4. Map reconstruction results. The 'w/ EO' means only using episodic observations in reconstruction, while 'w/ EO and GK' denotes leveraging both episodic observations and LLMs (ChatGLM). General knowledge enables the model to predict the completely unobserved contextual objects (see the regions highlighted by red circles). These sub-maps sourced from the val rooms of Gibson are unseen during training." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.37, + 0.835, + 0.385 + ], + "angle": 0, + "content": "and the step distance of move_forward is \\(25\\mathrm{cm}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.395, + 0.681, + 0.41 + ], + "angle": 0, + "content": "4.2. Evaluation Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Comparisons with previous map completion methods. Prior methods [19, 28] train a UNet [40] to directly predict unobserved regions based on the top-down map of a single timestamp. This comparison is to determine whether using UNet or learning contextual relations directly from the local map is more effective than our SGM (utilizing ViT and learning with randomly masked sub-maps). As shown in Tab. 1, we compare these two variants under identical training epochs and datasets. The UNet variant underperforms others in both map generation and navigation. In learning contextual relations, the random masking strategy (SGM) outperforms connected masking strategy [19, 28]. We infer that since visible patches are closely clustered in the connected masking strategy, the context of patches distant from the visible ones is completely absent, leading to difficulties for model in capturing the context relations of these patches during training. The results demonstrate that our SGM is more effective in capturing contextual relationships and assisting the navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Model complexity. We compare the impact of more complex models on map generation and navigation. As indicated by the row II in Tab. 1, the more complex model (i.e. ViT Large) only yields a marginal performance improvement. Hence, we conjecture that the ViT Base model is sufficiently capable for the task. Consequently, our SGM is ultimately implemented based on the ViT Base model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Impact of LLMs. Our SGM not only leverages episodic observations but also incorporates general knowledge obtained from LLMs for prediction. Compared to rows II and III in Tab. 1, there is a significant improvement on the recall metric, which suggests that LLMs can substantially bolster the prediction of object categories. As shown" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16419" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.218, + 0.09, + 0.756, + 0.099 + ], + "angle": 0, + "content": "□blank□floor wall □chair □couch □potted plant □bed □toilet □tv □oven □dining table □sink □refrigerator □book □clock □vase □cup □bottle" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.098, + 0.887, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.247, + 0.893, + 0.304 + ], + "angle": 0, + "content": "Figure 5. Navigation episode with SGM in Gibson (val). The top row displays the agent's RGB view and local semantic map, including the trajectory and long-term goal (indicated by the deep blue dot). The bottom row shows the generated map by SGM. At about \\(30\\%\\) of the navigation process (i.e. \\(t = 20\\)), the generated map accurately predicts the target's location even though the target has not yet been observed. Besides, SGM not only precisely predicts the target (couch), but also its contextual objects (e.g. potted plant)." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.31, + 0.458, + 0.615 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.621, + 0.47, + 0.665 + ], + "angle": 0, + "content": "Figure 6. More generated maps during navigation. As shown by the circled objects, the generated map accurately anticipates the location of unobserved objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "in the Fig. 4, the model with solely episodic observations is capable of completing the contours of partially observed objects, while it struggles to predict entirely unobserved categories. However, the general knowledge from LLMs provides rich semantic contextual priors, enables the model to predict the context objects that are completely unobserved (e.g. the chairs in the first row, and the potted plants and sinks in the second row). Additionally, we compare two LLMs: GPT-4 [34] and ChatGLM [17]. The results show that the choice of LLMs has minimal impact on performance. Moreover, as ChatGLM is publicly available, thus, we employ it to provide general knowledge. To improve inference speed, we extract all possible combinations of goal categories to pre-generate the prompt and obtain responses by using LLMs. The SGM directly leverages pre-extracted" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.31, + 0.893, + 0.38 + ], + "angle": 0, + "content": "Table 2. Ablation study of different components. GT means the long-term goal is set to the ground truth location of the target. 'EO' denotes the episodic observation, 'GK' represents the general knowledge and 'Explr' means using exploration strategy at the beginning of navigation." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.386, + 0.88, + 0.525 + ], + "angle": 0, + "content": "
IDModulesGibsonMP3D
GTEOGKExplrSR(%)SPL(%)DTS(m)SR(%)SPL(%)
I 21✓91.772.30.38--
2✓71.540.81.4631.912.2
3✓✓74.441.31.4934.713.2
II 64✓65.137.91.7625.911.6
5✓✓74.139.51.4833.011.8
6✓✓78.044.01.1137.614.7
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.536, + 0.875, + 0.551 + ], + "angle": 0, + "content": "responses for prediction during both training and testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.884 + ], + "angle": 0, + "content": "Visualization of navigating with SGM. We further visualize the generated maps of SGM during the navigation, as shown in Fig. 5 and 6, noting that the scenes are unseen. As Fig. 5 illustrated, at the beginning of navigation \\((t = 0)\\), the generated image offers limited additional information due to minimal observations. However, as more of the scene becomes observed, by \\(t = 20\\) (only about \\(30\\%\\) of the entire navigation), SGM successfully predicts the location of the target (couch) even though it has not yet been observed. Then, SGM continues to guide the agent by determining the long-term goal based on the generated map. Moreover, it is notable that SGM not only accurately locates the target but also anticipates its context objects (e.g. potted plant). Fig. 6 provides additional generated results, which is evident that the generated maps correctly estimate the approximate locations of objects and their context, while there is still a deviation in their absolute positions. However, we consider this deviation to be tolerable, as even humans cannot precisely locate unseen objects in unseen scenes. These two visualizations indicate that our SGM effectively scales up limited local maps by generating the unobserved regions, thereby guiding the agent to infer the target's location." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Ablations study. As shown in row I of Tab. 2, the agent" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16420" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.16 + ], + "angle": 0, + "content": "Table 3. Comparisons with the related works in Gibson and MP3D val. Note that THDA [32] and Habitat-Web [38] use additional data for training, while Red-Rabbit [53] utilizes auxiliary tasks to train the agent. For SemExp [5], L2M [19] and Stubborn [31], we report results from [57]. * denotes our implementation." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.165, + 0.472, + 0.445 + ], + "angle": 0, + "content": "
IDMethodGibsonMP3D
SR(%)SPL(%)DTS(m)SR(%)SPL(%)DTS(m)
1Random0.40.43.890.50.58.05
2DD-PPO [46]15.010.73.248.01.86.94
3Red-Rabbit [53]---34.67.9-
4THDA [32]---28.411.05.62
I5SSCNav* [28]---27.111.25.71
6EmbCLIP* [24]68.139.51.1529.210.15.42
7Habitat-Web [38]---35.410.2-
8ENTL [26]---17.05.0-
9FBE [50]48.528.92.5629.510.65.00
10ANS [7]67.134.91.6621.29.46.31
11SemExp [5]71.139.61.3928.310.96.06
II12PONI [37]73.641.01.2527.812.05.63
13L2M [19]---32.111.05.12
14Stubborn [31]---31.213.55.01
153D-aware [57]74.542.11.1634.014.64.78
16SGM (Ours)78.044.01.1137.714.74.93
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.642 + ], + "angle": 0, + "content": "only relying on SGM has already achieved comparable performance to some supervised methods [5, 37]. Furthermore, the row II of Tab. 2 indicates that introducing an exploration strategy in the early stages of navigation is effective, which prevents misguidance by low-confidence predictions resulted from limited observations. Our exploration strategy utilizes the area potential function from [37], which calculates the nearest frontier as the long-term goal. In contrast to the computation-based FBE [50], the area potential function learns to predict potential frontiers through supervised training. The ablation studies demonstrate the effectiveness of each component in our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Comparisons with the related works. Since there is no existing self-supervised work for ObjectNav task, our comparison is limited to previous supervised methods. We consider the following baselines: the end-to-end RL methods [9, 24, 26, 28, 32, 46, 53], the imitation learning method [38], and modular methods [5, 6, 19, 31, 37, 50, 56, 57] Note that, some works leverage additional data [10, 32, 38] or auxiliary task [9, 53] to improve the performance. Thus, it is challenging to compare all the methods in an equitable manner. Consequently, our focus is specifically on the most relevant baselines: SemExp [5], PONI [37], L2M [19], SSCNav [28], PEANUT [56], where PONI and PEANUT integrate goal-related function trained by supervised learning into SemExp, while L2M and SSCNav enhance navigation performance by learning to complete egocentric top-down map of single timestamp. They are also trained with supervised learning, while are limited to consider only single-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 4. Comparisons with the related works in HM3D val. * denotes our implementation." + }, + { + "type": "table", + "bbox": [ + 0.551, + 0.124, + 0.84, + 0.235 + ], + "angle": 0, + "content": "
IDMethodHM3D
SR(%)SPL(%)
1DD-PPO [46]27.914.2
2Habitat-Web [38]57.623.8
3RIM [9]57.827.2
4PEANUT* [56]59.130.3
5SGM (Ours)60.230.8
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.249, + 0.892, + 0.415 + ], + "angle": 0, + "content": "frame observations. In contrast, our SGM predicts the unobserved regions for the broader local map, which incorporates full observations from time 0 to t. Notably, PEANUT [56] initially reports results on MP3D and HM3D, however, they only release their code for HM3D. Therefore, we only compare with [56] on HM3D with re-implementation results in our setup. Besides, L2M and SSCNav are evaluated with their self-made validation data. Thus, for comparing their results, we report our own implementations or adopt re-implementation results from other work [57] with experimental settings that align with ours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.552 + ], + "angle": 0, + "content": "We compare our SGM with the related works on the validation set of Gibson, MP3D and HM3D datasets, as shown in Tab. 3 and 4. Despite our SGM being self-supervised, it achieves comparable performance with existing supervised methods across all metrics on these datasets. Particularly on the Gibson dataset, compared to the current state-of-the-art [57], our SGM outperforms 3D-aware [57] by \\(3.5\\%\\), \\(1.9\\%\\), and \\(-0.05\\mathrm{m}\\) in SR, SPL and DTS metrics, respectively. Note that lower value on DTS indicates better performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.569, + 0.628, + 0.585 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.838 + ], + "angle": 0, + "content": "In this work, we present the Self-supervised Generative Map (SGM) for the object goal navigation task. Our SGM captures contextual relationships of both objects and environments through self-supervised training. SGM utilizes two distinct yet complementary information for prediction: episodic observations and general knowledge from Large Language Models (LLMs), where episodic observations provide geometric details, and general knowledge offers semantic priors. During navigation, the local semantic map maintained by agent is sampled by proposed sampling strategy to select informative patches. Then the selected patches are fed into SGM to generate the unobserved regions. The generated map helps agent infer the likely location of the target. The experimental results indicate that despite being a self-supervised method, our SGM achieves comparable performance to previous supervised methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.845, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U23B2012, in part by Beijing Natural Science Foundation under Grant JQ22012, Z190020." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16421" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. Beit: BERT pre-training of image transformers. 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In 2017 IEEE International Conference on" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16424" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.11, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "Robotics and Automation, ICRA 2017, Singapore, Singapore, May 29 - June 3, 2017, pages 3357-3364, 2017. 2" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16425" + } + ] +] \ No newline at end of file diff --git a/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_origin.pdf b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..275fb8cf102437833dfa49eceafa597b7996e2bf --- /dev/null +++ b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/48dfab61-319b-4d14-baa1-3fef35834727_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0381c6e7925342a6d38d954d6c76c8ef89fed67276d5ea058044c82693bab314 +size 4028915 diff --git a/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/full.md b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d6aaa4649a476f1ee2372946e45464d4b69d68a7 --- /dev/null +++ b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/full.md @@ -0,0 +1,276 @@ +# Imagine Before Go: Self-Supervised Generative Map for Object Goal Navigation + +Sixian Zhang $^{1,2}$ , Xinyao Yu $^{1,2}$ , Xinhang Song $^{1,2}$ , Xiaohan Wang $^{1}$ , Shuqiang Jiang $^{1,2,3}$ + +1Key Lab of Intelligent Information Processing Laboratory of the Chinese Academy of Sciences (CAS), Institute of Computing Technology, Beijing, 2University of Chinese Academy of Sciences, Beijing + +3 Institute of Intelligent Computing Technology, Suzhou, CAS + +{sixian.zhang, xinyao.yu, xinhang.song, xiaohan.wang}@vipl.ict.ac.cn, sqjiang@ict.ac.cn + +# Abstract + +The Object Goal navigation (ObjectNav) task requires the agent to navigate to a specified target in an unseen environment. Since the environment layout is unknown, the agent needs to infer the unknown contextual objects from partially observations, thereby deducing the likely location of the target. Previous end-to-end RL methods capture contextual relationships through implicit representations while they lack notion of geometry. Alternatively, modular methods construct local maps for recording the observed geometric structure of unseen environment, however, lacking the reasoning of contextual relation limits the exploration efficiency. In this work, we propose the self-supervised generative map (SGM), a modular method that learns the explicit context relation via self-supervised learning. The SGM is trained to leverage both episodic observations and general knowledge to reconstruct the masked pixels of a cropped global map. During navigation, the agent maintains an incomplete local semantic map, meanwhile, the unknown regions of the local map are generated by the pretrained SGM. Based on the generated map, the agent sets the predicted location of the target as the goal and moves towards it. Experiments on Gibson, MP3D and HM3D show the effectiveness of our method. The code is available at https://github.com/sx-zhang/SGM. + +# 1. Introduction + +Navigating to specified targets [27, 44, 45, 55] is an essential capability for embodied AI systems to effectively manipulate and interact with real-world entities. Consequently, the visual object goal navigation (ObjectNav) task has recently gained widespread attention. In ObjectNav task, the agent is placed in an unseen and unmapped environment, and is tasked to navigate to an object of the user-specific category (e.g. couch) based on the visual observations. Since the environment is unseen, when the target is invisible, the agent needs to infer the likely location of the target. This + +![](images/9fd9a174456e73a104e3046a7ca9e51005c2151ddef1de001c4f63e7ba9f053b.jpg) +Figure 1. Agents employ SGM to 'imagine' details of unobserved regions during navigation. The SGM is trained in a self-supervised manner by predicting pixels in masked regions of sub-maps to capture contextual relations. The SGM leverages both episodic observations and general knowledge for map reconstruction. + +requires the agent to learn and understand the contextual relationships between objects (e.g. couches typically appear with cushions and coffee tables), which enables it to deduce the target's location based on observed visual clues. + +To learn the contextual relations, end-to-end reinforcement learning (RL) methods embed pre-constructed object relation graph [52, 54, 59] into the end-to-end navigation models, or learn object associations directly via the RL [14, 15, 33]. These pre-learned priors are implicitly encoded within the policy. However, since the priors are episode-agnostic and lack geometric memory of current environment, the end-to-end RL methods exhibit limited generalization in unseen environments [32, 60]. Alternatively, modular methods [5-7] construct an explicit semantic local map, merging observed geometry and semantics of the unseen environment. The agent can disregard the observed + +regions of the local map, where the target has not appeared, which simplifies the potential state space that needs to be explored. However, without learning the contextual object relation, the modular methods are still limited. + +Recently, some methods [37, 56, 61] attempt to introduce priors of object contextual relationships into modular methods for predicting the long-term goal. They learn the contextual relation based on the local map by predicting the potential frontier nearest to the target [37], estimating the distance to the target [61], or directly anticipating the coordinate of the target [56]. However, individually learning the relations of targets with supervised learning may not be reliable, as the absolute position of targets may vary with different room layouts. In contrast, the joint associative relations among multiple objects are more reliable, e.g. chairs, tables, and cups are commonly found together, similarly, couches, cushions, and coffee tables often appear in conjunction. Therefore, we propose learning the joint contextual relations of the objects in a self-supervised manner: without any need for data collection and labeling as supervised learning, the model is trained to reconstruct the masked regions of a cropped global map based on its visible neighboring regions. This preparatory phase allows it to grasp not only individual object specifics (e.g. location and size) but also the patterns of its contextual companions (i.e. contextual object relation) and the surrounding environments (e.g. potential obstacle and free path). Then the trained model can 'imagine' unobserved regions during navigation to help agent deduce the target location. + +In this paper, we propose self-supervised generative map (SGM) to scale up the coverage of the local map by generating the unobserved regions, as shown in Fig. 1. Specifically, given the global map of a training room, the global map is cropped into sub-maps with boxes of various scales, positions and angles, then uniformly resized to a fixed scale. Following the self-supervised learning settings of MAE [22], certain patches of the sub-maps are randomly masked. Our SGM is trained to predict the pixel values of the masked patches by leveraging both episodic observations and general knowledge. The episodic observations refer to the visible patches, which are encoded with a visual encoder, akin to many visual pre-training studies [8, 22]. However, contrary to image datasets, the quantity and diversity of training scenes for ObjectNav is notably limited. To enhance the generalization, general knowledge provided by Large Language Models (LLMs) is also considered. Visible patches are transformed into prompts for LLMs through a textual template, subsequently, LLMs (e.g. GPT-4 [34], ChatGLM [17]) predict the semantic contents of the masked patches in text. Furthermore, text predictions (general knowledge) and episodic observations merge via a cross-modality encoder. The decoder predicts the pixel values of the masked patches based on the encoded information. Episodic ob + +servations and general knowledge are orthogonal and complementary, where episodic observations provide more geometric details, while general knowledge with rich semantic prior enhances the inference of contextual categories. + +During navigation, the agent maintains a local semantic map that integrates observations of current unseen environment. Since the local map is incomplete, the trained SGM is employed to generate the unobserved regions of the local map. The local map is initially divided into non-overlapping patches. Then we propose a sample strategy that prioritizes the patches, which are informative or adjacent to unobserved regions. The selected patches are input into the SGM to predict the pixel values of the unknown regions. The agent selects the coordinates with the highest confidence of the target in the generated map as the long-term goal. The SGM continually generates the unknown regions based on updated local map until the target is found. We evaluate our SGM on photorealistic 3D environments of Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49]. The experimental results demonstrate the effectiveness of our SGM in generating unknown regions and assisting the agent in inferring the location of the target. + +# 2. Related Works + +ObjectGoal navigation. Existing visual object goal navigation can be categorized into: end-to-end methods and modular methods. The end-to-end methods learn to navigate by leveraging reinforcement learning (RL) [47, 58, 62] or imitation learning (IL) [38, 39]. Previous end-to-end RL methods attempt to learn object relation graph [14, 52, 54, 59], visual representation [24, 26, 33], historical states representation [16], auxiliary tasks [53] and data augmentation [10, 32] to enhance the navigation ability. To learn the contextual object relation for enhancing the deducing for target location, [52] constructs prior knowledge of object relations from external datasets [29], and [59] builds hierarchical object-to-zone graph. [14] proposes learning the object relations (i.e. the edges of predefined graph) by RL process. The learned contextual relations are implicitly encoded into the end-to-end model. However, lack of geometry memory and low sample efficiency of RL, the generalization of these methods in unseen environments remains limited. The modular methods [5-7] maintain a geometry semantic map for localization, memory and path planning. Recent modular methods [37, 56, 61] aim to address 'where to look?' subproblem (i.e. inferring the likely location of the target). These methods employ supervised learning to learn a target-related function. Based on a local map, they predict the nearest frontier to target [37], the minimal distance to target [61] or the absolute coordinates [56] of the target. Our SGM is also a modular method, while we learn joint contextual relations, i.e. the SGM predicts the unobserved regions, which contain both objects (not limited to + +target) and environments with self-supervised learning. + +Several recent works attempt to predict the unobserved regions. [36] proposes to anticipate occupancy for point goal navigation. [19] takes a further step by adding the semantic prediction via two-stage segmentation models. [28] also predicts the unobserved semantic map, while implicitly encoding it into an RL-based policy. All of these works [19, 28, 36] only predict unobserved regions of a top-down map projected from the egocentric RGB-D view at a single timestamp. However, our SGM has a wider prediction scope as it predicts based on a broader local map, which integrates all historical observations. Additionally, it is worth to highlight that our SGM is trained through self-supervised learning, which avoids the tedious data collection and annotation of imitation and supervised learning. + +Self-supervised learning. Reconstructing signals from masked inputs has been validated as an effective self-supervised learning within the communities of NLP [2, 12, 35], CV [1, 13, 22], and multimodal pretraining [43]. We adopt the settings of Masked Autoencoders (MAE) [22] to train our SGM, which has demonstrated its robust capacity for learning contextual associations in many visual tasks [8, 18, 51]. Recently, there are few self-supervised works for goal-oriented navigation tasks. [20] proposes a distance estimator from passive videos through self-supervised learning for image goal navigation. Our SGM is proposed for ObjectNav task, which learns the contextual object relation by self-supervised learning, thereby generating the map of unobserved regions during navigation. + +# 3. Approach + +# 3.1. Task Definition + +The ObjectNav task is defined as: the agent is required to navigate to an instance of a specified object category (e.g. potted plant) in an unseen environment. The agent is placed at a random location at the start of an episode. At each timestamp $t$ , the agent receives egocentric RGB-D observations $s_t$ , target object $o$ and senor pose $(x_t, y_t, \theta_t)$ , where $x_t, y_t$ and $\theta_t$ denote coordinates and orientation of the agent. The agent executes a discrete action, where the action space consists of move_forward, turn_left, turn_right and stop. The agent autonomously executes the action stop when it determines to complete the task. A successful episode is denoted as that, within certain number of steps, the agent stops at a position where the distance to the target is less than a threshold (e.g. 1m) and the target is visible in the egocentric observation. + +Our method is constructed based on the modular ObjectNav architecture. The modular methods typically build an accumulating semantic map during navigation [5] based on the RGB-D observations, sensor poses and segmentation models [21, 23]. The semantic map $m_{t} \in \mathbb{R}^{(N_{o} + N_{s}) \times H \times W}$ + +![](images/b6bc36ee6b52319d4f142ce17e305bac36ba0270cd2c4956d19e2cb7a12fc619.jpg) +Figure 2. Self-supervised training of SGM. 'Self', 'Cross' and 'FF' denotes self-attention, cross-attention and feed-forward layers, respectively. The SGM is trained to predict the pixel value of the masked patches by utilizing episodic observations and the general knowledge from LLMs. Examples of responses from LLMs are detailed in the supplements. + +utilizes multiple channels to represent different classes, where $N_{o}$ denotes the number occupancy classes including occupied and free, $N_{s}$ is the number of object classes and $H, W$ are the map size. The semantic map aggregates the observed object layout of the unseen environment from 0 to $t$ . However, since the semantic map is obtained only by partial observations of the entire environment, it is only a subset (i.e. local map) of the global map. Therefore, when the target is invisible, the agent needs to estimate its unobserved surroundings based on the learned context relation of the objects to infer the likely location of the target. + +# 3.2. Self-supervised Generative Map + +To predict the potential position of the target, the contextual relations between objects can be used to generate the unseen regions of local maps. In particular, we propose the self-supervised generative map (SGM) to learn the context relations of both objects and environments (e.g. obstacle and free path) with the self-supervised setting of MAE [22]. + +As shown in Fig. 1, given a global map of a training room, we first crop and sample a number of sub-maps from it using several boxes in various scales, positions and angles. Then the sub-maps are resized to a fixed scale and divided into non-overlapping patches. These patches are sampled without replacement by a uniform distribution strategy. The selected patches serve as the visible patches $m_{s}$ , while the remaining patches $m_{u}$ are masked. + +To learn the contextual relation, the SGM $P(m_u|m_s)$ is trained in a self-supervised manner by reconstructing the masked patches $m_{u}$ based on their visible neighboring patches $m_{s}$ . As shown in Fig. 2, the proposed SGM reconstructs the masked patches by leveraging the following + +two aspects of information: 1) episodic observations, and 2) general knowledge from large language models (LLMs). + +Episodic observations. The visible patches are embedded with a linear projection and added with positional embeddings, and then processed with the visual encoder $E_{v}$ . The visual encoder is implemented by several Transformer blocks of ViT [13], consisting of self-attention and feedforward layers. Then the episodic observations are embedded as $E_{v}(m_{s}) = f_{v} \in \mathbb{R}^{n_{v} \times n_{d}}$ , where $n_{v}$ is the number of visible patches and $n_{d}$ is the feature dimension. Following [22], the encoder only operates the visible patches, rather than all patches. Therefore, when the ratio of visible patches is small (e.g. 25%), the encoder consumes minimal computing and memory resources. + +General knowledge. Due to limited training environments, the quantity and diversity of available global maps for training is considerably less than that of image datasets [11, 29]. As a result, models trained merely on visual clues are prone to overfitting to the limited training environments, leading to poor generalization to unseen environments [32]. Currently, the LLMs demonstrate strong reasoning abilities on many complex tasks [3]. In our work, we employ the LLMs (e.g. GPT-4 [34], ChatGLM [17]) to provide general knowledge for reasoning the contextual relation and predicting the probable objects, thereby enhancing generalization for unseen environments. + +For all visible patches, an object category is considered as observed if there is a pixel with the value of 1 existing in the corresponding channel. Then we fill in the observed categories into a fixed sentence template to generate the text prompt for LLMs. For instance, when couches and chairs are observed, the generated prompt is 'In an indoor environment, if couches and chairs are observed, what other objects might be around them? Answer in one sentence.' The LLMs receive the text prompt and predict the probable neighboring categories around the observed categories. The predictions $L(m_{s})$ of LLMs are further processed by Tokenizer and embedded with pre-trained RoBERTa [30] by $E_{L}(L(m_{s})) = f_{l}\in \mathbb{R}^{n_{l}\times n_{d}}$ , where $n_l$ is the token number. Since LLMs are trained on massive data, the prediction $f_{l}$ can be regarded as an episode-agnostic, general knowledge. General knowledge $f_{l}$ provides a wealth of semantic priors, which is orthogonal and complementary to episodic observation $f_{v}$ that captures geometric details. + +Fusion and anticipation. We utilize the cross-modality encoder of LXMERT [42] to fuse $f_{v}$ and $f_{l}$ , which consists of cross-attention, self-attention and feed-forward layers. The cross-attention layers are used to fuse the information between $f_{v}$ and $f_{l}$ , which is formally given by + +$$ +C r o s s A t t n \left(f _ {v}, f _ {l}\right) = \sigma \left(\frac {f _ {v} W _ {q} \left(f _ {l} W _ {k}\right) ^ {T}}{\sqrt {n _ {d}}}\right) f _ {l} W _ {v} \tag {1} +$$ + +where $\sigma$ is the Softmax activation function, and $W_{*} \in$ + +$\mathbb{R}^{n_d\times n_d}$ are learned parameters and biases are omitted. The output of the cross-modality encoder serves as the final embedding for all visible patches. + +The decoder takes full patches (i.e. encoded visible patches and masked patches) as the inputs, where the masked patches are initialized to the learnable vectors of the same size as the encoded visible patches. All patches are added with positional embeddings that represent their spatial locations. The decoder is also implemented by a series of Transformer blocks. + +Training. The SGM is trained to predict the pixel value of the masked patches. Given the prediction $m_{u}$ , the training objective for all classes (i.e. occupancy and object classes) is given by + +$$ +L _ {B C E} = \frac {1}{n _ {u}} \sum_ {i = 0} ^ {n _ {u}} B C E \left(m _ {u} (i), \hat {m} _ {u} (i)\right) \tag {2} +$$ + +where $BCE$ denotes the pixel-wise binary cross entropy loss and $n_u$ is the number of masked patches. $m_u(i) \in \mathbb{R}^{(N_o + N_s) \times \delta \times \delta}$ represents one of the predicted patches, where $\delta$ is the size of a patch. $\hat{m}_u(i)$ is the ground-truth of the masked patches, and each pixel of $\hat{m}_u(i)$ is a binary value. Additionally, to enhance the accuracy of predicting the position and size of objects, an IoU loss is added specifically for the object classes + +$$ +L _ {I o U} = \frac {1}{n _ {u}} \sum_ {i = 0} ^ {n _ {u}} I o U \left(m _ {u} (i, N ^ {s}), \hat {m} _ {u} (i, N ^ {s})\right) \tag {3} +$$ + +where $IoU$ denotes the category-level pixel-wise intersection over union loss, and $m_u(i,N^s) \in \mathbb{R}^{N_s \times \delta \times \delta}$ only contains the object classes. We add up all the losses to train our SGM. The overall training objective is $L = L_{BCE} + \lambda L_{IoU}$ , where $\lambda$ denotes the loss weights. The advantages of our SGM are as following: 1) Data collection. The self-supervised training eliminates the requirement for target-oriented annotations or supervision from simulators. SGM requires only training with cropped and randomly masked global maps. 2) Scalability. SGM is compatible with various LLMs, allowing for concurrent improvements in our method as LLMs advance. + +# 3.3. ObjectNav with SGM + +The trained SGM is capable of generating unobserved regions based on their visible surroundings, which is utilized to help agent deduce the unobserved regions of the local maps during navigation. + +Unobserved regions generation. At each timestamp $t$ during navigation, the agent constructs a local semantic map $m_t$ (as introduced in Sec. 3.1), and each channel of $m_t$ contains binary-valued pixels. The local semantic map includes numerous unobserved regions as shown in Fig. 3, where the pixel values of these regions are 0 across all channels. + +Given the local semantic map $m_{t}$ of time $t$ , we first crop a sub-region of $m_{t}$ , where the size of this region is $\epsilon$ times that of the smallest fitting square box around the known regions of $m_{t}$ as shown in Fig. 3. The $\epsilon$ (e.g. $\epsilon = 140\%$ is decided via validation experiments) represents a scaled-up factor with a minimum value of $100\%$ . The cropped region is resized to a fixed scale $m_{t}^{\prime} \in \mathbb{R}^{(N_{o} + N_{s}) \times L \times L}$ (e.g. $L = 224$ for ViT-Base) and divided into non-overlapping patches. The size of each patch is $\delta$ . To eliminate noise and reduce computational complexity, we select a subset of patches to serve as the input of the SGM. The sampling strategy prioritizes the patches, which are 1) informative and 2) adjacent to unobserved regions. + +To construct the sampling strategy, we calculate the average pixel value in each patch by $W = \text{Avgpool}(m_t')$ , where $W \in \mathbb{R}^{\frac{L}{\delta} \times \frac{L}{\delta}}$ , and Avgpool represents the average pooling in each patch for all channels. For each element $w_i \in W$ , the higher value indicates that the corresponding patch is more informative, i.e., there are more observed object classes or larger observed regions in this patch. Furthermore, we leverage the Laplacian kernel $K$ as a gradient operator (i.e., edge detector), to operate the $W$ by $V = \text{Conv}(W, K)$ , where $V \in \mathbb{R}^{\frac{L}{\delta} \times \frac{L}{\delta}}$ and Conv denotes the convolution operation. The higher value of $v_i \in V$ demonstrates that the corresponding patch is more likely to be adjacent to the unobserved regions. + +The $W$ and $V$ are further processed by flattening and Softmax operations for probability normalization. Then the sampling probability $P$ of each patch is defined as + +$$ +P = \alpha \bar {W} + (1 - \alpha) \bar {V} \tag {4} +$$ + +where $\bar{W}$ and $\bar{V}$ denote the normalized $W$ and $V$ , respectively, and $\alpha$ is a trade-off weight. We employ a multinomial distribution for sampling patches. Specifically, given a set of patches $m_t' = \{m_t'(1), m_t'(2), \ldots, m_t'(n_p)\}$ ( $n_p = \left(\frac{L}{\delta}\right)^2$ ), and their associated probabilities $P = \{p_1, p_2, \ldots, p_{n_p}\}$ . The patches are sampled without replacement according to $m_t'(i) \sim \text{Multinomial}(n, P)$ . The number of sampled patches $n$ constitutes only a small fraction (e.g. $30\%$ ) of the total. + +Based on this strategy, sampled patches are fed into the SGM to predict unobserved regions. The predicted values are continuous, which reflect the confidence in its prediction. Furthermore, the raw prediction of SGM is enhanced by adding the actual local semantic map to form the final generated map, where if a coordinate has already been observed (having values in semantic map), its predicted value is replaced with the confirmed observed value. During ObjectNav task, the agent identifies the pixel with the highest confidence in the target's channel of the generated semantic map. Then the coordinates of this pixel are set as the long-term goal $g_{t}$ . Additionally, limited observation (e.g. no available contextual object is observed) may result in + +![](images/f0dac37d0d55f16e93ddd4876ca967a20a8bcf5c07b259f25460634c96b6e48c.jpg) +Figure 3. During navigation, the agent builds a local semantic map $m_t$ and crops it to $m_t'$ . The patches of $m_t'$ are sampled by multinomial distribution with probability $P$ . The SGM generates the unobserved regions based on selected $n$ patches. The long-term goal is determined by the generated map and the target. + +unreliable prediction of the target (i.e. the confidence of the predicted semantic map is low). Therefore, we adopt the exploration strategy [31, 50] at the beginning of navigation until the prediction confidence of the target exceeds a certain threshold. + +Navigation policy. Once the long-term goal is identified, the agent simply needs to navigate from its current location $(x_{t},y_{t})$ to the long-term goal $g_{t}$ . Following previous works [5, 37], the local policy is implemented by the Fast Marching Method [41], which calculates the shortest path from current location to the long-term goal based on the occupancy channels of the generated map. Then the local policy calculates deterministic actions for the agent based on its step distance and the shortest path. At each times- tamp, the local policy will re-plan the actions for the agent according to the updated semantic map. + +# 4. Experiments + +# 4.1. Experimental Setup + +Dataset. We evaluate our SGM on standard ObjectNav datasets, including Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49] dataset. + +For Gibson and MP3D, we follow the setup of [37, 57], we we utilize 25 train /5 val scenes from the Gibson tiny split and choose 6 goal categories with 1,000 val episodes for Gibson. For MP3D, we employ 56 train / 11 val scenes, 21 goal categories and 2,195 episodes for validation. For HM3D, our setup is consistent with [9], where we choose 80 train / 20 val scenes, 6 goal categories and 2,000 valida + +Table 1. Comparisons of different map generation variants in the Gibson (val). R/C means the training map is masked by random (R) or connected (C) strategy. The connected masking strategy requires that retained patches must be adjacent to each other (remaining patches are akin to a local map), which is similar to [19, 28] that learn contextual relations by completing the local map. For LLMs, we compare GPT-4 [34] and ChatGLM [17]. + +
IDModelMaskLLMMap GenerationNavigation
IoU(%)Recall(%)SR(%)SPL(%)DTS(m)
I 1UNet--19.2847.3667.537.81.76
2ViT-LC-24.1859.4273.839.51.45
3ViT-LR-26.8579.0574.239.61.49
4ViT-BC-22.3155.5073.139.31.53
5ViT-BR-25.4579.2374.139.51.48
6ViT-BCGPT-432.0672.3476.843.41.27
7ViT-BRGPT-439.4787.3377.443.81.15
8ViT-BCChatGLM30.8780.6777.043.51.31
9ViT-BRChatGLM31.7391.6878.044.01.11
+ +tion episodes. The goal categories adopted by these three datasets are listed in supplements. + +Evaluation metrics. For evaluating the navigation performance, we adopt three standard metrics following [5, 37, 56]: 1) SR: the ratio of success episodes. 2) SPL: the success rate weighted by the path length, which measures the efficiency of the path length. 3) DTS: the distance to the goal at the end of the episode. + +To assess the quality of map predictions, we employ the following two metrics: 1) IoU: the pixel intersection over union for all channels (both occupancy and object). 2) Recall: the proportion of true positive predicted object categories over the total number of ground-truth categories. + +Implementation details. For the self-supervised training of SGM, we sample 400,000 train /1,000 val sub-maps for training and validation in each dataset. We implement the SGM based on ViT-base/16, where the visual encoder, cross-modality encoder and decoder are respectively composed of 8, 4 and 2 Transformer blocks. The training mask ratio is set to $75\%$ , the input size $L = 224$ , and patch size $\delta = 16$ . We use the Adam optimizer [25] with a base learning rate of 0.00015. The warmup epoch is linearly scaled when the training epoch increases to 40. After warmup epochs, the learning rate is decayed by a factor of 0.05. The loss weights $\lambda = 0.2$ . + +For ObjectNav task, since constructing local semantic map requires the semantic segmentation model, we adopt publicly available Mask-RCNN [21] from [37] for Gibson, RedNet [23] from [37] for MP3D, and Mask-RCNN [21] from [56] for HM3D. The scaled-up factor $\epsilon = 140\%$ , the number of selected patches $n = 59$ , and sample weights $\alpha = 0.5$ . The experiments for these hyper-parameters are detailed in supplements. The turn angle is set to 30 degrees, + +![](images/3b448eed6905672d37daa9586ecece5b821bdc582b4f662966ff145c16c5946e.jpg) +Figure 4. Map reconstruction results. The 'w/ EO' means only using episodic observations in reconstruction, while 'w/ EO and GK' denotes leveraging both episodic observations and LLMs (ChatGLM). General knowledge enables the model to predict the completely unobserved contextual objects (see the regions highlighted by red circles). These sub-maps sourced from the val rooms of Gibson are unseen during training. + +and the step distance of move_forward is $25\mathrm{cm}$ + +# 4.2. Evaluation Results + +Comparisons with previous map completion methods. Prior methods [19, 28] train a UNet [40] to directly predict unobserved regions based on the top-down map of a single timestamp. This comparison is to determine whether using UNet or learning contextual relations directly from the local map is more effective than our SGM (utilizing ViT and learning with randomly masked sub-maps). As shown in Tab. 1, we compare these two variants under identical training epochs and datasets. The UNet variant underperforms others in both map generation and navigation. In learning contextual relations, the random masking strategy (SGM) outperforms connected masking strategy [19, 28]. We infer that since visible patches are closely clustered in the connected masking strategy, the context of patches distant from the visible ones is completely absent, leading to difficulties for model in capturing the context relations of these patches during training. The results demonstrate that our SGM is more effective in capturing contextual relationships and assisting the navigation. + +Model complexity. We compare the impact of more complex models on map generation and navigation. As indicated by the row II in Tab. 1, the more complex model (i.e. ViT Large) only yields a marginal performance improvement. Hence, we conjecture that the ViT Base model is sufficiently capable for the task. Consequently, our SGM is ultimately implemented based on the ViT Base model. + +Impact of LLMs. Our SGM not only leverages episodic observations but also incorporates general knowledge obtained from LLMs for prediction. Compared to rows II and III in Tab. 1, there is a significant improvement on the recall metric, which suggests that LLMs can substantially bolster the prediction of object categories. As shown + +![](images/8553ee42d187b371e0a505e69da743016e4735fc9c85bef7f9fe8727ecc20848.jpg) +Figure 5. Navigation episode with SGM in Gibson (val). The top row displays the agent's RGB view and local semantic map, including the trajectory and long-term goal (indicated by the deep blue dot). The bottom row shows the generated map by SGM. At about $30\%$ of the navigation process (i.e. $t = 20$ ), the generated map accurately predicts the target's location even though the target has not yet been observed. Besides, SGM not only precisely predicts the target (couch), but also its contextual objects (e.g. potted plant). + +![](images/3c1b74e8a5838876325b21c5ec73a473f51470c339a0e539bc31977d5d6400e9.jpg) +Figure 6. More generated maps during navigation. As shown by the circled objects, the generated map accurately anticipates the location of unobserved objects. + +in the Fig. 4, the model with solely episodic observations is capable of completing the contours of partially observed objects, while it struggles to predict entirely unobserved categories. However, the general knowledge from LLMs provides rich semantic contextual priors, enables the model to predict the context objects that are completely unobserved (e.g. the chairs in the first row, and the potted plants and sinks in the second row). Additionally, we compare two LLMs: GPT-4 [34] and ChatGLM [17]. The results show that the choice of LLMs has minimal impact on performance. Moreover, as ChatGLM is publicly available, thus, we employ it to provide general knowledge. To improve inference speed, we extract all possible combinations of goal categories to pre-generate the prompt and obtain responses by using LLMs. The SGM directly leverages pre-extracted + +Table 2. Ablation study of different components. GT means the long-term goal is set to the ground truth location of the target. 'EO' denotes the episodic observation, 'GK' represents the general knowledge and 'Explr' means using exploration strategy at the beginning of navigation. + +
IDModulesGibsonMP3D
GTEOGKExplrSR(%)SPL(%)DTS(m)SR(%)SPL(%)
I 21✓91.772.30.38--
2✓71.540.81.4631.912.2
3✓✓74.441.31.4934.713.2
II 64✓65.137.91.7625.911.6
5✓✓74.139.51.4833.011.8
6✓✓78.044.01.1137.614.7
+ +responses for prediction during both training and testing. + +Visualization of navigating with SGM. We further visualize the generated maps of SGM during the navigation, as shown in Fig. 5 and 6, noting that the scenes are unseen. As Fig. 5 illustrated, at the beginning of navigation $(t = 0)$ , the generated image offers limited additional information due to minimal observations. However, as more of the scene becomes observed, by $t = 20$ (only about $30\%$ of the entire navigation), SGM successfully predicts the location of the target (couch) even though it has not yet been observed. Then, SGM continues to guide the agent by determining the long-term goal based on the generated map. Moreover, it is notable that SGM not only accurately locates the target but also anticipates its context objects (e.g. potted plant). Fig. 6 provides additional generated results, which is evident that the generated maps correctly estimate the approximate locations of objects and their context, while there is still a deviation in their absolute positions. However, we consider this deviation to be tolerable, as even humans cannot precisely locate unseen objects in unseen scenes. These two visualizations indicate that our SGM effectively scales up limited local maps by generating the unobserved regions, thereby guiding the agent to infer the target's location. + +Ablations study. As shown in row I of Tab. 2, the agent + +Table 3. Comparisons with the related works in Gibson and MP3D val. Note that THDA [32] and Habitat-Web [38] use additional data for training, while Red-Rabbit [53] utilizes auxiliary tasks to train the agent. For SemExp [5], L2M [19] and Stubborn [31], we report results from [57]. * denotes our implementation. + +
IDMethodGibsonMP3D
SR(%)SPL(%)DTS(m)SR(%)SPL(%)DTS(m)
1Random0.40.43.890.50.58.05
2DD-PPO [46]15.010.73.248.01.86.94
3Red-Rabbit [53]---34.67.9-
4THDA [32]---28.411.05.62
I5SSCNav* [28]---27.111.25.71
6EmbCLIP* [24]68.139.51.1529.210.15.42
7Habitat-Web [38]---35.410.2-
8ENTL [26]---17.05.0-
9FBE [50]48.528.92.5629.510.65.00
10ANS [7]67.134.91.6621.29.46.31
11SemExp [5]71.139.61.3928.310.96.06
II12PONI [37]73.641.01.2527.812.05.63
13L2M [19]---32.111.05.12
14Stubborn [31]---31.213.55.01
153D-aware [57]74.542.11.1634.014.64.78
16SGM (Ours)78.044.01.1137.714.74.93
+ +only relying on SGM has already achieved comparable performance to some supervised methods [5, 37]. Furthermore, the row II of Tab. 2 indicates that introducing an exploration strategy in the early stages of navigation is effective, which prevents misguidance by low-confidence predictions resulted from limited observations. Our exploration strategy utilizes the area potential function from [37], which calculates the nearest frontier as the long-term goal. In contrast to the computation-based FBE [50], the area potential function learns to predict potential frontiers through supervised training. The ablation studies demonstrate the effectiveness of each component in our method. + +Comparisons with the related works. Since there is no existing self-supervised work for ObjectNav task, our comparison is limited to previous supervised methods. We consider the following baselines: the end-to-end RL methods [9, 24, 26, 28, 32, 46, 53], the imitation learning method [38], and modular methods [5, 6, 19, 31, 37, 50, 56, 57] Note that, some works leverage additional data [10, 32, 38] or auxiliary task [9, 53] to improve the performance. Thus, it is challenging to compare all the methods in an equitable manner. Consequently, our focus is specifically on the most relevant baselines: SemExp [5], PONI [37], L2M [19], SSCNav [28], PEANUT [56], where PONI and PEANUT integrate goal-related function trained by supervised learning into SemExp, while L2M and SSCNav enhance navigation performance by learning to complete egocentric top-down map of single timestamp. They are also trained with supervised learning, while are limited to consider only single- + +Table 4. Comparisons with the related works in HM3D val. * denotes our implementation. + +
IDMethodHM3D
SR(%)SPL(%)
1DD-PPO [46]27.914.2
2Habitat-Web [38]57.623.8
3RIM [9]57.827.2
4PEANUT* [56]59.130.3
5SGM (Ours)60.230.8
+ +frame observations. In contrast, our SGM predicts the unobserved regions for the broader local map, which incorporates full observations from time 0 to t. Notably, PEANUT [56] initially reports results on MP3D and HM3D, however, they only release their code for HM3D. Therefore, we only compare with [56] on HM3D with re-implementation results in our setup. Besides, L2M and SSCNav are evaluated with their self-made validation data. Thus, for comparing their results, we report our own implementations or adopt re-implementation results from other work [57] with experimental settings that align with ours. + +We compare our SGM with the related works on the validation set of Gibson, MP3D and HM3D datasets, as shown in Tab. 3 and 4. Despite our SGM being self-supervised, it achieves comparable performance with existing supervised methods across all metrics on these datasets. Particularly on the Gibson dataset, compared to the current state-of-the-art [57], our SGM outperforms 3D-aware [57] by $3.5\%$ , $1.9\%$ , and $-0.05\mathrm{m}$ in SR, SPL and DTS metrics, respectively. Note that lower value on DTS indicates better performance. + +# 5. Conclusions + +In this work, we present the Self-supervised Generative Map (SGM) for the object goal navigation task. Our SGM captures contextual relationships of both objects and environments through self-supervised training. SGM utilizes two distinct yet complementary information for prediction: episodic observations and general knowledge from Large Language Models (LLMs), where episodic observations provide geometric details, and general knowledge offers semantic priors. During navigation, the local semantic map maintained by agent is sampled by proposed sampling strategy to select informative patches. Then the selected patches are fed into SGM to generate the unobserved regions. The generated map helps agent infer the likely location of the target. The experimental results indicate that despite being a self-supervised method, our SGM achieves comparable performance to previous supervised methods. + +Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U23B2012, in part by Beijing Natural Science Foundation under Grant JQ22012, Z190020. + +# References + +[1] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. Beit: BERT pre-training of image transformers. In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. OpenReview.net, 2022.3 +[2] Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. 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In Computer Vision - ECCV 2022 - 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXXIX, pages 301-320. 2 +[59] Sixian Zhang, Xinhang Song, Yubing Bai, Weijie Li, Yakui Chu, and Shuqiang Jiang. Hierarchical object-to-zone graph for object navigation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 15130-15140, 2021. 1, 2 +[60] Sixian Zhang, Xinhang Song, Weijie Li, Yubing Bai, Xinyao Yu, and Shuqiang Jiang. Layout-based causal inference for object navigation. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023, pages 10792-10802. IEEE, 2023. 1 +[61] Minzhao Zhu, Binglei Zhao, and Tao Kong. Navigating to objects in unseen environments by distance prediction. In IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2022, Kyoto, Japan, October 23-27, 2022, pages 10571-10578. IEEE, 2022. 2 +[62] Yuke Zhu, Roozbeh Mottaghi, Eric Kolve, Joseph J. Lim, Abhinav Gupta, Li Fei-Fei, and Ali Farhadi. Target-driven visual navigation in indoor scenes using deep reinforcement learning. In 2017 IEEE International Conference on \ No newline at end of file diff --git a/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/images.zip b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..26f72023d930bab98047576c2fb63edf69092372 --- /dev/null +++ b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2b45bef86d64b81b6bcb7a0459703564a50589344942c9816ad26f1ddccde971 +size 562805 diff --git a/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/layout.json b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..82f5b1e5abb690e1f108db447968c50daa2c1d3c --- /dev/null +++ b/2024/Imagine Before Go_ Self-Supervised Generative Map for Object Goal Navigation/layout.json @@ -0,0 +1,8551 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 48, + 103, + 545, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 103, + 545, + 122 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 545, + 122 + ], + "type": "text", + "content": "Imagine Before Go: Self-Supervised Generative Map for Object Goal Navigation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "spans": [ + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "text", + "content": "Sixian Zhang" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "text", + "content": ", Xinyao Yu" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "text", + "content": ", Xinhang Song" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "text", + "content": ", Xiaohan Wang" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "text", + "content": ", Shuqiang Jiang" + }, + { + "bbox": [ + 89, + 142, + 503, + 158 + ], + "type": "inline_equation", + "content": "^{1,2,3}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 159, + 485, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 159, + 485, + 185 + ], + "spans": [ + { + "bbox": [ + 108, + 159, + 485, + 185 + ], + "type": "text", + "content": "1Key Lab of Intelligent Information Processing Laboratory of the Chinese Academy of Sciences (CAS), Institute of Computing Technology, Beijing, 2University of Chinese Academy of Sciences, Beijing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 182, + 186, + 410, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 186, + 410, + 198 + ], + "spans": [ + { + "bbox": [ + 182, + 186, + 410, + 198 + ], + "type": "text", + "content": "3 Institute of Intelligent Computing Technology, Suzhou, CAS" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 201, + 531, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 201, + 531, + 213 + ], + "spans": [ + { + "bbox": [ + 61, + 201, + 531, + 213 + ], + "type": "text", + "content": "{sixian.zhang, xinyao.yu, xinhang.song, xiaohan.wang}@vipl.ict.ac.cn, sqjiang@ict.ac.cn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 266, + 290, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 290, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 290, + 553 + ], + "type": "text", + "content": "The Object Goal navigation (ObjectNav) task requires the agent to navigate to a specified target in an unseen environment. Since the environment layout is unknown, the agent needs to infer the unknown contextual objects from partially observations, thereby deducing the likely location of the target. Previous end-to-end RL methods capture contextual relationships through implicit representations while they lack notion of geometry. Alternatively, modular methods construct local maps for recording the observed geometric structure of unseen environment, however, lacking the reasoning of contextual relation limits the exploration efficiency. In this work, we propose the self-supervised generative map (SGM), a modular method that learns the explicit context relation via self-supervised learning. The SGM is trained to leverage both episodic observations and general knowledge to reconstruct the masked pixels of a cropped global map. During navigation, the agent maintains an incomplete local semantic map, meanwhile, the unknown regions of the local map are generated by the pretrained SGM. Based on the generated map, the agent sets the predicted location of the target as the goal and moves towards it. Experiments on Gibson, MP3D and HM3D show the effectiveness of our method. The code is available at https://github.com/sx-zhang/SGM." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Navigating to specified targets [27, 44, 45, 55] is an essential capability for embodied AI systems to effectively manipulate and interact with real-world entities. Consequently, the visual object goal navigation (ObjectNav) task has recently gained widespread attention. In ObjectNav task, the agent is placed in an unseen and unmapped environment, and is tasked to navigate to an object of the user-specific category (e.g. couch) based on the visual observations. Since the environment is unseen, when the target is invisible, the agent needs to infer the likely location of the target. This" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 240, + 542, + 439 + ], + "blocks": [ + { + "bbox": [ + 310, + 240, + 542, + 439 + ], + "lines": [ + { + "bbox": [ + 310, + 240, + 542, + 439 + ], + "spans": [ + { + "bbox": [ + 310, + 240, + 542, + 439 + ], + "type": "image", + "image_path": "9fd9a174456e73a104e3046a7ca9e51005c2151ddef1de001c4f63e7ba9f053b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 445, + 547, + 500 + ], + "lines": [ + { + "bbox": [ + 305, + 445, + 547, + 500 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 547, + 500 + ], + "type": "text", + "content": "Figure 1. Agents employ SGM to 'imagine' details of unobserved regions during navigation. The SGM is trained in a self-supervised manner by predicting pixels in masked regions of sub-maps to capture contextual relations. The SGM leverages both episodic observations and general knowledge for map reconstruction." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 518, + 546, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 546, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 546, + 567 + ], + "type": "text", + "content": "requires the agent to learn and understand the contextual relationships between objects (e.g. couches typically appear with cushions and coffee tables), which enables it to deduce the target's location based on observed visual clues." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "To learn the contextual relations, end-to-end reinforcement learning (RL) methods embed pre-constructed object relation graph [52, 54, 59] into the end-to-end navigation models, or learn object associations directly via the RL [14, 15, 33]. These pre-learned priors are implicitly encoded within the policy. However, since the priors are episode-agnostic and lack geometric memory of current environment, the end-to-end RL methods exhibit limited generalization in unseen environments [32, 60]. Alternatively, modular methods [5-7] construct an explicit semantic local map, merging observed geometry and semantics of the unseen environment. The agent can disregard the observed" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16414" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 118 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 118 + ], + "type": "text", + "content": "regions of the local map, where the target has not appeared, which simplifies the potential state space that needs to be explored. However, without learning the contextual object relation, the modular methods are still limited." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 124, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 124, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 49, + 124, + 286, + 422 + ], + "type": "text", + "content": "Recently, some methods [37, 56, 61] attempt to introduce priors of object contextual relationships into modular methods for predicting the long-term goal. They learn the contextual relation based on the local map by predicting the potential frontier nearest to the target [37], estimating the distance to the target [61], or directly anticipating the coordinate of the target [56]. However, individually learning the relations of targets with supervised learning may not be reliable, as the absolute position of targets may vary with different room layouts. In contrast, the joint associative relations among multiple objects are more reliable, e.g. chairs, tables, and cups are commonly found together, similarly, couches, cushions, and coffee tables often appear in conjunction. Therefore, we propose learning the joint contextual relations of the objects in a self-supervised manner: without any need for data collection and labeling as supervised learning, the model is trained to reconstruct the masked regions of a cropped global map based on its visible neighboring regions. This preparatory phase allows it to grasp not only individual object specifics (e.g. location and size) but also the patterns of its contextual companions (i.e. contextual object relation) and the surrounding environments (e.g. potential obstacle and free path). Then the trained model can 'imagine' unobserved regions during navigation to help agent deduce the target location." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 427, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 427, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 427, + 286, + 712 + ], + "type": "text", + "content": "In this paper, we propose self-supervised generative map (SGM) to scale up the coverage of the local map by generating the unobserved regions, as shown in Fig. 1. Specifically, given the global map of a training room, the global map is cropped into sub-maps with boxes of various scales, positions and angles, then uniformly resized to a fixed scale. Following the self-supervised learning settings of MAE [22], certain patches of the sub-maps are randomly masked. Our SGM is trained to predict the pixel values of the masked patches by leveraging both episodic observations and general knowledge. The episodic observations refer to the visible patches, which are encoded with a visual encoder, akin to many visual pre-training studies [8, 22]. However, contrary to image datasets, the quantity and diversity of training scenes for ObjectNav is notably limited. To enhance the generalization, general knowledge provided by Large Language Models (LLMs) is also considered. Visible patches are transformed into prompts for LLMs through a textual template, subsequently, LLMs (e.g. GPT-4 [34], ChatGLM [17]) predict the semantic contents of the masked patches in text. Furthermore, text predictions (general knowledge) and episodic observations merge via a cross-modality encoder. The decoder predicts the pixel values of the masked patches based on the encoded information. Episodic ob" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 308, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 545, + 119 + ], + "type": "text", + "content": "servations and general knowledge are orthogonal and complementary, where episodic observations provide more geometric details, while general knowledge with rich semantic prior enhances the inference of contextual categories." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 121, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 121, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 308, + 121, + 545, + 335 + ], + "type": "text", + "content": "During navigation, the agent maintains a local semantic map that integrates observations of current unseen environment. Since the local map is incomplete, the trained SGM is employed to generate the unobserved regions of the local map. The local map is initially divided into non-overlapping patches. Then we propose a sample strategy that prioritizes the patches, which are informative or adjacent to unobserved regions. The selected patches are input into the SGM to predict the pixel values of the unknown regions. The agent selects the coordinates with the highest confidence of the target in the generated map as the long-term goal. The SGM continually generates the unknown regions based on updated local map until the target is found. We evaluate our SGM on photorealistic 3D environments of Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49]. The experimental results demonstrate the effectiveness of our SGM in generating unknown regions and assisting the agent in inferring the location of the target." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 346, + 395, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 346, + 395, + 358 + ], + "spans": [ + { + "bbox": [ + 308, + 346, + 395, + 358 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 367, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 367, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 367, + 545, + 712 + ], + "type": "text", + "content": "ObjectGoal navigation. Existing visual object goal navigation can be categorized into: end-to-end methods and modular methods. The end-to-end methods learn to navigate by leveraging reinforcement learning (RL) [47, 58, 62] or imitation learning (IL) [38, 39]. Previous end-to-end RL methods attempt to learn object relation graph [14, 52, 54, 59], visual representation [24, 26, 33], historical states representation [16], auxiliary tasks [53] and data augmentation [10, 32] to enhance the navigation ability. To learn the contextual object relation for enhancing the deducing for target location, [52] constructs prior knowledge of object relations from external datasets [29], and [59] builds hierarchical object-to-zone graph. [14] proposes learning the object relations (i.e. the edges of predefined graph) by RL process. The learned contextual relations are implicitly encoded into the end-to-end model. However, lack of geometry memory and low sample efficiency of RL, the generalization of these methods in unseen environments remains limited. The modular methods [5-7] maintain a geometry semantic map for localization, memory and path planning. Recent modular methods [37, 56, 61] aim to address 'where to look?' subproblem (i.e. inferring the likely location of the target). These methods employ supervised learning to learn a target-related function. Based on a local map, they predict the nearest frontier to target [37], the minimal distance to target [61] or the absolute coordinates [56] of the target. Our SGM is also a modular method, while we learn joint contextual relations, i.e. the SGM predicts the unobserved regions, which contain both objects (not limited to" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "text", + "content": "16415" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 270, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 270, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 270, + 84 + ], + "type": "text", + "content": "target) and environments with self-supervised learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 287, + 252 + ], + "type": "text", + "content": "Several recent works attempt to predict the unobserved regions. [36] proposes to anticipate occupancy for point goal navigation. [19] takes a further step by adding the semantic prediction via two-stage segmentation models. [28] also predicts the unobserved semantic map, while implicitly encoding it into an RL-based policy. All of these works [19, 28, 36] only predict unobserved regions of a top-down map projected from the egocentric RGB-D view at a single timestamp. However, our SGM has a wider prediction scope as it predicts based on a broader local map, which integrates all historical observations. Additionally, it is worth to highlight that our SGM is trained through self-supervised learning, which avoids the tedious data collection and annotation of imitation and supervised learning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 253, + 288, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 288, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 288, + 421 + ], + "type": "text", + "content": "Self-supervised learning. Reconstructing signals from masked inputs has been validated as an effective self-supervised learning within the communities of NLP [2, 12, 35], CV [1, 13, 22], and multimodal pretraining [43]. We adopt the settings of Masked Autoencoders (MAE) [22] to train our SGM, which has demonstrated its robust capacity for learning contextual associations in many visual tasks [8, 18, 51]. Recently, there are few self-supervised works for goal-oriented navigation tasks. [20] proposes a distance estimator from passive videos through self-supervised learning for image goal navigation. Our SGM is proposed for ObjectNav task, which learns the contextual object relation by self-supervised learning, thereby generating the map of unobserved regions during navigation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 434, + 113, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 113, + 447 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 113, + 447 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 454, + 141, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 141, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 141, + 466 + ], + "type": "text", + "content": "3.1. Task Definition" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": "The ObjectNav task is defined as: the agent is required to navigate to an instance of a specified object category (e.g. potted plant) in an unseen environment. The agent is placed at a random location at the start of an episode. At each timestamp " + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": ", the agent receives egocentric RGB-D observations " + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": ", target object " + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": " and senor pose " + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "inline_equation", + "content": "(x_t, y_t, \\theta_t)" + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "inline_equation", + "content": "x_t, y_t" + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 46, + 473, + 287, + 652 + ], + "type": "text", + "content": " denote coordinates and orientation of the agent. The agent executes a discrete action, where the action space consists of move_forward, turn_left, turn_right and stop. The agent autonomously executes the action stop when it determines to complete the task. A successful episode is denoted as that, within certain number of steps, the agent stops at a position where the distance to the target is less than a threshold (e.g. 1m) and the target is visible in the egocentric observation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "Our method is constructed based on the modular ObjectNav architecture. The modular methods typically build an accumulating semantic map during navigation [5] based on the RGB-D observations, sensor poses and segmentation models [21, 23]. The semantic map " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "m_{t} \\in \\mathbb{R}^{(N_{o} + N_{s}) \\times H \\times W}" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 313, + 71, + 541, + 244 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 541, + 244 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 541, + 244 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 541, + 244 + ], + "type": "image", + "image_path": "b6bc36ee6b52319d4f142ce17e305bac36ba0270cd2c4956d19e2cb7a12fc619.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 250, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 305, + 250, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 250, + 547, + 316 + ], + "type": "text", + "content": "Figure 2. Self-supervised training of SGM. 'Self', 'Cross' and 'FF' denotes self-attention, cross-attention and feed-forward layers, respectively. The SGM is trained to predict the pixel value of the masked patches by utilizing episodic observations and the general knowledge from LLMs. Examples of responses from LLMs are detailed in the supplements." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "text", + "content": "utilizes multiple channels to represent different classes, where " + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "inline_equation", + "content": "N_{o}" + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "text", + "content": " denotes the number occupancy classes including occupied and free, " + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "text", + "content": " is the number of object classes and " + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "text", + "content": " are the map size. The semantic map aggregates the observed object layout of the unseen environment from 0 to " + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 327, + 547, + 460 + ], + "type": "text", + "content": ". However, since the semantic map is obtained only by partial observations of the entire environment, it is only a subset (i.e. local map) of the global map. Therefore, when the target is invisible, the agent needs to estimate its unobserved surroundings based on the learned context relation of the objects to infer the likely location of the target." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 467, + 479, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 479, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 479, + 480 + ], + "type": "text", + "content": "3.2. Self-supervised Generative Map" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 485, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 557 + ], + "type": "text", + "content": "To predict the potential position of the target, the contextual relations between objects can be used to generate the unseen regions of local maps. In particular, we propose the self-supervised generative map (SGM) to learn the context relations of both objects and environments (e.g. obstacle and free path) with the self-supervised setting of MAE [22]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "content": "As shown in Fig. 1, given a global map of a training room, we first crop and sample a number of sub-maps from it using several boxes in various scales, positions and angles. Then the sub-maps are resized to a fixed scale and divided into non-overlapping patches. These patches are sampled without replacement by a uniform distribution strategy. The selected patches serve as the visible patches " + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "inline_equation", + "content": "m_{s}" + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "content": ", while the remaining patches " + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "inline_equation", + "content": "m_{u}" + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "content": " are masked." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "To learn the contextual relation, the SGM " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "P(m_u|m_s)" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " is trained in a self-supervised manner by reconstructing the masked patches " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "m_{u}" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " based on their visible neighboring patches " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "m_{s}" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ". As shown in Fig. 2, the proposed SGM reconstructs the masked patches by leveraging the following" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16416" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "two aspects of information: 1) episodic observations, and 2) general knowledge from large language models (LLMs)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "text", + "content": "Episodic observations. The visible patches are embedded with a linear projection and added with positional embeddings, and then processed with the visual encoder " + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "inline_equation", + "content": "E_{v}" + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "text", + "content": ". The visual encoder is implemented by several Transformer blocks of ViT [13], consisting of self-attention and feedforward layers. Then the episodic observations are embedded as " + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "inline_equation", + "content": "E_{v}(m_{s}) = f_{v} \\in \\mathbb{R}^{n_{v} \\times n_{d}}" + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "inline_equation", + "content": "n_{v}" + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "text", + "content": " is the number of visible patches and " + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "inline_equation", + "content": "n_{d}" + }, + { + "bbox": [ + 46, + 96, + 286, + 239 + ], + "type": "text", + "content": " is the feature dimension. Following [22], the encoder only operates the visible patches, rather than all patches. Therefore, when the ratio of visible patches is small (e.g. 25%), the encoder consumes minimal computing and memory resources." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 286, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 286, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 286, + 382 + ], + "type": "text", + "content": "General knowledge. Due to limited training environments, the quantity and diversity of available global maps for training is considerably less than that of image datasets [11, 29]. As a result, models trained merely on visual clues are prone to overfitting to the limited training environments, leading to poor generalization to unseen environments [32]. Currently, the LLMs demonstrate strong reasoning abilities on many complex tasks [3]. In our work, we employ the LLMs (e.g. GPT-4 [34], ChatGLM [17]) to provide general knowledge for reasoning the contextual relation and predicting the probable objects, thereby enhancing generalization for unseen environments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": "For all visible patches, an object category is considered as observed if there is a pixel with the value of 1 existing in the corresponding channel. Then we fill in the observed categories into a fixed sentence template to generate the text prompt for LLMs. For instance, when couches and chairs are observed, the generated prompt is 'In an indoor environment, if couches and chairs are observed, what other objects might be around them? Answer in one sentence.' The LLMs receive the text prompt and predict the probable neighboring categories around the observed categories. The predictions " + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "inline_equation", + "content": "L(m_{s})" + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": " of LLMs are further processed by Tokenizer and embedded with pre-trained RoBERTa [30] by " + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "inline_equation", + "content": "E_{L}(L(m_{s})) = f_{l}\\in \\mathbb{R}^{n_{l}\\times n_{d}}" + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "inline_equation", + "content": "n_l" + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": " is the token number. Since LLMs are trained on massive data, the prediction " + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "inline_equation", + "content": "f_{l}" + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": " can be regarded as an episode-agnostic, general knowledge. General knowledge " + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "inline_equation", + "content": "f_{l}" + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": " provides a wealth of semantic priors, which is orthogonal and complementary to episodic observation " + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 46, + 383, + 286, + 598 + ], + "type": "text", + "content": " that captures geometric details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "text", + "content": "Fusion and anticipation. We utilize the cross-modality encoder of LXMERT [42] to fuse " + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "inline_equation", + "content": "f_{l}" + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "text", + "content": ", which consists of cross-attention, self-attention and feed-forward layers. The cross-attention layers are used to fuse the information between " + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "inline_equation", + "content": "f_{l}" + }, + { + "bbox": [ + 46, + 598, + 286, + 658 + ], + "type": "text", + "content": ", which is formally given by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 663, + 286, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 663, + 286, + 696 + ], + "spans": [ + { + "bbox": [ + 58, + 663, + 286, + 696 + ], + "type": "interline_equation", + "content": "C r o s s A t t n \\left(f _ {v}, f _ {l}\\right) = \\sigma \\left(\\frac {f _ {v} W _ {q} \\left(f _ {l} W _ {k}\\right) ^ {T}}{\\sqrt {n _ {d}}}\\right) f _ {l} W _ {v} \\tag {1}", + "image_path": "5dbd23a375cae239dcfb1eb09bec9b2f52203c1914916de3ad68c65cd3d132db.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": " is the Softmax activation function, and " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "W_{*} \\in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{n_d\\times n_d}" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " are learned parameters and biases are omitted. The output of the cross-modality encoder serves as the final embedding for all visible patches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 108, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 190 + ], + "type": "text", + "content": "The decoder takes full patches (i.e. encoded visible patches and masked patches) as the inputs, where the masked patches are initialized to the learnable vectors of the same size as the encoded visible patches. All patches are added with positional embeddings that represent their spatial locations. The decoder is also implemented by a series of Transformer blocks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": "Training. The SGM is trained to predict the pixel value of the masked patches. Given the prediction " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "m_{u}" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": ", the training objective for all classes (i.e. occupancy and object classes) is given by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 342, + 247, + 545, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 247, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 342, + 247, + 545, + 277 + ], + "type": "interline_equation", + "content": "L _ {B C E} = \\frac {1}{n _ {u}} \\sum_ {i = 0} ^ {n _ {u}} B C E \\left(m _ {u} (i), \\hat {m} _ {u} (i)\\right) \\tag {2}", + "image_path": "cd126567c40be9e53aad4ecfcdb917ca9f575a8017a415f95e2e37a5e10a5035.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "BCE" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " denotes the pixel-wise binary cross entropy loss and " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "n_u" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " is the number of masked patches. " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "m_u(i) \\in \\mathbb{R}^{(N_o + N_s) \\times \\delta \\times \\delta}" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " represents one of the predicted patches, where " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " is the size of a patch. " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\hat{m}_u(i)" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " is the ground-truth of the masked patches, and each pixel of " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\hat{m}_u(i)" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " is a binary value. Additionally, to enhance the accuracy of predicting the position and size of objects, an IoU loss is added specifically for the object classes" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 387, + 545, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 387, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 329, + 387, + 545, + 418 + ], + "type": "interline_equation", + "content": "L _ {I o U} = \\frac {1}{n _ {u}} \\sum_ {i = 0} ^ {n _ {u}} I o U \\left(m _ {u} (i, N ^ {s}), \\hat {m} _ {u} (i, N ^ {s})\\right) \\tag {3}", + "image_path": "5091e14bf65c431120ca68423c4c01121061d7085fd46dafa89d2ac37b1d634c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "inline_equation", + "content": "IoU" + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "text", + "content": " denotes the category-level pixel-wise intersection over union loss, and " + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "inline_equation", + "content": "m_u(i,N^s) \\in \\mathbb{R}^{N_s \\times \\delta \\times \\delta}" + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "text", + "content": " only contains the object classes. We add up all the losses to train our SGM. The overall training objective is " + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "inline_equation", + "content": "L = L_{BCE} + \\lambda L_{IoU}" + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 425, + 545, + 568 + ], + "type": "text", + "content": " denotes the loss weights. The advantages of our SGM are as following: 1) Data collection. The self-supervised training eliminates the requirement for target-oriented annotations or supervision from simulators. SGM requires only training with cropped and randomly masked global maps. 2) Scalability. SGM is compatible with various LLMs, allowing for concurrent improvements in our method as LLMs advance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 574, + 429, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 429, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 429, + 588 + ], + "type": "text", + "content": "3.3. ObjectNav with SGM" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 641 + ], + "type": "text", + "content": "The trained SGM is capable of generating unobserved regions based on their visible surroundings, which is utilized to help agent deduce the unobserved regions of the local maps during navigation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Unobserved regions generation. At each timestamp " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " during navigation, the agent constructs a local semantic map " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "m_t" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " (as introduced in Sec. 3.1), and each channel of " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "m_t" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " contains binary-valued pixels. The local semantic map includes numerous unobserved regions as shown in Fig. 3, where the pixel values of these regions are 0 across all channels." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16417" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": "Given the local semantic map " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "m_{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " of time " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": ", we first crop a sub-region of " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "m_{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": ", where the size of this region is " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " times that of the smallest fitting square box around the known regions of " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "m_{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " as shown in Fig. 3. The " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " (e.g. " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "\\epsilon = 140\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " is decided via validation experiments) represents a scaled-up factor with a minimum value of " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": ". The cropped region is resized to a fixed scale " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "m_{t}^{\\prime} \\in \\mathbb{R}^{(N_{o} + N_{s}) \\times L \\times L}" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " (e.g. " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "L = 224" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": " for ViT-Base) and divided into non-overlapping patches. The size of each patch is " + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 72, + 289, + 227 + ], + "type": "text", + "content": ". To eliminate noise and reduce computational complexity, we select a subset of patches to serve as the input of the SGM. The sampling strategy prioritizes the patches, which are 1) informative and 2) adjacent to unobserved regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": "To construct the sampling strategy, we calculate the average pixel value in each patch by " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "W = \\text{Avgpool}(m_t')" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{\\frac{L}{\\delta} \\times \\frac{L}{\\delta}}" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": ", and Avgpool represents the average pooling in each patch for all channels. For each element " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "w_i \\in W" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": ", the higher value indicates that the corresponding patch is more informative, i.e., there are more observed object classes or larger observed regions in this patch. Furthermore, we leverage the Laplacian kernel " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": " as a gradient operator (i.e., edge detector), to operate the " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "V = \\text{Conv}(W, K)" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{\\frac{L}{\\delta} \\times \\frac{L}{\\delta}}" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": " and Conv denotes the convolution operation. The higher value of " + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "inline_equation", + "content": "v_i \\in V" + }, + { + "bbox": [ + 46, + 228, + 289, + 384 + ], + "type": "text", + "content": " demonstrates that the corresponding patch is more likely to be adjacent to the unobserved regions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "text", + "content": " are further processed by flattening and Softmax operations for probability normalization. Then the sampling probability " + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 384, + 288, + 421 + ], + "type": "text", + "content": " of each patch is defined as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 120, + 428, + 287, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 428, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 120, + 428, + 287, + 442 + ], + "type": "interline_equation", + "content": "P = \\alpha \\bar {W} + (1 - \\alpha) \\bar {V} \\tag {4}", + "image_path": "943ee8d916559245caa6dacbdbb541ac9e418976514cb487832472f06c255184.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\bar{W}" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\bar{V}" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": " denote the normalized " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": ", respectively, and " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": " is a trade-off weight. We employ a multinomial distribution for sampling patches. Specifically, given a set of patches " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "m_t' = \\{m_t'(1), m_t'(2), \\ldots, m_t'(n_p)\\}" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "n_p = \\left(\\frac{L}{\\delta}\\right)^2" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": "), and their associated probabilities " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "P = \\{p_1, p_2, \\ldots, p_{n_p}\\}" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": ". The patches are sampled without replacement according to " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "m_t'(i) \\sim \\text{Multinomial}(n, P)" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": ". The number of sampled patches " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": " constitutes only a small fraction (e.g. " + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 47, + 449, + 287, + 557 + ], + "type": "text", + "content": ") of the total." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Based on this strategy, sampled patches are fed into the SGM to predict unobserved regions. The predicted values are continuous, which reflect the confidence in its prediction. Furthermore, the raw prediction of SGM is enhanced by adding the actual local semantic map to form the final generated map, where if a coordinate has already been observed (having values in semantic map), its predicted value is replaced with the confirmed observed value. During ObjectNav task, the agent identifies the pixel with the highest confidence in the target's channel of the generated semantic map. Then the coordinates of this pixel are set as the long-term goal " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": ". Additionally, limited observation (e.g. no available contextual object is observed) may result in" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 313, + 70, + 541, + 274 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 541, + 274 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 541, + 274 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 541, + 274 + ], + "type": "image", + "image_path": "f0dac37d0d55f16e93ddd4876ca967a20a8bcf5c07b259f25460634c96b6e48c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "text", + "content": "Figure 3. During navigation, the agent builds a local semantic map " + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "m_t" + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "text", + "content": " and crops it to " + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "m_t'" + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "text", + "content": ". The patches of " + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "m_t'" + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "text", + "content": " are sampled by multinomial distribution with probability " + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "text", + "content": ". The SGM generates the unobserved regions based on selected " + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 278, + 547, + 335 + ], + "type": "text", + "content": " patches. The long-term goal is determined by the generated map and the target." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 346, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 547, + 407 + ], + "type": "text", + "content": "unreliable prediction of the target (i.e. the confidence of the predicted semantic map is low). Therefore, we adopt the exploration strategy [31, 50] at the beginning of navigation until the prediction confidence of the target exceeds a certain threshold." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "type": "text", + "content": "Navigation policy. Once the long-term goal is identified, the agent simply needs to navigate from its current location " + }, + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "type": "inline_equation", + "content": "(x_{t},y_{t})" + }, + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "type": "text", + "content": " to the long-term goal " + }, + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 304, + 407, + 547, + 540 + ], + "type": "text", + "content": ". Following previous works [5, 37], the local policy is implemented by the Fast Marching Method [41], which calculates the shortest path from current location to the long-term goal based on the occupancy channels of the generated map. Then the local policy calculates deterministic actions for the agent based on its step distance and the shortest path. At each times- tamp, the local policy will re-plan the actions for the agent according to the updated semantic map." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 553, + 388, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 553, + 388, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 553, + 388, + 567 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 574, + 422, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 422, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 422, + 586 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 593, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 628 + ], + "type": "text", + "content": "Dataset. We evaluate our SGM on standard ObjectNav datasets, including Gibson [48], Matterport3D (MP3D) [4] and Habitat-Matterport3D (HM3D) [49] dataset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "For Gibson and MP3D, we follow the setup of [37, 57], we we utilize 25 train /5 val scenes from the Gibson tiny split and choose 6 goal categories with 1,000 val episodes for Gibson. For MP3D, we employ 56 train / 11 val scenes, 21 goal categories and 2,195 episodes for validation. For HM3D, our setup is consistent with [9], where we choose 80 train / 20 val scenes, 6 goal categories and 2,000 valida" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16418" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 152, + 287, + 305 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 148 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 148 + ], + "type": "text", + "content": "Table 1. Comparisons of different map generation variants in the Gibson (val). R/C means the training map is masked by random (R) or connected (C) strategy. The connected masking strategy requires that retained patches must be adjacent to each other (remaining patches are akin to a local map), which is similar to [19, 28] that learn contextual relations by completing the local map. For LLMs, we compare GPT-4 [34] and ChatGLM [17]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 152, + 287, + 305 + ], + "lines": [ + { + "bbox": [ + 48, + 152, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 48, + 152, + 287, + 305 + ], + "type": "table", + "html": "
IDModelMaskLLMMap GenerationNavigation
IoU(%)Recall(%)SR(%)SPL(%)DTS(m)
I 1UNet--19.2847.3667.537.81.76
2ViT-LC-24.1859.4273.839.51.45
3ViT-LR-26.8579.0574.239.61.49
4ViT-BC-22.3155.5073.139.31.53
5ViT-BR-25.4579.2374.139.51.48
6ViT-BCGPT-432.0672.3476.843.41.27
7ViT-BRGPT-439.4787.3377.443.81.15
8ViT-BCChatGLM30.8780.6777.043.51.31
9ViT-BRChatGLM31.7391.6878.044.01.11
", + "image_path": "22acd425de35e67dfe8df2ef0a0c86604e212759bdf36fa82cddcbd3cbccb456.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 316, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 340 + ], + "type": "text", + "content": "tion episodes. The goal categories adopted by these three datasets are listed in supplements." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 341, + 287, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 412 + ], + "type": "text", + "content": "Evaluation metrics. For evaluating the navigation performance, we adopt three standard metrics following [5, 37, 56]: 1) SR: the ratio of success episodes. 2) SPL: the success rate weighted by the path length, which measures the efficiency of the path length. 3) DTS: the distance to the goal at the end of the episode." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 413, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 474 + ], + "type": "text", + "content": "To assess the quality of map predictions, we employ the following two metrics: 1) IoU: the pixel intersection over union for all channels (both occupancy and object). 2) Recall: the proportion of true positive predicted object categories over the total number of ground-truth categories." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "text", + "content": "Implementation details. For the self-supervised training of SGM, we sample 400,000 train /1,000 val sub-maps for training and validation in each dataset. We implement the SGM based on ViT-base/16, where the visual encoder, cross-modality encoder and decoder are respectively composed of 8, 4 and 2 Transformer blocks. The training mask ratio is set to " + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "text", + "content": ", the input size " + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "inline_equation", + "content": "L = 224" + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "text", + "content": ", and patch size " + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\delta = 16" + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "text", + "content": ". We use the Adam optimizer [25] with a base learning rate of 0.00015. The warmup epoch is linearly scaled when the training epoch increases to 40. After warmup epochs, the learning rate is decayed by a factor of 0.05. The loss weights " + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 46, + 474, + 287, + 617 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "For ObjectNav task, since constructing local semantic map requires the semantic segmentation model, we adopt publicly available Mask-RCNN [21] from [37] for Gibson, RedNet [23] from [37] for MP3D, and Mask-RCNN [21] from [56] for HM3D. The scaled-up factor " + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon = 140\\%" + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": ", the number of selected patches " + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "n = 59" + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": ", and sample weights " + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": ". The experiments for these hyper-parameters are detailed in supplements. The turn angle is set to 30 degrees," + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 543, + 201 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 543, + 201 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 543, + 201 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 543, + 201 + ], + "type": "image", + "image_path": "3b448eed6905672d37daa9586ecece5b821bdc582b4f662966ff145c16c5946e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 205, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 282 + ], + "type": "text", + "content": "Figure 4. Map reconstruction results. The 'w/ EO' means only using episodic observations in reconstruction, while 'w/ EO and GK' denotes leveraging both episodic observations and LLMs (ChatGLM). General knowledge enables the model to predict the completely unobserved contextual objects (see the regions highlighted by red circles). These sub-maps sourced from the val rooms of Gibson are unseen during training." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 293, + 511, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 511, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 511, + 304 + ], + "type": "text", + "content": "and the step distance of move_forward is " + }, + { + "bbox": [ + 306, + 293, + 511, + 304 + ], + "type": "inline_equation", + "content": "25\\mathrm{cm}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 312, + 416, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 416, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 416, + 324 + ], + "type": "text", + "content": "4.2. Evaluation Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 331, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 557 + ], + "type": "text", + "content": "Comparisons with previous map completion methods. Prior methods [19, 28] train a UNet [40] to directly predict unobserved regions based on the top-down map of a single timestamp. This comparison is to determine whether using UNet or learning contextual relations directly from the local map is more effective than our SGM (utilizing ViT and learning with randomly masked sub-maps). As shown in Tab. 1, we compare these two variants under identical training epochs and datasets. The UNet variant underperforms others in both map generation and navigation. In learning contextual relations, the random masking strategy (SGM) outperforms connected masking strategy [19, 28]. We infer that since visible patches are closely clustered in the connected masking strategy, the context of patches distant from the visible ones is completely absent, leading to difficulties for model in capturing the context relations of these patches during training. The results demonstrate that our SGM is more effective in capturing contextual relationships and assisting the navigation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "content": "Model complexity. We compare the impact of more complex models on map generation and navigation. As indicated by the row II in Tab. 1, the more complex model (i.e. ViT Large) only yields a marginal performance improvement. Hence, we conjecture that the ViT Base model is sufficiently capable for the task. Consequently, our SGM is ultimately implemented based on the ViT Base model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Impact of LLMs. Our SGM not only leverages episodic observations but also incorporates general knowledge obtained from LLMs for prediction. Compared to rows II and III in Tab. 1, there is a significant improvement on the recall metric, which suggests that LLMs can substantially bolster the prediction of object categories. As shown" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16419" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 77, + 542, + 191 + ], + "blocks": [ + { + "bbox": [ + 52, + 77, + 542, + 191 + ], + "lines": [ + { + "bbox": [ + 52, + 77, + 542, + 191 + ], + "spans": [ + { + "bbox": [ + 52, + 77, + 542, + 191 + ], + "type": "image", + "image_path": "8553ee42d187b371e0a505e69da743016e4735fc9c85bef7f9fe8727ecc20848.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "type": "text", + "content": "Figure 5. Navigation episode with SGM in Gibson (val). The top row displays the agent's RGB view and local semantic map, including the trajectory and long-term goal (indicated by the deep blue dot). The bottom row shows the generated map by SGM. At about " + }, + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "type": "text", + "content": " of the navigation process (i.e. " + }, + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "type": "inline_equation", + "content": "t = 20" + }, + { + "bbox": [ + 46, + 195, + 546, + 240 + ], + "type": "text", + "content": "), the generated map accurately predicts the target's location even though the target has not yet been observed. Besides, SGM not only precisely predicts the target (couch), but also its contextual objects (e.g. potted plant)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 245, + 280, + 487 + ], + "blocks": [ + { + "bbox": [ + 55, + 245, + 280, + 487 + ], + "lines": [ + { + "bbox": [ + 55, + 245, + 280, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 245, + 280, + 487 + ], + "type": "image", + "image_path": "3c1b74e8a5838876325b21c5ec73a473f51470c339a0e539bc31977d5d6400e9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 491, + 287, + 526 + ], + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 526 + ], + "type": "text", + "content": "Figure 6. More generated maps during navigation. As shown by the circled objects, the generated map accurately anticipates the location of unobserved objects." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": "in the Fig. 4, the model with solely episodic observations is capable of completing the contours of partially observed objects, while it struggles to predict entirely unobserved categories. However, the general knowledge from LLMs provides rich semantic contextual priors, enables the model to predict the context objects that are completely unobserved (e.g. the chairs in the first row, and the potted plants and sinks in the second row). Additionally, we compare two LLMs: GPT-4 [34] and ChatGLM [17]. The results show that the choice of LLMs has minimal impact on performance. Moreover, as ChatGLM is publicly available, thus, we employ it to provide general knowledge. To improve inference speed, we extract all possible combinations of goal categories to pre-generate the prompt and obtain responses by using LLMs. The SGM directly leverages pre-extracted" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 312, + 305, + 538, + 415 + ], + "blocks": [ + { + "bbox": [ + 305, + 245, + 546, + 300 + ], + "lines": [ + { + "bbox": [ + 305, + 245, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 546, + 300 + ], + "type": "text", + "content": "Table 2. Ablation study of different components. GT means the long-term goal is set to the ground truth location of the target. 'EO' denotes the episodic observation, 'GK' represents the general knowledge and 'Explr' means using exploration strategy at the beginning of navigation." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 305, + 538, + 415 + ], + "lines": [ + { + "bbox": [ + 312, + 305, + 538, + 415 + ], + "spans": [ + { + "bbox": [ + 312, + 305, + 538, + 415 + ], + "type": "table", + "html": "
IDModulesGibsonMP3D
GTEOGKExplrSR(%)SPL(%)DTS(m)SR(%)SPL(%)
I 21✓91.772.30.38--
2✓71.540.81.4631.912.2
3✓✓74.441.31.4934.713.2
II 64✓65.137.91.7625.911.6
5✓✓74.139.51.4833.011.8
6✓✓78.044.01.1137.614.7
", + "image_path": "0bedc864aee964f11a8db6772b8e5a3d6e5cb7ef959bcfa56a6dc0ece34cfab1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 424, + 535, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 424, + 535, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 424, + 535, + 436 + ], + "type": "text", + "content": "responses for prediction during both training and testing." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "text", + "content": "Visualization of navigating with SGM. We further visualize the generated maps of SGM during the navigation, as shown in Fig. 5 and 6, noting that the scenes are unseen. As Fig. 5 illustrated, at the beginning of navigation " + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "inline_equation", + "content": "(t = 0)" + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "text", + "content": ", the generated image offers limited additional information due to minimal observations. However, as more of the scene becomes observed, by " + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "inline_equation", + "content": "t = 20" + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "text", + "content": " (only about " + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 700 + ], + "type": "text", + "content": " of the entire navigation), SGM successfully predicts the location of the target (couch) even though it has not yet been observed. Then, SGM continues to guide the agent by determining the long-term goal based on the generated map. Moreover, it is notable that SGM not only accurately locates the target but also anticipates its context objects (e.g. potted plant). Fig. 6 provides additional generated results, which is evident that the generated maps correctly estimate the approximate locations of objects and their context, while there is still a deviation in their absolute positions. However, we consider this deviation to be tolerable, as even humans cannot precisely locate unseen objects in unseen scenes. These two visualizations indicate that our SGM effectively scales up limited local maps by generating the unobserved regions, thereby guiding the agent to infer the target's location." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "Ablations study. As shown in row I of Tab. 2, the agent" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 133, + 71, + 462, + 78 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 71, + 462, + 78 + ], + "spans": [ + { + "bbox": [ + 133, + 71, + 462, + 78 + ], + "type": "text", + "content": "□blank□floor wall □chair □couch □potted plant □bed □toilet □tv □oven □dining table □sink □refrigerator □book □clock □vase □cup □bottle" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16420" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 130, + 288, + 352 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "type": "text", + "content": "Table 3. Comparisons with the related works in Gibson and MP3D val. Note that THDA [32] and Habitat-Web [38] use additional data for training, while Red-Rabbit [53] utilizes auxiliary tasks to train the agent. For SemExp [5], L2M [19] and Stubborn [31], we report results from [57]. * denotes our implementation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 130, + 288, + 352 + ], + "lines": [ + { + "bbox": [ + 48, + 130, + 288, + 352 + ], + "spans": [ + { + "bbox": [ + 48, + 130, + 288, + 352 + ], + "type": "table", + "html": "
IDMethodGibsonMP3D
SR(%)SPL(%)DTS(m)SR(%)SPL(%)DTS(m)
1Random0.40.43.890.50.58.05
2DD-PPO [46]15.010.73.248.01.86.94
3Red-Rabbit [53]---34.67.9-
4THDA [32]---28.411.05.62
I5SSCNav* [28]---27.111.25.71
6EmbCLIP* [24]68.139.51.1529.210.15.42
7Habitat-Web [38]---35.410.2-
8ENTL [26]---17.05.0-
9FBE [50]48.528.92.5629.510.65.00
10ANS [7]67.134.91.6621.29.46.31
11SemExp [5]71.139.61.3928.310.96.06
II12PONI [37]73.641.01.2527.812.05.63
13L2M [19]---32.111.05.12
14Stubborn [31]---31.213.55.01
153D-aware [57]74.542.11.1634.014.64.78
16SGM (Ours)78.044.01.1137.714.74.93
", + "image_path": "804f05992ca774ab9e94350c3d3af05073467191f45d8d74d23305cc91c3c1c8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 364, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 508 + ], + "type": "text", + "content": "only relying on SGM has already achieved comparable performance to some supervised methods [5, 37]. Furthermore, the row II of Tab. 2 indicates that introducing an exploration strategy in the early stages of navigation is effective, which prevents misguidance by low-confidence predictions resulted from limited observations. Our exploration strategy utilizes the area potential function from [37], which calculates the nearest frontier as the long-term goal. In contrast to the computation-based FBE [50], the area potential function learns to predict potential frontiers through supervised training. The ablation studies demonstrate the effectiveness of each component in our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "content": "Comparisons with the related works. Since there is no existing self-supervised work for ObjectNav task, our comparison is limited to previous supervised methods. We consider the following baselines: the end-to-end RL methods [9, 24, 26, 28, 32, 46, 53], the imitation learning method [38], and modular methods [5, 6, 19, 31, 37, 50, 56, 57] Note that, some works leverage additional data [10, 32, 38] or auxiliary task [9, 53] to improve the performance. Thus, it is challenging to compare all the methods in an equitable manner. Consequently, our focus is specifically on the most relevant baselines: SemExp [5], PONI [37], L2M [19], SSCNav [28], PEANUT [56], where PONI and PEANUT integrate goal-related function trained by supervised learning into SemExp, while L2M and SSCNav enhance navigation performance by learning to complete egocentric top-down map of single timestamp. They are also trained with supervised learning, while are limited to consider only single-" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 337, + 98, + 514, + 186 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 4. Comparisons with the related works in HM3D val. * denotes our implementation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 337, + 98, + 514, + 186 + ], + "lines": [ + { + "bbox": [ + 337, + 98, + 514, + 186 + ], + "spans": [ + { + "bbox": [ + 337, + 98, + 514, + 186 + ], + "type": "table", + "html": "
IDMethodHM3D
SR(%)SPL(%)
1DD-PPO [46]27.914.2
2Habitat-Web [38]57.623.8
3RIM [9]57.827.2
4PEANUT* [56]59.130.3
5SGM (Ours)60.230.8
", + "image_path": "d1bc8e6bfb62abf3944f07f269de4746d61ed242096cd746b37a6f3392cab702.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 197, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 197, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 197, + 545, + 328 + ], + "type": "text", + "content": "frame observations. In contrast, our SGM predicts the unobserved regions for the broader local map, which incorporates full observations from time 0 to t. Notably, PEANUT [56] initially reports results on MP3D and HM3D, however, they only release their code for HM3D. Therefore, we only compare with [56] on HM3D with re-implementation results in our setup. Besides, L2M and SSCNav are evaluated with their self-made validation data. Thus, for comparing their results, we report our own implementations or adopt re-implementation results from other work [57] with experimental settings that align with ours." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "text", + "content": "We compare our SGM with the related works on the validation set of Gibson, MP3D and HM3D datasets, as shown in Tab. 3 and 4. Despite our SGM being self-supervised, it achieves comparable performance with existing supervised methods across all metrics on these datasets. Particularly on the Gibson dataset, compared to the current state-of-the-art [57], our SGM outperforms 3D-aware [57] by " + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "inline_equation", + "content": "-0.05\\mathrm{m}" + }, + { + "bbox": [ + 304, + 329, + 545, + 437 + ], + "type": "text", + "content": " in SR, SPL and DTS metrics, respectively. Note that lower value on DTS indicates better performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 450, + 384, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 450, + 384, + 463 + ], + "spans": [ + { + "bbox": [ + 306, + 450, + 384, + 463 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 471, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 663 + ], + "type": "text", + "content": "In this work, we present the Self-supervised Generative Map (SGM) for the object goal navigation task. Our SGM captures contextual relationships of both objects and environments through self-supervised training. SGM utilizes two distinct yet complementary information for prediction: episodic observations and general knowledge from Large Language Models (LLMs), where episodic observations provide geometric details, and general knowledge offers semantic priors. During navigation, the local semantic map maintained by agent is sampled by proposed sampling strategy to select informative patches. Then the selected patches are fed into SGM to generate the unobserved regions. The generated map helps agent infer the likely location of the target. The experimental results indicate that despite being a self-supervised method, our SGM achieves comparable performance to previous supervised methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 669, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 669, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 669, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U23B2012, in part by Beijing Natural Science Foundation under Grant JQ22012, Z190020." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16421" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. 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Existing works mainly focus on embedding images of different modalities into a unified space to mine modality-shared features. They only seek distinctive information within these shared features, while ignoring the identity-aware useful information that is implicit in the modality-specific features. To address this issue, we propose a novel Implicit Discriminative Knowledge Learning (IDKL) network to uncover and leverage the implicit discriminative information contained within the modality-specific. First, we extract modality-specific and modality-shared features using a novel dual-stream network. Then, the modality-specific features undergo purification to reduce their modality style discrepancies while preserving identity-aware discriminative knowledge. Subsequently, this kind of implicit knowledge is distilled into the modality-shared feature to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features. Extensive experiments on multiple public datasets demonstrate the superiority of IDKL network over the state-of-the-art methods. Code is available at https://github.com/1KK077/IDKL.", + "bbox": [ + 75, + 324, + 473, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 737, + 209, + 752 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visible-Infrared Person Re-Identification (VI-ReID) aims to match pedestrian images across multiple nonoverlapping camera views and different modalities. Advanced surveillance systems today are capable of automatically switching from visible to infrared mode at nightfall, ensuring an ample supply of trainable data. However, the unique modality of infrared images create significant domain discrepancies and a more complex environment. This makes previous single-modality methods, which are based", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c625676804a52ff86b1ad97cd2d73319cac1409b6d6023736052fa3ef8505d52.jpg", + "image_caption": [ + "Figure 1. Previous methods focused on seeking discriminative information within modality-shared features, overlooking the fact that there are discriminative clues implicit in modality-specific features. It is worth considering utilization of the implicit discriminative information to enhance shared invariant feature." + ], + "image_footnote": [], + "bbox": [ + 511, + 290, + 883, + 492 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "solely on visible images, less efficient for VI-ReID tasks.", + "bbox": [ + 500, + 592, + 877, + 607 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, numerous advanced methods have emerged in the field of VI-ReID. In conclusion, these approaches can generally be categorized into two types: the first aims to learn modality-shared features directly from raw modal data, and the second seeks to incorporate additional modal information to refine the feature space or bridge the modal gap, thereby facilitating the search for modality-shared features. Raw modal data based method [2, 4, 7, 8, 17, 19, 33, 49] is to embed different modality images into the same space and align them on feature-level so that model learn modality invariant feature directly. Despite original images based methods has achieved desirable results, they still remain a huge gap between different modalities in feature space. In order to bridge the gap between visible and infrared modalities and construct a continuous space for better learning modality-shared features, various methods based on introducing extra information [14, 29, 30, 34, 38, 42, 45] have emerged constantly.", + "bbox": [ + 496, + 609, + 892, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although significant improvements have been made in", + "bbox": [ + 519, + 885, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 1, + 807, + 18 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 323, + 16, + 723, + 30 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 31, + 754, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "393", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "current VI-ReID methods, these models inevitably discard some discriminative information that relies on modality-specific features, which is not fully exploited and utilized previously. These discriminative cues that exist in modality-specific features can be referred to as implicit discriminative information, as shown by the green area in Fig. 1, such as color, grayscale spectrum, contrast, saturation, and so on. Therefore, relying solely on modality-shared cues can limit the upper boundary of the discrimination ability of the feature representation. Utilizing implicit modality-specific characteristics effectively is essential to enhance the distinctiveness of modality-invariant features. However, we cannot directly use the modality-specific knowledge due to the modality discrepancies it contains. Instead, we need to reduce these discrepancies while preserving the identity-aware discriminative information inherent in the implicit knowledge. Meanwhile, traditional VI-ReID methods involving distillation, alignment, and mutual learning typically rely on logits [35, 44, 47]. However, there is no involvement of the classifier during the testing phase, with matching performed only at the feature level. Therefore, conducting discriminative information distillation at the feature level is also essential.", + "bbox": [ + 76, + 90, + 472, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above limitations, in this paper, we propose an Implicit Discriminative Knowledge Learning (IDKL) framework that captures implicit invariant information from modality-specific features and distills it into modality-shared features to enhance their discriminative capability. We first extract modality-specific and modality-shared features using the modality discriminator and modality confuser, respectively. The modality discriminator effectively distinguishes between different modal features, endowing them with specific characteristics; whereas the modality confuser is unable to differentiate between modal features, thereby imparting shared characteristics to them. Since the modality-specific feature after previous stage contains substantial modality discrepancies, it is not suitable for direct distillation into the shared feature. We initially employ Instance Normalization to reduce domain discrepancies. However, it is crucial to acknowledge that IN inevitably results in the loss of some discriminative features. Therefore, we aim to reduce its modality style discrepancy while preserving identity-aware discriminative knowledge. Subsequently, we distill this implicit knowledge into the modality-shared feature at both the feature-level through feature graph structure, and the semantic-level through the logit vector to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features.", + "bbox": [ + 76, + 441, + 472, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this paper can be summarized as follows:", + "bbox": [ + 76, + 837, + 470, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose the Implicit Discriminative Knowledge Learning (IDKL) network to utilize the discriminative", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "knowledge implicit in the modality-specific features to enhance the upper bound of discriminative power for the modality-shared feature.", + "bbox": [ + 511, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To reduce the modality style discrepancy without losing discriminative information of modality-specific information, we propose an IN-guided Information Purifier (IP), which is supervised by the discrimination enhancing loss and discrepancy reducing loss.", + "- The novel TGSA loss is developed to distill the discriminative modality-specific information into modality-shared feature and mitigate inter-modality discrepancy of modality-shared feature sufficiently. The substantial experimental results demonstrate the superiority of our method." + ], + "bbox": [ + 500, + 136, + 893, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 316, + 640, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visible Modality Person ReID. Person ReID has received increasing success in recent years, which aims to implement pedestrian retrieval between visible images. It has suffered huge challenges including various viewpoints, illuminations, postures and so on. To solve these problems, most methodologies [24, 25, 39, 48] are designed to obtain unified intra-class and discriminative inter-class representation by training CNN network. To further enhance the distinguishability of features, Sun et al. [27] proposed aligning part feature directly instead of using external cues. He et al. [9] caught the hot spot of transformer and first proposed the transformer variant applying on single-modality person ReID. Simultaneously, person ReID has developed some significant branches yet, such as Unsupervised Domain Adaptive Person ReID (UDA-ReID) and Domain Generalization Person ReID (DG-ReID) [41]. Although existing methods have made wide progress in visible modality person ReID, they suffer performance degradation when applied to visible-infrared person ReID due to the severe cross-modality discrepancy.", + "bbox": [ + 496, + 340, + 893, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visible-Infrared Person ReID (VI-ReID). VI-ReID is a cross-modality person retrieval problem, which aims at matching daytime visible and nighttime infrared images. It not only faces difficulties encountered in traditional single-motility person ReID task, but also the main challenge of huge modality discrepancy which caused by different camera spectra. To solve the these issues, numerous approaches are proposed to search shared feature[1, 5, 18, 20, 32, 36, 39, 46]. Wu et al. [32] first formulated the VI-REID issue and contributed a new cross-modality dataset SYSUMM01, which is of great significance to the following research. Ye et al. [36] proposed a part-level feature interaction and graph structure attention to enhance the discrimination of invariant feature. Meanwhile, some work begin to introduce additional modal information to jointly search for invariant features [14, 21, 28, 30, 45]. Wang et al. [30] combined RGB three channels feature and IR single", + "bbox": [ + 496, + 643, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "394", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ee84baa10c9a9a55770096e39ed7e4c62ae4a94a7d80d533426696e7004593ad.jpg", + "image_caption": [ + "Figure 2. Framework of the proposed Implicit Discriminative Knowledge Learning (IDKL) model. The dual one-stream network built by resnet blocks first extracts the modality-specific $F_{sp}$ and modality shared feature $F_{sh}$ under the constraint of modality discriminator and modality confuser accordingly, while the common ReID loss is used to optimize network basely. Then, the modality-specific feature is fed into the information purifier to regulate the modality style discrepancy while preserving the implicit discriminative information and obtain the purified modality-specific feature $\\widetilde{F}_{sp}$ . Subsequently, this implicit knowledge is distilled into the modality-shared feature through TGSA and CSA. Finally, the $\\mathcal{L}_{mdr}$ is further proposed to minimize modality discrepancy within the enhanced modality-shared feature." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 872, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "channel feature into united four channels feature to reduce modal differences. Jiang et al. [14] employed a global prototype to generate the missing modality counterpart through transformer. However, these generation based compensation methods inevitably introduce much noise and most of present methods aim to align modal discrepancy and extract modality invariant feature. They ignored use of beneficial style information contained in specific features to increase distinctiveness.", + "bbox": [ + 75, + 426, + 470, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Interactive Learning. In knowledge distillation, a teacher-student model is used to transfer the knowledge learned by a larger complex teacher model to a smaller simple student model. Different from the one-way transfer between a teacher and a student, deep mutual learning [44] is an ensemble of students which learns collaboratively and teaches each other throughout the training process. Some work applied this idea into VI-ReID for interactive learning in different modalities. Zheng et al. [47] enhanced invariant features learning by using interactive learning between two modality. Ye et al. [35] employed multi-classifier to reduce modality discrepancy on logits-level. Wu et al. [33] distilled RGB and IR knowledge mutually by four classifier to achieve inter shared representation. However, they only learn the knowledge within the semantic-level.", + "bbox": [ + 75, + 561, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 800, + 210, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we detail the proposed Implicit Discriminative Knowledge Learning (IDKL) framework as shown in Fig. 2. IDKL first distinguishes modality-specific features from modality-shared features through two network branches, which are constrained by modality discriminator", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and modality confuser, respectively. Simultaneously, common ReID loss is used to endow feature with representation. Then, an Information Purifier (IP) is developed to reduce the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. Finally, we distill the implicit discriminative knowledge across two branches into the modality-shared feature through Triplet Graph Structure Alignment (TGSA) at the feature-level and Class Semantic Alignment (CSA) at the logit-level. Additionally, to reduce modality discrepancy of shared feature, we proposed the Modality Discrepancy Reduction (MDR) loss within the modality-shared branch. As the discriminative information increases and modality discrepancy decreases constantly, the enhanced modality-shared feature can be obtained.", + "bbox": [ + 496, + 426, + 890, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, we represent visible and infrared images in a dataset as $V = \\{\\pmb{x}_i^V\\}_{i=1}^{N_V}$ and $I = \\{\\pmb{x}_i^I\\}_{i=1}^{N_I}$ , respectively. Typically, the number of images sampled in a mini-batch is equal across both modalities, i.e., $N_V = N_I = N = P \\times K$ , where $N_V$ and $N_I$ denote the number of images sampled from the visible and infrared modalities, respectively. Here, $N$ represents the number of images from a single modality, $2N$ is the total number of images in a mini-batch, $P$ is the number of distinct person classes, and $K$ is the number of images from each class within a single modality. We can therefore represent the images and their corresponding labels in a mini-batch as $X = \\{\\pmb{x}_i | \\pmb{x}_i \\in V \\cup I\\}_{i=1}^{2N}$ and $Y = \\{\\pmb{y}_i\\}_{i=1}^{N_p = P}$ , respectively. These images $X$ are fed into two separate network branches to extract the modality-specific features $F_{sp}$ which contains $F_{sp,V}, F_{sp,I}$ and the shared features $F_{sh}$ which contains $F_{sh,V}, F_{sh,I}$ as fol", + "bbox": [ + 496, + 656, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "395", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lows:", + "bbox": [ + 76, + 92, + 117, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {s p} = E _ {s p} (\\boldsymbol {x} \\mid \\Theta , \\Psi), \\boldsymbol {F} _ {s h} = E _ {s h} (\\boldsymbol {x} \\mid \\Theta , \\Phi), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 114, + 468, + 132 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $E_{sp}$ and $E_{sh}$ denote the specific and the shared feature extractor by employing ResNet-50, respectively. Among the sturctures of ResNet-50, the global average pooling replaced by Gem pooling[24, 39] which is a pooling operation between maximum pooling and average pooling. And $\\Theta$ is the shallow layer parameters with the first three blocks of ResNet-50, $\\Psi$ and $\\Phi$ is the deep layer parameters of different branches with the last two blocks of ResNet-50.", + "bbox": [ + 75, + 138, + 468, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Modality Confuser and Discriminator", + "text_level": 1, + "bbox": [ + 76, + 267, + 403, + 282 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modality Confuser. For each sample image $\\boldsymbol{x}_i$ , there is a modality label $t_i \\in \\{0,1\\}$ . To learn modality-irrelated shared information, similar to [6], our goal is to confuse different domains such that a domain classifier cannot distinguish the domain of origin for a sample. We employ an adversarial modality classifier based on the Gradient Reversed Layer (GRL) as the modality confuser. The constraint loss for the modality confuser is given by:", + "bbox": [ + 75, + 290, + 470, + 411 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C j} = - \\frac {1}{2 N} \\sum_ {i = 1} ^ {2 N} t _ {i} \\cdot \\log p \\left(C _ {j} \\left(G R L \\left(\\boldsymbol {F} _ {s h} ^ {i}\\right)\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 419, + 468, + 459 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C_j$ represents the $j$ -th modality confuser in the modality-shared branch, $p(\\cdot)$ is the prediction probability obtained via the softmax function, and $t_i$ is the modality label.", + "bbox": [ + 75, + 465, + 468, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modality Discriminator. To adequately learn modality-related specific information, we employ a modality classifier as the Modality Discriminator. This classifier, which does not use GRL, is applied on the specific branch to extract modality-specific features. The classification loss is formulated as follows:", + "bbox": [ + 75, + 526, + 468, + 614 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D j} = - \\frac {1}{2 N} \\sum_ {i = 1} ^ {2 N} t _ {i} \\cdot \\log p \\left(D _ {j} \\left(\\boldsymbol {F} _ {s p} ^ {i}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 622, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D_{j}$ denotes the j-th modality discriminator in the modality-specific branch.", + "bbox": [ + 75, + 669, + 468, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The combined loss from the modality confuser and discriminator is given by:", + "bbox": [ + 75, + 699, + 468, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C} = \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {C j}, \\quad \\mathcal {L} _ {D} = \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {D j}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 737, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To efficiently extract both modality-specific and modality-shared features, we combine these modality classifier losses with the standard ReID loss $\\mathcal{L}_{\\text{reid}}$ , which includes cross-entropy and hard triplet loss. These are applied to both the modality-specific and modality-shared branches as follows:", + "bbox": [ + 75, + 786, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s p} = \\mathcal {L} _ {\\text {r e i d}} \\left(\\boldsymbol {f} _ {s p}\\right) + \\mathcal {L} _ {D}, \\mathcal {L} _ {s h} = \\mathcal {L} _ {\\text {r e i d}} \\left(\\boldsymbol {f} _ {s h}\\right) + \\mathcal {L} _ {C}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb {f}\\in \\mathbb{R}^{B\\times C}$ is the pooling feature corresponding to $\\pmb {F}\\in \\mathbb{R}^{B\\times C\\times H\\times W}$", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, the base loss for our model is formulated as:", + "bbox": [ + 517, + 121, + 852, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b} = \\mathcal {L} _ {s h} + \\mathcal {L} _ {s p}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 143, + 890, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Information Purifier", + "text_level": 1, + "bbox": [ + 500, + 167, + 692, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Information Purifier (IP) is designed to minimize the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. The IP integrates Instance Normalization (IN), which is known to reduce domain discrepancies [13, 23, 48]. However, it is important to recognize that IN inevitably leads to the loss of some discriminative features [11, 15], potentially hindering the high performance of ReID.", + "bbox": [ + 496, + 191, + 890, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To overcome the aforementioned issues, we have designed a dual-mask network guided by Instance Normalization (IN) to alleviate modality style discrepancies while preserving implicit discriminative knowledge. Firstly, we apply IN on the modality-specific feature to obtain the normalized feature $\\widehat{\\pmb{F}}_{sp}$ by:", + "bbox": [ + 496, + 313, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\boldsymbol {F}} _ {s p} = \\operatorname {I N} \\left(\\boldsymbol {F} _ {s p}\\right) = \\frac {\\boldsymbol {F} _ {s p} - \\operatorname {E} \\left[ \\boldsymbol {F} _ {s p} \\right]}{\\sqrt {\\operatorname {V a r} \\left[ \\boldsymbol {F} _ {s p} \\right] + \\epsilon}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 411, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the $\\epsilon$ represents a safety factor to ensure the denominator is not zero. The mean $\\operatorname{E}[\\cdot]$ and variance $\\operatorname{Var}[\\cdot]$ are calculated along each channel.", + "bbox": [ + 496, + 453, + 890, + 497 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following the approach of SE-Net [10], we generate two channel-wise masks $\\mathbf{m}_e$ and $\\mathbf{m}_r$ by:", + "bbox": [ + 496, + 497, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {m} _ {e} = \\sigma \\left(\\mathrm {W} _ {2} \\delta \\left(\\mathrm {W} _ {1} g \\left(\\boldsymbol {F} _ {s p}\\right)\\right)\\right), \\mathbf {m} _ {r} = \\sigma \\left(\\mathrm {W} _ {4} \\delta \\left(\\mathrm {W} _ {3} g \\left(\\widehat {\\boldsymbol {F}} _ {s p}\\right)\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 534, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g(\\cdot)$ denotes the pooling operation, $W_{1}, W_{3} \\in \\mathbb{R}^{\\frac{c}{r} \\times c}$ and $W_{2}, W_{4} \\in \\mathbb{R}^{c \\times \\frac{c}{r}}$ are learnable parameters in the four fully-connected (FC) layers which are followed by the ReLU activation function $\\delta(\\cdot)$ and the sigmoid activation function $\\sigma(\\cdot)$ . To balance the calculate consumption, the dimension reduction ratio $r$ is set to 16.", + "bbox": [ + 496, + 566, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The channel-wise masks $\\mathbf{m}_e$ and $\\mathbf{m}_r$ indicate enhancement of discriminative characteristics and reduction of discrepancies attention mask, respectively. So we can obtain the stronger distinctiveness $F_{sp}^{d+}$ and the smaller modality differences $\\widehat{F}_{sp}^{m-}$ by:", + "bbox": [ + 496, + 657, + 890, + 741 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {s p} ^ {d +} = \\mathbf {m} _ {e} \\odot \\boldsymbol {F} _ {s p}, \\widehat {\\boldsymbol {F}} _ {s p} ^ {m -} = \\mathbf {m} _ {r} \\odot \\widehat {\\boldsymbol {F}} _ {s p}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 750, + 890, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, the discrimination enhancing loss $\\mathcal{L}_e$ and the discrepancy reducing loss $\\mathcal{L}_r$ are calculated to supervise $\\mathbf{m}_e$ and $\\mathbf{m}_r$ respectively as:", + "bbox": [ + 496, + 776, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e} = \\text {S o f t p l u s} \\left(h \\left(C _ {s p} \\left(\\boldsymbol {f} _ {s p} ^ {d +}\\right)\\right) - h \\left(C _ {s p} \\left(\\boldsymbol {f} _ {s p}\\right)\\right)\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 828, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r} = \\text {S o f t p l u s} \\left(d \\left(\\widehat {\\boldsymbol {f}} _ {s p, V} ^ {m -}, \\widehat {\\boldsymbol {f}} _ {s p, I} ^ {m -}\\right) - d \\left(\\widehat {\\boldsymbol {f}} _ {s p, V}, \\widehat {\\boldsymbol {f}} _ {s p, I}\\right)\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 861, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "396", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\mathcal{L}_e$ aims to imbue the generated $\\mathbf{F}_{sp}^{d+}$ with greater semantic distinctiveness compared to $\\mathbf{F}_{sp}$ , while $\\mathcal{L}_r$ seeks to ensure that $\\widehat{\\mathbf{F}}_{sp}^{m-}$ exhibit smaller modality differences than $\\widehat{\\mathbf{F}}_{sp}$ . And Softplus $(\\cdot) = \\ln(1 + \\exp(\\cdot))$ is a function with monotonic increase, designed to alleviate optimization challenges by circumventing negative values in loss.", + "bbox": [ + 76, + 90, + 467, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, an alternating integration strategy is employed to extract the distinctive information from $\\widetilde{\\mathbf{F}}_{sp}^{m - }$ by applying $\\mathbf{m}_e$ and the invariant information from $\\mathbf{F}_{sp}^{d + }$ by applying $\\mathbf{m}_r$ . Thus, The two sets of features extracted in this way both demonstrate smaller modality differences and stronger implicit discriminative information. By integrating them, we derive the purified modality-specific feature $\\widetilde{\\mathbf{F}}_{sp}$ as:", + "bbox": [ + 75, + 186, + 467, + 295 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {F}} _ {s p} = \\mathbf {m} _ {e} \\odot \\widehat {\\boldsymbol {F}} _ {s p} ^ {m -} + \\mathbf {m} _ {r} \\odot \\boldsymbol {F} _ {s p} ^ {d +}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 308, + 467, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Intuitively, the pooling feature $\\widetilde{f}_{sp}$ of implicit feature $\\widetilde{\\pmb{F}}_{sp}$ is also constraint with ReID loss. So the information purify loss $\\mathcal{L}_{ip}$ of this section is summarized as:", + "bbox": [ + 76, + 342, + 467, + 393 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i p} = \\mathcal {L} _ {e} + \\mathcal {L} _ {r} + \\mathcal {L} _ {\\text {r e i d}} (\\tilde {\\boldsymbol {f}} _ {s p}). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 404, + 467, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Implicit Knowledge Distillation", + "text_level": 1, + "bbox": [ + 76, + 440, + 352, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To ensure that the modality-shared feature comprehensively learns and integrates implicit information, we perform distillation from both the feature-level through TGSA and logit-level through CSA.", + "bbox": [ + 76, + 464, + 467, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.1 Triplet Graph Structure Alignment (TGSA)", + "text_level": 1, + "bbox": [ + 76, + 544, + 434, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To endow the shared feature with discriminative information and reduce modality discrepancy at the feature level, we develop a triplet feature graph structure alignment loss. This approach is motivated by the fact that the feature graph structure contains abundant information about the relationships and distribution between features, such as inter-class distinctiveness and intra-class diversity. These characteristics are utilized to unearth potential feature relationships and enhance the feature representation in [17, 36]. The graph structure affinity matrix which indicates the relationships between features is calculated by:", + "bbox": [ + 75, + 568, + 467, + 734 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i j} = \\frac {\\exp \\left(L \\left(\\left[ l \\left(\\boldsymbol {f} _ {i}\\right) \\| l \\left(\\boldsymbol {f} _ {j}\\right) \\right] \\cdot \\boldsymbol {w}\\right)\\right)}{\\sum_ {k \\in \\mathcal {N} _ {i}} \\exp \\left(L \\left(\\left[ l \\left(\\boldsymbol {f} _ {i}\\right) \\| l \\left(\\boldsymbol {f} _ {k}\\right) \\right] \\cdot \\boldsymbol {w}\\right)\\right)}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 744, + 467, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $L$ denote LeakyReLU activation function, $[\\cdot \\| \\cdot ]$ denote concatenate operation and $\\mathcal{N}_i$ denotes the neighbor samples which are used to normalize for the ith sample. $l(\\cdot)$ is feature dimension transformation layer and $\\pmb{w}$ is the full connection layer to calculate scores in a pair features. The affinity matrix is acquired making these scores through softmax function normalization.", + "bbox": [ + 76, + 794, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/92c3544ac8ece8a1ee09ff09c22c5197f14d723a23cdf8a37fbc3e9c0b02a73f.jpg", + "image_caption": [ + "Figure 3. Illustration of the proposed TGSA loss: 'a' and 'b' denote two different types of features. 'A' represents the graph structure affinity matrix. After aligning the three affinity matrices, the discrepancy in the graph structure distribution between features 'a' and features 'b' will be eliminated." + ], + "image_footnote": [], + "bbox": [ + 511, + 89, + 880, + 178 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Due to we utilize graph structure to align and distill knowledge, instead of augmenting the feature, and the Euclidean space distribution is more interesting for features, thus we replace the linear transformation with Euclidean distance to compute attention scores and redefine the graph structure expression for two groups of features as follows:", + "bbox": [ + 496, + 267, + 890, + 357 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {(a; b)} = \\left\\{\\alpha_ {i j} \\right\\} _ {i, j \\in N} = \\frac {\\exp \\left(D \\left(\\boldsymbol {f} _ {a} ^ {i} , \\boldsymbol {f} _ {b} ^ {j}\\right)\\right)}{\\sum_ {k \\in N} \\exp \\left(D \\left(\\boldsymbol {f} _ {a} ^ {i} , \\boldsymbol {f} _ {b} ^ {k}\\right)\\right)}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 366, + 888, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{ij}$ denotes the element of the affinity matrix, $N$ corresponds to the entirety of samples within one modality, $a$ and $b$ represent two modalities, $D(\\cdot)$ means Euclidean distance.", + "bbox": [ + 496, + 431, + 890, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, the triplet graph structure alignment loss $\\mathcal{L}_{tgsa}$ is developed for cross modality ReID to align two different modality types, enabling them to conform to the same graph structure distribution and reduce modality discrepancy. This loss encompasses two self-modal affinity matrices and one cross-modal affinity matrix, with the latter ensuring the overall consistency of the graph structure's distribution as shown in Fig. 3. These three matrices are aligned pairwise through the utilization of the Kullback-Leibler (KL) divergence. Therefore, the alignment loss $\\mathcal{L}_{tgsa}$ of two distinct modality types is defined as:", + "bbox": [ + 496, + 491, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {t g s a} ^ {(a; b)} = \\sum_ {p = 1} ^ {P} \\sum_ {k = 1} ^ {K} \\left(\\mathrm {K L} \\left(\\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \\boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\\right) \\right. \\\\ + \\operatorname {K L} \\left(\\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}\\right) + \\operatorname {K L} \\left(\\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}, \\boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\\right)). \\tag {16} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 667, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $A^{p_k}$ represents the graph structure distribution of the $k$ -th sample in the $p$ -th class, where $P$ is the number of person classes, and $K$ denotes the number of images for each class within a single modality.", + "bbox": [ + 496, + 751, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to convey the discriminative implicit modality-specific knowledge to shared feature on feature-level, the distillation loss across two branches on homogeneous features through TGSA can be formulated as:", + "bbox": [ + 496, + 811, + 890, + 871 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t g s a} = \\mathcal {L} _ {t g s a} ^ {(s p, V; s h, V)} + \\mathcal {L} _ {t g s a} ^ {(s p, I; s h, I)}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 881, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "397", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Class Sementic Alignment (CSA)", + "text_level": 1, + "bbox": [ + 76, + 90, + 361, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CSA is used to distill the semantic information of implicit modality-specific knowledge into the modality-shared branch for enhancing the feature representation of shared features. CSA operates on homogeneous features between two branches at logit-level. The logit matrix behind the classifier can be formulated as:", + "bbox": [ + 75, + 114, + 468, + 203 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Z} _ {s p} = C _ {s p} \\left(\\boldsymbol {f} _ {s p}\\right), \\boldsymbol {Z} _ {s h} = C _ {s h} \\left(\\boldsymbol {f} _ {s h}\\right), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 215, + 468, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $C_{sp}$ and $C_{sh}$ is the modality-specific and modality-shared classifier separately. And the logit $Z_{sp}$ and $Z_{sh} \\in \\mathbb{R}^{2N \\times C}$ of specific and shared branch both contain visible modality and infrared modality, $C$ is the total number of train dataset identities.", + "bbox": [ + 76, + 243, + 468, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For learning the implicit discriminative modality-specific knowledge on semantic-level, the CSA loss is implemented on the same modality logit between the two branches, which is formulated as:", + "bbox": [ + 75, + 319, + 468, + 378 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c s a} = \\sum_ {i = 1} ^ {N} \\left(\\mathrm {K L} \\left(\\boldsymbol {Z} _ {s h, V} ^ {i}, \\boldsymbol {Z} _ {s p, V} ^ {i}\\right) + \\mathrm {K L} \\left(\\boldsymbol {Z} _ {s h, I} ^ {i}, \\boldsymbol {Z} _ {s p, I} ^ {i}\\right)\\right). \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 388, + 468, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Modality Discrepancy Reduction (MDR)", + "text_level": 1, + "bbox": [ + 76, + 452, + 423, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "At this part, to guarantee the invariant representation of modality-shared feature, the TGSA and CSA are further used to reduce modality discrepancy within modality-shared branch as follow:", + "bbox": [ + 75, + 476, + 468, + 535 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m d r} = \\mathcal {L} _ {t g s a} ^ {(s h, V; s h, I)} + \\sum_ {i = 1} ^ {N} \\operatorname {K L} \\left(\\boldsymbol {Z} _ {s h, V} ^ {i}, \\boldsymbol {Z} _ {s h, I} ^ {i}\\right). \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 544, + 468, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this way, the visible feature and infrared feature in modality-shared branch can achieve mutual learning from feature-level and semantic-level. It makes two modalities feature aligning information each other, while alleviating modal gap and maintaining the invariant of modality-shared feature.", + "bbox": [ + 75, + 595, + 468, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Optimization", + "text_level": 1, + "bbox": [ + 76, + 694, + 217, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ultimately, by continuously distilling implicit discriminative knowledge from the modality-specific feature and consistently reducing modality discrepancies in the modality-shared feature, we can achieve a more discriminative and invariant modality-shared feature.", + "bbox": [ + 75, + 718, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The total loss of the model IDKL is defined as:", + "bbox": [ + 96, + 794, + 406, + 808 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {b} + \\lambda_ {1} \\mathcal {L} _ {i p} + \\lambda_ {2} \\mathcal {L} _ {t g s a} + \\lambda_ {3} \\mathcal {L} _ {c s a} + \\mathcal {L} _ {m d r}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 93, + 824, + 468, + 858 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{1},\\lambda_{2}$ and $\\lambda_{3}$ are hyper-parameters to balance the contribution of individual loss term.", + "bbox": [ + 75, + 869, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/88572ec55ee6e12b832640788e709d05ed0175a4c07112f70fd77c440a4c6aa3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 90, + 612, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/620d730a1fae94eb04d908658bc7f65b18ab8f2d2c812b2286ed6ae1a69083bb.jpg", + "image_caption": [ + "Figure 4. Observation the implicit discriminative information by Grad-CAM. And 'sh' and 'sp(im)' present the modality-shared feature and the modality-specific feature of trained IDKL w/o knowledge distillation, respectively; 'enhanced' denotes the modality-shared feature of IDKL w/ knowledge distillation." + ], + "image_footnote": [], + "bbox": [ + 511, + 207, + 611, + 309 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ebb08dbc55573406afd08cf4bde67698fabc4c99a99772c129343f5751ed7f99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 90, + 702, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4e298b6d20c9137e3012312e0b498a37d97b7ff8ff23cd2515336003b8b2db69.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 207, + 702, + 309 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/697b2e61cbc4f0b04fd8c161da8351ea02a8ad71d50ed2143c4663b42d658326.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 90, + 790, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ea031cd2c5dbd45e9f01f5742badab065b8ad3309c5965b9b6a45dbb2ee5d4a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 207, + 790, + 309 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fd5fb4ca2e3270b3956d8243c8278609e4b654d084f0e7a689490a63ca659b3a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 90, + 880, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/857cb09cd6f18c8b059ed1214f051dbc8d413cfa27b4946427683876d8bbcb8c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 207, + 880, + 309 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 407, + 630, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 438, + 808, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Three public VI-ReID datasets SYSU-MM01 [28], LLCM [43] and RegDB [22] are employed to evaluate our model. SYSU-MM01 is a popular large-scale dataset collected by four visible cameras and two near-infrared cameras, including indoor and outdoor environments. And the test protocols consist of all-search and indoor-search. LLCM dataset is a large-scale and low-light cross-modality dataset, which is divided into training and testing sets at a 2:1 ratio. RegDB is collected using dual-camera systems, where visible and infrared images are captured in pairs. Both LLCM and RegDB contain visible to infrared and infrared to visible two search modes.", + "bbox": [ + 496, + 465, + 890, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. The standard rank- $k$ matching accuracy and mean Average Precision (mAP) are adopted as the evaluation metrics. All the reported results are the average of 10 trials.", + "bbox": [ + 496, + 652, + 890, + 714 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. The proposed method and all experiments are implemented on a single NVIDIA GeForce 3090 GPU with PyTorch framework. The baseline model adopts the ResNet-50 pre-trained on ImageNet with the $\\mathcal{L}_b$ . The input images are resized to $3\\times 384\\times 128$ . The train mini-batch size is set as 120, which contains 12 random identities and 10 images for every identity. Adam optimizer with an initial learning rate $3\\times 10^{-5}$ is exploited, which decays at the 60th and 100th epoch with a decay factor of 0.1. The hype-parameters $\\lambda_{1}$ , $\\lambda_{2}$ and $\\lambda_{3}$ are set to 0.1, 0.6 and 0.8. During the testing phase, only modality-shared feature is used to evaluate performance.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "398", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6c13fd7c604121e2b8c87a9a5e9ddc8b4f9b70cfcb127d0e36fe6da5ac72f6a6.jpg", + "table_caption": [ + "Table 1. Comparison of CMC (%) and mAP (%) performances with the state-of-the-art methods on SYSU-MM01 dataset." + ], + "table_footnote": [], + "table_body": "
MethodsAll-searchIndoor-search
Single-shotMulti-shotSingle-shotMulti-shot
r=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20map
Zero-Padding [32]14.8054.1271.3315.9519.1361.4078.4110.8920.5868.3885.7926.9224.4375.8691.3218.86
D-HSME [8]20.6862.7477.9523.12------------
AlignGAN [28]42.4085.0093.7040.7051.5089.4095.7033.9045.9087.6094.4054.3057.1092.7097.4045.30
DDAG [36]54.7590.3995.8153.02----61.0294.0698.4167.98----
NFS [2]56.9191.3496.5255.4563.5194.4297.8148.5662.7996.5399.0769.7970.0397.7099.5161.45
PIC [47]57.5189.3595.0355.14----60.40--67.70----
MID [12]60.2792.90-59.40----64.8696.12-70.12----
cm-SSFT [21]61.6089.2093.9063.2063.4091.2095.7062.0070.5094.9097.7072.6073.0096.3099.1072.40
MCLNet [7]65.4093.3397.1461.98----72.5696.9899.2076.58----
FMCNet [42]66.34--62.5173.44--56.0668.15--74.0978.86--63.82
SMCL [31]67.3992.8796.7661.7872.1590.6694.3254.9368.8496.5598.7775.5679.5795.3398.0066.57
CAJ [37]69.8895.7198.466.89----76.2697.8899.4980.37----
MPANet [33]70.5896.2198.8068.2475.5897.9199.4362.9176.7498.2199.5780.9584.2299.6699.9675.11
CMT [14]71.8896.4598.8768.5780.2397.9199.5363.1376.997.6899.6479.9184.8799.4199.9774.11
DEEN [43]74.797.699.271.8----80.399.099.883.3----
SAAI [3]75.90--77.0382.8--82.3983.20--88.0190.73--91.30
MUN [40]76.2497.84-73.81----79.4298.09-82.06----
MSCLNet [45]76.9997.6399.1871.64----78.4999.3299.9181.17----
PartMix [16]77.78--74.6280.54--69.8481.52--84.3887.99--79.95
IDKL(Ours)81.4297.3898.8979.8584.3498.8999.7378.2287.1498.2899.2689.3794.3099.7199.9388.75
", + "bbox": [ + 81, + 104, + 893, + 376 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8fbb8e51bde2d6bf87b1faa04de8e3744ba878548ecd702947b6a49b793babe0.jpg", + "image_caption": [ + "Figure 5. Ablation analysis of hyper-parameter $\\lambda_{1}$ and $\\lambda_{2}$ , $\\lambda_{3}$ for $\\mathcal{L}_{ip},\\mathcal{L}_{tgsa}$ , and $\\mathcal{L}_{csa}$ respectively on SYSU-MM01 dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 398, + 205, + 486 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/96863ecd4cb31e453bbd3bc97cab69b5204d4bd4527529d82af6a77ba54a9a91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 205, + 398, + 334, + 486 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d089738f0890c9fa8ad72a365864e62b6210b5c645d026c8203632b60042a38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 334, + 398, + 464, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 527, + 441, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our IDKL model with the state-of-the-art VI-ReID methods published recent years on public VI-ReID datasets SYSU-MM01, RegDB and LLCM.", + "bbox": [ + 76, + 551, + 468, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on SYSU-MM01 dataset. The comparison experimental results is shown in Tab. 1 which displays the proposed IDKL method outperforms existing cutting-edge methods. Specifically, the IDKL method achieves the accuracy of $81.42\\%$ rank-1 and $79.85\\%$ map with single-shot all search protocol, while the accuracy of $87.14\\%$ rank-1 and $89.37\\%$ map with single-shot indoor search protocol. The compared SOTAs include various base methods, i.e., for the methods of learning the shared feature through network and loss function immediately, which contain D-HSME [8], NFS [2], CMT [14], DEEN[43] and MCLNet [7]. Based on graph structure augment method DDAG [36] and the mutual learning by logits skill (PIC [47] and MPANet [33]). Comparing with several other based modality-specific methods cm-SSFT[21], MUN[40] and MSCLNet[45], our results outperform them by a margin.", + "bbox": [ + 75, + 597, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on RegDB dataset. We also evaluate IDKL on a small-scale dataset RegDB as shown in Tab. 2. There is strong performance IDKL showed and outperforms the existing solutions. Specifically, we achieve rank-1 ac", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "curacy of $94.72\\%$ in visible to infrared mode, and rank-1 accuracy of $94.22\\%$ in infrared to visible mode.", + "bbox": [ + 498, + 398, + 888, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on LLCM dataset. The IDKL model achieves significant improvements on the large and complex LLCM dataset as shown in Tab. 3, demonstrating excellent rank-1 accuracy of $72.2\\%$ and $70.7\\%$ on two modes, respectively. This indicates that the IDKL model exhibits strong robustness in complex and multimodal scenarios.", + "bbox": [ + 498, + 430, + 890, + 521 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1760407fc89b7e4d0b2148191bae4ce4195a4ca6b0be845e7f96177f9d991f7c.jpg", + "table_caption": [ + "Table 2. Comparison of the CMC (\\%) and mAP (\\%) performances with state-of-the-art methods on RegDB dataset." + ], + "table_footnote": [], + "table_body": "
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
Zero-Padding [32]17.818.916.717.9
AlignGAN [28]57.953.656.353.4
DDAG [36]69.3463.4668.0661.80
cm-SSFT [21]72.372.971.071.7
MCLNet [7]80.3173.0775.9369.49
PIC [47]83.679.679.577.4
MPANet [33]83.780.982.880.7
SMCL [31]83.9379.8383.0578.57
MSCLNet [45]84.1780.9983.8678.31
CAJ [37]85.0377.8284.7577.82
MID [12]87.4584.8584.2981.41
FMCNet [42]89.1284.4388.3883.86
SAAI [3]91.0791.4592.0992.01
DEEN [43]91.185.189.583.4
CMT [14]95.1787.391.9784.46
MUN [40]95.1987.1591.8685.01
IDKL(Ours)94.7290.1994.2290.43
", + "bbox": [ + 504, + 564, + 888, + 829 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 845, + 653, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we conduct the ablation experiment to evaluate our proposed model exhaustively.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "399", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bbdbbf19bedcdf56e63913280519d005102589adca72ca2506870dcfc93e9b17.jpg", + "table_caption": [ + "Table 3. Comparison of the CMC (%) and mAP (%) performances with state-of-the-art methods on LLCM dataset." + ], + "table_footnote": [], + "table_body": "
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
DDAG [36]40.348.448.052.3
CAJ [37]56.559.848.856.6
DEEN [43]62.565.854.962.9
IDKL(Ours)72.2266.4370.7265.19
", + "bbox": [ + 81, + 106, + 465, + 200 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f961517c92f4a86d9e2332c34ddb991e653fc1169606c7d94a478bf847fe5a3a.jpg", + "table_caption": [ + "Table 4. Evaluation the impact of different components in terms of rank-1 $(\\%)$ and mAP $(\\%)$ on SYSU-MM01 dataset." + ], + "table_footnote": [], + "table_body": "
LbLipLtgsaLcsaLmdrSYSU-MM01
rank1map
✓××××67.6066.47
✓×✓××68.3867.30
✓✓✓××76.4074.83
✓✓×✓×76.2874.34
✓✓××✓77.0475.66
✓✓✓✓✓81.4279.85
", + "bbox": [ + 89, + 241, + 454, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of each component. We evaluate the effectiveness of each component on the SYSU-MM01 dataset under all search single-shot mode. Each component is added independently to reveal its the performance as Tab. 4. This indicates that each component is highly useful, with $\\mathcal{L}_{mdr}$ achieving significant performance improvements. This further suggests the effectiveness of TGSA and CSA in reducing modality discrepancies. Comparing the second row with the third row demonstrates the necessity of purifying implicit modality-specific information, and also proves the effectiveness of our Information Purifier module.", + "bbox": [ + 75, + 397, + 467, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyper-parameters analysis of IP, TGSA and CSA. In this part, we present a line chart to examine the detail influence of IP, TGSA and CSA by gradually increasing the value of hyperparameters. As depicted in Fig. 5, the maximum contributions of IP, TGSA and CSA are reached at 0.1, 0.6 and 0.8, respectively. The upward trend of the curve demonstrates the effectiveness of each module.", + "bbox": [ + 75, + 564, + 467, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization Analysis", + "text_level": 1, + "bbox": [ + 76, + 680, + 282, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attention maps Visualization. To further illustrate the effectiveness of IDKL, Grad-CAM [26] is utilized for a visual examination of different feature heatmaps. In Fig. 4, the areas of focus for implicit discriminative information typically differ from those of the shared feature, indicating that effectively and judiciously utilizing this information to strengthen the shared feature can be highly beneficial.", + "bbox": [ + 75, + 703, + 467, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Distribution Visualization. We utilize t-SNE [22] feature map visualization to observe the impact of the IDKL model and TGSA on the model. As shown in Fig. 6, each color represents a different identity, while the shapes of circles and triangles indicate the visible and infrared modality information, respectively. From Fig. 6(a),", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e9c4b0e07c777f31f3943a658867b06eb8f85554aa626ef57a15675a09b7d428.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 90, + 694, + 207 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7d3ae0b9f3bb711509dea1a030337d77b45737e509a3ed1cc731832ecdd7265d.jpg", + "image_caption": [ + "b (baseline)" + ], + "image_footnote": [], + "bbox": [ + 697, + 90, + 887, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/088b316aa60e2719a88d5f36c7a4a3960e4fa91e7b2d904c6e6b2d9a48a63c27.jpg", + "image_caption": [ + "a (pretrained resnet50)", + "c (IDKL w/o TGSA)", + "Figure 6. Visualization of learned features by t-SNE. Where \"a\" means the pre-training resnet50 on ImageNet; \"b\" represents the baseline; \"c\" is the IDKL model w/o TGSA; \"d\" is IDKL model w/ TGSA." + ], + "image_footnote": [], + "bbox": [ + 506, + 223, + 694, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b374cae388c2d31e37ca6865d8b7ae2fca16bcc8cd2cbbd0e98b63cd6dc2ccb7.jpg", + "image_caption": [ + "d (IDKL w/ TGSA)" + ], + "image_footnote": [], + "bbox": [ + 697, + 223, + 887, + 339 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a significant discrepancy between the two modalities is evident. Fig. 6(b) shows a reduction in modality discrepancy and the model exhibiting some discriminative capabilities. Comparing Fig. 6(b) with Fig. 6(c), it is observable that the IDKL model has a smaller intra-class discrepancy and better inter-class discrimination. In Fig. 6(d), the dark blue class appears more scattered than in Fig. 6(c), and the graph structures of the two modalities are more similar and closely aligned, demonstrating the effectiveness of TGSA in reducing modality discrepancies.", + "bbox": [ + 496, + 429, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 594, + 617, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper harnesses the implicit discriminative information within modality-specific features and introduces a robust model IDKL to exploit the potential discrimination of heterogeneous-related features and enhance the shared feature. The IDKL model comprises a dual one-stream network, a novel IN-guided information purifier, a triplet graph structure alignment solution, and refined distillation on logits. Collectively, these components demonstrate exceptional effectiveness and contribute to improved results.", + "bbox": [ + 496, + 619, + 890, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 768, + 658, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by National Key R&D Program of China (2021YFB3100800), National Natural Science Fund of China (62271090, 61771079), Chongqing Natural Science Fund (cstc2021jcyj-jqX0023) and National Youth Talent Project. This work is also supported by Huawei computational power of Chongqing Artificial Intelligence Innovation Center.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "400", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Cuiqun Chen, Mang Ye, Meibin Qi, Jingjing Wu, Jianguo Jiang, and Chia-Wen Lin. Structure-aware positional transformer for visible-infrared person re-identification. IEEE Transactions on Image Processing, 31:2352–2364, 2022. 2", + "[2] Yehansen Chen, Lin Wan, Zhihang Li, Qianyan Jing, and Zongyuan Sun. Neural feature search for rgb-infrared person re-identification. 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Neurocomputing, 386:97–109, 2020. 1" + ], + "bbox": [ + 501, + 92, + 893, + 896 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "402", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/b65ca941-cca6-4d10-a9af-cf9b0fc08ec1_model.json b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/b65ca941-cca6-4d10-a9af-cf9b0fc08ec1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..12f3ec55d64e1e95917970791ac9cc3772ef8d77 --- /dev/null +++ b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/b65ca941-cca6-4d10-a9af-cf9b0fc08ec1_model.json @@ -0,0 +1,2453 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.02 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.325, + 0.017, + 0.725, + 0.031 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.032, + 0.756, + 0.047 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.122, + 0.13, + 0.85, + 0.175 + ], + "angle": 0, + "content": "Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification" + }, + { + "type": "text", + "bbox": [ + 0.391, + 0.204, + 0.581, + 0.222 + ], + "angle": 0, + "content": "Kajjie Ren, Lei Zhang*" + }, + { + "type": "text", + "bbox": [ + 0.125, + 0.222, + 0.846, + 0.24 + ], + "angle": 0, + "content": "School of Microelectronics and Communication Engineering, Chongqing University, China" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.242, + 0.665, + 0.256 + ], + "angle": 0, + "content": "kaijieren@cqu.edu.cn, leizhang@cqu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.474, + 0.705 + ], + "angle": 0, + "content": "Visible-Infrared Person Re-identification (VI-ReID) is a challenging cross-modal pedestrian retrieval task, due to significant intra-class variations and cross-modal discrepancies among different cameras. Existing works mainly focus on embedding images of different modalities into a unified space to mine modality-shared features. They only seek distinctive information within these shared features, while ignoring the identity-aware useful information that is implicit in the modality-specific features. To address this issue, we propose a novel Implicit Discriminative Knowledge Learning (IDKL) network to uncover and leverage the implicit discriminative information contained within the modality-specific. First, we extract modality-specific and modality-shared features using a novel dual-stream network. Then, the modality-specific features undergo purification to reduce their modality style discrepancies while preserving identity-aware discriminative knowledge. Subsequently, this kind of implicit knowledge is distilled into the modality-shared feature to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features. Extensive experiments on multiple public datasets demonstrate the superiority of IDKL network over the state-of-the-art methods. Code is available at https://github.com/1KK077/IDKL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.738, + 0.21, + 0.753 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Visible-Infrared Person Re-Identification (VI-ReID) aims to match pedestrian images across multiple nonoverlapping camera views and different modalities. Advanced surveillance systems today are capable of automatically switching from visible to infrared mode at nightfall, ensuring an ample supply of trainable data. However, the unique modality of infrared images create significant domain discrepancies and a more complex environment. This makes previous single-modality methods, which are based" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.291, + 0.885, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.504, + 0.893, + 0.573 + ], + "angle": 0, + "content": "Figure 1. Previous methods focused on seeking discriminative information within modality-shared features, overlooking the fact that there are discriminative clues implicit in modality-specific features. It is worth considering utilization of the implicit discriminative information to enhance shared invariant feature." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.593, + 0.878, + 0.608 + ], + "angle": 0, + "content": "solely on visible images, less efficient for VI-ReID tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.893, + 0.883 + ], + "angle": 0, + "content": "Recently, numerous advanced methods have emerged in the field of VI-ReID. In conclusion, these approaches can generally be categorized into two types: the first aims to learn modality-shared features directly from raw modal data, and the second seeks to incorporate additional modal information to refine the feature space or bridge the modal gap, thereby facilitating the search for modality-shared features. Raw modal data based method [2, 4, 7, 8, 17, 19, 33, 49] is to embed different modality images into the same space and align them on feature-level so that model learn modality invariant feature directly. Despite original images based methods has achieved desirable results, they still remain a huge gap between different modalities in feature space. In order to bridge the gap between visible and infrared modalities and construct a continuous space for better learning modality-shared features, various methods based on introducing extra information [14, 29, 30, 34, 38, 42, 45] have emerged constantly." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Although significant improvements have been made in" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "393" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.438 + ], + "angle": 0, + "content": "current VI-ReID methods, these models inevitably discard some discriminative information that relies on modality-specific features, which is not fully exploited and utilized previously. These discriminative cues that exist in modality-specific features can be referred to as implicit discriminative information, as shown by the green area in Fig. 1, such as color, grayscale spectrum, contrast, saturation, and so on. Therefore, relying solely on modality-shared cues can limit the upper boundary of the discrimination ability of the feature representation. Utilizing implicit modality-specific characteristics effectively is essential to enhance the distinctiveness of modality-invariant features. However, we cannot directly use the modality-specific knowledge due to the modality discrepancies it contains. Instead, we need to reduce these discrepancies while preserving the identity-aware discriminative information inherent in the implicit knowledge. Meanwhile, traditional VI-ReID methods involving distillation, alignment, and mutual learning typically rely on logits [35, 44, 47]. However, there is no involvement of the classifier during the testing phase, with matching performed only at the feature level. Therefore, conducting discriminative information distillation at the feature level is also essential." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.442, + 0.473, + 0.835 + ], + "angle": 0, + "content": "To address the above limitations, in this paper, we propose an Implicit Discriminative Knowledge Learning (IDKL) framework that captures implicit invariant information from modality-specific features and distills it into modality-shared features to enhance their discriminative capability. We first extract modality-specific and modality-shared features using the modality discriminator and modality confuser, respectively. The modality discriminator effectively distinguishes between different modal features, endowing them with specific characteristics; whereas the modality confuser is unable to differentiate between modal features, thereby imparting shared characteristics to them. Since the modality-specific feature after previous stage contains substantial modality discrepancies, it is not suitable for direct distillation into the shared feature. We initially employ Instance Normalization to reduce domain discrepancies. However, it is crucial to acknowledge that IN inevitably results in the loss of some discriminative features. Therefore, we aim to reduce its modality style discrepancy while preserving identity-aware discriminative knowledge. Subsequently, we distill this implicit knowledge into the modality-shared feature at both the feature-level through feature graph structure, and the semantic-level through the logit vector to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.838, + 0.472, + 0.868 + ], + "angle": 0, + "content": "The main contributions of this paper can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "- We propose the Implicit Discriminative Knowledge Learning (IDKL) network to utilize the discriminative" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "knowledge implicit in the modality-specific features to enhance the upper bound of discriminative power for the modality-shared feature." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.137, + 0.894, + 0.213 + ], + "angle": 0, + "content": "- To reduce the modality style discrepancy without losing discriminative information of modality-specific information, we propose an IN-guided Information Purifier (IP), which is supervised by the discrimination enhancing loss and discrepancy reducing loss." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.212, + 0.895, + 0.303 + ], + "angle": 0, + "content": "- The novel TGSA loss is developed to distill the discriminative modality-specific information into modality-shared feature and mitigate inter-modality discrepancy of modality-shared feature sufficiently. The substantial experimental results demonstrate the superiority of our method." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.137, + 0.895, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.317, + 0.642, + 0.334 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.895, + 0.644 + ], + "angle": 0, + "content": "Visible Modality Person ReID. Person ReID has received increasing success in recent years, which aims to implement pedestrian retrieval between visible images. It has suffered huge challenges including various viewpoints, illuminations, postures and so on. To solve these problems, most methodologies [24, 25, 39, 48] are designed to obtain unified intra-class and discriminative inter-class representation by training CNN network. To further enhance the distinguishability of features, Sun et al. [27] proposed aligning part feature directly instead of using external cues. He et al. [9] caught the hot spot of transformer and first proposed the transformer variant applying on single-modality person ReID. Simultaneously, person ReID has developed some significant branches yet, such as Unsupervised Domain Adaptive Person ReID (UDA-ReID) and Domain Generalization Person ReID (DG-ReID) [41]. Although existing methods have made wide progress in visible modality person ReID, they suffer performance degradation when applied to visible-infrared person ReID due to the severe cross-modality discrepancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Visible-Infrared Person ReID (VI-ReID). VI-ReID is a cross-modality person retrieval problem, which aims at matching daytime visible and nighttime infrared images. It not only faces difficulties encountered in traditional single-motility person ReID task, but also the main challenge of huge modality discrepancy which caused by different camera spectra. To solve the these issues, numerous approaches are proposed to search shared feature[1, 5, 18, 20, 32, 36, 39, 46]. Wu et al. [32] first formulated the VI-REID issue and contributed a new cross-modality dataset SYSUMM01, which is of great significance to the following research. Ye et al. [36] proposed a part-level feature interaction and graph structure attention to enhance the discrimination of invariant feature. Meanwhile, some work begin to introduce additional modal information to jointly search for invariant features [14, 21, 28, 30, 45]. Wang et al. [30] combined RGB three channels feature and IR single" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "394" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.873, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.316, + 0.896, + 0.403 + ], + "angle": 0, + "content": "Figure 2. Framework of the proposed Implicit Discriminative Knowledge Learning (IDKL) model. The dual one-stream network built by resnet blocks first extracts the modality-specific \\( F_{sp} \\) and modality shared feature \\( F_{sh} \\) under the constraint of modality discriminator and modality confuser accordingly, while the common ReID loss is used to optimize network basely. Then, the modality-specific feature is fed into the information purifier to regulate the modality style discrepancy while preserving the implicit discriminative information and obtain the purified modality-specific feature \\( \\widetilde{F}_{sp} \\). Subsequently, this implicit knowledge is distilled into the modality-shared feature through TGSA and CSA. Finally, the \\( \\mathcal{L}_{mdr} \\) is further proposed to minimize modality discrepancy within the enhanced modality-shared feature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.471, + 0.56 + ], + "angle": 0, + "content": "channel feature into united four channels feature to reduce modal differences. Jiang et al. [14] employed a global prototype to generate the missing modality counterpart through transformer. However, these generation based compensation methods inevitably introduce much noise and most of present methods aim to align modal discrepancy and extract modality invariant feature. They ignored use of beneficial style information contained in specific features to increase distinctiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Interactive Learning. In knowledge distillation, a teacher-student model is used to transfer the knowledge learned by a larger complex teacher model to a smaller simple student model. Different from the one-way transfer between a teacher and a student, deep mutual learning [44] is an ensemble of students which learns collaboratively and teaches each other throughout the training process. Some work applied this idea into VI-ReID for interactive learning in different modalities. Zheng et al. [47] enhanced invariant features learning by using interactive learning between two modality. Ye et al. [35] employed multi-classifier to reduce modality discrepancy on logits-level. Wu et al. [33] distilled RGB and IR knowledge mutually by four classifier to achieve inter shared representation. However, they only learn the knowledge within the semantic-level." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.801, + 0.212, + 0.817 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this section, we detail the proposed Implicit Discriminative Knowledge Learning (IDKL) framework as shown in Fig. 2. IDKL first distinguishes modality-specific features from modality-shared features through two network branches, which are constrained by modality discriminator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.653 + ], + "angle": 0, + "content": "and modality confuser, respectively. Simultaneously, common ReID loss is used to endow feature with representation. Then, an Information Purifier (IP) is developed to reduce the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. Finally, we distill the implicit discriminative knowledge across two branches into the modality-shared feature through Triplet Graph Structure Alignment (TGSA) at the feature-level and Class Semantic Alignment (CSA) at the logit-level. Additionally, to reduce modality discrepancy of shared feature, we proposed the Modality Discrepancy Reduction (MDR) loss within the modality-shared branch. As the discriminative information increases and modality discrepancy decreases constantly, the enhanced modality-shared feature can be obtained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Formally, we represent visible and infrared images in a dataset as \\( V = \\{\\pmb{x}_i^V\\}_{i=1}^{N_V} \\) and \\( I = \\{\\pmb{x}_i^I\\}_{i=1}^{N_I} \\), respectively. Typically, the number of images sampled in a mini-batch is equal across both modalities, i.e., \\( N_V = N_I = N = P \\times K \\), where \\( N_V \\) and \\( N_I \\) denote the number of images sampled from the visible and infrared modalities, respectively. Here, \\( N \\) represents the number of images from a single modality, \\( 2N \\) is the total number of images in a mini-batch, \\( P \\) is the number of distinct person classes, and \\( K \\) is the number of images from each class within a single modality. We can therefore represent the images and their corresponding labels in a mini-batch as \\( X = \\{\\pmb{x}_i | \\pmb{x}_i \\in V \\cup I\\}_{i=1}^{2N} \\) and \\( Y = \\{\\pmb{y}_i\\}_{i=1}^{N_p = P} \\), respectively. These images \\( X \\) are fed into two separate network branches to extract the modality-specific features \\( F_{sp} \\) which contains \\( F_{sp,V}, F_{sp,I} \\) and the shared features \\( F_{sh} \\) which contains \\( F_{sh,V}, F_{sh,I} \\) as fol" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "395" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.093, + 0.118, + 0.105 + ], + "angle": 0, + "content": "lows:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.115, + 0.469, + 0.133 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {s p} = E _ {s p} (\\boldsymbol {x} \\mid \\Theta , \\Psi), \\boldsymbol {F} _ {s h} = E _ {s h} (\\boldsymbol {x} \\mid \\Theta , \\Phi), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.47, + 0.26 + ], + "angle": 0, + "content": "where \\( E_{sp} \\) and \\( E_{sh} \\) denote the specific and the shared feature extractor by employing ResNet-50, respectively. Among the sturctures of ResNet-50, the global average pooling replaced by Gem pooling[24, 39] which is a pooling operation between maximum pooling and average pooling. And \\( \\Theta \\) is the shallow layer parameters with the first three blocks of ResNet-50, \\( \\Psi \\) and \\( \\Phi \\) is the deep layer parameters of different branches with the last two blocks of ResNet-50." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.268, + 0.405, + 0.284 + ], + "angle": 0, + "content": "3.1. Modality Confuser and Discriminator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.471, + 0.412 + ], + "angle": 0, + "content": "Modality Confuser. For each sample image \\( \\boldsymbol{x}_i \\), there is a modality label \\( t_i \\in \\{0,1\\} \\). To learn modality-irrelated shared information, similar to [6], our goal is to confuse different domains such that a domain classifier cannot distinguish the domain of origin for a sample. We employ an adversarial modality classifier based on the Gradient Reversed Layer (GRL) as the modality confuser. The constraint loss for the modality confuser is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.42, + 0.469, + 0.46 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C j} = - \\frac {1}{2 N} \\sum_ {i = 1} ^ {2 N} t _ {i} \\cdot \\log p \\left(C _ {j} \\left(G R L \\left(\\boldsymbol {F} _ {s h} ^ {i}\\right)\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.469, + 0.525 + ], + "angle": 0, + "content": "where \\( C_j \\) represents the \\( j \\)-th modality confuser in the modality-shared branch, \\( p(\\cdot) \\) is the prediction probability obtained via the softmax function, and \\( t_i \\) is the modality label." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.469, + 0.616 + ], + "angle": 0, + "content": "Modality Discriminator. To adequately learn modality-related specific information, we employ a modality classifier as the Modality Discriminator. This classifier, which does not use GRL, is applied on the specific branch to extract modality-specific features. The classification loss is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.623, + 0.469, + 0.663 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D j} = - \\frac {1}{2 N} \\sum_ {i = 1} ^ {2 N} t _ {i} \\cdot \\log p \\left(D _ {j} \\left(\\boldsymbol {F} _ {s p} ^ {i}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.469, + 0.699 + ], + "angle": 0, + "content": "where \\(D_{j}\\) denotes the j-th modality discriminator in the modality-specific branch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.469, + 0.731 + ], + "angle": 0, + "content": "The combined loss from the modality confuser and discriminator is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.738, + 0.469, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C} = \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {C j}, \\quad \\mathcal {L} _ {D} = \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {D j}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.469, + 0.876 + ], + "angle": 0, + "content": "To efficiently extract both modality-specific and modality-shared features, we combine these modality classifier losses with the standard ReID loss \\(\\mathcal{L}_{\\text{reid}}\\), which includes cross-entropy and hard triplet loss. These are applied to both the modality-specific and modality-shared branches as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.884, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s p} = \\mathcal {L} _ {\\text {r e i d}} \\left(\\boldsymbol {f} _ {s p}\\right) + \\mathcal {L} _ {D}, \\mathcal {L} _ {s h} = \\mathcal {L} _ {\\text {r e i d}} \\left(\\boldsymbol {f} _ {s h}\\right) + \\mathcal {L} _ {C}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.12 + ], + "angle": 0, + "content": "where \\(\\pmb {f}\\in \\mathbb{R}^{B\\times C}\\) is the pooling feature corresponding to \\(\\pmb {F}\\in \\mathbb{R}^{B\\times C\\times H\\times W}\\)" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.122, + 0.854, + 0.136 + ], + "angle": 0, + "content": "Thus, the base loss for our model is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.145, + 0.892, + 0.162 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b} = \\mathcal {L} _ {s h} + \\mathcal {L} _ {s p}. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.169, + 0.694, + 0.184 + ], + "angle": 0, + "content": "3.2. Information Purifier" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.192, + 0.892, + 0.313 + ], + "angle": 0, + "content": "The Information Purifier (IP) is designed to minimize the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. The IP integrates Instance Normalization (IN), which is known to reduce domain discrepancies [13, 23, 48]. However, it is important to recognize that IN inevitably leads to the loss of some discriminative features [11, 15], potentially hindering the high performance of ReID." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.892, + 0.405 + ], + "angle": 0, + "content": "To overcome the aforementioned issues, we have designed a dual-mask network guided by Instance Normalization (IN) to alleviate modality style discrepancies while preserving implicit discriminative knowledge. Firstly, we apply IN on the modality-specific feature to obtain the normalized feature \\(\\widehat{\\pmb{F}}_{sp}\\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.412, + 0.891, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\boldsymbol {F}} _ {s p} = \\operatorname {I N} \\left(\\boldsymbol {F} _ {s p}\\right) = \\frac {\\boldsymbol {F} _ {s p} - \\operatorname {E} \\left[ \\boldsymbol {F} _ {s p} \\right]}{\\sqrt {\\operatorname {V a r} \\left[ \\boldsymbol {F} _ {s p} \\right] + \\epsilon}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.892, + 0.498 + ], + "angle": 0, + "content": "where the \\(\\epsilon\\) represents a safety factor to ensure the denominator is not zero. The mean \\(\\operatorname{E}[\\cdot]\\) and variance \\(\\operatorname{Var}[\\cdot]\\) are calculated along each channel." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.529 + ], + "angle": 0, + "content": "Following the approach of SE-Net [10], we generate two channel-wise masks \\(\\mathbf{m}_e\\) and \\(\\mathbf{m}_r\\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.535, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\mathbf {m} _ {e} = \\sigma \\left(\\mathrm {W} _ {2} \\delta \\left(\\mathrm {W} _ {1} g \\left(\\boldsymbol {F} _ {s p}\\right)\\right)\\right), \\mathbf {m} _ {r} = \\sigma \\left(\\mathrm {W} _ {4} \\delta \\left(\\mathrm {W} _ {3} g \\left(\\widehat {\\boldsymbol {F}} _ {s p}\\right)\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.657 + ], + "angle": 0, + "content": "where \\(g(\\cdot)\\) denotes the pooling operation, \\(W_{1}, W_{3} \\in \\mathbb{R}^{\\frac{c}{r} \\times c}\\) and \\(W_{2}, W_{4} \\in \\mathbb{R}^{c \\times \\frac{c}{r}}\\) are learnable parameters in the four fully-connected (FC) layers which are followed by the ReLU activation function \\(\\delta(\\cdot)\\) and the sigmoid activation function \\(\\sigma(\\cdot)\\). To balance the calculate consumption, the dimension reduction ratio \\(r\\) is set to 16." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.742 + ], + "angle": 0, + "content": "The channel-wise masks \\(\\mathbf{m}_e\\) and \\(\\mathbf{m}_r\\) indicate enhancement of discriminative characteristics and reduction of discrepancies attention mask, respectively. So we can obtain the stronger distinctiveness \\(F_{sp}^{d+}\\) and the smaller modality differences \\(\\widehat{F}_{sp}^{m-}\\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.75, + 0.891, + 0.772 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {s p} ^ {d +} = \\mathbf {m} _ {e} \\odot \\boldsymbol {F} _ {s p}, \\widehat {\\boldsymbol {F}} _ {s p} ^ {m -} = \\mathbf {m} _ {r} \\odot \\widehat {\\boldsymbol {F}} _ {s p}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.777, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Subsequently, the discrimination enhancing loss \\(\\mathcal{L}_e\\) and the discrepancy reducing loss \\(\\mathcal{L}_r\\) are calculated to supervise \\(\\mathbf{m}_e\\) and \\(\\mathbf{m}_r\\) respectively as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.829, + 0.892, + 0.856 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e} = \\text {S o f t p l u s} \\left(h \\left(C _ {s p} \\left(\\boldsymbol {f} _ {s p} ^ {d +}\\right)\\right) - h \\left(C _ {s p} \\left(\\boldsymbol {f} _ {s p}\\right)\\right)\\right), \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.862, + 0.891, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r} = \\text {S o f t p l u s} \\left(d \\left(\\widehat {\\boldsymbol {f}} _ {s p, V} ^ {m -}, \\widehat {\\boldsymbol {f}} _ {s p, I} ^ {m -}\\right) - d \\left(\\widehat {\\boldsymbol {f}} _ {s p, V}, \\widehat {\\boldsymbol {f}} _ {s p, I}\\right)\\right). \\tag {11}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "396" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.468, + 0.187 + ], + "angle": 0, + "content": "Here, \\(\\mathcal{L}_e\\) aims to imbue the generated \\(\\mathbf{F}_{sp}^{d+}\\) with greater semantic distinctiveness compared to \\(\\mathbf{F}_{sp}\\), while \\(\\mathcal{L}_r\\) seeks to ensure that \\(\\widehat{\\mathbf{F}}_{sp}^{m-}\\) exhibit smaller modality differences than \\(\\widehat{\\mathbf{F}}_{sp}\\). And Softplus \\((\\cdot) = \\ln(1 + \\exp(\\cdot))\\) is a function with monotonic increase, designed to alleviate optimization challenges by circumventing negative values in loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.188, + 0.468, + 0.296 + ], + "angle": 0, + "content": "Finally, an alternating integration strategy is employed to extract the distinctive information from \\(\\widetilde{\\mathbf{F}}_{sp}^{m - }\\) by applying \\(\\mathbf{m}_e\\) and the invariant information from \\(\\mathbf{F}_{sp}^{d + }\\) by applying \\(\\mathbf{m}_r\\). Thus, The two sets of features extracted in this way both demonstrate smaller modality differences and stronger implicit discriminative information. By integrating them, we derive the purified modality-specific feature \\(\\widetilde{\\mathbf{F}}_{sp}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.309, + 0.468, + 0.332 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {F}} _ {s p} = \\mathbf {m} _ {e} \\odot \\widehat {\\boldsymbol {F}} _ {s p} ^ {m -} + \\mathbf {m} _ {r} \\odot \\boldsymbol {F} _ {s p} ^ {d +}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.468, + 0.394 + ], + "angle": 0, + "content": "Intuitively, the pooling feature \\(\\widetilde{f}_{sp}\\) of implicit feature \\(\\widetilde{\\pmb{F}}_{sp}\\) is also constraint with ReID loss. So the information purify loss \\(\\mathcal{L}_{ip}\\) of this section is summarized as:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.405, + 0.468, + 0.431 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i p} = \\mathcal {L} _ {e} + \\mathcal {L} _ {r} + \\mathcal {L} _ {\\text {r e i d}} (\\tilde {\\boldsymbol {f}} _ {s p}). \\tag {13}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.441, + 0.354, + 0.457 + ], + "angle": 0, + "content": "3.3. Implicit Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.465, + 0.468, + 0.526 + ], + "angle": 0, + "content": "To ensure that the modality-shared feature comprehensively learns and integrates implicit information, we perform distillation from both the feature-level through TGSA and logit-level through CSA." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.436, + 0.56 + ], + "angle": 0, + "content": "3.3.1 Triplet Graph Structure Alignment (TGSA)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.468, + 0.735 + ], + "angle": 0, + "content": "To endow the shared feature with discriminative information and reduce modality discrepancy at the feature level, we develop a triplet feature graph structure alignment loss. This approach is motivated by the fact that the feature graph structure contains abundant information about the relationships and distribution between features, such as inter-class distinctiveness and intra-class diversity. These characteristics are utilized to unearth potential feature relationships and enhance the feature representation in [17, 36]. The graph structure affinity matrix which indicates the relationships between features is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.746, + 0.468, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i j} = \\frac {\\exp \\left(L \\left(\\left[ l \\left(\\boldsymbol {f} _ {i}\\right) \\| l \\left(\\boldsymbol {f} _ {j}\\right) \\right] \\cdot \\boldsymbol {w}\\right)\\right)}{\\sum_ {k \\in \\mathcal {N} _ {i}} \\exp \\left(L \\left(\\left[ l \\left(\\boldsymbol {f} _ {i}\\right) \\| l \\left(\\boldsymbol {f} _ {k}\\right) \\right] \\cdot \\boldsymbol {w}\\right)\\right)}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.468, + 0.9 + ], + "angle": 0, + "content": "where the \\(L\\) denote LeakyReLU activation function, \\([\\cdot \\| \\cdot ]\\) denote concatenate operation and \\(\\mathcal{N}_i\\) denotes the neighbor samples which are used to normalize for the ith sample. \\(l(\\cdot)\\) is feature dimension transformation layer and \\(\\pmb{w}\\) is the full connection layer to calculate scores in a pair features. The affinity matrix is acquired making these scores through softmax function normalization." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.09, + 0.882, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.191, + 0.892, + 0.26 + ], + "angle": 0, + "content": "Figure 3. Illustration of the proposed TGSA loss: 'a' and 'b' denote two different types of features. 'A' represents the graph structure affinity matrix. After aligning the three affinity matrices, the discrepancy in the graph structure distribution between features 'a' and features 'b' will be eliminated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.892, + 0.358 + ], + "angle": 0, + "content": "Due to we utilize graph structure to align and distill knowledge, instead of augmenting the feature, and the Euclidean space distribution is more interesting for features, thus we replace the linear transformation with Euclidean distance to compute attention scores and redefine the graph structure expression for two groups of features as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.367, + 0.89, + 0.432 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {(a; b)} = \\left\\{\\alpha_ {i j} \\right\\} _ {i, j \\in N} = \\frac {\\exp \\left(D \\left(\\boldsymbol {f} _ {a} ^ {i} , \\boldsymbol {f} _ {b} ^ {j}\\right)\\right)}{\\sum_ {k \\in N} \\exp \\left(D \\left(\\boldsymbol {f} _ {a} ^ {i} , \\boldsymbol {f} _ {b} ^ {k}\\right)\\right)}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.892, + 0.491 + ], + "angle": 0, + "content": "where \\(\\alpha_{ij}\\) denotes the element of the affinity matrix, \\(N\\) corresponds to the entirety of samples within one modality, \\(a\\) and \\(b\\) represent two modalities, \\(D(\\cdot)\\) means Euclidean distance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.659 + ], + "angle": 0, + "content": "Specifically, the triplet graph structure alignment loss \\(\\mathcal{L}_{tgsa}\\) is developed for cross modality ReID to align two different modality types, enabling them to conform to the same graph structure distribution and reduce modality discrepancy. This loss encompasses two self-modal affinity matrices and one cross-modal affinity matrix, with the latter ensuring the overall consistency of the graph structure's distribution as shown in Fig. 3. These three matrices are aligned pairwise through the utilization of the Kullback-Leibler (KL) divergence. Therefore, the alignment loss \\(\\mathcal{L}_{tgsa}\\) of two distinct modality types is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.668, + 0.891, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {t g s a} ^ {(a; b)} = \\sum_ {p = 1} ^ {P} \\sum_ {k = 1} ^ {K} \\left(\\mathrm {K L} \\left(\\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \\boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\\right) \\right. \\\\ + \\operatorname {K L} \\left(\\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}\\right) + \\operatorname {K L} \\left(\\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}, \\boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\\right)). \\tag {16} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.892, + 0.813 + ], + "angle": 0, + "content": "Here, \\( A^{p_k} \\) represents the graph structure distribution of the \\( k \\)-th sample in the \\( p \\)-th class, where \\( P \\) is the number of person classes, and \\( K \\) denotes the number of images for each class within a single modality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.813, + 0.892, + 0.872 + ], + "angle": 0, + "content": "In order to convey the discriminative implicit modality-specific knowledge to shared feature on feature-level, the distillation loss across two branches on homogeneous features through TGSA can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.882, + 0.891, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t g s a} = \\mathcal {L} _ {t g s a} ^ {(s p, V; s h, V)} + \\mathcal {L} _ {t g s a} ^ {(s p, I; s h, I)}. \\tag {17}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "397" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.362, + 0.108 + ], + "angle": 0, + "content": "3.3.2 Class Sementic Alignment (CSA)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.204 + ], + "angle": 0, + "content": "CSA is used to distill the semantic information of implicit modality-specific knowledge into the modality-shared branch for enhancing the feature representation of shared features. CSA operates on homogeneous features between two branches at logit-level. The logit matrix behind the classifier can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.216, + 0.469, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Z} _ {s p} = C _ {s p} \\left(\\boldsymbol {f} _ {s p}\\right), \\boldsymbol {Z} _ {s h} = C _ {s h} \\left(\\boldsymbol {f} _ {s h}\\right), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.244, + 0.469, + 0.318 + ], + "angle": 0, + "content": "where \\( C_{sp} \\) and \\( C_{sh} \\) is the modality-specific and modality-shared classifier separately. And the logit \\( Z_{sp} \\) and \\( Z_{sh} \\in \\mathbb{R}^{2N \\times C} \\) of specific and shared branch both contain visible modality and infrared modality, \\( C \\) is the total number of train dataset identities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.469, + 0.38 + ], + "angle": 0, + "content": "For learning the implicit discriminative modality-specific knowledge on semantic-level, the CSA loss is implemented on the same modality logit between the two branches, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.39, + 0.469, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c s a} = \\sum_ {i = 1} ^ {N} \\left(\\mathrm {K L} \\left(\\boldsymbol {Z} _ {s h, V} ^ {i}, \\boldsymbol {Z} _ {s p, V} ^ {i}\\right) + \\mathrm {K L} \\left(\\boldsymbol {Z} _ {s h, I} ^ {i}, \\boldsymbol {Z} _ {s p, I} ^ {i}\\right)\\right). \\tag {19}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.453, + 0.424, + 0.47 + ], + "angle": 0, + "content": "3.4. Modality Discrepancy Reduction (MDR)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.469, + 0.536 + ], + "angle": 0, + "content": "At this part, to guarantee the invariant representation of modality-shared feature, the TGSA and CSA are further used to reduce modality discrepancy within modality-shared branch as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.545, + 0.469, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m d r} = \\mathcal {L} _ {t g s a} ^ {(s h, V; s h, I)} + \\sum_ {i = 1} ^ {N} \\operatorname {K L} \\left(\\boldsymbol {Z} _ {s h, V} ^ {i}, \\boldsymbol {Z} _ {s h, I} ^ {i}\\right). \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.469, + 0.685 + ], + "angle": 0, + "content": "In this way, the visible feature and infrared feature in modality-shared branch can achieve mutual learning from feature-level and semantic-level. It makes two modalities feature aligning information each other, while alleviating modal gap and maintaining the invariant of modality-shared feature." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.218, + 0.712 + ], + "angle": 0, + "content": "3.5. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.469, + 0.794 + ], + "angle": 0, + "content": "Ultimately, by continuously distilling implicit discriminative knowledge from the modality-specific feature and consistently reducing modality discrepancies in the modality-shared feature, we can achieve a more discriminative and invariant modality-shared feature." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.795, + 0.408, + 0.809 + ], + "angle": 0, + "content": "The total loss of the model IDKL is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.094, + 0.825, + 0.469, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {b} + \\lambda_ {1} \\mathcal {L} _ {i p} + \\lambda_ {2} \\mathcal {L} _ {t g s a} + \\lambda_ {3} \\mathcal {L} _ {c s a} + \\mathcal {L} _ {m d r}, \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.9 + ], + "angle": 0, + "content": "where \\(\\lambda_{1},\\lambda_{2}\\) and \\(\\lambda_{3}\\) are hyper-parameters to balance the contribution of individual loss term." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.091, + 0.613, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.208, + 0.612, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.091, + 0.703, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.208, + 0.703, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.091, + 0.792, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.208, + 0.792, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.091, + 0.882, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.208, + 0.882, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.315, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Figure 4. Observation the implicit discriminative information by Grad-CAM. And 'sh' and 'sp(im)' present the modality-shared feature and the modality-specific feature of trained IDKL w/o knowledge distillation, respectively; 'enhanced' denotes the modality-shared feature of IDKL w/ knowledge distillation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.409, + 0.632, + 0.426 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.439, + 0.809, + 0.456 + ], + "angle": 0, + "content": "4.1. Datasets and Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.648 + ], + "angle": 0, + "content": "Datasets. Three public VI-ReID datasets SYSU-MM01 [28], LLCM [43] and RegDB [22] are employed to evaluate our model. SYSU-MM01 is a popular large-scale dataset collected by four visible cameras and two near-infrared cameras, including indoor and outdoor environments. And the test protocols consist of all-search and indoor-search. LLCM dataset is a large-scale and low-light cross-modality dataset, which is divided into training and testing sets at a 2:1 ratio. RegDB is collected using dual-camera systems, where visible and infrared images are captured in pairs. Both LLCM and RegDB contain visible to infrared and infrared to visible two search modes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.715 + ], + "angle": 0, + "content": "Evaluation metrics. The standard rank-\\(k\\) matching accuracy and mean Average Precision (mAP) are adopted as the evaluation metrics. All the reported results are the average of 10 trials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Implementation details. The proposed method and all experiments are implemented on a single NVIDIA GeForce 3090 GPU with PyTorch framework. The baseline model adopts the ResNet-50 pre-trained on ImageNet with the \\(\\mathcal{L}_b\\). The input images are resized to \\(3\\times 384\\times 128\\). The train mini-batch size is set as 120, which contains 12 random identities and 10 images for every identity. Adam optimizer with an initial learning rate \\(3\\times 10^{-5}\\) is exploited, which decays at the 60th and 100th epoch with a decay factor of 0.1. The hype-parameters \\(\\lambda_{1}\\), \\(\\lambda_{2}\\) and \\(\\lambda_{3}\\) are set to 0.1, 0.6 and 0.8. During the testing phase, only modality-shared feature is used to evaluate performance." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "398" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.123, + 0.09, + 0.846, + 0.103 + ], + "angle": 0, + "content": "Table 1. Comparison of CMC (%) and mAP (%) performances with the state-of-the-art methods on SYSU-MM01 dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.106, + 0.895, + 0.377 + ], + "angle": 0, + "content": "
MethodsAll-searchIndoor-search
Single-shotMulti-shotSingle-shotMulti-shot
r=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20map
Zero-Padding [32]14.8054.1271.3315.9519.1361.4078.4110.8920.5868.3885.7926.9224.4375.8691.3218.86
D-HSME [8]20.6862.7477.9523.12------------
AlignGAN [28]42.4085.0093.7040.7051.5089.4095.7033.9045.9087.6094.4054.3057.1092.7097.4045.30
DDAG [36]54.7590.3995.8153.02----61.0294.0698.4167.98----
NFS [2]56.9191.3496.5255.4563.5194.4297.8148.5662.7996.5399.0769.7970.0397.7099.5161.45
PIC [47]57.5189.3595.0355.14----60.40--67.70----
MID [12]60.2792.90-59.40----64.8696.12-70.12----
cm-SSFT [21]61.6089.2093.9063.2063.4091.2095.7062.0070.5094.9097.7072.6073.0096.3099.1072.40
MCLNet [7]65.4093.3397.1461.98----72.5696.9899.2076.58----
FMCNet [42]66.34--62.5173.44--56.0668.15--74.0978.86--63.82
SMCL [31]67.3992.8796.7661.7872.1590.6694.3254.9368.8496.5598.7775.5679.5795.3398.0066.57
CAJ [37]69.8895.7198.466.89----76.2697.8899.4980.37----
MPANet [33]70.5896.2198.8068.2475.5897.9199.4362.9176.7498.2199.5780.9584.2299.6699.9675.11
CMT [14]71.8896.4598.8768.5780.2397.9199.5363.1376.997.6899.6479.9184.8799.4199.9774.11
DEEN [43]74.797.699.271.8----80.399.099.883.3----
SAAI [3]75.90--77.0382.8--82.3983.20--88.0190.73--91.30
MUN [40]76.2497.84-73.81----79.4298.09-82.06----
MSCLNet [45]76.9997.6399.1871.64----78.4999.3299.9181.17----
PartMix [16]77.78--74.6280.54--69.8481.52--84.3887.99--79.95
IDKL(Ours)81.4297.3898.8979.8584.3498.8999.7378.2287.1498.2899.2689.3794.3099.7199.9388.75
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.399, + 0.207, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.207, + 0.399, + 0.335, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.399, + 0.465, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.491, + 0.47, + 0.521 + ], + "angle": 0, + "content": "Figure 5. Ablation analysis of hyper-parameter \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\), \\(\\lambda_{3}\\) for \\(\\mathcal{L}_{ip},\\mathcal{L}_{tgsa}\\), and \\(\\mathcal{L}_{csa}\\) respectively on SYSU-MM01 dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.442, + 0.544 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.552, + 0.47, + 0.597 + ], + "angle": 0, + "content": "We compare our IDKL model with the state-of-the-art VI-ReID methods published recent years on public VI-ReID datasets SYSU-MM01, RegDB and LLCM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Comparison on SYSU-MM01 dataset. The comparison experimental results is shown in Tab. 1 which displays the proposed IDKL method outperforms existing cutting-edge methods. Specifically, the IDKL method achieves the accuracy of \\(81.42\\%\\) rank-1 and \\(79.85\\%\\) map with single-shot all search protocol, while the accuracy of \\(87.14\\%\\) rank-1 and \\(89.37\\%\\) map with single-shot indoor search protocol. The compared SOTAs include various base methods, i.e., for the methods of learning the shared feature through network and loss function immediately, which contain D-HSME [8], NFS [2], CMT [14], DEEN[43] and MCLNet [7]. Based on graph structure augment method DDAG [36] and the mutual learning by logits skill (PIC [47] and MPANet [33]). Comparing with several other based modality-specific methods cm-SSFT[21], MUN[40] and MSCLNet[45], our results outperform them by a margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Comparison on RegDB dataset. We also evaluate IDKL on a small-scale dataset RegDB as shown in Tab. 2. There is strong performance IDKL showed and outperforms the existing solutions. Specifically, we achieve rank-1 ac" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.89, + 0.43 + ], + "angle": 0, + "content": "curacy of \\(94.72\\%\\) in visible to infrared mode, and rank-1 accuracy of \\(94.22\\%\\) in infrared to visible mode." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Comparison on LLCM dataset. The IDKL model achieves significant improvements on the large and complex LLCM dataset as shown in Tab. 3, demonstrating excellent rank-1 accuracy of \\(72.2\\%\\) and \\(70.7\\%\\) on two modes, respectively. This indicates that the IDKL model exhibits strong robustness in complex and multimodal scenarios." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.536, + 0.892, + 0.564 + ], + "angle": 0, + "content": "Table 2. Comparison of the CMC (\\%) and mAP (\\%) performances with state-of-the-art methods on RegDB dataset." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.565, + 0.889, + 0.83 + ], + "angle": 0, + "content": "
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
Zero-Padding [32]17.818.916.717.9
AlignGAN [28]57.953.656.353.4
DDAG [36]69.3463.4668.0661.80
cm-SSFT [21]72.372.971.071.7
MCLNet [7]80.3173.0775.9369.49
PIC [47]83.679.679.577.4
MPANet [33]83.780.982.880.7
SMCL [31]83.9379.8383.0578.57
MSCLNet [45]84.1780.9983.8678.31
CAJ [37]85.0377.8284.7577.82
MID [12]87.4584.8584.2981.41
FMCNet [42]89.1284.4388.3883.86
SAAI [3]91.0791.4592.0992.01
DEEN [43]91.185.189.583.4
CMT [14]95.1787.391.9784.46
MUN [40]95.1987.1591.8685.01
IDKL(Ours)94.7290.1994.2290.43
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.655, + 0.864 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this subsection, we conduct the ablation experiment to evaluate our proposed model exhaustively." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "399" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.077, + 0.468, + 0.103 + ], + "angle": 0, + "content": "Table 3. Comparison of the CMC (%) and mAP (%) performances with state-of-the-art methods on LLCM dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.107, + 0.466, + 0.202 + ], + "angle": 0, + "content": "
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
DDAG [36]40.348.448.052.3
CAJ [37]56.559.848.856.6
DEEN [43]62.565.854.962.9
IDKL(Ours)72.2266.4370.7265.19
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.213, + 0.468, + 0.24 + ], + "angle": 0, + "content": "Table 4. Evaluation the impact of different components in terms of rank-1 \\((\\%)\\) and mAP \\((\\%)\\) on SYSU-MM01 dataset." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.242, + 0.455, + 0.385 + ], + "angle": 0, + "content": "
LbLipLtgsaLcsaLmdrSYSU-MM01
rank1map
✓××××67.6066.47
✓×✓××68.3867.30
✓✓✓××76.4074.83
✓✓×✓×76.2874.34
✓✓××✓77.0475.66
✓✓✓✓✓81.4279.85
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.468, + 0.563 + ], + "angle": 0, + "content": "Effectiveness of each component. We evaluate the effectiveness of each component on the SYSU-MM01 dataset under all search single-shot mode. Each component is added independently to reveal its the performance as Tab. 4. This indicates that each component is highly useful, with \\(\\mathcal{L}_{mdr}\\) achieving significant performance improvements. This further suggests the effectiveness of TGSA and CSA in reducing modality discrepancies. Comparing the second row with the third row demonstrates the necessity of purifying implicit modality-specific information, and also proves the effectiveness of our Information Purifier module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.468, + 0.669 + ], + "angle": 0, + "content": "Hyper-parameters analysis of IP, TGSA and CSA. In this part, we present a line chart to examine the detail influence of IP, TGSA and CSA by gradually increasing the value of hyperparameters. As depicted in Fig. 5, the maximum contributions of IP, TGSA and CSA are reached at 0.1, 0.6 and 0.8, respectively. The upward trend of the curve demonstrates the effectiveness of each module." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.283, + 0.696 + ], + "angle": 0, + "content": "4.4. Visualization Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.809 + ], + "angle": 0, + "content": "Attention maps Visualization. To further illustrate the effectiveness of IDKL, Grad-CAM [26] is utilized for a visual examination of different feature heatmaps. In Fig. 4, the areas of focus for implicit discriminative information typically differ from those of the shared feature, indicating that effectively and judiciously utilizing this information to strengthen the shared feature can be highly beneficial." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Feature Distribution Visualization. We utilize t-SNE [22] feature map visualization to observe the impact of the IDKL model and TGSA on the model. As shown in Fig. 6, each color represents a different identity, while the shapes of circles and triangles indicate the visible and infrared modality information, respectively. From Fig. 6(a)," + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.092, + 0.696, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.211, + 0.667, + 0.223 + ], + "angle": 0, + "content": "a (pretrained resnet50)" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.092, + 0.888, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.212, + 0.827, + 0.223 + ], + "angle": 0, + "content": "b (baseline)" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.224, + 0.696, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.343, + 0.652, + 0.354 + ], + "angle": 0, + "content": "c (IDKL w/o TGSA)" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.224, + 0.888, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.343, + 0.841, + 0.354 + ], + "angle": 0, + "content": "d (IDKL w/ TGSA)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.366, + 0.892, + 0.421 + ], + "angle": 0, + "content": "Figure 6. Visualization of learned features by t-SNE. Where \"a\" means the pre-training resnet50 on ImageNet; \"b\" represents the baseline; \"c\" is the IDKL model w/o TGSA; \"d\" is IDKL model w/ TGSA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.581 + ], + "angle": 0, + "content": "a significant discrepancy between the two modalities is evident. Fig. 6(b) shows a reduction in modality discrepancy and the model exhibiting some discriminative capabilities. Comparing Fig. 6(b) with Fig. 6(c), it is observable that the IDKL model has a smaller intra-class discrepancy and better inter-class discrimination. In Fig. 6(d), the dark blue class appears more scattered than in Fig. 6(c), and the graph structures of the two modalities are more similar and closely aligned, demonstrating the effectiveness of TGSA in reducing modality discrepancies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.595, + 0.618, + 0.61 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.756 + ], + "angle": 0, + "content": "This paper harnesses the implicit discriminative information within modality-specific features and introduces a robust model IDKL to exploit the potential discrimination of heterogeneous-related features and enhance the shared feature. The IDKL model comprises a dual one-stream network, a novel IN-guided information purifier, a triplet graph structure alignment solution, and refined distillation on logits. Collectively, these components demonstrate exceptional effectiveness and contribute to improved results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.659, + 0.787 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was partially supported by National Key R&D Program of China (2021YFB3100800), National Natural Science Fund of China (62271090, 61771079), Chongqing Natural Science Fund (cstc2021jcyj-jqX0023) and National Youth Talent Project. This work is also supported by Huawei computational power of Chongqing Artificial Intelligence Innovation Center." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "400" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Cuiqun Chen, Mang Ye, Meibin Qi, Jingjing Wu, Jianguo Jiang, and Chia-Wen Lin. Structure-aware positional transformer for visible-infrared person re-identification. IEEE Transactions on Image Processing, 31:2352–2364, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Yehansen Chen, Lin Wan, Zhihang Li, Qianyan Jing, and Zongyuan Sun. Neural feature search for rgb-infrared person re-identification. 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Neurocomputing, 386:97–109, 2020. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.897 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "402" + } + ] +] \ No newline at end of file diff --git a/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/b65ca941-cca6-4d10-a9af-cf9b0fc08ec1_origin.pdf b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/b65ca941-cca6-4d10-a9af-cf9b0fc08ec1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a7e337f30ae48f468f7c5fe2ef3674de110016ea --- /dev/null +++ b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/b65ca941-cca6-4d10-a9af-cf9b0fc08ec1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:562f87cbb0d0cc06e7f48fe617a1d92770ef67bf27c0314a054923155ed86ec3 +size 1808949 diff --git a/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/full.md b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8239a19eae5d069dffd1bfa9fb0b694f28728c16 --- /dev/null +++ b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/full.md @@ -0,0 +1,387 @@ +# Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification + +Kajjie Ren, Lei Zhang* + +School of Microelectronics and Communication Engineering, Chongqing University, China + +kaijieren@cqu.edu.cn, leizhang@cqu.edu.cn + +# Abstract + +Visible-Infrared Person Re-identification (VI-ReID) is a challenging cross-modal pedestrian retrieval task, due to significant intra-class variations and cross-modal discrepancies among different cameras. Existing works mainly focus on embedding images of different modalities into a unified space to mine modality-shared features. They only seek distinctive information within these shared features, while ignoring the identity-aware useful information that is implicit in the modality-specific features. To address this issue, we propose a novel Implicit Discriminative Knowledge Learning (IDKL) network to uncover and leverage the implicit discriminative information contained within the modality-specific. First, we extract modality-specific and modality-shared features using a novel dual-stream network. Then, the modality-specific features undergo purification to reduce their modality style discrepancies while preserving identity-aware discriminative knowledge. Subsequently, this kind of implicit knowledge is distilled into the modality-shared feature to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features. Extensive experiments on multiple public datasets demonstrate the superiority of IDKL network over the state-of-the-art methods. Code is available at https://github.com/1KK077/IDKL. + +# 1. Introduction + +Visible-Infrared Person Re-Identification (VI-ReID) aims to match pedestrian images across multiple nonoverlapping camera views and different modalities. Advanced surveillance systems today are capable of automatically switching from visible to infrared mode at nightfall, ensuring an ample supply of trainable data. However, the unique modality of infrared images create significant domain discrepancies and a more complex environment. This makes previous single-modality methods, which are based + +![](images/c625676804a52ff86b1ad97cd2d73319cac1409b6d6023736052fa3ef8505d52.jpg) +Figure 1. Previous methods focused on seeking discriminative information within modality-shared features, overlooking the fact that there are discriminative clues implicit in modality-specific features. It is worth considering utilization of the implicit discriminative information to enhance shared invariant feature. + +solely on visible images, less efficient for VI-ReID tasks. + +Recently, numerous advanced methods have emerged in the field of VI-ReID. In conclusion, these approaches can generally be categorized into two types: the first aims to learn modality-shared features directly from raw modal data, and the second seeks to incorporate additional modal information to refine the feature space or bridge the modal gap, thereby facilitating the search for modality-shared features. Raw modal data based method [2, 4, 7, 8, 17, 19, 33, 49] is to embed different modality images into the same space and align them on feature-level so that model learn modality invariant feature directly. Despite original images based methods has achieved desirable results, they still remain a huge gap between different modalities in feature space. In order to bridge the gap between visible and infrared modalities and construct a continuous space for better learning modality-shared features, various methods based on introducing extra information [14, 29, 30, 34, 38, 42, 45] have emerged constantly. + +Although significant improvements have been made in + +current VI-ReID methods, these models inevitably discard some discriminative information that relies on modality-specific features, which is not fully exploited and utilized previously. These discriminative cues that exist in modality-specific features can be referred to as implicit discriminative information, as shown by the green area in Fig. 1, such as color, grayscale spectrum, contrast, saturation, and so on. Therefore, relying solely on modality-shared cues can limit the upper boundary of the discrimination ability of the feature representation. Utilizing implicit modality-specific characteristics effectively is essential to enhance the distinctiveness of modality-invariant features. However, we cannot directly use the modality-specific knowledge due to the modality discrepancies it contains. Instead, we need to reduce these discrepancies while preserving the identity-aware discriminative information inherent in the implicit knowledge. Meanwhile, traditional VI-ReID methods involving distillation, alignment, and mutual learning typically rely on logits [35, 44, 47]. However, there is no involvement of the classifier during the testing phase, with matching performed only at the feature level. Therefore, conducting discriminative information distillation at the feature level is also essential. + +To address the above limitations, in this paper, we propose an Implicit Discriminative Knowledge Learning (IDKL) framework that captures implicit invariant information from modality-specific features and distills it into modality-shared features to enhance their discriminative capability. We first extract modality-specific and modality-shared features using the modality discriminator and modality confuser, respectively. The modality discriminator effectively distinguishes between different modal features, endowing them with specific characteristics; whereas the modality confuser is unable to differentiate between modal features, thereby imparting shared characteristics to them. Since the modality-specific feature after previous stage contains substantial modality discrepancies, it is not suitable for direct distillation into the shared feature. We initially employ Instance Normalization to reduce domain discrepancies. However, it is crucial to acknowledge that IN inevitably results in the loss of some discriminative features. Therefore, we aim to reduce its modality style discrepancy while preserving identity-aware discriminative knowledge. Subsequently, we distill this implicit knowledge into the modality-shared feature at both the feature-level through feature graph structure, and the semantic-level through the logit vector to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features. + +The main contributions of this paper can be summarized as follows: + +- We propose the Implicit Discriminative Knowledge Learning (IDKL) network to utilize the discriminative + +knowledge implicit in the modality-specific features to enhance the upper bound of discriminative power for the modality-shared feature. + +- To reduce the modality style discrepancy without losing discriminative information of modality-specific information, we propose an IN-guided Information Purifier (IP), which is supervised by the discrimination enhancing loss and discrepancy reducing loss. +- The novel TGSA loss is developed to distill the discriminative modality-specific information into modality-shared feature and mitigate inter-modality discrepancy of modality-shared feature sufficiently. The substantial experimental results demonstrate the superiority of our method. + +# 2. Related Work + +Visible Modality Person ReID. Person ReID has received increasing success in recent years, which aims to implement pedestrian retrieval between visible images. It has suffered huge challenges including various viewpoints, illuminations, postures and so on. To solve these problems, most methodologies [24, 25, 39, 48] are designed to obtain unified intra-class and discriminative inter-class representation by training CNN network. To further enhance the distinguishability of features, Sun et al. [27] proposed aligning part feature directly instead of using external cues. He et al. [9] caught the hot spot of transformer and first proposed the transformer variant applying on single-modality person ReID. Simultaneously, person ReID has developed some significant branches yet, such as Unsupervised Domain Adaptive Person ReID (UDA-ReID) and Domain Generalization Person ReID (DG-ReID) [41]. Although existing methods have made wide progress in visible modality person ReID, they suffer performance degradation when applied to visible-infrared person ReID due to the severe cross-modality discrepancy. + +Visible-Infrared Person ReID (VI-ReID). VI-ReID is a cross-modality person retrieval problem, which aims at matching daytime visible and nighttime infrared images. It not only faces difficulties encountered in traditional single-motility person ReID task, but also the main challenge of huge modality discrepancy which caused by different camera spectra. To solve the these issues, numerous approaches are proposed to search shared feature[1, 5, 18, 20, 32, 36, 39, 46]. Wu et al. [32] first formulated the VI-REID issue and contributed a new cross-modality dataset SYSUMM01, which is of great significance to the following research. Ye et al. [36] proposed a part-level feature interaction and graph structure attention to enhance the discrimination of invariant feature. Meanwhile, some work begin to introduce additional modal information to jointly search for invariant features [14, 21, 28, 30, 45]. Wang et al. [30] combined RGB three channels feature and IR single + +![](images/ee84baa10c9a9a55770096e39ed7e4c62ae4a94a7d80d533426696e7004593ad.jpg) +Figure 2. Framework of the proposed Implicit Discriminative Knowledge Learning (IDKL) model. The dual one-stream network built by resnet blocks first extracts the modality-specific $F_{sp}$ and modality shared feature $F_{sh}$ under the constraint of modality discriminator and modality confuser accordingly, while the common ReID loss is used to optimize network basely. Then, the modality-specific feature is fed into the information purifier to regulate the modality style discrepancy while preserving the implicit discriminative information and obtain the purified modality-specific feature $\widetilde{F}_{sp}$ . Subsequently, this implicit knowledge is distilled into the modality-shared feature through TGSA and CSA. Finally, the $\mathcal{L}_{mdr}$ is further proposed to minimize modality discrepancy within the enhanced modality-shared feature. + +channel feature into united four channels feature to reduce modal differences. Jiang et al. [14] employed a global prototype to generate the missing modality counterpart through transformer. However, these generation based compensation methods inevitably introduce much noise and most of present methods aim to align modal discrepancy and extract modality invariant feature. They ignored use of beneficial style information contained in specific features to increase distinctiveness. + +Interactive Learning. In knowledge distillation, a teacher-student model is used to transfer the knowledge learned by a larger complex teacher model to a smaller simple student model. Different from the one-way transfer between a teacher and a student, deep mutual learning [44] is an ensemble of students which learns collaboratively and teaches each other throughout the training process. Some work applied this idea into VI-ReID for interactive learning in different modalities. Zheng et al. [47] enhanced invariant features learning by using interactive learning between two modality. Ye et al. [35] employed multi-classifier to reduce modality discrepancy on logits-level. Wu et al. [33] distilled RGB and IR knowledge mutually by four classifier to achieve inter shared representation. However, they only learn the knowledge within the semantic-level. + +# 3. Methodology + +In this section, we detail the proposed Implicit Discriminative Knowledge Learning (IDKL) framework as shown in Fig. 2. IDKL first distinguishes modality-specific features from modality-shared features through two network branches, which are constrained by modality discriminator + +and modality confuser, respectively. Simultaneously, common ReID loss is used to endow feature with representation. Then, an Information Purifier (IP) is developed to reduce the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. Finally, we distill the implicit discriminative knowledge across two branches into the modality-shared feature through Triplet Graph Structure Alignment (TGSA) at the feature-level and Class Semantic Alignment (CSA) at the logit-level. Additionally, to reduce modality discrepancy of shared feature, we proposed the Modality Discrepancy Reduction (MDR) loss within the modality-shared branch. As the discriminative information increases and modality discrepancy decreases constantly, the enhanced modality-shared feature can be obtained. + +Formally, we represent visible and infrared images in a dataset as $V = \{\pmb{x}_i^V\}_{i=1}^{N_V}$ and $I = \{\pmb{x}_i^I\}_{i=1}^{N_I}$ , respectively. Typically, the number of images sampled in a mini-batch is equal across both modalities, i.e., $N_V = N_I = N = P \times K$ , where $N_V$ and $N_I$ denote the number of images sampled from the visible and infrared modalities, respectively. Here, $N$ represents the number of images from a single modality, $2N$ is the total number of images in a mini-batch, $P$ is the number of distinct person classes, and $K$ is the number of images from each class within a single modality. We can therefore represent the images and their corresponding labels in a mini-batch as $X = \{\pmb{x}_i | \pmb{x}_i \in V \cup I\}_{i=1}^{2N}$ and $Y = \{\pmb{y}_i\}_{i=1}^{N_p = P}$ , respectively. These images $X$ are fed into two separate network branches to extract the modality-specific features $F_{sp}$ which contains $F_{sp,V}, F_{sp,I}$ and the shared features $F_{sh}$ which contains $F_{sh,V}, F_{sh,I}$ as fol + +lows: + +$$ +\boldsymbol {F} _ {s p} = E _ {s p} (\boldsymbol {x} \mid \Theta , \Psi), \boldsymbol {F} _ {s h} = E _ {s h} (\boldsymbol {x} \mid \Theta , \Phi), \tag {1} +$$ + +where $E_{sp}$ and $E_{sh}$ denote the specific and the shared feature extractor by employing ResNet-50, respectively. Among the sturctures of ResNet-50, the global average pooling replaced by Gem pooling[24, 39] which is a pooling operation between maximum pooling and average pooling. And $\Theta$ is the shallow layer parameters with the first three blocks of ResNet-50, $\Psi$ and $\Phi$ is the deep layer parameters of different branches with the last two blocks of ResNet-50. + +# 3.1. Modality Confuser and Discriminator + +Modality Confuser. For each sample image $\boldsymbol{x}_i$ , there is a modality label $t_i \in \{0,1\}$ . To learn modality-irrelated shared information, similar to [6], our goal is to confuse different domains such that a domain classifier cannot distinguish the domain of origin for a sample. We employ an adversarial modality classifier based on the Gradient Reversed Layer (GRL) as the modality confuser. The constraint loss for the modality confuser is given by: + +$$ +\mathcal {L} _ {C j} = - \frac {1}{2 N} \sum_ {i = 1} ^ {2 N} t _ {i} \cdot \log p \left(C _ {j} \left(G R L \left(\boldsymbol {F} _ {s h} ^ {i}\right)\right)\right), \tag {2} +$$ + +where $C_j$ represents the $j$ -th modality confuser in the modality-shared branch, $p(\cdot)$ is the prediction probability obtained via the softmax function, and $t_i$ is the modality label. + +Modality Discriminator. To adequately learn modality-related specific information, we employ a modality classifier as the Modality Discriminator. This classifier, which does not use GRL, is applied on the specific branch to extract modality-specific features. The classification loss is formulated as follows: + +$$ +\mathcal {L} _ {D j} = - \frac {1}{2 N} \sum_ {i = 1} ^ {2 N} t _ {i} \cdot \log p \left(D _ {j} \left(\boldsymbol {F} _ {s p} ^ {i}\right)\right), \tag {3} +$$ + +where $D_{j}$ denotes the j-th modality discriminator in the modality-specific branch. + +The combined loss from the modality confuser and discriminator is given by: + +$$ +\mathcal {L} _ {C} = \sum_ {j = 1} ^ {K} \mathcal {L} _ {C j}, \quad \mathcal {L} _ {D} = \sum_ {j = 1} ^ {K} \mathcal {L} _ {D j}. \tag {4} +$$ + +To efficiently extract both modality-specific and modality-shared features, we combine these modality classifier losses with the standard ReID loss $\mathcal{L}_{\text{reid}}$ , which includes cross-entropy and hard triplet loss. These are applied to both the modality-specific and modality-shared branches as follows: + +$$ +\mathcal {L} _ {s p} = \mathcal {L} _ {\text {r e i d}} \left(\boldsymbol {f} _ {s p}\right) + \mathcal {L} _ {D}, \mathcal {L} _ {s h} = \mathcal {L} _ {\text {r e i d}} \left(\boldsymbol {f} _ {s h}\right) + \mathcal {L} _ {C}, \tag {5} +$$ + +where $\pmb {f}\in \mathbb{R}^{B\times C}$ is the pooling feature corresponding to $\pmb {F}\in \mathbb{R}^{B\times C\times H\times W}$ + +Thus, the base loss for our model is formulated as: + +$$ +\mathcal {L} _ {b} = \mathcal {L} _ {s h} + \mathcal {L} _ {s p}. \tag {6} +$$ + +# 3.2. Information Purifier + +The Information Purifier (IP) is designed to minimize the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. The IP integrates Instance Normalization (IN), which is known to reduce domain discrepancies [13, 23, 48]. However, it is important to recognize that IN inevitably leads to the loss of some discriminative features [11, 15], potentially hindering the high performance of ReID. + +To overcome the aforementioned issues, we have designed a dual-mask network guided by Instance Normalization (IN) to alleviate modality style discrepancies while preserving implicit discriminative knowledge. Firstly, we apply IN on the modality-specific feature to obtain the normalized feature $\widehat{\pmb{F}}_{sp}$ by: + +$$ +\widehat {\boldsymbol {F}} _ {s p} = \operatorname {I N} \left(\boldsymbol {F} _ {s p}\right) = \frac {\boldsymbol {F} _ {s p} - \operatorname {E} \left[ \boldsymbol {F} _ {s p} \right]}{\sqrt {\operatorname {V a r} \left[ \boldsymbol {F} _ {s p} \right] + \epsilon}}, \tag {7} +$$ + +where the $\epsilon$ represents a safety factor to ensure the denominator is not zero. The mean $\operatorname{E}[\cdot]$ and variance $\operatorname{Var}[\cdot]$ are calculated along each channel. + +Following the approach of SE-Net [10], we generate two channel-wise masks $\mathbf{m}_e$ and $\mathbf{m}_r$ by: + +$$ +\mathbf {m} _ {e} = \sigma \left(\mathrm {W} _ {2} \delta \left(\mathrm {W} _ {1} g \left(\boldsymbol {F} _ {s p}\right)\right)\right), \mathbf {m} _ {r} = \sigma \left(\mathrm {W} _ {4} \delta \left(\mathrm {W} _ {3} g \left(\widehat {\boldsymbol {F}} _ {s p}\right)\right)\right), \tag {8} +$$ + +where $g(\cdot)$ denotes the pooling operation, $W_{1}, W_{3} \in \mathbb{R}^{\frac{c}{r} \times c}$ and $W_{2}, W_{4} \in \mathbb{R}^{c \times \frac{c}{r}}$ are learnable parameters in the four fully-connected (FC) layers which are followed by the ReLU activation function $\delta(\cdot)$ and the sigmoid activation function $\sigma(\cdot)$ . To balance the calculate consumption, the dimension reduction ratio $r$ is set to 16. + +The channel-wise masks $\mathbf{m}_e$ and $\mathbf{m}_r$ indicate enhancement of discriminative characteristics and reduction of discrepancies attention mask, respectively. So we can obtain the stronger distinctiveness $F_{sp}^{d+}$ and the smaller modality differences $\widehat{F}_{sp}^{m-}$ by: + +$$ +\boldsymbol {F} _ {s p} ^ {d +} = \mathbf {m} _ {e} \odot \boldsymbol {F} _ {s p}, \widehat {\boldsymbol {F}} _ {s p} ^ {m -} = \mathbf {m} _ {r} \odot \widehat {\boldsymbol {F}} _ {s p}. \tag {9} +$$ + +Subsequently, the discrimination enhancing loss $\mathcal{L}_e$ and the discrepancy reducing loss $\mathcal{L}_r$ are calculated to supervise $\mathbf{m}_e$ and $\mathbf{m}_r$ respectively as: + +$$ +\mathcal {L} _ {e} = \text {S o f t p l u s} \left(h \left(C _ {s p} \left(\boldsymbol {f} _ {s p} ^ {d +}\right)\right) - h \left(C _ {s p} \left(\boldsymbol {f} _ {s p}\right)\right)\right), \tag {10} +$$ + +$$ +\mathcal {L} _ {r} = \text {S o f t p l u s} \left(d \left(\widehat {\boldsymbol {f}} _ {s p, V} ^ {m -}, \widehat {\boldsymbol {f}} _ {s p, I} ^ {m -}\right) - d \left(\widehat {\boldsymbol {f}} _ {s p, V}, \widehat {\boldsymbol {f}} _ {s p, I}\right)\right). \tag {11} +$$ + +Here, $\mathcal{L}_e$ aims to imbue the generated $\mathbf{F}_{sp}^{d+}$ with greater semantic distinctiveness compared to $\mathbf{F}_{sp}$ , while $\mathcal{L}_r$ seeks to ensure that $\widehat{\mathbf{F}}_{sp}^{m-}$ exhibit smaller modality differences than $\widehat{\mathbf{F}}_{sp}$ . And Softplus $(\cdot) = \ln(1 + \exp(\cdot))$ is a function with monotonic increase, designed to alleviate optimization challenges by circumventing negative values in loss. + +Finally, an alternating integration strategy is employed to extract the distinctive information from $\widetilde{\mathbf{F}}_{sp}^{m - }$ by applying $\mathbf{m}_e$ and the invariant information from $\mathbf{F}_{sp}^{d + }$ by applying $\mathbf{m}_r$ . Thus, The two sets of features extracted in this way both demonstrate smaller modality differences and stronger implicit discriminative information. By integrating them, we derive the purified modality-specific feature $\widetilde{\mathbf{F}}_{sp}$ as: + +$$ +\widetilde {\boldsymbol {F}} _ {s p} = \mathbf {m} _ {e} \odot \widehat {\boldsymbol {F}} _ {s p} ^ {m -} + \mathbf {m} _ {r} \odot \boldsymbol {F} _ {s p} ^ {d +}. \tag {12} +$$ + +Intuitively, the pooling feature $\widetilde{f}_{sp}$ of implicit feature $\widetilde{\pmb{F}}_{sp}$ is also constraint with ReID loss. So the information purify loss $\mathcal{L}_{ip}$ of this section is summarized as: + +$$ +\mathcal {L} _ {i p} = \mathcal {L} _ {e} + \mathcal {L} _ {r} + \mathcal {L} _ {\text {r e i d}} (\tilde {\boldsymbol {f}} _ {s p}). \tag {13} +$$ + +# 3.3. Implicit Knowledge Distillation + +To ensure that the modality-shared feature comprehensively learns and integrates implicit information, we perform distillation from both the feature-level through TGSA and logit-level through CSA. + +# 3.3.1 Triplet Graph Structure Alignment (TGSA) + +To endow the shared feature with discriminative information and reduce modality discrepancy at the feature level, we develop a triplet feature graph structure alignment loss. This approach is motivated by the fact that the feature graph structure contains abundant information about the relationships and distribution between features, such as inter-class distinctiveness and intra-class diversity. These characteristics are utilized to unearth potential feature relationships and enhance the feature representation in [17, 36]. The graph structure affinity matrix which indicates the relationships between features is calculated by: + +$$ +\alpha_ {i j} = \frac {\exp \left(L \left(\left[ l \left(\boldsymbol {f} _ {i}\right) \| l \left(\boldsymbol {f} _ {j}\right) \right] \cdot \boldsymbol {w}\right)\right)}{\sum_ {k \in \mathcal {N} _ {i}} \exp \left(L \left(\left[ l \left(\boldsymbol {f} _ {i}\right) \| l \left(\boldsymbol {f} _ {k}\right) \right] \cdot \boldsymbol {w}\right)\right)}, \tag {14} +$$ + +where the $L$ denote LeakyReLU activation function, $[\cdot \| \cdot ]$ denote concatenate operation and $\mathcal{N}_i$ denotes the neighbor samples which are used to normalize for the ith sample. $l(\cdot)$ is feature dimension transformation layer and $\pmb{w}$ is the full connection layer to calculate scores in a pair features. The affinity matrix is acquired making these scores through softmax function normalization. + +![](images/92c3544ac8ece8a1ee09ff09c22c5197f14d723a23cdf8a37fbc3e9c0b02a73f.jpg) +Figure 3. Illustration of the proposed TGSA loss: 'a' and 'b' denote two different types of features. 'A' represents the graph structure affinity matrix. After aligning the three affinity matrices, the discrepancy in the graph structure distribution between features 'a' and features 'b' will be eliminated. + +Due to we utilize graph structure to align and distill knowledge, instead of augmenting the feature, and the Euclidean space distribution is more interesting for features, thus we replace the linear transformation with Euclidean distance to compute attention scores and redefine the graph structure expression for two groups of features as follows: + +$$ +\boldsymbol {A} _ {(a; b)} = \left\{\alpha_ {i j} \right\} _ {i, j \in N} = \frac {\exp \left(D \left(\boldsymbol {f} _ {a} ^ {i} , \boldsymbol {f} _ {b} ^ {j}\right)\right)}{\sum_ {k \in N} \exp \left(D \left(\boldsymbol {f} _ {a} ^ {i} , \boldsymbol {f} _ {b} ^ {k}\right)\right)}, \tag {15} +$$ + +where $\alpha_{ij}$ denotes the element of the affinity matrix, $N$ corresponds to the entirety of samples within one modality, $a$ and $b$ represent two modalities, $D(\cdot)$ means Euclidean distance. + +Specifically, the triplet graph structure alignment loss $\mathcal{L}_{tgsa}$ is developed for cross modality ReID to align two different modality types, enabling them to conform to the same graph structure distribution and reduce modality discrepancy. This loss encompasses two self-modal affinity matrices and one cross-modal affinity matrix, with the latter ensuring the overall consistency of the graph structure's distribution as shown in Fig. 3. These three matrices are aligned pairwise through the utilization of the Kullback-Leibler (KL) divergence. Therefore, the alignment loss $\mathcal{L}_{tgsa}$ of two distinct modality types is defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {t g s a} ^ {(a; b)} = \sum_ {p = 1} ^ {P} \sum_ {k = 1} ^ {K} \left(\mathrm {K L} \left(\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\right) \right. \\ + \operatorname {K L} \left(\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \boldsymbol {A} _ {(a; b)} ^ {p _ {k}}\right) + \operatorname {K L} \left(\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}, \boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\right)). \tag {16} \\ \end{array} +$$ + +Here, $A^{p_k}$ represents the graph structure distribution of the $k$ -th sample in the $p$ -th class, where $P$ is the number of person classes, and $K$ denotes the number of images for each class within a single modality. + +In order to convey the discriminative implicit modality-specific knowledge to shared feature on feature-level, the distillation loss across two branches on homogeneous features through TGSA can be formulated as: + +$$ +\mathcal {L} _ {t g s a} = \mathcal {L} _ {t g s a} ^ {(s p, V; s h, V)} + \mathcal {L} _ {t g s a} ^ {(s p, I; s h, I)}. \tag {17} +$$ + +# 3.3.2 Class Sementic Alignment (CSA) + +CSA is used to distill the semantic information of implicit modality-specific knowledge into the modality-shared branch for enhancing the feature representation of shared features. CSA operates on homogeneous features between two branches at logit-level. The logit matrix behind the classifier can be formulated as: + +$$ +\boldsymbol {Z} _ {s p} = C _ {s p} \left(\boldsymbol {f} _ {s p}\right), \boldsymbol {Z} _ {s h} = C _ {s h} \left(\boldsymbol {f} _ {s h}\right), \tag {18} +$$ + +where $C_{sp}$ and $C_{sh}$ is the modality-specific and modality-shared classifier separately. And the logit $Z_{sp}$ and $Z_{sh} \in \mathbb{R}^{2N \times C}$ of specific and shared branch both contain visible modality and infrared modality, $C$ is the total number of train dataset identities. + +For learning the implicit discriminative modality-specific knowledge on semantic-level, the CSA loss is implemented on the same modality logit between the two branches, which is formulated as: + +$$ +\mathcal {L} _ {c s a} = \sum_ {i = 1} ^ {N} \left(\mathrm {K L} \left(\boldsymbol {Z} _ {s h, V} ^ {i}, \boldsymbol {Z} _ {s p, V} ^ {i}\right) + \mathrm {K L} \left(\boldsymbol {Z} _ {s h, I} ^ {i}, \boldsymbol {Z} _ {s p, I} ^ {i}\right)\right). \tag {19} +$$ + +# 3.4. Modality Discrepancy Reduction (MDR) + +At this part, to guarantee the invariant representation of modality-shared feature, the TGSA and CSA are further used to reduce modality discrepancy within modality-shared branch as follow: + +$$ +\mathcal {L} _ {m d r} = \mathcal {L} _ {t g s a} ^ {(s h, V; s h, I)} + \sum_ {i = 1} ^ {N} \operatorname {K L} \left(\boldsymbol {Z} _ {s h, V} ^ {i}, \boldsymbol {Z} _ {s h, I} ^ {i}\right). \tag {20} +$$ + +In this way, the visible feature and infrared feature in modality-shared branch can achieve mutual learning from feature-level and semantic-level. It makes two modalities feature aligning information each other, while alleviating modal gap and maintaining the invariant of modality-shared feature. + +# 3.5. Optimization + +Ultimately, by continuously distilling implicit discriminative knowledge from the modality-specific feature and consistently reducing modality discrepancies in the modality-shared feature, we can achieve a more discriminative and invariant modality-shared feature. + +The total loss of the model IDKL is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {b} + \lambda_ {1} \mathcal {L} _ {i p} + \lambda_ {2} \mathcal {L} _ {t g s a} + \lambda_ {3} \mathcal {L} _ {c s a} + \mathcal {L} _ {m d r}, \tag {21} +$$ + +where $\lambda_{1},\lambda_{2}$ and $\lambda_{3}$ are hyper-parameters to balance the contribution of individual loss term. + +![](images/88572ec55ee6e12b832640788e709d05ed0175a4c07112f70fd77c440a4c6aa3.jpg) + +![](images/620d730a1fae94eb04d908658bc7f65b18ab8f2d2c812b2286ed6ae1a69083bb.jpg) +Figure 4. Observation the implicit discriminative information by Grad-CAM. And 'sh' and 'sp(im)' present the modality-shared feature and the modality-specific feature of trained IDKL w/o knowledge distillation, respectively; 'enhanced' denotes the modality-shared feature of IDKL w/ knowledge distillation. + +![](images/ebb08dbc55573406afd08cf4bde67698fabc4c99a99772c129343f5751ed7f99.jpg) + +![](images/4e298b6d20c9137e3012312e0b498a37d97b7ff8ff23cd2515336003b8b2db69.jpg) + +![](images/697b2e61cbc4f0b04fd8c161da8351ea02a8ad71d50ed2143c4663b42d658326.jpg) + +![](images/ea031cd2c5dbd45e9f01f5742badab065b8ad3309c5965b9b6a45dbb2ee5d4a8.jpg) + +![](images/fd5fb4ca2e3270b3956d8243c8278609e4b654d084f0e7a689490a63ca659b3a.jpg) + +![](images/857cb09cd6f18c8b059ed1214f051dbc8d413cfa27b4946427683876d8bbcb8c.jpg) + +# 4. Experiments + +# 4.1. Datasets and Experimental Settings + +Datasets. Three public VI-ReID datasets SYSU-MM01 [28], LLCM [43] and RegDB [22] are employed to evaluate our model. SYSU-MM01 is a popular large-scale dataset collected by four visible cameras and two near-infrared cameras, including indoor and outdoor environments. And the test protocols consist of all-search and indoor-search. LLCM dataset is a large-scale and low-light cross-modality dataset, which is divided into training and testing sets at a 2:1 ratio. RegDB is collected using dual-camera systems, where visible and infrared images are captured in pairs. Both LLCM and RegDB contain visible to infrared and infrared to visible two search modes. + +Evaluation metrics. The standard rank- $k$ matching accuracy and mean Average Precision (mAP) are adopted as the evaluation metrics. All the reported results are the average of 10 trials. + +Implementation details. The proposed method and all experiments are implemented on a single NVIDIA GeForce 3090 GPU with PyTorch framework. The baseline model adopts the ResNet-50 pre-trained on ImageNet with the $\mathcal{L}_b$ . The input images are resized to $3\times 384\times 128$ . The train mini-batch size is set as 120, which contains 12 random identities and 10 images for every identity. Adam optimizer with an initial learning rate $3\times 10^{-5}$ is exploited, which decays at the 60th and 100th epoch with a decay factor of 0.1. The hype-parameters $\lambda_{1}$ , $\lambda_{2}$ and $\lambda_{3}$ are set to 0.1, 0.6 and 0.8. During the testing phase, only modality-shared feature is used to evaluate performance. + +Table 1. Comparison of CMC (%) and mAP (%) performances with the state-of-the-art methods on SYSU-MM01 dataset. + +
MethodsAll-searchIndoor-search
Single-shotMulti-shotSingle-shotMulti-shot
r=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20map
Zero-Padding [32]14.8054.1271.3315.9519.1361.4078.4110.8920.5868.3885.7926.9224.4375.8691.3218.86
D-HSME [8]20.6862.7477.9523.12------------
AlignGAN [28]42.4085.0093.7040.7051.5089.4095.7033.9045.9087.6094.4054.3057.1092.7097.4045.30
DDAG [36]54.7590.3995.8153.02----61.0294.0698.4167.98----
NFS [2]56.9191.3496.5255.4563.5194.4297.8148.5662.7996.5399.0769.7970.0397.7099.5161.45
PIC [47]57.5189.3595.0355.14----60.40--67.70----
MID [12]60.2792.90-59.40----64.8696.12-70.12----
cm-SSFT [21]61.6089.2093.9063.2063.4091.2095.7062.0070.5094.9097.7072.6073.0096.3099.1072.40
MCLNet [7]65.4093.3397.1461.98----72.5696.9899.2076.58----
FMCNet [42]66.34--62.5173.44--56.0668.15--74.0978.86--63.82
SMCL [31]67.3992.8796.7661.7872.1590.6694.3254.9368.8496.5598.7775.5679.5795.3398.0066.57
CAJ [37]69.8895.7198.466.89----76.2697.8899.4980.37----
MPANet [33]70.5896.2198.8068.2475.5897.9199.4362.9176.7498.2199.5780.9584.2299.6699.9675.11
CMT [14]71.8896.4598.8768.5780.2397.9199.5363.1376.997.6899.6479.9184.8799.4199.9774.11
DEEN [43]74.797.699.271.8----80.399.099.883.3----
SAAI [3]75.90--77.0382.8--82.3983.20--88.0190.73--91.30
MUN [40]76.2497.84-73.81----79.4298.09-82.06----
MSCLNet [45]76.9997.6399.1871.64----78.4999.3299.9181.17----
PartMix [16]77.78--74.6280.54--69.8481.52--84.3887.99--79.95
IDKL(Ours)81.4297.3898.8979.8584.3498.8999.7378.2287.1498.2899.2689.3794.3099.7199.9388.75
+ +![](images/8fbb8e51bde2d6bf87b1faa04de8e3744ba878548ecd702947b6a49b793babe0.jpg) +Figure 5. Ablation analysis of hyper-parameter $\lambda_{1}$ and $\lambda_{2}$ , $\lambda_{3}$ for $\mathcal{L}_{ip},\mathcal{L}_{tgsa}$ , and $\mathcal{L}_{csa}$ respectively on SYSU-MM01 dataset. + +![](images/96863ecd4cb31e453bbd3bc97cab69b5204d4bd4527529d82af6a77ba54a9a91.jpg) + +![](images/8d089738f0890c9fa8ad72a365864e62b6210b5c645d026c8203632b60042a38.jpg) + +# 4.2. Comparison with State-of-the-art Methods + +We compare our IDKL model with the state-of-the-art VI-ReID methods published recent years on public VI-ReID datasets SYSU-MM01, RegDB and LLCM. + +Comparison on SYSU-MM01 dataset. The comparison experimental results is shown in Tab. 1 which displays the proposed IDKL method outperforms existing cutting-edge methods. Specifically, the IDKL method achieves the accuracy of $81.42\%$ rank-1 and $79.85\%$ map with single-shot all search protocol, while the accuracy of $87.14\%$ rank-1 and $89.37\%$ map with single-shot indoor search protocol. The compared SOTAs include various base methods, i.e., for the methods of learning the shared feature through network and loss function immediately, which contain D-HSME [8], NFS [2], CMT [14], DEEN[43] and MCLNet [7]. Based on graph structure augment method DDAG [36] and the mutual learning by logits skill (PIC [47] and MPANet [33]). Comparing with several other based modality-specific methods cm-SSFT[21], MUN[40] and MSCLNet[45], our results outperform them by a margin. + +Comparison on RegDB dataset. We also evaluate IDKL on a small-scale dataset RegDB as shown in Tab. 2. There is strong performance IDKL showed and outperforms the existing solutions. Specifically, we achieve rank-1 ac + +curacy of $94.72\%$ in visible to infrared mode, and rank-1 accuracy of $94.22\%$ in infrared to visible mode. + +Comparison on LLCM dataset. The IDKL model achieves significant improvements on the large and complex LLCM dataset as shown in Tab. 3, demonstrating excellent rank-1 accuracy of $72.2\%$ and $70.7\%$ on two modes, respectively. This indicates that the IDKL model exhibits strong robustness in complex and multimodal scenarios. + +Table 2. Comparison of the CMC (\%) and mAP (\%) performances with state-of-the-art methods on RegDB dataset. + +
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
Zero-Padding [32]17.818.916.717.9
AlignGAN [28]57.953.656.353.4
DDAG [36]69.3463.4668.0661.80
cm-SSFT [21]72.372.971.071.7
MCLNet [7]80.3173.0775.9369.49
PIC [47]83.679.679.577.4
MPANet [33]83.780.982.880.7
SMCL [31]83.9379.8383.0578.57
MSCLNet [45]84.1780.9983.8678.31
CAJ [37]85.0377.8284.7577.82
MID [12]87.4584.8584.2981.41
FMCNet [42]89.1284.4388.3883.86
SAAI [3]91.0791.4592.0992.01
DEEN [43]91.185.189.583.4
CMT [14]95.1787.391.9784.46
MUN [40]95.1987.1591.8685.01
IDKL(Ours)94.7290.1994.2290.43
+ +# 4.3. Ablation Study + +In this subsection, we conduct the ablation experiment to evaluate our proposed model exhaustively. + +Table 3. Comparison of the CMC (%) and mAP (%) performances with state-of-the-art methods on LLCM dataset. + +
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
DDAG [36]40.348.448.052.3
CAJ [37]56.559.848.856.6
DEEN [43]62.565.854.962.9
IDKL(Ours)72.2266.4370.7265.19
+ +Table 4. Evaluation the impact of different components in terms of rank-1 $(\%)$ and mAP $(\%)$ on SYSU-MM01 dataset. + +
LbLipLtgsaLcsaLmdrSYSU-MM01
rank1map
✓××××67.6066.47
✓×✓××68.3867.30
✓✓✓××76.4074.83
✓✓×✓×76.2874.34
✓✓××✓77.0475.66
✓✓✓✓✓81.4279.85
+ +Effectiveness of each component. We evaluate the effectiveness of each component on the SYSU-MM01 dataset under all search single-shot mode. Each component is added independently to reveal its the performance as Tab. 4. This indicates that each component is highly useful, with $\mathcal{L}_{mdr}$ achieving significant performance improvements. This further suggests the effectiveness of TGSA and CSA in reducing modality discrepancies. Comparing the second row with the third row demonstrates the necessity of purifying implicit modality-specific information, and also proves the effectiveness of our Information Purifier module. + +Hyper-parameters analysis of IP, TGSA and CSA. In this part, we present a line chart to examine the detail influence of IP, TGSA and CSA by gradually increasing the value of hyperparameters. As depicted in Fig. 5, the maximum contributions of IP, TGSA and CSA are reached at 0.1, 0.6 and 0.8, respectively. The upward trend of the curve demonstrates the effectiveness of each module. + +# 4.4. Visualization Analysis + +Attention maps Visualization. To further illustrate the effectiveness of IDKL, Grad-CAM [26] is utilized for a visual examination of different feature heatmaps. In Fig. 4, the areas of focus for implicit discriminative information typically differ from those of the shared feature, indicating that effectively and judiciously utilizing this information to strengthen the shared feature can be highly beneficial. + +Feature Distribution Visualization. We utilize t-SNE [22] feature map visualization to observe the impact of the IDKL model and TGSA on the model. As shown in Fig. 6, each color represents a different identity, while the shapes of circles and triangles indicate the visible and infrared modality information, respectively. From Fig. 6(a), + +![](images/e9c4b0e07c777f31f3943a658867b06eb8f85554aa626ef57a15675a09b7d428.jpg) + +![](images/7d3ae0b9f3bb711509dea1a030337d77b45737e509a3ed1cc731832ecdd7265d.jpg) +b (baseline) + +![](images/088b316aa60e2719a88d5f36c7a4a3960e4fa91e7b2d904c6e6b2d9a48a63c27.jpg) +a (pretrained resnet50) +c (IDKL w/o TGSA) +Figure 6. Visualization of learned features by t-SNE. Where "a" means the pre-training resnet50 on ImageNet; "b" represents the baseline; "c" is the IDKL model w/o TGSA; "d" is IDKL model w/ TGSA. + +![](images/b374cae388c2d31e37ca6865d8b7ae2fca16bcc8cd2cbbd0e98b63cd6dc2ccb7.jpg) +d (IDKL w/ TGSA) + +a significant discrepancy between the two modalities is evident. Fig. 6(b) shows a reduction in modality discrepancy and the model exhibiting some discriminative capabilities. Comparing Fig. 6(b) with Fig. 6(c), it is observable that the IDKL model has a smaller intra-class discrepancy and better inter-class discrimination. In Fig. 6(d), the dark blue class appears more scattered than in Fig. 6(c), and the graph structures of the two modalities are more similar and closely aligned, demonstrating the effectiveness of TGSA in reducing modality discrepancies. + +# 5. Conclusion + +This paper harnesses the implicit discriminative information within modality-specific features and introduces a robust model IDKL to exploit the potential discrimination of heterogeneous-related features and enhance the shared feature. The IDKL model comprises a dual one-stream network, a novel IN-guided information purifier, a triplet graph structure alignment solution, and refined distillation on logits. Collectively, these components demonstrate exceptional effectiveness and contribute to improved results. + +# Acknowledgments + +This work was partially supported by National Key R&D Program of China (2021YFB3100800), National Natural Science Fund of China (62271090, 61771079), Chongqing Natural Science Fund (cstc2021jcyj-jqX0023) and National Youth Talent Project. This work is also supported by Huawei computational power of Chongqing Artificial Intelligence Innovation Center. + +# References + +[1] Cuiqun Chen, Mang Ye, Meibin Qi, Jingjing Wu, Jianguo Jiang, and Chia-Wen Lin. Structure-aware positional transformer for visible-infrared person re-identification. IEEE Transactions on Image Processing, 31:2352–2364, 2022. 2 +[2] Yehansen Chen, Lin Wan, Zhihang Li, Qianyan Jing, and Zongyuan Sun. Neural feature search for rgb-infrared person re-identification. 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Visible-infrared person re-identification via partially interactive collaboration. IEEE Transactions on Image Processing, 31: 6951–6963, 2022. 2, 3, 7 +[48] Kaiyang Zhou, Yongxin Yang, Andrea Cavallaro, and Tao Xiang. Omni-scale feature learning for person re-identification. In Proceedings of the IEEE/CVF international conference on computer vision, pages 3702–3712, 2019. 2, 4 +[49] Yuanxin Zhu, Zhao Yang, Li Wang, Sai Zhao, Xiao Hu, and Dapeng Tao. Hetero-center loss for cross-modality person re-identification. Neurocomputing, 386:97–109, 2020. 1 \ No newline at end of file diff --git a/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/images.zip b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..22fb200932886b9bb255f267d1b4d6e7acd8135a --- /dev/null +++ b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:55785f17c0c31ade36c5b6fe77052148db68ffbf113ecc8916f77beb4c9932c7 +size 686421 diff --git a/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/layout.json b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..33e19fd31ba9acbf0099477491e7ba05cb683d40 --- /dev/null +++ b/2024/Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification/layout.json @@ -0,0 +1,9933 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 74, + 102, + 520, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 102, + 520, + 138 + ], + "spans": [ + { + "bbox": [ + 74, + 102, + 520, + 138 + ], + "type": "text", + "content": "Implicit Discriminative Knowledge Learning for Visible-Infrared Person Re-Identification" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 239, + 161, + 355, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 239, + 161, + 355, + 175 + ], + "spans": [ + { + "bbox": [ + 239, + 161, + 355, + 175 + ], + "type": "text", + "content": "Kajjie Ren, Lei Zhang*" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 76, + 175, + 517, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 175, + 517, + 190 + ], + "spans": [ + { + "bbox": [ + 76, + 175, + 517, + 190 + ], + "type": "text", + "content": "School of Microelectronics and Communication Engineering, Chongqing University, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 183, + 191, + 406, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 183, + 191, + 406, + 202 + ], + "spans": [ + { + "bbox": [ + 183, + 191, + 406, + 202 + ], + "type": "text", + "content": "kaijieren@cqu.edu.cn, leizhang@cqu.edu.cn" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 257, + 290, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 290, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 290, + 558 + ], + "type": "text", + "content": "Visible-Infrared Person Re-identification (VI-ReID) is a challenging cross-modal pedestrian retrieval task, due to significant intra-class variations and cross-modal discrepancies among different cameras. Existing works mainly focus on embedding images of different modalities into a unified space to mine modality-shared features. They only seek distinctive information within these shared features, while ignoring the identity-aware useful information that is implicit in the modality-specific features. To address this issue, we propose a novel Implicit Discriminative Knowledge Learning (IDKL) network to uncover and leverage the implicit discriminative information contained within the modality-specific. First, we extract modality-specific and modality-shared features using a novel dual-stream network. Then, the modality-specific features undergo purification to reduce their modality style discrepancies while preserving identity-aware discriminative knowledge. Subsequently, this kind of implicit knowledge is distilled into the modality-shared feature to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features. Extensive experiments on multiple public datasets demonstrate the superiority of IDKL network over the state-of-the-art methods. Code is available at https://github.com/1KK077/IDKL." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 584, + 128, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 584, + 128, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 584, + 128, + 596 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Visible-Infrared Person Re-Identification (VI-ReID) aims to match pedestrian images across multiple nonoverlapping camera views and different modalities. Advanced surveillance systems today are capable of automatically switching from visible to infrared mode at nightfall, ensuring an ample supply of trainable data. However, the unique modality of infrared images create significant domain discrepancies and a more complex environment. This makes previous single-modality methods, which are based" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 313, + 230, + 541, + 390 + ], + "blocks": [ + { + "bbox": [ + 313, + 230, + 541, + 390 + ], + "lines": [ + { + "bbox": [ + 313, + 230, + 541, + 390 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 541, + 390 + ], + "type": "image", + "image_path": "c625676804a52ff86b1ad97cd2d73319cac1409b6d6023736052fa3ef8505d52.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 399, + 546, + 453 + ], + "lines": [ + { + "bbox": [ + 305, + 399, + 546, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 546, + 453 + ], + "type": "text", + "content": "Figure 1. Previous methods focused on seeking discriminative information within modality-shared features, overlooking the fact that there are discriminative clues implicit in modality-specific features. It is worth considering utilization of the implicit discriminative information to enhance shared invariant feature." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 469, + 537, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 469, + 537, + 481 + ], + "spans": [ + { + "bbox": [ + 306, + 469, + 537, + 481 + ], + "type": "text", + "content": "solely on visible images, less efficient for VI-ReID tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 483, + 546, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 546, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 546, + 699 + ], + "type": "text", + "content": "Recently, numerous advanced methods have emerged in the field of VI-ReID. In conclusion, these approaches can generally be categorized into two types: the first aims to learn modality-shared features directly from raw modal data, and the second seeks to incorporate additional modal information to refine the feature space or bridge the modal gap, thereby facilitating the search for modality-shared features. Raw modal data based method [2, 4, 7, 8, 17, 19, 33, 49] is to embed different modality images into the same space and align them on feature-level so that model learn modality invariant feature directly. Despite original images based methods has achieved desirable results, they still remain a huge gap between different modalities in feature space. In order to bridge the gap between visible and infrared modalities and construct a continuous space for better learning modality-shared features, various methods based on introducing extra information [14, 29, 30, 34, 38, 42, 45] have emerged constantly." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 318, + 701, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 546, + 714 + ], + "type": "text", + "content": "Although significant improvements have been made in" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 15 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 15 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 15 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 198, + 13, + 443, + 24 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 13, + 443, + 24 + ], + "spans": [ + { + "bbox": [ + 198, + 13, + 443, + 24 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "spans": [ + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "393" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": "current VI-ReID methods, these models inevitably discard some discriminative information that relies on modality-specific features, which is not fully exploited and utilized previously. These discriminative cues that exist in modality-specific features can be referred to as implicit discriminative information, as shown by the green area in Fig. 1, such as color, grayscale spectrum, contrast, saturation, and so on. Therefore, relying solely on modality-shared cues can limit the upper boundary of the discrimination ability of the feature representation. Utilizing implicit modality-specific characteristics effectively is essential to enhance the distinctiveness of modality-invariant features. However, we cannot directly use the modality-specific knowledge due to the modality discrepancies it contains. Instead, we need to reduce these discrepancies while preserving the identity-aware discriminative information inherent in the implicit knowledge. Meanwhile, traditional VI-ReID methods involving distillation, alignment, and mutual learning typically rely on logits [35, 44, 47]. However, there is no involvement of the classifier during the testing phase, with matching performed only at the feature level. Therefore, conducting discriminative information distillation at the feature level is also essential." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 350, + 289, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 289, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 289, + 661 + ], + "type": "text", + "content": "To address the above limitations, in this paper, we propose an Implicit Discriminative Knowledge Learning (IDKL) framework that captures implicit invariant information from modality-specific features and distills it into modality-shared features to enhance their discriminative capability. We first extract modality-specific and modality-shared features using the modality discriminator and modality confuser, respectively. The modality discriminator effectively distinguishes between different modal features, endowing them with specific characteristics; whereas the modality confuser is unable to differentiate between modal features, thereby imparting shared characteristics to them. Since the modality-specific feature after previous stage contains substantial modality discrepancies, it is not suitable for direct distillation into the shared feature. We initially employ Instance Normalization to reduce domain discrepancies. However, it is crucial to acknowledge that IN inevitably results in the loss of some discriminative features. Therefore, we aim to reduce its modality style discrepancy while preserving identity-aware discriminative knowledge. Subsequently, we distill this implicit knowledge into the modality-shared feature at both the feature-level through feature graph structure, and the semantic-level through the logit vector to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on enhanced modality-shared features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 663, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 288, + 687 + ], + "type": "text", + "content": "The main contributions of this paper can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "- We propose the Implicit Discriminative Knowledge Learning (IDKL) network to utilize the discriminative" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 108 + ], + "type": "text", + "content": "knowledge implicit in the modality-specific features to enhance the upper bound of discriminative power for the modality-shared feature." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 108, + 547, + 239 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 306, + 108, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 108, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 547, + 168 + ], + "type": "text", + "content": "- To reduce the modality style discrepancy without losing discriminative information of modality-specific information, we propose an IN-guided Information Purifier (IP), which is supervised by the discrimination enhancing loss and discrepancy reducing loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 167, + 547, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 167, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 167, + 547, + 239 + ], + "type": "text", + "content": "- The novel TGSA loss is developed to distill the discriminative modality-specific information into modality-shared feature and mitigate inter-modality discrepancy of modality-shared feature sufficiently. The substantial experimental results demonstrate the superiority of our method." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 251, + 392, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 392, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 392, + 264 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 270, + 547, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 510 + ], + "type": "text", + "content": "Visible Modality Person ReID. Person ReID has received increasing success in recent years, which aims to implement pedestrian retrieval between visible images. It has suffered huge challenges including various viewpoints, illuminations, postures and so on. To solve these problems, most methodologies [24, 25, 39, 48] are designed to obtain unified intra-class and discriminative inter-class representation by training CNN network. To further enhance the distinguishability of features, Sun et al. [27] proposed aligning part feature directly instead of using external cues. He et al. [9] caught the hot spot of transformer and first proposed the transformer variant applying on single-modality person ReID. Simultaneously, person ReID has developed some significant branches yet, such as Unsupervised Domain Adaptive Person ReID (UDA-ReID) and Domain Generalization Person ReID (DG-ReID) [41]. Although existing methods have made wide progress in visible modality person ReID, they suffer performance degradation when applied to visible-infrared person ReID due to the severe cross-modality discrepancy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": "Visible-Infrared Person ReID (VI-ReID). VI-ReID is a cross-modality person retrieval problem, which aims at matching daytime visible and nighttime infrared images. It not only faces difficulties encountered in traditional single-motility person ReID task, but also the main challenge of huge modality discrepancy which caused by different camera spectra. To solve the these issues, numerous approaches are proposed to search shared feature[1, 5, 18, 20, 32, 36, 39, 46]. Wu et al. [32] first formulated the VI-REID issue and contributed a new cross-modality dataset SYSUMM01, which is of great significance to the following research. Ye et al. [36] proposed a part-level feature interaction and graph structure attention to enhance the discrimination of invariant feature. Meanwhile, some work begin to introduce additional modal information to jointly search for invariant features [14, 21, 28, 30, 45]. Wang et al. [30] combined RGB three channels feature and IR single" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "394" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 534, + 240 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 534, + 240 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 534, + 240 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 534, + 240 + ], + "type": "image", + "image_path": "ee84baa10c9a9a55770096e39ed7e4c62ae4a94a7d80d533426696e7004593ad.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "text", + "content": "Figure 2. Framework of the proposed Implicit Discriminative Knowledge Learning (IDKL) model. The dual one-stream network built by resnet blocks first extracts the modality-specific " + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "inline_equation", + "content": "F_{sp}" + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "text", + "content": " and modality shared feature " + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "inline_equation", + "content": "F_{sh}" + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "text", + "content": " under the constraint of modality discriminator and modality confuser accordingly, while the common ReID loss is used to optimize network basely. Then, the modality-specific feature is fed into the information purifier to regulate the modality style discrepancy while preserving the implicit discriminative information and obtain the purified modality-specific feature " + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{sp}" + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "text", + "content": ". Subsequently, this implicit knowledge is distilled into the modality-shared feature through TGSA and CSA. Finally, the " + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mdr}" + }, + { + "bbox": [ + 46, + 250, + 548, + 319 + ], + "type": "text", + "content": " is further proposed to minimize modality discrepancy within the enhanced modality-shared feature." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 338, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 443 + ], + "type": "text", + "content": "channel feature into united four channels feature to reduce modal differences. Jiang et al. [14] employed a global prototype to generate the missing modality counterpart through transformer. However, these generation based compensation methods inevitably introduce much noise and most of present methods aim to align modal discrepancy and extract modality invariant feature. They ignored use of beneficial style information contained in specific features to increase distinctiveness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 445, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 625 + ], + "type": "text", + "content": "Interactive Learning. In knowledge distillation, a teacher-student model is used to transfer the knowledge learned by a larger complex teacher model to a smaller simple student model. Different from the one-way transfer between a teacher and a student, deep mutual learning [44] is an ensemble of students which learns collaboratively and teaches each other throughout the training process. Some work applied this idea into VI-ReID for interactive learning in different modalities. Zheng et al. [47] enhanced invariant features learning by using interactive learning between two modality. Ye et al. [35] employed multi-classifier to reduce modality discrepancy on logits-level. Wu et al. [33] distilled RGB and IR knowledge mutually by four classifier to achieve inter shared representation. However, they only learn the knowledge within the semantic-level." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 634, + 129, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 129, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 129, + 647 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "In this section, we detail the proposed Implicit Discriminative Knowledge Learning (IDKL) framework as shown in Fig. 2. IDKL first distinguishes modality-specific features from modality-shared features through two network branches, which are constrained by modality discriminator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 338, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 517 + ], + "type": "text", + "content": "and modality confuser, respectively. Simultaneously, common ReID loss is used to endow feature with representation. Then, an Information Purifier (IP) is developed to reduce the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. Finally, we distill the implicit discriminative knowledge across two branches into the modality-shared feature through Triplet Graph Structure Alignment (TGSA) at the feature-level and Class Semantic Alignment (CSA) at the logit-level. Additionally, to reduce modality discrepancy of shared feature, we proposed the Modality Discrepancy Reduction (MDR) loss within the modality-shared branch. As the discriminative information increases and modality discrepancy decreases constantly, the enhanced modality-shared feature can be obtained." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": "Formally, we represent visible and infrared images in a dataset as " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "V = \\{\\pmb{x}_i^V\\}_{i=1}^{N_V}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "I = \\{\\pmb{x}_i^I\\}_{i=1}^{N_I}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": ", respectively. Typically, the number of images sampled in a mini-batch is equal across both modalities, i.e., " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "N_V = N_I = N = P \\times K" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "N_V" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "N_I" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " denote the number of images sampled from the visible and infrared modalities, respectively. Here, " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " represents the number of images from a single modality, " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "2N" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " is the total number of images in a mini-batch, " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " is the number of distinct person classes, and " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " is the number of images from each class within a single modality. We can therefore represent the images and their corresponding labels in a mini-batch as " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "X = \\{\\pmb{x}_i | \\pmb{x}_i \\in V \\cup I\\}_{i=1}^{2N}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "Y = \\{\\pmb{y}_i\\}_{i=1}^{N_p = P}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": ", respectively. These images " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " are fed into two separate network branches to extract the modality-specific features " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{sp}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " which contains " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{sp,V}, F_{sp,I}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " and the shared features " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{sh}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " which contains " + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{sh,V}, F_{sh,I}" + }, + { + "bbox": [ + 304, + 520, + 546, + 713 + ], + "type": "text", + "content": " as fol" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "395" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 73, + 72, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 73, + 72, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 73, + 72, + 83 + ], + "type": "text", + "content": "lows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 64, + 91, + 287, + 105 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 91, + 287, + 105 + ], + "spans": [ + { + "bbox": [ + 64, + 91, + 287, + 105 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {s p} = E _ {s p} (\\boldsymbol {x} \\mid \\Theta , \\Psi), \\boldsymbol {F} _ {s h} = E _ {s h} (\\boldsymbol {x} \\mid \\Theta , \\Phi), \\tag {1}", + "image_path": "18431abf1515333975124b19259e32bcc1635be4f2f0b80c2df1af48cfeaf3e3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "inline_equation", + "content": "E_{sp}" + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "inline_equation", + "content": "E_{sh}" + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "content": " denote the specific and the shared feature extractor by employing ResNet-50, respectively. Among the sturctures of ResNet-50, the global average pooling replaced by Gem pooling[24, 39] which is a pooling operation between maximum pooling and average pooling. And " + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "content": " is the shallow layer parameters with the first three blocks of ResNet-50, " + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 110, + 287, + 205 + ], + "type": "text", + "content": " is the deep layer parameters of different branches with the last two blocks of ResNet-50." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 212, + 247, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 212, + 247, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 212, + 247, + 224 + ], + "type": "text", + "content": "3.1. Modality Confuser and Discriminator" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "type": "text", + "content": "Modality Confuser. For each sample image " + }, + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "type": "text", + "content": ", there is a modality label " + }, + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "type": "inline_equation", + "content": "t_i \\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 230, + 288, + 326 + ], + "type": "text", + "content": ". To learn modality-irrelated shared information, similar to [6], our goal is to confuse different domains such that a domain classifier cannot distinguish the domain of origin for a sample. We employ an adversarial modality classifier based on the Gradient Reversed Layer (GRL) as the modality confuser. The constraint loss for the modality confuser is given by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 332, + 287, + 364 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 332, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 62, + 332, + 287, + 364 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C j} = - \\frac {1}{2 N} \\sum_ {i = 1} ^ {2 N} t _ {i} \\cdot \\log p \\left(C _ {j} \\left(G R L \\left(\\boldsymbol {F} _ {s h} ^ {i}\\right)\\right)\\right), \\tag {2}", + "image_path": "e659124056e04d26b74d60ad9e0372e886c03c44375cc3b3d79551df6f58124d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "inline_equation", + "content": "C_j" + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "text", + "content": "-th modality confuser in the modality-shared branch, " + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "inline_equation", + "content": "p(\\cdot)" + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "text", + "content": " is the prediction probability obtained via the softmax function, and " + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 369, + 287, + 415 + ], + "type": "text", + "content": " is the modality label." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 417, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 487 + ], + "type": "text", + "content": "Modality Discriminator. To adequately learn modality-related specific information, we employ a modality classifier as the Modality Discriminator. This classifier, which does not use GRL, is applied on the specific branch to extract modality-specific features. The classification loss is formulated as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 84, + 493, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 493, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 84, + 493, + 287, + 525 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D j} = - \\frac {1}{2 N} \\sum_ {i = 1} ^ {2 N} t _ {i} \\cdot \\log p \\left(D _ {j} \\left(\\boldsymbol {F} _ {s p} ^ {i}\\right)\\right), \\tag {3}", + "image_path": "d5d90f7c4a4a095dfdc4ddf09e83efd4e4bd1ccacdec58c27cc8246beb4488a0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 530, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 553 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 530, + 287, + 553 + ], + "type": "inline_equation", + "content": "D_{j}" + }, + { + "bbox": [ + 46, + 530, + 287, + 553 + ], + "type": "text", + "content": " denotes the j-th modality discriminator in the modality-specific branch." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "text", + "content": "The combined loss from the modality confuser and discriminator is given by:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 96, + 584, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 584, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 96, + 584, + 287, + 617 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C} = \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {C j}, \\quad \\mathcal {L} _ {D} = \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {D j}. \\tag {4}", + "image_path": "22372683dc5d6dbb3ee2e403e934754ad7478572147e372f76e6eaf4146c92cf.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 623, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 693 + ], + "type": "text", + "content": "To efficiently extract both modality-specific and modality-shared features, we combine these modality classifier losses with the standard ReID loss " + }, + { + "bbox": [ + 46, + 623, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{reid}}" + }, + { + "bbox": [ + 46, + 623, + 287, + 693 + ], + "type": "text", + "content": ", which includes cross-entropy and hard triplet loss. These are applied to both the modality-specific and modality-shared branches as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 53, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 53, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s p} = \\mathcal {L} _ {\\text {r e i d}} \\left(\\boldsymbol {f} _ {s p}\\right) + \\mathcal {L} _ {D}, \\mathcal {L} _ {s h} = \\mathcal {L} _ {\\text {r e i d}} \\left(\\boldsymbol {f} _ {s h}\\right) + \\mathcal {L} _ {C}, \\tag {5}", + "image_path": "0d55e917cf5a151ec27ec3494bb2dc9440842d504bdcbea822ae033f381b602d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\pmb {f}\\in \\mathbb{R}^{B\\times C}" + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": " is the pooling feature corresponding to " + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\pmb {F}\\in \\mathbb{R}^{B\\times C\\times H\\times W}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 96, + 522, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 96, + 522, + 107 + ], + "spans": [ + { + "bbox": [ + 317, + 96, + 522, + 107 + ], + "type": "text", + "content": "Thus, the base loss for our model is formulated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 389, + 114, + 545, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 114, + 545, + 128 + ], + "spans": [ + { + "bbox": [ + 389, + 114, + 545, + 128 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b} = \\mathcal {L} _ {s h} + \\mathcal {L} _ {s p}. \\tag {6}", + "image_path": "fbc7b541fdc40a277a7ee702095458b076723479f9e73b214683bb053ff97c26.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 133, + 424, + 145 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 424, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 424, + 145 + ], + "type": "text", + "content": "3.2. Information Purifier" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 152, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 152, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 152, + 545, + 247 + ], + "type": "text", + "content": "The Information Purifier (IP) is designed to minimize the impact of style variances while retaining identity-aware and discriminative knowledge in modality-specific features. The IP integrates Instance Normalization (IN), which is known to reduce domain discrepancies [13, 23, 48]. However, it is important to recognize that IN inevitably leads to the loss of some discriminative features [11, 15], potentially hindering the high performance of ReID." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 248, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 248, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 545, + 320 + ], + "type": "text", + "content": "To overcome the aforementioned issues, we have designed a dual-mask network guided by Instance Normalization (IN) to alleviate modality style discrepancies while preserving implicit discriminative knowledge. Firstly, we apply IN on the modality-specific feature to obtain the normalized feature " + }, + { + "bbox": [ + 304, + 248, + 545, + 320 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{F}}_{sp}" + }, + { + "bbox": [ + 304, + 248, + 545, + 320 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 348, + 326, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 326, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 348, + 326, + 545, + 354 + ], + "type": "interline_equation", + "content": "\\widehat {\\boldsymbol {F}} _ {s p} = \\operatorname {I N} \\left(\\boldsymbol {F} _ {s p}\\right) = \\frac {\\boldsymbol {F} _ {s p} - \\operatorname {E} \\left[ \\boldsymbol {F} _ {s p} \\right]}{\\sqrt {\\operatorname {V a r} \\left[ \\boldsymbol {F} _ {s p} \\right] + \\epsilon}}, \\tag {7}", + "image_path": "c71ee7dbbf4da7e41c6f462587df6290d64687cb1659bd514f3a8d7487204050.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "text", + "content": " represents a safety factor to ensure the denominator is not zero. The mean " + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\operatorname{E}[\\cdot]" + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\operatorname{Var}[\\cdot]" + }, + { + "bbox": [ + 304, + 359, + 545, + 394 + ], + "type": "text", + "content": " are calculated along each channel." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "text", + "content": "Following the approach of SE-Net [10], we generate two channel-wise masks " + }, + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_e" + }, + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_r" + }, + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 423, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 545, + 449 + ], + "type": "interline_equation", + "content": "\\mathbf {m} _ {e} = \\sigma \\left(\\mathrm {W} _ {2} \\delta \\left(\\mathrm {W} _ {1} g \\left(\\boldsymbol {F} _ {s p}\\right)\\right)\\right), \\mathbf {m} _ {r} = \\sigma \\left(\\mathrm {W} _ {4} \\delta \\left(\\mathrm {W} _ {3} g \\left(\\widehat {\\boldsymbol {F}} _ {s p}\\right)\\right)\\right), \\tag {8}", + "image_path": "d2411b6fe0a0ad7b7ecf78e505b8ba82506571f5cc1651d8bab446ba98850d4a.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": " denotes the pooling operation, " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "W_{1}, W_{3} \\in \\mathbb{R}^{\\frac{c}{r} \\times c}" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "W_{2}, W_{4} \\in \\mathbb{R}^{c \\times \\frac{c}{r}}" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": " are learnable parameters in the four fully-connected (FC) layers which are followed by the ReLU activation function " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\delta(\\cdot)" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": " and the sigmoid activation function " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": ". To balance the calculate consumption, the dimension reduction ratio " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": " is set to 16." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "text", + "content": "The channel-wise masks " + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_e" + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_r" + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "text", + "content": " indicate enhancement of discriminative characteristics and reduction of discrepancies attention mask, respectively. So we can obtain the stronger distinctiveness " + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "inline_equation", + "content": "F_{sp}^{d+}" + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "text", + "content": " and the smaller modality differences " + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\widehat{F}_{sp}^{m-}" + }, + { + "bbox": [ + 304, + 521, + 545, + 587 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 342, + 594, + 545, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 594, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 342, + 594, + 545, + 611 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {s p} ^ {d +} = \\mathbf {m} _ {e} \\odot \\boldsymbol {F} _ {s p}, \\widehat {\\boldsymbol {F}} _ {s p} ^ {m -} = \\mathbf {m} _ {r} \\odot \\widehat {\\boldsymbol {F}} _ {s p}. \\tag {9}", + "image_path": "ed7235b9fd94bb11c0c5fdecc2ca865929b500cd9be70af07ffea091d2f20eec.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "text", + "content": "Subsequently, the discrimination enhancing loss " + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_e" + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "text", + "content": " and the discrepancy reducing loss " + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r" + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "text", + "content": " are calculated to supervise " + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_e" + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_r" + }, + { + "bbox": [ + 304, + 615, + 545, + 652 + ], + "type": "text", + "content": " respectively as:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 312, + 656, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 656, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 312, + 656, + 545, + 677 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e} = \\text {S o f t p l u s} \\left(h \\left(C _ {s p} \\left(\\boldsymbol {f} _ {s p} ^ {d +}\\right)\\right) - h \\left(C _ {s p} \\left(\\boldsymbol {f} _ {s p}\\right)\\right)\\right), \\tag {10}", + "image_path": "507506a2ea78c9f51b05ac05a9d8d0751614970f6ca1adace95548c90c7de0e7.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 310, + 682, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 682, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 310, + 682, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r} = \\text {S o f t p l u s} \\left(d \\left(\\widehat {\\boldsymbol {f}} _ {s p, V} ^ {m -}, \\widehat {\\boldsymbol {f}} _ {s p, I} ^ {m -}\\right) - d \\left(\\widehat {\\boldsymbol {f}} _ {s p, V}, \\widehat {\\boldsymbol {f}} _ {s p, I}\\right)\\right). \\tag {11}", + "image_path": "3fe5d19089a7c9f97f4895fe7ac773a7f9d51200c1ea290201efbed7e50331dc.jpg" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "396" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_e" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": " aims to imbue the generated " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{sp}^{d+}" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": " with greater semantic distinctiveness compared to " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{sp}" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": " seeks to ensure that " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{F}}_{sp}^{m-}" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": " exhibit smaller modality differences than " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{F}}_{sp}" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": ". And Softplus " + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "inline_equation", + "content": "(\\cdot) = \\ln(1 + \\exp(\\cdot))" + }, + { + "bbox": [ + 47, + 72, + 286, + 148 + ], + "type": "text", + "content": " is a function with monotonic increase, designed to alleviate optimization challenges by circumventing negative values in loss." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "content": "Finally, an alternating integration strategy is employed to extract the distinctive information from " + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{F}}_{sp}^{m - }" + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "content": " by applying " + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_e" + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "content": " and the invariant information from " + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{sp}^{d + }" + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "content": " by applying " + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_r" + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "content": ". Thus, The two sets of features extracted in this way both demonstrate smaller modality differences and stronger implicit discriminative information. By integrating them, we derive the purified modality-specific feature " + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{F}}_{sp}" + }, + { + "bbox": [ + 46, + 148, + 286, + 234 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 96, + 244, + 286, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 244, + 286, + 262 + ], + "spans": [ + { + "bbox": [ + 96, + 244, + 286, + 262 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {F}} _ {s p} = \\mathbf {m} _ {e} \\odot \\widehat {\\boldsymbol {F}} _ {s p} ^ {m -} + \\mathbf {m} _ {r} \\odot \\boldsymbol {F} _ {s p} ^ {d +}. \\tag {12}", + "image_path": "9f35ad59a5301d90ee796658409afc241df1431741504ab5bb24c425d54eec47.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "text", + "content": "Intuitively, the pooling feature " + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "inline_equation", + "content": "\\widetilde{f}_{sp}" + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "text", + "content": " of implicit feature " + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "inline_equation", + "content": "\\widetilde{\\pmb{F}}_{sp}" + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "text", + "content": " is also constraint with ReID loss. So the information purify loss " + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ip}" + }, + { + "bbox": [ + 47, + 271, + 286, + 312 + ], + "type": "text", + "content": " of this section is summarized as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 100, + 320, + 286, + 341 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 320, + 286, + 341 + ], + "spans": [ + { + "bbox": [ + 100, + 320, + 286, + 341 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i p} = \\mathcal {L} _ {e} + \\mathcal {L} _ {r} + \\mathcal {L} _ {\\text {r e i d}} (\\tilde {\\boldsymbol {f}} _ {s p}). \\tag {13}", + "image_path": "32be93df5334e409b216f079b2a64c2d08afebac85fd3bec723fbe906ef1d9ad.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 349, + 216, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 216, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 216, + 361 + ], + "type": "text", + "content": "3.3. Implicit Knowledge Distillation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 368, + 286, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 368, + 286, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 368, + 286, + 416 + ], + "type": "text", + "content": "To ensure that the modality-shared feature comprehensively learns and integrates implicit information, we perform distillation from both the feature-level through TGSA and logit-level through CSA." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 431, + 266, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 266, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 266, + 443 + ], + "type": "text", + "content": "3.3.1 Triplet Graph Structure Alignment (TGSA)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 450, + 286, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 286, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 286, + 582 + ], + "type": "text", + "content": "To endow the shared feature with discriminative information and reduce modality discrepancy at the feature level, we develop a triplet feature graph structure alignment loss. This approach is motivated by the fact that the feature graph structure contains abundant information about the relationships and distribution between features, such as inter-class distinctiveness and intra-class diversity. These characteristics are utilized to unearth potential feature relationships and enhance the feature representation in [17, 36]. The graph structure affinity matrix which indicates the relationships between features is calculated by:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 590, + 286, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 590, + 286, + 620 + ], + "spans": [ + { + "bbox": [ + 67, + 590, + 286, + 620 + ], + "type": "interline_equation", + "content": "\\alpha_ {i j} = \\frac {\\exp \\left(L \\left(\\left[ l \\left(\\boldsymbol {f} _ {i}\\right) \\| l \\left(\\boldsymbol {f} _ {j}\\right) \\right] \\cdot \\boldsymbol {w}\\right)\\right)}{\\sum_ {k \\in \\mathcal {N} _ {i}} \\exp \\left(L \\left(\\left[ l \\left(\\boldsymbol {f} _ {i}\\right) \\| l \\left(\\boldsymbol {f} _ {k}\\right) \\right] \\cdot \\boldsymbol {w}\\right)\\right)}, \\tag {14}", + "image_path": "b4bdedb6444028d2459fb117803db8350fa7d3b2748045196c0cfdb0d304e11e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "content": " denote LeakyReLU activation function, " + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "inline_equation", + "content": "[\\cdot \\| \\cdot ]" + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "content": " denote concatenate operation and " + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "content": " denotes the neighbor samples which are used to normalize for the ith sample. " + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "inline_equation", + "content": "l(\\cdot)" + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "content": " is feature dimension transformation layer and " + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\pmb{w}" + }, + { + "bbox": [ + 47, + 629, + 286, + 712 + ], + "type": "text", + "content": " is the full connection layer to calculate scores in a pair features. The affinity matrix is acquired making these scores through softmax function normalization." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 71, + 539, + 141 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 539, + 141 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 539, + 141 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 539, + 141 + ], + "type": "image", + "image_path": "92c3544ac8ece8a1ee09ff09c22c5197f14d723a23cdf8a37fbc3e9c0b02a73f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 151, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 304, + 151, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 151, + 545, + 205 + ], + "type": "text", + "content": "Figure 3. Illustration of the proposed TGSA loss: 'a' and 'b' denote two different types of features. 'A' represents the graph structure affinity matrix. After aligning the three affinity matrices, the discrepancy in the graph structure distribution between features 'a' and features 'b' will be eliminated." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 212, + 545, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 545, + 283 + ], + "type": "text", + "content": "Due to we utilize graph structure to align and distill knowledge, instead of augmenting the feature, and the Euclidean space distribution is more interesting for features, thus we replace the linear transformation with Euclidean distance to compute attention scores and redefine the graph structure expression for two groups of features as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 290, + 544, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 290, + 544, + 342 + ], + "spans": [ + { + "bbox": [ + 318, + 290, + 544, + 342 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {(a; b)} = \\left\\{\\alpha_ {i j} \\right\\} _ {i, j \\in N} = \\frac {\\exp \\left(D \\left(\\boldsymbol {f} _ {a} ^ {i} , \\boldsymbol {f} _ {b} ^ {j}\\right)\\right)}{\\sum_ {k \\in N} \\exp \\left(D \\left(\\boldsymbol {f} _ {a} ^ {i} , \\boldsymbol {f} _ {b} ^ {k}\\right)\\right)}, \\tag {15}", + "image_path": "fab6c17b0d401adc310171905ef864f95b34247ad195120d920a83d1da36d9db.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\alpha_{ij}" + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "content": " denotes the element of the affinity matrix, " + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "content": " corresponds to the entirety of samples within one modality, " + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "content": " represent two modalities, " + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 304, + 342, + 545, + 388 + ], + "type": "text", + "content": " means Euclidean distance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "content": "Specifically, the triplet graph structure alignment loss " + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tgsa}" + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "content": " is developed for cross modality ReID to align two different modality types, enabling them to conform to the same graph structure distribution and reduce modality discrepancy. This loss encompasses two self-modal affinity matrices and one cross-modal affinity matrix, with the latter ensuring the overall consistency of the graph structure's distribution as shown in Fig. 3. These three matrices are aligned pairwise through the utilization of the Kullback-Leibler (KL) divergence. Therefore, the alignment loss " + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tgsa}" + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "content": " of two distinct modality types is defined as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 529, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 529, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 312, + 529, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {t g s a} ^ {(a; b)} = \\sum_ {p = 1} ^ {P} \\sum_ {k = 1} ^ {K} \\left(\\mathrm {K L} \\left(\\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \\boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\\right) \\right. \\\\ + \\operatorname {K L} \\left(\\boldsymbol {A} _ {(a; a)} ^ {p _ {k}}, \\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}\\right) + \\operatorname {K L} \\left(\\boldsymbol {A} _ {(a; b)} ^ {p _ {k}}, \\boldsymbol {A} _ {(b; b)} ^ {p _ {k}}\\right)). \\tag {16} \\\\ \\end{array}", + "image_path": "9d2c2ea1eb8852dc221f9ff99ed5651332389c9e7680a77b031ace6f08af34ab.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "A^{p_k}" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " represents the graph structure distribution of the " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "-th sample in the " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "-th class, where " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " is the number of person classes, and " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " denotes the number of images for each class within a single modality." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "content": "In order to convey the discriminative implicit modality-specific knowledge to shared feature on feature-level, the distillation loss across two branches on homogeneous features through TGSA can be formulated as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 698, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 698, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 351, + 698, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t g s a} = \\mathcal {L} _ {t g s a} ^ {(s p, V; s h, V)} + \\mathcal {L} _ {t g s a} ^ {(s p, I; s h, I)}. \\tag {17}", + "image_path": "2ae552e8c4e12c7e988e15bd2ee73f20ca2f0dc51894928ba0751b6489f3823a.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "397" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 221, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 221, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 221, + 85 + ], + "type": "text", + "content": "3.3.2 Class Sementic Alignment (CSA)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 161 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 161 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 161 + ], + "type": "text", + "content": "CSA is used to distill the semantic information of implicit modality-specific knowledge into the modality-shared branch for enhancing the feature representation of shared features. CSA operates on homogeneous features between two branches at logit-level. The logit matrix behind the classifier can be formulated as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 88, + 171, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 171, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 88, + 171, + 287, + 186 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Z} _ {s p} = C _ {s p} \\left(\\boldsymbol {f} _ {s p}\\right), \\boldsymbol {Z} _ {s h} = C _ {s h} \\left(\\boldsymbol {f} _ {s h}\\right), \\tag {18}", + "image_path": "60b559a896ff5478ff95620d4099c6eb80ada4c2ee19247f628de6b6e9160aac.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "inline_equation", + "content": "C_{sp}" + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "inline_equation", + "content": "C_{sh}" + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "content": " is the modality-specific and modality-shared classifier separately. And the logit " + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "inline_equation", + "content": "Z_{sp}" + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "inline_equation", + "content": "Z_{sh} \\in \\mathbb{R}^{2N \\times C}" + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "content": " of specific and shared branch both contain visible modality and infrared modality, " + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 193, + 287, + 251 + ], + "type": "text", + "content": " is the total number of train dataset identities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 253, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 300 + ], + "type": "text", + "content": "For learning the implicit discriminative modality-specific knowledge on semantic-level, the CSA loss is implemented on the same modality logit between the two branches, which is formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 308, + 287, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 308, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 49, + 308, + 287, + 352 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c s a} = \\sum_ {i = 1} ^ {N} \\left(\\mathrm {K L} \\left(\\boldsymbol {Z} _ {s h, V} ^ {i}, \\boldsymbol {Z} _ {s p, V} ^ {i}\\right) + \\mathrm {K L} \\left(\\boldsymbol {Z} _ {s h, I} ^ {i}, \\boldsymbol {Z} _ {s p, I} ^ {i}\\right)\\right). \\tag {19}", + "image_path": "46abcc742a1f0b479b05c6660ab293745bfcfee6fe02dabccd499e7e6fee23bf.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 358, + 259, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 259, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 259, + 372 + ], + "type": "text", + "content": "3.4. Modality Discrepancy Reduction (MDR)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 377, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 424 + ], + "type": "text", + "content": "At this part, to guarantee the invariant representation of modality-shared feature, the TGSA and CSA are further used to reduce modality discrepancy within modality-shared branch as follow:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 431, + 287, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 431, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 59, + 431, + 287, + 464 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m d r} = \\mathcal {L} _ {t g s a} ^ {(s h, V; s h, I)} + \\sum_ {i = 1} ^ {N} \\operatorname {K L} \\left(\\boldsymbol {Z} _ {s h, V} ^ {i}, \\boldsymbol {Z} _ {s h, I} ^ {i}\\right). \\tag {20}", + "image_path": "6ffc81fc8a98745c30422f0631f29384509f82c7ec5abcc85f47eaee72da766f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 472, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 542 + ], + "type": "text", + "content": "In this way, the visible feature and infrared feature in modality-shared branch can achieve mutual learning from feature-level and semantic-level. It makes two modalities feature aligning information each other, while alleviating modal gap and maintaining the invariant of modality-shared feature." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 550, + 133, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 133, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 133, + 563 + ], + "type": "text", + "content": "3.5. Optimization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 569, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 628 + ], + "type": "text", + "content": "Ultimately, by continuously distilling implicit discriminative knowledge from the modality-specific feature and consistently reducing modality discrepancies in the modality-shared feature, we can achieve a more discriminative and invariant modality-shared feature." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 629, + 249, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 629, + 249, + 640 + ], + "spans": [ + { + "bbox": [ + 59, + 629, + 249, + 640 + ], + "type": "text", + "content": "The total loss of the model IDKL is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 57, + 653, + 287, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 653, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 57, + 653, + 287, + 680 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {b} + \\lambda_ {1} \\mathcal {L} _ {i p} + \\lambda_ {2} \\mathcal {L} _ {t g s a} + \\lambda_ {3} \\mathcal {L} _ {c s a} + \\mathcal {L} _ {m d r}, \\tag {21}", + "image_path": "1154258afee44d5dbc30ab3e2648d6825481413061db16765e8f04000a71b1ef.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "content": " are hyper-parameters to balance the contribution of individual loss term." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 313, + 72, + 375, + 163 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 375, + 163 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 375, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 375, + 163 + ], + "type": "image", + "image_path": "88572ec55ee6e12b832640788e709d05ed0175a4c07112f70fd77c440a4c6aa3.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 313, + 164, + 374, + 245 + ], + "blocks": [ + { + "bbox": [ + 313, + 164, + 374, + 245 + ], + "lines": [ + { + "bbox": [ + 313, + 164, + 374, + 245 + ], + "spans": [ + { + "bbox": [ + 313, + 164, + 374, + 245 + ], + "type": "image", + "image_path": "620d730a1fae94eb04d908658bc7f65b18ab8f2d2c812b2286ed6ae1a69083bb.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 249, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 304, + 249, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 249, + 545, + 304 + ], + "type": "text", + "content": "Figure 4. Observation the implicit discriminative information by Grad-CAM. And 'sh' and 'sp(im)' present the modality-shared feature and the modality-specific feature of trained IDKL w/o knowledge distillation, respectively; 'enhanced' denotes the modality-shared feature of IDKL w/ knowledge distillation." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 381, + 72, + 430, + 163 + ], + "blocks": [ + { + "bbox": [ + 381, + 72, + 430, + 163 + ], + "lines": [ + { + "bbox": [ + 381, + 72, + 430, + 163 + ], + "spans": [ + { + "bbox": [ + 381, + 72, + 430, + 163 + ], + "type": "image", + "image_path": "ebb08dbc55573406afd08cf4bde67698fabc4c99a99772c129343f5751ed7f99.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 381, + 164, + 430, + 245 + ], + "blocks": [ + { + "bbox": [ + 381, + 164, + 430, + 245 + ], + "lines": [ + { + "bbox": [ + 381, + 164, + 430, + 245 + ], + "spans": [ + { + "bbox": [ + 381, + 164, + 430, + 245 + ], + "type": "image", + "image_path": "4e298b6d20c9137e3012312e0b498a37d97b7ff8ff23cd2515336003b8b2db69.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 436, + 72, + 484, + 163 + ], + "blocks": [ + { + "bbox": [ + 436, + 72, + 484, + 163 + ], + "lines": [ + { + "bbox": [ + 436, + 72, + 484, + 163 + ], + "spans": [ + { + "bbox": [ + 436, + 72, + 484, + 163 + ], + "type": "image", + "image_path": "697b2e61cbc4f0b04fd8c161da8351ea02a8ad71d50ed2143c4663b42d658326.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 436, + 164, + 484, + 245 + ], + "blocks": [ + { + "bbox": [ + 436, + 164, + 484, + 245 + ], + "lines": [ + { + "bbox": [ + 436, + 164, + 484, + 245 + ], + "spans": [ + { + "bbox": [ + 436, + 164, + 484, + 245 + ], + "type": "image", + "image_path": "ea031cd2c5dbd45e9f01f5742badab065b8ad3309c5965b9b6a45dbb2ee5d4a8.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 493, + 72, + 539, + 163 + ], + "blocks": [ + { + "bbox": [ + 493, + 72, + 539, + 163 + ], + "lines": [ + { + "bbox": [ + 493, + 72, + 539, + 163 + ], + "spans": [ + { + "bbox": [ + 493, + 72, + 539, + 163 + ], + "type": "image", + "image_path": "fd5fb4ca2e3270b3956d8243c8278609e4b654d084f0e7a689490a63ca659b3a.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 493, + 164, + 539, + 245 + ], + "blocks": [ + { + "bbox": [ + 493, + 164, + 539, + 245 + ], + "lines": [ + { + "bbox": [ + 493, + 164, + 539, + 245 + ], + "spans": [ + { + "bbox": [ + 493, + 164, + 539, + 245 + ], + "type": "image", + "image_path": "857cb09cd6f18c8b059ed1214f051dbc8d413cfa27b4946427683876d8bbcb8c.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 323, + 386, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 386, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 386, + 337 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 347, + 495, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 347, + 495, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 347, + 495, + 361 + ], + "type": "text", + "content": "4.1. Datasets and Experimental Settings" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 369, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 513 + ], + "type": "text", + "content": "Datasets. Three public VI-ReID datasets SYSU-MM01 [28], LLCM [43] and RegDB [22] are employed to evaluate our model. SYSU-MM01 is a popular large-scale dataset collected by four visible cameras and two near-infrared cameras, including indoor and outdoor environments. And the test protocols consist of all-search and indoor-search. LLCM dataset is a large-scale and low-light cross-modality dataset, which is divided into training and testing sets at a 2:1 ratio. RegDB is collected using dual-camera systems, where visible and infrared images are captured in pairs. Both LLCM and RegDB contain visible to infrared and infrared to visible two search modes." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 517, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 566 + ], + "type": "text", + "content": "Evaluation metrics. The standard rank-" + }, + { + "bbox": [ + 304, + 517, + 545, + 566 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 517, + 545, + 566 + ], + "type": "text", + "content": " matching accuracy and mean Average Precision (mAP) are adopted as the evaluation metrics. All the reported results are the average of 10 trials." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Implementation details. The proposed method and all experiments are implemented on a single NVIDIA GeForce 3090 GPU with PyTorch framework. The baseline model adopts the ResNet-50 pre-trained on ImageNet with the " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ". The input images are resized to " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "3\\times 384\\times 128" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ". The train mini-batch size is set as 120, which contains 12 random identities and 10 images for every identity. Adam optimizer with an initial learning rate " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "3\\times 10^{-5}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " is exploited, which decays at the 60th and 100th epoch with a decay factor of 0.1. The hype-parameters " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " are set to 0.1, 0.6 and 0.8. During the testing phase, only modality-shared feature is used to evaluate performance." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "398" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 83, + 547, + 298 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 517, + 81 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 517, + 81 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 517, + 81 + ], + "type": "text", + "content": "Table 1. Comparison of CMC (%) and mAP (%) performances with the state-of-the-art methods on SYSU-MM01 dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 83, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 547, + 298 + ], + "type": "table", + "html": "
MethodsAll-searchIndoor-search
Single-shotMulti-shotSingle-shotMulti-shot
r=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20mapr=1r=10r=20map
Zero-Padding [32]14.8054.1271.3315.9519.1361.4078.4110.8920.5868.3885.7926.9224.4375.8691.3218.86
D-HSME [8]20.6862.7477.9523.12------------
AlignGAN [28]42.4085.0093.7040.7051.5089.4095.7033.9045.9087.6094.4054.3057.1092.7097.4045.30
DDAG [36]54.7590.3995.8153.02----61.0294.0698.4167.98----
NFS [2]56.9191.3496.5255.4563.5194.4297.8148.5662.7996.5399.0769.7970.0397.7099.5161.45
PIC [47]57.5189.3595.0355.14----60.40--67.70----
MID [12]60.2792.90-59.40----64.8696.12-70.12----
cm-SSFT [21]61.6089.2093.9063.2063.4091.2095.7062.0070.5094.9097.7072.6073.0096.3099.1072.40
MCLNet [7]65.4093.3397.1461.98----72.5696.9899.2076.58----
FMCNet [42]66.34--62.5173.44--56.0668.15--74.0978.86--63.82
SMCL [31]67.3992.8796.7661.7872.1590.6694.3254.9368.8496.5598.7775.5679.5795.3398.0066.57
CAJ [37]69.8895.7198.466.89----76.2697.8899.4980.37----
MPANet [33]70.5896.2198.8068.2475.5897.9199.4362.9176.7498.2199.5780.9584.2299.6699.9675.11
CMT [14]71.8896.4598.8768.5780.2397.9199.5363.1376.997.6899.6479.9184.8799.4199.9774.11
DEEN [43]74.797.699.271.8----80.399.099.883.3----
SAAI [3]75.90--77.0382.8--82.3983.20--88.0190.73--91.30
MUN [40]76.2497.84-73.81----79.4298.09-82.06----
MSCLNet [45]76.9997.6399.1871.64----78.4999.3299.9181.17----
PartMix [16]77.78--74.6280.54--69.8481.52--84.3887.99--79.95
IDKL(Ours)81.4297.3898.8979.8584.3498.8999.7378.2287.1498.2899.2689.3794.3099.7199.9388.75
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Ablation analysis of hyper-parameter " + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ip},\\mathcal{L}_{tgsa}" + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{csa}" + }, + { + "bbox": [ + 47, + 388, + 287, + 412 + ], + "type": "text", + "content": " respectively on SYSU-MM01 dataset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 126, + 316, + 205, + 385 + ], + "blocks": [ + { + "bbox": [ + 126, + 316, + 205, + 385 + ], + "lines": [ + { + "bbox": [ + 126, + 316, + 205, + 385 + ], + "spans": [ + { + "bbox": [ + 126, + 316, + 205, + 385 + ], + "type": "image", + "image_path": "96863ecd4cb31e453bbd3bc97cab69b5204d4bd4527529d82af6a77ba54a9a91.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 205, + 316, + 284, + 386 + ], + "blocks": [ + { + "bbox": [ + 205, + 316, + 284, + 386 + ], + "lines": [ + { + "bbox": [ + 205, + 316, + 284, + 386 + ], + "spans": [ + { + "bbox": [ + 205, + 316, + 284, + 386 + ], + "type": "image", + "image_path": "8d089738f0890c9fa8ad72a365864e62b6210b5c645d026c8203632b60042a38.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 418, + 270, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 270, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 270, + 430 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 437, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 287, + 472 + ], + "type": "text", + "content": "We compare our IDKL model with the state-of-the-art VI-ReID methods published recent years on public VI-ReID datasets SYSU-MM01, RegDB and LLCM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "text", + "content": "Comparison on SYSU-MM01 dataset. The comparison experimental results is shown in Tab. 1 which displays the proposed IDKL method outperforms existing cutting-edge methods. Specifically, the IDKL method achieves the accuracy of " + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "inline_equation", + "content": "81.42\\%" + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "text", + "content": " rank-1 and " + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "inline_equation", + "content": "79.85\\%" + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "text", + "content": " map with single-shot all search protocol, while the accuracy of " + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "inline_equation", + "content": "87.14\\%" + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "text", + "content": " rank-1 and " + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "inline_equation", + "content": "89.37\\%" + }, + { + "bbox": [ + 46, + 473, + 287, + 665 + ], + "type": "text", + "content": " map with single-shot indoor search protocol. The compared SOTAs include various base methods, i.e., for the methods of learning the shared feature through network and loss function immediately, which contain D-HSME [8], NFS [2], CMT [14], DEEN[43] and MCLNet [7]. Based on graph structure augment method DDAG [36] and the mutual learning by logits skill (PIC [47] and MPANet [33]). Comparing with several other based modality-specific methods cm-SSFT[21], MUN[40] and MSCLNet[45], our results outperform them by a margin." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Comparison on RegDB dataset. We also evaluate IDKL on a small-scale dataset RegDB as shown in Tab. 2. There is strong performance IDKL showed and outperforms the existing solutions. Specifically, we achieve rank-1 ac" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "type": "text", + "content": "curacy of " + }, + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "type": "inline_equation", + "content": "94.72\\%" + }, + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "type": "text", + "content": " in visible to infrared mode, and rank-1 accuracy of " + }, + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "type": "inline_equation", + "content": "94.22\\%" + }, + { + "bbox": [ + 305, + 316, + 544, + 340 + ], + "type": "text", + "content": " in infrared to visible mode." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "type": "text", + "content": "Comparison on LLCM dataset. The IDKL model achieves significant improvements on the large and complex LLCM dataset as shown in Tab. 3, demonstrating excellent rank-1 accuracy of " + }, + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "type": "inline_equation", + "content": "72.2\\%" + }, + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "type": "inline_equation", + "content": "70.7\\%" + }, + { + "bbox": [ + 305, + 341, + 545, + 413 + ], + "type": "text", + "content": " on two modes, respectively. This indicates that the IDKL model exhibits strong robustness in complex and multimodal scenarios." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 447, + 544, + 657 + ], + "blocks": [ + { + "bbox": [ + 306, + 424, + 545, + 446 + ], + "lines": [ + { + "bbox": [ + 306, + 424, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 306, + 424, + 545, + 446 + ], + "type": "text", + "content": "Table 2. Comparison of the CMC (\\%) and mAP (\\%) performances with state-of-the-art methods on RegDB dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 447, + 544, + 657 + ], + "lines": [ + { + "bbox": [ + 309, + 447, + 544, + 657 + ], + "spans": [ + { + "bbox": [ + 309, + 447, + 544, + 657 + ], + "type": "table", + "html": "
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
Zero-Padding [32]17.818.916.717.9
AlignGAN [28]57.953.656.353.4
DDAG [36]69.3463.4668.0661.80
cm-SSFT [21]72.372.971.071.7
MCLNet [7]80.3173.0775.9369.49
PIC [47]83.679.679.577.4
MPANet [33]83.780.982.880.7
SMCL [31]83.9379.8383.0578.57
MSCLNet [45]84.1780.9983.8678.31
CAJ [37]85.0377.8284.7577.82
MID [12]87.4584.8584.2981.41
FMCNet [42]89.1284.4388.3883.86
SAAI [3]91.0791.4592.0992.01
DEEN [43]91.185.189.583.4
CMT [14]95.1787.391.9784.46
MUN [40]95.1987.1591.8685.01
IDKL(Ours)94.7290.1994.2290.43
", + "image_path": "1760407fc89b7e4d0b2148191bae4ce4195a4ca6b0be845e7f96177f9d991f7c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 670, + 400, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 400, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 400, + 684 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "In this subsection, we conduct the ablation experiment to evaluate our proposed model exhaustively." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "399" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 84, + 285, + 159 + ], + "blocks": [ + { + "bbox": [ + 47, + 60, + 286, + 81 + ], + "lines": [ + { + "bbox": [ + 47, + 60, + 286, + 81 + ], + "spans": [ + { + "bbox": [ + 47, + 60, + 286, + 81 + ], + "type": "text", + "content": "Table 3. Comparison of the CMC (%) and mAP (%) performances with state-of-the-art methods on LLCM dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 84, + 285, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 84, + 285, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 84, + 285, + 159 + ], + "type": "table", + "html": "
MethodsVisible to infraredInfrared to visible
rank-1maprank-1map
DDAG [36]40.348.448.052.3
CAJ [37]56.559.848.856.6
DEEN [43]62.565.854.962.9
IDKL(Ours)72.2266.4370.7265.19
", + "image_path": "bbdbbf19bedcdf56e63913280519d005102589adca72ca2506870dcfc93e9b17.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 55, + 191, + 278, + 304 + ], + "blocks": [ + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "type": "text", + "content": "Table 4. Evaluation the impact of different components in terms of rank-1 " + }, + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "type": "text", + "content": " and mAP " + }, + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 168, + 286, + 190 + ], + "type": "text", + "content": " on SYSU-MM01 dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 191, + 278, + 304 + ], + "lines": [ + { + "bbox": [ + 55, + 191, + 278, + 304 + ], + "spans": [ + { + "bbox": [ + 55, + 191, + 278, + 304 + ], + "type": "table", + "html": "
LbLipLtgsaLcsaLmdrSYSU-MM01
rank1map
✓××××67.6066.47
✓×✓××68.3867.30
✓✓✓××76.4074.83
✓✓×✓×76.2874.34
✓✓××✓77.0475.66
✓✓✓✓✓81.4279.85
", + "image_path": "f961517c92f4a86d9e2332c34ddb991e653fc1169606c7d94a478bf847fe5a3a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 315, + 286, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 286, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 286, + 445 + ], + "type": "text", + "content": "Effectiveness of each component. We evaluate the effectiveness of each component on the SYSU-MM01 dataset under all search single-shot mode. Each component is added independently to reveal its the performance as Tab. 4. This indicates that each component is highly useful, with " + }, + { + "bbox": [ + 46, + 315, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mdr}" + }, + { + "bbox": [ + 46, + 315, + 286, + 445 + ], + "type": "text", + "content": " achieving significant performance improvements. This further suggests the effectiveness of TGSA and CSA in reducing modality discrepancies. Comparing the second row with the third row demonstrates the necessity of purifying implicit modality-specific information, and also proves the effectiveness of our Information Purifier module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 447, + 286, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 286, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 286, + 529 + ], + "type": "text", + "content": "Hyper-parameters analysis of IP, TGSA and CSA. In this part, we present a line chart to examine the detail influence of IP, TGSA and CSA by gradually increasing the value of hyperparameters. As depicted in Fig. 5, the maximum contributions of IP, TGSA and CSA are reached at 0.1, 0.6 and 0.8, respectively. The upward trend of the curve demonstrates the effectiveness of each module." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 539, + 173, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 173, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 173, + 551 + ], + "type": "text", + "content": "4.4. Visualization Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "type": "text", + "content": "Attention maps Visualization. To further illustrate the effectiveness of IDKL, Grad-CAM [26] is utilized for a visual examination of different feature heatmaps. In Fig. 4, the areas of focus for implicit discriminative information typically differ from those of the shared feature, indicating that effectively and judiciously utilizing this information to strengthen the shared feature can be highly beneficial." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": "Feature Distribution Visualization. We utilize t-SNE [22] feature map visualization to observe the impact of the IDKL model and TGSA on the model. As shown in Fig. 6, each color represents a different identity, while the shapes of circles and triangles indicate the visible and infrared modality information, respectively. From Fig. 6(a)," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 425, + 164 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 425, + 164 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 425, + 164 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 425, + 164 + ], + "type": "image", + "image_path": "e9c4b0e07c777f31f3943a658867b06eb8f85554aa626ef57a15675a09b7d428.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 72, + 543, + 165 + ], + "blocks": [ + { + "bbox": [ + 427, + 72, + 543, + 165 + ], + "lines": [ + { + "bbox": [ + 427, + 72, + 543, + 165 + ], + "spans": [ + { + "bbox": [ + 427, + 72, + 543, + 165 + ], + "type": "image", + "image_path": "7d3ae0b9f3bb711509dea1a030337d77b45737e509a3ed1cc731832ecdd7265d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 464, + 167, + 506, + 176 + ], + "lines": [ + { + "bbox": [ + 464, + 167, + 506, + 176 + ], + "spans": [ + { + "bbox": [ + 464, + 167, + 506, + 176 + ], + "type": "text", + "content": "b (baseline)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 177, + 425, + 269 + ], + "blocks": [ + { + "bbox": [ + 328, + 167, + 408, + 176 + ], + "lines": [ + { + "bbox": [ + 328, + 167, + 408, + 176 + ], + "spans": [ + { + "bbox": [ + 328, + 167, + 408, + 176 + ], + "type": "text", + "content": "a (pretrained resnet50)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 177, + 425, + 269 + ], + "lines": [ + { + "bbox": [ + 310, + 177, + 425, + 269 + ], + "spans": [ + { + "bbox": [ + 310, + 177, + 425, + 269 + ], + "type": "image", + "image_path": "088b316aa60e2719a88d5f36c7a4a3960e4fa91e7b2d904c6e6b2d9a48a63c27.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 336, + 271, + 399, + 280 + ], + "lines": [ + { + "bbox": [ + 336, + 271, + 399, + 280 + ], + "spans": [ + { + "bbox": [ + 336, + 271, + 399, + 280 + ], + "type": "text", + "content": "c (IDKL w/o TGSA)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 289, + 545, + 333 + ], + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 333 + ], + "type": "text", + "content": "Figure 6. Visualization of learned features by t-SNE. Where \"a\" means the pre-training resnet50 on ImageNet; \"b\" represents the baseline; \"c\" is the IDKL model w/o TGSA; \"d\" is IDKL model w/ TGSA." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 427, + 177, + 543, + 269 + ], + "blocks": [ + { + "bbox": [ + 427, + 177, + 543, + 269 + ], + "lines": [ + { + "bbox": [ + 427, + 177, + 543, + 269 + ], + "spans": [ + { + "bbox": [ + 427, + 177, + 543, + 269 + ], + "type": "image", + "image_path": "b374cae388c2d31e37ca6865d8b7ae2fca16bcc8cd2cbbd0e98b63cd6dc2ccb7.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 455, + 271, + 514, + 280 + ], + "lines": [ + { + "bbox": [ + 455, + 271, + 514, + 280 + ], + "spans": [ + { + "bbox": [ + 455, + 271, + 514, + 280 + ], + "type": "text", + "content": "d (IDKL w/ TGSA)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 340, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 545, + 460 + ], + "type": "text", + "content": "a significant discrepancy between the two modalities is evident. Fig. 6(b) shows a reduction in modality discrepancy and the model exhibiting some discriminative capabilities. Comparing Fig. 6(b) with Fig. 6(c), it is observable that the IDKL model has a smaller intra-class discrepancy and better inter-class discrimination. In Fig. 6(d), the dark blue class appears more scattered than in Fig. 6(c), and the graph structures of the two modalities are more similar and closely aligned, demonstrating the effectiveness of TGSA in reducing modality discrepancies." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 491, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 598 + ], + "type": "text", + "content": "This paper harnesses the implicit discriminative information within modality-specific features and introduces a robust model IDKL to exploit the potential discrimination of heterogeneous-related features and enhance the shared feature. The IDKL model comprises a dual one-stream network, a novel IN-guided information purifier, a triplet graph structure alignment solution, and refined distillation on logits. Collectively, these components demonstrate exceptional effectiveness and contribute to improved results." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 609, + 403, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 403, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 403, + 623 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "This work was partially supported by National Key R&D Program of China (2021YFB3100800), National Natural Science Fund of China (62271090, 61771079), Chongqing Natural Science Fund (cstc2021jcyj-jqX0023) and National Youth Talent Project. This work is also supported by Huawei computational power of Chongqing Artificial Intelligence Innovation Center." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "400" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Cuiqun Chen, Mang Ye, Meibin Qi, Jingjing Wu, Jianguo Jiang, and Chia-Wen Lin. 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Neurocomputing, 386:97–109, 2020. 1" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "402" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_content_list.json b/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b0318ce1aead6dbaa1bc330827de40b0271e0 --- /dev/null +++ b/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_content_list.json @@ -0,0 +1,1803 @@ +[ + { + "type": "text", + "text": "Implicit Event-RGBD Neural SLAM", + "text_level": 1, + "bbox": [ + 297, + 130, + 671, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Delin $\\mathrm{Qu}^{1,2*}$ Chi Yan $^{2,5*}$ Dong Wang $^{2}$ Jie Yin $^{3}$ Qizhi Chen $^{2}$", + "bbox": [ + 205, + 178, + 763, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dan Xu5 Yiting Zhang2 Bin Zhao2,4† Xuelong Li2", + "bbox": [ + 253, + 198, + 715, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Fudan University $^{2}$ Shanghai AI Laboratory $^{3}$ Shanghai Jiao Tong University $^{4}$ Northwestern Polytechnical University $^{5}$ Hong Kong University of Sciences and Technology", + "bbox": [ + 104, + 215, + 861, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 285, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Implicit neural SLAM has achieved remarkable progress recently. Nevertheless, existing methods face significant challenges in non-ideal scenarios, such as motion blur or lighting variation, which often leads to issues like convergence failures, localization drifts, and distorted mapping. To address these challenges, we propose EN-SLAM, the first event-RGBD implicit neural SLAM framework, which effectively leverages the high rate and high dynamic range advantages of event data for tracking and mapping. Specifically, EN-SLAM proposes a differentiable CRF (Camera Response Function) rendering technique to generate distinct RGB and event camera data via a shared radiance field, which is optimized by learning a unified implicit representation with the captured event and RGBD supervision. Moreover, based on the temporal difference property of events, we propose a temporal aggregating optimization strategy for the event joint tracking and global bundle adjustment, capitalizing on the consecutive difference constraints of events, significantly enhancing tracking accuracy and robustness. Finally, we construct the simulated dataset DEV-Indoors and real captured dataset DEV-Reals containing 6 scenes, 17 sequences with practical motion blur and lighting changes for evaluations. Experimental results show that our method outperforms the SOTA methods in both tracking ATE and mapping ACC with a real-time 17 FPS in various challenging environments. Project page: https://delinqu.github.io/EN-SLAM.", + "bbox": [ + 75, + 318, + 473, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 758, + 209, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Simultaneous Localization and Mapping (SLAM) is an essential problem in computer vision and robotics, widely applied in tasks such as virtual and augmented reality [8], robot navigation [18] and autonomous driving [3] over last decades. Exploration in extreme environments [10, 31, 41]", + "bbox": [ + 75, + 785, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f617a732afa89f05f8e03b8200347a7d2f2710ca08a85621e96a446373edda81.jpg", + "image_caption": [ + "Figure 1. Illustration of the proposed implicit event-RGBD neural SLAM system EN-SLAM under non-ideal environments. The dynamic range of RGB sensors is relatively low and suffers from motion blur. Instead, event cameras show great potential in non-ideal environments due to their high dynamic range and low latency advantages. Our method samples rays from two independent RGBD and event cameras to jointly train a single implicit neural field with both modalities. This hybrid shared mechanism provides a natural fusion approach, avoiding alignment issues. It also leverages the advantages of both modalities, resulting in dense, more robust, and higher-quality reconstruction results." + ], + "image_footnote": [], + "bbox": [ + 504, + 276, + 893, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "remains challenging for visual SLAM (vSLAM) systems due to the lack of visual features caused by motion blur and lighting variation in diverse environments [42, 59, 68].", + "bbox": [ + 496, + 625, + 893, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As a novel representation for myriad of signals, Neural Radiance Fields (NeRF) [35] has innovated great progress in SLAM recently, demonstrating significant improvements in map memory consumption, hole filling, and mapping quality [23, 49, 52, 58, 67, 71]. While the existing NeRF-based neural vSLAM methods address the limitations of traditional SLAM frameworks [11, 36, 37, 50, 62] in accurate dense 3D map reconstruction, they are primarily designed for well-lit scenes and always fail in practical SLAM scenarios with motion blur [40, 66] and lighting variation [32, 48]. These methods produce unsatisfying results under non-ideal environments [58] because of the following limitations: 1) View-inconsistency: When the camera encounters rapid velocity variation in Fig. 2 (2nd), the scene may exhibit discontinuous blur, leading to view", + "bbox": [ + 496, + 674, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Authors contributed equally: dlqu22@m.fudan.edu.cn", + "bbox": [ + 99, + 875, + 397, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 99, + 888, + 230, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19584", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "inconsistency among frames, further causing heavy artifacts in the reconstructed map. 2) Low dynamic range: In light- ing variation scenes illustrated in Fig. 1, the dynamic range of the RGB sensor is relatively low, and the information on the dark and overexposure areas is lost, leading to tracking drifts and mapping distortions.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the issues in non-ideal scenarios of existing neural vSLAM, we introduce utilizing the advantages of high dynamic range (HDR) and temporal resolution of event data to compensate for the lost information, thereby improving the robustness, efficiency, and accuracy of current neural vSLAM in extreme environments. Fig. 2 shows the event generation model that an event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold $C$ . This asynchronous mechanism shows excellent potential in non-ideal environments due to its advantages in low latency [26, 43, 70], high dynamic range [46], and high temporal resolution [54, 55]. Fig. 1 and Fig. 2 illustrate its superiority in dark and fast motion, and event sensors capture higher-quality signals than RGB sensors. However, applying events into NeRF-based vSLAM is challenging due to the significant distinction in imaging mechanisms between event and RGB cameras. Moreover, the requirement of highly accurate camera poses and careful optimization in traditional surface density estimation [32] further complicates the integration.", + "bbox": [ + 75, + 183, + 470, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to overcome these obstacles, we present EN-SLAM, the first event-RGBD implicit neural SLAM framework that effectively harnesses the advantages of event and RGBD streams. The overview of EN-SLAM is shown in Fig. 3. Our method models the differentiable imaging process of two distinct cameras and utilizes shared radiance fields to jointly learn a hybrid unified representation from events and RGBD data. By integrating the event generation model into the optimization process, we introduce the event temporal aggregating (ETA) optimization strategy for event joint tracking and global bundle adjustment (BA). This strategy effectively leverages the temporal difference property of events, providing efficient consecutive difference constraints and significantly improving the performance. Additionally, we construct two datasets: the simulated dataset DEV-Indoors and the real captured dataset DEV-Reals, which consist of 6 scenes and 17 sequences with practical motion blur and lighting changes. Contributions can be summarized as follows:", + "bbox": [ + 75, + 487, + 468, + 772 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present EN-SLAM, the first event-RGBD implicit neural SLAM framework that efficiently leverages event stream and RGBD to overcome challenges in extreme motion blur and lighting variation scenes.", + "- A differentiable CRF rendering technique is proposed to map a unified representation in the shared radiance field to RGB and event camera data for addressing the significant distinction between event and RGB. A tempo" + ], + "bbox": [ + 78, + 779, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5eda0534f83d893336a8913d4b67e644443e6b5987b62cc8f3c4add304a3db46.jpg", + "image_caption": [ + "Figure 2. Illustration of the Event Generation Model (EGM). An event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold $C$ ." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 629, + 186 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d7aea2a7d9978f6101535ff0a9a5c1d1e5cc32a68699e5f1d6a11ca807c8e311.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 93, + 756, + 185 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ded92d95b63f77ffd09b5faed2cfb1b7f81e3187d3b4931802090d6bbd7cb755.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 758, + 93, + 890, + 185 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ral aggregating optimization strategy that capitalizes the consecutive difference constraints of the event stream is present and significantly improves the camera tracking accuracy and robustness.", + "bbox": [ + 513, + 238, + 890, + 297 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We construct a simulated DEV-Indoors and real captured DEV-Reals dataset containing 17 sequences with practical motion blur and lighting changes. A wide range of evaluations demonstrate competitive real-time performance under various challenging environments.", + "bbox": [ + 501, + 297, + 890, + 373 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 388, + 640, + 404 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Implicit vSLAM. Existing NeRF-based visual SLAM methods have made significant improvements in dense map reconstruction. iMAP [52] first introduces NeRF into SLAM, and NICE-SLAM [71] expands the reconstructable environment size by introducing multiscale feature grids. Vox-Fusion [64] utilizes an octree-based structure to expand the scene dynamically. Besides, CoSLAM [58] combines coordinate and sparse parametric encoding to achieve fast convergence and surface hole filling in reconstruction. Parallel works ESLAM [23] and Point-SLAM [49] represent scenes as multi-scale feature planes and neural point clouds, respectively, to improve the efficiency and accuracy. Beyond NeRF, GS-SLAM [63] utilizes 3D Gaussian [24] for scene representation and achieves photo-realistic reconstruction performance. However, these methods are designed for well-lit indoor scenes and commonly encounter challenges in non-ideal SLAM processes, such as motion blur and lighting variation. In contrast, we introduce utilizing the advantages of high dynamic range and temporal resolution of events to compensate for the lost information, thereby improving the robustness and accuracy of current neural implicit methods.", + "bbox": [ + 496, + 415, + 890, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event-based SLAM. Events have been incorporated into traditional visual SLAM systems to address the motion blur and lighting variation. These methods can be divided into three main types: feature-based methods, direct methods, and motion-compensation methods. Feature-based methods, such as USLAM [57], EIO [16] and PL-EVIO [17], track point or line features from event data [29, 44], and perform the camera tracking and mapping in parallel threads. However, the feature extraction algorithms [2, 33, 47, 56] rely heavily on frame-based feature detection, facing chal", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19585", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/838ff965dadfec0fef34dbb47d8f7c0a1349be1760dc0b4b55b361d27817b074.jpg", + "image_caption": [ + "Figure 3. Overview of EN-SLAM. EN-SLAM decodes the scene encoding to a shared geometry and radiance representation, and decomposes the radiance into RGB color $\\mathbf{c}(\\mathbf{x})$ and event luminance $\\mathbf{l}(\\mathbf{x})$ via differentiable CRF Mappers. We iteratively optimize the pose and scene representation by minimizing losses, in tracking and global BA with the event temporal aggregating techniques in Algorithm 1." + ], + "image_footnote": [], + "bbox": [ + 78, + 56, + 893, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lenges for motion-dependent event data appearance. Direct methods employ events without explicit data association by aligning the photometric event image [19, 25, 26] or utilizing the spatiotemporal information for event representations alignment [43, 45, 70]. Direct methods are well suited for events, but mainly focus on event-based visual odometry, leaving the visual dense mapping unexplored. Motion-compensation methods optimize event alignment in motion-compensated event frames by maximizing the contrast [39, 60], minimizing the dispersion [38] and align probabilistic [15]. However, they suffer from the collapse in a broad range of camera motions. Thus, currently, event-based SLAM demonstrates significant potential but lacks sufficient exploration in dense map reconstructions [20].", + "bbox": [ + 75, + 282, + 472, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Radiance Fields using Events. Event-based NeRF is in the nascent stages, and several studies have demonstrated the possibility of view synthesis from events via implicit neural fields. Event-NeRF [48] proposes an approach for inferring NeRF from a monocular color event stream that enables novel view synthesis. E-NeRF [27] and $\\mathrm{E}^2\\mathrm{NeRF}$ [40] tackle the NeRF estimation from event cameras under strong motion blur. They develop normalized and rendering loss to address varying contrast thresholds and enhance neural volumetric representation. The parallel work Ev-NeRF [22] conducts a threshold-bound loss with the ReLU function to address the lack of RGB images. In addition to reconstruction, $\\Delta_t$ NeRF [34] proposes an event camera tracker by minimizing the error between sparse events and the temporal gradient of the scene representation on the simplified intensity-change events. However, the traditional surface density estimation in NeRF requires highly accurate camera poses and careful optimization [32], thus making it exceptionally challenging to apply NeRF to the event-based SLAM.", + "bbox": [ + 75, + 496, + 470, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 814, + 210, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overview of our method is shown in Fig. 3. Given an input RGBD stream $\\{\\mathbf{I}_i, \\mathbf{D}_i\\}_{i=1}^J$ and event stream $\\{\\mathbf{E}_k\\}_{k=1}^N$ with known camera intrinsics $\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}$ and $\\mathbf{K}' \\in \\mathbb{R}^{3 \\times 3}$ , we aim to leverage event and RGBD to reconstruct the cam", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "era poses $\\{\\mathbf{P}_i\\}_{i = 1}^J$ and the implicit scene representation. In Sec. 3.1, the scene encoding is decoded to a unified geometry and radiance representation. Then, the shared radiance is decomposed into RGB color $\\mathbf{c}(\\mathbf{x})$ and event luminance $\\mathrm{l(x)}$ via differentiable CRF Mappers in Secs. 3.2 and 3.3 to address the imaging distinction of event and RGB cameras. Finally, EN-SLAM iteratively optimizes the pose and scene representation by minimizing the re-rendering loss between the observed RGBD-E (RGBD and events) and rendering results in tracking and global BA of Sec. 3.4.", + "bbox": [ + 496, + 282, + 890, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Unified Implicit Scene Representation", + "text_level": 1, + "bbox": [ + 498, + 443, + 826, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 3, we represent the scene S with multi-resolution geometric features and color grid features:", + "bbox": [ + 498, + 465, + 890, + 497 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} = \\left\\{\\left(F _ {\\mathbf {x}, \\theta} ^ {g}, F _ {\\mathbf {x}, \\theta} ^ {c}\\right) \\mid \\theta = 1, \\dots , \\Theta \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 507, + 890, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{x}$ and $\\theta$ denote the coordinate and resolution level. There are two challenges that hinder us from learning a scene representation from different RGB and event modalities. Firstly, the event data is sparse and records logarithmic changes in luminance. Secondly, different cameras hold distinct physical imaging process mechanisms. Despite this, the geometry and radiance fields remain consistent during the camera imaging. In this case, we propose to learn a shared unified geometry hidden feature $\\mathbf{h}_{\\mathbf{x}}^{g}$ and radiance representation $\\mathbf{e}(\\mathbf{x})$ across distinct cameras. The geometric grid feature $F_{\\mathbf{x},\\theta}^{g}$ and color feature $F_{\\mathbf{x},\\theta}^{c}$ are simultaneously mapped to geometry hidden vector $\\mathbf{h}_{\\mathbf{x}}^{g}$ , radiance fields $\\mathbf{e}(\\mathbf{x})$ and TSDF (truncated signed distance function) $\\mathbf{s}(\\mathbf{x})$ , by a geometry decoder $\\pmb{f}_{g}$ :", + "bbox": [ + 496, + 534, + 892, + 748 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {f} _ {\\boldsymbol {g}} \\left(F _ {\\mathbf {x}, \\theta} ^ {g}, F _ {\\mathbf {x}, \\theta} ^ {c}\\right) \\mapsto \\left(\\mathbf {h} _ {\\mathbf {x}} ^ {g}, \\mathbf {e} (\\mathbf {x}), \\mathbf {s} (\\mathbf {x})\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 756, + 890, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The geometry hidden vector $\\mathbf{h}_{\\mathbf{x}}^{g}$ and radiance fields $\\mathbf{e}(\\mathbf{x})$ are shared by the color and event CRF decoders.", + "bbox": [ + 498, + 792, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Decomposition of the Radiance Fields", + "text_level": 1, + "bbox": [ + 498, + 832, + 823, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In standard imaging devices, the incoming radiance undergoes linear and nonlinear image processing before being mapped into pixel values and stored in images. This entire", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19586", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "image processing can be represented by a single function $f_{c}$ called the camera response function (CRF) [9]. However, the traditional NeRF method [35] simplifies the imaging process, leading to discrepancies between the rendering and actual images. This deviation is further amplified in multi-modal implicit representations. As Fig. 10 shows, the captures of RGB and event cameras are significantly distinct, which can lead to joint optimization fluctuation. To address this issue, we model the radiance $\\mathbf{e}(\\mathbf{x})$ and exposure $\\Delta t_{c}$ of a ray $\\mathbf{r}$ but take the aperture and others as implicit factors to obtain the color field $\\mathbf{c}(\\mathbf{x})$ [21, 53] by differentiable tone-mapping:", + "bbox": [ + 76, + 90, + 472, + 272 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} (\\mathbf {x}) = \\boldsymbol {f} _ {c} \\left(\\mathbf {e} (\\mathbf {x}) \\Delta \\mathbf {t} _ {c}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 280, + 468, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To facilitate optimization, we convert all numerical values into the logarithmic domain and present the inverse function of $\\left(\\ln f_c^{-1}\\right)^{-1}$ as $\\Psi_{\\mathrm{c}}$ :", + "bbox": [ + 76, + 304, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {c} (\\mathbf {x}) = \\left(\\ln \\boldsymbol {f} _ {\\boldsymbol {c}} ^ {- 1}\\right) ^ {- 1} (\\ln \\mathbf {e} (\\mathbf {r}) + \\ln \\Delta \\mathbf {t} _ {c}) \\tag {4} \\\\ = \\boldsymbol {\\Psi} _ {\\mathbf {c}} (\\ln \\mathbf {e} (\\mathbf {x}) + \\ln \\Delta \\mathbf {t} _ {c}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 361, + 468, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As for the event camera, directly obtaining the event data is not feasible. However, we can predict high dynamic range luminance $l(\\mathbf{x})$ and derive events using the event generation model: As shown in Fig. 2, an event $E_{k} = (u_{k}, v_{k}, t_{k}, p_{k})$ at image coordinate $\\mathbf{m}_{k} = [u_{k}, v_{k}, 1]^{T}$ is triggered if the corresponding logarithmic brightness change $\\mathbf{L}(\\mathbf{m}, t)$ exceeds a threshold $C$ :", + "bbox": [ + 76, + 407, + 468, + 512 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} \\left(\\mathbf {m} _ {k}, t _ {k}\\right) - \\mathbf {L} \\left(\\mathbf {m} _ {k}, t _ {k - 1}\\right) = p _ {k} C, \\quad p _ {k} \\in \\{+ 1, - 1 \\}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 521, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The logarithmic brightness $\\mathbf{L}(\\mathbf{m},t)$ can be obtained by:", + "bbox": [ + 76, + 545, + 444, + 560 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} (\\mathbf {m}, t) = \\ln \\log \\left(\\mathbf {I} _ {e} (\\mathbf {m})\\right) = \\left\\{ \\begin{array}{l l} \\mathbf {I} _ {e} (\\mathbf {m}) \\cdot \\ln (B) / B, & \\text {i f} \\mathbf {I} _ {e} (\\mathbf {m}) < B \\\\ \\ln \\left(\\mathbf {I} _ {e} (\\mathbf {m})\\right), & \\text {e l s e} \\end{array} , \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 566, + 468, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $B$ denotes the linear region threshold [7] and the imaging brightness $\\mathbf{I}_e(\\mathbf{m})$ of event camera equals to the corresponding luminance of ray $\\mathbf{r}$ . By applying the modeling approach in Eqs. (3) and (4) to the CRF of an event camera, we establish the relation among the luminance field $l(\\mathbf{x})$ , the radiance $\\mathbf{e}(\\mathbf{x})$ and exposure:", + "bbox": [ + 76, + 597, + 468, + 688 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl (\\mathbf {x}) = \\boldsymbol {\\Psi} _ {l} \\left(\\ln \\mathbf {e} (\\mathbf {x}) + \\ln \\Delta \\mathbf {t} _ {l}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 696, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Psi_{l}$ and $\\Delta \\mathbf{t}_l$ denote the luminance tone-mapping and pseudo exposure of the event camera. In this way, we decompose the shared radiance field $\\mathbf{e}(\\mathbf{x})$ into the RGB and event camera imaging processes through two differentiable tone-mapping processes.", + "bbox": [ + 76, + 720, + 468, + 796 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Differentiable CRF Rendering", + "text_level": 1, + "bbox": [ + 76, + 804, + 346, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Upon obtaining the color and luminance fields in Sec. 3.2, we render the final imaging RGB, luminance, and depth by integrating predicted values along the samples in a ray $\\mathbf{r}$ :", + "bbox": [ + 76, + 827, + 468, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {i} = \\mathbf {O} + z _ {i} \\mathbf {d}, \\quad i \\in \\{1, \\dots , M \\}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 880, + 468, + 896 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b903c1a64e39a737a3d7c5be9205c71bbaa0c1514f37e881e0bfd73a9e23b58c.jpg", + "image_caption": [ + "a) Camera k trajectory", + "Figure 4. The illustration of event temporal aggregating optimization strategy. In the tracking and global BA stages, EN-SLAM adaptively forwards query the previous frame according to the previous index table, and sample rays from different views perform joint optimization in Eq. (13)." + ], + "image_footnote": [], + "bbox": [ + 501, + 82, + 648, + 210 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ac8bbf6c954fe79f12c4947426c19ef4d25e6f9531b11ac822e4a89466ff8f0d.jpg", + "image_caption": [ + "b) Previous Index Table" + ], + "image_footnote": [], + "bbox": [ + 648, + 85, + 764, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8edec6d2aeafff93576b1134e961ddd60fa2d94487a8da2af5ebe04bd0748e67.jpg", + "image_caption": [ + "c) Forward ray sampling" + ], + "image_footnote": [], + "bbox": [ + 776, + 85, + 890, + 204 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{O} \\in \\mathbb{R}^3$ is the camera origin, $\\mathbf{d} \\in \\mathbb{R}^3$ , $\\|\\mathbf{d}\\| = 1$ is the ray direction, and $z_i \\in \\mathbb{R}$ denotes the depth. Hence, we obtain the final imaging color $\\hat{\\mathbf{c}}$ , luminance $\\hat{l}$ and depth $\\hat{d}$ :", + "bbox": [ + 496, + 309, + 890, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {c}} (\\mathbf {r}, \\Delta t _ {c}) = \\sum_ {i = 1} ^ {i = M} w _ {i} \\boldsymbol {\\Psi} _ {\\mathbf {c}} \\left(\\ln \\mathbf {e} \\left(\\mathbf {x} _ {i}\\right) + \\ln \\Delta t _ {c}\\right), \\\\ \\hat {l} (\\mathbf {r}, \\Delta t _ {l}) = \\sum_ {i = 1} ^ {i = M} w _ {i} \\boldsymbol {\\Psi} _ {l} \\left(\\ln \\mathbf {e} \\left(\\mathbf {x} _ {i}\\right) + \\ln \\Delta t _ {l}\\right), \\tag {9} \\\\ \\hat {d} (\\mathbf {r}) = \\sum_ {i = 1} ^ {i = M} w _ {i} z _ {i}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 356, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We utilize the simple bell-shaped model [1] and compute weights $w_{i}$ by two sigmoid functions $\\sigma(\\cdot)$ to convert predicted TSDF $\\mathbf{s}(\\mathbf{x}_i)$ into weight $w_{i}$ :", + "bbox": [ + 496, + 473, + 890, + 518 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} = \\sigma \\left(\\frac {\\mathbf {s} \\left(\\mathbf {x} _ {i}\\right)}{t r}\\right) \\sigma \\left(- \\frac {\\mathbf {s} \\left(\\mathbf {x} _ {i}\\right)}{t r}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 529, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $tr$ is the truncation distance of a ray $\\mathbf{r}$ .", + "bbox": [ + 500, + 574, + 797, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Tracking and Bundle Adjustment", + "text_level": 1, + "bbox": [ + 500, + 598, + 794, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, to leverage the HDR and temporal difference properties of events, we propose an event joint tracking and global BA strategy in Sec. 3.4.1 that incorporates events into optimization, thus improving the accuracy and robustness. Besides, we introduce adaptive forward-query and sampling strategies in Sec. 3.4.2 and Sec. 3.4.3, which select event data and ray samples with more elevated confidence for optimization, thereby boosting the convergence.", + "bbox": [ + 496, + 622, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4.1 Event Temporal Aggregating Optimization", + "text_level": 1, + "bbox": [ + 498, + 746, + 851, + 761 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overview of ETA is shown in Fig. 4 and Algorithm 1. For tracking, we represent the camera pose $\\mathbf{P}_{cur} = \\exp (\\xi_t^{\\wedge})\\in \\mathbb{S}\\mathbb{E}(3)$ of current frame $\\mathbf{F}_{cur}$ and initialize with constant assumption. By selecting $N_{t}$ rays within $\\mathbf{F}_{cur}$ and performing an adaptive event forward query in Sec. 3.4.2 with a probability-weighted sampling in Sec. 3.4.3, we get the event stream and previous rays. Then, we iteratively optimize the pose by minimizing objective functions. For global BA, $N_{ba}$ rays from the global keyframe", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19587", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "list are sampled to be the subset of pixels $\\{PX_{cur}\\}$ . And then, the forward query and probability-weighted sampling are performed for each sample to get the previous subset $\\{PX_{prev}\\}$ and events $\\{E_k\\}_{k = prev}^{cur}$ . Finally, a joint optimization is performed to optimize the geometry decoder $f_{g}$ , differentiable CRF $\\{\\Psi_{\\mathbf{c}},\\Psi_{l}\\}$ , and poses $\\{\\mathbf{P_i}\\}_{i = 0}^{cur}$ .", + "bbox": [ + 76, + 90, + 468, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Adaptive Forward Event Query", + "text_level": 1, + "bbox": [ + 76, + 185, + 352, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 4, ETA performs an adaptive event forward window selection in tracking and BA by constructing a previous index table to prioritize reliable prior frames for optimization. Specifically, ETA uses a default window $w_{d}$ and performs a forward query. If the loss of a queried frame exceeds a threshold $\\mathcal{L}_{s}$ , we conduct a shift lookup within a neighborhood of length $2 \\times w_{k}$ , selecting the frame with the minimum loss as the forward frame for event loss calculation Eq. (13). This event temporal constraint provides a stable local constraint between the participating frames and effectively leverages the high HDR property of events.", + "bbox": [ + 75, + 203, + 470, + 369 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Event temporal aggregating optimization" + ], + "code_body": "Input: RGBD-E stream $\\{\\mathbf{I}_i,d_i\\}_{i = 1}^J$ and $\\{\\mathbf{E}_k\\}_{k = 1}^N$ Output: Loss $\\{\\mathcal{L}_{ev},\\mathcal{L}_{rgb},\\mathcal{L}_d,\\mathcal{L}_{sdf},\\mathcal{L}_{fs}\\}$ \nwhile $j < J$ do \nfor $i\\in \\{j\\}$ if not BA else $\\{0,1,\\dots,j\\}$ do /\\* Forward Query Sec. 3.4.2 \\*/ \n $\\mathbf{F}_{cur},\\mathbf{F}_{prev}\\gets \\mathrm{Tab}(i),\\mathrm{Tab}(i - w_d);$ if $\\mathcal{L}_{total} > \\mathcal{L}_s$ then \n $\\begin{array}{rlr}{\\bf F}_{prev}^{\\min}\\leftarrow \\mathrm{Tab}(i - w_s - w_d,i + w_s).Loss \\end{array}$ \nend \nProbability-weighted ray sampling: $\\mathrm{Rays}_{cur}$ Rays prev $\\leftarrow \\mathbf{F}_{cur},\\mathbf{F}_{prev}; / / \\mathrm{Sec.}3.4.3$ \nRay rendering: $\\hat{\\mathbf{L}} (\\mathbf{m},t_{\\beta}) - \\hat{\\mathbf{L}} (\\mathbf{m},t_{\\alpha});$ // Sec. 3.3 \nEvent accumulation: $\\sum_{t_k = t_{cur}}^{t_k = t_{prev}}p_kC;$ \nCalculate loss: $\\mathcal{L}_{ev},\\mathcal{L}_{rgb},\\mathcal{L}_d,\\mathcal{L}_{sdf},\\mathcal{L}_{fs};$ // Eqs. (13) to (15) \nTab(i) $\\leftarrow \\{\\mathcal{L}_{total},cur,prev\\}$ \nend \n13 end", + "bbox": [ + 81, + 395, + 444, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.3 Probability-weighted Sampling Strategy", + "text_level": 1, + "bbox": [ + 76, + 684, + 410, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To take advantage of hybrid multimodality and reduce computational costs, we propose to utilize the RGB loss to guide ray sampling in the event plane. As shown in Fig. 5, the algorithm starts by dividing the RGB image into $h \\times w$ patches and randomly sampling $\\mathbf{N}_c$ rays from each patch to obtain the loss for each sample. Then, we calculate the average loss of each patch and project the center $\\mathbf{m}_c$ to a downsampled mini-plan plane of the event camera:", + "bbox": [ + 75, + 702, + 468, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {m} = \\frac {1}{Z _ {e}} \\mathbf {K} _ {m} \\left[ \\mathbf {I} _ {3 \\times 3} | \\mathbf {0} _ {3 \\times 1} \\right] \\left[ \\begin{array}{c} \\mathbf {T} _ {e c} \\mathbf {K} ^ {- 1} \\mathbf {m} Z _ {c} \\\\ 1 \\end{array} \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 823, + 468, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Z_{c}$ and $Z_{e}$ are the depths of two planes, $\\mathbf{K}_m$ is the intrinsic of event mini-plane, and $\\mathbf{T}_{ec}$ denotes the transformation between cameras. We apply the bilinear interpolation", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/66fc7c3f3260953042e0804d6047eab3c8f3797db5c526565fcf442cc2bf66af.jpg", + "image_caption": [ + "Figure 5. Illustration of the proposed probability-weighted sampling strategy. We utilize the loss of the RGBD plane (left) to guide ray sampling in the event plane (right)." + ], + "image_footnote": [], + "bbox": [ + 540, + 59, + 854, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tion to compute the loss for each pixel in the mini-plan. Finally, the divided patches of the event plane query the loss $\\{\\mathcal{L}_e^q\\}_{q = 0}^Q$ from the mini-plane and sample rays with probability distribution $f(j) = \\frac{\\mathcal{L}_e^q}{\\sum_{q = 1}^Q\\mathcal{L}_e^q}$ .", + "bbox": [ + 498, + 258, + 890, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.4 Objective Functions", + "text_level": 1, + "bbox": [ + 500, + 330, + 692, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to the EGM in Eq. (5), although it is not possible to directly model the luminance signals supervision, the logarithmic brightness differences $\\hat{\\mathbf{L}} (\\mathbf{m},t_{\\beta}) - \\hat{\\mathbf{L}} (\\mathbf{m},t_{\\alpha})$ can be rendered from two camera poses $\\mathbf{P}_{\\alpha}$ and $\\mathbf{P}_{\\beta}$ with Eq. (9). By integrating it with Eqs. (5) and (6), we obtain:", + "bbox": [ + 496, + 348, + 890, + 425 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} (\\mathbf {m}, t _ {\\beta}) - \\mathbf {L} (\\mathbf {m}, t _ {\\alpha}) = \\sum_ {t _ {k} = t _ {\\alpha}} ^ {t _ {k} = t _ {\\beta}} p _ {k} C \\approx \\hat {\\mathbf {L}} (\\mathbf {m}, t _ {\\beta}) - \\hat {\\mathbf {L}} (\\mathbf {m}, t _ {\\alpha}). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 434, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus, we establish the relation between events and rendering, and define event reconstruction loss as:", + "bbox": [ + 498, + 479, + 888, + 510 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {e v}} \\left(t _ {\\beta}, t _ {\\alpha}\\right) = \\operatorname {M S E} \\left(\\sum_ {t _ {k} = t _ {\\alpha}} ^ {t _ {k} = t _ {\\beta}} p _ {k} C - \\hat {L} (\\mathbf {m}, t _ {\\beta}) + \\hat {L} (\\mathbf {m}, t _ {\\alpha})\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 521, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our implementation, we perform a normalization on Eq. (13) to eliminate $C$ when it is unavailable. The color and depth rendering losses [58] in a valid ray batch $R$ between the rendering and observations are also utilized:", + "bbox": [ + 496, + 566, + 890, + 626 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r g b}} = \\frac {1}{| R |} \\sum_ {\\mathbf {r} \\in \\mathbf {R}} (\\hat {\\mathbf {e}} (\\mathbf {r}, \\Delta t _ {c})) - c (\\mathbf {r})) ^ {2}, \\mathcal {L} _ {\\mathrm {d}} = \\frac {1}{| R |} \\sum_ {\\mathbf {r} \\in \\mathbf {R}} (\\hat {d} (\\mathbf {r}) - d (\\mathbf {r})) ^ {2}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 635, + 890, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $c(\\mathbf{r})$ and $d(\\mathbf{r})$ are the ground truth color and depth. To achieve an accurate geometry reconstruction, we apply the approximated SDF loss and free-space loss [58] to sampled point $\\mathbf{x}$ near the surface $(S_r^{tr} = \\{\\mathbf{x} \\mid |d(\\mathbf{r}) - d(\\mathbf{x})| \\leq tr\\})$ and far from the surface $(S_r^{fs} = \\{\\mathbf{x} \\mid |d(\\mathbf{r}) - d(\\mathbf{x})| > tr\\})$ :", + "bbox": [ + 496, + 674, + 890, + 751 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s d f} = \\frac {1}{| R |} \\sum_ {r \\in R} \\frac {1}{| S _ {r} ^ {t r} |} \\sum_ {\\mathbf {x} \\in S _ {r} ^ {t r}} \\left(\\mathbf {x} - \\left(\\hat {d} (\\mathbf {r}) - d (\\mathbf {r})\\right)\\right) ^ {2}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 753, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f s} = \\frac {1}{| R |} \\sum_ {r \\in R} \\frac {1}{\\left| S _ {r} ^ {f s} \\right|} \\sum_ {\\mathbf {x} \\in S _ {r} ^ {f s}} (\\mathbf {x} - t r) ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 791, + 766, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Dataset", + "text_level": 1, + "bbox": [ + 500, + 830, + 586, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To our knowledge, there is currently no SLAM dataset that satisfactorily tackles challenges posed by strong motion blur and lighting variations while encompassing RGBD and", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19588", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c0dc9f2f0e626786168e77c5ea33c84d4260e4ca7596ded2506b4bbba49e736b.jpg", + "image_caption": [ + "Figure 6. Overview of the DEV-Indoors and DEV-Reals datasets. DEV-Indoors is obtained through Blender [6] and simulator [14], covering normal, motion blur, and dark scenes, providing 9 subsets with RGB images, depth maps, event streams, meshes, and trajectories. DEV-Reals is captured from real scenes, providing 8 challenging subsets under motion blur and lighting variation." + ], + "image_footnote": [], + "bbox": [ + 89, + 56, + 880, + 294 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "event streams for NeRF-based SLAM. Common datasets lack depth [19] or ground truth meshes [61]. Additionally, they are primarily focused on outdoor scenes [65], without significant motion blur [4] or lighting variation [30]. Therefore, in this paper, we construct simulated Dynamic Event RGBD Indoor (DEV-Indoors) and Dynamic Event RGBD Real captured (DEV-Reals) datasets, as shown in Fig. 6. Besides, we use Vector [13] dataset for evaluation as well.", + "bbox": [ + 75, + 347, + 468, + 467 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1) DEV-Indoors is rendered from 3 Blender [6] models: #room, #apartment, and #workshop. We generated 9 subsets containing high-quality color images, depth, meshes, and ground truth trajectories by varying the scene lighting and camera exposure time. The events are further generated via the events simulator [14].", + "bbox": [ + 76, + 468, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2) Dev-Reals is captured from 3 real scenes: #Pioffice, #Garage and #Dormitory. Our capture system comprises a LiDAR (for ground truth pose), a Realsense D435I RGBD camera, and a DAVIS346 event camera. Eight subsequences are captured by modifying the lighting conditions and camera movement speed in the environment.", + "bbox": [ + 76, + 559, + 468, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 76, + 662, + 200, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. To the best of our knowledge, there is currently no event-based RGBD dense vSLAM with available public code that can be directly compared with our method. We opt EVO [43], ESVO [69], USLAM [57] as a reference from the most relevant event-based methods [5, 12, 19, 28, 61, 72]. We also compare our method with the existing SOTA NeRF-based methods: iMAP [52], NICE-SLAM [71], CoSLAM [58], and ESLAM [23].", + "bbox": [ + 75, + 688, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric. We use the absolute trajectory error [51] (ATE) (cm) to measure the localization accuracy. For map reconstruction, we use the 2D Depth L1 (cm) [71], 3D accuracy (cm), completion (cm), and completion ratio $(\\%)$ to measure the scene geometry with mesh culling [1, 23]. The evaluation datasets are generated by randomly conducting 2000", + "bbox": [ + 75, + 810, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f6d3da37132b524bc767efff44f91e03623d0cb01263deb76aeb6734c702948b.jpg", + "table_caption": [ + "Table 1. Tracking (ATE RSME [cm]) comparison on DEV-Indoors. Our method outperforms previous works, demonstrating its robustness under motion blur and luminance variation." + ], + "table_footnote": [], + "table_body": "
Method#Rnm#Rm blur#Rnm dark#Apt norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]41.0850.5870.7725.7514.411.06e5276.91891.86345.21214.57
NICE-SLAM [71]17.0629.5430.5325.1744.2248.28X94 %X33 %X33%32.47
CoSLAM[58]10.7110.8826.6410.0213.0330.757.9614.3717.8815.80
ESLAM [23]10.7215.5540.429.9912.7912.397.0115.077.9714.66
Ours9.629.729.948.628.779.216.747.516.948.56
", + "bbox": [ + 503, + 391, + 888, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "poses and depths in Blender [6]. We run all the methods 5 times and report the average results or $X +$ tracking success ratio if a method crashes.", + "bbox": [ + 498, + 487, + 890, + 531 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. EN-SLAM is implemented in Python and trained on a desktop PC with a 5.50GHz Intel Core i9-13900K CPU and NVIDIA RTX 4090 GPU. We run EN-SLAM at 17 FPS and sample 1024 and 2048 rays in tracking and BA stages with 10 iterations by default. The event joint global BA is performed every 5 frames with $5\\%$ of pixels from all keyframes. The model is trained using Adam optimizer with learning rate $lr_{rot} = 1e^{-3}, lr_{trans} = 1e^{-3}$ , and loss weights $\\lambda_{ev} = 0.05, \\lambda_{rgb} = 5.0, \\lambda_d = 0.1$ . Default window $w_d$ and neighborhood window are set as 5 and 2, respectively. The exposures of RGB and event cameras are $5.21e^{-5}$ in DEV-Indoors. We use two sigmoid functions to fit the exposures if they are unavailable. Detailed settings can be found in the supplemental materials.", + "bbox": [ + 496, + 532, + 890, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Evaluation of Tracking and Mapping", + "text_level": 1, + "bbox": [ + 500, + 755, + 821, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on DEV-Indoors. We report the trajectory accuracy and reconstruction quality in Tab. 1 and Tab. 2. As shown in Tab. 1, EN-SLAM performs the best in all 9 scenes and remains stable (fluctuation below 0.8) under all the blur and dark sequences. While the others perform sensitive and unstable when facing non-ideal environments, especially iMAP [52] and NICE-SLAM [71], which completely crushes in the blur and dark scenes. ESLAM [71]", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19589", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5a141d83ad61631a880e527b19f8aeb555d3e9e8fda4fdbec54e6d8cac960165.jpg", + "image_caption": [ + "Figure 7. Reconstruction Performance on DEV-Indoors. EN-SLAM achieves, on average, more precise reconstruction details than existing methods in motion blur and lighting varying environments with the assistance of high-quality event streams." + ], + "image_footnote": [], + "bbox": [ + 80, + 55, + 893, + 219 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/95855d52a35e3ec15a229483d6c6cbdfd45249c29dc7ba84cc3bd9c02df893c0.jpg", + "table_caption": [ + "Table 2. Reconstruction Performance [cm] of the proposed method vs. the state-of-the-art methods on DEV-Indoors dataset." + ], + "table_footnote": [], + "table_body": "
MethodMetric#Rm norm blur#Rm dark#Rm norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]Acc↓37.1637.6034.3025.5544.28854.4756.4051.7438.12
Comp↓48.6955.9733.7619.2823.9449.6165.4027.1847.11
Comp Ratio↑37.5637.7639.1160.0346.2742.5612.1448.4440.41
Depth L1↓79.9397.9864.9640.36128.45140.00131.79115.07124.69
NICESL AM [71]Acc↓18.4918.8616.6921.2716.5119.1726.3522.0928.40
Comp↓20.2621.9321.4320.6718.7021.2928.0449.8277.19
CompRatio↑60.4059.0358.1459.6063.4956.5550.9146.0035.58
Depth L1↓40.5942.0940.2641.5424.0034.8962.48104.20106.09
CoSLAM [58]Acc↓10.6611.3612.7715.4716.4230.7113.0217.5919.85
Comp↓13.2412.4412.2314.0915.3621.6713.9218.2619.46
Comp Ratio↑69.2276.8777.2670.6166.7555.2667.9261.2660.70
Depth L1↓24.7820.9120.6532.2935.9064.1428.6939.1742.85
ESLA M [23]Acc↓9.488.5811.8112.8616.2514.859.0110.0110.02
Comp↓7.947.547.088.51112.3710.408.8910.9510.44
Comp Ratio↑84.6085.6986.7082.9371.5380.9083.1780.0281.64
Depth L1↓15.3412.2719.0811.0727.8015.5030.0329.0628.02
OursAcc↓7.4810.537.079.469.919.349.239.289.25
Comp↓7.7012.517.709.879.289.619.959.929.92
Comp Ratio↑83.0074.4884.2685.3683.4084.0182.2782.3882.35
Depth L1↓15.1023.3611.9218.8611.9419.2123.1623.1423.39
", + "bbox": [ + 80, + 285, + 465, + 484 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2537580298cb9236f4ec9344f1df1fead3d4836aaca1a1557be22d5f9d0b4117.jpg", + "table_caption": [ + "Table 3. Tracking comparison (ATE median [cm]) of the proposed method vs. the state-of-the-art methods on DEV-Reals." + ], + "table_footnote": [], + "table_body": "
MethodPio1Pio2Gre1Gre2dorm1dorm2dorm3dorm4avg
ORBSLAM [19]x63%x63%x63%x63%x63%x63%x63%x63%x63%
NICE-SLAM [71]13.2123.35x63%x25%24.6910.6818.4444.04x22.40
COSLAM [58]11.1419.8382.5240.1615.9915.4230.1232.4530.95
ESLAM [23]11.2821.4263.6530.7537.9431.0416.1937.9131.27
Ours8.9419.0543.6321.1811.2611.9116.0019.7818.97
", + "bbox": [ + 80, + 530, + 467, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and CoSLAM [58] exhibit similar trends but achieve relatively stable results. Specifically, in #room sequences, they achieved 1.02 and 1.45 times the error on the blur subset and 2.49 and 3.77 times the error on the dark subset, respectively. The reconstruction quality in Tab. 2 and Fig. 7 show that EN-SLAM performs more accurately and robustly than the other methods. Specifically, our method reduces the error by 2.37, 0.48, and 1.90 in ACC, Comp, and Depth L1 compared with the second ESLAM [23]. Fig. 7 also shows that our method reconstructs the details of the scenes more accurately and produces fewer artifacts.", + "bbox": [ + 75, + 607, + 468, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation on DEV-Reals. Tab. 3 illustrates the tracking performance of our method and the state-of-the-art methods on the DEV-Reals dataset. Our method achieves the best performance in all the scenes (18.97), and the average error is 1.63 times lower than the second-best CoSLAM [58] (30.95). Note that DEV-Reals is challenging due to the large motion and varying light, leading to the crushes of ORBSLAM [36] and NICE-SLAM [71].", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a56a1b922ae0114cfef8fdffeeb8e07015a293454c05a929f15cb0729415b329.jpg", + "table_caption": [ + "Table 4. Tracking comparison (ATE mean [cm]) of the proposed method vs. the Event-based SLAM system on Vector[13] dataset." + ], + "table_footnote": [ + "E: event, V: RGB or gray image, D: depth, I: IMU, S: stereo, O: odometry, X: crashes." + ], + "table_body": "
Methodrobot normrobot fastdesk normdesk fastsofa normsofa fasthdr normhdr fastall avg
EVO [43]3.25✘✘✘✘✘✘✘3.25
ESVO [69]✘✘✘✘1.77✘✘✘1.77
USLAM [57] (EVIO)1.181.652.241.085.742.545.692.612.84
CoSLAM [58] (DV)1.00124.691.7697.651.7477.891.471.4238.45
ESLAM [23] (DV)1.393.302.543.647.9919.037.3812.237.19
Ours (EDV)1.061.731.762.692.021.841.031.221.67
", + "bbox": [ + 503, + 284, + 890, + 362 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b05f847a4c12d2b35315e02dda9f47720ee943fe3aea1d1d589755bc288f04ca.jpg", + "table_caption": [ + "Table 5. Run-time comparison on DEV-Indoors. EN-SLAM is comparable to the most efficient ESLAM and keeps lightweight." + ], + "table_footnote": [], + "table_body": "
MethodTracking [ms×it] ↓Mapping [ms×it] ↓FPS ↑#para.
iMAP [52]24.73×5041.18×3000.360.22 M
NICE-SLAM [71]6.46×1626.42×1201.555.86 M
CoSLAM[58]6.08×1513.52×1511.261.71 M
ESLAM [23]5.20×1316.68×1014.777.85 M
Ours5.75×1013.16×1017.401.95 M
", + "bbox": [ + 503, + 407, + 890, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Runtime Analysis", + "text_level": 1, + "bbox": [ + 500, + 474, + 671, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate all the frameworks on an NVIDIA RTX 4090 GPU and report average tracking and mapping iterations spending, FPS, and parameters number of the model in Tab. 5. The experimental results indicate that our method is fast, with an average of 17 FPS, comparable to the currently most efficient ESLAM [23]. Meanwhile, our method remains lightweight, with only 1.95M parameters, yet achieves the best accuracy.", + "bbox": [ + 496, + 500, + 890, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Evaluation of Rendering", + "text_level": 1, + "bbox": [ + 500, + 631, + 725, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare the rendering performance in Fig. 5.3 (left), EN-SLAM outperforms most SOTA works in image quality. The thumbnails in Fig. 5.3 (right) show that EN-SLAM achieves more precise rendering details than previous methods. Specifically, on #Rm Blur, EN-SLAM yields more refined results, while CoSLAM and ESLAM exhibit ghosting. Note that in #Rm Dark and #Wkp Dark, all the RGB rendering is dark and blurred, while our method can still generate high-quality luminance results with the assistance of the HDR event stream.", + "bbox": [ + 496, + 654, + 890, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 816, + 653, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of event and RGB modalities. Fig. 9 illustrates quantitative evaluation using ETA in tracking and mapping. Our full model achieve lower tracking error of 9.61 and 15.47 than the model w/o ETA in tracking (10.73 and 17.07)", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19590", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13d2119878820f66c7b199e1e992de6e49272dc2508512dce865b314b13d6906.jpg", + "image_caption": [ + "Figure 8. Rendering Performance on DEV-Indoors. left): Our method outperforms most previous works in image quality evaluation under non-ideal environments. right): EN-SLAM achieves more precise rendering details on average than previous methods." + ], + "image_footnote": [], + "bbox": [ + 91, + 55, + 903, + 244 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f41df484556fb4d130fc9808b78f1d930be6d5615ed31fb9c44718bd3dc7cb44.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Tracking EventMapping Event#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
XX11.898.6110.9876.3114.4618.75
X✓10.738.329.5381.8314.1717.07
✓X11.688.2810.2879.0516.0919.72
✓✓9.617.887.5983.5111.9115.47
RGB 1st-2nd only10.929.029.1582.8113.5217.80
W/o RGB12.0711.1211.0576.2722.5026.48
", + "bbox": [ + 86, + 286, + 464, + 391 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0f217ff0e8b0f8d734050ac600507f0e7f608c35ed4971fa6682b7f3f51e7ce1.jpg", + "image_caption": [ + "Figure 9. Ablation study of modalities on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations)." + ], + "image_footnote": [], + "bbox": [ + 81, + 393, + 207, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e1d305ec006d0c223c2e0e10634b2814a15091ac873e3225ddfccfa9bbaf93e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 393, + 336, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/76910319060adc007bb2dcc160317e93fd138d4ddca8162919b007ba4bf32ce5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 393, + 464, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and mapping (11.68 and 19.72) on the #Rm blur and #Dorm2, respectively. The results also show that the full model surpasses the model w/o ETA by 0.73 and $3.39\\%$ in ACC and completion. In addition, the RGB is also critical, but with the initialization of RGB in 2 frames, the performance is significantly improved, benefiting from the CRF.", + "bbox": [ + 75, + 571, + 468, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of CRF and probability-weighted sampling. Fig. 9 show the performance of differentiable CRF and probability-weighted sampling strategy (PWS). The system without CRF might suffer from the distinct event and RGB imaging process, resulting in fluctuating training and poor performance, especially in real datasets. It significantly reduces the tracking ATE RSME from 30.18 to 15.47 in #Drom2 and reconstruction completion from 9.78 to 7.59 in #Rm blur. The results also show that the full model surpasses the model w/o PWS by 0.25 and $1.9\\%$ in ATE and completion on #Rm blur. A visualization of CRF is shown in Fig. 10, on dark scene #Drom2, the model with CRF renders HDR luminance results and accurate mesh benefiting from events. In contrast, the model w/o CRF suffers from the low dynamic range RGB input.", + "bbox": [ + 75, + 672, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/03e5f7a7d63c8178beb3f990c3da913df7338a281281386007533f82ffe099d0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Setting#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
w/o CRF12.128.299.7883.5727.6730.18
w/o PWS9.867.889.4981.0416.5919.78
Full model9.617.887.5983.5111.9115.47
", + "bbox": [ + 509, + 286, + 887, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation study of CRF and PWS on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations).", + "bbox": [ + 500, + 359, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f88bd5021d37b74957e8f3e52ac8f5c222a987de13249e5096b5848569ef2f96.jpg", + "image_caption": [ + "Figure 10. CRF ablation on the #Dorm2 of DEV-Reals." + ], + "image_footnote": [], + "bbox": [ + 501, + 388, + 890, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Limitation", + "text_level": 1, + "bbox": [ + 500, + 573, + 750, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper first integrates the event stream into the implicit neural SLAM framework to overcome challenges in scenes with motion blur and lighting variation. A differentiable CRF rendering technique that maps the unified representation to color and luminance is proposed to address the significant distinction between event and RGB. An event temporal aggregating optimization strategy that capitalizes the consecutive difference constraints of events is presented to enhance the optimization. We construct DEV-Indoors and DEV-Reals datasets to evaluate the effectiveness of EN-SLAM under various environments. However, EN-SLAM relies on depth input, which might be unavailable in some scenarios. Besides, EN-SLAM focuses on indoor scenes and might face challenges in boundless long trajectories. In future work, we aim to extend it to large-scale outdoor environments and enhance the generalization capability.", + "bbox": [ + 496, + 599, + 890, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by the Shanghai AI Laboratory, National Key R&D Program of China (2022ZD0160101), the National Natural Science Foundation of China (62376222), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001).", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19591", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. In CVPR, pages 6290-6301, 2022. 4, 6", + "[2] Christian Brändli, Jonas Strubel, Susanne Keller, Davide Scaramuzza, and Tobi Delbruck. Elised—an event-based line segment detector. In *EBCCSP*, pages 1-7. 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IEEE, 2022. 6" + ], + "bbox": [ + 78, + 90, + 468, + 486 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19594", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_model.json b/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b34f317e93986e49e9497ecba6ffdc08c30be3a4 --- /dev/null +++ b/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_model.json @@ -0,0 +1,2653 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.299, + 0.131, + 0.673, + 0.154 + ], + "angle": 0, + "content": "Implicit Event-RGBD Neural SLAM" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.179, + 0.764, + 0.198 + ], + "angle": 0, + "content": "Delin \\(\\mathrm{Qu}^{1,2*}\\) Chi Yan\\(^{2,5*}\\) Dong Wang\\(^{2}\\) Jie Yin\\(^{3}\\) Qizhi Chen\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.254, + 0.199, + 0.716, + 0.217 + ], + "angle": 0, + "content": "Dan Xu5 Yiting Zhang2 Bin Zhao2,4† Xuelong Li2" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.217, + 0.862, + 0.253 + ], + "angle": 0, + "content": "\\(^{1}\\)Fudan University \\(^{2}\\)Shanghai AI Laboratory \\(^{3}\\)Shanghai Jiao Tong University \\(^{4}\\)Northwestern Polytechnical University \\(^{5}\\)Hong Kong University of Sciences and Technology" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.286, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.729 + ], + "angle": 0, + "content": "Implicit neural SLAM has achieved remarkable progress recently. Nevertheless, existing methods face significant challenges in non-ideal scenarios, such as motion blur or lighting variation, which often leads to issues like convergence failures, localization drifts, and distorted mapping. To address these challenges, we propose EN-SLAM, the first event-RGBD implicit neural SLAM framework, which effectively leverages the high rate and high dynamic range advantages of event data for tracking and mapping. Specifically, EN-SLAM proposes a differentiable CRF (Camera Response Function) rendering technique to generate distinct RGB and event camera data via a shared radiance field, which is optimized by learning a unified implicit representation with the captured event and RGBD supervision. Moreover, based on the temporal difference property of events, we propose a temporal aggregating optimization strategy for the event joint tracking and global bundle adjustment, capitalizing on the consecutive difference constraints of events, significantly enhancing tracking accuracy and robustness. Finally, we construct the simulated dataset DEV-Indoors and real captured dataset DEV-Reals containing 6 scenes, 17 sequences with practical motion blur and lighting changes for evaluations. Experimental results show that our method outperforms the SOTA methods in both tracking ATE and mapping ACC with a real-time 17 FPS in various challenging environments. Project page: https://delinqu.github.io/EN-SLAM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.759, + 0.21, + 0.775 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Simultaneous Localization and Mapping (SLAM) is an essential problem in computer vision and robotics, widely applied in tasks such as virtual and augmented reality [8], robot navigation [18] and autonomous driving [3] over last decades. Exploration in extreme environments [10, 31, 41]" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.277, + 0.895, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.614 + ], + "angle": 0, + "content": "Figure 1. Illustration of the proposed implicit event-RGBD neural SLAM system EN-SLAM under non-ideal environments. The dynamic range of RGB sensors is relatively low and suffers from motion blur. Instead, event cameras show great potential in non-ideal environments due to their high dynamic range and low latency advantages. Our method samples rays from two independent RGBD and event cameras to jointly train a single implicit neural field with both modalities. This hybrid shared mechanism provides a natural fusion approach, avoiding alignment issues. It also leverages the advantages of both modalities, resulting in dense, more robust, and higher-quality reconstruction results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.895, + 0.673 + ], + "angle": 0, + "content": "remains challenging for visual SLAM (vSLAM) systems due to the lack of visual features caused by motion blur and lighting variation in diverse environments [42, 59, 68]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.896, + 0.902 + ], + "angle": 0, + "content": "As a novel representation for myriad of signals, Neural Radiance Fields (NeRF) [35] has innovated great progress in SLAM recently, demonstrating significant improvements in map memory consumption, hole filling, and mapping quality [23, 49, 52, 58, 67, 71]. While the existing NeRF-based neural vSLAM methods address the limitations of traditional SLAM frameworks [11, 36, 37, 50, 62] in accurate dense 3D map reconstruction, they are primarily designed for well-lit scenes and always fail in practical SLAM scenarios with motion blur [40, 66] and lighting variation [32, 48]. These methods produce unsatisfying results under non-ideal environments [58] because of the following limitations: 1) View-inconsistency: When the camera encounters rapid velocity variation in Fig. 2 (2nd), the scene may exhibit discontinuous blur, leading to view" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.876, + 0.398, + 0.888 + ], + "angle": 0, + "content": "* Authors contributed equally: dlqu22@m.fudan.edu.cn" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.889, + 0.231, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.876, + 0.398, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19584" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "inconsistency among frames, further causing heavy artifacts in the reconstructed map. 2) Low dynamic range: In light- ing variation scenes illustrated in Fig. 1, the dynamic range of the RGB sensor is relatively low, and the information on the dark and overexposure areas is lost, leading to tracking drifts and mapping distortions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.184, + 0.471, + 0.486 + ], + "angle": 0, + "content": "To address the issues in non-ideal scenarios of existing neural vSLAM, we introduce utilizing the advantages of high dynamic range (HDR) and temporal resolution of event data to compensate for the lost information, thereby improving the robustness, efficiency, and accuracy of current neural vSLAM in extreme environments. Fig. 2 shows the event generation model that an event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold \\( C \\). This asynchronous mechanism shows excellent potential in non-ideal environments due to its advantages in low latency [26, 43, 70], high dynamic range [46], and high temporal resolution [54, 55]. Fig. 1 and Fig. 2 illustrate its superiority in dark and fast motion, and event sensors capture higher-quality signals than RGB sensors. However, applying events into NeRF-based vSLAM is challenging due to the significant distinction in imaging mechanisms between event and RGB cameras. Moreover, the requirement of highly accurate camera poses and careful optimization in traditional surface density estimation [32] further complicates the integration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.47, + 0.773 + ], + "angle": 0, + "content": "In order to overcome these obstacles, we present EN-SLAM, the first event-RGBD implicit neural SLAM framework that effectively harnesses the advantages of event and RGBD streams. The overview of EN-SLAM is shown in Fig. 3. Our method models the differentiable imaging process of two distinct cameras and utilizes shared radiance fields to jointly learn a hybrid unified representation from events and RGBD data. By integrating the event generation model into the optimization process, we introduce the event temporal aggregating (ETA) optimization strategy for event joint tracking and global bundle adjustment (BA). This strategy effectively leverages the temporal difference property of events, providing efficient consecutive difference constraints and significantly improving the performance. Additionally, we construct two datasets: the simulated dataset DEV-Indoors and the real captured dataset DEV-Reals, which consist of 6 scenes and 17 sequences with practical motion blur and lighting changes. Contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.78, + 0.469, + 0.839 + ], + "angle": 0, + "content": "- We present EN-SLAM, the first event-RGBD implicit neural SLAM framework that efficiently leverages event stream and RGBD to overcome challenges in extreme motion blur and lighting variation scenes." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.841, + 0.469, + 0.9 + ], + "angle": 0, + "content": "- A differentiable CRF rendering technique is proposed to map a unified representation in the shared radiance field to RGB and event camera data for addressing the significant distinction between event and RGB. A tempo" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.78, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.63, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.094, + 0.758, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.759, + 0.094, + 0.892, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.19, + 0.892, + 0.231 + ], + "angle": 0, + "content": "Figure 2. Illustration of the Event Generation Model (EGM). An event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold \\( C \\)." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.239, + 0.892, + 0.298 + ], + "angle": 0, + "content": "ral aggregating optimization strategy that capitalizes the consecutive difference constraints of the event stream is present and significantly improves the camera tracking accuracy and robustness." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.299, + 0.892, + 0.374 + ], + "angle": 0, + "content": "- We construct a simulated DEV-Indoors and real captured DEV-Reals dataset containing 17 sequences with practical motion blur and lighting changes. A wide range of evaluations demonstrate competitive real-time performance under various challenging environments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.39, + 0.641, + 0.405 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Neural Implicit vSLAM. Existing NeRF-based visual SLAM methods have made significant improvements in dense map reconstruction. iMAP [52] first introduces NeRF into SLAM, and NICE-SLAM [71] expands the reconstructable environment size by introducing multiscale feature grids. Vox-Fusion [64] utilizes an octree-based structure to expand the scene dynamically. Besides, CoSLAM [58] combines coordinate and sparse parametric encoding to achieve fast convergence and surface hole filling in reconstruction. Parallel works ESLAM [23] and Point-SLAM [49] represent scenes as multi-scale feature planes and neural point clouds, respectively, to improve the efficiency and accuracy. Beyond NeRF, GS-SLAM [63] utilizes 3D Gaussian [24] for scene representation and achieves photo-realistic reconstruction performance. However, these methods are designed for well-lit indoor scenes and commonly encounter challenges in non-ideal SLAM processes, such as motion blur and lighting variation. In contrast, we introduce utilizing the advantages of high dynamic range and temporal resolution of events to compensate for the lost information, thereby improving the robustness and accuracy of current neural implicit methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Event-based SLAM. Events have been incorporated into traditional visual SLAM systems to address the motion blur and lighting variation. These methods can be divided into three main types: feature-based methods, direct methods, and motion-compensation methods. Feature-based methods, such as USLAM [57], EIO [16] and PL-EVIO [17], track point or line features from event data [29, 44], and perform the camera tracking and mapping in parallel threads. However, the feature extraction algorithms [2, 33, 47, 56] rely heavily on frame-based feature detection, facing chal" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19585" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.058, + 0.895, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.234, + 0.895, + 0.278 + ], + "angle": 0, + "content": "Figure 3. Overview of EN-SLAM. EN-SLAM decodes the scene encoding to a shared geometry and radiance representation, and decomposes the radiance into RGB color \\(\\mathbf{c}(\\mathbf{x})\\) and event luminance \\(\\mathbf{l}(\\mathbf{x})\\) via differentiable CRF Mappers. We iteratively optimize the pose and scene representation by minimizing losses, in tracking and global BA with the event temporal aggregating techniques in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.473, + 0.496 + ], + "angle": 0, + "content": "lenges for motion-dependent event data appearance. Direct methods employ events without explicit data association by aligning the photometric event image [19, 25, 26] or utilizing the spatiotemporal information for event representations alignment [43, 45, 70]. Direct methods are well suited for events, but mainly focus on event-based visual odometry, leaving the visual dense mapping unexplored. Motion-compensation methods optimize event alignment in motion-compensated event frames by maximizing the contrast [39, 60], minimizing the dispersion [38] and align probabilistic [15]. However, they suffer from the collapse in a broad range of camera motions. Thus, currently, event-based SLAM demonstrates significant potential but lacks sufficient exploration in dense map reconstructions [20]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.472, + 0.799 + ], + "angle": 0, + "content": "Neural Radiance Fields using Events. Event-based NeRF is in the nascent stages, and several studies have demonstrated the possibility of view synthesis from events via implicit neural fields. Event-NeRF [48] proposes an approach for inferring NeRF from a monocular color event stream that enables novel view synthesis. E-NeRF [27] and \\(\\mathrm{E}^2\\mathrm{NeRF}\\) [40] tackle the NeRF estimation from event cameras under strong motion blur. They develop normalized and rendering loss to address varying contrast thresholds and enhance neural volumetric representation. The parallel work Ev-NeRF [22] conducts a threshold-bound loss with the ReLU function to address the lack of RGB images. In addition to reconstruction, \\(\\Delta_t\\) NeRF [34] proposes an event camera tracker by minimizing the error between sparse events and the temporal gradient of the scene representation on the simplified intensity-change events. However, the traditional surface density estimation in NeRF requires highly accurate camera poses and careful optimization [32], thus making it exceptionally challenging to apply NeRF to the event-based SLAM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.212, + 0.832 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The overview of our method is shown in Fig. 3. Given an input RGBD stream \\(\\{\\mathbf{I}_i, \\mathbf{D}_i\\}_{i=1}^J\\) and event stream \\(\\{\\mathbf{E}_k\\}_{k=1}^N\\) with known camera intrinsics \\(\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}\\) and \\(\\mathbf{K}' \\in \\mathbb{R}^{3 \\times 3}\\), we aim to leverage event and RGBD to reconstruct the cam" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.436 + ], + "angle": 0, + "content": "era poses \\(\\{\\mathbf{P}_i\\}_{i = 1}^J\\) and the implicit scene representation. In Sec. 3.1, the scene encoding is decoded to a unified geometry and radiance representation. Then, the shared radiance is decomposed into RGB color \\(\\mathbf{c}(\\mathbf{x})\\) and event luminance \\(\\mathrm{l(x)}\\) via differentiable CRF Mappers in Secs. 3.2 and 3.3 to address the imaging distinction of event and RGB cameras. Finally, EN-SLAM iteratively optimizes the pose and scene representation by minimizing the re-rendering loss between the observed RGBD-E (RGBD and events) and rendering results in tracking and global BA of Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.444, + 0.828, + 0.46 + ], + "angle": 0, + "content": "3.1. Unified Implicit Scene Representation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.892, + 0.498 + ], + "angle": 0, + "content": "As shown in Fig. 3, we represent the scene S with multi-resolution geometric features and color grid features:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.508, + 0.892, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} = \\left\\{\\left(F _ {\\mathbf {x}, \\theta} ^ {g}, F _ {\\mathbf {x}, \\theta} ^ {c}\\right) \\mid \\theta = 1, \\dots , \\Theta \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.893, + 0.749 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}\\) and \\(\\theta\\) denote the coordinate and resolution level. There are two challenges that hinder us from learning a scene representation from different RGB and event modalities. Firstly, the event data is sparse and records logarithmic changes in luminance. Secondly, different cameras hold distinct physical imaging process mechanisms. Despite this, the geometry and radiance fields remain consistent during the camera imaging. In this case, we propose to learn a shared unified geometry hidden feature \\(\\mathbf{h}_{\\mathbf{x}}^{g}\\) and radiance representation \\(\\mathbf{e}(\\mathbf{x})\\) across distinct cameras. The geometric grid feature \\(F_{\\mathbf{x},\\theta}^{g}\\) and color feature \\(F_{\\mathbf{x},\\theta}^{c}\\) are simultaneously mapped to geometry hidden vector \\(\\mathbf{h}_{\\mathbf{x}}^{g}\\), radiance fields \\(\\mathbf{e}(\\mathbf{x})\\) and TSDF (truncated signed distance function) \\(\\mathbf{s}(\\mathbf{x})\\), by a geometry decoder \\(\\pmb{f}_{g}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.757, + 0.892, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {f} _ {\\boldsymbol {g}} \\left(F _ {\\mathbf {x}, \\theta} ^ {g}, F _ {\\mathbf {x}, \\theta} ^ {c}\\right) \\mapsto \\left(\\mathbf {h} _ {\\mathbf {x}} ^ {g}, \\mathbf {e} (\\mathbf {x}), \\mathbf {s} (\\mathbf {x})\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.793, + 0.892, + 0.823 + ], + "angle": 0, + "content": "The geometry hidden vector \\(\\mathbf{h}_{\\mathbf{x}}^{g}\\) and radiance fields \\(\\mathbf{e}(\\mathbf{x})\\) are shared by the color and event CRF decoders." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.833, + 0.825, + 0.849 + ], + "angle": 0, + "content": "3.2. Decomposition of the Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In standard imaging devices, the incoming radiance undergoes linear and nonlinear image processing before being mapped into pixel values and stored in images. This entire" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19586" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "image processing can be represented by a single function \\( f_{c} \\) called the camera response function (CRF) [9]. However, the traditional NeRF method [35] simplifies the imaging process, leading to discrepancies between the rendering and actual images. This deviation is further amplified in multi-modal implicit representations. As Fig. 10 shows, the captures of RGB and event cameras are significantly distinct, which can lead to joint optimization fluctuation. To address this issue, we model the radiance \\( \\mathbf{e}(\\mathbf{x}) \\) and exposure \\( \\Delta t_{c} \\) of a ray \\( \\mathbf{r} \\) but take the aperture and others as implicit factors to obtain the color field \\( \\mathbf{c}(\\mathbf{x}) \\) [21, 53] by differentiable tone-mapping:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.281, + 0.47, + 0.298 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} (\\mathbf {x}) = \\boldsymbol {f} _ {c} \\left(\\mathbf {e} (\\mathbf {x}) \\Delta \\mathbf {t} _ {c}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.305, + 0.47, + 0.356 + ], + "angle": 0, + "content": "To facilitate optimization, we convert all numerical values into the logarithmic domain and present the inverse function of \\(\\left(\\ln f_c^{-1}\\right)^{-1}\\) as \\(\\Psi_{\\mathrm{c}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.362, + 0.47, + 0.401 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {c} (\\mathbf {x}) = \\left(\\ln \\boldsymbol {f} _ {\\boldsymbol {c}} ^ {- 1}\\right) ^ {- 1} (\\ln \\mathbf {e} (\\mathbf {r}) + \\ln \\Delta \\mathbf {t} _ {c}) \\tag {4} \\\\ = \\boldsymbol {\\Psi} _ {\\mathbf {c}} (\\ln \\mathbf {e} (\\mathbf {x}) + \\ln \\Delta \\mathbf {t} _ {c}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.408, + 0.47, + 0.513 + ], + "angle": 0, + "content": "As for the event camera, directly obtaining the event data is not feasible. However, we can predict high dynamic range luminance \\( l(\\mathbf{x}) \\) and derive events using the event generation model: As shown in Fig. 2, an event \\( E_{k} = (u_{k}, v_{k}, t_{k}, p_{k}) \\) at image coordinate \\( \\mathbf{m}_{k} = [u_{k}, v_{k}, 1]^{T} \\) is triggered if the corresponding logarithmic brightness change \\( \\mathbf{L}(\\mathbf{m}, t) \\) exceeds a threshold \\( C \\):" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.522, + 0.469, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} \\left(\\mathbf {m} _ {k}, t _ {k}\\right) - \\mathbf {L} \\left(\\mathbf {m} _ {k}, t _ {k - 1}\\right) = p _ {k} C, \\quad p _ {k} \\in \\{+ 1, - 1 \\}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.546, + 0.446, + 0.561 + ], + "angle": 0, + "content": "The logarithmic brightness \\(\\mathbf{L}(\\mathbf{m},t)\\) can be obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.568, + 0.469, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} (\\mathbf {m}, t) = \\ln \\log \\left(\\mathbf {I} _ {e} (\\mathbf {m})\\right) = \\left\\{ \\begin{array}{l l} \\mathbf {I} _ {e} (\\mathbf {m}) \\cdot \\ln (B) / B, & \\text {i f} \\mathbf {I} _ {e} (\\mathbf {m}) < B \\\\ \\ln \\left(\\mathbf {I} _ {e} (\\mathbf {m})\\right), & \\text {e l s e} \\end{array} , \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.598, + 0.469, + 0.689 + ], + "angle": 0, + "content": "where \\(B\\) denotes the linear region threshold [7] and the imaging brightness \\(\\mathbf{I}_e(\\mathbf{m})\\) of event camera equals to the corresponding luminance of ray \\(\\mathbf{r}\\). By applying the modeling approach in Eqs. (3) and (4) to the CRF of an event camera, we establish the relation among the luminance field \\(l(\\mathbf{x})\\), the radiance \\(\\mathbf{e}(\\mathbf{x})\\) and exposure:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.697, + 0.469, + 0.713 + ], + "angle": 0, + "content": "\\[\nl (\\mathbf {x}) = \\boldsymbol {\\Psi} _ {l} \\left(\\ln \\mathbf {e} (\\mathbf {x}) + \\ln \\Delta \\mathbf {t} _ {l}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.721, + 0.469, + 0.797 + ], + "angle": 0, + "content": "where \\(\\Psi_{l}\\) and \\(\\Delta \\mathbf{t}_l\\) denote the luminance tone-mapping and pseudo exposure of the event camera. In this way, we decompose the shared radiance field \\(\\mathbf{e}(\\mathbf{x})\\) into the RGB and event camera imaging processes through two differentiable tone-mapping processes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.805, + 0.348, + 0.821 + ], + "angle": 0, + "content": "3.3. Differentiable CRF Rendering" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.828, + 0.469, + 0.873 + ], + "angle": 0, + "content": "Upon obtaining the color and luminance fields in Sec. 3.2, we render the final imaging RGB, luminance, and depth by integrating predicted values along the samples in a ray \\(\\mathbf{r}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.881, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {i} = \\mathbf {O} + z _ {i} \\mathbf {d}, \\quad i \\in \\{1, \\dots , M \\}, \\tag {8}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.083, + 0.65, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.211, + 0.645, + 0.23 + ], + "angle": 0, + "content": "a) Camera k trajectory" + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.086, + 0.765, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.684, + 0.21, + 0.739, + 0.229 + ], + "angle": 0, + "content": "b) Previous Index Table" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.087, + 0.892, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.208, + 0.861, + 0.23 + ], + "angle": 0, + "content": "c) Forward ray sampling" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Figure 4. The illustration of event temporal aggregating optimization strategy. In the tracking and global BA stages, EN-SLAM adaptively forwards query the previous frame according to the previous index table, and sample rays from different views perform joint optimization in Eq. (13)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.356 + ], + "angle": 0, + "content": "where \\(\\mathbf{O} \\in \\mathbb{R}^3\\) is the camera origin, \\(\\mathbf{d} \\in \\mathbb{R}^3\\), \\(\\|\\mathbf{d}\\| = 1\\) is the ray direction, and \\(z_i \\in \\mathbb{R}\\) denotes the depth. Hence, we obtain the final imaging color \\(\\hat{\\mathbf{c}}\\), luminance \\(\\hat{l}\\) and depth \\(\\hat{d}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.357, + 0.891, + 0.475 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {c}} (\\mathbf {r}, \\Delta t _ {c}) = \\sum_ {i = 1} ^ {i = M} w _ {i} \\boldsymbol {\\Psi} _ {\\mathbf {c}} \\left(\\ln \\mathbf {e} \\left(\\mathbf {x} _ {i}\\right) + \\ln \\Delta t _ {c}\\right), \\\\ \\hat {l} (\\mathbf {r}, \\Delta t _ {l}) = \\sum_ {i = 1} ^ {i = M} w _ {i} \\boldsymbol {\\Psi} _ {l} \\left(\\ln \\mathbf {e} \\left(\\mathbf {x} _ {i}\\right) + \\ln \\Delta t _ {l}\\right), \\tag {9} \\\\ \\hat {d} (\\mathbf {r}) = \\sum_ {i = 1} ^ {i = M} w _ {i} z _ {i}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.52 + ], + "angle": 0, + "content": "We utilize the simple bell-shaped model [1] and compute weights \\( w_{i} \\) by two sigmoid functions \\( \\sigma(\\cdot) \\) to convert predicted TSDF \\( \\mathbf{s}(\\mathbf{x}_i) \\) into weight \\( w_{i} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.53, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\nw _ {i} = \\sigma \\left(\\frac {\\mathbf {s} \\left(\\mathbf {x} _ {i}\\right)}{t r}\\right) \\sigma \\left(- \\frac {\\mathbf {s} \\left(\\mathbf {x} _ {i}\\right)}{t r}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.575, + 0.799, + 0.589 + ], + "angle": 0, + "content": "where \\(tr\\) is the truncation distance of a ray \\(\\mathbf{r}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.599, + 0.795, + 0.615 + ], + "angle": 0, + "content": "3.4. Tracking and Bundle Adjustment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.744 + ], + "angle": 0, + "content": "In this section, to leverage the HDR and temporal difference properties of events, we propose an event joint tracking and global BA strategy in Sec. 3.4.1 that incorporates events into optimization, thus improving the accuracy and robustness. Besides, we introduce adaptive forward-query and sampling strategies in Sec. 3.4.2 and Sec. 3.4.3, which select event data and ray samples with more elevated confidence for optimization, thereby boosting the convergence." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.747, + 0.852, + 0.762 + ], + "angle": 0, + "content": "3.4.1 Event Temporal Aggregating Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The overview of ETA is shown in Fig. 4 and Algorithm 1. For tracking, we represent the camera pose \\(\\mathbf{P}_{cur} = \\exp (\\xi_t^{\\wedge})\\in \\mathbb{S}\\mathbb{E}(3)\\) of current frame \\(\\mathbf{F}_{cur}\\) and initialize with constant assumption. By selecting \\(N_{t}\\) rays within \\(\\mathbf{F}_{cur}\\) and performing an adaptive event forward query in Sec. 3.4.2 with a probability-weighted sampling in Sec. 3.4.3, we get the event stream and previous rays. Then, we iteratively optimize the pose by minimizing objective functions. For global BA, \\(N_{ba}\\) rays from the global keyframe" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19587" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.184 + ], + "angle": 0, + "content": "list are sampled to be the subset of pixels \\(\\{PX_{cur}\\}\\). And then, the forward query and probability-weighted sampling are performed for each sample to get the previous subset \\(\\{PX_{prev}\\}\\) and events \\(\\{E_k\\}_{k = prev}^{cur}\\). Finally, a joint optimization is performed to optimize the geometry decoder \\(f_{g}\\), differentiable CRF \\(\\{\\Psi_{\\mathbf{c}},\\Psi_{l}\\}\\), and poses \\(\\{\\mathbf{P_i}\\}_{i = 0}^{cur}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.186, + 0.353, + 0.202 + ], + "angle": 0, + "content": "3.4.2 Adaptive Forward Event Query" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.204, + 0.471, + 0.371 + ], + "angle": 0, + "content": "As shown in Fig. 4, ETA performs an adaptive event forward window selection in tracking and BA by constructing a previous index table to prioritize reliable prior frames for optimization. Specifically, ETA uses a default window \\( w_{d} \\) and performs a forward query. If the loss of a queried frame exceeds a threshold \\( \\mathcal{L}_{s} \\), we conduct a shift lookup within a neighborhood of length \\( 2 \\times w_{k} \\), selecting the frame with the minimum loss as the forward frame for event loss calculation Eq. (13). This event temporal constraint provides a stable local constraint between the participating frames and effectively leverages the high HDR property of events." + }, + { + "type": "code_caption", + "bbox": [ + 0.088, + 0.379, + 0.425, + 0.394 + ], + "angle": 0, + "content": "Algorithm 1: Event temporal aggregating optimization" + }, + { + "type": "algorithm", + "bbox": [ + 0.082, + 0.396, + 0.445, + 0.673 + ], + "angle": 0, + "content": "Input: RGBD-E stream \\(\\{\\mathbf{I}_i,d_i\\}_{i = 1}^J\\) and \\(\\{\\mathbf{E}_k\\}_{k = 1}^N\\) Output: Loss \\(\\{\\mathcal{L}_{ev},\\mathcal{L}_{rgb},\\mathcal{L}_d,\\mathcal{L}_{sdf},\\mathcal{L}_{fs}\\}\\) \nwhile \\(j < J\\) do \nfor \\(i\\in \\{j\\}\\) if not BA else \\(\\{0,1,\\dots,j\\}\\) do /\\* Forward Query Sec. 3.4.2 \\*/ \n\\(\\mathbf{F}_{cur},\\mathbf{F}_{prev}\\gets \\mathrm{Tab}(i),\\mathrm{Tab}(i - w_d);\\) if \\(\\mathcal{L}_{total} > \\mathcal{L}_s\\) then \n\\(\\begin{array}{rlr}{\\bf F}_{prev}^{\\min}\\leftarrow \\mathrm{Tab}(i - w_s - w_d,i + w_s).Loss \\end{array}\\) \nend \nProbability-weighted ray sampling: \\(\\mathrm{Rays}_{cur}\\) Rays prev \\(\\leftarrow \\mathbf{F}_{cur},\\mathbf{F}_{prev}; / / \\mathrm{Sec.}3.4.3\\) \nRay rendering: \\(\\hat{\\mathbf{L}} (\\mathbf{m},t_{\\beta}) - \\hat{\\mathbf{L}} (\\mathbf{m},t_{\\alpha});\\) // Sec. 3.3 \nEvent accumulation: \\(\\sum_{t_k = t_{cur}}^{t_k = t_{prev}}p_kC;\\) \nCalculate loss: \\(\\mathcal{L}_{ev},\\mathcal{L}_{rgb},\\mathcal{L}_d,\\mathcal{L}_{sdf},\\mathcal{L}_{fs};\\) // Eqs. (13) to (15) \nTab(i) \\(\\leftarrow \\{\\mathcal{L}_{total},cur,prev\\}\\) \nend \n13 end" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.685, + 0.411, + 0.7 + ], + "angle": 0, + "content": "3.4.3 Probability-weighted Sampling Strategy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.822 + ], + "angle": 0, + "content": "To take advantage of hybrid multimodality and reduce computational costs, we propose to utilize the RGB loss to guide ray sampling in the event plane. As shown in Fig. 5, the algorithm starts by dividing the RGB image into \\( h \\times w \\) patches and randomly sampling \\( \\mathbf{N}_c \\) rays from each patch to obtain the loss for each sample. Then, we calculate the average loss of each patch and project the center \\( \\mathbf{m}_c \\) to a downsampled mini-plan plane of the event camera:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.824, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\mathbf {m} = \\frac {1}{Z _ {e}} \\mathbf {K} _ {m} \\left[ \\mathbf {I} _ {3 \\times 3} | \\mathbf {0} _ {3 \\times 1} \\right] \\left[ \\begin{array}{c} \\mathbf {T} _ {e c} \\mathbf {K} ^ {- 1} \\mathbf {m} Z _ {c} \\\\ 1 \\end{array} \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(Z_{c}\\) and \\(Z_{e}\\) are the depths of two planes, \\(\\mathbf{K}_m\\) is the intrinsic of event mini-plane, and \\(\\mathbf{T}_{ec}\\) denotes the transformation between cameras. We apply the bilinear interpolation" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.06, + 0.856, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.21, + 0.892, + 0.252 + ], + "angle": 0, + "content": "Figure 5. Illustration of the proposed probability-weighted sampling strategy. We utilize the loss of the RGBD plane (left) to guide ray sampling in the event plane (right)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.259, + 0.892, + 0.331 + ], + "angle": 0, + "content": "tion to compute the loss for each pixel in the mini-plan. Finally, the divided patches of the event plane query the loss \\(\\{\\mathcal{L}_e^q\\}_{q = 0}^Q\\) from the mini-plane and sample rays with probability distribution \\(f(j) = \\frac{\\mathcal{L}_e^q}{\\sum_{q = 1}^Q\\mathcal{L}_e^q}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.331, + 0.694, + 0.346 + ], + "angle": 0, + "content": "3.4.4 Objective Functions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.426 + ], + "angle": 0, + "content": "According to the EGM in Eq. (5), although it is not possible to directly model the luminance signals supervision, the logarithmic brightness differences \\(\\hat{\\mathbf{L}} (\\mathbf{m},t_{\\beta}) - \\hat{\\mathbf{L}} (\\mathbf{m},t_{\\alpha})\\) can be rendered from two camera poses \\(\\mathbf{P}_{\\alpha}\\) and \\(\\mathbf{P}_{\\beta}\\) with Eq. (9). By integrating it with Eqs. (5) and (6), we obtain:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.435, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} (\\mathbf {m}, t _ {\\beta}) - \\mathbf {L} (\\mathbf {m}, t _ {\\alpha}) = \\sum_ {t _ {k} = t _ {\\alpha}} ^ {t _ {k} = t _ {\\beta}} p _ {k} C \\approx \\hat {\\mathbf {L}} (\\mathbf {m}, t _ {\\beta}) - \\hat {\\mathbf {L}} (\\mathbf {m}, t _ {\\alpha}). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.481, + 0.89, + 0.511 + ], + "angle": 0, + "content": "Thus, we establish the relation between events and rendering, and define event reconstruction loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.522, + 0.891, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {e v}} \\left(t _ {\\beta}, t _ {\\alpha}\\right) = \\operatorname {M S E} \\left(\\sum_ {t _ {k} = t _ {\\alpha}} ^ {t _ {k} = t _ {\\beta}} p _ {k} C - \\hat {L} (\\mathbf {m}, t _ {\\beta}) + \\hat {L} (\\mathbf {m}, t _ {\\alpha})\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.627 + ], + "angle": 0, + "content": "In our implementation, we perform a normalization on Eq. (13) to eliminate \\(C\\) when it is unavailable. The color and depth rendering losses [58] in a valid ray batch \\(R\\) between the rendering and observations are also utilized:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.636, + 0.891, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r g b}} = \\frac {1}{| R |} \\sum_ {\\mathbf {r} \\in \\mathbf {R}} (\\hat {\\mathbf {e}} (\\mathbf {r}, \\Delta t _ {c})) - c (\\mathbf {r})) ^ {2}, \\mathcal {L} _ {\\mathrm {d}} = \\frac {1}{| R |} \\sum_ {\\mathbf {r} \\in \\mathbf {R}} (\\hat {d} (\\mathbf {r}) - d (\\mathbf {r})) ^ {2}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.752 + ], + "angle": 0, + "content": "where \\(c(\\mathbf{r})\\) and \\(d(\\mathbf{r})\\) are the ground truth color and depth. To achieve an accurate geometry reconstruction, we apply the approximated SDF loss and free-space loss [58] to sampled point \\(\\mathbf{x}\\) near the surface \\((S_r^{tr} = \\{\\mathbf{x} \\mid |d(\\mathbf{r}) - d(\\mathbf{x})| \\leq tr\\})\\) and far from the surface \\((S_r^{fs} = \\{\\mathbf{x} \\mid |d(\\mathbf{r}) - d(\\mathbf{x})| > tr\\})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.755, + 0.892, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s d f} = \\frac {1}{| R |} \\sum_ {r \\in R} \\frac {1}{| S _ {r} ^ {t r} |} \\sum_ {\\mathbf {x} \\in S _ {r} ^ {t r}} \\left(\\mathbf {x} - \\left(\\hat {d} (\\mathbf {r}) - d (\\mathbf {r})\\right)\\right) ^ {2}, \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.792, + 0.767, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f s} = \\frac {1}{| R |} \\sum_ {r \\in R} \\frac {1}{\\left| S _ {r} ^ {f s} \\right|} \\sum_ {\\mathbf {x} \\in S _ {r} ^ {f s}} (\\mathbf {x} - t r) ^ {2}.\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.588, + 0.845 + ], + "angle": 0, + "content": "4. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To our knowledge, there is currently no SLAM dataset that satisfactorily tackles challenges posed by strong motion blur and lighting variations while encompassing RGBD and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19588" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.058, + 0.882, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.298, + 0.893, + 0.34 + ], + "angle": 0, + "content": "Figure 6. Overview of the DEV-Indoors and DEV-Reals datasets. DEV-Indoors is obtained through Blender [6] and simulator [14], covering normal, motion blur, and dark scenes, providing 9 subsets with RGB images, depth maps, event streams, meshes, and trajectories. DEV-Reals is captured from real scenes, providing 8 challenging subsets under motion blur and lighting variation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.468 + ], + "angle": 0, + "content": "event streams for NeRF-based SLAM. Common datasets lack depth [19] or ground truth meshes [61]. Additionally, they are primarily focused on outdoor scenes [65], without significant motion blur [4] or lighting variation [30]. Therefore, in this paper, we construct simulated Dynamic Event RGBD Indoor (DEV-Indoors) and Dynamic Event RGBD Real captured (DEV-Reals) datasets, as shown in Fig. 6. Besides, we use Vector [13] dataset for evaluation as well." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.469, + 0.47, + 0.558 + ], + "angle": 0, + "content": "1) DEV-Indoors is rendered from 3 Blender [6] models: #room, #apartment, and #workshop. We generated 9 subsets containing high-quality color images, depth, meshes, and ground truth trajectories by varying the scene lighting and camera exposure time. The events are further generated via the events simulator [14]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.56, + 0.47, + 0.65 + ], + "angle": 0, + "content": "2) Dev-Reals is captured from 3 real scenes: #Pioffice, #Garage and #Dormitory. Our capture system comprises a LiDAR (for ground truth pose), a Realsense D435I RGBD camera, and a DAVIS346 event camera. Eight subsequences are captured by modifying the lighting conditions and camera movement speed in the environment." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.202, + 0.681 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.809 + ], + "angle": 0, + "content": "Baselines. To the best of our knowledge, there is currently no event-based RGBD dense vSLAM with available public code that can be directly compared with our method. We opt EVO [43], ESVO [69], USLAM [57] as a reference from the most relevant event-based methods [5, 12, 19, 28, 61, 72]. We also compare our method with the existing SOTA NeRF-based methods: iMAP [52], NICE-SLAM [71], CoSLAM [58], and ESLAM [23]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Metric. We use the absolute trajectory error [51] (ATE) (cm) to measure the localization accuracy. For map reconstruction, we use the 2D Depth L1 (cm) [71], 3D accuracy (cm), completion (cm), and completion ratio \\((\\%)\\) to measure the scene geometry with mesh culling [1, 23]. The evaluation datasets are generated by randomly conducting 2000" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Table 1. Tracking (ATE RSME [cm]) comparison on DEV-Indoors. Our method outperforms previous works, demonstrating its robustness under motion blur and luminance variation." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.392, + 0.89, + 0.478 + ], + "angle": 0, + "content": "
Method#Rnm#Rm blur#Rnm dark#Apt norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]41.0850.5870.7725.7514.411.06e5276.91891.86345.21214.57
NICE-SLAM [71]17.0629.5430.5325.1744.2248.28X94 %X33 %X33%32.47
CoSLAM[58]10.7110.8826.6410.0213.0330.757.9614.3717.8815.80
ESLAM [23]10.7215.5540.429.9912.7912.397.0115.077.9714.66
Ours9.629.729.948.628.779.216.747.516.948.56
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.488, + 0.891, + 0.532 + ], + "angle": 0, + "content": "poses and depths in Blender [6]. We run all the methods 5 times and report the average results or \\(X + \\) tracking success ratio if a method crashes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.892, + 0.745 + ], + "angle": 0, + "content": "Implementation Details. EN-SLAM is implemented in Python and trained on a desktop PC with a 5.50GHz Intel Core i9-13900K CPU and NVIDIA RTX 4090 GPU. We run EN-SLAM at 17 FPS and sample 1024 and 2048 rays in tracking and BA stages with 10 iterations by default. The event joint global BA is performed every 5 frames with \\(5\\%\\) of pixels from all keyframes. The model is trained using Adam optimizer with learning rate \\(lr_{rot} = 1e^{-3}, lr_{trans} = 1e^{-3}\\), and loss weights \\(\\lambda_{ev} = 0.05, \\lambda_{rgb} = 5.0, \\lambda_d = 0.1\\). Default window \\(w_d\\) and neighborhood window are set as 5 and 2, respectively. The exposures of RGB and event cameras are \\(5.21e^{-5}\\) in DEV-Indoors. We use two sigmoid functions to fit the exposures if they are unavailable. Detailed settings can be found in the supplemental materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.822, + 0.772 + ], + "angle": 0, + "content": "5.1. Evaluation of Tracking and Mapping" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation on DEV-Indoors. We report the trajectory accuracy and reconstruction quality in Tab. 1 and Tab. 2. As shown in Tab. 1, EN-SLAM performs the best in all 9 scenes and remains stable (fluctuation below 0.8) under all the blur and dark sequences. While the others perform sensitive and unstable when facing non-ideal environments, especially iMAP [52] and NICE-SLAM [71], which completely crushes in the blur and dark scenes. ESLAM [71]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19589" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.056, + 0.894, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.223, + 0.893, + 0.251 + ], + "angle": 0, + "content": "Figure 7. Reconstruction Performance on DEV-Indoors. EN-SLAM achieves, on average, more precise reconstruction details than existing methods in motion blur and lighting varying environments with the assistance of high-quality event streams." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.255, + 0.47, + 0.282 + ], + "angle": 0, + "content": "Table 2. Reconstruction Performance [cm] of the proposed method vs. the state-of-the-art methods on DEV-Indoors dataset." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.286, + 0.467, + 0.485 + ], + "angle": 0, + "content": "
MethodMetric#Rm norm blur#Rm dark#Rm norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]Acc↓37.1637.6034.3025.5544.28854.4756.4051.7438.12
Comp↓48.6955.9733.7619.2823.9449.6165.4027.1847.11
Comp Ratio↑37.5637.7639.1160.0346.2742.5612.1448.4440.41
Depth L1↓79.9397.9864.9640.36128.45140.00131.79115.07124.69
NICESL AM [71]Acc↓18.4918.8616.6921.2716.5119.1726.3522.0928.40
Comp↓20.2621.9321.4320.6718.7021.2928.0449.8277.19
CompRatio↑60.4059.0358.1459.6063.4956.5550.9146.0035.58
Depth L1↓40.5942.0940.2641.5424.0034.8962.48104.20106.09
CoSLAM [58]Acc↓10.6611.3612.7715.4716.4230.7113.0217.5919.85
Comp↓13.2412.4412.2314.0915.3621.6713.9218.2619.46
Comp Ratio↑69.2276.8777.2670.6166.7555.2667.9261.2660.70
Depth L1↓24.7820.9120.6532.2935.9064.1428.6939.1742.85
ESLA M [23]Acc↓9.488.5811.8112.8616.2514.859.0110.0110.02
Comp↓7.947.547.088.51112.3710.408.8910.9510.44
Comp Ratio↑84.6085.6986.7082.9371.5380.9083.1780.0281.64
Depth L1↓15.3412.2719.0811.0727.8015.5030.0329.0628.02
OursAcc↓7.4810.537.079.469.919.349.239.289.25
Comp↓7.7012.517.709.879.289.619.959.929.92
Comp Ratio↑83.0074.4884.2685.3683.4084.0182.2782.3882.35
Depth L1↓15.1023.3611.9218.8611.9419.2123.1623.1423.39
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.501, + 0.469, + 0.528 + ], + "angle": 0, + "content": "Table 3. Tracking comparison (ATE median [cm]) of the proposed method vs. the state-of-the-art methods on DEV-Reals." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.531, + 0.468, + 0.594 + ], + "angle": 0, + "content": "
MethodPio1Pio2Gre1Gre2dorm1dorm2dorm3dorm4avg
ORBSLAM [19]x63%x63%x63%x63%x63%x63%x63%x63%x63%
NICE-SLAM [71]13.2123.35x63%x25%24.6910.6818.4444.04x22.40
COSLAM [58]11.1419.8382.5240.1615.9915.4230.1232.4530.95
ESLAM [23]11.2821.4263.6530.7537.9431.0416.1937.9131.27
Ours8.9419.0543.6321.1811.2611.9116.0019.7818.97
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.775 + ], + "angle": 0, + "content": "and CoSLAM [58] exhibit similar trends but achieve relatively stable results. Specifically, in #room sequences, they achieved 1.02 and 1.45 times the error on the blur subset and 2.49 and 3.77 times the error on the dark subset, respectively. The reconstruction quality in Tab. 2 and Fig. 7 show that EN-SLAM performs more accurately and robustly than the other methods. Specifically, our method reduces the error by 2.37, 0.48, and 1.90 in ACC, Comp, and Depth L1 compared with the second ESLAM [23]. Fig. 7 also shows that our method reconstructs the details of the scenes more accurately and produces fewer artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Evaluation on DEV-Reals. Tab. 3 illustrates the tracking performance of our method and the state-of-the-art methods on the DEV-Reals dataset. Our method achieves the best performance in all the scenes (18.97), and the average error is 1.63 times lower than the second-best CoSLAM [58] (30.95). Note that DEV-Reals is challenging due to the large motion and varying light, leading to the crushes of ORBSLAM [36] and NICE-SLAM [71]." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.255, + 0.892, + 0.282 + ], + "angle": 0, + "content": "Table 4. Tracking comparison (ATE mean [cm]) of the proposed method vs. the Event-based SLAM system on Vector[13] dataset." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.285, + 0.891, + 0.363 + ], + "angle": 0, + "content": "
Methodrobot normrobot fastdesk normdesk fastsofa normsofa fasthdr normhdr fastall avg
EVO [43]3.25✘✘✘✘✘✘✘3.25
ESVO [69]✘✘✘✘1.77✘✘✘1.77
USLAM [57] (EVIO)1.181.652.241.085.742.545.692.612.84
CoSLAM [58] (DV)1.00124.691.7697.651.7477.891.471.4238.45
ESLAM [23] (DV)1.393.302.543.647.9919.037.3812.237.19
Ours (EDV)1.061.731.762.692.021.841.031.221.67
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.554, + 0.363, + 0.838, + 0.372 + ], + "angle": 0, + "content": "E: event, V: RGB or gray image, D: depth, I: IMU, S: stereo, O: odometry, X: crashes." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.378, + 0.892, + 0.407 + ], + "angle": 0, + "content": "Table 5. Run-time comparison on DEV-Indoors. EN-SLAM is comparable to the most efficient ESLAM and keeps lightweight." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.409, + 0.891, + 0.472 + ], + "angle": 0, + "content": "
MethodTracking [ms×it] ↓Mapping [ms×it] ↓FPS ↑#para.
iMAP [52]24.73×5041.18×3000.360.22 M
NICE-SLAM [71]6.46×1626.42×1201.555.86 M
CoSLAM[58]6.08×1513.52×1511.261.71 M
ESLAM [23]5.20×1316.68×1014.777.85 M
Ours5.75×1013.16×1017.401.95 M
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.476, + 0.673, + 0.492 + ], + "angle": 0, + "content": "5.2. Runtime Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.621 + ], + "angle": 0, + "content": "We evaluate all the frameworks on an NVIDIA RTX 4090 GPU and report average tracking and mapping iterations spending, FPS, and parameters number of the model in Tab. 5. The experimental results indicate that our method is fast, with an average of 17 FPS, comparable to the currently most efficient ESLAM [23]. Meanwhile, our method remains lightweight, with only 1.95M parameters, yet achieves the best accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.727, + 0.648 + ], + "angle": 0, + "content": "5.3. Evaluation of Rendering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.806 + ], + "angle": 0, + "content": "We compare the rendering performance in Fig. 5.3 (left), EN-SLAM outperforms most SOTA works in image quality. The thumbnails in Fig. 5.3 (right) show that EN-SLAM achieves more precise rendering details than previous methods. Specifically, on #Rm Blur, EN-SLAM yields more refined results, while CoSLAM and ESLAM exhibit ghosting. Note that in #Rm Dark and #Wkp Dark, all the RGB rendering is dark and blurred, while our method can still generate high-quality luminance results with the assistance of the HDR event stream." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.654, + 0.833 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Effect of event and RGB modalities. Fig. 9 illustrates quantitative evaluation using ETA in tracking and mapping. Our full model achieve lower tracking error of 9.61 and 15.47 than the model w/o ETA in tracking (10.73 and 17.07)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19590" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.056, + 0.905, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.895, + 0.276 + ], + "angle": 0, + "content": "Figure 8. Rendering Performance on DEV-Indoors. left): Our method outperforms most previous works in image quality evaluation under non-ideal environments. right): EN-SLAM achieves more precise rendering details on average than previous methods." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.287, + 0.465, + 0.392 + ], + "angle": 0, + "content": "
Tracking EventMapping Event#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
XX11.898.6110.9876.3114.4618.75
X✓10.738.329.5381.8314.1717.07
✓X11.688.2810.2879.0516.0919.72
✓✓9.617.887.5983.5111.9115.47
RGB 1st-2nd only10.929.029.1582.8113.5217.80
W/o RGB12.0711.1211.0576.2722.5026.48
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.394, + 0.209, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.395, + 0.338, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.395, + 0.465, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.513, + 0.47, + 0.541 + ], + "angle": 0, + "content": "Figure 9. Ablation study of modalities on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.47, + 0.664 + ], + "angle": 0, + "content": "and mapping (11.68 and 19.72) on the #Rm blur and #Dorm2, respectively. The results also show that the full model surpasses the model w/o ETA by 0.73 and \\(3.39\\%\\) in ACC and completion. In addition, the RGB is also critical, but with the initialization of RGB in 2 frames, the performance is significantly improved, benefiting from the CRF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Effect of CRF and probability-weighted sampling. Fig. 9 show the performance of differentiable CRF and probability-weighted sampling strategy (PWS). The system without CRF might suffer from the distinct event and RGB imaging process, resulting in fluctuating training and poor performance, especially in real datasets. It significantly reduces the tracking ATE RSME from 30.18 to 15.47 in #Drom2 and reconstruction completion from 9.78 to 7.59 in #Rm blur. The results also show that the full model surpasses the model w/o PWS by 0.25 and \\(1.9\\%\\) in ATE and completion on #Rm blur. A visualization of CRF is shown in Fig. 10, on dark scene #Drom2, the model with CRF renders HDR luminance results and accurate mesh benefiting from events. In contrast, the model w/o CRF suffers from the low dynamic range RGB input." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.287, + 0.888, + 0.359 + ], + "angle": 0, + "content": "
Setting#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
w/o CRF12.128.299.7883.5727.6730.18
w/o PWS9.867.889.4981.0416.5919.78
Full model9.617.887.5983.5111.9115.47
" + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.361, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Table 6. Ablation study of CRF and PWS on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations)." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.39, + 0.892, + 0.547 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.55, + 0.866, + 0.564 + ], + "angle": 0, + "content": "Figure 10. CRF ablation on the #Dorm2 of DEV-Reals." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.75, + 0.59 + ], + "angle": 0, + "content": "6. Conclusion and Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.823 + ], + "angle": 0, + "content": "This paper first integrates the event stream into the implicit neural SLAM framework to overcome challenges in scenes with motion blur and lighting variation. A differentiable CRF rendering technique that maps the unified representation to color and luminance is proposed to address the significant distinction between event and RGB. An event temporal aggregating optimization strategy that capitalizes the consecutive difference constraints of events is presented to enhance the optimization. We construct DEV-Indoors and DEV-Reals datasets to evaluate the effectiveness of EN-SLAM under various environments. However, EN-SLAM relies on depth input, which might be unavailable in some scenarios. Besides, EN-SLAM focuses on indoor scenes and might face challenges in boundless long trajectories. In future work, we aim to extend it to large-scale outdoor environments and enhance the generalization capability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by the Shanghai AI Laboratory, National Key R&D Program of China (2022ZD0160101), the National Natural Science Foundation of China (62376222), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19591" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. In CVPR, pages 6290-6301, 2022. 4, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.472, + 0.212 + ], + "angle": 0, + "content": "[2] Christian Brändli, Jonas Strubel, Susanne Keller, Davide Scaramuzza, and Tobi Delbruck. 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IEEE, 2022. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "19594" + } + ] +] \ No newline at end of file diff --git a/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_origin.pdf b/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e9ea598331cd6e9342b8bdfc7188f16773432649 --- /dev/null +++ b/2024/Implicit Event-RGBD Neural SLAM/f9bb5455-cdd9-4999-bf90-4f084d0f2dbb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:05a73e81293b61406bb794c9d8ec38b23a1f3f83c604d40b7a27fe1c17299b75 +size 8937120 diff --git a/2024/Implicit Event-RGBD Neural SLAM/full.md b/2024/Implicit Event-RGBD Neural SLAM/full.md new file mode 100644 index 0000000000000000000000000000000000000000..6df1f9c6b98d4418689ff14169dc09171ed235fe --- /dev/null +++ b/2024/Implicit Event-RGBD Neural SLAM/full.md @@ -0,0 +1,395 @@ +# Implicit Event-RGBD Neural SLAM + +Delin $\mathrm{Qu}^{1,2*}$ Chi Yan $^{2,5*}$ Dong Wang $^{2}$ Jie Yin $^{3}$ Qizhi Chen $^{2}$ + +Dan Xu5 Yiting Zhang2 Bin Zhao2,4† Xuelong Li2 + +$^{1}$ Fudan University $^{2}$ Shanghai AI Laboratory $^{3}$ Shanghai Jiao Tong University $^{4}$ Northwestern Polytechnical University $^{5}$ Hong Kong University of Sciences and Technology + +# Abstract + +Implicit neural SLAM has achieved remarkable progress recently. Nevertheless, existing methods face significant challenges in non-ideal scenarios, such as motion blur or lighting variation, which often leads to issues like convergence failures, localization drifts, and distorted mapping. To address these challenges, we propose EN-SLAM, the first event-RGBD implicit neural SLAM framework, which effectively leverages the high rate and high dynamic range advantages of event data for tracking and mapping. Specifically, EN-SLAM proposes a differentiable CRF (Camera Response Function) rendering technique to generate distinct RGB and event camera data via a shared radiance field, which is optimized by learning a unified implicit representation with the captured event and RGBD supervision. Moreover, based on the temporal difference property of events, we propose a temporal aggregating optimization strategy for the event joint tracking and global bundle adjustment, capitalizing on the consecutive difference constraints of events, significantly enhancing tracking accuracy and robustness. Finally, we construct the simulated dataset DEV-Indoors and real captured dataset DEV-Reals containing 6 scenes, 17 sequences with practical motion blur and lighting changes for evaluations. Experimental results show that our method outperforms the SOTA methods in both tracking ATE and mapping ACC with a real-time 17 FPS in various challenging environments. Project page: https://delinqu.github.io/EN-SLAM. + +# 1. Introduction + +Simultaneous Localization and Mapping (SLAM) is an essential problem in computer vision and robotics, widely applied in tasks such as virtual and augmented reality [8], robot navigation [18] and autonomous driving [3] over last decades. Exploration in extreme environments [10, 31, 41] + +![](images/f617a732afa89f05f8e03b8200347a7d2f2710ca08a85621e96a446373edda81.jpg) +Figure 1. Illustration of the proposed implicit event-RGBD neural SLAM system EN-SLAM under non-ideal environments. The dynamic range of RGB sensors is relatively low and suffers from motion blur. Instead, event cameras show great potential in non-ideal environments due to their high dynamic range and low latency advantages. Our method samples rays from two independent RGBD and event cameras to jointly train a single implicit neural field with both modalities. This hybrid shared mechanism provides a natural fusion approach, avoiding alignment issues. It also leverages the advantages of both modalities, resulting in dense, more robust, and higher-quality reconstruction results. + +remains challenging for visual SLAM (vSLAM) systems due to the lack of visual features caused by motion blur and lighting variation in diverse environments [42, 59, 68]. + +As a novel representation for myriad of signals, Neural Radiance Fields (NeRF) [35] has innovated great progress in SLAM recently, demonstrating significant improvements in map memory consumption, hole filling, and mapping quality [23, 49, 52, 58, 67, 71]. While the existing NeRF-based neural vSLAM methods address the limitations of traditional SLAM frameworks [11, 36, 37, 50, 62] in accurate dense 3D map reconstruction, they are primarily designed for well-lit scenes and always fail in practical SLAM scenarios with motion blur [40, 66] and lighting variation [32, 48]. These methods produce unsatisfying results under non-ideal environments [58] because of the following limitations: 1) View-inconsistency: When the camera encounters rapid velocity variation in Fig. 2 (2nd), the scene may exhibit discontinuous blur, leading to view + +inconsistency among frames, further causing heavy artifacts in the reconstructed map. 2) Low dynamic range: In light- ing variation scenes illustrated in Fig. 1, the dynamic range of the RGB sensor is relatively low, and the information on the dark and overexposure areas is lost, leading to tracking drifts and mapping distortions. + +To address the issues in non-ideal scenarios of existing neural vSLAM, we introduce utilizing the advantages of high dynamic range (HDR) and temporal resolution of event data to compensate for the lost information, thereby improving the robustness, efficiency, and accuracy of current neural vSLAM in extreme environments. Fig. 2 shows the event generation model that an event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold $C$ . This asynchronous mechanism shows excellent potential in non-ideal environments due to its advantages in low latency [26, 43, 70], high dynamic range [46], and high temporal resolution [54, 55]. Fig. 1 and Fig. 2 illustrate its superiority in dark and fast motion, and event sensors capture higher-quality signals than RGB sensors. However, applying events into NeRF-based vSLAM is challenging due to the significant distinction in imaging mechanisms between event and RGB cameras. Moreover, the requirement of highly accurate camera poses and careful optimization in traditional surface density estimation [32] further complicates the integration. + +In order to overcome these obstacles, we present EN-SLAM, the first event-RGBD implicit neural SLAM framework that effectively harnesses the advantages of event and RGBD streams. The overview of EN-SLAM is shown in Fig. 3. Our method models the differentiable imaging process of two distinct cameras and utilizes shared radiance fields to jointly learn a hybrid unified representation from events and RGBD data. By integrating the event generation model into the optimization process, we introduce the event temporal aggregating (ETA) optimization strategy for event joint tracking and global bundle adjustment (BA). This strategy effectively leverages the temporal difference property of events, providing efficient consecutive difference constraints and significantly improving the performance. Additionally, we construct two datasets: the simulated dataset DEV-Indoors and the real captured dataset DEV-Reals, which consist of 6 scenes and 17 sequences with practical motion blur and lighting changes. Contributions can be summarized as follows: + +- We present EN-SLAM, the first event-RGBD implicit neural SLAM framework that efficiently leverages event stream and RGBD to overcome challenges in extreme motion blur and lighting variation scenes. +- A differentiable CRF rendering technique is proposed to map a unified representation in the shared radiance field to RGB and event camera data for addressing the significant distinction between event and RGB. A tempo + +![](images/5eda0534f83d893336a8913d4b67e644443e6b5987b62cc8f3c4add304a3db46.jpg) +Figure 2. Illustration of the Event Generation Model (EGM). An event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold $C$ . + +![](images/d7aea2a7d9978f6101535ff0a9a5c1d1e5cc32a68699e5f1d6a11ca807c8e311.jpg) + +![](images/ded92d95b63f77ffd09b5faed2cfb1b7f81e3187d3b4931802090d6bbd7cb755.jpg) + +ral aggregating optimization strategy that capitalizes the consecutive difference constraints of the event stream is present and significantly improves the camera tracking accuracy and robustness. + +- We construct a simulated DEV-Indoors and real captured DEV-Reals dataset containing 17 sequences with practical motion blur and lighting changes. A wide range of evaluations demonstrate competitive real-time performance under various challenging environments. + +# 2. Related Work + +Neural Implicit vSLAM. Existing NeRF-based visual SLAM methods have made significant improvements in dense map reconstruction. iMAP [52] first introduces NeRF into SLAM, and NICE-SLAM [71] expands the reconstructable environment size by introducing multiscale feature grids. Vox-Fusion [64] utilizes an octree-based structure to expand the scene dynamically. Besides, CoSLAM [58] combines coordinate and sparse parametric encoding to achieve fast convergence and surface hole filling in reconstruction. Parallel works ESLAM [23] and Point-SLAM [49] represent scenes as multi-scale feature planes and neural point clouds, respectively, to improve the efficiency and accuracy. Beyond NeRF, GS-SLAM [63] utilizes 3D Gaussian [24] for scene representation and achieves photo-realistic reconstruction performance. However, these methods are designed for well-lit indoor scenes and commonly encounter challenges in non-ideal SLAM processes, such as motion blur and lighting variation. In contrast, we introduce utilizing the advantages of high dynamic range and temporal resolution of events to compensate for the lost information, thereby improving the robustness and accuracy of current neural implicit methods. + +Event-based SLAM. Events have been incorporated into traditional visual SLAM systems to address the motion blur and lighting variation. These methods can be divided into three main types: feature-based methods, direct methods, and motion-compensation methods. Feature-based methods, such as USLAM [57], EIO [16] and PL-EVIO [17], track point or line features from event data [29, 44], and perform the camera tracking and mapping in parallel threads. However, the feature extraction algorithms [2, 33, 47, 56] rely heavily on frame-based feature detection, facing chal + +![](images/838ff965dadfec0fef34dbb47d8f7c0a1349be1760dc0b4b55b361d27817b074.jpg) +Figure 3. Overview of EN-SLAM. EN-SLAM decodes the scene encoding to a shared geometry and radiance representation, and decomposes the radiance into RGB color $\mathbf{c}(\mathbf{x})$ and event luminance $\mathbf{l}(\mathbf{x})$ via differentiable CRF Mappers. We iteratively optimize the pose and scene representation by minimizing losses, in tracking and global BA with the event temporal aggregating techniques in Algorithm 1. + +lenges for motion-dependent event data appearance. Direct methods employ events without explicit data association by aligning the photometric event image [19, 25, 26] or utilizing the spatiotemporal information for event representations alignment [43, 45, 70]. Direct methods are well suited for events, but mainly focus on event-based visual odometry, leaving the visual dense mapping unexplored. Motion-compensation methods optimize event alignment in motion-compensated event frames by maximizing the contrast [39, 60], minimizing the dispersion [38] and align probabilistic [15]. However, they suffer from the collapse in a broad range of camera motions. Thus, currently, event-based SLAM demonstrates significant potential but lacks sufficient exploration in dense map reconstructions [20]. + +Neural Radiance Fields using Events. Event-based NeRF is in the nascent stages, and several studies have demonstrated the possibility of view synthesis from events via implicit neural fields. Event-NeRF [48] proposes an approach for inferring NeRF from a monocular color event stream that enables novel view synthesis. E-NeRF [27] and $\mathrm{E}^2\mathrm{NeRF}$ [40] tackle the NeRF estimation from event cameras under strong motion blur. They develop normalized and rendering loss to address varying contrast thresholds and enhance neural volumetric representation. The parallel work Ev-NeRF [22] conducts a threshold-bound loss with the ReLU function to address the lack of RGB images. In addition to reconstruction, $\Delta_t$ NeRF [34] proposes an event camera tracker by minimizing the error between sparse events and the temporal gradient of the scene representation on the simplified intensity-change events. However, the traditional surface density estimation in NeRF requires highly accurate camera poses and careful optimization [32], thus making it exceptionally challenging to apply NeRF to the event-based SLAM. + +# 3. Methodology + +The overview of our method is shown in Fig. 3. Given an input RGBD stream $\{\mathbf{I}_i, \mathbf{D}_i\}_{i=1}^J$ and event stream $\{\mathbf{E}_k\}_{k=1}^N$ with known camera intrinsics $\mathbf{K} \in \mathbb{R}^{3 \times 3}$ and $\mathbf{K}' \in \mathbb{R}^{3 \times 3}$ , we aim to leverage event and RGBD to reconstruct the cam + +era poses $\{\mathbf{P}_i\}_{i = 1}^J$ and the implicit scene representation. In Sec. 3.1, the scene encoding is decoded to a unified geometry and radiance representation. Then, the shared radiance is decomposed into RGB color $\mathbf{c}(\mathbf{x})$ and event luminance $\mathrm{l(x)}$ via differentiable CRF Mappers in Secs. 3.2 and 3.3 to address the imaging distinction of event and RGB cameras. Finally, EN-SLAM iteratively optimizes the pose and scene representation by minimizing the re-rendering loss between the observed RGBD-E (RGBD and events) and rendering results in tracking and global BA of Sec. 3.4. + +# 3.1. Unified Implicit Scene Representation + +As shown in Fig. 3, we represent the scene S with multi-resolution geometric features and color grid features: + +$$ +\mathbf {S} = \left\{\left(F _ {\mathbf {x}, \theta} ^ {g}, F _ {\mathbf {x}, \theta} ^ {c}\right) \mid \theta = 1, \dots , \Theta \right\}, \tag {1} +$$ + +where $\mathbf{x}$ and $\theta$ denote the coordinate and resolution level. There are two challenges that hinder us from learning a scene representation from different RGB and event modalities. Firstly, the event data is sparse and records logarithmic changes in luminance. Secondly, different cameras hold distinct physical imaging process mechanisms. Despite this, the geometry and radiance fields remain consistent during the camera imaging. In this case, we propose to learn a shared unified geometry hidden feature $\mathbf{h}_{\mathbf{x}}^{g}$ and radiance representation $\mathbf{e}(\mathbf{x})$ across distinct cameras. The geometric grid feature $F_{\mathbf{x},\theta}^{g}$ and color feature $F_{\mathbf{x},\theta}^{c}$ are simultaneously mapped to geometry hidden vector $\mathbf{h}_{\mathbf{x}}^{g}$ , radiance fields $\mathbf{e}(\mathbf{x})$ and TSDF (truncated signed distance function) $\mathbf{s}(\mathbf{x})$ , by a geometry decoder $\pmb{f}_{g}$ : + +$$ +\boldsymbol {f} _ {\boldsymbol {g}} \left(F _ {\mathbf {x}, \theta} ^ {g}, F _ {\mathbf {x}, \theta} ^ {c}\right) \mapsto \left(\mathbf {h} _ {\mathbf {x}} ^ {g}, \mathbf {e} (\mathbf {x}), \mathbf {s} (\mathbf {x})\right). \tag {2} +$$ + +The geometry hidden vector $\mathbf{h}_{\mathbf{x}}^{g}$ and radiance fields $\mathbf{e}(\mathbf{x})$ are shared by the color and event CRF decoders. + +# 3.2. Decomposition of the Radiance Fields + +In standard imaging devices, the incoming radiance undergoes linear and nonlinear image processing before being mapped into pixel values and stored in images. This entire + +image processing can be represented by a single function $f_{c}$ called the camera response function (CRF) [9]. However, the traditional NeRF method [35] simplifies the imaging process, leading to discrepancies between the rendering and actual images. This deviation is further amplified in multi-modal implicit representations. As Fig. 10 shows, the captures of RGB and event cameras are significantly distinct, which can lead to joint optimization fluctuation. To address this issue, we model the radiance $\mathbf{e}(\mathbf{x})$ and exposure $\Delta t_{c}$ of a ray $\mathbf{r}$ but take the aperture and others as implicit factors to obtain the color field $\mathbf{c}(\mathbf{x})$ [21, 53] by differentiable tone-mapping: + +$$ +\mathbf {c} (\mathbf {x}) = \boldsymbol {f} _ {c} \left(\mathbf {e} (\mathbf {x}) \Delta \mathbf {t} _ {c}\right). \tag {3} +$$ + +To facilitate optimization, we convert all numerical values into the logarithmic domain and present the inverse function of $\left(\ln f_c^{-1}\right)^{-1}$ as $\Psi_{\mathrm{c}}$ : + +$$ +\begin{array}{l} \mathbf {c} (\mathbf {x}) = \left(\ln \boldsymbol {f} _ {\boldsymbol {c}} ^ {- 1}\right) ^ {- 1} (\ln \mathbf {e} (\mathbf {r}) + \ln \Delta \mathbf {t} _ {c}) \tag {4} \\ = \boldsymbol {\Psi} _ {\mathbf {c}} (\ln \mathbf {e} (\mathbf {x}) + \ln \Delta \mathbf {t} _ {c}), \\ \end{array} +$$ + +As for the event camera, directly obtaining the event data is not feasible. However, we can predict high dynamic range luminance $l(\mathbf{x})$ and derive events using the event generation model: As shown in Fig. 2, an event $E_{k} = (u_{k}, v_{k}, t_{k}, p_{k})$ at image coordinate $\mathbf{m}_{k} = [u_{k}, v_{k}, 1]^{T}$ is triggered if the corresponding logarithmic brightness change $\mathbf{L}(\mathbf{m}, t)$ exceeds a threshold $C$ : + +$$ +\mathbf {L} \left(\mathbf {m} _ {k}, t _ {k}\right) - \mathbf {L} \left(\mathbf {m} _ {k}, t _ {k - 1}\right) = p _ {k} C, \quad p _ {k} \in \{+ 1, - 1 \}. \tag {5} +$$ + +The logarithmic brightness $\mathbf{L}(\mathbf{m},t)$ can be obtained by: + +$$ +\mathbf {L} (\mathbf {m}, t) = \ln \log \left(\mathbf {I} _ {e} (\mathbf {m})\right) = \left\{ \begin{array}{l l} \mathbf {I} _ {e} (\mathbf {m}) \cdot \ln (B) / B, & \text {i f} \mathbf {I} _ {e} (\mathbf {m}) < B \\ \ln \left(\mathbf {I} _ {e} (\mathbf {m})\right), & \text {e l s e} \end{array} , \right. \tag {6} +$$ + +where $B$ denotes the linear region threshold [7] and the imaging brightness $\mathbf{I}_e(\mathbf{m})$ of event camera equals to the corresponding luminance of ray $\mathbf{r}$ . By applying the modeling approach in Eqs. (3) and (4) to the CRF of an event camera, we establish the relation among the luminance field $l(\mathbf{x})$ , the radiance $\mathbf{e}(\mathbf{x})$ and exposure: + +$$ +l (\mathbf {x}) = \boldsymbol {\Psi} _ {l} \left(\ln \mathbf {e} (\mathbf {x}) + \ln \Delta \mathbf {t} _ {l}\right), \tag {7} +$$ + +where $\Psi_{l}$ and $\Delta \mathbf{t}_l$ denote the luminance tone-mapping and pseudo exposure of the event camera. In this way, we decompose the shared radiance field $\mathbf{e}(\mathbf{x})$ into the RGB and event camera imaging processes through two differentiable tone-mapping processes. + +# 3.3. Differentiable CRF Rendering + +Upon obtaining the color and luminance fields in Sec. 3.2, we render the final imaging RGB, luminance, and depth by integrating predicted values along the samples in a ray $\mathbf{r}$ : + +$$ +\mathbf {x} _ {i} = \mathbf {O} + z _ {i} \mathbf {d}, \quad i \in \{1, \dots , M \}, \tag {8} +$$ + +![](images/b903c1a64e39a737a3d7c5be9205c71bbaa0c1514f37e881e0bfd73a9e23b58c.jpg) +a) Camera k trajectory +Figure 4. The illustration of event temporal aggregating optimization strategy. In the tracking and global BA stages, EN-SLAM adaptively forwards query the previous frame according to the previous index table, and sample rays from different views perform joint optimization in Eq. (13). + +![](images/ac8bbf6c954fe79f12c4947426c19ef4d25e6f9531b11ac822e4a89466ff8f0d.jpg) +b) Previous Index Table + +![](images/8edec6d2aeafff93576b1134e961ddd60fa2d94487a8da2af5ebe04bd0748e67.jpg) +c) Forward ray sampling + +where $\mathbf{O} \in \mathbb{R}^3$ is the camera origin, $\mathbf{d} \in \mathbb{R}^3$ , $\|\mathbf{d}\| = 1$ is the ray direction, and $z_i \in \mathbb{R}$ denotes the depth. Hence, we obtain the final imaging color $\hat{\mathbf{c}}$ , luminance $\hat{l}$ and depth $\hat{d}$ : + +$$ +\begin{array}{l} \hat {\mathbf {c}} (\mathbf {r}, \Delta t _ {c}) = \sum_ {i = 1} ^ {i = M} w _ {i} \boldsymbol {\Psi} _ {\mathbf {c}} \left(\ln \mathbf {e} \left(\mathbf {x} _ {i}\right) + \ln \Delta t _ {c}\right), \\ \hat {l} (\mathbf {r}, \Delta t _ {l}) = \sum_ {i = 1} ^ {i = M} w _ {i} \boldsymbol {\Psi} _ {l} \left(\ln \mathbf {e} \left(\mathbf {x} _ {i}\right) + \ln \Delta t _ {l}\right), \tag {9} \\ \hat {d} (\mathbf {r}) = \sum_ {i = 1} ^ {i = M} w _ {i} z _ {i}. \\ \end{array} +$$ + +We utilize the simple bell-shaped model [1] and compute weights $w_{i}$ by two sigmoid functions $\sigma(\cdot)$ to convert predicted TSDF $\mathbf{s}(\mathbf{x}_i)$ into weight $w_{i}$ : + +$$ +w _ {i} = \sigma \left(\frac {\mathbf {s} \left(\mathbf {x} _ {i}\right)}{t r}\right) \sigma \left(- \frac {\mathbf {s} \left(\mathbf {x} _ {i}\right)}{t r}\right), \tag {10} +$$ + +where $tr$ is the truncation distance of a ray $\mathbf{r}$ . + +# 3.4. Tracking and Bundle Adjustment + +In this section, to leverage the HDR and temporal difference properties of events, we propose an event joint tracking and global BA strategy in Sec. 3.4.1 that incorporates events into optimization, thus improving the accuracy and robustness. Besides, we introduce adaptive forward-query and sampling strategies in Sec. 3.4.2 and Sec. 3.4.3, which select event data and ray samples with more elevated confidence for optimization, thereby boosting the convergence. + +# 3.4.1 Event Temporal Aggregating Optimization + +The overview of ETA is shown in Fig. 4 and Algorithm 1. For tracking, we represent the camera pose $\mathbf{P}_{cur} = \exp (\xi_t^{\wedge})\in \mathbb{S}\mathbb{E}(3)$ of current frame $\mathbf{F}_{cur}$ and initialize with constant assumption. By selecting $N_{t}$ rays within $\mathbf{F}_{cur}$ and performing an adaptive event forward query in Sec. 3.4.2 with a probability-weighted sampling in Sec. 3.4.3, we get the event stream and previous rays. Then, we iteratively optimize the pose by minimizing objective functions. For global BA, $N_{ba}$ rays from the global keyframe + +list are sampled to be the subset of pixels $\{PX_{cur}\}$ . And then, the forward query and probability-weighted sampling are performed for each sample to get the previous subset $\{PX_{prev}\}$ and events $\{E_k\}_{k = prev}^{cur}$ . Finally, a joint optimization is performed to optimize the geometry decoder $f_{g}$ , differentiable CRF $\{\Psi_{\mathbf{c}},\Psi_{l}\}$ , and poses $\{\mathbf{P_i}\}_{i = 0}^{cur}$ . + +# 3.4.2 Adaptive Forward Event Query + +As shown in Fig. 4, ETA performs an adaptive event forward window selection in tracking and BA by constructing a previous index table to prioritize reliable prior frames for optimization. Specifically, ETA uses a default window $w_{d}$ and performs a forward query. If the loss of a queried frame exceeds a threshold $\mathcal{L}_{s}$ , we conduct a shift lookup within a neighborhood of length $2 \times w_{k}$ , selecting the frame with the minimum loss as the forward frame for event loss calculation Eq. (13). This event temporal constraint provides a stable local constraint between the participating frames and effectively leverages the high HDR property of events. + +Algorithm 1: Event temporal aggregating optimization +Input: RGBD-E stream $\{\mathbf{I}_i,d_i\}_{i = 1}^J$ and $\{\mathbf{E}_k\}_{k = 1}^N$ Output: Loss $\{\mathcal{L}_{ev},\mathcal{L}_{rgb},\mathcal{L}_d,\mathcal{L}_{sdf},\mathcal{L}_{fs}\}$ +while $j < J$ do +for $i\in \{j\}$ if not BA else $\{0,1,\dots,j\}$ do /\* Forward Query Sec. 3.4.2 \*/ + $\mathbf{F}_{cur},\mathbf{F}_{prev}\gets \mathrm{Tab}(i),\mathrm{Tab}(i - w_d);$ if $\mathcal{L}_{total} > \mathcal{L}_s$ then + $\begin{array}{rlr}{\bf F}_{prev}^{\min}\leftarrow \mathrm{Tab}(i - w_s - w_d,i + w_s).Loss \end{array}$ +end +Probability-weighted ray sampling: $\mathrm{Rays}_{cur}$ Rays prev $\leftarrow \mathbf{F}_{cur},\mathbf{F}_{prev}; / / \mathrm{Sec.}3.4.3$ +Ray rendering: $\hat{\mathbf{L}} (\mathbf{m},t_{\beta}) - \hat{\mathbf{L}} (\mathbf{m},t_{\alpha});$ // Sec. 3.3 +Event accumulation: $\sum_{t_k = t_{cur}}^{t_k = t_{prev}}p_kC;$ +Calculate loss: $\mathcal{L}_{ev},\mathcal{L}_{rgb},\mathcal{L}_d,\mathcal{L}_{sdf},\mathcal{L}_{fs};$ // Eqs. (13) to (15) +Tab(i) $\leftarrow \{\mathcal{L}_{total},cur,prev\}$ +end +13 end + +# 3.4.3 Probability-weighted Sampling Strategy + +To take advantage of hybrid multimodality and reduce computational costs, we propose to utilize the RGB loss to guide ray sampling in the event plane. As shown in Fig. 5, the algorithm starts by dividing the RGB image into $h \times w$ patches and randomly sampling $\mathbf{N}_c$ rays from each patch to obtain the loss for each sample. Then, we calculate the average loss of each patch and project the center $\mathbf{m}_c$ to a downsampled mini-plan plane of the event camera: + +$$ +\mathbf {m} = \frac {1}{Z _ {e}} \mathbf {K} _ {m} \left[ \mathbf {I} _ {3 \times 3} | \mathbf {0} _ {3 \times 1} \right] \left[ \begin{array}{c} \mathbf {T} _ {e c} \mathbf {K} ^ {- 1} \mathbf {m} Z _ {c} \\ 1 \end{array} \right], \tag {11} +$$ + +where $Z_{c}$ and $Z_{e}$ are the depths of two planes, $\mathbf{K}_m$ is the intrinsic of event mini-plane, and $\mathbf{T}_{ec}$ denotes the transformation between cameras. We apply the bilinear interpolation + +![](images/66fc7c3f3260953042e0804d6047eab3c8f3797db5c526565fcf442cc2bf66af.jpg) +Figure 5. Illustration of the proposed probability-weighted sampling strategy. We utilize the loss of the RGBD plane (left) to guide ray sampling in the event plane (right). + +tion to compute the loss for each pixel in the mini-plan. Finally, the divided patches of the event plane query the loss $\{\mathcal{L}_e^q\}_{q = 0}^Q$ from the mini-plane and sample rays with probability distribution $f(j) = \frac{\mathcal{L}_e^q}{\sum_{q = 1}^Q\mathcal{L}_e^q}$ . + +# 3.4.4 Objective Functions + +According to the EGM in Eq. (5), although it is not possible to directly model the luminance signals supervision, the logarithmic brightness differences $\hat{\mathbf{L}} (\mathbf{m},t_{\beta}) - \hat{\mathbf{L}} (\mathbf{m},t_{\alpha})$ can be rendered from two camera poses $\mathbf{P}_{\alpha}$ and $\mathbf{P}_{\beta}$ with Eq. (9). By integrating it with Eqs. (5) and (6), we obtain: + +$$ +\mathbf {L} (\mathbf {m}, t _ {\beta}) - \mathbf {L} (\mathbf {m}, t _ {\alpha}) = \sum_ {t _ {k} = t _ {\alpha}} ^ {t _ {k} = t _ {\beta}} p _ {k} C \approx \hat {\mathbf {L}} (\mathbf {m}, t _ {\beta}) - \hat {\mathbf {L}} (\mathbf {m}, t _ {\alpha}). \tag {12} +$$ + +Thus, we establish the relation between events and rendering, and define event reconstruction loss as: + +$$ +\mathcal {L} _ {\mathrm {e v}} \left(t _ {\beta}, t _ {\alpha}\right) = \operatorname {M S E} \left(\sum_ {t _ {k} = t _ {\alpha}} ^ {t _ {k} = t _ {\beta}} p _ {k} C - \hat {L} (\mathbf {m}, t _ {\beta}) + \hat {L} (\mathbf {m}, t _ {\alpha})\right). \tag {13} +$$ + +In our implementation, we perform a normalization on Eq. (13) to eliminate $C$ when it is unavailable. The color and depth rendering losses [58] in a valid ray batch $R$ between the rendering and observations are also utilized: + +$$ +\mathcal {L} _ {\mathrm {r g b}} = \frac {1}{| R |} \sum_ {\mathbf {r} \in \mathbf {R}} (\hat {\mathbf {e}} (\mathbf {r}, \Delta t _ {c})) - c (\mathbf {r})) ^ {2}, \mathcal {L} _ {\mathrm {d}} = \frac {1}{| R |} \sum_ {\mathbf {r} \in \mathbf {R}} (\hat {d} (\mathbf {r}) - d (\mathbf {r})) ^ {2}, \tag {14} +$$ + +where $c(\mathbf{r})$ and $d(\mathbf{r})$ are the ground truth color and depth. To achieve an accurate geometry reconstruction, we apply the approximated SDF loss and free-space loss [58] to sampled point $\mathbf{x}$ near the surface $(S_r^{tr} = \{\mathbf{x} \mid |d(\mathbf{r}) - d(\mathbf{x})| \leq tr\})$ and far from the surface $(S_r^{fs} = \{\mathbf{x} \mid |d(\mathbf{r}) - d(\mathbf{x})| > tr\})$ : + +$$ +\mathcal {L} _ {s d f} = \frac {1}{| R |} \sum_ {r \in R} \frac {1}{| S _ {r} ^ {t r} |} \sum_ {\mathbf {x} \in S _ {r} ^ {t r}} \left(\mathbf {x} - \left(\hat {d} (\mathbf {r}) - d (\mathbf {r})\right)\right) ^ {2}, \tag {15} +$$ + +$$ +\mathcal {L} _ {f s} = \frac {1}{| R |} \sum_ {r \in R} \frac {1}{\left| S _ {r} ^ {f s} \right|} \sum_ {\mathbf {x} \in S _ {r} ^ {f s}} (\mathbf {x} - t r) ^ {2}. +$$ + +# 4. Dataset + +To our knowledge, there is currently no SLAM dataset that satisfactorily tackles challenges posed by strong motion blur and lighting variations while encompassing RGBD and + +![](images/c0dc9f2f0e626786168e77c5ea33c84d4260e4ca7596ded2506b4bbba49e736b.jpg) +Figure 6. Overview of the DEV-Indoors and DEV-Reals datasets. DEV-Indoors is obtained through Blender [6] and simulator [14], covering normal, motion blur, and dark scenes, providing 9 subsets with RGB images, depth maps, event streams, meshes, and trajectories. DEV-Reals is captured from real scenes, providing 8 challenging subsets under motion blur and lighting variation. + +event streams for NeRF-based SLAM. Common datasets lack depth [19] or ground truth meshes [61]. Additionally, they are primarily focused on outdoor scenes [65], without significant motion blur [4] or lighting variation [30]. Therefore, in this paper, we construct simulated Dynamic Event RGBD Indoor (DEV-Indoors) and Dynamic Event RGBD Real captured (DEV-Reals) datasets, as shown in Fig. 6. Besides, we use Vector [13] dataset for evaluation as well. + +1) DEV-Indoors is rendered from 3 Blender [6] models: #room, #apartment, and #workshop. We generated 9 subsets containing high-quality color images, depth, meshes, and ground truth trajectories by varying the scene lighting and camera exposure time. The events are further generated via the events simulator [14]. + +2) Dev-Reals is captured from 3 real scenes: #Pioffice, #Garage and #Dormitory. Our capture system comprises a LiDAR (for ground truth pose), a Realsense D435I RGBD camera, and a DAVIS346 event camera. Eight subsequences are captured by modifying the lighting conditions and camera movement speed in the environment. + +# 5. Experiment + +Baselines. To the best of our knowledge, there is currently no event-based RGBD dense vSLAM with available public code that can be directly compared with our method. We opt EVO [43], ESVO [69], USLAM [57] as a reference from the most relevant event-based methods [5, 12, 19, 28, 61, 72]. We also compare our method with the existing SOTA NeRF-based methods: iMAP [52], NICE-SLAM [71], CoSLAM [58], and ESLAM [23]. + +Metric. We use the absolute trajectory error [51] (ATE) (cm) to measure the localization accuracy. For map reconstruction, we use the 2D Depth L1 (cm) [71], 3D accuracy (cm), completion (cm), and completion ratio $(\%)$ to measure the scene geometry with mesh culling [1, 23]. The evaluation datasets are generated by randomly conducting 2000 + +Table 1. Tracking (ATE RSME [cm]) comparison on DEV-Indoors. Our method outperforms previous works, demonstrating its robustness under motion blur and luminance variation. + +
Method#Rnm#Rm blur#Rnm dark#Apt norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]41.0850.5870.7725.7514.411.06e5276.91891.86345.21214.57
NICE-SLAM [71]17.0629.5430.5325.1744.2248.28X94 %X33 %X33%32.47
CoSLAM[58]10.7110.8826.6410.0213.0330.757.9614.3717.8815.80
ESLAM [23]10.7215.5540.429.9912.7912.397.0115.077.9714.66
Ours9.629.729.948.628.779.216.747.516.948.56
+ +poses and depths in Blender [6]. We run all the methods 5 times and report the average results or $X +$ tracking success ratio if a method crashes. + +Implementation Details. EN-SLAM is implemented in Python and trained on a desktop PC with a 5.50GHz Intel Core i9-13900K CPU and NVIDIA RTX 4090 GPU. We run EN-SLAM at 17 FPS and sample 1024 and 2048 rays in tracking and BA stages with 10 iterations by default. The event joint global BA is performed every 5 frames with $5\%$ of pixels from all keyframes. The model is trained using Adam optimizer with learning rate $lr_{rot} = 1e^{-3}, lr_{trans} = 1e^{-3}$ , and loss weights $\lambda_{ev} = 0.05, \lambda_{rgb} = 5.0, \lambda_d = 0.1$ . Default window $w_d$ and neighborhood window are set as 5 and 2, respectively. The exposures of RGB and event cameras are $5.21e^{-5}$ in DEV-Indoors. We use two sigmoid functions to fit the exposures if they are unavailable. Detailed settings can be found in the supplemental materials. + +# 5.1. Evaluation of Tracking and Mapping + +Evaluation on DEV-Indoors. We report the trajectory accuracy and reconstruction quality in Tab. 1 and Tab. 2. As shown in Tab. 1, EN-SLAM performs the best in all 9 scenes and remains stable (fluctuation below 0.8) under all the blur and dark sequences. While the others perform sensitive and unstable when facing non-ideal environments, especially iMAP [52] and NICE-SLAM [71], which completely crushes in the blur and dark scenes. ESLAM [71] + +![](images/5a141d83ad61631a880e527b19f8aeb555d3e9e8fda4fdbec54e6d8cac960165.jpg) +Figure 7. Reconstruction Performance on DEV-Indoors. EN-SLAM achieves, on average, more precise reconstruction details than existing methods in motion blur and lighting varying environments with the assistance of high-quality event streams. + +Table 2. Reconstruction Performance [cm] of the proposed method vs. the state-of-the-art methods on DEV-Indoors dataset. + +
MethodMetric#Rm norm blur#Rm dark#Rm norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]Acc↓37.1637.6034.3025.5544.28854.4756.4051.7438.12
Comp↓48.6955.9733.7619.2823.9449.6165.4027.1847.11
Comp Ratio↑37.5637.7639.1160.0346.2742.5612.1448.4440.41
Depth L1↓79.9397.9864.9640.36128.45140.00131.79115.07124.69
NICESL AM [71]Acc↓18.4918.8616.6921.2716.5119.1726.3522.0928.40
Comp↓20.2621.9321.4320.6718.7021.2928.0449.8277.19
CompRatio↑60.4059.0358.1459.6063.4956.5550.9146.0035.58
Depth L1↓40.5942.0940.2641.5424.0034.8962.48104.20106.09
CoSLAM [58]Acc↓10.6611.3612.7715.4716.4230.7113.0217.5919.85
Comp↓13.2412.4412.2314.0915.3621.6713.9218.2619.46
Comp Ratio↑69.2276.8777.2670.6166.7555.2667.9261.2660.70
Depth L1↓24.7820.9120.6532.2935.9064.1428.6939.1742.85
ESLA M [23]Acc↓9.488.5811.8112.8616.2514.859.0110.0110.02
Comp↓7.947.547.088.51112.3710.408.8910.9510.44
Comp Ratio↑84.6085.6986.7082.9371.5380.9083.1780.0281.64
Depth L1↓15.3412.2719.0811.0727.8015.5030.0329.0628.02
OursAcc↓7.4810.537.079.469.919.349.239.289.25
Comp↓7.7012.517.709.879.289.619.959.929.92
Comp Ratio↑83.0074.4884.2685.3683.4084.0182.2782.3882.35
Depth L1↓15.1023.3611.9218.8611.9419.2123.1623.1423.39
+ +Table 3. Tracking comparison (ATE median [cm]) of the proposed method vs. the state-of-the-art methods on DEV-Reals. + +
MethodPio1Pio2Gre1Gre2dorm1dorm2dorm3dorm4avg
ORBSLAM [19]x63%x63%x63%x63%x63%x63%x63%x63%x63%
NICE-SLAM [71]13.2123.35x63%x25%24.6910.6818.4444.04x22.40
COSLAM [58]11.1419.8382.5240.1615.9915.4230.1232.4530.95
ESLAM [23]11.2821.4263.6530.7537.9431.0416.1937.9131.27
Ours8.9419.0543.6321.1811.2611.9116.0019.7818.97
+ +and CoSLAM [58] exhibit similar trends but achieve relatively stable results. Specifically, in #room sequences, they achieved 1.02 and 1.45 times the error on the blur subset and 2.49 and 3.77 times the error on the dark subset, respectively. The reconstruction quality in Tab. 2 and Fig. 7 show that EN-SLAM performs more accurately and robustly than the other methods. Specifically, our method reduces the error by 2.37, 0.48, and 1.90 in ACC, Comp, and Depth L1 compared with the second ESLAM [23]. Fig. 7 also shows that our method reconstructs the details of the scenes more accurately and produces fewer artifacts. + +Evaluation on DEV-Reals. Tab. 3 illustrates the tracking performance of our method and the state-of-the-art methods on the DEV-Reals dataset. Our method achieves the best performance in all the scenes (18.97), and the average error is 1.63 times lower than the second-best CoSLAM [58] (30.95). Note that DEV-Reals is challenging due to the large motion and varying light, leading to the crushes of ORBSLAM [36] and NICE-SLAM [71]. + +Table 4. Tracking comparison (ATE mean [cm]) of the proposed method vs. the Event-based SLAM system on Vector[13] dataset. + +
Methodrobot normrobot fastdesk normdesk fastsofa normsofa fasthdr normhdr fastall avg
EVO [43]3.25✘✘✘✘✘✘✘3.25
ESVO [69]✘✘✘✘1.77✘✘✘1.77
USLAM [57] (EVIO)1.181.652.241.085.742.545.692.612.84
CoSLAM [58] (DV)1.00124.691.7697.651.7477.891.471.4238.45
ESLAM [23] (DV)1.393.302.543.647.9919.037.3812.237.19
Ours (EDV)1.061.731.762.692.021.841.031.221.67
+ +E: event, V: RGB or gray image, D: depth, I: IMU, S: stereo, O: odometry, X: crashes. + +Table 5. Run-time comparison on DEV-Indoors. EN-SLAM is comparable to the most efficient ESLAM and keeps lightweight. + +
MethodTracking [ms×it] ↓Mapping [ms×it] ↓FPS ↑#para.
iMAP [52]24.73×5041.18×3000.360.22 M
NICE-SLAM [71]6.46×1626.42×1201.555.86 M
CoSLAM[58]6.08×1513.52×1511.261.71 M
ESLAM [23]5.20×1316.68×1014.777.85 M
Ours5.75×1013.16×1017.401.95 M
+ +# 5.2. Runtime Analysis + +We evaluate all the frameworks on an NVIDIA RTX 4090 GPU and report average tracking and mapping iterations spending, FPS, and parameters number of the model in Tab. 5. The experimental results indicate that our method is fast, with an average of 17 FPS, comparable to the currently most efficient ESLAM [23]. Meanwhile, our method remains lightweight, with only 1.95M parameters, yet achieves the best accuracy. + +# 5.3. Evaluation of Rendering + +We compare the rendering performance in Fig. 5.3 (left), EN-SLAM outperforms most SOTA works in image quality. The thumbnails in Fig. 5.3 (right) show that EN-SLAM achieves more precise rendering details than previous methods. Specifically, on #Rm Blur, EN-SLAM yields more refined results, while CoSLAM and ESLAM exhibit ghosting. Note that in #Rm Dark and #Wkp Dark, all the RGB rendering is dark and blurred, while our method can still generate high-quality luminance results with the assistance of the HDR event stream. + +# 5.4. Ablation Study + +Effect of event and RGB modalities. Fig. 9 illustrates quantitative evaluation using ETA in tracking and mapping. Our full model achieve lower tracking error of 9.61 and 15.47 than the model w/o ETA in tracking (10.73 and 17.07) + +![](images/13d2119878820f66c7b199e1e992de6e49272dc2508512dce865b314b13d6906.jpg) +Figure 8. Rendering Performance on DEV-Indoors. left): Our method outperforms most previous works in image quality evaluation under non-ideal environments. right): EN-SLAM achieves more precise rendering details on average than previous methods. + +
Tracking EventMapping Event#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
XX11.898.6110.9876.3114.4618.75
X✓10.738.329.5381.8314.1717.07
✓X11.688.2810.2879.0516.0919.72
✓✓9.617.887.5983.5111.9115.47
RGB 1st-2nd only10.929.029.1582.8113.5217.80
W/o RGB12.0711.1211.0576.2722.5026.48
+ +![](images/0f217ff0e8b0f8d734050ac600507f0e7f608c35ed4971fa6682b7f3f51e7ce1.jpg) +Figure 9. Ablation study of modalities on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations). + +![](images/e1d305ec006d0c223c2e0e10634b2814a15091ac873e3225ddfccfa9bbaf93e0.jpg) + +![](images/76910319060adc007bb2dcc160317e93fd138d4ddca8162919b007ba4bf32ce5.jpg) + +and mapping (11.68 and 19.72) on the #Rm blur and #Dorm2, respectively. The results also show that the full model surpasses the model w/o ETA by 0.73 and $3.39\%$ in ACC and completion. In addition, the RGB is also critical, but with the initialization of RGB in 2 frames, the performance is significantly improved, benefiting from the CRF. + +Effect of CRF and probability-weighted sampling. Fig. 9 show the performance of differentiable CRF and probability-weighted sampling strategy (PWS). The system without CRF might suffer from the distinct event and RGB imaging process, resulting in fluctuating training and poor performance, especially in real datasets. It significantly reduces the tracking ATE RSME from 30.18 to 15.47 in #Drom2 and reconstruction completion from 9.78 to 7.59 in #Rm blur. The results also show that the full model surpasses the model w/o PWS by 0.25 and $1.9\%$ in ATE and completion on #Rm blur. A visualization of CRF is shown in Fig. 10, on dark scene #Drom2, the model with CRF renders HDR luminance results and accurate mesh benefiting from events. In contrast, the model w/o CRF suffers from the low dynamic range RGB input. + +
Setting#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
w/o CRF12.128.299.7883.5727.6730.18
w/o PWS9.867.889.4981.0416.5919.78
Full model9.617.887.5983.5111.9115.47
+ +Table 6. Ablation study of CRF and PWS on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations). + +![](images/f88bd5021d37b74957e8f3e52ac8f5c222a987de13249e5096b5848569ef2f96.jpg) +Figure 10. CRF ablation on the #Dorm2 of DEV-Reals. + +# 6. Conclusion and Limitation + +This paper first integrates the event stream into the implicit neural SLAM framework to overcome challenges in scenes with motion blur and lighting variation. A differentiable CRF rendering technique that maps the unified representation to color and luminance is proposed to address the significant distinction between event and RGB. An event temporal aggregating optimization strategy that capitalizes the consecutive difference constraints of events is presented to enhance the optimization. We construct DEV-Indoors and DEV-Reals datasets to evaluate the effectiveness of EN-SLAM under various environments. However, EN-SLAM relies on depth input, which might be unavailable in some scenarios. Besides, EN-SLAM focuses on indoor scenes and might face challenges in boundless long trajectories. In future work, we aim to extend it to large-scale outdoor environments and enhance the generalization capability. + +Acknowledgements. This work is supported by the Shanghai AI Laboratory, National Key R&D Program of China (2022ZD0160101), the National Natural Science Foundation of China (62376222), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). + +# References + +[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. In CVPR, pages 6290-6301, 2022. 4, 6 +[2] Christian Brändli, Jonas Strubel, Susanne Keller, Davide Scaramuzza, and Tobi Delbruck. Elised—an event-based line segment detector. In *EBCCSP*, pages 1-7. IEEE, 2016. 2 +[3] Guillaume Bresson, Zayed Alsayed, Li Yu, and Sébastien Glaser. Simultaneous localization and mapping: A survey of current trends in autonomous driving. 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Nevertheless, existing methods face significant challenges in non-ideal scenarios, such as motion blur or lighting variation, which often leads to issues like convergence failures, localization drifts, and distorted mapping. To address these challenges, we propose EN-SLAM, the first event-RGBD implicit neural SLAM framework, which effectively leverages the high rate and high dynamic range advantages of event data for tracking and mapping. Specifically, EN-SLAM proposes a differentiable CRF (Camera Response Function) rendering technique to generate distinct RGB and event camera data via a shared radiance field, which is optimized by learning a unified implicit representation with the captured event and RGBD supervision. Moreover, based on the temporal difference property of events, we propose a temporal aggregating optimization strategy for the event joint tracking and global bundle adjustment, capitalizing on the consecutive difference constraints of events, significantly enhancing tracking accuracy and robustness. Finally, we construct the simulated dataset DEV-Indoors and real captured dataset DEV-Reals containing 6 scenes, 17 sequences with practical motion blur and lighting changes for evaluations. Experimental results show that our method outperforms the SOTA methods in both tracking ATE and mapping ACC with a real-time 17 FPS in various challenging environments. Project page: https://delinqu.github.io/EN-SLAM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 601, + 128, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 128, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 128, + 613 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 622, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 287, + 684 + ], + "type": "text", + "content": "Simultaneous Localization and Mapping (SLAM) is an essential problem in computer vision and robotics, widely applied in tasks such as virtual and augmented reality [8], robot navigation [18] and autonomous driving [3] over last decades. Exploration in extreme environments [10, 31, 41]" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 219, + 547, + 358 + ], + "blocks": [ + { + "bbox": [ + 309, + 219, + 547, + 358 + ], + "lines": [ + { + "bbox": [ + 309, + 219, + 547, + 358 + ], + "spans": [ + { + "bbox": [ + 309, + 219, + 547, + 358 + ], + "type": "image", + "image_path": "f617a732afa89f05f8e03b8200347a7d2f2710ca08a85621e96a446373edda81.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 364, + 547, + 486 + ], + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 486 + ], + "type": "text", + "content": "Figure 1. Illustration of the proposed implicit event-RGBD neural SLAM system EN-SLAM under non-ideal environments. The dynamic range of RGB sensors is relatively low and suffers from motion blur. Instead, event cameras show great potential in non-ideal environments due to their high dynamic range and low latency advantages. Our method samples rays from two independent RGBD and event cameras to jointly train a single implicit neural field with both modalities. This hybrid shared mechanism provides a natural fusion approach, avoiding alignment issues. It also leverages the advantages of both modalities, resulting in dense, more robust, and higher-quality reconstruction results." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 495, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 533 + ], + "type": "text", + "content": "remains challenging for visual SLAM (vSLAM) systems due to the lack of visual features caused by motion blur and lighting variation in diverse environments [42, 59, 68]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "content": "As a novel representation for myriad of signals, Neural Radiance Fields (NeRF) [35] has innovated great progress in SLAM recently, demonstrating significant improvements in map memory consumption, hole filling, and mapping quality [23, 49, 52, 58, 67, 71]. While the existing NeRF-based neural vSLAM methods address the limitations of traditional SLAM frameworks [11, 36, 37, 50, 62] in accurate dense 3D map reconstruction, they are primarily designed for well-lit scenes and always fail in practical SLAM scenarios with motion blur [40, 66] and lighting variation [32, 48]. These methods produce unsatisfying results under non-ideal environments [58] because of the following limitations: 1) View-inconsistency: When the camera encounters rapid velocity variation in Fig. 2 (2nd), the scene may exhibit discontinuous blur, leading to view" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 243, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 243, + 703 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 243, + 703 + ], + "type": "text", + "content": "* Authors contributed equally: dlqu22@m.fudan.edu.cn" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 61, + 704, + 141, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 704, + 141, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 704, + 141, + 713 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19584" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "inconsistency among frames, further causing heavy artifacts in the reconstructed map. 2) Low dynamic range: In light- ing variation scenes illustrated in Fig. 1, the dynamic range of the RGB sensor is relatively low, and the information on the dark and overexposure areas is lost, leading to tracking drifts and mapping distortions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 145, + 288, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 145, + 288, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 145, + 288, + 384 + ], + "type": "text", + "content": "To address the issues in non-ideal scenarios of existing neural vSLAM, we introduce utilizing the advantages of high dynamic range (HDR) and temporal resolution of event data to compensate for the lost information, thereby improving the robustness, efficiency, and accuracy of current neural vSLAM in extreme environments. Fig. 2 shows the event generation model that an event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold " + }, + { + "bbox": [ + 46, + 145, + 288, + 384 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 145, + 288, + 384 + ], + "type": "text", + "content": ". This asynchronous mechanism shows excellent potential in non-ideal environments due to its advantages in low latency [26, 43, 70], high dynamic range [46], and high temporal resolution [54, 55]. Fig. 1 and Fig. 2 illustrate its superiority in dark and fast motion, and event sensors capture higher-quality signals than RGB sensors. However, applying events into NeRF-based vSLAM is challenging due to the significant distinction in imaging mechanisms between event and RGB cameras. Moreover, the requirement of highly accurate camera poses and careful optimization in traditional surface density estimation [32] further complicates the integration." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 386, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 287, + 612 + ], + "type": "text", + "content": "In order to overcome these obstacles, we present EN-SLAM, the first event-RGBD implicit neural SLAM framework that effectively harnesses the advantages of event and RGBD streams. The overview of EN-SLAM is shown in Fig. 3. Our method models the differentiable imaging process of two distinct cameras and utilizes shared radiance fields to jointly learn a hybrid unified representation from events and RGBD data. By integrating the event generation model into the optimization process, we introduce the event temporal aggregating (ETA) optimization strategy for event joint tracking and global bundle adjustment (BA). This strategy effectively leverages the temporal difference property of events, providing efficient consecutive difference constraints and significantly improving the performance. Additionally, we construct two datasets: the simulated dataset DEV-Indoors and the real captured dataset DEV-Reals, which consist of 6 scenes and 17 sequences with practical motion blur and lighting changes. Contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 617, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 48, + 617, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 617, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 48, + 617, + 287, + 664 + ], + "type": "text", + "content": "- We present EN-SLAM, the first event-RGBD implicit neural SLAM framework that efficiently leverages event stream and RGBD to overcome challenges in extreme motion blur and lighting variation scenes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 666, + 287, + 712 + ], + "type": "text", + "content": "- A differentiable CRF rendering technique is proposed to map a unified representation in the shared radiance field to RGB and event camera data for addressing the significant distinction between event and RGB. A tempo" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 385, + 148 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 385, + 148 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 385, + 148 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 385, + 148 + ], + "type": "image", + "image_path": "5eda0534f83d893336a8913d4b67e644443e6b5987b62cc8f3c4add304a3db46.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 150, + 545, + 182 + ], + "lines": [ + { + "bbox": [ + 306, + 150, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 306, + 150, + 545, + 182 + ], + "type": "text", + "content": "Figure 2. Illustration of the Event Generation Model (EGM). An event is triggered at a single pixel if the corresponding logarithmic change in luminance exceeds a threshold " + }, + { + "bbox": [ + 306, + 150, + 545, + 182 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 306, + 150, + 545, + 182 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 386, + 74, + 463, + 147 + ], + "blocks": [ + { + "bbox": [ + 386, + 74, + 463, + 147 + ], + "lines": [ + { + "bbox": [ + 386, + 74, + 463, + 147 + ], + "spans": [ + { + "bbox": [ + 386, + 74, + 463, + 147 + ], + "type": "image", + "image_path": "d7aea2a7d9978f6101535ff0a9a5c1d1e5cc32a68699e5f1d6a11ca807c8e311.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 464, + 74, + 545, + 147 + ], + "blocks": [ + { + "bbox": [ + 464, + 74, + 545, + 147 + ], + "lines": [ + { + "bbox": [ + 464, + 74, + 545, + 147 + ], + "spans": [ + { + "bbox": [ + 464, + 74, + 545, + 147 + ], + "type": "image", + "image_path": "ded92d95b63f77ffd09b5faed2cfb1b7f81e3187d3b4931802090d6bbd7cb755.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 189, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 189, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 314, + 189, + 545, + 236 + ], + "type": "text", + "content": "ral aggregating optimization strategy that capitalizes the consecutive difference constraints of the event stream is present and significantly improves the camera tracking accuracy and robustness." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 236, + 545, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 236, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 307, + 236, + 545, + 296 + ], + "type": "text", + "content": "- We construct a simulated DEV-Indoors and real captured DEV-Reals dataset containing 17 sequences with practical motion blur and lighting changes. A wide range of evaluations demonstrate competitive real-time performance under various challenging environments." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 308, + 392, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 392, + 320 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 392, + 320 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 329, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 592 + ], + "type": "text", + "content": "Neural Implicit vSLAM. Existing NeRF-based visual SLAM methods have made significant improvements in dense map reconstruction. iMAP [52] first introduces NeRF into SLAM, and NICE-SLAM [71] expands the reconstructable environment size by introducing multiscale feature grids. Vox-Fusion [64] utilizes an octree-based structure to expand the scene dynamically. Besides, CoSLAM [58] combines coordinate and sparse parametric encoding to achieve fast convergence and surface hole filling in reconstruction. Parallel works ESLAM [23] and Point-SLAM [49] represent scenes as multi-scale feature planes and neural point clouds, respectively, to improve the efficiency and accuracy. Beyond NeRF, GS-SLAM [63] utilizes 3D Gaussian [24] for scene representation and achieves photo-realistic reconstruction performance. However, these methods are designed for well-lit indoor scenes and commonly encounter challenges in non-ideal SLAM processes, such as motion blur and lighting variation. In contrast, we introduce utilizing the advantages of high dynamic range and temporal resolution of events to compensate for the lost information, thereby improving the robustness and accuracy of current neural implicit methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Event-based SLAM. Events have been incorporated into traditional visual SLAM systems to address the motion blur and lighting variation. These methods can be divided into three main types: feature-based methods, direct methods, and motion-compensation methods. Feature-based methods, such as USLAM [57], EIO [16] and PL-EVIO [17], track point or line features from event data [29, 44], and perform the camera tracking and mapping in parallel threads. However, the feature extraction algorithms [2, 33, 47, 56] rely heavily on frame-based feature detection, facing chal" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19585" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 45, + 547, + 178 + ], + "blocks": [ + { + "bbox": [ + 48, + 45, + 547, + 178 + ], + "lines": [ + { + "bbox": [ + 48, + 45, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 48, + 45, + 547, + 178 + ], + "type": "image", + "image_path": "838ff965dadfec0fef34dbb47d8f7c0a1349be1760dc0b4b55b361d27817b074.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "type": "text", + "content": "Figure 3. Overview of EN-SLAM. EN-SLAM decodes the scene encoding to a shared geometry and radiance representation, and decomposes the radiance into RGB color " + }, + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\mathbf{c}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "type": "text", + "content": " and event luminance " + }, + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\mathbf{l}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 185, + 547, + 220 + ], + "type": "text", + "content": " via differentiable CRF Mappers. We iteratively optimize the pose and scene representation by minimizing losses, in tracking and global BA with the event temporal aggregating techniques in Algorithm 1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 224, + 289, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 392 + ], + "type": "text", + "content": "lenges for motion-dependent event data appearance. Direct methods employ events without explicit data association by aligning the photometric event image [19, 25, 26] or utilizing the spatiotemporal information for event representations alignment [43, 45, 70]. Direct methods are well suited for events, but mainly focus on event-based visual odometry, leaving the visual dense mapping unexplored. Motion-compensation methods optimize event alignment in motion-compensated event frames by maximizing the contrast [39, 60], minimizing the dispersion [38] and align probabilistic [15]. However, they suffer from the collapse in a broad range of camera motions. Thus, currently, event-based SLAM demonstrates significant potential but lacks sufficient exploration in dense map reconstructions [20]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "type": "text", + "content": "Neural Radiance Fields using Events. Event-based NeRF is in the nascent stages, and several studies have demonstrated the possibility of view synthesis from events via implicit neural fields. Event-NeRF [48] proposes an approach for inferring NeRF from a monocular color event stream that enables novel view synthesis. E-NeRF [27] and " + }, + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "type": "text", + "content": " [40] tackle the NeRF estimation from event cameras under strong motion blur. They develop normalized and rendering loss to address varying contrast thresholds and enhance neural volumetric representation. The parallel work Ev-NeRF [22] conducts a threshold-bound loss with the ReLU function to address the lack of RGB images. In addition to reconstruction, " + }, + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "type": "inline_equation", + "content": "\\Delta_t" + }, + { + "bbox": [ + 46, + 393, + 288, + 632 + ], + "type": "text", + "content": " NeRF [34] proposes an event camera tracker by minimizing the error between sparse events and the temporal gradient of the scene representation on the simplified intensity-change events. However, the traditional surface density estimation in NeRF requires highly accurate camera poses and careful optimization [32], thus making it exceptionally challenging to apply NeRF to the event-based SLAM." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 645, + 129, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 129, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 129, + 658 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "The overview of our method is shown in Fig. 3. Given an input RGBD stream " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i, \\mathbf{D}_i\\}_{i=1}^J" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": " and event stream " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{E}_k\\}_{k=1}^N" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": " with known camera intrinsics " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{K}' \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": ", we aim to leverage event and RGBD to reconstruct the cam" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "text", + "content": "era poses " + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{P}_i\\}_{i = 1}^J" + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "text", + "content": " and the implicit scene representation. In Sec. 3.1, the scene encoding is decoded to a unified geometry and radiance representation. Then, the shared radiance is decomposed into RGB color " + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\mathbf{c}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "text", + "content": " and event luminance " + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\mathrm{l(x)}" + }, + { + "bbox": [ + 304, + 224, + 545, + 345 + ], + "type": "text", + "content": " via differentiable CRF Mappers in Secs. 3.2 and 3.3 to address the imaging distinction of event and RGB cameras. Finally, EN-SLAM iteratively optimizes the pose and scene representation by minimizing the re-rendering loss between the observed RGBD-E (RGBD and events) and rendering results in tracking and global BA of Sec. 3.4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 351, + 506, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 506, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 506, + 364 + ], + "type": "text", + "content": "3.1. Unified Implicit Scene Representation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 369, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 394 + ], + "type": "text", + "content": "As shown in Fig. 3, we represent the scene S with multi-resolution geometric features and color grid features:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 353, + 402, + 545, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 402, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 353, + 402, + 545, + 417 + ], + "type": "interline_equation", + "content": "\\mathbf {S} = \\left\\{\\left(F _ {\\mathbf {x}, \\theta} ^ {g}, F _ {\\mathbf {x}, \\theta} ^ {c}\\right) \\mid \\theta = 1, \\dots , \\Theta \\right\\}, \\tag {1}", + "image_path": "4f2d2d0b8ce6ca3d9353b96543063fc909129c5d309dd2ea606193d16ff8782c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " denote the coordinate and resolution level. There are two challenges that hinder us from learning a scene representation from different RGB and event modalities. Firstly, the event data is sparse and records logarithmic changes in luminance. Secondly, different cameras hold distinct physical imaging process mechanisms. Despite this, the geometry and radiance fields remain consistent during the camera imaging. In this case, we propose to learn a shared unified geometry hidden feature " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{\\mathbf{x}}^{g}" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " and radiance representation " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " across distinct cameras. The geometric grid feature " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "F_{\\mathbf{x},\\theta}^{g}" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " and color feature " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "F_{\\mathbf{x},\\theta}^{c}" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " are simultaneously mapped to geometry hidden vector " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{\\mathbf{x}}^{g}" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": ", radiance fields " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": " and TSDF (truncated signed distance function) " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": ", by a geometry decoder " + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "inline_equation", + "content": "\\pmb{f}_{g}" + }, + { + "bbox": [ + 304, + 423, + 546, + 593 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 349, + 599, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 599, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 349, + 599, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\boldsymbol {f} _ {\\boldsymbol {g}} \\left(F _ {\\mathbf {x}, \\theta} ^ {g}, F _ {\\mathbf {x}, \\theta} ^ {c}\\right) \\mapsto \\left(\\mathbf {h} _ {\\mathbf {x}} ^ {g}, \\mathbf {e} (\\mathbf {x}), \\mathbf {s} (\\mathbf {x})\\right). \\tag {2}", + "image_path": "7c6f7b4c79048c04567e715523cf30a64d6224043eb6b5978c4b867320689f97.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "type": "text", + "content": "The geometry hidden vector " + }, + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{\\mathbf{x}}^{g}" + }, + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "type": "text", + "content": " and radiance fields " + }, + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 628, + 545, + 651 + ], + "type": "text", + "content": " are shared by the color and event CRF decoders." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 659, + 504, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 659, + 504, + 672 + ], + "spans": [ + { + "bbox": [ + 305, + 659, + 504, + 672 + ], + "type": "text", + "content": "3.2. Decomposition of the Radiance Fields" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In standard imaging devices, the incoming radiance undergoes linear and nonlinear image processing before being mapped into pixel values and stored in images. This entire" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19586" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": "image processing can be represented by a single function " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " called the camera response function (CRF) [9]. However, the traditional NeRF method [35] simplifies the imaging process, leading to discrepancies between the rendering and actual images. This deviation is further amplified in multi-modal implicit representations. As Fig. 10 shows, the captures of RGB and event cameras are significantly distinct, which can lead to joint optimization fluctuation. To address this issue, we model the radiance " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " and exposure " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\Delta t_{c}" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " of a ray " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " but take the aperture and others as implicit factors to obtain the color field " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{c}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " [21, 53] by differentiable tone-mapping:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 119, + 222, + 287, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 222, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 119, + 222, + 287, + 236 + ], + "type": "interline_equation", + "content": "\\mathbf {c} (\\mathbf {x}) = \\boldsymbol {f} _ {c} \\left(\\mathbf {e} (\\mathbf {x}) \\Delta \\mathbf {t} _ {c}\\right). \\tag {3}", + "image_path": "cd345a2fb9f435458f1cc962b5c33b74b6789fc7f573b0e3ec357abad1d66cd3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "type": "text", + "content": "To facilitate optimization, we convert all numerical values into the logarithmic domain and present the inverse function of " + }, + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\left(\\ln f_c^{-1}\\right)^{-1}" + }, + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathrm{c}}" + }, + { + "bbox": [ + 47, + 241, + 287, + 281 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 286, + 287, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 286, + 287, + 317 + ], + "spans": [ + { + "bbox": [ + 85, + 286, + 287, + 317 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {c} (\\mathbf {x}) = \\left(\\ln \\boldsymbol {f} _ {\\boldsymbol {c}} ^ {- 1}\\right) ^ {- 1} (\\ln \\mathbf {e} (\\mathbf {r}) + \\ln \\Delta \\mathbf {t} _ {c}) \\tag {4} \\\\ = \\boldsymbol {\\Psi} _ {\\mathbf {c}} (\\ln \\mathbf {e} (\\mathbf {x}) + \\ln \\Delta \\mathbf {t} _ {c}), \\\\ \\end{array}", + "image_path": "d3f182b148dc2e77b1eba82d7aaebbd8754ec031174770805aa7f1c573803c8e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "content": "As for the event camera, directly obtaining the event data is not feasible. However, we can predict high dynamic range luminance " + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "l(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "content": " and derive events using the event generation model: As shown in Fig. 2, an event " + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "E_{k} = (u_{k}, v_{k}, t_{k}, p_{k})" + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "content": " at image coordinate " + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_{k} = [u_{k}, v_{k}, 1]^{T}" + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "content": " is triggered if the corresponding logarithmic brightness change " + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "\\mathbf{L}(\\mathbf{m}, t)" + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "content": " exceeds a threshold " + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 323, + 287, + 406 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 413, + 287, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 413, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 53, + 413, + 287, + 426 + ], + "type": "interline_equation", + "content": "\\mathbf {L} \\left(\\mathbf {m} _ {k}, t _ {k}\\right) - \\mathbf {L} \\left(\\mathbf {m} _ {k}, t _ {k - 1}\\right) = p _ {k} C, \\quad p _ {k} \\in \\{+ 1, - 1 \\}. \\tag {5}", + "image_path": "bcce90e116ab90d0e9e90ac37897e710b96bb92d53fff648cce59f96f4510979.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 432, + 272, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 272, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 272, + 444 + ], + "type": "text", + "content": "The logarithmic brightness " + }, + { + "bbox": [ + 47, + 432, + 272, + 444 + ], + "type": "inline_equation", + "content": "\\mathbf{L}(\\mathbf{m},t)" + }, + { + "bbox": [ + 47, + 432, + 272, + 444 + ], + "type": "text", + "content": " can be obtained by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 449, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 449, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 59, + 449, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\mathbf {L} (\\mathbf {m}, t) = \\ln \\log \\left(\\mathbf {I} _ {e} (\\mathbf {m})\\right) = \\left\\{ \\begin{array}{l l} \\mathbf {I} _ {e} (\\mathbf {m}) \\cdot \\ln (B) / B, & \\text {i f} \\mathbf {I} _ {e} (\\mathbf {m}) < B \\\\ \\ln \\left(\\mathbf {I} _ {e} (\\mathbf {m})\\right), & \\text {e l s e} \\end{array} , \\right. \\tag {6}", + "image_path": "c9245e37689b2fe2140f02d8d06e2c9d70888e64bf036c9d38ec62a07a904dc0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "content": " denotes the linear region threshold [7] and the imaging brightness " + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_e(\\mathbf{m})" + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "content": " of event camera equals to the corresponding luminance of ray " + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "content": ". By applying the modeling approach in Eqs. (3) and (4) to the CRF of an event camera, we establish the relation among the luminance field " + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "inline_equation", + "content": "l(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "content": ", the radiance " + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 473, + 287, + 545 + ], + "type": "text", + "content": " and exposure:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 103, + 552, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 552, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 103, + 552, + 287, + 564 + ], + "type": "interline_equation", + "content": "l (\\mathbf {x}) = \\boldsymbol {\\Psi} _ {l} \\left(\\ln \\mathbf {e} (\\mathbf {x}) + \\ln \\Delta \\mathbf {t} _ {l}\\right), \\tag {7}", + "image_path": "1bcf6f767f32320736fb4695a5b677adc418b362e6a971885ea31fb21e4337a5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\Psi_{l}" + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{t}_l" + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "text", + "content": " denote the luminance tone-mapping and pseudo exposure of the event camera. In this way, we decompose the shared radiance field " + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\mathbf{e}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 571, + 287, + 631 + ], + "type": "text", + "content": " into the RGB and event camera imaging processes through two differentiable tone-mapping processes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 637, + 212, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 637, + 212, + 650 + ], + "spans": [ + { + "bbox": [ + 47, + 637, + 212, + 650 + ], + "type": "text", + "content": "3.3. Differentiable CRF Rendering" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 655, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 287, + 691 + ], + "type": "text", + "content": "Upon obtaining the color and luminance fields in Sec. 3.2, we render the final imaging RGB, luminance, and depth by integrating predicted values along the samples in a ray " + }, + { + "bbox": [ + 47, + 655, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 47, + 655, + 287, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 96, + 697, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 697, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 96, + 697, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {i} = \\mathbf {O} + z _ {i} \\mathbf {d}, \\quad i \\in \\{1, \\dots , M \\}, \\tag {8}", + "image_path": "dbcd09baa78589cc9ba19a62023744834f69168e6b4193a99c7b63c19ec61464.jpg" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 65, + 397, + 167 + ], + "blocks": [ + { + "bbox": [ + 307, + 65, + 397, + 167 + ], + "lines": [ + { + "bbox": [ + 307, + 65, + 397, + 167 + ], + "spans": [ + { + "bbox": [ + 307, + 65, + 397, + 167 + ], + "type": "image", + "image_path": "b903c1a64e39a737a3d7c5be9205c71bbaa0c1514f37e881e0bfd73a9e23b58c.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 167, + 394, + 182 + ], + "lines": [ + { + "bbox": [ + 345, + 167, + 394, + 182 + ], + "spans": [ + { + "bbox": [ + 345, + 167, + 394, + 182 + ], + "type": "text", + "content": "a) Camera k trajectory" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 184, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 239 + ], + "type": "text", + "content": "Figure 4. The illustration of event temporal aggregating optimization strategy. In the tracking and global BA stages, EN-SLAM adaptively forwards query the previous frame according to the previous index table, and sample rays from different views perform joint optimization in Eq. (13)." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 397, + 68, + 468, + 162 + ], + "blocks": [ + { + "bbox": [ + 397, + 68, + 468, + 162 + ], + "lines": [ + { + "bbox": [ + 397, + 68, + 468, + 162 + ], + "spans": [ + { + "bbox": [ + 397, + 68, + 468, + 162 + ], + "type": "image", + "image_path": "ac8bbf6c954fe79f12c4947426c19ef4d25e6f9531b11ac822e4a89466ff8f0d.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 418, + 166, + 452, + 181 + ], + "lines": [ + { + "bbox": [ + 418, + 166, + 452, + 181 + ], + "spans": [ + { + "bbox": [ + 418, + 166, + 452, + 181 + ], + "type": "text", + "content": "b) Previous Index Table" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 475, + 68, + 545, + 162 + ], + "blocks": [ + { + "bbox": [ + 475, + 68, + 545, + 162 + ], + "lines": [ + { + "bbox": [ + 475, + 68, + 545, + 162 + ], + "spans": [ + { + "bbox": [ + 475, + 68, + 545, + 162 + ], + "type": "image", + "image_path": "8edec6d2aeafff93576b1134e961ddd60fa2d94487a8da2af5ebe04bd0748e67.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 484, + 164, + 526, + 182 + ], + "lines": [ + { + "bbox": [ + 484, + 164, + 526, + 182 + ], + "spans": [ + { + "bbox": [ + 484, + 164, + 526, + 182 + ], + "type": "text", + "content": "c) Forward ray sampling" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{O} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": " is the camera origin, " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{d} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\|\\mathbf{d}\\| = 1" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": " is the ray direction, and " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "z_i \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": " denotes the depth. Hence, we obtain the final imaging color " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": ", luminance " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\hat{l}" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\hat{d}" + }, + { + "bbox": [ + 304, + 245, + 545, + 281 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 343, + 282, + 545, + 376 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 282, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 343, + 282, + 545, + 376 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mathbf {c}} (\\mathbf {r}, \\Delta t _ {c}) = \\sum_ {i = 1} ^ {i = M} w _ {i} \\boldsymbol {\\Psi} _ {\\mathbf {c}} \\left(\\ln \\mathbf {e} \\left(\\mathbf {x} _ {i}\\right) + \\ln \\Delta t _ {c}\\right), \\\\ \\hat {l} (\\mathbf {r}, \\Delta t _ {l}) = \\sum_ {i = 1} ^ {i = M} w _ {i} \\boldsymbol {\\Psi} _ {l} \\left(\\ln \\mathbf {e} \\left(\\mathbf {x} _ {i}\\right) + \\ln \\Delta t _ {l}\\right), \\tag {9} \\\\ \\hat {d} (\\mathbf {r}) = \\sum_ {i = 1} ^ {i = M} w _ {i} z _ {i}. \\\\ \\end{array}", + "image_path": "d322b61b306bb3034085fa199419ebc95f3ca794b327e1cff21ece1a2950df04.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": "We utilize the simple bell-shaped model [1] and compute weights " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": " by two sigmoid functions " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": " to convert predicted TSDF " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": " into weight " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 359, + 419, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 419, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 359, + 419, + 545, + 447 + ], + "type": "interline_equation", + "content": "w _ {i} = \\sigma \\left(\\frac {\\mathbf {s} \\left(\\mathbf {x} _ {i}\\right)}{t r}\\right) \\sigma \\left(- \\frac {\\mathbf {s} \\left(\\mathbf {x} _ {i}\\right)}{t r}\\right), \\tag {10}", + "image_path": "259be7898aed02cbe095eadb36dcb5cca6dca8e3b1f89578c5f24dfcce4742b0.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "type": "inline_equation", + "content": "tr" + }, + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "type": "text", + "content": " is the truncation distance of a ray " + }, + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 306, + 455, + 488, + 466 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 474, + 486, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 486, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 486, + 487 + ], + "type": "text", + "content": "3.4. Tracking and Bundle Adjustment" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 493, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 589 + ], + "type": "text", + "content": "In this section, to leverage the HDR and temporal difference properties of events, we propose an event joint tracking and global BA strategy in Sec. 3.4.1 that incorporates events into optimization, thus improving the accuracy and robustness. Besides, we introduce adaptive forward-query and sampling strategies in Sec. 3.4.2 and Sec. 3.4.3, which select event data and ray samples with more elevated confidence for optimization, thereby boosting the convergence." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 591, + 521, + 603 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 591, + 521, + 603 + ], + "spans": [ + { + "bbox": [ + 305, + 591, + 521, + 603 + ], + "type": "text", + "content": "3.4.1 Event Temporal Aggregating Optimization" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The overview of ETA is shown in Fig. 4 and Algorithm 1. For tracking, we represent the camera pose " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{cur} = \\exp (\\xi_t^{\\wedge})\\in \\mathbb{S}\\mathbb{E}(3)" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " of current frame " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{cur}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and initialize with constant assumption. By selecting " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " rays within " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{cur}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and performing an adaptive event forward query in Sec. 3.4.2 with a probability-weighted sampling in Sec. 3.4.3, we get the event stream and previous rays. Then, we iteratively optimize the pose by minimizing objective functions. For global BA, " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{ba}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " rays from the global keyframe" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19587" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": "list are sampled to be the subset of pixels " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\{PX_{cur}\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": ". And then, the forward query and probability-weighted sampling are performed for each sample to get the previous subset " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\{PX_{prev}\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": " and events " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\{E_k\\}_{k = prev}^{cur}" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": ". Finally, a joint optimization is performed to optimize the geometry decoder " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": ", differentiable CRF " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\{\\Psi_{\\mathbf{c}},\\Psi_{l}\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": ", and poses " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{P_i}\\}_{i = 0}^{cur}" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 147, + 216, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 147, + 216, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 147, + 216, + 159 + ], + "type": "text", + "content": "3.4.2 Adaptive Forward Event Query" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "text", + "content": "As shown in Fig. 4, ETA performs an adaptive event forward window selection in tracking and BA by constructing a previous index table to prioritize reliable prior frames for optimization. Specifically, ETA uses a default window " + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "inline_equation", + "content": "w_{d}" + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "text", + "content": " and performs a forward query. If the loss of a queried frame exceeds a threshold " + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{s}" + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "text", + "content": ", we conduct a shift lookup within a neighborhood of length " + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "inline_equation", + "content": "2 \\times w_{k}" + }, + { + "bbox": [ + 46, + 161, + 288, + 293 + ], + "type": "text", + "content": ", selecting the frame with the minimum loss as the forward frame for event loss calculation Eq. (13). This event temporal constraint provides a stable local constraint between the participating frames and effectively leverages the high HDR property of events." + } + ] + } + ], + "index": 2 + }, + { + "type": "code", + "bbox": [ + 50, + 313, + 272, + 533 + ], + "blocks": [ + { + "bbox": [ + 53, + 300, + 260, + 312 + ], + "lines": [ + { + "bbox": [ + 53, + 300, + 260, + 312 + ], + "spans": [ + { + "bbox": [ + 53, + 300, + 260, + 312 + ], + "type": "text", + "content": "Algorithm 1: Event temporal aggregating optimization" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "lines": [ + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "spans": [ + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": "Input: RGBD-E stream " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i,d_i\\}_{i = 1}^J" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{E}_k\\}_{k = 1}^N" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " Output: Loss " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{L}_{ev},\\mathcal{L}_{rgb},\\mathcal{L}_d,\\mathcal{L}_{sdf},\\mathcal{L}_{fs}\\}" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " \nwhile " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "j < J" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " do \nfor " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "i\\in \\{j\\}" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " if not BA else " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\{0,1,\\dots,j\\}" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " do /\\* Forward Query Sec. 3.4.2 \\*/ \n" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{cur},\\mathbf{F}_{prev}\\gets \\mathrm{Tab}(i),\\mathrm{Tab}(i - w_d);" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total} > \\mathcal{L}_s" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " then \n" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\begin{array}{rlr}{\\bf F}_{prev}^{\\min}\\leftarrow \\mathrm{Tab}(i - w_s - w_d,i + w_s).Loss \\end{array}" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " \nend \nProbability-weighted ray sampling: " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\mathrm{Rays}_{cur}" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " Rays prev " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\leftarrow \\mathbf{F}_{cur},\\mathbf{F}_{prev}; / / \\mathrm{Sec.}3.4.3" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " \nRay rendering: " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}} (\\mathbf{m},t_{\\beta}) - \\hat{\\mathbf{L}} (\\mathbf{m},t_{\\alpha});" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " // Sec. 3.3 \nEvent accumulation: " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\sum_{t_k = t_{cur}}^{t_k = t_{prev}}p_kC;" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " \nCalculate loss: " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ev},\\mathcal{L}_{rgb},\\mathcal{L}_d,\\mathcal{L}_{sdf},\\mathcal{L}_{fs};" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " // Eqs. (13) to (15) \nTab(i) " + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "inline_equation", + "content": "\\leftarrow \\{\\mathcal{L}_{total},cur,prev\\}" + }, + { + "bbox": [ + 50, + 313, + 272, + 533 + ], + "type": "text", + "content": " \nend \n13 end" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "code_body" + } + ], + "index": 4, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 542, + 251, + 554 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 542, + 251, + 554 + ], + "spans": [ + { + "bbox": [ + 47, + 542, + 251, + 554 + ], + "type": "text", + "content": "3.4.3 Probability-weighted Sampling Strategy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "text", + "content": "To take advantage of hybrid multimodality and reduce computational costs, we propose to utilize the RGB loss to guide ray sampling in the event plane. As shown in Fig. 5, the algorithm starts by dividing the RGB image into " + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "text", + "content": " patches and randomly sampling " + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{N}_c" + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "text", + "content": " rays from each patch to obtain the loss for each sample. Then, we calculate the average loss of each patch and project the center " + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_c" + }, + { + "bbox": [ + 46, + 556, + 287, + 651 + ], + "type": "text", + "content": " to a downsampled mini-plan plane of the event camera:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 96, + 652, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 652, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 96, + 652, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\mathbf {m} = \\frac {1}{Z _ {e}} \\mathbf {K} _ {m} \\left[ \\mathbf {I} _ {3 \\times 3} | \\mathbf {0} _ {3 \\times 1} \\right] \\left[ \\begin{array}{c} \\mathbf {T} _ {e c} \\mathbf {K} ^ {- 1} \\mathbf {m} Z _ {c} \\\\ 1 \\end{array} \\right], \\tag {11}", + "image_path": "0ed3e40a9a36c43b10d173c62f6b78d3f667bc12e8ef4e791274cbeaad8243f3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "Z_{e}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " are the depths of two planes, " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_m" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " is the intrinsic of event mini-plane, and " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{ec}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " denotes the transformation between cameras. We apply the bilinear interpolation" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 331, + 47, + 523, + 163 + ], + "blocks": [ + { + "bbox": [ + 331, + 47, + 523, + 163 + ], + "lines": [ + { + "bbox": [ + 331, + 47, + 523, + 163 + ], + "spans": [ + { + "bbox": [ + 331, + 47, + 523, + 163 + ], + "type": "image", + "image_path": "66fc7c3f3260953042e0804d6047eab3c8f3797db5c526565fcf442cc2bf66af.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 166, + 545, + 199 + ], + "lines": [ + { + "bbox": [ + 304, + 166, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 304, + 166, + 545, + 199 + ], + "type": "text", + "content": "Figure 5. Illustration of the proposed probability-weighted sampling strategy. We utilize the loss of the RGBD plane (left) to guide ray sampling in the event plane (right)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "type": "text", + "content": "tion to compute the loss for each pixel in the mini-plan. Finally, the divided patches of the event plane query the loss " + }, + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{L}_e^q\\}_{q = 0}^Q" + }, + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "type": "text", + "content": " from the mini-plane and sample rays with probability distribution " + }, + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "type": "inline_equation", + "content": "f(j) = \\frac{\\mathcal{L}_e^q}{\\sum_{q = 1}^Q\\mathcal{L}_e^q}" + }, + { + "bbox": [ + 305, + 205, + 545, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 262, + 424, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 424, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 424, + 274 + ], + "type": "text", + "content": "3.4.4 Objective Functions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "text", + "content": "According to the EGM in Eq. (5), although it is not possible to directly model the luminance signals supervision, the logarithmic brightness differences " + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}} (\\mathbf{m},t_{\\beta}) - \\hat{\\mathbf{L}} (\\mathbf{m},t_{\\alpha})" + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "text", + "content": " can be rendered from two camera poses " + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\alpha}" + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\beta}" + }, + { + "bbox": [ + 304, + 276, + 545, + 337 + ], + "type": "text", + "content": " with Eq. (9). By integrating it with Eqs. (5) and (6), we obtain:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 344, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 344, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 545, + 373 + ], + "type": "interline_equation", + "content": "\\mathbf {L} (\\mathbf {m}, t _ {\\beta}) - \\mathbf {L} (\\mathbf {m}, t _ {\\alpha}) = \\sum_ {t _ {k} = t _ {\\alpha}} ^ {t _ {k} = t _ {\\beta}} p _ {k} C \\approx \\hat {\\mathbf {L}} (\\mathbf {m}, t _ {\\beta}) - \\hat {\\mathbf {L}} (\\mathbf {m}, t _ {\\alpha}). \\tag {12}", + "image_path": "2c9e0a96d6b1d8c3a6120799d97fd8d04eb9388aa9da3b448b41f59694e6d1fa.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 380, + 544, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 380, + 544, + 404 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 544, + 404 + ], + "type": "text", + "content": "Thus, we establish the relation between events and rendering, and define event reconstruction loss as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 413, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 413, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 317, + 413, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {e v}} \\left(t _ {\\beta}, t _ {\\alpha}\\right) = \\operatorname {M S E} \\left(\\sum_ {t _ {k} = t _ {\\alpha}} ^ {t _ {k} = t _ {\\beta}} p _ {k} C - \\hat {L} (\\mathbf {m}, t _ {\\beta}) + \\hat {L} (\\mathbf {m}, t _ {\\alpha})\\right). \\tag {13}", + "image_path": "89642f364d081eb7839ca126aa9f5759a0aa57596a4859bec7a163624eb7c07d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "content": "In our implementation, we perform a normalization on Eq. (13) to eliminate " + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "content": " when it is unavailable. The color and depth rendering losses [58] in a valid ray batch " + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "content": " between the rendering and observations are also utilized:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 503, + 545, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 503, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 313, + 503, + 545, + 526 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r g b}} = \\frac {1}{| R |} \\sum_ {\\mathbf {r} \\in \\mathbf {R}} (\\hat {\\mathbf {e}} (\\mathbf {r}, \\Delta t _ {c})) - c (\\mathbf {r})) ^ {2}, \\mathcal {L} _ {\\mathrm {d}} = \\frac {1}{| R |} \\sum_ {\\mathbf {r} \\in \\mathbf {R}} (\\hat {d} (\\mathbf {r}) - d (\\mathbf {r})) ^ {2}, \\tag {14}", + "image_path": "1acd78dbda8a8dd329bb5fb62cbe00518fe8d73be01cf20cc4729caf799276cb.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "inline_equation", + "content": "c(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "inline_equation", + "content": "d(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "content": " are the ground truth color and depth. To achieve an accurate geometry reconstruction, we apply the approximated SDF loss and free-space loss [58] to sampled point " + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "content": " near the surface " + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "inline_equation", + "content": "(S_r^{tr} = \\{\\mathbf{x} \\mid |d(\\mathbf{r}) - d(\\mathbf{x})| \\leq tr\\})" + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "content": " and far from the surface " + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "inline_equation", + "content": "(S_r^{fs} = \\{\\mathbf{x} \\mid |d(\\mathbf{r}) - d(\\mathbf{x})| > tr\\})" + }, + { + "bbox": [ + 304, + 534, + 545, + 595 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 323, + 597, + 545, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 597, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 323, + 597, + 545, + 633 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s d f} = \\frac {1}{| R |} \\sum_ {r \\in R} \\frac {1}{| S _ {r} ^ {t r} |} \\sum_ {\\mathbf {x} \\in S _ {r} ^ {t r}} \\left(\\mathbf {x} - \\left(\\hat {d} (\\mathbf {r}) - d (\\mathbf {r})\\right)\\right) ^ {2}, \\tag {15}", + "image_path": "0a7a0609cba9db031830aa165ccd625ba4edb0169b566a96aa3cdb193d56bb21.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 326, + 627, + 469, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 627, + 469, + 657 + ], + "spans": [ + { + "bbox": [ + 326, + 627, + 469, + 657 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f s} = \\frac {1}{| R |} \\sum_ {r \\in R} \\frac {1}{\\left| S _ {r} ^ {f s} \\right|} \\sum_ {\\mathbf {x} \\in S _ {r} ^ {f s}} (\\mathbf {x} - t r) ^ {2}.", + "image_path": "6fdcbd467e2bce1bf43cd27e9a4c8f02df8c670e5909c8e37eb0c81802e7bb24.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 658, + 359, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 359, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 359, + 669 + ], + "type": "text", + "content": "4. Dataset" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "To our knowledge, there is currently no SLAM dataset that satisfactorily tackles challenges posed by strong motion blur and lighting variations while encompassing RGBD and" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19588" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 45, + 539, + 233 + ], + "blocks": [ + { + "bbox": [ + 55, + 45, + 539, + 233 + ], + "lines": [ + { + "bbox": [ + 55, + 45, + 539, + 233 + ], + "spans": [ + { + "bbox": [ + 55, + 45, + 539, + 233 + ], + "type": "image", + "image_path": "c0dc9f2f0e626786168e77c5ea33c84d4260e4ca7596ded2506b4bbba49e736b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 546, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 546, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 546, + 269 + ], + "type": "text", + "content": "Figure 6. Overview of the DEV-Indoors and DEV-Reals datasets. DEV-Indoors is obtained through Blender [6] and simulator [14], covering normal, motion blur, and dark scenes, providing 9 subsets with RGB images, depth maps, event streams, meshes, and trajectories. DEV-Reals is captured from real scenes, providing 8 challenging subsets under motion blur and lighting variation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "text", + "content": "event streams for NeRF-based SLAM. Common datasets lack depth [19] or ground truth meshes [61]. Additionally, they are primarily focused on outdoor scenes [65], without significant motion blur [4] or lighting variation [30]. Therefore, in this paper, we construct simulated Dynamic Event RGBD Indoor (DEV-Indoors) and Dynamic Event RGBD Real captured (DEV-Reals) datasets, as shown in Fig. 6. Besides, we use Vector [13] dataset for evaluation as well." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 371, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 287, + 441 + ], + "type": "text", + "content": "1) DEV-Indoors is rendered from 3 Blender [6] models: #room, #apartment, and #workshop. We generated 9 subsets containing high-quality color images, depth, meshes, and ground truth trajectories by varying the scene lighting and camera exposure time. The events are further generated via the events simulator [14]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 443, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 287, + 514 + ], + "type": "text", + "content": "2) Dev-Reals is captured from 3 real scenes: #Pioffice, #Garage and #Dormitory. Our capture system comprises a LiDAR (for ground truth pose), a Realsense D435I RGBD camera, and a DAVIS346 event camera. Eight subsequences are captured by modifying the lighting conditions and camera movement speed in the environment." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 525, + 123, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 123, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 123, + 539 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 640 + ], + "type": "text", + "content": "Baselines. To the best of our knowledge, there is currently no event-based RGBD dense vSLAM with available public code that can be directly compared with our method. We opt EVO [43], ESVO [69], USLAM [57] as a reference from the most relevant event-based methods [5, 12, 19, 28, 61, 72]. We also compare our method with the existing SOTA NeRF-based methods: iMAP [52], NICE-SLAM [71], CoSLAM [58], and ESLAM [23]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": "Metric. We use the absolute trajectory error [51] (ATE) (cm) to measure the localization accuracy. For map reconstruction, we use the 2D Depth L1 (cm) [71], 3D accuracy (cm), completion (cm), and completion ratio " + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": " to measure the scene geometry with mesh culling [1, 23]. The evaluation datasets are generated by randomly conducting 2000" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 310, + 544, + 378 + ], + "blocks": [ + { + "bbox": [ + 305, + 275, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 308 + ], + "type": "text", + "content": "Table 1. Tracking (ATE RSME [cm]) comparison on DEV-Indoors. Our method outperforms previous works, demonstrating its robustness under motion blur and luminance variation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 310, + 544, + 378 + ], + "lines": [ + { + "bbox": [ + 308, + 310, + 544, + 378 + ], + "spans": [ + { + "bbox": [ + 308, + 310, + 544, + 378 + ], + "type": "table", + "html": "
Method#Rnm#Rm blur#Rnm dark#Apt norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]41.0850.5870.7725.7514.411.06e5276.91891.86345.21214.57
NICE-SLAM [71]17.0629.5430.5325.1744.2248.28X94 %X33 %X33%32.47
CoSLAM[58]10.7110.8826.6410.0213.0330.757.9614.3717.8815.80
ESLAM [23]10.7215.5540.429.9912.7912.397.0115.077.9714.66
Ours9.629.729.948.628.779.216.747.516.948.56
", + "image_path": "f6d3da37132b524bc767efff44f91e03623d0cb01263deb76aeb6734c702948b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 386, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 386, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 545, + 421 + ], + "type": "text", + "content": "poses and depths in Blender [6]. We run all the methods 5 times and report the average results or " + }, + { + "bbox": [ + 305, + 386, + 545, + 421 + ], + "type": "inline_equation", + "content": "X +" + }, + { + "bbox": [ + 305, + 386, + 545, + 421 + ], + "type": "text", + "content": " tracking success ratio if a method crashes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "content": "Implementation Details. EN-SLAM is implemented in Python and trained on a desktop PC with a 5.50GHz Intel Core i9-13900K CPU and NVIDIA RTX 4090 GPU. We run EN-SLAM at 17 FPS and sample 1024 and 2048 rays in tracking and BA stages with 10 iterations by default. The event joint global BA is performed every 5 frames with " + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "content": " of pixels from all keyframes. The model is trained using Adam optimizer with learning rate " + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "inline_equation", + "content": "lr_{rot} = 1e^{-3}, lr_{trans} = 1e^{-3}" + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "content": ", and loss weights " + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\lambda_{ev} = 0.05, \\lambda_{rgb} = 5.0, \\lambda_d = 0.1" + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "content": ". Default window " + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "inline_equation", + "content": "w_d" + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "content": " and neighborhood window are set as 5 and 2, respectively. The exposures of RGB and event cameras are " + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "inline_equation", + "content": "5.21e^{-5}" + }, + { + "bbox": [ + 304, + 422, + 545, + 590 + ], + "type": "text", + "content": " in DEV-Indoors. We use two sigmoid functions to fit the exposures if they are unavailable. Detailed settings can be found in the supplemental materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 598, + 503, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 503, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 503, + 611 + ], + "type": "text", + "content": "5.1. Evaluation of Tracking and Mapping" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Evaluation on DEV-Indoors. We report the trajectory accuracy and reconstruction quality in Tab. 1 and Tab. 2. As shown in Tab. 1, EN-SLAM performs the best in all 9 scenes and remains stable (fluctuation below 0.8) under all the blur and dark sequences. While the others perform sensitive and unstable when facing non-ideal environments, especially iMAP [52] and NICE-SLAM [71], which completely crushes in the blur and dark scenes. ESLAM [71]" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19589" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 44, + 547, + 174 + ], + "blocks": [ + { + "bbox": [ + 49, + 44, + 547, + 174 + ], + "lines": [ + { + "bbox": [ + 49, + 44, + 547, + 174 + ], + "spans": [ + { + "bbox": [ + 49, + 44, + 547, + 174 + ], + "type": "image", + "image_path": "5a141d83ad61631a880e527b19f8aeb555d3e9e8fda4fdbec54e6d8cac960165.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 176, + 546, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 176, + 546, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 546, + 198 + ], + "type": "text", + "content": "Figure 7. Reconstruction Performance on DEV-Indoors. EN-SLAM achieves, on average, more precise reconstruction details than existing methods in motion blur and lighting varying environments with the assistance of high-quality event streams." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 226, + 285, + 384 + ], + "blocks": [ + { + "bbox": [ + 47, + 201, + 287, + 223 + ], + "lines": [ + { + "bbox": [ + 47, + 201, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 287, + 223 + ], + "type": "text", + "content": "Table 2. Reconstruction Performance [cm] of the proposed method vs. the state-of-the-art methods on DEV-Indoors dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 226, + 285, + 384 + ], + "lines": [ + { + "bbox": [ + 49, + 226, + 285, + 384 + ], + "spans": [ + { + "bbox": [ + 49, + 226, + 285, + 384 + ], + "type": "table", + "html": "
MethodMetric#Rm norm blur#Rm dark#Rm norm#Apt blur#Apt dark#Wkp norm#Wkp blur#Wkp dark#all avg
iMAP [52]Acc↓37.1637.6034.3025.5544.28854.4756.4051.7438.12
Comp↓48.6955.9733.7619.2823.9449.6165.4027.1847.11
Comp Ratio↑37.5637.7639.1160.0346.2742.5612.1448.4440.41
Depth L1↓79.9397.9864.9640.36128.45140.00131.79115.07124.69
NICESL AM [71]Acc↓18.4918.8616.6921.2716.5119.1726.3522.0928.40
Comp↓20.2621.9321.4320.6718.7021.2928.0449.8277.19
CompRatio↑60.4059.0358.1459.6063.4956.5550.9146.0035.58
Depth L1↓40.5942.0940.2641.5424.0034.8962.48104.20106.09
CoSLAM [58]Acc↓10.6611.3612.7715.4716.4230.7113.0217.5919.85
Comp↓13.2412.4412.2314.0915.3621.6713.9218.2619.46
Comp Ratio↑69.2276.8777.2670.6166.7555.2667.9261.2660.70
Depth L1↓24.7820.9120.6532.2935.9064.1428.6939.1742.85
ESLA M [23]Acc↓9.488.5811.8112.8616.2514.859.0110.0110.02
Comp↓7.947.547.088.51112.3710.408.8910.9510.44
Comp Ratio↑84.6085.6986.7082.9371.5380.9083.1780.0281.64
Depth L1↓15.3412.2719.0811.0727.8015.5030.0329.0628.02
OursAcc↓7.4810.537.079.469.919.349.239.289.25
Comp↓7.7012.517.709.879.289.619.959.929.92
Comp Ratio↑83.0074.4884.2685.3683.4084.0182.2782.3882.35
Depth L1↓15.1023.3611.9218.8611.9419.2123.1623.1423.39
", + "image_path": "95855d52a35e3ec15a229483d6c6cbdfd45249c29dc7ba84cc3bd9c02df893c0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 49, + 420, + 286, + 470 + ], + "blocks": [ + { + "bbox": [ + 47, + 396, + 287, + 418 + ], + "lines": [ + { + "bbox": [ + 47, + 396, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 287, + 418 + ], + "type": "text", + "content": "Table 3. Tracking comparison (ATE median [cm]) of the proposed method vs. the state-of-the-art methods on DEV-Reals." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 420, + 286, + 470 + ], + "lines": [ + { + "bbox": [ + 49, + 420, + 286, + 470 + ], + "spans": [ + { + "bbox": [ + 49, + 420, + 286, + 470 + ], + "type": "table", + "html": "
MethodPio1Pio2Gre1Gre2dorm1dorm2dorm3dorm4avg
ORBSLAM [19]x63%x63%x63%x63%x63%x63%x63%x63%x63%
NICE-SLAM [71]13.2123.35x63%x25%24.6910.6818.4444.04x22.40
COSLAM [58]11.1419.8382.5240.1615.9915.4230.1232.4530.95
ESLAM [23]11.2821.4263.6530.7537.9431.0416.1937.9131.27
Ours8.9419.0543.6321.1811.2611.9116.0019.7818.97
", + "image_path": "2537580298cb9236f4ec9344f1df1fead3d4836aaca1a1557be22d5f9d0b4117.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 481, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 613 + ], + "type": "text", + "content": "and CoSLAM [58] exhibit similar trends but achieve relatively stable results. Specifically, in #room sequences, they achieved 1.02 and 1.45 times the error on the blur subset and 2.49 and 3.77 times the error on the dark subset, respectively. The reconstruction quality in Tab. 2 and Fig. 7 show that EN-SLAM performs more accurately and robustly than the other methods. Specifically, our method reduces the error by 2.37, 0.48, and 1.90 in ACC, Comp, and Depth L1 compared with the second ESLAM [23]. Fig. 7 also shows that our method reconstructs the details of the scenes more accurately and produces fewer artifacts." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Evaluation on DEV-Reals. Tab. 3 illustrates the tracking performance of our method and the state-of-the-art methods on the DEV-Reals dataset. Our method achieves the best performance in all the scenes (18.97), and the average error is 1.63 times lower than the second-best CoSLAM [58] (30.95). Note that DEV-Reals is challenging due to the large motion and varying light, leading to the crushes of ORBSLAM [36] and NICE-SLAM [71]." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 225, + 545, + 287 + ], + "blocks": [ + { + "bbox": [ + 305, + 201, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 223 + ], + "type": "text", + "content": "Table 4. Tracking comparison (ATE mean [cm]) of the proposed method vs. the Event-based SLAM system on Vector[13] dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 225, + 545, + 287 + ], + "lines": [ + { + "bbox": [ + 308, + 225, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 308, + 225, + 545, + 287 + ], + "type": "table", + "html": "
Methodrobot normrobot fastdesk normdesk fastsofa normsofa fasthdr normhdr fastall avg
EVO [43]3.25✘✘✘✘✘✘✘3.25
ESVO [69]✘✘✘✘1.77✘✘✘1.77
USLAM [57] (EVIO)1.181.652.241.085.742.545.692.612.84
CoSLAM [58] (DV)1.00124.691.7697.651.7477.891.471.4238.45
ESLAM [23] (DV)1.393.302.543.647.9919.037.3812.237.19
Ours (EDV)1.061.731.762.692.021.841.031.221.67
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MethodTracking [ms×it] ↓Mapping [ms×it] ↓FPS ↑#para.
iMAP [52]24.73×5041.18×3000.360.22 M
NICE-SLAM [71]6.46×1626.42×1201.555.86 M
CoSLAM[58]6.08×1513.52×1511.261.71 M
ESLAM [23]5.20×1316.68×1014.777.85 M
Ours5.75×1013.16×1017.401.95 M
", + "image_path": "b05f847a4c12d2b35315e02dda9f47720ee943fe3aea1d1d589755bc288f04ca.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 376, + 411, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 411, + 389 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 411, + 389 + ], + "type": "text", + "content": "5.2. Runtime Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 396, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 491 + ], + "type": "text", + "content": "We evaluate all the frameworks on an NVIDIA RTX 4090 GPU and report average tracking and mapping iterations spending, FPS, and parameters number of the model in Tab. 5. The experimental results indicate that our method is fast, with an average of 17 FPS, comparable to the currently most efficient ESLAM [23]. Meanwhile, our method remains lightweight, with only 1.95M parameters, yet achieves the best accuracy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 500, + 444, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 444, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 444, + 513 + ], + "type": "text", + "content": "5.3. Evaluation of Rendering" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 518, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 638 + ], + "type": "text", + "content": "We compare the rendering performance in Fig. 5.3 (left), EN-SLAM outperforms most SOTA works in image quality. The thumbnails in Fig. 5.3 (right) show that EN-SLAM achieves more precise rendering details than previous methods. Specifically, on #Rm Blur, EN-SLAM yields more refined results, while CoSLAM and ESLAM exhibit ghosting. Note that in #Rm Dark and #Wkp Dark, all the RGB rendering is dark and blurred, while our method can still generate high-quality luminance results with the assistance of the HDR event stream." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 647, + 400, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 400, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 400, + 659 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Effect of event and RGB modalities. Fig. 9 illustrates quantitative evaluation using ETA in tracking and mapping. Our full model achieve lower tracking error of 9.61 and 15.47 than the model w/o ETA in tracking (10.73 and 17.07)" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19590" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 44, + 553, + 194 + ], + "blocks": [ + { + "bbox": [ + 56, + 44, + 553, + 194 + ], + "lines": [ + { + "bbox": [ + 56, + 44, + 553, + 194 + ], + "spans": [ + { + "bbox": [ + 56, + 44, + 553, + 194 + ], + "type": "image", + "image_path": "13d2119878820f66c7b199e1e992de6e49272dc2508512dce865b314b13d6906.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 547, + 218 + ], + "type": "text", + "content": "Figure 8. Rendering Performance on DEV-Indoors. left): Our method outperforms most previous works in image quality evaluation under non-ideal environments. right): EN-SLAM achieves more precise rendering details on average than previous methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 227, + 284, + 310 + ], + "blocks": [ + { + "bbox": [ + 53, + 227, + 284, + 310 + ], + "lines": [ + { + "bbox": [ + 53, + 227, + 284, + 310 + ], + "spans": [ + { + "bbox": [ + 53, + 227, + 284, + 310 + ], + "type": "table", + "html": "
Tracking EventMapping Event#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
XX11.898.6110.9876.3114.4618.75
X✓10.738.329.5381.8314.1717.07
✓X11.688.2810.2879.0516.0919.72
✓✓9.617.887.5983.5111.9115.47
RGB 1st-2nd only10.929.029.1582.8113.5217.80
W/o RGB12.0711.1211.0576.2722.5026.48
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Setting#Rm blur#Dorm2
ATE↓ACC↓Comp↓Comp ratio↑Median↓RSME↓
w/o CRF12.128.299.7883.5727.6730.18
w/o PWS9.867.889.4981.0416.5919.78
Full model9.617.887.5983.5111.9115.47
", + "image_path": "03e5f7a7d63c8178beb3f990c3da913df7338a281281386007533f82ffe099d0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 285, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 306, + 285, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 545, + 308 + ], + "type": "text", + "content": "Table 6. Ablation study of CRF and PWS on the #Rm blur and #Drom2 subset of DEV-Indoors and DEV-Reals (15 iterations)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 308, + 545, + 433 + ], + "blocks": [ + { + "bbox": [ + 307, + 308, + 545, + 433 + ], + "lines": [ + { + "bbox": [ + 307, + 308, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 307, + 308, + 545, + 433 + ], + "type": "image", + "image_path": "f88bd5021d37b74957e8f3e52ac8f5c222a987de13249e5096b5848569ef2f96.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 435, + 529, + 446 + ], + "lines": [ + { + "bbox": [ + 321, + 435, + 529, + 446 + ], + "spans": [ + { + "bbox": [ + 321, + 435, + 529, + 446 + ], + "type": "text", + "content": "Figure 10. CRF ablation on the #Dorm2 of DEV-Reals." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 454, + 459, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 459, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 459, + 467 + ], + "type": "text", + "content": "6. Conclusion and Limitation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 475, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 651 + ], + "type": "text", + "content": "This paper first integrates the event stream into the implicit neural SLAM framework to overcome challenges in scenes with motion blur and lighting variation. A differentiable CRF rendering technique that maps the unified representation to color and luminance is proposed to address the significant distinction between event and RGB. An event temporal aggregating optimization strategy that capitalizes the consecutive difference constraints of events is presented to enhance the optimization. We construct DEV-Indoors and DEV-Reals datasets to evaluate the effectiveness of EN-SLAM under various environments. However, EN-SLAM relies on depth input, which might be unavailable in some scenarios. Besides, EN-SLAM focuses on indoor scenes and might face challenges in boundless long trajectories. In future work, we aim to extend it to large-scale outdoor environments and enhance the generalization capability." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by the Shanghai AI Laboratory, National Key R&D Program of China (2022ZD0160101), the National Natural Science Foundation of China (62376222), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19591" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. 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In addition, conventional encoder-decoder frameworks in video processing focus on modeling the correlation in the encoder, leading to limited generative capabilities and redundant intermediate representations. To address these challenges, this paper proposes a novel Implicit Motion Function (IMF) method. Our approach utilizes a low-dimensional latent token as the implicit representation, along with the use of cross-attention, to implicitly model the correlation between frames. This enables the implicit modeling of temporal correlations and understanding of object motions. Our method not only improves sparsity and efficiency in representation but also explores the generative capabilities of the decoder by integrating correlation modeling within it. The IMF framework facilitates video editing and other generative tasks by allowing the direct manipulation of latent tokens. We validate the effectiveness of IMF through extensive experiments on multiple video tasks, demonstrating superior performance in terms of reconstructed video quality, compression efficiency and generation ability.", + "bbox": [ + 75, + 305, + 473, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 678, + 207, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed an upsurge in the field of video modeling [44], processing [45, 62], compression [31, 38], prediction [19, 20], and generation [11, 64, 66]. A fundamental element in these diverse tasks is the use of optical flow, which encapsulates the relationship between consecutive frames. Existing approaches often employ readily available optical flow estimation models, such as RAFT [61], to facilitate this process. However, the definition of optical flow has inherent limitations. It lacks sparsity, capturing only the positional change of pixels, and fails to model the probabilistic aspects of object movements, thereby not comprehending the intrinsic motion and semantics of objects. Furthermore, the non-editability of explicit", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/920adad69aec24a285a14e8adb8e3c39456bea1588fba30b589dd9719a9b10c0.jpg", + "image_caption": [ + "Reference frame" + ], + "image_footnote": [], + "bbox": [ + 504, + 272, + 632, + 372 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3cc45988e91313902f74862d9d582b1dd773623bd096904bd449219e296e834e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 272, + 759, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c75d499620d9309517d0945452ca52a41749146f1bdb4ebd640d31aad16786c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 272, + 888, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b7c15ab6577af2d75f8a99b2498eaf7d7a4e0645699380cfd099f5f4756ad726.jpg", + "image_caption": [ + "Current frame" + ], + "image_footnote": [], + "bbox": [ + 504, + 383, + 630, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5da292f4bea66713dabfb72157b08665c7badac0074cccef1a2adfc6345aac48.jpg", + "image_caption": [ + "Dense optical flow" + ], + "image_footnote": [], + "bbox": [ + 632, + 383, + 758, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/44084b350e91b1f11423d984c191b775708168daf389f0b8e04d2de2e52d89f3.jpg", + "image_caption": [ + "Schematic latent space", + "IMF" + ], + "image_footnote": [], + "bbox": [ + 759, + 383, + 888, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c272b2a041f1d373eabfe5b21b023c9d55df751427139ea7ff9b16d46ab14a44.jpg", + "image_caption": [ + "Reference frame" + ], + "image_footnote": [], + "bbox": [ + 504, + 496, + 632, + 595 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0060484b7b344699e24cb9cc4dca630c66a4af74473fb4082fca7f98c42d78ae.jpg", + "image_caption": [ + "TPSMM [81]", + "Dense optical flow" + ], + "image_footnote": [], + "bbox": [ + 650, + 494, + 756, + 595 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/534d2c64db78b40e97131e48a50999383b97eb3486216b1e0a24caa29c257081.jpg", + "image_caption": [ + "Schematic latent space" + ], + "image_footnote": [], + "bbox": [ + 761, + 496, + 888, + 594 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2d345b17b02121c43063540528aebf35ae0b0ae5ffb1dd82d3da57d87742d2b4.jpg", + "image_caption": [ + "Current frame", + "Figure 1. IMF represents the motion in latent space and model the correlation implicitly. In the diagram, the blue shapes represent tokens from the reference frame, while the pink shapes represent tokens from the current frame. Tokens that are unmatched in the reference frame, indicating new content, are depicted with pink polygons. Successfully matched tokens, such as changes of the head pose or the magnification of flower, are indicated with green arrows. Compared to explicit methods PEChEad [11] and TPSMM [81], our IMF faithfully reconstructs the current frame." + ], + "image_footnote": [], + "bbox": [ + 504, + 608, + 630, + 705 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/691476c46d623c28c6c6dde127a7b33fe1ac0a5c10640eff10cd5109109451ca.jpg", + "image_caption": [ + "PECHead [11]" + ], + "image_footnote": [], + "bbox": [ + 632, + 608, + 758, + 705 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3bf527564159ced49170b1bd7221cbf21cb75a88eadfa8cd24dd1341bbd60c04.jpg", + "image_caption": [ + "IMF" + ], + "image_footnote": [], + "bbox": [ + 759, + 608, + 888, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "optical flow presents significant challenges in video generation tasks. This stems from its rigid structure, which lim", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19278", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "its the ability to manipulate or alter motion trajectories directly within the flow field. Consequently, this necessitates the integration of sophisticated neural networks for downstream generation tasks. These identified limitations underscore the need for an innovative approach in video modeling. It is in this context that we propose the Implicit Motion Function (IMF) method, a novel paradigm designed to address the aforementioned shortcomings by offering a more nuanced and editable representation of motion within video sequences.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our design of the IMF is based on the observation that, contrasting with the aforementioned limitations brought by the explicit optical flow, modeling the frame relations in the latent space offers a more nuanced and adaptable approach. Specifically, by operating in this latent space, it becomes feasible to effectively distinguish different objects and new content between two frames. Such capability is derived from the inherent property of the latent space by encoding a richer and more abstract representation of motion and object characteristics. This encoding allows for a more generalized understanding of object dynamics and interactions, thereby enabling the IMF to adapt to and accurately represent a broader range of object movements and behaviors, including the newly appeared objects. It is worth noting that we generalize the concept of motion to include the entry and exit of objects from the frame as a form of motion, rather than solely encompassing pixel displacement.", + "bbox": [ + 75, + 246, + 472, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The design of our pipeline, adopting an encoder-decoder style, can be highlighted in several aspects: (1) We employ a dense feature encoder and a latent token encoder to model dense features and latent tokens independently. This approach allows us to represent motion between two frames as a pair of low-dimensional tokens, significantly increasing the sparsity of the representation. (2) We design a latent token decoder to decode the tokens and a implicit motion alignment to model the correlation between two frames aligning the features from the reference frame to the current frame. They enable the model to understand the relationship between features across frames, thereby grasping the motion patterns of objects and increasing the sparsity of the motion representation. (3) By directly editing the latent token, we can facilitate editing and other generative tasks. In particular, the encoder independently extracts latent tokens from the current frame and the reference frame, so the frame-to-frame relationship is entirely modeled by the decoder. As shown in Fig. 1, we provide a schematic illustration of the correlation modeling process within the IMF latent space. Compared to explicit methods, our IMF allows for a faithful motion modeling of non-facial content (e.g., flowers) and even new content (e.g., appearing hand and blooming flower), demonstrating the semantic completeness is ensured by the proposed implicit modeling, for both talking head and general videos.", + "bbox": [ + 75, + 507, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In implementing the IMF, two primary challenges emerge. The first concerns defining and extracting sparse tokens. Conventional approaches [11, 41, 57, 66, 81] rely on sparse keypoints transformed into dense optical flow, but this method proves suboptimal, particularly for data lacking strong priors. Our approach circumvents this limitation by allowing the encoder to extract latent tokens without tying them to physical coordinates, preserving semantic integrity while maintaining sparsity. The second challenge involves modeling correlations with latent tokens. Drawing parallels to language model advancements [43, 48], we leverage cross-attention [65] mechanism, a sophisticated weight-based matrix operation that exceeds the capabilities of optical flow-based grid sampling [41]. By utilizing a latent token decoder to generate motion feature maps from compact latent tokens and processing these features through cross-attention, we model frame relationships and align reference appearance features to the current frame. This approach enables refined motion feature generation and feature alignment, bolstering both the reconstructive and generative abilities of the decoder and offering significant potential when integrated with foundation models for video applications.", + "bbox": [ + 496, + 90, + 893, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conducted comprehensive experiments to validate the superiority of our IMF model in video reconstruction, video compression, and talking head editing. In video reconstruction, IMF outperformed existing benchmarks in both talking head and general datasets, demonstrating its ability to accurately reconstruct non-facial objects and new content. For video compression, IMF achieved a superior rate-distortion trade-off compared to current methods, including neural video CODECs, highlighting the compactness of our latent tokens. In talking head editing, IMF surpassed state-of-the-art (SOTA) explicit editing methods, confirming the editability and robust generative capabilities of our latent tokens.", + "bbox": [ + 496, + 425, + 893, + 621 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 517, + 625, + 844, + 638 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the Implicit Motion Function (IMF), a novel framework for video modeling and video generation. The IMF is capable of faithfully reconstructing various videos at extremely low bit rates, while also enabling high-quality video generation.", + "- We incorporate the latent token decoder and the implicit motion alignment as the implicit motion function for correlation modeling. By integrating this step at the decoder, the generative capability of the decoder is unleashed.", + "- By manipulating the latent tokens, the proposed method can achieve high-quality editing results for talking head images, which also demonstrates the powerful expressive capability of our latent tokens.", + "- Extensive qualitative and quantitative results across several talking head and general datasets demonstrate the superiority of the our framework for video modeling and video generation." + ], + "bbox": [ + 500, + 641, + 890, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19279", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 89, + 225, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Image Animation and Video Generation", + "text_level": 1, + "bbox": [ + 76, + 116, + 419, + 132 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image animation, which involves transferring motion between images, has traditionally relied on methods utilizing face meshes [13, 49], human keypoints [78], or action units [22, 47]. Recent trends, however, are leaning towards self-supervised techniques that require only video input. Notable pioneering works such as FOMM [57], and MRAA [58] introduced motion representation through sparse keypoints or regions employing local affine transformations. TPSMM [81] employs thin-plate spline transformation for motion estimation. LIA [67] uses latent vector decomposition but relies on optical flow for warping, and its limited editability leads to artifacts and facial interference. Furthermore, Mallya et al. [41] proposed a warping method based on cross-attention mechanisms [65]. However, its reliance on explicit keypoints as an intermediate representation imposes limitations on performance, as its effectiveness in modeling non-facial data remains relatively limited.", + "bbox": [ + 75, + 142, + 472, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to methods targeting general data, the field of talking head video generation, which focuses on creating realistic videos of talking faces, has advanced significantly due to research in various areas. Unlike the image animation methods that do not need detailed facial models, talking head generation uses detailed information about the head to improve video quality. Progress in this field has been driven by large datasets of face images [8, 72, 73, 82], 3D models of faces [2, 10], face landmark detectors [6, 39], facial landmark detection [6, 39], neural radiance fields (NeRF) [14, 18, 28, 32, 42, 53, 75], and diffusion models [4, 15, 46, 51, 52, 59, 70, 79]. There are several approaches to generate talking head videos. (1). 3D Face Model-Based Methods [40, 63]: These methods use 3D models to track and recreate facial expressions. For example, Face2Face [63] tracks expressions from a source video and applies them to another face. (2). Direct Synthesis-Based Models [7, 76, 77]: These models create faces by transforming encoded representations of appearance and motion into images. They often use latent motion expressions but may also rely on explicit techniques like optical flow. (3). 3D Mesh-Based Methods [12, 26]: These methods use detailed 3D models to create lifelike head avatars from videos. (4). NeRF-Based Methods [14, 18, 18, 32, 53]: These utilize NeRF to represent head geometry and appearance in a novel 3D format. While effective, they can be complex and less versatile across different identities. (5). Warping-Based Methods [17, 50, 66, 69, 73]: These methods estimate motion fields to warp feature maps and generate images, often using learned keypoints. (6). Diffusion Model-Based Methods [9, 54, 60]: These methods create realistic videos from a single image and an audio sequence, enhancing lip-sync, video fidelity, and the naturalness of", + "bbox": [ + 75, + 401, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9b394b653b22e37e491abb2a632cd1a0fcc3f302e3aba9fc4b456fff5e827f72.jpg", + "image_caption": [ + "Figure 2. The overview of our method, which is encoder-decoder style. The reference latent token $t_r$ is obtained with the Latent Token Encoder. The $f_r^l$ and $t_r$ are shared across the whole video." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "head movements and poses. However, they involve complex training and inference pipelines, which can be a challenge in terms of computational resources and efficiency. Despite the successes of these methods, there are still opportunities for improvement, especially in handling non-facial data and enhancing editability for talking head videos. This paper aims to explore new approaches in video modeling that maintain high quality and efficiency while being adaptable to different models.", + "bbox": [ + 496, + 305, + 890, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Neural Video Codec", + "text_level": 1, + "bbox": [ + 500, + 452, + 691, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Many neural video CODECs [3, 34, 36, 38, 74] adopt the widely-used residual coding-based framework, where the predicted frame is firstly generated via motion estimation and motion compensation, and then the residual is coded. They aim to improve the prediction accuracy as much as possible, via scale-space flow [3], block-level prediction[36], and so on. Instead of generating pixel-domain predicted frame, the emerging conditional coding-based CODEcs [27, 29-31, 37, 55] extract feature-domain temporal context to help encoding, decoding, and the entropy model. However, most of them still rely on optical flow to generate the prediction or temporal context. Coding the optical flow requires non-trivial bitrate cost, even with the help of the learned entropy model [29-31]. By contrast, our IMF learns sparse latent token, which is naturally compact and efficient.", + "bbox": [ + 496, + 474, + 890, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 731, + 671, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 756, + 609, + 770 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of our framework is shown in Fig. 2, which follows the encoder-decoder style. The encoder contains the dense feature encoder $E_{F}$ and the latent token encoder $E_{T}$ . The decoder is composed of several implicit motion function (IMF) blocks and the frame decoder $D_{F}$ . Given input video $\\{x_{c}\\}_{c\\in \\Omega}$ and a reference frame $x_{r}$ , the appearance of the reference frame can be encoded into $f_{r}$ by $E_{F}$ and the correlation between $x_{c}$ and $x_{r}$ can be represented by", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19280", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e3f5f77ecd48d845b1ffca4e825bb6f3a083a8809331081059a9c78b4f49089b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 361, + 238 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/52bef632dd0a6c26f6ce00c1c95576ef6003bbce271ed48ff2aaca9e5026f0ad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 90, + 890, + 236 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4498787b873fd34475ca91a3287b8d97763544eeb09e0ccd79ea121c41c42786.jpg", + "image_caption": [ + "Figure 3. The illustration of our framework: a) the encoder contains the dense feature encoder $E_{F}$ and the latent token encoder $E_{T}$ ; b) the decoder contains the implicit motion function IMF and the feature decoder $D_{F}$ . IMF includes the latent token decoder $IMF_{D}$ and the implicit motion alignment $IMF_{A}$ . The motion features $m_{r}^{l}$ and $m_{c}^{l}$ are produced by $IMF_{D}$ from $t_{r}$ and $t_{c}$ , independently." + ], + "image_footnote": [], + "bbox": [ + 83, + 268, + 364, + 387 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/908a152b17e09266bd3b5b21ef8fbfe962f69b5d2e13343302ddbefc6bbcd46b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 370, + 238, + 866, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the tokens pair $(t_c, t_r)$ extracted respectively by $E_T$ from $x_c$ and $x_r$ . The decoder $D_F$ aims to faithfully reconstruct the $\\hat{x}_c$ with $(t_c, t_r, f_r)$ . The pipeline can be formulated as:", + "bbox": [ + 75, + 450, + 470, + 497 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} _ {c} = D _ {F} \\left(I M F \\left(t _ {c}, t _ {r}, f _ {r}\\right)\\right) \\quad \\text {w i t h} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 506, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {c} = E _ {T} (x _ {c}), \\quad t _ {r} = E _ {T} (x _ {r}), \\quad f _ {r} = E _ {F} (x _ {r}).\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 525, + 444, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that the reference frame $x_{r}$ is not necessarily selected from the input sequence $\\{x_{c}\\}$ . Taking the talking head generation as an example, our pipeline can support the reference having a different ID with the input. Furthermore, different from the former works such as optical flow, the correlation modeling by $(t_{c}, t_{r})$ does not require the reference input and the current input has the same dimension, not even the same modality.", + "bbox": [ + 75, + 547, + 468, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our framework, to learn sparse yet essential information, we will constrain the information flow in $t_c$ and $t_r$ . The optimization target can be formulated as:", + "bbox": [ + 75, + 667, + 468, + 713 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {c} L \\left(\\hat {x} _ {c}, x _ {c}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 719, + 468, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\text {s . t .} \\quad | t | < \\epsilon , t \\in \\left\\{t _ {c}, t _ {r} \\right\\}, \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 739, + 364, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L$ is the function that measures the similarity between $\\hat{x}_c$ and $x_c$ . $|t|$ is the size of the latent tokens, and $\\epsilon$ is the size limitation. To achieve this objective, we specially design the IMF at decoder to obtain high-fidelity $\\hat{x}_c$ . A detailed illustration of our full pipeline is shown in Fig. 3. The remaining part of this section will be organized as follows: In Sec. 3.2, we briefly introduce the encoder details of $E_F$ and $E_T$ . In Sec. 3.3, we describe the proposed IMF. Sec. 3.4 demonstrates the editability of the latent tokens on talking", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "head generation. In Sec. 3.5, we delve into the design and underlying rationale of our proposed framework.", + "bbox": [ + 498, + 450, + 890, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dense Feature & Latent Token Encoder", + "text_level": 1, + "bbox": [ + 500, + 505, + 841, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dense Feature Encoder. Given a reference frame $x_{r} \\in \\mathbb{R}^{H \\times W \\times 3}$ , the dense feature encoder $E_{F}$ extracts multiscale feature $f_{r}^{l} \\in \\mathbb{R}^{h_{l} \\times w_{l} \\times d_{l}}$ , $l \\in \\{1, L\\}$ , where $l$ is the layer index and $L$ is number of layers. $h_{l}, w_{l}$ is spatial size of the feature. $d_{l}$ is the depth dimension of the feature. The $E_{F}$ is only performed on the reference frame, which means the features $f_{r}^{l}$ are shared across the whole video if the reference frame is constant.", + "bbox": [ + 496, + 532, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Latent Token Encoder. The latent token encoder $E_{T}$ encodes the reference frame and the current frame to $t_r$ and $t_c$ , independently. It maps the space $\\mathbb{R}^{H \\times W \\times 3} \\Rightarrow \\mathbb{R}^{\\mathbf{d}}$ . Similar to $f_r$ , when the reference frame is constant, $t_r$ is also shared across the entire video. When $\\mathbf{d} = K \\times 2$ , where $K$ is the number of keypoints, our tokens can be viewed as the explicit coordinates representations from FOMM [57]. However, due to the limited information expressed by coordinates, the expressive capability of this kind of representation is limited, especially in terms of semantic integrity, i.e. the completeness to faithfully reconstruct the original frame. By contrast, we choose $\\mathbf{d} = 1 \\times d_m$ , a latent vector to ensure both completeness and compactness. We further discuss in Sec. 3.5 the choice between explicit and implicit representations of $t_c$ and reveal the pros and cons of each in the ablation experiments.", + "bbox": [ + 496, + 657, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19281", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Implicit Motion Function", + "text_level": 1, + "bbox": [ + 76, + 90, + 308, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the latent token $t_r$ and the appearance feature $f_r$ extracted from the reference frame, the target of IMF is to obtain the appearance feature $f_c$ of the current frame from its latent token $t_c$ . Specifically, the IMF is mainly composed of two parts. First, we design a latent token decoder $IMF_D$ module to transform the highly compact latent tokens into spatially aligned motion features that correspond with the frame. Subsequently, we utilize implicit motion alignment $IMF_A$ module to align and refine the appearance feature of the reference frame to the current frame.", + "bbox": [ + 75, + 112, + 468, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Latent Token Decoder. The $IMF_{D}$ decodes the compact tokens $t_r$ , $t_c$ to multiple motion features $m_r^l \\in \\mathbb{R}^{h_l \\times w_l \\times d_l}$ and $m_c^l \\in \\mathbb{R}^{h_l \\times w_l \\times d_l}$ where $l$ is the layer index. The \"style modulation\" utilizes Weight Modulation and Demodulation technique of StyleGAN2 [25], scales the convolution weights with the latent token, and normalizes them to unit standard deviation. Owing to the varying granularities, our latent tokens effectively compress multi-scale information, serving as a comprehensive representation. Furthermore, the fully implicit nature of our representation allows for flexible adjustment of the latent token dimension to accommodate different scenarios. Different from keypoint-based explicit representation [41, 57, 66], where the motion features are Gaussian heatmaps converted from the keypoints, our design enjoys better scalability and capability due to the latent token being directly learned by the encoder instead of coordinates with a limited value range.", + "bbox": [ + 75, + 265, + 470, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implicit Motion Alignment. As shown in Fig.3, with the motion features $m_r^l$ and $m_c^l$ , the $IMF_A$ will align the reference appearance features $f_r^l$ to the current frame. The $IMF_A$ contains two parts including the cross-attention [65] and transformer. The cross-attention module is implemented with scaled dot-product cross-attention. This attention module takes motion features $m_c^l$ , $m_r^l$ , and appearance features $f_r^l$ as $Q, K$ , and $V$ , respectively. The features are first flattened, then the positional embeddings $P_q$ , $P_k$ are added to the queries and keys. We compute the dot products of the queries with keys, divide each by $\\sqrt{d_k}$ , and apply a softmax function to obtain the weights on the values. Then the output-aligned values are computed through matrix multiplication. With the aligned values $V'$ , we further refine them using multi-head self-attention and feedforward network-based Transformer blocks [65], and finally obtain the appearance features $f_c^l$ of the current frame.", + "bbox": [ + 75, + 521, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Token Manipulation", + "text_level": 1, + "bbox": [ + 76, + 786, + 272, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In contrast to the explicit optical flow method, the implicit representation offers a distinct advantage in terms of editability. As the latent token is not task-specific, for a new controllable generation task, the decoder can be fixed and just train a small adapter with a small cost. Taking talking head generation as an example, in the training of the", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "latent space, the full network is only trained to reconstruct the current frame. After the latent space is trained, we can edit learned tokens through another independent token manipulation network. Formally, with an editing module $\\psi$ , source frame $x_{s}$ , and control condition $h$ , we can rewrite Eq. 1 to obtain the edited feature map $\\tilde{f}_{s}$ as:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {f} _ {s} = I M F \\left(\\psi \\left(t _ {s} \\mid h\\right), t _ {s}, f _ {s}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 184, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Passing $\\tilde{f}_s$ to the frame decoder trained before, we can get the edited frame $\\tilde{x}_s$ . In our experiments, we implement $\\psi$ with two MLP encoders to encode the source token and control condition (e.g., the 3DMM face coefficients), and one MLP decoder to output the edited token.", + "bbox": [ + 496, + 204, + 893, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Discussion", + "text_level": 1, + "bbox": [ + 500, + 287, + 617, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Explicit or Implicit. Based on the foundational works MonkeyNet [56], FOMM [57], and MRAA [58], introduced by Siarohin et al., several works employ explicit keypoints [17, 66], landmarks [11, 81], regions [58] or vectors [67] as intermediate representations for direct optical flow estimation. Given the pivotal role of optical flow in elucidating relationships between video frames, this explicit approach has become the predominant methodology in video modeling. However, explicit representations are inherently constrained. Optical flow, being a dense representation, poses optimization challenges due to the per-pixel operations in grid sampling. While keypoints offer sparsity, they compromise on detailed motion information. Additionally, keypoints are effective for quasi-rigid structures like human heads but falter in general video tasks due to the diverse shapes and motion patterns, which are difficult to encapsulate using explicit methods. Another notable drawback of keypoints is their limited scalability, where increased point usage for finer motion details often leads to redundancy and artifact-prone outputs.", + "bbox": [ + 496, + 311, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Encoder-centric (EC) or Decoder-centric (DC). Here, we discuss the placement of correlation modeling, whether it is within the encoder or the decoder. Most existing video compression and video modeling methods belong to EC, which requires a complex design for encoder. For example, the functioning of a video codec encoder is contingent on the decoder output to obtain the prediction or context. Such intertwined framework necessitates meticulous tuning. For instance, the previous SOTA codec DCVC-DC [31, 55] incorporates upwards of ten distinct complicate strategies during training phases. In contrast, recent advancements in Large Language Models (LLMs) [48] usually utilize a DC architecture to support diverse tasks. This paradigm shift prompts reconsideration of similar frameworks for video codec. Actually, Wyner-Ziv coding [71] has given the theoretical support that the rate of DC framework can be identical with that of the EC framework. Our IMF design aligns with successful DC-based LLMs, achieving significant enhancements in video modeling.", + "bbox": [ + 496, + 613, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19282", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/873855380b1cd46e41f3ef7dd89744086853c2bf77b76fb4a1353304c8e2da30.jpg", + "image_caption": [ + "Figure 4. Comparison of talking head video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 261, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a035199cd835038293987ca95b4cfe3c8b0b009eab517f08b0bf1923dd1da2de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 263, + 88, + 529, + 376 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d9f9e1c176acf2e7f627584257d958b206c319b2c68576ed03d65e572bd1c16c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 529, + 89, + 710, + 376 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6592b2503de6b9e33d52d229d66c5683c5c4c7d9a3d5c2e54f25a8c6517acaa5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 89, + 888, + 376 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7ed9bc1a2744e1039318a98fc1469822b079c9142f6a46f9af1b203d3d2c19d1.jpg", + "table_caption": [ + "Table 1. Quantitative results of video reconstruction on talking head datasets." + ], + "table_footnote": [], + "table_body": "
MethodsCelebV-HQ [82]LPIPSLFHQ [72]
L1SSIMPSNRFIDLPIPSL1SSIMPSNRFIDLPIPS
MRAA [58]0.05680.77722.3364.230.15390.04540.81222.6040.170.1117
F-Vid2Vid [66]0.05890.74621.5667.400.18890.04910.80421.7941.950.1054
LIA [67]0.06540.75420.7565.150.15410.05370.81521.4742.270.1099
IW [41]0.05390.80122.6757.650.12870.04260.86223.4634.050.0823
PECHEad [11]0.05520.80324.2956.680.13720.04350.85923.0331.200.0847
IMF0.04170.84925.2853.220.10570.02830.91826.8623.350.0540
", + "bbox": [ + 78, + 449, + 467, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 534, + 207, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. For talking head datasets, CelebVHQ [82] and VFHQ [72] are used. In addition, to verify the universality of our model, we also test three general datasets: Flower, Wavcloth and Foliage1. For visual results of the non-face datasets, we obtain in-the-wild video from the Internet to verify the generalization ability.", + "bbox": [ + 75, + 559, + 468, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We use $256 \\times 256$ as the frame spatial size. The latent token dimension is $d_m = 32$ for all experiments except for ablation studies. During the training, the perceptual Loss [23] and GAN loss [21, 33] are also used. More training details and network structure of each module are in supplementary materials.", + "bbox": [ + 75, + 650, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare four representative works: FOMM [57], MRAA [58], Face-Vid2Vid [66], and PEC-Head [11] on talking head data. Besides FOMM [57] and MRAA [58], we compare TPSMM [81], LIA [67] and IW [41] on general data. These methods were primarily proposed for face data, but can also be applied for general data because the models do not explicitly rely on prior knowledge of face.", + "bbox": [ + 75, + 741, + 468, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We use $L_{1}$ , SSIM [68] and PSNR to evaluate the", + "bbox": [ + 76, + 862, + 467, + 876 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/af32a63be762c7e095a929e0b576a1f331a8ed81ecb4bc7a46bbcd00209a4b05.jpg", + "table_caption": [ + "Table 2. Quantitative results of video reconstruction on general datasets." + ], + "table_footnote": [], + "table_body": "
MethodsFlowerWaveclothFoliage
L1SSIMLPIPSL1SSIMLPIPSL1SSIMLPIPS
FOMM [57]0.08370.6200.25590.07490.6840.20090.08010.68810.1761
MRAA [58]0.07920.6320.24600.06650.7100.17980.07570.71800.1925
TPSMM [81]0.06420.7040.20970.06250.7160.15370.06260.77710.1545
LIA [67]0.08480.5890.24530.07330.6820.18680.08260.66190.1679
IW [41]0.06390.7360.19830.05660.7900.13800.06970.74270.1479
IMF0.05440.7610.17460.04730.8040.12650.05480.82350.1209
", + "bbox": [ + 501, + 449, + 890, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "low-level similarity. FID [16] and LPIPS [80] are used to assess the perceptual quality. For video compression, BPP (bits per pixel) is used to measure the bit-stream size.", + "bbox": [ + 498, + 544, + 890, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Video Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 604, + 700, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 1 and Tab. 2 show the quantitative comparisons with previous SOTA models. Qualitative comparisons are presented in the Fig. 4 and Fig. 5. More results and videos are in supplemental material. These results show that our method significantly outperforms previous SOTA methods. For talking head data, although previous methods can approximately reconstruct the correct facial area, only our model accurately reconstructs the non-facial areas, such as hair and microphones. Our model also performs best for local motion changes, like blinking. For general data, our method is able to precisely reconstruct various contents with complex motion, such as blooming. However, the methods based on explicit representation and alignment [56, 57, 81] perform poorly in cases of drastic content changes and also have inferior modeling capabilities for subtle motions, such as minor positional changes in leaves and flowers. Implicit warping-based method IW [41] is better than previous methods, but the keypoints are still used. It", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1For more information about these datasets, please contact us.", + "bbox": [ + 94, + 886, + 421, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19283", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2ce98ee0800c1b9273782f8c78922613bdc71b6640fac8af332119e2e2f5f4c6.jpg", + "image_caption": [ + "Figure 5. Comparison of general video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles." + ], + "image_footnote": [], + "bbox": [ + 122, + 88, + 305, + 444 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38d9146e396a513f7d6c3bbb7e4bad01322a8ca7e50cef7b9a26a04a5cacd509.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 88, + 843, + 444 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef697b8fc16190a74942186f0179a2742926dddc5af160412c34cac9e8f2af29.jpg", + "image_caption": [ + "Figure 6. The rate-distortion curve on video compression." + ], + "image_footnote": [], + "bbox": [ + 86, + 484, + 459, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "lacks robustness, leading to the appearance of jitter artifacts in the videos.", + "bbox": [ + 75, + 728, + 468, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Video Compression", + "text_level": 1, + "bbox": [ + 76, + 770, + 264, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the efficiency and semantic completeness of our latent tokens, we also test the video compression task using VFHQ [72] dataset. The rate-distortion curves are presented in Fig. 6. Besides the existing methods of talking head generation, we also compare the best standard codec H.266/VTM [1, 5] and previous SOTA neural video codec DCVC-DC [31]. For the results of all methods, we only", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c5105730f847fd0eb6d125fe4c6a2c1663b21e7d4a9b32ef64588ee48ee69c8.jpg", + "image_caption": [ + "Figure 7. Comparison with explicit methods on both talking head and general datasets." + ], + "image_footnote": [], + "bbox": [ + 504, + 484, + 890, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "calculate the current BPP (bits per pixel). Our first approach is directly applying an offline array compressor [35] to compress the latent tokens, and we test different token sizes $d_m \\in \\{16, 32, 64, 128\\}$ , denoted as IMF- $d_m$ . To verify the compactness of the latent token, we also follow neural codec and implement an online learned entropy model [29, 31], where the token of the previous frame is used to predict the distribution of that of the current frame and then the arithmetic coding is applied. It is denoted as IMF- $d_m$ -online. From these results, we can see that our method is significantly better than all previous methods in terms of rate-distortion trade-off. Furthermore, the comparison with the online entropy model also reveals that our latent tokens are naturally compact, because the online entropy model only brings a very small bitrate reduction but with non-trivial quality degradation.", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19284", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/78880ece8ff6da4f66267a580247eafe3471007581c77e39dc2ed1ec68652997.jpg", + "image_caption": [ + "PECHead" + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 173, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ff0f476bf2b8a4231015fdec79e602e82ac9b145ea59b73cb4ec9222b822b88.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 173, + 88, + 251, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aa7e1c55fb9cfa457ffaf965fa0d3ed4895163a84f025e8caad93615a847e064.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 88, + 331, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d75b2f7605aaed3f3d9283f80a5cfefea4b4064d99a1c9496bcaa777a8056e7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 331, + 88, + 411, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4b99d2a5ac08d07cc9645e9c6a8bb416508612b4d2800320918db0a8ae8d9b95.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 88, + 491, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1d724c186ca1ddded91f53bcd7740d8f4c0152932fab475ec5dbec23c3ff397b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 88, + 571, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3e3bce34c338abce5e4e2595150a8832ae8b7035b5a1f49ea7ea7e79fecc0e62.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 88, + 651, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5ab6c114cf8f1cf75990cbfc8b50c248af4e20b2496d8a748a4a56a68f3eb55e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 88, + 730, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e2e744f2d58e5a63d17aa79ccd44c212381dded02ef593ce85083646759cf6c5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 88, + 810, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7547c35da1e403badb081fda9b94101f82e2d88673be133383d63fc4972ef423.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 810, + 88, + 890, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1224ceed195940cdd9f83ca9c039b1f0e4d9d9339dda164800d8de5b54ba8867.jpg", + "image_caption": [ + "Input", + "", + "", + "", + "", + "", + "", + "", + "公", + "$\\therefore m = \\frac{3}{11}$", + "$\\therefore m = \\frac{3}{11}$ ;", + "②", + "(1)", + "$\\therefore m = \\frac{3}{11}$ ;", + "#", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "", + "$\\left( {x - 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SettingsFlowerVFHQ [72]
IRIAL1SSIMPSNRLPIPSL1SSIMFIDLPIPS
0.06420.70422.230.20970.04350.85931.200.0847
✓0.06040.69321.580.19210.03960.87729.840.0612
✓0.05780.75822.460.17620.03660.88530.080.0713
✓✓0.05440.76123.330.17460.02830.91823.350.0540
", + "bbox": [ + 76, + 282, + 468, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Comparison with Explicit Methods", + "text_level": 1, + "bbox": [ + 76, + 373, + 382, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Fig. 7, we compare previous SOTA explicit methods on both talking head and general datasets. The optical flow-based TPS [81] cannot handle the correlation of facial and non-facial content, or new content, as the microphone and flower are not correctly modeled. The latent motion decomposition-based LIA [67] containing explicit flow in the model, fails when the corresponding regions are small or the motion is complex. The keypoints-based IW [41] cannot handle the local motion and can also cause jittering in the videos.", + "bbox": [ + 75, + 396, + 468, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Token Editing", + "text_level": 1, + "bbox": [ + 76, + 556, + 222, + 573 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In our framework, token manipulation facilitates the editing of facial features, enabling precise control over aspects such as head pose and facial expression. To demonstrate the generalization capability of our method, we applied token editing to images from the FFHQ dataset [24]. We benchmark our approach against previous SOTA explicit model for talking head editing, PECHead [11]. Qualitative results, as depicted in Fig. 8, demonstrate that our method not only parallels the editing performance of PECHead [11] but also surpasses it in terms of realism and naturalness, especially in intricate areas such as the eyes, mouth, and ears.", + "bbox": [ + 75, + 580, + 468, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 756, + 240, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare the implicit motion representation and alignment with the explicit motion representation (i.e., keypoints) and alignment (i.e., optical flow-based grid sample). For explicit motion representation and alignment method on general dataset Flower, we use the TPSMM [81] as the baseline model. For the talking head dataset VFHQ [72], we use the PECHad [11] as the baseline model. For implicit motion representation and explicit motion alignment, we keep", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8dc10c094697ea7db76ba8e2a90832573eab42bd3d6e2b51fd9055567259a377.jpg", + "image_caption": [ + "Reference" + ], + "image_footnote": [], + "bbox": [ + 504, + 257, + 566, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d95ee43ea2759b5de8ab3ade87192ce68eb6196828000009c2b242279b7cb502.jpg", + "image_caption": [ + "Current", + "Figure 9. Ablation studies on both talking head and general datasets. The IR and ER stand for implicit and explicit motion representation. The IA and EA stand for implicit and explicit motion alignment. The IR + IA is our full model." + ], + "image_footnote": [], + "bbox": [ + 566, + 258, + 630, + 357 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9858e13f72ce2842e281f41442c33579f990776a728499ed48653dc46135ad11.jpg", + "image_caption": [ + "ER + EA" + ], + "image_footnote": [], + "bbox": [ + 632, + 258, + 694, + 357 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f71f478af46dddfeac536f152a2250d24a4215a6619e39ba204ac290fab78fc6.jpg", + "image_caption": [ + "IR + EA", + "ER + IA" + ], + "image_footnote": [], + "bbox": [ + 696, + 258, + 823, + 357 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e69d0a5c5f8047f76aca9e7552379b389c1a09e742bddb9716bdf49ae1c48ae6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 258, + 825, + 357 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/38ea2acc13d83a53d5a5c13366a9335a99196d7b2b5b75fab311345767a54244.jpg", + "image_caption": [ + "IR+IA" + ], + "image_footnote": [], + "bbox": [ + 825, + 258, + 887, + 357 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the latent token encoder and decoder, and replace the implicit motion alignment with an optical flow estimator and flow-based grid sample to align the motion feature. For explicit motion representation and implicit motion alignment, we replace the latent token encoder with a keypoints extractor and the latent motion decoder with explicit keypoints to Gaussian heatmap [57], while keeping the implicit motion alignment. The results are shown in the Tab. 3 and Fig. 9. The results indicate that explicit representation can only model the face for facial data and is incapable of modeling hands: it either fails to generate results with hands, or it does not correctly reconstruct the position of the hands. The results on flower data also demonstrate the shortcomings of explicit representation and alignment: they either fail to capture complex motions or are unable to accurately reconstruct the frames.", + "bbox": [ + 496, + 445, + 890, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 700, + 617, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces the Implicit Motion Function (IMF), an innovative approach that advances beyond traditional optical flow in video modeling and generation. The implicit methodology of IMF not only achieves high-fidelity video reconstruction, especially in non-facial and new content regions, but also demonstrates a remarkable compression ratio improvement. Its capacity for directly editable latent tokens paves the way for superior editing performance. We believe IMF represents a meaningful step forward in video modeling, potentially inspiring further research and development in video reconstruction and generation.", + "bbox": [ + 496, + 726, + 890, + 892 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19285", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] VTM-17.0. https://vcgi.hhi.fraunhofer.de/jvet/VVCSoftware_VTM/.7", + "[2] Madhav Agarwal, Rudrabha Mukhopadhyay, Vinay P Namboodiri, and CV Jawahar. Audio-visual face reenactment. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5178-5187, 2023. 3", + "[3] Eirikur Agustsson, David Minnen, Nick Johnston, Johannes Balle, Sung Jin Hwang, and George Toderici. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.356, + 0.131, + 0.616, + 0.153 + ], + "angle": 0, + "content": "Implicit Motion Function" + }, + { + "type": "text", + "bbox": [ + 0.313, + 0.181, + 0.653, + 0.198 + ], + "angle": 0, + "content": "Yue Gao Jiahao Li Lei Chu Yan Lu" + }, + { + "type": "text", + "bbox": [ + 0.406, + 0.205, + 0.565, + 0.22 + ], + "angle": 0, + "content": "Microsoft Research" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.225, + 0.698, + 0.24 + ], + "angle": 0, + "content": "{yuegao, li.jiahao, leichu, yanlu}@microsoft.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.313, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.474, + 0.655 + ], + "angle": 0, + "content": "Recent advancements in video modeling extensively rely on optical flow to represent the relationships across frames, but this approach often lacks efficiency and fails to model the probability of the intrinsic motion of objects. In addition, conventional encoder-decoder frameworks in video processing focus on modeling the correlation in the encoder, leading to limited generative capabilities and redundant intermediate representations. To address these challenges, this paper proposes a novel Implicit Motion Function (IMF) method. Our approach utilizes a low-dimensional latent token as the implicit representation, along with the use of cross-attention, to implicitly model the correlation between frames. This enables the implicit modeling of temporal correlations and understanding of object motions. Our method not only improves sparsity and efficiency in representation but also explores the generative capabilities of the decoder by integrating correlation modeling within it. The IMF framework facilitates video editing and other generative tasks by allowing the direct manipulation of latent tokens. We validate the effectiveness of IMF through extensive experiments on multiple video tasks, demonstrating superior performance in terms of reconstructed video quality, compression efficiency and generation ability." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.679, + 0.209, + 0.695 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Recent years have witnessed an upsurge in the field of video modeling [44], processing [45, 62], compression [31, 38], prediction [19, 20], and generation [11, 64, 66]. A fundamental element in these diverse tasks is the use of optical flow, which encapsulates the relationship between consecutive frames. Existing approaches often employ readily available optical flow estimation models, such as RAFT [61], to facilitate this process. However, the definition of optical flow has inherent limitations. It lacks sparsity, capturing only the positional change of pixels, and fails to model the probabilistic aspects of object movements, thereby not comprehending the intrinsic motion and semantics of objects. Furthermore, the non-editability of explicit" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.273, + 0.633, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.373, + 0.614, + 0.383 + ], + "angle": 0, + "content": "Reference frame" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.273, + 0.761, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.373, + 0.747, + 0.384 + ], + "angle": 0, + "content": "Dense optical flow" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.273, + 0.889, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.373, + 0.885, + 0.384 + ], + "angle": 0, + "content": "Schematic latent space" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.385, + 0.632, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.485, + 0.607, + 0.495 + ], + "angle": 0, + "content": "Current frame" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.385, + 0.759, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.661, + 0.485, + 0.734, + 0.496 + ], + "angle": 0, + "content": "TPSMM [81]" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.385, + 0.889, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.811, + 0.485, + 0.839, + 0.495 + ], + "angle": 0, + "content": "IMF" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.497, + 0.633, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.597, + 0.612, + 0.607 + ], + "angle": 0, + "content": "Reference frame" + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.496, + 0.758, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.597, + 0.747, + 0.608 + ], + "angle": 0, + "content": "Dense optical flow" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.497, + 0.889, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.597, + 0.885, + 0.608 + ], + "angle": 0, + "content": "Schematic latent space" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.609, + 0.632, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.708, + 0.607, + 0.718 + ], + "angle": 0, + "content": "Current frame" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.609, + 0.759, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.657, + 0.708, + 0.736, + 0.719 + ], + "angle": 0, + "content": "PECHead [11]" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.609, + 0.889, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.811, + 0.708, + 0.839, + 0.718 + ], + "angle": 0, + "content": "IMF" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Figure 1. IMF represents the motion in latent space and model the correlation implicitly. In the diagram, the blue shapes represent tokens from the reference frame, while the pink shapes represent tokens from the current frame. Tokens that are unmatched in the reference frame, indicating new content, are depicted with pink polygons. Successfully matched tokens, such as changes of the head pose or the magnification of flower, are indicated with green arrows. Compared to explicit methods PEChEad [11] and TPSMM [81], our IMF faithfully reconstructs the current frame." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "optical flow presents significant challenges in video generation tasks. This stems from its rigid structure, which lim" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19278" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "its the ability to manipulate or alter motion trajectories directly within the flow field. Consequently, this necessitates the integration of sophisticated neural networks for downstream generation tasks. These identified limitations underscore the need for an innovative approach in video modeling. It is in this context that we propose the Implicit Motion Function (IMF) method, a novel paradigm designed to address the aforementioned shortcomings by offering a more nuanced and editable representation of motion within video sequences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.473, + 0.504 + ], + "angle": 0, + "content": "Our design of the IMF is based on the observation that, contrasting with the aforementioned limitations brought by the explicit optical flow, modeling the frame relations in the latent space offers a more nuanced and adaptable approach. Specifically, by operating in this latent space, it becomes feasible to effectively distinguish different objects and new content between two frames. Such capability is derived from the inherent property of the latent space by encoding a richer and more abstract representation of motion and object characteristics. This encoding allows for a more generalized understanding of object dynamics and interactions, thereby enabling the IMF to adapt to and accurately represent a broader range of object movements and behaviors, including the newly appeared objects. It is worth noting that we generalize the concept of motion to include the entry and exit of objects from the frame as a form of motion, rather than solely encompassing pixel displacement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The design of our pipeline, adopting an encoder-decoder style, can be highlighted in several aspects: (1) We employ a dense feature encoder and a latent token encoder to model dense features and latent tokens independently. This approach allows us to represent motion between two frames as a pair of low-dimensional tokens, significantly increasing the sparsity of the representation. (2) We design a latent token decoder to decode the tokens and a implicit motion alignment to model the correlation between two frames aligning the features from the reference frame to the current frame. They enable the model to understand the relationship between features across frames, thereby grasping the motion patterns of objects and increasing the sparsity of the motion representation. (3) By directly editing the latent token, we can facilitate editing and other generative tasks. In particular, the encoder independently extracts latent tokens from the current frame and the reference frame, so the frame-to-frame relationship is entirely modeled by the decoder. As shown in Fig. 1, we provide a schematic illustration of the correlation modeling process within the IMF latent space. Compared to explicit methods, our IMF allows for a faithful motion modeling of non-facial content (e.g., flowers) and even new content (e.g., appearing hand and blooming flower), demonstrating the semantic completeness is ensured by the proposed implicit modeling, for both talking head and general videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.424 + ], + "angle": 0, + "content": "In implementing the IMF, two primary challenges emerge. The first concerns defining and extracting sparse tokens. Conventional approaches [11, 41, 57, 66, 81] rely on sparse keypoints transformed into dense optical flow, but this method proves suboptimal, particularly for data lacking strong priors. Our approach circumvents this limitation by allowing the encoder to extract latent tokens without tying them to physical coordinates, preserving semantic integrity while maintaining sparsity. The second challenge involves modeling correlations with latent tokens. Drawing parallels to language model advancements [43, 48], we leverage cross-attention [65] mechanism, a sophisticated weight-based matrix operation that exceeds the capabilities of optical flow-based grid sampling [41]. By utilizing a latent token decoder to generate motion feature maps from compact latent tokens and processing these features through cross-attention, we model frame relationships and align reference appearance features to the current frame. This approach enables refined motion feature generation and feature alignment, bolstering both the reconstructive and generative abilities of the decoder and offering significant potential when integrated with foundation models for video applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.895, + 0.622 + ], + "angle": 0, + "content": "We conducted comprehensive experiments to validate the superiority of our IMF model in video reconstruction, video compression, and talking head editing. In video reconstruction, IMF outperformed existing benchmarks in both talking head and general datasets, demonstrating its ability to accurately reconstruct non-facial objects and new content. For video compression, IMF achieved a superior rate-distortion trade-off compared to current methods, including neural video CODECs, highlighting the compactness of our latent tokens. In talking head editing, IMF surpassed state-of-the-art (SOTA) explicit editing methods, confirming the editability and robust generative capabilities of our latent tokens." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.625, + 0.845, + 0.639 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.642, + 0.892, + 0.717 + ], + "angle": 0, + "content": "- We propose the Implicit Motion Function (IMF), a novel framework for video modeling and video generation. The IMF is capable of faithfully reconstructing various videos at extremely low bit rates, while also enabling high-quality video generation." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.718, + 0.892, + 0.777 + ], + "angle": 0, + "content": "- We incorporate the latent token decoder and the implicit motion alignment as the implicit motion function for correlation modeling. By integrating this step at the decoder, the generative capability of the decoder is unleashed." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.779, + 0.892, + 0.837 + ], + "angle": 0, + "content": "- By manipulating the latent tokens, the proposed method can achieve high-quality editing results for talking head images, which also demonstrates the powerful expressive capability of our latent tokens." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.839, + 0.892, + 0.898 + ], + "angle": 0, + "content": "- Extensive qualitative and quantitative results across several talking head and general datasets demonstrate the superiority of the our framework for video modeling and video generation." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.642, + 0.892, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19279" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.227, + 0.106 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.117, + 0.421, + 0.133 + ], + "angle": 0, + "content": "2.1. Image Animation and Video Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.143, + 0.473, + 0.4 + ], + "angle": 0, + "content": "Image animation, which involves transferring motion between images, has traditionally relied on methods utilizing face meshes [13, 49], human keypoints [78], or action units [22, 47]. Recent trends, however, are leaning towards self-supervised techniques that require only video input. Notable pioneering works such as FOMM [57], and MRAA [58] introduced motion representation through sparse keypoints or regions employing local affine transformations. TPSMM [81] employs thin-plate spline transformation for motion estimation. LIA [67] uses latent vector decomposition but relies on optical flow for warping, and its limited editability leads to artifacts and facial interference. Furthermore, Mallya et al. [41] proposed a warping method based on cross-attention mechanisms [65]. However, its reliance on explicit keypoints as an intermediate representation imposes limitations on performance, as its effectiveness in modeling non-facial data remains relatively limited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In contrast to methods targeting general data, the field of talking head video generation, which focuses on creating realistic videos of talking faces, has advanced significantly due to research in various areas. Unlike the image animation methods that do not need detailed facial models, talking head generation uses detailed information about the head to improve video quality. Progress in this field has been driven by large datasets of face images [8, 72, 73, 82], 3D models of faces [2, 10], face landmark detectors [6, 39], facial landmark detection [6, 39], neural radiance fields (NeRF) [14, 18, 28, 32, 42, 53, 75], and diffusion models [4, 15, 46, 51, 52, 59, 70, 79]. There are several approaches to generate talking head videos. (1). 3D Face Model-Based Methods [40, 63]: These methods use 3D models to track and recreate facial expressions. For example, Face2Face [63] tracks expressions from a source video and applies them to another face. (2). Direct Synthesis-Based Models [7, 76, 77]: These models create faces by transforming encoded representations of appearance and motion into images. They often use latent motion expressions but may also rely on explicit techniques like optical flow. (3). 3D Mesh-Based Methods [12, 26]: These methods use detailed 3D models to create lifelike head avatars from videos. (4). NeRF-Based Methods [14, 18, 18, 32, 53]: These utilize NeRF to represent head geometry and appearance in a novel 3D format. While effective, they can be complex and less versatile across different identities. (5). Warping-Based Methods [17, 50, 66, 69, 73]: These methods estimate motion fields to warp feature maps and generate images, often using learned keypoints. (6). Diffusion Model-Based Methods [9, 54, 60]: These methods create realistic videos from a single image and an audio sequence, enhancing lip-sync, video fidelity, and the naturalness of" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.257, + 0.892, + 0.299 + ], + "angle": 0, + "content": "Figure 2. The overview of our method, which is encoder-decoder style. The reference latent token \\( t_r \\) is obtained with the Latent Token Encoder. The \\( f_r^l \\) and \\( t_r \\) are shared across the whole video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.892, + 0.442 + ], + "angle": 0, + "content": "head movements and poses. However, they involve complex training and inference pipelines, which can be a challenge in terms of computational resources and efficiency. Despite the successes of these methods, there are still opportunities for improvement, especially in handling non-facial data and enhancing editability for talking head videos. This paper aims to explore new approaches in video modeling that maintain high quality and efficiency while being adaptable to different models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.453, + 0.692, + 0.467 + ], + "angle": 0, + "content": "2.2. Neural Video Codec" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Many neural video CODECs [3, 34, 36, 38, 74] adopt the widely-used residual coding-based framework, where the predicted frame is firstly generated via motion estimation and motion compensation, and then the residual is coded. They aim to improve the prediction accuracy as much as possible, via scale-space flow [3], block-level prediction[36], and so on. Instead of generating pixel-domain predicted frame, the emerging conditional coding-based CODEcs [27, 29-31, 37, 55] extract feature-domain temporal context to help encoding, decoding, and the entropy model. However, most of them still rely on optical flow to generate the prediction or temporal context. Coding the optical flow requires non-trivial bitrate cost, even with the help of the learned entropy model [29-31]. By contrast, our IMF learns sparse latent token, which is naturally compact and efficient." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.732, + 0.673, + 0.749 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.611, + 0.771 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "An overview of our framework is shown in Fig. 2, which follows the encoder-decoder style. The encoder contains the dense feature encoder \\( E_{F} \\) and the latent token encoder \\( E_{T} \\). The decoder is composed of several implicit motion function (IMF) blocks and the frame decoder \\( D_{F} \\). Given input video \\( \\{x_{c}\\}_{c\\in \\Omega} \\) and a reference frame \\( x_{r} \\), the appearance of the reference frame can be encoded into \\( f_{r} \\) by \\( E_{F} \\) and the correlation between \\( x_{c} \\) and \\( x_{r} \\) can be represented by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19280" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.362, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.091, + 0.891, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.269, + 0.365, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.239, + 0.867, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.397, + 0.893, + 0.441 + ], + "angle": 0, + "content": "Figure 3. The illustration of our framework: a) the encoder contains the dense feature encoder \\( E_{F} \\) and the latent token encoder \\( E_{T} \\); b) the decoder contains the implicit motion function IMF and the feature decoder \\( D_{F} \\). IMF includes the latent token decoder \\( IMF_{D} \\) and the implicit motion alignment \\( IMF_{A} \\). The motion features \\( m_{r}^{l} \\) and \\( m_{c}^{l} \\) are produced by \\( IMF_{D} \\) from \\( t_{r} \\) and \\( t_{c} \\), independently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.471, + 0.498 + ], + "angle": 0, + "content": "the tokens pair \\((t_c, t_r)\\) extracted respectively by \\(E_T\\) from \\(x_c\\) and \\(x_r\\). The decoder \\(D_F\\) aims to faithfully reconstruct the \\(\\hat{x}_c\\) with \\((t_c, t_r, f_r)\\). The pipeline can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.507, + 0.47, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\hat {x} _ {c} = D _ {F} \\left(I M F \\left(t _ {c}, t _ {r}, f _ {r}\\right)\\right) \\quad \\text {w i t h} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.526, + 0.445, + 0.542 + ], + "angle": 0, + "content": "\\[\nt _ {c} = E _ {T} (x _ {c}), \\quad t _ {r} = E _ {T} (x _ {r}), \\quad f _ {r} = E _ {F} (x _ {r}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.469, + 0.667 + ], + "angle": 0, + "content": "Note that the reference frame \\( x_{r} \\) is not necessarily selected from the input sequence \\( \\{x_{c}\\} \\). Taking the talking head generation as an example, our pipeline can support the reference having a different ID with the input. Furthermore, different from the former works such as optical flow, the correlation modeling by \\( (t_{c}, t_{r}) \\) does not require the reference input and the current input has the same dimension, not even the same modality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.47, + 0.714 + ], + "angle": 0, + "content": "In our framework, to learn sparse yet essential information, we will constrain the information flow in \\( t_c \\) and \\( t_r \\). The optimization target can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.72, + 0.469, + 0.745 + ], + "angle": 0, + "content": "\\[\n\\min _ {c} L \\left(\\hat {x} _ {c}, x _ {c}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.74, + 0.365, + 0.756 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\text {s . t .} \\quad | t | < \\epsilon , t \\in \\left\\{t _ {c}, t _ {r} \\right\\}, \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\( L \\) is the function that measures the similarity between \\( \\hat{x}_c \\) and \\( x_c \\). \\( |t| \\) is the size of the latent tokens, and \\( \\epsilon \\) is the size limitation. To achieve this objective, we specially design the IMF at decoder to obtain high-fidelity \\( \\hat{x}_c \\). A detailed illustration of our full pipeline is shown in Fig. 3. The remaining part of this section will be organized as follows: In Sec. 3.2, we briefly introduce the encoder details of \\( E_F \\) and \\( E_T \\). In Sec. 3.3, we describe the proposed IMF. Sec. 3.4 demonstrates the editability of the latent tokens on talking" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.452, + 0.892, + 0.483 + ], + "angle": 0, + "content": "head generation. In Sec. 3.5, we delve into the design and underlying rationale of our proposed framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.842, + 0.521 + ], + "angle": 0, + "content": "3.2. Dense Feature & Latent Token Encoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.892, + 0.653 + ], + "angle": 0, + "content": "Dense Feature Encoder. Given a reference frame \\( x_{r} \\in \\mathbb{R}^{H \\times W \\times 3} \\), the dense feature encoder \\( E_{F} \\) extracts multiscale feature \\( f_{r}^{l} \\in \\mathbb{R}^{h_{l} \\times w_{l} \\times d_{l}} \\), \\( l \\in \\{1, L\\} \\), where \\( l \\) is the layer index and \\( L \\) is number of layers. \\( h_{l}, w_{l} \\) is spatial size of the feature. \\( d_{l} \\) is the depth dimension of the feature. The \\( E_{F} \\) is only performed on the reference frame, which means the features \\( f_{r}^{l} \\) are shared across the whole video if the reference frame is constant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Latent Token Encoder. The latent token encoder \\( E_{T} \\) encodes the reference frame and the current frame to \\( t_r \\) and \\( t_c \\), independently. It maps the space \\( \\mathbb{R}^{H \\times W \\times 3} \\Rightarrow \\mathbb{R}^{\\mathbf{d}} \\). Similar to \\( f_r \\), when the reference frame is constant, \\( t_r \\) is also shared across the entire video. When \\( \\mathbf{d} = K \\times 2 \\), where \\( K \\) is the number of keypoints, our tokens can be viewed as the explicit coordinates representations from FOMM [57]. However, due to the limited information expressed by coordinates, the expressive capability of this kind of representation is limited, especially in terms of semantic integrity, i.e. the completeness to faithfully reconstruct the original frame. By contrast, we choose \\( \\mathbf{d} = 1 \\times d_m \\), a latent vector to ensure both completeness and compactness. We further discuss in Sec. 3.5 the choice between explicit and implicit representations of \\( t_c \\) and reveal the pros and cons of each in the ablation experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19281" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.31, + 0.108 + ], + "angle": 0, + "content": "3.3. Implicit Motion Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.47, + 0.265 + ], + "angle": 0, + "content": "With the latent token \\( t_r \\) and the appearance feature \\( f_r \\) extracted from the reference frame, the target of IMF is to obtain the appearance feature \\( f_c \\) of the current frame from its latent token \\( t_c \\). Specifically, the IMF is mainly composed of two parts. First, we design a latent token decoder \\( IMF_D \\) module to transform the highly compact latent tokens into spatially aligned motion features that correspond with the frame. Subsequently, we utilize implicit motion alignment \\( IMF_A \\) module to align and refine the appearance feature of the reference frame to the current frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.471, + 0.522 + ], + "angle": 0, + "content": "Latent Token Decoder. The \\(IMF_{D}\\) decodes the compact tokens \\(t_r\\), \\(t_c\\) to multiple motion features \\(m_r^l \\in \\mathbb{R}^{h_l \\times w_l \\times d_l}\\) and \\(m_c^l \\in \\mathbb{R}^{h_l \\times w_l \\times d_l}\\) where \\(l\\) is the layer index. The \"style modulation\" utilizes Weight Modulation and Demodulation technique of StyleGAN2 [25], scales the convolution weights with the latent token, and normalizes them to unit standard deviation. Owing to the varying granularities, our latent tokens effectively compress multi-scale information, serving as a comprehensive representation. Furthermore, the fully implicit nature of our representation allows for flexible adjustment of the latent token dimension to accommodate different scenarios. Different from keypoint-based explicit representation [41, 57, 66], where the motion features are Gaussian heatmaps converted from the keypoints, our design enjoys better scalability and capability due to the latent token being directly learned by the encoder instead of coordinates with a limited value range." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Implicit Motion Alignment. As shown in Fig.3, with the motion features \\( m_r^l \\) and \\( m_c^l \\), the \\( IMF_A \\) will align the reference appearance features \\( f_r^l \\) to the current frame. The \\( IMF_A \\) contains two parts including the cross-attention [65] and transformer. The cross-attention module is implemented with scaled dot-product cross-attention. This attention module takes motion features \\( m_c^l \\), \\( m_r^l \\), and appearance features \\( f_r^l \\) as \\( Q, K \\), and \\( V \\), respectively. The features are first flattened, then the positional embeddings \\( P_q \\), \\( P_k \\) are added to the queries and keys. We compute the dot products of the queries with keys, divide each by \\( \\sqrt{d_k} \\), and apply a softmax function to obtain the weights on the values. Then the output-aligned values are computed through matrix multiplication. With the aligned values \\( V' \\), we further refine them using multi-head self-attention and feedforward network-based Transformer blocks [65], and finally obtain the appearance features \\( f_c^l \\) of the current frame." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.273, + 0.803 + ], + "angle": 0, + "content": "3.4. Token Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In contrast to the explicit optical flow method, the implicit representation offers a distinct advantage in terms of editability. As the latent token is not task-specific, for a new controllable generation task, the decoder can be fixed and just train a small adapter with a small cost. Taking talking head generation as an example, in the training of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "latent space, the full network is only trained to reconstruct the current frame. After the latent space is trained, we can edit learned tokens through another independent token manipulation network. Formally, with an editing module \\(\\psi\\), source frame \\(x_{s}\\), and control condition \\(h\\), we can rewrite Eq. 1 to obtain the edited feature map \\(\\tilde{f}_{s}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.185, + 0.892, + 0.203 + ], + "angle": 0, + "content": "\\[\n\\tilde {f} _ {s} = I M F \\left(\\psi \\left(t _ {s} \\mid h\\right), t _ {s}, f _ {s}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.205, + 0.894, + 0.282 + ], + "angle": 0, + "content": "Passing \\(\\tilde{f}_s\\) to the frame decoder trained before, we can get the edited frame \\(\\tilde{x}_s\\). In our experiments, we implement \\(\\psi\\) with two MLP encoders to encode the source token and control condition (e.g., the 3DMM face coefficients), and one MLP decoder to output the edited token." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.289, + 0.618, + 0.304 + ], + "angle": 0, + "content": "3.5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.614 + ], + "angle": 0, + "content": "Explicit or Implicit. Based on the foundational works MonkeyNet [56], FOMM [57], and MRAA [58], introduced by Siarohin et al., several works employ explicit keypoints [17, 66], landmarks [11, 81], regions [58] or vectors [67] as intermediate representations for direct optical flow estimation. Given the pivotal role of optical flow in elucidating relationships between video frames, this explicit approach has become the predominant methodology in video modeling. However, explicit representations are inherently constrained. Optical flow, being a dense representation, poses optimization challenges due to the per-pixel operations in grid sampling. While keypoints offer sparsity, they compromise on detailed motion information. Additionally, keypoints are effective for quasi-rigid structures like human heads but falter in general video tasks due to the diverse shapes and motion patterns, which are difficult to encapsulate using explicit methods. Another notable drawback of keypoints is their limited scalability, where increased point usage for finer motion details often leads to redundancy and artifact-prone outputs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Encoder-centric (EC) or Decoder-centric (DC). Here, we discuss the placement of correlation modeling, whether it is within the encoder or the decoder. Most existing video compression and video modeling methods belong to EC, which requires a complex design for encoder. For example, the functioning of a video codec encoder is contingent on the decoder output to obtain the prediction or context. Such intertwined framework necessitates meticulous tuning. For instance, the previous SOTA codec DCVC-DC [31, 55] incorporates upwards of ten distinct complicate strategies during training phases. In contrast, recent advancements in Large Language Models (LLMs) [48] usually utilize a DC architecture to support diverse tasks. This paradigm shift prompts reconsideration of similar frameworks for video codec. Actually, Wyner-Ziv coding [71] has given the theoretical support that the rate of DC framework can be identical with that of the EC framework. Our IMF design aligns with successful DC-based LLMs, achieving significant enhancements in video modeling." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19282" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.263, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.089, + 0.531, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.09, + 0.712, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.09, + 0.89, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.379, + 0.892, + 0.407 + ], + "angle": 0, + "content": "Figure 4. Comparison of talking head video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.421, + 0.468, + 0.447 + ], + "angle": 0, + "content": "Table 1. Quantitative results of video reconstruction on talking head datasets." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.45, + 0.468, + 0.519 + ], + "angle": 0, + "content": "
MethodsCelebV-HQ [82]LPIPSLFHQ [72]
L1SSIMPSNRFIDLPIPSL1SSIMPSNRFIDLPIPS
MRAA [58]0.05680.77722.3364.230.15390.04540.81222.6040.170.1117
F-Vid2Vid [66]0.05890.74621.5667.400.18890.04910.80421.7941.950.1054
LIA [67]0.06540.75420.7565.150.15410.05370.81521.4742.270.1099
IW [41]0.05390.80122.6757.650.12870.04260.86223.4634.050.0823
PECHEad [11]0.05520.80324.2956.680.13720.04350.85923.0331.200.0847
IMF0.04170.84925.2853.220.10570.02830.91826.8623.350.0540
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.535, + 0.208, + 0.551 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.469, + 0.65 + ], + "angle": 0, + "content": "Datasets. For talking head datasets, CelebVHQ [82] and VFHQ [72] are used. In addition, to verify the universality of our model, we also test three general datasets: Flower, Wavcloth and Foliage1. For visual results of the non-face datasets, we obtain in-the-wild video from the Internet to verify the generalization ability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.651, + 0.469, + 0.741 + ], + "angle": 0, + "content": "Implementation details. We use \\(256 \\times 256\\) as the frame spatial size. The latent token dimension is \\(d_m = 32\\) for all experiments except for ablation studies. During the training, the perceptual Loss [23] and GAN loss [21, 33] are also used. More training details and network structure of each module are in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.469, + 0.862 + ], + "angle": 0, + "content": "Baselines. We compare four representative works: FOMM [57], MRAA [58], Face-Vid2Vid [66], and PEC-Head [11] on talking head data. Besides FOMM [57] and MRAA [58], we compare TPSMM [81], LIA [67] and IW [41] on general data. These methods were primarily proposed for face data, but can also be applied for general data because the models do not explicitly rely on prior knowledge of face." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.863, + 0.468, + 0.877 + ], + "angle": 0, + "content": "Metrics. We use \\( L_{1} \\), SSIM [68] and PSNR to evaluate the" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.421, + 0.89, + 0.447 + ], + "angle": 0, + "content": "Table 2. Quantitative results of video reconstruction on general datasets." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.45, + 0.891, + 0.529 + ], + "angle": 0, + "content": "
MethodsFlowerWaveclothFoliage
L1SSIMLPIPSL1SSIMLPIPSL1SSIMLPIPS
FOMM [57]0.08370.6200.25590.07490.6840.20090.08010.68810.1761
MRAA [58]0.07920.6320.24600.06650.7100.17980.07570.71800.1925
TPSMM [81]0.06420.7040.20970.06250.7160.15370.06260.77710.1545
LIA [67]0.08480.5890.24530.07330.6820.18680.08260.66190.1679
IW [41]0.06390.7360.19830.05660.7900.13800.06970.74270.1479
IMF0.05440.7610.17460.04730.8040.12650.05480.82350.1209
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.545, + 0.892, + 0.59 + ], + "angle": 0, + "content": "low-level similarity. FID [16] and LPIPS [80] are used to assess the perceptual quality. For video compression, BPP (bits per pixel) is used to measure the bit-stream size." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.702, + 0.619 + ], + "angle": 0, + "content": "4.1. Video Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Tab. 1 and Tab. 2 show the quantitative comparisons with previous SOTA models. Qualitative comparisons are presented in the Fig. 4 and Fig. 5. More results and videos are in supplemental material. These results show that our method significantly outperforms previous SOTA methods. For talking head data, although previous methods can approximately reconstruct the correct facial area, only our model accurately reconstructs the non-facial areas, such as hair and microphones. Our model also performs best for local motion changes, like blinking. For general data, our method is able to precisely reconstruct various contents with complex motion, such as blooming. However, the methods based on explicit representation and alignment [56, 57, 81] perform poorly in cases of drastic content changes and also have inferior modeling capabilities for subtle motions, such as minor positional changes in leaves and flowers. Implicit warping-based method IW [41] is better than previous methods, but the keypoints are still used. It" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.422, + 0.9 + ], + "angle": 0, + "content": "1For more information about these datasets, please contact us." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19283" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.124, + 0.089, + 0.306, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.089, + 0.844, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.447, + 0.893, + 0.474 + ], + "angle": 0, + "content": "Figure 5. Comparison of general video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.486, + 0.46, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.704, + 0.444, + 0.719 + ], + "angle": 0, + "content": "Figure 6. The rate-distortion curve on video compression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.759 + ], + "angle": 0, + "content": "lacks robustness, leading to the appearance of jitter artifacts in the videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.265, + 0.789 + ], + "angle": 0, + "content": "4.2. Video Compression" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To verify the efficiency and semantic completeness of our latent tokens, we also test the video compression task using VFHQ [72] dataset. The rate-distortion curves are presented in Fig. 6. Besides the existing methods of talking head generation, we also compare the best standard codec H.266/VTM [1, 5] and previous SOTA neural video codec DCVC-DC [31]. For the results of all methods, we only" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.486, + 0.891, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.605, + 0.892, + 0.634 + ], + "angle": 0, + "content": "Figure 7. Comparison with explicit methods on both talking head and general datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "calculate the current BPP (bits per pixel). Our first approach is directly applying an offline array compressor [35] to compress the latent tokens, and we test different token sizes \\( d_m \\in \\{16, 32, 64, 128\\} \\), denoted as IMF-\\( d_m \\). To verify the compactness of the latent token, we also follow neural codec and implement an online learned entropy model [29, 31], where the token of the previous frame is used to predict the distribution of that of the current frame and then the arithmetic coding is applied. It is denoted as IMF-\\( d_m \\)-online. From these results, we can see that our method is significantly better than all previous methods in terms of rate-distortion trade-off. Furthermore, the comparison with the online entropy model also reveals that our latent tokens are naturally compact, because the online entropy model only brings a very small bitrate reduction but with non-trivial quality degradation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19284" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.096, + 0.097, + 0.146 + ], + "angle": 270, + "content": "PECHead" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.174, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.089, + 0.253, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.089, + 0.333, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.089, + 0.412, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.089, + 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"content": "公" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.232, + 0.174, + 0.233 + ], + "angle": 0, + "content": "\\( \\therefore m = \\frac{3}{11} \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.233, + 0.174, + 0.234 + ], + "angle": 0, + "content": "\\( \\therefore m = \\frac{3}{11} \\) ;" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.234, + 0.174, + 0.235 + ], + "angle": 0, + "content": "②" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.235, + 0.174, + 0.236 + ], + "angle": 0, + "content": "\\( \\therefore m : x = 1 \\) 或 \\( {3x} + {4y} + 1 = 0 \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.236, + 0.174, + 0.237 + ], + "angle": 0, + "content": "(1)" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.237, + 0.174, + 0.238 + ], + "angle": 0, + "content": "\\( \\therefore m = \\frac{3}{11} \\) ;" + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.238, + 0.174, + 0.239 + ], + "angle": 0, + 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SettingsFlowerVFHQ [72]
IRIAL1SSIMPSNRLPIPSL1SSIMFIDLPIPS
0.06420.70422.230.20970.04350.85931.200.0847
✓0.06040.69321.580.19210.03960.87729.840.0612
✓0.05780.75822.460.17620.03660.88530.080.0713
✓✓0.05440.76123.330.17460.02830.91823.350.0540
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.374, + 0.383, + 0.39 + ], + "angle": 0, + "content": "4.3. Comparison with Explicit Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.47, + 0.547 + ], + "angle": 0, + "content": "As shown in Fig. 7, we compare previous SOTA explicit methods on both talking head and general datasets. The optical flow-based TPS [81] cannot handle the correlation of facial and non-facial content, or new content, as the microphone and flower are not correctly modeled. The latent motion decomposition-based LIA [67] containing explicit flow in the model, fails when the corresponding regions are small or the motion is complex. The keypoints-based IW [41] cannot handle the local motion and can also cause jittering in the videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.223, + 0.574 + ], + "angle": 0, + "content": "4.4. Token Editing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.469, + 0.747 + ], + "angle": 0, + "content": "In our framework, token manipulation facilitates the editing of facial features, enabling precise control over aspects such as head pose and facial expression. To demonstrate the generalization capability of our method, we applied token editing to images from the FFHQ dataset [24]. We benchmark our approach against previous SOTA explicit model for talking head editing, PECHead [11]. Qualitative results, as depicted in Fig. 8, demonstrate that our method not only parallels the editing performance of PECHead [11] but also surpasses it in terms of realism and naturalness, especially in intricate areas such as the eyes, mouth, and ears." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.241, + 0.772 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We compare the implicit motion representation and alignment with the explicit motion representation (i.e., keypoints) and alignment (i.e., optical flow-based grid sample). For explicit motion representation and alignment method on general dataset Flower, we use the TPSMM [81] as the baseline model. For the talking head dataset VFHQ [72], we use the PECHad [11] as the baseline model. For implicit motion representation and explicit motion alignment, we keep" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.258, + 0.568, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.358, + 0.564, + 0.367 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.259, + 0.632, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.579, + 0.358, + 0.623, + 0.367 + ], + "angle": 0, + "content": "Current" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.259, + 0.696, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.358, + 0.691, + 0.367 + ], + "angle": 0, + "content": "ER + EA" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.259, + 0.825, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.358, + 0.751, + 0.367 + ], + "angle": 0, + "content": "IR + EA" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.259, + 0.826, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.769, + 0.358, + 0.816, + 0.367 + ], + "angle": 0, + "content": "ER + IA" + }, + { + "type": "image", + "bbox": [ + 0.826, + 0.259, + 0.888, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.835, + 0.358, + 0.88, + 0.367 + ], + "angle": 0, + "content": "IR+IA" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.374, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Figure 9. Ablation studies on both talking head and general datasets. The IR and ER stand for implicit and explicit motion representation. The IA and EA stand for implicit and explicit motion alignment. The IR + IA is our full model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.688 + ], + "angle": 0, + "content": "the latent token encoder and decoder, and replace the implicit motion alignment with an optical flow estimator and flow-based grid sample to align the motion feature. For explicit motion representation and implicit motion alignment, we replace the latent token encoder with a keypoints extractor and the latent motion decoder with explicit keypoints to Gaussian heatmap [57], while keeping the implicit motion alignment. The results are shown in the Tab. 3 and Fig. 9. The results indicate that explicit representation can only model the face for facial data and is incapable of modeling hands: it either fails to generate results with hands, or it does not correctly reconstruct the position of the hands. The results on flower data also demonstrate the shortcomings of explicit representation and alignment: they either fail to capture complex motions or are unable to accurately reconstruct the frames." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.701, + 0.619, + 0.717 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.893 + ], + "angle": 0, + "content": "This paper introduces the Implicit Motion Function (IMF), an innovative approach that advances beyond traditional optical flow in video modeling and generation. The implicit methodology of IMF not only achieves high-fidelity video reconstruction, especially in non-facial and new content regions, but also demonstrates a remarkable compression ratio improvement. Its capacity for directly editable latent tokens paves the way for superior editing performance. We believe IMF represents a meaningful step forward in video modeling, potentially inspiring further research and development in video reconstruction and generation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19285" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] VTM-17.0. https://vcgi.hhi.fraunhofer.de/jvet/VVCSoftware_VTM/.7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.469, + 0.2 + ], + "angle": 0, + "content": "[2] Madhav Agarwal, Rudrabha Mukhopadhyay, Vinay P Namboodiri, and CV Jawahar. Audio-visual face reenactment. 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In addition, conventional encoder-decoder frameworks in video processing focus on modeling the correlation in the encoder, leading to limited generative capabilities and redundant intermediate representations. To address these challenges, this paper proposes a novel Implicit Motion Function (IMF) method. Our approach utilizes a low-dimensional latent token as the implicit representation, along with the use of cross-attention, to implicitly model the correlation between frames. This enables the implicit modeling of temporal correlations and understanding of object motions. Our method not only improves sparsity and efficiency in representation but also explores the generative capabilities of the decoder by integrating correlation modeling within it. The IMF framework facilitates video editing and other generative tasks by allowing the direct manipulation of latent tokens. We validate the effectiveness of IMF through extensive experiments on multiple video tasks, demonstrating superior performance in terms of reconstructed video quality, compression efficiency and generation ability. + +# 1. Introduction + +Recent years have witnessed an upsurge in the field of video modeling [44], processing [45, 62], compression [31, 38], prediction [19, 20], and generation [11, 64, 66]. A fundamental element in these diverse tasks is the use of optical flow, which encapsulates the relationship between consecutive frames. Existing approaches often employ readily available optical flow estimation models, such as RAFT [61], to facilitate this process. However, the definition of optical flow has inherent limitations. It lacks sparsity, capturing only the positional change of pixels, and fails to model the probabilistic aspects of object movements, thereby not comprehending the intrinsic motion and semantics of objects. Furthermore, the non-editability of explicit + +![](images/920adad69aec24a285a14e8adb8e3c39456bea1588fba30b589dd9719a9b10c0.jpg) +Reference frame + +![](images/3cc45988e91313902f74862d9d582b1dd773623bd096904bd449219e296e834e.jpg) + +![](images/c75d499620d9309517d0945452ca52a41749146f1bdb4ebd640d31aad16786c0.jpg) + +![](images/b7c15ab6577af2d75f8a99b2498eaf7d7a4e0645699380cfd099f5f4756ad726.jpg) +Current frame + +![](images/5da292f4bea66713dabfb72157b08665c7badac0074cccef1a2adfc6345aac48.jpg) +Dense optical flow + +![](images/44084b350e91b1f11423d984c191b775708168daf389f0b8e04d2de2e52d89f3.jpg) +Schematic latent space +IMF + +![](images/c272b2a041f1d373eabfe5b21b023c9d55df751427139ea7ff9b16d46ab14a44.jpg) +Reference frame + +![](images/0060484b7b344699e24cb9cc4dca630c66a4af74473fb4082fca7f98c42d78ae.jpg) +TPSMM [81] +Dense optical flow + +![](images/534d2c64db78b40e97131e48a50999383b97eb3486216b1e0a24caa29c257081.jpg) +Schematic latent space + +![](images/2d345b17b02121c43063540528aebf35ae0b0ae5ffb1dd82d3da57d87742d2b4.jpg) +Current frame +Figure 1. IMF represents the motion in latent space and model the correlation implicitly. In the diagram, the blue shapes represent tokens from the reference frame, while the pink shapes represent tokens from the current frame. Tokens that are unmatched in the reference frame, indicating new content, are depicted with pink polygons. Successfully matched tokens, such as changes of the head pose or the magnification of flower, are indicated with green arrows. Compared to explicit methods PEChEad [11] and TPSMM [81], our IMF faithfully reconstructs the current frame. + +![](images/691476c46d623c28c6c6dde127a7b33fe1ac0a5c10640eff10cd5109109451ca.jpg) +PECHead [11] + +![](images/3bf527564159ced49170b1bd7221cbf21cb75a88eadfa8cd24dd1341bbd60c04.jpg) +IMF + +optical flow presents significant challenges in video generation tasks. This stems from its rigid structure, which lim + +its the ability to manipulate or alter motion trajectories directly within the flow field. Consequently, this necessitates the integration of sophisticated neural networks for downstream generation tasks. These identified limitations underscore the need for an innovative approach in video modeling. It is in this context that we propose the Implicit Motion Function (IMF) method, a novel paradigm designed to address the aforementioned shortcomings by offering a more nuanced and editable representation of motion within video sequences. + +Our design of the IMF is based on the observation that, contrasting with the aforementioned limitations brought by the explicit optical flow, modeling the frame relations in the latent space offers a more nuanced and adaptable approach. Specifically, by operating in this latent space, it becomes feasible to effectively distinguish different objects and new content between two frames. Such capability is derived from the inherent property of the latent space by encoding a richer and more abstract representation of motion and object characteristics. This encoding allows for a more generalized understanding of object dynamics and interactions, thereby enabling the IMF to adapt to and accurately represent a broader range of object movements and behaviors, including the newly appeared objects. It is worth noting that we generalize the concept of motion to include the entry and exit of objects from the frame as a form of motion, rather than solely encompassing pixel displacement. + +The design of our pipeline, adopting an encoder-decoder style, can be highlighted in several aspects: (1) We employ a dense feature encoder and a latent token encoder to model dense features and latent tokens independently. This approach allows us to represent motion between two frames as a pair of low-dimensional tokens, significantly increasing the sparsity of the representation. (2) We design a latent token decoder to decode the tokens and a implicit motion alignment to model the correlation between two frames aligning the features from the reference frame to the current frame. They enable the model to understand the relationship between features across frames, thereby grasping the motion patterns of objects and increasing the sparsity of the motion representation. (3) By directly editing the latent token, we can facilitate editing and other generative tasks. In particular, the encoder independently extracts latent tokens from the current frame and the reference frame, so the frame-to-frame relationship is entirely modeled by the decoder. As shown in Fig. 1, we provide a schematic illustration of the correlation modeling process within the IMF latent space. Compared to explicit methods, our IMF allows for a faithful motion modeling of non-facial content (e.g., flowers) and even new content (e.g., appearing hand and blooming flower), demonstrating the semantic completeness is ensured by the proposed implicit modeling, for both talking head and general videos. + +In implementing the IMF, two primary challenges emerge. The first concerns defining and extracting sparse tokens. Conventional approaches [11, 41, 57, 66, 81] rely on sparse keypoints transformed into dense optical flow, but this method proves suboptimal, particularly for data lacking strong priors. Our approach circumvents this limitation by allowing the encoder to extract latent tokens without tying them to physical coordinates, preserving semantic integrity while maintaining sparsity. The second challenge involves modeling correlations with latent tokens. Drawing parallels to language model advancements [43, 48], we leverage cross-attention [65] mechanism, a sophisticated weight-based matrix operation that exceeds the capabilities of optical flow-based grid sampling [41]. By utilizing a latent token decoder to generate motion feature maps from compact latent tokens and processing these features through cross-attention, we model frame relationships and align reference appearance features to the current frame. This approach enables refined motion feature generation and feature alignment, bolstering both the reconstructive and generative abilities of the decoder and offering significant potential when integrated with foundation models for video applications. + +We conducted comprehensive experiments to validate the superiority of our IMF model in video reconstruction, video compression, and talking head editing. In video reconstruction, IMF outperformed existing benchmarks in both talking head and general datasets, demonstrating its ability to accurately reconstruct non-facial objects and new content. For video compression, IMF achieved a superior rate-distortion trade-off compared to current methods, including neural video CODECs, highlighting the compactness of our latent tokens. In talking head editing, IMF surpassed state-of-the-art (SOTA) explicit editing methods, confirming the editability and robust generative capabilities of our latent tokens. + +Our contributions can be summarized as follows: + +- We propose the Implicit Motion Function (IMF), a novel framework for video modeling and video generation. The IMF is capable of faithfully reconstructing various videos at extremely low bit rates, while also enabling high-quality video generation. +- We incorporate the latent token decoder and the implicit motion alignment as the implicit motion function for correlation modeling. By integrating this step at the decoder, the generative capability of the decoder is unleashed. +- By manipulating the latent tokens, the proposed method can achieve high-quality editing results for talking head images, which also demonstrates the powerful expressive capability of our latent tokens. +- Extensive qualitative and quantitative results across several talking head and general datasets demonstrate the superiority of the our framework for video modeling and video generation. + +# 2. Related Works + +# 2.1. Image Animation and Video Generation + +Image animation, which involves transferring motion between images, has traditionally relied on methods utilizing face meshes [13, 49], human keypoints [78], or action units [22, 47]. Recent trends, however, are leaning towards self-supervised techniques that require only video input. Notable pioneering works such as FOMM [57], and MRAA [58] introduced motion representation through sparse keypoints or regions employing local affine transformations. TPSMM [81] employs thin-plate spline transformation for motion estimation. LIA [67] uses latent vector decomposition but relies on optical flow for warping, and its limited editability leads to artifacts and facial interference. Furthermore, Mallya et al. [41] proposed a warping method based on cross-attention mechanisms [65]. However, its reliance on explicit keypoints as an intermediate representation imposes limitations on performance, as its effectiveness in modeling non-facial data remains relatively limited. + +In contrast to methods targeting general data, the field of talking head video generation, which focuses on creating realistic videos of talking faces, has advanced significantly due to research in various areas. Unlike the image animation methods that do not need detailed facial models, talking head generation uses detailed information about the head to improve video quality. Progress in this field has been driven by large datasets of face images [8, 72, 73, 82], 3D models of faces [2, 10], face landmark detectors [6, 39], facial landmark detection [6, 39], neural radiance fields (NeRF) [14, 18, 28, 32, 42, 53, 75], and diffusion models [4, 15, 46, 51, 52, 59, 70, 79]. There are several approaches to generate talking head videos. (1). 3D Face Model-Based Methods [40, 63]: These methods use 3D models to track and recreate facial expressions. For example, Face2Face [63] tracks expressions from a source video and applies them to another face. (2). Direct Synthesis-Based Models [7, 76, 77]: These models create faces by transforming encoded representations of appearance and motion into images. They often use latent motion expressions but may also rely on explicit techniques like optical flow. (3). 3D Mesh-Based Methods [12, 26]: These methods use detailed 3D models to create lifelike head avatars from videos. (4). NeRF-Based Methods [14, 18, 18, 32, 53]: These utilize NeRF to represent head geometry and appearance in a novel 3D format. While effective, they can be complex and less versatile across different identities. (5). Warping-Based Methods [17, 50, 66, 69, 73]: These methods estimate motion fields to warp feature maps and generate images, often using learned keypoints. (6). Diffusion Model-Based Methods [9, 54, 60]: These methods create realistic videos from a single image and an audio sequence, enhancing lip-sync, video fidelity, and the naturalness of + +![](images/9b394b653b22e37e491abb2a632cd1a0fcc3f302e3aba9fc4b456fff5e827f72.jpg) +Figure 2. The overview of our method, which is encoder-decoder style. The reference latent token $t_r$ is obtained with the Latent Token Encoder. The $f_r^l$ and $t_r$ are shared across the whole video. + +head movements and poses. However, they involve complex training and inference pipelines, which can be a challenge in terms of computational resources and efficiency. Despite the successes of these methods, there are still opportunities for improvement, especially in handling non-facial data and enhancing editability for talking head videos. This paper aims to explore new approaches in video modeling that maintain high quality and efficiency while being adaptable to different models. + +# 2.2. Neural Video Codec + +Many neural video CODECs [3, 34, 36, 38, 74] adopt the widely-used residual coding-based framework, where the predicted frame is firstly generated via motion estimation and motion compensation, and then the residual is coded. They aim to improve the prediction accuracy as much as possible, via scale-space flow [3], block-level prediction[36], and so on. Instead of generating pixel-domain predicted frame, the emerging conditional coding-based CODEcs [27, 29-31, 37, 55] extract feature-domain temporal context to help encoding, decoding, and the entropy model. However, most of them still rely on optical flow to generate the prediction or temporal context. Coding the optical flow requires non-trivial bitrate cost, even with the help of the learned entropy model [29-31]. By contrast, our IMF learns sparse latent token, which is naturally compact and efficient. + +# 3. Proposed Method + +# 3.1. Overview + +An overview of our framework is shown in Fig. 2, which follows the encoder-decoder style. The encoder contains the dense feature encoder $E_{F}$ and the latent token encoder $E_{T}$ . The decoder is composed of several implicit motion function (IMF) blocks and the frame decoder $D_{F}$ . Given input video $\{x_{c}\}_{c\in \Omega}$ and a reference frame $x_{r}$ , the appearance of the reference frame can be encoded into $f_{r}$ by $E_{F}$ and the correlation between $x_{c}$ and $x_{r}$ can be represented by + +![](images/e3f5f77ecd48d845b1ffca4e825bb6f3a083a8809331081059a9c78b4f49089b.jpg) + +![](images/52bef632dd0a6c26f6ce00c1c95576ef6003bbce271ed48ff2aaca9e5026f0ad.jpg) + +![](images/4498787b873fd34475ca91a3287b8d97763544eeb09e0ccd79ea121c41c42786.jpg) +Figure 3. The illustration of our framework: a) the encoder contains the dense feature encoder $E_{F}$ and the latent token encoder $E_{T}$ ; b) the decoder contains the implicit motion function IMF and the feature decoder $D_{F}$ . IMF includes the latent token decoder $IMF_{D}$ and the implicit motion alignment $IMF_{A}$ . The motion features $m_{r}^{l}$ and $m_{c}^{l}$ are produced by $IMF_{D}$ from $t_{r}$ and $t_{c}$ , independently. + +![](images/908a152b17e09266bd3b5b21ef8fbfe962f69b5d2e13343302ddbefc6bbcd46b.jpg) + +the tokens pair $(t_c, t_r)$ extracted respectively by $E_T$ from $x_c$ and $x_r$ . The decoder $D_F$ aims to faithfully reconstruct the $\hat{x}_c$ with $(t_c, t_r, f_r)$ . The pipeline can be formulated as: + +$$ +\hat {x} _ {c} = D _ {F} \left(I M F \left(t _ {c}, t _ {r}, f _ {r}\right)\right) \quad \text {w i t h} \tag {1} +$$ + +$$ +t _ {c} = E _ {T} (x _ {c}), \quad t _ {r} = E _ {T} (x _ {r}), \quad f _ {r} = E _ {F} (x _ {r}). +$$ + +Note that the reference frame $x_{r}$ is not necessarily selected from the input sequence $\{x_{c}\}$ . Taking the talking head generation as an example, our pipeline can support the reference having a different ID with the input. Furthermore, different from the former works such as optical flow, the correlation modeling by $(t_{c}, t_{r})$ does not require the reference input and the current input has the same dimension, not even the same modality. + +In our framework, to learn sparse yet essential information, we will constrain the information flow in $t_c$ and $t_r$ . The optimization target can be formulated as: + +$$ +\min _ {c} L \left(\hat {x} _ {c}, x _ {c}\right) \tag {2} +$$ + +$$ +\begin{array}{l} \text {s . t .} \quad | t | < \epsilon , t \in \left\{t _ {c}, t _ {r} \right\}, \end{array} +$$ + +where $L$ is the function that measures the similarity between $\hat{x}_c$ and $x_c$ . $|t|$ is the size of the latent tokens, and $\epsilon$ is the size limitation. To achieve this objective, we specially design the IMF at decoder to obtain high-fidelity $\hat{x}_c$ . A detailed illustration of our full pipeline is shown in Fig. 3. The remaining part of this section will be organized as follows: In Sec. 3.2, we briefly introduce the encoder details of $E_F$ and $E_T$ . In Sec. 3.3, we describe the proposed IMF. Sec. 3.4 demonstrates the editability of the latent tokens on talking + +head generation. In Sec. 3.5, we delve into the design and underlying rationale of our proposed framework. + +# 3.2. Dense Feature & Latent Token Encoder + +Dense Feature Encoder. Given a reference frame $x_{r} \in \mathbb{R}^{H \times W \times 3}$ , the dense feature encoder $E_{F}$ extracts multiscale feature $f_{r}^{l} \in \mathbb{R}^{h_{l} \times w_{l} \times d_{l}}$ , $l \in \{1, L\}$ , where $l$ is the layer index and $L$ is number of layers. $h_{l}, w_{l}$ is spatial size of the feature. $d_{l}$ is the depth dimension of the feature. The $E_{F}$ is only performed on the reference frame, which means the features $f_{r}^{l}$ are shared across the whole video if the reference frame is constant. + +Latent Token Encoder. The latent token encoder $E_{T}$ encodes the reference frame and the current frame to $t_r$ and $t_c$ , independently. It maps the space $\mathbb{R}^{H \times W \times 3} \Rightarrow \mathbb{R}^{\mathbf{d}}$ . Similar to $f_r$ , when the reference frame is constant, $t_r$ is also shared across the entire video. When $\mathbf{d} = K \times 2$ , where $K$ is the number of keypoints, our tokens can be viewed as the explicit coordinates representations from FOMM [57]. However, due to the limited information expressed by coordinates, the expressive capability of this kind of representation is limited, especially in terms of semantic integrity, i.e. the completeness to faithfully reconstruct the original frame. By contrast, we choose $\mathbf{d} = 1 \times d_m$ , a latent vector to ensure both completeness and compactness. We further discuss in Sec. 3.5 the choice between explicit and implicit representations of $t_c$ and reveal the pros and cons of each in the ablation experiments. + +# 3.3. Implicit Motion Function + +With the latent token $t_r$ and the appearance feature $f_r$ extracted from the reference frame, the target of IMF is to obtain the appearance feature $f_c$ of the current frame from its latent token $t_c$ . Specifically, the IMF is mainly composed of two parts. First, we design a latent token decoder $IMF_D$ module to transform the highly compact latent tokens into spatially aligned motion features that correspond with the frame. Subsequently, we utilize implicit motion alignment $IMF_A$ module to align and refine the appearance feature of the reference frame to the current frame. + +Latent Token Decoder. The $IMF_{D}$ decodes the compact tokens $t_r$ , $t_c$ to multiple motion features $m_r^l \in \mathbb{R}^{h_l \times w_l \times d_l}$ and $m_c^l \in \mathbb{R}^{h_l \times w_l \times d_l}$ where $l$ is the layer index. The "style modulation" utilizes Weight Modulation and Demodulation technique of StyleGAN2 [25], scales the convolution weights with the latent token, and normalizes them to unit standard deviation. Owing to the varying granularities, our latent tokens effectively compress multi-scale information, serving as a comprehensive representation. Furthermore, the fully implicit nature of our representation allows for flexible adjustment of the latent token dimension to accommodate different scenarios. Different from keypoint-based explicit representation [41, 57, 66], where the motion features are Gaussian heatmaps converted from the keypoints, our design enjoys better scalability and capability due to the latent token being directly learned by the encoder instead of coordinates with a limited value range. + +Implicit Motion Alignment. As shown in Fig.3, with the motion features $m_r^l$ and $m_c^l$ , the $IMF_A$ will align the reference appearance features $f_r^l$ to the current frame. The $IMF_A$ contains two parts including the cross-attention [65] and transformer. The cross-attention module is implemented with scaled dot-product cross-attention. This attention module takes motion features $m_c^l$ , $m_r^l$ , and appearance features $f_r^l$ as $Q, K$ , and $V$ , respectively. The features are first flattened, then the positional embeddings $P_q$ , $P_k$ are added to the queries and keys. We compute the dot products of the queries with keys, divide each by $\sqrt{d_k}$ , and apply a softmax function to obtain the weights on the values. Then the output-aligned values are computed through matrix multiplication. With the aligned values $V'$ , we further refine them using multi-head self-attention and feedforward network-based Transformer blocks [65], and finally obtain the appearance features $f_c^l$ of the current frame. + +# 3.4. Token Manipulation + +In contrast to the explicit optical flow method, the implicit representation offers a distinct advantage in terms of editability. As the latent token is not task-specific, for a new controllable generation task, the decoder can be fixed and just train a small adapter with a small cost. Taking talking head generation as an example, in the training of the + +latent space, the full network is only trained to reconstruct the current frame. After the latent space is trained, we can edit learned tokens through another independent token manipulation network. Formally, with an editing module $\psi$ , source frame $x_{s}$ , and control condition $h$ , we can rewrite Eq. 1 to obtain the edited feature map $\tilde{f}_{s}$ as: + +$$ +\tilde {f} _ {s} = I M F \left(\psi \left(t _ {s} \mid h\right), t _ {s}, f _ {s}\right). \tag {3} +$$ + +Passing $\tilde{f}_s$ to the frame decoder trained before, we can get the edited frame $\tilde{x}_s$ . In our experiments, we implement $\psi$ with two MLP encoders to encode the source token and control condition (e.g., the 3DMM face coefficients), and one MLP decoder to output the edited token. + +# 3.5. Discussion + +Explicit or Implicit. Based on the foundational works MonkeyNet [56], FOMM [57], and MRAA [58], introduced by Siarohin et al., several works employ explicit keypoints [17, 66], landmarks [11, 81], regions [58] or vectors [67] as intermediate representations for direct optical flow estimation. Given the pivotal role of optical flow in elucidating relationships between video frames, this explicit approach has become the predominant methodology in video modeling. However, explicit representations are inherently constrained. Optical flow, being a dense representation, poses optimization challenges due to the per-pixel operations in grid sampling. While keypoints offer sparsity, they compromise on detailed motion information. Additionally, keypoints are effective for quasi-rigid structures like human heads but falter in general video tasks due to the diverse shapes and motion patterns, which are difficult to encapsulate using explicit methods. Another notable drawback of keypoints is their limited scalability, where increased point usage for finer motion details often leads to redundancy and artifact-prone outputs. + +Encoder-centric (EC) or Decoder-centric (DC). Here, we discuss the placement of correlation modeling, whether it is within the encoder or the decoder. Most existing video compression and video modeling methods belong to EC, which requires a complex design for encoder. For example, the functioning of a video codec encoder is contingent on the decoder output to obtain the prediction or context. Such intertwined framework necessitates meticulous tuning. For instance, the previous SOTA codec DCVC-DC [31, 55] incorporates upwards of ten distinct complicate strategies during training phases. In contrast, recent advancements in Large Language Models (LLMs) [48] usually utilize a DC architecture to support diverse tasks. This paradigm shift prompts reconsideration of similar frameworks for video codec. Actually, Wyner-Ziv coding [71] has given the theoretical support that the rate of DC framework can be identical with that of the EC framework. Our IMF design aligns with successful DC-based LLMs, achieving significant enhancements in video modeling. + +![](images/873855380b1cd46e41f3ef7dd89744086853c2bf77b76fb4a1353304c8e2da30.jpg) +Figure 4. Comparison of talking head video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles. + +![](images/a035199cd835038293987ca95b4cfe3c8b0b009eab517f08b0bf1923dd1da2de.jpg) + +![](images/d9f9e1c176acf2e7f627584257d958b206c319b2c68576ed03d65e572bd1c16c.jpg) + +![](images/6592b2503de6b9e33d52d229d66c5683c5c4c7d9a3d5c2e54f25a8c6517acaa5.jpg) + +Table 1. Quantitative results of video reconstruction on talking head datasets. + +
MethodsCelebV-HQ [82]LPIPSLFHQ [72]
L1SSIMPSNRFIDLPIPSL1SSIMPSNRFIDLPIPS
MRAA [58]0.05680.77722.3364.230.15390.04540.81222.6040.170.1117
F-Vid2Vid [66]0.05890.74621.5667.400.18890.04910.80421.7941.950.1054
LIA [67]0.06540.75420.7565.150.15410.05370.81521.4742.270.1099
IW [41]0.05390.80122.6757.650.12870.04260.86223.4634.050.0823
PECHEad [11]0.05520.80324.2956.680.13720.04350.85923.0331.200.0847
IMF0.04170.84925.2853.220.10570.02830.91826.8623.350.0540
+ +# 4. Experiments + +Datasets. For talking head datasets, CelebVHQ [82] and VFHQ [72] are used. In addition, to verify the universality of our model, we also test three general datasets: Flower, Wavcloth and Foliage1. For visual results of the non-face datasets, we obtain in-the-wild video from the Internet to verify the generalization ability. + +Implementation details. We use $256 \times 256$ as the frame spatial size. The latent token dimension is $d_m = 32$ for all experiments except for ablation studies. During the training, the perceptual Loss [23] and GAN loss [21, 33] are also used. More training details and network structure of each module are in supplementary materials. + +Baselines. We compare four representative works: FOMM [57], MRAA [58], Face-Vid2Vid [66], and PEC-Head [11] on talking head data. Besides FOMM [57] and MRAA [58], we compare TPSMM [81], LIA [67] and IW [41] on general data. These methods were primarily proposed for face data, but can also be applied for general data because the models do not explicitly rely on prior knowledge of face. + +Metrics. We use $L_{1}$ , SSIM [68] and PSNR to evaluate the + +Table 2. Quantitative results of video reconstruction on general datasets. + +
MethodsFlowerWaveclothFoliage
L1SSIMLPIPSL1SSIMLPIPSL1SSIMLPIPS
FOMM [57]0.08370.6200.25590.07490.6840.20090.08010.68810.1761
MRAA [58]0.07920.6320.24600.06650.7100.17980.07570.71800.1925
TPSMM [81]0.06420.7040.20970.06250.7160.15370.06260.77710.1545
LIA [67]0.08480.5890.24530.07330.6820.18680.08260.66190.1679
IW [41]0.06390.7360.19830.05660.7900.13800.06970.74270.1479
IMF0.05440.7610.17460.04730.8040.12650.05480.82350.1209
+ +low-level similarity. FID [16] and LPIPS [80] are used to assess the perceptual quality. For video compression, BPP (bits per pixel) is used to measure the bit-stream size. + +# 4.1. Video Reconstruction + +Tab. 1 and Tab. 2 show the quantitative comparisons with previous SOTA models. Qualitative comparisons are presented in the Fig. 4 and Fig. 5. More results and videos are in supplemental material. These results show that our method significantly outperforms previous SOTA methods. For talking head data, although previous methods can approximately reconstruct the correct facial area, only our model accurately reconstructs the non-facial areas, such as hair and microphones. Our model also performs best for local motion changes, like blinking. For general data, our method is able to precisely reconstruct various contents with complex motion, such as blooming. However, the methods based on explicit representation and alignment [56, 57, 81] perform poorly in cases of drastic content changes and also have inferior modeling capabilities for subtle motions, such as minor positional changes in leaves and flowers. Implicit warping-based method IW [41] is better than previous methods, but the keypoints are still used. It + +![](images/2ce98ee0800c1b9273782f8c78922613bdc71b6640fac8af332119e2e2f5f4c6.jpg) +Figure 5. Comparison of general video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles. + +![](images/38d9146e396a513f7d6c3bbb7e4bad01322a8ca7e50cef7b9a26a04a5cacd509.jpg) + +![](images/ef697b8fc16190a74942186f0179a2742926dddc5af160412c34cac9e8f2af29.jpg) +Figure 6. The rate-distortion curve on video compression. + +lacks robustness, leading to the appearance of jitter artifacts in the videos. + +# 4.2. Video Compression + +To verify the efficiency and semantic completeness of our latent tokens, we also test the video compression task using VFHQ [72] dataset. The rate-distortion curves are presented in Fig. 6. Besides the existing methods of talking head generation, we also compare the best standard codec H.266/VTM [1, 5] and previous SOTA neural video codec DCVC-DC [31]. For the results of all methods, we only + +![](images/2c5105730f847fd0eb6d125fe4c6a2c1663b21e7d4a9b32ef64588ee48ee69c8.jpg) +Figure 7. Comparison with explicit methods on both talking head and general datasets. + +calculate the current BPP (bits per pixel). Our first approach is directly applying an offline array compressor [35] to compress the latent tokens, and we test different token sizes $d_m \in \{16, 32, 64, 128\}$ , denoted as IMF- $d_m$ . To verify the compactness of the latent token, we also follow neural codec and implement an online learned entropy model [29, 31], where the token of the previous frame is used to predict the distribution of that of the current frame and then the arithmetic coding is applied. It is denoted as IMF- $d_m$ -online. From these results, we can see that our method is significantly better than all previous methods in terms of rate-distortion trade-off. Furthermore, the comparison with the online entropy model also reveals that our latent tokens are naturally compact, because the online entropy model only brings a very small bitrate reduction but with non-trivial quality degradation. + +![](images/78880ece8ff6da4f66267a580247eafe3471007581c77e39dc2ed1ec68652997.jpg) +PECHead + +![](images/1ff0f476bf2b8a4231015fdec79e602e82ac9b145ea59b73cb4ec9222b822b88.jpg) + +![](images/aa7e1c55fb9cfa457ffaf965fa0d3ed4895163a84f025e8caad93615a847e064.jpg) + +![](images/d75b2f7605aaed3f3d9283f80a5cfefea4b4064d99a1c9496bcaa777a8056e7c.jpg) + +![](images/4b99d2a5ac08d07cc9645e9c6a8bb416508612b4d2800320918db0a8ae8d9b95.jpg) + +![](images/1d724c186ca1ddded91f53bcd7740d8f4c0152932fab475ec5dbec23c3ff397b.jpg) + +![](images/3e3bce34c338abce5e4e2595150a8832ae8b7035b5a1f49ea7ea7e79fecc0e62.jpg) + +![](images/5ab6c114cf8f1cf75990cbfc8b50c248af4e20b2496d8a748a4a56a68f3eb55e.jpg) + +![](images/e2e744f2d58e5a63d17aa79ccd44c212381dded02ef593ce85083646759cf6c5.jpg) + +![](images/7547c35da1e403badb081fda9b94101f82e2d88673be133383d63fc4972ef423.jpg) + +![](images/1224ceed195940cdd9f83ca9c039b1f0e4d9d9339dda164800d8de5b54ba8867.jpg) +Input + + + + + + + +公 +$\therefore m = \frac{3}{11}$ +$\therefore m = \frac{3}{11}$ ; +② +(1) +$\therefore m = \frac{3}{11}$ ; +# + + + + + + + + + + + + + + + +$\left( {x - {2x}}\right) t - x{y}^{2} = \left( {x - {2x}}\right) {f}^{\prime }t$ +# +1101 +11.11 +# +# + + + + + + +# +# +F5F1 +图1 +# + +![](images/c314f69b56c003265544683f1e34e6fdd37df98c28a7ed9c9db4b91de4350c6c.jpg) + +![](images/73cfce115bcc1e10ad6032bb0f4f0675f39a31db7269decf070e35e0dc4ee526.jpg) + +![](images/28111c360af59297ded033eb31f9ed7ccd0768b404eef7dba4d34f60e6d4ebc0.jpg) + +![](images/ccbd8229a8278d6fdaaeaf51828a3e2eba2b6359abc0be7961c0f1e9cce17bf4.jpg) + +![](images/4aabdd13a029af8512c92d585e4fb43d2ae1be9ee80e8ad7448a8536c091fa94.jpg) + +![](images/e2300788b335fa2bd5f20ecd8b11e756013db2948269301a1e9300d6303f989d.jpg) + +![](images/3e789891ec43605a40a01a7f5a6498a90740acdedede94813c4a4d35c898060d.jpg) + +![](images/d689ffa7d7cc1ff854d52cf52b952beac0a6030b9ae3445aed02a219c47587fb.jpg) + +![](images/37212fc8b26e72a155bc85b4e053b1f6b6eae75622e4bb4e690d9a2d5fdbb213.jpg) + +# + +$\therefore m : x = 1$ 或 ${3x} + {4y} + 1 = 0$ + +__________ + +# + +# + +
SettingsFlowerVFHQ [72]
IRIAL1SSIMPSNRLPIPSL1SSIMFIDLPIPS
0.06420.70422.230.20970.04350.85931.200.0847
✓0.06040.69321.580.19210.03960.87729.840.0612
✓0.05780.75822.460.17620.03660.88530.080.0713
✓✓0.05440.76123.330.17460.02830.91823.350.0540
+ +# 4.3. Comparison with Explicit Methods + +As shown in Fig. 7, we compare previous SOTA explicit methods on both talking head and general datasets. The optical flow-based TPS [81] cannot handle the correlation of facial and non-facial content, or new content, as the microphone and flower are not correctly modeled. The latent motion decomposition-based LIA [67] containing explicit flow in the model, fails when the corresponding regions are small or the motion is complex. The keypoints-based IW [41] cannot handle the local motion and can also cause jittering in the videos. + +# 4.4. Token Editing + +In our framework, token manipulation facilitates the editing of facial features, enabling precise control over aspects such as head pose and facial expression. To demonstrate the generalization capability of our method, we applied token editing to images from the FFHQ dataset [24]. We benchmark our approach against previous SOTA explicit model for talking head editing, PECHead [11]. Qualitative results, as depicted in Fig. 8, demonstrate that our method not only parallels the editing performance of PECHead [11] but also surpasses it in terms of realism and naturalness, especially in intricate areas such as the eyes, mouth, and ears. + +# 4.5. Ablation Studies + +We compare the implicit motion representation and alignment with the explicit motion representation (i.e., keypoints) and alignment (i.e., optical flow-based grid sample). For explicit motion representation and alignment method on general dataset Flower, we use the TPSMM [81] as the baseline model. For the talking head dataset VFHQ [72], we use the PECHad [11] as the baseline model. For implicit motion representation and explicit motion alignment, we keep + +![](images/8dc10c094697ea7db76ba8e2a90832573eab42bd3d6e2b51fd9055567259a377.jpg) +Reference + +![](images/d95ee43ea2759b5de8ab3ade87192ce68eb6196828000009c2b242279b7cb502.jpg) +Current +Figure 9. Ablation studies on both talking head and general datasets. The IR and ER stand for implicit and explicit motion representation. The IA and EA stand for implicit and explicit motion alignment. The IR + IA is our full model. + +![](images/9858e13f72ce2842e281f41442c33579f990776a728499ed48653dc46135ad11.jpg) +ER + EA + +![](images/f71f478af46dddfeac536f152a2250d24a4215a6619e39ba204ac290fab78fc6.jpg) +IR + EA +ER + IA + +![](images/e69d0a5c5f8047f76aca9e7552379b389c1a09e742bddb9716bdf49ae1c48ae6.jpg) + +![](images/38ea2acc13d83a53d5a5c13366a9335a99196d7b2b5b75fab311345767a54244.jpg) +IR+IA + +the latent token encoder and decoder, and replace the implicit motion alignment with an optical flow estimator and flow-based grid sample to align the motion feature. For explicit motion representation and implicit motion alignment, we replace the latent token encoder with a keypoints extractor and the latent motion decoder with explicit keypoints to Gaussian heatmap [57], while keeping the implicit motion alignment. The results are shown in the Tab. 3 and Fig. 9. The results indicate that explicit representation can only model the face for facial data and is incapable of modeling hands: it either fails to generate results with hands, or it does not correctly reconstruct the position of the hands. The results on flower data also demonstrate the shortcomings of explicit representation and alignment: they either fail to capture complex motions or are unable to accurately reconstruct the frames. + +# 5. Conclusion + +This paper introduces the Implicit Motion Function (IMF), an innovative approach that advances beyond traditional optical flow in video modeling and generation. The implicit methodology of IMF not only achieves high-fidelity video reconstruction, especially in non-facial and new content regions, but also demonstrates a remarkable compression ratio improvement. Its capacity for directly editable latent tokens paves the way for superior editing performance. We believe IMF represents a meaningful step forward in video modeling, potentially inspiring further research and development in video reconstruction and generation. + +# References + +[1] VTM-17.0. https://vcgi.hhi.fraunhofer.de/jvet/VVCSoftware_VTM/.7 +[2] Madhav Agarwal, Rudrabha Mukhopadhyay, Vinay P Namboodiri, and CV Jawahar. Audio-visual face reenactment. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5178-5187, 2023. 3 +[3] Eirikur Agustsson, David Minnen, Nick Johnston, Johannes Balle, Sung Jin Hwang, and George Toderici. Scale-space flow for end-to-end optimized video compression. 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Celebvehq: A large-scale video facial attributes dataset. arXiv preprint arXiv:2207.12393, 2022. 3, 6 \ No newline at end of file diff --git a/2024/Implicit Motion Function/images.zip b/2024/Implicit Motion Function/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..de184c57f33b2c1f3f4a2cb930d6cf5d2f219de0 --- /dev/null +++ b/2024/Implicit Motion Function/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a7e9016324a98d79d1f05d9243ce6799e9161caaf55b40bd98a551141063a2e1 +size 759759 diff --git a/2024/Implicit Motion Function/layout.json b/2024/Implicit Motion Function/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..2aec4a2f220a8d59d5ee62b55f37f74e1ab26472 --- /dev/null +++ b/2024/Implicit Motion Function/layout.json @@ -0,0 +1,13447 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 217, + 103, + 376, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 217, + 103, + 376, + 121 + ], + "spans": [ + { + "bbox": [ + 217, + 103, + 376, + 121 + ], + "type": "text", + "content": "Implicit Motion Function" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 191, + 143, + 399, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 191, + 143, + 399, + 156 + ], + "spans": [ + { + "bbox": [ + 191, + 143, + 399, + 156 + ], + "type": "text", + "content": "Yue Gao Jiahao Li Lei Chu Yan Lu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 248, + 162, + 345, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 248, + 162, + 345, + 174 + ], + "spans": [ + { + "bbox": [ + 248, + 162, + 345, + 174 + ], + "type": "text", + "content": "Microsoft Research" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 167, + 178, + 427, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 167, + 178, + 427, + 190 + ], + "spans": [ + { + "bbox": [ + 167, + 178, + 427, + 190 + ], + "type": "text", + "content": "{yuegao, li.jiahao, leichu, yanlu}@microsoft.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 217, + 191, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 191, + 229 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 191, + 229 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 242, + 290, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 290, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 290, + 518 + ], + "type": "text", + "content": "Recent advancements in video modeling extensively rely on optical flow to represent the relationships across frames, but this approach often lacks efficiency and fails to model the probability of the intrinsic motion of objects. 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IMF represents the motion in latent space and model the correlation implicitly. In the diagram, the blue shapes represent tokens from the reference frame, while the pink shapes represent tokens from the current frame. Tokens that are unmatched in the reference frame, indicating new content, are depicted with pink polygons. Successfully matched tokens, such as changes of the head pose or the magnification of flower, are indicated with green arrows. Compared to explicit methods PEChEad [11] and TPSMM [81], our IMF faithfully reconstructs the current frame." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 387, + 482, + 464, + 559 + ], + "blocks": [ + { + "bbox": [ + 387, + 482, + 464, + 559 + ], + "lines": [ + { + "bbox": [ + 387, + 482, + 464, + 559 + ], + "spans": [ + { + "bbox": [ + 387, + 482, + 464, + 559 + ], + "type": "image", + "image_path": "691476c46d623c28c6c6dde127a7b33fe1ac0a5c10640eff10cd5109109451ca.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 402, + 560, + 450, + 569 + ], + "lines": [ + { + "bbox": [ + 402, + 560, + 450, + 569 + ], + "spans": [ + { + "bbox": [ + 402, + 560, + 450, + 569 + ], + "type": "text", + "content": "PECHead [11]" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 465, + 482, + 544, + 559 + ], + "blocks": [ + { + "bbox": [ + 465, + 482, + 544, + 559 + ], + "lines": [ + { + "bbox": [ + 465, + 482, + 544, + 559 + ], + "spans": [ + { + "bbox": [ + 465, + 482, + 544, + 559 + ], + "type": "image", + "image_path": "3bf527564159ced49170b1bd7221cbf21cb75a88eadfa8cd24dd1341bbd60c04.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 496, + 560, + 513, + 568 + ], + "lines": [ + { + "bbox": [ + 496, + 560, + 513, + 568 + ], + "spans": [ + { + "bbox": [ + 496, + 560, + 513, + 568 + ], + "type": "text", + "content": "IMF" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "optical flow presents significant challenges in video generation tasks. This stems from its rigid structure, which lim" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19278" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "its the ability to manipulate or alter motion trajectories directly within the flow field. Consequently, this necessitates the integration of sophisticated neural networks for downstream generation tasks. These identified limitations underscore the need for an innovative approach in video modeling. It is in this context that we propose the Implicit Motion Function (IMF) method, a novel paradigm designed to address the aforementioned shortcomings by offering a more nuanced and editable representation of motion within video sequences." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 195, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 289, + 399 + ], + "type": "text", + "content": "Our design of the IMF is based on the observation that, contrasting with the aforementioned limitations brought by the explicit optical flow, modeling the frame relations in the latent space offers a more nuanced and adaptable approach. Specifically, by operating in this latent space, it becomes feasible to effectively distinguish different objects and new content between two frames. Such capability is derived from the inherent property of the latent space by encoding a richer and more abstract representation of motion and object characteristics. This encoding allows for a more generalized understanding of object dynamics and interactions, thereby enabling the IMF to adapt to and accurately represent a broader range of object movements and behaviors, including the newly appeared objects. It is worth noting that we generalize the concept of motion to include the entry and exit of objects from the frame as a form of motion, rather than solely encompassing pixel displacement." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": "The design of our pipeline, adopting an encoder-decoder style, can be highlighted in several aspects: (1) We employ a dense feature encoder and a latent token encoder to model dense features and latent tokens independently. This approach allows us to represent motion between two frames as a pair of low-dimensional tokens, significantly increasing the sparsity of the representation. (2) We design a latent token decoder to decode the tokens and a implicit motion alignment to model the correlation between two frames aligning the features from the reference frame to the current frame. They enable the model to understand the relationship between features across frames, thereby grasping the motion patterns of objects and increasing the sparsity of the motion representation. (3) By directly editing the latent token, we can facilitate editing and other generative tasks. In particular, the encoder independently extracts latent tokens from the current frame and the reference frame, so the frame-to-frame relationship is entirely modeled by the decoder. As shown in Fig. 1, we provide a schematic illustration of the correlation modeling process within the IMF latent space. Compared to explicit methods, our IMF allows for a faithful motion modeling of non-facial content (e.g., flowers) and even new content (e.g., appearing hand and blooming flower), demonstrating the semantic completeness is ensured by the proposed implicit modeling, for both talking head and general videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 335 + ], + "type": "text", + "content": "In implementing the IMF, two primary challenges emerge. The first concerns defining and extracting sparse tokens. Conventional approaches [11, 41, 57, 66, 81] rely on sparse keypoints transformed into dense optical flow, but this method proves suboptimal, particularly for data lacking strong priors. Our approach circumvents this limitation by allowing the encoder to extract latent tokens without tying them to physical coordinates, preserving semantic integrity while maintaining sparsity. The second challenge involves modeling correlations with latent tokens. Drawing parallels to language model advancements [43, 48], we leverage cross-attention [65] mechanism, a sophisticated weight-based matrix operation that exceeds the capabilities of optical flow-based grid sampling [41]. By utilizing a latent token decoder to generate motion feature maps from compact latent tokens and processing these features through cross-attention, we model frame relationships and align reference appearance features to the current frame. This approach enables refined motion feature generation and feature alignment, bolstering both the reconstructive and generative abilities of the decoder and offering significant potential when integrated with foundation models for video applications." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 337, + 547, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 547, + 492 + ], + "type": "text", + "content": "We conducted comprehensive experiments to validate the superiority of our IMF model in video reconstruction, video compression, and talking head editing. In video reconstruction, IMF outperformed existing benchmarks in both talking head and general datasets, demonstrating its ability to accurately reconstruct non-facial objects and new content. For video compression, IMF achieved a superior rate-distortion trade-off compared to current methods, including neural video CODECs, highlighting the compactness of our latent tokens. In talking head editing, IMF surpassed state-of-the-art (SOTA) explicit editing methods, confirming the editability and robust generative capabilities of our latent tokens." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 495, + 517, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 495, + 517, + 506 + ], + "spans": [ + { + "bbox": [ + 317, + 495, + 517, + 506 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 508, + 545, + 711 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 508, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 545, + 567 + ], + "type": "text", + "content": "- We propose the Implicit Motion Function (IMF), a novel framework for video modeling and video generation. The IMF is capable of faithfully reconstructing various videos at extremely low bit rates, while also enabling high-quality video generation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 568, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 568, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 568, + 545, + 615 + ], + "type": "text", + "content": "- We incorporate the latent token decoder and the implicit motion alignment as the implicit motion function for correlation modeling. By integrating this step at the decoder, the generative capability of the decoder is unleashed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 616, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 545, + 662 + ], + "type": "text", + "content": "- By manipulating the latent tokens, the proposed method can achieve high-quality editing results for talking head images, which also demonstrates the powerful expressive capability of our latent tokens." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 664, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 664, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 306, + 664, + 545, + 711 + ], + "type": "text", + "content": "- Extensive qualitative and quantitative results across several talking head and general datasets demonstrate the superiority of the our framework for video modeling and video generation." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19279" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 138, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 138, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 138, + 83 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 92, + 257, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 92, + 257, + 105 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 257, + 105 + ], + "type": "text", + "content": "2.1. Image Animation and Video Generation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 113, + 289, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 113, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 113, + 289, + 316 + ], + "type": "text", + "content": "Image animation, which involves transferring motion between images, has traditionally relied on methods utilizing face meshes [13, 49], human keypoints [78], or action units [22, 47]. Recent trends, however, are leaning towards self-supervised techniques that require only video input. Notable pioneering works such as FOMM [57], and MRAA [58] introduced motion representation through sparse keypoints or regions employing local affine transformations. TPSMM [81] employs thin-plate spline transformation for motion estimation. LIA [67] uses latent vector decomposition but relies on optical flow for warping, and its limited editability leads to artifacts and facial interference. Furthermore, Mallya et al. [41] proposed a warping method based on cross-attention mechanisms [65]. However, its reliance on explicit keypoints as an intermediate representation imposes limitations on performance, as its effectiveness in modeling non-facial data remains relatively limited." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 318, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 289, + 714 + ], + "type": "text", + "content": "In contrast to methods targeting general data, the field of talking head video generation, which focuses on creating realistic videos of talking faces, has advanced significantly due to research in various areas. Unlike the image animation methods that do not need detailed facial models, talking head generation uses detailed information about the head to improve video quality. Progress in this field has been driven by large datasets of face images [8, 72, 73, 82], 3D models of faces [2, 10], face landmark detectors [6, 39], facial landmark detection [6, 39], neural radiance fields (NeRF) [14, 18, 28, 32, 42, 53, 75], and diffusion models [4, 15, 46, 51, 52, 59, 70, 79]. There are several approaches to generate talking head videos. (1). 3D Face Model-Based Methods [40, 63]: These methods use 3D models to track and recreate facial expressions. For example, Face2Face [63] tracks expressions from a source video and applies them to another face. (2). Direct Synthesis-Based Models [7, 76, 77]: These models create faces by transforming encoded representations of appearance and motion into images. They often use latent motion expressions but may also rely on explicit techniques like optical flow. (3). 3D Mesh-Based Methods [12, 26]: These methods use detailed 3D models to create lifelike head avatars from videos. (4). NeRF-Based Methods [14, 18, 18, 32, 53]: These utilize NeRF to represent head geometry and appearance in a novel 3D format. While effective, they can be complex and less versatile across different identities. (5). Warping-Based Methods [17, 50, 66, 69, 73]: These methods estimate motion fields to warp feature maps and generate images, often using learned keypoints. (6). Diffusion Model-Based Methods [9, 54, 60]: These methods create realistic videos from a single image and an audio sequence, enhancing lip-sync, video fidelity, and the naturalness of" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 201 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 201 + ], + "type": "image", + "image_path": "9b394b653b22e37e491abb2a632cd1a0fcc3f302e3aba9fc4b456fff5e827f72.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "text", + "content": "Figure 2. The overview of our method, which is encoder-decoder style. The reference latent token " + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "text", + "content": " is obtained with the Latent Token Encoder. The " + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "inline_equation", + "content": "f_r^l" + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 305, + 203, + 545, + 236 + ], + "type": "text", + "content": " are shared across the whole video." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 242, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 545, + 350 + ], + "type": "text", + "content": "head movements and poses. However, they involve complex training and inference pipelines, which can be a challenge in terms of computational resources and efficiency. Despite the successes of these methods, there are still opportunities for improvement, especially in handling non-facial data and enhancing editability for talking head videos. This paper aims to explore new approaches in video modeling that maintain high quality and efficiency while being adaptable to different models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 358, + 423, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 423, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 423, + 369 + ], + "type": "text", + "content": "2.2. Neural Video Codec" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 376, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 568 + ], + "type": "text", + "content": "Many neural video CODECs [3, 34, 36, 38, 74] adopt the widely-used residual coding-based framework, where the predicted frame is firstly generated via motion estimation and motion compensation, and then the residual is coded. They aim to improve the prediction accuracy as much as possible, via scale-space flow [3], block-level prediction[36], and so on. Instead of generating pixel-domain predicted frame, the emerging conditional coding-based CODEcs [27, 29-31, 37, 55] extract feature-domain temporal context to help encoding, decoding, and the entropy model. However, most of them still rely on optical flow to generate the prediction or temporal context. Coding the optical flow requires non-trivial bitrate cost, even with the help of the learned entropy model [29-31]. By contrast, our IMF learns sparse latent token, which is naturally compact and efficient." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 579, + 411, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 579, + 411, + 593 + ], + "spans": [ + { + "bbox": [ + 306, + 579, + 411, + 593 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 599, + 373, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 373, + 610 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 373, + 610 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "An overview of our framework is shown in Fig. 2, which follows the encoder-decoder style. The encoder contains the dense feature encoder " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "E_{F}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " and the latent token encoder " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "E_{T}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": ". 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Given input video " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{x_{c}\\}_{c\\in \\Omega}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " and a reference frame " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "x_{r}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": ", the appearance of the reference frame can be encoded into " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_{r}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "E_{F}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " and the correlation between " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "x_{c}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "x_{r}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " can be represented by" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19280" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 221, + 189 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 221, + 189 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 221, + 189 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 221, + 189 + ], + "type": "image", + "image_path": "e3f5f77ecd48d845b1ffca4e825bb6f3a083a8809331081059a9c78b4f49089b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 225, + 72, + 545, + 187 + ], + "blocks": [ + { + "bbox": [ + 225, + 72, + 545, + 187 + ], + "lines": [ + { + "bbox": [ + 225, + 72, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 225, + 72, + 545, + 187 + ], + "type": "image", + "image_path": "52bef632dd0a6c26f6ce00c1c95576ef6003bbce271ed48ff2aaca9e5026f0ad.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 51, + 213, + 223, + 307 + ], + "blocks": [ + { + "bbox": [ + 51, + 213, + 223, + 307 + ], + "lines": [ + { + "bbox": [ + 51, + 213, + 223, + 307 + ], + "spans": [ + { + "bbox": [ + 51, + 213, + 223, + 307 + ], + "type": "image", + "image_path": "4498787b873fd34475ca91a3287b8d97763544eeb09e0ccd79ea121c41c42786.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "lines": [ + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "text", + "content": "Figure 3. The illustration of our framework: a) the encoder contains the dense feature encoder " + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "inline_equation", + "content": "E_{F}" + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "text", + "content": " and the latent token encoder " + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "inline_equation", + "content": "E_{T}" + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "text", + "content": "; b) the decoder contains the implicit motion function IMF and the feature decoder " + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "inline_equation", + "content": "D_{F}" + }, + { + "bbox": [ + 46, + 314, + 546, + 349 + ], + "type": "text", + "content": ". 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The decoder " + }, + { + "bbox": [ + 46, + 357, + 288, + 394 + ], + "type": "inline_equation", + "content": "D_F" + }, + { + "bbox": [ + 46, + 357, + 288, + 394 + ], + "type": "text", + "content": " aims to faithfully reconstruct the " + }, + { + "bbox": [ + 46, + 357, + 288, + 394 + ], + "type": "inline_equation", + "content": "\\hat{x}_c" + }, + { + "bbox": [ + 46, + 357, + 288, + 394 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 357, + 288, + 394 + ], + "type": "inline_equation", + "content": "(t_c, t_r, f_r)" + }, + { + "bbox": [ + 46, + 357, + 288, + 394 + ], + "type": "text", + "content": ". The pipeline can be formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 401, + 287, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 401, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 62, + 401, + 287, + 419 + ], + "type": "interline_equation", + "content": "\\hat {x} _ {c} = D _ {F} \\left(I M F \\left(t _ {c}, t _ {r}, f _ {r}\\right)\\right) \\quad \\text {w i t h} \\tag {1}", + "image_path": "39c8f8c2aa5f796b16ed97ca76c1451bf1b82548bf0055cb26c0cfa60b9d24d7.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 416, + 272, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 416, + 272, + 429 + ], + "spans": [ + { + "bbox": [ + 66, + 416, + 272, + 429 + ], + "type": "interline_equation", + "content": "t _ {c} = E _ {T} (x _ {c}), \\quad t _ {r} = E _ {T} (x _ {r}), \\quad f _ {r} = E _ {F} (x _ {r}).", + "image_path": "c0a94cd271721b53d48041b7c09a8cad4fc057864ee47429e7a3b2af6fb5d1ea.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "text", + "content": "Note that the reference frame " + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "inline_equation", + "content": "x_{r}" + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "text", + "content": " is not necessarily selected from the input sequence " + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\{x_{c}\\}" + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "text", + "content": ". Taking the talking head generation as an example, our pipeline can support the reference having a different ID with the input. Furthermore, different from the former works such as optical flow, the correlation modeling by " + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "inline_equation", + "content": "(t_{c}, t_{r})" + }, + { + "bbox": [ + 46, + 434, + 287, + 528 + ], + "type": "text", + "content": " does not require the reference input and the current input has the same dimension, not even the same modality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "type": "text", + "content": "In our framework, to learn sparse yet essential information, we will constrain the information flow in " + }, + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 46, + 529, + 287, + 565 + ], + "type": "text", + "content": ". The optimization target can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 110, + 570, + 287, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 570, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 110, + 570, + 287, + 590 + ], + "type": "interline_equation", + "content": "\\min _ {c} L \\left(\\hat {x} _ {c}, x _ {c}\\right) \\tag {2}", + "image_path": "81279e3cdd6f25436c6cb02ec6c1f879f97ad2bd6384574f3ae6eb1f89192a21.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 117, + 586, + 223, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 586, + 223, + 598 + ], + "spans": [ + { + "bbox": [ + 117, + 586, + 223, + 598 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\text {s . t .} \\quad | t | < \\epsilon , t \\in \\left\\{t _ {c}, t _ {r} \\right\\}, \\end{array}", + "image_path": "b188cb06bac3d8d6236f6e6eb56b6a09619faa96ed524a968af57c563dbd45c5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " is the function that measures the similarity between " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{x}_c" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_c" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "|t|" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " is the size of the latent tokens, and " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " is the size limitation. To achieve this objective, we specially design the IMF at decoder to obtain high-fidelity " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{x}_c" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ". A detailed illustration of our full pipeline is shown in Fig. 3. The remaining part of this section will be organized as follows: In Sec. 3.2, we briefly introduce the encoder details of " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "E_F" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "E_T" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ". In Sec. 3.3, we describe the proposed IMF. Sec. 3.4 demonstrates the editability of the latent tokens on talking" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 357, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 382 + ], + "type": "text", + "content": "head generation. In Sec. 3.5, we delve into the design and underlying rationale of our proposed framework." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 400, + 515, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 515, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 515, + 412 + ], + "type": "text", + "content": "3.2. Dense Feature & Latent Token Encoder" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": "Dense Feature Encoder. Given a reference frame " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "x_{r} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": ", the dense feature encoder " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "E_{F}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " extracts multiscale feature " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "f_{r}^{l} \\in \\mathbb{R}^{h_{l} \\times w_{l} \\times d_{l}}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "l \\in \\{1, L\\}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " is the layer index and " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " is number of layers. " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "h_{l}, w_{l}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " is spatial size of the feature. " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "d_{l}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " is the depth dimension of the feature. The " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "E_{F}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " is only performed on the reference frame, which means the features " + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "inline_equation", + "content": "f_{r}^{l}" + }, + { + "bbox": [ + 304, + 422, + 545, + 517 + ], + "type": "text", + "content": " are shared across the whole video if the reference frame is constant." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": "Latent Token Encoder. The latent token encoder " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "E_{T}" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": " encodes the reference frame and the current frame to " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": ", independently. It maps the space " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H \\times W \\times 3} \\Rightarrow \\mathbb{R}^{\\mathbf{d}}" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": ". Similar to " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "f_r" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": ", when the reference frame is constant, " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": " is also shared across the entire video. When " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{d} = K \\times 2" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": " is the number of keypoints, our tokens can be viewed as the explicit coordinates representations from FOMM [57]. However, due to the limited information expressed by coordinates, the expressive capability of this kind of representation is limited, especially in terms of semantic integrity, i.e. the completeness to faithfully reconstruct the original frame. By contrast, we choose " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{d} = 1 \\times d_m" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": ", a latent vector to ensure both completeness and compactness. We further discuss in Sec. 3.5 the choice between explicit and implicit representations of " + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": " and reveal the pros and cons of each in the ablation experiments." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19281" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 189, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 189, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 189, + 85 + ], + "type": "text", + "content": "3.3. Implicit Motion Function" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": "With the latent token " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": " and the appearance feature " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "f_r" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": " extracted from the reference frame, the target of IMF is to obtain the appearance feature " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "f_c" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": " of the current frame from its latent token " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": ". Specifically, the IMF is mainly composed of two parts. First, we design a latent token decoder " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "IMF_D" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": " module to transform the highly compact latent tokens into spatially aligned motion features that correspond with the frame. Subsequently, we utilize implicit motion alignment " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "IMF_A" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": " module to align and refine the appearance feature of the reference frame to the current frame." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": "Latent Token Decoder. The " + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "inline_equation", + "content": "IMF_{D}" + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": " decodes the compact tokens " + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "inline_equation", + "content": "t_r" + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": " to multiple motion features " + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "inline_equation", + "content": "m_r^l \\in \\mathbb{R}^{h_l \\times w_l \\times d_l}" + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "inline_equation", + "content": "m_c^l \\in \\mathbb{R}^{h_l \\times w_l \\times d_l}" + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 210, + 288, + 413 + ], + "type": "text", + "content": " is the layer index. The \"style modulation\" utilizes Weight Modulation and Demodulation technique of StyleGAN2 [25], scales the convolution weights with the latent token, and normalizes them to unit standard deviation. Owing to the varying granularities, our latent tokens effectively compress multi-scale information, serving as a comprehensive representation. Furthermore, the fully implicit nature of our representation allows for flexible adjustment of the latent token dimension to accommodate different scenarios. Different from keypoint-based explicit representation [41, 57, 66], where the motion features are Gaussian heatmaps converted from the keypoints, our design enjoys better scalability and capability due to the latent token being directly learned by the encoder instead of coordinates with a limited value range." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": "Implicit Motion Alignment. As shown in Fig.3, with the motion features " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "m_r^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "m_c^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "IMF_A" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " will align the reference appearance features " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "f_r^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " to the current frame. The " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "IMF_A" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " contains two parts including the cross-attention [65] and transformer. The cross-attention module is implemented with scaled dot-product cross-attention. This attention module takes motion features " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "m_c^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "m_r^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", and appearance features " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "f_r^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "Q, K" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", respectively. The features are first flattened, then the positional embeddings " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "P_q" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "P_k" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " are added to the queries and keys. We compute the dot products of the queries with keys, divide each by " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\sqrt{d_k}" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", and apply a softmax function to obtain the weights on the values. Then the output-aligned values are computed through matrix multiplication. With the aligned values " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "V'" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": ", we further refine them using multi-head self-attention and feedforward network-based Transformer blocks [65], and finally obtain the appearance features " + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "inline_equation", + "content": "f_c^l" + }, + { + "bbox": [ + 46, + 413, + 287, + 617 + ], + "type": "text", + "content": " of the current frame." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 623, + 167, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 167, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 167, + 635 + ], + "type": "text", + "content": "3.4. Token Manipulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "In contrast to the explicit optical flow method, the implicit representation offers a distinct advantage in terms of editability. As the latent token is not task-specific, for a new controllable generation task, the decoder can be fixed and just train a small adapter with a small cost. Taking talking head generation as an example, in the training of the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "latent space, the full network is only trained to reconstruct the current frame. After the latent space is trained, we can edit learned tokens through another independent token manipulation network. Formally, with an editing module " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", source frame " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "x_{s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", and control condition " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", we can rewrite Eq. 1 to obtain the edited feature map " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\tilde{f}_{s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 368, + 146, + 545, + 160 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 146, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 368, + 146, + 545, + 160 + ], + "type": "interline_equation", + "content": "\\tilde {f} _ {s} = I M F \\left(\\psi \\left(t _ {s} \\mid h\\right), t _ {s}, f _ {s}\\right). \\tag {3}", + "image_path": "278d2b09a2506037b2a32e7089191d88e9ef5a5f2b166eeaf4752f9f6738d42f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "spans": [ + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "text", + "content": "Passing " + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "inline_equation", + "content": "\\tilde{f}_s" + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "text", + "content": " to the frame decoder trained before, we can get the edited frame " + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "inline_equation", + "content": "\\tilde{x}_s" + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "text", + "content": ". In our experiments, we implement " + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 162, + 547, + 223 + ], + "type": "text", + "content": " with two MLP encoders to encode the source token and control condition (e.g., the 3DMM face coefficients), and one MLP decoder to output the edited token." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 228, + 378, + 240 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 378, + 240 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 378, + 240 + ], + "type": "text", + "content": "3.5. Discussion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 247, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 486 + ], + "type": "text", + "content": "Explicit or Implicit. Based on the foundational works MonkeyNet [56], FOMM [57], and MRAA [58], introduced by Siarohin et al., several works employ explicit keypoints [17, 66], landmarks [11, 81], regions [58] or vectors [67] as intermediate representations for direct optical flow estimation. Given the pivotal role of optical flow in elucidating relationships between video frames, this explicit approach has become the predominant methodology in video modeling. However, explicit representations are inherently constrained. Optical flow, being a dense representation, poses optimization challenges due to the per-pixel operations in grid sampling. While keypoints offer sparsity, they compromise on detailed motion information. Additionally, keypoints are effective for quasi-rigid structures like human heads but falter in general video tasks due to the diverse shapes and motion patterns, which are difficult to encapsulate using explicit methods. Another notable drawback of keypoints is their limited scalability, where increased point usage for finer motion details often leads to redundancy and artifact-prone outputs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": "Encoder-centric (EC) or Decoder-centric (DC). Here, we discuss the placement of correlation modeling, whether it is within the encoder or the decoder. Most existing video compression and video modeling methods belong to EC, which requires a complex design for encoder. For example, the functioning of a video codec encoder is contingent on the decoder output to obtain the prediction or context. Such intertwined framework necessitates meticulous tuning. For instance, the previous SOTA codec DCVC-DC [31, 55] incorporates upwards of ten distinct complicate strategies during training phases. In contrast, recent advancements in Large Language Models (LLMs) [48] usually utilize a DC architecture to support diverse tasks. This paradigm shift prompts reconsideration of similar frameworks for video codec. Actually, Wyner-Ziv coding [71] has given the theoretical support that the rate of DC framework can be identical with that of the EC framework. Our IMF design aligns with successful DC-based LLMs, achieving significant enhancements in video modeling." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19282" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 160, + 297 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 160, + 297 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 160, + 297 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 160, + 297 + ], + "type": "image", + "image_path": "873855380b1cd46e41f3ef7dd89744086853c2bf77b76fb4a1353304c8e2da30.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 545, + 322 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 545, + 322 + ], + "type": "text", + "content": "Figure 4. Comparison of talking head video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 161, + 70, + 324, + 298 + ], + "blocks": [ + { + "bbox": [ + 161, + 70, + 324, + 298 + ], + "lines": [ + { + "bbox": [ + 161, + 70, + 324, + 298 + ], + "spans": [ + { + "bbox": [ + 161, + 70, + 324, + 298 + ], + "type": "image", + "image_path": "a035199cd835038293987ca95b4cfe3c8b0b009eab517f08b0bf1923dd1da2de.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 324, + 71, + 435, + 298 + ], + "blocks": [ + { + "bbox": [ + 324, + 71, + 435, + 298 + ], + "lines": [ + { + "bbox": [ + 324, + 71, + 435, + 298 + ], + "spans": [ + { + "bbox": [ + 324, + 71, + 435, + 298 + ], + "type": "image", + "image_path": "d9f9e1c176acf2e7f627584257d958b206c319b2c68576ed03d65e572bd1c16c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 435, + 71, + 544, + 298 + ], + "blocks": [ + { + "bbox": [ + 435, + 71, + 544, + 298 + ], + "lines": [ + { + "bbox": [ + 435, + 71, + 544, + 298 + ], + "spans": [ + { + "bbox": [ + 435, + 71, + 544, + 298 + ], + "type": "image", + "image_path": "6592b2503de6b9e33d52d229d66c5683c5c4c7d9a3d5c2e54f25a8c6517acaa5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 356, + 286, + 411 + ], + "blocks": [ + { + "bbox": [ + 47, + 333, + 286, + 354 + ], + "lines": [ + { + "bbox": [ + 47, + 333, + 286, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 333, + 286, + 354 + ], + "type": "text", + "content": "Table 1. Quantitative results of video reconstruction on talking head datasets." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 356, + 286, + 411 + ], + "lines": [ + { + "bbox": [ + 48, + 356, + 286, + 411 + ], + "spans": [ + { + "bbox": [ + 48, + 356, + 286, + 411 + ], + "type": "table", + "html": "
MethodsCelebV-HQ [82]LPIPSLFHQ [72]
L1SSIMPSNRFIDLPIPSL1SSIMPSNRFIDLPIPS
MRAA [58]0.05680.77722.3364.230.15390.04540.81222.6040.170.1117
F-Vid2Vid [66]0.05890.74621.5667.400.18890.04910.80421.7941.950.1054
LIA [67]0.06540.75420.7565.150.15410.05370.81521.4742.270.1099
IW [41]0.05390.80122.6757.650.12870.04260.86223.4634.050.0823
PECHEad [11]0.05520.80324.2956.680.13720.04350.85923.0331.200.0847
IMF0.04170.84925.2853.220.10570.02830.91826.8623.350.0540
", + "image_path": "7ed9bc1a2744e1039318a98fc1469822b079c9142f6a46f9af1b203d3d2c19d1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 423, + 127, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 127, + 436 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 127, + 436 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 443, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 514 + ], + "type": "text", + "content": "Datasets. For talking head datasets, CelebVHQ [82] and VFHQ [72] are used. In addition, to verify the universality of our model, we also test three general datasets: Flower, Wavcloth and Foliage1. For visual results of the non-face datasets, we obtain in-the-wild video from the Internet to verify the generalization ability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "text", + "content": "Implementation details. We use " + }, + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "text", + "content": " as the frame spatial size. The latent token dimension is " + }, + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "inline_equation", + "content": "d_m = 32" + }, + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "text", + "content": " for all experiments except for ablation studies. During the training, the perceptual Loss [23] and GAN loss [21, 33] are also used. More training details and network structure of each module are in supplementary materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 587, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 287, + 682 + ], + "type": "text", + "content": "Baselines. We compare four representative works: FOMM [57], MRAA [58], Face-Vid2Vid [66], and PEC-Head [11] on talking head data. Besides FOMM [57] and MRAA [58], we compare TPSMM [81], LIA [67] and IW [41] on general data. These methods were primarily proposed for face data, but can also be applied for general data because the models do not explicitly rely on prior knowledge of face." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 683, + 286, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 286, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 286, + 694 + ], + "type": "text", + "content": "Metrics. We use " + }, + { + "bbox": [ + 47, + 683, + 286, + 694 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 683, + 286, + 694 + ], + "type": "text", + "content": ", SSIM [68] and PSNR to evaluate the" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 356, + 545, + 418 + ], + "blocks": [ + { + "bbox": [ + 306, + 333, + 544, + 354 + ], + "lines": [ + { + "bbox": [ + 306, + 333, + 544, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 333, + 544, + 354 + ], + "type": "text", + "content": "Table 2. Quantitative results of video reconstruction on general datasets." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 356, + 545, + 418 + ], + "lines": [ + { + "bbox": [ + 307, + 356, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 307, + 356, + 545, + 418 + ], + "type": "table", + "html": "
MethodsFlowerWaveclothFoliage
L1SSIMLPIPSL1SSIMLPIPSL1SSIMLPIPS
FOMM [57]0.08370.6200.25590.07490.6840.20090.08010.68810.1761
MRAA [58]0.07920.6320.24600.06650.7100.17980.07570.71800.1925
TPSMM [81]0.06420.7040.20970.06250.7160.15370.06260.77710.1545
LIA [67]0.08480.5890.24530.07330.6820.18680.08260.66190.1679
IW [41]0.06390.7360.19830.05660.7900.13800.06970.74270.1479
IMF0.05440.7610.17460.04730.8040.12650.05480.82350.1209
", + "image_path": "af32a63be762c7e095a929e0b576a1f331a8ed81ecb4bc7a46bbcd00209a4b05.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "type": "text", + "content": "low-level similarity. FID [16] and LPIPS [80] are used to assess the perceptual quality. For video compression, BPP (bits per pixel) is used to measure the bit-stream size." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 479, + 429, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 429, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 429, + 490 + ], + "type": "text", + "content": "4.1. Video Reconstruction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Tab. 1 and Tab. 2 show the quantitative comparisons with previous SOTA models. Qualitative comparisons are presented in the Fig. 4 and Fig. 5. More results and videos are in supplemental material. These results show that our method significantly outperforms previous SOTA methods. For talking head data, although previous methods can approximately reconstruct the correct facial area, only our model accurately reconstructs the non-facial areas, such as hair and microphones. Our model also performs best for local motion changes, like blinking. For general data, our method is able to precisely reconstruct various contents with complex motion, such as blooming. However, the methods based on explicit representation and alignment [56, 57, 81] perform poorly in cases of drastic content changes and also have inferior modeling capabilities for subtle motions, such as minor positional changes in leaves and flowers. Implicit warping-based method IW [41] is better than previous methods, but the keypoints are still used. It" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 258, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 258, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 258, + 712 + ], + "type": "text", + "content": "1For more information about these datasets, please contact us." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19283" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 70, + 187, + 352 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 187, + 352 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 187, + 352 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 187, + 352 + ], + "type": "image", + "image_path": "2ce98ee0800c1b9273782f8c78922613bdc71b6640fac8af332119e2e2f5f4c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 354, + 546, + 375 + ], + "lines": [ + { + "bbox": [ + 46, + 354, + 546, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 546, + 375 + ], + "type": "text", + "content": "Figure 5. Comparison of general video reconstruction results obtained by the proposed method and previous SOTA approaches. The main differences between reference frames and current frames are highlighted in circles." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 187, + 70, + 516, + 352 + ], + "blocks": [ + { + "bbox": [ + 187, + 70, + 516, + 352 + ], + "lines": [ + { + "bbox": [ + 187, + 70, + 516, + 352 + ], + "spans": [ + { + "bbox": [ + 187, + 70, + 516, + 352 + ], + "type": "image", + "image_path": "38d9146e396a513f7d6c3bbb7e4bad01322a8ca7e50cef7b9a26a04a5cacd509.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 384, + 281, + 553 + ], + "blocks": [ + { + "bbox": [ + 53, + 384, + 281, + 553 + ], + "lines": [ + { + "bbox": [ + 53, + 384, + 281, + 553 + ], + "spans": [ + { + "bbox": [ + 53, + 384, + 281, + 553 + ], + "type": "image", + "image_path": "ef697b8fc16190a74942186f0179a2742926dddc5af160412c34cac9e8f2af29.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 557, + 271, + 569 + ], + "lines": [ + { + "bbox": [ + 61, + 557, + 271, + 569 + ], + "spans": [ + { + "bbox": [ + 61, + 557, + 271, + 569 + ], + "type": "text", + "content": "Figure 6. The rate-distortion curve on video compression." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 577, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 577, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 577, + 287, + 601 + ], + "type": "text", + "content": "lacks robustness, leading to the appearance of jitter artifacts in the videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 610, + 162, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 162, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 162, + 624 + ], + "type": "text", + "content": "4.2. Video Compression" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "To verify the efficiency and semantic completeness of our latent tokens, we also test the video compression task using VFHQ [72] dataset. The rate-distortion curves are presented in Fig. 6. Besides the existing methods of talking head generation, we also compare the best standard codec H.266/VTM [1, 5] and previous SOTA neural video codec DCVC-DC [31]. For the results of all methods, we only" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 384, + 545, + 473 + ], + "blocks": [ + { + "bbox": [ + 309, + 384, + 545, + 473 + ], + "lines": [ + { + "bbox": [ + 309, + 384, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 309, + 384, + 545, + 473 + ], + "type": "image", + "image_path": "2c5105730f847fd0eb6d125fe4c6a2c1663b21e7d4a9b32ef64588ee48ee69c8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 479, + 545, + 502 + ], + "lines": [ + { + "bbox": [ + 305, + 479, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 545, + 502 + ], + "type": "text", + "content": "Figure 7. Comparison with explicit methods on both talking head and general datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "calculate the current BPP (bits per pixel). Our first approach is directly applying an offline array compressor [35] to compress the latent tokens, and we test different token sizes " + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "inline_equation", + "content": "d_m \\in \\{16, 32, 64, 128\\}" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": ", denoted as IMF-" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "inline_equation", + "content": "d_m" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": ". To verify the compactness of the latent token, we also follow neural codec and implement an online learned entropy model [29, 31], where the token of the previous frame is used to predict the distribution of that of the current frame and then the arithmetic coding is applied. It is denoted as IMF-" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "inline_equation", + "content": "d_m" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "-online. From these results, we can see that our method is significantly better than all previous methods in terms of rate-distortion trade-off. Furthermore, the comparison with the online entropy model also reveals that our latent tokens are naturally compact, because the online entropy model only brings a very small bitrate reduction but with non-trivial quality degradation." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19284" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 106, + 118 + ], + "blocks": [ + { + "bbox": [ + 49, + 76, + 59, + 115 + ], + "lines": [ + { + "bbox": [ + 49, + 76, + 59, + 115 + ], + "spans": [ + { + "bbox": [ + 49, + 76, + 59, + 115 + ], + "type": "text", + "content": "PECHead" + } + ] + } + ], + "index": 0, + "angle": 270, + 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The latent motion decomposition-based LIA [67] containing explicit flow in the model, fails when the corresponding regions are small or the motion is complex. The keypoints-based IW [41] cannot handle the local motion and can also cause jittering in the videos." + } + ] + } + ], + "index": 81 + }, + { + "bbox": [ + 47, + 441, + 136, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 136, + 454 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 136, + 454 + ], + "type": "text", + "content": "4.4. Token Editing" + } + ] + } + ], + "index": 82 + }, + { + "bbox": [ + 46, + 460, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 591 + ], + "type": "text", + "content": "In our framework, token manipulation facilitates the editing of facial features, enabling precise control over aspects such as head pose and facial expression. To demonstrate the generalization capability of our method, we applied token editing to images from the FFHQ dataset [24]. We benchmark our approach against previous SOTA explicit model for talking head editing, PECHead [11]. Qualitative results, as depicted in Fig. 8, demonstrate that our method not only parallels the editing performance of PECHead [11] but also surpasses it in terms of realism and naturalness, especially in intricate areas such as the eyes, mouth, and ears." + } + ] + } + ], + "index": 83 + }, + { + "bbox": [ + 47, + 599, + 147, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 147, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 147, + 611 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 84 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "We compare the implicit motion representation and alignment with the explicit motion representation (i.e., keypoints) and alignment (i.e., optical flow-based grid sample). For explicit motion representation and alignment method on general dataset Flower, we use the TPSMM [81] as the baseline model. For the talking head dataset VFHQ [72], we use the PECHad [11] as the baseline model. For implicit motion representation and explicit motion alignment, we keep" + } + ] + } + ], + "index": 85 + }, + { + "type": "image", + "bbox": [ + 309, + 204, + 347, + 281 + ], + "blocks": [ + { + "bbox": [ + 309, + 204, + 347, + 281 + ], + "lines": [ + { + "bbox": [ + 309, + 204, + 347, + 281 + ], + "spans": [ + { + "bbox": [ + 309, + 204, + 347, + 281 + ], + "type": "image", + "image_path": "8dc10c094697ea7db76ba8e2a90832573eab42bd3d6e2b51fd9055567259a377.jpg" + } + ] + } + ], + "index": 86, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 311, + 283, + 345, + 290 + ], + "lines": [ + { + "bbox": [ + 311, + 283, + 345, + 290 + ], + "spans": [ + { + "bbox": [ + 311, + 283, + 345, + 290 + ], + "type": "text", + "content": "Reference" + } + ] + } + ], + "index": 87, + "angle": 0, + "type": "image_caption" + } + ], + "index": 86 + }, + { + "type": "image", + "bbox": [ + 347, + 205, + 386, + 283 + ], + "blocks": [ + { + "bbox": [ + 347, + 205, + 386, + 283 + ], + "lines": [ + { + "bbox": [ + 347, + 205, + 386, + 283 + ], + "spans": [ + { + "bbox": [ + 347, + 205, + 386, + 283 + ], + "type": "image", + "image_path": "d95ee43ea2759b5de8ab3ade87192ce68eb6196828000009c2b242279b7cb502.jpg" + } + ] + } + ], + "index": 88, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 354, + 283, + 381, + 290 + ], + "lines": [ + { + "bbox": [ + 354, + 283, + 381, + 290 + ], + "spans": [ + { + "bbox": [ + 354, + 283, + 381, + 290 + ], + "type": "text", + "content": "Current" + } + ] + } + ], + "index": 89, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 296, + 545, + 340 + ], + "lines": [ + { + "bbox": [ + 305, + 296, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 296, + 545, + 340 + ], + "type": "text", + "content": "Figure 9. Ablation studies on both talking head and general datasets. The IR and ER stand for implicit and explicit motion representation. The IA and EA stand for implicit and explicit motion alignment. The IR + IA is our full model." + } + ] + } + ], + "index": 98, + "angle": 0, + "type": "image_caption" + } + ], + "index": 88 + }, + { + "type": "image", + "bbox": [ + 387, + 205, + 425, + 283 + ], + "blocks": [ + { + "bbox": [ + 387, + 205, + 425, + 283 + ], + "lines": [ + { + "bbox": [ + 387, + 205, + 425, + 283 + ], + "spans": [ + { + "bbox": [ + 387, + 205, + 425, + 283 + ], + "type": "image", + "image_path": "9858e13f72ce2842e281f41442c33579f990776a728499ed48653dc46135ad11.jpg" + } + ] + } + ], + "index": 90, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 391, + 283, + 422, + 290 + ], + "lines": [ + { + "bbox": [ + 391, + 283, + 422, + 290 + ], + "spans": [ + { + "bbox": [ + 391, + 283, + 422, + 290 + ], + "type": "text", + "content": "ER + EA" + } + ] + } + ], + "index": 91, + "angle": 0, + "type": "image_caption" + } + ], + "index": 90 + }, + { + "type": "image", + "bbox": [ + 426, + 205, + 504, + 283 + ], + "blocks": [ + { + "bbox": [ + 426, + 205, + 504, + 283 + ], + "lines": [ + { + "bbox": [ + 426, + 205, + 504, + 283 + ], + "spans": [ + { + "bbox": [ + 426, + 205, + 504, + 283 + ], + "type": "image", + "image_path": "f71f478af46dddfeac536f152a2250d24a4215a6619e39ba204ac290fab78fc6.jpg" + } + ] + } + ], + "index": 92, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 283, + 459, + 290 + ], + "lines": [ + { + "bbox": [ + 432, + 283, + 459, + 290 + ], + "spans": [ + { + "bbox": [ + 432, + 283, + 459, + 290 + ], + "type": "text", + "content": "IR + EA" + } + ] + } + ], + "index": 93, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 470, + 283, + 499, + 290 + ], + "lines": [ + { + "bbox": [ + 470, + 283, + 499, + 290 + ], + "spans": [ + { + "bbox": [ + 470, + 283, + 499, + 290 + ], + "type": "text", + "content": "ER + IA" + } + ] + } + ], + "index": 95, + "angle": 0, + "type": "image_caption" + } + ], + "index": 92 + }, + { + "type": "image", + "bbox": [ + 466, + 205, + 505, + 283 + ], + "blocks": [ + { + "bbox": [ + 466, + 205, + 505, + 283 + ], + "lines": [ + { + "bbox": [ + 466, + 205, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 466, + 205, + 505, + 283 + ], + "type": "image", + "image_path": "e69d0a5c5f8047f76aca9e7552379b389c1a09e742bddb9716bdf49ae1c48ae6.jpg" + } + ] + } + ], + "index": 94, + "angle": 0, + "type": "image_body" + } + ], + "index": 94 + }, + { + "type": "image", + "bbox": [ + 505, + 205, + 543, + 283 + ], + "blocks": [ + { + "bbox": [ + 505, + 205, + 543, + 283 + ], + "lines": [ + { + "bbox": [ + 505, + 205, + 543, + 283 + ], + "spans": [ + { + "bbox": [ + 505, + 205, + 543, + 283 + ], + "type": "image", + "image_path": "38ea2acc13d83a53d5a5c13366a9335a99196d7b2b5b75fab311345767a54244.jpg" + } + ] + } + ], + "index": 96, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 511, + 283, + 538, + 290 + ], + "lines": [ + { + "bbox": [ + 511, + 283, + 538, + 290 + ], + "spans": [ + { + "bbox": [ + 511, + 283, + 538, + 290 + ], + "type": "text", + "content": "IR+IA" + } + ] + } + ], + "index": 97, + "angle": 0, + "type": "image_caption" + } + ], + "index": 96 + }, + { + "bbox": [ + 304, + 353, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 544 + ], + "type": "text", + "content": "the latent token encoder and decoder, and replace the implicit motion alignment with an optical flow estimator and flow-based grid sample to align the motion feature. For explicit motion representation and implicit motion alignment, we replace the latent token encoder with a keypoints extractor and the latent motion decoder with explicit keypoints to Gaussian heatmap [57], while keeping the implicit motion alignment. The results are shown in the Tab. 3 and Fig. 9. The results indicate that explicit representation can only model the face for facial data and is incapable of modeling hands: it either fails to generate results with hands, or it does not correctly reconstruct the position of the hands. The results on flower data also demonstrate the shortcomings of explicit representation and alignment: they either fail to capture complex motions or are unable to accurately reconstruct the frames." + } + ] + } + ], + "index": 99 + }, + { + "bbox": [ + 306, + 555, + 378, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 555, + 378, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 555, + 378, + 567 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 100 + }, + { + "bbox": [ + 304, + 575, + 545, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 707 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 707 + ], + "type": "text", + "content": "This paper introduces the Implicit Motion Function (IMF), an innovative approach that advances beyond traditional optical flow in video modeling and generation. The implicit methodology of IMF not only achieves high-fidelity video reconstruction, especially in non-facial and new content regions, but also demonstrates a remarkable compression ratio improvement. Its capacity for directly editable latent tokens paves the way for superior editing performance. We believe IMF represents a meaningful step forward in video modeling, potentially inspiring further research and development in video reconstruction and generation." + } + ] + } + ], + "index": 101 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19285" + } + ] + } + ], + "index": 102 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] VTM-17.0. https://vcgi.hhi.fraunhofer.de/jvet/VVCSoftware_VTM/.7" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 287, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 287, + 158 + ], + "type": "text", + "content": "[2] Madhav Agarwal, Rudrabha Mukhopadhyay, Vinay P Namboodiri, and CV Jawahar. 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Celebvehq: A large-scale video facial attributes dataset. arXiv preprint arXiv:2207.12393, 2022. 3, 6" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19289" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_content_list.json b/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..639b04a36b650cf560be9a7e07dc673974b13d7a --- /dev/null +++ b/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_content_list.json @@ -0,0 +1,1374 @@ +[ + { + "type": "text", + "text": "Improved Baselines with Visual Instruction Tuning", + "text_level": 1, + "bbox": [ + 227, + 130, + 741, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haotian Liu1 Chunyuan Li2 Yuheng Li1 Yong Jae Lee1 \n1University of Wisconsin-Madison 2Microsoft Research, Redmond https://llava-vl.github.io", + "bbox": [ + 207, + 179, + 764, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large multimodal models (LMM) have recently shown encouraging progress with visual instruction tuning. In this paper, we present the first systematic study to investigate the design choices of LMMs in a controlled setting under the LLaVA framework. We show that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient. With simple modifications to LLaVA, namely, using CLIP-ViT-L-336px with an MLP projection and adding academic-task-oriented VQA data with response formatting prompts, we establish stronger baselines that achieve state-of-the-art across 11 benchmarks. Our final 13B checkpoint uses merely 1.2M publicly available data, and finishes full training in $\\sim 1$ day on a single 8-A100 node. Furthermore, we present some early exploration of open problems in LMMs, including scaling to higher resolution inputs, compositional capabilities, and model hallucination, etc. We hope this makes state-of-the-art LMM research more accessible. Code and model will be publicly available.", + "bbox": [ + 73, + 300, + 473, + 574 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 603, + 209, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large multimodal models (LMMs) have become increasingly popular in the research community, as they are the key building blocks towards general-purpose assistants [2, 29, 42]. Recent studies on LMMs are converging on a central concept known as visual instruction tuning [35]. The results are promising, e.g. LLaVA [35] and MiniGPT-4 [60] demonstrate impressive results on natural instruction-following and visual reasoning capabilities. To better understand the capability of LMMs, multiple benchmarks [16, 26, 33, 36, 54] have been proposed. Recent works further demonstrate improved performance by scaling up the pretraining data [3, 13, 53], instruction-following data [13, 17, 28, 57], visual encoders [3], or language models [38], respectively. The LLaVA architecture is also leveraged in different downstream tasks and domains, including region-level [8, 55] and pixel-level [25, 49] understanding, biomedical assistants [30], image generation [5], adversarial studies [6, 58].", + "bbox": [ + 73, + 628, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1dd41f9ee2e33172fee4a9962ad99eb5a2df0182e34e291c997b56f9580b389d.jpg", + "image_caption": [ + "Figure 1. LLaVA-1.5 achieves SoTA on a broad range of 11 tasks (Top), with high training sample efficiency (Left) and simple modifications to LLaVA (Right): an MLP connector and including academic-task-oriented data with response formatting prompts." + ], + "image_footnote": [], + "bbox": [ + 506, + 265, + 890, + 621 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, despite many benchmarks and developments, it still remains unclear what the best recipe is to train LMMs towards the goal of general-purpose assistants. For example, LLaVA [35] excels in conversational-style visual reasoning and even outperforms later approaches like InstructBLIP [13] on such benchmarks [54], while InstructBLIP excels in traditional VQA benchmarks that demands single-word or short answers. Given the significant differences in the model architecture and training data between them, the root cause of the disparity in their capabilities remains elusive, despite conjectures [36, 54]: the amount of training data, the usage of resamplers like Qformer [31], etc. To this", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26296", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "end, we present the first systematic study to investigate the design choices of LMMs in a controlled setting. Our study originates from LLaVA and builds a road map by carefully making effective contributions from the perspectives of the input, model, and data.", + "bbox": [ + 78, + 90, + 467, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "First, we unveil that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient, and we establish stronger and more feasible baselines built upon the LLaVA framework. We report that two simple improvements, namely, an MLP cross-modal connector and incorporating academic task related data such as VQA, are orthogonal to the framework of LLaVA, and when used with LLaVA, lead to better multimodal understanding capabilities. In contrast to InstructBLIP [13] or Qwen-VL [3], which trains specially designed visual resamplers on hundreds of millions or even billions of image-text paired data, LLaVA uses one of the simplest architecture design for LMMs and requires only training a simple fully-connected projection layer on merely 600K image-text pairs. Our final model can finish training in $\\sim 1$ day on a single 8-A100 machine and achieves state-of-the-art results on a wide range of benchmarks. Moreover, unlike Qwen-VL [3] that includes in-house data in training, LLaVA utilizes only publicly available data.", + "bbox": [ + 80, + 169, + 467, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Next, we delve into an early exploration of other open problems of large multimodal models. Our findings include: (1) Scaling to high-resolution image inputs. We show that LLaVA's architecture is versatile in scaling to higher resolutions by simply dividing images into grids and maintains its data efficiency; with the increased resolution, it improves the model's detailed perception capabilities and reduces hallucination. (2) Compositional capabilities. We find that large multimodal models are capable of generalizing to compositional capabilities. For example, training on long-form language reasoning together with shorter visual reasoning can improve the model's writing capability for multimodal questions. (3) Data efficiency. We show that randomly downsampling LLaVA's training data mixture by up to $75\\%$ does not significantly decrease the model's performance, suggesting that the possibility of a more sophisticated dataset compression strategy can further improve LLaVA's already efficient training pipeline. (4) Data scaling. We provide empirical evidence for the scaling of data granularity in conjunction with the model's capability is crucial for an improved capability without introducing artifacts like hallucination.", + "bbox": [ + 80, + 459, + 467, + 790 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In sum, we perform a systematic study on the training of large multimodal models, and introduce a simple yet effective approach to balance the multitask learning and effective scaling for large multimodal models. Our improved baselines, LLaVA-1.5, uses only public data, achieves the state-of-the-art on a broad range of 11 tasks, and is significantly more data-efficient than previous approaches. By", + "bbox": [ + 78, + 795, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rethinking the conventional approaches and exploring the open problems in visual instruction tuning, we pave the way for more robust and capable systems for LMMs. We hope these improved and easily-reproducible baselines will provide a reference for future research in open-source LMMs.", + "bbox": [ + 503, + 90, + 890, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 184, + 638, + 199 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instruction-following large multimodal models (LMMs). Common architectures include a pre-trained visual backbone to encode visual features, a pre-trained large language model (LLM) to comprehend the user instructions and produce responses, and a vision-language cross-modal connector to align the vision encoder outputs to the language models. As shown in Fig. 1, LLaVA [35] is perhaps the simplest architecture for LMMs. Optionally, visual resamplers (e.g. Qformer [31]) are used to reduce the number of visual patches [3, 13, 60]. Training an instruction-following LMM usually follows a two-stage protocol. First, the vision-language alignment pretraining stage leverages image-text pairs to align the visual features with the language model's word embedding space. Earlier works utilize relatively few image-text pairs (e.g. $\\sim 600\\mathrm{K}$ [35] or $\\sim 6\\mathrm{M}$ [60]), while some recent works pretrain the vision-language connector for a specific language model on a large amount of image-text pairs (e.g. 129M [13] and 1.4B [3]), to maximize the LMM's performance. Second, the visual instruction tuning stage tunes the model on visual instructions [35], to enable the model to follow users' diverse requests on instructions that involve the visual contents. Dealing with higher resolution with grids in LMM are studied in con-current works [1, 27, 52].", + "bbox": [ + 503, + 215, + 890, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multimodal instruction-following data. In NLP, studies show that the quality of instruction-following data largely affects the capability of the resulting instruction-following models [59]. For visual instruction tuning, LLaVA [35] is the pioneer to leverage text-only GPT-4 to expand the existing COCO [34] bounding box and caption dataset to a multimodal instruction-following dataset that contains three types of instruction-following data: conversational-style QA, detailed description, and complex reasoning. LLaVA's pipeline has been employed to expand to textual understanding [56], million-scales [57], and region-level conversations [8]. InstructBLIP [13] incorporates academic-task-oriented VQA datasets to further enhance the model's visual capabilities. Conversely, [7] identifies that such naive data merging can result in models that tend to overfit to VQA datasets and thus are unable to participate in natural conversations. The authors further propose to leverage the LLaVA pipeline to convert VQA datasets to a conversational style. While this proves effective for training, it introduces added complexities in data scaling. However, in NLP, the FLAN family [12, 50] shows that adding a large number of academic language tasks for instruction tuning can effectively improve the gen", + "bbox": [ + 503, + 569, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26297", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "eralization ability. In light of this, we consider investigating the root cause of the inability to balance between natural conversations and academic tasks in multimodal models.", + "bbox": [ + 76, + 90, + 470, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 151, + 184, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 176, + 217, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As the seminal work of visual instruction tuning, LLaVA [35] showcases commendable proficiency in visual reasoning capabilities, surpassing even more recent models on diverse benchmarks [4, 54] for real-life visual instruction-following tasks. LLaVA uses a single linear layer to project the visual features to language space, and optimizes the whole LLM for visual instruction tuning. However, LLaVA falls short on academic benchmarks that typically require short-form answers (e.g. single-word), and tends to answer yes for yes/no questions due to the lack of such data in the training distribution.", + "bbox": [ + 75, + 199, + 470, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the other hand, InstructBLIP [13] is the pioneer to incorporate academic-task-oriented datasets like VQA-v2 [18] along with LLaVA-Instruct [35], and demonstrates improved performance on VQA benchmarks. It pretrains Qformer [31] on 129M image-text pairs and only finetunes the instruction-aware Qformer for visual instruction tuning. However, recent studies [7, 54] show that it does not perform as well as LLaVA on engaging in real-life visual conversation tasks. More specifically, as shown in Table 1a, it can overfit to VQA training sets with short-answers, even on requests that require detailed responses.", + "bbox": [ + 75, + 367, + 470, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Response Format Prompting", + "text_level": 1, + "bbox": [ + 76, + 544, + 334, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We find that the inability [7] to balance between short- and long-form VQA for approaches like InstructBLIP [13], which leverages instruction following data that includes both natural responses and short-answers, is mainly due to the following reasons. First, ambiguous prompts on the response format. For example, $Q$ : {Question} A: {Answer}. Such prompts do not clearly indicate the desired output format, and can overfit an LLM behaviorally to short-form answers even for natural visual conversations. Second, not finetuning the LLM. The first issue is worsened by InstructBLIP only finetuning the Qformer for instruction-tuning. It requires the Qformer's visual output tokens to control the length of the LLM's output to be either long-form or short-form, as in prefix tuning [32], but Qformer may lack the capability of properly doing so, due to its limited capacity compared with LLMs like LLaMA.", + "bbox": [ + 73, + 568, + 468, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Thus, to enable LLaVA to better handle short-form answers while addressing the issues of InstructBLIP, we propose to use a single response formatting prompt that clearly indicates the output format. It is appended at the end of VQA questions when promoting short answers: Answer the question using a single word or phrase. We find that when the", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual input example, Multitask Balancing Problem:", + "text_level": 1, + "bbox": [ + 514, + 93, + 839, + 106 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a8a03c251ed3dc03720febd659389a06aad4958f288a8710d612a72b307d24d8.jpg", + "image_caption": [ + "User InstructBLIP", + "Is this unusual? Please explain in detail. yes" + ], + "image_footnote": [ + "(a) Example of InstructBLIP [13] (Vicuna-13B) having difficulty balancing between short- and long-form answers." + ], + "bbox": [ + 622, + 111, + 807, + 208 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/c2f9ac2bd6648d5de82e04bdf61a2f16904f951e8304b3b0f54d4c0c40f4e2a3.jpg", + "table_caption": [ + "Visual input example, Different Format Prompts:" + ], + "table_footnote": [ + "(b) Comparison of how different prompts regularize the output format. The results are obtained zero-shot directly after LLaVA undergoes the first-stage vision-language alignment pretraining, without the second-stage visual instruction tuning.", + "Table 1. Visual input example to illustrate the challenge of (a) multitask balancing and (b) different format prompts. The same image input is used." + ], + "table_body": "
Normal promptWhat is the color of the shirt that the man is wearing?
ResponseThe man is wearing a yellow shirt.
Ambiguous promptQ: What is the color of the shirt that the man is wearing? A:
ResponseThe man is wearing a yellow shirt.
Formatting promptWhat is the color of the shirt that the man is wearing? Answer the question using a single word or phrase.
ResponseYellow.
", + "bbox": [ + 506, + 299, + 888, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LLM is finetuned with such prompts, LLaVA is able to properly adjust the output format according to the user's instructions (see Table 1b), and does not require additional processing of the VQA answers using ChatGPT [7], which further enables scaling to various data sources. As shown in Table 2, by merely including VQAv2 [18] in training, LLaVA's performance on MME significantly improves (1323.8 vs 809.6) and outperforms InstructBLIP by 111 points.", + "bbox": [ + 496, + 583, + 893, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Scaling the Data and Model", + "text_level": 1, + "bbox": [ + 500, + 715, + 750, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MLP vision-language connector. Inspired by the improved performance in self-supervised learning by changing from a linear projection to an MLP [9, 10], we find that improving the vision-language connector's representation power with a two-layer MLP can improve LLaVA's multimodal capabilities, compared with the original linear projection.", + "bbox": [ + 496, + 744, + 893, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Academic task oriented data. We further include additional academic-task-oriented VQA datasets for VQA, OCR, and region-level perception, to enhance the model's capabilities in various ways, as shown in Table 2. We first include", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26298", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/34e28144874d491e764e69b7deb546aaee9460370ce7fe3e6b51ab8a593c8b50.jpg", + "image_caption": [ + "Figure 2. LLaVA-1.5-HD. Scaling LLaVA-1.5 to higher resolutions by splitting the image into grids and encoding them independently. This allows the model to scale to any resolution, without performing positional embedding interpolation for ViTs. We additionally concatenate the feature of a downsampled image to provide the LLM with a global context." + ], + "image_footnote": [], + "bbox": [ + 158, + 88, + 816, + 224 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/3f7c8ac3dd80c519516f0dcd60ba9aa71826e1cf02955277f8f061d74a847364.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLLMRes.GQAMMEMM-Vet
InstructBLIP14B22449.51212.825.6
Only using a subset of InstructBLIP training data
0LLaVA7B224-809.625.5
1+VQA-v27B22447.01197.027.7
2+Format prompt7B22446.81323.826.3
3+MLP VL connector7B22447.31355.227.8
4+OKVQA/OCR7B22450.01377.629.6
Additional scaling
5+Region-level VQA7B22450.31426.530.8
6+Scale up resolution7B33651.4145030.3
7+GQA7B33662.0*1469.230.7
8+ShareGPT7B33662.0*1510.731.1
9+Scale up LLM13B33663.3*1531.336.1
", + "bbox": [ + 81, + 301, + 467, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2. Scaling results on data, model, and resolution. We choose to conduct experiments on GQA [20], MME [16], and MM-Vet [54] to examine the representative capabilities of VQA with short answers, VQA with output formatting, and natural visual conversations, respectively. *Training images of GQA were observed during training.", + "bbox": [ + 75, + 508, + 470, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "four additional datasets that are used in InstructBLIP: open-knowledge VQA (OKVQA [40], A-OKVQA [44]) and OCR (OCRVQA [41], TextCaps [46]). A-OKVQA is converted to multiple choice questions and a specific response formatting prompt is used: Answer with the option's letter from the given choices directly. With only a subset of the datasets InstructBLIP uses, LLaVA already surpasses it on all three tasks in Table 2, suggesting LLaVA's effective design. Furthermore, we find further adding region-level VQA datasets (Visual Genome [24], RefCOCO [23, 39]) improves the model's capability of localizing fine-grained visual details.", + "bbox": [ + 75, + 622, + 470, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additional scaling. We further scale up the input image resolution to $336^2$ to allow the LLM to clearly \"see\" the details of images, by swapping the vision encoder to CLIPViT-L-336px (the highest resolution available for CLIP). In addition, we add the GQA dataset as an additional visual knowledge source. We also incorporate ShareGPT [45] data and scale up the LLM to 13B as in [3, 8, 38]. Results on MM", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Vet shows the most significant improvement when scaling the LLM to 13B, suggesting the importance of the base LLM's capability for visual conversations.", + "bbox": [ + 496, + 303, + 893, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LLaVA-1.5. We denote this final model with all the modifications as LLaVA-1.5 (the last two rows in Table 2), which achieves an impressive performance that significantly outperforms the original LLaVA [35].", + "bbox": [ + 496, + 354, + 893, + 416 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Computational cost. For LLaVA-1.5, we use the same pretraining dataset, and keep the training iterations and batch size roughly the same for instruction tuning as LLaVA [35]. Due to the increased image input resolution to $336^2$ , the training of LLaVA-1.5 is $\\sim 2\\times$ as long as LLaVA: $\\sim 6$ hours of pretraining and $\\sim 20$ hours of visual instruction tuning, using $8\\times$ A100s.", + "bbox": [ + 496, + 420, + 893, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Scaling to Higher Resolutions", + "text_level": 1, + "bbox": [ + 500, + 540, + 764, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Sec. 3.3, we observe the advantage that scaling up the input image resolution improves the model's capabilities. However, the image resolution of the existing open source CLIP vision encoders is limited to $336^{2}$ , preventing the support of higher resolution images by simply replacing the vision encoder as we did in Sec. 3.3. In this section, we present an early exploration of scaling the LMM to higher resolutions, while maintaining the data efficiency of LLaVA-1.5.", + "bbox": [ + 496, + 565, + 893, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When using ViT [14] as the vision encoder, to scale up the resolution, previous approaches mostly choose to perform positional embedding interpolation [3, 31] and adapt the ViT backbone to the new resolution during finetuning. However, this usually requires the model to be finetuned on a large-scale image-text paired dataset [3, 31], and limits the resolution of the image to a fixed size that the LMM can accept during inference.", + "bbox": [ + 496, + 702, + 893, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead, as shown in Fig. 2, we overcome this by dividing the image into smaller image patches of the resolution that the vision encoder is originally trained for, and encode them independently. After obtaining the feature maps of individual patches, we then combine them into a single large feature", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26299", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/e01856386f0da5f3890bb46ed80b59a052361df6acfec16253a26b680de717b5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLLMImage SizeSample SizeVQAv2 [18]GQA [20]VisWiz [19]SciQA-IMG [37]TextVQA [47]
BLIP-2 [31]Vicuna-13B2242129M-65.04119.66142.5
InstructBLIP [13]Vicuna-7B2242129M1.2M-49.234.560.550.1
InstructBLIP [13]Vicuna-13B2242129M1.2M-49.533.463.150.7
Shikra [8]Vicuna-13B2242600K5.5M77.4*----
IDEFICS-9B [21]LLaMA-7B2242353M1M50.938.435.5-25.9
IDEFICS-80B [21]LLaMA-65B2242353M1M60.045.236.0-30.9
Qwen-VL [3]Qwen-7B44821.4B†50M†78.8*59.3*35.267.163.8*
Qwen-VL-Chat [3]Qwen-7B44821.4B*50M†78.2*57.5*38.968.261.5*
LLaVA-1.5Vicuna-7B3362558K665K78.5*62.0*50.066.858.2
LLaVA-1.5Vicuna-13B3362558K665K80.0*63.3*53.671.661.3
LLaVA-1.5-HDVicuna-13B4482558K665K81.8*64.7*57.571.062.5
Specialist SOTA: PaLI-X-55B [11]86.1*72.1*70.9*-71.4*
", + "bbox": [ + 153, + 88, + 812, + 280 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0983acd05e07e5b70a3b8e7d81c58c02dc595985e2f93c546628319df77a22f3.jpg", + "table_caption": [ + "Table 3. Comparison with SoTA methods on academic-task-oriented datasets. LLaVA-1.5 achieves the best performance on 4/5 benchmarks, and ranks the second on the other. *The training images/annotations of the datasets are observed during training. †Includes in-house data that is not publicly accessible." + ], + "table_footnote": [], + "table_body": "
MethodPOPE [33]MME [16]MMBench [36]SEED-Bench [26]LLaVA-Wild [35]MM-Vet [54]
randpopadvencnallimgvid
BLIP2-14B [31]89.685.580.91293.8--46.449.736.738.122.4
InstructBLIP-8B [13]----3623.753.458.838.160.926.2
InstructBLIP-14B [13]87.777721212.8-----58.225.6
Shikra-13B [8]----58.8------
IDEFICS-9B [21]----48.225.2-44.5---
IDEFICS-80B [21]----54.538.1-53.2---
Qwen-VL [3]----38.27.456.362.339.1--
Qwen-VL-Chat [3]---1487.560.656.758.265.437.8--
LLaVA-7B [35]76.372.270.1809.638.736.433.537.023.862.825.5
LLaVA-1.5-7B87.386.184.21510.764.358.358.666.137.365.431.1
LLaVA-1.5-13B87.186.284.51531.367.763.661.668.242.772.536.1
LLaVA-1.5-13B-HD87.586.485.01500.168.861.962.670.141.372.039.4
", + "bbox": [ + 158, + 344, + 805, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 4. Comparison with SoTA methods on benchmarks for instruction-following LMMs. LLaVA-1.5 achieves the best overall performance.", + "bbox": [ + 75, + 539, + 892, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "map of the target resolution, and feed that into the LLM. To provide the LLM with the global context and to reduce the artifact of the split-encode-merge operation, we additionally concatenate the feature of a downsampled image to the merged feature map. This allows us to scale the input to any arbitrary resolution and maintain the data efficiency of LLaVA-1.5. We call this resulting model LLaVA-1.5-HD.", + "bbox": [ + 75, + 594, + 470, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Empirical Evaluation", + "text_level": 1, + "bbox": [ + 76, + 715, + 282, + 732 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Benchmarks", + "text_level": 1, + "bbox": [ + 76, + 739, + 210, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate LLaVA-1.5 on a collection of both academic-task-oriented benchmarks and recent benchmarks specifically proposed for instruction-following LMMs, totalling 12 benchmarks. For academic-task-oriented benchmarks, VQA-v2 [18] and GQA [20] evaluate model's visual perception capabilities on open-ended short answers. VizWiz [19] contains 8,000 images to evaluate model's zero-shot generalization on visual questions asked by visually impaired people. Following InstructBLIP [13], the image subset of", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ScienceQA [37] with multiple choice are used to evaluate the zero-shot generalization on scientific question answering. TextVQA [47] contains text-rich visual question answering.", + "bbox": [ + 496, + 594, + 893, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For recent benchmarks proposed for instruction-following LMMs, POPE [33] evaluates model's degree of hallucination on three sampled subsets of COCO [34]: random, common, and adversarial and we report the F1 score on all three splits. Other benchmarks evaluate the model's capabilities on a wide range of domains and applications, with different response formats. MME-Perception [16] evaluates model's visual perception with yes/no questions. MMBench [36] evaluates model's answer robustness with all-round shuffling on multiple choice answers. MMBench-CN [36] is the Chinese-translated version of MMBench. SEED-Bench [26] evaluates model's performance on both images and videos with multiple choice, and we sample the frame in the middle to evaluate the accuracy on videos. LLaVA-Bench-in-the-Wild [35] and MM-Vet [54] evaluate model's capabilities in engaging in visual conversations on a diverse range of tasks, and evaluates the correctness and the helpfulness of", + "bbox": [ + 496, + 643, + 895, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26300", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/eedfeda40e72d3345dfc73e77f105d041bc465ef06e12584466e597d02a63da1.jpg", + "table_caption": [ + "Visual input example, Tricky Question:" + ], + "table_footnote": [], + "table_body": "
UserIf there are factual errors in the questions, point it out; if not, proceed to answering the question. What's happening in the desert?
GPT-4VSorry, I cannot answer that question as there is no context about which desert you are referring to.
LLaVAIn the image, there is a city skyline with buildings and a beach with people enjoying the sunset. The scene is set in a desert, which is unusual for a beach setting.
LLaVA-1.5There are no deserts in the image. The image features a beach with palm trees, a city skyline, and a large body of water.
", + "bbox": [ + 83, + 107, + 459, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. LLaVA-1.5 can detect and answer tricky questions when prompted to verify the question.", + "bbox": [ + 76, + 376, + 465, + 405 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the response with GPT-4 evaluation.", + "bbox": [ + 76, + 430, + 316, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 76, + 454, + 169, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We show that LLaVA-1.5 achieves the best overall performance on 12 benchmarks, despite using magnitudes smaller pretraining and instruction tuning data compared with other methods [3, 13]. LLaVA-1.5 significantly outperforms LLaVA on all benchmarks for instruction-following LMMs. Note that it is challenging to evaluate the original LLaVA on academic datasets like VQA-v2 [18] that demand open-ended short answers.", + "bbox": [ + 75, + 477, + 468, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When we continue to scale up the image resolution to $448^{2}$ with LLaVA-1.5-HD, it further improves the overall performance on all benchmarks, especially on tasks that require perception of details in the images (e.g. OCR in MM-Vet, detailed description in LLaVA-Bench-in-the-Wild [35]). Moreover, we find that adding the global context effectively recovers the model from the split-and-merge artifacts and guides the model to more easily locate the relevant regions from the high-resolution features (see appendix).", + "bbox": [ + 75, + 598, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is encouraging that LLaVA-1.5 achieves the best performance with the simplest architecture, academic compute and public datasets, and yields a fully-reproducible and affordable baseline for future research. The results also suggest that visual instruction tuning plays an important role in improving an LMM's capabilities, and raises questions upon the common belief that LMMs require significant amount of vision-language alignment pretraining [3, 13, 31], despite that the vision encoders (e.g. CLIP [43], OpenCLIP [22], EVA-CLIP [15], etc.) are already pretrained on web-scale image-text paired data. LLaVA-1.5 (even the 7B model)", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3c60f64cf16f07ae315e6f9d58e0333b3dc01d2c922a2c1c4f99e327da845edc.jpg", + "table_caption": [ + "Visual input example, Constrained JSON Output:" + ], + "table_footnote": [], + "table_body": "
UserPlease read the text in this image and return the information in the following JSON format (note xxx is placeholder, if the information is not available in the image, put "N/A" instead). {"class": xxx, "DLN": xxx, "DOB": xxx, "Name": xxx, "Address": xxx, "EXP": xxx, "ISS": xxx, "SEX": xxx, "HGT": xxx, "WGT": xxx, "EYES": xxx, "HAIR": xxx, "DONOR": xxx}
GPT-4V{"class": "C", "DLN": "1234568", "DOB": "08/31/1977", "Name": "Ima Cardholder", "Address": "2570 24th Street, Anytown, CA 95818", "EXP": "08/31/2014", "ISS": "08/31/2011", "SEX": "F", "HGT": "5-05", "WGT": "125 lbs", "EYES": "BRN", "HAIR": "BRN", "DONOR": "VETERAN"}
LLaVA{"class": "Driver License", "DLN": "CA123 456 789", "DOB": "01/01/1990", "Name": "Amy", "Address": "Anytown, CA", "EXP": "08/31/2023", "ISS": "Veteran", "SEX": "F", "HGT": "5', "WGT": "130", "EYES": "Brown", "HAIR": "Brown", "DONOR": "Unknown"}
LLaVA-1.5{"class": "C", "DLN": "1132456789", "DOB": "08/23/1971", "Name": "Ima Cardholder", "Address": "Anytown, State, Zip", "EXP": "08/23/2014", "ISS": "California", "SEX": "F", "HGT": "5', "WGT": "123", "EYES": "Brown", "HAIR": "Brown", "DONOR": "N/A"}
", + "bbox": [ + 506, + 107, + 883, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "outperforms 80B IDEFICS [21], a Flamingo-like LMM with billions of trainable parameters for cross-modal connection. This also makes us rethink the benefits of the vision samplers and the necessity of the additional large-scale pretraining, in terms of multimodal instruction-following capabilities.", + "bbox": [ + 496, + 579, + 890, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Global context. For higher resolution, we pad and resize the image to a single image of $224^2$ , and concatenate it with the high resolution features to provide a global context. Ablation on a 7B model shows that the global context effectively boosts performance on all three validation benchmarks.", + "bbox": [ + 496, + 659, + 890, + 736 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1ca8c75467e62d7b6ead9289160e19a7e3df01185e52f8e7aab90926e6fc23ef.jpg", + "table_caption": [ + "Table 6. LLaVA-1.5 can extract information from the image and answer following the required format, despite a few errors compared with GPT-4V. GPT-4V results are obtained from [51]." + ], + "table_footnote": [], + "table_body": "
GQAMMEMM-Vet
high-res patch only62.91425.831.9
+global context63.8 (+0.9)1497.5 (+71)35.1 (+3.2)
", + "bbox": [ + 513, + 748, + 875, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Emerging Properties", + "text_level": 1, + "bbox": [ + 500, + 827, + 694, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Format instruction generalization. Although LLaVA-1.5 is only trained with a limited number of format instructions, it generalizes to others. First, VizWiz [19] requires the model", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26301", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3eb515929a578daf9ddeee23a2e254641b2d403b757ac7a8727167b3ab6aa06d.jpg", + "image_caption": [ + "Figure 3. Ablation on LLM choices. Data points represent the relative performance of the best performing variant for each dataset." + ], + "image_footnote": [], + "bbox": [ + 80, + 85, + 472, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to output \"Unanswerable\" when the provided content is insufficient to answer the question, and our response format prompt (see Appendix) effectively instructs the model to do so ( $11.1\\% \\rightarrow 67.8\\%$ on unanswerable questions). We additionally present qualitative examples on instructing LLaVA-1.5 to verify tricky questions (Fig. 5), respond in a constrained JSON format (Fig. 6), and more in appendix.", + "bbox": [ + 75, + 410, + 470, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multilingual multimodal capability. Though LLaVA-1.5 is not finetuned for multilingual multimodal instruction following at all (all visual instructions including VQA are in English), we find that it is capable of following multilingual instructions. This is partly due to the multilingual language instructions in ShareGPT [45]. Although ShareGPT does not contain images in its instructions, the model learns from this dataset the behavior of adaptively responding with the language that corresponds to the user's request. We empirically show that this behavior is transferred to visual conversations. We also quantitatively evaluate the model's generalization capability to Chinese on MMBench-CN [36], where the questions of MMBench are converted to Chinese. Notably, LLaVA-1.5 outperforms Qwen-VL-Chat by $+7.3\\%$ (63.6% vs 56.7%), despite Qwen being finetuned on Chinese multimodal instructions while LLaVA-1.5 is not.", + "bbox": [ + 75, + 520, + 472, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation on LLM Choices", + "text_level": 1, + "bbox": [ + 76, + 771, + 313, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In NLP, findings [48] suggest that the capability of the base LLM can affect its instruction-tuned successors. In this section, we explore two families of LLMs and study their contribution to the final model's multimodal capability: LLaMA-based (Vicuna-v1.1, Vicuna-v1.3) and LLaMA2-based (Vicuna-v1.5, LLaMA-2-Chat). Vicuna-v1.3 and Vicuna-v1.5 use the same $\\sim 150\\mathrm{K}$ ShareGPT [45] data ( $2\\times$", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e10f73ab5ee3c892687b2d911e92a705c28a2f1f9f40893e157a26b65f63aad.jpg", + "image_caption": [ + "Figure 4. Ablation on data efficiency. Data points represent the relative performance of the best performing variant for each dataset." + ], + "image_footnote": [], + "bbox": [ + 501, + 85, + 890, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that used in v1.1). Unlike Vicuna series that is only trained with supervised instruction finetuning (SFT), LLaMA-2-Chat is further optimized with reinforcement-learning from human-feedback (RLHF). We visualize the relative performance of these variants in Fig. 3.", + "bbox": [ + 496, + 414, + 893, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "First, we find that Vicuna-v1.5 achieves the best overall performance, and LLaMA-2-based models generally perform better than LLaMA-1-based, suggesting the importance of the base language model. This is further evidenced by the results on MMBench-CN [36]: despite Vicuna-v1.3 and v1.5 using the same ShareGPT data for instruction tuning, the performance in generalization to Chinese of Vicuna-v1.3 is significantly worse than v1.5.", + "bbox": [ + 496, + 491, + 893, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Second, language instruction-tuning matters on specific capabilities that are required by each dataset. For example, although LLaMA-2-Chat and Vicuna-v1.5 achieves almost the same performance on MMBench, the generalization to MMBench-CN [36] of LLaMA-2-Chat is worse than Vicuna-v1.5, which is partly due to that the most SFT/RLHF data of LLaMA-2-Chat is in English and does not contain as many multilingual data as in ShareGPT. Furthermore, TextVQA requires both the model's capability of identifying the text characters in the images, and also processing the noisy outputs from the OCR engine; such noise may be more commonly observed in the ShareGPT data, which is collected in-the-wild from daily usage of ChatGPT.", + "bbox": [ + 496, + 614, + 895, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Open Problems in LMMs", + "text_level": 1, + "bbox": [ + 500, + 828, + 740, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the successful scaling of LLaVA-1.5, we conduct additional studies on open problems in LMMs using the model design and data mixture of LLaVA-1.5.", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26302", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Data Efficiency", + "text_level": 1, + "bbox": [ + 76, + 90, + 230, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite the data efficiency of LLaVA-1.5 when compared with approaches like InstructBLIP [13], the training of LLaVA-1.5 still doubles when compared with LLaVA. In this section, we conduct experiments for further improving the data efficiency by randomly sub-sampling the training data mixture of LLaVA-1.5, with a sampling ratio ranging from 0.1 to 0.5. We visualize the relative performance of different sampling variants in Fig. 4.", + "bbox": [ + 75, + 112, + 468, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "First, the full data mixture provides the best knowledge coverage, and allows the model to achieve the best overall performance. To our surprise, with only $50\\%$ of the samples, the model still maintains more than $98\\%$ of the full dataset performance. This suggests that there is room for further improvements in data efficiency.", + "bbox": [ + 75, + 234, + 468, + 324 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Second, when downsampling the dataset to $50\\%$ , the model's performance on MMBench, ScienceQA, and POPE does not decrease at all, and it even slightly improves on MMBench. Similarly, the model's performance remains steady when further downscaling the data from $50\\%$ to $30\\%$ . These results show promise of having the less-is-more [59] benefit for multimodal models as well.", + "bbox": [ + 75, + 324, + 468, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Rethinking Hallucination in LMMs", + "text_level": 1, + "bbox": [ + 76, + 438, + 385, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hallucination is an important issue to tackle for LLMs and LMMs. Often in LMMs, we attribute the model's hallucination to the errors or hallucinations in the training dataset. For example, the detailed descriptions in LLaVA-Instruct [35] may contain a small amount of hallucinated content, and it is believed that training on such data may have caused the model to hallucinate when asked to \"describe the image in detail\". However, we find that such hallucination is significantly reduced, when we scale the model's inputs to higher resolutions like $448^{2}$ .", + "bbox": [ + 75, + 460, + 468, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This finding is interesting as it suggests that the LMMs may be robust to a few such errors in the training data. However, when the input resolution is not sufficient for the model to discern all details in the training data, and the amount of data that is at that granularity beyond the model's capability becomes large enough, the model learns to hallucinate. This further suggests that there needs to be a balance between improving the data annotation with more details and the model's capability to properly process the information at such granularities. We hope this finding provides a reference for future work in terms of dealing with hallucination and the scaling of the models and data.", + "bbox": [ + 75, + 612, + 470, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Compositional Capabilities", + "text_level": 1, + "bbox": [ + 76, + 801, + 321, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We demonstrate interesting compositional capabilities in LLaVA-1.5: the model trained on a set of tasks independently generalizes to tasks that require a combination of these capabilities without explicit joint training. We note some of the findings below.", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "First, we observe an improved language capability in visual conversations after including the ShareGPT [45] data, including the multimodal multilingual capability as discussed in Sec. 4.3. Moreover, the model is more capable at providing longer and more detailed responses in visual conversations. Second, the additional visual knowledge from the academic-task-oriented datasets, improves the visual groundness of LLaVA-1.5's responses in visual conversations, as evidenced quantitatively by the improved results on MMVet [54] and LLaVA-Wild [35] in Table 4.", + "bbox": [ + 496, + 90, + 893, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, there is still difficulty in achieving ideal performance for some tasks that require a certain combination of capabilities. For example, being able to correctly answer the attribute of a certain object in VQA, does not guarantee an accurate depiction of that object attribute in a detailed description of the whole image. Furthermore, the capability of engaging in conversations with certain foreign languages (e.g. Korean) still falls behind. See appendix for examples.", + "bbox": [ + 496, + 242, + 893, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "These findings suggest that the compositional capabilities of LMMs can be leveraged to improve the model's performance without significantly increasing the data by exhaustively including all task combinations. Yet, it can be further investigated, and a deeper understanding of the mechanism behind the compositional capabilities of LMMs can further improve the capability and the data efficiency of LLaVA-1.5.", + "bbox": [ + 496, + 364, + 893, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 486, + 617, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we take a step towards demystifying the design of large multimodal models, and propose a simple, effective, and data-efficient baseline, LLaVA-1.5, for large multimodal models. In addition, we explore the open problems in visual instruction tuning, scale LMMs to higher resolutions, and present some intriguing findings in terms of model hallucination and compositional capabilities for LMMs. We hope these improved and easily-reproducible baselines as well as the new findings will provide a reference for future research in open-source LMM.", + "bbox": [ + 496, + 512, + 893, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Despite the promising results demonstrated by LLaVA-1.5, it still has limitations including prolonged training for high-resolution images, lack of multiple-image understanding, limited problem solving capabilities in certain fields. It is not exempt from producing hallucinations, and should be used with caution in critical applications (e.g. medical). See appendix for a detailed discussion.", + "bbox": [ + 496, + 667, + 893, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported in part by NSF CAREER IIS2150012, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training).", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26303", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adept AI. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2" + ], + "bbox": [ + 78, + 90, + 470, + 530 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "26306", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_model.json b/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2ade3927bca006d4a82582829be620853a9088ea --- /dev/null +++ b/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_model.json @@ -0,0 +1,2103 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.228, + 0.131, + 0.743, + 0.154 + ], + "angle": 0, + "content": "Improved Baselines with Visual Instruction Tuning" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.18, + 0.765, + 0.234 + ], + "angle": 0, + "content": "Haotian Liu1 Chunyuan Li2 Yuheng Li1 Yong Jae Lee1 \n1University of Wisconsin-Madison 2Microsoft Research, Redmond https://llava-vl.github.io" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.301, + 0.474, + 0.575 + ], + "angle": 0, + "content": "Large multimodal models (LMM) have recently shown encouraging progress with visual instruction tuning. In this paper, we present the first systematic study to investigate the design choices of LMMs in a controlled setting under the LLaVA framework. We show that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient. With simple modifications to LLaVA, namely, using CLIP-ViT-L-336px with an MLP projection and adding academic-task-oriented VQA data with response formatting prompts, we establish stronger baselines that achieve state-of-the-art across 11 benchmarks. Our final 13B checkpoint uses merely 1.2M publicly available data, and finishes full training in \\(\\sim 1\\) day on a single 8-A100 node. Furthermore, we present some early exploration of open problems in LMMs, including scaling to higher resolution inputs, compositional capabilities, and model hallucination, etc. We hope this makes state-of-the-art LMM research more accessible. Code and model will be publicly available." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.604, + 0.21, + 0.619 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.629, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Large multimodal models (LMMs) have become increasingly popular in the research community, as they are the key building blocks towards general-purpose assistants [2, 29, 42]. Recent studies on LMMs are converging on a central concept known as visual instruction tuning [35]. The results are promising, e.g. LLaVA [35] and MiniGPT-4 [60] demonstrate impressive results on natural instruction-following and visual reasoning capabilities. To better understand the capability of LMMs, multiple benchmarks [16, 26, 33, 36, 54] have been proposed. Recent works further demonstrate improved performance by scaling up the pretraining data [3, 13, 53], instruction-following data [13, 17, 28, 57], visual encoders [3], or language models [38], respectively. The LLaVA architecture is also leveraged in different downstream tasks and domains, including region-level [8, 55] and pixel-level [25, 49] understanding, biomedical assistants [30], image generation [5], adversarial studies [6, 58]." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.266, + 0.891, + 0.622 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.633, + 0.895, + 0.689 + ], + "angle": 0, + "content": "Figure 1. LLaVA-1.5 achieves SoTA on a broad range of 11 tasks (Top), with high training sample efficiency (Left) and simple modifications to LLaVA (Right): an MLP connector and including academic-task-oriented data with response formatting prompts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "However, despite many benchmarks and developments, it still remains unclear what the best recipe is to train LMMs towards the goal of general-purpose assistants. For example, LLaVA [35] excels in conversational-style visual reasoning and even outperforms later approaches like InstructBLIP [13] on such benchmarks [54], while InstructBLIP excels in traditional VQA benchmarks that demands single-word or short answers. Given the significant differences in the model architecture and training data between them, the root cause of the disparity in their capabilities remains elusive, despite conjectures [36, 54]: the amount of training data, the usage of resamplers like Qformer [31], etc. To this" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26296" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.166 + ], + "angle": 0, + "content": "end, we present the first systematic study to investigate the design choices of LMMs in a controlled setting. Our study originates from LLaVA and builds a road map by carefully making effective contributions from the perspectives of the input, model, and data." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.17, + 0.468, + 0.456 + ], + "angle": 0, + "content": "First, we unveil that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient, and we establish stronger and more feasible baselines built upon the LLaVA framework. We report that two simple improvements, namely, an MLP cross-modal connector and incorporating academic task related data such as VQA, are orthogonal to the framework of LLaVA, and when used with LLaVA, lead to better multimodal understanding capabilities. In contrast to InstructBLIP [13] or Qwen-VL [3], which trains specially designed visual resamplers on hundreds of millions or even billions of image-text paired data, LLaVA uses one of the simplest architecture design for LMMs and requires only training a simple fully-connected projection layer on merely 600K image-text pairs. Our final model can finish training in \\(\\sim 1\\) day on a single 8-A100 machine and achieves state-of-the-art results on a wide range of benchmarks. Moreover, unlike Qwen-VL [3] that includes in-house data in training, LLaVA utilizes only publicly available data." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.46, + 0.468, + 0.791 + ], + "angle": 0, + "content": "Next, we delve into an early exploration of other open problems of large multimodal models. Our findings include: (1) Scaling to high-resolution image inputs. We show that LLaVA's architecture is versatile in scaling to higher resolutions by simply dividing images into grids and maintains its data efficiency; with the increased resolution, it improves the model's detailed perception capabilities and reduces hallucination. (2) Compositional capabilities. We find that large multimodal models are capable of generalizing to compositional capabilities. For example, training on long-form language reasoning together with shorter visual reasoning can improve the model's writing capability for multimodal questions. (3) Data efficiency. We show that randomly downsampling LLaVA's training data mixture by up to \\(75\\%\\) does not significantly decrease the model's performance, suggesting that the possibility of a more sophisticated dataset compression strategy can further improve LLaVA's already efficient training pipeline. (4) Data scaling. We provide empirical evidence for the scaling of data granularity in conjunction with the model's capability is crucial for an improved capability without introducing artifacts like hallucination." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.796, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In sum, we perform a systematic study on the training of large multimodal models, and introduce a simple yet effective approach to balance the multitask learning and effective scaling for large multimodal models. Our improved baselines, LLaVA-1.5, uses only public data, achieves the state-of-the-art on a broad range of 11 tasks, and is significantly more data-efficient than previous approaches. By" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "rethinking the conventional approaches and exploring the open problems in visual instruction tuning, we pave the way for more robust and capable systems for LMMs. We hope these improved and easily-reproducible baselines will provide a reference for future research in open-source LMMs." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.185, + 0.64, + 0.2 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.216, + 0.892, + 0.562 + ], + "angle": 0, + "content": "Instruction-following large multimodal models (LMMs). Common architectures include a pre-trained visual backbone to encode visual features, a pre-trained large language model (LLM) to comprehend the user instructions and produce responses, and a vision-language cross-modal connector to align the vision encoder outputs to the language models. As shown in Fig. 1, LLaVA [35] is perhaps the simplest architecture for LMMs. Optionally, visual resamplers (e.g. Qformer [31]) are used to reduce the number of visual patches [3, 13, 60]. Training an instruction-following LMM usually follows a two-stage protocol. First, the vision-language alignment pretraining stage leverages image-text pairs to align the visual features with the language model's word embedding space. Earlier works utilize relatively few image-text pairs (e.g. \\(\\sim 600\\mathrm{K}\\) [35] or \\(\\sim 6\\mathrm{M}\\) [60]), while some recent works pretrain the vision-language connector for a specific language model on a large amount of image-text pairs (e.g. 129M [13] and 1.4B [3]), to maximize the LMM's performance. Second, the visual instruction tuning stage tunes the model on visual instructions [35], to enable the model to follow users' diverse requests on instructions that involve the visual contents. Dealing with higher resolution with grids in LMM are studied in con-current works [1, 27, 52]." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.57, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Multimodal instruction-following data. In NLP, studies show that the quality of instruction-following data largely affects the capability of the resulting instruction-following models [59]. For visual instruction tuning, LLaVA [35] is the pioneer to leverage text-only GPT-4 to expand the existing COCO [34] bounding box and caption dataset to a multimodal instruction-following dataset that contains three types of instruction-following data: conversational-style QA, detailed description, and complex reasoning. LLaVA's pipeline has been employed to expand to textual understanding [56], million-scales [57], and region-level conversations [8]. InstructBLIP [13] incorporates academic-task-oriented VQA datasets to further enhance the model's visual capabilities. Conversely, [7] identifies that such naive data merging can result in models that tend to overfit to VQA datasets and thus are unable to participate in natural conversations. The authors further propose to leverage the LLaVA pipeline to convert VQA datasets to a conversational style. While this proves effective for training, it introduces added complexities in data scaling. However, in NLP, the FLAN family [12, 50] shows that adding a large number of academic language tasks for instruction tuning can effectively improve the gen" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "26297" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.471, + 0.136 + ], + "angle": 0, + "content": "eralization ability. In light of this, we consider investigating the root cause of the inability to balance between natural conversations and academic tasks in multimodal models." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.152, + 0.185, + 0.169 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.177, + 0.218, + 0.192 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.471, + 0.365 + ], + "angle": 0, + "content": "As the seminal work of visual instruction tuning, LLaVA [35] showcases commendable proficiency in visual reasoning capabilities, surpassing even more recent models on diverse benchmarks [4, 54] for real-life visual instruction-following tasks. LLaVA uses a single linear layer to project the visual features to language space, and optimizes the whole LLM for visual instruction tuning. However, LLaVA falls short on academic benchmarks that typically require short-form answers (e.g. single-word), and tends to answer yes for yes/no questions due to the lack of such data in the training distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.534 + ], + "angle": 0, + "content": "On the other hand, InstructBLIP [13] is the pioneer to incorporate academic-task-oriented datasets like VQA-v2 [18] along with LLaVA-Instruct [35], and demonstrates improved performance on VQA benchmarks. It pretrains Qformer [31] on 129M image-text pairs and only finetunes the instruction-aware Qformer for visual instruction tuning. However, recent studies [7, 54] show that it does not perform as well as LLaVA on engaging in real-life visual conversation tasks. More specifically, as shown in Table 1a, it can overfit to VQA training sets with short-answers, even on requests that require detailed responses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.336, + 0.561 + ], + "angle": 0, + "content": "3.2. Response Format Prompting" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.569, + 0.47, + 0.809 + ], + "angle": 0, + "content": "We find that the inability [7] to balance between short- and long-form VQA for approaches like InstructBLIP [13], which leverages instruction following data that includes both natural responses and short-answers, is mainly due to the following reasons. First, ambiguous prompts on the response format. For example, \\( Q \\): {Question} A: {Answer}. Such prompts do not clearly indicate the desired output format, and can overfit an LLM behaviorally to short-form answers even for natural visual conversations. Second, not finetuning the LLM. The first issue is worsened by InstructBLIP only finetuning the Qformer for instruction-tuning. It requires the Qformer's visual output tokens to control the length of the LLM's output to be either long-form or short-form, as in prefix tuning [32], but Qformer may lack the capability of properly doing so, due to its limited capacity compared with LLMs like LLaMA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Thus, to enable LLaVA to better handle short-form answers while addressing the issues of InstructBLIP, we propose to use a single response formatting prompt that clearly indicates the output format. It is appended at the end of VQA questions when promoting short answers: Answer the question using a single word or phrase. We find that when the" + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.094, + 0.84, + 0.107 + ], + "angle": 0, + "content": "Visual input example, Multitask Balancing Problem:" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.112, + 0.808, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.211, + 0.594, + 0.238 + ], + "angle": 0, + "content": "User InstructBLIP" + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.211, + 0.854, + 0.238 + ], + "angle": 0, + "content": "Is this unusual? Please explain in detail. yes" + }, + { + "type": "image_footnote", + "bbox": [ + 0.5, + 0.243, + 0.892, + 0.268 + ], + "angle": 0, + "content": "(a) Example of InstructBLIP [13] (Vicuna-13B) having difficulty balancing between short- and long-form answers." + }, + { + "type": "table_caption", + "bbox": [ + 0.515, + 0.283, + 0.82, + 0.298 + ], + "angle": 0, + "content": "Visual input example, Different Format Prompts:" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.3, + 0.889, + 0.45 + ], + "angle": 0, + "content": "
Normal promptWhat is the color of the shirt that the man is wearing?
ResponseThe man is wearing a yellow shirt.
Ambiguous promptQ: What is the color of the shirt that the man is wearing? A:
ResponseThe man is wearing a yellow shirt.
Formatting promptWhat is the color of the shirt that the man is wearing? Answer the question using a single word or phrase.
ResponseYellow.
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.453, + 0.892, + 0.502 + ], + "angle": 0, + "content": "(b) Comparison of how different prompts regularize the output format. The results are obtained zero-shot directly after LLaVA undergoes the first-stage vision-language alignment pretraining, without the second-stage visual instruction tuning." + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.514, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Table 1. Visual input example to illustrate the challenge of (a) multitask balancing and (b) different format prompts. The same image input is used." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.453, + 0.892, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.705 + ], + "angle": 0, + "content": "LLM is finetuned with such prompts, LLaVA is able to properly adjust the output format according to the user's instructions (see Table 1b), and does not require additional processing of the VQA answers using ChatGPT [7], which further enables scaling to various data sources. As shown in Table 2, by merely including VQAv2 [18] in training, LLaVA's performance on MME significantly improves (1323.8 vs 809.6) and outperforms InstructBLIP by 111 points." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.716, + 0.75, + 0.732 + ], + "angle": 0, + "content": "3.3. Scaling the Data and Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.894, + 0.836 + ], + "angle": 0, + "content": "MLP vision-language connector. Inspired by the improved performance in self-supervised learning by changing from a linear projection to an MLP [9, 10], we find that improving the vision-language connector's representation power with a two-layer MLP can improve LLaVA's multimodal capabilities, compared with the original linear projection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Academic task oriented data. We further include additional academic-task-oriented VQA datasets for VQA, OCR, and region-level perception, to enhance the model's capabilities in various ways, as shown in Table 2. We first include" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26298" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.089, + 0.817, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Figure 2. LLaVA-1.5-HD. Scaling LLaVA-1.5 to higher resolutions by splitting the image into grids and encoding them independently. This allows the model to scale to any resolution, without performing positional embedding interpolation for ViTs. We additionally concatenate the feature of a downsampled image to provide the LLM with a global context." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.302, + 0.468, + 0.499 + ], + "angle": 0, + "content": "
MethodLLMRes.GQAMMEMM-Vet
InstructBLIP14B22449.51212.825.6
Only using a subset of InstructBLIP training data
0LLaVA7B224-809.625.5
1+VQA-v27B22447.01197.027.7
2+Format prompt7B22446.81323.826.3
3+MLP VL connector7B22447.31355.227.8
4+OKVQA/OCR7B22450.01377.629.6
Additional scaling
5+Region-level VQA7B22450.31426.530.8
6+Scale up resolution7B33651.4145030.3
7+GQA7B33662.0*1469.230.7
8+ShareGPT7B33662.0*1510.731.1
9+Scale up LLM13B33663.3*1531.336.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.509, + 0.472, + 0.595 + ], + "angle": 0, + "content": "Table 2. Scaling results on data, model, and resolution. We choose to conduct experiments on GQA [20], MME [16], and MM-Vet [54] to examine the representative capabilities of VQA with short answers, VQA with output formatting, and natural visual conversations, respectively. *Training images of GQA were observed during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.472, + 0.79 + ], + "angle": 0, + "content": "four additional datasets that are used in InstructBLIP: open-knowledge VQA (OKVQA [40], A-OKVQA [44]) and OCR (OCRVQA [41], TextCaps [46]). A-OKVQA is converted to multiple choice questions and a specific response formatting prompt is used: Answer with the option's letter from the given choices directly. With only a subset of the datasets InstructBLIP uses, LLaVA already surpasses it on all three tasks in Table 2, suggesting LLaVA's effective design. Furthermore, we find further adding region-level VQA datasets (Visual Genome [24], RefCOCO [23, 39]) improves the model's capability of localizing fine-grained visual details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Additional scaling. We further scale up the input image resolution to \\(336^2\\) to allow the LLM to clearly \"see\" the details of images, by swapping the vision encoder to CLIPViT-L-336px (the highest resolution available for CLIP). In addition, we add the GQA dataset as an additional visual knowledge source. We also incorporate ShareGPT [45] data and scale up the LLM to 13B as in [3, 8, 38]. Results on MM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Vet shows the most significant improvement when scaling the LLM to 13B, suggesting the importance of the base LLM's capability for visual conversations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.895, + 0.417 + ], + "angle": 0, + "content": "LLaVA-1.5. We denote this final model with all the modifications as LLaVA-1.5 (the last two rows in Table 2), which achieves an impressive performance that significantly outperforms the original LLaVA [35]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.528 + ], + "angle": 0, + "content": "Computational cost. For LLaVA-1.5, we use the same pretraining dataset, and keep the training iterations and batch size roughly the same for instruction tuning as LLaVA [35]. Due to the increased image input resolution to \\(336^2\\), the training of LLaVA-1.5 is \\(\\sim 2\\times\\) as long as LLaVA: \\(\\sim 6\\) hours of pretraining and \\(\\sim 20\\) hours of visual instruction tuning, using \\(8\\times\\) A100s." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.541, + 0.766, + 0.558 + ], + "angle": 0, + "content": "3.4. Scaling to Higher Resolutions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.895, + 0.701 + ], + "angle": 0, + "content": "In Sec. 3.3, we observe the advantage that scaling up the input image resolution improves the model's capabilities. However, the image resolution of the existing open source CLIP vision encoders is limited to \\(336^{2}\\), preventing the support of higher resolution images by simply replacing the vision encoder as we did in Sec. 3.3. In this section, we present an early exploration of scaling the LMM to higher resolutions, while maintaining the data efficiency of LLaVA-1.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.895, + 0.825 + ], + "angle": 0, + "content": "When using ViT [14] as the vision encoder, to scale up the resolution, previous approaches mostly choose to perform positional embedding interpolation [3, 31] and adapt the ViT backbone to the new resolution during finetuning. However, this usually requires the model to be finetuned on a large-scale image-text paired dataset [3, 31], and limits the resolution of the image to a fixed size that the LMM can accept during inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Instead, as shown in Fig. 2, we overcome this by dividing the image into smaller image patches of the resolution that the vision encoder is originally trained for, and encode them independently. After obtaining the feature maps of individual patches, we then combine them into a single large feature" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26299" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.155, + 0.089, + 0.813, + 0.281 + ], + "angle": 0, + "content": "
MethodLLMImage SizeSample SizeVQAv2 [18]GQA [20]VisWiz [19]SciQA-IMG [37]TextVQA [47]
BLIP-2 [31]Vicuna-13B2242129M-65.04119.66142.5
InstructBLIP [13]Vicuna-7B2242129M1.2M-49.234.560.550.1
InstructBLIP [13]Vicuna-13B2242129M1.2M-49.533.463.150.7
Shikra [8]Vicuna-13B2242600K5.5M77.4*----
IDEFICS-9B [21]LLaMA-7B2242353M1M50.938.435.5-25.9
IDEFICS-80B [21]LLaMA-65B2242353M1M60.045.236.0-30.9
Qwen-VL [3]Qwen-7B44821.4B†50M†78.8*59.3*35.267.163.8*
Qwen-VL-Chat [3]Qwen-7B44821.4B*50M†78.2*57.5*38.968.261.5*
LLaVA-1.5Vicuna-7B3362558K665K78.5*62.0*50.066.858.2
LLaVA-1.5Vicuna-13B3362558K665K80.0*63.3*53.671.661.3
LLaVA-1.5-HDVicuna-13B4482558K665K81.8*64.7*57.571.062.5
Specialist SOTA: PaLI-X-55B [11]86.1*72.1*70.9*-71.4*
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.289, + 0.893, + 0.332 + ], + "angle": 0, + "content": "Table 3. Comparison with SoTA methods on academic-task-oriented datasets. LLaVA-1.5 achieves the best performance on 4/5 benchmarks, and ranks the second on the other. *The training images/annotations of the datasets are observed during training. †Includes in-house data that is not publicly accessible." + }, + { + "type": "table", + "bbox": [ + 0.16, + 0.345, + 0.807, + 0.533 + ], + "angle": 0, + "content": "
MethodPOPE [33]MME [16]MMBench [36]SEED-Bench [26]LLaVA-Wild [35]MM-Vet [54]
randpopadvencnallimgvid
BLIP2-14B [31]89.685.580.91293.8--46.449.736.738.122.4
InstructBLIP-8B [13]----3623.753.458.838.160.926.2
InstructBLIP-14B [13]87.777721212.8-----58.225.6
Shikra-13B [8]----58.8------
IDEFICS-9B [21]----48.225.2-44.5---
IDEFICS-80B [21]----54.538.1-53.2---
Qwen-VL [3]----38.27.456.362.339.1--
Qwen-VL-Chat [3]---1487.560.656.758.265.437.8--
LLaVA-7B [35]76.372.270.1809.638.736.433.537.023.862.825.5
LLaVA-1.5-7B87.386.184.21510.764.358.358.666.137.365.431.1
LLaVA-1.5-13B87.186.284.51531.367.763.661.668.242.772.536.1
LLaVA-1.5-13B-HD87.586.485.01500.168.861.962.670.141.372.039.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.54, + 0.893, + 0.569 + ], + "angle": 0, + "content": "Table 4. Comparison with SoTA methods on benchmarks for instruction-following LMMs. LLaVA-1.5 achieves the best overall performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.471, + 0.701 + ], + "angle": 0, + "content": "map of the target resolution, and feed that into the LLM. To provide the LLM with the global context and to reduce the artifact of the split-encode-merge operation, we additionally concatenate the feature of a downsampled image to the merged feature map. This allows us to scale the input to any arbitrary resolution and maintain the data efficiency of LLaVA-1.5. We call this resulting model LLaVA-1.5-HD." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.716, + 0.283, + 0.733 + ], + "angle": 0, + "content": "4. Empirical Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.212, + 0.756 + ], + "angle": 0, + "content": "4.1. Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We evaluate LLaVA-1.5 on a collection of both academic-task-oriented benchmarks and recent benchmarks specifically proposed for instruction-following LMMs, totalling 12 benchmarks. For academic-task-oriented benchmarks, VQA-v2 [18] and GQA [20] evaluate model's visual perception capabilities on open-ended short answers. VizWiz [19] contains 8,000 images to evaluate model's zero-shot generalization on visual questions asked by visually impaired people. Following InstructBLIP [13], the image subset of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.895, + 0.642 + ], + "angle": 0, + "content": "ScienceQA [37] with multiple choice are used to evaluate the zero-shot generalization on scientific question answering. TextVQA [47] contains text-rich visual question answering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.896, + 0.901 + ], + "angle": 0, + "content": "For recent benchmarks proposed for instruction-following LMMs, POPE [33] evaluates model's degree of hallucination on three sampled subsets of COCO [34]: random, common, and adversarial and we report the F1 score on all three splits. Other benchmarks evaluate the model's capabilities on a wide range of domains and applications, with different response formats. MME-Perception [16] evaluates model's visual perception with yes/no questions. MMBench [36] evaluates model's answer robustness with all-round shuffling on multiple choice answers. MMBench-CN [36] is the Chinese-translated version of MMBench. SEED-Bench [26] evaluates model's performance on both images and videos with multiple choice, and we sample the frame in the middle to evaluate the accuracy on videos. LLaVA-Bench-in-the-Wild [35] and MM-Vet [54] evaluate model's capabilities in engaging in visual conversations on a diverse range of tasks, and evaluates the correctness and the helpfulness of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26300" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.094, + 0.093, + 0.315, + 0.106 + ], + "angle": 0, + "content": "Visual input example, Tricky Question:" + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.108, + 0.46, + 0.367 + ], + "angle": 0, + "content": "
UserIf there are factual errors in the questions, point it out; if not, proceed to answering the question. What's happening in the desert?
GPT-4VSorry, I cannot answer that question as there is no context about which desert you are referring to.
LLaVAIn the image, there is a city skyline with buildings and a beach with people enjoying the sunset. The scene is set in a desert, which is unusual for a beach setting.
LLaVA-1.5There are no deserts in the image. The image features a beach with palm trees, a city skyline, and a large body of water.
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.377, + 0.466, + 0.406 + ], + "angle": 0, + "content": "Table 5. LLaVA-1.5 can detect and answer tricky questions when prompted to verify the question." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.431, + 0.318, + 0.446 + ], + "angle": 0, + "content": "the response with GPT-4 evaluation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.171, + 0.469 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.599 + ], + "angle": 0, + "content": "We show that LLaVA-1.5 achieves the best overall performance on 12 benchmarks, despite using magnitudes smaller pretraining and instruction tuning data compared with other methods [3, 13]. LLaVA-1.5 significantly outperforms LLaVA on all benchmarks for instruction-following LMMs. Note that it is challenging to evaluate the original LLaVA on academic datasets like VQA-v2 [18] that demand open-ended short answers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.736 + ], + "angle": 0, + "content": "When we continue to scale up the image resolution to \\(448^{2}\\) with LLaVA-1.5-HD, it further improves the overall performance on all benchmarks, especially on tasks that require perception of details in the images (e.g. OCR in MM-Vet, detailed description in LLaVA-Bench-in-the-Wild [35]). Moreover, we find that adding the global context effectively recovers the model from the split-and-merge artifacts and guides the model to more easily locate the relevant regions from the high-resolution features (see appendix)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.736, + 0.471, + 0.902 + ], + "angle": 0, + "content": "It is encouraging that LLaVA-1.5 achieves the best performance with the simplest architecture, academic compute and public datasets, and yields a fully-reproducible and affordable baseline for future research. The results also suggest that visual instruction tuning plays an important role in improving an LMM's capabilities, and raises questions upon the common belief that LMMs require significant amount of vision-language alignment pretraining [3, 13, 31], despite that the vision encoders (e.g. CLIP [43], OpenCLIP [22], EVA-CLIP [15], etc.) are already pretrained on web-scale image-text paired data. LLaVA-1.5 (even the 7B model)" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.093, + 0.794, + 0.106 + ], + "angle": 0, + "content": "Visual input example, Constrained JSON Output:" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.108, + 0.885, + 0.499 + ], + "angle": 0, + "content": "
UserPlease read the text in this image and return the information in the following JSON format (note xxx is placeholder, if the information is not available in the image, put "N/A" instead). {"class": xxx, "DLN": xxx, "DOB": xxx, "Name": xxx, "Address": xxx, "EXP": xxx, "ISS": xxx, "SEX": xxx, "HGT": xxx, "WGT": xxx, "EYES": xxx, "HAIR": xxx, "DONOR": xxx}
GPT-4V{"class": "C", "DLN": "1234568", "DOB": "08/31/1977", "Name": "Ima Cardholder", "Address": "2570 24th Street, Anytown, CA 95818", "EXP": "08/31/2014", "ISS": "08/31/2011", "SEX": "F", "HGT": "5-05", "WGT": "125 lbs", "EYES": "BRN", "HAIR": "BRN", "DONOR": "VETERAN"}
LLaVA{"class": "Driver License", "DLN": "CA123 456 789", "DOB": "01/01/1990", "Name": "Amy", "Address": "Anytown, CA", "EXP": "08/31/2023", "ISS": "Veteran", "SEX": "F", "HGT": "5', "WGT": "130", "EYES": "Brown", "HAIR": "Brown", "DONOR": "Unknown"}
LLaVA-1.5{"class": "C", "DLN": "1132456789", "DOB": "08/23/1971", "Name": "Ima Cardholder", "Address": "Anytown, State, Zip", "EXP": "08/23/2014", "ISS": "California", "SEX": "F", "HGT": "5', "WGT": "123", "EYES": "Brown", "HAIR": "Brown", "DONOR": "N/A"}
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.51, + 0.89, + 0.553 + ], + "angle": 0, + "content": "Table 6. LLaVA-1.5 can extract information from the image and answer following the required format, despite a few errors compared with GPT-4V. GPT-4V results are obtained from [51]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.656 + ], + "angle": 0, + "content": "outperforms 80B IDEFICS [21], a Flamingo-like LMM with billions of trainable parameters for cross-modal connection. This also makes us rethink the benefits of the vision samplers and the necessity of the additional large-scale pretraining, in terms of multimodal instruction-following capabilities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.737 + ], + "angle": 0, + "content": "Global context. For higher resolution, we pad and resize the image to a single image of \\(224^2\\), and concatenate it with the high resolution features to provide a global context. Ablation on a 7B model shows that the global context effectively boosts performance on all three validation benchmarks." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.749, + 0.876, + 0.801 + ], + "angle": 0, + "content": "
GQAMMEMM-Vet
high-res patch only62.91425.831.9
+global context63.8 (+0.9)1497.5 (+71)35.1 (+3.2)
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.828, + 0.696, + 0.844 + ], + "angle": 0, + "content": "4.3. Emerging Properties" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Format instruction generalization. Although LLaVA-1.5 is only trained with a limited number of format instructions, it generalizes to others. First, VizWiz [19] requires the model" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26301" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.087, + 0.473, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.358, + 0.471, + 0.389 + ], + "angle": 0, + "content": "Figure 3. Ablation on LLM choices. Data points represent the relative performance of the best performing variant for each dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.472, + 0.518 + ], + "angle": 0, + "content": "to output \"Unanswerable\" when the provided content is insufficient to answer the question, and our response format prompt (see Appendix) effectively instructs the model to do so (\\(11.1\\% \\rightarrow 67.8\\%\\) on unanswerable questions). We additionally present qualitative examples on instructing LLaVA-1.5 to verify tricky questions (Fig. 5), respond in a constrained JSON format (Fig. 6), and more in appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.473, + 0.765 + ], + "angle": 0, + "content": "Multilingual multimodal capability. Though LLaVA-1.5 is not finetuned for multilingual multimodal instruction following at all (all visual instructions including VQA are in English), we find that it is capable of following multilingual instructions. This is partly due to the multilingual language instructions in ShareGPT [45]. Although ShareGPT does not contain images in its instructions, the model learns from this dataset the behavior of adaptively responding with the language that corresponds to the user's request. We empirically show that this behavior is transferred to visual conversations. We also quantitatively evaluate the model's generalization capability to Chinese on MMBench-CN [36], where the questions of MMBench are converted to Chinese. Notably, LLaVA-1.5 outperforms Qwen-VL-Chat by \\(+7.3\\%\\) (63.6% vs 56.7%), despite Qwen being finetuned on Chinese multimodal instructions while LLaVA-1.5 is not." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.315, + 0.787 + ], + "angle": 0, + "content": "4.4. Ablation on LLM Choices" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.903 + ], + "angle": 0, + "content": "In NLP, findings [48] suggest that the capability of the base LLM can affect its instruction-tuned successors. In this section, we explore two families of LLMs and study their contribution to the final model's multimodal capability: LLaMA-based (Vicuna-v1.1, Vicuna-v1.3) and LLaMA2-based (Vicuna-v1.5, LLaMA-2-Chat). Vicuna-v1.3 and Vicuna-v1.5 use the same \\(\\sim 150\\mathrm{K}\\) ShareGPT [45] data (\\(2\\times\\)" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.087, + 0.891, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.358, + 0.893, + 0.389 + ], + "angle": 0, + "content": "Figure 4. Ablation on data efficiency. Data points represent the relative performance of the best performing variant for each dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.492 + ], + "angle": 0, + "content": "that used in v1.1). Unlike Vicuna series that is only trained with supervised instruction finetuning (SFT), LLaMA-2-Chat is further optimized with reinforcement-learning from human-feedback (RLHF). We visualize the relative performance of these variants in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.895, + 0.614 + ], + "angle": 0, + "content": "First, we find that Vicuna-v1.5 achieves the best overall performance, and LLaMA-2-based models generally perform better than LLaMA-1-based, suggesting the importance of the base language model. This is further evidenced by the results on MMBench-CN [36]: despite Vicuna-v1.3 and v1.5 using the same ShareGPT data for instruction tuning, the performance in generalization to Chinese of Vicuna-v1.3 is significantly worse than v1.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.897, + 0.812 + ], + "angle": 0, + "content": "Second, language instruction-tuning matters on specific capabilities that are required by each dataset. For example, although LLaMA-2-Chat and Vicuna-v1.5 achieves almost the same performance on MMBench, the generalization to MMBench-CN [36] of LLaMA-2-Chat is worse than Vicuna-v1.5, which is partly due to that the most SFT/RLHF data of LLaMA-2-Chat is in English and does not contain as many multilingual data as in ShareGPT. Furthermore, TextVQA requires both the model's capability of identifying the text characters in the images, and also processing the noisy outputs from the OCR engine; such noise may be more commonly observed in the ShareGPT data, which is collected in-the-wild from daily usage of ChatGPT." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.829, + 0.741, + 0.846 + ], + "angle": 0, + "content": "5. Open Problems in LMMs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Given the successful scaling of LLaVA-1.5, we conduct additional studies on open problems in LMMs using the model design and data mixture of LLaVA-1.5." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26302" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.232, + 0.108 + ], + "angle": 0, + "content": "5.1. Data Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.47, + 0.235 + ], + "angle": 0, + "content": "Despite the data efficiency of LLaVA-1.5 when compared with approaches like InstructBLIP [13], the training of LLaVA-1.5 still doubles when compared with LLaVA. In this section, we conduct experiments for further improving the data efficiency by randomly sub-sampling the training data mixture of LLaVA-1.5, with a sampling ratio ranging from 0.1 to 0.5. We visualize the relative performance of different sampling variants in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.235, + 0.47, + 0.325 + ], + "angle": 0, + "content": "First, the full data mixture provides the best knowledge coverage, and allows the model to achieve the best overall performance. To our surprise, with only \\(50\\%\\) of the samples, the model still maintains more than \\(98\\%\\) of the full dataset performance. This suggests that there is room for further improvements in data efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.47, + 0.432 + ], + "angle": 0, + "content": "Second, when downsampling the dataset to \\(50\\%\\), the model's performance on MMBench, ScienceQA, and POPE does not decrease at all, and it even slightly improves on MMBench. Similarly, the model's performance remains steady when further downscaling the data from \\(50\\%\\) to \\(30\\%\\). These results show promise of having the less-is-more [59] benefit for multimodal models as well." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.439, + 0.387, + 0.455 + ], + "angle": 0, + "content": "5.2. Rethinking Hallucination in LMMs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Hallucination is an important issue to tackle for LLMs and LMMs. Often in LMMs, we attribute the model's hallucination to the errors or hallucinations in the training dataset. For example, the detailed descriptions in LLaVA-Instruct [35] may contain a small amount of hallucinated content, and it is believed that training on such data may have caused the model to hallucinate when asked to \"describe the image in detail\". However, we find that such hallucination is significantly reduced, when we scale the model's inputs to higher resolutions like \\(448^{2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.471, + 0.794 + ], + "angle": 0, + "content": "This finding is interesting as it suggests that the LMMs may be robust to a few such errors in the training data. However, when the input resolution is not sufficient for the model to discern all details in the training data, and the amount of data that is at that granularity beyond the model's capability becomes large enough, the model learns to hallucinate. This further suggests that there needs to be a balance between improving the data annotation with more details and the model's capability to properly process the information at such granularities. We hope this finding provides a reference for future work in terms of dealing with hallucination and the scaling of the models and data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.322, + 0.818 + ], + "angle": 0, + "content": "5.3. Compositional Capabilities" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We demonstrate interesting compositional capabilities in LLaVA-1.5: the model trained on a set of tasks independently generalizes to tasks that require a combination of these capabilities without explicit joint training. We note some of the findings below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.242 + ], + "angle": 0, + "content": "First, we observe an improved language capability in visual conversations after including the ShareGPT [45] data, including the multimodal multilingual capability as discussed in Sec. 4.3. Moreover, the model is more capable at providing longer and more detailed responses in visual conversations. Second, the additional visual knowledge from the academic-task-oriented datasets, improves the visual groundness of LLaVA-1.5's responses in visual conversations, as evidenced quantitatively by the improved results on MMVet [54] and LLaVA-Wild [35] in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.895, + 0.365 + ], + "angle": 0, + "content": "However, there is still difficulty in achieving ideal performance for some tasks that require a certain combination of capabilities. For example, being able to correctly answer the attribute of a certain object in VQA, does not guarantee an accurate depiction of that object attribute in a detailed description of the whole image. Furthermore, the capability of engaging in conversations with certain foreign languages (e.g. Korean) still falls behind. See appendix for examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.895, + 0.471 + ], + "angle": 0, + "content": "These findings suggest that the compositional capabilities of LMMs can be leveraged to improve the model's performance without significantly increasing the data by exhaustively including all task combinations. Yet, it can be further investigated, and a deeper understanding of the mechanism behind the compositional capabilities of LMMs can further improve the capability and the data efficiency of LLaVA-1.5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.487, + 0.619, + 0.503 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.894, + 0.664 + ], + "angle": 0, + "content": "In this paper, we take a step towards demystifying the design of large multimodal models, and propose a simple, effective, and data-efficient baseline, LLaVA-1.5, for large multimodal models. In addition, we explore the open problems in visual instruction tuning, scale LMMs to higher resolutions, and present some intriguing findings in terms of model hallucination and compositional capabilities for LMMs. We hope these improved and easily-reproducible baselines as well as the new findings will provide a reference for future research in open-source LMM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.895, + 0.777 + ], + "angle": 0, + "content": "Limitations. Despite the promising results demonstrated by LLaVA-1.5, it still has limitations including prolonged training for high-resolution images, lack of multiple-image understanding, limited problem solving capabilities in certain fields. It is not exempt from producing hallucinations, and should be used with caution in critical applications (e.g. medical). See appendix for a detailed discussion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported in part by NSF CAREER IIS2150012, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26303" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.143 + ], + "angle": 0, + "content": "[1] Adept AI. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "26306" + } + ] +] \ No newline at end of file diff --git a/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_origin.pdf b/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e37c32818a0e80ef0f12a8ded4ae6f247340dade --- /dev/null +++ b/2024/Improved Baselines with Visual Instruction Tuning/82854e3f-7839-4652-bd17-7a90bb94eee7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5505eb027c8f7422f30c7915229a721ca95b80a3bb474d6df47175ab69294eab +size 1299100 diff --git a/2024/Improved Baselines with Visual Instruction Tuning/full.md b/2024/Improved Baselines with Visual Instruction Tuning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9e3648c82604eca695991afff6eaa7192eb06cad --- /dev/null +++ b/2024/Improved Baselines with Visual Instruction Tuning/full.md @@ -0,0 +1,274 @@ +# Improved Baselines with Visual Instruction Tuning + +Haotian Liu1 Chunyuan Li2 Yuheng Li1 Yong Jae Lee1 +1University of Wisconsin-Madison 2Microsoft Research, Redmond https://llava-vl.github.io + +# Abstract + +Large multimodal models (LMM) have recently shown encouraging progress with visual instruction tuning. In this paper, we present the first systematic study to investigate the design choices of LMMs in a controlled setting under the LLaVA framework. We show that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient. With simple modifications to LLaVA, namely, using CLIP-ViT-L-336px with an MLP projection and adding academic-task-oriented VQA data with response formatting prompts, we establish stronger baselines that achieve state-of-the-art across 11 benchmarks. Our final 13B checkpoint uses merely 1.2M publicly available data, and finishes full training in $\sim 1$ day on a single 8-A100 node. Furthermore, we present some early exploration of open problems in LMMs, including scaling to higher resolution inputs, compositional capabilities, and model hallucination, etc. We hope this makes state-of-the-art LMM research more accessible. Code and model will be publicly available. + +# 1. Introduction + +Large multimodal models (LMMs) have become increasingly popular in the research community, as they are the key building blocks towards general-purpose assistants [2, 29, 42]. Recent studies on LMMs are converging on a central concept known as visual instruction tuning [35]. The results are promising, e.g. LLaVA [35] and MiniGPT-4 [60] demonstrate impressive results on natural instruction-following and visual reasoning capabilities. To better understand the capability of LMMs, multiple benchmarks [16, 26, 33, 36, 54] have been proposed. Recent works further demonstrate improved performance by scaling up the pretraining data [3, 13, 53], instruction-following data [13, 17, 28, 57], visual encoders [3], or language models [38], respectively. The LLaVA architecture is also leveraged in different downstream tasks and domains, including region-level [8, 55] and pixel-level [25, 49] understanding, biomedical assistants [30], image generation [5], adversarial studies [6, 58]. + +![](images/1dd41f9ee2e33172fee4a9962ad99eb5a2df0182e34e291c997b56f9580b389d.jpg) +Figure 1. LLaVA-1.5 achieves SoTA on a broad range of 11 tasks (Top), with high training sample efficiency (Left) and simple modifications to LLaVA (Right): an MLP connector and including academic-task-oriented data with response formatting prompts. + +However, despite many benchmarks and developments, it still remains unclear what the best recipe is to train LMMs towards the goal of general-purpose assistants. For example, LLaVA [35] excels in conversational-style visual reasoning and even outperforms later approaches like InstructBLIP [13] on such benchmarks [54], while InstructBLIP excels in traditional VQA benchmarks that demands single-word or short answers. Given the significant differences in the model architecture and training data between them, the root cause of the disparity in their capabilities remains elusive, despite conjectures [36, 54]: the amount of training data, the usage of resamplers like Qformer [31], etc. To this + +end, we present the first systematic study to investigate the design choices of LMMs in a controlled setting. Our study originates from LLaVA and builds a road map by carefully making effective contributions from the perspectives of the input, model, and data. + +First, we unveil that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient, and we establish stronger and more feasible baselines built upon the LLaVA framework. We report that two simple improvements, namely, an MLP cross-modal connector and incorporating academic task related data such as VQA, are orthogonal to the framework of LLaVA, and when used with LLaVA, lead to better multimodal understanding capabilities. In contrast to InstructBLIP [13] or Qwen-VL [3], which trains specially designed visual resamplers on hundreds of millions or even billions of image-text paired data, LLaVA uses one of the simplest architecture design for LMMs and requires only training a simple fully-connected projection layer on merely 600K image-text pairs. Our final model can finish training in $\sim 1$ day on a single 8-A100 machine and achieves state-of-the-art results on a wide range of benchmarks. Moreover, unlike Qwen-VL [3] that includes in-house data in training, LLaVA utilizes only publicly available data. + +Next, we delve into an early exploration of other open problems of large multimodal models. Our findings include: (1) Scaling to high-resolution image inputs. We show that LLaVA's architecture is versatile in scaling to higher resolutions by simply dividing images into grids and maintains its data efficiency; with the increased resolution, it improves the model's detailed perception capabilities and reduces hallucination. (2) Compositional capabilities. We find that large multimodal models are capable of generalizing to compositional capabilities. For example, training on long-form language reasoning together with shorter visual reasoning can improve the model's writing capability for multimodal questions. (3) Data efficiency. We show that randomly downsampling LLaVA's training data mixture by up to $75\%$ does not significantly decrease the model's performance, suggesting that the possibility of a more sophisticated dataset compression strategy can further improve LLaVA's already efficient training pipeline. (4) Data scaling. We provide empirical evidence for the scaling of data granularity in conjunction with the model's capability is crucial for an improved capability without introducing artifacts like hallucination. + +In sum, we perform a systematic study on the training of large multimodal models, and introduce a simple yet effective approach to balance the multitask learning and effective scaling for large multimodal models. Our improved baselines, LLaVA-1.5, uses only public data, achieves the state-of-the-art on a broad range of 11 tasks, and is significantly more data-efficient than previous approaches. By + +rethinking the conventional approaches and exploring the open problems in visual instruction tuning, we pave the way for more robust and capable systems for LMMs. We hope these improved and easily-reproducible baselines will provide a reference for future research in open-source LMMs. + +# 2. Related Work + +Instruction-following large multimodal models (LMMs). Common architectures include a pre-trained visual backbone to encode visual features, a pre-trained large language model (LLM) to comprehend the user instructions and produce responses, and a vision-language cross-modal connector to align the vision encoder outputs to the language models. As shown in Fig. 1, LLaVA [35] is perhaps the simplest architecture for LMMs. Optionally, visual resamplers (e.g. Qformer [31]) are used to reduce the number of visual patches [3, 13, 60]. Training an instruction-following LMM usually follows a two-stage protocol. First, the vision-language alignment pretraining stage leverages image-text pairs to align the visual features with the language model's word embedding space. Earlier works utilize relatively few image-text pairs (e.g. $\sim 600\mathrm{K}$ [35] or $\sim 6\mathrm{M}$ [60]), while some recent works pretrain the vision-language connector for a specific language model on a large amount of image-text pairs (e.g. 129M [13] and 1.4B [3]), to maximize the LMM's performance. Second, the visual instruction tuning stage tunes the model on visual instructions [35], to enable the model to follow users' diverse requests on instructions that involve the visual contents. Dealing with higher resolution with grids in LMM are studied in con-current works [1, 27, 52]. + +Multimodal instruction-following data. In NLP, studies show that the quality of instruction-following data largely affects the capability of the resulting instruction-following models [59]. For visual instruction tuning, LLaVA [35] is the pioneer to leverage text-only GPT-4 to expand the existing COCO [34] bounding box and caption dataset to a multimodal instruction-following dataset that contains three types of instruction-following data: conversational-style QA, detailed description, and complex reasoning. LLaVA's pipeline has been employed to expand to textual understanding [56], million-scales [57], and region-level conversations [8]. InstructBLIP [13] incorporates academic-task-oriented VQA datasets to further enhance the model's visual capabilities. Conversely, [7] identifies that such naive data merging can result in models that tend to overfit to VQA datasets and thus are unable to participate in natural conversations. The authors further propose to leverage the LLaVA pipeline to convert VQA datasets to a conversational style. While this proves effective for training, it introduces added complexities in data scaling. However, in NLP, the FLAN family [12, 50] shows that adding a large number of academic language tasks for instruction tuning can effectively improve the gen + +eralization ability. In light of this, we consider investigating the root cause of the inability to balance between natural conversations and academic tasks in multimodal models. + +# 3. Approach + +# 3.1. Preliminaries + +As the seminal work of visual instruction tuning, LLaVA [35] showcases commendable proficiency in visual reasoning capabilities, surpassing even more recent models on diverse benchmarks [4, 54] for real-life visual instruction-following tasks. LLaVA uses a single linear layer to project the visual features to language space, and optimizes the whole LLM for visual instruction tuning. However, LLaVA falls short on academic benchmarks that typically require short-form answers (e.g. single-word), and tends to answer yes for yes/no questions due to the lack of such data in the training distribution. + +On the other hand, InstructBLIP [13] is the pioneer to incorporate academic-task-oriented datasets like VQA-v2 [18] along with LLaVA-Instruct [35], and demonstrates improved performance on VQA benchmarks. It pretrains Qformer [31] on 129M image-text pairs and only finetunes the instruction-aware Qformer for visual instruction tuning. However, recent studies [7, 54] show that it does not perform as well as LLaVA on engaging in real-life visual conversation tasks. More specifically, as shown in Table 1a, it can overfit to VQA training sets with short-answers, even on requests that require detailed responses. + +# 3.2. Response Format Prompting + +We find that the inability [7] to balance between short- and long-form VQA for approaches like InstructBLIP [13], which leverages instruction following data that includes both natural responses and short-answers, is mainly due to the following reasons. First, ambiguous prompts on the response format. For example, $Q$ : {Question} A: {Answer}. Such prompts do not clearly indicate the desired output format, and can overfit an LLM behaviorally to short-form answers even for natural visual conversations. Second, not finetuning the LLM. The first issue is worsened by InstructBLIP only finetuning the Qformer for instruction-tuning. It requires the Qformer's visual output tokens to control the length of the LLM's output to be either long-form or short-form, as in prefix tuning [32], but Qformer may lack the capability of properly doing so, due to its limited capacity compared with LLMs like LLaMA. + +Thus, to enable LLaVA to better handle short-form answers while addressing the issues of InstructBLIP, we propose to use a single response formatting prompt that clearly indicates the output format. It is appended at the end of VQA questions when promoting short answers: Answer the question using a single word or phrase. We find that when the + +# Visual input example, Multitask Balancing Problem: + +User InstructBLIP +Is this unusual? Please explain in detail. yes +![](images/a8a03c251ed3dc03720febd659389a06aad4958f288a8710d612a72b307d24d8.jpg) +(a) Example of InstructBLIP [13] (Vicuna-13B) having difficulty balancing between short- and long-form answers. + +Visual input example, Different Format Prompts: + +
Normal promptWhat is the color of the shirt that the man is wearing?
ResponseThe man is wearing a yellow shirt.
Ambiguous promptQ: What is the color of the shirt that the man is wearing? A:
ResponseThe man is wearing a yellow shirt.
Formatting promptWhat is the color of the shirt that the man is wearing? Answer the question using a single word or phrase.
ResponseYellow.
+ +(b) Comparison of how different prompts regularize the output format. The results are obtained zero-shot directly after LLaVA undergoes the first-stage vision-language alignment pretraining, without the second-stage visual instruction tuning. +Table 1. Visual input example to illustrate the challenge of (a) multitask balancing and (b) different format prompts. The same image input is used. + +LLM is finetuned with such prompts, LLaVA is able to properly adjust the output format according to the user's instructions (see Table 1b), and does not require additional processing of the VQA answers using ChatGPT [7], which further enables scaling to various data sources. As shown in Table 2, by merely including VQAv2 [18] in training, LLaVA's performance on MME significantly improves (1323.8 vs 809.6) and outperforms InstructBLIP by 111 points. + +# 3.3. Scaling the Data and Model + +MLP vision-language connector. Inspired by the improved performance in self-supervised learning by changing from a linear projection to an MLP [9, 10], we find that improving the vision-language connector's representation power with a two-layer MLP can improve LLaVA's multimodal capabilities, compared with the original linear projection. + +Academic task oriented data. We further include additional academic-task-oriented VQA datasets for VQA, OCR, and region-level perception, to enhance the model's capabilities in various ways, as shown in Table 2. We first include + +![](images/34e28144874d491e764e69b7deb546aaee9460370ce7fe3e6b51ab8a593c8b50.jpg) +Figure 2. LLaVA-1.5-HD. Scaling LLaVA-1.5 to higher resolutions by splitting the image into grids and encoding them independently. This allows the model to scale to any resolution, without performing positional embedding interpolation for ViTs. We additionally concatenate the feature of a downsampled image to provide the LLM with a global context. + +
MethodLLMRes.GQAMMEMM-Vet
InstructBLIP14B22449.51212.825.6
Only using a subset of InstructBLIP training data
0LLaVA7B224-809.625.5
1+VQA-v27B22447.01197.027.7
2+Format prompt7B22446.81323.826.3
3+MLP VL connector7B22447.31355.227.8
4+OKVQA/OCR7B22450.01377.629.6
Additional scaling
5+Region-level VQA7B22450.31426.530.8
6+Scale up resolution7B33651.4145030.3
7+GQA7B33662.0*1469.230.7
8+ShareGPT7B33662.0*1510.731.1
9+Scale up LLM13B33663.3*1531.336.1
+ +Table 2. Scaling results on data, model, and resolution. We choose to conduct experiments on GQA [20], MME [16], and MM-Vet [54] to examine the representative capabilities of VQA with short answers, VQA with output formatting, and natural visual conversations, respectively. *Training images of GQA were observed during training. + +four additional datasets that are used in InstructBLIP: open-knowledge VQA (OKVQA [40], A-OKVQA [44]) and OCR (OCRVQA [41], TextCaps [46]). A-OKVQA is converted to multiple choice questions and a specific response formatting prompt is used: Answer with the option's letter from the given choices directly. With only a subset of the datasets InstructBLIP uses, LLaVA already surpasses it on all three tasks in Table 2, suggesting LLaVA's effective design. Furthermore, we find further adding region-level VQA datasets (Visual Genome [24], RefCOCO [23, 39]) improves the model's capability of localizing fine-grained visual details. + +Additional scaling. We further scale up the input image resolution to $336^2$ to allow the LLM to clearly "see" the details of images, by swapping the vision encoder to CLIPViT-L-336px (the highest resolution available for CLIP). In addition, we add the GQA dataset as an additional visual knowledge source. We also incorporate ShareGPT [45] data and scale up the LLM to 13B as in [3, 8, 38]. Results on MM + +Vet shows the most significant improvement when scaling the LLM to 13B, suggesting the importance of the base LLM's capability for visual conversations. + +LLaVA-1.5. We denote this final model with all the modifications as LLaVA-1.5 (the last two rows in Table 2), which achieves an impressive performance that significantly outperforms the original LLaVA [35]. + +Computational cost. For LLaVA-1.5, we use the same pretraining dataset, and keep the training iterations and batch size roughly the same for instruction tuning as LLaVA [35]. Due to the increased image input resolution to $336^2$ , the training of LLaVA-1.5 is $\sim 2\times$ as long as LLaVA: $\sim 6$ hours of pretraining and $\sim 20$ hours of visual instruction tuning, using $8\times$ A100s. + +# 3.4. Scaling to Higher Resolutions + +In Sec. 3.3, we observe the advantage that scaling up the input image resolution improves the model's capabilities. However, the image resolution of the existing open source CLIP vision encoders is limited to $336^{2}$ , preventing the support of higher resolution images by simply replacing the vision encoder as we did in Sec. 3.3. In this section, we present an early exploration of scaling the LMM to higher resolutions, while maintaining the data efficiency of LLaVA-1.5. + +When using ViT [14] as the vision encoder, to scale up the resolution, previous approaches mostly choose to perform positional embedding interpolation [3, 31] and adapt the ViT backbone to the new resolution during finetuning. However, this usually requires the model to be finetuned on a large-scale image-text paired dataset [3, 31], and limits the resolution of the image to a fixed size that the LMM can accept during inference. + +Instead, as shown in Fig. 2, we overcome this by dividing the image into smaller image patches of the resolution that the vision encoder is originally trained for, and encode them independently. After obtaining the feature maps of individual patches, we then combine them into a single large feature + +
MethodLLMImage SizeSample SizeVQAv2 [18]GQA [20]VisWiz [19]SciQA-IMG [37]TextVQA [47]
BLIP-2 [31]Vicuna-13B2242129M-65.04119.66142.5
InstructBLIP [13]Vicuna-7B2242129M1.2M-49.234.560.550.1
InstructBLIP [13]Vicuna-13B2242129M1.2M-49.533.463.150.7
Shikra [8]Vicuna-13B2242600K5.5M77.4*----
IDEFICS-9B [21]LLaMA-7B2242353M1M50.938.435.5-25.9
IDEFICS-80B [21]LLaMA-65B2242353M1M60.045.236.0-30.9
Qwen-VL [3]Qwen-7B44821.4B†50M†78.8*59.3*35.267.163.8*
Qwen-VL-Chat [3]Qwen-7B44821.4B*50M†78.2*57.5*38.968.261.5*
LLaVA-1.5Vicuna-7B3362558K665K78.5*62.0*50.066.858.2
LLaVA-1.5Vicuna-13B3362558K665K80.0*63.3*53.671.661.3
LLaVA-1.5-HDVicuna-13B4482558K665K81.8*64.7*57.571.062.5
Specialist SOTA: PaLI-X-55B [11]86.1*72.1*70.9*-71.4*
+ +Table 3. Comparison with SoTA methods on academic-task-oriented datasets. LLaVA-1.5 achieves the best performance on 4/5 benchmarks, and ranks the second on the other. *The training images/annotations of the datasets are observed during training. †Includes in-house data that is not publicly accessible. + +
MethodPOPE [33]MME [16]MMBench [36]SEED-Bench [26]LLaVA-Wild [35]MM-Vet [54]
randpopadvencnallimgvid
BLIP2-14B [31]89.685.580.91293.8--46.449.736.738.122.4
InstructBLIP-8B [13]----3623.753.458.838.160.926.2
InstructBLIP-14B [13]87.777721212.8-----58.225.6
Shikra-13B [8]----58.8------
IDEFICS-9B [21]----48.225.2-44.5---
IDEFICS-80B [21]----54.538.1-53.2---
Qwen-VL [3]----38.27.456.362.339.1--
Qwen-VL-Chat [3]---1487.560.656.758.265.437.8--
LLaVA-7B [35]76.372.270.1809.638.736.433.537.023.862.825.5
LLaVA-1.5-7B87.386.184.21510.764.358.358.666.137.365.431.1
LLaVA-1.5-13B87.186.284.51531.367.763.661.668.242.772.536.1
LLaVA-1.5-13B-HD87.586.485.01500.168.861.962.670.141.372.039.4
+ +Table 4. Comparison with SoTA methods on benchmarks for instruction-following LMMs. LLaVA-1.5 achieves the best overall performance. + +map of the target resolution, and feed that into the LLM. To provide the LLM with the global context and to reduce the artifact of the split-encode-merge operation, we additionally concatenate the feature of a downsampled image to the merged feature map. This allows us to scale the input to any arbitrary resolution and maintain the data efficiency of LLaVA-1.5. We call this resulting model LLaVA-1.5-HD. + +# 4. Empirical Evaluation + +# 4.1. Benchmarks + +We evaluate LLaVA-1.5 on a collection of both academic-task-oriented benchmarks and recent benchmarks specifically proposed for instruction-following LMMs, totalling 12 benchmarks. For academic-task-oriented benchmarks, VQA-v2 [18] and GQA [20] evaluate model's visual perception capabilities on open-ended short answers. VizWiz [19] contains 8,000 images to evaluate model's zero-shot generalization on visual questions asked by visually impaired people. Following InstructBLIP [13], the image subset of + +ScienceQA [37] with multiple choice are used to evaluate the zero-shot generalization on scientific question answering. TextVQA [47] contains text-rich visual question answering. + +For recent benchmarks proposed for instruction-following LMMs, POPE [33] evaluates model's degree of hallucination on three sampled subsets of COCO [34]: random, common, and adversarial and we report the F1 score on all three splits. Other benchmarks evaluate the model's capabilities on a wide range of domains and applications, with different response formats. MME-Perception [16] evaluates model's visual perception with yes/no questions. MMBench [36] evaluates model's answer robustness with all-round shuffling on multiple choice answers. MMBench-CN [36] is the Chinese-translated version of MMBench. SEED-Bench [26] evaluates model's performance on both images and videos with multiple choice, and we sample the frame in the middle to evaluate the accuracy on videos. LLaVA-Bench-in-the-Wild [35] and MM-Vet [54] evaluate model's capabilities in engaging in visual conversations on a diverse range of tasks, and evaluates the correctness and the helpfulness of + +Visual input example, Tricky Question: + +
UserIf there are factual errors in the questions, point it out; if not, proceed to answering the question. What's happening in the desert?
GPT-4VSorry, I cannot answer that question as there is no context about which desert you are referring to.
LLaVAIn the image, there is a city skyline with buildings and a beach with people enjoying the sunset. The scene is set in a desert, which is unusual for a beach setting.
LLaVA-1.5There are no deserts in the image. The image features a beach with palm trees, a city skyline, and a large body of water.
+ +Table 5. LLaVA-1.5 can detect and answer tricky questions when prompted to verify the question. + +the response with GPT-4 evaluation. + +# 4.2. Results + +We show that LLaVA-1.5 achieves the best overall performance on 12 benchmarks, despite using magnitudes smaller pretraining and instruction tuning data compared with other methods [3, 13]. LLaVA-1.5 significantly outperforms LLaVA on all benchmarks for instruction-following LMMs. Note that it is challenging to evaluate the original LLaVA on academic datasets like VQA-v2 [18] that demand open-ended short answers. + +When we continue to scale up the image resolution to $448^{2}$ with LLaVA-1.5-HD, it further improves the overall performance on all benchmarks, especially on tasks that require perception of details in the images (e.g. OCR in MM-Vet, detailed description in LLaVA-Bench-in-the-Wild [35]). Moreover, we find that adding the global context effectively recovers the model from the split-and-merge artifacts and guides the model to more easily locate the relevant regions from the high-resolution features (see appendix). + +It is encouraging that LLaVA-1.5 achieves the best performance with the simplest architecture, academic compute and public datasets, and yields a fully-reproducible and affordable baseline for future research. The results also suggest that visual instruction tuning plays an important role in improving an LMM's capabilities, and raises questions upon the common belief that LMMs require significant amount of vision-language alignment pretraining [3, 13, 31], despite that the vision encoders (e.g. CLIP [43], OpenCLIP [22], EVA-CLIP [15], etc.) are already pretrained on web-scale image-text paired data. LLaVA-1.5 (even the 7B model) + +Visual input example, Constrained JSON Output: + +
UserPlease read the text in this image and return the information in the following JSON format (note xxx is placeholder, if the information is not available in the image, put "N/A" instead). {"class": xxx, "DLN": xxx, "DOB": xxx, "Name": xxx, "Address": xxx, "EXP": xxx, "ISS": xxx, "SEX": xxx, "HGT": xxx, "WGT": xxx, "EYES": xxx, "HAIR": xxx, "DONOR": xxx}
GPT-4V{"class": "C", "DLN": "1234568", "DOB": "08/31/1977", "Name": "Ima Cardholder", "Address": "2570 24th Street, Anytown, CA 95818", "EXP": "08/31/2014", "ISS": "08/31/2011", "SEX": "F", "HGT": "5-05", "WGT": "125 lbs", "EYES": "BRN", "HAIR": "BRN", "DONOR": "VETERAN"}
LLaVA{"class": "Driver License", "DLN": "CA123 456 789", "DOB": "01/01/1990", "Name": "Amy", "Address": "Anytown, CA", "EXP": "08/31/2023", "ISS": "Veteran", "SEX": "F", "HGT": "5', "WGT": "130", "EYES": "Brown", "HAIR": "Brown", "DONOR": "Unknown"}
LLaVA-1.5{"class": "C", "DLN": "1132456789", "DOB": "08/23/1971", "Name": "Ima Cardholder", "Address": "Anytown, State, Zip", "EXP": "08/23/2014", "ISS": "California", "SEX": "F", "HGT": "5', "WGT": "123", "EYES": "Brown", "HAIR": "Brown", "DONOR": "N/A"}
+ +outperforms 80B IDEFICS [21], a Flamingo-like LMM with billions of trainable parameters for cross-modal connection. This also makes us rethink the benefits of the vision samplers and the necessity of the additional large-scale pretraining, in terms of multimodal instruction-following capabilities. + +Global context. For higher resolution, we pad and resize the image to a single image of $224^2$ , and concatenate it with the high resolution features to provide a global context. Ablation on a 7B model shows that the global context effectively boosts performance on all three validation benchmarks. + +Table 6. LLaVA-1.5 can extract information from the image and answer following the required format, despite a few errors compared with GPT-4V. GPT-4V results are obtained from [51]. + +
GQAMMEMM-Vet
high-res patch only62.91425.831.9
+global context63.8 (+0.9)1497.5 (+71)35.1 (+3.2)
+ +# 4.3. Emerging Properties + +Format instruction generalization. Although LLaVA-1.5 is only trained with a limited number of format instructions, it generalizes to others. First, VizWiz [19] requires the model + +![](images/3eb515929a578daf9ddeee23a2e254641b2d403b757ac7a8727167b3ab6aa06d.jpg) +Figure 3. Ablation on LLM choices. Data points represent the relative performance of the best performing variant for each dataset. + +to output "Unanswerable" when the provided content is insufficient to answer the question, and our response format prompt (see Appendix) effectively instructs the model to do so ( $11.1\% \rightarrow 67.8\%$ on unanswerable questions). We additionally present qualitative examples on instructing LLaVA-1.5 to verify tricky questions (Fig. 5), respond in a constrained JSON format (Fig. 6), and more in appendix. + +Multilingual multimodal capability. Though LLaVA-1.5 is not finetuned for multilingual multimodal instruction following at all (all visual instructions including VQA are in English), we find that it is capable of following multilingual instructions. This is partly due to the multilingual language instructions in ShareGPT [45]. Although ShareGPT does not contain images in its instructions, the model learns from this dataset the behavior of adaptively responding with the language that corresponds to the user's request. We empirically show that this behavior is transferred to visual conversations. We also quantitatively evaluate the model's generalization capability to Chinese on MMBench-CN [36], where the questions of MMBench are converted to Chinese. Notably, LLaVA-1.5 outperforms Qwen-VL-Chat by $+7.3\%$ (63.6% vs 56.7%), despite Qwen being finetuned on Chinese multimodal instructions while LLaVA-1.5 is not. + +# 4.4. Ablation on LLM Choices + +In NLP, findings [48] suggest that the capability of the base LLM can affect its instruction-tuned successors. In this section, we explore two families of LLMs and study their contribution to the final model's multimodal capability: LLaMA-based (Vicuna-v1.1, Vicuna-v1.3) and LLaMA2-based (Vicuna-v1.5, LLaMA-2-Chat). Vicuna-v1.3 and Vicuna-v1.5 use the same $\sim 150\mathrm{K}$ ShareGPT [45] data ( $2\times$ + +![](images/8e10f73ab5ee3c892687b2d911e92a705c28a2f1f9f40893e157a26b65f63aad.jpg) +Figure 4. Ablation on data efficiency. Data points represent the relative performance of the best performing variant for each dataset. + +that used in v1.1). Unlike Vicuna series that is only trained with supervised instruction finetuning (SFT), LLaMA-2-Chat is further optimized with reinforcement-learning from human-feedback (RLHF). We visualize the relative performance of these variants in Fig. 3. + +First, we find that Vicuna-v1.5 achieves the best overall performance, and LLaMA-2-based models generally perform better than LLaMA-1-based, suggesting the importance of the base language model. This is further evidenced by the results on MMBench-CN [36]: despite Vicuna-v1.3 and v1.5 using the same ShareGPT data for instruction tuning, the performance in generalization to Chinese of Vicuna-v1.3 is significantly worse than v1.5. + +Second, language instruction-tuning matters on specific capabilities that are required by each dataset. For example, although LLaMA-2-Chat and Vicuna-v1.5 achieves almost the same performance on MMBench, the generalization to MMBench-CN [36] of LLaMA-2-Chat is worse than Vicuna-v1.5, which is partly due to that the most SFT/RLHF data of LLaMA-2-Chat is in English and does not contain as many multilingual data as in ShareGPT. Furthermore, TextVQA requires both the model's capability of identifying the text characters in the images, and also processing the noisy outputs from the OCR engine; such noise may be more commonly observed in the ShareGPT data, which is collected in-the-wild from daily usage of ChatGPT. + +# 5. Open Problems in LMMs + +Given the successful scaling of LLaVA-1.5, we conduct additional studies on open problems in LMMs using the model design and data mixture of LLaVA-1.5. + +# 5.1. Data Efficiency + +Despite the data efficiency of LLaVA-1.5 when compared with approaches like InstructBLIP [13], the training of LLaVA-1.5 still doubles when compared with LLaVA. In this section, we conduct experiments for further improving the data efficiency by randomly sub-sampling the training data mixture of LLaVA-1.5, with a sampling ratio ranging from 0.1 to 0.5. We visualize the relative performance of different sampling variants in Fig. 4. + +First, the full data mixture provides the best knowledge coverage, and allows the model to achieve the best overall performance. To our surprise, with only $50\%$ of the samples, the model still maintains more than $98\%$ of the full dataset performance. This suggests that there is room for further improvements in data efficiency. + +Second, when downsampling the dataset to $50\%$ , the model's performance on MMBench, ScienceQA, and POPE does not decrease at all, and it even slightly improves on MMBench. Similarly, the model's performance remains steady when further downscaling the data from $50\%$ to $30\%$ . These results show promise of having the less-is-more [59] benefit for multimodal models as well. + +# 5.2. Rethinking Hallucination in LMMs + +Hallucination is an important issue to tackle for LLMs and LMMs. Often in LMMs, we attribute the model's hallucination to the errors or hallucinations in the training dataset. For example, the detailed descriptions in LLaVA-Instruct [35] may contain a small amount of hallucinated content, and it is believed that training on such data may have caused the model to hallucinate when asked to "describe the image in detail". However, we find that such hallucination is significantly reduced, when we scale the model's inputs to higher resolutions like $448^{2}$ . + +This finding is interesting as it suggests that the LMMs may be robust to a few such errors in the training data. However, when the input resolution is not sufficient for the model to discern all details in the training data, and the amount of data that is at that granularity beyond the model's capability becomes large enough, the model learns to hallucinate. This further suggests that there needs to be a balance between improving the data annotation with more details and the model's capability to properly process the information at such granularities. We hope this finding provides a reference for future work in terms of dealing with hallucination and the scaling of the models and data. + +# 5.3. Compositional Capabilities + +We demonstrate interesting compositional capabilities in LLaVA-1.5: the model trained on a set of tasks independently generalizes to tasks that require a combination of these capabilities without explicit joint training. We note some of the findings below. + +First, we observe an improved language capability in visual conversations after including the ShareGPT [45] data, including the multimodal multilingual capability as discussed in Sec. 4.3. Moreover, the model is more capable at providing longer and more detailed responses in visual conversations. Second, the additional visual knowledge from the academic-task-oriented datasets, improves the visual groundness of LLaVA-1.5's responses in visual conversations, as evidenced quantitatively by the improved results on MMVet [54] and LLaVA-Wild [35] in Table 4. + +However, there is still difficulty in achieving ideal performance for some tasks that require a certain combination of capabilities. For example, being able to correctly answer the attribute of a certain object in VQA, does not guarantee an accurate depiction of that object attribute in a detailed description of the whole image. Furthermore, the capability of engaging in conversations with certain foreign languages (e.g. Korean) still falls behind. See appendix for examples. + +These findings suggest that the compositional capabilities of LMMs can be leveraged to improve the model's performance without significantly increasing the data by exhaustively including all task combinations. Yet, it can be further investigated, and a deeper understanding of the mechanism behind the compositional capabilities of LMMs can further improve the capability and the data efficiency of LLaVA-1.5. + +# 6. Conclusion + +In this paper, we take a step towards demystifying the design of large multimodal models, and propose a simple, effective, and data-efficient baseline, LLaVA-1.5, for large multimodal models. In addition, we explore the open problems in visual instruction tuning, scale LMMs to higher resolutions, and present some intriguing findings in terms of model hallucination and compositional capabilities for LMMs. We hope these improved and easily-reproducible baselines as well as the new findings will provide a reference for future research in open-source LMM. + +Limitations. Despite the promising results demonstrated by LLaVA-1.5, it still has limitations including prolonged training for high-resolution images, lack of multiple-image understanding, limited problem solving capabilities in certain fields. It is not exempt from producing hallucinations, and should be used with caution in critical applications (e.g. medical). See appendix for a detailed discussion. + +Acknowledgements. This work was supported in part by NSF CAREER IIS2150012, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training). + +# References + +[1] Adept AI. 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Vision: Large language model is also an open-ended decoder for vision-centric tasks. arXiv preprint arXiv:2305.11175, 2023. 1 +[50] Jason Wei, Maarten Bosma, Vincent Y Zhao, Kelvin Guu, Adams Wei Yu, Brian Lester, Nan Du, Andrew M Dai, and Quoc V Le. Finetuned language models are zero-shot learners. arXiv preprint arXiv:2109.01652, 2021. 2 +[51] Zhengyuan Yang, Linjie Li, Kevin Lin, Jianfeng Wang, Chung-Ching Lin, Zicheng Liu, and Lijuan Wang. The dawn of Imms: Preliminary explorations with gpt-4v (isdiction). arXiv preprint arXiv:2309.17421, 2023. 6 +[52] Jiabo Ye, Anwen Hu, Haiyang Xu, Qinghao Ye, Ming Yan, Guohai Xu, Chenliang Li, Junfeng Tian, Qi Qian, Ji Zhang, Qin Jin, Liang He, Xin Alex Lin, and Fei Huang. 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Llavar: Enhanced visual instruction tuning for text-rich image understanding. arXiv preprint arXiv:2306.17107, 2023. 2 +[57] Bo Zhao, Boya Wu, and Tiejun Huang. Svit: Scaling up visual instruction tuning. arXiv preprint arXiv:2307.04087, 2023. 1, 2 +[58] Yunqing Zhao, Tianyu Pang, Chao Du, Xiao Yang, Chongxuan Li, Ngai-Man Cheung, and Min Lin. On evaluating adversarial robustness of large vision-language models. arXiv preprint arXiv:2305.16934, 2023. 1 +[59] Chunting Zhou, Pengfei Liu, Puxin Xu, Srini Iyer, Jiao Sun, Yuning Mao, Xuezhe Ma, Avia Efrat, Ping Yu, Lili Yu, et al. Lima: Less is more for alignment. arXiv preprint arXiv:2305.11206, 2023. 2, 8 +[60] Deyao Zhu, Jun Chen, Xiaoqian Shen, Xiang Li, and Mohamed Elhoseiny. Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2 \ No newline at end of file diff --git a/2024/Improved Baselines with Visual Instruction Tuning/images.zip b/2024/Improved Baselines with Visual Instruction Tuning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..b6dea0fae275ee982e702430c6a4fb01aa4479b0 --- /dev/null +++ b/2024/Improved Baselines with Visual Instruction Tuning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:34dd9c9bc11ca2d200a7e501ec90ff183e6a660af5bd7cd50020408b84c54db2 +size 633939 diff --git a/2024/Improved Baselines with Visual Instruction Tuning/layout.json b/2024/Improved Baselines with Visual Instruction Tuning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7b4cdf3a8a9f8d74a1ef922c2f0b1436c0ac8469 --- /dev/null +++ b/2024/Improved Baselines with Visual Instruction Tuning/layout.json @@ -0,0 +1,6877 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 139, + 103, + 454, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 103, + 454, + 121 + ], + "spans": [ + { + "bbox": [ + 139, + 103, + 454, + 121 + ], + "type": "text", + "content": "Improved Baselines with Visual Instruction Tuning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 127, + 142, + 468, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 142, + 468, + 185 + ], + "spans": [ + { + "bbox": [ + 127, + 142, + 468, + 185 + ], + "type": "text", + "content": "Haotian Liu1 Chunyuan Li2 Yuheng Li1 Yong Jae Lee1 \n1University of Wisconsin-Madison 2Microsoft Research, Redmond https://llava-vl.github.io" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 238, + 290, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 238, + 290, + 455 + ], + "spans": [ + { + "bbox": [ + 45, + 238, + 290, + 455 + ], + "type": "text", + "content": "Large multimodal models (LMM) have recently shown encouraging progress with visual instruction tuning. In this paper, we present the first systematic study to investigate the design choices of LMMs in a controlled setting under the LLaVA framework. We show that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient. With simple modifications to LLaVA, namely, using CLIP-ViT-L-336px with an MLP projection and adding academic-task-oriented VQA data with response formatting prompts, we establish stronger baselines that achieve state-of-the-art across 11 benchmarks. Our final 13B checkpoint uses merely 1.2M publicly available data, and finishes full training in " + }, + { + "bbox": [ + 45, + 238, + 290, + 455 + ], + "type": "inline_equation", + "content": "\\sim 1" + }, + { + "bbox": [ + 45, + 238, + 290, + 455 + ], + "type": "text", + "content": " day on a single 8-A100 node. Furthermore, we present some early exploration of open problems in LMMs, including scaling to higher resolution inputs, compositional capabilities, and model hallucination, etc. We hope this makes state-of-the-art LMM research more accessible. Code and model will be publicly available." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 478, + 128, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 128, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 128, + 490 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 289, + 715 + ], + "type": "text", + "content": "Large multimodal models (LMMs) have become increasingly popular in the research community, as they are the key building blocks towards general-purpose assistants [2, 29, 42]. Recent studies on LMMs are converging on a central concept known as visual instruction tuning [35]. The results are promising, e.g. LLaVA [35] and MiniGPT-4 [60] demonstrate impressive results on natural instruction-following and visual reasoning capabilities. To better understand the capability of LMMs, multiple benchmarks [16, 26, 33, 36, 54] have been proposed. Recent works further demonstrate improved performance by scaling up the pretraining data [3, 13, 53], instruction-following data [13, 17, 28, 57], visual encoders [3], or language models [38], respectively. The LLaVA architecture is also leveraged in different downstream tasks and domains, including region-level [8, 55] and pixel-level [25, 49] understanding, biomedical assistants [30], image generation [5], adversarial studies [6, 58]." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 210, + 545, + 492 + ], + "blocks": [ + { + "bbox": [ + 310, + 210, + 545, + 492 + ], + "lines": [ + { + "bbox": [ + 310, + 210, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 310, + 210, + 545, + 492 + ], + "type": "image", + "image_path": "1dd41f9ee2e33172fee4a9962ad99eb5a2df0182e34e291c997b56f9580b389d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 501, + 547, + 545 + ], + "lines": [ + { + "bbox": [ + 305, + 501, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 305, + 501, + 547, + 545 + ], + "type": "text", + "content": "Figure 1. LLaVA-1.5 achieves SoTA on a broad range of 11 tasks (Top), with high training sample efficiency (Left) and simple modifications to LLaVA (Right): an MLP connector and including academic-task-oriented data with response formatting prompts." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "However, despite many benchmarks and developments, it still remains unclear what the best recipe is to train LMMs towards the goal of general-purpose assistants. For example, LLaVA [35] excels in conversational-style visual reasoning and even outperforms later approaches like InstructBLIP [13] on such benchmarks [54], while InstructBLIP excels in traditional VQA benchmarks that demands single-word or short answers. Given the significant differences in the model architecture and training data between them, the root cause of the disparity in their capabilities remains elusive, despite conjectures [36, 54]: the amount of training data, the usage of resamplers like Qformer [31], etc. To this" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "26296" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 131 + ], + "type": "text", + "content": "end, we present the first systematic study to investigate the design choices of LMMs in a controlled setting. Our study originates from LLaVA and builds a road map by carefully making effective contributions from the perspectives of the input, model, and data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 134, + 286, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 134, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 49, + 134, + 286, + 361 + ], + "type": "text", + "content": "First, we unveil that the fully-connected vision-language connector in LLaVA is surprisingly powerful and data-efficient, and we establish stronger and more feasible baselines built upon the LLaVA framework. We report that two simple improvements, namely, an MLP cross-modal connector and incorporating academic task related data such as VQA, are orthogonal to the framework of LLaVA, and when used with LLaVA, lead to better multimodal understanding capabilities. In contrast to InstructBLIP [13] or Qwen-VL [3], which trains specially designed visual resamplers on hundreds of millions or even billions of image-text paired data, LLaVA uses one of the simplest architecture design for LMMs and requires only training a simple fully-connected projection layer on merely 600K image-text pairs. Our final model can finish training in " + }, + { + "bbox": [ + 49, + 134, + 286, + 361 + ], + "type": "inline_equation", + "content": "\\sim 1" + }, + { + "bbox": [ + 49, + 134, + 286, + 361 + ], + "type": "text", + "content": " day on a single 8-A100 machine and achieves state-of-the-art results on a wide range of benchmarks. Moreover, unlike Qwen-VL [3] that includes in-house data in training, LLaVA utilizes only publicly available data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 364, + 286, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 364, + 286, + 626 + ], + "spans": [ + { + "bbox": [ + 49, + 364, + 286, + 626 + ], + "type": "text", + "content": "Next, we delve into an early exploration of other open problems of large multimodal models. Our findings include: (1) Scaling to high-resolution image inputs. We show that LLaVA's architecture is versatile in scaling to higher resolutions by simply dividing images into grids and maintains its data efficiency; with the increased resolution, it improves the model's detailed perception capabilities and reduces hallucination. (2) Compositional capabilities. We find that large multimodal models are capable of generalizing to compositional capabilities. For example, training on long-form language reasoning together with shorter visual reasoning can improve the model's writing capability for multimodal questions. (3) Data efficiency. We show that randomly downsampling LLaVA's training data mixture by up to " + }, + { + "bbox": [ + 49, + 364, + 286, + 626 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 49, + 364, + 286, + 626 + ], + "type": "text", + "content": " does not significantly decrease the model's performance, suggesting that the possibility of a more sophisticated dataset compression strategy can further improve LLaVA's already efficient training pipeline. (4) Data scaling. We provide empirical evidence for the scaling of data granularity in conjunction with the model's capability is crucial for an improved capability without introducing artifacts like hallucination." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "content": "In sum, we perform a systematic study on the training of large multimodal models, and introduce a simple yet effective approach to balance the multitask learning and effective scaling for large multimodal models. Our improved baselines, LLaVA-1.5, uses only public data, achieves the state-of-the-art on a broad range of 11 tasks, and is significantly more data-efficient than previous approaches. By" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 545, + 131 + ], + "type": "text", + "content": "rethinking the conventional approaches and exploring the open problems in visual instruction tuning, we pave the way for more robust and capable systems for LMMs. We hope these improved and easily-reproducible baselines will provide a reference for future research in open-source LMMs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 146, + 391, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 146, + 391, + 158 + ], + "spans": [ + { + "bbox": [ + 308, + 146, + 391, + 158 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "type": "text", + "content": "Instruction-following large multimodal models (LMMs). Common architectures include a pre-trained visual backbone to encode visual features, a pre-trained large language model (LLM) to comprehend the user instructions and produce responses, and a vision-language cross-modal connector to align the vision encoder outputs to the language models. As shown in Fig. 1, LLaVA [35] is perhaps the simplest architecture for LMMs. Optionally, visual resamplers (e.g. Qformer [31]) are used to reduce the number of visual patches [3, 13, 60]. Training an instruction-following LMM usually follows a two-stage protocol. First, the vision-language alignment pretraining stage leverages image-text pairs to align the visual features with the language model's word embedding space. Earlier works utilize relatively few image-text pairs (e.g. " + }, + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\sim 600\\mathrm{K}" + }, + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "type": "text", + "content": " [35] or " + }, + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\sim 6\\mathrm{M}" + }, + { + "bbox": [ + 308, + 171, + 545, + 445 + ], + "type": "text", + "content": " [60]), while some recent works pretrain the vision-language connector for a specific language model on a large amount of image-text pairs (e.g. 129M [13] and 1.4B [3]), to maximize the LMM's performance. Second, the visual instruction tuning stage tunes the model on visual instructions [35], to enable the model to follow users' diverse requests on instructions that involve the visual contents. Dealing with higher resolution with grids in LMM are studied in con-current works [1, 27, 52]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 451, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 451, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 451, + 545, + 712 + ], + "type": "text", + "content": "Multimodal instruction-following data. In NLP, studies show that the quality of instruction-following data largely affects the capability of the resulting instruction-following models [59]. For visual instruction tuning, LLaVA [35] is the pioneer to leverage text-only GPT-4 to expand the existing COCO [34] bounding box and caption dataset to a multimodal instruction-following dataset that contains three types of instruction-following data: conversational-style QA, detailed description, and complex reasoning. LLaVA's pipeline has been employed to expand to textual understanding [56], million-scales [57], and region-level conversations [8]. InstructBLIP [13] incorporates academic-task-oriented VQA datasets to further enhance the model's visual capabilities. Conversely, [7] identifies that such naive data merging can result in models that tend to overfit to VQA datasets and thus are unable to participate in natural conversations. The authors further propose to leverage the LLaVA pipeline to convert VQA datasets to a conversational style. While this proves effective for training, it introduces added complexities in data scaling. However, in NLP, the FLAN family [12, 50] shows that adding a large number of academic language tasks for instruction tuning can effectively improve the gen" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26297" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 288, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 288, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 288, + 107 + ], + "type": "text", + "content": "eralization ability. In light of this, we consider investigating the root cause of the inability to balance between natural conversations and academic tasks in multimodal models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 120, + 113, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 120, + 113, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 120, + 113, + 133 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 133, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 133, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 133, + 152 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 158, + 288, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 288, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 288, + 289 + ], + "type": "text", + "content": "As the seminal work of visual instruction tuning, LLaVA [35] showcases commendable proficiency in visual reasoning capabilities, surpassing even more recent models on diverse benchmarks [4, 54] for real-life visual instruction-following tasks. LLaVA uses a single linear layer to project the visual features to language space, and optimizes the whole LLM for visual instruction tuning. However, LLaVA falls short on academic benchmarks that typically require short-form answers (e.g. single-word), and tends to answer yes for yes/no questions due to the lack of such data in the training distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 291, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 422 + ], + "type": "text", + "content": "On the other hand, InstructBLIP [13] is the pioneer to incorporate academic-task-oriented datasets like VQA-v2 [18] along with LLaVA-Instruct [35], and demonstrates improved performance on VQA benchmarks. It pretrains Qformer [31] on 129M image-text pairs and only finetunes the instruction-aware Qformer for visual instruction tuning. However, recent studies [7, 54] show that it does not perform as well as LLaVA on engaging in real-life visual conversation tasks. More specifically, as shown in Table 1a, it can overfit to VQA training sets with short-answers, even on requests that require detailed responses." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 431, + 205, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 205, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 205, + 444 + ], + "type": "text", + "content": "3.2. Response Format Prompting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 450, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 450, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 45, + 450, + 287, + 640 + ], + "type": "text", + "content": "We find that the inability [7] to balance between short- and long-form VQA for approaches like InstructBLIP [13], which leverages instruction following data that includes both natural responses and short-answers, is mainly due to the following reasons. First, ambiguous prompts on the response format. For example, " + }, + { + "bbox": [ + 45, + 450, + 287, + 640 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 45, + 450, + 287, + 640 + ], + "type": "text", + "content": ": {Question} A: {Answer}. Such prompts do not clearly indicate the desired output format, and can overfit an LLM behaviorally to short-form answers even for natural visual conversations. Second, not finetuning the LLM. The first issue is worsened by InstructBLIP only finetuning the Qformer for instruction-tuning. It requires the Qformer's visual output tokens to control the length of the LLM's output to be either long-form or short-form, as in prefix tuning [32], but Qformer may lack the capability of properly doing so, due to its limited capacity compared with LLMs like LLaMA." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "Thus, to enable LLaVA to better handle short-form answers while addressing the issues of InstructBLIP, we propose to use a single response formatting prompt that clearly indicates the output format. It is appended at the end of VQA questions when promoting short answers: Answer the question using a single word or phrase. We find that when the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 74, + 514, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 74, + 514, + 84 + ], + "spans": [ + { + "bbox": [ + 315, + 74, + 514, + 84 + ], + "type": "text", + "content": "Visual input example, Multitask Balancing Problem:" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 381, + 88, + 494, + 165 + ], + "blocks": [ + { + "bbox": [ + 381, + 88, + 494, + 165 + ], + "lines": [ + { + "bbox": [ + 381, + 88, + 494, + 165 + ], + "spans": [ + { + "bbox": [ + 381, + 88, + 494, + 165 + ], + "type": "image", + "image_path": "a8a03c251ed3dc03720febd659389a06aad4958f288a8710d612a72b307d24d8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 167, + 363, + 188 + ], + "lines": [ + { + "bbox": [ + 315, + 167, + 363, + 188 + ], + "spans": [ + { + "bbox": [ + 315, + 167, + 363, + 188 + ], + "type": "text", + "content": "User InstructBLIP" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 381, + 167, + 522, + 188 + ], + "lines": [ + { + "bbox": [ + 381, + 167, + 522, + 188 + ], + "spans": [ + { + "bbox": [ + 381, + 167, + 522, + 188 + ], + "type": "text", + "content": "Is this unusual? Please explain in detail. yes" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 192, + 545, + 212 + ], + "lines": [ + { + "bbox": [ + 306, + 192, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 306, + 192, + 545, + 212 + ], + "type": "text", + "content": "(a) Example of InstructBLIP [13] (Vicuna-13B) having difficulty balancing between short- and long-form answers." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 310, + 237, + 544, + 356 + ], + "blocks": [ + { + "bbox": [ + 315, + 224, + 501, + 236 + ], + "lines": [ + { + "bbox": [ + 315, + 224, + 501, + 236 + ], + "spans": [ + { + "bbox": [ + 315, + 224, + 501, + 236 + ], + "type": "text", + "content": "Visual input example, Different Format Prompts:" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 237, + 544, + 356 + ], + "lines": [ + { + "bbox": [ + 310, + 237, + 544, + 356 + ], + "spans": [ + { + "bbox": [ + 310, + 237, + 544, + 356 + ], + "type": "table", + "html": "
Normal promptWhat is the color of the shirt that the man is wearing?
ResponseThe man is wearing a yellow shirt.
Ambiguous promptQ: What is the color of the shirt that the man is wearing? A:
ResponseThe man is wearing a yellow shirt.
Formatting promptWhat is the color of the shirt that the man is wearing? Answer the question using a single word or phrase.
ResponseYellow.
", + "image_path": "c2f9ac2bd6648d5de82e04bdf61a2f16904f951e8304b3b0f54d4c0c40f4e2a3.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 306, + 358, + 545, + 397 + ], + "lines": [ + { + "bbox": [ + 306, + 358, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 545, + 397 + ], + "type": "text", + "content": "(b) Comparison of how different prompts regularize the output format. The results are obtained zero-shot directly after LLaVA undergoes the first-stage vision-language alignment pretraining, without the second-stage visual instruction tuning." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 306, + 407, + 545, + 440 + ], + "lines": [ + { + "bbox": [ + 306, + 407, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 545, + 440 + ], + "type": "text", + "content": "Table 1. Visual input example to illustrate the challenge of (a) multitask balancing and (b) different format prompts. The same image input is used." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 462, + 547, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 558 + ], + "type": "text", + "content": "LLM is finetuned with such prompts, LLaVA is able to properly adjust the output format according to the user's instructions (see Table 1b), and does not require additional processing of the VQA answers using ChatGPT [7], which further enables scaling to various data sources. As shown in Table 2, by merely including VQAv2 [18] in training, LLaVA's performance on MME significantly improves (1323.8 vs 809.6) and outperforms InstructBLIP by 111 points." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 567, + 459, + 579 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 459, + 579 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 459, + 579 + ], + "type": "text", + "content": "3.3. Scaling the Data and Model" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 590, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 547, + 662 + ], + "type": "text", + "content": "MLP vision-language connector. Inspired by the improved performance in self-supervised learning by changing from a linear projection to an MLP [9, 10], we find that improving the vision-language connector's representation power with a two-layer MLP can improve LLaVA's multimodal capabilities, compared with the original linear projection." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Academic task oriented data. We further include additional academic-task-oriented VQA datasets for VQA, OCR, and region-level perception, to enhance the model's capabilities in various ways, as shown in Table 2. We first include" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26298" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 70, + 500, + 178 + ], + "blocks": [ + { + "bbox": [ + 97, + 70, + 500, + 178 + ], + "lines": [ + { + "bbox": [ + 97, + 70, + 500, + 178 + ], + "spans": [ + { + "bbox": [ + 97, + 70, + 500, + 178 + ], + "type": "image", + "image_path": "34e28144874d491e764e69b7deb546aaee9460370ce7fe3e6b51ab8a593c8b50.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 222 + ], + "type": "text", + "content": "Figure 2. LLaVA-1.5-HD. Scaling LLaVA-1.5 to higher resolutions by splitting the image into grids and encoding them independently. This allows the model to scale to any resolution, without performing positional embedding interpolation for ViTs. We additionally concatenate the feature of a downsampled image to provide the LLM with a global context." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 239, + 286, + 395 + ], + "blocks": [ + { + "bbox": [ + 50, + 239, + 286, + 395 + ], + "lines": [ + { + "bbox": [ + 50, + 239, + 286, + 395 + ], + "spans": [ + { + "bbox": [ + 50, + 239, + 286, + 395 + ], + "type": "table", + "html": "
MethodLLMRes.GQAMMEMM-Vet
InstructBLIP14B22449.51212.825.6
Only using a subset of InstructBLIP training data
0LLaVA7B224-809.625.5
1+VQA-v27B22447.01197.027.7
2+Format prompt7B22446.81323.826.3
3+MLP VL connector7B22447.31355.227.8
4+OKVQA/OCR7B22450.01377.629.6
Additional scaling
5+Region-level VQA7B22450.31426.530.8
6+Scale up resolution7B33651.4145030.3
7+GQA7B33662.0*1469.230.7
8+ShareGPT7B33662.0*1510.731.1
9+Scale up LLM13B33663.3*1531.336.1
", + "image_path": "3f7c8ac3dd80c519516f0dcd60ba9aa71826e1cf02955277f8f061d74a847364.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 403, + 288, + 471 + ], + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 471 + ], + "type": "text", + "content": "Table 2. Scaling results on data, model, and resolution. We choose to conduct experiments on GQA [20], MME [16], and MM-Vet [54] to examine the representative capabilities of VQA with short answers, VQA with output formatting, and natural visual conversations, respectively. *Training images of GQA were observed during training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 493, + 288, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 288, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 288, + 625 + ], + "type": "text", + "content": "four additional datasets that are used in InstructBLIP: open-knowledge VQA (OKVQA [40], A-OKVQA [44]) and OCR (OCRVQA [41], TextCaps [46]). A-OKVQA is converted to multiple choice questions and a specific response formatting prompt is used: Answer with the option's letter from the given choices directly. With only a subset of the datasets InstructBLIP uses, LLaVA already surpasses it on all three tasks in Table 2, suggesting LLaVA's effective design. Furthermore, we find further adding region-level VQA datasets (Visual Genome [24], RefCOCO [23, 39]) improves the model's capability of localizing fine-grained visual details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Additional scaling. We further scale up the input image resolution to " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "336^2" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": " to allow the LLM to clearly \"see\" the details of images, by swapping the vision encoder to CLIPViT-L-336px (the highest resolution available for CLIP). In addition, we add the GQA dataset as an additional visual knowledge source. We also incorporate ShareGPT [45] data and scale up the LLM to 13B as in [3, 8, 38]. Results on MM" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 240, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 547, + 277 + ], + "type": "text", + "content": "Vet shows the most significant improvement when scaling the LLM to 13B, suggesting the importance of the base LLM's capability for visual conversations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 281, + 547, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 330 + ], + "type": "text", + "content": "LLaVA-1.5. We denote this final model with all the modifications as LLaVA-1.5 (the last two rows in Table 2), which achieves an impressive performance that significantly outperforms the original LLaVA [35]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "content": "Computational cost. For LLaVA-1.5, we use the same pretraining dataset, and keep the training iterations and batch size roughly the same for instruction tuning as LLaVA [35]. Due to the increased image input resolution to " + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "inline_equation", + "content": "336^2" + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "content": ", the training of LLaVA-1.5 is " + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\sim 2\\times" + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "content": " as long as LLaVA: " + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\sim 6" + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "content": " hours of pretraining and " + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\sim 20" + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "content": " hours of visual instruction tuning, using " + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 304, + 333, + 547, + 418 + ], + "type": "text", + "content": " A100s." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 428, + 468, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 428, + 468, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 428, + 468, + 441 + ], + "type": "text", + "content": "3.4. Scaling to Higher Resolutions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 448, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 555 + ], + "type": "text", + "content": "In Sec. 3.3, we observe the advantage that scaling up the input image resolution improves the model's capabilities. However, the image resolution of the existing open source CLIP vision encoders is limited to " + }, + { + "bbox": [ + 304, + 448, + 547, + 555 + ], + "type": "inline_equation", + "content": "336^{2}" + }, + { + "bbox": [ + 304, + 448, + 547, + 555 + ], + "type": "text", + "content": ", preventing the support of higher resolution images by simply replacing the vision encoder as we did in Sec. 3.3. In this section, we present an early exploration of scaling the LMM to higher resolutions, while maintaining the data efficiency of LLaVA-1.5." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 556, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 547, + 653 + ], + "type": "text", + "content": "When using ViT [14] as the vision encoder, to scale up the resolution, previous approaches mostly choose to perform positional embedding interpolation [3, 31] and adapt the ViT backbone to the new resolution during finetuning. However, this usually requires the model to be finetuned on a large-scale image-text paired dataset [3, 31], and limits the resolution of the image to a fixed size that the LMM can accept during inference." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Instead, as shown in Fig. 2, we overcome this by dividing the image into smaller image patches of the resolution that the vision encoder is originally trained for, and encode them independently. After obtaining the feature maps of individual patches, we then combine them into a single large feature" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26299" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 70, + 497, + 222 + ], + "blocks": [ + { + "bbox": [ + 94, + 70, + 497, + 222 + ], + "lines": [ + { + "bbox": [ + 94, + 70, + 497, + 222 + ], + "spans": [ + { + "bbox": [ + 94, + 70, + 497, + 222 + ], + "type": "table", + "html": "
MethodLLMImage SizeSample SizeVQAv2 [18]GQA [20]VisWiz [19]SciQA-IMG [37]TextVQA [47]
BLIP-2 [31]Vicuna-13B2242129M-65.04119.66142.5
InstructBLIP [13]Vicuna-7B2242129M1.2M-49.234.560.550.1
InstructBLIP [13]Vicuna-13B2242129M1.2M-49.533.463.150.7
Shikra [8]Vicuna-13B2242600K5.5M77.4*----
IDEFICS-9B [21]LLaMA-7B2242353M1M50.938.435.5-25.9
IDEFICS-80B [21]LLaMA-65B2242353M1M60.045.236.0-30.9
Qwen-VL [3]Qwen-7B44821.4B†50M†78.8*59.3*35.267.163.8*
Qwen-VL-Chat [3]Qwen-7B44821.4B*50M†78.2*57.5*38.968.261.5*
LLaVA-1.5Vicuna-7B3362558K665K78.5*62.0*50.066.858.2
LLaVA-1.5Vicuna-13B3362558K665K80.0*63.3*53.671.661.3
LLaVA-1.5-HDVicuna-13B4482558K665K81.8*64.7*57.571.062.5
Specialist SOTA: PaLI-X-55B [11]86.1*72.1*70.9*-71.4*
", + "image_path": "e01856386f0da5f3890bb46ed80b59a052361df6acfec16253a26b680de717b5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 97, + 273, + 493, + 422 + ], + "blocks": [ + { + "bbox": [ + 46, + 228, + 546, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 262 + ], + "type": "text", + "content": "Table 3. Comparison with SoTA methods on academic-task-oriented datasets. LLaVA-1.5 achieves the best performance on 4/5 benchmarks, and ranks the second on the other. *The training images/annotations of the datasets are observed during training. †Includes in-house data that is not publicly accessible." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 97, + 273, + 493, + 422 + ], + "lines": [ + { + "bbox": [ + 97, + 273, + 493, + 422 + ], + "spans": [ + { + "bbox": [ + 97, + 273, + 493, + 422 + ], + "type": "table", + "html": "
MethodPOPE [33]MME [16]MMBench [36]SEED-Bench [26]LLaVA-Wild [35]MM-Vet [54]
randpopadvencnallimgvid
BLIP2-14B [31]89.685.580.91293.8--46.449.736.738.122.4
InstructBLIP-8B [13]----3623.753.458.838.160.926.2
InstructBLIP-14B [13]87.777721212.8-----58.225.6
Shikra-13B [8]----58.8------
IDEFICS-9B [21]----48.225.2-44.5---
IDEFICS-80B [21]----54.538.1-53.2---
Qwen-VL [3]----38.27.456.362.339.1--
Qwen-VL-Chat [3]---1487.560.656.758.265.437.8--
LLaVA-7B [35]76.372.270.1809.638.736.433.537.023.862.825.5
LLaVA-1.5-7B87.386.184.21510.764.358.358.666.137.365.431.1
LLaVA-1.5-13B87.186.284.51531.367.763.661.668.242.772.536.1
LLaVA-1.5-13B-HD87.586.485.01500.168.861.962.670.141.372.039.4
", + "image_path": "0983acd05e07e5b70a3b8e7d81c58c02dc595985e2f93c546628319df77a22f3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 427, + 546, + 450 + ], + "lines": [ + { + "bbox": [ + 46, + 427, + 546, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 546, + 450 + ], + "type": "text", + "content": "Table 4. Comparison with SoTA methods on benchmarks for instruction-following LMMs. LLaVA-1.5 achieves the best overall performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 471, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 288, + 555 + ], + "type": "text", + "content": "map of the target resolution, and feed that into the LLM. To provide the LLM with the global context and to reduce the artifact of the split-encode-merge operation, we additionally concatenate the feature of a downsampled image to the merged feature map. This allows us to scale the input to any arbitrary resolution and maintain the data efficiency of LLaVA-1.5. We call this resulting model LLaVA-1.5-HD." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 567, + 173, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 173, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 173, + 580 + ], + "type": "text", + "content": "4. Empirical Evaluation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 586, + 129, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 129, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 129, + 598 + ], + "type": "text", + "content": "4.1. Benchmarks" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "We evaluate LLaVA-1.5 on a collection of both academic-task-oriented benchmarks and recent benchmarks specifically proposed for instruction-following LMMs, totalling 12 benchmarks. For academic-task-oriented benchmarks, VQA-v2 [18] and GQA [20] evaluate model's visual perception capabilities on open-ended short answers. VizWiz [19] contains 8,000 images to evaluate model's zero-shot generalization on visual questions asked by visually impaired people. Following InstructBLIP [13], the image subset of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 471, + 547, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 547, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 547, + 508 + ], + "type": "text", + "content": "ScienceQA [37] with multiple choice are used to evaluate the zero-shot generalization on scientific question answering. TextVQA [47] contains text-rich visual question answering." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 510, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 713 + ], + "type": "text", + "content": "For recent benchmarks proposed for instruction-following LMMs, POPE [33] evaluates model's degree of hallucination on three sampled subsets of COCO [34]: random, common, and adversarial and we report the F1 score on all three splits. Other benchmarks evaluate the model's capabilities on a wide range of domains and applications, with different response formats. MME-Perception [16] evaluates model's visual perception with yes/no questions. MMBench [36] evaluates model's answer robustness with all-round shuffling on multiple choice answers. MMBench-CN [36] is the Chinese-translated version of MMBench. SEED-Bench [26] evaluates model's performance on both images and videos with multiple choice, and we sample the frame in the middle to evaluate the accuracy on videos. LLaVA-Bench-in-the-Wild [35] and MM-Vet [54] evaluate model's capabilities in engaging in visual conversations on a diverse range of tasks, and evaluates the correctness and the helpfulness of" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26300" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 85, + 281, + 290 + ], + "blocks": [ + { + "bbox": [ + 57, + 73, + 192, + 83 + ], + "lines": [ + { + "bbox": [ + 57, + 73, + 192, + 83 + ], + "spans": [ + { + "bbox": [ + 57, + 73, + 192, + 83 + ], + "type": "text", + "content": "Visual input example, Tricky Question:" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 85, + 281, + 290 + ], + "lines": [ + { + "bbox": [ + 51, + 85, + 281, + 290 + ], + "spans": [ + { + "bbox": [ + 51, + 85, + 281, + 290 + ], + "type": "table", + "html": "
UserIf there are factual errors in the questions, point it out; if not, proceed to answering the question. What's happening in the desert?
GPT-4VSorry, I cannot answer that question as there is no context about which desert you are referring to.
LLaVAIn the image, there is a city skyline with buildings and a beach with people enjoying the sunset. The scene is set in a desert, which is unusual for a beach setting.
LLaVA-1.5There are no deserts in the image. The image features a beach with palm trees, a city skyline, and a large body of water.
", + "image_path": "eedfeda40e72d3345dfc73e77f105d041bc465ef06e12584466e597d02a63da1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 298, + 285, + 321 + ], + "lines": [ + { + "bbox": [ + 47, + 298, + 285, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 285, + 321 + ], + "type": "text", + "content": "Table 5. LLaVA-1.5 can detect and answer tricky questions when prompted to verify the question." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 341, + 194, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 194, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 194, + 353 + ], + "type": "text", + "content": "the response with GPT-4 evaluation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 360, + 104, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 104, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 104, + 371 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 378, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 474 + ], + "type": "text", + "content": "We show that LLaVA-1.5 achieves the best overall performance on 12 benchmarks, despite using magnitudes smaller pretraining and instruction tuning data compared with other methods [3, 13]. LLaVA-1.5 significantly outperforms LLaVA on all benchmarks for instruction-following LMMs. Note that it is challenging to evaluate the original LLaVA on academic datasets like VQA-v2 [18] that demand open-ended short answers." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 582 + ], + "type": "text", + "content": "When we continue to scale up the image resolution to " + }, + { + "bbox": [ + 46, + 474, + 287, + 582 + ], + "type": "inline_equation", + "content": "448^{2}" + }, + { + "bbox": [ + 46, + 474, + 287, + 582 + ], + "type": "text", + "content": " with LLaVA-1.5-HD, it further improves the overall performance on all benchmarks, especially on tasks that require perception of details in the images (e.g. OCR in MM-Vet, detailed description in LLaVA-Bench-in-the-Wild [35]). Moreover, we find that adding the global context effectively recovers the model from the split-and-merge artifacts and guides the model to more easily locate the relevant regions from the high-resolution features (see appendix)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "It is encouraging that LLaVA-1.5 achieves the best performance with the simplest architecture, academic compute and public datasets, and yields a fully-reproducible and affordable baseline for future research. The results also suggest that visual instruction tuning plays an important role in improving an LMM's capabilities, and raises questions upon the common belief that LMMs require significant amount of vision-language alignment pretraining [3, 13, 31], despite that the vision encoders (e.g. CLIP [43], OpenCLIP [22], EVA-CLIP [15], etc.) are already pretrained on web-scale image-text paired data. LLaVA-1.5 (even the 7B model)" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 85, + 541, + 395 + ], + "blocks": [ + { + "bbox": [ + 314, + 73, + 485, + 83 + ], + "lines": [ + { + "bbox": [ + 314, + 73, + 485, + 83 + ], + "spans": [ + { + "bbox": [ + 314, + 73, + 485, + 83 + ], + "type": "text", + "content": "Visual input example, Constrained JSON Output:" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 85, + 541, + 395 + ], + "lines": [ + { + "bbox": [ + 310, + 85, + 541, + 395 + ], + "spans": [ + { + "bbox": [ + 310, + 85, + 541, + 395 + ], + "type": "table", + "html": "
UserPlease read the text in this image and return the information in the following JSON format (note xxx is placeholder, if the information is not available in the image, put "N/A" instead). {"class": xxx, "DLN": xxx, "DOB": xxx, "Name": xxx, "Address": xxx, "EXP": xxx, "ISS": xxx, "SEX": xxx, "HGT": xxx, "WGT": xxx, "EYES": xxx, "HAIR": xxx, "DONOR": xxx}
GPT-4V{"class": "C", "DLN": "1234568", "DOB": "08/31/1977", "Name": "Ima Cardholder", "Address": "2570 24th Street, Anytown, CA 95818", "EXP": "08/31/2014", "ISS": "08/31/2011", "SEX": "F", "HGT": "5-05", "WGT": "125 lbs", "EYES": "BRN", "HAIR": "BRN", "DONOR": "VETERAN"}
LLaVA{"class": "Driver License", "DLN": "CA123 456 789", "DOB": "01/01/1990", "Name": "Amy", "Address": "Anytown, CA", "EXP": "08/31/2023", "ISS": "Veteran", "SEX": "F", "HGT": "5', "WGT": "130", "EYES": "Brown", "HAIR": "Brown", "DONOR": "Unknown"}
LLaVA-1.5{"class": "C", "DLN": "1132456789", "DOB": "08/23/1971", "Name": "Ima Cardholder", "Address": "Anytown, State, Zip", "EXP": "08/23/2014", "ISS": "California", "SEX": "F", "HGT": "5', "WGT": "123", "EYES": "Brown", "HAIR": "Brown", "DONOR": "N/A"}
", + "image_path": "3c60f64cf16f07ae315e6f9d58e0333b3dc01d2c922a2c1c4f99e327da845edc.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 459, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 519 + ], + "type": "text", + "content": "outperforms 80B IDEFICS [21], a Flamingo-like LMM with billions of trainable parameters for cross-modal connection. This also makes us rethink the benefits of the vision samplers and the necessity of the additional large-scale pretraining, in terms of multimodal instruction-following capabilities." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 545, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 583 + ], + "type": "text", + "content": "Global context. For higher resolution, we pad and resize the image to a single image of " + }, + { + "bbox": [ + 304, + 522, + 545, + 583 + ], + "type": "inline_equation", + "content": "224^2" + }, + { + "bbox": [ + 304, + 522, + 545, + 583 + ], + "type": "text", + "content": ", and concatenate it with the high resolution features to provide a global context. Ablation on a 7B model shows that the global context effectively boosts performance on all three validation benchmarks." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 314, + 593, + 536, + 634 + ], + "blocks": [ + { + "bbox": [ + 305, + 403, + 544, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 544, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 544, + 437 + ], + "type": "text", + "content": "Table 6. LLaVA-1.5 can extract information from the image and answer following the required format, despite a few errors compared with GPT-4V. GPT-4V results are obtained from [51]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 314, + 593, + 536, + 634 + ], + "lines": [ + { + "bbox": [ + 314, + 593, + 536, + 634 + ], + "spans": [ + { + "bbox": [ + 314, + 593, + 536, + 634 + ], + "type": "table", + "html": "
GQAMMEMM-Vet
high-res patch only62.91425.831.9
+global context63.8 (+0.9)1497.5 (+71)35.1 (+3.2)
", + "image_path": "1ca8c75467e62d7b6ead9289160e19a7e3df01185e52f8e7aab90926e6fc23ef.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 655, + 425, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 655, + 425, + 668 + ], + "spans": [ + { + "bbox": [ + 306, + 655, + 425, + 668 + ], + "type": "text", + "content": "4.3. Emerging Properties" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Format instruction generalization. Although LLaVA-1.5 is only trained with a limited number of format instructions, it generalizes to others. First, VizWiz [19] requires the model" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26301" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 68, + 289, + 276 + ], + "blocks": [ + { + "bbox": [ + 49, + 68, + 289, + 276 + ], + "lines": [ + { + "bbox": [ + 49, + 68, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 49, + 68, + 289, + 276 + ], + "type": "image", + "image_path": "3eb515929a578daf9ddeee23a2e254641b2d403b757ac7a8727167b3ab6aa06d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 283, + 288, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 283, + 288, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 288, + 308 + ], + "type": "text", + "content": "Figure 3. Ablation on LLM choices. Data points represent the relative performance of the best performing variant for each dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 325, + 288, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 288, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 288, + 410 + ], + "type": "text", + "content": "to output \"Unanswerable\" when the provided content is insufficient to answer the question, and our response format prompt (see Appendix) effectively instructs the model to do so (" + }, + { + "bbox": [ + 46, + 325, + 288, + 410 + ], + "type": "inline_equation", + "content": "11.1\\% \\rightarrow 67.8\\%" + }, + { + "bbox": [ + 46, + 325, + 288, + 410 + ], + "type": "text", + "content": " on unanswerable questions). We additionally present qualitative examples on instructing LLaVA-1.5 to verify tricky questions (Fig. 5), respond in a constrained JSON format (Fig. 6), and more in appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 412, + 289, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 289, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 289, + 605 + ], + "type": "text", + "content": "Multilingual multimodal capability. Though LLaVA-1.5 is not finetuned for multilingual multimodal instruction following at all (all visual instructions including VQA are in English), we find that it is capable of following multilingual instructions. This is partly due to the multilingual language instructions in ShareGPT [45]. Although ShareGPT does not contain images in its instructions, the model learns from this dataset the behavior of adaptively responding with the language that corresponds to the user's request. We empirically show that this behavior is transferred to visual conversations. We also quantitatively evaluate the model's generalization capability to Chinese on MMBench-CN [36], where the questions of MMBench are converted to Chinese. Notably, LLaVA-1.5 outperforms Qwen-VL-Chat by " + }, + { + "bbox": [ + 46, + 412, + 289, + 605 + ], + "type": "inline_equation", + "content": "+7.3\\%" + }, + { + "bbox": [ + 46, + 412, + 289, + 605 + ], + "type": "text", + "content": " (63.6% vs 56.7%), despite Qwen being finetuned on Chinese multimodal instructions while LLaVA-1.5 is not." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 611, + 192, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 192, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 192, + 623 + ], + "type": "text", + "content": "4.4. Ablation on LLM Choices" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "In NLP, findings [48] suggest that the capability of the base LLM can affect its instruction-tuned successors. In this section, we explore two families of LLMs and study their contribution to the final model's multimodal capability: LLaMA-based (Vicuna-v1.1, Vicuna-v1.3) and LLaMA2-based (Vicuna-v1.5, LLaMA-2-Chat). Vicuna-v1.3 and Vicuna-v1.5 use the same " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\sim 150\\mathrm{K}" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": " ShareGPT [45] data (" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "2\\times" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 68, + 545, + 276 + ], + "blocks": [ + { + "bbox": [ + 307, + 68, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 307, + 68, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 307, + 68, + 545, + 276 + ], + "type": "image", + "image_path": "8e10f73ab5ee3c892687b2d911e92a705c28a2f1f9f40893e157a26b65f63aad.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 283, + 546, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 283, + 546, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 546, + 308 + ], + "type": "text", + "content": "Figure 4. Ablation on data efficiency. Data points represent the relative performance of the best performing variant for each dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 328, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 547, + 389 + ], + "type": "text", + "content": "that used in v1.1). Unlike Vicuna series that is only trained with supervised instruction finetuning (SFT), LLaMA-2-Chat is further optimized with reinforcement-learning from human-feedback (RLHF). We visualize the relative performance of these variants in Fig. 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 389, + 547, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 547, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 547, + 486 + ], + "type": "text", + "content": "First, we find that Vicuna-v1.5 achieves the best overall performance, and LLaMA-2-based models generally perform better than LLaMA-1-based, suggesting the importance of the base language model. This is further evidenced by the results on MMBench-CN [36]: despite Vicuna-v1.3 and v1.5 using the same ShareGPT data for instruction tuning, the performance in generalization to Chinese of Vicuna-v1.3 is significantly worse than v1.5." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 487, + 548, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 548, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 548, + 643 + ], + "type": "text", + "content": "Second, language instruction-tuning matters on specific capabilities that are required by each dataset. For example, although LLaMA-2-Chat and Vicuna-v1.5 achieves almost the same performance on MMBench, the generalization to MMBench-CN [36] of LLaMA-2-Chat is worse than Vicuna-v1.5, which is partly due to that the most SFT/RLHF data of LLaMA-2-Chat is in English and does not contain as many multilingual data as in ShareGPT. Furthermore, TextVQA requires both the model's capability of identifying the text characters in the images, and also processing the noisy outputs from the OCR engine; such noise may be more commonly observed in the ShareGPT data, which is collected in-the-wild from daily usage of ChatGPT." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 656, + 453, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 656, + 453, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 656, + 453, + 670 + ], + "type": "text", + "content": "5. Open Problems in LMMs" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Given the successful scaling of LLaVA-1.5, we conduct additional studies on open problems in LMMs using the model design and data mixture of LLaVA-1.5." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26302" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 141, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 141, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 141, + 85 + ], + "type": "text", + "content": "5.1. Data Efficiency" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 287, + 186 + ], + "type": "text", + "content": "Despite the data efficiency of LLaVA-1.5 when compared with approaches like InstructBLIP [13], the training of LLaVA-1.5 still doubles when compared with LLaVA. In this section, we conduct experiments for further improving the data efficiency by randomly sub-sampling the training data mixture of LLaVA-1.5, with a sampling ratio ranging from 0.1 to 0.5. We visualize the relative performance of different sampling variants in Fig. 4." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "type": "text", + "content": "First, the full data mixture provides the best knowledge coverage, and allows the model to achieve the best overall performance. To our surprise, with only " + }, + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "type": "text", + "content": " of the samples, the model still maintains more than " + }, + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 186, + 287, + 257 + ], + "type": "text", + "content": " of the full dataset performance. This suggests that there is room for further improvements in data efficiency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "text", + "content": "Second, when downsampling the dataset to " + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "text", + "content": ", the model's performance on MMBench, ScienceQA, and POPE does not decrease at all, and it even slightly improves on MMBench. Similarly, the model's performance remains steady when further downscaling the data from " + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 257, + 287, + 342 + ], + "type": "text", + "content": ". These results show promise of having the less-is-more [59] benefit for multimodal models as well." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 347, + 236, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 236, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 236, + 360 + ], + "type": "text", + "content": "5.2. Rethinking Hallucination in LMMs" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "type": "text", + "content": "Hallucination is an important issue to tackle for LLMs and LMMs. Often in LMMs, we attribute the model's hallucination to the errors or hallucinations in the training dataset. For example, the detailed descriptions in LLaVA-Instruct [35] may contain a small amount of hallucinated content, and it is believed that training on such data may have caused the model to hallucinate when asked to \"describe the image in detail\". However, we find that such hallucination is significantly reduced, when we scale the model's inputs to higher resolutions like " + }, + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "type": "inline_equation", + "content": "448^{2}" + }, + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 485, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 628 + ], + "type": "text", + "content": "This finding is interesting as it suggests that the LMMs may be robust to a few such errors in the training data. However, when the input resolution is not sufficient for the model to discern all details in the training data, and the amount of data that is at that granularity beyond the model's capability becomes large enough, the model learns to hallucinate. This further suggests that there needs to be a balance between improving the data annotation with more details and the model's capability to properly process the information at such granularities. We hope this finding provides a reference for future work in terms of dealing with hallucination and the scaling of the models and data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 635, + 197, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 197, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 197, + 647 + ], + "type": "text", + "content": "5.3. Compositional Capabilities" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "We demonstrate interesting compositional capabilities in LLaVA-1.5: the model trained on a set of tasks independently generalizes to tasks that require a combination of these capabilities without explicit joint training. We note some of the findings below." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 191 + ], + "type": "text", + "content": "First, we observe an improved language capability in visual conversations after including the ShareGPT [45] data, including the multimodal multilingual capability as discussed in Sec. 4.3. Moreover, the model is more capable at providing longer and more detailed responses in visual conversations. Second, the additional visual knowledge from the academic-task-oriented datasets, improves the visual groundness of LLaVA-1.5's responses in visual conversations, as evidenced quantitatively by the improved results on MMVet [54] and LLaVA-Wild [35] in Table 4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 192, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 547, + 289 + ], + "type": "text", + "content": "However, there is still difficulty in achieving ideal performance for some tasks that require a certain combination of capabilities. For example, being able to correctly answer the attribute of a certain object in VQA, does not guarantee an accurate depiction of that object attribute in a detailed description of the whole image. Furthermore, the capability of engaging in conversations with certain foreign languages (e.g. Korean) still falls behind. See appendix for examples." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 289, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 373 + ], + "type": "text", + "content": "These findings suggest that the compositional capabilities of LMMs can be leveraged to improve the model's performance without significantly increasing the data by exhaustively including all task combinations. Yet, it can be further investigated, and a deeper understanding of the mechanism behind the compositional capabilities of LMMs can further improve the capability and the data efficiency of LLaVA-1.5." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 385, + 378, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 378, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 378, + 398 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 406, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 547, + 525 + ], + "type": "text", + "content": "In this paper, we take a step towards demystifying the design of large multimodal models, and propose a simple, effective, and data-efficient baseline, LLaVA-1.5, for large multimodal models. In addition, we explore the open problems in visual instruction tuning, scale LMMs to higher resolutions, and present some intriguing findings in terms of model hallucination and compositional capabilities for LMMs. We hope these improved and easily-reproducible baselines as well as the new findings will provide a reference for future research in open-source LMM." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 529, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 615 + ], + "type": "text", + "content": "Limitations. Despite the promising results demonstrated by LLaVA-1.5, it still has limitations including prolonged training for high-resolution images, lack of multiple-image understanding, limited problem solving capabilities in certain fields. It is not exempt from producing hallucinations, and should be used with caution in critical applications (e.g. medical). See appendix for a detailed discussion." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Acknowledgements. This work was supported in part by NSF CAREER IIS2150012, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26303" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 113 + ], + "type": "text", + "content": "[1] Adept AI. 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Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26306" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_content_list.json b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8fdec29e3ba248275e609af142635c6dd7fc2a81 --- /dev/null +++ b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_content_list.json @@ -0,0 +1,1773 @@ +[ + { + "type": "text", + "text": "Improved Implicit Neural Representation with Fourier Reparameterized Training", + "text_level": 1, + "bbox": [ + 274, + 130, + 694, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kexuan Shi Xingyu Zhou Shuhang Gu* \nSchool of Computer Science and Engineering, UESTC \n{kexuanshi712, xy.chous526, shuhanggu}@gmail.com", + "bbox": [ + 267, + 203, + 700, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 277, + 313, + 294 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data. The codes are available at https://github.com/LabShuHangGU/FR-INR.", + "bbox": [ + 75, + 310, + 473, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, a novel signal representation paradigm called implicit neural representation (INR) has gained great attention in the field of computer vision and graphics. The main idea of INR is using multi-layer perceptron (MLP) to parameterize continuous and differentiable functions in an implicit manner. For example, given a gray scale image, INR takes the coordinates of the pixels as inputs to MLP and trains it to output the exact gray values using gradient-based optimization methods. Benefiting from the continuity nature and the expressive power of MLP, a more versatile continuous representation can be learned than traditional dis", + "bbox": [ + 75, + 710, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/37a9284f623a1afcbc58158b5110a3f2344f1cdb66c56aadfc27058400b86a51.jpg", + "image_caption": [ + "Figure 1. A conceptual illustration of our Fourier reparameterization method. We reparameterize the linear weight $\\mathbf{W}$ with a trainable coefficient matrix $\\pmb{\\Lambda}$ and a fixed Fourier basis matrix $\\mathbf{B}$ . More balanced eigenvalue distribution of neural tangent kernel (NTK) matrix implies that our method is able to alleviate the low-frequency bias of deep neural network, and therefore leads to better implicit neural representation." + ], + "image_footnote": [], + "bbox": [ + 503, + 277, + 883, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "crete grid-based methods. Consequently, INR has achieved state-of-the-art performance across a variety of tasks such as signal representation [34, 35], 3D shape reconstruction [3, 6, 30] and novel view synthesis [26, 28, 37].", + "bbox": [ + 496, + 672, + 890, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the universal approximation capabilities of MLP which have been proved in [16], obtaining highly accurate INR is not trivial. Specifically, MLP with ReLU activation function often fails to represent the high-frequency components of the signal such as the complex texture information in images and the intricate geometric shapes involved in 3D shape reconstruction. Such tendency of MLP to learn simple patterns of the target function is referred to as spectral bias [31] or low-frequency bias [43]. To improve the performance of INR, great efforts have been made to alleviate or circumvent the spectral bias of MLP. One main category", + "bbox": [ + 496, + 734, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25985", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of approaches find that the difficulty of learning high frequencies becomes easier by increasing the complexity of the input data manifold [31] and explicitly extracting high-frequency features (for example, positional encoding [26]) to deal with the spectral bias issue. While, inspired by the pioneer work of [35], another main class of approaches exploit advanced activation functions [13, 34, 45] for pursuing more accurate approximation.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we dive into details of the spectral bias issue and prove that reparameterizing weights of MLP with appropriate bases could provide us with a chance to narrow the gap between the magnitude of low-frequency and high-frequency loss, i.e. to alleviate the spectral bias during the training of deep neural networks. We propose a Fourier reparameterization strategy (see Fig. 1) and evaluate our method on simple 1D function approximation task and several real-world vision applications. Experimental results clearly validate our advantages in alleviating the low-frequency bias issue for improving approximation accuracy. Our study provides the literature with a practical reparameterization solution for improving the approximation accuracy of MLP without modifying its network architecture, previously, which so far has only been studied for the convolutional architectures. Moreover, our theoretical analysis sheds new light on the advantage of reparameterized training by connecting it with the spectral bias issue. We hope our study could inspire future works in improving training dynamics of deep neural networks with sophisticated reparameterization methods.", + "bbox": [ + 75, + 212, + 472, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 96, + 529, + 401, + 542 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We connect network training bias with reparameterization technique and theoretically prove that appropriate reparameterization could alleviate the spectral bias issue by altering the magnitude of gradients from different frequencies.", + "- We propose a practical reparameterization method for multi-layer perceptron, i.e. the Fourier reparameterization scheme, which could effectively improve the approximation accuracy of implicit neural representation without modifying its network architecture.", + "- We provide detailed experimental analysis on a wide range of implicit neural representation tasks. Our Fourier reparameterization method allows the improvement of commonly used network architectures and provides an representation with more high-frequency details." + ], + "bbox": [ + 76, + 545, + 470, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 784, + 218, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit neural representation. The novel signal representation paradigm representing a signal as an implicit continuous function by neural networks has gained lots of attention. Recent works have demonstrated the remarkable performance and memory-efficient property in many representation tasks such as 2D image representa", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion [13, 22, 32, 34, 35], occupancy volume representation [7, 24, 30, 36], view synthesis [4, 25, 26, 28, 37, 40] and virtual reality [8]. However, the popular activation function ReLU empirically can't achieve the satisfactory performance with vanilla MLP. Therefore, various modifications have been studied. The mainstream modifications can be classified into two aspects. The first aspect focuses on the input domain. Rahaman et al. [31] show that learning high frequency components gets easier with the increasing of the complexity of the input data manifold. Inspired by this phenomenon, Mildenhall et al. [26] use the positional encoding which adopts the sinusoidal mapping of the input features as the new input in the view synthesis and achieve remarkable performance. Zhong et al. [47] also use this method to reconstruct more accurate continuous distributions of 3D protein structure. Recent studies [19, 23, 38] propose to encode input coordinates by learned features. Inspired by this, Xie et al. [42] rearrange the order of input coordinates and obtain more low-frequency components, avoiding confrontation with spectral bias. The second aspect focuses on the activation function. Sitzmann et al. [35] find that using periodic functions, such as the sinusoidal function, as activation functions can achieve remarkable performance in signal fitting. Sinusoidal functions are also explored by Fathony et al. [13] in multiplicative filter networks. Yüce et al. [45] explain the success of the usage of periodic function from a structured dictionary perspective. Inspired by this perspective, Saragadam et al. [35] use a complex Gabor wavelet activation and achieve robust and accurate representations.", + "bbox": [ + 496, + 90, + 893, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spectral bias. The term spectral bias [31] also known as the low-frequency bias [43] implies that MLP tends to learn simple patterns of the real data [2] or the low-frequency components of the target function [43]. Arpit et al. [2] first find this phenomenon which has attracted lots of follow up studies. Rahaman et al. [31] exploit the structure of ReLU networks to evaluate its Fourier spectrum and estimate the relationships between the spectral norm of MLP weights and the amplitude of the output of MLP at different frequencies. Xu [43] builds a theoretical framework by Fourier Analysis to decompose gradients in the frequency domain and discusses the distributions of the absolute gradients of the parameters at different frequencies. From the perspective of the neural tangent kernel (NTK) theory [18], components of the target function corresponding to larger kernel eigenvalues will be learned faster [5, 33]. Therefore, Tancik et al. [39] propose to leverage the eigenvalues of the NTK matrix to analyze the spectral bias of MLP. In this paper, we dive into details of the low-frequency bias issue and find that network reparameterization could provide us a chance to alleviate the bias in network training. We analyze our proposed method with the frequency decomposed loss, gradient [43] and NTK theory [39]. Our experiment", + "bbox": [ + 496, + 544, + 893, + 892 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25986", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tal results validate our idea of improving spectral bias with weight reparameterization.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Weight reparameterization. In order to reduce the inference cost of deep learning models [15, 17], weight reparameterization method is proposed by Zagoruyko et al. [46]. Inspired by this work, various reparameterization methods have been explored to train networks with mergeable auxiliary structures [9-11, 27, 29, 41]. Recently, there are still researches which exploit the idea of reparameterization to design network optimizer for advanced training [12]. In this paper, we adopt the idea of weight reparameterization to improve the approximation accuracy of MLP. For the first time, we link the reparameterization technique with network training bias and theoretically prove the possibility of mitigating frequency-bias with reparameterized training. We hope our theoretical analysis could shed new light on network reparameterization and inspire future studies on advanced reparameterization method.", + "bbox": [ + 75, + 136, + 472, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 401, + 210, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The formulation of INR", + "text_level": 1, + "bbox": [ + 76, + 425, + 295, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The task of INR is to approximate a target function with a multi-layer perceptron (MLP): $f_{\\Theta}(x) \\approx g(x)$ ; where $g(x) : \\mathbb{R}^{d_0} \\mapsto \\mathbb{R}^{d_N}$ is the target function which defines a mapping from a $d_0$ -dimensional real space to a $d_N$ -dimensional real space, and $f_{\\Theta}(x)$ is a N-layer MLP with the learnable parameters set $\\Theta$ . Denote the output of $n$ -th layer as:", + "bbox": [ + 76, + 449, + 468, + 540 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} ^ {(\\mathbf {n})} = \\sigma (\\mathbf {W} ^ {(\\mathbf {n})} \\mathbf {y} ^ {(\\mathbf {n} - \\mathbf {1})} + \\mathbf {b} ^ {(\\mathbf {n})}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 559, + 468, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma$ is an element-wise nonlinear activation function; $\\mathbf{W}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times d_{n - 1}}$ and $\\mathbf{b}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n}$ are the weight and bias for the $n$ -th layer; $\\mathbf{y}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n}$ and $\\mathbf{y}^{(\\mathbf{n} - \\mathbf{1})}\\in \\mathbb{R}^{d_{n - 1}}$ are the output and input of the $n$ -th layer, respectively. For $n = N$ , we have that $\\mathbf{y}^{(\\mathbf{N})} = \\mathbf{W}^{(\\mathbf{N})}\\mathbf{y}^{(\\mathbf{N} - \\mathbf{1})} + \\mathbf{b}^{(\\mathbf{N})}$ . The MLP parameters set $\\Theta = \\{\\mathbf{W}^{(\\mathrm{i})},\\mathbf{b}^{(\\mathrm{i})}\\}_{\\mathrm{i = 1,\\dots,N}}$ is learned by minimizing the loss with gradient-based methods.", + "bbox": [ + 76, + 599, + 468, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The above idea of INR is memory efficient, and the continuous nature of MLP allows INR to model fine detail that is not limited by the grid resolution. However, during the practical optimization process, gradients of parameters are dominated by the error of low-frequency components. Such a spectral bias hinders the accurate learning pace of MLP. Various modifications, including input feature adjustments [39, 42] and activation function adjustments [13, 32, 34, 35], have been exploited for alleviating the spectral bias issue. In this paper, we show that appropriate reparameterization of MLP is also beneficial for narrowing the gap between the gradient magnitude of high-frequency components and low-frequency components.", + "bbox": [ + 75, + 704, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Fourier reparameterization", + "text_level": 1, + "bbox": [ + 500, + 90, + 746, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As we have introduced in the previous subsection, the weight matrix in the $n$ -th layer of MLP is denoted as $\\mathbf{W}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times d_{n - 1}}$ . Instead of directly calculating the gradient of $\\mathbf{W}^{(\\mathbf{n})}$ respect to the loss function, we reparameterize each row of $\\mathbf{W}^{(\\mathbf{n})}$ as a weighted combination of fixed Fourier bases:", + "bbox": [ + 498, + 113, + 890, + 202 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} ^ {(\\mathbf {n})} = \\boldsymbol {\\Lambda} ^ {(\\mathbf {n})} \\mathbf {B} ^ {(\\mathbf {n})}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 202, + 890, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{\\Lambda}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times M}$ are the coefficient matrix, and $\\mathbf{B}^{(\\mathbf{n})}\\in \\mathbb{R}^{M\\times d_{n - 1}}$ are $M$ Fourier bases. Each Fourier basis is achieved by changing the frequency $\\omega$ and phase $\\varphi$ of a cosine function $\\cos (\\omega z + \\varphi)$ :", + "bbox": [ + 498, + 224, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nb _ {i j} = \\cos \\left(\\omega_ {i} z _ {j} + \\varphi_ {i}\\right), f o r i = 1, \\dots , M; j = 1, \\dots , d _ {n - 1}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 299, + 890, + 328 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{z} = \\{z_{j}\\}_{j = 1,\\dots,d_{n - 1}}$ is the sampling position sequence. More details will be introduced in section 5.4.3. Generally, we have $M\\geq d_{n - 1}$ which means that we reparameterize the weight matrix with over complete bases.", + "bbox": [ + 498, + 330, + 890, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Please note that in Eq. 2, each basis is with the same dimension as the input feature $\\mathbf{y}^{(n - 1)}$ , which means that our reparameterization scheme firstly projects the input features onto a series of Fourier bases and weighted combines the projection coefficients:", + "bbox": [ + 498, + 391, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} ^ {(\\mathbf {n})} = \\sigma \\left(\\boldsymbol {\\Lambda} ^ {(\\mathbf {n})} \\mathbf {B} ^ {(\\mathbf {n})} \\mathbf {y} ^ {(\\mathbf {n} - 1)} + \\mathbf {b} ^ {(\\mathbf {n})}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 474, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the above equation, $\\mathbf{B}^{(\\mathbf{n})}$ is fixed and we only learn $\\Lambda^{(\\mathbf{n})}$ during the training phase. After training, we combine $\\Lambda^{(\\mathbf{n})}$ and $\\mathbf{B}^{(\\mathbf{n})}$ to form the weight matrix $\\mathbf{W}^{(\\mathbf{n})}$ in the inference. Therefore, our reparameterization approach only adjusts the training dynamic and will not affect the inference process of INR. Moreover, the proposed Fourier reparameterization approach does not affect the input feature space as well as nonlinear activation functions. Our method is compatible with existing techniques, including but not limited to positional encoding [39] and periodic activation functions [35].", + "bbox": [ + 498, + 503, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Discussion", + "text_level": 1, + "bbox": [ + 500, + 666, + 617, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this subsection, we analyze our reparameterization scheme in the frequency domain. By carefully analyzing the gradients of learning parameters respect to different frequencies, we show that appropriate weight reparameterization provides us with a chance to alleviate the low-frequency bias in the network training.", + "bbox": [ + 498, + 689, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start our analysis with the definition of some basic concepts [43]. We denote the Fourier Transform of the target function and the MLP representation of INR at frequency $k$ as: $\\mathcal{F}[g](k)$ and $\\mathcal{F}[f_{\\Theta}](k)$ , respectively. Then, the approximation error at frequency $k$ can be naturally achieved by $E(k) = \\mathcal{F}[g](k) - \\mathcal{F}[f_{\\Theta}](k)$ . We further define the following notations: $E(k) = A(k)e^{i\\theta (k)}$ and $\\mathbb{L}(k) = |E(k)|^2$ ; where $A(k)$ and $\\theta (k)\\in [\\pi ,\\pi ]$ indicate the", + "bbox": [ + 498, + 780, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25987", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "amplitude and phase of $E(k)$ ; $\\mathbb{L}(k)$ is the loss component of frequency $k$ ; $|\\cdot|$ is the norm of the complex number.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the above definitions, Xu [43] shows that the spectral bias can be reflected on the absolute gradient values of parameters at different frequencies:", + "bbox": [ + 75, + 121, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1. (Theorem 1 in [43]) Consider a MLP with one hidden layer using tanh function $\\sigma(x)$ as the activation function. For any frequencies $k_{1}$ and $k_{2}$ such that $k_{1} > k_{2} > 0$ and there exist $c_{1}, c_{2}$ , such that $A(k_{1}) > c_{1} > 0$ , $A(k_{1}) < c_{2} < \\infty$ , we have", + "bbox": [ + 76, + 181, + 468, + 257 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lim _ {\\delta \\rightarrow 0} \\frac {\\mu \\left( \\right.\\left\\{ \\right.w _ {j}: \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial \\Theta_ {j l}} \\left. \\right| > \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial \\Theta_ {j l}} \\mid f o r a l l j , l \\left. \\right\\} \\cap B _ {\\delta})}{\\mu \\left(B _ {\\delta}\\right)} = 1, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 265, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $B_{\\delta}$ is a ball with radius $\\delta$ centered at the origin and $\\mu (\\cdot)$ is the Lebesgue measure of a set and $\\Theta_{jl}$ is a leannable parameter in the parameters set.", + "bbox": [ + 75, + 316, + 468, + 362 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generally, Theorem 1 shows that in the case of one hidden layer MLP, the gradient respect to low-frequency loss $\\mathbb{L}(k_2)$ is almost always larger than the one respect to high-frequency part. Although the condition of one hidden layer MLP is not applicable in most of practical cases, based on recent observations of low-frequency bias [2, 18, 31, 43], the above Theorem 1 inspires us to assume such relationship to MLP with more hidden layers. Then, we could have the following Theorem 2:", + "bbox": [ + 75, + 362, + 468, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2. Given a MLP with multiple hidden layers, reparameterize the weight matrix $\\mathbf{W} \\in \\mathbb{R}^{d \\times d}$ of one hidden layer with a trainable coefficient matrix $\\boldsymbol{\\Lambda} \\in \\mathbb{R}^{d \\times M}$ and the fixed basis matrix $\\mathbf{B} \\in \\mathbb{R}^{M \\times d}$ . For any frequencies $k_{1}$ and $k_{2}$ such that $k_{1} > k_{2} > 0$ , given any $\\epsilon \\geq 0$ and fixed $i$ , for $j = 1, 2, \\ldots, M$ , there must exist a set of basis matrices such that", + "bbox": [ + 75, + 513, + 468, + 618 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial \\lambda_ {i j}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial \\lambda_ {i j}} \\right| \\geq \\max \\left\\{\\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial w _ {i 1}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial w _ {i 1}} \\right|, \\dots , \\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial w _ {i d}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial w _ {i d}} \\right| \\right\\} - \\epsilon , \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 623, + 468, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}(i,j) = w_{ij}$ and $\\pmb {\\Lambda}(i,j) = \\lambda_{ij}$", + "bbox": [ + 80, + 657, + 352, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed proof of Theorem 2 can be found in our supplementary file. Theorem 2 implies that reparameterizing MLP weights with appropriate bases is able to enlarge the portion of high-frequency loss components in comparison to low-frequency components, i.e. improving the spectral bias in training MLP. Although the optimal basis for frequency-bias adjustment is related to the training data and we are not able to achieve the optimal basis with negligible efforts, we experimentally find that fixed Fourier basis is able to improve the low-frequency bias and provide better INR for various function approximation tasks.", + "bbox": [ + 75, + 672, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 847, + 290, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Basis construction. As we have introduced in section 3.2, we establish Fourier bases with various frequencies and", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "phase parameters. We adopt $P$ different phases and $2F$ different frequencies. Concretely, the $\\varphi$ in Eq. 3 varies from 0 to $2\\pi (P - 1) / P$ with step length $2\\pi /P$ ; for each phase value, we have a group of low-frequency bases with $\\omega = \\{1 / F,2 / F,\\dots ,1\\}$ and a group of high-frequency bases with $\\omega = \\{1,2,\\ldots ,F\\}$ . Based on the above basis construction scheme, we could obtain $M = 2FP$ bases. Details of the selected $F$ and $P$ values for different settings will be introduced in the experimental section. We also provide ablation experiments in our supplementary field to analyze the effects of different design choices of $F$ and $P$ .", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sampling strategy. The cosine basis function used in Eq. 3 is a continuous function. We need to sample values from the continuous function to achieve discrete basis for weight reparameterization. As the number of sampling points is determined by the neuron number of input feature, the only key hyper-parameter during the sampling process is the range of sampling. To reflect characteristics of different frequency bases, we choose the maximum period $(T_{max} = 2\\pi F)$ of the adopted Fourier Bases as the sampling range. To maintain the periodicity of bases, uniform sampling is employed. Due to the symmetry of bases, we set the sampling interval as $[- \\frac{1}{2} T_{max}, \\frac{1}{2} T_{max}]$ . The length of interval will be discussed in our ablation studies.", + "bbox": [ + 496, + 272, + 890, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initialization scheme. Initialization techniques are one of the prerequisites for successfully training a deep neural network. The basic idea of the existing popular initialization strategies [14, 15] is to let the network start in a regime with constant variance between inputs and outputs. While our method reparameterizes the network weights as the fixed Fourier bases and trainable coefficients, initializing the learnable coefficients $\\Lambda$ with existing initialization techniques will deactivate the constant variance requirement. We therefore adjust the initialization strategy for $\\Lambda$ . For ReLU activation function [15], we initialize the trainable coefficient matrix $\\Lambda^{(\\mathbf{n})}$ using the following equation:", + "bbox": [ + 496, + 483, + 890, + 664 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {i j} ^ {(n)} \\sim U (- \\sqrt {\\frac {6}{M \\sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}, \\sqrt {\\frac {6}{M \\sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 664, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{ij}^{(n)}, b_{ij}^{(n)}$ is in the $i$ -th row and $j$ -th column of $\\mathbf{\\Lambda}^{(\\mathbf{n})} \\in \\mathbb{R}^{d_n \\times M}$ and $\\mathbf{B}^{(\\mathbf{n})} \\in \\mathbb{R}^{M \\times d_{n-1}}$ , respectively. For SIREN [35], we have the similar initialization scheme. The detailed derivation can be found in our supplementary file.", + "bbox": [ + 498, + 719, + 890, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experimental Analysis on Simple Function Approximation", + "text_level": 1, + "bbox": [ + 498, + 796, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We firstly conduct experiments on the simple function approximation task. Thanks to the simplicity of the target function, the behaviour of MLP can be analyzed with various techniques. In the remaining of this section, we firstly", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25988", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e5a7d4931d31566c870d89948d82492667150d28b2741f230e8a8adfe67eafdd.jpg", + "image_caption": [ + "Figure 2. Visualization of simple function. The left side of the first row displays the visualization of the 1D simple function on the $x - y$ coordinate axis. The left side of the second row shows the amplitude of the function in the frequency domain. The right side presents the average loss curve with the shaded area indicating the fluctuation from 100 repetitions." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 467, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "introduce our experimental settings and then analyze the property of our proposed Fourier reparameterization (FR).", + "bbox": [ + 75, + 354, + 468, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental settings", + "text_level": 1, + "bbox": [ + 76, + 396, + 282, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to thoroughly analyze the advantage of FR, we establish a 1D function $g(x)$ by combining sine functions of different frequencies:", + "bbox": [ + 75, + 419, + 470, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n2 R \\left(\\frac {\\sin (3 \\pi x) + \\sin (5 \\pi x) + \\sin (7 \\pi x) + \\sin (9 \\pi x)}{2}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 476, + 468, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $R(\\cdot)$ is the rounding function for increasing the complexity of approximation. A similar rounded periodic function has been adopted in [43] to analyze the spectral-bias of MLP. A visualization of our adopted 1D function and its spectrum can be found in the first column of Fig. 2. As designed by purpose, four distinct peaks marked by red dots can be observed in the stem plot of the spectrum.", + "bbox": [ + 75, + 518, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilize a four-hidden-layer MLP to approximate the $g(x)$ with 300 discrete values uniformly sampled in the interval $[-1,1]$ , where each hidden layer consists of 128 neurons. We conduct experiments on both the ReLU and the periodic activation function Sin. The $\\omega_0$ in Sin activation function is set as 5 for the pursuit of fast convergence [35]. For our reparameterization approach, we reparameterize the weight matrices between consecutive hidden layers and set $F = 64$ and $P = 16$ . Therefore, we have $M = 2048$ bases in total. The four comparison methods are denoted as: MLP+ReLU, MLP+ReLU+FR, MLP+Sin, MLP+Sin+FR. All the methods are trained with Adam optimizer [21] for 10000 iterations with a learning rate 1e-6 and full-batch.", + "bbox": [ + 75, + 625, + 470, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Approximation results and analysis", + "text_level": 1, + "bbox": [ + 76, + 832, + 383, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The convergence curves by different methods can be found in Fig. 2. For both the ReLU and Sin activation function cases, Our FR approach improves the convergence", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "speed as well as approximation error of vanilla MLP. Especially for the naive MLP+ReLU case, training network with our proposed reparameterization method could improve the original training paradigm by a large margin.", + "bbox": [ + 496, + 90, + 892, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Frequency-specific error analysis. In [43], using Discrete Fourier Transform, Xu et al. compute the relative difference $\\Delta_{k}$ between the target signal and the output of MLP at frequency $k$ and empirically show the low-frequency bias of MLP:", + "bbox": [ + 496, + 166, + 893, + 239 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta_ {k} = \\frac {\\left| \\mathcal {F} _ {D} [ g ] (k) - \\mathcal {F} _ {D} [ f _ {\\Theta} ] (k) \\right|}{\\left| \\mathcal {F} _ {D} [ g ] (k) \\right|}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 241, + 892, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_D$ denotes the Discrete Fourier Transform. We follow [43] and use Eq. 9 to analyze the frequency-specific approximation error after different numbers of iterations. As can be found in Fig. 3, the evolution of frequency-specific error clearly shows the low-frequency bias in network training: the error of low-frequency components generally reduces much faster than that of high-frequency components. The proposed FR method narrows the gap in dropping speed of low-frequency error and high-frequency error, thereby leading to overall faster convergence speed.", + "bbox": [ + 496, + 282, + 893, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Neural tangent kernel. Neural tangent kernel (NTK) [18] is a theory to analyze the dynamic training process of neural networks. Tancik et al. [39] have shown that components of the target function that correspond to larger kernel eigenvalues will be learned faster and adopt kernel eigenvalues [5, 33, 39] to analyze the spectral bias. Since the conditions of the standard NTK theory are not applicable to commonly used networks, we follow [1, 45] and utilize the following empirical NTK to analyze the training dynamics of different networks:", + "bbox": [ + 496, + 450, + 892, + 601 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nk _ {N T K} ^ {\\prime} \\left(x _ {i}, x _ {j}\\right) = J _ {f _ {\\Theta}} \\left(x _ {i}\\right) J _ {f _ {\\Theta}} \\left(x _ {j}\\right) ^ {T}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 614, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $J_{f_\\Theta}(x_i)$ denotes the Jacobian matrix of the function $f_\\Theta$ at the $i$ -th sample $x_i$ and $k_{NTK}'(x_i, x_j)$ is the element in the $i$ -th row and $j$ -th column of the empirical NTK matrix.", + "bbox": [ + 496, + 647, + 890, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The first four and the summation of the remaining eigenvalues by different methods are shown in Fig. 4. Consistent with the conclusion of [39], the eigenvalues of $\\mathrm{MLP} + \\mathrm{ReLU}$ decay rapidly, which means the model suffers severe spectral bias during training. While, our FR scheme is able to reduce the percentage of the first eigenvalue and enlarge the other eigenvalues of the empirical NTK matrix, leading to more balanced eigenvalue distribution during training.", + "bbox": [ + 496, + 693, + 890, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental Results on Vision Applications", + "text_level": 1, + "bbox": [ + 500, + 830, + 890, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implicit neural representation has been utilized in different vision applications. In this section, we evaluate the proposed FR method on different vision applications.", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25989", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/04bad5a76569d078766dc837ada9cae242894f08f563d7b4ddd4324fcfeace12.jpg", + "image_caption": [ + "Figure 3. Evolution of frequency-specific approximation error with training iterations of four different methods (x-axis for training step, y-axis for frequency and colormap for relative approximation error)." + ], + "image_footnote": [], + "bbox": [ + 88, + 89, + 269, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/adc523b7ddd87b4e8dab99eaa8b50c4aa9041f94c151bec86666cd341dc99556.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 88, + 464, + 209 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ffab144ed7c5824bc3dc82369a73a25a51e32183b61632b77a0b403e9811f8e6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 663, + 209 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b8eeab4f821bbebc70ec7e0e808550df3f09768fbf1b292ebfc659858186ff61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 683, + 88, + 861, + 209 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2745a81b873537c274b14eb5442dc495511427e2ec79ca91ad9282570e693c9a.jpg", + "image_caption": [ + "Figure 4. The distribution of different NTK eigenvalues. 'First' denotes the percentage of the largest eigenvalue, and so on. 'Remain' refers to the percentage of the summation of remaining eigenvalues." + ], + "image_footnote": [], + "bbox": [ + 83, + 277, + 460, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. 2D Color image approximation", + "text_level": 1, + "bbox": [ + 76, + 469, + 352, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Natural images are extremely complex functions which simultaneously encompass rich low- and high-frequency components [20]. Single image fitting has become an ideal test bed [34, 35, 42] to evaluate the capability of implicit neural representation. In our experiments, we attempt to parameterize a function $\\phi : \\mathbb{R}^2 \\mapsto \\mathbb{R}^3$ , $x \\mapsto \\phi(x)$ that represents a given discrete image in a continuous fashion.", + "bbox": [ + 75, + 492, + 468, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We establish MLP with four hidden layers and each hidden layer contains 256 neurons. We conduct experiments on three MLP architectures, i.e. (1) MLP with RLU as the activation function $(\\mathrm{MLP} + \\mathrm{ReLU})$ , (2) $\\mathrm{MLP} + \\mathrm{ReLU}$ with Fourier positional encoding $(\\mathrm{MLP} + \\mathrm{ReLU} + \\mathrm{PE})$ [39], and (3) MLP with Periodic Sin activation function $(\\mathrm{MLP} + \\mathrm{Sin})$ [35]. $\\mathrm{MLP} + \\mathrm{ReLU} + \\mathrm{PE}$ and $\\mathrm{MLP} + \\mathrm{Sin}$ represent two important categories of techniques in INR. Experimental results on more activation functions and other input adjustments can be found in our supplementary file. For each MLP architecture, we train baseline model which trains network parameters directly with the standard back-propagation approach and (+FR) model which utilizes our proposed FR scheme in the training phase. We reparameterize the weight matrices between consecutive hidden layers and set $F = 128$ , $P = 32$ for all the images in the experiment. We use Adam optimizer to minimize the $\\ell_2$ loss between ground truth pixel values and INR approximations. The MLPs are trained with an initial learning rate of $10^{-4}$ for 3000 iterations, and then we drop the learning rate to $10^{-5}$ for another", + "bbox": [ + 75, + 598, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8056440c6004256d7d5c64b540d38bbbe618443670606dd6cda1e47cb2da0c7b.jpg", + "image_caption": [ + "MLP+ReLU (17.31dB)" + ], + "image_footnote": [], + "bbox": [ + 506, + 276, + 696, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e022585dc03d901b4790e21bd10d212a7591a407f6218af71153d53129958cc8.jpg", + "image_caption": [ + "MLP+ReLU+FR (18.33dB)" + ], + "image_footnote": [], + "bbox": [ + 696, + 276, + 888, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/86c8010ab8d9250342f88673a864807aaeb42186f81ee972e0543c5b119adf0c.jpg", + "image_caption": [ + "$\\mathrm{MLP + RELU + PE}$ (22.87dB)" + ], + "image_footnote": [], + "bbox": [ + 504, + 385, + 696, + 484 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8f829e54fde690c8b8c1c8a14e631e7e6a5989cd6ea9201ba62dc16858f3ff4d.jpg", + "image_caption": [ + "MLP+ReLU+PE+FR (26.78dB)" + ], + "image_footnote": [], + "bbox": [ + 696, + 385, + 888, + 484 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/41714c0b5f359bc8e93fe5bd094feabf1cb36c981b363af6f4947f5e711ea401.jpg", + "image_caption": [ + "MLP+Sin (33.05dB)", + "Figure 5. Visual examples of the 2D color image approximation results (PSNR) by different methods. Detailed experimental settings can be found in section 5.1." + ], + "image_footnote": [], + "bbox": [ + 504, + 494, + 696, + 594 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cee7c8cf590f2834a0c06f73fed328a7f00969f648fa4962568baeee23db3bac.jpg", + "image_caption": [ + "MLP+Sin+FR (34.64dB)" + ], + "image_footnote": [], + "bbox": [ + 696, + 494, + 888, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "7000 iterations. Full-batch training is adopted.", + "bbox": [ + 500, + 690, + 807, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 1, we report the PSNR values achieved by different INRs for approximating the first 8 images in the Kodak 24 dataset. More evaluation metrics can be found in our supplementary file. Our FR method is able to improve the approximation accuracy for all the three network architectures. Some visual examples of the learned approximations can be found in Fig. 5. Our FR method enables the network to capture more fine details.", + "bbox": [ + 496, + 705, + 890, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Representing shapes with signed distance functions", + "text_level": 1, + "bbox": [ + 500, + 832, + 890, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Representing shapes with differentiable signed distance functions (SDFs) has the advantage of modeling arbitrary", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25990", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/820479e7414c5d400b50eb428bab18a699ba53e93949e61ba0ba812084341f9a.jpg", + "table_caption": [ + "Table 1. Peak signal to noise ratio (PSNR) of 2D color image approximation results by different methods. Detailed experimental settings can be found in section 5.1." + ], + "table_footnote": [], + "table_body": "
MethodKodim 01Kodim 02Kodim 03Kodim 04Kodim 05Kodim 06Kodim 07Kodim 08Average
MLP + ReLU19.3726.1225.1124.5717.3121.6920.7915.6821.33
MLP + ReLU + FR20.3426.5827.2125.7218.3322.2522.4716.6422.44
MLP + ReLU + PE24.4731.4131.5330.1622.8726.5429.3321.1427.18
MLP + ReLU + PE + FR27.6433.9234.4533.2326.7829.8334.1324.7030.59
MLP + Sin31.5936.5539.5936.6633.0534.1039.9631.0035.31
MLP + Sin + FR33.4538.6839.5837.9634.6434.4539.7632.1636.34
", + "bbox": [ + 124, + 128, + 844, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4dd7c7ae3fdbd8847d3d489e65460bc2449d524c527ad502049aa1916b46e0a8.jpg", + "image_caption": [ + "Figure 6. Visual examples of the shape representation results (IOU) by different methods. More experimental details can be found in section 5.2." + ], + "image_footnote": [], + "bbox": [ + 86, + 247, + 197, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4707867b958928569ca2aaec759ee58b0f58738bed6787b4e3564e8c0cdb808c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 248, + 313, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17c9dc6139c980b609945e77af91d9ace552fb337904c4f22edb8cd7b73afc02.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 316, + 248, + 428, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a45cbbae3e1775210eed36d7ab8119e27262c4d410e981b20bb428afa67a34c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 436, + 248, + 540, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ff578b3a7d1c520dfa49af54201dcc5e84501bffda0e571f49004d08f414a1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 545, + 248, + 656, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2d89c63f1477cccb6aa80b81e5a83928053297cf54162b92a667ffa36a181b91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 661, + 248, + 771, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7d4ae188babde6f24bcc29e06f14aad292c0fd677200ae1e67d9ee498119325.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 776, + 248, + 887, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "topologies [35]. In this section, we evaluate the proposed FR method on the shape representation task. We follow the experimental setting of [34], which sample points over a $512 \\times 512 \\times 512$ grid. We establish MLP with two hidden layers and each hidden layer contains 256 neurons. We reparameterize the weight matrices between consecutive hidden layers and set $F = 256$ , $P = 8$ . We use Adam optimizer to minimize the $\\ell_2$ loss between sampled voxel values and INR approximations. We train all the networks for 200 epochs with an initial learning rate of $5 \\times 10^{-3}$ . The learning rate is reduced exponentially to $5 \\times 10^{-4}$ .", + "bbox": [ + 75, + 506, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 6, we visualize the shape representation results by different methods, the intersection over union (IOU) metrics are also provided for reference. FR method represents intricate geometric shape with less artifacts and more details.", + "bbox": [ + 75, + 672, + 470, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Learning neural radiance fields", + "text_level": 1, + "bbox": [ + 76, + 741, + 354, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Learning neural radience fields for view synthesis is also a main application of INR [26, 28, 37]. The main process of the view synthesis task is to reconstruct 3D representation of an object from the given 2D images taken at various given angles. In this section, we evaluate our FR method in this task. The original NeRF and two recent SOTAs by neural networks, i.e. the InstantNGP [28] and the DVGO [37], are adopted. We follow the experimental settings of these works and train the models on the all objects of the", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Blender dataset [26] with $800 \\times 800$ resolutions. For the original NeRF, we reparameterize the weight matrices of last three hidden layers with $F = 128$ , $P = 32$ and the \"NeRF-pytorch\" codebase [44] is used. The complete results for the InstantNGP and DVGO can be found in our supplementary file.", + "bbox": [ + 496, + 506, + 892, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 7, we show some view synthesis results of the original NeRF. With our proposed FR, the INR is able to capture more details of the complex texture, also representing the more accurate reflection of light.", + "bbox": [ + 496, + 597, + 890, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 661, + 650, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this part, we conduct ablation studies to analyze our design choices. All the ablation experiments are conducted on the first three images of the Kodak 24 dataset, and the structure of the 2D image fitting task is adopted.", + "bbox": [ + 496, + 684, + 893, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4.1 Weight reparameterization with Fourier basis", + "text_level": 1, + "bbox": [ + 498, + 748, + 872, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Theorem 2, we show that appropriate bases selection could alleviate the low-frequency bias issue. In this paper, we select fixed Fourier bases to reparameterize our MLP and show its superiority approximation accuracy on several applications. In this section, we conduct experiments to show that the selection of basis plays a crucial role in our approach. We generate random basis from a uniform distribution and denote the model as random reparameterization (RR). Moreover, we also adopt a similar strategy as", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25991", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/856039f87444d9fa10f27b78680c75308e95c5ef5f9c758a41a58175c64799ba.jpg", + "image_caption": [ + "Figure 7. Visual examples of the view synthesis results (PSNR) by learning neural radiance field with the original NeRF [26]." + ], + "image_footnote": [], + "bbox": [ + 81, + 94, + 267, + 251 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8cbb54888018e8c9974b3a76b10d1fea04c2b40ae51868d5bd9315afd8f031dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 95, + 475, + 251 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/811fc93219f4cfd7838784c470a8e91cb2a064803348bf4e24386361b767410b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 95, + 697, + 251 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8aa6f3e0cce6142410ed519e59e6a48ecb7201e00a461736229febd0c76e156d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 95, + 890, + 251 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/53360a06352f0c02bddc7f770f87713f802c34abbf1850592ed04fcfd1ebceaa.jpg", + "table_caption": [ + "Table 2. Ablation experiments on the reparameterization bases. Our Fourier bases achieve the average approximation results (PSNR) on all the three network architectures. Detailed experimental results can be found in Section 5.4.1." + ], + "table_footnote": [], + "table_body": "
MethodKodim 01Kodim 02Kodim 03Average
MLP+ReLU+RR19.6426.1925.6623.83
MLP+ReLU+RIR20.2226.4826.6724.46
MLP+ReLU+FR20.3426.5827.2124.71
MLP+ReLU+PE+RR27.0532.1633.3830.86
MLP+ReLU+PE+RIR26.9132.0432.8530.60
MLP+ReLU+PE+FR27.6433.9234.4532.00
MLP+Sin+RR34.2837.8430.4834.20
MLP+Sin+RIR25.1928.6127.1226.97
MLP+Sin+FR33.4538.6839.5837.24
", + "bbox": [ + 80, + 369, + 460, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the existing reparameterization works [11] which updates all the random initialized parameters instead of fixed basis during the training phase, and denote the model as randomly initialized reparameterization (RIR). The average approximation results by different reparameterization schemes are shown in Table 2. The results clearly show that bases play a pivotal role in reparameterized training, and our selected Fourier bases have advantages in 2D image fitting.", + "bbox": [ + 75, + 507, + 468, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4.2 Training speed", + "text_level": 1, + "bbox": [ + 76, + 633, + 235, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Fig. 2, in terms of learning iterations, our FR accelerates the convergence speed of network training. While, since our FR will lead to more computations in each training step, we present the detailed training time by different methods. In Table 3, we show the average per epoch training time by different methods in the simple function approximation experiment. The additional time introduced by our FR is not significant. Although it takes an additional $17.3\\%$ time (from $2.89 \\times 10^{-3}$ seconds to $3.31 \\times 10^{-3}$ seconds) for training a MLP + ReLu architecture, our FR could lead to $86\\%$ improvement on accuracy.", + "bbox": [ + 75, + 657, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4.3 Sampling interval analysis", + "text_level": 1, + "bbox": [ + 76, + 845, + 316, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Another important hyper-parameter for our method is our sampling interval. In this section, we conduct experi", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/170cd9393ff6c9efe19297ba95358f6f84f249075f0b91d5e420e25f1d2cadea.jpg", + "table_caption": [ + "Table 3. Average per epoch training time by different methods in the simple function approximation experiment. Detaild experimental results can be found in Section 4.1 and Section 5.4.1." + ], + "table_footnote": [], + "table_body": "
MethodMLP+ReLUMLP+ReLU+FRMLP+SinMLP+Sin+FR
Time (ms)2.893.313.503.59
", + "bbox": [ + 501, + 347, + 897, + 385 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f46ccb759ad0e3d77549fb7509ce169667d896827f07da8db2fcc70229eaca6e.jpg", + "table_caption": [ + "Table 4. Ablation experiments on sampling intervals. Our method could achieve good results (PSNR) on a wide range of sampling intervals. More experimental details can be found in section 5.4.3." + ], + "table_footnote": [], + "table_body": "
Length (×Tmax)0.10.250.512410
Average23.3424.0724.3824.6224.7124.5323.14
", + "bbox": [ + 504, + 445, + 879, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ments to analyze the effect of different sampling intervals. Denote the maximum period of the adopted Fourier function as $T_{max}$ . We vary the sampling interval from $0.1T_{max}$ to $10T_{max}$ . The approximation accuracy with different sampling intervals can be found in Table 4. Our method could achieve good results with a wide range of sampling intervals, i.e. $0.5T_{max}$ to $4T_{max}$ . While sampling points from a very small range fails to represent an entire period for many bases and leads to a performance drop.", + "bbox": [ + 496, + 500, + 890, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 664, + 625, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed a novel FR method for advanced INR. We theoretically analyzed the low-frequency bias issue of MLP for INR and show that appropriate network reparameterization is able to alleviate the low-frequency bias in training MLP. Based on our theoretical analysis, we proposed our FR method which learns coefficient matrix of fixed Fourier bases to compose network weights instead of directly learning them from training data. Experiments were conducted on simple function task and real-world vision applications. Our method improved the representation accuracy for a wide range of commonly used INR network architectures. We hope our initial study could inspire future works in adjusting the learning bias of network by advanced network reparameterization.", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25992", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] What can linearized neural networks actually say about generalization? Advances in Neural Information Processing Systems, 34:8998-9010, 2021. 5", + "[2] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S. Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, and Simon Lacoste-Julien. A closer look at memorization in deep networks, 2017. 2, 4", + "[3] Matan Atzmon and Yaron Lipman. 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Diracnets: Training very deep neural networks without skip-connections. arXiv preprint arXiv:1706.00388, 2017. 3", + "[47] Ellen D Zhong, Tristan Bepler, Joseph H Davis, and Bonnie Berger. Reconstructing continuous distributions of 3d protein structure from cryo-em images. arXiv preprint arXiv:1909.05215, 2019. 2" + ], + "bbox": [ + 501, + 92, + 890, + 473 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "25994", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_model.json b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2f2226b2526dc0d9b581c593934c565c9c1eb25f --- /dev/null +++ b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_model.json @@ -0,0 +1,2365 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.275, + 0.131, + 0.696, + 0.177 + ], + "angle": 0, + "content": "Improved Implicit Neural Representation with Fourier Reparameterized Training" + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.204, + 0.701, + 0.257 + ], + "angle": 0, + "content": "Kexuan Shi Xingyu Zhou Shuhang Gu* \nSchool of Computer Science and Engineering, UESTC \n{kexuanshi712, xy.chous526, shuhanggu}@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.279, + 0.314, + 0.295 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.474, + 0.658 + ], + "angle": 0, + "content": "Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data. The codes are available at https://github.com/LabShuHangGU/FR-INR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.687, + 0.21, + 0.702 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Recently, a novel signal representation paradigm called implicit neural representation (INR) has gained great attention in the field of computer vision and graphics. The main idea of INR is using multi-layer perceptron (MLP) to parameterize continuous and differentiable functions in an implicit manner. For example, given a gray scale image, INR takes the coordinates of the pixels as inputs to MLP and trains it to output the exact gray values using gradient-based optimization methods. Benefiting from the continuity nature and the expressive power of MLP, a more versatile continuous representation can be learned than traditional dis" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.279, + 0.885, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.557, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Figure 1. A conceptual illustration of our Fourier reparameterization method. We reparameterize the linear weight \\(\\mathbf{W}\\) with a trainable coefficient matrix \\(\\pmb{\\Lambda}\\) and a fixed Fourier basis matrix \\(\\mathbf{B}\\). More balanced eigenvalue distribution of neural tangent kernel (NTK) matrix implies that our method is able to alleviate the low-frequency bias of deep neural network, and therefore leads to better implicit neural representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.735 + ], + "angle": 0, + "content": "crete grid-based methods. Consequently, INR has achieved state-of-the-art performance across a variety of tasks such as signal representation [34, 35], 3D shape reconstruction [3, 6, 30] and novel view synthesis [26, 28, 37]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Despite the universal approximation capabilities of MLP which have been proved in [16], obtaining highly accurate INR is not trivial. Specifically, MLP with ReLU activation function often fails to represent the high-frequency components of the signal such as the complex texture information in images and the intricate geometric shapes involved in 3D shape reconstruction. Such tendency of MLP to learn simple patterns of the target function is referred to as spectral bias [31] or low-frequency bias [43]. To improve the performance of INR, great efforts have been made to alleviate or circumvent the spectral bias of MLP. One main category" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25985" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "of approaches find that the difficulty of learning high frequencies becomes easier by increasing the complexity of the input data manifold [31] and explicitly extracting high-frequency features (for example, positional encoding [26]) to deal with the spectral bias issue. While, inspired by the pioneer work of [35], another main class of approaches exploit advanced activation functions [13, 34, 45] for pursuing more accurate approximation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.529 + ], + "angle": 0, + "content": "In this paper, we dive into details of the spectral bias issue and prove that reparameterizing weights of MLP with appropriate bases could provide us with a chance to narrow the gap between the magnitude of low-frequency and high-frequency loss, i.e. to alleviate the spectral bias during the training of deep neural networks. We propose a Fourier reparameterization strategy (see Fig. 1) and evaluate our method on simple 1D function approximation task and several real-world vision applications. Experimental results clearly validate our advantages in alleviating the low-frequency bias issue for improving approximation accuracy. Our study provides the literature with a practical reparameterization solution for improving the approximation accuracy of MLP without modifying its network architecture, previously, which so far has only been studied for the convolutional architectures. Moreover, our theoretical analysis sheds new light on the advantage of reparameterized training by connecting it with the spectral bias issue. We hope our study could inspire future works in improving training dynamics of deep neural networks with sophisticated reparameterization methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.53, + 0.402, + 0.544 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.546, + 0.47, + 0.62 + ], + "angle": 0, + "content": "- We connect network training bias with reparameterization technique and theoretically prove that appropriate reparameterization could alleviate the spectral bias issue by altering the magnitude of gradients from different frequencies." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.621, + 0.47, + 0.696 + ], + "angle": 0, + "content": "- We propose a practical reparameterization method for multi-layer perceptron, i.e. the Fourier reparameterization scheme, which could effectively improve the approximation accuracy of implicit neural representation without modifying its network architecture." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.697, + 0.471, + 0.773 + ], + "angle": 0, + "content": "- We provide detailed experimental analysis on a wide range of implicit neural representation tasks. Our Fourier reparameterization method allows the improvement of commonly used network architectures and provides an representation with more high-frequency details." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.546, + 0.471, + 0.773 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.785, + 0.22, + 0.801 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Implicit neural representation. The novel signal representation paradigm representing a signal as an implicit continuous function by neural networks has gained lots of attention. Recent works have demonstrated the remarkable performance and memory-efficient property in many representation tasks such as 2D image representa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.531 + ], + "angle": 0, + "content": "tion [13, 22, 32, 34, 35], occupancy volume representation [7, 24, 30, 36], view synthesis [4, 25, 26, 28, 37, 40] and virtual reality [8]. However, the popular activation function ReLU empirically can't achieve the satisfactory performance with vanilla MLP. Therefore, various modifications have been studied. The mainstream modifications can be classified into two aspects. The first aspect focuses on the input domain. Rahaman et al. [31] show that learning high frequency components gets easier with the increasing of the complexity of the input data manifold. Inspired by this phenomenon, Mildenhall et al. [26] use the positional encoding which adopts the sinusoidal mapping of the input features as the new input in the view synthesis and achieve remarkable performance. Zhong et al. [47] also use this method to reconstruct more accurate continuous distributions of 3D protein structure. Recent studies [19, 23, 38] propose to encode input coordinates by learned features. Inspired by this, Xie et al. [42] rearrange the order of input coordinates and obtain more low-frequency components, avoiding confrontation with spectral bias. The second aspect focuses on the activation function. Sitzmann et al. [35] find that using periodic functions, such as the sinusoidal function, as activation functions can achieve remarkable performance in signal fitting. Sinusoidal functions are also explored by Fathony et al. [13] in multiplicative filter networks. Yüce et al. [45] explain the success of the usage of periodic function from a structured dictionary perspective. Inspired by this perspective, Saragadam et al. [35] use a complex Gabor wavelet activation and achieve robust and accurate representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.895, + 0.893 + ], + "angle": 0, + "content": "Spectral bias. The term spectral bias [31] also known as the low-frequency bias [43] implies that MLP tends to learn simple patterns of the real data [2] or the low-frequency components of the target function [43]. Arpit et al. [2] first find this phenomenon which has attracted lots of follow up studies. Rahaman et al. [31] exploit the structure of ReLU networks to evaluate its Fourier spectrum and estimate the relationships between the spectral norm of MLP weights and the amplitude of the output of MLP at different frequencies. Xu [43] builds a theoretical framework by Fourier Analysis to decompose gradients in the frequency domain and discusses the distributions of the absolute gradients of the parameters at different frequencies. From the perspective of the neural tangent kernel (NTK) theory [18], components of the target function corresponding to larger kernel eigenvalues will be learned faster [5, 33]. Therefore, Tancik et al. [39] propose to leverage the eigenvalues of the NTK matrix to analyze the spectral bias of MLP. In this paper, we dive into details of the low-frequency bias issue and find that network reparameterization could provide us a chance to alleviate the bias in network training. We analyze our proposed method with the frequency decomposed loss, gradient [43] and NTK theory [39]. Our experiment" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25986" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "tal results validate our idea of improving spectral bias with weight reparameterization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.473, + 0.381 + ], + "angle": 0, + "content": "Weight reparameterization. In order to reduce the inference cost of deep learning models [15, 17], weight reparameterization method is proposed by Zagoruyko et al. [46]. Inspired by this work, various reparameterization methods have been explored to train networks with mergeable auxiliary structures [9-11, 27, 29, 41]. Recently, there are still researches which exploit the idea of reparameterization to design network optimizer for advanced training [12]. In this paper, we adopt the idea of weight reparameterization to improve the approximation accuracy of MLP. For the first time, we link the reparameterization technique with network training bias and theoretically prove the possibility of mitigating frequency-bias with reparameterized training. We hope our theoretical analysis could shed new light on network reparameterization and inspire future studies on advanced reparameterization method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.402, + 0.212, + 0.419 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.426, + 0.296, + 0.44 + ], + "angle": 0, + "content": "3.1. The formulation of INR" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.45, + 0.47, + 0.541 + ], + "angle": 0, + "content": "The task of INR is to approximate a target function with a multi-layer perceptron (MLP): \\( f_{\\Theta}(x) \\approx g(x) \\); where \\( g(x) : \\mathbb{R}^{d_0} \\mapsto \\mathbb{R}^{d_N} \\) is the target function which defines a mapping from a \\( d_0 \\)-dimensional real space to a \\( d_N \\)-dimensional real space, and \\( f_{\\Theta}(x) \\) is a N-layer MLP with the learnable parameters set \\( \\Theta \\). Denote the output of \\( n \\)-th layer as:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.56, + 0.469, + 0.579 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} ^ {(\\mathbf {n})} = \\sigma (\\mathbf {W} ^ {(\\mathbf {n})} \\mathbf {y} ^ {(\\mathbf {n} - \\mathbf {1})} + \\mathbf {b} ^ {(\\mathbf {n})}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.6, + 0.469, + 0.704 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is an element-wise nonlinear activation function; \\(\\mathbf{W}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times d_{n - 1}}\\) and \\(\\mathbf{b}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n}\\) are the weight and bias for the \\(n\\)-th layer; \\(\\mathbf{y}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n}\\) and \\(\\mathbf{y}^{(\\mathbf{n} - \\mathbf{1})}\\in \\mathbb{R}^{d_{n - 1}}\\) are the output and input of the \\(n\\)-th layer, respectively. For \\(n = N\\), we have that \\(\\mathbf{y}^{(\\mathbf{N})} = \\mathbf{W}^{(\\mathbf{N})}\\mathbf{y}^{(\\mathbf{N} - \\mathbf{1})} + \\mathbf{b}^{(\\mathbf{N})}\\). The MLP parameters set \\(\\Theta = \\{\\mathbf{W}^{(\\mathrm{i})},\\mathbf{b}^{(\\mathrm{i})}\\}_{\\mathrm{i = 1,\\dots,N}}\\) is learned by minimizing the loss with gradient-based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The above idea of INR is memory efficient, and the continuous nature of MLP allows INR to model fine detail that is not limited by the grid resolution. However, during the practical optimization process, gradients of parameters are dominated by the error of low-frequency components. Such a spectral bias hinders the accurate learning pace of MLP. Various modifications, including input feature adjustments [39, 42] and activation function adjustments [13, 32, 34, 35], have been exploited for alleviating the spectral bias issue. In this paper, we show that appropriate reparameterization of MLP is also beneficial for narrowing the gap between the gradient magnitude of high-frequency components and low-frequency components." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.747, + 0.107 + ], + "angle": 0, + "content": "3.2. Fourier reparameterization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.114, + 0.892, + 0.203 + ], + "angle": 0, + "content": "As we have introduced in the previous subsection, the weight matrix in the \\(n\\)-th layer of MLP is denoted as \\(\\mathbf{W}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times d_{n - 1}}\\). Instead of directly calculating the gradient of \\(\\mathbf{W}^{(\\mathbf{n})}\\) respect to the loss function, we reparameterize each row of \\(\\mathbf{W}^{(\\mathbf{n})}\\) as a weighted combination of fixed Fourier bases:" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.203, + 0.892, + 0.22 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} ^ {(\\mathbf {n})} = \\boldsymbol {\\Lambda} ^ {(\\mathbf {n})} \\mathbf {B} ^ {(\\mathbf {n})}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.226, + 0.892, + 0.289 + ], + "angle": 0, + "content": "where \\(\\mathbf{\\Lambda}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times M}\\) are the coefficient matrix, and \\(\\mathbf{B}^{(\\mathbf{n})}\\in \\mathbb{R}^{M\\times d_{n - 1}}\\) are \\(M\\) Fourier bases. Each Fourier basis is achieved by changing the frequency \\(\\omega\\) and phase \\(\\varphi\\) of a cosine function \\(\\cos (\\omega z + \\varphi)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.3, + 0.892, + 0.329 + ], + "angle": 0, + "content": "\\[\nb _ {i j} = \\cos \\left(\\omega_ {i} z _ {j} + \\varphi_ {i}\\right), f o r i = 1, \\dots , M; j = 1, \\dots , d _ {n - 1}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.331, + 0.892, + 0.39 + ], + "angle": 0, + "content": "where \\(\\mathbf{z} = \\{z_{j}\\}_{j = 1,\\dots,d_{n - 1}}\\) is the sampling position sequence. More details will be introduced in section 5.4.3. Generally, we have \\(M\\geq d_{n - 1}\\) which means that we reparameterize the weight matrix with over complete bases." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.392, + 0.892, + 0.466 + ], + "angle": 0, + "content": "Please note that in Eq. 2, each basis is with the same dimension as the input feature \\(\\mathbf{y}^{(n - 1)}\\), which means that our reparameterization scheme firstly projects the input features onto a series of Fourier bases and weighted combines the projection coefficients:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.476, + 0.891, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} ^ {(\\mathbf {n})} = \\sigma \\left(\\boldsymbol {\\Lambda} ^ {(\\mathbf {n})} \\mathbf {B} ^ {(\\mathbf {n})} \\mathbf {y} ^ {(\\mathbf {n} - 1)} + \\mathbf {b} ^ {(\\mathbf {n})}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.505, + 0.892, + 0.657 + ], + "angle": 0, + "content": "In the above equation, \\(\\mathbf{B}^{(\\mathbf{n})}\\) is fixed and we only learn \\(\\Lambda^{(\\mathbf{n})}\\) during the training phase. After training, we combine \\(\\Lambda^{(\\mathbf{n})}\\) and \\(\\mathbf{B}^{(\\mathbf{n})}\\) to form the weight matrix \\(\\mathbf{W}^{(\\mathbf{n})}\\) in the inference. Therefore, our reparameterization approach only adjusts the training dynamic and will not affect the inference process of INR. Moreover, the proposed Fourier reparameterization approach does not affect the input feature space as well as nonlinear activation functions. Our method is compatible with existing techniques, including but not limited to positional encoding [39] and periodic activation functions [35]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.618, + 0.681 + ], + "angle": 0, + "content": "3.3. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.69, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In this subsection, we analyze our reparameterization scheme in the frequency domain. By carefully analyzing the gradients of learning parameters respect to different frequencies, we show that appropriate weight reparameterization provides us with a chance to alleviate the low-frequency bias in the network training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.781, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We start our analysis with the definition of some basic concepts [43]. We denote the Fourier Transform of the target function and the MLP representation of INR at frequency \\( k \\) as: \\( \\mathcal{F}[g](k) \\) and \\( \\mathcal{F}[f_{\\Theta}](k) \\), respectively. Then, the approximation error at frequency \\( k \\) can be naturally achieved by \\( E(k) = \\mathcal{F}[g](k) - \\mathcal{F}[f_{\\Theta}](k) \\). We further define the following notations: \\( E(k) = A(k)e^{i\\theta (k)} \\) and \\( \\mathbb{L}(k) = |E(k)|^2 \\); where \\( A(k) \\) and \\( \\theta (k)\\in [\\pi ,\\pi ] \\) indicate the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25987" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "amplitude and phase of \\( E(k) \\); \\( \\mathbb{L}(k) \\) is the loss component of frequency \\( k \\); \\( |\\cdot| \\) is the norm of the complex number." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.469, + 0.168 + ], + "angle": 0, + "content": "Based on the above definitions, Xu [43] shows that the spectral bias can be reflected on the absolute gradient values of parameters at different frequencies:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.182, + 0.47, + 0.258 + ], + "angle": 0, + "content": "Theorem 1. (Theorem 1 in [43]) Consider a MLP with one hidden layer using tanh function \\(\\sigma(x)\\) as the activation function. For any frequencies \\(k_{1}\\) and \\(k_{2}\\) such that \\(k_{1} > k_{2} > 0\\) and there exist \\(c_{1}, c_{2}\\), such that \\(A(k_{1}) > c_{1} > 0\\), \\(A(k_{1}) < c_{2} < \\infty\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.266, + 0.469, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\lim _ {\\delta \\rightarrow 0} \\frac {\\mu \\left( \\right.\\left\\{ \\right.w _ {j}: \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial \\Theta_ {j l}} \\left. \\right| > \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial \\Theta_ {j l}} \\mid f o r a l l j , l \\left. \\right\\} \\cap B _ {\\delta})}{\\mu \\left(B _ {\\delta}\\right)} = 1, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.47, + 0.363 + ], + "angle": 0, + "content": "where \\(B_{\\delta}\\) is a ball with radius \\(\\delta\\) centered at the origin and \\(\\mu (\\cdot)\\) is the Lebesgue measure of a set and \\(\\Theta_{jl}\\) is a leannable parameter in the parameters set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.469, + 0.499 + ], + "angle": 0, + "content": "Generally, Theorem 1 shows that in the case of one hidden layer MLP, the gradient respect to low-frequency loss \\(\\mathbb{L}(k_2)\\) is almost always larger than the one respect to high-frequency part. Although the condition of one hidden layer MLP is not applicable in most of practical cases, based on recent observations of low-frequency bias [2, 18, 31, 43], the above Theorem 1 inspires us to assume such relationship to MLP with more hidden layers. Then, we could have the following Theorem 2:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.469, + 0.619 + ], + "angle": 0, + "content": "Theorem 2. Given a MLP with multiple hidden layers, reparameterize the weight matrix \\(\\mathbf{W} \\in \\mathbb{R}^{d \\times d}\\) of one hidden layer with a trainable coefficient matrix \\(\\boldsymbol{\\Lambda} \\in \\mathbb{R}^{d \\times M}\\) and the fixed basis matrix \\(\\mathbf{B} \\in \\mathbb{R}^{M \\times d}\\). For any frequencies \\(k_{1}\\) and \\(k_{2}\\) such that \\(k_{1} > k_{2} > 0\\), given any \\(\\epsilon \\geq 0\\) and fixed \\(i\\), for \\(j = 1, 2, \\ldots, M\\), there must exist a set of basis matrices such that" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.624, + 0.469, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial \\lambda_ {i j}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial \\lambda_ {i j}} \\right| \\geq \\max \\left\\{\\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial w _ {i 1}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial w _ {i 1}} \\right|, \\dots , \\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial w _ {i d}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial w _ {i d}} \\right| \\right\\} - \\epsilon , \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.658, + 0.353, + 0.674 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}(i,j) = w_{ij}\\) and \\(\\pmb {\\Lambda}(i,j) = \\lambda_{ij}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.84 + ], + "angle": 0, + "content": "The detailed proof of Theorem 2 can be found in our supplementary file. Theorem 2 implies that reparameterizing MLP weights with appropriate bases is able to enlarge the portion of high-frequency loss components in comparison to low-frequency components, i.e. improving the spectral bias in training MLP. Although the optimal basis for frequency-bias adjustment is related to the training data and we are not able to achieve the optimal basis with negligible efforts, we experimentally find that fixed Fourier basis is able to improve the low-frequency bias and provide better INR for various function approximation tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.292, + 0.864 + ], + "angle": 0, + "content": "3.4. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Basis construction. As we have introduced in section 3.2, we establish Fourier bases with various frequencies and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "phase parameters. We adopt \\(P\\) different phases and \\(2F\\) different frequencies. Concretely, the \\(\\varphi\\) in Eq. 3 varies from 0 to \\(2\\pi (P - 1) / P\\) with step length \\(2\\pi /P\\); for each phase value, we have a group of low-frequency bases with \\(\\omega = \\{1 / F,2 / F,\\dots ,1\\}\\) and a group of high-frequency bases with \\(\\omega = \\{1,2,\\ldots ,F\\}\\). Based on the above basis construction scheme, we could obtain \\(M = 2FP\\) bases. Details of the selected \\(F\\) and \\(P\\) values for different settings will be introduced in the experimental section. We also provide ablation experiments in our supplementary field to analyze the effects of different design choices of \\(F\\) and \\(P\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.892, + 0.469 + ], + "angle": 0, + "content": "Sampling strategy. The cosine basis function used in Eq. 3 is a continuous function. We need to sample values from the continuous function to achieve discrete basis for weight reparameterization. As the number of sampling points is determined by the neuron number of input feature, the only key hyper-parameter during the sampling process is the range of sampling. To reflect characteristics of different frequency bases, we choose the maximum period \\((T_{max} = 2\\pi F)\\) of the adopted Fourier Bases as the sampling range. To maintain the periodicity of bases, uniform sampling is employed. Due to the symmetry of bases, we set the sampling interval as \\([- \\frac{1}{2} T_{max}, \\frac{1}{2} T_{max}]\\). The length of interval will be discussed in our ablation studies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Initialization scheme. Initialization techniques are one of the prerequisites for successfully training a deep neural network. The basic idea of the existing popular initialization strategies [14, 15] is to let the network start in a regime with constant variance between inputs and outputs. While our method reparameterizes the network weights as the fixed Fourier bases and trainable coefficients, initializing the learnable coefficients \\(\\Lambda\\) with existing initialization techniques will deactivate the constant variance requirement. We therefore adjust the initialization strategy for \\(\\Lambda\\). For ReLU activation function [15], we initialize the trainable coefficient matrix \\(\\Lambda^{(\\mathbf{n})}\\) using the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.665, + 0.891, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {i j} ^ {(n)} \\sim U (- \\sqrt {\\frac {6}{M \\sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}, \\sqrt {\\frac {6}{M \\sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.892, + 0.787 + ], + "angle": 0, + "content": "where \\(\\lambda_{ij}^{(n)}, b_{ij}^{(n)}\\) is in the \\(i\\)-th row and \\(j\\)-th column of \\(\\mathbf{\\Lambda}^{(\\mathbf{n})} \\in \\mathbb{R}^{d_n \\times M}\\) and \\(\\mathbf{B}^{(\\mathbf{n})} \\in \\mathbb{R}^{M \\times d_{n-1}}\\), respectively. For SIREN [35], we have the similar initialization scheme. The detailed derivation can be found in our supplementary file." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.797, + 0.891, + 0.833 + ], + "angle": 0, + "content": "4. Experimental Analysis on Simple Function Approximation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We firstly conduct experiments on the simple function approximation task. Thanks to the simplicity of the target function, the behaviour of MLP can be analyzed with various techniques. In the remaining of this section, we firstly" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25988" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.329 + ], + "angle": 0, + "content": "Figure 2. Visualization of simple function. The left side of the first row displays the visualization of the 1D simple function on the \\( x - y \\) coordinate axis. The left side of the second row shows the amplitude of the function in the frequency domain. The right side presents the average loss curve with the shaded area indicating the fluctuation from 100 repetitions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.47, + 0.387 + ], + "angle": 0, + "content": "introduce our experimental settings and then analyze the property of our proposed Fourier reparameterization (FR)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.397, + 0.283, + 0.414 + ], + "angle": 0, + "content": "4.1. Experimental settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.471, + 0.466 + ], + "angle": 0, + "content": "In order to thoroughly analyze the advantage of FR, we establish a 1D function \\( g(x) \\) by combining sine functions of different frequencies:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.477, + 0.47, + 0.508 + ], + "angle": 0, + "content": "\\[\n2 R \\left(\\frac {\\sin (3 \\pi x) + \\sin (5 \\pi x) + \\sin (7 \\pi x) + \\sin (9 \\pi x)}{2}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.625 + ], + "angle": 0, + "content": "where \\( R(\\cdot) \\) is the rounding function for increasing the complexity of approximation. A similar rounded periodic function has been adopted in [43] to analyze the spectral-bias of MLP. A visualization of our adopted 1D function and its spectrum can be found in the first column of Fig. 2. As designed by purpose, four distinct peaks marked by red dots can be observed in the stem plot of the spectrum." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.471, + 0.822 + ], + "angle": 0, + "content": "We utilize a four-hidden-layer MLP to approximate the \\( g(x) \\) with 300 discrete values uniformly sampled in the interval \\([-1,1]\\), where each hidden layer consists of 128 neurons. We conduct experiments on both the ReLU and the periodic activation function Sin. The \\( \\omega_0 \\) in Sin activation function is set as 5 for the pursuit of fast convergence [35]. For our reparameterization approach, we reparameterize the weight matrices between consecutive hidden layers and set \\( F = 64 \\) and \\( P = 16 \\). Therefore, we have \\( M = 2048 \\) bases in total. The four comparison methods are denoted as: MLP+ReLU, MLP+ReLU+FR, MLP+Sin, MLP+Sin+FR. All the methods are trained with Adam optimizer [21] for 10000 iterations with a learning rate 1e-6 and full-batch." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.385, + 0.85 + ], + "angle": 0, + "content": "4.2. Approximation results and analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The convergence curves by different methods can be found in Fig. 2. For both the ReLU and Sin activation function cases, Our FR approach improves the convergence" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.153 + ], + "angle": 0, + "content": "speed as well as approximation error of vanilla MLP. Especially for the naive MLP+ReLU case, training network with our proposed reparameterization method could improve the original training paradigm by a large margin." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.167, + 0.894, + 0.241 + ], + "angle": 0, + "content": "Frequency-specific error analysis. In [43], using Discrete Fourier Transform, Xu et al. compute the relative difference \\(\\Delta_{k}\\) between the target signal and the output of MLP at frequency \\(k\\) and empirically show the low-frequency bias of MLP:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.242, + 0.893, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\Delta_ {k} = \\frac {\\left| \\mathcal {F} _ {D} [ g ] (k) - \\mathcal {F} _ {D} [ f _ {\\Theta} ] (k) \\right|}{\\left| \\mathcal {F} _ {D} [ g ] (k) \\right|}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.895, + 0.436 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_D\\) denotes the Discrete Fourier Transform. We follow [43] and use Eq. 9 to analyze the frequency-specific approximation error after different numbers of iterations. As can be found in Fig. 3, the evolution of frequency-specific error clearly shows the low-frequency bias in network training: the error of low-frequency components generally reduces much faster than that of high-frequency components. The proposed FR method narrows the gap in dropping speed of low-frequency error and high-frequency error, thereby leading to overall faster convergence speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.893, + 0.602 + ], + "angle": 0, + "content": "Neural tangent kernel. Neural tangent kernel (NTK) [18] is a theory to analyze the dynamic training process of neural networks. Tancik et al. [39] have shown that components of the target function that correspond to larger kernel eigenvalues will be learned faster and adopt kernel eigenvalues [5, 33, 39] to analyze the spectral bias. Since the conditions of the standard NTK theory are not applicable to commonly used networks, we follow [1, 45] and utilize the following empirical NTK to analyze the training dynamics of different networks:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.615, + 0.892, + 0.635 + ], + "angle": 0, + "content": "\\[\nk _ {N T K} ^ {\\prime} \\left(x _ {i}, x _ {j}\\right) = J _ {f _ {\\Theta}} \\left(x _ {i}\\right) J _ {f _ {\\Theta}} \\left(x _ {j}\\right) ^ {T}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.693 + ], + "angle": 0, + "content": "where \\( J_{f_\\Theta}(x_i) \\) denotes the Jacobian matrix of the function \\( f_\\Theta \\) at the \\( i \\)-th sample \\( x_i \\) and \\( k_{NTK}'(x_i, x_j) \\) is the element in the \\( i \\)-th row and \\( j \\)-th column of the empirical NTK matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.814 + ], + "angle": 0, + "content": "The first four and the summation of the remaining eigenvalues by different methods are shown in Fig. 4. Consistent with the conclusion of [39], the eigenvalues of \\(\\mathrm{MLP} + \\mathrm{ReLU}\\) decay rapidly, which means the model suffers severe spectral bias during training. While, our FR scheme is able to reduce the percentage of the first eigenvalue and enlarge the other eigenvalues of the empirical NTK matrix, leading to more balanced eigenvalue distribution during training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.892, + 0.849 + ], + "angle": 0, + "content": "5. Experimental Results on Vision Applications" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Implicit neural representation has been utilized in different vision applications. In this section, we evaluate the proposed FR method on different vision applications." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25989" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.09, + 0.27, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.089, + 0.465, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.665, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.089, + 0.862, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.221, + 0.894, + 0.25 + ], + "angle": 0, + "content": "Figure 3. Evolution of frequency-specific approximation error with training iterations of four different methods (x-axis for training step, y-axis for frequency and colormap for relative approximation error)." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.279, + 0.461, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.471, + 0.436 + ], + "angle": 0, + "content": "Figure 4. The distribution of different NTK eigenvalues. 'First' denotes the percentage of the largest eigenvalue, and so on. 'Remain' refers to the percentage of the summation of remaining eigenvalues." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.47, + 0.353, + 0.485 + ], + "angle": 0, + "content": "5.1. 2D Color image approximation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.599 + ], + "angle": 0, + "content": "Natural images are extremely complex functions which simultaneously encompass rich low- and high-frequency components [20]. Single image fitting has become an ideal test bed [34, 35, 42] to evaluate the capability of implicit neural representation. In our experiments, we attempt to parameterize a function \\(\\phi : \\mathbb{R}^2 \\mapsto \\mathbb{R}^3\\), \\(x \\mapsto \\phi(x)\\) that represents a given discrete image in a continuous fashion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We establish MLP with four hidden layers and each hidden layer contains 256 neurons. We conduct experiments on three MLP architectures, i.e. (1) MLP with RLU as the activation function \\((\\mathrm{MLP} + \\mathrm{ReLU})\\), (2) \\(\\mathrm{MLP} + \\mathrm{ReLU}\\) with Fourier positional encoding \\((\\mathrm{MLP} + \\mathrm{ReLU} + \\mathrm{PE})\\) [39], and (3) MLP with Periodic Sin activation function \\((\\mathrm{MLP} + \\mathrm{Sin})\\) [35]. \\(\\mathrm{MLP} + \\mathrm{ReLU} + \\mathrm{PE}\\) and \\(\\mathrm{MLP} + \\mathrm{Sin}\\) represent two important categories of techniques in INR. Experimental results on more activation functions and other input adjustments can be found in our supplementary file. For each MLP architecture, we train baseline model which trains network parameters directly with the standard back-propagation approach and (+FR) model which utilizes our proposed FR scheme in the training phase. We reparameterize the weight matrices between consecutive hidden layers and set \\(F = 128\\), \\(P = 32\\) for all the images in the experiment. We use Adam optimizer to minimize the \\(\\ell_2\\) loss between ground truth pixel values and INR approximations. The MLPs are trained with an initial learning rate of \\(10^{-4}\\) for 3000 iterations, and then we drop the learning rate to \\(10^{-5}\\) for another" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.277, + 0.697, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.374, + 0.667, + 0.385 + ], + "angle": 0, + "content": "MLP+ReLU (17.31dB)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.277, + 0.889, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.374, + 0.865, + 0.386 + ], + "angle": 0, + "content": "MLP+ReLU+FR (18.33dB)" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.386, + 0.697, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.485, + 0.673, + 0.496 + ], + "angle": 0, + "content": "\\(\\mathrm{MLP + RELU + PE}\\) (22.87dB)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.386, + 0.889, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.485, + 0.875, + 0.496 + ], + "angle": 0, + "content": "MLP+ReLU+PE+FR (26.78dB)" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.496, + 0.697, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.595, + 0.66, + 0.606 + ], + "angle": 0, + "content": "MLP+Sin (33.05dB)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.496, + 0.889, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.595, + 0.857, + 0.606 + ], + "angle": 0, + "content": "MLP+Sin+FR (34.64dB)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Figure 5. Visual examples of the 2D color image approximation results (PSNR) by different methods. Detailed experimental settings can be found in section 5.1." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.691, + 0.808, + 0.706 + ], + "angle": 0, + "content": "7000 iterations. Full-batch training is adopted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.892, + 0.827 + ], + "angle": 0, + "content": "In Table 1, we report the PSNR values achieved by different INRs for approximating the first 8 images in the Kodak 24 dataset. More evaluation metrics can be found in our supplementary file. Our FR method is able to improve the approximation accuracy for all the three network architectures. Some visual examples of the learned approximations can be found in Fig. 5. Our FR method enables the network to capture more fine details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.892, + 0.862 + ], + "angle": 0, + "content": "5.2. Representing shapes with signed distance functions" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Representing shapes with differentiable signed distance functions (SDFs) has the advantage of modeling arbitrary" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25990" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 1. Peak signal to noise ratio (PSNR) of 2D color image approximation results by different methods. Detailed experimental settings can be found in section 5.1." + }, + { + "type": "table", + "bbox": [ + 0.125, + 0.129, + 0.846, + 0.23 + ], + "angle": 0, + "content": "
MethodKodim 01Kodim 02Kodim 03Kodim 04Kodim 05Kodim 06Kodim 07Kodim 08Average
MLP + ReLU19.3726.1225.1124.5717.3121.6920.7915.6821.33
MLP + ReLU + FR20.3426.5827.2125.7218.3322.2522.4716.6422.44
MLP + ReLU + PE24.4731.4131.5330.1622.8726.5429.3321.1427.18
MLP + ReLU + PE + FR27.6433.9234.4533.2326.7829.8334.1324.7030.59
MLP + Sin31.5936.5539.5936.6633.0534.1039.9631.0035.31
MLP + Sin + FR33.4538.6839.5837.9634.6434.4539.7632.1636.34
" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.248, + 0.199, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.203, + 0.249, + 0.314, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.249, + 0.429, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.249, + 0.542, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.249, + 0.658, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.249, + 0.772, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.249, + 0.888, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.462, + 0.895, + 0.491 + ], + "angle": 0, + "content": "Figure 6. Visual examples of the shape representation results (IOU) by different methods. More experimental details can be found in section 5.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.673 + ], + "angle": 0, + "content": "topologies [35]. In this section, we evaluate the proposed FR method on the shape representation task. We follow the experimental setting of [34], which sample points over a \\( 512 \\times 512 \\times 512 \\) grid. We establish MLP with two hidden layers and each hidden layer contains 256 neurons. We reparameterize the weight matrices between consecutive hidden layers and set \\( F = 256 \\), \\( P = 8 \\). We use Adam optimizer to minimize the \\( \\ell_2 \\) loss between sampled voxel values and INR approximations. We train all the networks for 200 epochs with an initial learning rate of \\( 5 \\times 10^{-3} \\). The learning rate is reduced exponentially to \\( 5 \\times 10^{-4} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.471, + 0.735 + ], + "angle": 0, + "content": "In Fig. 6, we visualize the shape representation results by different methods, the intersection over union (IOU) metrics are also provided for reference. FR method represents intricate geometric shape with less artifacts and more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.356, + 0.759 + ], + "angle": 0, + "content": "5.3. Learning neural radiance fields" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Learning neural radience fields for view synthesis is also a main application of INR [26, 28, 37]. The main process of the view synthesis task is to reconstruct 3D representation of an object from the given 2D images taken at various given angles. In this section, we evaluate our FR method in this task. The original NeRF and two recent SOTAs by neural networks, i.e. the InstantNGP [28] and the DVGO [37], are adopted. We follow the experimental settings of these works and train the models on the all objects of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.893, + 0.598 + ], + "angle": 0, + "content": "Blender dataset [26] with \\(800 \\times 800\\) resolutions. For the original NeRF, we reparameterize the weight matrices of last three hidden layers with \\(F = 128\\), \\(P = 32\\) and the \"NeRF-pytorch\" codebase [44] is used. The complete results for the InstantNGP and DVGO can be found in our supplementary file." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.659 + ], + "angle": 0, + "content": "In Fig. 7, we show some view synthesis results of the original NeRF. With our proposed FR, the INR is able to capture more details of the complex texture, also representing the more accurate reflection of light." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.662, + 0.651, + 0.679 + ], + "angle": 0, + "content": "5.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.894, + 0.746 + ], + "angle": 0, + "content": "In this part, we conduct ablation studies to analyze our design choices. All the ablation experiments are conducted on the first three images of the Kodak 24 dataset, and the structure of the 2D image fitting task is adopted." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.749, + 0.874, + 0.764 + ], + "angle": 0, + "content": "5.4.1 Weight reparameterization with Fourier basis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In Theorem 2, we show that appropriate bases selection could alleviate the low-frequency bias issue. In this paper, we select fixed Fourier bases to reparameterize our MLP and show its superiority approximation accuracy on several applications. In this section, we conduct experiments to show that the selection of basis plays a crucial role in our approach. We generate random basis from a uniform distribution and denote the model as random reparameterization (RR). Moreover, we also adopt a similar strategy as" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "25991" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.095, + 0.268, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.096, + 0.477, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.096, + 0.698, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.096, + 0.891, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.263, + 0.856, + 0.278 + ], + "angle": 0, + "content": "Figure 7. Visual examples of the view synthesis results (PSNR) by learning neural radiance field with the original NeRF [26]." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.303, + 0.47, + 0.358 + ], + "angle": 0, + "content": "Table 2. Ablation experiments on the reparameterization bases. Our Fourier bases achieve the average approximation results (PSNR) on all the three network architectures. Detailed experimental results can be found in Section 5.4.1." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.37, + 0.462, + 0.499 + ], + "angle": 0, + "content": "
MethodKodim 01Kodim 02Kodim 03Average
MLP+ReLU+RR19.6426.1925.6623.83
MLP+ReLU+RIR20.2226.4826.6724.46
MLP+ReLU+FR20.3426.5827.2124.71
MLP+ReLU+PE+RR27.0532.1633.3830.86
MLP+ReLU+PE+RIR26.9132.0432.8530.60
MLP+ReLU+PE+FR27.6433.9234.4532.00
MLP+Sin+RR34.2837.8430.4834.20
MLP+Sin+RIR25.1928.6127.1226.97
MLP+Sin+FR33.4538.6839.5837.24
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.631 + ], + "angle": 0, + "content": "the existing reparameterization works [11] which updates all the random initialized parameters instead of fixed basis during the training phase, and denote the model as randomly initialized reparameterization (RIR). The average approximation results by different reparameterization schemes are shown in Table 2. The results clearly show that bases play a pivotal role in reparameterized training, and our selected Fourier bases have advantages in 2D image fitting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.236, + 0.649 + ], + "angle": 0, + "content": "5.4.2 Training speed" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.825 + ], + "angle": 0, + "content": "As shown in Fig. 2, in terms of learning iterations, our FR accelerates the convergence speed of network training. While, since our FR will lead to more computations in each training step, we present the detailed training time by different methods. In Table 3, we show the average per epoch training time by different methods in the simple function approximation experiment. The additional time introduced by our FR is not significant. Although it takes an additional \\(17.3\\%\\) time (from \\(2.89 \\times 10^{-3}\\) seconds to \\(3.31 \\times 10^{-3}\\) seconds) for training a MLP + ReLu architecture, our FR could lead to \\(86\\%\\) improvement on accuracy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.317, + 0.862 + ], + "angle": 0, + "content": "5.4.3 Sampling interval analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Another important hyper-parameter for our method is our sampling interval. In this section, we conduct experi" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.303, + 0.893, + 0.344 + ], + "angle": 0, + "content": "Table 3. Average per epoch training time by different methods in the simple function approximation experiment. Detaild experimental results can be found in Section 4.1 and Section 5.4.1." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.348, + 0.898, + 0.386 + ], + "angle": 0, + "content": "
MethodMLP+ReLUMLP+ReLU+FRMLP+SinMLP+Sin+FR
Time (ms)2.893.313.503.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.403, + 0.892, + 0.444 + ], + "angle": 0, + "content": "Table 4. Ablation experiments on sampling intervals. Our method could achieve good results (PSNR) on a wide range of sampling intervals. More experimental details can be found in section 5.4.3." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.446, + 0.88, + 0.484 + ], + "angle": 0, + "content": "
Length (×Tmax)0.10.250.512410
Average23.3424.0724.3824.6224.7124.5323.14
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.637 + ], + "angle": 0, + "content": "ments to analyze the effect of different sampling intervals. Denote the maximum period of the adopted Fourier function as \\( T_{max} \\). We vary the sampling interval from \\( 0.1T_{max} \\) to \\( 10T_{max} \\). The approximation accuracy with different sampling intervals can be found in Table 4. Our method could achieve good results with a wide range of sampling intervals, i.e. \\( 0.5T_{max} \\) to \\( 4T_{max} \\). While sampling points from a very small range fails to represent an entire period for many bases and leads to a performance drop." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.627, + 0.68 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we proposed a novel FR method for advanced INR. We theoretically analyzed the low-frequency bias issue of MLP for INR and show that appropriate network reparameterization is able to alleviate the low-frequency bias in training MLP. Based on our theoretical analysis, we proposed our FR method which learns coefficient matrix of fixed Fourier bases to compose network weights instead of directly learning them from training data. Experiments were conducted on simple function task and real-world vision applications. Our method improved the representation accuracy for a wide range of commonly used INR network architectures. We hope our initial study could inspire future works in adjusting the learning bias of network by advanced network reparameterization." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25992" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] What can linearized neural networks actually say about generalization? Advances in Neural Information Processing Systems, 34:8998-9010, 2021. 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.472, + 0.228 + ], + "angle": 0, + "content": "[2] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S. Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, and Simon Lacoste-Julien. 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Reconstructing continuous distributions of 3d protein structure from cryo-em images. arXiv preprint arXiv:1909.05215, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25994" + } + ] +] \ No newline at end of file diff --git a/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_origin.pdf b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..262f5a23874b92e577aa9bd46de3a0f33798d397 --- /dev/null +++ b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/cb3f94d3-0c17-46df-9543-5d0cd59a45b0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b2c5a4e459950610edf6e9fa74a9da6202ae01731a3853b9fab4a02a9b8d03ea +size 5835715 diff --git a/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/full.md b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/full.md new file mode 100644 index 0000000000000000000000000000000000000000..312a7acac227184c04939b547e12e318c883ff16 --- /dev/null +++ b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/full.md @@ -0,0 +1,351 @@ +# Improved Implicit Neural Representation with Fourier Reparameterized Training + +Kexuan Shi Xingyu Zhou Shuhang Gu* +School of Computer Science and Engineering, UESTC +{kexuanshi712, xy.chous526, shuhanggu}@gmail.com + +# Abstract + +Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data. The codes are available at https://github.com/LabShuHangGU/FR-INR. + +# 1. Introduction + +Recently, a novel signal representation paradigm called implicit neural representation (INR) has gained great attention in the field of computer vision and graphics. The main idea of INR is using multi-layer perceptron (MLP) to parameterize continuous and differentiable functions in an implicit manner. For example, given a gray scale image, INR takes the coordinates of the pixels as inputs to MLP and trains it to output the exact gray values using gradient-based optimization methods. Benefiting from the continuity nature and the expressive power of MLP, a more versatile continuous representation can be learned than traditional dis + +![](images/37a9284f623a1afcbc58158b5110a3f2344f1cdb66c56aadfc27058400b86a51.jpg) +Figure 1. A conceptual illustration of our Fourier reparameterization method. We reparameterize the linear weight $\mathbf{W}$ with a trainable coefficient matrix $\pmb{\Lambda}$ and a fixed Fourier basis matrix $\mathbf{B}$ . More balanced eigenvalue distribution of neural tangent kernel (NTK) matrix implies that our method is able to alleviate the low-frequency bias of deep neural network, and therefore leads to better implicit neural representation. + +crete grid-based methods. Consequently, INR has achieved state-of-the-art performance across a variety of tasks such as signal representation [34, 35], 3D shape reconstruction [3, 6, 30] and novel view synthesis [26, 28, 37]. + +Despite the universal approximation capabilities of MLP which have been proved in [16], obtaining highly accurate INR is not trivial. Specifically, MLP with ReLU activation function often fails to represent the high-frequency components of the signal such as the complex texture information in images and the intricate geometric shapes involved in 3D shape reconstruction. Such tendency of MLP to learn simple patterns of the target function is referred to as spectral bias [31] or low-frequency bias [43]. To improve the performance of INR, great efforts have been made to alleviate or circumvent the spectral bias of MLP. One main category + +of approaches find that the difficulty of learning high frequencies becomes easier by increasing the complexity of the input data manifold [31] and explicitly extracting high-frequency features (for example, positional encoding [26]) to deal with the spectral bias issue. While, inspired by the pioneer work of [35], another main class of approaches exploit advanced activation functions [13, 34, 45] for pursuing more accurate approximation. + +In this paper, we dive into details of the spectral bias issue and prove that reparameterizing weights of MLP with appropriate bases could provide us with a chance to narrow the gap between the magnitude of low-frequency and high-frequency loss, i.e. to alleviate the spectral bias during the training of deep neural networks. We propose a Fourier reparameterization strategy (see Fig. 1) and evaluate our method on simple 1D function approximation task and several real-world vision applications. Experimental results clearly validate our advantages in alleviating the low-frequency bias issue for improving approximation accuracy. Our study provides the literature with a practical reparameterization solution for improving the approximation accuracy of MLP without modifying its network architecture, previously, which so far has only been studied for the convolutional architectures. Moreover, our theoretical analysis sheds new light on the advantage of reparameterized training by connecting it with the spectral bias issue. We hope our study could inspire future works in improving training dynamics of deep neural networks with sophisticated reparameterization methods. + +Our contributions are summarized as follows: + +- We connect network training bias with reparameterization technique and theoretically prove that appropriate reparameterization could alleviate the spectral bias issue by altering the magnitude of gradients from different frequencies. +- We propose a practical reparameterization method for multi-layer perceptron, i.e. the Fourier reparameterization scheme, which could effectively improve the approximation accuracy of implicit neural representation without modifying its network architecture. +- We provide detailed experimental analysis on a wide range of implicit neural representation tasks. Our Fourier reparameterization method allows the improvement of commonly used network architectures and provides an representation with more high-frequency details. + +# 2. Related Work + +Implicit neural representation. The novel signal representation paradigm representing a signal as an implicit continuous function by neural networks has gained lots of attention. Recent works have demonstrated the remarkable performance and memory-efficient property in many representation tasks such as 2D image representa + +tion [13, 22, 32, 34, 35], occupancy volume representation [7, 24, 30, 36], view synthesis [4, 25, 26, 28, 37, 40] and virtual reality [8]. However, the popular activation function ReLU empirically can't achieve the satisfactory performance with vanilla MLP. Therefore, various modifications have been studied. The mainstream modifications can be classified into two aspects. The first aspect focuses on the input domain. Rahaman et al. [31] show that learning high frequency components gets easier with the increasing of the complexity of the input data manifold. Inspired by this phenomenon, Mildenhall et al. [26] use the positional encoding which adopts the sinusoidal mapping of the input features as the new input in the view synthesis and achieve remarkable performance. Zhong et al. [47] also use this method to reconstruct more accurate continuous distributions of 3D protein structure. Recent studies [19, 23, 38] propose to encode input coordinates by learned features. Inspired by this, Xie et al. [42] rearrange the order of input coordinates and obtain more low-frequency components, avoiding confrontation with spectral bias. The second aspect focuses on the activation function. Sitzmann et al. [35] find that using periodic functions, such as the sinusoidal function, as activation functions can achieve remarkable performance in signal fitting. Sinusoidal functions are also explored by Fathony et al. [13] in multiplicative filter networks. Yüce et al. [45] explain the success of the usage of periodic function from a structured dictionary perspective. Inspired by this perspective, Saragadam et al. [35] use a complex Gabor wavelet activation and achieve robust and accurate representations. + +Spectral bias. The term spectral bias [31] also known as the low-frequency bias [43] implies that MLP tends to learn simple patterns of the real data [2] or the low-frequency components of the target function [43]. Arpit et al. [2] first find this phenomenon which has attracted lots of follow up studies. Rahaman et al. [31] exploit the structure of ReLU networks to evaluate its Fourier spectrum and estimate the relationships between the spectral norm of MLP weights and the amplitude of the output of MLP at different frequencies. Xu [43] builds a theoretical framework by Fourier Analysis to decompose gradients in the frequency domain and discusses the distributions of the absolute gradients of the parameters at different frequencies. From the perspective of the neural tangent kernel (NTK) theory [18], components of the target function corresponding to larger kernel eigenvalues will be learned faster [5, 33]. Therefore, Tancik et al. [39] propose to leverage the eigenvalues of the NTK matrix to analyze the spectral bias of MLP. In this paper, we dive into details of the low-frequency bias issue and find that network reparameterization could provide us a chance to alleviate the bias in network training. We analyze our proposed method with the frequency decomposed loss, gradient [43] and NTK theory [39]. Our experiment + +tal results validate our idea of improving spectral bias with weight reparameterization. + +Weight reparameterization. In order to reduce the inference cost of deep learning models [15, 17], weight reparameterization method is proposed by Zagoruyko et al. [46]. Inspired by this work, various reparameterization methods have been explored to train networks with mergeable auxiliary structures [9-11, 27, 29, 41]. Recently, there are still researches which exploit the idea of reparameterization to design network optimizer for advanced training [12]. In this paper, we adopt the idea of weight reparameterization to improve the approximation accuracy of MLP. For the first time, we link the reparameterization technique with network training bias and theoretically prove the possibility of mitigating frequency-bias with reparameterized training. We hope our theoretical analysis could shed new light on network reparameterization and inspire future studies on advanced reparameterization method. + +# 3. Methodology + +# 3.1. The formulation of INR + +The task of INR is to approximate a target function with a multi-layer perceptron (MLP): $f_{\Theta}(x) \approx g(x)$ ; where $g(x) : \mathbb{R}^{d_0} \mapsto \mathbb{R}^{d_N}$ is the target function which defines a mapping from a $d_0$ -dimensional real space to a $d_N$ -dimensional real space, and $f_{\Theta}(x)$ is a N-layer MLP with the learnable parameters set $\Theta$ . Denote the output of $n$ -th layer as: + +$$ +\mathbf {y} ^ {(\mathbf {n})} = \sigma (\mathbf {W} ^ {(\mathbf {n})} \mathbf {y} ^ {(\mathbf {n} - \mathbf {1})} + \mathbf {b} ^ {(\mathbf {n})}), \tag {1} +$$ + +where $\sigma$ is an element-wise nonlinear activation function; $\mathbf{W}^{(\mathbf{n})}\in \mathbb{R}^{d_n\times d_{n - 1}}$ and $\mathbf{b}^{(\mathbf{n})}\in \mathbb{R}^{d_n}$ are the weight and bias for the $n$ -th layer; $\mathbf{y}^{(\mathbf{n})}\in \mathbb{R}^{d_n}$ and $\mathbf{y}^{(\mathbf{n} - \mathbf{1})}\in \mathbb{R}^{d_{n - 1}}$ are the output and input of the $n$ -th layer, respectively. For $n = N$ , we have that $\mathbf{y}^{(\mathbf{N})} = \mathbf{W}^{(\mathbf{N})}\mathbf{y}^{(\mathbf{N} - \mathbf{1})} + \mathbf{b}^{(\mathbf{N})}$ . The MLP parameters set $\Theta = \{\mathbf{W}^{(\mathrm{i})},\mathbf{b}^{(\mathrm{i})}\}_{\mathrm{i = 1,\dots,N}}$ is learned by minimizing the loss with gradient-based methods. + +The above idea of INR is memory efficient, and the continuous nature of MLP allows INR to model fine detail that is not limited by the grid resolution. However, during the practical optimization process, gradients of parameters are dominated by the error of low-frequency components. Such a spectral bias hinders the accurate learning pace of MLP. Various modifications, including input feature adjustments [39, 42] and activation function adjustments [13, 32, 34, 35], have been exploited for alleviating the spectral bias issue. In this paper, we show that appropriate reparameterization of MLP is also beneficial for narrowing the gap between the gradient magnitude of high-frequency components and low-frequency components. + +# 3.2. Fourier reparameterization + +As we have introduced in the previous subsection, the weight matrix in the $n$ -th layer of MLP is denoted as $\mathbf{W}^{(\mathbf{n})}\in \mathbb{R}^{d_n\times d_{n - 1}}$ . Instead of directly calculating the gradient of $\mathbf{W}^{(\mathbf{n})}$ respect to the loss function, we reparameterize each row of $\mathbf{W}^{(\mathbf{n})}$ as a weighted combination of fixed Fourier bases: + +$$ +\mathbf {W} ^ {(\mathbf {n})} = \boldsymbol {\Lambda} ^ {(\mathbf {n})} \mathbf {B} ^ {(\mathbf {n})}, \tag {2} +$$ + +where $\mathbf{\Lambda}^{(\mathbf{n})}\in \mathbb{R}^{d_n\times M}$ are the coefficient matrix, and $\mathbf{B}^{(\mathbf{n})}\in \mathbb{R}^{M\times d_{n - 1}}$ are $M$ Fourier bases. Each Fourier basis is achieved by changing the frequency $\omega$ and phase $\varphi$ of a cosine function $\cos (\omega z + \varphi)$ : + +$$ +b _ {i j} = \cos \left(\omega_ {i} z _ {j} + \varphi_ {i}\right), f o r i = 1, \dots , M; j = 1, \dots , d _ {n - 1}, \tag {3} +$$ + +where $\mathbf{z} = \{z_{j}\}_{j = 1,\dots,d_{n - 1}}$ is the sampling position sequence. More details will be introduced in section 5.4.3. Generally, we have $M\geq d_{n - 1}$ which means that we reparameterize the weight matrix with over complete bases. + +Please note that in Eq. 2, each basis is with the same dimension as the input feature $\mathbf{y}^{(n - 1)}$ , which means that our reparameterization scheme firstly projects the input features onto a series of Fourier bases and weighted combines the projection coefficients: + +$$ +\mathbf {y} ^ {(\mathbf {n})} = \sigma \left(\boldsymbol {\Lambda} ^ {(\mathbf {n})} \mathbf {B} ^ {(\mathbf {n})} \mathbf {y} ^ {(\mathbf {n} - 1)} + \mathbf {b} ^ {(\mathbf {n})}\right). \tag {4} +$$ + +In the above equation, $\mathbf{B}^{(\mathbf{n})}$ is fixed and we only learn $\Lambda^{(\mathbf{n})}$ during the training phase. After training, we combine $\Lambda^{(\mathbf{n})}$ and $\mathbf{B}^{(\mathbf{n})}$ to form the weight matrix $\mathbf{W}^{(\mathbf{n})}$ in the inference. Therefore, our reparameterization approach only adjusts the training dynamic and will not affect the inference process of INR. Moreover, the proposed Fourier reparameterization approach does not affect the input feature space as well as nonlinear activation functions. Our method is compatible with existing techniques, including but not limited to positional encoding [39] and periodic activation functions [35]. + +# 3.3. Discussion + +In this subsection, we analyze our reparameterization scheme in the frequency domain. By carefully analyzing the gradients of learning parameters respect to different frequencies, we show that appropriate weight reparameterization provides us with a chance to alleviate the low-frequency bias in the network training. + +We start our analysis with the definition of some basic concepts [43]. We denote the Fourier Transform of the target function and the MLP representation of INR at frequency $k$ as: $\mathcal{F}[g](k)$ and $\mathcal{F}[f_{\Theta}](k)$ , respectively. Then, the approximation error at frequency $k$ can be naturally achieved by $E(k) = \mathcal{F}[g](k) - \mathcal{F}[f_{\Theta}](k)$ . We further define the following notations: $E(k) = A(k)e^{i\theta (k)}$ and $\mathbb{L}(k) = |E(k)|^2$ ; where $A(k)$ and $\theta (k)\in [\pi ,\pi ]$ indicate the + +amplitude and phase of $E(k)$ ; $\mathbb{L}(k)$ is the loss component of frequency $k$ ; $|\cdot|$ is the norm of the complex number. + +Based on the above definitions, Xu [43] shows that the spectral bias can be reflected on the absolute gradient values of parameters at different frequencies: + +Theorem 1. (Theorem 1 in [43]) Consider a MLP with one hidden layer using tanh function $\sigma(x)$ as the activation function. For any frequencies $k_{1}$ and $k_{2}$ such that $k_{1} > k_{2} > 0$ and there exist $c_{1}, c_{2}$ , such that $A(k_{1}) > c_{1} > 0$ , $A(k_{1}) < c_{2} < \infty$ , we have + +$$ +\lim _ {\delta \rightarrow 0} \frac {\mu \left( \right.\left\{ \right.w _ {j}: \frac {\partial \mathbb {L} \left(k _ {2}\right)}{\partial \Theta_ {j l}} \left. \right| > \frac {\partial \mathbb {L} \left(k _ {1}\right)}{\partial \Theta_ {j l}} \mid f o r a l l j , l \left. \right\} \cap B _ {\delta})}{\mu \left(B _ {\delta}\right)} = 1, \tag {5} +$$ + +where $B_{\delta}$ is a ball with radius $\delta$ centered at the origin and $\mu (\cdot)$ is the Lebesgue measure of a set and $\Theta_{jl}$ is a leannable parameter in the parameters set. + +Generally, Theorem 1 shows that in the case of one hidden layer MLP, the gradient respect to low-frequency loss $\mathbb{L}(k_2)$ is almost always larger than the one respect to high-frequency part. Although the condition of one hidden layer MLP is not applicable in most of practical cases, based on recent observations of low-frequency bias [2, 18, 31, 43], the above Theorem 1 inspires us to assume such relationship to MLP with more hidden layers. Then, we could have the following Theorem 2: + +Theorem 2. Given a MLP with multiple hidden layers, reparameterize the weight matrix $\mathbf{W} \in \mathbb{R}^{d \times d}$ of one hidden layer with a trainable coefficient matrix $\boldsymbol{\Lambda} \in \mathbb{R}^{d \times M}$ and the fixed basis matrix $\mathbf{B} \in \mathbb{R}^{M \times d}$ . For any frequencies $k_{1}$ and $k_{2}$ such that $k_{1} > k_{2} > 0$ , given any $\epsilon \geq 0$ and fixed $i$ , for $j = 1, 2, \ldots, M$ , there must exist a set of basis matrices such that + +$$ +\left| \frac {\partial \mathbb {L} \left(k _ {1}\right)}{\partial \lambda_ {i j}} / \frac {\partial \mathbb {L} \left(k _ {2}\right)}{\partial \lambda_ {i j}} \right| \geq \max \left\{\left| \frac {\partial \mathbb {L} \left(k _ {1}\right)}{\partial w _ {i 1}} / \frac {\partial \mathbb {L} \left(k _ {2}\right)}{\partial w _ {i 1}} \right|, \dots , \left| \frac {\partial \mathbb {L} \left(k _ {1}\right)}{\partial w _ {i d}} / \frac {\partial \mathbb {L} \left(k _ {2}\right)}{\partial w _ {i d}} \right| \right\} - \epsilon , \tag {6} +$$ + +where $\mathbf{W}(i,j) = w_{ij}$ and $\pmb {\Lambda}(i,j) = \lambda_{ij}$ + +The detailed proof of Theorem 2 can be found in our supplementary file. Theorem 2 implies that reparameterizing MLP weights with appropriate bases is able to enlarge the portion of high-frequency loss components in comparison to low-frequency components, i.e. improving the spectral bias in training MLP. Although the optimal basis for frequency-bias adjustment is related to the training data and we are not able to achieve the optimal basis with negligible efforts, we experimentally find that fixed Fourier basis is able to improve the low-frequency bias and provide better INR for various function approximation tasks. + +# 3.4. Implementation details + +Basis construction. As we have introduced in section 3.2, we establish Fourier bases with various frequencies and + +phase parameters. We adopt $P$ different phases and $2F$ different frequencies. Concretely, the $\varphi$ in Eq. 3 varies from 0 to $2\pi (P - 1) / P$ with step length $2\pi /P$ ; for each phase value, we have a group of low-frequency bases with $\omega = \{1 / F,2 / F,\dots ,1\}$ and a group of high-frequency bases with $\omega = \{1,2,\ldots ,F\}$ . Based on the above basis construction scheme, we could obtain $M = 2FP$ bases. Details of the selected $F$ and $P$ values for different settings will be introduced in the experimental section. We also provide ablation experiments in our supplementary field to analyze the effects of different design choices of $F$ and $P$ . + +Sampling strategy. The cosine basis function used in Eq. 3 is a continuous function. We need to sample values from the continuous function to achieve discrete basis for weight reparameterization. As the number of sampling points is determined by the neuron number of input feature, the only key hyper-parameter during the sampling process is the range of sampling. To reflect characteristics of different frequency bases, we choose the maximum period $(T_{max} = 2\pi F)$ of the adopted Fourier Bases as the sampling range. To maintain the periodicity of bases, uniform sampling is employed. Due to the symmetry of bases, we set the sampling interval as $[- \frac{1}{2} T_{max}, \frac{1}{2} T_{max}]$ . The length of interval will be discussed in our ablation studies. + +Initialization scheme. Initialization techniques are one of the prerequisites for successfully training a deep neural network. The basic idea of the existing popular initialization strategies [14, 15] is to let the network start in a regime with constant variance between inputs and outputs. While our method reparameterizes the network weights as the fixed Fourier bases and trainable coefficients, initializing the learnable coefficients $\Lambda$ with existing initialization techniques will deactivate the constant variance requirement. We therefore adjust the initialization strategy for $\Lambda$ . For ReLU activation function [15], we initialize the trainable coefficient matrix $\Lambda^{(\mathbf{n})}$ using the following equation: + +$$ +\lambda_ {i j} ^ {(n)} \sim U (- \sqrt {\frac {6}{M \sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}, \sqrt {\frac {6}{M \sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}), \tag {7} +$$ + +where $\lambda_{ij}^{(n)}, b_{ij}^{(n)}$ is in the $i$ -th row and $j$ -th column of $\mathbf{\Lambda}^{(\mathbf{n})} \in \mathbb{R}^{d_n \times M}$ and $\mathbf{B}^{(\mathbf{n})} \in \mathbb{R}^{M \times d_{n-1}}$ , respectively. For SIREN [35], we have the similar initialization scheme. The detailed derivation can be found in our supplementary file. + +# 4. Experimental Analysis on Simple Function Approximation + +We firstly conduct experiments on the simple function approximation task. Thanks to the simplicity of the target function, the behaviour of MLP can be analyzed with various techniques. In the remaining of this section, we firstly + +![](images/e5a7d4931d31566c870d89948d82492667150d28b2741f230e8a8adfe67eafdd.jpg) +Figure 2. Visualization of simple function. The left side of the first row displays the visualization of the 1D simple function on the $x - y$ coordinate axis. The left side of the second row shows the amplitude of the function in the frequency domain. The right side presents the average loss curve with the shaded area indicating the fluctuation from 100 repetitions. + +introduce our experimental settings and then analyze the property of our proposed Fourier reparameterization (FR). + +# 4.1. Experimental settings + +In order to thoroughly analyze the advantage of FR, we establish a 1D function $g(x)$ by combining sine functions of different frequencies: + +$$ +2 R \left(\frac {\sin (3 \pi x) + \sin (5 \pi x) + \sin (7 \pi x) + \sin (9 \pi x)}{2}\right), \tag {8} +$$ + +where $R(\cdot)$ is the rounding function for increasing the complexity of approximation. A similar rounded periodic function has been adopted in [43] to analyze the spectral-bias of MLP. A visualization of our adopted 1D function and its spectrum can be found in the first column of Fig. 2. As designed by purpose, four distinct peaks marked by red dots can be observed in the stem plot of the spectrum. + +We utilize a four-hidden-layer MLP to approximate the $g(x)$ with 300 discrete values uniformly sampled in the interval $[-1,1]$ , where each hidden layer consists of 128 neurons. We conduct experiments on both the ReLU and the periodic activation function Sin. The $\omega_0$ in Sin activation function is set as 5 for the pursuit of fast convergence [35]. For our reparameterization approach, we reparameterize the weight matrices between consecutive hidden layers and set $F = 64$ and $P = 16$ . Therefore, we have $M = 2048$ bases in total. The four comparison methods are denoted as: MLP+ReLU, MLP+ReLU+FR, MLP+Sin, MLP+Sin+FR. All the methods are trained with Adam optimizer [21] for 10000 iterations with a learning rate 1e-6 and full-batch. + +# 4.2. Approximation results and analysis + +The convergence curves by different methods can be found in Fig. 2. For both the ReLU and Sin activation function cases, Our FR approach improves the convergence + +speed as well as approximation error of vanilla MLP. Especially for the naive MLP+ReLU case, training network with our proposed reparameterization method could improve the original training paradigm by a large margin. + +Frequency-specific error analysis. In [43], using Discrete Fourier Transform, Xu et al. compute the relative difference $\Delta_{k}$ between the target signal and the output of MLP at frequency $k$ and empirically show the low-frequency bias of MLP: + +$$ +\Delta_ {k} = \frac {\left| \mathcal {F} _ {D} [ g ] (k) - \mathcal {F} _ {D} [ f _ {\Theta} ] (k) \right|}{\left| \mathcal {F} _ {D} [ g ] (k) \right|}, \tag {9} +$$ + +where $\mathcal{F}_D$ denotes the Discrete Fourier Transform. We follow [43] and use Eq. 9 to analyze the frequency-specific approximation error after different numbers of iterations. As can be found in Fig. 3, the evolution of frequency-specific error clearly shows the low-frequency bias in network training: the error of low-frequency components generally reduces much faster than that of high-frequency components. The proposed FR method narrows the gap in dropping speed of low-frequency error and high-frequency error, thereby leading to overall faster convergence speed. + +Neural tangent kernel. Neural tangent kernel (NTK) [18] is a theory to analyze the dynamic training process of neural networks. Tancik et al. [39] have shown that components of the target function that correspond to larger kernel eigenvalues will be learned faster and adopt kernel eigenvalues [5, 33, 39] to analyze the spectral bias. Since the conditions of the standard NTK theory are not applicable to commonly used networks, we follow [1, 45] and utilize the following empirical NTK to analyze the training dynamics of different networks: + +$$ +k _ {N T K} ^ {\prime} \left(x _ {i}, x _ {j}\right) = J _ {f _ {\Theta}} \left(x _ {i}\right) J _ {f _ {\Theta}} \left(x _ {j}\right) ^ {T}, \tag {10} +$$ + +where $J_{f_\Theta}(x_i)$ denotes the Jacobian matrix of the function $f_\Theta$ at the $i$ -th sample $x_i$ and $k_{NTK}'(x_i, x_j)$ is the element in the $i$ -th row and $j$ -th column of the empirical NTK matrix. + +The first four and the summation of the remaining eigenvalues by different methods are shown in Fig. 4. Consistent with the conclusion of [39], the eigenvalues of $\mathrm{MLP} + \mathrm{ReLU}$ decay rapidly, which means the model suffers severe spectral bias during training. While, our FR scheme is able to reduce the percentage of the first eigenvalue and enlarge the other eigenvalues of the empirical NTK matrix, leading to more balanced eigenvalue distribution during training. + +# 5. Experimental Results on Vision Applications + +Implicit neural representation has been utilized in different vision applications. In this section, we evaluate the proposed FR method on different vision applications. + +![](images/04bad5a76569d078766dc837ada9cae242894f08f563d7b4ddd4324fcfeace12.jpg) +Figure 3. Evolution of frequency-specific approximation error with training iterations of four different methods (x-axis for training step, y-axis for frequency and colormap for relative approximation error). + +![](images/adc523b7ddd87b4e8dab99eaa8b50c4aa9041f94c151bec86666cd341dc99556.jpg) + +![](images/ffab144ed7c5824bc3dc82369a73a25a51e32183b61632b77a0b403e9811f8e6.jpg) + +![](images/b8eeab4f821bbebc70ec7e0e808550df3f09768fbf1b292ebfc659858186ff61.jpg) + +![](images/2745a81b873537c274b14eb5442dc495511427e2ec79ca91ad9282570e693c9a.jpg) +Figure 4. The distribution of different NTK eigenvalues. 'First' denotes the percentage of the largest eigenvalue, and so on. 'Remain' refers to the percentage of the summation of remaining eigenvalues. + +# 5.1. 2D Color image approximation + +Natural images are extremely complex functions which simultaneously encompass rich low- and high-frequency components [20]. Single image fitting has become an ideal test bed [34, 35, 42] to evaluate the capability of implicit neural representation. In our experiments, we attempt to parameterize a function $\phi : \mathbb{R}^2 \mapsto \mathbb{R}^3$ , $x \mapsto \phi(x)$ that represents a given discrete image in a continuous fashion. + +We establish MLP with four hidden layers and each hidden layer contains 256 neurons. We conduct experiments on three MLP architectures, i.e. (1) MLP with RLU as the activation function $(\mathrm{MLP} + \mathrm{ReLU})$ , (2) $\mathrm{MLP} + \mathrm{ReLU}$ with Fourier positional encoding $(\mathrm{MLP} + \mathrm{ReLU} + \mathrm{PE})$ [39], and (3) MLP with Periodic Sin activation function $(\mathrm{MLP} + \mathrm{Sin})$ [35]. $\mathrm{MLP} + \mathrm{ReLU} + \mathrm{PE}$ and $\mathrm{MLP} + \mathrm{Sin}$ represent two important categories of techniques in INR. Experimental results on more activation functions and other input adjustments can be found in our supplementary file. For each MLP architecture, we train baseline model which trains network parameters directly with the standard back-propagation approach and (+FR) model which utilizes our proposed FR scheme in the training phase. We reparameterize the weight matrices between consecutive hidden layers and set $F = 128$ , $P = 32$ for all the images in the experiment. We use Adam optimizer to minimize the $\ell_2$ loss between ground truth pixel values and INR approximations. The MLPs are trained with an initial learning rate of $10^{-4}$ for 3000 iterations, and then we drop the learning rate to $10^{-5}$ for another + +![](images/8056440c6004256d7d5c64b540d38bbbe618443670606dd6cda1e47cb2da0c7b.jpg) +MLP+ReLU (17.31dB) + +![](images/e022585dc03d901b4790e21bd10d212a7591a407f6218af71153d53129958cc8.jpg) +MLP+ReLU+FR (18.33dB) + +![](images/86c8010ab8d9250342f88673a864807aaeb42186f81ee972e0543c5b119adf0c.jpg) +$\mathrm{MLP + RELU + PE}$ (22.87dB) + +![](images/8f829e54fde690c8b8c1c8a14e631e7e6a5989cd6ea9201ba62dc16858f3ff4d.jpg) +MLP+ReLU+PE+FR (26.78dB) + +![](images/41714c0b5f359bc8e93fe5bd094feabf1cb36c981b363af6f4947f5e711ea401.jpg) +MLP+Sin (33.05dB) +Figure 5. Visual examples of the 2D color image approximation results (PSNR) by different methods. Detailed experimental settings can be found in section 5.1. + +![](images/cee7c8cf590f2834a0c06f73fed328a7f00969f648fa4962568baeee23db3bac.jpg) +MLP+Sin+FR (34.64dB) + +7000 iterations. Full-batch training is adopted. + +In Table 1, we report the PSNR values achieved by different INRs for approximating the first 8 images in the Kodak 24 dataset. More evaluation metrics can be found in our supplementary file. Our FR method is able to improve the approximation accuracy for all the three network architectures. Some visual examples of the learned approximations can be found in Fig. 5. Our FR method enables the network to capture more fine details. + +# 5.2. Representing shapes with signed distance functions + +Representing shapes with differentiable signed distance functions (SDFs) has the advantage of modeling arbitrary + +Table 1. Peak signal to noise ratio (PSNR) of 2D color image approximation results by different methods. Detailed experimental settings can be found in section 5.1. + +
MethodKodim 01Kodim 02Kodim 03Kodim 04Kodim 05Kodim 06Kodim 07Kodim 08Average
MLP + ReLU19.3726.1225.1124.5717.3121.6920.7915.6821.33
MLP + ReLU + FR20.3426.5827.2125.7218.3322.2522.4716.6422.44
MLP + ReLU + PE24.4731.4131.5330.1622.8726.5429.3321.1427.18
MLP + ReLU + PE + FR27.6433.9234.4533.2326.7829.8334.1324.7030.59
MLP + Sin31.5936.5539.5936.6633.0534.1039.9631.0035.31
MLP + Sin + FR33.4538.6839.5837.9634.6434.4539.7632.1636.34
+ +![](images/4dd7c7ae3fdbd8847d3d489e65460bc2449d524c527ad502049aa1916b46e0a8.jpg) +Figure 6. Visual examples of the shape representation results (IOU) by different methods. More experimental details can be found in section 5.2. + +![](images/4707867b958928569ca2aaec759ee58b0f58738bed6787b4e3564e8c0cdb808c.jpg) + +![](images/17c9dc6139c980b609945e77af91d9ace552fb337904c4f22edb8cd7b73afc02.jpg) + +![](images/a45cbbae3e1775210eed36d7ab8119e27262c4d410e981b20bb428afa67a34c2.jpg) + +![](images/7ff578b3a7d1c520dfa49af54201dcc5e84501bffda0e571f49004d08f414a1b.jpg) + +![](images/2d89c63f1477cccb6aa80b81e5a83928053297cf54162b92a667ffa36a181b91.jpg) + +![](images/a7d4ae188babde6f24bcc29e06f14aad292c0fd677200ae1e67d9ee498119325.jpg) + +topologies [35]. In this section, we evaluate the proposed FR method on the shape representation task. We follow the experimental setting of [34], which sample points over a $512 \times 512 \times 512$ grid. We establish MLP with two hidden layers and each hidden layer contains 256 neurons. We reparameterize the weight matrices between consecutive hidden layers and set $F = 256$ , $P = 8$ . We use Adam optimizer to minimize the $\ell_2$ loss between sampled voxel values and INR approximations. We train all the networks for 200 epochs with an initial learning rate of $5 \times 10^{-3}$ . The learning rate is reduced exponentially to $5 \times 10^{-4}$ . + +In Fig. 6, we visualize the shape representation results by different methods, the intersection over union (IOU) metrics are also provided for reference. FR method represents intricate geometric shape with less artifacts and more details. + +# 5.3. Learning neural radiance fields + +Learning neural radience fields for view synthesis is also a main application of INR [26, 28, 37]. The main process of the view synthesis task is to reconstruct 3D representation of an object from the given 2D images taken at various given angles. In this section, we evaluate our FR method in this task. The original NeRF and two recent SOTAs by neural networks, i.e. the InstantNGP [28] and the DVGO [37], are adopted. We follow the experimental settings of these works and train the models on the all objects of the + +Blender dataset [26] with $800 \times 800$ resolutions. For the original NeRF, we reparameterize the weight matrices of last three hidden layers with $F = 128$ , $P = 32$ and the "NeRF-pytorch" codebase [44] is used. The complete results for the InstantNGP and DVGO can be found in our supplementary file. + +In Fig. 7, we show some view synthesis results of the original NeRF. With our proposed FR, the INR is able to capture more details of the complex texture, also representing the more accurate reflection of light. + +# 5.4. Ablation study + +In this part, we conduct ablation studies to analyze our design choices. All the ablation experiments are conducted on the first three images of the Kodak 24 dataset, and the structure of the 2D image fitting task is adopted. + +# 5.4.1 Weight reparameterization with Fourier basis + +In Theorem 2, we show that appropriate bases selection could alleviate the low-frequency bias issue. In this paper, we select fixed Fourier bases to reparameterize our MLP and show its superiority approximation accuracy on several applications. In this section, we conduct experiments to show that the selection of basis plays a crucial role in our approach. We generate random basis from a uniform distribution and denote the model as random reparameterization (RR). Moreover, we also adopt a similar strategy as + +![](images/856039f87444d9fa10f27b78680c75308e95c5ef5f9c758a41a58175c64799ba.jpg) +Figure 7. Visual examples of the view synthesis results (PSNR) by learning neural radiance field with the original NeRF [26]. + +![](images/8cbb54888018e8c9974b3a76b10d1fea04c2b40ae51868d5bd9315afd8f031dc.jpg) + +![](images/811fc93219f4cfd7838784c470a8e91cb2a064803348bf4e24386361b767410b.jpg) + +![](images/8aa6f3e0cce6142410ed519e59e6a48ecb7201e00a461736229febd0c76e156d.jpg) + +Table 2. Ablation experiments on the reparameterization bases. Our Fourier bases achieve the average approximation results (PSNR) on all the three network architectures. Detailed experimental results can be found in Section 5.4.1. + +
MethodKodim 01Kodim 02Kodim 03Average
MLP+ReLU+RR19.6426.1925.6623.83
MLP+ReLU+RIR20.2226.4826.6724.46
MLP+ReLU+FR20.3426.5827.2124.71
MLP+ReLU+PE+RR27.0532.1633.3830.86
MLP+ReLU+PE+RIR26.9132.0432.8530.60
MLP+ReLU+PE+FR27.6433.9234.4532.00
MLP+Sin+RR34.2837.8430.4834.20
MLP+Sin+RIR25.1928.6127.1226.97
MLP+Sin+FR33.4538.6839.5837.24
+ +the existing reparameterization works [11] which updates all the random initialized parameters instead of fixed basis during the training phase, and denote the model as randomly initialized reparameterization (RIR). The average approximation results by different reparameterization schemes are shown in Table 2. The results clearly show that bases play a pivotal role in reparameterized training, and our selected Fourier bases have advantages in 2D image fitting. + +# 5.4.2 Training speed + +As shown in Fig. 2, in terms of learning iterations, our FR accelerates the convergence speed of network training. While, since our FR will lead to more computations in each training step, we present the detailed training time by different methods. In Table 3, we show the average per epoch training time by different methods in the simple function approximation experiment. The additional time introduced by our FR is not significant. Although it takes an additional $17.3\%$ time (from $2.89 \times 10^{-3}$ seconds to $3.31 \times 10^{-3}$ seconds) for training a MLP + ReLu architecture, our FR could lead to $86\%$ improvement on accuracy. + +# 5.4.3 Sampling interval analysis + +Another important hyper-parameter for our method is our sampling interval. In this section, we conduct experi + +Table 3. Average per epoch training time by different methods in the simple function approximation experiment. Detaild experimental results can be found in Section 4.1 and Section 5.4.1. + +
MethodMLP+ReLUMLP+ReLU+FRMLP+SinMLP+Sin+FR
Time (ms)2.893.313.503.59
+ +Table 4. Ablation experiments on sampling intervals. Our method could achieve good results (PSNR) on a wide range of sampling intervals. More experimental details can be found in section 5.4.3. + +
Length (×Tmax)0.10.250.512410
Average23.3424.0724.3824.6224.7124.5323.14
+ +ments to analyze the effect of different sampling intervals. Denote the maximum period of the adopted Fourier function as $T_{max}$ . We vary the sampling interval from $0.1T_{max}$ to $10T_{max}$ . The approximation accuracy with different sampling intervals can be found in Table 4. Our method could achieve good results with a wide range of sampling intervals, i.e. $0.5T_{max}$ to $4T_{max}$ . While sampling points from a very small range fails to represent an entire period for many bases and leads to a performance drop. + +# 6. Conclusions + +In this paper, we proposed a novel FR method for advanced INR. We theoretically analyzed the low-frequency bias issue of MLP for INR and show that appropriate network reparameterization is able to alleviate the low-frequency bias in training MLP. Based on our theoretical analysis, we proposed our FR method which learns coefficient matrix of fixed Fourier bases to compose network weights instead of directly learning them from training data. 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Diner: Disorder-invariant implicit neural representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6143-6152, 2023. 2, 3, 6 +[43] Zhiqin John Xu. Understanding training and generalization in deep learning by fourier analysis, 2018. 1, 2, 3, 4, 5 +[44] Lin Yen-Chen. Nerf-pytorch. https://github.com/yenchenlin/nerf-pytorch/, 2020.7 +[45] Gizem Yüce, Guillermo Ortiz-Jiménez, Beril Besbinar, and Pascal Frossard. A structured dictionary perspective on implicit neural representations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19228-19238, 2022. 2, 5 +[46] Sergey Zagoruyko and Nikos Komodakis. Diracnets: Training very deep neural networks without skip-connections. arXiv preprint arXiv:1706.00388, 2017. 3 +[47] Ellen D Zhong, Tristan Bepler, Joseph H Davis, and Bonnie Berger. Reconstructing continuous distributions of 3d protein structure from cryo-em images. arXiv preprint arXiv:1909.05215, 2019. 2 \ No newline at end of file diff --git a/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/images.zip b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..87a738eb64b11742e016512aec3d27493c0a7a92 --- /dev/null +++ b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:83b797d9ceee0da4ebdc3521690386f16d134cb074127f9ebeab15a3bd27769a +size 512181 diff --git a/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/layout.json b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..45d5fad1276a83a665bb385f02684ee95d0113a1 --- /dev/null +++ b/2024/Improved Implicit Neural Representation with Fourier Reparameterized Training/layout.json @@ -0,0 +1,10340 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 168, + 103, + 425, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 103, + 425, + 140 + ], + "spans": [ + { + "bbox": [ + 168, + 103, + 425, + 140 + ], + "type": "text", + "content": "Improved Implicit Neural Representation with Fourier Reparameterized Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 164, + 161, + 429, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 164, + 161, + 429, + 203 + ], + "spans": [ + { + "bbox": [ + 164, + 161, + 429, + 203 + ], + "type": "text", + "content": "Kexuan Shi Xingyu Zhou Shuhang Gu* \nSchool of Computer Science and Engineering, UESTC \n{kexuanshi712, xy.chous526, shuhanggu}@gmail.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 220, + 192, + 233 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 220, + 192, + 233 + ], + "spans": [ + { + "bbox": [ + 143, + 220, + 192, + 233 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 246, + 290, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 290, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 290, + 521 + ], + "type": "text", + "content": "Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data. The codes are available at https://github.com/LabShuHangGU/FR-INR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 544, + 128, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 128, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 128, + 555 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "type": "text", + "content": "Recently, a novel signal representation paradigm called implicit neural representation (INR) has gained great attention in the field of computer vision and graphics. The main idea of INR is using multi-layer perceptron (MLP) to parameterize continuous and differentiable functions in an implicit manner. For example, given a gray scale image, INR takes the coordinates of the pixels as inputs to MLP and trains it to output the exact gray values using gradient-based optimization methods. Benefiting from the continuity nature and the expressive power of MLP, a more versatile continuous representation can be learned than traditional dis" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 220, + 541, + 434 + ], + "blocks": [ + { + "bbox": [ + 308, + 220, + 541, + 434 + ], + "lines": [ + { + "bbox": [ + 308, + 220, + 541, + 434 + ], + "spans": [ + { + "bbox": [ + 308, + 220, + 541, + 434 + ], + "type": "image", + "image_path": "37a9284f623a1afcbc58158b5110a3f2344f1cdb66c56aadfc27058400b86a51.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "text", + "content": "Figure 1. A conceptual illustration of our Fourier reparameterization method. We reparameterize the linear weight " + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "text", + "content": " with a trainable coefficient matrix " + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\pmb{\\Lambda}" + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "text", + "content": " and a fixed Fourier basis matrix " + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 441, + 545, + 519 + ], + "type": "text", + "content": ". More balanced eigenvalue distribution of neural tangent kernel (NTK) matrix implies that our method is able to alleviate the low-frequency bias of deep neural network, and therefore leads to better implicit neural representation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 533, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 582 + ], + "type": "text", + "content": "crete grid-based methods. Consequently, INR has achieved state-of-the-art performance across a variety of tasks such as signal representation [34, 35], 3D shape reconstruction [3, 6, 30] and novel view synthesis [26, 28, 37]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 714 + ], + "type": "text", + "content": "Despite the universal approximation capabilities of MLP which have been proved in [16], obtaining highly accurate INR is not trivial. Specifically, MLP with ReLU activation function often fails to represent the high-frequency components of the signal such as the complex texture information in images and the intricate geometric shapes involved in 3D shape reconstruction. Such tendency of MLP to learn simple patterns of the target function is referred to as spectral bias [31] or low-frequency bias [43]. To improve the performance of INR, great efforts have been made to alleviate or circumvent the spectral bias of MLP. One main category" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25985" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "of approaches find that the difficulty of learning high frequencies becomes easier by increasing the complexity of the input data manifold [31] and explicitly extracting high-frequency features (for example, positional encoding [26]) to deal with the spectral bias issue. While, inspired by the pioneer work of [35], another main class of approaches exploit advanced activation functions [13, 34, 45] for pursuing more accurate approximation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 418 + ], + "type": "text", + "content": "In this paper, we dive into details of the spectral bias issue and prove that reparameterizing weights of MLP with appropriate bases could provide us with a chance to narrow the gap between the magnitude of low-frequency and high-frequency loss, i.e. to alleviate the spectral bias during the training of deep neural networks. We propose a Fourier reparameterization strategy (see Fig. 1) and evaluate our method on simple 1D function approximation task and several real-world vision applications. Experimental results clearly validate our advantages in alleviating the low-frequency bias issue for improving approximation accuracy. Our study provides the literature with a practical reparameterization solution for improving the approximation accuracy of MLP without modifying its network architecture, previously, which so far has only been studied for the convolutional architectures. Moreover, our theoretical analysis sheds new light on the advantage of reparameterized training by connecting it with the spectral bias issue. We hope our study could inspire future works in improving training dynamics of deep neural networks with sophisticated reparameterization methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 419, + 246, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 419, + 246, + 430 + ], + "spans": [ + { + "bbox": [ + 59, + 419, + 246, + 430 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 432, + 288, + 612 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 432, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 491 + ], + "type": "text", + "content": "- We connect network training bias with reparameterization technique and theoretically prove that appropriate reparameterization could alleviate the spectral bias issue by altering the magnitude of gradients from different frequencies." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 491, + 287, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 551 + ], + "type": "text", + "content": "- We propose a practical reparameterization method for multi-layer perceptron, i.e. the Fourier reparameterization scheme, which could effectively improve the approximation accuracy of implicit neural representation without modifying its network architecture." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 552, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 288, + 612 + ], + "type": "text", + "content": "- We provide detailed experimental analysis on a wide range of implicit neural representation tasks. Our Fourier reparameterization method allows the improvement of commonly used network architectures and provides an representation with more high-frequency details." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 621, + 134, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 134, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 134, + 634 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "Implicit neural representation. The novel signal representation paradigm representing a signal as an implicit continuous function by neural networks has gained lots of attention. Recent works have demonstrated the remarkable performance and memory-efficient property in many representation tasks such as 2D image representa" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 420 + ], + "type": "text", + "content": "tion [13, 22, 32, 34, 35], occupancy volume representation [7, 24, 30, 36], view synthesis [4, 25, 26, 28, 37, 40] and virtual reality [8]. However, the popular activation function ReLU empirically can't achieve the satisfactory performance with vanilla MLP. Therefore, various modifications have been studied. The mainstream modifications can be classified into two aspects. The first aspect focuses on the input domain. Rahaman et al. [31] show that learning high frequency components gets easier with the increasing of the complexity of the input data manifold. Inspired by this phenomenon, Mildenhall et al. [26] use the positional encoding which adopts the sinusoidal mapping of the input features as the new input in the view synthesis and achieve remarkable performance. Zhong et al. [47] also use this method to reconstruct more accurate continuous distributions of 3D protein structure. Recent studies [19, 23, 38] propose to encode input coordinates by learned features. Inspired by this, Xie et al. [42] rearrange the order of input coordinates and obtain more low-frequency components, avoiding confrontation with spectral bias. The second aspect focuses on the activation function. Sitzmann et al. [35] find that using periodic functions, such as the sinusoidal function, as activation functions can achieve remarkable performance in signal fitting. Sinusoidal functions are also explored by Fathony et al. [13] in multiplicative filter networks. Yüce et al. [45] explain the success of the usage of periodic function from a structured dictionary perspective. Inspired by this perspective, Saragadam et al. [35] use a complex Gabor wavelet activation and achieve robust and accurate representations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 431, + 547, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 707 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 707 + ], + "type": "text", + "content": "Spectral bias. The term spectral bias [31] also known as the low-frequency bias [43] implies that MLP tends to learn simple patterns of the real data [2] or the low-frequency components of the target function [43]. Arpit et al. [2] first find this phenomenon which has attracted lots of follow up studies. Rahaman et al. [31] exploit the structure of ReLU networks to evaluate its Fourier spectrum and estimate the relationships between the spectral norm of MLP weights and the amplitude of the output of MLP at different frequencies. Xu [43] builds a theoretical framework by Fourier Analysis to decompose gradients in the frequency domain and discusses the distributions of the absolute gradients of the parameters at different frequencies. From the perspective of the neural tangent kernel (NTK) theory [18], components of the target function corresponding to larger kernel eigenvalues will be learned faster [5, 33]. Therefore, Tancik et al. [39] propose to leverage the eigenvalues of the NTK matrix to analyze the spectral bias of MLP. In this paper, we dive into details of the low-frequency bias issue and find that network reparameterization could provide us a chance to alleviate the bias in network training. We analyze our proposed method with the frequency decomposed loss, gradient [43] and NTK theory [39]. Our experiment" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "25986" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "tal results validate our idea of improving spectral bias with weight reparameterization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 289, + 301 + ], + "type": "text", + "content": "Weight reparameterization. In order to reduce the inference cost of deep learning models [15, 17], weight reparameterization method is proposed by Zagoruyko et al. [46]. Inspired by this work, various reparameterization methods have been explored to train networks with mergeable auxiliary structures [9-11, 27, 29, 41]. Recently, there are still researches which exploit the idea of reparameterization to design network optimizer for advanced training [12]. In this paper, we adopt the idea of weight reparameterization to improve the approximation accuracy of MLP. For the first time, we link the reparameterization technique with network training bias and theoretically prove the possibility of mitigating frequency-bias with reparameterized training. We hope our theoretical analysis could shed new light on network reparameterization and inspire future studies on advanced reparameterization method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 318, + 129, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 318, + 129, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 318, + 129, + 331 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 337, + 181, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 181, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 181, + 348 + ], + "type": "text", + "content": "3.1. The formulation of INR" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": "The task of INR is to approximate a target function with a multi-layer perceptron (MLP): " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "f_{\\Theta}(x) \\approx g(x)" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": "; where " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "g(x) : \\mathbb{R}^{d_0} \\mapsto \\mathbb{R}^{d_N}" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": " is the target function which defines a mapping from a " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "d_0" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": "-dimensional real space to a " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "d_N" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": "-dimensional real space, and " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "f_{\\Theta}(x)" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": " is a N-layer MLP with the learnable parameters set " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": ". Denote the output of " + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 356, + 287, + 428 + ], + "type": "text", + "content": "-th layer as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 443, + 287, + 458 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 443, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 99, + 443, + 287, + 458 + ], + "type": "interline_equation", + "content": "\\mathbf {y} ^ {(\\mathbf {n})} = \\sigma (\\mathbf {W} ^ {(\\mathbf {n})} \\mathbf {y} ^ {(\\mathbf {n} - \\mathbf {1})} + \\mathbf {b} ^ {(\\mathbf {n})}), \\tag {1}", + "image_path": "1ab81a581a42d5dc7477bc1b1eac4c98dd47f0438d8176bdb6867485809b3eba.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": " is an element-wise nonlinear activation function; " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times d_{n - 1}}" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{b}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n}" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": " are the weight and bias for the " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": "-th layer; " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n}" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{(\\mathbf{n} - \\mathbf{1})}\\in \\mathbb{R}^{d_{n - 1}}" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": " are the output and input of the " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": "-th layer, respectively. For " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "n = N" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": ", we have that " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{(\\mathbf{N})} = \\mathbf{W}^{(\\mathbf{N})}\\mathbf{y}^{(\\mathbf{N} - \\mathbf{1})} + \\mathbf{b}^{(\\mathbf{N})}" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": ". The MLP parameters set " + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\Theta = \\{\\mathbf{W}^{(\\mathrm{i})},\\mathbf{b}^{(\\mathrm{i})}\\}_{\\mathrm{i = 1,\\dots,N}}" + }, + { + "bbox": [ + 47, + 475, + 287, + 557 + ], + "type": "text", + "content": " is learned by minimizing the loss with gradient-based methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "content": "The above idea of INR is memory efficient, and the continuous nature of MLP allows INR to model fine detail that is not limited by the grid resolution. However, during the practical optimization process, gradients of parameters are dominated by the error of low-frequency components. Such a spectral bias hinders the accurate learning pace of MLP. Various modifications, including input feature adjustments [39, 42] and activation function adjustments [13, 32, 34, 35], have been exploited for alleviating the spectral bias issue. In this paper, we show that appropriate reparameterization of MLP is also beneficial for narrowing the gap between the gradient magnitude of high-frequency components and low-frequency components." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 457, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 457, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 457, + 84 + ], + "type": "text", + "content": "3.2. Fourier reparameterization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "text", + "content": "As we have introduced in the previous subsection, the weight matrix in the " + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "text", + "content": "-th layer of MLP is denoted as " + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times d_{n - 1}}" + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "text", + "content": ". Instead of directly calculating the gradient of " + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "text", + "content": " respect to the loss function, we reparameterize each row of " + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 90, + 545, + 160 + ], + "type": "text", + "content": " as a weighted combination of fixed Fourier bases:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 384, + 160, + 545, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 160, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 384, + 160, + 545, + 174 + ], + "type": "interline_equation", + "content": "\\mathbf {W} ^ {(\\mathbf {n})} = \\boldsymbol {\\Lambda} ^ {(\\mathbf {n})} \\mathbf {B} ^ {(\\mathbf {n})}, \\tag {2}", + "image_path": "4a23279e8fec48e8fa9284144d7e45c820f198a0052f50fec22695632e5696d7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{\\Lambda}^{(\\mathbf{n})}\\in \\mathbb{R}^{d_n\\times M}" + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": " are the coefficient matrix, and " + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^{(\\mathbf{n})}\\in \\mathbb{R}^{M\\times d_{n - 1}}" + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": " Fourier bases. Each Fourier basis is achieved by changing the frequency " + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": " and phase " + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": " of a cosine function " + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\cos (\\omega z + \\varphi)" + }, + { + "bbox": [ + 305, + 178, + 545, + 228 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 237, + 545, + 260 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 545, + 260 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 545, + 260 + ], + "type": "interline_equation", + "content": "b _ {i j} = \\cos \\left(\\omega_ {i} z _ {j} + \\varphi_ {i}\\right), f o r i = 1, \\dots , M; j = 1, \\dots , d _ {n - 1}, \\tag {3}", + "image_path": "ec107f30fd1e478cc36a563cacf82d99fb1e58120050bbbafb88723c3bf7bd35.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\{z_{j}\\}_{j = 1,\\dots,d_{n - 1}}" + }, + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "type": "text", + "content": " is the sampling position sequence. More details will be introduced in section 5.4.3. Generally, we have " + }, + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "type": "inline_equation", + "content": "M\\geq d_{n - 1}" + }, + { + "bbox": [ + 305, + 262, + 545, + 308 + ], + "type": "text", + "content": " which means that we reparameterize the weight matrix with over complete bases." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 310, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 310, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 310, + 545, + 369 + ], + "type": "text", + "content": "Please note that in Eq. 2, each basis is with the same dimension as the input feature " + }, + { + "bbox": [ + 305, + 310, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{(n - 1)}" + }, + { + "bbox": [ + 305, + 310, + 545, + 369 + ], + "type": "text", + "content": ", which means that our reparameterization scheme firstly projects the input features onto a series of Fourier bases and weighted combines the projection coefficients:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 376, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 376, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 350, + 376, + 545, + 392 + ], + "type": "interline_equation", + "content": "\\mathbf {y} ^ {(\\mathbf {n})} = \\sigma \\left(\\boldsymbol {\\Lambda} ^ {(\\mathbf {n})} \\mathbf {B} ^ {(\\mathbf {n})} \\mathbf {y} ^ {(\\mathbf {n} - 1)} + \\mathbf {b} ^ {(\\mathbf {n})}\\right). \\tag {4}", + "image_path": "2855737baaf3315fdc5dcabf1265cd718bb57b769092b90d3be8afa0c441332c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "content": "In the above equation, " + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "content": " is fixed and we only learn " + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\Lambda^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "content": " during the training phase. After training, we combine " + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\Lambda^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "content": " to form the weight matrix " + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(\\mathbf{n})}" + }, + { + "bbox": [ + 305, + 399, + 545, + 520 + ], + "type": "text", + "content": " in the inference. Therefore, our reparameterization approach only adjusts the training dynamic and will not affect the inference process of INR. Moreover, the proposed Fourier reparameterization approach does not affect the input feature space as well as nonlinear activation functions. Our method is compatible with existing techniques, including but not limited to positional encoding [39] and periodic activation functions [35]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 528, + 378, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 378, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 378, + 539 + ], + "type": "text", + "content": "3.3. Discussion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 546, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 546, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 546, + 545, + 617 + ], + "type": "text", + "content": "In this subsection, we analyze our reparameterization scheme in the frequency domain. By carefully analyzing the gradients of learning parameters respect to different frequencies, we show that appropriate weight reparameterization provides us with a chance to alleviate the low-frequency bias in the network training." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": "We start our analysis with the definition of some basic concepts [43]. We denote the Fourier Transform of the target function and the MLP representation of INR at frequency " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": " as: " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}[g](k)" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}[f_{\\Theta}](k)" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": ", respectively. Then, the approximation error at frequency " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": " can be naturally achieved by " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "E(k) = \\mathcal{F}[g](k) - \\mathcal{F}[f_{\\Theta}](k)" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": ". We further define the following notations: " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "E(k) = A(k)e^{i\\theta (k)}" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{L}(k) = |E(k)|^2" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": "; where " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "A(k)" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\theta (k)\\in [\\pi ,\\pi ]" + }, + { + "bbox": [ + 305, + 618, + 545, + 714 + ], + "type": "text", + "content": " indicate the" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25987" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "amplitude and phase of " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "E(k)" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathbb{L}(k)" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " is the loss component of frequency " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "|\\cdot|" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " is the norm of the complex number." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 133 + ], + "type": "text", + "content": "Based on the above definitions, Xu [43] shows that the spectral bias can be reflected on the absolute gradient values of parameters at different frequencies:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": "Theorem 1. (Theorem 1 in [43]) Consider a MLP with one hidden layer using tanh function " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "\\sigma(x)" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": " as the activation function. For any frequencies " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "k_{1}" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "k_{2}" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "k_{1} > k_{2} > 0" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": " and there exist " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "c_{1}, c_{2}" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "A(k_{1}) > c_{1} > 0" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "inline_equation", + "content": "A(k_{1}) < c_{2} < \\infty" + }, + { + "bbox": [ + 47, + 144, + 287, + 204 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 51, + 210, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 210, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 51, + 210, + 287, + 251 + ], + "type": "interline_equation", + "content": "\\lim _ {\\delta \\rightarrow 0} \\frac {\\mu \\left( \\right.\\left\\{ \\right.w _ {j}: \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial \\Theta_ {j l}} \\left. \\right| > \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial \\Theta_ {j l}} \\mid f o r a l l j , l \\left. \\right\\} \\cap B _ {\\delta})}{\\mu \\left(B _ {\\delta}\\right)} = 1, \\tag {5}", + "image_path": "bf756ed7052216d64923cf0ff78a0f5a3be63fb7dcd09a5c1408fd4e51e5ddd4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "inline_equation", + "content": "B_{\\delta}" + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "content": " is a ball with radius " + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "content": " centered at the origin and " + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\mu (\\cdot)" + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "content": " is the Lebesgue measure of a set and " + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\Theta_{jl}" + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "content": " is a leannable parameter in the parameters set." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 287, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 287, + 395 + ], + "type": "text", + "content": "Generally, Theorem 1 shows that in the case of one hidden layer MLP, the gradient respect to low-frequency loss " + }, + { + "bbox": [ + 46, + 287, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbb{L}(k_2)" + }, + { + "bbox": [ + 46, + 287, + 287, + 395 + ], + "type": "text", + "content": " is almost always larger than the one respect to high-frequency part. Although the condition of one hidden layer MLP is not applicable in most of practical cases, based on recent observations of low-frequency bias [2, 18, 31, 43], the above Theorem 1 inspires us to assume such relationship to MLP with more hidden layers. Then, we could have the following Theorem 2:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": "Theorem 2. Given a MLP with multiple hidden layers, reparameterize the weight matrix " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": " of one hidden layer with a trainable coefficient matrix " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Lambda} \\in \\mathbb{R}^{d \\times M}" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": " and the fixed basis matrix " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{B} \\in \\mathbb{R}^{M \\times d}" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": ". For any frequencies " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "k_{1}" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "k_{2}" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "k_{1} > k_{2} > 0" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": ", given any " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\epsilon \\geq 0" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": " and fixed " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "inline_equation", + "content": "j = 1, 2, \\ldots, M" + }, + { + "bbox": [ + 46, + 407, + 287, + 490 + ], + "type": "text", + "content": ", there must exist a set of basis matrices such that" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 494, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 287, + 520 + ], + "type": "interline_equation", + "content": "\\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial \\lambda_ {i j}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial \\lambda_ {i j}} \\right| \\geq \\max \\left\\{\\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial w _ {i 1}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial w _ {i 1}} \\right|, \\dots , \\left| \\frac {\\partial \\mathbb {L} \\left(k _ {1}\\right)}{\\partial w _ {i d}} / \\frac {\\partial \\mathbb {L} \\left(k _ {2}\\right)}{\\partial w _ {i d}} \\right| \\right\\} - \\epsilon , \\tag {6}", + "image_path": "b7b3ab1ca88b181768d2b7b340ebaeb5872ecb5c394ec069870c7c2724749d27.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 49, + 521, + 216, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 521, + 216, + 533 + ], + "spans": [ + { + "bbox": [ + 49, + 521, + 216, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 49, + 521, + 216, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{W}(i,j) = w_{ij}" + }, + { + "bbox": [ + 49, + 521, + 216, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 49, + 521, + 216, + 533 + ], + "type": "inline_equation", + "content": "\\pmb {\\Lambda}(i,j) = \\lambda_{ij}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 665 + ], + "type": "text", + "content": "The detailed proof of Theorem 2 can be found in our supplementary file. Theorem 2 implies that reparameterizing MLP weights with appropriate bases is able to enlarge the portion of high-frequency loss components in comparison to low-frequency components, i.e. improving the spectral bias in training MLP. Although the optimal basis for frequency-bias adjustment is related to the training data and we are not able to achieve the optimal basis with negligible efforts, we experimentally find that fixed Fourier basis is able to improve the low-frequency bias and provide better INR for various function approximation tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 178, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 178, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 178, + 684 + ], + "type": "text", + "content": "3.4. Implementation details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Basis construction. As we have introduced in section 3.2, we establish Fourier bases with various frequencies and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "phase parameters. We adopt " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " different phases and " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "2F" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " different frequencies. Concretely, the " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " in Eq. 3 varies from 0 to " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "2\\pi (P - 1) / P" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " with step length " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "2\\pi /P" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "; for each phase value, we have a group of low-frequency bases with " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\omega = \\{1 / F,2 / F,\\dots ,1\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " and a group of high-frequency bases with " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\omega = \\{1,2,\\ldots ,F\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ". Based on the above basis construction scheme, we could obtain " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "M = 2FP" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " bases. Details of the selected " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " values for different settings will be introduced in the experimental section. We also provide ablation experiments in our supplementary field to analyze the effects of different design choices of " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "type": "text", + "content": "Sampling strategy. The cosine basis function used in Eq. 3 is a continuous function. We need to sample values from the continuous function to achieve discrete basis for weight reparameterization. As the number of sampling points is determined by the neuron number of input feature, the only key hyper-parameter during the sampling process is the range of sampling. To reflect characteristics of different frequency bases, we choose the maximum period " + }, + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "type": "inline_equation", + "content": "(T_{max} = 2\\pi F)" + }, + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "type": "text", + "content": " of the adopted Fourier Bases as the sampling range. To maintain the periodicity of bases, uniform sampling is employed. Due to the symmetry of bases, we set the sampling interval as " + }, + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "type": "inline_equation", + "content": "[- \\frac{1}{2} T_{max}, \\frac{1}{2} T_{max}]" + }, + { + "bbox": [ + 304, + 216, + 545, + 371 + ], + "type": "text", + "content": ". The length of interval will be discussed in our ablation studies." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "text", + "content": "Initialization scheme. Initialization techniques are one of the prerequisites for successfully training a deep neural network. The basic idea of the existing popular initialization strategies [14, 15] is to let the network start in a regime with constant variance between inputs and outputs. While our method reparameterizes the network weights as the fixed Fourier bases and trainable coefficients, initializing the learnable coefficients " + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "text", + "content": " with existing initialization techniques will deactivate the constant variance requirement. We therefore adjust the initialization strategy for " + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "text", + "content": ". For ReLU activation function [15], we initialize the trainable coefficient matrix " + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\Lambda^{(\\mathbf{n})}" + }, + { + "bbox": [ + 304, + 383, + 545, + 526 + ], + "type": "text", + "content": " using the following equation:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 311, + 526, + 545, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 526, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 311, + 526, + 545, + 564 + ], + "type": "interline_equation", + "content": "\\lambda_ {i j} ^ {(n)} \\sim U (- \\sqrt {\\frac {6}{M \\sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}, \\sqrt {\\frac {6}{M \\sum_ {t = 1} ^ {d _ {n - 1}} b _ {j t} ^ {(n) ^ {2}}}}), \\tag {7}", + "image_path": "0d01f22604e487acfb854ceca6b54703e1af46d060f72cd24271c5ec391d3684.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\lambda_{ij}^{(n)}, b_{ij}^{(n)}" + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "content": " is in the " + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "content": "-th row and " + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "content": "-th column of " + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{\\Lambda}^{(\\mathbf{n})} \\in \\mathbb{R}^{d_n \\times M}" + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^{(\\mathbf{n})} \\in \\mathbb{R}^{M \\times d_{n-1}}" + }, + { + "bbox": [ + 305, + 570, + 545, + 623 + ], + "type": "text", + "content": ", respectively. For SIREN [35], we have the similar initialization scheme. The detailed derivation can be found in our supplementary file." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 631, + 545, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 631, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 305, + 631, + 545, + 659 + ], + "type": "text", + "content": "4. Experimental Analysis on Simple Function Approximation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We firstly conduct experiments on the simple function approximation task. Thanks to the simplicity of the target function, the behaviour of MLP can be analyzed with various techniques. In the remaining of this section, we firstly" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25988" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 286, + 183 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 183 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 183 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 183 + ], + "type": "image", + "image_path": "e5a7d4931d31566c870d89948d82492667150d28b2741f230e8a8adfe67eafdd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 192, + 289, + 260 + ], + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 260 + ], + "type": "text", + "content": "Figure 2. Visualization of simple function. The left side of the first row displays the visualization of the 1D simple function on the " + }, + { + "bbox": [ + 46, + 192, + 289, + 260 + ], + "type": "inline_equation", + "content": "x - y" + }, + { + "bbox": [ + 46, + 192, + 289, + 260 + ], + "type": "text", + "content": " coordinate axis. The left side of the second row shows the amplitude of the function in the frequency domain. The right side presents the average loss curve with the shaded area indicating the fluctuation from 100 repetitions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 281, + 287, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 306 + ], + "type": "text", + "content": "introduce our experimental settings and then analyze the property of our proposed Fourier reparameterization (FR)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 314, + 173, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 314, + 173, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 314, + 173, + 327 + ], + "type": "text", + "content": "4.1. Experimental settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 332, + 288, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 288, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 288, + 369 + ], + "type": "text", + "content": "In order to thoroughly analyze the advantage of FR, we establish a 1D function " + }, + { + "bbox": [ + 46, + 332, + 288, + 369 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 46, + 332, + 288, + 369 + ], + "type": "text", + "content": " by combining sine functions of different frequencies:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 377, + 287, + 402 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 377, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 56, + 377, + 287, + 402 + ], + "type": "interline_equation", + "content": "2 R \\left(\\frac {\\sin (3 \\pi x) + \\sin (5 \\pi x) + \\sin (7 \\pi x) + \\sin (9 \\pi x)}{2}\\right), \\tag {8}", + "image_path": "d0096db036875d70ce41469615fca89b855c4f12333e712b757780cdc1902440.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 411, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 495 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 411, + 287, + 495 + ], + "type": "inline_equation", + "content": "R(\\cdot)" + }, + { + "bbox": [ + 46, + 411, + 287, + 495 + ], + "type": "text", + "content": " is the rounding function for increasing the complexity of approximation. A similar rounded periodic function has been adopted in [43] to analyze the spectral-bias of MLP. A visualization of our adopted 1D function and its spectrum can be found in the first column of Fig. 2. As designed by purpose, four distinct peaks marked by red dots can be observed in the stem plot of the spectrum." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": "We utilize a four-hidden-layer MLP to approximate the " + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "inline_equation", + "content": "g(x)" + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": " with 300 discrete values uniformly sampled in the interval " + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": ", where each hidden layer consists of 128 neurons. We conduct experiments on both the ReLU and the periodic activation function Sin. The " + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "inline_equation", + "content": "\\omega_0" + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": " in Sin activation function is set as 5 for the pursuit of fast convergence [35]. For our reparameterization approach, we reparameterize the weight matrices between consecutive hidden layers and set " + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "inline_equation", + "content": "F = 64" + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "inline_equation", + "content": "P = 16" + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": ". Therefore, we have " + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "inline_equation", + "content": "M = 2048" + }, + { + "bbox": [ + 46, + 495, + 288, + 651 + ], + "type": "text", + "content": " bases in total. The four comparison methods are denoted as: MLP+ReLU, MLP+ReLU+FR, MLP+Sin, MLP+Sin+FR. All the methods are trained with Adam optimizer [21] for 10000 iterations with a learning rate 1e-6 and full-batch." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 659, + 235, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 235, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 235, + 673 + ], + "type": "text", + "content": "4.2. Approximation results and analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "The convergence curves by different methods can be found in Fig. 2. For both the ReLU and Sin activation function cases, Our FR approach improves the convergence" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 546, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 121 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 121 + ], + "type": "text", + "content": "speed as well as approximation error of vanilla MLP. Especially for the naive MLP+ReLU case, training network with our proposed reparameterization method could improve the original training paradigm by a large margin." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "type": "text", + "content": "Frequency-specific error analysis. In [43], using Discrete Fourier Transform, Xu et al. compute the relative difference " + }, + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\Delta_{k}" + }, + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "type": "text", + "content": " between the target signal and the output of MLP at frequency " + }, + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 132, + 547, + 190 + ], + "type": "text", + "content": " and empirically show the low-frequency bias of MLP:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 357, + 191, + 546, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 191, + 546, + 219 + ], + "spans": [ + { + "bbox": [ + 357, + 191, + 546, + 219 + ], + "type": "interline_equation", + "content": "\\Delta_ {k} = \\frac {\\left| \\mathcal {F} _ {D} [ g ] (k) - \\mathcal {F} _ {D} [ f _ {\\Theta} ] (k) \\right|}{\\left| \\mathcal {F} _ {D} [ g ] (k) \\right|}, \\tag {9}", + "image_path": "f964cc1a792e33b4849d8e54dcb2cd3cf4f5367f45e7321b76c582cfe945bb27.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 224, + 547, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 345 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 224, + 547, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_D" + }, + { + "bbox": [ + 304, + 224, + 547, + 345 + ], + "type": "text", + "content": " denotes the Discrete Fourier Transform. We follow [43] and use Eq. 9 to analyze the frequency-specific approximation error after different numbers of iterations. As can be found in Fig. 3, the evolution of frequency-specific error clearly shows the low-frequency bias in network training: the error of low-frequency components generally reduces much faster than that of high-frequency components. The proposed FR method narrows the gap in dropping speed of low-frequency error and high-frequency error, thereby leading to overall faster convergence speed." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 357, + 546, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 546, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 546, + 476 + ], + "type": "text", + "content": "Neural tangent kernel. Neural tangent kernel (NTK) [18] is a theory to analyze the dynamic training process of neural networks. Tancik et al. [39] have shown that components of the target function that correspond to larger kernel eigenvalues will be learned faster and adopt kernel eigenvalues [5, 33, 39] to analyze the spectral bias. Since the conditions of the standard NTK theory are not applicable to commonly used networks, we follow [1, 45] and utilize the following empirical NTK to analyze the training dynamics of different networks:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 487, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 487, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 350, + 487, + 545, + 502 + ], + "type": "interline_equation", + "content": "k _ {N T K} ^ {\\prime} \\left(x _ {i}, x _ {j}\\right) = J _ {f _ {\\Theta}} \\left(x _ {i}\\right) J _ {f _ {\\Theta}} \\left(x _ {j}\\right) ^ {T}, \\tag {10}", + "image_path": "50ee490886d05fb0715025a68ebde197976a0bcaff9c7fb2c7384886a19a8034.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "J_{f_\\Theta}(x_i)" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": " denotes the Jacobian matrix of the function " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "f_\\Theta" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th sample " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "k_{NTK}'(x_i, x_j)" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": " is the element in the " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th row and " + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 513, + 545, + 548 + ], + "type": "text", + "content": "-th column of the empirical NTK matrix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 549, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 644 + ], + "type": "text", + "content": "The first four and the summation of the remaining eigenvalues by different methods are shown in Fig. 4. Consistent with the conclusion of [39], the eigenvalues of " + }, + { + "bbox": [ + 304, + 549, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP} + \\mathrm{ReLU}" + }, + { + "bbox": [ + 304, + 549, + 545, + 644 + ], + "type": "text", + "content": " decay rapidly, which means the model suffers severe spectral bias during training. While, our FR scheme is able to reduce the percentage of the first eigenvalue and enlarge the other eigenvalues of the empirical NTK matrix, leading to more balanced eigenvalue distribution during training." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 658, + 545, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 545, + 672 + ], + "type": "text", + "content": "5. Experimental Results on Vision Applications" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "Implicit neural representation has been utilized in different vision applications. In this section, we evaluate the proposed FR method on different vision applications." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25989" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 71, + 165, + 163 + ], + "blocks": [ + { + "bbox": [ + 54, + 71, + 165, + 163 + ], + "lines": [ + { + "bbox": [ + 54, + 71, + 165, + 163 + ], + "spans": [ + { + "bbox": [ + 54, + 71, + 165, + 163 + ], + "type": "image", + "image_path": "04bad5a76569d078766dc837ada9cae242894f08f563d7b4ddd4324fcfeace12.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 175, + 547, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 547, + 198 + ], + "type": "text", + "content": "Figure 3. Evolution of frequency-specific approximation error with training iterations of four different methods (x-axis for training step, y-axis for frequency and colormap for relative approximation error)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 70, + 284, + 166 + ], + "blocks": [ + { + "bbox": [ + 175, + 70, + 284, + 166 + ], + "lines": [ + { + "bbox": [ + 175, + 70, + 284, + 166 + ], + "spans": [ + { + "bbox": [ + 175, + 70, + 284, + 166 + ], + "type": "image", + "image_path": "adc523b7ddd87b4e8dab99eaa8b50c4aa9041f94c151bec86666cd341dc99556.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 406, + 166 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 406, + 166 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 406, + 166 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 406, + 166 + ], + "type": "image", + "image_path": "ffab144ed7c5824bc3dc82369a73a25a51e32183b61632b77a0b403e9811f8e6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 418, + 70, + 527, + 166 + ], + "blocks": [ + { + "bbox": [ + 418, + 70, + 527, + 166 + ], + "lines": [ + { + "bbox": [ + 418, + 70, + 527, + 166 + ], + "spans": [ + { + "bbox": [ + 418, + 70, + 527, + 166 + ], + "type": "image", + "image_path": "b8eeab4f821bbebc70ec7e0e808550df3f09768fbf1b292ebfc659858186ff61.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 51, + 220, + 282, + 289 + ], + "blocks": [ + { + "bbox": [ + 51, + 220, + 282, + 289 + ], + "lines": [ + { + "bbox": [ + 51, + 220, + 282, + 289 + ], + "spans": [ + { + "bbox": [ + 51, + 220, + 282, + 289 + ], + "type": "image", + "image_path": "2745a81b873537c274b14eb5442dc495511427e2ec79ca91ad9282570e693c9a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 288, + 345 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 288, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 288, + 345 + ], + "type": "text", + "content": "Figure 4. The distribution of different NTK eigenvalues. 'First' denotes the percentage of the largest eigenvalue, and so on. 'Remain' refers to the percentage of the summation of remaining eigenvalues." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 372, + 216, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 216, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 216, + 384 + ], + "type": "text", + "content": "5.1. 2D Color image approximation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "text", + "content": "Natural images are extremely complex functions which simultaneously encompass rich low- and high-frequency components [20]. Single image fitting has become an ideal test bed [34, 35, 42] to evaluate the capability of implicit neural representation. In our experiments, we attempt to parameterize a function " + }, + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "inline_equation", + "content": "\\phi : \\mathbb{R}^2 \\mapsto \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "inline_equation", + "content": "x \\mapsto \\phi(x)" + }, + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "text", + "content": " that represents a given discrete image in a continuous fashion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": "We establish MLP with four hidden layers and each hidden layer contains 256 neurons. We conduct experiments on three MLP architectures, i.e. (1) MLP with RLU as the activation function " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathrm{MLP} + \\mathrm{ReLU})" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": ", (2) " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP} + \\mathrm{ReLU}" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " with Fourier positional encoding " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathrm{MLP} + \\mathrm{ReLU} + \\mathrm{PE})" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " [39], and (3) MLP with Periodic Sin activation function " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathrm{MLP} + \\mathrm{Sin})" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " [35]. " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP} + \\mathrm{ReLU} + \\mathrm{PE}" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP} + \\mathrm{Sin}" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " represent two important categories of techniques in INR. Experimental results on more activation functions and other input adjustments can be found in our supplementary file. For each MLP architecture, we train baseline model which trains network parameters directly with the standard back-propagation approach and (+FR) model which utilizes our proposed FR scheme in the training phase. We reparameterize the weight matrices between consecutive hidden layers and set " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "F = 128" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "P = 32" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " for all the images in the experiment. We use Adam optimizer to minimize the " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " loss between ground truth pixel values and INR approximations. The MLPs are trained with an initial learning rate of " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " for 3000 iterations, and then we drop the learning rate to " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " for another" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 219, + 426, + 297 + ], + "blocks": [ + { + "bbox": [ + 310, + 219, + 426, + 297 + ], + "lines": [ + { + "bbox": [ + 310, + 219, + 426, + 297 + ], + "spans": [ + { + "bbox": [ + 310, + 219, + 426, + 297 + ], + "type": "image", + "image_path": "8056440c6004256d7d5c64b540d38bbbe618443670606dd6cda1e47cb2da0c7b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 296, + 408, + 304 + ], + "lines": [ + { + "bbox": [ + 333, + 296, + 408, + 304 + ], + "spans": [ + { + "bbox": [ + 333, + 296, + 408, + 304 + ], + "type": "text", + "content": "MLP+ReLU (17.31dB)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 426, + 219, + 544, + 297 + ], + "blocks": [ + { + "bbox": [ + 426, + 219, + 544, + 297 + ], + "lines": [ + { + "bbox": [ + 426, + 219, + 544, + 297 + ], + "spans": [ + { + "bbox": [ + 426, + 219, + 544, + 297 + ], + "type": "image", + "image_path": "e022585dc03d901b4790e21bd10d212a7591a407f6218af71153d53129958cc8.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 296, + 529, + 305 + ], + "lines": [ + { + "bbox": [ + 440, + 296, + 529, + 305 + ], + "spans": [ + { + "bbox": [ + 440, + 296, + 529, + 305 + ], + "type": "text", + "content": "MLP+ReLU+FR (18.33dB)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 305, + 426, + 384 + ], + "blocks": [ + { + "bbox": [ + 309, + 305, + 426, + 384 + ], + "lines": [ + { + "bbox": [ + 309, + 305, + 426, + 384 + ], + "spans": [ + { + "bbox": [ + 309, + 305, + 426, + 384 + ], + "type": "image", + "image_path": "86c8010ab8d9250342f88673a864807aaeb42186f81ee972e0543c5b119adf0c.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 384, + 411, + 392 + ], + "lines": [ + { + "bbox": [ + 323, + 384, + 411, + 392 + ], + "spans": [ + { + "bbox": [ + 323, + 384, + 411, + 392 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP + RELU + PE}" + }, + { + "bbox": [ + 323, + 384, + 411, + 392 + ], + "type": "text", + "content": " (22.87dB)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 426, + 305, + 544, + 384 + ], + "blocks": [ + { + "bbox": [ + 426, + 305, + 544, + 384 + ], + "lines": [ + { + "bbox": [ + 426, + 305, + 544, + 384 + ], + "spans": [ + { + "bbox": [ + 426, + 305, + 544, + 384 + ], + "type": "image", + "image_path": "8f829e54fde690c8b8c1c8a14e631e7e6a5989cd6ea9201ba62dc16858f3ff4d.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 433, + 384, + 535, + 392 + ], + "lines": [ + { + "bbox": [ + 433, + 384, + 535, + 392 + ], + "spans": [ + { + "bbox": [ + 433, + 384, + 535, + 392 + ], + "type": "text", + "content": "MLP+ReLU+PE+FR (26.78dB)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 309, + 392, + 426, + 471 + ], + "blocks": [ + { + "bbox": [ + 309, + 392, + 426, + 471 + ], + "lines": [ + { + "bbox": [ + 309, + 392, + 426, + 471 + ], + "spans": [ + { + "bbox": [ + 309, + 392, + 426, + 471 + ], + "type": "image", + "image_path": "41714c0b5f359bc8e93fe5bd094feabf1cb36c981b363af6f4947f5e711ea401.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 471, + 403, + 479 + ], + "lines": [ + { + "bbox": [ + 337, + 471, + 403, + 479 + ], + "spans": [ + { + "bbox": [ + 337, + 471, + 403, + 479 + ], + "type": "text", + "content": "MLP+Sin (33.05dB)" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 490, + 545, + 523 + ], + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 523 + ], + "type": "text", + "content": "Figure 5. Visual examples of the 2D color image approximation results (PSNR) by different methods. Detailed experimental settings can be found in section 5.1." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 426, + 392, + 544, + 471 + ], + "blocks": [ + { + "bbox": [ + 426, + 392, + 544, + 471 + ], + "lines": [ + { + "bbox": [ + 426, + 392, + 544, + 471 + ], + "spans": [ + { + "bbox": [ + 426, + 392, + 544, + 471 + ], + "type": "image", + "image_path": "cee7c8cf590f2834a0c06f73fed328a7f00969f648fa4962568baeee23db3bac.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 471, + 524, + 479 + ], + "lines": [ + { + "bbox": [ + 443, + 471, + 524, + 479 + ], + "spans": [ + { + "bbox": [ + 443, + 471, + 524, + 479 + ], + "type": "text", + "content": "MLP+Sin+FR (34.64dB)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 547, + 494, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 494, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 494, + 559 + ], + "type": "text", + "content": "7000 iterations. Full-batch training is adopted." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 559, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 654 + ], + "type": "text", + "content": "In Table 1, we report the PSNR values achieved by different INRs for approximating the first 8 images in the Kodak 24 dataset. More evaluation metrics can be found in our supplementary file. Our FR method is able to improve the approximation accuracy for all the three network architectures. Some visual examples of the learned approximations can be found in Fig. 5. Our FR method enables the network to capture more fine details." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 659, + 545, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 545, + 682 + ], + "type": "text", + "content": "5.2. Representing shapes with signed distance functions" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Representing shapes with differentiable signed distance functions (SDFs) has the advantage of modeling arbitrary" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25990" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 76, + 102, + 517, + 182 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. Peak signal to noise ratio (PSNR) of 2D color image approximation results by different methods. Detailed experimental settings can be found in section 5.1." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 76, + 102, + 517, + 182 + ], + "lines": [ + { + "bbox": [ + 76, + 102, + 517, + 182 + ], + "spans": [ + { + "bbox": [ + 76, + 102, + 517, + 182 + ], + "type": "table", + "html": "
MethodKodim 01Kodim 02Kodim 03Kodim 04Kodim 05Kodim 06Kodim 07Kodim 08Average
MLP + ReLU19.3726.1225.1124.5717.3121.6920.7915.6821.33
MLP + ReLU + FR20.3426.5827.2125.7218.3322.2522.4716.6422.44
MLP + ReLU + PE24.4731.4131.5330.1622.8726.5429.3321.1427.18
MLP + ReLU + PE + FR27.6433.9234.4533.2326.7829.8334.1324.7030.59
MLP + Sin31.5936.5539.5936.6633.0534.1039.9631.0035.31
MLP + Sin + FR33.4538.6839.5837.9634.6434.4539.7632.1636.34
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More experimental details can be found in section 5.2." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 124, + 197, + 192, + 353 + ], + "blocks": [ + { + "bbox": [ + 124, + 197, + 192, + 353 + ], + "lines": [ + { + "bbox": [ + 124, + 197, + 192, + 353 + ], + "spans": [ + { + "bbox": [ + 124, + 197, + 192, + 353 + ], + "type": "image", + "image_path": "4707867b958928569ca2aaec759ee58b0f58738bed6787b4e3564e8c0cdb808c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 194, + 197, + 262, + 353 + ], + "blocks": [ + { + "bbox": [ + 194, + 197, + 262, + 353 + ], + "lines": [ + { + "bbox": [ + 194, + 197, + 262, + 353 + ], + "spans": [ + { + "bbox": [ + 194, + 197, + 262, + 353 + ], + "type": "image", + "image_path": "17c9dc6139c980b609945e77af91d9ace552fb337904c4f22edb8cd7b73afc02.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 267, + 197, + 331, + 353 + ], + "blocks": [ + { + "bbox": [ + 267, + 197, + 331, + 353 + ], + "lines": [ + { + "bbox": [ + 267, + 197, + 331, + 353 + ], + "spans": [ + { + "bbox": [ + 267, + 197, + 331, + 353 + ], + "type": "image", + "image_path": "a45cbbae3e1775210eed36d7ab8119e27262c4d410e981b20bb428afa67a34c2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 334, + 197, + 402, + 353 + ], + "blocks": [ + { + "bbox": [ + 334, + 197, + 402, + 353 + ], + "lines": [ + { + "bbox": [ + 334, + 197, + 402, + 353 + ], + "spans": [ + { + "bbox": [ + 334, + 197, + 402, + 353 + ], + "type": "image", + "image_path": "7ff578b3a7d1c520dfa49af54201dcc5e84501bffda0e571f49004d08f414a1b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 405, + 197, + 472, + 353 + ], + "blocks": [ + { + "bbox": [ + 405, + 197, + 472, + 353 + ], + "lines": [ + { + "bbox": [ + 405, + 197, + 472, + 353 + ], + "spans": [ + { + "bbox": [ + 405, + 197, + 472, + 353 + ], + "type": "image", + "image_path": "2d89c63f1477cccb6aa80b81e5a83928053297cf54162b92a667ffa36a181b91.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 475, + 197, + 543, + 353 + ], + "blocks": [ + { + "bbox": [ + 475, + 197, + 543, + 353 + ], + "lines": [ + { + "bbox": [ + 475, + 197, + 543, + 353 + ], + "spans": [ + { + "bbox": [ + 475, + 197, + 543, + 353 + ], + "type": "image", + "image_path": "a7d4ae188babde6f24bcc29e06f14aad292c0fd677200ae1e67d9ee498119325.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": "topologies [35]. In this section, we evaluate the proposed FR method on the shape representation task. We follow the experimental setting of [34], which sample points over a " + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "inline_equation", + "content": "512 \\times 512 \\times 512" + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": " grid. We establish MLP with two hidden layers and each hidden layer contains 256 neurons. We reparameterize the weight matrices between consecutive hidden layers and set " + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "inline_equation", + "content": "F = 256" + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "inline_equation", + "content": "P = 8" + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": ". We use Adam optimizer to minimize the " + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": " loss between sampled voxel values and INR approximations. We train all the networks for 200 epochs with an initial learning rate of " + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": ". The learning rate is reduced exponentially to " + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 401, + 287, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "content": "In Fig. 6, we visualize the shape representation results by different methods, the intersection over union (IOU) metrics are also provided for reference. FR method represents intricate geometric shape with less artifacts and more details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 587, + 217, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 217, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 217, + 601 + ], + "type": "text", + "content": "5.3. Learning neural radiance fields" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Learning neural radience fields for view synthesis is also a main application of INR [26, 28, 37]. The main process of the view synthesis task is to reconstruct 3D representation of an object from the given 2D images taken at various given angles. In this section, we evaluate our FR method in this task. The original NeRF and two recent SOTAs by neural networks, i.e. the InstantNGP [28] and the DVGO [37], are adopted. We follow the experimental settings of these works and train the models on the all objects of the" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "text", + "content": "Blender dataset [26] with " + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "text", + "content": " resolutions. For the original NeRF, we reparameterize the weight matrices of last three hidden layers with " + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "inline_equation", + "content": "F = 128" + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "inline_equation", + "content": "P = 32" + }, + { + "bbox": [ + 304, + 401, + 546, + 473 + ], + "type": "text", + "content": " and the \"NeRF-pytorch\" codebase [44] is used. The complete results for the InstantNGP and DVGO can be found in our supplementary file." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": "In Fig. 7, we show some view synthesis results of the original NeRF. With our proposed FR, the INR is able to capture more details of the complex texture, also representing the more accurate reflection of light." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 524, + 398, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 398, + 537 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 398, + 537 + ], + "type": "text", + "content": "5.4. Ablation study" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 542, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 547, + 590 + ], + "type": "text", + "content": "In this part, we conduct ablation studies to analyze our design choices. All the ablation experiments are conducted on the first three images of the Kodak 24 dataset, and the structure of the 2D image fitting task is adopted." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 593, + 534, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 593, + 534, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 593, + 534, + 605 + ], + "type": "text", + "content": "5.4.1 Weight reparameterization with Fourier basis" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "In Theorem 2, we show that appropriate bases selection could alleviate the low-frequency bias issue. In this paper, we select fixed Fourier bases to reparameterize our MLP and show its superiority approximation accuracy on several applications. In this section, we conduct experiments to show that the selection of basis plays a crucial role in our approach. We generate random basis from a uniform distribution and denote the model as random reparameterization (RR). Moreover, we also adopt a similar strategy as" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "25991" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 75, + 164, + 199 + ], + "blocks": [ + { + "bbox": [ + 50, + 75, + 164, + 199 + ], + "lines": [ + { + "bbox": [ + 50, + 75, + 164, + 199 + ], + "spans": [ + { + "bbox": [ + 50, + 75, + 164, + 199 + ], + "type": "image", + "image_path": "856039f87444d9fa10f27b78680c75308e95c5ef5f9c758a41a58175c64799ba.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 208, + 523, + 220 + ], + "lines": [ + { + "bbox": [ + 68, + 208, + 523, + 220 + ], + "spans": [ + { + "bbox": [ + 68, + 208, + 523, + 220 + ], + "type": "text", + "content": "Figure 7. Visual examples of the view synthesis results (PSNR) by learning neural radiance field with the original NeRF [26]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 176, + 76, + 291, + 199 + ], + "blocks": [ + { + "bbox": [ + 176, + 76, + 291, + 199 + ], + "lines": [ + { + "bbox": [ + 176, + 76, + 291, + 199 + ], + "spans": [ + { + "bbox": [ + 176, + 76, + 291, + 199 + ], + "type": "image", + "image_path": "8cbb54888018e8c9974b3a76b10d1fea04c2b40ae51868d5bd9315afd8f031dc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 311, + 76, + 427, + 199 + ], + "blocks": [ + { + "bbox": [ + 311, + 76, + 427, + 199 + ], + "lines": [ + { + "bbox": [ + 311, + 76, + 427, + 199 + ], + "spans": [ + { + "bbox": [ + 311, + 76, + 427, + 199 + ], + "type": "image", + "image_path": "811fc93219f4cfd7838784c470a8e91cb2a064803348bf4e24386361b767410b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 429, + 76, + 545, + 199 + ], + "blocks": [ + { + "bbox": [ + 429, + 76, + 545, + 199 + ], + "lines": [ + { + "bbox": [ + 429, + 76, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 429, + 76, + 545, + 199 + ], + "type": "image", + "image_path": "8aa6f3e0cce6142410ed519e59e6a48ecb7201e00a461736229febd0c76e156d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 49, + 293, + 282, + 395 + ], + "blocks": [ + { + "bbox": [ + 46, + 239, + 287, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 283 + ], + "type": "text", + "content": "Table 2. Ablation experiments on the reparameterization bases. Our Fourier bases achieve the average approximation results (PSNR) on all the three network architectures. Detailed experimental results can be found in Section 5.4.1." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 293, + 282, + 395 + ], + "lines": [ + { + "bbox": [ + 49, + 293, + 282, + 395 + ], + "spans": [ + { + "bbox": [ + 49, + 293, + 282, + 395 + ], + "type": "table", + "html": "
MethodKodim 01Kodim 02Kodim 03Average
MLP+ReLU+RR19.6426.1925.6623.83
MLP+ReLU+RIR20.2226.4826.6724.46
MLP+ReLU+FR20.3426.5827.2124.71
MLP+ReLU+PE+RR27.0532.1633.3830.86
MLP+ReLU+PE+RIR26.9132.0432.8530.60
MLP+ReLU+PE+FR27.6433.9234.4532.00
MLP+Sin+RR34.2837.8430.4834.20
MLP+Sin+RIR25.1928.6127.1226.97
MLP+Sin+FR33.4538.6839.5837.24
", + "image_path": "53360a06352f0c02bddc7f770f87713f802c34abbf1850592ed04fcfd1ebceaa.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 402, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 499 + ], + "type": "text", + "content": "the existing reparameterization works [11] which updates all the random initialized parameters instead of fixed basis during the training phase, and denote the model as randomly initialized reparameterization (RIR). The average approximation results by different reparameterization schemes are shown in Table 2. The results clearly show that bases play a pivotal role in reparameterized training, and our selected Fourier bases have advantages in 2D image fitting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 502, + 144, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 144, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 144, + 514 + ], + "type": "text", + "content": "5.4.2 Training speed" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": "As shown in Fig. 2, in terms of learning iterations, our FR accelerates the convergence speed of network training. While, since our FR will lead to more computations in each training step, we present the detailed training time by different methods. In Table 3, we show the average per epoch training time by different methods in the simple function approximation experiment. The additional time introduced by our FR is not significant. Although it takes an additional " + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "inline_equation", + "content": "17.3\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": " time (from " + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "inline_equation", + "content": "2.89 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": " seconds to " + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "inline_equation", + "content": "3.31 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": " seconds) for training a MLP + ReLu architecture, our FR could lead to " + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "inline_equation", + "content": "86\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": " improvement on accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 670, + 194, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 194, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 194, + 682 + ], + "type": "text", + "content": "5.4.3 Sampling interval analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Another important hyper-parameter for our method is our sampling interval. In this section, we conduct experi" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 275, + 549, + 305 + ], + "blocks": [ + { + "bbox": [ + 305, + 239, + 546, + 272 + ], + "lines": [ + { + "bbox": [ + 305, + 239, + 546, + 272 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 546, + 272 + ], + "type": "text", + "content": "Table 3. Average per epoch training time by different methods in the simple function approximation experiment. Detaild experimental results can be found in Section 4.1 and Section 5.4.1." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 275, + 549, + 305 + ], + "lines": [ + { + "bbox": [ + 307, + 275, + 549, + 305 + ], + "spans": [ + { + "bbox": [ + 307, + 275, + 549, + 305 + ], + "type": "table", + "html": "
MethodMLP+ReLUMLP+ReLU+FRMLP+SinMLP+Sin+FR
Time (ms)2.893.313.503.59
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Length (×Tmax)0.10.250.512410
Average23.3424.0724.3824.6224.7124.5323.14
", + "image_path": "f46ccb759ad0e3d77549fb7509ce169667d896827f07da8db2fcc70229eaca6e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "content": "ments to analyze the effect of different sampling intervals. Denote the maximum period of the adopted Fourier function as " + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "inline_equation", + "content": "T_{max}" + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "content": ". We vary the sampling interval from " + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "inline_equation", + "content": "0.1T_{max}" + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "inline_equation", + "content": "10T_{max}" + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "content": ". The approximation accuracy with different sampling intervals can be found in Table 4. Our method could achieve good results with a wide range of sampling intervals, i.e. " + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "inline_equation", + "content": "0.5T_{max}" + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "inline_equation", + "content": "4T_{max}" + }, + { + "bbox": [ + 304, + 396, + 545, + 504 + ], + "type": "text", + "content": ". While sampling points from a very small range fails to represent an entire period for many bases and leads to a performance drop." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 526, + 383, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 383, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 383, + 538 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we proposed a novel FR method for advanced INR. We theoretically analyzed the low-frequency bias issue of MLP for INR and show that appropriate network reparameterization is able to alleviate the low-frequency bias in training MLP. Based on our theoretical analysis, we proposed our FR method which learns coefficient matrix of fixed Fourier bases to compose network weights instead of directly learning them from training data. Experiments were conducted on simple function task and real-world vision applications. Our method improved the representation accuracy for a wide range of commonly used INR network architectures. We hope our initial study could inspire future works in adjusting the learning bias of network by advanced network reparameterization." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25992" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] What can linearized neural networks actually say about generalization? 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However, existing self-trained TTA methods often face the challenges of unreliable pseudo-labels and unstable model optimization. In this paper, we propose an Improved Self-Training (IST) approach, which addresses these challenges by enhancing the pseudo-label quality and stabilizing the adaptation process. Specifically, we use a simple augmentation strategy to generate multiple views of each test sample, and construct a graph structure to correct the pseudo-labels based on the similarity of the latent features. Moreover, we adopt a parameter moving average scheme to smooth the model updates and prevent catastrophic forgetting. Instead of using a model with fixed label space, we explore the adaptability of the foundation model CLIP to various downstream tasks at test time. Extensive experiments on various benchmarks show that IST can achieve significant and consistent improvements over the existing TTA methods in classification, detection, and segmentation tasks.", + "bbox": [ + 75, + 300, + 473, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 632, + 209, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep Neural Networks have performed superiorly in a broad scope of tasks, and exhibit surprising zero-shot generalization capabilities. However, in practical applications, behavior decline may occur owing to the distribution shifts of unknown domains, which leads to laborious efforts in data collection and model retraining. To address this issue, Test-Time Adaptation (TTA), aims to adapt the model to the target domain at test time, has emerged as a promising paradigm of increasing attention and research [19, 29, 30].", + "bbox": [ + 75, + 657, + 468, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Early methods of TTA [22, 27, 30, 32] explore adapting the activation statistics and updating the affine transformation parameters of batch normalization layers to mitigate the distribution shifts from clean to corrupted images. These approaches are easily scalable to deep neural networks with different architectures, but their performance is often confined to specific ranges of distribution shifts due to the lim", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/edec926d0ab0ee9b0823530bff93a056de96d6fc33cd1af5141c71389f1adb3c.jpg", + "image_caption": [ + "Figure 1. An illustration of test-time adaptation. The approach employs source models from a model zoo, where the source data is unknown. Source models adapt to target domains using one batch of test samples at a time. Self-training is a key component for updating models and providing more accurate online predictions." + ], + "image_footnote": [], + "bbox": [ + 521, + 265, + 874, + 434 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ited adaptive capacity of batch normalization [2]. A series of works [4, 8, 20, 29] leverage self-supervised learning for test-time training (TTT) to update the model parameters before making predictions, which is conditional on having correlated gradients between the loss functions of the auxiliary and main tasks. However, an inappropriate pretext task may be detrimental to the learned model [20]. Moreover, although TTT is not restricted by the type of main task, it typically requires modifying the training process to accommodate a self-supervised task, which increases the cost of applying TTT to pre-trained models [36].", + "bbox": [ + 496, + 522, + 893, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another line of research seeks to utilize the predictions of the model itself as pseudo-labels and re-train the model, which is known as the self-training strategy. Owing to the poor calibration of neural networks [10], pseudo-labels generated by the source model may be inaccurate and noisy for target data. Liang, et al. [19] propose to attain class-wise prototypes by clustering and further obtain cleaner pseudolabels. Recent works [3, 18, 28, 31, 35] suggest performing different data augmentations on a test sample to improve the model's prediction. On the other hand, some works [3, 24, 31, 32] focus on stabilizing the adaptation procedure at test time by adopting active selection, re-weighting strategy, or knowledge distillation. Generally, self-training-based approaches make no strong assumptions about distrib", + "bbox": [ + 496, + 689, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23701", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "bution shifts and types of task, thus they are more ubiquitous for real-world applications. However, existing methods still suffer from the following limitations: 1) Test-time augmentation may degrade performance for voluminous and aggregated categories, 2) Pseudo-label correction has not fully exploited the model's intermediate representations of the target domain. 3) Error accumulation and catastrophic forgetting may occur during the adaptation process.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we aim to address the above issues by analyzing the key components of self-training, i.e., pseudolabel generation, correction, and model optimization. We challenge the task of fully test-time adaptation [30], which supposes that any information about source data is unavailable, including original samples, intermediate features, and all kinds of statistics. To this end, we propose an Improved Self-Training (IST) method. In contrast to applying complex transformations, IST generates pseudo-labels with a simple test-time augmentation strategy to mitigate the poor calibration caused by unused functions. Moreover, an algorithm is proposed to correct the pseudo-labels by leveraging graph structures constructed with target samples in the latent space. Furthermore, we compare common optimization policies and propose parameter moving average to stabilize the adaptation process and alleviate catastrophic forgetting. Finally, we scale up IST to basic computer vision tasks and conduct extensive experiments on various benchmarks. The results demonstrate that IST achieves credible and consistent performance gains over existing TTA methods.", + "bbox": [ + 75, + 212, + 472, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows:", + "bbox": [ + 96, + 513, + 433, + 527 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a plug-and-play strategy for generating and correcting pseudo-labels, which is effective and efficient for test-time augmentation without additional retraining.", + "- We propose an improved self-training method for fully test-time adaptation, which is scalable to a variety of pretrained models and application tasks.", + "- We exhibit the effectiveness and robustness of our method on various benchmarks, including image classification, object detection, and semantic segmentation." + ], + "bbox": [ + 76, + 529, + 468, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 676, + 218, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Test-Time Adaptation (TTA) is a challenging task, that aims to adapt the model to arbitrary distributions and achieve improved performance at test time. BN Adapt [27] replaces the activation statistics of batch normalization layers with the estimated statistics of the corrupted images to improve the robustness of the model. Further, Tent [30] discards the statistics from the source data and updates the affine transformation parameters by entropy minimization. Sun, et al. [29] propose introducing the self-supervised pretext task to adapt the main task by updating the model parameters before making predictions. Following this way, TTT [29] and", + "bbox": [ + 75, + 700, + 472, + 868 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "TTT-MAE [8] employ rotation prediction and image generation as auxiliary tasks, respectively. TTT++ [20] and ITTA [4] rely on more general contrastive learning tasks. To effectively utilize a model without source data to solve domain adaptation problems, SHOT [19] exploits information maximization and self-supervised pseudo-labeling to align the target representation to the source hypothesis. MEMO [35] and SFOD [18] augment test samples to obtain robust pseudo labels and self-train the model with entropy descent. AdaContrast [3] denoises pseudo-labels via soft voting among nearest neighbors and applies weak-strong augmentation consistency as a regularizer. For non-stationary and continually changing environments, RoTTA [32] and CoTTA [31] are proposed to effectively stabilize the adaptation procedure and avoid catastrophic forgetting.", + "bbox": [ + 500, + 90, + 890, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing approaches tend to address the distribution shift caused by image corruption, but infrequently consider unconstrained conditions in nature, such as label shift and correlation shift. Hence, we propose to employ the Contrastive Language-Image Pre-trained model (CLIP) [25] as the source model for test-time adaptation. In this way, we have no need to pre-train models on different benchmarks, thus avoiding additional assumptions of the label distribution. Meanwhile, CLIP can provide a suitable starting point for the adaptation process due to its zero-shot capability and generalized feature properties, which have been proven to have a significant impact on post-adaptation [36]. From an application perspective, exploring how to improve the performance of CLIP in realistic environments at test time has important practical value for foundation models.", + "bbox": [ + 496, + 318, + 893, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 558, + 589, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We address the problem of adapting a pre-trained model to new domains at test time. Given a source model $f_{\\theta}$ with parameters $\\theta_S$ trained on the source domain $\\mathcal{D}_S$ , the goal is to adapt it to the target domain $\\mathcal{D}_T$ with only unlabeled data $\\{x_i\\}_{i=1}^n$ . We explicitly divide the model into encoder $g_{\\varphi}$ and predictor $h_{\\phi}$ , and denote $f = h \\circ g$ . By default, we define the final linear layer as the predictor and the rest as the encoder. A data point $x_i \\in \\mathcal{X}$ is projected into a latent space $z_i \\in \\mathcal{Z}$ by the encoder, and then mapped to a label space $y_i \\in \\mathcal{Y}$ by the predictor. Our proposed method applies a Simple Augmentation (SimpAug) to the original image and produces augmented points $\\widetilde{x} \\sim \\mathcal{U}(x)$ . Expanded data sets $\\{x\\} \\cap \\{\\widetilde{x}\\}$ , consisting of original and augmented samples, are fed into the encoder to generate intermediate features $\\{z\\}$ . Subsequently, we perform a Pseudo-Label Correction Algorithm (PLCA) to reinforce the prediction of unlabeled data by utilizing the graph structure in the latent space. To stabilize the self-training process at test time, we analyze the primary optimization algorithms and adopt Parameter Moving Average (PMA) for iterative updating. The pipeline of our method can be referred to Fig. 3.", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1The code is available at https://github.com/JingInAI/IST4TTA", + "bbox": [ + 76, + 875, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23702", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d679df4ad291ae18b05f1336629df6800a0f1c4177ab10aa453ada0a3a1d00b8.jpg", + "image_caption": [ + "bustard" + ], + "image_footnote": [], + "bbox": [ + 107, + 88, + 207, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d471d996d49986a5c54d9afb2149372ff2045ef2e01e819ecb47385856cb0d2c.jpg", + "image_caption": [ + "43.41%", + "prison" + ], + "image_footnote": [], + "bbox": [ + 117, + 196, + 197, + 258 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2aaf1fab63f4cd3e6ff8f5b5fac5c30fe06aada208b15f438548c37ed39c1d3b.jpg", + "image_caption": [ + "17.32%", + "Figure 2. (a) Visualization of images in ImageNet [6] with two kinds of test-time augmentation polices. Predictions are provided by CLIP (ViT-B/32), with correct and incorrect classes marked in green and red, respectively. (b) Error rate of pseudo-labeling counted on the test/validation set for each benchmark. (c) Computational speed of three pseudo-label correction algorithms on a fixed-size 10K sample set, averaged over 10 runs. The dimension of latent space is 1024 for RN50 and 512 for ViT-B/32." + ], + "image_footnote": [], + "bbox": [ + 117, + 277, + 197, + 340 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/162e3fb7127a1b3b0a3af4b537dce8a479465b2272cba2b3eb506e7a8235d9ac.jpg", + "image_caption": [ + "steel drum", + "29.60%（17.26%）", + "limpkin" + ], + "image_footnote": [], + "bbox": [ + 230, + 116, + 310, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c1a9a9037809ea4baca2e730d49d89f537df795a2865663f2a87118f9381dee7.jpg", + "image_caption": [ + "33.96% (32.12%)", + "chainlink fence" + ], + "image_footnote": [], + "bbox": [ + 230, + 196, + 310, + 258 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a2a251441cd4b17f6c59830b7569d337bb5ea0683affc96754909bae2a560b94.jpg", + "image_caption": [ + "12.09%（9.55%）", + "(a)" + ], + "image_footnote": [], + "bbox": [ + 230, + 277, + 310, + 340 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/586f3ee9b30786e948537f8009c1ca9ef28ef97c591647feb7d282381a15cea4.jpg", + "image_caption": [ + "AugMix w/ Avg.", + "SimpAug w/NMS", + "membranophone", + "32.86%", + "bustard" + ], + "image_footnote": [], + "bbox": [ + 341, + 116, + 421, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2c217e1a2b980dd2a79874098fca07e79b8912ef336f8b3ff720d6d217ba6187.jpg", + "image_caption": [ + "78.65%", + "prison" + ], + "image_footnote": [], + "bbox": [ + 341, + 196, + 421, + 258 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2664c6e728538ffc4d8a20c06283cbac25522bff4333ca678de30853b2b59946.jpg", + "image_caption": [ + "40.01%" + ], + "image_footnote": [], + "bbox": [ + 341, + 277, + 421, + 340 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b7962c3353b041744c3bae920562559c708c699c52d653f2c3bcbd813d389d7c.jpg", + "image_caption": [ + "(b)", + "(c)" + ], + "image_footnote": [], + "bbox": [ + 449, + 88, + 861, + 268 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/acacaeaa6cfa1763e052d210f0559ca833d6dd57030f98008ede573c85a5b11a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Usage Time (seconds)SHOTKNNOurs
CLIP - RN507.5011.5283.911
CLIP - ViT-B/323.2391.2393.601
", + "bbox": [ + 459, + 282, + 839, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Simple Augmentation Strategy", + "text_level": 1, + "bbox": [ + 76, + 422, + 348, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Typically, existing test-time augmentation methods tend to employ sophisticated augmentation functions to be applied to the test image [35]. Although this is a reasonable approach to extract invariant encodings from data augmentations, it may lead to serious corruption of original attributes. Fig. 2 (a) shows that the differences between classes are reflected in a few attribute variations for class-dense or fine-grained tasks. Complex augmentations, such as altering the brightness, contrast, saturation, and hue of the image, will impair the representative attributes of the category. Another type of augmentation, such as image rotation and adding Gaussian noise, will cause high-confidence erroneous predictions, especially for models without the use of similar transformations during training, e.g. CLIP [25].", + "bbox": [ + 75, + 446, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To this end, we consider the standard policy (crops, scales, and horizontal flips) for test-time augmentation. On the one hand, crops and scales can zoom in on the local regions of the image, reduce the interference of background pixels, and increase the model's attention to tiny objects. On the other hand, we preserve the position information of augmented versions in the original coordinate system and project the predictions to the primal image space, which is beneficial for solving regression problems, e.g. detection and segmentation. Specifically, we define the ratio of the cropped region to the original area as $r \\sim U(r_{min}, r_{max})$ and the aspect ratio as $a \\sim U(a_{min}, a_{max})$ . Given an image $x$ with the size of $H \\times W$ , the length and width of the cropped region are calculated as", + "bbox": [ + 75, + 657, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw = \\sqrt {H \\times W \\times r \\times a}, \\quad h = \\sqrt {H \\times W \\times r / a}. (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 878, + 468, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, we randomly select the top-left corner of the cropped region $(i,j)$ from $U(0,H - h)$ and $U(0,W - w)$ , respectively. The cropped sub-image is flipped horizontally with a probability of $p_{hf}$ and scaled to the original size $H\\times W$ . In general, we set $r_{min} = 0.7$ , $r_{max} = 1.0$ to ensure the clarity of augmented images, and $a_{min} = 0.75\\times H / W$ , $a_{max} = 1.33\\times H / W$ to avoid the distortion of the aspect ratio. $p_{hf}$ is set to 0.5 by default. We save the set of parameters $(i,j,h,w,hf)$ for each augmented version, where $hf$ is a binary variable indicating whether the image is flipped.", + "bbox": [ + 496, + 422, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We discard the operation of averaging the predictions of augmented samples, since it implicitly assumes that the augmentation functions have no influence on which predictions are corrected and which are corrupted [28]. Instead, motivated by Non-Maximum Suppression (NMS) [23], we extract the predictive probabilities of images in the augmentation space $\\{\\widetilde{x}_j\\}_{j=1}^m \\sim \\mathcal{U}(x_i)$ , and select the most confident class as the final prediction, which is formulated as", + "bbox": [ + 496, + 575, + 890, + 696 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} \\left(x _ {i}\\right) = \\arg \\max _ {c} \\left\\{p _ {c} \\left(\\widetilde {x} _ {j}\\right) \\right\\} _ {j = 1} ^ {m}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 704, + 890, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $c \\in \\mathcal{V}$ is the class label, and $p_c$ is the probability of class $c$ . In contrast to the image classification task, NMS is applied to the set of detected boxes with high confidence scores and IOU values for object detection, and applied to the set of predictions for a single pixel from augmented versions for semantic segmentation.", + "bbox": [ + 496, + 734, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We compare the performance with MEMO [35], using AugMix [13] and averaging predictive probabilities for test-time augmentation, referred to Fig. 2 (a, b). Results demonstrate that SimpAug is more robust in class-dense and fine-grained benchmarks, e.g. ImageNet [6] and Food101 [1].", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23703", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/097d02906f8726db376037ddc0755fbf0b93a7cbb9681a7e473c659b12a2fb0b.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 107, + 88, + 385, + 316 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/576754eaec460be4c575161c27fa9b1b23ead223c1e6a398bc2ffb7312ca5df1.jpg", + "image_caption": [ + "(b)", + "Figure 3. The framework of our approach. At the beginning of test-time adaptation, the model is initialized with the source parameters $\\hat{\\theta}_0 = \\theta_S$ . A target sample $x_{t}$ arriving at time step $t$ is transformed by SimpAug. We maintain a fixed-size memory queue for storing feature vectors and probabilities of target samples and their augmented versions. PLCA utilizes the graph structure formed by the stored vectors to correct the pseudo-labels generated by the model $\\hat{\\theta}_{t - 1}$ , and then employs NMS to select the most reliable prediction. PMA modifies the optimized parameters $\\theta_{t}$ to preserve the knowledge of the source model. We visualize the features extracted by the image encoder of CLIP (RN50) on CIFAR10. Translucent-colored dots represent correctly classified images, gray dots represent failure cases, and opaque dots represent misclassified samples corrected by PLCA." + ], + "image_footnote": [], + "bbox": [ + 385, + 88, + 857, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Pseudo-Label Correction Algorithm", + "text_level": 1, + "bbox": [ + 76, + 446, + 390, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although test-time augmentation can improve the robustness of distribution shifts, the pseudo labels annotated by the source model are still inaccurate and noisy for target data. To obtain cleaner labels, a series of methods [3, 19] explore the latent space of the source model to correct erroneous labeling. By visualizing the features on target domains using CLIP's visual encoder [25] in Fig. 3, we observe that the representation of different classes in the latent space exhibits clustering patterns. However, numerous target samples in the same cluster or manifold are misclassified. Inspired by [37], we propose a pseudo-label correction algorithm through learning from the graph structure constructed with only target data.", + "bbox": [ + 75, + 469, + 468, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We consider feature vectors in the latent space $\\{z_i\\}_{i=1}^n \\in \\mathcal{Z}$ as vertices in a graph, and the edges between vertices are defined by the distances between a point and its K-nearest neighbors. Specifically, the edges are weighted by", + "bbox": [ + 76, + 666, + 468, + 726 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i j} = \\left\\{ \\begin{array}{l l} 1, & i = j, \\\\ 1 - \\frac {\\| z _ {i} - z _ {j} \\| _ {2}}{\\max _ {j} \\| z _ {i} - z _ {j} \\| _ {2}}, & z _ {j} \\in \\mathcal {N} _ {K} (z _ {i}), \\\\ 0, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 734, + 468, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that self-reinforcement is added to prevent the instability caused by the accumulation of erroneous predictions in the spread process. By default, we set $K = 50$ . To guarantee the information spread symmetrically, we build a symmetric non-negative matrix $W = (w_{ij})_{n\\times n} + (w_{ji})_{n\\times n}$ and normalize it by $S = D^{-1 / 2}WD^{-1 / 2}$ for following iterations, where $D$ is a diagonal matrix with $D_{ii} = \\sum_{j}w_{ij}$ .", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We define an initial label matrix $Y(0) = (y_{ij})_{n \\times m}$ , where $y_{ij} = p_j(x_i)$ is the predictive probability of the sample $x_i$ belonging to the class $j$ . Afterward, we iteratively update the label matrix by", + "bbox": [ + 498, + 446, + 890, + 507 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY (t + 1) = \\alpha S Y (t) + (1 - \\alpha) Y (0), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 516, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is a hyper-parameter to balance the influence of initial labels and the information spread. By repeating the Eqn. 4 for $T$ times, we obtain the final label matrix", + "bbox": [ + 498, + 541, + 890, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY (T) = \\alpha^ {T} S ^ {T} Y (0) + (1 - \\alpha) \\sum_ {t = 0} ^ {T - 1} \\alpha^ {t} S ^ {t} Y (0). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 594, + 890, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since $0 < \\alpha < 1$ and the spectral radius of $S$ is less than or equal to 1, we have", + "bbox": [ + 498, + 642, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lim _ {T \\to \\infty} \\alpha^ {T} S ^ {T} Y (0) = 0,\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 679, + 709, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lim _ {T \\rightarrow \\infty} \\sum_ {t = 0} ^ {T - 1} \\alpha^ {t} S ^ {t} Y (0) = (I - \\alpha S) ^ {- 1} Y (0). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 705, + 890, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, the final label matrix can be approximated by", + "bbox": [ + 500, + 756, + 880, + 772 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY ^ {*} = \\lim _ {T \\rightarrow \\infty} Y (T) = (1 - \\alpha) (I - \\alpha S) ^ {- 1} Y (0). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 779, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we correct the pseudo labels in Eqn. 2 by", + "bbox": [ + 500, + 809, + 826, + 824 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} \\left(x _ {i}\\right) = \\arg \\max _ {c} \\left\\{p _ {c} \\left(\\widetilde {x} _ {j}\\right) \\times \\mathbb {1} _ {\\arg \\max _ {k} y _ {j k} ^ {*} = c} \\right\\} _ {j = 1} ^ {m}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 833, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2This linear system can be solved by the conjugate gradient method because $I - \\alpha S$ is symmetric and positive definite. By default, we set $\\alpha = 0.99$ and iterate for at most 20 times following [14].", + "bbox": [ + 498, + 862, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23704", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/57ebcf8e18df5b5469e35a7d8ab1204d9a54fb730874435feaa21535ef3fe250.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 318, + 253 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1dcc5f191330c488a8cfa4ec126d96903694da0c9ea57a7d4572780f75deaf37.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 321, + 88, + 553, + 253 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e3efb23a8cba61c207d1335b5dece7bc8dd195f403a79863cfdbbd8aa6f9e5ad.jpg", + "image_caption": [ + "(c)", + "Figure 4. Online test-time adaptation following [29]. We compare the impact of updating different parts of CLIP and show the top-1 accuracy $(\\%)$ in five benchmarks with RN50 (a) and ViT-B/32 (b). To explore the impact of three optimizers on CNN-based and Transformer-based models, we freeze the text encoder in CLIP and update the image encoder. The adaptation process is visualized in (c)." + ], + "image_footnote": [], + "bbox": [ + 558, + 88, + 880, + 255 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8de40d1a38228ea265d19fabd2d65c7be5f1a483a91b104972e400245bb01e27.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsModelsCIFAR10CIFAR100Food101CutsImageNetModelsCIFAR10CIFAR100Food101CutsImageNet
CLIP (zero-shot) [25]ResNet-5068.7±0.037.9±0.074.4±0.053.9±0.055.8±0.0ResNet-10178.1±0.041.2±0.077.5±0.060.7±0.058.2±0.0
Ours (SimpAug)69.0±0.138.7±0.175.4±0.054.0±0.056.8±0.078.8±0.142.0±0.178.7±0.061.0±0.059.2±0.0
Ours (PLCA)78.9±0.149.0±0.180.8±0.062.0±0.060.9±0.084.2±0.155.0±0.183.9±0.068.8±0.063.2±0.0
Ours (Online)83.0±0.252.8±0.479.5±0.256.9±0.458.3±0.189.1±0.159.0±0.282.6±0.264.0±0.360.1±0.0
Ours (Offline)84.6±0.154.1±0.581.0±0.065.9±0.160.2±0.092.1±0.163.4±0.185.1±0.071.4±0.262.6±0.0
CLIP (zero-shot) [25]ViT-B/3288.8±0.061.1±0.080.7±0.058.6±0.059.8±0.0ViT-B/1689.3±0.064.0±0.086.6±0.063.9±0.064.5±0.0
Ours (SimpAug)89.6±0.162.1±0.182.3±0.058.9±0.061.1±0.090.1±0.165.7±0.187.6±0.064.3±0.065.5±0.0
Ours (PLCA)92.8±0.169.7±0.186.1±0.065.7±0.065.8±0.094.3±0.073.0±0.190.3±0.071.0±0.069.9±0.0
Ours (Online)92.9±0.172.1±0.286.3±0.162.1±0.362.1±0.194.8±0.074.6±0.190.2±0.067.0±0.167.2±0.1
Ours (Offline)95.7±0.075.9±0.187.1±0.169.3±0.066.2±0.096.4±0.078.5±0.191.8±0.073.4±0.172.0±0.1
", + "bbox": [ + 94, + 318, + 877, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Top-1 Classification Accuracy (%) for five benchmarks with CLIP models. Higher is better. For ease of reading, we highlight the highest accuracy in bold and the second best as underline, which also applies to the following tables.", + "bbox": [ + 75, + 511, + 892, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y_{jk}^{*}$ is the $k$ -th element of the $j$ -th row of the matrix $Y^{*}$ , and $\\mathbb{1}$ is the indicator function.", + "bbox": [ + 76, + 546, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, SHOT [19] employs class-wise prototypes for K-means clustering, and AdaContrast [3] utilizes KNN to rectify the pseudo-labeling bias by averaging the probabilities of K-nearest neighbors. In contrast to SHOT which focuses on the global distribution in the latent space and KNN which concentrates on local similarity, our PLCA builds a local relation network for a sample and iteratively updates its pseudo-label in the global graph structure. We compare the effectiveness and computational speed for these three algorithms in Fig. 2 (b, c). Our PLCA achieves fewer pseudolabeling errors and maintains a more stable speed in the latent space with different dimensions.", + "bbox": [ + 75, + 578, + 468, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark. We treat the corrected pseudo-labels as targets for test-time training and adopt the same loss functions as the training stage, which scales our method to various tasks.", + "bbox": [ + 75, + 758, + 468, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Test-Time Optimization", + "text_level": 1, + "bbox": [ + 76, + 816, + 295, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this subsection, we explore a scalable and efficient optimization method for test-time adaptation, and this problem involves two key questions: Which parameters need to be updated and how to update them?", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To analyze the impact of updating different parts of CLIP, we compare several common policies:", + "bbox": [ + 498, + 547, + 892, + 575 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- BN Adapt [27] advices to combine the normalization statistics computed on the training dataset with the estimated ones on target samples, which is suitable for image corruption and has no extra training cost at test time.", + "- Tent [30] removes the statistics from the source data and updates the affine transformation parameters of BN layers, which is widely used in recent methods [22].", + "Full-tune the model, which is the most expensive one." + ], + "bbox": [ + 500, + 579, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We show the experimental results in Fig. 4 (a, b) and ensure that only the updated scopes are different. Because counting the mean and variance of target domains on a mini-batch leads to severe bias, especially when the batch size is small, it brings hard-to-recover errors to pseudo-labeling at the first few iterations. However, for Vision Transformer (ViT) [7] with LayerNorm, normalization statistics are counted for each sample, and it will not suffer from the above problem. Therefore, we freeze all the normalization layers and update other parameters to avoid such model corruption.", + "bbox": [ + 496, + 702, + 890, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The choice of optimizer has a great impact on test-time adaptation [8]. We experiment with various learning rates for three representative optimizers, including stochastic gra", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23705", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a1716dea0cf1ff0d761e615332f6d6ab4d6e4b7d94c23ce1b5b306e1c7090696.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓28.822.926.29.520.610.69.314.215.317.57.620.914.741.314.718.3±0.00
TTT++ (Offline) [20]✓12.811.111.27.317.18.26.59.49.97.95.05.113.78.810.69.6±0.00
SHOT (Offline) [19]✓13.411.616.37.315.98.27.19.49.410.26.38.312.89.813.610.6±0.00
BN Adapt [27]✓15.913.718.07.818.38.98.010.89.612.76.19.413.514.314.512.1±0.01
TENT [30]✓14.512.417.77.717.78.87.910.39.612.06.19.013.411.314.511.5±0.02
MEMO [35]✓13.912.216.37.416.68.27.49.89.310.76.19.312.610.014.310.9±0.02
TTT++ (Online) [20]✓15.514.123.69.125.111.48.113.213.113.46.66.917.612.513.613.6±0.03
SHOT (Online) [19]✓14.512.317.77.817.88.77.910.49.612.16.19.013.411.414.411.5±0.02
Ours (Online)✓12.811.414.96.715.87.76.98.98.610.15.68.011.910.512.810.2±0.04
", + "bbox": [ + 81, + 88, + 890, + 231 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fa0d8b980703d8715f281e3ee7f566dec4320b2f0f65298f72214daeb97978e2.jpg", + "table_caption": [ + "Table 2. Top-1 Classification Error (%) for all corruptions on CIFAR-10C (level 5). Lower is Better. SF denotes source free." + ], + "table_footnote": [], + "table_body": "
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓98.497.798.490.692.589.881.889.585.086.351.197.285.376.971.786.2±0.00
SHOT (Offline) [19]✓73.870.572.279.280.658.554.053.663.047.339.297.748.746.153.062.5±0.00
BN Adapt [27]✓87.190.689.587.693.480.071.970.681.565.946.889.873.563.267.577.3±0.30
TTT [29]✓73.771.473.176.393.471.366.664.481.352.441.764.755.752.255.766.3±0.00
MEMO [35]✓85.481.083.594.192.572.560.564.072.552.041.497.155.850.757.570.7±0.05
TENT [30]✓80.878.680.482.582.572.160.563.766.752.139.284.255.550.858.267.2±0.02
SHOT (Online) [19]✓83.982.383.783.983.872.661.965.768.654.839.485.958.153.162.369.3±0.03
Ours (Online)✓72.970.873.180.779.769.657.459.863.150.039.383.951.848.550.863.4±0.03
", + "bbox": [ + 80, + 255, + 890, + 386 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/88b621620c7d417ea0b40a4484e2c834e69a711bb3545bf7a4b36067c0f1c86a.jpg", + "table_caption": [ + "Table 3. Top-1 Classification Error (%) for all corruptions on ImageNet-C (level 5). Lower is Better. SF denotes source free." + ], + "table_footnote": [], + "table_body": "
MethodsSourceBN AdaptTENTMEMOCoTTAOurs
CIFAR-10C18.3±0.013.8±0.412.1±0.710.9±0.311.5±0.110.4±0.1
ImageNet-C86.2±0.074.9±0.470.7±0.679.8±1.067.8±0.365.4±0.1
", + "bbox": [ + 78, + 414, + 470, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Continuous online adaptation following CoTTA [31]. We report the top-1 classification error $(\\%)$ . Lower is Better.", + "bbox": [ + 76, + 477, + 468, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dient descent (SGD), SGD with momentum, and Adam [15]. Fig. 4 (c) exhibits the online adaptation process under the best learning rate. Optimizers with first/second-order momentum can adapt fast to the target distribution in most cases, but also cause fluctuations (e.g., SGD with momentum for RN50) and even continuing decline due to error accumulation (e.g., Adam for ViT-B/32). In contrast, vanilla SGD with a small learning rate can achieve stable and ascending performance. Since vanilla SGD can update the model parameters in the current optimal direction without being affected by historical gradients.", + "bbox": [ + 75, + 517, + 468, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Avoiding catastrophic forgetting during long-time adaptation is a problem worth paying attention to [24, 31]. This issue is also important for maintaining the zero-shot robustness of CLIP. We propose the parameter moving average to preserve the knowledge from the source model. Specifically, at any iteration $t \\geq 1$ , we define the parameters after optimization as $\\theta_t$ and update the moving average $\\hat{\\theta}_t$ as", + "bbox": [ + 75, + 688, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\theta} _ {t} = \\pi \\cdot \\hat {\\theta} _ {t - 1} + (1 - \\pi) \\cdot \\theta_ {t}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 813, + 468, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{\\theta}_0$ is initialized as the parameters of source model $\\theta_S$ and $\\pi \\in [0,1]$ is the momentum coefficient, which determines the degree of knowledge preservation.", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 414, + 624, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 500, + 439, + 581, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate on the following datasets:", + "bbox": [ + 500, + 462, + 823, + 477 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- CIFAR10 [17] and CIFAR100 [17] are two datasets consisting of low-resolution images, which differ from the common size of the training data of CLIP. We use them to evaluate the adaptability of our method to the distribution shift from image distortion caused by resize operations.", + "- Food101 [1] and Stanford Cars [16] are fine-grained datasets contains 101 food categories and 196 car categories, respectively. We use them for fine-grained tasks.", + "- ImageNet [6] is a large-scale dataset with 1000 classes, which is suitable for evaluating our method on category-intensive and real-world classification tasks.", + "- CIFAR-10C [12] and ImageNet-C [12] are created by test images of CIFAR10 and ImageNet with 15 types of corruptions in 5 levels, which are widely used to evaluate the robustness of test-time adaptation methods. Following the common protocol [27, 29, 30], we evaluate our method on the 5-level (worst) corruptions of all 15 types.", + "- For object detection, we use KITTI [9] to evaluate our method for automotive applications. KITTI comprises 8 categories of traffic participants and is mostly recorded in clear weather conditions. We follow Mirza et al. [22] to simulate degrading weathers of fog, rain and snow.", + "- For semantic segmentation, we use CarlaTTA [21] to conduct experiments. CarlaTTA contains five gradually changing scenarios, including day2night, clear2fog, clear2rain, dynamic, and highway. It challenges the methods to adapt to distribution shift over time." + ], + "bbox": [ + 500, + 477, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. For test-time adaptation with", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23706", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3a594480495f98db8e5dafa9b869ecd94731344da64a543163b35c61d0e1b88f.jpg", + "image_caption": [ + "Figure 5. Visualization of the detection results on KITTI in the weather conditions of fog, rain, and snow." + ], + "image_footnote": [], + "bbox": [ + 109, + 80, + 859, + 233 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a6db65cc42faafde768ba2c7af0caaef9d99efcbb01cce2c30e0609803c41b31.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSFFogRainSnow
Source✓22.8±0.065.5±0.025.6±0.0
ActMAD [22]✗47.7±1.081.4±0.264.5±0.0
BN Adapt [27]✓32.3±0.170.6±0.144.9±0.2
TTT [29]✓29.4±0.571.5±0.447.5±0.7
Ours (SimpAug)✓27.3±0.475.2±0.436.0±0.3
Ours (Online)✓43.2±0.381.6±0.252.3±0.2
", + "bbox": [ + 89, + 258, + 457, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CLIP [25], we use the publicly available pretrained model as the source model, and evaluate our method on the test/validation sets of CIFAR10, CIFAR100, Food101, Cars, and ImageNet. We uniformly use \"a photo of a {class}\" as the prompt template, where the class token is replaced by the specific class name, such as \"airplane\", \"deer\", and \"frog\". Our method is run with a learning rate of 1e-6 for ResNet [11] backbone and 1e-5 for Vision Transformer [7] backbone. A batch size of 64 is adopted considering the memory constraint, while different batch sizes have little impact on our method, analyzed in the ablation study 4.4. Following Mirza et al. [22], we adapt a Wide-ResNet-40-2 [34] (WRN-40-2) pre-trained with AugMix [13] on CIFAR-10C, and an ImageNet pre-trained ResNet-18 [11] from PyTorch model zoo on ImageNet-C. We adopt a batch size of 128 and a learning rate of 1e-3, while all the compared methods and baselines use the hyperparameters reported by their authors. For object detection task, we adapt a YOLOv3 [26] pretrained on KITTI in clear weather to fog, rain and snow. For semantic segmentation task, we adapt a DeepLab-V2 [5] with a ResNet-101 backbone pretrained on clear split of CarlaTTA to the other five scenarios. We run experiments on 5 random seeds and report the mean and standard deviation for these runs.", + "bbox": [ + 75, + 430, + 472, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Offline and online adaptation. We evaluate our method in both offline and online settings. In the offline scenario, we can access all the test data and train the model on the entire test sets for 50 epochs, without considering the storage limitation. In the online scenario, the test samples arrive sequentially and do not reappear. We maintain a memory queue to store a certain amount of feature vectors, $10K$ by", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9082807d47870f60ced66083a279b329da628eb28e1f0860e973da7922795176.jpg", + "table_caption": [ + "Table 5. Mean Average Precision (mAP@50) in KITTI with the most severe weather conditions, i.e. fog with only $30\\mathrm{m}$ visibility, rain with $200\\mathrm{mm/hr}$ intensity, and snow in level 5. Higher is better. SF denotes source free." + ], + "table_footnote": [], + "table_body": "
MethodsSFday2nightclear2fogclear2raindynamichighway
Source✓58.452.871.846.628.7
BN Adapt [27]✓62.056.871.452.632.8
TENT [30]✓61.556.070.950.332.0
MEMO [35]✓61.055.171.650.335.2
CoTTA [31]✓61.456.870.746.433.8
Ours (SimpAug)✓60.153.972.648.931.9
Ours (Online)✓62.456.873.951.534.7
", + "bbox": [ + 508, + 258, + 883, + 397 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Mean Intersection over Union (mIoU, %) on CarlaTTA. Higher is Better. SF denotes source free.", + "bbox": [ + 498, + 400, + 890, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "default, for our PLCA. We also study the effect of adopting different memory capacities on our method in Sec. 4.4. Furthermore, our method maintains the performance in the more challenging single sample online adaptation task.", + "bbox": [ + 498, + 431, + 892, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Image Classification", + "text_level": 1, + "bbox": [ + 498, + 500, + 692, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results for adapting CLIP model are reported in Table 1. We find that updating both image and text encoders simultaneously can further improve the adaptability of CLIP model than freezing the text encoder as shown in Fig. 4 (c). We also compare with the method of using SimpAug and PLCA without re-training. The number of augmented verions for each test sample is set to 8 by default, which contains an original version. PLCA outperforms the our online method on multiple benchmarks, which may be due to the fact that online training does not sufficiently learn from the test samples with pseudo-labels, while offline adaptation addresses this issue by training repeatedly and providing more accurate pseudo-labels after each epoch.", + "bbox": [ + 496, + 522, + 892, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present the results on CIFAR-10C and ImageNet-C in Table 2 and 3. Our method outperforms other online methods by a fair margin. Compared to works designed for offline adaptation, our method achieves comparable or even higher performance. It is noteworthy that MEMO [35] achieves higher performance than other baselines on adapting WRN-40-2, perhaps because of applying the same augmentation strategy, AugMix [13], for TTA as the training stage. However, when adapting ResNet-18 pre-trained with standard augmentation, MEMO does not maintain advantages due to the poor calibration of deep neural networks to augmented images with complex unseen transformations.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23707", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/717d938afd9da903dccf0f8c12190fd2b4f42595e410f7133c8df61ca5043dee.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelsMethodsImageNet-V2-Sketch-A-R
RN-50CLIP (zero-shot)55.851.133.221.856.0
Ours (π = 0)57.253.133.822.559.2
Ours (π = 0.9)58.353.836.024.060.3
Ours (π = 0.99)57.452.636.224.059.1
RN-101CLIP (zero-shot)58.254.338.028.163.9
Ours (π = 0)59.755.939.827.066.9
Ours (π = 0.9)60.156.240.930.467.3
Ours (π = 0.99)59.355.440.831.066.6
ViT-B/32CLIP (zero-shot)59.854.740.930.266.7
Ours (π = 0)63.758.144.132.771.4
Ours (π = 0.9)62.157.143.633.470.5
Ours (π = 0.99)60.956.543.233.169.7
ViT-B/16CLIP (zero-shot)64.560.646.047.873.8
Ours (π = 0)69.163.650.151.479.1
Ours (π = 0.9)67.262.549.152.977.6
Ours (π = 0.99)65.961.848.552.076.6
", + "bbox": [ + 86, + 88, + 460, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Continuous online adaptation. Following CoTTA [31] to continuously adapt the model to different corruptions, we test our method on CIFAR-10C and ImageNet-C, referred to Table 4. Our method outperforms other baselines.", + "bbox": [ + 76, + 343, + 468, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Object Detection and Semantic Segmentation", + "text_level": 1, + "bbox": [ + 76, + 416, + 460, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the effectiveness of our method in solving regression problems, we conduct experiments on KITTI using YOLOv3. We report the results in Table 5 and visualize the detecting boxes in Fig. 5. Our method outperforms BN Adapt [27] and TTT [29], which are scalable to other models and not limited by the main task, and also beats ActMAD [22], which utilizes statistics in source data to TTA, in clear-to-rain task. Note that when only using SimpAug for test-time augmentation, we improve the source model up to $10.4\\%$ . The visualization shows that SimpAug helps the model recognize distant and occluded objects that are hard to detect, while online training with pseudo-labels further boosts the accuracy and filter out duplicate boxes.", + "bbox": [ + 75, + 439, + 468, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the semantic segmentation task, building a graph with all pixels is computationally expensive. We are inspired by COMUS [33] and collect object-level features, which represent the nodes in the graph. The results are listed in Table 6. BN Adapt exhibits robustness in the distribution shifts over time, while other methods seem to have limited improvement in gradually changing environments. Our method outperforms CoTTA [31], which is designed for continuous test-time adaptation.", + "bbox": [ + 75, + 637, + 468, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "More implementation details and comparison results can be found in the supplemental material.", + "bbox": [ + 76, + 773, + 468, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 816, + 230, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of augmentations. We study how the number of augmentation for single sample affects the performance of SimpAug, and conduct experiments on KITTI using YOLOv3, referred to Table 8. SimpAug improves the ac", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3f72907357a561e003a3cd7d56e9eebfe882c38fae5b7dfae1520132c132ab0e.jpg", + "table_caption": [ + "Table 7. Comparison with different $\\pi$ values on robustness to distribution shift. Higher is Better." + ], + "table_footnote": [], + "table_body": "
Num1286432168421 (Source)
Fog28.227.727.326.425.925.024.622.8
Rain75.975.975.273.873.472.168.965.5
Snow37.637.036.034.632.830.628.725.6
", + "bbox": [ + 509, + 89, + 883, + 151 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a584932c624447548d0b65e625e0578f0910195e70ecec70ef1f4efe1777e857.jpg", + "table_caption": [ + "Table 8. mAP@50 of SimpAug with different augmentation numbers on KITTI. Higher is Better." + ], + "table_footnote": [], + "table_body": "
Memory Size100K10K1K100100Source
RN50CIFAR1083.083.083.482.982.282.168.7
ViT-B/32Food10186.486.385.885.785.785.780.7
", + "bbox": [ + 511, + 183, + 879, + 232 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ea69afeaa864d2334ae13e100016d476133af9fbcd107eeb06197fbaa205d638.jpg", + "table_caption": [ + "Table 9. Accuracy $(\\%)$ of our online method with CLIP model in different sizes of memory queue. Higher is Better." + ], + "table_footnote": [], + "table_body": "
Batch Size12864321681Source
RN50CIFAR1082.883.083.582.983.381.068.7
ViT-B/32Food10186.486.386.386.686.587.180.7
", + "bbox": [ + 514, + 263, + 877, + 315 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Accuracy $(\\%)$ of our online method with different batch sizes. Source denotes zero-shot performance of the CLIP model.", + "bbox": [ + 500, + 316, + 890, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "curacy with the increase of augmentation numbers until the performance bottleneck. Large number of augmentation requires computational resources and storage.", + "bbox": [ + 498, + 351, + 890, + 397 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Size of memory queue. The memory size affects the inference speed and the accuracy of corrected pseudo-labels by PLCA. We conduct ablation experiments for online adaptation, as shown in Table 9. A large memory improves the ability of graph modeling the relations between samples. However, in online settings, old stored feature vectors have a higher error rate than the new ones, which affects the prediction of pseudo-labels for the current image.", + "bbox": [ + 496, + 397, + 890, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Momentum coefficient. $\\pi$ is a momentum coefficient that affects the models' update speed and avoids catastrophic forgetting. We test the performance of the CLIP model without using PMA and with two $\\pi$ values. The results listed in Table 7 show that ViT backbone is more resistant to catastrophic forgetting than ResNet, and our method can maintain the robustness of the CLIP model to distribution shift while performing test-time adaptation.", + "bbox": [ + 496, + 518, + 890, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Batch size. Most existing methods suffer from a small batch size in online adaptation, especially for those that rely on modifying normalization statistics of BN layers. As shown in Table 10, our method maintains comparable performance even in single sample online adaptation.", + "bbox": [ + 496, + 638, + 890, + 714 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 724, + 617, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose an improved self-training method for fully test-time adaptation. In contrast to previous TTA methods, our IST explores the adaptability of the foundation model by employing CLIP as the source model. It goes beyond image classification and can be applied to object detection and semantic segmentation. IST outperforms existing TTA methods on different benchmarks and tasks by improving the quality of pseudo-labels and stabilizing the adaptation process. Experiments show that IST is scalable to a variety of pre-trained models and application tasks.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23708", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part VI 13, pages 446-461. Springer, 2014. 3, 6", + "[2] Collin Burns and Jacob Steinhardt. Limitations of post-hoc feature alignment for robustness. 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Advances in neural information processing systems, 16, 2003. 4" + ], + "bbox": [ + 78, + 92, + 470, + 671 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23710", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improved Self-Training for Test-Time Adaptation/dc47adbd-48af-4fc3-a882-67b2a96aeb19_model.json b/2024/Improved Self-Training for Test-Time Adaptation/dc47adbd-48af-4fc3-a882-67b2a96aeb19_model.json new file mode 100644 index 0000000000000000000000000000000000000000..878be91f394eb8fe06d650fa3ab2f18a1921489f --- /dev/null +++ b/2024/Improved Self-Training for Test-Time Adaptation/dc47adbd-48af-4fc3-a882-67b2a96aeb19_model.json @@ -0,0 +1,2442 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.131, + 0.737, + 0.154 + ], + "angle": 0, + "content": "Improved Self-Training for Test-Time Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.182, + 0.681, + 0.218 + ], + "angle": 0, + "content": "Jing Ma \nHuazhong University of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.394, + 0.22, + 0.573, + 0.234 + ], + "angle": 0, + "content": "jingma001@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.604 + ], + "angle": 0, + "content": "Test-time adaptation (TTA) is a technique to improve the performance of a pre-trained source model on a target distribution without using any labeled data. However, existing self-trained TTA methods often face the challenges of unreliable pseudo-labels and unstable model optimization. In this paper, we propose an Improved Self-Training (IST) approach, which addresses these challenges by enhancing the pseudo-label quality and stabilizing the adaptation process. Specifically, we use a simple augmentation strategy to generate multiple views of each test sample, and construct a graph structure to correct the pseudo-labels based on the similarity of the latent features. Moreover, we adopt a parameter moving average scheme to smooth the model updates and prevent catastrophic forgetting. Instead of using a model with fixed label space, we explore the adaptability of the foundation model CLIP to various downstream tasks at test time. Extensive experiments on various benchmarks show that IST can achieve significant and consistent improvements over the existing TTA methods in classification, detection, and segmentation tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.633, + 0.21, + 0.649 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Deep Neural Networks have performed superiorly in a broad scope of tasks, and exhibit surprising zero-shot generalization capabilities. However, in practical applications, behavior decline may occur owing to the distribution shifts of unknown domains, which leads to laborious efforts in data collection and model retraining. To address this issue, Test-Time Adaptation (TTA), aims to adapt the model to the target domain at test time, has emerged as a promising paradigm of increasing attention and research [19, 29, 30]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Early methods of TTA [22, 27, 30, 32] explore adapting the activation statistics and updating the affine transformation parameters of batch normalization layers to mitigate the distribution shifts from clean to corrupted images. These approaches are easily scalable to deep neural networks with different architectures, but their performance is often confined to specific ranges of distribution shifts due to the lim" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.266, + 0.875, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.443, + 0.895, + 0.514 + ], + "angle": 0, + "content": "Figure 1. An illustration of test-time adaptation. The approach employs source models from a model zoo, where the source data is unknown. Source models adapt to target domains using one batch of test samples at a time. Self-training is a key component for updating models and providing more accurate online predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.895, + 0.689 + ], + "angle": 0, + "content": "ited adaptive capacity of batch normalization [2]. A series of works [4, 8, 20, 29] leverage self-supervised learning for test-time training (TTT) to update the model parameters before making predictions, which is conditional on having correlated gradients between the loss functions of the auxiliary and main tasks. However, an inappropriate pretext task may be detrimental to the learned model [20]. Moreover, although TTT is not restricted by the type of main task, it typically requires modifying the training process to accommodate a self-supervised task, which increases the cost of applying TTT to pre-trained models [36]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Another line of research seeks to utilize the predictions of the model itself as pseudo-labels and re-train the model, which is known as the self-training strategy. Owing to the poor calibration of neural networks [10], pseudo-labels generated by the source model may be inaccurate and noisy for target data. Liang, et al. [19] propose to attain class-wise prototypes by clustering and further obtain cleaner pseudolabels. Recent works [3, 18, 28, 31, 35] suggest performing different data augmentations on a test sample to improve the model's prediction. On the other hand, some works [3, 24, 31, 32] focus on stabilizing the adaptation procedure at test time by adopting active selection, re-weighting strategy, or knowledge distillation. Generally, self-training-based approaches make no strong assumptions about distrib" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23701" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "bution shifts and types of task, thus they are more ubiquitous for real-world applications. However, existing methods still suffer from the following limitations: 1) Test-time augmentation may degrade performance for voluminous and aggregated categories, 2) Pseudo-label correction has not fully exploited the model's intermediate representations of the target domain. 3) Error accumulation and catastrophic forgetting may occur during the adaptation process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.514 + ], + "angle": 0, + "content": "In this paper, we aim to address the above issues by analyzing the key components of self-training, i.e., pseudolabel generation, correction, and model optimization. We challenge the task of fully test-time adaptation [30], which supposes that any information about source data is unavailable, including original samples, intermediate features, and all kinds of statistics. To this end, we propose an Improved Self-Training (IST) method. In contrast to applying complex transformations, IST generates pseudo-labels with a simple test-time augmentation strategy to mitigate the poor calibration caused by unused functions. Moreover, an algorithm is proposed to correct the pseudo-labels by leveraging graph structures constructed with target samples in the latent space. Furthermore, we compare common optimization policies and propose parameter moving average to stabilize the adaptation process and alleviate catastrophic forgetting. Finally, we scale up IST to basic computer vision tasks and conduct extensive experiments on various benchmarks. The results demonstrate that IST achieves credible and consistent performance gains over existing TTA methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.515, + 0.434, + 0.529 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.53, + 0.47, + 0.575 + ], + "angle": 0, + "content": "- We propose a plug-and-play strategy for generating and correcting pseudo-labels, which is effective and efficient for test-time augmentation without additional retraining." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.575, + 0.47, + 0.62 + ], + "angle": 0, + "content": "- We propose an improved self-training method for fully test-time adaptation, which is scalable to a variety of pretrained models and application tasks." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.62, + 0.47, + 0.665 + ], + "angle": 0, + "content": "- We exhibit the effectiveness and robustness of our method on various benchmarks, including image classification, object detection, and semantic segmentation." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.53, + 0.47, + 0.665 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.677, + 0.22, + 0.693 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.473, + 0.869 + ], + "angle": 0, + "content": "Test-Time Adaptation (TTA) is a challenging task, that aims to adapt the model to arbitrary distributions and achieve improved performance at test time. BN Adapt [27] replaces the activation statistics of batch normalization layers with the estimated statistics of the corrupted images to improve the robustness of the model. Further, Tent [30] discards the statistics from the source data and updates the affine transformation parameters by entropy minimization. Sun, et al. [29] propose introducing the self-supervised pretext task to adapt the main task by updating the model parameters before making predictions. Following this way, TTT [29] and" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "TTT-MAE [8] employ rotation prediction and image generation as auxiliary tasks, respectively. TTT++ [20] and ITTA [4] rely on more general contrastive learning tasks. To effectively utilize a model without source data to solve domain adaptation problems, SHOT [19] exploits information maximization and self-supervised pseudo-labeling to align the target representation to the source hypothesis. MEMO [35] and SFOD [18] augment test samples to obtain robust pseudo labels and self-train the model with entropy descent. AdaContrast [3] denoises pseudo-labels via soft voting among nearest neighbors and applies weak-strong augmentation consistency as a regularizer. For non-stationary and continually changing environments, RoTTA [32] and CoTTA [31] are proposed to effectively stabilize the adaptation procedure and avoid catastrophic forgetting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.895, + 0.545 + ], + "angle": 0, + "content": "Existing approaches tend to address the distribution shift caused by image corruption, but infrequently consider unconstrained conditions in nature, such as label shift and correlation shift. Hence, we propose to employ the Contrastive Language-Image Pre-trained model (CLIP) [25] as the source model for test-time adaptation. In this way, we have no need to pre-train models on different benchmarks, thus avoiding additional assumptions of the label distribution. Meanwhile, CLIP can provide a suitable starting point for the adaptation process due to its zero-shot capability and generalized feature properties, which have been proven to have a significant impact on post-adaptation [36]. From an application perspective, exploring how to improve the performance of CLIP in realistic environments at test time has important practical value for foundation models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.591, + 0.573 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We address the problem of adapting a pre-trained model to new domains at test time. Given a source model \\( f_{\\theta} \\) with parameters \\( \\theta_S \\) trained on the source domain \\( \\mathcal{D}_S \\), the goal is to adapt it to the target domain \\( \\mathcal{D}_T \\) with only unlabeled data \\( \\{x_i\\}_{i=1}^n \\). We explicitly divide the model into encoder \\( g_{\\varphi} \\) and predictor \\( h_{\\phi} \\), and denote \\( f = h \\circ g \\). By default, we define the final linear layer as the predictor and the rest as the encoder. A data point \\( x_i \\in \\mathcal{X} \\) is projected into a latent space \\( z_i \\in \\mathcal{Z} \\) by the encoder, and then mapped to a label space \\( y_i \\in \\mathcal{Y} \\) by the predictor. Our proposed method applies a Simple Augmentation (SimpAug) to the original image and produces augmented points \\( \\widetilde{x} \\sim \\mathcal{U}(x) \\). Expanded data sets \\( \\{x\\} \\cap \\{\\widetilde{x}\\} \\), consisting of original and augmented samples, are fed into the encoder to generate intermediate features \\( \\{z\\} \\). Subsequently, we perform a Pseudo-Label Correction Algorithm (PLCA) to reinforce the prediction of unlabeled data by utilizing the graph structure in the latent space. To stabilize the self-training process at test time, we analyze the primary optimization algorithms and adopt Parameter Moving Average (PMA) for iterative updating. The pipeline of our method can be referred to Fig. 3." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.468, + 0.9 + ], + "angle": 0, + "content": "1The code is available at https://github.com/JingInAI/IST4TTA" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23702" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.089, + 0.208, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.182, + 0.172, + 0.189 + ], + "angle": 0, + "content": "bustard" + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.189, + 0.172, + 0.196 + ], + "angle": 0, + "content": "43.41%" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.198, + 0.199, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.264, + 0.171, + 0.27 + ], + "angle": 0, + "content": "prison" + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.27, + 0.172, + 0.276 + ], + "angle": 0, + "content": "17.32%" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.278, + 0.199, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.239, + 0.092, + 0.303, + 0.1 + ], + "angle": 0, + "content": "AugMix w/ Avg." + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.102, + 0.29, + 0.108 + ], + "angle": 0, + "content": "steel drum" + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.109, + 0.305, + 0.116 + ], + "angle": 0, + "content": "29.60%（17.26%）" + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.117, + 0.312, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.258, + 0.182, + 0.285, + 0.189 + ], + "angle": 0, + "content": "limpkin" + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.189, + 0.304, + 0.197 + ], + "angle": 0, + "content": "33.96% (32.12%)" + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.198, + 0.312, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.263, + 0.299, + 0.269 + ], + "angle": 0, + "content": "chainlink fence" + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.27, + 0.302, + 0.277 + ], + "angle": 0, + "content": "12.09%（9.55%）" + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.278, + 0.312, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.344, + 0.279, + 0.354 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.091, + 0.417, + 0.1 + ], + "angle": 0, + "content": "SimpAug w/NMS" + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.101, + 0.408, + 0.107 + ], + "angle": 0, + "content": "membranophone" + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.108, + 0.395, + 0.114 + ], + "angle": 0, + "content": "32.86%" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.117, + 0.422, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.183, + 0.394, + 0.189 + ], + "angle": 0, + "content": "bustard" + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.189, + 0.395, + 0.196 + ], + "angle": 0, + "content": "78.65%" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.198, + 0.422, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.264, + 0.393, + 0.27 + ], + "angle": 0, + "content": "prison" + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.27, + 0.394, + 0.276 + ], + "angle": 0, + "content": "40.01%" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.278, + 0.422, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.45, + 0.089, + 0.862, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.65, + 0.271, + 0.665, + 0.28 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "table", + "bbox": [ + 0.46, + 0.284, + 0.841, + 0.342 + ], + "angle": 0, + "content": "
Usage Time (seconds)SHOTKNNOurs
CLIP - RN507.5011.5283.911
CLIP - ViT-B/323.2391.2393.601
" + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.344, + 0.664, + 0.354 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.356, + 0.894, + 0.412 + ], + "angle": 0, + "content": "Figure 2. (a) Visualization of images in ImageNet [6] with two kinds of test-time augmentation polices. Predictions are provided by CLIP (ViT-B/32), with correct and incorrect classes marked in green and red, respectively. (b) Error rate of pseudo-labeling counted on the test/validation set for each benchmark. (c) Computational speed of three pseudo-label correction algorithms on a fixed-size 10K sample set, averaged over 10 runs. The dimension of latent space is 1024 for RN50 and 512 for ViT-B/32." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.349, + 0.44 + ], + "angle": 0, + "content": "3.1. Simple Augmentation Strategy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.658 + ], + "angle": 0, + "content": "Typically, existing test-time augmentation methods tend to employ sophisticated augmentation functions to be applied to the test image [35]. Although this is a reasonable approach to extract invariant encodings from data augmentations, it may lead to serious corruption of original attributes. Fig. 2 (a) shows that the differences between classes are reflected in a few attribute variations for class-dense or fine-grained tasks. Complex augmentations, such as altering the brightness, contrast, saturation, and hue of the image, will impair the representative attributes of the category. Another type of augmentation, such as image rotation and adding Gaussian noise, will cause high-confidence erroneous predictions, especially for models without the use of similar transformations during training, e.g. CLIP [25]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.87 + ], + "angle": 0, + "content": "To this end, we consider the standard policy (crops, scales, and horizontal flips) for test-time augmentation. On the one hand, crops and scales can zoom in on the local regions of the image, reduce the interference of background pixels, and increase the model's attention to tiny objects. On the other hand, we preserve the position information of augmented versions in the original coordinate system and project the predictions to the primal image space, which is beneficial for solving regression problems, e.g. detection and segmentation. Specifically, we define the ratio of the cropped region to the original area as \\( r \\sim U(r_{min}, r_{max}) \\) and the aspect ratio as \\( a \\sim U(a_{min}, a_{max}) \\). Given an image \\( x \\) with the size of \\( H \\times W \\), the length and width of the cropped region are calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.879, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\nw = \\sqrt {H \\times W \\times r \\times a}, \\quad h = \\sqrt {H \\times W \\times r / a}. (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Then, we randomly select the top-left corner of the cropped region \\((i,j)\\) from \\(U(0,H - h)\\) and \\(U(0,W - w)\\), respectively. The cropped sub-image is flipped horizontally with a probability of \\(p_{hf}\\) and scaled to the original size \\(H\\times W\\). In general, we set \\(r_{min} = 0.7\\), \\(r_{max} = 1.0\\) to ensure the clarity of augmented images, and \\(a_{min} = 0.75\\times H / W\\), \\(a_{max} = 1.33\\times H / W\\) to avoid the distortion of the aspect ratio. \\(p_{hf}\\) is set to 0.5 by default. We save the set of parameters \\((i,j,h,w,hf)\\) for each augmented version, where \\(hf\\) is a binary variable indicating whether the image is flipped." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.892, + 0.697 + ], + "angle": 0, + "content": "We discard the operation of averaging the predictions of augmented samples, since it implicitly assumes that the augmentation functions have no influence on which predictions are corrected and which are corrupted [28]. Instead, motivated by Non-Maximum Suppression (NMS) [23], we extract the predictive probabilities of images in the augmentation space \\(\\{\\widetilde{x}_j\\}_{j=1}^m \\sim \\mathcal{U}(x_i)\\), and select the most confident class as the final prediction, which is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.705, + 0.892, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\hat {y} \\left(x _ {i}\\right) = \\arg \\max _ {c} \\left\\{p _ {c} \\left(\\widetilde {x} _ {j}\\right) \\right\\} _ {j = 1} ^ {m}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.825 + ], + "angle": 0, + "content": "where \\( c \\in \\mathcal{V} \\) is the class label, and \\( p_c \\) is the probability of class \\( c \\). In contrast to the image classification task, NMS is applied to the set of detected boxes with high confidence scores and IOU values for object detection, and applied to the set of predictions for a single pixel from augmented versions for semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We compare the performance with MEMO [35], using AugMix [13] and averaging predictive probabilities for test-time augmentation, referred to Fig. 2 (a, b). Results demonstrate that SimpAug is more robust in class-dense and fine-grained benchmarks, e.g. ImageNet [6] and Food101 [1]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23703" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.089, + 0.387, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.239, + 0.332, + 0.255, + 0.342 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.089, + 0.858, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.651, + 0.332, + 0.668, + 0.342 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.892, + 0.442 + ], + "angle": 0, + "content": "Figure 3. The framework of our approach. At the beginning of test-time adaptation, the model is initialized with the source parameters \\(\\hat{\\theta}_0 = \\theta_S\\). A target sample \\(x_{t}\\) arriving at time step \\(t\\) is transformed by SimpAug. We maintain a fixed-size memory queue for storing feature vectors and probabilities of target samples and their augmented versions. PLCA utilizes the graph structure formed by the stored vectors to correct the pseudo-labels generated by the model \\(\\hat{\\theta}_{t - 1}\\), and then employs NMS to select the most reliable prediction. PMA modifies the optimized parameters \\(\\theta_{t}\\) to preserve the knowledge of the source model. We visualize the features extracted by the image encoder of CLIP (RN50) on CIFAR10. Translucent-colored dots represent correctly classified images, gray dots represent failure cases, and opaque dots represent misclassified samples corrected by PLCA." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.447, + 0.391, + 0.463 + ], + "angle": 0, + "content": "3.2. Pseudo-Label Correction Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.469, + 0.666 + ], + "angle": 0, + "content": "Although test-time augmentation can improve the robustness of distribution shifts, the pseudo labels annotated by the source model are still inaccurate and noisy for target data. To obtain cleaner labels, a series of methods [3, 19] explore the latent space of the source model to correct erroneous labeling. By visualizing the features on target domains using CLIP's visual encoder [25] in Fig. 3, we observe that the representation of different classes in the latent space exhibits clustering patterns. However, numerous target samples in the same cluster or manifold are misclassified. Inspired by [37], we propose a pseudo-label correction algorithm through learning from the graph structure constructed with only target data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.667, + 0.47, + 0.727 + ], + "angle": 0, + "content": "We consider feature vectors in the latent space \\(\\{z_i\\}_{i=1}^n \\in \\mathcal{Z}\\) as vertices in a graph, and the edges between vertices are defined by the distances between a point and its K-nearest neighbors. Specifically, the edges are weighted by" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.736, + 0.469, + 0.786 + ], + "angle": 0, + "content": "\\[\nw _ {i j} = \\left\\{ \\begin{array}{l l} 1, & i = j, \\\\ 1 - \\frac {\\| z _ {i} - z _ {j} \\| _ {2}}{\\max _ {j} \\| z _ {i} - z _ {j} \\| _ {2}}, & z _ {j} \\in \\mathcal {N} _ {K} (z _ {i}), \\\\ 0, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.904 + ], + "angle": 0, + "content": "Note that self-reinforcement is added to prevent the instability caused by the accumulation of erroneous predictions in the spread process. By default, we set \\( K = 50 \\). To guarantee the information spread symmetrically, we build a symmetric non-negative matrix \\( W = (w_{ij})_{n\\times n} + (w_{ji})_{n\\times n} \\) and normalize it by \\( S = D^{-1 / 2}WD^{-1 / 2} \\) for following iterations, where \\( D \\) is a diagonal matrix with \\( D_{ii} = \\sum_{j}w_{ij} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.448, + 0.892, + 0.508 + ], + "angle": 0, + "content": "We define an initial label matrix \\( Y(0) = (y_{ij})_{n \\times m} \\), where \\( y_{ij} = p_j(x_i) \\) is the predictive probability of the sample \\( x_i \\) belonging to the class \\( j \\). Afterward, we iteratively update the label matrix by" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.517, + 0.891, + 0.533 + ], + "angle": 0, + "content": "\\[\nY (t + 1) = \\alpha S Y (t) + (1 - \\alpha) Y (0), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.542, + 0.892, + 0.587 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a hyper-parameter to balance the influence of initial labels and the information spread. By repeating the Eqn. 4 for \\(T\\) times, we obtain the final label matrix" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.595, + 0.891, + 0.636 + ], + "angle": 0, + "content": "\\[\nY (T) = \\alpha^ {T} S ^ {T} Y (0) + (1 - \\alpha) \\sum_ {t = 0} ^ {T - 1} \\alpha^ {t} S ^ {t} Y (0). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.643, + 0.891, + 0.673 + ], + "angle": 0, + "content": "Since \\(0 < \\alpha < 1\\) and the spectral radius of \\(S\\) is less than or equal to 1, we have" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.68, + 0.71, + 0.704 + ], + "angle": 0, + "content": "\\[\n\\lim _ {T \\to \\infty} \\alpha^ {T} S ^ {T} Y (0) = 0,\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.707, + 0.891, + 0.749 + ], + "angle": 0, + "content": "\\[\n\\lim _ {T \\rightarrow \\infty} \\sum_ {t = 0} ^ {T - 1} \\alpha^ {t} S ^ {t} Y (0) = (I - \\alpha S) ^ {- 1} Y (0). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.757, + 0.882, + 0.773 + ], + "angle": 0, + "content": "Therefore, the final label matrix can be approximated by" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.78, + 0.891, + 0.803 + ], + "angle": 0, + "content": "\\[\nY ^ {*} = \\lim _ {T \\rightarrow \\infty} Y (T) = (1 - \\alpha) (I - \\alpha S) ^ {- 1} Y (0). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.81, + 0.827, + 0.825 + ], + "angle": 0, + "content": "Finally, we correct the pseudo labels in Eqn. 2 by" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.834, + 0.891, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\hat {y} \\left(x _ {i}\\right) = \\arg \\max _ {c} \\left\\{p _ {c} \\left(\\widetilde {x} _ {j}\\right) \\times \\mathbb {1} _ {\\arg \\max _ {k} y _ {j k} ^ {*} = c} \\right\\} _ {j = 1} ^ {m}, \\tag {8}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2This linear system can be solved by the conjugate gradient method because \\(I - \\alpha S\\) is symmetric and positive definite. By default, we set \\(\\alpha = 0.99\\) and iterate for at most 20 times following [14]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23704" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.319, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.195, + 0.256, + 0.209, + 0.264 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.089, + 0.554, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.431, + 0.256, + 0.445, + 0.264 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.559, + 0.089, + 0.882, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.715, + 0.256, + 0.728, + 0.264 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.893, + 0.313 + ], + "angle": 0, + "content": "Figure 4. Online test-time adaptation following [29]. We compare the impact of updating different parts of CLIP and show the top-1 accuracy \\((\\%)\\) in five benchmarks with RN50 (a) and ViT-B/32 (b). To explore the impact of three optimizers on CNN-based and Transformer-based models, we freeze the text encoder in CLIP and update the image encoder. The adaptation process is visualized in (c)." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.319, + 0.879, + 0.508 + ], + "angle": 0, + "content": "
MethodsModelsCIFAR10CIFAR100Food101CutsImageNetModelsCIFAR10CIFAR100Food101CutsImageNet
CLIP (zero-shot) [25]ResNet-5068.7±0.037.9±0.074.4±0.053.9±0.055.8±0.0ResNet-10178.1±0.041.2±0.077.5±0.060.7±0.058.2±0.0
Ours (SimpAug)69.0±0.138.7±0.175.4±0.054.0±0.056.8±0.078.8±0.142.0±0.178.7±0.061.0±0.059.2±0.0
Ours (PLCA)78.9±0.149.0±0.180.8±0.062.0±0.060.9±0.084.2±0.155.0±0.183.9±0.068.8±0.063.2±0.0
Ours (Online)83.0±0.252.8±0.479.5±0.256.9±0.458.3±0.189.1±0.159.0±0.282.6±0.264.0±0.360.1±0.0
Ours (Offline)84.6±0.154.1±0.581.0±0.065.9±0.160.2±0.092.1±0.163.4±0.185.1±0.071.4±0.262.6±0.0
CLIP (zero-shot) [25]ViT-B/3288.8±0.061.1±0.080.7±0.058.6±0.059.8±0.0ViT-B/1689.3±0.064.0±0.086.6±0.063.9±0.064.5±0.0
Ours (SimpAug)89.6±0.162.1±0.182.3±0.058.9±0.061.1±0.090.1±0.165.7±0.187.6±0.064.3±0.065.5±0.0
Ours (PLCA)92.8±0.169.7±0.186.1±0.065.7±0.065.8±0.094.3±0.073.0±0.190.3±0.071.0±0.069.9±0.0
Ours (Online)92.9±0.172.1±0.286.3±0.162.1±0.362.1±0.194.8±0.074.6±0.190.2±0.067.0±0.167.2±0.1
Ours (Offline)95.7±0.075.9±0.187.1±0.169.3±0.066.2±0.096.4±0.078.5±0.191.8±0.073.4±0.172.0±0.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.512, + 0.893, + 0.541 + ], + "angle": 0, + "content": "Table 1. Top-1 Classification Accuracy (%) for five benchmarks with CLIP models. Higher is better. For ease of reading, we highlight the highest accuracy in bold and the second best as underline, which also applies to the following tables." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.547, + 0.469, + 0.576 + ], + "angle": 0, + "content": "where \\( y_{jk}^{*} \\) is the \\( k \\)-th element of the \\( j \\)-th row of the matrix \\( Y^{*} \\), and \\( \\mathbb{1} \\) is the indicator function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Similarly, SHOT [19] employs class-wise prototypes for K-means clustering, and AdaContrast [3] utilizes KNN to rectify the pseudo-labeling bias by averaging the probabilities of K-nearest neighbors. In contrast to SHOT which focuses on the global distribution in the latent space and KNN which concentrates on local similarity, our PLCA builds a local relation network for a sample and iteratively updates its pseudo-label in the global graph structure. We compare the effectiveness and computational speed for these three algorithms in Fig. 2 (b, c). Our PLCA achieves fewer pseudolabeling errors and maintains a more stable speed in the latent space with different dimensions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.76, + 0.47, + 0.805 + ], + "angle": 0, + "content": "Remark. We treat the corrected pseudo-labels as targets for test-time training and adopt the same loss functions as the training stage, which scales our method to various tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.296, + 0.833 + ], + "angle": 0, + "content": "3.3. Test-Time Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this subsection, we explore a scalable and efficient optimization method for test-time adaptation, and this problem involves two key questions: Which parameters need to be updated and how to update them?" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.548, + 0.893, + 0.577 + ], + "angle": 0, + "content": "To analyze the impact of updating different parts of CLIP, we compare several common policies:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.58, + 0.892, + 0.64 + ], + "angle": 0, + "content": "- BN Adapt [27] advices to combine the normalization statistics computed on the training dataset with the estimated ones on target samples, which is suitable for image corruption and has no extra training cost at test time." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.64, + 0.892, + 0.685 + ], + "angle": 0, + "content": "- Tent [30] removes the statistics from the source data and updates the affine transformation parameters of BN layers, which is widely used in recent methods [22]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.686, + 0.871, + 0.701 + ], + "angle": 0, + "content": "Full-tune the model, which is the most expensive one." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.58, + 0.892, + 0.701 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.853 + ], + "angle": 0, + "content": "We show the experimental results in Fig. 4 (a, b) and ensure that only the updated scopes are different. Because counting the mean and variance of target domains on a mini-batch leads to severe bias, especially when the batch size is small, it brings hard-to-recover errors to pseudo-labeling at the first few iterations. However, for Vision Transformer (ViT) [7] with LayerNorm, normalization statistics are counted for each sample, and it will not suffer from the above problem. Therefore, we freeze all the normalization layers and update other parameters to avoid such model corruption." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The choice of optimizer has a great impact on test-time adaptation [8]. We experiment with various learning rates for three representative optimizers, including stochastic gra" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23705" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.232 + ], + "angle": 0, + "content": "
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓28.822.926.29.520.610.69.314.215.317.57.620.914.741.314.718.3±0.00
TTT++ (Offline) [20]✓12.811.111.27.317.18.26.59.49.97.95.05.113.78.810.69.6±0.00
SHOT (Offline) [19]✓13.411.616.37.315.98.27.19.49.410.26.38.312.89.813.610.6±0.00
BN Adapt [27]✓15.913.718.07.818.38.98.010.89.612.76.19.413.514.314.512.1±0.01
TENT [30]✓14.512.417.77.717.78.87.910.39.612.06.19.013.411.314.511.5±0.02
MEMO [35]✓13.912.216.37.416.68.27.49.89.310.76.19.312.610.014.310.9±0.02
TTT++ (Online) [20]✓15.514.123.69.125.111.48.113.213.113.46.66.917.612.513.613.6±0.03
SHOT (Online) [19]✓14.512.317.77.817.88.77.910.49.612.16.19.013.411.414.411.5±0.02
Ours (Online)✓12.811.414.96.715.87.76.98.98.610.15.68.011.910.512.810.2±0.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.118, + 0.235, + 0.851, + 0.25 + ], + "angle": 0, + "content": "Table 2. Top-1 Classification Error (%) for all corruptions on CIFAR-10C (level 5). Lower is Better. SF denotes source free." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.256, + 0.892, + 0.387 + ], + "angle": 0, + "content": "
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓98.497.798.490.692.589.881.889.585.086.351.197.285.376.971.786.2±0.00
SHOT (Offline) [19]✓73.870.572.279.280.658.554.053.663.047.339.297.748.746.153.062.5±0.00
BN Adapt [27]✓87.190.689.587.693.480.071.970.681.565.946.889.873.563.267.577.3±0.30
TTT [29]✓73.771.473.176.393.471.366.664.481.352.441.764.755.752.255.766.3±0.00
MEMO [35]✓85.481.083.594.192.572.560.564.072.552.041.497.155.850.757.570.7±0.05
TENT [30]✓80.878.680.482.582.572.160.563.766.752.139.284.255.550.858.267.2±0.02
SHOT (Online) [19]✓83.982.383.783.983.872.661.965.768.654.839.485.958.153.162.369.3±0.03
Ours (Online)✓72.970.873.180.779.769.657.459.863.150.039.383.951.848.550.863.4±0.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.117, + 0.391, + 0.851, + 0.405 + ], + "angle": 0, + "content": "Table 3. Top-1 Classification Error (%) for all corruptions on ImageNet-C (level 5). Lower is Better. SF denotes source free." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.415, + 0.472, + 0.474 + ], + "angle": 0, + "content": "
MethodsSourceBN AdaptTENTMEMOCoTTAOurs
CIFAR-10C18.3±0.013.8±0.412.1±0.710.9±0.311.5±0.110.4±0.1
ImageNet-C86.2±0.074.9±0.470.7±0.679.8±1.067.8±0.365.4±0.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.478, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Table 4. Continuous online adaptation following CoTTA [31]. We report the top-1 classification error \\((\\%)\\). Lower is Better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.47, + 0.686 + ], + "angle": 0, + "content": "dient descent (SGD), SGD with momentum, and Adam [15]. Fig. 4 (c) exhibits the online adaptation process under the best learning rate. Optimizers with first/second-order momentum can adapt fast to the target distribution in most cases, but also cause fluctuations (e.g., SGD with momentum for RN50) and even continuing decline due to error accumulation (e.g., Adam for ViT-B/32). In contrast, vanilla SGD with a small learning rate can achieve stable and ascending performance. Since vanilla SGD can update the model parameters in the current optimal direction without being affected by historical gradients." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Avoiding catastrophic forgetting during long-time adaptation is a problem worth paying attention to [24, 31]. This issue is also important for maintaining the zero-shot robustness of CLIP. We propose the parameter moving average to preserve the knowledge from the source model. Specifically, at any iteration \\( t \\geq 1 \\), we define the parameters after optimization as \\( \\theta_t \\) and update the moving average \\( \\hat{\\theta}_t \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.814, + 0.47, + 0.833 + ], + "angle": 0, + "content": "\\[\n\\hat {\\theta} _ {t} = \\pi \\cdot \\hat {\\theta} _ {t - 1} + (1 - \\pi) \\cdot \\theta_ {t}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.469, + 0.903 + ], + "angle": 0, + "content": "where \\(\\hat{\\theta}_0\\) is initialized as the parameters of source model \\(\\theta_S\\) and \\(\\pi \\in [0,1]\\) is the momentum coefficient, which determines the degree of knowledge preservation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.415, + 0.625, + 0.433 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.583, + 0.456 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.463, + 0.824, + 0.478 + ], + "angle": 0, + "content": "Datasets. We evaluate on the following datasets:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.478, + 0.892, + 0.553 + ], + "angle": 0, + "content": "- CIFAR10 [17] and CIFAR100 [17] are two datasets consisting of low-resolution images, which differ from the common size of the training data of CLIP. We use them to evaluate the adaptability of our method to the distribution shift from image distortion caused by resize operations." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.554, + 0.892, + 0.599 + ], + "angle": 0, + "content": "- Food101 [1] and Stanford Cars [16] are fine-grained datasets contains 101 food categories and 196 car categories, respectively. We use them for fine-grained tasks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.599, + 0.891, + 0.643 + ], + "angle": 0, + "content": "- ImageNet [6] is a large-scale dataset with 1000 classes, which is suitable for evaluating our method on category-intensive and real-world classification tasks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.644, + 0.892, + 0.735 + ], + "angle": 0, + "content": "- CIFAR-10C [12] and ImageNet-C [12] are created by test images of CIFAR10 and ImageNet with 15 types of corruptions in 5 levels, which are widely used to evaluate the robustness of test-time adaptation methods. Following the common protocol [27, 29, 30], we evaluate our method on the 5-level (worst) corruptions of all 15 types." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.735, + 0.892, + 0.81 + ], + "angle": 0, + "content": "- For object detection, we use KITTI [9] to evaluate our method for automotive applications. KITTI comprises 8 categories of traffic participants and is mostly recorded in clear weather conditions. We follow Mirza et al. [22] to simulate degrading weathers of fog, rain and snow." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.81, + 0.892, + 0.884 + ], + "angle": 0, + "content": "- For semantic segmentation, we use CarlaTTA [21] to conduct experiments. CarlaTTA contains five gradually changing scenarios, including day2night, clear2fog, clear2rain, dynamic, and highway. It challenges the methods to adapt to distribution shift over time." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.478, + 0.892, + 0.884 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. For test-time adaptation with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23706" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.082, + 0.861, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.172, + 0.238, + 0.796, + 0.253 + ], + "angle": 0, + "content": "Figure 5. Visualization of the detection results on KITTI in the weather conditions of fog, rain, and snow." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.259, + 0.459, + 0.365 + ], + "angle": 0, + "content": "
MethodsSFFogRainSnow
Source✓22.8±0.065.5±0.025.6±0.0
ActMAD [22]✗47.7±1.081.4±0.264.5±0.0
BN Adapt [27]✓32.3±0.170.6±0.144.9±0.2
TTT [29]✓29.4±0.571.5±0.447.5±0.7
Ours (SimpAug)✓27.3±0.475.2±0.436.0±0.3
Ours (Online)✓43.2±0.381.6±0.252.3±0.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.368, + 0.47, + 0.424 + ], + "angle": 0, + "content": "Table 5. Mean Average Precision (mAP@50) in KITTI with the most severe weather conditions, i.e. fog with only \\(30\\mathrm{m}\\) visibility, rain with \\(200\\mathrm{mm/hr}\\) intensity, and snow in level 5. Higher is better. SF denotes source free." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.473, + 0.793 + ], + "angle": 0, + "content": "CLIP [25], we use the publicly available pretrained model as the source model, and evaluate our method on the test/validation sets of CIFAR10, CIFAR100, Food101, Cars, and ImageNet. We uniformly use \"a photo of a {class}\" as the prompt template, where the class token is replaced by the specific class name, such as \"airplane\", \"deer\", and \"frog\". Our method is run with a learning rate of 1e-6 for ResNet [11] backbone and 1e-5 for Vision Transformer [7] backbone. A batch size of 64 is adopted considering the memory constraint, while different batch sizes have little impact on our method, analyzed in the ablation study 4.4. Following Mirza et al. [22], we adapt a Wide-ResNet-40-2 [34] (WRN-40-2) pre-trained with AugMix [13] on CIFAR-10C, and an ImageNet pre-trained ResNet-18 [11] from PyTorch model zoo on ImageNet-C. We adopt a batch size of 128 and a learning rate of 1e-3, while all the compared methods and baselines use the hyperparameters reported by their authors. For object detection task, we adapt a YOLOv3 [26] pretrained on KITTI in clear weather to fog, rain and snow. For semantic segmentation task, we adapt a DeepLab-V2 [5] with a ResNet-101 backbone pretrained on clear split of CarlaTTA to the other five scenarios. We run experiments on 5 random seeds and report the mean and standard deviation for these runs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Offline and online adaptation. We evaluate our method in both offline and online settings. In the offline scenario, we can access all the test data and train the model on the entire test sets for 50 epochs, without considering the storage limitation. In the online scenario, the test samples arrive sequentially and do not reappear. We maintain a memory queue to store a certain amount of feature vectors, \\(10K\\) by" + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.259, + 0.885, + 0.398 + ], + "angle": 0, + "content": "
MethodsSFday2nightclear2fogclear2raindynamichighway
Source✓58.452.871.846.628.7
BN Adapt [27]✓62.056.871.452.632.8
TENT [30]✓61.556.070.950.332.0
MEMO [35]✓61.055.171.650.335.2
CoTTA [31]✓61.456.870.746.433.8
Ours (SimpAug)✓60.153.972.648.931.9
Ours (Online)✓62.456.873.951.534.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.401, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Table 6. Mean Intersection over Union (mIoU, %) on CarlaTTA. Higher is Better. SF denotes source free." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.893, + 0.495 + ], + "angle": 0, + "content": "default, for our PLCA. We also study the effect of adopting different memory capacities on our method in Sec. 4.4. Furthermore, our method maintains the performance in the more challenging single sample online adaptation task." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.5, + 0.693, + 0.516 + ], + "angle": 0, + "content": "4.2. Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.719 + ], + "angle": 0, + "content": "Results for adapting CLIP model are reported in Table 1. We find that updating both image and text encoders simultaneously can further improve the adaptability of CLIP model than freezing the text encoder as shown in Fig. 4 (c). We also compare with the method of using SimpAug and PLCA without re-training. The number of augmented verions for each test sample is set to 8 by default, which contains an original version. PLCA outperforms the our online method on multiple benchmarks, which may be due to the fact that online training does not sufficiently learn from the test samples with pseudo-labels, while offline adaptation addresses this issue by training repeatedly and providing more accurate pseudo-labels after each epoch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We present the results on CIFAR-10C and ImageNet-C in Table 2 and 3. Our method outperforms other online methods by a fair margin. Compared to works designed for offline adaptation, our method achieves comparable or even higher performance. It is noteworthy that MEMO [35] achieves higher performance than other baselines on adapting WRN-40-2, perhaps because of applying the same augmentation strategy, AugMix [13], for TTA as the training stage. However, when adapting ResNet-18 pre-trained with standard augmentation, MEMO does not maintain advantages due to the poor calibration of deep neural networks to augmented images with complex unseen transformations." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23707" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.462, + 0.307 + ], + "angle": 0, + "content": "
ModelsMethodsImageNet-V2-Sketch-A-R
RN-50CLIP (zero-shot)55.851.133.221.856.0
Ours (π = 0)57.253.133.822.559.2
Ours (π = 0.9)58.353.836.024.060.3
Ours (π = 0.99)57.452.636.224.059.1
RN-101CLIP (zero-shot)58.254.338.028.163.9
Ours (π = 0)59.755.939.827.066.9
Ours (π = 0.9)60.156.240.930.467.3
Ours (π = 0.99)59.355.440.831.066.6
ViT-B/32CLIP (zero-shot)59.854.740.930.266.7
Ours (π = 0)63.758.144.132.771.4
Ours (π = 0.9)62.157.143.633.470.5
Ours (π = 0.99)60.956.543.233.169.7
ViT-B/16CLIP (zero-shot)64.560.646.047.873.8
Ours (π = 0)69.163.650.151.479.1
Ours (π = 0.9)67.262.549.152.977.6
Ours (π = 0.99)65.961.848.552.076.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.311, + 0.47, + 0.339 + ], + "angle": 0, + "content": "Table 7. Comparison with different \\( \\pi \\) values on robustness to distribution shift. Higher is Better." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.344, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Continuous online adaptation. Following CoTTA [31] to continuously adapt the model to different corruptions, we test our method on CIFAR-10C and ImageNet-C, referred to Table 4. Our method outperforms other baselines." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.417, + 0.462, + 0.433 + ], + "angle": 0, + "content": "4.3. Object Detection and Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.637 + ], + "angle": 0, + "content": "To evaluate the effectiveness of our method in solving regression problems, we conduct experiments on KITTI using YOLOv3. We report the results in Table 5 and visualize the detecting boxes in Fig. 5. Our method outperforms BN Adapt [27] and TTT [29], which are scalable to other models and not limited by the main task, and also beats ActMAD [22], which utilizes statistics in source data to TTA, in clear-to-rain task. Note that when only using SimpAug for test-time augmentation, we improve the source model up to \\(10.4\\%\\). The visualization shows that SimpAug helps the model recognize distant and occluded objects that are hard to detect, while online training with pseudo-labels further boosts the accuracy and filter out duplicate boxes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.773 + ], + "angle": 0, + "content": "For the semantic segmentation task, building a graph with all pixels is computationally expensive. We are inspired by COMUS [33] and collect object-level features, which represent the nodes in the graph. The results are listed in Table 6. BN Adapt exhibits robustness in the distribution shifts over time, while other methods seem to have limited improvement in gradually changing environments. Our method outperforms CoTTA [31], which is designed for continuous test-time adaptation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.775, + 0.47, + 0.806 + ], + "angle": 0, + "content": "More implementation details and comparison results can be found in the supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.231, + 0.833 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Number of augmentations. We study how the number of augmentation for single sample affects the performance of SimpAug, and conduct experiments on KITTI using YOLOv3, referred to Table 8. SimpAug improves the ac" + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.09, + 0.885, + 0.152 + ], + "angle": 0, + "content": "
Num1286432168421 (Source)
Fog28.227.727.326.425.925.024.622.8
Rain75.975.975.273.873.472.168.965.5
Snow37.637.036.034.632.830.628.725.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.153, + 0.892, + 0.181 + ], + "angle": 0, + "content": "Table 8. mAP@50 of SimpAug with different augmentation numbers on KITTI. Higher is Better." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.184, + 0.88, + 0.233 + ], + "angle": 0, + "content": "
Memory Size100K10K1K100100Source
RN50CIFAR1083.083.083.482.982.282.168.7
ViT-B/32Food10186.486.385.885.785.785.780.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.235, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Table 9. Accuracy \\((\\%)\\) of our online method with CLIP model in different sizes of memory queue. Higher is Better." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.265, + 0.878, + 0.316 + ], + "angle": 0, + "content": "
Batch Size12864321681Source
RN50CIFAR1082.883.083.582.983.381.068.7
ViT-B/32Food10186.486.386.386.686.587.180.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.317, + 0.892, + 0.345 + ], + "angle": 0, + "content": "Table 10. Accuracy \\((\\%)\\) of our online method with different batch sizes. Source denotes zero-shot performance of the CLIP model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.892, + 0.398 + ], + "angle": 0, + "content": "curacy with the increase of augmentation numbers until the performance bottleneck. Large number of augmentation requires computational resources and storage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Size of memory queue. The memory size affects the inference speed and the accuracy of corrected pseudo-labels by PLCA. We conduct ablation experiments for online adaptation, as shown in Table 9. A large memory improves the ability of graph modeling the relations between samples. However, in online settings, old stored feature vectors have a higher error rate than the new ones, which affects the prediction of pseudo-labels for the current image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Momentum coefficient. \\(\\pi\\) is a momentum coefficient that affects the models' update speed and avoids catastrophic forgetting. We test the performance of the CLIP model without using PMA and with two \\(\\pi\\) values. The results listed in Table 7 show that ViT backbone is more resistant to catastrophic forgetting than ResNet, and our method can maintain the robustness of the CLIP model to distribution shift while performing test-time adaptation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.715 + ], + "angle": 0, + "content": "Batch size. Most existing methods suffer from a small batch size in online adaptation, especially for those that rely on modifying normalization statistics of BN layers. As shown in Table 10, our method maintains comparable performance even in single sample online adaptation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.619, + 0.74 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we propose an improved self-training method for fully test-time adaptation. In contrast to previous TTA methods, our IST explores the adaptability of the foundation model by employing CLIP as the source model. It goes beyond image classification and can be applied to object detection and semantic segmentation. IST outperforms existing TTA methods on different benchmarks and tasks by improving the quality of pseudo-labels and stabilizing the adaptation process. Experiments show that IST is scalable to a variety of pre-trained models and application tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23708" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part VI 13, pages 446-461. Springer, 2014. 3, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.201, + 0.472, + 0.257 + ], + "angle": 0, + "content": "[2] Collin Burns and Jacob Steinhardt. Limitations of post-hoc feature alignment for robustness. 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Advances in neural information processing systems, 16, 2003. 4" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.472, + 0.672 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23710" + } + ] +] \ No newline at end of file diff --git a/2024/Improved Self-Training for Test-Time Adaptation/dc47adbd-48af-4fc3-a882-67b2a96aeb19_origin.pdf b/2024/Improved Self-Training for Test-Time Adaptation/dc47adbd-48af-4fc3-a882-67b2a96aeb19_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aba83deec72e9c9b61e2ff60347cc976f63c9be7 --- /dev/null +++ b/2024/Improved Self-Training for Test-Time Adaptation/dc47adbd-48af-4fc3-a882-67b2a96aeb19_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09ff582f777e2d3e3dc93f3bb5bb9746d33e0aa66620c79a0ba3277842407815 +size 6376381 diff --git a/2024/Improved Self-Training for Test-Time Adaptation/full.md b/2024/Improved Self-Training for Test-Time Adaptation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e174513e56eea6bd332eeee51c53709731fc8284 --- /dev/null +++ b/2024/Improved Self-Training for Test-Time Adaptation/full.md @@ -0,0 +1,344 @@ +# Improved Self-Training for Test-Time Adaptation + +Jing Ma +Huazhong University of Science and Technology + +jingma001@gmail.com + +# Abstract + +Test-time adaptation (TTA) is a technique to improve the performance of a pre-trained source model on a target distribution without using any labeled data. However, existing self-trained TTA methods often face the challenges of unreliable pseudo-labels and unstable model optimization. In this paper, we propose an Improved Self-Training (IST) approach, which addresses these challenges by enhancing the pseudo-label quality and stabilizing the adaptation process. Specifically, we use a simple augmentation strategy to generate multiple views of each test sample, and construct a graph structure to correct the pseudo-labels based on the similarity of the latent features. Moreover, we adopt a parameter moving average scheme to smooth the model updates and prevent catastrophic forgetting. Instead of using a model with fixed label space, we explore the adaptability of the foundation model CLIP to various downstream tasks at test time. Extensive experiments on various benchmarks show that IST can achieve significant and consistent improvements over the existing TTA methods in classification, detection, and segmentation tasks. + +# 1. Introduction + +Deep Neural Networks have performed superiorly in a broad scope of tasks, and exhibit surprising zero-shot generalization capabilities. However, in practical applications, behavior decline may occur owing to the distribution shifts of unknown domains, which leads to laborious efforts in data collection and model retraining. To address this issue, Test-Time Adaptation (TTA), aims to adapt the model to the target domain at test time, has emerged as a promising paradigm of increasing attention and research [19, 29, 30]. + +Early methods of TTA [22, 27, 30, 32] explore adapting the activation statistics and updating the affine transformation parameters of batch normalization layers to mitigate the distribution shifts from clean to corrupted images. These approaches are easily scalable to deep neural networks with different architectures, but their performance is often confined to specific ranges of distribution shifts due to the lim + +![](images/edec926d0ab0ee9b0823530bff93a056de96d6fc33cd1af5141c71389f1adb3c.jpg) +Figure 1. An illustration of test-time adaptation. The approach employs source models from a model zoo, where the source data is unknown. Source models adapt to target domains using one batch of test samples at a time. Self-training is a key component for updating models and providing more accurate online predictions. + +ited adaptive capacity of batch normalization [2]. A series of works [4, 8, 20, 29] leverage self-supervised learning for test-time training (TTT) to update the model parameters before making predictions, which is conditional on having correlated gradients between the loss functions of the auxiliary and main tasks. However, an inappropriate pretext task may be detrimental to the learned model [20]. Moreover, although TTT is not restricted by the type of main task, it typically requires modifying the training process to accommodate a self-supervised task, which increases the cost of applying TTT to pre-trained models [36]. + +Another line of research seeks to utilize the predictions of the model itself as pseudo-labels and re-train the model, which is known as the self-training strategy. Owing to the poor calibration of neural networks [10], pseudo-labels generated by the source model may be inaccurate and noisy for target data. Liang, et al. [19] propose to attain class-wise prototypes by clustering and further obtain cleaner pseudolabels. Recent works [3, 18, 28, 31, 35] suggest performing different data augmentations on a test sample to improve the model's prediction. On the other hand, some works [3, 24, 31, 32] focus on stabilizing the adaptation procedure at test time by adopting active selection, re-weighting strategy, or knowledge distillation. Generally, self-training-based approaches make no strong assumptions about distrib + +bution shifts and types of task, thus they are more ubiquitous for real-world applications. However, existing methods still suffer from the following limitations: 1) Test-time augmentation may degrade performance for voluminous and aggregated categories, 2) Pseudo-label correction has not fully exploited the model's intermediate representations of the target domain. 3) Error accumulation and catastrophic forgetting may occur during the adaptation process. + +In this paper, we aim to address the above issues by analyzing the key components of self-training, i.e., pseudolabel generation, correction, and model optimization. We challenge the task of fully test-time adaptation [30], which supposes that any information about source data is unavailable, including original samples, intermediate features, and all kinds of statistics. To this end, we propose an Improved Self-Training (IST) method. In contrast to applying complex transformations, IST generates pseudo-labels with a simple test-time augmentation strategy to mitigate the poor calibration caused by unused functions. Moreover, an algorithm is proposed to correct the pseudo-labels by leveraging graph structures constructed with target samples in the latent space. Furthermore, we compare common optimization policies and propose parameter moving average to stabilize the adaptation process and alleviate catastrophic forgetting. Finally, we scale up IST to basic computer vision tasks and conduct extensive experiments on various benchmarks. The results demonstrate that IST achieves credible and consistent performance gains over existing TTA methods. + +In summary, our main contributions are as follows: + +- We propose a plug-and-play strategy for generating and correcting pseudo-labels, which is effective and efficient for test-time augmentation without additional retraining. +- We propose an improved self-training method for fully test-time adaptation, which is scalable to a variety of pretrained models and application tasks. +- We exhibit the effectiveness and robustness of our method on various benchmarks, including image classification, object detection, and semantic segmentation. + +# 2. Related Work + +Test-Time Adaptation (TTA) is a challenging task, that aims to adapt the model to arbitrary distributions and achieve improved performance at test time. BN Adapt [27] replaces the activation statistics of batch normalization layers with the estimated statistics of the corrupted images to improve the robustness of the model. Further, Tent [30] discards the statistics from the source data and updates the affine transformation parameters by entropy minimization. Sun, et al. [29] propose introducing the self-supervised pretext task to adapt the main task by updating the model parameters before making predictions. Following this way, TTT [29] and + +TTT-MAE [8] employ rotation prediction and image generation as auxiliary tasks, respectively. TTT++ [20] and ITTA [4] rely on more general contrastive learning tasks. To effectively utilize a model without source data to solve domain adaptation problems, SHOT [19] exploits information maximization and self-supervised pseudo-labeling to align the target representation to the source hypothesis. MEMO [35] and SFOD [18] augment test samples to obtain robust pseudo labels and self-train the model with entropy descent. AdaContrast [3] denoises pseudo-labels via soft voting among nearest neighbors and applies weak-strong augmentation consistency as a regularizer. For non-stationary and continually changing environments, RoTTA [32] and CoTTA [31] are proposed to effectively stabilize the adaptation procedure and avoid catastrophic forgetting. + +Existing approaches tend to address the distribution shift caused by image corruption, but infrequently consider unconstrained conditions in nature, such as label shift and correlation shift. Hence, we propose to employ the Contrastive Language-Image Pre-trained model (CLIP) [25] as the source model for test-time adaptation. In this way, we have no need to pre-train models on different benchmarks, thus avoiding additional assumptions of the label distribution. Meanwhile, CLIP can provide a suitable starting point for the adaptation process due to its zero-shot capability and generalized feature properties, which have been proven to have a significant impact on post-adaptation [36]. From an application perspective, exploring how to improve the performance of CLIP in realistic environments at test time has important practical value for foundation models. + +# 3. Method + +We address the problem of adapting a pre-trained model to new domains at test time. Given a source model $f_{\theta}$ with parameters $\theta_S$ trained on the source domain $\mathcal{D}_S$ , the goal is to adapt it to the target domain $\mathcal{D}_T$ with only unlabeled data $\{x_i\}_{i=1}^n$ . We explicitly divide the model into encoder $g_{\varphi}$ and predictor $h_{\phi}$ , and denote $f = h \circ g$ . By default, we define the final linear layer as the predictor and the rest as the encoder. A data point $x_i \in \mathcal{X}$ is projected into a latent space $z_i \in \mathcal{Z}$ by the encoder, and then mapped to a label space $y_i \in \mathcal{Y}$ by the predictor. Our proposed method applies a Simple Augmentation (SimpAug) to the original image and produces augmented points $\widetilde{x} \sim \mathcal{U}(x)$ . Expanded data sets $\{x\} \cap \{\widetilde{x}\}$ , consisting of original and augmented samples, are fed into the encoder to generate intermediate features $\{z\}$ . Subsequently, we perform a Pseudo-Label Correction Algorithm (PLCA) to reinforce the prediction of unlabeled data by utilizing the graph structure in the latent space. To stabilize the self-training process at test time, we analyze the primary optimization algorithms and adopt Parameter Moving Average (PMA) for iterative updating. The pipeline of our method can be referred to Fig. 3. + +![](images/d679df4ad291ae18b05f1336629df6800a0f1c4177ab10aa453ada0a3a1d00b8.jpg) +bustard + +![](images/d471d996d49986a5c54d9afb2149372ff2045ef2e01e819ecb47385856cb0d2c.jpg) +43.41% +prison + +![](images/2aaf1fab63f4cd3e6ff8f5b5fac5c30fe06aada208b15f438548c37ed39c1d3b.jpg) +17.32% +Figure 2. (a) Visualization of images in ImageNet [6] with two kinds of test-time augmentation polices. Predictions are provided by CLIP (ViT-B/32), with correct and incorrect classes marked in green and red, respectively. (b) Error rate of pseudo-labeling counted on the test/validation set for each benchmark. (c) Computational speed of three pseudo-label correction algorithms on a fixed-size 10K sample set, averaged over 10 runs. The dimension of latent space is 1024 for RN50 and 512 for ViT-B/32. + +![](images/162e3fb7127a1b3b0a3af4b537dce8a479465b2272cba2b3eb506e7a8235d9ac.jpg) +steel drum +29.60%（17.26%） +limpkin + +![](images/c1a9a9037809ea4baca2e730d49d89f537df795a2865663f2a87118f9381dee7.jpg) +33.96% (32.12%) +chainlink fence + +![](images/a2a251441cd4b17f6c59830b7569d337bb5ea0683affc96754909bae2a560b94.jpg) +12.09%（9.55%） +(a) + +![](images/586f3ee9b30786e948537f8009c1ca9ef28ef97c591647feb7d282381a15cea4.jpg) +AugMix w/ Avg. +SimpAug w/NMS +membranophone +32.86% +bustard + +![](images/2c217e1a2b980dd2a79874098fca07e79b8912ef336f8b3ff720d6d217ba6187.jpg) +78.65% +prison + +![](images/2664c6e728538ffc4d8a20c06283cbac25522bff4333ca678de30853b2b59946.jpg) +40.01% + +![](images/b7962c3353b041744c3bae920562559c708c699c52d653f2c3bcbd813d389d7c.jpg) +(b) +(c) + +
Usage Time (seconds)SHOTKNNOurs
CLIP - RN507.5011.5283.911
CLIP - ViT-B/323.2391.2393.601
+ +# 3.1. Simple Augmentation Strategy + +Typically, existing test-time augmentation methods tend to employ sophisticated augmentation functions to be applied to the test image [35]. Although this is a reasonable approach to extract invariant encodings from data augmentations, it may lead to serious corruption of original attributes. Fig. 2 (a) shows that the differences between classes are reflected in a few attribute variations for class-dense or fine-grained tasks. Complex augmentations, such as altering the brightness, contrast, saturation, and hue of the image, will impair the representative attributes of the category. Another type of augmentation, such as image rotation and adding Gaussian noise, will cause high-confidence erroneous predictions, especially for models without the use of similar transformations during training, e.g. CLIP [25]. + +To this end, we consider the standard policy (crops, scales, and horizontal flips) for test-time augmentation. On the one hand, crops and scales can zoom in on the local regions of the image, reduce the interference of background pixels, and increase the model's attention to tiny objects. On the other hand, we preserve the position information of augmented versions in the original coordinate system and project the predictions to the primal image space, which is beneficial for solving regression problems, e.g. detection and segmentation. Specifically, we define the ratio of the cropped region to the original area as $r \sim U(r_{min}, r_{max})$ and the aspect ratio as $a \sim U(a_{min}, a_{max})$ . Given an image $x$ with the size of $H \times W$ , the length and width of the cropped region are calculated as + +$$ +w = \sqrt {H \times W \times r \times a}, \quad h = \sqrt {H \times W \times r / a}. (1) +$$ + +Then, we randomly select the top-left corner of the cropped region $(i,j)$ from $U(0,H - h)$ and $U(0,W - w)$ , respectively. The cropped sub-image is flipped horizontally with a probability of $p_{hf}$ and scaled to the original size $H\times W$ . In general, we set $r_{min} = 0.7$ , $r_{max} = 1.0$ to ensure the clarity of augmented images, and $a_{min} = 0.75\times H / W$ , $a_{max} = 1.33\times H / W$ to avoid the distortion of the aspect ratio. $p_{hf}$ is set to 0.5 by default. We save the set of parameters $(i,j,h,w,hf)$ for each augmented version, where $hf$ is a binary variable indicating whether the image is flipped. + +We discard the operation of averaging the predictions of augmented samples, since it implicitly assumes that the augmentation functions have no influence on which predictions are corrected and which are corrupted [28]. Instead, motivated by Non-Maximum Suppression (NMS) [23], we extract the predictive probabilities of images in the augmentation space $\{\widetilde{x}_j\}_{j=1}^m \sim \mathcal{U}(x_i)$ , and select the most confident class as the final prediction, which is formulated as + +$$ +\hat {y} \left(x _ {i}\right) = \arg \max _ {c} \left\{p _ {c} \left(\widetilde {x} _ {j}\right) \right\} _ {j = 1} ^ {m}, \tag {2} +$$ + +where $c \in \mathcal{V}$ is the class label, and $p_c$ is the probability of class $c$ . In contrast to the image classification task, NMS is applied to the set of detected boxes with high confidence scores and IOU values for object detection, and applied to the set of predictions for a single pixel from augmented versions for semantic segmentation. + +We compare the performance with MEMO [35], using AugMix [13] and averaging predictive probabilities for test-time augmentation, referred to Fig. 2 (a, b). Results demonstrate that SimpAug is more robust in class-dense and fine-grained benchmarks, e.g. ImageNet [6] and Food101 [1]. + +![](images/097d02906f8726db376037ddc0755fbf0b93a7cbb9681a7e473c659b12a2fb0b.jpg) +(a) + +![](images/576754eaec460be4c575161c27fa9b1b23ead223c1e6a398bc2ffb7312ca5df1.jpg) +(b) +Figure 3. The framework of our approach. At the beginning of test-time adaptation, the model is initialized with the source parameters $\hat{\theta}_0 = \theta_S$ . A target sample $x_{t}$ arriving at time step $t$ is transformed by SimpAug. We maintain a fixed-size memory queue for storing feature vectors and probabilities of target samples and their augmented versions. PLCA utilizes the graph structure formed by the stored vectors to correct the pseudo-labels generated by the model $\hat{\theta}_{t - 1}$ , and then employs NMS to select the most reliable prediction. PMA modifies the optimized parameters $\theta_{t}$ to preserve the knowledge of the source model. We visualize the features extracted by the image encoder of CLIP (RN50) on CIFAR10. Translucent-colored dots represent correctly classified images, gray dots represent failure cases, and opaque dots represent misclassified samples corrected by PLCA. + +# 3.2. Pseudo-Label Correction Algorithm + +Although test-time augmentation can improve the robustness of distribution shifts, the pseudo labels annotated by the source model are still inaccurate and noisy for target data. To obtain cleaner labels, a series of methods [3, 19] explore the latent space of the source model to correct erroneous labeling. By visualizing the features on target domains using CLIP's visual encoder [25] in Fig. 3, we observe that the representation of different classes in the latent space exhibits clustering patterns. However, numerous target samples in the same cluster or manifold are misclassified. Inspired by [37], we propose a pseudo-label correction algorithm through learning from the graph structure constructed with only target data. + +We consider feature vectors in the latent space $\{z_i\}_{i=1}^n \in \mathcal{Z}$ as vertices in a graph, and the edges between vertices are defined by the distances between a point and its K-nearest neighbors. Specifically, the edges are weighted by + +$$ +w _ {i j} = \left\{ \begin{array}{l l} 1, & i = j, \\ 1 - \frac {\| z _ {i} - z _ {j} \| _ {2}}{\max _ {j} \| z _ {i} - z _ {j} \| _ {2}}, & z _ {j} \in \mathcal {N} _ {K} (z _ {i}), \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {3} +$$ + +Note that self-reinforcement is added to prevent the instability caused by the accumulation of erroneous predictions in the spread process. By default, we set $K = 50$ . To guarantee the information spread symmetrically, we build a symmetric non-negative matrix $W = (w_{ij})_{n\times n} + (w_{ji})_{n\times n}$ and normalize it by $S = D^{-1 / 2}WD^{-1 / 2}$ for following iterations, where $D$ is a diagonal matrix with $D_{ii} = \sum_{j}w_{ij}$ . + +We define an initial label matrix $Y(0) = (y_{ij})_{n \times m}$ , where $y_{ij} = p_j(x_i)$ is the predictive probability of the sample $x_i$ belonging to the class $j$ . Afterward, we iteratively update the label matrix by + +$$ +Y (t + 1) = \alpha S Y (t) + (1 - \alpha) Y (0), \tag {4} +$$ + +where $\alpha$ is a hyper-parameter to balance the influence of initial labels and the information spread. By repeating the Eqn. 4 for $T$ times, we obtain the final label matrix + +$$ +Y (T) = \alpha^ {T} S ^ {T} Y (0) + (1 - \alpha) \sum_ {t = 0} ^ {T - 1} \alpha^ {t} S ^ {t} Y (0). \tag {5} +$$ + +Since $0 < \alpha < 1$ and the spectral radius of $S$ is less than or equal to 1, we have + +$$ +\lim _ {T \to \infty} \alpha^ {T} S ^ {T} Y (0) = 0, +$$ + +$$ +\lim _ {T \rightarrow \infty} \sum_ {t = 0} ^ {T - 1} \alpha^ {t} S ^ {t} Y (0) = (I - \alpha S) ^ {- 1} Y (0). \tag {6} +$$ + +Therefore, the final label matrix can be approximated by + +$$ +Y ^ {*} = \lim _ {T \rightarrow \infty} Y (T) = (1 - \alpha) (I - \alpha S) ^ {- 1} Y (0). \tag {7} +$$ + +Finally, we correct the pseudo labels in Eqn. 2 by + +$$ +\hat {y} \left(x _ {i}\right) = \arg \max _ {c} \left\{p _ {c} \left(\widetilde {x} _ {j}\right) \times \mathbb {1} _ {\arg \max _ {k} y _ {j k} ^ {*} = c} \right\} _ {j = 1} ^ {m}, \tag {8} +$$ + +![](images/57ebcf8e18df5b5469e35a7d8ab1204d9a54fb730874435feaa21535ef3fe250.jpg) +(a) + +![](images/1dcc5f191330c488a8cfa4ec126d96903694da0c9ea57a7d4572780f75deaf37.jpg) +(b) + +![](images/e3efb23a8cba61c207d1335b5dece7bc8dd195f403a79863cfdbbd8aa6f9e5ad.jpg) +(c) +Figure 4. Online test-time adaptation following [29]. We compare the impact of updating different parts of CLIP and show the top-1 accuracy $(\%)$ in five benchmarks with RN50 (a) and ViT-B/32 (b). To explore the impact of three optimizers on CNN-based and Transformer-based models, we freeze the text encoder in CLIP and update the image encoder. The adaptation process is visualized in (c). + +
MethodsModelsCIFAR10CIFAR100Food101CutsImageNetModelsCIFAR10CIFAR100Food101CutsImageNet
CLIP (zero-shot) [25]ResNet-5068.7±0.037.9±0.074.4±0.053.9±0.055.8±0.0ResNet-10178.1±0.041.2±0.077.5±0.060.7±0.058.2±0.0
Ours (SimpAug)69.0±0.138.7±0.175.4±0.054.0±0.056.8±0.078.8±0.142.0±0.178.7±0.061.0±0.059.2±0.0
Ours (PLCA)78.9±0.149.0±0.180.8±0.062.0±0.060.9±0.084.2±0.155.0±0.183.9±0.068.8±0.063.2±0.0
Ours (Online)83.0±0.252.8±0.479.5±0.256.9±0.458.3±0.189.1±0.159.0±0.282.6±0.264.0±0.360.1±0.0
Ours (Offline)84.6±0.154.1±0.581.0±0.065.9±0.160.2±0.092.1±0.163.4±0.185.1±0.071.4±0.262.6±0.0
CLIP (zero-shot) [25]ViT-B/3288.8±0.061.1±0.080.7±0.058.6±0.059.8±0.0ViT-B/1689.3±0.064.0±0.086.6±0.063.9±0.064.5±0.0
Ours (SimpAug)89.6±0.162.1±0.182.3±0.058.9±0.061.1±0.090.1±0.165.7±0.187.6±0.064.3±0.065.5±0.0
Ours (PLCA)92.8±0.169.7±0.186.1±0.065.7±0.065.8±0.094.3±0.073.0±0.190.3±0.071.0±0.069.9±0.0
Ours (Online)92.9±0.172.1±0.286.3±0.162.1±0.362.1±0.194.8±0.074.6±0.190.2±0.067.0±0.167.2±0.1
Ours (Offline)95.7±0.075.9±0.187.1±0.169.3±0.066.2±0.096.4±0.078.5±0.191.8±0.073.4±0.172.0±0.1
+ +Table 1. Top-1 Classification Accuracy (%) for five benchmarks with CLIP models. Higher is better. For ease of reading, we highlight the highest accuracy in bold and the second best as underline, which also applies to the following tables. + +where $y_{jk}^{*}$ is the $k$ -th element of the $j$ -th row of the matrix $Y^{*}$ , and $\mathbb{1}$ is the indicator function. + +Similarly, SHOT [19] employs class-wise prototypes for K-means clustering, and AdaContrast [3] utilizes KNN to rectify the pseudo-labeling bias by averaging the probabilities of K-nearest neighbors. In contrast to SHOT which focuses on the global distribution in the latent space and KNN which concentrates on local similarity, our PLCA builds a local relation network for a sample and iteratively updates its pseudo-label in the global graph structure. We compare the effectiveness and computational speed for these three algorithms in Fig. 2 (b, c). Our PLCA achieves fewer pseudolabeling errors and maintains a more stable speed in the latent space with different dimensions. + +Remark. We treat the corrected pseudo-labels as targets for test-time training and adopt the same loss functions as the training stage, which scales our method to various tasks. + +# 3.3. Test-Time Optimization + +In this subsection, we explore a scalable and efficient optimization method for test-time adaptation, and this problem involves two key questions: Which parameters need to be updated and how to update them? + +To analyze the impact of updating different parts of CLIP, we compare several common policies: + +- BN Adapt [27] advices to combine the normalization statistics computed on the training dataset with the estimated ones on target samples, which is suitable for image corruption and has no extra training cost at test time. +- Tent [30] removes the statistics from the source data and updates the affine transformation parameters of BN layers, which is widely used in recent methods [22]. +Full-tune the model, which is the most expensive one. + +We show the experimental results in Fig. 4 (a, b) and ensure that only the updated scopes are different. Because counting the mean and variance of target domains on a mini-batch leads to severe bias, especially when the batch size is small, it brings hard-to-recover errors to pseudo-labeling at the first few iterations. However, for Vision Transformer (ViT) [7] with LayerNorm, normalization statistics are counted for each sample, and it will not suffer from the above problem. Therefore, we freeze all the normalization layers and update other parameters to avoid such model corruption. + +The choice of optimizer has a great impact on test-time adaptation [8]. We experiment with various learning rates for three representative optimizers, including stochastic gra + +
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓28.822.926.29.520.610.69.314.215.317.57.620.914.741.314.718.3±0.00
TTT++ (Offline) [20]✓12.811.111.27.317.18.26.59.49.97.95.05.113.78.810.69.6±0.00
SHOT (Offline) [19]✓13.411.616.37.315.98.27.19.49.410.26.38.312.89.813.610.6±0.00
BN Adapt [27]✓15.913.718.07.818.38.98.010.89.612.76.19.413.514.314.512.1±0.01
TENT [30]✓14.512.417.77.717.78.87.910.39.612.06.19.013.411.314.511.5±0.02
MEMO [35]✓13.912.216.37.416.68.27.49.89.310.76.19.312.610.014.310.9±0.02
TTT++ (Online) [20]✓15.514.123.69.125.111.48.113.213.113.46.66.917.612.513.613.6±0.03
SHOT (Online) [19]✓14.512.317.77.817.88.77.910.49.612.16.19.013.411.414.411.5±0.02
Ours (Online)✓12.811.414.96.715.87.76.98.98.610.15.68.011.910.512.810.2±0.04
+ +Table 2. Top-1 Classification Error (%) for all corruptions on CIFAR-10C (level 5). Lower is Better. SF denotes source free. + +
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓98.497.798.490.692.589.881.889.585.086.351.197.285.376.971.786.2±0.00
SHOT (Offline) [19]✓73.870.572.279.280.658.554.053.663.047.339.297.748.746.153.062.5±0.00
BN Adapt [27]✓87.190.689.587.693.480.071.970.681.565.946.889.873.563.267.577.3±0.30
TTT [29]✓73.771.473.176.393.471.366.664.481.352.441.764.755.752.255.766.3±0.00
MEMO [35]✓85.481.083.594.192.572.560.564.072.552.041.497.155.850.757.570.7±0.05
TENT [30]✓80.878.680.482.582.572.160.563.766.752.139.284.255.550.858.267.2±0.02
SHOT (Online) [19]✓83.982.383.783.983.872.661.965.768.654.839.485.958.153.162.369.3±0.03
Ours (Online)✓72.970.873.180.779.769.657.459.863.150.039.383.951.848.550.863.4±0.03
+ +Table 3. Top-1 Classification Error (%) for all corruptions on ImageNet-C (level 5). Lower is Better. SF denotes source free. + +
MethodsSourceBN AdaptTENTMEMOCoTTAOurs
CIFAR-10C18.3±0.013.8±0.412.1±0.710.9±0.311.5±0.110.4±0.1
ImageNet-C86.2±0.074.9±0.470.7±0.679.8±1.067.8±0.365.4±0.1
+ +Table 4. Continuous online adaptation following CoTTA [31]. We report the top-1 classification error $(\%)$ . Lower is Better. + +dient descent (SGD), SGD with momentum, and Adam [15]. Fig. 4 (c) exhibits the online adaptation process under the best learning rate. Optimizers with first/second-order momentum can adapt fast to the target distribution in most cases, but also cause fluctuations (e.g., SGD with momentum for RN50) and even continuing decline due to error accumulation (e.g., Adam for ViT-B/32). In contrast, vanilla SGD with a small learning rate can achieve stable and ascending performance. Since vanilla SGD can update the model parameters in the current optimal direction without being affected by historical gradients. + +Avoiding catastrophic forgetting during long-time adaptation is a problem worth paying attention to [24, 31]. This issue is also important for maintaining the zero-shot robustness of CLIP. We propose the parameter moving average to preserve the knowledge from the source model. Specifically, at any iteration $t \geq 1$ , we define the parameters after optimization as $\theta_t$ and update the moving average $\hat{\theta}_t$ as + +$$ +\hat {\theta} _ {t} = \pi \cdot \hat {\theta} _ {t - 1} + (1 - \pi) \cdot \theta_ {t}, \tag {9} +$$ + +where $\hat{\theta}_0$ is initialized as the parameters of source model $\theta_S$ and $\pi \in [0,1]$ is the momentum coefficient, which determines the degree of knowledge preservation. + +# 4. Experiment + +# 4.1. Setup + +Datasets. We evaluate on the following datasets: + +- CIFAR10 [17] and CIFAR100 [17] are two datasets consisting of low-resolution images, which differ from the common size of the training data of CLIP. We use them to evaluate the adaptability of our method to the distribution shift from image distortion caused by resize operations. +- Food101 [1] and Stanford Cars [16] are fine-grained datasets contains 101 food categories and 196 car categories, respectively. We use them for fine-grained tasks. +- ImageNet [6] is a large-scale dataset with 1000 classes, which is suitable for evaluating our method on category-intensive and real-world classification tasks. +- CIFAR-10C [12] and ImageNet-C [12] are created by test images of CIFAR10 and ImageNet with 15 types of corruptions in 5 levels, which are widely used to evaluate the robustness of test-time adaptation methods. Following the common protocol [27, 29, 30], we evaluate our method on the 5-level (worst) corruptions of all 15 types. +- For object detection, we use KITTI [9] to evaluate our method for automotive applications. KITTI comprises 8 categories of traffic participants and is mostly recorded in clear weather conditions. We follow Mirza et al. [22] to simulate degrading weathers of fog, rain and snow. +- For semantic segmentation, we use CarlaTTA [21] to conduct experiments. CarlaTTA contains five gradually changing scenarios, including day2night, clear2fog, clear2rain, dynamic, and highway. It challenges the methods to adapt to distribution shift over time. + +Implementation details. For test-time adaptation with + +![](images/3a594480495f98db8e5dafa9b869ecd94731344da64a543163b35c61d0e1b88f.jpg) +Figure 5. Visualization of the detection results on KITTI in the weather conditions of fog, rain, and snow. + +
MethodsSFFogRainSnow
Source✓22.8±0.065.5±0.025.6±0.0
ActMAD [22]✗47.7±1.081.4±0.264.5±0.0
BN Adapt [27]✓32.3±0.170.6±0.144.9±0.2
TTT [29]✓29.4±0.571.5±0.447.5±0.7
Ours (SimpAug)✓27.3±0.475.2±0.436.0±0.3
Ours (Online)✓43.2±0.381.6±0.252.3±0.2
+ +CLIP [25], we use the publicly available pretrained model as the source model, and evaluate our method on the test/validation sets of CIFAR10, CIFAR100, Food101, Cars, and ImageNet. We uniformly use "a photo of a {class}" as the prompt template, where the class token is replaced by the specific class name, such as "airplane", "deer", and "frog". Our method is run with a learning rate of 1e-6 for ResNet [11] backbone and 1e-5 for Vision Transformer [7] backbone. A batch size of 64 is adopted considering the memory constraint, while different batch sizes have little impact on our method, analyzed in the ablation study 4.4. Following Mirza et al. [22], we adapt a Wide-ResNet-40-2 [34] (WRN-40-2) pre-trained with AugMix [13] on CIFAR-10C, and an ImageNet pre-trained ResNet-18 [11] from PyTorch model zoo on ImageNet-C. We adopt a batch size of 128 and a learning rate of 1e-3, while all the compared methods and baselines use the hyperparameters reported by their authors. For object detection task, we adapt a YOLOv3 [26] pretrained on KITTI in clear weather to fog, rain and snow. For semantic segmentation task, we adapt a DeepLab-V2 [5] with a ResNet-101 backbone pretrained on clear split of CarlaTTA to the other five scenarios. We run experiments on 5 random seeds and report the mean and standard deviation for these runs. + +Offline and online adaptation. We evaluate our method in both offline and online settings. In the offline scenario, we can access all the test data and train the model on the entire test sets for 50 epochs, without considering the storage limitation. In the online scenario, the test samples arrive sequentially and do not reappear. We maintain a memory queue to store a certain amount of feature vectors, $10K$ by + +Table 5. Mean Average Precision (mAP@50) in KITTI with the most severe weather conditions, i.e. fog with only $30\mathrm{m}$ visibility, rain with $200\mathrm{mm/hr}$ intensity, and snow in level 5. Higher is better. SF denotes source free. + +
MethodsSFday2nightclear2fogclear2raindynamichighway
Source✓58.452.871.846.628.7
BN Adapt [27]✓62.056.871.452.632.8
TENT [30]✓61.556.070.950.332.0
MEMO [35]✓61.055.171.650.335.2
CoTTA [31]✓61.456.870.746.433.8
Ours (SimpAug)✓60.153.972.648.931.9
Ours (Online)✓62.456.873.951.534.7
+ +Table 6. Mean Intersection over Union (mIoU, %) on CarlaTTA. Higher is Better. SF denotes source free. + +default, for our PLCA. We also study the effect of adopting different memory capacities on our method in Sec. 4.4. Furthermore, our method maintains the performance in the more challenging single sample online adaptation task. + +# 4.2. Image Classification + +Results for adapting CLIP model are reported in Table 1. We find that updating both image and text encoders simultaneously can further improve the adaptability of CLIP model than freezing the text encoder as shown in Fig. 4 (c). We also compare with the method of using SimpAug and PLCA without re-training. The number of augmented verions for each test sample is set to 8 by default, which contains an original version. PLCA outperforms the our online method on multiple benchmarks, which may be due to the fact that online training does not sufficiently learn from the test samples with pseudo-labels, while offline adaptation addresses this issue by training repeatedly and providing more accurate pseudo-labels after each epoch. + +We present the results on CIFAR-10C and ImageNet-C in Table 2 and 3. Our method outperforms other online methods by a fair margin. Compared to works designed for offline adaptation, our method achieves comparable or even higher performance. It is noteworthy that MEMO [35] achieves higher performance than other baselines on adapting WRN-40-2, perhaps because of applying the same augmentation strategy, AugMix [13], for TTA as the training stage. However, when adapting ResNet-18 pre-trained with standard augmentation, MEMO does not maintain advantages due to the poor calibration of deep neural networks to augmented images with complex unseen transformations. + +
ModelsMethodsImageNet-V2-Sketch-A-R
RN-50CLIP (zero-shot)55.851.133.221.856.0
Ours (π = 0)57.253.133.822.559.2
Ours (π = 0.9)58.353.836.024.060.3
Ours (π = 0.99)57.452.636.224.059.1
RN-101CLIP (zero-shot)58.254.338.028.163.9
Ours (π = 0)59.755.939.827.066.9
Ours (π = 0.9)60.156.240.930.467.3
Ours (π = 0.99)59.355.440.831.066.6
ViT-B/32CLIP (zero-shot)59.854.740.930.266.7
Ours (π = 0)63.758.144.132.771.4
Ours (π = 0.9)62.157.143.633.470.5
Ours (π = 0.99)60.956.543.233.169.7
ViT-B/16CLIP (zero-shot)64.560.646.047.873.8
Ours (π = 0)69.163.650.151.479.1
Ours (π = 0.9)67.262.549.152.977.6
Ours (π = 0.99)65.961.848.552.076.6
+ +Continuous online adaptation. Following CoTTA [31] to continuously adapt the model to different corruptions, we test our method on CIFAR-10C and ImageNet-C, referred to Table 4. Our method outperforms other baselines. + +# 4.3. Object Detection and Semantic Segmentation + +To evaluate the effectiveness of our method in solving regression problems, we conduct experiments on KITTI using YOLOv3. We report the results in Table 5 and visualize the detecting boxes in Fig. 5. Our method outperforms BN Adapt [27] and TTT [29], which are scalable to other models and not limited by the main task, and also beats ActMAD [22], which utilizes statistics in source data to TTA, in clear-to-rain task. Note that when only using SimpAug for test-time augmentation, we improve the source model up to $10.4\%$ . The visualization shows that SimpAug helps the model recognize distant and occluded objects that are hard to detect, while online training with pseudo-labels further boosts the accuracy and filter out duplicate boxes. + +For the semantic segmentation task, building a graph with all pixels is computationally expensive. We are inspired by COMUS [33] and collect object-level features, which represent the nodes in the graph. The results are listed in Table 6. BN Adapt exhibits robustness in the distribution shifts over time, while other methods seem to have limited improvement in gradually changing environments. Our method outperforms CoTTA [31], which is designed for continuous test-time adaptation. + +More implementation details and comparison results can be found in the supplemental material. + +# 4.4. Ablation Study + +Number of augmentations. We study how the number of augmentation for single sample affects the performance of SimpAug, and conduct experiments on KITTI using YOLOv3, referred to Table 8. SimpAug improves the ac + +Table 7. Comparison with different $\pi$ values on robustness to distribution shift. Higher is Better. + +
Num1286432168421 (Source)
Fog28.227.727.326.425.925.024.622.8
Rain75.975.975.273.873.472.168.965.5
Snow37.637.036.034.632.830.628.725.6
+ +Table 8. mAP@50 of SimpAug with different augmentation numbers on KITTI. Higher is Better. + +
Memory Size100K10K1K100100Source
RN50CIFAR1083.083.083.482.982.282.168.7
ViT-B/32Food10186.486.385.885.785.785.780.7
+ +Table 9. Accuracy $(\%)$ of our online method with CLIP model in different sizes of memory queue. Higher is Better. + +
Batch Size12864321681Source
RN50CIFAR1082.883.083.582.983.381.068.7
ViT-B/32Food10186.486.386.386.686.587.180.7
+ +Table 10. Accuracy $(\%)$ of our online method with different batch sizes. Source denotes zero-shot performance of the CLIP model. + +curacy with the increase of augmentation numbers until the performance bottleneck. Large number of augmentation requires computational resources and storage. + +Size of memory queue. The memory size affects the inference speed and the accuracy of corrected pseudo-labels by PLCA. We conduct ablation experiments for online adaptation, as shown in Table 9. A large memory improves the ability of graph modeling the relations between samples. However, in online settings, old stored feature vectors have a higher error rate than the new ones, which affects the prediction of pseudo-labels for the current image. + +Momentum coefficient. $\pi$ is a momentum coefficient that affects the models' update speed and avoids catastrophic forgetting. We test the performance of the CLIP model without using PMA and with two $\pi$ values. The results listed in Table 7 show that ViT backbone is more resistant to catastrophic forgetting than ResNet, and our method can maintain the robustness of the CLIP model to distribution shift while performing test-time adaptation. + +Batch size. Most existing methods suffer from a small batch size in online adaptation, especially for those that rely on modifying normalization statistics of BN layers. As shown in Table 10, our method maintains comparable performance even in single sample online adaptation. + +# 5. Conclusion + +In this work, we propose an improved self-training method for fully test-time adaptation. In contrast to previous TTA methods, our IST explores the adaptability of the foundation model by employing CLIP as the source model. It goes beyond image classification and can be applied to object detection and semantic segmentation. IST outperforms existing TTA methods on different benchmarks and tasks by improving the quality of pseudo-labels and stabilizing the adaptation process. Experiments show that IST is scalable to a variety of pre-trained models and application tasks. + +# References + +[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part VI 13, pages 446-461. Springer, 2014. 3, 6 +[2] Collin Burns and Jacob Steinhardt. Limitations of post-hoc feature alignment for robustness. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2525-2533, 2021. 1 +[3] Dian Chen, Dequan Wang, Trevor Darrell, and Sayna Ebrahimi. Contrastive test-time adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 295-305, 2022. 1, 2, 4, 5 +[4] Liang Chen, Yong Zhang, Yibing Song, Ying Shan, and Lingqiao Liu. Improved test-time adaptation for domain generalization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24172-24182, 2023. 1, 2 +[5] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence, 40(4):834-848, 2017. 7 +[6] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248-255. 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In Proceedings of the IEEE international conference on computer vision workshops, pages 554–561, 2013. 6 +[17] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. 6 +[18] Xianfeng Li, Weijie Chen, Di Xie, Shicai Yang, Peng Yuan, Shiliang Pu, and Yueting Zhuang. A free lunch for unsupervised domain adaptive object detection without source data. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 8474-8481, 2021. 1, 2 +[19] Jian Liang, Dapeng Hu, and Jiashi Feng. Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation. In International conference on machine learning, pages 6028-6039. PMLR, 2020. 1, 2, 4, 5, 6 +[20] Yuejiang Liu, Parth Kothari, Bastien Van Delft, Baptiste Bellot-Gurlet, Taylor Mordan, and Alexandre Alahi. Ttt++: When does self-supervised test-time training fail or thrive? Advances in Neural Information Processing Systems, 34: 21808-21820, 2021. 1, 2, 6 +[21] Robert A Marsden, Mario Döbler, and Bin Yang. Introducing intermediate domains for effective self-training during test-time. arXiv preprint arXiv:2208.07736, 1(2):5, 2022. 6 +[22] Muhammad Jehanzeb Mirza, Pol Jane Soneira, Wei Lin, Mateusz Kozinski, Horst Possegger, and Horst Bischof. Actmad: Activation matching to align distributions for test-time-training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24152-24161, 2023. 1, 5, 6, 7, 8 +[23] Alexander Neubeck and Luc Van Gool. Efficient nonmaximum suppression. In 18th international conference on pattern recognition (ICPR'06), pages 850-855. IEEE, 2006. 3 +[24] Shuaicheng Niu, Jiaxiang Wu, Yifan Zhang, Yafo Chen, Shijian Zheng, Peilin Zhao, and Mingkui Tan. Efficient test-time model adaptation without forgetting. In International conference on machine learning, pages 16888-16905. PMLR, 2022. 1, 6 +[25] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748-8763. PMLR, 2021. 2, 3, 4, 5, 7 +[26] Joseph Redmon and Ali Farhadi. Yolov3: An incremental improvement. arXiv preprint arXiv:1804.02767, 2018. 7 +[27] Steffen Schneider, Evgenia Rusak, Luisa Eck, Oliver Bringmann, Wieland Brendel, and Matthias Bethge. Improving + +robustness against common corruptions by covariate shift adaptation. Advances in neural information processing systems, 33:11539-11551, 2020. 1, 2, 5, 6, 7, 8 +[28] Divya Shanmugam, Davis Blalock, Guha Balakrishnan, and John Guttag. Better aggregation in test-time augmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 1214-1223, 2021. 1, 3 +[29] Yu Sun, Xiaolong Wang, Zhuang Liu, John Miller, Alexei Efros, and Moritz Hardt. Test-time training with self-supervision for generalization under distribution shifts. In International conference on machine learning, pages 9229-9248. PMLR, 2020. 1, 2, 5, 6, 7, 8 +[30] Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell. Tent: Fully test-time adaptation by entropy minimization. arXiv preprint arXiv:2006.10726, 2020. 1, 2, 5, 6, 7 +[31] Qin Wang, Olga Fink, Luc Van Gool, and Dengxin Dai. Continual test-time domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7201-7211, 2022. 1, 2, 6, 7, 8 +[32] Longhui Yuan, Binhui Xie, and Shuang Li. Robust test-time adaptation in dynamic scenarios. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15922-15932, 2023. 1, 2 +[33] Andrii Zadaianchuk, Matthaeus Kleindessner, Yi Zhu, Francesco Locatello, and Thomas Brox. Unsupervised semantic segmentation with self-supervised object-centric representations. arXiv preprint arXiv:2207.05027, 2022. 8 +[34] Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. arXiv preprint arXiv:1605.07146, 2016. 7 +[35] Marvin Zhang, Sergey Levine, and Chelsea Finn. Memo: Test time robustness via adaptation and augmentation. Advances in Neural Information Processing Systems, 35: 38629-38642, 2022. 1, 2, 3, 6, 7 +[36] Hao Zhao, Yuejiang Liu, Alexandre Alahi, and Tao Lin. On pitfalls of test-time adaptation. arXiv preprint arXiv:2306.03536, 2023. 1, 2 +[37] Dengyong Zhou, Olivier Bousquet, Thomas Lal, Jason Weston, and Bernhard Schölkopf. Learning with local and global consistency. Advances in neural information processing systems, 16, 2003. 4 \ No newline at end of file diff --git a/2024/Improved Self-Training for Test-Time Adaptation/images.zip b/2024/Improved Self-Training for Test-Time Adaptation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..375c853e4f9ac45e3e3420059dd966ae8b6844c9 --- /dev/null +++ b/2024/Improved Self-Training for Test-Time Adaptation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c02f84ff4fd3be4a7a2e4f56b02bfe6a24ddaf37cd16fe386f26994779b9e643 +size 859531 diff --git a/2024/Improved Self-Training for Test-Time Adaptation/layout.json b/2024/Improved Self-Training for Test-Time Adaptation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b53d5ff72a290cd35551c14ad28406b4a357474c --- /dev/null +++ b/2024/Improved Self-Training for Test-Time Adaptation/layout.json @@ -0,0 +1,9159 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 143, + 103, + 451, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 103, + 451, + 121 + ], + "spans": [ + { + "bbox": [ + 143, + 103, + 451, + 121 + ], + "type": "text", + "content": "Improved Self-Training for Test-Time Adaptation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 177, + 144, + 416, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 177, + 144, + 416, + 172 + ], + "spans": [ + { + "bbox": [ + 177, + 144, + 416, + 172 + ], + "type": "text", + "content": "Jing Ma \nHuazhong University of Science and Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 241, + 174, + 350, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 241, + 174, + 350, + 185 + ], + "spans": [ + { + "bbox": [ + 241, + 174, + 350, + 185 + ], + "type": "text", + "content": "jingma001@gmail.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "text", + "content": "Test-time adaptation (TTA) is a technique to improve the performance of a pre-trained source model on a target distribution without using any labeled data. However, existing self-trained TTA methods often face the challenges of unreliable pseudo-labels and unstable model optimization. In this paper, we propose an Improved Self-Training (IST) approach, which addresses these challenges by enhancing the pseudo-label quality and stabilizing the adaptation process. Specifically, we use a simple augmentation strategy to generate multiple views of each test sample, and construct a graph structure to correct the pseudo-labels based on the similarity of the latent features. Moreover, we adopt a parameter moving average scheme to smooth the model updates and prevent catastrophic forgetting. Instead of using a model with fixed label space, we explore the adaptability of the foundation model CLIP to various downstream tasks at test time. Extensive experiments on various benchmarks show that IST can achieve significant and consistent improvements over the existing TTA methods in classification, detection, and segmentation tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 629 + ], + "type": "text", + "content": "Deep Neural Networks have performed superiorly in a broad scope of tasks, and exhibit surprising zero-shot generalization capabilities. However, in practical applications, behavior decline may occur owing to the distribution shifts of unknown domains, which leads to laborious efforts in data collection and model retraining. To address this issue, Test-Time Adaptation (TTA), aims to adapt the model to the target domain at test time, has emerged as a promising paradigm of increasing attention and research [19, 29, 30]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Early methods of TTA [22, 27, 30, 32] explore adapting the activation statistics and updating the affine transformation parameters of batch normalization layers to mitigate the distribution shifts from clean to corrupted images. These approaches are easily scalable to deep neural networks with different architectures, but their performance is often confined to specific ranges of distribution shifts due to the lim" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 319, + 210, + 535, + 344 + ], + "blocks": [ + { + "bbox": [ + 319, + 210, + 535, + 344 + ], + "lines": [ + { + "bbox": [ + 319, + 210, + 535, + 344 + ], + "spans": [ + { + "bbox": [ + 319, + 210, + 535, + 344 + ], + "type": "image", + "image_path": "edec926d0ab0ee9b0823530bff93a056de96d6fc33cd1af5141c71389f1adb3c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 350, + 547, + 407 + ], + "lines": [ + { + "bbox": [ + 304, + 350, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 547, + 407 + ], + "type": "text", + "content": "Figure 1. An illustration of test-time adaptation. The approach employs source models from a model zoo, where the source data is unknown. Source models adapt to target domains using one batch of test samples at a time. Self-training is a key component for updating models and providing more accurate online predictions." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 414, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 547, + 545 + ], + "type": "text", + "content": "ited adaptive capacity of batch normalization [2]. A series of works [4, 8, 20, 29] leverage self-supervised learning for test-time training (TTT) to update the model parameters before making predictions, which is conditional on having correlated gradients between the loss functions of the auxiliary and main tasks. However, an inappropriate pretext task may be detrimental to the learned model [20]. Moreover, although TTT is not restricted by the type of main task, it typically requires modifying the training process to accommodate a self-supervised task, which increases the cost of applying TTT to pre-trained models [36]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "type": "text", + "content": "Another line of research seeks to utilize the predictions of the model itself as pseudo-labels and re-train the model, which is known as the self-training strategy. Owing to the poor calibration of neural networks [10], pseudo-labels generated by the source model may be inaccurate and noisy for target data. Liang, et al. [19] propose to attain class-wise prototypes by clustering and further obtain cleaner pseudolabels. Recent works [3, 18, 28, 31, 35] suggest performing different data augmentations on a test sample to improve the model's prediction. On the other hand, some works [3, 24, 31, 32] focus on stabilizing the adaptation procedure at test time by adopting active selection, re-weighting strategy, or knowledge distillation. Generally, self-training-based approaches make no strong assumptions about distrib" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23701" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "bution shifts and types of task, thus they are more ubiquitous for real-world applications. However, existing methods still suffer from the following limitations: 1) Test-time augmentation may degrade performance for voluminous and aggregated categories, 2) Pseudo-label correction has not fully exploited the model's intermediate representations of the target domain. 3) Error accumulation and catastrophic forgetting may occur during the adaptation process." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 407 + ], + "type": "text", + "content": "In this paper, we aim to address the above issues by analyzing the key components of self-training, i.e., pseudolabel generation, correction, and model optimization. We challenge the task of fully test-time adaptation [30], which supposes that any information about source data is unavailable, including original samples, intermediate features, and all kinds of statistics. To this end, we propose an Improved Self-Training (IST) method. In contrast to applying complex transformations, IST generates pseudo-labels with a simple test-time augmentation strategy to mitigate the poor calibration caused by unused functions. Moreover, an algorithm is proposed to correct the pseudo-labels by leveraging graph structures constructed with target samples in the latent space. Furthermore, we compare common optimization policies and propose parameter moving average to stabilize the adaptation process and alleviate catastrophic forgetting. Finally, we scale up IST to basic computer vision tasks and conduct extensive experiments on various benchmarks. The results demonstrate that IST achieves credible and consistent performance gains over existing TTA methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 407, + 265, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 407, + 265, + 418 + ], + "spans": [ + { + "bbox": [ + 59, + 407, + 265, + 418 + ], + "type": "text", + "content": "In summary, our main contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 419, + 287, + 526 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 419, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 419, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 287, + 455 + ], + "type": "text", + "content": "- We propose a plug-and-play strategy for generating and correcting pseudo-labels, which is effective and efficient for test-time augmentation without additional retraining." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 455, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 287, + 491 + ], + "type": "text", + "content": "- We propose an improved self-training method for fully test-time adaptation, which is scalable to a variety of pretrained models and application tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 491, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 526 + ], + "type": "text", + "content": "- We exhibit the effectiveness and robustness of our method on various benchmarks, including image classification, object detection, and semantic segmentation." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 536, + 134, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 134, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 134, + 548 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 555, + 289, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 289, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 289, + 688 + ], + "type": "text", + "content": "Test-Time Adaptation (TTA) is a challenging task, that aims to adapt the model to arbitrary distributions and achieve improved performance at test time. BN Adapt [27] replaces the activation statistics of batch normalization layers with the estimated statistics of the corrupted images to improve the robustness of the model. Further, Tent [30] discards the statistics from the source data and updates the affine transformation parameters by entropy minimization. Sun, et al. [29] propose introducing the self-supervised pretext task to adapt the main task by updating the model parameters before making predictions. Following this way, TTT [29] and" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 251 + ], + "type": "text", + "content": "TTT-MAE [8] employ rotation prediction and image generation as auxiliary tasks, respectively. TTT++ [20] and ITTA [4] rely on more general contrastive learning tasks. To effectively utilize a model without source data to solve domain adaptation problems, SHOT [19] exploits information maximization and self-supervised pseudo-labeling to align the target representation to the source hypothesis. MEMO [35] and SFOD [18] augment test samples to obtain robust pseudo labels and self-train the model with entropy descent. AdaContrast [3] denoises pseudo-labels via soft voting among nearest neighbors and applies weak-strong augmentation consistency as a regularizer. For non-stationary and continually changing environments, RoTTA [32] and CoTTA [31] are proposed to effectively stabilize the adaptation procedure and avoid catastrophic forgetting." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 252, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 547, + 431 + ], + "type": "text", + "content": "Existing approaches tend to address the distribution shift caused by image corruption, but infrequently consider unconstrained conditions in nature, such as label shift and correlation shift. Hence, we propose to employ the Contrastive Language-Image Pre-trained model (CLIP) [25] as the source model for test-time adaptation. In this way, we have no need to pre-train models on different benchmarks, thus avoiding additional assumptions of the label distribution. Meanwhile, CLIP can provide a suitable starting point for the adaptation process due to its zero-shot capability and generalized feature properties, which have been proven to have a significant impact on post-adaptation [36]. From an application perspective, exploring how to improve the performance of CLIP in realistic environments at test time has important practical value for foundation models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 442, + 361, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 361, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 361, + 453 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "We address the problem of adapting a pre-trained model to new domains at test time. Given a source model " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\theta_S" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " trained on the source domain " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ", the goal is to adapt it to the target domain " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " with only unlabeled data " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ". We explicitly divide the model into encoder " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "g_{\\varphi}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " and predictor " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ", and denote " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "f = h \\circ g" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ". By default, we define the final linear layer as the predictor and the rest as the encoder. A data point " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "x_i \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " is projected into a latent space " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_i \\in \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " by the encoder, and then mapped to a label space " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "y_i \\in \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": " by the predictor. Our proposed method applies a Simple Augmentation (SimpAug) to the original image and produces augmented points " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\widetilde{x} \\sim \\mathcal{U}(x)" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ". Expanded data sets " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{x\\} \\cap \\{\\widetilde{x}\\}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ", consisting of original and augmented samples, are fed into the encoder to generate intermediate features " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{z\\}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": ". Subsequently, we perform a Pseudo-Label Correction Algorithm (PLCA) to reinforce the prediction of unlabeled data by utilizing the graph structure in the latent space. To stabilize the self-training process at test time, we analyze the primary optimization algorithms and adopt Parameter Moving Average (PMA) for iterative updating. The pipeline of our method can be referred to Fig. 3." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": "1The code is available at https://github.com/JingInAI/IST4TTA" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23702" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 127, + 142 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 127, + 142 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 127, + 142 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 127, + 142 + ], + "type": "image", + "image_path": "d679df4ad291ae18b05f1336629df6800a0f1c4177ab10aa453ada0a3a1d00b8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 144, + 105, + 149 + ], + "lines": [ + { + "bbox": [ + 88, + 144, + 105, + 149 + ], + "spans": [ + { + "bbox": [ + 88, + 144, + 105, + 149 + ], + "type": "text", + "content": "bustard" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 72, + 156, + 121, + 205 + ], + "blocks": [ + { + "bbox": [ + 88, + 149, + 105, + 155 + ], + "lines": [ + { + "bbox": [ + 88, + 149, + 105, + 155 + ], + "spans": [ + { + "bbox": [ + 88, + 149, + 105, + 155 + ], + "type": "text", + "content": "43.41%" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 72, + 156, + 121, + 205 + ], + "lines": [ + { + "bbox": [ + 72, + 156, + 121, + 205 + ], + "spans": [ + { + "bbox": [ + 72, + 156, + 121, + 205 + ], + "type": "image", + "image_path": "d471d996d49986a5c54d9afb2149372ff2045ef2e01e819ecb47385856cb0d2c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 209, + 104, + 213 + ], + "lines": [ + { + "bbox": [ + 89, + 209, + 104, + 213 + ], + "spans": [ + { + "bbox": [ + 89, + 209, + 104, + 213 + ], + "type": "text", + "content": "prison" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 72, + 220, + 121, + 270 + ], + "blocks": [ + { + "bbox": [ + 88, + 213, + 105, + 218 + ], + "lines": [ + { + "bbox": [ + 88, + 213, + 105, + 218 + ], + "spans": [ + { + "bbox": [ + 88, + 213, + 105, + 218 + ], + "type": "text", + "content": "17.32%" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 72, + 220, + 121, + 270 + ], + "lines": [ + { + "bbox": [ + 72, + 220, + 121, + 270 + ], + "spans": [ + { + "bbox": [ + 72, + 220, + 121, + 270 + ], + "type": "image", + "image_path": "2aaf1fab63f4cd3e6ff8f5b5fac5c30fe06aada208b15f438548c37ed39c1d3b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 281, + 547, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 547, + 326 + ], + "type": "text", + "content": "Figure 2. (a) Visualization of images in ImageNet [6] with two kinds of test-time augmentation polices. Predictions are provided by CLIP (ViT-B/32), with correct and incorrect classes marked in green and red, respectively. (b) Error rate of pseudo-labeling counted on the test/validation set for each benchmark. (c) Computational speed of three pseudo-label correction algorithms on a fixed-size 10K sample set, averaged over 10 runs. 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Usage Time (seconds)SHOTKNNOurs
CLIP - RN507.5011.5283.911
CLIP - ViT-B/323.2391.2393.601
", + "image_path": "acacaeaa6cfa1763e052d210f0559ca833d6dd57030f98008ede573c85a5b11a.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "table_body" + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 335, + 213, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 213, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 213, + 348 + ], + "type": "text", + "content": "3.1. Simple Augmentation Strategy" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 354, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 521 + ], + "type": "text", + "content": "Typically, existing test-time augmentation methods tend to employ sophisticated augmentation functions to be applied to the test image [35]. Although this is a reasonable approach to extract invariant encodings from data augmentations, it may lead to serious corruption of original attributes. Fig. 2 (a) shows that the differences between classes are reflected in a few attribute variations for class-dense or fine-grained tasks. Complex augmentations, such as altering the brightness, contrast, saturation, and hue of the image, will impair the representative attributes of the category. Another type of augmentation, such as image rotation and adding Gaussian noise, will cause high-confidence erroneous predictions, especially for models without the use of similar transformations during training, e.g. CLIP [25]." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "content": "To this end, we consider the standard policy (crops, scales, and horizontal flips) for test-time augmentation. On the one hand, crops and scales can zoom in on the local regions of the image, reduce the interference of background pixels, and increase the model's attention to tiny objects. On the other hand, we preserve the position information of augmented versions in the original coordinate system and project the predictions to the primal image space, which is beneficial for solving regression problems, e.g. detection and segmentation. Specifically, we define the ratio of the cropped region to the original area as " + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "inline_equation", + "content": "r \\sim U(r_{min}, r_{max})" + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "content": " and the aspect ratio as " + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "inline_equation", + "content": "a \\sim U(a_{min}, a_{max})" + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "content": ". Given an image " + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "content": " with the size of " + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "content": ", the length and width of the cropped region are calculated as" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 56, + 696, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 696, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 56, + 696, + 287, + 711 + ], + "type": "interline_equation", + "content": "w = \\sqrt {H \\times W \\times r \\times a}, \\quad h = \\sqrt {H \\times W \\times r / a}. (1)", + "image_path": "387bc2138fcff36b3ca024ec85727d8719b7add94cd150b0202676d887aa1780.jpg" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": "Then, we randomly select the top-left corner of the cropped region " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "U(0,H - h)" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "U(0,W - w)" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": ", respectively. The cropped sub-image is flipped horizontally with a probability of " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "p_{hf}" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " and scaled to the original size " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": ". In general, we set " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "r_{min} = 0.7" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "r_{max} = 1.0" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " to ensure the clarity of augmented images, and " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "a_{min} = 0.75\\times H / W" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "a_{max} = 1.33\\times H / W" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " to avoid the distortion of the aspect ratio. " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "p_{hf}" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " is set to 0.5 by default. We save the set of parameters " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "(i,j,h,w,hf)" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " for each augmented version, where " + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "hf" + }, + { + "bbox": [ + 304, + 335, + 545, + 456 + ], + "type": "text", + "content": " is a binary variable indicating whether the image is flipped." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 456, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 552 + ], + "type": "text", + "content": "We discard the operation of averaging the predictions of augmented samples, since it implicitly assumes that the augmentation functions have no influence on which predictions are corrected and which are corrupted [28]. Instead, motivated by Non-Maximum Suppression (NMS) [23], we extract the predictive probabilities of images in the augmentation space " + }, + { + "bbox": [ + 304, + 456, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{x}_j\\}_{j=1}^m \\sim \\mathcal{U}(x_i)" + }, + { + "bbox": [ + 304, + 456, + 545, + 552 + ], + "type": "text", + "content": ", and select the most confident class as the final prediction, which is formulated as" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 361, + 558, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 558, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 361, + 558, + 545, + 574 + ], + "type": "interline_equation", + "content": "\\hat {y} \\left(x _ {i}\\right) = \\arg \\max _ {c} \\left\\{p _ {c} \\left(\\widetilde {x} _ {j}\\right) \\right\\} _ {j = 1} ^ {m}, \\tag {2}", + "image_path": "e8073a07a5c2f2bef3603ae1bf79fb520a574b054d000b56573875cc820bfd7d.jpg" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "content": " is the class label, and " + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "content": " is the probability of class " + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "content": ". In contrast to the image classification task, NMS is applied to the set of detected boxes with high confidence scores and IOU values for object detection, and applied to the set of predictions for a single pixel from augmented versions for semantic segmentation." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We compare the performance with MEMO [35], using AugMix [13] and averaging predictive probabilities for test-time augmentation, referred to Fig. 2 (a, b). Results demonstrate that SimpAug is more robust in class-dense and fine-grained benchmarks, e.g. ImageNet [6] and Food101 [1]." + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23703" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 236, + 251 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 236, + 251 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 236, + 251 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 236, + 251 + ], + "type": "image", + "image_path": "097d02906f8726db376037ddc0755fbf0b93a7cbb9681a7e473c659b12a2fb0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 146, + 262, + 156, + 270 + ], + "lines": [ + { + "bbox": [ + 146, + 262, + 156, + 270 + ], + "spans": [ + { + "bbox": [ + 146, + 262, + 156, + 270 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 236, + 70, + 525, + 260 + ], + "blocks": [ + { + "bbox": [ + 236, + 70, + 525, + 260 + ], + "lines": [ + { + "bbox": [ + 236, + 70, + 525, + 260 + ], + "spans": [ + { + "bbox": [ + 236, + 70, + 525, + 260 + ], + "type": "image", + "image_path": "576754eaec460be4c575161c27fa9b1b23ead223c1e6a398bc2ffb7312ca5df1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 398, + 262, + 408, + 270 + ], + "lines": [ + { + "bbox": [ + 398, + 262, + 408, + 270 + ], + "spans": [ + { + "bbox": [ + 398, + 262, + 408, + 270 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "text", + "content": "Figure 3. The framework of our approach. At the beginning of test-time adaptation, the model is initialized with the source parameters " + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_0 = \\theta_S" + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "text", + "content": ". A target sample " + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "text", + "content": " arriving at time step " + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "text", + "content": " is transformed by SimpAug. We maintain a fixed-size memory queue for storing feature vectors and probabilities of target samples and their augmented versions. PLCA utilizes the graph structure formed by the stored vectors to correct the pseudo-labels generated by the model " + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_{t - 1}" + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "text", + "content": ", and then employs NMS to select the most reliable prediction. PMA modifies the optimized parameters " + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 46, + 273, + 545, + 350 + ], + "type": "text", + "content": " to preserve the knowledge of the source model. We visualize the features extracted by the image encoder of CLIP (RN50) on CIFAR10. Translucent-colored dots represent correctly classified images, gray dots represent failure cases, and opaque dots represent misclassified samples corrected by PLCA." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 354, + 239, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 239, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 239, + 366 + ], + "type": "text", + "content": "3.2. Pseudo-Label Correction Algorithm" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 372, + 287, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 527 + ], + "type": "text", + "content": "Although test-time augmentation can improve the robustness of distribution shifts, the pseudo labels annotated by the source model are still inaccurate and noisy for target data. To obtain cleaner labels, a series of methods [3, 19] explore the latent space of the source model to correct erroneous labeling. By visualizing the features on target domains using CLIP's visual encoder [25] in Fig. 3, we observe that the representation of different classes in the latent space exhibits clustering patterns. However, numerous target samples in the same cluster or manifold are misclassified. Inspired by [37], we propose a pseudo-label correction algorithm through learning from the graph structure constructed with only target data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 287, + 575 + ], + "type": "text", + "content": "We consider feature vectors in the latent space " + }, + { + "bbox": [ + 47, + 528, + 287, + 575 + ], + "type": "inline_equation", + "content": "\\{z_i\\}_{i=1}^n \\in \\mathcal{Z}" + }, + { + "bbox": [ + 47, + 528, + 287, + 575 + ], + "type": "text", + "content": " as vertices in a graph, and the edges between vertices are defined by the distances between a point and its K-nearest neighbors. Specifically, the edges are weighted by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 71, + 582, + 287, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 582, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 71, + 582, + 287, + 622 + ], + "type": "interline_equation", + "content": "w _ {i j} = \\left\\{ \\begin{array}{l l} 1, & i = j, \\\\ 1 - \\frac {\\| z _ {i} - z _ {j} \\| _ {2}}{\\max _ {j} \\| z _ {i} - z _ {j} \\| _ {2}}, & z _ {j} \\in \\mathcal {N} _ {K} (z _ {i}), \\\\ 0, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}", + "image_path": "cd69ebcb7c66186b8efda4cc76f37aeec50d0fc9c543f22c6ce186916dd3c105.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Note that self-reinforcement is added to prevent the instability caused by the accumulation of erroneous predictions in the spread process. By default, we set " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "K = 50" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ". To guarantee the information spread symmetrically, we build a symmetric non-negative matrix " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "W = (w_{ij})_{n\\times n} + (w_{ji})_{n\\times n}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " and normalize it by " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "S = D^{-1 / 2}WD^{-1 / 2}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " for following iterations, where " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " is a diagonal matrix with " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "D_{ii} = \\sum_{j}w_{ij}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "text", + "content": "We define an initial label matrix " + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "inline_equation", + "content": "Y(0) = (y_{ij})_{n \\times m}" + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "inline_equation", + "content": "y_{ij} = p_j(x_i)" + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "text", + "content": " is the predictive probability of the sample " + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "text", + "content": " belonging to the class " + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 354, + 545, + 402 + ], + "type": "text", + "content": ". Afterward, we iteratively update the label matrix by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 349, + 409, + 545, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 409, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 349, + 409, + 545, + 422 + ], + "type": "interline_equation", + "content": "Y (t + 1) = \\alpha S Y (t) + (1 - \\alpha) Y (0), \\tag {4}", + "image_path": "9c359209ce2521a8e68314be136808be2c143cde1a7aff642d7b9764aa178446.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "type": "text", + "content": " is a hyper-parameter to balance the influence of initial labels and the information spread. By repeating the Eqn. 4 for " + }, + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 429, + 545, + 464 + ], + "type": "text", + "content": " times, we obtain the final label matrix" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 471, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 471, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 329, + 471, + 545, + 503 + ], + "type": "interline_equation", + "content": "Y (T) = \\alpha^ {T} S ^ {T} Y (0) + (1 - \\alpha) \\sum_ {t = 0} ^ {T - 1} \\alpha^ {t} S ^ {t} Y (0). \\tag {5}", + "image_path": "147f41dd65e333dcbb24e907d863d7d5f81e57667a57d1eac4c3d1dfd65d329b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "type": "inline_equation", + "content": "0 < \\alpha < 1" + }, + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "type": "text", + "content": " and the spectral radius of " + }, + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 509, + 545, + 533 + ], + "type": "text", + "content": " is less than or equal to 1, we have" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 538, + 434, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 538, + 434, + 557 + ], + "spans": [ + { + "bbox": [ + 340, + 538, + 434, + 557 + ], + "type": "interline_equation", + "content": "\\lim _ {T \\to \\infty} \\alpha^ {T} S ^ {T} Y (0) = 0,", + "image_path": "4e0bf9ad63c6f9a4fb4f5b7f15c636f76103c908baa0236d7bfc29b5ed25b65a.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 341, + 559, + 545, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 559, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 341, + 559, + 545, + 593 + ], + "type": "interline_equation", + "content": "\\lim _ {T \\rightarrow \\infty} \\sum_ {t = 0} ^ {T - 1} \\alpha^ {t} S ^ {t} Y (0) = (I - \\alpha S) ^ {- 1} Y (0). \\tag {6}", + "image_path": "db260db022ac717048a519946760a5a7c97f158bb9e9749c29679868c4440519.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 599, + 539, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 539, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 539, + 612 + ], + "type": "text", + "content": "Therefore, the final label matrix can be approximated by" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 329, + 617, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 617, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 329, + 617, + 545, + 635 + ], + "type": "interline_equation", + "content": "Y ^ {*} = \\lim _ {T \\rightarrow \\infty} Y (T) = (1 - \\alpha) (I - \\alpha S) ^ {- 1} Y (0). \\tag {7}", + "image_path": "484d5696cad30253ac7af53c6434b0b98757433106b9a087e3880aa7e5c2f368.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 641, + 506, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 641, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 641, + 506, + 653 + ], + "type": "text", + "content": "Finally, we correct the pseudo labels in Eqn. 2 by" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 660, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 660, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 318, + 660, + 545, + 677 + ], + "type": "interline_equation", + "content": "\\hat {y} \\left(x _ {i}\\right) = \\arg \\max _ {c} \\left\\{p _ {c} \\left(\\widetilde {x} _ {j}\\right) \\times \\mathbb {1} _ {\\arg \\max _ {k} y _ {j k} ^ {*} = c} \\right\\} _ {j = 1} ^ {m}, \\tag {8}", + "image_path": "b5d93c6ed70cf0a8afa1e446cd7ef43e0c8f24706c20389c2155daffae572241.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "type": "text", + "content": "2This linear system can be solved by the conjugate gradient method because " + }, + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "type": "inline_equation", + "content": "I - \\alpha S" + }, + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "type": "text", + "content": " is symmetric and positive definite. 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Online test-time adaptation following [29]. We compare the impact of updating different parts of CLIP and show the top-1 accuracy " + }, + { + "bbox": [ + 46, + 213, + 546, + 247 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 213, + 546, + 247 + ], + "type": "text", + "content": " in five benchmarks with RN50 (a) and ViT-B/32 (b). To explore the impact of three optimizers on CNN-based and Transformer-based models, we freeze the text encoder in CLIP and update the image encoder. The adaptation process is visualized in (c)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 58, + 252, + 537, + 402 + ], + "blocks": [ + { + "bbox": [ + 58, + 252, + 537, + 402 + ], + "lines": [ + { + "bbox": [ + 58, + 252, + 537, + 402 + ], + "spans": [ + { + "bbox": [ + 58, + 252, + 537, + 402 + ], + "type": "table", + "html": "
MethodsModelsCIFAR10CIFAR100Food101CutsImageNetModelsCIFAR10CIFAR100Food101CutsImageNet
CLIP (zero-shot) [25]ResNet-5068.7±0.037.9±0.074.4±0.053.9±0.055.8±0.0ResNet-10178.1±0.041.2±0.077.5±0.060.7±0.058.2±0.0
Ours (SimpAug)69.0±0.138.7±0.175.4±0.054.0±0.056.8±0.078.8±0.142.0±0.178.7±0.061.0±0.059.2±0.0
Ours (PLCA)78.9±0.149.0±0.180.8±0.062.0±0.060.9±0.084.2±0.155.0±0.183.9±0.068.8±0.063.2±0.0
Ours (Online)83.0±0.252.8±0.479.5±0.256.9±0.458.3±0.189.1±0.159.0±0.282.6±0.264.0±0.360.1±0.0
Ours (Offline)84.6±0.154.1±0.581.0±0.065.9±0.160.2±0.092.1±0.163.4±0.185.1±0.071.4±0.262.6±0.0
CLIP (zero-shot) [25]ViT-B/3288.8±0.061.1±0.080.7±0.058.6±0.059.8±0.0ViT-B/1689.3±0.064.0±0.086.6±0.063.9±0.064.5±0.0
Ours (SimpAug)89.6±0.162.1±0.182.3±0.058.9±0.061.1±0.090.1±0.165.7±0.187.6±0.064.3±0.065.5±0.0
Ours (PLCA)92.8±0.169.7±0.186.1±0.065.7±0.065.8±0.094.3±0.073.0±0.190.3±0.071.0±0.069.9±0.0
Ours (Online)92.9±0.172.1±0.286.3±0.162.1±0.362.1±0.194.8±0.074.6±0.190.2±0.067.0±0.167.2±0.1
Ours (Offline)95.7±0.075.9±0.187.1±0.169.3±0.066.2±0.096.4±0.078.5±0.191.8±0.073.4±0.172.0±0.1
", + "image_path": "8de40d1a38228ea265d19fabd2d65c7be5f1a483a91b104972e400245bb01e27.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 405, + 546, + 428 + ], + "lines": [ + { + "bbox": [ + 46, + 405, + 546, + 428 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 546, + 428 + ], + "type": "text", + "content": "Table 1. Top-1 Classification Accuracy (%) for five benchmarks with CLIP models. Higher is better. For ease of reading, we highlight the highest accuracy in bold and the second best as underline, which also applies to the following tables." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "inline_equation", + "content": "y_{jk}^{*}" + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "content": "-th element of the " + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "content": "-th row of the matrix " + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "inline_equation", + "content": "Y^{*}" + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathbb{1}" + }, + { + "bbox": [ + 47, + 433, + 287, + 456 + ], + "type": "text", + "content": " is the indicator function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 458, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 601 + ], + "type": "text", + "content": "Similarly, SHOT [19] employs class-wise prototypes for K-means clustering, and AdaContrast [3] utilizes KNN to rectify the pseudo-labeling bias by averaging the probabilities of K-nearest neighbors. In contrast to SHOT which focuses on the global distribution in the latent space and KNN which concentrates on local similarity, our PLCA builds a local relation network for a sample and iteratively updates its pseudo-label in the global graph structure. We compare the effectiveness and computational speed for these three algorithms in Fig. 2 (b, c). Our PLCA achieves fewer pseudolabeling errors and maintains a more stable speed in the latent space with different dimensions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 601, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 637 + ], + "type": "text", + "content": "Remark. We treat the corrected pseudo-labels as targets for test-time training and adopt the same loss functions as the training stage, which scales our method to various tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 647, + 181, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 181, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 181, + 659 + ], + "type": "text", + "content": "3.3. Test-Time Optimization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "In this subsection, we explore a scalable and efficient optimization method for test-time adaptation, and this problem involves two key questions: Which parameters need to be updated and how to update them?" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 434, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 546, + 456 + ], + "type": "text", + "content": "To analyze the impact of updating different parts of CLIP, we compare several common policies:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 459, + 545, + 555 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 306, + 459, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 545, + 506 + ], + "type": "text", + "content": "- BN Adapt [27] advices to combine the normalization statistics computed on the training dataset with the estimated ones on target samples, which is suitable for image corruption and has no extra training cost at test time." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 506, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 545, + 542 + ], + "type": "text", + "content": "- Tent [30] removes the statistics from the source data and updates the affine transformation parameters of BN layers, which is widely used in recent methods [22]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 543, + 533, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 543, + 533, + 555 + ], + "spans": [ + { + "bbox": [ + 306, + 543, + 533, + 555 + ], + "type": "text", + "content": "Full-tune the model, which is the most expensive one." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 556, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 675 + ], + "type": "text", + "content": "We show the experimental results in Fig. 4 (a, b) and ensure that only the updated scopes are different. Because counting the mean and variance of target domains on a mini-batch leads to severe bias, especially when the batch size is small, it brings hard-to-recover errors to pseudo-labeling at the first few iterations. However, for Vision Transformer (ViT) [7] with LayerNorm, normalization statistics are counted for each sample, and it will not suffer from the above problem. Therefore, we freeze all the normalization layers and update other parameters to avoid such model corruption." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "The choice of optimizer has a great impact on test-time adaptation [8]. We experiment with various learning rates for three representative optimizers, including stochastic gra" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23705" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 183 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 183 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 183 + ], + "type": "table", + "html": "
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓28.822.926.29.520.610.69.314.215.317.57.620.914.741.314.718.3±0.00
TTT++ (Offline) [20]✓12.811.111.27.317.18.26.59.49.97.95.05.113.78.810.69.6±0.00
SHOT (Offline) [19]✓13.411.616.37.315.98.27.19.49.410.26.38.312.89.813.610.6±0.00
BN Adapt [27]✓15.913.718.07.818.38.98.010.89.612.76.19.413.514.314.512.1±0.01
TENT [30]✓14.512.417.77.717.78.87.910.39.612.06.19.013.411.314.511.5±0.02
MEMO [35]✓13.912.216.37.416.68.27.49.89.310.76.19.312.610.014.310.9±0.02
TTT++ (Online) [20]✓15.514.123.69.125.111.48.113.213.113.46.66.917.612.513.613.6±0.03
SHOT (Online) [19]✓14.512.317.77.817.88.77.910.49.612.16.19.013.411.414.411.5±0.02
Ours (Online)✓12.811.414.96.715.87.76.98.98.610.15.68.011.910.512.810.2±0.04
", + "image_path": "a1716dea0cf1ff0d761e615332f6d6ab4d6e4b7d94c23ce1b5b306e1c7090696.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 202, + 545, + 306 + ], + "blocks": [ + { + "bbox": [ + 72, + 186, + 520, + 198 + ], + "lines": [ + { + "bbox": [ + 72, + 186, + 520, + 198 + ], + "spans": [ + { + "bbox": [ + 72, + 186, + 520, + 198 + ], + "type": "text", + "content": "Table 2. Top-1 Classification Error (%) for all corruptions on CIFAR-10C (level 5). Lower is Better. SF denotes source free." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 202, + 545, + 306 + ], + "lines": [ + { + "bbox": [ + 49, + 202, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 49, + 202, + 545, + 306 + ], + "type": "table", + "html": "
MethodsSFGaussShotImpulDefcsGlsMtnZmSnwFrstFgBrtCntElsPxJpgMean
Source✓98.497.798.490.692.589.881.889.585.086.351.197.285.376.971.786.2±0.00
SHOT (Offline) [19]✓73.870.572.279.280.658.554.053.663.047.339.297.748.746.153.062.5±0.00
BN Adapt [27]✓87.190.689.587.693.480.071.970.681.565.946.889.873.563.267.577.3±0.30
TTT [29]✓73.771.473.176.393.471.366.664.481.352.441.764.755.752.255.766.3±0.00
MEMO [35]✓85.481.083.594.192.572.560.564.072.552.041.497.155.850.757.570.7±0.05
TENT [30]✓80.878.680.482.582.572.160.563.766.752.139.284.255.550.858.267.2±0.02
SHOT (Online) [19]✓83.982.383.783.983.872.661.965.768.654.839.485.958.153.162.369.3±0.03
Ours (Online)✓72.970.873.180.779.769.657.459.863.150.039.383.951.848.550.863.4±0.03
", + "image_path": "fa0d8b980703d8715f281e3ee7f566dec4320b2f0f65298f72214daeb97978e2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 328, + 288, + 375 + ], + "blocks": [ + { + "bbox": [ + 71, + 309, + 520, + 320 + ], + "lines": [ + { + "bbox": [ + 71, + 309, + 520, + 320 + ], + "spans": [ + { + "bbox": [ + 71, + 309, + 520, + 320 + ], + "type": "text", + "content": "Table 3. Top-1 Classification Error (%) for all corruptions on ImageNet-C (level 5). Lower is Better. SF denotes source free." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 328, + 288, + 375 + ], + "lines": [ + { + "bbox": [ + 48, + 328, + 288, + 375 + ], + "spans": [ + { + "bbox": [ + 48, + 328, + 288, + 375 + ], + "type": "table", + "html": "
MethodsSourceBN AdaptTENTMEMOCoTTAOurs
CIFAR-10C18.3±0.013.8±0.412.1±0.710.9±0.311.5±0.110.4±0.1
ImageNet-C86.2±0.074.9±0.470.7±0.679.8±1.067.8±0.365.4±0.1
", + "image_path": "88b621620c7d417ea0b40a4484e2c834e69a711bb3545bf7a4b36067c0f1c86a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 378, + 287, + 400 + ], + "lines": [ + { + "bbox": [ + 47, + 378, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 287, + 400 + ], + "type": "text", + "content": "Table 4. Continuous online adaptation following CoTTA [31]. We report the top-1 classification error " + }, + { + "bbox": [ + 47, + 378, + 287, + 400 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 378, + 287, + 400 + ], + "type": "text", + "content": ". Lower is Better." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 410, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 543 + ], + "type": "text", + "content": "dient descent (SGD), SGD with momentum, and Adam [15]. Fig. 4 (c) exhibits the online adaptation process under the best learning rate. Optimizers with first/second-order momentum can adapt fast to the target distribution in most cases, but also cause fluctuations (e.g., SGD with momentum for RN50) and even continuing decline due to error accumulation (e.g., Adam for ViT-B/32). In contrast, vanilla SGD with a small learning rate can achieve stable and ascending performance. Since vanilla SGD can update the model parameters in the current optimal direction without being affected by historical gradients." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": "Avoiding catastrophic forgetting during long-time adaptation is a problem worth paying attention to [24, 31]. This issue is also important for maintaining the zero-shot robustness of CLIP. We propose the parameter moving average to preserve the knowledge from the source model. Specifically, at any iteration " + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "inline_equation", + "content": "t \\geq 1" + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": ", we define the parameters after optimization as " + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": " and update the moving average " + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_t" + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 107, + 644, + 287, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 644, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 107, + 644, + 287, + 659 + ], + "type": "interline_equation", + "content": "\\hat {\\theta} _ {t} = \\pi \\cdot \\hat {\\theta} _ {t - 1} + (1 - \\pi) \\cdot \\theta_ {t}, \\tag {9}", + "image_path": "7d3ad0da240a87f17c9e65bedf15dd43a3dcf31d5c158d1a971fc38f2b2f5eb3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_0" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " is initialized as the parameters of source model " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\theta_S" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pi \\in [0,1]" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " is the momentum coefficient, which determines the degree of knowledge preservation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 328, + 382, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 328, + 382, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 328, + 382, + 342 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 348, + 356, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 356, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 356, + 361 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 366, + 504, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 366, + 504, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 366, + 504, + 378 + ], + "type": "text", + "content": "Datasets. We evaluate on the following datasets:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 378, + 545, + 700 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 306, + 378, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 545, + 437 + ], + "type": "text", + "content": "- CIFAR10 [17] and CIFAR100 [17] are two datasets consisting of low-resolution images, which differ from the common size of the training data of CLIP. We use them to evaluate the adaptability of our method to the distribution shift from image distortion caused by resize operations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 438, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 545, + 474 + ], + "type": "text", + "content": "- Food101 [1] and Stanford Cars [16] are fine-grained datasets contains 101 food categories and 196 car categories, respectively. We use them for fine-grained tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 474, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 545, + 509 + ], + "type": "text", + "content": "- ImageNet [6] is a large-scale dataset with 1000 classes, which is suitable for evaluating our method on category-intensive and real-world classification tasks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 510, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 545, + 582 + ], + "type": "text", + "content": "- CIFAR-10C [12] and ImageNet-C [12] are created by test images of CIFAR10 and ImageNet with 15 types of corruptions in 5 levels, which are widely used to evaluate the robustness of test-time adaptation methods. Following the common protocol [27, 29, 30], we evaluate our method on the 5-level (worst) corruptions of all 15 types." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 582, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 545, + 641 + ], + "type": "text", + "content": "- For object detection, we use KITTI [9] to evaluate our method for automotive applications. KITTI comprises 8 categories of traffic participants and is mostly recorded in clear weather conditions. We follow Mirza et al. [22] to simulate degrading weathers of fog, rain and snow." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 641, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 641, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 306, + 641, + 545, + 700 + ], + "type": "text", + "content": "- For semantic segmentation, we use CarlaTTA [21] to conduct experiments. CarlaTTA contains five gradually changing scenarios, including day2night, clear2fog, clear2rain, dynamic, and highway. It challenges the methods to adapt to distribution shift over time." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. For test-time adaptation with" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23706" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 64, + 526, + 185 + ], + "blocks": [ + { + "bbox": [ + 67, + 64, + 526, + 185 + ], + "lines": [ + { + "bbox": [ + 67, + 64, + 526, + 185 + ], + "spans": [ + { + "bbox": [ + 67, + 64, + 526, + 185 + ], + "type": "image", + "image_path": "3a594480495f98db8e5dafa9b869ecd94731344da64a543163b35c61d0e1b88f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 105, + 188, + 487, + 200 + ], + "lines": [ + { + "bbox": [ + 105, + 188, + 487, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 188, + 487, + 200 + ], + "type": "text", + "content": "Figure 5. Visualization of the detection results on KITTI in the weather conditions of fog, rain, and snow." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 205, + 280, + 289 + ], + "blocks": [ + { + "bbox": [ + 55, + 205, + 280, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 205, + 280, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 205, + 280, + 289 + ], + "type": "table", + "html": "
MethodsSFFogRainSnow
Source✓22.8±0.065.5±0.025.6±0.0
ActMAD [22]✗47.7±1.081.4±0.264.5±0.0
BN Adapt [27]✓32.3±0.170.6±0.144.9±0.2
TTT [29]✓29.4±0.571.5±0.447.5±0.7
Ours (SimpAug)✓27.3±0.475.2±0.436.0±0.3
Ours (Online)✓43.2±0.381.6±0.252.3±0.2
", + "image_path": "a6db65cc42faafde768ba2c7af0caaef9d99efcbb01cce2c30e0609803c41b31.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 341, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 289, + 628 + ], + "type": "text", + "content": "CLIP [25], we use the publicly available pretrained model as the source model, and evaluate our method on the test/validation sets of CIFAR10, CIFAR100, Food101, Cars, and ImageNet. We uniformly use \"a photo of a {class}\" as the prompt template, where the class token is replaced by the specific class name, such as \"airplane\", \"deer\", and \"frog\". Our method is run with a learning rate of 1e-6 for ResNet [11] backbone and 1e-5 for Vision Transformer [7] backbone. A batch size of 64 is adopted considering the memory constraint, while different batch sizes have little impact on our method, analyzed in the ablation study 4.4. Following Mirza et al. [22], we adapt a Wide-ResNet-40-2 [34] (WRN-40-2) pre-trained with AugMix [13] on CIFAR-10C, and an ImageNet pre-trained ResNet-18 [11] from PyTorch model zoo on ImageNet-C. We adopt a batch size of 128 and a learning rate of 1e-3, while all the compared methods and baselines use the hyperparameters reported by their authors. For object detection task, we adapt a YOLOv3 [26] pretrained on KITTI in clear weather to fog, rain and snow. For semantic segmentation task, we adapt a DeepLab-V2 [5] with a ResNet-101 backbone pretrained on clear split of CarlaTTA to the other five scenarios. We run experiments on 5 random seeds and report the mean and standard deviation for these runs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Offline and online adaptation. We evaluate our method in both offline and online settings. In the offline scenario, we can access all the test data and train the model on the entire test sets for 50 epochs, without considering the storage limitation. In the online scenario, the test samples arrive sequentially and do not reappear. We maintain a memory queue to store a certain amount of feature vectors, " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "10K" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 311, + 205, + 541, + 315 + ], + "blocks": [ + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "type": "text", + "content": "Table 5. Mean Average Precision (mAP@50) in KITTI with the most severe weather conditions, i.e. fog with only " + }, + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "type": "inline_equation", + "content": "30\\mathrm{m}" + }, + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "type": "text", + "content": " visibility, rain with " + }, + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "type": "inline_equation", + "content": "200\\mathrm{mm/hr}" + }, + { + "bbox": [ + 46, + 291, + 287, + 335 + ], + "type": "text", + "content": " intensity, and snow in level 5. Higher is better. SF denotes source free." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 311, + 205, + 541, + 315 + ], + "lines": [ + { + "bbox": [ + 311, + 205, + 541, + 315 + ], + "spans": [ + { + "bbox": [ + 311, + 205, + 541, + 315 + ], + "type": "table", + "html": "
MethodsSFday2nightclear2fogclear2raindynamichighway
Source✓58.452.871.846.628.7
BN Adapt [27]✓62.056.871.452.632.8
TENT [30]✓61.556.070.950.332.0
MEMO [35]✓61.055.171.650.335.2
CoTTA [31]✓61.456.870.746.433.8
Ours (SimpAug)✓60.153.972.648.931.9
Ours (Online)✓62.456.873.951.534.7
", + "image_path": "9082807d47870f60ced66083a279b329da628eb28e1f0860e973da7922795176.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 317, + 545, + 340 + ], + "lines": [ + { + "bbox": [ + 305, + 317, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 317, + 545, + 340 + ], + "type": "text", + "content": "Table 6. Mean Intersection over Union (mIoU, %) on CarlaTTA. Higher is Better. SF denotes source free." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 342, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 546, + 392 + ], + "type": "text", + "content": "default, for our PLCA. We also study the effect of adopting different memory capacities on our method in Sec. 4.4. Furthermore, our method maintains the performance in the more challenging single sample online adaptation task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 396, + 424, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 424, + 408 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 424, + 408 + ], + "type": "text", + "content": "4.2. Image Classification" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 414, + 546, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 569 + ], + "type": "text", + "content": "Results for adapting CLIP model are reported in Table 1. We find that updating both image and text encoders simultaneously can further improve the adaptability of CLIP model than freezing the text encoder as shown in Fig. 4 (c). We also compare with the method of using SimpAug and PLCA without re-training. The number of augmented verions for each test sample is set to 8 by default, which contains an original version. PLCA outperforms the our online method on multiple benchmarks, which may be due to the fact that online training does not sufficiently learn from the test samples with pseudo-labels, while offline adaptation addresses this issue by training repeatedly and providing more accurate pseudo-labels after each epoch." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "We present the results on CIFAR-10C and ImageNet-C in Table 2 and 3. Our method outperforms other online methods by a fair margin. Compared to works designed for offline adaptation, our method achieves comparable or even higher performance. It is noteworthy that MEMO [35] achieves higher performance than other baselines on adapting WRN-40-2, perhaps because of applying the same augmentation strategy, AugMix [13], for TTA as the training stage. However, when adapting ResNet-18 pre-trained with standard augmentation, MEMO does not maintain advantages due to the poor calibration of deep neural networks to augmented images with complex unseen transformations." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23707" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 282, + 243 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 282, + 243 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 282, + 243 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 282, + 243 + ], + "type": "table", + "html": "
ModelsMethodsImageNet-V2-Sketch-A-R
RN-50CLIP (zero-shot)55.851.133.221.856.0
Ours (π = 0)57.253.133.822.559.2
Ours (π = 0.9)58.353.836.024.060.3
Ours (π = 0.99)57.452.636.224.059.1
RN-101CLIP (zero-shot)58.254.338.028.163.9
Ours (π = 0)59.755.939.827.066.9
Ours (π = 0.9)60.156.240.930.467.3
Ours (π = 0.99)59.355.440.831.066.6
ViT-B/32CLIP (zero-shot)59.854.740.930.266.7
Ours (π = 0)63.758.144.132.771.4
Ours (π = 0.9)62.157.143.633.470.5
Ours (π = 0.99)60.956.543.233.169.7
ViT-B/16CLIP (zero-shot)64.560.646.047.873.8
Ours (π = 0)69.163.650.151.479.1
Ours (π = 0.9)67.262.549.152.977.6
Ours (π = 0.99)65.961.848.552.076.6
", + "image_path": "717d938afd9da903dccf0f8c12190fd2b4f42595e410f7133c8df61ca5043dee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 272, + 287, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 287, + 321 + ], + "type": "text", + "content": "Continuous online adaptation. Following CoTTA [31] to continuously adapt the model to different corruptions, we test our method on CIFAR-10C and ImageNet-C, referred to Table 4. Our method outperforms other baselines." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 330, + 282, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 330, + 282, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 330, + 282, + 342 + ], + "type": "text", + "content": "4.3. Object Detection and Semantic Segmentation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 348, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 504 + ], + "type": "text", + "content": "To evaluate the effectiveness of our method in solving regression problems, we conduct experiments on KITTI using YOLOv3. We report the results in Table 5 and visualize the detecting boxes in Fig. 5. Our method outperforms BN Adapt [27] and TTT [29], which are scalable to other models and not limited by the main task, and also beats ActMAD [22], which utilizes statistics in source data to TTA, in clear-to-rain task. Note that when only using SimpAug for test-time augmentation, we improve the source model up to " + }, + { + "bbox": [ + 46, + 348, + 287, + 504 + ], + "type": "inline_equation", + "content": "10.4\\%" + }, + { + "bbox": [ + 46, + 348, + 287, + 504 + ], + "type": "text", + "content": ". The visualization shows that SimpAug helps the model recognize distant and occluded objects that are hard to detect, while online training with pseudo-labels further boosts the accuracy and filter out duplicate boxes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 505, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 612 + ], + "type": "text", + "content": "For the semantic segmentation task, building a graph with all pixels is computationally expensive. We are inspired by COMUS [33] and collect object-level features, which represent the nodes in the graph. The results are listed in Table 6. BN Adapt exhibits robustness in the distribution shifts over time, while other methods seem to have limited improvement in gradually changing environments. Our method outperforms CoTTA [31], which is designed for continuous test-time adaptation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "type": "text", + "content": "More implementation details and comparison results can be found in the supplemental material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 141, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 141, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 141, + 659 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "Number of augmentations. We study how the number of augmentation for single sample affects the performance of SimpAug, and conduct experiments on KITTI using YOLOv3, referred to Table 8. SimpAug improves the ac" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 312, + 71, + 541, + 120 + ], + "blocks": [ + { + "bbox": [ + 47, + 246, + 287, + 268 + ], + "lines": [ + { + "bbox": [ + 47, + 246, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 246, + 287, + 268 + ], + "type": "text", + "content": "Table 7. Comparison with different " + }, + { + "bbox": [ + 47, + 246, + 287, + 268 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 246, + 287, + 268 + ], + "type": "text", + "content": " values on robustness to distribution shift. Higher is Better." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 71, + 541, + 120 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 541, + 120 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 541, + 120 + ], + "type": "table", + "html": "
Num1286432168421 (Source)
Fog28.227.727.326.425.925.024.622.8
Rain75.975.975.273.873.472.168.965.5
Snow37.637.036.034.632.830.628.725.6
", + "image_path": "3f72907357a561e003a3cd7d56e9eebfe882c38fae5b7dfae1520132c132ab0e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 313, + 145, + 538, + 184 + ], + "blocks": [ + { + "bbox": [ + 306, + 121, + 545, + 143 + ], + "lines": [ + { + "bbox": [ + 306, + 121, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 545, + 143 + ], + "type": "text", + "content": "Table 8. mAP@50 of SimpAug with different augmentation numbers on KITTI. Higher is Better." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 145, + 538, + 184 + ], + "lines": [ + { + "bbox": [ + 313, + 145, + 538, + 184 + ], + "spans": [ + { + "bbox": [ + 313, + 145, + 538, + 184 + ], + "type": "table", + "html": "
Memory Size100K10K1K100100Source
RN50CIFAR1083.083.083.482.982.282.168.7
ViT-B/32Food10186.486.385.885.785.785.780.7
", + "image_path": "a584932c624447548d0b65e625e0578f0910195e70ecec70ef1f4efe1777e857.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 209, + 537, + 250 + ], + "blocks": [ + { + "bbox": [ + 306, + 186, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 306, + 186, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 545, + 208 + ], + "type": "text", + "content": "Table 9. Accuracy " + }, + { + "bbox": [ + 306, + 186, + 545, + 208 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 306, + 186, + 545, + 208 + ], + "type": "text", + "content": " of our online method with CLIP model in different sizes of memory queue. Higher is Better." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 209, + 537, + 250 + ], + "lines": [ + { + "bbox": [ + 315, + 209, + 537, + 250 + ], + "spans": [ + { + "bbox": [ + 315, + 209, + 537, + 250 + ], + "type": "table", + "html": "
Batch Size12864321681Source
RN50CIFAR1082.883.083.582.983.381.068.7
ViT-B/32Food10186.486.386.386.686.587.180.7
", + "image_path": "ea69afeaa864d2334ae13e100016d476133af9fbcd107eeb06197fbaa205d638.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 251, + 545, + 273 + ], + "lines": [ + { + "bbox": [ + 306, + 251, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 545, + 273 + ], + "type": "text", + "content": "Table 10. Accuracy " + }, + { + "bbox": [ + 306, + 251, + 545, + 273 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 306, + 251, + 545, + 273 + ], + "type": "text", + "content": " of our online method with different batch sizes. Source denotes zero-shot performance of the CLIP model." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 278, + 545, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 545, + 315 + ], + "type": "text", + "content": "curacy with the increase of augmentation numbers until the performance bottleneck. Large number of augmentation requires computational resources and storage." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 315, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 410 + ], + "type": "text", + "content": "Size of memory queue. The memory size affects the inference speed and the accuracy of corrected pseudo-labels by PLCA. We conduct ablation experiments for online adaptation, as shown in Table 9. A large memory improves the ability of graph modeling the relations between samples. However, in online settings, old stored feature vectors have a higher error rate than the new ones, which affects the prediction of pseudo-labels for the current image." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "type": "text", + "content": "Momentum coefficient. " + }, + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "type": "text", + "content": " is a momentum coefficient that affects the models' update speed and avoids catastrophic forgetting. We test the performance of the CLIP model without using PMA and with two " + }, + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 411, + 545, + 506 + ], + "type": "text", + "content": " values. The results listed in Table 7 show that ViT backbone is more resistant to catastrophic forgetting than ResNet, and our method can maintain the robustness of the CLIP model to distribution shift while performing test-time adaptation." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 506, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 566 + ], + "type": "text", + "content": "Batch size. Most existing methods suffer from a small batch size in online adaptation, especially for those that rely on modifying normalization statistics of BN layers. As shown in Table 10, our method maintains comparable performance even in single sample online adaptation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 574, + 378, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 378, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 378, + 586 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "In this work, we propose an improved self-training method for fully test-time adaptation. In contrast to previous TTA methods, our IST explores the adaptability of the foundation model by employing CLIP as the source model. It goes beyond image classification and can be applied to object detection and semantic segmentation. IST outperforms existing TTA methods on different benchmarks and tasks by improving the quality of pseudo-labels and stabilizing the adaptation process. Experiments show that IST is scalable to a variety of pre-trained models and application tasks." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23708" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. 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Advances in neural information processing systems, 16, 2003. 4" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23710" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improved Visual Grounding through Self-Consistent Explanations/10bbab27-77ad-411f-b190-f41874ca342d_content_list.json b/2024/Improved Visual Grounding through Self-Consistent Explanations/10bbab27-77ad-411f-b190-f41874ca342d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d48a92e866f6b1e1d7068c2e6b8d2dcb24bbd4a5 --- /dev/null +++ b/2024/Improved Visual Grounding through Self-Consistent Explanations/10bbab27-77ad-411f-b190-f41874ca342d_content_list.json @@ -0,0 +1,1868 @@ +[ + { + "type": "text", + "text": "Improved Visual Grounding through Self-Consistent Explanations", + "text_level": 1, + "bbox": [ + 150, + 130, + 818, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ruozhen He1 Paola Cascante-Bonilla1 Ziyan Yang1 Alexander C. Berg2 Vicente Ordonez1 \n1Rice University 2University of California, Irvine", + "bbox": [ + 89, + 179, + 879, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "catherine.he@rice.edu, pc51@rice.edu, zy47@rice.edu, bergac@uci.edu, vicenteor@rice.edu", + "bbox": [ + 96, + 219, + 867, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-and-language models trained to match images with text can be combined with visual explanation methods to point to the locations of specific objects in an image. Our work shows that the localization – “grounding”– abilities of these models can be further improved by finetuning for self-consistent visual explanations. We propose a strategy for augmenting existing text-image datasets with paraphrases using a large language model, and SelfEQ, a weakly-supervised strategy on visual explanation maps for paraphrases that encourages self-consistency. Specifically, for an input textual phrase, we attempt to generate a paraphrase and finetune the model so that the phrase and paraphrase map to the same region in the image. We posit that this both expands the vocabulary that the model is able to handle, and improves the quality of the object locations highlighted by gradient-based visual explanation methods (e.g. GradCAM). We demonstrate that SelfEQ improves performance on Flickr30k, ReferIt, and RefCOCO+ over a strong baseline method and several prior works. Particularly, comparing to other methods that do not use any type of box annotations, we obtain $84.07\\%$ on Flickr30k (an absolute improvement of $4.69\\%$ ), $67.40\\%$ on ReferIt (an absolute improvement of $7.68\\%$ ), and $75.10\\%$ $55.49\\%$ on RefCOCO+ test sets A and B respectively (an absolute improvement of $3.74\\%$ on average).", + "bbox": [ + 75, + 300, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 708, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-and-language models that are trained to associate images with text have shown to be effective for many tasks and benchmarks [21, 27, 31, 41], including object detection [18, 54] and image segmentation [15, 36, 50]. Since these models are typically trained with in-the-wild data from the web, they can handle a wide range of vocabulary for objects as long as they are well represented in the training data. These models are often remarkably accurate [16, 22, 28, 47] even without tuning them to perform well in any particular downstream task [14, 32, 52]. The ALBEF model [27] was particularly capable of visual", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f8bff9e87446fa658b4891dd1b2484bdd5bb31d4f5ec00254b86767b0464741e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 296, + 888, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6398610bc06f60cea807a09e1dd468cf67a623a891b30ec5bef7912f24ba985d.jpg", + "image_caption": [ + "Figure 1. Previous models can localize the word frisbee, but struggle with equivalent but more uncommon referents such as disc. A model tuned with our proposed SelfEQ objective encourages consistent visual explanations for paraphrased prompts and performs well on both examples. SelfEQ not only enables a larger working vocabulary but also improves overall localization performance." + ], + "image_footnote": [], + "bbox": [ + 504, + 400, + 888, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"grounding\" - or in other words - the ability to localize objects in images by simply using it in conjunction with a visual explanation method such as GradCAM [43]. This capability is particularly remarkable given that this model was only supervised with images and text but no object location annotations of any type.", + "bbox": [ + 496, + 611, + 892, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In order to improve the ability of vision-and-language models to perform localization, many methods have incorporated further finetuning with either box or segment annotations, or rely on pretrained object detectors or box proposal networks [5, 12, 19, 23, 30, 51]. Our work instead aims to improve the localization capabilities of models trained only on image-text pairs through weak supervision. But, how can we improve the ability of a model to localize objects without access to object location annotations? Consider the example in Figure 1 where a model is tasked with pointing to the location of the object frisbee in this image. The baseline model succeeds at finding the object but is unsuccessful at locating the object when prompted with the", + "bbox": [ + 496, + 704, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13095", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "equivalent but more generic name disc. Regardless of the ability for the base model to find either of these, the visual explanations for these two prompts should be the same since the query refers to the very same object in both cases. Our work exploits this property by first generating paraphrases using a large language model and then proposing a weakly-supervised Self-consistency EQuivalence Tuning (SelfEQ) objective that encourages consistent visual explanations between paraphrased input text pairs that refer to the same object or region in a given image.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a base pre-trained vision-and-language model purely trained on image-text pairs such as ALBEF [27], SelfEQ tunes the model so that for a given input image and text pair, the visual attention map extracted using GradCAM [43] produces a similar visual attention map when provided with the same image and a text paraphrase. Figure 2 provides an overview of our method. Another contribution of our work consists in exploiting a large language model (LLM) to automatically generate paraphrases for existing datasets such as Visual Genome [26] that contains textual descriptions of individual objects and regions, or MS-COCO [33] and CC3M [46] that contain global image descriptions. We find that SelfEQ not only expands the vocabulary of objects that the base model is able to localize but more importantly, improves the visual grounding capabilities of the model on standard benchmarks such as referring expression comprehension on the ReferIt benchmark [24] and region-phrase grounding in the Flickr30K Entities benchmark [40]. In summary, our key contributions are as follows:", + "bbox": [ + 75, + 242, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design a novel objective, SelfEQ, to encourage vision-and-language models to generate self-consistent visual explanations for equivalent text phrases, thereby improving grounding capabilities while expanding the working vocabulary of the model.", + "- We propose to prompt large language models for generating paraphrased image descriptions of individual objects or regions. Particularly, we adopt Vicuna-13B [6] and design text prompts to obtain high quality paraphrases.", + "- We demonstrate the effectiveness of our method by outperforming previous methods, leading to $4.69\\%$ improvement on Flickr30k, $7.68\\%$ improvement on ReferIt, and $3.74\\%$ improvement on RefCOCO+." + ], + "bbox": [ + 76, + 545, + 468, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, we plan to release our code, generated paraphrases and model checkpoints upon publication.", + "bbox": [ + 75, + 743, + 468, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 784, + 218, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is related to previous methods on visual grounding, especially those that are trained under weak supervision understood as without the use of bounding box or segment annotations and relying only on image-text pairs. From a technical perspective our work is related to methods that optimize visual explanations to improve the underlying model.", + "bbox": [ + 75, + 809, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual grounding consists of localizing an input textual description in an image. Supervised methods are provided with text-image pairs and corresponding bounding boxes [8, 9, 12, 23, 51]. Other supervised methods leverage pretrained object detectors to obtain a region of interest and then identify the region that aligns most closely under their textual representations [5, 7, 17, 19, 35, 48]. In both cases, these methods use some form of box supervision during pre-training or at test time by relying on a pre-trained object detector. In contrast, our work focuses exclusively in the scenario where no bounding boxes or segment annotations are available at any stage.", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Weakly-Supervised Grounding. Our setup is similar to that of Arbelle et al [3] where no box annotations or object detectors are used for grounding. This work proposes Grounding by Separation (GbS) where a model is trained on randomly alpha-blended pairs of images and the goal is to separate them conditioned on text prompts. Our method instead relies on data augmentation on the text side and while our method shows favorable results, our contribution is orthogonal. Shaharabany et al [45] builds a weakly-supervised phrase grounding model by creating a large amount of data by combining region boxes with a BLIP captioning model. Later work by Shaharabany and Wolf [44] employs layerwise relevance propagation [38] to integrate relevancy and gradient information with the scores computed from each attention head in the transformer layers [4], or residual connections [1]. Our work compares favorably or on par with these methods but since we rely on gradient-based explanations, our work does not require making any modifications to the base network.", + "bbox": [ + 496, + 276, + 892, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Explanation Tuning. Related to our method is the strategy used by ALBEF [27] where the model is only supervised on image-text pairs and performs grounding through GradCAM [43], a gradient-based visual explanation method that outputs a heatmap indicating spatial relevance. Earlier, Xiao et al [49] used a similar strategy but further optimized gradient-based explanations using structural constraints derived from text. Recently, AMC [51] follows this strategy but further adds box supervision on the output maps using a margin-based loss. We adopt ALBEF [27] as our base model and also adopt a gradient-based explanation strategy but unlike AMC [51] we do not rely on box annotations for tuning this model and use our proposed SelfEQ objective instead. Javed et al [20] proposed an objective function that encourages consistent representations in embedding space for the same input prompt on different images. In contrast SelfEQ encourages consistent visual explanations for different prompts on the same image by relying on automatically generated paraphrases. Akbari et al [2] also optimizes attention maps but in their formulation the model backbone is modified to explicitly incorporate attention instead of relying on gradient-based attention maps.", + "bbox": [ + 496, + 568, + 892, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13096", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a8a916b3ad207ffd9fc2d96d3d31fa36392304059a7816fabb05d3c9148f26fc.jpg", + "image_caption": [ + "Figure 2. Overview of our proposed weakly-supervised Self-consistency EQuivalence tuning objective. We input image-text and image-paraphrase pairs $\\langle V, T \\rangle$ and $\\langle V, T^e \\rangle$ to our base pretrained vision-and-language model. We then obtain gradient-based visual explanations $\\langle G, G^e \\rangle$ and compute a similarity loss between them. We also define an overlapping region of interest mask and encourage the model to predict consistently high saliency scores within this mask for each input pair." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 472, + 251 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 388, + 169, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start from a base vision-language model composed of a text encoder $\\phi_t$ , an image encoder $\\phi_v$ , and a multimodal fusion encoder $\\phi_f$ , along with a dataset $D$ to finetune this model consisting of image-text pairs $\\langle T, V \\rangle$ . Section 3.1, introduces the training objectives for the base model which we also adopt for finetuning our baseline and are also used in conjunction with SelfEQ to finetune our final model. Section 3.2 introduces in detail SelfEQ, our self-consistency equivalence tuning objective that assumes the existence of paraphrases $T^e$ for each input image-text pair $\\langle T, V \\rangle$ , and Section 3.3 describes our approach for automatically generating paraphrases $T^e$ using LLM-prompting. Figure 2 presents an overview of our proposed method.", + "bbox": [ + 75, + 415, + 472, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Base Model: Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 626, + 318, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our base vision-and-language model is ALBEF [27] which relies on three widely used objectives for visual and textual representation learning: image-text matching, masked language modeling and a contrastive loss. We describe them here briefly as they are also re-used during fine-tuning.", + "bbox": [ + 75, + 650, + 468, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-Text Matching Loss (ITM). This loss is calculated using the output of the [CLS] token to predict if the input image and the input text are matching or not and is defined as follows:", + "bbox": [ + 75, + 733, + 470, + 792 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {i t m}} = \\mathbb {E} _ {(V, T) \\sim D} \\mathcal {H} \\left(\\vec {y}, \\phi_ {f} ^ {\\mathrm {c l s}} \\left(\\phi_ {v} (V), \\phi_ {t} (T)\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 804, + 468, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\vec{y}$ denotes a two-dimensional one-hot vector, indicating whether the sample $\\langle V,T\\rangle$ constitutes a match, $\\phi_f^{\\mathrm{cls}}$ represents a linear layer followed by a softmax function, and $\\mathcal{H}$ is the cross entropy loss function.", + "bbox": [ + 76, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Masking Language Modeling Loss (MLM). This loss has been applied for various vision-language pretraining models [5, 27, 29, 34]. It integrates the contextual text and the input image to infer masked words in the input text. After utilizing a linear layer and a softmax activation function $\\phi_f^{\\mathrm{m}}$ to individual output embeddings, the objective is expressed as:", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {m l m}} = \\mathbb {E} _ {(V, T ^ {- \\mathrm {m}}) \\sim D} \\mathcal {H} \\left(\\bar {t} ^ {\\mathrm {m}}, \\phi_ {f} ^ {\\mathrm {m}} \\left(\\phi_ {v} (V), \\phi_ {t} \\left(T ^ {- \\mathrm {m}}\\right)\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 205, + 890, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the one-hot vector $t^{\\mathrm{m}}$ denotes the masked token, and $T^{-\\mathrm{m}}$ represents the input masked text.", + "bbox": [ + 500, + 234, + 890, + 266 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-Text Contrastive Loss (ITC). It improves the alignment between visual and textual representations by bringing closer the representations for corresponding text-image pairs relative to text-image pairs that do not correspond. This objective can be defined as follows:", + "bbox": [ + 496, + 275, + 890, + 351 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {i t c}} = \\mathbb {E} _ {(V, T) \\sim D} \\frac {1}{2} \\left[ \\mathcal {H} \\left(\\vec {y}, \\frac {\\exp \\left(\\phi_ {v} (V) \\cdot \\phi_ {t} (T)\\right) / \\tau}{\\sum_ {b = 1} ^ {B} \\mathrm {s} (V , T _ {b})}\\right) \\right. \\tag {3} \\\\ \\left. + \\mathcal {H} \\left(\\vec {y}, \\frac {\\exp \\left(\\phi_ {t} (T) \\cdot \\phi_ {v} (V)\\right) / \\tau}{\\sum_ {b = 1} ^ {B} \\mathrm {s} (T , V _ {b})}\\right) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 359, + 890, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $B$ is the number of negative sample pairs, and $\\tau$ is a temperature parameter for the softmax function.", + "bbox": [ + 496, + 436, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The training objective for the base model is a combination of the previous three loss functions:", + "bbox": [ + 498, + 467, + 890, + 496 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {v l}} = \\mathcal {L} _ {\\mathrm {i t m}} + \\mathcal {L} _ {\\mathrm {m l m}} + \\mathcal {L} _ {\\mathrm {i t c}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 508, + 890, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This loss $\\mathcal{L}_{\\mathrm{vl}}$ will also be used to tune our baseline model.", + "bbox": [ + 500, + 534, + 883, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Self-Consistency Equivalence Tuning", + "text_level": 1, + "bbox": [ + 500, + 559, + 820, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SelfEQ assumes that the model has access to paraphrases $T^e$ for each input image-text pair $\\langle V, T \\rangle$ or, in practice, for a subset of those samples. Therefore we assume a finetuning dataset $D'$ with triplets $\\langle V, T, T^e \\rangle$ such that $T^e$ exists for a corresponding input text $T$ . The first step to define our SelfEQ objective is to generate the explanation heatmaps (i.e., attention maps) through GradCAM [43] conditioned on the input text. We extract intermediate feature maps from the multimodal interactive encoder $\\phi_f$ for input pairs $\\langle V, T \\rangle$ and $\\langle V, T^e \\rangle$ as follows:", + "bbox": [ + 496, + 582, + 890, + 733 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF = \\phi (\\phi_ {v} (V), \\phi_ {t} (T)), F ^ {e} = \\phi (\\phi_ {v} (V), \\phi_ {t} (T ^ {e})), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 743, + 890, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\phi$ denotes the feature map extraction operation. We then proceed to calculate the gradient of $F$ and $F^{e}$ related to the image-text matching score $\\mathcal{L}_{\\mathrm{itm}}$ . This computation yields the attention maps for the original text and paraphrased text, referred to as $G$ and $G^{e}$ , respectively:", + "bbox": [ + 496, + 768, + 890, + 845 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nG = \\operatorname {R e L U} \\left(F \\odot \\nabla \\mathcal {H} \\left(\\vec {y}, \\phi_ {f} ^ {c l s} \\left(\\phi_ {v} (V), \\phi_ {t} (T)\\right)\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 854, + 890, + 886 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nG ^ {e} = \\operatorname {R e L U} \\left(F ^ {e} \\odot \\nabla \\mathcal {H} \\left(\\vec {\\mathcal {y}}, \\phi_ {f} ^ {c l s} \\left(\\phi_ {v} (V), \\phi_ {t} \\left(T ^ {e}\\right)\\right)\\right)\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 880, + 852, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13097", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our SelfEQ tuning is based on the premise that if a vision-language model is identified as self-consistent, the attention maps produced for both the text and its equivalent paraphrase should yield nearly identical results. To achieve this, we first apply a simple mean squared error loss over the produced heatmaps so that their $\\ell_2$ distance is minimized and thus become more similar.", + "bbox": [ + 76, + 90, + 472, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s i m}} = \\mathbb {E} _ {(V, T, T ^ {e}) \\sim D ^ {\\prime}} \\left[ \\frac {1}{N} \\sum_ {i, j} \\left(G _ {i, j} - G _ {i, j} ^ {e}\\right) ^ {2} \\right]. \\qquad (7)\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 203, + 468, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Nevertheless, while minimizing a sum of pixel-wise distances contributes to self-consistency, without a regularization term this loss can easily fall into a trivial solution. For instance, it could lead to attention maps with uniformly negative or positive predictions, or just really small values. To address this limitation, we propose to integrate these heatmaps by defining a Region of Interest (RoI) mask. This mask is designed to preserve regions within the attention maps that possibly contain correct predictions. Our approach hinges on the observation that, despite the predictions of equivalent textual inputs being inconsistent, sometimes regions with large values or regions that overlap between the two heatmaps tend to be correct. As such, we assume that if the sum of attention scores at a given position $(i,j)$ exceeds a certain threshold $k$ , it is likely indicative of a correct prediction. We formalize the condition as follows:", + "bbox": [ + 76, + 247, + 472, + 489 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {i, j} = \\left\\{ \\begin{array}{l} 1, \\left(G _ {i, j} + G _ {i, j} ^ {e}\\right) \\geq k \\\\ 0, \\left(G _ {i, j} + G _ {i, j} ^ {e}\\right) < k \\end{array} \\right.. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 500, + 468, + 536 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The attention maps within RoI masks are obtained by element-wise multiplication as follows:", + "bbox": [ + 76, + 544, + 468, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR = G \\odot M, \\quad R ^ {e} = G ^ {e} \\odot M. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 584, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The integration of RoI masks allows us to use equivalent texts for mutual supervision, refining and improving the accuracy and providing regularization for the previously defined distance-based loss. Moreover, it could potentially address errors owing to unknown or less common words by working vocabulary expansion. Presuming one of the textual expressions is known and correctly understood, the model could extrapolate the meaning of the other equivalent expression via weak supervision. To implement it, we first compute the mean $\\mu_{RoI},\\mu_{RoI}^{e}$ and the standard deviation $\\sigma_{RoI},\\sigma_{RoI}^{e}$ within the RoI as follows:", + "bbox": [ + 76, + 609, + 472, + 777 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {R o I} = \\frac {\\sum_ {i , j} R _ {i , j}}{\\sum_ {i , j} M _ {i , j}}, \\mu_ {R o I} ^ {e} = \\frac {\\sum_ {i , j} R _ {i , j} ^ {e}}{\\sum_ {i , j} M _ {i , j}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 786, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {R o I} = \\sqrt {\\frac {\\sum_ {i , j} M _ {i , j} \\cdot \\left(R _ {i , j} - \\mu_ {R o I}\\right) ^ {2}}{\\sum_ {i , j} M _ {i , j}}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 827, + 468, + 871 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {R o I} ^ {e} = \\sqrt {\\frac {\\sum_ {i , j} M _ {i , j} \\cdot (R _ {i , j} ^ {e} - \\mu_ {R o I} ^ {e}) ^ {2}}{\\sum_ {i , j} M _ {i , j}}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 867, + 395, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose a consistency loss $(\\mathcal{L}_{\\mathrm{cst}})$ , expecting the RoI regions of attention maps to achieve consistently high scores, further reinforcing self-consistency, accuracy, and potential working vocabulary expansion. This objective is formulated as follows:", + "bbox": [ + 500, + 90, + 890, + 166 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c s t}} = \\mathbb {E} _ {(V, T, T ^ {e}) \\sim D ^ {\\prime}} \\left[ \\sigma_ {R o I} + \\sigma_ {R o I} ^ {e} + \\right. \\tag {12} \\\\ \\left. \\max (0, k / 2 - \\mu_ {R o I}) + \\max (0, k / 2 - \\mu_ {R o I} ^ {e}) \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 174, + 890, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the objective of our self-consistency equivalence tuning is expressed as:", + "bbox": [ + 500, + 246, + 890, + 277 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {S e l f E Q}} = \\mathcal {L} _ {\\text {s i m}} + \\lambda \\cdot \\mathcal {L} _ {\\text {c s t}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 292, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyperparameter to control the relative influence of each loss.", + "bbox": [ + 498, + 311, + 890, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Self-Consistency Data Augmentation", + "text_level": 1, + "bbox": [ + 500, + 354, + 816, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section we define a function $\\mathcal{F}$ that can automatically map input textual phrases $T$ as paraphrases $T^{e}$ without the need to rely on human annotations such that $T^{e} \\sim \\mathcal{F}(T)$ . We achieve this goal through a two-level prompting approach using a large language model which we describe in detail below.", + "bbox": [ + 498, + 377, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Phrase Chunking: Using our first-level prompts, we aim to augment the original text using phrase chunking to encourage global captions to concentrate on more specific regions. Visual grounding seeks to localize objects in images based on textual inputs. In contrast, global captions usually describe the entire image, typically describing several objects. While training on global captions could be beneficial for learning cross-modal information, it may lead the model to predict a broader region (i.e., global context) rather than a specific region. Phrase chunking (i.e., shallow parsing [55]) aims to identify continuous sequences of tokens representing syntactic units, enabling the extraction of phrases from unstructured text. We leverage an LLM to segment global captions into object-centric short phrases. During training, we use these image-chunk pairs instead of global captions, effectively guiding the model attention toward localized regions of interest. We refer the reader to the supplementary material for prompting details and generated examples.", + "bbox": [ + 498, + 472, + 892, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Paraphrase Generation: Our SelfEQ approach involves feeding the model with pairs of textual descriptions that refer to the same underlying concept, with the expectation that the model can make similar predictions for these equivalent description pairs $\\langle T, T^e \\rangle$ . We augment our dataset by transforming the region-based captions (i.e., text that only refers to a region in the image) and the object-centric short phrases we obtained from phrase chunking into equivalent paraphrases referring to the same concept through our second-level LLM-prompts.", + "bbox": [ + 498, + 750, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13098", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Q:\"a smiling, holding something and standing man\" \nA:{\"group\": \"man\", \"synonym\": [\"adult male\",\"gentleman\"], \"antonym\": [\"woman\"], \"hypernym\": [\"adult\",\"grownup\",\"male\",\"male person\",\"human being\",\"human\"], \"meronym\": [\"man body\",\"man head\",\"man arms\",\"man legs\"]} \nQ:\"a desk\" \nA:{\"group\": \"desk\", \"synonym\": [\"table\",\"writing desk\"], \"antonym\": [], \"hypernym\": [\"writer tool\",\"furniture\"], \"meronym\": [\"desktop\",\"desk leg\"]}", + "guess_lang": "jsonl", + "bbox": [ + 81, + 89, + 467, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 3. Two samples from our LLM-prompt for paraphrase generation. The first set showcases an example of a region-based caption, and the second set shows a non-sentence phrase. $\\mathbf{Q}$ is the query text and $\\mathbf{A}$ is the expected answer.", + "bbox": [ + 75, + 200, + 468, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "There are many ways to paraphrase, including substituting words, altering sentence structures, and rewriting sentences based on semantics. However, considering that self-consistency in vision and language is relatively underexplored, we adopt a straightforward strategy: Replacing the primary object in the sentence while retaining all other attributes. This strategy yields several benefits. First, it provides a consistent context, which serves as a reference for the model to identify equivalent descriptions. This enables the equivalent relationships of paraphrases to be learned intuitively. Second, it simplifies prompt designing and post-processing by detecting the primary object and generating its synonym.", + "bbox": [ + 75, + 267, + 468, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To generate paraphrases for the dataset consisting of region-based captions, we select four textual descriptions in which the primary noun plays different syntactic roles. We further select two non-sentence phrases as examples of query texts in our prompts. We show an example of a region-based caption and a non-sentence phrase in Figure 3. To design our prompt, we identify the primary object in the query text Q. Then we use WordNet [37] to obtain synonyms automatically and further remove inaccurate or invalid words. We add A to indicate the expected answer and include other relationships such as antonym, hy- pernym and meronym to provide richer contexts for LLM in-context learning. Additional prompting details and paraphrase samples are provided in the supplementary material.", + "bbox": [ + 75, + 464, + 468, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This two-level prompt-based LLM augmentation approach ensures that our model is exposed to textual inputs that share the same concept while varying in linguistic representation, thereby promoting self-consistency and working vocabulary expansion.", + "bbox": [ + 75, + 676, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 768, + 287, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. We use ALBEF [27] as our base model in all our experiments, given its reported off-the-shelf visual grounding performance via GradCAM [43]. ALBEF combines a ViT-B [11] model for encoding images and a BERT-base [10] model for encoding text. It is pre-trained on a range of datasets, including ImageNet-1K [42], Conceptual Captions [46], SBU Captions [39], MS-COCO [33], and", + "bbox": [ + 75, + 794, + 467, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/bd7c38847e068faede53f1e852bfefbe6b43dc486d67ee5f949c9357e6d65190.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrainingFlickr30kReferIt
Box SupervisionAlign2Ground [7]VG-boxes71.00-
12-in-1 [35]VG-boxes76.40-
InfoGround [19]VG-boxes76.74-
VMRM [12]VG-boxes81.11-
AMC [51]VG-boxes86.5973.17
Without Box SupervisionTD [56]VG42.4031.97
SSS [20]VG49.1039.98
MG-BiLSTM [2]VG57.9162.76
MG-ELMo [2]VG60.0860.01
GbS [3]VG73.3962.24
g [45]VG75.6365.95
g++ [44]VG79.9570.25
SelfEQ (ours)VG81.9067.40
FCVC [13]MS-COCO29.0333.52
MG-BiLSTM [2]MS-COCO53.2947.89
MG-ELMo [2]MS-COCO61.6647.52
GbS [3]MS-COCO74.5049.26
g [45]MS-COCO75.4361.03
g++ [44]MS-COCO78.1061.53
SelfEQ (ours)MS-COCO84.0762.75
", + "bbox": [ + 501, + 89, + 893, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Visual Grounding results on two benchmarks using pointing game accuracy with two training datasets. SelfEQ yields generally the best overall performance among weakly-supervised methods, and comes second to $\\mathrm{g} + +$ on the ReferIt benchmark when trained using VG. We also show at the top the results of methods using additional box supervision from Visual Genome (VG) either directly or through an object detector.", + "bbox": [ + 496, + 476, + 893, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visual Genome (VG) [26] excluding box annotations. We finetune ALBEF with image-text pairs from VG and MS-COCO without any type of box supervision (i.e., no bounding boxes or object detectors), following prior work [2]. We further leverage Vicuna-13B [6] as our LLM-prompting model to generate the object-centric short phrases (via shallow parsing or chunking) and the equivalent paraphrases for our self-consistency data augmentation. Additionally, we validate the effectiveness of our SelfEQ tuning and self-consistency data augmentation method by training on a preprocessed subset of the Conceptual Captions 3M (CC3M) dataset [46], which contains many noisy or unaligned web-crawled AltText-image pairs. With this subset, we achieve an absolute improvement of $2.15\\%$ on Flickr30k, $3.32\\%$ on ReferIt, and $1.33\\%$ on RefCOCO+; refer to the supplementary material for detailed CC3M experiments.", + "bbox": [ + 496, + 590, + 890, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation. We conduct evaluations using Flickr30k [40] and ReferIt [24] under pointing game accuracy following previous weakly-supervised visual grounding works [2, 3]. To underscore the competitive edge of our method, we also", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13099", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/cc9a83c0894c4ea99676d6ffb463adab1135fe75f3d706ca3878dd08b9720c03.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBox SupervisionRefCOCO+
Test ATest B
InfoGround [19]Yes39.8041.11
VMRM [12]Yes58.8750.32
AMC [51]Yes80.3464.55
ALBEF [27]No69.3553.77
SelfEQ (ours)No75.1055.49
", + "bbox": [ + 93, + 88, + 455, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Results on RefCOCO+ pointing game accuracy. SelfEQ shows significant improvements over off-the-shelf ALBEF and competitive results compared to box-supervised methods.", + "bbox": [ + 76, + 244, + 468, + 286 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "present its performance on RefCOCO+ [53], a challenging benchmark more commonly used for testing box-supervised methods [7, 12, 19, 35, 51].", + "bbox": [ + 76, + 297, + 468, + 342 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 351, + 294, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our experiments are conducted on a single computing node with 8 NVIDIA A40 GPUs. During the training phase, input images are resized to $256 \\times 256$ and augmented with horizontal flipping, color jittering, and random grayscale conversion. We set up an Adam optimizer [25] with a learning rate of 1e-5 and a batch size of 448 across all experiments. We empirically set the RoI threshold $k$ to 0.8 and the hyperparameter $\\lambda$ to 1.0. For training with raw image-text pairs from the datasets, we employ the vision-language objective $\\mathcal{L}_{\\mathrm{vl}}$ (Sec. 3.1), while for the subset with equivalent paraphrases, we use our self-consistency equivalence tuning objective $\\mathcal{L}_{\\mathrm{SelfEQ}}$ (Sec. 3.2) and corresponding vision-language objective $\\mathcal{L}_{\\mathrm{vl}}^e$ . The composite objective function is given by $\\mathcal{L} = \\alpha \\cdot \\mathcal{L}_{\\mathrm{vl}} + (1 - \\alpha) \\cdot (\\mathcal{L}_{\\mathrm{SelfEQ}} + \\mathcal{L}_{\\mathrm{vl}}^e)$ , where $\\alpha$ is initially set to 0 and increments to 1, remaining constant after the second epoch. Our hyperparameter values and schedules were determined empirically on a small validation subset.", + "bbox": [ + 75, + 375, + 470, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 659, + 282, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our resulting model obtains the best performance on the task of weakly-supervised visual grounding compared to most methods under this setting and is comparable to several prior works that rely on some of box supervision. Moreover, our qualitative results show that our method can handle paraphrases and a larger working vocabulary without the needed to increment the training dataset significantly.", + "bbox": [ + 75, + 684, + 468, + 790 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flickr30k and ReferIt. We evaluate the effectiveness of our proposed SelfEQ method in Table 1, demonstrating its substantial lead over GradCAM-based weakly-supervised approaches. Our self-consistency equivalent tuning adapts well for both region-based (i.e., VG) and global-based (i.e., COCO) image-text pairs, yielding a performance gain of $4.69\\%$ on Flickr30k and $7.68\\%$ on ReferIt, compared to", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/105888ffed6fd16cb4d84d67516d6329cac6a916d973bd201a403e4355a86d57.jpg", + "image_caption": [ + "Text: \"trees on the right\"", + "Image" + ], + "image_footnote": [], + "bbox": [ + 509, + 109, + 604, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2961438ff455512f612744005dfdd23a5c6189c02d1ffccf77bf6e103592b00c.jpg", + "image_caption": [ + "ALBEF" + ], + "image_footnote": [], + "bbox": [ + 604, + 109, + 696, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/45a6fa338a3438facf8b3783af3d731bc29db03b354b08ddea3e76ef67c5cb86.jpg", + "image_caption": [ + "AMC" + ], + "image_footnote": [], + "bbox": [ + 697, + 109, + 789, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8b31a5c821a3094aa6568f6c2b63ed5b9ce162b0dfebc73f7ddb879c88f3293c.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 790, + 109, + 885, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6a42500bee4806295b5ce97a878f420680970b986ca22cdf9655c5375d77b796.jpg", + "image_caption": [ + "Text: \"blue thermos very bottom\"", + "Image" + ], + "image_footnote": [], + "bbox": [ + 511, + 191, + 604, + 246 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/502db3a97101a86b95abb745604e97b37e18328d8e04d03f369313150864d007.jpg", + "image_caption": [ + "ALBEF" + ], + "image_footnote": [], + "bbox": [ + 604, + 191, + 697, + 246 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/991db022fde3c93fa1b5e0fdde53856e8441257cf6b994e43f1b5215b72e79a8.jpg", + "image_caption": [ + "AMC" + ], + "image_footnote": [], + "bbox": [ + 697, + 191, + 789, + 246 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0e62e5bbf210669161d5a925e6fc2c993eaeeb4df3c5d0d5cfe696c1474510fa.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 790, + 191, + 885, + 246 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cc3f291f8a0ecf6d6b7d5b0b0fb2ad53a39a7cee49c213c4eb0fd201c5a31a1e.jpg", + "image_caption": [ + "Text: \"person right corner\"", + "Image" + ], + "image_footnote": [], + "bbox": [ + 509, + 275, + 604, + 330 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8be2ae858df8fc9cb013ba428f526582b2595e2e8ed9ccbe7e087b507063b598.jpg", + "image_caption": [ + "ALBEF" + ], + "image_footnote": [], + "bbox": [ + 607, + 275, + 697, + 330 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/45ebe99d74808e2f5a9539380355c2e02badec0da12d56aeb4dde4758dc3be80.jpg", + "image_caption": [ + "AMC" + ], + "image_footnote": [], + "bbox": [ + 697, + 275, + 790, + 330 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/444986c4da65e4f4b35ffd26fc67ac090f271f84d19d405cd07308fbd85fc34a.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 790, + 275, + 885, + 330 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3729c61bd9059ab6e36b298700fc554d415f47d7340533392b619ea7043bf911.jpg", + "image_caption": [ + "Text: \"kangaroo furthest away facing right\"", + "Image" + ], + "image_footnote": [], + "bbox": [ + 509, + 358, + 602, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/efe802e7d80fe99a34472cf5b4a86888370a9eaaf3834e307d71e3dc6e8913dd.jpg", + "image_caption": [ + "ALBEF" + ], + "image_footnote": [], + "bbox": [ + 607, + 358, + 697, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d4a2bd87ac87bf940176320578297c244b6146feb7de5895920b654fa6a77907.jpg", + "image_caption": [ + "AMC" + ], + "image_footnote": [], + "bbox": [ + 697, + 358, + 789, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2ecda2b9698cbbddfe882a4667f3a80fbd6e15b7f1ef23cc5b1cc694e99316c8.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 790, + 358, + 885, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b5c1513b0f309d1cfd53168834fc8342b616bacf1ae210d0700f55377b383889.jpg", + "image_caption": [ + "Text: \"white bldg\"", + "Image", + "Figure 4. Qualitative results of our method in challenging visual grounding scenarios compared to prior works. On top of each row we show the reference text, the first column shows the image, then we show our base model ALBEF, the SotA box-supervised method AMC, and finally we show results with our method SelfEQ." + ], + "image_footnote": [], + "bbox": [ + 517, + 440, + 599, + 523 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/05221046499fde22d165e7c0df470546cac1e848528cff56f6db50b65869ed79.jpg", + "image_caption": [ + "ALBEF" + ], + "image_footnote": [], + "bbox": [ + 609, + 440, + 692, + 523 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1aa0821b4cd677e43a98e3baf350fd07e451ffd5b64915516e4fec3ebe524ff2.jpg", + "image_caption": [ + "AMC" + ], + "image_footnote": [], + "bbox": [ + 702, + 439, + 785, + 523 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0364ae426a36de47b099f6a4769efe7ed407d649ac68c9906d9dbdf1cac4f36c.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 795, + 439, + 880, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "our base model ALBEF (see first row in Table 3). Notably, our method outperforms almost all box-supervised methods on Flickr30k [7, 12, 19, 35]. In the weakly-supervised setting, our method only comes second on ReferIt compared to $\\mathrm{g + + }[44]$ when trained on Visual Genome imagedtext pairs. This method leverages a custom architecture to produce a mask and uses heatmap supervision from a CLIP [41] model as pseudo-labels during training. We posit that our contribution is orthogonal and our approach would likely also benefit from similar supervision, since CLIP is trained in a much larger image-text pair dataset. Despite differences, our method still obtains higher performance when trained on MS-COCO and the best performance compared to all weakly-supervised methods on Flickr30K region-phrase grounding.", + "bbox": [ + 496, + 623, + 890, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RefCOCO+. RefCOCO+ [53] serves as a rigorous benchmark for visual grounding, typically used to evaluate box-supervised techniques. In Table 2, we present the per", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13100", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2e32c90976951268df0c16e9a9177a244e32197358102315a4d05ed3ee176fa3.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Ablation studies on different ways to utilize extra equivalent paraphrased data. The first row is off-the-shelf ALBEF performance before tuning. $T$ denotes the textual captions from the dataset, and ${T}^{e}$ corresponds to the associated equivalent paraphrases. ${\\mathcal{L}}_{\\mathrm{{vl}}}$ is the vision-language objective,and ${\\mathcal{L}}_{\\text{SelfEQ }}$ is our self-consistency equivalence tuning objective." + ], + "table_body": "
DataObjectiveRefCOCO+Flickr30kReferIt
Test ATest B
-\\( \\mathcal{L}_{\\mathrm{vl}} \\)69.3553.7779.3859.72
T\\( \\mathcal{L}_{\\mathrm{vl}} \\)72.3054.2278.7565.86
T+Te\\( \\mathcal{L}_{\\mathrm{vl}} \\)71.5553.5178.0564.57
T+Te\\( \\mathcal{L}_{\\text{SelfEQ}} \\)75.1055.4981.9067.40
", + "bbox": [ + 86, + 88, + 460, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "formance of our weakly-supervised method (VG trained) against box-supervised methods. Our results indicate that our approach is competitive without reliance on any form of box annotations and significantly improves over the base ALBEF model.", + "bbox": [ + 75, + 308, + 470, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual Grounding Analysis. Figure 4 provides qualitative results of our method in challenging scenarios, including occluded objects (row 1), small objects within complex scenes (row 2), objects partially shown in the corner of the image (row 3), multiple similar objects (row 4), and abbreviated text inputs (row 5). Our self-consistency equivalency tuning approach exhibits substantial improvements in the grounding capability of the base ALBEF [27] model. Remarkably, our approach even outperforms the state-of-the-art box-supervised method AMC [51] in multiple scenarios.", + "bbox": [ + 75, + 388, + 468, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Self-Consistency Analysis. Figure 5 demonstrates qualitative results for the self-consistency capability across different equivalent paraphrases, encompassing terminology (row 1), synonym substitutions (row 2), and regional slang combining with different sentence structures (row 3). Although other methods succeed in localizing certain phrases, they demonstrate inconsistencies for the equivalent paraphrases. In contrast, our model finetuned with SelfEQ effectively establishes connections between semantically equivalent paraphrases, thereby enhancing the model self-consistency ability and potentially expanding its working vocabulary.", + "bbox": [ + 75, + 544, + 470, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 720, + 241, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data Quantity. We assess the impact of the data quantity of our generated paraphrases and compare our tuning strategy against standard vision-language objectives. We randomly sample portions of data from VG by $10\\%$ associated with our augmented equivalent paraphrases three times. To compare, we use the vision-language objective with VG text-image pairs as baselines. In Figure 6, we show the mean and standard deviation pointing game accuracy. The performance of the base vision-language objective does not exhibit a steady improvement with more text-image pairs. Al-", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/93e02ff69731fc5109cb0e56f4e4b82bbb3158886b98e69b95d3d5937874106d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 92, + 887, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ec7829f18c58bca6218f49d76349e0252b7b7d79594ea9c8938c447bb31d67e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 227, + 885, + 362 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/920376e4140cf3bf27d52458840f59fcf6fed0eafbe15081dce7ef2e32b3809c.jpg", + "image_caption": [ + "Figure 5. Qualitative results across equivalent paraphrases among different methods. For each image, we show a caption referring to an object in the first row and an equivalent paraphrase in the second row. Each column shows the results of ALBEF, the SotA box-supervised method AMC, and our SelfEQ method." + ], + "image_footnote": [], + "bbox": [ + 506, + 364, + 885, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "though ReferIt performance increases, the performance on RefCOCO+ Test A remains mostly unchanged. Additionally, the performance on Flickr30k notably decreases, and there is a mixed effect on RefCOCO+ Test B, with half of the accuracy falling below the off-the-shelf ALBEF performance of $53.77\\%$ .", + "bbox": [ + 498, + 592, + 890, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In contrast, SelfEQ consistently leads to performance enhancements with more equivalent paraphrases. Clear upward trends are observed on Flickr30k, ReferIt, and RefCOCO+ Test A as more data with corresponding equivalent paraphrases are added, meanwhile the gaps between the baselines generally widen. Notably, SelfEQ tuning maintains performance gains on Flickr30k, whereas the baselines performances drop. Although the trend on RefCOCO+ Test B is not consistently increasing, it is essential to emphasize that RefCOCO+ Test B is only a subset, and SelfEQ illustrates more stable and effective tuning performance on it, compared to the base vision-language objective.", + "bbox": [ + 496, + 686, + 890, + 867 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "These observations indicate that more equivalent paraphrases connecting with associated text phrases enable the", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13101", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/283e0434cffe2589dd3dec8351141ecdab4db15e468c61f9d5bd52c1b837619b.jpg", + "image_caption": [ + "Figure 6. Tuning performance with different data quantities on Flickr30k, ReferIt, RefCOCO+ Test A and Test B. The purple and cyan lines represent SelfEQ (ours) and ALBEF baseline losses (vision-language objective), respectively. We show the impact of progressively augmenting captions via LLM-prompting for generating equivalent paraphrases tuned with our SelfEQ objective. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 282, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/390a6ecb5040342d64ca85d13530f2efb55dd2486dfb31950ade8f0ce4dff533.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 88, + 480, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c1cb77ce1321c5115cbddaa3edb89d2fca214e6f12c3faf808466d5fa57cd134.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 88, + 678, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/12a2add7f4d5936d9c28197e7ed661811ee223b6984f9f0d3593607277e40dd8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 88, + 875, + 184 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/eb44b90ea93482e76f673d8ca9fafe671a100374b87940f613c9f6049cdf86aa.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
FormatObjectiveFlickr30kReferIt
-\\( \\mathcal{L}_{\\mathrm{vl}} \\)79.3859.72
C\\( \\mathcal{L}_{\\mathrm{vl}} \\)79.9060.64
C\\( \\mathcal{L}_{\\text{SelfEQ}} \\)81.2862.04
P\\( \\mathcal{L}_{\\mathrm{vl}} \\)81.1861.18
P\\( \\mathcal{L}_{\\text{SelfEQ}} \\)84.0762.75
", + "bbox": [ + 122, + 244, + 419, + 357 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model to acquire more valuable information during tuning. SelfEQ proves to be an effective and robust strategy for consistently improving performance with our generated paraphrases. With increased self-consistency augmented data, SelfEQ guides the model toward better grounding performance by enhancing its self-consistency capabilities.", + "bbox": [ + 75, + 441, + 468, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method generates equivalent paraphrases for self-consistency enhancement, but it also contributes additional data for training. To ascertain the specific impact of our SelfEQ tuning strategy, we run a control experiment on this variable. As shown in Table 3, we assess the model's performance when equivalent paraphrases are integrated as regular image-text pairs with vision-language objectives (Sec. 3.1). This comparison reveals that merely augmenting the dataset with extra image-paraphrase pairs, without forming explicit linkages between the original text and its paraphrases, does not yield performance improvements.", + "bbox": [ + 75, + 532, + 468, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Data Augmentation. For global-based captions in MS-COCO, we preprocess the captions $C$ to object-centric short phrases $P$ via LLM-prompting. As shown in Table 4, tuning with phrases $P$ leads to better performance, benefiting both the vision-language objective $(\\mathcal{L}_{\\mathrm{vl}})$ and our self-consistency equivalence tuning objective $(\\mathcal{L}_{\\mathrm{SelfEQ}})$ . This improvement is probably attributed to short phrases allowing the model to focus on a specific region rather than the entire scene, aligning more closely with the objective of visual grounding. By utilizing equivalent paraphrases with our SelfEQ objective (row 3 and 5), phrase chunking helps SelfEQ even more, indicating the important role of equivalent paraphrases in promoting self-consistency and grounding ability.", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5f0da444fd58d2b9909ee1aac936256338450a21e66cc0deeedbff48db1640ce.jpg", + "table_caption": [ + "Table 4. Comparisons on data augmentation strategy for global-based captions in MS-COCO with or without the paraphrases. $C$ is the global-based captions from MS-COCO, and $P$ is our Vicuna-13B processed object-centric phrases separately. The first row is the off-the-shelf ALBEF performance before tuning." + ], + "table_footnote": [], + "table_body": "
\\( \\mathcal{L}_{\\text{sim}} \\)\\( \\mathcal{L}_{\\text{cst}} \\)RefCOCO+Flickr30kReferIt
Test ATest B
✓66.4247.2168.2655.96
✓73.3355.8880.9466.57
✓✓75.1055.4981.9067.40
", + "bbox": [ + 513, + 244, + 877, + 337 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation studies on objective components of self-consistency equivalence tuning objective ${\\mathcal{L}}_{\\text{SelfEQ }}$ .", + "bbox": [ + 498, + 342, + 890, + 372 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Objective. Table 5 evaluates each component within our self-consistency equivalence tuning objective. The $\\mathcal{L}_{\\mathrm{sim}}$ loss targets pixel-wise similarity, ensuring that maps for a caption and its equivalent paraphrase are identical. However, focusing solely on pixel-level similarity may neglect the precise spatial positioning of objects. To address this, the $\\mathcal{L}_{\\mathrm{cst}}$ loss is proposed to identify the most likely correct object positions within the two maps (i.e., RoI). It then encourages the model to yield consistently high attention scores within the RoI. By integrating both $\\mathcal{L}_{\\mathrm{sim}}$ and $\\mathcal{L}_{\\mathrm{cst}}$ , self-consistency equivalence tuning objective fosters the model to not only align global similarities but also to pinpoint accurate object locations through the mutual supervision provided by a caption and its paraphrase, thereby enhancing self-consistency and accuracy.", + "bbox": [ + 496, + 386, + 892, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 627, + 619, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a novel weakly-supervised tuning approach coupled with a data augmentation strategy to enhance the localization capabilities of an image-text supervised model through self-consistency. Using an open-source LLM, we expand a dataset with equivalent paraphrases tailored to be object-centric. The augmented data is used to finetune a base model employing our novel self-consistency equivalence tuning objective. Our approach has been rigorously validated across pretraining on diverse datasets, ranging from region-based captions (i.e., VG) to global-based captions (i.e., COCO). Our method achieves superior and self-consistent performance on three benchmarks and is even competitive with some box-supervised methods.", + "bbox": [ + 496, + 652, + 890, + 848 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was partially funded by NSF Award #2201710 and a Ken Kennedy Institute's SLB PhD Fellowship.", + "bbox": [ + 498, + 852, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13102", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samira Abnar and Willem Zuidema. Quantifying attention flow in transformers. arXiv preprint arXiv:2005.00928, 2020. 2", + "[2] Hassan Akbari, Svebor Karaman, Surabhi Bhargava, Brian Chen, Carl Vondrick, and Shih-Fu Chang. Multi-level multimodal common semantic space for image-phrase grounding. 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Filip: Fine-grained interactive language-image pre-training. arXiv preprint arXiv:2111.07783, 2021. 1", + "[53] Licheng Yu, Patrick Poirson, Shan Yang, Alexander C Berg, and Tamara L Berg. Modeling context in referring expressions. In Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part II 14, pages 69-85. Springer, 2016. 6", + "[54] Alireza Zareian, Kevin Dela Rosa, Derek Hao Hu, and Shih-Fu Chang. Open-vocabulary object detection using captions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14393-14402, 2021. 1", + "[55] Feifei Zhai, Saloni Potdar, Bing Xiang, and Bowen Zhou. Neural models for sequence chunking. In Proceedings of the AAAI conference on artificial intelligence, 2017. 4", + "[56] Jianming Zhang, Sarah Adel Bargal, Zhe Lin, Jonathan Brandt, Xiaohui Shen, and Stan Sclaroff. Top-down neural attention by excitation backprop. International Journal of Computer Vision, 126(10):1084-1102, 2018. 5" + ], + "bbox": [ + 78, + 90, + 470, + 655 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13105", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improved Visual Grounding through Self-Consistent Explanations/10bbab27-77ad-411f-b190-f41874ca342d_model.json b/2024/Improved Visual Grounding through Self-Consistent Explanations/10bbab27-77ad-411f-b190-f41874ca342d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..81e3b9919e1ee97f4b86f875ce7db53922008c7f --- /dev/null +++ b/2024/Improved Visual Grounding through Self-Consistent Explanations/10bbab27-77ad-411f-b190-f41874ca342d_model.json @@ -0,0 +1,2675 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.151, + 0.131, + 0.82, + 0.154 + ], + "angle": 0, + "content": "Improved Visual Grounding through Self-Consistent Explanations" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.18, + 0.88, + 0.217 + ], + "angle": 0, + "content": "Ruozhen He1 Paola Cascante-Bonilla1 Ziyan Yang1 Alexander C. Berg2 Vicente Ordonez1 \n1Rice University 2University of California, Irvine" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.22, + 0.868, + 0.234 + ], + "angle": 0, + "content": "catherine.he@rice.edu, pc51@rice.edu, zy47@rice.edu, bergac@uci.edu, vicenteor@rice.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.681 + ], + "angle": 0, + "content": "Vision-and-language models trained to match images with text can be combined with visual explanation methods to point to the locations of specific objects in an image. Our work shows that the localization – “grounding”– abilities of these models can be further improved by finetuning for self-consistent visual explanations. We propose a strategy for augmenting existing text-image datasets with paraphrases using a large language model, and SelfEQ, a weakly-supervised strategy on visual explanation maps for paraphrases that encourages self-consistency. Specifically, for an input textual phrase, we attempt to generate a paraphrase and finetune the model so that the phrase and paraphrase map to the same region in the image. We posit that this both expands the vocabulary that the model is able to handle, and improves the quality of the object locations highlighted by gradient-based visual explanation methods (e.g. GradCAM). We demonstrate that SelfEQ improves performance on Flickr30k, ReferIt, and RefCOCO+ over a strong baseline method and several prior works. Particularly, comparing to other methods that do not use any type of box annotations, we obtain \\(84.07\\%\\) on Flickr30k (an absolute improvement of \\(4.69\\%\\)), \\(67.40\\%\\) on ReferIt (an absolute improvement of \\(7.68\\%\\)), and \\(75.10\\%\\) \\(55.49\\%\\) on RefCOCO+ test sets A and B respectively (an absolute improvement of \\(3.74\\%\\) on average)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.709, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Vision-and-language models that are trained to associate images with text have shown to be effective for many tasks and benchmarks [21, 27, 31, 41], including object detection [18, 54] and image segmentation [15, 36, 50]. Since these models are typically trained with in-the-wild data from the web, they can handle a wide range of vocabulary for objects as long as they are well represented in the training data. These models are often remarkably accurate [16, 22, 28, 47] even without tuning them to perform well in any particular downstream task [14, 32, 52]. The ALBEF model [27] was particularly capable of visual" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.297, + 0.89, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.401, + 0.889, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.511, + 0.893, + 0.596 + ], + "angle": 0, + "content": "Figure 1. Previous models can localize the word frisbee, but struggle with equivalent but more uncommon referents such as disc. A model tuned with our proposed SelfEQ objective encourages consistent visual explanations for paraphrased prompts and performs well on both examples. SelfEQ not only enables a larger working vocabulary but also improves overall localization performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.893, + 0.704 + ], + "angle": 0, + "content": "\"grounding\" - or in other words - the ability to localize objects in images by simply using it in conjunction with a visual explanation method such as GradCAM [43]. This capability is particularly remarkable given that this model was only supervised with images and text but no object location annotations of any type." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In order to improve the ability of vision-and-language models to perform localization, many methods have incorporated further finetuning with either box or segment annotations, or rely on pretrained object detectors or box proposal networks [5, 12, 19, 23, 30, 51]. Our work instead aims to improve the localization capabilities of models trained only on image-text pairs through weak supervision. But, how can we improve the ability of a model to localize objects without access to object location annotations? Consider the example in Figure 1 where a model is tasked with pointing to the location of the object frisbee in this image. The baseline model succeeds at finding the object but is unsuccessful at locating the object when prompted with the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13095" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "equivalent but more generic name disc. Regardless of the ability for the base model to find either of these, the visual explanations for these two prompts should be the same since the query refers to the very same object in both cases. Our work exploits this property by first generating paraphrases using a large language model and then proposing a weakly-supervised Self-consistency EQuivalence Tuning (SelfEQ) objective that encourages consistent visual explanations between paraphrased input text pairs that refer to the same object or region in a given image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.544 + ], + "angle": 0, + "content": "Given a base pre-trained vision-and-language model purely trained on image-text pairs such as ALBEF [27], SelfEQ tunes the model so that for a given input image and text pair, the visual attention map extracted using GradCAM [43] produces a similar visual attention map when provided with the same image and a text paraphrase. Figure 2 provides an overview of our method. Another contribution of our work consists in exploiting a large language model (LLM) to automatically generate paraphrases for existing datasets such as Visual Genome [26] that contains textual descriptions of individual objects and regions, or MS-COCO [33] and CC3M [46] that contain global image descriptions. We find that SelfEQ not only expands the vocabulary of objects that the base model is able to localize but more importantly, improves the visual grounding capabilities of the model on standard benchmarks such as referring expression comprehension on the ReferIt benchmark [24] and region-phrase grounding in the Flickr30K Entities benchmark [40]. In summary, our key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.546, + 0.47, + 0.621 + ], + "angle": 0, + "content": "- We design a novel objective, SelfEQ, to encourage vision-and-language models to generate self-consistent visual explanations for equivalent text phrases, thereby improving grounding capabilities while expanding the working vocabulary of the model." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.622, + 0.47, + 0.681 + ], + "angle": 0, + "content": "- We propose to prompt large language models for generating paraphrased image descriptions of individual objects or regions. Particularly, we adopt Vicuna-13B [6] and design text prompts to obtain high quality paraphrases." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.682, + 0.47, + 0.741 + ], + "angle": 0, + "content": "- We demonstrate the effectiveness of our method by outperforming previous methods, leading to \\(4.69\\%\\) improvement on Flickr30k, \\(7.68\\%\\) improvement on ReferIt, and \\(3.74\\%\\) improvement on RefCOCO+." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.546, + 0.47, + 0.741 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.774 + ], + "angle": 0, + "content": "Finally, we plan to release our code, generated paraphrases and model checkpoints upon publication." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.785, + 0.22, + 0.801 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Our work is related to previous methods on visual grounding, especially those that are trained under weak supervision understood as without the use of bounding box or segment annotations and relying only on image-text pairs. From a technical perspective our work is related to methods that optimize visual explanations to improve the underlying model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Visual grounding consists of localizing an input textual description in an image. Supervised methods are provided with text-image pairs and corresponding bounding boxes [8, 9, 12, 23, 51]. Other supervised methods leverage pretrained object detectors to obtain a region of interest and then identify the region that aligns most closely under their textual representations [5, 7, 17, 19, 35, 48]. In both cases, these methods use some form of box supervision during pre-training or at test time by relying on a pre-trained object detector. In contrast, our work focuses exclusively in the scenario where no bounding boxes or segment annotations are available at any stage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.893, + 0.563 + ], + "angle": 0, + "content": "Weakly-Supervised Grounding. Our setup is similar to that of Arbelle et al [3] where no box annotations or object detectors are used for grounding. This work proposes Grounding by Separation (GbS) where a model is trained on randomly alpha-blended pairs of images and the goal is to separate them conditioned on text prompts. Our method instead relies on data augmentation on the text side and while our method shows favorable results, our contribution is orthogonal. Shaharabany et al [45] builds a weakly-supervised phrase grounding model by creating a large amount of data by combining region boxes with a BLIP captioning model. Later work by Shaharabany and Wolf [44] employs layerwise relevance propagation [38] to integrate relevancy and gradient information with the scores computed from each attention head in the transformer layers [4], or residual connections [1]. Our work compares favorably or on par with these methods but since we rely on gradient-based explanations, our work does not require making any modifications to the base network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Visual Explanation Tuning. Related to our method is the strategy used by ALBEF [27] where the model is only supervised on image-text pairs and performs grounding through GradCAM [43], a gradient-based visual explanation method that outputs a heatmap indicating spatial relevance. Earlier, Xiao et al [49] used a similar strategy but further optimized gradient-based explanations using structural constraints derived from text. Recently, AMC [51] follows this strategy but further adds box supervision on the output maps using a margin-based loss. We adopt ALBEF [27] as our base model and also adopt a gradient-based explanation strategy but unlike AMC [51] we do not rely on box annotations for tuning this model and use our proposed SelfEQ objective instead. Javed et al [20] proposed an objective function that encourages consistent representations in embedding space for the same input prompt on different images. In contrast SelfEQ encourages consistent visual explanations for different prompts on the same image by relying on automatically generated paraphrases. Akbari et al [2] also optimizes attention maps but in their formulation the model backbone is modified to explicitly incorporate attention instead of relying on gradient-based attention maps." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "13096" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.089, + 0.473, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.473, + 0.373 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed weakly-supervised Self-consistency EQuivalence tuning objective. We input image-text and image-paraphrase pairs \\(\\langle V, T \\rangle\\) and \\(\\langle V, T^e \\rangle\\) to our base pretrained vision-and-language model. We then obtain gradient-based visual explanations \\(\\langle G, G^e \\rangle\\) and compute a similarity loss between them. We also define an overlapping region of interest mask and encourage the model to predict consistently high saliency scores within this mask for each input pair." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.39, + 0.17, + 0.405 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.473, + 0.614 + ], + "angle": 0, + "content": "We start from a base vision-language model composed of a text encoder \\(\\phi_t\\), an image encoder \\(\\phi_v\\), and a multimodal fusion encoder \\(\\phi_f\\), along with a dataset \\(D\\) to finetune this model consisting of image-text pairs \\(\\langle T, V \\rangle\\). Section 3.1, introduces the training objectives for the base model which we also adopt for finetuning our baseline and are also used in conjunction with SelfEQ to finetune our final model. Section 3.2 introduces in detail SelfEQ, our self-consistency equivalence tuning objective that assumes the existence of paraphrases \\(T^e\\) for each input image-text pair \\(\\langle T, V \\rangle\\), and Section 3.3 describes our approach for automatically generating paraphrases \\(T^e\\) using LLM-prompting. Figure 2 presents an overview of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.627, + 0.32, + 0.642 + ], + "angle": 0, + "content": "3.1. Base Model: Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.651, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Our base vision-and-language model is ALBEF [27] which relies on three widely used objectives for visual and textual representation learning: image-text matching, masked language modeling and a contrastive loss. We describe them here briefly as they are also re-used during fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.471, + 0.794 + ], + "angle": 0, + "content": "Image-Text Matching Loss (ITM). This loss is calculated using the output of the [CLS] token to predict if the input image and the input text are matching or not and is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.805, + 0.47, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {i t m}} = \\mathbb {E} _ {(V, T) \\sim D} \\mathcal {H} \\left(\\vec {y}, \\phi_ {f} ^ {\\mathrm {c l s}} \\left(\\phi_ {v} (V), \\phi_ {t} (T)\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(\\vec{y}\\) denotes a two-dimensional one-hot vector, indicating whether the sample \\(\\langle V,T\\rangle\\) constitutes a match, \\(\\phi_f^{\\mathrm{cls}}\\) represents a linear layer followed by a softmax function, and \\(\\mathcal{H}\\) is the cross entropy loss function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Masking Language Modeling Loss (MLM). This loss has been applied for various vision-language pretraining models [5, 27, 29, 34]. It integrates the contextual text and the input image to infer masked words in the input text. After utilizing a linear layer and a softmax activation function \\(\\phi_f^{\\mathrm{m}}\\) to individual output embeddings, the objective is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.207, + 0.892, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {m l m}} = \\mathbb {E} _ {(V, T ^ {- \\mathrm {m}}) \\sim D} \\mathcal {H} \\left(\\bar {t} ^ {\\mathrm {m}}, \\phi_ {f} ^ {\\mathrm {m}} \\left(\\phi_ {v} (V), \\phi_ {t} \\left(T ^ {- \\mathrm {m}}\\right)\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.235, + 0.892, + 0.267 + ], + "angle": 0, + "content": "where the one-hot vector \\(t^{\\mathrm{m}}\\) denotes the masked token, and \\(T^{-\\mathrm{m}}\\) represents the input masked text." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Image-Text Contrastive Loss (ITC). It improves the alignment between visual and textual representations by bringing closer the representations for corresponding text-image pairs relative to text-image pairs that do not correspond. This objective can be defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.361, + 0.892, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {i t c}} = \\mathbb {E} _ {(V, T) \\sim D} \\frac {1}{2} \\left[ \\mathcal {H} \\left(\\vec {y}, \\frac {\\exp \\left(\\phi_ {v} (V) \\cdot \\phi_ {t} (T)\\right) / \\tau}{\\sum_ {b = 1} ^ {B} \\mathrm {s} (V , T _ {b})}\\right) \\right. \\tag {3} \\\\ \\left. + \\mathcal {H} \\left(\\vec {y}, \\frac {\\exp \\left(\\phi_ {t} (T) \\cdot \\phi_ {v} (V)\\right) / \\tau}{\\sum_ {b = 1} ^ {B} \\mathrm {s} (T , V _ {b})}\\right) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.892, + 0.467 + ], + "angle": 0, + "content": "where \\(B\\) is the number of negative sample pairs, and \\(\\tau\\) is a temperature parameter for the softmax function." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.468, + 0.892, + 0.497 + ], + "angle": 0, + "content": "The training objective for the base model is a combination of the previous three loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.509, + 0.892, + 0.523 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {v l}} = \\mathcal {L} _ {\\mathrm {i t m}} + \\mathcal {L} _ {\\mathrm {m l m}} + \\mathcal {L} _ {\\mathrm {i t c}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.535, + 0.884, + 0.549 + ], + "angle": 0, + "content": "This loss \\(\\mathcal{L}_{\\mathrm{vl}}\\) will also be used to tune our baseline model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.56, + 0.821, + 0.575 + ], + "angle": 0, + "content": "3.2. Self-Consistency Equivalence Tuning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.734 + ], + "angle": 0, + "content": "SelfEQ assumes that the model has access to paraphrases \\( T^e \\) for each input image-text pair \\( \\langle V, T \\rangle \\) or, in practice, for a subset of those samples. Therefore we assume a finetuning dataset \\( D' \\) with triplets \\( \\langle V, T, T^e \\rangle \\) such that \\( T^e \\) exists for a corresponding input text \\( T \\). The first step to define our SelfEQ objective is to generate the explanation heatmaps (i.e., attention maps) through GradCAM [43] conditioned on the input text. We extract intermediate feature maps from the multimodal interactive encoder \\( \\phi_f \\) for input pairs \\( \\langle V, T \\rangle \\) and \\( \\langle V, T^e \\rangle \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.744, + 0.892, + 0.761 + ], + "angle": 0, + "content": "\\[\nF = \\phi (\\phi_ {v} (V), \\phi_ {t} (T)), F ^ {e} = \\phi (\\phi_ {v} (V), \\phi_ {t} (T ^ {e})), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.847 + ], + "angle": 0, + "content": "where \\(\\phi\\) denotes the feature map extraction operation. We then proceed to calculate the gradient of \\(F\\) and \\(F^{e}\\) related to the image-text matching score \\(\\mathcal{L}_{\\mathrm{itm}}\\). This computation yields the attention maps for the original text and paraphrased text, referred to as \\(G\\) and \\(G^{e}\\), respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.856, + 0.892, + 0.887 + ], + "angle": 0, + "content": "\\[\nG = \\operatorname {R e L U} \\left(F \\odot \\nabla \\mathcal {H} \\left(\\vec {y}, \\phi_ {f} ^ {c l s} \\left(\\phi_ {v} (V), \\phi_ {t} (T)\\right)\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.881, + 0.853, + 0.905 + ], + "angle": 0, + "content": "\\[\nG ^ {e} = \\operatorname {R e L U} \\left(F ^ {e} \\odot \\nabla \\mathcal {H} \\left(\\vec {\\mathcal {y}}, \\phi_ {f} ^ {c l s} \\left(\\phi_ {v} (V), \\phi_ {t} \\left(T ^ {e}\\right)\\right)\\right)\\right).\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13097" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "Our SelfEQ tuning is based on the premise that if a vision-language model is identified as self-consistent, the attention maps produced for both the text and its equivalent paraphrase should yield nearly identical results. To achieve this, we first apply a simple mean squared error loss over the produced heatmaps so that their \\(\\ell_2\\) distance is minimized and thus become more similar." + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.204, + 0.47, + 0.24 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s i m}} = \\mathbb {E} _ {(V, T, T ^ {e}) \\sim D ^ {\\prime}} \\left[ \\frac {1}{N} \\sum_ {i, j} \\left(G _ {i, j} - G _ {i, j} ^ {e}\\right) ^ {2} \\right]. \\qquad (7)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.248, + 0.473, + 0.491 + ], + "angle": 0, + "content": "Nevertheless, while minimizing a sum of pixel-wise distances contributes to self-consistency, without a regularization term this loss can easily fall into a trivial solution. For instance, it could lead to attention maps with uniformly negative or positive predictions, or just really small values. To address this limitation, we propose to integrate these heatmaps by defining a Region of Interest (RoI) mask. This mask is designed to preserve regions within the attention maps that possibly contain correct predictions. Our approach hinges on the observation that, despite the predictions of equivalent textual inputs being inconsistent, sometimes regions with large values or regions that overlap between the two heatmaps tend to be correct. As such, we assume that if the sum of attention scores at a given position \\((i,j)\\) exceeds a certain threshold \\(k\\), it is likely indicative of a correct prediction. We formalize the condition as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.5, + 0.47, + 0.537 + ], + "angle": 0, + "content": "\\[\nM _ {i, j} = \\left\\{ \\begin{array}{l} 1, \\left(G _ {i, j} + G _ {i, j} ^ {e}\\right) \\geq k \\\\ 0, \\left(G _ {i, j} + G _ {i, j} ^ {e}\\right) < k \\end{array} \\right.. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.545, + 0.47, + 0.576 + ], + "angle": 0, + "content": "The attention maps within RoI masks are obtained by element-wise multiplication as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.585, + 0.47, + 0.6 + ], + "angle": 0, + "content": "\\[\nR = G \\odot M, \\quad R ^ {e} = G ^ {e} \\odot M. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.611, + 0.473, + 0.779 + ], + "angle": 0, + "content": "The integration of RoI masks allows us to use equivalent texts for mutual supervision, refining and improving the accuracy and providing regularization for the previously defined distance-based loss. Moreover, it could potentially address errors owing to unknown or less common words by working vocabulary expansion. Presuming one of the textual expressions is known and correctly understood, the model could extrapolate the meaning of the other equivalent expression via weak supervision. To implement it, we first compute the mean \\(\\mu_{RoI},\\mu_{RoI}^{e}\\) and the standard deviation \\(\\sigma_{RoI},\\sigma_{RoI}^{e}\\) within the RoI as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.787, + 0.47, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\mu_ {R o I} = \\frac {\\sum_ {i , j} R _ {i , j}}{\\sum_ {i , j} M _ {i , j}}, \\mu_ {R o I} ^ {e} = \\frac {\\sum_ {i , j} R _ {i , j} ^ {e}}{\\sum_ {i , j} M _ {i , j}}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.828, + 0.469, + 0.872 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {R o I} = \\sqrt {\\frac {\\sum_ {i , j} M _ {i , j} \\cdot \\left(R _ {i , j} - \\mu_ {R o I}\\right) ^ {2}}{\\sum_ {i , j} M _ {i , j}}}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.868, + 0.396, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {R o I} ^ {e} = \\sqrt {\\frac {\\sum_ {i , j} M _ {i , j} \\cdot (R _ {i , j} ^ {e} - \\mu_ {R o I} ^ {e}) ^ {2}}{\\sum_ {i , j} M _ {i , j}}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "We propose a consistency loss \\((\\mathcal{L}_{\\mathrm{cst}})\\), expecting the RoI regions of attention maps to achieve consistently high scores, further reinforcing self-consistency, accuracy, and potential working vocabulary expansion. This objective is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.175, + 0.892, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c s t}} = \\mathbb {E} _ {(V, T, T ^ {e}) \\sim D ^ {\\prime}} \\left[ \\sigma_ {R o I} + \\sigma_ {R o I} ^ {e} + \\right. \\tag {12} \\\\ \\left. \\max (0, k / 2 - \\mu_ {R o I}) + \\max (0, k / 2 - \\mu_ {R o I} ^ {e}) \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.247, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Finally, the objective of our self-consistency equivalence tuning is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.293, + 0.892, + 0.308 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {S e l f E Q}} = \\mathcal {L} _ {\\text {s i m}} + \\lambda \\cdot \\mathcal {L} _ {\\text {c s t}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.313, + 0.892, + 0.343 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyperparameter to control the relative influence of each loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.355, + 0.818, + 0.371 + ], + "angle": 0, + "content": "3.3. Self-Consistency Data Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.378, + 0.892, + 0.467 + ], + "angle": 0, + "content": "In this section we define a function \\(\\mathcal{F}\\) that can automatically map input textual phrases \\(T\\) as paraphrases \\(T^{e}\\) without the need to rely on human annotations such that \\(T^{e} \\sim \\mathcal{F}(T)\\). We achieve this goal through a two-level prompting approach using a large language model which we describe in detail below." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.473, + 0.893, + 0.746 + ], + "angle": 0, + "content": "Phrase Chunking: Using our first-level prompts, we aim to augment the original text using phrase chunking to encourage global captions to concentrate on more specific regions. Visual grounding seeks to localize objects in images based on textual inputs. In contrast, global captions usually describe the entire image, typically describing several objects. While training on global captions could be beneficial for learning cross-modal information, it may lead the model to predict a broader region (i.e., global context) rather than a specific region. Phrase chunking (i.e., shallow parsing [55]) aims to identify continuous sequences of tokens representing syntactic units, enabling the extraction of phrases from unstructured text. We leverage an LLM to segment global captions into object-centric short phrases. During training, we use these image-chunk pairs instead of global captions, effectively guiding the model attention toward localized regions of interest. We refer the reader to the supplementary material for prompting details and generated examples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Paraphrase Generation: Our SelfEQ approach involves feeding the model with pairs of textual descriptions that refer to the same underlying concept, with the expectation that the model can make similar predictions for these equivalent description pairs \\(\\langle T, T^e \\rangle\\). We augment our dataset by transforming the region-based captions (i.e., text that only refers to a region in the image) and the object-centric short phrases we obtained from phrase chunking into equivalent paraphrases referring to the same concept through our second-level LLM-prompts." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13098" + } + ], + [ + { + "type": "code", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.192 + ], + "angle": 0, + "content": "Q:\"a smiling, holding something and standing man\" \nA:{\"group\": \"man\", \"synonym\": [\"adult male\",\"gentleman\"], \"antonym\": [\"woman\"], \"hypernym\": [\"adult\",\"grownup\",\"male\",\"male person\",\"human being\",\"human\"], \"meronym\": [\"man body\",\"man head\",\"man arms\",\"man legs\"]} \nQ:\"a desk\" \nA:{\"group\": \"desk\", \"synonym\": [\"table\",\"writing desk\"], \"antonym\": [], \"hypernym\": [\"writer tool\",\"furniture\"], \"meronym\": [\"desktop\",\"desk leg\"]}" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.201, + 0.47, + 0.258 + ], + "angle": 0, + "content": "Figure 3. Two samples from our LLM-prompt for paraphrase generation. The first set showcases an example of a region-based caption, and the second set shows a non-sentence phrase. \\(\\mathbf{Q}\\) is the query text and \\(\\mathbf{A}\\) is the expected answer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.268, + 0.47, + 0.463 + ], + "angle": 0, + "content": "There are many ways to paraphrase, including substituting words, altering sentence structures, and rewriting sentences based on semantics. However, considering that self-consistency in vision and language is relatively underexplored, we adopt a straightforward strategy: Replacing the primary object in the sentence while retaining all other attributes. This strategy yields several benefits. First, it provides a consistent context, which serves as a reference for the model to identify equivalent descriptions. This enables the equivalent relationships of paraphrases to be learned intuitively. Second, it simplifies prompt designing and post-processing by detecting the primary object and generating its synonym." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.47, + 0.675 + ], + "angle": 0, + "content": "To generate paraphrases for the dataset consisting of region-based captions, we select four textual descriptions in which the primary noun plays different syntactic roles. We further select two non-sentence phrases as examples of query texts in our prompts. We show an example of a region-based caption and a non-sentence phrase in Figure 3. To design our prompt, we identify the primary object in the query text Q. Then we use WordNet [37] to obtain synonyms automatically and further remove inaccurate or invalid words. We add A to indicate the expected answer and include other relationships such as antonym, hy- pernym and meronym to provide richer contexts for LLM in-context learning. Additional prompting details and paraphrase samples are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.47, + 0.754 + ], + "angle": 0, + "content": "This two-level prompt-based LLM augmentation approach ensures that our model is exposed to textual inputs that share the same concept while varying in linguistic representation, thereby promoting self-consistency and working vocabulary expansion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.289, + 0.788 + ], + "angle": 0, + "content": "4. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.903 + ], + "angle": 0, + "content": "Training. We use ALBEF [27] as our base model in all our experiments, given its reported off-the-shelf visual grounding performance via GradCAM [43]. ALBEF combines a ViT-B [11] model for encoding images and a BERT-base [10] model for encoding text. It is pre-trained on a range of datasets, including ImageNet-1K [42], Conceptual Captions [46], SBU Captions [39], MS-COCO [33], and" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.09, + 0.895, + 0.466 + ], + "angle": 0, + "content": "
MethodTrainingFlickr30kReferIt
Box SupervisionAlign2Ground [7]VG-boxes71.00-
12-in-1 [35]VG-boxes76.40-
InfoGround [19]VG-boxes76.74-
VMRM [12]VG-boxes81.11-
AMC [51]VG-boxes86.5973.17
Without Box SupervisionTD [56]VG42.4031.97
SSS [20]VG49.1039.98
MG-BiLSTM [2]VG57.9162.76
MG-ELMo [2]VG60.0860.01
GbS [3]VG73.3962.24
g [45]VG75.6365.95
g++ [44]VG79.9570.25
SelfEQ (ours)VG81.9067.40
FCVC [13]MS-COCO29.0333.52
MG-BiLSTM [2]MS-COCO53.2947.89
MG-ELMo [2]MS-COCO61.6647.52
GbS [3]MS-COCO74.5049.26
g [45]MS-COCO75.4361.03
g++ [44]MS-COCO78.1061.53
SelfEQ (ours)MS-COCO84.0762.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.477, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Table 1. Visual Grounding results on two benchmarks using pointing game accuracy with two training datasets. SelfEQ yields generally the best overall performance among weakly-supervised methods, and comes second to \\( \\mathrm{g} + + \\) on the ReferIt benchmark when trained using VG. We also show at the top the results of methods using additional box supervision from Visual Genome (VG) either directly or through an object detector." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Visual Genome (VG) [26] excluding box annotations. We finetune ALBEF with image-text pairs from VG and MS-COCO without any type of box supervision (i.e., no bounding boxes or object detectors), following prior work [2]. We further leverage Vicuna-13B [6] as our LLM-prompting model to generate the object-centric short phrases (via shallow parsing or chunking) and the equivalent paraphrases for our self-consistency data augmentation. Additionally, we validate the effectiveness of our SelfEQ tuning and self-consistency data augmentation method by training on a preprocessed subset of the Conceptual Captions 3M (CC3M) dataset [46], which contains many noisy or unaligned web-crawled AltText-image pairs. With this subset, we achieve an absolute improvement of \\(2.15\\%\\) on Flickr30k, \\(3.32\\%\\) on ReferIt, and \\(1.33\\%\\) on RefCOCO+; refer to the supplementary material for detailed CC3M experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Evaluation. We conduct evaluations using Flickr30k [40] and ReferIt [24] under pointing game accuracy following previous weakly-supervised visual grounding works [2, 3]. To underscore the competitive edge of our method, we also" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13099" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.457, + 0.235 + ], + "angle": 0, + "content": "
MethodBox SupervisionRefCOCO+
Test ATest B
InfoGround [19]Yes39.8041.11
VMRM [12]Yes58.8750.32
AMC [51]Yes80.3464.55
ALBEF [27]No69.3553.77
SelfEQ (ours)No75.1055.49
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.245, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Table 2. Results on RefCOCO+ pointing game accuracy. SelfEQ shows significant improvements over off-the-shelf ALBEF and competitive results compared to box-supervised methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.298, + 0.47, + 0.343 + ], + "angle": 0, + "content": "present its performance on RefCOCO+ [53], a challenging benchmark more commonly used for testing box-supervised methods [7, 12, 19, 35, 51]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.352, + 0.295, + 0.368 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.471, + 0.646 + ], + "angle": 0, + "content": "Our experiments are conducted on a single computing node with 8 NVIDIA A40 GPUs. During the training phase, input images are resized to \\(256 \\times 256\\) and augmented with horizontal flipping, color jittering, and random grayscale conversion. We set up an Adam optimizer [25] with a learning rate of 1e-5 and a batch size of 448 across all experiments. We empirically set the RoI threshold \\(k\\) to 0.8 and the hyperparameter \\(\\lambda\\) to 1.0. For training with raw image-text pairs from the datasets, we employ the vision-language objective \\(\\mathcal{L}_{\\mathrm{vl}}\\) (Sec. 3.1), while for the subset with equivalent paraphrases, we use our self-consistency equivalence tuning objective \\(\\mathcal{L}_{\\mathrm{SelfEQ}}\\) (Sec. 3.2) and corresponding vision-language objective \\(\\mathcal{L}_{\\mathrm{vl}}^e\\). The composite objective function is given by \\(\\mathcal{L} = \\alpha \\cdot \\mathcal{L}_{\\mathrm{vl}} + (1 - \\alpha) \\cdot (\\mathcal{L}_{\\mathrm{SelfEQ}} + \\mathcal{L}_{\\mathrm{vl}}^e)\\), where \\(\\alpha\\) is initially set to 0 and increments to 1, remaining constant after the second epoch. Our hyperparameter values and schedules were determined empirically on a small validation subset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.283, + 0.677 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.791 + ], + "angle": 0, + "content": "Our resulting model obtains the best performance on the task of weakly-supervised visual grounding compared to most methods under this setting and is comparable to several prior works that rely on some of box supervision. Moreover, our qualitative results show that our method can handle paraphrases and a larger working vocabulary without the needed to increment the training dataset significantly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Flickr30k and ReferIt. We evaluate the effectiveness of our proposed SelfEQ method in Table 1, demonstrating its substantial lead over GradCAM-based weakly-supervised approaches. Our self-consistency equivalent tuning adapts well for both region-based (i.e., VG) and global-based (i.e., COCO) image-text pairs, yielding a performance gain of \\(4.69\\%\\) on Flickr30k and \\(7.68\\%\\) on ReferIt, compared to" + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.096, + 0.65, + 0.109 + ], + "angle": 0, + "content": "Text: \"trees on the right\"" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.11, + 0.605, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.165, + 0.573, + 0.174 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.11, + 0.697, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.165, + 0.663, + 0.174 + ], + "angle": 0, + "content": "ALBEF" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.11, + 0.79, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.732, + 0.165, + 0.755, + 0.173 + ], + "angle": 0, + "content": "AMC" + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.11, + 0.887, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.165, + 0.849, + 0.173 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.179, + 0.692, + 0.19 + ], + "angle": 0, + "content": "Text: \"blue thermos very bottom\"" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.192, + 0.605, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.248, + 0.573, + 0.257 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.192, + 0.698, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.248, + 0.664, + 0.256 + ], + "angle": 0, + "content": "ALBEF" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.192, + 0.79, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.733, + 0.248, + 0.756, + 0.256 + ], + "angle": 0, + "content": "AMC" + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.192, + 0.886, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.827, + 0.248, + 0.848, + 0.256 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.263, + 0.66, + 0.274 + ], + "angle": 0, + "content": "Text: \"person right corner\"" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.276, + 0.606, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.332, + 0.573, + 0.34 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.276, + 0.699, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.332, + 0.664, + 0.34 + ], + "angle": 0, + "content": "ALBEF" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.276, + 0.791, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.332, + 0.756, + 0.339 + ], + "angle": 0, + "content": "AMC" + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.276, + 0.886, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.332, + 0.848, + 0.339 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.346, + 0.746, + 0.358 + ], + "angle": 0, + "content": "Text: \"kangaroo furthest away facing right\"" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.359, + 0.604, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.414, + 0.573, + 0.422 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.359, + 0.698, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.414, + 0.664, + 0.422 + ], + "angle": 0, + "content": "ALBEF" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.359, + 0.79, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.414, + 0.756, + 0.421 + ], + "angle": 0, + "content": "AMC" + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.359, + 0.886, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.414, + 0.848, + 0.422 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.428, + 0.612, + 0.44 + ], + "angle": 0, + "content": "Text: \"white bldg\"" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.441, + 0.6, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.525, + 0.573, + 0.534 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.611, + 0.441, + 0.693, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.525, + 0.664, + 0.533 + ], + "angle": 0, + "content": "ALBEF" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.44, + 0.786, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.525, + 0.756, + 0.533 + ], + "angle": 0, + "content": "AMC" + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.44, + 0.881, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.525, + 0.848, + 0.533 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.541, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Figure 4. Qualitative results of our method in challenging visual grounding scenarios compared to prior works. On top of each row we show the reference text, the first column shows the image, then we show our base model ALBEF, the SotA box-supervised method AMC, and finally we show results with our method SelfEQ." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.851 + ], + "angle": 0, + "content": "our base model ALBEF (see first row in Table 3). Notably, our method outperforms almost all box-supervised methods on Flickr30k [7, 12, 19, 35]. In the weakly-supervised setting, our method only comes second on ReferIt compared to \\(\\mathrm{g + + }[44]\\) when trained on Visual Genome imagedtext pairs. This method leverages a custom architecture to produce a mask and uses heatmap supervision from a CLIP [41] model as pseudo-labels during training. We posit that our contribution is orthogonal and our approach would likely also benefit from similar supervision, since CLIP is trained in a much larger image-text pair dataset. Despite differences, our method still obtains higher performance when trained on MS-COCO and the best performance compared to all weakly-supervised methods on Flickr30K region-phrase grounding." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "RefCOCO+. RefCOCO+ [53] serves as a rigorous benchmark for visual grounding, typically used to evaluate box-supervised techniques. In Table 2, we present the per" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13100" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.462, + 0.202 + ], + "angle": 0, + "content": "
DataObjectiveRefCOCO+Flickr30kReferIt
Test ATest B
-\\( \\mathcal{L}_{\\mathrm{vl}} \\)69.3553.7779.3859.72
T\\( \\mathcal{L}_{\\mathrm{vl}} \\)72.3054.2278.7565.86
T+Te\\( \\mathcal{L}_{\\mathrm{vl}} \\)71.5553.5178.0564.57
T+Te\\( \\mathcal{L}_{\\text{SelfEQ}} \\)75.1055.4981.9067.40
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.212, + 0.47, + 0.296 + ], + "angle": 0, + "content": "Table 3. Ablation studies on different ways to utilize extra equivalent paraphrased data. The first row is off-the-shelf ALBEF performance before tuning. \\( T \\) denotes the textual captions from the dataset, and \\( {T}^{e} \\) corresponds to the associated equivalent paraphrases. \\( {\\mathcal{L}}_{\\mathrm{{vl}}} \\) is the vision-language objective,and \\( {\\mathcal{L}}_{\\text{SelfEQ }} \\) is our self-consistency equivalence tuning objective." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.471, + 0.384 + ], + "angle": 0, + "content": "formance of our weakly-supervised method (VG trained) against box-supervised methods. Our results indicate that our approach is competitive without reliance on any form of box annotations and significantly improves over the base ALBEF model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.542 + ], + "angle": 0, + "content": "Visual Grounding Analysis. Figure 4 provides qualitative results of our method in challenging scenarios, including occluded objects (row 1), small objects within complex scenes (row 2), objects partially shown in the corner of the image (row 3), multiple similar objects (row 4), and abbreviated text inputs (row 5). Our self-consistency equivalency tuning approach exhibits substantial improvements in the grounding capability of the base ALBEF [27] model. Remarkably, our approach even outperforms the state-of-the-art box-supervised method AMC [51] in multiple scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.471, + 0.713 + ], + "angle": 0, + "content": "Self-Consistency Analysis. Figure 5 demonstrates qualitative results for the self-consistency capability across different equivalent paraphrases, encompassing terminology (row 1), synonym substitutions (row 2), and regional slang combining with different sentence structures (row 3). Although other methods succeed in localizing certain phrases, they demonstrate inconsistencies for the equivalent paraphrases. In contrast, our model finetuned with SelfEQ effectively establishes connections between semantically equivalent paraphrases, thereby enhancing the model self-consistency ability and potentially expanding its working vocabulary." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.722, + 0.242, + 0.736 + ], + "angle": 0, + "content": "5.1. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Data Quantity. We assess the impact of the data quantity of our generated paraphrases and compare our tuning strategy against standard vision-language objectives. We randomly sample portions of data from VG by \\(10\\%\\) associated with our augmented equivalent paraphrases three times. To compare, we use the vision-language objective with VG text-image pairs as baselines. In Figure 6, we show the mean and standard deviation pointing game accuracy. The performance of the base vision-language objective does not exhibit a steady improvement with more text-image pairs. Al-" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.093, + 0.888, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.228, + 0.887, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.365, + 0.887, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.509, + 0.892, + 0.579 + ], + "angle": 0, + "content": "Figure 5. Qualitative results across equivalent paraphrases among different methods. For each image, we show a caption referring to an object in the first row and an equivalent paraphrase in the second row. Each column shows the results of ALBEF, the SotA box-supervised method AMC, and our SelfEQ method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.593, + 0.892, + 0.683 + ], + "angle": 0, + "content": "though ReferIt performance increases, the performance on RefCOCO+ Test A remains mostly unchanged. Additionally, the performance on Flickr30k notably decreases, and there is a mixed effect on RefCOCO+ Test B, with half of the accuracy falling below the off-the-shelf ALBEF performance of \\(53.77\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.868 + ], + "angle": 0, + "content": "In contrast, SelfEQ consistently leads to performance enhancements with more equivalent paraphrases. Clear upward trends are observed on Flickr30k, ReferIt, and RefCOCO+ Test A as more data with corresponding equivalent paraphrases are added, meanwhile the gaps between the baselines generally widen. Notably, SelfEQ tuning maintains performance gains on Flickr30k, whereas the baselines performances drop. Although the trend on RefCOCO+ Test B is not consistently increasing, it is essential to emphasize that RefCOCO+ Test B is only a subset, and SelfEQ illustrates more stable and effective tuning performance on it, compared to the base vision-language objective." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "These observations indicate that more equivalent paraphrases connecting with associated text phrases enable the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13101" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.283, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.481, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.089, + 0.679, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.089, + 0.877, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.189, + 0.894, + 0.232 + ], + "angle": 0, + "content": "Figure 6. Tuning performance with different data quantities on Flickr30k, ReferIt, RefCOCO+ Test A and Test B. The purple and cyan lines represent SelfEQ (ours) and ALBEF baseline losses (vision-language objective), respectively. We show the impact of progressively augmenting captions via LLM-prompting for generating equivalent paraphrases tuned with our SelfEQ objective. Best viewed in color." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.246, + 0.421, + 0.358 + ], + "angle": 0, + "content": "
FormatObjectiveFlickr30kReferIt
-\\( \\mathcal{L}_{\\mathrm{vl}} \\)79.3859.72
C\\( \\mathcal{L}_{\\mathrm{vl}} \\)79.9060.64
C\\( \\mathcal{L}_{\\text{SelfEQ}} \\)81.2862.04
P\\( \\mathcal{L}_{\\mathrm{vl}} \\)81.1861.18
P\\( \\mathcal{L}_{\\text{SelfEQ}} \\)84.0762.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.364, + 0.47, + 0.435 + ], + "angle": 0, + "content": "Table 4. Comparisons on data augmentation strategy for global-based captions in MS-COCO with or without the paraphrases. \\( C \\) is the global-based captions from MS-COCO, and \\( P \\) is our Vicuna-13B processed object-centric phrases separately. The first row is the off-the-shelf ALBEF performance before tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.469, + 0.534 + ], + "angle": 0, + "content": "model to acquire more valuable information during tuning. SelfEQ proves to be an effective and robust strategy for consistently improving performance with our generated paraphrases. With increased self-consistency augmented data, SelfEQ guides the model toward better grounding performance by enhancing its self-consistency capabilities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Our method generates equivalent paraphrases for self-consistency enhancement, but it also contributes additional data for training. To ascertain the specific impact of our SelfEQ tuning strategy, we run a control experiment on this variable. As shown in Table 3, we assess the model's performance when equivalent paraphrases are integrated as regular image-text pairs with vision-language objectives (Sec. 3.1). This comparison reveals that merely augmenting the dataset with extra image-paraphrase pairs, without forming explicit linkages between the original text and its paraphrases, does not yield performance improvements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Data Augmentation. For global-based captions in MS-COCO, we preprocess the captions \\(C\\) to object-centric short phrases \\(P\\) via LLM-prompting. As shown in Table 4, tuning with phrases \\(P\\) leads to better performance, benefiting both the vision-language objective \\((\\mathcal{L}_{\\mathrm{vl}})\\) and our self-consistency equivalence tuning objective \\((\\mathcal{L}_{\\mathrm{SelfEQ}})\\). This improvement is probably attributed to short phrases allowing the model to focus on a specific region rather than the entire scene, aligning more closely with the objective of visual grounding. By utilizing equivalent paraphrases with our SelfEQ objective (row 3 and 5), phrase chunking helps SelfEQ even more, indicating the important role of equivalent paraphrases in promoting self-consistency and grounding ability." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.246, + 0.878, + 0.338 + ], + "angle": 0, + "content": "
\\( \\mathcal{L}_{\\text{sim}} \\)\\( \\mathcal{L}_{\\text{cst}} \\)RefCOCO+Flickr30kReferIt
Test ATest B
✓66.4247.2168.2655.96
✓73.3355.8880.9466.57
✓✓75.1055.4981.9067.40
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.343, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Table 5. Ablation studies on objective components of self-consistency equivalence tuning objective \\( {\\mathcal{L}}_{\\text{SelfEQ }} \\) ." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.893, + 0.614 + ], + "angle": 0, + "content": "Objective. Table 5 evaluates each component within our self-consistency equivalence tuning objective. The \\(\\mathcal{L}_{\\mathrm{sim}}\\) loss targets pixel-wise similarity, ensuring that maps for a caption and its equivalent paraphrase are identical. However, focusing solely on pixel-level similarity may neglect the precise spatial positioning of objects. To address this, the \\(\\mathcal{L}_{\\mathrm{cst}}\\) loss is proposed to identify the most likely correct object positions within the two maps (i.e., RoI). It then encourages the model to yield consistently high attention scores within the RoI. By integrating both \\(\\mathcal{L}_{\\mathrm{sim}}\\) and \\(\\mathcal{L}_{\\mathrm{cst}}\\), self-consistency equivalence tuning objective fosters the model to not only align global similarities but also to pinpoint accurate object locations through the mutual supervision provided by a caption and its paraphrase, thereby enhancing self-consistency and accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.628, + 0.62, + 0.643 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.849 + ], + "angle": 0, + "content": "We propose a novel weakly-supervised tuning approach coupled with a data augmentation strategy to enhance the localization capabilities of an image-text supervised model through self-consistency. Using an open-source LLM, we expand a dataset with equivalent paraphrases tailored to be object-centric. The augmented data is used to finetune a base model employing our novel self-consistency equivalence tuning objective. Our approach has been rigorously validated across pretraining on diverse datasets, ranging from region-based captions (i.e., VG) to global-based captions (i.e., COCO). Our method achieves superior and self-consistent performance on three benchmarks and is even competitive with some box-supervised methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.853, + 0.892, + 0.899 + ], + "angle": 0, + "content": "Acknowledgments. This work was partially funded by NSF Award #2201710 and a Ken Kennedy Institute's SLB PhD Fellowship." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13102" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.155 + ], + "angle": 0, + "content": "[1] Samira Abnar and Willem Zuidema. Quantifying attention flow in transformers. arXiv preprint arXiv:2005.00928, 2020. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.239 + ], + "angle": 0, + "content": "[2] Hassan Akbari, Svebor Karaman, Surabhi Bhargava, Brian Chen, Carl Vondrick, and Shih-Fu Chang. Multi-level multimodal common semantic space for image-phrase grounding. 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Berg2 Vicente Ordonez1 +1Rice University 2University of California, Irvine + +catherine.he@rice.edu, pc51@rice.edu, zy47@rice.edu, bergac@uci.edu, vicenteor@rice.edu + +# Abstract + +Vision-and-language models trained to match images with text can be combined with visual explanation methods to point to the locations of specific objects in an image. Our work shows that the localization – “grounding”– abilities of these models can be further improved by finetuning for self-consistent visual explanations. We propose a strategy for augmenting existing text-image datasets with paraphrases using a large language model, and SelfEQ, a weakly-supervised strategy on visual explanation maps for paraphrases that encourages self-consistency. Specifically, for an input textual phrase, we attempt to generate a paraphrase and finetune the model so that the phrase and paraphrase map to the same region in the image. We posit that this both expands the vocabulary that the model is able to handle, and improves the quality of the object locations highlighted by gradient-based visual explanation methods (e.g. GradCAM). We demonstrate that SelfEQ improves performance on Flickr30k, ReferIt, and RefCOCO+ over a strong baseline method and several prior works. Particularly, comparing to other methods that do not use any type of box annotations, we obtain $84.07\%$ on Flickr30k (an absolute improvement of $4.69\%$ ), $67.40\%$ on ReferIt (an absolute improvement of $7.68\%$ ), and $75.10\%$ $55.49\%$ on RefCOCO+ test sets A and B respectively (an absolute improvement of $3.74\%$ on average). + +# 1. Introduction + +Vision-and-language models that are trained to associate images with text have shown to be effective for many tasks and benchmarks [21, 27, 31, 41], including object detection [18, 54] and image segmentation [15, 36, 50]. Since these models are typically trained with in-the-wild data from the web, they can handle a wide range of vocabulary for objects as long as they are well represented in the training data. These models are often remarkably accurate [16, 22, 28, 47] even without tuning them to perform well in any particular downstream task [14, 32, 52]. The ALBEF model [27] was particularly capable of visual + +![](images/f8bff9e87446fa658b4891dd1b2484bdd5bb31d4f5ec00254b86767b0464741e.jpg) + +![](images/6398610bc06f60cea807a09e1dd468cf67a623a891b30ec5bef7912f24ba985d.jpg) +Figure 1. Previous models can localize the word frisbee, but struggle with equivalent but more uncommon referents such as disc. A model tuned with our proposed SelfEQ objective encourages consistent visual explanations for paraphrased prompts and performs well on both examples. SelfEQ not only enables a larger working vocabulary but also improves overall localization performance. + +"grounding" - or in other words - the ability to localize objects in images by simply using it in conjunction with a visual explanation method such as GradCAM [43]. This capability is particularly remarkable given that this model was only supervised with images and text but no object location annotations of any type. + +In order to improve the ability of vision-and-language models to perform localization, many methods have incorporated further finetuning with either box or segment annotations, or rely on pretrained object detectors or box proposal networks [5, 12, 19, 23, 30, 51]. Our work instead aims to improve the localization capabilities of models trained only on image-text pairs through weak supervision. But, how can we improve the ability of a model to localize objects without access to object location annotations? Consider the example in Figure 1 where a model is tasked with pointing to the location of the object frisbee in this image. The baseline model succeeds at finding the object but is unsuccessful at locating the object when prompted with the + +equivalent but more generic name disc. Regardless of the ability for the base model to find either of these, the visual explanations for these two prompts should be the same since the query refers to the very same object in both cases. Our work exploits this property by first generating paraphrases using a large language model and then proposing a weakly-supervised Self-consistency EQuivalence Tuning (SelfEQ) objective that encourages consistent visual explanations between paraphrased input text pairs that refer to the same object or region in a given image. + +Given a base pre-trained vision-and-language model purely trained on image-text pairs such as ALBEF [27], SelfEQ tunes the model so that for a given input image and text pair, the visual attention map extracted using GradCAM [43] produces a similar visual attention map when provided with the same image and a text paraphrase. Figure 2 provides an overview of our method. Another contribution of our work consists in exploiting a large language model (LLM) to automatically generate paraphrases for existing datasets such as Visual Genome [26] that contains textual descriptions of individual objects and regions, or MS-COCO [33] and CC3M [46] that contain global image descriptions. We find that SelfEQ not only expands the vocabulary of objects that the base model is able to localize but more importantly, improves the visual grounding capabilities of the model on standard benchmarks such as referring expression comprehension on the ReferIt benchmark [24] and region-phrase grounding in the Flickr30K Entities benchmark [40]. In summary, our key contributions are as follows: + +- We design a novel objective, SelfEQ, to encourage vision-and-language models to generate self-consistent visual explanations for equivalent text phrases, thereby improving grounding capabilities while expanding the working vocabulary of the model. +- We propose to prompt large language models for generating paraphrased image descriptions of individual objects or regions. Particularly, we adopt Vicuna-13B [6] and design text prompts to obtain high quality paraphrases. +- We demonstrate the effectiveness of our method by outperforming previous methods, leading to $4.69\%$ improvement on Flickr30k, $7.68\%$ improvement on ReferIt, and $3.74\%$ improvement on RefCOCO+. + +Finally, we plan to release our code, generated paraphrases and model checkpoints upon publication. + +# 2. Related Work + +Our work is related to previous methods on visual grounding, especially those that are trained under weak supervision understood as without the use of bounding box or segment annotations and relying only on image-text pairs. From a technical perspective our work is related to methods that optimize visual explanations to improve the underlying model. + +Visual grounding consists of localizing an input textual description in an image. Supervised methods are provided with text-image pairs and corresponding bounding boxes [8, 9, 12, 23, 51]. Other supervised methods leverage pretrained object detectors to obtain a region of interest and then identify the region that aligns most closely under their textual representations [5, 7, 17, 19, 35, 48]. In both cases, these methods use some form of box supervision during pre-training or at test time by relying on a pre-trained object detector. In contrast, our work focuses exclusively in the scenario where no bounding boxes or segment annotations are available at any stage. + +Weakly-Supervised Grounding. Our setup is similar to that of Arbelle et al [3] where no box annotations or object detectors are used for grounding. This work proposes Grounding by Separation (GbS) where a model is trained on randomly alpha-blended pairs of images and the goal is to separate them conditioned on text prompts. Our method instead relies on data augmentation on the text side and while our method shows favorable results, our contribution is orthogonal. Shaharabany et al [45] builds a weakly-supervised phrase grounding model by creating a large amount of data by combining region boxes with a BLIP captioning model. Later work by Shaharabany and Wolf [44] employs layerwise relevance propagation [38] to integrate relevancy and gradient information with the scores computed from each attention head in the transformer layers [4], or residual connections [1]. Our work compares favorably or on par with these methods but since we rely on gradient-based explanations, our work does not require making any modifications to the base network. + +Visual Explanation Tuning. Related to our method is the strategy used by ALBEF [27] where the model is only supervised on image-text pairs and performs grounding through GradCAM [43], a gradient-based visual explanation method that outputs a heatmap indicating spatial relevance. Earlier, Xiao et al [49] used a similar strategy but further optimized gradient-based explanations using structural constraints derived from text. Recently, AMC [51] follows this strategy but further adds box supervision on the output maps using a margin-based loss. We adopt ALBEF [27] as our base model and also adopt a gradient-based explanation strategy but unlike AMC [51] we do not rely on box annotations for tuning this model and use our proposed SelfEQ objective instead. Javed et al [20] proposed an objective function that encourages consistent representations in embedding space for the same input prompt on different images. In contrast SelfEQ encourages consistent visual explanations for different prompts on the same image by relying on automatically generated paraphrases. Akbari et al [2] also optimizes attention maps but in their formulation the model backbone is modified to explicitly incorporate attention instead of relying on gradient-based attention maps. + +![](images/a8a916b3ad207ffd9fc2d96d3d31fa36392304059a7816fabb05d3c9148f26fc.jpg) +Figure 2. Overview of our proposed weakly-supervised Self-consistency EQuivalence tuning objective. We input image-text and image-paraphrase pairs $\langle V, T \rangle$ and $\langle V, T^e \rangle$ to our base pretrained vision-and-language model. We then obtain gradient-based visual explanations $\langle G, G^e \rangle$ and compute a similarity loss between them. We also define an overlapping region of interest mask and encourage the model to predict consistently high saliency scores within this mask for each input pair. + +# 3. Method + +We start from a base vision-language model composed of a text encoder $\phi_t$ , an image encoder $\phi_v$ , and a multimodal fusion encoder $\phi_f$ , along with a dataset $D$ to finetune this model consisting of image-text pairs $\langle T, V \rangle$ . Section 3.1, introduces the training objectives for the base model which we also adopt for finetuning our baseline and are also used in conjunction with SelfEQ to finetune our final model. Section 3.2 introduces in detail SelfEQ, our self-consistency equivalence tuning objective that assumes the existence of paraphrases $T^e$ for each input image-text pair $\langle T, V \rangle$ , and Section 3.3 describes our approach for automatically generating paraphrases $T^e$ using LLM-prompting. Figure 2 presents an overview of our proposed method. + +# 3.1. Base Model: Preliminaries + +Our base vision-and-language model is ALBEF [27] which relies on three widely used objectives for visual and textual representation learning: image-text matching, masked language modeling and a contrastive loss. We describe them here briefly as they are also re-used during fine-tuning. + +Image-Text Matching Loss (ITM). This loss is calculated using the output of the [CLS] token to predict if the input image and the input text are matching or not and is defined as follows: + +$$ +\mathcal {L} _ {\mathrm {i t m}} = \mathbb {E} _ {(V, T) \sim D} \mathcal {H} \left(\vec {y}, \phi_ {f} ^ {\mathrm {c l s}} \left(\phi_ {v} (V), \phi_ {t} (T)\right)\right), \tag {1} +$$ + +where $\vec{y}$ denotes a two-dimensional one-hot vector, indicating whether the sample $\langle V,T\rangle$ constitutes a match, $\phi_f^{\mathrm{cls}}$ represents a linear layer followed by a softmax function, and $\mathcal{H}$ is the cross entropy loss function. + +Masking Language Modeling Loss (MLM). This loss has been applied for various vision-language pretraining models [5, 27, 29, 34]. It integrates the contextual text and the input image to infer masked words in the input text. After utilizing a linear layer and a softmax activation function $\phi_f^{\mathrm{m}}$ to individual output embeddings, the objective is expressed as: + +$$ +\mathcal {L} _ {\mathrm {m l m}} = \mathbb {E} _ {(V, T ^ {- \mathrm {m}}) \sim D} \mathcal {H} \left(\bar {t} ^ {\mathrm {m}}, \phi_ {f} ^ {\mathrm {m}} \left(\phi_ {v} (V), \phi_ {t} \left(T ^ {- \mathrm {m}}\right)\right)\right), \tag {2} +$$ + +where the one-hot vector $t^{\mathrm{m}}$ denotes the masked token, and $T^{-\mathrm{m}}$ represents the input masked text. + +Image-Text Contrastive Loss (ITC). It improves the alignment between visual and textual representations by bringing closer the representations for corresponding text-image pairs relative to text-image pairs that do not correspond. This objective can be defined as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {i t c}} = \mathbb {E} _ {(V, T) \sim D} \frac {1}{2} \left[ \mathcal {H} \left(\vec {y}, \frac {\exp \left(\phi_ {v} (V) \cdot \phi_ {t} (T)\right) / \tau}{\sum_ {b = 1} ^ {B} \mathrm {s} (V , T _ {b})}\right) \right. \tag {3} \\ \left. + \mathcal {H} \left(\vec {y}, \frac {\exp \left(\phi_ {t} (T) \cdot \phi_ {v} (V)\right) / \tau}{\sum_ {b = 1} ^ {B} \mathrm {s} (T , V _ {b})}\right) \right], \\ \end{array} +$$ + +where $B$ is the number of negative sample pairs, and $\tau$ is a temperature parameter for the softmax function. + +The training objective for the base model is a combination of the previous three loss functions: + +$$ +\mathcal {L} _ {\mathrm {v l}} = \mathcal {L} _ {\mathrm {i t m}} + \mathcal {L} _ {\mathrm {m l m}} + \mathcal {L} _ {\mathrm {i t c}}. \tag {4} +$$ + +This loss $\mathcal{L}_{\mathrm{vl}}$ will also be used to tune our baseline model. + +# 3.2. Self-Consistency Equivalence Tuning + +SelfEQ assumes that the model has access to paraphrases $T^e$ for each input image-text pair $\langle V, T \rangle$ or, in practice, for a subset of those samples. Therefore we assume a finetuning dataset $D'$ with triplets $\langle V, T, T^e \rangle$ such that $T^e$ exists for a corresponding input text $T$ . The first step to define our SelfEQ objective is to generate the explanation heatmaps (i.e., attention maps) through GradCAM [43] conditioned on the input text. We extract intermediate feature maps from the multimodal interactive encoder $\phi_f$ for input pairs $\langle V, T \rangle$ and $\langle V, T^e \rangle$ as follows: + +$$ +F = \phi (\phi_ {v} (V), \phi_ {t} (T)), F ^ {e} = \phi (\phi_ {v} (V), \phi_ {t} (T ^ {e})), \tag {5} +$$ + +where $\phi$ denotes the feature map extraction operation. We then proceed to calculate the gradient of $F$ and $F^{e}$ related to the image-text matching score $\mathcal{L}_{\mathrm{itm}}$ . This computation yields the attention maps for the original text and paraphrased text, referred to as $G$ and $G^{e}$ , respectively: + +$$ +G = \operatorname {R e L U} \left(F \odot \nabla \mathcal {H} \left(\vec {y}, \phi_ {f} ^ {c l s} \left(\phi_ {v} (V), \phi_ {t} (T)\right)\right)\right), \tag {6} +$$ + +$$ +G ^ {e} = \operatorname {R e L U} \left(F ^ {e} \odot \nabla \mathcal {H} \left(\vec {\mathcal {y}}, \phi_ {f} ^ {c l s} \left(\phi_ {v} (V), \phi_ {t} \left(T ^ {e}\right)\right)\right)\right). +$$ + +Our SelfEQ tuning is based on the premise that if a vision-language model is identified as self-consistent, the attention maps produced for both the text and its equivalent paraphrase should yield nearly identical results. To achieve this, we first apply a simple mean squared error loss over the produced heatmaps so that their $\ell_2$ distance is minimized and thus become more similar. + +$$ +\mathcal {L} _ {\mathrm {s i m}} = \mathbb {E} _ {(V, T, T ^ {e}) \sim D ^ {\prime}} \left[ \frac {1}{N} \sum_ {i, j} \left(G _ {i, j} - G _ {i, j} ^ {e}\right) ^ {2} \right]. \qquad (7) +$$ + +Nevertheless, while minimizing a sum of pixel-wise distances contributes to self-consistency, without a regularization term this loss can easily fall into a trivial solution. For instance, it could lead to attention maps with uniformly negative or positive predictions, or just really small values. To address this limitation, we propose to integrate these heatmaps by defining a Region of Interest (RoI) mask. This mask is designed to preserve regions within the attention maps that possibly contain correct predictions. Our approach hinges on the observation that, despite the predictions of equivalent textual inputs being inconsistent, sometimes regions with large values or regions that overlap between the two heatmaps tend to be correct. As such, we assume that if the sum of attention scores at a given position $(i,j)$ exceeds a certain threshold $k$ , it is likely indicative of a correct prediction. We formalize the condition as follows: + +$$ +M _ {i, j} = \left\{ \begin{array}{l} 1, \left(G _ {i, j} + G _ {i, j} ^ {e}\right) \geq k \\ 0, \left(G _ {i, j} + G _ {i, j} ^ {e}\right) < k \end{array} \right.. \tag {8} +$$ + +The attention maps within RoI masks are obtained by element-wise multiplication as follows: + +$$ +R = G \odot M, \quad R ^ {e} = G ^ {e} \odot M. \tag {9} +$$ + +The integration of RoI masks allows us to use equivalent texts for mutual supervision, refining and improving the accuracy and providing regularization for the previously defined distance-based loss. Moreover, it could potentially address errors owing to unknown or less common words by working vocabulary expansion. Presuming one of the textual expressions is known and correctly understood, the model could extrapolate the meaning of the other equivalent expression via weak supervision. To implement it, we first compute the mean $\mu_{RoI},\mu_{RoI}^{e}$ and the standard deviation $\sigma_{RoI},\sigma_{RoI}^{e}$ within the RoI as follows: + +$$ +\mu_ {R o I} = \frac {\sum_ {i , j} R _ {i , j}}{\sum_ {i , j} M _ {i , j}}, \mu_ {R o I} ^ {e} = \frac {\sum_ {i , j} R _ {i , j} ^ {e}}{\sum_ {i , j} M _ {i , j}}, \tag {10} +$$ + +$$ +\sigma_ {R o I} = \sqrt {\frac {\sum_ {i , j} M _ {i , j} \cdot \left(R _ {i , j} - \mu_ {R o I}\right) ^ {2}}{\sum_ {i , j} M _ {i , j}}}, \tag {11} +$$ + +$$ +\sigma_ {R o I} ^ {e} = \sqrt {\frac {\sum_ {i , j} M _ {i , j} \cdot (R _ {i , j} ^ {e} - \mu_ {R o I} ^ {e}) ^ {2}}{\sum_ {i , j} M _ {i , j}}}. +$$ + +We propose a consistency loss $(\mathcal{L}_{\mathrm{cst}})$ , expecting the RoI regions of attention maps to achieve consistently high scores, further reinforcing self-consistency, accuracy, and potential working vocabulary expansion. This objective is formulated as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {c s t}} = \mathbb {E} _ {(V, T, T ^ {e}) \sim D ^ {\prime}} \left[ \sigma_ {R o I} + \sigma_ {R o I} ^ {e} + \right. \tag {12} \\ \left. \max (0, k / 2 - \mu_ {R o I}) + \max (0, k / 2 - \mu_ {R o I} ^ {e}) \right]. \\ \end{array} +$$ + +Finally, the objective of our self-consistency equivalence tuning is expressed as: + +$$ +\mathcal {L} _ {\text {S e l f E Q}} = \mathcal {L} _ {\text {s i m}} + \lambda \cdot \mathcal {L} _ {\text {c s t}}, \tag {13} +$$ + +where $\lambda$ is a hyperparameter to control the relative influence of each loss. + +# 3.3. Self-Consistency Data Augmentation + +In this section we define a function $\mathcal{F}$ that can automatically map input textual phrases $T$ as paraphrases $T^{e}$ without the need to rely on human annotations such that $T^{e} \sim \mathcal{F}(T)$ . We achieve this goal through a two-level prompting approach using a large language model which we describe in detail below. + +Phrase Chunking: Using our first-level prompts, we aim to augment the original text using phrase chunking to encourage global captions to concentrate on more specific regions. Visual grounding seeks to localize objects in images based on textual inputs. In contrast, global captions usually describe the entire image, typically describing several objects. While training on global captions could be beneficial for learning cross-modal information, it may lead the model to predict a broader region (i.e., global context) rather than a specific region. Phrase chunking (i.e., shallow parsing [55]) aims to identify continuous sequences of tokens representing syntactic units, enabling the extraction of phrases from unstructured text. We leverage an LLM to segment global captions into object-centric short phrases. During training, we use these image-chunk pairs instead of global captions, effectively guiding the model attention toward localized regions of interest. We refer the reader to the supplementary material for prompting details and generated examples. + +Paraphrase Generation: Our SelfEQ approach involves feeding the model with pairs of textual descriptions that refer to the same underlying concept, with the expectation that the model can make similar predictions for these equivalent description pairs $\langle T, T^e \rangle$ . We augment our dataset by transforming the region-based captions (i.e., text that only refers to a region in the image) and the object-centric short phrases we obtained from phrase chunking into equivalent paraphrases referring to the same concept through our second-level LLM-prompts. + +```jsonl +Q:"a smiling, holding something and standing man" +A:{"group": "man", "synonym": ["adult male","gentleman"], "antonym": ["woman"], "hypernym": ["adult","grownup","male","male person","human being","human"], "meronym": ["man body","man head","man arms","man legs"]} +Q:"a desk" +A:{"group": "desk", "synonym": ["table","writing desk"], "antonym": [], "hypernym": ["writer tool","furniture"], "meronym": ["desktop","desk leg"]} +``` + +Figure 3. Two samples from our LLM-prompt for paraphrase generation. The first set showcases an example of a region-based caption, and the second set shows a non-sentence phrase. $\mathbf{Q}$ is the query text and $\mathbf{A}$ is the expected answer. + +There are many ways to paraphrase, including substituting words, altering sentence structures, and rewriting sentences based on semantics. However, considering that self-consistency in vision and language is relatively underexplored, we adopt a straightforward strategy: Replacing the primary object in the sentence while retaining all other attributes. This strategy yields several benefits. First, it provides a consistent context, which serves as a reference for the model to identify equivalent descriptions. This enables the equivalent relationships of paraphrases to be learned intuitively. Second, it simplifies prompt designing and post-processing by detecting the primary object and generating its synonym. + +To generate paraphrases for the dataset consisting of region-based captions, we select four textual descriptions in which the primary noun plays different syntactic roles. We further select two non-sentence phrases as examples of query texts in our prompts. We show an example of a region-based caption and a non-sentence phrase in Figure 3. To design our prompt, we identify the primary object in the query text Q. Then we use WordNet [37] to obtain synonyms automatically and further remove inaccurate or invalid words. We add A to indicate the expected answer and include other relationships such as antonym, hy- pernym and meronym to provide richer contexts for LLM in-context learning. Additional prompting details and paraphrase samples are provided in the supplementary material. + +This two-level prompt-based LLM augmentation approach ensures that our model is exposed to textual inputs that share the same concept while varying in linguistic representation, thereby promoting self-consistency and working vocabulary expansion. + +# 4. Experimental Settings + +Training. We use ALBEF [27] as our base model in all our experiments, given its reported off-the-shelf visual grounding performance via GradCAM [43]. ALBEF combines a ViT-B [11] model for encoding images and a BERT-base [10] model for encoding text. It is pre-trained on a range of datasets, including ImageNet-1K [42], Conceptual Captions [46], SBU Captions [39], MS-COCO [33], and + +
MethodTrainingFlickr30kReferIt
Box SupervisionAlign2Ground [7]VG-boxes71.00-
12-in-1 [35]VG-boxes76.40-
InfoGround [19]VG-boxes76.74-
VMRM [12]VG-boxes81.11-
AMC [51]VG-boxes86.5973.17
Without Box SupervisionTD [56]VG42.4031.97
SSS [20]VG49.1039.98
MG-BiLSTM [2]VG57.9162.76
MG-ELMo [2]VG60.0860.01
GbS [3]VG73.3962.24
g [45]VG75.6365.95
g++ [44]VG79.9570.25
SelfEQ (ours)VG81.9067.40
FCVC [13]MS-COCO29.0333.52
MG-BiLSTM [2]MS-COCO53.2947.89
MG-ELMo [2]MS-COCO61.6647.52
GbS [3]MS-COCO74.5049.26
g [45]MS-COCO75.4361.03
g++ [44]MS-COCO78.1061.53
SelfEQ (ours)MS-COCO84.0762.75
+ +Table 1. Visual Grounding results on two benchmarks using pointing game accuracy with two training datasets. SelfEQ yields generally the best overall performance among weakly-supervised methods, and comes second to $\mathrm{g} + +$ on the ReferIt benchmark when trained using VG. We also show at the top the results of methods using additional box supervision from Visual Genome (VG) either directly or through an object detector. + +Visual Genome (VG) [26] excluding box annotations. We finetune ALBEF with image-text pairs from VG and MS-COCO without any type of box supervision (i.e., no bounding boxes or object detectors), following prior work [2]. We further leverage Vicuna-13B [6] as our LLM-prompting model to generate the object-centric short phrases (via shallow parsing or chunking) and the equivalent paraphrases for our self-consistency data augmentation. Additionally, we validate the effectiveness of our SelfEQ tuning and self-consistency data augmentation method by training on a preprocessed subset of the Conceptual Captions 3M (CC3M) dataset [46], which contains many noisy or unaligned web-crawled AltText-image pairs. With this subset, we achieve an absolute improvement of $2.15\%$ on Flickr30k, $3.32\%$ on ReferIt, and $1.33\%$ on RefCOCO+; refer to the supplementary material for detailed CC3M experiments. + +Evaluation. We conduct evaluations using Flickr30k [40] and ReferIt [24] under pointing game accuracy following previous weakly-supervised visual grounding works [2, 3]. To underscore the competitive edge of our method, we also + +
MethodBox SupervisionRefCOCO+
Test ATest B
InfoGround [19]Yes39.8041.11
VMRM [12]Yes58.8750.32
AMC [51]Yes80.3464.55
ALBEF [27]No69.3553.77
SelfEQ (ours)No75.1055.49
+ +Table 2. Results on RefCOCO+ pointing game accuracy. SelfEQ shows significant improvements over off-the-shelf ALBEF and competitive results compared to box-supervised methods. + +present its performance on RefCOCO+ [53], a challenging benchmark more commonly used for testing box-supervised methods [7, 12, 19, 35, 51]. + +# 4.1. Implementation Details + +Our experiments are conducted on a single computing node with 8 NVIDIA A40 GPUs. During the training phase, input images are resized to $256 \times 256$ and augmented with horizontal flipping, color jittering, and random grayscale conversion. We set up an Adam optimizer [25] with a learning rate of 1e-5 and a batch size of 448 across all experiments. We empirically set the RoI threshold $k$ to 0.8 and the hyperparameter $\lambda$ to 1.0. For training with raw image-text pairs from the datasets, we employ the vision-language objective $\mathcal{L}_{\mathrm{vl}}$ (Sec. 3.1), while for the subset with equivalent paraphrases, we use our self-consistency equivalence tuning objective $\mathcal{L}_{\mathrm{SelfEQ}}$ (Sec. 3.2) and corresponding vision-language objective $\mathcal{L}_{\mathrm{vl}}^e$ . The composite objective function is given by $\mathcal{L} = \alpha \cdot \mathcal{L}_{\mathrm{vl}} + (1 - \alpha) \cdot (\mathcal{L}_{\mathrm{SelfEQ}} + \mathcal{L}_{\mathrm{vl}}^e)$ , where $\alpha$ is initially set to 0 and increments to 1, remaining constant after the second epoch. Our hyperparameter values and schedules were determined empirically on a small validation subset. + +# 5. Experimental Results + +Our resulting model obtains the best performance on the task of weakly-supervised visual grounding compared to most methods under this setting and is comparable to several prior works that rely on some of box supervision. Moreover, our qualitative results show that our method can handle paraphrases and a larger working vocabulary without the needed to increment the training dataset significantly. + +Flickr30k and ReferIt. We evaluate the effectiveness of our proposed SelfEQ method in Table 1, demonstrating its substantial lead over GradCAM-based weakly-supervised approaches. Our self-consistency equivalent tuning adapts well for both region-based (i.e., VG) and global-based (i.e., COCO) image-text pairs, yielding a performance gain of $4.69\%$ on Flickr30k and $7.68\%$ on ReferIt, compared to + +![](images/105888ffed6fd16cb4d84d67516d6329cac6a916d973bd201a403e4355a86d57.jpg) +Text: "trees on the right" +Image + +![](images/2961438ff455512f612744005dfdd23a5c6189c02d1ffccf77bf6e103592b00c.jpg) +ALBEF + +![](images/45a6fa338a3438facf8b3783af3d731bc29db03b354b08ddea3e76ef67c5cb86.jpg) +AMC + +![](images/8b31a5c821a3094aa6568f6c2b63ed5b9ce162b0dfebc73f7ddb879c88f3293c.jpg) +Ours + +![](images/6a42500bee4806295b5ce97a878f420680970b986ca22cdf9655c5375d77b796.jpg) +Text: "blue thermos very bottom" +Image + +![](images/502db3a97101a86b95abb745604e97b37e18328d8e04d03f369313150864d007.jpg) +ALBEF + +![](images/991db022fde3c93fa1b5e0fdde53856e8441257cf6b994e43f1b5215b72e79a8.jpg) +AMC + +![](images/0e62e5bbf210669161d5a925e6fc2c993eaeeb4df3c5d0d5cfe696c1474510fa.jpg) +Ours + +![](images/cc3f291f8a0ecf6d6b7d5b0b0fb2ad53a39a7cee49c213c4eb0fd201c5a31a1e.jpg) +Text: "person right corner" +Image + +![](images/8be2ae858df8fc9cb013ba428f526582b2595e2e8ed9ccbe7e087b507063b598.jpg) +ALBEF + +![](images/45ebe99d74808e2f5a9539380355c2e02badec0da12d56aeb4dde4758dc3be80.jpg) +AMC + +![](images/444986c4da65e4f4b35ffd26fc67ac090f271f84d19d405cd07308fbd85fc34a.jpg) +Ours + +![](images/3729c61bd9059ab6e36b298700fc554d415f47d7340533392b619ea7043bf911.jpg) +Text: "kangaroo furthest away facing right" +Image + +![](images/efe802e7d80fe99a34472cf5b4a86888370a9eaaf3834e307d71e3dc6e8913dd.jpg) +ALBEF + +![](images/d4a2bd87ac87bf940176320578297c244b6146feb7de5895920b654fa6a77907.jpg) +AMC + +![](images/2ecda2b9698cbbddfe882a4667f3a80fbd6e15b7f1ef23cc5b1cc694e99316c8.jpg) +Ours + +![](images/b5c1513b0f309d1cfd53168834fc8342b616bacf1ae210d0700f55377b383889.jpg) +Text: "white bldg" +Image +Figure 4. Qualitative results of our method in challenging visual grounding scenarios compared to prior works. On top of each row we show the reference text, the first column shows the image, then we show our base model ALBEF, the SotA box-supervised method AMC, and finally we show results with our method SelfEQ. + +![](images/05221046499fde22d165e7c0df470546cac1e848528cff56f6db50b65869ed79.jpg) +ALBEF + +![](images/1aa0821b4cd677e43a98e3baf350fd07e451ffd5b64915516e4fec3ebe524ff2.jpg) +AMC + +![](images/0364ae426a36de47b099f6a4769efe7ed407d649ac68c9906d9dbdf1cac4f36c.jpg) +Ours + +our base model ALBEF (see first row in Table 3). Notably, our method outperforms almost all box-supervised methods on Flickr30k [7, 12, 19, 35]. In the weakly-supervised setting, our method only comes second on ReferIt compared to $\mathrm{g + + }[44]$ when trained on Visual Genome imagedtext pairs. This method leverages a custom architecture to produce a mask and uses heatmap supervision from a CLIP [41] model as pseudo-labels during training. We posit that our contribution is orthogonal and our approach would likely also benefit from similar supervision, since CLIP is trained in a much larger image-text pair dataset. Despite differences, our method still obtains higher performance when trained on MS-COCO and the best performance compared to all weakly-supervised methods on Flickr30K region-phrase grounding. + +RefCOCO+. RefCOCO+ [53] serves as a rigorous benchmark for visual grounding, typically used to evaluate box-supervised techniques. In Table 2, we present the per + +
DataObjectiveRefCOCO+Flickr30kReferIt
Test ATest B
-\( \mathcal{L}_{\mathrm{vl}} \)69.3553.7779.3859.72
T\( \mathcal{L}_{\mathrm{vl}} \)72.3054.2278.7565.86
T+Te\( \mathcal{L}_{\mathrm{vl}} \)71.5553.5178.0564.57
T+Te\( \mathcal{L}_{\text{SelfEQ}} \)75.1055.4981.9067.40
+ +Table 3. Ablation studies on different ways to utilize extra equivalent paraphrased data. The first row is off-the-shelf ALBEF performance before tuning. $T$ denotes the textual captions from the dataset, and ${T}^{e}$ corresponds to the associated equivalent paraphrases. ${\mathcal{L}}_{\mathrm{{vl}}}$ is the vision-language objective,and ${\mathcal{L}}_{\text{SelfEQ }}$ is our self-consistency equivalence tuning objective. + +formance of our weakly-supervised method (VG trained) against box-supervised methods. Our results indicate that our approach is competitive without reliance on any form of box annotations and significantly improves over the base ALBEF model. + +Visual Grounding Analysis. Figure 4 provides qualitative results of our method in challenging scenarios, including occluded objects (row 1), small objects within complex scenes (row 2), objects partially shown in the corner of the image (row 3), multiple similar objects (row 4), and abbreviated text inputs (row 5). Our self-consistency equivalency tuning approach exhibits substantial improvements in the grounding capability of the base ALBEF [27] model. Remarkably, our approach even outperforms the state-of-the-art box-supervised method AMC [51] in multiple scenarios. + +Self-Consistency Analysis. Figure 5 demonstrates qualitative results for the self-consistency capability across different equivalent paraphrases, encompassing terminology (row 1), synonym substitutions (row 2), and regional slang combining with different sentence structures (row 3). Although other methods succeed in localizing certain phrases, they demonstrate inconsistencies for the equivalent paraphrases. In contrast, our model finetuned with SelfEQ effectively establishes connections between semantically equivalent paraphrases, thereby enhancing the model self-consistency ability and potentially expanding its working vocabulary. + +# 5.1. Ablation Studies + +Data Quantity. We assess the impact of the data quantity of our generated paraphrases and compare our tuning strategy against standard vision-language objectives. We randomly sample portions of data from VG by $10\%$ associated with our augmented equivalent paraphrases three times. To compare, we use the vision-language objective with VG text-image pairs as baselines. In Figure 6, we show the mean and standard deviation pointing game accuracy. The performance of the base vision-language objective does not exhibit a steady improvement with more text-image pairs. Al- + +![](images/93e02ff69731fc5109cb0e56f4e4b82bbb3158886b98e69b95d3d5937874106d.jpg) + +![](images/2ec7829f18c58bca6218f49d76349e0252b7b7d79594ea9c8938c447bb31d67e.jpg) + +![](images/920376e4140cf3bf27d52458840f59fcf6fed0eafbe15081dce7ef2e32b3809c.jpg) +Figure 5. Qualitative results across equivalent paraphrases among different methods. For each image, we show a caption referring to an object in the first row and an equivalent paraphrase in the second row. Each column shows the results of ALBEF, the SotA box-supervised method AMC, and our SelfEQ method. + +though ReferIt performance increases, the performance on RefCOCO+ Test A remains mostly unchanged. Additionally, the performance on Flickr30k notably decreases, and there is a mixed effect on RefCOCO+ Test B, with half of the accuracy falling below the off-the-shelf ALBEF performance of $53.77\%$ . + +In contrast, SelfEQ consistently leads to performance enhancements with more equivalent paraphrases. Clear upward trends are observed on Flickr30k, ReferIt, and RefCOCO+ Test A as more data with corresponding equivalent paraphrases are added, meanwhile the gaps between the baselines generally widen. Notably, SelfEQ tuning maintains performance gains on Flickr30k, whereas the baselines performances drop. Although the trend on RefCOCO+ Test B is not consistently increasing, it is essential to emphasize that RefCOCO+ Test B is only a subset, and SelfEQ illustrates more stable and effective tuning performance on it, compared to the base vision-language objective. + +These observations indicate that more equivalent paraphrases connecting with associated text phrases enable the + +![](images/283e0434cffe2589dd3dec8351141ecdab4db15e468c61f9d5bd52c1b837619b.jpg) +Figure 6. Tuning performance with different data quantities on Flickr30k, ReferIt, RefCOCO+ Test A and Test B. The purple and cyan lines represent SelfEQ (ours) and ALBEF baseline losses (vision-language objective), respectively. We show the impact of progressively augmenting captions via LLM-prompting for generating equivalent paraphrases tuned with our SelfEQ objective. Best viewed in color. + +![](images/390a6ecb5040342d64ca85d13530f2efb55dd2486dfb31950ade8f0ce4dff533.jpg) + +![](images/c1cb77ce1321c5115cbddaa3edb89d2fca214e6f12c3faf808466d5fa57cd134.jpg) + +![](images/12a2add7f4d5936d9c28197e7ed661811ee223b6984f9f0d3593607277e40dd8.jpg) + +
FormatObjectiveFlickr30kReferIt
-\( \mathcal{L}_{\mathrm{vl}} \)79.3859.72
C\( \mathcal{L}_{\mathrm{vl}} \)79.9060.64
C\( \mathcal{L}_{\text{SelfEQ}} \)81.2862.04
P\( \mathcal{L}_{\mathrm{vl}} \)81.1861.18
P\( \mathcal{L}_{\text{SelfEQ}} \)84.0762.75
+ +model to acquire more valuable information during tuning. SelfEQ proves to be an effective and robust strategy for consistently improving performance with our generated paraphrases. With increased self-consistency augmented data, SelfEQ guides the model toward better grounding performance by enhancing its self-consistency capabilities. + +Our method generates equivalent paraphrases for self-consistency enhancement, but it also contributes additional data for training. To ascertain the specific impact of our SelfEQ tuning strategy, we run a control experiment on this variable. As shown in Table 3, we assess the model's performance when equivalent paraphrases are integrated as regular image-text pairs with vision-language objectives (Sec. 3.1). This comparison reveals that merely augmenting the dataset with extra image-paraphrase pairs, without forming explicit linkages between the original text and its paraphrases, does not yield performance improvements. + +Data Augmentation. For global-based captions in MS-COCO, we preprocess the captions $C$ to object-centric short phrases $P$ via LLM-prompting. As shown in Table 4, tuning with phrases $P$ leads to better performance, benefiting both the vision-language objective $(\mathcal{L}_{\mathrm{vl}})$ and our self-consistency equivalence tuning objective $(\mathcal{L}_{\mathrm{SelfEQ}})$ . This improvement is probably attributed to short phrases allowing the model to focus on a specific region rather than the entire scene, aligning more closely with the objective of visual grounding. By utilizing equivalent paraphrases with our SelfEQ objective (row 3 and 5), phrase chunking helps SelfEQ even more, indicating the important role of equivalent paraphrases in promoting self-consistency and grounding ability. + +Table 4. Comparisons on data augmentation strategy for global-based captions in MS-COCO with or without the paraphrases. $C$ is the global-based captions from MS-COCO, and $P$ is our Vicuna-13B processed object-centric phrases separately. The first row is the off-the-shelf ALBEF performance before tuning. + +
\( \mathcal{L}_{\text{sim}} \)\( \mathcal{L}_{\text{cst}} \)RefCOCO+Flickr30kReferIt
Test ATest B
✓66.4247.2168.2655.96
✓73.3355.8880.9466.57
✓✓75.1055.4981.9067.40
+ +Table 5. Ablation studies on objective components of self-consistency equivalence tuning objective ${\mathcal{L}}_{\text{SelfEQ }}$ . + +Objective. Table 5 evaluates each component within our self-consistency equivalence tuning objective. The $\mathcal{L}_{\mathrm{sim}}$ loss targets pixel-wise similarity, ensuring that maps for a caption and its equivalent paraphrase are identical. However, focusing solely on pixel-level similarity may neglect the precise spatial positioning of objects. To address this, the $\mathcal{L}_{\mathrm{cst}}$ loss is proposed to identify the most likely correct object positions within the two maps (i.e., RoI). It then encourages the model to yield consistently high attention scores within the RoI. By integrating both $\mathcal{L}_{\mathrm{sim}}$ and $\mathcal{L}_{\mathrm{cst}}$ , self-consistency equivalence tuning objective fosters the model to not only align global similarities but also to pinpoint accurate object locations through the mutual supervision provided by a caption and its paraphrase, thereby enhancing self-consistency and accuracy. + +# 6. Conclusion + +We propose a novel weakly-supervised tuning approach coupled with a data augmentation strategy to enhance the localization capabilities of an image-text supervised model through self-consistency. Using an open-source LLM, we expand a dataset with equivalent paraphrases tailored to be object-centric. The augmented data is used to finetune a base model employing our novel self-consistency equivalence tuning objective. Our approach has been rigorously validated across pretraining on diverse datasets, ranging from region-based captions (i.e., VG) to global-based captions (i.e., COCO). 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Berg2 Vicente Ordonez1 \n1Rice University 2University of California, Irvine" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 174, + 531, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 174, + 531, + 185 + ], + "spans": [ + { + "bbox": [ + 59, + 174, + 531, + 185 + ], + "type": "text", + "content": "catherine.he@rice.edu, pc51@rice.edu, zy47@rice.edu, bergac@uci.edu, vicenteor@rice.edu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": "Vision-and-language models trained to match images with text can be combined with visual explanation methods to point to the locations of specific objects in an image. Our work shows that the localization – “grounding”– abilities of these models can be further improved by finetuning for self-consistent visual explanations. We propose a strategy for augmenting existing text-image datasets with paraphrases using a large language model, and SelfEQ, a weakly-supervised strategy on visual explanation maps for paraphrases that encourages self-consistency. Specifically, for an input textual phrase, we attempt to generate a paraphrase and finetune the model so that the phrase and paraphrase map to the same region in the image. We posit that this both expands the vocabulary that the model is able to handle, and improves the quality of the object locations highlighted by gradient-based visual explanation methods (e.g. GradCAM). We demonstrate that SelfEQ improves performance on Flickr30k, ReferIt, and RefCOCO+ over a strong baseline method and several prior works. Particularly, comparing to other methods that do not use any type of box annotations, we obtain " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "84.07\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": " on Flickr30k (an absolute improvement of " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "4.69\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "67.40\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": " on ReferIt (an absolute improvement of " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "7.68\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": "), and " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "75.10\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "55.49\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": " on RefCOCO+ test sets A and B respectively (an absolute improvement of " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "3.74\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": " on average)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "Vision-and-language models that are trained to associate images with text have shown to be effective for many tasks and benchmarks [21, 27, 31, 41], including object detection [18, 54] and image segmentation [15, 36, 50]. Since these models are typically trained with in-the-wild data from the web, they can handle a wide range of vocabulary for objects as long as they are well represented in the training data. These models are often remarkably accurate [16, 22, 28, 47] even without tuning them to perform well in any particular downstream task [14, 32, 52]. The ALBEF model [27] was particularly capable of visual" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 235, + 544, + 314 + ], + "blocks": [ + { + "bbox": [ + 310, + 235, + 544, + 314 + ], + "lines": [ + { + "bbox": [ + 310, + 235, + 544, + 314 + ], + "spans": [ + { + "bbox": [ + 310, + 235, + 544, + 314 + ], + "type": "image", + "image_path": "f8bff9e87446fa658b4891dd1b2484bdd5bb31d4f5ec00254b86767b0464741e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 317, + 544, + 393 + ], + "blocks": [ + { + "bbox": [ + 309, + 317, + 544, + 393 + ], + "lines": [ + { + "bbox": [ + 309, + 317, + 544, + 393 + ], + "spans": [ + { + "bbox": [ + 309, + 317, + 544, + 393 + ], + "type": "image", + "image_path": "6398610bc06f60cea807a09e1dd468cf67a623a891b30ec5bef7912f24ba985d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 404, + 546, + 472 + ], + "lines": [ + { + "bbox": [ + 305, + 404, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 404, + 546, + 472 + ], + "type": "text", + "content": "Figure 1. Previous models can localize the word frisbee, but struggle with equivalent but more uncommon referents such as disc. A model tuned with our proposed SelfEQ objective encourages consistent visual explanations for paraphrased prompts and performs well on both examples. SelfEQ not only enables a larger working vocabulary but also improves overall localization performance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 484, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 546, + 557 + ], + "type": "text", + "content": "\"grounding\" - or in other words - the ability to localize objects in images by simply using it in conjunction with a visual explanation method such as GradCAM [43]. This capability is particularly remarkable given that this model was only supervised with images and text but no object location annotations of any type." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "In order to improve the ability of vision-and-language models to perform localization, many methods have incorporated further finetuning with either box or segment annotations, or rely on pretrained object detectors or box proposal networks [5, 12, 19, 23, 30, 51]. Our work instead aims to improve the localization capabilities of models trained only on image-text pairs through weak supervision. But, how can we improve the ability of a model to localize objects without access to object location annotations? Consider the example in Figure 1 where a model is tasked with pointing to the location of the object frisbee in this image. The baseline model succeeds at finding the object but is unsuccessful at locating the object when prompted with the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13095" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "equivalent but more generic name disc. Regardless of the ability for the base model to find either of these, the visual explanations for these two prompts should be the same since the query refers to the very same object in both cases. Our work exploits this property by first generating paraphrases using a large language model and then proposing a weakly-supervised Self-consistency EQuivalence Tuning (SelfEQ) objective that encourages consistent visual explanations between paraphrased input text pairs that refer to the same object or region in a given image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 430 + ], + "type": "text", + "content": "Given a base pre-trained vision-and-language model purely trained on image-text pairs such as ALBEF [27], SelfEQ tunes the model so that for a given input image and text pair, the visual attention map extracted using GradCAM [43] produces a similar visual attention map when provided with the same image and a text paraphrase. Figure 2 provides an overview of our method. Another contribution of our work consists in exploiting a large language model (LLM) to automatically generate paraphrases for existing datasets such as Visual Genome [26] that contains textual descriptions of individual objects and regions, or MS-COCO [33] and CC3M [46] that contain global image descriptions. We find that SelfEQ not only expands the vocabulary of objects that the base model is able to localize but more importantly, improves the visual grounding capabilities of the model on standard benchmarks such as referring expression comprehension on the ReferIt benchmark [24] and region-phrase grounding in the Flickr30K Entities benchmark [40]. In summary, our key contributions are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 432, + 287, + 586 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 432, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 491 + ], + "type": "text", + "content": "- We design a novel objective, SelfEQ, to encourage vision-and-language models to generate self-consistent visual explanations for equivalent text phrases, thereby improving grounding capabilities while expanding the working vocabulary of the model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 492, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 492, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 287, + 539 + ], + "type": "text", + "content": "- We propose to prompt large language models for generating paraphrased image descriptions of individual objects or regions. Particularly, we adopt Vicuna-13B [6] and design text prompts to obtain high quality paraphrases." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "text", + "content": "- We demonstrate the effectiveness of our method by outperforming previous methods, leading to " + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "inline_equation", + "content": "4.69\\%" + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "text", + "content": " improvement on Flickr30k, " + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "inline_equation", + "content": "7.68\\%" + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "text", + "content": " improvement on ReferIt, and " + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "inline_equation", + "content": "3.74\\%" + }, + { + "bbox": [ + 47, + 540, + 287, + 586 + ], + "type": "text", + "content": " improvement on RefCOCO+." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 589, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 613 + ], + "type": "text", + "content": "Finally, we plan to release our code, generated paraphrases and model checkpoints upon publication." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 621, + 134, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 134, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 134, + 634 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": "Our work is related to previous methods on visual grounding, especially those that are trained under weak supervision understood as without the use of bounding box or segment annotations and relying only on image-text pairs. From a technical perspective our work is related to methods that optimize visual explanations to improve the underlying model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "Visual grounding consists of localizing an input textual description in an image. Supervised methods are provided with text-image pairs and corresponding bounding boxes [8, 9, 12, 23, 51]. Other supervised methods leverage pretrained object detectors to obtain a region of interest and then identify the region that aligns most closely under their textual representations [5, 7, 17, 19, 35, 48]. In both cases, these methods use some form of box supervision during pre-training or at test time by relying on a pre-trained object detector. In contrast, our work focuses exclusively in the scenario where no bounding boxes or segment annotations are available at any stage." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 219, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 546, + 445 + ], + "type": "text", + "content": "Weakly-Supervised Grounding. Our setup is similar to that of Arbelle et al [3] where no box annotations or object detectors are used for grounding. This work proposes Grounding by Separation (GbS) where a model is trained on randomly alpha-blended pairs of images and the goal is to separate them conditioned on text prompts. Our method instead relies on data augmentation on the text side and while our method shows favorable results, our contribution is orthogonal. Shaharabany et al [45] builds a weakly-supervised phrase grounding model by creating a large amount of data by combining region boxes with a BLIP captioning model. Later work by Shaharabany and Wolf [44] employs layerwise relevance propagation [38] to integrate relevancy and gradient information with the scores computed from each attention head in the transformer layers [4], or residual connections [1]. Our work compares favorably or on par with these methods but since we rely on gradient-based explanations, our work does not require making any modifications to the base network." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "content": "Visual Explanation Tuning. Related to our method is the strategy used by ALBEF [27] where the model is only supervised on image-text pairs and performs grounding through GradCAM [43], a gradient-based visual explanation method that outputs a heatmap indicating spatial relevance. Earlier, Xiao et al [49] used a similar strategy but further optimized gradient-based explanations using structural constraints derived from text. Recently, AMC [51] follows this strategy but further adds box supervision on the output maps using a margin-based loss. We adopt ALBEF [27] as our base model and also adopt a gradient-based explanation strategy but unlike AMC [51] we do not rely on box annotations for tuning this model and use our proposed SelfEQ objective instead. Javed et al [20] proposed an objective function that encourages consistent representations in embedding space for the same input prompt on different images. In contrast SelfEQ encourages consistent visual explanations for different prompts on the same image by relying on automatically generated paraphrases. Akbari et al [2] also optimizes attention maps but in their formulation the model backbone is modified to explicitly incorporate attention instead of relying on gradient-based attention maps." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13096" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 289, + 199 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 199 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 199 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 199 + ], + "type": "image", + "image_path": "a8a916b3ad207ffd9fc2d96d3d31fa36392304059a7816fabb05d3c9148f26fc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed weakly-supervised Self-consistency EQuivalence tuning objective. We input image-text and image-paraphrase pairs " + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "inline_equation", + "content": "\\langle V, T \\rangle" + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "inline_equation", + "content": "\\langle V, T^e \\rangle" + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "text", + "content": " to our base pretrained vision-and-language model. We then obtain gradient-based visual explanations " + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "inline_equation", + "content": "\\langle G, G^e \\rangle" + }, + { + "bbox": [ + 46, + 205, + 289, + 295 + ], + "type": "text", + "content": " and compute a similarity loss between them. We also define an overlapping region of interest mask and encourage the model to predict consistently high saliency scores within this mask for each input pair." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 308, + 104, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 104, + 320 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 104, + 320 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": "We start from a base vision-language model composed of a text encoder " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": ", an image encoder " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\phi_v" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": ", and a multimodal fusion encoder " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\phi_f" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": ", along with a dataset " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": " to finetune this model consisting of image-text pairs " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\langle T, V \\rangle" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": ". Section 3.1, introduces the training objectives for the base model which we also adopt for finetuning our baseline and are also used in conjunction with SelfEQ to finetune our final model. Section 3.2 introduces in detail SelfEQ, our self-consistency equivalence tuning objective that assumes the existence of paraphrases " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "T^e" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": " for each input image-text pair " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\langle T, V \\rangle" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": ", and Section 3.3 describes our approach for automatically generating paraphrases " + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "inline_equation", + "content": "T^e" + }, + { + "bbox": [ + 46, + 329, + 289, + 486 + ], + "type": "text", + "content": " using LLM-prompting. Figure 2 presents an overview of our proposed method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 496, + 195, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 496, + 195, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 496, + 195, + 508 + ], + "type": "text", + "content": "3.1. Base Model: Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 515, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 515, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 287, + 576 + ], + "type": "text", + "content": "Our base vision-and-language model is ALBEF [27] which relies on three widely used objectives for visual and textual representation learning: image-text matching, masked language modeling and a contrastive loss. We describe them here briefly as they are also re-used during fine-tuning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 581, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 288, + 628 + ], + "type": "text", + "content": "Image-Text Matching Loss (ITM). This loss is calculated using the output of the [CLS] token to predict if the input image and the input text are matching or not and is defined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 73, + 637, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 637, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 73, + 637, + 287, + 657 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {i t m}} = \\mathbb {E} _ {(V, T) \\sim D} \\mathcal {H} \\left(\\vec {y}, \\phi_ {f} ^ {\\mathrm {c l s}} \\left(\\phi_ {v} (V), \\phi_ {t} (T)\\right)\\right), \\tag {1}", + "image_path": "e123fe50a82026f7cb60ae437353db3ea08bc4f2c59aff29440e4504a3406e4d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\vec{y}" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " denotes a two-dimensional one-hot vector, indicating whether the sample " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\langle V,T\\rangle" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " constitutes a match, " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\phi_f^{\\mathrm{cls}}" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " represents a linear layer followed by a softmax function, and " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " is the cross entropy loss function." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "Masking Language Modeling Loss (MLM). This loss has been applied for various vision-language pretraining models [5, 27, 29, 34]. It integrates the contextual text and the input image to infer masked words in the input text. After utilizing a linear layer and a softmax activation function " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\phi_f^{\\mathrm{m}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " to individual output embeddings, the objective is expressed as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 163, + 545, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 163, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 312, + 163, + 545, + 178 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {m l m}} = \\mathbb {E} _ {(V, T ^ {- \\mathrm {m}}) \\sim D} \\mathcal {H} \\left(\\bar {t} ^ {\\mathrm {m}}, \\phi_ {f} ^ {\\mathrm {m}} \\left(\\phi_ {v} (V), \\phi_ {t} \\left(T ^ {- \\mathrm {m}}\\right)\\right)\\right), \\tag {2}", + "image_path": "aa71f15850737449abf0c6ca6522302abb4ee73aa62c8891a925b3400cd1e951.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "type": "text", + "content": "where the one-hot vector " + }, + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "type": "inline_equation", + "content": "t^{\\mathrm{m}}" + }, + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "type": "text", + "content": " denotes the masked token, and " + }, + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "type": "inline_equation", + "content": "T^{-\\mathrm{m}}" + }, + { + "bbox": [ + 306, + 186, + 545, + 211 + ], + "type": "text", + "content": " represents the input masked text." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 218, + 545, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 278 + ], + "type": "text", + "content": "Image-Text Contrastive Loss (ITC). It improves the alignment between visual and textual representations by bringing closer the representations for corresponding text-image pairs relative to text-image pairs that do not correspond. This objective can be defined as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 320, + 285, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 285, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 320, + 285, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {i t c}} = \\mathbb {E} _ {(V, T) \\sim D} \\frac {1}{2} \\left[ \\mathcal {H} \\left(\\vec {y}, \\frac {\\exp \\left(\\phi_ {v} (V) \\cdot \\phi_ {t} (T)\\right) / \\tau}{\\sum_ {b = 1} ^ {B} \\mathrm {s} (V , T _ {b})}\\right) \\right. \\tag {3} \\\\ \\left. + \\mathcal {H} \\left(\\vec {y}, \\frac {\\exp \\left(\\phi_ {t} (T) \\cdot \\phi_ {v} (V)\\right) / \\tau}{\\sum_ {b = 1} ^ {B} \\mathrm {s} (T , V _ {b})}\\right) \\right], \\\\ \\end{array}", + "image_path": "c9542f567cc17b3abc1856bdd754bba4689fdd416c8685c2c97ea7780a120edc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "type": "text", + "content": " is the number of negative sample pairs, and " + }, + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 346, + 545, + 369 + ], + "type": "text", + "content": " is a temperature parameter for the softmax function." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 370, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 545, + 393 + ], + "type": "text", + "content": "The training objective for the base model is a combination of the previous three loss functions:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 372, + 403, + 545, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 403, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 372, + 403, + 545, + 414 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {v l}} = \\mathcal {L} _ {\\mathrm {i t m}} + \\mathcal {L} _ {\\mathrm {m l m}} + \\mathcal {L} _ {\\mathrm {i t c}}. \\tag {4}", + "image_path": "b24cb23d524682988482b6306b8b7b8d05560d5e033996b1b60c3ed60fe9d6eb.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 423, + 541, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 541, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 541, + 434 + ], + "type": "text", + "content": "This loss " + }, + { + "bbox": [ + 306, + 423, + 541, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{vl}}" + }, + { + "bbox": [ + 306, + 423, + 541, + 434 + ], + "type": "text", + "content": " will also be used to tune our baseline model." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 443, + 502, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 443, + 502, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 502, + 455 + ], + "type": "text", + "content": "3.2. Self-Consistency Equivalence Tuning" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": "SelfEQ assumes that the model has access to paraphrases " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "T^e" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " for each input image-text pair " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\langle V, T \\rangle" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " or, in practice, for a subset of those samples. Therefore we assume a finetuning dataset " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "D'" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " with triplets " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\langle V, T, T^e \\rangle" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "T^e" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " exists for a corresponding input text " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": ". The first step to define our SelfEQ objective is to generate the explanation heatmaps (i.e., attention maps) through GradCAM [43] conditioned on the input text. We extract intermediate feature maps from the multimodal interactive encoder " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\phi_f" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " for input pairs " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\langle V, T \\rangle" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\langle V, T^e \\rangle" + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 330, + 589, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 589, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 330, + 589, + 545, + 602 + ], + "type": "interline_equation", + "content": "F = \\phi (\\phi_ {v} (V), \\phi_ {t} (T)), F ^ {e} = \\phi (\\phi_ {v} (V), \\phi_ {t} (T ^ {e})), \\tag {5}", + "image_path": "ba1fb72a1ef6d861f78609a17f28fb811b0e282a13456259bc82efb279fdf8c8.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": " denotes the feature map extraction operation. We then proceed to calculate the gradient of " + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "inline_equation", + "content": "F^{e}" + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": " related to the image-text matching score " + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{itm}}" + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": ". This computation yields the attention maps for the original text and paraphrased text, referred to as " + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "inline_equation", + "content": "G^{e}" + }, + { + "bbox": [ + 304, + 609, + 545, + 670 + ], + "type": "text", + "content": ", respectively:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 321, + 677, + 545, + 702 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 677, + 545, + 702 + ], + "spans": [ + { + "bbox": [ + 321, + 677, + 545, + 702 + ], + "type": "interline_equation", + "content": "G = \\operatorname {R e L U} \\left(F \\odot \\nabla \\mathcal {H} \\left(\\vec {y}, \\phi_ {f} ^ {c l s} \\left(\\phi_ {v} (V), \\phi_ {t} (T)\\right)\\right)\\right), \\tag {6}", + "image_path": "7f70b47e4e6be6f781755b9e89f915dfd3274911acfe8035f7d11e71c3a4fb4d.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 320, + 697, + 522, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 697, + 522, + 716 + ], + "spans": [ + { + "bbox": [ + 320, + 697, + 522, + 716 + ], + "type": "interline_equation", + "content": "G ^ {e} = \\operatorname {R e L U} \\left(F ^ {e} \\odot \\nabla \\mathcal {H} \\left(\\vec {\\mathcal {y}}, \\phi_ {f} ^ {c l s} \\left(\\phi_ {v} (V), \\phi_ {t} \\left(T ^ {e}\\right)\\right)\\right)\\right).", + "image_path": "b42c350637a3a1e86c3d1530304de9f642ce90cda39e486e29dfb994eb7f6bdd.jpg" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13097" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": "Our SelfEQ tuning is based on the premise that if a vision-language model is identified as self-consistent, the attention maps produced for both the text and its equivalent paraphrase should yield nearly identical results. To achieve this, we first apply a simple mean squared error loss over the produced heatmaps so that their " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " distance is minimized and thus become more similar." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 79, + 161, + 287, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 161, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 79, + 161, + 287, + 190 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s i m}} = \\mathbb {E} _ {(V, T, T ^ {e}) \\sim D ^ {\\prime}} \\left[ \\frac {1}{N} \\sum_ {i, j} \\left(G _ {i, j} - G _ {i, j} ^ {e}\\right) ^ {2} \\right]. \\qquad (7)", + "image_path": "84b86b165c441892357522bff81f3e218d4e482ea6f56666d43d751c4d08b380.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "type": "text", + "content": "Nevertheless, while minimizing a sum of pixel-wise distances contributes to self-consistency, without a regularization term this loss can easily fall into a trivial solution. For instance, it could lead to attention maps with uniformly negative or positive predictions, or just really small values. To address this limitation, we propose to integrate these heatmaps by defining a Region of Interest (RoI) mask. This mask is designed to preserve regions within the attention maps that possibly contain correct predictions. Our approach hinges on the observation that, despite the predictions of equivalent textual inputs being inconsistent, sometimes regions with large values or regions that overlap between the two heatmaps tend to be correct. As such, we assume that if the sum of attention scores at a given position " + }, + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "type": "text", + "content": " exceeds a certain threshold " + }, + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 196, + 289, + 388 + ], + "type": "text", + "content": ", it is likely indicative of a correct prediction. We formalize the condition as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 396, + 287, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 396, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 101, + 396, + 287, + 425 + ], + "type": "interline_equation", + "content": "M _ {i, j} = \\left\\{ \\begin{array}{l} 1, \\left(G _ {i, j} + G _ {i, j} ^ {e}\\right) \\geq k \\\\ 0, \\left(G _ {i, j} + G _ {i, j} ^ {e}\\right) < k \\end{array} \\right.. \\tag {8}", + "image_path": "34b5445cd3c73702f720b440fb4cbd38abf56745d6ecfc243dcd7a8a0a52449f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 431, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 287, + 456 + ], + "type": "text", + "content": "The attention maps within RoI masks are obtained by element-wise multiplication as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 463, + 287, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 463, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 107, + 463, + 287, + 475 + ], + "type": "interline_equation", + "content": "R = G \\odot M, \\quad R ^ {e} = G ^ {e} \\odot M. \\tag {9}", + "image_path": "8c4761951dd988b459783698687be68c86406622246f7289104331a5e3ec28da.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "type": "text", + "content": "The integration of RoI masks allows us to use equivalent texts for mutual supervision, refining and improving the accuracy and providing regularization for the previously defined distance-based loss. Moreover, it could potentially address errors owing to unknown or less common words by working vocabulary expansion. Presuming one of the textual expressions is known and correctly understood, the model could extrapolate the meaning of the other equivalent expression via weak supervision. To implement it, we first compute the mean " + }, + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "type": "inline_equation", + "content": "\\mu_{RoI},\\mu_{RoI}^{e}" + }, + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "type": "text", + "content": " and the standard deviation " + }, + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "type": "inline_equation", + "content": "\\sigma_{RoI},\\sigma_{RoI}^{e}" + }, + { + "bbox": [ + 47, + 483, + 289, + 616 + ], + "type": "text", + "content": " within the RoI as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 90, + 623, + 287, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 623, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 90, + 623, + 287, + 651 + ], + "type": "interline_equation", + "content": "\\mu_ {R o I} = \\frac {\\sum_ {i , j} R _ {i , j}}{\\sum_ {i , j} M _ {i , j}}, \\mu_ {R o I} ^ {e} = \\frac {\\sum_ {i , j} R _ {i , j} ^ {e}}{\\sum_ {i , j} M _ {i , j}}, \\tag {10}", + "image_path": "ef4c697aab5def0ddbc515c2f01e4b6537b099d9315f8ba600412429bb102ba5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 655, + 287, + 690 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 655, + 287, + 690 + ], + "spans": [ + { + "bbox": [ + 91, + 655, + 287, + 690 + ], + "type": "interline_equation", + "content": "\\sigma_ {R o I} = \\sqrt {\\frac {\\sum_ {i , j} M _ {i , j} \\cdot \\left(R _ {i , j} - \\mu_ {R o I}\\right) ^ {2}}{\\sum_ {i , j} M _ {i , j}}}, \\tag {11}", + "image_path": "78a2ffc483e0ae539fb3f01aab110f929bc8c9bdfd709fa9d473a231fcb27f95.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 91, + 687, + 242, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 687, + 242, + 716 + ], + "spans": [ + { + "bbox": [ + 91, + 687, + 242, + 716 + ], + "type": "interline_equation", + "content": "\\sigma_ {R o I} ^ {e} = \\sqrt {\\frac {\\sum_ {i , j} M _ {i , j} \\cdot (R _ {i , j} ^ {e} - \\mu_ {R o I} ^ {e}) ^ {2}}{\\sum_ {i , j} M _ {i , j}}}.", + "image_path": "473b46953dbbd99c946f9ac109f26e63755deeeded3ada2fbc0f472e7c6fa126.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 132 + ], + "type": "text", + "content": "We propose a consistency loss " + }, + { + "bbox": [ + 306, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{cst}})" + }, + { + "bbox": [ + 306, + 72, + 545, + 132 + ], + "type": "text", + "content": ", expecting the RoI regions of attention maps to achieve consistently high scores, further reinforcing self-consistency, accuracy, and potential working vocabulary expansion. This objective is formulated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 138, + 545, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 138, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 317, + 138, + 545, + 188 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c s t}} = \\mathbb {E} _ {(V, T, T ^ {e}) \\sim D ^ {\\prime}} \\left[ \\sigma_ {R o I} + \\sigma_ {R o I} ^ {e} + \\right. \\tag {12} \\\\ \\left. \\max (0, k / 2 - \\mu_ {R o I}) + \\max (0, k / 2 - \\mu_ {R o I} ^ {e}) \\right]. \\\\ \\end{array}", + "image_path": "f3a18661b6681196498f124b083c42a633bc7e83aa5881b27ea444f4f9b34e92.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 195, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 195, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 195, + 545, + 220 + ], + "type": "text", + "content": "Finally, the objective of our self-consistency equivalence tuning is expressed as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 373, + 232, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 232, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 373, + 232, + 545, + 243 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {S e l f E Q}} = \\mathcal {L} _ {\\text {s i m}} + \\lambda \\cdot \\mathcal {L} _ {\\text {c s t}}, \\tag {13}", + "image_path": "67ea167a723838b725f9628b2253e498d596e9281878113db57cc6ac21228eef.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 247, + 545, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 545, + 271 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 247, + 545, + 271 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 247, + 545, + 271 + ], + "type": "text", + "content": " is a hyperparameter to control the relative influence of each loss." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 281, + 500, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 500, + 293 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 500, + 293 + ], + "type": "text", + "content": "3.3. Self-Consistency Data Augmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "text", + "content": "In this section we define a function " + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "text", + "content": " that can automatically map input textual phrases " + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "text", + "content": " as paraphrases " + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "inline_equation", + "content": "T^{e}" + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "text", + "content": " without the need to rely on human annotations such that " + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "inline_equation", + "content": "T^{e} \\sim \\mathcal{F}(T)" + }, + { + "bbox": [ + 305, + 299, + 545, + 369 + ], + "type": "text", + "content": ". We achieve this goal through a two-level prompting approach using a large language model which we describe in detail below." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 374, + 546, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 374, + 546, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 546, + 590 + ], + "type": "text", + "content": "Phrase Chunking: Using our first-level prompts, we aim to augment the original text using phrase chunking to encourage global captions to concentrate on more specific regions. Visual grounding seeks to localize objects in images based on textual inputs. In contrast, global captions usually describe the entire image, typically describing several objects. While training on global captions could be beneficial for learning cross-modal information, it may lead the model to predict a broader region (i.e., global context) rather than a specific region. Phrase chunking (i.e., shallow parsing [55]) aims to identify continuous sequences of tokens representing syntactic units, enabling the extraction of phrases from unstructured text. We leverage an LLM to segment global captions into object-centric short phrases. During training, we use these image-chunk pairs instead of global captions, effectively guiding the model attention toward localized regions of interest. We refer the reader to the supplementary material for prompting details and generated examples." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": "Paraphrase Generation: Our SelfEQ approach involves feeding the model with pairs of textual descriptions that refer to the same underlying concept, with the expectation that the model can make similar predictions for these equivalent description pairs " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\langle T, T^e \\rangle" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": ". We augment our dataset by transforming the region-based captions (i.e., text that only refers to a region in the image) and the object-centric short phrases we obtained from phrase chunking into equivalent paraphrases referring to the same concept through our second-level LLM-prompts." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13098" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 50, + 71, + 286, + 152 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 152 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 152 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 152 + ], + "type": "text", + "content": "Q:\"a smiling, holding something and standing man\" \nA:{\"group\": \"man\", \"synonym\": [\"adult male\",\"gentleman\"], \"antonym\": [\"woman\"], \"hypernym\": [\"adult\",\"grownup\",\"male\",\"male person\",\"human being\",\"human\"], \"meronym\": [\"man body\",\"man head\",\"man arms\",\"man legs\"]} \nQ:\"a desk\" \nA:{\"group\": \"desk\", \"synonym\": [\"table\",\"writing desk\"], \"antonym\": [], \"hypernym\": [\"writer tool\",\"furniture\"], \"meronym\": [\"desktop\",\"desk leg\"]}" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + } + ], + "index": 0, + "sub_type": "code", + "guess_lang": "jsonl" + }, + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "type": "text", + "content": "Figure 3. Two samples from our LLM-prompt for paraphrase generation. The first set showcases an example of a region-based caption, and the second set shows a non-sentence phrase. " + }, + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "type": "text", + "content": " is the query text and " + }, + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 159, + 287, + 204 + ], + "type": "text", + "content": " is the expected answer." + } + ] + } + ], + "index": 1, + "type": "text" + }, + { + "bbox": [ + 46, + 212, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 212, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 287, + 366 + ], + "type": "text", + "content": "There are many ways to paraphrase, including substituting words, altering sentence structures, and rewriting sentences based on semantics. However, considering that self-consistency in vision and language is relatively underexplored, we adopt a straightforward strategy: Replacing the primary object in the sentence while retaining all other attributes. This strategy yields several benefits. First, it provides a consistent context, which serves as a reference for the model to identify equivalent descriptions. This enables the equivalent relationships of paraphrases to be learned intuitively. Second, it simplifies prompt designing and post-processing by detecting the primary object and generating its synonym." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 368, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 534 + ], + "type": "text", + "content": "To generate paraphrases for the dataset consisting of region-based captions, we select four textual descriptions in which the primary noun plays different syntactic roles. We further select two non-sentence phrases as examples of query texts in our prompts. We show an example of a region-based caption and a non-sentence phrase in Figure 3. To design our prompt, we identify the primary object in the query text Q. Then we use WordNet [37] to obtain synonyms automatically and further remove inaccurate or invalid words. We add A to indicate the expected answer and include other relationships such as antonym, hy- pernym and meronym to provide richer contexts for LLM in-context learning. Additional prompting details and paraphrase samples are provided in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "content": "This two-level prompt-based LLM augmentation approach ensures that our model is exposed to textual inputs that share the same concept while varying in linguistic representation, thereby promoting self-consistency and working vocabulary expansion." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 609, + 176, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 176, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 176, + 624 + ], + "type": "text", + "content": "4. Experimental Settings" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 715 + ], + "type": "text", + "content": "Training. We use ALBEF [27] as our base model in all our experiments, given its reported off-the-shelf visual grounding performance via GradCAM [43]. ALBEF combines a ViT-B [11] model for encoding images and a BERT-base [10] model for encoding text. It is pre-trained on a range of datasets, including ImageNet-1K [42], Conceptual Captions [46], SBU Captions [39], MS-COCO [33], and" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 547, + 369 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 547, + 369 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 547, + 369 + ], + "type": "table", + "html": "
MethodTrainingFlickr30kReferIt
Box SupervisionAlign2Ground [7]VG-boxes71.00-
12-in-1 [35]VG-boxes76.40-
InfoGround [19]VG-boxes76.74-
VMRM [12]VG-boxes81.11-
AMC [51]VG-boxes86.5973.17
Without Box SupervisionTD [56]VG42.4031.97
SSS [20]VG49.1039.98
MG-BiLSTM [2]VG57.9162.76
MG-ELMo [2]VG60.0860.01
GbS [3]VG73.3962.24
g [45]VG75.6365.95
g++ [44]VG79.9570.25
SelfEQ (ours)VG81.9067.40
FCVC [13]MS-COCO29.0333.52
MG-BiLSTM [2]MS-COCO53.2947.89
MG-ELMo [2]MS-COCO61.6647.52
GbS [3]MS-COCO74.5049.26
g [45]MS-COCO75.4361.03
g++ [44]MS-COCO78.1061.53
SelfEQ (ours)MS-COCO84.0762.75
", + "image_path": "bd7c38847e068faede53f1e852bfefbe6b43dc486d67ee5f949c9357e6d65190.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 377, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 304, + 377, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 547, + 456 + ], + "type": "text", + "content": "Table 1. Visual Grounding results on two benchmarks using pointing game accuracy with two training datasets. SelfEQ yields generally the best overall performance among weakly-supervised methods, and comes second to " + }, + { + "bbox": [ + 304, + 377, + 547, + 456 + ], + "type": "inline_equation", + "content": "\\mathrm{g} + +" + }, + { + "bbox": [ + 304, + 377, + 547, + 456 + ], + "type": "text", + "content": " on the ReferIt benchmark when trained using VG. We also show at the top the results of methods using additional box supervision from Visual Genome (VG) either directly or through an object detector." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "text", + "content": "Visual Genome (VG) [26] excluding box annotations. We finetune ALBEF with image-text pairs from VG and MS-COCO without any type of box supervision (i.e., no bounding boxes or object detectors), following prior work [2]. We further leverage Vicuna-13B [6] as our LLM-prompting model to generate the object-centric short phrases (via shallow parsing or chunking) and the equivalent paraphrases for our self-consistency data augmentation. Additionally, we validate the effectiveness of our SelfEQ tuning and self-consistency data augmentation method by training on a preprocessed subset of the Conceptual Captions 3M (CC3M) dataset [46], which contains many noisy or unaligned web-crawled AltText-image pairs. With this subset, we achieve an absolute improvement of " + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "inline_equation", + "content": "2.15\\%" + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "text", + "content": " on Flickr30k, " + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "inline_equation", + "content": "3.32\\%" + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "text", + "content": " on ReferIt, and " + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "inline_equation", + "content": "1.33\\%" + }, + { + "bbox": [ + 304, + 468, + 545, + 659 + ], + "type": "text", + "content": " on RefCOCO+; refer to the supplementary material for detailed CC3M experiments." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Evaluation. We conduct evaluations using Flickr30k [40] and ReferIt [24] under pointing game accuracy following previous weakly-supervised visual grounding works [2, 3]. To underscore the competitive edge of our method, we also" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13099" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 279, + 186 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 279, + 186 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 279, + 186 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 279, + 186 + ], + "type": "table", + "html": "
MethodBox SupervisionRefCOCO+
Test ATest B
InfoGround [19]Yes39.8041.11
VMRM [12]Yes58.8750.32
AMC [51]Yes80.3464.55
ALBEF [27]No69.3553.77
SelfEQ (ours)No75.1055.49
", + "image_path": "cc9a83c0894c4ea99676d6ffb463adab1135fe75f3d706ca3878dd08b9720c03.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 194, + 287, + 227 + ], + "lines": [ + { + "bbox": [ + 47, + 194, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 287, + 227 + ], + "type": "text", + "content": "Table 2. Results on RefCOCO+ pointing game accuracy. SelfEQ shows significant improvements over off-the-shelf ALBEF and competitive results compared to box-supervised methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 236, + 287, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 287, + 271 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 287, + 271 + ], + "type": "text", + "content": "present its performance on RefCOCO+ [53], a challenging benchmark more commonly used for testing box-supervised methods [7, 12, 19, 35, 51]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 278, + 180, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 180, + 291 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 180, + 291 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": "Our experiments are conducted on a single computing node with 8 NVIDIA A40 GPUs. During the training phase, input images are resized to " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": " and augmented with horizontal flipping, color jittering, and random grayscale conversion. We set up an Adam optimizer [25] with a learning rate of 1e-5 and a batch size of 448 across all experiments. We empirically set the RoI threshold " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": " to 0.8 and the hyperparameter " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": " to 1.0. For training with raw image-text pairs from the datasets, we employ the vision-language objective " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{vl}}" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": " (Sec. 3.1), while for the subset with equivalent paraphrases, we use our self-consistency equivalence tuning objective " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SelfEQ}}" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": " (Sec. 3.2) and corresponding vision-language objective " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{vl}}^e" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": ". The composite objective function is given by " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\alpha \\cdot \\mathcal{L}_{\\mathrm{vl}} + (1 - \\alpha) \\cdot (\\mathcal{L}_{\\mathrm{SelfEQ}} + \\mathcal{L}_{\\mathrm{vl}}^e)" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 297, + 288, + 511 + ], + "type": "text", + "content": " is initially set to 0 and increments to 1, remaining constant after the second epoch. Our hyperparameter values and schedules were determined empirically on a small validation subset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 522, + 173, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 173, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 173, + 536 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 542, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 626 + ], + "type": "text", + "content": "Our resulting model obtains the best performance on the task of weakly-supervised visual grounding compared to most methods under this setting and is comparable to several prior works that rely on some of box supervision. Moreover, our qualitative results show that our method can handle paraphrases and a larger working vocabulary without the needed to increment the training dataset significantly." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "Flickr30k and ReferIt. We evaluate the effectiveness of our proposed SelfEQ method in Table 1, demonstrating its substantial lead over GradCAM-based weakly-supervised approaches. Our self-consistency equivalent tuning adapts well for both region-based (i.e., VG) and global-based (i.e., COCO) image-text pairs, yielding a performance gain of " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "4.69\\%" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": " on Flickr30k and " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "7.68\\%" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": " on ReferIt, compared to" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 87, + 370, + 129 + ], + "blocks": [ + { + "bbox": [ + 312, + 76, + 397, + 86 + ], + "lines": [ + { + "bbox": [ + 312, + 76, + 397, + 86 + ], + "spans": [ + { + "bbox": [ + 312, + 76, + 397, + 86 + ], + "type": "text", + "content": "Text: \"trees on the right\"" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + 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348 + ], + "type": "text", + "content": "Text: \"white bldg\"" + } + ] + } + ], + "index": 44, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 349, + 367, + 415 + ], + "lines": [ + { + "bbox": [ + 317, + 349, + 367, + 415 + ], + "spans": [ + { + "bbox": [ + 317, + 349, + 367, + 415 + ], + "type": "image", + "image_path": "b5c1513b0f309d1cfd53168834fc8342b616bacf1ae210d0700f55377b383889.jpg" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 415, + 350, + 422 + ], + "lines": [ + { + "bbox": [ + 333, + 415, + 350, + 422 + ], + "spans": [ + { + "bbox": [ + 333, + 415, + 350, + 422 + ], + "type": "text", + "content": "Image" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 428, + 545, + 483 + ], + "lines": [ + { + "bbox": [ + 306, + 428, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 428, + 545, + 483 + ], + "type": "text", + "content": "Figure 4. Qualitative results of our method in challenging visual grounding scenarios compared to prior works. On top of each row we show the reference text, the first column shows the image, then we show our base model ALBEF, the SotA box-supervised method AMC, and finally we show results with our method SelfEQ." + } + ] + } + ], + "index": 53, + "angle": 0, + "type": "image_caption" + } + ], + "index": 45 + }, + { + "type": "image", + "bbox": [ + 373, + 349, + 424, + 415 + ], + "blocks": [ + { + "bbox": [ + 373, + 349, + 424, + 415 + ], + "lines": [ + { + "bbox": [ + 373, + 349, + 424, + 415 + ], + "spans": [ + { + "bbox": [ + 373, + 349, + 424, + 415 + ], + "type": "image", + "image_path": "05221046499fde22d165e7c0df470546cac1e848528cff56f6db50b65869ed79.jpg" + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 415, + 406, + 422 + ], + "lines": [ + { + "bbox": [ + 390, + 415, + 406, + 422 + ], + "spans": [ + { + "bbox": [ + 390, + 415, + 406, + 422 + ], + "type": "text", + "content": "ALBEF" + } + ] + } + ], + "index": 48, + "angle": 0, + "type": "image_caption" + } + ], + "index": 47 + }, + { + "type": "image", + "bbox": [ + 430, + 348, + 481, + 415 + ], + "blocks": [ + { + "bbox": [ + 430, + 348, + 481, + 415 + ], + "lines": [ + { + "bbox": [ + 430, + 348, + 481, + 415 + ], + "spans": [ + { + "bbox": [ + 430, + 348, + 481, + 415 + ], + "type": "image", + "image_path": "1aa0821b4cd677e43a98e3baf350fd07e451ffd5b64915516e4fec3ebe524ff2.jpg" + } + ] + } + ], + "index": 49, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 415, + 462, + 422 + ], + "lines": [ + { + "bbox": [ + 449, + 415, + 462, + 422 + ], + "spans": [ + { + "bbox": [ + 449, + 415, + 462, + 422 + ], + "type": "text", + "content": "AMC" + } + ] + } + ], + "index": 50, + "angle": 0, + "type": "image_caption" + } + ], + "index": 49 + }, + { + "type": "image", + "bbox": [ + 487, + 348, + 539, + 415 + ], + "blocks": [ + { + "bbox": [ + 487, + 348, + 539, + 415 + ], + "lines": [ + { + "bbox": [ + 487, + 348, + 539, + 415 + ], + "spans": [ + { + "bbox": [ + 487, + 348, + 539, + 415 + ], + "type": "image", + "image_path": "0364ae426a36de47b099f6a4769efe7ed407d649ac68c9906d9dbdf1cac4f36c.jpg" + } + ] + } + ], + "index": 51, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 506, + 415, + 518, + 422 + ], + "lines": [ + { + "bbox": [ + 506, + 415, + 518, + 422 + ], + "spans": [ + { + "bbox": [ + 506, + 415, + 518, + 422 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_caption" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 494, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 673 + ], + "type": "text", + "content": "our base model ALBEF (see first row in Table 3). Notably, our method outperforms almost all box-supervised methods on Flickr30k [7, 12, 19, 35]. In the weakly-supervised setting, our method only comes second on ReferIt compared to " + }, + { + "bbox": [ + 304, + 494, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathrm{g + + }[44]" + }, + { + "bbox": [ + 304, + 494, + 545, + 673 + ], + "type": "text", + "content": " when trained on Visual Genome imagedtext pairs. This method leverages a custom architecture to produce a mask and uses heatmap supervision from a CLIP [41] model as pseudo-labels during training. We posit that our contribution is orthogonal and our approach would likely also benefit from similar supervision, since CLIP is trained in a much larger image-text pair dataset. Despite differences, our method still obtains higher performance when trained on MS-COCO and the best performance compared to all weakly-supervised methods on Flickr30K region-phrase grounding." + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "RefCOCO+. RefCOCO+ [53] serves as a rigorous benchmark for visual grounding, typically used to evaluate box-supervised techniques. In Table 2, we present the per" + } + ] + } + ], + "index": 55 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13100" + } + ] + } + ], + "index": 56 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 282, + 159 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 282, + 159 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 282, + 159 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 282, + 159 + ], + "type": "table", + "html": "
DataObjectiveRefCOCO+Flickr30kReferIt
Test ATest B
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", + "image_path": "2e32c90976951268df0c16e9a9177a244e32197358102315a4d05ed3ee176fa3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "text", + "content": "Table 3. Ablation studies on different ways to utilize extra equivalent paraphrased data. The first row is off-the-shelf ALBEF performance before tuning. " + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "text", + "content": " denotes the textual captions from the dataset, and " + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "inline_equation", + "content": "{T}^{e}" + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "text", + "content": " corresponds to the associated equivalent paraphrases. " + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{\\mathrm{{vl}}}" + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "text", + "content": " is the vision-language objective,and " + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{\\text{SelfEQ }}" + }, + { + "bbox": [ + 46, + 167, + 287, + 234 + ], + "type": "text", + "content": " is our self-consistency equivalence tuning objective." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 244, + 288, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 288, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 288, + 304 + ], + "type": "text", + "content": "formance of our weakly-supervised method (VG trained) against box-supervised methods. Our results indicate that our approach is competitive without reliance on any form of box annotations and significantly improves over the base ALBEF model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 429 + ], + "type": "text", + "content": "Visual Grounding Analysis. Figure 4 provides qualitative results of our method in challenging scenarios, including occluded objects (row 1), small objects within complex scenes (row 2), objects partially shown in the corner of the image (row 3), multiple similar objects (row 4), and abbreviated text inputs (row 5). Our self-consistency equivalency tuning approach exhibits substantial improvements in the grounding capability of the base ALBEF [27] model. Remarkably, our approach even outperforms the state-of-the-art box-supervised method AMC [51] in multiple scenarios." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 431, + 288, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 288, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 288, + 564 + ], + "type": "text", + "content": "Self-Consistency Analysis. Figure 5 demonstrates qualitative results for the self-consistency capability across different equivalent paraphrases, encompassing terminology (row 1), synonym substitutions (row 2), and regional slang combining with different sentence structures (row 3). Although other methods succeed in localizing certain phrases, they demonstrate inconsistencies for the equivalent paraphrases. In contrast, our model finetuned with SelfEQ effectively establishes connections between semantically equivalent paraphrases, thereby enhancing the model self-consistency ability and potentially expanding its working vocabulary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 571, + 148, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 148, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 148, + 582 + ], + "type": "text", + "content": "5.1. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Data Quantity. We assess the impact of the data quantity of our generated paraphrases and compare our tuning strategy against standard vision-language objectives. We randomly sample portions of data from VG by " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " associated with our augmented equivalent paraphrases three times. To compare, we use the vision-language objective with VG text-image pairs as baselines. In Figure 6, we show the mean and standard deviation pointing game accuracy. The performance of the base vision-language objective does not exhibit a steady improvement with more text-image pairs. Al-" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 73, + 543, + 178 + ], + "blocks": [ + { + "bbox": [ + 310, + 73, + 543, + 178 + ], + "lines": [ + { + "bbox": [ + 310, + 73, + 543, + 178 + ], + "spans": [ + { + "bbox": [ + 310, + 73, + 543, + 178 + ], + "type": "image", + "image_path": "93e02ff69731fc5109cb0e56f4e4b82bbb3158886b98e69b95d3d5937874106d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 311, + 180, + 542, + 287 + ], + "blocks": [ + { + "bbox": [ + 311, + 180, + 542, + 287 + ], + "lines": [ + { + "bbox": [ + 311, + 180, + 542, + 287 + ], + "spans": [ + { + "bbox": [ + 311, + 180, + 542, + 287 + ], + "type": "image", + "image_path": "2ec7829f18c58bca6218f49d76349e0252b7b7d79594ea9c8938c447bb31d67e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 289, + 542, + 395 + ], + "blocks": [ + { + "bbox": [ + 310, + 289, + 542, + 395 + ], + "lines": [ + { + "bbox": [ + 310, + 289, + 542, + 395 + ], + "spans": [ + { + "bbox": [ + 310, + 289, + 542, + 395 + ], + "type": "image", + "image_path": "920376e4140cf3bf27d52458840f59fcf6fed0eafbe15081dce7ef2e32b3809c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 403, + 545, + 458 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 545, + 458 + ], + "type": "text", + "content": "Figure 5. Qualitative results across equivalent paraphrases among different methods. For each image, we show a caption referring to an object in the first row and an equivalent paraphrase in the second row. Each column shows the results of ALBEF, the SotA box-supervised method AMC, and our SelfEQ method." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 469, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 545, + 540 + ], + "type": "text", + "content": "though ReferIt performance increases, the performance on RefCOCO+ Test A remains mostly unchanged. Additionally, the performance on Flickr30k notably decreases, and there is a mixed effect on RefCOCO+ Test B, with half of the accuracy falling below the off-the-shelf ALBEF performance of " + }, + { + "bbox": [ + 305, + 469, + 545, + 540 + ], + "type": "inline_equation", + "content": "53.77\\%" + }, + { + "bbox": [ + 305, + 469, + 545, + 540 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 544, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 687 + ], + "type": "text", + "content": "In contrast, SelfEQ consistently leads to performance enhancements with more equivalent paraphrases. Clear upward trends are observed on Flickr30k, ReferIt, and RefCOCO+ Test A as more data with corresponding equivalent paraphrases are added, meanwhile the gaps between the baselines generally widen. Notably, SelfEQ tuning maintains performance gains on Flickr30k, whereas the baselines performances drop. Although the trend on RefCOCO+ Test B is not consistently increasing, it is essential to emphasize that RefCOCO+ Test B is only a subset, and SelfEQ illustrates more stable and effective tuning performance on it, compared to the base vision-language objective." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "These observations indicate that more equivalent paraphrases connecting with associated text phrases enable the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13101" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 173, + 146 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 173, + 146 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 173, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 173, + 146 + ], + "type": "image", + "image_path": "283e0434cffe2589dd3dec8351141ecdab4db15e468c61f9d5bd52c1b837619b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 149, + 547, + 183 + ], + "lines": [ + { + "bbox": [ + 46, + 149, + 547, + 183 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 547, + 183 + ], + "type": "text", + "content": "Figure 6. Tuning performance with different data quantities on Flickr30k, ReferIt, RefCOCO+ Test A and Test B. The purple and cyan lines represent SelfEQ (ours) and ALBEF baseline losses (vision-language objective), respectively. We show the impact of progressively augmenting captions via LLM-prompting for generating equivalent paraphrases tuned with our SelfEQ objective. 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FormatObjectiveFlickr30kReferIt
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Ablation studies on objective components of self-consistency equivalence tuning objective " + }, + { + "bbox": [ + 305, + 271, + 545, + 295 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{\\text{SelfEQ }}" + }, + { + "bbox": [ + 305, + 271, + 545, + 295 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "text", + "content": "Objective. Table 5 evaluates each component within our self-consistency equivalence tuning objective. The " + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sim}}" + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "text", + "content": " loss targets pixel-wise similarity, ensuring that maps for a caption and its equivalent paraphrase are identical. However, focusing solely on pixel-level similarity may neglect the precise spatial positioning of objects. To address this, the " + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cst}}" + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "text", + "content": " loss is proposed to identify the most likely correct object positions within the two maps (i.e., RoI). It then encourages the model to yield consistently high attention scores within the RoI. By integrating both " + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sim}}" + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cst}}" + }, + { + "bbox": [ + 304, + 306, + 546, + 486 + ], + "type": "text", + "content": ", self-consistency equivalence tuning objective fosters the model to not only align global similarities but also to pinpoint accurate object locations through the mutual supervision provided by a caption and its paraphrase, thereby enhancing self-consistency and accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 517, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 672 + ], + "type": "text", + "content": "We propose a novel weakly-supervised tuning approach coupled with a data augmentation strategy to enhance the localization capabilities of an image-text supervised model through self-consistency. Using an open-source LLM, we expand a dataset with equivalent paraphrases tailored to be object-centric. The augmented data is used to finetune a base model employing our novel self-consistency equivalence tuning objective. Our approach has been rigorously validated across pretraining on diverse datasets, ranging from region-based captions (i.e., VG) to global-based captions (i.e., COCO). Our method achieves superior and self-consistent performance on three benchmarks and is even competitive with some box-supervised methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 675, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 675, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 675, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments. This work was partially funded by NSF Award #2201710 and a Ken Kennedy Institute's SLB PhD Fellowship." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13102" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "type": "text", + "content": "[1] Samira Abnar and Willem Zuidema. 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International Journal of Computer Vision, 126(10):1084-1102, 2018. 5" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "13105" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_content_list.json b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ae6357e9c9e74740af9cab93a9182985f450f984 --- /dev/null +++ b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_content_list.json @@ -0,0 +1,1721 @@ +[ + { + "type": "text", + "text": "Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions", + "text_level": 1, + "bbox": [ + 94, + 130, + 875, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Oindrila Saha Grant Van Horn Subhransu Maji University of Massachusetts, Amherst {osaha, gvanhorn, smaji}@umass.edu", + "bbox": [ + 258, + 180, + 710, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The zero-shot performance of existing vision-language models (VLMs) such as CLIP [29] is limited by the availability of large-scale, aligned image and text datasets in specific domains. In this work, we leverage two complementary sources of information—descriptions of categories generated by large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across fine-grained domains. On the technical side, we develop methods to train VLMs with this \"bag-level\" image-text supervision. We find that simply using these attributes at test-time does not improve performance, but our training strategy, for example, on the iNaturalist [41] dataset, leads to an average improvement of $4 - 5\\%$ in zero-shot classification accuracy for novel categories of birds [42] and flowers [23]. Similar improvements are observed in domains where a subset of the categories was used to fine-tune the model. By prompting LLMs in various ways, we generate descriptions that capture visual appearance, habitat, and geographic regions and pair them with existing attributes such as the taxonomic structure of the categories. We systematically evaluate their ability to improve zero-shot categorization in natural domains. Our findings suggest that geographic priors can be just as effective and are complementary to visual appearance. Our method also outperforms prior work on prompt-based tuning of VLMs. We release the benchmark, consisting of 14 datasets at https://github.com/cvl-umass/AdaptCLIPZS, which will contribute to future research in zero-shot recognition.", + "bbox": [ + 75, + 300, + 473, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 768, + 209, + 784 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent improvements in zero-shot classification have been due, in part, to success in training VLMs at scale. Models such as CLIP [29], ALIGN [11], and BLIP [16] use massive datasets of image and text pairs to learn a common embedding between visual and natural language domains. However, we find existing VLMs show poor performance in encoding visual attributes in fine-grained domains, beyond", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bddf8a38260c140cab794284ddcba734e003b5adc86b65816abe2dc822643ae9.jpg", + "image_caption": [ + "Figure 1. Motivation. Collecting image captions in fine-grained domains requires expertise (top row), but LLMs can generate structured (e.g., shape or appearance) and accurate descriptions of categories at both the coarse (e.g., birds) and fine-grained level (e.g., Vesper Sparrow). Rich descriptions of fine-grained categories can be paired with existing datasets, such as iNaturalist [41] and NABirds [39] to generate coarsely-aligned image-text datasets for fine-tuning VLMs. This improves their zero-shot performance on a range of benchmarks, generalizing to novel categories and tasks." + ], + "image_footnote": [], + "bbox": [ + 501, + 268, + 890, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "simply recognizing the name of the category. For example, we observe concatenating visual attribute descriptions to the species name for the bird species in the CUB [42] dataset improves the zero-shot classification from $50.5\\%$ to only $50.7\\%$ , while for Cars [14], the performance even drops slightly (see Tab. 1). Although the datasets on which VLMs are trained are extensive, they often lack the details that experts may require for fine-grained categorization. At the same time, collecting large-scale image-caption datasets in these domains requires significant effort, making training similar models challenging.", + "bbox": [ + 496, + 580, + 892, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we leverage two complementary sources of information—large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across a variety of fine-grained domains. Concretely, we generate large datasets of images aligned with text by pairing images within a category with descriptions of that category generated by LLMs as seen in Fig. 1. We find this approach works well, as images within a fine-grained domain share many attributes, unlike in coarse categories with", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17542", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "larger intra-category variation. At the same time, we find that LLMs are capable of accurately describing appearance, habitat, and other properties for a wide range of categories, allowing us to systematically generate datasets in a scalable manner. In other words, fine-grained labels allow us to bridge the gap between image-level captions required for VLM training, and general information about visual categories contained in LLMs.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the technical side, we develop methods to train VLMs with \"bag-level\" supervision. In our dataset a set of images are grouped with a set of descriptions and lack the image-text correspondences. Some of the descriptions may not apply to an image (e.g., the part may be occluded). However, we find that training by stochastically pairing the images and text within a category, followed by a category-level contrastive loss similar to CLIP objective offers robust improvements in performance. Adapting semi-supervised learning approaches such as FixMatch [35] or Knowledge distillation [3] results in minor improvements ( $\\S 5.7$ ). A detailed investigation of the image-text association within a category suggests the model is able to correctly associate the visual attributes with the corresponding text even they are paired randomly during training (Fig. 2).", + "bbox": [ + 75, + 212, + 468, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We systematically evaluate the effectiveness of our method by assessing the zero-shot classification performance on novel classes. We find that simply using these attributes of novel classes generated by LLMs does not improve performance when using CLIP (Tab. 1). However, our training strategy leads to an average improvement of $4 - 5\\%$ in accuracy across 12 datasets, and outperforms baselines (Tab. 2). For natural domains (e.g., iNaturalist and NABirds), we prompt LLMs in various ways to generate descriptions that capture visual appearance, habitat, and geographic regions, and pair them with existing attributes within the dataset, such as taxonomic structure. Our results indicate that geographic priors are equally effective and complementary to visual appearance cues (see Tab. 3). Training on iNaturalist without any bird classes improves the performance of CLIP on CUB by more than $3\\%$ , and we observe similar improvements when evaluating across other domains (see Tab. 4). Improvements are consistent across text generated by different LLMs, as well as by humans (see Tab. 5). Our model also results in relative error reduction of $4.1\\%$ over CLIP on the challenging NeWT dataset [40].", + "bbox": [ + 75, + 439, + 472, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 768, + 218, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Zero-shot Image Classification using VLMs. Vision Language models (VLMs) [6, 11, 29, 33, 45] learn to associate images with their corresponding text captions. Learning a shared embedding makes them perform exceptionally well in zero-shot classification tasks when paired with an appropriate text such as the class name during test time. FLAVA [33] learns using paired as well as unpaired im", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/71a3ad2b6d05ba340f71b6cfb17cc6d2e698e23b22419f1de9392cb45b81c909.jpg", + "image_caption": [ + "Figure 2. Visualizing image-text similarity. All images within a category are sorted in order of similarity to a given text predicted by CLIP and our fine-tuned $\\mathrm{CLIP^{FT} + A}$ . For example, our method identifies birds which show olive-green tint on their back as the top images, whereas CLIP selects birds with visibly brown upperparts or occluded back. The image with lowest similarity which has the occluded back remains the same for both models, showing our model does not learn incorrect attribute associations even though we stochastically pair every attribute with every image during training. On the aircraft example our model predicts higher similarity to images with prominently visible fuselage. CLIP identifies the least similar image as one in which fuselage is visible, but ours chooses one where aircrafts are too far to make out the shape of fuselage." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ages and texts using different losses for multimodal and unimodal understanding. ALIGN [11] uses a large number of noisy image-text data by obtaining alt-texts for images and trains using a contrastive loss. CLIP [29] is trained on a smaller and cleaner dataset of image-text pairs using a similar objective function. It employs a vision model and a language model to learn joint embeddings of images and text. While training, it maximizes the similarity between related image-text pairs and minimizes similarity between unrelated pairs. At test time the similarity over captions such “a photo of a [class name]” over all classes in the domain for each image is found. The image is classified to the class with the caption with highest probability. The original paper shows that manual prompt tuning can boost zero-shot classification accuracy.", + "bbox": [ + 496, + 460, + 892, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generating Better Prompts. Prior work on prompt tuning [7, 12, 13, 32, 51] has focused on improving the text descriptions of classes. For example, CoOp [50] appends learnable context vectors to the class name texts to improve classification. CoCoOp [49] and related methods have also explored prompting the vision encoder simultaneously. While prompt tuning has proven useful for adapting models to a set of \"base categories\", its performance on novel categories still falls short of the CLIP baseline.", + "bbox": [ + 496, + 688, + 890, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of research aims at querying LLMs to generate prompts or attributes of categories. CHiLS [24] refines classes based on GPT descriptions (e.g., taxonomic structure) and maps the image to one of the subcategories to improve classification. We also explore the ability to", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17543", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "learn taxonomy-based attributes in our work. Menon et al. [20] and CuPL [28] append class-specific attributes obtained from GPT [2] to simple prompts, e.g. \"a photo of a [class]\" to improve zero-shot performance at test-time, similar to our approach. However, we find that CLIP struggles to recognize nuanced attributes in fine-grained domains where we observe little to no improvement in classification performance, motivating the need for fine-tuning VLMs.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fine-tuning VLMs. Most work on fine-tuning VLMs has focused on parameter efficient updates using lightweight adapters [8,19,25,27,46,47] for improving few-shot classification. For example, CLIP adapter [8] trains a few learnable layers on top of the encoders, while Maniparambil et al. [19] query LLMs for class-wise descriptions for tuning an external adapter network. Their work improves over CoCoOp and CLIP adapter for unseen classes, however, as before, most approaches show no improvement over CLIP, especially on novel classes in fine-grained datasets.", + "bbox": [ + 75, + 212, + 470, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another line of research [9, 34, 37, 43, 48] involves fine-tuning CLIP for robustness to domain shifts. For instance, WiSE-FT [43] utilizes weight-space ensembling to improve performance on a sketch version of ImageNet. Similarly, LaFTer [21] employs fine-tuning both the image and text encoders using unpaired images and texts obtained by querying LLMs. These techniques focus on adapting to a target distribution, such as a specific set of test images or classes, rather than on generalizing to novel classes.", + "bbox": [ + 75, + 364, + 468, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Two works similar to ours, GIST [15] and I2MVFormer [22], also utilize GPT to generate category-specific texts for fine-grained domains. GIST pairs each image with the $n$ most similar texts within the category based on CLIP similarity and consolidates them into a caption. In contrast, our approach stochastically pairs images with text, a strategy we found to be more robust. Notably, our experiments showed that biasing sampling towards similar image and text pairs led to inferior results (see § 5.7). I2MVFormer uses a LLM to generate class descriptions based on texts provided by annotators and Wikipedia documents. The key differences between their work and ours lie in the use of human effort in their training data generation and starting from scratch resulting in much lower performance compared to ours. Finally, in contrast to both these works, we explore training using visual, habitat, and location information, as well as training on larger datasets such as NABirds and iNaturalist.", + "bbox": [ + 75, + 500, + 470, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Summary To the best of our knowledge, ours is the first method demonstrating that fine-tuning CLIP with class-specific descriptions obtained by querying LLMs improves the zero-shot performance in fine-grained domains. Our approach leverages LLMs to generate image-text data that are coarsely aligned, making it particularly effective for fine-grained categories. Moreover, unlike prior work [19, 20],", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "our method queries LLMs along various dimensions such as visual, taxonomy, habitat and geographic priors, and systematically evaluates their effectiveness.", + "bbox": [ + 496, + 90, + 890, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 150, + 591, + 166 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a dataset $\\mathcal{D} = \\{(x_i, y_i)\\}_{i=1}^n$ consisting of images $x_i \\in \\mathcal{X}$ and labels $y_i \\in \\mathcal{Y}$ . A VLM such as CLIP [29] consists of an image encoder $\\Theta$ and a text encoder $\\Phi$ such that $\\Theta(x) \\approx \\Phi(y)$ for images $x$ with label $y$ . We want to improve the zero-shot performance of CLIP on novel categories in fine-grained domains by fine-tuning the image and the text encoders. We do so either by splitting a dataset $\\mathcal{D}$ into $\\mathbf{K}_{\\mathrm{train}}$ training and $\\mathbf{K}_{\\mathrm{test}}$ testing classes, or train our model on large datasets such as iNaturalist and NABirds by excluding classes or domains overlapping with our test set. Our framework consists of: 1) generating textual descriptions given the class names by prompting LLMs in different ways ( $\\S 3.1$ ); 2) fine-tuning CLIP using these descriptions using our proposed approach ( $\\S 3.2$ ); and 3) evaluating the models on downstream tasks ( $\\S 3.3$ ). Fig. 3 provides an illustration of our method.", + "bbox": [ + 496, + 176, + 890, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dataset Generation", + "text_level": 1, + "bbox": [ + 500, + 428, + 684, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For each dataset we generate texts for every class which can be used to differentiate it from other classes in the domain using visual attributes. We query an LLM as:", + "bbox": [ + 496, + 452, + 890, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "What characteristics can be used to differentiate [class] from other [domain] based on just a photo? Provide an exhaustive list of all attributes that can be used to identify the [domain] uniquely. Texts should be of the form \"[domain] with [characteristic)\".", + "bbox": [ + 506, + 512, + 885, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here [class] is the class name for the $K$ classes in the dataset [domain]. Each domain is associated to different datasets, for example for the CUB200 dataset, [domain] is \"bird\" and for iNaturalist dataset it is \"organism\". Appending the domain [domain] is helpful because it provides context about the set of the other classes to distinguish from, and reduces confusion across similar class names in other domains. The LLM produces $l_{k}$ descriptions for category $k$ . We append \"a photo of [class]\" to the generated texts resulting in descriptions of the form \"a photo of a [class] [domain] with [characteristic]\" for each class (more details in the experiment section). This results in a set of descriptions $\\mathbf{Y}^{\\mathbf{k}}$ for each category.", + "bbox": [ + 496, + 590, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We also separately query about the habitat and geographic location of occurrence for the classes in CUB200, Flowers102, NABirds and iNaturalist datasets. For this purpose we use the prompt:", + "bbox": [ + 496, + 787, + 890, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Where can we find a [class]? Produce a list of habitat and geographic location information that can be used to identify the [domain].", + "bbox": [ + 508, + 861, + 885, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17544", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/93e7cddf8659b870237fbc7fc658de8b2e03868d53810de90da058be3d2e2f1f.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 493, + 313 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/adcad86024e407732ff4c509c37201d0e03e5b59639188badd61bdb94c0f4b2a.jpg", + "image_caption": [ + "(b)", + "Figure 3. Fine-tuning VLMs to improve zero-shot performance. a) Our framework for $①$ generating fine-grained attributes per class using LLMs, $②$ category-level fine-tuning of VLMs and $③$ evaluating on a series of challenging unseen scenarios. b) We show examples of texts produced in step $①$ ." + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 893, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We add the texts obtained to the category-level corpus $\\mathbf{Y}^{\\mathbf{k}}$ . The impact of these location-specific texts and the improvements offered are described in the results section. Examples of visual and habitat descriptions are in the Appendix. We determine the correctness of the texts produced for 4-6 classes of CUB, Aircraft and Cars by manual fact-checking texts with the help of online sources. We find that $96\\%$ (CUB), $90\\%$ (Aircraft) and $96\\%$ (Cars) are marked as correct by study participants (more details in Appendix). However, a challenge is that this manual vetting does not scale to large datasets, and we therefore rely on empirical results to support the utility of the generated text.", + "bbox": [ + 75, + 373, + 473, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. VLM Fine-Tuning", + "text_level": 1, + "bbox": [ + 76, + 588, + 254, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CLIP [29] is trained with image caption pairs. However, in our case we have a set of images $\\mathbf{X}^{\\mathbf{k}}$ and a set of texts $\\mathbf{Y}^{\\mathbf{k}}$ for classes $k\\in \\mathbf{K}_{\\mathrm{train}}$ in our training set. We address this by pairing every image with randomly sampled text from the corresponding category during training. However, we cannot directly use the batch-level cross-entropy loss used by CLIP which treats the paired text as positive and rest of the texts as negative. This is because the same batch can contain multiple pairs with images and texts belonging to the same category. Below we describe our modification of the objective function that addresses this.", + "bbox": [ + 75, + 619, + 468, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In each iteration of training we sample a batch of size $N$ consisting of $\\{(x_i, y_i)\\}_{i=1}^N$ pairs where both $x_i$ and $y_i$ is an image and text from the same class. Let the similarity score obtained using the forward pass of CLIP for image $x_i$ and text $y_j$ be $S_{ij}$ . Let $\\mathsf{c}(i)$ be the category of image-text pair $(x_i, y_i)$ . Let $G_i = \\{j \\mid \\mathsf{c}(j) = \\mathsf{c}(i)\\}$ denote the indices of pairs that belong to the same class as pair $(x_i, y_i)$ . Then the", + "bbox": [ + 76, + 794, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "loss function for images is:", + "bbox": [ + 500, + 373, + 681, + 388 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i m a g e}} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {1}{| G _ {i} |} \\sum_ {j \\in G _ {i}} \\log \\frac {\\exp \\left(S _ {i , j} / \\tau\\right)}{\\sum_ {r = 1} ^ {N} \\exp \\left(S _ {i , r} / \\tau\\right)} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 400, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and the corresponding one for texts is:", + "bbox": [ + 500, + 455, + 754, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t e x t} = - \\frac {1}{N} \\sum_ {j = 1} ^ {N} \\frac {1}{| G _ {j} |} \\sum_ {i \\in G _ {j}} \\log \\frac {\\exp \\left(S _ {i , j} / \\tau\\right)}{\\sum_ {r = 1} ^ {N} \\exp \\left(S _ {r , j} / \\tau\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 482, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is a learnable temperature parameter. The overall loss for fine-tuning is:", + "bbox": [ + 498, + 537, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f t} = \\mathcal {L} _ {i m a g e} + \\mathcal {L} _ {t e x t}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 580, + 772, + 597 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The objective aggregates the image text similarity across all image and text pairs from the same category within the batch. To avoid overfitting on small datasets we maintain momentum encoders whose weights $(\\theta_{EMA},\\phi_{EMA})$ are updated with the exponential moving average (EMA) of the weights of the encoders $(\\theta ,\\phi)$ which is trained using the objective $\\mathcal{L}_{ft}$ :", + "bbox": [ + 496, + 609, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\theta_ {E M A} \\leftarrow m \\theta_ {E M A} + (1 - m) \\theta_ {E} \\\\ \\phi_ {E M A} \\leftarrow m \\phi_ {E M A} + (1 - m) \\phi_ {E}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 728, + 810, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $m$ is a momentum parameter. All encoders are initialized using the pre-trained weights of CLIP.", + "bbox": [ + 498, + 775, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Evaluation for Zero-shot Classification", + "text_level": 1, + "bbox": [ + 500, + 816, + 833, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To evaluate a model on unseen classes we similarly query the LLM as described in §3.1 to obtain texts $\\mathbf{Y}^{\\mathbf{k}}$ , for $k \\in \\mathbf{K}_{\\mathrm{test}}$ . For any given image $x$ we can find the similarity score using a VLM for every text $y_{m}^{k}$ for $m \\in \\{1, \\dots, l_{k}\\}$", + "bbox": [ + 498, + 839, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17545", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and $k \\in \\mathbf{K}_{\\mathrm{test}}$ . Denote the similarity between image $x$ and text $y_{m}^{k}$ as $S_{m}^{k}$ . The predicted class is:", + "bbox": [ + 75, + 90, + 468, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {k} {\\operatorname {a r g m a x}} \\frac {1}{l _ {k}} \\sum_ {m = 1} ^ {l _ {k}} \\frac {\\exp \\left(S _ {m} ^ {k}\\right)}{\\sum_ {p \\in \\mathbf {K} _ {\\text {t e s t}}} \\sum_ {q = 1} ^ {l _ {p}} \\exp \\left(S _ {q} ^ {p}\\right)} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 143, + 468, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The score represents average similarity between an image and the texts corresponding to each class. Our initial experiments suggested that simple averaging of probabilities is more robust than alternatives such as the geometric mean.", + "bbox": [ + 75, + 196, + 468, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 268, + 209, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section we present the experimental details of our approach. We outline the datasets we use, the particulars of implementation for each part of the method as well as the details of the baselines we compare our method to.", + "bbox": [ + 75, + 294, + 468, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 364, + 179, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use a variety of fine-grained classification datasets including CUB [42] (200 classes), Flowers 102 [23] (102 classes), Stanford Cars [14] (196 classes), FGVC Aircrafts [18] (100 classes) and Food101 [1] (101 classes). We also apply our method on some coarser datasets including EuroSAT [10] (10 classes), ImageNet [31] (1000 classes), CalTech101 [5] (100 classes), DTD [4] (47 classes), Oxford Pets [26] (37 classes), Sun397 [44] (397 classes) and UCF101 [36] (101 classes). For all these datasets, we use the first half of the classes (ordered by ids of the original dataset) for training and second half for zero-shot testing.", + "bbox": [ + 75, + 387, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also use NABirds [39] which contains 404 bird classes at species level. We remove the overlapping classes of the CUB testing set from these to obtain 331 training classes. Along with train and test classes being different, this setting also represents a distribution shift in the images of training and testing as images for CUB and NABirds have been obtained in different manners.", + "bbox": [ + 75, + 551, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "iNaturalist [41] 2021 is another dataset we utilize to illustrate that our method scales and generalizes. iNaturalist contains 10k classes belonging to 11 general categories (such as birds, plants, fishes). First, in a similar setting to NABirds we remove overlapping test classes of CUB to train a model for testing on CUB. Secondly, we remove all bird classes from iNat and train a model on the remaining classes to test on CUB. We follow similar settings for testing on Flowers 102. Even in these challenging circumstances our method offers improvement over the baselines(§ 5.3).", + "bbox": [ + 75, + 657, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For CUB, NABirds and iNaturalist we also have taxonomy information including family, order and scientific name. We also append separate texts containing these to the category-wise text corpus to show improvements (Tab. 3).", + "bbox": [ + 75, + 810, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NeWT [40] provides a benchmark for a set of 164 complex binary classification tasks in the natural world that ex", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tend beyond species classification. These tasks include determining 1) appearance 2) behavior, 3) context, 4) counting and 5) gestalt. NeWT contains 36k images with 200-400 images per task. We randomly select 50 of the 164 tasks to evaluate our trained model. We manually associate two texts for each task, positive and negative. For example, \"a photo of a raptor bird which is not on a utility pole\" and \"a photo of a raptor bird which is on a utility pole\". We show improvements over CLIP (§ 5.5). All details of texts used as well as categories selected are in the Appendix.", + "bbox": [ + 496, + 90, + 890, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 256, + 718, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For generating category-level texts for training, we utilize the \"gpt-4-0613\" API. We set the temperature parameter as 0 so that texts generated are deterministic.", + "bbox": [ + 496, + 282, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For all queries concerning the classes of iNaturalist (both visual and location) we also append the type of organism as well as it's scientific name in the question. For example, for the class \"Bay Laurel\" the query for location information is", + "bbox": [ + 496, + 328, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where can we find a Bay Laurel, a type of plant with scientific name Laurus nobilis? Produce a list of habitat and geographic location information that can be used to identify the plant.", + "bbox": [ + 506, + 409, + 885, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This is required because there exist organisms with the same common name but different domains. Also, we need to append the scientific name as otherwise GPT4 does not recognise the organism in many cases. We provide more details in Appendix.", + "bbox": [ + 496, + 469, + 890, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additionally, we experiment with using taxonomy information for training and testing on datasets where it is available (Tab. 3). We form the following texts", + "bbox": [ + 496, + 547, + 890, + 592 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. a photo of [class] [domain], with scientific name [s_name]", + "2. a photo of [class] [domain], with family name [family]", + "3. a photo of [class] [domain], of the order [order]" + ], + "bbox": [ + 509, + 613, + 880, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While fine-tuning using the texts obtained from an LLM, we train for only 15 epochs on each dataset. On iNaturalist, we train for only 5 epochs. We find hyperparameters by splitting the train classes into two equal parts, training on the first half, and validating on the second. We then fix the best hyperparameters found and train on all train classes.", + "bbox": [ + 496, + 672, + 890, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The CLIP architecture consists of an image encoder and a text encoder. Both contain transformers followed by a linear projection layer at the end. We use different learning rate and weight decay for the projection layers compared to rest of the encoders. The temperature parameter $\\tau$ in our model (§ 3.2) is trainable. We provide the details of the initialization of $\\tau$ , the momentum parameter for the EMA encoder as well as learning rates and weight decays of every parameter for all datasets in the Appendix.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17546", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/30239383a99ad6a3492f40f4fa2585aabe6977e35e17c334f09d65a2a6b95f31.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsCUBStanford CarsFGVC AircractsFlowers 102Food 101
CLIP50.5469.7229.2771.7888.32
CLIP + A50.7169.4730.3575.3790.08
CLIPFT50.81 ± 0.0469.61 ± 0.0731.10 ± 0.0273.68 ± 0.0088.32 ± 0.00
CLIPFT + A53.34 ± 0.0871.63 ± 0.0636.41 ± 0.0277.05 ± 0.0093.71 ± 0.01
", + "bbox": [ + 156, + 87, + 812, + 167 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f68a5c8624eeb066c7248d11631378b106cf4cfa39680193b882cfec9410067d.jpg", + "table_caption": [ + "Table 1. Comparison with CLIP ViT-B/32 on zero-shot performance on fine-grained domains. We compare our method $\\mathrm{CLIP^{FT}} + \\mathrm{A}$ to the baselines defined in § 4.3. We significantly improve over baseline CLIP evaluated with both \"a photo of a [class] [domain]\" and LLM attributes. We also fine-tune CLIP with only \"a photo of a [class] [domain]\" text and compare with our method to show that our improvements are not due to seeing domain-specific images but also by learning correlations between images and fine-grained attributes." + ], + "table_footnote": [], + "table_body": "
Stanford CarsFGVC AircraticsFlowers 102EuroSATFood 101ImageNet
CLIP74.9436.4777.0564.0592.4967.41
CLIP + A73.8336.4780.8471.5193.7269.74
CLIP-A-self [19]72.9033.0075.3070.5091.2068.30
CLIPFT + A75.7840.7581.2681.8295.0871.87
", + "bbox": [ + 125, + 229, + 844, + 308 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5005ce144f228fad5efc7040ffcd802b0469031426fdc884ff8a4bede794d813.jpg", + "table_caption": [ + "Table 2. Comparison to prior work using ViT B/16 architecture on zero-shot classification. We show that across a variety of datasets from finer to coarser domains we considerably boost performance over baselines. Here we train using only 16 images per class and test on unseen classes for fair comparison to CLIP-A-self. We do not compare on CUB dataset as CLIP-A-self uses a 3:1 split on CUB, whereas we use 1:1 across all datasets." + ], + "table_footnote": [], + "table_body": "
TextsCUBFlowers 102
Visual53.3477.05
Taxonomy53.07-
Habitat53.6976.00
Vis. + Hab.54.0177.22
Vis. + Tax. + Hab.54.23-
", + "bbox": [ + 125, + 359, + 423, + 452 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ba066b2daf8565ea2051938465774a8f41b218700504c569bb4eafeb22fcaa67.jpg", + "table_caption": [ + "Table 3. Evaluating $\\mathbf{CLIP^{FT}} + \\mathbf{A}$ using different types of text. We query LLMs to produce visual (vis.) and habitat (hab.) information separately and use taxonomy (tax.) information available with dataset. We train with the type of text specified in each row and test with the same type. Using habitat information works slightly better than using visual information for CUB. All three types of texts are complementary." + ], + "table_footnote": [], + "table_body": "
Train SetCUBFlowers 102
NABirds\\overlap55.32-
iNat\\overlap54.5877.05
iNat\\Birds53.89-
iNat\\Plants-76.63
", + "bbox": [ + 125, + 541, + 419, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Baselines", + "text_level": 1, + "bbox": [ + 76, + 694, + 184, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we discuss the various methods for which we compare zero-shot classification accuracy.", + "bbox": [ + 75, + 718, + 467, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CLIP refers to pre-trained CLIP tested with \"a photo of a [class] [domain]\" texts like the original paper.", + "bbox": [ + 76, + 750, + 467, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathbf{CLIP} + \\mathbf{A}$ is evaluating pre-trained CLIP with attributes obtained from LLMs as outlined in § 3.3.", + "bbox": [ + 75, + 779, + 467, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CLIPFT involves fine-tuning CLIP on training classes using \"a photo of [class] [domain]\" texts and evaluating on test classes using \"a photo of [class] [domain]\" texts.", + "bbox": [ + 75, + 809, + 467, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathbf{CLIP}^{\\mathrm{FT}} + \\mathbf{A}$ is our method where we fine-tune CLIP (§ 3.2) using attributes obtained from a LLM (§ 3.1) for training classes and evaluate using LLM attributes of testing classes", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bb664dfd667cbb410dacfdc9f1f3d289e15bc7a3f5f68cc9bf12467e2fe64338.jpg", + "table_caption": [ + "Table 4. Evaluating domain transfer performance. Our method offers substantial gain over baseline CLIP (Tab. 1) even when trained on external datasets. Performance boost is competitive even when removing all bird or plant classes from iNat to test on CUB and Flowers respectively." + ], + "table_footnote": [], + "table_body": "
Testing TextsCLIP + ACLIPFT + A
[class] [domain]50.5452.29
GPT 4 Vis.50.7153.34
GPT 3 Vis.51.0853.35
LLaMA Vis.50.1052.52
Ground Truth Vis.52.5353.99
GPT 4 Vis. + Tax. + Hab.52.8354.23
GPT 3 Vis. + Tax. + Hab.52.6353.58
LLaMA Vis. + Tax. + Hab.50.8552.64
", + "bbox": [ + 500, + 359, + 885, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Evaluating model trained using GPT4 with texts obtained from other models. Our model consistently improves over pre-trained CLIP when evaluated with texts obtained from different LLM models (GPT3.5 and LLaMA2-7B) as well as GT aggregated captions and \"a photo of a [class] [domain]\".", + "bbox": [ + 496, + 510, + 890, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "at test time as described in $\\S 3.3$", + "bbox": [ + 498, + 589, + 718, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CLIP-A-self [19] is prior work which uses text obtained from GPT to train an adapter network attached after the text and image encoders of CLIP. For comparing with this, we use the numbers stated by them under their training and evaluation scheme. We test our model on the same classes as them to show improvement.", + "bbox": [ + 496, + 604, + 890, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 500, + 708, + 586, + 723 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare our method to baselines and evaluate it under various settings. We discuss our performance improvements over various datasets and architectures. We show that for natural domains using taxonomy and habitat information offers improvements with habitat information especially being a strong factor. Our model scales across architectures and needs only a few epochs of training. We further show that our method performs better than baseline CLIP even under more difficult evaluation settings such as 1) using texts from different LLM models during testing and training; 2) training a model in a do", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17547", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "main very different from testing domain, and 3) evaluating on tasks other than identifying categories at test time. Additionally, we discuss other training strategies for category-level fine-tuning and how they perform.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Comparison with Baselines", + "text_level": 1, + "bbox": [ + 76, + 161, + 321, + 176 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 1 compares our method to three baselines CLIP, $\\mathrm{CLIP} + \\mathrm{A}$ and $\\mathrm{CLIP^{FT}}$ , all evaluated on unseen classes. Here we use the ViT B/32 architecture for all methods. Our method offers considerable improvements over pre-trained CLIP when using \"a photo of a [class] [domain]\" text and when using GPT generated text. In difficult fine-grained domains such as CUB, Stanford Cars and FGVC Aircrafts pre-trained CLIP does not utilize text attributes generated by GPT resulting in negligible improvement (decrease on Stanford Cars) compared to \"a photo of a [class] [domain]\" (see $\\mathrm{CLIP} + \\mathrm{A}$ vs CLIP). This motivates the need to fine-tune using these attributes, resulting in significant improvement across all datasets. We also compare to fine-tuning CLIP with \"a photo of a [class] [domain]\" texts ( $\\mathrm{CLIP^{FT}}$ ) to show that the improvement our method achieves is not due to just being trained on images of concerned domain.", + "bbox": [ + 75, + 184, + 468, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method to previous work CLIP-A-self [19] in Tab. 2. We follow [19] and use the ViT B/16 architecture and only 16 images per class for training. Again we evaluate on unseen classes. Our method outperforms CLIP-A-self significantly across all datasets. Also, our method offers substantial improvement over CLIP, showing that it scales across architectures. We discuss why CLIP-A-self underperforms in detail in the Appendix. We also show results on the 14 datasets benchmark in Appendix.", + "bbox": [ + 75, + 441, + 468, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Using more than just Visual Information", + "text_level": 1, + "bbox": [ + 76, + 587, + 423, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We explore using information other than visual attributes for natural domains such as birds and flowers. For humans identifying a bird in an image it is crucial to know where the image was taken, because that reveals habitat and location information. We therefore query GPT for an organism's habitat and geographic range. In Tab. 3 we show that for CUB using only habitat information performs better than using only visual information. A reason for this is that habitat information describes the background of the images of birds, which is helping to differentiate between categories. We also show that combining visual + taxonomy + habitat information for CUB and visual + habitat information for Flowers102 offers best improvement.", + "bbox": [ + 75, + 611, + 468, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Training on External Domains", + "text_level": 1, + "bbox": [ + 76, + 816, + 346, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now evaluate under more difficult settings. We train and test on different datasets, always removing any overlapping classes. For training on iNat and NABirds we use all visual + taxonomy + habitat information. While testing", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "on CUB we use visual + taxonomy + habitat. For Flowers 102 we use visual + habitat information. Tab. 4 we show the accuracy on CUB test classes improves considerably when training using NABirds and iNat even though the images of these datasets have a distribution shift w.r.t. CUB. More strikingly, we show that even when we remove all bird classes from iNat we still offer improvement on CUB test classes compared to CLIP + A (52.83 → 53.89). Similarly when we remove all plant classes from iNat, we still get improvement on Flowers 102 test set. This proves that our model is also able to generalize well. It is learning to associate fine-grained attributes to images irrespective of the domain differences in training and testing.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Using Novel Texts during Test Time", + "text_level": 1, + "bbox": [ + 498, + 297, + 808, + 313 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate how our model would perform in the absence of the LLM used to generate training texts, during test time (Tab 5). We use GPT3.5 turbo (0613) and LLaMA2-7B [38] for generating visual and habitat texts. We show that our method consistently improves performance over pre-trained CLIP for all types of texts explored. Please refer to Appendix for examples of texts produced. Our model also improves performance over pre-trained CLIP while using \"a photo of a [class] [domain]\" texts.", + "bbox": [ + 496, + 320, + 890, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Reed et al. [30] present a dataset of human-labelled captions per image for the CUB dataset. We use these ground truth texts at test time to evaluate our model. The dataset contains 10 captions for every image, which are all visual attributes of the bird in the image. Since many attributes in the captions are repeated for each image as well as across images of the same class, and to limit the size of the text corpus, we randomly select one caption per image of a given class and aggregate them to form a category corpus. In Tab. 5 last row, we notice that CLIP does better using these image-level GT texts compared to using GPT4 Visual texts which were category-level (row 2). However, our method still outperforms showing that it is able learn meaningful attributes through noisy labels.", + "bbox": [ + 496, + 458, + 890, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Evaluation on Novel Tasks", + "text_level": 1, + "bbox": [ + 500, + 678, + 738, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use the NeWT [40] benchmark to evaluate on tasks beyond categorization. These include identifying age, attribute, health, photo quality, species, context and behavior. We evaluate the model and baseline CLIP using average Mean Average Precision (MAP) across tasks. Our model trained on iNaturalist using visual + taxonomy + location information outperforms baseline CLIP: 60.25 vs 61.90 MAP $\\rightarrow$ $4.1\\%$ relative error reduction. We present all tasks and texts we use to evaluate as well as MAP per task in the Appendix. Below is an example prediction:", + "bbox": [ + 496, + 702, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1LLaMA model does not always produce texts in the specified format and thus needs post-processing. The texts formed finally are considerably different grammatically from the sentences our model has been trained on.", + "bbox": [ + 498, + 862, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17548", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/824569385b38f230282dd66a3506485c13201441cc831d2ce6f598b83468a218.jpg", + "image_caption": [ + "a photo of a raptor bird which is not on a utility pole" + ], + "image_footnote": [], + "bbox": [ + 80, + 92, + 187, + 157 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Probability: 0.38", + "bbox": [ + 230, + 138, + 316, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a photo of a raptor bird which is on a utility pole", + "bbox": [ + 361, + 95, + 465, + 125 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Probability: 0.62", + "bbox": [ + 370, + 138, + 455, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Resource Requirements", + "text_level": 1, + "bbox": [ + 76, + 185, + 295, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We fine-tune our model using a 1024 batch size on a single NVIDIA A100 80GB. We need to train only for a maximum of 15 epochs. For smaller datasets such as CUB, FGVC Aircraft, and Stanford Cars, this takes less than 5 minutes. For iNaturalist, which is a large dataset, we train only for 5 epochs, taking about 4 hours.", + "bbox": [ + 75, + 209, + 468, + 300 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The cost of using the GPT-4 API to query text descriptions for a dataset with 100-200 classes (such as CUB) is about \\(1-\\)5. This is low because it scales with the number of categories and not the number of images. Generating captions per image is both time-consuming and expensive; an estimate for doing this for the CUB dataset using the GPT-4 Vision API is more than \\)100. This cost scales significantly for larger datasets with more images.", + "bbox": [ + 75, + 301, + 468, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.7. Alternate Training Strategies", + "text_level": 1, + "bbox": [ + 76, + 434, + 336, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here we discuss other training strategies for improving VLMs using category-level training data. Our simple finetuning strategy of stochastically pairing images with texts within categories is simple, efficient, and offers similar improvements compared to more complex approaches.", + "bbox": [ + 75, + 459, + 468, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Firstly, since we pair a given image of a category to every text of that category, we might be pairing texts that describe attributes that are not visible. For CUB dataset we have the ground truth visibility annotations of various bird parts, which we use to ignore texts that are occluded for each image. This strategy offers improvement to our scores (54.23 $\\rightarrow$ 54.47). However, this depends on visibility information that is time-consuming to generate.", + "bbox": [ + 75, + 536, + 468, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The next step is to assume that pre-trained CLIP itself is able to correctly identify if a part is visible. Assuming this we mask texts during training time based on CLIP predictions by doing 1) a forward pass for a image and all texts of the category to find the texts above a threshold that can be paired with the image, 2) max pooling at instance level for images and texts. We find that none of these strategies offer any improvement and that pairing images with low scoring texts also (like in our method) is improving performance because CLIP does not accurately identify which fine-grained attributes correctly correspond to given image.", + "bbox": [ + 75, + 657, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also try well-known semi-supervised learning strategies such as FixMatch [35] and knowledge distillation [3]. We find that these offer small $(< 0.2\\%)$ to no improvements over our method. Please see the Appendix for details of implementation of all the methods and accuracies.", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.8. Performance of image captioning models.", + "text_level": 1, + "bbox": [ + 500, + 90, + 852, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We test the recently released GPT4 Vision API for checking quality of image captions obtained. Even though it performs better than previous captioning models such as LLaVA [17] and BLIP2 [16], we find that the captions obtained are general descriptions without fine-grained details. The captions are specific to the image but do not describe information helpful to identify the category. An example is:", + "bbox": [ + 496, + 113, + 890, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/287811afec208d567aa8977cd83912572cbc854d8329aca6c031dec183f65a75.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 231, + 575, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A slender, streaked brown songbird with keen eyes and a pointed beak perches atop a weathered wooden fence post amidst a backdrop of natural grassland under a clear blue sky.", + "bbox": [ + 581, + 233, + 887, + 285 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For this image of a Vesper Sparrow, GPT4 provides a general description of the bird and suggests the presence of clear blue sky which is not visible in the image. We provide more detail including prompt and examples in Appendix.", + "bbox": [ + 496, + 305, + 890, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitation", + "text_level": 1, + "bbox": [ + 500, + 377, + 612, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Since our method is trained on texts generated by LLMs, it is important to verify the correctness of these texts to assess the level of noise in our training dataset. As described in § 3.1, we conduct spot checks across some categories on our evaluation sets. However, for our larger training datasets, vetting becomes impractical. Improved performance on human-generated texts on CUB, as well as the vetted evaluation sets, supports our model's ability to learn meaningful information from somewhat noisy training data.", + "bbox": [ + 496, + 402, + 890, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 550, + 617, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a method to improve the zero-shot performance of VLMs using attributes generated by LLMs on fine-grained domains. Our evaluation strategy involves testing the trained model on unseen classes, texts generated from different LLMs as well as humans, dissimilar domains, and novel tasks. We show that fine-tuning CLIP using category-level descriptions from GPT4 significantly improves performance compared to baselines in this challenging downstream evaluation framework. Our findings suggest that habitat and geographic priors are equally effective and complementary to visual information for zero-shot classification in natural domains. We publicly release our benchmark across all 14 datasets.", + "bbox": [ + 496, + 575, + 890, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 784, + 686, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank Aaron Sun, Gustavo Perez, Rangel Daroya, and Mustafa Chasmai for participating in the verification of attributes generated by GPT4. The project is supported in part by NSF Grants #2329927 and #1749833. Our experiments were performed on the GPU cluster funded by the Mass. Technology Collaborative.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17549", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101 – mining discriminative components with random forests. 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Domain prompt learning for efficiently adapting" + ], + "bbox": [ + 503, + 92, + 890, + 901 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17551", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "clip to unseen domains. arXiv preprint arXiv:2111.12853, 2021.3", + "[49] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Conditional prompt learning for vision-language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16816-16825, 2022. 2", + "[50] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. International Journal of Computer Vision, 130(9):2337-2348, 2022. 2", + "[51] Beier Zhu, Yulei Niu, Yucheng Han, Yue Wu, and Hanwang Zhang. Prompt-aligned gradient for prompt tuning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15659-15669, 2023. 2" + ], + "bbox": [ + 78, + 90, + 467, + 303 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17552", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_model.json b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..77d326a8f7cb14f93de2c34a276438e349c42d7b --- /dev/null +++ b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_model.json @@ -0,0 +1,2345 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.131, + 0.877, + 0.155 + ], + "angle": 0, + "content": "Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions" + }, + { + "type": "text", + "bbox": [ + 0.259, + 0.181, + 0.711, + 0.234 + ], + "angle": 0, + "content": "Oindrila Saha Grant Van Horn Subhransu Maji University of Massachusetts, Amherst {osaha, gvanhorn, smaji}@umass.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.742 + ], + "angle": 0, + "content": "The zero-shot performance of existing vision-language models (VLMs) such as CLIP [29] is limited by the availability of large-scale, aligned image and text datasets in specific domains. In this work, we leverage two complementary sources of information—descriptions of categories generated by large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across fine-grained domains. On the technical side, we develop methods to train VLMs with this \"bag-level\" image-text supervision. We find that simply using these attributes at test-time does not improve performance, but our training strategy, for example, on the iNaturalist [41] dataset, leads to an average improvement of \\(4 - 5\\%\\) in zero-shot classification accuracy for novel categories of birds [42] and flowers [23]. Similar improvements are observed in domains where a subset of the categories was used to fine-tune the model. By prompting LLMs in various ways, we generate descriptions that capture visual appearance, habitat, and geographic regions and pair them with existing attributes such as the taxonomic structure of the categories. We systematically evaluate their ability to improve zero-shot categorization in natural domains. Our findings suggest that geographic priors can be just as effective and are complementary to visual appearance. Our method also outperforms prior work on prompt-based tuning of VLMs. We release the benchmark, consisting of 14 datasets at https://github.com/cvl-umass/AdaptCLIPZS, which will contribute to future research in zero-shot recognition." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.769, + 0.21, + 0.785 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Recent improvements in zero-shot classification have been due, in part, to success in training VLMs at scale. Models such as CLIP [29], ALIGN [11], and BLIP [16] use massive datasets of image and text pairs to learn a common embedding between visual and natural language domains. However, we find existing VLMs show poor performance in encoding visual attributes in fine-grained domains, beyond" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.269, + 0.891, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.558 + ], + "angle": 0, + "content": "Figure 1. Motivation. Collecting image captions in fine-grained domains requires expertise (top row), but LLMs can generate structured (e.g., shape or appearance) and accurate descriptions of categories at both the coarse (e.g., birds) and fine-grained level (e.g., Vesper Sparrow). Rich descriptions of fine-grained categories can be paired with existing datasets, such as iNaturalist [41] and NABirds [39] to generate coarsely-aligned image-text datasets for fine-tuning VLMs. This improves their zero-shot performance on a range of benchmarks, generalizing to novel categories and tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.893, + 0.748 + ], + "angle": 0, + "content": "simply recognizing the name of the category. For example, we observe concatenating visual attribute descriptions to the species name for the bird species in the CUB [42] dataset improves the zero-shot classification from \\(50.5\\%\\) to only \\(50.7\\%\\), while for Cars [14], the performance even drops slightly (see Tab. 1). Although the datasets on which VLMs are trained are extensive, they often lack the details that experts may require for fine-grained categorization. At the same time, collecting large-scale image-caption datasets in these domains requires significant effort, making training similar models challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this work, we leverage two complementary sources of information—large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across a variety of fine-grained domains. Concretely, we generate large datasets of images aligned with text by pairing images within a category with descriptions of that category generated by LLMs as seen in Fig. 1. We find this approach works well, as images within a fine-grained domain share many attributes, unlike in coarse categories with" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17542" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "larger intra-category variation. At the same time, we find that LLMs are capable of accurately describing appearance, habitat, and other properties for a wide range of categories, allowing us to systematically generate datasets in a scalable manner. In other words, fine-grained labels allow us to bridge the gap between image-level captions required for VLM training, and general information about visual categories contained in LLMs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.439 + ], + "angle": 0, + "content": "On the technical side, we develop methods to train VLMs with \"bag-level\" supervision. In our dataset a set of images are grouped with a set of descriptions and lack the image-text correspondences. Some of the descriptions may not apply to an image (e.g., the part may be occluded). However, we find that training by stochastically pairing the images and text within a category, followed by a category-level contrastive loss similar to CLIP objective offers robust improvements in performance. Adapting semi-supervised learning approaches such as FixMatch [35] or Knowledge distillation [3] results in minor improvements (\\(\\S 5.7\\)). A detailed investigation of the image-text association within a category suggests the model is able to correctly associate the visual attributes with the corresponding text even they are paired randomly during training (Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.473, + 0.758 + ], + "angle": 0, + "content": "We systematically evaluate the effectiveness of our method by assessing the zero-shot classification performance on novel classes. We find that simply using these attributes of novel classes generated by LLMs does not improve performance when using CLIP (Tab. 1). However, our training strategy leads to an average improvement of \\(4 - 5\\%\\) in accuracy across 12 datasets, and outperforms baselines (Tab. 2). For natural domains (e.g., iNaturalist and NABirds), we prompt LLMs in various ways to generate descriptions that capture visual appearance, habitat, and geographic regions, and pair them with existing attributes within the dataset, such as taxonomic structure. Our results indicate that geographic priors are equally effective and complementary to visual appearance cues (see Tab. 3). Training on iNaturalist without any bird classes improves the performance of CLIP on CUB by more than \\(3\\%\\), and we observe similar improvements when evaluating across other domains (see Tab. 4). Improvements are consistent across text generated by different LLMs, as well as by humans (see Tab. 5). Our model also results in relative error reduction of \\(4.1\\%\\) over CLIP on the challenging NeWT dataset [40]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.22, + 0.785 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Zero-shot Image Classification using VLMs. Vision Language models (VLMs) [6, 11, 29, 33, 45] learn to associate images with their corresponding text captions. Learning a shared embedding makes them perform exceptionally well in zero-shot classification tasks when paired with an appropriate text such as the class name during test time. FLAVA [33] learns using paired as well as unpaired im" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.294, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Figure 2. Visualizing image-text similarity. All images within a category are sorted in order of similarity to a given text predicted by CLIP and our fine-tuned \\(\\mathrm{CLIP^{FT} + A}\\). For example, our method identifies birds which show olive-green tint on their back as the top images, whereas CLIP selects birds with visibly brown upperparts or occluded back. The image with lowest similarity which has the occluded back remains the same for both models, showing our model does not learn incorrect attribute associations even though we stochastically pair every attribute with every image during training. On the aircraft example our model predicts higher similarity to images with prominently visible fuselage. CLIP identifies the least similar image as one in which fuselage is visible, but ours chooses one where aircrafts are too far to make out the shape of fuselage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.893, + 0.687 + ], + "angle": 0, + "content": "ages and texts using different losses for multimodal and unimodal understanding. ALIGN [11] uses a large number of noisy image-text data by obtaining alt-texts for images and trains using a contrastive loss. CLIP [29] is trained on a smaller and cleaner dataset of image-text pairs using a similar objective function. It employs a vision model and a language model to learn joint embeddings of images and text. While training, it maximizes the similarity between related image-text pairs and minimizes similarity between unrelated pairs. At test time the similarity over captions such “a photo of a [class name]” over all classes in the domain for each image is found. The image is classified to the class with the caption with highest probability. The original paper shows that manual prompt tuning can boost zero-shot classification accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Generating Better Prompts. Prior work on prompt tuning [7, 12, 13, 32, 51] has focused on improving the text descriptions of classes. For example, CoOp [50] appends learnable context vectors to the class name texts to improve classification. CoCoOp [49] and related methods have also explored prompting the vision encoder simultaneously. While prompt tuning has proven useful for adapting models to a set of \"base categories\", its performance on novel categories still falls short of the CLIP baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Another line of research aims at querying LLMs to generate prompts or attributes of categories. CHiLS [24] refines classes based on GPT descriptions (e.g., taxonomic structure) and maps the image to one of the subcategories to improve classification. We also explore the ability to" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17543" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "learn taxonomy-based attributes in our work. Menon et al. [20] and CuPL [28] append class-specific attributes obtained from GPT [2] to simple prompts, e.g. \"a photo of a [class]\" to improve zero-shot performance at test-time, similar to our approach. However, we find that CLIP struggles to recognize nuanced attributes in fine-grained domains where we observe little to no improvement in classification performance, motivating the need for fine-tuning VLMs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.471, + 0.365 + ], + "angle": 0, + "content": "Fine-tuning VLMs. Most work on fine-tuning VLMs has focused on parameter efficient updates using lightweight adapters [8,19,25,27,46,47] for improving few-shot classification. For example, CLIP adapter [8] trains a few learnable layers on top of the encoders, while Maniparambil et al. [19] query LLMs for class-wise descriptions for tuning an external adapter network. Their work improves over CoCoOp and CLIP adapter for unseen classes, however, as before, most approaches show no improvement over CLIP, especially on novel classes in fine-grained datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.501 + ], + "angle": 0, + "content": "Another line of research [9, 34, 37, 43, 48] involves fine-tuning CLIP for robustness to domain shifts. For instance, WiSE-FT [43] utilizes weight-space ensembling to improve performance on a sketch version of ImageNet. Similarly, LaFTer [21] employs fine-tuning both the image and text encoders using unpaired images and texts obtained by querying LLMs. These techniques focus on adapting to a target distribution, such as a specific set of test images or classes, rather than on generalizing to novel classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.773 + ], + "angle": 0, + "content": "Two works similar to ours, GIST [15] and I2MVFormer [22], also utilize GPT to generate category-specific texts for fine-grained domains. GIST pairs each image with the \\( n \\) most similar texts within the category based on CLIP similarity and consolidates them into a caption. In contrast, our approach stochastically pairs images with text, a strategy we found to be more robust. Notably, our experiments showed that biasing sampling towards similar image and text pairs led to inferior results (see § 5.7). I2MVFormer uses a LLM to generate class descriptions based on texts provided by annotators and Wikipedia documents. The key differences between their work and ours lie in the use of human effort in their training data generation and starting from scratch resulting in much lower performance compared to ours. Finally, in contrast to both these works, we explore training using visual, habitat, and location information, as well as training on larger datasets such as NABirds and iNaturalist." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Summary To the best of our knowledge, ours is the first method demonstrating that fine-tuning CLIP with class-specific descriptions obtained by querying LLMs improves the zero-shot performance in fine-grained domains. Our approach leverages LLMs to generate image-text data that are coarsely aligned, making it particularly effective for fine-grained categories. Moreover, unlike prior work [19, 20]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "our method queries LLMs along various dimensions such as visual, taxonomy, habitat and geographic priors, and systematically evaluates their effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.151, + 0.593, + 0.167 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.177, + 0.892, + 0.419 + ], + "angle": 0, + "content": "Consider a dataset \\(\\mathcal{D} = \\{(x_i, y_i)\\}_{i=1}^n\\) consisting of images \\(x_i \\in \\mathcal{X}\\) and labels \\(y_i \\in \\mathcal{Y}\\). A VLM such as CLIP [29] consists of an image encoder \\(\\Theta\\) and a text encoder \\(\\Phi\\) such that \\(\\Theta(x) \\approx \\Phi(y)\\) for images \\(x\\) with label \\(y\\). We want to improve the zero-shot performance of CLIP on novel categories in fine-grained domains by fine-tuning the image and the text encoders. We do so either by splitting a dataset \\(\\mathcal{D}\\) into \\(\\mathbf{K}_{\\mathrm{train}}\\) training and \\(\\mathbf{K}_{\\mathrm{test}}\\) testing classes, or train our model on large datasets such as iNaturalist and NABirds by excluding classes or domains overlapping with our test set. Our framework consists of: 1) generating textual descriptions given the class names by prompting LLMs in different ways (\\(\\S 3.1\\)); 2) fine-tuning CLIP using these descriptions using our proposed approach (\\(\\S 3.2\\)); and 3) evaluating the models on downstream tasks (\\(\\S 3.3\\)). Fig. 3 provides an illustration of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.429, + 0.686, + 0.443 + ], + "angle": 0, + "content": "3.1. Dataset Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.499 + ], + "angle": 0, + "content": "For each dataset we generate texts for every class which can be used to differentiate it from other classes in the domain using visual attributes. We query an LLM as:" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.513, + 0.887, + 0.577 + ], + "angle": 0, + "content": "What characteristics can be used to differentiate [class] from other [domain] based on just a photo? Provide an exhaustive list of all attributes that can be used to identify the [domain] uniquely. Texts should be of the form \"[domain] with [characteristic)\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.788 + ], + "angle": 0, + "content": "Here [class] is the class name for the \\(K\\) classes in the dataset [domain]. Each domain is associated to different datasets, for example for the CUB200 dataset, [domain] is \"bird\" and for iNaturalist dataset it is \"organism\". Appending the domain [domain] is helpful because it provides context about the set of the other classes to distinguish from, and reduces confusion across similar class names in other domains. The LLM produces \\(l_{k}\\) descriptions for category \\(k\\). We append \"a photo of [class]\" to the generated texts resulting in descriptions of the form \"a photo of a [class] [domain] with [characteristic]\" for each class (more details in the experiment section). This results in a set of descriptions \\(\\mathbf{Y}^{\\mathbf{k}}\\) for each category." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.788, + 0.892, + 0.849 + ], + "angle": 0, + "content": "We also separately query about the habitat and geographic location of occurrence for the classes in CUB200, Flowers102, NABirds and iNaturalist datasets. For this purpose we use the prompt:" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.862, + 0.887, + 0.903 + ], + "angle": 0, + "content": "Where can we find a [class]? Produce a list of habitat and geographic location information that can be used to identify the [domain]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17544" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.495, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.347, + 0.325, + 0.366, + 0.338 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.895, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.325, + 0.765, + 0.337 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.34, + 0.892, + 0.366 + ], + "angle": 0, + "content": "Figure 3. Fine-tuning VLMs to improve zero-shot performance. a) Our framework for \\(①\\) generating fine-grained attributes per class using LLMs, \\(②\\) category-level fine-tuning of VLMs and \\(③\\) evaluating on a series of challenging unseen scenarios. b) We show examples of texts produced in step \\(①\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.474, + 0.555 + ], + "angle": 0, + "content": "We add the texts obtained to the category-level corpus \\(\\mathbf{Y}^{\\mathbf{k}}\\). The impact of these location-specific texts and the improvements offered are described in the results section. Examples of visual and habitat descriptions are in the Appendix. We determine the correctness of the texts produced for 4-6 classes of CUB, Aircraft and Cars by manual fact-checking texts with the help of online sources. We find that \\(96\\%\\) (CUB), \\(90\\%\\) (Aircraft) and \\(96\\%\\) (Cars) are marked as correct by study participants (more details in Appendix). However, a challenge is that this manual vetting does not scale to large datasets, and we therefore rely on empirical results to support the utility of the generated text." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.589, + 0.255, + 0.606 + ], + "angle": 0, + "content": "3.2. VLM Fine-Tuning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.47, + 0.786 + ], + "angle": 0, + "content": "CLIP [29] is trained with image caption pairs. However, in our case we have a set of images \\(\\mathbf{X}^{\\mathbf{k}}\\) and a set of texts \\(\\mathbf{Y}^{\\mathbf{k}}\\) for classes \\(k\\in \\mathbf{K}_{\\mathrm{train}}\\) in our training set. We address this by pairing every image with randomly sampled text from the corresponding category during training. However, we cannot directly use the batch-level cross-entropy loss used by CLIP which treats the paired text as positive and rest of the texts as negative. This is because the same batch can contain multiple pairs with images and texts belonging to the same category. Below we describe our modification of the objective function that addresses this." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In each iteration of training we sample a batch of size \\(N\\) consisting of \\(\\{(x_i, y_i)\\}_{i=1}^N\\) pairs where both \\(x_i\\) and \\(y_i\\) is an image and text from the same class. Let the similarity score obtained using the forward pass of CLIP for image \\(x_i\\) and text \\(y_j\\) be \\(S_{ij}\\). Let \\(\\mathsf{c}(i)\\) be the category of image-text pair \\((x_i, y_i)\\). Let \\(G_i = \\{j \\mid \\mathsf{c}(j) = \\mathsf{c}(i)\\}\\) denote the indices of pairs that belong to the same class as pair \\((x_i, y_i)\\). Then the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.374, + 0.682, + 0.389 + ], + "angle": 0, + "content": "loss function for images is:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.401, + 0.892, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i m a g e}} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {1}{| G _ {i} |} \\sum_ {j \\in G _ {i}} \\log \\frac {\\exp \\left(S _ {i , j} / \\tau\\right)}{\\sum_ {r = 1} ^ {N} \\exp \\left(S _ {i , r} / \\tau\\right)} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.456, + 0.756, + 0.47 + ], + "angle": 0, + "content": "and the corresponding one for texts is:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.483, + 0.892, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t e x t} = - \\frac {1}{N} \\sum_ {j = 1} ^ {N} \\frac {1}{| G _ {j} |} \\sum_ {i \\in G _ {j}} \\log \\frac {\\exp \\left(S _ {i , j} / \\tau\\right)}{\\sum_ {r = 1} ^ {N} \\exp \\left(S _ {r , j} / \\tau\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.568 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a learnable temperature parameter. The overall loss for fine-tuning is:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.581, + 0.774, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f t} = \\mathcal {L} _ {i m a g e} + \\mathcal {L} _ {t e x t}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.716 + ], + "angle": 0, + "content": "The objective aggregates the image text similarity across all image and text pairs from the same category within the batch. To avoid overfitting on small datasets we maintain momentum encoders whose weights \\((\\theta_{EMA},\\phi_{EMA})\\) are updated with the exponential moving average (EMA) of the weights of the encoders \\((\\theta ,\\phi)\\) which is trained using the objective \\(\\mathcal{L}_{ft}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.729, + 0.812, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\theta_ {E M A} \\leftarrow m \\theta_ {E M A} + (1 - m) \\theta_ {E} \\\\ \\phi_ {E M A} \\leftarrow m \\phi_ {E M A} + (1 - m) \\phi_ {E}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.776, + 0.891, + 0.807 + ], + "angle": 0, + "content": "where \\( m \\) is a momentum parameter. All encoders are initialized using the pre-trained weights of CLIP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.834, + 0.832 + ], + "angle": 0, + "content": "3.3. Evaluation for Zero-shot Classification" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.903 + ], + "angle": 0, + "content": "To evaluate a model on unseen classes we similarly query the LLM as described in §3.1 to obtain texts \\(\\mathbf{Y}^{\\mathbf{k}}\\), for \\(k \\in \\mathbf{K}_{\\mathrm{test}}\\). For any given image \\(x\\) we can find the similarity score using a VLM for every text \\(y_{m}^{k}\\) for \\(m \\in \\{1, \\dots, l_{k}\\}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17545" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "and \\( k \\in \\mathbf{K}_{\\mathrm{test}} \\). Denote the similarity between image \\( x \\) and text \\( y_{m}^{k} \\) as \\( S_{m}^{k} \\). The predicted class is:" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.145, + 0.469, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\underset {k} {\\operatorname {a r g m a x}} \\frac {1}{l _ {k}} \\sum_ {m = 1} ^ {l _ {k}} \\frac {\\exp \\left(S _ {m} ^ {k}\\right)}{\\sum_ {p \\in \\mathbf {K} _ {\\text {t e s t}}} \\sum_ {q = 1} ^ {l _ {p}} \\exp \\left(S _ {q} ^ {p}\\right)} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.469, + 0.258 + ], + "angle": 0, + "content": "The score represents average similarity between an image and the texts corresponding to each class. Our initial experiments suggested that simple averaging of probabilities is more robust than alternatives such as the geometric mean." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.27, + 0.21, + 0.287 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.47, + 0.356 + ], + "angle": 0, + "content": "In this section we present the experimental details of our approach. We outline the datasets we use, the particulars of implementation for each part of the method as well as the details of the baselines we compare our method to." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.365, + 0.18, + 0.379 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.469, + 0.553 + ], + "angle": 0, + "content": "We use a variety of fine-grained classification datasets including CUB [42] (200 classes), Flowers 102 [23] (102 classes), Stanford Cars [14] (196 classes), FGVC Aircrafts [18] (100 classes) and Food101 [1] (101 classes). We also apply our method on some coarser datasets including EuroSAT [10] (10 classes), ImageNet [31] (1000 classes), CalTech101 [5] (100 classes), DTD [4] (47 classes), Oxford Pets [26] (37 classes), Sun397 [44] (397 classes) and UCF101 [36] (101 classes). For all these datasets, we use the first half of the classes (ordered by ids of the original dataset) for training and second half for zero-shot testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.658 + ], + "angle": 0, + "content": "We also use NABirds [39] which contains 404 bird classes at species level. We remove the overlapping classes of the CUB testing set from these to obtain 331 training classes. Along with train and test classes being different, this setting also represents a distribution shift in the images of training and testing as images for CUB and NABirds have been obtained in different manners." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.81 + ], + "angle": 0, + "content": "iNaturalist [41] 2021 is another dataset we utilize to illustrate that our method scales and generalizes. iNaturalist contains 10k classes belonging to 11 general categories (such as birds, plants, fishes). First, in a similar setting to NABirds we remove overlapping test classes of CUB to train a model for testing on CUB. Secondly, we remove all bird classes from iNat and train a model on the remaining classes to test on CUB. We follow similar settings for testing on Flowers 102. Even in these challenging circumstances our method offers improvement over the baselines(§ 5.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.871 + ], + "angle": 0, + "content": "For CUB, NABirds and iNaturalist we also have taxonomy information including family, order and scientific name. We also append separate texts containing these to the category-wise text corpus to show improvements (Tab. 3)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "NeWT [40] provides a benchmark for a set of 164 complex binary classification tasks in the natural world that ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.244 + ], + "angle": 0, + "content": "tend beyond species classification. These tasks include determining 1) appearance 2) behavior, 3) context, 4) counting and 5) gestalt. NeWT contains 36k images with 200-400 images per task. We randomly select 50 of the 164 tasks to evaluate our trained model. We manually associate two texts for each task, positive and negative. For example, \"a photo of a raptor bird which is not on a utility pole\" and \"a photo of a raptor bird which is on a utility pole\". We show improvements over CLIP (§ 5.5). All details of texts used as well as categories selected are in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.257, + 0.719, + 0.273 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.327 + ], + "angle": 0, + "content": "For generating category-level texts for training, we utilize the \"gpt-4-0613\" API. We set the temperature parameter as 0 so that texts generated are deterministic." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.39 + ], + "angle": 0, + "content": "For all queries concerning the classes of iNaturalist (both visual and location) we also append the type of organism as well as it's scientific name in the question. For example, for the class \"Bay Laurel\" the query for location information is" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.41, + 0.887, + 0.451 + ], + "angle": 0, + "content": "Where can we find a Bay Laurel, a type of plant with scientific name Laurus nobilis? Produce a list of habitat and geographic location information that can be used to identify the plant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.546 + ], + "angle": 0, + "content": "This is required because there exist organisms with the same common name but different domains. Also, we need to append the scientific name as otherwise GPT4 does not recognise the organism in many cases. We provide more details in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Additionally, we experiment with using taxonomy information for training and testing on datasets where it is available (Tab. 3). We form the following texts" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.614, + 0.882, + 0.626 + ], + "angle": 0, + "content": "1. a photo of [class] [domain], with scientific name [s_name]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.627, + 0.875, + 0.639 + ], + "angle": 0, + "content": "2. a photo of [class] [domain], with family name [family]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.64, + 0.836, + 0.652 + ], + "angle": 0, + "content": "3. a photo of [class] [domain], of the order [order]" + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.614, + 0.882, + 0.652 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.763 + ], + "angle": 0, + "content": "While fine-tuning using the texts obtained from an LLM, we train for only 15 epochs on each dataset. On iNaturalist, we train for only 5 epochs. We find hyperparameters by splitting the train classes into two equal parts, training on the first half, and validating on the second. We then fix the best hyperparameters found and train on all train classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The CLIP architecture consists of an image encoder and a text encoder. Both contain transformers followed by a linear projection layer at the end. We use different learning rate and weight decay for the projection layers compared to rest of the encoders. The temperature parameter \\(\\tau\\) in our model (§ 3.2) is trainable. We provide the details of the initialization of \\(\\tau\\), the momentum parameter for the EMA encoder as well as learning rates and weight decays of every parameter for all datasets in the Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17546" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.158, + 0.088, + 0.813, + 0.168 + ], + "angle": 0, + "content": "
MethodsCUBStanford CarsFGVC AircractsFlowers 102Food 101
CLIP50.5469.7229.2771.7888.32
CLIP + A50.7169.4730.3575.3790.08
CLIPFT50.81 ± 0.0469.61 ± 0.0731.10 ± 0.0273.68 ± 0.0088.32 ± 0.00
CLIPFT + A53.34 ± 0.0871.63 ± 0.0636.41 ± 0.0277.05 ± 0.0093.71 ± 0.01
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.178, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Table 1. Comparison with CLIP ViT-B/32 on zero-shot performance on fine-grained domains. We compare our method \\(\\mathrm{CLIP^{FT}} + \\mathrm{A}\\) to the baselines defined in § 4.3. We significantly improve over baseline CLIP evaluated with both \"a photo of a [class] [domain]\" and LLM attributes. We also fine-tune CLIP with only \"a photo of a [class] [domain]\" text and compare with our method to show that our improvements are not due to seeing domain-specific images but also by learning correlations between images and fine-grained attributes." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.23, + 0.845, + 0.309 + ], + "angle": 0, + "content": "
Stanford CarsFGVC AircraticsFlowers 102EuroSATFood 101ImageNet
CLIP74.9436.4777.0564.0592.4967.41
CLIP + A73.8336.4780.8471.5193.7269.74
CLIP-A-self [19]72.9033.0075.3070.5091.2068.30
CLIPFT + A75.7840.7581.2681.8295.0871.87
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.318, + 0.893, + 0.357 + ], + "angle": 0, + "content": "Table 2. Comparison to prior work using ViT B/16 architecture on zero-shot classification. We show that across a variety of datasets from finer to coarser domains we considerably boost performance over baselines. Here we train using only 16 images per class and test on unseen classes for fair comparison to CLIP-A-self. We do not compare on CUB dataset as CLIP-A-self uses a 3:1 split on CUB, whereas we use 1:1 across all datasets." + }, + { + "type": "table", + "bbox": [ + 0.126, + 0.361, + 0.424, + 0.453 + ], + "angle": 0, + "content": "
TextsCUBFlowers 102
Visual53.3477.05
Taxonomy53.07-
Habitat53.6976.00
Vis. + Hab.54.0177.22
Vis. + Tax. + Hab.54.23-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.465, + 0.47, + 0.539 + ], + "angle": 0, + "content": "Table 3. Evaluating \\(\\mathbf{CLIP^{FT}} + \\mathbf{A}\\) using different types of text. We query LLMs to produce visual (vis.) and habitat (hab.) information separately and use taxonomy (tax.) information available with dataset. We train with the type of text specified in each row and test with the same type. Using habitat information works slightly better than using visual information for CUB. All three types of texts are complementary." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.542, + 0.421, + 0.62 + ], + "angle": 0, + "content": "
Train SetCUBFlowers 102
NABirds\\overlap55.32-
iNat\\overlap54.5877.05
iNat\\Birds53.89-
iNat\\Plants-76.63
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.681 + ], + "angle": 0, + "content": "Table 4. Evaluating domain transfer performance. Our method offers substantial gain over baseline CLIP (Tab. 1) even when trained on external datasets. Performance boost is competitive even when removing all bird or plant classes from iNat to test on CUB and Flowers respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.185, + 0.71 + ], + "angle": 0, + "content": "4.3. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.468, + 0.749 + ], + "angle": 0, + "content": "In this section, we discuss the various methods for which we compare zero-shot classification accuracy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.468, + 0.779 + ], + "angle": 0, + "content": "CLIP refers to pre-trained CLIP tested with \"a photo of a [class] [domain]\" texts like the original paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.809 + ], + "angle": 0, + "content": "\\(\\mathbf{CLIP} + \\mathbf{A}\\) is evaluating pre-trained CLIP with attributes obtained from LLMs as outlined in § 3.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.855 + ], + "angle": 0, + "content": "CLIPFT involves fine-tuning CLIP on training classes using \"a photo of [class] [domain]\" texts and evaluating on test classes using \"a photo of [class] [domain]\" texts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "\\(\\mathbf{CLIP}^{\\mathrm{FT}} + \\mathbf{A}\\) is our method where we fine-tune CLIP (§ 3.2) using attributes obtained from a LLM (§ 3.1) for training classes and evaluate using LLM attributes of testing classes" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.361, + 0.886, + 0.502 + ], + "angle": 0, + "content": "
Testing TextsCLIP + ACLIPFT + A
[class] [domain]50.5452.29
GPT 4 Vis.50.7153.34
GPT 3 Vis.51.0853.35
LLaMA Vis.50.1052.52
Ground Truth Vis.52.5353.99
GPT 4 Vis. + Tax. + Hab.52.8354.23
GPT 3 Vis. + Tax. + Hab.52.6353.58
LLaMA Vis. + Tax. + Hab.50.8552.64
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.573 + ], + "angle": 0, + "content": "Table 5. Evaluating model trained using GPT4 with texts obtained from other models. Our model consistently improves over pre-trained CLIP when evaluated with texts obtained from different LLM models (GPT3.5 and LLaMA2-7B) as well as GT aggregated captions and \"a photo of a [class] [domain]\"." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.59, + 0.719, + 0.604 + ], + "angle": 0, + "content": "at test time as described in \\(\\S 3.3\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.697 + ], + "angle": 0, + "content": "CLIP-A-self [19] is prior work which uses text obtained from GPT to train an adapter network attached after the text and image encoders of CLIP. For comparing with this, we use the numbers stated by them under their training and evaluation scheme. We test our model on the same classes as them to show improvement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.709, + 0.587, + 0.724 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we compare our method to baselines and evaluate it under various settings. We discuss our performance improvements over various datasets and architectures. We show that for natural domains using taxonomy and habitat information offers improvements with habitat information especially being a strong factor. Our model scales across architectures and needs only a few epochs of training. We further show that our method performs better than baseline CLIP even under more difficult evaluation settings such as 1) using texts from different LLM models during testing and training; 2) training a model in a do" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17547" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "main very different from testing domain, and 3) evaluating on tasks other than identifying categories at test time. Additionally, we discuss other training strategies for category-level fine-tuning and how they perform." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.162, + 0.323, + 0.178 + ], + "angle": 0, + "content": "5.1. Comparison with Baselines" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Tab. 1 compares our method to three baselines CLIP, \\(\\mathrm{CLIP} + \\mathrm{A}\\) and \\(\\mathrm{CLIP^{FT}}\\), all evaluated on unseen classes. Here we use the ViT B/32 architecture for all methods. Our method offers considerable improvements over pre-trained CLIP when using \"a photo of a [class] [domain]\" text and when using GPT generated text. In difficult fine-grained domains such as CUB, Stanford Cars and FGVC Aircrafts pre-trained CLIP does not utilize text attributes generated by GPT resulting in negligible improvement (decrease on Stanford Cars) compared to \"a photo of a [class] [domain]\" (see \\(\\mathrm{CLIP} + \\mathrm{A}\\) vs CLIP). This motivates the need to fine-tune using these attributes, resulting in significant improvement across all datasets. We also compare to fine-tuning CLIP with \"a photo of a [class] [domain]\" texts (\\(\\mathrm{CLIP^{FT}}\\)) to show that the improvement our method achieves is not due to just being trained on images of concerned domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.579 + ], + "angle": 0, + "content": "We compare our method to previous work CLIP-A-self [19] in Tab. 2. We follow [19] and use the ViT B/16 architecture and only 16 images per class for training. Again we evaluate on unseen classes. Our method outperforms CLIP-A-self significantly across all datasets. Also, our method offers substantial improvement over CLIP, showing that it scales across architectures. We discuss why CLIP-A-self underperforms in detail in the Appendix. We also show results on the 14 datasets benchmark in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.588, + 0.424, + 0.604 + ], + "angle": 0, + "content": "5.2. Using more than just Visual Information" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.807 + ], + "angle": 0, + "content": "We explore using information other than visual attributes for natural domains such as birds and flowers. For humans identifying a bird in an image it is crucial to know where the image was taken, because that reveals habitat and location information. We therefore query GPT for an organism's habitat and geographic range. In Tab. 3 we show that for CUB using only habitat information performs better than using only visual information. A reason for this is that habitat information describes the background of the images of birds, which is helping to differentiate between categories. We also show that combining visual + taxonomy + habitat information for CUB and visual + habitat information for Flowers102 offers best improvement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.348, + 0.833 + ], + "angle": 0, + "content": "5.3. Training on External Domains" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We now evaluate under more difficult settings. We train and test on different datasets, always removing any overlapping classes. For training on iNat and NABirds we use all visual + taxonomy + habitat information. While testing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "on CUB we use visual + taxonomy + habitat. For Flowers 102 we use visual + habitat information. Tab. 4 we show the accuracy on CUB test classes improves considerably when training using NABirds and iNat even though the images of these datasets have a distribution shift w.r.t. CUB. More strikingly, we show that even when we remove all bird classes from iNat we still offer improvement on CUB test classes compared to CLIP + A (52.83 → 53.89). Similarly when we remove all plant classes from iNat, we still get improvement on Flowers 102 test set. This proves that our model is also able to generalize well. It is learning to associate fine-grained attributes to images irrespective of the domain differences in training and testing." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.298, + 0.809, + 0.314 + ], + "angle": 0, + "content": "5.4. Using Novel Texts during Test Time" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.457 + ], + "angle": 0, + "content": "We evaluate how our model would perform in the absence of the LLM used to generate training texts, during test time (Tab 5). We use GPT3.5 turbo (0613) and LLaMA2-7B [38] for generating visual and habitat texts. We show that our method consistently improves performance over pre-trained CLIP for all types of texts explored. Please refer to Appendix for examples of texts produced. Our model also improves performance over pre-trained CLIP while using \"a photo of a [class] [domain]\" texts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Reed et al. [30] present a dataset of human-labelled captions per image for the CUB dataset. We use these ground truth texts at test time to evaluate our model. The dataset contains 10 captions for every image, which are all visual attributes of the bird in the image. Since many attributes in the captions are repeated for each image as well as across images of the same class, and to limit the size of the text corpus, we randomly select one caption per image of a given class and aggregate them to form a category corpus. In Tab. 5 last row, we notice that CLIP does better using these image-level GT texts compared to using GPT4 Visual texts which were category-level (row 2). However, our method still outperforms showing that it is able learn meaningful attributes through noisy labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.74, + 0.694 + ], + "angle": 0, + "content": "5.5. Evaluation on Novel Tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.854 + ], + "angle": 0, + "content": "We use the NeWT [40] benchmark to evaluate on tasks beyond categorization. These include identifying age, attribute, health, photo quality, species, context and behavior. We evaluate the model and baseline CLIP using average Mean Average Precision (MAP) across tasks. Our model trained on iNaturalist using visual + taxonomy + location information outperforms baseline CLIP: 60.25 vs 61.90 MAP \\(\\rightarrow\\) \\(4.1\\%\\) relative error reduction. We present all tasks and texts we use to evaluate as well as MAP per task in the Appendix. Below is an example prediction:" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1LLaMA model does not always produce texts in the specified format and thus needs post-processing. The texts formed finally are considerably different grammatically from the sentences our model has been trained on." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17548" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.093, + 0.189, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.216, + 0.096, + 0.335, + 0.125 + ], + "angle": 0, + "content": "a photo of a raptor bird which is not on a utility pole" + }, + { + "type": "text", + "bbox": [ + 0.231, + 0.139, + 0.317, + 0.151 + ], + "angle": 0, + "content": "Probability: 0.38" + }, + { + "type": "text", + "bbox": [ + 0.362, + 0.096, + 0.466, + 0.125 + ], + "angle": 0, + "content": "a photo of a raptor bird which is on a utility pole" + }, + { + "type": "text", + "bbox": [ + 0.372, + 0.139, + 0.457, + 0.151 + ], + "angle": 0, + "content": "Probability: 0.62" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.186, + 0.296, + 0.202 + ], + "angle": 0, + "content": "5.6. Resource Requirements" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.21, + 0.469, + 0.301 + ], + "angle": 0, + "content": "We fine-tune our model using a 1024 batch size on a single NVIDIA A100 80GB. We need to train only for a maximum of 15 epochs. For smaller datasets such as CUB, FGVC Aircraft, and Stanford Cars, this takes less than 5 minutes. For iNaturalist, which is a large dataset, we train only for 5 epochs, taking about 4 hours." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.469, + 0.424 + ], + "angle": 0, + "content": "The cost of using the GPT-4 API to query text descriptions for a dataset with 100-200 classes (such as CUB) is about \\(1-\\)5. This is low because it scales with the number of categories and not the number of images. Generating captions per image is both time-consuming and expensive; an estimate for doing this for the CUB dataset using the GPT-4 Vision API is more than \\)100. This cost scales significantly for larger datasets with more images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.435, + 0.338, + 0.452 + ], + "angle": 0, + "content": "5.7. Alternate Training Strategies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.469, + 0.536 + ], + "angle": 0, + "content": "Here we discuss other training strategies for improving VLMs using category-level training data. Our simple finetuning strategy of stochastically pairing images with texts within categories is simple, efficient, and offers similar improvements compared to more complex approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.469, + 0.657 + ], + "angle": 0, + "content": "Firstly, since we pair a given image of a category to every text of that category, we might be pairing texts that describe attributes that are not visible. For CUB dataset we have the ground truth visibility annotations of various bird parts, which we use to ignore texts that are occluded for each image. This strategy offers improvement to our scores (54.23 \\(\\rightarrow\\) 54.47). However, this depends on visibility information that is time-consuming to generate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.824 + ], + "angle": 0, + "content": "The next step is to assume that pre-trained CLIP itself is able to correctly identify if a part is visible. Assuming this we mask texts during training time based on CLIP predictions by doing 1) a forward pass for a image and all texts of the category to find the texts above a threshold that can be paired with the image, 2) max pooling at instance level for images and texts. We find that none of these strategies offer any improvement and that pairing images with low scoring texts also (like in our method) is improving performance because CLIP does not accurately identify which fine-grained attributes correctly correspond to given image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We also try well-known semi-supervised learning strategies such as FixMatch [35] and knowledge distillation [3]. We find that these offer small \\((< 0.2\\%)\\) to no improvements over our method. Please see the Appendix for details of implementation of all the methods and accuracies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.853, + 0.108 + ], + "angle": 0, + "content": "5.8. Performance of image captioning models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.221 + ], + "angle": 0, + "content": "We test the recently released GPT4 Vision API for checking quality of image captions obtained. Even though it performs better than previous captioning models such as LLaVA [17] and BLIP2 [16], we find that the captions obtained are general descriptions without fine-grained details. The captions are specific to the image but do not describe information helpful to identify the category. An example is:" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.232, + 0.576, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.582, + 0.234, + 0.888, + 0.286 + ], + "angle": 0, + "content": "A slender, streaked brown songbird with keen eyes and a pointed beak perches atop a weathered wooden fence post amidst a backdrop of natural grassland under a clear blue sky." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.892, + 0.367 + ], + "angle": 0, + "content": "For this image of a Vesper Sparrow, GPT4 provides a general description of the bird and suggests the presence of clear blue sky which is not visible in the image. We provide more detail including prompt and examples in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.378, + 0.614, + 0.394 + ], + "angle": 0, + "content": "6. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Since our method is trained on texts generated by LLMs, it is important to verify the correctness of these texts to assess the level of noise in our training dataset. As described in § 3.1, we conduct spot checks across some categories on our evaluation sets. However, for our larger training datasets, vetting becomes impractical. Improved performance on human-generated texts on CUB, as well as the vetted evaluation sets, supports our model's ability to learn meaningful information from somewhat noisy training data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.619, + 0.567 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.773 + ], + "angle": 0, + "content": "We present a method to improve the zero-shot performance of VLMs using attributes generated by LLMs on fine-grained domains. Our evaluation strategy involves testing the trained model on unseen classes, texts generated from different LLMs as well as humans, dissimilar domains, and novel tasks. We show that fine-tuning CLIP using category-level descriptions from GPT4 significantly improves performance compared to baselines in this challenging downstream evaluation framework. Our findings suggest that habitat and geographic priors are equally effective and complementary to visual information for zero-shot classification in natural domains. We publicly release our benchmark across all 14 datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.687, + 0.802 + ], + "angle": 0, + "content": "8. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We thank Aaron Sun, Gustavo Perez, Rangel Daroya, and Mustafa Chasmai for participating in the verification of attributes generated by GPT4. The project is supported in part by NSF Grants #2329927 and #1749833. Our experiments were performed on the GPU cluster funded by the Mass. Technology Collaborative." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17549" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101 – mining discriminative components with random forests. In European Conference on Computer Vision, 2014. 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.47, + 0.241 + ], + "angle": 0, + "content": "[2] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. 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Domain prompt learning for efficiently adapting" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17551" + } + ], + [ + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.092, + 0.468, + 0.119 + ], + "angle": 0, + "content": "clip to unseen domains. arXiv preprint arXiv:2111.12853, 2021.3" + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.122, + 0.468, + 0.189 + ], + "angle": 0, + "content": "[49] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Conditional prompt learning for vision-language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16816-16825, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.192, + 0.468, + 0.246 + ], + "angle": 0, + "content": "[50] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15659-15669, 2023. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17552" + } + ] +] \ No newline at end of file diff --git a/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_origin.pdf b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ffee64f8c114671c9009f229bf9b7ee321b3e119 --- /dev/null +++ b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/54ac6e92-bc80-4537-bc0c-01614b64b2c9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5b7989ed2fb8f83e9ccee901d7acbd31235bbebd5a515f87fe3690788a03eeb9 +size 4907116 diff --git a/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/full.md b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/full.md new file mode 100644 index 0000000000000000000000000000000000000000..df671f68be2b0e5a7b62e16a7dce3f49d330b8bd --- /dev/null +++ b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/full.md @@ -0,0 +1,333 @@ +# Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions + +Oindrila Saha Grant Van Horn Subhransu Maji University of Massachusetts, Amherst {osaha, gvanhorn, smaji}@umass.edu + +# Abstract + +The zero-shot performance of existing vision-language models (VLMs) such as CLIP [29] is limited by the availability of large-scale, aligned image and text datasets in specific domains. In this work, we leverage two complementary sources of information—descriptions of categories generated by large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across fine-grained domains. On the technical side, we develop methods to train VLMs with this "bag-level" image-text supervision. We find that simply using these attributes at test-time does not improve performance, but our training strategy, for example, on the iNaturalist [41] dataset, leads to an average improvement of $4 - 5\%$ in zero-shot classification accuracy for novel categories of birds [42] and flowers [23]. Similar improvements are observed in domains where a subset of the categories was used to fine-tune the model. By prompting LLMs in various ways, we generate descriptions that capture visual appearance, habitat, and geographic regions and pair them with existing attributes such as the taxonomic structure of the categories. We systematically evaluate their ability to improve zero-shot categorization in natural domains. Our findings suggest that geographic priors can be just as effective and are complementary to visual appearance. Our method also outperforms prior work on prompt-based tuning of VLMs. We release the benchmark, consisting of 14 datasets at https://github.com/cvl-umass/AdaptCLIPZS, which will contribute to future research in zero-shot recognition. + +# 1. Introduction + +Recent improvements in zero-shot classification have been due, in part, to success in training VLMs at scale. Models such as CLIP [29], ALIGN [11], and BLIP [16] use massive datasets of image and text pairs to learn a common embedding between visual and natural language domains. However, we find existing VLMs show poor performance in encoding visual attributes in fine-grained domains, beyond + +![](images/bddf8a38260c140cab794284ddcba734e003b5adc86b65816abe2dc822643ae9.jpg) +Figure 1. Motivation. Collecting image captions in fine-grained domains requires expertise (top row), but LLMs can generate structured (e.g., shape or appearance) and accurate descriptions of categories at both the coarse (e.g., birds) and fine-grained level (e.g., Vesper Sparrow). Rich descriptions of fine-grained categories can be paired with existing datasets, such as iNaturalist [41] and NABirds [39] to generate coarsely-aligned image-text datasets for fine-tuning VLMs. This improves their zero-shot performance on a range of benchmarks, generalizing to novel categories and tasks. + +simply recognizing the name of the category. For example, we observe concatenating visual attribute descriptions to the species name for the bird species in the CUB [42] dataset improves the zero-shot classification from $50.5\%$ to only $50.7\%$ , while for Cars [14], the performance even drops slightly (see Tab. 1). Although the datasets on which VLMs are trained are extensive, they often lack the details that experts may require for fine-grained categorization. At the same time, collecting large-scale image-caption datasets in these domains requires significant effort, making training similar models challenging. + +In this work, we leverage two complementary sources of information—large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across a variety of fine-grained domains. Concretely, we generate large datasets of images aligned with text by pairing images within a category with descriptions of that category generated by LLMs as seen in Fig. 1. We find this approach works well, as images within a fine-grained domain share many attributes, unlike in coarse categories with + +larger intra-category variation. At the same time, we find that LLMs are capable of accurately describing appearance, habitat, and other properties for a wide range of categories, allowing us to systematically generate datasets in a scalable manner. In other words, fine-grained labels allow us to bridge the gap between image-level captions required for VLM training, and general information about visual categories contained in LLMs. + +On the technical side, we develop methods to train VLMs with "bag-level" supervision. In our dataset a set of images are grouped with a set of descriptions and lack the image-text correspondences. Some of the descriptions may not apply to an image (e.g., the part may be occluded). However, we find that training by stochastically pairing the images and text within a category, followed by a category-level contrastive loss similar to CLIP objective offers robust improvements in performance. Adapting semi-supervised learning approaches such as FixMatch [35] or Knowledge distillation [3] results in minor improvements ( $\S 5.7$ ). A detailed investigation of the image-text association within a category suggests the model is able to correctly associate the visual attributes with the corresponding text even they are paired randomly during training (Fig. 2). + +We systematically evaluate the effectiveness of our method by assessing the zero-shot classification performance on novel classes. We find that simply using these attributes of novel classes generated by LLMs does not improve performance when using CLIP (Tab. 1). However, our training strategy leads to an average improvement of $4 - 5\%$ in accuracy across 12 datasets, and outperforms baselines (Tab. 2). For natural domains (e.g., iNaturalist and NABirds), we prompt LLMs in various ways to generate descriptions that capture visual appearance, habitat, and geographic regions, and pair them with existing attributes within the dataset, such as taxonomic structure. Our results indicate that geographic priors are equally effective and complementary to visual appearance cues (see Tab. 3). Training on iNaturalist without any bird classes improves the performance of CLIP on CUB by more than $3\%$ , and we observe similar improvements when evaluating across other domains (see Tab. 4). Improvements are consistent across text generated by different LLMs, as well as by humans (see Tab. 5). Our model also results in relative error reduction of $4.1\%$ over CLIP on the challenging NeWT dataset [40]. + +# 2. Related Work + +Zero-shot Image Classification using VLMs. Vision Language models (VLMs) [6, 11, 29, 33, 45] learn to associate images with their corresponding text captions. Learning a shared embedding makes them perform exceptionally well in zero-shot classification tasks when paired with an appropriate text such as the class name during test time. FLAVA [33] learns using paired as well as unpaired im + +![](images/71a3ad2b6d05ba340f71b6cfb17cc6d2e698e23b22419f1de9392cb45b81c909.jpg) +Figure 2. Visualizing image-text similarity. All images within a category are sorted in order of similarity to a given text predicted by CLIP and our fine-tuned $\mathrm{CLIP^{FT} + A}$ . For example, our method identifies birds which show olive-green tint on their back as the top images, whereas CLIP selects birds with visibly brown upperparts or occluded back. The image with lowest similarity which has the occluded back remains the same for both models, showing our model does not learn incorrect attribute associations even though we stochastically pair every attribute with every image during training. On the aircraft example our model predicts higher similarity to images with prominently visible fuselage. CLIP identifies the least similar image as one in which fuselage is visible, but ours chooses one where aircrafts are too far to make out the shape of fuselage. + +ages and texts using different losses for multimodal and unimodal understanding. ALIGN [11] uses a large number of noisy image-text data by obtaining alt-texts for images and trains using a contrastive loss. CLIP [29] is trained on a smaller and cleaner dataset of image-text pairs using a similar objective function. It employs a vision model and a language model to learn joint embeddings of images and text. While training, it maximizes the similarity between related image-text pairs and minimizes similarity between unrelated pairs. At test time the similarity over captions such “a photo of a [class name]” over all classes in the domain for each image is found. The image is classified to the class with the caption with highest probability. The original paper shows that manual prompt tuning can boost zero-shot classification accuracy. + +Generating Better Prompts. Prior work on prompt tuning [7, 12, 13, 32, 51] has focused on improving the text descriptions of classes. For example, CoOp [50] appends learnable context vectors to the class name texts to improve classification. CoCoOp [49] and related methods have also explored prompting the vision encoder simultaneously. While prompt tuning has proven useful for adapting models to a set of "base categories", its performance on novel categories still falls short of the CLIP baseline. + +Another line of research aims at querying LLMs to generate prompts or attributes of categories. CHiLS [24] refines classes based on GPT descriptions (e.g., taxonomic structure) and maps the image to one of the subcategories to improve classification. We also explore the ability to + +learn taxonomy-based attributes in our work. Menon et al. [20] and CuPL [28] append class-specific attributes obtained from GPT [2] to simple prompts, e.g. "a photo of a [class]" to improve zero-shot performance at test-time, similar to our approach. However, we find that CLIP struggles to recognize nuanced attributes in fine-grained domains where we observe little to no improvement in classification performance, motivating the need for fine-tuning VLMs. + +Fine-tuning VLMs. Most work on fine-tuning VLMs has focused on parameter efficient updates using lightweight adapters [8,19,25,27,46,47] for improving few-shot classification. For example, CLIP adapter [8] trains a few learnable layers on top of the encoders, while Maniparambil et al. [19] query LLMs for class-wise descriptions for tuning an external adapter network. Their work improves over CoCoOp and CLIP adapter for unseen classes, however, as before, most approaches show no improvement over CLIP, especially on novel classes in fine-grained datasets. + +Another line of research [9, 34, 37, 43, 48] involves fine-tuning CLIP for robustness to domain shifts. For instance, WiSE-FT [43] utilizes weight-space ensembling to improve performance on a sketch version of ImageNet. Similarly, LaFTer [21] employs fine-tuning both the image and text encoders using unpaired images and texts obtained by querying LLMs. These techniques focus on adapting to a target distribution, such as a specific set of test images or classes, rather than on generalizing to novel classes. + +Two works similar to ours, GIST [15] and I2MVFormer [22], also utilize GPT to generate category-specific texts for fine-grained domains. GIST pairs each image with the $n$ most similar texts within the category based on CLIP similarity and consolidates them into a caption. In contrast, our approach stochastically pairs images with text, a strategy we found to be more robust. Notably, our experiments showed that biasing sampling towards similar image and text pairs led to inferior results (see § 5.7). I2MVFormer uses a LLM to generate class descriptions based on texts provided by annotators and Wikipedia documents. The key differences between their work and ours lie in the use of human effort in their training data generation and starting from scratch resulting in much lower performance compared to ours. Finally, in contrast to both these works, we explore training using visual, habitat, and location information, as well as training on larger datasets such as NABirds and iNaturalist. + +Summary To the best of our knowledge, ours is the first method demonstrating that fine-tuning CLIP with class-specific descriptions obtained by querying LLMs improves the zero-shot performance in fine-grained domains. Our approach leverages LLMs to generate image-text data that are coarsely aligned, making it particularly effective for fine-grained categories. Moreover, unlike prior work [19, 20], + +our method queries LLMs along various dimensions such as visual, taxonomy, habitat and geographic priors, and systematically evaluates their effectiveness. + +# 3. Method + +Consider a dataset $\mathcal{D} = \{(x_i, y_i)\}_{i=1}^n$ consisting of images $x_i \in \mathcal{X}$ and labels $y_i \in \mathcal{Y}$ . A VLM such as CLIP [29] consists of an image encoder $\Theta$ and a text encoder $\Phi$ such that $\Theta(x) \approx \Phi(y)$ for images $x$ with label $y$ . We want to improve the zero-shot performance of CLIP on novel categories in fine-grained domains by fine-tuning the image and the text encoders. We do so either by splitting a dataset $\mathcal{D}$ into $\mathbf{K}_{\mathrm{train}}$ training and $\mathbf{K}_{\mathrm{test}}$ testing classes, or train our model on large datasets such as iNaturalist and NABirds by excluding classes or domains overlapping with our test set. Our framework consists of: 1) generating textual descriptions given the class names by prompting LLMs in different ways ( $\S 3.1$ ); 2) fine-tuning CLIP using these descriptions using our proposed approach ( $\S 3.2$ ); and 3) evaluating the models on downstream tasks ( $\S 3.3$ ). Fig. 3 provides an illustration of our method. + +# 3.1. Dataset Generation + +For each dataset we generate texts for every class which can be used to differentiate it from other classes in the domain using visual attributes. We query an LLM as: + +What characteristics can be used to differentiate [class] from other [domain] based on just a photo? Provide an exhaustive list of all attributes that can be used to identify the [domain] uniquely. Texts should be of the form "[domain] with [characteristic)". + +Here [class] is the class name for the $K$ classes in the dataset [domain]. Each domain is associated to different datasets, for example for the CUB200 dataset, [domain] is "bird" and for iNaturalist dataset it is "organism". Appending the domain [domain] is helpful because it provides context about the set of the other classes to distinguish from, and reduces confusion across similar class names in other domains. The LLM produces $l_{k}$ descriptions for category $k$ . We append "a photo of [class]" to the generated texts resulting in descriptions of the form "a photo of a [class] [domain] with [characteristic]" for each class (more details in the experiment section). This results in a set of descriptions $\mathbf{Y}^{\mathbf{k}}$ for each category. + +We also separately query about the habitat and geographic location of occurrence for the classes in CUB200, Flowers102, NABirds and iNaturalist datasets. For this purpose we use the prompt: + +Where can we find a [class]? Produce a list of habitat and geographic location information that can be used to identify the [domain]. + +![](images/93e7cddf8659b870237fbc7fc658de8b2e03868d53810de90da058be3d2e2f1f.jpg) +(a) + +![](images/adcad86024e407732ff4c509c37201d0e03e5b59639188badd61bdb94c0f4b2a.jpg) +(b) +Figure 3. Fine-tuning VLMs to improve zero-shot performance. a) Our framework for $①$ generating fine-grained attributes per class using LLMs, $②$ category-level fine-tuning of VLMs and $③$ evaluating on a series of challenging unseen scenarios. b) We show examples of texts produced in step $①$ . + +We add the texts obtained to the category-level corpus $\mathbf{Y}^{\mathbf{k}}$ . The impact of these location-specific texts and the improvements offered are described in the results section. Examples of visual and habitat descriptions are in the Appendix. We determine the correctness of the texts produced for 4-6 classes of CUB, Aircraft and Cars by manual fact-checking texts with the help of online sources. We find that $96\%$ (CUB), $90\%$ (Aircraft) and $96\%$ (Cars) are marked as correct by study participants (more details in Appendix). However, a challenge is that this manual vetting does not scale to large datasets, and we therefore rely on empirical results to support the utility of the generated text. + +# 3.2. VLM Fine-Tuning + +CLIP [29] is trained with image caption pairs. However, in our case we have a set of images $\mathbf{X}^{\mathbf{k}}$ and a set of texts $\mathbf{Y}^{\mathbf{k}}$ for classes $k\in \mathbf{K}_{\mathrm{train}}$ in our training set. We address this by pairing every image with randomly sampled text from the corresponding category during training. However, we cannot directly use the batch-level cross-entropy loss used by CLIP which treats the paired text as positive and rest of the texts as negative. This is because the same batch can contain multiple pairs with images and texts belonging to the same category. Below we describe our modification of the objective function that addresses this. + +In each iteration of training we sample a batch of size $N$ consisting of $\{(x_i, y_i)\}_{i=1}^N$ pairs where both $x_i$ and $y_i$ is an image and text from the same class. Let the similarity score obtained using the forward pass of CLIP for image $x_i$ and text $y_j$ be $S_{ij}$ . Let $\mathsf{c}(i)$ be the category of image-text pair $(x_i, y_i)$ . Let $G_i = \{j \mid \mathsf{c}(j) = \mathsf{c}(i)\}$ denote the indices of pairs that belong to the same class as pair $(x_i, y_i)$ . Then the + +loss function for images is: + +$$ +\mathcal {L} _ {\text {i m a g e}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {1}{| G _ {i} |} \sum_ {j \in G _ {i}} \log \frac {\exp \left(S _ {i , j} / \tau\right)}{\sum_ {r = 1} ^ {N} \exp \left(S _ {i , r} / \tau\right)} \tag {1} +$$ + +and the corresponding one for texts is: + +$$ +\mathcal {L} _ {t e x t} = - \frac {1}{N} \sum_ {j = 1} ^ {N} \frac {1}{| G _ {j} |} \sum_ {i \in G _ {j}} \log \frac {\exp \left(S _ {i , j} / \tau\right)}{\sum_ {r = 1} ^ {N} \exp \left(S _ {r , j} / \tau\right)} \tag {2} +$$ + +where $\tau$ is a learnable temperature parameter. The overall loss for fine-tuning is: + +$$ +\mathcal {L} _ {f t} = \mathcal {L} _ {i m a g e} + \mathcal {L} _ {t e x t} +$$ + +The objective aggregates the image text similarity across all image and text pairs from the same category within the batch. To avoid overfitting on small datasets we maintain momentum encoders whose weights $(\theta_{EMA},\phi_{EMA})$ are updated with the exponential moving average (EMA) of the weights of the encoders $(\theta ,\phi)$ which is trained using the objective $\mathcal{L}_{ft}$ : + +$$ +\begin{array}{l} \theta_ {E M A} \leftarrow m \theta_ {E M A} + (1 - m) \theta_ {E} \\ \phi_ {E M A} \leftarrow m \phi_ {E M A} + (1 - m) \phi_ {E}, \\ \end{array} +$$ + +where $m$ is a momentum parameter. All encoders are initialized using the pre-trained weights of CLIP. + +# 3.3. Evaluation for Zero-shot Classification + +To evaluate a model on unseen classes we similarly query the LLM as described in §3.1 to obtain texts $\mathbf{Y}^{\mathbf{k}}$ , for $k \in \mathbf{K}_{\mathrm{test}}$ . For any given image $x$ we can find the similarity score using a VLM for every text $y_{m}^{k}$ for $m \in \{1, \dots, l_{k}\}$ + +and $k \in \mathbf{K}_{\mathrm{test}}$ . Denote the similarity between image $x$ and text $y_{m}^{k}$ as $S_{m}^{k}$ . The predicted class is: + +$$ +\underset {k} {\operatorname {a r g m a x}} \frac {1}{l _ {k}} \sum_ {m = 1} ^ {l _ {k}} \frac {\exp \left(S _ {m} ^ {k}\right)}{\sum_ {p \in \mathbf {K} _ {\text {t e s t}}} \sum_ {q = 1} ^ {l _ {p}} \exp \left(S _ {q} ^ {p}\right)} \tag {3} +$$ + +The score represents average similarity between an image and the texts corresponding to each class. Our initial experiments suggested that simple averaging of probabilities is more robust than alternatives such as the geometric mean. + +# 4. Experiments + +In this section we present the experimental details of our approach. We outline the datasets we use, the particulars of implementation for each part of the method as well as the details of the baselines we compare our method to. + +# 4.1. Datasets + +We use a variety of fine-grained classification datasets including CUB [42] (200 classes), Flowers 102 [23] (102 classes), Stanford Cars [14] (196 classes), FGVC Aircrafts [18] (100 classes) and Food101 [1] (101 classes). We also apply our method on some coarser datasets including EuroSAT [10] (10 classes), ImageNet [31] (1000 classes), CalTech101 [5] (100 classes), DTD [4] (47 classes), Oxford Pets [26] (37 classes), Sun397 [44] (397 classes) and UCF101 [36] (101 classes). For all these datasets, we use the first half of the classes (ordered by ids of the original dataset) for training and second half for zero-shot testing. + +We also use NABirds [39] which contains 404 bird classes at species level. We remove the overlapping classes of the CUB testing set from these to obtain 331 training classes. Along with train and test classes being different, this setting also represents a distribution shift in the images of training and testing as images for CUB and NABirds have been obtained in different manners. + +iNaturalist [41] 2021 is another dataset we utilize to illustrate that our method scales and generalizes. iNaturalist contains 10k classes belonging to 11 general categories (such as birds, plants, fishes). First, in a similar setting to NABirds we remove overlapping test classes of CUB to train a model for testing on CUB. Secondly, we remove all bird classes from iNat and train a model on the remaining classes to test on CUB. We follow similar settings for testing on Flowers 102. Even in these challenging circumstances our method offers improvement over the baselines(§ 5.3). + +For CUB, NABirds and iNaturalist we also have taxonomy information including family, order and scientific name. We also append separate texts containing these to the category-wise text corpus to show improvements (Tab. 3). + +NeWT [40] provides a benchmark for a set of 164 complex binary classification tasks in the natural world that ex + +tend beyond species classification. These tasks include determining 1) appearance 2) behavior, 3) context, 4) counting and 5) gestalt. NeWT contains 36k images with 200-400 images per task. We randomly select 50 of the 164 tasks to evaluate our trained model. We manually associate two texts for each task, positive and negative. For example, "a photo of a raptor bird which is not on a utility pole" and "a photo of a raptor bird which is on a utility pole". We show improvements over CLIP (§ 5.5). All details of texts used as well as categories selected are in the Appendix. + +# 4.2. Implementation Details + +For generating category-level texts for training, we utilize the "gpt-4-0613" API. We set the temperature parameter as 0 so that texts generated are deterministic. + +For all queries concerning the classes of iNaturalist (both visual and location) we also append the type of organism as well as it's scientific name in the question. For example, for the class "Bay Laurel" the query for location information is + +Where can we find a Bay Laurel, a type of plant with scientific name Laurus nobilis? Produce a list of habitat and geographic location information that can be used to identify the plant. + +This is required because there exist organisms with the same common name but different domains. Also, we need to append the scientific name as otherwise GPT4 does not recognise the organism in many cases. We provide more details in Appendix. + +Additionally, we experiment with using taxonomy information for training and testing on datasets where it is available (Tab. 3). We form the following texts + +1. a photo of [class] [domain], with scientific name [s_name] +2. a photo of [class] [domain], with family name [family] +3. a photo of [class] [domain], of the order [order] + +While fine-tuning using the texts obtained from an LLM, we train for only 15 epochs on each dataset. On iNaturalist, we train for only 5 epochs. We find hyperparameters by splitting the train classes into two equal parts, training on the first half, and validating on the second. We then fix the best hyperparameters found and train on all train classes. + +The CLIP architecture consists of an image encoder and a text encoder. Both contain transformers followed by a linear projection layer at the end. We use different learning rate and weight decay for the projection layers compared to rest of the encoders. The temperature parameter $\tau$ in our model (§ 3.2) is trainable. We provide the details of the initialization of $\tau$ , the momentum parameter for the EMA encoder as well as learning rates and weight decays of every parameter for all datasets in the Appendix. + +
MethodsCUBStanford CarsFGVC AircractsFlowers 102Food 101
CLIP50.5469.7229.2771.7888.32
CLIP + A50.7169.4730.3575.3790.08
CLIPFT50.81 ± 0.0469.61 ± 0.0731.10 ± 0.0273.68 ± 0.0088.32 ± 0.00
CLIPFT + A53.34 ± 0.0871.63 ± 0.0636.41 ± 0.0277.05 ± 0.0093.71 ± 0.01
+ +Table 1. Comparison with CLIP ViT-B/32 on zero-shot performance on fine-grained domains. We compare our method $\mathrm{CLIP^{FT}} + \mathrm{A}$ to the baselines defined in § 4.3. We significantly improve over baseline CLIP evaluated with both "a photo of a [class] [domain]" and LLM attributes. We also fine-tune CLIP with only "a photo of a [class] [domain]" text and compare with our method to show that our improvements are not due to seeing domain-specific images but also by learning correlations between images and fine-grained attributes. + +
Stanford CarsFGVC AircraticsFlowers 102EuroSATFood 101ImageNet
CLIP74.9436.4777.0564.0592.4967.41
CLIP + A73.8336.4780.8471.5193.7269.74
CLIP-A-self [19]72.9033.0075.3070.5091.2068.30
CLIPFT + A75.7840.7581.2681.8295.0871.87
+ +Table 2. Comparison to prior work using ViT B/16 architecture on zero-shot classification. We show that across a variety of datasets from finer to coarser domains we considerably boost performance over baselines. Here we train using only 16 images per class and test on unseen classes for fair comparison to CLIP-A-self. We do not compare on CUB dataset as CLIP-A-self uses a 3:1 split on CUB, whereas we use 1:1 across all datasets. + +
TextsCUBFlowers 102
Visual53.3477.05
Taxonomy53.07-
Habitat53.6976.00
Vis. + Hab.54.0177.22
Vis. + Tax. + Hab.54.23-
+ +Table 3. Evaluating $\mathbf{CLIP^{FT}} + \mathbf{A}$ using different types of text. We query LLMs to produce visual (vis.) and habitat (hab.) information separately and use taxonomy (tax.) information available with dataset. We train with the type of text specified in each row and test with the same type. Using habitat information works slightly better than using visual information for CUB. All three types of texts are complementary. + +
Train SetCUBFlowers 102
NABirds\overlap55.32-
iNat\overlap54.5877.05
iNat\Birds53.89-
iNat\Plants-76.63
+ +# 4.3. Baselines + +In this section, we discuss the various methods for which we compare zero-shot classification accuracy. + +CLIP refers to pre-trained CLIP tested with "a photo of a [class] [domain]" texts like the original paper. + +$\mathbf{CLIP} + \mathbf{A}$ is evaluating pre-trained CLIP with attributes obtained from LLMs as outlined in § 3.3. + +CLIPFT involves fine-tuning CLIP on training classes using "a photo of [class] [domain]" texts and evaluating on test classes using "a photo of [class] [domain]" texts. + +$\mathbf{CLIP}^{\mathrm{FT}} + \mathbf{A}$ is our method where we fine-tune CLIP (§ 3.2) using attributes obtained from a LLM (§ 3.1) for training classes and evaluate using LLM attributes of testing classes + +Table 4. Evaluating domain transfer performance. Our method offers substantial gain over baseline CLIP (Tab. 1) even when trained on external datasets. Performance boost is competitive even when removing all bird or plant classes from iNat to test on CUB and Flowers respectively. + +
Testing TextsCLIP + ACLIPFT + A
[class] [domain]50.5452.29
GPT 4 Vis.50.7153.34
GPT 3 Vis.51.0853.35
LLaMA Vis.50.1052.52
Ground Truth Vis.52.5353.99
GPT 4 Vis. + Tax. + Hab.52.8354.23
GPT 3 Vis. + Tax. + Hab.52.6353.58
LLaMA Vis. + Tax. + Hab.50.8552.64
+ +Table 5. Evaluating model trained using GPT4 with texts obtained from other models. Our model consistently improves over pre-trained CLIP when evaluated with texts obtained from different LLM models (GPT3.5 and LLaMA2-7B) as well as GT aggregated captions and "a photo of a [class] [domain]". + +at test time as described in $\S 3.3$ + +CLIP-A-self [19] is prior work which uses text obtained from GPT to train an adapter network attached after the text and image encoders of CLIP. For comparing with this, we use the numbers stated by them under their training and evaluation scheme. We test our model on the same classes as them to show improvement. + +# 5. Results + +In this section, we compare our method to baselines and evaluate it under various settings. We discuss our performance improvements over various datasets and architectures. We show that for natural domains using taxonomy and habitat information offers improvements with habitat information especially being a strong factor. Our model scales across architectures and needs only a few epochs of training. We further show that our method performs better than baseline CLIP even under more difficult evaluation settings such as 1) using texts from different LLM models during testing and training; 2) training a model in a do + +main very different from testing domain, and 3) evaluating on tasks other than identifying categories at test time. Additionally, we discuss other training strategies for category-level fine-tuning and how they perform. + +# 5.1. Comparison with Baselines + +Tab. 1 compares our method to three baselines CLIP, $\mathrm{CLIP} + \mathrm{A}$ and $\mathrm{CLIP^{FT}}$ , all evaluated on unseen classes. Here we use the ViT B/32 architecture for all methods. Our method offers considerable improvements over pre-trained CLIP when using "a photo of a [class] [domain]" text and when using GPT generated text. In difficult fine-grained domains such as CUB, Stanford Cars and FGVC Aircrafts pre-trained CLIP does not utilize text attributes generated by GPT resulting in negligible improvement (decrease on Stanford Cars) compared to "a photo of a [class] [domain]" (see $\mathrm{CLIP} + \mathrm{A}$ vs CLIP). This motivates the need to fine-tune using these attributes, resulting in significant improvement across all datasets. We also compare to fine-tuning CLIP with "a photo of a [class] [domain]" texts ( $\mathrm{CLIP^{FT}}$ ) to show that the improvement our method achieves is not due to just being trained on images of concerned domain. + +We compare our method to previous work CLIP-A-self [19] in Tab. 2. We follow [19] and use the ViT B/16 architecture and only 16 images per class for training. Again we evaluate on unseen classes. Our method outperforms CLIP-A-self significantly across all datasets. Also, our method offers substantial improvement over CLIP, showing that it scales across architectures. We discuss why CLIP-A-self underperforms in detail in the Appendix. We also show results on the 14 datasets benchmark in Appendix. + +# 5.2. Using more than just Visual Information + +We explore using information other than visual attributes for natural domains such as birds and flowers. For humans identifying a bird in an image it is crucial to know where the image was taken, because that reveals habitat and location information. We therefore query GPT for an organism's habitat and geographic range. In Tab. 3 we show that for CUB using only habitat information performs better than using only visual information. A reason for this is that habitat information describes the background of the images of birds, which is helping to differentiate between categories. We also show that combining visual + taxonomy + habitat information for CUB and visual + habitat information for Flowers102 offers best improvement. + +# 5.3. Training on External Domains + +We now evaluate under more difficult settings. We train and test on different datasets, always removing any overlapping classes. For training on iNat and NABirds we use all visual + taxonomy + habitat information. While testing + +on CUB we use visual + taxonomy + habitat. For Flowers 102 we use visual + habitat information. Tab. 4 we show the accuracy on CUB test classes improves considerably when training using NABirds and iNat even though the images of these datasets have a distribution shift w.r.t. CUB. More strikingly, we show that even when we remove all bird classes from iNat we still offer improvement on CUB test classes compared to CLIP + A (52.83 → 53.89). Similarly when we remove all plant classes from iNat, we still get improvement on Flowers 102 test set. This proves that our model is also able to generalize well. It is learning to associate fine-grained attributes to images irrespective of the domain differences in training and testing. + +# 5.4. Using Novel Texts during Test Time + +We evaluate how our model would perform in the absence of the LLM used to generate training texts, during test time (Tab 5). We use GPT3.5 turbo (0613) and LLaMA2-7B [38] for generating visual and habitat texts. We show that our method consistently improves performance over pre-trained CLIP for all types of texts explored. Please refer to Appendix for examples of texts produced. Our model also improves performance over pre-trained CLIP while using "a photo of a [class] [domain]" texts. + +Reed et al. [30] present a dataset of human-labelled captions per image for the CUB dataset. We use these ground truth texts at test time to evaluate our model. The dataset contains 10 captions for every image, which are all visual attributes of the bird in the image. Since many attributes in the captions are repeated for each image as well as across images of the same class, and to limit the size of the text corpus, we randomly select one caption per image of a given class and aggregate them to form a category corpus. In Tab. 5 last row, we notice that CLIP does better using these image-level GT texts compared to using GPT4 Visual texts which were category-level (row 2). However, our method still outperforms showing that it is able learn meaningful attributes through noisy labels. + +# 5.5. Evaluation on Novel Tasks + +We use the NeWT [40] benchmark to evaluate on tasks beyond categorization. These include identifying age, attribute, health, photo quality, species, context and behavior. We evaluate the model and baseline CLIP using average Mean Average Precision (MAP) across tasks. Our model trained on iNaturalist using visual + taxonomy + location information outperforms baseline CLIP: 60.25 vs 61.90 MAP $\rightarrow$ $4.1\%$ relative error reduction. We present all tasks and texts we use to evaluate as well as MAP per task in the Appendix. Below is an example prediction: + +![](images/824569385b38f230282dd66a3506485c13201441cc831d2ce6f598b83468a218.jpg) +a photo of a raptor bird which is not on a utility pole + +Probability: 0.38 + +a photo of a raptor bird which is on a utility pole + +Probability: 0.62 + +# 5.6. Resource Requirements + +We fine-tune our model using a 1024 batch size on a single NVIDIA A100 80GB. We need to train only for a maximum of 15 epochs. For smaller datasets such as CUB, FGVC Aircraft, and Stanford Cars, this takes less than 5 minutes. For iNaturalist, which is a large dataset, we train only for 5 epochs, taking about 4 hours. + +The cost of using the GPT-4 API to query text descriptions for a dataset with 100-200 classes (such as CUB) is about \(1-\)5. This is low because it scales with the number of categories and not the number of images. Generating captions per image is both time-consuming and expensive; an estimate for doing this for the CUB dataset using the GPT-4 Vision API is more than \)100. This cost scales significantly for larger datasets with more images. + +# 5.7. Alternate Training Strategies + +Here we discuss other training strategies for improving VLMs using category-level training data. Our simple finetuning strategy of stochastically pairing images with texts within categories is simple, efficient, and offers similar improvements compared to more complex approaches. + +Firstly, since we pair a given image of a category to every text of that category, we might be pairing texts that describe attributes that are not visible. For CUB dataset we have the ground truth visibility annotations of various bird parts, which we use to ignore texts that are occluded for each image. This strategy offers improvement to our scores (54.23 $\rightarrow$ 54.47). However, this depends on visibility information that is time-consuming to generate. + +The next step is to assume that pre-trained CLIP itself is able to correctly identify if a part is visible. Assuming this we mask texts during training time based on CLIP predictions by doing 1) a forward pass for a image and all texts of the category to find the texts above a threshold that can be paired with the image, 2) max pooling at instance level for images and texts. We find that none of these strategies offer any improvement and that pairing images with low scoring texts also (like in our method) is improving performance because CLIP does not accurately identify which fine-grained attributes correctly correspond to given image. + +We also try well-known semi-supervised learning strategies such as FixMatch [35] and knowledge distillation [3]. We find that these offer small $(< 0.2\%)$ to no improvements over our method. Please see the Appendix for details of implementation of all the methods and accuracies. + +# 5.8. Performance of image captioning models. + +We test the recently released GPT4 Vision API for checking quality of image captions obtained. Even though it performs better than previous captioning models such as LLaVA [17] and BLIP2 [16], we find that the captions obtained are general descriptions without fine-grained details. The captions are specific to the image but do not describe information helpful to identify the category. An example is: + +![](images/287811afec208d567aa8977cd83912572cbc854d8329aca6c031dec183f65a75.jpg) + +A slender, streaked brown songbird with keen eyes and a pointed beak perches atop a weathered wooden fence post amidst a backdrop of natural grassland under a clear blue sky. + +For this image of a Vesper Sparrow, GPT4 provides a general description of the bird and suggests the presence of clear blue sky which is not visible in the image. We provide more detail including prompt and examples in Appendix. + +# 6. Limitation + +Since our method is trained on texts generated by LLMs, it is important to verify the correctness of these texts to assess the level of noise in our training dataset. As described in § 3.1, we conduct spot checks across some categories on our evaluation sets. However, for our larger training datasets, vetting becomes impractical. Improved performance on human-generated texts on CUB, as well as the vetted evaluation sets, supports our model's ability to learn meaningful information from somewhat noisy training data. + +# 7. Conclusion + +We present a method to improve the zero-shot performance of VLMs using attributes generated by LLMs on fine-grained domains. Our evaluation strategy involves testing the trained model on unseen classes, texts generated from different LLMs as well as humans, dissimilar domains, and novel tasks. We show that fine-tuning CLIP using category-level descriptions from GPT4 significantly improves performance compared to baselines in this challenging downstream evaluation framework. Our findings suggest that habitat and geographic priors are equally effective and complementary to visual information for zero-shot classification in natural domains. We publicly release our benchmark across all 14 datasets. + +# 8. Acknowledgements + +We thank Aaron Sun, Gustavo Perez, Rangel Daroya, and Mustafa Chasmai for participating in the verification of attributes generated by GPT4. The project is supported in part by NSF Grants #2329927 and #1749833. Our experiments were performed on the GPU cluster funded by the Mass. Technology Collaborative. + +# References + +[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101 – mining discriminative components with random forests. In European Conference on Computer Vision, 2014. 5 +[2] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15659-15669, 2023. 2 \ No newline at end of file diff --git a/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/images.zip b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d2c8ca438848f785c1025940d234aa7a802320a1 --- /dev/null +++ b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:daf4e41c5a5ae94569a5060abab2d3e059e2c53751802fc71d643e859d7ec7d3 +size 396423 diff --git a/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/layout.json b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6a63ae71b541359c74ae662c36911fb7e548c297 --- /dev/null +++ b/2024/Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions/layout.json @@ -0,0 +1,8628 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 103, + 536, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 103, + 536, + 122 + ], + "spans": [ + { + "bbox": [ + 58, + 103, + 536, + 122 + ], + "type": "text", + "content": "Improved Zero-Shot Classification by Adapting VLMs with Text Descriptions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 158, + 143, + 435, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 158, + 143, + 435, + 185 + ], + "spans": [ + { + "bbox": [ + 158, + 143, + 435, + 185 + ], + "type": "text", + "content": "Oindrila Saha Grant Van Horn Subhransu Maji University of Massachusetts, Amherst {osaha, gvanhorn, smaji}@umass.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 238, + 290, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 587 + ], + "type": "text", + "content": "The zero-shot performance of existing vision-language models (VLMs) such as CLIP [29] is limited by the availability of large-scale, aligned image and text datasets in specific domains. In this work, we leverage two complementary sources of information—descriptions of categories generated by large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across fine-grained domains. On the technical side, we develop methods to train VLMs with this \"bag-level\" image-text supervision. We find that simply using these attributes at test-time does not improve performance, but our training strategy, for example, on the iNaturalist [41] dataset, leads to an average improvement of " + }, + { + "bbox": [ + 46, + 238, + 290, + 587 + ], + "type": "inline_equation", + "content": "4 - 5\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 587 + ], + "type": "text", + "content": " in zero-shot classification accuracy for novel categories of birds [42] and flowers [23]. Similar improvements are observed in domains where a subset of the categories was used to fine-tune the model. By prompting LLMs in various ways, we generate descriptions that capture visual appearance, habitat, and geographic regions and pair them with existing attributes such as the taxonomic structure of the categories. We systematically evaluate their ability to improve zero-shot categorization in natural domains. Our findings suggest that geographic priors can be just as effective and are complementary to visual appearance. Our method also outperforms prior work on prompt-based tuning of VLMs. We release the benchmark, consisting of 14 datasets at https://github.com/cvl-umass/AdaptCLIPZS, which will contribute to future research in zero-shot recognition." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Recent improvements in zero-shot classification have been due, in part, to success in training VLMs at scale. Models such as CLIP [29], ALIGN [11], and BLIP [16] use massive datasets of image and text pairs to learn a common embedding between visual and natural language domains. However, we find existing VLMs show poor performance in encoding visual attributes in fine-grained domains, beyond" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 213, + 545, + 356 + ], + "blocks": [ + { + "bbox": [ + 307, + 213, + 545, + 356 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 545, + 356 + ], + "type": "image", + "image_path": "bddf8a38260c140cab794284ddcba734e003b5adc86b65816abe2dc822643ae9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 364, + 547, + 441 + ], + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 441 + ], + "type": "text", + "content": "Figure 1. Motivation. Collecting image captions in fine-grained domains requires expertise (top row), but LLMs can generate structured (e.g., shape or appearance) and accurate descriptions of categories at both the coarse (e.g., birds) and fine-grained level (e.g., Vesper Sparrow). Rich descriptions of fine-grained categories can be paired with existing datasets, such as iNaturalist [41] and NABirds [39] to generate coarsely-aligned image-text datasets for fine-tuning VLMs. This improves their zero-shot performance on a range of benchmarks, generalizing to novel categories and tasks." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "type": "text", + "content": "simply recognizing the name of the category. For example, we observe concatenating visual attribute descriptions to the species name for the bird species in the CUB [42] dataset improves the zero-shot classification from " + }, + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "type": "inline_equation", + "content": "50.5\\%" + }, + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "type": "text", + "content": " to only " + }, + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "type": "inline_equation", + "content": "50.7\\%" + }, + { + "bbox": [ + 304, + 460, + 546, + 592 + ], + "type": "text", + "content": ", while for Cars [14], the performance even drops slightly (see Tab. 1). Although the datasets on which VLMs are trained are extensive, they often lack the details that experts may require for fine-grained categorization. At the same time, collecting large-scale image-caption datasets in these domains requires significant effort, making training similar models challenging." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "In this work, we leverage two complementary sources of information—large language models (LLMs) and abundant, fine-grained image classification datasets—to improve the zero-shot classification performance of VLMs across a variety of fine-grained domains. Concretely, we generate large datasets of images aligned with text by pairing images within a category with descriptions of that category generated by LLMs as seen in Fig. 1. We find this approach works well, as images within a fine-grained domain share many attributes, unlike in coarse categories with" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "17542" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "larger intra-category variation. At the same time, we find that LLMs are capable of accurately describing appearance, habitat, and other properties for a wide range of categories, allowing us to systematically generate datasets in a scalable manner. In other words, fine-grained labels allow us to bridge the gap between image-level captions required for VLM training, and general information about visual categories contained in LLMs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 347 + ], + "type": "text", + "content": "On the technical side, we develop methods to train VLMs with \"bag-level\" supervision. In our dataset a set of images are grouped with a set of descriptions and lack the image-text correspondences. Some of the descriptions may not apply to an image (e.g., the part may be occluded). However, we find that training by stochastically pairing the images and text within a category, followed by a category-level contrastive loss similar to CLIP objective offers robust improvements in performance. Adapting semi-supervised learning approaches such as FixMatch [35] or Knowledge distillation [3] results in minor improvements (" + }, + { + "bbox": [ + 46, + 168, + 287, + 347 + ], + "type": "inline_equation", + "content": "\\S 5.7" + }, + { + "bbox": [ + 46, + 168, + 287, + 347 + ], + "type": "text", + "content": "). A detailed investigation of the image-text association within a category suggests the model is able to correctly associate the visual attributes with the corresponding text even they are paired randomly during training (Fig. 2)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "text", + "content": "We systematically evaluate the effectiveness of our method by assessing the zero-shot classification performance on novel classes. We find that simply using these attributes of novel classes generated by LLMs does not improve performance when using CLIP (Tab. 1). However, our training strategy leads to an average improvement of " + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "inline_equation", + "content": "4 - 5\\%" + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "text", + "content": " in accuracy across 12 datasets, and outperforms baselines (Tab. 2). For natural domains (e.g., iNaturalist and NABirds), we prompt LLMs in various ways to generate descriptions that capture visual appearance, habitat, and geographic regions, and pair them with existing attributes within the dataset, such as taxonomic structure. Our results indicate that geographic priors are equally effective and complementary to visual appearance cues (see Tab. 3). Training on iNaturalist without any bird classes improves the performance of CLIP on CUB by more than " + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "text", + "content": ", and we observe similar improvements when evaluating across other domains (see Tab. 4). Improvements are consistent across text generated by different LLMs, as well as by humans (see Tab. 5). Our model also results in relative error reduction of " + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 46, + 348, + 289, + 600 + ], + "type": "text", + "content": " over CLIP on the challenging NeWT dataset [40]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 609, + 134, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 134, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 134, + 621 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Zero-shot Image Classification using VLMs. Vision Language models (VLMs) [6, 11, 29, 33, 45] learn to associate images with their corresponding text captions. Learning a shared embedding makes them perform exceptionally well in zero-shot classification tasks when paired with an appropriate text such as the class name during test time. FLAVA [33] learns using paired as well as unpaired im" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 223 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 223 + ], + "type": "image", + "image_path": "71a3ad2b6d05ba340f71b6cfb17cc6d2e698e23b22419f1de9392cb45b81c909.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 232, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 348 + ], + "type": "text", + "content": "Figure 2. Visualizing image-text similarity. All images within a category are sorted in order of similarity to a given text predicted by CLIP and our fine-tuned " + }, + { + "bbox": [ + 304, + 232, + 547, + 348 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP^{FT} + A}" + }, + { + "bbox": [ + 304, + 232, + 547, + 348 + ], + "type": "text", + "content": ". For example, our method identifies birds which show olive-green tint on their back as the top images, whereas CLIP selects birds with visibly brown upperparts or occluded back. The image with lowest similarity which has the occluded back remains the same for both models, showing our model does not learn incorrect attribute associations even though we stochastically pair every attribute with every image during training. On the aircraft example our model predicts higher similarity to images with prominently visible fuselage. CLIP identifies the least similar image as one in which fuselage is visible, but ours chooses one where aircrafts are too far to make out the shape of fuselage." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 365, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 544 + ], + "type": "text", + "content": "ages and texts using different losses for multimodal and unimodal understanding. ALIGN [11] uses a large number of noisy image-text data by obtaining alt-texts for images and trains using a contrastive loss. CLIP [29] is trained on a smaller and cleaner dataset of image-text pairs using a similar objective function. It employs a vision model and a language model to learn joint embeddings of images and text. While training, it maximizes the similarity between related image-text pairs and minimizes similarity between unrelated pairs. At test time the similarity over captions such “a photo of a [class name]” over all classes in the domain for each image is found. The image is classified to the class with the caption with highest probability. The original paper shows that manual prompt tuning can boost zero-shot classification accuracy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 545, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 652 + ], + "type": "text", + "content": "Generating Better Prompts. Prior work on prompt tuning [7, 12, 13, 32, 51] has focused on improving the text descriptions of classes. For example, CoOp [50] appends learnable context vectors to the class name texts to improve classification. CoCoOp [49] and related methods have also explored prompting the vision encoder simultaneously. While prompt tuning has proven useful for adapting models to a set of \"base categories\", its performance on novel categories still falls short of the CLIP baseline." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "Another line of research aims at querying LLMs to generate prompts or attributes of categories. CHiLS [24] refines classes based on GPT descriptions (e.g., taxonomic structure) and maps the image to one of the subcategories to improve classification. We also explore the ability to" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "17543" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "learn taxonomy-based attributes in our work. Menon et al. [20] and CuPL [28] append class-specific attributes obtained from GPT [2] to simple prompts, e.g. \"a photo of a [class]\" to improve zero-shot performance at test-time, similar to our approach. However, we find that CLIP struggles to recognize nuanced attributes in fine-grained domains where we observe little to no improvement in classification performance, motivating the need for fine-tuning VLMs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 288, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 288, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 288, + 289 + ], + "type": "text", + "content": "Fine-tuning VLMs. Most work on fine-tuning VLMs has focused on parameter efficient updates using lightweight adapters [8,19,25,27,46,47] for improving few-shot classification. For example, CLIP adapter [8] trains a few learnable layers on top of the encoders, while Maniparambil et al. [19] query LLMs for class-wise descriptions for tuning an external adapter network. Their work improves over CoCoOp and CLIP adapter for unseen classes, however, as before, most approaches show no improvement over CLIP, especially on novel classes in fine-grained datasets." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 289, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 396 + ], + "type": "text", + "content": "Another line of research [9, 34, 37, 43, 48] involves fine-tuning CLIP for robustness to domain shifts. For instance, WiSE-FT [43] utilizes weight-space ensembling to improve performance on a sketch version of ImageNet. Similarly, LaFTer [21] employs fine-tuning both the image and text encoders using unpaired images and texts obtained by querying LLMs. These techniques focus on adapting to a target distribution, such as a specific set of test images or classes, rather than on generalizing to novel classes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 612 + ], + "type": "text", + "content": "Two works similar to ours, GIST [15] and I2MVFormer [22], also utilize GPT to generate category-specific texts for fine-grained domains. GIST pairs each image with the " + }, + { + "bbox": [ + 46, + 396, + 288, + 612 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 396, + 288, + 612 + ], + "type": "text", + "content": " most similar texts within the category based on CLIP similarity and consolidates them into a caption. In contrast, our approach stochastically pairs images with text, a strategy we found to be more robust. Notably, our experiments showed that biasing sampling towards similar image and text pairs led to inferior results (see § 5.7). I2MVFormer uses a LLM to generate class descriptions based on texts provided by annotators and Wikipedia documents. The key differences between their work and ours lie in the use of human effort in their training data generation and starting from scratch resulting in much lower performance compared to ours. Finally, in contrast to both these works, we explore training using visual, habitat, and location information, as well as training on larger datasets such as NABirds and iNaturalist." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Summary To the best of our knowledge, ours is the first method demonstrating that fine-tuning CLIP with class-specific descriptions obtained by querying LLMs improves the zero-shot performance in fine-grained domains. Our approach leverages LLMs to generate image-text data that are coarsely aligned, making it particularly effective for fine-grained categories. Moreover, unlike prior work [19, 20]," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "type": "text", + "content": "our method queries LLMs along various dimensions such as visual, taxonomy, habitat and geographic priors, and systematically evaluates their effectiveness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 119, + 362, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 119, + 362, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 119, + 362, + 132 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": "Consider a dataset " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_i, y_i)\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " consisting of images " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "x_i \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " and labels " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "y_i \\in \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": ". A VLM such as CLIP [29] consists of an image encoder " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\Theta(x) \\approx \\Phi(y)" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " for images " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " with label " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": ". We want to improve the zero-shot performance of CLIP on novel categories in fine-grained domains by fine-tuning the image and the text encoders. We do so either by splitting a dataset " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " training and " + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathrm{test}}" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": " testing classes, or train our model on large datasets such as iNaturalist and NABirds by excluding classes or domains overlapping with our test set. Our framework consists of: 1) generating textual descriptions given the class names by prompting LLMs in different ways (" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\S 3.1" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": "); 2) fine-tuning CLIP using these descriptions using our proposed approach (" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\S 3.2" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": "); and 3) evaluating the models on downstream tasks (" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\S 3.3" + }, + { + "bbox": [ + 304, + 140, + 545, + 331 + ], + "type": "text", + "content": "). Fig. 3 provides an illustration of our method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 339, + 419, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 339, + 419, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 339, + 419, + 350 + ], + "type": "text", + "content": "3.1. Dataset Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 358, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 545, + 395 + ], + "type": "text", + "content": "For each dataset we generate texts for every class which can be used to differentiate it from other classes in the domain using visual attributes. We query an LLM as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 406, + 542, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 406, + 542, + 456 + ], + "spans": [ + { + "bbox": [ + 310, + 406, + 542, + 456 + ], + "type": "text", + "content": "What characteristics can be used to differentiate [class] from other [domain] based on just a photo? Provide an exhaustive list of all attributes that can be used to identify the [domain] uniquely. Texts should be of the form \"[domain] with [characteristic)\"." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "text", + "content": "Here [class] is the class name for the " + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "text", + "content": " classes in the dataset [domain]. Each domain is associated to different datasets, for example for the CUB200 dataset, [domain] is \"bird\" and for iNaturalist dataset it is \"organism\". Appending the domain [domain] is helpful because it provides context about the set of the other classes to distinguish from, and reduces confusion across similar class names in other domains. The LLM produces " + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "inline_equation", + "content": "l_{k}" + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "text", + "content": " descriptions for category " + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "text", + "content": ". We append \"a photo of [class]\" to the generated texts resulting in descriptions of the form \"a photo of a [class] [domain] with [characteristic]\" for each class (more details in the experiment section). This results in a set of descriptions " + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\mathbf{k}}" + }, + { + "bbox": [ + 304, + 468, + 545, + 624 + ], + "type": "text", + "content": " for each category." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "type": "text", + "content": "We also separately query about the habitat and geographic location of occurrence for the classes in CUB200, Flowers102, NABirds and iNaturalist datasets. For this purpose we use the prompt:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 682, + 542, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 682, + 542, + 715 + ], + "spans": [ + { + "bbox": [ + 311, + 682, + 542, + 715 + ], + "type": "text", + "content": "Where can we find a [class]? Produce a list of habitat and geographic location information that can be used to identify the [domain]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17544" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 302, + 248 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 302, + 248 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 302, + 248 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 302, + 248 + ], + "type": "image", + "image_path": "93e7cddf8659b870237fbc7fc658de8b2e03868d53810de90da058be3d2e2f1f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 212, + 257, + 223, + 267 + ], + "lines": [ + { + "bbox": [ + 212, + 257, + 223, + 267 + ], + "spans": [ + { + "bbox": [ + 212, + 257, + 223, + 267 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 547, + 248 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 547, + 248 + ], + "type": "image", + "image_path": "adcad86024e407732ff4c509c37201d0e03e5b59639188badd61bdb94c0f4b2a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 457, + 257, + 468, + 266 + ], + "lines": [ + { + "bbox": [ + 457, + 257, + 468, + 266 + ], + "spans": [ + { + "bbox": [ + 457, + 257, + 468, + 266 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "text", + "content": "Figure 3. Fine-tuning VLMs to improve zero-shot performance. a) Our framework for " + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "inline_equation", + "content": "①" + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "text", + "content": " generating fine-grained attributes per class using LLMs, " + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "inline_equation", + "content": "②" + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "text", + "content": " category-level fine-tuning of VLMs and " + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "inline_equation", + "content": "③" + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "text", + "content": " evaluating on a series of challenging unseen scenarios. b) We show examples of texts produced in step " + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "inline_equation", + "content": "①" + }, + { + "bbox": [ + 46, + 269, + 545, + 289 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "text", + "content": "We add the texts obtained to the category-level corpus " + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\mathbf{k}}" + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "text", + "content": ". The impact of these location-specific texts and the improvements offered are described in the results section. Examples of visual and habitat descriptions are in the Appendix. We determine the correctness of the texts produced for 4-6 classes of CUB, Aircraft and Cars by manual fact-checking texts with the help of online sources. We find that " + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "inline_equation", + "content": "96\\%" + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "text", + "content": " (CUB), " + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "text", + "content": " (Aircraft) and " + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "inline_equation", + "content": "96\\%" + }, + { + "bbox": [ + 46, + 296, + 290, + 439 + ], + "type": "text", + "content": " (Cars) are marked as correct by study participants (more details in Appendix). However, a challenge is that this manual vetting does not scale to large datasets, and we therefore rely on empirical results to support the utility of the generated text." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 466, + 156, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 156, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 156, + 479 + ], + "type": "text", + "content": "3.2. VLM Fine-Tuning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "text", + "content": "CLIP [29] is trained with image caption pairs. However, in our case we have a set of images " + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^{\\mathbf{k}}" + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "text", + "content": " and a set of texts " + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\mathbf{k}}" + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "text", + "content": " for classes " + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "inline_equation", + "content": "k\\in \\mathbf{K}_{\\mathrm{train}}" + }, + { + "bbox": [ + 46, + 491, + 287, + 622 + ], + "type": "text", + "content": " in our training set. We address this by pairing every image with randomly sampled text from the corresponding category during training. However, we cannot directly use the batch-level cross-entropy loss used by CLIP which treats the paired text as positive and rest of the texts as negative. This is because the same batch can contain multiple pairs with images and texts belonging to the same category. Below we describe our modification of the objective function that addresses this." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": "In each iteration of training we sample a batch of size " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " consisting of " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{(x_i, y_i)\\}_{i=1}^N" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " pairs where both " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " is an image and text from the same class. Let the similarity score obtained using the forward pass of CLIP for image " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " and text " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "y_j" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " be " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "S_{ij}" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathsf{c}(i)" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " be the category of image-text pair " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "(x_i, y_i)" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "G_i = \\{j \\mid \\mathsf{c}(j) = \\mathsf{c}(i)\\}" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": " denote the indices of pairs that belong to the same class as pair " + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "(x_i, y_i)" + }, + { + "bbox": [ + 47, + 629, + 288, + 715 + ], + "type": "text", + "content": ". Then the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 296, + 417, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 296, + 417, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 417, + 308 + ], + "type": "text", + "content": "loss function for images is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 311, + 317, + 545, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 317, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 311, + 317, + 545, + 352 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i m a g e}} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {1}{| G _ {i} |} \\sum_ {j \\in G _ {i}} \\log \\frac {\\exp \\left(S _ {i , j} / \\tau\\right)}{\\sum_ {r = 1} ^ {N} \\exp \\left(S _ {i , r} / \\tau\\right)} \\tag {1}", + "image_path": "a820c47a7706e99e8ac66ac783025c2d328b91752883e233df6040ed51d396d2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 361, + 462, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 462, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 462, + 372 + ], + "type": "text", + "content": "and the corresponding one for texts is:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 382, + 545, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 382, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 315, + 382, + 545, + 417 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t e x t} = - \\frac {1}{N} \\sum_ {j = 1} ^ {N} \\frac {1}{| G _ {j} |} \\sum_ {i \\in G _ {j}} \\log \\frac {\\exp \\left(S _ {i , j} / \\tau\\right)}{\\sum_ {r = 1} ^ {N} \\exp \\left(S _ {r , j} / \\tau\\right)} \\tag {2}", + "image_path": "bc255c51b14f1fa2e8f71117542cc30d841ed61a92117926e7735ac711f7689c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "content": " is a learnable temperature parameter. The overall loss for fine-tuning is:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 378, + 460, + 473, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 460, + 473, + 473 + ], + "spans": [ + { + "bbox": [ + 378, + 460, + 473, + 473 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f t} = \\mathcal {L} _ {i m a g e} + \\mathcal {L} _ {t e x t}", + "image_path": "310663dc83662365628cfecf9f51f72e38c94dc4be29ba95e0ca6bb6bb081d1d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "content": "The objective aggregates the image text similarity across all image and text pairs from the same category within the batch. To avoid overfitting on small datasets we maintain momentum encoders whose weights " + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "inline_equation", + "content": "(\\theta_{EMA},\\phi_{EMA})" + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "content": " are updated with the exponential moving average (EMA) of the weights of the encoders " + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "inline_equation", + "content": "(\\theta ,\\phi)" + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "content": " which is trained using the objective " + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ft}" + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 354, + 577, + 496, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 577, + 496, + 604 + ], + "spans": [ + { + "bbox": [ + 354, + 577, + 496, + 604 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\theta_ {E M A} \\leftarrow m \\theta_ {E M A} + (1 - m) \\theta_ {E} \\\\ \\phi_ {E M A} \\leftarrow m \\phi_ {E M A} + (1 - m) \\phi_ {E}, \\\\ \\end{array}", + "image_path": "69061fc8626a08a9d1f32c42f1b813889d00fd57fb66c852214dbd15d1e5c3a3.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 614, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 614, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 614, + 545, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 614, + 545, + 639 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 614, + 545, + 639 + ], + "type": "text", + "content": " is a momentum parameter. All encoders are initialized using the pre-trained weights of CLIP." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 647, + 510, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 510, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 510, + 658 + ], + "type": "text", + "content": "3.3. Evaluation for Zero-shot Classification" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "content": "To evaluate a model on unseen classes we similarly query the LLM as described in §3.1 to obtain texts " + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\mathbf{k}}" + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "k \\in \\mathbf{K}_{\\mathrm{test}}" + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "content": ". For any given image " + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "content": " we can find the similarity score using a VLM for every text " + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "y_{m}^{k}" + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "m \\in \\{1, \\dots, l_{k}\\}" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "17545" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "k \\in \\mathbf{K}_{\\mathrm{test}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "text", + "content": ". Denote the similarity between image " + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "text", + "content": " and text " + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "y_{m}^{k}" + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "S_{m}^{k}" + }, + { + "bbox": [ + 46, + 72, + 287, + 97 + ], + "type": "text", + "content": ". The predicted class is:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 114, + 287, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 114, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 80, + 114, + 287, + 148 + ], + "type": "interline_equation", + "content": "\\underset {k} {\\operatorname {a r g m a x}} \\frac {1}{l _ {k}} \\sum_ {m = 1} ^ {l _ {k}} \\frac {\\exp \\left(S _ {m} ^ {k}\\right)}{\\sum_ {p \\in \\mathbf {K} _ {\\text {t e s t}}} \\sum_ {q = 1} ^ {l _ {p}} \\exp \\left(S _ {q} ^ {p}\\right)} \\tag {3}", + "image_path": "4428d447cea959315721f0c8e2eff92d45c6fefcfde7cfe2ceb2323455ca756d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 156, + 287, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 204 + ], + "type": "text", + "content": "The score represents average similarity between an image and the texts corresponding to each class. Our initial experiments suggested that simple averaging of probabilities is more robust than alternatives such as the geometric mean." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 213, + 128, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 128, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 128, + 227 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "text", + "content": "In this section we present the experimental details of our approach. We outline the datasets we use, the particulars of implementation for each part of the method as well as the details of the baselines we compare our method to." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 289, + 110, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 110, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 110, + 300 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 307, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 287, + 437 + ], + "type": "text", + "content": "We use a variety of fine-grained classification datasets including CUB [42] (200 classes), Flowers 102 [23] (102 classes), Stanford Cars [14] (196 classes), FGVC Aircrafts [18] (100 classes) and Food101 [1] (101 classes). We also apply our method on some coarser datasets including EuroSAT [10] (10 classes), ImageNet [31] (1000 classes), CalTech101 [5] (100 classes), DTD [4] (47 classes), Oxford Pets [26] (37 classes), Sun397 [44] (397 classes) and UCF101 [36] (101 classes). For all these datasets, we use the first half of the classes (ordered by ids of the original dataset) for training and second half for zero-shot testing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 521 + ], + "type": "text", + "content": "We also use NABirds [39] which contains 404 bird classes at species level. We remove the overlapping classes of the CUB testing set from these to obtain 331 training classes. Along with train and test classes being different, this setting also represents a distribution shift in the images of training and testing as images for CUB and NABirds have been obtained in different manners." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "type": "text", + "content": "iNaturalist [41] 2021 is another dataset we utilize to illustrate that our method scales and generalizes. iNaturalist contains 10k classes belonging to 11 general categories (such as birds, plants, fishes). First, in a similar setting to NABirds we remove overlapping test classes of CUB to train a model for testing on CUB. Secondly, we remove all bird classes from iNat and train a model on the remaining classes to test on CUB. We follow similar settings for testing on Flowers 102. Even in these challenging circumstances our method offers improvement over the baselines(§ 5.3)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": "For CUB, NABirds and iNaturalist we also have taxonomy information including family, order and scientific name. We also append separate texts containing these to the category-wise text corpus to show improvements (Tab. 3)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "NeWT [40] provides a benchmark for a set of 164 complex binary classification tasks in the natural world that ex" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": "tend beyond species classification. These tasks include determining 1) appearance 2) behavior, 3) context, 4) counting and 5) gestalt. NeWT contains 36k images with 200-400 images per task. We randomly select 50 of the 164 tasks to evaluate our trained model. We manually associate two texts for each task, positive and negative. For example, \"a photo of a raptor bird which is not on a utility pole\" and \"a photo of a raptor bird which is on a utility pole\". We show improvements over CLIP (§ 5.5). All details of texts used as well as categories selected are in the Appendix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 203, + 440, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 203, + 440, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 203, + 440, + 216 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 224, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 258 + ], + "type": "text", + "content": "For generating category-level texts for training, we utilize the \"gpt-4-0613\" API. We set the temperature parameter as 0 so that texts generated are deterministic." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "type": "text", + "content": "For all queries concerning the classes of iNaturalist (both visual and location) we also append the type of organism as well as it's scientific name in the question. For example, for the class \"Bay Laurel\" the query for location information is" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 324, + 542, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 324, + 542, + 357 + ], + "spans": [ + { + "bbox": [ + 310, + 324, + 542, + 357 + ], + "type": "text", + "content": "Where can we find a Bay Laurel, a type of plant with scientific name Laurus nobilis? Produce a list of habitat and geographic location information that can be used to identify the plant." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 372, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 432 + ], + "type": "text", + "content": "This is required because there exist organisms with the same common name but different domains. Also, we need to append the scientific name as otherwise GPT4 does not recognise the organism in many cases. We provide more details in Appendix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 434, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 469 + ], + "type": "text", + "content": "Additionally, we experiment with using taxonomy information for training and testing on datasets where it is available (Tab. 3). We form the following texts" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 312, + 486, + 539, + 516 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 312, + 486, + 539, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 486, + 539, + 495 + ], + "spans": [ + { + "bbox": [ + 312, + 486, + 539, + 495 + ], + "type": "text", + "content": "1. a photo of [class] [domain], with scientific name [s_name]" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 496, + 535, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 496, + 535, + 506 + ], + "spans": [ + { + "bbox": [ + 313, + 496, + 535, + 506 + ], + "type": "text", + "content": "2. a photo of [class] [domain], with family name [family]" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 506, + 511, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 511, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 511, + 516 + ], + "type": "text", + "content": "3. a photo of [class] [domain], of the order [order]" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 533, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 604 + ], + "type": "text", + "content": "While fine-tuning using the texts obtained from an LLM, we train for only 15 epochs on each dataset. On iNaturalist, we train for only 5 epochs. We find hyperparameters by splitting the train classes into two equal parts, training on the first half, and validating on the second. We then fix the best hyperparameters found and train on all train classes." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The CLIP architecture consists of an image encoder and a text encoder. Both contain transformers followed by a linear projection layer at the end. We use different learning rate and weight decay for the projection layers compared to rest of the encoders. The temperature parameter " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " in our model (§ 3.2) is trainable. We provide the details of the initialization of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", the momentum parameter for the EMA encoder as well as learning rates and weight decays of every parameter for all datasets in the Appendix." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17546" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 96, + 69, + 497, + 133 + ], + "blocks": [ + { + "bbox": [ + 96, + 69, + 497, + 133 + ], + "lines": [ + { + "bbox": [ + 96, + 69, + 497, + 133 + ], + "spans": [ + { + "bbox": [ + 96, + 69, + 497, + 133 + ], + "type": "table", + "html": "
MethodsCUBStanford CarsFGVC AircractsFlowers 102Food 101
CLIP50.5469.7229.2771.7888.32
CLIP + A50.7169.4730.3575.3790.08
CLIPFT50.81 ± 0.0469.61 ± 0.0731.10 ± 0.0273.68 ± 0.0088.32 ± 0.00
CLIPFT + A53.34 ± 0.0871.63 ± 0.0636.41 ± 0.0277.05 ± 0.0093.71 ± 0.01
", + "image_path": "30239383a99ad6a3492f40f4fa2585aabe6977e35e17c334f09d65a2a6b95f31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 77, + 182, + 517, + 244 + ], + "blocks": [ + { + "bbox": [ + 46, + 140, + 545, + 180 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 545, + 180 + ], + "type": "text", + "content": "Table 1. Comparison with CLIP ViT-B/32 on zero-shot performance on fine-grained domains. We compare our method " + }, + { + "bbox": [ + 46, + 140, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP^{FT}} + \\mathrm{A}" + }, + { + "bbox": [ + 46, + 140, + 545, + 180 + ], + "type": "text", + "content": " to the baselines defined in § 4.3. We significantly improve over baseline CLIP evaluated with both \"a photo of a [class] [domain]\" and LLM attributes. We also fine-tune CLIP with only \"a photo of a [class] [domain]\" text and compare with our method to show that our improvements are not due to seeing domain-specific images but also by learning correlations between images and fine-grained attributes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 182, + 517, + 244 + ], + "lines": [ + { + "bbox": [ + 77, + 182, + 517, + 244 + ], + "spans": [ + { + "bbox": [ + 77, + 182, + 517, + 244 + ], + "type": "table", + "html": "
Stanford CarsFGVC AircraticsFlowers 102EuroSATFood 101ImageNet
CLIP74.9436.4777.0564.0592.4967.41
CLIP + A73.8336.4780.8471.5193.7269.74
CLIP-A-self [19]72.9033.0075.3070.5091.2068.30
CLIPFT + A75.7840.7581.2681.8295.0871.87
", + "image_path": "f68a5c8624eeb066c7248d11631378b106cf4cfa39680193b882cfec9410067d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 77, + 285, + 259, + 358 + ], + "blocks": [ + { + "bbox": [ + 46, + 251, + 546, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 546, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 546, + 282 + ], + "type": "text", + "content": "Table 2. Comparison to prior work using ViT B/16 architecture on zero-shot classification. We show that across a variety of datasets from finer to coarser domains we considerably boost performance over baselines. Here we train using only 16 images per class and test on unseen classes for fair comparison to CLIP-A-self. We do not compare on CUB dataset as CLIP-A-self uses a 3:1 split on CUB, whereas we use 1:1 across all datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 285, + 259, + 358 + ], + "lines": [ + { + "bbox": [ + 77, + 285, + 259, + 358 + ], + "spans": [ + { + "bbox": [ + 77, + 285, + 259, + 358 + ], + "type": "table", + "html": "
TextsCUBFlowers 102
Visual53.3477.05
Taxonomy53.07-
Habitat53.6976.00
Vis. + Hab.54.0177.22
Vis. + Tax. + Hab.54.23-
", + "image_path": "5005ce144f228fad5efc7040ffcd802b0469031426fdc884ff8a4bede794d813.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 77, + 429, + 257, + 491 + ], + "blocks": [ + { + "bbox": [ + 46, + 368, + 287, + 426 + ], + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 426 + ], + "type": "text", + "content": "Table 3. Evaluating " + }, + { + "bbox": [ + 46, + 368, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{CLIP^{FT}} + \\mathbf{A}" + }, + { + "bbox": [ + 46, + 368, + 287, + 426 + ], + "type": "text", + "content": " using different types of text. We query LLMs to produce visual (vis.) and habitat (hab.) information separately and use taxonomy (tax.) information available with dataset. We train with the type of text specified in each row and test with the same type. Using habitat information works slightly better than using visual information for CUB. All three types of texts are complementary." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 429, + 257, + 491 + ], + "lines": [ + { + "bbox": [ + 77, + 429, + 257, + 491 + ], + "spans": [ + { + "bbox": [ + 77, + 429, + 257, + 491 + ], + "type": "table", + "html": "
Train SetCUBFlowers 102
NABirds\\overlap55.32-
iNat\\overlap54.5877.05
iNat\\Birds53.89-
iNat\\Plants-76.63
", + "image_path": "ba066b2daf8565ea2051938465774a8f41b218700504c569bb4eafeb22fcaa67.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 550, + 113, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 113, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 113, + 562 + ], + "type": "text", + "content": "4.3. Baselines" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 569, + 286, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 286, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 286, + 593 + ], + "type": "text", + "content": "In this section, we discuss the various methods for which we compare zero-shot classification accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 594, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 286, + 616 + ], + "type": "text", + "content": "CLIP refers to pre-trained CLIP tested with \"a photo of a [class] [domain]\" texts like the original paper." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{CLIP} + \\mathbf{A}" + }, + { + "bbox": [ + 46, + 617, + 286, + 640 + ], + "type": "text", + "content": " is evaluating pre-trained CLIP with attributes obtained from LLMs as outlined in § 3.3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 641, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 677 + ], + "type": "text", + "content": "CLIPFT involves fine-tuning CLIP on training classes using \"a photo of [class] [domain]\" texts and evaluating on test classes using \"a photo of [class] [domain]\" texts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{CLIP}^{\\mathrm{FT}} + \\mathbf{A}" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": " is our method where we fine-tune CLIP (§ 3.2) using attributes obtained from a LLM (§ 3.1) for training classes and evaluate using LLM attributes of testing classes" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 306, + 285, + 542, + 397 + ], + "blocks": [ + { + "bbox": [ + 46, + 499, + 287, + 539 + ], + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 539 + ], + "type": "text", + "content": "Table 4. Evaluating domain transfer performance. Our method offers substantial gain over baseline CLIP (Tab. 1) even when trained on external datasets. Performance boost is competitive even when removing all bird or plant classes from iNat to test on CUB and Flowers respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 285, + 542, + 397 + ], + "lines": [ + { + "bbox": [ + 306, + 285, + 542, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 542, + 397 + ], + "type": "table", + "html": "
Testing TextsCLIP + ACLIPFT + A
[class] [domain]50.5452.29
GPT 4 Vis.50.7153.34
GPT 3 Vis.51.0853.35
LLaMA Vis.50.1052.52
Ground Truth Vis.52.5353.99
GPT 4 Vis. + Tax. + Hab.52.8354.23
GPT 3 Vis. + Tax. + Hab.52.6353.58
LLaMA Vis. + Tax. + Hab.50.8552.64
", + "image_path": "bb664dfd667cbb410dacfdc9f1f3d289e15bc7a3f5f68cc9bf12467e2fe64338.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "lines": [ + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "type": "text", + "content": "Table 5. Evaluating model trained using GPT4 with texts obtained from other models. Our model consistently improves over pre-trained CLIP when evaluated with texts obtained from different LLM models (GPT3.5 and LLaMA2-7B) as well as GT aggregated captions and \"a photo of a [class] [domain]\"." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 467, + 440, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 467, + 440, + 478 + ], + "spans": [ + { + "bbox": [ + 305, + 467, + 440, + 478 + ], + "type": "text", + "content": "at test time as described in " + }, + { + "bbox": [ + 305, + 467, + 440, + 478 + ], + "type": "inline_equation", + "content": "\\S 3.3" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 479, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 552 + ], + "type": "text", + "content": "CLIP-A-self [19] is prior work which uses text obtained from GPT to train an adapter network attached after the text and image encoders of CLIP. For comparing with this, we use the numbers stated by them under their training and evaluation scheme. We test our model on the same classes as them to show improvement." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 561, + 359, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 359, + 573 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 359, + 573 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "In this section, we compare our method to baselines and evaluate it under various settings. We discuss our performance improvements over various datasets and architectures. We show that for natural domains using taxonomy and habitat information offers improvements with habitat information especially being a strong factor. Our model scales across architectures and needs only a few epochs of training. We further show that our method performs better than baseline CLIP even under more difficult evaluation settings such as 1) using texts from different LLM models during testing and training; 2) training a model in a do" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "17547" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "main very different from testing domain, and 3) evaluating on tasks other than identifying categories at test time. Additionally, we discuss other training strategies for category-level fine-tuning and how they perform." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 128, + 197, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 128, + 197, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 128, + 197, + 140 + ], + "type": "text", + "content": "5.1. Comparison with Baselines" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "text", + "content": "Tab. 1 compares our method to three baselines CLIP, " + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP} + \\mathrm{A}" + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP^{FT}}" + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "text", + "content": ", all evaluated on unseen classes. Here we use the ViT B/32 architecture for all methods. Our method offers considerable improvements over pre-trained CLIP when using \"a photo of a [class] [domain]\" text and when using GPT generated text. In difficult fine-grained domains such as CUB, Stanford Cars and FGVC Aircrafts pre-trained CLIP does not utilize text attributes generated by GPT resulting in negligible improvement (decrease on Stanford Cars) compared to \"a photo of a [class] [domain]\" (see " + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP} + \\mathrm{A}" + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "text", + "content": " vs CLIP). This motivates the need to fine-tune using these attributes, resulting in significant improvement across all datasets. We also compare to fine-tuning CLIP with \"a photo of a [class] [domain]\" texts (" + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathrm{CLIP^{FT}}" + }, + { + "bbox": [ + 46, + 146, + 287, + 350 + ], + "type": "text", + "content": ") to show that the improvement our method achieves is not due to just being trained on images of concerned domain." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 350, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 458 + ], + "type": "text", + "content": "We compare our method to previous work CLIP-A-self [19] in Tab. 2. We follow [19] and use the ViT B/16 architecture and only 16 images per class for training. Again we evaluate on unseen classes. Our method outperforms CLIP-A-self significantly across all datasets. Also, our method offers substantial improvement over CLIP, showing that it scales across architectures. We discuss why CLIP-A-self underperforms in detail in the Appendix. We also show results on the 14 datasets benchmark in Appendix." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 465, + 259, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 259, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 259, + 478 + ], + "type": "text", + "content": "5.2. Using more than just Visual Information" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 639 + ], + "type": "text", + "content": "We explore using information other than visual attributes for natural domains such as birds and flowers. For humans identifying a bird in an image it is crucial to know where the image was taken, because that reveals habitat and location information. We therefore query GPT for an organism's habitat and geographic range. In Tab. 3 we show that for CUB using only habitat information performs better than using only visual information. A reason for this is that habitat information describes the background of the images of birds, which is helping to differentiate between categories. We also show that combining visual + taxonomy + habitat information for CUB and visual + habitat information for Flowers102 offers best improvement." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 647, + 212, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 212, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 212, + 659 + ], + "type": "text", + "content": "5.3. Training on External Domains" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "We now evaluate under more difficult settings. We train and test on different datasets, always removing any overlapping classes. For training on iNat and NABirds we use all visual + taxonomy + habitat information. While testing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "on CUB we use visual + taxonomy + habitat. For Flowers 102 we use visual + habitat information. Tab. 4 we show the accuracy on CUB test classes improves considerably when training using NABirds and iNat even though the images of these datasets have a distribution shift w.r.t. CUB. More strikingly, we show that even when we remove all bird classes from iNat we still offer improvement on CUB test classes compared to CLIP + A (52.83 → 53.89). Similarly when we remove all plant classes from iNat, we still get improvement on Flowers 102 test set. This proves that our model is also able to generalize well. It is learning to associate fine-grained attributes to images irrespective of the domain differences in training and testing." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 236, + 495, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 236, + 495, + 248 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 495, + 248 + ], + "type": "text", + "content": "5.4. Using Novel Texts during Test Time" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 254, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 361 + ], + "type": "text", + "content": "We evaluate how our model would perform in the absence of the LLM used to generate training texts, during test time (Tab 5). We use GPT3.5 turbo (0613) and LLaMA2-7B [38] for generating visual and habitat texts. We show that our method consistently improves performance over pre-trained CLIP for all types of texts explored. Please refer to Appendix for examples of texts produced. Our model also improves performance over pre-trained CLIP while using \"a photo of a [class] [domain]\" texts." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 363, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 529 + ], + "type": "text", + "content": "Reed et al. [30] present a dataset of human-labelled captions per image for the CUB dataset. We use these ground truth texts at test time to evaluate our model. The dataset contains 10 captions for every image, which are all visual attributes of the bird in the image. Since many attributes in the captions are repeated for each image as well as across images of the same class, and to limit the size of the text corpus, we randomly select one caption per image of a given class and aggregate them to form a category corpus. In Tab. 5 last row, we notice that CLIP does better using these image-level GT texts compared to using GPT4 Visual texts which were category-level (row 2). However, our method still outperforms showing that it is able learn meaningful attributes through noisy labels." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 537, + 452, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 452, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 452, + 549 + ], + "type": "text", + "content": "5.5. Evaluation on Novel Tasks" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "text", + "content": "We use the NeWT [40] benchmark to evaluate on tasks beyond categorization. These include identifying age, attribute, health, photo quality, species, context and behavior. We evaluate the model and baseline CLIP using average Mean Average Precision (MAP) across tasks. Our model trained on iNaturalist using visual + taxonomy + location information outperforms baseline CLIP: 60.25 vs 61.90 MAP " + }, + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "text", + "content": " relative error reduction. We present all tasks and texts we use to evaluate as well as MAP per task in the Appendix. Below is an example prediction:" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 545, + 713 + ], + "type": "text", + "content": "1LLaMA model does not always produce texts in the specified format and thus needs post-processing. The texts formed finally are considerably different grammatically from the sentences our model has been trained on." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17548" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 73, + 115, + 125 + ], + "blocks": [ + { + "bbox": [ + 49, + 73, + 115, + 125 + ], + "lines": [ + { + "bbox": [ + 49, + 73, + 115, + 125 + ], + "spans": [ + { + "bbox": [ + 49, + 73, + 115, + 125 + ], + "type": "image", + "image_path": "824569385b38f230282dd66a3506485c13201441cc831d2ce6f598b83468a218.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 132, + 76, + 205, + 99 + ], + "lines": [ + { + "bbox": [ + 132, + 76, + 205, + 99 + ], + "spans": [ + { + "bbox": [ + 132, + 76, + 205, + 99 + ], + "type": "text", + "content": "a photo of a raptor bird which is not on a utility pole" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 110, + 194, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 110, + 194, + 119 + ], + "spans": [ + { + "bbox": [ + 141, + 110, + 194, + 119 + ], + "type": "text", + "content": "Probability: 0.38" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 221, + 76, + 285, + 99 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 221, + 76, + 285, + 99 + ], + "spans": [ + { + "bbox": [ + 221, + 76, + 285, + 99 + ], + "type": "text", + "content": "a photo of a raptor bird which is on a utility pole" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 227, + 110, + 279, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 227, + 110, + 279, + 119 + ], + "spans": [ + { + "bbox": [ + 227, + 110, + 279, + 119 + ], + "type": "text", + "content": "Probability: 0.62" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 147, + 181, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 147, + 181, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 147, + 181, + 159 + ], + "type": "text", + "content": "5.6. Resource Requirements" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 166, + 287, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 238 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 238 + ], + "type": "text", + "content": "We fine-tune our model using a 1024 batch size on a single NVIDIA A100 80GB. We need to train only for a maximum of 15 epochs. For smaller datasets such as CUB, FGVC Aircraft, and Stanford Cars, this takes less than 5 minutes. For iNaturalist, which is a large dataset, we train only for 5 epochs, taking about 4 hours." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": "The cost of using the GPT-4 API to query text descriptions for a dataset with 100-200 classes (such as CUB) is about \\(1-\\)5. This is low because it scales with the number of categories and not the number of images. Generating captions per image is both time-consuming and expensive; an estimate for doing this for the CUB dataset using the GPT-4 Vision API is more than \\)100. This cost scales significantly for larger datasets with more images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 344, + 206, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 206, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 206, + 357 + ], + "type": "text", + "content": "5.7. Alternate Training Strategies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 364, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 424 + ], + "type": "text", + "content": "Here we discuss other training strategies for improving VLMs using category-level training data. Our simple finetuning strategy of stochastically pairing images with texts within categories is simple, efficient, and offers similar improvements compared to more complex approaches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "type": "text", + "content": "Firstly, since we pair a given image of a category to every text of that category, we might be pairing texts that describe attributes that are not visible. For CUB dataset we have the ground truth visibility annotations of various bird parts, which we use to ignore texts that are occluded for each image. This strategy offers improvement to our scores (54.23 " + }, + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "type": "text", + "content": " 54.47). However, this depends on visibility information that is time-consuming to generate." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "content": "The next step is to assume that pre-trained CLIP itself is able to correctly identify if a part is visible. Assuming this we mask texts during training time based on CLIP predictions by doing 1) a forward pass for a image and all texts of the category to find the texts above a threshold that can be paired with the image, 2) max pooling at instance level for images and texts. We find that none of these strategies offer any improvement and that pairing images with low scoring texts also (like in our method) is improving performance because CLIP does not accurately identify which fine-grained attributes correctly correspond to given image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "We also try well-known semi-supervised learning strategies such as FixMatch [35] and knowledge distillation [3]. We find that these offer small " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "(< 0.2\\%)" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " to no improvements over our method. Please see the Appendix for details of implementation of all the methods and accuracies." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 522, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 522, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 522, + 85 + ], + "type": "text", + "content": "5.8. Performance of image captioning models." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 90, + 545, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 175 + ], + "type": "text", + "content": "We test the recently released GPT4 Vision API for checking quality of image captions obtained. Even though it performs better than previous captioning models such as LLaVA [17] and BLIP2 [16], we find that the captions obtained are general descriptions without fine-grained details. The captions are specific to the image but do not describe information helpful to identify the category. An example is:" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 307, + 183, + 352, + 228 + ], + "blocks": [ + { + "bbox": [ + 307, + 183, + 352, + 228 + ], + "lines": [ + { + "bbox": [ + 307, + 183, + 352, + 228 + ], + "spans": [ + { + "bbox": [ + 307, + 183, + 352, + 228 + ], + "type": "image", + "image_path": "287811afec208d567aa8977cd83912572cbc854d8329aca6c031dec183f65a75.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 356, + 185, + 543, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 185, + 543, + 226 + ], + "spans": [ + { + "bbox": [ + 356, + 185, + 543, + 226 + ], + "type": "text", + "content": "A slender, streaked brown songbird with keen eyes and a pointed beak perches atop a weathered wooden fence post amidst a backdrop of natural grassland under a clear blue sky." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 242, + 545, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 545, + 290 + ], + "type": "text", + "content": "For this image of a Vesper Sparrow, GPT4 provides a general description of the bird and suggests the presence of clear blue sky which is not visible in the image. We provide more detail including prompt and examples in Appendix." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 299, + 375, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 299, + 375, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 375, + 312 + ], + "type": "text", + "content": "6. Limitation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 319, + 545, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 428 + ], + "type": "text", + "content": "Since our method is trained on texts generated by LLMs, it is important to verify the correctness of these texts to assess the level of noise in our training dataset. As described in § 3.1, we conduct spot checks across some categories on our evaluation sets. However, for our larger training datasets, vetting becomes impractical. Improved performance on human-generated texts on CUB, as well as the vetted evaluation sets, supports our model's ability to learn meaningful information from somewhat noisy training data." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 436, + 378, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 378, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 378, + 449 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "text", + "content": "We present a method to improve the zero-shot performance of VLMs using attributes generated by LLMs on fine-grained domains. Our evaluation strategy involves testing the trained model on unseen classes, texts generated from different LLMs as well as humans, dissimilar domains, and novel tasks. We show that fine-tuning CLIP using category-level descriptions from GPT4 significantly improves performance compared to baselines in this challenging downstream evaluation framework. Our findings suggest that habitat and geographic priors are equally effective and complementary to visual information for zero-shot classification in natural domains. We publicly release our benchmark across all 14 datasets." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 621, + 420, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 420, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 420, + 635 + ], + "type": "text", + "content": "8. Acknowledgements" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "We thank Aaron Sun, Gustavo Perez, Rangel Daroya, and Mustafa Chasmai for participating in the verification of attributes generated by GPT4. The project is supported in part by NSF Grants #2329927 and #1749833. Our experiments were performed on the GPU cluster funded by the Mass. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15659-15669, 2023. 2" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "17552" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/64afc4ea-9f99-49c3-ab03-ca65285f08d0_content_list.json b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/64afc4ea-9f99-49c3-ab03-ca65285f08d0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9076743e41ef7dd52f516f1b0a9e831f7ecc2356 --- /dev/null +++ b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/64afc4ea-9f99-49c3-ab03-ca65285f08d0_content_list.json @@ -0,0 +1,1634 @@ +[ + { + "type": "text", + "text": "Improving Bird's Eye View Semantic Segmentation by Task Decomposition", + "text_level": 1, + "bbox": [ + 106, + 130, + 864, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tianhao Zhao $^{1*}$ Yongcan Chen $^{1*}$ Yu Wu $^{1}$ Tianyang Liu $^{1}$ Bo Du $^{1\\dagger}$ \nPeilun Xiao $^{2}$ Shi Qiu $^{2}$ Hongda Yang $^{2}$ Guozhen Li $^{2}$ Yi Yang $^{2}$ Yutian Lin $^{1\\dagger}$ $^{1}$ Institute of Artificial Intelligence, School of Computer Science, Hubei Luojia Laboratory, Wuhan University, Wuhan, China \n $^{2}$ Didi Chuxing, China \n{happytianhao, chenyongcan, wuyucs, bodu, yutian.lin}@whu.edu.cn", + "bbox": [ + 156, + 179, + 836, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 321, + 313, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation in bird's eye view (BEV) plays a crucial role in autonomous driving. Previous methods usually follow an end-to-end pipeline, directly predicting the BEV segmentation map from monocular RGB inputs. However, the challenge arises when the RGB inputs and BEV targets from distinct perspectives, making the direct point-to-point predicting hard to optimize. In this paper, we decompose the original BEV segmentation task into two stages, namely BEV map reconstruction and RGB-BEV feature alignment. In the first stage, we train a BEV autoencoder to reconstruct the BEV segmentation maps given corrupted noisy latent representation, which urges the decoder to learn fundamental knowledge of typical BEV patterns. The second stage involves mapping RGB input images into the BEV latent space of the first stage, directly optimizing the correlations between the two views at the feature level. Our approach simplifies the complexity of combining perception and generation into distinct steps, equipping the model to handle intricate and challenging scenes effectively. Besides, we propose to transform the BEV segmentation map from the Cartesian to the polar coordinate system to establish the column-wise correspondence between RGB images and BEV maps. Moreover, our method requires neither multi-scale features nor camera intrinsic parameters for depth estimation and saves computational overhead. Extensive experiments on nuScenes and Argoverse show the effectiveness and efficiency of our method. Code is available at https://github.com/happytianhao/TaDe.", + "bbox": [ + 76, + 354, + 473, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 806, + 209, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the field of autonomous driving, bird's eye view (BEV) perception tasks can obtain adequate semantic in", + "bbox": [ + 76, + 833, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e040d1292070b63a6e169303d7142f7a790b13f4216371a4ff928d1d6ec51276.jpg", + "image_caption": [ + "Figure 1. Qualitative comparison between traditional end-to-end method and our method. (a) shows the perspective view RGB image, (b) and (c) show the BEV segmentation maps predicted without and with the method of task decomposition, respectively." + ], + "image_footnote": [], + "bbox": [ + 501, + 320, + 681, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9e6a0628b1b4dd3be42d68ce1019581c63e039e198860820792e09fcf5979b73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 683, + 320, + 785, + 414 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81851a0c53dc7d09a1e6136f3fa51216272b5577b2b53d90c498b7f840173e5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 320, + 890, + 415 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "formation such as road layout, object categories, positions, and scales around vehicles. This kind of information is called BEV representation and can be directly applied to downstream tasks such as layout mapping, action prediction, route planning, and collision avoidance. In this work, we focus on the monocular BEV segmentation task, which is a fundamental task that aims to predict road segments from camera inputs.", + "bbox": [ + 496, + 505, + 890, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous BEV segmentation methods [6,16,18,23,25,28, 31,34,40,41] usually follow an end-to-end pipeline, which adopts a transformer-based architecture to directly predict BEV segmentation maps from the input RGB images. However, different from the general segmentation task, the input images and targets in BEV are of distinct views (perspective view versus bird's eye view), thus it is hard to train the model by direct point-to-point optimization. And it is even harder when attempting to achieve both source information perception and target view generation in a single step. As shown in Figure 1 (b), the generated BEV segmentation map of the end-to-end baseline looks distorted and does not conform to the expected regular patterns found in real-world traffic scenes.", + "bbox": [ + 496, + 627, + 892, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To achieve the complex cross-view BEV segmentation, we propose a Task Decomposition (TaDe) method that decompose the traditional end-to-end pipeline into two distinct but goal-oriented stages. In the first stage, we train an", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15512", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "autoencoder model to learn a basic understanding of typical BEV scene patterns, enabling it to generate coherent and rational BEV segmentation maps independent from RGB images. In the second stage, given input RGB images, we only intend to obtain the latent BEV feature, leaving the workload of BEV segmentation map prediction to the pretrained decoder of the first stage. This two-stage approach, with each stage focusing on only one mission, equips the model with the capacity to handle more intricate and challenging scene perception. As shown in Figure 1 (c), with the help of task decomposition, the predicted BEV segmentation maps share greater structural similarity with the RGB image.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To be specific, in the first stage, to generate BEV maps that are consistent with physical rules, it is crucial to have a specific expert to comprehend the global traffic layout. For instance, walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow circles. To incorporate this prior knowledge, we employ an autoencoder to learn how to reconstruct/generate the target BEV segmentation maps. To learn a more intrinsic and robust generating ability, we disturb the autoencoder by corrupting the latent representation with random noise during training and enforce the model perfectly reconstruct the ground truth with only the noised latent. This reconstruction can locally recognize and predict typical patterns in BEV segmentation maps, thereby ensuring reasonable BEV map generation given imperfect latent representations.", + "bbox": [ + 75, + 275, + 472, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the second stage, we aim to learn a smooth transition from the perspective RGB input to the BEV semantic latent space. Specifically, the model encodes the input RGB images into features and leverages a column-wise transformer to transit them into the BEV latent space. The training objective of the second stage is to ensure that the transited RGB representations align seamlessly with the target BEV latent space. Thus we input the BEV label maps to the frozen BEV encoder of Stage I to get the BEV latent feature, and then take this BEV feature as the optimization target for the transition model of Stage II. Different from existing works, the optimization is in the autoencoder latent space, rather than the traditional pixel segmentation classification space. During inference, since the representations of both views have been already aligned, the transited RGB feature can directly go through the BEV decoder of Stage I for the final BEV segmentation mask prediction.", + "bbox": [ + 75, + 518, + 472, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, to achieve better cross-view alignment, we introduce a coordinate transform step that converts the original BEV segmentation map from Cartesian to polar coordinates. In the transformed BEV map, each column shares the same spatial information with the input monocular RGB images, which also benefits the smooth transition of cross-view features in the second stage. Extensive experiments on two large-scale datasets including nuScenes [2] and Argo", + "bbox": [ + 75, + 780, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "verse [4] clearly demonstrate our superiority compared to prior end-to-end works.", + "bbox": [ + 496, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 517, + 121, + 844, + 135 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We break down the traditional end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception).", + "- We propose a BEV autoencoder to automatically learn typical patterns by reconstructing BEV maps from corrupted latent features, ensuring the decoder prediction is rational and adheres to the real world.", + "- We also transform the BEV label map from Cartesian to polar coordinates to learn better alignment across perspective views and bird's eye views." + ], + "bbox": [ + 517, + 148, + 890, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 335, + 650, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Bird's Eye View (BEV) Perception", + "text_level": 1, + "bbox": [ + 500, + 359, + 799, + 376 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As BEV representations contain rich semantic information and can be directly applied to numerous downstream tasks, BEV perception has received widespread attention in the field of autonomous driving. However, converting the perspective view captured by cameras to the bird's eye view is an ill-posed problem, which makes it hard to meet the autonomous driving requirements of complex real-world scenarios. Early works [13, 14, 17, 22, 26, 27, 29, 39] addressed this challenge based on a bottom-up strategy. They first predict the position in the 3D space by estimating the depth of each pixel in the perspective view and then project the 3D position to the BEV space based on the internal and external parameters of the cameras. Nevertheless, despite being intuitive, bottom-up methods depend on the accuracy of depth estimation and have high computational complexity. Recent works follow a top-down strategy. Inspired by DETR [3], DETR3D [36] detects objects from object queries in 3D space with a transformer. BEVFormer [18] and BEVFormer v2 [37] add dense object queries based on DETR3D to achieve map segmentation. PETR [20] and PETRv2 [21] introduce 3D position encoding to DETR3D and significantly simplify the pipeline.", + "bbox": [ + 496, + 383, + 890, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Monocular BEV Segmentation", + "text_level": 1, + "bbox": [ + 500, + 726, + 772, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional BEV perception methods focus on calculating the corresponding relationship between the coordinates of the perspective view and the bird's eye view by using the internal and external parameters of the cameras. However, due to the geometric distortion and the presence of overlapping parts and gaps between the perspective views, the perception effect is not ideal. In this regard, some works [1, 5, 10, 11, 24, 33] propose to predict the BEV segmentation map of road layout and objects directly in the case of giving a monocular perspective view.", + "bbox": [ + 496, + 750, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15513", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "PYVA [38] proposes a GAN-based framework and designs a cross-view conversion module to handle significant differences between views. VED [23] employs a variational encoder-decoder network to directly anticipate a semantic occupancy grid from an image. However, the inclusion of a fully connected bottleneck layer in the network results in the loss of significant spatial context and an output that is relatively coarse and incapable of capturing smaller objects like pedestrians. CVT [40] designs a transformer and utilizes the camera's intrinsic and extrinsic calibrations to efficiently understand the surrounding environment. PON [31] adopts a semantic Bayesian occupancy grid framework to estimate BEV segmentation maps directly from monocular perspective views. HFT [41] provides a balanced approach that combines structured geometric information from model-based methods with the global context-capturing ability of model-free methods to overcome their respective limitations in image processing. DiffBEV [42] and DDP [15] propose an end-to-end framework to generate a more comprehensive BEV representation and denoise noisy samples by applying the diffusion model to BEV perception.", + "bbox": [ + 76, + 90, + 472, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Polar-based Methods", + "text_level": 1, + "bbox": [ + 76, + 416, + 276, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "So far, many works have made significant progress in the BEV segmentation task. However, due to the fact that the perspective view is established in a 3D polar coordinate system, while the bird's eye view is established in a 2D Cartesian coordinate system with the camera as the origin, this gap has led to the previous method's unsatisfactory performance. Therefore, in order to reduce this gap, some methods choose to convert the ground truth of the bird's eye view in the Cartesian coordinate system to the polar coordinate system, corresponding to the perspective view, in order to better learn the relationship between them. PolarDETR [6] converts the object representation in DETR3D from the Cartesian coordinate system to the polar coordinate system. PolarFormer [16] incorporates a polar alignment module to aggregate rays from multiple cameras and generate a structured polar feature map. TIM [34] formulates BEV segmentation map generation from an image as a set of sequence-to-sequence translations and proposes a novel form of end-to-end transformer network to translate between a vertical scanline in the image and rays passing through the camera location in the bird's eye view. GitNet [9] first learns visibility-aware features and learnable geometry to translate into BEV space and then deforms the pre-aligned coarse BEV features with visibility knowledge by ray-based transformers.", + "bbox": [ + 76, + 440, + 472, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 829, + 166, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose TaDe (Task Decomposition) to break down the traditional end-to-end training pipeline into two simple and distinct stages: (1) With the BEV autoencoder, BEV", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fd99876f9472f96c35a3ba49d19f49b41b37880130d0a8af99a588b301b79396.jpg", + "image_caption": [ + "Figure 2. Illustration of the transformation between Cartesian (left) and polar (right) coordinate system for BEV segmentation maps. This transformation can achieve a column-wise correspondence between the BEV segmentation maps and the RGB images." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 890, + 218 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "segmentation maps with $50\\%$ noise are reconstructed to recognize and predict the typical patterns and obtain the BEV latent representations. (2) With the RGB-BEV alignment, the input monocular RGB images are mapped into the BEV latent space via a column-wise transformer to achieve view alignment. During testing, the BEV decoder is employed to generate BEV semantic segmentation maps. In this section, we first introduce the coordinate system transformation of target BEV maps in Section 3.1. After that, we elaborate on the BEV autoencoder and column-wise feature mapping in Section 3.2. and Section 3.3., respectively.", + "bbox": [ + 498, + 306, + 893, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. BEV Coordinate System Transformation", + "text_level": 1, + "bbox": [ + 500, + 483, + 849, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the monocular BEV semantic segmentation task, the input RGB images are captured from a perspective view in polar coordinates, while the segmented output targets originate from the bird's eye view in Cartesian coordinates. Consequently, there exists no pixel-level correspondence between the input RGB images and the target segmentation maps, unlike traditional semantic segmentation tasks, which makes this task extremely challenging. However, previous polar-based methods [9, 34] have identified a corresponding relationship between the columns of RGB images and the rays in BEV segmentation maps with the camera position as the origin. To establish this correspondence, they conducted resampling from polar to Cartesian coordinates in the feature space. In contrast, to facilitate BEV autoencoder training and achieve column-wise feature alignment, we directly apply coordinate system transformation on the BEV segmentation maps.", + "bbox": [ + 498, + 507, + 890, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To be specific, as illustrated in Figure 2, we employ a resampling method to transform the BEV segmentation maps between the Cartesian and polar coordinate systems to achieve a column-wise spatial correspondence between the BEV segmentation maps and RGB images. For instance, in the Cartesian to polar conversion, for each pixel in the polar map, we calculate the corresponding coordinate in the Cartesian map according to the field of view (FOV) and resample from the nearby pixels, and vice versa. Note that", + "bbox": [ + 498, + 765, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15514", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9dd3092f825a23a6afe0c44e7690ce5791dd505ee8f76b6c1138574b2e06f83a.jpg", + "image_caption": [ + "(b) Stage 2: RGB-BEV Alignment", + "Figure 3. Overview of our two-stage method. (a) In the first stage, a BEV autoencoder is trained by BEV segmentation maps independent from RGB images. (b) In the second stage, the BEV autoencoder is frozen and the RGB-BEV alignment is conducted to match the RGB images to BEV latent representations for decoding." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 890, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "this transform is deterministic and does not require training. During training, we transform the BEV segmentation maps from the Cartesian to the polar coordinate system for reconstruction and encoding. During testing, we transform the predicted BEV segmentation maps from the polar to the Cartesian coordinate system for further quantitative and qualitative validation.", + "bbox": [ + 75, + 377, + 468, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. BEV Autoencoder", + "text_level": 1, + "bbox": [ + 76, + 494, + 253, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve rational BEV map generation, it is essential to possess a profound understanding of the traffic scene occupancy patterns. In the real world, there is prior knowledge within the traffic BEV segmentation map, where walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow shapes. However, in previous methods, the generated BEV segmentation map does not match real traffic patterns effectively. To address this issue, we introduce a BEV autoencoder, which is designed to reconstruct the BEV segmentation map in polar coordinates. Notably, we introduce $50\\%$ noise into the BEV latent representation for reconstruction. This addition of noise renders the reconstruction task more challenging, which requires a holistic understanding of the traffic scene patterns and thus ensures the creation of rational BEV maps that align more closely with real-world expectations.", + "bbox": [ + 75, + 518, + 468, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Figure 3 (a), the BEV autoencoder consists of a BEV encoder denoted as $E(\\cdot)$ , and a BEV decoder denoted as $D(\\cdot)$ . Given a BEV segmentation map $y$ in polar coordinates, the BEV autoencoder is outlined as follows:", + "bbox": [ + 75, + 777, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz = E (y), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 235, + 851, + 468, + 867 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = D (\\tilde {z}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 235, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z$ and $\\hat{z}$ denotes the BEV latent representation, $\\hat{y}$ denotes the reconstructed vector in input space. Note that we obtain $z$ with a low scale of $8 \\times 22$ , which can thus be seen as a latent representation of $y$ .", + "bbox": [ + 496, + 377, + 890, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the simplicity of BEV segmentation maps, the criterion is not sufficient to obtain a useful representation or effective decoder. Therefore, we added a large amount of Gaussian noise (e.g. $50\\%$ ) to the latent feature map $z$ , to force the BEV decoder to predict the regular traffic scene patterns from noise. The latent feature with noise is calculated by:", + "bbox": [ + 496, + 438, + 892, + 542 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {z} = \\sqrt {1 - \\eta} z + \\sqrt {\\eta} \\varepsilon , \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 542, + 890, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\eta$ is set to 0.5 in our experiments and $\\varepsilon$ denotes the standard Gaussian distribution, which shares the same dimensionality with $z$ .", + "bbox": [ + 496, + 564, + 890, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ultimately, we train the BEV autoencoder utilizing a weighted BCE loss to reconstruct the input $y$ as accurately as possible, ensuring that the latent feature map $z$ retains as much information from the original input $y$ as possible:", + "bbox": [ + 496, + 609, + 890, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {B C E} = - w (y \\log \\hat {y} + (1 - y) \\log (1 - \\hat {y})), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 678, + 890, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w$ denotes the training weights of each class. During implementation, the reciprocal of the frequency of occurrence is used as the weight for each class, which enables balanced learning for each type of object.", + "bbox": [ + 496, + 703, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the pretrained BEV autoencoder, the BEV latent representation is leveraged for RGV-BEV alignment, while the BEV decoder is utilized for BEV segmentation map generation during testing.", + "bbox": [ + 496, + 763, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. RGB-BEV Alignment", + "text_level": 1, + "bbox": [ + 500, + 832, + 702, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of RGB-BEV alignment is to learn a transition from the perspective RGB images to the BEV latent representations. As shown in Figure 3 (b), the perspective RGB", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15515", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "image is taken as the input into the pipeline, where the output is supposed to predict the latent representation $z$ .", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following previous works [31, 34], we first resize the input RGB images from $900 \\times 1600$ to $396 \\times 704$ , and then crop off the upper part that contains inessential information like the sky and buildings, leaving only the bottom $256 \\times 704$ , in order to better adapt to our model.", + "bbox": [ + 75, + 121, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At the beginning of the pipeline, we primarily utilize ResNet [12] and FPN [19], denoted as $F(\\cdot)$ together, to extract the feature maps $f$ with a lower scale of $64 \\times 176$ from the preprocessed input RGB image $x$ :", + "bbox": [ + 75, + 196, + 467, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf = F (x). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 233, + 268, + 467, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Despite the fact that we have transformed the BEV segmentation map from Cartesian to polar coordinates to establish spatial correspondence with RGB images from a perspective view of polar coordinates, it is noteworthy that for each column, objects in the RGB image adhere to the characteristic of being larger closer and smaller farther away, whereas objects in the BEV segmentation map maintain the same scale regardless of their distance. To address this, we treat this task as a column-wise sequence-to-sequence translation problem and employ a transformer [35] following [9, 34]. Specifically, we first permute and reshape the feature map from $f^{N \\times C \\times H \\times W}$ to $f^{H \\times (N \\times W) \\times C}$ and treat each column as a sequence input to the transformer [35] to produce a feature map $t^{H \\times (N \\times W) \\times C}$ , which is then resized back to the scale of $t^{N \\times C \\times H \\times W}$ .", + "bbox": [ + 75, + 295, + 467, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the last module of the pipeline, we apply multiple convolutional layers, denoted as $conv(\\cdot)$ , to reduce the scale $(64 \\times 176)$ of the feature map $t$ obtained from the transformer to match the scale $(8 \\times 22)$ of the feature map $z$ ,", + "bbox": [ + 75, + 522, + 467, + 583 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} = \\operatorname {c o n v} (t), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 598, + 467, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{z}$ is the output of the whole pipeline.", + "bbox": [ + 76, + 619, + 364, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the training phase, we utilize the mean squared error (MSE) loss to facilitate the output of the pipeline to approach the latent feature map $z$ generated by the frozen BEV encoder according to Equation 1:", + "bbox": [ + 75, + 636, + 467, + 695 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {M S E} = (\\hat {z} - z) ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 705, + 467, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During testing, we use the frozen BEV decoder to decode the feature map $\\hat{z}$ predicted by the pipeline into the BEV segmentation map according to Equation 2. Finally, we transform it from the polar to the Cartesian coordinates system following Section 3.1.", + "bbox": [ + 75, + 734, + 467, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although we can decode the aligned latent feature map $\\hat{z}$ predicted from the pipeline with the frozen BEV decoder into the BEV segmentation map and achieve good performance, we observe that the decoder has only been exposed to samples of BEV segmentation maps during its training process and thus struggles to adequately adapt to the data", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "distribution of input RGB images. To address this issue, we introduce a fine-tuning strategy that enables the decoder to better adapt to the data distributions of both input RGB images and latent features, thus establishing a connection between the data distribution of BEV segmentation maps and that of input RGB images. To achieve this, we freeze the parameters of the pipeline and only apply fine-tuning to the BEV decoder using the BCE loss in Equation 4.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 227, + 630, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 252, + 689, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. The nuScenes dataset [2] comprises 1,000 scenes captured by six cameras in Boston and Singapore. Each scene spans approximately 20 seconds. For semantic mapping, nuScenes provides detailed vectorized maps covering 11 semantic classes. In terms of dynamic objects, the dataset includes comprehensive annotations of 3D bounding boxes for 23 classes, complemented by 8 unique attributes. The Argoverse dataset [4] includes 65 training and 24 validation sequences recorded in Miami and Pittsburgh, utilizing seven surround-view cameras. Similar to the nuScenes dataset, Argoverse offers 3D object annotations across 15 categories and detailed semantic map data that encompasses road masks, lane geometry, and ground elevation. For a fair comparison, we use the same ground truth generation process, layout and object classes, and training/validation splits outlined in PON [31].", + "bbox": [ + 496, + 275, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metric. We present our results using the Intersection-over-Union (IoU) metric across background classes. Additionally, we compute the class-averaged mean IoU to assess overall performance. We ignore invisible grid cells during the evaluation process, as a LiDAR ray that cannot penetrate them will render them invisible in the image. Considering the possibility of class overlap, such as a car driving in the drivable area, we perform an independent binary segmentation evaluation for each category. We then determine the best performance by selecting the maximum IoU from various thresholds.", + "bbox": [ + 496, + 518, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Referring to PON [31], we perform segmentation in a $[0, 50] \\times [-25, 25]$ square meters region around the ego car with a resolution of 0.25 meters per pixel, resulting in a final map size of $200 \\times 200$ . For each stage and fine-tuning, we conduct training for 50 epochs. We employ the Lion optimizer [7], set the initial learning rates at $5 \\times 10^{-4}$ , $2 \\times 10^{-5}$ , and $2 \\times 10^{-4}$ for the first, second, and fine-tuning stages, respectively. Additionally, we use a weight decay factor of 0.01, complemented by warm-up and cosine learning rate decay strategies.", + "bbox": [ + 496, + 684, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Quantitative Comparison", + "text_level": 1, + "bbox": [ + 500, + 845, + 732, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although our method predicts based on monocular RGB images without exploring the relationships between multi", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15516", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a2a841e7889869a4c84a7dc20e5c52f58c3dd5bd108636a28c666555d8e1a333.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLayoutObjectMean
DrivableCrossingWalkwayCarparkBusBikeCarC.V.Motor.TrailerTruckPed.ConeBarrier
IPM [31]40.1-14.0-3.00.24.9-0.8--0.6---
Depth Unpr. [31]27.1-14.1-6.71.311.3-2.8--2.2---
VED [23]54.712.020.713.50.00.08.80.00.07.40.20.00.04.08.7
VPN [26]58.027.329.412.920.04.425.54.95.616.617.37.14.610.817.5
Sim2real [30]60.527.119.218.36.93.87.10.34.53.24.71.84.212.112.4
OFT [32]62.430.934.523.523.24.634.73.76.618.217.41.21.112.919.6
PON [31]60.428.031.018.420.89.424.712.37.016.616.88.25.78.119.1
EPOSH [8]61.133.537.825.431.86.737.82.710.514.220.45.97.613.422.1
DiffBEV [42]65.441.341.128.433.713.238.98.414.421.123.19.67.516.725.9
GitNet [9]65.141.642.131.935.413.843.49.715.022.525.514.111.618.627.9
TaDe (Ours)65.940.942.330.738.514.242.811.418.226.326.914.015.021.429.2
", + "bbox": [ + 81, + 88, + 890, + 263 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b86fd467183a2f6fd24e2cbbb4d2a1522e3037465049577f0ab961ca4dd6247f.jpg", + "table_caption": [ + "Table 1. Quantitative results of IoU (%) on the nuScenes [2] validation set. \"Mean\" indicates IoU across all classes. \"Crossing\", \"C.V.\", \"Motor.\", \"Ped.\", and \"Cone\" denote pedestrian crossing, construction vehicle, motorcycle, pedestrian, and traffic cone, respectively. IPM and Depth Unpr. are proposed in PON [31]." + ], + "table_footnote": [], + "table_body": "
MethodDrivableVehiclePedestrianLarge VehicleBicycleBusTrailerMotorcycleMean
IPM [31]43.77.51.5-0.47.4-0.8-
Depth Unpr. [31]33.012.73.3-1.120.6-1.6-
VED [23]62.914.01.03.90.012.31.30.011.9
VPN [26]64.923.96.29.70.93.00.41.913.9
PON [31]65.431.47.411.13.611.00.75.717.0
TaDe (Ours)68.334.59.314.74.437.83.16.422.3
", + "bbox": [ + 150, + 328, + 823, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ple cameras, we conducted experiments on all available surrounding cameras in nuScenes [2] and Argoverse [4] and showed the average results on their validation set following most previous works [9, 31] in Table 1 and Table 2.", + "bbox": [ + 75, + 482, + 468, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "nuScenes. As shown in Table 1, we observe that our method surpasses IPM-based approaches like IPM [31] and Sim2real [30] by at least $16.8\\mathrm{mIoU}$ , without relying on the assumption of a perfectly flat ground plane. Our method also outperforms bottleneck-based approaches, including VED [23], VPN [26], and PON [31], because our BEV decoder can effectively decode latent features. Compared to depth-based approaches like Depth Unprojection-based (DepthUnpr.) [31], OFT [32], EPOSH [8], and DiffBEV [42], our method outperforms them by at least 3.3 mIoU, without depending on depth estimation results. Furthermore, our method achieves the highest performance of 29.2 on mIoU and surpasses the state-of-the-art method GitNet [9] in 10 classes. The above experimental results demonstrate that our method has achieved a higher level of accuracy, particularly in the segmentation of objects such as motorcycles, trailers, and traffic cones.", + "bbox": [ + 75, + 547, + 470, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Argoverse. As shown in Table 2, we observe that our method achieves the highest performance in terms of mIoU and consistently exhibits improvement across all classes compared with PON [31]. This observation demonstrates the superiority and robustness of our method across diverse datasets.", + "bbox": [ + 75, + 810, + 470, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b648fc53033850ab7554dec9ee1986c035e40f06927157859e7140d8dc5c6f2f.jpg", + "table_caption": [ + "Table 2. Quantitative results of IoU (%) on the Argoverse [4] validation set." + ], + "table_footnote": [], + "table_body": "
MethodParams↓FLOPs↓FPS↑GPU Hours↓
PON [31]38.6M60.9G43.8100
TIM [34]45.7M268.3G18.1160
TaDe (Ours)41.5M48.5G51.48 + 48 + 24 = 80
", + "bbox": [ + 509, + 479, + 887, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison of computational overhead on nuScenes [2]. We report the GPU hours of BEV autoencoder, RGB-BEV alignment, and fine-tuning of our method respectively.", + "bbox": [ + 498, + 556, + 890, + 599 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Computational Overhead. We compare the computational overhead with two open-source methods, considering the following four metrics: parameters, FLOPs, FPS, and GPU hours, as presented in Table 3. GPU hours represent the estimated GPU (NVIDIA GeForce RTX 4090) hours required for training to converge. Notably, in inference, our method achieves the best FLOPs and FPS. In terms of training, despite three stages, our method consumes 80 GPU hours in total, while TIM [34] requires 160 GPU hours. In summary, compared with state-of-the-art methods, our method achieves the best results and maintains low computational overhead thanks to not using multi-scale features.", + "bbox": [ + 496, + 625, + 890, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "IoU over Distance. We further discuss the experimental results of IoU over distance. We divide the BEV maps into 5-meter intervals along the distance from the camera and report the mIoU for layouts and objects at various distances in Figure 5. The experimental results met our expectations, with IoU showing a decreasing trend as the distance", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15517", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7169ea59d31cfb401e708b0a62d63dca5d24578b8a76ca24a9a8bad4fe5b74d2.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 264, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e758e98b3fd6592b8c012662791c6a1e05061c0fc4c72f10434bae11b1fbfb1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 90, + 367, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fdc8f1166bed1515726a696e369d86e4335b3a59cbc12898eb2a85335496f3f7.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 264, + 171, + 367, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c216a25a07c5f9136f14a048d0df12a1af25dded19a7cf5d1208403b660449b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 370, + 90, + 472, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/608ed9c85b54b6a379a6854ee40857012f9e4f0646a7661bf8fb8c374877aa2b.jpg", + "image_caption": [ + "VPN" + ], + "image_footnote": [], + "bbox": [ + 370, + 171, + 472, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9126c525de0560aa7f63c84f277e5548a149746c66a5a3594cb19ef0c6d1fa13.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 472, + 90, + 575, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51a6b294e996930aaaee654665601ab6bb82a04c61de77edb1017e6c6e29e153.jpg", + "image_caption": [ + "PON" + ], + "image_footnote": [], + "bbox": [ + 472, + 171, + 575, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86fc7b2fdeaf3a56b89718378b68624d4334f29df780da0631a40607d10cd396.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 90, + 679, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3861a16d4f0004f1939a2e9bd558fca42535dfec7f5e5a5f350a86a1e42d28b1.jpg", + "image_caption": [ + "STA" + ], + "image_footnote": [], + "bbox": [ + 576, + 171, + 679, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/96547aec453b97e1410e4af3e7b7c5344083623e85399995a314027f64628edf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 90, + 782, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e81c08c841568255de088b2f956158ea6820a103c0e64033f5761df25ff0e696.jpg", + "image_caption": [ + "GitNet" + ], + "image_footnote": [], + "bbox": [ + 681, + 171, + 782, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e3792860c8c76a03397d13a6590be617cbabfbf9915b6af659deb38566c9c74.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 90, + 887, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/69232fbae5a7d4606f18e413cf2ae6b8734dcdf64b4a3046ba1ff0377c14fb93.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 785, + 171, + 887, + 251 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/532e674d7dab0ca3783cae0c906759cae5a7bddd704c99c80e200fbb98423231.jpg", + "image_caption": [ + "Figure 4. Qualitative results on nuScenes [2]. We compare with other methods following the color scheme used in PON [31].", + "(a) Quantitative Comparison" + ], + "image_footnote": [], + "bbox": [ + 81, + 310, + 272, + 407 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2fb5276f1ceecbf9e81d4ae0c0227b69bb8c55d0cd142d8db54f97b4a0e034f1.jpg", + "image_caption": [ + "(b) Percentage Improvement", + "Figure 5. Trend demonstration and comparison with PON [31] of IoU over distance (0-50m) on nuScenes [2]." + ], + "image_footnote": [], + "bbox": [ + 274, + 310, + 464, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "between the target and the camera increases. Compared to PON [31], we achieve significant and consistent improvements across distances. Notably, for layouts such as drivable areas, we obtain even more absolute performance gains at larger distances. As for small objects like pedestrians and bikes, we observe a relative performance improvement of $200\\%$ (5.4 vs 1.8) at 45-50 meters, while the relative improvement at 0-5 meters is $173\\%$ (38.7 vs 14.2). In summary, our method shows its superiority, especially at large distances for both layouts and objects.", + "bbox": [ + 75, + 486, + 468, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 648, + 228, + 665 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we explore the effectiveness of each proposed component through an ablation study on nuScenes [2]. The experimental groups and results are shown in Table 4.", + "bbox": [ + 75, + 672, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Coordinate System Transformation. In Table 4, Groups I and III, compared with Groups II and IV, are designated as control groups. Following the adoption of the BEV segmentation map in polar coordinates, there is an overall increase in mIoU by 4.3 and 3, respectively. This improvement can be attributed to the column-wise correspondence established between the BEV segmentation map in polar coordinates and the perspective image, enabling the model to make more accurate predictions. Additionally, Group III exhibits a notable improvement, showing increases of 6.5 in layout and 3.6 in small objects compared to Group I.", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/72092e7c3b2af9860b743133c77dfbd23ca118cfd167eaef58b4d639eb446f5c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
GroupComponentsIoU
CSTTDCWTFTLayoutLarge Obj.Small Obj.Mean
I35.022.010.421.6
II✓41.922.911.724.4
III✓41.525.613.825.9
IV✓✓44.127.513.927.4
V✓✓41.226.415.526.7
VI✓✓✓44.828.615.928.7
VII✓✓✓✓45.029.216.629.2
", + "bbox": [ + 506, + 310, + 888, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablations of different key components on nuScenes [2]. CST, TD, CWT, and FT denote coordinate system transformation, task decomposition, column-wise transformer, and fine-tuning, respectively. Large objects include bus, car, construction vehicle, trailer, and truck. Small objects include barrier, bike, motorcycle, pedestrian, and traffic cone.", + "bbox": [ + 498, + 431, + 890, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Task Decomposition. We deploy ablations to demonstrate the effectiveness of task decomposition. For Groups I, III, and V in Table 4, we train the pipeline and the BEV decoder simultaneously with the BCE loss in an end-to-end paradigm. Comparing Group V and Group VI, we observe that task decomposition brings a significant improvement to layouts (41.2 vs 44.8) and large objects (26.4 vs 28.6) which commonly appearing typical patterns. Similar improvements could be observed in the comparison between Group III and Group IV, especially between Group I and Group II (6.9 IoU improvement to layouts). The above ablations demonstrate that the BEV autoencoder successfully learned prior patterns of traffic scenes to decode a more rational BEV segmentation map.", + "bbox": [ + 496, + 537, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Column-wise Transformer. In RGB images, objects exhibit the characteristic of appearing larger when closer and smaller when farther away, while in BEV segmentation maps, objects maintain the same scale regardless of their distance. Motivated by TIM [34], we adopt a column-wise transformer to translate each column of the feature map to match the characteristics between the perspective view and the bird's eye view. As shown in Table 4, when compared with Group IV and Group VI, the column-wise transformer improves the IoU of small objects significantly (13.9 vs", + "bbox": [ + 496, + 750, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15518", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/50819bf7cf19f9e8e161d6494e083ed4718904493ead8a82ec64826bfda48e51.jpg", + "image_caption": [ + "Figure 6. Qualitative results of ablations on nuScenes [2]. I, III, V, and VI are corresponded to the relevant ablations in Table 4." + ], + "image_footnote": [], + "bbox": [ + 140, + 88, + 831, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "15.9) while also improving the IoU of large objects (27.5 vs 28.6). Similar improvements are observed in the comparison between Group III and Group V. These experimental results prove that the column-wise transformer could better capture the information of objects.", + "bbox": [ + 75, + 383, + 468, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fine-tuning. Although Stage 1 and Stage 2 for training are sufficient to achieve good results, the BEV decoder was trained independently from RGB images so that could not decode typical patterns in RGB images to a detailed BEV segmentation map. Thus we freeze the pipeline as a pretrained RGB image feature extractor and fine-tune the BEV decoder in an end-to-end manner to establish connections between RGB images and BEV segmentation maps. Compared to Group VI in Table 4, Group VII achieves better results across all classes, especially on objects that occupy small regions (0.7 IoU improvement).", + "bbox": [ + 75, + 460, + 470, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Comparison", + "text_level": 1, + "bbox": [ + 76, + 635, + 299, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 4 shows qualitative results on nuScenes [2], comparing our predicted segmentation maps with other methods and the ground truth. Our segmentation maps appear more precise and rational, benefiting from our task decomposition into two stages. Specifically, our model demonstrates a more coherent road layout, pedestrian crossing, and walkway layout, thanks to prior knowledge learned in advance. For dynamic objects, our model effectively leverages the polar coordinate system to predict nearby and distant objects with high accuracy, particularly excelling in determining the scale of cars and buses.", + "bbox": [ + 75, + 659, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 6 provides further qualitative results of our ablation experiments. Groups III, V, and VI in the first row display more coherent and accurate road layouts due to the introduction of the coordinate system transformation. Group V in the second row successfully predicts distant", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cars, thanks to the effectiveness of the column-wise transformer in translating each column. In the third row of Figure 6, Group VI demonstrates that the BEV autoencoder has successfully learned prior patterns about layouts and objects, accurately predicting the size of cars and the layout of pedestrian crossings compared to other experiments.", + "bbox": [ + 496, + 383, + 893, + 476 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 494, + 619, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we leverage a clearer and more direct optimization target, by decomposing the end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception). Specifically, in the first stage, we propose a BEV autoencoder to reconstruct the BEV segmentation map with corrupted noise, where the decoder is forced to learn typical BEV traffic scene patterns. In the second stage, a mapping from input RGB images and BEV latent representations is learned. Furthermore, we transform the BEV segmentation map from a Cartesian coordinate system to a polar one, thus enhancing its alignment with RGB input. Notably, our method abstains from utilizing multi-scale features or camera intrinsic parameters for depth estimation, resulting in a significantly lower computational overhead. Additionally, our method consistently achieves outstanding prediction accuracy across varying distances from the camera. Extensive experiments on two datasets demonstrate our effectiveness.", + "bbox": [ + 496, + 521, + 893, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 813, + 660, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by the National Natural Science Foundation of China under Grant 62372341 and sponsored by CCF-DiDi GAIA Collaborative Research Funds for Young Scholars.", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15519", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Florent Bartoccioni, Éloi Zablocki, Andrei Bursuc, Patrick Pérez, Matthieu Cord, and Karteek Alahari. 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Diffbev: Conditional diffusion model for bird's eye view perception. arXiv preprint arXiv:2303.08333, 2023. 3, 6" + ], + "bbox": [ + 501, + 92, + 890, + 513 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15521", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/64afc4ea-9f99-49c3-ab03-ca65285f08d0_model.json b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/64afc4ea-9f99-49c3-ab03-ca65285f08d0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f427d9e68862793ec4e684ea4675a3f13464a439 --- /dev/null +++ b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/64afc4ea-9f99-49c3-ab03-ca65285f08d0_model.json @@ -0,0 +1,2200 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "Improving Bird's Eye View Semantic Segmentation by Task Decomposition" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.18, + 0.838, + 0.288 + ], + "angle": 0, + "content": "Tianhao Zhao\\(^{1*}\\) Yongcan Chen\\(^{1*}\\) Yu Wu\\(^{1}\\) Tianyang Liu\\(^{1}\\) Bo Du\\(^{1\\dagger}\\) \nPeilun Xiao\\(^{2}\\) Shi Qiu\\(^{2}\\) Hongda Yang\\(^{2}\\) Guozhen Li\\(^{2}\\) Yi Yang\\(^{2}\\) Yutian Lin\\(^{1\\dagger}\\) \n\\(^{1}\\) Institute of Artificial Intelligence, School of Computer Science, Hubei Luojia Laboratory, Wuhan University, Wuhan, China \n\\(^{2}\\) Didi Chuxing, China \n{happytianhao, chenyongcan, wuyucs, bodu, yutian.lin}@whu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.355, + 0.474, + 0.779 + ], + "angle": 0, + "content": "Semantic segmentation in bird's eye view (BEV) plays a crucial role in autonomous driving. Previous methods usually follow an end-to-end pipeline, directly predicting the BEV segmentation map from monocular RGB inputs. However, the challenge arises when the RGB inputs and BEV targets from distinct perspectives, making the direct point-to-point predicting hard to optimize. In this paper, we decompose the original BEV segmentation task into two stages, namely BEV map reconstruction and RGB-BEV feature alignment. In the first stage, we train a BEV autoencoder to reconstruct the BEV segmentation maps given corrupted noisy latent representation, which urges the decoder to learn fundamental knowledge of typical BEV patterns. The second stage involves mapping RGB input images into the BEV latent space of the first stage, directly optimizing the correlations between the two views at the feature level. Our approach simplifies the complexity of combining perception and generation into distinct steps, equipping the model to handle intricate and challenging scenes effectively. Besides, we propose to transform the BEV segmentation map from the Cartesian to the polar coordinate system to establish the column-wise correspondence between RGB images and BEV maps. Moreover, our method requires neither multi-scale features nor camera intrinsic parameters for depth estimation and saves computational overhead. Extensive experiments on nuScenes and Argoverse show the effectiveness and efficiency of our method. Code is available at https://github.com/happytianhao/TaDe." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.808, + 0.21, + 0.823 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.834, + 0.47, + 0.864 + ], + "angle": 0, + "content": "In the field of autonomous driving, bird's eye view (BEV) perception tasks can obtain adequate semantic in" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.321, + 0.682, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.321, + 0.787, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.321, + 0.892, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.427, + 0.894, + 0.484 + ], + "angle": 0, + "content": "Figure 1. Qualitative comparison between traditional end-to-end method and our method. (a) shows the perspective view RGB image, (b) and (c) show the BEV segmentation maps predicted without and with the method of task decomposition, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.627 + ], + "angle": 0, + "content": "formation such as road layout, object categories, positions, and scales around vehicles. This kind of information is called BEV representation and can be directly applied to downstream tasks such as layout mapping, action prediction, route planning, and collision avoidance. In this work, we focus on the monocular BEV segmentation task, which is a fundamental task that aims to predict road segments from camera inputs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.838 + ], + "angle": 0, + "content": "Previous BEV segmentation methods [6,16,18,23,25,28, 31,34,40,41] usually follow an end-to-end pipeline, which adopts a transformer-based architecture to directly predict BEV segmentation maps from the input RGB images. However, different from the general segmentation task, the input images and targets in BEV are of distinct views (perspective view versus bird's eye view), thus it is hard to train the model by direct point-to-point optimization. And it is even harder when attempting to achieve both source information perception and target view generation in a single step. As shown in Figure 1 (b), the generated BEV segmentation map of the end-to-end baseline looks distorted and does not conform to the expected regular patterns found in real-world traffic scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To achieve the complex cross-view BEV segmentation, we propose a Task Decomposition (TaDe) method that decompose the traditional end-to-end pipeline into two distinct but goal-oriented stages. In the first stage, we train an" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.203, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.222, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15512" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "autoencoder model to learn a basic understanding of typical BEV scene patterns, enabling it to generate coherent and rational BEV segmentation maps independent from RGB images. In the second stage, given input RGB images, we only intend to obtain the latent BEV feature, leaving the workload of BEV segmentation map prediction to the pretrained decoder of the first stage. This two-stage approach, with each stage focusing on only one mission, equips the model with the capacity to handle more intricate and challenging scene perception. As shown in Figure 1 (c), with the help of task decomposition, the predicted BEV segmentation maps share greater structural similarity with the RGB image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.276, + 0.473, + 0.518 + ], + "angle": 0, + "content": "To be specific, in the first stage, to generate BEV maps that are consistent with physical rules, it is crucial to have a specific expert to comprehend the global traffic layout. For instance, walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow circles. To incorporate this prior knowledge, we employ an autoencoder to learn how to reconstruct/generate the target BEV segmentation maps. To learn a more intrinsic and robust generating ability, we disturb the autoencoder by corrupting the latent representation with random noise during training and enforce the model perfectly reconstruct the ground truth with only the noised latent. This reconstruction can locally recognize and predict typical patterns in BEV segmentation maps, thereby ensuring reasonable BEV map generation given imperfect latent representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.473, + 0.779 + ], + "angle": 0, + "content": "In the second stage, we aim to learn a smooth transition from the perspective RGB input to the BEV semantic latent space. Specifically, the model encodes the input RGB images into features and leverages a column-wise transformer to transit them into the BEV latent space. The training objective of the second stage is to ensure that the transited RGB representations align seamlessly with the target BEV latent space. Thus we input the BEV label maps to the frozen BEV encoder of Stage I to get the BEV latent feature, and then take this BEV feature as the optimization target for the transition model of Stage II. Different from existing works, the optimization is in the autoencoder latent space, rather than the traditional pixel segmentation classification space. During inference, since the representations of both views have been already aligned, the transited RGB feature can directly go through the BEV decoder of Stage I for the final BEV segmentation mask prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Furthermore, to achieve better cross-view alignment, we introduce a coordinate transform step that converts the original BEV segmentation map from Cartesian to polar coordinates. In the transformed BEV map, each column shares the same spatial information with the input monocular RGB images, which also benefits the smooth transition of cross-view features in the second stage. Extensive experiments on two large-scale datasets including nuScenes [2] and Argo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "verse [4] clearly demonstrate our superiority compared to prior end-to-end works." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.122, + 0.845, + 0.136 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.15, + 0.892, + 0.196 + ], + "angle": 0, + "content": "- We break down the traditional end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.206, + 0.892, + 0.265 + ], + "angle": 0, + "content": "- We propose a BEV autoencoder to automatically learn typical patterns by reconstructing BEV maps from corrupted latent features, ensuring the decoder prediction is rational and adheres to the real world." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.277, + 0.892, + 0.323 + ], + "angle": 0, + "content": "- We also transform the BEV label map from Cartesian to polar coordinates to learn better alignment across perspective views and bird's eye views." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.15, + 0.892, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.336, + 0.651, + 0.352 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.361, + 0.8, + 0.377 + ], + "angle": 0, + "content": "2.1. Bird's Eye View (BEV) Perception" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.718 + ], + "angle": 0, + "content": "As BEV representations contain rich semantic information and can be directly applied to numerous downstream tasks, BEV perception has received widespread attention in the field of autonomous driving. However, converting the perspective view captured by cameras to the bird's eye view is an ill-posed problem, which makes it hard to meet the autonomous driving requirements of complex real-world scenarios. Early works [13, 14, 17, 22, 26, 27, 29, 39] addressed this challenge based on a bottom-up strategy. They first predict the position in the 3D space by estimating the depth of each pixel in the perspective view and then project the 3D position to the BEV space based on the internal and external parameters of the cameras. Nevertheless, despite being intuitive, bottom-up methods depend on the accuracy of depth estimation and have high computational complexity. Recent works follow a top-down strategy. Inspired by DETR [3], DETR3D [36] detects objects from object queries in 3D space with a transformer. BEVFormer [18] and BEVFormer v2 [37] add dense object queries based on DETR3D to achieve map segmentation. PETR [20] and PETRv2 [21] introduce 3D position encoding to DETR3D and significantly simplify the pipeline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.773, + 0.743 + ], + "angle": 0, + "content": "2.2. Monocular BEV Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Traditional BEV perception methods focus on calculating the corresponding relationship between the coordinates of the perspective view and the bird's eye view by using the internal and external parameters of the cameras. However, due to the geometric distortion and the presence of overlapping parts and gaps between the perspective views, the perception effect is not ideal. In this regard, some works [1, 5, 10, 11, 24, 33] propose to predict the BEV segmentation map of road layout and objects directly in the case of giving a monocular perspective view." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15513" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.41 + ], + "angle": 0, + "content": "PYVA [38] proposes a GAN-based framework and designs a cross-view conversion module to handle significant differences between views. VED [23] employs a variational encoder-decoder network to directly anticipate a semantic occupancy grid from an image. However, the inclusion of a fully connected bottleneck layer in the network results in the loss of significant spatial context and an output that is relatively coarse and incapable of capturing smaller objects like pedestrians. CVT [40] designs a transformer and utilizes the camera's intrinsic and extrinsic calibrations to efficiently understand the surrounding environment. PON [31] adopts a semantic Bayesian occupancy grid framework to estimate BEV segmentation maps directly from monocular perspective views. HFT [41] provides a balanced approach that combines structured geometric information from model-based methods with the global context-capturing ability of model-free methods to overcome their respective limitations in image processing. DiffBEV [42] and DDP [15] propose an end-to-end framework to generate a more comprehensive BEV representation and denoise noisy samples by applying the diffusion model to BEV perception." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.417, + 0.277, + 0.431 + ], + "angle": 0, + "content": "2.3. Polar-based Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.441, + 0.473, + 0.819 + ], + "angle": 0, + "content": "So far, many works have made significant progress in the BEV segmentation task. However, due to the fact that the perspective view is established in a 3D polar coordinate system, while the bird's eye view is established in a 2D Cartesian coordinate system with the camera as the origin, this gap has led to the previous method's unsatisfactory performance. Therefore, in order to reduce this gap, some methods choose to convert the ground truth of the bird's eye view in the Cartesian coordinate system to the polar coordinate system, corresponding to the perspective view, in order to better learn the relationship between them. PolarDETR [6] converts the object representation in DETR3D from the Cartesian coordinate system to the polar coordinate system. PolarFormer [16] incorporates a polar alignment module to aggregate rays from multiple cameras and generate a structured polar feature map. TIM [34] formulates BEV segmentation map generation from an image as a set of sequence-to-sequence translations and proposes a novel form of end-to-end transformer network to translate between a vertical scanline in the image and rays passing through the camera location in the bird's eye view. GitNet [9] first learns visibility-aware features and learnable geometry to translate into BEV space and then deforms the pre-aligned coarse BEV features with visibility knowledge by ray-based transformers." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.168, + 0.845 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We propose TaDe (Task Decomposition) to break down the traditional end-to-end training pipeline into two simple and distinct stages: (1) With the BEV autoencoder, BEV" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.892, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.23, + 0.894, + 0.286 + ], + "angle": 0, + "content": "Figure 2. Illustration of the transformation between Cartesian (left) and polar (right) coordinate system for BEV segmentation maps. This transformation can achieve a column-wise correspondence between the BEV segmentation maps and the RGB images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.307, + 0.895, + 0.473 + ], + "angle": 0, + "content": "segmentation maps with \\(50\\%\\) noise are reconstructed to recognize and predict the typical patterns and obtain the BEV latent representations. (2) With the RGB-BEV alignment, the input monocular RGB images are mapped into the BEV latent space via a column-wise transformer to achieve view alignment. During testing, the BEV decoder is employed to generate BEV semantic segmentation maps. In this section, we first introduce the coordinate system transformation of target BEV maps in Section 3.1. After that, we elaborate on the BEV autoencoder and column-wise feature mapping in Section 3.2. and Section 3.3., respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.85, + 0.5 + ], + "angle": 0, + "content": "3.1. BEV Coordinate System Transformation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.508, + 0.892, + 0.765 + ], + "angle": 0, + "content": "In the monocular BEV semantic segmentation task, the input RGB images are captured from a perspective view in polar coordinates, while the segmented output targets originate from the bird's eye view in Cartesian coordinates. Consequently, there exists no pixel-level correspondence between the input RGB images and the target segmentation maps, unlike traditional semantic segmentation tasks, which makes this task extremely challenging. However, previous polar-based methods [9, 34] have identified a corresponding relationship between the columns of RGB images and the rays in BEV segmentation maps with the camera position as the origin. To establish this correspondence, they conducted resampling from polar to Cartesian coordinates in the feature space. In contrast, to facilitate BEV autoencoder training and achieve column-wise feature alignment, we directly apply coordinate system transformation on the BEV segmentation maps." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.766, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To be specific, as illustrated in Figure 2, we employ a resampling method to transform the BEV segmentation maps between the Cartesian and polar coordinate systems to achieve a column-wise spatial correspondence between the BEV segmentation maps and RGB images. For instance, in the Cartesian to polar conversion, for each pixel in the polar map, we calculate the corresponding coordinate in the Cartesian map according to the field of view (FOV) and resample from the nearby pixels, and vice versa. Note that" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15514" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.891, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.288, + 0.434, + 0.302 + ], + "angle": 0, + "content": "(b) Stage 2: RGB-BEV Alignment" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.316, + 0.894, + 0.358 + ], + "angle": 0, + "content": "Figure 3. Overview of our two-stage method. (a) In the first stage, a BEV autoencoder is trained by BEV segmentation maps independent from RGB images. (b) In the second stage, the BEV autoencoder is frozen and the RGB-BEV alignment is conducted to match the RGB images to BEV latent representations for decoding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.47, + 0.484 + ], + "angle": 0, + "content": "this transform is deterministic and does not require training. During training, we transform the BEV segmentation maps from the Cartesian to the polar coordinate system for reconstruction and encoding. During testing, we transform the predicted BEV segmentation maps from the polar to the Cartesian coordinate system for further quantitative and qualitative validation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.254, + 0.51 + ], + "angle": 0, + "content": "3.2. BEV Autoencoder" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.776 + ], + "angle": 0, + "content": "To achieve rational BEV map generation, it is essential to possess a profound understanding of the traffic scene occupancy patterns. In the real world, there is prior knowledge within the traffic BEV segmentation map, where walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow shapes. However, in previous methods, the generated BEV segmentation map does not match real traffic patterns effectively. To address this issue, we introduce a BEV autoencoder, which is designed to reconstruct the BEV segmentation map in polar coordinates. Notably, we introduce \\(50\\%\\) noise into the BEV latent representation for reconstruction. This addition of noise renders the reconstruction task more challenging, which requires a holistic understanding of the traffic scene patterns and thus ensures the creation of rational BEV maps that align more closely with real-world expectations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.47, + 0.837 + ], + "angle": 0, + "content": "As illustrated in Figure 3 (a), the BEV autoencoder consists of a BEV encoder denoted as \\( E(\\cdot) \\), and a BEV decoder denoted as \\( D(\\cdot) \\). Given a BEV segmentation map \\( y \\) in polar coordinates, the BEV autoencoder is outlined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.236, + 0.852, + 0.469, + 0.868 + ], + "angle": 0, + "content": "\\[\nz = E (y), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.236, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = D (\\tilde {z}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.892, + 0.438 + ], + "angle": 0, + "content": "where \\( z \\) and \\( \\hat{z} \\) denotes the BEV latent representation, \\( \\hat{y} \\) denotes the reconstructed vector in input space. Note that we obtain \\( z \\) with a low scale of \\( 8 \\times 22 \\), which can thus be seen as a latent representation of \\( y \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.893, + 0.543 + ], + "angle": 0, + "content": "Due to the simplicity of BEV segmentation maps, the criterion is not sufficient to obtain a useful representation or effective decoder. Therefore, we added a large amount of Gaussian noise (e.g. \\(50\\%\\) ) to the latent feature map \\(z\\), to force the BEV decoder to predict the regular traffic scene patterns from noise. The latent feature with noise is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.543, + 0.891, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\tilde {z} = \\sqrt {1 - \\eta} z + \\sqrt {\\eta} \\varepsilon , \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.61 + ], + "angle": 0, + "content": "where \\(\\eta\\) is set to 0.5 in our experiments and \\(\\varepsilon\\) denotes the standard Gaussian distribution, which shares the same dimensionality with \\(z\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.671 + ], + "angle": 0, + "content": "Ultimately, we train the BEV autoencoder utilizing a weighted BCE loss to reconstruct the input \\( y \\) as accurately as possible, ensuring that the latent feature map \\( z \\) retains as much information from the original input \\( y \\) as possible:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.679, + 0.891, + 0.696 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {B C E} = - w (y \\log \\hat {y} + (1 - y) \\log (1 - \\hat {y})), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.764 + ], + "angle": 0, + "content": "where \\( w \\) denotes the training weights of each class. During implementation, the reciprocal of the frequency of occurrence is used as the weight for each class, which enables balanced learning for each type of object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.825 + ], + "angle": 0, + "content": "With the pretrained BEV autoencoder, the BEV latent representation is leveraged for RGV-BEV alignment, while the BEV decoder is utilized for BEV segmentation map generation during testing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.704, + 0.849 + ], + "angle": 0, + "content": "3.3. RGB-BEV Alignment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The goal of RGB-BEV alignment is to learn a transition from the perspective RGB images to the BEV latent representations. As shown in Figure 3 (b), the perspective RGB" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15515" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "image is taken as the input into the pipeline, where the output is supposed to predict the latent representation \\( z \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.197 + ], + "angle": 0, + "content": "Following previous works [31, 34], we first resize the input RGB images from \\(900 \\times 1600\\) to \\(396 \\times 704\\), and then crop off the upper part that contains inessential information like the sky and buildings, leaving only the bottom \\(256 \\times 704\\), in order to better adapt to our model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.468, + 0.258 + ], + "angle": 0, + "content": "At the beginning of the pipeline, we primarily utilize ResNet [12] and FPN [19], denoted as \\(F(\\cdot)\\) together, to extract the feature maps \\(f\\) with a lower scale of \\(64 \\times 176\\) from the preprocessed input RGB image \\(x\\):" + }, + { + "type": "equation", + "bbox": [ + 0.235, + 0.269, + 0.468, + 0.285 + ], + "angle": 0, + "content": "\\[\nf = F (x). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.468, + 0.522 + ], + "angle": 0, + "content": "Despite the fact that we have transformed the BEV segmentation map from Cartesian to polar coordinates to establish spatial correspondence with RGB images from a perspective view of polar coordinates, it is noteworthy that for each column, objects in the RGB image adhere to the characteristic of being larger closer and smaller farther away, whereas objects in the BEV segmentation map maintain the same scale regardless of their distance. To address this, we treat this task as a column-wise sequence-to-sequence translation problem and employ a transformer [35] following [9, 34]. Specifically, we first permute and reshape the feature map from \\( f^{N \\times C \\times H \\times W} \\) to \\( f^{H \\times (N \\times W) \\times C} \\) and treat each column as a sequence input to the transformer [35] to produce a feature map \\( t^{H \\times (N \\times W) \\times C} \\), which is then resized back to the scale of \\( t^{N \\times C \\times H \\times W} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.584 + ], + "angle": 0, + "content": "For the last module of the pipeline, we apply multiple convolutional layers, denoted as \\( conv(\\cdot) \\), to reduce the scale \\( (64 \\times 176) \\) of the feature map \\( t \\) obtained from the transformer to match the scale \\( (8 \\times 22) \\) of the feature map \\( z \\)," + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.599, + 0.468, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\hat {z} = \\operatorname {c o n v} (t), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.621, + 0.365, + 0.635 + ], + "angle": 0, + "content": "where \\(\\hat{z}\\) is the output of the whole pipeline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.468, + 0.696 + ], + "angle": 0, + "content": "In the training phase, we utilize the mean squared error (MSE) loss to facilitate the output of the pipeline to approach the latent feature map \\( z \\) generated by the frozen BEV encoder according to Equation 1:" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.707, + 0.468, + 0.724 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {M S E} = (\\hat {z} - z) ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.81 + ], + "angle": 0, + "content": "During testing, we use the frozen BEV decoder to decode the feature map \\(\\hat{z}\\) predicted by the pipeline into the BEV segmentation map according to Equation 2. Finally, we transform it from the polar to the Cartesian coordinates system following Section 3.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Although we can decode the aligned latent feature map \\(\\hat{z}\\) predicted from the pipeline with the frozen BEV decoder into the BEV segmentation map and achieve good performance, we observe that the decoder has only been exposed to samples of BEV segmentation maps during its training process and thus struggles to adequately adapt to the data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "distribution of input RGB images. To address this issue, we introduce a fine-tuning strategy that enables the decoder to better adapt to the data distributions of both input RGB images and latent features, thus establishing a connection between the data distribution of BEV segmentation maps and that of input RGB images. To achieve this, we freeze the parameters of the pipeline and only apply fine-tuning to the BEV decoder using the BCE loss in Equation 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.228, + 0.632, + 0.244 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.253, + 0.691, + 0.269 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Datasets. The nuScenes dataset [2] comprises 1,000 scenes captured by six cameras in Boston and Singapore. Each scene spans approximately 20 seconds. For semantic mapping, nuScenes provides detailed vectorized maps covering 11 semantic classes. In terms of dynamic objects, the dataset includes comprehensive annotations of 3D bounding boxes for 23 classes, complemented by 8 unique attributes. The Argoverse dataset [4] includes 65 training and 24 validation sequences recorded in Miami and Pittsburgh, utilizing seven surround-view cameras. Similar to the nuScenes dataset, Argoverse offers 3D object annotations across 15 categories and detailed semantic map data that encompasses road masks, lane geometry, and ground elevation. For a fair comparison, we use the same ground truth generation process, layout and object classes, and training/validation splits outlined in PON [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.683 + ], + "angle": 0, + "content": "Evaluation Metric. We present our results using the Intersection-over-Union (IoU) metric across background classes. Additionally, we compute the class-averaged mean IoU to assess overall performance. We ignore invisible grid cells during the evaluation process, as a LiDAR ray that cannot penetrate them will render them invisible in the image. Considering the possibility of class overlap, such as a car driving in the drivable area, we perform an independent binary segmentation evaluation for each category. We then determine the best performance by selecting the maximum IoU from various thresholds." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.836 + ], + "angle": 0, + "content": "Implementation Details. Referring to PON [31], we perform segmentation in a \\([0, 50] \\times [-25, 25]\\) square meters region around the ego car with a resolution of 0.25 meters per pixel, resulting in a final map size of \\(200 \\times 200\\). For each stage and fine-tuning, we conduct training for 50 epochs. We employ the Lion optimizer [7], set the initial learning rates at \\(5 \\times 10^{-4}\\), \\(2 \\times 10^{-5}\\), and \\(2 \\times 10^{-4}\\) for the first, second, and fine-tuning stages, respectively. Additionally, we use a weight decay factor of 0.01, complemented by warm-up and cosine learning rate decay strategies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.733, + 0.864 + ], + "angle": 0, + "content": "4.2. Quantitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Although our method predicts based on monocular RGB images without exploring the relationships between multi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15516" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.264 + ], + "angle": 0, + "content": "
MethodLayoutObjectMean
DrivableCrossingWalkwayCarparkBusBikeCarC.V.Motor.TrailerTruckPed.ConeBarrier
IPM [31]40.1-14.0-3.00.24.9-0.8--0.6---
Depth Unpr. [31]27.1-14.1-6.71.311.3-2.8--2.2---
VED [23]54.712.020.713.50.00.08.80.00.07.40.20.00.04.08.7
VPN [26]58.027.329.412.920.04.425.54.95.616.617.37.14.610.817.5
Sim2real [30]60.527.119.218.36.93.87.10.34.53.24.71.84.212.112.4
OFT [32]62.430.934.523.523.24.634.73.76.618.217.41.21.112.919.6
PON [31]60.428.031.018.420.89.424.712.37.016.616.88.25.78.119.1
EPOSH [8]61.133.537.825.431.86.737.82.710.514.220.45.97.613.422.1
DiffBEV [42]65.441.341.128.433.713.238.98.414.421.123.19.67.516.725.9
GitNet [9]65.141.642.131.935.413.843.49.715.022.525.514.111.618.627.9
TaDe (Ours)65.940.942.330.738.514.242.811.418.226.326.914.015.021.429.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.273, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Table 1. Quantitative results of IoU (%) on the nuScenes [2] validation set. \"Mean\" indicates IoU across all classes. \"Crossing\", \"C.V.\", \"Motor.\", \"Ped.\", and \"Cone\" denote pedestrian crossing, construction vehicle, motorcycle, pedestrian, and traffic cone, respectively. IPM and Depth Unpr. are proposed in PON [31]." + }, + { + "type": "table", + "bbox": [ + 0.151, + 0.329, + 0.825, + 0.439 + ], + "angle": 0, + "content": "
MethodDrivableVehiclePedestrianLarge VehicleBicycleBusTrailerMotorcycleMean
IPM [31]43.77.51.5-0.47.4-0.8-
Depth Unpr. [31]33.012.73.3-1.120.6-1.6-
VED [23]62.914.01.03.90.012.31.30.011.9
VPN [26]64.923.96.29.70.93.00.41.913.9
PON [31]65.431.47.411.13.611.00.75.717.0
TaDe (Ours)68.334.59.314.74.437.83.16.422.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.26, + 0.449, + 0.71, + 0.463 + ], + "angle": 0, + "content": "Table 2. Quantitative results of IoU (%) on the Argoverse [4] validation set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.47, + 0.545 + ], + "angle": 0, + "content": "ple cameras, we conducted experiments on all available surrounding cameras in nuScenes [2] and Argoverse [4] and showed the average results on their validation set following most previous works [9, 31] in Table 1 and Table 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.471, + 0.806 + ], + "angle": 0, + "content": "nuScenes. As shown in Table 1, we observe that our method surpasses IPM-based approaches like IPM [31] and Sim2real [30] by at least \\(16.8\\mathrm{mIoU}\\), without relying on the assumption of a perfectly flat ground plane. Our method also outperforms bottleneck-based approaches, including VED [23], VPN [26], and PON [31], because our BEV decoder can effectively decode latent features. Compared to depth-based approaches like Depth Unprojection-based (DepthUnpr.) [31], OFT [32], EPOSH [8], and DiffBEV [42], our method outperforms them by at least 3.3 mIoU, without depending on depth estimation results. Furthermore, our method achieves the highest performance of 29.2 on mIoU and surpasses the state-of-the-art method GitNet [9] in 10 classes. The above experimental results demonstrate that our method has achieved a higher level of accuracy, particularly in the segmentation of objects such as motorcycles, trailers, and traffic cones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.9 + ], + "angle": 0, + "content": "Argoverse. As shown in Table 2, we observe that our method achieves the highest performance in terms of mIoU and consistently exhibits improvement across all classes compared with PON [31]. This observation demonstrates the superiority and robustness of our method across diverse datasets." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.481, + 0.888, + 0.548 + ], + "angle": 0, + "content": "
MethodParams↓FLOPs↓FPS↑GPU Hours↓
PON [31]38.6M60.9G43.8100
TIM [34]45.7M268.3G18.1160
TaDe (Ours)41.5M48.5G51.48 + 48 + 24 = 80
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.557, + 0.892, + 0.6 + ], + "angle": 0, + "content": "Table 3. Comparison of computational overhead on nuScenes [2]. We report the GPU hours of BEV autoencoder, RGB-BEV alignment, and fine-tuning of our method respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Computational Overhead. We compare the computational overhead with two open-source methods, considering the following four metrics: parameters, FLOPs, FPS, and GPU hours, as presented in Table 3. GPU hours represent the estimated GPU (NVIDIA GeForce RTX 4090) hours required for training to converge. Notably, in inference, our method achieves the best FLOPs and FPS. In terms of training, despite three stages, our method consumes 80 GPU hours in total, while TIM [34] requires 160 GPU hours. In summary, compared with state-of-the-art methods, our method achieves the best results and maintains low computational overhead thanks to not using multi-scale features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "IoU over Distance. We further discuss the experimental results of IoU over distance. We divide the BEV maps into 5-meter intervals along the distance from the camera and report the mIoU for layouts and objects at various distances in Figure 5. The experimental results met our expectations, with IoU showing a decreasing trend as the distance" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15517" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.265, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.255, + 0.192, + 0.265 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.091, + 0.369, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.172, + 0.369, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.255, + 0.352, + 0.265 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.092, + 0.473, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.172, + 0.473, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.409, + 0.255, + 0.434, + 0.264 + ], + "angle": 0, + "content": "VPN" + }, + { + "type": "image", + "bbox": [ + 0.473, + 0.092, + 0.576, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.473, + 0.172, + 0.576, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.255, + 0.538, + 0.264 + ], + "angle": 0, + "content": "PON" + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.092, + 0.68, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.172, + 0.68, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.255, + 0.641, + 0.264 + ], + "angle": 0, + "content": "STA" + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.092, + 0.784, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.172, + 0.784, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.715, + 0.255, + 0.75, + 0.264 + ], + "angle": 0, + "content": "GitNet" + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.092, + 0.888, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.172, + 0.888, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.255, + 0.849, + 0.264 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.279, + 0.853, + 0.294 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on nuScenes [2]. We compare with other methods following the color scheme used in PON [31]." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.311, + 0.273, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.413, + 0.255, + 0.424 + ], + "angle": 0, + "content": "(a) Quantitative Comparison" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.311, + 0.465, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.296, + 0.413, + 0.448, + 0.424 + ], + "angle": 0, + "content": "(b) Percentage Improvement" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.436, + 0.47, + 0.465 + ], + "angle": 0, + "content": "Figure 5. Trend demonstration and comparison with PON [31] of IoU over distance (0-50m) on nuScenes [2]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.469, + 0.637 + ], + "angle": 0, + "content": "between the target and the camera increases. Compared to PON [31], we achieve significant and consistent improvements across distances. Notably, for layouts such as drivable areas, we obtain even more absolute performance gains at larger distances. As for small objects like pedestrians and bikes, we observe a relative performance improvement of \\(200\\%\\) (5.4 vs 1.8) at 45-50 meters, while the relative improvement at 0-5 meters is \\(173\\%\\) (38.7 vs 14.2). In summary, our method shows its superiority, especially at large distances for both layouts and objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.229, + 0.666 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.734 + ], + "angle": 0, + "content": "In this section, we explore the effectiveness of each proposed component through an ablation study on nuScenes [2]. The experimental groups and results are shown in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Coordinate System Transformation. In Table 4, Groups I and III, compared with Groups II and IV, are designated as control groups. Following the adoption of the BEV segmentation map in polar coordinates, there is an overall increase in mIoU by 4.3 and 3, respectively. This improvement can be attributed to the column-wise correspondence established between the BEV segmentation map in polar coordinates and the perspective image, enabling the model to make more accurate predictions. Additionally, Group III exhibits a notable improvement, showing increases of 6.5 in layout and 3.6 in small objects compared to Group I." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.311, + 0.89, + 0.422 + ], + "angle": 0, + "content": "
GroupComponentsIoU
CSTTDCWTFTLayoutLarge Obj.Small Obj.Mean
I35.022.010.421.6
II✓41.922.911.724.4
III✓41.525.613.825.9
IV✓✓44.127.513.927.4
V✓✓41.226.415.526.7
VI✓✓✓44.828.615.928.7
VII✓✓✓✓45.029.216.629.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.432, + 0.892, + 0.515 + ], + "angle": 0, + "content": "Table 4. Ablations of different key components on nuScenes [2]. CST, TD, CWT, and FT denote coordinate system transformation, task decomposition, column-wise transformer, and fine-tuning, respectively. Large objects include bus, car, construction vehicle, trailer, and truck. Small objects include barrier, bike, motorcycle, pedestrian, and traffic cone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Task Decomposition. We deploy ablations to demonstrate the effectiveness of task decomposition. For Groups I, III, and V in Table 4, we train the pipeline and the BEV decoder simultaneously with the BCE loss in an end-to-end paradigm. Comparing Group V and Group VI, we observe that task decomposition brings a significant improvement to layouts (41.2 vs 44.8) and large objects (26.4 vs 28.6) which commonly appearing typical patterns. Similar improvements could be observed in the comparison between Group III and Group IV, especially between Group I and Group II (6.9 IoU improvement to layouts). The above ablations demonstrate that the BEV autoencoder successfully learned prior patterns of traffic scenes to decode a more rational BEV segmentation map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Column-wise Transformer. In RGB images, objects exhibit the characteristic of appearing larger when closer and smaller when farther away, while in BEV segmentation maps, objects maintain the same scale regardless of their distance. Motivated by TIM [34], we adopt a column-wise transformer to translate each column of the feature map to match the characteristics between the perspective view and the bird's eye view. As shown in Table 4, when compared with Group IV and Group VI, the column-wise transformer improves the IoU of small objects significantly (13.9 vs" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15518" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.142, + 0.089, + 0.832, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.35, + 0.861, + 0.366 + ], + "angle": 0, + "content": "Figure 6. Qualitative results of ablations on nuScenes [2]. I, III, V, and VI are corresponded to the relevant ablations in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.461 + ], + "angle": 0, + "content": "15.9) while also improving the IoU of large objects (27.5 vs 28.6). Similar improvements are observed in the comparison between Group III and Group V. These experimental results prove that the column-wise transformer could better capture the information of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.471, + 0.627 + ], + "angle": 0, + "content": "Fine-tuning. Although Stage 1 and Stage 2 for training are sufficient to achieve good results, the BEV decoder was trained independently from RGB images so that could not decode typical patterns in RGB images to a detailed BEV segmentation map. Thus we freeze the pipeline as a pretrained RGB image feature extractor and fine-tune the BEV decoder in an end-to-end manner to establish connections between RGB images and BEV segmentation maps. Compared to Group VI in Table 4, Group VII achieves better results across all classes, especially on objects that occupy small regions (0.7 IoU improvement)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.3, + 0.652 + ], + "angle": 0, + "content": "4.4. Qualitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Figure 4 shows qualitative results on nuScenes [2], comparing our predicted segmentation maps with other methods and the ground truth. Our segmentation maps appear more precise and rational, benefiting from our task decomposition into two stages. Specifically, our model demonstrates a more coherent road layout, pedestrian crossing, and walkway layout, thanks to prior knowledge learned in advance. For dynamic objects, our model effectively leverages the polar coordinate system to predict nearby and distant objects with high accuracy, particularly excelling in determining the scale of cars and buses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Figure 6 provides further qualitative results of our ablation experiments. Groups III, V, and VI in the first row display more coherent and accurate road layouts due to the introduction of the coordinate system transformation. Group V in the second row successfully predicts distant" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.895, + 0.477 + ], + "angle": 0, + "content": "cars, thanks to the effectiveness of the column-wise transformer in translating each column. In the third row of Figure 6, Group VI demonstrates that the BEV autoencoder has successfully learned prior patterns about layouts and objects, accurately predicting the size of cars and the layout of pedestrian crossings compared to other experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.495, + 0.62, + 0.51 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.895, + 0.794 + ], + "angle": 0, + "content": "In this paper, we leverage a clearer and more direct optimization target, by decomposing the end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception). Specifically, in the first stage, we propose a BEV autoencoder to reconstruct the BEV segmentation map with corrupted noise, where the decoder is forced to learn typical BEV traffic scene patterns. In the second stage, a mapping from input RGB images and BEV latent representations is learned. Furthermore, we transform the BEV segmentation map from a Cartesian coordinate system to a polar one, thus enhancing its alignment with RGB input. Notably, our method abstains from utilizing multi-scale features or camera intrinsic parameters for depth estimation, resulting in a significantly lower computational overhead. Additionally, our method consistently achieves outstanding prediction accuracy across varying distances from the camera. Extensive experiments on two datasets demonstrate our effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.661, + 0.831 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "This work was partially supported by the National Natural Science Foundation of China under Grant 62372341 and sponsored by CCF-DiDi GAIA Collaborative Research Funds for Young Scholars." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15519" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Florent Bartoccioni, Éloi Zablocki, Andrei Bursuc, Patrick Pérez, Matthieu Cord, and Karteek Alahari. 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Previous methods usually follow an end-to-end pipeline, directly predicting the BEV segmentation map from monocular RGB inputs. However, the challenge arises when the RGB inputs and BEV targets from distinct perspectives, making the direct point-to-point predicting hard to optimize. In this paper, we decompose the original BEV segmentation task into two stages, namely BEV map reconstruction and RGB-BEV feature alignment. In the first stage, we train a BEV autoencoder to reconstruct the BEV segmentation maps given corrupted noisy latent representation, which urges the decoder to learn fundamental knowledge of typical BEV patterns. The second stage involves mapping RGB input images into the BEV latent space of the first stage, directly optimizing the correlations between the two views at the feature level. Our approach simplifies the complexity of combining perception and generation into distinct steps, equipping the model to handle intricate and challenging scenes effectively. Besides, we propose to transform the BEV segmentation map from the Cartesian to the polar coordinate system to establish the column-wise correspondence between RGB images and BEV maps. Moreover, our method requires neither multi-scale features nor camera intrinsic parameters for depth estimation and saves computational overhead. Extensive experiments on nuScenes and Argoverse show the effectiveness and efficiency of our method. Code is available at https://github.com/happytianhao/TaDe. + +# 1. Introduction + +In the field of autonomous driving, bird's eye view (BEV) perception tasks can obtain adequate semantic in + +![](images/e040d1292070b63a6e169303d7142f7a790b13f4216371a4ff928d1d6ec51276.jpg) +Figure 1. Qualitative comparison between traditional end-to-end method and our method. (a) shows the perspective view RGB image, (b) and (c) show the BEV segmentation maps predicted without and with the method of task decomposition, respectively. + +![](images/9e6a0628b1b4dd3be42d68ce1019581c63e039e198860820792e09fcf5979b73.jpg) + +![](images/81851a0c53dc7d09a1e6136f3fa51216272b5577b2b53d90c498b7f840173e5d.jpg) + +formation such as road layout, object categories, positions, and scales around vehicles. This kind of information is called BEV representation and can be directly applied to downstream tasks such as layout mapping, action prediction, route planning, and collision avoidance. In this work, we focus on the monocular BEV segmentation task, which is a fundamental task that aims to predict road segments from camera inputs. + +Previous BEV segmentation methods [6,16,18,23,25,28, 31,34,40,41] usually follow an end-to-end pipeline, which adopts a transformer-based architecture to directly predict BEV segmentation maps from the input RGB images. However, different from the general segmentation task, the input images and targets in BEV are of distinct views (perspective view versus bird's eye view), thus it is hard to train the model by direct point-to-point optimization. And it is even harder when attempting to achieve both source information perception and target view generation in a single step. As shown in Figure 1 (b), the generated BEV segmentation map of the end-to-end baseline looks distorted and does not conform to the expected regular patterns found in real-world traffic scenes. + +To achieve the complex cross-view BEV segmentation, we propose a Task Decomposition (TaDe) method that decompose the traditional end-to-end pipeline into two distinct but goal-oriented stages. In the first stage, we train an + +autoencoder model to learn a basic understanding of typical BEV scene patterns, enabling it to generate coherent and rational BEV segmentation maps independent from RGB images. In the second stage, given input RGB images, we only intend to obtain the latent BEV feature, leaving the workload of BEV segmentation map prediction to the pretrained decoder of the first stage. This two-stage approach, with each stage focusing on only one mission, equips the model with the capacity to handle more intricate and challenging scene perception. As shown in Figure 1 (c), with the help of task decomposition, the predicted BEV segmentation maps share greater structural similarity with the RGB image. + +To be specific, in the first stage, to generate BEV maps that are consistent with physical rules, it is crucial to have a specific expert to comprehend the global traffic layout. For instance, walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow circles. To incorporate this prior knowledge, we employ an autoencoder to learn how to reconstruct/generate the target BEV segmentation maps. To learn a more intrinsic and robust generating ability, we disturb the autoencoder by corrupting the latent representation with random noise during training and enforce the model perfectly reconstruct the ground truth with only the noised latent. This reconstruction can locally recognize and predict typical patterns in BEV segmentation maps, thereby ensuring reasonable BEV map generation given imperfect latent representations. + +In the second stage, we aim to learn a smooth transition from the perspective RGB input to the BEV semantic latent space. Specifically, the model encodes the input RGB images into features and leverages a column-wise transformer to transit them into the BEV latent space. The training objective of the second stage is to ensure that the transited RGB representations align seamlessly with the target BEV latent space. Thus we input the BEV label maps to the frozen BEV encoder of Stage I to get the BEV latent feature, and then take this BEV feature as the optimization target for the transition model of Stage II. Different from existing works, the optimization is in the autoencoder latent space, rather than the traditional pixel segmentation classification space. During inference, since the representations of both views have been already aligned, the transited RGB feature can directly go through the BEV decoder of Stage I for the final BEV segmentation mask prediction. + +Furthermore, to achieve better cross-view alignment, we introduce a coordinate transform step that converts the original BEV segmentation map from Cartesian to polar coordinates. In the transformed BEV map, each column shares the same spatial information with the input monocular RGB images, which also benefits the smooth transition of cross-view features in the second stage. Extensive experiments on two large-scale datasets including nuScenes [2] and Argo + +verse [4] clearly demonstrate our superiority compared to prior end-to-end works. + +Our contributions can be summarized as follows: + +- We break down the traditional end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception). +- We propose a BEV autoencoder to automatically learn typical patterns by reconstructing BEV maps from corrupted latent features, ensuring the decoder prediction is rational and adheres to the real world. +- We also transform the BEV label map from Cartesian to polar coordinates to learn better alignment across perspective views and bird's eye views. + +# 2. Related Works + +# 2.1. Bird's Eye View (BEV) Perception + +As BEV representations contain rich semantic information and can be directly applied to numerous downstream tasks, BEV perception has received widespread attention in the field of autonomous driving. However, converting the perspective view captured by cameras to the bird's eye view is an ill-posed problem, which makes it hard to meet the autonomous driving requirements of complex real-world scenarios. Early works [13, 14, 17, 22, 26, 27, 29, 39] addressed this challenge based on a bottom-up strategy. They first predict the position in the 3D space by estimating the depth of each pixel in the perspective view and then project the 3D position to the BEV space based on the internal and external parameters of the cameras. Nevertheless, despite being intuitive, bottom-up methods depend on the accuracy of depth estimation and have high computational complexity. Recent works follow a top-down strategy. Inspired by DETR [3], DETR3D [36] detects objects from object queries in 3D space with a transformer. BEVFormer [18] and BEVFormer v2 [37] add dense object queries based on DETR3D to achieve map segmentation. PETR [20] and PETRv2 [21] introduce 3D position encoding to DETR3D and significantly simplify the pipeline. + +# 2.2. Monocular BEV Segmentation + +Traditional BEV perception methods focus on calculating the corresponding relationship between the coordinates of the perspective view and the bird's eye view by using the internal and external parameters of the cameras. However, due to the geometric distortion and the presence of overlapping parts and gaps between the perspective views, the perception effect is not ideal. In this regard, some works [1, 5, 10, 11, 24, 33] propose to predict the BEV segmentation map of road layout and objects directly in the case of giving a monocular perspective view. + +PYVA [38] proposes a GAN-based framework and designs a cross-view conversion module to handle significant differences between views. VED [23] employs a variational encoder-decoder network to directly anticipate a semantic occupancy grid from an image. However, the inclusion of a fully connected bottleneck layer in the network results in the loss of significant spatial context and an output that is relatively coarse and incapable of capturing smaller objects like pedestrians. CVT [40] designs a transformer and utilizes the camera's intrinsic and extrinsic calibrations to efficiently understand the surrounding environment. PON [31] adopts a semantic Bayesian occupancy grid framework to estimate BEV segmentation maps directly from monocular perspective views. HFT [41] provides a balanced approach that combines structured geometric information from model-based methods with the global context-capturing ability of model-free methods to overcome their respective limitations in image processing. DiffBEV [42] and DDP [15] propose an end-to-end framework to generate a more comprehensive BEV representation and denoise noisy samples by applying the diffusion model to BEV perception. + +# 2.3. Polar-based Methods + +So far, many works have made significant progress in the BEV segmentation task. However, due to the fact that the perspective view is established in a 3D polar coordinate system, while the bird's eye view is established in a 2D Cartesian coordinate system with the camera as the origin, this gap has led to the previous method's unsatisfactory performance. Therefore, in order to reduce this gap, some methods choose to convert the ground truth of the bird's eye view in the Cartesian coordinate system to the polar coordinate system, corresponding to the perspective view, in order to better learn the relationship between them. PolarDETR [6] converts the object representation in DETR3D from the Cartesian coordinate system to the polar coordinate system. PolarFormer [16] incorporates a polar alignment module to aggregate rays from multiple cameras and generate a structured polar feature map. TIM [34] formulates BEV segmentation map generation from an image as a set of sequence-to-sequence translations and proposes a novel form of end-to-end transformer network to translate between a vertical scanline in the image and rays passing through the camera location in the bird's eye view. GitNet [9] first learns visibility-aware features and learnable geometry to translate into BEV space and then deforms the pre-aligned coarse BEV features with visibility knowledge by ray-based transformers. + +# 3. Method + +We propose TaDe (Task Decomposition) to break down the traditional end-to-end training pipeline into two simple and distinct stages: (1) With the BEV autoencoder, BEV + +![](images/fd99876f9472f96c35a3ba49d19f49b41b37880130d0a8af99a588b301b79396.jpg) +Figure 2. Illustration of the transformation between Cartesian (left) and polar (right) coordinate system for BEV segmentation maps. This transformation can achieve a column-wise correspondence between the BEV segmentation maps and the RGB images. + +segmentation maps with $50\%$ noise are reconstructed to recognize and predict the typical patterns and obtain the BEV latent representations. (2) With the RGB-BEV alignment, the input monocular RGB images are mapped into the BEV latent space via a column-wise transformer to achieve view alignment. During testing, the BEV decoder is employed to generate BEV semantic segmentation maps. In this section, we first introduce the coordinate system transformation of target BEV maps in Section 3.1. After that, we elaborate on the BEV autoencoder and column-wise feature mapping in Section 3.2. and Section 3.3., respectively. + +# 3.1. BEV Coordinate System Transformation + +In the monocular BEV semantic segmentation task, the input RGB images are captured from a perspective view in polar coordinates, while the segmented output targets originate from the bird's eye view in Cartesian coordinates. Consequently, there exists no pixel-level correspondence between the input RGB images and the target segmentation maps, unlike traditional semantic segmentation tasks, which makes this task extremely challenging. However, previous polar-based methods [9, 34] have identified a corresponding relationship between the columns of RGB images and the rays in BEV segmentation maps with the camera position as the origin. To establish this correspondence, they conducted resampling from polar to Cartesian coordinates in the feature space. In contrast, to facilitate BEV autoencoder training and achieve column-wise feature alignment, we directly apply coordinate system transformation on the BEV segmentation maps. + +To be specific, as illustrated in Figure 2, we employ a resampling method to transform the BEV segmentation maps between the Cartesian and polar coordinate systems to achieve a column-wise spatial correspondence between the BEV segmentation maps and RGB images. For instance, in the Cartesian to polar conversion, for each pixel in the polar map, we calculate the corresponding coordinate in the Cartesian map according to the field of view (FOV) and resample from the nearby pixels, and vice versa. Note that + +![](images/9dd3092f825a23a6afe0c44e7690ce5791dd505ee8f76b6c1138574b2e06f83a.jpg) +(b) Stage 2: RGB-BEV Alignment +Figure 3. Overview of our two-stage method. (a) In the first stage, a BEV autoencoder is trained by BEV segmentation maps independent from RGB images. (b) In the second stage, the BEV autoencoder is frozen and the RGB-BEV alignment is conducted to match the RGB images to BEV latent representations for decoding. + +this transform is deterministic and does not require training. During training, we transform the BEV segmentation maps from the Cartesian to the polar coordinate system for reconstruction and encoding. During testing, we transform the predicted BEV segmentation maps from the polar to the Cartesian coordinate system for further quantitative and qualitative validation. + +# 3.2. BEV Autoencoder + +To achieve rational BEV map generation, it is essential to possess a profound understanding of the traffic scene occupancy patterns. In the real world, there is prior knowledge within the traffic BEV segmentation map, where walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow shapes. However, in previous methods, the generated BEV segmentation map does not match real traffic patterns effectively. To address this issue, we introduce a BEV autoencoder, which is designed to reconstruct the BEV segmentation map in polar coordinates. Notably, we introduce $50\%$ noise into the BEV latent representation for reconstruction. This addition of noise renders the reconstruction task more challenging, which requires a holistic understanding of the traffic scene patterns and thus ensures the creation of rational BEV maps that align more closely with real-world expectations. + +As illustrated in Figure 3 (a), the BEV autoencoder consists of a BEV encoder denoted as $E(\cdot)$ , and a BEV decoder denoted as $D(\cdot)$ . Given a BEV segmentation map $y$ in polar coordinates, the BEV autoencoder is outlined as follows: + +$$ +z = E (y), \tag {1} +$$ + +$$ +\hat {y} = D (\tilde {z}), \tag {2} +$$ + +where $z$ and $\hat{z}$ denotes the BEV latent representation, $\hat{y}$ denotes the reconstructed vector in input space. Note that we obtain $z$ with a low scale of $8 \times 22$ , which can thus be seen as a latent representation of $y$ . + +Due to the simplicity of BEV segmentation maps, the criterion is not sufficient to obtain a useful representation or effective decoder. Therefore, we added a large amount of Gaussian noise (e.g. $50\%$ ) to the latent feature map $z$ , to force the BEV decoder to predict the regular traffic scene patterns from noise. The latent feature with noise is calculated by: + +$$ +\tilde {z} = \sqrt {1 - \eta} z + \sqrt {\eta} \varepsilon , \tag {3} +$$ + +where $\eta$ is set to 0.5 in our experiments and $\varepsilon$ denotes the standard Gaussian distribution, which shares the same dimensionality with $z$ . + +Ultimately, we train the BEV autoencoder utilizing a weighted BCE loss to reconstruct the input $y$ as accurately as possible, ensuring that the latent feature map $z$ retains as much information from the original input $y$ as possible: + +$$ +\mathcal {L} _ {B C E} = - w (y \log \hat {y} + (1 - y) \log (1 - \hat {y})), \tag {4} +$$ + +where $w$ denotes the training weights of each class. During implementation, the reciprocal of the frequency of occurrence is used as the weight for each class, which enables balanced learning for each type of object. + +With the pretrained BEV autoencoder, the BEV latent representation is leveraged for RGV-BEV alignment, while the BEV decoder is utilized for BEV segmentation map generation during testing. + +# 3.3. RGB-BEV Alignment + +The goal of RGB-BEV alignment is to learn a transition from the perspective RGB images to the BEV latent representations. As shown in Figure 3 (b), the perspective RGB + +image is taken as the input into the pipeline, where the output is supposed to predict the latent representation $z$ . + +Following previous works [31, 34], we first resize the input RGB images from $900 \times 1600$ to $396 \times 704$ , and then crop off the upper part that contains inessential information like the sky and buildings, leaving only the bottom $256 \times 704$ , in order to better adapt to our model. + +At the beginning of the pipeline, we primarily utilize ResNet [12] and FPN [19], denoted as $F(\cdot)$ together, to extract the feature maps $f$ with a lower scale of $64 \times 176$ from the preprocessed input RGB image $x$ : + +$$ +f = F (x). \tag {5} +$$ + +Despite the fact that we have transformed the BEV segmentation map from Cartesian to polar coordinates to establish spatial correspondence with RGB images from a perspective view of polar coordinates, it is noteworthy that for each column, objects in the RGB image adhere to the characteristic of being larger closer and smaller farther away, whereas objects in the BEV segmentation map maintain the same scale regardless of their distance. To address this, we treat this task as a column-wise sequence-to-sequence translation problem and employ a transformer [35] following [9, 34]. Specifically, we first permute and reshape the feature map from $f^{N \times C \times H \times W}$ to $f^{H \times (N \times W) \times C}$ and treat each column as a sequence input to the transformer [35] to produce a feature map $t^{H \times (N \times W) \times C}$ , which is then resized back to the scale of $t^{N \times C \times H \times W}$ . + +For the last module of the pipeline, we apply multiple convolutional layers, denoted as $conv(\cdot)$ , to reduce the scale $(64 \times 176)$ of the feature map $t$ obtained from the transformer to match the scale $(8 \times 22)$ of the feature map $z$ , + +$$ +\hat {z} = \operatorname {c o n v} (t), \tag {6} +$$ + +where $\hat{z}$ is the output of the whole pipeline. + +In the training phase, we utilize the mean squared error (MSE) loss to facilitate the output of the pipeline to approach the latent feature map $z$ generated by the frozen BEV encoder according to Equation 1: + +$$ +\mathcal {L} _ {M S E} = (\hat {z} - z) ^ {2}. \tag {7} +$$ + +During testing, we use the frozen BEV decoder to decode the feature map $\hat{z}$ predicted by the pipeline into the BEV segmentation map according to Equation 2. Finally, we transform it from the polar to the Cartesian coordinates system following Section 3.1. + +Although we can decode the aligned latent feature map $\hat{z}$ predicted from the pipeline with the frozen BEV decoder into the BEV segmentation map and achieve good performance, we observe that the decoder has only been exposed to samples of BEV segmentation maps during its training process and thus struggles to adequately adapt to the data + +distribution of input RGB images. To address this issue, we introduce a fine-tuning strategy that enables the decoder to better adapt to the data distributions of both input RGB images and latent features, thus establishing a connection between the data distribution of BEV segmentation maps and that of input RGB images. To achieve this, we freeze the parameters of the pipeline and only apply fine-tuning to the BEV decoder using the BCE loss in Equation 4. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. The nuScenes dataset [2] comprises 1,000 scenes captured by six cameras in Boston and Singapore. Each scene spans approximately 20 seconds. For semantic mapping, nuScenes provides detailed vectorized maps covering 11 semantic classes. In terms of dynamic objects, the dataset includes comprehensive annotations of 3D bounding boxes for 23 classes, complemented by 8 unique attributes. The Argoverse dataset [4] includes 65 training and 24 validation sequences recorded in Miami and Pittsburgh, utilizing seven surround-view cameras. Similar to the nuScenes dataset, Argoverse offers 3D object annotations across 15 categories and detailed semantic map data that encompasses road masks, lane geometry, and ground elevation. For a fair comparison, we use the same ground truth generation process, layout and object classes, and training/validation splits outlined in PON [31]. + +Evaluation Metric. We present our results using the Intersection-over-Union (IoU) metric across background classes. Additionally, we compute the class-averaged mean IoU to assess overall performance. We ignore invisible grid cells during the evaluation process, as a LiDAR ray that cannot penetrate them will render them invisible in the image. Considering the possibility of class overlap, such as a car driving in the drivable area, we perform an independent binary segmentation evaluation for each category. We then determine the best performance by selecting the maximum IoU from various thresholds. + +Implementation Details. Referring to PON [31], we perform segmentation in a $[0, 50] \times [-25, 25]$ square meters region around the ego car with a resolution of 0.25 meters per pixel, resulting in a final map size of $200 \times 200$ . For each stage and fine-tuning, we conduct training for 50 epochs. We employ the Lion optimizer [7], set the initial learning rates at $5 \times 10^{-4}$ , $2 \times 10^{-5}$ , and $2 \times 10^{-4}$ for the first, second, and fine-tuning stages, respectively. Additionally, we use a weight decay factor of 0.01, complemented by warm-up and cosine learning rate decay strategies. + +# 4.2. Quantitative Comparison + +Although our method predicts based on monocular RGB images without exploring the relationships between multi + +
MethodLayoutObjectMean
DrivableCrossingWalkwayCarparkBusBikeCarC.V.Motor.TrailerTruckPed.ConeBarrier
IPM [31]40.1-14.0-3.00.24.9-0.8--0.6---
Depth Unpr. [31]27.1-14.1-6.71.311.3-2.8--2.2---
VED [23]54.712.020.713.50.00.08.80.00.07.40.20.00.04.08.7
VPN [26]58.027.329.412.920.04.425.54.95.616.617.37.14.610.817.5
Sim2real [30]60.527.119.218.36.93.87.10.34.53.24.71.84.212.112.4
OFT [32]62.430.934.523.523.24.634.73.76.618.217.41.21.112.919.6
PON [31]60.428.031.018.420.89.424.712.37.016.616.88.25.78.119.1
EPOSH [8]61.133.537.825.431.86.737.82.710.514.220.45.97.613.422.1
DiffBEV [42]65.441.341.128.433.713.238.98.414.421.123.19.67.516.725.9
GitNet [9]65.141.642.131.935.413.843.49.715.022.525.514.111.618.627.9
TaDe (Ours)65.940.942.330.738.514.242.811.418.226.326.914.015.021.429.2
+ +Table 1. Quantitative results of IoU (%) on the nuScenes [2] validation set. "Mean" indicates IoU across all classes. "Crossing", "C.V.", "Motor.", "Ped.", and "Cone" denote pedestrian crossing, construction vehicle, motorcycle, pedestrian, and traffic cone, respectively. IPM and Depth Unpr. are proposed in PON [31]. + +
MethodDrivableVehiclePedestrianLarge VehicleBicycleBusTrailerMotorcycleMean
IPM [31]43.77.51.5-0.47.4-0.8-
Depth Unpr. [31]33.012.73.3-1.120.6-1.6-
VED [23]62.914.01.03.90.012.31.30.011.9
VPN [26]64.923.96.29.70.93.00.41.913.9
PON [31]65.431.47.411.13.611.00.75.717.0
TaDe (Ours)68.334.59.314.74.437.83.16.422.3
+ +ple cameras, we conducted experiments on all available surrounding cameras in nuScenes [2] and Argoverse [4] and showed the average results on their validation set following most previous works [9, 31] in Table 1 and Table 2. + +nuScenes. As shown in Table 1, we observe that our method surpasses IPM-based approaches like IPM [31] and Sim2real [30] by at least $16.8\mathrm{mIoU}$ , without relying on the assumption of a perfectly flat ground plane. Our method also outperforms bottleneck-based approaches, including VED [23], VPN [26], and PON [31], because our BEV decoder can effectively decode latent features. Compared to depth-based approaches like Depth Unprojection-based (DepthUnpr.) [31], OFT [32], EPOSH [8], and DiffBEV [42], our method outperforms them by at least 3.3 mIoU, without depending on depth estimation results. Furthermore, our method achieves the highest performance of 29.2 on mIoU and surpasses the state-of-the-art method GitNet [9] in 10 classes. The above experimental results demonstrate that our method has achieved a higher level of accuracy, particularly in the segmentation of objects such as motorcycles, trailers, and traffic cones. + +Argoverse. As shown in Table 2, we observe that our method achieves the highest performance in terms of mIoU and consistently exhibits improvement across all classes compared with PON [31]. This observation demonstrates the superiority and robustness of our method across diverse datasets. + +Table 2. Quantitative results of IoU (%) on the Argoverse [4] validation set. + +
MethodParams↓FLOPs↓FPS↑GPU Hours↓
PON [31]38.6M60.9G43.8100
TIM [34]45.7M268.3G18.1160
TaDe (Ours)41.5M48.5G51.48 + 48 + 24 = 80
+ +Table 3. Comparison of computational overhead on nuScenes [2]. We report the GPU hours of BEV autoencoder, RGB-BEV alignment, and fine-tuning of our method respectively. + +Computational Overhead. We compare the computational overhead with two open-source methods, considering the following four metrics: parameters, FLOPs, FPS, and GPU hours, as presented in Table 3. GPU hours represent the estimated GPU (NVIDIA GeForce RTX 4090) hours required for training to converge. Notably, in inference, our method achieves the best FLOPs and FPS. In terms of training, despite three stages, our method consumes 80 GPU hours in total, while TIM [34] requires 160 GPU hours. In summary, compared with state-of-the-art methods, our method achieves the best results and maintains low computational overhead thanks to not using multi-scale features. + +IoU over Distance. We further discuss the experimental results of IoU over distance. We divide the BEV maps into 5-meter intervals along the distance from the camera and report the mIoU for layouts and objects at various distances in Figure 5. The experimental results met our expectations, with IoU showing a decreasing trend as the distance + +![](images/7169ea59d31cfb401e708b0a62d63dca5d24578b8a76ca24a9a8bad4fe5b74d2.jpg) +Image + +![](images/7e758e98b3fd6592b8c012662791c6a1e05061c0fc4c72f10434bae11b1fbfb1.jpg) + +![](images/fdc8f1166bed1515726a696e369d86e4335b3a59cbc12898eb2a85335496f3f7.jpg) +Ground Truth + +![](images/2c216a25a07c5f9136f14a048d0df12a1af25dded19a7cf5d1208403b660449b.jpg) + +![](images/608ed9c85b54b6a379a6854ee40857012f9e4f0646a7661bf8fb8c374877aa2b.jpg) +VPN + +![](images/9126c525de0560aa7f63c84f277e5548a149746c66a5a3594cb19ef0c6d1fa13.jpg) + +![](images/51a6b294e996930aaaee654665601ab6bb82a04c61de77edb1017e6c6e29e153.jpg) +PON + +![](images/86fc7b2fdeaf3a56b89718378b68624d4334f29df780da0631a40607d10cd396.jpg) + +![](images/3861a16d4f0004f1939a2e9bd558fca42535dfec7f5e5a5f350a86a1e42d28b1.jpg) +STA + +![](images/96547aec453b97e1410e4af3e7b7c5344083623e85399995a314027f64628edf.jpg) + +![](images/e81c08c841568255de088b2f956158ea6820a103c0e64033f5761df25ff0e696.jpg) +GitNet + +![](images/0e3792860c8c76a03397d13a6590be617cbabfbf9915b6af659deb38566c9c74.jpg) + +![](images/69232fbae5a7d4606f18e413cf2ae6b8734dcdf64b4a3046ba1ff0377c14fb93.jpg) +Ours + +![](images/532e674d7dab0ca3783cae0c906759cae5a7bddd704c99c80e200fbb98423231.jpg) +Figure 4. Qualitative results on nuScenes [2]. We compare with other methods following the color scheme used in PON [31]. +(a) Quantitative Comparison + +![](images/2fb5276f1ceecbf9e81d4ae0c0227b69bb8c55d0cd142d8db54f97b4a0e034f1.jpg) +(b) Percentage Improvement +Figure 5. Trend demonstration and comparison with PON [31] of IoU over distance (0-50m) on nuScenes [2]. + +between the target and the camera increases. Compared to PON [31], we achieve significant and consistent improvements across distances. Notably, for layouts such as drivable areas, we obtain even more absolute performance gains at larger distances. As for small objects like pedestrians and bikes, we observe a relative performance improvement of $200\%$ (5.4 vs 1.8) at 45-50 meters, while the relative improvement at 0-5 meters is $173\%$ (38.7 vs 14.2). In summary, our method shows its superiority, especially at large distances for both layouts and objects. + +# 4.3. Ablation Study + +In this section, we explore the effectiveness of each proposed component through an ablation study on nuScenes [2]. The experimental groups and results are shown in Table 4. + +Coordinate System Transformation. In Table 4, Groups I and III, compared with Groups II and IV, are designated as control groups. Following the adoption of the BEV segmentation map in polar coordinates, there is an overall increase in mIoU by 4.3 and 3, respectively. This improvement can be attributed to the column-wise correspondence established between the BEV segmentation map in polar coordinates and the perspective image, enabling the model to make more accurate predictions. Additionally, Group III exhibits a notable improvement, showing increases of 6.5 in layout and 3.6 in small objects compared to Group I. + +
GroupComponentsIoU
CSTTDCWTFTLayoutLarge Obj.Small Obj.Mean
I35.022.010.421.6
II✓41.922.911.724.4
III✓41.525.613.825.9
IV✓✓44.127.513.927.4
V✓✓41.226.415.526.7
VI✓✓✓44.828.615.928.7
VII✓✓✓✓45.029.216.629.2
+ +Table 4. Ablations of different key components on nuScenes [2]. CST, TD, CWT, and FT denote coordinate system transformation, task decomposition, column-wise transformer, and fine-tuning, respectively. Large objects include bus, car, construction vehicle, trailer, and truck. Small objects include barrier, bike, motorcycle, pedestrian, and traffic cone. + +Task Decomposition. We deploy ablations to demonstrate the effectiveness of task decomposition. For Groups I, III, and V in Table 4, we train the pipeline and the BEV decoder simultaneously with the BCE loss in an end-to-end paradigm. Comparing Group V and Group VI, we observe that task decomposition brings a significant improvement to layouts (41.2 vs 44.8) and large objects (26.4 vs 28.6) which commonly appearing typical patterns. Similar improvements could be observed in the comparison between Group III and Group IV, especially between Group I and Group II (6.9 IoU improvement to layouts). The above ablations demonstrate that the BEV autoencoder successfully learned prior patterns of traffic scenes to decode a more rational BEV segmentation map. + +Column-wise Transformer. In RGB images, objects exhibit the characteristic of appearing larger when closer and smaller when farther away, while in BEV segmentation maps, objects maintain the same scale regardless of their distance. Motivated by TIM [34], we adopt a column-wise transformer to translate each column of the feature map to match the characteristics between the perspective view and the bird's eye view. As shown in Table 4, when compared with Group IV and Group VI, the column-wise transformer improves the IoU of small objects significantly (13.9 vs + +![](images/50819bf7cf19f9e8e161d6494e083ed4718904493ead8a82ec64826bfda48e51.jpg) +Figure 6. Qualitative results of ablations on nuScenes [2]. I, III, V, and VI are corresponded to the relevant ablations in Table 4. + +15.9) while also improving the IoU of large objects (27.5 vs 28.6). Similar improvements are observed in the comparison between Group III and Group V. These experimental results prove that the column-wise transformer could better capture the information of objects. + +Fine-tuning. Although Stage 1 and Stage 2 for training are sufficient to achieve good results, the BEV decoder was trained independently from RGB images so that could not decode typical patterns in RGB images to a detailed BEV segmentation map. Thus we freeze the pipeline as a pretrained RGB image feature extractor and fine-tune the BEV decoder in an end-to-end manner to establish connections between RGB images and BEV segmentation maps. Compared to Group VI in Table 4, Group VII achieves better results across all classes, especially on objects that occupy small regions (0.7 IoU improvement). + +# 4.4. Qualitative Comparison + +Figure 4 shows qualitative results on nuScenes [2], comparing our predicted segmentation maps with other methods and the ground truth. Our segmentation maps appear more precise and rational, benefiting from our task decomposition into two stages. Specifically, our model demonstrates a more coherent road layout, pedestrian crossing, and walkway layout, thanks to prior knowledge learned in advance. For dynamic objects, our model effectively leverages the polar coordinate system to predict nearby and distant objects with high accuracy, particularly excelling in determining the scale of cars and buses. + +Figure 6 provides further qualitative results of our ablation experiments. Groups III, V, and VI in the first row display more coherent and accurate road layouts due to the introduction of the coordinate system transformation. Group V in the second row successfully predicts distant + +cars, thanks to the effectiveness of the column-wise transformer in translating each column. In the third row of Figure 6, Group VI demonstrates that the BEV autoencoder has successfully learned prior patterns about layouts and objects, accurately predicting the size of cars and the layout of pedestrian crossings compared to other experiments. + +# 5. Conclusion + +In this paper, we leverage a clearer and more direct optimization target, by decomposing the end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception). Specifically, in the first stage, we propose a BEV autoencoder to reconstruct the BEV segmentation map with corrupted noise, where the decoder is forced to learn typical BEV traffic scene patterns. In the second stage, a mapping from input RGB images and BEV latent representations is learned. 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Time will tell: New outlooks and a baseline for temporal multiview 3d object detection. In The Eleventh International Conference on Learning Representations, 2022. 2 +[28] Lang Peng, Zhirong Chen, Zhangjie Fu, Pengpeng Liang, and Erkang Cheng. Bevsegformer: Bird's eye view semantic segmentation from arbitrary camera rigs. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5935-5943, 2023. 1 +[29] Jonah Philion and Sanja Fidler. Lift, splat, shoot: Encoding images from arbitrary camera rigs by implicitly unprojecting to 3d. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XIV 16, pages 194-210. Springer, 2020. 2 +[30] Lennart Reiher, Bastian Lampe, and Lutz Eckstein. A sim2real deep learning approach for the transformation of images from multiple vehicle-mounted cameras to a semantically segmented image in bird's eye view. 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Projecting your view attentively: Monocular road scene layout estimation via cross-view transformation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 15536-15545, 2021. 3 +[39] Yunpeng Zhang, Zheng Zhu, Wenzhao Zheng, Junjie Huang, Guan Huang, Jie Zhou, and Jiwen Lu. Beverse: Unified perception and prediction in birds-eye-view for vision-centric autonomous driving. arXiv preprint arXiv:2205.09743, 2022. 2 +[40] Brady Zhou and Philipp Krahenbuhl. Cross-view transformers for real-time map-view semantic segmentation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 13760-13769, 2022. 1, 3 +[41] Jiayu Zou, Zheng Zhu, Junjie Huang, Tian Yang, Guan Huang, and Xingang Wang. Hft: Lifting perspective representations via hybrid feature transformation for bev perception. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 7046-7053. IEEE, 2023. 1, 3 +[42] Jiayu Zou, Zheng Zhu, Yun Ye, and Xingang Wang. Diffbev: Conditional diffusion model for bird's eye view perception. arXiv preprint arXiv:2303.08333, 2023. 3, 6 \ No newline at end of file diff --git a/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/images.zip b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..02517bcca55b0a767cb0a67699e3023627c49b17 --- /dev/null +++ b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ca7b18352f554e4f2474e7ee9ce947a26c740820c8bbfad9dcf8c0b1eca51a9a +size 432770 diff --git a/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/layout.json b/2024/Improving Bird's Eye View Semantic Segmentation by Task Decomposition/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..192b0de949a0132ce052521db24877d8625fdd98 --- 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Previous methods usually follow an end-to-end pipeline, directly predicting the BEV segmentation map from monocular RGB inputs. However, the challenge arises when the RGB inputs and BEV targets from distinct perspectives, making the direct point-to-point predicting hard to optimize. In this paper, we decompose the original BEV segmentation task into two stages, namely BEV map reconstruction and RGB-BEV feature alignment. In the first stage, we train a BEV autoencoder to reconstruct the BEV segmentation maps given corrupted noisy latent representation, which urges the decoder to learn fundamental knowledge of typical BEV patterns. The second stage involves mapping RGB input images into the BEV latent space of the first stage, directly optimizing the correlations between the two views at the feature level. Our approach simplifies the complexity of combining perception and generation into distinct steps, equipping the model to handle intricate and challenging scenes effectively. Besides, we propose to transform the BEV segmentation map from the Cartesian to the polar coordinate system to establish the column-wise correspondence between RGB images and BEV maps. Moreover, our method requires neither multi-scale features nor camera intrinsic parameters for depth estimation and saves computational overhead. Extensive experiments on nuScenes and Argoverse show the effectiveness and efficiency of our method. Code is available at https://github.com/happytianhao/TaDe." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 639, + 128, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 128, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 128, + 651 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 660, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 660, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 660, + 287, + 684 + ], + "type": "text", + "content": "In the field of autonomous driving, bird's eye view (BEV) perception tasks can obtain adequate semantic in" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 254, + 417, + 329 + ], + "blocks": [ + { + "bbox": [ + 307, + 254, + 417, + 329 + ], + "lines": [ + { + "bbox": [ + 307, + 254, + 417, + 329 + ], + "spans": [ + { + "bbox": [ + 307, + 254, + 417, + 329 + ], + "type": "image", + "image_path": "e040d1292070b63a6e169303d7142f7a790b13f4216371a4ff928d1d6ec51276.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 338, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 305, + 338, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 547, + 383 + ], + "type": "text", + "content": "Figure 1. Qualitative comparison between traditional end-to-end method and our method. (a) shows the perspective view RGB image, (b) and (c) show the BEV segmentation maps predicted without and with the method of task decomposition, respectively." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 418, + 254, + 481, + 328 + ], + "blocks": [ + { + "bbox": [ + 418, + 254, + 481, + 328 + ], + "lines": [ + { + "bbox": [ + 418, + 254, + 481, + 328 + ], + "spans": [ + { + "bbox": [ + 418, + 254, + 481, + 328 + ], + "type": "image", + "image_path": "9e6a0628b1b4dd3be42d68ce1019581c63e039e198860820792e09fcf5979b73.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 482, + 254, + 545, + 329 + ], + "blocks": [ + { + "bbox": [ + 482, + 254, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 482, + 254, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 482, + 254, + 545, + 329 + ], + "type": "image", + "image_path": "81851a0c53dc7d09a1e6136f3fa51216272b5577b2b53d90c498b7f840173e5d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 400, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 496 + ], + "type": "text", + "content": "formation such as road layout, object categories, positions, and scales around vehicles. This kind of information is called BEV representation and can be directly applied to downstream tasks such as layout mapping, action prediction, route planning, and collision avoidance. In this work, we focus on the monocular BEV segmentation task, which is a fundamental task that aims to predict road segments from camera inputs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 497, + 546, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 663 + ], + "type": "text", + "content": "Previous BEV segmentation methods [6,16,18,23,25,28, 31,34,40,41] usually follow an end-to-end pipeline, which adopts a transformer-based architecture to directly predict BEV segmentation maps from the input RGB images. However, different from the general segmentation task, the input images and targets in BEV are of distinct views (perspective view versus bird's eye view), thus it is hard to train the model by direct point-to-point optimization. And it is even harder when attempting to achieve both source information perception and target view generation in a single step. As shown in Figure 1 (b), the generated BEV segmentation map of the end-to-end baseline looks distorted and does not conform to the expected regular patterns found in real-world traffic scenes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "To achieve the complex cross-view BEV segmentation, we propose a Task Decomposition (TaDe) method that decompose the traditional end-to-end pipeline into two distinct but goal-oriented stages. In the first stage, we train an" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15512" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "autoencoder model to learn a basic understanding of typical BEV scene patterns, enabling it to generate coherent and rational BEV segmentation maps independent from RGB images. In the second stage, given input RGB images, we only intend to obtain the latent BEV feature, leaving the workload of BEV segmentation map prediction to the pretrained decoder of the first stage. This two-stage approach, with each stage focusing on only one mission, equips the model with the capacity to handle more intricate and challenging scene perception. As shown in Figure 1 (c), with the help of task decomposition, the predicted BEV segmentation maps share greater structural similarity with the RGB image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 218, + 289, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 218, + 289, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 289, + 410 + ], + "type": "text", + "content": "To be specific, in the first stage, to generate BEV maps that are consistent with physical rules, it is crucial to have a specific expert to comprehend the global traffic layout. For instance, walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow circles. To incorporate this prior knowledge, we employ an autoencoder to learn how to reconstruct/generate the target BEV segmentation maps. To learn a more intrinsic and robust generating ability, we disturb the autoencoder by corrupting the latent representation with random noise during training and enforce the model perfectly reconstruct the ground truth with only the noised latent. This reconstruction can locally recognize and predict typical patterns in BEV segmentation maps, thereby ensuring reasonable BEV map generation given imperfect latent representations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 411, + 289, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 289, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 289, + 616 + ], + "type": "text", + "content": "In the second stage, we aim to learn a smooth transition from the perspective RGB input to the BEV semantic latent space. Specifically, the model encodes the input RGB images into features and leverages a column-wise transformer to transit them into the BEV latent space. The training objective of the second stage is to ensure that the transited RGB representations align seamlessly with the target BEV latent space. Thus we input the BEV label maps to the frozen BEV encoder of Stage I to get the BEV latent feature, and then take this BEV feature as the optimization target for the transition model of Stage II. Different from existing works, the optimization is in the autoencoder latent space, rather than the traditional pixel segmentation classification space. During inference, since the representations of both views have been already aligned, the transited RGB feature can directly go through the BEV decoder of Stage I for the final BEV segmentation mask prediction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "type": "text", + "content": "Furthermore, to achieve better cross-view alignment, we introduce a coordinate transform step that converts the original BEV segmentation map from Cartesian to polar coordinates. In the transformed BEV map, each column shares the same spatial information with the input monocular RGB images, which also benefits the smooth transition of cross-view features in the second stage. Extensive experiments on two large-scale datasets including nuScenes [2] and Argo" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "content": "verse [4] clearly demonstrate our superiority compared to prior end-to-end works." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 96, + 517, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 96, + 517, + 107 + ], + "spans": [ + { + "bbox": [ + 317, + 96, + 517, + 107 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 118, + 545, + 255 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 118, + 545, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 118, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 317, + 118, + 545, + 155 + ], + "type": "text", + "content": "- We break down the traditional end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 163, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 163, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 317, + 163, + 545, + 209 + ], + "type": "text", + "content": "- We propose a BEV autoencoder to automatically learn typical patterns by reconstructing BEV maps from corrupted latent features, ensuring the decoder prediction is rational and adheres to the real world." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 219, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 219, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 317, + 219, + 545, + 255 + ], + "type": "text", + "content": "- We also transform the BEV label map from Cartesian to polar coordinates to learn better alignment across perspective views and bird's eye views." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 266, + 398, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 266, + 398, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 398, + 278 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 285, + 489, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 489, + 298 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 489, + 298 + ], + "type": "text", + "content": "2.1. Bird's Eye View (BEV) Perception" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 304, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 568 + ], + "type": "text", + "content": "As BEV representations contain rich semantic information and can be directly applied to numerous downstream tasks, BEV perception has received widespread attention in the field of autonomous driving. However, converting the perspective view captured by cameras to the bird's eye view is an ill-posed problem, which makes it hard to meet the autonomous driving requirements of complex real-world scenarios. Early works [13, 14, 17, 22, 26, 27, 29, 39] addressed this challenge based on a bottom-up strategy. They first predict the position in the 3D space by estimating the depth of each pixel in the perspective view and then project the 3D position to the BEV space based on the internal and external parameters of the cameras. Nevertheless, despite being intuitive, bottom-up methods depend on the accuracy of depth estimation and have high computational complexity. Recent works follow a top-down strategy. Inspired by DETR [3], DETR3D [36] detects objects from object queries in 3D space with a transformer. BEVFormer [18] and BEVFormer v2 [37] add dense object queries based on DETR3D to achieve map segmentation. PETR [20] and PETRv2 [21] introduce 3D position encoding to DETR3D and significantly simplify the pipeline." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "type": "text", + "content": "2.2. Monocular BEV Segmentation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": "Traditional BEV perception methods focus on calculating the corresponding relationship between the coordinates of the perspective view and the bird's eye view by using the internal and external parameters of the cameras. However, due to the geometric distortion and the presence of overlapping parts and gaps between the perspective views, the perception effect is not ideal. In this regard, some works [1, 5, 10, 11, 24, 33] propose to predict the BEV segmentation map of road layout and objects directly in the case of giving a monocular perspective view." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15513" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "content": "PYVA [38] proposes a GAN-based framework and designs a cross-view conversion module to handle significant differences between views. VED [23] employs a variational encoder-decoder network to directly anticipate a semantic occupancy grid from an image. However, the inclusion of a fully connected bottleneck layer in the network results in the loss of significant spatial context and an output that is relatively coarse and incapable of capturing smaller objects like pedestrians. CVT [40] designs a transformer and utilizes the camera's intrinsic and extrinsic calibrations to efficiently understand the surrounding environment. PON [31] adopts a semantic Bayesian occupancy grid framework to estimate BEV segmentation maps directly from monocular perspective views. HFT [41] provides a balanced approach that combines structured geometric information from model-based methods with the global context-capturing ability of model-free methods to overcome their respective limitations in image processing. DiffBEV [42] and DDP [15] propose an end-to-end framework to generate a more comprehensive BEV representation and denoise noisy samples by applying the diffusion model to BEV perception." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 330, + 169, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 330, + 169, + 341 + ], + "spans": [ + { + "bbox": [ + 47, + 330, + 169, + 341 + ], + "type": "text", + "content": "2.3. Polar-based Methods" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 349, + 289, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 289, + 648 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 289, + 648 + ], + "type": "text", + "content": "So far, many works have made significant progress in the BEV segmentation task. However, due to the fact that the perspective view is established in a 3D polar coordinate system, while the bird's eye view is established in a 2D Cartesian coordinate system with the camera as the origin, this gap has led to the previous method's unsatisfactory performance. Therefore, in order to reduce this gap, some methods choose to convert the ground truth of the bird's eye view in the Cartesian coordinate system to the polar coordinate system, corresponding to the perspective view, in order to better learn the relationship between them. PolarDETR [6] converts the object representation in DETR3D from the Cartesian coordinate system to the polar coordinate system. PolarFormer [16] incorporates a polar alignment module to aggregate rays from multiple cameras and generate a structured polar feature map. TIM [34] formulates BEV segmentation map generation from an image as a set of sequence-to-sequence translations and proposes a novel form of end-to-end transformer network to translate between a vertical scanline in the image and rays passing through the camera location in the bird's eye view. GitNet [9] first learns visibility-aware features and learnable geometry to translate into BEV space and then deforms the pre-aligned coarse BEV features with visibility knowledge by ray-based transformers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 657, + 102, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 102, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 102, + 669 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "We propose TaDe (Task Decomposition) to break down the traditional end-to-end training pipeline into two simple and distinct stages: (1) With the BEV autoencoder, BEV" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 545, + 173 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 173 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 173 + ], + "type": "image", + "image_path": "fd99876f9472f96c35a3ba49d19f49b41b37880130d0a8af99a588b301b79396.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 182, + 547, + 226 + ], + "lines": [ + { + "bbox": [ + 305, + 182, + 547, + 226 + ], + "spans": [ + { + "bbox": [ + 305, + 182, + 547, + 226 + ], + "type": "text", + "content": "Figure 2. Illustration of the transformation between Cartesian (left) and polar (right) coordinate system for BEV segmentation maps. This transformation can achieve a column-wise correspondence between the BEV segmentation maps and the RGB images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 243, + 547, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 547, + 374 + ], + "type": "text", + "content": "segmentation maps with " + }, + { + "bbox": [ + 305, + 243, + 547, + 374 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 305, + 243, + 547, + 374 + ], + "type": "text", + "content": " noise are reconstructed to recognize and predict the typical patterns and obtain the BEV latent representations. (2) With the RGB-BEV alignment, the input monocular RGB images are mapped into the BEV latent space via a column-wise transformer to achieve view alignment. During testing, the BEV decoder is employed to generate BEV semantic segmentation maps. In this section, we first introduce the coordinate system transformation of target BEV maps in Section 3.1. After that, we elaborate on the BEV autoencoder and column-wise feature mapping in Section 3.2. and Section 3.3., respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 383, + 520, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 520, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 520, + 396 + ], + "type": "text", + "content": "3.1. BEV Coordinate System Transformation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 402, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 402, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 545, + 605 + ], + "type": "text", + "content": "In the monocular BEV semantic segmentation task, the input RGB images are captured from a perspective view in polar coordinates, while the segmented output targets originate from the bird's eye view in Cartesian coordinates. Consequently, there exists no pixel-level correspondence between the input RGB images and the target segmentation maps, unlike traditional semantic segmentation tasks, which makes this task extremely challenging. However, previous polar-based methods [9, 34] have identified a corresponding relationship between the columns of RGB images and the rays in BEV segmentation maps with the camera position as the origin. To establish this correspondence, they conducted resampling from polar to Cartesian coordinates in the feature space. In contrast, to facilitate BEV autoencoder training and achieve column-wise feature alignment, we directly apply coordinate system transformation on the BEV segmentation maps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 606, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 606, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 606, + 547, + 713 + ], + "type": "text", + "content": "To be specific, as illustrated in Figure 2, we employ a resampling method to transform the BEV segmentation maps between the Cartesian and polar coordinate systems to achieve a column-wise spatial correspondence between the BEV segmentation maps and RGB images. For instance, in the Cartesian to polar conversion, for each pixel in the polar map, we calculate the corresponding coordinate in the Cartesian map according to the field of view (FOV) and resample from the nearby pixels, and vice versa. Note that" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15514" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 545, + 227 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 545, + 227 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 545, + 227 + ], + "type": "image", + "image_path": "9dd3092f825a23a6afe0c44e7690ce5791dd505ee8f76b6c1138574b2e06f83a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 228, + 265, + 239 + ], + "lines": [ + { + "bbox": [ + 141, + 228, + 265, + 239 + ], + "spans": [ + { + "bbox": [ + 141, + 228, + 265, + 239 + ], + "type": "text", + "content": "(b) Stage 2: RGB-BEV Alignment" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "type": "text", + "content": "Figure 3. Overview of our two-stage method. (a) In the first stage, a BEV autoencoder is trained by BEV segmentation maps independent from RGB images. (b) In the second stage, the BEV autoencoder is frozen and the RGB-BEV alignment is conducted to match the RGB images to BEV latent representations for decoding." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 299, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 287, + 383 + ], + "type": "text", + "content": "this transform is deterministic and does not require training. During training, we transform the BEV segmentation maps from the Cartesian to the polar coordinate system for reconstruction and encoding. During testing, we transform the predicted BEV segmentation maps from the polar to the Cartesian coordinate system for further quantitative and qualitative validation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 392, + 155, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 155, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 155, + 403 + ], + "type": "text", + "content": "3.2. BEV Autoencoder" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 411, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 614 + ], + "type": "text", + "content": "To achieve rational BEV map generation, it is essential to possess a profound understanding of the traffic scene occupancy patterns. In the real world, there is prior knowledge within the traffic BEV segmentation map, where walkways are usually to be continuous rather than discontinuous, and cars are supposed to be shaped as filled rectangles instead of hollow shapes. However, in previous methods, the generated BEV segmentation map does not match real traffic patterns effectively. To address this issue, we introduce a BEV autoencoder, which is designed to reconstruct the BEV segmentation map in polar coordinates. Notably, we introduce " + }, + { + "bbox": [ + 46, + 411, + 287, + 614 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 614 + ], + "type": "text", + "content": " noise into the BEV latent representation for reconstruction. This addition of noise renders the reconstruction task more challenging, which requires a holistic understanding of the traffic scene patterns and thus ensures the creation of rational BEV maps that align more closely with real-world expectations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "text", + "content": "As illustrated in Figure 3 (a), the BEV autoencoder consists of a BEV encoder denoted as " + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "text", + "content": ", and a BEV decoder denoted as " + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "text", + "content": ". Given a BEV segmentation map " + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 616, + 287, + 662 + ], + "type": "text", + "content": " in polar coordinates, the BEV autoencoder is outlined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 144, + 674, + 287, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 674, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 144, + 674, + 287, + 687 + ], + "type": "interline_equation", + "content": "z = E (y), \\tag {1}", + "image_path": "ae2a3c340471676d3f62eae06b1510051d4c19bf90289f7ab2d7208872a2358d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 144, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 144, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\hat {y} = D (\\tilde {z}), \\tag {2}", + "image_path": "ee39116f6e9b36cd0f7699d276e98bc0125bd3c2e7728ae4181545790b20dd07.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " denotes the BEV latent representation, " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " denotes the reconstructed vector in input space. Note that we obtain " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " with a low scale of " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "8 \\times 22" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": ", which can thus be seen as a latent representation of " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "type": "text", + "content": "Due to the simplicity of BEV segmentation maps, the criterion is not sufficient to obtain a useful representation or effective decoder. Therefore, we added a large amount of Gaussian noise (e.g. " + }, + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "type": "text", + "content": " ) to the latent feature map " + }, + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 347, + 546, + 430 + ], + "type": "text", + "content": ", to force the BEV decoder to predict the regular traffic scene patterns from noise. The latent feature with noise is calculated by:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 379, + 430, + 545, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 430, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 379, + 430, + 545, + 444 + ], + "type": "interline_equation", + "content": "\\tilde {z} = \\sqrt {1 - \\eta} z + \\sqrt {\\eta} \\varepsilon , \\tag {3}", + "image_path": "832e4f2a9a08098a558aee8f75aa7d615575fdba116b96e68466b84ce4ff3b64.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "content": " is set to 0.5 in our experiments and " + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "content": " denotes the standard Gaussian distribution, which shares the same dimensionality with " + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "text", + "content": "Ultimately, we train the BEV autoencoder utilizing a weighted BCE loss to reconstruct the input " + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "text", + "content": " as accurately as possible, ensuring that the latent feature map " + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "text", + "content": " retains as much information from the original input " + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 483, + 545, + 531 + ], + "type": "text", + "content": " as possible:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 334, + 537, + 545, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 537, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 334, + 537, + 545, + 551 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {B C E} = - w (y \\log \\hat {y} + (1 - y) \\log (1 - \\hat {y})), \\tag {4}", + "image_path": "cefc86742a4d8722ba143ddc28356479cd6524d3dd3e4d5963aa0df55cfdb4cd.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "content": " denotes the training weights of each class. During implementation, the reciprocal of the frequency of occurrence is used as the weight for each class, which enables balanced learning for each type of object." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 653 + ], + "type": "text", + "content": "With the pretrained BEV autoencoder, the BEV latent representation is leveraged for RGV-BEV alignment, while the BEV decoder is utilized for BEV segmentation map generation during testing." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 659, + 430, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 430, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 430, + 672 + ], + "type": "text", + "content": "3.3. RGB-BEV Alignment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "The goal of RGB-BEV alignment is to learn a transition from the perspective RGB images to the BEV latent representations. As shown in Figure 3 (b), the perspective RGB" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "15515" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "image is taken as the input into the pipeline, where the output is supposed to predict the latent representation " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "text", + "content": "Following previous works [31, 34], we first resize the input RGB images from " + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "inline_equation", + "content": "900 \\times 1600" + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "inline_equation", + "content": "396 \\times 704" + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "text", + "content": ", and then crop off the upper part that contains inessential information like the sky and buildings, leaving only the bottom " + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "inline_equation", + "content": "256 \\times 704" + }, + { + "bbox": [ + 46, + 96, + 286, + 156 + ], + "type": "text", + "content": ", in order to better adapt to our model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "text", + "content": "At the beginning of the pipeline, we primarily utilize ResNet [12] and FPN [19], denoted as " + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "inline_equation", + "content": "F(\\cdot)" + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "text", + "content": " together, to extract the feature maps " + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "text", + "content": " with a lower scale of " + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "inline_equation", + "content": "64 \\times 176" + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "text", + "content": " from the preprocessed input RGB image " + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 156, + 286, + 204 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 213, + 286, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 286, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 286, + 225 + ], + "type": "interline_equation", + "content": "f = F (x). \\tag {5}", + "image_path": "0ccd700660a582e37b53520ce970933cd984ac90fa82ca735decf951e92078be.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "text", + "content": "Despite the fact that we have transformed the BEV segmentation map from Cartesian to polar coordinates to establish spatial correspondence with RGB images from a perspective view of polar coordinates, it is noteworthy that for each column, objects in the RGB image adhere to the characteristic of being larger closer and smaller farther away, whereas objects in the BEV segmentation map maintain the same scale regardless of their distance. To address this, we treat this task as a column-wise sequence-to-sequence translation problem and employ a transformer [35] following [9, 34]. Specifically, we first permute and reshape the feature map from " + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "inline_equation", + "content": "f^{N \\times C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "inline_equation", + "content": "f^{H \\times (N \\times W) \\times C}" + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "text", + "content": " and treat each column as a sequence input to the transformer [35] to produce a feature map " + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "inline_equation", + "content": "t^{H \\times (N \\times W) \\times C}" + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "text", + "content": ", which is then resized back to the scale of " + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "inline_equation", + "content": "t^{N \\times C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 234, + 286, + 413 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": "For the last module of the pipeline, we apply multiple convolutional layers, denoted as " + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "inline_equation", + "content": "conv(\\cdot)" + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": ", to reduce the scale " + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "inline_equation", + "content": "(64 \\times 176)" + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": " of the feature map " + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": " obtained from the transformer to match the scale " + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "inline_equation", + "content": "(8 \\times 22)" + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": " of the feature map " + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 139, + 474, + 286, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 474, + 286, + 487 + ], + "spans": [ + { + "bbox": [ + 139, + 474, + 286, + 487 + ], + "type": "interline_equation", + "content": "\\hat {z} = \\operatorname {c o n v} (t), \\tag {6}", + "image_path": "a4b35542dbea230f003510ca897a9ecd56e63f36d78fbba6bd21b8e7b13a9169.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 491, + 223, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 223, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 223, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 491, + 223, + 502 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 47, + 491, + 223, + 502 + ], + "type": "text", + "content": " is the output of the whole pipeline." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 504, + 286, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 286, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 286, + 551 + ], + "type": "text", + "content": "In the training phase, we utilize the mean squared error (MSE) loss to facilitate the output of the pipeline to approach the latent feature map " + }, + { + "bbox": [ + 46, + 504, + 286, + 551 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 504, + 286, + 551 + ], + "type": "text", + "content": " generated by the frozen BEV encoder according to Equation 1:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 559, + 286, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 559, + 286, + 573 + ], + "spans": [ + { + "bbox": [ + 126, + 559, + 286, + 573 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {M S E} = (\\hat {z} - z) ^ {2}. \\tag {7}", + "image_path": "227bf4f82d6b2938d8c850a6b0afdfec0218978608ea078bffa1cf24d7b21fa4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 286, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 641 + ], + "type": "text", + "content": "During testing, we use the frozen BEV decoder to decode the feature map " + }, + { + "bbox": [ + 46, + 582, + 286, + 641 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 582, + 286, + 641 + ], + "type": "text", + "content": " predicted by the pipeline into the BEV segmentation map according to Equation 2. Finally, we transform it from the polar to the Cartesian coordinates system following Section 3.1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": "Although we can decode the aligned latent feature map " + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": " predicted from the pipeline with the frozen BEV decoder into the BEV segmentation map and achieve good performance, we observe that the decoder has only been exposed to samples of BEV segmentation maps during its training process and thus struggles to adequately adapt to the data" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "distribution of input RGB images. To address this issue, we introduce a fine-tuning strategy that enables the decoder to better adapt to the data distributions of both input RGB images and latent features, thus establishing a connection between the data distribution of BEV segmentation maps and that of input RGB images. To achieve this, we freeze the parameters of the pipeline and only apply fine-tuning to the BEV decoder using the BCE loss in Equation 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 180, + 386, + 193 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 180, + 386, + 193 + ], + "spans": [ + { + "bbox": [ + 306, + 180, + 386, + 193 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 200, + 422, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 200, + 422, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 200, + 422, + 213 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 218, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 410 + ], + "type": "text", + "content": "Datasets. The nuScenes dataset [2] comprises 1,000 scenes captured by six cameras in Boston and Singapore. Each scene spans approximately 20 seconds. For semantic mapping, nuScenes provides detailed vectorized maps covering 11 semantic classes. In terms of dynamic objects, the dataset includes comprehensive annotations of 3D bounding boxes for 23 classes, complemented by 8 unique attributes. The Argoverse dataset [4] includes 65 training and 24 validation sequences recorded in Miami and Pittsburgh, utilizing seven surround-view cameras. Similar to the nuScenes dataset, Argoverse offers 3D object annotations across 15 categories and detailed semantic map data that encompasses road masks, lane geometry, and ground elevation. For a fair comparison, we use the same ground truth generation process, layout and object classes, and training/validation splits outlined in PON [31]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 411, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 540 + ], + "type": "text", + "content": "Evaluation Metric. We present our results using the Intersection-over-Union (IoU) metric across background classes. Additionally, we compute the class-averaged mean IoU to assess overall performance. We ignore invisible grid cells during the evaluation process, as a LiDAR ray that cannot penetrate them will render them invisible in the image. Considering the possibility of class overlap, such as a car driving in the drivable area, we perform an independent binary segmentation evaluation for each category. We then determine the best performance by selecting the maximum IoU from various thresholds." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "content": "Implementation Details. Referring to PON [31], we perform segmentation in a " + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "inline_equation", + "content": "[0, 50] \\times [-25, 25]" + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "content": " square meters region around the ego car with a resolution of 0.25 meters per pixel, resulting in a final map size of " + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "inline_equation", + "content": "200 \\times 200" + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "content": ". For each stage and fine-tuning, we conduct training for 50 epochs. We employ the Lion optimizer [7], set the initial learning rates at " + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 542, + 545, + 662 + ], + "type": "text", + "content": " for the first, second, and fine-tuning stages, respectively. Additionally, we use a weight decay factor of 0.01, complemented by warm-up and cosine learning rate decay strategies." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 670, + 448, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 448, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 448, + 684 + ], + "type": "text", + "content": "4.2. Quantitative Comparison" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Although our method predicts based on monocular RGB images without exploring the relationships between multi" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15516" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 209 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 209 + ], + "type": "table", + "html": "
MethodLayoutObjectMean
DrivableCrossingWalkwayCarparkBusBikeCarC.V.Motor.TrailerTruckPed.ConeBarrier
IPM [31]40.1-14.0-3.00.24.9-0.8--0.6---
Depth Unpr. [31]27.1-14.1-6.71.311.3-2.8--2.2---
VED [23]54.712.020.713.50.00.08.80.00.07.40.20.00.04.08.7
VPN [26]58.027.329.412.920.04.425.54.95.616.617.37.14.610.817.5
Sim2real [30]60.527.119.218.36.93.87.10.34.53.24.71.84.212.112.4
OFT [32]62.430.934.523.523.24.634.73.76.618.217.41.21.112.919.6
PON [31]60.428.031.018.420.89.424.712.37.016.616.88.25.78.119.1
EPOSH [8]61.133.537.825.431.86.737.82.710.514.220.45.97.613.422.1
DiffBEV [42]65.441.341.128.433.713.238.98.414.421.123.19.67.516.725.9
GitNet [9]65.141.642.131.935.413.843.49.715.022.525.514.111.618.627.9
TaDe (Ours)65.940.942.330.738.514.242.811.418.226.326.914.015.021.429.2
", + "image_path": "a2a841e7889869a4c84a7dc20e5c52f58c3dd5bd108636a28c666555d8e1a333.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 92, + 260, + 504, + 347 + ], + "blocks": [ + { + "bbox": [ + 46, + 216, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 546, + 251 + ], + "type": "text", + "content": "Table 1. Quantitative results of IoU (%) on the nuScenes [2] validation set. \"Mean\" indicates IoU across all classes. \"Crossing\", \"C.V.\", \"Motor.\", \"Ped.\", and \"Cone\" denote pedestrian crossing, construction vehicle, motorcycle, pedestrian, and traffic cone, respectively. IPM and Depth Unpr. are proposed in PON [31]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 92, + 260, + 504, + 347 + ], + "lines": [ + { + "bbox": [ + 92, + 260, + 504, + 347 + ], + "spans": [ + { + "bbox": [ + 92, + 260, + 504, + 347 + ], + "type": "table", + "html": "
MethodDrivableVehiclePedestrianLarge VehicleBicycleBusTrailerMotorcycleMean
IPM [31]43.77.51.5-0.47.4-0.8-
Depth Unpr. [31]33.012.73.3-1.120.6-1.6-
VED [23]62.914.01.03.90.012.31.30.011.9
VPN [26]64.923.96.29.70.93.00.41.913.9
PON [31]65.431.47.411.13.611.00.75.717.0
TaDe (Ours)68.334.59.314.74.437.83.16.422.3
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MethodParams↓FLOPs↓FPS↑GPU Hours↓
PON [31]38.6M60.9G43.8100
TIM [34]45.7M268.3G18.1160
TaDe (Ours)41.5M48.5G51.48 + 48 + 24 = 80
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We compare the computational overhead with two open-source methods, considering the following four metrics: parameters, FLOPs, FPS, and GPU hours, as presented in Table 3. GPU hours represent the estimated GPU (NVIDIA GeForce RTX 4090) hours required for training to converge. Notably, in inference, our method achieves the best FLOPs and FPS. In terms of training, despite three stages, our method consumes 80 GPU hours in total, while TIM [34] requires 160 GPU hours. In summary, compared with state-of-the-art methods, our method achieves the best results and maintains low computational overhead thanks to not using multi-scale features." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "IoU over Distance. We further discuss the experimental results of IoU over distance. We divide the BEV maps into 5-meter intervals along the distance from the camera and report the mIoU for layouts and objects at various distances in Figure 5. The experimental results met our expectations, with IoU showing a decreasing trend as the distance" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15517" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 162, + 199 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 162, + 199 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 162, + 199 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 162, + 199 + ], + "type": "image", + "image_path": "7169ea59d31cfb401e708b0a62d63dca5d24578b8a76ca24a9a8bad4fe5b74d2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 96, + 201, + 117, + 209 + ], 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Qualitative results on nuScenes [2]. We compare with other methods following the color scheme used in PON [31]." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 246, + 167, + 323 + ], + "lines": [ + { + "bbox": [ + 50, + 246, + 167, + 323 + ], + "spans": [ + { + "bbox": [ + 50, + 246, + 167, + 323 + ], + "type": "image", + "image_path": "532e674d7dab0ca3783cae0c906759cae5a7bddd704c99c80e200fbb98423231.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 327, + 156, + 335 + ], + "lines": [ + { + "bbox": [ + 63, + 327, + 156, + 335 + ], + "spans": [ + { + "bbox": [ + 63, + 327, + 156, + 335 + ], + "type": "text", + "content": "(a) Quantitative Comparison" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 168, + 246, + 284, + 324 + ], + "blocks": [ + { + "bbox": [ + 168, + 246, + 284, + 324 + ], + "lines": [ + { + "bbox": [ + 168, + 246, + 284, + 324 + ], + "spans": [ + { + "bbox": [ + 168, + 246, + 284, + 324 + ], + "type": "image", + "image_path": "2fb5276f1ceecbf9e81d4ae0c0227b69bb8c55d0cd142d8db54f97b4a0e034f1.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 181, + 327, + 274, + 335 + ], + "lines": [ + { + "bbox": [ + 181, + 327, + 274, + 335 + ], + "spans": [ + { + "bbox": [ + 181, + 327, + 274, + 335 + ], + "type": "text", + "content": "(b) Percentage Improvement" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 345, + 287, + 368 + ], + "lines": [ + { + "bbox": [ + 47, + 345, + 287, + 368 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 287, + 368 + ], + "type": "text", + "content": "Figure 5. Trend demonstration and comparison with PON [31] of IoU over distance (0-50m) on nuScenes [2]." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "type": "text", + "content": "between the target and the camera increases. Compared to PON [31], we achieve significant and consistent improvements across distances. Notably, for layouts such as drivable areas, we obtain even more absolute performance gains at larger distances. As for small objects like pedestrians and bikes, we observe a relative performance improvement of " + }, + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "type": "inline_equation", + "content": "200\\%" + }, + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "type": "text", + "content": " (5.4 vs 1.8) at 45-50 meters, while the relative improvement at 0-5 meters is " + }, + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "type": "inline_equation", + "content": "173\\%" + }, + { + "bbox": [ + 46, + 385, + 287, + 504 + ], + "type": "text", + "content": " (38.7 vs 14.2). In summary, our method shows its superiority, especially at large distances for both layouts and objects." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 514, + 140, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 140, + 527 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 140, + 527 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 533, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 581 + ], + "type": "text", + "content": "In this section, we explore the effectiveness of each proposed component through an ablation study on nuScenes [2]. The experimental groups and results are shown in Table 4." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "Coordinate System Transformation. In Table 4, Groups I and III, compared with Groups II and IV, are designated as control groups. Following the adoption of the BEV segmentation map in polar coordinates, there is an overall increase in mIoU by 4.3 and 3, respectively. This improvement can be attributed to the column-wise correspondence established between the BEV segmentation map in polar coordinates and the perspective image, enabling the model to make more accurate predictions. Additionally, Group III exhibits a notable improvement, showing increases of 6.5 in layout and 3.6 in small objects compared to Group I." + } + ] + } + ], + "index": 29 + }, + { + "type": "table", + "bbox": [ + 310, + 246, + 544, + 334 + ], + "blocks": [ + { + "bbox": [ + 310, + 246, + 544, + 334 + ], + "lines": [ + { + "bbox": [ + 310, + 246, + 544, + 334 + ], + "spans": [ + { + "bbox": [ + 310, + 246, + 544, + 334 + ], + "type": "table", + "html": "
GroupComponentsIoU
CSTTDCWTFTLayoutLarge Obj.Small Obj.Mean
I35.022.010.421.6
II✓41.922.911.724.4
III✓41.525.613.825.9
IV✓✓44.127.513.927.4
V✓✓41.226.415.526.7
VI✓✓✓44.828.615.928.7
VII✓✓✓✓45.029.216.629.2
", + "image_path": "72092e7c3b2af9860b743133c77dfbd23ca118cfd167eaef58b4d639eb446f5c.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "table_body" + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 342, + 545, + 407 + ], + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 407 + ], + "type": "text", + "content": "Table 4. Ablations of different key components on nuScenes [2]. CST, TD, CWT, and FT denote coordinate system transformation, task decomposition, column-wise transformer, and fine-tuning, respectively. Large objects include bus, car, construction vehicle, trailer, and truck. Small objects include barrier, bike, motorcycle, pedestrian, and traffic cone." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 426, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 593 + ], + "type": "text", + "content": "Task Decomposition. We deploy ablations to demonstrate the effectiveness of task decomposition. For Groups I, III, and V in Table 4, we train the pipeline and the BEV decoder simultaneously with the BCE loss in an end-to-end paradigm. Comparing Group V and Group VI, we observe that task decomposition brings a significant improvement to layouts (41.2 vs 44.8) and large objects (26.4 vs 28.6) which commonly appearing typical patterns. Similar improvements could be observed in the comparison between Group III and Group IV, especially between Group I and Group II (6.9 IoU improvement to layouts). The above ablations demonstrate that the BEV autoencoder successfully learned prior patterns of traffic scenes to decode a more rational BEV segmentation map." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "Column-wise Transformer. In RGB images, objects exhibit the characteristic of appearing larger when closer and smaller when farther away, while in BEV segmentation maps, objects maintain the same scale regardless of their distance. Motivated by TIM [34], we adopt a column-wise transformer to translate each column of the feature map to match the characteristics between the perspective view and the bird's eye view. As shown in Table 4, when compared with Group IV and Group VI, the column-wise transformer improves the IoU of small objects significantly (13.9 vs" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15518" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 70, + 509, + 270 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 509, + 270 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 509, + 270 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 509, + 270 + ], + "type": "image", + "image_path": "50819bf7cf19f9e8e161d6494e083ed4718904493ead8a82ec64826bfda48e51.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 277, + 526, + 289 + ], + "lines": [ + { + "bbox": [ + 66, + 277, + 526, + 289 + ], + "spans": [ + { + "bbox": [ + 66, + 277, + 526, + 289 + ], + "type": "text", + "content": "Figure 6. Qualitative results of ablations on nuScenes [2]. I, III, V, and VI are corresponded to the relevant ablations in Table 4." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 365 + ], + "type": "text", + "content": "15.9) while also improving the IoU of large objects (27.5 vs 28.6). Similar improvements are observed in the comparison between Group III and Group V. These experimental results prove that the column-wise transformer could better capture the information of objects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 288, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 288, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 288, + 496 + ], + "type": "text", + "content": "Fine-tuning. Although Stage 1 and Stage 2 for training are sufficient to achieve good results, the BEV decoder was trained independently from RGB images so that could not decode typical patterns in RGB images to a detailed BEV segmentation map. Thus we freeze the pipeline as a pretrained RGB image feature extractor and fine-tune the BEV decoder in an end-to-end manner to establish connections between RGB images and BEV segmentation maps. Compared to Group VI in Table 4, Group VII achieves better results across all classes, especially on objects that occupy small regions (0.7 IoU improvement)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 503, + 183, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 183, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 183, + 516 + ], + "type": "text", + "content": "4.4. Qualitative Comparison" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 522, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 653 + ], + "type": "text", + "content": "Figure 4 shows qualitative results on nuScenes [2], comparing our predicted segmentation maps with other methods and the ground truth. Our segmentation maps appear more precise and rational, benefiting from our task decomposition into two stages. Specifically, our model demonstrates a more coherent road layout, pedestrian crossing, and walkway layout, thanks to prior knowledge learned in advance. For dynamic objects, our model effectively leverages the polar coordinate system to predict nearby and distant objects with high accuracy, particularly excelling in determining the scale of cars and buses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "Figure 6 provides further qualitative results of our ablation experiments. Groups III, V, and VI in the first row display more coherent and accurate road layouts due to the introduction of the coordinate system transformation. Group V in the second row successfully predicts distant" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 304, + 547, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 377 + ], + "type": "text", + "content": "cars, thanks to the effectiveness of the column-wise transformer in translating each column. In the third row of Figure 6, Group VI demonstrates that the BEV autoencoder has successfully learned prior patterns about layouts and objects, accurately predicting the size of cars and the layout of pedestrian crossings compared to other experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 392, + 379, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 379, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 379, + 403 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 413, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 547, + 628 + ], + "type": "text", + "content": "In this paper, we leverage a clearer and more direct optimization target, by decomposing the end-to-end pipeline into two separate stages, with each stage focusing on only one mission (either generation or perception). Specifically, in the first stage, we propose a BEV autoencoder to reconstruct the BEV segmentation map with corrupted noise, where the decoder is forced to learn typical BEV traffic scene patterns. In the second stage, a mapping from input RGB images and BEV latent representations is learned. Furthermore, we transform the BEV segmentation map from a Cartesian coordinate system to a polar one, thus enhancing its alignment with RGB input. Notably, our method abstains from utilizing multi-scale features or camera intrinsic parameters for depth estimation, resulting in a significantly lower computational overhead. Additionally, our method consistently achieves outstanding prediction accuracy across varying distances from the camera. Extensive experiments on two datasets demonstrate our effectiveness." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 644, + 404, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 404, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 404, + 658 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "This work was partially supported by the National Natural Science Foundation of China under Grant 62372341 and sponsored by CCF-DiDi GAIA Collaborative Research Funds for Young Scholars." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15519" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Florent Bartoccioni, Éloi Zablocki, Andrei Bursuc, Patrick Pérez, Matthieu Cord, and Karteek Alahari. 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Typical method (S2D [22]) based on the encoder-decoder network (ED-Net) and its intermediate features are visualized by the heatmap [46]. The sparse decoder feature $f_{di}$ derived from the dense fused encoder-decoder feature $f_{edi}$ tends to complement the corresponding encoder feature $f_{ei}$ , where the \"dense $\\Rightarrow$ sparse\" process destroys the completeness of features multiple times." + ], + "image_footnote": [], + "bbox": [ + 86, + 257, + 344, + 449 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e21e4c25fb10c3846be6acf40f5e2a68591f2e6913e0171a85ab1485ac8b7050.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 344, + 255, + 890, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 510, + 313, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The encoder-decoder network (ED-Net) is a commonly employed choice for existing depth completion methods, but its working mechanism is ambiguous. In this paper, we visualize the internal feature maps to analyze how the network densifies the input sparse depth. We find that the encoder feature of ED-Net focuses on the areas with input depth points around. To obtain a dense feature and thus estimate complete depth, the decoder feature tends to complement and enhance the encoder feature by skip-connection to make the fused encoder-decoder feature dense, resulting in the decoder feature also exhibits sparse. However, ED-Net obtains the sparse decoder feature from the dense fused feature at the previous stage, where the \"dense $\\Rightarrow$ sparse\" process destroys the completeness of features and loses information. To address this issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. Furthermore, we propose a confidence-aware guidance module (CGM), which is confidence-aware and performs guidance", + "bbox": [ + 73, + 542, + 473, + 877 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "with adaptive receptive fields (GARF), to fully exploit the potential of these dense features as guidance. Experimental results show that our DFU, a plug-and-play module, can significantly improve the performance of existing ED-Net based methods with limited computational overheads, and new SOTA results are achieved. Besides, the generalization capability on sparser depth is also enhanced. Project page: https://npucvr.github.io/DFU.", + "bbox": [ + 500, + 512, + 893, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 662, + 633, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Accurate and dense scene depth is crucial for various applications [13, 34, 41], such as autonomous navigation [33] and augmented reality [24]. Existing active depth sensors have been widely applied because they can obtain accurate depth information. However, the depth acquired by these sensors is generally highly sparse due to the imaging principles and power limitation. For instance, roughly $4\\%$ pixels in the depth provided by 64-line LiDAR have values [21, 22, 35]. To facilitate the use of the depth data, we need to address a sparse-to-dense problem in which the given sparse depth map is densified to the dense depth map, usually guided by the corresponding RGB image.", + "bbox": [ + 496, + 688, + 890, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Depth completion is a challenging task as the input depth information is scarce. Existing approaches commonly", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: daiyuchao@nwpu.edu.cn.", + "bbox": [ + 94, + 886, + 362, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21104", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "consider this task as a pixel-wise regression problem and utilize an encoder-decoder network with skip-connection (ED-Net) to address it. For instance, the single-branch ED-Net [2, 14, 21, 22, 25] uses standard backbone networks [6, 19] as the encoder to extract features from the sparse depth and RGB images. Then, the decoder employs operations, such as the element-wise addition and transpose convolution, to fuse the encoder feature and upsampling. Recently, some multi-branch ED-Nets [4, 31, 32, 44, 47], including the dual-encoder ED-Net [4, 47] and the double encoder-decoder ED-Net[31, 32], etc., have been proposed. These methods employ separate branches to extract features from the sparse depth and RGB images, and internal features are fused at multiple scales. Although existing ED-Nets based methods have achieved considerable success [39, 48, 51], the ED-Net is often employed as a black box. how the network recovers a dense depth map from the input sparse depth has always been ambiguous.", + "bbox": [ + 75, + 90, + 472, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To gain a deeper understanding of the ED-Net employed by depth completion, Fig. 1 visualizes internal features of the representative method S2D [22] through the feature heatmap [46]. The feature heatmap [46] is obtained by summing the value of the feature along the channel dimension and normalizing them to a range of $(0,1)$ , which reflects the spatial locations that the network focuses on at different stages and provides valuable insights to infer the behaviors of the network. We observe that although the sparse depth map and dense RGB image are both fed to the network, the shallow feature of the encoder primarily focuses on few regions where the sparse depth map has values. Through multiple downsampling and convolution, the sparse regions of interest continue to expand and aggregate, the encoder feature gradually becomes more \"dense\". As shown in Fig. 1, the lowest-resolution encoder feature $f_{e4}$ has rich information at most spatial locations. However, to obtain a dense feature and thus estimate complete depth, the decoder tends to obtain a complementary feature for the corresponding encoder feature, which contains multiple \"dense $\\Rightarrow$ sparse\" processes. For instance, the decoder feature $f_{d1}$ , which is skip-connected to $f_{e1}$ , tends to complement and enhance existing $f_{e1}$ to make the fused encoder-decoder feature $f_{ed1}$ dense. Therefore, the decoder feature $f_{d1}$ also exhibits sparse. However, the sparse $f_{d1}$ is derived from the dense $f_{ed2}$ at the previous stage, where the \"dense $\\Rightarrow$ sparse\" process destroys the completeness of features and loses information. Experiments on multi-branch networks also validate this observation, which is provided in the supplemental material. To conclude, existing ED-Nets have not fully utilized the internal dense features, thereby restricting the performance of ED-Net based methods.", + "bbox": [ + 75, + 367, + 472, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR)", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. The multiscale dense features that cover comprehensive scene depth information can progressively resolve ambiguity in super-resolving the feature of uneven depth distribution areas. Meanwhile, the upsampling process can also effectively integrate these dense features into the HR depth feature to predict the dense depth. To further improve the effectiveness of the DFU, we propose a confidence-aware guidance module (CGM) to fully exploit the potential of these dense features as guidance. Specifically, we first filter out unreliable values of the depth feature by predicting its confidence map, and then perform the guidance operation with adaptive receptive fields. In addition, the proposed network can be extended to multi-layer to achieve better results.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are summarized as:", + "bbox": [ + 517, + 334, + 805, + 347 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We analyze the working mechanism of popular ED-Nets by visualizing the internal feature maps and reveal that multiple \"dense $\\Rightarrow$ sparse\" processes exist in the decoder network, which destroy the completeness of features and lose information.", + "- We propose a depth feature upsampling network with confidence-aware guidance module, which is a plug-and-play module, to significantly improve the performance of existing ED-Net based methods and enhance the generalization ability on sparser depth with limited computational overheads.", + "- Extensive experiments on popular datasets prove the effectiveness of our method on existing popular ED-Nets, including single-branch, multi-branch, and SPN-based networks, and new SOTA results are achieved." + ], + "bbox": [ + 500, + 356, + 890, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 602, + 640, + 617 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single-branch ED-Nets. The single-branch ED-Net contains one encoder and one decoder. The pioneer approaches [21, 26] concatenates the sparse depth and RGB image directly, and feeds them into a standard encoder-decoder network to predict the dense depth. Unlike using convolution in the last layer, [28] proposes to use the least squares to fit the relationship between the extracted features and depth values. Considering the gap between the RGB and depth information, subsequent methods [10, 20, 42] generally use two separate convolutional layers to extract features from the sparse depth and RGB image, respectively. Then, the multi-modal features are concatenated and fed into the network. This type of approach is simple and straightforward, but its performance is generally limited.", + "bbox": [ + 496, + 628, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-branch ED-Nets. Recently, some multi-branch ED-Nets [31, 32, 40, 44, 47] have been proposed for better extraction and fusion of the RGB and depth information. For example, the dual-encoder ED-Net [4, 47]", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21105", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2b71000cd9092358bca43740297f558359be64c02fc34034cb0b011fa429ec98.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 127, + 88, + 851, + 252 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7c4eeb0feba97621cd7c8984debb0f8192c0ce6ea1d5576d0ab914f487a9808d.jpg", + "image_caption": [ + "(a) Three-layer Depth feature upsampling network", + "(b) Single-branch ED-Net" + ], + "image_footnote": [], + "bbox": [ + 109, + 263, + 372, + 359 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e313afa190bd65bf5da1e5c11f0aaeb7aa89c616b025cc7aae01fb8e1d874ea9.jpg", + "image_caption": [ + "(c) Multi-branch ED-Net" + ], + "image_footnote": [], + "bbox": [ + 375, + 263, + 665, + 361 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8129bb0bcb33f9dd77ba0f7aafb144468f546e3883cb3baa5da4db17e8b6f812.jpg", + "image_caption": [ + "Figure 2. The proposed depth feature upsampling network (DFU). It explicitly employs the internal dense features of ED-Nets that are not fully utilized by existing methods to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one." + ], + "image_footnote": [], + "bbox": [ + 673, + 263, + 859, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "commonly employs two separate encoders to extract features from RGB images and sparse depth, respectively. Then, the extracted RGB and depth features are fused at single-scale or multi-scale by the channel-wise concatenation, element-wise summation, or other sophisticated fusion modules [32, 37, 44, 47]. GuideNet [32] proposes a double encoder-decoder network, which extracts the RGB and depth feature by a whole encoder-decoder network. The decoder feature of the RGB branch and the encoder feature of the depth branch are fused by the guided convolutional network at multiple scales. The multiple encoder-decoder network is proposed by RigNet [44], which uses repetitive hourglass networks to extract discriminative RGB features, and the fusion of RGB and depth information is also performed in a repetitive manner.", + "bbox": [ + 75, + 417, + 468, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SPN-based Networks. The spatial propagation network (SPN) [2, 3, 14, 18, 25, 43] is a hot topic, which iteratively refines the predicted depth by aggregating the reference and neighbor pixels. The initial SPN [17] updates each pixel by three adjacent pixels from the previous row or column. CSPN [2] improves it by updating all pixels simultaneously by fixed-local neighbors, and $\\mathrm{CSPN}++$ [3] assembles the results predicted by using the neighbors in different ranges. To obtain non-local neighbors, DSPN [43] and NLSPN [25] learn the offsets to the regular grid. DySPN [14] gives variable weights to neighbors with different distances to make the kernel weights change dynamically during the update process. GraphCSPN [18] integrates 3D information into the update process. LRRU [36] proposes to employ multiscale guidance features to guide the prediction of neighbors and weights, which makes them change adaptively throughout the update process.", + "bbox": [ + 75, + 643, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 415, + 633, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present a depth feature upsampling network (DFU) that effectively utilizes internal dense features of ED-Net to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The DFU is introduced in three parts: (1) feature extraction, including extracting the LR depth feature and multi-scale dense features from ED-Net as guidance, (2) depth feature upsampling guided by the proposed confidence-aware module, (3) going deeper, where DFU is extended to multi-layer to obtain better results. For descriptive convenience, the feature is marked as $f_{i}$ , where $i = \\{1,2,3,4,5\\}$ denotes the feature of different resolutions, namely $f_{i} \\in \\mathbb{R}^{H / n \\times W / n \\times D_{i}}$ , $n = 2^{i - 1}$ .", + "bbox": [ + 496, + 441, + 890, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Features Extraction", + "text_level": 1, + "bbox": [ + 500, + 648, + 687, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The LR depth feature $f_{dd4} \\in \\mathbb{R}^{H/8 \\times W/8 \\times D_{dd4}}$ is extracted from the sparse input depth using a convolutional network, where $D_{dd4}$ is set to 64 in this paper. The network consists of 8 residual blocks, 2 at full-resolution, 2 at 1/2-resolution, 2 at 1/4-resolution, and 2 at 1/8-resolution. Although the input depth is sparse, the depth information continues to expand and aggregate by multiple downsampling and convolutional layers, making the LR feature $f_{dd4}$ dense (most spatial positions of the feature contain rich information).", + "bbox": [ + 496, + 672, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2 (b) and (c), the guidance feature can be obtained from any ED-Net, including single-branch ED-Net, multi-branch ED-Net, etc. In this paper, we generally extract five encoder features $\\{f_{e1}, f_{e2}, f_{e3}, f_{e4}, f_{e5}\\}$ at different resolution. Then, the decoder features $\\{f_{d4}, f_{d3}, f_{d2}, f_{d1}\\}$ and fused encoder-decoder features", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21106", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}$ are obtained in the decoder. We select the features $\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}$ to guide the upsampling of the LR depth feature. These features are generally dense and cover comprehensive scene depth information, which can progressively resolve ambiguity in superresolving the feature of uneven depth distribution areas. Furthermore, the upsampling process effectively integrates these dense features that are underutilized in existing ED-Nets, thus improving the accuracy of depth completion.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To reduce computational complexity, we reduce the channel number of these features $\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}$ to the same as the LR depth feature by", + "bbox": [ + 75, + 227, + 468, + 272 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {g i} = \\mathbf {C o n v} _ {\\mathbf {1} \\times \\mathbf {1}} (f _ {e d i}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 284, + 468, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{Conv}_{\\mathbf{1}\\times \\mathbf{1}}$ is a $1\\times 1$ convolutional layer, and the feature $f_{gi}$ is employed as the guidance feature in the DFU.", + "bbox": [ + 75, + 311, + 468, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Depth Feature Upsampling", + "text_level": 1, + "bbox": [ + 76, + 352, + 320, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2 (a), the LR depth feature is upsampled to HR through four stages, which are guided by the features $\\{f_{g4}, f_{g3}, f_{g2}, f_{g1}\\}$ , respectively. To fully exploit the potential of the guidance feature, we propose a Confidence-aware Guidance Module (CGM), which first filters out unreliable values of the depth feature by predicting its confidence map, and performs the guidance operation with adaptive receptive fields to handle uneven depth distribution. The first stage of the DFU consists of a CGM, while other stages adopt the \"upsampling + CGM\". As shown in Fig. 3, for the depth feature $f_{ddi}$ , we denote the output feature of the CGM as $f_{ddi}'$ . In this paper, the upsampling is implemented by using a deconvolutional layer of stride 2, and the details of the CGM are introduced as follows:", + "bbox": [ + 75, + 375, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confidence-aware. The LR depth feature is extracted from the input depth that is highly sparse and noisy. Besides, ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, we predict an elementwise attention map to filter out unreliable feature values. Specifically, we concatenate the depth feature $f_{ddi}$ and the guidance feature $f_{gi}$ . The confidence map $c_i$ is predicted by a $3 \\times 3$ convolutional layer as:", + "bbox": [ + 75, + 587, + 468, + 707 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc _ {i} = \\sigma \\left(\\mathbf {C o n v} _ {\\mathbf {3} \\times \\mathbf {3}} \\left(\\mathbf {c o n c}. \\left(f _ {d d i}, f _ {g i}\\right)\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 720, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "here $\\sigma$ denotes the sigmoid function to compress the confidence value to $0 - 1$ .", + "bbox": [ + 75, + 748, + 467, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Guidance with Adaptive Receptive Fields (GARF). In the field of depth completion, guided convolutional networks have been studied widely for multi-modal feature fusion. For example, the pioneering GuideNet [32] predicts spatially-variant depthwise convolutional kernels [30] $\\mathbf{W} \\in \\mathbb{R}^{hw \\times k^2 \\times c}$ from the RGB feature, and then applies them to extract the depth feature. Here, $h$ , $w$ , and $c$ are the height, weight, and channel number of the feature map,", + "bbox": [ + 75, + 777, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eb9867639c37d32f4a0004f70f382cbf483b2524b310546234122d9edfa2674f.jpg", + "image_caption": [ + "Figure 3. The Confidence-aware Guidance Module (CGM) and $k$ is the kernel size. To reduce computational complexity, [37] decomposes the depthwise kernel $\\mathbf{W}_{\\mathbf{P}_i} \\in \\mathbb{R}^{k^2 \\times c}$ at each spatial location $\\mathbf{p}_i$ into content-adaptive adaptors $\\mathbf{A} \\in \\mathbb{R}^{k^2 \\times m}$ multiplied by the spatially-shared component $\\mathbf{D} \\in \\mathbb{R}^{m \\times c}$ . The guided convolutional network has been proven to be effective since it can transfer structural information from the guidance feature to the target feature [12]. Therefore, in our method, we adopt this strategy to fully utilize the guidance feature. However, the kernel size of existing guided convolutional networks is usually fixed, which cannot handle the areas with uneven depth distribution well. To address this issue, we propose a guidance module with adaptive receptive fields." + ], + "image_footnote": [], + "bbox": [ + 517, + 92, + 893, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recently, some novel dynamic convolution networks [27, 38] have shown that the convolutional kernel can be equivalently represented as a combination of pre-fixed bases, such as Fourier-Bessel(FB) bases [1]. Inspired by these works [27, 38], we further decompose the adaptors over multi-scale FB bases to selectively choose a receptive field at each spatial position. Specifically, we pre-generate $n$ FB bases of different sizes, such as $3 \\times 3$ , $5 \\times 5$ , and $7 \\times 7$ , and then unify them to the same size by zero padding. Unlike [37] directly predicts the adaptors, we predict the weight of the multi-scale FB bases. As shown in Fig. 3, the adaptors with adaptive receptive fields can be obtained by multiplying the predicted weight with the FB bases. Then, we preform the guidance operation similar as [37] and obtain the refined depth feature $f_{gdi}$ by:", + "bbox": [ + 496, + 489, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {g d i} = G A R F \\left(c _ {i} \\odot f _ {d d i}, f _ {g i}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 724, + 890, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature Updating. The confidence map $c_{i}$ assigns low confidence to the unreliable depth features, which are exactly the areas we want the guidance module to prioritize. Therefore, we obtain the output of CGM $f_{ddi}'$ by:", + "bbox": [ + 496, + 751, + 890, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {d d i} ^ {\\prime} = c _ {i} \\odot f _ {d d i} + (1 - c _ {i}) \\odot f _ {g d i} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 821, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Going Deeper", + "text_level": 1, + "bbox": [ + 500, + 847, + 640, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further enhance the performance of the proposed method, we extend the depth feature upsampling network", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21107", + "bbox": [ + 478, + 924, + 517, + 935 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/822a7f903f09503c02b5fe4e8e4a0d930422237fee38e058470cc6a84dd9309a.jpg", + "table_caption": [ + "Table 1. The performance comparison between the baseline models and their improved model by using the multi-layer DFU." + ], + "table_footnote": [], + "table_body": "
KITTI Validate Dataset [5]NYUv2 Depth Dataset [23]
Params. [M]FLOPs [G]RMSE ↓ [mm]MAE ↓ [mm]iRMSE ↓ [1/km]iMAE ↓ [1/km]RMSE ↓ [mm]REL ↓ (×1000)δ1.25 ↑ [%]δ1.252 ↑ [%]δ1.253 ↑ [%]
Our single-branch ED-Net11.95291.24772.87210.262.280.95111.9416.6299.3299.8899.98
Improving by One-layer DFU+ 1.67+ 43.79750.58205.322.140.93100.6713.9299.4699.9199.98
Improving by Two-layer DFU+ 2.41+ 65.65745.27202.342.180.9398.9913.6399.4899.9199.98
Improving by Three-layer DFU+ 3.14+ 87.52746.98201.082.090.8997.7813.5999.4999.9199.98
Our Dual-branch ED-Net22.28498.84753.81204.392.120.92101.1214.4099.4699.9199.98
Improving by One-layer DFU+ 1.65+ 38.34741.39199.652.000.8898.6314.2199.4999.9299.98
Improving by Two-layer DFU+ 2.38+ 57.24738.20198.852.030.8797.6213.7099.5099.9299.98
Improving by Three-layer DFU+ 3.10+ 76.15736.60198.612.010.8796.2712.9299.5099.9299.98
", + "bbox": [ + 78, + 104, + 893, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to multi-layer. In this subsection, the feature is marked as $f_{i}^{j}$ , where the superscript $j$ denotes the feature in the $j$ -th layer DFU. As shown in Fig. 2, we deepen the depth of each stage of the network. Specifically, we employ the feature $f_{ddi}^{j}$ of the $j$ -th layer DFU as the guidance feature $f_{gi}^{j+1}$ of the corresponding module of the $j+1$ -th layer DFU.", + "bbox": [ + 75, + 297, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 405, + 209, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 430, + 294, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We employ PyTorch to implement our model, and conduct experiments with GeForce RTX 3090 GPUs. Our training process is divided into two stages, which both employ the $L1 + L2$ loss to train 35 epochs. The initial learning rate is $10^{-3}$ , and it is reduced by $50\\%$ every 5 epochs. We employ the AdamW optimizer with a batch size of 8, and set $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ , weight decay is $10^{-6}$ . In the first stage, we first train the ED-Net to obtain the internal dense features that cover comprehensive scene depth information. Then, we train the depth feature upsampling network (DFU), in which these dense features are explicitly employed as the guidance features. For the multi-layer DFU, we only supervise the output of the last-layer DFU.", + "bbox": [ + 75, + 455, + 468, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 76, + 662, + 274, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "KITTI Dataset [5] consists of sparse depth maps projected from raw LiDAR scans and corresponding RGB images, which is a popular real-world autonomous driving dataset. The dataset contains 86k frames for training, 1k selected frames for validation, and 1k frames without ground truth that need to be tested on the online benchmark.", + "bbox": [ + 75, + 686, + 468, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NYUv2 Dataset [23] is a popular indoor RGBD dataset. Following existing works [16, 36, 45, 51], our model is trained with 50K images sampled from the training set, and tested on 654 officially labeled images. The images of size $640 \\times 480$ are downsampled to half and then center-cropped to $304 \\times 228$ for both training and inference.", + "bbox": [ + 75, + 777, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following exiting methods [25, 36, 52], we employ Root Mean Squared Error (RMSE), Mean", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Absolute Error (MAE), inverse RMSE (iRMSE), inverse MAE (iMAE), mean absolute relative error (REL), and percentage of pixels satisfying $\\delta_{\\tau}$ for quantitative evaluation.", + "bbox": [ + 498, + 297, + 890, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Improving Single-branch ED-Net", + "text_level": 1, + "bbox": [ + 498, + 368, + 792, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following most methods [10, 20, 22, 42], the single-branch ED-Net used in this paper first extracts the depth and RGB features by two independent convolutional layers, and the features are concatenated and fed into an encoder-decoder network. The encoder consists of five stages, and each stage contains 2 residual blocks. The encoder feature is extracted at full-resolution in the first stage and is progressively halved in the next four stages. The feature channels of the five stages are 64, 128, 256, 256 and 256. We use the deconvolutional layer with stride 2 to upsample features, and fuse the encoder and decoder feature by the concatenate. As shown in Fig. 2 (b), the fused encoder-decoder features $f_{ed4}$ , $f_{ed3}$ , $f_{ed2}$ , $f_{ed1}$ are employed as the guidance features in the proposed DFU.", + "bbox": [ + 496, + 396, + 890, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 1, our single-branch ED-Net contains $11.95\\mathrm{M}$ parameters and requires $291.24\\mathrm{G}$ FLOPs, and the RMSE and MAE are $772.87\\mathrm{mm}$ and $210.26\\mathrm{mm}$ . Note that our single-branch ED-Net outperforms S2D [22] built on the Resnet-34 with fewer parameters since we use the effective stochastic depth strategy [8] in the residual block as [14]. We observe that the single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, the improvement in terms of various metrics is $22.29\\mathrm{mm}$ in RMSE, $4.94\\mathrm{mm}$ in MAE, 0.14 in iRMSE, and 0.02 in iMAE. Meanwhile, the performance in terms of RMSE and MAE is further improved when we deepen the DFU to two layers. However, this improvement is relatively small compared to the previous one. When we extend the DFU to three layers, the MAE is further reduced, while the results in the term of RMSE appear saturated. In addition, the experimental results conducted on the NYUv2 dataset consistently demonstrate that our DFU can effectively improve the performance of the single-branch ED-Net.", + "bbox": [ + 496, + 613, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21108", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d117afc8578ff2fa25a74c03e19d48246752bcfcfcbe1daa9607986cac0a06f8.jpg", + "table_caption": [ + "Table 2. The performance comparison between LRRUs (SPN-based method) and their improved model by using the multi-layer DFU." + ], + "table_footnote": [], + "table_body": "
LRRU-MiniLRRU-TinyLRRU-SmallLRRU-Base
KITTI [5]Validate DatasetRMSE↓[mm]MAE↓[mm]iRMSE↓[1/km]iMAE↓[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]
Baseline806.27210.162.280.89763.80198.892.120.85745.31195.692.000.83729.49188.781.920.80
+ One-layer DFU787.28206.562.270.88747.39195.682.040.83732.42192.271.960.81718.27188.051.890.80
+ Two-layer DFU775.93202.712.200.86744.92193.102.000.82730.89190.561.940.81716.02186.691.890.80
+ Three-layer DFU767.67199.482.160.85742.83192.311.990.81729.24189.411.930.80713.32185.551.870.79
NYUv2 [23]Depth DatasetRMSE↓[mm]REL↓(x1000)δ1.25↑δ1.252↑RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252
Baseline100.8613.3499.4499.9195.3612.2599.5199.9293.3611.8599.5399.9291.2711.2199.5699.92
+ One-layer DFU99.2212.7799.4699.9192.5811.7699.5499.9391.5711.4899.5699.9390.7911.1999.5799.93
+ Two-layer DFU98.9412.7399.4799.9192.3111.6399.5599.9391.1511.4399.5699.9890.6111.2299.5799.93
+ Three-layer DFU98.2912.6999.4799.9192.2911.5999.5599.9291.0811.4399.5699.9890.7711.2799.5799.93
", + "bbox": [ + 78, + 103, + 893, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Improving Multi-branch ED-Net", + "text_level": 1, + "bbox": [ + 76, + 311, + 366, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We experimentally found that the performance gap between dual-branch networks, double encoder-decoder networks, and multiple encoder-decoder networks is not significant. Therefore, we select the most cost-effective dual-encoder network as the baseline model to verify the improvement effect of our proposed method on the multi-branch ED-Net. As shown in Fig. 2 (c), the difference between the dual-encoder ED-Net and single-branch ED-Net is that the dual-encoder ED-Net utilizes two encoders to extract features from the sparse depth and corresponding RGB image, respectively. Specifically, the RGB encoder works independently, and the extracted RGB features at multiple scales are gradually injected into the depth encoder to effectively integrate information from different modalities.", + "bbox": [ + 75, + 334, + 468, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table 1, our dual-encoder ED-Net has nearly double the number of parameters and computational complexity in comparison to the single-branch ED-Net as it employs two encoders and the multi-scale fusion strategy. However, the dual-encoder ED-Net also outperforms the single-branch ED-Net significantly. When we apply one-layer DFU to the dual-encoder ED-Net, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by $12.42\\mathrm{mm}$ , $4.74\\mathrm{mm}$ , 0.12 and 0.04, respectively. The performance of the method is continuously improved as the DFU deepens, while the magnitude of the performance improvement gradually decreases. We observe that the performance of the method closes saturation when using the three-layer DFU. Additionally, similar conclusions can be drawn from the results on the NYUv2 dataset, which adequately demonstrate that our proposed method can effectively improve the performance of the dual-branch ED-Net.", + "bbox": [ + 75, + 547, + 470, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Improving SPN-based Model", + "text_level": 1, + "bbox": [ + 76, + 816, + 336, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The SPN is a popular module to refine the predicted depth map. To validate the effectiveness of our method for SPN-based methods, we apply the proposed DFU to LRRU [36], which introduces an effective SPN model and achieves top", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ranking performance on the KITTI benchmark. As described in [36], LRRU has already utilized internal dense features of the guided-feature extraction network to guide the SPN model. However, these features are employed individually, and the features at different scales can not be aggregated to improve the robustness and effectiveness of the SPN model. To address this issue, we add the DFU between the guided-feature extraction network and the recurrent update process of the LRRU to integrate the information from the multi-scale guidance features (more details in the supplementary materials).", + "bbox": [ + 496, + 311, + 890, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table 2, we conduct comprehensive experiments on four variants of LRRU with varying network scales. On the KITTI dataset, the performance of all four variants of LRRU is significantly improved by using the DFU, especially for the mini model. Specifically, by using one-layer DFU, the RMSE of LRRU-Mini is reduced by $18.99\\mathrm{mm}$ , and the RMSE of LRRU-Base is reduced by $11.22\\mathrm{mm}$ . Furthermore, the performance of LRRUs continues to enhance at a gradually decreasing rate when utilizing the multi-layer DFU. The experimental results on the NYUv2 dataset consistently demonstrate the effectiveness of our method. Noted that, due to the limited number of samples of the NYUv2 dataset, when we continue to add our method to the LRRU-Base model with a large network size, the network appears to be overfitting. Therefore, on the NYUv2 dataset, our method only has a limited performance improvement effect on the LRRU-Base model.", + "bbox": [ + 496, + 478, + 892, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.6. Comparison with state-of-the-arts", + "text_level": 1, + "bbox": [ + 498, + 742, + 797, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate our methods against state-of-the-art (SOTA) methods, we compare their experimental results on the KITTI benchmark (outdoor) and NYUv2 (indoor). As shown in Table 3, we report the results of our baseline methods and the improved methods by using three-layer DFU. Meanwhile, we select some representative methods from the last three years for comparison. Since most SOTA methods employ the multi-branch ED-Net structure, the performance of our single-branch ED-Net is slightly worse", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21109", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2b775439bb912edcd77e13c88fc89c9b57446ad19e3409e8f7bfde0d5248e062.jpg", + "table_caption": [ + "Table 3. Quantitative evaluation on the KITTI online leaderboard and NYUv2. The results of improved methods by using the three-layer DFU are highlighted with a gray background and the best and second-best results are highlighted in red and blue colors, respectively." + ], + "table_footnote": [], + "table_body": "
KITTI Online Benchmark [5]NYUv2 Depth Dataset [23]Publication
RMSE[mm]↓MAE[mm]↓iRMSE[1/km]↓iMAE[1/km]↓RMSE[m]↓REL↓δ1.25↑δ1.252↑δ1.252↑
TWISE [11]840.20195.582.080.820.0970.01399.699.9100.0CVPR 2021
FCFRNet [15]735.81217.152.200.980.1060.01599.599.9100.0AAAI 2021
PENet [7]730.08210.552.170.94-----ICRA 2021
ACMNet [49]744.91206.092.080.900.1050.01599.599.9100.0TIP 2021
PointFusion [9]741.90201.101.970.850.0900.01499.699.9100.0ICCV 2021
GFormer [29]721.48207.762.140.97-----CVPR 2022
DySPN [14]709.12192.711.880.820.0900.01299.699.9100.0AAAI 2022
GraphCSPN [18]738.41199.311.960.840.0900.01299.699.9100.0ECCV 2022
RigNet [44]712.66203.252.080.900.0900.01399.699.9100.0ECCV 2022
CompletionFormer [48]708.30203.452.010.880.0910.01299.699.9100.0CVPR 2023
BEV@DC [51]697.44189.441.830.820.0890.01299.699.9100.0CVPR 2023
PointDC [45]736.07201.871.970.870.0890.01299.699.9100.0ICCV 2023
Our Single-branch ED-Net745.16209.862.220.950.1120.01699.399.9100.0-
Improved Single-branch719.65201.922.060.910.0980.01499.599.9100.0-
Our Dual-branch ED-Net720.96203.732.070.920.1010.01499.599.9100.0-
Improved Dual-branch706.23199.141.990.890.0960.01399.599.9100.0-
LRRU-Base (SPN-based) [36]696.51189.961.870.810.0910.01199.699.9100.0ICCV 2023
Improved LRRU-Base686.46187.951.830.810.0910.01199.699.9100.0-
", + "bbox": [ + 76, + 118, + 893, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in comparison. However, the performance of our single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, on the KITTI benchmark, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by $25.51 \\mathrm{~mm}$ , $7.94 \\mathrm{~mm}$ , 0.16, and 0.04, respectively. Besides, five metrics evaluated on the NYUv2 are also enhanced considerably. The experimental results demonstrate that the proposed DFU can effectively improve the performance of the single-branch ED-Net. Compared to the single-branch ED-Net, our dual-branch ED-Net shows better performance, which already outperforms the latest PointDC [45], GraphCSPN [18], GFormer [29], etc. in the term of RMSE. However, the proposed DFU still greatly improves the performance of the dual-branch ED-Net on two benchmarks. Note that our method is effective for the LRRU-Base (SPN-based method) as well, which is the current SOTA method on the KITTI benchmark. Specifically, the improved LRRU-Base by using three-layer DFU achieves new SOTA results, which ranks Top-1 on the KITTI benchmark.", + "bbox": [ + 75, + 398, + 472, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results on the NYUv2 show that the methods [9, 18, 51, 51] that fuse 3D information generally achieve better results, such as BEV@DC [51] and PointDC [51]. Our method can also greatly improve the performance of the single-branch ED-Net and dual-branch ED-Net on NYUv2, while the performance improvement on LRRU-Base is negligible due to overfitting. Fig. 4 and Fig. 5 show the qualitative results of the baseline models and improved models by using three-layer DFU. Since our DFU effectively uses internal dense features of ED-Nets that cover comprehensive scene depth information, the improved method has more accurate results in fine and small structures, such as the gap area between two adjacent objects.", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86fc4bd26b2b5a3e18616478a8b0b2c54b8c468cac44408008262a074903d2b7.jpg", + "image_caption": [ + "Figure 4. Qualitative results on the NYUv2 depth dataset." + ], + "image_footnote": [], + "bbox": [ + 504, + 398, + 877, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.7. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 588, + 663, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct experiments on the KITTI dataset to verify the effectiveness of the confidence-aware guidance module, which consists of the confidence-aware model and the guidance model with adaptive receptive fields. As shown in Table 4 (a) and (e), we choose our single-branch ED-Net as the baseline, and its results are significantly improved by using standard one-layer DFU.", + "bbox": [ + 496, + 612, + 890, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Confidence-aware. In this paper, the LR depth feature is extracted from a highly sparse and noisy depth map, and ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, some values of the depth feature are unreliable. To filter out the unreliable depth feature values before the guidance module, we propose to predict an element-wise confidence map, which assigns these unreliable values a lower weight. Besides, we also employ the confidence map in the feature updating, which makes the guidance module focus on the unreliable values of the depth features. As shown in Table 4 (d) and (e), removing the confidence map increases the RMSE and", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21110", + "bbox": [ + 478, + 926, + 519, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51d8664aec3078399ac081e3d1b887d63ca3c7d7c254542df074083120c0fec0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 92, + 354, + 147 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/faf364be559aa62806220c7335f196930d99441b1ab98ecf540953b9053e5487.jpg", + "image_caption": [ + "A.2 RGB Image" + ], + "image_footnote": [], + "bbox": [ + 354, + 92, + 609, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01a99a459214160df3a4885361c055466da6cda844615abde10f4ec1de34d325.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 611, + 92, + 862, + 147 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/67d8d74f2ad0012ce2c53ad48f39f5f6544cfef5bf863139d713782f6e0afcd7.jpg", + "image_caption": [ + "A.1 RGB Image", + "B.1 Our Single-branch Result" + ], + "image_footnote": [], + "bbox": [ + 101, + 161, + 354, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d3da858926fc0130df96034070b96a22ca8f55190c5b934888abfc0e6051b01.jpg", + "image_caption": [ + "B.2 Our Dual-branch Result" + ], + "image_footnote": [], + "bbox": [ + 354, + 161, + 607, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/46bb1f2fd016bc1a7252db7e17831005c2701aae88ca1be30038ab878d024b11.jpg", + "image_caption": [ + "A.3 RGB Image", + "B.2 The LRRU-Base Result" + ], + "image_footnote": [], + "bbox": [ + 611, + 161, + 862, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/02bcc16540f0cf11d807a655051321fef0bd620daec879cfd379806d747686d5.jpg", + "image_caption": [ + "C.1 Improved Single-branch Result" + ], + "image_footnote": [], + "bbox": [ + 101, + 231, + 354, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9403dd2218f412e0be2cf176530c5be0276b19aeb0e8ad08608f14684a5386e.jpg", + "image_caption": [ + "C.2 Improved Dual-branch Result" + ], + "image_footnote": [], + "bbox": [ + 354, + 231, + 607, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5b2cca80dc933742c3bb4430600f5afb2940e2f45b6f3c22a6fe4ec4b21356cc.jpg", + "image_caption": [ + "C.3 Improved LRRU-Base Result" + ], + "image_footnote": [], + "bbox": [ + 611, + 231, + 862, + 284 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ee145e8db45d142326357d293275ec54db0f711cb94c442fd17c5e8b690054eb.jpg", + "table_caption": [ + "Table 4. Ablation studies on the KITTI validation dataset." + ], + "table_footnote": [], + "table_body": "
Confidence awareGARFRMSE [mm]MAE [mm]
(a)Our Single-branch ED-Net--772.87210.26
(b)Improving by one-layer DFU--761.24209.04
(c)Improving by one-layer DFU✓-758.67207.51
(d)Improving by one-layer DFU-✓756.31206.82
(e)Improving by one-layer DFU✓✓751.76203.09
", + "bbox": [ + 78, + 344, + 462, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MAE of the improved method by $4.55\\mathrm{mm}$ and $3.73\\mathrm{mm}$ .", + "bbox": [ + 76, + 460, + 454, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Guidance with Adaptive Receptive Fields. Traditional guided convolutional networks [32, 37, 44] generally predict spatially-variant convolutional kernels from the guidance feature, and then employ the predicted kernels to extract the target feature. These networks have been proven effective since they can transfer the structural information from the guidance feature to the target feature. However, the predicted per-pixel kernel has a fixed size, which cannot be suitable for the areas with different depth distributions. To address this issue, we propose the guidance module with adaptive receptive fields (GARF). The results in Table 4 (c) and (e) show that the performance of the improved method without GARF is significantly decreased, which demonstrates the effectiveness of GARF.", + "bbox": [ + 75, + 476, + 468, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.8. Experiments on fewer points", + "text_level": 1, + "bbox": [ + 76, + 696, + 333, + 713 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "It is crucial to analyze the generalization ability for sparser depth maps, which are usually provided in many practical applications. We train our baseline methods and their improved methods by using three-layer DFU on the standard KITTI (64-line LiDAR depth) and test the performance (MAE[mm]) on the depth map with fewer lines. The sparser depth map is obtained by the method provided by [50]. As shown in Fig. 6, the performance improvement by using the proposed DFU is more significant on sparser depth maps. The experimental results demonstrate that our approach not only improves the performance of the method, but also enhances the generalization ability for sparser depth maps.", + "bbox": [ + 75, + 719, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26e3284e4089965dfb893a873ddca8b1962e8e3c41a9210d2028414bc49f404e.jpg", + "image_caption": [ + "Figure 5. Qualitative results on the KITTI online leaderboard, including the baseline and improved models by using three-layer DFU.", + "Figure 6. The performance (MAE [mm]) on fewer points." + ], + "image_footnote": [], + "bbox": [ + 509, + 330, + 875, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.9. Computational Cost", + "text_level": 1, + "bbox": [ + 500, + 450, + 692, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We report the parameters and FLOPs of the method in Table 1. Since we pre-reduce the channel number of the feature, our method improves the performance of existing ED-Nets with limited computational overheads. Specifically, using one-layer DFU approximately requires extra $1.7\\mathrm{M}$ parameters and $40\\mathrm{G}$ FLOPs, which are small compared to those of the ED-Net itself.", + "bbox": [ + 496, + 474, + 890, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 594, + 617, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed the depth feature upsampling network (DFU), a plug-and-play module to improve existing ED-Net based methods. By the proposed confidence-aware guidance module, DFU effectively utilizes internal dense features of ED-Net to guide the depth feature upsampling, the completeness of these dense features is maintained in DFU. Furthermore, DFU can be extended to multi-layer to achieve better results. Experimental results show that our method can significantly improve existing ED-Nets, including single-branch ED-Nets, multi-branch ED-Nets, and SPN-based methods, with limited computational overheads. Meanwhile, the generalization ability for sparser depth is also enhanced.", + "bbox": [ + 496, + 619, + 890, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 830, + 658, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Science Fund of China (Grant Nos.62001394, 62271410, 62306238) and the Fundamental Research Funds for the Central Universities.", + "bbox": [ + 498, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21111", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Milton Abramowitz, Irene A Stegun, and Robert H Romer. 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In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2022. 5" + ], + "bbox": [ + 501, + 92, + 890, + 839 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21113", + "bbox": [ + 478, + 926, + 519, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Depth Completion via Depth Feature Upsampling/0ed38fa6-aa40-45ef-a200-06326c698546_model.json b/2024/Improving Depth Completion via Depth Feature Upsampling/0ed38fa6-aa40-45ef-a200-06326c698546_model.json new file mode 100644 index 0000000000000000000000000000000000000000..41c6e026faa9046df04517aebd7b7557a8448f41 --- /dev/null +++ b/2024/Improving Depth Completion via Depth Feature Upsampling/0ed38fa6-aa40-45ef-a200-06326c698546_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.048 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.131, + 0.795, + 0.156 + ], + "angle": 0, + "content": "Improving Depth Completion via Depth Feature Upsampling" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.18, + 0.819, + 0.201 + ], + "angle": 0, + "content": "Yufei Wang\\(^{1}\\), Ge Zhang\\(^{2}\\), Shaoqian Wang\\(^{1}\\), Bo Li\\(^{1}\\), Qi Liu\\(^{1}\\), Le Hui\\(^{1}\\), Yuchao Dai\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.203, + 0.856, + 0.241 + ], + "angle": 0, + "content": "1Northwestern Polytechnical University and Shaanxi Key Laboratory of Information Acquisition and Processing 2Beijing Institute of Tracking and Telecommunication Technology" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.258, + 0.345, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.256, + 0.891, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.454, + 0.895, + 0.497 + ], + "angle": 0, + "content": "Figure 1. Typical method (S2D [22]) based on the encoder-decoder network (ED-Net) and its intermediate features are visualized by the heatmap [46]. The sparse decoder feature \\( f_{di} \\) derived from the dense fused encoder-decoder feature \\( f_{edi} \\) tends to complement the corresponding encoder feature \\( f_{ei} \\), where the \"dense \\(\\Rightarrow\\) sparse\" process destroys the completeness of features multiple times." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.511, + 0.314, + 0.527 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.544, + 0.474, + 0.878 + ], + "angle": 0, + "content": "The encoder-decoder network (ED-Net) is a commonly employed choice for existing depth completion methods, but its working mechanism is ambiguous. In this paper, we visualize the internal feature maps to analyze how the network densifies the input sparse depth. We find that the encoder feature of ED-Net focuses on the areas with input depth points around. To obtain a dense feature and thus estimate complete depth, the decoder feature tends to complement and enhance the encoder feature by skip-connection to make the fused encoder-decoder feature dense, resulting in the decoder feature also exhibits sparse. However, ED-Net obtains the sparse decoder feature from the dense fused feature at the previous stage, where the \"dense \\(\\Rightarrow\\) sparse\" process destroys the completeness of features and loses information. To address this issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. Furthermore, we propose a confidence-aware guidance module (CGM), which is confidence-aware and performs guidance" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.513, + 0.895, + 0.634 + ], + "angle": 0, + "content": "with adaptive receptive fields (GARF), to fully exploit the potential of these dense features as guidance. Experimental results show that our DFU, a plug-and-play module, can significantly improve the performance of existing ED-Net based methods with limited computational overheads, and new SOTA results are achieved. Besides, the generalization capability on sparser depth is also enhanced. Project page: https://npucvr.github.io/DFU." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.664, + 0.634, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Accurate and dense scene depth is crucial for various applications [13, 34, 41], such as autonomous navigation [33] and augmented reality [24]. Existing active depth sensors have been widely applied because they can obtain accurate depth information. However, the depth acquired by these sensors is generally highly sparse due to the imaging principles and power limitation. For instance, roughly \\(4\\%\\) pixels in the depth provided by 64-line LiDAR have values [21, 22, 35]. To facilitate the use of the depth data, we need to address a sparse-to-dense problem in which the given sparse depth map is densified to the dense depth map, usually guided by the corresponding RGB image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Depth completion is a challenging task as the input depth information is scarce. Existing approaches commonly" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.363, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: daiyuchao@nwpu.edu.cn." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "21104" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.364 + ], + "angle": 0, + "content": "consider this task as a pixel-wise regression problem and utilize an encoder-decoder network with skip-connection (ED-Net) to address it. For instance, the single-branch ED-Net [2, 14, 21, 22, 25] uses standard backbone networks [6, 19] as the encoder to extract features from the sparse depth and RGB images. Then, the decoder employs operations, such as the element-wise addition and transpose convolution, to fuse the encoder feature and upsampling. Recently, some multi-branch ED-Nets [4, 31, 32, 44, 47], including the dual-encoder ED-Net [4, 47] and the double encoder-decoder ED-Net[31, 32], etc., have been proposed. These methods employ separate branches to extract features from the sparse depth and RGB images, and internal features are fused at multiple scales. Although existing ED-Nets based methods have achieved considerable success [39, 48, 51], the ED-Net is often employed as a black box. how the network recovers a dense depth map from the input sparse depth has always been ambiguous." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.473, + 0.852 + ], + "angle": 0, + "content": "To gain a deeper understanding of the ED-Net employed by depth completion, Fig. 1 visualizes internal features of the representative method S2D [22] through the feature heatmap [46]. The feature heatmap [46] is obtained by summing the value of the feature along the channel dimension and normalizing them to a range of \\((0,1)\\), which reflects the spatial locations that the network focuses on at different stages and provides valuable insights to infer the behaviors of the network. We observe that although the sparse depth map and dense RGB image are both fed to the network, the shallow feature of the encoder primarily focuses on few regions where the sparse depth map has values. Through multiple downsampling and convolution, the sparse regions of interest continue to expand and aggregate, the encoder feature gradually becomes more \"dense\". As shown in Fig. 1, the lowest-resolution encoder feature \\(f_{e4}\\) has rich information at most spatial locations. However, to obtain a dense feature and thus estimate complete depth, the decoder tends to obtain a complementary feature for the corresponding encoder feature, which contains multiple \"dense \\(\\Rightarrow\\) sparse\" processes. For instance, the decoder feature \\(f_{d1}\\), which is skip-connected to \\(f_{e1}\\), tends to complement and enhance existing \\(f_{e1}\\) to make the fused encoder-decoder feature \\(f_{ed1}\\) dense. Therefore, the decoder feature \\(f_{d1}\\) also exhibits sparse. However, the sparse \\(f_{d1}\\) is derived from the dense \\(f_{ed2}\\) at the previous stage, where the \"dense \\(\\Rightarrow\\) sparse\" process destroys the completeness of features and loses information. Experiments on multi-branch networks also validate this observation, which is provided in the supplemental material. To conclude, existing ED-Nets have not fully utilized the internal dense features, thereby restricting the performance of ED-Net based methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "To address the issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. The multiscale dense features that cover comprehensive scene depth information can progressively resolve ambiguity in super-resolving the feature of uneven depth distribution areas. Meanwhile, the upsampling process can also effectively integrate these dense features into the HR depth feature to predict the dense depth. To further improve the effectiveness of the DFU, we propose a confidence-aware guidance module (CGM) to fully exploit the potential of these dense features as guidance. Specifically, we first filter out unreliable values of the depth feature by predicting its confidence map, and then perform the guidance operation with adaptive receptive fields. In addition, the proposed network can be extended to multi-layer to achieve better results." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.335, + 0.807, + 0.348 + ], + "angle": 0, + "content": "Our main contributions are summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.357, + 0.892, + 0.431 + ], + "angle": 0, + "content": "- We analyze the working mechanism of popular ED-Nets by visualizing the internal feature maps and reveal that multiple \"dense \\(\\Rightarrow\\) sparse\" processes exist in the decoder network, which destroy the completeness of features and lose information." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.434, + 0.892, + 0.524 + ], + "angle": 0, + "content": "- We propose a depth feature upsampling network with confidence-aware guidance module, which is a plug-and-play module, to significantly improve the performance of existing ED-Net based methods and enhance the generalization ability on sparser depth with limited computational overheads." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.527, + 0.892, + 0.587 + ], + "angle": 0, + "content": "- Extensive experiments on popular datasets prove the effectiveness of our method on existing popular ED-Nets, including single-branch, multi-branch, and SPN-based networks, and new SOTA results are achieved." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.357, + 0.892, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.603, + 0.642, + 0.618 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Single-branch ED-Nets. The single-branch ED-Net contains one encoder and one decoder. The pioneer approaches [21, 26] concatenates the sparse depth and RGB image directly, and feeds them into a standard encoder-decoder network to predict the dense depth. Unlike using convolution in the last layer, [28] proposes to use the least squares to fit the relationship between the extracted features and depth values. Considering the gap between the RGB and depth information, subsequent methods [10, 20, 42] generally use two separate convolutional layers to extract features from the sparse depth and RGB image, respectively. Then, the multi-modal features are concatenated and fed into the network. This type of approach is simple and straightforward, but its performance is generally limited." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Multi-branch ED-Nets. Recently, some multi-branch ED-Nets [31, 32, 40, 44, 47] have been proposed for better extraction and fusion of the RGB and depth information. For example, the dual-encoder ED-Net [4, 47]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "21105" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.089, + 0.852, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.254, + 0.621, + 0.264 + ], + "angle": 0, + "content": "(a) Three-layer Depth feature upsampling network" + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.264, + 0.373, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.363, + 0.306, + 0.374 + ], + "angle": 0, + "content": "(b) Single-branch ED-Net" + }, + { + "type": "image", + "bbox": [ + 0.376, + 0.264, + 0.666, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.46, + 0.363, + 0.583, + 0.374 + ], + "angle": 0, + "content": "(c) Multi-branch ED-Net" + }, + { + "type": "image", + "bbox": [ + 0.674, + 0.264, + 0.861, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.377, + 0.892, + 0.406 + ], + "angle": 0, + "content": "Figure 2. The proposed depth feature upsampling network (DFU). It explicitly employs the internal dense features of ED-Nets that are not fully utilized by existing methods to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.643 + ], + "angle": 0, + "content": "commonly employs two separate encoders to extract features from RGB images and sparse depth, respectively. Then, the extracted RGB and depth features are fused at single-scale or multi-scale by the channel-wise concatenation, element-wise summation, or other sophisticated fusion modules [32, 37, 44, 47]. GuideNet [32] proposes a double encoder-decoder network, which extracts the RGB and depth feature by a whole encoder-decoder network. The decoder feature of the RGB branch and the encoder feature of the depth branch are fused by the guided convolutional network at multiple scales. The multiple encoder-decoder network is proposed by RigNet [44], which uses repetitive hourglass networks to extract discriminative RGB features, and the fusion of RGB and depth information is also performed in a repetitive manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.471, + 0.902 + ], + "angle": 0, + "content": "SPN-based Networks. The spatial propagation network (SPN) [2, 3, 14, 18, 25, 43] is a hot topic, which iteratively refines the predicted depth by aggregating the reference and neighbor pixels. The initial SPN [17] updates each pixel by three adjacent pixels from the previous row or column. CSPN [2] improves it by updating all pixels simultaneously by fixed-local neighbors, and \\(\\mathrm{CSPN}++\\) [3] assembles the results predicted by using the neighbors in different ranges. To obtain non-local neighbors, DSPN [43] and NLSPN [25] learn the offsets to the regular grid. DySPN [14] gives variable weights to neighbors with different distances to make the kernel weights change dynamically during the update process. GraphCSPN [18] integrates 3D information into the update process. LRRU [36] proposes to employ multiscale guidance features to guide the prediction of neighbors and weights, which makes them change adaptively throughout the update process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.416, + 0.634, + 0.433 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.637 + ], + "angle": 0, + "content": "In this section, we present a depth feature upsampling network (DFU) that effectively utilizes internal dense features of ED-Net to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The DFU is introduced in three parts: (1) feature extraction, including extracting the LR depth feature and multi-scale dense features from ED-Net as guidance, (2) depth feature upsampling guided by the proposed confidence-aware module, (3) going deeper, where DFU is extended to multi-layer to obtain better results. For descriptive convenience, the feature is marked as \\( f_{i} \\), where \\( i = \\{1,2,3,4,5\\} \\) denotes the feature of different resolutions, namely \\( f_{i} \\in \\mathbb{R}^{H / n \\times W / n \\times D_{i}} \\), \\( n = 2^{i - 1} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.689, + 0.665 + ], + "angle": 0, + "content": "3.1. Features Extraction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.809 + ], + "angle": 0, + "content": "The LR depth feature \\( f_{dd4} \\in \\mathbb{R}^{H/8 \\times W/8 \\times D_{dd4}} \\) is extracted from the sparse input depth using a convolutional network, where \\( D_{dd4} \\) is set to 64 in this paper. The network consists of 8 residual blocks, 2 at full-resolution, 2 at 1/2-resolution, 2 at 1/4-resolution, and 2 at 1/8-resolution. Although the input depth is sparse, the depth information continues to expand and aggregate by multiple downsampling and convolutional layers, making the LR feature \\( f_{dd4} \\) dense (most spatial positions of the feature contain rich information)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 2 (b) and (c), the guidance feature can be obtained from any ED-Net, including single-branch ED-Net, multi-branch ED-Net, etc. In this paper, we generally extract five encoder features \\(\\{f_{e1}, f_{e2}, f_{e3}, f_{e4}, f_{e5}\\}\\) at different resolution. Then, the decoder features \\(\\{f_{d4}, f_{d3}, f_{d2}, f_{d1}\\}\\) and fused encoder-decoder features" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "21106" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.227 + ], + "angle": 0, + "content": "\\(\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}\\) are obtained in the decoder. We select the features \\(\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}\\) to guide the upsampling of the LR depth feature. These features are generally dense and cover comprehensive scene depth information, which can progressively resolve ambiguity in superresolving the feature of uneven depth distribution areas. Furthermore, the upsampling process effectively integrates these dense features that are underutilized in existing ED-Nets, thus improving the accuracy of depth completion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.469, + 0.273 + ], + "angle": 0, + "content": "To reduce computational complexity, we reduce the channel number of these features \\(\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}\\) to the same as the LR depth feature by" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.285, + 0.469, + 0.302 + ], + "angle": 0, + "content": "\\[\nf _ {g i} = \\mathbf {C o n v} _ {\\mathbf {1} \\times \\mathbf {1}} (f _ {e d i}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.469, + 0.344 + ], + "angle": 0, + "content": "where \\(\\mathbf{Conv}_{\\mathbf{1}\\times \\mathbf{1}}\\) is a \\(1\\times 1\\) convolutional layer, and the feature \\(f_{gi}\\) is employed as the guidance feature in the DFU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.353, + 0.321, + 0.369 + ], + "angle": 0, + "content": "3.2. Depth Feature Upsampling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.469, + 0.587 + ], + "angle": 0, + "content": "As shown in Fig. 2 (a), the LR depth feature is upsampled to HR through four stages, which are guided by the features \\(\\{f_{g4}, f_{g3}, f_{g2}, f_{g1}\\}\\), respectively. To fully exploit the potential of the guidance feature, we propose a Confidence-aware Guidance Module (CGM), which first filters out unreliable values of the depth feature by predicting its confidence map, and performs the guidance operation with adaptive receptive fields to handle uneven depth distribution. The first stage of the DFU consists of a CGM, while other stages adopt the \"upsampling + CGM\". As shown in Fig. 3, for the depth feature \\(f_{ddi}\\), we denote the output feature of the CGM as \\(f_{ddi}'\\). In this paper, the upsampling is implemented by using a deconvolutional layer of stride 2, and the details of the CGM are introduced as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.469, + 0.708 + ], + "angle": 0, + "content": "Confidence-aware. The LR depth feature is extracted from the input depth that is highly sparse and noisy. Besides, ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, we predict an elementwise attention map to filter out unreliable feature values. Specifically, we concatenate the depth feature \\( f_{ddi} \\) and the guidance feature \\( f_{gi} \\). The confidence map \\( c_i \\) is predicted by a \\( 3 \\times 3 \\) convolutional layer as:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.721, + 0.469, + 0.737 + ], + "angle": 0, + "content": "\\[\nc _ {i} = \\sigma \\left(\\mathbf {C o n v} _ {\\mathbf {3} \\times \\mathbf {3}} \\left(\\mathbf {c o n c}. \\left(f _ {d d i}, f _ {g i}\\right)\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.468, + 0.776 + ], + "angle": 0, + "content": "here \\(\\sigma\\) denotes the sigmoid function to compress the confidence value to \\(0 - 1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Guidance with Adaptive Receptive Fields (GARF). In the field of depth completion, guided convolutional networks have been studied widely for multi-modal feature fusion. For example, the pioneering GuideNet [32] predicts spatially-variant depthwise convolutional kernels [30] \\(\\mathbf{W} \\in \\mathbb{R}^{hw \\times k^2 \\times c}\\) from the RGB feature, and then applies them to extract the depth feature. Here, \\(h\\), \\(w\\), and \\(c\\) are the height, weight, and channel number of the feature map," + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.093, + 0.895, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.277, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Figure 3. The Confidence-aware Guidance Module (CGM) and \\( k \\) is the kernel size. To reduce computational complexity, [37] decomposes the depthwise kernel \\( \\mathbf{W}_{\\mathbf{P}_i} \\in \\mathbb{R}^{k^2 \\times c} \\) at each spatial location \\( \\mathbf{p}_i \\) into content-adaptive adaptors \\( \\mathbf{A} \\in \\mathbb{R}^{k^2 \\times m} \\) multiplied by the spatially-shared component \\( \\mathbf{D} \\in \\mathbb{R}^{m \\times c} \\). The guided convolutional network has been proven to be effective since it can transfer structural information from the guidance feature to the target feature [12]. Therefore, in our method, we adopt this strategy to fully utilize the guidance feature. However, the kernel size of existing guided convolutional networks is usually fixed, which cannot handle the areas with uneven depth distribution well. To address this issue, we propose a guidance module with adaptive receptive fields." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.717 + ], + "angle": 0, + "content": "Recently, some novel dynamic convolution networks [27, 38] have shown that the convolutional kernel can be equivalently represented as a combination of pre-fixed bases, such as Fourier-Bessel(FB) bases [1]. Inspired by these works [27, 38], we further decompose the adaptors over multi-scale FB bases to selectively choose a receptive field at each spatial position. Specifically, we pre-generate \\( n \\) FB bases of different sizes, such as \\( 3 \\times 3 \\), \\( 5 \\times 5 \\), and \\( 7 \\times 7 \\), and then unify them to the same size by zero padding. Unlike [37] directly predicts the adaptors, we predict the weight of the multi-scale FB bases. As shown in Fig. 3, the adaptors with adaptive receptive fields can be obtained by multiplying the predicted weight with the FB bases. Then, we preform the guidance operation similar as [37] and obtain the refined depth feature \\( f_{gdi} \\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.726, + 0.891, + 0.743 + ], + "angle": 0, + "content": "\\[\nf _ {g d i} = G A R F \\left(c _ {i} \\odot f _ {d d i}, f _ {g i}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.891, + 0.813 + ], + "angle": 0, + "content": "Feature Updating. The confidence map \\( c_{i} \\) assigns low confidence to the unreliable depth features, which are exactly the areas we want the guidance module to prioritize. Therefore, we obtain the output of CGM \\( f_{ddi}' \\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.822, + 0.891, + 0.839 + ], + "angle": 0, + "content": "\\[\nf _ {d d i} ^ {\\prime} = c _ {i} \\odot f _ {d d i} + (1 - c _ {i}) \\odot f _ {g d i} \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.642, + 0.864 + ], + "angle": 0, + "content": "3.3. Going Deeper" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To further enhance the performance of the proposed method, we extend the depth feature upsampling network" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.518, + 0.936 + ], + "angle": 0, + "content": "21107" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.116, + 0.09, + 0.852, + 0.103 + ], + "angle": 0, + "content": "Table 1. The performance comparison between the baseline models and their improved model by using the multi-layer DFU." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.105, + 0.894, + 0.284 + ], + "angle": 0, + "content": "
KITTI Validate Dataset [5]NYUv2 Depth Dataset [23]
Params. [M]FLOPs [G]RMSE ↓ [mm]MAE ↓ [mm]iRMSE ↓ [1/km]iMAE ↓ [1/km]RMSE ↓ [mm]REL ↓ (×1000)δ1.25 ↑ [%]δ1.252 ↑ [%]δ1.253 ↑ [%]
Our single-branch ED-Net11.95291.24772.87210.262.280.95111.9416.6299.3299.8899.98
Improving by One-layer DFU+ 1.67+ 43.79750.58205.322.140.93100.6713.9299.4699.9199.98
Improving by Two-layer DFU+ 2.41+ 65.65745.27202.342.180.9398.9913.6399.4899.9199.98
Improving by Three-layer DFU+ 3.14+ 87.52746.98201.082.090.8997.7813.5999.4999.9199.98
Our Dual-branch ED-Net22.28498.84753.81204.392.120.92101.1214.4099.4699.9199.98
Improving by One-layer DFU+ 1.65+ 38.34741.39199.652.000.8898.6314.2199.4999.9299.98
Improving by Two-layer DFU+ 2.38+ 57.24738.20198.852.030.8797.6213.7099.5099.9299.98
Improving by Three-layer DFU+ 3.10+ 76.15736.60198.612.010.8796.2712.9299.5099.9299.98
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.299, + 0.47, + 0.39 + ], + "angle": 0, + "content": "to multi-layer. In this subsection, the feature is marked as \\( f_{i}^{j} \\), where the superscript \\( j \\) denotes the feature in the \\( j \\)-th layer DFU. As shown in Fig. 2, we deepen the depth of each stage of the network. Specifically, we employ the feature \\( f_{ddi}^{j} \\) of the \\( j \\)-th layer DFU as the guidance feature \\( f_{gi}^{j+1} \\) of the corresponding module of the \\( j+1 \\)-th layer DFU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.406, + 0.21, + 0.423 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.431, + 0.295, + 0.448 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.47, + 0.651 + ], + "angle": 0, + "content": "We employ PyTorch to implement our model, and conduct experiments with GeForce RTX 3090 GPUs. Our training process is divided into two stages, which both employ the \\( L1 + L2 \\) loss to train 35 epochs. The initial learning rate is \\( 10^{-3} \\), and it is reduced by \\( 50\\% \\) every 5 epochs. We employ the AdamW optimizer with a batch size of 8, and set \\( \\beta_{1} = 0.9 \\), \\( \\beta_{2} = 0.999 \\), weight decay is \\( 10^{-6} \\). In the first stage, we first train the ED-Net to obtain the internal dense features that cover comprehensive scene depth information. Then, we train the depth feature upsampling network (DFU), in which these dense features are explicitly employed as the guidance features. For the multi-layer DFU, we only supervise the output of the last-layer DFU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.276, + 0.679 + ], + "angle": 0, + "content": "4.2. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.777 + ], + "angle": 0, + "content": "KITTI Dataset [5] consists of sparse depth maps projected from raw LiDAR scans and corresponding RGB images, which is a popular real-world autonomous driving dataset. The dataset contains 86k frames for training, 1k selected frames for validation, and 1k frames without ground truth that need to be tested on the online benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.869 + ], + "angle": 0, + "content": "NYUv2 Dataset [23] is a popular indoor RGBD dataset. Following existing works [16, 36, 45, 51], our model is trained with 50K images sampled from the training set, and tested on 654 officially labeled images. The images of size \\(640 \\times 480\\) are downsampled to half and then center-cropped to \\(304 \\times 228\\) for both training and inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. Following exiting methods [25, 36, 52], we employ Root Mean Squared Error (RMSE), Mean" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.299, + 0.892, + 0.346 + ], + "angle": 0, + "content": "Absolute Error (MAE), inverse RMSE (iRMSE), inverse MAE (iMAE), mean absolute relative error (REL), and percentage of pixels satisfying \\(\\delta_{\\tau}\\) for quantitative evaluation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.369, + 0.794, + 0.386 + ], + "angle": 0, + "content": "4.3. Improving Single-branch ED-Net" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.609 + ], + "angle": 0, + "content": "Following most methods [10, 20, 22, 42], the single-branch ED-Net used in this paper first extracts the depth and RGB features by two independent convolutional layers, and the features are concatenated and fed into an encoder-decoder network. The encoder consists of five stages, and each stage contains 2 residual blocks. The encoder feature is extracted at full-resolution in the first stage and is progressively halved in the next four stages. The feature channels of the five stages are 64, 128, 256, 256 and 256. We use the deconvolutional layer with stride 2 to upsample features, and fuse the encoder and decoder feature by the concatenate. As shown in Fig. 2 (b), the fused encoder-decoder features \\( f_{ed4} \\), \\( f_{ed3} \\), \\( f_{ed2} \\), \\( f_{ed1} \\) are employed as the guidance features in the proposed DFU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 1, our single-branch ED-Net contains \\(11.95\\mathrm{M}\\) parameters and requires \\(291.24\\mathrm{G}\\) FLOPs, and the RMSE and MAE are \\(772.87\\mathrm{mm}\\) and \\(210.26\\mathrm{mm}\\). Note that our single-branch ED-Net outperforms S2D [22] built on the Resnet-34 with fewer parameters since we use the effective stochastic depth strategy [8] in the residual block as [14]. We observe that the single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, the improvement in terms of various metrics is \\(22.29\\mathrm{mm}\\) in RMSE, \\(4.94\\mathrm{mm}\\) in MAE, 0.14 in iRMSE, and 0.02 in iMAE. Meanwhile, the performance in terms of RMSE and MAE is further improved when we deepen the DFU to two layers. However, this improvement is relatively small compared to the previous one. When we extend the DFU to three layers, the MAE is further reduced, while the results in the term of RMSE appear saturated. In addition, the experimental results conducted on the NYUv2 dataset consistently demonstrate that our DFU can effectively improve the performance of the single-branch ED-Net." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "21108" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.089, + 0.09, + 0.88, + 0.103 + ], + "angle": 0, + "content": "Table 2. The performance comparison between LRRUs (SPN-based method) and their improved model by using the multi-layer DFU." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.104, + 0.894, + 0.297 + ], + "angle": 0, + "content": "
LRRU-MiniLRRU-TinyLRRU-SmallLRRU-Base
KITTI [5]Validate DatasetRMSE↓[mm]MAE↓[mm]iRMSE↓[1/km]iMAE↓[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]
Baseline806.27210.162.280.89763.80198.892.120.85745.31195.692.000.83729.49188.781.920.80
+ One-layer DFU787.28206.562.270.88747.39195.682.040.83732.42192.271.960.81718.27188.051.890.80
+ Two-layer DFU775.93202.712.200.86744.92193.102.000.82730.89190.561.940.81716.02186.691.890.80
+ Three-layer DFU767.67199.482.160.85742.83192.311.990.81729.24189.411.930.80713.32185.551.870.79
NYUv2 [23]Depth DatasetRMSE↓[mm]REL↓(x1000)δ1.25↑δ1.252↑RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252
Baseline100.8613.3499.4499.9195.3612.2599.5199.9293.3611.8599.5399.9291.2711.2199.5699.92
+ One-layer DFU99.2212.7799.4699.9192.5811.7699.5499.9391.5711.4899.5699.9390.7911.1999.5799.93
+ Two-layer DFU98.9412.7399.4799.9192.3111.6399.5599.9391.1511.4399.5699.9890.6111.2299.5799.93
+ Three-layer DFU98.2912.6999.4799.9192.2911.5999.5599.9291.0811.4399.5699.9890.7711.2799.5799.93
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.312, + 0.367, + 0.328 + ], + "angle": 0, + "content": "4.4. Improving Multi-branch ED-Net" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.47, + 0.546 + ], + "angle": 0, + "content": "We experimentally found that the performance gap between dual-branch networks, double encoder-decoder networks, and multiple encoder-decoder networks is not significant. Therefore, we select the most cost-effective dual-encoder network as the baseline model to verify the improvement effect of our proposed method on the multi-branch ED-Net. As shown in Fig. 2 (c), the difference between the dual-encoder ED-Net and single-branch ED-Net is that the dual-encoder ED-Net utilizes two encoders to extract features from the sparse depth and corresponding RGB image, respectively. Specifically, the RGB encoder works independently, and the extracted RGB features at multiple scales are gradually injected into the depth encoder to effectively integrate information from different modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.471, + 0.805 + ], + "angle": 0, + "content": "As shown in Table 1, our dual-encoder ED-Net has nearly double the number of parameters and computational complexity in comparison to the single-branch ED-Net as it employs two encoders and the multi-scale fusion strategy. However, the dual-encoder ED-Net also outperforms the single-branch ED-Net significantly. When we apply one-layer DFU to the dual-encoder ED-Net, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by \\(12.42\\mathrm{mm}\\), \\(4.74\\mathrm{mm}\\), 0.12 and 0.04, respectively. The performance of the method is continuously improved as the DFU deepens, while the magnitude of the performance improvement gradually decreases. We observe that the performance of the method closes saturation when using the three-layer DFU. Additionally, similar conclusions can be drawn from the results on the NYUv2 dataset, which adequately demonstrate that our proposed method can effectively improve the performance of the dual-branch ED-Net." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.338, + 0.833 + ], + "angle": 0, + "content": "4.5. Improving SPN-based Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The SPN is a popular module to refine the predicted depth map. To validate the effectiveness of our method for SPN-based methods, we apply the proposed DFU to LRRU [36], which introduces an effective SPN model and achieves top" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.478 + ], + "angle": 0, + "content": "ranking performance on the KITTI benchmark. As described in [36], LRRU has already utilized internal dense features of the guided-feature extraction network to guide the SPN model. However, these features are employed individually, and the features at different scales can not be aggregated to improve the robustness and effectiveness of the SPN model. To address this issue, we add the DFU between the guided-feature extraction network and the recurrent update process of the LRRU to integrate the information from the multi-scale guidance features (more details in the supplementary materials)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.893, + 0.735 + ], + "angle": 0, + "content": "As shown in Table 2, we conduct comprehensive experiments on four variants of LRRU with varying network scales. On the KITTI dataset, the performance of all four variants of LRRU is significantly improved by using the DFU, especially for the mini model. Specifically, by using one-layer DFU, the RMSE of LRRU-Mini is reduced by \\(18.99\\mathrm{mm}\\), and the RMSE of LRRU-Base is reduced by \\(11.22\\mathrm{mm}\\). Furthermore, the performance of LRRUs continues to enhance at a gradually decreasing rate when utilizing the multi-layer DFU. The experimental results on the NYUv2 dataset consistently demonstrate the effectiveness of our method. Noted that, due to the limited number of samples of the NYUv2 dataset, when we continue to add our method to the LRRU-Base model with a large network size, the network appears to be overfitting. Therefore, on the NYUv2 dataset, our method only has a limited performance improvement effect on the LRRU-Base model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.743, + 0.798, + 0.758 + ], + "angle": 0, + "content": "4.6. Comparison with state-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "To evaluate our methods against state-of-the-art (SOTA) methods, we compare their experimental results on the KITTI benchmark (outdoor) and NYUv2 (indoor). As shown in Table 3, we report the results of our baseline methods and the improved methods by using three-layer DFU. Meanwhile, we select some representative methods from the last three years for comparison. Since most SOTA methods employ the multi-branch ED-Net structure, the performance of our single-branch ED-Net is slightly worse" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "21109" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation on the KITTI online leaderboard and NYUv2. The results of improved methods by using the three-layer DFU are highlighted with a gray background and the best and second-best results are highlighted in red and blue colors, respectively." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.119, + 0.895, + 0.387 + ], + "angle": 0, + "content": "
KITTI Online Benchmark [5]NYUv2 Depth Dataset [23]Publication
RMSE[mm]↓MAE[mm]↓iRMSE[1/km]↓iMAE[1/km]↓RMSE[m]↓REL↓δ1.25↑δ1.252↑δ1.252↑
TWISE [11]840.20195.582.080.820.0970.01399.699.9100.0CVPR 2021
FCFRNet [15]735.81217.152.200.980.1060.01599.599.9100.0AAAI 2021
PENet [7]730.08210.552.170.94-----ICRA 2021
ACMNet [49]744.91206.092.080.900.1050.01599.599.9100.0TIP 2021
PointFusion [9]741.90201.101.970.850.0900.01499.699.9100.0ICCV 2021
GFormer [29]721.48207.762.140.97-----CVPR 2022
DySPN [14]709.12192.711.880.820.0900.01299.699.9100.0AAAI 2022
GraphCSPN [18]738.41199.311.960.840.0900.01299.699.9100.0ECCV 2022
RigNet [44]712.66203.252.080.900.0900.01399.699.9100.0ECCV 2022
CompletionFormer [48]708.30203.452.010.880.0910.01299.699.9100.0CVPR 2023
BEV@DC [51]697.44189.441.830.820.0890.01299.699.9100.0CVPR 2023
PointDC [45]736.07201.871.970.870.0890.01299.699.9100.0ICCV 2023
Our Single-branch ED-Net745.16209.862.220.950.1120.01699.399.9100.0-
Improved Single-branch719.65201.922.060.910.0980.01499.599.9100.0-
Our Dual-branch ED-Net720.96203.732.070.920.1010.01499.599.9100.0-
Improved Dual-branch706.23199.141.990.890.0960.01399.599.9100.0-
LRRU-Base (SPN-based) [36]696.51189.961.870.810.0910.01199.699.9100.0ICCV 2023
Improved LRRU-Base686.46187.951.830.810.0910.01199.699.9100.0-
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.473, + 0.702 + ], + "angle": 0, + "content": "in comparison. However, the performance of our single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, on the KITTI benchmark, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by \\(25.51 \\mathrm{~mm}\\), \\(7.94 \\mathrm{~mm}\\), 0.16, and 0.04, respectively. Besides, five metrics evaluated on the NYUv2 are also enhanced considerably. The experimental results demonstrate that the proposed DFU can effectively improve the performance of the single-branch ED-Net. Compared to the single-branch ED-Net, our dual-branch ED-Net shows better performance, which already outperforms the latest PointDC [45], GraphCSPN [18], GFormer [29], etc. in the term of RMSE. However, the proposed DFU still greatly improves the performance of the dual-branch ED-Net on two benchmarks. Note that our method is effective for the LRRU-Base (SPN-based method) as well, which is the current SOTA method on the KITTI benchmark. Specifically, the improved LRRU-Base by using three-layer DFU achieves new SOTA results, which ranks Top-1 on the KITTI benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The results on the NYUv2 show that the methods [9, 18, 51, 51] that fuse 3D information generally achieve better results, such as BEV@DC [51] and PointDC [51]. Our method can also greatly improve the performance of the single-branch ED-Net and dual-branch ED-Net on NYUv2, while the performance improvement on LRRU-Base is negligible due to overfitting. Fig. 4 and Fig. 5 show the qualitative results of the baseline models and improved models by using three-layer DFU. Since our DFU effectively uses internal dense features of ED-Nets that cover comprehensive scene depth information, the improved method has more accurate results in fine and small structures, such as the gap area between two adjacent objects." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.399, + 0.878, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.568, + 0.867, + 0.581 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on the NYUv2 depth dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.665, + 0.603 + ], + "angle": 0, + "content": "4.7. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.719 + ], + "angle": 0, + "content": "In this section, we conduct experiments on the KITTI dataset to verify the effectiveness of the confidence-aware guidance module, which consists of the confidence-aware model and the guidance model with adaptive receptive fields. As shown in Table 4 (a) and (e), we choose our single-branch ED-Net as the baseline, and its results are significantly improved by using standard one-layer DFU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Confidence-aware. In this paper, the LR depth feature is extracted from a highly sparse and noisy depth map, and ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, some values of the depth feature are unreliable. To filter out the unreliable depth feature values before the guidance module, we propose to predict an element-wise confidence map, which assigns these unreliable values a lower weight. Besides, we also employ the confidence map in the feature updating, which makes the guidance module focus on the unreliable values of the depth features. As shown in Table 4 (d) and (e), removing the confidence map increases the RMSE and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.927, + 0.521, + 0.938 + ], + "angle": 0, + "content": "21110" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.093, + 0.355, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.178, + 0.15, + 0.282, + 0.163 + ], + "angle": 0, + "content": "A.1 RGB Image" + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.093, + 0.611, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.431, + 0.15, + 0.534, + 0.163 + ], + "angle": 0, + "content": "A.2 RGB Image" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.093, + 0.864, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.686, + 0.15, + 0.79, + 0.163 + ], + "angle": 0, + "content": "A.3 RGB Image" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.162, + 0.355, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.218, + 0.323, + 0.231 + ], + "angle": 0, + "content": "B.1 Our Single-branch Result" + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.162, + 0.609, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.218, + 0.572, + 0.23 + ], + "angle": 0, + "content": "B.2 Our Dual-branch Result" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.162, + 0.864, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.218, + 0.826, + 0.23 + ], + "angle": 0, + "content": "B.2 The LRRU-Base Result" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.232, + 0.355, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.287, + 0.341, + 0.301 + ], + "angle": 0, + "content": "C.1 Improved Single-branch Result" + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.232, + 0.609, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.376, + 0.287, + 0.59, + 0.3 + ], + "angle": 0, + "content": "C.2 Improved Dual-branch Result" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.232, + 0.864, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.631, + 0.287, + 0.844, + 0.3 + ], + "angle": 0, + "content": "C.3 Improved LRRU-Base Result" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.302, + 0.878, + 0.317 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on the KITTI online leaderboard, including the baseline and improved models by using three-layer DFU." + }, + { + "type": "table_caption", + "bbox": [ + 0.102, + 0.331, + 0.444, + 0.344 + ], + "angle": 0, + "content": "Table 4. Ablation studies on the KITTI validation dataset." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.345, + 0.464, + 0.455 + ], + "angle": 0, + "content": "
Confidence awareGARFRMSE [mm]MAE [mm]
(a)Our Single-branch ED-Net--772.87210.26
(b)Improving by one-layer DFU--761.24209.04
(c)Improving by one-layer DFU✓-758.67207.51
(d)Improving by one-layer DFU-✓756.31206.82
(e)Improving by one-layer DFU✓✓751.76203.09
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.461, + 0.455, + 0.476 + ], + "angle": 0, + "content": "MAE of the improved method by \\(4.55\\mathrm{mm}\\) and \\(3.73\\mathrm{mm}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.469, + 0.686 + ], + "angle": 0, + "content": "Guidance with Adaptive Receptive Fields. Traditional guided convolutional networks [32, 37, 44] generally predict spatially-variant convolutional kernels from the guidance feature, and then employ the predicted kernels to extract the target feature. These networks have been proven effective since they can transfer the structural information from the guidance feature to the target feature. However, the predicted per-pixel kernel has a fixed size, which cannot be suitable for the areas with different depth distributions. To address this issue, we propose the guidance module with adaptive receptive fields (GARF). The results in Table 4 (c) and (e) show that the performance of the improved method without GARF is significantly decreased, which demonstrates the effectiveness of GARF." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.334, + 0.714 + ], + "angle": 0, + "content": "4.8. Experiments on fewer points" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.902 + ], + "angle": 0, + "content": "It is crucial to analyze the generalization ability for sparser depth maps, which are usually provided in many practical applications. We train our baseline methods and their improved methods by using three-layer DFU on the standard KITTI (64-line LiDAR depth) and test the performance (MAE[mm]) on the depth map with fewer lines. The sparser depth map is obtained by the method provided by [50]. As shown in Fig. 6, the performance improvement by using the proposed DFU is more significant on sparser depth maps. The experimental results demonstrate that our approach not only improves the performance of the method, but also enhances the generalization ability for sparser depth maps." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.331, + 0.877, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.437, + 0.866, + 0.451 + ], + "angle": 0, + "content": "Figure 6. The performance (MAE [mm]) on fewer points." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.452, + 0.693, + 0.468 + ], + "angle": 0, + "content": "4.9. Computational Cost" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.58 + ], + "angle": 0, + "content": "We report the parameters and FLOPs of the method in Table 1. Since we pre-reduce the channel number of the feature, our method improves the performance of existing ED-Nets with limited computational overheads. Specifically, using one-layer DFU approximately requires extra \\(1.7\\mathrm{M}\\) parameters and \\(40\\mathrm{G}\\) FLOPs, which are small compared to those of the ED-Net itself." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.595, + 0.618, + 0.61 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.816 + ], + "angle": 0, + "content": "In this paper, we have proposed the depth feature upsampling network (DFU), a plug-and-play module to improve existing ED-Net based methods. By the proposed confidence-aware guidance module, DFU effectively utilizes internal dense features of ED-Net to guide the depth feature upsampling, the completeness of these dense features is maintained in DFU. Furthermore, DFU can be extended to multi-layer to achieve better results. Experimental results show that our method can significantly improve existing ED-Nets, including single-branch ED-Nets, multi-branch ED-Nets, and SPN-based methods, with limited computational overheads. Meanwhile, the generalization ability for sparser depth is also enhanced." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.659, + 0.847 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was supported by the National Science Fund of China (Grant Nos.62001394, 62271410, 62306238) and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "21111" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Milton Abramowitz, Irene A Stegun, and Robert H Romer. 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In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 2022. 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.84 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.927, + 0.52, + 0.938 + ], + "angle": 0, + "content": "21113" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Depth Completion via Depth Feature Upsampling/0ed38fa6-aa40-45ef-a200-06326c698546_origin.pdf b/2024/Improving Depth Completion via Depth Feature Upsampling/0ed38fa6-aa40-45ef-a200-06326c698546_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f44f46043aa38d4877156745f31c3adbb043fe19 --- /dev/null +++ b/2024/Improving Depth Completion via Depth Feature Upsampling/0ed38fa6-aa40-45ef-a200-06326c698546_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed2373ebdb26ac2db673c589b194eba88b9d2ffda4578b5b157ba13db38a342f +size 4409064 diff --git a/2024/Improving Depth Completion via Depth Feature Upsampling/full.md b/2024/Improving Depth Completion via Depth Feature Upsampling/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3f1dd2cc7126997292e379f0dfd8680c59d2d551 --- /dev/null +++ b/2024/Improving Depth Completion via Depth Feature Upsampling/full.md @@ -0,0 +1,293 @@ +# Improving Depth Completion via Depth Feature Upsampling + +Yufei Wang $^{1}$ , Ge Zhang $^{2}$ , Shaoqian Wang $^{1}$ , Bo Li $^{1}$ , Qi Liu $^{1}$ , Le Hui $^{1}$ , Yuchao Dai $^{1*}$ + +1Northwestern Polytechnical University and Shaanxi Key Laboratory of Information Acquisition and Processing 2Beijing Institute of Tracking and Telecommunication Technology + +![](images/3bdf78b0cbe2db6a8dc1deada73b197cf9c3d8d355eeeca5bdefc27e05be16db.jpg) +Figure 1. Typical method (S2D [22]) based on the encoder-decoder network (ED-Net) and its intermediate features are visualized by the heatmap [46]. The sparse decoder feature $f_{di}$ derived from the dense fused encoder-decoder feature $f_{edi}$ tends to complement the corresponding encoder feature $f_{ei}$ , where the "dense $\Rightarrow$ sparse" process destroys the completeness of features multiple times. + +![](images/e21e4c25fb10c3846be6acf40f5e2a68591f2e6913e0171a85ab1485ac8b7050.jpg) + +# Abstract + +The encoder-decoder network (ED-Net) is a commonly employed choice for existing depth completion methods, but its working mechanism is ambiguous. In this paper, we visualize the internal feature maps to analyze how the network densifies the input sparse depth. We find that the encoder feature of ED-Net focuses on the areas with input depth points around. To obtain a dense feature and thus estimate complete depth, the decoder feature tends to complement and enhance the encoder feature by skip-connection to make the fused encoder-decoder feature dense, resulting in the decoder feature also exhibits sparse. However, ED-Net obtains the sparse decoder feature from the dense fused feature at the previous stage, where the "dense $\Rightarrow$ sparse" process destroys the completeness of features and loses information. To address this issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. Furthermore, we propose a confidence-aware guidance module (CGM), which is confidence-aware and performs guidance + +with adaptive receptive fields (GARF), to fully exploit the potential of these dense features as guidance. Experimental results show that our DFU, a plug-and-play module, can significantly improve the performance of existing ED-Net based methods with limited computational overheads, and new SOTA results are achieved. Besides, the generalization capability on sparser depth is also enhanced. Project page: https://npucvr.github.io/DFU. + +# 1. Introduction + +Accurate and dense scene depth is crucial for various applications [13, 34, 41], such as autonomous navigation [33] and augmented reality [24]. Existing active depth sensors have been widely applied because they can obtain accurate depth information. However, the depth acquired by these sensors is generally highly sparse due to the imaging principles and power limitation. For instance, roughly $4\%$ pixels in the depth provided by 64-line LiDAR have values [21, 22, 35]. To facilitate the use of the depth data, we need to address a sparse-to-dense problem in which the given sparse depth map is densified to the dense depth map, usually guided by the corresponding RGB image. + +Depth completion is a challenging task as the input depth information is scarce. Existing approaches commonly + +consider this task as a pixel-wise regression problem and utilize an encoder-decoder network with skip-connection (ED-Net) to address it. For instance, the single-branch ED-Net [2, 14, 21, 22, 25] uses standard backbone networks [6, 19] as the encoder to extract features from the sparse depth and RGB images. Then, the decoder employs operations, such as the element-wise addition and transpose convolution, to fuse the encoder feature and upsampling. Recently, some multi-branch ED-Nets [4, 31, 32, 44, 47], including the dual-encoder ED-Net [4, 47] and the double encoder-decoder ED-Net[31, 32], etc., have been proposed. These methods employ separate branches to extract features from the sparse depth and RGB images, and internal features are fused at multiple scales. Although existing ED-Nets based methods have achieved considerable success [39, 48, 51], the ED-Net is often employed as a black box. how the network recovers a dense depth map from the input sparse depth has always been ambiguous. + +To gain a deeper understanding of the ED-Net employed by depth completion, Fig. 1 visualizes internal features of the representative method S2D [22] through the feature heatmap [46]. The feature heatmap [46] is obtained by summing the value of the feature along the channel dimension and normalizing them to a range of $(0,1)$ , which reflects the spatial locations that the network focuses on at different stages and provides valuable insights to infer the behaviors of the network. We observe that although the sparse depth map and dense RGB image are both fed to the network, the shallow feature of the encoder primarily focuses on few regions where the sparse depth map has values. Through multiple downsampling and convolution, the sparse regions of interest continue to expand and aggregate, the encoder feature gradually becomes more "dense". As shown in Fig. 1, the lowest-resolution encoder feature $f_{e4}$ has rich information at most spatial locations. However, to obtain a dense feature and thus estimate complete depth, the decoder tends to obtain a complementary feature for the corresponding encoder feature, which contains multiple "dense $\Rightarrow$ sparse" processes. For instance, the decoder feature $f_{d1}$ , which is skip-connected to $f_{e1}$ , tends to complement and enhance existing $f_{e1}$ to make the fused encoder-decoder feature $f_{ed1}$ dense. Therefore, the decoder feature $f_{d1}$ also exhibits sparse. However, the sparse $f_{d1}$ is derived from the dense $f_{ed2}$ at the previous stage, where the "dense $\Rightarrow$ sparse" process destroys the completeness of features and loses information. Experiments on multi-branch networks also validate this observation, which is provided in the supplemental material. To conclude, existing ED-Nets have not fully utilized the internal dense features, thereby restricting the performance of ED-Net based methods. + +To address the issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR) + +depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. The multiscale dense features that cover comprehensive scene depth information can progressively resolve ambiguity in super-resolving the feature of uneven depth distribution areas. Meanwhile, the upsampling process can also effectively integrate these dense features into the HR depth feature to predict the dense depth. To further improve the effectiveness of the DFU, we propose a confidence-aware guidance module (CGM) to fully exploit the potential of these dense features as guidance. Specifically, we first filter out unreliable values of the depth feature by predicting its confidence map, and then perform the guidance operation with adaptive receptive fields. In addition, the proposed network can be extended to multi-layer to achieve better results. + +Our main contributions are summarized as: + +- We analyze the working mechanism of popular ED-Nets by visualizing the internal feature maps and reveal that multiple "dense $\Rightarrow$ sparse" processes exist in the decoder network, which destroy the completeness of features and lose information. +- We propose a depth feature upsampling network with confidence-aware guidance module, which is a plug-and-play module, to significantly improve the performance of existing ED-Net based methods and enhance the generalization ability on sparser depth with limited computational overheads. +- Extensive experiments on popular datasets prove the effectiveness of our method on existing popular ED-Nets, including single-branch, multi-branch, and SPN-based networks, and new SOTA results are achieved. + +# 2. Related Work + +Single-branch ED-Nets. The single-branch ED-Net contains one encoder and one decoder. The pioneer approaches [21, 26] concatenates the sparse depth and RGB image directly, and feeds them into a standard encoder-decoder network to predict the dense depth. Unlike using convolution in the last layer, [28] proposes to use the least squares to fit the relationship between the extracted features and depth values. Considering the gap between the RGB and depth information, subsequent methods [10, 20, 42] generally use two separate convolutional layers to extract features from the sparse depth and RGB image, respectively. Then, the multi-modal features are concatenated and fed into the network. This type of approach is simple and straightforward, but its performance is generally limited. + +Multi-branch ED-Nets. Recently, some multi-branch ED-Nets [31, 32, 40, 44, 47] have been proposed for better extraction and fusion of the RGB and depth information. For example, the dual-encoder ED-Net [4, 47] + +![](images/2b71000cd9092358bca43740297f558359be64c02fc34034cb0b011fa429ec98.jpg) + +![](images/7c4eeb0feba97621cd7c8984debb0f8192c0ce6ea1d5576d0ab914f487a9808d.jpg) +(a) Three-layer Depth feature upsampling network +(b) Single-branch ED-Net + +![](images/e313afa190bd65bf5da1e5c11f0aaeb7aa89c616b025cc7aae01fb8e1d874ea9.jpg) +(c) Multi-branch ED-Net + +![](images/8129bb0bcb33f9dd77ba0f7aafb144468f546e3883cb3baa5da4db17e8b6f812.jpg) +Figure 2. The proposed depth feature upsampling network (DFU). It explicitly employs the internal dense features of ED-Nets that are not fully utilized by existing methods to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. + +commonly employs two separate encoders to extract features from RGB images and sparse depth, respectively. Then, the extracted RGB and depth features are fused at single-scale or multi-scale by the channel-wise concatenation, element-wise summation, or other sophisticated fusion modules [32, 37, 44, 47]. GuideNet [32] proposes a double encoder-decoder network, which extracts the RGB and depth feature by a whole encoder-decoder network. The decoder feature of the RGB branch and the encoder feature of the depth branch are fused by the guided convolutional network at multiple scales. The multiple encoder-decoder network is proposed by RigNet [44], which uses repetitive hourglass networks to extract discriminative RGB features, and the fusion of RGB and depth information is also performed in a repetitive manner. + +SPN-based Networks. The spatial propagation network (SPN) [2, 3, 14, 18, 25, 43] is a hot topic, which iteratively refines the predicted depth by aggregating the reference and neighbor pixels. The initial SPN [17] updates each pixel by three adjacent pixels from the previous row or column. CSPN [2] improves it by updating all pixels simultaneously by fixed-local neighbors, and $\mathrm{CSPN}++$ [3] assembles the results predicted by using the neighbors in different ranges. To obtain non-local neighbors, DSPN [43] and NLSPN [25] learn the offsets to the regular grid. DySPN [14] gives variable weights to neighbors with different distances to make the kernel weights change dynamically during the update process. GraphCSPN [18] integrates 3D information into the update process. LRRU [36] proposes to employ multiscale guidance features to guide the prediction of neighbors and weights, which makes them change adaptively throughout the update process. + +# 3. Methodology + +In this section, we present a depth feature upsampling network (DFU) that effectively utilizes internal dense features of ED-Net to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The DFU is introduced in three parts: (1) feature extraction, including extracting the LR depth feature and multi-scale dense features from ED-Net as guidance, (2) depth feature upsampling guided by the proposed confidence-aware module, (3) going deeper, where DFU is extended to multi-layer to obtain better results. For descriptive convenience, the feature is marked as $f_{i}$ , where $i = \{1,2,3,4,5\}$ denotes the feature of different resolutions, namely $f_{i} \in \mathbb{R}^{H / n \times W / n \times D_{i}}$ , $n = 2^{i - 1}$ . + +# 3.1. Features Extraction + +The LR depth feature $f_{dd4} \in \mathbb{R}^{H/8 \times W/8 \times D_{dd4}}$ is extracted from the sparse input depth using a convolutional network, where $D_{dd4}$ is set to 64 in this paper. The network consists of 8 residual blocks, 2 at full-resolution, 2 at 1/2-resolution, 2 at 1/4-resolution, and 2 at 1/8-resolution. Although the input depth is sparse, the depth information continues to expand and aggregate by multiple downsampling and convolutional layers, making the LR feature $f_{dd4}$ dense (most spatial positions of the feature contain rich information). + +As shown in Fig. 2 (b) and (c), the guidance feature can be obtained from any ED-Net, including single-branch ED-Net, multi-branch ED-Net, etc. In this paper, we generally extract five encoder features $\{f_{e1}, f_{e2}, f_{e3}, f_{e4}, f_{e5}\}$ at different resolution. Then, the decoder features $\{f_{d4}, f_{d3}, f_{d2}, f_{d1}\}$ and fused encoder-decoder features + +$\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\}$ are obtained in the decoder. We select the features $\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\}$ to guide the upsampling of the LR depth feature. These features are generally dense and cover comprehensive scene depth information, which can progressively resolve ambiguity in superresolving the feature of uneven depth distribution areas. Furthermore, the upsampling process effectively integrates these dense features that are underutilized in existing ED-Nets, thus improving the accuracy of depth completion. + +To reduce computational complexity, we reduce the channel number of these features $\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\}$ to the same as the LR depth feature by + +$$ +f _ {g i} = \mathbf {C o n v} _ {\mathbf {1} \times \mathbf {1}} (f _ {e d i}), \tag {1} +$$ + +where $\mathbf{Conv}_{\mathbf{1}\times \mathbf{1}}$ is a $1\times 1$ convolutional layer, and the feature $f_{gi}$ is employed as the guidance feature in the DFU. + +# 3.2. Depth Feature Upsampling + +As shown in Fig. 2 (a), the LR depth feature is upsampled to HR through four stages, which are guided by the features $\{f_{g4}, f_{g3}, f_{g2}, f_{g1}\}$ , respectively. To fully exploit the potential of the guidance feature, we propose a Confidence-aware Guidance Module (CGM), which first filters out unreliable values of the depth feature by predicting its confidence map, and performs the guidance operation with adaptive receptive fields to handle uneven depth distribution. The first stage of the DFU consists of a CGM, while other stages adopt the "upsampling + CGM". As shown in Fig. 3, for the depth feature $f_{ddi}$ , we denote the output feature of the CGM as $f_{ddi}'$ . In this paper, the upsampling is implemented by using a deconvolutional layer of stride 2, and the details of the CGM are introduced as follows: + +Confidence-aware. The LR depth feature is extracted from the input depth that is highly sparse and noisy. Besides, ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, we predict an elementwise attention map to filter out unreliable feature values. Specifically, we concatenate the depth feature $f_{ddi}$ and the guidance feature $f_{gi}$ . The confidence map $c_i$ is predicted by a $3 \times 3$ convolutional layer as: + +$$ +c _ {i} = \sigma \left(\mathbf {C o n v} _ {\mathbf {3} \times \mathbf {3}} \left(\mathbf {c o n c}. \left(f _ {d d i}, f _ {g i}\right)\right)\right), \tag {2} +$$ + +here $\sigma$ denotes the sigmoid function to compress the confidence value to $0 - 1$ . + +Guidance with Adaptive Receptive Fields (GARF). In the field of depth completion, guided convolutional networks have been studied widely for multi-modal feature fusion. For example, the pioneering GuideNet [32] predicts spatially-variant depthwise convolutional kernels [30] $\mathbf{W} \in \mathbb{R}^{hw \times k^2 \times c}$ from the RGB feature, and then applies them to extract the depth feature. Here, $h$ , $w$ , and $c$ are the height, weight, and channel number of the feature map, + +![](images/eb9867639c37d32f4a0004f70f382cbf483b2524b310546234122d9edfa2674f.jpg) +Figure 3. The Confidence-aware Guidance Module (CGM) and $k$ is the kernel size. To reduce computational complexity, [37] decomposes the depthwise kernel $\mathbf{W}_{\mathbf{P}_i} \in \mathbb{R}^{k^2 \times c}$ at each spatial location $\mathbf{p}_i$ into content-adaptive adaptors $\mathbf{A} \in \mathbb{R}^{k^2 \times m}$ multiplied by the spatially-shared component $\mathbf{D} \in \mathbb{R}^{m \times c}$ . The guided convolutional network has been proven to be effective since it can transfer structural information from the guidance feature to the target feature [12]. Therefore, in our method, we adopt this strategy to fully utilize the guidance feature. However, the kernel size of existing guided convolutional networks is usually fixed, which cannot handle the areas with uneven depth distribution well. To address this issue, we propose a guidance module with adaptive receptive fields. + +Recently, some novel dynamic convolution networks [27, 38] have shown that the convolutional kernel can be equivalently represented as a combination of pre-fixed bases, such as Fourier-Bessel(FB) bases [1]. Inspired by these works [27, 38], we further decompose the adaptors over multi-scale FB bases to selectively choose a receptive field at each spatial position. Specifically, we pre-generate $n$ FB bases of different sizes, such as $3 \times 3$ , $5 \times 5$ , and $7 \times 7$ , and then unify them to the same size by zero padding. Unlike [37] directly predicts the adaptors, we predict the weight of the multi-scale FB bases. As shown in Fig. 3, the adaptors with adaptive receptive fields can be obtained by multiplying the predicted weight with the FB bases. Then, we preform the guidance operation similar as [37] and obtain the refined depth feature $f_{gdi}$ by: + +$$ +f _ {g d i} = G A R F \left(c _ {i} \odot f _ {d d i}, f _ {g i}\right) \tag {3} +$$ + +Feature Updating. The confidence map $c_{i}$ assigns low confidence to the unreliable depth features, which are exactly the areas we want the guidance module to prioritize. Therefore, we obtain the output of CGM $f_{ddi}'$ by: + +$$ +f _ {d d i} ^ {\prime} = c _ {i} \odot f _ {d d i} + (1 - c _ {i}) \odot f _ {g d i} \tag {4} +$$ + +# 3.3. Going Deeper + +To further enhance the performance of the proposed method, we extend the depth feature upsampling network + +Table 1. The performance comparison between the baseline models and their improved model by using the multi-layer DFU. + +
KITTI Validate Dataset [5]NYUv2 Depth Dataset [23]
Params. [M]FLOPs [G]RMSE ↓ [mm]MAE ↓ [mm]iRMSE ↓ [1/km]iMAE ↓ [1/km]RMSE ↓ [mm]REL ↓ (×1000)δ1.25 ↑ [%]δ1.252 ↑ [%]δ1.253 ↑ [%]
Our single-branch ED-Net11.95291.24772.87210.262.280.95111.9416.6299.3299.8899.98
Improving by One-layer DFU+ 1.67+ 43.79750.58205.322.140.93100.6713.9299.4699.9199.98
Improving by Two-layer DFU+ 2.41+ 65.65745.27202.342.180.9398.9913.6399.4899.9199.98
Improving by Three-layer DFU+ 3.14+ 87.52746.98201.082.090.8997.7813.5999.4999.9199.98
Our Dual-branch ED-Net22.28498.84753.81204.392.120.92101.1214.4099.4699.9199.98
Improving by One-layer DFU+ 1.65+ 38.34741.39199.652.000.8898.6314.2199.4999.9299.98
Improving by Two-layer DFU+ 2.38+ 57.24738.20198.852.030.8797.6213.7099.5099.9299.98
Improving by Three-layer DFU+ 3.10+ 76.15736.60198.612.010.8796.2712.9299.5099.9299.98
+ +to multi-layer. In this subsection, the feature is marked as $f_{i}^{j}$ , where the superscript $j$ denotes the feature in the $j$ -th layer DFU. As shown in Fig. 2, we deepen the depth of each stage of the network. Specifically, we employ the feature $f_{ddi}^{j}$ of the $j$ -th layer DFU as the guidance feature $f_{gi}^{j+1}$ of the corresponding module of the $j+1$ -th layer DFU. + +# 4. Experiments + +# 4.1. Implementation Details + +We employ PyTorch to implement our model, and conduct experiments with GeForce RTX 3090 GPUs. Our training process is divided into two stages, which both employ the $L1 + L2$ loss to train 35 epochs. The initial learning rate is $10^{-3}$ , and it is reduced by $50\%$ every 5 epochs. We employ the AdamW optimizer with a batch size of 8, and set $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , weight decay is $10^{-6}$ . In the first stage, we first train the ED-Net to obtain the internal dense features that cover comprehensive scene depth information. Then, we train the depth feature upsampling network (DFU), in which these dense features are explicitly employed as the guidance features. For the multi-layer DFU, we only supervise the output of the last-layer DFU. + +# 4.2. Datasets and Metrics + +KITTI Dataset [5] consists of sparse depth maps projected from raw LiDAR scans and corresponding RGB images, which is a popular real-world autonomous driving dataset. The dataset contains 86k frames for training, 1k selected frames for validation, and 1k frames without ground truth that need to be tested on the online benchmark. + +NYUv2 Dataset [23] is a popular indoor RGBD dataset. Following existing works [16, 36, 45, 51], our model is trained with 50K images sampled from the training set, and tested on 654 officially labeled images. The images of size $640 \times 480$ are downsampled to half and then center-cropped to $304 \times 228$ for both training and inference. + +Evaluation Metrics. Following exiting methods [25, 36, 52], we employ Root Mean Squared Error (RMSE), Mean + +Absolute Error (MAE), inverse RMSE (iRMSE), inverse MAE (iMAE), mean absolute relative error (REL), and percentage of pixels satisfying $\delta_{\tau}$ for quantitative evaluation. + +# 4.3. Improving Single-branch ED-Net + +Following most methods [10, 20, 22, 42], the single-branch ED-Net used in this paper first extracts the depth and RGB features by two independent convolutional layers, and the features are concatenated and fed into an encoder-decoder network. The encoder consists of five stages, and each stage contains 2 residual blocks. The encoder feature is extracted at full-resolution in the first stage and is progressively halved in the next four stages. The feature channels of the five stages are 64, 128, 256, 256 and 256. We use the deconvolutional layer with stride 2 to upsample features, and fuse the encoder and decoder feature by the concatenate. As shown in Fig. 2 (b), the fused encoder-decoder features $f_{ed4}$ , $f_{ed3}$ , $f_{ed2}$ , $f_{ed1}$ are employed as the guidance features in the proposed DFU. + +As shown in Table 1, our single-branch ED-Net contains $11.95\mathrm{M}$ parameters and requires $291.24\mathrm{G}$ FLOPs, and the RMSE and MAE are $772.87\mathrm{mm}$ and $210.26\mathrm{mm}$ . Note that our single-branch ED-Net outperforms S2D [22] built on the Resnet-34 with fewer parameters since we use the effective stochastic depth strategy [8] in the residual block as [14]. We observe that the single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, the improvement in terms of various metrics is $22.29\mathrm{mm}$ in RMSE, $4.94\mathrm{mm}$ in MAE, 0.14 in iRMSE, and 0.02 in iMAE. Meanwhile, the performance in terms of RMSE and MAE is further improved when we deepen the DFU to two layers. However, this improvement is relatively small compared to the previous one. When we extend the DFU to three layers, the MAE is further reduced, while the results in the term of RMSE appear saturated. In addition, the experimental results conducted on the NYUv2 dataset consistently demonstrate that our DFU can effectively improve the performance of the single-branch ED-Net. + +Table 2. The performance comparison between LRRUs (SPN-based method) and their improved model by using the multi-layer DFU. + +
LRRU-MiniLRRU-TinyLRRU-SmallLRRU-Base
KITTI [5]Validate DatasetRMSE↓[mm]MAE↓[mm]iRMSE↓[1/km]iMAE↓[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]
Baseline806.27210.162.280.89763.80198.892.120.85745.31195.692.000.83729.49188.781.920.80
+ One-layer DFU787.28206.562.270.88747.39195.682.040.83732.42192.271.960.81718.27188.051.890.80
+ Two-layer DFU775.93202.712.200.86744.92193.102.000.82730.89190.561.940.81716.02186.691.890.80
+ Three-layer DFU767.67199.482.160.85742.83192.311.990.81729.24189.411.930.80713.32185.551.870.79
NYUv2 [23]Depth DatasetRMSE↓[mm]REL↓(x1000)δ1.25↑δ1.252↑RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252
Baseline100.8613.3499.4499.9195.3612.2599.5199.9293.3611.8599.5399.9291.2711.2199.5699.92
+ One-layer DFU99.2212.7799.4699.9192.5811.7699.5499.9391.5711.4899.5699.9390.7911.1999.5799.93
+ Two-layer DFU98.9412.7399.4799.9192.3111.6399.5599.9391.1511.4399.5699.9890.6111.2299.5799.93
+ Three-layer DFU98.2912.6999.4799.9192.2911.5999.5599.9291.0811.4399.5699.9890.7711.2799.5799.93
+ +# 4.4. Improving Multi-branch ED-Net + +We experimentally found that the performance gap between dual-branch networks, double encoder-decoder networks, and multiple encoder-decoder networks is not significant. Therefore, we select the most cost-effective dual-encoder network as the baseline model to verify the improvement effect of our proposed method on the multi-branch ED-Net. As shown in Fig. 2 (c), the difference between the dual-encoder ED-Net and single-branch ED-Net is that the dual-encoder ED-Net utilizes two encoders to extract features from the sparse depth and corresponding RGB image, respectively. Specifically, the RGB encoder works independently, and the extracted RGB features at multiple scales are gradually injected into the depth encoder to effectively integrate information from different modalities. + +As shown in Table 1, our dual-encoder ED-Net has nearly double the number of parameters and computational complexity in comparison to the single-branch ED-Net as it employs two encoders and the multi-scale fusion strategy. However, the dual-encoder ED-Net also outperforms the single-branch ED-Net significantly. When we apply one-layer DFU to the dual-encoder ED-Net, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by $12.42\mathrm{mm}$ , $4.74\mathrm{mm}$ , 0.12 and 0.04, respectively. The performance of the method is continuously improved as the DFU deepens, while the magnitude of the performance improvement gradually decreases. We observe that the performance of the method closes saturation when using the three-layer DFU. Additionally, similar conclusions can be drawn from the results on the NYUv2 dataset, which adequately demonstrate that our proposed method can effectively improve the performance of the dual-branch ED-Net. + +# 4.5. Improving SPN-based Model + +The SPN is a popular module to refine the predicted depth map. To validate the effectiveness of our method for SPN-based methods, we apply the proposed DFU to LRRU [36], which introduces an effective SPN model and achieves top + +ranking performance on the KITTI benchmark. As described in [36], LRRU has already utilized internal dense features of the guided-feature extraction network to guide the SPN model. However, these features are employed individually, and the features at different scales can not be aggregated to improve the robustness and effectiveness of the SPN model. To address this issue, we add the DFU between the guided-feature extraction network and the recurrent update process of the LRRU to integrate the information from the multi-scale guidance features (more details in the supplementary materials). + +As shown in Table 2, we conduct comprehensive experiments on four variants of LRRU with varying network scales. On the KITTI dataset, the performance of all four variants of LRRU is significantly improved by using the DFU, especially for the mini model. Specifically, by using one-layer DFU, the RMSE of LRRU-Mini is reduced by $18.99\mathrm{mm}$ , and the RMSE of LRRU-Base is reduced by $11.22\mathrm{mm}$ . Furthermore, the performance of LRRUs continues to enhance at a gradually decreasing rate when utilizing the multi-layer DFU. The experimental results on the NYUv2 dataset consistently demonstrate the effectiveness of our method. Noted that, due to the limited number of samples of the NYUv2 dataset, when we continue to add our method to the LRRU-Base model with a large network size, the network appears to be overfitting. Therefore, on the NYUv2 dataset, our method only has a limited performance improvement effect on the LRRU-Base model. + +# 4.6. Comparison with state-of-the-arts + +To evaluate our methods against state-of-the-art (SOTA) methods, we compare their experimental results on the KITTI benchmark (outdoor) and NYUv2 (indoor). As shown in Table 3, we report the results of our baseline methods and the improved methods by using three-layer DFU. Meanwhile, we select some representative methods from the last three years for comparison. Since most SOTA methods employ the multi-branch ED-Net structure, the performance of our single-branch ED-Net is slightly worse + +Table 3. Quantitative evaluation on the KITTI online leaderboard and NYUv2. The results of improved methods by using the three-layer DFU are highlighted with a gray background and the best and second-best results are highlighted in red and blue colors, respectively. + +
KITTI Online Benchmark [5]NYUv2 Depth Dataset [23]Publication
RMSE[mm]↓MAE[mm]↓iRMSE[1/km]↓iMAE[1/km]↓RMSE[m]↓REL↓δ1.25↑δ1.252↑δ1.252↑
TWISE [11]840.20195.582.080.820.0970.01399.699.9100.0CVPR 2021
FCFRNet [15]735.81217.152.200.980.1060.01599.599.9100.0AAAI 2021
PENet [7]730.08210.552.170.94-----ICRA 2021
ACMNet [49]744.91206.092.080.900.1050.01599.599.9100.0TIP 2021
PointFusion [9]741.90201.101.970.850.0900.01499.699.9100.0ICCV 2021
GFormer [29]721.48207.762.140.97-----CVPR 2022
DySPN [14]709.12192.711.880.820.0900.01299.699.9100.0AAAI 2022
GraphCSPN [18]738.41199.311.960.840.0900.01299.699.9100.0ECCV 2022
RigNet [44]712.66203.252.080.900.0900.01399.699.9100.0ECCV 2022
CompletionFormer [48]708.30203.452.010.880.0910.01299.699.9100.0CVPR 2023
BEV@DC [51]697.44189.441.830.820.0890.01299.699.9100.0CVPR 2023
PointDC [45]736.07201.871.970.870.0890.01299.699.9100.0ICCV 2023
Our Single-branch ED-Net745.16209.862.220.950.1120.01699.399.9100.0-
Improved Single-branch719.65201.922.060.910.0980.01499.599.9100.0-
Our Dual-branch ED-Net720.96203.732.070.920.1010.01499.599.9100.0-
Improved Dual-branch706.23199.141.990.890.0960.01399.599.9100.0-
LRRU-Base (SPN-based) [36]696.51189.961.870.810.0910.01199.699.9100.0ICCV 2023
Improved LRRU-Base686.46187.951.830.810.0910.01199.699.9100.0-
+ +in comparison. However, the performance of our single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, on the KITTI benchmark, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by $25.51 \mathrm{~mm}$ , $7.94 \mathrm{~mm}$ , 0.16, and 0.04, respectively. Besides, five metrics evaluated on the NYUv2 are also enhanced considerably. The experimental results demonstrate that the proposed DFU can effectively improve the performance of the single-branch ED-Net. Compared to the single-branch ED-Net, our dual-branch ED-Net shows better performance, which already outperforms the latest PointDC [45], GraphCSPN [18], GFormer [29], etc. in the term of RMSE. However, the proposed DFU still greatly improves the performance of the dual-branch ED-Net on two benchmarks. Note that our method is effective for the LRRU-Base (SPN-based method) as well, which is the current SOTA method on the KITTI benchmark. Specifically, the improved LRRU-Base by using three-layer DFU achieves new SOTA results, which ranks Top-1 on the KITTI benchmark. + +The results on the NYUv2 show that the methods [9, 18, 51, 51] that fuse 3D information generally achieve better results, such as BEV@DC [51] and PointDC [51]. Our method can also greatly improve the performance of the single-branch ED-Net and dual-branch ED-Net on NYUv2, while the performance improvement on LRRU-Base is negligible due to overfitting. Fig. 4 and Fig. 5 show the qualitative results of the baseline models and improved models by using three-layer DFU. Since our DFU effectively uses internal dense features of ED-Nets that cover comprehensive scene depth information, the improved method has more accurate results in fine and small structures, such as the gap area between two adjacent objects. + +![](images/86fc4bd26b2b5a3e18616478a8b0b2c54b8c468cac44408008262a074903d2b7.jpg) +Figure 4. Qualitative results on the NYUv2 depth dataset. + +# 4.7. Ablation Studies + +In this section, we conduct experiments on the KITTI dataset to verify the effectiveness of the confidence-aware guidance module, which consists of the confidence-aware model and the guidance model with adaptive receptive fields. As shown in Table 4 (a) and (e), we choose our single-branch ED-Net as the baseline, and its results are significantly improved by using standard one-layer DFU. + +Confidence-aware. In this paper, the LR depth feature is extracted from a highly sparse and noisy depth map, and ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, some values of the depth feature are unreliable. To filter out the unreliable depth feature values before the guidance module, we propose to predict an element-wise confidence map, which assigns these unreliable values a lower weight. Besides, we also employ the confidence map in the feature updating, which makes the guidance module focus on the unreliable values of the depth features. As shown in Table 4 (d) and (e), removing the confidence map increases the RMSE and + +![](images/51d8664aec3078399ac081e3d1b887d63ca3c7d7c254542df074083120c0fec0.jpg) + +![](images/faf364be559aa62806220c7335f196930d99441b1ab98ecf540953b9053e5487.jpg) +A.2 RGB Image + +![](images/01a99a459214160df3a4885361c055466da6cda844615abde10f4ec1de34d325.jpg) + +![](images/67d8d74f2ad0012ce2c53ad48f39f5f6544cfef5bf863139d713782f6e0afcd7.jpg) +A.1 RGB Image +B.1 Our Single-branch Result + +![](images/2d3da858926fc0130df96034070b96a22ca8f55190c5b934888abfc0e6051b01.jpg) +B.2 Our Dual-branch Result + +![](images/46bb1f2fd016bc1a7252db7e17831005c2701aae88ca1be30038ab878d024b11.jpg) +A.3 RGB Image +B.2 The LRRU-Base Result + +![](images/02bcc16540f0cf11d807a655051321fef0bd620daec879cfd379806d747686d5.jpg) +C.1 Improved Single-branch Result + +![](images/b9403dd2218f412e0be2cf176530c5be0276b19aeb0e8ad08608f14684a5386e.jpg) +C.2 Improved Dual-branch Result + +![](images/5b2cca80dc933742c3bb4430600f5afb2940e2f45b6f3c22a6fe4ec4b21356cc.jpg) +C.3 Improved LRRU-Base Result + +Table 4. Ablation studies on the KITTI validation dataset. + +
Confidence awareGARFRMSE [mm]MAE [mm]
(a)Our Single-branch ED-Net--772.87210.26
(b)Improving by one-layer DFU--761.24209.04
(c)Improving by one-layer DFU✓-758.67207.51
(d)Improving by one-layer DFU-✓756.31206.82
(e)Improving by one-layer DFU✓✓751.76203.09
+ +MAE of the improved method by $4.55\mathrm{mm}$ and $3.73\mathrm{mm}$ . + +Guidance with Adaptive Receptive Fields. Traditional guided convolutional networks [32, 37, 44] generally predict spatially-variant convolutional kernels from the guidance feature, and then employ the predicted kernels to extract the target feature. These networks have been proven effective since they can transfer the structural information from the guidance feature to the target feature. However, the predicted per-pixel kernel has a fixed size, which cannot be suitable for the areas with different depth distributions. To address this issue, we propose the guidance module with adaptive receptive fields (GARF). The results in Table 4 (c) and (e) show that the performance of the improved method without GARF is significantly decreased, which demonstrates the effectiveness of GARF. + +# 4.8. Experiments on fewer points + +It is crucial to analyze the generalization ability for sparser depth maps, which are usually provided in many practical applications. We train our baseline methods and their improved methods by using three-layer DFU on the standard KITTI (64-line LiDAR depth) and test the performance (MAE[mm]) on the depth map with fewer lines. The sparser depth map is obtained by the method provided by [50]. As shown in Fig. 6, the performance improvement by using the proposed DFU is more significant on sparser depth maps. The experimental results demonstrate that our approach not only improves the performance of the method, but also enhances the generalization ability for sparser depth maps. + +![](images/26e3284e4089965dfb893a873ddca8b1962e8e3c41a9210d2028414bc49f404e.jpg) +Figure 5. Qualitative results on the KITTI online leaderboard, including the baseline and improved models by using three-layer DFU. +Figure 6. The performance (MAE [mm]) on fewer points. + +# 4.9. Computational Cost + +We report the parameters and FLOPs of the method in Table 1. Since we pre-reduce the channel number of the feature, our method improves the performance of existing ED-Nets with limited computational overheads. Specifically, using one-layer DFU approximately requires extra $1.7\mathrm{M}$ parameters and $40\mathrm{G}$ FLOPs, which are small compared to those of the ED-Net itself. + +# 5. Conclusion + +In this paper, we have proposed the depth feature upsampling network (DFU), a plug-and-play module to improve existing ED-Net based methods. By the proposed confidence-aware guidance module, DFU effectively utilizes internal dense features of ED-Net to guide the depth feature upsampling, the completeness of these dense features is maintained in DFU. Furthermore, DFU can be extended to multi-layer to achieve better results. Experimental results show that our method can significantly improve existing ED-Nets, including single-branch ED-Nets, multi-branch ED-Nets, and SPN-based methods, with limited computational overheads. Meanwhile, the generalization ability for sparser depth is also enhanced. + +# Acknowledgments + +This work was supported by the National Science Fund of China (Grant Nos.62001394, 62271410, 62306238) and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Milton Abramowitz, Irene A Stegun, and Robert H Romer. Handbook of mathematical functions with formulas, graphs, and mathematical tables. courier corporation, 1988. 4 +[2] Xinjing Cheng, Peng Wang, and Ruigang Yang. Learning depth with convolutional spatial propagation network. IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 2019. 2, 3 +[3] Xinjing Cheng, Peng Wang, Chenye Guan, and Ruigang Yang. 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In this paper, we visualize the internal feature maps to analyze how the network densifies the input sparse depth. We find that the encoder feature of ED-Net focuses on the areas with input depth points around. To obtain a dense feature and thus estimate complete depth, the decoder feature tends to complement and enhance the encoder feature by skip-connection to make the fused encoder-decoder feature dense, resulting in the decoder feature also exhibits sparse. However, ED-Net obtains the sparse decoder feature from the dense fused feature at the previous stage, where the \"dense " + }, + { + "bbox": [ + 45, + 430, + 290, + 695 + ], + "type": "inline_equation", + "content": "\\Rightarrow" + }, + { + "bbox": [ + 45, + 430, + 290, + 695 + ], + "type": "text", + "content": " sparse\" process destroys the completeness of features and loses information. To address this issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. Furthermore, we propose a confidence-aware guidance module (CGM), which is confidence-aware and performs guidance" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 406, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 547, + 502 + ], + "type": "text", + "content": "with adaptive receptive fields (GARF), to fully exploit the potential of these dense features as guidance. Experimental results show that our DFU, a plug-and-play module, can significantly improve the performance of existing ED-Net based methods with limited computational overheads, and new SOTA results are achieved. Besides, the generalization capability on sparser depth is also enhanced. Project page: https://npucvr.github.io/DFU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 525, + 388, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 388, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 388, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": "Accurate and dense scene depth is crucial for various applications [13, 34, 41], such as autonomous navigation [33] and augmented reality [24]. Existing active depth sensors have been widely applied because they can obtain accurate depth information. However, the depth acquired by these sensors is generally highly sparse due to the imaging principles and power limitation. For instance, roughly " + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": " pixels in the depth provided by 64-line LiDAR have values [21, 22, 35]. To facilitate the use of the depth data, we need to address a sparse-to-dense problem in which the given sparse depth map is densified to the dense depth map, usually guided by the corresponding RGB image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "Depth completion is a challenging task as the input depth information is scarce. Existing approaches commonly" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 222, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 222, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 222, + 713 + ], + "type": "text", + "content": "*Corresponding author: daiyuchao@nwpu.edu.cn." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "21104" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "content": "consider this task as a pixel-wise regression problem and utilize an encoder-decoder network with skip-connection (ED-Net) to address it. For instance, the single-branch ED-Net [2, 14, 21, 22, 25] uses standard backbone networks [6, 19] as the encoder to extract features from the sparse depth and RGB images. Then, the decoder employs operations, such as the element-wise addition and transpose convolution, to fuse the encoder feature and upsampling. Recently, some multi-branch ED-Nets [4, 31, 32, 44, 47], including the dual-encoder ED-Net [4, 47] and the double encoder-decoder ED-Net[31, 32], etc., have been proposed. These methods employ separate branches to extract features from the sparse depth and RGB images, and internal features are fused at multiple scales. Although existing ED-Nets based methods have achieved considerable success [39, 48, 51], the ED-Net is often employed as a black box. how the network recovers a dense depth map from the input sparse depth has always been ambiguous." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": "To gain a deeper understanding of the ED-Net employed by depth completion, Fig. 1 visualizes internal features of the representative method S2D [22] through the feature heatmap [46]. The feature heatmap [46] is obtained by summing the value of the feature along the channel dimension and normalizing them to a range of " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "(0,1)" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": ", which reflects the spatial locations that the network focuses on at different stages and provides valuable insights to infer the behaviors of the network. We observe that although the sparse depth map and dense RGB image are both fed to the network, the shallow feature of the encoder primarily focuses on few regions where the sparse depth map has values. Through multiple downsampling and convolution, the sparse regions of interest continue to expand and aggregate, the encoder feature gradually becomes more \"dense\". As shown in Fig. 1, the lowest-resolution encoder feature " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{e4}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " has rich information at most spatial locations. However, to obtain a dense feature and thus estimate complete depth, the decoder tends to obtain a complementary feature for the corresponding encoder feature, which contains multiple \"dense " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "\\Rightarrow" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " sparse\" processes. For instance, the decoder feature " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{d1}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": ", which is skip-connected to " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{e1}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": ", tends to complement and enhance existing " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{e1}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " to make the fused encoder-decoder feature " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{ed1}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " dense. Therefore, the decoder feature " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{d1}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " also exhibits sparse. However, the sparse " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{d1}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " is derived from the dense " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "f_{ed2}" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " at the previous stage, where the \"dense " + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "inline_equation", + "content": "\\Rightarrow" + }, + { + "bbox": [ + 46, + 291, + 289, + 674 + ], + "type": "text", + "content": " sparse\" process destroys the completeness of features and loses information. Experiments on multi-branch networks also validate this observation, which is provided in the supplemental material. To conclude, existing ED-Nets have not fully utilized the internal dense features, thereby restricting the performance of ED-Net based methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "To address the issue, we present a depth feature upsampling network (DFU) that explicitly utilizes these dense features to guide the upsampling of a low-resolution (LR)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "depth feature to a high-resolution (HR) one. The completeness of features is maintained throughout the upsampling process, thus avoiding information loss. The multiscale dense features that cover comprehensive scene depth information can progressively resolve ambiguity in super-resolving the feature of uneven depth distribution areas. Meanwhile, the upsampling process can also effectively integrate these dense features into the HR depth feature to predict the dense depth. To further improve the effectiveness of the DFU, we propose a confidence-aware guidance module (CGM) to fully exploit the potential of these dense features as guidance. Specifically, we first filter out unreliable values of the depth feature by predicting its confidence map, and then perform the guidance operation with adaptive receptive fields. In addition, the proposed network can be extended to multi-layer to achieve better results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 265, + 493, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 265, + 493, + 275 + ], + "spans": [ + { + "bbox": [ + 317, + 265, + 493, + 275 + ], + "type": "text", + "content": "Our main contributions are summarized as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 282, + 545, + 464 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 282, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 282, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 306, + 282, + 545, + 341 + ], + "type": "text", + "content": "- We analyze the working mechanism of popular ED-Nets by visualizing the internal feature maps and reveal that multiple \"dense " + }, + { + "bbox": [ + 306, + 282, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\Rightarrow" + }, + { + "bbox": [ + 306, + 282, + 545, + 341 + ], + "type": "text", + "content": " sparse\" processes exist in the decoder network, which destroy the completeness of features and lose information." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 343, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 343, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 343, + 545, + 415 + ], + "type": "text", + "content": "- We propose a depth feature upsampling network with confidence-aware guidance module, which is a plug-and-play module, to significantly improve the performance of existing ED-Net based methods and enhance the generalization ability on sparser depth with limited computational overheads." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 417, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 417, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 545, + 464 + ], + "type": "text", + "content": "- Extensive experiments on popular datasets prove the effectiveness of our method on existing popular ED-Nets, including single-branch, multi-branch, and SPN-based networks, and new SOTA results are achieved." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 477, + 392, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 392, + 489 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 392, + 489 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": "Single-branch ED-Nets. The single-branch ED-Net contains one encoder and one decoder. The pioneer approaches [21, 26] concatenates the sparse depth and RGB image directly, and feeds them into a standard encoder-decoder network to predict the dense depth. Unlike using convolution in the last layer, [28] proposes to use the least squares to fit the relationship between the extracted features and depth values. Considering the gap between the RGB and depth information, subsequent methods [10, 20, 42] generally use two separate convolutional layers to extract features from the sparse depth and RGB image, respectively. Then, the multi-modal features are concatenated and fed into the network. This type of approach is simple and straightforward, but its performance is generally limited." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Multi-branch ED-Nets. Recently, some multi-branch ED-Nets [31, 32, 40, 44, 47] have been proposed for better extraction and fusion of the RGB and depth information. For example, the dual-encoder ED-Net [4, 47]" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "21105" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 70, + 521, + 200 + ], + "blocks": [ + { + "bbox": [ + 78, + 70, + 521, + 200 + ], + "lines": [ + { + "bbox": [ + 78, + 70, + 521, + 200 + ], + "spans": [ + { + "bbox": [ + 78, + 70, + 521, + 200 + ], + "type": "image", + "image_path": "2b71000cd9092358bca43740297f558359be64c02fc34034cb0b011fa429ec98.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 67, + 209, + 228, + 285 + ], + "blocks": [ + { + "bbox": [ + 227, + 201, + 380, + 209 + ], + "lines": [ + { + "bbox": [ + 227, + 201, + 380, + 209 + ], + "spans": [ + { + "bbox": [ + 227, + 201, + 380, + 209 + ], + "type": "text", + "content": "(a) Three-layer Depth feature upsampling network" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 67, + 209, + 228, + 285 + ], + "lines": [ + { + "bbox": [ + 67, + 209, + 228, + 285 + ], + "spans": [ + { + "bbox": [ + 67, + 209, + 228, + 285 + ], + "type": "image", + "image_path": "7c4eeb0feba97621cd7c8984debb0f8192c0ce6ea1d5576d0ab914f487a9808d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 109, + 287, + 187, + 296 + ], + "lines": [ + { + "bbox": [ + 109, + 287, + 187, + 296 + ], + "spans": [ + { + "bbox": [ + 109, + 287, + 187, + 296 + ], + "type": "text", + "content": "(b) Single-branch ED-Net" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 230, + 209, + 407, + 286 + ], + "blocks": [ + { + "bbox": [ + 230, + 209, + 407, + 286 + ], + "lines": [ + { + "bbox": [ + 230, + 209, + 407, + 286 + ], + "spans": [ + { + "bbox": [ + 230, + 209, + 407, + 286 + ], + "type": "image", + "image_path": "e313afa190bd65bf5da1e5c11f0aaeb7aa89c616b025cc7aae01fb8e1d874ea9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 281, + 287, + 356, + 296 + ], + "lines": [ + { + "bbox": [ + 281, + 287, + 356, + 296 + ], + "spans": [ + { + "bbox": [ + 281, + 287, + 356, + 296 + ], + "type": "text", + "content": "(c) Multi-branch ED-Net" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 412, + 209, + 526, + 287 + ], + "blocks": [ + { + "bbox": [ + 412, + 209, + 526, + 287 + ], + "lines": [ + { + "bbox": [ + 412, + 209, + 526, + 287 + ], + "spans": [ + { + "bbox": [ + 412, + 209, + 526, + 287 + ], + "type": "image", + "image_path": "8129bb0bcb33f9dd77ba0f7aafb144468f546e3883cb3baa5da4db17e8b6f812.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 298, + 545, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 298, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 545, + 321 + ], + "type": "text", + "content": "Figure 2. The proposed depth feature upsampling network (DFU). It explicitly employs the internal dense features of ED-Nets that are not fully utilized by existing methods to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 331, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 509 + ], + "type": "text", + "content": "commonly employs two separate encoders to extract features from RGB images and sparse depth, respectively. Then, the extracted RGB and depth features are fused at single-scale or multi-scale by the channel-wise concatenation, element-wise summation, or other sophisticated fusion modules [32, 37, 44, 47]. GuideNet [32] proposes a double encoder-decoder network, which extracts the RGB and depth feature by a whole encoder-decoder network. The decoder feature of the RGB branch and the encoder feature of the depth branch are fused by the guided convolutional network at multiple scales. The multiple encoder-decoder network is proposed by RigNet [44], which uses repetitive hourglass networks to extract discriminative RGB features, and the fusion of RGB and depth information is also performed in a repetitive manner." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": "SPN-based Networks. The spatial propagation network (SPN) [2, 3, 14, 18, 25, 43] is a hot topic, which iteratively refines the predicted depth by aggregating the reference and neighbor pixels. The initial SPN [17] updates each pixel by three adjacent pixels from the previous row or column. CSPN [2] improves it by updating all pixels simultaneously by fixed-local neighbors, and " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{CSPN}++" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " [3] assembles the results predicted by using the neighbors in different ranges. To obtain non-local neighbors, DSPN [43] and NLSPN [25] learn the offsets to the regular grid. DySPN [14] gives variable weights to neighbors with different distances to make the kernel weights change dynamically during the update process. GraphCSPN [18] integrates 3D information into the update process. LRRU [36] proposes to employ multiscale guidance features to guide the prediction of neighbors and weights, which makes them change adaptively throughout the update process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 329, + 388, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 329, + 388, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 329, + 388, + 342 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "text", + "content": "In this section, we present a depth feature upsampling network (DFU) that effectively utilizes internal dense features of ED-Net to guide the upsampling of a low-resolution (LR) depth feature to a high-resolution (HR) one. The DFU is introduced in three parts: (1) feature extraction, including extracting the LR depth feature and multi-scale dense features from ED-Net as guidance, (2) depth feature upsampling guided by the proposed confidence-aware module, (3) going deeper, where DFU is extended to multi-layer to obtain better results. For descriptive convenience, the feature is marked as " + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "inline_equation", + "content": "i = \\{1,2,3,4,5\\}" + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "text", + "content": " denotes the feature of different resolutions, namely " + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "inline_equation", + "content": "f_{i} \\in \\mathbb{R}^{H / n \\times W / n \\times D_{i}}" + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "inline_equation", + "content": "n = 2^{i - 1}" + }, + { + "bbox": [ + 304, + 350, + 545, + 504 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 514, + 421, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 421, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 421, + 526 + ], + "type": "text", + "content": "3.1. Features Extraction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "The LR depth feature " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "f_{dd4} \\in \\mathbb{R}^{H/8 \\times W/8 \\times D_{dd4}}" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " is extracted from the sparse input depth using a convolutional network, where " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "D_{dd4}" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " is set to 64 in this paper. The network consists of 8 residual blocks, 2 at full-resolution, 2 at 1/2-resolution, 2 at 1/4-resolution, and 2 at 1/8-resolution. Although the input depth is sparse, the depth information continues to expand and aggregate by multiple downsampling and convolutional layers, making the LR feature " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "f_{dd4}" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " dense (most spatial positions of the feature contain rich information)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "As shown in Fig. 2 (b) and (c), the guidance feature can be obtained from any ED-Net, including single-branch ED-Net, multi-branch ED-Net, etc. In this paper, we generally extract five encoder features " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{f_{e1}, f_{e2}, f_{e3}, f_{e4}, f_{e5}\\}" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " at different resolution. Then, the decoder features " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{f_{d4}, f_{d3}, f_{d2}, f_{d1}\\}" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " and fused encoder-decoder features" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "text", + "content": "21106" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " are obtained in the decoder. We select the features " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " to guide the upsampling of the LR depth feature. These features are generally dense and cover comprehensive scene depth information, which can progressively resolve ambiguity in superresolving the feature of uneven depth distribution areas. Furthermore, the upsampling process effectively integrates these dense features that are underutilized in existing ED-Nets, thus improving the accuracy of depth completion." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 287, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 287, + 216 + ], + "type": "text", + "content": "To reduce computational complexity, we reduce the channel number of these features " + }, + { + "bbox": [ + 46, + 180, + 287, + 216 + ], + "type": "inline_equation", + "content": "\\{f_{ed4}, f_{ed3}, f_{ed2}, f_{ed1}\\}" + }, + { + "bbox": [ + 46, + 180, + 287, + 216 + ], + "type": "text", + "content": " to the same as the LR depth feature by" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 118, + 225, + 287, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 225, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 118, + 225, + 287, + 239 + ], + "type": "interline_equation", + "content": "f _ {g i} = \\mathbf {C o n v} _ {\\mathbf {1} \\times \\mathbf {1}} (f _ {e d i}), \\tag {1}", + "image_path": "443c8fc1a20aec46b5bb231d18029c00492e4dce6876726dceb0985947408023.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "inline_equation", + "content": "\\mathbf{Conv}_{\\mathbf{1}\\times \\mathbf{1}}" + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "text", + "content": " convolutional layer, and the feature " + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "inline_equation", + "content": "f_{gi}" + }, + { + "bbox": [ + 46, + 247, + 287, + 272 + ], + "type": "text", + "content": " is employed as the guidance feature in the DFU." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 279, + 196, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 196, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 196, + 292 + ], + "type": "text", + "content": "3.2. Depth Feature Upsampling" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "text", + "content": "As shown in Fig. 2 (a), the LR depth feature is upsampled to HR through four stages, which are guided by the features " + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\{f_{g4}, f_{g3}, f_{g2}, f_{g1}\\}" + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "text", + "content": ", respectively. To fully exploit the potential of the guidance feature, we propose a Confidence-aware Guidance Module (CGM), which first filters out unreliable values of the depth feature by predicting its confidence map, and performs the guidance operation with adaptive receptive fields to handle uneven depth distribution. The first stage of the DFU consists of a CGM, while other stages adopt the \"upsampling + CGM\". As shown in Fig. 3, for the depth feature " + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "inline_equation", + "content": "f_{ddi}" + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "text", + "content": ", we denote the output feature of the CGM as " + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "inline_equation", + "content": "f_{ddi}'" + }, + { + "bbox": [ + 46, + 297, + 287, + 464 + ], + "type": "text", + "content": ". In this paper, the upsampling is implemented by using a deconvolutional layer of stride 2, and the details of the CGM are introduced as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "text", + "content": "Confidence-aware. The LR depth feature is extracted from the input depth that is highly sparse and noisy. Besides, ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, we predict an elementwise attention map to filter out unreliable feature values. Specifically, we concatenate the depth feature " + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "inline_equation", + "content": "f_{ddi}" + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "text", + "content": " and the guidance feature " + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "inline_equation", + "content": "f_{gi}" + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "text", + "content": ". The confidence map " + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "text", + "content": " is predicted by a " + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 465, + 287, + 560 + ], + "type": "text", + "content": " convolutional layer as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 571, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 571, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 88, + 571, + 287, + 583 + ], + "type": "interline_equation", + "content": "c _ {i} = \\sigma \\left(\\mathbf {C o n v} _ {\\mathbf {3} \\times \\mathbf {3}} \\left(\\mathbf {c o n c}. \\left(f _ {d d i}, f _ {g i}\\right)\\right)\\right), \\tag {2}", + "image_path": "cef39c7e3af7bbf678a298fa56cdadd31776568a1aa31fbcd92e3c2c2818ef67.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "type": "text", + "content": "here " + }, + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "type": "text", + "content": " denotes the sigmoid function to compress the confidence value to " + }, + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "type": "inline_equation", + "content": "0 - 1" + }, + { + "bbox": [ + 46, + 593, + 286, + 614 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": "Guidance with Adaptive Receptive Fields (GARF). In the field of depth completion, guided convolutional networks have been studied widely for multi-modal feature fusion. For example, the pioneering GuideNet [32] predicts spatially-variant depthwise convolutional kernels [30] " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{hw \\times k^2 \\times c}" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " from the RGB feature, and then applies them to extract the depth feature. Here, " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " are the height, weight, and channel number of the feature map," + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 73, + 547, + 215 + ], + "blocks": [ + { + "bbox": [ + 317, + 73, + 547, + 215 + ], + "lines": [ + { + "bbox": [ + 317, + 73, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 547, + 215 + ], + "type": "image", + "image_path": "eb9867639c37d32f4a0004f70f382cbf483b2524b310546234122d9edfa2674f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "lines": [ + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "text", + "content": "Figure 3. The Confidence-aware Guidance Module (CGM) and " + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "text", + "content": " is the kernel size. To reduce computational complexity, [37] decomposes the depthwise kernel " + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathbf{P}_i} \\in \\mathbb{R}^{k^2 \\times c}" + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "text", + "content": " at each spatial location " + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "text", + "content": " into content-adaptive adaptors " + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{k^2 \\times m}" + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "text", + "content": " multiplied by the spatially-shared component " + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\in \\mathbb{R}^{m \\times c}" + }, + { + "bbox": [ + 304, + 219, + 545, + 387 + ], + "type": "text", + "content": ". The guided convolutional network has been proven to be effective since it can transfer structural information from the guidance feature to the target feature [12]. Therefore, in our method, we adopt this strategy to fully utilize the guidance feature. However, the kernel size of existing guided convolutional networks is usually fixed, which cannot handle the areas with uneven depth distribution well. To address this issue, we propose a guidance module with adaptive receptive fields." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "content": "Recently, some novel dynamic convolution networks [27, 38] have shown that the convolutional kernel can be equivalently represented as a combination of pre-fixed bases, such as Fourier-Bessel(FB) bases [1]. Inspired by these works [27, 38], we further decompose the adaptors over multi-scale FB bases to selectively choose a receptive field at each spatial position. Specifically, we pre-generate " + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "content": " FB bases of different sizes, such as " + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "content": ", and then unify them to the same size by zero padding. Unlike [37] directly predicts the adaptors, we predict the weight of the multi-scale FB bases. As shown in Fig. 3, the adaptors with adaptive receptive fields can be obtained by multiplying the predicted weight with the FB bases. Then, we preform the guidance operation similar as [37] and obtain the refined depth feature " + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "inline_equation", + "content": "f_{gdi}" + }, + { + "bbox": [ + 304, + 388, + 545, + 567 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 362, + 574, + 545, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 574, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 362, + 574, + 545, + 588 + ], + "type": "interline_equation", + "content": "f _ {g d i} = G A R F \\left(c _ {i} \\odot f _ {d d i}, f _ {g i}\\right) \\tag {3}", + "image_path": "30b0f7f5821b6b2f904eb7a874718f57ed02ae84670412c2e3dac145670b95b9.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "Feature Updating. The confidence map " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " assigns low confidence to the unreliable depth features, which are exactly the areas we want the guidance module to prioritize. Therefore, we obtain the output of CGM " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "f_{ddi}'" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 353, + 651, + 545, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 651, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 353, + 651, + 545, + 664 + ], + "type": "interline_equation", + "content": "f _ {d d i} ^ {\\prime} = c _ {i} \\odot f _ {d d i} + (1 - c _ {i}) \\odot f _ {g d i} \\tag {4}", + "image_path": "fbaad9eb042f4a95dcd86ef8befaf803ba57917dc33c93f9f953665477400351.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 671, + 392, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 392, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 392, + 684 + ], + "type": "text", + "content": "3.3. Going Deeper" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "To further enhance the performance of the proposed method, we extend the depth feature upsampling network" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 741 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 741 + ], + "type": "text", + "content": "21107" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 83, + 547, + 224 + ], + "blocks": [ + { + "bbox": [ + 70, + 71, + 521, + 81 + ], + "lines": [ + { + "bbox": [ + 70, + 71, + 521, + 81 + ], + "spans": [ + { + "bbox": [ + 70, + 71, + 521, + 81 + ], + "type": "text", + "content": "Table 1. The performance comparison between the baseline models and their improved model by using the multi-layer DFU." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 83, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 48, + 83, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 48, + 83, + 547, + 224 + ], + "type": "table", + "html": "
KITTI Validate Dataset [5]NYUv2 Depth Dataset [23]
Params. [M]FLOPs [G]RMSE ↓ [mm]MAE ↓ [mm]iRMSE ↓ [1/km]iMAE ↓ [1/km]RMSE ↓ [mm]REL ↓ (×1000)δ1.25 ↑ [%]δ1.252 ↑ [%]δ1.253 ↑ [%]
Our single-branch ED-Net11.95291.24772.87210.262.280.95111.9416.6299.3299.8899.98
Improving by One-layer DFU+ 1.67+ 43.79750.58205.322.140.93100.6713.9299.4699.9199.98
Improving by Two-layer DFU+ 2.41+ 65.65745.27202.342.180.9398.9913.6399.4899.9199.98
Improving by Three-layer DFU+ 3.14+ 87.52746.98201.082.090.8997.7813.5999.4999.9199.98
Our Dual-branch ED-Net22.28498.84753.81204.392.120.92101.1214.4099.4699.9199.98
Improving by One-layer DFU+ 1.65+ 38.34741.39199.652.000.8898.6314.2199.4999.9299.98
Improving by Two-layer DFU+ 2.38+ 57.24738.20198.852.030.8797.6213.7099.5099.9299.98
Improving by Three-layer DFU+ 3.10+ 76.15736.60198.612.010.8796.2712.9299.5099.9299.98
", + "image_path": "822a7f903f09503c02b5fe4e8e4a0d930422237fee38e058470cc6a84dd9309a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": "to multi-layer. In this subsection, the feature is marked as " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "f_{i}^{j}" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": ", where the superscript " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": " denotes the feature in the " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": "-th layer DFU. As shown in Fig. 2, we deepen the depth of each stage of the network. Specifically, we employ the feature " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "f_{ddi}^{j}" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": "-th layer DFU as the guidance feature " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "f_{gi}^{j+1}" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": " of the corresponding module of the " + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "inline_equation", + "content": "j+1" + }, + { + "bbox": [ + 46, + 236, + 287, + 308 + ], + "type": "text", + "content": "-th layer DFU." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 321, + 128, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 321, + 128, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 128, + 335 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 341, + 180, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 180, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 180, + 354 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": "We employ PyTorch to implement our model, and conduct experiments with GeForce RTX 3090 GPUs. Our training process is divided into two stages, which both employ the " + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "inline_equation", + "content": "L1 + L2" + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": " loss to train 35 epochs. The initial learning rate is " + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": ", and it is reduced by " + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": " every 5 epochs. We employ the AdamW optimizer with a batch size of 8, and set " + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": ", weight decay is " + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "inline_equation", + "content": "10^{-6}" + }, + { + "bbox": [ + 46, + 361, + 287, + 515 + ], + "type": "text", + "content": ". In the first stage, we first train the ED-Net to obtain the internal dense features that cover comprehensive scene depth information. Then, we train the depth feature upsampling network (DFU), in which these dense features are explicitly employed as the guidance features. For the multi-layer DFU, we only supervise the output of the last-layer DFU." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 525, + 168, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 168, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 168, + 537 + ], + "type": "text", + "content": "4.2. Datasets and Metrics" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 544, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 615 + ], + "type": "text", + "content": "KITTI Dataset [5] consists of sparse depth maps projected from raw LiDAR scans and corresponding RGB images, which is a popular real-world autonomous driving dataset. The dataset contains 86k frames for training, 1k selected frames for validation, and 1k frames without ground truth that need to be tested on the online benchmark." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "text", + "content": "NYUv2 Dataset [23] is a popular indoor RGBD dataset. Following existing works [16, 36, 45, 51], our model is trained with 50K images sampled from the training set, and tested on 654 officially labeled images. The images of size " + }, + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "text", + "content": " are downsampled to half and then center-cropped to " + }, + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "inline_equation", + "content": "304 \\times 228" + }, + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "text", + "content": " for both training and inference." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. Following exiting methods [25, 36, 52], we employ Root Mean Squared Error (RMSE), Mean" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 236, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 236, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 545, + 274 + ], + "type": "text", + "content": "Absolute Error (MAE), inverse RMSE (iRMSE), inverse MAE (iMAE), mean absolute relative error (REL), and percentage of pixels satisfying " + }, + { + "bbox": [ + 305, + 236, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\delta_{\\tau}" + }, + { + "bbox": [ + 305, + 236, + 545, + 274 + ], + "type": "text", + "content": " for quantitative evaluation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 292, + 485, + 305 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 292, + 485, + 305 + ], + "spans": [ + { + "bbox": [ + 305, + 292, + 485, + 305 + ], + "type": "text", + "content": "4.3. Improving Single-branch ED-Net" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "text", + "content": "Following most methods [10, 20, 22, 42], the single-branch ED-Net used in this paper first extracts the depth and RGB features by two independent convolutional layers, and the features are concatenated and fed into an encoder-decoder network. The encoder consists of five stages, and each stage contains 2 residual blocks. The encoder feature is extracted at full-resolution in the first stage and is progressively halved in the next four stages. The feature channels of the five stages are 64, 128, 256, 256 and 256. We use the deconvolutional layer with stride 2 to upsample features, and fuse the encoder and decoder feature by the concatenate. As shown in Fig. 2 (b), the fused encoder-decoder features " + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "inline_equation", + "content": "f_{ed4}" + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "inline_equation", + "content": "f_{ed3}" + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "inline_equation", + "content": "f_{ed2}" + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "inline_equation", + "content": "f_{ed1}" + }, + { + "bbox": [ + 304, + 314, + 545, + 482 + ], + "type": "text", + "content": " are employed as the guidance features in the proposed DFU." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": "As shown in Table 1, our single-branch ED-Net contains " + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "inline_equation", + "content": "11.95\\mathrm{M}" + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": " parameters and requires " + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "inline_equation", + "content": "291.24\\mathrm{G}" + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": " FLOPs, and the RMSE and MAE are " + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "inline_equation", + "content": "772.87\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "inline_equation", + "content": "210.26\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": ". Note that our single-branch ED-Net outperforms S2D [22] built on the Resnet-34 with fewer parameters since we use the effective stochastic depth strategy [8] in the residual block as [14]. We observe that the single-branch ED-Net is significantly improved by using one-layer DFU. Specifically, the improvement in terms of various metrics is " + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "inline_equation", + "content": "22.29\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": " in RMSE, " + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "inline_equation", + "content": "4.94\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": " in MAE, 0.14 in iRMSE, and 0.02 in iMAE. Meanwhile, the performance in terms of RMSE and MAE is further improved when we deepen the DFU to two layers. However, this improvement is relatively small compared to the previous one. When we extend the DFU to three layers, the MAE is further reduced, while the results in the term of RMSE appear saturated. In addition, the experimental results conducted on the NYUv2 dataset consistently demonstrate that our DFU can effectively improve the performance of the single-branch ED-Net." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "21108" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 82, + 547, + 235 + ], + "blocks": [ + { + "bbox": [ + 54, + 71, + 538, + 81 + ], + "lines": [ + { + "bbox": [ + 54, + 71, + 538, + 81 + ], + "spans": [ + { + "bbox": [ + 54, + 71, + 538, + 81 + ], + "type": "text", + "content": "Table 2. The performance comparison between LRRUs (SPN-based method) and their improved model by using the multi-layer DFU." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 82, + 547, + 235 + ], + "lines": [ + { + "bbox": [ + 48, + 82, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 48, + 82, + 547, + 235 + ], + "type": "table", + "html": "
LRRU-MiniLRRU-TinyLRRU-SmallLRRU-Base
KITTI [5]Validate DatasetRMSE↓[mm]MAE↓[mm]iRMSE↓[1/km]iMAE↓[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]RMSE[mm]MAE[mm]iRMSE[1/km]iMAE[1/km]
Baseline806.27210.162.280.89763.80198.892.120.85745.31195.692.000.83729.49188.781.920.80
+ One-layer DFU787.28206.562.270.88747.39195.682.040.83732.42192.271.960.81718.27188.051.890.80
+ Two-layer DFU775.93202.712.200.86744.92193.102.000.82730.89190.561.940.81716.02186.691.890.80
+ Three-layer DFU767.67199.482.160.85742.83192.311.990.81729.24189.411.930.80713.32185.551.870.79
NYUv2 [23]Depth DatasetRMSE↓[mm]REL↓(x1000)δ1.25↑δ1.252↑RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252RMSE[mm]REL(x1000)δ1.25δ1.252
Baseline100.8613.3499.4499.9195.3612.2599.5199.9293.3611.8599.5399.9291.2711.2199.5699.92
+ One-layer DFU99.2212.7799.4699.9192.5811.7699.5499.9391.5711.4899.5699.9390.7911.1999.5799.93
+ Two-layer DFU98.9412.7399.4799.9192.3111.6399.5599.9391.1511.4399.5699.9890.6111.2299.5799.93
+ Three-layer DFU98.2912.6999.4799.9192.2911.5999.5599.9291.0811.4399.5699.9890.7711.2799.5799.93
", + "image_path": "d117afc8578ff2fa25a74c03e19d48246752bcfcfcbe1daa9607986cac0a06f8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 247, + 224, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 224, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 224, + 259 + ], + "type": "text", + "content": "4.4. Improving Multi-branch ED-Net" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 265, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 432 + ], + "type": "text", + "content": "We experimentally found that the performance gap between dual-branch networks, double encoder-decoder networks, and multiple encoder-decoder networks is not significant. Therefore, we select the most cost-effective dual-encoder network as the baseline model to verify the improvement effect of our proposed method on the multi-branch ED-Net. As shown in Fig. 2 (c), the difference between the dual-encoder ED-Net and single-branch ED-Net is that the dual-encoder ED-Net utilizes two encoders to extract features from the sparse depth and corresponding RGB image, respectively. Specifically, the RGB encoder works independently, and the extracted RGB features at multiple scales are gradually injected into the depth encoder to effectively integrate information from different modalities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "type": "text", + "content": "As shown in Table 1, our dual-encoder ED-Net has nearly double the number of parameters and computational complexity in comparison to the single-branch ED-Net as it employs two encoders and the multi-scale fusion strategy. However, the dual-encoder ED-Net also outperforms the single-branch ED-Net significantly. When we apply one-layer DFU to the dual-encoder ED-Net, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by " + }, + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "type": "inline_equation", + "content": "12.42\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "type": "inline_equation", + "content": "4.74\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 434, + 288, + 637 + ], + "type": "text", + "content": ", 0.12 and 0.04, respectively. The performance of the method is continuously improved as the DFU deepens, while the magnitude of the performance improvement gradually decreases. We observe that the performance of the method closes saturation when using the three-layer DFU. Additionally, similar conclusions can be drawn from the results on the NYUv2 dataset, which adequately demonstrate that our proposed method can effectively improve the performance of the dual-branch ED-Net." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 206, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 206, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 206, + 659 + ], + "type": "text", + "content": "4.5. Improving SPN-based Model" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "The SPN is a popular module to refine the predicted depth map. To validate the effectiveness of our method for SPN-based methods, we apply the proposed DFU to LRRU [36], which introduces an effective SPN model and achieves top" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 247, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 378 + ], + "type": "text", + "content": "ranking performance on the KITTI benchmark. As described in [36], LRRU has already utilized internal dense features of the guided-feature extraction network to guide the SPN model. However, these features are employed individually, and the features at different scales can not be aggregated to improve the robustness and effectiveness of the SPN model. To address this issue, we add the DFU between the guided-feature extraction network and the recurrent update process of the LRRU to integrate the information from the multi-scale guidance features (more details in the supplementary materials)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "type": "text", + "content": "As shown in Table 2, we conduct comprehensive experiments on four variants of LRRU with varying network scales. On the KITTI dataset, the performance of all four variants of LRRU is significantly improved by using the DFU, especially for the mini model. Specifically, by using one-layer DFU, the RMSE of LRRU-Mini is reduced by " + }, + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "type": "inline_equation", + "content": "18.99\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "type": "text", + "content": ", and the RMSE of LRRU-Base is reduced by " + }, + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "type": "inline_equation", + "content": "11.22\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 379, + 546, + 582 + ], + "type": "text", + "content": ". Furthermore, the performance of LRRUs continues to enhance at a gradually decreasing rate when utilizing the multi-layer DFU. The experimental results on the NYUv2 dataset consistently demonstrate the effectiveness of our method. Noted that, due to the limited number of samples of the NYUv2 dataset, when we continue to add our method to the LRRU-Base model with a large network size, the network appears to be overfitting. Therefore, on the NYUv2 dataset, our method only has a limited performance improvement effect on the LRRU-Base model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 588, + 488, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 588, + 488, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 588, + 488, + 600 + ], + "type": "text", + "content": "4.6. Comparison with state-of-the-arts" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "To evaluate our methods against state-of-the-art (SOTA) methods, we compare their experimental results on the KITTI benchmark (outdoor) and NYUv2 (indoor). As shown in Table 3, we report the results of our baseline methods and the improved methods by using three-layer DFU. Meanwhile, we select some representative methods from the last three years for comparison. Since most SOTA methods employ the multi-branch ED-Net structure, the performance of our single-branch ED-Net is slightly worse" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "21109" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 94, + 547, + 306 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation on the KITTI online leaderboard and NYUv2. The results of improved methods by using the three-layer DFU are highlighted with a gray background and the best and second-best results are highlighted in red and blue colors, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 94, + 547, + 306 + ], + "lines": [ + { + "bbox": [ + 47, + 94, + 547, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 94, + 547, + 306 + ], + "type": "table", + "html": "
KITTI Online Benchmark [5]NYUv2 Depth Dataset [23]Publication
RMSE[mm]↓MAE[mm]↓iRMSE[1/km]↓iMAE[1/km]↓RMSE[m]↓REL↓δ1.25↑δ1.252↑δ1.252↑
TWISE [11]840.20195.582.080.820.0970.01399.699.9100.0CVPR 2021
FCFRNet [15]735.81217.152.200.980.1060.01599.599.9100.0AAAI 2021
PENet [7]730.08210.552.170.94-----ICRA 2021
ACMNet [49]744.91206.092.080.900.1050.01599.599.9100.0TIP 2021
PointFusion [9]741.90201.101.970.850.0900.01499.699.9100.0ICCV 2021
GFormer [29]721.48207.762.140.97-----CVPR 2022
DySPN [14]709.12192.711.880.820.0900.01299.699.9100.0AAAI 2022
GraphCSPN [18]738.41199.311.960.840.0900.01299.699.9100.0ECCV 2022
RigNet [44]712.66203.252.080.900.0900.01399.699.9100.0ECCV 2022
CompletionFormer [48]708.30203.452.010.880.0910.01299.699.9100.0CVPR 2023
BEV@DC [51]697.44189.441.830.820.0890.01299.699.9100.0CVPR 2023
PointDC [45]736.07201.871.970.870.0890.01299.699.9100.0ICCV 2023
Our Single-branch ED-Net745.16209.862.220.950.1120.01699.399.9100.0-
Improved Single-branch719.65201.922.060.910.0980.01499.599.9100.0-
Our Dual-branch ED-Net720.96203.732.070.920.1010.01499.599.9100.0-
Improved Dual-branch706.23199.141.990.890.0960.01399.599.9100.0-
LRRU-Base (SPN-based) [36]696.51189.961.870.810.0910.01199.699.9100.0ICCV 2023
Improved LRRU-Base686.46187.951.830.810.0910.01199.699.9100.0-
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Specifically, on the KITTI benchmark, the errors including RMSE, MAE, iRMSE, and iMAE are reduced by " + }, + { + "bbox": [ + 46, + 316, + 289, + 555 + ], + "type": "inline_equation", + "content": "25.51 \\mathrm{~mm}" + }, + { + "bbox": [ + 46, + 316, + 289, + 555 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 316, + 289, + 555 + ], + "type": "inline_equation", + "content": "7.94 \\mathrm{~mm}" + }, + { + "bbox": [ + 46, + 316, + 289, + 555 + ], + "type": "text", + "content": ", 0.16, and 0.04, respectively. Besides, five metrics evaluated on the NYUv2 are also enhanced considerably. The experimental results demonstrate that the proposed DFU can effectively improve the performance of the single-branch ED-Net. Compared to the single-branch ED-Net, our dual-branch ED-Net shows better performance, which already outperforms the latest PointDC [45], GraphCSPN [18], GFormer [29], etc. in the term of RMSE. However, the proposed DFU still greatly improves the performance of the dual-branch ED-Net on two benchmarks. Note that our method is effective for the LRRU-Base (SPN-based method) as well, which is the current SOTA method on the KITTI benchmark. Specifically, the improved LRRU-Base by using three-layer DFU achieves new SOTA results, which ranks Top-1 on the KITTI benchmark." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "The results on the NYUv2 show that the methods [9, 18, 51, 51] that fuse 3D information generally achieve better results, such as BEV@DC [51] and PointDC [51]. Our method can also greatly improve the performance of the single-branch ED-Net and dual-branch ED-Net on NYUv2, while the performance improvement on LRRU-Base is negligible due to overfitting. Fig. 4 and Fig. 5 show the qualitative results of the baseline models and improved models by using three-layer DFU. Since our DFU effectively uses internal dense features of ED-Nets that cover comprehensive scene depth information, the improved method has more accurate results in fine and small structures, such as the gap area between two adjacent objects." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 309, + 316, + 537, + 449 + ], + "blocks": [ + { + "bbox": [ + 309, + 316, + 537, + 449 + ], + "lines": [ + { + "bbox": [ + 309, + 316, + 537, + 449 + ], + "spans": [ + { + "bbox": [ + 309, + 316, + 537, + 449 + ], + "type": "image", + "image_path": "86fc4bd26b2b5a3e18616478a8b0b2c54b8c468cac44408008262a074903d2b7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 449, + 530, + 460 + ], + "lines": [ + { + "bbox": [ + 321, + 449, + 530, + 460 + ], + "spans": [ + { + "bbox": [ + 321, + 449, + 530, + 460 + ], + "type": "text", + "content": "Figure 4. Qualitative results on the NYUv2 depth dataset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 466, + 406, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 406, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 406, + 477 + ], + "type": "text", + "content": "4.7. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 485, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 569 + ], + "type": "text", + "content": "In this section, we conduct experiments on the KITTI dataset to verify the effectiveness of the confidence-aware guidance module, which consists of the confidence-aware model and the guidance model with adaptive receptive fields. As shown in Table 4 (a) and (e), we choose our single-branch ED-Net as the baseline, and its results are significantly improved by using standard one-layer DFU." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Confidence-aware. In this paper, the LR depth feature is extracted from a highly sparse and noisy depth map, and ambiguity in super-resolving the feature of uneven depth distribution areas often exists. Therefore, some values of the depth feature are unreliable. To filter out the unreliable depth feature values before the guidance module, we propose to predict an element-wise confidence map, which assigns these unreliable values a lower weight. 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Ablation studies on the KITTI validation dataset." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 273, + 283, + 360 + ], + "lines": [ + { + "bbox": [ + 48, + 273, + 283, + 360 + ], + "spans": [ + { + "bbox": [ + 48, + 273, + 283, + 360 + ], + "type": "table", + "html": "
Confidence awareGARFRMSE [mm]MAE [mm]
(a)Our Single-branch ED-Net--772.87210.26
(b)Improving by one-layer DFU--761.24209.04
(c)Improving by one-layer DFU✓-758.67207.51
(d)Improving by one-layer DFU-✓756.31206.82
(e)Improving by one-layer DFU✓✓751.76203.09
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Traditional guided convolutional networks [32, 37, 44] generally predict spatially-variant convolutional kernels from the guidance feature, and then employ the predicted kernels to extract the target feature. These networks have been proven effective since they can transfer the structural information from the guidance feature to the target feature. However, the predicted per-pixel kernel has a fixed size, which cannot be suitable for the areas with different depth distributions. To address this issue, we propose the guidance module with adaptive receptive fields (GARF). The results in Table 4 (c) and (e) show that the performance of the improved method without GARF is significantly decreased, which demonstrates the effectiveness of GARF." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 552, + 204, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 204, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 204, + 565 + ], + "type": "text", + "content": "4.8. Experiments on fewer points" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": "It is crucial to analyze the generalization ability for sparser depth maps, which are usually provided in many practical applications. We train our baseline methods and their improved methods by using three-layer DFU on the standard KITTI (64-line LiDAR depth) and test the performance (MAE[mm]) on the depth map with fewer lines. The sparser depth map is obtained by the method provided by [50]. As shown in Fig. 6, the performance improvement by using the proposed DFU is more significant on sparser depth maps. The experimental results demonstrate that our approach not only improves the performance of the method, but also enhances the generalization ability for sparser depth maps." + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 312, + 262, + 536, + 344 + ], + "blocks": [ + { + "bbox": [ + 55, + 239, + 537, + 251 + ], + "lines": [ + { + "bbox": [ + 55, + 239, + 537, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 239, + 537, + 251 + ], + "type": "text", + "content": "Figure 5. Qualitative results on the KITTI online leaderboard, including the baseline and improved models by using three-layer DFU." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 262, + 536, + 344 + ], + "lines": [ + { + "bbox": [ + 312, + 262, + 536, + 344 + ], + "spans": [ + { + "bbox": [ + 312, + 262, + 536, + 344 + ], + "type": "image", + "image_path": "26e3284e4089965dfb893a873ddca8b1962e8e3c41a9210d2028414bc49f404e.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 346, + 529, + 357 + ], + "lines": [ + { + "bbox": [ + 321, + 346, + 529, + 357 + ], + "spans": [ + { + "bbox": [ + 321, + 346, + 529, + 357 + ], + "type": "text", + "content": "Figure 6. The performance (MAE [mm]) on fewer points." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 357, + 424, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 424, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 424, + 370 + ], + "type": "text", + "content": "4.9. Computational Cost" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "type": "text", + "content": "We report the parameters and FLOPs of the method in Table 1. Since we pre-reduce the channel number of the feature, our method improves the performance of existing ED-Nets with limited computational overheads. Specifically, using one-layer DFU approximately requires extra " + }, + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "type": "inline_equation", + "content": "1.7\\mathrm{M}" + }, + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "type": "text", + "content": " parameters and " + }, + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "type": "inline_equation", + "content": "40\\mathrm{G}" + }, + { + "bbox": [ + 304, + 376, + 545, + 459 + ], + "type": "text", + "content": " FLOPs, which are small compared to those of the ED-Net itself." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 491, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 646 + ], + "type": "text", + "content": "In this paper, we have proposed the depth feature upsampling network (DFU), a plug-and-play module to improve existing ED-Net based methods. By the proposed confidence-aware guidance module, DFU effectively utilizes internal dense features of ED-Net to guide the depth feature upsampling, the completeness of these dense features is maintained in DFU. Furthermore, DFU can be extended to multi-layer to achieve better results. Experimental results show that our method can significantly improve existing ED-Nets, including single-branch ED-Nets, multi-branch ED-Nets, and SPN-based methods, with limited computational overheads. 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Alvarez $^{2}$", + "bbox": [ + 84, + 179, + 890, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ CUHK $^{2}$ NVIDIA $^{3}$ UC Berkeley $^{4}$ Caltech", + "bbox": [ + 279, + 210, + 692, + 231 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/403c9b7771c31a6773df33add2d2ccdd1c324155623c44f8ad4f132053e8a7c4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 257, + 890, + 385 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e00e77f6bf713c203e8490e2363f5ff370d4b7d83c9e731fa573f8fbd97af517.jpg", + "image_caption": [ + "DID-M3D" + ], + "image_footnote": [], + "bbox": [ + 81, + 392, + 480, + 467 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3ed62fcae65dc8d232aa06bd15db7076cf51340c7edceebf29625bd795282350.jpg", + "image_caption": [ + "LR3D (Ours)", + "Figure 1. Upper: Without 3D annotations beyond $40\\mathrm{m}$ , LR3D enables the predictions of 3D boxes for extremely distant objects over $200\\mathrm{m}$ (right, in green) based on the inputs of image and 2D box (left). Lower: Existing methods fail to detect 3D objects beyond the 3D supervision range, e.g., $40\\mathrm{m}$ for this case. With LR3D, these remote missing objects are well detected." + ], + "image_footnote": [], + "bbox": [ + 488, + 393, + 887, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 537, + 313, + 553 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Improving the detection of distant 3d objects is an important yet challenging task. For camera-based 3D perception, the annotation of 3d bounding relies heavily on LiDAR for accurate depth information. As such, the distance of annotation is often limited due to the sparsity of LiDAR points on distant objects, which hampers the capability of existing detectors for long-range scenarios. We address this challenge by considering only 2D box supervision for distant objects since they are easy to annotate. We propose LR3D, a framework that learns to recover the missing depth of distant objects. LR3D adopts an implicit projection head to learn the generation of mapping between 2D boxes and depth using the 3D supervision on close objects. This mapping allows the depth estimation of distant objects conditioned on their 2D boxes, making long-range 3D detection with 2D supervision feasible. Experiments show that without distant 3D annotations, LR3D allows camera-based methods to detect distant objects (over $200m$ ) with comparable accuracy to full 3D supervision. Our framework is general, and could widely benefit 3D detection methods to a large extent.", + "bbox": [ + 73, + 561, + 473, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 537, + 630, + 553 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Camera-based 3D object detection [1-7] is an important task in autonomous driving aiming to localize and classify objects in 3D space with monocular or multi-view image input. Detecting distant objects with camera input is both important and challenging. On one hand, the ability to detect objects at distance is needed for planning, especially for highway scenarios. According to [8], at 60 miles/hour, the typical stopping distance for a vehicle is 73 meters and it grows significantly under harsh road conditions such as having wet surface [9-11]. On the other hand, the detection range of camera-based methods depends heavily on the distance range of 3D annotations. For example, these methods work well within the distance range with abundant 3D annotations (e.g., $\\sim 70$ meters on KITTI [12] and nuScenes [13]), but often fail beyond this range where 3D annotations are missing. This indicates the importance to improve distant 3D object detection with longer 3D annotation range.", + "bbox": [ + 496, + 566, + 890, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Though of great importance, increasing the range of 3D annotation is not easy. One main challenge is the sparsity of LiDAR points at longer distances. LiDAR is typically the main reference for axial depth information in 3D annotation. For distant objects with few or even no LiDAR points,", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during internship / affiliation with NVIDIA.", + "bbox": [ + 93, + 875, + 393, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author: zhidingy@nvidia.com", + "bbox": [ + 98, + 888, + 341, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14853", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "labeling their 3D bounding boxes is an ill-posed, noisy, and time-consuming task for human annotators. For this reason, distant 3D box annotations are rare, and most datasets [12-14] provide 3D annotations around 70 meters. A few datasets [15, 16] provide far-away annotations. They obtain long-range 3D annotations either by using costly Li-DAR sensors with very long sensing ranges or by taking significant efforts in annotating 3D boxes with consistency among sequences of stereo images. Both of these strategies are more expensive and less scalable, compared to drawing precise 2D boxes on images. Thus, in this paper, we explore an efficient camera-based approach to achieve high-quality long-range 3D object detection, which uses only 2D annotations for long-range objects of which the 3D annotations are hardly available due to sparse or no interior LiDAR points.", + "bbox": [ + 75, + 90, + 472, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach: We present LR3D, a camera-based detection framework that detects distant 3D objects using only 2D bounding box annotations. The core of LR3D is an Implicit Projection Head (IP-Head) design that can be plugged into existing camera-based detectors and enables them to effectively predict 3D bounding boxes at all ranges, using the supervision from close 2D/3D and distant 2D box labels.", + "bbox": [ + 75, + 319, + 472, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "IP-Head learns to generate specific mapping for each instance from their 2D bounding box prediction to the corresponding depth, and thus is capable of estimating depth for distant objects relying on 2D supervision only. We also design a projection augmentation strategy to force the generated implicit function to correctly model the mapping between 2D boxes and 3D depth of target instances and estimate different depth outputs if the 2D box input changes.", + "bbox": [ + 75, + 426, + 472, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also notice issues in evaluating camera-based detectors for long-range 3D detection. Existing evaluation metrics [12, 13], based on mean average precision (mAP) with fixed thresholds, neglect the inaccuracy of depth estimation of distant objects from cameras and lead to meaningless numbers even for state-of-the-art methods, e.g., only $0.43\\%$ mAP of DID-M3D [6] on KITTI Dataset for objects farther than $40\\mathrm{m}$ . This motivates us to design a novel metric, Long-range Detection Score (LDS), which sets a dynamic threshold for judging TP prediction regarding associated ground truth depth, for informative qualitative comparison.", + "bbox": [ + 75, + 549, + 472, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct experiments on five popular 3D detection datasets including KITTI [12], nuScenes [13], and Waymo [14] for objects within $80\\mathrm{m}$ , as well as Cityscapes3D [16] and Argoverse 2 [15] for objects farther than $200\\mathrm{m}$ . We remove the 3D annotations of farther objects in the train set and evaluate the performance on 3D objects at all ranges.", + "bbox": [ + 75, + 717, + 472, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Experiments show that, with LR3D, state-of-the-art detectors gain significant improvement in detecting distant objects without 3D annotation, i.e., $14.8\\%$ improvement of DID-M3D [6] on KITTI [12], $15.9\\%$ improvement of BEVFormer [2] on nuScenes [13], $34.5\\%$ and $14.17\\%$ improvement of FCOS3D [1] on Cityscapes3D and Argoverse", + "bbox": [ + 75, + 809, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2, $7.09\\%$ improvement of MV-FCOS3D++ [7] on Waymo. With LR3D, these methods yield competitive performance even compared to fully 3D supervised counterparts. Notably, LR3D enables them to detect extremely distant 3D objects as shown in Figure 1.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 498, + 181, + 640, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LiDAR-based Detectors. LiDAR methods detect 3D objects from point clouds. According to inputs, these methods can be divided into point, voxel, and range-view detectors. Point methods [17-21] make 3D predictions from raw point clouds [22-27]. Voxel methods [28-31] transform point clouds into voxels and extract features by convolutions [32-37]. Other methods project point clouds into range-view [38-42] and process them as images [43]. Albeit impressively performed, LiDAR methods are 3D-label-greedy, and limited by the perspective range of LiDAR sensors, i.e., usually fail for areas with few or no LiDAR points.", + "bbox": [ + 496, + 200, + 893, + 369 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Camera-based Detectors. Camera-based methods do 3D detection from images. Monocular methods predict 3D boxes in single image directly [1, 44-47]. Stereo methods based on multi-view images formulate a 3D volume [48-50]. Recent methods [2, 51-57] build a bird-eye-view (BEV) representation for detection.", + "bbox": [ + 496, + 369, + 893, + 460 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The advantages of Camera-based methods lie in the unbounded perception range of cameras, which makes them suitable for distant 3D detection. Some methods, e.g., Far3D [58], are designed for long-range 3D detection, but still heavily rely on abundant high-quality distant 3D annotations, which are hard to collect. Some datasets [15, 16] provide distant annotations. However, their labeling is time-consuming and requires huge human efforts to take hints from multi-modal sensors and temporal consistency to label distant objects with few or no interior LiDAR points. The workload of the labeling process and the 3D-label-greedy character of existing detectors limit the applications of long-range 3D detection. Instead, we propose to detect distant 3D objects without long-range 3D box supervision. It is the simplest setting and is practical for scalability.", + "bbox": [ + 496, + 460, + 895, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object Distance Estimation. Another related topic is monocular distance estimation, which estimates the object distance from an RGB image. SVR [59] and DisNet [60] estimate object distance through pixel height and width. They base on an assumption of projected 2D box size determined by the distance of object only. However, other factors, like size and orientation, also affect the projected 2D box size.", + "bbox": [ + 496, + 688, + 893, + 795 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Method of [61] develops a FastRCNN [62] pipeline for end-to-end distance estimation by directly regressing the distance from RoI features. R4D [9] utilizes reference objects for further improvements. These methods are limited by their requirements of abundant annotations. Given the difficulty in labeling distant 3D objects, in this paper, we develop a simpler 2D setting that even achieves competitive", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14854", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e60418d9f80d61bf84553077e043fd61e694efc9e8683bc4b332cbde2e8fec07.jpg", + "image_caption": [ + "Figure 2. Illustration of LR3D which detects 3D boxes for both close and distant objects using the supervision of close 2D/3D and distant 2D bounding box annotations." + ], + "image_footnote": [], + "bbox": [ + 81, + 71, + 467, + 210 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/07ae5a3ccc619e2ccd9615adf065ad0ffabd977b1b0e7cf1bdc5d4ce8463d62f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Distant 3D Groundtruth?Location Err.Size Err.Orientation Err.
✓0.090.210.37
-0.34 (+0.25)0.23 (+0.02)0.41 (+0.04)
", + "bbox": [ + 78, + 263, + 464, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Performance comparison between FastRCNN3D trained with and without distant 3D supervision.", + "bbox": [ + 76, + 316, + 467, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "performance to their 3D supervised counterparts.", + "bbox": [ + 76, + 354, + 400, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 383, + 166, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LR3D is a long-range 3D detection framework that detects 3D bounding boxes, including locations, sizes, and orientations, of distant objects using only their 2D supervision (Figure 2). In this section, we first analyze the main challenge of directly utilizing existing 3D detectors on LR3D in Section 3.1 and then introduce our solution in Section 3.2.", + "bbox": [ + 76, + 409, + 468, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Analysis", + "text_level": 1, + "bbox": [ + 76, + 510, + 179, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Albeit important and critical, long-range 3D object detection is seldom explored. One difficulty is to obtain sufficient high-quality 3D bounding box annotations for distant objects. We discard this high-human-labor-cost setting and propose a new framework, LR3D, to predict 3D boxes for distant objects only from their 2D image supervision.", + "bbox": [ + 76, + 534, + 468, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Can Existing Methods Use only 2D Supervision? We first analyze if existing methods can use only 2D supervision for detecting distant 3D objects. To this end, we use FastRCNN3D, a FastRCNN-like [62] 3D detector where the original head for 2D detection is replaced by the FCOS3D head [1] for 3D detection. For training, we first manually assign objects over $40\\mathrm{m}$ as distant objects and remove their 3D annotations. Then, we train FastRCNN3D with close 2D/3D and distant 2D box labels as Figure 2. At test time, we use the 2D ground truth of distant objects as proposals, predict their 3D boxes, and evaluate their errors in location, size, and orientation. Note that we use relative distance as location error, IoU with aligned location and orientation as size error, and absolute difference as orientation error.", + "bbox": [ + 76, + 628, + 468, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1 compares errors between the LR3D configuration and traditional full supervision. As shown, errors in size and orientation are comparable. The main gap comes from the location error, in which depth estimation plays the", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/306247ae5d24106d41ea8885261a7cd788cde6da4d2fdc36e1433c2725cff874.jpg", + "image_caption": [ + "Figure 3. Illustration of IP-Head. We use an MLP $f^{(\\theta)}$ to fit the implicit function from 2D box to 3D depth, of which the weights $\\theta$ are dynamically determined by instance features including information of size and orientation." + ], + "image_footnote": [], + "bbox": [ + 501, + 71, + 890, + 228 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "essential role. Due to the lack of depth information in 2D box supervision, directly regressing the depth as previous methods cannot produce accurate depth prediction for distant objects and leads to a significant drop. Therefore, we seek a new method to implicitly estimate the depth.", + "bbox": [ + 498, + 303, + 890, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Implicit Projection Head", + "text_level": 1, + "bbox": [ + 500, + 387, + 725, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we introduce Implicit Projection head (IP-Head), our proposal to estimate depth of distant objects using only 2D supervision. Given a 3D object with fixed depth, size, and orientation $^1$ , through the camera calibration matrix, it is easy to obtain the corresponding projected 2D bounding box (described by its width $w_{2d}$ and height $h_{2d}$ ) on the target image. We use a function $f$ , determined by the calibration matrix, to indicate the mapping between depth $(d)$ , size $(s)$ , orientation $(o)$ and 2D box $(b_{2d} = (w_{2d}, h_{2d}))$ as", + "bbox": [ + 498, + 409, + 890, + 547 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (d, s, o) = b _ {2 d}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 555, + 890, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Eq. (1) shows the ubiquitous relation between $d$ and $b_{2d}$ if the object size $s$ and orientation $o$ are fixed – for objects with the same size and orientation, the further these objects locate, the smaller their projected 2D boxes on image are. Inspired by this fact, we ask if it is possible to estimate the inverse function $f^{-1}$ to transfer the 2D bounding box to the corresponding depth conditioned by $s$ and $o$ , formulated as", + "bbox": [ + 498, + 579, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {- 1} \\left(b _ {2 d} | s, o\\right) = d. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 694, + 890, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the power of neural networks to fit complicated functions, we utilize a small-size network with a multi-layer perceptron (MLP) to estimate the implicit inverse function $f^{-1}$ . For simplicity, we use $f^{(\\theta)}$ to represent this network, of which the parameter weights are represented as $\\theta$ .", + "bbox": [ + 498, + 719, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the implicit inverse function $f^{-1}$ depends on the size and orientation of the specific 3D objects, $f^{(\\theta)}$ should also be different across multiple objects, which means weights $\\theta$ should be dynamic.", + "bbox": [ + 498, + 795, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1The mentioned orientation is the relative one to the camera, i.e., the observed orientation on the image. We refer the readers to FCOS3D [1] and Stereo-RCNN [63] for more details on obtaining relative orientation.", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14855", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d4be4de832e4ac872246bbb1b105f3f0ed46be6b4de2bd84798b297f3d9cddba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 73, + 478, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/11e3e94197473f455cc8cbbaa8d30448ca329543eede56ee6a38aa3f55cd1789.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 71, + 883, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/15db0a060d0f36c1fd719909bf162acdddc41fa05c84c99278c008ec4e069fa3.jpg", + "image_caption": [ + "Figure 4. Illustration of the training and testing pipeline of IP-Head. (a). Training: During training, we use 2D/3D annotation pairs of close objects to supervise $f_{g}$ to generate dynamic weights of MLP $f^{(\\theta)}$ which models the transformation of target 3D object from 2D box to corresponding depth in Eq. (3). (b). Testing: During testing, we use a 2D detection head (2D Det. Head) $f_{2d}$ to generate 2D detection results for all objects. They are then transferred to corresponding depth by IP-Head.", + "Figure 5. Illustration of deploying IP-Head to monocular 3D detectors: (a) FCOS3D; (b) FastRCNN3D." + ], + "image_footnote": [], + "bbox": [ + 89, + 287, + 455, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With these considerations, rather than utilizing a shared $\\theta$ for all objects, we use a trainable MLP $f_{g}$ to generate a set of dynamic weights $\\theta_{i}$ according to the features $F_{i}$ of each object $i$ . We then utilize those $\\theta_{i}$ as the weights of network $f^{(\\theta)}$ to estimate the corresponding depth of the $i$ -th 2D box. This process generates the specific Implicit inverse function of each object to Project its 2D box to 3D depth. We illustrate this procedure in Figure 3, in which \"2D Box Encoding\", $f_{\\mathrm{PE}}$ , is a positional encoding function [64] to encode 2-channel 2D box descriptors (with width $w_{2d}$ and height $h_{2d}$ ) into informative high-dimensional features and $f_{2d}$ is a 2D detection network for predicting 2D bounding boxes on the image. The overall procedure is formulated as", + "bbox": [ + 75, + 527, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} = f ^ {\\left(f _ {g} \\left(F _ {i}\\right)\\right)} \\left(f _ {\\mathrm {P E}} \\left(b _ {2 d _ {i}}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 734, + 468, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{g}$ estimates the weights of $f^{(\\theta_i)}$ from instance features $F_{i}$ to transfer the $i$ -th 2D bounding boxes to its corresponding depth. Its condition information, including size $s_i$ and orientation $o_i$ , is included in feature $F_{i}$ , from which information can be obtained like that of [1, 65, 66].", + "bbox": [ + 75, + 763, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During training, we make use of 2D/3D annotation pairs of close objects to supervise IP-Head for obtaining a reliable dynamic weight generator $f_{g}$ . Specifically, for a close object, after obtaining its corresponding dynamic weights,", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8d0ffe2e921adc39f46f70b18725120558a65c435bf808727e330e6fe0d59e98.jpg", + "image_caption": [ + "Figure 6. Illustration of extending IP-Head to all camera-based 3D detectors through a teacher-student pipeline." + ], + "image_footnote": [], + "bbox": [ + 503, + 287, + 888, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we transfer its 2D ground truth box for depth prediction by IP-Head, and optimize $f_{g}$ by computing the loss between the predicted depth and the 3D annotation.", + "bbox": [ + 498, + 483, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During inference, we first use the backbone network to extract instance features $F_{i}^{\\prime}$ . Then, we extract dynamic weights using $f_{g}$ and use a detection network $f_{2d}$ , supervised by 2D bounding box ground truth, to predict the associated 2D bounding box $b_{2d_i}'$ as $b_{2d_i}' = f_{2d}(F_i')$ . Finally, we use Eq. (3) to obtain depth predictions for each instance in the image. The overall process is illustrated in Figure 4.", + "bbox": [ + 496, + 529, + 890, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using neural networks to directly estimate a hard-to-optimize function was successful in other research areas. For example, NeRF [67] uses MLP networks to learn a shared mapping from positions to colors and densities; classification models use a shared CNN model to learn the function from pixels to classification confidence. In contrast to previous methods, we first study the estimation of transformation function from 2D boxes on images to 3D depths. Moreover, instead of learning a shared mapping, IP-Head generates dynamic mappings from 2D box sizes to 3D depth according to the 3D size and orientation of target objects, which equips IP-Head with great generalization ability and potential applied to complex autonomous driving scenarios.", + "bbox": [ + 496, + 638, + 892, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Projection Augmentation. The implicit inverse function $f^{(\\theta)}$ needs to model the relation between the 2D box and corresponding depth, and generate different depth predictions based on 2D box input. To further improve effective", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14856", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ness, we also propose an augmentation strategy, called projection augmentation. The idea is to generate more depth $d$ and 2D box $b_{2d}$ pairs for each close object during training, so as to enable $f_{g}$ to estimate a more accurate $b_{2d} - d$ relation.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "These extra $b_{2d} - d$ training pairs come from Eq. (1). Given an object with fixed size and orientation, we randomly choose different depth values $d^{*}$ , calculate their corresponding 2D boxes $b_{2d}^{*}$ through Eq. (1), and utilize these augmented $b_{2d}^{*} - d^{*}$ pairs, along with the ground truth $b_{2d} - d$ pair, to train the IP-Head for higher performance.", + "bbox": [ + 75, + 152, + 468, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Long-range Teacher The proposed IP-Head can be used in existing monocular 3D detectors, like FCOS3D [1], to boost their performance in LR3D. As illustrated in Figure 5, only two additional branches, i.e., a 2D detection branch $f_{2d}$ and a weight generation MLP $f_{g}$ , are needed to utilize IP-Head in FCOS3D. Apart from monocular methods, BEV methods become popular due to their strong performance and multi-tasking ability. We extend IP-Head to BEV methods to alleviate their demand of 3D annotations.", + "bbox": [ + 75, + 247, + 468, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our solution is to utilize a monocular method equipped with IP-Head as the detector of the LR3D model which then serves as the long-range teacher to generate pseudo distant 3D annotations. With close 2D/3D annotations and distant 2D annotations, we first apply LR3D to generate 3D predictions for distant objects. Then, we treat these predictions as pseudo 3D box labels, which are, together with close 3D ground truth, taken as the whole supervision to train BEV methods. Our pipeline is shown in Figure 6. Experiments show that, it works decently for various 3D detectors on long-range objects without distant 3D box annotation.", + "bbox": [ + 75, + 383, + 468, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Long-range Detection Score", + "text_level": 1, + "bbox": [ + 76, + 561, + 334, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Existing detection metrics are built upon mAP based on either IoU [12, 14] or absolute distance error [13]. They use fixed IoU or error thresholds as criterion to calculate AP.", + "bbox": [ + 75, + 582, + 468, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, the fixed threshold is not suitable for distant objects due to its neglect of the increasing error in depth estimation when objects go farther. For example, though DID-M3D [6] is the state-of-the-art camera-based detector, it only achieves $0.43\\%$ mAP under fixed IoU criterion on objects over $40\\mathrm{m}$ . Fixed threshold metrics hardly bring informative results. In fact, further objects should have a larger tolerance to closer ones, since estimating their depth is more ill-posed. Similar ideas were taken in tasks like dense depth estimation [68] and object distance estimation [9]. They all prefer relative distance errors as their metrics.", + "bbox": [ + 75, + 628, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this limitation, we introduce Long-range Detection Score (LDS), a new metric for long-range 3D object detection. LDS is based on the widely applied nuScenes Detection Score (NDS) [13] and it is defined as", + "bbox": [ + 75, + 796, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {L D S} = \\frac {1}{6} [ 3 \\mathrm {m A P} + \\operatorname {R e c} \\times \\sum_ {\\mathrm {m T P} \\in \\mathrm {m T P}} (1 - \\min (1, \\mathrm {m T P})) ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 867, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where Rec is the recall rate and mTP represents the mean True Positive metric.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LDS improves NDS in two main aspects: the criterion of mAP and the multiplication of Rec and summation of mTP. Improvements on mAP. In LDS, we compute mAP based on the relative distance error of", + "bbox": [ + 498, + 121, + 890, + 184 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {R e l . D i s t . E r r .} = \\frac {\\left\\| P _ {c} - G _ {c} \\right\\|}{G _ {d}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 193, + 890, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{c}$ , $G_{c}$ and $G_{d}$ represent the center of predicted 3D box, center of ground truth 3D box and the distance of ground truth 3D box towards ego vehicle, respectively. Predictions with a relative error smaller than a threshold $r$ are counted as true positive, and false positive otherwise, for computing AP. We choose 4 thresholds $\\mathbb{R} = \\{0.025, 0.05, 0.1, 0.2\\}$ and take average over these thresholds and the class set $\\mathbb{C}$ . Finally, we obtain mAP as", + "bbox": [ + 498, + 234, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {m A P} = \\frac {1}{| \\mathbb {C} | | \\mathbb {R} |} \\sum_ {c \\in \\mathbb {C}} \\sum_ {r \\in \\mathbb {R}} \\mathrm {A P} _ {c, r}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 366, + 890, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Improvement on mTP. Also, we multiply the recall rate and mTP before adding to mAP. The mTP is utilized to measure errors on the location (mATE), size (mASE) and orientation (mAOE) for TP prediction, whose relative distance to the ground truth is smaller than $r = 0.1$ during matching. mATE is computed as the relative distance, normalized by 0.1 to ensure range falling within 0 and 1.", + "bbox": [ + 498, + 417, + 890, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "mASE and mAOE are the same as those in nuScenes Dataset [13]. The intuition of multiplying the recall rate to the mTP is simple. The larger the recall rate is, the more predictions are involved in the statistics of mTP. Compared to simply setting a recall threshold [13], the multiplication improvement adjusts the weight of mTP to LDS according to its comprehensiveness, and thus brings a more informative quantitative result.", + "bbox": [ + 496, + 523, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 657, + 633, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our method on five popular 3D detection datasets of KITTI [12], nuScenes [13], Cityscapes3D [16], Waymo Open Dataset [14] and Argoverse 2 [15], which have plenty of high-quality 3D annotations for both close and distant objects. Due to the space limitation, we show the experimental results on Cityscapes3D, Waymo and Argoverse 2 datasets in the supplementary material.", + "bbox": [ + 496, + 681, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Results on KITTI", + "text_level": 1, + "bbox": [ + 500, + 797, + 671, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Preparation. KITTI Dataset [12] provides high-quality 2D/3D annotations for objects in \"Car\", \"Pedestrian\" and \"Cyclist\" within the range of $\\sim 80\\mathrm{m}$ . For extremely distant objects, due to lack of points, it only labels their 2D ground truth boxes on images and marks them as", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14857", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9fe27d165dfd29de9e2565a766703c16ff5229f916c607ae69055c4f41408d70.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDistant 3D Groundtruth?Overall (0m-Inf)Close (0m-40m)Distant (40m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√48.044.749.947.538.232.6
FCOS3D [1]-42.138.950.547.14.93.3
LR3D (IP-FCOS3D)50.046.752.149.436.231.0
", + "bbox": [ + 96, + 69, + 870, + 138 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/df0a32c82763043989e67c41cbc756c1de2ee17f61ea9b0db839b9ab815c83e7.jpg", + "table_caption": [ + "Long-range Teacher" + ], + "table_footnote": [], + "table_body": "
ImVoxelNet [52]√44.845.248.148.426.224.7
ImVoxelNet [52]-40.339.948.648.14.44.1
+LR3D teacher44.945.147.947.926.925.3
CaDDN [53]√51.150.157.856.319.318.5
CaDDN [53]-48.948.658.557.95.55.7
+LR3D teacher51.150.657.656.820.919.8
MonoFlex [65]√55.552.457.755.240.634.8
MonoFlex [65]-50.147.359.356.18.46.6
+LR3D teacher54.351.657.354.835.832.9
GUPNet [66]√49.347.554.052.126.725.1
GUPNet [66]-46.845.254.052.317.616.5
+LR3D teacher49.447.854.252.826.424.4
DID-M3D [6]√56.155.158.557.238.936.7
DID-M3D [6]-52.551.458.957.824.222.5
+LR3D teacher56.355.058.757.239.036.2
", + "bbox": [ + 96, + 151, + 870, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the KITTI val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated.", + "bbox": [ + 75, + 354, + 890, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"DontCare\". Given these labels, we accordingly conduct quantitative and qualitative evaluations on KITTI Dataset.", + "bbox": [ + 75, + 390, + 468, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative evaluation is conducted on objects with 3D annotations. Specifically, based on the official provided 3D annotations, we mark annotations over $40\\mathrm{m}$ as distant ones following [9], only using their 2D labels for training. For those closer than $40\\mathrm{m}$ , we keep both 2D and 3D labels for training. We report LDS on both close and distant objects for statistical results. The split of train and val sets follows [69]. Due to the lack of \"Pedestrian\" and \"Cyclist\" labels beyond $40\\mathrm{m}$ , we only report results on class \"Car\".", + "bbox": [ + 75, + 422, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative evaluation is designed for \"DontCare\" objects which are extremely far away and without 3D annotations due to no LiDAR points. We visualize the 3D detection results of our model conditioned by their 2D ground truth boxes. Through this evaluation, we manifest the capacity of our model for extremely distant 3D detection.", + "bbox": [ + 75, + 559, + 468, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Setting. For quantitative evaluation, we utilize FCOS3D [1] as our baseline for its simplicity and implementation platform. FCOS3D is implemented on the MMDetection3D [70] platform including multiple methods and datasets. We extend FCOS3D with our IP-Head (IP-FCOS3D, Figure 5) as the detector in the LR3D framework. For qualitative evaluation, we utilize FastRCNN3D with IP-Head (Figure 5) as LR3D detector, to utilize 2D conditions.", + "bbox": [ + 75, + 654, + 468, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results. We compare our LR3D, using IP-FCOS3D as its detector, and the baseline FCOS3D [1] for distant 3D detection without 3D annotations in Table 2. It is obvious that our LR3D outperforms FCOS3D on detecting distant objects by a large margin, i.e., $31.3\\%$ and $27.7\\%$ on LDS and mAP, respectively. Even compared to FCOS3D with distant 3D ground truth supervision, LR3D still shows competitive performance on distant objects.", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further evaluate the performance of using LR3D as the teacher model to generate pseudo long-range 3D labels to train state-of-the-art camera-based detectors. The results are listed in Table 2. Surprisingly, models trained with the combination of close 3D ground truth and distant 3D pseudo labels even achieve comparable or even better performance to their fully 3D supervised counterparts.", + "bbox": [ + 496, + 390, + 890, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results in Table 2 demonstrate the effectiveness of our LR3D framework, as well as the potential of our method in relieving the great demand of accurate 3D bounding box annotations for long-range object detection.", + "bbox": [ + 496, + 497, + 890, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. We visualize the 3D prediction results of LR3D conditioned with \"DontCare\" objects in Figure 7. It is also clear that supervised by close 3D annotations only (maximum to $40\\mathrm{m}$ away), our method infers reasonable 3D bounding boxes (3rd & 4th rows) for those extremely distant objects much beyond the 3D supervision range according to the corresponding 2D bounding boxes (1st & 2nd rows). These qualitative results further demonstrate the potential to extend LR3D to the labeling process. Annotators can first simply label 2D boxes for distant objects and then generate associated 3D annotations by LR3D.", + "bbox": [ + 496, + 561, + 890, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results on nuScenes", + "text_level": 1, + "bbox": [ + 500, + 737, + 691, + 752 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data Preparation. NuScenes [13] is a large-scale dataset with 1,000 autonomous driving sequences labeled with 3D boxes in 10 classes. In nuScenes, we set the distance threshold of marking long-range objects as $40\\mathrm{m}$ . We mark those annotations beyond the threshold as distant objects, remove the 3D annotations and only use 2D box labels for training. For those closer than $40\\mathrm{m}$ , we keep their both 2D/3D labels.", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate different models among all 10 classes, and do not set the detection range upper-bound for different", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14858", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7f771391cce88f1c6aff2331e8d8c22ed612a95160648ed09615c930c48ab2c1.jpg", + "image_caption": [ + "Figure 7. Qualitative results on KITTI Dataset in detecting extremely far away 3D objects. LiDAR points are projected to images shown with different colors related to depth. The distances of 3D bounding boxes are marked on the top-left. 1st & 2nd rows: 2D annotations of extremely distant objects; 3rd & 4th rows: 3D box prediction of corresponding objects." + ], + "image_footnote": [], + "bbox": [ + 81, + 71, + 344, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/306d758af43e976897e5447b16f63542303903b67f2f093bd3641372784e9bec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 71, + 617, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3031037c79f91dee2901d03736e84e3fc586a95b3a1887c830f83a8857ff8db1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 71, + 888, + 273 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e8f558926f121e5b24a064a079b103cf6bda3a2b5ae43b53d3b2bb678eef3872.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDistant 3D Groundtruth?OverallClose (0m-40m)Distant (40m-51.2m)Distant (51.2m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√26.627.429.130.116.412.711.38.6
FCOS3D [1]-22.623.429.930.31.81.40.00.0
LR3D (IP-FCOS3D)24.124.428.528.416.111.36.44.3
", + "bbox": [ + 89, + 321, + 875, + 391 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/eee3aab9ba1dd8787985f23812e2fbeb5008566368bd17ac328bf2156a0f67bd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Long-range Teacher
BEVFormer-S [2]√36.937.238.338.719.615.2--
BEVFormer-S [2] +LR3D teacher-33.634.238.038.52.41.7--
36.336.838.038.918.310.9--
BEVFormer-S† [2]√33.734.037.437.919.414.514.410.2
BEVFormer-S† [2] +LR3D teacher-29.129.938.038.72.41.00.00.0
33.033.637.538.017.910.712.76.4
", + "bbox": [ + 89, + 391, + 875, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the nuScenes val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated.", + "bbox": [ + 75, + 488, + 888, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "classes as the official benchmark [13]. This setting helps keep distant predictions. Following [13], we train our model on 700 training scenes and test it on 150 validation scenes.", + "bbox": [ + 75, + 523, + 468, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Model Setting. We utilize FCOS3D [1] as our monocular baseline and enhance it with IP-Head (IP-FCOS3D) for LR3D with 2D supervision only. To demonstrate the effectiveness of LR3D as a long-range teacher on nuScenes, we choose BEVFormer [2] as the student for its effectiveness, and test its performance without distant 3D supervision.", + "bbox": [ + 75, + 575, + 468, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Main Results. The experimental results are illustrated in Table 3. With IP-Head, LR3D outperforms its baseline FCOS3D by $14.3\\%$ and $9.9\\%$ performance improvement in terms of LDS and mAP for distant objects from $40\\mathrm{m}$ to $51.2\\mathrm{m}$ . It is significant. Compared to the fully 3D supervised FCOS3D with distant 3D ground truth, LR3D still yields competitive capacity on long-range 3D detection.", + "bbox": [ + 75, + 670, + 468, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also list the results of BEVFormer [2] with and without LR3D teacher on detecting distant 3D objects without 3D supervision. As illustrated, with the LR3D teacher, BEVFormer-S yields strong performance, comparable to its fully-supervised counterparts with 3D box labels.", + "bbox": [ + 75, + 777, + 468, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the limited perception range of official BEVFormer $(-51.2\\mathrm{m}$ to $51.2\\mathrm{m})$ we enlarge the perception range of BEVFormer from $51.2\\mathrm{m}$ to $76.8\\mathrm{m}$ for further verifica", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion, denoted as BEVFormer- $S^{\\dagger}$ . Still, as shown in Table 3, with LR3D teacher, BEVFormer- $S^{\\dagger}$ achieves impressive improvement compared to its baseline, and yields comparable results to those of the fully-supervised model.", + "bbox": [ + 496, + 523, + 890, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 598, + 663, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "All ablation studies are conducted on KITTI Dataset, using IP-FCOS3D as the detector of the LR3D model.", + "bbox": [ + 496, + 622, + 890, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on the IP-Head. IP-Head learns to estimate implicit inverse function $f^{-1}$ , which is the mapping from 2D bounding box on image to corresponding depth, through two MLP networks $f_{g}$ and $f^{(\\theta)}$ . We evaluate its effectiveness by comparing the mapping curve from 2D box size to the depth of a fixed 3D object generated by ground truth transformation and estimated transformation.", + "bbox": [ + 496, + 657, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The generation of the ground truth curve follows Eq. (1), from which we obtain multiple $d - b_{2d}$ pairs by modifying depth $d$ . The estimated curve is generated through Eq. (3) by changing the 2D box inputs. As illustrated in Figure 8, our IP-Head can estimate specific implicit inverse functions for different objects (by comparison across rows). The estimated function by MLP network $f^{(\\theta)}$ well models the mapping from 2D bounding box size to the corresponding depth of target 3D object (through comparison inside each row).", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14859", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/429cc12ffa905fbddd3f5c457c8fdc2f67c1205987474cb1af913172c76a9568.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
f(θ) Weight Learning StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
Shared45.046.632.5
Dynamic50.052.136.2
", + "bbox": [ + 88, + 70, + 326, + 138 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/63bdc7ddf0b057e00ad414060f7e2209927bf43be2d672b4afe8aab79e2cb325.jpg", + "table_caption": [ + "(a) Effect of parameter learning in $f^{(\\theta)}$ ." + ], + "table_footnote": [ + "(d) Effect of the number of layers in $f^{(\\theta)}$ ." + ], + "table_body": "
No. of layersOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
148.651.332.4
250.052.136.2
349.752.035.2
449.051.434.9
", + "bbox": [ + 88, + 170, + 331, + 261 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7591bccb614bf99e96d5449c4f5b498f40a00fe931ed6784db965a3ae9f99d0b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Pos. Enc.Overall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
None19.920.213.3
Sin. Cos. [64]50.052.136.2
", + "bbox": [ + 367, + 70, + 616, + 138 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/29a878c331a48d772195586c00ee273bee15092fc3a2b8d32cbb475a26b73246.jpg", + "table_caption": [ + "(b) Effect of positional encoding in $f^{(\\theta)}$ ." + ], + "table_footnote": [], + "table_body": "
No. of channelsOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
848.450.934.5
1650.052.136.2
3249.952.335.6
6449.751.936.1
", + "bbox": [ + 367, + 170, + 622, + 261 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f527bb6e367854e52342f8101d0ecee74443b493366ebfab3e1407bec41edfd3.jpg", + "table_caption": [ + "(e) Effect of the channel number in $f^{(\\theta)}$ ." + ], + "table_footnote": [], + "table_body": "
2D Box (b2d) \nDescriptorsOverall \n(0m-Inf) \nLDS (%)Close \n(0m-40m) \nLDS (%)Distant \n(40m-Inf) \nLDS (%)
box width (w2d)48.551.730.6
box height (h2d)49.451.834.9
both (w2d, h2d)50.052.136.2
", + "bbox": [ + 645, + 71, + 908, + 150 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d61c81e56955eb2c13972bef40ee350d7fd6db3db84ddfa9f17fee0fc834c615.jpg", + "table_caption": [ + "(c) Effect of 2D box descriptors." + ], + "table_footnote": [], + "table_body": "
Aug. StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
FCOS3D [1]42.150.54.9
+Copy-PasteN/AN/AN/A
LR3D48.352.726.5
+Proj. Aug.50.052.136.2
", + "bbox": [ + 645, + 169, + 898, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(f) Effect of the projection augmentation.", + "bbox": [ + 651, + 263, + 869, + 275 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation studies on IP-Head structure and projection augmentation. Default settings are highlighted in lightcyan .", + "bbox": [ + 119, + 281, + 844, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a3be5b60b4b309feddc8aaea93efe8fcfb2da05869d553d0ac7c5bd0e419621b.jpg", + "image_caption": [ + "Figure 8. Illustration of the ground truth and estimated $b_{2d} - d$ mappings. Each row indicates the target 3D object and its mapping from 2D box width and height to the depth." + ], + "image_footnote": [], + "bbox": [ + 78, + 306, + 468, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further provide quantitative analysis of using MLP network $f_{g}$ to dynamically determine weights of $f^{(\\theta)}$ to estimate specific implicit inverse functions of different 3D objects. As listed in Table 4a, compared to the design of shared weights, using dynamic weights assignment in $f^{(\\theta)}$ well models the difference of implicit inverse functions due to size and orientation of 3D objects, and thus outperforms the model using a shared weight $\\theta$ across 3D objects.", + "bbox": [ + 75, + 542, + 468, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on the IP-Head Structure. We first describe the default structure of IP-Head. $f^{(\\theta)}$ is a 2-layer perceptron with channels of 16 and 1. The 2D boxes $b_{2d}$ are described as height $(h_{2d})$ and width $(w_{2d})$ . The positional encoding function $f_{\\mathrm{PE}}$ is the sine-cosine function illustrated in [64].", + "bbox": [ + 75, + 670, + 468, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 4b, we evaluate the contribution of positional encoding. With positional encoding [64], the 2D descriptors are well encoded into more informative features, which thus outperforms the model without positional encoding (\"None\"). In Table 4c, we compare the model with different 2D box descriptors. Utilizing both 2D box width $w_{2d}$ and height $h_{2d}$ as descriptors yields the best performance. In Table 4d and Table 4e, we conduct ablation studies on MLP structures of network $f^{(\\theta)}$ with different numbers of layers and channels. As illustrated, the model with 2-layer", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and channel number 16 achieves the best results.", + "bbox": [ + 498, + 306, + 821, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on the Projection Augmentation. The projection augmentation ensures the estimated implicit inverse function $f^{(\\theta)}$ models the relation between 2D box sizes and depths by generating more training $b_{2d} - d$ pairs. We analyze it by comparing the performance of LR3D trained with and without this augmentation. As shown in Table 4f, compared to FCOS3D baseline (1st row), LR3D can model mapping functions from 2D sizes to depths and produces good results on distant objects without 3D supervision. Moreover, equipped with projection augmentation, LR3D further shows a huge performance improvement on distant objects.", + "bbox": [ + 496, + 330, + 890, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A similar augmentation to projection augmentation is copy-paste augmentation [71, 72], which simulates distant training samples by cropping close objects with image patches and pasting them to distant areas by Eq. (1). However, this augmentation brings noises in image distribution, is hard to optimize, and thus leads to a great performance drop (Table 4f (2nd row)). In contrast, projection augmentation is simple to implement without changing training images, and able to augment to any depth without extra effort.", + "bbox": [ + 496, + 502, + 890, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Results on Other Datasets", + "text_level": 1, + "bbox": [ + 500, + 662, + 735, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Please find additional results on Cityscapes3D [16], Waymo [14], and Argoverse 2 [15] in the supplementary materials.", + "bbox": [ + 500, + 690, + 890, + 722 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 750, + 617, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed the LR3D framework for long-range 3D detection using 2D supervision and designed the IP-Head as the key component. We developed a teacher-student pipeline to benefit all camera-based detectors. Our LDS, a metric with relative distance criterion, helps obtain informative quantitative results for distant objects. With these designs, we demonstrate the feasibility of using 2D supervision only for long-range 3D detection.", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14860", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tai Wang, Xinge Zhu, Jiangmiao Pang, and Dahua Lin. FCOS3D: Fully convolutional one-stage monocular 3d object detection. In ICCV Workshops, 2021. 1, 2, 3, 4, 5, 6, 7, 8", + "[2] Zhiqi Li, Wenhai Wang, Hongyang Li, Enze Xie, Chonghao Sima, Tong Lu, Yu Qiao, and Jifeng Dai. 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In CVPR, 2021. 8" + ], + "bbox": [ + 78, + 90, + 468, + 359 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14863", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improving Distant 3D Object Detection Using 2D Box Supervision/34f5dadc-28a4-4c87-abd0-683d3827eb2b_model.json b/2024/Improving Distant 3D Object Detection Using 2D Box Supervision/34f5dadc-28a4-4c87-abd0-683d3827eb2b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b33330ef8bd4d7cde49a428869c1d5127b937f7e --- /dev/null +++ b/2024/Improving Distant 3D Object Detection Using 2D Box Supervision/34f5dadc-28a4-4c87-abd0-683d3827eb2b_model.json @@ -0,0 +1,2620 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.152, + 0.131, + 0.819, + 0.154 + ], + "angle": 0, + "content": "Improving Distant 3D Object Detection Using 2D Box Supervision" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.18, + 0.892, + 0.201 + ], + "angle": 0, + "content": "Zetong Yang\\(^{1*}\\) Zhiding Yu\\(^{2\\dagger}\\) Chris Choy\\(^{2}\\) Renhao Wang\\(^{3*}\\) Anima Anandkumar\\(^{4*}\\) Jose M. Alvarez\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.281, + 0.212, + 0.694, + 0.232 + ], + "angle": 0, + "content": "\\(^{1}\\)CUHK \\(^{2}\\)NVIDIA \\(^{3}\\)UC Berkeley \\(^{4}\\)Caltech" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.258, + 0.891, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.393, + 0.482, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.469, + 0.32, + 0.482 + ], + "angle": 0, + "content": "DID-M3D" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.394, + 0.888, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.469, + 0.751, + 0.483 + ], + "angle": 0, + "content": "LR3D (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.483, + 0.893, + 0.525 + ], + "angle": 0, + "content": "Figure 1. Upper: Without 3D annotations beyond \\(40\\mathrm{m}\\), LR3D enables the predictions of 3D boxes for extremely distant objects over \\(200\\mathrm{m}\\) (right, in green) based on the inputs of image and 2D box (left). Lower: Existing methods fail to detect 3D objects beyond the 3D supervision range, e.g., \\(40\\mathrm{m}\\) for this case. With LR3D, these remote missing objects are well detected." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.539, + 0.314, + 0.554 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.563, + 0.474, + 0.866 + ], + "angle": 0, + "content": "Improving the detection of distant 3d objects is an important yet challenging task. For camera-based 3D perception, the annotation of 3d bounding relies heavily on LiDAR for accurate depth information. As such, the distance of annotation is often limited due to the sparsity of LiDAR points on distant objects, which hampers the capability of existing detectors for long-range scenarios. We address this challenge by considering only 2D box supervision for distant objects since they are easy to annotate. We propose LR3D, a framework that learns to recover the missing depth of distant objects. LR3D adopts an implicit projection head to learn the generation of mapping between 2D boxes and depth using the 3D supervision on close objects. This mapping allows the depth estimation of distant objects conditioned on their 2D boxes, making long-range 3D detection with 2D supervision feasible. Experiments show that without distant 3D annotations, LR3D allows camera-based methods to detect distant objects (over \\(200m\\)) with comparable accuracy to full 3D supervision. Our framework is general, and could widely benefit 3D detection methods to a large extent." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.539, + 0.631, + 0.554 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Camera-based 3D object detection [1-7] is an important task in autonomous driving aiming to localize and classify objects in 3D space with monocular or multi-view image input. Detecting distant objects with camera input is both important and challenging. On one hand, the ability to detect objects at distance is needed for planning, especially for highway scenarios. According to [8], at 60 miles/hour, the typical stopping distance for a vehicle is 73 meters and it grows significantly under harsh road conditions such as having wet surface [9-11]. On the other hand, the detection range of camera-based methods depends heavily on the distance range of 3D annotations. For example, these methods work well within the distance range with abundant 3D annotations (e.g., \\(\\sim 70\\) meters on KITTI [12] and nuScenes [13]), but often fail beyond this range where 3D annotations are missing. This indicates the importance to improve distant 3D object detection with longer 3D annotation range." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.827, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Though of great importance, increasing the range of 3D annotation is not easy. One main challenge is the sparsity of LiDAR points at longer distances. LiDAR is typically the main reference for axial depth information in 3D annotation. For distant objects with few or even no LiDAR points," + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.876, + 0.395, + 0.888 + ], + "angle": 0, + "content": "*Work done during internship / affiliation with NVIDIA." + }, + { + "type": "page_footnote", + "bbox": [ + 0.099, + 0.889, + 0.343, + 0.902 + ], + "angle": 0, + "content": "†Corresponding author: zhidingy@nvidia.com" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.876, + 0.395, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14853" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.319 + ], + "angle": 0, + "content": "labeling their 3D bounding boxes is an ill-posed, noisy, and time-consuming task for human annotators. For this reason, distant 3D box annotations are rare, and most datasets [12-14] provide 3D annotations around 70 meters. A few datasets [15, 16] provide far-away annotations. They obtain long-range 3D annotations either by using costly Li-DAR sensors with very long sensing ranges or by taking significant efforts in annotating 3D boxes with consistency among sequences of stereo images. Both of these strategies are more expensive and less scalable, compared to drawing precise 2D boxes on images. Thus, in this paper, we explore an efficient camera-based approach to achieve high-quality long-range 3D object detection, which uses only 2D annotations for long-range objects of which the 3D annotations are hardly available due to sparse or no interior LiDAR points." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.473, + 0.426 + ], + "angle": 0, + "content": "Our approach: We present LR3D, a camera-based detection framework that detects distant 3D objects using only 2D bounding box annotations. The core of LR3D is an Implicit Projection Head (IP-Head) design that can be plugged into existing camera-based detectors and enables them to effectively predict 3D bounding boxes at all ranges, using the supervision from close 2D/3D and distant 2D box labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.473, + 0.549 + ], + "angle": 0, + "content": "IP-Head learns to generate specific mapping for each instance from their 2D bounding box prediction to the corresponding depth, and thus is capable of estimating depth for distant objects relying on 2D supervision only. We also design a projection augmentation strategy to force the generated implicit function to correctly model the mapping between 2D boxes and 3D depth of target instances and estimate different depth outputs if the 2D box input changes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.473, + 0.718 + ], + "angle": 0, + "content": "We also notice issues in evaluating camera-based detectors for long-range 3D detection. Existing evaluation metrics [12, 13], based on mean average precision (mAP) with fixed thresholds, neglect the inaccuracy of depth estimation of distant objects from cameras and lead to meaningless numbers even for state-of-the-art methods, e.g., only \\(0.43\\%\\) mAP of DID-M3D [6] on KITTI Dataset for objects farther than \\(40\\mathrm{m}\\). This motivates us to design a novel metric, Long-range Detection Score (LDS), which sets a dynamic threshold for judging TP prediction regarding associated ground truth depth, for informative qualitative comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.473, + 0.81 + ], + "angle": 0, + "content": "We conduct experiments on five popular 3D detection datasets including KITTI [12], nuScenes [13], and Waymo [14] for objects within \\(80\\mathrm{m}\\), as well as Cityscapes3D [16] and Argoverse 2 [15] for objects farther than \\(200\\mathrm{m}\\). We remove the 3D annotations of farther objects in the train set and evaluate the performance on 3D objects at all ranges." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Experiments show that, with LR3D, state-of-the-art detectors gain significant improvement in detecting distant objects without 3D annotation, i.e., \\(14.8\\%\\) improvement of DID-M3D [6] on KITTI [12], \\(15.9\\%\\) improvement of BEVFormer [2] on nuScenes [13], \\(34.5\\%\\) and \\(14.17\\%\\) improvement of FCOS3D [1] on Cityscapes3D and Argoverse" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.169 + ], + "angle": 0, + "content": "2, \\(7.09\\%\\) improvement of MV-FCOS3D++ [7] on Waymo. With LR3D, these methods yield competitive performance even compared to fully 3D supervised counterparts. Notably, LR3D enables them to detect extremely distant 3D objects as shown in Figure 1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.182, + 0.642, + 0.198 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.202, + 0.895, + 0.37 + ], + "angle": 0, + "content": "LiDAR-based Detectors. LiDAR methods detect 3D objects from point clouds. According to inputs, these methods can be divided into point, voxel, and range-view detectors. Point methods [17-21] make 3D predictions from raw point clouds [22-27]. Voxel methods [28-31] transform point clouds into voxels and extract features by convolutions [32-37]. Other methods project point clouds into range-view [38-42] and process them as images [43]. Albeit impressively performed, LiDAR methods are 3D-label-greedy, and limited by the perspective range of LiDAR sensors, i.e., usually fail for areas with few or no LiDAR points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.895, + 0.462 + ], + "angle": 0, + "content": "Camera-based Detectors. Camera-based methods do 3D detection from images. Monocular methods predict 3D boxes in single image directly [1, 44-47]. Stereo methods based on multi-view images formulate a 3D volume [48-50]. Recent methods [2, 51-57] build a bird-eye-view (BEV) representation for detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.896, + 0.689 + ], + "angle": 0, + "content": "The advantages of Camera-based methods lie in the unbounded perception range of cameras, which makes them suitable for distant 3D detection. Some methods, e.g., Far3D [58], are designed for long-range 3D detection, but still heavily rely on abundant high-quality distant 3D annotations, which are hard to collect. Some datasets [15, 16] provide distant annotations. However, their labeling is time-consuming and requires huge human efforts to take hints from multi-modal sensors and temporal consistency to label distant objects with few or no interior LiDAR points. The workload of the labeling process and the 3D-label-greedy character of existing detectors limit the applications of long-range 3D detection. Instead, we propose to detect distant 3D objects without long-range 3D box supervision. It is the simplest setting and is practical for scalability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.796 + ], + "angle": 0, + "content": "Object Distance Estimation. Another related topic is monocular distance estimation, which estimates the object distance from an RGB image. SVR [59] and DisNet [60] estimate object distance through pixel height and width. They base on an assumption of projected 2D box size determined by the distance of object only. However, other factors, like size and orientation, also affect the projected 2D box size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Method of [61] develops a FastRCNN [62] pipeline for end-to-end distance estimation by directly regressing the distance from RoI features. R4D [9] utilizes reference objects for further improvements. These methods are limited by their requirements of abundant annotations. Given the difficulty in labeling distant 3D objects, in this paper, we develop a simpler 2D setting that even achieves competitive" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "14854" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.072, + 0.468, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.217, + 0.47, + 0.259 + ], + "angle": 0, + "content": "Figure 2. Illustration of LR3D which detects 3D boxes for both close and distant objects using the supervision of close 2D/3D and distant 2D bounding box annotations." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.264, + 0.465, + 0.316 + ], + "angle": 0, + "content": "
Distant 3D Groundtruth?Location Err.Size Err.Orientation Err.
✓0.090.210.37
-0.34 (+0.25)0.23 (+0.02)0.41 (+0.04)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.318, + 0.468, + 0.346 + ], + "angle": 0, + "content": "Table 1. Performance comparison between FastRCNN3D trained with and without distant 3D supervision." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.355, + 0.401, + 0.371 + ], + "angle": 0, + "content": "performance to their 3D supervised counterparts." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.384, + 0.168, + 0.4 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.41, + 0.469, + 0.501 + ], + "angle": 0, + "content": "LR3D is a long-range 3D detection framework that detects 3D bounding boxes, including locations, sizes, and orientations, of distant objects using only their 2D supervision (Figure 2). In this section, we first analyze the main challenge of directly utilizing existing 3D detectors on LR3D in Section 3.1 and then introduce our solution in Section 3.2." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.511, + 0.18, + 0.527 + ], + "angle": 0, + "content": "3.1. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.469, + 0.626 + ], + "angle": 0, + "content": "Albeit important and critical, long-range 3D object detection is seldom explored. One difficulty is to obtain sufficient high-quality 3D bounding box annotations for distant objects. We discard this high-human-labor-cost setting and propose a new framework, LR3D, to predict 3D boxes for distant objects only from their 2D image supervision." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.629, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Can Existing Methods Use only 2D Supervision? We first analyze if existing methods can use only 2D supervision for detecting distant 3D objects. To this end, we use FastRCNN3D, a FastRCNN-like [62] 3D detector where the original head for 2D detection is replaced by the FCOS3D head [1] for 3D detection. For training, we first manually assign objects over \\(40\\mathrm{m}\\) as distant objects and remove their 3D annotations. Then, we train FastRCNN3D with close 2D/3D and distant 2D box labels as Figure 2. At test time, we use the 2D ground truth of distant objects as proposals, predict their 3D boxes, and evaluate their errors in location, size, and orientation. Note that we use relative distance as location error, IoU with aligned location and orientation as size error, and absolute difference as orientation error." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Table 1 compares errors between the LR3D configuration and traditional full supervision. As shown, errors in size and orientation are comparable. The main gap comes from the location error, in which depth estimation plays the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.072, + 0.891, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.233, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Figure 3. Illustration of IP-Head. We use an MLP \\( f^{(\\theta)} \\) to fit the implicit function from 2D box to 3D depth, of which the weights \\( \\theta \\) are dynamically determined by instance features including information of size and orientation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.381 + ], + "angle": 0, + "content": "essential role. Due to the lack of depth information in 2D box supervision, directly regressing the depth as previous methods cannot produce accurate depth prediction for distant objects and leads to a significant drop. Therefore, we seek a new method to implicitly estimate the depth." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.388, + 0.727, + 0.404 + ], + "angle": 0, + "content": "3.2. Implicit Projection Head" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.41, + 0.892, + 0.548 + ], + "angle": 0, + "content": "Here, we introduce Implicit Projection head (IP-Head), our proposal to estimate depth of distant objects using only 2D supervision. Given a 3D object with fixed depth, size, and orientation \\( ^1 \\), through the camera calibration matrix, it is easy to obtain the corresponding projected 2D bounding box (described by its width \\( w_{2d} \\) and height \\( h_{2d} \\)) on the target image. We use a function \\( f \\), determined by the calibration matrix, to indicate the mapping between depth \\( (d) \\), size \\( (s) \\), orientation \\( (o) \\) and 2D box \\( (b_{2d} = (w_{2d}, h_{2d})) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.64, + 0.556, + 0.891, + 0.573 + ], + "angle": 0, + "content": "\\[\nf (d, s, o) = b _ {2 d}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.58, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Eq. (1) shows the ubiquitous relation between \\( d \\) and \\( b_{2d} \\) if the object size \\( s \\) and orientation \\( o \\) are fixed – for objects with the same size and orientation, the further these objects locate, the smaller their projected 2D boxes on image are. Inspired by this fact, we ask if it is possible to estimate the inverse function \\( f^{-1} \\) to transfer the 2D bounding box to the corresponding depth conditioned by \\( s \\) and \\( o \\), formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.632, + 0.695, + 0.891, + 0.712 + ], + "angle": 0, + "content": "\\[\nf ^ {- 1} \\left(b _ {2 d} | s, o\\right) = d. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.892, + 0.795 + ], + "angle": 0, + "content": "With the power of neural networks to fit complicated functions, we utilize a small-size network with a multi-layer perceptron (MLP) to estimate the implicit inverse function \\( f^{-1} \\). For simplicity, we use \\( f^{(\\theta)} \\) to represent this network, of which the parameter weights are represented as \\( \\theta \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.796, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Since the implicit inverse function \\( f^{-1} \\) depends on the size and orientation of the specific 3D objects, \\( f^{(\\theta)} \\) should also be different across multiple objects, which means weights \\( \\theta \\) should be dynamic." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1The mentioned orientation is the relative one to the camera, i.e., the observed orientation on the image. We refer the readers to FCOS3D [1] and Stereo-RCNN [63] for more details on obtaining relative orientation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14855" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.074, + 0.48, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.073, + 0.885, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.231, + 0.894, + 0.287 + ], + "angle": 0, + "content": "Figure 4. Illustration of the training and testing pipeline of IP-Head. (a). Training: During training, we use 2D/3D annotation pairs of close objects to supervise \\( f_{g} \\) to generate dynamic weights of MLP \\( f^{(\\theta)} \\) which models the transformation of target 3D object from 2D box to corresponding depth in Eq. (3). (b). Testing: During testing, we use a 2D detection head (2D Det. Head) \\( f_{2d} \\) to generate 2D detection results for all objects. They are then transferred to corresponding depth by IP-Head." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.289, + 0.457, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.494, + 0.468, + 0.521 + ], + "angle": 0, + "content": "Figure 5. Illustration of deploying IP-Head to monocular 3D detectors: (a) FCOS3D; (b) FastRCNN3D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.47, + 0.726 + ], + "angle": 0, + "content": "With these considerations, rather than utilizing a shared \\(\\theta\\) for all objects, we use a trainable MLP \\(f_{g}\\) to generate a set of dynamic weights \\(\\theta_{i}\\) according to the features \\(F_{i}\\) of each object \\(i\\). We then utilize those \\(\\theta_{i}\\) as the weights of network \\(f^{(\\theta)}\\) to estimate the corresponding depth of the \\(i\\)-th 2D box. This process generates the specific Implicit inverse function of each object to Project its 2D box to 3D depth. We illustrate this procedure in Figure 3, in which \"2D Box Encoding\", \\(f_{\\mathrm{PE}}\\), is a positional encoding function [64] to encode 2-channel 2D box descriptors (with width \\(w_{2d}\\) and height \\(h_{2d}\\)) into informative high-dimensional features and \\(f_{2d}\\) is a 2D detection network for predicting 2D bounding boxes on the image. The overall procedure is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.735, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\nd _ {i} = f ^ {\\left(f _ {g} \\left(F _ {i}\\right)\\right)} \\left(f _ {\\mathrm {P E}} \\left(b _ {2 d _ {i}}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.84 + ], + "angle": 0, + "content": "where \\( f_{g} \\) estimates the weights of \\( f^{(\\theta_i)} \\) from instance features \\( F_{i} \\) to transfer the \\( i \\)-th 2D bounding boxes to its corresponding depth. Its condition information, including size \\( s_i \\) and orientation \\( o_i \\), is included in feature \\( F_{i} \\), from which information can be obtained like that of [1, 65, 66]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "During training, we make use of 2D/3D annotation pairs of close objects to supervise IP-Head for obtaining a reliable dynamic weight generator \\( f_{g} \\). Specifically, for a close object, after obtaining its corresponding dynamic weights," + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.289, + 0.89, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.471 + ], + "angle": 0, + "content": "Figure 6. Illustration of extending IP-Head to all camera-based 3D detectors through a teacher-student pipeline." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.484, + 0.891, + 0.528 + ], + "angle": 0, + "content": "we transfer its 2D ground truth box for depth prediction by IP-Head, and optimize \\( f_{g} \\) by computing the loss between the predicted depth and the 3D annotation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.892, + 0.637 + ], + "angle": 0, + "content": "During inference, we first use the backbone network to extract instance features \\( F_{i}^{\\prime} \\). Then, we extract dynamic weights using \\( f_{g} \\) and use a detection network \\( f_{2d} \\), supervised by 2D bounding box ground truth, to predict the associated 2D bounding box \\( b_{2d_i}' \\) as \\( b_{2d_i}' = f_{2d}(F_i') \\). Finally, we use Eq. (3) to obtain depth predictions for each instance in the image. The overall process is illustrated in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.893, + 0.835 + ], + "angle": 0, + "content": "Using neural networks to directly estimate a hard-to-optimize function was successful in other research areas. For example, NeRF [67] uses MLP networks to learn a shared mapping from positions to colors and densities; classification models use a shared CNN model to learn the function from pixels to classification confidence. In contrast to previous methods, we first study the estimation of transformation function from 2D boxes on images to 3D depths. Moreover, instead of learning a shared mapping, IP-Head generates dynamic mappings from 2D box sizes to 3D depth according to the 3D size and orientation of target objects, which equips IP-Head with great generalization ability and potential applied to complex autonomous driving scenarios." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Projection Augmentation. The implicit inverse function \\( f^{(\\theta)} \\) needs to model the relation between the 2D box and corresponding depth, and generate different depth predictions based on 2D box input. To further improve effective" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14856" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "ness, we also propose an augmentation strategy, called projection augmentation. The idea is to generate more depth \\(d\\) and 2D box \\(b_{2d}\\) pairs for each close object during training, so as to enable \\(f_{g}\\) to estimate a more accurate \\(b_{2d} - d\\) relation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.47, + 0.244 + ], + "angle": 0, + "content": "These extra \\( b_{2d} - d \\) training pairs come from Eq. (1). Given an object with fixed size and orientation, we randomly choose different depth values \\( d^{*} \\), calculate their corresponding 2D boxes \\( b_{2d}^{*} \\) through Eq. (1), and utilize these augmented \\( b_{2d}^{*} - d^{*} \\) pairs, along with the ground truth \\( b_{2d} - d \\) pair, to train the IP-Head for higher performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.469, + 0.382 + ], + "angle": 0, + "content": "Long-range Teacher The proposed IP-Head can be used in existing monocular 3D detectors, like FCOS3D [1], to boost their performance in LR3D. As illustrated in Figure 5, only two additional branches, i.e., a 2D detection branch \\( f_{2d} \\) and a weight generation MLP \\( f_{g} \\), are needed to utilize IP-Head in FCOS3D. Apart from monocular methods, BEV methods become popular due to their strong performance and multi-tasking ability. We extend IP-Head to BEV methods to alleviate their demand of 3D annotations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.469, + 0.55 + ], + "angle": 0, + "content": "Our solution is to utilize a monocular method equipped with IP-Head as the detector of the LR3D model which then serves as the long-range teacher to generate pseudo distant 3D annotations. With close 2D/3D annotations and distant 2D annotations, we first apply LR3D to generate 3D predictions for distant objects. Then, we treat these predictions as pseudo 3D box labels, which are, together with close 3D ground truth, taken as the whole supervision to train BEV methods. Our pipeline is shown in Figure 6. Experiments show that, it works decently for various 3D detectors on long-range objects without distant 3D box annotation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.562, + 0.336, + 0.579 + ], + "angle": 0, + "content": "4. Long-range Detection Score" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.627 + ], + "angle": 0, + "content": "Existing detection metrics are built upon mAP based on either IoU [12, 14] or absolute distance error [13]. They use fixed IoU or error thresholds as criterion to calculate AP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.795 + ], + "angle": 0, + "content": "However, the fixed threshold is not suitable for distant objects due to its neglect of the increasing error in depth estimation when objects go farther. For example, though DID-M3D [6] is the state-of-the-art camera-based detector, it only achieves \\(0.43\\%\\) mAP under fixed IoU criterion on objects over \\(40\\mathrm{m}\\). Fixed threshold metrics hardly bring informative results. In fact, further objects should have a larger tolerance to closer ones, since estimating their depth is more ill-posed. Similar ideas were taken in tasks like dense depth estimation [68] and object distance estimation [9]. They all prefer relative distance errors as their metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.469, + 0.856 + ], + "angle": 0, + "content": "To address this limitation, we introduce Long-range Detection Score (LDS), a new metric for long-range 3D object detection. LDS is based on the widely applied nuScenes Detection Score (NDS) [13] and it is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.868, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathrm {L D S} = \\frac {1}{6} [ 3 \\mathrm {m A P} + \\operatorname {R e c} \\times \\sum_ {\\mathrm {m T P} \\in \\mathrm {m T P}} (1 - \\min (1, \\mathrm {m T P})) ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.12 + ], + "angle": 0, + "content": "where Rec is the recall rate and mTP represents the mean True Positive metric." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.892, + 0.185 + ], + "angle": 0, + "content": "LDS improves NDS in two main aspects: the criterion of mAP and the multiplication of Rec and summation of mTP. Improvements on mAP. In LDS, we compute mAP based on the relative distance error of" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.194, + 0.892, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\text {R e l . D i s t . E r r .} = \\frac {\\left\\| P _ {c} - G _ {c} \\right\\|}{G _ {d}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.236, + 0.892, + 0.356 + ], + "angle": 0, + "content": "where \\(P_{c}\\), \\(G_{c}\\) and \\(G_{d}\\) represent the center of predicted 3D box, center of ground truth 3D box and the distance of ground truth 3D box towards ego vehicle, respectively. Predictions with a relative error smaller than a threshold \\(r\\) are counted as true positive, and false positive otherwise, for computing AP. We choose 4 thresholds \\(\\mathbb{R} = \\{0.025, 0.05, 0.1, 0.2\\}\\) and take average over these thresholds and the class set \\(\\mathbb{C}\\). Finally, we obtain mAP as" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.367, + 0.892, + 0.404 + ], + "angle": 0, + "content": "\\[\n\\mathrm {m A P} = \\frac {1}{| \\mathbb {C} | | \\mathbb {R} |} \\sum_ {c \\in \\mathbb {C}} \\sum_ {r \\in \\mathbb {R}} \\mathrm {A P} _ {c, r}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.418, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Improvement on mTP. Also, we multiply the recall rate and mTP before adding to mAP. The mTP is utilized to measure errors on the location (mATE), size (mASE) and orientation (mAOE) for TP prediction, whose relative distance to the ground truth is smaller than \\( r = 0.1 \\) during matching. mATE is computed as the relative distance, normalized by 0.1 to ensure range falling within 0 and 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.644 + ], + "angle": 0, + "content": "mASE and mAOE are the same as those in nuScenes Dataset [13]. The intuition of multiplying the recall rate to the mTP is simple. The larger the recall rate is, the more predictions are involved in the statistics of mTP. Compared to simply setting a recall threshold [13], the multiplication improvement adjusts the weight of mTP to LDS according to its comprehensiveness, and thus brings a more informative quantitative result." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.658, + 0.634, + 0.675 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.789 + ], + "angle": 0, + "content": "We evaluate our method on five popular 3D detection datasets of KITTI [12], nuScenes [13], Cityscapes3D [16], Waymo Open Dataset [14] and Argoverse 2 [15], which have plenty of high-quality 3D annotations for both close and distant objects. Due to the space limitation, we show the experimental results on Cityscapes3D, Waymo and Argoverse 2 datasets in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.673, + 0.813 + ], + "angle": 0, + "content": "5.1. Results on KITTI" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Data Preparation. KITTI Dataset [12] provides high-quality 2D/3D annotations for objects in \"Car\", \"Pedestrian\" and \"Cyclist\" within the range of \\(\\sim 80\\mathrm{m}\\). For extremely distant objects, due to lack of points, it only labels their 2D ground truth boxes on images and marks them as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14857" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.07, + 0.872, + 0.14 + ], + "angle": 0, + "content": "
MethodDistant 3D Groundtruth?Overall (0m-Inf)Close (0m-40m)Distant (40m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√48.044.749.947.538.232.6
FCOS3D [1]-42.138.950.547.14.93.3
LR3D (IP-FCOS3D)50.046.752.149.436.231.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.14, + 0.231, + 0.151 + ], + "angle": 0, + "content": "Long-range Teacher" + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.152, + 0.872, + 0.352 + ], + "angle": 0, + "content": "
ImVoxelNet [52]√44.845.248.148.426.224.7
ImVoxelNet [52]-40.339.948.648.14.44.1
+LR3D teacher44.945.147.947.926.925.3
CaDDN [53]√51.150.157.856.319.318.5
CaDDN [53]-48.948.658.557.95.55.7
+LR3D teacher51.150.657.656.820.919.8
MonoFlex [65]√55.552.457.755.240.634.8
MonoFlex [65]-50.147.359.356.18.46.6
+LR3D teacher54.351.657.354.835.832.9
GUPNet [66]√49.347.554.052.126.725.1
GUPNet [66]-46.845.254.052.317.616.5
+LR3D teacher49.447.854.252.826.424.4
DID-M3D [6]√56.155.158.557.238.936.7
DID-M3D [6]-52.551.458.957.824.222.5
+LR3D teacher56.355.058.757.239.036.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.355, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Table 2. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the KITTI val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.469, + 0.422 + ], + "angle": 0, + "content": "\"DontCare\". Given these labels, we accordingly conduct quantitative and qualitative evaluations on KITTI Dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.469, + 0.558 + ], + "angle": 0, + "content": "Quantitative evaluation is conducted on objects with 3D annotations. Specifically, based on the official provided 3D annotations, we mark annotations over \\(40\\mathrm{m}\\) as distant ones following [9], only using their 2D labels for training. For those closer than \\(40\\mathrm{m}\\), we keep both 2D and 3D labels for training. We report LDS on both close and distant objects for statistical results. The split of train and val sets follows [69]. Due to the lack of \"Pedestrian\" and \"Cyclist\" labels beyond \\(40\\mathrm{m}\\), we only report results on class \"Car\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Qualitative evaluation is designed for \"DontCare\" objects which are extremely far away and without 3D annotations due to no LiDAR points. We visualize the 3D detection results of our model conditioned by their 2D ground truth boxes. Through this evaluation, we manifest the capacity of our model for extremely distant 3D detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.469, + 0.777 + ], + "angle": 0, + "content": "Model Setting. For quantitative evaluation, we utilize FCOS3D [1] as our baseline for its simplicity and implementation platform. FCOS3D is implemented on the MMDetection3D [70] platform including multiple methods and datasets. We extend FCOS3D with our IP-Head (IP-FCOS3D, Figure 5) as the detector in the LR3D framework. For qualitative evaluation, we utilize FastRCNN3D with IP-Head (Figure 5) as LR3D detector, to utilize 2D conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Quantitative Results. We compare our LR3D, using IP-FCOS3D as its detector, and the baseline FCOS3D [1] for distant 3D detection without 3D annotations in Table 2. It is obvious that our LR3D outperforms FCOS3D on detecting distant objects by a large margin, i.e., \\(31.3\\%\\) and \\(27.7\\%\\) on LDS and mAP, respectively. Even compared to FCOS3D with distant 3D ground truth supervision, LR3D still shows competitive performance on distant objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.391, + 0.892, + 0.497 + ], + "angle": 0, + "content": "We further evaluate the performance of using LR3D as the teacher model to generate pseudo long-range 3D labels to train state-of-the-art camera-based detectors. The results are listed in Table 2. Surprisingly, models trained with the combination of close 3D ground truth and distant 3D pseudo labels even achieve comparable or even better performance to their fully 3D supervised counterparts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.559 + ], + "angle": 0, + "content": "Quantitative results in Table 2 demonstrate the effectiveness of our LR3D framework, as well as the potential of our method in relieving the great demand of accurate 3D bounding box annotations for long-range object detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Qualitative Results. We visualize the 3D prediction results of LR3D conditioned with \"DontCare\" objects in Figure 7. It is also clear that supervised by close 3D annotations only (maximum to \\(40\\mathrm{m}\\) away), our method infers reasonable 3D bounding boxes (3rd & 4th rows) for those extremely distant objects much beyond the 3D supervision range according to the corresponding 2D bounding boxes (1st & 2nd rows). These qualitative results further demonstrate the potential to extend LR3D to the labeling process. Annotators can first simply label 2D boxes for distant objects and then generate associated 3D annotations by LR3D." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.738, + 0.692, + 0.753 + ], + "angle": 0, + "content": "5.2. Results on nuScenes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Data Preparation. NuScenes [13] is a large-scale dataset with 1,000 autonomous driving sequences labeled with 3D boxes in 10 classes. In nuScenes, we set the distance threshold of marking long-range objects as \\(40\\mathrm{m}\\). We mark those annotations beyond the threshold as distant objects, remove the 3D annotations and only use 2D box labels for training. For those closer than \\(40\\mathrm{m}\\), we keep their both 2D/3D labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate different models among all 10 classes, and do not set the detection range upper-bound for different" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14858" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.072, + 0.346, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.072, + 0.618, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.072, + 0.89, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.277, + 0.893, + 0.319 + ], + "angle": 0, + "content": "Figure 7. Qualitative results on KITTI Dataset in detecting extremely far away 3D objects. LiDAR points are projected to images shown with different colors related to depth. The distances of 3D bounding boxes are marked on the top-left. 1st & 2nd rows: 2D annotations of extremely distant objects; 3rd & 4th rows: 3D box prediction of corresponding objects." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.323, + 0.877, + 0.392 + ], + "angle": 0, + "content": "
MethodDistant 3D Groundtruth?OverallClose (0m-40m)Distant (40m-51.2m)Distant (51.2m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√26.627.429.130.116.412.711.38.6
FCOS3D [1]-22.623.429.930.31.81.40.00.0
LR3D (IP-FCOS3D)24.124.428.528.416.111.36.44.3
" + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.392, + 0.877, + 0.487 + ], + "angle": 0, + "content": "
Long-range Teacher
BEVFormer-S [2]√36.937.238.338.719.615.2--
BEVFormer-S [2] +LR3D teacher-33.634.238.038.52.41.7--
36.336.838.038.918.310.9--
BEVFormer-S† [2]√33.734.037.437.919.414.514.410.2
BEVFormer-S† [2] +LR3D teacher-29.129.938.038.72.41.00.00.0
33.033.637.538.017.910.712.76.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.489, + 0.89, + 0.517 + ], + "angle": 0, + "content": "Table 3. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the nuScenes val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.469, + 0.571 + ], + "angle": 0, + "content": "classes as the official benchmark [13]. This setting helps keep distant predictions. Following [13], we train our model on 700 training scenes and test it on 150 validation scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.469, + 0.667 + ], + "angle": 0, + "content": "Model Setting. We utilize FCOS3D [1] as our monocular baseline and enhance it with IP-Head (IP-FCOS3D) for LR3D with 2D supervision only. To demonstrate the effectiveness of LR3D as a long-range teacher on nuScenes, we choose BEVFormer [2] as the student for its effectiveness, and test its performance without distant 3D supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.469, + 0.777 + ], + "angle": 0, + "content": "Main Results. The experimental results are illustrated in Table 3. With IP-Head, LR3D outperforms its baseline FCOS3D by \\(14.3\\%\\) and \\(9.9\\%\\) performance improvement in terms of LDS and mAP for distant objects from \\(40\\mathrm{m}\\) to \\(51.2\\mathrm{m}\\). It is significant. Compared to the fully 3D supervised FCOS3D with distant 3D ground truth, LR3D still yields competitive capacity on long-range 3D detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.854 + ], + "angle": 0, + "content": "We also list the results of BEVFormer [2] with and without LR3D teacher on detecting distant 3D objects without 3D supervision. As illustrated, with the LR3D teacher, BEVFormer-S yields strong performance, comparable to its fully-supervised counterparts with 3D box labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.899 + ], + "angle": 0, + "content": "Given the limited perception range of official BEVFormer \\((-51.2\\mathrm{m}\\) to \\(51.2\\mathrm{m})\\) we enlarge the perception range of BEVFormer from \\(51.2\\mathrm{m}\\) to \\(76.8\\mathrm{m}\\) for further verifica" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.892, + 0.587 + ], + "angle": 0, + "content": "tion, denoted as BEVFormer-\\(S^{\\dagger}\\). Still, as shown in Table 3, with LR3D teacher, BEVFormer-\\(S^{\\dagger}\\) achieves impressive improvement compared to its baseline, and yields comparable results to those of the fully-supervised model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.599, + 0.664, + 0.613 + ], + "angle": 0, + "content": "5.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.653 + ], + "angle": 0, + "content": "All ablation studies are conducted on KITTI Dataset, using IP-FCOS3D as the detector of the LR3D model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Analysis on the IP-Head. IP-Head learns to estimate implicit inverse function \\( f^{-1} \\), which is the mapping from 2D bounding box on image to corresponding depth, through two MLP networks \\( f_{g} \\) and \\( f^{(\\theta)} \\). We evaluate its effectiveness by comparing the mapping curve from 2D box size to the depth of a fixed 3D object generated by ground truth transformation and estimated transformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The generation of the ground truth curve follows Eq. (1), from which we obtain multiple \\(d - b_{2d}\\) pairs by modifying depth \\(d\\). The estimated curve is generated through Eq. (3) by changing the 2D box inputs. As illustrated in Figure 8, our IP-Head can estimate specific implicit inverse functions for different objects (by comparison across rows). The estimated function by MLP network \\(f^{(\\theta)}\\) well models the mapping from 2D bounding box size to the corresponding depth of target 3D object (through comparison inside each row)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14859" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.089, + 0.071, + 0.328, + 0.14 + ], + "angle": 0, + "content": "
f(θ) Weight Learning StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
Shared45.046.632.5
Dynamic50.052.136.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.097, + 0.152, + 0.31, + 0.167 + ], + "angle": 0, + "content": "(a) Effect of parameter learning in \\( f^{(\\theta)} \\)." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.171, + 0.333, + 0.262 + ], + "angle": 0, + "content": "
No. of layersOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
148.651.332.4
250.052.136.2
349.752.035.2
449.051.434.9
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.093, + 0.264, + 0.314, + 0.277 + ], + "angle": 0, + "content": "(d) Effect of the number of layers in \\( f^{(\\theta)} \\)." + }, + { + "type": "table", + "bbox": [ + 0.368, + 0.071, + 0.617, + 0.14 + ], + "angle": 0, + "content": "
Pos. Enc.Overall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
None19.920.213.3
Sin. Cos. [64]50.052.136.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.375, + 0.152, + 0.591, + 0.166 + ], + "angle": 0, + "content": "(b) Effect of positional encoding in \\( f^{(\\theta)} \\)." + }, + { + "type": "table", + "bbox": [ + 0.368, + 0.171, + 0.624, + 0.262 + ], + "angle": 0, + "content": "
No. of channelsOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
848.450.934.5
1650.052.136.2
3249.952.335.6
6449.751.936.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.375, + 0.264, + 0.59, + 0.277 + ], + "angle": 0, + "content": "(e) Effect of the channel number in \\( f^{(\\theta)} \\)." + }, + { + "type": "table", + "bbox": [ + 0.647, + 0.072, + 0.909, + 0.151 + ], + "angle": 0, + "content": "
2D Box (b2d) \nDescriptorsOverall \n(0m-Inf) \nLDS (%)Close \n(0m-40m) \nLDS (%)Distant \n(40m-Inf) \nLDS (%)
box width (w2d)48.551.730.6
box height (h2d)49.451.834.9
both (w2d, h2d)50.052.136.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.677, + 0.153, + 0.847, + 0.165 + ], + "angle": 0, + "content": "(c) Effect of 2D box descriptors." + }, + { + "type": "table", + "bbox": [ + 0.647, + 0.17, + 0.899, + 0.263 + ], + "angle": 0, + "content": "
Aug. StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
FCOS3D [1]42.150.54.9
+Copy-PasteN/AN/AN/A
LR3D48.352.726.5
+Proj. Aug.50.052.136.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.653, + 0.265, + 0.87, + 0.276 + ], + "angle": 0, + "content": "(f) Effect of the projection augmentation." + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.282, + 0.846, + 0.298 + ], + "angle": 0, + "content": "Table 4. Ablation studies on IP-Head structure and projection augmentation. Default settings are highlighted in lightcyan ." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.308, + 0.47, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.485, + 0.47, + 0.528 + ], + "angle": 0, + "content": "Figure 8. Illustration of the ground truth and estimated \\( b_{2d} - d \\) mappings. Each row indicates the target 3D object and its mapping from 2D box width and height to the depth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.664 + ], + "angle": 0, + "content": "We further provide quantitative analysis of using MLP network \\( f_{g} \\) to dynamically determine weights of \\( f^{(\\theta)} \\) to estimate specific implicit inverse functions of different 3D objects. As listed in Table 4a, compared to the design of shared weights, using dynamic weights assignment in \\( f^{(\\theta)} \\) well models the difference of implicit inverse functions due to size and orientation of 3D objects, and thus outperforms the model using a shared weight \\( \\theta \\) across 3D objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.47, + 0.747 + ], + "angle": 0, + "content": "Analysis on the IP-Head Structure. We first describe the default structure of IP-Head. \\( f^{(\\theta)} \\) is a 2-layer perceptron with channels of 16 and 1. The 2D boxes \\( b_{2d} \\) are described as height \\( (h_{2d}) \\) and width \\( (w_{2d}) \\). The positional encoding function \\( f_{\\mathrm{PE}} \\) is the sine-cosine function illustrated in [64]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In Table 4b, we evaluate the contribution of positional encoding. With positional encoding [64], the 2D descriptors are well encoded into more informative features, which thus outperforms the model without positional encoding (\"None\"). In Table 4c, we compare the model with different 2D box descriptors. Utilizing both 2D box width \\( w_{2d} \\) and height \\( h_{2d} \\) as descriptors yields the best performance. In Table 4d and Table 4e, we conduct ablation studies on MLP structures of network \\( f^{(\\theta)} \\) with different numbers of layers and channels. As illustrated, the model with 2-layer" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.308, + 0.822, + 0.323 + ], + "angle": 0, + "content": "and channel number 16 achieves the best results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.498 + ], + "angle": 0, + "content": "Analysis on the Projection Augmentation. The projection augmentation ensures the estimated implicit inverse function \\( f^{(\\theta)} \\) models the relation between 2D box sizes and depths by generating more training \\( b_{2d} - d \\) pairs. We analyze it by comparing the performance of LR3D trained with and without this augmentation. As shown in Table 4f, compared to FCOS3D baseline (1st row), LR3D can model mapping functions from 2D sizes to depths and produces good results on distant objects without 3D supervision. Moreover, equipped with projection augmentation, LR3D further shows a huge performance improvement on distant objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.64 + ], + "angle": 0, + "content": "A similar augmentation to projection augmentation is copy-paste augmentation [71, 72], which simulates distant training samples by cropping close objects with image patches and pasting them to distant areas by Eq. (1). However, this augmentation brings noises in image distribution, is hard to optimize, and thus leads to a great performance drop (Table 4f (2nd row)). In contrast, projection augmentation is simple to implement without changing training images, and able to augment to any depth without extra effort." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.663, + 0.736, + 0.678 + ], + "angle": 0, + "content": "5.4. Results on Other Datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.691, + 0.892, + 0.723 + ], + "angle": 0, + "content": "Please find additional results on Cityscapes3D [16], Waymo [14], and Argoverse 2 [15] in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.75, + 0.619, + 0.765 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this paper, we proposed the LR3D framework for long-range 3D detection using 2D supervision and designed the IP-Head as the key component. We developed a teacher-student pipeline to benefit all camera-based detectors. Our LDS, a metric with relative distance criterion, helps obtain informative quantitative results for distant objects. With these designs, we demonstrate the feasibility of using 2D supervision only for long-range 3D detection." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14860" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Tai Wang, Xinge Zhu, Jiangmiao Pang, and Dahua Lin. FCOS3D: Fully convolutional one-stage monocular 3d object detection. In ICCV Workshops, 2021. 1, 2, 3, 4, 5, 6, 7, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.241 + ], + "angle": 0, + "content": "[2] Zhiqi Li, Wenhai Wang, Hongyang Li, Enze Xie, Chonghao Sima, Tong Lu, Yu Qiao, and Jifeng Dai. 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Alvarez $^{2}$ + +$^{1}$ CUHK $^{2}$ NVIDIA $^{3}$ UC Berkeley $^{4}$ Caltech + +![](images/403c9b7771c31a6773df33add2d2ccdd1c324155623c44f8ad4f132053e8a7c4.jpg) + +![](images/e00e77f6bf713c203e8490e2363f5ff370d4b7d83c9e731fa573f8fbd97af517.jpg) +DID-M3D + +![](images/3ed62fcae65dc8d232aa06bd15db7076cf51340c7edceebf29625bd795282350.jpg) +LR3D (Ours) +Figure 1. Upper: Without 3D annotations beyond $40\mathrm{m}$ , LR3D enables the predictions of 3D boxes for extremely distant objects over $200\mathrm{m}$ (right, in green) based on the inputs of image and 2D box (left). Lower: Existing methods fail to detect 3D objects beyond the 3D supervision range, e.g., $40\mathrm{m}$ for this case. With LR3D, these remote missing objects are well detected. + +# Abstract + +Improving the detection of distant 3d objects is an important yet challenging task. For camera-based 3D perception, the annotation of 3d bounding relies heavily on LiDAR for accurate depth information. As such, the distance of annotation is often limited due to the sparsity of LiDAR points on distant objects, which hampers the capability of existing detectors for long-range scenarios. We address this challenge by considering only 2D box supervision for distant objects since they are easy to annotate. We propose LR3D, a framework that learns to recover the missing depth of distant objects. LR3D adopts an implicit projection head to learn the generation of mapping between 2D boxes and depth using the 3D supervision on close objects. This mapping allows the depth estimation of distant objects conditioned on their 2D boxes, making long-range 3D detection with 2D supervision feasible. Experiments show that without distant 3D annotations, LR3D allows camera-based methods to detect distant objects (over $200m$ ) with comparable accuracy to full 3D supervision. Our framework is general, and could widely benefit 3D detection methods to a large extent. + +# 1. Introduction + +Camera-based 3D object detection [1-7] is an important task in autonomous driving aiming to localize and classify objects in 3D space with monocular or multi-view image input. Detecting distant objects with camera input is both important and challenging. On one hand, the ability to detect objects at distance is needed for planning, especially for highway scenarios. According to [8], at 60 miles/hour, the typical stopping distance for a vehicle is 73 meters and it grows significantly under harsh road conditions such as having wet surface [9-11]. On the other hand, the detection range of camera-based methods depends heavily on the distance range of 3D annotations. For example, these methods work well within the distance range with abundant 3D annotations (e.g., $\sim 70$ meters on KITTI [12] and nuScenes [13]), but often fail beyond this range where 3D annotations are missing. This indicates the importance to improve distant 3D object detection with longer 3D annotation range. + +Though of great importance, increasing the range of 3D annotation is not easy. One main challenge is the sparsity of LiDAR points at longer distances. LiDAR is typically the main reference for axial depth information in 3D annotation. For distant objects with few or even no LiDAR points, + +labeling their 3D bounding boxes is an ill-posed, noisy, and time-consuming task for human annotators. For this reason, distant 3D box annotations are rare, and most datasets [12-14] provide 3D annotations around 70 meters. A few datasets [15, 16] provide far-away annotations. They obtain long-range 3D annotations either by using costly Li-DAR sensors with very long sensing ranges or by taking significant efforts in annotating 3D boxes with consistency among sequences of stereo images. Both of these strategies are more expensive and less scalable, compared to drawing precise 2D boxes on images. Thus, in this paper, we explore an efficient camera-based approach to achieve high-quality long-range 3D object detection, which uses only 2D annotations for long-range objects of which the 3D annotations are hardly available due to sparse or no interior LiDAR points. + +Our approach: We present LR3D, a camera-based detection framework that detects distant 3D objects using only 2D bounding box annotations. The core of LR3D is an Implicit Projection Head (IP-Head) design that can be plugged into existing camera-based detectors and enables them to effectively predict 3D bounding boxes at all ranges, using the supervision from close 2D/3D and distant 2D box labels. + +IP-Head learns to generate specific mapping for each instance from their 2D bounding box prediction to the corresponding depth, and thus is capable of estimating depth for distant objects relying on 2D supervision only. We also design a projection augmentation strategy to force the generated implicit function to correctly model the mapping between 2D boxes and 3D depth of target instances and estimate different depth outputs if the 2D box input changes. + +We also notice issues in evaluating camera-based detectors for long-range 3D detection. Existing evaluation metrics [12, 13], based on mean average precision (mAP) with fixed thresholds, neglect the inaccuracy of depth estimation of distant objects from cameras and lead to meaningless numbers even for state-of-the-art methods, e.g., only $0.43\%$ mAP of DID-M3D [6] on KITTI Dataset for objects farther than $40\mathrm{m}$ . This motivates us to design a novel metric, Long-range Detection Score (LDS), which sets a dynamic threshold for judging TP prediction regarding associated ground truth depth, for informative qualitative comparison. + +We conduct experiments on five popular 3D detection datasets including KITTI [12], nuScenes [13], and Waymo [14] for objects within $80\mathrm{m}$ , as well as Cityscapes3D [16] and Argoverse 2 [15] for objects farther than $200\mathrm{m}$ . We remove the 3D annotations of farther objects in the train set and evaluate the performance on 3D objects at all ranges. + +Experiments show that, with LR3D, state-of-the-art detectors gain significant improvement in detecting distant objects without 3D annotation, i.e., $14.8\%$ improvement of DID-M3D [6] on KITTI [12], $15.9\%$ improvement of BEVFormer [2] on nuScenes [13], $34.5\%$ and $14.17\%$ improvement of FCOS3D [1] on Cityscapes3D and Argoverse + +2, $7.09\%$ improvement of MV-FCOS3D++ [7] on Waymo. With LR3D, these methods yield competitive performance even compared to fully 3D supervised counterparts. Notably, LR3D enables them to detect extremely distant 3D objects as shown in Figure 1. + +# 2. Related Work + +LiDAR-based Detectors. LiDAR methods detect 3D objects from point clouds. According to inputs, these methods can be divided into point, voxel, and range-view detectors. Point methods [17-21] make 3D predictions from raw point clouds [22-27]. Voxel methods [28-31] transform point clouds into voxels and extract features by convolutions [32-37]. Other methods project point clouds into range-view [38-42] and process them as images [43]. Albeit impressively performed, LiDAR methods are 3D-label-greedy, and limited by the perspective range of LiDAR sensors, i.e., usually fail for areas with few or no LiDAR points. + +Camera-based Detectors. Camera-based methods do 3D detection from images. Monocular methods predict 3D boxes in single image directly [1, 44-47]. Stereo methods based on multi-view images formulate a 3D volume [48-50]. Recent methods [2, 51-57] build a bird-eye-view (BEV) representation for detection. + +The advantages of Camera-based methods lie in the unbounded perception range of cameras, which makes them suitable for distant 3D detection. Some methods, e.g., Far3D [58], are designed for long-range 3D detection, but still heavily rely on abundant high-quality distant 3D annotations, which are hard to collect. Some datasets [15, 16] provide distant annotations. However, their labeling is time-consuming and requires huge human efforts to take hints from multi-modal sensors and temporal consistency to label distant objects with few or no interior LiDAR points. The workload of the labeling process and the 3D-label-greedy character of existing detectors limit the applications of long-range 3D detection. Instead, we propose to detect distant 3D objects without long-range 3D box supervision. It is the simplest setting and is practical for scalability. + +Object Distance Estimation. Another related topic is monocular distance estimation, which estimates the object distance from an RGB image. SVR [59] and DisNet [60] estimate object distance through pixel height and width. They base on an assumption of projected 2D box size determined by the distance of object only. However, other factors, like size and orientation, also affect the projected 2D box size. + +Method of [61] develops a FastRCNN [62] pipeline for end-to-end distance estimation by directly regressing the distance from RoI features. R4D [9] utilizes reference objects for further improvements. These methods are limited by their requirements of abundant annotations. Given the difficulty in labeling distant 3D objects, in this paper, we develop a simpler 2D setting that even achieves competitive + +![](images/e60418d9f80d61bf84553077e043fd61e694efc9e8683bc4b332cbde2e8fec07.jpg) +Figure 2. Illustration of LR3D which detects 3D boxes for both close and distant objects using the supervision of close 2D/3D and distant 2D bounding box annotations. + +
Distant 3D Groundtruth?Location Err.Size Err.Orientation Err.
✓0.090.210.37
-0.34 (+0.25)0.23 (+0.02)0.41 (+0.04)
+ +Table 1. Performance comparison between FastRCNN3D trained with and without distant 3D supervision. + +performance to their 3D supervised counterparts. + +# 3. Method + +LR3D is a long-range 3D detection framework that detects 3D bounding boxes, including locations, sizes, and orientations, of distant objects using only their 2D supervision (Figure 2). In this section, we first analyze the main challenge of directly utilizing existing 3D detectors on LR3D in Section 3.1 and then introduce our solution in Section 3.2. + +# 3.1. Analysis + +Albeit important and critical, long-range 3D object detection is seldom explored. One difficulty is to obtain sufficient high-quality 3D bounding box annotations for distant objects. We discard this high-human-labor-cost setting and propose a new framework, LR3D, to predict 3D boxes for distant objects only from their 2D image supervision. + +Can Existing Methods Use only 2D Supervision? We first analyze if existing methods can use only 2D supervision for detecting distant 3D objects. To this end, we use FastRCNN3D, a FastRCNN-like [62] 3D detector where the original head for 2D detection is replaced by the FCOS3D head [1] for 3D detection. For training, we first manually assign objects over $40\mathrm{m}$ as distant objects and remove their 3D annotations. Then, we train FastRCNN3D with close 2D/3D and distant 2D box labels as Figure 2. At test time, we use the 2D ground truth of distant objects as proposals, predict their 3D boxes, and evaluate their errors in location, size, and orientation. Note that we use relative distance as location error, IoU with aligned location and orientation as size error, and absolute difference as orientation error. + +Table 1 compares errors between the LR3D configuration and traditional full supervision. As shown, errors in size and orientation are comparable. The main gap comes from the location error, in which depth estimation plays the + +![](images/306247ae5d24106d41ea8885261a7cd788cde6da4d2fdc36e1433c2725cff874.jpg) +Figure 3. Illustration of IP-Head. We use an MLP $f^{(\theta)}$ to fit the implicit function from 2D box to 3D depth, of which the weights $\theta$ are dynamically determined by instance features including information of size and orientation. + +essential role. Due to the lack of depth information in 2D box supervision, directly regressing the depth as previous methods cannot produce accurate depth prediction for distant objects and leads to a significant drop. Therefore, we seek a new method to implicitly estimate the depth. + +# 3.2. Implicit Projection Head + +Here, we introduce Implicit Projection head (IP-Head), our proposal to estimate depth of distant objects using only 2D supervision. Given a 3D object with fixed depth, size, and orientation $^1$ , through the camera calibration matrix, it is easy to obtain the corresponding projected 2D bounding box (described by its width $w_{2d}$ and height $h_{2d}$ ) on the target image. We use a function $f$ , determined by the calibration matrix, to indicate the mapping between depth $(d)$ , size $(s)$ , orientation $(o)$ and 2D box $(b_{2d} = (w_{2d}, h_{2d}))$ as + +$$ +f (d, s, o) = b _ {2 d}. \tag {1} +$$ + +Eq. (1) shows the ubiquitous relation between $d$ and $b_{2d}$ if the object size $s$ and orientation $o$ are fixed – for objects with the same size and orientation, the further these objects locate, the smaller their projected 2D boxes on image are. Inspired by this fact, we ask if it is possible to estimate the inverse function $f^{-1}$ to transfer the 2D bounding box to the corresponding depth conditioned by $s$ and $o$ , formulated as + +$$ +f ^ {- 1} \left(b _ {2 d} | s, o\right) = d. \tag {2} +$$ + +With the power of neural networks to fit complicated functions, we utilize a small-size network with a multi-layer perceptron (MLP) to estimate the implicit inverse function $f^{-1}$ . For simplicity, we use $f^{(\theta)}$ to represent this network, of which the parameter weights are represented as $\theta$ . + +Since the implicit inverse function $f^{-1}$ depends on the size and orientation of the specific 3D objects, $f^{(\theta)}$ should also be different across multiple objects, which means weights $\theta$ should be dynamic. + +![](images/d4be4de832e4ac872246bbb1b105f3f0ed46be6b4de2bd84798b297f3d9cddba.jpg) + +![](images/11e3e94197473f455cc8cbbaa8d30448ca329543eede56ee6a38aa3f55cd1789.jpg) + +![](images/15db0a060d0f36c1fd719909bf162acdddc41fa05c84c99278c008ec4e069fa3.jpg) +Figure 4. Illustration of the training and testing pipeline of IP-Head. (a). Training: During training, we use 2D/3D annotation pairs of close objects to supervise $f_{g}$ to generate dynamic weights of MLP $f^{(\theta)}$ which models the transformation of target 3D object from 2D box to corresponding depth in Eq. (3). (b). Testing: During testing, we use a 2D detection head (2D Det. Head) $f_{2d}$ to generate 2D detection results for all objects. They are then transferred to corresponding depth by IP-Head. +Figure 5. Illustration of deploying IP-Head to monocular 3D detectors: (a) FCOS3D; (b) FastRCNN3D. + +With these considerations, rather than utilizing a shared $\theta$ for all objects, we use a trainable MLP $f_{g}$ to generate a set of dynamic weights $\theta_{i}$ according to the features $F_{i}$ of each object $i$ . We then utilize those $\theta_{i}$ as the weights of network $f^{(\theta)}$ to estimate the corresponding depth of the $i$ -th 2D box. This process generates the specific Implicit inverse function of each object to Project its 2D box to 3D depth. We illustrate this procedure in Figure 3, in which "2D Box Encoding", $f_{\mathrm{PE}}$ , is a positional encoding function [64] to encode 2-channel 2D box descriptors (with width $w_{2d}$ and height $h_{2d}$ ) into informative high-dimensional features and $f_{2d}$ is a 2D detection network for predicting 2D bounding boxes on the image. The overall procedure is formulated as + +$$ +d _ {i} = f ^ {\left(f _ {g} \left(F _ {i}\right)\right)} \left(f _ {\mathrm {P E}} \left(b _ {2 d _ {i}}\right)\right), \tag {3} +$$ + +where $f_{g}$ estimates the weights of $f^{(\theta_i)}$ from instance features $F_{i}$ to transfer the $i$ -th 2D bounding boxes to its corresponding depth. Its condition information, including size $s_i$ and orientation $o_i$ , is included in feature $F_{i}$ , from which information can be obtained like that of [1, 65, 66]. + +During training, we make use of 2D/3D annotation pairs of close objects to supervise IP-Head for obtaining a reliable dynamic weight generator $f_{g}$ . Specifically, for a close object, after obtaining its corresponding dynamic weights, + +![](images/8d0ffe2e921adc39f46f70b18725120558a65c435bf808727e330e6fe0d59e98.jpg) +Figure 6. Illustration of extending IP-Head to all camera-based 3D detectors through a teacher-student pipeline. + +we transfer its 2D ground truth box for depth prediction by IP-Head, and optimize $f_{g}$ by computing the loss between the predicted depth and the 3D annotation. + +During inference, we first use the backbone network to extract instance features $F_{i}^{\prime}$ . Then, we extract dynamic weights using $f_{g}$ and use a detection network $f_{2d}$ , supervised by 2D bounding box ground truth, to predict the associated 2D bounding box $b_{2d_i}'$ as $b_{2d_i}' = f_{2d}(F_i')$ . Finally, we use Eq. (3) to obtain depth predictions for each instance in the image. The overall process is illustrated in Figure 4. + +Using neural networks to directly estimate a hard-to-optimize function was successful in other research areas. For example, NeRF [67] uses MLP networks to learn a shared mapping from positions to colors and densities; classification models use a shared CNN model to learn the function from pixels to classification confidence. In contrast to previous methods, we first study the estimation of transformation function from 2D boxes on images to 3D depths. Moreover, instead of learning a shared mapping, IP-Head generates dynamic mappings from 2D box sizes to 3D depth according to the 3D size and orientation of target objects, which equips IP-Head with great generalization ability and potential applied to complex autonomous driving scenarios. + +Projection Augmentation. The implicit inverse function $f^{(\theta)}$ needs to model the relation between the 2D box and corresponding depth, and generate different depth predictions based on 2D box input. To further improve effective + +ness, we also propose an augmentation strategy, called projection augmentation. The idea is to generate more depth $d$ and 2D box $b_{2d}$ pairs for each close object during training, so as to enable $f_{g}$ to estimate a more accurate $b_{2d} - d$ relation. + +These extra $b_{2d} - d$ training pairs come from Eq. (1). Given an object with fixed size and orientation, we randomly choose different depth values $d^{*}$ , calculate their corresponding 2D boxes $b_{2d}^{*}$ through Eq. (1), and utilize these augmented $b_{2d}^{*} - d^{*}$ pairs, along with the ground truth $b_{2d} - d$ pair, to train the IP-Head for higher performance. + +Long-range Teacher The proposed IP-Head can be used in existing monocular 3D detectors, like FCOS3D [1], to boost their performance in LR3D. As illustrated in Figure 5, only two additional branches, i.e., a 2D detection branch $f_{2d}$ and a weight generation MLP $f_{g}$ , are needed to utilize IP-Head in FCOS3D. Apart from monocular methods, BEV methods become popular due to their strong performance and multi-tasking ability. We extend IP-Head to BEV methods to alleviate their demand of 3D annotations. + +Our solution is to utilize a monocular method equipped with IP-Head as the detector of the LR3D model which then serves as the long-range teacher to generate pseudo distant 3D annotations. With close 2D/3D annotations and distant 2D annotations, we first apply LR3D to generate 3D predictions for distant objects. Then, we treat these predictions as pseudo 3D box labels, which are, together with close 3D ground truth, taken as the whole supervision to train BEV methods. Our pipeline is shown in Figure 6. Experiments show that, it works decently for various 3D detectors on long-range objects without distant 3D box annotation. + +# 4. Long-range Detection Score + +Existing detection metrics are built upon mAP based on either IoU [12, 14] or absolute distance error [13]. They use fixed IoU or error thresholds as criterion to calculate AP. + +However, the fixed threshold is not suitable for distant objects due to its neglect of the increasing error in depth estimation when objects go farther. For example, though DID-M3D [6] is the state-of-the-art camera-based detector, it only achieves $0.43\%$ mAP under fixed IoU criterion on objects over $40\mathrm{m}$ . Fixed threshold metrics hardly bring informative results. In fact, further objects should have a larger tolerance to closer ones, since estimating their depth is more ill-posed. Similar ideas were taken in tasks like dense depth estimation [68] and object distance estimation [9]. They all prefer relative distance errors as their metrics. + +To address this limitation, we introduce Long-range Detection Score (LDS), a new metric for long-range 3D object detection. LDS is based on the widely applied nuScenes Detection Score (NDS) [13] and it is defined as + +$$ +\mathrm {L D S} = \frac {1}{6} [ 3 \mathrm {m A P} + \operatorname {R e c} \times \sum_ {\mathrm {m T P} \in \mathrm {m T P}} (1 - \min (1, \mathrm {m T P})) ], \tag {4} +$$ + +where Rec is the recall rate and mTP represents the mean True Positive metric. + +LDS improves NDS in two main aspects: the criterion of mAP and the multiplication of Rec and summation of mTP. Improvements on mAP. In LDS, we compute mAP based on the relative distance error of + +$$ +\text {R e l . D i s t . E r r .} = \frac {\left\| P _ {c} - G _ {c} \right\|}{G _ {d}}, \tag {5} +$$ + +where $P_{c}$ , $G_{c}$ and $G_{d}$ represent the center of predicted 3D box, center of ground truth 3D box and the distance of ground truth 3D box towards ego vehicle, respectively. Predictions with a relative error smaller than a threshold $r$ are counted as true positive, and false positive otherwise, for computing AP. We choose 4 thresholds $\mathbb{R} = \{0.025, 0.05, 0.1, 0.2\}$ and take average over these thresholds and the class set $\mathbb{C}$ . Finally, we obtain mAP as + +$$ +\mathrm {m A P} = \frac {1}{| \mathbb {C} | | \mathbb {R} |} \sum_ {c \in \mathbb {C}} \sum_ {r \in \mathbb {R}} \mathrm {A P} _ {c, r}. \tag {6} +$$ + +Improvement on mTP. Also, we multiply the recall rate and mTP before adding to mAP. The mTP is utilized to measure errors on the location (mATE), size (mASE) and orientation (mAOE) for TP prediction, whose relative distance to the ground truth is smaller than $r = 0.1$ during matching. mATE is computed as the relative distance, normalized by 0.1 to ensure range falling within 0 and 1. + +mASE and mAOE are the same as those in nuScenes Dataset [13]. The intuition of multiplying the recall rate to the mTP is simple. The larger the recall rate is, the more predictions are involved in the statistics of mTP. Compared to simply setting a recall threshold [13], the multiplication improvement adjusts the weight of mTP to LDS according to its comprehensiveness, and thus brings a more informative quantitative result. + +# 5. Experiments + +We evaluate our method on five popular 3D detection datasets of KITTI [12], nuScenes [13], Cityscapes3D [16], Waymo Open Dataset [14] and Argoverse 2 [15], which have plenty of high-quality 3D annotations for both close and distant objects. Due to the space limitation, we show the experimental results on Cityscapes3D, Waymo and Argoverse 2 datasets in the supplementary material. + +# 5.1. Results on KITTI + +Data Preparation. KITTI Dataset [12] provides high-quality 2D/3D annotations for objects in "Car", "Pedestrian" and "Cyclist" within the range of $\sim 80\mathrm{m}$ . For extremely distant objects, due to lack of points, it only labels their 2D ground truth boxes on images and marks them as + +
MethodDistant 3D Groundtruth?Overall (0m-Inf)Close (0m-40m)Distant (40m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√48.044.749.947.538.232.6
FCOS3D [1]-42.138.950.547.14.93.3
LR3D (IP-FCOS3D)50.046.752.149.436.231.0
+ +Long-range Teacher + +
ImVoxelNet [52]√44.845.248.148.426.224.7
ImVoxelNet [52]-40.339.948.648.14.44.1
+LR3D teacher44.945.147.947.926.925.3
CaDDN [53]√51.150.157.856.319.318.5
CaDDN [53]-48.948.658.557.95.55.7
+LR3D teacher51.150.657.656.820.919.8
MonoFlex [65]√55.552.457.755.240.634.8
MonoFlex [65]-50.147.359.356.18.46.6
+LR3D teacher54.351.657.354.835.832.9
GUPNet [66]√49.347.554.052.126.725.1
GUPNet [66]-46.845.254.052.317.616.5
+LR3D teacher49.447.854.252.826.424.4
DID-M3D [6]√56.155.158.557.238.936.7
DID-M3D [6]-52.551.458.957.824.222.5
+LR3D teacher56.355.058.757.239.036.2
+ +Table 2. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the KITTI val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated. + +"DontCare". Given these labels, we accordingly conduct quantitative and qualitative evaluations on KITTI Dataset. + +Quantitative evaluation is conducted on objects with 3D annotations. Specifically, based on the official provided 3D annotations, we mark annotations over $40\mathrm{m}$ as distant ones following [9], only using their 2D labels for training. For those closer than $40\mathrm{m}$ , we keep both 2D and 3D labels for training. We report LDS on both close and distant objects for statistical results. The split of train and val sets follows [69]. Due to the lack of "Pedestrian" and "Cyclist" labels beyond $40\mathrm{m}$ , we only report results on class "Car". + +Qualitative evaluation is designed for "DontCare" objects which are extremely far away and without 3D annotations due to no LiDAR points. We visualize the 3D detection results of our model conditioned by their 2D ground truth boxes. Through this evaluation, we manifest the capacity of our model for extremely distant 3D detection. + +Model Setting. For quantitative evaluation, we utilize FCOS3D [1] as our baseline for its simplicity and implementation platform. FCOS3D is implemented on the MMDetection3D [70] platform including multiple methods and datasets. We extend FCOS3D with our IP-Head (IP-FCOS3D, Figure 5) as the detector in the LR3D framework. For qualitative evaluation, we utilize FastRCNN3D with IP-Head (Figure 5) as LR3D detector, to utilize 2D conditions. + +Quantitative Results. We compare our LR3D, using IP-FCOS3D as its detector, and the baseline FCOS3D [1] for distant 3D detection without 3D annotations in Table 2. It is obvious that our LR3D outperforms FCOS3D on detecting distant objects by a large margin, i.e., $31.3\%$ and $27.7\%$ on LDS and mAP, respectively. Even compared to FCOS3D with distant 3D ground truth supervision, LR3D still shows competitive performance on distant objects. + +We further evaluate the performance of using LR3D as the teacher model to generate pseudo long-range 3D labels to train state-of-the-art camera-based detectors. The results are listed in Table 2. Surprisingly, models trained with the combination of close 3D ground truth and distant 3D pseudo labels even achieve comparable or even better performance to their fully 3D supervised counterparts. + +Quantitative results in Table 2 demonstrate the effectiveness of our LR3D framework, as well as the potential of our method in relieving the great demand of accurate 3D bounding box annotations for long-range object detection. + +Qualitative Results. We visualize the 3D prediction results of LR3D conditioned with "DontCare" objects in Figure 7. It is also clear that supervised by close 3D annotations only (maximum to $40\mathrm{m}$ away), our method infers reasonable 3D bounding boxes (3rd & 4th rows) for those extremely distant objects much beyond the 3D supervision range according to the corresponding 2D bounding boxes (1st & 2nd rows). These qualitative results further demonstrate the potential to extend LR3D to the labeling process. Annotators can first simply label 2D boxes for distant objects and then generate associated 3D annotations by LR3D. + +# 5.2. Results on nuScenes + +Data Preparation. NuScenes [13] is a large-scale dataset with 1,000 autonomous driving sequences labeled with 3D boxes in 10 classes. In nuScenes, we set the distance threshold of marking long-range objects as $40\mathrm{m}$ . We mark those annotations beyond the threshold as distant objects, remove the 3D annotations and only use 2D box labels for training. For those closer than $40\mathrm{m}$ , we keep their both 2D/3D labels. + +We evaluate different models among all 10 classes, and do not set the detection range upper-bound for different + +![](images/7f771391cce88f1c6aff2331e8d8c22ed612a95160648ed09615c930c48ab2c1.jpg) +Figure 7. Qualitative results on KITTI Dataset in detecting extremely far away 3D objects. LiDAR points are projected to images shown with different colors related to depth. The distances of 3D bounding boxes are marked on the top-left. 1st & 2nd rows: 2D annotations of extremely distant objects; 3rd & 4th rows: 3D box prediction of corresponding objects. + +![](images/306d758af43e976897e5447b16f63542303903b67f2f093bd3641372784e9bec.jpg) + +![](images/3031037c79f91dee2901d03736e84e3fc586a95b3a1887c830f83a8857ff8db1.jpg) + +
MethodDistant 3D Groundtruth?OverallClose (0m-40m)Distant (40m-51.2m)Distant (51.2m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√26.627.429.130.116.412.711.38.6
FCOS3D [1]-22.623.429.930.31.81.40.00.0
LR3D (IP-FCOS3D)24.124.428.528.416.111.36.44.3
+ +
Long-range Teacher
BEVFormer-S [2]√36.937.238.338.719.615.2--
BEVFormer-S [2] +LR3D teacher-33.634.238.038.52.41.7--
36.336.838.038.918.310.9--
BEVFormer-S† [2]√33.734.037.437.919.414.514.410.2
BEVFormer-S† [2] +LR3D teacher-29.129.938.038.72.41.00.00.0
33.033.637.538.017.910.712.76.4
+ +Table 3. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the nuScenes val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated. + +classes as the official benchmark [13]. This setting helps keep distant predictions. Following [13], we train our model on 700 training scenes and test it on 150 validation scenes. + +Model Setting. We utilize FCOS3D [1] as our monocular baseline and enhance it with IP-Head (IP-FCOS3D) for LR3D with 2D supervision only. To demonstrate the effectiveness of LR3D as a long-range teacher on nuScenes, we choose BEVFormer [2] as the student for its effectiveness, and test its performance without distant 3D supervision. + +Main Results. The experimental results are illustrated in Table 3. With IP-Head, LR3D outperforms its baseline FCOS3D by $14.3\%$ and $9.9\%$ performance improvement in terms of LDS and mAP for distant objects from $40\mathrm{m}$ to $51.2\mathrm{m}$ . It is significant. Compared to the fully 3D supervised FCOS3D with distant 3D ground truth, LR3D still yields competitive capacity on long-range 3D detection. + +We also list the results of BEVFormer [2] with and without LR3D teacher on detecting distant 3D objects without 3D supervision. As illustrated, with the LR3D teacher, BEVFormer-S yields strong performance, comparable to its fully-supervised counterparts with 3D box labels. + +Given the limited perception range of official BEVFormer $(-51.2\mathrm{m}$ to $51.2\mathrm{m})$ we enlarge the perception range of BEVFormer from $51.2\mathrm{m}$ to $76.8\mathrm{m}$ for further verifica + +tion, denoted as BEVFormer- $S^{\dagger}$ . Still, as shown in Table 3, with LR3D teacher, BEVFormer- $S^{\dagger}$ achieves impressive improvement compared to its baseline, and yields comparable results to those of the fully-supervised model. + +# 5.3. Ablation Studies + +All ablation studies are conducted on KITTI Dataset, using IP-FCOS3D as the detector of the LR3D model. + +Analysis on the IP-Head. IP-Head learns to estimate implicit inverse function $f^{-1}$ , which is the mapping from 2D bounding box on image to corresponding depth, through two MLP networks $f_{g}$ and $f^{(\theta)}$ . We evaluate its effectiveness by comparing the mapping curve from 2D box size to the depth of a fixed 3D object generated by ground truth transformation and estimated transformation. + +The generation of the ground truth curve follows Eq. (1), from which we obtain multiple $d - b_{2d}$ pairs by modifying depth $d$ . The estimated curve is generated through Eq. (3) by changing the 2D box inputs. As illustrated in Figure 8, our IP-Head can estimate specific implicit inverse functions for different objects (by comparison across rows). The estimated function by MLP network $f^{(\theta)}$ well models the mapping from 2D bounding box size to the corresponding depth of target 3D object (through comparison inside each row). + +
f(θ) Weight Learning StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
Shared45.046.632.5
Dynamic50.052.136.2
+ +(a) Effect of parameter learning in $f^{(\theta)}$ . + +
No. of layersOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
148.651.332.4
250.052.136.2
349.752.035.2
449.051.434.9
+ +(d) Effect of the number of layers in $f^{(\theta)}$ . + +
Pos. Enc.Overall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
None19.920.213.3
Sin. Cos. [64]50.052.136.2
+ +(b) Effect of positional encoding in $f^{(\theta)}$ . + +
No. of channelsOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
848.450.934.5
1650.052.136.2
3249.952.335.6
6449.751.936.1
+ +(e) Effect of the channel number in $f^{(\theta)}$ . + +
2D Box (b2d) +DescriptorsOverall +(0m-Inf) +LDS (%)Close +(0m-40m) +LDS (%)Distant +(40m-Inf) +LDS (%)
box width (w2d)48.551.730.6
box height (h2d)49.451.834.9
both (w2d, h2d)50.052.136.2
+ +(c) Effect of 2D box descriptors. + +
Aug. StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
FCOS3D [1]42.150.54.9
+Copy-PasteN/AN/AN/A
LR3D48.352.726.5
+Proj. Aug.50.052.136.2
+ +(f) Effect of the projection augmentation. + +Table 4. Ablation studies on IP-Head structure and projection augmentation. Default settings are highlighted in lightcyan . + +![](images/a3be5b60b4b309feddc8aaea93efe8fcfb2da05869d553d0ac7c5bd0e419621b.jpg) +Figure 8. Illustration of the ground truth and estimated $b_{2d} - d$ mappings. Each row indicates the target 3D object and its mapping from 2D box width and height to the depth. + +We further provide quantitative analysis of using MLP network $f_{g}$ to dynamically determine weights of $f^{(\theta)}$ to estimate specific implicit inverse functions of different 3D objects. As listed in Table 4a, compared to the design of shared weights, using dynamic weights assignment in $f^{(\theta)}$ well models the difference of implicit inverse functions due to size and orientation of 3D objects, and thus outperforms the model using a shared weight $\theta$ across 3D objects. + +Analysis on the IP-Head Structure. We first describe the default structure of IP-Head. $f^{(\theta)}$ is a 2-layer perceptron with channels of 16 and 1. The 2D boxes $b_{2d}$ are described as height $(h_{2d})$ and width $(w_{2d})$ . The positional encoding function $f_{\mathrm{PE}}$ is the sine-cosine function illustrated in [64]. + +In Table 4b, we evaluate the contribution of positional encoding. With positional encoding [64], the 2D descriptors are well encoded into more informative features, which thus outperforms the model without positional encoding ("None"). In Table 4c, we compare the model with different 2D box descriptors. Utilizing both 2D box width $w_{2d}$ and height $h_{2d}$ as descriptors yields the best performance. In Table 4d and Table 4e, we conduct ablation studies on MLP structures of network $f^{(\theta)}$ with different numbers of layers and channels. As illustrated, the model with 2-layer + +and channel number 16 achieves the best results. + +Analysis on the Projection Augmentation. The projection augmentation ensures the estimated implicit inverse function $f^{(\theta)}$ models the relation between 2D box sizes and depths by generating more training $b_{2d} - d$ pairs. We analyze it by comparing the performance of LR3D trained with and without this augmentation. As shown in Table 4f, compared to FCOS3D baseline (1st row), LR3D can model mapping functions from 2D sizes to depths and produces good results on distant objects without 3D supervision. Moreover, equipped with projection augmentation, LR3D further shows a huge performance improvement on distant objects. + +A similar augmentation to projection augmentation is copy-paste augmentation [71, 72], which simulates distant training samples by cropping close objects with image patches and pasting them to distant areas by Eq. (1). However, this augmentation brings noises in image distribution, is hard to optimize, and thus leads to a great performance drop (Table 4f (2nd row)). In contrast, projection augmentation is simple to implement without changing training images, and able to augment to any depth without extra effort. + +# 5.4. Results on Other Datasets + +Please find additional results on Cityscapes3D [16], Waymo [14], and Argoverse 2 [15] in the supplementary materials. + +# 6. Conclusion + +In this paper, we proposed the LR3D framework for long-range 3D detection using 2D supervision and designed the IP-Head as the key component. We developed a teacher-student pipeline to benefit all camera-based detectors. Our LDS, a metric with relative distance criterion, helps obtain informative quantitative results for distant objects. With these designs, we demonstrate the feasibility of using 2D supervision only for long-range 3D detection. + +# References + +[1] Tai Wang, Xinge Zhu, Jiangmiao Pang, and Dahua Lin. FCOS3D: Fully convolutional one-stage monocular 3d object detection. 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Upper: Without 3D annotations beyond " + }, + { + "bbox": [ + 46, + 382, + 546, + 415 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 382, + 546, + 415 + ], + "type": "text", + "content": ", LR3D enables the predictions of 3D boxes for extremely distant objects over " + }, + { + "bbox": [ + 46, + 382, + 546, + 415 + ], + "type": "inline_equation", + "content": "200\\mathrm{m}" + }, + { + "bbox": [ + 46, + 382, + 546, + 415 + ], + "type": "text", + "content": " (right, in green) based on the inputs of image and 2D box (left). Lower: Existing methods fail to detect 3D objects beyond the 3D supervision range, e.g., " + }, + { + "bbox": [ + 46, + 382, + 546, + 415 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 382, + 546, + 415 + ], + "type": "text", + "content": " for this case. With LR3D, these remote missing objects are well detected." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 426, + 192, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 426, + 192, + 438 + ], + "spans": [ + { + "bbox": [ + 143, + 426, + 192, + 438 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 445, + 290, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 445, + 290, + 685 + ], + "spans": [ + { + "bbox": [ + 45, + 445, + 290, + 685 + ], + "type": "text", + "content": "Improving the detection of distant 3d objects is an important yet challenging task. For camera-based 3D perception, the annotation of 3d bounding relies heavily on LiDAR for accurate depth information. As such, the distance of annotation is often limited due to the sparsity of LiDAR points on distant objects, which hampers the capability of existing detectors for long-range scenarios. We address this challenge by considering only 2D box supervision for distant objects since they are easy to annotate. We propose LR3D, a framework that learns to recover the missing depth of distant objects. LR3D adopts an implicit projection head to learn the generation of mapping between 2D boxes and depth using the 3D supervision on close objects. This mapping allows the depth estimation of distant objects conditioned on their 2D boxes, making long-range 3D detection with 2D supervision feasible. Experiments show that without distant 3D annotations, LR3D allows camera-based methods to detect distant objects (over " + }, + { + "bbox": [ + 45, + 445, + 290, + 685 + ], + "type": "inline_equation", + "content": "200m" + }, + { + "bbox": [ + 45, + 445, + 290, + 685 + ], + "type": "text", + "content": ") with comparable accuracy to full 3D supervision. Our framework is general, and could widely benefit 3D detection methods to a large extent." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 426, + 386, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 386, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 386, + 438 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 449, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 653 + ], + "type": "text", + "content": "Camera-based 3D object detection [1-7] is an important task in autonomous driving aiming to localize and classify objects in 3D space with monocular or multi-view image input. Detecting distant objects with camera input is both important and challenging. On one hand, the ability to detect objects at distance is needed for planning, especially for highway scenarios. According to [8], at 60 miles/hour, the typical stopping distance for a vehicle is 73 meters and it grows significantly under harsh road conditions such as having wet surface [9-11]. On the other hand, the detection range of camera-based methods depends heavily on the distance range of 3D annotations. For example, these methods work well within the distance range with abundant 3D annotations (e.g., " + }, + { + "bbox": [ + 304, + 449, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\sim 70" + }, + { + "bbox": [ + 304, + 449, + 545, + 653 + ], + "type": "text", + "content": " meters on KITTI [12] and nuScenes [13]), but often fail beyond this range where 3D annotations are missing. This indicates the importance to improve distant 3D object detection with longer 3D annotation range." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Though of great importance, increasing the range of 3D annotation is not easy. One main challenge is the sparsity of LiDAR points at longer distances. LiDAR is typically the main reference for axial depth information in 3D annotation. For distant objects with few or even no LiDAR points," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 241, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 241, + 703 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 241, + 703 + ], + "type": "text", + "content": "*Work done during internship / affiliation with NVIDIA." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 60, + 704, + 209, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 704, + 209, + 714 + ], + "spans": [ + { + "bbox": [ + 60, + 704, + 209, + 714 + ], + "type": "text", + "content": "†Corresponding author: zhidingy@nvidia.com" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14853" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": "labeling their 3D bounding boxes is an ill-posed, noisy, and time-consuming task for human annotators. For this reason, distant 3D box annotations are rare, and most datasets [12-14] provide 3D annotations around 70 meters. A few datasets [15, 16] provide far-away annotations. They obtain long-range 3D annotations either by using costly Li-DAR sensors with very long sensing ranges or by taking significant efforts in annotating 3D boxes with consistency among sequences of stereo images. Both of these strategies are more expensive and less scalable, compared to drawing precise 2D boxes on images. Thus, in this paper, we explore an efficient camera-based approach to achieve high-quality long-range 3D object detection, which uses only 2D annotations for long-range objects of which the 3D annotations are hardly available due to sparse or no interior LiDAR points." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 253, + 289, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 289, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 289, + 337 + ], + "type": "text", + "content": "Our approach: We present LR3D, a camera-based detection framework that detects distant 3D objects using only 2D bounding box annotations. The core of LR3D is an Implicit Projection Head (IP-Head) design that can be plugged into existing camera-based detectors and enables them to effectively predict 3D bounding boxes at all ranges, using the supervision from close 2D/3D and distant 2D box labels." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 338, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 289, + 434 + ], + "type": "text", + "content": "IP-Head learns to generate specific mapping for each instance from their 2D bounding box prediction to the corresponding depth, and thus is capable of estimating depth for distant objects relying on 2D supervision only. We also design a projection augmentation strategy to force the generated implicit function to correctly model the mapping between 2D boxes and 3D depth of target instances and estimate different depth outputs if the 2D box input changes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "type": "text", + "content": "We also notice issues in evaluating camera-based detectors for long-range 3D detection. Existing evaluation metrics [12, 13], based on mean average precision (mAP) with fixed thresholds, neglect the inaccuracy of depth estimation of distant objects from cameras and lead to meaningless numbers even for state-of-the-art methods, e.g., only " + }, + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "type": "inline_equation", + "content": "0.43\\%" + }, + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "type": "text", + "content": " mAP of DID-M3D [6] on KITTI Dataset for objects farther than " + }, + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 435, + 289, + 568 + ], + "type": "text", + "content": ". This motivates us to design a novel metric, Long-range Detection Score (LDS), which sets a dynamic threshold for judging TP prediction regarding associated ground truth depth, for informative qualitative comparison." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "type": "text", + "content": "We conduct experiments on five popular 3D detection datasets including KITTI [12], nuScenes [13], and Waymo [14] for objects within " + }, + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "type": "inline_equation", + "content": "80\\mathrm{m}" + }, + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "type": "text", + "content": ", as well as Cityscapes3D [16] and Argoverse 2 [15] for objects farther than " + }, + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "type": "inline_equation", + "content": "200\\mathrm{m}" + }, + { + "bbox": [ + 46, + 568, + 289, + 641 + ], + "type": "text", + "content": ". We remove the 3D annotations of farther objects in the train set and evaluate the performance on 3D objects at all ranges." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": "Experiments show that, with LR3D, state-of-the-art detectors gain significant improvement in detecting distant objects without 3D annotation, i.e., " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "14.8\\%" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " improvement of DID-M3D [6] on KITTI [12], " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "15.9\\%" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " improvement of BEVFormer [2] on nuScenes [13], " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "34.5\\%" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "14.17\\%" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " improvement of FCOS3D [1] on Cityscapes3D and Argoverse" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "2, " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "7.09\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " improvement of MV-FCOS3D++ [7] on Waymo. With LR3D, these methods yield competitive performance even compared to fully 3D supervised counterparts. Notably, LR3D enables them to detect extremely distant 3D objects as shown in Figure 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 144, + 392, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 144, + 392, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 144, + 392, + 156 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 159, + 547, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 547, + 293 + ], + "type": "text", + "content": "LiDAR-based Detectors. LiDAR methods detect 3D objects from point clouds. According to inputs, these methods can be divided into point, voxel, and range-view detectors. Point methods [17-21] make 3D predictions from raw point clouds [22-27]. Voxel methods [28-31] transform point clouds into voxels and extract features by convolutions [32-37]. Other methods project point clouds into range-view [38-42] and process them as images [43]. Albeit impressively performed, LiDAR methods are 3D-label-greedy, and limited by the perspective range of LiDAR sensors, i.e., usually fail for areas with few or no LiDAR points." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 293, + 547, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 365 + ], + "type": "text", + "content": "Camera-based Detectors. Camera-based methods do 3D detection from images. Monocular methods predict 3D boxes in single image directly [1, 44-47]. Stereo methods based on multi-view images formulate a 3D volume [48-50]. Recent methods [2, 51-57] build a bird-eye-view (BEV) representation for detection." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 365, + 548, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 548, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 548, + 545 + ], + "type": "text", + "content": "The advantages of Camera-based methods lie in the unbounded perception range of cameras, which makes them suitable for distant 3D detection. Some methods, e.g., Far3D [58], are designed for long-range 3D detection, but still heavily rely on abundant high-quality distant 3D annotations, which are hard to collect. Some datasets [15, 16] provide distant annotations. However, their labeling is time-consuming and requires huge human efforts to take hints from multi-modal sensors and temporal consistency to label distant objects with few or no interior LiDAR points. The workload of the labeling process and the 3D-label-greedy character of existing detectors limit the applications of long-range 3D detection. Instead, we propose to detect distant 3D objects without long-range 3D box supervision. It is the simplest setting and is practical for scalability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "text", + "content": "Object Distance Estimation. Another related topic is monocular distance estimation, which estimates the object distance from an RGB image. SVR [59] and DisNet [60] estimate object distance through pixel height and width. They base on an assumption of projected 2D box size determined by the distance of object only. However, other factors, like size and orientation, also affect the projected 2D box size." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Method of [61] develops a FastRCNN [62] pipeline for end-to-end distance estimation by directly regressing the distance from RoI features. R4D [9] utilizes reference objects for further improvements. These methods are limited by their requirements of abundant annotations. Given the difficulty in labeling distant 3D objects, in this paper, we develop a simpler 2D setting that even achieves competitive" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14854" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 57, + 286, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 57, + 286, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 57, + 286, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 57, + 286, + 167 + ], + "type": "image", + "image_path": "e60418d9f80d61bf84553077e043fd61e694efc9e8683bc4b332cbde2e8fec07.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 171, + 287, + 205 + ], + "lines": [ + { + "bbox": [ + 47, + 171, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 287, + 205 + ], + "type": "text", + "content": "Figure 2. Illustration of LR3D which detects 3D boxes for both close and distant objects using the supervision of close 2D/3D and distant 2D bounding box annotations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 209, + 284, + 250 + ], + "blocks": [ + { + "bbox": [ + 48, + 209, + 284, + 250 + ], + "lines": [ + { + "bbox": [ + 48, + 209, + 284, + 250 + ], + "spans": [ + { + "bbox": [ + 48, + 209, + 284, + 250 + ], + "type": "table", + "html": "
Distant 3D Groundtruth?Location Err.Size Err.Orientation Err.
✓0.090.210.37
-0.34 (+0.25)0.23 (+0.02)0.41 (+0.04)
", + "image_path": "07ae5a3ccc619e2ccd9615adf065ad0ffabd977b1b0e7cf1bdc5d4ce8463d62f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 251, + 286, + 274 + ], + "lines": [ + { + "bbox": [ + 47, + 251, + 286, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 286, + 274 + ], + "type": "text", + "content": "Table 1. Performance comparison between FastRCNN3D trained with and without distant 3D supervision." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 281, + 245, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 245, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 245, + 293 + ], + "type": "text", + "content": "performance to their 3D supervised counterparts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 304, + 102, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 102, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 102, + 316 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 324, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 287, + 396 + ], + "type": "text", + "content": "LR3D is a long-range 3D detection framework that detects 3D bounding boxes, including locations, sizes, and orientations, of distant objects using only their 2D supervision (Figure 2). In this section, we first analyze the main challenge of directly utilizing existing 3D detectors on LR3D in Section 3.1 and then introduce our solution in Section 3.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 404, + 110, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 110, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 110, + 417 + ], + "type": "text", + "content": "3.1. Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 423, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 287, + 495 + ], + "type": "text", + "content": "Albeit important and critical, long-range 3D object detection is seldom explored. One difficulty is to obtain sufficient high-quality 3D bounding box annotations for distant objects. We discard this high-human-labor-cost setting and propose a new framework, LR3D, to predict 3D boxes for distant objects only from their 2D image supervision." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 498, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 664 + ], + "type": "text", + "content": "Can Existing Methods Use only 2D Supervision? We first analyze if existing methods can use only 2D supervision for detecting distant 3D objects. To this end, we use FastRCNN3D, a FastRCNN-like [62] 3D detector where the original head for 2D detection is replaced by the FCOS3D head [1] for 3D detection. For training, we first manually assign objects over " + }, + { + "bbox": [ + 47, + 498, + 287, + 664 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 47, + 498, + 287, + 664 + ], + "type": "text", + "content": " as distant objects and remove their 3D annotations. Then, we train FastRCNN3D with close 2D/3D and distant 2D box labels as Figure 2. At test time, we use the 2D ground truth of distant objects as proposals, predict their 3D boxes, and evaluate their errors in location, size, and orientation. Note that we use relative distance as location error, IoU with aligned location and orientation as size error, and absolute difference as orientation error." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "Table 1 compares errors between the LR3D configuration and traditional full supervision. As shown, errors in size and orientation are comparable. The main gap comes from the location error, in which depth estimation plays the" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 57, + 545, + 181 + ], + "blocks": [ + { + "bbox": [ + 307, + 57, + 545, + 181 + ], + "lines": [ + { + "bbox": [ + 307, + 57, + 545, + 181 + ], + "spans": [ + { + "bbox": [ + 307, + 57, + 545, + 181 + ], + "type": "image", + "image_path": "306247ae5d24106d41ea8885261a7cd788cde6da4d2fdc36e1433c2725cff874.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "type": "text", + "content": "Figure 3. Illustration of IP-Head. We use an MLP " + }, + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "type": "text", + "content": " to fit the implicit function from 2D box to 3D depth, of which the weights " + }, + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 184, + 545, + 228 + ], + "type": "text", + "content": " are dynamically determined by instance features including information of size and orientation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 240, + 545, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 301 + ], + "type": "text", + "content": "essential role. Due to the lack of depth information in 2D box supervision, directly regressing the depth as previous methods cannot produce accurate depth prediction for distant objects and leads to a significant drop. Therefore, we seek a new method to implicitly estimate the depth." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 307, + 444, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 307, + 444, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 307, + 444, + 319 + ], + "type": "text", + "content": "3.2. Implicit Projection Head" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": "Here, we introduce Implicit Projection head (IP-Head), our proposal to estimate depth of distant objects using only 2D supervision. Given a 3D object with fixed depth, size, and orientation " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": ", through the camera calibration matrix, it is easy to obtain the corresponding projected 2D bounding box (described by its width " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "w_{2d}" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": " and height " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "h_{2d}" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": ") on the target image. We use a function " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": ", determined by the calibration matrix, to indicate the mapping between depth " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "(d)" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": ", size " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "(s)" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": ", orientation " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "(o)" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": " and 2D box " + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "inline_equation", + "content": "(b_{2d} = (w_{2d}, h_{2d}))" + }, + { + "bbox": [ + 305, + 324, + 545, + 434 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 391, + 440, + 545, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 440, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 391, + 440, + 545, + 453 + ], + "type": "interline_equation", + "content": "f (d, s, o) = b _ {2 d}. \\tag {1}", + "image_path": "7b090bde52ab148a51d7b9096136beeb012de81faed8b8c6086b8acabf5fff37.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": "Eq. (1) shows the ubiquitous relation between " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "b_{2d}" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": " if the object size " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": " and orientation " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": " are fixed – for objects with the same size and orientation, the further these objects locate, the smaller their projected 2D boxes on image are. Inspired by this fact, we ask if it is possible to estimate the inverse function " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "f^{-1}" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": " to transfer the 2D bounding box to the corresponding depth conditioned by " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 305, + 459, + 545, + 544 + ], + "type": "text", + "content": ", formulated as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 386, + 550, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 550, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 386, + 550, + 545, + 563 + ], + "type": "interline_equation", + "content": "f ^ {- 1} \\left(b _ {2 d} | s, o\\right) = d. \\tag {2}", + "image_path": "2dd88f1c20454dae875ad7b23a79d4128ec859a25ff371d6e308eee7895810d2.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "text", + "content": "With the power of neural networks to fit complicated functions, we utilize a small-size network with a multi-layer perceptron (MLP) to estimate the implicit inverse function " + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "inline_equation", + "content": "f^{-1}" + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "text", + "content": ". For simplicity, we use " + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "text", + "content": " to represent this network, of which the parameter weights are represented as " + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 570, + 545, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "text", + "content": "Since the implicit inverse function " + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "inline_equation", + "content": "f^{-1}" + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "text", + "content": " depends on the size and orientation of the specific 3D objects, " + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "text", + "content": " should also be different across multiple objects, which means weights " + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 630, + 545, + 677 + ], + "type": "text", + "content": " should be dynamic." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "1The mentioned orientation is the relative one to the camera, i.e., the observed orientation on the image. We refer the readers to FCOS3D [1] and Stereo-RCNN [63] for more details on obtaining relative orientation." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14855" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 58, + 293, + 178 + ], + "blocks": [ + { + "bbox": [ + 50, + 58, + 293, + 178 + ], + "lines": [ + { + "bbox": [ + 50, + 58, + 293, + 178 + ], + "spans": [ + { + "bbox": [ + 50, + 58, + 293, + 178 + ], + "type": "image", + "image_path": "d4be4de832e4ac872246bbb1b105f3f0ed46be6b4de2bd84798b297f3d9cddba.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 57, + 541, + 178 + ], + "blocks": [ + { + "bbox": [ + 299, + 57, + 541, + 178 + ], + "lines": [ + { + "bbox": [ + 299, + 57, + 541, + 178 + ], + "spans": [ + { + "bbox": [ + 299, + 57, + 541, + 178 + ], + "type": "image", + "image_path": "11e3e94197473f455cc8cbbaa8d30448ca329543eede56ee6a38aa3f55cd1789.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 228, + 279, + 387 + ], + "blocks": [ + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "text", + "content": "Figure 4. Illustration of the training and testing pipeline of IP-Head. (a). Training: During training, we use 2D/3D annotation pairs of close objects to supervise " + }, + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "text", + "content": " to generate dynamic weights of MLP " + }, + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "text", + "content": " which models the transformation of target 3D object from 2D box to corresponding depth in Eq. (3). (b). Testing: During testing, we use a 2D detection head (2D Det. Head) " + }, + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "inline_equation", + "content": "f_{2d}" + }, + { + "bbox": [ + 46, + 182, + 547, + 227 + ], + "type": "text", + "content": " to generate 2D detection results for all objects. They are then transferred to corresponding depth by IP-Head." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 228, + 279, + 387 + ], + "lines": [ + { + "bbox": [ + 55, + 228, + 279, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 228, + 279, + 387 + ], + "type": "image", + "image_path": "15db0a060d0f36c1fd719909bf162acdddc41fa05c84c99278c008ec4e069fa3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 391, + 286, + 412 + ], + "lines": [ + { + "bbox": [ + 46, + 391, + 286, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 286, + 412 + ], + "type": "text", + "content": "Figure 5. Illustration of deploying IP-Head to monocular 3D detectors: (a) FCOS3D; (b) FastRCNN3D." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": "With these considerations, rather than utilizing a shared " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " for all objects, we use a trainable MLP " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " to generate a set of dynamic weights " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " according to the features " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " of each object " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": ". We then utilize those " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " as the weights of network " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " to estimate the corresponding depth of the " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": "-th 2D box. This process generates the specific Implicit inverse function of each object to Project its 2D box to 3D depth. We illustrate this procedure in Figure 3, in which \"2D Box Encoding\", " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{PE}}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": ", is a positional encoding function [64] to encode 2-channel 2D box descriptors (with width " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "w_{2d}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " and height " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "h_{2d}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": ") into informative high-dimensional features and " + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "inline_equation", + "content": "f_{2d}" + }, + { + "bbox": [ + 46, + 418, + 287, + 574 + ], + "type": "text", + "content": " is a 2D detection network for predicting 2D bounding boxes on the image. The overall procedure is formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 112, + 582, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 582, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 112, + 582, + 287, + 596 + ], + "type": "interline_equation", + "content": "d _ {i} = f ^ {\\left(f _ {g} \\left(F _ {i}\\right)\\right)} \\left(f _ {\\mathrm {P E}} \\left(b _ {2 d _ {i}}\\right)\\right), \\tag {3}", + "image_path": "0548488aea8e0ccd03148133ecad20b869786f0d155fe17ce1e7d5025c50e3b9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": " estimates the weights of " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "f^{(\\theta_i)}" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": " from instance features " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": " to transfer the " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": "-th 2D bounding boxes to its corresponding depth. Its condition information, including size " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": " and orientation " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": ", is included in feature " + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": ", from which information can be obtained like that of [1, 65, 66]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "During training, we make use of 2D/3D annotation pairs of close objects to supervise IP-Head for obtaining a reliable dynamic weight generator " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": ". Specifically, for a close object, after obtaining its corresponding dynamic weights," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 228, + 544, + 348 + ], + "blocks": [ + { + "bbox": [ + 308, + 228, + 544, + 348 + ], + "lines": [ + { + "bbox": [ + 308, + 228, + 544, + 348 + ], + "spans": [ + { + "bbox": [ + 308, + 228, + 544, + 348 + ], + "type": "image", + "image_path": "8d0ffe2e921adc39f46f70b18725120558a65c435bf808727e330e6fe0d59e98.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 350, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 373 + ], + "type": "text", + "content": "Figure 6. Illustration of extending IP-Head to all camera-based 3D detectors through a teacher-student pipeline." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 383, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 545, + 418 + ], + "type": "text", + "content": "we transfer its 2D ground truth box for depth prediction by IP-Head, and optimize " + }, + { + "bbox": [ + 305, + 383, + 545, + 418 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 305, + 383, + 545, + 418 + ], + "type": "text", + "content": " by computing the loss between the predicted depth and the 3D annotation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "content": "During inference, we first use the backbone network to extract instance features " + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "inline_equation", + "content": "F_{i}^{\\prime}" + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "content": ". Then, we extract dynamic weights using " + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "content": " and use a detection network " + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "inline_equation", + "content": "f_{2d}" + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "content": ", supervised by 2D bounding box ground truth, to predict the associated 2D bounding box " + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "inline_equation", + "content": "b_{2d_i}'" + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "inline_equation", + "content": "b_{2d_i}' = f_{2d}(F_i')" + }, + { + "bbox": [ + 304, + 419, + 545, + 504 + ], + "type": "text", + "content": ". Finally, we use Eq. (3) to obtain depth predictions for each instance in the image. The overall process is illustrated in Figure 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 506, + 546, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 546, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 546, + 661 + ], + "type": "text", + "content": "Using neural networks to directly estimate a hard-to-optimize function was successful in other research areas. For example, NeRF [67] uses MLP networks to learn a shared mapping from positions to colors and densities; classification models use a shared CNN model to learn the function from pixels to classification confidence. In contrast to previous methods, we first study the estimation of transformation function from 2D boxes on images to 3D depths. Moreover, instead of learning a shared mapping, IP-Head generates dynamic mappings from 2D box sizes to 3D depth according to the 3D size and orientation of target objects, which equips IP-Head with great generalization ability and potential applied to complex autonomous driving scenarios." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Projection Augmentation. The implicit inverse function " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": " needs to model the relation between the 2D box and corresponding depth, and generate different depth predictions based on 2D box input. To further improve effective" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14856" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "ness, we also propose an augmentation strategy, called projection augmentation. The idea is to generate more depth " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " and 2D box " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "b_{2d}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " pairs for each close object during training, so as to enable " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " to estimate a more accurate " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "b_{2d} - d" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " relation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "content": "These extra " + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "b_{2d} - d" + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "content": " training pairs come from Eq. (1). Given an object with fixed size and orientation, we randomly choose different depth values " + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "d^{*}" + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "content": ", calculate their corresponding 2D boxes " + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "b_{2d}^{*}" + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "content": " through Eq. (1), and utilize these augmented " + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "b_{2d}^{*} - d^{*}" + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "content": " pairs, along with the ground truth " + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "b_{2d} - d" + }, + { + "bbox": [ + 46, + 121, + 287, + 193 + ], + "type": "text", + "content": " pair, to train the IP-Head for higher performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "type": "text", + "content": "Long-range Teacher The proposed IP-Head can be used in existing monocular 3D detectors, like FCOS3D [1], to boost their performance in LR3D. As illustrated in Figure 5, only two additional branches, i.e., a 2D detection branch " + }, + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "type": "inline_equation", + "content": "f_{2d}" + }, + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "type": "text", + "content": " and a weight generation MLP " + }, + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 196, + 287, + 302 + ], + "type": "text", + "content": ", are needed to utilize IP-Head in FCOS3D. Apart from monocular methods, BEV methods become popular due to their strong performance and multi-tasking ability. We extend IP-Head to BEV methods to alleviate their demand of 3D annotations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 435 + ], + "type": "text", + "content": "Our solution is to utilize a monocular method equipped with IP-Head as the detector of the LR3D model which then serves as the long-range teacher to generate pseudo distant 3D annotations. With close 2D/3D annotations and distant 2D annotations, we first apply LR3D to generate 3D predictions for distant objects. Then, we treat these predictions as pseudo 3D box labels, which are, together with close 3D ground truth, taken as the whole supervision to train BEV methods. Our pipeline is shown in Figure 6. Experiments show that, it works decently for various 3D detectors on long-range objects without distant 3D box annotation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 445, + 205, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 205, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 205, + 458 + ], + "type": "text", + "content": "4. Long-range Detection Score" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 461, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 496 + ], + "type": "text", + "content": "Existing detection metrics are built upon mAP based on either IoU [12, 14] or absolute distance error [13]. They use fixed IoU or error thresholds as criterion to calculate AP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": "However, the fixed threshold is not suitable for distant objects due to its neglect of the increasing error in depth estimation when objects go farther. For example, though DID-M3D [6] is the state-of-the-art camera-based detector, it only achieves " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "0.43\\%" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": " mAP under fixed IoU criterion on objects over " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": ". Fixed threshold metrics hardly bring informative results. In fact, further objects should have a larger tolerance to closer ones, since estimating their depth is more ill-posed. Similar ideas were taken in tasks like dense depth estimation [68] and object distance estimation [9]. They all prefer relative distance errors as their metrics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 631, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 287, + 677 + ], + "type": "text", + "content": "To address this limitation, we introduce Long-range Detection Score (LDS), a new metric for long-range 3D object detection. LDS is based on the widely applied nuScenes Detection Score (NDS) [13] and it is defined as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 687, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 687, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 52, + 687, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathrm {L D S} = \\frac {1}{6} [ 3 \\mathrm {m A P} + \\operatorname {R e c} \\times \\sum_ {\\mathrm {m T P} \\in \\mathrm {m T P}} (1 - \\min (1, \\mathrm {m T P})) ], \\tag {4}", + "image_path": "28bf5ab66d43a9ea2bbfdf8821b961dc1a2ed7f8228681f47064c0279bb2ed8a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "where Rec is the recall rate and mTP represents the mean True Positive metric." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "content": "LDS improves NDS in two main aspects: the criterion of mAP and the multiplication of Rec and summation of mTP. Improvements on mAP. In LDS, we compute mAP based on the relative distance error of" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 153, + 545, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 153, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 364, + 153, + 545, + 178 + ], + "type": "interline_equation", + "content": "\\text {R e l . D i s t . E r r .} = \\frac {\\left\\| P _ {c} - G _ {c} \\right\\|}{G _ {d}}, \\tag {5}", + "image_path": "ee85af913942318495b643baad55bf97e66eb54715788f7dc467791d7c72823c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "P_{c}" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "G_{c}" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "G_{d}" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": " represent the center of predicted 3D box, center of ground truth 3D box and the distance of ground truth 3D box towards ego vehicle, respectively. Predictions with a relative error smaller than a threshold " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": " are counted as true positive, and false positive otherwise, for computing AP. We choose 4 thresholds " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbb{R} = \\{0.025, 0.05, 0.1, 0.2\\}" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": " and take average over these thresholds and the class set " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbb{C}" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": ". Finally, we obtain mAP as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 362, + 290, + 545, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 290, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 362, + 290, + 545, + 319 + ], + "type": "interline_equation", + "content": "\\mathrm {m A P} = \\frac {1}{| \\mathbb {C} | | \\mathbb {R} |} \\sum_ {c \\in \\mathbb {C}} \\sum_ {r \\in \\mathbb {R}} \\mathrm {A P} _ {c, r}. \\tag {6}", + "image_path": "fc4b19745fc5dea2819abd25185d245c056f44bf97ed8e166de033128ac94ccb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 331, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 413 + ], + "type": "text", + "content": "Improvement on mTP. Also, we multiply the recall rate and mTP before adding to mAP. The mTP is utilized to measure errors on the location (mATE), size (mASE) and orientation (mAOE) for TP prediction, whose relative distance to the ground truth is smaller than " + }, + { + "bbox": [ + 305, + 331, + 545, + 413 + ], + "type": "inline_equation", + "content": "r = 0.1" + }, + { + "bbox": [ + 305, + 331, + 545, + 413 + ], + "type": "text", + "content": " during matching. mATE is computed as the relative distance, normalized by 0.1 to ensure range falling within 0 and 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 415, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 510 + ], + "type": "text", + "content": "mASE and mAOE are the same as those in nuScenes Dataset [13]. The intuition of multiplying the recall rate to the mTP is simple. The larger the recall rate is, the more predictions are involved in the statistics of mTP. Compared to simply setting a recall threshold [13], the multiplication improvement adjusts the weight of mTP to LDS according to its comprehensiveness, and thus brings a more informative quantitative result." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 521, + 388, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 388, + 534 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 388, + 534 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": "We evaluate our method on five popular 3D detection datasets of KITTI [12], nuScenes [13], Cityscapes3D [16], Waymo Open Dataset [14] and Argoverse 2 [15], which have plenty of high-quality 3D annotations for both close and distant objects. Due to the space limitation, we show the experimental results on Cityscapes3D, Waymo and Argoverse 2 datasets in the supplementary material." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 632, + 411, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 411, + 643 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 411, + 643 + ], + "type": "text", + "content": "5.1. Results on KITTI" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Data Preparation. KITTI Dataset [12] provides high-quality 2D/3D annotations for objects in \"Car\", \"Pedestrian\" and \"Cyclist\" within the range of " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sim 80\\mathrm{m}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": ". For extremely distant objects, due to lack of points, it only labels their 2D ground truth boxes on images and marks them as" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14857" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 55, + 533, + 110 + ], + "blocks": [ + { + "bbox": [ + 59, + 55, + 533, + 110 + ], + "lines": [ + { + "bbox": [ + 59, + 55, + 533, + 110 + ], + "spans": [ + { + "bbox": [ + 59, + 55, + 533, + 110 + ], + "type": "table", + "html": "
MethodDistant 3D Groundtruth?Overall (0m-Inf)Close (0m-40m)Distant (40m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√48.044.749.947.538.232.6
FCOS3D [1]-42.138.950.547.14.93.3
LR3D (IP-FCOS3D)50.046.752.149.436.231.0
", + "image_path": "9fe27d165dfd29de9e2565a766703c16ff5229f916c607ae69055c4f41408d70.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 120, + 533, + 278 + ], + "blocks": [ + { + "bbox": [ + 69, + 110, + 141, + 119 + ], + "lines": [ + { + "bbox": [ + 69, + 110, + 141, + 119 + ], + "spans": [ + { + "bbox": [ + 69, + 110, + 141, + 119 + ], + "type": "text", + "content": "Long-range Teacher" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 120, + 533, + 278 + ], + "lines": [ + { + "bbox": [ + 59, + 120, + 533, + 278 + ], + "spans": [ + { + "bbox": [ + 59, + 120, + 533, + 278 + ], + "type": "table", + "html": "
ImVoxelNet [52]√44.845.248.148.426.224.7
ImVoxelNet [52]-40.339.948.648.14.44.1
+LR3D teacher44.945.147.947.926.925.3
CaDDN [53]√51.150.157.856.319.318.5
CaDDN [53]-48.948.658.557.95.55.7
+LR3D teacher51.150.657.656.820.919.8
MonoFlex [65]√55.552.457.755.240.634.8
MonoFlex [65]-50.147.359.356.18.46.6
+LR3D teacher54.351.657.354.835.832.9
GUPNet [66]√49.347.554.052.126.725.1
GUPNet [66]-46.845.254.052.317.616.5
+LR3D teacher49.447.854.252.826.424.4
DID-M3D [6]√56.155.158.557.238.936.7
DID-M3D [6]-52.551.458.957.824.222.5
+LR3D teacher56.355.058.757.239.036.2
", + "image_path": "df0a32c82763043989e67c41cbc756c1de2ee17f61ea9b0db839b9ab815c83e7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 545, + 304 + ], + "type": "text", + "content": "Table 2. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the KITTI val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 309, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 287, + 334 + ], + "type": "text", + "content": "\"DontCare\". Given these labels, we accordingly conduct quantitative and qualitative evaluations on KITTI Dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": "Quantitative evaluation is conducted on objects with 3D annotations. Specifically, based on the official provided 3D annotations, we mark annotations over " + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": " as distant ones following [9], only using their 2D labels for training. For those closer than " + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": ", we keep both 2D and 3D labels for training. We report LDS on both close and distant objects for statistical results. The split of train and val sets follows [69]. Due to the lack of \"Pedestrian\" and \"Cyclist\" labels beyond " + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": ", we only report results on class \"Car\"." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 443, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 515 + ], + "type": "text", + "content": "Qualitative evaluation is designed for \"DontCare\" objects which are extremely far away and without 3D annotations due to no LiDAR points. We visualize the 3D detection results of our model conditioned by their 2D ground truth boxes. Through this evaluation, we manifest the capacity of our model for extremely distant 3D detection." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 518, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 615 + ], + "type": "text", + "content": "Model Setting. For quantitative evaluation, we utilize FCOS3D [1] as our baseline for its simplicity and implementation platform. FCOS3D is implemented on the MMDetection3D [70] platform including multiple methods and datasets. We extend FCOS3D with our IP-Head (IP-FCOS3D, Figure 5) as the detector in the LR3D framework. For qualitative evaluation, we utilize FastRCNN3D with IP-Head (Figure 5) as LR3D detector, to utilize 2D conditions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Quantitative Results. We compare our LR3D, using IP-FCOS3D as its detector, and the baseline FCOS3D [1] for distant 3D detection without 3D annotations in Table 2. It is obvious that our LR3D outperforms FCOS3D on detecting distant objects by a large margin, i.e., " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "31.3\\%" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "27.7\\%" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " on LDS and mAP, respectively. Even compared to FCOS3D with distant 3D ground truth supervision, LR3D still shows competitive performance on distant objects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 309, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 545, + 393 + ], + "type": "text", + "content": "We further evaluate the performance of using LR3D as the teacher model to generate pseudo long-range 3D labels to train state-of-the-art camera-based detectors. The results are listed in Table 2. Surprisingly, models trained with the combination of close 3D ground truth and distant 3D pseudo labels even achieve comparable or even better performance to their fully 3D supervised counterparts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 394, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 442 + ], + "type": "text", + "content": "Quantitative results in Table 2 demonstrate the effectiveness of our LR3D framework, as well as the potential of our method in relieving the great demand of accurate 3D bounding box annotations for long-range object detection." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 445, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 576 + ], + "type": "text", + "content": "Qualitative Results. We visualize the 3D prediction results of LR3D conditioned with \"DontCare\" objects in Figure 7. It is also clear that supervised by close 3D annotations only (maximum to " + }, + { + "bbox": [ + 304, + 445, + 545, + 576 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 304, + 445, + 545, + 576 + ], + "type": "text", + "content": " away), our method infers reasonable 3D bounding boxes (3rd & 4th rows) for those extremely distant objects much beyond the 3D supervision range according to the corresponding 2D bounding boxes (1st & 2nd rows). These qualitative results further demonstrate the potential to extend LR3D to the labeling process. Annotators can first simply label 2D boxes for distant objects and then generate associated 3D annotations by LR3D." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 584, + 423, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 584, + 423, + 596 + ], + "spans": [ + { + "bbox": [ + 306, + 584, + 423, + 596 + ], + "type": "text", + "content": "5.2. Results on nuScenes" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "Data Preparation. NuScenes [13] is a large-scale dataset with 1,000 autonomous driving sequences labeled with 3D boxes in 10 classes. In nuScenes, we set the distance threshold of marking long-range objects as " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ". We mark those annotations beyond the threshold as distant objects, remove the 3D annotations and only use 2D box labels for training. For those closer than " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ", we keep their both 2D/3D labels." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "We evaluate different models among all 10 classes, and do not set the detection range upper-bound for different" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14858" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 57, + 211, + 217 + ], + "blocks": [ + { + "bbox": [ + 50, + 57, + 211, + 217 + ], + "lines": [ + { + "bbox": [ + 50, + 57, + 211, + 217 + ], + "spans": [ + { + "bbox": [ + 50, + 57, + 211, + 217 + ], + "type": "image", + "image_path": "7f771391cce88f1c6aff2331e8d8c22ed612a95160648ed09615c930c48ab2c1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 219, + 546, + 252 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 546, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 546, + 252 + ], + "type": "text", + "content": "Figure 7. Qualitative results on KITTI Dataset in detecting extremely far away 3D objects. LiDAR points are projected to images shown with different colors related to depth. The distances of 3D bounding boxes are marked on the top-left. 1st & 2nd rows: 2D annotations of extremely distant objects; 3rd & 4th rows: 3D box prediction of corresponding objects." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 57, + 378, + 217 + ], + "blocks": [ + { + "bbox": [ + 215, + 57, + 378, + 217 + ], + "lines": [ + { + "bbox": [ + 215, + 57, + 378, + 217 + ], + "spans": [ + { + "bbox": [ + 215, + 57, + 378, + 217 + ], + "type": "image", + "image_path": "306d758af43e976897e5447b16f63542303903b67f2f093bd3641372784e9bec.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 383, + 57, + 544, + 217 + ], + "blocks": [ + { + "bbox": [ + 383, + 57, + 544, + 217 + ], + "lines": [ + { + "bbox": [ + 383, + 57, + 544, + 217 + ], + "spans": [ + { + "bbox": [ + 383, + 57, + 544, + 217 + ], + "type": "image", + "image_path": "3031037c79f91dee2901d03736e84e3fc586a95b3a1887c830f83a8857ff8db1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 55, + 255, + 536, + 310 + ], + "blocks": [ + { + "bbox": [ + 55, + 255, + 536, + 310 + ], + "lines": [ + { + "bbox": [ + 55, + 255, + 536, + 310 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 536, + 310 + ], + "type": "table", + "html": "
MethodDistant 3D Groundtruth?OverallClose (0m-40m)Distant (40m-51.2m)Distant (51.2m-Inf)
LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)LDS (%)mAP (%)
FCOS3D [1]√26.627.429.130.116.412.711.38.6
FCOS3D [1]-22.623.429.930.31.81.40.00.0
LR3D (IP-FCOS3D)24.124.428.528.416.111.36.44.3
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Long-range Teacher
BEVFormer-S [2]√36.937.238.338.719.615.2--
BEVFormer-S [2] +LR3D teacher-33.634.238.038.52.41.7--
36.336.838.038.918.310.9--
BEVFormer-S† [2]√33.734.037.437.919.414.514.410.2
BEVFormer-S† [2] +LR3D teacher-29.129.938.038.72.41.00.00.0
33.033.637.538.017.910.712.76.4
", + "image_path": "eee3aab9ba1dd8787985f23812e2fbeb5008566368bd17ac328bf2156a0f67bd.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 387, + 544, + 409 + ], + "lines": [ + { + "bbox": [ + 46, + 387, + 544, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 544, + 409 + ], + "type": "text", + "content": "Table 3. Comparison on state-of-the-art methods with and without IP-Head or LR3D teacher supervised by distant 2D ground truth only on the nuScenes val dataset. Their fully supervised counterparts (with distant 3D ground truth) are also illustrated." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 415, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 452 + ], + "type": "text", + "content": "classes as the official benchmark [13]. This setting helps keep distant predictions. Following [13], we train our model on 700 training scenes and test it on 150 validation scenes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "type": "text", + "content": "Model Setting. We utilize FCOS3D [1] as our monocular baseline and enhance it with IP-Head (IP-FCOS3D) for LR3D with 2D supervision only. To demonstrate the effectiveness of LR3D as a long-range teacher on nuScenes, we choose BEVFormer [2] as the student for its effectiveness, and test its performance without distant 3D supervision." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "text", + "content": "Main Results. The experimental results are illustrated in Table 3. With IP-Head, LR3D outperforms its baseline FCOS3D by " + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "inline_equation", + "content": "14.3\\%" + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "inline_equation", + "content": "9.9\\%" + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "text", + "content": " performance improvement in terms of LDS and mAP for distant objects from " + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "inline_equation", + "content": "40\\mathrm{m}" + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "inline_equation", + "content": "51.2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 531, + 287, + 615 + ], + "type": "text", + "content": ". It is significant. Compared to the fully 3D supervised FCOS3D with distant 3D ground truth, LR3D still yields competitive capacity on long-range 3D detection." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 616, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 676 + ], + "type": "text", + "content": "We also list the results of BEVFormer [2] with and without LR3D teacher on detecting distant 3D objects without 3D supervision. As illustrated, with the LR3D teacher, BEVFormer-S yields strong performance, comparable to its fully-supervised counterparts with 3D box labels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": "Given the limited perception range of official BEVFormer " + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "(-51.2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "51.2\\mathrm{m})" + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": " we enlarge the perception range of BEVFormer from " + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "51.2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "76.8\\mathrm{m}" + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": " for further verifica" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "type": "text", + "content": "tion, denoted as BEVFormer-" + }, + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "type": "inline_equation", + "content": "S^{\\dagger}" + }, + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "type": "text", + "content": ". Still, as shown in Table 3, with LR3D teacher, BEVFormer-" + }, + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "type": "inline_equation", + "content": "S^{\\dagger}" + }, + { + "bbox": [ + 304, + 415, + 545, + 464 + ], + "type": "text", + "content": " achieves impressive improvement compared to its baseline, and yields comparable results to those of the fully-supervised model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 474, + 406, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 406, + 485 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 406, + 485 + ], + "type": "text", + "content": "5.3. Ablation Studies" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 493, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 517 + ], + "type": "text", + "content": "All ablation studies are conducted on KITTI Dataset, using IP-FCOS3D as the detector of the LR3D model." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "text", + "content": "Analysis on the IP-Head. IP-Head learns to estimate implicit inverse function " + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "inline_equation", + "content": "f^{-1}" + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "text", + "content": ", which is the mapping from 2D bounding box on image to corresponding depth, through two MLP networks " + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 304, + 521, + 545, + 604 + ], + "type": "text", + "content": ". We evaluate its effectiveness by comparing the mapping curve from 2D box size to the depth of a fixed 3D object generated by ground truth transformation and estimated transformation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The generation of the ground truth curve follows Eq. (1), from which we obtain multiple " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "d - b_{2d}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " pairs by modifying depth " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The estimated curve is generated through Eq. (3) by changing the 2D box inputs. As illustrated in Figure 8, our IP-Head can estimate specific implicit inverse functions for different objects (by comparison across rows). The estimated function by MLP network " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " well models the mapping from 2D bounding box size to the corresponding depth of target 3D object (through comparison inside each row)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14859" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 54, + 56, + 200, + 110 + ], + "blocks": [ + { + "bbox": [ + 54, + 56, + 200, + 110 + ], + "lines": [ + { + "bbox": [ + 54, + 56, + 200, + 110 + ], + "spans": [ + { + "bbox": [ + 54, + 56, + 200, + 110 + ], + "type": "table", + "html": "
f(θ) Weight Learning StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
Shared45.046.632.5
Dynamic50.052.136.2
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No. of layersOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
148.651.332.4
250.052.136.2
349.752.035.2
449.051.434.9
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Pos. Enc.Overall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
None19.920.213.3
Sin. Cos. [64]50.052.136.2
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No. of channelsOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
848.450.934.5
1650.052.136.2
3249.952.335.6
6449.751.936.1
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2D Box (b2d) \nDescriptorsOverall \n(0m-Inf) \nLDS (%)Close \n(0m-40m) \nLDS (%)Distant \n(40m-Inf) \nLDS (%)
box width (w2d)48.551.730.6
box height (h2d)49.451.834.9
both (w2d, h2d)50.052.136.2
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Aug. StrategyOverall (0m-Inf) LDS (%)Close (0m-40m) LDS (%)Distant (40m-Inf) LDS (%)
FCOS3D [1]42.150.54.9
+Copy-PasteN/AN/AN/A
LR3D48.352.726.5
+Proj. Aug.50.052.136.2
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Default settings are highlighted in lightcyan ." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 243, + 287, + 381 + ], + "blocks": [ + { + "bbox": [ + 48, + 243, + 287, + 381 + ], + "lines": [ + { + "bbox": [ + 48, + 243, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 48, + 243, + 287, + 381 + ], + "type": "image", + "image_path": "a3be5b60b4b309feddc8aaea93efe8fcfb2da05869d553d0ac7c5bd0e419621b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 384, + 287, + 418 + ], + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 418 + ], + "type": "text", + "content": "Figure 8. Illustration of the ground truth and estimated " + }, + { + "bbox": [ + 46, + 384, + 287, + 418 + ], + "type": "inline_equation", + "content": "b_{2d} - d" + }, + { + "bbox": [ + 46, + 384, + 287, + 418 + ], + "type": "text", + "content": " mappings. Each row indicates the target 3D object and its mapping from 2D box width and height to the depth." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": "We further provide quantitative analysis of using MLP network " + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": " to dynamically determine weights of " + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": " to estimate specific implicit inverse functions of different 3D objects. As listed in Table 4a, compared to the design of shared weights, using dynamic weights assignment in " + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": " well models the difference of implicit inverse functions due to size and orientation of 3D objects, and thus outperforms the model using a shared weight " + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": " across 3D objects." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "content": "Analysis on the IP-Head Structure. We first describe the default structure of IP-Head. " + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "content": " is a 2-layer perceptron with channels of 16 and 1. The 2D boxes " + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "inline_equation", + "content": "b_{2d}" + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "content": " are described as height " + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "inline_equation", + "content": "(h_{2d})" + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "content": " and width " + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "inline_equation", + "content": "(w_{2d})" + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "content": ". The positional encoding function " + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{PE}}" + }, + { + "bbox": [ + 46, + 531, + 287, + 591 + ], + "type": "text", + "content": " is the sine-cosine function illustrated in [64]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "In Table 4b, we evaluate the contribution of positional encoding. With positional encoding [64], the 2D descriptors are well encoded into more informative features, which thus outperforms the model without positional encoding (\"None\"). In Table 4c, we compare the model with different 2D box descriptors. Utilizing both 2D box width " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "w_{2d}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and height " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "h_{2d}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " as descriptors yields the best performance. In Table 4d and Table 4e, we conduct ablation studies on MLP structures of network " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " with different numbers of layers and channels. As illustrated, the model with 2-layer" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 243, + 503, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 503, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 503, + 255 + ], + "type": "text", + "content": "and channel number 16 achieves the best results." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": "Analysis on the Projection Augmentation. The projection augmentation ensures the estimated implicit inverse function " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "f^{(\\theta)}" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": " models the relation between 2D box sizes and depths by generating more training " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "b_{2d} - d" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": " pairs. We analyze it by comparing the performance of LR3D trained with and without this augmentation. As shown in Table 4f, compared to FCOS3D baseline (1st row), LR3D can model mapping functions from 2D sizes to depths and produces good results on distant objects without 3D supervision. Moreover, equipped with projection augmentation, LR3D further shows a huge performance improvement on distant objects." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 398, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 506 + ], + "type": "text", + "content": "A similar augmentation to projection augmentation is copy-paste augmentation [71, 72], which simulates distant training samples by cropping close objects with image patches and pasting them to distant areas by Eq. (1). However, this augmentation brings noises in image distribution, is hard to optimize, and thus leads to a great performance drop (Table 4f (2nd row)). In contrast, projection augmentation is simple to implement without changing training images, and able to augment to any depth without extra effort." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 525, + 450, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 450, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 450, + 536 + ], + "type": "text", + "content": "5.4. Results on Other Datasets" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 547, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 545, + 572 + ], + "type": "text", + "content": "Please find additional results on Cityscapes3D [16], Waymo [14], and Argoverse 2 [15] in the supplementary materials." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 594, + 378, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 378, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 378, + 605 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "In this paper, we proposed the LR3D framework for long-range 3D detection using 2D supervision and designed the IP-Head as the key component. We developed a teacher-student pipeline to benefit all camera-based detectors. Our LDS, a metric with relative distance criterion, helps obtain informative quantitative results for distant objects. 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In CVPR, 2021. 8" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14863" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_content_list.json b/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..58128cb26c447296fca3beb7e7a99368cbcfbe2c --- /dev/null +++ b/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_content_list.json @@ -0,0 +1,1578 @@ +[ + { + "type": "text", + "text": "Improving Generalization via Meta-Learning on Hard Samples", + "text_level": 1, + "bbox": [ + 166, + 130, + 803, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nishant Jain Arun S. Suggala Pradeep Shenoy Google Research India", + "bbox": [ + 271, + 181, + 696, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{nishantjn,arunss,shenoypradeep}@google.com", + "bbox": [ + 295, + 219, + 674, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learned reweighting (LRW) approaches to supervised learning use an optimization criterion to assign weights for training instances, in order to maximize performance on a representative validation dataset. We pose and formalize the problem of optimized selection of the validation set used in LRW training, to improve classifier generalization. In particular, we show that using hard-to-classify instances in the validation set has both a theoretical connection to, and strong empirical evidence of generalization. We provide an efficient algorithm for training this meta-optimized model, as well as a simple train-twice heuristic for careful comparative study. We demonstrate that LRW with easy validation data performs consistently worse than LRW with hard validation data, establishing the validity of our meta-optimization problem. Our proposed algorithm outperforms a wide range of baselines on a range of datasets and domain shift challenges (Imagenet-1K, CIFAR-100, Clothing-1M, CAMELYON, WILDS, etc.), with $1\\%$ gains using VIT-B on Imagenet. We also show that using naturally hard examples for validation (Imagenet-R / Imagenet-A) in LRW training for Imagenet improves performance on both clean and naturally hard test instances by $1 - 2\\%$ . Secondary analyses show that using hard validation data in an LRW framework improves margins on test data, hinting at the mechanism underlying our empirical gains. We believe this work opens up new research directions for the meta-optimization of meta-learning in a supervised learning context.", + "bbox": [ + 75, + 300, + 472, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 739, + 209, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Overparameterized models, common in supervised learning [27], carry the risk of overfitting to training data. Typically, model generalization is measured on a validation dataset separate from the training data, for purposes of hyperparameter selection. Increasingly, this validation dataset is itself used as part of the learning objective in nested formulations, e.g., for hyperparameter tuning via gradient descent on the validation loss [11]. In particular, learned reweighting (LRW) approaches learn importance weights", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "associated with training instances [14, 16, 17, 31, 32, 40] or groups of training instances [25, 41] by optimizing a weighted training loss alongside an unweighted metal-loss on the validation data. This bilevel optimization aligns training loss with the validation data distribution via reweighting, a useful property in addressing covariate shift [34], and for group DRO [9, 41]. Even for in-domain test data, Ren et al. [31] show that using \"clean\" validation data with bilevel optimization can overcome significant amounts of label noise in training data.", + "bbox": [ + 496, + 268, + 893, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thus the choice of validation set in a LRW paradigm can greatly influence the quality and properties of the learned classifier. We therefore ask the question: can we optimize the choice of validation data in LRW so as to maximize generalization of the resulting classifier? We refer to this problem of validation set selection as meta-optimization, since it produces data that is the input of another optimization (the meta-learning approach underlying LRW). The closest related work to our proposal is [40] which constructs a validation dataset on the fly during training of an LRW classifier, with a criterion of choosing representative instances.", + "bbox": [ + 496, + 422, + 893, + 589 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our primary hypothesis is that we can improve classifier generalization by using a validation set consisting of hard-to-classify instances from the training distribution. We therefore pose and formalize the problem of Meta-Optimized LEarned REweighting (MOLERE) where the partitioning of data into train and validation splits, and the LRW classifier corresponding to that split, are jointly optimized. We design an efficient algorithm to tackle this meta-optimization, and make the following contributions:", + "bbox": [ + 496, + 592, + 893, + 728 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We formalize the problem statement of validation set optimization in learned reweighting (LRW) classifiers for improved generalization. We prove that asymptotically our optimization objective exactly achieves our stated goal of maximizing accuracy on the hardest samples.", + "- We simplify the nested optimization of our proposal into a tractable bi-level optimization with a min-max game between two auxiliary networks: a \"splitter\" that finds the hardest samples, and a \"reweighter\" that minimizes loss on those samples using LRW. We also provide a simple train-twice heuristic that can be used for careful analysis" + ], + "bbox": [ + 500, + 734, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27600", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of the choice of validation data in LRW.", + "bbox": [ + 89, + 90, + 356, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We show strict accuracy ordering of LRW models based on validation set: easy $<$ random $<$ hard, demonstrating the importance of optimizing LRW validation sets. We obtain reliable gains over ERM across datasets (e.g., $1\\%$ on Imagenet/VIT-B backbone), and in domain-generalization (e.g., $1.36\\%$ on iWildCam dataset [4, 18]) and noisy-label settings (e.g., $4.2\\%$ on Clothing1M dataset [37]). We outperform a range of baselines including reweighting, meta-learning among others. Analyses show improved margins on test set in MOLERE classifiers, suggesting an explanation of our gains.", + "- We extend our results to natural hard samples as validation (Imagenet withImagenet-R /Imagenet-A), showing $1 - 3\\%$ gains on both in-domain and out-of-domain test sets. This shows the value of our ideas even in scenarios where we pay no additional cost for meta-optimization." + ], + "bbox": [ + 76, + 106, + 467, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We hope that our work will be seen as an initial step in establishing the value of meta-optimization of meta-learning, with our findings providing a strong proof-of-concept for the general research direction.", + "bbox": [ + 76, + 349, + 467, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 422, + 217, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Importance weighting for robustness. There have been several works on learning robust representations via example re-weighting lately. Mostly, these work aim at avoiding noisy labels in the train set by analyzing the effect of decreasing loss on a given instance on a clean validation set. This line of work includes either learning a per-instance free parameter [31] or learning a simple MLP network [32] to predict importance of an instance based on its loss value. However, the requirement of a clean validation set limits their applicability to realistic scenarios. To deal with this, a meta-learning based re-weighting scheme (Fast Sample Reweighting [40]) was proposed based on generating some sort of pseudo-clean data as a proxy validation set. It also proposed certain approximations to make the training process more computation efficient. On a different note, a recent proposal called RHO-loss [24] proposed to select only worthy points for training which increased generalization property of the model, calculated as the difference of the training loss and a hold-out set loss.", + "bbox": [ + 76, + 446, + 467, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A recent line of work [16, 17] proposed weighting based on context/relevance of an instance compared with the overall data distribution. These papers target slow temporal drift in longitudinal datasets, and the development of better uncertainty measures for selective classification, respectively. In particular, Jain et al. [17], suggest that using target domain data in the validation set can improve domain shift performance of classifiers.", + "bbox": [ + 76, + 734, + 467, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Meta Learning. The sample re-weighting task using a validation set comes under the umbrella of meta-learning [15], which follows the learning-to-learn paradigm. It", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is conceptually similar to model agnostic meta learning (MAML) [10], which learns a single set of parameters that can easily be customized (few-shot) to multiple tasks. Learning these shared parameters involves a nested optimization similar to the one presented here, and significantly optimized for efficiency by recent work[28, 30, 42].", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Probabilistic Margins. Recent work [22] showed that the probabilistic margin in multi-class problems can be used to improve how neural networks deal with adversarial examples. The margin is defined as the difference between the probability of the true label and the largest of the remaining label probabilities, indicating the difficulty of classifying that instance. Liu et al. [22] propose re-weighting training instances, in presence of an adversarial attack, inversely related to their probability margins.", + "bbox": [ + 496, + 181, + 890, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Just Train Twice. A recent work [21] proposed an effective strategy to improve sensitivity of ERM models towards certain groups by training the ERM model in 2 stages. The first stage is a standard training procedure, whereas the second stage involves giving more importance to the incorrectly classified examples in the first stage by up-weighting their loss in the aggregate loss term for updating the parameters. This can be interpreted as similar to giving more importance to low margin examples (here essentially a hard separation between positive and negative).", + "bbox": [ + 496, + 320, + 890, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries: Learned ReWeighting", + "text_level": 1, + "bbox": [ + 500, + 502, + 833, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We work with learned reweighting (LRW) classifiers where training data is reweighted in order to optimize some specified metric on validation data. The basic LRW formulation [31] works with two datasets $S_{tr} = \\{(x_i, y_i)\\}_{i=1}^N$ and $S_{val} = \\{(x_i, y_i)\\}_{i=1}^M$ (training & validation, respectively). Given a desired loss function $\\ell(y, \\hat{y})$ , LRW learns a classifier $f_\\theta(\\cdot)$ , (with parameters $\\theta$ ) and an instance-wise weighting function $\\phi(\\cdot)$ that minimize following bi-level objective:", + "bbox": [ + 496, + 527, + 890, + 650 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\theta^ {*} (\\phi) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in S _ {t r}} \\phi (x) \\ell (y, f _ {\\theta} (x)), \\\\ s. t. \\quad \\phi^ {*} = \\arg \\min _ {\\phi} \\sum_ {(x, y) \\in S _ {v a l}} \\ell (y, f _ {\\theta^ {*} (\\phi)} (x)) \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 664, + 890, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notice that the validation loss is unweighted, while the training objective is a weighted loss. Essentially, the above bilevel objective computes an estimate of classifier performance on the validation set, and optimizes it indirectly via reweighting of training data to influence the learned classifier. The weighted-loss-minimizing classifier $f_{\\theta^{*}}(\\cdot)$ , and the weights $\\phi^{*}(\\cdot)$ , are learned jointly, typically using alternating stochastic updates over minibatches to make the learning tractable [31]; this is in line with other meta-learning approaches such as MAML [10]. Following more", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27601", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "recent work [16], we use an instance-dependent neural network $\\phi(x)$ for learning the training instance weights, instead of free parameters [31].", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Intuition: LRW has been used for overcoming training label noise [31, 32] and for handling covariate shift [16, 41]. In these cases, the validation set is assumed to be representative of test samples (i.e., clean labels, or covariateshifted data, respectively). The intuition is that the learned reweighting of the training loss aligns it with the (possibly different) validation distribution in the process of indirectly minimizing the meta-loss (Eq. 1). In particular, Shu et al. [32] show analytically that \"validation-like\" instances are upweighted. Thus, the validation set in LRW can be thought of as a target for generalization, with the learned classifier being optimized for performance on that target set.", + "bbox": [ + 75, + 136, + 470, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. MOLERE: Optimizing LRW models", + "text_level": 1, + "bbox": [ + 76, + 329, + 408, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Hypothesis and formal objective", + "text_level": 1, + "bbox": [ + 76, + 354, + 362, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our primary hypothesis is that we can improve generalization capabilities of supervised learning by combining two ingredients: a) a learned-reweighting classifier, as described in the previous section, and b) an optimized validation set that strongly encourages desired properties in the reweighting classifier. We refer to this idea as Meta-Optimization of the Learned Reweighting framework.", + "bbox": [ + 75, + 378, + 468, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In particular, we propose learning an LRW classifier with hard samples as validation set, to improve accuracy and generalization of learned classifiers. Since LRW by definition maximizes classifier performance on a given validation set, we believe that this choice of validation set will maximize generalization. Thus, given a dataset for training a predictive model, we need to 1) select the \"hard instances\" from the dataset and separate it into a validation set, and 2) train a classifier on the remaining data using this validation set for LRW. Notice that hardness of instances is determined in terms of the learned model itself; thus, formalizing the above idea leads to a joint optimization problem of data partitioning (train, validation), and LRW training. We present the formal problem below.", + "bbox": [ + 75, + 484, + 470, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Objective: Let $S = \\{(x,y)\\}_{i=1}^{N+M}$ be the available data, and let $\\Theta$ be the splitting function that splits $S$ into training and validation datasets; to be precise, we let $\\Theta(S)$ be the validation set and $\\Theta(S)^c$ be its complement. MOLERE aims to solve the following tri-level optimization problem", + "bbox": [ + 75, + 694, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Theta^ {*} = \\arg \\max _ {\\Theta} \\sum_ {(x, y) \\in \\Theta (S)} \\ell (y, f _ {\\theta^ {*} (\\phi^ {*} (\\Theta), \\Theta)} (x)) \\\\ \\text{where}\\phi^{*}(\\Theta) = \\arg \\min_{\\phi}\\sum_{(x,y)\\in \\Theta (S)}\\ell (y,f_{\\theta^{*}(\\phi ,\\Theta)}(x)) \\\\ s. t. \\theta^ {*} (\\phi , \\Theta) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in \\Theta (S) ^ {c}} \\phi (x) \\ell (y, f _ {\\theta} (x)). \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 779, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In words: Find a data split, such that across all possible splits the LRW classifier learned on the split has maximal error on the chosen validation set. In practice, we impose an additional constraint on the validation set size: $|\\Theta (S)| / (N + M)\\leq \\delta$ , where $\\delta$ is some predefined fractional constant.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. MOLERE objective and generalization", + "text_level": 1, + "bbox": [ + 498, + 190, + 828, + 207 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now study the asymptotic properties of our proposed meta-optimization as $N + M \\to \\infty$ , as a means of gaining theoretical insights into its generalization capabilities in comparison to classical empirical risk minimization (ERM). This analysis assumes a weighting function $\\phi(\\cdot)$ dependent on both $x$ and $y$ . Interestingly, our experiments revealed similar performance between this formulation of $\\phi$ and one relying solely on $x$ . The following proposition shows that asymptotically MOLERE solves a robust optimization objective.", + "bbox": [ + 496, + 214, + 890, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1 (Asymptotics). Consider the tri-level optimization in Equation (2). Suppose the weighting function $\\phi(\\cdot)$ , and splitting function $\\Theta(\\cdot)$ are dependent on both $x$ and $y$ . Let's suppose $N + M \\to \\infty$ , and $\\lim_{N, M \\to \\infty} \\frac{M}{N + M} = \\delta$ . Moreover, suppose the domains of $\\phi, \\theta, \\Theta$ are very large and contain the set of all measurable functions. Then the objective of MOLERE is equivalent to", + "bbox": [ + 496, + 373, + 890, + 479 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {S: | S | = \\delta (N + M)} \\min _ {\\theta} \\sum_ {(x, y) \\in S} \\ell (y, f _ {\\theta} (x)). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 488, + 890, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proof Sketch. The proof of the theorem relies on the observation that there exists a weighting function $\\phi$ that can transform any probability distribution $P$ to any another distribution $Q$ (as long as the support of $Q$ is a subset of $P$ ). Using this observation, one can show that the second, third level optimization problems in Equation (2) is equivalent to following problem: $\\min_{\\theta} \\sum_{(x,y) \\in \\Theta(S)^c} \\ell(y, f_{\\theta}(x))$ .", + "bbox": [ + 496, + 532, + 890, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A similar result holds when both $\\Theta(\\cdot), \\phi(\\cdot)$ rely solely on $x$ . Intuitively, the above theorem shows that in the limit of infinite samples, MOLERE identifies the hardest samples in the training data, and learns a classifier that minimizes the error on those samples. This is exactly the goal laid out in our hypothesis above.", + "bbox": [ + 496, + 648, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Connections to DRO. Interestingly, the objective in Equation (3) is the dual of the following Distributionally Robust Optimization (DRO) objective [5]", + "bbox": [ + 496, + 741, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\max _ {S: | S | = \\delta (N + M)} \\sum_ {(x, y) \\in S} \\ell (y, f _ {\\theta} (x)). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 796, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DRO is a well studied framework for learning robust models [8, 26]. However, to the best of our knowledge, dual DRO is not studied in the literature; we will explore this connection more deeply in future work.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27602", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.3. Efficient algorithm for validation optimization", + "text_level": 1, + "bbox": [ + 76, + 90, + 468, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Designing a tractable algorithm for meta-optimization runs into two technical challenges: a) How can we learn to assign instances to train and validation sets? and b) How do we efficiently solve the tri-level objective proposed in Sec. 4.1? We address these two challenges in this section. First, we use a second auxiliary network for soft-assigning instances to train and validation datasets. Second, we collapse the outer two loops of the trilevel objective into a minimax formulation, and thereby reduce it to a bi-level optimization problem. We describe each of these in order below.", + "bbox": [ + 75, + 113, + 468, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Soft data assignment: Inspired by a recent work [3], we use a partitioning network to predict probability for each instance to be included in the validation set. At any point in time, the \"splitter\" network outputs soft assignments $\\mathbb{P}(z|x,y)$ with $z\\in \\{0,1\\}$ indicating whether the example $(x,y)$ belongs to the pseudotest set $(z = 0)$ or the pseudotrain set. The pseudotrain set is used to train a classifier using standard cross-entropy. The splitter is then updated to identify easy instances for the classifier and assign them to the pseudotrain partition in the next round; this is achieved by minimizing the cross-entropy between its soft-assignment and classifier accuracy:", + "bbox": [ + 75, + 265, + 470, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s p l i t} = C E \\left(\\mathbb {P} _ {s p l i t t e r} \\left(z _ {i} \\mid x _ {i}, y _ {i}\\right), \\mathbb {I} _ {y _ {i}} (\\hat {y})\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 455, + 468, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw h e r e \\quad \\hat {y} = \\arg \\max \\mathbb {P} _ {\\text {p r e d i c t o r}} (y | x _ {i})\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 477, + 401, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to maintain the label distribution and train-to-test ratio, two regularizers [3] are added to penalize shift from the prior distribution, and to push label margins in the training split and testing split close to the original label margin (see supplementary for details).", + "bbox": [ + 75, + 502, + 468, + 578 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Meta-optimization with min-max objective: To simplify the tri-level optimization in Sec. 4.1, we propose a bi-level approximation where the outer loop combines the data splitting and instance reweighting objectives. Specifically, we propose a min-max game between the splitter (parametrized by $\\Theta$ ) and the meta-network (parametrized by $\\phi$ ), where the splitter has to maximize validation set error whereas instance weights are focused on minimizing it:", + "bbox": [ + 75, + 578, + 468, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Theta^ {*}, \\phi^ {*} = \\arg \\max _ {\\Theta} \\min _ {\\phi} \\sum_ {(x, y) \\in S _ {t} ^ {c}} \\left(\\ell (y, f _ {\\theta^ {*} (\\phi , \\Theta)} (x)) - \\mathcal {L} _ {s p l i t}\\right) \\\\ w h e r e \\quad \\theta^ {*} (\\phi , \\Theta) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in S _ {t}} \\phi (x) \\ell (y, f _ {\\theta} (x)) \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 709, + 472, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the set $S_{t} = \\{(x,y):(x,y)\\in S,\\mathbb{I}\\{\\Theta (x,y) > 0.5\\} \\}$ and $S_{t}^{c} = S\\setminus S_{t}$ , $\\mathbb{I}$ denotes the indicator function. The overall algorithm updates the splitter and instance weighting network once every $Q$ steps of classifier update, and also regularizes the splitter with $\\Omega_{ratio} + \\Omega_{ld}$ at set intervals (every R steps). The complete description of this method is provided in Algorithm 1 and analysis of the loss function", + "bbox": [ + 75, + 794, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "at the outer level, derivation of update equations for all parameters $(\\Theta, \\phi, \\theta)$ are provided in the supplementary. Both the instance weight network and Splitter are parameterized as neural networks. The meta-network for instance weights predict the weight for a training instance $(x_i, y_i)$ by using $(x_i)$ as input, $w_i = g_{\\phi}(x_i)$ and the Splitter predicts a probability of $(x_i, y_i)$ being in the train set by taking both of them as inputs $z_i = g_{\\Theta}(x_i, y_i)$ . In experiments, we refer to this end-to-end optimization method as LRWOpt.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 LRWOpt: The Overall One-Shot Algorithm." + ], + "code_body": "Require: $\\theta, \\Theta, \\phi$ , learning rates $(\\beta_{1}, \\beta_{2}, \\beta_{3}), S, N, M$ . \nEnsure: Robustly trained classifier parameters $\\theta$ . \n1: Randomly initialize $\\theta, \\Theta$ and $\\phi$ ; \n2: initialize ge = 0; ▷ Difference b/w train and val error \n3: for e=1 to MaxEpochs do \n4: $S_{tr}, S_{val} = \\text{GenerateSplit}(\\mathcal{D}, \\Theta)$ \n5: for $b = 1$ to M/m do ▷ m is the batch size \n6: $\\{(x_i^v, y_i^v)\\}_{i=1}^m = \\text{SampleMiniBatch}(\\mathcal{S}_{val}, m)$ ; \n7: $\\Theta \\gets \\Theta - \\beta_1 \\nabla_\\Theta \\sum (\\mathcal{L}_{split} - \\ell(y_i^v, f_\\theta(x_i^v)))$ \n8: $\\phi \\gets \\phi - \\beta_2 \\nabla_\\phi \\sum (\\ell(y_i^v, f_\\theta(x_i^v)) - \\mathcal{L}_{split})$ \n9: for $j = 1$ to Q do \n10: $\\{(x_i, y_i)\\}_{i=1}^n$ SampleMiniBatch( $\\mathcal{D}_t, n$ ); \n11: $\\theta \\gets \\theta - \\beta_3 \\nabla_\\theta \\sum g_\\phi(x_i) \\ell(f_\\theta(x_i), y_i)$ ; \n12: end for \n13: end for \n14: if $\\sum \\ell(y_i^v, f_\\theta(x_i^v)) - \\sum \\ell(y_i, f_\\theta(x_i)) < \\text{ge then}$ \n15: break; \n16: end if \n17: ge = $\\sum \\frac{1}{M} \\ell(y_i^v, f_\\theta(x_i^v)) - \\frac{1}{N} \\sum \\ell(y_i, f_\\theta(x_i))$ \n18: end for", + "bbox": [ + 500, + 260, + 890, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. A simple train-twice heuristic", + "text_level": 1, + "bbox": [ + 500, + 592, + 763, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now describe a simple train-twice heuristic that can be used to establish the importance of validation set optimization in LRW. We first train an ERM classifier on the available training data, and use the probabilistic margin (PM) as a proxy for instance hardness:", + "bbox": [ + 496, + 614, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP M (x, y, \\theta) = \\mathbf {p} _ {y} (x, \\theta) - \\max _ {j, j \\neq y} \\mathbf {p} _ {j} (x, \\theta) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 700, + 890, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $\\theta$ denotes the ERM classifier's parameters. This criterion was used to manually reweight adversarial examples in recent work [22]. Although this proxy score is inexact1, it nevertheless allows us to design interesting heuristic LRW variants based on its rank-ordering of training instances: (1) LRW-Hard, where we use the lowest margin instances as validation data, and the rest of the instances as training data, (2) LRW-Easy, in which the highest margin instances are", + "bbox": [ + 496, + 733, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "For instance, it measures instance hardness under an ERM classifier, not the to-be-trained LRW model; further, an overtrained classifier may give incorrectly overconfident margins [21].", + "bbox": [ + 496, + 862, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "27603", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/00e46469fcc757580c369fec1576da05407846059f9bc9b9610addd4f6e6a79e.jpg", + "image_caption": [ + "Figure 1. Robustness analysis on benchmark datasets. Left: Comparing different LRW variants, based on the choice of validation set (Easy, Random, Hard, corresponding to the rank-ordering of training data by probabilistic margin of an ERM classifier). $y$ -axis shows accuracy gains over ERM for each dataset ( $x$ -axis). We see consistent ordering of performance, with LRW-Easy $<$ LRW-Random $<$ LRW-Hard, showing the importance of validation set optimization. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. In-1K corresponds to ImageNet-1K. For absolute accuracy values refer supplementary." + ], + "image_footnote": [], + "bbox": [ + 84, + 108, + 483, + 308 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d263a7f4ede6b116fe1224db24bfc1d8df10dd9d7c79fc1c6718b76aabfb25a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 108, + 883, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "used as validation data, and (3) LRW-Random, a control which uses a randomly selected validation set that does not depend on the ERM margin.", + "bbox": [ + 75, + 435, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We can use these variants to quantify the impact of perturbing the validation set in LRW, and to provide an existence proof of validation optimization techniques that materially improve learned classifiers. In particular, we expect to see a clear ordering of classifier test accuracy - LRW-Easy $<$ LRW-Random $<$ LRW-Hard.", + "bbox": [ + 75, + 479, + 468, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 585, + 209, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform extensive experimentation on multiple classification tasks including distribution shift benchmarks. For all datasets, if a train-validation split is already available, we use the training data for the ERM classifier in the train twice heuristic before pooling, ranking, and repartitioning. For the end-to-end optimization, we start with pooled train-validation data and simultaneously learn the data splits and the corresponding LRWOpt model.", + "bbox": [ + 75, + 609, + 468, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 741, + 179, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use popular classification benchmarks including CIFAR-100 [20], ImageNet-100 [35], ImageNet-1K [7], Aircraft [23], Stanford Cars [19], Oxford-IIIT Fine-grained classification (Cats v/s Dogs) [29] and Diabetic Retinopathy (DR) dataset. Furthermore, for OOD analysis we use the ImageNet-A [13], ImageNet-R [12] datasets for models trained on ImageNet-1K. We also use the Camelyon [2], iWildCam [4] dataset from the widely popular WILDS benchmark [18] and also the country shifted test set for the", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DR [1] dataset. We further analyze for robustness in presence of instance dependent noise on the noisy version of CIFAR-10 dataset (Inst.C-10) proposed by Xia et al. [36] and Clothing-1M [37] dataset. Please refer supplementary (supp.) for more details, setup for these datasets.", + "bbox": [ + 496, + 435, + 893, + 511 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Baselines", + "text_level": 1, + "bbox": [ + 500, + 518, + 607, + 534 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Along with ERM, we also compare our method against various re-weighting based methods designed for improving robustness or handling noisy scenarios. These include learned re-weighting methods: MWN [32], FSR [40], L2R [31], MAPLE [41], BiLAW [14], GDW [6], StableNet [39] along with Margin Based Reweighting (MBR) [22] and Rho-Loss [24]. Please refer supp. for more details regarding them.", + "bbox": [ + 496, + 542, + 893, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Results", + "text_level": 1, + "bbox": [ + 500, + 660, + 586, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1. In-Distribution Generalization", + "text_level": 1, + "bbox": [ + 500, + 685, + 769, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1.1 MOLERE improves classification accuracy", + "text_level": 1, + "bbox": [ + 500, + 709, + 852, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 1 (left) shows the LRW advantage (gains over an ERM baseline) for a range of datasets. Shown are 4 alternatives—LRW-Easy, LRW-Random, and LRW-Hard, corresponding to easy, random, and hard validation sets per the train-twice heuristic (Sec. 4.4), and LRWOpt, which is the end-to-end optimization of LRW classifier and train-validation split (Sec. 4.3). Refer supplementary for absolute accuracy values.", + "bbox": [ + 496, + 732, + 890, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Gains vs ERM are strictly ordered in nearly all datasets—LRW-Easy $<$ LRW-Random $<$ LRW-Hard—robustly confirming our hypothesis that validation sets in LRW classi", + "bbox": [ + 500, + 854, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27604", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f8c39ccef9276b658574f3f2cfd43328594f164b5b14b8362a228450e6f22942.jpg", + "image_caption": [ + "Figure 2. OOD generalization. Left: Comparison of LRW variants on domain shift benchmarks. The ordering between the validation selection methods is reconfirmed on domain shift benchmark datasets as well, suggesting that earlier gains are not via overfitting to training distribution. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. For absolute values refer supp." + ], + "image_footnote": [], + "bbox": [ + 86, + 108, + 433, + 294 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/46aab2494a2382063fc962b892cb3dfef0227f7d5f113f6105640afbdc3c5172.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 437, + 108, + 880, + 294 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "fiers need to be optimized. The difference between LRW-Hard and LRW-Easy is over $2.5\\%$ relative gain for ImageNet & CIFAR-100, and $1.6\\%$ relative for Clothing-1M.", + "bbox": [ + 91, + 395, + 467, + 439 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- LRW-Random shows modest gains over ERM in most datasets². LRW-Hard shows significant gains, underscoring the benefit of combining LRW with validation set optimization - 0.8% relative gain on Imagenet, 1.3% on Clothing-1M, 2.15% relative on CIFAR-100.", + "- The end-to-end LRWOpt matches or exceeds LRW-Hard, showcasing its effectiveness without the need for training twice. On a minority of datasets, LRW-Hard is nominally better; we believe this is due to the small-sample nature of real-world datasets, and attendant estimation noise." + ], + "bbox": [ + 76, + 441, + 467, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although the presented accuracy is on unseen test sets, a concern may be that LRW-Hard overfits to the training data distribution and results in brittle classifiers. To address this, we performed a number of experiments on datasets with matched out-of-domain test sets (Diabetic retinopathy [1, 33], Camelyon [2], WildCam [4]) in next subsection.", + "bbox": [ + 75, + 595, + 467, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1.2 MOLERE outperforms existing re-weighting baselines", + "text_level": 1, + "bbox": [ + 76, + 708, + 467, + 737 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We now compare our LRWOpt method against other reweighting methods- FSR [40]), MBR [22], MAPLE [41], MWN [32], StableNet [39], BiLAW [14])-see Fig. 1 (right) for more details. While FSR, RHO-Loss, MBR, MAPLE, StableNet and BiLAW are proposals in the literature for learned reweighting of the training data (via meta-learning)", + "bbox": [ + 75, + 748, + 467, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in order to address various clean- and noisy-label scenarios, MBR is an extrapolation of a proposal for ad-hoc upweighting of adversarial examples alone [22], for increased robustness against those specific adversarial attacks. In similar spirit, the proposal \"just train twice\" [21] also suggests an ad-hoc upweighting of poor performing instances in a second round of training. RHO-loss [24], on the other hand, follows the harder version as against all these methods and selects only some points from a batch which minimize the holdout set loss for efficient training.", + "bbox": [ + 500, + 395, + 890, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On the datasets tested, we see that LRWOpt clearly outperforms all these baseline methods consistently across all the datasets. It is followed by MAPLE, StableNet which are designed keeping group/OOD robustness in mind. FSR and Rho-Loss perform similar to ERM only. Interestingly, MBR and MWN are among the worst performers, showing that it is insufficient to simply upweight instances based on a first-round estimate of margin and the commonly followed bilevel optimization procedure by using free-parameters/loss based re-weighting, even though capable of providing unbiasedness, is not sufficient and requires another level of optimization for finding the appropriate validation set.", + "bbox": [ + 496, + 546, + 890, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2. Out-Of-Distribution (OD) generalization", + "text_level": 1, + "bbox": [ + 500, + 739, + 861, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further evaluate the robustness of our learned representations on the standard out-of-distribution datasets from the Wilds benchmark namely the camelyon [2] and the iwildcam [4] datasets along with the Diabetic Retinopathy dataset with a country shifted test set (APTOS test dataset) [1]. For the first two, $10\\%$ examples from the train set, sampled randomly, are used as val set. For the last one, a separate validation set, with same domain as the train set, is provided. Refer supplementary for more details regarding", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2Previous results [31] had shown neutral or slightly negative gains over ERM, focusing chiefly on training with noisy training labels + clean validation data. The improvement in our results are driven by the use of the meta-network.", + "bbox": [ + 75, + 849, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27605", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the dataset details and our evaluation setup. Furthermore, we also analyze the performance on the ImageNet-A dataset by using both training and validation data from ImageNet-1K. Our primary goal here is to check whether the gains we saw above are primarily driven by in-domain learning, or a broader improvement in generalization capacity over the existing learned reweighting methods –as a result, we restrict ourselves to comparison among ERM, the LRW variants along with LRWOpt and the re-weighting baselines, rather than the substantial literature on domain shift. Fig. 2 (left) confirms that our learned classifiers generalize better to domain shift data as compared to ERM classifiers; further, the ordering between the different validation datasets is largely preserved. Fig. 2 (right) provides evaluation of our methods and other re-weighting baselines. These include the standard bi-level optimization based ones like MWN, FSR along with ones designed for OOD generalization/robustness like MAPLE, StableNet, Rho-Loss and MBR. It can be observed that our method surpasses all of these baselines thereby showing the importance of validation set optimization problem for the bi-level optimization based re-weighting methods, introduced in the paper. StableNet comes out to be the closest competitor of our method which has been designed explicitly for OOD learning. Rest all the re-weighting methods perform similar to ERM with minor gains/losses. Absolute accuracy values for this analysis are provided in the supplementary.", + "bbox": [ + 76, + 90, + 472, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Practical Label Noise Settings", + "text_level": 1, + "bbox": [ + 76, + 523, + 344, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now study the noisy label setting with a focus on real-world label noise using datasets like Clothing1M [37], and noisy CIFAR-10 (Inst. C-10 [36]), which contain instance conditioned noise as against randomly flipping labels or adding uniform noise. This noise can be treated as a measure of instance hardness rather than labeling error (refer supplementary for more details). Table 3 compares LR-WOpt method against bi-level optimization approaches like MWN, FSR, L2R, GDW which although specifically designed for noisy labels have been primarily tested on label flipping, uniform noise data. We also compare against MAPLE, designed for general robustness. On Inst. C-10, our method clearly surpasses all baselines, with $1.53\\%$ accuracy gain. On Clothing-1M, we show about $0.85\\%$ gain over the best performing GDW baseline. For other noisy settings like random label flips, prior work on outlier robust DRO [38] has shown good results using loss clipping (e.g. exclude $\\mathrm{k}\\%$ of highest loss as label noise), which could be co-opted into our work.", + "bbox": [ + 75, + 547, + 472, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.4. Skewed Labels", + "text_level": 1, + "bbox": [ + 76, + 845, + 230, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now study the skewed label setting, comparing against instance based reweighting schemes proposed with this set-", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/41335917a075e6674e269c78c72c67f3d75bbbcf31594094c04cec192e825912.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodEasyHardRandomLRWoptMWNERM
Acc.83.1785.0983.8784.9484.0284.11
", + "bbox": [ + 501, + 89, + 893, + 128 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b4006aa55522e33205370dc34db083af043facb64296b6fdfc0fee0c30d834fe.jpg", + "table_caption": [ + "Table 1. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and 12s baselines." + ], + "table_footnote": [], + "table_body": "
class skew20050101
MWN [32]40.11 ± 0.948.67 ± 0.761.32 ± 0.674.23 ± 0.3
FSR [40]38.04 ± 0.845.12 ± 0.958.38 ± 0.674.68 ± 0.2
GDW [6]40.36 ± 1.048.89 ± 0.861.67 ± 0.574.41 ± 0.4
LRWOpt42.33 ± 0.850.77 ± 0.763.28 ± 0.875.12 ± 0.3
", + "bbox": [ + 501, + 195, + 913, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b033fcf4b9825e72e863e3b97603ecc481339e5677b945ea54362eabd2033c68.jpg", + "table_caption": [ + "Table 2. Comparison, on CIFAR-100 dataset, of our LRWOpt method with existing meta-learning based reweighting methods in a label skew setup for which these methods were defined." + ], + "table_footnote": [], + "table_body": "
MWNFSRL2RMAPLEGDWOurs
Inst. C-1065.8967.1270.2170.3469.1271.87
Clothing-1M72.7972.0772.2271.6773.1273.97
", + "bbox": [ + 501, + 344, + 906, + 397 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Instance-dependent noise. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and l2s baselines.", + "bbox": [ + 498, + 406, + 893, + 449 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ting in mind (Meta-Weight-Net, FSR and another recently proposed re-weighting method GDW [6]). Table 2 shows the results for this analysis on the CIFAR-100 datasets with various skew levels ranging from 1 to 200. It can be observed that our LRWOpt significantly outperform the existing loss based reweighting methods at all of the skew levels showing accuracy gains upto $2.22\\%$ .", + "bbox": [ + 496, + 473, + 893, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.5. MOLERE scales to large pretrained models", + "text_level": 1, + "bbox": [ + 498, + 588, + 864, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further analyze the LRW-Hard, Easy and Random methods along with the ERM baseline on ViT-B/16 pretrained backbone trained using these techniques and evaluated on the ImageNet-1K dataset. Table 1 shows the results from this experiments. Again LRW-Hard emerges the winner and improves significantly (around $1\\%$ ) w.r.t. other methods and the baseline advocating robustness using hard examples. Furthermore, there is $1.92\\%$ difference in accuracy between LRW-Easy and LRW-Hard, even though we warm-started all the techniques with a pretrained backbone, showing the sensitivity of techniques to choice of validation set.", + "bbox": [ + 496, + 611, + 893, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.6. Leveraging OOD val set: A heuristic solution", + "text_level": 1, + "bbox": [ + 498, + 786, + 883, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now turn to the use of known hard instance, or OOD, datasets when available, in the MOLERE context. For the well-studied Imagenet-1K dataset, two datasets are frequently used to gauge generalization properties of learned classifiers – IN-A (“natural adversarial instances”, examples known to be misclassified by a trained Resnet-50", + "bbox": [ + 496, + 809, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27606", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa74da41d1295bb3729e621f718ef61eca0c145da396b8bd5bbe3d4ad2909491.jpg", + "image_caption": [ + "Figure 3. MOLERE improves margins of learned classifiers. (a,b): paired margin deltas between LRWOpt and ERM are moderately right-skewed with mean/median greater than zero. (c,d): As a function of ERM margin, clear separation seen between LRW-Hard (better) and LRW-Easy (worse) in terms of margin gain over ERM (errors bars are SEM). All results on unseen test data; Imagenet-100, CIFAR100 shown for brevity, with similar results for other datasets in appendix." + ], + "image_footnote": [], + "bbox": [ + 76, + 114, + 267, + 227 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9596f7b71389992551cef4f6d0678793848bf9930f664ee71dd055fff3a3c4a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 114, + 491, + 228 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fdf16d2063be349c7fd0c085533e1e2225396c80bb2429992bf3263a5bdd69bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 113, + 684, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a07077c1468e2f9c57063201516d24f45e8f92fa021b8ddd17429f4179b45a15.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 114, + 890, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model), and IN-R (renditions of objects, such as drawings, paintings, sculptures, etc). For each of these, we used a portion of the dataset as LRW validation set, and retained another portion for testing. Table 4 shows the results of this study. We report the following two surprising results: (1) our approach outperforms the baseline ERM classifier on not just the OOD test set, but also on the in-domain test set (1.7-3% and 0.5-0.7% gains respectively), and (2) simply adding the OOD data to the train set only moderately improves OOD test set performance while degrading ID accuracy. These findings were replicated for both IN-A and IN-R as LRW validation sets, underscoring the real-world applicability of our findings, on large-scale datasets.", + "bbox": [ + 75, + 327, + 472, + 523 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cbc936439e3d0e4654f4f2ee8388c0fa8b7735d4026f78d78cf5643e6a8025d9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IN-R val (ResNet50)IN-A val (ResNet152)
IN1K TestINR TestIN1k TestINA Test
LRWOpt + INR val76.1449.178.127.9
ERM (IN1K)75.6546.177.316.2
ERM (IN1K+INR)74.8947.477.086.6
", + "bbox": [ + 78, + 547, + 483, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Natural hard examples as validation. LRW classifiers on Imagenet (IN1k) data and OOD validation sets (IN-A & IN-R respectively) outperform ERM on both in-domain and OOD test sets. Simply augmenting training data of ERM baseline does not match this (see text for details).", + "bbox": [ + 75, + 633, + 468, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.7. Margin maximization via meta-learning", + "text_level": 1, + "bbox": [ + 75, + 722, + 419, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present empirical evidence showing that MOLERE has a margin maximization effect, i.e., the learned classifiers have wider margins than ERM classifiers. Since our validation data is selected to be low-margin instances, our LRW classifier upweights, and improves performance on, training instances most similar to the low-margin validation set. 3 shows two views of margin differences between MOLERE and ERM on the test set, to confirm this expectation3. Pan-", + "bbox": [ + 75, + 746, + 468, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "els (a,b) shows a histogram of paired margin differences between ERM and LRWOpt, indicating a modest right-skew with mean & median to the right of 0. Panels (c,d) shows LRW-Hard and LRW-Easy deltas w.r.t. ERM, averaged over ERM margin buckets (mean and S.E.M. errorbars)—across the board (i.e., for most values of ERM margin), LRW-Hard contrasts with ERM better than LRW-Easy.", + "bbox": [ + 496, + 327, + 890, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Further details on Algorithm 1, proof of Theorem 1, the time complexity of the proposed scheme compared to ERM, the training setup, ablation study over the validation set selection/loss, and discussion regarding the early-stage performance of the proposed scheme are provided in the supplementary.", + "bbox": [ + 496, + 436, + 892, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Discussion & conclusion", + "text_level": 1, + "bbox": [ + 500, + 554, + 725, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed the novel idea of optimizing the choice of validation data in a learned-reweighting setting, and showed that it gives significant gains over ERM on a range of datasets and domain generalization benchmarks. In particular, in most experiments on clean data, we saw a clear ordering between choosing easy, random, and hard samples as validation data in an LRW setup, with the latter performing best and delivering consistent gains over ERM. This ordering provides broad support to our primary hypothesis: meta-optimization of the metalearning workflow in LRW is an important area of research with potential for substantial impact. Our specific heuristic of choosing low-margin points is a simple, straightforward instantiation of what we believe is a family of optimization algorithms that can be brought to bear on the general problem of optimizing metalelearned classifiers. Indeed, our heuristic is not competitive under very high label noise scenarios, suggesting the need for follow-on work that explores more formal, optimization-driven approaches towards this problem. We are also excited about elucidating the theoretical basis of observed gains in the MOLERE framework.", + "bbox": [ + 496, + 583, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "3We show Imagenet-100 & CIFAR100 for brevity; findings consistent across all datasets (see Appendix).", + "bbox": [ + 75, + 875, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27607", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kaggle. diabetic retinopathy detection challenge, 2015, 2015. 5, 6", + "[2] Peter Bandi, Oscar Geessink, Quirine Manson, Marcory Van Dijk, Maschenka Balkenhol, Meyke Hermsen, Babak Ehteshami Bejnordi, Byungjae Lee, Kyunghyun Paeng, Aoxiao Zhong, et al. 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Caml: Fast context adaptation via meta-learning. 2018. 2" + ], + "bbox": [ + 78, + 90, + 468, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "27609", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_model.json b/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f6b05f024ac7d77baa27233e5a1e30efbb7dbe82 --- /dev/null +++ b/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.167, + 0.131, + 0.804, + 0.154 + ], + "angle": 0, + "content": "Improving Generalization via Meta-Learning on Hard Samples" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.182, + 0.697, + 0.217 + ], + "angle": 0, + "content": "Nishant Jain Arun S. Suggala Pradeep Shenoy Google Research India" + }, + { + "type": "text", + "bbox": [ + 0.296, + 0.22, + 0.675, + 0.234 + ], + "angle": 0, + "content": "{nishantjn,arunss,shenoypradeep}@google.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.473, + 0.71 + ], + "angle": 0, + "content": "Learned reweighting (LRW) approaches to supervised learning use an optimization criterion to assign weights for training instances, in order to maximize performance on a representative validation dataset. We pose and formalize the problem of optimized selection of the validation set used in LRW training, to improve classifier generalization. In particular, we show that using hard-to-classify instances in the validation set has both a theoretical connection to, and strong empirical evidence of generalization. We provide an efficient algorithm for training this meta-optimized model, as well as a simple train-twice heuristic for careful comparative study. We demonstrate that LRW with easy validation data performs consistently worse than LRW with hard validation data, establishing the validity of our meta-optimization problem. Our proposed algorithm outperforms a wide range of baselines on a range of datasets and domain shift challenges (Imagenet-1K, CIFAR-100, Clothing-1M, CAMELYON, WILDS, etc.), with \\(1\\%\\) gains using VIT-B on Imagenet. We also show that using naturally hard examples for validation (Imagenet-R / Imagenet-A) in LRW training for Imagenet improves performance on both clean and naturally hard test instances by \\(1 - 2\\%\\). Secondary analyses show that using hard validation data in an LRW framework improves margins on test data, hinting at the mechanism underlying our empirical gains. We believe this work opens up new research directions for the meta-optimization of meta-learning in a supervised learning context." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.21, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Overparameterized models, common in supervised learning [27], carry the risk of overfitting to training data. Typically, model generalization is measured on a validation dataset separate from the training data, for purposes of hyperparameter selection. Increasingly, this validation dataset is itself used as part of the learning objective in nested formulations, e.g., for hyperparameter tuning via gradient descent on the validation loss [11]. In particular, learned reweighting (LRW) approaches learn importance weights" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.895, + 0.422 + ], + "angle": 0, + "content": "associated with training instances [14, 16, 17, 31, 32, 40] or groups of training instances [25, 41] by optimizing a weighted training loss alongside an unweighted metal-loss on the validation data. This bilevel optimization aligns training loss with the validation data distribution via reweighting, a useful property in addressing covariate shift [34], and for group DRO [9, 41]. Even for in-domain test data, Ren et al. [31] show that using \"clean\" validation data with bilevel optimization can overcome significant amounts of label noise in training data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.895, + 0.59 + ], + "angle": 0, + "content": "Thus the choice of validation set in a LRW paradigm can greatly influence the quality and properties of the learned classifier. We therefore ask the question: can we optimize the choice of validation data in LRW so as to maximize generalization of the resulting classifier? We refer to this problem of validation set selection as meta-optimization, since it produces data that is the input of another optimization (the meta-learning approach underlying LRW). The closest related work to our proposal is [40] which constructs a validation dataset on the fly during training of an LRW classifier, with a criterion of choosing representative instances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.894, + 0.729 + ], + "angle": 0, + "content": "Our primary hypothesis is that we can improve classifier generalization by using a validation set consisting of hard-to-classify instances from the training distribution. We therefore pose and formalize the problem of Meta-Optimized LEarned REweighting (MOLERE) where the partitioning of data into train and validation splits, and the LRW classifier corresponding to that split, are jointly optimized. We design an efficient algorithm to tackle this meta-optimization, and make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.735, + 0.892, + 0.81 + ], + "angle": 0, + "content": "- We formalize the problem statement of validation set optimization in learned reweighting (LRW) classifiers for improved generalization. We prove that asymptotically our optimization objective exactly achieves our stated goal of maximizing accuracy on the hardest samples." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.894, + 0.901 + ], + "angle": 0, + "content": "- We simplify the nested optimization of our proposal into a tractable bi-level optimization with a min-max game between two auxiliary networks: a \"splitter\" that finds the hardest samples, and a \"reweighter\" that minimizes loss on those samples using LRW. We also provide a simple train-twice heuristic that can be used for careful analysis" + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27600" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.357, + 0.105 + ], + "angle": 0, + "content": "of the choice of validation data in LRW." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.107, + 0.468, + 0.272 + ], + "angle": 0, + "content": "- We show strict accuracy ordering of LRW models based on validation set: easy \\(<\\) random \\(<\\) hard, demonstrating the importance of optimizing LRW validation sets. We obtain reliable gains over ERM across datasets (e.g., \\(1\\%\\) on Imagenet/VIT-B backbone), and in domain-generalization (e.g., \\(1.36\\%\\) on iWildCam dataset [4, 18]) and noisy-label settings (e.g., \\(4.2\\%\\) on Clothing1M dataset [37]). We outperform a range of baselines including reweighting, meta-learning among others. Analyses show improved margins on test set in MOLERE classifiers, suggesting an explanation of our gains." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.273, + 0.468, + 0.348 + ], + "angle": 0, + "content": "- We extend our results to natural hard samples as validation (Imagenet withImagenet-R /Imagenet-A), showing \\(1 - 3\\%\\) gains on both in-domain and out-of-domain test sets. This shows the value of our ideas even in scenarios where we pay no additional cost for meta-optimization." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.107, + 0.468, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.35, + 0.468, + 0.41 + ], + "angle": 0, + "content": "We hope that our work will be seen as an initial step in establishing the value of meta-optimization of meta-learning, with our findings providing a strong proof-of-concept for the general research direction." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.423, + 0.218, + 0.437 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.448, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Importance weighting for robustness. There have been several works on learning robust representations via example re-weighting lately. Mostly, these work aim at avoiding noisy labels in the train set by analyzing the effect of decreasing loss on a given instance on a clean validation set. This line of work includes either learning a per-instance free parameter [31] or learning a simple MLP network [32] to predict importance of an instance based on its loss value. However, the requirement of a clean validation set limits their applicability to realistic scenarios. To deal with this, a meta-learning based re-weighting scheme (Fast Sample Reweighting [40]) was proposed based on generating some sort of pseudo-clean data as a proxy validation set. It also proposed certain approximations to make the training process more computation efficient. On a different note, a recent proposal called RHO-loss [24] proposed to select only worthy points for training which increased generalization property of the model, calculated as the difference of the training loss and a hold-out set loss." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.468, + 0.854 + ], + "angle": 0, + "content": "A recent line of work [16, 17] proposed weighting based on context/relevance of an instance compared with the overall data distribution. These papers target slow temporal drift in longitudinal datasets, and the development of better uncertainty measures for selective classification, respectively. In particular, Jain et al. [17], suggest that using target domain data in the validation set can improve domain shift performance of classifiers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Meta Learning. The sample re-weighting task using a validation set comes under the umbrella of meta-learning [15], which follows the learning-to-learn paradigm. It" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.891, + 0.182 + ], + "angle": 0, + "content": "is conceptually similar to model agnostic meta learning (MAML) [10], which learns a single set of parameters that can easily be customized (few-shot) to multiple tasks. Learning these shared parameters involves a nested optimization similar to the one presented here, and significantly optimized for efficiency by recent work[28, 30, 42]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Probabilistic Margins. Recent work [22] showed that the probabilistic margin in multi-class problems can be used to improve how neural networks deal with adversarial examples. The margin is defined as the difference between the probability of the true label and the largest of the remaining label probabilities, indicating the difficulty of classifying that instance. Liu et al. [22] propose re-weighting training instances, in presence of an adversarial attack, inversely related to their probability margins." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Just Train Twice. A recent work [21] proposed an effective strategy to improve sensitivity of ERM models towards certain groups by training the ERM model in 2 stages. The first stage is a standard training procedure, whereas the second stage involves giving more importance to the incorrectly classified examples in the first stage by up-weighting their loss in the aggregate loss term for updating the parameters. This can be interpreted as similar to giving more importance to low margin examples (here essentially a hard separation between positive and negative)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.503, + 0.834, + 0.521 + ], + "angle": 0, + "content": "3. Preliminaries: Learned ReWeighting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.651 + ], + "angle": 0, + "content": "We work with learned reweighting (LRW) classifiers where training data is reweighted in order to optimize some specified metric on validation data. The basic LRW formulation [31] works with two datasets \\( S_{tr} = \\{(x_i, y_i)\\}_{i=1}^N \\) and \\( S_{val} = \\{(x_i, y_i)\\}_{i=1}^M \\) (training & validation, respectively). Given a desired loss function \\( \\ell(y, \\hat{y}) \\), LRW learns a classifier \\( f_\\theta(\\cdot) \\), (with parameters \\( \\theta \\)) and an instance-wise weighting function \\( \\phi(\\cdot) \\) that minimize following bi-level objective:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.665, + 0.891, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\theta^ {*} (\\phi) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in S _ {t r}} \\phi (x) \\ell (y, f _ {\\theta} (x)), \\\\ s. t. \\quad \\phi^ {*} = \\arg \\min _ {\\phi} \\sum_ {(x, y) \\in S _ {v a l}} \\ell (y, f _ {\\theta^ {*} (\\phi)} (x)) \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Notice that the validation loss is unweighted, while the training objective is a weighted loss. Essentially, the above bilevel objective computes an estimate of classifier performance on the validation set, and optimizes it indirectly via reweighting of training data to influence the learned classifier. The weighted-loss-minimizing classifier \\( f_{\\theta^{*}}(\\cdot) \\), and the weights \\( \\phi^{*}(\\cdot) \\), are learned jointly, typically using alternating stochastic updates over minibatches to make the learning tractable [31]; this is in line with other meta-learning approaches such as MAML [10]. Following more" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27601" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "recent work [16], we use an instance-dependent neural network \\(\\phi(x)\\) for learning the training instance weights, instead of free parameters [31]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.319 + ], + "angle": 0, + "content": "Intuition: LRW has been used for overcoming training label noise [31, 32] and for handling covariate shift [16, 41]. In these cases, the validation set is assumed to be representative of test samples (i.e., clean labels, or covariateshifted data, respectively). The intuition is that the learned reweighting of the training loss aligns it with the (possibly different) validation distribution in the process of indirectly minimizing the meta-loss (Eq. 1). In particular, Shu et al. [32] show analytically that \"validation-like\" instances are upweighted. Thus, the validation set in LRW can be thought of as a target for generalization, with the learned classifier being optimized for performance on that target set." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.41, + 0.348 + ], + "angle": 0, + "content": "4. MOLERE: Optimizing LRW models" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.355, + 0.363, + 0.372 + ], + "angle": 0, + "content": "4.1. Hypothesis and formal objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.484 + ], + "angle": 0, + "content": "Our primary hypothesis is that we can improve generalization capabilities of supervised learning by combining two ingredients: a) a learned-reweighting classifier, as described in the previous section, and b) an optimized validation set that strongly encourages desired properties in the reweighting classifier. We refer to this idea as Meta-Optimization of the Learned Reweighting framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.471, + 0.695 + ], + "angle": 0, + "content": "In particular, we propose learning an LRW classifier with hard samples as validation set, to improve accuracy and generalization of learned classifiers. Since LRW by definition maximizes classifier performance on a given validation set, we believe that this choice of validation set will maximize generalization. Thus, given a dataset for training a predictive model, we need to 1) select the \"hard instances\" from the dataset and separate it into a validation set, and 2) train a classifier on the remaining data using this validation set for LRW. Notice that hardness of instances is determined in terms of the learned model itself; thus, formalizing the above idea leads to a joint optimization problem of data partitioning (train, validation), and LRW training. We present the formal problem below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Objective: Let \\( S = \\{(x,y)\\}_{i=1}^{N+M} \\) be the available data, and let \\( \\Theta \\) be the splitting function that splits \\( S \\) into training and validation datasets; to be precise, we let \\( \\Theta(S) \\) be the validation set and \\( \\Theta(S)^c \\) be its complement. MOLERE aims to solve the following tri-level optimization problem" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Theta^ {*} = \\arg \\max _ {\\Theta} \\sum_ {(x, y) \\in \\Theta (S)} \\ell (y, f _ {\\theta^ {*} (\\phi^ {*} (\\Theta), \\Theta)} (x)) \\\\ \\text{where}\\phi^{*}(\\Theta) = \\arg \\min_{\\phi}\\sum_{(x,y)\\in \\Theta (S)}\\ell (y,f_{\\theta^{*}(\\phi ,\\Theta)}(x)) \\\\ s. t. \\theta^ {*} (\\phi , \\Theta) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in \\Theta (S) ^ {c}} \\phi (x) \\ell (y, f _ {\\theta} (x)). \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "In words: Find a data split, such that across all possible splits the LRW classifier learned on the split has maximal error on the chosen validation set. In practice, we impose an additional constraint on the validation set size: \\(|\\Theta (S)| / (N + M)\\leq \\delta\\), where \\(\\delta\\) is some predefined fractional constant." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.191, + 0.829, + 0.208 + ], + "angle": 0, + "content": "4.2. MOLERE objective and generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.215, + 0.892, + 0.365 + ], + "angle": 0, + "content": "We now study the asymptotic properties of our proposed meta-optimization as \\( N + M \\to \\infty \\), as a means of gaining theoretical insights into its generalization capabilities in comparison to classical empirical risk minimization (ERM). This analysis assumes a weighting function \\( \\phi(\\cdot) \\) dependent on both \\( x \\) and \\( y \\). Interestingly, our experiments revealed similar performance between this formulation of \\( \\phi \\) and one relying solely on \\( x \\). The following proposition shows that asymptotically MOLERE solves a robust optimization objective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.892, + 0.48 + ], + "angle": 0, + "content": "Theorem 1 (Asymptotics). Consider the tri-level optimization in Equation (2). Suppose the weighting function \\(\\phi(\\cdot)\\), and splitting function \\(\\Theta(\\cdot)\\) are dependent on both \\(x\\) and \\(y\\). Let's suppose \\(N + M \\to \\infty\\), and \\(\\lim_{N, M \\to \\infty} \\frac{M}{N + M} = \\delta\\). Moreover, suppose the domains of \\(\\phi, \\theta, \\Theta\\) are very large and contain the set of all measurable functions. Then the objective of MOLERE is equivalent to" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.489, + 0.892, + 0.524 + ], + "angle": 0, + "content": "\\[\n\\max _ {S: | S | = \\delta (N + M)} \\min _ {\\theta} \\sum_ {(x, y) \\in S} \\ell (y, f _ {\\theta} (x)). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Proof Sketch. The proof of the theorem relies on the observation that there exists a weighting function \\(\\phi\\) that can transform any probability distribution \\(P\\) to any another distribution \\(Q\\) (as long as the support of \\(Q\\) is a subset of \\(P\\)). Using this observation, one can show that the second, third level optimization problems in Equation (2) is equivalent to following problem: \\(\\min_{\\theta} \\sum_{(x,y) \\in \\Theta(S)^c} \\ell(y, f_{\\theta}(x))\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.892, + 0.74 + ], + "angle": 0, + "content": "A similar result holds when both \\(\\Theta(\\cdot), \\phi(\\cdot)\\) rely solely on \\(x\\). Intuitively, the above theorem shows that in the limit of infinite samples, MOLERE identifies the hardest samples in the training data, and learns a classifier that minimizes the error on those samples. This is exactly the goal laid out in our hypothesis above." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.788 + ], + "angle": 0, + "content": "Connections to DRO. Interestingly, the objective in Equation (3) is the dual of the following Distributionally Robust Optimization (DRO) objective [5]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.797, + 0.892, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\max _ {S: | S | = \\delta (N + M)} \\sum_ {(x, y) \\in S} \\ell (y, f _ {\\theta} (x)). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "DRO is a well studied framework for learning robust models [8, 26]. However, to the best of our knowledge, dual DRO is not studied in the literature; we will explore this connection more deeply in future work." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27602" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.469, + 0.108 + ], + "angle": 0, + "content": "4.3. Efficient algorithm for validation optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.265 + ], + "angle": 0, + "content": "Designing a tractable algorithm for meta-optimization runs into two technical challenges: a) How can we learn to assign instances to train and validation sets? and b) How do we efficiently solve the tri-level objective proposed in Sec. 4.1? We address these two challenges in this section. First, we use a second auxiliary network for soft-assigning instances to train and validation datasets. Second, we collapse the outer two loops of the trilevel objective into a minimax formulation, and thereby reduce it to a bi-level optimization problem. We describe each of these in order below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.471, + 0.448 + ], + "angle": 0, + "content": "Soft data assignment: Inspired by a recent work [3], we use a partitioning network to predict probability for each instance to be included in the validation set. At any point in time, the \"splitter\" network outputs soft assignments \\(\\mathbb{P}(z|x,y)\\) with \\(z\\in \\{0,1\\}\\) indicating whether the example \\((x,y)\\) belongs to the pseudotest set \\((z = 0)\\) or the pseudotrain set. The pseudotrain set is used to train a classifier using standard cross-entropy. The splitter is then updated to identify easy instances for the classifier and assign them to the pseudotrain partition in the next round; this is achieved by minimizing the cross-entropy between its soft-assignment and classifier accuracy:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.457, + 0.47, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s p l i t} = C E \\left(\\mathbb {P} _ {s p l i t t e r} \\left(z _ {i} \\mid x _ {i}, y _ {i}\\right), \\mathbb {I} _ {y _ {i}} (\\hat {y})\\right) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.478, + 0.402, + 0.493 + ], + "angle": 0, + "content": "\\[\nw h e r e \\quad \\hat {y} = \\arg \\max \\mathbb {P} _ {\\text {p r e d i c t o r}} (y | x _ {i})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.47, + 0.579 + ], + "angle": 0, + "content": "In order to maintain the label distribution and train-to-test ratio, two regularizers [3] are added to penalize shift from the prior distribution, and to push label margins in the training split and testing split close to the original label margin (see supplementary for details)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Meta-optimization with min-max objective: To simplify the tri-level optimization in Sec. 4.1, we propose a bi-level approximation where the outer loop combines the data splitting and instance reweighting objectives. Specifically, we propose a min-max game between the splitter (parametrized by \\(\\Theta\\)) and the meta-network (parametrized by \\(\\phi\\)), where the splitter has to maximize validation set error whereas instance weights are focused on minimizing it:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.71, + 0.473, + 0.794 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Theta^ {*}, \\phi^ {*} = \\arg \\max _ {\\Theta} \\min _ {\\phi} \\sum_ {(x, y) \\in S _ {t} ^ {c}} \\left(\\ell (y, f _ {\\theta^ {*} (\\phi , \\Theta)} (x)) - \\mathcal {L} _ {s p l i t}\\right) \\\\ w h e r e \\quad \\theta^ {*} (\\phi , \\Theta) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in S _ {t}} \\phi (x) \\ell (y, f _ {\\theta} (x)) \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where the set \\( S_{t} = \\{(x,y):(x,y)\\in S,\\mathbb{I}\\{\\Theta (x,y) > 0.5\\} \\} \\) and \\( S_{t}^{c} = S\\setminus S_{t} \\), \\( \\mathbb{I} \\) denotes the indicator function. The overall algorithm updates the splitter and instance weighting network once every \\( Q \\) steps of classifier update, and also regularizes the splitter with \\( \\Omega_{ratio} + \\Omega_{ld} \\) at set intervals (every R steps). The complete description of this method is provided in Algorithm 1 and analysis of the loss function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "at the outer level, derivation of update equations for all parameters \\((\\Theta, \\phi, \\theta)\\) are provided in the supplementary. Both the instance weight network and Splitter are parameterized as neural networks. The meta-network for instance weights predict the weight for a training instance \\((x_i, y_i)\\) by using \\((x_i)\\) as input, \\(w_i = g_{\\phi}(x_i)\\) and the Splitter predicts a probability of \\((x_i, y_i)\\) being in the train set by taking both of them as inputs \\(z_i = g_{\\Theta}(x_i, y_i)\\). In experiments, we refer to this end-to-end optimization method as LRWOpt." + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.242, + 0.885, + 0.259 + ], + "angle": 0, + "content": "Algorithm 1 LRWOpt: The Overall One-Shot Algorithm." + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.261, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Require: \\(\\theta, \\Theta, \\phi\\), learning rates \\((\\beta_{1}, \\beta_{2}, \\beta_{3}), S, N, M\\). \nEnsure: Robustly trained classifier parameters \\(\\theta\\). \n1: Randomly initialize \\(\\theta, \\Theta\\) and \\(\\phi\\); \n2: initialize ge = 0; ▷ Difference b/w train and val error \n3: for e=1 to MaxEpochs do \n4: \\(S_{tr}, S_{val} = \\text{GenerateSplit}(\\mathcal{D}, \\Theta)\\) \n5: for \\(b = 1\\) to M/m do ▷ m is the batch size \n6: \\(\\{(x_i^v, y_i^v)\\}_{i=1}^m = \\text{SampleMiniBatch}(\\mathcal{S}_{val}, m)\\); \n7: \\(\\Theta \\gets \\Theta - \\beta_1 \\nabla_\\Theta \\sum (\\mathcal{L}_{split} - \\ell(y_i^v, f_\\theta(x_i^v)))\\) \n8: \\(\\phi \\gets \\phi - \\beta_2 \\nabla_\\phi \\sum (\\ell(y_i^v, f_\\theta(x_i^v)) - \\mathcal{L}_{split})\\) \n9: for \\(j = 1\\) to Q do \n10: \\(\\{(x_i, y_i)\\}_{i=1}^n\\) SampleMiniBatch(\\(\\mathcal{D}_t, n\\)); \n11: \\(\\theta \\gets \\theta - \\beta_3 \\nabla_\\theta \\sum g_\\phi(x_i) \\ell(f_\\theta(x_i), y_i)\\); \n12: end for \n13: end for \n14: if \\(\\sum \\ell(y_i^v, f_\\theta(x_i^v)) - \\sum \\ell(y_i, f_\\theta(x_i)) < \\text{ge then}\\) \n15: break; \n16: end if \n17: ge = \\(\\sum \\frac{1}{M} \\ell(y_i^v, f_\\theta(x_i^v)) - \\frac{1}{N} \\sum \\ell(y_i, f_\\theta(x_i))\\) \n18: end for" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.593, + 0.764, + 0.609 + ], + "angle": 0, + "content": "4.4. A simple train-twice heuristic" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.692 + ], + "angle": 0, + "content": "We now describe a simple train-twice heuristic that can be used to establish the importance of validation set optimization in LRW. We first train an ERM classifier on the available training data, and use the probabilistic margin (PM) as a proxy for instance hardness:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.702, + 0.892, + 0.727 + ], + "angle": 0, + "content": "\\[\nP M (x, y, \\theta) = \\mathbf {p} _ {y} (x, \\theta) - \\max _ {j, j \\neq y} \\mathbf {p} _ {j} (x, \\theta) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Here \\(\\theta\\) denotes the ERM classifier's parameters. This criterion was used to manually reweight adversarial examples in recent work [22]. Although this proxy score is inexact1, it nevertheless allows us to design interesting heuristic LRW variants based on its rank-ordering of training instances: (1) LRW-Hard, where we use the lowest margin instances as validation data, and the rest of the instances as training data, (2) LRW-Easy, in which the highest margin instances are" + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For instance, it measures instance hardness under an ERM classifier, not the to-be-trained LRW model; further, an overtrained classifier may give incorrectly overconfident margins [21]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27603" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.109, + 0.485, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.109, + 0.885, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.894, + 0.404 + ], + "angle": 0, + "content": "Figure 1. Robustness analysis on benchmark datasets. Left: Comparing different LRW variants, based on the choice of validation set (Easy, Random, Hard, corresponding to the rank-ordering of training data by probabilistic margin of an ERM classifier). \\(y\\)-axis shows accuracy gains over ERM for each dataset (\\(x\\)-axis). We see consistent ordering of performance, with LRW-Easy \\(<\\) LRW-Random \\(<\\) LRW-Hard, showing the importance of validation set optimization. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. In-1K corresponds to ImageNet-1K. For absolute accuracy values refer supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.48 + ], + "angle": 0, + "content": "used as validation data, and (3) LRW-Random, a control which uses a randomly selected validation set that does not depend on the ERM margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.571 + ], + "angle": 0, + "content": "We can use these variants to quantify the impact of perturbing the validation set in LRW, and to provide an existence proof of validation optimization techniques that materially improve learned classifiers. In particular, we expect to see a clear ordering of classifier test accuracy - LRW-Easy \\(<\\) LRW-Random \\(<\\) LRW-Hard." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.586, + 0.21, + 0.603 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.47, + 0.732 + ], + "angle": 0, + "content": "We perform extensive experimentation on multiple classification tasks including distribution shift benchmarks. For all datasets, if a train-validation split is already available, we use the training data for the ERM classifier in the train twice heuristic before pooling, ranking, and repartitioning. For the end-to-end optimization, we start with pooled train-validation data and simultaneously learn the data splits and the corresponding LRWOpt model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.18, + 0.756 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We use popular classification benchmarks including CIFAR-100 [20], ImageNet-100 [35], ImageNet-1K [7], Aircraft [23], Stanford Cars [19], Oxford-IIIT Fine-grained classification (Cats v/s Dogs) [29] and Diabetic Retinopathy (DR) dataset. Furthermore, for OOD analysis we use the ImageNet-A [13], ImageNet-R [12] datasets for models trained on ImageNet-1K. We also use the Camelyon [2], iWildCam [4] dataset from the widely popular WILDS benchmark [18] and also the country shifted test set for the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.894, + 0.512 + ], + "angle": 0, + "content": "DR [1] dataset. We further analyze for robustness in presence of instance dependent noise on the noisy version of CIFAR-10 dataset (Inst.C-10) proposed by Xia et al. [36] and Clothing-1M [37] dataset. Please refer supplementary (supp.) for more details, setup for these datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.608, + 0.535 + ], + "angle": 0, + "content": "5.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.894, + 0.65 + ], + "angle": 0, + "content": "Along with ERM, we also compare our method against various re-weighting based methods designed for improving robustness or handling noisy scenarios. These include learned re-weighting methods: MWN [32], FSR [40], L2R [31], MAPLE [41], BiLAW [14], GDW [6], StableNet [39] along with Margin Based Reweighting (MBR) [22] and Rho-Loss [24]. Please refer supp. for more details regarding them." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.661, + 0.587, + 0.677 + ], + "angle": 0, + "content": "6. Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.686, + 0.771, + 0.701 + ], + "angle": 0, + "content": "6.1. In-Distribution Generalization" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.853, + 0.725 + ], + "angle": 0, + "content": "6.1.1 MOLERE improves classification accuracy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Figure 1 (left) shows the LRW advantage (gains over an ERM baseline) for a range of datasets. Shown are 4 alternatives—LRW-Easy, LRW-Random, and LRW-Hard, corresponding to easy, random, and hard validation sets per the train-twice heuristic (Sec. 4.4), and LRWOpt, which is the end-to-end optimization of LRW classifier and train-validation split (Sec. 4.3). Refer supplementary for absolute accuracy values." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "- Gains vs ERM are strictly ordered in nearly all datasets—LRW-Easy \\(<\\) LRW-Random \\(<\\) LRW-Hard—robustly confirming our hypothesis that validation sets in LRW classi" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27604" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.109, + 0.434, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.439, + 0.109, + 0.882, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.307, + 0.894, + 0.366 + ], + "angle": 0, + "content": "Figure 2. OOD generalization. Left: Comparison of LRW variants on domain shift benchmarks. The ordering between the validation selection methods is reconfirmed on domain shift benchmark datasets as well, suggesting that earlier gains are not via overfitting to training distribution. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. For absolute values refer supp." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.396, + 0.468, + 0.44 + ], + "angle": 0, + "content": "fiers need to be optimized. The difference between LRW-Hard and LRW-Easy is over \\(2.5\\%\\) relative gain for ImageNet & CIFAR-100, and \\(1.6\\%\\) relative for Clothing-1M." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.442, + 0.468, + 0.516 + ], + "angle": 0, + "content": "- LRW-Random shows modest gains over ERM in most datasets². LRW-Hard shows significant gains, underscoring the benefit of combining LRW with validation set optimization - 0.8% relative gain on Imagenet, 1.3% on Clothing-1M, 2.15% relative on CIFAR-100." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.516, + 0.468, + 0.591 + ], + "angle": 0, + "content": "- The end-to-end LRWOpt matches or exceeds LRW-Hard, showcasing its effectiveness without the need for training twice. On a minority of datasets, LRW-Hard is nominally better; we believe this is due to the small-sample nature of real-world datasets, and attendant estimation noise." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.442, + 0.468, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.468, + 0.687 + ], + "angle": 0, + "content": "Although the presented accuracy is on unseen test sets, a concern may be that LRW-Hard overfits to the training data distribution and results in brittle classifiers. To address this, we performed a number of experiments on datasets with matched out-of-domain test sets (Diabetic retinopathy [1, 33], Camelyon [2], WildCam [4]) in next subsection." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.709, + 0.468, + 0.738 + ], + "angle": 0, + "content": "6.1.2 MOLERE outperforms existing re-weighting baselines" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.468, + 0.84 + ], + "angle": 0, + "content": "We now compare our LRWOpt method against other reweighting methods- FSR [40]), MBR [22], MAPLE [41], MWN [32], StableNet [39], BiLAW [14])-see Fig. 1 (right) for more details. While FSR, RHO-Loss, MBR, MAPLE, StableNet and BiLAW are proposals in the literature for learned reweighting of the training data (via meta-learning)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.396, + 0.892, + 0.546 + ], + "angle": 0, + "content": "in order to address various clean- and noisy-label scenarios, MBR is an extrapolation of a proposal for ad-hoc upweighting of adversarial examples alone [22], for increased robustness against those specific adversarial attacks. In similar spirit, the proposal \"just train twice\" [21] also suggests an ad-hoc upweighting of poor performing instances in a second round of training. RHO-loss [24], on the other hand, follows the harder version as against all these methods and selects only some points from a batch which minimize the holdout set loss for efficient training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.728 + ], + "angle": 0, + "content": "On the datasets tested, we see that LRWOpt clearly outperforms all these baseline methods consistently across all the datasets. It is followed by MAPLE, StableNet which are designed keeping group/OOD robustness in mind. FSR and Rho-Loss perform similar to ERM only. Interestingly, MBR and MWN are among the worst performers, showing that it is insufficient to simply upweight instances based on a first-round estimate of margin and the commonly followed bilevel optimization procedure by using free-parameters/loss based re-weighting, even though capable of providing unbiasedness, is not sufficient and requires another level of optimization for finding the appropriate validation set." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.862, + 0.758 + ], + "angle": 0, + "content": "6.2. Out-Of-Distribution (OD) generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We further evaluate the robustness of our learned representations on the standard out-of-distribution datasets from the Wilds benchmark namely the camelyon [2] and the iwildcam [4] datasets along with the Diabetic Retinopathy dataset with a country shifted test set (APTOS test dataset) [1]. For the first two, \\(10\\%\\) examples from the train set, sampled randomly, are used as val set. For the last one, a separate validation set, with same domain as the train set, is provided. Refer supplementary for more details regarding" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.468, + 0.9 + ], + "angle": 0, + "content": "2Previous results [31] had shown neutral or slightly negative gains over ERM, focusing chiefly on training with noisy training labels + clean validation data. The improvement in our results are driven by the use of the meta-network." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27605" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.501 + ], + "angle": 0, + "content": "the dataset details and our evaluation setup. Furthermore, we also analyze the performance on the ImageNet-A dataset by using both training and validation data from ImageNet-1K. Our primary goal here is to check whether the gains we saw above are primarily driven by in-domain learning, or a broader improvement in generalization capacity over the existing learned reweighting methods –as a result, we restrict ourselves to comparison among ERM, the LRW variants along with LRWOpt and the re-weighting baselines, rather than the substantial literature on domain shift. Fig. 2 (left) confirms that our learned classifiers generalize better to domain shift data as compared to ERM classifiers; further, the ordering between the different validation datasets is largely preserved. Fig. 2 (right) provides evaluation of our methods and other re-weighting baselines. These include the standard bi-level optimization based ones like MWN, FSR along with ones designed for OOD generalization/robustness like MAPLE, StableNet, Rho-Loss and MBR. It can be observed that our method surpasses all of these baselines thereby showing the importance of validation set optimization problem for the bi-level optimization based re-weighting methods, introduced in the paper. StableNet comes out to be the closest competitor of our method which has been designed explicitly for OOD learning. Rest all the re-weighting methods perform similar to ERM with minor gains/losses. Absolute accuracy values for this analysis are provided in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.525, + 0.345, + 0.541 + ], + "angle": 0, + "content": "6.3. Practical Label Noise Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.473, + 0.837 + ], + "angle": 0, + "content": "We now study the noisy label setting with a focus on real-world label noise using datasets like Clothing1M [37], and noisy CIFAR-10 (Inst. C-10 [36]), which contain instance conditioned noise as against randomly flipping labels or adding uniform noise. This noise can be treated as a measure of instance hardness rather than labeling error (refer supplementary for more details). Table 3 compares LR-WOpt method against bi-level optimization approaches like MWN, FSR, L2R, GDW which although specifically designed for noisy labels have been primarily tested on label flipping, uniform noise data. We also compare against MAPLE, designed for general robustness. On Inst. C-10, our method clearly surpasses all baselines, with \\(1.53\\%\\) accuracy gain. On Clothing-1M, we show about \\(0.85\\%\\) gain over the best performing GDW baseline. For other noisy settings like random label flips, prior work on outlier robust DRO [38] has shown good results using loss clipping (e.g. exclude \\(\\mathrm{k}\\%\\) of highest loss as label noise), which could be co-opted into our work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.231, + 0.862 + ], + "angle": 0, + "content": "6.4. Skewed Labels" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We now study the skewed label setting, comparing against instance based reweighting schemes proposed with this set-" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.09, + 0.895, + 0.13 + ], + "angle": 0, + "content": "
MethodEasyHardRandomLRWoptMWNERM
Acc.83.1785.0983.8784.9484.0284.11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.14, + 0.895, + 0.182 + ], + "angle": 0, + "content": "Table 1. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and 12s baselines." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.196, + 0.915, + 0.279 + ], + "angle": 0, + "content": "
class skew20050101
MWN [32]40.11 ± 0.948.67 ± 0.761.32 ± 0.674.23 ± 0.3
FSR [40]38.04 ± 0.845.12 ± 0.958.38 ± 0.674.68 ± 0.2
GDW [6]40.36 ± 1.048.89 ± 0.861.67 ± 0.574.41 ± 0.4
LRWOpt42.33 ± 0.850.77 ± 0.763.28 ± 0.875.12 ± 0.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.289, + 0.895, + 0.331 + ], + "angle": 0, + "content": "Table 2. Comparison, on CIFAR-100 dataset, of our LRWOpt method with existing meta-learning based reweighting methods in a label skew setup for which these methods were defined." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.345, + 0.907, + 0.398 + ], + "angle": 0, + "content": "
MWNFSRL2RMAPLEGDWOurs
Inst. C-1065.8967.1270.2170.3469.1271.87
Clothing-1M72.7972.0772.2271.6773.1273.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.407, + 0.895, + 0.45 + ], + "angle": 0, + "content": "Table 3. Instance-dependent noise. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and l2s baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.895, + 0.581 + ], + "angle": 0, + "content": "ting in mind (Meta-Weight-Net, FSR and another recently proposed re-weighting method GDW [6]). Table 2 shows the results for this analysis on the CIFAR-100 datasets with various skew levels ranging from 1 to 200. It can be observed that our LRWOpt significantly outperform the existing loss based reweighting methods at all of the skew levels showing accuracy gains upto \\(2.22\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.589, + 0.866, + 0.605 + ], + "angle": 0, + "content": "6.5. MOLERE scales to large pretrained models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.895, + 0.78 + ], + "angle": 0, + "content": "We further analyze the LRW-Hard, Easy and Random methods along with the ERM baseline on ViT-B/16 pretrained backbone trained using these techniques and evaluated on the ImageNet-1K dataset. Table 1 shows the results from this experiments. Again LRW-Hard emerges the winner and improves significantly (around \\(1\\%\\)) w.r.t. other methods and the baseline advocating robustness using hard examples. Furthermore, there is \\(1.92\\%\\) difference in accuracy between LRW-Easy and LRW-Hard, even though we warm-started all the techniques with a pretrained backbone, showing the sensitivity of techniques to choice of validation set." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.787, + 0.885, + 0.803 + ], + "angle": 0, + "content": "6.6. Leveraging OOD val set: A heuristic solution" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.897, + 0.903 + ], + "angle": 0, + "content": "We now turn to the use of known hard instance, or OOD, datasets when available, in the MOLERE context. For the well-studied Imagenet-1K dataset, two datasets are frequently used to gauge generalization properties of learned classifiers – IN-A (“natural adversarial instances”, examples known to be misclassified by a trained Resnet-50" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27606" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.116, + 0.268, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.116, + 0.493, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.114, + 0.685, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.116, + 0.892, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.24, + 0.894, + 0.296 + ], + "angle": 0, + "content": "Figure 3. MOLERE improves margins of learned classifiers. (a,b): paired margin deltas between LRWOpt and ERM are moderately right-skewed with mean/median greater than zero. (c,d): As a function of ERM margin, clear separation seen between LRW-Hard (better) and LRW-Easy (worse) in terms of margin gain over ERM (errors bars are SEM). All results on unseen test data; Imagenet-100, CIFAR100 shown for brevity, with similar results for other datasets in appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.473, + 0.525 + ], + "angle": 0, + "content": "model), and IN-R (renditions of objects, such as drawings, paintings, sculptures, etc). For each of these, we used a portion of the dataset as LRW validation set, and retained another portion for testing. Table 4 shows the results of this study. We report the following two surprising results: (1) our approach outperforms the baseline ERM classifier on not just the OOD test set, but also on the in-domain test set (1.7-3% and 0.5-0.7% gains respectively), and (2) simply adding the OOD data to the train set only moderately improves OOD test set performance while degrading ID accuracy. These findings were replicated for both IN-A and IN-R as LRW validation sets, underscoring the real-world applicability of our findings, on large-scale datasets." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.548, + 0.485, + 0.624 + ], + "angle": 0, + "content": "
IN-R val (ResNet50)IN-A val (ResNet152)
IN1K TestINR TestIN1k TestINA Test
LRWOpt + INR val76.1449.178.127.9
ERM (IN1K)75.6546.177.316.2
ERM (IN1K+INR)74.8947.477.086.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.635, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Table 4. Natural hard examples as validation. LRW classifiers on Imagenet (IN1k) data and OOD validation sets (IN-A & IN-R respectively) outperform ERM on both in-domain and OOD test sets. Simply augmenting training data of ERM baseline does not match this (see text for details)." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.723, + 0.421, + 0.74 + ], + "angle": 0, + "content": "6.7. Margin maximization via meta-learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.868 + ], + "angle": 0, + "content": "We present empirical evidence showing that MOLERE has a margin maximization effect, i.e., the learned classifiers have wider margins than ERM classifiers. Since our validation data is selected to be low-margin instances, our LRW classifier upweights, and improves performance on, training instances most similar to the low-margin validation set. 3 shows two views of margin differences between MOLERE and ERM on the test set, to confirm this expectation3. Pan-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.902 + ], + "angle": 0, + "content": "3We show Imagenet-100 & CIFAR100 for brevity; findings consistent across all datasets (see Appendix)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.435 + ], + "angle": 0, + "content": "els (a,b) shows a histogram of paired margin differences between ERM and LRWOpt, indicating a modest right-skew with mean & median to the right of 0. Panels (c,d) shows LRW-Hard and LRW-Easy deltas w.r.t. ERM, averaged over ERM margin buckets (mean and S.E.M. errorbars)—across the board (i.e., for most values of ERM margin), LRW-Hard contrasts with ERM better than LRW-Easy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Further details on Algorithm 1, proof of Theorem 1, the time complexity of the proposed scheme compared to ERM, the training setup, ablation study over the validation set selection/loss, and discussion regarding the early-stage performance of the proposed scheme are provided in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.555, + 0.727, + 0.57 + ], + "angle": 0, + "content": "7. Discussion & conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We proposed the novel idea of optimizing the choice of validation data in a learned-reweighting setting, and showed that it gives significant gains over ERM on a range of datasets and domain generalization benchmarks. In particular, in most experiments on clean data, we saw a clear ordering between choosing easy, random, and hard samples as validation data in an LRW setup, with the latter performing best and delivering consistent gains over ERM. This ordering provides broad support to our primary hypothesis: meta-optimization of the metalearning workflow in LRW is an important area of research with potential for substantial impact. Our specific heuristic of choosing low-margin points is a simple, straightforward instantiation of what we believe is a family of optimization algorithms that can be brought to bear on the general problem of optimizing metalelearned classifiers. Indeed, our heuristic is not competitive under very high label noise scenarios, suggesting the need for follow-on work that explores more formal, optimization-driven approaches towards this problem. We are also excited about elucidating the theoretical basis of observed gains in the MOLERE framework." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27607" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Kaggle. diabetic retinopathy detection challenge, 2015, 2015. 5, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.468, + 0.24 + ], + "angle": 0, + "content": "[2] Peter Bandi, Oscar Geessink, Quirine Manson, Marcory Van Dijk, Maschenka Balkenhol, Meyke Hermsen, Babak Ehteshami Bejnordi, Byungjae Lee, Kyunghyun Paeng, Aoxiao Zhong, et al. From detection of individual metastases to classification of lymph node status at the patient level: the camelyon17 challenge. 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Caml: Fast context adaptation via meta-learning. 2018. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27609" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_origin.pdf b/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..631228613332fb1d7e309a3b8849239341f37816 --- /dev/null +++ b/2024/Improving Generalization via Meta-Learning on Hard Samples/ceb0ccb0-32b0-4bdb-8488-9b62f8a01ad9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1e6a3cf792fbd35ce178367990236682d4dfdbbf96012fe91f59532fcd9cb7bc +size 884140 diff --git a/2024/Improving Generalization via Meta-Learning on Hard Samples/full.md b/2024/Improving Generalization via Meta-Learning on Hard Samples/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fa186a64aee0f88c3473568a8fed938a100bc6c6 --- /dev/null +++ b/2024/Improving Generalization via Meta-Learning on Hard Samples/full.md @@ -0,0 +1,316 @@ +# Improving Generalization via Meta-Learning on Hard Samples + +Nishant Jain Arun S. Suggala Pradeep Shenoy Google Research India + +{nishantjn,arunss,shenoypradeep}@google.com + +# Abstract + +Learned reweighting (LRW) approaches to supervised learning use an optimization criterion to assign weights for training instances, in order to maximize performance on a representative validation dataset. We pose and formalize the problem of optimized selection of the validation set used in LRW training, to improve classifier generalization. In particular, we show that using hard-to-classify instances in the validation set has both a theoretical connection to, and strong empirical evidence of generalization. We provide an efficient algorithm for training this meta-optimized model, as well as a simple train-twice heuristic for careful comparative study. We demonstrate that LRW with easy validation data performs consistently worse than LRW with hard validation data, establishing the validity of our meta-optimization problem. Our proposed algorithm outperforms a wide range of baselines on a range of datasets and domain shift challenges (Imagenet-1K, CIFAR-100, Clothing-1M, CAMELYON, WILDS, etc.), with $1\%$ gains using VIT-B on Imagenet. We also show that using naturally hard examples for validation (Imagenet-R / Imagenet-A) in LRW training for Imagenet improves performance on both clean and naturally hard test instances by $1 - 2\%$ . Secondary analyses show that using hard validation data in an LRW framework improves margins on test data, hinting at the mechanism underlying our empirical gains. We believe this work opens up new research directions for the meta-optimization of meta-learning in a supervised learning context. + +# 1. Introduction + +Overparameterized models, common in supervised learning [27], carry the risk of overfitting to training data. Typically, model generalization is measured on a validation dataset separate from the training data, for purposes of hyperparameter selection. Increasingly, this validation dataset is itself used as part of the learning objective in nested formulations, e.g., for hyperparameter tuning via gradient descent on the validation loss [11]. In particular, learned reweighting (LRW) approaches learn importance weights + +associated with training instances [14, 16, 17, 31, 32, 40] or groups of training instances [25, 41] by optimizing a weighted training loss alongside an unweighted metal-loss on the validation data. This bilevel optimization aligns training loss with the validation data distribution via reweighting, a useful property in addressing covariate shift [34], and for group DRO [9, 41]. Even for in-domain test data, Ren et al. [31] show that using "clean" validation data with bilevel optimization can overcome significant amounts of label noise in training data. + +Thus the choice of validation set in a LRW paradigm can greatly influence the quality and properties of the learned classifier. We therefore ask the question: can we optimize the choice of validation data in LRW so as to maximize generalization of the resulting classifier? We refer to this problem of validation set selection as meta-optimization, since it produces data that is the input of another optimization (the meta-learning approach underlying LRW). The closest related work to our proposal is [40] which constructs a validation dataset on the fly during training of an LRW classifier, with a criterion of choosing representative instances. + +Our primary hypothesis is that we can improve classifier generalization by using a validation set consisting of hard-to-classify instances from the training distribution. We therefore pose and formalize the problem of Meta-Optimized LEarned REweighting (MOLERE) where the partitioning of data into train and validation splits, and the LRW classifier corresponding to that split, are jointly optimized. We design an efficient algorithm to tackle this meta-optimization, and make the following contributions: + +- We formalize the problem statement of validation set optimization in learned reweighting (LRW) classifiers for improved generalization. We prove that asymptotically our optimization objective exactly achieves our stated goal of maximizing accuracy on the hardest samples. +- We simplify the nested optimization of our proposal into a tractable bi-level optimization with a min-max game between two auxiliary networks: a "splitter" that finds the hardest samples, and a "reweighter" that minimizes loss on those samples using LRW. We also provide a simple train-twice heuristic that can be used for careful analysis + +of the choice of validation data in LRW. + +- We show strict accuracy ordering of LRW models based on validation set: easy $<$ random $<$ hard, demonstrating the importance of optimizing LRW validation sets. We obtain reliable gains over ERM across datasets (e.g., $1\%$ on Imagenet/VIT-B backbone), and in domain-generalization (e.g., $1.36\%$ on iWildCam dataset [4, 18]) and noisy-label settings (e.g., $4.2\%$ on Clothing1M dataset [37]). We outperform a range of baselines including reweighting, meta-learning among others. Analyses show improved margins on test set in MOLERE classifiers, suggesting an explanation of our gains. +- We extend our results to natural hard samples as validation (Imagenet withImagenet-R /Imagenet-A), showing $1 - 3\%$ gains on both in-domain and out-of-domain test sets. This shows the value of our ideas even in scenarios where we pay no additional cost for meta-optimization. + +We hope that our work will be seen as an initial step in establishing the value of meta-optimization of meta-learning, with our findings providing a strong proof-of-concept for the general research direction. + +# 2. Related Work + +Importance weighting for robustness. There have been several works on learning robust representations via example re-weighting lately. Mostly, these work aim at avoiding noisy labels in the train set by analyzing the effect of decreasing loss on a given instance on a clean validation set. This line of work includes either learning a per-instance free parameter [31] or learning a simple MLP network [32] to predict importance of an instance based on its loss value. However, the requirement of a clean validation set limits their applicability to realistic scenarios. To deal with this, a meta-learning based re-weighting scheme (Fast Sample Reweighting [40]) was proposed based on generating some sort of pseudo-clean data as a proxy validation set. It also proposed certain approximations to make the training process more computation efficient. On a different note, a recent proposal called RHO-loss [24] proposed to select only worthy points for training which increased generalization property of the model, calculated as the difference of the training loss and a hold-out set loss. + +A recent line of work [16, 17] proposed weighting based on context/relevance of an instance compared with the overall data distribution. These papers target slow temporal drift in longitudinal datasets, and the development of better uncertainty measures for selective classification, respectively. In particular, Jain et al. [17], suggest that using target domain data in the validation set can improve domain shift performance of classifiers. + +Meta Learning. The sample re-weighting task using a validation set comes under the umbrella of meta-learning [15], which follows the learning-to-learn paradigm. It + +is conceptually similar to model agnostic meta learning (MAML) [10], which learns a single set of parameters that can easily be customized (few-shot) to multiple tasks. Learning these shared parameters involves a nested optimization similar to the one presented here, and significantly optimized for efficiency by recent work[28, 30, 42]. + +Probabilistic Margins. Recent work [22] showed that the probabilistic margin in multi-class problems can be used to improve how neural networks deal with adversarial examples. The margin is defined as the difference between the probability of the true label and the largest of the remaining label probabilities, indicating the difficulty of classifying that instance. Liu et al. [22] propose re-weighting training instances, in presence of an adversarial attack, inversely related to their probability margins. + +Just Train Twice. A recent work [21] proposed an effective strategy to improve sensitivity of ERM models towards certain groups by training the ERM model in 2 stages. The first stage is a standard training procedure, whereas the second stage involves giving more importance to the incorrectly classified examples in the first stage by up-weighting their loss in the aggregate loss term for updating the parameters. This can be interpreted as similar to giving more importance to low margin examples (here essentially a hard separation between positive and negative). + +# 3. Preliminaries: Learned ReWeighting + +We work with learned reweighting (LRW) classifiers where training data is reweighted in order to optimize some specified metric on validation data. The basic LRW formulation [31] works with two datasets $S_{tr} = \{(x_i, y_i)\}_{i=1}^N$ and $S_{val} = \{(x_i, y_i)\}_{i=1}^M$ (training & validation, respectively). Given a desired loss function $\ell(y, \hat{y})$ , LRW learns a classifier $f_\theta(\cdot)$ , (with parameters $\theta$ ) and an instance-wise weighting function $\phi(\cdot)$ that minimize following bi-level objective: + +$$ +\begin{array}{l} \theta^ {*} (\phi) = \arg \min _ {\theta} \sum_ {(x, y) \in S _ {t r}} \phi (x) \ell (y, f _ {\theta} (x)), \\ s. t. \quad \phi^ {*} = \arg \min _ {\phi} \sum_ {(x, y) \in S _ {v a l}} \ell (y, f _ {\theta^ {*} (\phi)} (x)) \tag {1} \\ \end{array} +$$ + +Notice that the validation loss is unweighted, while the training objective is a weighted loss. Essentially, the above bilevel objective computes an estimate of classifier performance on the validation set, and optimizes it indirectly via reweighting of training data to influence the learned classifier. The weighted-loss-minimizing classifier $f_{\theta^{*}}(\cdot)$ , and the weights $\phi^{*}(\cdot)$ , are learned jointly, typically using alternating stochastic updates over minibatches to make the learning tractable [31]; this is in line with other meta-learning approaches such as MAML [10]. Following more + +recent work [16], we use an instance-dependent neural network $\phi(x)$ for learning the training instance weights, instead of free parameters [31]. + +Intuition: LRW has been used for overcoming training label noise [31, 32] and for handling covariate shift [16, 41]. In these cases, the validation set is assumed to be representative of test samples (i.e., clean labels, or covariateshifted data, respectively). The intuition is that the learned reweighting of the training loss aligns it with the (possibly different) validation distribution in the process of indirectly minimizing the meta-loss (Eq. 1). In particular, Shu et al. [32] show analytically that "validation-like" instances are upweighted. Thus, the validation set in LRW can be thought of as a target for generalization, with the learned classifier being optimized for performance on that target set. + +# 4. MOLERE: Optimizing LRW models + +# 4.1. Hypothesis and formal objective + +Our primary hypothesis is that we can improve generalization capabilities of supervised learning by combining two ingredients: a) a learned-reweighting classifier, as described in the previous section, and b) an optimized validation set that strongly encourages desired properties in the reweighting classifier. We refer to this idea as Meta-Optimization of the Learned Reweighting framework. + +In particular, we propose learning an LRW classifier with hard samples as validation set, to improve accuracy and generalization of learned classifiers. Since LRW by definition maximizes classifier performance on a given validation set, we believe that this choice of validation set will maximize generalization. Thus, given a dataset for training a predictive model, we need to 1) select the "hard instances" from the dataset and separate it into a validation set, and 2) train a classifier on the remaining data using this validation set for LRW. Notice that hardness of instances is determined in terms of the learned model itself; thus, formalizing the above idea leads to a joint optimization problem of data partitioning (train, validation), and LRW training. We present the formal problem below. + +Objective: Let $S = \{(x,y)\}_{i=1}^{N+M}$ be the available data, and let $\Theta$ be the splitting function that splits $S$ into training and validation datasets; to be precise, we let $\Theta(S)$ be the validation set and $\Theta(S)^c$ be its complement. MOLERE aims to solve the following tri-level optimization problem + +$$ +\begin{array}{l} \Theta^ {*} = \arg \max _ {\Theta} \sum_ {(x, y) \in \Theta (S)} \ell (y, f _ {\theta^ {*} (\phi^ {*} (\Theta), \Theta)} (x)) \\ \text{where}\phi^{*}(\Theta) = \arg \min_{\phi}\sum_{(x,y)\in \Theta (S)}\ell (y,f_{\theta^{*}(\phi ,\Theta)}(x)) \\ s. t. \theta^ {*} (\phi , \Theta) = \arg \min _ {\theta} \sum_ {(x, y) \in \Theta (S) ^ {c}} \phi (x) \ell (y, f _ {\theta} (x)). \tag {2} \\ \end{array} +$$ + +In words: Find a data split, such that across all possible splits the LRW classifier learned on the split has maximal error on the chosen validation set. In practice, we impose an additional constraint on the validation set size: $|\Theta (S)| / (N + M)\leq \delta$ , where $\delta$ is some predefined fractional constant. + +# 4.2. MOLERE objective and generalization + +We now study the asymptotic properties of our proposed meta-optimization as $N + M \to \infty$ , as a means of gaining theoretical insights into its generalization capabilities in comparison to classical empirical risk minimization (ERM). This analysis assumes a weighting function $\phi(\cdot)$ dependent on both $x$ and $y$ . Interestingly, our experiments revealed similar performance between this formulation of $\phi$ and one relying solely on $x$ . The following proposition shows that asymptotically MOLERE solves a robust optimization objective. + +Theorem 1 (Asymptotics). Consider the tri-level optimization in Equation (2). Suppose the weighting function $\phi(\cdot)$ , and splitting function $\Theta(\cdot)$ are dependent on both $x$ and $y$ . Let's suppose $N + M \to \infty$ , and $\lim_{N, M \to \infty} \frac{M}{N + M} = \delta$ . Moreover, suppose the domains of $\phi, \theta, \Theta$ are very large and contain the set of all measurable functions. Then the objective of MOLERE is equivalent to + +$$ +\max _ {S: | S | = \delta (N + M)} \min _ {\theta} \sum_ {(x, y) \in S} \ell (y, f _ {\theta} (x)). \tag {3} +$$ + +Proof Sketch. The proof of the theorem relies on the observation that there exists a weighting function $\phi$ that can transform any probability distribution $P$ to any another distribution $Q$ (as long as the support of $Q$ is a subset of $P$ ). Using this observation, one can show that the second, third level optimization problems in Equation (2) is equivalent to following problem: $\min_{\theta} \sum_{(x,y) \in \Theta(S)^c} \ell(y, f_{\theta}(x))$ . + +A similar result holds when both $\Theta(\cdot), \phi(\cdot)$ rely solely on $x$ . Intuitively, the above theorem shows that in the limit of infinite samples, MOLERE identifies the hardest samples in the training data, and learns a classifier that minimizes the error on those samples. This is exactly the goal laid out in our hypothesis above. + +Connections to DRO. Interestingly, the objective in Equation (3) is the dual of the following Distributionally Robust Optimization (DRO) objective [5] + +$$ +\min _ {\theta} \max _ {S: | S | = \delta (N + M)} \sum_ {(x, y) \in S} \ell (y, f _ {\theta} (x)). \tag {4} +$$ + +DRO is a well studied framework for learning robust models [8, 26]. However, to the best of our knowledge, dual DRO is not studied in the literature; we will explore this connection more deeply in future work. + +# 4.3. Efficient algorithm for validation optimization + +Designing a tractable algorithm for meta-optimization runs into two technical challenges: a) How can we learn to assign instances to train and validation sets? and b) How do we efficiently solve the tri-level objective proposed in Sec. 4.1? We address these two challenges in this section. First, we use a second auxiliary network for soft-assigning instances to train and validation datasets. Second, we collapse the outer two loops of the trilevel objective into a minimax formulation, and thereby reduce it to a bi-level optimization problem. We describe each of these in order below. + +Soft data assignment: Inspired by a recent work [3], we use a partitioning network to predict probability for each instance to be included in the validation set. At any point in time, the "splitter" network outputs soft assignments $\mathbb{P}(z|x,y)$ with $z\in \{0,1\}$ indicating whether the example $(x,y)$ belongs to the pseudotest set $(z = 0)$ or the pseudotrain set. The pseudotrain set is used to train a classifier using standard cross-entropy. The splitter is then updated to identify easy instances for the classifier and assign them to the pseudotrain partition in the next round; this is achieved by minimizing the cross-entropy between its soft-assignment and classifier accuracy: + +$$ +\mathcal {L} _ {s p l i t} = C E \left(\mathbb {P} _ {s p l i t t e r} \left(z _ {i} \mid x _ {i}, y _ {i}\right), \mathbb {I} _ {y _ {i}} (\hat {y})\right) \tag {5} +$$ + +$$ +w h e r e \quad \hat {y} = \arg \max \mathbb {P} _ {\text {p r e d i c t o r}} (y | x _ {i}) +$$ + +In order to maintain the label distribution and train-to-test ratio, two regularizers [3] are added to penalize shift from the prior distribution, and to push label margins in the training split and testing split close to the original label margin (see supplementary for details). + +Meta-optimization with min-max objective: To simplify the tri-level optimization in Sec. 4.1, we propose a bi-level approximation where the outer loop combines the data splitting and instance reweighting objectives. Specifically, we propose a min-max game between the splitter (parametrized by $\Theta$ ) and the meta-network (parametrized by $\phi$ ), where the splitter has to maximize validation set error whereas instance weights are focused on minimizing it: + +$$ +\begin{array}{l} \Theta^ {*}, \phi^ {*} = \arg \max _ {\Theta} \min _ {\phi} \sum_ {(x, y) \in S _ {t} ^ {c}} \left(\ell (y, f _ {\theta^ {*} (\phi , \Theta)} (x)) - \mathcal {L} _ {s p l i t}\right) \\ w h e r e \quad \theta^ {*} (\phi , \Theta) = \arg \min _ {\theta} \sum_ {(x, y) \in S _ {t}} \phi (x) \ell (y, f _ {\theta} (x)) \tag {6} \\ \end{array} +$$ + +where the set $S_{t} = \{(x,y):(x,y)\in S,\mathbb{I}\{\Theta (x,y) > 0.5\} \}$ and $S_{t}^{c} = S\setminus S_{t}$ , $\mathbb{I}$ denotes the indicator function. The overall algorithm updates the splitter and instance weighting network once every $Q$ steps of classifier update, and also regularizes the splitter with $\Omega_{ratio} + \Omega_{ld}$ at set intervals (every R steps). The complete description of this method is provided in Algorithm 1 and analysis of the loss function + +at the outer level, derivation of update equations for all parameters $(\Theta, \phi, \theta)$ are provided in the supplementary. Both the instance weight network and Splitter are parameterized as neural networks. The meta-network for instance weights predict the weight for a training instance $(x_i, y_i)$ by using $(x_i)$ as input, $w_i = g_{\phi}(x_i)$ and the Splitter predicts a probability of $(x_i, y_i)$ being in the train set by taking both of them as inputs $z_i = g_{\Theta}(x_i, y_i)$ . In experiments, we refer to this end-to-end optimization method as LRWOpt. + +Algorithm 1 LRWOpt: The Overall One-Shot Algorithm. +Require: $\theta, \Theta, \phi$ , learning rates $(\beta_{1}, \beta_{2}, \beta_{3}), S, N, M$ . +Ensure: Robustly trained classifier parameters $\theta$ . +1: Randomly initialize $\theta, \Theta$ and $\phi$ ; +2: initialize ge = 0; ▷ Difference b/w train and val error +3: for e=1 to MaxEpochs do +4: $S_{tr}, S_{val} = \text{GenerateSplit}(\mathcal{D}, \Theta)$ +5: for $b = 1$ to M/m do ▷ m is the batch size +6: $\{(x_i^v, y_i^v)\}_{i=1}^m = \text{SampleMiniBatch}(\mathcal{S}_{val}, m)$ ; +7: $\Theta \gets \Theta - \beta_1 \nabla_\Theta \sum (\mathcal{L}_{split} - \ell(y_i^v, f_\theta(x_i^v)))$ +8: $\phi \gets \phi - \beta_2 \nabla_\phi \sum (\ell(y_i^v, f_\theta(x_i^v)) - \mathcal{L}_{split})$ +9: for $j = 1$ to Q do +10: $\{(x_i, y_i)\}_{i=1}^n$ SampleMiniBatch( $\mathcal{D}_t, n$ ); +11: $\theta \gets \theta - \beta_3 \nabla_\theta \sum g_\phi(x_i) \ell(f_\theta(x_i), y_i)$ ; +12: end for +13: end for +14: if $\sum \ell(y_i^v, f_\theta(x_i^v)) - \sum \ell(y_i, f_\theta(x_i)) < \text{ge then}$ +15: break; +16: end if +17: ge = $\sum \frac{1}{M} \ell(y_i^v, f_\theta(x_i^v)) - \frac{1}{N} \sum \ell(y_i, f_\theta(x_i))$ +18: end for + +# 4.4. A simple train-twice heuristic + +We now describe a simple train-twice heuristic that can be used to establish the importance of validation set optimization in LRW. We first train an ERM classifier on the available training data, and use the probabilistic margin (PM) as a proxy for instance hardness: + +$$ +P M (x, y, \theta) = \mathbf {p} _ {y} (x, \theta) - \max _ {j, j \neq y} \mathbf {p} _ {j} (x, \theta) \tag {7} +$$ + +Here $\theta$ denotes the ERM classifier's parameters. This criterion was used to manually reweight adversarial examples in recent work [22]. Although this proxy score is inexact1, it nevertheless allows us to design interesting heuristic LRW variants based on its rank-ordering of training instances: (1) LRW-Hard, where we use the lowest margin instances as validation data, and the rest of the instances as training data, (2) LRW-Easy, in which the highest margin instances are + +![](images/00e46469fcc757580c369fec1576da05407846059f9bc9b9610addd4f6e6a79e.jpg) +Figure 1. Robustness analysis on benchmark datasets. Left: Comparing different LRW variants, based on the choice of validation set (Easy, Random, Hard, corresponding to the rank-ordering of training data by probabilistic margin of an ERM classifier). $y$ -axis shows accuracy gains over ERM for each dataset ( $x$ -axis). We see consistent ordering of performance, with LRW-Easy $<$ LRW-Random $<$ LRW-Hard, showing the importance of validation set optimization. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. In-1K corresponds to ImageNet-1K. For absolute accuracy values refer supplementary. + +![](images/d263a7f4ede6b116fe1224db24bfc1d8df10dd9d7c79fc1c6718b76aabfb25a2.jpg) + +used as validation data, and (3) LRW-Random, a control which uses a randomly selected validation set that does not depend on the ERM margin. + +We can use these variants to quantify the impact of perturbing the validation set in LRW, and to provide an existence proof of validation optimization techniques that materially improve learned classifiers. In particular, we expect to see a clear ordering of classifier test accuracy - LRW-Easy $<$ LRW-Random $<$ LRW-Hard. + +# 5. Experiments + +We perform extensive experimentation on multiple classification tasks including distribution shift benchmarks. For all datasets, if a train-validation split is already available, we use the training data for the ERM classifier in the train twice heuristic before pooling, ranking, and repartitioning. For the end-to-end optimization, we start with pooled train-validation data and simultaneously learn the data splits and the corresponding LRWOpt model. + +# 5.1. Datasets + +We use popular classification benchmarks including CIFAR-100 [20], ImageNet-100 [35], ImageNet-1K [7], Aircraft [23], Stanford Cars [19], Oxford-IIIT Fine-grained classification (Cats v/s Dogs) [29] and Diabetic Retinopathy (DR) dataset. Furthermore, for OOD analysis we use the ImageNet-A [13], ImageNet-R [12] datasets for models trained on ImageNet-1K. We also use the Camelyon [2], iWildCam [4] dataset from the widely popular WILDS benchmark [18] and also the country shifted test set for the + +DR [1] dataset. We further analyze for robustness in presence of instance dependent noise on the noisy version of CIFAR-10 dataset (Inst.C-10) proposed by Xia et al. [36] and Clothing-1M [37] dataset. Please refer supplementary (supp.) for more details, setup for these datasets. + +# 5.2. Baselines + +Along with ERM, we also compare our method against various re-weighting based methods designed for improving robustness or handling noisy scenarios. These include learned re-weighting methods: MWN [32], FSR [40], L2R [31], MAPLE [41], BiLAW [14], GDW [6], StableNet [39] along with Margin Based Reweighting (MBR) [22] and Rho-Loss [24]. Please refer supp. for more details regarding them. + +# 6. Results + +# 6.1. In-Distribution Generalization + +# 6.1.1 MOLERE improves classification accuracy + +Figure 1 (left) shows the LRW advantage (gains over an ERM baseline) for a range of datasets. Shown are 4 alternatives—LRW-Easy, LRW-Random, and LRW-Hard, corresponding to easy, random, and hard validation sets per the train-twice heuristic (Sec. 4.4), and LRWOpt, which is the end-to-end optimization of LRW classifier and train-validation split (Sec. 4.3). Refer supplementary for absolute accuracy values. + +- Gains vs ERM are strictly ordered in nearly all datasets—LRW-Easy $<$ LRW-Random $<$ LRW-Hard—robustly confirming our hypothesis that validation sets in LRW classi + +![](images/f8c39ccef9276b658574f3f2cfd43328594f164b5b14b8362a228450e6f22942.jpg) +Figure 2. OOD generalization. Left: Comparison of LRW variants on domain shift benchmarks. The ordering between the validation selection methods is reconfirmed on domain shift benchmark datasets as well, suggesting that earlier gains are not via overfitting to training distribution. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. For absolute values refer supp. + +![](images/46aab2494a2382063fc962b892cb3dfef0227f7d5f113f6105640afbdc3c5172.jpg) + +fiers need to be optimized. The difference between LRW-Hard and LRW-Easy is over $2.5\%$ relative gain for ImageNet & CIFAR-100, and $1.6\%$ relative for Clothing-1M. + +- LRW-Random shows modest gains over ERM in most datasets². LRW-Hard shows significant gains, underscoring the benefit of combining LRW with validation set optimization - 0.8% relative gain on Imagenet, 1.3% on Clothing-1M, 2.15% relative on CIFAR-100. +- The end-to-end LRWOpt matches or exceeds LRW-Hard, showcasing its effectiveness without the need for training twice. On a minority of datasets, LRW-Hard is nominally better; we believe this is due to the small-sample nature of real-world datasets, and attendant estimation noise. + +Although the presented accuracy is on unseen test sets, a concern may be that LRW-Hard overfits to the training data distribution and results in brittle classifiers. To address this, we performed a number of experiments on datasets with matched out-of-domain test sets (Diabetic retinopathy [1, 33], Camelyon [2], WildCam [4]) in next subsection. + +# 6.1.2 MOLERE outperforms existing re-weighting baselines + +We now compare our LRWOpt method against other reweighting methods- FSR [40]), MBR [22], MAPLE [41], MWN [32], StableNet [39], BiLAW [14])-see Fig. 1 (right) for more details. While FSR, RHO-Loss, MBR, MAPLE, StableNet and BiLAW are proposals in the literature for learned reweighting of the training data (via meta-learning) + +in order to address various clean- and noisy-label scenarios, MBR is an extrapolation of a proposal for ad-hoc upweighting of adversarial examples alone [22], for increased robustness against those specific adversarial attacks. In similar spirit, the proposal "just train twice" [21] also suggests an ad-hoc upweighting of poor performing instances in a second round of training. RHO-loss [24], on the other hand, follows the harder version as against all these methods and selects only some points from a batch which minimize the holdout set loss for efficient training. + +On the datasets tested, we see that LRWOpt clearly outperforms all these baseline methods consistently across all the datasets. It is followed by MAPLE, StableNet which are designed keeping group/OOD robustness in mind. FSR and Rho-Loss perform similar to ERM only. Interestingly, MBR and MWN are among the worst performers, showing that it is insufficient to simply upweight instances based on a first-round estimate of margin and the commonly followed bilevel optimization procedure by using free-parameters/loss based re-weighting, even though capable of providing unbiasedness, is not sufficient and requires another level of optimization for finding the appropriate validation set. + +# 6.2. Out-Of-Distribution (OD) generalization + +We further evaluate the robustness of our learned representations on the standard out-of-distribution datasets from the Wilds benchmark namely the camelyon [2] and the iwildcam [4] datasets along with the Diabetic Retinopathy dataset with a country shifted test set (APTOS test dataset) [1]. For the first two, $10\%$ examples from the train set, sampled randomly, are used as val set. For the last one, a separate validation set, with same domain as the train set, is provided. Refer supplementary for more details regarding + +the dataset details and our evaluation setup. Furthermore, we also analyze the performance on the ImageNet-A dataset by using both training and validation data from ImageNet-1K. Our primary goal here is to check whether the gains we saw above are primarily driven by in-domain learning, or a broader improvement in generalization capacity over the existing learned reweighting methods –as a result, we restrict ourselves to comparison among ERM, the LRW variants along with LRWOpt and the re-weighting baselines, rather than the substantial literature on domain shift. Fig. 2 (left) confirms that our learned classifiers generalize better to domain shift data as compared to ERM classifiers; further, the ordering between the different validation datasets is largely preserved. Fig. 2 (right) provides evaluation of our methods and other re-weighting baselines. These include the standard bi-level optimization based ones like MWN, FSR along with ones designed for OOD generalization/robustness like MAPLE, StableNet, Rho-Loss and MBR. It can be observed that our method surpasses all of these baselines thereby showing the importance of validation set optimization problem for the bi-level optimization based re-weighting methods, introduced in the paper. StableNet comes out to be the closest competitor of our method which has been designed explicitly for OOD learning. Rest all the re-weighting methods perform similar to ERM with minor gains/losses. Absolute accuracy values for this analysis are provided in the supplementary. + +# 6.3. Practical Label Noise Settings + +We now study the noisy label setting with a focus on real-world label noise using datasets like Clothing1M [37], and noisy CIFAR-10 (Inst. C-10 [36]), which contain instance conditioned noise as against randomly flipping labels or adding uniform noise. This noise can be treated as a measure of instance hardness rather than labeling error (refer supplementary for more details). Table 3 compares LR-WOpt method against bi-level optimization approaches like MWN, FSR, L2R, GDW which although specifically designed for noisy labels have been primarily tested on label flipping, uniform noise data. We also compare against MAPLE, designed for general robustness. On Inst. C-10, our method clearly surpasses all baselines, with $1.53\%$ accuracy gain. On Clothing-1M, we show about $0.85\%$ gain over the best performing GDW baseline. For other noisy settings like random label flips, prior work on outlier robust DRO [38] has shown good results using loss clipping (e.g. exclude $\mathrm{k}\%$ of highest loss as label noise), which could be co-opted into our work. + +# 6.4. Skewed Labels + +We now study the skewed label setting, comparing against instance based reweighting schemes proposed with this set- + +
MethodEasyHardRandomLRWoptMWNERM
Acc.83.1785.0983.8784.9484.0284.11
+ +Table 1. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and 12s baselines. + +
class skew20050101
MWN [32]40.11 ± 0.948.67 ± 0.761.32 ± 0.674.23 ± 0.3
FSR [40]38.04 ± 0.845.12 ± 0.958.38 ± 0.674.68 ± 0.2
GDW [6]40.36 ± 1.048.89 ± 0.861.67 ± 0.574.41 ± 0.4
LRWOpt42.33 ± 0.850.77 ± 0.763.28 ± 0.875.12 ± 0.3
+ +Table 2. Comparison, on CIFAR-100 dataset, of our LRWOpt method with existing meta-learning based reweighting methods in a label skew setup for which these methods were defined. + +
MWNFSRL2RMAPLEGDWOurs
Inst. C-1065.8967.1270.2170.3469.1271.87
Clothing-1M72.7972.0772.2271.6773.1273.97
+ +Table 3. Instance-dependent noise. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and l2s baselines. + +ting in mind (Meta-Weight-Net, FSR and another recently proposed re-weighting method GDW [6]). Table 2 shows the results for this analysis on the CIFAR-100 datasets with various skew levels ranging from 1 to 200. It can be observed that our LRWOpt significantly outperform the existing loss based reweighting methods at all of the skew levels showing accuracy gains upto $2.22\%$ . + +# 6.5. MOLERE scales to large pretrained models + +We further analyze the LRW-Hard, Easy and Random methods along with the ERM baseline on ViT-B/16 pretrained backbone trained using these techniques and evaluated on the ImageNet-1K dataset. Table 1 shows the results from this experiments. Again LRW-Hard emerges the winner and improves significantly (around $1\%$ ) w.r.t. other methods and the baseline advocating robustness using hard examples. Furthermore, there is $1.92\%$ difference in accuracy between LRW-Easy and LRW-Hard, even though we warm-started all the techniques with a pretrained backbone, showing the sensitivity of techniques to choice of validation set. + +# 6.6. Leveraging OOD val set: A heuristic solution + +We now turn to the use of known hard instance, or OOD, datasets when available, in the MOLERE context. For the well-studied Imagenet-1K dataset, two datasets are frequently used to gauge generalization properties of learned classifiers – IN-A (“natural adversarial instances”, examples known to be misclassified by a trained Resnet-50 + +![](images/fa74da41d1295bb3729e621f718ef61eca0c145da396b8bd5bbe3d4ad2909491.jpg) +Figure 3. MOLERE improves margins of learned classifiers. (a,b): paired margin deltas between LRWOpt and ERM are moderately right-skewed with mean/median greater than zero. (c,d): As a function of ERM margin, clear separation seen between LRW-Hard (better) and LRW-Easy (worse) in terms of margin gain over ERM (errors bars are SEM). All results on unseen test data; Imagenet-100, CIFAR100 shown for brevity, with similar results for other datasets in appendix. + +![](images/9596f7b71389992551cef4f6d0678793848bf9930f664ee71dd055fff3a3c4a5.jpg) + +![](images/fdf16d2063be349c7fd0c085533e1e2225396c80bb2429992bf3263a5bdd69bd.jpg) + +![](images/a07077c1468e2f9c57063201516d24f45e8f92fa021b8ddd17429f4179b45a15.jpg) + +model), and IN-R (renditions of objects, such as drawings, paintings, sculptures, etc). For each of these, we used a portion of the dataset as LRW validation set, and retained another portion for testing. Table 4 shows the results of this study. We report the following two surprising results: (1) our approach outperforms the baseline ERM classifier on not just the OOD test set, but also on the in-domain test set (1.7-3% and 0.5-0.7% gains respectively), and (2) simply adding the OOD data to the train set only moderately improves OOD test set performance while degrading ID accuracy. These findings were replicated for both IN-A and IN-R as LRW validation sets, underscoring the real-world applicability of our findings, on large-scale datasets. + +
IN-R val (ResNet50)IN-A val (ResNet152)
IN1K TestINR TestIN1k TestINA Test
LRWOpt + INR val76.1449.178.127.9
ERM (IN1K)75.6546.177.316.2
ERM (IN1K+INR)74.8947.477.086.6
+ +Table 4. Natural hard examples as validation. LRW classifiers on Imagenet (IN1k) data and OOD validation sets (IN-A & IN-R respectively) outperform ERM on both in-domain and OOD test sets. Simply augmenting training data of ERM baseline does not match this (see text for details). + +# 6.7. Margin maximization via meta-learning + +We present empirical evidence showing that MOLERE has a margin maximization effect, i.e., the learned classifiers have wider margins than ERM classifiers. Since our validation data is selected to be low-margin instances, our LRW classifier upweights, and improves performance on, training instances most similar to the low-margin validation set. 3 shows two views of margin differences between MOLERE and ERM on the test set, to confirm this expectation3. Pan- + +els (a,b) shows a histogram of paired margin differences between ERM and LRWOpt, indicating a modest right-skew with mean & median to the right of 0. Panels (c,d) shows LRW-Hard and LRW-Easy deltas w.r.t. ERM, averaged over ERM margin buckets (mean and S.E.M. errorbars)—across the board (i.e., for most values of ERM margin), LRW-Hard contrasts with ERM better than LRW-Easy. + +Further details on Algorithm 1, proof of Theorem 1, the time complexity of the proposed scheme compared to ERM, the training setup, ablation study over the validation set selection/loss, and discussion regarding the early-stage performance of the proposed scheme are provided in the supplementary. + +# 7. Discussion & conclusion + +We proposed the novel idea of optimizing the choice of validation data in a learned-reweighting setting, and showed that it gives significant gains over ERM on a range of datasets and domain generalization benchmarks. In particular, in most experiments on clean data, we saw a clear ordering between choosing easy, random, and hard samples as validation data in an LRW setup, with the latter performing best and delivering consistent gains over ERM. This ordering provides broad support to our primary hypothesis: meta-optimization of the metalearning workflow in LRW is an important area of research with potential for substantial impact. Our specific heuristic of choosing low-margin points is a simple, straightforward instantiation of what we believe is a family of optimization algorithms that can be brought to bear on the general problem of optimizing metalelearned classifiers. Indeed, our heuristic is not competitive under very high label noise scenarios, suggesting the need for follow-on work that explores more formal, optimization-driven approaches towards this problem. We are also excited about elucidating the theoretical basis of observed gains in the MOLERE framework. + +# References + +[1] Kaggle. diabetic retinopathy detection challenge, 2015, 2015. 5, 6 +[2] Peter Bandi, Oscar Geessink, Quirine Manson, Marcory Van Dijk, Maschenka Balkenhol, Meyke Hermsen, Babak Ehteshami Bejnordi, Byungjae Lee, Kyunghyun Paeng, Aoxiao Zhong, et al. From detection of individual metastases to classification of lymph node status at the patient level: the camelyon17 challenge. IEEE transactions on medical imaging, 38(2):550-560, 2018. 5, 6 +[3] Yujia Bao and Regina Barzilay. Learning to split for automatic bias detection. arXiv preprint arXiv:2204.13749, 2022. 4 +[4] Sara Beery, Elijah Cole, and Arvi Gjoka. The iwildcam 2020 competition dataset. arXiv preprint arXiv:2004.10340, 2020. 2, 5, 6 +[5] Aharon Ben-Tal, Dick Den Hertog, Anja De Waegenaere, Bertrand Mellenberg, and Gijs Rennen. Robust solutions of optimization problems affected by uncertain probabilities. 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In International Conference on Machine Learning, pages 27203-27221. PMLR, 2022. 1, 3, 5, 6 +[42] Luisa M Zintgraf, Kyriacos Shiarlis, Vitaly Kurin, Katja Hofmann, and Shimon Whiteson. Caml: Fast context adaptation via meta-learning. 2018. 2 \ No newline at end of file diff --git a/2024/Improving Generalization via Meta-Learning on Hard Samples/images.zip b/2024/Improving Generalization via Meta-Learning on Hard Samples/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f891fa876e069e4f54a4b46c623d5a1c323139fd --- /dev/null +++ b/2024/Improving Generalization via Meta-Learning on Hard Samples/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a331e0645c812c2b4489b1b72e20dca51bcb38e8885f813f72553bb3fee0f4c0 +size 317747 diff --git a/2024/Improving Generalization via Meta-Learning on Hard Samples/layout.json b/2024/Improving Generalization via Meta-Learning on Hard Samples/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6e090cd0d92a001a97c302620ba00d75c8d9fa96 --- /dev/null +++ b/2024/Improving Generalization via Meta-Learning on Hard Samples/layout.json @@ -0,0 +1,8196 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 102, + 103, + 492, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 103, + 492, + 121 + ], + "spans": [ + { + "bbox": [ + 102, + 103, + 492, + 121 + ], + "type": "text", + "content": "Improving Generalization via Meta-Learning on Hard Samples" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 166, + 144, + 426, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 166, + 144, + 426, + 171 + ], + "spans": [ + { + "bbox": [ + 166, + 144, + 426, + 171 + ], + "type": "text", + "content": "Nishant Jain Arun S. Suggala Pradeep Shenoy Google Research India" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 181, + 174, + 413, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 174, + 413, + 185 + ], + "spans": [ + { + "bbox": [ + 181, + 174, + 413, + 185 + ], + "type": "text", + "content": "{nishantjn,arunss,shenoypradeep}@google.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "type": "text", + "content": "Learned reweighting (LRW) approaches to supervised learning use an optimization criterion to assign weights for training instances, in order to maximize performance on a representative validation dataset. We pose and formalize the problem of optimized selection of the validation set used in LRW training, to improve classifier generalization. In particular, we show that using hard-to-classify instances in the validation set has both a theoretical connection to, and strong empirical evidence of generalization. We provide an efficient algorithm for training this meta-optimized model, as well as a simple train-twice heuristic for careful comparative study. We demonstrate that LRW with easy validation data performs consistently worse than LRW with hard validation data, establishing the validity of our meta-optimization problem. Our proposed algorithm outperforms a wide range of baselines on a range of datasets and domain shift challenges (Imagenet-1K, CIFAR-100, Clothing-1M, CAMELYON, WILDS, etc.), with " + }, + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "type": "text", + "content": " gains using VIT-B on Imagenet. We also show that using naturally hard examples for validation (Imagenet-R / Imagenet-A) in LRW training for Imagenet improves performance on both clean and naturally hard test instances by " + }, + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "type": "inline_equation", + "content": "1 - 2\\%" + }, + { + "bbox": [ + 46, + 238, + 289, + 562 + ], + "type": "text", + "content": ". Secondary analyses show that using hard validation data in an LRW framework improves margins on test data, hinting at the mechanism underlying our empirical gains. We believe this work opens up new research directions for the meta-optimization of meta-learning in a supervised learning context." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Overparameterized models, common in supervised learning [27], carry the risk of overfitting to training data. Typically, model generalization is measured on a validation dataset separate from the training data, for purposes of hyperparameter selection. Increasingly, this validation dataset is itself used as part of the learning objective in nested formulations, e.g., for hyperparameter tuning via gradient descent on the validation loss [11]. In particular, learned reweighting (LRW) approaches learn importance weights" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 213, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 334 + ], + "type": "text", + "content": "associated with training instances [14, 16, 17, 31, 32, 40] or groups of training instances [25, 41] by optimizing a weighted training loss alongside an unweighted metal-loss on the validation data. This bilevel optimization aligns training loss with the validation data distribution via reweighting, a useful property in addressing covariate shift [34], and for group DRO [9, 41]. Even for in-domain test data, Ren et al. [31] show that using \"clean\" validation data with bilevel optimization can overcome significant amounts of label noise in training data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 335, + 547, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 467 + ], + "type": "text", + "content": "Thus the choice of validation set in a LRW paradigm can greatly influence the quality and properties of the learned classifier. We therefore ask the question: can we optimize the choice of validation data in LRW so as to maximize generalization of the resulting classifier? We refer to this problem of validation set selection as meta-optimization, since it produces data that is the input of another optimization (the meta-learning approach underlying LRW). The closest related work to our proposal is [40] which constructs a validation dataset on the fly during training of an LRW classifier, with a criterion of choosing representative instances." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 469, + 547, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 547, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 547, + 577 + ], + "type": "text", + "content": "Our primary hypothesis is that we can improve classifier generalization by using a validation set consisting of hard-to-classify instances from the training distribution. We therefore pose and formalize the problem of Meta-Optimized LEarned REweighting (MOLERE) where the partitioning of data into train and validation splits, and the LRW classifier corresponding to that split, are jointly optimized. We design an efficient algorithm to tackle this meta-optimization, and make the following contributions:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 582, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 306, + 582, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 545, + 641 + ], + "type": "text", + "content": "- We formalize the problem statement of validation set optimization in learned reweighting (LRW) classifiers for improved generalization. We prove that asymptotically our optimization objective exactly achieves our stated goal of maximizing accuracy on the hardest samples." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "text", + "content": "- We simplify the nested optimization of our proposal into a tractable bi-level optimization with a min-max game between two auxiliary networks: a \"splitter\" that finds the hardest samples, and a \"reweighter\" that minimizes loss on those samples using LRW. We also provide a simple train-twice heuristic that can be used for careful analysis" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27600" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 218, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 218, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 218, + 83 + ], + "type": "text", + "content": "of the choice of validation data in LRW." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 84, + 286, + 275 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "content": "- We show strict accuracy ordering of LRW models based on validation set: easy " + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "content": " random " + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "content": " hard, demonstrating the importance of optimizing LRW validation sets. We obtain reliable gains over ERM across datasets (e.g., " + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "content": " on Imagenet/VIT-B backbone), and in domain-generalization (e.g., " + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "inline_equation", + "content": "1.36\\%" + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "content": " on iWildCam dataset [4, 18]) and noisy-label settings (e.g., " + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 47, + 84, + 286, + 215 + ], + "type": "text", + "content": " on Clothing1M dataset [37]). We outperform a range of baselines including reweighting, meta-learning among others. Analyses show improved margins on test set in MOLERE classifiers, suggesting an explanation of our gains." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 216, + 286, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 286, + 275 + ], + "type": "text", + "content": "- We extend our results to natural hard samples as validation (Imagenet withImagenet-R /Imagenet-A), showing " + }, + { + "bbox": [ + 47, + 216, + 286, + 275 + ], + "type": "inline_equation", + "content": "1 - 3\\%" + }, + { + "bbox": [ + 47, + 216, + 286, + 275 + ], + "type": "text", + "content": " gains on both in-domain and out-of-domain test sets. This shows the value of our ideas even in scenarios where we pay no additional cost for meta-optimization." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 277, + 286, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 286, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 286, + 324 + ], + "type": "text", + "content": "We hope that our work will be seen as an initial step in establishing the value of meta-optimization of meta-learning, with our findings providing a strong proof-of-concept for the general research direction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 335, + 133, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 133, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 133, + 346 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 354, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 286, + 581 + ], + "type": "text", + "content": "Importance weighting for robustness. There have been several works on learning robust representations via example re-weighting lately. Mostly, these work aim at avoiding noisy labels in the train set by analyzing the effect of decreasing loss on a given instance on a clean validation set. This line of work includes either learning a per-instance free parameter [31] or learning a simple MLP network [32] to predict importance of an instance based on its loss value. However, the requirement of a clean validation set limits their applicability to realistic scenarios. To deal with this, a meta-learning based re-weighting scheme (Fast Sample Reweighting [40]) was proposed based on generating some sort of pseudo-clean data as a proxy validation set. It also proposed certain approximations to make the training process more computation efficient. On a different note, a recent proposal called RHO-loss [24] proposed to select only worthy points for training which increased generalization property of the model, calculated as the difference of the training loss and a hold-out set loss." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 582, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 286, + 676 + ], + "type": "text", + "content": "A recent line of work [16, 17] proposed weighting based on context/relevance of an instance compared with the overall data distribution. These papers target slow temporal drift in longitudinal datasets, and the development of better uncertainty measures for selective classification, respectively. In particular, Jain et al. [17], suggest that using target domain data in the validation set can improve domain shift performance of classifiers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Meta Learning. The sample re-weighting task using a validation set comes under the umbrella of meta-learning [15], which follows the learning-to-learn paradigm. It" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "is conceptually similar to model agnostic meta learning (MAML) [10], which learns a single set of parameters that can easily be customized (few-shot) to multiple tasks. Learning these shared parameters involves a nested optimization similar to the one presented here, and significantly optimized for efficiency by recent work[28, 30, 42]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 144, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 252 + ], + "type": "text", + "content": "Probabilistic Margins. Recent work [22] showed that the probabilistic margin in multi-class problems can be used to improve how neural networks deal with adversarial examples. The margin is defined as the difference between the probability of the true label and the largest of the remaining label probabilities, indicating the difficulty of classifying that instance. Liu et al. [22] propose re-weighting training instances, in presence of an adversarial attack, inversely related to their probability margins." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 254, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 373 + ], + "type": "text", + "content": "Just Train Twice. A recent work [21] proposed an effective strategy to improve sensitivity of ERM models towards certain groups by training the ERM model in 2 stages. The first stage is a standard training procedure, whereas the second stage involves giving more importance to the incorrectly classified examples in the first stage by up-weighting their loss in the aggregate loss term for updating the parameters. This can be interpreted as similar to giving more importance to low margin examples (here essentially a hard separation between positive and negative)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 398, + 510, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 398, + 510, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 398, + 510, + 412 + ], + "type": "text", + "content": "3. Preliminaries: Learned ReWeighting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": "We work with learned reweighting (LRW) classifiers where training data is reweighted in order to optimize some specified metric on validation data. The basic LRW formulation [31] works with two datasets " + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "inline_equation", + "content": "S_{tr} = \\{(x_i, y_i)\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "inline_equation", + "content": "S_{val} = \\{(x_i, y_i)\\}_{i=1}^M" + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": " (training & validation, respectively). Given a desired loss function " + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\ell(y, \\hat{y})" + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": ", LRW learns a classifier " + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "inline_equation", + "content": "f_\\theta(\\cdot)" + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": ", (with parameters " + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": ") and an instance-wise weighting function " + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": " that minimize following bi-level objective:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 526, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 526, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 326, + 526, + 545, + 582 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\theta^ {*} (\\phi) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in S _ {t r}} \\phi (x) \\ell (y, f _ {\\theta} (x)), \\\\ s. t. \\quad \\phi^ {*} = \\arg \\min _ {\\phi} \\sum_ {(x, y) \\in S _ {v a l}} \\ell (y, f _ {\\theta^ {*} (\\phi)} (x)) \\tag {1} \\\\ \\end{array}", + "image_path": "f5cc354b69edb351f5bea53e2c445ff7e9ab628fa6f98449be2f9e3a37a36bb3.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Notice that the validation loss is unweighted, while the training objective is a weighted loss. Essentially, the above bilevel objective computes an estimate of classifier performance on the validation set, and optimizes it indirectly via reweighting of training data to influence the learned classifier. The weighted-loss-minimizing classifier " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta^{*}}(\\cdot)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", and the weights " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\phi^{*}(\\cdot)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", are learned jointly, typically using alternating stochastic updates over minibatches to make the learning tractable [31]; this is in line with other meta-learning approaches such as MAML [10]. Following more" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27601" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "recent work [16], we use an instance-dependent neural network " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\phi(x)" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " for learning the training instance weights, instead of free parameters [31]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 252 + ], + "type": "text", + "content": "Intuition: LRW has been used for overcoming training label noise [31, 32] and for handling covariate shift [16, 41]. In these cases, the validation set is assumed to be representative of test samples (i.e., clean labels, or covariateshifted data, respectively). The intuition is that the learned reweighting of the training loss aligns it with the (possibly different) validation distribution in the process of indirectly minimizing the meta-loss (Eq. 1). In particular, Shu et al. [32] show analytically that \"validation-like\" instances are upweighted. Thus, the validation set in LRW can be thought of as a target for generalization, with the learned classifier being optimized for performance on that target set." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 261, + 250, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 250, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 250, + 275 + ], + "type": "text", + "content": "4. MOLERE: Optimizing LRW models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 281, + 222, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 222, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 222, + 294 + ], + "type": "text", + "content": "4.1. Hypothesis and formal objective" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 300, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 383 + ], + "type": "text", + "content": "Our primary hypothesis is that we can improve generalization capabilities of supervised learning by combining two ingredients: a) a learned-reweighting classifier, as described in the previous section, and b) an optimized validation set that strongly encourages desired properties in the reweighting classifier. We refer to this idea as Meta-Optimization of the Learned Reweighting framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 384, + 288, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 550 + ], + "type": "text", + "content": "In particular, we propose learning an LRW classifier with hard samples as validation set, to improve accuracy and generalization of learned classifiers. Since LRW by definition maximizes classifier performance on a given validation set, we believe that this choice of validation set will maximize generalization. Thus, given a dataset for training a predictive model, we need to 1) select the \"hard instances\" from the dataset and separate it into a validation set, and 2) train a classifier on the remaining data using this validation set for LRW. Notice that hardness of instances is determined in terms of the learned model itself; thus, formalizing the above idea leads to a joint optimization problem of data partitioning (train, validation), and LRW training. We present the formal problem below." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "content": "Objective: Let " + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "S = \\{(x,y)\\}_{i=1}^{N+M}" + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "content": " be the available data, and let " + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "content": " be the splitting function that splits " + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "content": " into training and validation datasets; to be precise, we let " + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\Theta(S)" + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "content": " be the validation set and " + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\Theta(S)^c" + }, + { + "bbox": [ + 46, + 550, + 287, + 612 + ], + "type": "text", + "content": " be its complement. MOLERE aims to solve the following tri-level optimization problem" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 617, + 287, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 617, + 287, + 713 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Theta^ {*} = \\arg \\max _ {\\Theta} \\sum_ {(x, y) \\in \\Theta (S)} \\ell (y, f _ {\\theta^ {*} (\\phi^ {*} (\\Theta), \\Theta)} (x)) \\\\ \\text{where}\\phi^{*}(\\Theta) = \\arg \\min_{\\phi}\\sum_{(x,y)\\in \\Theta (S)}\\ell (y,f_{\\theta^{*}(\\phi ,\\Theta)}(x)) \\\\ s. t. \\theta^ {*} (\\phi , \\Theta) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in \\Theta (S) ^ {c}} \\phi (x) \\ell (y, f _ {\\theta} (x)). \\tag {2} \\\\ \\end{array}", + "image_path": "6e80434d3488dbbfd137de283950df291f40473eaf88b09be789c2f668fdb4da.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "In words: Find a data split, such that across all possible splits the LRW classifier learned on the split has maximal error on the chosen validation set. In practice, we impose an additional constraint on the validation set size: " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "|\\Theta (S)| / (N + M)\\leq \\delta" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " is some predefined fractional constant." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 151, + 507, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 151, + 507, + 164 + ], + "spans": [ + { + "bbox": [ + 305, + 151, + 507, + 164 + ], + "type": "text", + "content": "4.2. MOLERE objective and generalization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": "We now study the asymptotic properties of our proposed meta-optimization as " + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "inline_equation", + "content": "N + M \\to \\infty" + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": ", as a means of gaining theoretical insights into its generalization capabilities in comparison to classical empirical risk minimization (ERM). This analysis assumes a weighting function " + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": " dependent on both " + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": ". Interestingly, our experiments revealed similar performance between this formulation of " + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": " and one relying solely on " + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 170, + 545, + 289 + ], + "type": "text", + "content": ". The following proposition shows that asymptotically MOLERE solves a robust optimization objective." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": "Theorem 1 (Asymptotics). Consider the tri-level optimization in Equation (2). Suppose the weighting function " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": ", and splitting function " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\Theta(\\cdot)" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": " are dependent on both " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": ". Let's suppose " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "N + M \\to \\infty" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\lim_{N, M \\to \\infty} \\frac{M}{N + M} = \\delta" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": ". Moreover, suppose the domains of " + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\phi, \\theta, \\Theta" + }, + { + "bbox": [ + 304, + 296, + 545, + 380 + ], + "type": "text", + "content": " are very large and contain the set of all measurable functions. Then the objective of MOLERE is equivalent to" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 348, + 387, + 545, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 387, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 348, + 387, + 545, + 415 + ], + "type": "interline_equation", + "content": "\\max _ {S: | S | = \\delta (N + M)} \\min _ {\\theta} \\sum_ {(x, y) \\in S} \\ell (y, f _ {\\theta} (x)). \\tag {3}", + "image_path": "75bd0be144d77f9d866b54d03773ec9af87d90b8e760c84db23f3061f67f4b38.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": "Proof Sketch. The proof of the theorem relies on the observation that there exists a weighting function " + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": " that can transform any probability distribution " + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": " to any another distribution " + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": " (as long as the support of " + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": " is a subset of " + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": "). Using this observation, one can show that the second, third level optimization problems in Equation (2) is equivalent to following problem: " + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\min_{\\theta} \\sum_{(x,y) \\in \\Theta(S)^c} \\ell(y, f_{\\theta}(x))" + }, + { + "bbox": [ + 304, + 422, + 545, + 509 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "type": "text", + "content": "A similar result holds when both " + }, + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\Theta(\\cdot), \\phi(\\cdot)" + }, + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "type": "text", + "content": " rely solely on " + }, + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 514, + 545, + 586 + ], + "type": "text", + "content": ". Intuitively, the above theorem shows that in the limit of infinite samples, MOLERE identifies the hardest samples in the training data, and learns a classifier that minimizes the error on those samples. This is exactly the goal laid out in our hypothesis above." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 587, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 545, + 624 + ], + "type": "text", + "content": "Connections to DRO. Interestingly, the objective in Equation (3) is the dual of the following Distributionally Robust Optimization (DRO) objective [5]" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 347, + 631, + 545, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 631, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 347, + 631, + 545, + 658 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\max _ {S: | S | = \\delta (N + M)} \\sum_ {(x, y) \\in S} \\ell (y, f _ {\\theta} (x)). \\tag {4}", + "image_path": "bb60fe75ded363b22db320063b291ac541dd49335e593e0ddb74cdb8b5239726.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "DRO is a well studied framework for learning robust models [8, 26]. However, to the best of our knowledge, dual DRO is not studied in the literature; we will explore this connection more deeply in future work." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27602" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 85 + ], + "type": "text", + "content": "4.3. Efficient algorithm for validation optimization" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 209 + ], + "type": "text", + "content": "Designing a tractable algorithm for meta-optimization runs into two technical challenges: a) How can we learn to assign instances to train and validation sets? and b) How do we efficiently solve the tri-level objective proposed in Sec. 4.1? We address these two challenges in this section. First, we use a second auxiliary network for soft-assigning instances to train and validation datasets. Second, we collapse the outer two loops of the trilevel objective into a minimax formulation, and thereby reduce it to a bi-level optimization problem. We describe each of these in order below." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "text", + "content": "Soft data assignment: Inspired by a recent work [3], we use a partitioning network to predict probability for each instance to be included in the validation set. At any point in time, the \"splitter\" network outputs soft assignments " + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(z|x,y)" + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "inline_equation", + "content": "z\\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "text", + "content": " indicating whether the example " + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "text", + "content": " belongs to the pseudotest set " + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "inline_equation", + "content": "(z = 0)" + }, + { + "bbox": [ + 46, + 210, + 288, + 354 + ], + "type": "text", + "content": " or the pseudotrain set. The pseudotrain set is used to train a classifier using standard cross-entropy. The splitter is then updated to identify easy instances for the classifier and assign them to the pseudotrain partition in the next round; this is achieved by minimizing the cross-entropy between its soft-assignment and classifier accuracy:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 361, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 361, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 83, + 361, + 287, + 380 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s p l i t} = C E \\left(\\mathbb {P} _ {s p l i t t e r} \\left(z _ {i} \\mid x _ {i}, y _ {i}\\right), \\mathbb {I} _ {y _ {i}} (\\hat {y})\\right) \\tag {5}", + "image_path": "1df382d96b045ab5773435a5c09e559de5e36c91e1a8f8c2f2b0485bd6c158ce.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 378, + 246, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 378, + 246, + 390 + ], + "spans": [ + { + "bbox": [ + 85, + 378, + 246, + 390 + ], + "type": "interline_equation", + "content": "w h e r e \\quad \\hat {y} = \\arg \\max \\mathbb {P} _ {\\text {p r e d i c t o r}} (y | x _ {i})", + "image_path": "102abe09a64c7a7dbe79ec97e636cdf80943f0ce2ea66ea9bc6be2007b329f0e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 398, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 287, + 458 + ], + "type": "text", + "content": "In order to maintain the label distribution and train-to-test ratio, two regularizers [3] are added to penalize shift from the prior distribution, and to push label margins in the training split and testing split close to the original label margin (see supplementary for details)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "type": "text", + "content": "Meta-optimization with min-max objective: To simplify the tri-level optimization in Sec. 4.1, we propose a bi-level approximation where the outer loop combines the data splitting and instance reweighting objectives. Specifically, we propose a min-max game between the splitter (parametrized by " + }, + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "type": "text", + "content": ") and the meta-network (parametrized by " + }, + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 458, + 287, + 555 + ], + "type": "text", + "content": "), where the splitter has to maximize validation set error whereas instance weights are focused on minimizing it:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 562, + 289, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 289, + 628 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Theta^ {*}, \\phi^ {*} = \\arg \\max _ {\\Theta} \\min _ {\\phi} \\sum_ {(x, y) \\in S _ {t} ^ {c}} \\left(\\ell (y, f _ {\\theta^ {*} (\\phi , \\Theta)} (x)) - \\mathcal {L} _ {s p l i t}\\right) \\\\ w h e r e \\quad \\theta^ {*} (\\phi , \\Theta) = \\arg \\min _ {\\theta} \\sum_ {(x, y) \\in S _ {t}} \\phi (x) \\ell (y, f _ {\\theta} (x)) \\tag {6} \\\\ \\end{array}", + "image_path": "93e9579847f93cb5aed588e371f063349e50f8aaedf8ab5af98ffd81142d7097.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": "where the set " + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "inline_equation", + "content": "S_{t} = \\{(x,y):(x,y)\\in S,\\mathbb{I}\\{\\Theta (x,y) > 0.5\\} \\}" + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "inline_equation", + "content": "S_{t}^{c} = S\\setminus S_{t}" + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": " denotes the indicator function. The overall algorithm updates the splitter and instance weighting network once every " + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": " steps of classifier update, and also regularizes the splitter with " + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\Omega_{ratio} + \\Omega_{ld}" + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": " at set intervals (every R steps). The complete description of this method is provided in Algorithm 1 and analysis of the loss function" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "at the outer level, derivation of update equations for all parameters " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "(\\Theta, \\phi, \\theta)" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " are provided in the supplementary. Both the instance weight network and Splitter are parameterized as neural networks. The meta-network for instance weights predict the weight for a training instance " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "(x_i, y_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " by using " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "(x_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " as input, " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "w_i = g_{\\phi}(x_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " and the Splitter predicts a probability of " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "(x_i, y_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " being in the train set by taking both of them as inputs " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "z_i = g_{\\Theta}(x_i, y_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": ". In experiments, we refer to this end-to-end optimization method as LRWOpt." + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 306, + 206, + 545, + 448 + ], + "blocks": [ + { + "bbox": [ + 306, + 191, + 541, + 205 + ], + "lines": [ + { + "bbox": [ + 306, + 191, + 541, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 191, + 541, + 205 + ], + "type": "text", + "content": "Algorithm 1 LRWOpt: The Overall One-Shot Algorithm." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "lines": [ + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\theta, \\Theta, \\phi" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": ", learning rates " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "(\\beta_{1}, \\beta_{2}, \\beta_{3}), S, N, M" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": ". \nEnsure: Robustly trained classifier parameters " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": ". \n1: Randomly initialize " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\theta, \\Theta" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": "; \n2: initialize ge = 0; ▷ Difference b/w train and val error \n3: for e=1 to MaxEpochs do \n4: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "S_{tr}, S_{val} = \\text{GenerateSplit}(\\mathcal{D}, \\Theta)" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " \n5: for " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "b = 1" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " to M/m do ▷ m is the batch size \n6: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\{(x_i^v, y_i^v)\\}_{i=1}^m = \\text{SampleMiniBatch}(\\mathcal{S}_{val}, m)" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": "; \n7: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\Theta \\gets \\Theta - \\beta_1 \\nabla_\\Theta \\sum (\\mathcal{L}_{split} - \\ell(y_i^v, f_\\theta(x_i^v)))" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " \n8: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\phi \\gets \\phi - \\beta_2 \\nabla_\\phi \\sum (\\ell(y_i^v, f_\\theta(x_i^v)) - \\mathcal{L}_{split})" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " \n9: for " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "j = 1" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " to Q do \n10: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\{(x_i, y_i)\\}_{i=1}^n" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " SampleMiniBatch(" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t, n" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": "); \n11: " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\theta \\gets \\theta - \\beta_3 \\nabla_\\theta \\sum g_\\phi(x_i) \\ell(f_\\theta(x_i), y_i)" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": "; \n12: end for \n13: end for \n14: if " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\sum \\ell(y_i^v, f_\\theta(x_i^v)) - \\sum \\ell(y_i, f_\\theta(x_i)) < \\text{ge then}" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " \n15: break; \n16: end if \n17: ge = " + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\sum \\frac{1}{M} \\ell(y_i^v, f_\\theta(x_i^v)) - \\frac{1}{N} \\sum \\ell(y_i, f_\\theta(x_i))" + }, + { + "bbox": [ + 306, + 206, + 545, + 448 + ], + "type": "text", + "content": " \n18: end for" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 469, + 467, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 469, + 467, + 482 + ], + "spans": [ + { + "bbox": [ + 306, + 469, + 467, + 482 + ], + "type": "text", + "content": "4.4. A simple train-twice heuristic" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "content": "We now describe a simple train-twice heuristic that can be used to establish the importance of validation set optimization in LRW. We first train an ERM classifier on the available training data, and use the probabilistic margin (PM) as a proxy for instance hardness:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 342, + 555, + 545, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 555, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 342, + 555, + 545, + 575 + ], + "type": "interline_equation", + "content": "P M (x, y, \\theta) = \\mathbf {p} _ {y} (x, \\theta) - \\max _ {j, j \\neq y} \\mathbf {p} _ {j} (x, \\theta) \\tag {7}", + "image_path": "1b71a53c232b11a7c7d098c9b0d77d0e99b5e998d2f11b7c2d4e73b7c028013c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "type": "text", + "content": " denotes the ERM classifier's parameters. This criterion was used to manually reweight adversarial examples in recent work [22]. Although this proxy score is inexact1, it nevertheless allows us to design interesting heuristic LRW variants based on its rank-ordering of training instances: (1) LRW-Hard, where we use the lowest margin instances as validation data, and the rest of the instances as training data, (2) LRW-Easy, in which the highest margin instances are" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 683, + 545, + 713 + ], + "type": "text", + "content": "For instance, it measures instance hardness under an ERM classifier, not the to-be-trained LRW model; further, an overtrained classifier may give incorrectly overconfident margins [21]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27603" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 86, + 296, + 244 + ], + "blocks": [ + { + "bbox": [ + 52, + 86, + 296, + 244 + ], + "lines": [ + { + "bbox": [ + 52, + 86, + 296, + 244 + ], + "spans": [ + { + "bbox": [ + 52, + 86, + 296, + 244 + ], + "type": "image", + "image_path": "00e46469fcc757580c369fec1576da05407846059f9bc9b9610addd4f6e6a79e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "text", + "content": "Figure 1. Robustness analysis on benchmark datasets. Left: Comparing different LRW variants, based on the choice of validation set (Easy, Random, Hard, corresponding to the rank-ordering of training data by probabilistic margin of an ERM classifier). " + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "text", + "content": "-axis shows accuracy gains over ERM for each dataset (" + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "text", + "content": "-axis). We see consistent ordering of performance, with LRW-Easy " + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "text", + "content": " LRW-Random " + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 253, + 547, + 319 + ], + "type": "text", + "content": " LRW-Hard, showing the importance of validation set optimization. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. In-1K corresponds to ImageNet-1K. For absolute accuracy values refer supplementary." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 86, + 541, + 243 + ], + "blocks": [ + { + "bbox": [ + 298, + 86, + 541, + 243 + ], + "lines": [ + { + "bbox": [ + 298, + 86, + 541, + 243 + ], + "spans": [ + { + "bbox": [ + 298, + 86, + 541, + 243 + ], + "type": "image", + "image_path": "d263a7f4ede6b116fe1224db24bfc1d8df10dd9d7c79fc1c6718b76aabfb25a2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 345, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 380 + ], + "type": "text", + "content": "used as validation data, and (3) LRW-Random, a control which uses a randomly selected validation set that does not depend on the ERM margin." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "type": "text", + "content": "We can use these variants to quantify the impact of perturbing the validation set in LRW, and to provide an existence proof of validation optimization techniques that materially improve learned classifiers. In particular, we expect to see a clear ordering of classifier test accuracy - LRW-Easy " + }, + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "type": "text", + "content": " LRW-Random " + }, + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 380, + 287, + 452 + ], + "type": "text", + "content": " LRW-Hard." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 464, + 128, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 128, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 128, + 477 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 483, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 579 + ], + "type": "text", + "content": "We perform extensive experimentation on multiple classification tasks including distribution shift benchmarks. For all datasets, if a train-validation split is already available, we use the training data for the ERM classifier in the train twice heuristic before pooling, ranking, and repartitioning. For the end-to-end optimization, we start with pooled train-validation data and simultaneously learn the data splits and the corresponding LRWOpt model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 110, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 110, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 110, + 598 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "We use popular classification benchmarks including CIFAR-100 [20], ImageNet-100 [35], ImageNet-1K [7], Aircraft [23], Stanford Cars [19], Oxford-IIIT Fine-grained classification (Cats v/s Dogs) [29] and Diabetic Retinopathy (DR) dataset. Furthermore, for OOD analysis we use the ImageNet-A [13], ImageNet-R [12] datasets for models trained on ImageNet-1K. We also use the Camelyon [2], iWildCam [4] dataset from the widely popular WILDS benchmark [18] and also the country shifted test set for the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 345, + 547, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 547, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 547, + 405 + ], + "type": "text", + "content": "DR [1] dataset. We further analyze for robustness in presence of instance dependent noise on the noisy version of CIFAR-10 dataset (Inst.C-10) proposed by Xia et al. [36] and Clothing-1M [37] dataset. Please refer supplementary (supp.) for more details, setup for these datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 411, + 372, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 372, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 372, + 423 + ], + "type": "text", + "content": "5.2. Baselines" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "type": "text", + "content": "Along with ERM, we also compare our method against various re-weighting based methods designed for improving robustness or handling noisy scenarios. These include learned re-weighting methods: MWN [32], FSR [40], L2R [31], MAPLE [41], BiLAW [14], GDW [6], StableNet [39] along with Margin Based Reweighting (MBR) [22] and Rho-Loss [24]. Please refer supp. for more details regarding them." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 523, + 359, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 523, + 359, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 523, + 359, + 536 + ], + "type": "text", + "content": "6. Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 543, + 471, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 543, + 471, + 555 + ], + "spans": [ + { + "bbox": [ + 306, + 543, + 471, + 555 + ], + "type": "text", + "content": "6.1. In-Distribution Generalization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 562, + 522, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 522, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 522, + 574 + ], + "type": "text", + "content": "6.1.1 MOLERE improves classification accuracy" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "type": "text", + "content": "Figure 1 (left) shows the LRW advantage (gains over an ERM baseline) for a range of datasets. Shown are 4 alternatives—LRW-Easy, LRW-Random, and LRW-Hard, corresponding to easy, random, and hard validation sets per the train-twice heuristic (Sec. 4.4), and LRWOpt, which is the end-to-end optimization of LRW classifier and train-validation split (Sec. 4.3). Refer supplementary for absolute accuracy values." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "type": "text", + "content": "- Gains vs ERM are strictly ordered in nearly all datasets—LRW-Easy " + }, + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "type": "text", + "content": " LRW-Random " + }, + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 306, + 677, + 547, + 713 + ], + "type": "text", + "content": " LRW-Hard—robustly confirming our hypothesis that validation sets in LRW classi" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27604" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 86, + 265, + 233 + ], + "blocks": [ + { + "bbox": [ + 53, + 86, + 265, + 233 + ], + "lines": [ + { + "bbox": [ + 53, + 86, + 265, + 233 + ], + "spans": [ + { + "bbox": [ + 53, + 86, + 265, + 233 + ], + "type": "image", + "image_path": "f8c39ccef9276b658574f3f2cfd43328594f164b5b14b8362a228450e6f22942.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 547, + 289 + ], + "type": "text", + "content": "Figure 2. OOD generalization. Left: Comparison of LRW variants on domain shift benchmarks. The ordering between the validation selection methods is reconfirmed on domain shift benchmark datasets as well, suggesting that earlier gains are not via overfitting to training distribution. Right: Comparing against other re-weighting methods. The figure shows that our proposal (LRW-Hard) outperforms the other reweighting techniques on average, with fast sample re-weighting (FSR) begin competitive in some datasets. For absolute values refer supp." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 268, + 86, + 539, + 233 + ], + "blocks": [ + { + "bbox": [ + 268, + 86, + 539, + 233 + ], + "lines": [ + { + "bbox": [ + 268, + 86, + 539, + 233 + ], + "spans": [ + { + "bbox": [ + 268, + 86, + 539, + 233 + ], + "type": "image", + "image_path": "46aab2494a2382063fc962b892cb3dfef0227f7d5f113f6105640afbdc3c5172.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "spans": [ + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "type": "text", + "content": "fiers need to be optimized. The difference between LRW-Hard and LRW-Easy is over " + }, + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "type": "text", + "content": " relative gain for ImageNet & CIFAR-100, and " + }, + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 56, + 313, + 286, + 348 + ], + "type": "text", + "content": " relative for Clothing-1M." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 350, + 286, + 468 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 350, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 286, + 408 + ], + "type": "text", + "content": "- LRW-Random shows modest gains over ERM in most datasets². LRW-Hard shows significant gains, underscoring the benefit of combining LRW with validation set optimization - 0.8% relative gain on Imagenet, 1.3% on Clothing-1M, 2.15% relative on CIFAR-100." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 408, + 286, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 286, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 286, + 468 + ], + "type": "text", + "content": "- The end-to-end LRWOpt matches or exceeds LRW-Hard, showcasing its effectiveness without the need for training twice. On a minority of datasets, LRW-Hard is nominally better; we believe this is due to the small-sample nature of real-world datasets, and attendant estimation noise." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 472, + 286, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 286, + 544 + ], + "type": "text", + "content": "Although the presented accuracy is on unseen test sets, a concern may be that LRW-Hard overfits to the training data distribution and results in brittle classifiers. To address this, we performed a number of experiments on datasets with matched out-of-domain test sets (Diabetic retinopathy [1, 33], Camelyon [2], WildCam [4]) in next subsection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 561, + 286, + 584 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 286, + 584 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 286, + 584 + ], + "type": "text", + "content": "6.1.2 MOLERE outperforms existing re-weighting baselines" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 593, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 286, + 665 + ], + "type": "text", + "content": "We now compare our LRWOpt method against other reweighting methods- FSR [40]), MBR [22], MAPLE [41], MWN [32], StableNet [39], BiLAW [14])-see Fig. 1 (right) for more details. While FSR, RHO-Loss, MBR, MAPLE, StableNet and BiLAW are proposals in the literature for learned reweighting of the training data (via meta-learning)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 313, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 313, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 306, + 313, + 545, + 432 + ], + "type": "text", + "content": "in order to address various clean- and noisy-label scenarios, MBR is an extrapolation of a proposal for ad-hoc upweighting of adversarial examples alone [22], for increased robustness against those specific adversarial attacks. In similar spirit, the proposal \"just train twice\" [21] also suggests an ad-hoc upweighting of poor performing instances in a second round of training. RHO-loss [24], on the other hand, follows the harder version as against all these methods and selects only some points from a batch which minimize the holdout set loss for efficient training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 433, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 576 + ], + "type": "text", + "content": "On the datasets tested, we see that LRWOpt clearly outperforms all these baseline methods consistently across all the datasets. It is followed by MAPLE, StableNet which are designed keeping group/OOD robustness in mind. FSR and Rho-Loss perform similar to ERM only. Interestingly, MBR and MWN are among the worst performers, showing that it is insufficient to simply upweight instances based on a first-round estimate of margin and the commonly followed bilevel optimization procedure by using free-parameters/loss based re-weighting, even though capable of providing unbiasedness, is not sufficient and requires another level of optimization for finding the appropriate validation set." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 586, + 527, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 527, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 527, + 600 + ], + "type": "text", + "content": "6.2. Out-Of-Distribution (OD) generalization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "We further evaluate the robustness of our learned representations on the standard out-of-distribution datasets from the Wilds benchmark namely the camelyon [2] and the iwildcam [4] datasets along with the Diabetic Retinopathy dataset with a country shifted test set (APTOS test dataset) [1]. For the first two, " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " examples from the train set, sampled randomly, are used as val set. For the last one, a separate validation set, with same domain as the train set, is provided. Refer supplementary for more details regarding" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 673, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 286, + 712 + ], + "type": "text", + "content": "2Previous results [31] had shown neutral or slightly negative gains over ERM, focusing chiefly on training with noisy training labels + clean validation data. The improvement in our results are driven by the use of the meta-network." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27605" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 396 + ], + "type": "text", + "content": "the dataset details and our evaluation setup. Furthermore, we also analyze the performance on the ImageNet-A dataset by using both training and validation data from ImageNet-1K. Our primary goal here is to check whether the gains we saw above are primarily driven by in-domain learning, or a broader improvement in generalization capacity over the existing learned reweighting methods –as a result, we restrict ourselves to comparison among ERM, the LRW variants along with LRWOpt and the re-weighting baselines, rather than the substantial literature on domain shift. Fig. 2 (left) confirms that our learned classifiers generalize better to domain shift data as compared to ERM classifiers; further, the ordering between the different validation datasets is largely preserved. Fig. 2 (right) provides evaluation of our methods and other re-weighting baselines. These include the standard bi-level optimization based ones like MWN, FSR along with ones designed for OOD generalization/robustness like MAPLE, StableNet, Rho-Loss and MBR. It can be observed that our method surpasses all of these baselines thereby showing the importance of validation set optimization problem for the bi-level optimization based re-weighting methods, introduced in the paper. StableNet comes out to be the closest competitor of our method which has been designed explicitly for OOD learning. Rest all the re-weighting methods perform similar to ERM with minor gains/losses. Absolute accuracy values for this analysis are provided in the supplementary." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 415, + 211, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 211, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 211, + 428 + ], + "type": "text", + "content": "6.3. Practical Label Noise Settings" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "text", + "content": "We now study the noisy label setting with a focus on real-world label noise using datasets like Clothing1M [37], and noisy CIFAR-10 (Inst. C-10 [36]), which contain instance conditioned noise as against randomly flipping labels or adding uniform noise. This noise can be treated as a measure of instance hardness rather than labeling error (refer supplementary for more details). Table 3 compares LR-WOpt method against bi-level optimization approaches like MWN, FSR, L2R, GDW which although specifically designed for noisy labels have been primarily tested on label flipping, uniform noise data. We also compare against MAPLE, designed for general robustness. On Inst. C-10, our method clearly surpasses all baselines, with " + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "inline_equation", + "content": "1.53\\%" + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "text", + "content": " accuracy gain. On Clothing-1M, we show about " + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "inline_equation", + "content": "0.85\\%" + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "text", + "content": " gain over the best performing GDW baseline. For other noisy settings like random label flips, prior work on outlier robust DRO [38] has shown good results using loss clipping (e.g. exclude " + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "inline_equation", + "content": "\\mathrm{k}\\%" + }, + { + "bbox": [ + 46, + 434, + 289, + 662 + ], + "type": "text", + "content": " of highest loss as label noise), which could be co-opted into our work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 670, + 141, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 141, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 141, + 682 + ], + "type": "text", + "content": "6.4. Skewed Labels" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "We now study the skewed label setting, comparing against instance based reweighting schemes proposed with this set-" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 547, + 102 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 547, + 102 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 547, + 102 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 547, + 102 + ], + "type": "table", + "html": "
MethodEasyHardRandomLRWoptMWNERM
Acc.83.1785.0983.8784.9484.0284.11
", + "image_path": "41335917a075e6674e269c78c72c67f3d75bbbcf31594094c04cec192e825912.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 155, + 559, + 220 + ], + "blocks": [ + { + "bbox": [ + 305, + 110, + 547, + 144 + ], + "lines": [ + { + "bbox": [ + 305, + 110, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 110, + 547, + 144 + ], + "type": "text", + "content": "Table 1. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and 12s baselines." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 155, + 559, + 220 + ], + "lines": [ + { + "bbox": [ + 307, + 155, + 559, + 220 + ], + "spans": [ + { + "bbox": [ + 307, + 155, + 559, + 220 + ], + "type": "table", + "html": "
class skew20050101
MWN [32]40.11 ± 0.948.67 ± 0.761.32 ± 0.674.23 ± 0.3
FSR [40]38.04 ± 0.845.12 ± 0.958.38 ± 0.674.68 ± 0.2
GDW [6]40.36 ± 1.048.89 ± 0.861.67 ± 0.574.41 ± 0.4
LRWOpt42.33 ± 0.850.77 ± 0.763.28 ± 0.875.12 ± 0.3
", + "image_path": "b4006aa55522e33205370dc34db083af043facb64296b6fdfc0fee0c30d834fe.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 273, + 555, + 315 + ], + "blocks": [ + { + "bbox": [ + 305, + 228, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 305, + 228, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 547, + 262 + ], + "type": "text", + "content": "Table 2. Comparison, on CIFAR-100 dataset, of our LRWOpt method with existing meta-learning based reweighting methods in a label skew setup for which these methods were defined." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 273, + 555, + 315 + ], + "lines": [ + { + "bbox": [ + 307, + 273, + 555, + 315 + ], + "spans": [ + { + "bbox": [ + 307, + 273, + 555, + 315 + ], + "type": "table", + "html": "
MWNFSRL2RMAPLEGDWOurs
Inst. C-1065.8967.1270.2170.3469.1271.87
Clothing-1M72.7972.0772.2271.6773.1273.97
", + "image_path": "b033fcf4b9825e72e863e3b97603ecc481339e5677b945ea54362eabd2033c68.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 322, + 547, + 356 + ], + "lines": [ + { + "bbox": [ + 305, + 322, + 547, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 322, + 547, + 356 + ], + "type": "text", + "content": "Table 3. Instance-dependent noise. ImageNet-1k dataset with a ViT-B/16 pretrained backbone. We compare various versions of our method with the ERM, Meta-Weight and l2s baselines." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 375, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 547, + 460 + ], + "type": "text", + "content": "ting in mind (Meta-Weight-Net, FSR and another recently proposed re-weighting method GDW [6]). Table 2 shows the results for this analysis on the CIFAR-100 datasets with various skew levels ranging from 1 to 200. It can be observed that our LRWOpt significantly outperform the existing loss based reweighting methods at all of the skew levels showing accuracy gains upto " + }, + { + "bbox": [ + 304, + 375, + 547, + 460 + ], + "type": "inline_equation", + "content": "2.22\\%" + }, + { + "bbox": [ + 304, + 375, + 547, + 460 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 466, + 529, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 466, + 529, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 466, + 529, + 479 + ], + "type": "text", + "content": "6.5. MOLERE scales to large pretrained models" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "type": "text", + "content": "We further analyze the LRW-Hard, Easy and Random methods along with the ERM baseline on ViT-B/16 pretrained backbone trained using these techniques and evaluated on the ImageNet-1K dataset. Table 1 shows the results from this experiments. Again LRW-Hard emerges the winner and improves significantly (around " + }, + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "type": "text", + "content": ") w.r.t. other methods and the baseline advocating robustness using hard examples. Furthermore, there is " + }, + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "type": "inline_equation", + "content": "1.92\\%" + }, + { + "bbox": [ + 304, + 484, + 547, + 617 + ], + "type": "text", + "content": " difference in accuracy between LRW-Easy and LRW-Hard, even though we warm-started all the techniques with a pretrained backbone, showing the sensitivity of techniques to choice of validation set." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 623, + 541, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 623, + 541, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 623, + 541, + 635 + ], + "type": "text", + "content": "6.6. Leveraging OOD val set: A heuristic solution" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "content": "We now turn to the use of known hard instance, or OOD, datasets when available, in the MOLERE context. For the well-studied Imagenet-1K dataset, two datasets are frequently used to gauge generalization properties of learned classifiers – IN-A (“natural adversarial instances”, examples known to be misclassified by a trained Resnet-50" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27606" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 91, + 164, + 180 + ], + "blocks": [ + { + "bbox": [ + 47, + 91, + 164, + 180 + ], + "lines": [ + { + "bbox": [ + 47, + 91, + 164, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 164, + 180 + ], + "type": "image", + "image_path": "fa74da41d1295bb3729e621f718ef61eca0c145da396b8bd5bbe3d4ad2909491.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 190, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 45, + 190, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 45, + 190, + 547, + 234 + ], + "type": "text", + "content": "Figure 3. MOLERE improves margins of learned classifiers. (a,b): paired margin deltas between LRWOpt and ERM are moderately right-skewed with mean/median greater than zero. (c,d): As a function of ERM margin, clear separation seen between LRW-Hard (better) and LRW-Easy (worse) in terms of margin gain over ERM (errors bars are SEM). All results on unseen test data; Imagenet-100, CIFAR100 shown for brevity, with similar results for other datasets in appendix." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 172, + 91, + 301, + 181 + ], + "blocks": [ + { + "bbox": [ + 172, + 91, + 301, + 181 + ], + "lines": [ + { + "bbox": [ + 172, + 91, + 301, + 181 + ], + "spans": [ + { + "bbox": [ + 172, + 91, + 301, + 181 + ], + "type": "image", + "image_path": "9596f7b71389992551cef4f6d0678793848bf9930f664ee71dd055fff3a3c4a5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 306, + 90, + 419, + 176 + ], + "blocks": [ + { + "bbox": [ + 306, + 90, + 419, + 176 + ], + "lines": [ + { + "bbox": [ + 306, + 90, + 419, + 176 + ], + "spans": [ + { + "bbox": [ + 306, + 90, + 419, + 176 + ], + "type": "image", + "image_path": "fdf16d2063be349c7fd0c085533e1e2225396c80bb2429992bf3263a5bdd69bd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 428, + 91, + 545, + 180 + ], + "blocks": [ + { + "bbox": [ + 428, + 91, + 545, + 180 + ], + "lines": [ + { + "bbox": [ + 428, + 91, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 428, + 91, + 545, + 180 + ], + "type": "image", + "image_path": "a07077c1468e2f9c57063201516d24f45e8f92fa021b8ddd17429f4179b45a15.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 259, + 289, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 289, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 289, + 415 + ], + "type": "text", + "content": "model), and IN-R (renditions of objects, such as drawings, paintings, sculptures, etc). For each of these, we used a portion of the dataset as LRW validation set, and retained another portion for testing. Table 4 shows the results of this study. We report the following two surprising results: (1) our approach outperforms the baseline ERM classifier on not just the OOD test set, but also on the in-domain test set (1.7-3% and 0.5-0.7% gains respectively), and (2) simply adding the OOD data to the train set only moderately improves OOD test set performance while degrading ID accuracy. These findings were replicated for both IN-A and IN-R as LRW validation sets, underscoring the real-world applicability of our findings, on large-scale datasets." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 48, + 434, + 296, + 494 + ], + "blocks": [ + { + "bbox": [ + 48, + 434, + 296, + 494 + ], + "lines": [ + { + "bbox": [ + 48, + 434, + 296, + 494 + ], + "spans": [ + { + "bbox": [ + 48, + 434, + 296, + 494 + ], + "type": "table", + "html": "
IN-R val (ResNet50)IN-A val (ResNet152)
IN1K TestINR TestIN1k TestINA Test
LRWOpt + INR val76.1449.178.127.9
ERM (IN1K)75.6546.177.316.2
ERM (IN1K+INR)74.8947.477.086.6
", + "image_path": "cbc936439e3d0e4654f4f2ee8388c0fa8b7735d4026f78d78cf5643e6a8025d9.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 502, + 287, + 557 + ], + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 557 + ], + "type": "text", + "content": "Table 4. Natural hard examples as validation. LRW classifiers on Imagenet (IN1k) data and OOD validation sets (IN-A & IN-R respectively) outperform ERM on both in-domain and OOD test sets. Simply augmenting training data of ERM baseline does not match this (see text for details)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 572, + 257, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 257, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 257, + 586 + ], + "type": "text", + "content": "6.7. Margin maximization via meta-learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 591, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 687 + ], + "type": "text", + "content": "We present empirical evidence showing that MOLERE has a margin maximization effect, i.e., the learned classifiers have wider margins than ERM classifiers. Since our validation data is selected to be low-margin instances, our LRW classifier upweights, and improves performance on, training instances most similar to the low-margin validation set. 3 shows two views of margin differences between MOLERE and ERM on the test set, to confirm this expectation3. Pan-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 259, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 344 + ], + "type": "text", + "content": "els (a,b) shows a histogram of paired margin differences between ERM and LRWOpt, indicating a modest right-skew with mean & median to the right of 0. Panels (c,d) shows LRW-Hard and LRW-Easy deltas w.r.t. ERM, averaged over ERM margin buckets (mean and S.E.M. errorbars)—across the board (i.e., for most values of ERM margin), LRW-Hard contrasts with ERM better than LRW-Easy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 346, + 546, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 546, + 419 + ], + "type": "text", + "content": "Further details on Algorithm 1, proof of Theorem 1, the time complexity of the proposed scheme compared to ERM, the training setup, ablation study over the validation set selection/loss, and discussion regarding the early-stage performance of the proposed scheme are provided in the supplementary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 439, + 444, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 439, + 444, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 439, + 444, + 451 + ], + "type": "text", + "content": "7. Discussion & conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": "We proposed the novel idea of optimizing the choice of validation data in a learned-reweighting setting, and showed that it gives significant gains over ERM on a range of datasets and domain generalization benchmarks. In particular, in most experiments on clean data, we saw a clear ordering between choosing easy, random, and hard samples as validation data in an LRW setup, with the latter performing best and delivering consistent gains over ERM. This ordering provides broad support to our primary hypothesis: meta-optimization of the metalearning workflow in LRW is an important area of research with potential for substantial impact. Our specific heuristic of choosing low-margin points is a simple, straightforward instantiation of what we believe is a family of optimization algorithms that can be brought to bear on the general problem of optimizing metalelearned classifiers. Indeed, our heuristic is not competitive under very high label noise scenarios, suggesting the need for follow-on work that explores more formal, optimization-driven approaches towards this problem. We are also excited about elucidating the theoretical basis of observed gains in the MOLERE framework." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 714 + ], + "type": "text", + "content": "3We show Imagenet-100 & CIFAR100 for brevity; findings consistent across all datasets (see Appendix)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27607" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Kaggle. diabetic retinopathy detection challenge, 2015, 2015. 5, 6" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 286, + 190 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 286, + 190 + ], + "type": "text", + "content": "[2] Peter Bandi, Oscar Geessink, Quirine Manson, Marcory Van Dijk, Maschenka Balkenhol, Meyke Hermsen, Babak Ehteshami Bejnordi, Byungjae Lee, Kyunghyun Paeng, Aoxiao Zhong, et al. 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Caml: Fast context adaptation via meta-learning. 2018. 2" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "27609" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names/eeeede11-1438-46b6-b66c-0eb160635025_content_list.json b/2024/Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names/eeeede11-1438-46b6-b66c-0eb160635025_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7d2f967a9d79aebbb50bc5155c3bfa0dd72fcf12 --- /dev/null +++ b/2024/Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names/eeeede11-1438-46b6-b66c-0eb160635025_content_list.json @@ -0,0 +1,1591 @@ +[ + { + "type": "text", + "text": "Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names", + "text_level": 1, + "bbox": [ + 83, + 128, + 888, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yapeng Li $^{1}$ , Yong Luo $^{1,2}$ , Zengmao Wang $^{1}$ , Bo Du $^{1,2*}$", + "bbox": [ + 254, + 202, + 712, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ National Engineering Research Center for Multimedia Software, Institute of Artificial Intelligence, Hubei Key Laboratory of Multimedia and Network Communication Engineering, School of Computer Science, Wuhan University, Wuhan, China.", + "bbox": [ + 91, + 220, + 875, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Hubei Luojia Laboratory, Wuhan, China.", + "bbox": [ + 315, + 273, + 653, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/1i-yapeng/DSECN", + "bbox": [ + 328, + 294, + 635, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generalized Zero-Shot Learning (GZSL) methods often assume that the unseen classes are similar to seen classes, and thus perform poor when unseen classes are dissimilar to seen classes. Although some existing GZSL approaches can alleviate this issue by leveraging additional semantic information from test unseen classes, their generalization ability to dissimilar unseen classes is still unsatisfactory. This motivates us to study GZSL in the more practical setting, where unseen classes can be either similar or dissimilar to seen classes. In this paper, we propose a simple yet effective GZSL framework by exploring diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes. This is achieved by introducing diverse semantics from external class names and aligning the introduced semantics to visual space using the classification head of pre-trained network. Furthermore, we show that the design idea of DSECN can easily be integrate into other advanced GZSL approaches, such as the generative-based ones, and enhance their robustness for dissimilar unseen classes. Extensive experiments in the practical setting including both similar and dissimilar unseen classes show that our method significantly outperforms the state-of-the-art approaches on all datasets and can be trained very efficiently.", + "bbox": [ + 76, + 376, + 473, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 771, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the high cost of annotation and the complexity of real-world test scenarios, the presence of unseen classes is often inevitable [34, 43]. Unfortunately, traditional machine learning models are unable to handle samples from classes that have not been covered by the training data [8].", + "bbox": [ + 75, + 797, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/24dde050104dfd755ddb73363db423e05af8d590448c8b6c3fa5f3a3a96de4f0.jpg", + "image_caption": [ + "(a) Our Setting" + ], + "image_footnote": [], + "bbox": [ + 514, + 343, + 877, + 455 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/86a24f0161f409aede503f30384b80727ea06a6e7a6f4339f5d07f356229c650.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModeCN [38]TransZero [9]ZLA [4]DGZ [5]Ours (Δ)
Similar42.5047.9942.6543.1648.45 (+0.46)
Dissimilar5.092.478.5212.3047.44 (+35.14)
", + "bbox": [ + 501, + 470, + 906, + 520 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(b) Results", + "bbox": [ + 666, + 521, + 727, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1. Setting illustration and results: (a) Comparison with the existing setting, our setting takes into account the scenario where the unseen classes are dissimilar to seen classes; (b) Performance of existing GZSL methods on similar and dissimilar unseen classes on the CUB dataset. The similar unseen classes were obtained from the same CUB dataset, while the dissimilar unseen classes come from AWA2 and SUN dataset.", + "bbox": [ + 496, + 537, + 893, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To tackle this challenge, zero-shot learning (ZSL) has been proposed to recognize new classes via transferring knowledge obtained from seen classes with the help of semantic information [14, 15, 23, 52]. In contrast, Generalized ZSL (GZSL) is a more challenging task which handle test samples from both seen and unseen classes [3, 25, 29, 34].", + "bbox": [ + 496, + 641, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The core idea of GZSL is to introduce auxiliary semantic information and establish the connection between semantic and visual space for the recognition of unseen classes [34]. Since unseen samples are not available during training, existing GZSL models often misclassify unseen class samples into seen classes during test (known as the bias issue) [21, 22]. To alleviate this issue, several strategies have been introduced. A common strategy is to utilize a backbone pre-trained on the ImageNet-1K dataset [13] to extract visual features [7, 24, 26, 36, 50], which is beneficial to improve the generalization ability of visual features. However,", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors: Zengmao Wang, Bo Du", + "bbox": [ + 94, + 886, + 357, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23344", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the rich semantics that implicitly contained in the backbone classification heads are simply ignored in these approaches, and thus their ability to exploit diverse semantics is limited. Generative-based GZSL methods [4-6, 16, 51] alleviate the bias problem by introducing the semantics from test unseen classes, and some semantic augmentation approaches focus on enhancing the semantics of each class by leveraging the textual documents [30], large language model [31], etc [19, 50]. However, these approaches share a common limitation that they heavily rely on the semantics and visual features from seen classes to build the relations between visual and semantic space. This makes these models perform poorly on dissimilar unseen classes (see Fig. 1b), as little information can be transferred from seen to dissimilar unseen classes. That is, these methods can only deal with the unrealistic setting that the unseen classes are similar with seen classes (see existing setting of Fig. 1a). However, it is inevitable that unseen classes may be quite different from seen classes in the real-world applications, and hence it is desirable to enhance GZSL models to effectively handle dissimilar unseen classes.", + "bbox": [ + 76, + 90, + 472, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve this goal, we need to address three main challenges: (I) how to obtain the information that can be transferred to dissimilar unseen classes; (II) how to enable effective information transfer without labeled training data; and (III) how to reduce costs as much as possible while ensuring effectiveness. If the cost of the solution exceeds the cost of collecting the data and retraining the model, then such a solution would be meaningless. Therefore, we propose a simple yet effective GZSL framework by exploring Diverse Semantics from External Class Names (DSECN), which is robust on both the similar and dissimilar unseen classes. Specifically, we introduce the diverse semantics from external (not test unseen classes) class names as the bridge to reduce the gap between the seen and unseen classes, which is beneficial for the recognition of unseen classes (challenge I). Then we utilize the classification head pre-trained on large-scale dataset, e.g., ImageNet-1K [13], to align the introduced semantics to the visual space (challenge II). Finally, the hierarchical taxonomy of WordNet [28] for the classes in large-scale dataset is introduced to further improve the diversity of semantics from class names. Since the class name and pre-trained classification head are quite easy to collect, the cost of our method is quite low (challenge III).", + "bbox": [ + 76, + 411, + 472, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, the main contributions of this paper are:", + "bbox": [ + 94, + 776, + 462, + 792 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To the best of our knowledge, we are the first that explicitly study the realistic GZSL setting that both similar and dissimilar unseen classes exist (see our setting in Fig. 1a).", + "- We propose a GZSL method that explores the diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes." + ], + "bbox": [ + 76, + 795, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We show that the proposed idea can be easily integrated into other GZSL approaches, such as generative-based ones, and improve their robustness for dissimilar unseen classes.", + "bbox": [ + 500, + 90, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct extensive experiments on diverse real-world datasets. The results show that in the practical setting including both similar and dissimilar unseen classes, the harmonic mean accuracies of our method significantly outperform all counterparts. Besides, our model can be trained within one minute on all three datasets.", + "bbox": [ + 498, + 152, + 893, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 257, + 640, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Generalized Zero-shot Learning", + "text_level": 1, + "bbox": [ + 500, + 282, + 782, + 299 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing GZSL methods can be broadly categorized into embedding-based [9, 18, 25, 38] and generative-based ones [2, 5, 12, 16]. Early global embedding-based methods [15, 18, 25, 38, 45] align global visual features with corresponding category semantic information into a common embedding space, which enables knowledge transfer from seen to unseen classes. Recently proposed local embedding-based methods [9-11, 42, 48, 49] utilize attribute descriptions as guidance to discover the discriminative local features between seen classes and unseen classes. Besides, generative-based methods [4, 5, 12, 37, 38, 47] introduce the semantic from test unseen classes to alleviate the bias problem in GZSL [34]. However, these methods focus on the unrealistic setting where unseen classes are assumed to be similar to seen classes, and perform poorly in identifying dissimilar unseen classes. In contrast, our work focuses on a realistic GZSL setting that includes both similar and dissimilar unseen classes, and the proposed DSECN can robustly identify similar and dissimilar unseen classes.", + "bbox": [ + 498, + 306, + 890, + 594 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Semantic Information for GZSL", + "text_level": 1, + "bbox": [ + 500, + 604, + 784, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic information is a bridge that transfers knowledge from seen classes to unseen class recognition and is crucial to GZSL [30, 34, 50]. Most of prior works rely on human-annotated attributes [2, 32, 49] or word vectors [20, 39] as the semantic information. While attributes are accurate, they are costly to annotate and are not suitable for a large-scale problem [20, 50]. In contrast, word vectors require less human labor and are suitable for large-scale datasets [34]. However, word vectors often do not reflect visual similarities, thus limiting the performance [30, 49]. Xu et al. [49] propose a visually-grounded semantic embedding (VGSE) network to discover semantic embeddings containing discriminative visual properties. Naeem et al. [30] propose a transformer-based model I2DFormer that learns semantic embeddings from raw online textual documents. However, these methods only consider semantic enhancement within a single category. When an unseen class is dissimilar to seen classes, the transferable semantic infor", + "bbox": [ + 498, + 628, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23345", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mation from seen classes is still little, which limits their performance. In contrast, we introduce diverse semantic information from external category names and align the introduced semantics into visual space using the classification head pre-trained on a large-scale dataset , thus assisting in the identification of dissimilar unseen categories.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 196, + 250, + 213 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem Formulation. In ZSL and GZSL, we define two sets of classes: seen classes in $Y^s$ and unseen classes in $Y^u$ . The seen classes $Y^s$ and the unseen classes $Y^u$ are disjoint, i.e., $Y^s \\cap Y^u = \\emptyset$ and $Y^s \\cup Y^u = \\mathcal{Y}$ . The unseen classes may be similar or dissimilar to seen classes in practice. Hence, in this work, the unseen classes $Y^u$ contain similar unseen classes $Y_s^u$ and dissimilar unseen classes $Y_d^u$ , i.e., $Y^u = Y_s^u \\cup Y_d^u$ . The seen data are expressed as $D^s = \\{(x_i^s, y_i^s)\\}$ , where $x_i^s \\in X$ indicates the $i$ -th sample features extracted by the pretrained backbone network, e.g., ResNet101 [17], and $y_i^s \\in Y^s$ is its class label. The $D^s$ is split into a training set $D_{tr}^s$ and a testing set $D_{te}^s$ . On the other hand, the unseen data are denoted as $D^u = \\{(x_i^u, y_i^u)\\}$ , where $x_i^u \\in X^u$ and $y_i^u \\in Y^u$ are the sample features of unseen classes and the corresponding ground-truth label for evaluation, respectively. The goal of ZSL is to learn a classifier for classifying test samples from unseen classes, i.e., $X \\xrightarrow{f_{ZSL}} Y^u$ . In contrast to ZSL, the goal of GZSL is to learn a classifier for classifying test samples from both seen and unseen classes, i.e., $X \\xrightarrow{f_{GZSL}} Y^s \\cup Y^u$ . In ZSL and GZSL, the auxiliary semantic information $A$ is obtained by transforming the class labels $\\mathcal{V}$ using human-annotated attributes [9] or language models [27, 35].", + "bbox": [ + 75, + 222, + 472, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview of framework. As shown in Fig. 2, the framework contains three components: visual flow (§ 3.1), diverse semantic enhancement (DSE, § 3.2), and hierarchy taxonomy enhancement (HTE, § 3.3). The visual flow aligns seen class semantics into visual space. Diverse semantic and hierarchy taxonomy enhancement are proposed to enhance the diversity of semantics available to the model, thereby assisting the identification of dissimilar unseen classes.", + "bbox": [ + 75, + 594, + 468, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Visual Flow", + "text_level": 1, + "bbox": [ + 76, + 724, + 204, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The visual flow is designed to classify visual objects from both seen and unseen classes by transferring knowledge from the seen classes to the unseen ones with the help of semantic information. The visual flow contains two parts: semantic-to-visual sub-network $(S2V)$ and visual classifier. The $S2V$ sub-network is a learnable multilayer perceptron (MLP), and is used to link the semantic and visual representation. This enables the model to transfer the knowledge from seen classes to the unseen classes through semantic information. The visual classifier uses the relation", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ship between the visual sample and all categories to obtain the classification result of the sample. Because the visual flow requires paired visual samples and category labels, in the training phase, the visual flow can only be trained on the paired visual feature and label dataset $D_{tr}^{s}$ . Specifically, the $S2V$ sub-network takes the seen semantic feature $A^{s}$ as input to generate the class-level visual prototype of seen classes $V^{s}$ . The process to generate the class-level visual prototype of seen classes $V^{s}$ can be expressed by", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {s} \\in \\mathbb {R} ^ {C ^ {s} \\times d ^ {a}} \\xrightarrow {S 2 V} V ^ {s} \\in \\mathbb {R} ^ {C ^ {s} \\times d ^ {v}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 239, + 890, + 260 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $C^s, d^a, d^v$ denote the number of seen classes, the dimensionality of semantic representation and the dimensionality of visual representation, respectively. $A^s$ signifies the semantic representations of seen classes and is extracted by language models [27, 35].", + "bbox": [ + 496, + 270, + 890, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, the visual classifier (VC) computes the scaled cosine similarity between the visual feature of seen classes $X_{tr}^{s} \\in \\mathbb{R}^{N_{tr}^{s} \\times d^{v}}$ and the class-level visual feature of seen classes $V^{s} \\in \\mathbb{R}^{C^{s} \\times d^{v}}$ as logits $l^{s} \\in \\mathbb{R}^{N_{tr}^{s} \\times C^{s}}$ , where $N_{tr}^{s}$ is the number of seen class samples in the training set. Formally, the logits $l^{s}$ can be obtained as follows:", + "bbox": [ + 496, + 347, + 890, + 438 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nl ^ {s} = \\gamma^ {2} \\frac {X _ {t r} ^ {s} V ^ {s} {} ^ {\\top}}{\\| X _ {t r} ^ {s} \\| \\| V ^ {s} \\|}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 448, + 890, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\gamma$ is the scale factor.", + "bbox": [ + 500, + 493, + 679, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, we adopt the Cross-Entropy (CE) loss to update the visual flow:", + "bbox": [ + 496, + 508, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {V} = \\mathcal {L} _ {C E} \\left(\\sigma \\left(l ^ {s}\\right), Y _ {t r} ^ {s}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 551, + 890, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma$ denotes the softmax function.", + "bbox": [ + 500, + 580, + 767, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Diverse Semantic Enhancement", + "text_level": 1, + "bbox": [ + 500, + 604, + 779, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivation of DSE. When the unseen classes are dissimilar with seen classes, the visual flow can transfer only little information from seen classes to unseen classes, resulting in poor recognition performance of unseen classes. Motivated by this, we propose the diverse semantic enhancement module, which introduces the semantic information from external class names to help the recognition of unseen classes. To successfully transfer semantic information to unseen classes, establishing a substantial linkage between the semantics inherent in class names and their corresponding visual features is imperative. Nonetheless, the visual feature of the class name is unknown, which poses the primary obstacle in leveraging semantics from class names to enhance Generalized Zero-Shot Learning (GZSL). Considering the visual representation $X$ obtained through the pretrained backbone, e.g. ResNet101, on the large-scale dataset, we use the classification head corresponding to pretrained backbone as semantic classifier (SC) to constrain the", + "bbox": [ + 496, + 628, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23346", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d4d7ef52d30ea1a23fa9db0dc035fb574b8eac3070f2d06ed25bc23d397667d1.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed DSECN framework. During the training phase, our method contains three components: visual flow, diverse semantic enhancement, and hierarchy taxonomy enhancement. In the visual flow, we employ the visual cosine classifier to align the semantics and visual features of seen classes. Then the diverse semantic enhancement and hierarchy taxonomy enhancement introduce more diverse information from the external base class names and the augmented class names. The introduced diverse semantics are aligned to the visual space using pre-trained classification head, which enables our model to learn a robust union space for both similar and dissimilar unseen classes. During the inference phase, benefiting from the learned union space that contains visual-semantic correspondence of diverse classes, the test image from dissimilar unseen classes can be accurately classified." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 885, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "generated class-level visual prototype of class names to visual space. Besides, the introduced semantics from class names should be diverse. Hence, we choose the class names of large-scale dataset to extract diverse semantics.", + "bbox": [ + 75, + 568, + 468, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Construction of DSE. We first introduce the class names $CN^{EB}$ of large-scale dataset corresponding to pretrained network and extract the semantic information $A^{EB} \\in \\mathbb{R}^{C^{EB} \\times d^a}$ of $CN^{EB}$ using the Language Model (LM), i.e.,", + "bbox": [ + 76, + 628, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {E B} = L M \\left(C N ^ {E B}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 704, + 468, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$C^{EB}$ denotes the number of external base class names from the large-scale dataset. Then the semantic information $A^{EB}$ are taken as the input of $S2V$ sub-network to generate class-level visual prototype $V^{EB} \\in \\mathbb{R}^{C^{EB} \\times d^v}$ , i.e.,", + "bbox": [ + 75, + 729, + 468, + 794 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV ^ {E B} = S 2 V \\left(A ^ {E B}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 804, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, the generated visual prototype $V^{EB}$ is fed into the semantic classifier (SC) to get the logits $l^{EB} \\in \\mathbb{R}^{C^{EB} \\times C^{PR}}$ , i.e.,", + "bbox": [ + 75, + 835, + 468, + 882 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl ^ {E B} = S C (V ^ {E B}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $SC$ is the frozen classification head from pretrained network. $C^{PR}$ is the class number of pretraining dataset.", + "bbox": [ + 498, + 568, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the backbone pretrained in large-scale dataset, we can obtain the label of $CN^{EB}$ as follows:", + "bbox": [ + 500, + 598, + 890, + 627 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY ^ {E B} = C N 2 Y \\left(C N ^ {E B}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 637, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $CN2Y$ is the dictionary mapping from class names to labels in the large-scale dataset corresponding to the pretrained backbone.", + "bbox": [ + 498, + 666, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the Cross-Entropy (CE) Loss is adopted to update the diverse semantic enhancement module:", + "bbox": [ + 498, + 710, + 890, + 741 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E B} = \\mathcal {L} _ {C E} (\\sigma (l ^ {E B}), Y ^ {E B}). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 751, + 890, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comparison with Analogous Methods. The prevailing GZSL approach depends on transferring semantic knowledge from seen to unseen classes. However, these techniques falter in a realistic GZSL setting that encompasses both similar and dissimilar unseen classes. Our method introduces varied semantics derived from external class names and aligns them with the visual domain through a pre-trained classification head. This process allows our", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23347", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "model to leverage newly introduced semantics as a bridge connecting seen and dissimilar unseen classes, thus enhancing the identification of dissimilar unseen classes. Notably, the procurement cost of class names and pre-trained classification heads is low, rendering our approach more feasible in practice.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Hierarchy Taxonomy Enhancement", + "text_level": 1, + "bbox": [ + 76, + 188, + 387, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Chihuahua is a kind of pet dog, and the dog is also a kind of animal. That is, there is a hierarchical structure between different categories. Therefore, we can utilize the hierarchy structure of classes to augment more classes. Based on the assumption, we propose a class name augment method based on hierarchy structure of classes. Specifically, we first employ WordNet [28] to extract the subclass names of external base class names $(CN^{EB})$ as hierarchically augmented class names $(CN^{HA})$ .", + "bbox": [ + 75, + 212, + 472, + 348 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC N ^ {H A} = h y p o n y m s \\left(C N ^ {E B}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 359, + 468, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where hyponyms denotes the mapping function for extracting hyponyms using WordNet [28]. The semantic information $A^{HA} \\in \\mathbb{R}^{C^{HA} \\times d^a}$ of the $CN^{HA}$ can be extracted by the language model, i.e., $A^{HA} = LM(CN^{HA})$ . $C^{HA}$ denotes the number of the augmented class names.", + "bbox": [ + 75, + 383, + 468, + 458 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then we can obtain the predicted probability $l^{HA} \\in \\mathbb{R}^{C^{HA} \\times C^{PR}}$ of the augmented classes as follows:", + "bbox": [ + 76, + 458, + 468, + 492 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nl ^ {H A} = S C \\left(S 2 V \\left(A ^ {H A}\\right)\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 497, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S2V$ and $SC$ is the semantic-to-visual ( $S2V$ ) subnetwork and the semantic classifier ( $SC$ ), respectively. Considering that the subclass is one of the parent classes, we assign the label of the corresponding parent class as the label of the subclass. For example, fire ant is the subclass of ant, and thus the label of fire ant $y^{fire-ant}$ is assigned as the label of ant in the pretraining large-scale dataset, i.e., $y^{fire-ant} = y^{ant} = CN2Y(ant)$ . Based on the idea, the label $Y^{HA}$ of $CN^{HA}$ can be obtained as follows:", + "bbox": [ + 75, + 521, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nY ^ {H A} = C N 2 Y \\left(h y p e r n y m s \\left(C N ^ {H A}\\right)\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 662, + 468, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where hypernyms denotes the mapping function for extracting hypernyms using WordNet [28], $CN2Y$ is the dictionary mapping from class names to labels in the largescale dataset corresponding to the pretrained backbone.", + "bbox": [ + 75, + 688, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the Cross-Entropy (CE) Loss is adopted to obtain the loss of hierarchy taxonomy enhancement:", + "bbox": [ + 75, + 750, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {H A} = \\mathcal {L} _ {C E} (\\sigma (l ^ {H A}), Y ^ {H A}). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 784, + 468, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training and Inference", + "text_level": 1, + "bbox": [ + 76, + 809, + 290, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed DSECN, which contains three components, is trained in an end-to-end manner, and the total loss function is given as follows:", + "bbox": [ + 75, + 832, + 468, + 878 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {V} + \\lambda_ {E B} \\mathcal {L} _ {E B} + \\lambda_ {H A} \\mathcal {L} _ {H A}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Training Process of DSECN" + ], + "code_body": "Input: Training seen data $\\{X_{tr}^{s},CN^{s},Y_{tr}^{s}\\}$ , external base class names $C N^{E B}$ and hierarchy augmented class names $CN^{HA}$ \nOutput: The final S2V model \n// Generate Semantics and Labels \n $A^s,A^{EB},A^{HA} = LM(CN^s,CN^{EB},CN^{HA})$ $Y^{EB}\\gets \\{CNEB\\}$ in Eq.(7), \n $Y^{HA}\\leftarrow \\{CN^{HA}\\}$ in Eq.(11). \nfor $e = 1,2,\\ldots ,E$ do \n// Visual Flow \n $V^{s} = S2V(A^{s})$ $l^s\\gets \\{V^s,X_{tr}^s\\}$ in Eq.(2), \n $\\mathcal{L}_V\\gets \\{l^s,Y_{tr}^s\\}$ in Eq.(3). \n// Diverse Semantic Enhancement \n $V^{EB} = S2V(A^{EB})$ $l^{EB} = SC(V^{EB})$ $\\mathcal{L}_{EB}\\gets \\{l^{EB},Y^{EB}\\}$ in Eq.(8). \n// Hierarchy Taxonomy Enhancement \n $V^{HA} = S2V(A^{HA})$ $l^{HA} = SC(V^{HA})$ $\\mathcal{L}_{HA}\\gets \\{l^{HA},Y^{HA}\\}$ in Eq.(12). \n// Compute Total Loss \n $\\mathcal{L}_{total} = \\mathcal{L}_V + \\mathcal{L}_{EB} + \\mathcal{L}_{HA}$ \n// Update Parameters \nUpdate the parameters of S2V using Adam.", + "bbox": [ + 519, + 112, + 841, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end", + "bbox": [ + 521, + 465, + 547, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{EB}$ and $\\lambda_{HA}$ are trade-off hyper-parameters. The training pseudo-code is presented in Algorithm 1. It is noteworthy that we only update the parameters of $S2V$ .", + "bbox": [ + 498, + 511, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the inference phase, given a visual feature $x$ and the semantic feature $A$ of all classes, we apply the visual flow to obtain the final class prediction $\\hat{y}$ . Specifically, the semantic features $A = A^s \\cup A^u$ of all classes are first fed into $S2V$ sub-network to generate the class-level visual prototype, i.e., $V = S2V(A)$ . Then the final class prediction can be obtained according to:", + "bbox": [ + 498, + 556, + 890, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\underset {y \\in \\mathcal {Y}} {\\arg \\max } \\left(\\operatorname {s o f t m a x} \\left(\\gamma^ {2} \\frac {x V ^ {\\top}}{\\| x \\| \\| V \\|}\\right)\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 672, + 890, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{Y} = Y^{s}\\cup Y^{u}$ is the union of seen classes $Y^{s}$ and unseen classes $Y^{u}$ .", + "bbox": [ + 498, + 715, + 890, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Integrating into Existing GZSL Methods", + "text_level": 1, + "bbox": [ + 498, + 756, + 848, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed DSECN can be easily integrated into other mainstream GZSL approaches to improve their robustness for dissimilar unseen classes. The GZSL method essentially models the relationship between visual and semantic features, so that semantic features can be used as a bridge to accurately classify visual features of unseen classes. DSECN can effectively build such relationship between \"diverse\" semantic and visual features at low cost, and thus signif", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23348", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "icantly improving the performance of existing GZSL approaches. Taking generative-based methods as an example, the generator can generate visual features of the introduced diverse semantic from external class names. Then the pretrained classification head is used to align the generated visual features to visual space. This enables the generator to adapt to more classes and generate more accurate visual features for unseen classes. Finally, the refined visual features of unseen classes are used to train the GZSL classifier, thus improving the model performance. More details on the integration of our idea with the generative-based methods and other types of GZSL approaches can be found in the supplementary material A.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 304, + 209, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 76, + 329, + 277, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We conduct our experiments on three widely used ZSL benchmark datasets, which are AWA2 [46], CUB [40] and SUN [33]. Since the main focus of this work is to study the more practical GZSL setting that includes both similar and dissimilar unseen classes, the learned GZSL model needs to recognize the dissimilar unseen classes from other datasets. Hence, we do not use the human-annotated attributes, but rather use language models, e.g., W2V [27] and CLIP [35], to extract the semantic embedding of classes.", + "bbox": [ + 75, + 353, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation. Unlike most existing methods that only consider similar settings, we comprehensively evaluate the GZSL model on three testing settings, including similar, dissimilar and practical settings. To better describe these settings, we define the set of datasets as $Set = \\{AWA2, CUB, SUN\\}$ . The dataset of seen classes and unseen classes are respectively expressed as $ds$ and $du$ , where $ds \\subseteq Set$ and $du \\subseteq Set$ . To simulate the similar scene, the dataset $ds$ of seen classes is same as the dataset $du$ of unseen classes, i.e., $ds = du$ . To simulate the dissimilar scene, we use the complementary set of $ds$ as $du$ , i.e., $du = \\complement_{Set} ds$ . For practical scene, the unseen classes may either be similar or dissimilar to the seen classes. Therefore, in our practical setting, we use all datasets to evaluate unseen classes, i.e., $du = Set$ . For all three settings, we follow [46] to evaluate model for both ZSL and GZSL. In the ZSL, the average per-class top-1 accuracy ( $T$ ) on unseen classes is taken as the evaluation metric. In the GZSL, the evaluation metric is the harmonic mean $H$ between seen classes accuracy $S$ and unseen class accuracy $U$ , i.e., $H = (2 \\times U \\times S) / (U + S)$ .", + "bbox": [ + 75, + 506, + 472, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. The implementation details are provided in the supplementary material B.", + "bbox": [ + 75, + 824, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fair-comparison Guarantee. All methods are trained on seen class images of the training set $D_{tr}^{s}$ , ensuring that the labeled training data are the same for different approaches.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "They all adopt the same backbone weights pretrained on large-scale dataset, which means that the pre-training data implicitly utilized by the model is completely consistent. They all use the same language model to extract semantic features, ensuring the fairness of the semantic extraction method. Therefore, the same data are utilized for different methods, and the fairness of comparison is guaranteed. Notably, introducing additional information is a common strategy to mitigate bias issue in GZSL. For example, generative-based GZSL methods [2, 16] introduce semantic information of test unseen classes to mitigate bias. The transductive GZSL methods [1, 41, 44] utilize test unseen class samples to mitigate bias. Unlike these methods, our method does not utilize any semantic or sample information of test unseen classes, thus making our method more suitable for practical GZSL.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 498, + 343, + 803, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance. We comprehensively compare our method with several SOTA GZSL approaches on the similar, dissimilar, and practical settings. Tab. 1 shows that: 1) the performance of all counterparts in identifying dissimilar unseen classes is very poor, which proves that existing models have difficulty in identifying common dissimilar unseen classes in the real world; 2) our method achieves the SOTA performance on all datasets, semantic embeddings and settings, which demonstrates the effectiveness of our method. In particular, our method significantly outperforms all counterparts under dissimilar and practical settings. Take the CUB dataset under dissimilar setting as an example, our method outperforms the most competitive counterpart by $21.76\\%$ and $35.14\\%$ on the W2V [27] and CLIP text embedding [35], respectively.", + "bbox": [ + 496, + 367, + 890, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Efficiency. We conduct training efficiency comparison experiments on all datasets using CLIP [35] text embedding. Tab. 2 reports the training time of each method. Benefiting from the simple network design, the training costs of CN and the proposed method are much lower than other approaches. Although our method is slightly slower than the CN method because of the introducing semantics from external class names, our method can be trained within one minute.", + "bbox": [ + 496, + 594, + 890, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 739, + 653, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the benefits of tackling GZSL with the diverse semantic enhancement (DSE) and the hierarchy taxonomy enhancement (HTE), we conduct an ablation study on all semantics, datasets and settings. The results using CLIP [35] and W2V [27] semantic embedding are reported in Fig. 3 and Fig. S3 of supplementary material C, respectively. From these results, we can see that: 1) regardless of W2V or CLIP semantic representation, the baseline model $b$ has poor recognition performance on dissimilar unseen classes.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23349", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6f725f0c8ae2d3fd3901cffc770e0e083ab0a17ec86ae363318df89151d12ab5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Train DataMethodsW2VCLIP
SimilarDissimilarPracticalSimilarDissimilarPractical
ZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSL
CUB\\( ZLA^†[IJCAI22] [4] \\)17.2416.033.356.007.4111.0446.5642.654.668.5219.3224.89
\\( DGZ^†[AAAI23] [5] \\)18.0018.423.245.675.477.4247.1243.167.1512.3020.6126.60
\\( CN^‡[ICLR21] [38] \\)18.1622.101.122.035.698.7443.7442.503.825.0917.8123.25
\\( TransZero^‡[AAAI22] [9] \\)17.1515.650.900.866.496.4149.7747.993.562.4719.1824.81
\\( MSDN^‡[CVPR22] [10] \\)18.3018.461.733.334.846.4449.1747.692.652.7918.6023.40
\\( HASZSL^‡[MM23] [11] \\)13.4616.911.042.035.266.7542.5143.642.172.8116.2617.12
DSECN (Ours)18.8023.4017.7327.7617.8123.6350.7048.4535.5447.4440.8545.29
AWA2\\( ZLA^†[IJCAI22] [4] \\)49.7854.653.416.214.678.2076.5975.095.159.329.2514.87
\\( DGZ^†[AAAI23] [5] \\)54.5957.023.125.874.848.5478.2776.597.0312.5910.3017.26
\\( CN^‡[ICLR21] [38] \\)41.1249.621.662.763.476.3079.4573.385.489.958.6014.72
\\( TransZero^‡[AAAI22] [9] \\)39.7042.901.071.943.345.3069.5859.782.113.942.674.79
\\( MSDN^‡[AAAI22] [9] \\)45.9048.521.632.523.475.0564.4264.213.666.035.899.46
\\( HASZSL^‡[MM23] [11] \\)36.5945.040.880.981.261.0660.3456.066.767.7337.9537.25
DSECN (Ours)69.2370.7111.2119.8814.3723.7986.9781.2837.0152.5240.0053.74
SUN\\( ZLA^†[IJCAI22] [4] \\)33.5423.909.1213.0618.7018.8654.6536.708.5211.7931.5928.31
\\( DGZ^†[IJCAI22] [4] \\)31.3225.089.3113.7617.5317.8553.5437.7311.8717.4931.6128.31
\\( CN^‡[ICLR21] [38] \\)33.8226.275.177.0518.8018.1455.5638.879.6913.6432.8030.00
\\( TransZero^‡[AAAI22] [9] \\)30.4221.813.682.6616.6914.6354.5135.865.282.8929.9825.39
\\( MSDN^‡[AAAI22] [9] \\)28.1316.231.512.789.967.5853.3331.735.578.2028.3122.56
\\( HASZSL^‡[MM23] [11] \\)19.5111.413.720.1210.691.4136.5321.154.570.1220.028.34
DSECN (Ours)37.8526.8110.5416.4724.1921.6960.2840.3337.1140.1949.1038.54
", + "bbox": [ + 80, + 88, + 885, + 431 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3061b91c6d49cab246c0bd8f4e276685c61e9ef4710d7f2f7301a7684d24286.jpg", + "image_caption": [ + "Figure 3. Effect of diverse semantic enhancement $(s)$ and hierarchy taxonomy enhancement $(h)$ for GZSL. We remove these two components as our baseline $(b)$ . In the ablation study, we add DSE $(s)$ and HTE $(h)$ step by step to show their effect on GZSL. Refer to § 4.3." + ], + "image_footnote": [], + "bbox": [ + 89, + 463, + 339, + 614 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/deae76973fc78c7ee8939f5633c96404f4a89cbd7dbf1acebb7601704e195b1e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 463, + 612, + 614 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cece79792b9fd0202a37c48acb8dbc8fc2582ad9914b66b91e5554f4d43ba8be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 463, + 883, + 614 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1255569b10afdefaa70f057e81d229e13a70cb855aece09f92a19547844f9471.jpg", + "table_caption": [ + "Table 1. Comparison with the state-of-the-art GZSL approaches in the three settings, † and ‡ signify the generative-based method and embedding-based approach. Please see details in § 4.2." + ], + "table_footnote": [], + "table_body": "
MethodsCUBAWA2SUNMean
ZLA* [4]4.4 hours9.5 hours7.7 hours7.2 hours
DGZ* [5]8.3 hours12.2 hours16.1 hours12.2 hours
CN* [38]8.6 sec25.8 sec12.2 sec15.5 sec
TransZero° [9]40.7 min2.0 hours1.6 hours1.4 hours
MSDN° [10]4.4 min21.9 min14.5 min13.6 min
HAS° [11]5.4 hours17.3 hours7.4 hours10.0 hours
DSECN* (Ours)13.9 sec37.9 sec19.7 sec23.8 sec
", + "bbox": [ + 78, + 651, + 477, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Training time for the recent GZSL methods that made their official implementations publicly available. * and $\\diamond$ respectively indicate that the model uses the 2048-dimensional vector and ${14} \\times {14} \\times {2048}$ -dimensional feature map extracted by pretrained Resnet101 as input. $\\bullet$ denotes that the model takes original image as input and finetunes the pretrained backbone. See § 4.2.", + "bbox": [ + 75, + 770, + 468, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This indicates that the problem of identifying dissimilar unseen classes cannot be solved by enhancing the semantic information contained in seen classes; 2) after adding DSE", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$s$ and HTE $h$ to the baseline, the $b + s + h$ model achieves the best performance on all semantics, datasets and settings. This proves that both the DSE $s$ and the HTE $h$ are critical to GZSL and complementary to each other on all three test settings; 3) the less similar the unseen classes are to the seen classes in the test setting, the greater the performance improvement gain brought by the proposed module $s$ and $h$ . Taking the CUB dataset with CLIP semantic embedding as an example, $b + s + h$ improves the harmonic mean accuracy by $42.38\\%$ , $21.76\\%$ , and $4.73\\%$ on dissimilar, practical and similar settings, respectively. This may be because when the unseen classes are dissimilar to seen classes, the baseline model can only transfer little information from seen classes to unseen classes, while $b + s + h$ introduces a variety of semantic information from class names that can be transferred to unseen classes to improve the recognition performance of", + "bbox": [ + 496, + 655, + 890, + 896 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23350", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ac42e8e3cda92354cef98a55d08b7ed9b05dee3f07367e78833972354d88d35f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsCUBAWA2SUN
W2VCLIPW2VCLIPW2VCLIP
CN [38]2.035.092.769.957.0513.64
CN+DSECN22.0837.6814.3533.0412.6429.11
TransZero [9]0.862.471.943.942.662.89
TransZero+DSECN2.414.442.515.413.593.02
DGZ [5]5.6712.305.8712.5913.7617.49
DGZ+DSECN26.3448.3917.0247.6817.7639.11
", + "bbox": [ + 91, + 88, + 452, + 207 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8c6688478614c4f9c0cada279a6ed9a79900d5ead3e0bbb35a40da65e12071b7.jpg", + "table_caption": [ + "Table 3. Effect of integrating DSECN into existing GZSL methods under dissimilar setting. CN [38], TransZero [9], and DGZ [5] belong to the global embedding-based, local embedding-based, and generation-based GZSL methods respectively. See details in § 4.4." + ], + "table_footnote": [], + "table_body": "
SemanticsMethodsCUBAWA2SUN
1K21K1K21K1K21K
W2Vb2.961.965.512.8211.175.50
b+s+h27.7656.9719.8840.6816.4728.24
↑24.8055.0114.3737.865.3022.74
CLIPb5.066.877.747.9412.6615.55
b+s+h47.4477.6052.5271.2540.1961.59
↑42.3870.7344.7863.3127.5346.04
", + "bbox": [ + 81, + 263, + 460, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Effect of the number of external class names. $\\uparrow$ signifies the performance improvement. Please see § 4.5 for details.", + "bbox": [ + 76, + 383, + 467, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "unseen classes. Furthermore, we also qualitatively analyzed the reasons why the proposed module is effective in the supplementary materials D.", + "bbox": [ + 76, + 422, + 467, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Integration with other GZSL Approaches", + "text_level": 1, + "bbox": [ + 76, + 494, + 431, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have integrated DSECN into three mainstream GZSL methods and analysed the effect of integrating DSECN. From the results in Tab. 3, we can observe that: 1) benefiting from the introduction of diverse semantic information from class names (DSECN), the performance of global embedding-based (CN) and generative-based methods (DGZ) is significantly improved. For example, when unseen classes are not similar to seen classes, DSECN improves DGZ's GZSL performance by $20.67\\%$ in the CUB dataset using W2V [27] embedding. This proves that the DSECN can be integrated into existing global embedding-based and generative-based GZSL methods to improve the model's robustness to dissimilar unseen classes; 2) the improvement with the local embedding-based GZSL method (TransZero) is smaller than that of global embedding-based and generative-based methods. This may be attributed to the fact that the performance improvement of integrating DSECN is limited by the accuracy of the generated visual feature maps. It is challenging to accurately generate not visible visual feature maps from semantic vectors, which is why existing generative-based GZSL methods mostly generate global visual features rather than local visual features. Overall, the proposed DSECN can easily be integrated into existing mainstream GZSL methods to improve the robustness for dissimilar unseen classes.", + "bbox": [ + 76, + 523, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Effect of the External Class Name Number", + "text_level": 1, + "bbox": [ + 500, + 90, + 864, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To investigate the effect of the ECN number on identifying dissimilar unseen classes, we introduce the class names from ImageNet-1K and ImageNet-21K separately as the external base class names, and then remove the unseen class names from the external class names. Notably, we use the ResNet101 pretrained on ImageNet-21K when introducing ImageNet-21K class names. The results are shown in Tab. 4. We can observe that as the introduced ECN increases, performance of the model improves significantly. This proves that increasing the ECN is important to improve the performance of dissimilar unseen class recognition.", + "bbox": [ + 496, + 114, + 890, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 297, + 619, + 313 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce and investigate the practical GZSL setting, where unseen classes can be either similar and dissimilar to seen classes. We empirically show that existing GZSL methods are difficult in identifying dissimilar unseen classes, and propose a simple yet effective method, which exploits diverse semantics from external class names (DSECN), and is simultaneously robust for both similar and dissimilar unseen classes. From the results, we mainly conclude that: 1) the semantics contained in the external unseen class names are quite helpful to improve the generalization ability of GZSL approach; 2) It is critical to align the augmented semantics to their corresponding visual features. In the future, we intend to incorporate the proposed idea into more GZSL approaches and improve their performance.", + "bbox": [ + 496, + 324, + 890, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Potential Impacts. The existing GZSL methods perform poorly when unseen classes are dissimilar to seen classes, which hinders the practical application of the existing GZSL methods. The paper will help attract researchers' attention to dissimilar unseen classes and help the GZSL field develop in a more practical direction. In addition, the proposed DSECN is simultaneously robust on similar and dissimilar unseen classes, and can easily be integrated into other GZSL methods to improve their robustness for dissimilar unseen classes. This capability is beneficial for improving the practicality of the GZSL model. From an evaluation perspective, existing methods assess using visible and invisible classes from the same dataset. This leads to excessive focus on similar unseen classes during evaluation, thereby overestimating the generalizability of existing GZSL methods. In contrast, the cross-dataset evaluation protocol proposed in the paper can more comprehensively reflect the performance of existing GZSL methods on similar, dissimilar and practical settings.", + "bbox": [ + 496, + 537, + 890, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported by the National Key Research and Development Program of China 2023YFC2705700, National Natural Science Foundation of China under Grants 62225113 and 62276195, and Special Fund of Hubei Luojia Laboratory under Grant 220100014.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23351", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Liu Bo, Qiulei Dong, and Zhanyi Hu. Hardness sampling for self-training based transductive zero-shot learning. In CVPR, pages 16499-16508, 2021. 6", + "[2] Samet Cetin, Orhun Bugra Baran, and Ramazan Gokberk Cinbis. Closed-form sample probing for learning generative models in zero-shot learning. 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In CVPR, pages 6034-6042, 2016. 1" + ], + "bbox": [ + 501, + 90, + 890, + 330 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23353", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names/eeeede11-1438-46b6-b66c-0eb160635025_model.json b/2024/Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names/eeeede11-1438-46b6-b66c-0eb160635025_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7a569d2e78c20640be2c2809020ebb2de9160af9 --- /dev/null +++ b/2024/Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names/eeeede11-1438-46b6-b66c-0eb160635025_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.13, + 0.89, + 0.175 + ], + "angle": 0, + "content": "Improving Generalized Zero-Shot Learning by Exploring the Diverse Semantics from External Class Names" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.203, + 0.714, + 0.222 + ], + "angle": 0, + "content": "Yapeng Li\\(^{1}\\), Yong Luo\\(^{1,2}\\), Zengmao Wang\\(^{1}\\), Bo Du\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.222, + 0.877, + 0.274 + ], + "angle": 0, + "content": "\\(^{1}\\)National Engineering Research Center for Multimedia Software, Institute of Artificial Intelligence, Hubei Key Laboratory of Multimedia and Network Communication Engineering, School of Computer Science, Wuhan University, Wuhan, China." + }, + { + "type": "text", + "bbox": [ + 0.316, + 0.275, + 0.654, + 0.292 + ], + "angle": 0, + "content": "\\(^{2}\\) Hubei Luojia Laboratory, Wuhan, China." + }, + { + "type": "text", + "bbox": [ + 0.329, + 0.295, + 0.636, + 0.31 + ], + "angle": 0, + "content": "https://github.com/1i-yapeng/DSECN" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.474, + 0.741 + ], + "angle": 0, + "content": "Generalized Zero-Shot Learning (GZSL) methods often assume that the unseen classes are similar to seen classes, and thus perform poor when unseen classes are dissimilar to seen classes. Although some existing GZSL approaches can alleviate this issue by leveraging additional semantic information from test unseen classes, their generalization ability to dissimilar unseen classes is still unsatisfactory. This motivates us to study GZSL in the more practical setting, where unseen classes can be either similar or dissimilar to seen classes. In this paper, we propose a simple yet effective GZSL framework by exploring diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes. This is achieved by introducing diverse semantics from external class names and aligning the introduced semantics to visual space using the classification head of pre-trained network. Furthermore, we show that the design idea of DSECN can easily be integrate into other advanced GZSL approaches, such as the generative-based ones, and enhance their robustness for dissimilar unseen classes. Extensive experiments in the practical setting including both similar and dissimilar unseen classes show that our method significantly outperforms the state-of-the-art approaches on all datasets and can be trained very efficiently." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.772, + 0.21, + 0.788 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Due to the high cost of annotation and the complexity of real-world test scenarios, the presence of unseen classes is often inevitable [34, 43]. Unfortunately, traditional machine learning models are unable to handle samples from classes that have not been covered by the training data [8]." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.344, + 0.878, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.459, + 0.738, + 0.471 + ], + "angle": 0, + "content": "(a) Our Setting" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.472, + 0.908, + 0.521 + ], + "angle": 0, + "content": "
ModeCN [38]TransZero [9]ZLA [4]DGZ [5]Ours (Δ)
Similar42.5047.9942.6543.1648.45 (+0.46)
Dissimilar5.092.478.5212.3047.44 (+35.14)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.667, + 0.522, + 0.728, + 0.534 + ], + "angle": 0, + "content": "(b) Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.635 + ], + "angle": 0, + "content": "Figure 1. Setting illustration and results: (a) Comparison with the existing setting, our setting takes into account the scenario where the unseen classes are dissimilar to seen classes; (b) Performance of existing GZSL methods on similar and dissimilar unseen classes on the CUB dataset. The similar unseen classes were obtained from the same CUB dataset, while the dissimilar unseen classes come from AWA2 and SUN dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.894, + 0.734 + ], + "angle": 0, + "content": "To tackle this challenge, zero-shot learning (ZSL) has been proposed to recognize new classes via transferring knowledge obtained from seen classes with the help of semantic information [14, 15, 23, 52]. In contrast, Generalized ZSL (GZSL) is a more challenging task which handle test samples from both seen and unseen classes [3, 25, 29, 34]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The core idea of GZSL is to introduce auxiliary semantic information and establish the connection between semantic and visual space for the recognition of unseen classes [34]. Since unseen samples are not available during training, existing GZSL models often misclassify unseen class samples into seen classes during test (known as the bias issue) [21, 22]. To alleviate this issue, several strategies have been introduced. A common strategy is to utilize a backbone pre-trained on the ImageNet-1K dataset [13] to extract visual features [7, 24, 26, 36, 50], which is beneficial to improve the generalization ability of visual features. However," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.358, + 0.901 + ], + "angle": 0, + "content": "*Corresponding authors: Zengmao Wang, Bo Du" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23344" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.408 + ], + "angle": 0, + "content": "the rich semantics that implicitly contained in the backbone classification heads are simply ignored in these approaches, and thus their ability to exploit diverse semantics is limited. Generative-based GZSL methods [4-6, 16, 51] alleviate the bias problem by introducing the semantics from test unseen classes, and some semantic augmentation approaches focus on enhancing the semantics of each class by leveraging the textual documents [30], large language model [31], etc [19, 50]. However, these approaches share a common limitation that they heavily rely on the semantics and visual features from seen classes to build the relations between visual and semantic space. This makes these models perform poorly on dissimilar unseen classes (see Fig. 1b), as little information can be transferred from seen to dissimilar unseen classes. That is, these methods can only deal with the unrealistic setting that the unseen classes are similar with seen classes (see existing setting of Fig. 1a). However, it is inevitable that unseen classes may be quite different from seen classes in the real-world applications, and hence it is desirable to enhance GZSL models to effectively handle dissimilar unseen classes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.473, + 0.775 + ], + "angle": 0, + "content": "To achieve this goal, we need to address three main challenges: (I) how to obtain the information that can be transferred to dissimilar unseen classes; (II) how to enable effective information transfer without labeled training data; and (III) how to reduce costs as much as possible while ensuring effectiveness. If the cost of the solution exceeds the cost of collecting the data and retraining the model, then such a solution would be meaningless. Therefore, we propose a simple yet effective GZSL framework by exploring Diverse Semantics from External Class Names (DSECN), which is robust on both the similar and dissimilar unseen classes. Specifically, we introduce the diverse semantics from external (not test unseen classes) class names as the bridge to reduce the gap between the seen and unseen classes, which is beneficial for the recognition of unseen classes (challenge I). Then we utilize the classification head pre-trained on large-scale dataset, e.g., ImageNet-1K [13], to align the introduced semantics to the visual space (challenge II). Finally, the hierarchical taxonomy of WordNet [28] for the classes in large-scale dataset is introduced to further improve the diversity of semantics from class names. Since the class name and pre-trained classification head are quite easy to collect, the cost of our method is quite low (challenge III)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.777, + 0.464, + 0.793 + ], + "angle": 0, + "content": "To summarize, the main contributions of this paper are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.796, + 0.47, + 0.841 + ], + "angle": 0, + "content": "- To the best of our knowledge, we are the first that explicitly study the realistic GZSL setting that both similar and dissimilar unseen classes exist (see our setting in Fig. 1a)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.841, + 0.47, + 0.9 + ], + "angle": 0, + "content": "- We propose a GZSL method that explores the diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.796, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "- We show that the proposed idea can be easily integrated into other GZSL approaches, such as generative-based ones, and improve their robustness for dissimilar unseen classes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.153, + 0.894, + 0.243 + ], + "angle": 0, + "content": "We conduct extensive experiments on diverse real-world datasets. The results show that in the practical setting including both similar and dissimilar unseen classes, the harmonic mean accuracies of our method significantly outperform all counterparts. Besides, our model can be trained within one minute on all three datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.258, + 0.642, + 0.274 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.284, + 0.783, + 0.3 + ], + "angle": 0, + "content": "2.1. Generalized Zero-shot Learning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.307, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Existing GZSL methods can be broadly categorized into embedding-based [9, 18, 25, 38] and generative-based ones [2, 5, 12, 16]. Early global embedding-based methods [15, 18, 25, 38, 45] align global visual features with corresponding category semantic information into a common embedding space, which enables knowledge transfer from seen to unseen classes. Recently proposed local embedding-based methods [9-11, 42, 48, 49] utilize attribute descriptions as guidance to discover the discriminative local features between seen classes and unseen classes. Besides, generative-based methods [4, 5, 12, 37, 38, 47] introduce the semantic from test unseen classes to alleviate the bias problem in GZSL [34]. However, these methods focus on the unrealistic setting where unseen classes are assumed to be similar to seen classes, and perform poorly in identifying dissimilar unseen classes. In contrast, our work focuses on a realistic GZSL setting that includes both similar and dissimilar unseen classes, and the proposed DSECN can robustly identify similar and dissimilar unseen classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.785, + 0.62 + ], + "angle": 0, + "content": "2.2. Semantic Information for GZSL" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Semantic information is a bridge that transfers knowledge from seen classes to unseen class recognition and is crucial to GZSL [30, 34, 50]. Most of prior works rely on human-annotated attributes [2, 32, 49] or word vectors [20, 39] as the semantic information. While attributes are accurate, they are costly to annotate and are not suitable for a large-scale problem [20, 50]. In contrast, word vectors require less human labor and are suitable for large-scale datasets [34]. However, word vectors often do not reflect visual similarities, thus limiting the performance [30, 49]. Xu et al. [49] propose a visually-grounded semantic embedding (VGSE) network to discover semantic embeddings containing discriminative visual properties. Naeem et al. [30] propose a transformer-based model I2DFormer that learns semantic embeddings from raw online textual documents. However, these methods only consider semantic enhancement within a single category. When an unseen class is dissimilar to seen classes, the transferable semantic infor" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23345" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "mation from seen classes is still little, which limits their performance. In contrast, we introduce diverse semantic information from external category names and align the introduced semantics into visual space using the classification head pre-trained on a large-scale dataset , thus assisting in the identification of dissimilar unseen categories." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.197, + 0.251, + 0.214 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.473, + 0.593 + ], + "angle": 0, + "content": "Problem Formulation. In ZSL and GZSL, we define two sets of classes: seen classes in \\( Y^s \\) and unseen classes in \\( Y^u \\). The seen classes \\( Y^s \\) and the unseen classes \\( Y^u \\) are disjoint, i.e., \\( Y^s \\cap Y^u = \\emptyset \\) and \\( Y^s \\cup Y^u = \\mathcal{Y} \\). The unseen classes may be similar or dissimilar to seen classes in practice. Hence, in this work, the unseen classes \\( Y^u \\) contain similar unseen classes \\( Y_s^u \\) and dissimilar unseen classes \\( Y_d^u \\), i.e., \\( Y^u = Y_s^u \\cup Y_d^u \\). The seen data are expressed as \\( D^s = \\{(x_i^s, y_i^s)\\} \\), where \\( x_i^s \\in X \\) indicates the \\( i \\)-th sample features extracted by the pretrained backbone network, e.g., ResNet101 [17], and \\( y_i^s \\in Y^s \\) is its class label. The \\( D^s \\) is split into a training set \\( D_{tr}^s \\) and a testing set \\( D_{te}^s \\). On the other hand, the unseen data are denoted as \\( D^u = \\{(x_i^u, y_i^u)\\} \\), where \\( x_i^u \\in X^u \\) and \\( y_i^u \\in Y^u \\) are the sample features of unseen classes and the corresponding ground-truth label for evaluation, respectively. The goal of ZSL is to learn a classifier for classifying test samples from unseen classes, i.e., \\( X \\xrightarrow{f_{ZSL}} Y^u \\). In contrast to ZSL, the goal of GZSL is to learn a classifier for classifying test samples from both seen and unseen classes, i.e., \\( X \\xrightarrow{f_{GZSL}} Y^s \\cup Y^u \\). In ZSL and GZSL, the auxiliary semantic information \\( A \\) is obtained by transforming the class labels \\( \\mathcal{V} \\) using human-annotated attributes [9] or language models [27, 35]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Overview of framework. As shown in Fig. 2, the framework contains three components: visual flow (§ 3.1), diverse semantic enhancement (DSE, § 3.2), and hierarchy taxonomy enhancement (HTE, § 3.3). The visual flow aligns seen class semantics into visual space. Diverse semantic and hierarchy taxonomy enhancement are proposed to enhance the diversity of semantics available to the model, thereby assisting the identification of dissimilar unseen classes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.205, + 0.74 + ], + "angle": 0, + "content": "3.1. Visual Flow" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "The visual flow is designed to classify visual objects from both seen and unseen classes by transferring knowledge from the seen classes to the unseen ones with the help of semantic information. The visual flow contains two parts: semantic-to-visual sub-network \\((S2V)\\) and visual classifier. The \\(S2V\\) sub-network is a learnable multilayer perceptron (MLP), and is used to link the semantic and visual representation. This enables the model to transfer the knowledge from seen classes to the unseen classes through semantic information. The visual classifier uses the relation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "ship between the visual sample and all categories to obtain the classification result of the sample. Because the visual flow requires paired visual samples and category labels, in the training phase, the visual flow can only be trained on the paired visual feature and label dataset \\( D_{tr}^{s} \\). Specifically, the \\( S2V \\) sub-network takes the seen semantic feature \\( A^{s} \\) as input to generate the class-level visual prototype of seen classes \\( V^{s} \\). The process to generate the class-level visual prototype of seen classes \\( V^{s} \\) can be expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.24, + 0.892, + 0.261 + ], + "angle": 0, + "content": "\\[\nA ^ {s} \\in \\mathbb {R} ^ {C ^ {s} \\times d ^ {a}} \\xrightarrow {S 2 V} V ^ {s} \\in \\mathbb {R} ^ {C ^ {s} \\times d ^ {v}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.271, + 0.892, + 0.348 + ], + "angle": 0, + "content": "where \\( C^s, d^a, d^v \\) denote the number of seen classes, the dimensionality of semantic representation and the dimensionality of visual representation, respectively. \\( A^s \\) signifies the semantic representations of seen classes and is extracted by language models [27, 35]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Next, the visual classifier (VC) computes the scaled cosine similarity between the visual feature of seen classes \\( X_{tr}^{s} \\in \\mathbb{R}^{N_{tr}^{s} \\times d^{v}} \\) and the class-level visual feature of seen classes \\( V^{s} \\in \\mathbb{R}^{C^{s} \\times d^{v}} \\) as logits \\( l^{s} \\in \\mathbb{R}^{N_{tr}^{s} \\times C^{s}} \\), where \\( N_{tr}^{s} \\) is the number of seen class samples in the training set. Formally, the logits \\( l^{s} \\) can be obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.449, + 0.892, + 0.485 + ], + "angle": 0, + "content": "\\[\nl ^ {s} = \\gamma^ {2} \\frac {X _ {t r} ^ {s} V ^ {s} {} ^ {\\top}}{\\| X _ {t r} ^ {s} \\| \\| V ^ {s} \\|}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.494, + 0.68, + 0.508 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the scale factor." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Finally, we adopt the Cross-Entropy (CE) loss to update the visual flow:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.552, + 0.892, + 0.57 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {V} = \\mathcal {L} _ {C E} \\left(\\sigma \\left(l ^ {s}\\right), Y _ {t r} ^ {s}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.581, + 0.768, + 0.596 + ], + "angle": 0, + "content": "where \\(\\sigma\\) denotes the softmax function." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.78, + 0.621 + ], + "angle": 0, + "content": "3.2. Diverse Semantic Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Motivation of DSE. When the unseen classes are dissimilar with seen classes, the visual flow can transfer only little information from seen classes to unseen classes, resulting in poor recognition performance of unseen classes. Motivated by this, we propose the diverse semantic enhancement module, which introduces the semantic information from external class names to help the recognition of unseen classes. To successfully transfer semantic information to unseen classes, establishing a substantial linkage between the semantics inherent in class names and their corresponding visual features is imperative. Nonetheless, the visual feature of the class name is unknown, which poses the primary obstacle in leveraging semantics from class names to enhance Generalized Zero-Shot Learning (GZSL). Considering the visual representation \\( X \\) obtained through the pretrained backbone, e.g. ResNet101, on the large-scale dataset, we use the classification head corresponding to pretrained backbone as semantic classifier (SC) to constrain the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23346" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.887, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.467, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed DSECN framework. During the training phase, our method contains three components: visual flow, diverse semantic enhancement, and hierarchy taxonomy enhancement. In the visual flow, we employ the visual cosine classifier to align the semantics and visual features of seen classes. Then the diverse semantic enhancement and hierarchy taxonomy enhancement introduce more diverse information from the external base class names and the augmented class names. The introduced diverse semantics are aligned to the visual space using pre-trained classification head, which enables our model to learn a robust union space for both similar and dissimilar unseen classes. During the inference phase, benefiting from the learned union space that contains visual-semantic correspondence of diverse classes, the test image from dissimilar unseen classes can be accurately classified." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.628 + ], + "angle": 0, + "content": "generated class-level visual prototype of class names to visual space. Besides, the introduced semantics from class names should be diverse. Hence, we choose the class names of large-scale dataset to extract diverse semantics." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.47, + 0.691 + ], + "angle": 0, + "content": "Construction of DSE. We first introduce the class names \\(CN^{EB}\\) of large-scale dataset corresponding to pretrained network and extract the semantic information \\(A^{EB} \\in \\mathbb{R}^{C^{EB} \\times d^a}\\) of \\(CN^{EB}\\) using the Language Model (LM), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.705, + 0.47, + 0.723 + ], + "angle": 0, + "content": "\\[\nA ^ {E B} = L M \\left(C N ^ {E B}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.795 + ], + "angle": 0, + "content": "\\(C^{EB}\\) denotes the number of external base class names from the large-scale dataset. Then the semantic information \\(A^{EB}\\) are taken as the input of \\(S2V\\) sub-network to generate class-level visual prototype \\(V^{EB} \\in \\mathbb{R}^{C^{EB} \\times d^v}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.805, + 0.47, + 0.824 + ], + "angle": 0, + "content": "\\[\nV ^ {E B} = S 2 V \\left(A ^ {E B}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.836, + 0.47, + 0.883 + ], + "angle": 0, + "content": "Next, the generated visual prototype \\(V^{EB}\\) is fed into the semantic classifier (SC) to get the logits \\(l^{EB} \\in \\mathbb{R}^{C^{EB} \\times C^{PR}}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.884, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\nl ^ {E B} = S C (V ^ {E B}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.569, + 0.892, + 0.599 + ], + "angle": 0, + "content": "where \\(SC\\) is the frozen classification head from pretrained network. \\(C^{PR}\\) is the class number of pretraining dataset." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.599, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Due to the backbone pretrained in large-scale dataset, we can obtain the label of \\(CN^{EB}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.638, + 0.892, + 0.657 + ], + "angle": 0, + "content": "\\[\nY ^ {E B} = C N 2 Y \\left(C N ^ {E B}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.667, + 0.892, + 0.711 + ], + "angle": 0, + "content": "where \\(CN2Y\\) is the dictionary mapping from class names to labels in the large-scale dataset corresponding to the pretrained backbone." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.712, + 0.892, + 0.742 + ], + "angle": 0, + "content": "Finally, the Cross-Entropy (CE) Loss is adopted to update the diverse semantic enhancement module:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.752, + 0.892, + 0.77 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E B} = \\mathcal {L} _ {C E} (\\sigma (l ^ {E B}), Y ^ {E B}). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Comparison with Analogous Methods. The prevailing GZSL approach depends on transferring semantic knowledge from seen to unseen classes. However, these techniques falter in a realistic GZSL setting that encompasses both similar and dissimilar unseen classes. Our method introduces varied semantics derived from external class names and aligns them with the visual domain through a pre-trained classification head. This process allows our" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23347" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "model to leverage newly introduced semantics as a bridge connecting seen and dissimilar unseen classes, thus enhancing the identification of dissimilar unseen classes. Notably, the procurement cost of class names and pre-trained classification heads is low, rendering our approach more feasible in practice." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.189, + 0.388, + 0.207 + ], + "angle": 0, + "content": "3.3. Hierarchy Taxonomy Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.349 + ], + "angle": 0, + "content": "Chihuahua is a kind of pet dog, and the dog is also a kind of animal. That is, there is a hierarchical structure between different categories. Therefore, we can utilize the hierarchy structure of classes to augment more classes. Based on the assumption, we propose a class name augment method based on hierarchy structure of classes. Specifically, we first employ WordNet [28] to extract the subclass names of external base class names \\((CN^{EB})\\) as hierarchically augmented class names \\((CN^{HA})\\)." + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.361, + 0.47, + 0.381 + ], + "angle": 0, + "content": "\\[\nC N ^ {H A} = h y p o n y m s \\left(C N ^ {E B}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.459 + ], + "angle": 0, + "content": "where hyponyms denotes the mapping function for extracting hyponyms using WordNet [28]. The semantic information \\(A^{HA} \\in \\mathbb{R}^{C^{HA} \\times d^a}\\) of the \\(CN^{HA}\\) can be extracted by the language model, i.e., \\(A^{HA} = LM(CN^{HA})\\). \\(C^{HA}\\) denotes the number of the augmented class names." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.459, + 0.47, + 0.493 + ], + "angle": 0, + "content": "Then we can obtain the predicted probability \\( l^{HA} \\in \\mathbb{R}^{C^{HA} \\times C^{PR}} \\) of the augmented classes as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.498, + 0.469, + 0.517 + ], + "angle": 0, + "content": "\\[\nl ^ {H A} = S C \\left(S 2 V \\left(A ^ {H A}\\right)\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.658 + ], + "angle": 0, + "content": "where \\( S2V \\) and \\( SC \\) is the semantic-to-visual (\\( S2V \\)) subnetwork and the semantic classifier (\\( SC \\)), respectively. Considering that the subclass is one of the parent classes, we assign the label of the corresponding parent class as the label of the subclass. For example, fire ant is the subclass of ant, and thus the label of fire ant \\( y^{fire-ant} \\) is assigned as the label of ant in the pretraining large-scale dataset, i.e., \\( y^{fire-ant} = y^{ant} = CN2Y(ant) \\). Based on the idea, the label \\( Y^{HA} \\) of \\( CN^{HA} \\) can be obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.664, + 0.47, + 0.683 + ], + "angle": 0, + "content": "\\[\nY ^ {H A} = C N 2 Y \\left(h y p e r n y m s \\left(C N ^ {H A}\\right)\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.749 + ], + "angle": 0, + "content": "where hypernyms denotes the mapping function for extracting hypernyms using WordNet [28], \\(CN2Y\\) is the dictionary mapping from class names to labels in the largescale dataset corresponding to the pretrained backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Finally, the Cross-Entropy (CE) Loss is adopted to obtain the loss of hierarchy taxonomy enhancement:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.785, + 0.469, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {H A} = \\mathcal {L} _ {C E} (\\sigma (l ^ {H A}), Y ^ {H A}). \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.81, + 0.292, + 0.827 + ], + "angle": 0, + "content": "3.4. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.833, + 0.469, + 0.879 + ], + "angle": 0, + "content": "The proposed DSECN, which contains three components, is trained in an end-to-end manner, and the total loss function is given as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {V} + \\lambda_ {E B} \\mathcal {L} _ {E B} + \\lambda_ {H A} \\mathcal {L} _ {H A}, \\tag {13}\n\\]" + }, + { + "type": "code_caption", + "bbox": [ + 0.511, + 0.095, + 0.794, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Training Process of DSECN" + }, + { + "type": "algorithm", + "bbox": [ + 0.52, + 0.113, + 0.842, + 0.467 + ], + "angle": 0, + "content": "Input: Training seen data \\(\\{X_{tr}^{s},CN^{s},Y_{tr}^{s}\\}\\) , external base class names \\(C N^{E B}\\) and hierarchy augmented class names \\(CN^{HA}\\) \nOutput: The final S2V model \n// Generate Semantics and Labels \n\\(A^s,A^{EB},A^{HA} = LM(CN^s,CN^{EB},CN^{HA})\\) \n\\(Y^{EB}\\gets \\{CNEB\\}\\) in Eq.(7), \n\\(Y^{HA}\\leftarrow \\{CN^{HA}\\}\\) in Eq.(11). \nfor \\(e = 1,2,\\ldots ,E\\) do \n// Visual Flow \n\\(V^{s} = S2V(A^{s})\\) \n\\(l^s\\gets \\{V^s,X_{tr}^s\\}\\) in Eq.(2), \n\\(\\mathcal{L}_V\\gets \\{l^s,Y_{tr}^s\\}\\) in Eq.(3). \n// Diverse Semantic Enhancement \n\\(V^{EB} = S2V(A^{EB})\\) \n\\(l^{EB} = SC(V^{EB})\\) \n\\(\\mathcal{L}_{EB}\\gets \\{l^{EB},Y^{EB}\\}\\) in Eq.(8). \n// Hierarchy Taxonomy Enhancement \n\\(V^{HA} = S2V(A^{HA})\\) \n\\(l^{HA} = SC(V^{HA})\\) \n\\(\\mathcal{L}_{HA}\\gets \\{l^{HA},Y^{HA}\\}\\) in Eq.(12). \n// Compute Total Loss \n\\(\\mathcal{L}_{total} = \\mathcal{L}_V + \\mathcal{L}_{EB} + \\mathcal{L}_{HA}\\) \n// Update Parameters \nUpdate the parameters of S2V using Adam." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.467, + 0.548, + 0.477 + ], + "angle": 0, + "content": "end" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.512, + 0.892, + 0.557 + ], + "angle": 0, + "content": "where \\(\\lambda_{EB}\\) and \\(\\lambda_{HA}\\) are trade-off hyper-parameters. The training pseudo-code is presented in Algorithm 1. It is noteworthy that we only update the parameters of \\(S2V\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.558, + 0.892, + 0.664 + ], + "angle": 0, + "content": "In the inference phase, given a visual feature \\( x \\) and the semantic feature \\( A \\) of all classes, we apply the visual flow to obtain the final class prediction \\( \\hat{y} \\). Specifically, the semantic features \\( A = A^s \\cup A^u \\) of all classes are first fed into \\( S2V \\) sub-network to generate the class-level visual prototype, i.e., \\( V = S2V(A) \\). Then the final class prediction can be obtained according to:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.673, + 0.892, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\underset {y \\in \\mathcal {Y}} {\\arg \\max } \\left(\\operatorname {s o f t m a x} \\left(\\gamma^ {2} \\frac {x V ^ {\\top}}{\\| x \\| \\| V \\|}\\right)\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.717, + 0.892, + 0.748 + ], + "angle": 0, + "content": "where \\(\\mathcal{Y} = Y^{s}\\cup Y^{u}\\) is the union of seen classes \\(Y^{s}\\) and unseen classes \\(Y^{u}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.849, + 0.774 + ], + "angle": 0, + "content": "3.5. Integrating into Existing GZSL Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The proposed DSECN can be easily integrated into other mainstream GZSL approaches to improve their robustness for dissimilar unseen classes. The GZSL method essentially models the relationship between visual and semantic features, so that semantic features can be used as a bridge to accurately classify visual features of unseen classes. DSECN can effectively build such relationship between \"diverse\" semantic and visual features at low cost, and thus signif" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23348" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "icantly improving the performance of existing GZSL approaches. Taking generative-based methods as an example, the generator can generate visual features of the introduced diverse semantic from external class names. Then the pretrained classification head is used to align the generated visual features to visual space. This enables the generator to adapt to more classes and generate more accurate visual features for unseen classes. Finally, the refined visual features of unseen classes are used to train the GZSL classifier, thus improving the model performance. More details on the integration of our idea with the generative-based methods and other types of GZSL approaches can be found in the supplementary material A." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.305, + 0.21, + 0.321 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.279, + 0.347 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Datasets. We conduct our experiments on three widely used ZSL benchmark datasets, which are AWA2 [46], CUB [40] and SUN [33]. Since the main focus of this work is to study the more practical GZSL setting that includes both similar and dissimilar unseen classes, the learned GZSL model needs to recognize the dissimilar unseen classes from other datasets. Hence, we do not use the human-annotated attributes, but rather use language models, e.g., W2V [27] and CLIP [35], to extract the semantic embedding of classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.473, + 0.824 + ], + "angle": 0, + "content": "Evaluation. Unlike most existing methods that only consider similar settings, we comprehensively evaluate the GZSL model on three testing settings, including similar, dissimilar and practical settings. To better describe these settings, we define the set of datasets as \\( Set = \\{AWA2, CUB, SUN\\} \\). The dataset of seen classes and unseen classes are respectively expressed as \\( ds \\) and \\( du \\), where \\( ds \\subseteq Set \\) and \\( du \\subseteq Set \\). To simulate the similar scene, the dataset \\( ds \\) of seen classes is same as the dataset \\( du \\) of unseen classes, i.e., \\( ds = du \\). To simulate the dissimilar scene, we use the complementary set of \\( ds \\) as \\( du \\), i.e., \\( du = \\complement_{Set} ds \\). For practical scene, the unseen classes may either be similar or dissimilar to the seen classes. Therefore, in our practical setting, we use all datasets to evaluate unseen classes, i.e., \\( du = Set \\). For all three settings, we follow [46] to evaluate model for both ZSL and GZSL. In the ZSL, the average per-class top-1 accuracy (\\( T \\)) on unseen classes is taken as the evaluation metric. In the GZSL, the evaluation metric is the harmonic mean \\( H \\) between seen classes accuracy \\( S \\) and unseen class accuracy \\( U \\), i.e., \\( H = (2 \\times U \\times S) / (U + S) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.855 + ], + "angle": 0, + "content": "Implementation Details. The implementation details are provided in the supplementary material B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Fair-comparison Guarantee. All methods are trained on seen class images of the training set \\( D_{tr}^{s} \\), ensuring that the labeled training data are the same for different approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "They all adopt the same backbone weights pretrained on large-scale dataset, which means that the pre-training data implicitly utilized by the model is completely consistent. They all use the same language model to extract semantic features, ensuring the fairness of the semantic extraction method. Therefore, the same data are utilized for different methods, and the fairness of comparison is guaranteed. Notably, introducing additional information is a common strategy to mitigate bias issue in GZSL. For example, generative-based GZSL methods [2, 16] introduce semantic information of test unseen classes to mitigate bias. The transductive GZSL methods [1, 41, 44] utilize test unseen class samples to mitigate bias. Unlike these methods, our method does not utilize any semantic or sample information of test unseen classes, thus making our method more suitable for practical GZSL." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.344, + 0.805, + 0.36 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Performance. We comprehensively compare our method with several SOTA GZSL approaches on the similar, dissimilar, and practical settings. Tab. 1 shows that: 1) the performance of all counterparts in identifying dissimilar unseen classes is very poor, which proves that existing models have difficulty in identifying common dissimilar unseen classes in the real world; 2) our method achieves the SOTA performance on all datasets, semantic embeddings and settings, which demonstrates the effectiveness of our method. In particular, our method significantly outperforms all counterparts under dissimilar and practical settings. Take the CUB dataset under dissimilar setting as an example, our method outperforms the most competitive counterpart by \\(21.76\\%\\) and \\(35.14\\%\\) on the W2V [27] and CLIP text embedding [35], respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.73 + ], + "angle": 0, + "content": "Training Efficiency. We conduct training efficiency comparison experiments on all datasets using CLIP [35] text embedding. Tab. 2 reports the training time of each method. Benefiting from the simple network design, the training costs of CN and the proposed method are much lower than other approaches. Although our method is slightly slower than the CN method because of the introducing semantics from external class names, our method can be trained within one minute." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.741, + 0.655, + 0.758 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To evaluate the benefits of tackling GZSL with the diverse semantic enhancement (DSE) and the hierarchy taxonomy enhancement (HTE), we conduct an ablation study on all semantics, datasets and settings. The results using CLIP [35] and W2V [27] semantic embedding are reported in Fig. 3 and Fig. S3 of supplementary material C, respectively. From these results, we can see that: 1) regardless of W2V or CLIP semantic representation, the baseline model \\( b \\) has poor recognition performance on dissimilar unseen classes." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23349" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.887, + 0.432 + ], + "angle": 0, + "content": "
Train DataMethodsW2VCLIP
SimilarDissimilarPracticalSimilarDissimilarPractical
ZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSL
CUB\\( ZLA^†[IJCAI22] [4] \\)17.2416.033.356.007.4111.0446.5642.654.668.5219.3224.89
\\( DGZ^†[AAAI23] [5] \\)18.0018.423.245.675.477.4247.1243.167.1512.3020.6126.60
\\( CN^‡[ICLR21] [38] \\)18.1622.101.122.035.698.7443.7442.503.825.0917.8123.25
\\( TransZero^‡[AAAI22] [9] \\)17.1515.650.900.866.496.4149.7747.993.562.4719.1824.81
\\( MSDN^‡[CVPR22] [10] \\)18.3018.461.733.334.846.4449.1747.692.652.7918.6023.40
\\( HASZSL^‡[MM23] [11] \\)13.4616.911.042.035.266.7542.5143.642.172.8116.2617.12
DSECN (Ours)18.8023.4017.7327.7617.8123.6350.7048.4535.5447.4440.8545.29
AWA2\\( ZLA^†[IJCAI22] [4] \\)49.7854.653.416.214.678.2076.5975.095.159.329.2514.87
\\( DGZ^†[AAAI23] [5] \\)54.5957.023.125.874.848.5478.2776.597.0312.5910.3017.26
\\( CN^‡[ICLR21] [38] \\)41.1249.621.662.763.476.3079.4573.385.489.958.6014.72
\\( TransZero^‡[AAAI22] [9] \\)39.7042.901.071.943.345.3069.5859.782.113.942.674.79
\\( MSDN^‡[AAAI22] [9] \\)45.9048.521.632.523.475.0564.4264.213.666.035.899.46
\\( HASZSL^‡[MM23] [11] \\)36.5945.040.880.981.261.0660.3456.066.767.7337.9537.25
DSECN (Ours)69.2370.7111.2119.8814.3723.7986.9781.2837.0152.5240.0053.74
SUN\\( ZLA^†[IJCAI22] [4] \\)33.5423.909.1213.0618.7018.8654.6536.708.5211.7931.5928.31
\\( DGZ^†[IJCAI22] [4] \\)31.3225.089.3113.7617.5317.8553.5437.7311.8717.4931.6128.31
\\( CN^‡[ICLR21] [38] \\)33.8226.275.177.0518.8018.1455.5638.879.6913.6432.8030.00
\\( TransZero^‡[AAAI22] [9] \\)30.4221.813.682.6616.6914.6354.5135.865.282.8929.9825.39
\\( MSDN^‡[AAAI22] [9] \\)28.1316.231.512.789.967.5853.3331.735.578.2028.3122.56
\\( HASZSL^‡[MM23] [11] \\)19.5111.413.720.1210.691.4136.5321.154.570.1220.028.34
DSECN (Ours)37.8526.8110.5416.4724.1921.6960.2840.3337.1140.1949.1038.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.434, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Table 1. Comparison with the state-of-the-art GZSL approaches in the three settings, † and ‡ signify the generative-based method and embedding-based approach. Please see details in § 4.2." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.464, + 0.341, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.464, + 0.614, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.464, + 0.885, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.615, + 0.89, + 0.642 + ], + "angle": 0, + "content": "Figure 3. Effect of diverse semantic enhancement \\((s)\\) and hierarchy taxonomy enhancement \\((h)\\) for GZSL. We remove these two components as our baseline \\((b)\\). In the ablation study, we add DSE \\((s)\\) and HTE \\((h)\\) step by step to show their effect on GZSL. Refer to § 4.3." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.652, + 0.478, + 0.77 + ], + "angle": 0, + "content": "
MethodsCUBAWA2SUNMean
ZLA* [4]4.4 hours9.5 hours7.7 hours7.2 hours
DGZ* [5]8.3 hours12.2 hours16.1 hours12.2 hours
CN* [38]8.6 sec25.8 sec12.2 sec15.5 sec
TransZero° [9]40.7 min2.0 hours1.6 hours1.4 hours
MSDN° [10]4.4 min21.9 min14.5 min13.6 min
HAS° [11]5.4 hours17.3 hours7.4 hours10.0 hours
DSECN* (Ours)13.9 sec37.9 sec19.7 sec23.8 sec
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.771, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Table 2. Training time for the recent GZSL methods that made their official implementations publicly available. * and \\( \\diamond \\) respectively indicate that the model uses the 2048-dimensional vector and \\( {14} \\times {14} \\times {2048} \\) -dimensional feature map extracted by pretrained Resnet101 as input. \\( \\bullet \\) denotes that the model takes original image as input and finetunes the pretrained backbone. See § 4.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "This indicates that the problem of identifying dissimilar unseen classes cannot be solved by enhancing the semantic information contained in seen classes; 2) after adding DSE" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.897 + ], + "angle": 0, + "content": "\\(s\\) and HTE \\(h\\) to the baseline, the \\(b + s + h\\) model achieves the best performance on all semantics, datasets and settings. This proves that both the DSE \\(s\\) and the HTE \\(h\\) are critical to GZSL and complementary to each other on all three test settings; 3) the less similar the unseen classes are to the seen classes in the test setting, the greater the performance improvement gain brought by the proposed module \\(s\\) and \\(h\\). Taking the CUB dataset with CLIP semantic embedding as an example, \\(b + s + h\\) improves the harmonic mean accuracy by \\(42.38\\%\\), \\(21.76\\%\\), and \\(4.73\\%\\) on dissimilar, practical and similar settings, respectively. This may be because when the unseen classes are dissimilar to seen classes, the baseline model can only transfer little information from seen classes to unseen classes, while \\(b + s + h\\) introduces a variety of semantic information from class names that can be transferred to unseen classes to improve the recognition performance of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23350" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.089, + 0.454, + 0.208 + ], + "angle": 0, + "content": "
MethodsCUBAWA2SUN
W2VCLIPW2VCLIPW2VCLIP
CN [38]2.035.092.769.957.0513.64
CN+DSECN22.0837.6814.3533.0412.6429.11
TransZero [9]0.862.471.943.942.662.89
TransZero+DSECN2.414.442.515.413.593.02
DGZ [5]5.6712.305.8712.5913.7617.49
DGZ+DSECN26.3448.3917.0247.6817.7639.11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.209, + 0.47, + 0.264 + ], + "angle": 0, + "content": "Table 3. Effect of integrating DSECN into existing GZSL methods under dissimilar setting. CN [38], TransZero [9], and DGZ [5] belong to the global embedding-based, local embedding-based, and generation-based GZSL methods respectively. See details in § 4.4." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.265, + 0.462, + 0.382 + ], + "angle": 0, + "content": "
SemanticsMethodsCUBAWA2SUN
1K21K1K21K1K21K
W2Vb2.961.965.512.8211.175.50
b+s+h27.7656.9719.8840.6816.4728.24
↑24.8055.0114.3737.865.3022.74
CLIPb5.066.877.747.9412.6615.55
b+s+h47.4477.6052.5271.2540.1961.59
↑42.3870.7344.7863.3127.5346.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.384, + 0.468, + 0.411 + ], + "angle": 0, + "content": "Table 4. Effect of the number of external class names. \\( \\uparrow \\) signifies the performance improvement. Please see § 4.5 for details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.468, + 0.469 + ], + "angle": 0, + "content": "unseen classes. Furthermore, we also qualitatively analyzed the reasons why the proposed module is effective in the supplementary materials D." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.433, + 0.511 + ], + "angle": 0, + "content": "4.4. Integration with other GZSL Approaches" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.524, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We have integrated DSECN into three mainstream GZSL methods and analysed the effect of integrating DSECN. From the results in Tab. 3, we can observe that: 1) benefiting from the introduction of diverse semantic information from class names (DSECN), the performance of global embedding-based (CN) and generative-based methods (DGZ) is significantly improved. For example, when unseen classes are not similar to seen classes, DSECN improves DGZ's GZSL performance by \\(20.67\\%\\) in the CUB dataset using W2V [27] embedding. This proves that the DSECN can be integrated into existing global embedding-based and generative-based GZSL methods to improve the model's robustness to dissimilar unseen classes; 2) the improvement with the local embedding-based GZSL method (TransZero) is smaller than that of global embedding-based and generative-based methods. This may be attributed to the fact that the performance improvement of integrating DSECN is limited by the accuracy of the generated visual feature maps. It is challenging to accurately generate not visible visual feature maps from semantic vectors, which is why existing generative-based GZSL methods mostly generate global visual features rather than local visual features. Overall, the proposed DSECN can easily be integrated into existing mainstream GZSL methods to improve the robustness for dissimilar unseen classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.866, + 0.107 + ], + "angle": 0, + "content": "4.5. Effect of the External Class Name Number" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.283 + ], + "angle": 0, + "content": "To investigate the effect of the ECN number on identifying dissimilar unseen classes, we introduce the class names from ImageNet-1K and ImageNet-21K separately as the external base class names, and then remove the unseen class names from the external class names. Notably, we use the ResNet101 pretrained on ImageNet-21K when introducing ImageNet-21K class names. The results are shown in Tab. 4. We can observe that as the introduced ECN increases, performance of the model improves significantly. This proves that increasing the ECN is important to improve the performance of dissimilar unseen class recognition." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.299, + 0.62, + 0.314 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.536 + ], + "angle": 0, + "content": "In this paper, we introduce and investigate the practical GZSL setting, where unseen classes can be either similar and dissimilar to seen classes. We empirically show that existing GZSL methods are difficult in identifying dissimilar unseen classes, and propose a simple yet effective method, which exploits diverse semantics from external class names (DSECN), and is simultaneously robust for both similar and dissimilar unseen classes. From the results, we mainly conclude that: 1) the semantics contained in the external unseen class names are quite helpful to improve the generalization ability of GZSL approach; 2) It is critical to align the augmented semantics to their corresponding visual features. In the future, we intend to incorporate the proposed idea into more GZSL approaches and improve their performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Potential Impacts. The existing GZSL methods perform poorly when unseen classes are dissimilar to seen classes, which hinders the practical application of the existing GZSL methods. The paper will help attract researchers' attention to dissimilar unseen classes and help the GZSL field develop in a more practical direction. In addition, the proposed DSECN is simultaneously robust on similar and dissimilar unseen classes, and can easily be integrated into other GZSL methods to improve their robustness for dissimilar unseen classes. This capability is beneficial for improving the practicality of the GZSL model. From an evaluation perspective, existing methods assess using visible and invisible classes from the same dataset. This leads to excessive focus on similar unseen classes during evaluation, thereby overestimating the generalizability of existing GZSL methods. In contrast, the cross-dataset evaluation protocol proposed in the paper can more comprehensively reflect the performance of existing GZSL methods on similar, dissimilar and practical settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported by the National Key Research and Development Program of China 2023YFC2705700, National Natural Science Foundation of China under Grants 62225113 and 62276195, and Special Fund of Hubei Luojia Laboratory under Grant 220100014." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23351" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Liu Bo, Qiulei Dong, and Zhanyi Hu. Hardness sampling for self-training based transductive zero-shot learning. In CVPR, pages 16499-16508, 2021. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.471, + 0.2 + ], + "angle": 0, + "content": "[2] Samet Cetin, Orhun Bugra Baran, and Ramazan Gokberk Cinbis. 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Although some existing GZSL approaches can alleviate this issue by leveraging additional semantic information from test unseen classes, their generalization ability to dissimilar unseen classes is still unsatisfactory. This motivates us to study GZSL in the more practical setting, where unseen classes can be either similar or dissimilar to seen classes. In this paper, we propose a simple yet effective GZSL framework by exploring diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes. This is achieved by introducing diverse semantics from external class names and aligning the introduced semantics to visual space using the classification head of pre-trained network. Furthermore, we show that the design idea of DSECN can easily be integrate into other advanced GZSL approaches, such as the generative-based ones, and enhance their robustness for dissimilar unseen classes. Extensive experiments in the practical setting including both similar and dissimilar unseen classes show that our method significantly outperforms the state-of-the-art approaches on all datasets and can be trained very efficiently. + +# 1. Introduction + +Due to the high cost of annotation and the complexity of real-world test scenarios, the presence of unseen classes is often inevitable [34, 43]. Unfortunately, traditional machine learning models are unable to handle samples from classes that have not been covered by the training data [8]. + +![](images/24dde050104dfd755ddb73363db423e05af8d590448c8b6c3fa5f3a3a96de4f0.jpg) +(a) Our Setting + +
ModeCN [38]TransZero [9]ZLA [4]DGZ [5]Ours (Δ)
Similar42.5047.9942.6543.1648.45 (+0.46)
Dissimilar5.092.478.5212.3047.44 (+35.14)
+ +(b) Results + +Figure 1. Setting illustration and results: (a) Comparison with the existing setting, our setting takes into account the scenario where the unseen classes are dissimilar to seen classes; (b) Performance of existing GZSL methods on similar and dissimilar unseen classes on the CUB dataset. The similar unseen classes were obtained from the same CUB dataset, while the dissimilar unseen classes come from AWA2 and SUN dataset. + +To tackle this challenge, zero-shot learning (ZSL) has been proposed to recognize new classes via transferring knowledge obtained from seen classes with the help of semantic information [14, 15, 23, 52]. In contrast, Generalized ZSL (GZSL) is a more challenging task which handle test samples from both seen and unseen classes [3, 25, 29, 34]. + +The core idea of GZSL is to introduce auxiliary semantic information and establish the connection between semantic and visual space for the recognition of unseen classes [34]. Since unseen samples are not available during training, existing GZSL models often misclassify unseen class samples into seen classes during test (known as the bias issue) [21, 22]. To alleviate this issue, several strategies have been introduced. A common strategy is to utilize a backbone pre-trained on the ImageNet-1K dataset [13] to extract visual features [7, 24, 26, 36, 50], which is beneficial to improve the generalization ability of visual features. However, + +the rich semantics that implicitly contained in the backbone classification heads are simply ignored in these approaches, and thus their ability to exploit diverse semantics is limited. Generative-based GZSL methods [4-6, 16, 51] alleviate the bias problem by introducing the semantics from test unseen classes, and some semantic augmentation approaches focus on enhancing the semantics of each class by leveraging the textual documents [30], large language model [31], etc [19, 50]. However, these approaches share a common limitation that they heavily rely on the semantics and visual features from seen classes to build the relations between visual and semantic space. This makes these models perform poorly on dissimilar unseen classes (see Fig. 1b), as little information can be transferred from seen to dissimilar unseen classes. That is, these methods can only deal with the unrealistic setting that the unseen classes are similar with seen classes (see existing setting of Fig. 1a). However, it is inevitable that unseen classes may be quite different from seen classes in the real-world applications, and hence it is desirable to enhance GZSL models to effectively handle dissimilar unseen classes. + +To achieve this goal, we need to address three main challenges: (I) how to obtain the information that can be transferred to dissimilar unseen classes; (II) how to enable effective information transfer without labeled training data; and (III) how to reduce costs as much as possible while ensuring effectiveness. If the cost of the solution exceeds the cost of collecting the data and retraining the model, then such a solution would be meaningless. Therefore, we propose a simple yet effective GZSL framework by exploring Diverse Semantics from External Class Names (DSECN), which is robust on both the similar and dissimilar unseen classes. Specifically, we introduce the diverse semantics from external (not test unseen classes) class names as the bridge to reduce the gap between the seen and unseen classes, which is beneficial for the recognition of unseen classes (challenge I). Then we utilize the classification head pre-trained on large-scale dataset, e.g., ImageNet-1K [13], to align the introduced semantics to the visual space (challenge II). Finally, the hierarchical taxonomy of WordNet [28] for the classes in large-scale dataset is introduced to further improve the diversity of semantics from class names. Since the class name and pre-trained classification head are quite easy to collect, the cost of our method is quite low (challenge III). + +To summarize, the main contributions of this paper are: + +- To the best of our knowledge, we are the first that explicitly study the realistic GZSL setting that both similar and dissimilar unseen classes exist (see our setting in Fig. 1a). +- We propose a GZSL method that explores the diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes. + +- We show that the proposed idea can be easily integrated into other GZSL approaches, such as generative-based ones, and improve their robustness for dissimilar unseen classes. + +We conduct extensive experiments on diverse real-world datasets. The results show that in the practical setting including both similar and dissimilar unseen classes, the harmonic mean accuracies of our method significantly outperform all counterparts. Besides, our model can be trained within one minute on all three datasets. + +# 2. Related Work + +# 2.1. Generalized Zero-shot Learning + +Existing GZSL methods can be broadly categorized into embedding-based [9, 18, 25, 38] and generative-based ones [2, 5, 12, 16]. Early global embedding-based methods [15, 18, 25, 38, 45] align global visual features with corresponding category semantic information into a common embedding space, which enables knowledge transfer from seen to unseen classes. Recently proposed local embedding-based methods [9-11, 42, 48, 49] utilize attribute descriptions as guidance to discover the discriminative local features between seen classes and unseen classes. Besides, generative-based methods [4, 5, 12, 37, 38, 47] introduce the semantic from test unseen classes to alleviate the bias problem in GZSL [34]. However, these methods focus on the unrealistic setting where unseen classes are assumed to be similar to seen classes, and perform poorly in identifying dissimilar unseen classes. In contrast, our work focuses on a realistic GZSL setting that includes both similar and dissimilar unseen classes, and the proposed DSECN can robustly identify similar and dissimilar unseen classes. + +# 2.2. Semantic Information for GZSL + +Semantic information is a bridge that transfers knowledge from seen classes to unseen class recognition and is crucial to GZSL [30, 34, 50]. Most of prior works rely on human-annotated attributes [2, 32, 49] or word vectors [20, 39] as the semantic information. While attributes are accurate, they are costly to annotate and are not suitable for a large-scale problem [20, 50]. In contrast, word vectors require less human labor and are suitable for large-scale datasets [34]. However, word vectors often do not reflect visual similarities, thus limiting the performance [30, 49]. Xu et al. [49] propose a visually-grounded semantic embedding (VGSE) network to discover semantic embeddings containing discriminative visual properties. Naeem et al. [30] propose a transformer-based model I2DFormer that learns semantic embeddings from raw online textual documents. However, these methods only consider semantic enhancement within a single category. When an unseen class is dissimilar to seen classes, the transferable semantic infor + +mation from seen classes is still little, which limits their performance. In contrast, we introduce diverse semantic information from external category names and align the introduced semantics into visual space using the classification head pre-trained on a large-scale dataset , thus assisting in the identification of dissimilar unseen categories. + +# 3. Proposed Method + +Problem Formulation. In ZSL and GZSL, we define two sets of classes: seen classes in $Y^s$ and unseen classes in $Y^u$ . The seen classes $Y^s$ and the unseen classes $Y^u$ are disjoint, i.e., $Y^s \cap Y^u = \emptyset$ and $Y^s \cup Y^u = \mathcal{Y}$ . The unseen classes may be similar or dissimilar to seen classes in practice. Hence, in this work, the unseen classes $Y^u$ contain similar unseen classes $Y_s^u$ and dissimilar unseen classes $Y_d^u$ , i.e., $Y^u = Y_s^u \cup Y_d^u$ . The seen data are expressed as $D^s = \{(x_i^s, y_i^s)\}$ , where $x_i^s \in X$ indicates the $i$ -th sample features extracted by the pretrained backbone network, e.g., ResNet101 [17], and $y_i^s \in Y^s$ is its class label. The $D^s$ is split into a training set $D_{tr}^s$ and a testing set $D_{te}^s$ . On the other hand, the unseen data are denoted as $D^u = \{(x_i^u, y_i^u)\}$ , where $x_i^u \in X^u$ and $y_i^u \in Y^u$ are the sample features of unseen classes and the corresponding ground-truth label for evaluation, respectively. The goal of ZSL is to learn a classifier for classifying test samples from unseen classes, i.e., $X \xrightarrow{f_{ZSL}} Y^u$ . In contrast to ZSL, the goal of GZSL is to learn a classifier for classifying test samples from both seen and unseen classes, i.e., $X \xrightarrow{f_{GZSL}} Y^s \cup Y^u$ . In ZSL and GZSL, the auxiliary semantic information $A$ is obtained by transforming the class labels $\mathcal{V}$ using human-annotated attributes [9] or language models [27, 35]. + +Overview of framework. As shown in Fig. 2, the framework contains three components: visual flow (§ 3.1), diverse semantic enhancement (DSE, § 3.2), and hierarchy taxonomy enhancement (HTE, § 3.3). The visual flow aligns seen class semantics into visual space. Diverse semantic and hierarchy taxonomy enhancement are proposed to enhance the diversity of semantics available to the model, thereby assisting the identification of dissimilar unseen classes. + +# 3.1. Visual Flow + +The visual flow is designed to classify visual objects from both seen and unseen classes by transferring knowledge from the seen classes to the unseen ones with the help of semantic information. The visual flow contains two parts: semantic-to-visual sub-network $(S2V)$ and visual classifier. The $S2V$ sub-network is a learnable multilayer perceptron (MLP), and is used to link the semantic and visual representation. This enables the model to transfer the knowledge from seen classes to the unseen classes through semantic information. The visual classifier uses the relation + +ship between the visual sample and all categories to obtain the classification result of the sample. Because the visual flow requires paired visual samples and category labels, in the training phase, the visual flow can only be trained on the paired visual feature and label dataset $D_{tr}^{s}$ . Specifically, the $S2V$ sub-network takes the seen semantic feature $A^{s}$ as input to generate the class-level visual prototype of seen classes $V^{s}$ . The process to generate the class-level visual prototype of seen classes $V^{s}$ can be expressed by + +$$ +A ^ {s} \in \mathbb {R} ^ {C ^ {s} \times d ^ {a}} \xrightarrow {S 2 V} V ^ {s} \in \mathbb {R} ^ {C ^ {s} \times d ^ {v}}, \tag {1} +$$ + +where $C^s, d^a, d^v$ denote the number of seen classes, the dimensionality of semantic representation and the dimensionality of visual representation, respectively. $A^s$ signifies the semantic representations of seen classes and is extracted by language models [27, 35]. + +Next, the visual classifier (VC) computes the scaled cosine similarity between the visual feature of seen classes $X_{tr}^{s} \in \mathbb{R}^{N_{tr}^{s} \times d^{v}}$ and the class-level visual feature of seen classes $V^{s} \in \mathbb{R}^{C^{s} \times d^{v}}$ as logits $l^{s} \in \mathbb{R}^{N_{tr}^{s} \times C^{s}}$ , where $N_{tr}^{s}$ is the number of seen class samples in the training set. Formally, the logits $l^{s}$ can be obtained as follows: + +$$ +l ^ {s} = \gamma^ {2} \frac {X _ {t r} ^ {s} V ^ {s} {} ^ {\top}}{\| X _ {t r} ^ {s} \| \| V ^ {s} \|}, \tag {2} +$$ + +where $\gamma$ is the scale factor. + +Finally, we adopt the Cross-Entropy (CE) loss to update the visual flow: + +$$ +\mathcal {L} _ {V} = \mathcal {L} _ {C E} \left(\sigma \left(l ^ {s}\right), Y _ {t r} ^ {s}\right), \tag {3} +$$ + +where $\sigma$ denotes the softmax function. + +# 3.2. Diverse Semantic Enhancement + +Motivation of DSE. When the unseen classes are dissimilar with seen classes, the visual flow can transfer only little information from seen classes to unseen classes, resulting in poor recognition performance of unseen classes. Motivated by this, we propose the diverse semantic enhancement module, which introduces the semantic information from external class names to help the recognition of unseen classes. To successfully transfer semantic information to unseen classes, establishing a substantial linkage between the semantics inherent in class names and their corresponding visual features is imperative. Nonetheless, the visual feature of the class name is unknown, which poses the primary obstacle in leveraging semantics from class names to enhance Generalized Zero-Shot Learning (GZSL). Considering the visual representation $X$ obtained through the pretrained backbone, e.g. ResNet101, on the large-scale dataset, we use the classification head corresponding to pretrained backbone as semantic classifier (SC) to constrain the + +![](images/d4d7ef52d30ea1a23fa9db0dc035fb574b8eac3070f2d06ed25bc23d397667d1.jpg) +Figure 2. Overview of the proposed DSECN framework. During the training phase, our method contains three components: visual flow, diverse semantic enhancement, and hierarchy taxonomy enhancement. In the visual flow, we employ the visual cosine classifier to align the semantics and visual features of seen classes. Then the diverse semantic enhancement and hierarchy taxonomy enhancement introduce more diverse information from the external base class names and the augmented class names. The introduced diverse semantics are aligned to the visual space using pre-trained classification head, which enables our model to learn a robust union space for both similar and dissimilar unseen classes. During the inference phase, benefiting from the learned union space that contains visual-semantic correspondence of diverse classes, the test image from dissimilar unseen classes can be accurately classified. + +generated class-level visual prototype of class names to visual space. Besides, the introduced semantics from class names should be diverse. Hence, we choose the class names of large-scale dataset to extract diverse semantics. + +Construction of DSE. We first introduce the class names $CN^{EB}$ of large-scale dataset corresponding to pretrained network and extract the semantic information $A^{EB} \in \mathbb{R}^{C^{EB} \times d^a}$ of $CN^{EB}$ using the Language Model (LM), i.e., + +$$ +A ^ {E B} = L M \left(C N ^ {E B}\right). \tag {4} +$$ + +$C^{EB}$ denotes the number of external base class names from the large-scale dataset. Then the semantic information $A^{EB}$ are taken as the input of $S2V$ sub-network to generate class-level visual prototype $V^{EB} \in \mathbb{R}^{C^{EB} \times d^v}$ , i.e., + +$$ +V ^ {E B} = S 2 V \left(A ^ {E B}\right). \tag {5} +$$ + +Next, the generated visual prototype $V^{EB}$ is fed into the semantic classifier (SC) to get the logits $l^{EB} \in \mathbb{R}^{C^{EB} \times C^{PR}}$ , i.e., + +$$ +l ^ {E B} = S C (V ^ {E B}), \tag {6} +$$ + +where $SC$ is the frozen classification head from pretrained network. $C^{PR}$ is the class number of pretraining dataset. + +Due to the backbone pretrained in large-scale dataset, we can obtain the label of $CN^{EB}$ as follows: + +$$ +Y ^ {E B} = C N 2 Y \left(C N ^ {E B}\right), \tag {7} +$$ + +where $CN2Y$ is the dictionary mapping from class names to labels in the large-scale dataset corresponding to the pretrained backbone. + +Finally, the Cross-Entropy (CE) Loss is adopted to update the diverse semantic enhancement module: + +$$ +\mathcal {L} _ {E B} = \mathcal {L} _ {C E} (\sigma (l ^ {E B}), Y ^ {E B}). \tag {8} +$$ + +Comparison with Analogous Methods. The prevailing GZSL approach depends on transferring semantic knowledge from seen to unseen classes. However, these techniques falter in a realistic GZSL setting that encompasses both similar and dissimilar unseen classes. Our method introduces varied semantics derived from external class names and aligns them with the visual domain through a pre-trained classification head. This process allows our + +model to leverage newly introduced semantics as a bridge connecting seen and dissimilar unseen classes, thus enhancing the identification of dissimilar unseen classes. Notably, the procurement cost of class names and pre-trained classification heads is low, rendering our approach more feasible in practice. + +# 3.3. Hierarchy Taxonomy Enhancement + +Chihuahua is a kind of pet dog, and the dog is also a kind of animal. That is, there is a hierarchical structure between different categories. Therefore, we can utilize the hierarchy structure of classes to augment more classes. Based on the assumption, we propose a class name augment method based on hierarchy structure of classes. Specifically, we first employ WordNet [28] to extract the subclass names of external base class names $(CN^{EB})$ as hierarchically augmented class names $(CN^{HA})$ . + +$$ +C N ^ {H A} = h y p o n y m s \left(C N ^ {E B}\right), \tag {9} +$$ + +where hyponyms denotes the mapping function for extracting hyponyms using WordNet [28]. The semantic information $A^{HA} \in \mathbb{R}^{C^{HA} \times d^a}$ of the $CN^{HA}$ can be extracted by the language model, i.e., $A^{HA} = LM(CN^{HA})$ . $C^{HA}$ denotes the number of the augmented class names. + +Then we can obtain the predicted probability $l^{HA} \in \mathbb{R}^{C^{HA} \times C^{PR}}$ of the augmented classes as follows: + +$$ +l ^ {H A} = S C \left(S 2 V \left(A ^ {H A}\right)\right), \tag {10} +$$ + +where $S2V$ and $SC$ is the semantic-to-visual ( $S2V$ ) subnetwork and the semantic classifier ( $SC$ ), respectively. Considering that the subclass is one of the parent classes, we assign the label of the corresponding parent class as the label of the subclass. For example, fire ant is the subclass of ant, and thus the label of fire ant $y^{fire-ant}$ is assigned as the label of ant in the pretraining large-scale dataset, i.e., $y^{fire-ant} = y^{ant} = CN2Y(ant)$ . Based on the idea, the label $Y^{HA}$ of $CN^{HA}$ can be obtained as follows: + +$$ +Y ^ {H A} = C N 2 Y \left(h y p e r n y m s \left(C N ^ {H A}\right)\right), \tag {11} +$$ + +where hypernyms denotes the mapping function for extracting hypernyms using WordNet [28], $CN2Y$ is the dictionary mapping from class names to labels in the largescale dataset corresponding to the pretrained backbone. + +Finally, the Cross-Entropy (CE) Loss is adopted to obtain the loss of hierarchy taxonomy enhancement: + +$$ +\mathcal {L} _ {H A} = \mathcal {L} _ {C E} (\sigma (l ^ {H A}), Y ^ {H A}). \tag {12} +$$ + +# 3.4. Training and Inference + +The proposed DSECN, which contains three components, is trained in an end-to-end manner, and the total loss function is given as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {V} + \lambda_ {E B} \mathcal {L} _ {E B} + \lambda_ {H A} \mathcal {L} _ {H A}, \tag {13} +$$ + +Algorithm 1: Training Process of DSECN +Input: Training seen data $\{X_{tr}^{s},CN^{s},Y_{tr}^{s}\}$ , external base class names $C N^{E B}$ and hierarchy augmented class names $CN^{HA}$ +Output: The final S2V model +// Generate Semantics and Labels + $A^s,A^{EB},A^{HA} = LM(CN^s,CN^{EB},CN^{HA})$ $Y^{EB}\gets \{CNEB\}$ in Eq.(7), + $Y^{HA}\leftarrow \{CN^{HA}\}$ in Eq.(11). +for $e = 1,2,\ldots ,E$ do +// Visual Flow + $V^{s} = S2V(A^{s})$ $l^s\gets \{V^s,X_{tr}^s\}$ in Eq.(2), + $\mathcal{L}_V\gets \{l^s,Y_{tr}^s\}$ in Eq.(3). +// Diverse Semantic Enhancement + $V^{EB} = S2V(A^{EB})$ $l^{EB} = SC(V^{EB})$ $\mathcal{L}_{EB}\gets \{l^{EB},Y^{EB}\}$ in Eq.(8). +// Hierarchy Taxonomy Enhancement + $V^{HA} = S2V(A^{HA})$ $l^{HA} = SC(V^{HA})$ $\mathcal{L}_{HA}\gets \{l^{HA},Y^{HA}\}$ in Eq.(12). +// Compute Total Loss + $\mathcal{L}_{total} = \mathcal{L}_V + \mathcal{L}_{EB} + \mathcal{L}_{HA}$ +// Update Parameters +Update the parameters of S2V using Adam. + +end + +where $\lambda_{EB}$ and $\lambda_{HA}$ are trade-off hyper-parameters. The training pseudo-code is presented in Algorithm 1. It is noteworthy that we only update the parameters of $S2V$ . + +In the inference phase, given a visual feature $x$ and the semantic feature $A$ of all classes, we apply the visual flow to obtain the final class prediction $\hat{y}$ . Specifically, the semantic features $A = A^s \cup A^u$ of all classes are first fed into $S2V$ sub-network to generate the class-level visual prototype, i.e., $V = S2V(A)$ . Then the final class prediction can be obtained according to: + +$$ +\hat {y} = \underset {y \in \mathcal {Y}} {\arg \max } \left(\operatorname {s o f t m a x} \left(\gamma^ {2} \frac {x V ^ {\top}}{\| x \| \| V \|}\right)\right), \tag {14} +$$ + +where $\mathcal{Y} = Y^{s}\cup Y^{u}$ is the union of seen classes $Y^{s}$ and unseen classes $Y^{u}$ . + +# 3.5. Integrating into Existing GZSL Methods + +The proposed DSECN can be easily integrated into other mainstream GZSL approaches to improve their robustness for dissimilar unseen classes. The GZSL method essentially models the relationship between visual and semantic features, so that semantic features can be used as a bridge to accurately classify visual features of unseen classes. DSECN can effectively build such relationship between "diverse" semantic and visual features at low cost, and thus signif + +icantly improving the performance of existing GZSL approaches. Taking generative-based methods as an example, the generator can generate visual features of the introduced diverse semantic from external class names. Then the pretrained classification head is used to align the generated visual features to visual space. This enables the generator to adapt to more classes and generate more accurate visual features for unseen classes. Finally, the refined visual features of unseen classes are used to train the GZSL classifier, thus improving the model performance. More details on the integration of our idea with the generative-based methods and other types of GZSL approaches can be found in the supplementary material A. + +# 4. Experiments + +# 4.1. Experimental Setting + +Datasets. We conduct our experiments on three widely used ZSL benchmark datasets, which are AWA2 [46], CUB [40] and SUN [33]. Since the main focus of this work is to study the more practical GZSL setting that includes both similar and dissimilar unseen classes, the learned GZSL model needs to recognize the dissimilar unseen classes from other datasets. Hence, we do not use the human-annotated attributes, but rather use language models, e.g., W2V [27] and CLIP [35], to extract the semantic embedding of classes. + +Evaluation. Unlike most existing methods that only consider similar settings, we comprehensively evaluate the GZSL model on three testing settings, including similar, dissimilar and practical settings. To better describe these settings, we define the set of datasets as $Set = \{AWA2, CUB, SUN\}$ . The dataset of seen classes and unseen classes are respectively expressed as $ds$ and $du$ , where $ds \subseteq Set$ and $du \subseteq Set$ . To simulate the similar scene, the dataset $ds$ of seen classes is same as the dataset $du$ of unseen classes, i.e., $ds = du$ . To simulate the dissimilar scene, we use the complementary set of $ds$ as $du$ , i.e., $du = \complement_{Set} ds$ . For practical scene, the unseen classes may either be similar or dissimilar to the seen classes. Therefore, in our practical setting, we use all datasets to evaluate unseen classes, i.e., $du = Set$ . For all three settings, we follow [46] to evaluate model for both ZSL and GZSL. In the ZSL, the average per-class top-1 accuracy ( $T$ ) on unseen classes is taken as the evaluation metric. In the GZSL, the evaluation metric is the harmonic mean $H$ between seen classes accuracy $S$ and unseen class accuracy $U$ , i.e., $H = (2 \times U \times S) / (U + S)$ . + +Implementation Details. The implementation details are provided in the supplementary material B. + +Fair-comparison Guarantee. All methods are trained on seen class images of the training set $D_{tr}^{s}$ , ensuring that the labeled training data are the same for different approaches. + +They all adopt the same backbone weights pretrained on large-scale dataset, which means that the pre-training data implicitly utilized by the model is completely consistent. They all use the same language model to extract semantic features, ensuring the fairness of the semantic extraction method. Therefore, the same data are utilized for different methods, and the fairness of comparison is guaranteed. Notably, introducing additional information is a common strategy to mitigate bias issue in GZSL. For example, generative-based GZSL methods [2, 16] introduce semantic information of test unseen classes to mitigate bias. The transductive GZSL methods [1, 41, 44] utilize test unseen class samples to mitigate bias. Unlike these methods, our method does not utilize any semantic or sample information of test unseen classes, thus making our method more suitable for practical GZSL. + +# 4.2. Comparison with State-of-the-Arts + +Performance. We comprehensively compare our method with several SOTA GZSL approaches on the similar, dissimilar, and practical settings. Tab. 1 shows that: 1) the performance of all counterparts in identifying dissimilar unseen classes is very poor, which proves that existing models have difficulty in identifying common dissimilar unseen classes in the real world; 2) our method achieves the SOTA performance on all datasets, semantic embeddings and settings, which demonstrates the effectiveness of our method. In particular, our method significantly outperforms all counterparts under dissimilar and practical settings. Take the CUB dataset under dissimilar setting as an example, our method outperforms the most competitive counterpart by $21.76\%$ and $35.14\%$ on the W2V [27] and CLIP text embedding [35], respectively. + +Training Efficiency. We conduct training efficiency comparison experiments on all datasets using CLIP [35] text embedding. Tab. 2 reports the training time of each method. Benefiting from the simple network design, the training costs of CN and the proposed method are much lower than other approaches. Although our method is slightly slower than the CN method because of the introducing semantics from external class names, our method can be trained within one minute. + +# 4.3. Ablation Study + +To evaluate the benefits of tackling GZSL with the diverse semantic enhancement (DSE) and the hierarchy taxonomy enhancement (HTE), we conduct an ablation study on all semantics, datasets and settings. The results using CLIP [35] and W2V [27] semantic embedding are reported in Fig. 3 and Fig. S3 of supplementary material C, respectively. From these results, we can see that: 1) regardless of W2V or CLIP semantic representation, the baseline model $b$ has poor recognition performance on dissimilar unseen classes. + +
Train DataMethodsW2VCLIP
SimilarDissimilarPracticalSimilarDissimilarPractical
ZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSL
CUB\( ZLA^†[IJCAI22] [4] \)17.2416.033.356.007.4111.0446.5642.654.668.5219.3224.89
\( DGZ^†[AAAI23] [5] \)18.0018.423.245.675.477.4247.1243.167.1512.3020.6126.60
\( CN^‡[ICLR21] [38] \)18.1622.101.122.035.698.7443.7442.503.825.0917.8123.25
\( TransZero^‡[AAAI22] [9] \)17.1515.650.900.866.496.4149.7747.993.562.4719.1824.81
\( MSDN^‡[CVPR22] [10] \)18.3018.461.733.334.846.4449.1747.692.652.7918.6023.40
\( HASZSL^‡[MM23] [11] \)13.4616.911.042.035.266.7542.5143.642.172.8116.2617.12
DSECN (Ours)18.8023.4017.7327.7617.8123.6350.7048.4535.5447.4440.8545.29
AWA2\( ZLA^†[IJCAI22] [4] \)49.7854.653.416.214.678.2076.5975.095.159.329.2514.87
\( DGZ^†[AAAI23] [5] \)54.5957.023.125.874.848.5478.2776.597.0312.5910.3017.26
\( CN^‡[ICLR21] [38] \)41.1249.621.662.763.476.3079.4573.385.489.958.6014.72
\( TransZero^‡[AAAI22] [9] \)39.7042.901.071.943.345.3069.5859.782.113.942.674.79
\( MSDN^‡[AAAI22] [9] \)45.9048.521.632.523.475.0564.4264.213.666.035.899.46
\( HASZSL^‡[MM23] [11] \)36.5945.040.880.981.261.0660.3456.066.767.7337.9537.25
DSECN (Ours)69.2370.7111.2119.8814.3723.7986.9781.2837.0152.5240.0053.74
SUN\( ZLA^†[IJCAI22] [4] \)33.5423.909.1213.0618.7018.8654.6536.708.5211.7931.5928.31
\( DGZ^†[IJCAI22] [4] \)31.3225.089.3113.7617.5317.8553.5437.7311.8717.4931.6128.31
\( CN^‡[ICLR21] [38] \)33.8226.275.177.0518.8018.1455.5638.879.6913.6432.8030.00
\( TransZero^‡[AAAI22] [9] \)30.4221.813.682.6616.6914.6354.5135.865.282.8929.9825.39
\( MSDN^‡[AAAI22] [9] \)28.1316.231.512.789.967.5853.3331.735.578.2028.3122.56
\( HASZSL^‡[MM23] [11] \)19.5111.413.720.1210.691.4136.5321.154.570.1220.028.34
DSECN (Ours)37.8526.8110.5416.4724.1921.6960.2840.3337.1140.1949.1038.54
+ +![](images/e3061b91c6d49cab246c0bd8f4e276685c61e9ef4710d7f2f7301a7684d24286.jpg) +Figure 3. Effect of diverse semantic enhancement $(s)$ and hierarchy taxonomy enhancement $(h)$ for GZSL. We remove these two components as our baseline $(b)$ . In the ablation study, we add DSE $(s)$ and HTE $(h)$ step by step to show their effect on GZSL. Refer to § 4.3. + +![](images/deae76973fc78c7ee8939f5633c96404f4a89cbd7dbf1acebb7601704e195b1e.jpg) + +![](images/cece79792b9fd0202a37c48acb8dbc8fc2582ad9914b66b91e5554f4d43ba8be.jpg) + +Table 1. Comparison with the state-of-the-art GZSL approaches in the three settings, † and ‡ signify the generative-based method and embedding-based approach. Please see details in § 4.2. + +
MethodsCUBAWA2SUNMean
ZLA* [4]4.4 hours9.5 hours7.7 hours7.2 hours
DGZ* [5]8.3 hours12.2 hours16.1 hours12.2 hours
CN* [38]8.6 sec25.8 sec12.2 sec15.5 sec
TransZero° [9]40.7 min2.0 hours1.6 hours1.4 hours
MSDN° [10]4.4 min21.9 min14.5 min13.6 min
HAS° [11]5.4 hours17.3 hours7.4 hours10.0 hours
DSECN* (Ours)13.9 sec37.9 sec19.7 sec23.8 sec
+ +Table 2. Training time for the recent GZSL methods that made their official implementations publicly available. * and $\diamond$ respectively indicate that the model uses the 2048-dimensional vector and ${14} \times {14} \times {2048}$ -dimensional feature map extracted by pretrained Resnet101 as input. $\bullet$ denotes that the model takes original image as input and finetunes the pretrained backbone. See § 4.2. + +This indicates that the problem of identifying dissimilar unseen classes cannot be solved by enhancing the semantic information contained in seen classes; 2) after adding DSE + +$s$ and HTE $h$ to the baseline, the $b + s + h$ model achieves the best performance on all semantics, datasets and settings. This proves that both the DSE $s$ and the HTE $h$ are critical to GZSL and complementary to each other on all three test settings; 3) the less similar the unseen classes are to the seen classes in the test setting, the greater the performance improvement gain brought by the proposed module $s$ and $h$ . Taking the CUB dataset with CLIP semantic embedding as an example, $b + s + h$ improves the harmonic mean accuracy by $42.38\%$ , $21.76\%$ , and $4.73\%$ on dissimilar, practical and similar settings, respectively. This may be because when the unseen classes are dissimilar to seen classes, the baseline model can only transfer little information from seen classes to unseen classes, while $b + s + h$ introduces a variety of semantic information from class names that can be transferred to unseen classes to improve the recognition performance of + +
MethodsCUBAWA2SUN
W2VCLIPW2VCLIPW2VCLIP
CN [38]2.035.092.769.957.0513.64
CN+DSECN22.0837.6814.3533.0412.6429.11
TransZero [9]0.862.471.943.942.662.89
TransZero+DSECN2.414.442.515.413.593.02
DGZ [5]5.6712.305.8712.5913.7617.49
DGZ+DSECN26.3448.3917.0247.6817.7639.11
+ +Table 3. Effect of integrating DSECN into existing GZSL methods under dissimilar setting. CN [38], TransZero [9], and DGZ [5] belong to the global embedding-based, local embedding-based, and generation-based GZSL methods respectively. See details in § 4.4. + +
SemanticsMethodsCUBAWA2SUN
1K21K1K21K1K21K
W2Vb2.961.965.512.8211.175.50
b+s+h27.7656.9719.8840.6816.4728.24
↑24.8055.0114.3737.865.3022.74
CLIPb5.066.877.747.9412.6615.55
b+s+h47.4477.6052.5271.2540.1961.59
↑42.3870.7344.7863.3127.5346.04
+ +Table 4. Effect of the number of external class names. $\uparrow$ signifies the performance improvement. Please see § 4.5 for details. + +unseen classes. Furthermore, we also qualitatively analyzed the reasons why the proposed module is effective in the supplementary materials D. + +# 4.4. Integration with other GZSL Approaches + +We have integrated DSECN into three mainstream GZSL methods and analysed the effect of integrating DSECN. From the results in Tab. 3, we can observe that: 1) benefiting from the introduction of diverse semantic information from class names (DSECN), the performance of global embedding-based (CN) and generative-based methods (DGZ) is significantly improved. For example, when unseen classes are not similar to seen classes, DSECN improves DGZ's GZSL performance by $20.67\%$ in the CUB dataset using W2V [27] embedding. This proves that the DSECN can be integrated into existing global embedding-based and generative-based GZSL methods to improve the model's robustness to dissimilar unseen classes; 2) the improvement with the local embedding-based GZSL method (TransZero) is smaller than that of global embedding-based and generative-based methods. This may be attributed to the fact that the performance improvement of integrating DSECN is limited by the accuracy of the generated visual feature maps. It is challenging to accurately generate not visible visual feature maps from semantic vectors, which is why existing generative-based GZSL methods mostly generate global visual features rather than local visual features. Overall, the proposed DSECN can easily be integrated into existing mainstream GZSL methods to improve the robustness for dissimilar unseen classes. + +# 4.5. Effect of the External Class Name Number + +To investigate the effect of the ECN number on identifying dissimilar unseen classes, we introduce the class names from ImageNet-1K and ImageNet-21K separately as the external base class names, and then remove the unseen class names from the external class names. Notably, we use the ResNet101 pretrained on ImageNet-21K when introducing ImageNet-21K class names. The results are shown in Tab. 4. We can observe that as the introduced ECN increases, performance of the model improves significantly. This proves that increasing the ECN is important to improve the performance of dissimilar unseen class recognition. + +# 5. Conclusion + +In this paper, we introduce and investigate the practical GZSL setting, where unseen classes can be either similar and dissimilar to seen classes. We empirically show that existing GZSL methods are difficult in identifying dissimilar unseen classes, and propose a simple yet effective method, which exploits diverse semantics from external class names (DSECN), and is simultaneously robust for both similar and dissimilar unseen classes. From the results, we mainly conclude that: 1) the semantics contained in the external unseen class names are quite helpful to improve the generalization ability of GZSL approach; 2) It is critical to align the augmented semantics to their corresponding visual features. In the future, we intend to incorporate the proposed idea into more GZSL approaches and improve their performance. + +Potential Impacts. The existing GZSL methods perform poorly when unseen classes are dissimilar to seen classes, which hinders the practical application of the existing GZSL methods. The paper will help attract researchers' attention to dissimilar unseen classes and help the GZSL field develop in a more practical direction. In addition, the proposed DSECN is simultaneously robust on similar and dissimilar unseen classes, and can easily be integrated into other GZSL methods to improve their robustness for dissimilar unseen classes. This capability is beneficial for improving the practicality of the GZSL model. From an evaluation perspective, existing methods assess using visible and invisible classes from the same dataset. This leads to excessive focus on similar unseen classes during evaluation, thereby overestimating the generalizability of existing GZSL methods. In contrast, the cross-dataset evaluation protocol proposed in the paper can more comprehensively reflect the performance of existing GZSL methods on similar, dissimilar and practical settings. + +Acknowledgement. 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ModeCN [38]TransZero [9]ZLA [4]DGZ [5]Ours (Δ)
Similar42.5047.9942.6543.1648.45 (+0.46)
Dissimilar5.092.478.5212.3047.44 (+35.14)
", + "image_path": "86a24f0161f409aede503f30384b80727ea06a6e7a6f4339f5d07f356229c650.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 408, + 413, + 445, + 422 + ], + "lines": [ + { + "bbox": [ + 408, + 413, + 445, + 422 + ], + "spans": [ + { + "bbox": [ + 408, + 413, + 445, + 422 + ], + "type": "text", + "content": "(b) Results" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 426, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 502 + ], + "type": "text", + "content": "Figure 1. Setting illustration and results: (a) Comparison with the existing setting, our setting takes into account the scenario where the unseen classes are dissimilar to seen classes; (b) Performance of existing GZSL methods on similar and dissimilar unseen classes on the CUB dataset. The similar unseen classes were obtained from the same CUB dataset, while the dissimilar unseen classes come from AWA2 and SUN dataset." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 508, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 581 + ], + "type": "text", + "content": "To tackle this challenge, zero-shot learning (ZSL) has been proposed to recognize new classes via transferring knowledge obtained from seen classes with the help of semantic information [14, 15, 23, 52]. In contrast, Generalized ZSL (GZSL) is a more challenging task which handle test samples from both seen and unseen classes [3, 25, 29, 34]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "The core idea of GZSL is to introduce auxiliary semantic information and establish the connection between semantic and visual space for the recognition of unseen classes [34]. Since unseen samples are not available during training, existing GZSL models often misclassify unseen class samples into seen classes during test (known as the bias issue) [21, 22]. To alleviate this issue, several strategies have been introduced. A common strategy is to utilize a backbone pre-trained on the ImageNet-1K dataset [13] to extract visual features [7, 24, 26, 36, 50], which is beneficial to improve the generalization ability of visual features. However," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 219, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 219, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 219, + 713 + ], + "type": "text", + "content": "*Corresponding authors: Zengmao Wang, Bo Du" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23344" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "content": "the rich semantics that implicitly contained in the backbone classification heads are simply ignored in these approaches, and thus their ability to exploit diverse semantics is limited. Generative-based GZSL methods [4-6, 16, 51] alleviate the bias problem by introducing the semantics from test unseen classes, and some semantic augmentation approaches focus on enhancing the semantics of each class by leveraging the textual documents [30], large language model [31], etc [19, 50]. However, these approaches share a common limitation that they heavily rely on the semantics and visual features from seen classes to build the relations between visual and semantic space. This makes these models perform poorly on dissimilar unseen classes (see Fig. 1b), as little information can be transferred from seen to dissimilar unseen classes. That is, these methods can only deal with the unrealistic setting that the unseen classes are similar with seen classes (see existing setting of Fig. 1a). However, it is inevitable that unseen classes may be quite different from seen classes in the real-world applications, and hence it is desirable to enhance GZSL models to effectively handle dissimilar unseen classes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 326, + 289, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 289, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 289, + 613 + ], + "type": "text", + "content": "To achieve this goal, we need to address three main challenges: (I) how to obtain the information that can be transferred to dissimilar unseen classes; (II) how to enable effective information transfer without labeled training data; and (III) how to reduce costs as much as possible while ensuring effectiveness. If the cost of the solution exceeds the cost of collecting the data and retraining the model, then such a solution would be meaningless. Therefore, we propose a simple yet effective GZSL framework by exploring Diverse Semantics from External Class Names (DSECN), which is robust on both the similar and dissimilar unseen classes. Specifically, we introduce the diverse semantics from external (not test unseen classes) class names as the bridge to reduce the gap between the seen and unseen classes, which is beneficial for the recognition of unseen classes (challenge I). Then we utilize the classification head pre-trained on large-scale dataset, e.g., ImageNet-1K [13], to align the introduced semantics to the visual space (challenge II). Finally, the hierarchical taxonomy of WordNet [28] for the classes in large-scale dataset is introduced to further improve the diversity of semantics from class names. Since the class name and pre-trained classification head are quite easy to collect, the cost of our method is quite low (challenge III)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 615, + 283, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 615, + 283, + 628 + ], + "spans": [ + { + "bbox": [ + 58, + 615, + 283, + 628 + ], + "type": "text", + "content": "To summarize, the main contributions of this paper are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 630, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "content": "- To the best of our knowledge, we are the first that explicitly study the realistic GZSL setting that both similar and dissimilar unseen classes exist (see our setting in Fig. 1a)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": "- We propose a GZSL method that explores the diverse semantics from external class names (DSECN), which is simultaneously robust on the similar and dissimilar unseen classes." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 119 + ], + "type": "text", + "content": "- We show that the proposed idea can be easily integrated into other GZSL approaches, such as generative-based ones, and improve their robustness for dissimilar unseen classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 121, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 547, + 192 + ], + "type": "text", + "content": "We conduct extensive experiments on diverse real-world datasets. The results show that in the practical setting including both similar and dissimilar unseen classes, the harmonic mean accuracies of our method significantly outperform all counterparts. Besides, our model can be trained within one minute on all three datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 204, + 392, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 204, + 392, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 204, + 392, + 217 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 224, + 479, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 479, + 237 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 479, + 237 + ], + "type": "text", + "content": "2.1. Generalized Zero-shot Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 243, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 545, + 471 + ], + "type": "text", + "content": "Existing GZSL methods can be broadly categorized into embedding-based [9, 18, 25, 38] and generative-based ones [2, 5, 12, 16]. Early global embedding-based methods [15, 18, 25, 38, 45] align global visual features with corresponding category semantic information into a common embedding space, which enables knowledge transfer from seen to unseen classes. Recently proposed local embedding-based methods [9-11, 42, 48, 49] utilize attribute descriptions as guidance to discover the discriminative local features between seen classes and unseen classes. Besides, generative-based methods [4, 5, 12, 37, 38, 47] introduce the semantic from test unseen classes to alleviate the bias problem in GZSL [34]. However, these methods focus on the unrealistic setting where unseen classes are assumed to be similar to seen classes, and perform poorly in identifying dissimilar unseen classes. In contrast, our work focuses on a realistic GZSL setting that includes both similar and dissimilar unseen classes, and the proposed DSECN can robustly identify similar and dissimilar unseen classes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 479, + 480, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 480, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 480, + 491 + ], + "type": "text", + "content": "2.2. Semantic Information for GZSL" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": "Semantic information is a bridge that transfers knowledge from seen classes to unseen class recognition and is crucial to GZSL [30, 34, 50]. Most of prior works rely on human-annotated attributes [2, 32, 49] or word vectors [20, 39] as the semantic information. While attributes are accurate, they are costly to annotate and are not suitable for a large-scale problem [20, 50]. In contrast, word vectors require less human labor and are suitable for large-scale datasets [34]. However, word vectors often do not reflect visual similarities, thus limiting the performance [30, 49]. Xu et al. [49] propose a visually-grounded semantic embedding (VGSE) network to discover semantic embeddings containing discriminative visual properties. Naeem et al. [30] propose a transformer-based model I2DFormer that learns semantic embeddings from raw online textual documents. However, these methods only consider semantic enhancement within a single category. When an unseen class is dissimilar to seen classes, the transferable semantic infor" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23345" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "mation from seen classes is still little, which limits their performance. In contrast, we introduce diverse semantic information from external category names and align the introduced semantics into visual space using the classification head pre-trained on a large-scale dataset , thus assisting in the identification of dissimilar unseen categories." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 156, + 153, + 169 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 153, + 169 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 153, + 169 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": "Problem Formulation. In ZSL and GZSL, we define two sets of classes: seen classes in " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^s" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " and unseen classes in " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ". The seen classes " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^s" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " and the unseen classes " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " are disjoint, i.e., " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^s \\cap Y^u = \\emptyset" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^s \\cup Y^u = \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ". The unseen classes may be similar or dissimilar to seen classes in practice. Hence, in this work, the unseen classes " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " contain similar unseen classes " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y_s^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " and dissimilar unseen classes " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y_d^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "Y^u = Y_s^u \\cup Y_d^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ". The seen data are expressed as " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "D^s = \\{(x_i^s, y_i^s)\\}" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "x_i^s \\in X" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": "-th sample features extracted by the pretrained backbone network, e.g., ResNet101 [17], and " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "y_i^s \\in Y^s" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " is its class label. The " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "D^s" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " is split into a training set " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "D_{tr}^s" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " and a testing set " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "D_{te}^s" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ". On the other hand, the unseen data are denoted as " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "D^u = \\{(x_i^u, y_i^u)\\}" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "x_i^u \\in X^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "y_i^u \\in Y^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " are the sample features of unseen classes and the corresponding ground-truth label for evaluation, respectively. The goal of ZSL is to learn a classifier for classifying test samples from unseen classes, i.e., " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "X \\xrightarrow{f_{ZSL}} Y^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ". In contrast to ZSL, the goal of GZSL is to learn a classifier for classifying test samples from both seen and unseen classes, i.e., " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "X \\xrightarrow{f_{GZSL}} Y^s \\cup Y^u" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": ". In ZSL and GZSL, the auxiliary semantic information " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " is obtained by transforming the class labels " + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 176, + 289, + 469 + ], + "type": "text", + "content": " using human-annotated attributes [9] or language models [27, 35]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 471, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 567 + ], + "type": "text", + "content": "Overview of framework. As shown in Fig. 2, the framework contains three components: visual flow (§ 3.1), diverse semantic enhancement (DSE, § 3.2), and hierarchy taxonomy enhancement (HTE, § 3.3). The visual flow aligns seen class semantics into visual space. Diverse semantic and hierarchy taxonomy enhancement are proposed to enhance the diversity of semantics available to the model, thereby assisting the identification of dissimilar unseen classes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 574, + 125, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 125, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 125, + 586 + ], + "type": "text", + "content": "3.1. Visual Flow" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "The visual flow is designed to classify visual objects from both seen and unseen classes by transferring knowledge from the seen classes to the unseen ones with the help of semantic information. The visual flow contains two parts: semantic-to-visual sub-network " + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "(S2V)" + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": " and visual classifier. The " + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": " sub-network is a learnable multilayer perceptron (MLP), and is used to link the semantic and visual representation. This enables the model to transfer the knowledge from seen classes to the unseen classes through semantic information. The visual classifier uses the relation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "ship between the visual sample and all categories to obtain the classification result of the sample. Because the visual flow requires paired visual samples and category labels, in the training phase, the visual flow can only be trained on the paired visual feature and label dataset " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "D_{tr}^{s}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": ". Specifically, the " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " sub-network takes the seen semantic feature " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "A^{s}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " as input to generate the class-level visual prototype of seen classes " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "V^{s}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": ". The process to generate the class-level visual prototype of seen classes " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "V^{s}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " can be expressed by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 352, + 190, + 545, + 206 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 190, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 352, + 190, + 545, + 206 + ], + "type": "interline_equation", + "content": "A ^ {s} \\in \\mathbb {R} ^ {C ^ {s} \\times d ^ {a}} \\xrightarrow {S 2 V} V ^ {s} \\in \\mathbb {R} ^ {C ^ {s} \\times d ^ {v}}, \\tag {1}", + "image_path": "a1d751674483e4bf7c067325d58e7e3b6e5aa35722fc84ad40b966c0d164578c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "type": "inline_equation", + "content": "C^s, d^a, d^v" + }, + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "type": "text", + "content": " denote the number of seen classes, the dimensionality of semantic representation and the dimensionality of visual representation, respectively. " + }, + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "type": "inline_equation", + "content": "A^s" + }, + { + "bbox": [ + 304, + 214, + 545, + 275 + ], + "type": "text", + "content": " signifies the semantic representations of seen classes and is extracted by language models [27, 35]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "content": "Next, the visual classifier (VC) computes the scaled cosine similarity between the visual feature of seen classes " + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "inline_equation", + "content": "X_{tr}^{s} \\in \\mathbb{R}^{N_{tr}^{s} \\times d^{v}}" + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "content": " and the class-level visual feature of seen classes " + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "inline_equation", + "content": "V^{s} \\in \\mathbb{R}^{C^{s} \\times d^{v}}" + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "content": " as logits " + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "inline_equation", + "content": "l^{s} \\in \\mathbb{R}^{N_{tr}^{s} \\times C^{s}}" + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "inline_equation", + "content": "N_{tr}^{s}" + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "content": " is the number of seen class samples in the training set. Formally, the logits " + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "inline_equation", + "content": "l^{s}" + }, + { + "bbox": [ + 304, + 275, + 545, + 347 + ], + "type": "text", + "content": " can be obtained as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 380, + 355, + 545, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 355, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 380, + 355, + 545, + 384 + ], + "type": "interline_equation", + "content": "l ^ {s} = \\gamma^ {2} \\frac {X _ {t r} ^ {s} V ^ {s} {} ^ {\\top}}{\\| X _ {t r} ^ {s} \\| \\| V ^ {s} \\|}, \\tag {2}", + "image_path": "97b7254df5c508a699316e158be13833455e999006375fae4b4c419a0d0397de.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 391, + 416, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 391, + 416, + 402 + ], + "spans": [ + { + "bbox": [ + 306, + 391, + 416, + 402 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 391, + 416, + 402 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 391, + 416, + 402 + ], + "type": "text", + "content": " is the scale factor." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "content": "Finally, we adopt the Cross-Entropy (CE) loss to update the visual flow:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 376, + 437, + 545, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 437, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 376, + 437, + 545, + 451 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {V} = \\mathcal {L} _ {C E} \\left(\\sigma \\left(l ^ {s}\\right), Y _ {t r} ^ {s}\\right), \\tag {3}", + "image_path": "9754a12ab2f56066893a243ccff7c84d26bfcf49bd7c598eb43795e2a7df6a60.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 460, + 470, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 470, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 470, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 460, + 470, + 472 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 306, + 460, + 470, + 472 + ], + "type": "text", + "content": " denotes the softmax function." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 479, + 477, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 477, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 477, + 491 + ], + "type": "text", + "content": "3.2. Diverse Semantic Enhancement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "type": "text", + "content": "Motivation of DSE. When the unseen classes are dissimilar with seen classes, the visual flow can transfer only little information from seen classes to unseen classes, resulting in poor recognition performance of unseen classes. Motivated by this, we propose the diverse semantic enhancement module, which introduces the semantic information from external class names to help the recognition of unseen classes. To successfully transfer semantic information to unseen classes, establishing a substantial linkage between the semantics inherent in class names and their corresponding visual features is imperative. Nonetheless, the visual feature of the class name is unknown, which poses the primary obstacle in leveraging semantics from class names to enhance Generalized Zero-Shot Learning (GZSL). Considering the visual representation " + }, + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "type": "text", + "content": " obtained through the pretrained backbone, e.g. ResNet101, on the large-scale dataset, we use the classification head corresponding to pretrained backbone as semantic classifier (SC) to constrain the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23346" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 542, + 366 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 542, + 366 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 542, + 366 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 542, + 366 + ], + "type": "image", + "image_path": "d4d7ef52d30ea1a23fa9db0dc035fb574b8eac3070f2d06ed25bc23d397667d1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 369, + 545, + 447 + ], + "lines": [ + { + "bbox": [ + 46, + 369, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 545, + 447 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed DSECN framework. During the training phase, our method contains three components: visual flow, diverse semantic enhancement, and hierarchy taxonomy enhancement. In the visual flow, we employ the visual cosine classifier to align the semantics and visual features of seen classes. Then the diverse semantic enhancement and hierarchy taxonomy enhancement introduce more diverse information from the external base class names and the augmented class names. The introduced diverse semantics are aligned to the visual space using pre-trained classification head, which enables our model to learn a robust union space for both similar and dissimilar unseen classes. During the inference phase, benefiting from the learned union space that contains visual-semantic correspondence of diverse classes, the test image from dissimilar unseen classes can be accurately classified." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 450, + 287, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 497 + ], + "type": "text", + "content": "generated class-level visual prototype of class names to visual space. Besides, the introduced semantics from class names should be diverse. Hence, we choose the class names of large-scale dataset to extract diverse semantics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "content": "Construction of DSE. We first introduce the class names " + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "inline_equation", + "content": "CN^{EB}" + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "content": " of large-scale dataset corresponding to pretrained network and extract the semantic information " + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "inline_equation", + "content": "A^{EB} \\in \\mathbb{R}^{C^{EB} \\times d^a}" + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "inline_equation", + "content": "CN^{EB}" + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "content": " using the Language Model (LM), i.e.," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 119, + 558, + 287, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 558, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 119, + 558, + 287, + 572 + ], + "type": "interline_equation", + "content": "A ^ {E B} = L M \\left(C N ^ {E B}\\right). \\tag {4}", + "image_path": "0d95dccf3d2ba8250916d4caed39b1a5832f87cc2a8bdd4183e2c38ba6692882.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "inline_equation", + "content": "C^{EB}" + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "text", + "content": " denotes the number of external base class names from the large-scale dataset. Then the semantic information " + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "inline_equation", + "content": "A^{EB}" + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "text", + "content": " are taken as the input of " + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "text", + "content": " sub-network to generate class-level visual prototype " + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "inline_equation", + "content": "V^{EB} \\in \\mathbb{R}^{C^{EB} \\times d^v}" + }, + { + "bbox": [ + 46, + 578, + 287, + 629 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 123, + 637, + 287, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 637, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 123, + 637, + 287, + 652 + ], + "type": "interline_equation", + "content": "V ^ {E B} = S 2 V \\left(A ^ {E B}\\right). \\tag {5}", + "image_path": "dc10d07c8077c181204be721cb1f108389fca1c1e4003e6ee68f776378faecc8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "type": "text", + "content": "Next, the generated visual prototype " + }, + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "type": "inline_equation", + "content": "V^{EB}" + }, + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "type": "text", + "content": " is fed into the semantic classifier (SC) to get the logits " + }, + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "type": "inline_equation", + "content": "l^{EB} \\in \\mathbb{R}^{C^{EB} \\times C^{PR}}" + }, + { + "bbox": [ + 46, + 662, + 287, + 699 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 127, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 127, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "l ^ {E B} = S C (V ^ {E B}), \\tag {6}", + "image_path": "582684d8c61207f01e898d5bbaeb488509c2b1f65e8328e9dbda2a4c9e323ff9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "type": "inline_equation", + "content": "SC" + }, + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "type": "text", + "content": " is the frozen classification head from pretrained network. " + }, + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "type": "inline_equation", + "content": "C^{PR}" + }, + { + "bbox": [ + 305, + 450, + 545, + 474 + ], + "type": "text", + "content": " is the class number of pretraining dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 474, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 545, + 497 + ], + "type": "text", + "content": "Due to the backbone pretrained in large-scale dataset, we can obtain the label of " + }, + { + "bbox": [ + 306, + 474, + 545, + 497 + ], + "type": "inline_equation", + "content": "CN^{EB}" + }, + { + "bbox": [ + 306, + 474, + 545, + 497 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 371, + 505, + 545, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 505, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 371, + 505, + 545, + 520 + ], + "type": "interline_equation", + "content": "Y ^ {E B} = C N 2 Y \\left(C N ^ {E B}\\right), \\tag {7}", + "image_path": "fee80673ec543cd50a642c484201e7caca4bec5c52eadcb7556bef11d210679f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 528, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 528, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 528, + 545, + 563 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 528, + 545, + 563 + ], + "type": "inline_equation", + "content": "CN2Y" + }, + { + "bbox": [ + 305, + 528, + 545, + 563 + ], + "type": "text", + "content": " is the dictionary mapping from class names to labels in the large-scale dataset corresponding to the pretrained backbone." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "type": "text", + "content": "Finally, the Cross-Entropy (CE) Loss is adopted to update the diverse semantic enhancement module:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 364, + 595, + 545, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 595, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 364, + 595, + 545, + 609 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E B} = \\mathcal {L} _ {C E} (\\sigma (l ^ {E B}), Y ^ {E B}). \\tag {8}", + "image_path": "8fc7f5bf1c292b46011fed3258ee8e543bdcf236249d998c57fc2b5bcc796a45.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "Comparison with Analogous Methods. The prevailing GZSL approach depends on transferring semantic knowledge from seen to unseen classes. However, these techniques falter in a realistic GZSL setting that encompasses both similar and dissimilar unseen classes. Our method introduces varied semantics derived from external class names and aligns them with the visual domain through a pre-trained classification head. This process allows our" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23347" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "model to leverage newly introduced semantics as a bridge connecting seen and dissimilar unseen classes, thus enhancing the identification of dissimilar unseen classes. Notably, the procurement cost of class names and pre-trained classification heads is low, rendering our approach more feasible in practice." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 149, + 237, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 149, + 237, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 149, + 237, + 163 + ], + "type": "text", + "content": "3.3. Hierarchy Taxonomy Enhancement" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "type": "text", + "content": "Chihuahua is a kind of pet dog, and the dog is also a kind of animal. That is, there is a hierarchical structure between different categories. Therefore, we can utilize the hierarchy structure of classes to augment more classes. Based on the assumption, we propose a class name augment method based on hierarchy structure of classes. Specifically, we first employ WordNet [28] to extract the subclass names of external base class names " + }, + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "type": "inline_equation", + "content": "(CN^{EB})" + }, + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "type": "text", + "content": " as hierarchically augmented class names " + }, + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "type": "inline_equation", + "content": "(CN^{HA})" + }, + { + "bbox": [ + 46, + 168, + 289, + 276 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 285, + 287, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 285, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 100, + 285, + 287, + 301 + ], + "type": "interline_equation", + "content": "C N ^ {H A} = h y p o n y m s \\left(C N ^ {E B}\\right), \\tag {9}", + "image_path": "08158a4131afe482ce556154c6a7f0e4c4761f2bddf3819b4d1e4e28e6e29d46.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "text", + "content": "where hyponyms denotes the mapping function for extracting hyponyms using WordNet [28]. The semantic information " + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "inline_equation", + "content": "A^{HA} \\in \\mathbb{R}^{C^{HA} \\times d^a}" + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "inline_equation", + "content": "CN^{HA}" + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "text", + "content": " can be extracted by the language model, i.e., " + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "inline_equation", + "content": "A^{HA} = LM(CN^{HA})" + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "inline_equation", + "content": "C^{HA}" + }, + { + "bbox": [ + 46, + 304, + 287, + 363 + ], + "type": "text", + "content": " denotes the number of the augmented class names." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 363, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 363, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 287, + 390 + ], + "type": "text", + "content": "Then we can obtain the predicted probability " + }, + { + "bbox": [ + 47, + 363, + 287, + 390 + ], + "type": "inline_equation", + "content": "l^{HA} \\in \\mathbb{R}^{C^{HA} \\times C^{PR}}" + }, + { + "bbox": [ + 47, + 363, + 287, + 390 + ], + "type": "text", + "content": " of the augmented classes as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 394, + 287, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 394, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 113, + 394, + 287, + 409 + ], + "type": "interline_equation", + "content": "l ^ {H A} = S C \\left(S 2 V \\left(A ^ {H A}\\right)\\right), \\tag {10}", + "image_path": "93a132a17b5eb9b804548cae392e903673a3b3f15d39c3d1f6d6b790835f47e9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "SC" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": " is the semantic-to-visual (" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": ") subnetwork and the semantic classifier (" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "SC" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": "), respectively. Considering that the subclass is one of the parent classes, we assign the label of the corresponding parent class as the label of the subclass. For example, fire ant is the subclass of ant, and thus the label of fire ant " + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "y^{fire-ant}" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": " is assigned as the label of ant in the pretraining large-scale dataset, i.e., " + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "y^{fire-ant} = y^{ant} = CN2Y(ant)" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": ". Based on the idea, the label " + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "Y^{HA}" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "inline_equation", + "content": "CN^{HA}" + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": " can be obtained as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 525, + 287, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 525, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 83, + 525, + 287, + 540 + ], + "type": "interline_equation", + "content": "Y ^ {H A} = C N 2 Y \\left(h y p e r n y m s \\left(C N ^ {H A}\\right)\\right), \\tag {11}", + "image_path": "cb932015f4a40b7ab586d400c1b6acb8db447b1e128d0bedaf2afd8bc70e8d48.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 593 + ], + "type": "text", + "content": "where hypernyms denotes the mapping function for extracting hypernyms using WordNet [28], " + }, + { + "bbox": [ + 46, + 545, + 287, + 593 + ], + "type": "inline_equation", + "content": "CN2Y" + }, + { + "bbox": [ + 46, + 545, + 287, + 593 + ], + "type": "text", + "content": " is the dictionary mapping from class names to labels in the largescale dataset corresponding to the pretrained backbone." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "type": "text", + "content": "Finally, the Cross-Entropy (CE) Loss is adopted to obtain the loss of hierarchy taxonomy enhancement:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 621, + 287, + 636 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 621, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 287, + 636 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {H A} = \\mathcal {L} _ {C E} (\\sigma (l ^ {H A}), Y ^ {H A}). \\tag {12}", + "image_path": "c24cb8722c0e0f3e613d5bac1c8c4cf2637539b2c762455cd0c5d217d260a592.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 641, + 178, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 178, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 178, + 654 + ], + "type": "text", + "content": "3.4. Training and Inference" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 659, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 659, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 659, + 287, + 696 + ], + "type": "text", + "content": "The proposed DSECN, which contains three components, is trained in an end-to-end manner, and the total loss function is given as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 86, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 86, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {V} + \\lambda_ {E B} \\mathcal {L} _ {E B} + \\lambda_ {H A} \\mathcal {L} _ {H A}, \\tag {13}", + "image_path": "030753593bc1dfc82245b638fb9fd9bbb98dc009a2a6a075c8c8893d789ed539.jpg" + } + ] + } + ], + "index": 14 + }, + { + "type": "code", + "bbox": [ + 318, + 89, + 515, + 369 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 485, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 485, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 485, + 87 + ], + "type": "text", + "content": "Algorithm 1: Training Process of DSECN" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "lines": [ + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "spans": [ + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": "Input: Training seen data " + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "\\{X_{tr}^{s},CN^{s},Y_{tr}^{s}\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " , external base class names " + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "C N^{E B}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " and hierarchy augmented class names " + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "CN^{HA}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " \nOutput: The final S2V model \n// Generate Semantics and Labels \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "A^s,A^{EB},A^{HA} = LM(CN^s,CN^{EB},CN^{HA})" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "Y^{EB}\\gets \\{CNEB\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " in Eq.(7), \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "Y^{HA}\\leftarrow \\{CN^{HA}\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " in Eq.(11). \nfor " + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "e = 1,2,\\ldots ,E" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " do \n// Visual Flow \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "V^{s} = S2V(A^{s})" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "l^s\\gets \\{V^s,X_{tr}^s\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " in Eq.(2), \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_V\\gets \\{l^s,Y_{tr}^s\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " in Eq.(3). \n// Diverse Semantic Enhancement \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "V^{EB} = S2V(A^{EB})" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "l^{EB} = SC(V^{EB})" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{EB}\\gets \\{l^{EB},Y^{EB}\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " in Eq.(8). \n// Hierarchy Taxonomy Enhancement \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "V^{HA} = S2V(A^{HA})" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "l^{HA} = SC(V^{HA})" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{HA}\\gets \\{l^{HA},Y^{HA}\\}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " in Eq.(12). \n// Compute Total Loss \n" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total} = \\mathcal{L}_V + \\mathcal{L}_{EB} + \\mathcal{L}_{HA}" + }, + { + "bbox": [ + 318, + 89, + 515, + 369 + ], + "type": "text", + "content": " \n// Update Parameters \nUpdate the parameters of S2V using Adam." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "code_body" + } + ], + "index": 16, + "sub_type": "algorithm" + }, + { + "bbox": [ + 319, + 369, + 335, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 369, + 335, + 377 + ], + "spans": [ + { + "bbox": [ + 319, + 369, + 335, + 377 + ], + "type": "text", + "content": "end" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\lambda_{EB}" + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\lambda_{HA}" + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": " are trade-off hyper-parameters. The training pseudo-code is presented in Algorithm 1. It is noteworthy that we only update the parameters of " + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": "In the inference phase, given a visual feature " + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": " and the semantic feature " + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": " of all classes, we apply the visual flow to obtain the final class prediction " + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": ". Specifically, the semantic features " + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "A = A^s \\cup A^u" + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": " of all classes are first fed into " + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "S2V" + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": " sub-network to generate the class-level visual prototype, i.e., " + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "V = S2V(A)" + }, + { + "bbox": [ + 305, + 441, + 545, + 525 + ], + "type": "text", + "content": ". Then the final class prediction can be obtained according to:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 345, + 533, + 545, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 533, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 345, + 533, + 545, + 561 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\underset {y \\in \\mathcal {Y}} {\\arg \\max } \\left(\\operatorname {s o f t m a x} \\left(\\gamma^ {2} \\frac {x V ^ {\\top}}{\\| x \\| \\| V \\|}\\right)\\right), \\tag {14}", + "image_path": "db1494b46bbb11843d0a35a872d29e88ce708a28b6f92aa8d5a833725467bf70.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = Y^{s}\\cup Y^{u}" + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "text", + "content": " is the union of seen classes " + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "inline_equation", + "content": "Y^{s}" + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "text", + "content": " and unseen classes " + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "inline_equation", + "content": "Y^{u}" + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 599, + 519, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 519, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 519, + 613 + ], + "type": "text", + "content": "3.5. Integrating into Existing GZSL Methods" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "The proposed DSECN can be easily integrated into other mainstream GZSL approaches to improve their robustness for dissimilar unseen classes. The GZSL method essentially models the relationship between visual and semantic features, so that semantic features can be used as a bridge to accurately classify visual features of unseen classes. DSECN can effectively build such relationship between \"diverse\" semantic and visual features at low cost, and thus signif" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23348" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "icantly improving the performance of existing GZSL approaches. Taking generative-based methods as an example, the generator can generate visual features of the introduced diverse semantic from external class names. Then the pretrained classification head is used to align the generated visual features to visual space. This enables the generator to adapt to more classes and generate more accurate visual features for unseen classes. Finally, the refined visual features of unseen classes are used to train the GZSL classifier, thus improving the model performance. More details on the integration of our idea with the generative-based methods and other types of GZSL approaches can be found in the supplementary material A." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 241, + 128, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 241, + 128, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 241, + 128, + 254 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 261, + 170, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 170, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 170, + 274 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 280, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 287, + 399 + ], + "type": "text", + "content": "Datasets. We conduct our experiments on three widely used ZSL benchmark datasets, which are AWA2 [46], CUB [40] and SUN [33]. Since the main focus of this work is to study the more practical GZSL setting that includes both similar and dissimilar unseen classes, the learned GZSL model needs to recognize the dissimilar unseen classes from other datasets. Hence, we do not use the human-annotated attributes, but rather use language models, e.g., W2V [27] and CLIP [35], to extract the semantic embedding of classes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": "Evaluation. Unlike most existing methods that only consider similar settings, we comprehensively evaluate the GZSL model on three testing settings, including similar, dissimilar and practical settings. To better describe these settings, we define the set of datasets as " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "Set = \\{AWA2, CUB, SUN\\}" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ". The dataset of seen classes and unseen classes are respectively expressed as " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "ds" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "du" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "ds \\subseteq Set" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "du \\subseteq Set" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ". To simulate the similar scene, the dataset " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "ds" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " of seen classes is same as the dataset " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "du" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " of unseen classes, i.e., " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "ds = du" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ". To simulate the dissimilar scene, we use the complementary set of " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "ds" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "du" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "du = \\complement_{Set} ds" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ". For practical scene, the unseen classes may either be similar or dissimilar to the seen classes. Therefore, in our practical setting, we use all datasets to evaluate unseen classes, i.e., " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "du = Set" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ". For all three settings, we follow [46] to evaluate model for both ZSL and GZSL. In the ZSL, the average per-class top-1 accuracy (" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ") on unseen classes is taken as the evaluation metric. In the GZSL, the evaluation metric is the harmonic mean " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " between seen classes accuracy " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": " and unseen class accuracy " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "inline_equation", + "content": "H = (2 \\times U \\times S) / (U + S)" + }, + { + "bbox": [ + 46, + 401, + 289, + 652 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": "Implementation Details. The implementation details are provided in the supplementary material B." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Fair-comparison Guarantee. All methods are trained on seen class images of the training set " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "D_{tr}^{s}" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": ", ensuring that the labeled training data are the same for different approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "They all adopt the same backbone weights pretrained on large-scale dataset, which means that the pre-training data implicitly utilized by the model is completely consistent. They all use the same language model to extract semantic features, ensuring the fairness of the semantic extraction method. Therefore, the same data are utilized for different methods, and the fairness of comparison is guaranteed. Notably, introducing additional information is a common strategy to mitigate bias issue in GZSL. For example, generative-based GZSL methods [2, 16] introduce semantic information of test unseen classes to mitigate bias. The transductive GZSL methods [1, 41, 44] utilize test unseen class samples to mitigate bias. Unlike these methods, our method does not utilize any semantic or sample information of test unseen classes, thus making our method more suitable for practical GZSL." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 272, + 492, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 272, + 492, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 272, + 492, + 285 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-Arts" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "type": "text", + "content": "Performance. We comprehensively compare our method with several SOTA GZSL approaches on the similar, dissimilar, and practical settings. Tab. 1 shows that: 1) the performance of all counterparts in identifying dissimilar unseen classes is very poor, which proves that existing models have difficulty in identifying common dissimilar unseen classes in the real world; 2) our method achieves the SOTA performance on all datasets, semantic embeddings and settings, which demonstrates the effectiveness of our method. In particular, our method significantly outperforms all counterparts under dissimilar and practical settings. Take the CUB dataset under dissimilar setting as an example, our method outperforms the most competitive counterpart by " + }, + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "type": "inline_equation", + "content": "21.76\\%" + }, + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "type": "inline_equation", + "content": "35.14\\%" + }, + { + "bbox": [ + 304, + 291, + 545, + 470 + ], + "type": "text", + "content": " on the W2V [27] and CLIP text embedding [35], respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 471, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 578 + ], + "type": "text", + "content": "Training Efficiency. We conduct training efficiency comparison experiments on all datasets using CLIP [35] text embedding. Tab. 2 reports the training time of each method. Benefiting from the simple network design, the training costs of CN and the proposed method are much lower than other approaches. Although our method is slightly slower than the CN method because of the introducing semantics from external class names, our method can be trained within one minute." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 586, + 400, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 400, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 400, + 600 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "To evaluate the benefits of tackling GZSL with the diverse semantic enhancement (DSE) and the hierarchy taxonomy enhancement (HTE), we conduct an ablation study on all semantics, datasets and settings. The results using CLIP [35] and W2V [27] semantic embedding are reported in Fig. 3 and Fig. S3 of supplementary material C, respectively. From these results, we can see that: 1) regardless of W2V or CLIP semantic representation, the baseline model " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " has poor recognition performance on dissimilar unseen classes." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23349" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 542, + 342 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 542, + 342 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 542, + 342 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 542, + 342 + ], + "type": "table", + "html": "
Train DataMethodsW2VCLIP
SimilarDissimilarPracticalSimilarDissimilarPractical
ZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSLZSLGZSL
CUB\\( ZLA^†[IJCAI22] [4] \\)17.2416.033.356.007.4111.0446.5642.654.668.5219.3224.89
\\( DGZ^†[AAAI23] [5] \\)18.0018.423.245.675.477.4247.1243.167.1512.3020.6126.60
\\( CN^‡[ICLR21] [38] \\)18.1622.101.122.035.698.7443.7442.503.825.0917.8123.25
\\( TransZero^‡[AAAI22] [9] \\)17.1515.650.900.866.496.4149.7747.993.562.4719.1824.81
\\( MSDN^‡[CVPR22] [10] \\)18.3018.461.733.334.846.4449.1747.692.652.7918.6023.40
\\( HASZSL^‡[MM23] [11] \\)13.4616.911.042.035.266.7542.5143.642.172.8116.2617.12
DSECN (Ours)18.8023.4017.7327.7617.8123.6350.7048.4535.5447.4440.8545.29
AWA2\\( ZLA^†[IJCAI22] [4] \\)49.7854.653.416.214.678.2076.5975.095.159.329.2514.87
\\( DGZ^†[AAAI23] [5] \\)54.5957.023.125.874.848.5478.2776.597.0312.5910.3017.26
\\( CN^‡[ICLR21] [38] \\)41.1249.621.662.763.476.3079.4573.385.489.958.6014.72
\\( TransZero^‡[AAAI22] [9] \\)39.7042.901.071.943.345.3069.5859.782.113.942.674.79
\\( MSDN^‡[AAAI22] [9] \\)45.9048.521.632.523.475.0564.4264.213.666.035.899.46
\\( HASZSL^‡[MM23] [11] \\)36.5945.040.880.981.261.0660.3456.066.767.7337.9537.25
DSECN (Ours)69.2370.7111.2119.8814.3723.7986.9781.2837.0152.5240.0053.74
SUN\\( ZLA^†[IJCAI22] [4] \\)33.5423.909.1213.0618.7018.8654.6536.708.5211.7931.5928.31
\\( DGZ^†[IJCAI22] [4] \\)31.3225.089.3113.7617.5317.8553.5437.7311.8717.4931.6128.31
\\( CN^‡[ICLR21] [38] \\)33.8226.275.177.0518.8018.1455.5638.879.6913.6432.8030.00
\\( TransZero^‡[AAAI22] [9] \\)30.4221.813.682.6616.6914.6354.5135.865.282.8929.9825.39
\\( MSDN^‡[AAAI22] [9] \\)28.1316.231.512.789.967.5853.3331.735.578.2028.3122.56
\\( HASZSL^‡[MM23] [11] \\)19.5111.413.720.1210.691.4136.5321.154.570.1220.028.34
DSECN (Ours)37.8526.8110.5416.4724.1921.6960.2840.3337.1140.1949.1038.54
", + "image_path": "6f725f0c8ae2d3fd3901cffc770e0e083ab0a17ec86ae363318df89151d12ab5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 367, + 208, + 487 + ], + "blocks": [ + { + "bbox": [ + 55, + 367, + 208, + 487 + ], + "lines": [ + { + "bbox": [ + 55, + 367, + 208, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 367, + 208, + 487 + ], + "type": "image", + "image_path": "e3061b91c6d49cab246c0bd8f4e276685c61e9ef4710d7f2f7301a7684d24286.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "lines": [ + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "text", + "content": "Figure 3. Effect of diverse semantic enhancement " + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "inline_equation", + "content": "(s)" + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "text", + "content": " and hierarchy taxonomy enhancement " + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "inline_equation", + "content": "(h)" + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "text", + "content": " for GZSL. We remove these two components as our baseline " + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "inline_equation", + "content": "(b)" + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "text", + "content": ". In the ablation study, we add DSE " + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "inline_equation", + "content": "(s)" + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "text", + "content": " and HTE " + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "inline_equation", + "content": "(h)" + }, + { + "bbox": [ + 47, + 487, + 544, + 508 + ], + "type": "text", + "content": " step by step to show their effect on GZSL. Refer to § 4.3." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 221, + 367, + 375, + 487 + ], + "blocks": [ + { + "bbox": [ + 221, + 367, + 375, + 487 + ], + "lines": [ + { + "bbox": [ + 221, + 367, + 375, + 487 + ], + "spans": [ + { + "bbox": [ + 221, + 367, + 375, + 487 + ], + "type": "image", + "image_path": "deae76973fc78c7ee8939f5633c96404f4a89cbd7dbf1acebb7601704e195b1e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 388, + 367, + 541, + 487 + ], + "blocks": [ + { + "bbox": [ + 388, + 367, + 541, + 487 + ], + "lines": [ + { + "bbox": [ + 388, + 367, + 541, + 487 + ], + "spans": [ + { + "bbox": [ + 388, + 367, + 541, + 487 + ], + "type": "image", + "image_path": "cece79792b9fd0202a37c48acb8dbc8fc2582ad9914b66b91e5554f4d43ba8be.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 516, + 292, + 609 + ], + "blocks": [ + { + "bbox": [ + 47, + 343, + 545, + 365 + ], + "lines": [ + { + "bbox": [ + 47, + 343, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 343, + 545, + 365 + ], + "type": "text", + "content": "Table 1. Comparison with the state-of-the-art GZSL approaches in the three settings, † and ‡ signify the generative-based method and embedding-based approach. Please see details in § 4.2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 516, + 292, + 609 + ], + "lines": [ + { + "bbox": [ + 48, + 516, + 292, + 609 + ], + "spans": [ + { + "bbox": [ + 48, + 516, + 292, + 609 + ], + "type": "table", + "html": "
MethodsCUBAWA2SUNMean
ZLA* [4]4.4 hours9.5 hours7.7 hours7.2 hours
DGZ* [5]8.3 hours12.2 hours16.1 hours12.2 hours
CN* [38]8.6 sec25.8 sec12.2 sec15.5 sec
TransZero° [9]40.7 min2.0 hours1.6 hours1.4 hours
MSDN° [10]4.4 min21.9 min14.5 min13.6 min
HAS° [11]5.4 hours17.3 hours7.4 hours10.0 hours
DSECN* (Ours)13.9 sec37.9 sec19.7 sec23.8 sec
", + "image_path": "1255569b10afdefaa70f057e81d229e13a70cb855aece09f92a19547844f9471.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "lines": [ + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "text", + "content": "Table 2. Training time for the recent GZSL methods that made their official implementations publicly available. * and " + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "text", + "content": " respectively indicate that the model uses the 2048-dimensional vector and " + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "inline_equation", + "content": "{14} \\times {14} \\times {2048}" + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "text", + "content": " -dimensional feature map extracted by pretrained Resnet101 as input. " + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 610, + 287, + 676 + ], + "type": "text", + "content": " denotes that the model takes original image as input and finetunes the pretrained backbone. See § 4.2." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "This indicates that the problem of identifying dissimilar unseen classes cannot be solved by enhancing the semantic information contained in seen classes; 2) after adding DSE" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " and HTE " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " to the baseline, the " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "b + s + h" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " model achieves the best performance on all semantics, datasets and settings. This proves that both the DSE " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " and the HTE " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " are critical to GZSL and complementary to each other on all three test settings; 3) the less similar the unseen classes are to the seen classes in the test setting, the greater the performance improvement gain brought by the proposed module " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": ". Taking the CUB dataset with CLIP semantic embedding as an example, " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "b + s + h" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " improves the harmonic mean accuracy by " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "42.38\\%" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "21.76\\%" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "4.73\\%" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " on dissimilar, practical and similar settings, respectively. This may be because when the unseen classes are dissimilar to seen classes, the baseline model can only transfer little information from seen classes to unseen classes, while " + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "inline_equation", + "content": "b + s + h" + }, + { + "bbox": [ + 304, + 519, + 545, + 710 + ], + "type": "text", + "content": " introduces a variety of semantic information from class names that can be transferred to unseen classes to improve the recognition performance of" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "23350" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 277, + 164 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 277, + 164 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 277, + 164 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 277, + 164 + ], + "type": "table", + "html": "
MethodsCUBAWA2SUN
W2VCLIPW2VCLIPW2VCLIP
CN [38]2.035.092.769.957.0513.64
CN+DSECN22.0837.6814.3533.0412.6429.11
TransZero [9]0.862.471.943.942.662.89
TransZero+DSECN2.414.442.515.413.593.02
DGZ [5]5.6712.305.8712.5913.7617.49
DGZ+DSECN26.3448.3917.0247.6817.7639.11
", + "image_path": "ac42e8e3cda92354cef98a55d08b7ed9b05dee3f07367e78833972354d88d35f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 209, + 282, + 302 + ], + "blocks": [ + { + "bbox": [ + 47, + 165, + 287, + 209 + ], + "lines": [ + { + "bbox": [ + 47, + 165, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 287, + 209 + ], + "type": "text", + "content": "Table 3. Effect of integrating DSECN into existing GZSL methods under dissimilar setting. CN [38], TransZero [9], and DGZ [5] belong to the global embedding-based, local embedding-based, and generation-based GZSL methods respectively. See details in § 4.4." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 209, + 282, + 302 + ], + "lines": [ + { + "bbox": [ + 50, + 209, + 282, + 302 + ], + "spans": [ + { + "bbox": [ + 50, + 209, + 282, + 302 + ], + "type": "table", + "html": "
SemanticsMethodsCUBAWA2SUN
1K21K1K21K1K21K
W2Vb2.961.965.512.8211.175.50
b+s+h27.7656.9719.8840.6816.4728.24
↑24.8055.0114.3737.865.3022.74
CLIPb5.066.877.747.9412.6615.55
b+s+h47.4477.6052.5271.2540.1961.59
↑42.3870.7344.7863.3127.5346.04
", + "image_path": "8c6688478614c4f9c0cada279a6ed9a79900d5ead3e0bbb35a40da65e12071b7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 304, + 286, + 325 + ], + "lines": [ + { + "bbox": [ + 47, + 304, + 286, + 325 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 286, + 325 + ], + "type": "text", + "content": "Table 4. Effect of the number of external class names. " + }, + { + "bbox": [ + 47, + 304, + 286, + 325 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 304, + 286, + 325 + ], + "type": "text", + "content": " signifies the performance improvement. Please see § 4.5 for details." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 335, + 286, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 286, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 286, + 371 + ], + "type": "text", + "content": "unseen classes. Furthermore, we also qualitatively analyzed the reasons why the proposed module is effective in the supplementary materials D." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 392, + 264, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 264, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 264, + 404 + ], + "type": "text", + "content": "4.4. Integration with other GZSL Approaches" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 415, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 287, + 713 + ], + "type": "text", + "content": "We have integrated DSECN into three mainstream GZSL methods and analysed the effect of integrating DSECN. From the results in Tab. 3, we can observe that: 1) benefiting from the introduction of diverse semantic information from class names (DSECN), the performance of global embedding-based (CN) and generative-based methods (DGZ) is significantly improved. For example, when unseen classes are not similar to seen classes, DSECN improves DGZ's GZSL performance by " + }, + { + "bbox": [ + 47, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "20.67\\%" + }, + { + "bbox": [ + 47, + 415, + 287, + 713 + ], + "type": "text", + "content": " in the CUB dataset using W2V [27] embedding. This proves that the DSECN can be integrated into existing global embedding-based and generative-based GZSL methods to improve the model's robustness to dissimilar unseen classes; 2) the improvement with the local embedding-based GZSL method (TransZero) is smaller than that of global embedding-based and generative-based methods. This may be attributed to the fact that the performance improvement of integrating DSECN is limited by the accuracy of the generated visual feature maps. It is challenging to accurately generate not visible visual feature maps from semantic vectors, which is why existing generative-based GZSL methods mostly generate global visual features rather than local visual features. Overall, the proposed DSECN can easily be integrated into existing mainstream GZSL methods to improve the robustness for dissimilar unseen classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 529, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 529, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 529, + 84 + ], + "type": "text", + "content": "4.5. Effect of the External Class Name Number" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "content": "To investigate the effect of the ECN number on identifying dissimilar unseen classes, we introduce the class names from ImageNet-1K and ImageNet-21K separately as the external base class names, and then remove the unseen class names from the external class names. Notably, we use the ResNet101 pretrained on ImageNet-21K when introducing ImageNet-21K class names. The results are shown in Tab. 4. We can observe that as the introduced ECN increases, performance of the model improves significantly. This proves that increasing the ECN is important to improve the performance of dissimilar unseen class recognition." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 236, + 379, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 379, + 248 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 379, + 248 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 257, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 424 + ], + "type": "text", + "content": "In this paper, we introduce and investigate the practical GZSL setting, where unseen classes can be either similar and dissimilar to seen classes. We empirically show that existing GZSL methods are difficult in identifying dissimilar unseen classes, and propose a simple yet effective method, which exploits diverse semantics from external class names (DSECN), and is simultaneously robust for both similar and dissimilar unseen classes. From the results, we mainly conclude that: 1) the semantics contained in the external unseen class names are quite helpful to improve the generalization ability of GZSL approach; 2) It is critical to align the augmented semantics to their corresponding visual features. In the future, we intend to incorporate the proposed idea into more GZSL approaches and improve their performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 653 + ], + "type": "text", + "content": "Potential Impacts. The existing GZSL methods perform poorly when unseen classes are dissimilar to seen classes, which hinders the practical application of the existing GZSL methods. The paper will help attract researchers' attention to dissimilar unseen classes and help the GZSL field develop in a more practical direction. In addition, the proposed DSECN is simultaneously robust on similar and dissimilar unseen classes, and can easily be integrated into other GZSL methods to improve their robustness for dissimilar unseen classes. This capability is beneficial for improving the practicality of the GZSL model. From an evaluation perspective, existing methods assess using visible and invisible classes from the same dataset. This leads to excessive focus on similar unseen classes during evaluation, thereby overestimating the generalizability of existing GZSL methods. In contrast, the cross-dataset evaluation protocol proposed in the paper can more comprehensively reflect the performance of existing GZSL methods on similar, dissimilar and practical settings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work was supported by the National Key Research and Development Program of China 2023YFC2705700, National Natural Science Foundation of China under Grants 62225113 and 62276195, and Special Fund of Hubei Luojia Laboratory under Grant 220100014." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23351" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Liu Bo, Qiulei Dong, and Zhanyi Hu. 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In CVPR, pages 6034-6042, 2016. 1" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23353" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_content_list.json b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c35efc488fc1a246acf47f5ee516d09d45dc4617 --- /dev/null +++ b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_content_list.json @@ -0,0 +1,1579 @@ +[ + { + "type": "text", + "text": "Improving Graph Contrastive Learning via Adaptive Positive Sampling", + "text_level": 1, + "bbox": [ + 124, + 130, + 844, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiaming Zhuo $^{1}$ , Feiyang Qin $^{1}$ , Can Cui $^{1}$ , Kun Fu $^{1}$ , Bingxin Niu $^{1}$ , Mengzhu Wang $^{1}$ , Yuanfang Guo $^{2}$ , Chuan Wang $^{3*}$ , Zhen Wang $^{4,5}$ , Xiaochun Cao $^{6}$ , Liang Yang $^{1*}$", + "bbox": [ + 156, + 179, + 813, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Artificial Intelligence, Hebei University of Technology, Tianjin, China", + "bbox": [ + 163, + 215, + 805, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Computer Science and Engineering, Beihang University, Beijing, China", + "bbox": [ + 156, + 233, + 812, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Institute of Information Engineering Chinese Academy of Sciences, Beijing, China", + "bbox": [ + 155, + 251, + 815, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ School of Cybersecurity, Northwestern Polytechnical University, Xi'an, China", + "bbox": [ + 173, + 268, + 797, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "5OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, Xi'an, China", + "bbox": [ + 140, + 286, + 830, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{6}$ School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China", + "bbox": [ + 151, + 304, + 818, + 321 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jiaming.zhuo@outlook.com, feiyangqinzzu@163.com, 594021820@qq.com, fukun@hebut.edu.cn, niubingxin666@163.com, dreamkily@gmail.com, andyguo@buaa.edu.cn, wangchuan@iie.ac.cn, w-zhen@nwpu.edu.cn, caoxiaochun@mail.sysu.edu.cn, yangliang@vip.qq.com", + "bbox": [ + 104, + 325, + 861, + 375 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 409, + 312, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graph Contrastive Learning (GCL), a Self-Supervised Learning (SSL) architecture tailored for graphs, has shown notable potential for mitigating label scarcity. Its core idea is to amplify feature similarities between the positive sample pairs and reduce them between the negative sample pairs. Unfortunately, most existing GCLs consistently present suboptimal performances on both homophilic and heterophilic graphs. This is primarily attributed to two limitations of positive sampling, that is, incomplete local sampling and blind sampling. To address these limitations, this paper introduces a novel GCL framework with an adaptive positive sampling module, named graphH contrastiveE Adaptive positive Samples (HEATS). Motivated by the observation that the affinity matrix corresponding to optimal positive sample sets has a block-diagonal structure with equal weights within each block, a self-expressive learning objective incorporating the block and idempotent constraint is presented. This learning objective and the contrastive learning objective are iteratively optimized to improve the adaptability and robustness of HEATS. Extensive experiments on graphs and images validate the effectiveness and generality of HEATS.", + "bbox": [ + 75, + 441, + 472, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 804, + 207, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-supervised learning (SSL), has been a highly regarded methodology within the unsupervised learning field. It generates supervision signals for model training by extracting", + "bbox": [ + 75, + 829, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "latent data patterns from the unannotated data [8]. As a notable branch of SSL, Contrastive Learning (CL) emphasizes producing the supervision signals using the established rule, i.e., bringing similar samples (positive samples) closer and pushing dissimilar samples (negative samples) apart. Based on this rule, Graph Contrastive Learning (GCL) extends the applied range to non-Euclidean graphs by employing techniques like graph augmentations and graph encoders. It has achieved remarkable performance on various downstream tasks, such as node classification [15, 32].", + "bbox": [ + 500, + 410, + 890, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To generate the discriminative node representations from GCLs, the positive sample set of each node should contain all nodes from the same class (i.e., TRUE positive samples), while the negative ones should consist of nodes from different classes (i.e., TRUE negative samples). Subsequently, to extend the TRUE positive sample sets, certain research endeavors in GCLs focus on identifying semantically relevant samples within node neighborhoods [12, 20, 26, 30, 34], leveraging the homophily assumption [1, 16]. Despite their consistent performance improvements on the homophilic graphs, where adjacent nodes typically belong to the same class, the improvements are limited. More critically, their robustness to the heterophilic graphs, where adjacent nodes tend to be from different classes, is severely constrained.", + "bbox": [ + 496, + 565, + 890, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These drawbacks are attributed to two limitations of positive sampling. (1) Incomplete local sampling. Most graphs are sparse, and nodes of the same class are typically situated beyond each other's neighborhoods. Therefore, the positive sample sets for most GCLs tend to be incomplete, which could lead to the absence of shared information between the same class. (2) Blind sampling. In dealing with blindness caused by a lack of supervised guidance, the endeavors of", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Chuan Wang and Liang Yang are corresponding authors.", + "bbox": [ + 94, + 886, + 401, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23179", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "GCLs to establish the criterion for positive sampling beyond the neighborhoods are insufficient. Concretely, most GCLs always center on exploring semantic relevance in neighborhoods utilizing various homophily measures [6, 12, 34]. In fact, these criteria do not apply beyond neighborhoods because of their local property. Due to the incompleteness and blindness of positive sampling, GCLs can not obtain all TRUE positive sample pairs. This hampers the representation ability of GCLs, resulting in their poor performances on both homophilic and heterophilic graphs.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these deficiencies, this paper proposes a novel GCL framework, named grapH contrastive Adaptive positive Sampling (HEATS). The idea is to devise a criterion to guide global positive sampling. Toward this end, the characteristic of an affinity matrix (termed positive sample matrix) associated with the optimal positive sample set is first investigated. The conclusion drawn is that the optimal positive sample matrix obeys the block diagonal property (BDP) and is idempotent, as depicted in Figure 1(a). To be specific, this matrix can be decomposed into a batch of diagonal submatrices (blocks), where each block characterizes semantic relevance among nodes from the same class. Moreover, each block is fully connected and the weights within it are equal. Motivated by this, a novel positive sampling module is presented, focusing on constructing such block-diagonal and idempotent affinity matrices. To capture long-range dependencies, positive sample matrices are generated by optimizing a self-expressive objective incorporating block and idempotent constraints, leveraging the features of all nodes within batches. In light of the intrinsic denoising capability of GCLs [14, 35], an alternating update mechanism of matrix construction and contrastive optimization is introduced to obtain reciprocal benefits, thereby improving the robustness and adaptability of HEATS. In theory, HEATS has a stricter lower bound on the mutual information (MI) between node attributes and node embeddings compared to the baselines that select positive samples from neighborhoods, which guarantees its effectiveness and robustness.", + "bbox": [ + 75, + 242, + 472, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are summarized below.", + "bbox": [ + 96, + 665, + 455, + 679 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We investigate the characteristics of an affinity matrix associated with the optimal positive sample set.", + "- We present a novel graph contrastive learning framework HEATS with an adaptive positive sampling module.", + "- We theoretically analyze the effectiveness and robustness of the proposed HEATS from a Mutual Information Maximization perspective.", + "- We conduct extensive evaluations to demonstrate the superior performance and generality of HEATS." + ], + "bbox": [ + 76, + 680, + 468, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 829, + 215, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This section starts by explaining the notations used throughout the paper. It then introduces the basic concepts in Graph Contrastive Learning (GCL).", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Notations", + "text_level": 1, + "bbox": [ + 500, + 90, + 609, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Capital italic letters stand for sets (e.g., set $\\mathcal{V}$ ), capital bold letters represent matrices (e.g., matrix $\\mathbf{Q}$ ), bold lowercase letters term vectors (e.g., vector $\\mathbf{q}_v$ ), and lowercase letters denote scalars (e.g., scalar $q_{v,u}$ ).", + "bbox": [ + 496, + 113, + 890, + 174 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For generality, this paper focuses on attribute undirected graphs. It considers a graph $\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathbf{X})$ , where the node set $\\mathcal{V}$ contains $n$ node instances $\\{(\\mathbf{x}_v,\\mathbf{y}_v)\\}_{v\\in \\mathcal{V}}$ . $\\mathbf{x}_v\\in \\mathbb{R}^f$ and $\\mathbf{y}_v\\in \\mathbb{R}^c$ denote the attribute and label vector of the node $v$ , respectively. The node embeddings $\\mathbf{H}\\in \\mathbb{R}^{n\\times d}$ are learned on entire graphs in an unsupervised manner, then utilized in downstream tasks, such as node classification, where the labels $\\mathbf{Y}$ are used for fine-tuning linear classifiers.", + "bbox": [ + 496, + 174, + 892, + 295 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Graph Contrastive Learning", + "text_level": 1, + "bbox": [ + 498, + 303, + 756, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Being typical of a graph-based self-supervised learning SSL architecture, GCL aims to generate supervised signals based on a predefined rule. It involves bringing the similar samples (i.e., positive samples) closer while pushing the dissimilar samples (i.e., negative samples) apart simultaneously. Take GRACE [32], which is an oft-discussed baseline, as an example, its architecture is described below.", + "bbox": [ + 496, + 325, + 890, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In line with SimCLR [2], a contrastive learning baseline in computer vision (CV), GRACE adopts a two-channel architecture. For graph $\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathbf{X})$ , both channels are responsible for generating node embeddings (represented as $\\mathbf{H}$ and $\\tilde{\\mathbf{H}}$ ) for its two augmented graphs through graph augmentations [32] and encoders [11]. The description of these processes can be found in the appendix.", + "bbox": [ + 496, + 431, + 890, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Once the node features are obtained, InfoNCE [22] loss, is calculated as a guide for its update. For node $v$ , the positive sample of the anchor node $(\\mathbf{h}_v)$ is the same node $(\\tilde{\\mathbf{h}}_v)$ in another view, while the negative samples are other nodes in both views. This contrastive loss (denoted as $\\ell_{gc}$ ) can be formulated as", + "bbox": [ + 496, + 537, + 890, + 626 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\ell_ {g c} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) = - l o g \\frac {\\mathrm {p o} _ {v}}{\\mathrm {p o} _ {v} + \\mathrm {n e} _ {v}}, \\\\ \\mathrm {p o} _ {v} = \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {v})}{\\tau}}, \\mathrm {n e} _ {v} = \\sum_ {t \\in V \\backslash v} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\mathbf {h} _ {t})}{\\tau}} + \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {t})}{\\tau}}, \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 632, + 890, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\theta (\\mathbf{h}_v,\\tilde{\\mathbf{h}}_v) = s(f(\\mathbf{h}_v),f(\\tilde{\\mathbf{h}}_v))$ , $s(,)$ terms the cosine similarity, and $f(\\cdot)$ denotes the projection head [2], which is a two-layer multilayer perceptron (MLP). $\\tau$ represents a scalar, which is positively correlated with the uniformity of the feature distribution. The overall contrastive loss is set as the average over all nodes based on the mutually symmetric form of Equation 1. This can be formulated as", + "bbox": [ + 496, + 710, + 890, + 818 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g r a c e}} = \\frac {1}{2 | V |} \\sum_ {v \\in V} \\left(\\ell_ {g c} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) + \\ell_ {g c} \\left(\\tilde {\\mathbf {h}} _ {v}, \\mathbf {h} _ {v}\\right)\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 825, + 890, + 861 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to the above pairwise positive sampling, several local positive sampling techniques have been presented", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23180", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/76115030afeef6a5f7c6144389fce79fe824820d2d4cdbc26983a1375c6e7e31.jpg", + "image_caption": [ + "(a) Optimal positive sample set for GCLs and the corresponding matrix.", + "(b) The proposed HEATS Framework.", + "Figure 1. Overview of the proposed GCL framework, named HEATS, and its design motivation. (a) An intuitive example of the optimal positive sample matrix for GCLs, where the colors of nodes stand for classes. (b) The proposed HEATS framework with adaptive positive sampling. The optimal positive sample set should consist of all nodes from the same class. Accordingly, the optimal positive sample matrix should be block-diagonal, where each block is fully connected and weights within it are equal." + ], + "image_footnote": [], + "bbox": [ + 135, + 92, + 851, + 228 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[12, 34]. They propose to add the specified neighbor nodes into the positive sample sets, leveraging the homophily assumption [1, 16].", + "bbox": [ + 75, + 316, + 468, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 378, + 210, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, following the introduction of design motivation, a graph contrastive learning (GCL) framework, named grapH contrastive Adaptive positive Sampling (HEATS), is devised. Subsequently, theoretical analysis of its efficacy are presented.", + "bbox": [ + 75, + 405, + 468, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Motivation", + "text_level": 1, + "bbox": [ + 76, + 494, + 197, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As previously discussed in the introduction, existing positive sampling strategies utilized in GCLs tend to be incomplete and blind, leading to a loss of discriminative power of node representations.", + "bbox": [ + 75, + 518, + 468, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1. Block Diagonal Property (BDP) [9]. The given matrix $\\mathbf{Z} \\in \\mathbb{R}^{n \\times n}$ satisfies block diagonal property if it can be decomposed into submatrices as follows:", + "bbox": [ + 75, + 592, + 468, + 638 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} = \\left[ \\begin{array}{c c c c} \\mathbf {Z} _ {1} & 0 & \\dots & 0 \\\\ 0 & \\mathbf {Z} _ {2} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & \\mathbf {Z} _ {k} \\end{array} \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 650, + 369, + 722 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{Z}_i\\in \\mathbb{R}^{n_i\\times n_i}$ stands for the $i$ -th square submatrix (block), and $\\sum_{i = 0}^{k}n_{i} = n$", + "bbox": [ + 76, + 734, + 468, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An intuitive and optimal solution is provide target nodes with positive sample sets that consists of all nodes from the same class (i.e., optimal positive sample set), as depicted in Figure 1(a). It is evident that the relationships among these positive samples can be succinctly expressed as a block diagonal matrix, where each block describes the relationships among a class of nodes. Additionally, this matrix should exhibit the following properties: each block is full connected", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and weights within it are equal. Therefore, the optimal positive sample matrix should be formulated as:", + "bbox": [ + 498, + 316, + 888, + 347 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} = \\left[ \\begin{array}{c c c c} \\frac {1}{n _ {1}} \\mathbf {1} _ {n _ {1}} \\mathbf {1} _ {n _ {1}} ^ {\\top} & 0 & \\dots & 0 \\\\ 0 & \\frac {1}{n _ {2}} \\mathbf {1} _ {n _ {2}} \\mathbf {1} _ {n _ {2}} ^ {\\top} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & \\frac {1}{n _ {k}} \\mathbf {1} _ {n _ {k}} \\mathbf {1} _ {n _ {k}} ^ {\\top} \\end{array} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 357, + 890, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{1}_{n_i} \\in \\mathbb{R}^{n_i}$ denotes an all-one column vector.", + "bbox": [ + 500, + 444, + 839, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. HEATS framework", + "text_level": 1, + "bbox": [ + 500, + 468, + 684, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the above analysis, this paper devises a novel GCL framework HEATS, which directs the positive sampling by employing constructed block diagonal affinity matrices. As overviewed in Figure 1(b), HEATS consists of two key components: (1) Matrix Construction and (2) Contrastive Optimization. These two components engage in an alternating refinement process, gradually converging to the optimum.", + "bbox": [ + 498, + 492, + 890, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Matrix Construction", + "text_level": 1, + "bbox": [ + 500, + 616, + 697, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This component aims to construct affinity matrices, which possess inter-class sparsity and intra-class connectivity (i.e., obey BDP), to guide the selection of positive samples. Particularly, it adopts a self-expressive learning objective, commonly utilized in subspace clustering [13], to acquire such affinity matrices. This objective posits that each sample can be represented by linearly combining all other samples in the same subspace (i.e., block). This objective can be formulated as the following equation:", + "bbox": [ + 496, + 640, + 890, + 776 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {Z}, \\mathbf {E}} {\\operatorname {a r g m i n}} \\mathcal {O} (\\mathbf {Z}) + \\lambda \\mathcal {T} (\\mathbf {E}), \\quad \\text {s . t .} \\mathbf {X} = \\mathbf {Z} \\mathbf {X} + \\mathbf {E}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 787, + 890, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{Z}$ denotes the affinity matrix, which depicts the combination coefficients, and $\\mathbf{E}$ stands for the noise. Moreover, $\\mathcal{O}$ and $\\mathcal{T}$ term the constraint on affinity matrices and noise matrices, respectively. $\\lambda$ is a hyperparameter that balances the two terms of the objective function.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23181", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To obtain a high-quality affinity matrix, as expressed in Equation 3, several constraints should be incorporated into the learning objective: idempotent and $k$ -block. Firstly, the affinity matrix $\\mathbf{Z}$ in Equation 3 is idempotent [27] because of $\\mathbf{Z}_i = \\mathbf{Z}_i \\times \\mathbf{Z}_i = \\mathbf{Z}_i^2$ . Secondly, the number of blocks in the affinity matrices should be controlled as $k$ . Furthermore, the affinity matrices also should be normalized, symmetric, and non-negative. To achieve these properties and enhance effectiveness, the self-expressive learning objective can be reformulated as:", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname *{argmin}_{\\substack{\\mathbf{Z},\\mathbf{S}}}\\| \\mathbf{Z} - \\mathbf{S}\\|_{F}^{2} + \\gamma \\| \\mathbf{S}\\|_{id} + \\lambda \\| \\mathbf{E}\\|_{2,1}, \\\\ \\mathrm {s . t .} \\mathbf {H} = \\mathbf {Z H} + \\mathbf {E}, \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 250, + 468, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} \\mathbf {1} _ {n} = \\mathbf {1} _ {n}, \\mathbf {S} = \\mathbf {S} ^ {\\top}, \\mathbf {S} \\geq \\mathbf {0}, \\operatorname {T r} (\\mathbf {S}) = k,\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 299, + 400, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{S}$ denotes an intermediate-term to mitigate the loss of representation capability. And, $\\| \\mathbf{S}\\|_{id} = \\| \\mathbf{S} - \\mathbf{S}^2\\| _F^2$ terms the idempotent constraint and $\\gamma$ is a scalar that controls the impacts of this term. The terms $\\mathbf{S1}_n = \\mathbf{1}_n$ $\\mathbf{S} = \\mathbf{S}^{\\top}$ ,and $\\mathbf{S}\\geq 0$ stand for the column-normalized, symmetric, and nonnegative constraints, respectively. Based on the above constraints, the term $\\mathrm{Tr}(\\mathbf{S}) = k$ is introduced to make the matrix have $k$ blocks. $\\| \\mathbf{E}\\|_{2,1} = \\sum_{j = 1}^{n}\\sqrt{\\sum_{i = 1}^{n}([\\mathbf{E}]_{ij})^2}$ is the $\\ell_{2,1}$ -norm of noise, which characterizes sample-specific outliers. Finally, the affinity matrix, a guide of positive sampling, can be obtained by optimizing Equation 5. Please refer to the appendix for optimization details. Once the affinity matrix M (i.e., $\\mathbf{Z}$ or S) is obtained, it is necessary to sparsify it to enhance training efficiency. The sparsification process can be formulated as:", + "bbox": [ + 75, + 327, + 472, + 554 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nm _ {v, u} = \\left\\{ \\begin{array}{l l} 0, & m _ {v, u} < \\beta , \\\\ m _ {v, u}, & \\text {o t h e r w i s e}. \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 563, + 370, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ denotes the threshold parameter, which is utilized to indicate filter out the values below it.", + "bbox": [ + 75, + 613, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1. The affinity matrix $\\mathbf{M}$ , which is generated by optimizing Equation (5), satisfies the BDP in Definition 1.", + "bbox": [ + 75, + 652, + 468, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 theoretically demonstrates that the proposed matrix construction strategy aligns with the motivation. For the proof, please refer to the appendix.", + "bbox": [ + 75, + 691, + 468, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Contrastive Optimization", + "text_level": 1, + "bbox": [ + 76, + 756, + 308, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This subsection delineates the methodology for formulating the contrastive loss leveraging the constructed affinity matrix $\\mathbf{M}$ . Firstly, it is utilized to direct the sampling process. By identifying non-zero values in the vector $\\mathbf{m}_v$ , nodes that are semantically associated with node $v$ can be marked out. These nodes collectively constitute the positive sample set of node $v$ , denoted as $\\mathcal{P}_v^M = \\{u|m_{v,u} > 0\\}$ . Following the baselines [2, 32], the negative sample set is composed of", + "bbox": [ + 75, + 779, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the remaining nodes, that is $\\mathcal{N}_v^M = V\\setminus \\{\\mathcal{P}_v^M\\cup v\\}$ . Secondly, the matrix $\\mathbf{M}$ is also interpreted as a measure of the relationships, and the values within it are treated as weights.", + "bbox": [ + 496, + 89, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In implementation, HEATS follows the baseline GRACE [32], which is mentioned in Section 2.2. Therefore, the contrastive loss of HEATS with respect to anchor node $\\mathbf{h}_v$ can be reformulated from Equation 1 as", + "bbox": [ + 496, + 136, + 893, + 198 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\ell_ {h t} (\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}) = - l o g \\frac {\\mathrm {p o} _ {v}}{\\mathrm {p o} _ {v} + \\mathrm {n e} _ {v}}, \\\\ \\mathrm {p o} _ {v} = \\mathrm {e} ^ {\\frac {\\theta \\left(\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {v}\\right)}{\\tau}} + \\sum_ {u \\in \\mathcal {P} _ {v} ^ {M}} m _ {v, u} \\cdot \\mathrm {e} ^ {\\frac {\\theta \\left(\\mathbf {h} _ {v} , \\mathbf {h} _ {u}\\right)}{\\tau}}, \\tag {6} \\\\ \\mathrm {n e} _ {v} = \\sum_ {t \\in \\mathcal {N} _ {v} ^ {M}} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\bar {\\mathbf {h}} _ {t})}{\\tau}} + \\sum_ {t \\in \\mathcal {N} _ {v} ^ {M}} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\bar {\\mathbf {h}} _ {t})}{\\tau}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 207, + 890, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall contrastive loss of HEATS, denoted as $\\mathcal{L}_{\\text{heats}}$", + "bbox": [ + 500, + 327, + 885, + 343 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {h e a t s}} = \\frac {1}{2 | V |} \\sum_ {v \\in V} \\left(\\ell_ {h t} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) + \\ell_ {h t} \\left(\\tilde {\\mathbf {h}} _ {v}, \\mathbf {h} _ {v}\\right)\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 353, + 890, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In comparison to the existing GCLs [12, 20, 34], the proposed HEATS exhibits several characteristics. (1) Generality. Since the positive sample matrices are constructed globally, that is, independent of the underlying graph topology, HEATS can be reasonably extended to non-graph domains such as computer vision (CV). (2) Robustness. Due to the fact that the positive sample matrix is obtained by optimizing a robust self-expressive learning objective, as formulated in Equation (5), the robustness is strengthened through positive sampling on these matrices.", + "bbox": [ + 496, + 400, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2. The contrastive loss of HEATS $(\\mathcal{L}_{\\text {heats }})$ is a more stringent estimate of mutual information (MI) between node attributes and embeddings than that of the local baseline HomoGCL [12], that is,", + "bbox": [ + 496, + 561, + 893, + 622 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {h o m o g c l}} \\leq \\mathcal {L} _ {\\text {h e a t s}} \\leq I (\\mathbf {X}; \\mathbf {H}, \\tilde {\\mathbf {H}}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 633, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X}$ denotes the node attributes, and $\\mathbf{H}$ and $\\tilde{\\mathbf{H}}$ represent the node embeddings in two augmented views.", + "bbox": [ + 496, + 664, + 890, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2 demonstrates that the proposed HEATS provides a refined approximation to the TRUE mutual information, enabling it to promote model robustness and stability.", + "bbox": [ + 496, + 705, + 890, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.3 Alternating Update", + "text_level": 1, + "bbox": [ + 500, + 771, + 689, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enhance the adaptivity of HEATS, the two fundamental components, matrix construction and contrastive optimization, engage in iterative updates in an alternating fashion, as visually depicted in Figure 1(b). The former is tasked with solving Equation 5 to construct positive sample matrices in the feature space. The latter focuses on representation (feature) learning by optimizing the contrastive loss using these", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23182", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/3b0f0fdd2841cca019e0441cfa4589628efcb3edb5d3b7c58c7406b37cf260ab.jpg", + "table_caption": [ + "Table 1. Statistics of twelve graph datasets. Homophily is the edge homophily in [17]." + ], + "table_footnote": [], + "table_body": "
DatasetNodesEdgesFeaturesClassesHomophily
Cora2,7085,2781,43370.81
CiteSeer3,3274,5523,70360.74
PubMed19,71744,32450030.80
Wiki-CS11,701216,123300100.65
Computers13,752245,861767100.78
Photo7,650238,16374580.83
Cornell1832951,70350.13
Texas1833091,70350.11
Wisconsin2514991,70350.20
Chameleon2,27736,1012,32550.23
Squirrel5,201217,0732,08950.22
Actor7,60033,54493150.22
", + "bbox": [ + 80, + 122, + 467, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "positive sample matrices, which is formulated as Equation 6. These two components are updated alternately.", + "bbox": [ + 76, + 315, + 467, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The alternating update procedure offers several benefits to GCLs. (1) Adaptive positive samples. Note that the positive sample matrices are constructed in the feature space. Hence, this procedure can continually provide adaptive positive samples for the subsequent contrastive optimization, adapting to feature changes. (2) Discriminative node representations. GCLs have the denoising ability, to some extent, which is attributed to the fact that it obtains the invariant information [28]. As a result, the discriminative feature space can be provided for the construction of positive sample matrices, eventually resulting in more discriminative features through contrastive learning. Furthermore, benefits also involve the risk reduction of each component falling into the local optimum and accelerating the convergence speed.", + "bbox": [ + 75, + 345, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 570, + 207, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, the proposed framework HEATS is validated by empirically evaluating its performances on node and image classification tasks in the unsupervised setting. Next, an in-depth understanding of the efficacy of this framework is provided through several experiment analyses.", + "bbox": [ + 75, + 595, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 76, + 680, + 253, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. To illustrate the effectiveness and generality of the proposed HEATS, twelve non-Euclidean graph datasets, and three 2-D spatial image datasets are adopted in the experiments. According to graph homophily [17], these graph datasets can be divided into two categories: six homophilic graphs, including Cora, CiteSeer, PubMed, Wiki-CS, Computers, and Photo, and six heterophilic graphs, containing Cornell, Texas, Wisconsin, Chameleon, Squirrel, and Actor. Moreover, the image datasets are CIFAR-10, STL-10, and CIFAR-100. The statistics of the graph datasets are presented in Table 1. Due to space limitations, the introduction of all datasets is presented in the appendix.", + "bbox": [ + 75, + 703, + 468, + 885 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Splitting. To ensure experimental fairness, the dataset split", + "bbox": [ + 76, + 885, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ting follows commonly employed schemes. Specifically, for three homophilic graphs (Cora, CiteSeer, and PubMed) and all six heterophilic graphs, the training, validation, and testing sets constitute $48\\%$ , $32\\%$ , and $20\\%$ of the data, respectively. For the remaining homophilic graphs (Wiki-CS, Computers, and Photo), the proportions amount to $10\\%$ , $10\\%$ and $80\\%$ . Besides, for the CIFAR-10 dataset, 5000 and 1000 images per class are selected for training and testing, respectively. For the STL-10 dataset, 10500 and 800 images per class are assigned to the training and testing sets, respectively. For the CIFAR-100 dataset, 500 and 100 images per class are served in training and testing, respectively.", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. These experiments involve two types of downstream tasks: node classification for graphs and image classification. For the node classification, the baselines include two types: semi-supervised graph neural networks (GCN [11], GAT [24] and JKNet [29]), and unsupervised graph learning models (Deepwalk [18], Node2vec [4], GAE [10], VGAE [10], DGI [25], MVGRL [5], GRACE [32], GCA [33], BGRL [21], SELENE [31], and HomoGCL [12]). For the image classification, the baseline is CL model SimCLR [2], which is implemented with two backbones (ResNet-18 and ResNet-50) [7]. Please refer to the appendix for an introduction to related works.", + "bbox": [ + 496, + 272, + 890, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Configurations. In the node classification, the proposed HEATS framework is implemented with the configurations following GRACE [32]. To be specific, each branch corresponds to an augmented graph, which is initially obtained through the edge deletion and attribute masking [3], with the random ratio among $\\{0.2, 0.4, 0.6, 0.8\\}$ . Furthermore, the node features are obtained through a two-layer GCN [11] encoding and a two-layer MLP [19] projecting, where both dimensions are 64. The node features are trained by minimizing the contrastive loss, where the temperature coefficient is taken from $\\{0.2, 0.4, 0.6, 0.8, 1\\}$ . In this process, an Adam optimizer with the learning rate of 0.01 and the weight decay rate among $\\{0, 5 \\times 10^{-5}\\}$ is to be employed for optimization and regularization, respectively. Minibatch training is adopted for larger node numbers, such as PubMed. For the unique parameters of HEATS, namely $\\gamma$ and $\\lambda$ , both are selected from $\\{1 \\times 10^{-3}, 1 \\times 10^{-2}, 1 \\times 10^{-1}, 1, 10\\}$ . Furthermore, the number of blocks $k$ is selected from a set with no more than the number of classes, and its impact is analyzed in Section 4.3.2. All experiments are conducted in PyTorch on a single RTX4090 24GB GPU.", + "bbox": [ + 496, + 453, + 890, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Protocol. For both node and image classification tasks, the experimental evaluations adopt the standard linear evaluation protocol [25]. Concretely, all models undergo initial unsupervised pre-training, followed by utilizing the obtained embeddings to train linear classifiers and subsequently presenting the test accuracy results. Throughout the evaluation phases, the Adam optimizer with a learning rate of 0.01 is utilized. The experiment results are re", + "bbox": [ + 496, + 770, + 890, + 891 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23183", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/41ca89b6c5f5048dba5b39cfbfcb62e2263721266d465adfc79ef82f91c5c07e.jpg", + "table_caption": [ + "Table 2. Node classification accuracy (mean ± std) is reported for six homophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information." + ], + "table_footnote": [], + "table_body": "
ModelTraining DataCoraCiteSeerPubMedWiki-CSComputersPhoto
GCNA,X,Y85.77 ± 0.2573.68 ± 0.3188.13 ± 0.2876.89 ± 0.3786.34 ± 0.4892.35 ± 0.25
GATA,X,Y86.37 ± 0.3074.32 ± 0.2787.62 ± 0.2677.42 ± 0.1987.06 ± 0.3592.64 ± 0.42
JKNetA,X,Y85.93 ± 1.3574.37 ± 1.5387.68 ± 0.3079.52 ± 0.2185.28 ± 0.7292.68 ± 0.13
DeepWalkA73.96 ± 0.1261.91 ± 0.4274.79 ± 0.9874.35 ± 0.0685.68 ± 0.0689.44 ± 0.11
Node2VecA75.87 ± 0.2262.54 ± 0.1376.49 ± 0.3271.79 ± 0.0584.39 ± 0.0889.67 ± 0.12
GAEA,X76.83 ± 1.2265.43 ± 1.1376.52 ± 0.3370.15 ± 0.0185.27 ± 0.1991.62 ± 0.13
VGAEA,X79.36 ± 0.8369.18 ± 0.2779.17 ± 0.4476.63 ± 0.1986.37 ± 0.2192.20 ± 0.11
DGIA,X85.90 ± 0.5772.57 ± 0.2383.52 ± 1.2475.73 ± 0.1384.09 ± 0.3991.49 ± 0.25
MVGRLA,X86.77 ± 0.3373.71 ± 0.4884.63 ± 0.7377.97 ± 0.1887.09 ± 0.2792.01 ± 0.13
GRACEA,X84.79 ± 0.6472.94 ± 0.7284.51 ± 0.6879.16 ± 0.3687.21 ± 0.4492.65 ± 0.32
GCAA,X85.16 ± 0.5172.73 ± 0.4585.22 ± 0.7379.35 ± 0.1287.84 ± 0.2792.78 ± 0.17
BGRLA,X85.37 ± 0.7473.45 ± 0.8384.61 ± 0.3278.74 ± 0.2288.92 ± 0.3393.24 ± 0.29
SELENEA,X85.28 ± 0.8373.48 ± 0.6584.70 ± 0.5278.31 ± 0.6388.13 ± 0.5192.93 ± 0.34
HomoGCLA,X85.02 ± 0.6873.67 ± 0.7882.33 ± 0.4977.47 ± 0.4587.84 ± 0.2893.59 ± 0.27
HEATSA,X87.10 ± 1.4075.26 ± 1.2585.41 ± 0.8279.99 ± 1.5989.29 ± 1.1294.65 ± 1.71
", + "bbox": [ + 99, + 128, + 867, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ported as an average of over ten random runs.", + "bbox": [ + 76, + 380, + 379, + 396 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results on benchmark datasets", + "text_level": 1, + "bbox": [ + 76, + 407, + 352, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Homophilic Graphs. Table 2 presents the experimental results of node classification on six homophilic graphs. It is evident that compared to all unsupervised baseline models, the proposed HEATS achieves the best performance across all datasets. It even surpasses all supervised comparison models on datasets other than PubMed. To be specific, on the CiteSeer dataset, HEATS outperforms the second-best unsupervised model (i.e., MVGRL) by $1.55\\%$ and the baseline model (i.e., GRACE) by $2.32\\%$ in classification accuracy. This highlights the effectiveness of HEATS in exploring positive samples by modeling high-order relationships.", + "bbox": [ + 75, + 431, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Homophilic Graphs. A similar phenomenon can be observed from the experiment results on heterophilic graphs, as illustrated in Table 3. To be specific, compared to the baseline model (i.e., GRACE), HEATS achieves performance improvements across all datasets. Particularly noteworthy are improvements in accuracy by $12.11\\%$ , $7.29\\%$ , and $15.88\\%$ on the Cornell, Texas, and Wisconsin datasets, respectively. This emphasizes the contribution of the proposed positive sampling based on matrix construction in enriching the universality of the baselines. Moreover, HEATS outperforms other unsupervised baselines on three datasets, except the Chameleon, Squirrel, and Actor datasets, showcasing its superior performance.", + "bbox": [ + 75, + 613, + 468, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualization. This experiment aims to intuitively demonstrate the representation ability of the proposed HEATS. For this purpose, the t-SNE [23] method is exploited to perform feature reduction and visualization of the trained representations. Figure 2 exhibits the experiment results (scatter plots) on three benchmark datasets (i.e., Cora, CiteSeer, and", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5852a8bcde22a7d8927cedd6d2ec2cdaf2eea9f7d2e0505fd7364dc453c98cfa.jpg", + "image_caption": [ + "Figure 2. t-SNE visualization of node embeddings from HEATS, BGRL, and GRACE on Cora, CiteSeer, and Photo datasets." + ], + "image_footnote": [], + "bbox": [ + 526, + 383, + 877, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Photo), where colors stand for the classes of nodes. It can be observed that compared to all the comparison models (i.e., GRACE and BGRL), the proposed HEATS framework is enabled to produce the most informative representations. As exemplified by the Cora and CiteSeer dataset, compared to the baseline model (i.e., GRACE), HEATS achieves more compact clusters in node embeddings. Specifically, the embeddings of the same class are closer, while the embeddings of different classes exhibit more significant differences. The experiment results emphasize the effectiveness of HEATS in enhancing representation ability.", + "bbox": [ + 496, + 628, + 890, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Image Datasets. As previously mentioned, the proposed HEATS designs a positive sampling strategy from a global perspective, which effectively mitigates graph structural constraints. In essence, this improves its generality to various domains. To substantiate this claim, the experiment compares a contrastive learning (CL) model tailored for images (i.e., SimCLR) with the proposed variants.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23184", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d6877a2dafb26dafccda6b006f585b01bf8e2f44c1ef58742dd98548fb5a8a4c.jpg", + "table_caption": [ + "Table 3. Node classification accuracy (mean ± std) is reported for six heterophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information." + ], + "table_footnote": [], + "table_body": "
ModelTraining DataCornellTexasWisconsinChameleonSquirrelActor
GCNA,X,Y55.14 ± 7.5755.68 ± 9.6158.42 ± 5.1059.82 ± 2.5836.89 ± 1.3430.64 ± 1.49
GATA,X,Y58.92 ± 3.3258.38 ± 4.4555.29 ± 8.7160.26 ± 2.5040.72 ± 1.5527.44 ± 0.89
JKNetA,X,Y56.49 ± 3.2265.35 ± 4.8651.37 ± 3.2160.31 ± 2.7644.24 ± 2.1136.47 ± 0.51
DeepWalkA39.18 ± 5.5746.49 ± 6.4933.53 ± 4.9247.74 ± 2.0532.93 ± 1.5822.78 ± 0.64
Node2VecA42.94 ± 7.4641.92 ± 7.7637.45 ± 7.0941.93 ± 3.2922.84 ± 0.7228.28 ± 1.27
GAEA,X58.85 ± 3.2158.64 ± 4.5352.55 ± 3.8033.84 ± 2.7728.03 ± 1.6128.03 ± 1.18
VGAEA,X59.19 ± 4.0959.20 ± 4.2656.67 ± 5.5135.22 ± 2.7129.48 ± 1.4826.99 ± 1.56
DGIA,X63.35 ± 4.6160.59 ± 7.5655.41 ± 5.9639.95 ± 1.7531.80 ± 0.7729.82 ± 0.69
MVGRLA,X64.30 ± 5.4362.38 ± 5.6162.37 ± 4.3251.07 ± 2.6835.47 ± 1.2930.02 ± 0.70
GRACEA,X54.86 ± 6.9557.57 ± 5.6850.00 ± 5.8348.05 ± 1.8131.33 ± 1.2229.01 ± 0.78
GCAA,X55.41 ± 4.5659.46 ± 6.1650.78 ± 4.0649.80 ± 1.8135.50 ± 0.9129.65 ± 1.47
BGRLA,X57.30 ± 5.5159.19 ± 5.8552.35 ± 4.1247.46 ± 2.7432.64 ± 0.7829.86 ± 0.75
SELENEA,X59.94 ± 5.1261.87 ± 4.2561.87 ± 4.7942.13 ± 2.1533.28 ± 0.8230.12 ± 0.76
HomoGCLA,X48.64 ± 2.5954.05 ± 2.3239.21 ± 5.7548.68 ± 1.1638.71 ± 0.8528.81 ± 0.78
HEATSA,X66.97 ± 6.7464.86 ± 4.6865.88 ± 5.5649.96 ± 1.8636.24 ± 1.1129.91 ± 1.16
", + "bbox": [ + 99, + 128, + 867, + 363 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/10765011227722854b65f10187fd259ae2813b409c84dc56afed7618b2ea7569.jpg", + "table_caption": [ + "Table 4. Image classification accuracy (mean) of SimCLR and its HEATS-based variants. $\\uparrow$ dentoes the performance improvement." + ], + "table_footnote": [], + "table_body": "
BackboneMethodCIFAR-10STL-10CIFAR-100
ResNet-18SimCLR78.5978.4449.60
+HEATS79.1978.8352.62
↑+0.60+0.39+3.02
ResNet-50SimCLR75.0376.7349.31
+HEATS77.5877.8053.81
↑+2.55+1.07+4.50
", + "bbox": [ + 99, + 417, + 444, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The configurations of these variants align with that of the baselines, including standard parameters such as learning rate and training epochs. Please refer to the appendix for experiment setups. Table 4 exhibits the image classification results after 30 epochs using ResNet-18 and ResNet-50 backbones. It can be seen that compared to the baseline (i.e., SimCLR), the proposed HEATS framework consistently improves performance across all three datasets. To be specific, HEATS showcases superior performance compared to the two baselines utilizing ResNet-18 and ResNet-50 backbones on the CIFAR-100 dataset by $3.02\\%$ and $4.5\\%$ , respectively, accentuating the generality to image-centric tasks. More importantly, it provides valuable insights for applying HEATS in a wide range of domains.", + "bbox": [ + 75, + 541, + 468, + 752 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Further Analysis", + "text_level": 1, + "bbox": [ + 76, + 762, + 243, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.1 Effectiveness Justify", + "text_level": 1, + "bbox": [ + 76, + 785, + 272, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The experiment intends to justify the effectiveness of the two proposed approaches to enhance positive sampling, i.e., matrix construction and alternating updates, to pursue the block-diagonal matrices. Therefore, three matrices, which include the adjacent matrix, the matrix computed using the initial features, and the matrix computed using the features", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc656502431c4a5d12bbed467d40bc7ebe279067015b3b9d29d179a8eca25f04.jpg", + "image_caption": [ + "Figure 3. Visualization of the adjacent matrices, the matrices computed using the initial features (Matrix 1), and the matrices computed using the learned features after 200 iterations (Matrix 2) on the Cora and CiteSeer datasets. The nodes are sorted by class. The weights between nodes are not considered here." + ], + "image_footnote": [], + "bbox": [ + 526, + 383, + 867, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "after 200 iterations, are visualized in Figure 3 to provide an intuitive understanding.", + "bbox": [ + 498, + 824, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Based on the observations in Figure 3, three significant conclusions can be drawn. (1) The constructed matrices are approximately block diagonal. In particular, on all datasets", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23185", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/665bad5c92f1db3f2841252b392eb544083555d625e5df857f538bd445aa98ab.jpg", + "image_caption": [ + "Figure 4. Impact of the number of blocks $k$ ." + ], + "image_footnote": [], + "bbox": [ + 83, + 94, + 460, + 195 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0348dee2a57cacc8dc7b2208de43e49ef0d310cd1d8cbd7ad69c2dd0e609084f.jpg", + "image_caption": [ + "(a) Topology attacks", + "Figure 5. Results of GCLs under graph attacks" + ], + "image_footnote": [], + "bbox": [ + 78, + 233, + 254, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dbba3ddee58e5c2a3e75a7ba7a25ef1786d83255a1afc4f658b24077077e047c.jpg", + "image_caption": [ + "(b) Attribute attacks" + ], + "image_footnote": [], + "bbox": [ + 272, + 233, + 446, + 342 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(i.e., Cora and CiteSeer), the edges between nodes from the same class outnumber those between nodes from different classes. This indicates that the proposed HEATS framework can serve as an effective strategy to obtain more TRUE positive samples. (2) Compared to the adjacent matrices, the constructed matrices exhibit denser diagonal blocks. This implies that the proposed matrix construction approach is feasible in contrastive learning by offering more TRUE positive samples beyond graph topology. (3) Compared to the matrices constructed in the initial feature space, those constructed in the updated feature space exhibit a more distinct block-diagonal structure, e.g., results of the Cora dataset. This emphasizes the effectiveness of the proposed alternating update approach. In summary, the experiment confirms the efficacy of the two proposed approaches in constructing block-diagonal matrices for positive sample collection.", + "bbox": [ + 75, + 390, + 472, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.2 Hyperparameter Study", + "text_level": 1, + "bbox": [ + 76, + 650, + 294, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The experiment aims to provide a guide on choosing the parameter $k$ , which represents the number of blocks, by investigating its impact on the performance. This parameter is selected from 2 to the number of classes, as setting it to 1 seems ineffective. Figure 4 exhibits the experiment results on three datasets (i.e., Cora, CiteSeer, and Cornell). Incorporating the results in Table 2, it can be observed that HEATS consistently performs well within a specific parameter range. For example, on the Cora dataset, when the parameter selects from the set $\\{4,5,6\\}$ , HEATS consistently outperforms the baseline model (i.e., GRACE) by $2.21\\%$ , $2.31\\%$ , and $2.25\\%$ , respectively. This indicates HEATS insensitivity to changes in this parameter. Additionally, with a small value (e.g., 2), HEATS performs better than the baseline GRACE, which offers guidance to select the parameter.", + "bbox": [ + 75, + 674, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.3 Robustness Analysis", + "text_level": 1, + "bbox": [ + 498, + 90, + 694, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This experiment is intended to evaluate the robustness of the proposed HEATS framework to noise. The topology attack (adding edges) and the attribute attack (flipping attributes) are applied to create noisy data on the Cora dataset. Figure 5 shows the performance variation of the GCL, HEATS, and the baseline GRACE under topology and attribute attacks.", + "bbox": [ + 496, + 114, + 890, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "It can be seen from Figure 5a that GRACE is somewhat resistant to robust against topology attacks, but the performance degrades significantly with higher attack levels. For example, the accuracy decreases by about $2\\%$ compared to the attack-free accuracy at an edge deletion rate of 0.1. This is attributed to their centers on capturing the invariant information from multiple augmented graphs, to some extent, resulting in them being insensitive to topology changes. However, the accuracy decreases $5\\%$ when the edge deletion rate increases to 0.3. In contrast, HEAT exhibits greater robustness to this attack. Specifically, it achieves about $4.5\\%$ increase in accuracy compared to the baseline GRACE when the edges deletion reaches an extreme $0.2\\%$ . This is mainly due to HEATS incorporating noise simulation and alternating update approach to extract high-order positive samples, thereby enhancing the robustness. Furthermore, as shown in Figure 5b, HEATS consistently outperforms the baseline GRACE, showcasing its denoising ability.", + "bbox": [ + 496, + 205, + 892, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 498, + 489, + 625, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, a novel graph contrastive learning framework, named HEATS, is proposed to address two key limitations of the existing positive sampling techniques: incomplete local sampling and blind sampling. Drawing inspiration from the observation that the affinity matrix associated with the optimal positive sample set is block-diagonal and idempotent, the idea of constructing such matrices to guide positive sampling is proposed. To enhance the adaptability and robustness of HEATS, an approach that alternately updates the positive sampling and contrastive optimization is proposed. Extensive experiments reveal the efficacy and robustness of HEATS. Future research directions include improving the scalability of the framework to accommodate large datasets and improving its generality to multimodal data.", + "bbox": [ + 496, + 513, + 890, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 498, + 739, + 679, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China (No. 62376088, 61972442, 62272020, 62102413, 62132006, U2001202, and U22B2036), in part by the National Science Fund for Distinguished Young Scholars (No. 62025602), in part by the National Social Science Fund of China under Grant 22VMG037, in part by the Natural Science Foundation of Hebei Province of China under Grant F2020202040, and in part by the Tencent Foundation and XPLORER PRIZE.", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23186", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kristen M Altenburger and Johan Ugander. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12682-12691, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 859 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "23187", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_model.json b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..697933ea4227dd1287d67bae5e19141b99d7fbff --- /dev/null +++ b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_model.json @@ -0,0 +1,2044 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.131, + 0.846, + 0.154 + ], + "angle": 0, + "content": "Improving Graph Contrastive Learning via Adaptive Positive Sampling" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.18, + 0.814, + 0.217 + ], + "angle": 0, + "content": "Jiaming Zhuo\\(^{1}\\), Feiyang Qin\\(^{1}\\), Can Cui\\(^{1}\\), Kun Fu\\(^{1}\\), Bingxin Niu\\(^{1}\\), Mengzhu Wang\\(^{1}\\), Yuanfang Guo\\(^{2}\\), Chuan Wang\\(^{3*}\\), Zhen Wang\\(^{4,5}\\), Xiaochun Cao\\(^{6}\\), Liang Yang\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.164, + 0.217, + 0.806, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Artificial Intelligence, Hebei University of Technology, Tianjin, China" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.234, + 0.813, + 0.252 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Computer Science and Engineering, Beihang University, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.156, + 0.252, + 0.816, + 0.27 + ], + "angle": 0, + "content": "\\(^{3}\\)Institute of Information Engineering Chinese Academy of Sciences, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.27, + 0.798, + 0.287 + ], + "angle": 0, + "content": "\\(^{4}\\)School of Cybersecurity, Northwestern Polytechnical University, Xi'an, China" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.287, + 0.831, + 0.304 + ], + "angle": 0, + "content": "5OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, Xi'an, China" + }, + { + "type": "text", + "bbox": [ + 0.153, + 0.305, + 0.819, + 0.322 + ], + "angle": 0, + "content": "\\(^{6}\\)School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.326, + 0.862, + 0.375 + ], + "angle": 0, + "content": "jiaming.zhuo@outlook.com, feiyangqinzzu@163.com, 594021820@qq.com, fukun@hebut.edu.cn, niubingxin666@163.com, dreamkily@gmail.com, andyguo@buaa.edu.cn, wangchuan@iie.ac.cn, w-zhen@nwpu.edu.cn, caoxiaochun@mail.sysu.edu.cn, yangliang@vip.qq.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.41, + 0.313, + 0.426 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.473, + 0.775 + ], + "angle": 0, + "content": "Graph Contrastive Learning (GCL), a Self-Supervised Learning (SSL) architecture tailored for graphs, has shown notable potential for mitigating label scarcity. Its core idea is to amplify feature similarities between the positive sample pairs and reduce them between the negative sample pairs. Unfortunately, most existing GCLs consistently present suboptimal performances on both homophilic and heterophilic graphs. This is primarily attributed to two limitations of positive sampling, that is, incomplete local sampling and blind sampling. To address these limitations, this paper introduces a novel GCL framework with an adaptive positive sampling module, named graphH contrastiveE Adaptive positive Samples (HEATS). Motivated by the observation that the affinity matrix corresponding to optimal positive sample sets has a block-diagonal structure with equal weights within each block, a self-expressive learning objective incorporating the block and idempotent constraint is presented. This learning objective and the contrastive learning objective are iteratively optimized to improve the adaptability and robustness of HEATS. Extensive experiments on graphs and images validate the effectiveness and generality of HEATS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.805, + 0.208, + 0.82 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.83, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Self-supervised learning (SSL), has been a highly regarded methodology within the unsupervised learning field. It generates supervision signals for model training by extracting" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.411, + 0.892, + 0.562 + ], + "angle": 0, + "content": "latent data patterns from the unannotated data [8]. As a notable branch of SSL, Contrastive Learning (CL) emphasizes producing the supervision signals using the established rule, i.e., bringing similar samples (positive samples) closer and pushing dissimilar samples (negative samples) apart. Based on this rule, Graph Contrastive Learning (GCL) extends the applied range to non-Euclidean graphs by employing techniques like graph augmentations and graph encoders. It has achieved remarkable performance on various downstream tasks, such as node classification [15, 32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.777 + ], + "angle": 0, + "content": "To generate the discriminative node representations from GCLs, the positive sample set of each node should contain all nodes from the same class (i.e., TRUE positive samples), while the negative ones should consist of nodes from different classes (i.e., TRUE negative samples). Subsequently, to extend the TRUE positive sample sets, certain research endeavors in GCLs focus on identifying semantically relevant samples within node neighborhoods [12, 20, 26, 30, 34], leveraging the homophily assumption [1, 16]. Despite their consistent performance improvements on the homophilic graphs, where adjacent nodes typically belong to the same class, the improvements are limited. More critically, their robustness to the heterophilic graphs, where adjacent nodes tend to be from different classes, is severely constrained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "These drawbacks are attributed to two limitations of positive sampling. (1) Incomplete local sampling. Most graphs are sparse, and nodes of the same class are typically situated beyond each other's neighborhoods. Therefore, the positive sample sets for most GCLs tend to be incomplete, which could lead to the absence of shared information between the same class. (2) Blind sampling. In dealing with blindness caused by a lack of supervised guidance, the endeavors of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.402, + 0.901 + ], + "angle": 0, + "content": "*Chuan Wang and Liang Yang are corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23179" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "GCLs to establish the criterion for positive sampling beyond the neighborhoods are insufficient. Concretely, most GCLs always center on exploring semantic relevance in neighborhoods utilizing various homophily measures [6, 12, 34]. In fact, these criteria do not apply beyond neighborhoods because of their local property. Due to the incompleteness and blindness of positive sampling, GCLs can not obtain all TRUE positive sample pairs. This hampers the representation ability of GCLs, resulting in their poor performances on both homophilic and heterophilic graphs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.665 + ], + "angle": 0, + "content": "To address these deficiencies, this paper proposes a novel GCL framework, named grapH contrastive Adaptive positive Sampling (HEATS). The idea is to devise a criterion to guide global positive sampling. Toward this end, the characteristic of an affinity matrix (termed positive sample matrix) associated with the optimal positive sample set is first investigated. The conclusion drawn is that the optimal positive sample matrix obeys the block diagonal property (BDP) and is idempotent, as depicted in Figure 1(a). To be specific, this matrix can be decomposed into a batch of diagonal submatrices (blocks), where each block characterizes semantic relevance among nodes from the same class. Moreover, each block is fully connected and the weights within it are equal. Motivated by this, a novel positive sampling module is presented, focusing on constructing such block-diagonal and idempotent affinity matrices. To capture long-range dependencies, positive sample matrices are generated by optimizing a self-expressive objective incorporating block and idempotent constraints, leveraging the features of all nodes within batches. In light of the intrinsic denoising capability of GCLs [14, 35], an alternating update mechanism of matrix construction and contrastive optimization is introduced to obtain reciprocal benefits, thereby improving the robustness and adaptability of HEATS. In theory, HEATS has a stricter lower bound on the mutual information (MI) between node attributes and node embeddings compared to the baselines that select positive samples from neighborhoods, which guarantees its effectiveness and robustness." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.666, + 0.456, + 0.68 + ], + "angle": 0, + "content": "The contributions of this paper are summarized below." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.681, + 0.469, + 0.71 + ], + "angle": 0, + "content": "- We investigate the characteristics of an affinity matrix associated with the optimal positive sample set." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.712, + 0.469, + 0.741 + ], + "angle": 0, + "content": "- We present a novel graph contrastive learning framework HEATS with an adaptive positive sampling module." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.741, + 0.469, + 0.786 + ], + "angle": 0, + "content": "- We theoretically analyze the effectiveness and robustness of the proposed HEATS from a Mutual Information Maximization perspective." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.787, + 0.469, + 0.817 + ], + "angle": 0, + "content": "- We conduct extensive evaluations to demonstrate the superior performance and generality of HEATS." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.681, + 0.469, + 0.817 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.216, + 0.846 + ], + "angle": 0, + "content": "2. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "This section starts by explaining the notations used throughout the paper. It then introduces the basic concepts in Graph Contrastive Learning (GCL)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.611, + 0.105 + ], + "angle": 0, + "content": "2.1. Notations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.175 + ], + "angle": 0, + "content": "Capital italic letters stand for sets (e.g., set \\(\\mathcal{V}\\)), capital bold letters represent matrices (e.g., matrix \\(\\mathbf{Q}\\)), bold lowercase letters term vectors (e.g., vector \\(\\mathbf{q}_v\\)), and lowercase letters denote scalars (e.g., scalar \\(q_{v,u}\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.175, + 0.893, + 0.296 + ], + "angle": 0, + "content": "For generality, this paper focuses on attribute undirected graphs. It considers a graph \\(\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathbf{X})\\), where the node set \\(\\mathcal{V}\\) contains \\(n\\) node instances \\(\\{(\\mathbf{x}_v,\\mathbf{y}_v)\\}_{v\\in \\mathcal{V}}\\). \\(\\mathbf{x}_v\\in \\mathbb{R}^f\\) and \\(\\mathbf{y}_v\\in \\mathbb{R}^c\\) denote the attribute and label vector of the node \\(v\\), respectively. The node embeddings \\(\\mathbf{H}\\in \\mathbb{R}^{n\\times d}\\) are learned on entire graphs in an unsupervised manner, then utilized in downstream tasks, such as node classification, where the labels \\(\\mathbf{Y}\\) are used for fine-tuning linear classifiers." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.304, + 0.757, + 0.32 + ], + "angle": 0, + "content": "2.2. Graph Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.892, + 0.432 + ], + "angle": 0, + "content": "Being typical of a graph-based self-supervised learning SSL architecture, GCL aims to generate supervised signals based on a predefined rule. It involves bringing the similar samples (i.e., positive samples) closer while pushing the dissimilar samples (i.e., negative samples) apart simultaneously. Take GRACE [32], which is an oft-discussed baseline, as an example, its architecture is described below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.538 + ], + "angle": 0, + "content": "In line with SimCLR [2], a contrastive learning baseline in computer vision (CV), GRACE adopts a two-channel architecture. For graph \\(\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathbf{X})\\), both channels are responsible for generating node embeddings (represented as \\(\\mathbf{H}\\) and \\(\\tilde{\\mathbf{H}}\\)) for its two augmented graphs through graph augmentations [32] and encoders [11]. The description of these processes can be found in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Once the node features are obtained, InfoNCE [22] loss, is calculated as a guide for its update. For node \\( v \\), the positive sample of the anchor node \\( (\\mathbf{h}_v) \\) is the same node \\( (\\tilde{\\mathbf{h}}_v) \\) in another view, while the negative samples are other nodes in both views. This contrastive loss (denoted as \\( \\ell_{gc} \\)) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.633, + 0.891, + 0.701 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\ell_ {g c} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) = - l o g \\frac {\\mathrm {p o} _ {v}}{\\mathrm {p o} _ {v} + \\mathrm {n e} _ {v}}, \\\\ \\mathrm {p o} _ {v} = \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {v})}{\\tau}}, \\mathrm {n e} _ {v} = \\sum_ {t \\in V \\backslash v} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\mathbf {h} _ {t})}{\\tau}} + \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {t})}{\\tau}}, \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.819 + ], + "angle": 0, + "content": "where \\(\\theta (\\mathbf{h}_v,\\tilde{\\mathbf{h}}_v) = s(f(\\mathbf{h}_v),f(\\tilde{\\mathbf{h}}_v))\\), \\(s(,)\\) terms the cosine similarity, and \\(f(\\cdot)\\) denotes the projection head [2], which is a two-layer multilayer perceptron (MLP). \\(\\tau\\) represents a scalar, which is positively correlated with the uniformity of the feature distribution. The overall contrastive loss is set as the average over all nodes based on the mutually symmetric form of Equation 1. This can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.827, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g r a c e}} = \\frac {1}{2 | V |} \\sum_ {v \\in V} \\left(\\ell_ {g c} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) + \\ell_ {g c} \\left(\\tilde {\\mathbf {h}} _ {v}, \\mathbf {h} _ {v}\\right)\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In addition to the above pairwise positive sampling, several local positive sampling techniques have been presented" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23180" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.093, + 0.852, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.231, + 0.51, + 0.244 + ], + "angle": 0, + "content": "(a) Optimal positive sample set for GCLs and the corresponding matrix." + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.231, + 0.794, + 0.243 + ], + "angle": 0, + "content": "(b) The proposed HEATS Framework." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed GCL framework, named HEATS, and its design motivation. (a) An intuitive example of the optimal positive sample matrix for GCLs, where the colors of nodes stand for classes. (b) The proposed HEATS framework with adaptive positive sampling. The optimal positive sample set should consist of all nodes from the same class. Accordingly, the optimal positive sample matrix should be block-diagonal, where each block is fully connected and weights within it are equal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.469, + 0.364 + ], + "angle": 0, + "content": "[12, 34]. They propose to add the specified neighbor nodes into the positive sample sets, leveraging the homophily assumption [1, 16]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.38, + 0.212, + 0.397 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.469, + 0.482 + ], + "angle": 0, + "content": "In this section, following the introduction of design motivation, a graph contrastive learning (GCL) framework, named grapH contrastive Adaptive positive Sampling (HEATS), is devised. Subsequently, theoretical analysis of its efficacy are presented." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.198, + 0.509 + ], + "angle": 0, + "content": "3.1. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.469, + 0.58 + ], + "angle": 0, + "content": "As previously discussed in the introduction, existing positive sampling strategies utilized in GCLs tend to be incomplete and blind, leading to a loss of discriminative power of node representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.469, + 0.639 + ], + "angle": 0, + "content": "Definition 1. Block Diagonal Property (BDP) [9]. The given matrix \\(\\mathbf{Z} \\in \\mathbb{R}^{n \\times n}\\) satisfies block diagonal property if it can be decomposed into submatrices as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.651, + 0.37, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} = \\left[ \\begin{array}{c c c c} \\mathbf {Z} _ {1} & 0 & \\dots & 0 \\\\ 0 & \\mathbf {Z} _ {2} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & \\mathbf {Z} _ {k} \\end{array} \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.736, + 0.469, + 0.768 + ], + "angle": 0, + "content": "where \\(\\mathbf{Z}_i\\in \\mathbb{R}^{n_i\\times n_i}\\) stands for the \\(i\\) -th square submatrix (block), and \\(\\sum_{i = 0}^{k}n_{i} = n\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "An intuitive and optimal solution is provide target nodes with positive sample sets that consists of all nodes from the same class (i.e., optimal positive sample set), as depicted in Figure 1(a). It is evident that the relationships among these positive samples can be succinctly expressed as a block diagonal matrix, where each block describes the relationships among a class of nodes. Additionally, this matrix should exhibit the following properties: each block is full connected" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.318, + 0.89, + 0.348 + ], + "angle": 0, + "content": "and weights within it are equal. Therefore, the optimal positive sample matrix should be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.358, + 0.892, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} = \\left[ \\begin{array}{c c c c} \\frac {1}{n _ {1}} \\mathbf {1} _ {n _ {1}} \\mathbf {1} _ {n _ {1}} ^ {\\top} & 0 & \\dots & 0 \\\\ 0 & \\frac {1}{n _ {2}} \\mathbf {1} _ {n _ {2}} \\mathbf {1} _ {n _ {2}} ^ {\\top} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & \\frac {1}{n _ {k}} \\mathbf {1} _ {n _ {k}} \\mathbf {1} _ {n _ {k}} ^ {\\top} \\end{array} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.445, + 0.841, + 0.46 + ], + "angle": 0, + "content": "where \\(\\mathbf{1}_{n_i} \\in \\mathbb{R}^{n_i}\\) denotes an all-one column vector." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.469, + 0.686, + 0.484 + ], + "angle": 0, + "content": "3.2. HEATS framework" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.493, + 0.892, + 0.6 + ], + "angle": 0, + "content": "Based on the above analysis, this paper devises a novel GCL framework HEATS, which directs the positive sampling by employing constructed block diagonal affinity matrices. As overviewed in Figure 1(b), HEATS consists of two key components: (1) Matrix Construction and (2) Contrastive Optimization. These two components engage in an alternating refinement process, gradually converging to the optimum." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.617, + 0.698, + 0.631 + ], + "angle": 0, + "content": "3.2.1 Matrix Construction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.777 + ], + "angle": 0, + "content": "This component aims to construct affinity matrices, which possess inter-class sparsity and intra-class connectivity (i.e., obey BDP), to guide the selection of positive samples. Particularly, it adopts a self-expressive learning objective, commonly utilized in subspace clustering [13], to acquire such affinity matrices. This objective posits that each sample can be represented by linearly combining all other samples in the same subspace (i.e., block). This objective can be formulated as the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.789, + 0.891, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {Z}, \\mathbf {E}} {\\operatorname {a r g m i n}} \\mathcal {O} (\\mathbf {Z}) + \\lambda \\mathcal {T} (\\mathbf {E}), \\quad \\text {s . t .} \\mathbf {X} = \\mathbf {Z} \\mathbf {X} + \\mathbf {E}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{Z}\\) denotes the affinity matrix, which depicts the combination coefficients, and \\(\\mathbf{E}\\) stands for the noise. Moreover, \\(\\mathcal{O}\\) and \\(\\mathcal{T}\\) term the constraint on affinity matrices and noise matrices, respectively. \\(\\lambda\\) is a hyperparameter that balances the two terms of the objective function." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23181" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "To obtain a high-quality affinity matrix, as expressed in Equation 3, several constraints should be incorporated into the learning objective: idempotent and \\(k\\)-block. Firstly, the affinity matrix \\(\\mathbf{Z}\\) in Equation 3 is idempotent [27] because of \\(\\mathbf{Z}_i = \\mathbf{Z}_i \\times \\mathbf{Z}_i = \\mathbf{Z}_i^2\\). Secondly, the number of blocks in the affinity matrices should be controlled as \\(k\\). Furthermore, the affinity matrices also should be normalized, symmetric, and non-negative. To achieve these properties and enhance effectiveness, the self-expressive learning objective can be reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.25, + 0.469, + 0.295 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname *{argmin}_{\\substack{\\mathbf{Z},\\mathbf{S}}}\\| \\mathbf{Z} - \\mathbf{S}\\|_{F}^{2} + \\gamma \\| \\mathbf{S}\\|_{id} + \\lambda \\| \\mathbf{E}\\|_{2,1}, \\\\ \\mathrm {s . t .} \\mathbf {H} = \\mathbf {Z H} + \\mathbf {E}, \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.3, + 0.401, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} \\mathbf {1} _ {n} = \\mathbf {1} _ {n}, \\mathbf {S} = \\mathbf {S} ^ {\\top}, \\mathbf {S} \\geq \\mathbf {0}, \\operatorname {T r} (\\mathbf {S}) = k,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.473, + 0.555 + ], + "angle": 0, + "content": "where \\(\\mathbf{S}\\) denotes an intermediate-term to mitigate the loss of representation capability. And, \\(\\| \\mathbf{S}\\|_{id} = \\| \\mathbf{S} - \\mathbf{S}^2\\| _F^2\\) terms the idempotent constraint and \\(\\gamma\\) is a scalar that controls the impacts of this term. The terms \\(\\mathbf{S1}_n = \\mathbf{1}_n\\) \\(\\mathbf{S} = \\mathbf{S}^{\\top}\\) ,and \\(\\mathbf{S}\\geq 0\\) stand for the column-normalized, symmetric, and nonnegative constraints, respectively. Based on the above constraints, the term \\(\\mathrm{Tr}(\\mathbf{S}) = k\\) is introduced to make the matrix have \\(k\\) blocks. \\(\\| \\mathbf{E}\\|_{2,1} = \\sum_{j = 1}^{n}\\sqrt{\\sum_{i = 1}^{n}([\\mathbf{E}]_{ij})^2}\\) is the \\(\\ell_{2,1}\\) -norm of noise, which characterizes sample-specific outliers. Finally, the affinity matrix, a guide of positive sampling, can be obtained by optimizing Equation 5. Please refer to the appendix for optimization details. Once the affinity matrix M (i.e., \\(\\mathbf{Z}\\) or S) is obtained, it is necessary to sparsify it to enhance training efficiency. The sparsification process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.564, + 0.372, + 0.605 + ], + "angle": 0, + "content": "\\[\nm _ {v, u} = \\left\\{ \\begin{array}{l l} 0, & m _ {v, u} < \\beta , \\\\ m _ {v, u}, & \\text {o t h e r w i s e}. \\end{array} \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.644 + ], + "angle": 0, + "content": "where \\(\\beta\\) denotes the threshold parameter, which is utilized to indicate filter out the values below it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Theorem 1. The affinity matrix \\(\\mathbf{M}\\), which is generated by optimizing Equation (5), satisfies the BDP in Definition 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.47, + 0.739 + ], + "angle": 0, + "content": "Theorem 1 theoretically demonstrates that the proposed matrix construction strategy aligns with the motivation. For the proof, please refer to the appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.31, + 0.772 + ], + "angle": 0, + "content": "3.2.2 Contrastive Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.902 + ], + "angle": 0, + "content": "This subsection delineates the methodology for formulating the contrastive loss leveraging the constructed affinity matrix \\(\\mathbf{M}\\). Firstly, it is utilized to direct the sampling process. By identifying non-zero values in the vector \\(\\mathbf{m}_v\\), nodes that are semantically associated with node \\(v\\) can be marked out. These nodes collectively constitute the positive sample set of node \\(v\\), denoted as \\(\\mathcal{P}_v^M = \\{u|m_{v,u} > 0\\}\\). Following the baselines [2, 32], the negative sample set is composed of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.137 + ], + "angle": 0, + "content": "the remaining nodes, that is \\(\\mathcal{N}_v^M = V\\setminus \\{\\mathcal{P}_v^M\\cup v\\}\\). Secondly, the matrix \\(\\mathbf{M}\\) is also interpreted as a measure of the relationships, and the values within it are treated as weights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.894, + 0.199 + ], + "angle": 0, + "content": "In implementation, HEATS follows the baseline GRACE [32], which is mentioned in Section 2.2. Therefore, the contrastive loss of HEATS with respect to anchor node \\(\\mathbf{h}_v\\) can be reformulated from Equation 1 as" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.208, + 0.892, + 0.318 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\ell_ {h t} (\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}) = - l o g \\frac {\\mathrm {p o} _ {v}}{\\mathrm {p o} _ {v} + \\mathrm {n e} _ {v}}, \\\\ \\mathrm {p o} _ {v} = \\mathrm {e} ^ {\\frac {\\theta \\left(\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {v}\\right)}{\\tau}} + \\sum_ {u \\in \\mathcal {P} _ {v} ^ {M}} m _ {v, u} \\cdot \\mathrm {e} ^ {\\frac {\\theta \\left(\\mathbf {h} _ {v} , \\mathbf {h} _ {u}\\right)}{\\tau}}, \\tag {6} \\\\ \\mathrm {n e} _ {v} = \\sum_ {t \\in \\mathcal {N} _ {v} ^ {M}} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\bar {\\mathbf {h}} _ {t})}{\\tau}} + \\sum_ {t \\in \\mathcal {N} _ {v} ^ {M}} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\bar {\\mathbf {h}} _ {t})}{\\tau}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.328, + 0.886, + 0.344 + ], + "angle": 0, + "content": "The overall contrastive loss of HEATS, denoted as \\(\\mathcal{L}_{\\text{heats}}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.354, + 0.892, + 0.39 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {h e a t s}} = \\frac {1}{2 | V |} \\sum_ {v \\in V} \\left(\\ell_ {h t} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) + \\ell_ {h t} \\left(\\tilde {\\mathbf {h}} _ {v}, \\mathbf {h} _ {v}\\right)\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.552 + ], + "angle": 0, + "content": "In comparison to the existing GCLs [12, 20, 34], the proposed HEATS exhibits several characteristics. (1) Generality. Since the positive sample matrices are constructed globally, that is, independent of the underlying graph topology, HEATS can be reasonably extended to non-graph domains such as computer vision (CV). (2) Robustness. Due to the fact that the positive sample matrix is obtained by optimizing a robust self-expressive learning objective, as formulated in Equation (5), the robustness is strengthened through positive sampling on these matrices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.894, + 0.623 + ], + "angle": 0, + "content": "Theorem 2. The contrastive loss of HEATS \\((\\mathcal{L}_{\\text {heats }})\\) is a more stringent estimate of mutual information (MI) between node attributes and embeddings than that of the local baseline HomoGCL [12], that is," + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.635, + 0.892, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {h o m o g c l}} \\leq \\mathcal {L} _ {\\text {h e a t s}} \\leq I (\\mathbf {X}; \\mathbf {H}, \\tilde {\\mathbf {H}}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.665, + 0.892, + 0.697 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}\\) denotes the node attributes, and \\(\\mathbf{H}\\) and \\(\\tilde{\\mathbf{H}}\\) represent the node embeddings in two augmented views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.892, + 0.753 + ], + "angle": 0, + "content": "Theorem 2 demonstrates that the proposed HEATS provides a refined approximation to the TRUE mutual information, enabling it to promote model robustness and stability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.691, + 0.787 + ], + "angle": 0, + "content": "3.2.3 Alternating Update" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To enhance the adaptivity of HEATS, the two fundamental components, matrix construction and contrastive optimization, engage in iterative updates in an alternating fashion, as visually depicted in Figure 1(b). The former is tasked with solving Equation 5 to construct positive sample matrices in the feature space. The latter focuses on representation (feature) learning by optimizing the contrastive loss using these" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23182" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 1. Statistics of twelve graph datasets. Homophily is the edge homophily in [17]." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.123, + 0.468, + 0.301 + ], + "angle": 0, + "content": "
DatasetNodesEdgesFeaturesClassesHomophily
Cora2,7085,2781,43370.81
CiteSeer3,3274,5523,70360.74
PubMed19,71744,32450030.80
Wiki-CS11,701216,123300100.65
Computers13,752245,861767100.78
Photo7,650238,16374580.83
Cornell1832951,70350.13
Texas1833091,70350.11
Wisconsin2514991,70350.20
Chameleon2,27736,1012,32550.23
Squirrel5,201217,0732,08950.22
Actor7,60033,54493150.22
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.316, + 0.468, + 0.345 + ], + "angle": 0, + "content": "positive sample matrices, which is formulated as Equation 6. These two components are updated alternately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.346, + 0.47, + 0.557 + ], + "angle": 0, + "content": "The alternating update procedure offers several benefits to GCLs. (1) Adaptive positive samples. Note that the positive sample matrices are constructed in the feature space. Hence, this procedure can continually provide adaptive positive samples for the subsequent contrastive optimization, adapting to feature changes. (2) Discriminative node representations. GCLs have the denoising ability, to some extent, which is attributed to the fact that it obtains the invariant information [28]. As a result, the discriminative feature space can be provided for the construction of positive sample matrices, eventually resulting in more discriminative features through contrastive learning. Furthermore, benefits also involve the risk reduction of each component falling into the local optimum and accelerating the convergence speed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.571, + 0.209, + 0.587 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.673 + ], + "angle": 0, + "content": "In this section, the proposed framework HEATS is validated by empirically evaluating its performances on node and image classification tasks in the unsupervised setting. Next, an in-depth understanding of the efficacy of this framework is provided through several experiment analyses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.254, + 0.698 + ], + "angle": 0, + "content": "4.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Datasets. To illustrate the effectiveness and generality of the proposed HEATS, twelve non-Euclidean graph datasets, and three 2-D spatial image datasets are adopted in the experiments. According to graph homophily [17], these graph datasets can be divided into two categories: six homophilic graphs, including Cora, CiteSeer, PubMed, Wiki-CS, Computers, and Photo, and six heterophilic graphs, containing Cornell, Texas, Wisconsin, Chameleon, Squirrel, and Actor. Moreover, the image datasets are CIFAR-10, STL-10, and CIFAR-100. The statistics of the graph datasets are presented in Table 1. Due to space limitations, the introduction of all datasets is presented in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Splitting. To ensure experimental fairness, the dataset split" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "ting follows commonly employed schemes. Specifically, for three homophilic graphs (Cora, CiteSeer, and PubMed) and all six heterophilic graphs, the training, validation, and testing sets constitute \\(48\\%\\), \\(32\\%\\), and \\(20\\%\\) of the data, respectively. For the remaining homophilic graphs (Wiki-CS, Computers, and Photo), the proportions amount to \\(10\\%\\), \\(10\\%\\) and \\(80\\%\\). Besides, for the CIFAR-10 dataset, 5000 and 1000 images per class are selected for training and testing, respectively. For the STL-10 dataset, 10500 and 800 images per class are assigned to the training and testing sets, respectively. For the CIFAR-100 dataset, 500 and 100 images per class are served in training and testing, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.892, + 0.452 + ], + "angle": 0, + "content": "Baselines. These experiments involve two types of downstream tasks: node classification for graphs and image classification. For the node classification, the baselines include two types: semi-supervised graph neural networks (GCN [11], GAT [24] and JKNet [29]), and unsupervised graph learning models (Deepwalk [18], Node2vec [4], GAE [10], VGAE [10], DGI [25], MVGRL [5], GRACE [32], GCA [33], BGRL [21], SELENE [31], and HomoGCL [12]). For the image classification, the baseline is CL model SimCLR [2], which is implemented with two backbones (ResNet-18 and ResNet-50) [7]. Please refer to the appendix for an introduction to related works." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.892, + 0.77 + ], + "angle": 0, + "content": "Configurations. In the node classification, the proposed HEATS framework is implemented with the configurations following GRACE [32]. To be specific, each branch corresponds to an augmented graph, which is initially obtained through the edge deletion and attribute masking [3], with the random ratio among \\(\\{0.2, 0.4, 0.6, 0.8\\}\\). Furthermore, the node features are obtained through a two-layer GCN [11] encoding and a two-layer MLP [19] projecting, where both dimensions are 64. The node features are trained by minimizing the contrastive loss, where the temperature coefficient is taken from \\(\\{0.2, 0.4, 0.6, 0.8, 1\\}\\). In this process, an Adam optimizer with the learning rate of 0.01 and the weight decay rate among \\(\\{0, 5 \\times 10^{-5}\\}\\) is to be employed for optimization and regularization, respectively. Minibatch training is adopted for larger node numbers, such as PubMed. For the unique parameters of HEATS, namely \\(\\gamma\\) and \\(\\lambda\\), both are selected from \\(\\{1 \\times 10^{-3}, 1 \\times 10^{-2}, 1 \\times 10^{-1}, 1, 10\\}\\). Furthermore, the number of blocks \\(k\\) is selected from a set with no more than the number of classes, and its impact is analyzed in Section 4.3.2. All experiments are conducted in PyTorch on a single RTX4090 24GB GPU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.771, + 0.892, + 0.892 + ], + "angle": 0, + "content": "Evaluation Protocol. For both node and image classification tasks, the experimental evaluations adopt the standard linear evaluation protocol [25]. Concretely, all models undergo initial unsupervised pre-training, followed by utilizing the obtained embeddings to train linear classifiers and subsequently presenting the test accuracy results. Throughout the evaluation phases, the Adam optimizer with a learning rate of 0.01 is utilized. The experiment results are re" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23183" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 2. Node classification accuracy (mean ± std) is reported for six homophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.129, + 0.868, + 0.364 + ], + "angle": 0, + "content": "
ModelTraining DataCoraCiteSeerPubMedWiki-CSComputersPhoto
GCNA,X,Y85.77 ± 0.2573.68 ± 0.3188.13 ± 0.2876.89 ± 0.3786.34 ± 0.4892.35 ± 0.25
GATA,X,Y86.37 ± 0.3074.32 ± 0.2787.62 ± 0.2677.42 ± 0.1987.06 ± 0.3592.64 ± 0.42
JKNetA,X,Y85.93 ± 1.3574.37 ± 1.5387.68 ± 0.3079.52 ± 0.2185.28 ± 0.7292.68 ± 0.13
DeepWalkA73.96 ± 0.1261.91 ± 0.4274.79 ± 0.9874.35 ± 0.0685.68 ± 0.0689.44 ± 0.11
Node2VecA75.87 ± 0.2262.54 ± 0.1376.49 ± 0.3271.79 ± 0.0584.39 ± 0.0889.67 ± 0.12
GAEA,X76.83 ± 1.2265.43 ± 1.1376.52 ± 0.3370.15 ± 0.0185.27 ± 0.1991.62 ± 0.13
VGAEA,X79.36 ± 0.8369.18 ± 0.2779.17 ± 0.4476.63 ± 0.1986.37 ± 0.2192.20 ± 0.11
DGIA,X85.90 ± 0.5772.57 ± 0.2383.52 ± 1.2475.73 ± 0.1384.09 ± 0.3991.49 ± 0.25
MVGRLA,X86.77 ± 0.3373.71 ± 0.4884.63 ± 0.7377.97 ± 0.1887.09 ± 0.2792.01 ± 0.13
GRACEA,X84.79 ± 0.6472.94 ± 0.7284.51 ± 0.6879.16 ± 0.3687.21 ± 0.4492.65 ± 0.32
GCAA,X85.16 ± 0.5172.73 ± 0.4585.22 ± 0.7379.35 ± 0.1287.84 ± 0.2792.78 ± 0.17
BGRLA,X85.37 ± 0.7473.45 ± 0.8384.61 ± 0.3278.74 ± 0.2288.92 ± 0.3393.24 ± 0.29
SELENEA,X85.28 ± 0.8373.48 ± 0.6584.70 ± 0.5278.31 ± 0.6388.13 ± 0.5192.93 ± 0.34
HomoGCLA,X85.02 ± 0.6873.67 ± 0.7882.33 ± 0.4977.47 ± 0.4587.84 ± 0.2893.59 ± 0.27
HEATSA,X87.10 ± 1.4075.26 ± 1.2585.41 ± 0.8279.99 ± 1.5989.29 ± 1.1294.65 ± 1.71
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.381, + 0.38, + 0.397 + ], + "angle": 0, + "content": "ported as an average of over ten random runs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.353, + 0.423 + ], + "angle": 0, + "content": "4.2. Results on benchmark datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Results on Homophilic Graphs. Table 2 presents the experimental results of node classification on six homophilic graphs. It is evident that compared to all unsupervised baseline models, the proposed HEATS achieves the best performance across all datasets. It even surpasses all supervised comparison models on datasets other than PubMed. To be specific, on the CiteSeer dataset, HEATS outperforms the second-best unsupervised model (i.e., MVGRL) by \\(1.55\\%\\) and the baseline model (i.e., GRACE) by \\(2.32\\%\\) in classification accuracy. This highlights the effectiveness of HEATS in exploring positive samples by modeling high-order relationships." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Results on Homophilic Graphs. A similar phenomenon can be observed from the experiment results on heterophilic graphs, as illustrated in Table 3. To be specific, compared to the baseline model (i.e., GRACE), HEATS achieves performance improvements across all datasets. Particularly noteworthy are improvements in accuracy by \\(12.11\\%\\), \\(7.29\\%\\), and \\(15.88\\%\\) on the Cornell, Texas, and Wisconsin datasets, respectively. This emphasizes the contribution of the proposed positive sampling based on matrix construction in enriching the universality of the baselines. Moreover, HEATS outperforms other unsupervised baselines on three datasets, except the Chameleon, Squirrel, and Actor datasets, showcasing its superior performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Visualization. This experiment aims to intuitively demonstrate the representation ability of the proposed HEATS. For this purpose, the t-SNE [23] method is exploited to perform feature reduction and visualization of the trained representations. Figure 2 exhibits the experiment results (scatter plots) on three benchmark datasets (i.e., Cora, CiteSeer, and" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.385, + 0.878, + 0.584 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.595, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Figure 2. t-SNE visualization of node embeddings from HEATS, BGRL, and GRACE on Cora, CiteSeer, and Photo datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Photo), where colors stand for the classes of nodes. It can be observed that compared to all the comparison models (i.e., GRACE and BGRL), the proposed HEATS framework is enabled to produce the most informative representations. As exemplified by the Cora and CiteSeer dataset, compared to the baseline model (i.e., GRACE), HEATS achieves more compact clusters in node embeddings. Specifically, the embeddings of the same class are closer, while the embeddings of different classes exhibit more significant differences. The experiment results emphasize the effectiveness of HEATS in enhancing representation ability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on Image Datasets. As previously mentioned, the proposed HEATS designs a positive sampling strategy from a global perspective, which effectively mitigates graph structural constraints. In essence, this improves its generality to various domains. To substantiate this claim, the experiment compares a contrastive learning (CL) model tailored for images (i.e., SimCLR) with the proposed variants." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23184" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 3. Node classification accuracy (mean ± std) is reported for six heterophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.129, + 0.869, + 0.364 + ], + "angle": 0, + "content": "
ModelTraining DataCornellTexasWisconsinChameleonSquirrelActor
GCNA,X,Y55.14 ± 7.5755.68 ± 9.6158.42 ± 5.1059.82 ± 2.5836.89 ± 1.3430.64 ± 1.49
GATA,X,Y58.92 ± 3.3258.38 ± 4.4555.29 ± 8.7160.26 ± 2.5040.72 ± 1.5527.44 ± 0.89
JKNetA,X,Y56.49 ± 3.2265.35 ± 4.8651.37 ± 3.2160.31 ± 2.7644.24 ± 2.1136.47 ± 0.51
DeepWalkA39.18 ± 5.5746.49 ± 6.4933.53 ± 4.9247.74 ± 2.0532.93 ± 1.5822.78 ± 0.64
Node2VecA42.94 ± 7.4641.92 ± 7.7637.45 ± 7.0941.93 ± 3.2922.84 ± 0.7228.28 ± 1.27
GAEA,X58.85 ± 3.2158.64 ± 4.5352.55 ± 3.8033.84 ± 2.7728.03 ± 1.6128.03 ± 1.18
VGAEA,X59.19 ± 4.0959.20 ± 4.2656.67 ± 5.5135.22 ± 2.7129.48 ± 1.4826.99 ± 1.56
DGIA,X63.35 ± 4.6160.59 ± 7.5655.41 ± 5.9639.95 ± 1.7531.80 ± 0.7729.82 ± 0.69
MVGRLA,X64.30 ± 5.4362.38 ± 5.6162.37 ± 4.3251.07 ± 2.6835.47 ± 1.2930.02 ± 0.70
GRACEA,X54.86 ± 6.9557.57 ± 5.6850.00 ± 5.8348.05 ± 1.8131.33 ± 1.2229.01 ± 0.78
GCAA,X55.41 ± 4.5659.46 ± 6.1650.78 ± 4.0649.80 ± 1.8135.50 ± 0.9129.65 ± 1.47
BGRLA,X57.30 ± 5.5159.19 ± 5.8552.35 ± 4.1247.46 ± 2.7432.64 ± 0.7829.86 ± 0.75
SELENEA,X59.94 ± 5.1261.87 ± 4.2561.87 ± 4.7942.13 ± 2.1533.28 ± 0.8230.12 ± 0.76
HomoGCLA,X48.64 ± 2.5954.05 ± 2.3239.21 ± 5.7548.68 ± 1.1638.71 ± 0.8528.81 ± 0.78
HEATSA,X66.97 ± 6.7464.86 ± 4.6865.88 ± 5.5649.96 ± 1.8636.24 ± 1.1129.91 ± 1.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.379, + 0.47, + 0.407 + ], + "angle": 0, + "content": "Table 4. Image classification accuracy (mean) of SimCLR and its HEATS-based variants. \\(\\uparrow\\) dentoes the performance improvement." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.418, + 0.445, + 0.523 + ], + "angle": 0, + "content": "
BackboneMethodCIFAR-10STL-10CIFAR-100
ResNet-18SimCLR78.5978.4449.60
+HEATS79.1978.8352.62
↑+0.60+0.39+3.02
ResNet-50SimCLR75.0376.7349.31
+HEATS77.5877.8053.81
↑+2.55+1.07+4.50
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.47, + 0.753 + ], + "angle": 0, + "content": "The configurations of these variants align with that of the baselines, including standard parameters such as learning rate and training epochs. Please refer to the appendix for experiment setups. Table 4 exhibits the image classification results after 30 epochs using ResNet-18 and ResNet-50 backbones. It can be seen that compared to the baseline (i.e., SimCLR), the proposed HEATS framework consistently improves performance across all three datasets. To be specific, HEATS showcases superior performance compared to the two baselines utilizing ResNet-18 and ResNet-50 backbones on the CIFAR-100 dataset by \\(3.02\\%\\) and \\(4.5\\%\\), respectively, accentuating the generality to image-centric tasks. More importantly, it provides valuable insights for applying HEATS in a wide range of domains." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.763, + 0.245, + 0.779 + ], + "angle": 0, + "content": "4.3. Further Analysis" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.273, + 0.801 + ], + "angle": 0, + "content": "4.3.1 Effectiveness Justify" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The experiment intends to justify the effectiveness of the two proposed approaches to enhance positive sampling, i.e., matrix construction and alternating updates, to pursue the block-diagonal matrices. Therefore, three matrices, which include the adjacent matrix, the matrix computed using the initial features, and the matrix computed using the features" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.384, + 0.868, + 0.735 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.74, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Figure 3. Visualization of the adjacent matrices, the matrices computed using the initial features (Matrix 1), and the matrices computed using the learned features after 200 iterations (Matrix 2) on the Cora and CiteSeer datasets. The nodes are sorted by class. The weights between nodes are not considered here." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.854 + ], + "angle": 0, + "content": "after 200 iterations, are visualized in Figure 3 to provide an intuitive understanding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Based on the observations in Figure 3, three significant conclusions can be drawn. (1) The constructed matrices are approximately block diagonal. In particular, on all datasets" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23185" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.095, + 0.462, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.202, + 0.405, + 0.216 + ], + "angle": 0, + "content": "Figure 4. Impact of the number of blocks \\( k \\)." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.234, + 0.255, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.345, + 0.23, + 0.357 + ], + "angle": 0, + "content": "(a) Topology attacks" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.234, + 0.447, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.345, + 0.422, + 0.357 + ], + "angle": 0, + "content": "(b) Attribute attacks" + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.363, + 0.414, + 0.377 + ], + "angle": 0, + "content": "Figure 5. Results of GCLs under graph attacks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.473, + 0.633 + ], + "angle": 0, + "content": "(i.e., Cora and CiteSeer), the edges between nodes from the same class outnumber those between nodes from different classes. This indicates that the proposed HEATS framework can serve as an effective strategy to obtain more TRUE positive samples. (2) Compared to the adjacent matrices, the constructed matrices exhibit denser diagonal blocks. This implies that the proposed matrix construction approach is feasible in contrastive learning by offering more TRUE positive samples beyond graph topology. (3) Compared to the matrices constructed in the initial feature space, those constructed in the updated feature space exhibit a more distinct block-diagonal structure, e.g., results of the Cora dataset. This emphasizes the effectiveness of the proposed alternating update approach. In summary, the experiment confirms the efficacy of the two proposed approaches in constructing block-diagonal matrices for positive sample collection." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.295, + 0.667 + ], + "angle": 0, + "content": "4.3.2 Hyperparameter Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.902 + ], + "angle": 0, + "content": "The experiment aims to provide a guide on choosing the parameter \\( k \\), which represents the number of blocks, by investigating its impact on the performance. This parameter is selected from 2 to the number of classes, as setting it to 1 seems ineffective. Figure 4 exhibits the experiment results on three datasets (i.e., Cora, CiteSeer, and Cornell). Incorporating the results in Table 2, it can be observed that HEATS consistently performs well within a specific parameter range. For example, on the Cora dataset, when the parameter selects from the set \\(\\{4,5,6\\}\\), HEATS consistently outperforms the baseline model (i.e., GRACE) by \\(2.21\\%\\), \\(2.31\\%\\), and \\(2.25\\%\\), respectively. This indicates HEATS insensitivity to changes in this parameter. Additionally, with a small value (e.g., 2), HEATS performs better than the baseline GRACE, which offers guidance to select the parameter." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.092, + 0.696, + 0.107 + ], + "angle": 0, + "content": "4.3.3 Robustness Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.206 + ], + "angle": 0, + "content": "This experiment is intended to evaluate the robustness of the proposed HEATS framework to noise. The topology attack (adding edges) and the attribute attack (flipping attributes) are applied to create noisy data on the Cora dataset. Figure 5 shows the performance variation of the GCL, HEATS, and the baseline GRACE under topology and attribute attacks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.207, + 0.893, + 0.478 + ], + "angle": 0, + "content": "It can be seen from Figure 5a that GRACE is somewhat resistant to robust against topology attacks, but the performance degrades significantly with higher attack levels. For example, the accuracy decreases by about \\(2\\%\\) compared to the attack-free accuracy at an edge deletion rate of 0.1. This is attributed to their centers on capturing the invariant information from multiple augmented graphs, to some extent, resulting in them being insensitive to topology changes. However, the accuracy decreases \\(5\\%\\) when the edge deletion rate increases to 0.3. In contrast, HEAT exhibits greater robustness to this attack. Specifically, it achieves about \\(4.5\\%\\) increase in accuracy compared to the baseline GRACE when the edges deletion reaches an extreme \\(0.2\\%\\). This is mainly due to HEATS incorporating noise simulation and alternating update approach to extract high-order positive samples, thereby enhancing the robustness. Furthermore, as shown in Figure 5b, HEATS consistently outperforms the baseline GRACE, showcasing its denoising ability." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.49, + 0.627, + 0.506 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.728 + ], + "angle": 0, + "content": "In this paper, a novel graph contrastive learning framework, named HEATS, is proposed to address two key limitations of the existing positive sampling techniques: incomplete local sampling and blind sampling. Drawing inspiration from the observation that the affinity matrix associated with the optimal positive sample set is block-diagonal and idempotent, the idea of constructing such matrices to guide positive sampling is proposed. To enhance the adaptability and robustness of HEATS, an approach that alternately updates the positive sampling and contrastive optimization is proposed. Extensive experiments reveal the efficacy and robustness of HEATS. Future research directions include improving the scalability of the framework to accommodate large datasets and improving its generality to multimodal data." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.74, + 0.681, + 0.758 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China (No. 62376088, 61972442, 62272020, 62102413, 62132006, U2001202, and U22B2036), in part by the National Science Fund for Distinguished Young Scholars (No. 62025602), in part by the National Social Science Fund of China under Grant 22VMG037, in part by the Natural Science Foundation of Hebei Province of China under Grant F2020202040, and in part by the Tencent Foundation and XPLORER PRIZE." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23186" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Kristen M Altenburger and Johan Ugander. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12682-12691, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.86 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23187" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_origin.pdf b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d4e0cf7ffcb0ec6fea0226adafc3a8670c426cda --- /dev/null +++ b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/39e494d0-f5b1-4e1a-9fa4-55c8eca880a8_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:76ed5d0e225ed157f0961be8d0384918c3ba2c631b1c0dc72eb036fcdadf1c80 +size 1981971 diff --git a/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/full.md b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9543f0d2370d0a4efff4da25f6684f11cca3e5c7 --- /dev/null +++ b/2024/Improving Graph Contrastive Learning via Adaptive Positive Sampling/full.md @@ -0,0 +1,314 @@ +# Improving Graph Contrastive Learning via Adaptive Positive Sampling + +Jiaming Zhuo $^{1}$ , Feiyang Qin $^{1}$ , Can Cui $^{1}$ , Kun Fu $^{1}$ , Bingxin Niu $^{1}$ , Mengzhu Wang $^{1}$ , Yuanfang Guo $^{2}$ , Chuan Wang $^{3*}$ , Zhen Wang $^{4,5}$ , Xiaochun Cao $^{6}$ , Liang Yang $^{1*}$ + +$^{1}$ School of Artificial Intelligence, Hebei University of Technology, Tianjin, China + +$^{2}$ School of Computer Science and Engineering, Beihang University, Beijing, China + +$^{3}$ Institute of Information Engineering Chinese Academy of Sciences, Beijing, China + +$^{4}$ School of Cybersecurity, Northwestern Polytechnical University, Xi'an, China + +5OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, Xi'an, China + +$^{6}$ School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China + +jiaming.zhuo@outlook.com, feiyangqinzzu@163.com, 594021820@qq.com, fukun@hebut.edu.cn, niubingxin666@163.com, dreamkily@gmail.com, andyguo@buaa.edu.cn, wangchuan@iie.ac.cn, w-zhen@nwpu.edu.cn, caoxiaochun@mail.sysu.edu.cn, yangliang@vip.qq.com + +# Abstract + +Graph Contrastive Learning (GCL), a Self-Supervised Learning (SSL) architecture tailored for graphs, has shown notable potential for mitigating label scarcity. Its core idea is to amplify feature similarities between the positive sample pairs and reduce them between the negative sample pairs. Unfortunately, most existing GCLs consistently present suboptimal performances on both homophilic and heterophilic graphs. This is primarily attributed to two limitations of positive sampling, that is, incomplete local sampling and blind sampling. To address these limitations, this paper introduces a novel GCL framework with an adaptive positive sampling module, named graphH contrastiveE Adaptive positive Samples (HEATS). Motivated by the observation that the affinity matrix corresponding to optimal positive sample sets has a block-diagonal structure with equal weights within each block, a self-expressive learning objective incorporating the block and idempotent constraint is presented. This learning objective and the contrastive learning objective are iteratively optimized to improve the adaptability and robustness of HEATS. Extensive experiments on graphs and images validate the effectiveness and generality of HEATS. + +# 1. Introduction + +Self-supervised learning (SSL), has been a highly regarded methodology within the unsupervised learning field. It generates supervision signals for model training by extracting + +latent data patterns from the unannotated data [8]. As a notable branch of SSL, Contrastive Learning (CL) emphasizes producing the supervision signals using the established rule, i.e., bringing similar samples (positive samples) closer and pushing dissimilar samples (negative samples) apart. Based on this rule, Graph Contrastive Learning (GCL) extends the applied range to non-Euclidean graphs by employing techniques like graph augmentations and graph encoders. It has achieved remarkable performance on various downstream tasks, such as node classification [15, 32]. + +To generate the discriminative node representations from GCLs, the positive sample set of each node should contain all nodes from the same class (i.e., TRUE positive samples), while the negative ones should consist of nodes from different classes (i.e., TRUE negative samples). Subsequently, to extend the TRUE positive sample sets, certain research endeavors in GCLs focus on identifying semantically relevant samples within node neighborhoods [12, 20, 26, 30, 34], leveraging the homophily assumption [1, 16]. Despite their consistent performance improvements on the homophilic graphs, where adjacent nodes typically belong to the same class, the improvements are limited. More critically, their robustness to the heterophilic graphs, where adjacent nodes tend to be from different classes, is severely constrained. + +These drawbacks are attributed to two limitations of positive sampling. (1) Incomplete local sampling. Most graphs are sparse, and nodes of the same class are typically situated beyond each other's neighborhoods. Therefore, the positive sample sets for most GCLs tend to be incomplete, which could lead to the absence of shared information between the same class. (2) Blind sampling. In dealing with blindness caused by a lack of supervised guidance, the endeavors of + +GCLs to establish the criterion for positive sampling beyond the neighborhoods are insufficient. Concretely, most GCLs always center on exploring semantic relevance in neighborhoods utilizing various homophily measures [6, 12, 34]. In fact, these criteria do not apply beyond neighborhoods because of their local property. Due to the incompleteness and blindness of positive sampling, GCLs can not obtain all TRUE positive sample pairs. This hampers the representation ability of GCLs, resulting in their poor performances on both homophilic and heterophilic graphs. + +To address these deficiencies, this paper proposes a novel GCL framework, named grapH contrastive Adaptive positive Sampling (HEATS). The idea is to devise a criterion to guide global positive sampling. Toward this end, the characteristic of an affinity matrix (termed positive sample matrix) associated with the optimal positive sample set is first investigated. The conclusion drawn is that the optimal positive sample matrix obeys the block diagonal property (BDP) and is idempotent, as depicted in Figure 1(a). To be specific, this matrix can be decomposed into a batch of diagonal submatrices (blocks), where each block characterizes semantic relevance among nodes from the same class. Moreover, each block is fully connected and the weights within it are equal. Motivated by this, a novel positive sampling module is presented, focusing on constructing such block-diagonal and idempotent affinity matrices. To capture long-range dependencies, positive sample matrices are generated by optimizing a self-expressive objective incorporating block and idempotent constraints, leveraging the features of all nodes within batches. In light of the intrinsic denoising capability of GCLs [14, 35], an alternating update mechanism of matrix construction and contrastive optimization is introduced to obtain reciprocal benefits, thereby improving the robustness and adaptability of HEATS. In theory, HEATS has a stricter lower bound on the mutual information (MI) between node attributes and node embeddings compared to the baselines that select positive samples from neighborhoods, which guarantees its effectiveness and robustness. + +The contributions of this paper are summarized below. + +- We investigate the characteristics of an affinity matrix associated with the optimal positive sample set. +- We present a novel graph contrastive learning framework HEATS with an adaptive positive sampling module. +- We theoretically analyze the effectiveness and robustness of the proposed HEATS from a Mutual Information Maximization perspective. +- We conduct extensive evaluations to demonstrate the superior performance and generality of HEATS. + +# 2. Preliminaries + +This section starts by explaining the notations used throughout the paper. It then introduces the basic concepts in Graph Contrastive Learning (GCL). + +# 2.1. Notations + +Capital italic letters stand for sets (e.g., set $\mathcal{V}$ ), capital bold letters represent matrices (e.g., matrix $\mathbf{Q}$ ), bold lowercase letters term vectors (e.g., vector $\mathbf{q}_v$ ), and lowercase letters denote scalars (e.g., scalar $q_{v,u}$ ). + +For generality, this paper focuses on attribute undirected graphs. It considers a graph $\mathcal{G}(\mathcal{V},\mathcal{E},\mathbf{X})$ , where the node set $\mathcal{V}$ contains $n$ node instances $\{(\mathbf{x}_v,\mathbf{y}_v)\}_{v\in \mathcal{V}}$ . $\mathbf{x}_v\in \mathbb{R}^f$ and $\mathbf{y}_v\in \mathbb{R}^c$ denote the attribute and label vector of the node $v$ , respectively. The node embeddings $\mathbf{H}\in \mathbb{R}^{n\times d}$ are learned on entire graphs in an unsupervised manner, then utilized in downstream tasks, such as node classification, where the labels $\mathbf{Y}$ are used for fine-tuning linear classifiers. + +# 2.2. Graph Contrastive Learning + +Being typical of a graph-based self-supervised learning SSL architecture, GCL aims to generate supervised signals based on a predefined rule. It involves bringing the similar samples (i.e., positive samples) closer while pushing the dissimilar samples (i.e., negative samples) apart simultaneously. Take GRACE [32], which is an oft-discussed baseline, as an example, its architecture is described below. + +In line with SimCLR [2], a contrastive learning baseline in computer vision (CV), GRACE adopts a two-channel architecture. For graph $\mathcal{G}(\mathcal{V},\mathcal{E},\mathbf{X})$ , both channels are responsible for generating node embeddings (represented as $\mathbf{H}$ and $\tilde{\mathbf{H}}$ ) for its two augmented graphs through graph augmentations [32] and encoders [11]. The description of these processes can be found in the appendix. + +Once the node features are obtained, InfoNCE [22] loss, is calculated as a guide for its update. For node $v$ , the positive sample of the anchor node $(\mathbf{h}_v)$ is the same node $(\tilde{\mathbf{h}}_v)$ in another view, while the negative samples are other nodes in both views. This contrastive loss (denoted as $\ell_{gc}$ ) can be formulated as + +$$ +\begin{array}{l} \ell_ {g c} \left(\mathbf {h} _ {v}, \tilde {\mathbf {h}} _ {v}\right) = - l o g \frac {\mathrm {p o} _ {v}}{\mathrm {p o} _ {v} + \mathrm {n e} _ {v}}, \\ \mathrm {p o} _ {v} = \mathrm {e} ^ {\frac {\theta (\mathbf {h} _ {v} , \tilde {\mathbf {h}} _ {v})}{\tau}}, \mathrm {n e} _ {v} = \sum_ {t \in V \backslash v} \mathrm {e} ^ {\frac {\theta (\mathbf {h} _ {v} , \mathbf {h} _ {t})}{\tau}} + \mathrm {e} ^ {\frac {\theta (\mathbf {h} _ {v} , \tilde {\mathbf {h}} _ {t})}{\tau}}, \tag {1} \\ \end{array} +$$ + +where $\theta (\mathbf{h}_v,\tilde{\mathbf{h}}_v) = s(f(\mathbf{h}_v),f(\tilde{\mathbf{h}}_v))$ , $s(,)$ terms the cosine similarity, and $f(\cdot)$ denotes the projection head [2], which is a two-layer multilayer perceptron (MLP). $\tau$ represents a scalar, which is positively correlated with the uniformity of the feature distribution. The overall contrastive loss is set as the average over all nodes based on the mutually symmetric form of Equation 1. This can be formulated as + +$$ +\mathcal {L} _ {\text {g r a c e}} = \frac {1}{2 | V |} \sum_ {v \in V} \left(\ell_ {g c} \left(\mathbf {h} _ {v}, \tilde {\mathbf {h}} _ {v}\right) + \ell_ {g c} \left(\tilde {\mathbf {h}} _ {v}, \mathbf {h} _ {v}\right)\right). \tag {2} +$$ + +In addition to the above pairwise positive sampling, several local positive sampling techniques have been presented + +![](images/76115030afeef6a5f7c6144389fce79fe824820d2d4cdbc26983a1375c6e7e31.jpg) +(a) Optimal positive sample set for GCLs and the corresponding matrix. +(b) The proposed HEATS Framework. +Figure 1. Overview of the proposed GCL framework, named HEATS, and its design motivation. (a) An intuitive example of the optimal positive sample matrix for GCLs, where the colors of nodes stand for classes. (b) The proposed HEATS framework with adaptive positive sampling. The optimal positive sample set should consist of all nodes from the same class. Accordingly, the optimal positive sample matrix should be block-diagonal, where each block is fully connected and weights within it are equal. + +[12, 34]. They propose to add the specified neighbor nodes into the positive sample sets, leveraging the homophily assumption [1, 16]. + +# 3. Methodology + +In this section, following the introduction of design motivation, a graph contrastive learning (GCL) framework, named grapH contrastive Adaptive positive Sampling (HEATS), is devised. Subsequently, theoretical analysis of its efficacy are presented. + +# 3.1. Motivation + +As previously discussed in the introduction, existing positive sampling strategies utilized in GCLs tend to be incomplete and blind, leading to a loss of discriminative power of node representations. + +Definition 1. Block Diagonal Property (BDP) [9]. The given matrix $\mathbf{Z} \in \mathbb{R}^{n \times n}$ satisfies block diagonal property if it can be decomposed into submatrices as follows: + +$$ +\mathbf {Z} = \left[ \begin{array}{c c c c} \mathbf {Z} _ {1} & 0 & \dots & 0 \\ 0 & \mathbf {Z} _ {2} & \dots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \dots & \mathbf {Z} _ {k} \end{array} \right], +$$ + +where $\mathbf{Z}_i\in \mathbb{R}^{n_i\times n_i}$ stands for the $i$ -th square submatrix (block), and $\sum_{i = 0}^{k}n_{i} = n$ + +An intuitive and optimal solution is provide target nodes with positive sample sets that consists of all nodes from the same class (i.e., optimal positive sample set), as depicted in Figure 1(a). It is evident that the relationships among these positive samples can be succinctly expressed as a block diagonal matrix, where each block describes the relationships among a class of nodes. Additionally, this matrix should exhibit the following properties: each block is full connected + +and weights within it are equal. Therefore, the optimal positive sample matrix should be formulated as: + +$$ +\mathbf {Z} = \left[ \begin{array}{c c c c} \frac {1}{n _ {1}} \mathbf {1} _ {n _ {1}} \mathbf {1} _ {n _ {1}} ^ {\top} & 0 & \dots & 0 \\ 0 & \frac {1}{n _ {2}} \mathbf {1} _ {n _ {2}} \mathbf {1} _ {n _ {2}} ^ {\top} & \dots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \dots & \frac {1}{n _ {k}} \mathbf {1} _ {n _ {k}} \mathbf {1} _ {n _ {k}} ^ {\top} \end{array} \right], \tag {3} +$$ + +where $\mathbf{1}_{n_i} \in \mathbb{R}^{n_i}$ denotes an all-one column vector. + +# 3.2. HEATS framework + +Based on the above analysis, this paper devises a novel GCL framework HEATS, which directs the positive sampling by employing constructed block diagonal affinity matrices. As overviewed in Figure 1(b), HEATS consists of two key components: (1) Matrix Construction and (2) Contrastive Optimization. These two components engage in an alternating refinement process, gradually converging to the optimum. + +# 3.2.1 Matrix Construction + +This component aims to construct affinity matrices, which possess inter-class sparsity and intra-class connectivity (i.e., obey BDP), to guide the selection of positive samples. Particularly, it adopts a self-expressive learning objective, commonly utilized in subspace clustering [13], to acquire such affinity matrices. This objective posits that each sample can be represented by linearly combining all other samples in the same subspace (i.e., block). This objective can be formulated as the following equation: + +$$ +\underset {\mathbf {Z}, \mathbf {E}} {\operatorname {a r g m i n}} \mathcal {O} (\mathbf {Z}) + \lambda \mathcal {T} (\mathbf {E}), \quad \text {s . t .} \mathbf {X} = \mathbf {Z} \mathbf {X} + \mathbf {E}, \tag {4} +$$ + +where $\mathbf{Z}$ denotes the affinity matrix, which depicts the combination coefficients, and $\mathbf{E}$ stands for the noise. Moreover, $\mathcal{O}$ and $\mathcal{T}$ term the constraint on affinity matrices and noise matrices, respectively. $\lambda$ is a hyperparameter that balances the two terms of the objective function. + +To obtain a high-quality affinity matrix, as expressed in Equation 3, several constraints should be incorporated into the learning objective: idempotent and $k$ -block. Firstly, the affinity matrix $\mathbf{Z}$ in Equation 3 is idempotent [27] because of $\mathbf{Z}_i = \mathbf{Z}_i \times \mathbf{Z}_i = \mathbf{Z}_i^2$ . Secondly, the number of blocks in the affinity matrices should be controlled as $k$ . Furthermore, the affinity matrices also should be normalized, symmetric, and non-negative. To achieve these properties and enhance effectiveness, the self-expressive learning objective can be reformulated as: + +$$ +\begin{array}{l} \operatorname *{argmin}_{\substack{\mathbf{Z},\mathbf{S}}}\| \mathbf{Z} - \mathbf{S}\|_{F}^{2} + \gamma \| \mathbf{S}\|_{id} + \lambda \| \mathbf{E}\|_{2,1}, \\ \mathrm {s . t .} \mathbf {H} = \mathbf {Z H} + \mathbf {E}, \tag {5} \\ \end{array} +$$ + +$$ +\mathbf {S} \mathbf {1} _ {n} = \mathbf {1} _ {n}, \mathbf {S} = \mathbf {S} ^ {\top}, \mathbf {S} \geq \mathbf {0}, \operatorname {T r} (\mathbf {S}) = k, +$$ + +where $\mathbf{S}$ denotes an intermediate-term to mitigate the loss of representation capability. And, $\| \mathbf{S}\|_{id} = \| \mathbf{S} - \mathbf{S}^2\| _F^2$ terms the idempotent constraint and $\gamma$ is a scalar that controls the impacts of this term. The terms $\mathbf{S1}_n = \mathbf{1}_n$ $\mathbf{S} = \mathbf{S}^{\top}$ ,and $\mathbf{S}\geq 0$ stand for the column-normalized, symmetric, and nonnegative constraints, respectively. Based on the above constraints, the term $\mathrm{Tr}(\mathbf{S}) = k$ is introduced to make the matrix have $k$ blocks. $\| \mathbf{E}\|_{2,1} = \sum_{j = 1}^{n}\sqrt{\sum_{i = 1}^{n}([\mathbf{E}]_{ij})^2}$ is the $\ell_{2,1}$ -norm of noise, which characterizes sample-specific outliers. Finally, the affinity matrix, a guide of positive sampling, can be obtained by optimizing Equation 5. Please refer to the appendix for optimization details. Once the affinity matrix M (i.e., $\mathbf{Z}$ or S) is obtained, it is necessary to sparsify it to enhance training efficiency. The sparsification process can be formulated as: + +$$ +m _ {v, u} = \left\{ \begin{array}{l l} 0, & m _ {v, u} < \beta , \\ m _ {v, u}, & \text {o t h e r w i s e}. \end{array} \right. +$$ + +where $\beta$ denotes the threshold parameter, which is utilized to indicate filter out the values below it. + +Theorem 1. The affinity matrix $\mathbf{M}$ , which is generated by optimizing Equation (5), satisfies the BDP in Definition 1. + +Theorem 1 theoretically demonstrates that the proposed matrix construction strategy aligns with the motivation. For the proof, please refer to the appendix. + +# 3.2.2 Contrastive Optimization + +This subsection delineates the methodology for formulating the contrastive loss leveraging the constructed affinity matrix $\mathbf{M}$ . Firstly, it is utilized to direct the sampling process. By identifying non-zero values in the vector $\mathbf{m}_v$ , nodes that are semantically associated with node $v$ can be marked out. These nodes collectively constitute the positive sample set of node $v$ , denoted as $\mathcal{P}_v^M = \{u|m_{v,u} > 0\}$ . Following the baselines [2, 32], the negative sample set is composed of + +the remaining nodes, that is $\mathcal{N}_v^M = V\setminus \{\mathcal{P}_v^M\cup v\}$ . Secondly, the matrix $\mathbf{M}$ is also interpreted as a measure of the relationships, and the values within it are treated as weights. + +In implementation, HEATS follows the baseline GRACE [32], which is mentioned in Section 2.2. Therefore, the contrastive loss of HEATS with respect to anchor node $\mathbf{h}_v$ can be reformulated from Equation 1 as + +$$ +\begin{array}{l} \ell_ {h t} (\mathbf {h} _ {v}, \tilde {\mathbf {h}} _ {v}) = - l o g \frac {\mathrm {p o} _ {v}}{\mathrm {p o} _ {v} + \mathrm {n e} _ {v}}, \\ \mathrm {p o} _ {v} = \mathrm {e} ^ {\frac {\theta \left(\mathbf {h} _ {v} , \tilde {\mathbf {h}} _ {v}\right)}{\tau}} + \sum_ {u \in \mathcal {P} _ {v} ^ {M}} m _ {v, u} \cdot \mathrm {e} ^ {\frac {\theta \left(\mathbf {h} _ {v} , \mathbf {h} _ {u}\right)}{\tau}}, \tag {6} \\ \mathrm {n e} _ {v} = \sum_ {t \in \mathcal {N} _ {v} ^ {M}} \mathrm {e} ^ {\frac {\theta (\mathbf {h} _ {v} , \bar {\mathbf {h}} _ {t})}{\tau}} + \sum_ {t \in \mathcal {N} _ {v} ^ {M}} \mathrm {e} ^ {\frac {\theta (\mathbf {h} _ {v} , \bar {\mathbf {h}} _ {t})}{\tau}}, \\ \end{array} +$$ + +The overall contrastive loss of HEATS, denoted as $\mathcal{L}_{\text{heats}}$ + +$$ +\mathcal {L} _ {\text {h e a t s}} = \frac {1}{2 | V |} \sum_ {v \in V} \left(\ell_ {h t} \left(\mathbf {h} _ {v}, \tilde {\mathbf {h}} _ {v}\right) + \ell_ {h t} \left(\tilde {\mathbf {h}} _ {v}, \mathbf {h} _ {v}\right)\right). \tag {7} +$$ + +In comparison to the existing GCLs [12, 20, 34], the proposed HEATS exhibits several characteristics. (1) Generality. Since the positive sample matrices are constructed globally, that is, independent of the underlying graph topology, HEATS can be reasonably extended to non-graph domains such as computer vision (CV). (2) Robustness. Due to the fact that the positive sample matrix is obtained by optimizing a robust self-expressive learning objective, as formulated in Equation (5), the robustness is strengthened through positive sampling on these matrices. + +Theorem 2. The contrastive loss of HEATS $(\mathcal{L}_{\text {heats }})$ is a more stringent estimate of mutual information (MI) between node attributes and embeddings than that of the local baseline HomoGCL [12], that is, + +$$ +\mathcal {L} _ {\text {h o m o g c l}} \leq \mathcal {L} _ {\text {h e a t s}} \leq I (\mathbf {X}; \mathbf {H}, \tilde {\mathbf {H}}), \tag {8} +$$ + +where $\mathbf{X}$ denotes the node attributes, and $\mathbf{H}$ and $\tilde{\mathbf{H}}$ represent the node embeddings in two augmented views. + +Theorem 2 demonstrates that the proposed HEATS provides a refined approximation to the TRUE mutual information, enabling it to promote model robustness and stability. + +# 3.2.3 Alternating Update + +To enhance the adaptivity of HEATS, the two fundamental components, matrix construction and contrastive optimization, engage in iterative updates in an alternating fashion, as visually depicted in Figure 1(b). The former is tasked with solving Equation 5 to construct positive sample matrices in the feature space. The latter focuses on representation (feature) learning by optimizing the contrastive loss using these + +Table 1. Statistics of twelve graph datasets. Homophily is the edge homophily in [17]. + +
DatasetNodesEdgesFeaturesClassesHomophily
Cora2,7085,2781,43370.81
CiteSeer3,3274,5523,70360.74
PubMed19,71744,32450030.80
Wiki-CS11,701216,123300100.65
Computers13,752245,861767100.78
Photo7,650238,16374580.83
Cornell1832951,70350.13
Texas1833091,70350.11
Wisconsin2514991,70350.20
Chameleon2,27736,1012,32550.23
Squirrel5,201217,0732,08950.22
Actor7,60033,54493150.22
+ +positive sample matrices, which is formulated as Equation 6. These two components are updated alternately. + +The alternating update procedure offers several benefits to GCLs. (1) Adaptive positive samples. Note that the positive sample matrices are constructed in the feature space. Hence, this procedure can continually provide adaptive positive samples for the subsequent contrastive optimization, adapting to feature changes. (2) Discriminative node representations. GCLs have the denoising ability, to some extent, which is attributed to the fact that it obtains the invariant information [28]. As a result, the discriminative feature space can be provided for the construction of positive sample matrices, eventually resulting in more discriminative features through contrastive learning. Furthermore, benefits also involve the risk reduction of each component falling into the local optimum and accelerating the convergence speed. + +# 4. Experiments + +In this section, the proposed framework HEATS is validated by empirically evaluating its performances on node and image classification tasks in the unsupervised setting. Next, an in-depth understanding of the efficacy of this framework is provided through several experiment analyses. + +# 4.1. Experiment Setup + +Datasets. To illustrate the effectiveness and generality of the proposed HEATS, twelve non-Euclidean graph datasets, and three 2-D spatial image datasets are adopted in the experiments. According to graph homophily [17], these graph datasets can be divided into two categories: six homophilic graphs, including Cora, CiteSeer, PubMed, Wiki-CS, Computers, and Photo, and six heterophilic graphs, containing Cornell, Texas, Wisconsin, Chameleon, Squirrel, and Actor. Moreover, the image datasets are CIFAR-10, STL-10, and CIFAR-100. The statistics of the graph datasets are presented in Table 1. Due to space limitations, the introduction of all datasets is presented in the appendix. + +Splitting. To ensure experimental fairness, the dataset split + +ting follows commonly employed schemes. Specifically, for three homophilic graphs (Cora, CiteSeer, and PubMed) and all six heterophilic graphs, the training, validation, and testing sets constitute $48\%$ , $32\%$ , and $20\%$ of the data, respectively. For the remaining homophilic graphs (Wiki-CS, Computers, and Photo), the proportions amount to $10\%$ , $10\%$ and $80\%$ . Besides, for the CIFAR-10 dataset, 5000 and 1000 images per class are selected for training and testing, respectively. For the STL-10 dataset, 10500 and 800 images per class are assigned to the training and testing sets, respectively. For the CIFAR-100 dataset, 500 and 100 images per class are served in training and testing, respectively. + +Baselines. These experiments involve two types of downstream tasks: node classification for graphs and image classification. For the node classification, the baselines include two types: semi-supervised graph neural networks (GCN [11], GAT [24] and JKNet [29]), and unsupervised graph learning models (Deepwalk [18], Node2vec [4], GAE [10], VGAE [10], DGI [25], MVGRL [5], GRACE [32], GCA [33], BGRL [21], SELENE [31], and HomoGCL [12]). For the image classification, the baseline is CL model SimCLR [2], which is implemented with two backbones (ResNet-18 and ResNet-50) [7]. Please refer to the appendix for an introduction to related works. + +Configurations. In the node classification, the proposed HEATS framework is implemented with the configurations following GRACE [32]. To be specific, each branch corresponds to an augmented graph, which is initially obtained through the edge deletion and attribute masking [3], with the random ratio among $\{0.2, 0.4, 0.6, 0.8\}$ . Furthermore, the node features are obtained through a two-layer GCN [11] encoding and a two-layer MLP [19] projecting, where both dimensions are 64. The node features are trained by minimizing the contrastive loss, where the temperature coefficient is taken from $\{0.2, 0.4, 0.6, 0.8, 1\}$ . In this process, an Adam optimizer with the learning rate of 0.01 and the weight decay rate among $\{0, 5 \times 10^{-5}\}$ is to be employed for optimization and regularization, respectively. Minibatch training is adopted for larger node numbers, such as PubMed. For the unique parameters of HEATS, namely $\gamma$ and $\lambda$ , both are selected from $\{1 \times 10^{-3}, 1 \times 10^{-2}, 1 \times 10^{-1}, 1, 10\}$ . Furthermore, the number of blocks $k$ is selected from a set with no more than the number of classes, and its impact is analyzed in Section 4.3.2. All experiments are conducted in PyTorch on a single RTX4090 24GB GPU. + +Evaluation Protocol. For both node and image classification tasks, the experimental evaluations adopt the standard linear evaluation protocol [25]. Concretely, all models undergo initial unsupervised pre-training, followed by utilizing the obtained embeddings to train linear classifiers and subsequently presenting the test accuracy results. Throughout the evaluation phases, the Adam optimizer with a learning rate of 0.01 is utilized. The experiment results are re + +Table 2. Node classification accuracy (mean ± std) is reported for six homophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information. + +
ModelTraining DataCoraCiteSeerPubMedWiki-CSComputersPhoto
GCNA,X,Y85.77 ± 0.2573.68 ± 0.3188.13 ± 0.2876.89 ± 0.3786.34 ± 0.4892.35 ± 0.25
GATA,X,Y86.37 ± 0.3074.32 ± 0.2787.62 ± 0.2677.42 ± 0.1987.06 ± 0.3592.64 ± 0.42
JKNetA,X,Y85.93 ± 1.3574.37 ± 1.5387.68 ± 0.3079.52 ± 0.2185.28 ± 0.7292.68 ± 0.13
DeepWalkA73.96 ± 0.1261.91 ± 0.4274.79 ± 0.9874.35 ± 0.0685.68 ± 0.0689.44 ± 0.11
Node2VecA75.87 ± 0.2262.54 ± 0.1376.49 ± 0.3271.79 ± 0.0584.39 ± 0.0889.67 ± 0.12
GAEA,X76.83 ± 1.2265.43 ± 1.1376.52 ± 0.3370.15 ± 0.0185.27 ± 0.1991.62 ± 0.13
VGAEA,X79.36 ± 0.8369.18 ± 0.2779.17 ± 0.4476.63 ± 0.1986.37 ± 0.2192.20 ± 0.11
DGIA,X85.90 ± 0.5772.57 ± 0.2383.52 ± 1.2475.73 ± 0.1384.09 ± 0.3991.49 ± 0.25
MVGRLA,X86.77 ± 0.3373.71 ± 0.4884.63 ± 0.7377.97 ± 0.1887.09 ± 0.2792.01 ± 0.13
GRACEA,X84.79 ± 0.6472.94 ± 0.7284.51 ± 0.6879.16 ± 0.3687.21 ± 0.4492.65 ± 0.32
GCAA,X85.16 ± 0.5172.73 ± 0.4585.22 ± 0.7379.35 ± 0.1287.84 ± 0.2792.78 ± 0.17
BGRLA,X85.37 ± 0.7473.45 ± 0.8384.61 ± 0.3278.74 ± 0.2288.92 ± 0.3393.24 ± 0.29
SELENEA,X85.28 ± 0.8373.48 ± 0.6584.70 ± 0.5278.31 ± 0.6388.13 ± 0.5192.93 ± 0.34
HomoGCLA,X85.02 ± 0.6873.67 ± 0.7882.33 ± 0.4977.47 ± 0.4587.84 ± 0.2893.59 ± 0.27
HEATSA,X87.10 ± 1.4075.26 ± 1.2585.41 ± 0.8279.99 ± 1.5989.29 ± 1.1294.65 ± 1.71
+ +ported as an average of over ten random runs. + +# 4.2. Results on benchmark datasets + +Results on Homophilic Graphs. Table 2 presents the experimental results of node classification on six homophilic graphs. It is evident that compared to all unsupervised baseline models, the proposed HEATS achieves the best performance across all datasets. It even surpasses all supervised comparison models on datasets other than PubMed. To be specific, on the CiteSeer dataset, HEATS outperforms the second-best unsupervised model (i.e., MVGRL) by $1.55\%$ and the baseline model (i.e., GRACE) by $2.32\%$ in classification accuracy. This highlights the effectiveness of HEATS in exploring positive samples by modeling high-order relationships. + +Results on Homophilic Graphs. A similar phenomenon can be observed from the experiment results on heterophilic graphs, as illustrated in Table 3. To be specific, compared to the baseline model (i.e., GRACE), HEATS achieves performance improvements across all datasets. Particularly noteworthy are improvements in accuracy by $12.11\%$ , $7.29\%$ , and $15.88\%$ on the Cornell, Texas, and Wisconsin datasets, respectively. This emphasizes the contribution of the proposed positive sampling based on matrix construction in enriching the universality of the baselines. Moreover, HEATS outperforms other unsupervised baselines on three datasets, except the Chameleon, Squirrel, and Actor datasets, showcasing its superior performance. + +Visualization. This experiment aims to intuitively demonstrate the representation ability of the proposed HEATS. For this purpose, the t-SNE [23] method is exploited to perform feature reduction and visualization of the trained representations. Figure 2 exhibits the experiment results (scatter plots) on three benchmark datasets (i.e., Cora, CiteSeer, and + +![](images/5852a8bcde22a7d8927cedd6d2ec2cdaf2eea9f7d2e0505fd7364dc453c98cfa.jpg) +Figure 2. t-SNE visualization of node embeddings from HEATS, BGRL, and GRACE on Cora, CiteSeer, and Photo datasets. + +Photo), where colors stand for the classes of nodes. It can be observed that compared to all the comparison models (i.e., GRACE and BGRL), the proposed HEATS framework is enabled to produce the most informative representations. As exemplified by the Cora and CiteSeer dataset, compared to the baseline model (i.e., GRACE), HEATS achieves more compact clusters in node embeddings. Specifically, the embeddings of the same class are closer, while the embeddings of different classes exhibit more significant differences. The experiment results emphasize the effectiveness of HEATS in enhancing representation ability. + +Results on Image Datasets. As previously mentioned, the proposed HEATS designs a positive sampling strategy from a global perspective, which effectively mitigates graph structural constraints. In essence, this improves its generality to various domains. To substantiate this claim, the experiment compares a contrastive learning (CL) model tailored for images (i.e., SimCLR) with the proposed variants. + +Table 3. Node classification accuracy (mean ± std) is reported for six heterophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information. + +
ModelTraining DataCornellTexasWisconsinChameleonSquirrelActor
GCNA,X,Y55.14 ± 7.5755.68 ± 9.6158.42 ± 5.1059.82 ± 2.5836.89 ± 1.3430.64 ± 1.49
GATA,X,Y58.92 ± 3.3258.38 ± 4.4555.29 ± 8.7160.26 ± 2.5040.72 ± 1.5527.44 ± 0.89
JKNetA,X,Y56.49 ± 3.2265.35 ± 4.8651.37 ± 3.2160.31 ± 2.7644.24 ± 2.1136.47 ± 0.51
DeepWalkA39.18 ± 5.5746.49 ± 6.4933.53 ± 4.9247.74 ± 2.0532.93 ± 1.5822.78 ± 0.64
Node2VecA42.94 ± 7.4641.92 ± 7.7637.45 ± 7.0941.93 ± 3.2922.84 ± 0.7228.28 ± 1.27
GAEA,X58.85 ± 3.2158.64 ± 4.5352.55 ± 3.8033.84 ± 2.7728.03 ± 1.6128.03 ± 1.18
VGAEA,X59.19 ± 4.0959.20 ± 4.2656.67 ± 5.5135.22 ± 2.7129.48 ± 1.4826.99 ± 1.56
DGIA,X63.35 ± 4.6160.59 ± 7.5655.41 ± 5.9639.95 ± 1.7531.80 ± 0.7729.82 ± 0.69
MVGRLA,X64.30 ± 5.4362.38 ± 5.6162.37 ± 4.3251.07 ± 2.6835.47 ± 1.2930.02 ± 0.70
GRACEA,X54.86 ± 6.9557.57 ± 5.6850.00 ± 5.8348.05 ± 1.8131.33 ± 1.2229.01 ± 0.78
GCAA,X55.41 ± 4.5659.46 ± 6.1650.78 ± 4.0649.80 ± 1.8135.50 ± 0.9129.65 ± 1.47
BGRLA,X57.30 ± 5.5159.19 ± 5.8552.35 ± 4.1247.46 ± 2.7432.64 ± 0.7829.86 ± 0.75
SELENEA,X59.94 ± 5.1261.87 ± 4.2561.87 ± 4.7942.13 ± 2.1533.28 ± 0.8230.12 ± 0.76
HomoGCLA,X48.64 ± 2.5954.05 ± 2.3239.21 ± 5.7548.68 ± 1.1638.71 ± 0.8528.81 ± 0.78
HEATSA,X66.97 ± 6.7464.86 ± 4.6865.88 ± 5.5649.96 ± 1.8636.24 ± 1.1129.91 ± 1.16
+ +Table 4. Image classification accuracy (mean) of SimCLR and its HEATS-based variants. $\uparrow$ dentoes the performance improvement. + +
BackboneMethodCIFAR-10STL-10CIFAR-100
ResNet-18SimCLR78.5978.4449.60
+HEATS79.1978.8352.62
↑+0.60+0.39+3.02
ResNet-50SimCLR75.0376.7349.31
+HEATS77.5877.8053.81
↑+2.55+1.07+4.50
+ +The configurations of these variants align with that of the baselines, including standard parameters such as learning rate and training epochs. Please refer to the appendix for experiment setups. Table 4 exhibits the image classification results after 30 epochs using ResNet-18 and ResNet-50 backbones. It can be seen that compared to the baseline (i.e., SimCLR), the proposed HEATS framework consistently improves performance across all three datasets. To be specific, HEATS showcases superior performance compared to the two baselines utilizing ResNet-18 and ResNet-50 backbones on the CIFAR-100 dataset by $3.02\%$ and $4.5\%$ , respectively, accentuating the generality to image-centric tasks. More importantly, it provides valuable insights for applying HEATS in a wide range of domains. + +# 4.3. Further Analysis + +# 4.3.1 Effectiveness Justify + +The experiment intends to justify the effectiveness of the two proposed approaches to enhance positive sampling, i.e., matrix construction and alternating updates, to pursue the block-diagonal matrices. Therefore, three matrices, which include the adjacent matrix, the matrix computed using the initial features, and the matrix computed using the features + +![](images/bc656502431c4a5d12bbed467d40bc7ebe279067015b3b9d29d179a8eca25f04.jpg) +Figure 3. Visualization of the adjacent matrices, the matrices computed using the initial features (Matrix 1), and the matrices computed using the learned features after 200 iterations (Matrix 2) on the Cora and CiteSeer datasets. The nodes are sorted by class. The weights between nodes are not considered here. + +after 200 iterations, are visualized in Figure 3 to provide an intuitive understanding. + +Based on the observations in Figure 3, three significant conclusions can be drawn. (1) The constructed matrices are approximately block diagonal. In particular, on all datasets + +![](images/665bad5c92f1db3f2841252b392eb544083555d625e5df857f538bd445aa98ab.jpg) +Figure 4. Impact of the number of blocks $k$ . + +![](images/0348dee2a57cacc8dc7b2208de43e49ef0d310cd1d8cbd7ad69c2dd0e609084f.jpg) +(a) Topology attacks +Figure 5. Results of GCLs under graph attacks + +![](images/dbba3ddee58e5c2a3e75a7ba7a25ef1786d83255a1afc4f658b24077077e047c.jpg) +(b) Attribute attacks + +(i.e., Cora and CiteSeer), the edges between nodes from the same class outnumber those between nodes from different classes. This indicates that the proposed HEATS framework can serve as an effective strategy to obtain more TRUE positive samples. (2) Compared to the adjacent matrices, the constructed matrices exhibit denser diagonal blocks. This implies that the proposed matrix construction approach is feasible in contrastive learning by offering more TRUE positive samples beyond graph topology. (3) Compared to the matrices constructed in the initial feature space, those constructed in the updated feature space exhibit a more distinct block-diagonal structure, e.g., results of the Cora dataset. This emphasizes the effectiveness of the proposed alternating update approach. In summary, the experiment confirms the efficacy of the two proposed approaches in constructing block-diagonal matrices for positive sample collection. + +# 4.3.2 Hyperparameter Study + +The experiment aims to provide a guide on choosing the parameter $k$ , which represents the number of blocks, by investigating its impact on the performance. This parameter is selected from 2 to the number of classes, as setting it to 1 seems ineffective. Figure 4 exhibits the experiment results on three datasets (i.e., Cora, CiteSeer, and Cornell). Incorporating the results in Table 2, it can be observed that HEATS consistently performs well within a specific parameter range. For example, on the Cora dataset, when the parameter selects from the set $\{4,5,6\}$ , HEATS consistently outperforms the baseline model (i.e., GRACE) by $2.21\%$ , $2.31\%$ , and $2.25\%$ , respectively. This indicates HEATS insensitivity to changes in this parameter. Additionally, with a small value (e.g., 2), HEATS performs better than the baseline GRACE, which offers guidance to select the parameter. + +# 4.3.3 Robustness Analysis + +This experiment is intended to evaluate the robustness of the proposed HEATS framework to noise. The topology attack (adding edges) and the attribute attack (flipping attributes) are applied to create noisy data on the Cora dataset. Figure 5 shows the performance variation of the GCL, HEATS, and the baseline GRACE under topology and attribute attacks. + +It can be seen from Figure 5a that GRACE is somewhat resistant to robust against topology attacks, but the performance degrades significantly with higher attack levels. For example, the accuracy decreases by about $2\%$ compared to the attack-free accuracy at an edge deletion rate of 0.1. This is attributed to their centers on capturing the invariant information from multiple augmented graphs, to some extent, resulting in them being insensitive to topology changes. However, the accuracy decreases $5\%$ when the edge deletion rate increases to 0.3. In contrast, HEAT exhibits greater robustness to this attack. Specifically, it achieves about $4.5\%$ increase in accuracy compared to the baseline GRACE when the edges deletion reaches an extreme $0.2\%$ . This is mainly due to HEATS incorporating noise simulation and alternating update approach to extract high-order positive samples, thereby enhancing the robustness. Furthermore, as shown in Figure 5b, HEATS consistently outperforms the baseline GRACE, showcasing its denoising ability. + +# 5. Conclusions + +In this paper, a novel graph contrastive learning framework, named HEATS, is proposed to address two key limitations of the existing positive sampling techniques: incomplete local sampling and blind sampling. Drawing inspiration from the observation that the affinity matrix associated with the optimal positive sample set is block-diagonal and idempotent, the idea of constructing such matrices to guide positive sampling is proposed. To enhance the adaptability and robustness of HEATS, an approach that alternately updates the positive sampling and contrastive optimization is proposed. Extensive experiments reveal the efficacy and robustness of HEATS. Future research directions include improving the scalability of the framework to accommodate large datasets and improving its generality to multimodal data. + +# 6. Acknowledgments + +This work was supported in part by the National Natural Science Foundation of China (No. 62376088, 61972442, 62272020, 62102413, 62132006, U2001202, and U22B2036), in part by the National Science Fund for Distinguished Young Scholars (No. 62025602), in part by the National Social Science Fund of China under Grant 22VMG037, in part by the Natural Science Foundation of Hebei Province of China under Grant F2020202040, and in part by the Tencent Foundation and XPLORER PRIZE. + +# References + +[1] Kristen M Altenburger and Johan Ugander. Monophily in social networks introduces similarity among friends-of-friends. Nature human behaviour, 2(4):284-290, 2018. 1, 3 +[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey E. Hinton. A simple framework for contrastive learning of visual representations. In ICML, pages 1597-1607, 2020. 2, 4, 5 +[3] Kaize Ding, Zhe Xu, Hanghang Tong, and Huan Liu. Data augmentation for deep graph learning: A survey. 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}, + { + "bbox": [ + 143, + 324, + 191, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 324, + 191, + 337 + ], + "spans": [ + { + "bbox": [ + 143, + 324, + 191, + 337 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 350, + 289, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 289, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 289, + 613 + ], + "type": "text", + "content": "Graph Contrastive Learning (GCL), a Self-Supervised Learning (SSL) architecture tailored for graphs, has shown notable potential for mitigating label scarcity. Its core idea is to amplify feature similarities between the positive sample pairs and reduce them between the negative sample pairs. Unfortunately, most existing GCLs consistently present suboptimal performances on both homophilic and heterophilic graphs. This is primarily attributed to two limitations of positive sampling, that is, incomplete local sampling and blind sampling. To address these limitations, this paper introduces a novel GCL framework with an adaptive positive sampling module, named graphH contrastiveE Adaptive positive Samples (HEATS). Motivated by the observation that the affinity matrix corresponding to optimal positive sample sets has a block-diagonal structure with equal weights within each block, a self-expressive learning objective incorporating the block and idempotent constraint is presented. This learning objective and the contrastive learning objective are iteratively optimized to improve the adaptability and robustness of HEATS. 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It generates supervision signals for model training by extracting" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 325, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 325, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 325, + 545, + 445 + ], + "type": "text", + "content": "latent data patterns from the unannotated data [8]. As a notable branch of SSL, Contrastive Learning (CL) emphasizes producing the supervision signals using the established rule, i.e., bringing similar samples (positive samples) closer and pushing dissimilar samples (negative samples) apart. Based on this rule, Graph Contrastive Learning (GCL) extends the applied range to non-Euclidean graphs by employing techniques like graph augmentations and graph encoders. It has achieved remarkable performance on various downstream tasks, such as node classification [15, 32]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 448, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 615 + ], + "type": "text", + "content": "To generate the discriminative node representations from GCLs, the positive sample set of each node should contain all nodes from the same class (i.e., TRUE positive samples), while the negative ones should consist of nodes from different classes (i.e., TRUE negative samples). Subsequently, to extend the TRUE positive sample sets, certain research endeavors in GCLs focus on identifying semantically relevant samples within node neighborhoods [12, 20, 26, 30, 34], leveraging the homophily assumption [1, 16]. Despite their consistent performance improvements on the homophilic graphs, where adjacent nodes typically belong to the same class, the improvements are limited. More critically, their robustness to the heterophilic graphs, where adjacent nodes tend to be from different classes, is severely constrained." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "These drawbacks are attributed to two limitations of positive sampling. (1) Incomplete local sampling. Most graphs are sparse, and nodes of the same class are typically situated beyond each other's neighborhoods. Therefore, the positive sample sets for most GCLs tend to be incomplete, which could lead to the absence of shared information between the same class. (2) Blind sampling. In dealing with blindness caused by a lack of supervised guidance, the endeavors of" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "type": "text", + "content": "*Chuan Wang and Liang Yang are corresponding authors." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23179" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "GCLs to establish the criterion for positive sampling beyond the neighborhoods are insufficient. Concretely, most GCLs always center on exploring semantic relevance in neighborhoods utilizing various homophily measures [6, 12, 34]. In fact, these criteria do not apply beyond neighborhoods because of their local property. Due to the incompleteness and blindness of positive sampling, GCLs can not obtain all TRUE positive sample pairs. This hampers the representation ability of GCLs, resulting in their poor performances on both homophilic and heterophilic graphs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 526 + ], + "type": "text", + "content": "To address these deficiencies, this paper proposes a novel GCL framework, named grapH contrastive Adaptive positive Sampling (HEATS). The idea is to devise a criterion to guide global positive sampling. Toward this end, the characteristic of an affinity matrix (termed positive sample matrix) associated with the optimal positive sample set is first investigated. The conclusion drawn is that the optimal positive sample matrix obeys the block diagonal property (BDP) and is idempotent, as depicted in Figure 1(a). To be specific, this matrix can be decomposed into a batch of diagonal submatrices (blocks), where each block characterizes semantic relevance among nodes from the same class. Moreover, each block is fully connected and the weights within it are equal. Motivated by this, a novel positive sampling module is presented, focusing on constructing such block-diagonal and idempotent affinity matrices. To capture long-range dependencies, positive sample matrices are generated by optimizing a self-expressive objective incorporating block and idempotent constraints, leveraging the features of all nodes within batches. In light of the intrinsic denoising capability of GCLs [14, 35], an alternating update mechanism of matrix construction and contrastive optimization is introduced to obtain reciprocal benefits, thereby improving the robustness and adaptability of HEATS. In theory, HEATS has a stricter lower bound on the mutual information (MI) between node attributes and node embeddings compared to the baselines that select positive samples from neighborhoods, which guarantees its effectiveness and robustness." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 527, + 279, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 527, + 279, + 538 + ], + "spans": [ + { + "bbox": [ + 59, + 527, + 279, + 538 + ], + "type": "text", + "content": "The contributions of this paper are summarized below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 539, + 287, + 647 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 539, + 287, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 287, + 562 + ], + "type": "text", + "content": "- We investigate the characteristics of an affinity matrix associated with the optimal positive sample set." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 563, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 287, + 586 + ], + "type": "text", + "content": "- We present a novel graph contrastive learning framework HEATS with an adaptive positive sampling module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 586, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 287, + 622 + ], + "type": "text", + "content": "- We theoretically analyze the effectiveness and robustness of the proposed HEATS from a Mutual Information Maximization perspective." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 623, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 287, + 647 + ], + "type": "text", + "content": "- We conduct extensive evaluations to demonstrate the superior performance and generality of HEATS." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "type": "text", + "content": "2. Preliminaries" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "This section starts by explaining the notations used throughout the paper. It then introduces the basic concepts in Graph Contrastive Learning (GCL)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 373, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 373, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 373, + 83 + ], + "type": "text", + "content": "2.1. Notations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "text", + "content": "Capital italic letters stand for sets (e.g., set " + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "text", + "content": "), capital bold letters represent matrices (e.g., matrix " + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "text", + "content": "), bold lowercase letters term vectors (e.g., vector " + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_v" + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "text", + "content": "), and lowercase letters denote scalars (e.g., scalar " + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "inline_equation", + "content": "q_{v,u}" + }, + { + "bbox": [ + 304, + 90, + 545, + 138 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": "For generality, this paper focuses on attribute undirected graphs. It considers a graph " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathbf{X})" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": ", where the node set " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": " contains " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": " node instances " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{x}_v,\\mathbf{y}_v)\\}_{v\\in \\mathcal{V}}" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_v\\in \\mathbb{R}^f" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_v\\in \\mathbb{R}^c" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": " denote the attribute and label vector of the node " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": ", respectively. The node embeddings " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{H}\\in \\mathbb{R}^{n\\times d}" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": " are learned on entire graphs in an unsupervised manner, then utilized in downstream tasks, such as node classification, where the labels " + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 138, + 546, + 234 + ], + "type": "text", + "content": " are used for fine-tuning linear classifiers." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 240, + 463, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 240, + 463, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 463, + 253 + ], + "type": "text", + "content": "2.2. Graph Contrastive Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 258, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 342 + ], + "type": "text", + "content": "Being typical of a graph-based self-supervised learning SSL architecture, GCL aims to generate supervised signals based on a predefined rule. It involves bringing the similar samples (i.e., positive samples) closer while pushing the dissimilar samples (i.e., negative samples) apart simultaneously. Take GRACE [32], which is an oft-discussed baseline, as an example, its architecture is described below." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": "In line with SimCLR [2], a contrastive learning baseline in computer vision (CV), GRACE adopts a two-channel architecture. For graph " + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathbf{X})" + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": ", both channels are responsible for generating node embeddings (represented as " + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{H}}" + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": ") for its two augmented graphs through graph augmentations [32] and encoders [11]. The description of these processes can be found in the appendix." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "text", + "content": "Once the node features are obtained, InfoNCE [22] loss, is calculated as a guide for its update. For node " + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "text", + "content": ", the positive sample of the anchor node " + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "inline_equation", + "content": "(\\mathbf{h}_v)" + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "text", + "content": " is the same node " + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "inline_equation", + "content": "(\\tilde{\\mathbf{h}}_v)" + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "text", + "content": " in another view, while the negative samples are other nodes in both views. This contrastive loss (denoted as " + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\ell_{gc}" + }, + { + "bbox": [ + 304, + 426, + 545, + 496 + ], + "type": "text", + "content": ") can be formulated as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 501, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 501, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 313, + 501, + 545, + 555 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\ell_ {g c} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) = - l o g \\frac {\\mathrm {p o} _ {v}}{\\mathrm {p o} _ {v} + \\mathrm {n e} _ {v}}, \\\\ \\mathrm {p o} _ {v} = \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {v})}{\\tau}}, \\mathrm {n e} _ {v} = \\sum_ {t \\in V \\backslash v} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\mathbf {h} _ {t})}{\\tau}} + \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {t})}{\\tau}}, \\tag {1} \\\\ \\end{array}", + "image_path": "b791c1805317e8a6093e884eb10d8bbf079c913797d76fd47a7e510fdbf5ad28.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "inline_equation", + "content": "\\theta (\\mathbf{h}_v,\\tilde{\\mathbf{h}}_v) = s(f(\\mathbf{h}_v),f(\\tilde{\\mathbf{h}}_v))" + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "inline_equation", + "content": "s(,)" + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "text", + "content": " terms the cosine similarity, and " + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "text", + "content": " denotes the projection head [2], which is a two-layer multilayer perceptron (MLP). " + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 563, + 545, + 648 + ], + "type": "text", + "content": " represents a scalar, which is positively correlated with the uniformity of the feature distribution. The overall contrastive loss is set as the average over all nodes based on the mutually symmetric form of Equation 1. This can be formulated as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 316, + 654, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 654, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 316, + 654, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g r a c e}} = \\frac {1}{2 | V |} \\sum_ {v \\in V} \\left(\\ell_ {g c} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) + \\ell_ {g c} \\left(\\tilde {\\mathbf {h}} _ {v}, \\mathbf {h} _ {v}\\right)\\right). \\tag {2}", + "image_path": "425daa8af51a0948331114786127c989b658fdcba22880857790cd07f026dfd5.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "In addition to the above pairwise positive sampling, several local positive sampling techniques have been presented" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23180" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 73, + 521, + 181 + ], + "blocks": [ + { + "bbox": [ + 83, + 73, + 521, + 181 + ], + "lines": [ + { + "bbox": [ + 83, + 73, + 521, + 181 + ], + "spans": [ + { + "bbox": [ + 83, + 73, + 521, + 181 + ], + "type": "image", + "image_path": "76115030afeef6a5f7c6144389fce79fe824820d2d4cdbc26983a1375c6e7e31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 182, + 312, + 193 + ], + "lines": [ + { + "bbox": [ + 76, + 182, + 312, + 193 + ], + "spans": [ + { + "bbox": [ + 76, + 182, + 312, + 193 + ], + "type": "text", + "content": "(a) Optimal positive sample set for GCLs and the corresponding matrix." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 359, + 182, + 485, + 192 + ], + "lines": [ + { + "bbox": [ + 359, + 182, + 485, + 192 + ], + "spans": [ + { + "bbox": [ + 359, + 182, + 485, + 192 + ], + "type": "text", + "content": "(b) The proposed HEATS Framework." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 196, + 545, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 545, + 240 + ], + "type": "text", + "content": "Figure 1. Overview of the proposed GCL framework, named HEATS, and its design motivation. (a) An intuitive example of the optimal positive sample matrix for GCLs, where the colors of nodes stand for classes. (b) The proposed HEATS framework with adaptive positive sampling. The optimal positive sample set should consist of all nodes from the same class. Accordingly, the optimal positive sample matrix should be block-diagonal, where each block is fully connected and weights within it are equal." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 287, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 288 + ], + "type": "text", + "content": "[12, 34]. They propose to add the specified neighbor nodes into the positive sample sets, leveraging the homophily assumption [1, 16]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 300, + 129, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 129, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 129, + 314 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 321, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 287, + 381 + ], + "type": "text", + "content": "In this section, following the introduction of design motivation, a graph contrastive learning (GCL) framework, named grapH contrastive Adaptive positive Sampling (HEATS), is devised. Subsequently, theoretical analysis of its efficacy are presented." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 392, + 121, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 121, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 121, + 403 + ], + "type": "text", + "content": "3.1. Motivation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 411, + 287, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 459 + ], + "type": "text", + "content": "As previously discussed in the introduction, existing positive sampling strategies utilized in GCLs tend to be incomplete and blind, leading to a loss of discriminative power of node representations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 469, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 506 + ], + "type": "text", + "content": "Definition 1. Block Diagonal Property (BDP) [9]. The given matrix " + }, + { + "bbox": [ + 46, + 469, + 287, + 506 + ], + "type": "inline_equation", + "content": "\\mathbf{Z} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 46, + 469, + 287, + 506 + ], + "type": "text", + "content": " satisfies block diagonal property if it can be decomposed into submatrices as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 107, + 515, + 226, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 515, + 226, + 572 + ], + "spans": [ + { + "bbox": [ + 107, + 515, + 226, + 572 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} = \\left[ \\begin{array}{c c c c} \\mathbf {Z} _ {1} & 0 & \\dots & 0 \\\\ 0 & \\mathbf {Z} _ {2} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & \\mathbf {Z} _ {k} \\end{array} \\right],", + "image_path": "b701354828ca051b300103ce3bcb6e9b6912495689eeb724a0f78a42c4a98a4a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_i\\in \\mathbb{R}^{n_i\\times n_i}" + }, + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "text", + "content": " stands for the " + }, + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "text", + "content": " -th square submatrix (block), and " + }, + { + "bbox": [ + 47, + 582, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\sum_{i = 0}^{k}n_{i} = n" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "An intuitive and optimal solution is provide target nodes with positive sample sets that consists of all nodes from the same class (i.e., optimal positive sample set), as depicted in Figure 1(a). It is evident that the relationships among these positive samples can be succinctly expressed as a block diagonal matrix, where each block describes the relationships among a class of nodes. Additionally, this matrix should exhibit the following properties: each block is full connected" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 251, + 544, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 544, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 544, + 275 + ], + "type": "text", + "content": "and weights within it are equal. Therefore, the optimal positive sample matrix should be formulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 283, + 545, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 283, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 315, + 283, + 545, + 344 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} = \\left[ \\begin{array}{c c c c} \\frac {1}{n _ {1}} \\mathbf {1} _ {n _ {1}} \\mathbf {1} _ {n _ {1}} ^ {\\top} & 0 & \\dots & 0 \\\\ 0 & \\frac {1}{n _ {2}} \\mathbf {1} _ {n _ {2}} \\mathbf {1} _ {n _ {2}} ^ {\\top} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & \\frac {1}{n _ {k}} \\mathbf {1} _ {n _ {k}} \\mathbf {1} _ {n _ {k}} ^ {\\top} \\end{array} \\right], \\tag {3}", + "image_path": "fad041bcbf27dac6c605c97b30497d025141572c3ae11ffafdc49144830d4339.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 352, + 514, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 514, + 364 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 514, + 364 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 352, + 514, + 364 + ], + "type": "inline_equation", + "content": "\\mathbf{1}_{n_i} \\in \\mathbb{R}^{n_i}" + }, + { + "bbox": [ + 306, + 352, + 514, + 364 + ], + "type": "text", + "content": " denotes an all-one column vector." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 371, + 419, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 371, + 419, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 371, + 419, + 383 + ], + "type": "text", + "content": "3.2. HEATS framework" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 390, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 545, + 475 + ], + "type": "text", + "content": "Based on the above analysis, this paper devises a novel GCL framework HEATS, which directs the positive sampling by employing constructed block diagonal affinity matrices. As overviewed in Figure 1(b), HEATS consists of two key components: (1) Matrix Construction and (2) Contrastive Optimization. These two components engage in an alternating refinement process, gradually converging to the optimum." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 488, + 427, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 488, + 427, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 488, + 427, + 499 + ], + "type": "text", + "content": "3.2.1 Matrix Construction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 507, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 615 + ], + "type": "text", + "content": "This component aims to construct affinity matrices, which possess inter-class sparsity and intra-class connectivity (i.e., obey BDP), to guide the selection of positive samples. Particularly, it adopts a self-expressive learning objective, commonly utilized in subspace clustering [13], to acquire such affinity matrices. This objective posits that each sample can be represented by linearly combining all other samples in the same subspace (i.e., block). This objective can be formulated as the following equation:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 331, + 624, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 624, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 331, + 624, + 545, + 644 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {Z}, \\mathbf {E}} {\\operatorname {a r g m i n}} \\mathcal {O} (\\mathbf {Z}) + \\lambda \\mathcal {T} (\\mathbf {E}), \\quad \\text {s . t .} \\mathbf {X} = \\mathbf {Z} \\mathbf {X} + \\mathbf {E}, \\tag {4}", + "image_path": "9af1a331a2890ad18cf6491b2a716c87ea028f34adf5302bbb6df929529196d0.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " denotes the affinity matrix, which depicts the combination coefficients, and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " stands for the noise. Moreover, " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " term the constraint on affinity matrices and noise matrices, respectively. " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " is a hyperparameter that balances the two terms of the objective function." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23181" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "To obtain a high-quality affinity matrix, as expressed in Equation 3, several constraints should be incorporated into the learning objective: idempotent and " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "-block. Firstly, the affinity matrix " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " in Equation 3 is idempotent [27] because of " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_i = \\mathbf{Z}_i \\times \\mathbf{Z}_i = \\mathbf{Z}_i^2" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ". Secondly, the number of blocks in the affinity matrices should be controlled as " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ". Furthermore, the affinity matrices also should be normalized, symmetric, and non-negative. To achieve these properties and enhance effectiveness, the self-expressive learning objective can be reformulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 198, + 287, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 198, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 83, + 198, + 287, + 233 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname *{argmin}_{\\substack{\\mathbf{Z},\\mathbf{S}}}\\| \\mathbf{Z} - \\mathbf{S}\\|_{F}^{2} + \\gamma \\| \\mathbf{S}\\|_{id} + \\lambda \\| \\mathbf{E}\\|_{2,1}, \\\\ \\mathrm {s . t .} \\mathbf {H} = \\mathbf {Z H} + \\mathbf {E}, \\tag {5} \\\\ \\end{array}", + "image_path": "4572d49e42fe5f172d458ea2fce4c9faba9671c956d50ac1a19539f7474f5b89.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 82, + 237, + 245, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 237, + 245, + 251 + ], + "spans": [ + { + "bbox": [ + 82, + 237, + 245, + 251 + ], + "type": "interline_equation", + "content": "\\mathbf {S} \\mathbf {1} _ {n} = \\mathbf {1} _ {n}, \\mathbf {S} = \\mathbf {S} ^ {\\top}, \\mathbf {S} \\geq \\mathbf {0}, \\operatorname {T r} (\\mathbf {S}) = k,", + "image_path": "e06c95ba05563079fd2187f23193bdcc147d354f49768cafd07028165a9a6552.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " denotes an intermediate-term to mitigate the loss of representation capability. And, " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{S}\\|_{id} = \\| \\mathbf{S} - \\mathbf{S}^2\\| _F^2" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " terms the idempotent constraint and " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " is a scalar that controls the impacts of this term. The terms " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{S1}_n = \\mathbf{1}_n" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = \\mathbf{S}^{\\top}" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{S}\\geq 0" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " stand for the column-normalized, symmetric, and nonnegative constraints, respectively. Based on the above constraints, the term " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\mathrm{Tr}(\\mathbf{S}) = k" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " is introduced to make the matrix have " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " blocks. " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{E}\\|_{2,1} = \\sum_{j = 1}^{n}\\sqrt{\\sum_{i = 1}^{n}([\\mathbf{E}]_{ij})^2}" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\ell_{2,1}" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " -norm of noise, which characterizes sample-specific outliers. Finally, the affinity matrix, a guide of positive sampling, can be obtained by optimizing Equation 5. Please refer to the appendix for optimization details. Once the affinity matrix M (i.e., " + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 46, + 259, + 289, + 439 + ], + "type": "text", + "content": " or S) is obtained, it is necessary to sparsify it to enhance training efficiency. The sparsification process can be formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 446, + 227, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 446, + 227, + 479 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 227, + 479 + ], + "type": "interline_equation", + "content": "m _ {v, u} = \\left\\{ \\begin{array}{l l} 0, & m _ {v, u} < \\beta , \\\\ m _ {v, u}, & \\text {o t h e r w i s e}. \\end{array} \\right.", + "image_path": "e84ba1cb0fd00c6cf33cf43e478753cfccc70a0c56d97aca993bf4f2865a338b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 486, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 486, + 287, + 510 + ], + "type": "text", + "content": " denotes the threshold parameter, which is utilized to indicate filter out the values below it." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 517, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 541 + ], + "type": "text", + "content": "Theorem 1. The affinity matrix " + }, + { + "bbox": [ + 46, + 517, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 517, + 287, + 541 + ], + "type": "text", + "content": ", which is generated by optimizing Equation (5), satisfies the BDP in Definition 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 548, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 585 + ], + "type": "text", + "content": "Theorem 1 theoretically demonstrates that the proposed matrix construction strategy aligns with the motivation. For the proof, please refer to the appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 599, + 189, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 189, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 189, + 611 + ], + "type": "text", + "content": "3.2.2 Contrastive Optimization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": "This subsection delineates the methodology for formulating the contrastive loss leveraging the constructed affinity matrix " + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": ". Firstly, it is utilized to direct the sampling process. By identifying non-zero values in the vector " + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_v" + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": ", nodes that are semantically associated with node " + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": " can be marked out. These nodes collectively constitute the positive sample set of node " + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_v^M = \\{u|m_{v,u} > 0\\}" + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": ". Following the baselines [2, 32], the negative sample set is composed of" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": "the remaining nodes, that is " + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_v^M = V\\setminus \\{\\mathcal{P}_v^M\\cup v\\}" + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": ". Secondly, the matrix " + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": " is also interpreted as a measure of the relationships, and the values within it are treated as weights." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 108, + 547, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 157 + ], + "type": "text", + "content": "In implementation, HEATS follows the baseline GRACE [32], which is mentioned in Section 2.2. Therefore, the contrastive loss of HEATS with respect to anchor node " + }, + { + "bbox": [ + 304, + 108, + 547, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_v" + }, + { + "bbox": [ + 304, + 108, + 547, + 157 + ], + "type": "text", + "content": " can be reformulated from Equation 1 as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 339, + 164, + 545, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 164, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 339, + 164, + 545, + 251 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\ell_ {h t} (\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}) = - l o g \\frac {\\mathrm {p o} _ {v}}{\\mathrm {p o} _ {v} + \\mathrm {n e} _ {v}}, \\\\ \\mathrm {p o} _ {v} = \\mathrm {e} ^ {\\frac {\\theta \\left(\\mathbf {h} _ {v} , \\tilde {\\mathbf {h}} _ {v}\\right)}{\\tau}} + \\sum_ {u \\in \\mathcal {P} _ {v} ^ {M}} m _ {v, u} \\cdot \\mathrm {e} ^ {\\frac {\\theta \\left(\\mathbf {h} _ {v} , \\mathbf {h} _ {u}\\right)}{\\tau}}, \\tag {6} \\\\ \\mathrm {n e} _ {v} = \\sum_ {t \\in \\mathcal {N} _ {v} ^ {M}} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\bar {\\mathbf {h}} _ {t})}{\\tau}} + \\sum_ {t \\in \\mathcal {N} _ {v} ^ {M}} \\mathrm {e} ^ {\\frac {\\theta (\\mathbf {h} _ {v} , \\bar {\\mathbf {h}} _ {t})}{\\tau}}, \\\\ \\end{array}", + "image_path": "aaab48afc90e1c5fa31b7a9fea9174d9a06804b234f61e7a6b8291928141eb5e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 259, + 542, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 259, + 542, + 272 + ], + "spans": [ + { + "bbox": [ + 306, + 259, + 542, + 272 + ], + "type": "text", + "content": "The overall contrastive loss of HEATS, denoted as " + }, + { + "bbox": [ + 306, + 259, + 542, + 272 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{heats}}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 280, + 545, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 280, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 317, + 280, + 545, + 308 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {h e a t s}} = \\frac {1}{2 | V |} \\sum_ {v \\in V} \\left(\\ell_ {h t} \\left(\\mathbf {h} _ {v}, \\tilde {\\mathbf {h}} _ {v}\\right) + \\ell_ {h t} \\left(\\tilde {\\mathbf {h}} _ {v}, \\mathbf {h} _ {v}\\right)\\right). \\tag {7}", + "image_path": "ede67b63f7406f886baa68c1103e6b281ea2c8b8d82a97100c22bab9e6bfb310.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "type": "text", + "content": "In comparison to the existing GCLs [12, 20, 34], the proposed HEATS exhibits several characteristics. (1) Generality. Since the positive sample matrices are constructed globally, that is, independent of the underlying graph topology, HEATS can be reasonably extended to non-graph domains such as computer vision (CV). (2) Robustness. Due to the fact that the positive sample matrix is obtained by optimizing a robust self-expressive learning objective, as formulated in Equation (5), the robustness is strengthened through positive sampling on these matrices." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 445, + 547, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 493 + ], + "type": "text", + "content": "Theorem 2. The contrastive loss of HEATS " + }, + { + "bbox": [ + 304, + 445, + 547, + 493 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\text {heats }})" + }, + { + "bbox": [ + 304, + 445, + 547, + 493 + ], + "type": "text", + "content": " is a more stringent estimate of mutual information (MI) between node attributes and embeddings than that of the local baseline HomoGCL [12], that is," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 353, + 502, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 502, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 353, + 502, + 545, + 517 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {h o m o g c l}} \\leq \\mathcal {L} _ {\\text {h e a t s}} \\leq I (\\mathbf {X}; \\mathbf {H}, \\tilde {\\mathbf {H}}), \\tag {8}", + "image_path": "0b48b7c1dfc247a4e49377b0514ea070bfc7c5b1b0df069123fe2e183a126f56.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "text", + "content": " denotes the node attributes, and " + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{H}}" + }, + { + "bbox": [ + 304, + 526, + 545, + 552 + ], + "type": "text", + "content": " represent the node embeddings in two augmented views." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 559, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 596 + ], + "type": "text", + "content": "Theorem 2 demonstrates that the proposed HEATS provides a refined approximation to the TRUE mutual information, enabling it to promote model robustness and stability." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 611, + 422, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 422, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 422, + 623 + ], + "type": "text", + "content": "3.2.3 Alternating Update" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "To enhance the adaptivity of HEATS, the two fundamental components, matrix construction and contrastive optimization, engage in iterative updates in an alternating fashion, as visually depicted in Figure 1(b). The former is tasked with solving Equation 5 to construct positive sample matrices in the feature space. The latter focuses on representation (feature) learning by optimizing the contrastive loss using these" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23182" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 97, + 286, + 238 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "type": "text", + "content": "Table 1. Statistics of twelve graph datasets. Homophily is the edge homophily in [17]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 97, + 286, + 238 + ], + "lines": [ + { + "bbox": [ + 49, + 97, + 286, + 238 + ], + "spans": [ + { + "bbox": [ + 49, + 97, + 286, + 238 + ], + "type": "table", + "html": "
DatasetNodesEdgesFeaturesClassesHomophily
Cora2,7085,2781,43370.81
CiteSeer3,3274,5523,70360.74
PubMed19,71744,32450030.80
Wiki-CS11,701216,123300100.65
Computers13,752245,861767100.78
Photo7,650238,16374580.83
Cornell1832951,70350.13
Texas1833091,70350.11
Wisconsin2514991,70350.20
Chameleon2,27736,1012,32550.23
Squirrel5,201217,0732,08950.22
Actor7,60033,54493150.22
", + "image_path": "3b0f0fdd2841cca019e0441cfa4589628efcb3edb5d3b7c58c7406b37cf260ab.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 250, + 286, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 250, + 286, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 250, + 286, + 273 + ], + "type": "text", + "content": "positive sample matrices, which is formulated as Equation 6. These two components are updated alternately." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 274, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 441 + ], + "type": "text", + "content": "The alternating update procedure offers several benefits to GCLs. (1) Adaptive positive samples. Note that the positive sample matrices are constructed in the feature space. Hence, this procedure can continually provide adaptive positive samples for the subsequent contrastive optimization, adapting to feature changes. (2) Discriminative node representations. GCLs have the denoising ability, to some extent, which is attributed to the fact that it obtains the invariant information [28]. As a result, the discriminative feature space can be provided for the construction of positive sample matrices, eventually resulting in more discriminative features through contrastive learning. Furthermore, benefits also involve the risk reduction of each component falling into the local optimum and accelerating the convergence speed." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 452, + 127, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 127, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 127, + 464 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 472, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 533 + ], + "type": "text", + "content": "In this section, the proposed framework HEATS is validated by empirically evaluating its performances on node and image classification tasks in the unsupervised setting. Next, an in-depth understanding of the efficacy of this framework is provided through several experiment analyses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 539, + 155, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 155, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 155, + 552 + ], + "type": "text", + "content": "4.1. Experiment Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "type": "text", + "content": "Datasets. To illustrate the effectiveness and generality of the proposed HEATS, twelve non-Euclidean graph datasets, and three 2-D spatial image datasets are adopted in the experiments. According to graph homophily [17], these graph datasets can be divided into two categories: six homophilic graphs, including Cora, CiteSeer, PubMed, Wiki-CS, Computers, and Photo, and six heterophilic graphs, containing Cornell, Texas, Wisconsin, Chameleon, Squirrel, and Actor. Moreover, the image datasets are CIFAR-10, STL-10, and CIFAR-100. The statistics of the graph datasets are presented in Table 1. Due to space limitations, the introduction of all datasets is presented in the appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "content": "Splitting. To ensure experimental fairness, the dataset split" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "ting follows commonly employed schemes. Specifically, for three homophilic graphs (Cora, CiteSeer, and PubMed) and all six heterophilic graphs, the training, validation, and testing sets constitute " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "48\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "32\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " of the data, respectively. For the remaining homophilic graphs (Wiki-CS, Computers, and Photo), the proportions amount to " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": ". Besides, for the CIFAR-10 dataset, 5000 and 1000 images per class are selected for training and testing, respectively. For the STL-10 dataset, 10500 and 800 images per class are assigned to the training and testing sets, respectively. For the CIFAR-100 dataset, 500 and 100 images per class are served in training and testing, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 216, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 545, + 357 + ], + "type": "text", + "content": "Baselines. These experiments involve two types of downstream tasks: node classification for graphs and image classification. For the node classification, the baselines include two types: semi-supervised graph neural networks (GCN [11], GAT [24] and JKNet [29]), and unsupervised graph learning models (Deepwalk [18], Node2vec [4], GAE [10], VGAE [10], DGI [25], MVGRL [5], GRACE [32], GCA [33], BGRL [21], SELENE [31], and HomoGCL [12]). For the image classification, the baseline is CL model SimCLR [2], which is implemented with two backbones (ResNet-18 and ResNet-50) [7]. Please refer to the appendix for an introduction to related works." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": "Configurations. In the node classification, the proposed HEATS framework is implemented with the configurations following GRACE [32]. To be specific, each branch corresponds to an augmented graph, which is initially obtained through the edge deletion and attribute masking [3], with the random ratio among " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\{0.2, 0.4, 0.6, 0.8\\}" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": ". Furthermore, the node features are obtained through a two-layer GCN [11] encoding and a two-layer MLP [19] projecting, where both dimensions are 64. The node features are trained by minimizing the contrastive loss, where the temperature coefficient is taken from " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\{0.2, 0.4, 0.6, 0.8, 1\\}" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": ". In this process, an Adam optimizer with the learning rate of 0.01 and the weight decay rate among " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\{0, 5 \\times 10^{-5}\\}" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": " is to be employed for optimization and regularization, respectively. Minibatch training is adopted for larger node numbers, such as PubMed. For the unique parameters of HEATS, namely " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": ", both are selected from " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\{1 \\times 10^{-3}, 1 \\times 10^{-2}, 1 \\times 10^{-1}, 1, 10\\}" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": ". Furthermore, the number of blocks " + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 359, + 545, + 609 + ], + "type": "text", + "content": " is selected from a set with no more than the number of classes, and its impact is analyzed in Section 4.3.2. All experiments are conducted in PyTorch on a single RTX4090 24GB GPU." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 610, + 545, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 610, + 545, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 610, + 545, + 706 + ], + "type": "text", + "content": "Evaluation Protocol. For both node and image classification tasks, the experimental evaluations adopt the standard linear evaluation protocol [25]. Concretely, all models undergo initial unsupervised pre-training, followed by utilizing the obtained embeddings to train linear classifiers and subsequently presenting the test accuracy results. Throughout the evaluation phases, the Adam optimizer with a learning rate of 0.01 is utilized. The experiment results are re" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23183" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 102, + 531, + 288 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 2. Node classification accuracy (mean ± std) is reported for six homophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 102, + 531, + 288 + ], + "lines": [ + { + "bbox": [ + 61, + 102, + 531, + 288 + ], + "spans": [ + { + "bbox": [ + 61, + 102, + 531, + 288 + ], + "type": "table", + "html": "
ModelTraining DataCoraCiteSeerPubMedWiki-CSComputersPhoto
GCNA,X,Y85.77 ± 0.2573.68 ± 0.3188.13 ± 0.2876.89 ± 0.3786.34 ± 0.4892.35 ± 0.25
GATA,X,Y86.37 ± 0.3074.32 ± 0.2787.62 ± 0.2677.42 ± 0.1987.06 ± 0.3592.64 ± 0.42
JKNetA,X,Y85.93 ± 1.3574.37 ± 1.5387.68 ± 0.3079.52 ± 0.2185.28 ± 0.7292.68 ± 0.13
DeepWalkA73.96 ± 0.1261.91 ± 0.4274.79 ± 0.9874.35 ± 0.0685.68 ± 0.0689.44 ± 0.11
Node2VecA75.87 ± 0.2262.54 ± 0.1376.49 ± 0.3271.79 ± 0.0584.39 ± 0.0889.67 ± 0.12
GAEA,X76.83 ± 1.2265.43 ± 1.1376.52 ± 0.3370.15 ± 0.0185.27 ± 0.1991.62 ± 0.13
VGAEA,X79.36 ± 0.8369.18 ± 0.2779.17 ± 0.4476.63 ± 0.1986.37 ± 0.2192.20 ± 0.11
DGIA,X85.90 ± 0.5772.57 ± 0.2383.52 ± 1.2475.73 ± 0.1384.09 ± 0.3991.49 ± 0.25
MVGRLA,X86.77 ± 0.3373.71 ± 0.4884.63 ± 0.7377.97 ± 0.1887.09 ± 0.2792.01 ± 0.13
GRACEA,X84.79 ± 0.6472.94 ± 0.7284.51 ± 0.6879.16 ± 0.3687.21 ± 0.4492.65 ± 0.32
GCAA,X85.16 ± 0.5172.73 ± 0.4585.22 ± 0.7379.35 ± 0.1287.84 ± 0.2792.78 ± 0.17
BGRLA,X85.37 ± 0.7473.45 ± 0.8384.61 ± 0.3278.74 ± 0.2288.92 ± 0.3393.24 ± 0.29
SELENEA,X85.28 ± 0.8373.48 ± 0.6584.70 ± 0.5278.31 ± 0.6388.13 ± 0.5192.93 ± 0.34
HomoGCLA,X85.02 ± 0.6873.67 ± 0.7882.33 ± 0.4977.47 ± 0.4587.84 ± 0.2893.59 ± 0.27
HEATSA,X87.10 ± 1.4075.26 ± 1.2585.41 ± 0.8279.99 ± 1.5989.29 ± 1.1294.65 ± 1.71
", + "image_path": "41ca89b6c5f5048dba5b39cfbfcb62e2263721266d465adfc79ef82f91c5c07e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 301, + 232, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 301, + 232, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 301, + 232, + 314 + ], + "type": "text", + "content": "ported as an average of over ten random runs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 216, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 216, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 216, + 335 + ], + "type": "text", + "content": "4.2. Results on benchmark datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "type": "text", + "content": "Results on Homophilic Graphs. Table 2 presents the experimental results of node classification on six homophilic graphs. It is evident that compared to all unsupervised baseline models, the proposed HEATS achieves the best performance across all datasets. It even surpasses all supervised comparison models on datasets other than PubMed. To be specific, on the CiteSeer dataset, HEATS outperforms the second-best unsupervised model (i.e., MVGRL) by " + }, + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "type": "inline_equation", + "content": "1.55\\%" + }, + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "type": "text", + "content": " and the baseline model (i.e., GRACE) by " + }, + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "type": "inline_equation", + "content": "2.32\\%" + }, + { + "bbox": [ + 46, + 342, + 287, + 485 + ], + "type": "text", + "content": " in classification accuracy. This highlights the effectiveness of HEATS in exploring positive samples by modeling high-order relationships." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": "Results on Homophilic Graphs. A similar phenomenon can be observed from the experiment results on heterophilic graphs, as illustrated in Table 3. To be specific, compared to the baseline model (i.e., GRACE), HEATS achieves performance improvements across all datasets. Particularly noteworthy are improvements in accuracy by " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "12.11\\%" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "7.29\\%" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "15.88\\%" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": " on the Cornell, Texas, and Wisconsin datasets, respectively. This emphasizes the contribution of the proposed positive sampling based on matrix construction in enriching the universality of the baselines. Moreover, HEATS outperforms other unsupervised baselines on three datasets, except the Chameleon, Squirrel, and Actor datasets, showcasing its superior performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "Visualization. This experiment aims to intuitively demonstrate the representation ability of the proposed HEATS. For this purpose, the t-SNE [23] method is exploited to perform feature reduction and visualization of the trained representations. Figure 2 exhibits the experiment results (scatter plots) on three benchmark datasets (i.e., Cora, CiteSeer, and" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 322, + 304, + 537, + 462 + ], + "blocks": [ + { + "bbox": [ + 322, + 304, + 537, + 462 + ], + "lines": [ + { + "bbox": [ + 322, + 304, + 537, + 462 + ], + "spans": [ + { + "bbox": [ + 322, + 304, + 537, + 462 + ], + "type": "image", + "image_path": "5852a8bcde22a7d8927cedd6d2ec2cdaf2eea9f7d2e0505fd7364dc453c98cfa.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 471, + 545, + 493 + ], + "lines": [ + { + "bbox": [ + 305, + 471, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 545, + 493 + ], + "type": "text", + "content": "Figure 2. t-SNE visualization of node embeddings from HEATS, BGRL, and GRACE on Cora, CiteSeer, and Photo datasets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "content": "Photo), where colors stand for the classes of nodes. It can be observed that compared to all the comparison models (i.e., GRACE and BGRL), the proposed HEATS framework is enabled to produce the most informative representations. As exemplified by the Cora and CiteSeer dataset, compared to the baseline model (i.e., GRACE), HEATS achieves more compact clusters in node embeddings. Specifically, the embeddings of the same class are closer, while the embeddings of different classes exhibit more significant differences. The experiment results emphasize the effectiveness of HEATS in enhancing representation ability." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Results on Image Datasets. As previously mentioned, the proposed HEATS designs a positive sampling strategy from a global perspective, which effectively mitigates graph structural constraints. In essence, this improves its generality to various domains. To substantiate this claim, the experiment compares a contrastive learning (CL) model tailored for images (i.e., SimCLR) with the proposed variants." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23184" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 102, + 531, + 288 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 3. Node classification accuracy (mean ± std) is reported for six heterophilic datasets. The top-performing unsupervised model is denoted in **bold**, and the second-best unsupervised model is **underline**. The second column specifies the training information." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 102, + 531, + 288 + ], + "lines": [ + { + "bbox": [ + 61, + 102, + 531, + 288 + ], + "spans": [ + { + "bbox": [ + 61, + 102, + 531, + 288 + ], + "type": "table", + "html": "
ModelTraining DataCornellTexasWisconsinChameleonSquirrelActor
GCNA,X,Y55.14 ± 7.5755.68 ± 9.6158.42 ± 5.1059.82 ± 2.5836.89 ± 1.3430.64 ± 1.49
GATA,X,Y58.92 ± 3.3258.38 ± 4.4555.29 ± 8.7160.26 ± 2.5040.72 ± 1.5527.44 ± 0.89
JKNetA,X,Y56.49 ± 3.2265.35 ± 4.8651.37 ± 3.2160.31 ± 2.7644.24 ± 2.1136.47 ± 0.51
DeepWalkA39.18 ± 5.5746.49 ± 6.4933.53 ± 4.9247.74 ± 2.0532.93 ± 1.5822.78 ± 0.64
Node2VecA42.94 ± 7.4641.92 ± 7.7637.45 ± 7.0941.93 ± 3.2922.84 ± 0.7228.28 ± 1.27
GAEA,X58.85 ± 3.2158.64 ± 4.5352.55 ± 3.8033.84 ± 2.7728.03 ± 1.6128.03 ± 1.18
VGAEA,X59.19 ± 4.0959.20 ± 4.2656.67 ± 5.5135.22 ± 2.7129.48 ± 1.4826.99 ± 1.56
DGIA,X63.35 ± 4.6160.59 ± 7.5655.41 ± 5.9639.95 ± 1.7531.80 ± 0.7729.82 ± 0.69
MVGRLA,X64.30 ± 5.4362.38 ± 5.6162.37 ± 4.3251.07 ± 2.6835.47 ± 1.2930.02 ± 0.70
GRACEA,X54.86 ± 6.9557.57 ± 5.6850.00 ± 5.8348.05 ± 1.8131.33 ± 1.2229.01 ± 0.78
GCAA,X55.41 ± 4.5659.46 ± 6.1650.78 ± 4.0649.80 ± 1.8135.50 ± 0.9129.65 ± 1.47
BGRLA,X57.30 ± 5.5159.19 ± 5.8552.35 ± 4.1247.46 ± 2.7432.64 ± 0.7829.86 ± 0.75
SELENEA,X59.94 ± 5.1261.87 ± 4.2561.87 ± 4.7942.13 ± 2.1533.28 ± 0.8230.12 ± 0.76
HomoGCLA,X48.64 ± 2.5954.05 ± 2.3239.21 ± 5.7548.68 ± 1.1638.71 ± 0.8528.81 ± 0.78
HEATSA,X66.97 ± 6.7464.86 ± 4.6865.88 ± 5.5649.96 ± 1.8636.24 ± 1.1129.91 ± 1.16
", + "image_path": "d6877a2dafb26dafccda6b006f585b01bf8e2f44c1ef58742dd98548fb5a8a4c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 61, + 331, + 272, + 414 + ], + "blocks": [ + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "type": "text", + "content": "Table 4. Image classification accuracy (mean) of SimCLR and its HEATS-based variants. " + }, + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "type": "text", + "content": " dentoes the performance improvement." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 331, + 272, + 414 + ], + "lines": [ + { + "bbox": [ + 61, + 331, + 272, + 414 + ], + "spans": [ + { + "bbox": [ + 61, + 331, + 272, + 414 + ], + "type": "table", + "html": "
BackboneMethodCIFAR-10STL-10CIFAR-100
ResNet-18SimCLR78.5978.4449.60
+HEATS79.1978.8352.62
↑+0.60+0.39+3.02
ResNet-50SimCLR75.0376.7349.31
+HEATS77.5877.8053.81
↑+2.55+1.07+4.50
", + "image_path": "10765011227722854b65f10187fd259ae2813b409c84dc56afed7618b2ea7569.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": "The configurations of these variants align with that of the baselines, including standard parameters such as learning rate and training epochs. Please refer to the appendix for experiment setups. Table 4 exhibits the image classification results after 30 epochs using ResNet-18 and ResNet-50 backbones. It can be seen that compared to the baseline (i.e., SimCLR), the proposed HEATS framework consistently improves performance across all three datasets. To be specific, HEATS showcases superior performance compared to the two baselines utilizing ResNet-18 and ResNet-50 backbones on the CIFAR-100 dataset by " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "3.02\\%" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "4.5\\%" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": ", respectively, accentuating the generality to image-centric tasks. More importantly, it provides valuable insights for applying HEATS in a wide range of domains." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 604, + 149, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 149, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 149, + 616 + ], + "type": "text", + "content": "4.3. Further Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 622, + 167, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 167, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 167, + 634 + ], + "type": "text", + "content": "4.3.1 Effectiveness Justify" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "The experiment intends to justify the effectiveness of the two proposed approaches to enhance positive sampling, i.e., matrix construction and alternating updates, to pursue the block-diagonal matrices. Therefore, three matrices, which include the adjacent matrix, the matrix computed using the initial features, and the matrix computed using the features" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 322, + 304, + 531, + 582 + ], + "blocks": [ + { + "bbox": [ + 322, + 304, + 531, + 582 + ], + "lines": [ + { + "bbox": [ + 322, + 304, + 531, + 582 + ], + "spans": [ + { + "bbox": [ + 322, + 304, + 531, + 582 + ], + "type": "image", + "image_path": "bc656502431c4a5d12bbed467d40bc7ebe279067015b3b9d29d179a8eca25f04.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 586, + 545, + 640 + ], + "lines": [ + { + "bbox": [ + 305, + 586, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 545, + 640 + ], + "type": "text", + "content": "Figure 3. Visualization of the adjacent matrices, the matrices computed using the initial features (Matrix 1), and the matrices computed using the learned features after 200 iterations (Matrix 2) on the Cora and CiteSeer datasets. The nodes are sorted by class. The weights between nodes are not considered here." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 653, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 676 + ], + "type": "text", + "content": "after 200 iterations, are visualized in Figure 3 to provide an intuitive understanding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Based on the observations in Figure 3, three significant conclusions can be drawn. (1) The constructed matrices are approximately block diagonal. In particular, on all datasets" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23185" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 75, + 282, + 155 + ], + "blocks": [ + { + "bbox": [ + 51, + 75, + 282, + 155 + ], + "lines": [ + { + "bbox": [ + 51, + 75, + 282, + 155 + ], + "spans": [ + { + "bbox": [ + 51, + 75, + 282, + 155 + ], + "type": "image", + "image_path": "665bad5c92f1db3f2841252b392eb544083555d625e5df857f538bd445aa98ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 159, + 247, + 171 + ], + "lines": [ + { + "bbox": [ + 86, + 159, + 247, + 171 + ], + "spans": [ + { + "bbox": [ + 86, + 159, + 247, + 171 + ], + "type": "text", + "content": "Figure 4. Impact of the number of blocks " + }, + { + "bbox": [ + 86, + 159, + 247, + 171 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 86, + 159, + 247, + 171 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 185, + 156, + 271 + ], + "blocks": [ + { + "bbox": [ + 48, + 185, + 156, + 271 + ], + "lines": [ + { + "bbox": [ + 48, + 185, + 156, + 271 + ], + "spans": [ + { + "bbox": [ + 48, + 185, + 156, + 271 + ], + "type": "image", + "image_path": "0348dee2a57cacc8dc7b2208de43e49ef0d310cd1d8cbd7ad69c2dd0e609084f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 74, + 273, + 140, + 282 + ], + "lines": [ + { + "bbox": [ + 74, + 273, + 140, + 282 + ], + "spans": [ + { + "bbox": [ + 74, + 273, + 140, + 282 + ], + "type": "text", + "content": "(a) Topology attacks" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 81, + 287, + 253, + 298 + ], + "lines": [ + { + "bbox": [ + 81, + 287, + 253, + 298 + ], + "spans": [ + { + "bbox": [ + 81, + 287, + 253, + 298 + ], + "type": "text", + "content": "Figure 5. Results of GCLs under graph attacks" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 185, + 273, + 271 + ], + "blocks": [ + { + "bbox": [ + 167, + 185, + 273, + 271 + ], + "lines": [ + { + "bbox": [ + 167, + 185, + 273, + 271 + ], + "spans": [ + { + "bbox": [ + 167, + 185, + 273, + 271 + ], + "type": "image", + "image_path": "dbba3ddee58e5c2a3e75a7ba7a25ef1786d83255a1afc4f658b24077077e047c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 192, + 273, + 258, + 282 + ], + "lines": [ + { + "bbox": [ + 192, + 273, + 258, + 282 + ], + "spans": [ + { + "bbox": [ + 192, + 273, + 258, + 282 + ], + "type": "text", + "content": "(b) Attribute attacks" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 309, + 289, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 289, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 289, + 501 + ], + "type": "text", + "content": "(i.e., Cora and CiteSeer), the edges between nodes from the same class outnumber those between nodes from different classes. This indicates that the proposed HEATS framework can serve as an effective strategy to obtain more TRUE positive samples. (2) Compared to the adjacent matrices, the constructed matrices exhibit denser diagonal blocks. This implies that the proposed matrix construction approach is feasible in contrastive learning by offering more TRUE positive samples beyond graph topology. (3) Compared to the matrices constructed in the initial feature space, those constructed in the updated feature space exhibit a more distinct block-diagonal structure, e.g., results of the Cora dataset. This emphasizes the effectiveness of the proposed alternating update approach. In summary, the experiment confirms the efficacy of the two proposed approaches in constructing block-diagonal matrices for positive sample collection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "type": "text", + "content": "4.3.2 Hyperparameter Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": "The experiment aims to provide a guide on choosing the parameter " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", which represents the number of blocks, by investigating its impact on the performance. This parameter is selected from 2 to the number of classes, as setting it to 1 seems ineffective. Figure 4 exhibits the experiment results on three datasets (i.e., Cora, CiteSeer, and Cornell). Incorporating the results in Table 2, it can be observed that HEATS consistently performs well within a specific parameter range. For example, on the Cora dataset, when the parameter selects from the set " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\{4,5,6\\}" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", HEATS consistently outperforms the baseline model (i.e., GRACE) by " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "2.21\\%" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "2.31\\%" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "2.25\\%" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", respectively. This indicates HEATS insensitivity to changes in this parameter. Additionally, with a small value (e.g., 2), HEATS performs better than the baseline GRACE, which offers guidance to select the parameter." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 425, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 425, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 425, + 84 + ], + "type": "text", + "content": "4.3.3 Robustness Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 91, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 163 + ], + "type": "text", + "content": "This experiment is intended to evaluate the robustness of the proposed HEATS framework to noise. The topology attack (adding edges) and the attribute attack (flipping attributes) are applied to create noisy data on the Cora dataset. Figure 5 shows the performance variation of the GCL, HEATS, and the baseline GRACE under topology and attribute attacks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "text", + "content": "It can be seen from Figure 5a that GRACE is somewhat resistant to robust against topology attacks, but the performance degrades significantly with higher attack levels. For example, the accuracy decreases by about " + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "text", + "content": " compared to the attack-free accuracy at an edge deletion rate of 0.1. This is attributed to their centers on capturing the invariant information from multiple augmented graphs, to some extent, resulting in them being insensitive to topology changes. However, the accuracy decreases " + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "text", + "content": " when the edge deletion rate increases to 0.3. In contrast, HEAT exhibits greater robustness to this attack. Specifically, it achieves about " + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "inline_equation", + "content": "4.5\\%" + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "text", + "content": " increase in accuracy compared to the baseline GRACE when the edges deletion reaches an extreme " + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 163, + 546, + 378 + ], + "type": "text", + "content": ". This is mainly due to HEATS incorporating noise simulation and alternating update approach to extract high-order positive samples, thereby enhancing the robustness. Furthermore, as shown in Figure 5b, HEATS consistently outperforms the baseline GRACE, showcasing its denoising ability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 388, + 383, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 383, + 400 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 383, + 400 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": "In this paper, a novel graph contrastive learning framework, named HEATS, is proposed to address two key limitations of the existing positive sampling techniques: incomplete local sampling and blind sampling. Drawing inspiration from the observation that the affinity matrix associated with the optimal positive sample set is block-diagonal and idempotent, the idea of constructing such matrices to guide positive sampling is proposed. To enhance the adaptability and robustness of HEATS, an approach that alternately updates the positive sampling and contrastive optimization is proposed. Extensive experiments reveal the efficacy and robustness of HEATS. Future research directions include improving the scalability of the framework to accommodate large datasets and improving its generality to multimodal data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 586, + 416, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 416, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 416, + 600 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China (No. 62376088, 61972442, 62272020, 62102413, 62132006, U2001202, and U22B2036), in part by the National Science Fund for Distinguished Young Scholars (No. 62025602), in part by the National Social Science Fund of China under Grant 22VMG037, in part by the Natural Science Foundation of Hebei Province of China under Grant F2020202040, and in part by the Tencent Foundation and XPLORER PRIZE." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23186" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Kristen M Altenburger and Johan Ugander. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12682-12691, 2022. 2" + } + ] + } + ], + "index": 36 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23187" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_content_list.json b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f54c56cc8c42b8102657e691b9d7987a5455d395 --- /dev/null +++ b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_content_list.json @@ -0,0 +1,2159 @@ +[ + { + "type": "text", + "text": "Improving Image Restoration through Removing Degradations in Textual Representations", + "text_level": 1, + "bbox": [ + 225, + 130, + 743, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jingbo Lin $^{1}$ , Zhilu Zhang $^{1}$ , Yuxiang Wei $^{1}$ , Dongwei Ren $^{1,*}$ , Dongsheng Jiang $^{2}$ , Qi Tian $^{2}$ , Wangmeng Zuo $^{1}$ , Harbin Institute of Technology ${}^{2}$ Huawei Cloud Computing Co., Ltd.", + "bbox": [ + 86, + 202, + 916, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jb1ncs1996@gmail.com, cszlzhang@outlook.com, yuxiang.wei.cs@gmail.com,", + "bbox": [ + 184, + 241, + 810, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rendongweihit@gmail.com, dongsheng_jiang@outlook.com, tian.qil@huawei.com, cswmzuo@gmail.com", + "bbox": [ + 94, + 258, + 906, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we introduce a new perspective for improving image restoration by removing degradation in the textual representations of a given degraded image. Intuitively, restoration is much easier on text modality than image one. For example, it can be easily conducted by removing degradation-related words while keeping the content-aware words. Hence, we combine the advantages of images in detail description and ones of text in degradation removal to perform restoration. To address the cross-modal assistance, we propose to map the degraded images into textual representations for removing the degradations, and then convert the restored textual representations into a guidance image for assisting image restoration. In particular, We ingeniously embed an image-to-text mapper and text restoration module into CLIP-equipped text-to-image models to generate the guidance. Then, we adopt a simple coarse-to-fine approach to dynamically inject multiscale information from guidance to image restoration networks. Extensive experiments are conducted on various image restoration tasks, including deblurring, dehazing, detraining, and denoising, and all-in-one image restoration. The results showcase that our method outperforms state-of-the-art ones across all these tasks. The codes and models are available at https://github.com/mrluin/TextualDegRemoval.", + "bbox": [ + 76, + 340, + 472, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 746, + 209, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image restoration aims to reconstruct a high-quality clean image from its degraded observations. Most existing methods design deep networks for specific restoration tasks, including image denoising [55, 111, 115, 117, 119], deblurring [13, 14, 18, 93, 110], deraining [16, 93, 98, 110], dehazing [8, 19, 36, 88, 90], etc. Recent works [15, 50, 69, 71, 114, 124] expect to explore a unified model for multiple", + "bbox": [ + 75, + 772, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "degradations. However, the severely ill-posed nature of the task makes it non-trivial to separate degradations and desired image content. Especially for unified models, the potential conflicts in dealing with various degradations bring more uncertainty.", + "bbox": [ + 500, + 310, + 890, + 385 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "From a broader perspective, the purpose of the restoration is to enhance the clarity of scenes for human perception and recognition, while performing it on image modality is just one option. Moreover, degradations in image modality are tightly coupled with desirable content, making their removal challenging. When recording the scenes in some other modalities, this problem can be alleviated. Let us take the text modality as an example. Assume the textual description of a clean scene is represented by 'a scene of *'. When this scene is subjected to rainfall, the description can be converted into 'a rainy scene of *'. Thus, deraining can be readily achieved by simply removing the rain-related text 'rainy'. Furthermore, it is also convenient to remove multiple degradations in textual space with one unified model. Note that text modality may only describe rough aspects and ignore some details. We can further introduce image modality to combine their complementary potential in degradation removal and image restoration.", + "bbox": [ + 496, + 386, + 892, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motivated by the above, we propose to perform restoration first in a modality where degradations and content are loosely coupled, and then utilize the corrected content to guide image restoration. In particular, we adopt the commonly used textual modality. Note that the text corresponding to the scene is not always available and the cross-modal assistance is difficult to achieve directly. The gap between text and image should be bridged. First, degraded images should be mapped into textual space for removing degradations. Second, the restored text should be mapped into a guidance image to assist restoration of the degraded image. As shown in Fig. 1, for the former, we have tried to convert degraded images to textual captions by image-to-text (I2T) models (e.g., BLIP [51, 52]), and find the captions can explicitly express both degradation types (e.g., blur, rain, haze, and noise) and content information. For the latter, we can", + "bbox": [ + 496, + 659, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Correspondence author.", + "bbox": [ + 94, + 886, + 228, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2866", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e83e9e500ff6b129087a9b809985e755bd038cc5c70a94258fe2bd476bd8186.jpg", + "image_caption": [ + "Figure 1. Overview of the proposed method. We propose to improve image restoration by performing restoration on the textual level, in which content and degradation information are loosely coupled. We first encode image concepts into textual space and then remove degradation-related information. To achieve cross-modal assistance, we employ pre-trained T2I models to generate clean guidance for the image restoration process." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 883, + 343 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "utilize the text-to-image (T2I) models (e.g.,Imagen [82]), which have demonstrated impressive image generation capability from the given texts.", + "bbox": [ + 75, + 409, + 470, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although such a scheme is conceptually feasible, converting to explicit text may lose a lot of information from images, and additional degraded-clean text pairs need to be collected to train the text restoration module. Fortunately, Contrastive Language-Image Pre-training (CLIP) [74] implicitly aligns concepts of images and text. And we can leverage the CLIP-equipped T2I models (e.g., Stable Diffusion [81]) to build an end-to-end framework for generating clear guidance from degraded images gracefully. Specifically, CLIP has been demonstrated as an effective I2T converter [23]. For converting degraded images into degraded textual representations, we adopt the image encoder of CLIP, and add an I2T mapper after the encoder. For restoring degraded representations, we further append a textual restoration module after I2T mapper. Then, I2T mapper and textual restoration module can be sequentially trained by employing paired data from different image restoration datasets, without additional text data.", + "bbox": [ + 75, + 458, + 472, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to the ease of removing degradations on textual level, we train the I2T mapper and textual restoration module with multiple degradations at once. When training is done, it can serve multiple tasks, generating content-related and degradation-free guidance images from degraded images. Finally, we adopt a simple coarse-to-fine approach to dynamically inject multi-scale information from guidance to classic image restoration networks. Extensive experiments are conducted on multiple tasks, including all-in-one restoration, image debunking, dehazing, deraining, and denoising. The results show our method achieves better uni-", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "versally than corresponding state-of-the-art methods. Especially for all-in-one restoration, 0.5 dB PSNR improvement is obtained in comparison with PromptIR [71].", + "bbox": [ + 496, + 409, + 893, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions can be summarized as follows:", + "bbox": [ + 517, + 455, + 880, + 469 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new perspective for image restoration, i.e., performing restoration first in textual space where degradations and content are loosely coupled, and then utilizing the restored content to guide image restoration.", + "- To address the cross-modal assistance, we propose to embed an image-to-text mapper and textual restoration module into CLIP-equipped text-to-image models to generate clear guidance from degraded images.", + "- Extensive experiments on multiple tasks demonstrate that our method improves the performance of state-of-the-art image restoration networks." + ], + "bbox": [ + 500, + 470, + 890, + 637 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 654, + 640, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Restoration", + "text_level": 1, + "bbox": [ + 500, + 679, + 679, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Restoration for Specific Tasks. Image restoration is a fundamental computer vision problem, which aims to reconstruct high-quality images from corresponding degraded inputs. In recent years, deep learning has achieved great progress in image restoration. Starting from some simple convolutional neural networks (CNNs) [24, 115], the introduction of channel-attention [121], spatial-attention [35, 109], non-local operation [57, 122], skip-connection architectures [54, 109] and multi-stage scheme [93, 110] enables image restoration performance continuously improve. With the emergence of vision transformers [26, 60], the capability of capturing long-range dependencies in the image allows transformer-based", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2867", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d5f851b74c68a03334ec9da82c3265b3137baca3a366e469b653c87e6a5d1b10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 85, + 872, + 172 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d8239d3120b71cb03531321560028c46d00f50950c541bf3ba5a02947748c88d.jpg", + "image_caption": [ + "(a) Guidance Generation", + "(b) Guided Image Restoration.", + "Figure 2. Illustration of the proposed pipeline. (a) We sequentially train image-to-text mapper $\\mathcal{M}_{i2t}$ and textual restoration module $\\mathcal{M}_{clean}$ to convert image concepts into textual representations and remove textual degradation information, respectively. (b) The guidance image is used to assist the image restoration process." + ], + "image_footnote": [], + "bbox": [ + 98, + 184, + 870, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods to achieve better performance, gradually replacing previous CNN-based methods. To balance computational cost, window-based attention [17, 55] and transposed attention [111] are also introduced into image restoration tasks. Albeit image restoration performance has benefited from various advanced architecture designs, most of the works only focus on one specific degradation, due to the difficulty of learning to remove multiple degradations.", + "bbox": [ + 75, + 356, + 468, + 476 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "All-in-One Image Restoration. Promoting by the development of unified model, some works focus on the solution to the all-in-one image restoration [15, 50, 69, 71, 114, 124]. The first all-in-one image restoration work, i.e., IPT [12], employs ViT-based backbone with multi-heads and multi-tails for inputs with different degradations. However, the method is limited in handling specific synthesized degradations and cannot directly generalize to unknown tasks. AirNet [50] develops the unified model for denoising-deraining-dehazing, which utilizes contrastive learning to capture degradation representations of different tasks and adaptively injects the degradation priors into backbone restoration framework for aiding in learning better results. ADMS [69] exploits FAIG [99] in all-in-one image restoration, by learning specific filters and degradation classifiers, achieving better performance on deraining-denoising-deblurring and deraining-desnowing-dehazing tasks. IDR [114] proposes a two-stage training strategy, which first learns separate task-oriented hubs for each degradation. Then, in the second stage, it reformulates the learned hubs into a single ingredient-oriented hub by learnable PCA and adopts the reformulated hub as prior to adaptively aid in restoring corrupted images. PromptIR [71] learns to encode and adopt degradation information as prompts for dehazing-deraining-denoising task. Although existing works can unify a set of image restoration tasks into one unified model, the performance is still limited caused by the large gap among different degradations.", + "bbox": [ + 75, + 478, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prior-Based Image Restoration. Prior-based restoration aims at improving performance by introducing external priors, including structures, images, pre-trained models, etc. For instance, some works [9, 42, 61] adopt information from the high-resolution reference image to help improve the performance of super-resolution. Recent works [56, 92, 100] utilize pre-trained generative priors to restore more realistic and natural results. TextIR [6] develops a text-driven image restoration framework by incorporating information on textual representation.", + "bbox": [ + 496, + 356, + 890, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we provide a new perspective, i.e., utilizing restoration in textual space to assist image restoration. We also combine the advantages of both text-based prior (by learning degradations in textual level) and image-based prior (by giving clean guidance) for better performance.", + "bbox": [ + 496, + 507, + 890, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Text-to-Image Generation", + "text_level": 1, + "bbox": [ + 500, + 590, + 735, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-image generation models [22, 31, 67, 75, 76, 83, 96] have attracted intensive attention in recent years due to its ability to generate high-quality and diverse images based on given text descriptions. A variety of techniques, including generative adversarial networks (GAN) [34], autoregressive models, and diffusion models have been investigated. Initial studies [48, 83, 96] mainly rely on GAN-based architectures, and train a conditional model from given paired image-caption datasets to generate samples. Some efforts focus on autoregressive models [10, 21, 31, 75, 104] have also shown exciting results. These models, such as CogView [21] and Muse [10] first learn a discrete codebook through training an autoencoder, and then adopt an autoregressive transformer to predict the tokens sequentially. With the development of diffusion models [38, 87], text conditioned image synthesis has shown remarkable improvement. By training with huge corpora, large diffusion models, such as DALLE-2 [76], Imagen [82], Stable Diffusion [80], and DALLE-3 [7] have demonstrated excel", + "bbox": [ + 496, + 613, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2868", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lent semantic understanding, and can generate diverse and photo-realistic images.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 133, + 250, + 150 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we present our proposed method for image restoration. As illustrated in Fig. 2, we suggest first conducting restoration in the textual modality, in which degradation is loosely coupled with the content and can be easily removed. Then we in turn utilize the restored results as guidance to improve image restoration. Specifically, in Sec. 3.2, we propose an image-to-text mapper $\\mathcal{M}_{i2t}$ and a textual restoration module $\\mathcal{M}_{clean}$ to extract the degradation-free textual representations $\\mathbf{E}_{txt}^{\\prime}$ from degraded images $\\mathbf{X} \\in \\mathbb{R}^{H \\times W \\times 3}$ . Then with a pre-trained T2I model, we can generate a guidance image $\\mathbf{G} \\in \\mathbb{R}^{H \\times W \\times 3}$ that is related to the content of $\\mathbf{X}$ but free of degradation. In Sec. 3.3, to leverage clean content information from $\\mathbf{G}$ for enhancing image restoration performance, we introduce a coarse-to-fine approach that dynamically incorporates multi-scale information from guidance $\\mathbf{G}$ into restoration frameworks. Besides, we first give a preliminary knowledge of the T2I model in Sec. 3.1.", + "bbox": [ + 75, + 157, + 472, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 439, + 207, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we employ Stable Diffusion [81] as our text-to-image model. Stable Diffusion pretrains an autoencoder $(\\mathcal{E}(\\cdot),\\mathcal{D}(\\cdot))$ to map the input image $\\mathbf{X}$ into a lower dimensional latent space by $\\mathbf{z} = \\mathcal{E}(\\mathbf{X})$ . The decoder $\\mathcal{D}(\\cdot)$ learns to map the latent code back to the image as $\\mathcal{D}(\\mathcal{E}(\\mathbf{X}))\\approx \\mathbf{X}$ . Then, the conditional diffusion model $\\epsilon_{\\theta}(\\cdot)$ is trained on the latent space to generate latent codes based on text condition $\\mathbf{p}$ . To train the diffusion model, simple mean-squared loss is adopted as,", + "bbox": [ + 75, + 462, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {L D M} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathcal {E} (\\mathbf {X}), \\mathbf {p}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\tau_ {\\theta} ^ {t} (\\mathbf {p})\\right) \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 606, + 468, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon$ denotes the unscaled noise, $t$ is the timestep, $\\mathbf{z}_t$ is the latent noised to time $t$ , and $\\tau_{\\theta}^{t}(\\cdot)$ represents the pretrained CLIP [74] text encoder. During inference, a random Gaussian noise $\\mathbf{z}_T$ is iteratively denoised to $\\mathbf{z}_0$ , and the final image is obtained through the decoder $\\mathbf{X}' = \\mathcal{D}(\\mathbf{z}_0)$ .", + "bbox": [ + 75, + 642, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Degradation-Free Guidance Generation", + "text_level": 1, + "bbox": [ + 76, + 726, + 419, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image captioning models (e.g., BLIP2 [52]) can generate text descriptions of degraded images, which can be taken into the text restoration module and text-to-image models to reconstruct clean guidance images. However, such descriptions may lose too many details, resulting in severely inconsistent content between the guidance and the input images. To address these problems, we propose an image-to-text mapper $\\mathcal{M}_{i2t}$ to encode the degraded image $\\mathbf{X}$ as implicit textual representations $\\mathbf{E}_{txt}$ rather than explicit texts, which can be used to reconstruct the content more faithfully.", + "bbox": [ + 75, + 750, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we utilize a textual restoration module $\\mathcal{M}_{clean}$ to remove the degradation from $\\mathbf{E}_{txt}$ and obtain degradation-free textual representations $\\mathbf{E}_{txt}^{\\prime}$ .", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image-to-Text Mapping. Following [94], we adopt the textual word embedding space of CLIP [74] as the target space in image-to-text mapping. Benefiting from the aligned vision-language feature space of CLIP, we first adopt pre-trained CLIP image encoder $\\tau_{\\theta}^{i}(\\cdot)$ to encode input $\\mathbf{X}$ into CLIP image embedding $\\mathbf{E}_{img}$ . Then, we propose an image-to-text mapper $\\mathcal{M}_{i2t}$ to project CLIP image embedding into textual word embedding $\\mathbf{E}_{txt}$ ,", + "bbox": [ + 496, + 136, + 890, + 258 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} _ {t x t} = \\mathcal {M} _ {i 2 t} \\left(\\tau_ {\\theta} ^ {i} (\\mathbf {X})\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 270, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{E}_{\\text{txt}} \\in \\mathbb{R}^{N \\times D}$ and $D$ is the dimension of textual word embedding. $N$ is the number of learned words. To make the obtained word embedding describe more details of the input image, we set $N$ to a large number (e.g., $N = 20$ ).", + "bbox": [ + 496, + 297, + 890, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Textual Restoration. Although $\\mathcal{M}_{i2t}$ can project images into the textual word embedding space, the projected textual word embedding will include corresponding degradation information if input $\\mathbf{X}$ is degraded. Condition on the degraded textual word embedding, the synthesized guidance inevitably reflects the corresponding degradation pattern. Therefore, we further propose a textual restoration module $\\mathcal{M}_{clean}$ to remove the degradation information from the textual word embedding $\\mathbf{E}_{txt}$ ,", + "bbox": [ + 496, + 359, + 890, + 496 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} _ {t x t} ^ {\\prime} = \\mathcal {M} _ {c l e a n} (\\mathbf {E} _ {t x t}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 508, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{E}_{txt}^{\\prime}$ denote the restored textual representations. When feeding $\\mathbf{E}_{txt}^{\\prime}$ into Stable Diffusion, we can obtain a degradation-free image $\\mathbf{G}$ , which has similar content as $\\mathbf{X}$ but is free of degradation, as shown in Fig. 1.", + "bbox": [ + 496, + 537, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model Optimization. During training, the image-to-text mapper $\\mathcal{M}_{i2t}$ and textual restoration module $\\mathcal{M}_{clean}$ are optimized sequentially. In the first training stage, we collect both clean and degraded images from different restoration tasks as training data. We adopt Eq. (1) as a loss function, which constrains the diffusion model to reconstruct clean and degraded images conditioning on their own projected embedding $\\mathbf{E}_{txt}$ . In the second training stage, we use pairs of degraded-clean images from different image restoration datasets as training data. Based on pre-trained $\\mathcal{M}_{i2t}$ , we further deploy $\\mathcal{M}_{clean}$ to remove degradation-related concepts from degraded embedding $\\mathbf{E}_{txt}$ , obtaining $\\mathbf{E}_{txt}^{\\prime}$ . We still adopt Eq. (1), which constrains the diffusion model to reconstruct clean images conditioning on restored embedding $\\mathbf{E}_{txt}^{\\prime}$ . Note that, due to the ease of removing degradations in the textual space, it is feasible to train $\\mathcal{M}_{i2t}$ and $\\mathcal{M}_{clean}$ with multiple degradations simultaneously. When training is done, it can serve multiple image restoration tasks, generating content-related and degradation-free guidance images $\\mathbf{G}$ from degraded images", + "bbox": [ + 496, + 598, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2869", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/1250fc165e51d38ada28c07a3944c6ebe1f834b6de2687e9169e5e3db20e59fe.jpg", + "table_caption": [ + "Table 1. All-in-one image restoration results. Following PromptIR [71], we train and evaluate the proposed method in all-in-one image restoration task, our method outperforms PromptIR across all the benchmark datasets." + ], + "table_footnote": [], + "table_body": "
MethodDehazing on SOTSDerain on Rain100LDenoise on BSD68Average
σ = 15σ = 25σ = 50
BRDNet [89]23.23/0.89527.42/0.89532.26/0.89829.74/0.83626.34/0.83627.80/0.843
LPNet [33]20.84/0.82824.88/0.78426.47/0.77824.77/0.74821.26/0.55223.64/0.738
FDGAN [32]24.71/0.92429.89/0.93330.25/0.91028.81/0.86826.43/0.77628.02/0.883
MPRNet [110]25.28/0.95433.57/0.95433.54/0.92730.89/0.88027.56/0.77930.17/0.899
DL [27]26.92/0.39132.62/0.93133.05/0.91430.41/0.86126.90/0.74029.98/0.875
AirNet [50]27.94/0.96234.90/0.96733.92/0.93331.26/0.88828.00/0.79731.20/0.910
PromptIR [71]30.58/0.97436.37/0.97233.98/0.93331.31/0.88828.06/0.79932.06/0.913
Ours31.63/0.98037.58/0.97934.01/0.93331.39/0.89028.18/0.80232.56/0.916
", + "bbox": [ + 78, + 147, + 475, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with one unified model (as shown in Fig. 1). More training details can be seen in the Suppl.", + "bbox": [ + 76, + 272, + 468, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Guided Restoration", + "text_level": 1, + "bbox": [ + 76, + 313, + 264, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although guidance image $\\mathbf{G}$ is clean, it is inevitable that there are content differences between $\\mathbf{G}$ and degraded image $\\mathbf{X}$ . Simplyfusing the features of $\\mathbf{G}$ and $\\mathbf{X}$ is not enough to improve image restoration. Instead, we suggest a dynamic aggregation module to extract and exploit helpful information from $\\mathbf{G}$ .", + "bbox": [ + 75, + 335, + 468, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dynamic Aggregation. First, we perform feature matching [61] between the guidance $\\mathbf{G}$ and given degraded image $\\mathbf{X}$ . Specifically, we use a shared image encoder to extract multi-scale features for $\\mathbf{X}$ and $\\mathbf{G}$ , named $\\mathbf{F}_x$ and $\\mathbf{F}_g$ , respectively. According to the similarity score between $\\mathbf{F}_x$ and $\\mathbf{F}_g$ , we search for the most useful feature from $\\mathbf{F}_g$ for each small patch in $\\mathbf{F}_x$ in a coarse-to-fine manner. After searching, we get a set of guidance features $\\hat{\\mathbf{F}}_g$ , whose content is aligned spatially with the input content. Second, we integrate the matched feature $\\hat{\\mathbf{F}}_g$ into the image restoration backbone. Both CNN-based and transformer-based restoration networks can be adopted. Without bells and whistles, we modulate the original input features as,", + "bbox": [ + 75, + 428, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {x} = \\mathbf {F} _ {x} + \\alpha \\cdot \\mathcal {B} ([ \\mathbf {F} _ {x}, \\hat {\\mathbf {F}} _ {g} ]), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 636, + 468, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $[\\cdot, \\cdot]$ represents concatenation operation, $\\mathcal{B}$ represents one CNN-based block or transformer-based block, $\\alpha$ is the hyper-parameter to trade-off feature integration. Moreover, we perform it over multiple layers or levels. More details can be seen in the Suppl.", + "bbox": [ + 75, + 664, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Function. To train guided restoration framework, we simply adopt $\\ell_1$ loss as the reconstruction loss between predicted results $\\hat{\\mathbf{Y}}$ and target $\\mathbf{Y}$ , i.e.,", + "bbox": [ + 75, + 741, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {1} = \\left| \\left| \\hat {\\mathbf {Y}} - \\mathbf {Y} \\right| \\right| _ {1}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 799, + 468, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 829, + 209, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the proposed method on five image restoration tasks, including (1) all-in-one image restoration [71], (2) image deblurring [14, 111] (i.e., motion image deblurring", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/16cdba6d17df12a8a2f86e72519c5fa5cdddf7ecc37c2086b4d5752458190c23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 89, + 602, + 145 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fb30a7220c85e1a31321e3ac97e74570ac49cd8dbe9422448b12e7bf4555f0b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 146, + 602, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/92a1a95a88aecce55d107d831c89f8395fb34c661b23324a0bc1c916e0c39ebb.jpg", + "image_caption": [ + "Degraded", + "Figure 3. All-in-one image restoration results. Top: image denoising, mid: image deraining, bottom: image dehazing." + ], + "image_footnote": [], + "bbox": [ + 506, + 196, + 602, + 242 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2e4fef983d0ee1af22d92cc6da75128ca64b263577c2f5dbcc3d9ec4503ffe08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 90, + 697, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f99c6316de07aea3a1724346fbe01d46696605216f06a828c8bc03c2140ab71d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 146, + 697, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/538e97884d78205c419e5c480968c5609e6df57af17f04d92bd5ae2e83239a00.jpg", + "image_caption": [ + "Label" + ], + "image_footnote": [], + "bbox": [ + 604, + 196, + 697, + 242 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7b8686d6006f54497fff179e1e90d84bb14c5eff0838e322c94589f794d8c4c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 90, + 795, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c1dd166a4118278af0b0ed459f2016274364616df2c17744a4c288801062b00b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 146, + 795, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cfdb9ee57bc86b0fcc1003d0dbb827d9f2f5ff87777cafb1e8cfc653ce4f1a26.jpg", + "image_caption": [ + "PromptIR [71]" + ], + "image_footnote": [], + "bbox": [ + 700, + 196, + 795, + 242 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/637aacf85a070b539830068ccabe151324f894d6f92b80d92e815b8b9854a6be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 90, + 893, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/090d30dc87e250f5bc0349d169196285b0974340c0015c2ff38f61a747001358.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 146, + 893, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2f44d661368b587a771a2c12359cc41c8b248cfdca67f9d6f55e6685880860fd.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 797, + 196, + 893, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and defocus image deblurring), (3) image dehazing [19], (4) image deraining [16], and (5) image denoising [111] (i.e., grayscale and color image denoising on Gaussian noise, and real-world image denoising).", + "bbox": [ + 498, + 294, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We adopt publicly released stable-diffusion-v2.1-base as our T2I generative model. $N$ is set to 20 in image-to-text mapper. Moreover, we employ the state-of-the-art methods as our image restoration backbone in different image restoration tasks: (1) we adopt PromptIR [71] in all-in-one image restoration, (2) we adopt NAFNet [14] and Restormer [111] in single-image motion deblurring, and Restormer [111] in defocus deblurring, (3) we adopt SFNet [19] in image dehazing, (4) we adopt DRSformer [16] in image deraining, (5) we adopt Restormer [111] in image denoising. The training settings of our guided restoration network are consistent with those of the corresponding backbone methods. Details of datasets, network architecture, and training hyperparameters are provided in Suppl.", + "bbox": [ + 498, + 354, + 890, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. All-in-One Restoration Results", + "text_level": 1, + "bbox": [ + 500, + 590, + 772, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [71], we adopt BSD400 [5] and WED [62] for color image denoising, Rain100L [27] for image deraining, and SOTS [49] for image dehazing. We train and evaluate the proposed method on these three tasks in all-in-one image restoration setting. The large difference among different degradations makes unifying multiple image restoration tasks into one unified network difficult, and thus the performance of existing all-in-one image restoration methods is limited. Compared with performing all-in-one restoration in the image level, it is much easier for us to conduct all-in-one restoration in the textual level. Once trained, our method can generate clean textual representation for different image restoration tasks, and thus we can synthesize guidance images for various types of degradation. Comparison results in Table 1 show that our method outperforms PromptIR [71] across all the benchmark datasets, achieving $+1.05$ dB PSNR on dehazing task, $+1.21$ dB PSNR on deraining task, and $+0.5$ dB PSNR on average improvement. As shown in Fig. 3, the prediction of the proposed method", + "bbox": [ + 498, + 613, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2870", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/de34989e8cfb669e9e53ada652065148572b34f5375b7e6db703b3733a0babc3.jpg", + "table_caption": [ + "Table 2. Motion image deblurring results. We train models with GoPro training data. We evaluate our method on GoPro, HIDE, RealBlur benchmark datasets. PSNR and SSIM scores are calculated on RGB-channels." + ], + "table_footnote": [], + "table_body": "
MethodGoPro [66]HIDE [84]RealBlur-R [79]RealBlur-J [79]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DBGAN [118]31.100.94228.940.91533.780.90924.930.745
MT-RNN [68]31.150.94529.150.91835.790.95128.440.862
DMPHN [113]31.200.94029.090.92435.700.94828.420.860
SPAIR [72]32.060.95330.290.931--28.810.875
MIMO-Unet+ [18]32.450.95729.990.93035.540.94727.630.837
IPT [12]32.52-------
MPRNet [110]32.660.95930.960.93935.990.95228.700.873
HINet [13]32.710.95930.320.932----
Uformer [93]32.970.967------
Restormer [111]32.920.96131.220.94236.190.95728.960.879
Ours-Restormer33.110.96231.260.94336.470.95929.170.875
NAFNet [14]33.690.96631.320.94333.620.94426.330.856
Ours-NAFNet33.970.96831.570.94633.870.95026.760.861
", + "bbox": [ + 80, + 152, + 496, + 335 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e5d6d16da12c2e313a1ea0823508f7e07ff77897cc9c10c4e6c90f6e124f4e45.jpg", + "table_caption": [ + "Table 3. Defocus image deblurring results. We train and evaluate methods on DPDD dataset [2]. $S$ denotes single-image defocus deblurring model. $D$ denotes dual-pixel defocus deblurring. PSNR and SSIM scores are calculated on RGB channels." + ], + "table_footnote": [], + "table_body": "
MethodIndoor ScenesOutdoor ScenesCombined
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
EBDBS[43]25.770.77221.250.59923.450.683
DMENetS[45]25.500.78821.430.64423.410.714
JNBS[85]26.730.82821.100.60823.840.715
DPDNetS[2]26.540.81622.250.68224.340.747
KPACS[86]27.970.85222.620.70125.220.774
IFANs[46]28.110.86122.760.72025.370.789
RestormerS[111]28.870.88223.240.74325.980.811
OursS29.110.88923.350.74826.150.817
DPDNetD[2]27.480.84922.900.72625.130.786
RDPD3[3]28.100.84322.820.70425.390.772
UformerD[93]28.230.86023.100.72825.650.795
IFAND[46]28.660.86823.460.74325.990.804
RestormerD[111]29.480.89523.970.77326.660.833
OursD29.620.89924.160.77526.820.835
", + "bbox": [ + 527, + 148, + 862, + 337 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4b91084df9a845fe7b3b3823b9fe7f178e132220c26220029af6be138c4d7a47.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 78, + 340, + 325, + 449 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/444eb028048aa47693017b97314d5530fc4343dceafde547d9995fa8ae9be0c8.jpg", + "image_caption": [ + "Degraded" + ], + "image_footnote": [], + "bbox": [ + 326, + 340, + 464, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ee6fb9a5780a8e4a38047e1cae1080580aa7bff528d49e310605783dfe7cda36.jpg", + "image_caption": [ + "Label" + ], + "image_footnote": [], + "bbox": [ + 465, + 340, + 602, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bd4ab74709442f9a54494af9e175733a7db89c114ec2e41661d73deba4ddb1a9.jpg", + "image_caption": [ + "DMPHN [113]" + ], + "image_footnote": [], + "bbox": [ + 604, + 340, + 743, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b0510d76d068cfe06138e9b07dd02e978d10681997ee89a53e177f43e53cbb3e.jpg", + "image_caption": [ + "MT-RNN [68]" + ], + "image_footnote": [], + "bbox": [ + 745, + 340, + 883, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e3f18f48ff0ec709f3fae0d66e118b3aced61e7df2ecb4b694e3ba2c3cbbf192.jpg", + "image_caption": [ + "Figure 4. Motion image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries.", + "Input image", + "Figure 5. Defocus image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries." + ], + "image_footnote": [], + "bbox": [ + 91, + 486, + 318, + 604 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a10cf74a2bee9ec5aff9ab08e246dac1267de0efa70ebdc83bf4f780766f5a1e.jpg", + "image_caption": [ + "Degraded" + ], + "image_footnote": [], + "bbox": [ + 320, + 487, + 455, + 539 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bba765f6a8aa6826b48af3f9e75403f0e9fe8ee892fae72e90f096c7b53c6a67.jpg", + "image_caption": [ + "Label" + ], + "image_footnote": [], + "bbox": [ + 457, + 487, + 594, + 539 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/af3c87b2acc9385826e9edde729ad94287893061aa2cc48c8a1ba05ab7fb317d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 487, + 730, + 539 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/32de0b3ead792b9925c885d9427d25062b3e293d2aec63fc4c67ba7924030052.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 732, + 487, + 867, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is finer and more detailed compared with PromptIR.", + "bbox": [ + 76, + 638, + 419, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Image Deblurring Results", + "text_level": 1, + "bbox": [ + 76, + 664, + 310, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Motion Deblurring. Following [14, 111], we train the proposed method on GoPro training data and evaluate our method on GoPro [66], HIDE [84], and real-world datasets (RealBlur-R [79] and RealBlur-J [79]). As shown in Table 2, benefiting from synthesized high-quality guidance, Ours-Restormer and Ours-NAFNet outperform the state-of-the-art methods on all four benchmark datasets. Our method achieves $+0.28$ dB PSNR improvement on GoPro testing data. The visual results in Fig. 4 show that our method can restore images with sharper boundaries and details, demonstrating its effectiveness.", + "bbox": [ + 75, + 688, + 468, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Defocus Deblurring. Following [111], we train and evaluate the proposed method on DPDD [2] dataset for single-image defocus deblurring and dual-pixel defocus deblur", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6e649a5e6bd3bf4532a569212d6f19546512e0fc77e9a70b04a8fd629c0eae48.jpg", + "image_caption": [ + "DMPHN [113]", + "Restormer [111]" + ], + "image_footnote": [], + "bbox": [ + 594, + 551, + 730, + 604 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0414d094787e7d111b58867aaaed95e7585111e3dfcd43d9fa6839f51304480e.jpg", + "image_caption": [ + "MPRNet [110]", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 732, + 551, + 867, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ring. From Table 3, compared with Restormer [111], our method achieves $+0.17$ dB PSNR and $+0.16$ dB PSNR gains on single-image defocus deblurring and dual-pixel defocus deblurring, respectively. As illustrated in Fig. 5, the prediction of our method shows a clearer structure.", + "bbox": [ + 496, + 638, + 890, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Image Dehazing Results", + "text_level": 1, + "bbox": [ + 500, + 736, + 720, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For image dehazing task, we conduct experiments on the synthetic benchmark RESIDE [49] dataset. We train the proposed method on indoor scene and outdoor scene data, and evaluate the performance on SOTS-indoor and SOTS-outdoor testing dataset [49] separately. Table 4 reports the quantitative comparison results. One can see that our method outperforms existing methods on both indoor and outdoor scenes, achieving $+0.24$ dB PSNR average improvement. Visual comparisons can be found in the Suppl.", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2871", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Image dehazing results. We separately train and evaluate our method indoor scene and outdoor scene. PSNR and SSIM scores are calculated on RGB-channels.", + "bbox": [ + 76, + 90, + 447, + 133 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/535032fb7a100131faf3050844d170753e6de05b3c338b8a241f7691724640a3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSOTS-Indoor [49]SOTS-Outdoor [49]
PSNR↑SSIM↑PSNR↑SSIM↑
DehazeNet [8]19.820.82124.750.927
AOD-Net [47]20.510.86124.140.920
GridDehazeNet [59]32.160.98430.860.982
MSBDN [25]33.670.98533.480.982
FFA-Net [73]36.390.98933.570.984
ACER-Net [95]37.170.990--
DeHamer [36]36.630.98835.180.986
MAXIM-2S [90]38.110.99134.190.985
PMNet [102]38.410.99034.740.985
DehazeFormer-L [88]40.050.996--
SFNet [19]41.240.99640.050.996
Ours41.480.99640.290.996
", + "bbox": [ + 106, + 142, + 423, + 319 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/39081979b92e0bb055457422b11f6150d7af14612ee3e1fead65e5b371204488.jpg", + "table_caption": [ + "Table 6. Grayscale image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level." + ], + "table_footnote": [], + "table_body": "
MethodSet12 [115]BSD68 [63]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
DnCNN [115]32.6730.3527.1831.6229.1626.2332.2829.8026.35
FFDNet [117]32.7530.4327.3231.6329.1926.2932.4029.9026.50
IRCNN [116]32.7630.3727.1231.6329.1526.1932.4629.8026.22
DRUNet [119]33.2530.9427.9031.9129.4826.5933.4431.1127.96
Restormer[111]33.3531.0428.0131.9529.5126.6233.6731.3928.33
Ours33.3531.3028.1331.9829.5826.7733.6231.4728.46
FOCNet [40]33.0730.7327.6831.8329.3826.5033.1530.6427.40
MWCNN [58]33.1530.7927.7431.8629.4126.5333.1730.6627.42
NLRN [57]33.1630.8027.6431.8829.4126.4733.4530.9427.49
RNAN [122]--27.70--26.48--27.65
DeamNet [77]33.1930.8127.7431.9129.4426.5433.3730.8527.53
DAGL [65]33.2830.9327.8131.9329.4626.5133.7931.3927.97
SwinIR [55]33.3631.0127.9131.9729.5026.5833.7031.3027.98
Restormer [111]33.4231.0828.0031.9629.5226.6233.7931.4628.29
Ours33.4731.1528.1231.9229.6726.7833.7831.5828.38
", + "bbox": [ + 80, + 378, + 439, + 588 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ee373afe9d346fffe7daa52dadd4445cc78bcba3e09a7e0e1be36c8fb4eb4ba2.jpg", + "table_caption": [ + "le 5. Image deraining results. We separately train and evaluate our hod on Rain200H, Rain200L, DID-Data, and DDN-Data. PSNR and M scores are calculated on Y channel in YCbCr color space." + ], + "table_footnote": [], + "table_body": "
MethodRain200L [101]Rain200H [101]DID-Data [112]DDN-Data [29]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DDN [28]34.680.96726.050.80530.970.91130.000.904
RESCAN [53]36.090.96726.750.83533.380.94131.940.935
PReNet [78]37.800.98129.040.89933.170.94832.600.946
MSPFN [41]38.530.98329.360.90333.720.95532.990.933
RCDNet [91]39.170.98930.240.90434.080.95333.040.947
MPRNet [110]39.470.98230.670.91133.990.95933.100.935
DualGCN [30]40.730.98931.150.91234.370.96233.010.949
SPDNet [103]40.500.98831.280.92034.570.95633.150.946
Uformer [93]40.200.98630.800.91035.020.96233.950.955
Restormer [111]40.990.98932.000.93235.290.96434.200.957
IDT [98]40.740.98832.100.93434.890.96233.840.955
DRSformer [16]41.210.98932.160.93335.240.96234.230.955
Ours41.590.99031.970.93135.460.96434.570.958
", + "bbox": [ + 457, + 132, + 890, + 321 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/90f59b25852e15a294bdcdb95ef174527f0a8dcbb307329ca589d492f9e5fad2.jpg", + "table_caption": [ + "Table 7. Color image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level. PSNR is calculated on RGB channels." + ], + "table_footnote": [], + "table_body": "
MethodCBSD68 [64]Kodak24McMaster [120]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
IRCNN [116]33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [117]33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [115]33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [70]33.9131.2828.0534.6332.1629.0534.6732.4029.28---
DRUNet [119]34.3031.6928.5135.3132.8929.8635.4033.1430.0834.8132.6029.61
Restormer [111]34.3931.7828.5935.4433.0230.0035.5533.3130.2935.0632.9130.02
Ours34.3731.8728.6835.5233.1330.1535.6233.3830.4035.0332.9730.19
RPCNN [97]-31.2428.06-32.3429.25-32.3329.33-31.8128.62
BRDNet [89]34.1031.4328.1634.8832.4129.2235.0832.7529.5234.4231.9928.56
RNAN [122]--28.27--29.58--29.72--29.08
RDN [123]--28.31--29.66-----29.38
IPT [12]--28.39--29.64--29.98--29.71
SwinIR [55]34.4231.7828.5635.3432.8929.7935.6133.2030.2235.1332.9029.82
Restormer [111]34.4031.7928.6035.4733.0430.0135.6133.3430.3035.1332.9630.02
Ours34.4831.9728.8335.5833.2130.2335.7533.5630.4635.1133.1330.27
", + "bbox": [ + 447, + 377, + 900, + 588 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e01b55f9fcba6967de203a6313016f39c9572bef0b206d41b5f939ee2521871.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 78, + 598, + 218, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7a643d8d8de13c3d9f4722faaf2773ac91e7b7ae3071ccffa327553abfa04305.jpg", + "image_caption": [ + "Degraded" + ], + "image_footnote": [], + "bbox": [ + 218, + 598, + 312, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f96d21c006d55ae8dc92c72acaca4c8d3c24986299a24e428e41fcd628b1d39a.jpg", + "image_caption": [ + "Label" + ], + "image_footnote": [], + "bbox": [ + 313, + 598, + 406, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/87aa146a92f96f7e2110b9f4d0c734fb13c7a3390e732ea8223addcd38c69482.jpg", + "image_caption": [ + "RDN [123]" + ], + "image_footnote": [], + "bbox": [ + 408, + 598, + 500, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/52a3d48235e761093100993fcd0dd1e14992b02ac1fec36cc12aaa42203fed12.jpg", + "image_caption": [ + "RNAN [122]" + ], + "image_footnote": [], + "bbox": [ + 501, + 598, + 594, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9fd21e6c0e43a564b52b9f92e6f5f2a483dcb95d225e2e221746229b03f19122.jpg", + "image_caption": [ + "SwinIR [55]" + ], + "image_footnote": [], + "bbox": [ + 594, + 598, + 687, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/58a696a653e7dda2686a82f76b4ae1ed824af9ea0d7b90796ca131e24bd6e7e1.jpg", + "image_caption": [ + "Restormer [111]" + ], + "image_footnote": [], + "bbox": [ + 692, + 598, + 787, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/865e55f77af705b27b0e4862f49424320d896002ee95c46157fa93eba854ea45.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 790, + 598, + 883, + 665 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8660514c930676c545e11cd67c250950f3b6d8d0eed840d1ed560c114fb2c3f3.jpg", + "image_caption": [ + "Figure 6. Color image denoising results on Gaussian noise. Compared with others, the proposed method can obtain finer results.", + "Input image", + "Figure 7. Grayscale image denoising results on Gaussian noise. Our method can restore detailed results especially in texture regions." + ], + "image_footnote": [], + "bbox": [ + 78, + 705, + 184, + 777 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba8fb1754ce1d2086413ab2e175da4377b286264c6732424a853ab91c59c1506.jpg", + "image_caption": [ + "Degraded" + ], + "image_footnote": [], + "bbox": [ + 186, + 705, + 285, + 773 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d17c5c67ef740266854c6f5a23f26e391ca28e6a31543c23d43254c981d9e81.jpg", + "image_caption": [ + "Label" + ], + "image_footnote": [], + "bbox": [ + 285, + 705, + 385, + 773 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7aba0ea0246a0dde027a718b874f28afe39dccda43faabdfb56da2030feb0253.jpg", + "image_caption": [ + "DeamNet [77]" + ], + "image_footnote": [], + "bbox": [ + 385, + 705, + 483, + 773 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0b9ecfc5ad3c1d98804b51fc2ef703306818f9e34c22a4a41a413c9da750e701.jpg", + "image_caption": [ + "RNAN [122]" + ], + "image_footnote": [], + "bbox": [ + 485, + 705, + 584, + 773 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38d137aa6e4c8113f19011fdcce0d4c33cced812624acf9b17c442906f4c71e6.jpg", + "image_caption": [ + "SwinIR [55]" + ], + "image_footnote": [], + "bbox": [ + 586, + 705, + 684, + 773 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/721c232f8acb41c9e6613aac0ab2368e5b77b9b7cd564f0bd54a163fd3b14c94.jpg", + "image_caption": [ + "Restormer [111]" + ], + "image_footnote": [], + "bbox": [ + 684, + 705, + 784, + 773 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/924be009daa1f576958ad0fb703868116f5a90b0c93fd0b3c95172ab4712e2b0.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 785, + 705, + 883, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Image Deraining Results", + "text_level": 1, + "bbox": [ + 76, + 819, + 303, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following [16], we train and evaluate the proposed method separately on Rain200L [101], Rain200H [101], DIDData [112], and DDN-Data [29] datasets. From Table 5,", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "our method achieves $+0.31$ dB PSNR average improvement on Rain200L, DID-Data,and DDN-Data against DRSformer [16].On the Rain200H dataset, we only have comparable performance, as its severe rain streak may interfere with the dynamic aggregation process between the guidance", + "bbox": [ + 498, + 819, + 890, + 895 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2872", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d08abb0fb43783bdb15adcf0fa5259ef6b881d1509d8223730e4b0f78422bc29.jpg", + "table_caption": [ + "Table 8. Real-world image denoising results. We train and evaluate our mehtod on SIDD [1] datasets. * denotes methods using additional training data. PSNR and SSIM scores are calculated on RGB channels." + ], + "table_footnote": [], + "table_body": "
DatasetMethodDnCNN [115]BM3D [20]CBDNet* [37]RIDNet* [4]AINDNet* [44]VDN [105]SADNet* [11]DANet+* [106]CycleISP* [107]MIRNet [108]DeamNet* [77]MPRNet [110]DAGL [65]Uformer [93]Restormer [111]Ours
SIDD [1]PSNR ↑23.6625.6530.7838.7139.0839.2839.4639.4739.5239.7239.4739.7138.9439.7740.0240.09
SSIM ↑0.5830.6850.8010.9510.9540.9560.9570.9570.9570.9590.9570.9580.9530.9590.9600.960
", + "bbox": [ + 84, + 121, + 888, + 176 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/49e4f1a94513f509ef691dfe7314273401bd40c98bcd70a2408d9f65f24723e3.jpg", + "table_caption": [ + "Table 9. Effect of ${\\mathbf{E}}_{txt}$ with different $N$ ." + ], + "table_footnote": [], + "table_body": "
MethodbaselineN=5N=10N=20N=30N=40
PSNR↑30.1631.1331.3631.5731.5131.60
SSIM↑0.9320.9410.9450.9470.9470.948
", + "bbox": [ + 94, + 198, + 372, + 248 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/379b86a3e085b7a4f66d444e5604e4ce42d4d8adda3288262b9050b7f067e692.jpg", + "table_caption": [ + "Table 10. Effect of integration strategy." + ], + "table_footnote": [], + "table_body": "
MethodbaselineEnc.Dec.Enc. & Dec.
PSNR↑30.1631.3730.3131.57
SSIM↑0.9320.9460.9340.947
", + "bbox": [ + 403, + 200, + 629, + 247 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2d7d9c3f1c87d942699b4b28b7f46a69b975c8b98fc93295434f163b27dbe391.jpg", + "table_caption": [ + "Table 11. Effect of generated guidance." + ], + "table_footnote": [], + "table_body": "
Methodbaselineonly I2TDegra.BLIP2Ours
PSNR↑30.1630.1030.1330.3431.57
SSIM↑0.9320.9290.9310.9400.947
", + "bbox": [ + 643, + 199, + 893, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "information and the degraded images. Visual comparisons of deraining results will be provided in the Suppl.", + "bbox": [ + 76, + 258, + 468, + 291 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Image Denoising Results", + "text_level": 1, + "bbox": [ + 76, + 299, + 302, + 315 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Image Denoising on Gaussian Noise. Following [111], we train the blind denoising model ( $\\sigma$ with range of $[0, 50]$ ) and non-blind denoising models ( $\\sigma = 15, 25, 50$ ) for grayscale and color image denoising on Gaussian noise. We train the proposed method on DFBW dataset with synthetic noise degradation. For grayscale image denoising, we evaluate our method on Set12 [115], BSD68 [64], and Urban100 [39]. For color image denoising, we evaluate our method on CBSD68 [64], Kodak24, McMaster [120], and Urban100 [39]. As shown in Table 6 and Table 7, our method achieves comparable performance with baseline on low noise-level ( $\\sigma = 15$ ), while our method outperforms baseline when noise becomes heavier, e.g., achieving $+0.25$ dB PSNR gain on Urban100 [39] with Gaussian color noise $\\sigma = 50$ . Qualitative comparisons in Fig. 6 and Fig. 7 show that our method can restore finer texture and sharper boundaries while other methods tend to generate smoother results.", + "bbox": [ + 75, + 321, + 468, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real-World Image Denoising. Furthermore, We train and evaluate the proposed method on real-world denoising dataset SIDD [1]. From Table 8, although Restormer [111] has already achieved superior performance on real-world denoising task, our method can also bring $+0.07$ dB PSNR improvement, demonstrating its effectiveness. Visual comparison results can be found in Suppl.", + "bbox": [ + 75, + 579, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 696, + 240, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In ablation studies, we adopt NAFNet with 32 channels as our baseline. We train and evaluate each method on GoPro datasets.", + "bbox": [ + 76, + 719, + 468, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of $\\mathbf{E}_{\\text {txt }}$ with different $N$ . In our method, we use the number of words $N$ to control the representation ability of $\\mathbf{E}_{\\text {txt }}$ , which is used as condition information to generate guidance. We conduct the experiments on five settings, i.e., $N = 5, 10, 20, 30, 40$ . As shown in Table 9, the restoration performance generally improves from $N = 5$ to $N = 40$ , as more informative textual descriptions can help T2I model generate more faithful guidance. Since the performance only improves slightly when $N$ is larger than 20, we finally", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "set $N$ to 20 to make a trade-off between performance and computational cost.", + "bbox": [ + 496, + 258, + 890, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Integrating Strategy. To evaluate the effect of different guidance integrating strategies, we conduct experiments by integrating guidance information into different modules of image restoration networks, i.e., Enc. (encoder only), Dec. (decoder only), and Enc. & Dec. (both encoder and decoder). As shown in Table 10, the experimental results show that integrating guidance information into both encoder and decoder achieves better performance.", + "bbox": [ + 496, + 289, + 892, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Proposed Modules. To validate the effectiveness of our proposed modules, we conduct comparison with only using I2T mapper ('only I2T'), using explicit representation ('BLIP2'), and replacing guidance with degraded input ('Degra.') From comparison results in Table 11, since 'only I2T' and 'Degra.' cannot provide clean information to restoration process, they fail to obtain improvement upon baseline. Since using explicit representation ('BLIP2') cannot keep the content information of input as good as ours, our method can gain more from guidance. Guidance comparisons of 'only I2T', 'BLIP2', and ours can be found in Suppl.", + "bbox": [ + 496, + 409, + 892, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 599, + 617, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we provide a new perspective for image restoration. Considering that content and degradation are tightly coupled in image representation, while decoupled in textual representation. Rather than direct restoration on image level, we suggest conducting restoration on textual level and in turn utilizing the restored textual content to assist image restoration. To this end, we propose a plug-and-play approach that first encodes degraded images into degraded textual representations and then removes textual degradation information to obtain restored textual representations. Conditioned on the representations, we employ a pre-trained T2I model to synthesize clean guidance images for improving image restoration. We evaluate our method on various image restoration tasks. The experimental results demonstrate it outperforms the state-of-the-art ones.", + "bbox": [ + 496, + 626, + 890, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. U22B2035 and No. 62371164.", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2873", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S. Brown. A high-quality denoising dataset for smartphone cameras. In CVPR, pages 1692-1700, 2018. 8", + "[2] Abdullah Abuolaim and Michael S. Brown. Defocus deblurring using dual-pixel data. 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In CVPR, pages 21747-21758, 2023. 1, 3" + ], + "bbox": [ + 78, + 90, + 467, + 473 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "2878", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_model.json b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_model.json new file mode 100644 index 0000000000000000000000000000000000000000..71c9806bf7c871b920e3e8ca03315ca1c7083862 --- /dev/null +++ b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_model.json @@ -0,0 +1,3790 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.226, + 0.131, + 0.745, + 0.177 + ], + "angle": 0, + "content": "Improving Image Restoration through Removing Degradations in Textual Representations" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.203, + 0.918, + 0.24 + ], + "angle": 0, + "content": "Jingbo Lin\\(^{1}\\), Zhilu Zhang\\(^{1}\\), Yuxiang Wei\\(^{1}\\), Dongwei Ren\\(^{1,*}\\), Dongsheng Jiang\\(^{2}\\), Qi Tian\\(^{2}\\), Wangmeng Zuo\\(^{1}\\), Harbin Institute of Technology \\({}^{2}\\)Huawei Cloud Computing Co., Ltd." + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.242, + 0.812, + 0.258 + ], + "angle": 0, + "content": "jb1ncs1996@gmail.com, cszlzhang@outlook.com, yuxiang.wei.cs@gmail.com," + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.26, + 0.908, + 0.275 + ], + "angle": 0, + "content": "rendongweihit@gmail.com, dongsheng_jiang@outlook.com, tian.qil@huawei.com, cswmzuo@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.473, + 0.718 + ], + "angle": 0, + "content": "In this paper, we introduce a new perspective for improving image restoration by removing degradation in the textual representations of a given degraded image. Intuitively, restoration is much easier on text modality than image one. For example, it can be easily conducted by removing degradation-related words while keeping the content-aware words. Hence, we combine the advantages of images in detail description and ones of text in degradation removal to perform restoration. To address the cross-modal assistance, we propose to map the degraded images into textual representations for removing the degradations, and then convert the restored textual representations into a guidance image for assisting image restoration. In particular, We ingeniously embed an image-to-text mapper and text restoration module into CLIP-equipped text-to-image models to generate the guidance. Then, we adopt a simple coarse-to-fine approach to dynamically inject multiscale information from guidance to image restoration networks. Extensive experiments are conducted on various image restoration tasks, including deblurring, dehazing, detraining, and denoising, and all-in-one image restoration. The results showcase that our method outperforms state-of-the-art ones across all these tasks. The codes and models are available at https://github.com/mrluin/TextualDegRemoval." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.747, + 0.21, + 0.763 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.773, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Image restoration aims to reconstruct a high-quality clean image from its degraded observations. Most existing methods design deep networks for specific restoration tasks, including image denoising [55, 111, 115, 117, 119], deblurring [13, 14, 18, 93, 110], deraining [16, 93, 98, 110], dehazing [8, 19, 36, 88, 90], etc. Recent works [15, 50, 69, 71, 114, 124] expect to explore a unified model for multiple" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.311, + 0.892, + 0.386 + ], + "angle": 0, + "content": "degradations. However, the severely ill-posed nature of the task makes it non-trivial to separate degradations and desired image content. Especially for unified models, the potential conflicts in dealing with various degradations bring more uncertainty." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.893, + 0.658 + ], + "angle": 0, + "content": "From a broader perspective, the purpose of the restoration is to enhance the clarity of scenes for human perception and recognition, while performing it on image modality is just one option. Moreover, degradations in image modality are tightly coupled with desirable content, making their removal challenging. When recording the scenes in some other modalities, this problem can be alleviated. Let us take the text modality as an example. Assume the textual description of a clean scene is represented by 'a scene of *'. When this scene is subjected to rainfall, the description can be converted into 'a rainy scene of *'. Thus, deraining can be readily achieved by simply removing the rain-related text 'rainy'. Furthermore, it is also convenient to remove multiple degradations in textual space with one unified model. Note that text modality may only describe rough aspects and ignore some details. We can further introduce image modality to combine their complementary potential in degradation removal and image restoration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Motivated by the above, we propose to perform restoration first in a modality where degradations and content are loosely coupled, and then utilize the corrected content to guide image restoration. In particular, we adopt the commonly used textual modality. Note that the text corresponding to the scene is not always available and the cross-modal assistance is difficult to achieve directly. The gap between text and image should be bridged. First, degraded images should be mapped into textual space for removing degradations. Second, the restored text should be mapped into a guidance image to assist restoration of the degraded image. As shown in Fig. 1, for the former, we have tried to convert degraded images to textual captions by image-to-text (I2T) models (e.g., BLIP [51, 52]), and find the captions can explicitly express both degradation types (e.g., blur, rain, haze, and noise) and content information. For the latter, we can" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.23, + 0.9 + ], + "angle": 0, + "content": "*Correspondence author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "2866" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.885, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.348, + 0.895, + 0.406 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed method. We propose to improve image restoration by performing restoration on the textual level, in which content and degradation information are loosely coupled. We first encode image concepts into textual space and then remove degradation-related information. To achieve cross-modal assistance, we employ pre-trained T2I models to generate clean guidance for the image restoration process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.471, + 0.455 + ], + "angle": 0, + "content": "utilize the text-to-image (T2I) models (e.g.,Imagen [82]), which have demonstrated impressive image generation capability from the given texts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.732 + ], + "angle": 0, + "content": "Although such a scheme is conceptually feasible, converting to explicit text may lose a lot of information from images, and additional degraded-clean text pairs need to be collected to train the text restoration module. Fortunately, Contrastive Language-Image Pre-training (CLIP) [74] implicitly aligns concepts of images and text. And we can leverage the CLIP-equipped T2I models (e.g., Stable Diffusion [81]) to build an end-to-end framework for generating clear guidance from degraded images gracefully. Specifically, CLIP has been demonstrated as an effective I2T converter [23]. For converting degraded images into degraded textual representations, we adopt the image encoder of CLIP, and add an I2T mapper after the encoder. For restoring degraded representations, we further append a textual restoration module after I2T mapper. Then, I2T mapper and textual restoration module can be sequentially trained by employing paired data from different image restoration datasets, without additional text data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Due to the ease of removing degradations on textual level, we train the I2T mapper and textual restoration module with multiple degradations at once. When training is done, it can serve multiple tasks, generating content-related and degradation-free guidance images from degraded images. Finally, we adopt a simple coarse-to-fine approach to dynamically inject multi-scale information from guidance to classic image restoration networks. Extensive experiments are conducted on multiple tasks, including all-in-one restoration, image debunking, dehazing, deraining, and denoising. The results show our method achieves better uni-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.455 + ], + "angle": 0, + "content": "versally than corresponding state-of-the-art methods. Especially for all-in-one restoration, 0.5 dB PSNR improvement is obtained in comparison with PromptIR [71]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.456, + 0.882, + 0.47 + ], + "angle": 0, + "content": "The main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.472, + 0.892, + 0.533 + ], + "angle": 0, + "content": "- We introduce a new perspective for image restoration, i.e., performing restoration first in textual space where degradations and content are loosely coupled, and then utilizing the restored content to guide image restoration." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.533, + 0.892, + 0.593 + ], + "angle": 0, + "content": "- To address the cross-modal assistance, we propose to embed an image-to-text mapper and textual restoration module into CLIP-equipped text-to-image models to generate clear guidance from degraded images." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.593, + 0.892, + 0.638 + ], + "angle": 0, + "content": "- Extensive experiments on multiple tasks demonstrate that our method improves the performance of state-of-the-art image restoration networks." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.472, + 0.892, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.642, + 0.671 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.681, + 0.696 + ], + "angle": 0, + "content": "2.1. Image Restoration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Image Restoration for Specific Tasks. Image restoration is a fundamental computer vision problem, which aims to reconstruct high-quality images from corresponding degraded inputs. In recent years, deep learning has achieved great progress in image restoration. Starting from some simple convolutional neural networks (CNNs) [24, 115], the introduction of channel-attention [121], spatial-attention [35, 109], non-local operation [57, 122], skip-connection architectures [54, 109] and multi-stage scheme [93, 110] enables image restoration performance continuously improve. With the emergence of vision transformers [26, 60], the capability of capturing long-range dependencies in the image allows transformer-based" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2867" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.087, + 0.874, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.411, + 0.175, + 0.553, + 0.187 + ], + "angle": 0, + "content": "(a) Guidance Generation" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.185, + 0.871, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.407, + 0.296, + 0.581, + 0.309 + ], + "angle": 0, + "content": "(b) Guided Image Restoration." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.31, + 0.893, + 0.352 + ], + "angle": 0, + "content": "Figure 2. Illustration of the proposed pipeline. (a) We sequentially train image-to-text mapper \\(\\mathcal{M}_{i2t}\\) and textual restoration module \\(\\mathcal{M}_{clean}\\) to convert image concepts into textual representations and remove textual degradation information, respectively. (b) The guidance image is used to assist the image restoration process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.469, + 0.477 + ], + "angle": 0, + "content": "methods to achieve better performance, gradually replacing previous CNN-based methods. To balance computational cost, window-based attention [17, 55] and transposed attention [111] are also introduced into image restoration tasks. Albeit image restoration performance has benefited from various advanced architecture designs, most of the works only focus on one specific degradation, due to the difficulty of learning to remove multiple degradations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.902 + ], + "angle": 0, + "content": "All-in-One Image Restoration. Promoting by the development of unified model, some works focus on the solution to the all-in-one image restoration [15, 50, 69, 71, 114, 124]. The first all-in-one image restoration work, i.e., IPT [12], employs ViT-based backbone with multi-heads and multi-tails for inputs with different degradations. However, the method is limited in handling specific synthesized degradations and cannot directly generalize to unknown tasks. AirNet [50] develops the unified model for denoising-deraining-dehazing, which utilizes contrastive learning to capture degradation representations of different tasks and adaptively injects the degradation priors into backbone restoration framework for aiding in learning better results. ADMS [69] exploits FAIG [99] in all-in-one image restoration, by learning specific filters and degradation classifiers, achieving better performance on deraining-denoising-deblurring and deraining-desnowing-dehazing tasks. IDR [114] proposes a two-stage training strategy, which first learns separate task-oriented hubs for each degradation. Then, in the second stage, it reformulates the learned hubs into a single ingredient-oriented hub by learnable PCA and adopts the reformulated hub as prior to adaptively aid in restoring corrupted images. PromptIR [71] learns to encode and adopt degradation information as prompts for dehazing-deraining-denoising task. Although existing works can unify a set of image restoration tasks into one unified model, the performance is still limited caused by the large gap among different degradations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.508 + ], + "angle": 0, + "content": "Prior-Based Image Restoration. Prior-based restoration aims at improving performance by introducing external priors, including structures, images, pre-trained models, etc. For instance, some works [9, 42, 61] adopt information from the high-resolution reference image to help improve the performance of super-resolution. Recent works [56, 92, 100] utilize pre-trained generative priors to restore more realistic and natural results. TextIR [6] develops a text-driven image restoration framework by incorporating information on textual representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.584 + ], + "angle": 0, + "content": "In this work, we provide a new perspective, i.e., utilizing restoration in textual space to assist image restoration. We also combine the advantages of both text-based prior (by learning degradations in textual level) and image-based prior (by giving clean guidance) for better performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.736, + 0.607 + ], + "angle": 0, + "content": "2.2. Text-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Text-to-image generation models [22, 31, 67, 75, 76, 83, 96] have attracted intensive attention in recent years due to its ability to generate high-quality and diverse images based on given text descriptions. A variety of techniques, including generative adversarial networks (GAN) [34], autoregressive models, and diffusion models have been investigated. Initial studies [48, 83, 96] mainly rely on GAN-based architectures, and train a conditional model from given paired image-caption datasets to generate samples. Some efforts focus on autoregressive models [10, 21, 31, 75, 104] have also shown exciting results. These models, such as CogView [21] and Muse [10] first learn a discrete codebook through training an autoencoder, and then adopt an autoregressive transformer to predict the tokens sequentially. With the development of diffusion models [38, 87], text conditioned image synthesis has shown remarkable improvement. By training with huge corpora, large diffusion models, such as DALLE-2 [76], Imagen [82], Stable Diffusion [80], and DALLE-3 [7] have demonstrated excel" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2868" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "lent semantic understanding, and can generate diverse and photo-realistic images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.134, + 0.251, + 0.151 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.159, + 0.473, + 0.432 + ], + "angle": 0, + "content": "In this section, we present our proposed method for image restoration. As illustrated in Fig. 2, we suggest first conducting restoration in the textual modality, in which degradation is loosely coupled with the content and can be easily removed. Then we in turn utilize the restored results as guidance to improve image restoration. Specifically, in Sec. 3.2, we propose an image-to-text mapper \\(\\mathcal{M}_{i2t}\\) and a textual restoration module \\(\\mathcal{M}_{clean}\\) to extract the degradation-free textual representations \\(\\mathbf{E}_{txt}^{\\prime}\\) from degraded images \\(\\mathbf{X} \\in \\mathbb{R}^{H \\times W \\times 3}\\). Then with a pre-trained T2I model, we can generate a guidance image \\(\\mathbf{G} \\in \\mathbb{R}^{H \\times W \\times 3}\\) that is related to the content of \\(\\mathbf{X}\\) but free of degradation. In Sec. 3.3, to leverage clean content information from \\(\\mathbf{G}\\) for enhancing image restoration performance, we introduce a coarse-to-fine approach that dynamically incorporates multi-scale information from guidance \\(\\mathbf{G}\\) into restoration frameworks. Besides, we first give a preliminary knowledge of the T2I model in Sec. 3.1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.44, + 0.208, + 0.456 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.601 + ], + "angle": 0, + "content": "In this work, we employ Stable Diffusion [81] as our text-to-image model. Stable Diffusion pretrains an autoencoder \\((\\mathcal{E}(\\cdot),\\mathcal{D}(\\cdot))\\) to map the input image \\(\\mathbf{X}\\) into a lower dimensional latent space by \\(\\mathbf{z} = \\mathcal{E}(\\mathbf{X})\\). The decoder \\(\\mathcal{D}(\\cdot)\\) learns to map the latent code back to the image as \\(\\mathcal{D}(\\mathcal{E}(\\mathbf{X}))\\approx \\mathbf{X}\\). Then, the conditional diffusion model \\(\\epsilon_{\\theta}(\\cdot)\\) is trained on the latent space to generate latent codes based on text condition \\(\\mathbf{p}\\). To train the diffusion model, simple mean-squared loss is adopted as," + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.607, + 0.469, + 0.642 + ], + "angle": 0, + "content": "\\[\nL _ {L D M} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathcal {E} (\\mathbf {X}), \\mathbf {p}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\tau_ {\\theta} ^ {t} (\\mathbf {p})\\right) \\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.469, + 0.719 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) denotes the unscaled noise, \\(t\\) is the timestep, \\(\\mathbf{z}_t\\) is the latent noised to time \\(t\\), and \\(\\tau_{\\theta}^{t}(\\cdot)\\) represents the pretrained CLIP [74] text encoder. During inference, a random Gaussian noise \\(\\mathbf{z}_T\\) is iteratively denoised to \\(\\mathbf{z}_0\\), and the final image is obtained through the decoder \\(\\mathbf{X}' = \\mathcal{D}(\\mathbf{z}_0)\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.421, + 0.743 + ], + "angle": 0, + "content": "3.2. Degradation-Free Guidance Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Image captioning models (e.g., BLIP2 [52]) can generate text descriptions of degraded images, which can be taken into the text restoration module and text-to-image models to reconstruct clean guidance images. However, such descriptions may lose too many details, resulting in severely inconsistent content between the guidance and the input images. To address these problems, we propose an image-to-text mapper \\(\\mathcal{M}_{i2t}\\) to encode the degraded image \\(\\mathbf{X}\\) as implicit textual representations \\(\\mathbf{E}_{txt}\\) rather than explicit texts, which can be used to reconstruct the content more faithfully." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "Then, we utilize a textual restoration module \\(\\mathcal{M}_{clean}\\) to remove the degradation from \\(\\mathbf{E}_{txt}\\) and obtain degradation-free textual representations \\(\\mathbf{E}_{txt}^{\\prime}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.259 + ], + "angle": 0, + "content": "Image-to-Text Mapping. Following [94], we adopt the textual word embedding space of CLIP [74] as the target space in image-to-text mapping. Benefiting from the aligned vision-language feature space of CLIP, we first adopt pre-trained CLIP image encoder \\(\\tau_{\\theta}^{i}(\\cdot)\\) to encode input \\(\\mathbf{X}\\) into CLIP image embedding \\(\\mathbf{E}_{img}\\). Then, we propose an image-to-text mapper \\(\\mathcal{M}_{i2t}\\) to project CLIP image embedding into textual word embedding \\(\\mathbf{E}_{txt}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.271, + 0.892, + 0.288 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} _ {t x t} = \\mathcal {M} _ {i 2 t} \\left(\\tau_ {\\theta} ^ {i} (\\mathbf {X})\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.36 + ], + "angle": 0, + "content": "where \\(\\mathbf{E}_{\\text{txt}} \\in \\mathbb{R}^{N \\times D}\\) and \\(D\\) is the dimension of textual word embedding. \\(N\\) is the number of learned words. To make the obtained word embedding describe more details of the input image, we set \\(N\\) to a large number (e.g., \\(N = 20\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.497 + ], + "angle": 0, + "content": "Textual Restoration. Although \\(\\mathcal{M}_{i2t}\\) can project images into the textual word embedding space, the projected textual word embedding will include corresponding degradation information if input \\(\\mathbf{X}\\) is degraded. Condition on the degraded textual word embedding, the synthesized guidance inevitably reflects the corresponding degradation pattern. Therefore, we further propose a textual restoration module \\(\\mathcal{M}_{clean}\\) to remove the degradation information from the textual word embedding \\(\\mathbf{E}_{txt}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.509, + 0.891, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} _ {t x t} ^ {\\prime} = \\mathcal {M} _ {c l e a n} (\\mathbf {E} _ {t x t}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.599 + ], + "angle": 0, + "content": "where \\(\\mathbf{E}_{txt}^{\\prime}\\) denote the restored textual representations. When feeding \\(\\mathbf{E}_{txt}^{\\prime}\\) into Stable Diffusion, we can obtain a degradation-free image \\(\\mathbf{G}\\), which has similar content as \\(\\mathbf{X}\\) but is free of degradation, as shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Model Optimization. During training, the image-to-text mapper \\(\\mathcal{M}_{i2t}\\) and textual restoration module \\(\\mathcal{M}_{clean}\\) are optimized sequentially. In the first training stage, we collect both clean and degraded images from different restoration tasks as training data. We adopt Eq. (1) as a loss function, which constrains the diffusion model to reconstruct clean and degraded images conditioning on their own projected embedding \\(\\mathbf{E}_{txt}\\). In the second training stage, we use pairs of degraded-clean images from different image restoration datasets as training data. Based on pre-trained \\(\\mathcal{M}_{i2t}\\), we further deploy \\(\\mathcal{M}_{clean}\\) to remove degradation-related concepts from degraded embedding \\(\\mathbf{E}_{txt}\\), obtaining \\(\\mathbf{E}_{txt}^{\\prime}\\). We still adopt Eq. (1), which constrains the diffusion model to reconstruct clean images conditioning on restored embedding \\(\\mathbf{E}_{txt}^{\\prime}\\). Note that, due to the ease of removing degradations in the textual space, it is feasible to train \\(\\mathcal{M}_{i2t}\\) and \\(\\mathcal{M}_{clean}\\) with multiple degradations simultaneously. When training is done, it can serve multiple image restoration tasks, generating content-related and degradation-free guidance images \\(\\mathbf{G}\\) from degraded images" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2869" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.145 + ], + "angle": 0, + "content": "Table 1. All-in-one image restoration results. Following PromptIR [71], we train and evaluate the proposed method in all-in-one image restoration task, our method outperforms PromptIR across all the benchmark datasets." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.148, + 0.477, + 0.261 + ], + "angle": 0, + "content": "
MethodDehazing on SOTSDerain on Rain100LDenoise on BSD68Average
σ = 15σ = 25σ = 50
BRDNet [89]23.23/0.89527.42/0.89532.26/0.89829.74/0.83626.34/0.83627.80/0.843
LPNet [33]20.84/0.82824.88/0.78426.47/0.77824.77/0.74821.26/0.55223.64/0.738
FDGAN [32]24.71/0.92429.89/0.93330.25/0.91028.81/0.86826.43/0.77628.02/0.883
MPRNet [110]25.28/0.95433.57/0.95433.54/0.92730.89/0.88027.56/0.77930.17/0.899
DL [27]26.92/0.39132.62/0.93133.05/0.91430.41/0.86126.90/0.74029.98/0.875
AirNet [50]27.94/0.96234.90/0.96733.92/0.93331.26/0.88828.00/0.79731.20/0.910
PromptIR [71]30.58/0.97436.37/0.97233.98/0.93331.31/0.88828.06/0.79932.06/0.913
Ours31.63/0.98037.58/0.97934.01/0.93331.39/0.89028.18/0.80232.56/0.916
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.47, + 0.306 + ], + "angle": 0, + "content": "with one unified model (as shown in Fig. 1). More training details can be seen in the Suppl." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.314, + 0.266, + 0.329 + ], + "angle": 0, + "content": "3.3. Guided Restoration" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.469, + 0.426 + ], + "angle": 0, + "content": "Although guidance image \\(\\mathbf{G}\\) is clean, it is inevitable that there are content differences between \\(\\mathbf{G}\\) and degraded image \\(\\mathbf{X}\\). Simplyfusing the features of \\(\\mathbf{G}\\) and \\(\\mathbf{X}\\) is not enough to improve image restoration. Instead, we suggest a dynamic aggregation module to extract and exploit helpful information from \\(\\mathbf{G}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.47, + 0.625 + ], + "angle": 0, + "content": "Dynamic Aggregation. First, we perform feature matching [61] between the guidance \\(\\mathbf{G}\\) and given degraded image \\(\\mathbf{X}\\). Specifically, we use a shared image encoder to extract multi-scale features for \\(\\mathbf{X}\\) and \\(\\mathbf{G}\\), named \\(\\mathbf{F}_x\\) and \\(\\mathbf{F}_g\\), respectively. According to the similarity score between \\(\\mathbf{F}_x\\) and \\(\\mathbf{F}_g\\), we search for the most useful feature from \\(\\mathbf{F}_g\\) for each small patch in \\(\\mathbf{F}_x\\) in a coarse-to-fine manner. After searching, we get a set of guidance features \\(\\hat{\\mathbf{F}}_g\\), whose content is aligned spatially with the input content. Second, we integrate the matched feature \\(\\hat{\\mathbf{F}}_g\\) into the image restoration backbone. Both CNN-based and transformer-based restoration networks can be adopted. Without bells and whistles, we modulate the original input features as," + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.637, + 0.469, + 0.656 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {x} = \\mathbf {F} _ {x} + \\alpha \\cdot \\mathcal {B} ([ \\mathbf {F} _ {x}, \\hat {\\mathbf {F}} _ {g} ]), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.665, + 0.469, + 0.741 + ], + "angle": 0, + "content": "where \\([\\cdot, \\cdot]\\) represents concatenation operation, \\(\\mathcal{B}\\) represents one CNN-based block or transformer-based block, \\(\\alpha\\) is the hyper-parameter to trade-off feature integration. Moreover, we perform it over multiple layers or levels. More details can be seen in the Suppl." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.469, + 0.788 + ], + "angle": 0, + "content": "Loss Function. To train guided restoration framework, we simply adopt \\(\\ell_1\\) loss as the reconstruction loss between predicted results \\(\\hat{\\mathbf{Y}}\\) and target \\(\\mathbf{Y}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.213, + 0.8, + 0.469, + 0.816 + ], + "angle": 0, + "content": "\\[\n\\ell_ {1} = \\left| \\left| \\hat {\\mathbf {Y}} - \\mathbf {Y} \\right| \\right| _ {1}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.21, + 0.848 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We evaluate the proposed method on five image restoration tasks, including (1) all-in-one image restoration [71], (2) image deblurring [14, 111] (i.e., motion image deblurring" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.09, + 0.603, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.147, + 0.603, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.198, + 0.603, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.243, + 0.585, + 0.255 + ], + "angle": 0, + "content": "Degraded" + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.091, + 0.699, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.147, + 0.699, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.198, + 0.699, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.243, + 0.671, + 0.254 + ], + "angle": 0, + "content": "Label" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.091, + 0.796, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.147, + 0.796, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.198, + 0.796, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.243, + 0.79, + 0.255 + ], + "angle": 0, + "content": "PromptIR [71]" + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.091, + 0.894, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.147, + 0.894, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.198, + 0.894, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.833, + 0.243, + 0.863, + 0.254 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.258, + 0.892, + 0.286 + ], + "angle": 0, + "content": "Figure 3. All-in-one image restoration results. Top: image denoising, mid: image deraining, bottom: image dehazing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.295, + 0.892, + 0.356 + ], + "angle": 0, + "content": "and defocus image deblurring), (3) image dehazing [19], (4) image deraining [16], and (5) image denoising [111] (i.e., grayscale and color image denoising on Gaussian noise, and real-world image denoising)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.356, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Implementation Details. We adopt publicly released stable-diffusion-v2.1-base as our T2I generative model. \\(N\\) is set to 20 in image-to-text mapper. Moreover, we employ the state-of-the-art methods as our image restoration backbone in different image restoration tasks: (1) we adopt PromptIR [71] in all-in-one image restoration, (2) we adopt NAFNet [14] and Restormer [111] in single-image motion deblurring, and Restormer [111] in defocus deblurring, (3) we adopt SFNet [19] in image dehazing, (4) we adopt DRSformer [16] in image deraining, (5) we adopt Restormer [111] in image denoising. The training settings of our guided restoration network are consistent with those of the corresponding backbone methods. Details of datasets, network architecture, and training hyperparameters are provided in Suppl." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.774, + 0.606 + ], + "angle": 0, + "content": "4.1. All-in-One Restoration Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.614, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Following [71], we adopt BSD400 [5] and WED [62] for color image denoising, Rain100L [27] for image deraining, and SOTS [49] for image dehazing. We train and evaluate the proposed method on these three tasks in all-in-one image restoration setting. The large difference among different degradations makes unifying multiple image restoration tasks into one unified network difficult, and thus the performance of existing all-in-one image restoration methods is limited. Compared with performing all-in-one restoration in the image level, it is much easier for us to conduct all-in-one restoration in the textual level. Once trained, our method can generate clean textual representation for different image restoration tasks, and thus we can synthesize guidance images for various types of degradation. Comparison results in Table 1 show that our method outperforms PromptIR [71] across all the benchmark datasets, achieving \\(+1.05\\) dB PSNR on dehazing task, \\(+1.21\\) dB PSNR on deraining task, and \\(+0.5\\) dB PSNR on average improvement. As shown in Fig. 3, the prediction of the proposed method" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2870" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.092, + 0.49, + 0.146 + ], + "angle": 0, + "content": "Table 2. Motion image deblurring results. We train models with GoPro training data. We evaluate our method on GoPro, HIDE, RealBlur benchmark datasets. PSNR and SSIM scores are calculated on RGB-channels." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.153, + 0.497, + 0.337 + ], + "angle": 0, + "content": "
MethodGoPro [66]HIDE [84]RealBlur-R [79]RealBlur-J [79]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DBGAN [118]31.100.94228.940.91533.780.90924.930.745
MT-RNN [68]31.150.94529.150.91835.790.95128.440.862
DMPHN [113]31.200.94029.090.92435.700.94828.420.860
SPAIR [72]32.060.95330.290.931--28.810.875
MIMO-Unet+ [18]32.450.95729.990.93035.540.94727.630.837
IPT [12]32.52-------
MPRNet [110]32.660.95930.960.93935.990.95228.700.873
HINet [13]32.710.95930.320.932----
Uformer [93]32.970.967------
Restormer [111]32.920.96131.220.94236.190.95728.960.879
Ours-Restormer33.110.96231.260.94336.470.95929.170.875
NAFNet [14]33.690.96631.320.94333.620.94426.330.856
Ours-NAFNet33.970.96831.570.94633.870.95026.760.861
" + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.09, + 0.888, + 0.145 + ], + "angle": 0, + "content": "Table 3. Defocus image deblurring results. We train and evaluate methods on DPDD dataset [2]. \\( S \\) denotes single-image defocus deblurring model. \\( D \\) denotes dual-pixel defocus deblurring. PSNR and SSIM scores are calculated on RGB channels." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.15, + 0.864, + 0.338 + ], + "angle": 0, + "content": "
MethodIndoor ScenesOutdoor ScenesCombined
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
EBDBS[43]25.770.77221.250.59923.450.683
DMENetS[45]25.500.78821.430.64423.410.714
JNBS[85]26.730.82821.100.60823.840.715
DPDNetS[2]26.540.81622.250.68224.340.747
KPACS[86]27.970.85222.620.70125.220.774
IFANs[46]28.110.86122.760.72025.370.789
RestormerS[111]28.870.88223.240.74325.980.811
OursS29.110.88923.350.74826.150.817
DPDNetD[2]27.480.84922.900.72625.130.786
RDPD3[3]28.100.84322.820.70425.390.772
UformerD[93]28.230.86023.100.72825.650.795
IFAND[46]28.660.86823.460.74325.990.804
RestormerD[111]29.480.89523.970.77326.660.833
OursD29.620.89924.160.77526.820.835
" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.342, + 0.326, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.45, + 0.249, + 0.462 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.342, + 0.465, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.369, + 0.39, + 0.426, + 0.402 + ], + "angle": 0, + "content": "Degraded" + }, + { + "type": "image", + "bbox": [ + 0.466, + 0.342, + 0.604, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.39, + 0.554, + 0.401 + ], + "angle": 0, + "content": "Label" + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.342, + 0.744, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.39, + 0.72, + 0.401 + ], + "angle": 0, + "content": "DMPHN [113]" + }, + { + "type": "image", + "bbox": [ + 0.746, + 0.342, + 0.884, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.39, + 0.858, + 0.401 + ], + "angle": 0, + "content": "MT-RNN [68]" + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.466, + 0.872, + 0.481 + ], + "angle": 0, + "content": "Figure 4. Motion image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.487, + 0.32, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.175, + 0.606, + 0.253, + 0.618 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.488, + 0.456, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.541, + 0.42, + 0.553 + ], + "angle": 0, + "content": "Degraded" + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.488, + 0.595, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.541, + 0.545, + 0.551 + ], + "angle": 0, + "content": "Label" + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.488, + 0.732, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.622, + 0.541, + 0.709, + 0.552 + ], + "angle": 0, + "content": "DMPHN [113]" + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.488, + 0.869, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.541, + 0.846, + 0.552 + ], + "angle": 0, + "content": "MPRNet [110]" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.622, + 0.874, + 0.636 + ], + "angle": 0, + "content": "Figure 5. Defocus image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.639, + 0.421, + 0.654 + ], + "angle": 0, + "content": "is finer and more detailed compared with PromptIR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.312, + 0.681 + ], + "angle": 0, + "content": "4.2. Image Deblurring Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Motion Deblurring. Following [14, 111], we train the proposed method on GoPro training data and evaluate our method on GoPro [66], HIDE [84], and real-world datasets (RealBlur-R [79] and RealBlur-J [79]). As shown in Table 2, benefiting from synthesized high-quality guidance, Ours-Restormer and Ours-NAFNet outperform the state-of-the-art methods on all four benchmark datasets. Our method achieves \\(+0.28\\) dB PSNR improvement on GoPro testing data. The visual results in Fig. 4 show that our method can restore images with sharper boundaries and details, demonstrating its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Defocus Deblurring. Following [111], we train and evaluate the proposed method on DPDD [2] dataset for single-image defocus deblurring and dual-pixel defocus deblur" + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.553, + 0.732, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.606, + 0.713, + 0.617 + ], + "angle": 0, + "content": "Restormer [111]" + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.553, + 0.869, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.606, + 0.82, + 0.616 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.713 + ], + "angle": 0, + "content": "ring. From Table 3, compared with Restormer [111], our method achieves \\(+0.17\\) dB PSNR and \\(+0.16\\) dB PSNR gains on single-image defocus deblurring and dual-pixel defocus deblurring, respectively. As illustrated in Fig. 5, the prediction of our method shows a clearer structure." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.737, + 0.722, + 0.754 + ], + "angle": 0, + "content": "4.3. Image Dehazing Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For image dehazing task, we conduct experiments on the synthetic benchmark RESIDE [49] dataset. We train the proposed method on indoor scene and outdoor scene data, and evaluate the performance on SOTS-indoor and SOTS-outdoor testing dataset [49] separately. Table 4 reports the quantitative comparison results. One can see that our method outperforms existing methods on both indoor and outdoor scenes, achieving \\(+0.24\\) dB PSNR average improvement. Visual comparisons can be found in the Suppl." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2871" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.092, + 0.448, + 0.134 + ], + "angle": 0, + "content": "Table 4. Image dehazing results. We separately train and evaluate our method indoor scene and outdoor scene. PSNR and SSIM scores are calculated on RGB-channels." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.143, + 0.424, + 0.32 + ], + "angle": 0, + "content": "
MethodSOTS-Indoor [49]SOTS-Outdoor [49]
PSNR↑SSIM↑PSNR↑SSIM↑
DehazeNet [8]19.820.82124.750.927
AOD-Net [47]20.510.86124.140.920
GridDehazeNet [59]32.160.98430.860.982
MSBDN [25]33.670.98533.480.982
FFA-Net [73]36.390.98933.570.984
ACER-Net [95]37.170.990--
DeHamer [36]36.630.98835.180.986
MAXIM-2S [90]38.110.99134.190.985
PMNet [102]38.410.99034.740.985
DehazeFormer-L [88]40.050.996--
SFNet [19]41.240.99640.050.996
Ours41.480.99640.290.996
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.332, + 0.434, + 0.373 + ], + "angle": 0, + "content": "Table 6. Grayscale image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.379, + 0.44, + 0.589 + ], + "angle": 0, + "content": "
MethodSet12 [115]BSD68 [63]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
DnCNN [115]32.6730.3527.1831.6229.1626.2332.2829.8026.35
FFDNet [117]32.7530.4327.3231.6329.1926.2932.4029.9026.50
IRCNN [116]32.7630.3727.1231.6329.1526.1932.4629.8026.22
DRUNet [119]33.2530.9427.9031.9129.4826.5933.4431.1127.96
Restormer[111]33.3531.0428.0131.9529.5126.6233.6731.3928.33
Ours33.3531.3028.1331.9829.5826.7733.6231.4728.46
FOCNet [40]33.0730.7327.6831.8329.3826.5033.1530.6427.40
MWCNN [58]33.1530.7927.7431.8629.4126.5333.1730.6627.42
NLRN [57]33.1630.8027.6431.8829.4126.4733.4530.9427.49
RNAN [122]--27.70--26.48--27.65
DeamNet [77]33.1930.8127.7431.9129.4426.5433.3730.8527.53
DAGL [65]33.2830.9327.8131.9329.4626.5133.7931.3927.97
SwinIR [55]33.3631.0127.9131.9729.5026.5833.7031.3027.98
Restormer [111]33.4231.0828.0031.9629.5226.6233.7931.4628.29
Ours33.4731.1528.1231.9229.6726.7833.7831.5828.38
" + }, + { + "type": "table_caption", + "bbox": [ + 0.48, + 0.09, + 0.889, + 0.132 + ], + "angle": 0, + "content": "le 5. Image deraining results. We separately train and evaluate our hod on Rain200H, Rain200L, DID-Data, and DDN-Data. PSNR and M scores are calculated on Y channel in YCbCr color space." + }, + { + "type": "table", + "bbox": [ + 0.458, + 0.133, + 0.892, + 0.322 + ], + "angle": 0, + "content": "
MethodRain200L [101]Rain200H [101]DID-Data [112]DDN-Data [29]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DDN [28]34.680.96726.050.80530.970.91130.000.904
RESCAN [53]36.090.96726.750.83533.380.94131.940.935
PReNet [78]37.800.98129.040.89933.170.94832.600.946
MSPFN [41]38.530.98329.360.90333.720.95532.990.933
RCDNet [91]39.170.98930.240.90434.080.95333.040.947
MPRNet [110]39.470.98230.670.91133.990.95933.100.935
DualGCN [30]40.730.98931.150.91234.370.96233.010.949
SPDNet [103]40.500.98831.280.92034.570.95633.150.946
Uformer [93]40.200.98630.800.91035.020.96233.950.955
Restormer [111]40.990.98932.000.93235.290.96434.200.957
IDT [98]40.740.98832.100.93434.890.96233.840.955
DRSformer [16]41.210.98932.160.93335.240.96234.230.955
Ours41.590.99031.970.93135.460.96434.570.958
" + }, + { + "type": "table_caption", + "bbox": [ + 0.445, + 0.332, + 0.889, + 0.373 + ], + "angle": 0, + "content": "Table 7. Color image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level. PSNR is calculated on RGB channels." + }, + { + "type": "table", + "bbox": [ + 0.449, + 0.378, + 0.901, + 0.589 + ], + "angle": 0, + "content": "
MethodCBSD68 [64]Kodak24McMaster [120]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
IRCNN [116]33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [117]33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [115]33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [70]33.9131.2828.0534.6332.1629.0534.6732.4029.28---
DRUNet [119]34.3031.6928.5135.3132.8929.8635.4033.1430.0834.8132.6029.61
Restormer [111]34.3931.7828.5935.4433.0230.0035.5533.3130.2935.0632.9130.02
Ours34.3731.8728.6835.5233.1330.1535.6233.3830.4035.0332.9730.19
RPCNN [97]-31.2428.06-32.3429.25-32.3329.33-31.8128.62
BRDNet [89]34.1031.4328.1634.8832.4129.2235.0832.7529.5234.4231.9928.56
RNAN [122]--28.27--29.58--29.72--29.08
RDN [123]--28.31--29.66-----29.38
IPT [12]--28.39--29.64--29.98--29.71
SwinIR [55]34.4231.7828.5635.3432.8929.7935.6133.2030.2235.1332.9029.82
Restormer [111]34.4031.7928.6035.4733.0430.0135.6133.3430.3035.1332.9630.02
Ours34.4831.9728.8335.5833.2130.2335.7533.5630.4635.1133.1330.27
" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.599, + 0.219, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.669, + 0.192, + 0.68 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.22, + 0.599, + 0.313, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.239, + 0.668, + 0.296, + 0.68 + ], + "angle": 0, + "content": "Degraded" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.599, + 0.408, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.668, + 0.379, + 0.679 + ], + "angle": 0, + "content": "Label" + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.599, + 0.501, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.423, + 0.668, + 0.49, + 0.68 + ], + "angle": 0, + "content": "RDN [123]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.599, + 0.596, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.668, + 0.588, + 0.68 + ], + "angle": 0, + "content": "RNAN [122]" + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.599, + 0.688, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.668, + 0.681, + 0.68 + ], + "angle": 0, + "content": "SwinIR [55]" + }, + { + "type": "image", + "bbox": [ + 0.694, + 0.599, + 0.788, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.695, + 0.668, + 0.789, + 0.68 + ], + "angle": 0, + "content": "Restormer [111]" + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.599, + 0.885, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.668, + 0.857, + 0.679 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.681, + 0.87, + 0.695 + ], + "angle": 0, + "content": "Figure 6. Color image denoising results on Gaussian noise. Compared with others, the proposed method can obtain finer results." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.707, + 0.186, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.779, + 0.177, + 0.79 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.707, + 0.286, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.21, + 0.778, + 0.267, + 0.79 + ], + "angle": 0, + "content": "Degraded" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.707, + 0.386, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.778, + 0.355, + 0.789 + ], + "angle": 0, + "content": "Label" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.707, + 0.485, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.396, + 0.778, + 0.48, + 0.79 + ], + "angle": 0, + "content": "DeamNet [77]" + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.707, + 0.585, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.778, + 0.575, + 0.79 + ], + "angle": 0, + "content": "RNAN [122]" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.707, + 0.685, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.778, + 0.673, + 0.79 + ], + "angle": 0, + "content": "SwinIR [55]" + }, + { + "type": "image", + "bbox": [ + 0.686, + 0.707, + 0.785, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.778, + 0.785, + 0.79 + ], + "angle": 0, + "content": "Restormer [111]" + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.707, + 0.885, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.821, + 0.778, + 0.855, + 0.789 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.791, + 0.884, + 0.805 + ], + "angle": 0, + "content": "Figure 7. Grayscale image denoising results on Gaussian noise. Our method can restore detailed results especially in texture regions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.82, + 0.304, + 0.836 + ], + "angle": 0, + "content": "4.4. Image Deraining Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Following [16], we train and evaluate the proposed method separately on Rain200L [101], Rain200H [101], DIDData [112], and DDN-Data [29] datasets. From Table 5," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.82, + 0.892, + 0.896 + ], + "angle": 0, + "content": "our method achieves \\(+0.31\\) dB PSNR average improvement on Rain200L, DID-Data,and DDN-Data against DRSformer [16].On the Rain200H dataset, we only have comparable performance, as its severe rain streak may interfere with the dynamic aggregation process between the guidance" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2872" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 8. Real-world image denoising results. We train and evaluate our mehtod on SIDD [1] datasets. * denotes methods using additional training data. PSNR and SSIM scores are calculated on RGB channels." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.122, + 0.89, + 0.178 + ], + "angle": 0, + "content": "
DatasetMethodDnCNN [115]BM3D [20]CBDNet* [37]RIDNet* [4]AINDNet* [44]VDN [105]SADNet* [11]DANet+* [106]CycleISP* [107]MIRNet [108]DeamNet* [77]MPRNet [110]DAGL [65]Uformer [93]Restormer [111]Ours
SIDD [1]PSNR ↑23.6625.6530.7838.7139.0839.2839.4639.4739.5239.7239.4739.7138.9439.7740.0240.09
SSIM ↑0.5830.6850.8010.9510.9540.9560.9570.9570.9570.9590.9570.9580.9530.9590.9600.960
" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.185, + 0.356, + 0.198 + ], + "angle": 0, + "content": "Table 9. Effect of \\( {\\mathbf{E}}_{txt} \\) with different \\( N \\) ." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.199, + 0.374, + 0.249 + ], + "angle": 0, + "content": "
MethodbaselineN=5N=10N=20N=30N=40
PSNR↑30.1631.1331.3631.5731.5131.60
SSIM↑0.9320.9410.9450.9470.9470.948
" + }, + { + "type": "table_caption", + "bbox": [ + 0.399, + 0.185, + 0.631, + 0.199 + ], + "angle": 0, + "content": "Table 10. Effect of integration strategy." + }, + { + "type": "table", + "bbox": [ + 0.405, + 0.201, + 0.63, + 0.248 + ], + "angle": 0, + "content": "
MethodbaselineEnc.Dec.Enc. & Dec.
PSNR↑30.1631.3730.3131.57
SSIM↑0.9320.9460.9340.947
" + }, + { + "type": "table_caption", + "bbox": [ + 0.647, + 0.185, + 0.88, + 0.199 + ], + "angle": 0, + "content": "Table 11. Effect of generated guidance." + }, + { + "type": "table", + "bbox": [ + 0.645, + 0.2, + 0.894, + 0.248 + ], + "angle": 0, + "content": "
Methodbaselineonly I2TDegra.BLIP2Ours
PSNR↑30.1630.1030.1330.3431.57
SSIM↑0.9320.9290.9310.9400.947
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.26, + 0.47, + 0.292 + ], + "angle": 0, + "content": "information and the degraded images. Visual comparisons of deraining results will be provided in the Suppl." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.3, + 0.303, + 0.316 + ], + "angle": 0, + "content": "4.5. Image Denoising Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.47, + 0.58 + ], + "angle": 0, + "content": "Image Denoising on Gaussian Noise. Following [111], we train the blind denoising model (\\(\\sigma\\) with range of \\([0, 50]\\)) and non-blind denoising models (\\(\\sigma = 15, 25, 50\\)) for grayscale and color image denoising on Gaussian noise. We train the proposed method on DFBW dataset with synthetic noise degradation. For grayscale image denoising, we evaluate our method on Set12 [115], BSD68 [64], and Urban100 [39]. For color image denoising, we evaluate our method on CBSD68 [64], Kodak24, McMaster [120], and Urban100 [39]. As shown in Table 6 and Table 7, our method achieves comparable performance with baseline on low noise-level (\\(\\sigma = 15\\)), while our method outperforms baseline when noise becomes heavier, e.g., achieving \\(+0.25\\) dB PSNR gain on Urban100 [39] with Gaussian color noise \\(\\sigma = 50\\). Qualitative comparisons in Fig. 6 and Fig. 7 show that our method can restore finer texture and sharper boundaries while other methods tend to generate smoother results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Real-World Image Denoising. Furthermore, We train and evaluate the proposed method on real-world denoising dataset SIDD [1]. From Table 8, although Restormer [111] has already achieved superior performance on real-world denoising task, our method can also bring \\(+0.07\\) dB PSNR improvement, demonstrating its effectiveness. Visual comparison results can be found in Suppl." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.241, + 0.71 + ], + "angle": 0, + "content": "4.6. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.47, + 0.763 + ], + "angle": 0, + "content": "In ablation studies, we adopt NAFNet with 32 channels as our baseline. We train and evaluate each method on GoPro datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Effect of \\(\\mathbf{E}_{\\text {txt }}\\) with different \\(N\\). In our method, we use the number of words \\(N\\) to control the representation ability of \\(\\mathbf{E}_{\\text {txt }}\\), which is used as condition information to generate guidance. We conduct the experiments on five settings, i.e., \\(N = 5, 10, 20, 30, 40\\). As shown in Table 9, the restoration performance generally improves from \\(N = 5\\) to \\(N = 40\\), as more informative textual descriptions can help T2I model generate more faithful guidance. Since the performance only improves slightly when \\(N\\) is larger than 20, we finally" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.26, + 0.892, + 0.289 + ], + "angle": 0, + "content": "set \\(N\\) to 20 to make a trade-off between performance and computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.893, + 0.41 + ], + "angle": 0, + "content": "Effect of Integrating Strategy. To evaluate the effect of different guidance integrating strategies, we conduct experiments by integrating guidance information into different modules of image restoration networks, i.e., Enc. (encoder only), Dec. (decoder only), and Enc. & Dec. (both encoder and decoder). As shown in Table 10, the experimental results show that integrating guidance information into both encoder and decoder achieves better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.591 + ], + "angle": 0, + "content": "Effect of Proposed Modules. To validate the effectiveness of our proposed modules, we conduct comparison with only using I2T mapper ('only I2T'), using explicit representation ('BLIP2'), and replacing guidance with degraded input ('Degra.') From comparison results in Table 11, since 'only I2T' and 'Degra.' cannot provide clean information to restoration process, they fail to obtain improvement upon baseline. Since using explicit representation ('BLIP2') cannot keep the content information of input as good as ours, our method can gain more from guidance. Guidance comparisons of 'only I2T', 'BLIP2', and ours can be found in Suppl." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.601, + 0.619, + 0.617 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.853 + ], + "angle": 0, + "content": "In this paper, we provide a new perspective for image restoration. Considering that content and degradation are tightly coupled in image representation, while decoupled in textual representation. Rather than direct restoration on image level, we suggest conducting restoration on textual level and in turn utilizing the restored textual content to assist image restoration. To this end, we propose a plug-and-play approach that first encodes degraded images into degraded textual representations and then removes textual degradation information to obtain restored textual representations. Conditioned on the representations, we employ a pre-trained T2I model to synthesize clean guidance images for improving image restoration. We evaluate our method on various image restoration tasks. The experimental results demonstrate it outperforms the state-of-the-art ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. U22B2035 and No. 62371164." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2873" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S. Brown. 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In CVPR, pages 21747-21758, 2023. 1, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2878" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_origin.pdf b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bef4dd6b64198b711b66188b42245cea89f18382 --- /dev/null +++ b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/c7ee9b17-7c3b-4549-9cfe-7a14b5397358_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c15042d855030edca3babeb0158be0803058ebd3d4f186da2f65854969906391 +size 1408975 diff --git a/2024/Improving Image Restoration through Removing Degradations in Textual Representations/full.md b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b184b642c37df3725be3d5d3d408bfc450569daf --- /dev/null +++ b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/full.md @@ -0,0 +1,480 @@ +# Improving Image Restoration through Removing Degradations in Textual Representations + +Jingbo Lin $^{1}$ , Zhilu Zhang $^{1}$ , Yuxiang Wei $^{1}$ , Dongwei Ren $^{1,*}$ , Dongsheng Jiang $^{2}$ , Qi Tian $^{2}$ , Wangmeng Zuo $^{1}$ , Harbin Institute of Technology ${}^{2}$ Huawei Cloud Computing Co., Ltd. + +jb1ncs1996@gmail.com, cszlzhang@outlook.com, yuxiang.wei.cs@gmail.com, + +rendongweihit@gmail.com, dongsheng_jiang@outlook.com, tian.qil@huawei.com, cswmzuo@gmail.com + +# Abstract + +In this paper, we introduce a new perspective for improving image restoration by removing degradation in the textual representations of a given degraded image. Intuitively, restoration is much easier on text modality than image one. For example, it can be easily conducted by removing degradation-related words while keeping the content-aware words. Hence, we combine the advantages of images in detail description and ones of text in degradation removal to perform restoration. To address the cross-modal assistance, we propose to map the degraded images into textual representations for removing the degradations, and then convert the restored textual representations into a guidance image for assisting image restoration. In particular, We ingeniously embed an image-to-text mapper and text restoration module into CLIP-equipped text-to-image models to generate the guidance. Then, we adopt a simple coarse-to-fine approach to dynamically inject multiscale information from guidance to image restoration networks. Extensive experiments are conducted on various image restoration tasks, including deblurring, dehazing, detraining, and denoising, and all-in-one image restoration. The results showcase that our method outperforms state-of-the-art ones across all these tasks. The codes and models are available at https://github.com/mrluin/TextualDegRemoval. + +# 1. Introduction + +Image restoration aims to reconstruct a high-quality clean image from its degraded observations. Most existing methods design deep networks for specific restoration tasks, including image denoising [55, 111, 115, 117, 119], deblurring [13, 14, 18, 93, 110], deraining [16, 93, 98, 110], dehazing [8, 19, 36, 88, 90], etc. Recent works [15, 50, 69, 71, 114, 124] expect to explore a unified model for multiple + +degradations. However, the severely ill-posed nature of the task makes it non-trivial to separate degradations and desired image content. Especially for unified models, the potential conflicts in dealing with various degradations bring more uncertainty. + +From a broader perspective, the purpose of the restoration is to enhance the clarity of scenes for human perception and recognition, while performing it on image modality is just one option. Moreover, degradations in image modality are tightly coupled with desirable content, making their removal challenging. When recording the scenes in some other modalities, this problem can be alleviated. Let us take the text modality as an example. Assume the textual description of a clean scene is represented by 'a scene of *'. When this scene is subjected to rainfall, the description can be converted into 'a rainy scene of *'. Thus, deraining can be readily achieved by simply removing the rain-related text 'rainy'. Furthermore, it is also convenient to remove multiple degradations in textual space with one unified model. Note that text modality may only describe rough aspects and ignore some details. We can further introduce image modality to combine their complementary potential in degradation removal and image restoration. + +Motivated by the above, we propose to perform restoration first in a modality where degradations and content are loosely coupled, and then utilize the corrected content to guide image restoration. In particular, we adopt the commonly used textual modality. Note that the text corresponding to the scene is not always available and the cross-modal assistance is difficult to achieve directly. The gap between text and image should be bridged. First, degraded images should be mapped into textual space for removing degradations. Second, the restored text should be mapped into a guidance image to assist restoration of the degraded image. As shown in Fig. 1, for the former, we have tried to convert degraded images to textual captions by image-to-text (I2T) models (e.g., BLIP [51, 52]), and find the captions can explicitly express both degradation types (e.g., blur, rain, haze, and noise) and content information. For the latter, we can + +![](images/0e83e9e500ff6b129087a9b809985e755bd038cc5c70a94258fe2bd476bd8186.jpg) +Figure 1. Overview of the proposed method. We propose to improve image restoration by performing restoration on the textual level, in which content and degradation information are loosely coupled. We first encode image concepts into textual space and then remove degradation-related information. To achieve cross-modal assistance, we employ pre-trained T2I models to generate clean guidance for the image restoration process. + +utilize the text-to-image (T2I) models (e.g.,Imagen [82]), which have demonstrated impressive image generation capability from the given texts. + +Although such a scheme is conceptually feasible, converting to explicit text may lose a lot of information from images, and additional degraded-clean text pairs need to be collected to train the text restoration module. Fortunately, Contrastive Language-Image Pre-training (CLIP) [74] implicitly aligns concepts of images and text. And we can leverage the CLIP-equipped T2I models (e.g., Stable Diffusion [81]) to build an end-to-end framework for generating clear guidance from degraded images gracefully. Specifically, CLIP has been demonstrated as an effective I2T converter [23]. For converting degraded images into degraded textual representations, we adopt the image encoder of CLIP, and add an I2T mapper after the encoder. For restoring degraded representations, we further append a textual restoration module after I2T mapper. Then, I2T mapper and textual restoration module can be sequentially trained by employing paired data from different image restoration datasets, without additional text data. + +Due to the ease of removing degradations on textual level, we train the I2T mapper and textual restoration module with multiple degradations at once. When training is done, it can serve multiple tasks, generating content-related and degradation-free guidance images from degraded images. Finally, we adopt a simple coarse-to-fine approach to dynamically inject multi-scale information from guidance to classic image restoration networks. Extensive experiments are conducted on multiple tasks, including all-in-one restoration, image debunking, dehazing, deraining, and denoising. The results show our method achieves better uni- + +versally than corresponding state-of-the-art methods. Especially for all-in-one restoration, 0.5 dB PSNR improvement is obtained in comparison with PromptIR [71]. + +The main contributions can be summarized as follows: + +- We introduce a new perspective for image restoration, i.e., performing restoration first in textual space where degradations and content are loosely coupled, and then utilizing the restored content to guide image restoration. +- To address the cross-modal assistance, we propose to embed an image-to-text mapper and textual restoration module into CLIP-equipped text-to-image models to generate clear guidance from degraded images. +- Extensive experiments on multiple tasks demonstrate that our method improves the performance of state-of-the-art image restoration networks. + +# 2. Related Work + +# 2.1. Image Restoration + +Image Restoration for Specific Tasks. Image restoration is a fundamental computer vision problem, which aims to reconstruct high-quality images from corresponding degraded inputs. In recent years, deep learning has achieved great progress in image restoration. Starting from some simple convolutional neural networks (CNNs) [24, 115], the introduction of channel-attention [121], spatial-attention [35, 109], non-local operation [57, 122], skip-connection architectures [54, 109] and multi-stage scheme [93, 110] enables image restoration performance continuously improve. With the emergence of vision transformers [26, 60], the capability of capturing long-range dependencies in the image allows transformer-based + +![](images/d5f851b74c68a03334ec9da82c3265b3137baca3a366e469b653c87e6a5d1b10.jpg) + +![](images/d8239d3120b71cb03531321560028c46d00f50950c541bf3ba5a02947748c88d.jpg) +(a) Guidance Generation +(b) Guided Image Restoration. +Figure 2. Illustration of the proposed pipeline. (a) We sequentially train image-to-text mapper $\mathcal{M}_{i2t}$ and textual restoration module $\mathcal{M}_{clean}$ to convert image concepts into textual representations and remove textual degradation information, respectively. (b) The guidance image is used to assist the image restoration process. + +methods to achieve better performance, gradually replacing previous CNN-based methods. To balance computational cost, window-based attention [17, 55] and transposed attention [111] are also introduced into image restoration tasks. Albeit image restoration performance has benefited from various advanced architecture designs, most of the works only focus on one specific degradation, due to the difficulty of learning to remove multiple degradations. + +All-in-One Image Restoration. Promoting by the development of unified model, some works focus on the solution to the all-in-one image restoration [15, 50, 69, 71, 114, 124]. The first all-in-one image restoration work, i.e., IPT [12], employs ViT-based backbone with multi-heads and multi-tails for inputs with different degradations. However, the method is limited in handling specific synthesized degradations and cannot directly generalize to unknown tasks. AirNet [50] develops the unified model for denoising-deraining-dehazing, which utilizes contrastive learning to capture degradation representations of different tasks and adaptively injects the degradation priors into backbone restoration framework for aiding in learning better results. ADMS [69] exploits FAIG [99] in all-in-one image restoration, by learning specific filters and degradation classifiers, achieving better performance on deraining-denoising-deblurring and deraining-desnowing-dehazing tasks. IDR [114] proposes a two-stage training strategy, which first learns separate task-oriented hubs for each degradation. Then, in the second stage, it reformulates the learned hubs into a single ingredient-oriented hub by learnable PCA and adopts the reformulated hub as prior to adaptively aid in restoring corrupted images. PromptIR [71] learns to encode and adopt degradation information as prompts for dehazing-deraining-denoising task. Although existing works can unify a set of image restoration tasks into one unified model, the performance is still limited caused by the large gap among different degradations. + +Prior-Based Image Restoration. Prior-based restoration aims at improving performance by introducing external priors, including structures, images, pre-trained models, etc. For instance, some works [9, 42, 61] adopt information from the high-resolution reference image to help improve the performance of super-resolution. Recent works [56, 92, 100] utilize pre-trained generative priors to restore more realistic and natural results. TextIR [6] develops a text-driven image restoration framework by incorporating information on textual representation. + +In this work, we provide a new perspective, i.e., utilizing restoration in textual space to assist image restoration. We also combine the advantages of both text-based prior (by learning degradations in textual level) and image-based prior (by giving clean guidance) for better performance. + +# 2.2. Text-to-Image Generation + +Text-to-image generation models [22, 31, 67, 75, 76, 83, 96] have attracted intensive attention in recent years due to its ability to generate high-quality and diverse images based on given text descriptions. A variety of techniques, including generative adversarial networks (GAN) [34], autoregressive models, and diffusion models have been investigated. Initial studies [48, 83, 96] mainly rely on GAN-based architectures, and train a conditional model from given paired image-caption datasets to generate samples. Some efforts focus on autoregressive models [10, 21, 31, 75, 104] have also shown exciting results. These models, such as CogView [21] and Muse [10] first learn a discrete codebook through training an autoencoder, and then adopt an autoregressive transformer to predict the tokens sequentially. With the development of diffusion models [38, 87], text conditioned image synthesis has shown remarkable improvement. By training with huge corpora, large diffusion models, such as DALLE-2 [76], Imagen [82], Stable Diffusion [80], and DALLE-3 [7] have demonstrated excel + +lent semantic understanding, and can generate diverse and photo-realistic images. + +# 3. Proposed Method + +In this section, we present our proposed method for image restoration. As illustrated in Fig. 2, we suggest first conducting restoration in the textual modality, in which degradation is loosely coupled with the content and can be easily removed. Then we in turn utilize the restored results as guidance to improve image restoration. Specifically, in Sec. 3.2, we propose an image-to-text mapper $\mathcal{M}_{i2t}$ and a textual restoration module $\mathcal{M}_{clean}$ to extract the degradation-free textual representations $\mathbf{E}_{txt}^{\prime}$ from degraded images $\mathbf{X} \in \mathbb{R}^{H \times W \times 3}$ . Then with a pre-trained T2I model, we can generate a guidance image $\mathbf{G} \in \mathbb{R}^{H \times W \times 3}$ that is related to the content of $\mathbf{X}$ but free of degradation. In Sec. 3.3, to leverage clean content information from $\mathbf{G}$ for enhancing image restoration performance, we introduce a coarse-to-fine approach that dynamically incorporates multi-scale information from guidance $\mathbf{G}$ into restoration frameworks. Besides, we first give a preliminary knowledge of the T2I model in Sec. 3.1. + +# 3.1. Preliminary + +In this work, we employ Stable Diffusion [81] as our text-to-image model. Stable Diffusion pretrains an autoencoder $(\mathcal{E}(\cdot),\mathcal{D}(\cdot))$ to map the input image $\mathbf{X}$ into a lower dimensional latent space by $\mathbf{z} = \mathcal{E}(\mathbf{X})$ . The decoder $\mathcal{D}(\cdot)$ learns to map the latent code back to the image as $\mathcal{D}(\mathcal{E}(\mathbf{X}))\approx \mathbf{X}$ . Then, the conditional diffusion model $\epsilon_{\theta}(\cdot)$ is trained on the latent space to generate latent codes based on text condition $\mathbf{p}$ . To train the diffusion model, simple mean-squared loss is adopted as, + +$$ +L _ {L D M} = \mathbb {E} _ {\mathbf {z} \sim \mathcal {E} (\mathbf {X}), \mathbf {p}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, \tau_ {\theta} ^ {t} (\mathbf {p})\right) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $\epsilon$ denotes the unscaled noise, $t$ is the timestep, $\mathbf{z}_t$ is the latent noised to time $t$ , and $\tau_{\theta}^{t}(\cdot)$ represents the pretrained CLIP [74] text encoder. During inference, a random Gaussian noise $\mathbf{z}_T$ is iteratively denoised to $\mathbf{z}_0$ , and the final image is obtained through the decoder $\mathbf{X}' = \mathcal{D}(\mathbf{z}_0)$ . + +# 3.2. Degradation-Free Guidance Generation + +Image captioning models (e.g., BLIP2 [52]) can generate text descriptions of degraded images, which can be taken into the text restoration module and text-to-image models to reconstruct clean guidance images. However, such descriptions may lose too many details, resulting in severely inconsistent content between the guidance and the input images. To address these problems, we propose an image-to-text mapper $\mathcal{M}_{i2t}$ to encode the degraded image $\mathbf{X}$ as implicit textual representations $\mathbf{E}_{txt}$ rather than explicit texts, which can be used to reconstruct the content more faithfully. + +Then, we utilize a textual restoration module $\mathcal{M}_{clean}$ to remove the degradation from $\mathbf{E}_{txt}$ and obtain degradation-free textual representations $\mathbf{E}_{txt}^{\prime}$ . + +Image-to-Text Mapping. Following [94], we adopt the textual word embedding space of CLIP [74] as the target space in image-to-text mapping. Benefiting from the aligned vision-language feature space of CLIP, we first adopt pre-trained CLIP image encoder $\tau_{\theta}^{i}(\cdot)$ to encode input $\mathbf{X}$ into CLIP image embedding $\mathbf{E}_{img}$ . Then, we propose an image-to-text mapper $\mathcal{M}_{i2t}$ to project CLIP image embedding into textual word embedding $\mathbf{E}_{txt}$ , + +$$ +\mathbf {E} _ {t x t} = \mathcal {M} _ {i 2 t} \left(\tau_ {\theta} ^ {i} (\mathbf {X})\right), \tag {2} +$$ + +where $\mathbf{E}_{\text{txt}} \in \mathbb{R}^{N \times D}$ and $D$ is the dimension of textual word embedding. $N$ is the number of learned words. To make the obtained word embedding describe more details of the input image, we set $N$ to a large number (e.g., $N = 20$ ). + +Textual Restoration. Although $\mathcal{M}_{i2t}$ can project images into the textual word embedding space, the projected textual word embedding will include corresponding degradation information if input $\mathbf{X}$ is degraded. Condition on the degraded textual word embedding, the synthesized guidance inevitably reflects the corresponding degradation pattern. Therefore, we further propose a textual restoration module $\mathcal{M}_{clean}$ to remove the degradation information from the textual word embedding $\mathbf{E}_{txt}$ , + +$$ +\mathbf {E} _ {t x t} ^ {\prime} = \mathcal {M} _ {c l e a n} (\mathbf {E} _ {t x t}), \tag {3} +$$ + +where $\mathbf{E}_{txt}^{\prime}$ denote the restored textual representations. When feeding $\mathbf{E}_{txt}^{\prime}$ into Stable Diffusion, we can obtain a degradation-free image $\mathbf{G}$ , which has similar content as $\mathbf{X}$ but is free of degradation, as shown in Fig. 1. + +Model Optimization. During training, the image-to-text mapper $\mathcal{M}_{i2t}$ and textual restoration module $\mathcal{M}_{clean}$ are optimized sequentially. In the first training stage, we collect both clean and degraded images from different restoration tasks as training data. We adopt Eq. (1) as a loss function, which constrains the diffusion model to reconstruct clean and degraded images conditioning on their own projected embedding $\mathbf{E}_{txt}$ . In the second training stage, we use pairs of degraded-clean images from different image restoration datasets as training data. Based on pre-trained $\mathcal{M}_{i2t}$ , we further deploy $\mathcal{M}_{clean}$ to remove degradation-related concepts from degraded embedding $\mathbf{E}_{txt}$ , obtaining $\mathbf{E}_{txt}^{\prime}$ . We still adopt Eq. (1), which constrains the diffusion model to reconstruct clean images conditioning on restored embedding $\mathbf{E}_{txt}^{\prime}$ . Note that, due to the ease of removing degradations in the textual space, it is feasible to train $\mathcal{M}_{i2t}$ and $\mathcal{M}_{clean}$ with multiple degradations simultaneously. When training is done, it can serve multiple image restoration tasks, generating content-related and degradation-free guidance images $\mathbf{G}$ from degraded images + +Table 1. All-in-one image restoration results. Following PromptIR [71], we train and evaluate the proposed method in all-in-one image restoration task, our method outperforms PromptIR across all the benchmark datasets. + +
MethodDehazing on SOTSDerain on Rain100LDenoise on BSD68Average
σ = 15σ = 25σ = 50
BRDNet [89]23.23/0.89527.42/0.89532.26/0.89829.74/0.83626.34/0.83627.80/0.843
LPNet [33]20.84/0.82824.88/0.78426.47/0.77824.77/0.74821.26/0.55223.64/0.738
FDGAN [32]24.71/0.92429.89/0.93330.25/0.91028.81/0.86826.43/0.77628.02/0.883
MPRNet [110]25.28/0.95433.57/0.95433.54/0.92730.89/0.88027.56/0.77930.17/0.899
DL [27]26.92/0.39132.62/0.93133.05/0.91430.41/0.86126.90/0.74029.98/0.875
AirNet [50]27.94/0.96234.90/0.96733.92/0.93331.26/0.88828.00/0.79731.20/0.910
PromptIR [71]30.58/0.97436.37/0.97233.98/0.93331.31/0.88828.06/0.79932.06/0.913
Ours31.63/0.98037.58/0.97934.01/0.93331.39/0.89028.18/0.80232.56/0.916
+ +with one unified model (as shown in Fig. 1). More training details can be seen in the Suppl. + +# 3.3. Guided Restoration + +Although guidance image $\mathbf{G}$ is clean, it is inevitable that there are content differences between $\mathbf{G}$ and degraded image $\mathbf{X}$ . Simplyfusing the features of $\mathbf{G}$ and $\mathbf{X}$ is not enough to improve image restoration. Instead, we suggest a dynamic aggregation module to extract and exploit helpful information from $\mathbf{G}$ . + +Dynamic Aggregation. First, we perform feature matching [61] between the guidance $\mathbf{G}$ and given degraded image $\mathbf{X}$ . Specifically, we use a shared image encoder to extract multi-scale features for $\mathbf{X}$ and $\mathbf{G}$ , named $\mathbf{F}_x$ and $\mathbf{F}_g$ , respectively. According to the similarity score between $\mathbf{F}_x$ and $\mathbf{F}_g$ , we search for the most useful feature from $\mathbf{F}_g$ for each small patch in $\mathbf{F}_x$ in a coarse-to-fine manner. After searching, we get a set of guidance features $\hat{\mathbf{F}}_g$ , whose content is aligned spatially with the input content. Second, we integrate the matched feature $\hat{\mathbf{F}}_g$ into the image restoration backbone. Both CNN-based and transformer-based restoration networks can be adopted. Without bells and whistles, we modulate the original input features as, + +$$ +\mathbf {F} _ {x} = \mathbf {F} _ {x} + \alpha \cdot \mathcal {B} ([ \mathbf {F} _ {x}, \hat {\mathbf {F}} _ {g} ]), \tag {4} +$$ + +where $[\cdot, \cdot]$ represents concatenation operation, $\mathcal{B}$ represents one CNN-based block or transformer-based block, $\alpha$ is the hyper-parameter to trade-off feature integration. Moreover, we perform it over multiple layers or levels. More details can be seen in the Suppl. + +Loss Function. To train guided restoration framework, we simply adopt $\ell_1$ loss as the reconstruction loss between predicted results $\hat{\mathbf{Y}}$ and target $\mathbf{Y}$ , i.e., + +$$ +\ell_ {1} = \left| \left| \hat {\mathbf {Y}} - \mathbf {Y} \right| \right| _ {1}. \tag {5} +$$ + +# 4. Experiments + +We evaluate the proposed method on five image restoration tasks, including (1) all-in-one image restoration [71], (2) image deblurring [14, 111] (i.e., motion image deblurring + +![](images/16cdba6d17df12a8a2f86e72519c5fa5cdddf7ecc37c2086b4d5752458190c23.jpg) + +![](images/fb30a7220c85e1a31321e3ac97e74570ac49cd8dbe9422448b12e7bf4555f0b1.jpg) + +![](images/92a1a95a88aecce55d107d831c89f8395fb34c661b23324a0bc1c916e0c39ebb.jpg) +Degraded +Figure 3. All-in-one image restoration results. Top: image denoising, mid: image deraining, bottom: image dehazing. + +![](images/2e4fef983d0ee1af22d92cc6da75128ca64b263577c2f5dbcc3d9ec4503ffe08.jpg) + +![](images/f99c6316de07aea3a1724346fbe01d46696605216f06a828c8bc03c2140ab71d.jpg) + +![](images/538e97884d78205c419e5c480968c5609e6df57af17f04d92bd5ae2e83239a00.jpg) +Label + +![](images/7b8686d6006f54497fff179e1e90d84bb14c5eff0838e322c94589f794d8c4c6.jpg) + +![](images/c1dd166a4118278af0b0ed459f2016274364616df2c17744a4c288801062b00b.jpg) + +![](images/cfdb9ee57bc86b0fcc1003d0dbb827d9f2f5ff87777cafb1e8cfc653ce4f1a26.jpg) +PromptIR [71] + +![](images/637aacf85a070b539830068ccabe151324f894d6f92b80d92e815b8b9854a6be.jpg) + +![](images/090d30dc87e250f5bc0349d169196285b0974340c0015c2ff38f61a747001358.jpg) + +![](images/2f44d661368b587a771a2c12359cc41c8b248cfdca67f9d6f55e6685880860fd.jpg) +Ours + +and defocus image deblurring), (3) image dehazing [19], (4) image deraining [16], and (5) image denoising [111] (i.e., grayscale and color image denoising on Gaussian noise, and real-world image denoising). + +Implementation Details. We adopt publicly released stable-diffusion-v2.1-base as our T2I generative model. $N$ is set to 20 in image-to-text mapper. Moreover, we employ the state-of-the-art methods as our image restoration backbone in different image restoration tasks: (1) we adopt PromptIR [71] in all-in-one image restoration, (2) we adopt NAFNet [14] and Restormer [111] in single-image motion deblurring, and Restormer [111] in defocus deblurring, (3) we adopt SFNet [19] in image dehazing, (4) we adopt DRSformer [16] in image deraining, (5) we adopt Restormer [111] in image denoising. The training settings of our guided restoration network are consistent with those of the corresponding backbone methods. Details of datasets, network architecture, and training hyperparameters are provided in Suppl. + +# 4.1. All-in-One Restoration Results + +Following [71], we adopt BSD400 [5] and WED [62] for color image denoising, Rain100L [27] for image deraining, and SOTS [49] for image dehazing. We train and evaluate the proposed method on these three tasks in all-in-one image restoration setting. The large difference among different degradations makes unifying multiple image restoration tasks into one unified network difficult, and thus the performance of existing all-in-one image restoration methods is limited. Compared with performing all-in-one restoration in the image level, it is much easier for us to conduct all-in-one restoration in the textual level. Once trained, our method can generate clean textual representation for different image restoration tasks, and thus we can synthesize guidance images for various types of degradation. Comparison results in Table 1 show that our method outperforms PromptIR [71] across all the benchmark datasets, achieving $+1.05$ dB PSNR on dehazing task, $+1.21$ dB PSNR on deraining task, and $+0.5$ dB PSNR on average improvement. As shown in Fig. 3, the prediction of the proposed method + +Table 2. Motion image deblurring results. We train models with GoPro training data. We evaluate our method on GoPro, HIDE, RealBlur benchmark datasets. PSNR and SSIM scores are calculated on RGB-channels. + +
MethodGoPro [66]HIDE [84]RealBlur-R [79]RealBlur-J [79]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DBGAN [118]31.100.94228.940.91533.780.90924.930.745
MT-RNN [68]31.150.94529.150.91835.790.95128.440.862
DMPHN [113]31.200.94029.090.92435.700.94828.420.860
SPAIR [72]32.060.95330.290.931--28.810.875
MIMO-Unet+ [18]32.450.95729.990.93035.540.94727.630.837
IPT [12]32.52-------
MPRNet [110]32.660.95930.960.93935.990.95228.700.873
HINet [13]32.710.95930.320.932----
Uformer [93]32.970.967------
Restormer [111]32.920.96131.220.94236.190.95728.960.879
Ours-Restormer33.110.96231.260.94336.470.95929.170.875
NAFNet [14]33.690.96631.320.94333.620.94426.330.856
Ours-NAFNet33.970.96831.570.94633.870.95026.760.861
+ +Table 3. Defocus image deblurring results. We train and evaluate methods on DPDD dataset [2]. $S$ denotes single-image defocus deblurring model. $D$ denotes dual-pixel defocus deblurring. PSNR and SSIM scores are calculated on RGB channels. + +
MethodIndoor ScenesOutdoor ScenesCombined
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
EBDBS[43]25.770.77221.250.59923.450.683
DMENetS[45]25.500.78821.430.64423.410.714
JNBS[85]26.730.82821.100.60823.840.715
DPDNetS[2]26.540.81622.250.68224.340.747
KPACS[86]27.970.85222.620.70125.220.774
IFANs[46]28.110.86122.760.72025.370.789
RestormerS[111]28.870.88223.240.74325.980.811
OursS29.110.88923.350.74826.150.817
DPDNetD[2]27.480.84922.900.72625.130.786
RDPD3[3]28.100.84322.820.70425.390.772
UformerD[93]28.230.86023.100.72825.650.795
IFAND[46]28.660.86823.460.74325.990.804
RestormerD[111]29.480.89523.970.77326.660.833
OursD29.620.89924.160.77526.820.835
+ +![](images/4b91084df9a845fe7b3b3823b9fe7f178e132220c26220029af6be138c4d7a47.jpg) +Input image + +![](images/444eb028048aa47693017b97314d5530fc4343dceafde547d9995fa8ae9be0c8.jpg) +Degraded + +![](images/ee6fb9a5780a8e4a38047e1cae1080580aa7bff528d49e310605783dfe7cda36.jpg) +Label + +![](images/bd4ab74709442f9a54494af9e175733a7db89c114ec2e41661d73deba4ddb1a9.jpg) +DMPHN [113] + +![](images/b0510d76d068cfe06138e9b07dd02e978d10681997ee89a53e177f43e53cbb3e.jpg) +MT-RNN [68] + +![](images/e3f18f48ff0ec709f3fae0d66e118b3aced61e7df2ecb4b694e3ba2c3cbbf192.jpg) +Figure 4. Motion image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries. +Input image +Figure 5. Defocus image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries. + +![](images/a10cf74a2bee9ec5aff9ab08e246dac1267de0efa70ebdc83bf4f780766f5a1e.jpg) +Degraded + +![](images/bba765f6a8aa6826b48af3f9e75403f0e9fe8ee892fae72e90f096c7b53c6a67.jpg) +Label + +![](images/af3c87b2acc9385826e9edde729ad94287893061aa2cc48c8a1ba05ab7fb317d.jpg) + +![](images/32de0b3ead792b9925c885d9427d25062b3e293d2aec63fc4c67ba7924030052.jpg) + +is finer and more detailed compared with PromptIR. + +# 4.2. Image Deblurring Results + +Motion Deblurring. Following [14, 111], we train the proposed method on GoPro training data and evaluate our method on GoPro [66], HIDE [84], and real-world datasets (RealBlur-R [79] and RealBlur-J [79]). As shown in Table 2, benefiting from synthesized high-quality guidance, Ours-Restormer and Ours-NAFNet outperform the state-of-the-art methods on all four benchmark datasets. Our method achieves $+0.28$ dB PSNR improvement on GoPro testing data. The visual results in Fig. 4 show that our method can restore images with sharper boundaries and details, demonstrating its effectiveness. + +Defocus Deblurring. Following [111], we train and evaluate the proposed method on DPDD [2] dataset for single-image defocus deblurring and dual-pixel defocus deblur + +![](images/6e649a5e6bd3bf4532a569212d6f19546512e0fc77e9a70b04a8fd629c0eae48.jpg) +DMPHN [113] +Restormer [111] + +![](images/0414d094787e7d111b58867aaaed95e7585111e3dfcd43d9fa6839f51304480e.jpg) +MPRNet [110] +Ours + +ring. From Table 3, compared with Restormer [111], our method achieves $+0.17$ dB PSNR and $+0.16$ dB PSNR gains on single-image defocus deblurring and dual-pixel defocus deblurring, respectively. As illustrated in Fig. 5, the prediction of our method shows a clearer structure. + +# 4.3. Image Dehazing Results + +For image dehazing task, we conduct experiments on the synthetic benchmark RESIDE [49] dataset. We train the proposed method on indoor scene and outdoor scene data, and evaluate the performance on SOTS-indoor and SOTS-outdoor testing dataset [49] separately. Table 4 reports the quantitative comparison results. One can see that our method outperforms existing methods on both indoor and outdoor scenes, achieving $+0.24$ dB PSNR average improvement. Visual comparisons can be found in the Suppl. + +Table 4. Image dehazing results. We separately train and evaluate our method indoor scene and outdoor scene. PSNR and SSIM scores are calculated on RGB-channels. + +
MethodSOTS-Indoor [49]SOTS-Outdoor [49]
PSNR↑SSIM↑PSNR↑SSIM↑
DehazeNet [8]19.820.82124.750.927
AOD-Net [47]20.510.86124.140.920
GridDehazeNet [59]32.160.98430.860.982
MSBDN [25]33.670.98533.480.982
FFA-Net [73]36.390.98933.570.984
ACER-Net [95]37.170.990--
DeHamer [36]36.630.98835.180.986
MAXIM-2S [90]38.110.99134.190.985
PMNet [102]38.410.99034.740.985
DehazeFormer-L [88]40.050.996--
SFNet [19]41.240.99640.050.996
Ours41.480.99640.290.996
+ +Table 6. Grayscale image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level. + +
MethodSet12 [115]BSD68 [63]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
DnCNN [115]32.6730.3527.1831.6229.1626.2332.2829.8026.35
FFDNet [117]32.7530.4327.3231.6329.1926.2932.4029.9026.50
IRCNN [116]32.7630.3727.1231.6329.1526.1932.4629.8026.22
DRUNet [119]33.2530.9427.9031.9129.4826.5933.4431.1127.96
Restormer[111]33.3531.0428.0131.9529.5126.6233.6731.3928.33
Ours33.3531.3028.1331.9829.5826.7733.6231.4728.46
FOCNet [40]33.0730.7327.6831.8329.3826.5033.1530.6427.40
MWCNN [58]33.1530.7927.7431.8629.4126.5333.1730.6627.42
NLRN [57]33.1630.8027.6431.8829.4126.4733.4530.9427.49
RNAN [122]--27.70--26.48--27.65
DeamNet [77]33.1930.8127.7431.9129.4426.5433.3730.8527.53
DAGL [65]33.2830.9327.8131.9329.4626.5133.7931.3927.97
SwinIR [55]33.3631.0127.9131.9729.5026.5833.7031.3027.98
Restormer [111]33.4231.0828.0031.9629.5226.6233.7931.4628.29
Ours33.4731.1528.1231.9229.6726.7833.7831.5828.38
+ +le 5. Image deraining results. We separately train and evaluate our hod on Rain200H, Rain200L, DID-Data, and DDN-Data. PSNR and M scores are calculated on Y channel in YCbCr color space. + +
MethodRain200L [101]Rain200H [101]DID-Data [112]DDN-Data [29]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DDN [28]34.680.96726.050.80530.970.91130.000.904
RESCAN [53]36.090.96726.750.83533.380.94131.940.935
PReNet [78]37.800.98129.040.89933.170.94832.600.946
MSPFN [41]38.530.98329.360.90333.720.95532.990.933
RCDNet [91]39.170.98930.240.90434.080.95333.040.947
MPRNet [110]39.470.98230.670.91133.990.95933.100.935
DualGCN [30]40.730.98931.150.91234.370.96233.010.949
SPDNet [103]40.500.98831.280.92034.570.95633.150.946
Uformer [93]40.200.98630.800.91035.020.96233.950.955
Restormer [111]40.990.98932.000.93235.290.96434.200.957
IDT [98]40.740.98832.100.93434.890.96233.840.955
DRSformer [16]41.210.98932.160.93335.240.96234.230.955
Ours41.590.99031.970.93135.460.96434.570.958
+ +Table 7. Color image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level. PSNR is calculated on RGB channels. + +
MethodCBSD68 [64]Kodak24McMaster [120]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
IRCNN [116]33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [117]33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [115]33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [70]33.9131.2828.0534.6332.1629.0534.6732.4029.28---
DRUNet [119]34.3031.6928.5135.3132.8929.8635.4033.1430.0834.8132.6029.61
Restormer [111]34.3931.7828.5935.4433.0230.0035.5533.3130.2935.0632.9130.02
Ours34.3731.8728.6835.5233.1330.1535.6233.3830.4035.0332.9730.19
RPCNN [97]-31.2428.06-32.3429.25-32.3329.33-31.8128.62
BRDNet [89]34.1031.4328.1634.8832.4129.2235.0832.7529.5234.4231.9928.56
RNAN [122]--28.27--29.58--29.72--29.08
RDN [123]--28.31--29.66-----29.38
IPT [12]--28.39--29.64--29.98--29.71
SwinIR [55]34.4231.7828.5635.3432.8929.7935.6133.2030.2235.1332.9029.82
Restormer [111]34.4031.7928.6035.4733.0430.0135.6133.3430.3035.1332.9630.02
Ours34.4831.9728.8335.5833.2130.2335.7533.5630.4635.1133.1330.27
+ +![](images/8e01b55f9fcba6967de203a6313016f39c9572bef0b206d41b5f939ee2521871.jpg) +Input image + +![](images/7a643d8d8de13c3d9f4722faaf2773ac91e7b7ae3071ccffa327553abfa04305.jpg) +Degraded + +![](images/f96d21c006d55ae8dc92c72acaca4c8d3c24986299a24e428e41fcd628b1d39a.jpg) +Label + +![](images/87aa146a92f96f7e2110b9f4d0c734fb13c7a3390e732ea8223addcd38c69482.jpg) +RDN [123] + +![](images/52a3d48235e761093100993fcd0dd1e14992b02ac1fec36cc12aaa42203fed12.jpg) +RNAN [122] + +![](images/9fd21e6c0e43a564b52b9f92e6f5f2a483dcb95d225e2e221746229b03f19122.jpg) +SwinIR [55] + +![](images/58a696a653e7dda2686a82f76b4ae1ed824af9ea0d7b90796ca131e24bd6e7e1.jpg) +Restormer [111] + +![](images/865e55f77af705b27b0e4862f49424320d896002ee95c46157fa93eba854ea45.jpg) +Ours + +![](images/8660514c930676c545e11cd67c250950f3b6d8d0eed840d1ed560c114fb2c3f3.jpg) +Figure 6. Color image denoising results on Gaussian noise. Compared with others, the proposed method can obtain finer results. +Input image +Figure 7. Grayscale image denoising results on Gaussian noise. Our method can restore detailed results especially in texture regions. + +![](images/ba8fb1754ce1d2086413ab2e175da4377b286264c6732424a853ab91c59c1506.jpg) +Degraded + +![](images/6d17c5c67ef740266854c6f5a23f26e391ca28e6a31543c23d43254c981d9e81.jpg) +Label + +![](images/7aba0ea0246a0dde027a718b874f28afe39dccda43faabdfb56da2030feb0253.jpg) +DeamNet [77] + +![](images/0b9ecfc5ad3c1d98804b51fc2ef703306818f9e34c22a4a41a413c9da750e701.jpg) +RNAN [122] + +![](images/38d137aa6e4c8113f19011fdcce0d4c33cced812624acf9b17c442906f4c71e6.jpg) +SwinIR [55] + +![](images/721c232f8acb41c9e6613aac0ab2368e5b77b9b7cd564f0bd54a163fd3b14c94.jpg) +Restormer [111] + +![](images/924be009daa1f576958ad0fb703868116f5a90b0c93fd0b3c95172ab4712e2b0.jpg) +Ours + +# 4.4. Image Deraining Results + +Following [16], we train and evaluate the proposed method separately on Rain200L [101], Rain200H [101], DIDData [112], and DDN-Data [29] datasets. From Table 5, + +our method achieves $+0.31$ dB PSNR average improvement on Rain200L, DID-Data,and DDN-Data against DRSformer [16].On the Rain200H dataset, we only have comparable performance, as its severe rain streak may interfere with the dynamic aggregation process between the guidance + +Table 8. Real-world image denoising results. We train and evaluate our mehtod on SIDD [1] datasets. * denotes methods using additional training data. PSNR and SSIM scores are calculated on RGB channels. + +
DatasetMethodDnCNN [115]BM3D [20]CBDNet* [37]RIDNet* [4]AINDNet* [44]VDN [105]SADNet* [11]DANet+* [106]CycleISP* [107]MIRNet [108]DeamNet* [77]MPRNet [110]DAGL [65]Uformer [93]Restormer [111]Ours
SIDD [1]PSNR ↑23.6625.6530.7838.7139.0839.2839.4639.4739.5239.7239.4739.7138.9439.7740.0240.09
SSIM ↑0.5830.6850.8010.9510.9540.9560.9570.9570.9570.9590.9570.9580.9530.9590.9600.960
+ +Table 9. Effect of ${\mathbf{E}}_{txt}$ with different $N$ . + +
MethodbaselineN=5N=10N=20N=30N=40
PSNR↑30.1631.1331.3631.5731.5131.60
SSIM↑0.9320.9410.9450.9470.9470.948
+ +Table 10. Effect of integration strategy. + +
MethodbaselineEnc.Dec.Enc. & Dec.
PSNR↑30.1631.3730.3131.57
SSIM↑0.9320.9460.9340.947
+ +Table 11. Effect of generated guidance. + +
Methodbaselineonly I2TDegra.BLIP2Ours
PSNR↑30.1630.1030.1330.3431.57
SSIM↑0.9320.9290.9310.9400.947
+ +information and the degraded images. Visual comparisons of deraining results will be provided in the Suppl. + +# 4.5. Image Denoising Results + +Image Denoising on Gaussian Noise. Following [111], we train the blind denoising model ( $\sigma$ with range of $[0, 50]$ ) and non-blind denoising models ( $\sigma = 15, 25, 50$ ) for grayscale and color image denoising on Gaussian noise. We train the proposed method on DFBW dataset with synthetic noise degradation. For grayscale image denoising, we evaluate our method on Set12 [115], BSD68 [64], and Urban100 [39]. For color image denoising, we evaluate our method on CBSD68 [64], Kodak24, McMaster [120], and Urban100 [39]. As shown in Table 6 and Table 7, our method achieves comparable performance with baseline on low noise-level ( $\sigma = 15$ ), while our method outperforms baseline when noise becomes heavier, e.g., achieving $+0.25$ dB PSNR gain on Urban100 [39] with Gaussian color noise $\sigma = 50$ . Qualitative comparisons in Fig. 6 and Fig. 7 show that our method can restore finer texture and sharper boundaries while other methods tend to generate smoother results. + +Real-World Image Denoising. Furthermore, We train and evaluate the proposed method on real-world denoising dataset SIDD [1]. From Table 8, although Restormer [111] has already achieved superior performance on real-world denoising task, our method can also bring $+0.07$ dB PSNR improvement, demonstrating its effectiveness. Visual comparison results can be found in Suppl. + +# 4.6. Ablation Studies + +In ablation studies, we adopt NAFNet with 32 channels as our baseline. We train and evaluate each method on GoPro datasets. + +Effect of $\mathbf{E}_{\text {txt }}$ with different $N$ . In our method, we use the number of words $N$ to control the representation ability of $\mathbf{E}_{\text {txt }}$ , which is used as condition information to generate guidance. We conduct the experiments on five settings, i.e., $N = 5, 10, 20, 30, 40$ . As shown in Table 9, the restoration performance generally improves from $N = 5$ to $N = 40$ , as more informative textual descriptions can help T2I model generate more faithful guidance. Since the performance only improves slightly when $N$ is larger than 20, we finally + +set $N$ to 20 to make a trade-off between performance and computational cost. + +Effect of Integrating Strategy. To evaluate the effect of different guidance integrating strategies, we conduct experiments by integrating guidance information into different modules of image restoration networks, i.e., Enc. (encoder only), Dec. (decoder only), and Enc. & Dec. (both encoder and decoder). As shown in Table 10, the experimental results show that integrating guidance information into both encoder and decoder achieves better performance. + +Effect of Proposed Modules. To validate the effectiveness of our proposed modules, we conduct comparison with only using I2T mapper ('only I2T'), using explicit representation ('BLIP2'), and replacing guidance with degraded input ('Degra.') From comparison results in Table 11, since 'only I2T' and 'Degra.' cannot provide clean information to restoration process, they fail to obtain improvement upon baseline. Since using explicit representation ('BLIP2') cannot keep the content information of input as good as ours, our method can gain more from guidance. Guidance comparisons of 'only I2T', 'BLIP2', and ours can be found in Suppl. + +# 5. Conclusion + +In this paper, we provide a new perspective for image restoration. Considering that content and degradation are tightly coupled in image representation, while decoupled in textual representation. Rather than direct restoration on image level, we suggest conducting restoration on textual level and in turn utilizing the restored textual content to assist image restoration. To this end, we propose a plug-and-play approach that first encodes degraded images into degraded textual representations and then removes textual degradation information to obtain restored textual representations. Conditioned on the representations, we employ a pre-trained T2I model to synthesize clean guidance images for improving image restoration. We evaluate our method on various image restoration tasks. The experimental results demonstrate it outperforms the state-of-the-art ones. + +Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. U22B2035 and No. 62371164. + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S. Brown. A high-quality denoising dataset for smartphone cameras. 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In CVPR, pages 21747-21758, 2023. 1, 3 \ No newline at end of file diff --git a/2024/Improving Image Restoration through Removing Degradations in Textual Representations/images.zip b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f7ef0f411eeea1de68f0aec9414a04c681a23331 --- /dev/null +++ b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3adb856e6a31500a76cc1ba8e3a0c37e882e6dfa85d605d0ec3715fe502c0cdc +size 983032 diff --git a/2024/Improving Image Restoration through Removing Degradations in Textual Representations/layout.json b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c3636be73a714833ff5c220675c0dfe58075237e --- /dev/null +++ b/2024/Improving Image Restoration through Removing Degradations in Textual Representations/layout.json @@ -0,0 +1,14329 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 138, + 103, + 455, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 103, + 455, + 140 + ], + "spans": [ + { + "bbox": [ + 138, + 103, + 455, + 140 + ], + "type": "text", + "content": "Improving Image Restoration through Removing Degradations in Textual Representations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "spans": [ + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": "Jingbo Lin" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Zhilu Zhang" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Yuxiang Wei" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Dongwei Ren" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Dongsheng Jiang" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Qi Tian" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Wangmeng Zuo" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": ", Harbin Institute of Technology " + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "inline_equation", + "content": "{}^{2}" + }, + { + "bbox": [ + 53, + 160, + 561, + 190 + ], + "type": "text", + "content": "Huawei Cloud Computing Co., Ltd." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 113, + 191, + 496, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 191, + 496, + 204 + ], + "spans": [ + { + "bbox": [ + 113, + 191, + 496, + 204 + ], + "type": "text", + "content": "jb1ncs1996@gmail.com, cszlzhang@outlook.com, yuxiang.wei.cs@gmail.com," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 205, + 555, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 205, + 555, + 217 + ], + "spans": [ + { + "bbox": [ + 58, + 205, + 555, + 217 + ], + "type": "text", + "content": "rendongweihit@gmail.com, dongsheng_jiang@outlook.com, tian.qil@huawei.com, cswmzuo@gmail.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 270, + 289, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 289, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 289, + 568 + ], + "type": "text", + "content": "In this paper, we introduce a new perspective for improving image restoration by removing degradation in the textual representations of a given degraded image. Intuitively, restoration is much easier on text modality than image one. For example, it can be easily conducted by removing degradation-related words while keeping the content-aware words. Hence, we combine the advantages of images in detail description and ones of text in degradation removal to perform restoration. To address the cross-modal assistance, we propose to map the degraded images into textual representations for removing the degradations, and then convert the restored textual representations into a guidance image for assisting image restoration. In particular, We ingeniously embed an image-to-text mapper and text restoration module into CLIP-equipped text-to-image models to generate the guidance. Then, we adopt a simple coarse-to-fine approach to dynamically inject multiscale information from guidance to image restoration networks. Extensive experiments are conducted on various image restoration tasks, including deblurring, dehazing, detraining, and denoising, and all-in-one image restoration. The results showcase that our method outperforms state-of-the-art ones across all these tasks. The codes and models are available at https://github.com/mrluin/TextualDegRemoval." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 591, + 128, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 128, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 128, + 604 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 612, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 612, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 612, + 287, + 696 + ], + "type": "text", + "content": "Image restoration aims to reconstruct a high-quality clean image from its degraded observations. Most existing methods design deep networks for specific restoration tasks, including image denoising [55, 111, 115, 117, 119], deblurring [13, 14, 18, 93, 110], deraining [16, 93, 98, 110], dehazing [8, 19, 36, 88, 90], etc. Recent works [15, 50, 69, 71, 114, 124] expect to explore a unified model for multiple" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 246, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 246, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 545, + 305 + ], + "type": "text", + "content": "degradations. However, the severely ill-posed nature of the task makes it non-trivial to separate degradations and desired image content. Especially for unified models, the potential conflicts in dealing with various degradations bring more uncertainty." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 306, + 546, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 546, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 546, + 521 + ], + "type": "text", + "content": "From a broader perspective, the purpose of the restoration is to enhance the clarity of scenes for human perception and recognition, while performing it on image modality is just one option. Moreover, degradations in image modality are tightly coupled with desirable content, making their removal challenging. When recording the scenes in some other modalities, this problem can be alleviated. Let us take the text modality as an example. Assume the textual description of a clean scene is represented by 'a scene of *'. When this scene is subjected to rainfall, the description can be converted into 'a rainy scene of *'. Thus, deraining can be readily achieved by simply removing the rain-related text 'rainy'. Furthermore, it is also convenient to remove multiple degradations in textual space with one unified model. Note that text modality may only describe rough aspects and ignore some details. We can further introduce image modality to combine their complementary potential in degradation removal and image restoration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": "Motivated by the above, we propose to perform restoration first in a modality where degradations and content are loosely coupled, and then utilize the corrected content to guide image restoration. In particular, we adopt the commonly used textual modality. Note that the text corresponding to the scene is not always available and the cross-modal assistance is difficult to achieve directly. The gap between text and image should be bridged. First, degraded images should be mapped into textual space for removing degradations. Second, the restored text should be mapped into a guidance image to assist restoration of the degraded image. As shown in Fig. 1, for the former, we have tried to convert degraded images to textual captions by image-to-text (I2T) models (e.g., BLIP [51, 52]), and find the captions can explicitly express both degradation types (e.g., blur, rain, haze, and noise) and content information. For the latter, we can" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 140, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 140, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 140, + 712 + ], + "type": "text", + "content": "*Correspondence author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "2866" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 541, + 272 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 541, + 272 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 541, + 272 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 541, + 272 + ], + "type": "image", + "image_path": "0e83e9e500ff6b129087a9b809985e755bd038cc5c70a94258fe2bd476bd8186.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 275, + 547, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 547, + 321 + ], + "type": "text", + "content": "Figure 1. Overview of the proposed method. We propose to improve image restoration by performing restoration on the textual level, in which content and degradation information are loosely coupled. We first encode image concepts into textual space and then remove degradation-related information. To achieve cross-modal assistance, we employ pre-trained T2I models to generate clean guidance for the image restoration process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 324, + 288, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 288, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 288, + 360 + ], + "type": "text", + "content": "utilize the text-to-image (T2I) models (e.g.,Imagen [82]), which have demonstrated impressive image generation capability from the given texts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 363, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 579 + ], + "type": "text", + "content": "Although such a scheme is conceptually feasible, converting to explicit text may lose a lot of information from images, and additional degraded-clean text pairs need to be collected to train the text restoration module. Fortunately, Contrastive Language-Image Pre-training (CLIP) [74] implicitly aligns concepts of images and text. And we can leverage the CLIP-equipped T2I models (e.g., Stable Diffusion [81]) to build an end-to-end framework for generating clear guidance from degraded images gracefully. Specifically, CLIP has been demonstrated as an effective I2T converter [23]. For converting degraded images into degraded textual representations, we adopt the image encoder of CLIP, and add an I2T mapper after the encoder. For restoring degraded representations, we further append a textual restoration module after I2T mapper. Then, I2T mapper and textual restoration module can be sequentially trained by employing paired data from different image restoration datasets, without additional text data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "Due to the ease of removing degradations on textual level, we train the I2T mapper and textual restoration module with multiple degradations at once. When training is done, it can serve multiple tasks, generating content-related and degradation-free guidance images from degraded images. Finally, we adopt a simple coarse-to-fine approach to dynamically inject multi-scale information from guidance to classic image restoration networks. Extensive experiments are conducted on multiple tasks, including all-in-one restoration, image debunking, dehazing, deraining, and denoising. The results show our method achieves better uni-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 324, + 547, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 360 + ], + "type": "text", + "content": "versally than corresponding state-of-the-art methods. Especially for all-in-one restoration, 0.5 dB PSNR improvement is obtained in comparison with PromptIR [71]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 361, + 539, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 361, + 539, + 372 + ], + "spans": [ + { + "bbox": [ + 317, + 361, + 539, + 372 + ], + "type": "text", + "content": "The main contributions can be summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 373, + 545, + 505 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 373, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 545, + 422 + ], + "type": "text", + "content": "- We introduce a new perspective for image restoration, i.e., performing restoration first in textual space where degradations and content are loosely coupled, and then utilizing the restored content to guide image restoration." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 422, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 545, + 469 + ], + "type": "text", + "content": "- To address the cross-modal assistance, we propose to embed an image-to-text mapper and textual restoration module into CLIP-equipped text-to-image models to generate clear guidance from degraded images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 469, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 469, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 306, + 469, + 545, + 505 + ], + "type": "text", + "content": "- Extensive experiments on multiple tasks demonstrate that our method improves the performance of state-of-the-art image restoration networks." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 518, + 392, + 531 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 392, + 531 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 392, + 531 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 538, + 416, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 416, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 416, + 551 + ], + "type": "text", + "content": "2.1. Image Restoration" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "Image Restoration for Specific Tasks. Image restoration is a fundamental computer vision problem, which aims to reconstruct high-quality images from corresponding degraded inputs. In recent years, deep learning has achieved great progress in image restoration. Starting from some simple convolutional neural networks (CNNs) [24, 115], the introduction of channel-attention [121], spatial-attention [35, 109], non-local operation [57, 122], skip-connection architectures [54, 109] and multi-stage scheme [93, 110] enables image restoration performance continuously improve. With the emergence of vision transformers [26, 60], the capability of capturing long-range dependencies in the image allows transformer-based" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2867" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 68, + 534, + 137 + ], + "blocks": [ + { + "bbox": [ + 60, + 68, + 534, + 137 + ], + "lines": [ + { + "bbox": [ + 60, + 68, + 534, + 137 + ], + "spans": [ + { + "bbox": [ + 60, + 68, + 534, + 137 + ], + "type": "image", + "image_path": "d5f851b74c68a03334ec9da82c3265b3137baca3a366e469b653c87e6a5d1b10.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 146, + 533, + 232 + ], + "blocks": [ + { + "bbox": [ + 251, + 138, + 338, + 148 + ], + "lines": [ + { + "bbox": [ + 251, + 138, + 338, + 148 + ], + "spans": [ + { + "bbox": [ + 251, + 138, + 338, + 148 + ], + "type": "text", + "content": "(a) Guidance Generation" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 60, + 146, + 533, + 232 + ], + "lines": [ + { + "bbox": [ + 60, + 146, + 533, + 232 + ], + "spans": [ + { + "bbox": [ + 60, + 146, + 533, + 232 + ], + "type": "image", + "image_path": "d8239d3120b71cb03531321560028c46d00f50950c541bf3ba5a02947748c88d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 249, + 234, + 355, + 244 + ], + "lines": [ + { + "bbox": [ + 249, + 234, + 355, + 244 + ], + "spans": [ + { + "bbox": [ + 249, + 234, + 355, + 244 + ], + "type": "text", + "content": "(b) Guided Image Restoration." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "type": "text", + "content": "Figure 2. Illustration of the proposed pipeline. (a) We sequentially train image-to-text mapper " + }, + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "type": "text", + "content": " and textual restoration module " + }, + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 46, + 245, + 546, + 278 + ], + "type": "text", + "content": " to convert image concepts into textual representations and remove textual degradation information, respectively. (b) The guidance image is used to assist the image restoration process." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 282, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 377 + ], + "type": "text", + "content": "methods to achieve better performance, gradually replacing previous CNN-based methods. To balance computational cost, window-based attention [17, 55] and transposed attention [111] are also introduced into image restoration tasks. Albeit image restoration performance has benefited from various advanced architecture designs, most of the works only focus on one specific degradation, due to the difficulty of learning to remove multiple degradations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 379, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 714 + ], + "type": "text", + "content": "All-in-One Image Restoration. Promoting by the development of unified model, some works focus on the solution to the all-in-one image restoration [15, 50, 69, 71, 114, 124]. The first all-in-one image restoration work, i.e., IPT [12], employs ViT-based backbone with multi-heads and multi-tails for inputs with different degradations. However, the method is limited in handling specific synthesized degradations and cannot directly generalize to unknown tasks. AirNet [50] develops the unified model for denoising-deraining-dehazing, which utilizes contrastive learning to capture degradation representations of different tasks and adaptively injects the degradation priors into backbone restoration framework for aiding in learning better results. ADMS [69] exploits FAIG [99] in all-in-one image restoration, by learning specific filters and degradation classifiers, achieving better performance on deraining-denoising-deblurring and deraining-desnowing-dehazing tasks. IDR [114] proposes a two-stage training strategy, which first learns separate task-oriented hubs for each degradation. Then, in the second stage, it reformulates the learned hubs into a single ingredient-oriented hub by learnable PCA and adopts the reformulated hub as prior to adaptively aid in restoring corrupted images. PromptIR [71] learns to encode and adopt degradation information as prompts for dehazing-deraining-denoising task. Although existing works can unify a set of image restoration tasks into one unified model, the performance is still limited caused by the large gap among different degradations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 282, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 402 + ], + "type": "text", + "content": "Prior-Based Image Restoration. Prior-based restoration aims at improving performance by introducing external priors, including structures, images, pre-trained models, etc. For instance, some works [9, 42, 61] adopt information from the high-resolution reference image to help improve the performance of super-resolution. Recent works [56, 92, 100] utilize pre-trained generative priors to restore more realistic and natural results. TextIR [6] develops a text-driven image restoration framework by incorporating information on textual representation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 402, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 462 + ], + "type": "text", + "content": "In this work, we provide a new perspective, i.e., utilizing restoration in textual space to assist image restoration. We also combine the advantages of both text-based prior (by learning degradations in textual level) and image-based prior (by giving clean guidance) for better performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 468, + 450, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 450, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 450, + 480 + ], + "type": "text", + "content": "2.2. Text-to-Image Generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": "Text-to-image generation models [22, 31, 67, 75, 76, 83, 96] have attracted intensive attention in recent years due to its ability to generate high-quality and diverse images based on given text descriptions. A variety of techniques, including generative adversarial networks (GAN) [34], autoregressive models, and diffusion models have been investigated. Initial studies [48, 83, 96] mainly rely on GAN-based architectures, and train a conditional model from given paired image-caption datasets to generate samples. Some efforts focus on autoregressive models [10, 21, 31, 75, 104] have also shown exciting results. These models, such as CogView [21] and Muse [10] first learn a discrete codebook through training an autoencoder, and then adopt an autoregressive transformer to predict the tokens sequentially. With the development of diffusion models [38, 87], text conditioned image synthesis has shown remarkable improvement. By training with huge corpora, large diffusion models, such as DALLE-2 [76], Imagen [82], Stable Diffusion [80], and DALLE-3 [7] have demonstrated excel" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2868" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "lent semantic understanding, and can generate diverse and photo-realistic images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 106, + 153, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 106, + 153, + 119 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 153, + 119 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": "In this section, we present our proposed method for image restoration. As illustrated in Fig. 2, we suggest first conducting restoration in the textual modality, in which degradation is loosely coupled with the content and can be easily removed. Then we in turn utilize the restored results as guidance to improve image restoration. Specifically, in Sec. 3.2, we propose an image-to-text mapper " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " and a textual restoration module " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " to extract the degradation-free textual representations " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}^{\\prime}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " from degraded images " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": ". Then with a pre-trained T2I model, we can generate a guidance image " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{G} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " that is related to the content of " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " but free of degradation. In Sec. 3.3, to leverage clean content information from " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " for enhancing image restoration performance, we introduce a coarse-to-fine approach that dynamically incorporates multi-scale information from guidance " + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 125, + 289, + 342 + ], + "type": "text", + "content": " into restoration frameworks. Besides, we first give a preliminary knowledge of the T2I model in Sec. 3.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 348, + 127, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 127, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 127, + 361 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": "In this work, we employ Stable Diffusion [81] as our text-to-image model. Stable Diffusion pretrains an autoencoder " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "(\\mathcal{E}(\\cdot),\\mathcal{D}(\\cdot))" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": " to map the input image " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": " into a lower dimensional latent space by " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{E}(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": ". The decoder " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot)" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": " learns to map the latent code back to the image as " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathcal{E}(\\mathbf{X}))\\approx \\mathbf{X}" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": ". Then, the conditional diffusion model " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": " is trained on the latent space to generate latent codes based on text condition " + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 366, + 287, + 475 + ], + "type": "text", + "content": ". To train the diffusion model, simple mean-squared loss is adopted as," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 480, + 287, + 508 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 480, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 55, + 480, + 287, + 508 + ], + "type": "interline_equation", + "content": "L _ {L D M} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathcal {E} (\\mathbf {X}), \\mathbf {p}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\tau_ {\\theta} ^ {t} (\\mathbf {p})\\right) \\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "ce5914db0a9be99db35e73c09924aaabffc6ae204d7fce724f9b657635dae857.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": " denotes the unscaled noise, " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": " is the timestep, " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": " is the latent noised to time " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}^{t}(\\cdot)" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": " represents the pretrained CLIP [74] text encoder. During inference, a random Gaussian noise " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": " is iteratively denoised to " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": ", and the final image is obtained through the decoder " + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{X}' = \\mathcal{D}(\\mathbf{z}_0)" + }, + { + "bbox": [ + 46, + 509, + 287, + 569 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 575, + 257, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 257, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 257, + 588 + ], + "type": "text", + "content": "3.2. Degradation-Free Guidance Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": "Image captioning models (e.g., BLIP2 [52]) can generate text descriptions of degraded images, which can be taken into the text restoration module and text-to-image models to reconstruct clean guidance images. However, such descriptions may lose too many details, resulting in severely inconsistent content between the guidance and the input images. To address these problems, we propose an image-to-text mapper " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " to encode the degraded image " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " as implicit textual representations " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " rather than explicit texts, which can be used to reconstruct the content more faithfully." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "Then, we utilize a textual restoration module " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " to remove the degradation from " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " and obtain degradation-free textual representations " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "content": "Image-to-Text Mapping. Following [94], we adopt the textual word embedding space of CLIP [74] as the target space in image-to-text mapping. Benefiting from the aligned vision-language feature space of CLIP, we first adopt pre-trained CLIP image encoder " + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}^{i}(\\cdot)" + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "content": " to encode input " + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "content": " into CLIP image embedding " + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{img}" + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "content": ". Then, we propose an image-to-text mapper " + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "content": " to project CLIP image embedding into textual word embedding " + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}" + }, + { + "bbox": [ + 304, + 108, + 545, + 205 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 379, + 214, + 545, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 214, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 379, + 214, + 545, + 228 + ], + "type": "interline_equation", + "content": "\\mathbf {E} _ {t x t} = \\mathcal {M} _ {i 2 t} \\left(\\tau_ {\\theta} ^ {i} (\\mathbf {X})\\right), \\tag {2}", + "image_path": "1ec96ce859b827e5e9caf66ec56f7574cefd7bb91c6d4cd3d6b862410cfc0020.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\text{txt}} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " is the dimension of textual word embedding. " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " is the number of learned words. To make the obtained word embedding describe more details of the input image, we set " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " to a large number (e.g., " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "N = 20" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "text", + "content": "Textual Restoration. Although " + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "text", + "content": " can project images into the textual word embedding space, the projected textual word embedding will include corresponding degradation information if input " + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "text", + "content": " is degraded. Condition on the degraded textual word embedding, the synthesized guidance inevitably reflects the corresponding degradation pattern. Therefore, we further propose a textual restoration module " + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "text", + "content": " to remove the degradation information from the textual word embedding " + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}" + }, + { + "bbox": [ + 304, + 285, + 545, + 393 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 377, + 403, + 545, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 403, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 377, + 403, + 545, + 417 + ], + "type": "interline_equation", + "content": "\\mathbf {E} _ {t x t} ^ {\\prime} = \\mathcal {M} _ {c l e a n} (\\mathbf {E} _ {t x t}), \\tag {3}", + "image_path": "548b525882cc7b50e9ceafe1e6aa5cae06075972da89ba87eb4f2d80be32f7cb.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}^{\\prime}" + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "text", + "content": " denote the restored textual representations. When feeding " + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}^{\\prime}" + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "text", + "content": " into Stable Diffusion, we can obtain a degradation-free image " + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "text", + "content": ", which has similar content as " + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 426, + 545, + 474 + ], + "type": "text", + "content": " but is free of degradation, as shown in Fig. 1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": "Model Optimization. During training, the image-to-text mapper " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": " and textual restoration module " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": " are optimized sequentially. In the first training stage, we collect both clean and degraded images from different restoration tasks as training data. We adopt Eq. (1) as a loss function, which constrains the diffusion model to reconstruct clean and degraded images conditioning on their own projected embedding " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": ". In the second training stage, we use pairs of degraded-clean images from different image restoration datasets as training data. Based on pre-trained " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": ", we further deploy " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": " to remove degradation-related concepts from degraded embedding " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": ", obtaining " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}^{\\prime}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": ". We still adopt Eq. (1), which constrains the diffusion model to reconstruct clean images conditioning on restored embedding " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{txt}^{\\prime}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": ". Note that, due to the ease of removing degradations in the textual space, it is feasible to train " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{i2t}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{clean}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": " with multiple degradations simultaneously. When training is done, it can serve multiple image restoration tasks, generating content-related and degradation-free guidance images " + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 474, + 546, + 714 + ], + "type": "text", + "content": " from degraded images" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2869" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 117, + 291, + 206 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 114 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 114 + ], + "type": "text", + "content": "Table 1. All-in-one image restoration results. Following PromptIR [71], we train and evaluate the proposed method in all-in-one image restoration task, our method outperforms PromptIR across all the benchmark datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 117, + 291, + 206 + ], + "lines": [ + { + "bbox": [ + 48, + 117, + 291, + 206 + ], + "spans": [ + { + "bbox": [ + 48, + 117, + 291, + 206 + ], + "type": "table", + "html": "
MethodDehazing on SOTSDerain on Rain100LDenoise on BSD68Average
σ = 15σ = 25σ = 50
BRDNet [89]23.23/0.89527.42/0.89532.26/0.89829.74/0.83626.34/0.83627.80/0.843
LPNet [33]20.84/0.82824.88/0.78426.47/0.77824.77/0.74821.26/0.55223.64/0.738
FDGAN [32]24.71/0.92429.89/0.93330.25/0.91028.81/0.86826.43/0.77628.02/0.883
MPRNet [110]25.28/0.95433.57/0.95433.54/0.92730.89/0.88027.56/0.77930.17/0.899
DL [27]26.92/0.39132.62/0.93133.05/0.91430.41/0.86126.90/0.74029.98/0.875
AirNet [50]27.94/0.96234.90/0.96733.92/0.93331.26/0.88828.00/0.79731.20/0.910
PromptIR [71]30.58/0.97436.37/0.97233.98/0.93331.31/0.88828.06/0.79932.06/0.913
Ours31.63/0.98037.58/0.97934.01/0.93331.39/0.89028.18/0.80232.56/0.916
", + "image_path": "1250fc165e51d38ada28c07a3944c6ebe1f834b6de2687e9169e5e3db20e59fe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 216, + 287, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 242 + ], + "type": "text", + "content": "with one unified model (as shown in Fig. 1). More training details can be seen in the Suppl." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 248, + 162, + 260 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 248, + 162, + 260 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 162, + 260 + ], + "type": "text", + "content": "3.3. Guided Restoration" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": "Although guidance image " + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": " is clean, it is inevitable that there are content differences between " + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": " and degraded image " + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": ". Simplyfusing the features of " + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": " is not enough to improve image restoration. Instead, we suggest a dynamic aggregation module to extract and exploit helpful information from " + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 266, + 287, + 337 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": "Dynamic Aggregation. First, we perform feature matching [61] between the guidance " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " and given degraded image " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": ". Specifically, we use a shared image encoder to extract multi-scale features for " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": ", named " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_x" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_g" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": ", respectively. According to the similarity score between " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_x" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_g" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": ", we search for the most useful feature from " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_g" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " for each small patch in " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_x" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " in a coarse-to-fine manner. After searching, we get a set of guidance features " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_g" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": ", whose content is aligned spatially with the input content. Second, we integrate the matched feature " + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_g" + }, + { + "bbox": [ + 46, + 339, + 287, + 495 + ], + "type": "text", + "content": " into the image restoration backbone. Both CNN-based and transformer-based restoration networks can be adopted. Without bells and whistles, we modulate the original input features as," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 504, + 287, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 504, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 107, + 504, + 287, + 519 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {x} = \\mathbf {F} _ {x} + \\alpha \\cdot \\mathcal {B} ([ \\mathbf {F} _ {x}, \\hat {\\mathbf {F}} _ {g} ]), \\tag {4}", + "image_path": "d19e576ff3b148c74664bbd554a1c54c4fd53010c77cd34622c941c9d788f9de.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "inline_equation", + "content": "[\\cdot, \\cdot]" + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "text", + "content": " represents concatenation operation, " + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "text", + "content": " represents one CNN-based block or transformer-based block, " + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 526, + 287, + 586 + ], + "type": "text", + "content": " is the hyper-parameter to trade-off feature integration. Moreover, we perform it over multiple layers or levels. More details can be seen in the Suppl." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "text", + "content": "Loss Function. To train guided restoration framework, we simply adopt " + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "text", + "content": " loss as the reconstruction loss between predicted results " + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Y}}" + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 587, + 287, + 624 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 130, + 633, + 287, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 633, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 130, + 633, + 287, + 646 + ], + "type": "interline_equation", + "content": "\\ell_ {1} = \\left| \\left| \\hat {\\mathbf {Y}} - \\mathbf {Y} \\right| \\right| _ {1}. \\tag {5}", + "image_path": "413eaab5f44e9c7563db88c3d411be4b3544bf734c39bd852936453ef065c7ab.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 657, + 128, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 128, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 128, + 671 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "We evaluate the proposed method on five image restoration tasks, including (1) all-in-one image restoration [71], (2) image deblurring [14, 111] (i.e., motion image deblurring" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 369, + 115 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 369, + 115 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 369, + 115 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 369, + 115 + ], + "type": "image", + "image_path": "16cdba6d17df12a8a2f86e72519c5fa5cdddf7ecc37c2086b4d5752458190c23.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 116, + 369, + 156 + ], + "blocks": [ + { + "bbox": [ + 310, + 116, + 369, + 156 + ], + "lines": [ + { + "bbox": [ + 310, + 116, + 369, + 156 + ], + "spans": [ + { + "bbox": [ + 310, + 116, + 369, + 156 + ], + "type": "image", + "image_path": "fb30a7220c85e1a31321e3ac97e74570ac49cd8dbe9422448b12e7bf4555f0b1.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 310, + 156, + 369, + 192 + ], + "blocks": [ + { + "bbox": [ + 310, + 156, + 369, + 192 + ], + "lines": [ + { + "bbox": [ + 310, + 156, + 369, + 192 + ], + "spans": [ + { + "bbox": [ + 310, + 156, + 369, + 192 + ], + "type": "image", + "image_path": "92a1a95a88aecce55d107d831c89f8395fb34c661b23324a0bc1c916e0c39ebb.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 192, + 358, + 201 + ], + "lines": [ + { + "bbox": [ + 325, + 192, + 358, + 201 + ], + "spans": [ + { + "bbox": [ + 325, + 192, + 358, + 201 + ], + "type": "text", + "content": "Degraded" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 204, + 545, + 226 + ], + "lines": [ + { + "bbox": [ + 305, + 204, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 305, + 204, + 545, + 226 + ], + "type": "text", + "content": "Figure 3. All-in-one image restoration results. Top: image denoising, mid: image deraining, bottom: image dehazing." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 370, + 72, + 427, + 114 + ], + "blocks": [ + { + "bbox": [ + 370, + 72, + 427, + 114 + ], + "lines": [ + { + "bbox": [ + 370, + 72, + 427, + 114 + ], + "spans": [ + { + "bbox": [ + 370, + 72, + 427, + 114 + ], + "type": "image", + "image_path": "2e4fef983d0ee1af22d92cc6da75128ca64b263577c2f5dbcc3d9ec4503ffe08.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 370, + 116, + 427, + 156 + ], + "blocks": [ + { + "bbox": [ + 370, + 116, + 427, + 156 + ], + "lines": [ + { + "bbox": [ + 370, + 116, + 427, + 156 + ], + "spans": [ + { + "bbox": [ + 370, + 116, + 427, + 156 + ], + "type": "image", + "image_path": "f99c6316de07aea3a1724346fbe01d46696605216f06a828c8bc03c2140ab71d.jpg" + } + ] + } + ], + 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"text", + "content": "Ours" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 233, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 233, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 233, + 545, + 281 + ], + "type": "text", + "content": "and defocus image deblurring), (3) image dehazing [19], (4) image deraining [16], and (5) image denoising [111] (i.e., grayscale and color image denoising on Gaussian noise, and real-world image denoising)." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 281, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 281, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 281, + 545, + 461 + ], + "type": "text", + "content": "Implementation Details. We adopt publicly released stable-diffusion-v2.1-base as our T2I generative model. " + }, + { + "bbox": [ + 305, + 281, + 545, + 461 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 281, + 545, + 461 + ], + "type": "text", + "content": " is set to 20 in image-to-text mapper. Moreover, we employ the state-of-the-art methods as our image restoration backbone in different image restoration tasks: (1) we adopt PromptIR [71] in all-in-one image restoration, (2) we adopt NAFNet [14] and Restormer [111] in single-image motion deblurring, and Restormer [111] in defocus deblurring, (3) we adopt SFNet [19] in image dehazing, (4) we adopt DRSformer [16] in image deraining, (5) we adopt Restormer [111] in image denoising. The training settings of our guided restoration network are consistent with those of the corresponding backbone methods. Details of datasets, network architecture, and training hyperparameters are provided in Suppl." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 468, + 473, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 473, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 473, + 479 + ], + "type": "text", + "content": "4.1. All-in-One Restoration Results" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "text", + "content": "Following [71], we adopt BSD400 [5] and WED [62] for color image denoising, Rain100L [27] for image deraining, and SOTS [49] for image dehazing. We train and evaluate the proposed method on these three tasks in all-in-one image restoration setting. The large difference among different degradations makes unifying multiple image restoration tasks into one unified network difficult, and thus the performance of existing all-in-one image restoration methods is limited. Compared with performing all-in-one restoration in the image level, it is much easier for us to conduct all-in-one restoration in the textual level. Once trained, our method can generate clean textual representation for different image restoration tasks, and thus we can synthesize guidance images for various types of degradation. Comparison results in Table 1 show that our method outperforms PromptIR [71] across all the benchmark datasets, achieving " + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "inline_equation", + "content": "+1.05" + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "text", + "content": " dB PSNR on dehazing task, " + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "inline_equation", + "content": "+1.21" + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "text", + "content": " dB PSNR on deraining task, and " + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "inline_equation", + "content": "+0.5" + }, + { + "bbox": [ + 305, + 486, + 545, + 713 + ], + "type": "text", + "content": " dB PSNR on average improvement. As shown in Fig. 3, the prediction of the proposed method" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2870" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 121, + 304, + 266 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 299, + 115 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 299, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 299, + 115 + ], + "type": "text", + "content": "Table 2. Motion image deblurring results. We train models with GoPro training data. We evaluate our method on GoPro, HIDE, RealBlur benchmark datasets. PSNR and SSIM scores are calculated on RGB-channels." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 121, + 304, + 266 + ], + "lines": [ + { + "bbox": [ + 49, + 121, + 304, + 266 + ], + "spans": [ + { + "bbox": [ + 49, + 121, + 304, + 266 + ], + "type": "table", + "html": "
MethodGoPro [66]HIDE [84]RealBlur-R [79]RealBlur-J [79]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DBGAN [118]31.100.94228.940.91533.780.90924.930.745
MT-RNN [68]31.150.94529.150.91835.790.95128.440.862
DMPHN [113]31.200.94029.090.92435.700.94828.420.860
SPAIR [72]32.060.95330.290.931--28.810.875
MIMO-Unet+ [18]32.450.95729.990.93035.540.94727.630.837
IPT [12]32.52-------
MPRNet [110]32.660.95930.960.93935.990.95228.700.873
HINet [13]32.710.95930.320.932----
Uformer [93]32.970.967------
Restormer [111]32.920.96131.220.94236.190.95728.960.879
Ours-Restormer33.110.96231.260.94336.470.95929.170.875
NAFNet [14]33.690.96631.320.94333.620.94426.330.856
Ours-NAFNet33.970.96831.570.94633.870.95026.760.861
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MethodIndoor ScenesOutdoor ScenesCombined
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
EBDBS[43]25.770.77221.250.59923.450.683
DMENetS[45]25.500.78821.430.64423.410.714
JNBS[85]26.730.82821.100.60823.840.715
DPDNetS[2]26.540.81622.250.68224.340.747
KPACS[86]27.970.85222.620.70125.220.774
IFANs[46]28.110.86122.760.72025.370.789
RestormerS[111]28.870.88223.240.74325.980.811
OursS29.110.88923.350.74826.150.817
DPDNetD[2]27.480.84922.900.72625.130.786
RDPD3[3]28.100.84322.820.70425.390.772
UformerD[93]28.230.86023.100.72825.650.795
IFAND[46]28.660.86823.460.74325.990.804
RestormerD[111]29.480.89523.970.77326.660.833
OursD29.620.89924.160.77526.820.835
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Motion image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 385, + 195, + 479 + ], + "lines": [ + { + "bbox": [ + 56, + 385, + 195, + 479 + ], + "spans": [ + { + "bbox": [ + 56, + 385, + 195, + 479 + ], + "type": "image", + "image_path": "e3f18f48ff0ec709f3fae0d66e118b3aced61e7df2ecb4b694e3ba2c3cbbf192.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 479, + 154, + 489 + ], + "lines": [ + { + "bbox": [ + 107, + 479, + 154, + 489 + ], + "spans": [ + { + "bbox": [ + 107, + 479, + 154, + 489 + ], + "type": "text", + "content": "Input image" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 492, + 534, + 503 + ], + "lines": [ + { + "bbox": [ + 47, + 492, + 534, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 534, + 503 + ], + "type": "text", + "content": "Figure 5. Defocus image deblurring results. Compared with others, our method can predict clearer results with clearer boundaries." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 196, + 386, + 279, + 427 + ], + "blocks": [ + { + "bbox": [ + 196, + 386, + 279, + 427 + ], + "lines": [ + { + "bbox": [ + 196, + 386, + 279, + 427 + ], + "spans": [ + { + "bbox": [ + 196, + 386, + 279, + 427 + ], + "type": "image", + "image_path": "a10cf74a2bee9ec5aff9ab08e246dac1267de0efa70ebdc83bf4f780766f5a1e.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 221, + 428, + 257, + 437 + ], + "lines": [ + { + "bbox": [ + 221, + 428, + 257, + 437 + ], + "spans": [ + { + "bbox": [ + 221, + 428, + 257, + 437 + ], + "type": "text", + "content": "Degraded" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 280, + 386, + 364, + 427 + ], + "blocks": [ + { + "bbox": [ + 280, + 386, + 364, + 427 + ], + "lines": [ + { + "bbox": [ + 280, + 386, + 364, + 427 + ], + "spans": [ + { + "bbox": [ + 280, + 386, + 364, + 427 + ], + "type": "image", + "image_path": "bba765f6a8aa6826b48af3f9e75403f0e9fe8ee892fae72e90f096c7b53c6a67.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 428, + 333, + 436 + ], + "lines": [ + { + "bbox": [ + 312, + 428, + 333, + 436 + ], + "spans": [ + { + "bbox": [ + 312, + 428, + 333, + 436 + ], + "type": "text", + "content": "Label" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 364, + 386, + 447, + 427 + ], + "blocks": [ + { + "bbox": [ + 364, + 386, + 447, + 427 + ], + "lines": [ + { + "bbox": [ + 364, + 386, + 447, + 427 + ], + "spans": [ + { + "bbox": [ + 364, + 386, + 447, + 427 + ], + "type": "image", + "image_path": "af3c87b2acc9385826e9edde729ad94287893061aa2cc48c8a1ba05ab7fb317d.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 448, + 386, + 531, + 427 + ], + "blocks": [ + { + "bbox": [ + 448, + 386, + 531, + 427 + ], + "lines": [ + { + "bbox": [ + 448, + 386, + 531, + 427 + ], + "spans": [ + { + "bbox": [ + 448, + 386, + 531, + 427 + ], + "type": "image", + "image_path": "32de0b3ead792b9925c885d9427d25062b3e293d2aec63fc4c67ba7924030052.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 506, + 257, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 257, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 257, + 517 + ], + "type": "text", + "content": "is finer and more detailed compared with PromptIR." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 526, + 190, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 190, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 190, + 539 + ], + "type": "text", + "content": "4.2. Image Deblurring Results" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "content": "Motion Deblurring. Following [14, 111], we train the proposed method on GoPro training data and evaluate our method on GoPro [66], HIDE [84], and real-world datasets (RealBlur-R [79] and RealBlur-J [79]). As shown in Table 2, benefiting from synthesized high-quality guidance, Ours-Restormer and Ours-NAFNet outperform the state-of-the-art methods on all four benchmark datasets. Our method achieves " + }, + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "inline_equation", + "content": "+0.28" + }, + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "content": " dB PSNR improvement on GoPro testing data. The visual results in Fig. 4 show that our method can restore images with sharper boundaries and details, demonstrating its effectiveness." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Defocus Deblurring. Following [111], we train and evaluate the proposed method on DPDD [2] dataset for single-image defocus deblurring and dual-pixel defocus deblur" + } + ] + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 364, + 437, + 447, + 479 + ], + "blocks": [ + { + "bbox": [ + 380, + 428, + 433, + 437 + ], + "lines": [ + { + "bbox": [ + 380, + 428, + 433, + 437 + ], + "spans": [ + { + "bbox": [ + 380, + 428, + 433, + 437 + ], + "type": "text", + "content": "DMPHN [113]" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 364, + 437, + 447, + 479 + ], + "lines": [ + { + "bbox": [ + 364, + 437, + 447, + 479 + ], + "spans": [ + { + "bbox": [ + 364, + 437, + 447, + 479 + ], + "type": "image", + "image_path": "6e649a5e6bd3bf4532a569212d6f19546512e0fc77e9a70b04a8fd629c0eae48.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 377, + 479, + 436, + 488 + ], + "lines": [ + { + "bbox": [ + 377, + 479, + 436, + 488 + ], + "spans": [ + { + "bbox": [ + 377, + 479, + 436, + 488 + ], + "type": "text", + "content": "Restormer [111]" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 448, + 437, + 531, + 479 + ], + "blocks": [ + { + "bbox": [ + 464, + 428, + 517, + 437 + ], + "lines": [ + { + "bbox": [ + 464, + 428, + 517, + 437 + ], + "spans": [ + { + "bbox": [ + 464, + 428, + 517, + 437 + ], + "type": "text", + "content": "MPRNet [110]" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 448, + 437, + 531, + 479 + ], + "lines": [ + { + "bbox": [ + 448, + 437, + 531, + 479 + ], + "spans": [ + { + "bbox": [ + 448, + 437, + 531, + 479 + ], + "type": "image", + "image_path": "0414d094787e7d111b58867aaaed95e7585111e3dfcd43d9fa6839f51304480e.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 479, + 501, + 487 + ], + "lines": [ + { + "bbox": [ + 481, + 479, + 501, + 487 + ], + "spans": [ + { + "bbox": [ + 481, + 479, + 501, + 487 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": "ring. From Table 3, compared with Restormer [111], our method achieves " + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "inline_equation", + "content": "+0.17" + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": " dB PSNR and " + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "inline_equation", + "content": "+0.16" + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": " dB PSNR gains on single-image defocus deblurring and dual-pixel defocus deblurring, respectively. As illustrated in Fig. 5, the prediction of our method shows a clearer structure." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 583, + 441, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 583, + 441, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 583, + 441, + 597 + ], + "type": "text", + "content": "4.3. Image Dehazing Results" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "For image dehazing task, we conduct experiments on the synthetic benchmark RESIDE [49] dataset. We train the proposed method on indoor scene and outdoor scene data, and evaluate the performance on SOTS-indoor and SOTS-outdoor testing dataset [49] separately. Table 4 reports the quantitative comparison results. One can see that our method outperforms existing methods on both indoor and outdoor scenes, achieving " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "+0.24" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " dB PSNR average improvement. Visual comparisons can be found in the Suppl." + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "2871" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 274, + 106 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 274, + 106 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 274, + 106 + ], + "type": "text", + "content": "Table 4. Image dehazing results. We separately train and evaluate our method indoor scene and outdoor scene. PSNR and SSIM scores are calculated on RGB-channels." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "text" + }, + { + "type": "table", + "bbox": [ + 65, + 113, + 259, + 253 + ], + "blocks": [ + { + "bbox": [ + 65, + 113, + 259, + 253 + ], + "lines": [ + { + "bbox": [ + 65, + 113, + 259, + 253 + ], + "spans": [ + { + "bbox": [ + 65, + 113, + 259, + 253 + ], + "type": "table", + "html": "
MethodSOTS-Indoor [49]SOTS-Outdoor [49]
PSNR↑SSIM↑PSNR↑SSIM↑
DehazeNet [8]19.820.82124.750.927
AOD-Net [47]20.510.86124.140.920
GridDehazeNet [59]32.160.98430.860.982
MSBDN [25]33.670.98533.480.982
FFA-Net [73]36.390.98933.570.984
ACER-Net [95]37.170.990--
DeHamer [36]36.630.98835.180.986
MAXIM-2S [90]38.110.99134.190.985
PMNet [102]38.410.99034.740.985
DehazeFormer-L [88]40.050.996--
SFNet [19]41.240.99640.050.996
Ours41.480.99640.290.996
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MethodSet12 [115]BSD68 [63]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
DnCNN [115]32.6730.3527.1831.6229.1626.2332.2829.8026.35
FFDNet [117]32.7530.4327.3231.6329.1926.2932.4029.9026.50
IRCNN [116]32.7630.3727.1231.6329.1526.1932.4629.8026.22
DRUNet [119]33.2530.9427.9031.9129.4826.5933.4431.1127.96
Restormer[111]33.3531.0428.0131.9529.5126.6233.6731.3928.33
Ours33.3531.3028.1331.9829.5826.7733.6231.4728.46
FOCNet [40]33.0730.7327.6831.8329.3826.5033.1530.6427.40
MWCNN [58]33.1530.7927.7431.8629.4126.5333.1730.6627.42
NLRN [57]33.1630.8027.6431.8829.4126.4733.4530.9427.49
RNAN [122]--27.70--26.48--27.65
DeamNet [77]33.1930.8127.7431.9129.4426.5433.3730.8527.53
DAGL [65]33.2830.9327.8131.9329.4626.5133.7931.3927.97
SwinIR [55]33.3631.0127.9131.9729.5026.5833.7031.3027.98
Restormer [111]33.4231.0828.0031.9629.5226.6233.7931.4628.29
Ours33.4731.1528.1231.9229.6726.7833.7831.5828.38
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MethodRain200L [101]Rain200H [101]DID-Data [112]DDN-Data [29]
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DDN [28]34.680.96726.050.80530.970.91130.000.904
RESCAN [53]36.090.96726.750.83533.380.94131.940.935
PReNet [78]37.800.98129.040.89933.170.94832.600.946
MSPFN [41]38.530.98329.360.90333.720.95532.990.933
RCDNet [91]39.170.98930.240.90434.080.95333.040.947
MPRNet [110]39.470.98230.670.91133.990.95933.100.935
DualGCN [30]40.730.98931.150.91234.370.96233.010.949
SPDNet [103]40.500.98831.280.92034.570.95633.150.946
Uformer [93]40.200.98630.800.91035.020.96233.950.955
Restormer [111]40.990.98932.000.93235.290.96434.200.957
IDT [98]40.740.98832.100.93434.890.96233.840.955
DRSformer [16]41.210.98932.160.93335.240.96234.230.955
Ours41.590.99031.970.93135.460.96434.570.958
", + "image_path": "ee373afe9d346fffe7daa52dadd4445cc78bcba3e09a7e0e1be36c8fb4eb4ba2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 274, + 299, + 551, + 466 + ], + "blocks": [ + { + "bbox": [ + 272, + 262, + 544, + 295 + ], + "lines": [ + { + "bbox": [ + 272, + 262, + 544, + 295 + ], + "spans": [ + { + "bbox": [ + 272, + 262, + 544, + 295 + ], + "type": "text", + "content": "Table 7. Color image denoising on Gaussian noise. Upper-bracket: models are trained on a range of noise levels. Lower-bracket: models are trained on the fixed noise level. PSNR is calculated on RGB channels." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 274, + 299, + 551, + 466 + ], + "lines": [ + { + "bbox": [ + 274, + 299, + 551, + 466 + ], + "spans": [ + { + "bbox": [ + 274, + 299, + 551, + 466 + ], + "type": "table", + "html": "
MethodCBSD68 [64]Kodak24McMaster [120]Urban100 [39]
σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50σ=15σ=25σ=50
IRCNN [116]33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [117]33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [115]33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [70]33.9131.2828.0534.6332.1629.0534.6732.4029.28---
DRUNet [119]34.3031.6928.5135.3132.8929.8635.4033.1430.0834.8132.6029.61
Restormer [111]34.3931.7828.5935.4433.0230.0035.5533.3130.2935.0632.9130.02
Ours34.3731.8728.6835.5233.1330.1535.6233.3830.4035.0332.9730.19
RPCNN [97]-31.2428.06-32.3429.25-32.3329.33-31.8128.62
BRDNet [89]34.1031.4328.1634.8832.4129.2235.0832.7529.5234.4231.9928.56
RNAN [122]--28.27--29.58--29.72--29.08
RDN [123]--28.31--29.66-----29.38
IPT [12]--28.39--29.64--29.98--29.71
SwinIR [55]34.4231.7828.5635.3432.8929.7935.6133.2030.2235.1332.9029.82
Restormer [111]34.4031.7928.6035.4733.0430.0135.6133.3430.3035.1332.9630.02
Ours34.4831.9728.8335.5833.2130.2335.7533.5630.4635.1133.1330.27
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Color image denoising results on Gaussian noise. 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Grayscale image denoising results on Gaussian noise. 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Image Deraining Results" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Following [16], we train and evaluate the proposed method separately on Rain200L [101], Rain200H [101], DIDData [112], and DDN-Data [29] datasets. From Table 5," + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 305, + 649, + 545, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 649, + 545, + 709 + ], + "spans": [ + { + "bbox": [ + 305, + 649, + 545, + 709 + ], + "type": "text", + "content": "our method achieves " + }, + { + "bbox": [ + 305, + 649, + 545, + 709 + ], + "type": "inline_equation", + "content": "+0.31" + }, + { + "bbox": [ + 305, + 649, + 545, + 709 + ], + "type": "text", + "content": " dB PSNR average improvement on Rain200L, DID-Data,and DDN-Data against DRSformer [16].On the Rain200H dataset, we only have comparable performance, as its severe rain streak may interfere with the dynamic aggregation process between the guidance" + } + ] + } + ], + "index": 44 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2872" + } + ] + } + ], + "index": 45 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 96, + 544, + 140 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 8. Real-world image denoising results. We train and evaluate our mehtod on SIDD [1] datasets. * denotes methods using additional training data. PSNR and SSIM scores are calculated on RGB channels." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 96, + 544, + 140 + ], + "lines": [ + { + "bbox": [ + 52, + 96, + 544, + 140 + ], + "spans": [ + { + "bbox": [ + 52, + 96, + 544, + 140 + ], + "type": "table", + "html": "
DatasetMethodDnCNN [115]BM3D [20]CBDNet* [37]RIDNet* [4]AINDNet* [44]VDN [105]SADNet* [11]DANet+* [106]CycleISP* [107]MIRNet [108]DeamNet* [77]MPRNet [110]DAGL [65]Uformer [93]Restormer [111]Ours
SIDD [1]PSNR ↑23.6625.6530.7838.7139.0839.2839.4639.4739.5239.7239.4739.7138.9439.7740.0240.09
SSIM ↑0.5830.6850.8010.9510.9540.9560.9570.9570.9570.9590.9570.9580.9530.9590.9600.960
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MethodbaselineN=5N=10N=20N=30N=40
PSNR↑30.1631.1331.3631.5731.5131.60
SSIM↑0.9320.9410.9450.9470.9470.948
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MethodbaselineEnc.Dec.Enc. & Dec.
PSNR↑30.1631.3730.3131.57
SSIM↑0.9320.9460.9340.947
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Methodbaselineonly I2TDegra.BLIP2Ours
PSNR↑30.1630.1030.1330.3431.57
SSIM↑0.9320.9290.9310.9400.947
", + "image_path": "2d7d9c3f1c87d942699b4b28b7f46a69b975c8b98fc93295434f163b27dbe391.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 205, + 287, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 205, + 287, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 287, + 231 + ], + "type": "text", + "content": "information and the degraded images. Visual comparisons of deraining results will be provided in the Suppl." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 237, + 185, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 237, + 185, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 237, + 185, + 250 + ], + "type": "text", + "content": "4.5. Image Denoising Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": "Image Denoising on Gaussian Noise. Following [111], we train the blind denoising model (" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": " with range of " + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "inline_equation", + "content": "[0, 50]" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": ") and non-blind denoising models (" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\sigma = 15, 25, 50" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": ") for grayscale and color image denoising on Gaussian noise. We train the proposed method on DFBW dataset with synthetic noise degradation. For grayscale image denoising, we evaluate our method on Set12 [115], BSD68 [64], and Urban100 [39]. For color image denoising, we evaluate our method on CBSD68 [64], Kodak24, McMaster [120], and Urban100 [39]. As shown in Table 6 and Table 7, our method achieves comparable performance with baseline on low noise-level (" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\sigma = 15" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": "), while our method outperforms baseline when noise becomes heavier, e.g., achieving " + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "inline_equation", + "content": "+0.25" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": " dB PSNR gain on Urban100 [39] with Gaussian color noise " + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\sigma = 50" + }, + { + "bbox": [ + 46, + 255, + 287, + 459 + ], + "type": "text", + "content": ". Qualitative comparisons in Fig. 6 and Fig. 7 show that our method can restore finer texture and sharper boundaries while other methods tend to generate smoother results." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 459, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 544 + ], + "type": "text", + "content": "Real-World Image Denoising. Furthermore, We train and evaluate the proposed method on real-world denoising dataset SIDD [1]. From Table 8, although Restormer [111] has already achieved superior performance on real-world denoising task, our method can also bring " + }, + { + "bbox": [ + 46, + 459, + 287, + 544 + ], + "type": "inline_equation", + "content": "+0.07" + }, + { + "bbox": [ + 46, + 459, + 287, + 544 + ], + "type": "text", + "content": " dB PSNR improvement, demonstrating its effectiveness. Visual comparison results can be found in Suppl." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 552, + 147, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 147, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 147, + 562 + ], + "type": "text", + "content": "4.6. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 570, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 604 + ], + "type": "text", + "content": "In ablation studies, we adopt NAFNet with 32 channels as our baseline. We train and evaluate each method on GoPro datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\text {txt }}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " with different " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": ". In our method, we use the number of words " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " to control the representation ability of " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\text {txt }}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": ", which is used as condition information to generate guidance. We conduct the experiments on five settings, i.e., " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N = 5, 10, 20, 30, 40" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": ". As shown in Table 9, the restoration performance generally improves from " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N = 40" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": ", as more informative textual descriptions can help T2I model generate more faithful guidance. Since the performance only improves slightly when " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " is larger than 20, we finally" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 205, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 228 + ], + "type": "text", + "content": "set " + }, + { + "bbox": [ + 304, + 205, + 545, + 228 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 205, + 545, + 228 + ], + "type": "text", + "content": " to 20 to make a trade-off between performance and computational cost." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 229, + 546, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 546, + 324 + ], + "type": "text", + "content": "Effect of Integrating Strategy. To evaluate the effect of different guidance integrating strategies, we conduct experiments by integrating guidance information into different modules of image restoration networks, i.e., Enc. (encoder only), Dec. (decoder only), and Enc. & Dec. (both encoder and decoder). As shown in Table 10, the experimental results show that integrating guidance information into both encoder and decoder achieves better performance." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 324, + 546, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 468 + ], + "type": "text", + "content": "Effect of Proposed Modules. To validate the effectiveness of our proposed modules, we conduct comparison with only using I2T mapper ('only I2T'), using explicit representation ('BLIP2'), and replacing guidance with degraded input ('Degra.') From comparison results in Table 11, since 'only I2T' and 'Degra.' cannot provide clean information to restoration process, they fail to obtain improvement upon baseline. Since using explicit representation ('BLIP2') cannot keep the content information of input as good as ours, our method can gain more from guidance. Guidance comparisons of 'only I2T', 'BLIP2', and ours can be found in Suppl." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 475, + 378, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 378, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 378, + 488 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 496, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 675 + ], + "type": "text", + "content": "In this paper, we provide a new perspective for image restoration. Considering that content and degradation are tightly coupled in image representation, while decoupled in textual representation. Rather than direct restoration on image level, we suggest conducting restoration on textual level and in turn utilizing the restored textual content to assist image restoration. To this end, we propose a plug-and-play approach that first encodes degraded images into degraded textual representations and then removes textual degradation information to obtain restored textual representations. Conditioned on the representations, we employ a pre-trained T2I model to synthesize clean guidance images for improving image restoration. We evaluate our method on various image restoration tasks. The experimental results demonstrate it outperforms the state-of-the-art ones." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. This work is partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. U22B2035 and No. 62371164." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2873" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 58, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S. 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In CVPR, pages 21747-21758, 2023. 1, 3" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2878" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_content_list.json b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8031e7cdec6319922f03340234feeac7c770b01a --- /dev/null +++ b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_content_list.json @@ -0,0 +1,1486 @@ +[ + { + "type": "text", + "text": "Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments", + "text_level": 1, + "bbox": [ + 197, + 130, + 776, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yinhua Piao $^{1}$ , Sangseon Lee $^{2}$ , Yijingxiu Lu $^{1}$ , Sun Kim $^{1,3,4}$", + "bbox": [ + 254, + 202, + 714, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Department of Computer Science and Engineering, Seoul National University1 \nInstitute of Computer Technology, Seoul National University2, AIGENDRUG Co., Ltd.3 \nInterdisciplinary Program in Artificial Intelligence, Seoul National University4", + "bbox": [ + 135, + 238, + 833, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{2018-27910, sangseon486, solanoon0113, sunkim.bioinfo}@snu.ac.kr", + "bbox": [ + 194, + 294, + 769, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Out-of-distribution (OOD) generalization in the graph domain is challenging due to complex distribution shifts and a lack of environmental contexts. Recent methods attempt to enhance graph OOD generalization by generating flat environments. However, such flat environments come with inherent limitations to capture more complex data distributions. Considering the DrugOOD dataset, which contains diverse training environments (e.g., scaffold, size, etc.), flat contexts cannot sufficiently address its high heterogeneity. Thus, a new challenge is posed to generate more semantically enriched environments to enhance graph invariant learning for handling distribution shifts. In this paper, we propose a novel approach to generate hierarchical semantic environments for each graph. Firstly, given an input graph, we explicitly extract variant subgraphs from the input graph to generate proxy predictions on local environments. Then, stochastic attention mechanisms are employed to re-extract the subgraphs for regenerating global environments in a hierarchical manner. In addition, we introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies. This approach enables our model to consider the relationships between environments and facilitates robust graph invariant learning. Extensive experiments on real-world graph data have demonstrated the effectiveness of our framework. Particularly, in the challenging dataset DrugOOD, our method achieves up to $1.29\\%$ and $2.83\\%$ improvement over the best baselines on IC50 and EC50 prediction tasks, respectively.", + "bbox": [ + 76, + 376, + 473, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 844, + 209, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graph-structured data is ubiquitous in real-world applications, from social networks to biological networks and", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c355ad2f6378a7f8a9da5e06a35da78dcd8d9b60d9c77443ad176ef8f40f4fec.jpg", + "image_caption": [ + "Figure 1. (a) Results on IC50-SCA dataset from DrugOOD [20]. (b) Flat environments from existing approaches. (c) Hierarchical environments from our methods. For visualization, we set #real environments as 10." + ], + "image_footnote": [], + "bbox": [ + 498, + 340, + 890, + 491 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chemical molecules [14, 16, 21, 48]. One notable advancement in this area is the emergence of Graph Neural Networks (GNNs). GNN-based models have pioneered end-to-end learning strategies to extract valuable information from graphs and have demonstrated remarkable success across various applications [13, 24, 42]. However, the success of GNNs encounters challenges in out-of-distribution (OOD) scenarios primarily due to the intricate nature of graph distribution shifts [3, 9, 28]. Graph data, characterized by nodes, edges, and potential attributes, poses additional challenges compared to other domains such as natural language processing (NLP) or computer vision (CV). Unlike those domains where context is often provided by sentences, paragraphs, or spatial information in images [4, 15, 36], graph lacks a built-in contextual framework, making it inherently challenging to discern the relevance and context of individual graph elements in OOD scenarios [12, 49].", + "bbox": [ + 496, + 583, + 892, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Invariant Risk Minimization (IRM) [2] is a widely used strategy in the Euclidean domain, relying on the assumption that training data is sourced from distinct environments with varied data distributions. Motivated by the success of", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27631", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "invariant learning in the Euclidean domain [1, 2, 8, 17, 26, 29, 31, 32], invariant learning methods for non-Euclidean graphs [6, 7, 10, 27, 27, 30, 43] extend the concept to address the unique challenges posed by graph-structured data. Despite commendable progress in addressing OOD scenarios within the graph domain, existing studies have predominantly adhered to the assumption of a flat environmental situation [5, 33]. For example, in the DrugOOD dataset, there are nearly 7000 diverse training environments in IC50-SCA subset, including a wide variety of distinct substructures. Fig. 1 illustrates three existing approaches to acquire environments when performing invariant learning on this data: \"Real\" means directly utilizing provided environments [27], \"Rand#2\" means randomly splitting samples into two environments [2, 6], and \"Infer#2\" means inferring samples into two environments [8, 17]. As shown in Fig. 1, all existing approaches exhibit poor or comparable performance to empirical risk minimization (ERM), which is consistent with the findings of Yang [43]. These phenomena indicate the shortcomings of flat environments: (1) Limited consideration of local environment similarity degrades performance in numerous environments (e.g., 'Real' case in Fig. 1) (2) Inferring from a small number of environments may fail to capture global environment similarities and interrelationships. (e.g., 'Infer#2' case in Fig. 1)", + "bbox": [ + 76, + 90, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Considering that graphs exhibit a hierarchical structure, with semantic information organized across various levels. This inherent hierarchy is fundamental to understanding structures and properties within graphs [44]. In addition, inspired by the recent works [1, 17, 29], which show that the diversity of environments is recognized as the key to effectively handling graph OOD scenarios, we aim to bridge the gap of flat environments while leveraging the inherent hierarchy of graphs. In this paper, we propose a hierarchical approach to generate semantic environments of each graph for effective graph invariant learning. Initially, we extract variant subgraphs from the input graph, enabling the generation of proxy predictions on local environments. Employing stochastic attention mechanisms, we iteratively re-extract subgraphs, building global environments hierarchically. To guide the robustness of hierarchical environment inference, we introduce a hierarchical environment diversification loss which encourages our model to diversify environments within the same hierarchy while maintaining consistency across different hierarchical levels. This approach not only aids our model in considering relationships between environments but also strengthens graph invariant learning robustness. By modeling relationships between different environments within a hierarchical framework, our approach acquires the rich source of environmental information embedded in the hierarchical structure of graphs. Extensive experiments demonstrate our approach to graph OOD classification datasets. Our contributions can be sum", + "bbox": [ + 76, + 477, + 472, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "marized as follows:", + "bbox": [ + 500, + 90, + 633, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a hierarchical approach to generate semantic environments for effective graph invariant learning. To the best of our knowledge, our proposed method is the first attempt to generate the environments in a hierarchical way in graph OOD generalization.", + "- We introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies.", + "- Extensive experiments have demonstrated our model yields significant improvements over various domains. In molecule graph benchmarks DrugOOD, our method achieves up to $1.29\\%$ and $2.83\\%$ higher ROC-AUC compared to SOTA graph invariant learning approaches." + ], + "bbox": [ + 500, + 106, + 893, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 329, + 650, + 345 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Out-of-Distribution Generalization In the Euclidean domain, such as computer vision, OOD generalization has been studied extensively using a variety of strategies, such as Invariant Risk Minimization (IRM) [2], data augmentation [47], and domain adaptation methods [39]. Unlike deep neural networks with ERM, which suffer performance degradation under data distributional shifts, IRM-based studies [1, 26] have shown powerful and robust performance when providing environmental information. Recently, a two-step optimization framework EIIL [8] has been proposed to train the invariant learning model without explicit environment labels. EIIL trains the environment inference model to learn and infer the environment labels in the first step, and in the second step, EIIL uses inferred environments to conduct invariant learning. Other recent approaches, such as ZIN [29], HRM [31], KerHRM[32], and EDNIL [17] improve the OOD generalization by augmenting the environment to address its high heterogeneity. These augmentation strategies, such as the assistant model, clustering-based model, or effective diversification objective function all enhance the learning stage to infer diverse environments for effective invariant learning.", + "bbox": [ + 496, + 354, + 893, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graph Invariant Learning While general invariant learning methods are effective for the Euclidean domain, challenges arise when applying them to non-Euclidean domains like graph structures. In the realm of graph invariant learning, since graph data have an inherent nature of complex distribution shifts, often lacks explicit environment labels. To address this issue, methodologies have been widely developed and implemented. Approaches such as EERM [41], LiSA [45], and GREA [30] proposed to generate new environments, offering effective strategies to discover invariant patterns without environment label knowledge. While methods like MoleOOD [43] and GIL[27] focus on the inference of environments, providing solutions to", + "bbox": [ + 496, + 704, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27632", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "deal with challenging or unexplored environments. Another dimension of exploration involves learning with auxiliary assistance to ensure sufficient variation, with typical techniques found in CIGA [6], GALA[7]. Collectively, these innovative methods offer detailed strategies to navigate the challenges inherent in graph invariant learning.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problem Definition and Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 193, + 415, + 209 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Sec. 3.1, we introduce notations about out-of-distribution generalization and the background knowledge of graph invariant learning. In Sec. 3.2, we introduce environment inference to explain how recent research works on the graph dataset without environmental information.", + "bbox": [ + 75, + 218, + 468, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 76, + 301, + 261, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following general settings of OOD generalization, we assume that the training datasets are collected from multiple training environments. Let $\\mathcal{G}_{tr} = \\{G^{e}\\}_{e\\in \\mathrm{supp}(\\mathcal{E}_{tr})}$ with different graphs $G^{e} = \\{(G_{i}^{e},y_{i}^{e})|1\\leq i\\leq N^{e}\\}$ be the training datasets, where $G^{e}$ represents the graphs drawn from environment $e$ and $\\mathcal{E}_{tr}$ indicates the environment labels in the training datasets. We denote the environments $\\mathcal{E}_{all}$ as all possible environment labels in the real world. Then, the test datasets contain graphs $\\mathcal{G}_{test} = \\{G^{e^{\\prime}}\\}$ with unknown environment labels $e^\\prime$ ,where $e^\\prime \\in \\operatorname {supp}(\\mathcal{E}_{all})\\setminus \\operatorname {supp}(\\mathcal{E}_{tr})$ Our approach addresses out-of-distribution challenges in graph-level classification by incorporating invariant learning within environments derived from complex heterogeneous data hierarchically.", + "bbox": [ + 75, + 324, + 472, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 542, + 217, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Graph Invariant Learning. Recently, several studies have identified the cause of performance deterioration in out-of-distribution (OOD) graphs, attributing it to the introduction of spurious features. It is widely acknowledged that spurious features exhibit sensitivity to environmental changes, often referred to as environmental factors. The incorporation of spurious features diminishes the significance of invariant features, resulting in a decline in OOD performance. As a result, recent research [6, 7, 27, 45] often involves graph decomposition to extract both variant subgraphs $G_{v}$ and invariant subgraphs $G_{inv}$ from the original graphs $G$ , thereby facilitating the invariant GNN encoder $f$ [24] to learn relationships between invariant features $h_{inv}$ and labels $y$ . Following the invariant risk minimization [2], the encoder $f$ is trained with a regularization term enforcing jointly optimize the encoder $f$ in training environments $e$ , which can generalize to unseen testing environments $e'$ :", + "bbox": [ + 75, + 566, + 472, + 824 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {e \\in \\operatorname {s u p p} \\left\\{\\mathcal {E} _ {t r} \\right\\}} \\mathcal {R} ^ {e} (f) + \\lambda | | \\nabla \\mathcal {R} ^ {e} (f) | | ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 829, + 468, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{R}^e (f) = \\mathbb{E}_{G,y}^e [\\mathcal{L}(f(G),y)]$ denotes the risk of $f$ in environment $e$ , and $\\mathcal{L}(\\cdot ,\\cdot)$ denotes the loss function.", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Environment Inference for GIL. In most cases, environmental information is difficult to obtain, especially in the context of graph generalization. While some datasets may provide metadata that could serve as environmental information, it is not reliable to fully use such information as the ground truth of the environment is not guaranteed. Therefore, existing methods [8, 17, 29, 31, 32] often infer the environmental labels $\\mathcal{E}_{infer}$ by using variant subgraphs $G_{v}$ that are related to the environment. A variant GNN encoder $f^{e}$ is used to learn the variant features $h_v$ from $G_{v}$ and infer the label $\\hat{e}$ of the environment $e$ . This approach allows joint optimization of environment inference and graph invariant learning through a learning process.", + "bbox": [ + 496, + 90, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methods", + "text_level": 1, + "bbox": [ + 498, + 299, + 598, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method consists of three components: hierarchical stochastic subgraph generation Sec. 4.1, hierarchical semantic environment inference Sec. 4.2, and robust graph invariant learning (GIL) with inferred environments Sec. 4.3. In Sec. 4.1, we generate invariant and variant subgraphs hierarchically for hierarchical semantic environment inference. In Sec. 4.2, we learn hierarchical semantic environments using the proposed hierarchical loss. Finally, in Sec. 4.3, we leverage the inferred hierarchical semantic environments to facilitate robust graph invariant learning, enabling us to uncover the invariant relationships between input graphs and their corresponding labels. These three steps together form a comprehensive approach for enhanced graph analysis and understanding.", + "bbox": [ + 496, + 324, + 893, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Hierarchical Stochastic Subgraph Generation", + "text_level": 1, + "bbox": [ + 498, + 542, + 885, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a graph $G = (V, E)$ , where $V$ represents the set of nodes and $E$ represents the set of edges, the goal is to generate the invariant subgraph $G_{v}^{k}$ and variant subgraph $G_{inv}^{k}$ from the original graph $G$ at each hierarchy $k \\in K$ , where $K$ denotes the number of environmental hierarchies. At each hierarchy $k$ , we employ a graph neural network denoted as $\\mathrm{GNN}_k$ to update the hidden embedding $h_i^k = \\mathrm{GNN}_k(h_i^{k-1}, A)$ for each node $v_i \\in V$ . We use graph neural networks as $\\mathrm{GNN}_k$ [42] to aggregate information from neighboring nodes for node embedding updating. In the process of learning variant and invariant subgraphs at each hierarchy, we define a probability distribution function $S^k(\\cdot)$ for edge selection as follows. We omit the hierarchy notations, while the computation of probability distribution is conducted within each hierarchy:", + "bbox": [ + 496, + 566, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i j} = S \\left(h _ {i j}\\right) = \\sigma \\left(\\operatorname {M L P} \\left(\\left[ h _ {i}, h _ {j} \\right]\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 800, + 890, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $s_{ij}$ is the probability of selecting edge $e_{ij}$ , $\\sigma$ is the sigmoid function, and $\\mathrm{MLP}(h_i, h_j)$ is a multi-layer perceptron (MLP) that takes node embeddings $v_i$ and $v_j$ as inputs.", + "bbox": [ + 496, + 825, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To introduce stochasticity in edge selection, we generate a sampler $\\mathbf{p}_{ij} \\in \\{0,1\\}$ from the Bernoulli distribution", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27633", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/11373bc5f57aaf4a8855afe13348729e7334907bfa8cb1f361b5f466462c5327.jpg", + "image_caption": [ + "Figure 2. Our Framework consists of (a) Hierarchical Stochastic Subgraph Generation in Sec. 4.1, (b) Hierarchical Semantic Environments in Sec. 4.2, (c) Robust GIL with Hierarchical Semantic Environments in Sec. 4.3." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 893, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{p}_{ij} \\sim \\{\\pi_1 := s_{ij}, \\pi_0 := 1 - s_{ij}\\}$ . Gumbel-Softmax [19] is then applied to obtain differentiable edge selection probabilities for each edge:", + "bbox": [ + 75, + 478, + 470, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {p}} _ {i j} = \\frac {\\exp \\left(\\left(\\log \\pi_ {1} + \\mathbf {g} _ {1}\\right) / \\tau\\right)}{\\sum_ {i \\in \\{0 , 1 \\}} \\exp \\left(\\left(\\log \\pi_ {i} + \\mathbf {g} _ {i}\\right) / \\tau\\right)} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 534, + 468, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\mathbf{g}_1$ and $\\mathbf{g}_0$ are i.i.d variables sampled from the Gumbel distribution, and $\\tau$ is a temperature parameter that controls the smoothness of the sampling process. A lower $\\tau$ leads to more categorical (hard) selections, while a higher $\\tau$ results in smoother (soft) probabilities. As $\\tau$ approaches 0, $\\hat{\\mathbf{p}}_{ij}$ can be annealed to a categorical distribution.", + "bbox": [ + 75, + 574, + 468, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure hierarchical neighborhood consistency [38] in the generation of stochastic subgraphs, we introduce an additional hierarchical neighbor masking function denoted as $N^k$ . This masking function compares the neighbor matrix from the previous hierarchy ( $k - 1$ ) with the currently selected neighbors, ensuring that nodes within the hierarchical neighborhood are consistently either included or excluded. The hierarchical neighbor mask $N_{ij}^{k}$ can be defined as:", + "bbox": [ + 75, + 665, + 470, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nN _ {i j} ^ {k} = N _ {i j} ^ {k - 1} + \\mathbf {1} \\left\\{N _ {i j} ^ {k - 1} = 0 \\text {a n d} \\mathbf {p} _ {i j} ^ {k} > T \\right\\} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 797, + 468, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T$ denotes the threshold for selecting the edges based on $\\mathbf{p}_{ij}^{(k)}$ , and $\\mathbf{1}$ denotes indicator function. Then we obtain the variant and invariant subgraph at each hierarchy $k$ as:", + "bbox": [ + 76, + 825, + 470, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {v} ^ {k} \\leftarrow A \\odot N ^ {k}, A _ {i n v} ^ {k} \\leftarrow A - A _ {v} ^ {k} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the adjacency matrix of the variant subgraph, denoted as $A_v^k$ , is derived by performing element-wise multiplication between the original edge matrix $A$ and the hierarchical neighbor mask matrix $N^k$ . Conversely, the adjacency matrix of the invariant subgraph, denoted as $A_{inv}^k$ , is obtained by subtracting the edges included in the variant subgraph $A_v^k$ from the original edge matrix $A$ [5, 7, 27]. By following this process iteratively across hierarchies, we construct a series of variant and invariant subgraphs that capture the hierarchical and structural nuances within the original graph, enabling a multi-level analysis of downstream tasks and analysis.", + "bbox": [ + 496, + 478, + 893, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Hierarchical Semantic Environments", + "text_level": 1, + "bbox": [ + 498, + 667, + 821, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the existing environmental information is not reliable or available, we design an environment inference model to assign the graphs to relatively reliable environments. Given prior $p(e|G)$ , we maximize the log-likelihood of $p(y|G)$ to obtain the posterior $p(e|G,y)$ . As there is no solution to the true posterior, existing methods use clustering-based or variational distribution to approximate and infer the posterior. Inspired by a multi-class classification problem, we estimate the posterior using the softmax function as:", + "bbox": [ + 496, + 690, + 893, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP (\\hat {e} \\in \\mathcal {E} _ {t r} | X, Y) = \\frac {\\exp \\left(- l \\left(f ^ {e} \\left(\\Phi (X) , Y\\right)\\right)\\right)}{\\sum_ {e ^ {\\prime} \\in \\operatorname {s u p p} \\left(\\mathcal {E} _ {t r}\\right)} \\exp \\left(- l \\left(f ^ {e ^ {\\prime}} \\left(\\Phi (X) , Y\\right)\\right)\\right)}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 830, + 898, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f^{e}$ denotes neural network with $y^{e}$ -class classifier and $\\Phi$ indicates the variant subgraph generator.", + "bbox": [ + 498, + 869, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "27634", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.1 Intra-Hierarchy Environment Diversification", + "text_level": 1, + "bbox": [ + 76, + 90, + 444, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the previous section, we discussed the extraction of variant subgraphs $\\{G_v^k | k \\in K\\}$ utilizing GNN encoders in conjunction with corresponding stochastic masking $\\{p_{ij}^k | k \\in K\\}$ at each hierarchy $k$ . To guide the learning process effectively, we incorporate an intra-hierarchy environment diversification loss with variant subgraph and estimated posteriors, denoted as $L_{ED}$ :", + "bbox": [ + 75, + 114, + 467, + 220 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {E D} ^ {k} = - \\sum_ {i} \\max _ {e ^ {k}} \\log P \\left(e ^ {k} \\mid f ^ {k} \\left(G _ {v i} ^ {k}, y _ {i}\\right)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 228, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, $L_{ED}$ is designed to guide the network $f^{k}$ to maximize the dependency between $e^{k}$ and $Y$ given the variant subgraph $G_{v}^{k}$ at each hierarchy $k$ . By optimizing this loss, the network $f^{k}$ is ensured to distinguish relationships between the generated environments, fostering diversity within hierarchies.", + "bbox": [ + 75, + 268, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.2 Inter-Hierarchy Environment Augmentation", + "text_level": 1, + "bbox": [ + 76, + 378, + 441, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The goal of inter-hierarchy environment augmentation is to maximize the intra-class mutual information of the estimated invariant subgraphs while maximizing the intra-environment mutual information of the estimated variant subgraphs. Before introducing our objective function, a standard InfoNCE loss [37] can maximize the similarity between positive pairs and minimize the similarities between some randomly sampled negative pairs, which is defined as:", + "bbox": [ + 75, + 402, + 468, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {I n f o N C E}} (z, \\mathcal {N} _ {p}, \\tau) = - \\log \\left(\\frac {\\exp (z \\cdot \\mathcal {N} _ {p} (z) / \\tau)}{\\sum_ {n \\in \\mathcal {N} (z)} \\exp (z \\cdot n / \\tau)}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 531, + 454, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_p(z)$ denotes positive samples for $z$ , and $\\mathcal{N}(z)$ denotes the batch samples for $z$ , and $\\tau$ denotes a temperature parameter. To ensure the reliability and diversification of learned hierarchical environments, we introduce two inter-hierarchy semantic invariants: label-invariant and neighborhood-invariant. Inspired by [5, 7], we introduce two contrastive learning losses: (1) Environment-based Contrastive learning loss $\\mathcal{L}_{\\mathrm{EnvCon}}$ and (2) Label-based Contrastive learning loss $\\mathcal{L}_{\\mathrm{LabelCon}}$ . For environment-based contrastive learning, we define an environment-based neighborhood function $\\mathcal{N}_{p_e}^k$ that constructs the positive set for the anchor sample, where samples have the same inferred environment. To preserve neighborhood consistency across hierarchies, the hierarchical neighborhood function $\\mathcal{N}_{p_e}^k$ can be defined as:", + "bbox": [ + 75, + 580, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} _ {p _ {e}} ^ {k} (z) = \\mathcal {N} _ {p _ {e}} ^ {k - 1} (z) \\cup \\left\\{z _ {i} \\mid e _ {i} ^ {k} = e _ {z} ^ {k}, z _ {i} \\in \\mathcal {N} (z) \\right\\} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 815, + 468, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Using $\\mathcal{N}_{p_e}^k$ , we formulate the environment consistency loss $\\mathcal{L}_{\\mathrm{EnvCon}}$ as follows:", + "bbox": [ + 76, + 844, + 468, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {E n v C o n}} ^ {k} = \\mathbb {E} _ {G _ {v} ^ {k} \\sim p _ {d}} \\left[ \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {v} ^ {k}, \\mathcal {N} _ {p _ {e}} ^ {k} \\left(z _ {v} ^ {k}\\right), \\tau\\right) \\right] \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 883, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_d$ denotes the batch of data, and $z_v^k$ denotes the embedding of variant subgraph $G_v^k$ from a multi-layer perception MLP at $k$ -th hierarchy. Environment consistency loss $\\mathcal{L}_{\\mathrm{EnvCon}}^k$ attracts the variant subgraphs with the same environment labels and pushes the variant subgraphs with different environments, which can augment the power of learning the sufficiency of the environment.", + "bbox": [ + 498, + 90, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For label-based contrastive loss, we define a label-based neighborhood function that represents the positive samples given ground truth label $y$ , which can be defined as $\\mathcal{N}_{p_y}(z) = \\{z_i \\mid y_i = y_z, z_i \\in \\mathcal{N}(z)\\}$ . To measure the label consistency loss, we formulate $\\mathcal{L}_{\\mathrm{LabelCon}}$ as follows:", + "bbox": [ + 498, + 196, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {L a b e l C o n}} ^ {k} = \\mathbb {E} _ {G _ {\\text {i n v}} ^ {k} \\sim p _ {d}} \\left[ \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {\\text {i n v}} ^ {k}, \\mathcal {N} _ {p _ {y}} \\left(z _ {\\text {i n v}} ^ {k}\\right), \\tau\\right) \\right] \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 285, + 890, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{\\mathrm{inv}}$ denotes the embedding of invariant subgraph $G_{\\mathrm{inv}}^k$ from MLP at $k$ -th hierarchy.", + "bbox": [ + 500, + 316, + 890, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.3 Overall Objective Function", + "text_level": 1, + "bbox": [ + 500, + 369, + 743, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering the diversity of intra-hierarchy and consistency of inter-hierarchy, we define a total loss of each hierarchy $k$ as follows:", + "bbox": [ + 498, + 393, + 890, + 438 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {h i e r} _ {k}} = \\mathcal {L} _ {\\mathrm {E D}} ^ {k} + \\alpha \\cdot \\mathcal {L} _ {\\text {E n v C o n}} ^ {k} + \\beta \\cdot \\mathcal {L} _ {\\text {L a b e l C o n}} ^ {k} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 452, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ denote coefficient parameters. And the overall objective loss can be defined as $\\mathcal{L}_{\\mathrm{HEI}} = \\sum_{k=1}^{K} \\mathcal{L}_{\\mathrm{hier}_k}$ . This formulation ensures a unified optimization objective, allowing the model to learn invariant subgraphs that capture both label and environment information effectively.", + "bbox": [ + 498, + 483, + 890, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Robust GIL with Hierarchical Semantic Environments", + "text_level": 1, + "bbox": [ + 498, + 570, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the hierarchical learning stage of environment generation, we extract the generated environment $e^{K - 1}$ from the last hierarchy $K - 1$ . Our objective is to minimize the invariant risk given by Eq. (1), employing the hierarchically generated semantic environments $e^{K - 1}$ . The objective function to calculate $\\mathcal{L}_{inv}$ is as follows:", + "bbox": [ + 498, + 609, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {f} \\mathcal {L} _ {c l s} (f) + \\nabla_ {\\hat {e}} \\left(\\mathcal {L} _ {c l s} (f)\\right) \\text {s . t .} \\hat {e} = \\arg \\min _ {e} \\mathcal {L} _ {\\mathrm {H E I}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 713, + 890, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This equation represents an optimization problem where the goal is to find a function $f$ that minimizes the sum of two terms. The first term $\\mathcal{L}_{cls}(f)$ corresponds to the cross entropy loss of the classification task. The second term $\\nabla_{\\hat{e}}(\\mathcal{L}_{cls}(f))$ represents the gradient with respect to $\\hat{e}$ , which is a specific environment. In essence, the objective is to discover a function $f$ that performs well on a classification task while maintaining stability in performance across different environments, adhering to the specified environmental minimization condition.", + "bbox": [ + 496, + 750, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27635", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/43ff0168d232966610d2b685e64c03eb4cff5769151b34ccfbc01f8b6b51de36.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METHODS\n#ENVIC50-ASSAY\n311IC50-SCA\n6881IC50-SIZE\n190EC50-ASSAY\n47EC50-SCA\n850EC50-SIZE\n167
ERM[40]71.79±0.2768.85±0.6266.70±1.0876.42±1.5964.56±1.2562.79±1.15
IRM[2]72.12±0.4968.69±0.6566.54±0.4276.51±1.8964.82±0.5563.23±0.56
V-REX[26]72.05±1.2568.92±0.9866.33±0.7476.73±2.2662.83±1.2059.27±1.65
EIIL[8]72.60±0.4768.45±0.5366.38±0.6676.96±0.2564.95±1.1262.65±1.88
IB-IRM[1]72.50±0.4968.50±0.4066.64±0.2876.72±0.9864.43±0.8564.10±0.61
GREA [30]72.77±1.2568.33±0.3266.16±0.4672.44±2.5567.98±1.0063.93±3.01
CIGAV1 [6]72.71±0.5269.04±0.8667.24±0.8878.46±0.4566.05±1.2966.01±0.84
CIGAV2 [6]73.17±0.3969.70±0.2767.78±0.76---
MOLEOOD [43]71.38±0.6868.02±0.5566.51±0.5573.25±1.2466.69±0.3465.09±0.90
GALA [7]---79.24±1.3666.00±1.8666.01±0.84
OURS74.01±0.1170.72±0.3068.64±0.2380.82±0.2169.73±0.2166.87±0.38
", + "bbox": [ + 109, + 88, + 859, + 313 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Test ROC-AUC of various models on DrugOOD benchmark datasets. The mean ± standard deviation of all models is reported as an average of 5 executions of each model. The best methods are highlighted in bold and the second best methods are underlined.", + "bbox": [ + 75, + 324, + 893, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 377, + 209, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Extensive experiments were conducted on real-world graph data from diverse domains.", + "bbox": [ + 75, + 404, + 468, + 434 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- CMNIST-75sp. The task is to classify each graph that is converted from an image in the ColoredMNIST dataset [2] into the corresponding handwritten digit using the superpixels algorithm [25]. Distribution shifts exist on node attributes by adding random noises in the testing set.", + "- Graph-SST datasets. We utilize sentiment graph data from SST5 and SST-Twitter datasets from [46]. For the Graph-SST5 dataset, graphs are split into different sets based on averaged node degrees to create distribution shifts. For the Graph-Twitter dataset, we invert the split order to assess the out-of-distribution generalization capability of GNNs trained on large-degree graphs to smaller ones.", + "- DrugOOD. We use six datasets in DrugOOD [20] that are provided with manually specified environment labels. DrugOOD provides more diverse splitting indicators, including assay, scaffold, and size. To comprehensively evaluate the performance of our method under different environment definitions, we adopt these three different splitting schemes on categories IC50 and EC50 provided in DrugOOD. Then we obtain six datasets, EC50-* and IC50-* where the suffix * specifies the splitting scheme i.e. IC50/EC50-ASSAY/SCAFFOLD/SIZE." + ], + "bbox": [ + 76, + 436, + 470, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We comprehensively compare our methods with the following categories of baselines: (1) ERM denotes supervised learning with empirical risk minimization [40]. (2) Euclidean OOD methods: We compare with SOTA invariant learning methods from the Euclidean regime, including IRM [2], V-REX [26], EIIL [8], IB-IRM [1]. (3)", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Graph OOD methods: We also compare with SOTA invariant learning methods from the graph regime. Graph OOD methods can be further split into three groups: environment generation-based baseline methods including GREA [30] and LiSA [45], environment augmentation-based baseline methods including DisC [10] and CIGA [6] and environment inference-based baseline methods including GIL [27], MoleOOD [43], and GALA [7].", + "bbox": [ + 496, + 378, + 893, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Environmental Setup. All methods use the same GIN backbone [42] and the same optimization protocol for fair comparisons. Each of the methods is configured using the same parameters reported in the original paper or selected by grid search. For a fair comparison, we use the same embedding size for all methods. We tune the hyperparameters following the common practice. All details are given in Appendix. We report the ROC-AUC score in the DrugOOD dataset and the accuracy score for the rest of the datasets.", + "bbox": [ + 496, + 518, + 893, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Performance Comparison", + "text_level": 1, + "bbox": [ + 498, + 666, + 736, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first provide a detailed report on the DrugOOD benchmark dataset in Tab. 1. We conduct IC50 and EC50 predictions with different split settings. As shown in Tab. 1 and mentioned in Sec. 1, the DrugOOD dataset includes molecular datasets with complex distributions, such as assay, scaffold, and size split with various numbers of environments. Our approach consistently outperforms existing methods, demonstrating the importance of hierarchical environment learning in addressing complex drug OOD generalization applications. As shown in Tab. 1, compared to Empirical Risk Minimization (ERM), Euclidean-based invariant learning methods, such as IRM [2], V-REX [26], EIIL [8], etc, show comparable or even degraded performance in most experimental settings. This suggests that di", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27636", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8c4f922d971c709641420f9220acaaae6c944ca6c83a9ea717ce230b2bd90d17.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METHODSIC50-SCAIC50-SIZE
w/ env#non-infer RAND=268.54±0.6467.63±0.33
w/ env#non-infer=real68.77±0.7267.60±0.32
w/ env#infer=269.14±0.8067.55±0.34
w/ env#infer=real69.08±0.6467.74±0.13
w/ env#hier-infer (OURS)70.72±0.3068.64±0.23
", + "bbox": [ + 84, + 88, + 460, + 208 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "rectly applying general invariant learning struggles to handle shifts in graph distributions. In contrast, graph-based OOD methods exhibit better performance, as they learn invariant subgraph patterns for graph OOD generalization.", + "bbox": [ + 75, + 265, + 467, + 325 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, in the performance comparison of graph-based OOD methods, the MoleOOD [43] pointed out that simple ERM sometimes outperforms several existing methods when faced with a large number of provided environments in graph OOD datasets, which is aligned with the results of Tab. 1. For example, IC50-SCA dataset is provided with 6881 environments, where 6881 scaffolds or substructures construct a vast amount of environmental information for the dataset. In IC50-SCA dataset, GREA and MoleOOD show poor performance compared to ERM, as shown in Tab. 1. We analyze this phenomenon for two potential reasons: (1) The first reason is that the provided environments are overly fine-grained, thereby similar substructure environments in the training and testing sets. ERM can capture similar substructures to learn similar data distributions, showing better performance. (2) The second reason is that GREA and MoleOOD only generate a small number of environments, which overly simplifies the environment and neglects the relationships between environments. This limits their ability to learn heterogeneous and interrelated environments, resulting in noticeable performance degradation.", + "bbox": [ + 75, + 327, + 467, + 645 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method performs a hierarchical approach to learn relationships between redundant environments and maximize the diversity of environments. Leveraging the high-level semantic environments from the last hierarchy, we minimize invariant prediction risk, thereby achieving better graph OOD generalization. In Appendix, we report performance comparisons showing that our performance is better or comparable to existing methods in general domains.", + "bbox": [ + 75, + 646, + 467, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Effect of Hierarchical Semantic Environments", + "text_level": 1, + "bbox": [ + 76, + 784, + 467, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, similar to existing environment inference-based works for OOD generalization [7, 8], we first analyze the role of environment inference, and then we discuss the effects of hierarchical environments learned by our model, showing the necessity of learning the hierarchical environments for graph invariant learning.", + "bbox": [ + 75, + 810, + 467, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e967cd99c7e779fed7b8122c95bda3d0152d5e45d470f8821daa1a57e34e410d.jpg", + "table_caption": [ + "Table 2. The ablation study on IC50-SCA and IC50-SIZE datasets." + ], + "table_footnote": [], + "table_body": "
CONFIGURATIONSIC50-SCAIC50-SIZE
#real = [#ep]69.08±0.6467.60±0.32
#env = [5]69.35±0.6767.70±0.50
#env = [2]69.14±0.8067.73±0.64
#env=[#ep→#ep/2→5]70.12±0.1468.62±0.34
#env=[#ep→#ep/2→2]70.72±0.3068.64±0.23
", + "bbox": [ + 500, + 88, + 890, + 202 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Sensitivity analysis on generated environments. $\\# e_{p}$ denotes the number of provided environments in datasets.", + "bbox": [ + 498, + 212, + 890, + 239 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Environment Inference. As shown in Tab. 2, we analyze the role of environment inference by comparing the direct usage of non-inferred and inferred environments. Direct usage of the non-inferred environments can be divided into two scenarios: (1) When environments are unavailable, existing methods randomly assign two environments for graph invariant learning, which is shown as 'w/ env#non-infer (rand)' from Tab. 2. (2) DrugOOD dataset provides environmental information, e.g., scaffold information in IC50-SCA dataset. As shown in Tab. 1, we can know the number of environments for both dataset IC50-SCA and dataset IC50-SIZE. In such cases, we use environments for invariant learning, as illustrated by the 'w/ env#non-infer (real)' in Tab. 2.", + "bbox": [ + 496, + 268, + 890, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Secondly, we consider the usage of inferred environments for invariant learning, as indicated in Tab. 2. Through the model of environment inference, we directly predict the flat environment and use it in invariant learning, as illustrated by 'w/ env#infer=*. From Tab. 2, it can be observed that the model with inferred environments exhibits better performance, indicating that learned environments from data are more effective than direct usage of non-inferred environments. Moreover, in dataset IC50-SCA, the effects of inference are more pronounced, emphasizing the necessity of performing environment inference operations in situations with complex real-world environments.", + "bbox": [ + 496, + 467, + 890, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hierarchical Environment Inference. We further analyze the effects of hierarchical environments by comparing them with flat environments. Our model adopts a hierarchical approach to learning environmental information, regulating semantic environmental content between hierarchies through both intra-hierarchy and inter-hierarchy mechanisms. Upon comparing experimental results in IC50-SCA and IC50-SIZE datasets, as shown in Tab. 2, our hierarchical model consistently outperforms invariant learning models with flat environments. This indicates that in real-world datasets, the environmental factors influencing label predictions are complex and interdependent. Consequently, investigating graph invariant learning with hierarchical environment inference is essential for attaining more sophisticated and effective in graph OOD generalization.", + "bbox": [ + 496, + 672, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27637", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Sensitive analysis on hierarchy", + "text_level": 1, + "bbox": [ + 76, + 90, + 346, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also conduct sensitive analysis on the number of hierarchies and the number of environments at each hierarchy. Specifically, in hierarchical settings, we start from the number of environments as the number of environments provided in the first hierarchy for a fair comparison. By comparing the results shown in Tab. 3, we find inferred environments with hierarchical settings help OOD generalization in the graph domain. Inferring flat environments is worse than environment inference with three hierarchies. In addition, inferring a large number of environments $\\# e_{p}$ in a single hierarchy shows poor performance compared to inferring a small number of environments. This is because the model with a large number of environments learns too local and redundant to capture the relationships between environments. However, in a hierarchical setting, even if inference starts from a large number of environments to a small number of environments, different hierarchies can capture the local relationships among a huge number of environments and dynamically maximize the diversity of inferred high-level environments. Therefore, despite the final number of inferred environments is still small, these environments learn the semantic information from complex data distribution hierarchically and can improve the Graph OOD generalization using the high-level semantic environments.", + "bbox": [ + 75, + 113, + 472, + 476 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Discussions", + "text_level": 1, + "bbox": [ + 76, + 484, + 202, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We discuss the diversity of environments generated by different methods as shown in Fig. 3. we compare two environment assignment methods with our method, which are random sampling-based method rand#2, and flat environment inference-based method infer#2, respectively. For a fair comparison, we set two environments for both methods and set the hierarchical environment as $[6881\\to 3440\\to 2]$ for our method using the IC50-sCA dataset from DrugOOD.", + "bbox": [ + 75, + 508, + 468, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As mentioned in [8], the diversity of environments is important to obtain effective IRM models, and large discrepancy of spurious correlations between environments benefits the IRM model. We measure the diversity of environments by calculating the distance of distributions among the acquired environments for each method. More specifically, we measure the Kolomogorov-Smirnov (K-S) statistic [34] as a distance between the two inferred scaffold distributions for each method, respectively. The K-S test can capture the dissimilarity between cumulative distribution functions, making it suitable for our analysis. As shown in Fig. 3, the two environments generated by rand#2 methods are almost the same since they assign the sample to two environments using random sampling, showing the lowest diversity of environments. infer#2 shows better diversity of generated environment distributions with significant p-values $(p = 1.86e - 26)$ . Our method generates more significantly diverse environment distributions $(p = 4.52e - 73)$", + "bbox": [ + 75, + 628, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c8c33da69befed183f47f42b73d4143ed02609657a6f72fee2f416370642dffd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 563, + 88, + 692, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3346f1deaf78852b55033272a522524f9b3642fa35d34e6329ece14dde9cd7dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 88, + 830, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8eaa30a0e0d51c25b16c50d856e4893e185bcc8b60df573b650284ce6c30f9af.jpg", + "image_caption": [ + "Figure 3. Discussions on the diversity of generated environments. We show distributions of two generated environments $env_0$ and $env_1$ for (a) random sampling methods, (b) flat environment inference methods, and (c) our hierarchical environment inference methods. (d) We employ the Kolmogorov-Smirnov test [34] to calculate the diversity of three methods." + ], + "image_footnote": [], + "bbox": [ + 563, + 191, + 692, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/64d51654036bf6b98343ac6c3284af567a56578a8886ca62f96d89bdde0c16e6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 191, + 828, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "compared to other methods, surpassing them in inter-env-distance by a large margin. Moreover, the results are aligned with Fig. 1, our methods outperform other methods in IC50-SCA dataset, indicating that diverse environments can give a clear indication of distribution shifts, therefore IRM can easily identify and eliminate variant features.", + "bbox": [ + 496, + 398, + 893, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 501, + 619, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In our research, we take on the formidable challenge of improving out-of-distribution (OOD) generalization in the graph domain. We observe that recent works often overlook the crucial aspect of studying hierarchical environments in graph invariant learning. To address this gap, we introduce a novel method that generates hierarchical dynamic environments for each graph. Our approach involves hierarchical stochastic subgraph generation, hierarchical environment inference, and a carefully designed learning objective. By incorporating graph invariant learning with inferred high-level environments, our model not only achieves meaningful and diverse environments within the same hierarchy but also ensures consistency across different hierarchies. The effectiveness of our method is particularly pronounced in the DrugOOD dataset, shedding light on the potential for further exploration in hierarchical graph learning within OOD scenarios.", + "bbox": [ + 496, + 527, + 893, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 791, + 679, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by Bio & Medical Technology Development Program of the NRF funded by the Ministry of Science & ICT(NRF-2022M3E5F3085677, RS-2023-00257479), and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00246586).", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27638", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Jean-Christophe Gagnon-Audet, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. 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AI open, 1:57-81, 2020. 1" + ], + "bbox": [ + 501, + 92, + 890, + 643 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "27640", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_model.json b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_model.json new file mode 100644 index 0000000000000000000000000000000000000000..dafe570b67d557022e431f87fc0ee5dcbef10c78 --- /dev/null +++ b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_model.json @@ -0,0 +1,2024 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.199, + 0.131, + 0.777, + 0.175 + ], + "angle": 0, + "content": "Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.203, + 0.715, + 0.222 + ], + "angle": 0, + "content": "Yinhua Piao\\(^{1}\\), Sangseon Lee\\(^{2}\\), Yijingxiu Lu\\(^{1}\\), Sun Kim\\(^{1,3,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.239, + 0.834, + 0.293 + ], + "angle": 0, + "content": "Department of Computer Science and Engineering, Seoul National University1 \nInstitute of Computer Technology, Seoul National University2, AIGENDRUG Co., Ltd.3 \nInterdisciplinary Program in Artificial Intelligence, Seoul National University4" + }, + { + "type": "text", + "bbox": [ + 0.195, + 0.295, + 0.771, + 0.31 + ], + "angle": 0, + "content": "{2018-27910, sangseon486, solanoon0113, sunkim.bioinfo}@snu.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.474, + 0.817 + ], + "angle": 0, + "content": "Out-of-distribution (OOD) generalization in the graph domain is challenging due to complex distribution shifts and a lack of environmental contexts. Recent methods attempt to enhance graph OOD generalization by generating flat environments. However, such flat environments come with inherent limitations to capture more complex data distributions. Considering the DrugOOD dataset, which contains diverse training environments (e.g., scaffold, size, etc.), flat contexts cannot sufficiently address its high heterogeneity. Thus, a new challenge is posed to generate more semantically enriched environments to enhance graph invariant learning for handling distribution shifts. In this paper, we propose a novel approach to generate hierarchical semantic environments for each graph. Firstly, given an input graph, we explicitly extract variant subgraphs from the input graph to generate proxy predictions on local environments. Then, stochastic attention mechanisms are employed to re-extract the subgraphs for regenerating global environments in a hierarchical manner. In addition, we introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies. This approach enables our model to consider the relationships between environments and facilitates robust graph invariant learning. Extensive experiments on real-world graph data have demonstrated the effectiveness of our framework. Particularly, in the challenging dataset DrugOOD, our method achieves up to \\(1.29\\%\\) and \\(2.83\\%\\) improvement over the best baselines on IC50 and EC50 prediction tasks, respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.21, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Graph-structured data is ubiquitous in real-world applications, from social networks to biological networks and" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.342, + 0.892, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.501, + 0.894, + 0.556 + ], + "angle": 0, + "content": "Figure 1. (a) Results on IC50-SCA dataset from DrugOOD [20]. (b) Flat environments from existing approaches. (c) Hierarchical environments from our methods. For visualization, we set #real environments as 10." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.84 + ], + "angle": 0, + "content": "chemical molecules [14, 16, 21, 48]. One notable advancement in this area is the emergence of Graph Neural Networks (GNNs). GNN-based models have pioneered end-to-end learning strategies to extract valuable information from graphs and have demonstrated remarkable success across various applications [13, 24, 42]. However, the success of GNNs encounters challenges in out-of-distribution (OOD) scenarios primarily due to the intricate nature of graph distribution shifts [3, 9, 28]. Graph data, characterized by nodes, edges, and potential attributes, poses additional challenges compared to other domains such as natural language processing (NLP) or computer vision (CV). Unlike those domains where context is often provided by sentences, paragraphs, or spatial information in images [4, 15, 36], graph lacks a built-in contextual framework, making it inherently challenging to discern the relevance and context of individual graph elements in OOD scenarios [12, 49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Invariant Risk Minimization (IRM) [2] is a widely used strategy in the Euclidean domain, relying on the assumption that training data is sourced from distinct environments with varied data distributions. Motivated by the success of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27631" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.471 + ], + "angle": 0, + "content": "invariant learning in the Euclidean domain [1, 2, 8, 17, 26, 29, 31, 32], invariant learning methods for non-Euclidean graphs [6, 7, 10, 27, 27, 30, 43] extend the concept to address the unique challenges posed by graph-structured data. Despite commendable progress in addressing OOD scenarios within the graph domain, existing studies have predominantly adhered to the assumption of a flat environmental situation [5, 33]. For example, in the DrugOOD dataset, there are nearly 7000 diverse training environments in IC50-SCA subset, including a wide variety of distinct substructures. Fig. 1 illustrates three existing approaches to acquire environments when performing invariant learning on this data: \"Real\" means directly utilizing provided environments [27], \"Rand#2\" means randomly splitting samples into two environments [2, 6], and \"Infer#2\" means inferring samples into two environments [8, 17]. As shown in Fig. 1, all existing approaches exhibit poor or comparable performance to empirical risk minimization (ERM), which is consistent with the findings of Yang [43]. These phenomena indicate the shortcomings of flat environments: (1) Limited consideration of local environment similarity degrades performance in numerous environments (e.g., 'Real' case in Fig. 1) (2) Inferring from a small number of environments may fail to capture global environment similarities and interrelationships. (e.g., 'Infer#2' case in Fig. 1)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.478, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Considering that graphs exhibit a hierarchical structure, with semantic information organized across various levels. This inherent hierarchy is fundamental to understanding structures and properties within graphs [44]. In addition, inspired by the recent works [1, 17, 29], which show that the diversity of environments is recognized as the key to effectively handling graph OOD scenarios, we aim to bridge the gap of flat environments while leveraging the inherent hierarchy of graphs. In this paper, we propose a hierarchical approach to generate semantic environments of each graph for effective graph invariant learning. Initially, we extract variant subgraphs from the input graph, enabling the generation of proxy predictions on local environments. Employing stochastic attention mechanisms, we iteratively re-extract subgraphs, building global environments hierarchically. To guide the robustness of hierarchical environment inference, we introduce a hierarchical environment diversification loss which encourages our model to diversify environments within the same hierarchy while maintaining consistency across different hierarchical levels. This approach not only aids our model in considering relationships between environments but also strengthens graph invariant learning robustness. By modeling relationships between different environments within a hierarchical framework, our approach acquires the rich source of environmental information embedded in the hierarchical structure of graphs. Extensive experiments demonstrate our approach to graph OOD classification datasets. Our contributions can be sum" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.634, + 0.105 + ], + "angle": 0, + "content": "marized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.107, + 0.894, + 0.182 + ], + "angle": 0, + "content": "- We propose a hierarchical approach to generate semantic environments for effective graph invariant learning. To the best of our knowledge, our proposed method is the first attempt to generate the environments in a hierarchical way in graph OOD generalization." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.183, + 0.894, + 0.242 + ], + "angle": 0, + "content": "- We introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.243, + 0.894, + 0.32 + ], + "angle": 0, + "content": "- Extensive experiments have demonstrated our model yields significant improvements over various domains. In molecule graph benchmarks DrugOOD, our method achieves up to \\(1.29\\%\\) and \\(2.83\\%\\) higher ROC-AUC compared to SOTA graph invariant learning approaches." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.107, + 0.894, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.33, + 0.651, + 0.346 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.895, + 0.689 + ], + "angle": 0, + "content": "Out-of-Distribution Generalization In the Euclidean domain, such as computer vision, OOD generalization has been studied extensively using a variety of strategies, such as Invariant Risk Minimization (IRM) [2], data augmentation [47], and domain adaptation methods [39]. Unlike deep neural networks with ERM, which suffer performance degradation under data distributional shifts, IRM-based studies [1, 26] have shown powerful and robust performance when providing environmental information. Recently, a two-step optimization framework EIIL [8] has been proposed to train the invariant learning model without explicit environment labels. EIIL trains the environment inference model to learn and infer the environment labels in the first step, and in the second step, EIIL uses inferred environments to conduct invariant learning. Other recent approaches, such as ZIN [29], HRM [31], KerHRM[32], and EDNIL [17] improve the OOD generalization by augmenting the environment to address its high heterogeneity. These augmentation strategies, such as the assistant model, clustering-based model, or effective diversification objective function all enhance the learning stage to infer diverse environments for effective invariant learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Graph Invariant Learning While general invariant learning methods are effective for the Euclidean domain, challenges arise when applying them to non-Euclidean domains like graph structures. In the realm of graph invariant learning, since graph data have an inherent nature of complex distribution shifts, often lacks explicit environment labels. To address this issue, methodologies have been widely developed and implemented. Approaches such as EERM [41], LiSA [45], and GREA [30] proposed to generate new environments, offering effective strategies to discover invariant patterns without environment label knowledge. While methods like MoleOOD [43] and GIL[27] focus on the inference of environments, providing solutions to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27632" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "deal with challenging or unexplored environments. Another dimension of exploration involves learning with auxiliary assistance to ensure sufficient variation, with typical techniques found in CIGA [6], GALA[7]. Collectively, these innovative methods offer detailed strategies to navigate the challenges inherent in graph invariant learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.194, + 0.416, + 0.21 + ], + "angle": 0, + "content": "3. Problem Definition and Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.219, + 0.47, + 0.295 + ], + "angle": 0, + "content": "In Sec. 3.1, we introduce notations about out-of-distribution generalization and the background knowledge of graph invariant learning. In Sec. 3.2, we introduce environment inference to explain how recent research works on the graph dataset without environmental information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.302, + 0.262, + 0.317 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.473, + 0.538 + ], + "angle": 0, + "content": "Following general settings of OOD generalization, we assume that the training datasets are collected from multiple training environments. Let \\(\\mathcal{G}_{tr} = \\{G^{e}\\}_{e\\in \\mathrm{supp}(\\mathcal{E}_{tr})}\\) with different graphs \\(G^{e} = \\{(G_{i}^{e},y_{i}^{e})|1\\leq i\\leq N^{e}\\}\\) be the training datasets, where \\(G^{e}\\) represents the graphs drawn from environment \\(e\\) and \\(\\mathcal{E}_{tr}\\) indicates the environment labels in the training datasets. We denote the environments \\(\\mathcal{E}_{all}\\) as all possible environment labels in the real world. Then, the test datasets contain graphs \\(\\mathcal{G}_{test} = \\{G^{e^{\\prime}}\\}\\) with unknown environment labels \\(e^\\prime\\) ,where \\(e^\\prime \\in \\operatorname {supp}(\\mathcal{E}_{all})\\setminus \\operatorname {supp}(\\mathcal{E}_{tr})\\) Our approach addresses out-of-distribution challenges in graph-level classification by incorporating invariant learning within environments derived from complex heterogeneous data hierarchically." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.218, + 0.558 + ], + "angle": 0, + "content": "3.2. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.473, + 0.825 + ], + "angle": 0, + "content": "Graph Invariant Learning. Recently, several studies have identified the cause of performance deterioration in out-of-distribution (OOD) graphs, attributing it to the introduction of spurious features. It is widely acknowledged that spurious features exhibit sensitivity to environmental changes, often referred to as environmental factors. The incorporation of spurious features diminishes the significance of invariant features, resulting in a decline in OOD performance. As a result, recent research [6, 7, 27, 45] often involves graph decomposition to extract both variant subgraphs \\( G_{v} \\) and invariant subgraphs \\( G_{inv} \\) from the original graphs \\( G \\), thereby facilitating the invariant GNN encoder \\( f \\) [24] to learn relationships between invariant features \\( h_{inv} \\) and labels \\( y \\). Following the invariant risk minimization [2], the encoder \\( f \\) is trained with a regularization term enforcing jointly optimize the encoder \\( f \\) in training environments \\( e \\), which can generalize to unseen testing environments \\( e' \\):" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.83, + 0.47, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\sum_ {e \\in \\operatorname {s u p p} \\left\\{\\mathcal {E} _ {t r} \\right\\}} \\mathcal {R} ^ {e} (f) + \\lambda | | \\nabla \\mathcal {R} ^ {e} (f) | | ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}^e (f) = \\mathbb{E}_{G,y}^e [\\mathcal{L}(f(G),y)]\\) denotes the risk of \\(f\\) in environment \\(e\\), and \\(\\mathcal{L}(\\cdot ,\\cdot)\\) denotes the loss function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.289 + ], + "angle": 0, + "content": "Environment Inference for GIL. In most cases, environmental information is difficult to obtain, especially in the context of graph generalization. While some datasets may provide metadata that could serve as environmental information, it is not reliable to fully use such information as the ground truth of the environment is not guaranteed. Therefore, existing methods [8, 17, 29, 31, 32] often infer the environmental labels \\(\\mathcal{E}_{infer}\\) by using variant subgraphs \\(G_{v}\\) that are related to the environment. A variant GNN encoder \\(f^{e}\\) is used to learn the variant features \\(h_v\\) from \\(G_{v}\\) and infer the label \\(\\hat{e}\\) of the environment \\(e\\). This approach allows joint optimization of environment inference and graph invariant learning through a learning process." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.3, + 0.599, + 0.315 + ], + "angle": 0, + "content": "4. Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.538 + ], + "angle": 0, + "content": "Our method consists of three components: hierarchical stochastic subgraph generation Sec. 4.1, hierarchical semantic environment inference Sec. 4.2, and robust graph invariant learning (GIL) with inferred environments Sec. 4.3. In Sec. 4.1, we generate invariant and variant subgraphs hierarchically for hierarchical semantic environment inference. In Sec. 4.2, we learn hierarchical semantic environments using the proposed hierarchical loss. Finally, in Sec. 4.3, we leverage the inferred hierarchical semantic environments to facilitate robust graph invariant learning, enabling us to uncover the invariant relationships between input graphs and their corresponding labels. These three steps together form a comprehensive approach for enhanced graph analysis and understanding." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.544, + 0.887, + 0.56 + ], + "angle": 0, + "content": "4.1. Hierarchical Stochastic Subgraph Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Given a graph \\( G = (V, E) \\), where \\( V \\) represents the set of nodes and \\( E \\) represents the set of edges, the goal is to generate the invariant subgraph \\( G_{v}^{k} \\) and variant subgraph \\( G_{inv}^{k} \\) from the original graph \\( G \\) at each hierarchy \\( k \\in K \\), where \\( K \\) denotes the number of environmental hierarchies. At each hierarchy \\( k \\), we employ a graph neural network denoted as \\( \\mathrm{GNN}_k \\) to update the hidden embedding \\( h_i^k = \\mathrm{GNN}_k(h_i^{k-1}, A) \\) for each node \\( v_i \\in V \\). We use graph neural networks as \\( \\mathrm{GNN}_k \\) [42] to aggregate information from neighboring nodes for node embedding updating. In the process of learning variant and invariant subgraphs at each hierarchy, we define a probability distribution function \\( S^k(\\cdot) \\) for edge selection as follows. We omit the hierarchy notations, while the computation of probability distribution is conducted within each hierarchy:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.801, + 0.891, + 0.82 + ], + "angle": 0, + "content": "\\[\ns _ {i j} = S \\left(h _ {i j}\\right) = \\sigma \\left(\\operatorname {M L P} \\left(\\left[ h _ {i}, h _ {j} \\right]\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Here, \\( s_{ij} \\) is the probability of selecting edge \\( e_{ij} \\), \\( \\sigma \\) is the sigmoid function, and \\( \\mathrm{MLP}(h_i, h_j) \\) is a multi-layer perceptron (MLP) that takes node embeddings \\( v_i \\) and \\( v_j \\) as inputs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To introduce stochasticity in edge selection, we generate a sampler \\(\\mathbf{p}_{ij} \\in \\{0,1\\}\\) from the Bernoulli distribution" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27633" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.895, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.424, + 0.895, + 0.455 + ], + "angle": 0, + "content": "Figure 2. Our Framework consists of (a) Hierarchical Stochastic Subgraph Generation in Sec. 4.1, (b) Hierarchical Semantic Environments in Sec. 4.2, (c) Robust GIL with Hierarchical Semantic Environments in Sec. 4.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.471, + 0.526 + ], + "angle": 0, + "content": "\\(\\mathbf{p}_{ij} \\sim \\{\\pi_1 := s_{ij}, \\pi_0 := 1 - s_{ij}\\}\\). Gumbel-Softmax [19] is then applied to obtain differentiable edge selection probabilities for each edge:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.535, + 0.47, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {p}} _ {i j} = \\frac {\\exp \\left(\\left(\\log \\pi_ {1} + \\mathbf {g} _ {1}\\right) / \\tau\\right)}{\\sum_ {i \\in \\{0 , 1 \\}} \\exp \\left(\\left(\\log \\pi_ {i} + \\mathbf {g} _ {i}\\right) / \\tau\\right)} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.47, + 0.666 + ], + "angle": 0, + "content": "Here, \\(\\mathbf{g}_1\\) and \\(\\mathbf{g}_0\\) are i.i.d variables sampled from the Gumbel distribution, and \\(\\tau\\) is a temperature parameter that controls the smoothness of the sampling process. A lower \\(\\tau\\) leads to more categorical (hard) selections, while a higher \\(\\tau\\) results in smoother (soft) probabilities. As \\(\\tau\\) approaches 0, \\(\\hat{\\mathbf{p}}_{ij}\\) can be annealed to a categorical distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.471, + 0.789 + ], + "angle": 0, + "content": "To ensure hierarchical neighborhood consistency [38] in the generation of stochastic subgraphs, we introduce an additional hierarchical neighbor masking function denoted as \\( N^k \\). This masking function compares the neighbor matrix from the previous hierarchy (\\( k - 1 \\)) with the currently selected neighbors, ensuring that nodes within the hierarchical neighborhood are consistently either included or excluded. The hierarchical neighbor mask \\( N_{ij}^{k} \\) can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.798, + 0.47, + 0.82 + ], + "angle": 0, + "content": "\\[\nN _ {i j} ^ {k} = N _ {i j} ^ {k - 1} + \\mathbf {1} \\left\\{N _ {i j} ^ {k - 1} = 0 \\text {a n d} \\mathbf {p} _ {i j} ^ {k} > T \\right\\} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.827, + 0.471, + 0.876 + ], + "angle": 0, + "content": "where \\(T\\) denotes the threshold for selecting the edges based on \\(\\mathbf{p}_{ij}^{(k)}\\), and \\(\\mathbf{1}\\) denotes indicator function. Then we obtain the variant and invariant subgraph at each hierarchy \\(k\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.884, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\nA _ {v} ^ {k} \\leftarrow A \\odot N ^ {k}, A _ {i n v} ^ {k} \\leftarrow A - A _ {v} ^ {k} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.895, + 0.661 + ], + "angle": 0, + "content": "where the adjacency matrix of the variant subgraph, denoted as \\( A_v^k \\), is derived by performing element-wise multiplication between the original edge matrix \\( A \\) and the hierarchical neighbor mask matrix \\( N^k \\). Conversely, the adjacency matrix of the invariant subgraph, denoted as \\( A_{inv}^k \\), is obtained by subtracting the edges included in the variant subgraph \\( A_v^k \\) from the original edge matrix \\( A \\) [5, 7, 27]. By following this process iteratively across hierarchies, we construct a series of variant and invariant subgraphs that capture the hierarchical and structural nuances within the original graph, enabling a multi-level analysis of downstream tasks and analysis." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.668, + 0.822, + 0.683 + ], + "angle": 0, + "content": "4.2. Hierarchical Semantic Environments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.691, + 0.894, + 0.827 + ], + "angle": 0, + "content": "Since the existing environmental information is not reliable or available, we design an environment inference model to assign the graphs to relatively reliable environments. Given prior \\( p(e|G) \\), we maximize the log-likelihood of \\( p(y|G) \\) to obtain the posterior \\( p(e|G,y) \\). As there is no solution to the true posterior, existing methods use clustering-based or variational distribution to approximate and infer the posterior. Inspired by a multi-class classification problem, we estimate the posterior using the softmax function as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.831, + 0.9, + 0.868 + ], + "angle": 0, + "content": "\\[\nP (\\hat {e} \\in \\mathcal {E} _ {t r} | X, Y) = \\frac {\\exp \\left(- l \\left(f ^ {e} \\left(\\Phi (X) , Y\\right)\\right)\\right)}{\\sum_ {e ^ {\\prime} \\in \\operatorname {s u p p} \\left(\\mathcal {E} _ {t r}\\right)} \\exp \\left(- l \\left(f ^ {e ^ {\\prime}} \\left(\\Phi (X) , Y\\right)\\right)\\right)}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "where \\( f^{e} \\) denotes neural network with \\( y^{e} \\)-class classifier and \\( \\Phi \\) indicates the variant subgraph generator." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27634" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.445, + 0.107 + ], + "angle": 0, + "content": "4.2.1 Intra-Hierarchy Environment Diversification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.468, + 0.221 + ], + "angle": 0, + "content": "In the previous section, we discussed the extraction of variant subgraphs \\(\\{G_v^k | k \\in K\\}\\) utilizing GNN encoders in conjunction with corresponding stochastic masking \\(\\{p_{ij}^k | k \\in K\\}\\) at each hierarchy \\(k\\). To guide the learning process effectively, we incorporate an intra-hierarchy environment diversification loss with variant subgraph and estimated posteriors, denoted as \\(L_{ED}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.229, + 0.469, + 0.259 + ], + "angle": 0, + "content": "\\[\nL _ {E D} ^ {k} = - \\sum_ {i} \\max _ {e ^ {k}} \\log P \\left(e ^ {k} \\mid f ^ {k} \\left(G _ {v i} ^ {k}, y _ {i}\\right)\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.469, + 0.362 + ], + "angle": 0, + "content": "Specifically, \\(L_{ED}\\) is designed to guide the network \\(f^{k}\\) to maximize the dependency between \\(e^{k}\\) and \\(Y\\) given the variant subgraph \\(G_{v}^{k}\\) at each hierarchy \\(k\\). By optimizing this loss, the network \\(f^{k}\\) is ensured to distinguish relationships between the generated environments, fostering diversity within hierarchies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.38, + 0.442, + 0.395 + ], + "angle": 0, + "content": "4.2.2 Inter-Hierarchy Environment Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.469, + 0.524 + ], + "angle": 0, + "content": "The goal of inter-hierarchy environment augmentation is to maximize the intra-class mutual information of the estimated invariant subgraphs while maximizing the intra-environment mutual information of the estimated variant subgraphs. Before introducing our objective function, a standard InfoNCE loss [37] can maximize the similarity between positive pairs and minimize the similarities between some randomly sampled negative pairs, which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.532, + 0.455, + 0.573 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {I n f o N C E}} (z, \\mathcal {N} _ {p}, \\tau) = - \\log \\left(\\frac {\\exp (z \\cdot \\mathcal {N} _ {p} (z) / \\tau)}{\\sum_ {n \\in \\mathcal {N} (z)} \\exp (z \\cdot n / \\tau)}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.469, + 0.807 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_p(z)\\) denotes positive samples for \\(z\\), and \\(\\mathcal{N}(z)\\) denotes the batch samples for \\(z\\), and \\(\\tau\\) denotes a temperature parameter. To ensure the reliability and diversification of learned hierarchical environments, we introduce two inter-hierarchy semantic invariants: label-invariant and neighborhood-invariant. Inspired by [5, 7], we introduce two contrastive learning losses: (1) Environment-based Contrastive learning loss \\(\\mathcal{L}_{\\mathrm{EnvCon}}\\) and (2) Label-based Contrastive learning loss \\(\\mathcal{L}_{\\mathrm{LabelCon}}\\). For environment-based contrastive learning, we define an environment-based neighborhood function \\(\\mathcal{N}_{p_e}^k\\) that constructs the positive set for the anchor sample, where samples have the same inferred environment. To preserve neighborhood consistency across hierarchies, the hierarchical neighborhood function \\(\\mathcal{N}_{p_e}^k\\) can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.816, + 0.469, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} _ {p _ {e}} ^ {k} (z) = \\mathcal {N} _ {p _ {e}} ^ {k - 1} (z) \\cup \\left\\{z _ {i} \\mid e _ {i} ^ {k} = e _ {z} ^ {k}, z _ {i} \\in \\mathcal {N} (z) \\right\\} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.845, + 0.469, + 0.876 + ], + "angle": 0, + "content": "Using \\(\\mathcal{N}_{p_e}^k\\), we formulate the environment consistency loss \\(\\mathcal{L}_{\\mathrm{EnvCon}}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.884, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {E n v C o n}} ^ {k} = \\mathbb {E} _ {G _ {v} ^ {k} \\sim p _ {d}} \\left[ \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {v} ^ {k}, \\mathcal {N} _ {p _ {e}} ^ {k} \\left(z _ {v} ^ {k}\\right), \\tau\\right) \\right] \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.197 + ], + "angle": 0, + "content": "where \\( p_d \\) denotes the batch of data, and \\( z_v^k \\) denotes the embedding of variant subgraph \\( G_v^k \\) from a multi-layer perception MLP at \\( k \\)-th hierarchy. Environment consistency loss \\( \\mathcal{L}_{\\mathrm{EnvCon}}^k \\) attracts the variant subgraphs with the same environment labels and pushes the variant subgraphs with different environments, which can augment the power of learning the sufficiency of the environment." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.198, + 0.892, + 0.274 + ], + "angle": 0, + "content": "For label-based contrastive loss, we define a label-based neighborhood function that represents the positive samples given ground truth label \\(y\\), which can be defined as \\(\\mathcal{N}_{p_y}(z) = \\{z_i \\mid y_i = y_z, z_i \\in \\mathcal{N}(z)\\}\\). To measure the label consistency loss, we formulate \\(\\mathcal{L}_{\\mathrm{LabelCon}}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.286, + 0.892, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {L a b e l C o n}} ^ {k} = \\mathbb {E} _ {G _ {\\text {i n v}} ^ {k} \\sim p _ {d}} \\left[ \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {\\text {i n v}} ^ {k}, \\mathcal {N} _ {p _ {y}} \\left(z _ {\\text {i n v}} ^ {k}\\right), \\tau\\right) \\right] \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.317, + 0.892, + 0.349 + ], + "angle": 0, + "content": "where \\(z_{\\mathrm{inv}}\\) denotes the embedding of invariant subgraph \\(G_{\\mathrm{inv}}^k\\) from MLP at \\(k\\)-th hierarchy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.37, + 0.744, + 0.385 + ], + "angle": 0, + "content": "4.2.3 Overall Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Considering the diversity of intra-hierarchy and consistency of inter-hierarchy, we define a total loss of each hierarchy \\( k \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.453, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {h i e r} _ {k}} = \\mathcal {L} _ {\\mathrm {E D}} ^ {k} + \\alpha \\cdot \\mathcal {L} _ {\\text {E n v C o n}} ^ {k} + \\beta \\cdot \\mathcal {L} _ {\\text {L a b e l C o n}} ^ {k} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.484, + 0.892, + 0.56 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) denote coefficient parameters. And the overall objective loss can be defined as \\(\\mathcal{L}_{\\mathrm{HEI}} = \\sum_{k=1}^{K} \\mathcal{L}_{\\mathrm{hier}_k}\\). This formulation ensures a unified optimization objective, allowing the model to learn invariant subgraphs that capture both label and environment information effectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.571, + 0.892, + 0.601 + ], + "angle": 0, + "content": "4.3. Robust GIL with Hierarchical Semantic Environments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.61, + 0.892, + 0.701 + ], + "angle": 0, + "content": "After the hierarchical learning stage of environment generation, we extract the generated environment \\( e^{K - 1} \\) from the last hierarchy \\( K - 1 \\). Our objective is to minimize the invariant risk given by Eq. (1), employing the hierarchically generated semantic environments \\( e^{K - 1} \\). The objective function to calculate \\( \\mathcal{L}_{inv} \\) is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.714, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\min _ {f} \\mathcal {L} _ {c l s} (f) + \\nabla_ {\\hat {e}} \\left(\\mathcal {L} _ {c l s} (f)\\right) \\text {s . t .} \\hat {e} = \\arg \\min _ {e} \\mathcal {L} _ {\\mathrm {H E I}} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This equation represents an optimization problem where the goal is to find a function \\( f \\) that minimizes the sum of two terms. The first term \\( \\mathcal{L}_{cls}(f) \\) corresponds to the cross entropy loss of the classification task. The second term \\( \\nabla_{\\hat{e}}(\\mathcal{L}_{cls}(f)) \\) represents the gradient with respect to \\( \\hat{e} \\), which is a specific environment. In essence, the objective is to discover a function \\( f \\) that performs well on a classification task while maintaining stability in performance across different environments, adhering to the specified environmental minimization condition." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27635" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.86, + 0.314 + ], + "angle": 0, + "content": "
METHODS\n#ENVIC50-ASSAY\n311IC50-SCA\n6881IC50-SIZE\n190EC50-ASSAY\n47EC50-SCA\n850EC50-SIZE\n167
ERM[40]71.79±0.2768.85±0.6266.70±1.0876.42±1.5964.56±1.2562.79±1.15
IRM[2]72.12±0.4968.69±0.6566.54±0.4276.51±1.8964.82±0.5563.23±0.56
V-REX[26]72.05±1.2568.92±0.9866.33±0.7476.73±2.2662.83±1.2059.27±1.65
EIIL[8]72.60±0.4768.45±0.5366.38±0.6676.96±0.2564.95±1.1262.65±1.88
IB-IRM[1]72.50±0.4968.50±0.4066.64±0.2876.72±0.9864.43±0.8564.10±0.61
GREA [30]72.77±1.2568.33±0.3266.16±0.4672.44±2.5567.98±1.0063.93±3.01
CIGAV1 [6]72.71±0.5269.04±0.8667.24±0.8878.46±0.4566.05±1.2966.01±0.84
CIGAV2 [6]73.17±0.3969.70±0.2767.78±0.76---
MOLEOOD [43]71.38±0.6868.02±0.5566.51±0.5573.25±1.2466.69±0.3465.09±0.90
GALA [7]---79.24±1.3666.00±1.8666.01±0.84
OURS74.01±0.1170.72±0.3068.64±0.2380.82±0.2169.73±0.2166.87±0.38
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.325, + 0.894, + 0.355 + ], + "angle": 0, + "content": "Table 1. Test ROC-AUC of various models on DrugOOD benchmark datasets. The mean ± standard deviation of all models is reported as an average of 5 executions of each model. The best methods are highlighted in bold and the second best methods are underlined." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.378, + 0.21, + 0.396 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.469, + 0.435 + ], + "angle": 0, + "content": "Datasets. Extensive experiments were conducted on real-world graph data from diverse domains." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.437, + 0.47, + 0.513 + ], + "angle": 0, + "content": "- CMNIST-75sp. The task is to classify each graph that is converted from an image in the ColoredMNIST dataset [2] into the corresponding handwritten digit using the superpixels algorithm [25]. Distribution shifts exist on node attributes by adding random noises in the testing set." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.512, + 0.47, + 0.633 + ], + "angle": 0, + "content": "- Graph-SST datasets. We utilize sentiment graph data from SST5 and SST-Twitter datasets from [46]. For the Graph-SST5 dataset, graphs are split into different sets based on averaged node degrees to create distribution shifts. For the Graph-Twitter dataset, we invert the split order to assess the out-of-distribution generalization capability of GNNs trained on large-degree graphs to smaller ones." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.633, + 0.471, + 0.785 + ], + "angle": 0, + "content": "- DrugOOD. We use six datasets in DrugOOD [20] that are provided with manually specified environment labels. DrugOOD provides more diverse splitting indicators, including assay, scaffold, and size. To comprehensively evaluate the performance of our method under different environment definitions, we adopt these three different splitting schemes on categories IC50 and EC50 provided in DrugOOD. Then we obtain six datasets, EC50-* and IC50-* where the suffix * specifies the splitting scheme i.e. IC50/EC50-ASSAY/SCAFFOLD/SIZE." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.437, + 0.471, + 0.785 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.904 + ], + "angle": 0, + "content": "Baselines. We comprehensively compare our methods with the following categories of baselines: (1) ERM denotes supervised learning with empirical risk minimization [40]. (2) Euclidean OOD methods: We compare with SOTA invariant learning methods from the Euclidean regime, including IRM [2], V-REX [26], EIIL [8], IB-IRM [1]. (3)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.895, + 0.503 + ], + "angle": 0, + "content": "Graph OOD methods: We also compare with SOTA invariant learning methods from the graph regime. Graph OOD methods can be further split into three groups: environment generation-based baseline methods including GREA [30] and LiSA [45], environment augmentation-based baseline methods including DisC [10] and CIGA [6] and environment inference-based baseline methods including GIL [27], MoleOOD [43], and GALA [7]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.895, + 0.657 + ], + "angle": 0, + "content": "Environmental Setup. All methods use the same GIN backbone [42] and the same optimization protocol for fair comparisons. Each of the methods is configured using the same parameters reported in the original paper or selected by grid search. For a fair comparison, we use the same embedding size for all methods. We tune the hyperparameters following the common practice. All details are given in Appendix. We report the ROC-AUC score in the DrugOOD dataset and the accuracy score for the rest of the datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.667, + 0.737, + 0.683 + ], + "angle": 0, + "content": "5.1. Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We first provide a detailed report on the DrugOOD benchmark dataset in Tab. 1. We conduct IC50 and EC50 predictions with different split settings. As shown in Tab. 1 and mentioned in Sec. 1, the DrugOOD dataset includes molecular datasets with complex distributions, such as assay, scaffold, and size split with various numbers of environments. Our approach consistently outperforms existing methods, demonstrating the importance of hierarchical environment learning in addressing complex drug OOD generalization applications. As shown in Tab. 1, compared to Empirical Risk Minimization (ERM), Euclidean-based invariant learning methods, such as IRM [2], V-REX [26], EIIL [8], etc, show comparable or even degraded performance in most experimental settings. This suggests that di" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27636" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.462, + 0.209 + ], + "angle": 0, + "content": "
METHODSIC50-SCAIC50-SIZE
w/ env#non-infer RAND=268.54±0.6467.63±0.33
w/ env#non-infer=real68.77±0.7267.60±0.32
w/ env#infer=269.14±0.8067.55±0.34
w/ env#infer=real69.08±0.6467.74±0.13
w/ env#hier-infer (OURS)70.72±0.3068.64±0.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.219, + 0.468, + 0.234 + ], + "angle": 0, + "content": "Table 2. The ablation study on IC50-SCA and IC50-SIZE datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.468, + 0.327 + ], + "angle": 0, + "content": "rectly applying general invariant learning struggles to handle shifts in graph distributions. In contrast, graph-based OOD methods exhibit better performance, as they learn invariant subgraph patterns for graph OOD generalization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.468, + 0.646 + ], + "angle": 0, + "content": "In addition, in the performance comparison of graph-based OOD methods, the MoleOOD [43] pointed out that simple ERM sometimes outperforms several existing methods when faced with a large number of provided environments in graph OOD datasets, which is aligned with the results of Tab. 1. For example, IC50-SCA dataset is provided with 6881 environments, where 6881 scaffolds or substructures construct a vast amount of environmental information for the dataset. In IC50-SCA dataset, GREA and MoleOOD show poor performance compared to ERM, as shown in Tab. 1. We analyze this phenomenon for two potential reasons: (1) The first reason is that the provided environments are overly fine-grained, thereby similar substructure environments in the training and testing sets. ERM can capture similar substructures to learn similar data distributions, showing better performance. (2) The second reason is that GREA and MoleOOD only generate a small number of environments, which overly simplifies the environment and neglects the relationships between environments. This limits their ability to learn heterogeneous and interrelated environments, resulting in noticeable performance degradation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.647, + 0.468, + 0.769 + ], + "angle": 0, + "content": "Our method performs a hierarchical approach to learn relationships between redundant environments and maximize the diversity of environments. Leveraging the high-level semantic environments from the last hierarchy, we minimize invariant prediction risk, thereby achieving better graph OOD generalization. In Appendix, we report performance comparisons showing that our performance is better or comparable to existing methods in general domains." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.468, + 0.801 + ], + "angle": 0, + "content": "5.2. Effect of Hierarchical Semantic Environments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.902 + ], + "angle": 0, + "content": "In this section, similar to existing environment inference-based works for OOD generalization [7, 8], we first analyze the role of environment inference, and then we discuss the effects of hierarchical environments learned by our model, showing the necessity of learning the hierarchical environments for graph invariant learning." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.892, + 0.203 + ], + "angle": 0, + "content": "
CONFIGURATIONSIC50-SCAIC50-SIZE
#real = [#ep]69.08±0.6467.60±0.32
#env = [5]69.35±0.6767.70±0.50
#env = [2]69.14±0.8067.73±0.64
#env=[#ep→#ep/2→5]70.12±0.1468.62±0.34
#env=[#ep→#ep/2→2]70.72±0.3068.64±0.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.213, + 0.892, + 0.241 + ], + "angle": 0, + "content": "Table 3. Sensitivity analysis on generated environments. \\( \\# e_{p} \\) denotes the number of provided environments in datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.892, + 0.468 + ], + "angle": 0, + "content": "Environment Inference. As shown in Tab. 2, we analyze the role of environment inference by comparing the direct usage of non-inferred and inferred environments. Direct usage of the non-inferred environments can be divided into two scenarios: (1) When environments are unavailable, existing methods randomly assign two environments for graph invariant learning, which is shown as 'w/ env#non-infer (rand)' from Tab. 2. (2) DrugOOD dataset provides environmental information, e.g., scaffold information in IC50-SCA dataset. As shown in Tab. 1, we can know the number of environments for both dataset IC50-SCA and dataset IC50-SIZE. In such cases, we use environments for invariant learning, as illustrated by the 'w/ env#non-infer (real)' in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.649 + ], + "angle": 0, + "content": "Secondly, we consider the usage of inferred environments for invariant learning, as indicated in Tab. 2. Through the model of environment inference, we directly predict the flat environment and use it in invariant learning, as illustrated by 'w/ env#infer=*. From Tab. 2, it can be observed that the model with inferred environments exhibits better performance, indicating that learned environments from data are more effective than direct usage of non-inferred environments. Moreover, in dataset IC50-SCA, the effects of inference are more pronounced, emphasizing the necessity of performing environment inference operations in situations with complex real-world environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Hierarchical Environment Inference. We further analyze the effects of hierarchical environments by comparing them with flat environments. Our model adopts a hierarchical approach to learning environmental information, regulating semantic environmental content between hierarchies through both intra-hierarchy and inter-hierarchy mechanisms. Upon comparing experimental results in IC50-SCA and IC50-SIZE datasets, as shown in Tab. 2, our hierarchical model consistently outperforms invariant learning models with flat environments. This indicates that in real-world datasets, the environmental factors influencing label predictions are complex and interdependent. Consequently, investigating graph invariant learning with hierarchical environment inference is essential for attaining more sophisticated and effective in graph OOD generalization." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27637" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.348, + 0.108 + ], + "angle": 0, + "content": "5.3. Sensitive analysis on hierarchy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.477 + ], + "angle": 0, + "content": "We also conduct sensitive analysis on the number of hierarchies and the number of environments at each hierarchy. Specifically, in hierarchical settings, we start from the number of environments as the number of environments provided in the first hierarchy for a fair comparison. By comparing the results shown in Tab. 3, we find inferred environments with hierarchical settings help OOD generalization in the graph domain. Inferring flat environments is worse than environment inference with three hierarchies. In addition, inferring a large number of environments \\(\\# e_{p}\\) in a single hierarchy shows poor performance compared to inferring a small number of environments. This is because the model with a large number of environments learns too local and redundant to capture the relationships between environments. However, in a hierarchical setting, even if inference starts from a large number of environments to a small number of environments, different hierarchies can capture the local relationships among a huge number of environments and dynamically maximize the diversity of inferred high-level environments. Therefore, despite the final number of inferred environments is still small, these environments learn the semantic information from complex data distribution hierarchically and can improve the Graph OOD generalization using the high-level semantic environments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.204, + 0.5 + ], + "angle": 0, + "content": "5.4. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.629 + ], + "angle": 0, + "content": "We discuss the diversity of environments generated by different methods as shown in Fig. 3. we compare two environment assignment methods with our method, which are random sampling-based method rand#2, and flat environment inference-based method infer#2, respectively. For a fair comparison, we set two environments for both methods and set the hierarchical environment as \\([6881\\to 3440\\to 2]\\) for our method using the IC50-sCA dataset from DrugOOD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.471, + 0.902 + ], + "angle": 0, + "content": "As mentioned in [8], the diversity of environments is important to obtain effective IRM models, and large discrepancy of spurious correlations between environments benefits the IRM model. We measure the diversity of environments by calculating the distance of distributions among the acquired environments for each method. More specifically, we measure the Kolomogorov-Smirnov (K-S) statistic [34] as a distance between the two inferred scaffold distributions for each method, respectively. The K-S test can capture the dissimilarity between cumulative distribution functions, making it suitable for our analysis. As shown in Fig. 3, the two environments generated by rand#2 methods are almost the same since they assign the sample to two environments using random sampling, showing the lowest diversity of environments. infer#2 shows better diversity of generated environment distributions with significant p-values \\((p = 1.86e - 26)\\). Our method generates more significantly diverse environment distributions \\((p = 4.52e - 73)\\)" + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.089, + 0.693, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.089, + 0.831, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.192, + 0.693, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.192, + 0.83, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.307, + 0.895, + 0.391 + ], + "angle": 0, + "content": "Figure 3. Discussions on the diversity of generated environments. We show distributions of two generated environments \\(env_0\\) and \\(env_1\\) for (a) random sampling methods, (b) flat environment inference methods, and (c) our hierarchical environment inference methods. (d) We employ the Kolmogorov-Smirnov test [34] to calculate the diversity of three methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.895, + 0.49 + ], + "angle": 0, + "content": "compared to other methods, surpassing them in inter-env-distance by a large margin. Moreover, the results are aligned with Fig. 1, our methods outperform other methods in IC50-SCA dataset, indicating that diverse environments can give a clear indication of distribution shifts, therefore IRM can easily identify and eliminate variant features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.502, + 0.62, + 0.518 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.895, + 0.784 + ], + "angle": 0, + "content": "In our research, we take on the formidable challenge of improving out-of-distribution (OOD) generalization in the graph domain. We observe that recent works often overlook the crucial aspect of studying hierarchical environments in graph invariant learning. To address this gap, we introduce a novel method that generates hierarchical dynamic environments for each graph. Our approach involves hierarchical stochastic subgraph generation, hierarchical environment inference, and a carefully designed learning objective. By incorporating graph invariant learning with inferred high-level environments, our model not only achieves meaningful and diverse environments within the same hierarchy but also ensures consistency across different hierarchies. The effectiveness of our method is particularly pronounced in the DrugOOD dataset, shedding light on the potential for further exploration in hierarchical graph learning within OOD scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.792, + 0.681, + 0.808 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "This work was supported by Bio & Medical Technology Development Program of the NRF funded by the Ministry of Science & ICT(NRF-2022M3E5F3085677, RS-2023-00257479), and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00246586)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27638" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Jean-Christophe Gagnon-Audet, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. 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AI open, 1:57-81, 2020. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.644 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "27640" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_origin.pdf b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..39e16ffc4b2d8072c8a3b3469a1e8fd57f8fd848 --- /dev/null +++ b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/bf45557d-430d-42a3-9a68-3f81e133f486_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:89e29a28f48cffebedabcf88e6937fd4f3b8a92fba844bb9c5cf0cd003dfeda7 +size 797711 diff --git a/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/full.md b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ddcebf10e53e0b5002c97e7b575bbecd411fb02b --- /dev/null +++ b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/full.md @@ -0,0 +1,310 @@ +# Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments + +Yinhua Piao $^{1}$ , Sangseon Lee $^{2}$ , Yijingxiu Lu $^{1}$ , Sun Kim $^{1,3,4}$ + +Department of Computer Science and Engineering, Seoul National University1 +Institute of Computer Technology, Seoul National University2, AIGENDRUG Co., Ltd.3 +Interdisciplinary Program in Artificial Intelligence, Seoul National University4 + +{2018-27910, sangseon486, solanoon0113, sunkim.bioinfo}@snu.ac.kr + +# Abstract + +Out-of-distribution (OOD) generalization in the graph domain is challenging due to complex distribution shifts and a lack of environmental contexts. Recent methods attempt to enhance graph OOD generalization by generating flat environments. However, such flat environments come with inherent limitations to capture more complex data distributions. Considering the DrugOOD dataset, which contains diverse training environments (e.g., scaffold, size, etc.), flat contexts cannot sufficiently address its high heterogeneity. Thus, a new challenge is posed to generate more semantically enriched environments to enhance graph invariant learning for handling distribution shifts. In this paper, we propose a novel approach to generate hierarchical semantic environments for each graph. Firstly, given an input graph, we explicitly extract variant subgraphs from the input graph to generate proxy predictions on local environments. Then, stochastic attention mechanisms are employed to re-extract the subgraphs for regenerating global environments in a hierarchical manner. In addition, we introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies. This approach enables our model to consider the relationships between environments and facilitates robust graph invariant learning. Extensive experiments on real-world graph data have demonstrated the effectiveness of our framework. Particularly, in the challenging dataset DrugOOD, our method achieves up to $1.29\%$ and $2.83\%$ improvement over the best baselines on IC50 and EC50 prediction tasks, respectively. + +# 1. Introduction + +Graph-structured data is ubiquitous in real-world applications, from social networks to biological networks and + +![](images/c355ad2f6378a7f8a9da5e06a35da78dcd8d9b60d9c77443ad176ef8f40f4fec.jpg) +Figure 1. (a) Results on IC50-SCA dataset from DrugOOD [20]. (b) Flat environments from existing approaches. (c) Hierarchical environments from our methods. For visualization, we set #real environments as 10. + +chemical molecules [14, 16, 21, 48]. One notable advancement in this area is the emergence of Graph Neural Networks (GNNs). GNN-based models have pioneered end-to-end learning strategies to extract valuable information from graphs and have demonstrated remarkable success across various applications [13, 24, 42]. However, the success of GNNs encounters challenges in out-of-distribution (OOD) scenarios primarily due to the intricate nature of graph distribution shifts [3, 9, 28]. Graph data, characterized by nodes, edges, and potential attributes, poses additional challenges compared to other domains such as natural language processing (NLP) or computer vision (CV). Unlike those domains where context is often provided by sentences, paragraphs, or spatial information in images [4, 15, 36], graph lacks a built-in contextual framework, making it inherently challenging to discern the relevance and context of individual graph elements in OOD scenarios [12, 49]. + +Invariant Risk Minimization (IRM) [2] is a widely used strategy in the Euclidean domain, relying on the assumption that training data is sourced from distinct environments with varied data distributions. Motivated by the success of + +invariant learning in the Euclidean domain [1, 2, 8, 17, 26, 29, 31, 32], invariant learning methods for non-Euclidean graphs [6, 7, 10, 27, 27, 30, 43] extend the concept to address the unique challenges posed by graph-structured data. Despite commendable progress in addressing OOD scenarios within the graph domain, existing studies have predominantly adhered to the assumption of a flat environmental situation [5, 33]. For example, in the DrugOOD dataset, there are nearly 7000 diverse training environments in IC50-SCA subset, including a wide variety of distinct substructures. Fig. 1 illustrates three existing approaches to acquire environments when performing invariant learning on this data: "Real" means directly utilizing provided environments [27], "Rand#2" means randomly splitting samples into two environments [2, 6], and "Infer#2" means inferring samples into two environments [8, 17]. As shown in Fig. 1, all existing approaches exhibit poor or comparable performance to empirical risk minimization (ERM), which is consistent with the findings of Yang [43]. These phenomena indicate the shortcomings of flat environments: (1) Limited consideration of local environment similarity degrades performance in numerous environments (e.g., 'Real' case in Fig. 1) (2) Inferring from a small number of environments may fail to capture global environment similarities and interrelationships. (e.g., 'Infer#2' case in Fig. 1) + +Considering that graphs exhibit a hierarchical structure, with semantic information organized across various levels. This inherent hierarchy is fundamental to understanding structures and properties within graphs [44]. In addition, inspired by the recent works [1, 17, 29], which show that the diversity of environments is recognized as the key to effectively handling graph OOD scenarios, we aim to bridge the gap of flat environments while leveraging the inherent hierarchy of graphs. In this paper, we propose a hierarchical approach to generate semantic environments of each graph for effective graph invariant learning. Initially, we extract variant subgraphs from the input graph, enabling the generation of proxy predictions on local environments. Employing stochastic attention mechanisms, we iteratively re-extract subgraphs, building global environments hierarchically. To guide the robustness of hierarchical environment inference, we introduce a hierarchical environment diversification loss which encourages our model to diversify environments within the same hierarchy while maintaining consistency across different hierarchical levels. This approach not only aids our model in considering relationships between environments but also strengthens graph invariant learning robustness. By modeling relationships between different environments within a hierarchical framework, our approach acquires the rich source of environmental information embedded in the hierarchical structure of graphs. Extensive experiments demonstrate our approach to graph OOD classification datasets. Our contributions can be sum + +marized as follows: + +- We propose a hierarchical approach to generate semantic environments for effective graph invariant learning. To the best of our knowledge, our proposed method is the first attempt to generate the environments in a hierarchical way in graph OOD generalization. +- We introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies. +- Extensive experiments have demonstrated our model yields significant improvements over various domains. In molecule graph benchmarks DrugOOD, our method achieves up to $1.29\%$ and $2.83\%$ higher ROC-AUC compared to SOTA graph invariant learning approaches. + +# 2. Related Works + +Out-of-Distribution Generalization In the Euclidean domain, such as computer vision, OOD generalization has been studied extensively using a variety of strategies, such as Invariant Risk Minimization (IRM) [2], data augmentation [47], and domain adaptation methods [39]. Unlike deep neural networks with ERM, which suffer performance degradation under data distributional shifts, IRM-based studies [1, 26] have shown powerful and robust performance when providing environmental information. Recently, a two-step optimization framework EIIL [8] has been proposed to train the invariant learning model without explicit environment labels. EIIL trains the environment inference model to learn and infer the environment labels in the first step, and in the second step, EIIL uses inferred environments to conduct invariant learning. Other recent approaches, such as ZIN [29], HRM [31], KerHRM[32], and EDNIL [17] improve the OOD generalization by augmenting the environment to address its high heterogeneity. These augmentation strategies, such as the assistant model, clustering-based model, or effective diversification objective function all enhance the learning stage to infer diverse environments for effective invariant learning. + +Graph Invariant Learning While general invariant learning methods are effective for the Euclidean domain, challenges arise when applying them to non-Euclidean domains like graph structures. In the realm of graph invariant learning, since graph data have an inherent nature of complex distribution shifts, often lacks explicit environment labels. To address this issue, methodologies have been widely developed and implemented. Approaches such as EERM [41], LiSA [45], and GREA [30] proposed to generate new environments, offering effective strategies to discover invariant patterns without environment label knowledge. While methods like MoleOOD [43] and GIL[27] focus on the inference of environments, providing solutions to + +deal with challenging or unexplored environments. Another dimension of exploration involves learning with auxiliary assistance to ensure sufficient variation, with typical techniques found in CIGA [6], GALA[7]. Collectively, these innovative methods offer detailed strategies to navigate the challenges inherent in graph invariant learning. + +# 3. Problem Definition and Preliminaries + +In Sec. 3.1, we introduce notations about out-of-distribution generalization and the background knowledge of graph invariant learning. In Sec. 3.2, we introduce environment inference to explain how recent research works on the graph dataset without environmental information. + +# 3.1. Problem Definition + +Following general settings of OOD generalization, we assume that the training datasets are collected from multiple training environments. Let $\mathcal{G}_{tr} = \{G^{e}\}_{e\in \mathrm{supp}(\mathcal{E}_{tr})}$ with different graphs $G^{e} = \{(G_{i}^{e},y_{i}^{e})|1\leq i\leq N^{e}\}$ be the training datasets, where $G^{e}$ represents the graphs drawn from environment $e$ and $\mathcal{E}_{tr}$ indicates the environment labels in the training datasets. We denote the environments $\mathcal{E}_{all}$ as all possible environment labels in the real world. Then, the test datasets contain graphs $\mathcal{G}_{test} = \{G^{e^{\prime}}\}$ with unknown environment labels $e^\prime$ ,where $e^\prime \in \operatorname {supp}(\mathcal{E}_{all})\setminus \operatorname {supp}(\mathcal{E}_{tr})$ Our approach addresses out-of-distribution challenges in graph-level classification by incorporating invariant learning within environments derived from complex heterogeneous data hierarchically. + +# 3.2. Preliminaries + +Graph Invariant Learning. Recently, several studies have identified the cause of performance deterioration in out-of-distribution (OOD) graphs, attributing it to the introduction of spurious features. It is widely acknowledged that spurious features exhibit sensitivity to environmental changes, often referred to as environmental factors. The incorporation of spurious features diminishes the significance of invariant features, resulting in a decline in OOD performance. As a result, recent research [6, 7, 27, 45] often involves graph decomposition to extract both variant subgraphs $G_{v}$ and invariant subgraphs $G_{inv}$ from the original graphs $G$ , thereby facilitating the invariant GNN encoder $f$ [24] to learn relationships between invariant features $h_{inv}$ and labels $y$ . Following the invariant risk minimization [2], the encoder $f$ is trained with a regularization term enforcing jointly optimize the encoder $f$ in training environments $e$ , which can generalize to unseen testing environments $e'$ : + +$$ +\sum_ {e \in \operatorname {s u p p} \left\{\mathcal {E} _ {t r} \right\}} \mathcal {R} ^ {e} (f) + \lambda | | \nabla \mathcal {R} ^ {e} (f) | | ^ {2}, \tag {1} +$$ + +where $\mathcal{R}^e (f) = \mathbb{E}_{G,y}^e [\mathcal{L}(f(G),y)]$ denotes the risk of $f$ in environment $e$ , and $\mathcal{L}(\cdot ,\cdot)$ denotes the loss function. + +Environment Inference for GIL. In most cases, environmental information is difficult to obtain, especially in the context of graph generalization. While some datasets may provide metadata that could serve as environmental information, it is not reliable to fully use such information as the ground truth of the environment is not guaranteed. Therefore, existing methods [8, 17, 29, 31, 32] often infer the environmental labels $\mathcal{E}_{infer}$ by using variant subgraphs $G_{v}$ that are related to the environment. A variant GNN encoder $f^{e}$ is used to learn the variant features $h_v$ from $G_{v}$ and infer the label $\hat{e}$ of the environment $e$ . This approach allows joint optimization of environment inference and graph invariant learning through a learning process. + +# 4. Methods + +Our method consists of three components: hierarchical stochastic subgraph generation Sec. 4.1, hierarchical semantic environment inference Sec. 4.2, and robust graph invariant learning (GIL) with inferred environments Sec. 4.3. In Sec. 4.1, we generate invariant and variant subgraphs hierarchically for hierarchical semantic environment inference. In Sec. 4.2, we learn hierarchical semantic environments using the proposed hierarchical loss. Finally, in Sec. 4.3, we leverage the inferred hierarchical semantic environments to facilitate robust graph invariant learning, enabling us to uncover the invariant relationships between input graphs and their corresponding labels. These three steps together form a comprehensive approach for enhanced graph analysis and understanding. + +# 4.1. Hierarchical Stochastic Subgraph Generation + +Given a graph $G = (V, E)$ , where $V$ represents the set of nodes and $E$ represents the set of edges, the goal is to generate the invariant subgraph $G_{v}^{k}$ and variant subgraph $G_{inv}^{k}$ from the original graph $G$ at each hierarchy $k \in K$ , where $K$ denotes the number of environmental hierarchies. At each hierarchy $k$ , we employ a graph neural network denoted as $\mathrm{GNN}_k$ to update the hidden embedding $h_i^k = \mathrm{GNN}_k(h_i^{k-1}, A)$ for each node $v_i \in V$ . We use graph neural networks as $\mathrm{GNN}_k$ [42] to aggregate information from neighboring nodes for node embedding updating. In the process of learning variant and invariant subgraphs at each hierarchy, we define a probability distribution function $S^k(\cdot)$ for edge selection as follows. We omit the hierarchy notations, while the computation of probability distribution is conducted within each hierarchy: + +$$ +s _ {i j} = S \left(h _ {i j}\right) = \sigma \left(\operatorname {M L P} \left(\left[ h _ {i}, h _ {j} \right]\right)\right) \tag {2} +$$ + +Here, $s_{ij}$ is the probability of selecting edge $e_{ij}$ , $\sigma$ is the sigmoid function, and $\mathrm{MLP}(h_i, h_j)$ is a multi-layer perceptron (MLP) that takes node embeddings $v_i$ and $v_j$ as inputs. + +To introduce stochasticity in edge selection, we generate a sampler $\mathbf{p}_{ij} \in \{0,1\}$ from the Bernoulli distribution + +![](images/11373bc5f57aaf4a8855afe13348729e7334907bfa8cb1f361b5f466462c5327.jpg) +Figure 2. Our Framework consists of (a) Hierarchical Stochastic Subgraph Generation in Sec. 4.1, (b) Hierarchical Semantic Environments in Sec. 4.2, (c) Robust GIL with Hierarchical Semantic Environments in Sec. 4.3. + +$\mathbf{p}_{ij} \sim \{\pi_1 := s_{ij}, \pi_0 := 1 - s_{ij}\}$ . Gumbel-Softmax [19] is then applied to obtain differentiable edge selection probabilities for each edge: + +$$ +\hat {\mathbf {p}} _ {i j} = \frac {\exp \left(\left(\log \pi_ {1} + \mathbf {g} _ {1}\right) / \tau\right)}{\sum_ {i \in \{0 , 1 \}} \exp \left(\left(\log \pi_ {i} + \mathbf {g} _ {i}\right) / \tau\right)} \tag {3} +$$ + +Here, $\mathbf{g}_1$ and $\mathbf{g}_0$ are i.i.d variables sampled from the Gumbel distribution, and $\tau$ is a temperature parameter that controls the smoothness of the sampling process. A lower $\tau$ leads to more categorical (hard) selections, while a higher $\tau$ results in smoother (soft) probabilities. As $\tau$ approaches 0, $\hat{\mathbf{p}}_{ij}$ can be annealed to a categorical distribution. + +To ensure hierarchical neighborhood consistency [38] in the generation of stochastic subgraphs, we introduce an additional hierarchical neighbor masking function denoted as $N^k$ . This masking function compares the neighbor matrix from the previous hierarchy ( $k - 1$ ) with the currently selected neighbors, ensuring that nodes within the hierarchical neighborhood are consistently either included or excluded. The hierarchical neighbor mask $N_{ij}^{k}$ can be defined as: + +$$ +N _ {i j} ^ {k} = N _ {i j} ^ {k - 1} + \mathbf {1} \left\{N _ {i j} ^ {k - 1} = 0 \text {a n d} \mathbf {p} _ {i j} ^ {k} > T \right\} \tag {4} +$$ + +where $T$ denotes the threshold for selecting the edges based on $\mathbf{p}_{ij}^{(k)}$ , and $\mathbf{1}$ denotes indicator function. Then we obtain the variant and invariant subgraph at each hierarchy $k$ as: + +$$ +A _ {v} ^ {k} \leftarrow A \odot N ^ {k}, A _ {i n v} ^ {k} \leftarrow A - A _ {v} ^ {k} \tag {5} +$$ + +where the adjacency matrix of the variant subgraph, denoted as $A_v^k$ , is derived by performing element-wise multiplication between the original edge matrix $A$ and the hierarchical neighbor mask matrix $N^k$ . Conversely, the adjacency matrix of the invariant subgraph, denoted as $A_{inv}^k$ , is obtained by subtracting the edges included in the variant subgraph $A_v^k$ from the original edge matrix $A$ [5, 7, 27]. By following this process iteratively across hierarchies, we construct a series of variant and invariant subgraphs that capture the hierarchical and structural nuances within the original graph, enabling a multi-level analysis of downstream tasks and analysis. + +# 4.2. Hierarchical Semantic Environments + +Since the existing environmental information is not reliable or available, we design an environment inference model to assign the graphs to relatively reliable environments. Given prior $p(e|G)$ , we maximize the log-likelihood of $p(y|G)$ to obtain the posterior $p(e|G,y)$ . As there is no solution to the true posterior, existing methods use clustering-based or variational distribution to approximate and infer the posterior. Inspired by a multi-class classification problem, we estimate the posterior using the softmax function as: + +$$ +P (\hat {e} \in \mathcal {E} _ {t r} | X, Y) = \frac {\exp \left(- l \left(f ^ {e} \left(\Phi (X) , Y\right)\right)\right)}{\sum_ {e ^ {\prime} \in \operatorname {s u p p} \left(\mathcal {E} _ {t r}\right)} \exp \left(- l \left(f ^ {e ^ {\prime}} \left(\Phi (X) , Y\right)\right)\right)} +$$ + +where $f^{e}$ denotes neural network with $y^{e}$ -class classifier and $\Phi$ indicates the variant subgraph generator. + +# 4.2.1 Intra-Hierarchy Environment Diversification + +In the previous section, we discussed the extraction of variant subgraphs $\{G_v^k | k \in K\}$ utilizing GNN encoders in conjunction with corresponding stochastic masking $\{p_{ij}^k | k \in K\}$ at each hierarchy $k$ . To guide the learning process effectively, we incorporate an intra-hierarchy environment diversification loss with variant subgraph and estimated posteriors, denoted as $L_{ED}$ : + +$$ +L _ {E D} ^ {k} = - \sum_ {i} \max _ {e ^ {k}} \log P \left(e ^ {k} \mid f ^ {k} \left(G _ {v i} ^ {k}, y _ {i}\right)\right) \tag {6} +$$ + +Specifically, $L_{ED}$ is designed to guide the network $f^{k}$ to maximize the dependency between $e^{k}$ and $Y$ given the variant subgraph $G_{v}^{k}$ at each hierarchy $k$ . By optimizing this loss, the network $f^{k}$ is ensured to distinguish relationships between the generated environments, fostering diversity within hierarchies. + +# 4.2.2 Inter-Hierarchy Environment Augmentation + +The goal of inter-hierarchy environment augmentation is to maximize the intra-class mutual information of the estimated invariant subgraphs while maximizing the intra-environment mutual information of the estimated variant subgraphs. Before introducing our objective function, a standard InfoNCE loss [37] can maximize the similarity between positive pairs and minimize the similarities between some randomly sampled negative pairs, which is defined as: + +$$ +\mathcal {L} _ {\mathrm {I n f o N C E}} (z, \mathcal {N} _ {p}, \tau) = - \log \left(\frac {\exp (z \cdot \mathcal {N} _ {p} (z) / \tau)}{\sum_ {n \in \mathcal {N} (z)} \exp (z \cdot n / \tau)}\right) +$$ + +where $\mathcal{N}_p(z)$ denotes positive samples for $z$ , and $\mathcal{N}(z)$ denotes the batch samples for $z$ , and $\tau$ denotes a temperature parameter. To ensure the reliability and diversification of learned hierarchical environments, we introduce two inter-hierarchy semantic invariants: label-invariant and neighborhood-invariant. Inspired by [5, 7], we introduce two contrastive learning losses: (1) Environment-based Contrastive learning loss $\mathcal{L}_{\mathrm{EnvCon}}$ and (2) Label-based Contrastive learning loss $\mathcal{L}_{\mathrm{LabelCon}}$ . For environment-based contrastive learning, we define an environment-based neighborhood function $\mathcal{N}_{p_e}^k$ that constructs the positive set for the anchor sample, where samples have the same inferred environment. To preserve neighborhood consistency across hierarchies, the hierarchical neighborhood function $\mathcal{N}_{p_e}^k$ can be defined as: + +$$ +\mathcal {N} _ {p _ {e}} ^ {k} (z) = \mathcal {N} _ {p _ {e}} ^ {k - 1} (z) \cup \left\{z _ {i} \mid e _ {i} ^ {k} = e _ {z} ^ {k}, z _ {i} \in \mathcal {N} (z) \right\} \tag {7} +$$ + +Using $\mathcal{N}_{p_e}^k$ , we formulate the environment consistency loss $\mathcal{L}_{\mathrm{EnvCon}}$ as follows: + +$$ +\mathcal {L} _ {\text {E n v C o n}} ^ {k} = \mathbb {E} _ {G _ {v} ^ {k} \sim p _ {d}} \left[ \mathcal {L} _ {\text {I n f o N C E}} \left(z _ {v} ^ {k}, \mathcal {N} _ {p _ {e}} ^ {k} \left(z _ {v} ^ {k}\right), \tau\right) \right] \tag {8} +$$ + +where $p_d$ denotes the batch of data, and $z_v^k$ denotes the embedding of variant subgraph $G_v^k$ from a multi-layer perception MLP at $k$ -th hierarchy. Environment consistency loss $\mathcal{L}_{\mathrm{EnvCon}}^k$ attracts the variant subgraphs with the same environment labels and pushes the variant subgraphs with different environments, which can augment the power of learning the sufficiency of the environment. + +For label-based contrastive loss, we define a label-based neighborhood function that represents the positive samples given ground truth label $y$ , which can be defined as $\mathcal{N}_{p_y}(z) = \{z_i \mid y_i = y_z, z_i \in \mathcal{N}(z)\}$ . To measure the label consistency loss, we formulate $\mathcal{L}_{\mathrm{LabelCon}}$ as follows: + +$$ +\mathcal {L} _ {\text {L a b e l C o n}} ^ {k} = \mathbb {E} _ {G _ {\text {i n v}} ^ {k} \sim p _ {d}} \left[ \mathcal {L} _ {\text {I n f o N C E}} \left(z _ {\text {i n v}} ^ {k}, \mathcal {N} _ {p _ {y}} \left(z _ {\text {i n v}} ^ {k}\right), \tau\right) \right] \tag {9} +$$ + +where $z_{\mathrm{inv}}$ denotes the embedding of invariant subgraph $G_{\mathrm{inv}}^k$ from MLP at $k$ -th hierarchy. + +# 4.2.3 Overall Objective Function + +Considering the diversity of intra-hierarchy and consistency of inter-hierarchy, we define a total loss of each hierarchy $k$ as follows: + +$$ +\mathcal {L} _ {\text {h i e r} _ {k}} = \mathcal {L} _ {\mathrm {E D}} ^ {k} + \alpha \cdot \mathcal {L} _ {\text {E n v C o n}} ^ {k} + \beta \cdot \mathcal {L} _ {\text {L a b e l C o n}} ^ {k} \tag {10} +$$ + +where $\alpha$ and $\beta$ denote coefficient parameters. And the overall objective loss can be defined as $\mathcal{L}_{\mathrm{HEI}} = \sum_{k=1}^{K} \mathcal{L}_{\mathrm{hier}_k}$ . This formulation ensures a unified optimization objective, allowing the model to learn invariant subgraphs that capture both label and environment information effectively. + +# 4.3. Robust GIL with Hierarchical Semantic Environments + +After the hierarchical learning stage of environment generation, we extract the generated environment $e^{K - 1}$ from the last hierarchy $K - 1$ . Our objective is to minimize the invariant risk given by Eq. (1), employing the hierarchically generated semantic environments $e^{K - 1}$ . The objective function to calculate $\mathcal{L}_{inv}$ is as follows: + +$$ +\min _ {f} \mathcal {L} _ {c l s} (f) + \nabla_ {\hat {e}} \left(\mathcal {L} _ {c l s} (f)\right) \text {s . t .} \hat {e} = \arg \min _ {e} \mathcal {L} _ {\mathrm {H E I}} \tag {11} +$$ + +This equation represents an optimization problem where the goal is to find a function $f$ that minimizes the sum of two terms. The first term $\mathcal{L}_{cls}(f)$ corresponds to the cross entropy loss of the classification task. The second term $\nabla_{\hat{e}}(\mathcal{L}_{cls}(f))$ represents the gradient with respect to $\hat{e}$ , which is a specific environment. In essence, the objective is to discover a function $f$ that performs well on a classification task while maintaining stability in performance across different environments, adhering to the specified environmental minimization condition. + +
METHODS +#ENVIC50-ASSAY +311IC50-SCA +6881IC50-SIZE +190EC50-ASSAY +47EC50-SCA +850EC50-SIZE +167
ERM[40]71.79±0.2768.85±0.6266.70±1.0876.42±1.5964.56±1.2562.79±1.15
IRM[2]72.12±0.4968.69±0.6566.54±0.4276.51±1.8964.82±0.5563.23±0.56
V-REX[26]72.05±1.2568.92±0.9866.33±0.7476.73±2.2662.83±1.2059.27±1.65
EIIL[8]72.60±0.4768.45±0.5366.38±0.6676.96±0.2564.95±1.1262.65±1.88
IB-IRM[1]72.50±0.4968.50±0.4066.64±0.2876.72±0.9864.43±0.8564.10±0.61
GREA [30]72.77±1.2568.33±0.3266.16±0.4672.44±2.5567.98±1.0063.93±3.01
CIGAV1 [6]72.71±0.5269.04±0.8667.24±0.8878.46±0.4566.05±1.2966.01±0.84
CIGAV2 [6]73.17±0.3969.70±0.2767.78±0.76---
MOLEOOD [43]71.38±0.6868.02±0.5566.51±0.5573.25±1.2466.69±0.3465.09±0.90
GALA [7]---79.24±1.3666.00±1.8666.01±0.84
OURS74.01±0.1170.72±0.3068.64±0.2380.82±0.2169.73±0.2166.87±0.38
+ +Table 1. Test ROC-AUC of various models on DrugOOD benchmark datasets. The mean ± standard deviation of all models is reported as an average of 5 executions of each model. The best methods are highlighted in bold and the second best methods are underlined. + +# 5. Experiments + +Datasets. Extensive experiments were conducted on real-world graph data from diverse domains. + +- CMNIST-75sp. The task is to classify each graph that is converted from an image in the ColoredMNIST dataset [2] into the corresponding handwritten digit using the superpixels algorithm [25]. Distribution shifts exist on node attributes by adding random noises in the testing set. +- Graph-SST datasets. We utilize sentiment graph data from SST5 and SST-Twitter datasets from [46]. For the Graph-SST5 dataset, graphs are split into different sets based on averaged node degrees to create distribution shifts. For the Graph-Twitter dataset, we invert the split order to assess the out-of-distribution generalization capability of GNNs trained on large-degree graphs to smaller ones. +- DrugOOD. We use six datasets in DrugOOD [20] that are provided with manually specified environment labels. DrugOOD provides more diverse splitting indicators, including assay, scaffold, and size. To comprehensively evaluate the performance of our method under different environment definitions, we adopt these three different splitting schemes on categories IC50 and EC50 provided in DrugOOD. Then we obtain six datasets, EC50-* and IC50-* where the suffix * specifies the splitting scheme i.e. IC50/EC50-ASSAY/SCAFFOLD/SIZE. + +Baselines. We comprehensively compare our methods with the following categories of baselines: (1) ERM denotes supervised learning with empirical risk minimization [40]. (2) Euclidean OOD methods: We compare with SOTA invariant learning methods from the Euclidean regime, including IRM [2], V-REX [26], EIIL [8], IB-IRM [1]. (3) + +Graph OOD methods: We also compare with SOTA invariant learning methods from the graph regime. Graph OOD methods can be further split into three groups: environment generation-based baseline methods including GREA [30] and LiSA [45], environment augmentation-based baseline methods including DisC [10] and CIGA [6] and environment inference-based baseline methods including GIL [27], MoleOOD [43], and GALA [7]. + +Environmental Setup. All methods use the same GIN backbone [42] and the same optimization protocol for fair comparisons. Each of the methods is configured using the same parameters reported in the original paper or selected by grid search. For a fair comparison, we use the same embedding size for all methods. We tune the hyperparameters following the common practice. All details are given in Appendix. We report the ROC-AUC score in the DrugOOD dataset and the accuracy score for the rest of the datasets. + +# 5.1. Performance Comparison + +We first provide a detailed report on the DrugOOD benchmark dataset in Tab. 1. We conduct IC50 and EC50 predictions with different split settings. As shown in Tab. 1 and mentioned in Sec. 1, the DrugOOD dataset includes molecular datasets with complex distributions, such as assay, scaffold, and size split with various numbers of environments. Our approach consistently outperforms existing methods, demonstrating the importance of hierarchical environment learning in addressing complex drug OOD generalization applications. As shown in Tab. 1, compared to Empirical Risk Minimization (ERM), Euclidean-based invariant learning methods, such as IRM [2], V-REX [26], EIIL [8], etc, show comparable or even degraded performance in most experimental settings. This suggests that di + +
METHODSIC50-SCAIC50-SIZE
w/ env#non-infer RAND=268.54±0.6467.63±0.33
w/ env#non-infer=real68.77±0.7267.60±0.32
w/ env#infer=269.14±0.8067.55±0.34
w/ env#infer=real69.08±0.6467.74±0.13
w/ env#hier-infer (OURS)70.72±0.3068.64±0.23
+ +rectly applying general invariant learning struggles to handle shifts in graph distributions. In contrast, graph-based OOD methods exhibit better performance, as they learn invariant subgraph patterns for graph OOD generalization. + +In addition, in the performance comparison of graph-based OOD methods, the MoleOOD [43] pointed out that simple ERM sometimes outperforms several existing methods when faced with a large number of provided environments in graph OOD datasets, which is aligned with the results of Tab. 1. For example, IC50-SCA dataset is provided with 6881 environments, where 6881 scaffolds or substructures construct a vast amount of environmental information for the dataset. In IC50-SCA dataset, GREA and MoleOOD show poor performance compared to ERM, as shown in Tab. 1. We analyze this phenomenon for two potential reasons: (1) The first reason is that the provided environments are overly fine-grained, thereby similar substructure environments in the training and testing sets. ERM can capture similar substructures to learn similar data distributions, showing better performance. (2) The second reason is that GREA and MoleOOD only generate a small number of environments, which overly simplifies the environment and neglects the relationships between environments. This limits their ability to learn heterogeneous and interrelated environments, resulting in noticeable performance degradation. + +Our method performs a hierarchical approach to learn relationships between redundant environments and maximize the diversity of environments. Leveraging the high-level semantic environments from the last hierarchy, we minimize invariant prediction risk, thereby achieving better graph OOD generalization. In Appendix, we report performance comparisons showing that our performance is better or comparable to existing methods in general domains. + +# 5.2. Effect of Hierarchical Semantic Environments + +In this section, similar to existing environment inference-based works for OOD generalization [7, 8], we first analyze the role of environment inference, and then we discuss the effects of hierarchical environments learned by our model, showing the necessity of learning the hierarchical environments for graph invariant learning. + +Table 2. The ablation study on IC50-SCA and IC50-SIZE datasets. + +
CONFIGURATIONSIC50-SCAIC50-SIZE
#real = [#ep]69.08±0.6467.60±0.32
#env = [5]69.35±0.6767.70±0.50
#env = [2]69.14±0.8067.73±0.64
#env=[#ep→#ep/2→5]70.12±0.1468.62±0.34
#env=[#ep→#ep/2→2]70.72±0.3068.64±0.23
+ +Table 3. Sensitivity analysis on generated environments. $\# e_{p}$ denotes the number of provided environments in datasets. + +Environment Inference. As shown in Tab. 2, we analyze the role of environment inference by comparing the direct usage of non-inferred and inferred environments. Direct usage of the non-inferred environments can be divided into two scenarios: (1) When environments are unavailable, existing methods randomly assign two environments for graph invariant learning, which is shown as 'w/ env#non-infer (rand)' from Tab. 2. (2) DrugOOD dataset provides environmental information, e.g., scaffold information in IC50-SCA dataset. As shown in Tab. 1, we can know the number of environments for both dataset IC50-SCA and dataset IC50-SIZE. In such cases, we use environments for invariant learning, as illustrated by the 'w/ env#non-infer (real)' in Tab. 2. + +Secondly, we consider the usage of inferred environments for invariant learning, as indicated in Tab. 2. Through the model of environment inference, we directly predict the flat environment and use it in invariant learning, as illustrated by 'w/ env#infer=*. From Tab. 2, it can be observed that the model with inferred environments exhibits better performance, indicating that learned environments from data are more effective than direct usage of non-inferred environments. Moreover, in dataset IC50-SCA, the effects of inference are more pronounced, emphasizing the necessity of performing environment inference operations in situations with complex real-world environments. + +Hierarchical Environment Inference. We further analyze the effects of hierarchical environments by comparing them with flat environments. Our model adopts a hierarchical approach to learning environmental information, regulating semantic environmental content between hierarchies through both intra-hierarchy and inter-hierarchy mechanisms. Upon comparing experimental results in IC50-SCA and IC50-SIZE datasets, as shown in Tab. 2, our hierarchical model consistently outperforms invariant learning models with flat environments. This indicates that in real-world datasets, the environmental factors influencing label predictions are complex and interdependent. Consequently, investigating graph invariant learning with hierarchical environment inference is essential for attaining more sophisticated and effective in graph OOD generalization. + +# 5.3. Sensitive analysis on hierarchy + +We also conduct sensitive analysis on the number of hierarchies and the number of environments at each hierarchy. Specifically, in hierarchical settings, we start from the number of environments as the number of environments provided in the first hierarchy for a fair comparison. By comparing the results shown in Tab. 3, we find inferred environments with hierarchical settings help OOD generalization in the graph domain. Inferring flat environments is worse than environment inference with three hierarchies. In addition, inferring a large number of environments $\# e_{p}$ in a single hierarchy shows poor performance compared to inferring a small number of environments. This is because the model with a large number of environments learns too local and redundant to capture the relationships between environments. However, in a hierarchical setting, even if inference starts from a large number of environments to a small number of environments, different hierarchies can capture the local relationships among a huge number of environments and dynamically maximize the diversity of inferred high-level environments. Therefore, despite the final number of inferred environments is still small, these environments learn the semantic information from complex data distribution hierarchically and can improve the Graph OOD generalization using the high-level semantic environments. + +# 5.4. Discussions + +We discuss the diversity of environments generated by different methods as shown in Fig. 3. we compare two environment assignment methods with our method, which are random sampling-based method rand#2, and flat environment inference-based method infer#2, respectively. For a fair comparison, we set two environments for both methods and set the hierarchical environment as $[6881\to 3440\to 2]$ for our method using the IC50-sCA dataset from DrugOOD. + +As mentioned in [8], the diversity of environments is important to obtain effective IRM models, and large discrepancy of spurious correlations between environments benefits the IRM model. We measure the diversity of environments by calculating the distance of distributions among the acquired environments for each method. More specifically, we measure the Kolomogorov-Smirnov (K-S) statistic [34] as a distance between the two inferred scaffold distributions for each method, respectively. The K-S test can capture the dissimilarity between cumulative distribution functions, making it suitable for our analysis. As shown in Fig. 3, the two environments generated by rand#2 methods are almost the same since they assign the sample to two environments using random sampling, showing the lowest diversity of environments. infer#2 shows better diversity of generated environment distributions with significant p-values $(p = 1.86e - 26)$ . Our method generates more significantly diverse environment distributions $(p = 4.52e - 73)$ + +![](images/c8c33da69befed183f47f42b73d4143ed02609657a6f72fee2f416370642dffd.jpg) + +![](images/3346f1deaf78852b55033272a522524f9b3642fa35d34e6329ece14dde9cd7dd.jpg) + +![](images/8eaa30a0e0d51c25b16c50d856e4893e185bcc8b60df573b650284ce6c30f9af.jpg) +Figure 3. Discussions on the diversity of generated environments. We show distributions of two generated environments $env_0$ and $env_1$ for (a) random sampling methods, (b) flat environment inference methods, and (c) our hierarchical environment inference methods. (d) We employ the Kolmogorov-Smirnov test [34] to calculate the diversity of three methods. + +![](images/64d51654036bf6b98343ac6c3284af567a56578a8886ca62f96d89bdde0c16e6.jpg) + +compared to other methods, surpassing them in inter-env-distance by a large margin. Moreover, the results are aligned with Fig. 1, our methods outperform other methods in IC50-SCA dataset, indicating that diverse environments can give a clear indication of distribution shifts, therefore IRM can easily identify and eliminate variant features. + +# 6. Conclusion + +In our research, we take on the formidable challenge of improving out-of-distribution (OOD) generalization in the graph domain. We observe that recent works often overlook the crucial aspect of studying hierarchical environments in graph invariant learning. To address this gap, we introduce a novel method that generates hierarchical dynamic environments for each graph. Our approach involves hierarchical stochastic subgraph generation, hierarchical environment inference, and a carefully designed learning objective. By incorporating graph invariant learning with inferred high-level environments, our model not only achieves meaningful and diverse environments within the same hierarchy but also ensures consistency across different hierarchies. The effectiveness of our method is particularly pronounced in the DrugOOD dataset, shedding light on the potential for further exploration in hierarchical graph learning within OOD scenarios. + +# 7. Acknowledgement + +This work was supported by Bio & Medical Technology Development Program of the NRF funded by the Ministry of Science & ICT(NRF-2022M3E5F3085677, RS-2023-00257479), and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00246586). + +# References + +[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Jean-Christophe Gagnon-Audet, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. Invariance principle meets information bottleneck for out-of-distribution generalization. Advances in Neural Information Processing Systems, 34: 3438-3450, 2021. 2, 6, 12 +[2] Martin Arjovsky, León Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019. 1, 2, 3, 6, 12, 14 +[3] Beatrice Bevilacqua, Yangze Zhou, and Bruno Ribeiro. Size-invariant graph representations for graph classification extrapolations. 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Delving into out-of-distribution detection with vision-language representations. Advances in Neural Information Processing Systems, 35:35087-35102, 2022. 1 +[37] Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748, 2018. 5 +[38] Yinhua Piao, Sangseon Lee, Dohoon Lee, and Sun Kim. Sparse structure learning via graph neural networks for inductive document classification. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 11165–11173, 2022. 4 +[39] Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. In Computer Vision-ECCV 2016 Workshops: Amsterdam, The Netherlands, October 8-10 and 15-16, 2016, Proceedings, Part III 14, pages 443-450. Springer, 2016. 2 + +[40] Vladimir Vapnik. Principles of risk minimization for learning theory. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11620-11630, 2023. 2, 3, 6, 12, 14 +[46] Hao Yuan, Haiyang Yu, Shurui Gui, and Shuiwang Ji. Explainability in graph neural networks: A taxonomic survey. IEEE transactions on pattern analysis and machine intelligence, 45(5):5782-5799, 2022. 6 +[47] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017. 2 +[48] Yanfu Zhang, Hongchang Gao, Jian Pei, and Heng Huang. Robust self-supervised structural graph neural network for social network prediction. In Proceedings of the ACM Web Conference 2022, pages 1352-1361, 2022. 1 +[49] Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun. Graph neural networks: A review of methods and applications. AI open, 1:57-81, 2020. 1 \ No newline at end of file diff --git a/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/images.zip b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..256e946adcf0fe7a327fb0f8bb113df89cf5b411 --- /dev/null +++ b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fb08d91e57ecd7c703e3a336108e5c07c12d0f814f0df005cce333b6a067a060 +size 417563 diff --git a/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/layout.json b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5ced10ce025cc4ff7f18f2b8c7041a10ab465ab4 --- /dev/null +++ b/2024/Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments/layout.json @@ -0,0 +1,8882 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 121, + 103, + 475, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 103, + 475, + 138 + ], + "spans": [ + { + "bbox": [ + 121, + 103, + 475, + 138 + ], + "type": "text", + "content": "Improving Out-of-Distribution Generalization in Graphs via Hierarchical Semantic Environments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "spans": [ + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "text", + "content": "Yinhua Piao" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "text", + "content": ", Sangseon Lee" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "text", + "content": ", Yijingxiu Lu" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "text", + "content": ", Sun Kim" + }, + { + "bbox": [ + 156, + 160, + 437, + 175 + ], + "type": "inline_equation", + "content": "^{1,3,4}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 189, + 510, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 189, + 510, + 232 + ], + "spans": [ + { + "bbox": [ + 83, + 189, + 510, + 232 + ], + "type": "text", + "content": "Department of Computer Science and Engineering, Seoul National University1 \nInstitute of Computer Technology, Seoul National University2, AIGENDRUG Co., Ltd.3 \nInterdisciplinary Program in Artificial Intelligence, Seoul National University4" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 119, + 233, + 471, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 233, + 471, + 245 + ], + "spans": [ + { + "bbox": [ + 119, + 233, + 471, + 245 + ], + "type": "text", + "content": "{2018-27910, sangseon486, solanoon0113, sunkim.bioinfo}@snu.ac.kr" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "spans": [ + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "type": "text", + "content": "Out-of-distribution (OOD) generalization in the graph domain is challenging due to complex distribution shifts and a lack of environmental contexts. Recent methods attempt to enhance graph OOD generalization by generating flat environments. However, such flat environments come with inherent limitations to capture more complex data distributions. Considering the DrugOOD dataset, which contains diverse training environments (e.g., scaffold, size, etc.), flat contexts cannot sufficiently address its high heterogeneity. Thus, a new challenge is posed to generate more semantically enriched environments to enhance graph invariant learning for handling distribution shifts. In this paper, we propose a novel approach to generate hierarchical semantic environments for each graph. Firstly, given an input graph, we explicitly extract variant subgraphs from the input graph to generate proxy predictions on local environments. Then, stochastic attention mechanisms are employed to re-extract the subgraphs for regenerating global environments in a hierarchical manner. In addition, we introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies. This approach enables our model to consider the relationships between environments and facilitates robust graph invariant learning. Extensive experiments on real-world graph data have demonstrated the effectiveness of our framework. Particularly, in the challenging dataset DrugOOD, our method achieves up to " + }, + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "type": "inline_equation", + "content": "1.29\\%" + }, + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "type": "inline_equation", + "content": "2.83\\%" + }, + { + "bbox": [ + 47, + 298, + 290, + 647 + ], + "type": "text", + "content": " improvement over the best baselines on IC50 and EC50 prediction tasks, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 669, + 128, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 128, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 128, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Graph-structured data is ubiquitous in real-world applications, from social networks to biological networks and" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 305, + 270, + 545, + 389 + ], + "blocks": [ + { + "bbox": [ + 305, + 270, + 545, + 389 + ], + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 389 + ], + "type": "image", + "image_path": "c355ad2f6378a7f8a9da5e06a35da78dcd8d9b60d9c77443ad176ef8f40f4fec.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 396, + 547, + 440 + ], + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 440 + ], + "type": "text", + "content": "Figure 1. (a) Results on IC50-SCA dataset from DrugOOD [20]. (b) Flat environments from existing approaches. (c) Hierarchical environments from our methods. For visualization, we set #real environments as 10." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 462, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 665 + ], + "type": "text", + "content": "chemical molecules [14, 16, 21, 48]. One notable advancement in this area is the emergence of Graph Neural Networks (GNNs). GNN-based models have pioneered end-to-end learning strategies to extract valuable information from graphs and have demonstrated remarkable success across various applications [13, 24, 42]. However, the success of GNNs encounters challenges in out-of-distribution (OOD) scenarios primarily due to the intricate nature of graph distribution shifts [3, 9, 28]. Graph data, characterized by nodes, edges, and potential attributes, poses additional challenges compared to other domains such as natural language processing (NLP) or computer vision (CV). Unlike those domains where context is often provided by sentences, paragraphs, or spatial information in images [4, 15, 36], graph lacks a built-in contextual framework, making it inherently challenging to discern the relevance and context of individual graph elements in OOD scenarios [12, 49]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Invariant Risk Minimization (IRM) [2] is a widely used strategy in the Euclidean domain, relying on the assumption that training data is sourced from distinct environments with varied data distributions. Motivated by the success of" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27631" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "type": "text", + "content": "invariant learning in the Euclidean domain [1, 2, 8, 17, 26, 29, 31, 32], invariant learning methods for non-Euclidean graphs [6, 7, 10, 27, 27, 30, 43] extend the concept to address the unique challenges posed by graph-structured data. Despite commendable progress in addressing OOD scenarios within the graph domain, existing studies have predominantly adhered to the assumption of a flat environmental situation [5, 33]. For example, in the DrugOOD dataset, there are nearly 7000 diverse training environments in IC50-SCA subset, including a wide variety of distinct substructures. Fig. 1 illustrates three existing approaches to acquire environments when performing invariant learning on this data: \"Real\" means directly utilizing provided environments [27], \"Rand#2\" means randomly splitting samples into two environments [2, 6], and \"Infer#2\" means inferring samples into two environments [8, 17]. As shown in Fig. 1, all existing approaches exhibit poor or comparable performance to empirical risk minimization (ERM), which is consistent with the findings of Yang [43]. These phenomena indicate the shortcomings of flat environments: (1) Limited consideration of local environment similarity degrades performance in numerous environments (e.g., 'Real' case in Fig. 1) (2) Inferring from a small number of environments may fail to capture global environment similarities and interrelationships. (e.g., 'Infer#2' case in Fig. 1)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 378, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 289, + 713 + ], + "type": "text", + "content": "Considering that graphs exhibit a hierarchical structure, with semantic information organized across various levels. This inherent hierarchy is fundamental to understanding structures and properties within graphs [44]. In addition, inspired by the recent works [1, 17, 29], which show that the diversity of environments is recognized as the key to effectively handling graph OOD scenarios, we aim to bridge the gap of flat environments while leveraging the inherent hierarchy of graphs. In this paper, we propose a hierarchical approach to generate semantic environments of each graph for effective graph invariant learning. Initially, we extract variant subgraphs from the input graph, enabling the generation of proxy predictions on local environments. Employing stochastic attention mechanisms, we iteratively re-extract subgraphs, building global environments hierarchically. To guide the robustness of hierarchical environment inference, we introduce a hierarchical environment diversification loss which encourages our model to diversify environments within the same hierarchy while maintaining consistency across different hierarchical levels. This approach not only aids our model in considering relationships between environments but also strengthens graph invariant learning robustness. By modeling relationships between different environments within a hierarchical framework, our approach acquires the rich source of environmental information embedded in the hierarchical structure of graphs. Extensive experiments demonstrate our approach to graph OOD classification datasets. Our contributions can be sum" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 72, + 388, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 388, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 388, + 83 + ], + "type": "text", + "content": "marized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 84, + 547, + 253 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 306, + 84, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 84, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 84, + 547, + 144 + ], + "type": "text", + "content": "- We propose a hierarchical approach to generate semantic environments for effective graph invariant learning. To the best of our knowledge, our proposed method is the first attempt to generate the environments in a hierarchical way in graph OOD generalization." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 144, + 547, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 144, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 144, + 547, + 191 + ], + "type": "text", + "content": "- We introduce a new learning objective that guides our model to learn the diversity of environments within the same hierarchy while maintaining consistency across different hierarchies." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "type": "text", + "content": "- Extensive experiments have demonstrated our model yields significant improvements over various domains. In molecule graph benchmarks DrugOOD, our method achieves up to " + }, + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "type": "inline_equation", + "content": "1.29\\%" + }, + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "type": "inline_equation", + "content": "2.83\\%" + }, + { + "bbox": [ + 306, + 192, + 547, + 253 + ], + "type": "text", + "content": " higher ROC-AUC compared to SOTA graph invariant learning approaches." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 261, + 398, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 261, + 398, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 398, + 274 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 281, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 545 + ], + "type": "text", + "content": "Out-of-Distribution Generalization In the Euclidean domain, such as computer vision, OOD generalization has been studied extensively using a variety of strategies, such as Invariant Risk Minimization (IRM) [2], data augmentation [47], and domain adaptation methods [39]. Unlike deep neural networks with ERM, which suffer performance degradation under data distributional shifts, IRM-based studies [1, 26] have shown powerful and robust performance when providing environmental information. Recently, a two-step optimization framework EIIL [8] has been proposed to train the invariant learning model without explicit environment labels. EIIL trains the environment inference model to learn and infer the environment labels in the first step, and in the second step, EIIL uses inferred environments to conduct invariant learning. Other recent approaches, such as ZIN [29], HRM [31], KerHRM[32], and EDNIL [17] improve the OOD generalization by augmenting the environment to address its high heterogeneity. These augmentation strategies, such as the assistant model, clustering-based model, or effective diversification objective function all enhance the learning stage to infer diverse environments for effective invariant learning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "type": "text", + "content": "Graph Invariant Learning While general invariant learning methods are effective for the Euclidean domain, challenges arise when applying them to non-Euclidean domains like graph structures. In the realm of graph invariant learning, since graph data have an inherent nature of complex distribution shifts, often lacks explicit environment labels. To address this issue, methodologies have been widely developed and implemented. Approaches such as EERM [41], LiSA [45], and GREA [30] proposed to generate new environments, offering effective strategies to discover invariant patterns without environment label knowledge. While methods like MoleOOD [43] and GIL[27] focus on the inference of environments, providing solutions to" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27632" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "deal with challenging or unexplored environments. Another dimension of exploration involves learning with auxiliary assistance to ensure sufficient variation, with typical techniques found in CIGA [6], GALA[7]. Collectively, these innovative methods offer detailed strategies to navigate the challenges inherent in graph invariant learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 153, + 254, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 153, + 254, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 153, + 254, + 166 + ], + "type": "text", + "content": "3. Problem Definition and Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 173, + 287, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 173, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 287, + 233 + ], + "type": "text", + "content": "In Sec. 3.1, we introduce notations about out-of-distribution generalization and the background knowledge of graph invariant learning. In Sec. 3.2, we introduce environment inference to explain how recent research works on the graph dataset without environmental information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 239, + 160, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 160, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 160, + 251 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": "Following general settings of OOD generalization, we assume that the training datasets are collected from multiple training environments. Let " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{tr} = \\{G^{e}\\}_{e\\in \\mathrm{supp}(\\mathcal{E}_{tr})}" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " with different graphs " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "G^{e} = \\{(G_{i}^{e},y_{i}^{e})|1\\leq i\\leq N^{e}\\}" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " be the training datasets, where " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "G^{e}" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " represents the graphs drawn from environment " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{tr}" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " indicates the environment labels in the training datasets. We denote the environments " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{all}" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " as all possible environment labels in the real world. Then, the test datasets contain graphs " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{test} = \\{G^{e^{\\prime}}\\}" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " with unknown environment labels " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "e^\\prime" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " ,where " + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "inline_equation", + "content": "e^\\prime \\in \\operatorname {supp}(\\mathcal{E}_{all})\\setminus \\operatorname {supp}(\\mathcal{E}_{tr})" + }, + { + "bbox": [ + 46, + 257, + 289, + 426 + ], + "type": "text", + "content": " Our approach addresses out-of-distribution challenges in graph-level classification by incorporating invariant learning within environments derived from complex heterogeneous data hierarchically." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 430, + 133, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 133, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 133, + 441 + ], + "type": "text", + "content": "3.2. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": "Graph Invariant Learning. Recently, several studies have identified the cause of performance deterioration in out-of-distribution (OOD) graphs, attributing it to the introduction of spurious features. It is widely acknowledged that spurious features exhibit sensitivity to environmental changes, often referred to as environmental factors. The incorporation of spurious features diminishes the significance of invariant features, resulting in a decline in OOD performance. As a result, recent research [6, 7, 27, 45] often involves graph decomposition to extract both variant subgraphs " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "G_{v}" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": " and invariant subgraphs " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "G_{inv}" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": " from the original graphs " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": ", thereby facilitating the invariant GNN encoder " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": " [24] to learn relationships between invariant features " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "h_{inv}" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": " and labels " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": ". Following the invariant risk minimization [2], the encoder " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": " is trained with a regularization term enforcing jointly optimize the encoder " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": " in training environments " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": ", which can generalize to unseen testing environments " + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "inline_equation", + "content": "e'" + }, + { + "bbox": [ + 46, + 449, + 289, + 653 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 93, + 657, + 287, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 657, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 93, + 657, + 287, + 685 + ], + "type": "interline_equation", + "content": "\\sum_ {e \\in \\operatorname {s u p p} \\left\\{\\mathcal {E} _ {t r} \\right\\}} \\mathcal {R} ^ {e} (f) + \\lambda | | \\nabla \\mathcal {R} ^ {e} (f) | | ^ {2}, \\tag {1}", + "image_path": "a869eaf013a78d88db087abd48a03fb94e2221e92aba4416c550e86c584f2088.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}^e (f) = \\mathbb{E}_{G,y}^e [\\mathcal{L}(f(G),y)]" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " denotes the risk of " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " in environment " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " denotes the loss function." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "Environment Inference for GIL. In most cases, environmental information is difficult to obtain, especially in the context of graph generalization. While some datasets may provide metadata that could serve as environmental information, it is not reliable to fully use such information as the ground truth of the environment is not guaranteed. Therefore, existing methods [8, 17, 29, 31, 32] often infer the environmental labels " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{infer}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " by using variant subgraphs " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "G_{v}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " that are related to the environment. A variant GNN encoder " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "f^{e}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " is used to learn the variant features " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "h_v" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "G_{v}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " and infer the label " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\hat{e}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " of the environment " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": ". This approach allows joint optimization of environment inference and graph invariant learning through a learning process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 237, + 366, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 366, + 249 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 366, + 249 + ], + "type": "text", + "content": "4. Methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 257, + 547, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 426 + ], + "type": "text", + "content": "Our method consists of three components: hierarchical stochastic subgraph generation Sec. 4.1, hierarchical semantic environment inference Sec. 4.2, and robust graph invariant learning (GIL) with inferred environments Sec. 4.3. In Sec. 4.1, we generate invariant and variant subgraphs hierarchically for hierarchical semantic environment inference. In Sec. 4.2, we learn hierarchical semantic environments using the proposed hierarchical loss. Finally, in Sec. 4.3, we leverage the inferred hierarchical semantic environments to facilitate robust graph invariant learning, enabling us to uncover the invariant relationships between input graphs and their corresponding labels. These three steps together form a comprehensive approach for enhanced graph analysis and understanding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 430, + 542, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 542, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 542, + 443 + ], + "type": "text", + "content": "4.1. Hierarchical Stochastic Subgraph Generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": "Given a graph " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "G = (V, E)" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " represents the set of nodes and " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " represents the set of edges, the goal is to generate the invariant subgraph " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "G_{v}^{k}" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " and variant subgraph " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "G_{inv}^{k}" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " from the original graph " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " at each hierarchy " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "k \\in K" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " denotes the number of environmental hierarchies. At each hierarchy " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": ", we employ a graph neural network denoted as " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{GNN}_k" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " to update the hidden embedding " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "h_i^k = \\mathrm{GNN}_k(h_i^{k-1}, A)" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " for each node " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "v_i \\in V" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": ". We use graph neural networks as " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{GNN}_k" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " [42] to aggregate information from neighboring nodes for node embedding updating. In the process of learning variant and invariant subgraphs at each hierarchy, we define a probability distribution function " + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "inline_equation", + "content": "S^k(\\cdot)" + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": " for edge selection as follows. We omit the hierarchy notations, while the computation of probability distribution is conducted within each hierarchy:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 355, + 634, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 634, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 355, + 634, + 545, + 649 + ], + "type": "interline_equation", + "content": "s _ {i j} = S \\left(h _ {i j}\\right) = \\sigma \\left(\\operatorname {M L P} \\left(\\left[ h _ {i}, h _ {j} \\right]\\right)\\right) \\tag {2}", + "image_path": "7fb5cea96a3f3caa1bc9632019c5cc24f660262dd4e8d40e56478f040a3ffe13.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "s_{ij}" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " is the probability of selecting edge " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "e_{ij}" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " is the sigmoid function, and " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}(h_i, h_j)" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " is a multi-layer perceptron (MLP) that takes node embeddings " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " as inputs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "To introduce stochasticity in edge selection, we generate a sampler " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{ij} \\in \\{0,1\\}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " from the Bernoulli distribution" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27633" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 547, + 319 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 547, + 319 + ], + "type": "image", + "image_path": "11373bc5f57aaf4a8855afe13348729e7334907bfa8cb1f361b5f466462c5327.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 335, + 547, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 547, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 547, + 360 + ], + "type": "text", + "content": "Figure 2. Our Framework consists of (a) Hierarchical Stochastic Subgraph Generation in Sec. 4.1, (b) Hierarchical Semantic Environments in Sec. 4.2, (c) Robust GIL with Hierarchical Semantic Environments in Sec. 4.3." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 379, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 288, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{ij} \\sim \\{\\pi_1 := s_{ij}, \\pi_0 := 1 - s_{ij}\\}" + }, + { + "bbox": [ + 46, + 379, + 288, + 416 + ], + "type": "text", + "content": ". Gumbel-Softmax [19] is then applied to obtain differentiable edge selection probabilities for each edge:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 423, + 287, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 423, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 86, + 423, + 287, + 452 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {p}} _ {i j} = \\frac {\\exp \\left(\\left(\\log \\pi_ {1} + \\mathbf {g} _ {1}\\right) / \\tau\\right)}{\\sum_ {i \\in \\{0 , 1 \\}} \\exp \\left(\\left(\\log \\pi_ {i} + \\mathbf {g} _ {i}\\right) / \\tau\\right)} \\tag {3}", + "image_path": "b79a528d4ffb4ebff687bd21f7cb4c64444be0652767195d62f5878e8663aa80.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_1" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_0" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " are i.i.d variables sampled from the Gumbel distribution, and " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " is a temperature parameter that controls the smoothness of the sampling process. A lower " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " leads to more categorical (hard) selections, while a higher " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " results in smoother (soft) probabilities. As " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " approaches 0, " + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_{ij}" + }, + { + "bbox": [ + 46, + 455, + 287, + 527 + ], + "type": "text", + "content": " can be annealed to a categorical distribution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "text", + "content": "To ensure hierarchical neighborhood consistency [38] in the generation of stochastic subgraphs, we introduce an additional hierarchical neighbor masking function denoted as " + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "inline_equation", + "content": "N^k" + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "text", + "content": ". This masking function compares the neighbor matrix from the previous hierarchy (" + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "inline_equation", + "content": "k - 1" + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "text", + "content": ") with the currently selected neighbors, ensuring that nodes within the hierarchical neighborhood are consistently either included or excluded. The hierarchical neighbor mask " + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "inline_equation", + "content": "N_{ij}^{k}" + }, + { + "bbox": [ + 46, + 527, + 288, + 624 + ], + "type": "text", + "content": " can be defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 632, + 287, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 632, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 77, + 632, + 287, + 649 + ], + "type": "interline_equation", + "content": "N _ {i j} ^ {k} = N _ {i j} ^ {k - 1} + \\mathbf {1} \\left\\{N _ {i j} ^ {k - 1} = 0 \\text {a n d} \\mathbf {p} _ {i j} ^ {k} > T \\right\\} \\tag {4}", + "image_path": "d0fe1e9264dd8f51155658db2df294ebb1023a43d5a09a4ab5cfbb4f5eb3ae82.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "text", + "content": " denotes the threshold for selecting the edges based on " + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{ij}^{(k)}" + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{1}" + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "text", + "content": " denotes indicator function. Then we obtain the variant and invariant subgraph at each hierarchy " + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 654, + 288, + 693 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 99, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 99, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "A _ {v} ^ {k} \\leftarrow A \\odot N ^ {k}, A _ {i n v} ^ {k} \\leftarrow A - A _ {v} ^ {k} \\tag {5}", + "image_path": "030280a0934be3c57cb9459b556fda75f1026998c94430ea319fa5ff12527d37.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": "where the adjacency matrix of the variant subgraph, denoted as " + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "inline_equation", + "content": "A_v^k" + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": ", is derived by performing element-wise multiplication between the original edge matrix " + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": " and the hierarchical neighbor mask matrix " + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "inline_equation", + "content": "N^k" + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": ". Conversely, the adjacency matrix of the invariant subgraph, denoted as " + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "inline_equation", + "content": "A_{inv}^k" + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": ", is obtained by subtracting the edges included in the variant subgraph " + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "inline_equation", + "content": "A_v^k" + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": " from the original edge matrix " + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 379, + 547, + 523 + ], + "type": "text", + "content": " [5, 7, 27]. By following this process iteratively across hierarchies, we construct a series of variant and invariant subgraphs that capture the hierarchical and structural nuances within the original graph, enabling a multi-level analysis of downstream tasks and analysis." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 529, + 503, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 529, + 503, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 529, + 503, + 540 + ], + "type": "text", + "content": "4.2. Hierarchical Semantic Environments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "text", + "content": "Since the existing environmental information is not reliable or available, we design an environment inference model to assign the graphs to relatively reliable environments. Given prior " + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "inline_equation", + "content": "p(e|G)" + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "text", + "content": ", we maximize the log-likelihood of " + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "inline_equation", + "content": "p(y|G)" + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "text", + "content": " to obtain the posterior " + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "inline_equation", + "content": "p(e|G,y)" + }, + { + "bbox": [ + 304, + 547, + 547, + 654 + ], + "type": "text", + "content": ". As there is no solution to the true posterior, existing methods use clustering-based or variational distribution to approximate and infer the posterior. Inspired by a multi-class classification problem, we estimate the posterior using the softmax function as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 658, + 550, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 550, + 687 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 550, + 687 + ], + "type": "interline_equation", + "content": "P (\\hat {e} \\in \\mathcal {E} _ {t r} | X, Y) = \\frac {\\exp \\left(- l \\left(f ^ {e} \\left(\\Phi (X) , Y\\right)\\right)\\right)}{\\sum_ {e ^ {\\prime} \\in \\operatorname {s u p p} \\left(\\mathcal {E} _ {t r}\\right)} \\exp \\left(- l \\left(f ^ {e ^ {\\prime}} \\left(\\Phi (X) , Y\\right)\\right)\\right)}", + "image_path": "f0c9933c05057e6f56ea93981b20b9954dd97fa2dbbd21726ff3d0f2c7ece443.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "inline_equation", + "content": "f^{e}" + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": " denotes neural network with " + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "inline_equation", + "content": "y^{e}" + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "-class classifier and " + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": " indicates the variant subgraph generator." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27634" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 272, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 272, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 272, + 84 + ], + "type": "text", + "content": "4.2.1 Intra-Hierarchy Environment Diversification" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "content": "In the previous section, we discussed the extraction of variant subgraphs " + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "inline_equation", + "content": "\\{G_v^k | k \\in K\\}" + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "content": " utilizing GNN encoders in conjunction with corresponding stochastic masking " + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "inline_equation", + "content": "\\{p_{ij}^k | k \\in K\\}" + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "content": " at each hierarchy " + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "content": ". To guide the learning process effectively, we incorporate an intra-hierarchy environment diversification loss with variant subgraph and estimated posteriors, denoted as " + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "inline_equation", + "content": "L_{ED}" + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 81, + 181, + 287, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 181, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 81, + 181, + 287, + 205 + ], + "type": "interline_equation", + "content": "L _ {E D} ^ {k} = - \\sum_ {i} \\max _ {e ^ {k}} \\log P \\left(e ^ {k} \\mid f ^ {k} \\left(G _ {v i} ^ {k}, y _ {i}\\right)\\right) \\tag {6}", + "image_path": "351b07c971a1d4efb80bf395861c9dfd69c9d1bac8bd7ddf0fc95e4277c512c7.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": "Specifically, " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "L_{ED}" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": " is designed to guide the network " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "f^{k}" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": " to maximize the dependency between " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "e^{k}" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": " given the variant subgraph " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "G_{v}^{k}" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": " at each hierarchy " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": ". By optimizing this loss, the network " + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "inline_equation", + "content": "f^{k}" + }, + { + "bbox": [ + 46, + 213, + 287, + 286 + ], + "type": "text", + "content": " is ensured to distinguish relationships between the generated environments, fostering diversity within hierarchies." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 300, + 270, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 270, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 270, + 312 + ], + "type": "text", + "content": "4.2.2 Inter-Hierarchy Environment Augmentation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 319, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 415 + ], + "type": "text", + "content": "The goal of inter-hierarchy environment augmentation is to maximize the intra-class mutual information of the estimated invariant subgraphs while maximizing the intra-environment mutual information of the estimated variant subgraphs. Before introducing our objective function, a standard InfoNCE loss [37] can maximize the similarity between positive pairs and minimize the similarities between some randomly sampled negative pairs, which is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 421, + 278, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 421, + 278, + 453 + ], + "spans": [ + { + "bbox": [ + 55, + 421, + 278, + 453 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {I n f o N C E}} (z, \\mathcal {N} _ {p}, \\tau) = - \\log \\left(\\frac {\\exp (z \\cdot \\mathcal {N} _ {p} (z) / \\tau)}{\\sum_ {n \\in \\mathcal {N} (z)} \\exp (z \\cdot n / \\tau)}\\right)", + "image_path": "e73756afda559c6e177713d76fad9bddd9870d763c36a9ca22757fc3527598d3.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_p(z)" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": " denotes positive samples for " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(z)" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": " denotes the batch samples for " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": " denotes a temperature parameter. To ensure the reliability and diversification of learned hierarchical environments, we introduce two inter-hierarchy semantic invariants: label-invariant and neighborhood-invariant. Inspired by [5, 7], we introduce two contrastive learning losses: (1) Environment-based Contrastive learning loss " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{EnvCon}}" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": " and (2) Label-based Contrastive learning loss " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{LabelCon}}" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": ". For environment-based contrastive learning, we define an environment-based neighborhood function " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{p_e}^k" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": " that constructs the positive set for the anchor sample, where samples have the same inferred environment. To preserve neighborhood consistency across hierarchies, the hierarchical neighborhood function " + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{p_e}^k" + }, + { + "bbox": [ + 46, + 460, + 287, + 639 + ], + "type": "text", + "content": " can be defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 60, + 646, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 646, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 60, + 646, + 287, + 662 + ], + "type": "interline_equation", + "content": "\\mathcal {N} _ {p _ {e}} ^ {k} (z) = \\mathcal {N} _ {p _ {e}} ^ {k - 1} (z) \\cup \\left\\{z _ {i} \\mid e _ {i} ^ {k} = e _ {z} ^ {k}, z _ {i} \\in \\mathcal {N} (z) \\right\\} \\tag {7}", + "image_path": "885f987f8505a11d1d732b464aeef2b931df72a8d6cf2746080c80157150ac41.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "type": "text", + "content": "Using " + }, + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{p_e}^k" + }, + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "type": "text", + "content": ", we formulate the environment consistency loss " + }, + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{EnvCon}}" + }, + { + "bbox": [ + 47, + 669, + 287, + 693 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 73, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 73, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {E n v C o n}} ^ {k} = \\mathbb {E} _ {G _ {v} ^ {k} \\sim p _ {d}} \\left[ \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {v} ^ {k}, \\mathcal {N} _ {p _ {e}} ^ {k} \\left(z _ {v} ^ {k}\\right), \\tau\\right) \\right] \\tag {8}", + "image_path": "9c2c9622d4816f977b6a1bacac1377f078345d20377d7c992d73964ec33c56b5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "p_d" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " denotes the batch of data, and " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "z_v^k" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " denotes the embedding of variant subgraph " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "G_v^k" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " from a multi-layer perception MLP at " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": "-th hierarchy. Environment consistency loss " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{EnvCon}}^k" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " attracts the variant subgraphs with the same environment labels and pushes the variant subgraphs with different environments, which can augment the power of learning the sufficiency of the environment." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "text", + "content": "For label-based contrastive loss, we define a label-based neighborhood function that represents the positive samples given ground truth label " + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "text", + "content": ", which can be defined as " + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{p_y}(z) = \\{z_i \\mid y_i = y_z, z_i \\in \\mathcal{N}(z)\\}" + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "text", + "content": ". To measure the label consistency loss, we formulate " + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{LabelCon}}" + }, + { + "bbox": [ + 305, + 156, + 545, + 217 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 226, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 226, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 318, + 226, + 545, + 243 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {L a b e l C o n}} ^ {k} = \\mathbb {E} _ {G _ {\\text {i n v}} ^ {k} \\sim p _ {d}} \\left[ \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {\\text {i n v}} ^ {k}, \\mathcal {N} _ {p _ {y}} \\left(z _ {\\text {i n v}} ^ {k}\\right), \\tau\\right) \\right] \\tag {9}", + "image_path": "6e86dc4110e008c0191c95904544916e0364091e497c0faf152028ab0d5a65c8.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{inv}}" + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "text", + "content": " denotes the embedding of invariant subgraph " + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{inv}}^k" + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "text", + "content": " from MLP at " + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 251, + 545, + 276 + ], + "type": "text", + "content": "-th hierarchy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 293, + 455, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 455, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 455, + 304 + ], + "type": "text", + "content": "4.2.3 Overall Objective Function" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 312, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 347 + ], + "type": "text", + "content": "Considering the diversity of intra-hierarchy and consistency of inter-hierarchy, we define a total loss of each hierarchy " + }, + { + "bbox": [ + 305, + 312, + 545, + 347 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 312, + 545, + 347 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 339, + 358, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 358, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 339, + 358, + 545, + 373 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {h i e r} _ {k}} = \\mathcal {L} _ {\\mathrm {E D}} ^ {k} + \\alpha \\cdot \\mathcal {L} _ {\\text {E n v C o n}} ^ {k} + \\beta \\cdot \\mathcal {L} _ {\\text {L a b e l C o n}} ^ {k} \\tag {10}", + "image_path": "54b05cf4028eb3fe6ebf21520c93695b9bd8f68e6b4b37ef3e22c4038b6c9656.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "text", + "content": " denote coefficient parameters. And the overall objective loss can be defined as " + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{HEI}} = \\sum_{k=1}^{K} \\mathcal{L}_{\\mathrm{hier}_k}" + }, + { + "bbox": [ + 305, + 383, + 545, + 443 + ], + "type": "text", + "content": ". This formulation ensures a unified optimization objective, allowing the model to learn invariant subgraphs that capture both label and environment information effectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 452, + 545, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 452, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 452, + 545, + 475 + ], + "type": "text", + "content": "4.3. Robust GIL with Hierarchical Semantic Environments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "text", + "content": "After the hierarchical learning stage of environment generation, we extract the generated environment " + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "inline_equation", + "content": "e^{K - 1}" + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "text", + "content": " from the last hierarchy " + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "inline_equation", + "content": "K - 1" + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "text", + "content": ". Our objective is to minimize the invariant risk given by Eq. (1), employing the hierarchically generated semantic environments " + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "inline_equation", + "content": "e^{K - 1}" + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "text", + "content": ". The objective function to calculate " + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{inv}" + }, + { + "bbox": [ + 305, + 483, + 545, + 555 + ], + "type": "text", + "content": " is as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 315, + 565, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 565, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 315, + 565, + 545, + 583 + ], + "type": "interline_equation", + "content": "\\min _ {f} \\mathcal {L} _ {c l s} (f) + \\nabla_ {\\hat {e}} \\left(\\mathcal {L} _ {c l s} (f)\\right) \\text {s . t .} \\hat {e} = \\arg \\min _ {e} \\mathcal {L} _ {\\mathrm {H E I}} \\tag {11}", + "image_path": "cae227535571d7635430cb769fe57c259df3bf74e492d7f184a0e65010171265.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": "This equation represents an optimization problem where the goal is to find a function " + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": " that minimizes the sum of two terms. The first term " + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}(f)" + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": " corresponds to the cross entropy loss of the classification task. The second term " + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\nabla_{\\hat{e}}(\\mathcal{L}_{cls}(f))" + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": " represents the gradient with respect to " + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\hat{e}" + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": ", which is a specific environment. In essence, the objective is to discover a function " + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": " that performs well on a classification task while maintaining stability in performance across different environments, adhering to the specified environmental minimization condition." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27635" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 526, + 248 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 526, + 248 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 526, + 248 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 526, + 248 + ], + "type": "table", + "html": "
METHODS\n#ENVIC50-ASSAY\n311IC50-SCA\n6881IC50-SIZE\n190EC50-ASSAY\n47EC50-SCA\n850EC50-SIZE\n167
ERM[40]71.79±0.2768.85±0.6266.70±1.0876.42±1.5964.56±1.2562.79±1.15
IRM[2]72.12±0.4968.69±0.6566.54±0.4276.51±1.8964.82±0.5563.23±0.56
V-REX[26]72.05±1.2568.92±0.9866.33±0.7476.73±2.2662.83±1.2059.27±1.65
EIIL[8]72.60±0.4768.45±0.5366.38±0.6676.96±0.2564.95±1.1262.65±1.88
IB-IRM[1]72.50±0.4968.50±0.4066.64±0.2876.72±0.9864.43±0.8564.10±0.61
GREA [30]72.77±1.2568.33±0.3266.16±0.4672.44±2.5567.98±1.0063.93±3.01
CIGAV1 [6]72.71±0.5269.04±0.8667.24±0.8878.46±0.4566.05±1.2966.01±0.84
CIGAV2 [6]73.17±0.3969.70±0.2767.78±0.76---
MOLEOOD [43]71.38±0.6868.02±0.5566.51±0.5573.25±1.2466.69±0.3465.09±0.90
GALA [7]---79.24±1.3666.00±1.8666.01±0.84
OURS74.01±0.1170.72±0.3068.64±0.2380.82±0.2169.73±0.2166.87±0.38
", + "image_path": "43ff0168d232966610d2b685e64c03eb4cff5769151b34ccfbc01f8b6b51de36.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 257, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 547, + 281 + ], + "type": "text", + "content": "Table 1. Test ROC-AUC of various models on DrugOOD benchmark datasets. The mean ± standard deviation of all models is reported as an average of 5 executions of each model. The best methods are highlighted in bold and the second best methods are underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 299, + 128, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 299, + 128, + 313 + ], + "spans": [ + { + "bbox": [ + 47, + 299, + 128, + 313 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 320, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 287, + 344 + ], + "type": "text", + "content": "Datasets. Extensive experiments were conducted on real-world graph data from diverse domains." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 346, + 288, + 621 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 346, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 406 + ], + "type": "text", + "content": "- CMNIST-75sp. The task is to classify each graph that is converted from an image in the ColoredMNIST dataset [2] into the corresponding handwritten digit using the superpixels algorithm [25]. Distribution shifts exist on node attributes by adding random noises in the testing set." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 405, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 287, + 501 + ], + "type": "text", + "content": "- Graph-SST datasets. We utilize sentiment graph data from SST5 and SST-Twitter datasets from [46]. For the Graph-SST5 dataset, graphs are split into different sets based on averaged node degrees to create distribution shifts. For the Graph-Twitter dataset, we invert the split order to assess the out-of-distribution generalization capability of GNNs trained on large-degree graphs to smaller ones." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 501, + 288, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 288, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 288, + 621 + ], + "type": "text", + "content": "- DrugOOD. We use six datasets in DrugOOD [20] that are provided with manually specified environment labels. DrugOOD provides more diverse splitting indicators, including assay, scaffold, and size. To comprehensively evaluate the performance of our method under different environment definitions, we adopt these three different splitting schemes on categories IC50 and EC50 provided in DrugOOD. Then we obtain six datasets, EC50-* and IC50-* where the suffix * specifies the splitting scheme i.e. IC50/EC50-ASSAY/SCAFFOLD/SIZE." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Baselines. We comprehensively compare our methods with the following categories of baselines: (1) ERM denotes supervised learning with empirical risk minimization [40]. (2) Euclidean OOD methods: We compare with SOTA invariant learning methods from the Euclidean regime, including IRM [2], V-REX [26], EIIL [8], IB-IRM [1]. (3)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 300, + 547, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 547, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 547, + 398 + ], + "type": "text", + "content": "Graph OOD methods: We also compare with SOTA invariant learning methods from the graph regime. Graph OOD methods can be further split into three groups: environment generation-based baseline methods including GREA [30] and LiSA [45], environment augmentation-based baseline methods including DisC [10] and CIGA [6] and environment inference-based baseline methods including GIL [27], MoleOOD [43], and GALA [7]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 411, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 520 + ], + "type": "text", + "content": "Environmental Setup. All methods use the same GIN backbone [42] and the same optimization protocol for fair comparisons. Each of the methods is configured using the same parameters reported in the original paper or selected by grid search. For a fair comparison, we use the same embedding size for all methods. We tune the hyperparameters following the common practice. All details are given in Appendix. We report the ROC-AUC score in the DrugOOD dataset and the accuracy score for the rest of the datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 528, + 451, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 528, + 451, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 528, + 451, + 540 + ], + "type": "text", + "content": "5.1. Performance Comparison" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "We first provide a detailed report on the DrugOOD benchmark dataset in Tab. 1. We conduct IC50 and EC50 predictions with different split settings. As shown in Tab. 1 and mentioned in Sec. 1, the DrugOOD dataset includes molecular datasets with complex distributions, such as assay, scaffold, and size split with various numbers of environments. Our approach consistently outperforms existing methods, demonstrating the importance of hierarchical environment learning in addressing complex drug OOD generalization applications. As shown in Tab. 1, compared to Empirical Risk Minimization (ERM), Euclidean-based invariant learning methods, such as IRM [2], V-REX [26], EIIL [8], etc, show comparable or even degraded performance in most experimental settings. This suggests that di" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27636" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 282, + 165 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 282, + 165 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 282, + 165 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 282, + 165 + ], + "type": "table", + "html": "
METHODSIC50-SCAIC50-SIZE
w/ env#non-infer RAND=268.54±0.6467.63±0.33
w/ env#non-infer=real68.77±0.7267.60±0.32
w/ env#infer=269.14±0.8067.55±0.34
w/ env#infer=real69.08±0.6467.74±0.13
w/ env#hier-infer (OURS)70.72±0.3068.64±0.23
", + "image_path": "8c4f922d971c709641420f9220acaaae6c944ca6c83a9ea717ce230b2bd90d17.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 210, + 286, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 286, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 286, + 258 + ], + "type": "text", + "content": "rectly applying general invariant learning struggles to handle shifts in graph distributions. In contrast, graph-based OOD methods exhibit better performance, as they learn invariant subgraph patterns for graph OOD generalization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 259, + 286, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 286, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 286, + 511 + ], + "type": "text", + "content": "In addition, in the performance comparison of graph-based OOD methods, the MoleOOD [43] pointed out that simple ERM sometimes outperforms several existing methods when faced with a large number of provided environments in graph OOD datasets, which is aligned with the results of Tab. 1. For example, IC50-SCA dataset is provided with 6881 environments, where 6881 scaffolds or substructures construct a vast amount of environmental information for the dataset. In IC50-SCA dataset, GREA and MoleOOD show poor performance compared to ERM, as shown in Tab. 1. We analyze this phenomenon for two potential reasons: (1) The first reason is that the provided environments are overly fine-grained, thereby similar substructure environments in the training and testing sets. ERM can capture similar substructures to learn similar data distributions, showing better performance. (2) The second reason is that GREA and MoleOOD only generate a small number of environments, which overly simplifies the environment and neglects the relationships between environments. This limits their ability to learn heterogeneous and interrelated environments, resulting in noticeable performance degradation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 512, + 286, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 512, + 286, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 512, + 286, + 609 + ], + "type": "text", + "content": "Our method performs a hierarchical approach to learn relationships between redundant environments and maximize the diversity of environments. Leveraging the high-level semantic environments from the last hierarchy, we minimize invariant prediction risk, thereby achieving better graph OOD generalization. In Appendix, we report performance comparisons showing that our performance is better or comparable to existing methods in general domains." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 621, + 286, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 286, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 286, + 634 + ], + "type": "text", + "content": "5.2. Effect of Hierarchical Semantic Environments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "content": "In this section, similar to existing environment inference-based works for OOD generalization [7, 8], we first analyze the role of environment inference, and then we discuss the effects of hierarchical environments learned by our model, showing the necessity of learning the hierarchical environments for graph invariant learning." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 545, + 160 + ], + "blocks": [ + { + "bbox": [ + 47, + 173, + 286, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 173, + 286, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 173, + 286, + 185 + ], + "type": "text", + "content": "Table 2. The ablation study on IC50-SCA and IC50-SIZE datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 70, + 545, + 160 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 160 + ], + "type": "table", + "html": "
CONFIGURATIONSIC50-SCAIC50-SIZE
#real = [#ep]69.08±0.6467.60±0.32
#env = [5]69.35±0.6767.70±0.50
#env = [2]69.14±0.8067.73±0.64
#env=[#ep→#ep/2→5]70.12±0.1468.62±0.34
#env=[#ep→#ep/2→2]70.72±0.3068.64±0.23
", + "image_path": "e967cd99c7e779fed7b8122c95bda3d0152d5e45d470f8821daa1a57e34e410d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "type": "text", + "content": "Table 3. Sensitivity analysis on generated environments. " + }, + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\# e_{p}" + }, + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "type": "text", + "content": " denotes the number of provided environments in datasets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 213, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 370 + ], + "type": "text", + "content": "Environment Inference. As shown in Tab. 2, we analyze the role of environment inference by comparing the direct usage of non-inferred and inferred environments. Direct usage of the non-inferred environments can be divided into two scenarios: (1) When environments are unavailable, existing methods randomly assign two environments for graph invariant learning, which is shown as 'w/ env#non-infer (rand)' from Tab. 2. (2) DrugOOD dataset provides environmental information, e.g., scaffold information in IC50-SCA dataset. As shown in Tab. 1, we can know the number of environments for both dataset IC50-SCA and dataset IC50-SIZE. In such cases, we use environments for invariant learning, as illustrated by the 'w/ env#non-infer (real)' in Tab. 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 370, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 514 + ], + "type": "text", + "content": "Secondly, we consider the usage of inferred environments for invariant learning, as indicated in Tab. 2. Through the model of environment inference, we directly predict the flat environment and use it in invariant learning, as illustrated by 'w/ env#infer=*. From Tab. 2, it can be observed that the model with inferred environments exhibits better performance, indicating that learned environments from data are more effective than direct usage of non-inferred environments. Moreover, in dataset IC50-SCA, the effects of inference are more pronounced, emphasizing the necessity of performing environment inference operations in situations with complex real-world environments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": "Hierarchical Environment Inference. We further analyze the effects of hierarchical environments by comparing them with flat environments. Our model adopts a hierarchical approach to learning environmental information, regulating semantic environmental content between hierarchies through both intra-hierarchy and inter-hierarchy mechanisms. Upon comparing experimental results in IC50-SCA and IC50-SIZE datasets, as shown in Tab. 2, our hierarchical model consistently outperforms invariant learning models with flat environments. This indicates that in real-world datasets, the environmental factors influencing label predictions are complex and interdependent. Consequently, investigating graph invariant learning with hierarchical environment inference is essential for attaining more sophisticated and effective in graph OOD generalization." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27637" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 212, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 212, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 212, + 85 + ], + "type": "text", + "content": "5.3. Sensitive analysis on hierarchy" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 377 + ], + "type": "text", + "content": "We also conduct sensitive analysis on the number of hierarchies and the number of environments at each hierarchy. Specifically, in hierarchical settings, we start from the number of environments as the number of environments provided in the first hierarchy for a fair comparison. By comparing the results shown in Tab. 3, we find inferred environments with hierarchical settings help OOD generalization in the graph domain. Inferring flat environments is worse than environment inference with three hierarchies. In addition, inferring a large number of environments " + }, + { + "bbox": [ + 46, + 90, + 289, + 377 + ], + "type": "inline_equation", + "content": "\\# e_{p}" + }, + { + "bbox": [ + 46, + 90, + 289, + 377 + ], + "type": "text", + "content": " in a single hierarchy shows poor performance compared to inferring a small number of environments. This is because the model with a large number of environments learns too local and redundant to capture the relationships between environments. However, in a hierarchical setting, even if inference starts from a large number of environments to a small number of environments, different hierarchies can capture the local relationships among a huge number of environments and dynamically maximize the diversity of inferred high-level environments. Therefore, despite the final number of inferred environments is still small, these environments learn the semantic information from complex data distribution hierarchically and can improve the Graph OOD generalization using the high-level semantic environments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 384, + 124, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 124, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 124, + 396 + ], + "type": "text", + "content": "5.4. Discussions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 403, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 498 + ], + "type": "text", + "content": "We discuss the diversity of environments generated by different methods as shown in Fig. 3. we compare two environment assignment methods with our method, which are random sampling-based method rand#2, and flat environment inference-based method infer#2, respectively. For a fair comparison, we set two environments for both methods and set the hierarchical environment as " + }, + { + "bbox": [ + 46, + 403, + 287, + 498 + ], + "type": "inline_equation", + "content": "[6881\\to 3440\\to 2]" + }, + { + "bbox": [ + 46, + 403, + 287, + 498 + ], + "type": "text", + "content": " for our method using the IC50-sCA dataset from DrugOOD." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": "As mentioned in [8], the diversity of environments is important to obtain effective IRM models, and large discrepancy of spurious correlations between environments benefits the IRM model. We measure the diversity of environments by calculating the distance of distributions among the acquired environments for each method. More specifically, we measure the Kolomogorov-Smirnov (K-S) statistic [34] as a distance between the two inferred scaffold distributions for each method, respectively. The K-S test can capture the dissimilarity between cumulative distribution functions, making it suitable for our analysis. As shown in Fig. 3, the two environments generated by rand#2 methods are almost the same since they assign the sample to two environments using random sampling, showing the lowest diversity of environments. infer#2 shows better diversity of generated environment distributions with significant p-values " + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "inline_equation", + "content": "(p = 1.86e - 26)" + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": ". Our method generates more significantly diverse environment distributions " + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "inline_equation", + "content": "(p = 4.52e - 73)" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 345, + 70, + 424, + 151 + ], + "blocks": [ + { + "bbox": [ + 345, + 70, + 424, + 151 + ], + "lines": [ + { + "bbox": [ + 345, + 70, + 424, + 151 + ], + "spans": [ + { + "bbox": [ + 345, + 70, + 424, + 151 + ], + "type": "image", + "image_path": "c8c33da69befed183f47f42b73d4143ed02609657a6f72fee2f416370642dffd.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 427, + 70, + 508, + 151 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 508, + 151 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 508, + 151 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 508, + 151 + ], + "type": "image", + "image_path": "3346f1deaf78852b55033272a522524f9b3642fa35d34e6329ece14dde9cd7dd.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 345, + 152, + 424, + 232 + ], + "blocks": [ + { + "bbox": [ + 345, + 152, + 424, + 232 + ], + "lines": [ + { + "bbox": [ + 345, + 152, + 424, + 232 + ], + "spans": [ + { + "bbox": [ + 345, + 152, + 424, + 232 + ], + "type": "image", + "image_path": "8eaa30a0e0d51c25b16c50d856e4893e185bcc8b60df573b650284ce6c30f9af.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "type": "text", + "content": "Figure 3. Discussions on the diversity of generated environments. We show distributions of two generated environments " + }, + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "type": "inline_equation", + "content": "env_0" + }, + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "type": "inline_equation", + "content": "env_1" + }, + { + "bbox": [ + 304, + 243, + 547, + 309 + ], + "type": "text", + "content": " for (a) random sampling methods, (b) flat environment inference methods, and (c) our hierarchical environment inference methods. (d) We employ the Kolmogorov-Smirnov test [34] to calculate the diversity of three methods." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 427, + 152, + 507, + 232 + ], + "blocks": [ + { + "bbox": [ + 427, + 152, + 507, + 232 + ], + "lines": [ + { + "bbox": [ + 427, + 152, + 507, + 232 + ], + "spans": [ + { + "bbox": [ + 427, + 152, + 507, + 232 + ], + "type": "image", + "image_path": "64d51654036bf6b98343ac6c3284af567a56578a8886ca62f96d89bdde0c16e6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 316, + 547, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 388 + ], + "type": "text", + "content": "compared to other methods, surpassing them in inter-env-distance by a large margin. Moreover, the results are aligned with Fig. 1, our methods outperform other methods in IC50-SCA dataset, indicating that diverse environments can give a clear indication of distribution shifts, therefore IRM can easily identify and eliminate variant features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 397, + 379, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 397, + 379, + 410 + ], + "spans": [ + { + "bbox": [ + 306, + 397, + 379, + 410 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 418, + 547, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 620 + ], + "type": "text", + "content": "In our research, we take on the formidable challenge of improving out-of-distribution (OOD) generalization in the graph domain. We observe that recent works often overlook the crucial aspect of studying hierarchical environments in graph invariant learning. To address this gap, we introduce a novel method that generates hierarchical dynamic environments for each graph. Our approach involves hierarchical stochastic subgraph generation, hierarchical environment inference, and a carefully designed learning objective. By incorporating graph invariant learning with inferred high-level environments, our model not only achieves meaningful and diverse environments within the same hierarchy but also ensures consistency across different hierarchies. The effectiveness of our method is particularly pronounced in the DrugOOD dataset, shedding light on the potential for further exploration in hierarchical graph learning within OOD scenarios." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 627, + 416, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 627, + 416, + 639 + ], + "spans": [ + { + "bbox": [ + 306, + 627, + 416, + 639 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "This work was supported by Bio & Medical Technology Development Program of the NRF funded by the Ministry of Science & ICT(NRF-2022M3E5F3085677, RS-2023-00257479), and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00246586)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27638" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Jean-Christophe Gagnon-Audet, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. 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AI open, 1:57-81, 2020. 1" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "27640" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/4b87738e-8519-4923-9186-4d7b85e26126_content_list.json b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/4b87738e-8519-4923-9186-4d7b85e26126_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9e15894b56394d15b5c93464986e832fdcae9661 --- /dev/null +++ b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/4b87738e-8519-4923-9186-4d7b85e26126_content_list.json @@ -0,0 +1,1521 @@ +[ + { + "type": "text", + "text": "Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization", + "text_level": 1, + "bbox": [ + 76, + 128, + 893, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Takuhiro Kaneko \nNTT Corporation", + "bbox": [ + 411, + 200, + 557, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Geometry-agnostic system identification is a technique for identifying the geometry and physical properties of an object from video sequences without any geometric assumptions. Recently, physics-augmented continuum neural radiance fields (PAC-NeRF) has demonstrated promising results for this technique by utilizing a hybrid Eulerian-Lagrangian representation, in which the geometry is represented by the Eulerian grid representations of NeRF, the physics is described by a material point method (MPM), and they are connected via Lagrangian particles. However, a notable limitation of PAC-NeRF is that its performance is sensitive to the learning of the geometry from the first frames owing to its two-step optimization. First, the grid representations are optimized with the first frames of video sequences, and then the physical properties are optimized through video sequences utilizing the fixed first-frame grid representations. This limitation can be critical when learning of the geometric structure is difficult, for example, in a few-shot (sparse view) setting. To overcome this limitation, we propose Lagrangian particle optimization (LPO), in which the positions and features of particles are optimized through video sequences in Lagrangian space. This method allows for the optimization of the geometric structure across the entire video sequence within the physical constraints imposed by the MPM. The experimental results demonstrate that the LPO is useful for geometric correction and physical identification in sparse-view settings. $^{1}$", + "bbox": [ + 75, + 301, + 473, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 722, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "System identification is a technique used to identify the geometry and physical properties of an object based on visual observations. It has been actively studied in computer vision and physics because of its wide range of applications, including 3D reproduction, environmental understanding, and content creation. To solve this problem in a realistic environment, it is important to adequately address both the extrinsic geometry structure and the intrinsic physical prop", + "bbox": [ + 75, + 747, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6a4fee893f99e78038c235f21cd85c6f3dd1520c7c968295981ab9c8ad89f127.jpg", + "image_caption": [ + "(a) Ground truth $E = 1.00\\times 10^{6}$ $\\nu = 0.300$" + ], + "image_footnote": [], + "bbox": [ + 516, + 268, + 619, + 405 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33e3557af9be976d8466c43f4065c81e8ea3b33d9d1581f7c1bad9a221d0400f.jpg", + "image_caption": [ + "PSNR: 23.99", + "(c) +LPO (proposed) $E = 1.15\\times 10^{6}$ $\\nu = 0.299$", + "Figure 1. Impact of the proposed Lagrangian particle optimization (LPO) in sparse-view geometric-agnostic system identification. We aim to identify the geometry and physical properties of an object from visual observations without any geometric assumptions in severe (e.g., sparse-view) settings. As shown in (b), a standard PAC-NeRF [41] has difficulty learning the geometry in a sparse-view setting (particularly, when the number of viewpoints is three). Consequently, it also fails to estimate the physical properties (Young's modulus $E$ and Poisson's ratio $\\mu$ ). As shown in (c), LPO is useful for correcting this failure and succeeds in improving the identification of both geometry and physical properties." + ], + "image_footnote": [], + "bbox": [ + 640, + 268, + 751, + 409 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e32000abb2c1beb17073fdc14762e93a125ef12f9620f38e586baab9d9da3d3.jpg", + "image_caption": [ + "PSNR: 30.07", + "(b) PAC-NeRF $E = 1.89\\times 10^{6}$ $\\nu = 0.215$" + ], + "image_footnote": [], + "bbox": [ + 769, + 268, + 880, + 404 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "erties. For example, to identify the geometry and physical properties of an object from the observation that it collides with the ground, it is necessary to understand not only the appearance and shape change in the geometry but also other internal factors in physics which are necessary to explain this phenomenon without any discrepancies over time. Generally, this problem is ill-posed and challenging to resolve. However, the emergence of powerful geometric representations by neural fields [82], 2D-3D connections by neural rendering [74], and trainable physical simulations using differentiable physical simulators [1] provide clues for solving this problem. For instance, previous studies [34, 35, 47] succeeded in estimating physical properties such as velocity, mass, friction, inertia, and elasticity directly from video sequences by combining differentiable physical simulators with differentiable renderers.", + "bbox": [ + 496, + 623, + 893, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although these studies have yielded promising results in terms of physical property estimation, their applicability is restricted by the assumption that the geometric struc", + "bbox": [ + 496, + 856, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Video samples are available at https://www.kecl.ntt.co.jp/people/kaneko.takuhiro/projects/lpo/.", + "bbox": [ + 76, + 875, + 467, + 902 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5470", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ture of a scene is completely known, which makes it difficult to apply them in practical scenarios. To eliminate this assumption, geometry-agnostic system identification, which is a technique for identifying the geometry and physical properties of an object from visual observations without any geometric assumptions, has been studied. Specifically, a pioneering model involves physics-augmented continuum neural radiance fields (PAC-NeRF) [41], which is an extension of NeRF [50] that is enforced to follow the conservation laws of continuum mechanics. PAC-NeRF obtains this functionality utilizing a hybrid Eulerian-Lagrangian representation, that is, the geometry (volume density and color fields) is represented with the Eulerian grid representations of NeRF [72], which is transformed into a material space via Lagrangian particles, and physical simulation is conducted on the particles using a material point method (MPM) (particularly, differentiable MPM (DiffMPM) [32]). Because all modules are differentiable, PAC-NeRF can be trained directly with multi-view video sequences and can optimize the geometry and physics without explicit supervision.", + "bbox": [ + 76, + 90, + 472, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although PAC-NeRF has enabled the tackling of new tasks, its notable limitation is that its performance is sensitive to the learning of the geometry from the first frames of the video sequences owing to its two-step optimization. First, the grid representations were trained with the first frames of the video sequences, and then the physical properties were optimized across the video sequences by utilizing the frozen first-frame grid representations. This limitation makes it difficult to apply it to cases in which geometry learning is difficult, for example, in a few-shot (sparse-view) setting, as shown in Figure 1(b).", + "bbox": [ + 76, + 383, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One possible solution is to train the Eulerian grid representations using all video sequences and not just the first frame. However, a critical problem with this approach is that Eulerian grid representations cannot be trained with explicit physical constraints on the particles because they are optimized in Eulerian (i.e., world) space and cannot reflect all physical phenomena occurring in Lagrangian (i.e., material or particle) space; for example, they cannot propagate gradients calculated for particle positions.", + "bbox": [ + 76, + 546, + 472, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve this problem, we propose Lagrangian particle optimization (LPO), in which the positions and features (i.e., volume density and color) of the particles are optimized in Lagrangian space and not in Eulerian space. Contrary to the abovementioned possible solution, this method allows for the optimization of the geometric structure across video sequences with explicit physical constraints on the particles imposed by the MPM. Thus, the gradients calculated for the particle positions are reflected.", + "bbox": [ + 76, + 679, + 472, + 811 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, LPO is useful not only for geometry correction, but also for corrections to the physical identification because this task is closely related, that is, an accurate geometry is useful for accurately identifying the physical properties, and vice versa. This motivated us to utilize the geometry corrected by LPO to re-identify the phys", + "bbox": [ + 76, + 813, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ical properties and propose iterative geometry-physics optimization for gradually seeking the optimized states. Figure 1(c) shows the effectiveness of this method.", + "bbox": [ + 496, + 90, + 890, + 133 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluated the effectiveness of LPO in sparse-view settings. In particular, we first applied LPO to a pretrained PAC-NeRF and demonstrated that LPO is useful for correcting geometric structures through video sequences. Subsequently, we employed LPO in iterative geometry-physics optimization and demonstrated that LPO contributes to improving the performance of physical identification. Ablation and comparative studies were conducted to determine the importance of each component.", + "bbox": [ + 496, + 135, + 890, + 266 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 517, + 266, + 844, + 279 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To improve the performance of geometry-agnostic system identification, we propose LPO, which optimizes the position and features of the particles in Lagrangian space to optimize the geometrical structures across video sequences within the physical constraints of an MPM.", + "- We propose iterative geometry-physics optimization to utilize the geometry corrected by LPO for re-identifying physical properties in an iterative manner.", + "- We experimentally demonstrated that LPO is useful for geometric correction and physical identification in sparse-view settings. We also provide detailed analyses and extended results in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript." + ], + "bbox": [ + 500, + 281, + 890, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 497, + 637, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural radiance fields (NeRF). Novel view synthesis is a fundamental problem in computer vision and graphics and has been addressed in a large body of research. Recently, a substantial breakthrough has been achieved with the emergence of neural fields that represent a scene utilizing a coordinate-based network (e.g., a survey paper [82]). NeRF [50] is a representative variant of such neural fields and has attracted significant attention because of its geometrical consistency and high-fidelity novel view synthesis. Various studies have been conducted since the emergence of NeRF. These can be categorized into three topics. (1) Improvements to the image quality and expanding of the applicable settings, such as wild or few-shot settings (e.g., [2-4, 8, 11, 12, 14, 30, 33, 48, 51, 56, 65, 76, 79, 85, 87, 89, 91]), (2) speeding up the training or inference speed (e.g., [4, 6, 9, 18, 20, 26, 29, 30, 38, 40, 45, 46, 52, 53, 58, 63, 64, 72, 80, 81, 86]), and (3) incorporating other models or functionalities, such as generative models [22, 28, 71] (e.g., [5-7, 15, 23, 37, 54, 55, 59, 67, 70, 84]) and dynamics/physics (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). Among these, this study relates to the first in terms of its application to few-shot settings. This study relates to the third in terms of seeking physics-informed models. As studies on NeRF are benefiting from developments in adjacent categories, applying our ideas to other categories and models will be an interesting future research direction.", + "bbox": [ + 496, + 523, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5471", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NeRF with dynamics/physics. As mentioned above, NeRFs with dynamics/physics have been actively studied (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). These studies have one characteristic in common: they learned time-varying neural fields from video sequences. These can be roughly categorized into two models: (1) non- (or weak) physics-informed models (e.g., [19, 25, 43, 57, 60, 68, 75, 90]) and (2) physics-informed models (e.g., [13, 24, 41]). The advantage of the first is that it can be applied to scenes or objects that are difficult to describe physically; however, its disadvantage is that it requires a large amount of training data to learn dynamics from scratch, and the learned representations are not necessarily interpretable because they are not based on physics. The advantage of the second is that it can obtain interpretable representations based on physics; however, the disadvantage is that its application is limited to physically describable objects or scenes. In particular, PI-NeRF [13] targets smoke scenes and does not address the boundary conditions; therefore, it cannot handle solid or contact materials. NeuroFluid [24] focuses on fluid dynamics grounding and solves it using an intuitive physics-based approach in which formal instruction in physics is not explicitly defined. In contrast, PAC-NeRF [41] is based on a principled and interpretable physical simulator and can be applied to various materials, including Newtonian/non-Newtonian fluids, granular media, deformable solids, and plasticine. This study focused on the PAC-NeRF and attempted to widen its applicability while prioritizing its interpretability. However, a Lagrangian particle representation is commonly utilized in physics (e.g., NeuroFluid $[24]^2$ ); therefore, applying our ideas, that is, LPO, to other models is an interesting research topic.", + "bbox": [ + 76, + 90, + 472, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NeRF for few-shot (sparse-view) settings. In practice, it is often laborious or impractical to collect multi-view images. Recent studies [8, 12-14, 33, 56, 65, 68, 79, 85, 87, 89] addressed this problem by refining NeRF such that it could be applied to few-shot (sparse-view) settings. These methods can be roughly divided into three approaches. (1) Regularization using external models. For example, normalizing flow [16]-based [56], VGG [69]-based [89], depth-based [14, 65, 79], and CLIP [62]-based [33] regularizations have been proposed. (2) Utilization of general and transferable models [8, 12, 68, 87]. They are trained using external datasets, and in several studies, they are finetuned for each scene. (3) Introduction of advanced training methods, such as gradual training to prevent overfitting to sparse views, including frequency regularization [85] and layer-by-layer growing strategies [13]. Among these categories, the proposed LPO is categorized as the third one, that is, optimization is conducted for each scene, and external models/datasets are not required. The main difference between", + "bbox": [ + 76, + 556, + 472, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2Note that NeuroFluid optimizes the transition probability of particles under the assumption that the initial particle positions are known, that is, fixed. In contrast, LPO optimizes the initial particle positions to correct the geometry estimation of the first frames. Therefore, NeuroFluid and LPO are complementary.", + "bbox": [ + 75, + 840, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the LPO and previous methods is that LPO attempts to optimize geometric structures through video sequences with the physical constraints of an MPM. However, previous studies have not sufficiently considered these constraints. Owing to this difference in applications, the proposed method is complementary to, rather than competitive with, other methods.", + "bbox": [ + 496, + 90, + 890, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "System identification of soft bodies. Soft bodies are not only high-dimensional, but also allow large deformations; therefore, it is challenging to identify their geometry and physical properties. Typical methods can be categorized into three types. (1) Gradient-free methods [73, 77], (2) neural network-based methods [42, 66, 83], and (3) differentiable physics-simulation-based methods [10, 17, 21, 27, 35, 41, 47, 61]. The strength of the methods in the first and second categories is that they are flexible; however, they have difficulty achieving a high accuracy owing to their black-box modeling. Methods in the third category require sophisticated modeling to fill the gap between simulations and the real world; however, they have recently demonstrated promising results owing to advancements in differentiable physical simulators. The third category can be further divided into two subcategories. (i) Methods that assume that watertight geometric mesh representations of objects are available [17, 21, 27, 35, 47, 61] and (2) methods that do not assume this [10, 41]. Among these methods, we focused on the final category, PAC-NeRF [41], which prioritizes general and fast characteristics. Specifically, PAC-NeRF adopts an MPM that can be applied to various materials, including elastic objects, sand [39], fluids [36], and foam [88]. In particular, PAC-NeRF utilizes a differentiable MPM (DiffMPM) [32] to construct a fully differentiable simulation rendering system. This study is based on this advancement. In particular, sensitivity to geometry learning from the first frames is one of the bottlenecks of PAC-NeRF. Therefore, this study focused on alleviating this bottleneck and attempted to widen its applicability to severe (e.g., sparse-view) settings.", + "bbox": [ + 496, + 181, + 892, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 646, + 591, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first define the problem statement (Section 3.1) and then briefly review PAC-NeRF [41], upon which our method is built (Section 3.2). Subsequently, we explain the main idea of the proposed method, that is, geometric correction using LPO (Section 3.3), and then introduce its application to physical identification (Section 3.4).", + "bbox": [ + 496, + 671, + 890, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem statement", + "text_level": 1, + "bbox": [ + 500, + 768, + 684, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of multi-view video sequences, our objectives are as follows: (1) to recover geometric representations3 of the target dynamic object (particularly continuum materials) through video sequences and (2) identify its physical properties. More formally, the training data comprise", + "bbox": [ + 496, + 791, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "3Here, both appearance and shape are treated as part of the geometric representation. We attempted to recover both.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5472", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f181108a197c39887f014830553f1e5fe9f1c3fdfa0407d68255a9268faafb3.jpg", + "image_caption": [ + "(1) Eulerian static voxel grid optimization (PAC-NeRF)" + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 885, + 179 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4e619bb5fa17dc898229f626060a5f9441d5f52513e5193879e12b4afe8b7dd3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 75, + 202, + 880, + 368 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1e63532372324b5738d78e64d7dca11671bb8e8418e924ee538b4f8841fbc615.jpg", + "image_caption": [ + "(2) Physical property optimization (PAC-NeRF)", + "(3) Lagrangian particle optimization (proposed)", + "Figure 2. Training pipelines of PAC-NeRF (1)(2) and the proposed LPO (3)." + ], + "image_footnote": [], + "bbox": [ + 76, + 383, + 879, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ground truth color observations, that is, $\\hat{\\mathbf{C}} (\\mathbf{r},t)$ . Here, $\\mathbf{r}(s)\\in \\mathbb{R}^3$ is a camera ray defined as $\\mathbf{r}(s) = \\mathbf{o} + s\\mathbf{d}$ , where $\\mathbf{o}\\in \\mathbb{R}^3$ is the camera origin, $\\mathbf{d}\\in \\mathbb{S}^2$ is the view direction, and $s\\in [s_n,s_f]$ is a distance from the origin. $\\mathbf{r}$ is sampled from a set of ray collections in the training data, that is, $\\hat{\\mathcal{R}}$ . $t\\in \\mathbb{R}^{+}$ is a time variable, and during training, it is sampled from $\\{t_0,\\dots ,t_{N - 1}\\}$ , where $N$ is the number of frames. Given these training data, we attempt to (1) predict the color observation $\\mathbf{C}(\\mathbf{r},t)$ that can recover $\\hat{\\mathbf{C}} (\\mathbf{r},t)$ from the training data and those for novel views, and (2) identify the physical properties. In particular, to widen its applicability, we addressed a scenario in which input views are sparse, that is, $\\hat{\\mathcal{R}}$ is limited.", + "bbox": [ + 75, + 603, + 472, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Preliminary: PAC-NeRF", + "text_level": 1, + "bbox": [ + 76, + 810, + 305, + 828 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve the abovementioned problem, PAC-NeRF employs three core components: a continuum NeRF, particle-grid interconverters, and a Lagrangian field.", + "bbox": [ + 75, + 835, + 468, + 880 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Continuum NeRF. PAC-NeRF extends the standard (static)", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "NeRF to a continuum NeRF to address the dynamics of continuum materials. To achieve this, a standard NeRF is first extended to a dynamic NeRF [60] for dynamic scenarios. In a dynamic NeRF, the volume density and color fields are defined as $\\sigma (\\mathbf{r},t)$ and $\\mathbf{c}(\\mathbf{r},\\mathbf{d},t)$ , respectively, where the time variable $t$ is introduced to represent the dynamics. The color of each pixel $\\mathbf{C}(\\mathbf{r},t)$ is calculated using volume rendering [49]", + "bbox": [ + 496, + 604, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} (\\mathbf {r}, t) = \\int_ {s _ {n}} ^ {s _ {f}} T (s, t) \\sigma (\\mathbf {r} (s), t) \\mathbf {c} (\\mathbf {r}, \\mathbf {d}, t) d s + \\mathbf {c} _ {b g} T (s _ {f}, t), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 726, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT (s, t) = \\exp \\left(- \\int_ {s _ {n}} ^ {s} \\sigma (\\mathbf {r} (u), t) d u\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 777, + 890, + 813 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{c}_{bg}$ denotes the background color. The model is trained with pixel-wise loss.", + "bbox": [ + 500, + 816, + 890, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p i x e l}} = \\frac {1}{N} \\sum_ {i = 0} ^ {N - 1} \\frac {1}{| \\hat {\\mathcal {R}} |} \\sum_ {\\mathbf {r} \\in \\hat {\\mathcal {R}}} \\| \\mathbf {C} (\\mathbf {r}, t _ {i}) - \\hat {\\mathbf {C}} (\\mathbf {r}, t _ {i}) \\| _ {2} ^ {2}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 852, + 890, + 897 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5473", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, dynamic NeRF is extended to a continuum NeRF to represent continuum materials. To achieve this, conservation laws for the velocity field are imposed on the volume density and color fields.", + "bbox": [ + 75, + 90, + 468, + 148 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {D \\sigma}{D t} = 0, \\frac {D \\mathbf {c}}{D t} = \\mathbf {0}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 156, + 468, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "whereas the material derivative of an arbitrary time-dependent field $\\phi (\\mathbf{x},t)$ is defined as $\\frac{D\\phi}{Dt} = \\frac{\\partial\\phi}{\\partial t} +\\mathbf{v}\\cdot \\nabla \\phi$ Here, $\\mathbf{v}$ is the velocity field and follows momentum conservation for continuum materials:", + "bbox": [ + 76, + 191, + 468, + 251 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\rho \\frac {D \\mathbf {v}}{D t} = \\nabla \\cdot \\boldsymbol {T} + \\rho \\mathbf {g}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 255, + 468, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\rho$ is the physical density field, $T$ is the internal Cauchy stress tensor, and $\\mathbf{g}$ is the acceleration owing to gravity. This equation is solved using DiffMPM [32].", + "bbox": [ + 75, + 291, + 468, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Particle-grid interconverters. As shown in Figure 2(1)(2), in PAC-NeRF, a physical simulation is conducted in Lagrangian particle space using DiffMPM [32], whereas neural rendering is performed in Eulerian grid space with a discretized voxel-based NeRF [72]. To bridge these two spaces, grid-to-particle (G2P) and particle-to-grid (P2G) conversions are conducted.", + "bbox": [ + 75, + 338, + 468, + 439 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {p} ^ {P} \\approx \\sum_ {i} w _ {i p} \\mathcal {F} _ {i} ^ {G}, \\mathcal {F} _ {i} ^ {G} \\approx \\frac {\\sum_ {p} w _ {i p} \\mathcal {F} _ {p} ^ {P}}{\\sum_ {p} w _ {i p}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 445, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_*$ is a field (e.g., volume density or color field); $P$ and $G$ denote particle and grid views, respectively; $i$ and $p$ indicate the index of the grid node and particle, respectively; and $w_{ip}$ is the weight of the trilinear shape function defined on $i$ and evaluated at $p$ .", + "bbox": [ + 75, + 491, + 468, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lagrangian field. As shown in Figure 2(1), during training, the Eulerian voxel field $\\mathcal{F}^{G^{\\prime}}(t_0)$ is optimized for the first frames of the video sequences. Subsequently, this field is converted into a Lagrangian particle field $\\mathcal{F}^P (t_0)$ using G2P, in which the positions of the particles are determined by random sampling around voxel grids. The geometric shape is represented in Lagrangian space by removing the particles whose alpha values are small, that is, the remaining particles represent the shape of the object. As shown in Figure 2(2), the particle field in the next step, that is, $\\mathcal{F}^P (t_1)$ , where $t_1 = t_0 + \\delta t$ and $\\delta t$ is the duration of the simulation time step, is calculated based on $\\mathcal{F}^P (t_0)$ using DiffMPM [32]. After this process, $\\mathcal{F}^P (t_1)$ is converted to the Eulerian voxel field $\\mathcal{F}^G (t_1)$ using P2G, and pixels are rendered based on this field using voxel-based volume rendering [72], in which the volume density and color of a sample on a ray are rendered as follows:", + "bbox": [ + 75, + 566, + 468, + 816 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma (\\mathbf {x}, t) = \\operatorname {s o f t p l u s} \\left(\\operatorname {i n t e r p} \\left(\\mathbf {x}, \\sigma^ {G}\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 823, + 467, + 840 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, t) = \\operatorname {M L P} \\left(\\operatorname {i n t e r p} (\\mathbf {x}, \\mathbf {c} ^ {G}), \\mathbf {d}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 844, + 468, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma^G$ and $\\mathbf{c}^G$ denote the volume density and color fields, respectively, discretized on fixed voxel grids.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Geometric correction with LPO", + "text_level": 1, + "bbox": [ + 500, + 90, + 779, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As explained above, in PAC-NeRF, the Eulerian voxel fields $\\mathcal{F}^{G^{\\prime}}(t_0)$ are optimized for the first frames of the video sequences (Figure 2(1)). These are fixed while optimizing the physical properties using video sequences (Figure 2(2)). This approach is problematic when the learning of the Eulerian voxel field from the first frames is difficult, for example, in sparse-view settings, because failure of this learning cannot be corrected after the process. This also means that in dynamic scenes, information over time is useful for covering a lack of information owing to sparse views; however, this approach cannot utilize this information to optimize the volume density and color.", + "bbox": [ + 498, + 113, + 890, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One possible solution is to train $\\mathcal{F}^{G^{\\prime}}(t_0)$ with the entire video sequence and not just the first frame. However, in this approach, the optimization targets are limited to the volume density and color of the grids; therefore, it is difficult to reflect the physics-based optimization that occurs in Lagrangian particle space. This can cause excessive modification of the geometry beyond physical constraints.", + "bbox": [ + 496, + 290, + 890, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Alternatively, we developed Lagrangian particle optimization (LPO), in which the geometric structure is optimized not in Eulerian grid space but in Lagrangian particle space, as shown in Figure 2(3). More formally, in the Eulerian voxel grid optimization, $\\sigma^G$ (Equation (7)) and $\\mathbf{c}^G$ (Equation (8)) are optimized for the fixed voxel grid $\\mathbf{x}^G$ . In contrast, in LPO, not only the volume density and color fields of the particles, that is, $\\sigma^P$ and $\\mathbf{c}^P$ , but also the particle position, that is $\\mathbf{x}^P$ , are optimized. Because $\\mathbf{x}^P$ is defined in Lagrangian space, it can reflect the physical constraints of the MPM. Consequently, we can optimize the geometric structures within the physical allowance.", + "bbox": [ + 496, + 393, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Physical identification with LPO", + "text_level": 1, + "bbox": [ + 500, + 578, + 784, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Identifying both the geometry and physical properties from limited observations is ill-posed and challenging because there is a chicken-and-egg relationship between the geometric structure and the physical properties, that is, accurate geometry estimation is necessary for accurate physical identification and vice versa. Considering that particle-based geometric correction is highly challenging when there is a large gap between the ground truth and the predicted pixels owing to the high-dimensional nature (e.g., in extreme cases, particles can diverge), in practice, we apply LPO after physical property optimization, as shown in Figure 2.", + "bbox": [ + 496, + 601, + 890, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, an interesting question is whether the corrected geometric structures can be utilized to improve the", + "bbox": [ + 500, + 762, + 890, + 792 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "4More precisely, as explained in Section 3.2, particles are randomly sampled around equally spaced voxel grids, and the Eulerian voxel fields (precisely, alpha values calculated from them) are only utilized to mask them (with a non-differentiable way). Consequently, gradients calculated for the particle positions cannot propagate to $\\mathcal{F}^{G^{\\prime}}(t_0)$", + "bbox": [ + 500, + 803, + 890, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "5Note that the values of $\\sigma^P$ and $\\mathbf{c}^P$ are changed in training but they are time-invariant, i.e., have the same values across sequences. Therefore, the conservation laws (Equation (4)) are preserved.", + "bbox": [ + 500, + 864, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5474", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Iterative geometry-physics optimization" + ], + "code_body": "Input: Ground-truth color observations $\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)$ $\\hat{\\mathbf{r}}\\in \\hat{\\mathcal{R}}$ : Rays from observed viewpoints $t\\in \\{t_0,\\dots ,t_{N - 1}\\}$ : Time \nOutput: Physical properties \n1: for $i = 1$ to $R$ do \n2: // (1) Eulerian static voxel grid optimization \n3: if $i = 1$ then \n4: Optimize voxel grids with $\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t_0)$ \n5: else \n6: Optimize voxel grids with $\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t_0)$ and $\\check{\\mathbf{C}} (\\check{\\mathbf{r}},t_0)$ \n7: end if \n8: // (2) Physical property optimization \n9: Optimize physical properties with $\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)$ \n10: // (3) Lagrangian particle optimization \n11: Optimize particles with $\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)$ \n12: // (4) Color prediction for unobserved views $\\check{\\mathbf{r}}\\in \\check{\\mathcal{R}}$ \n13: Predict $\\check{\\mathbf{C}} (\\check{\\mathbf{r}},t_0)$ \n14: end for", + "bbox": [ + 76, + 111, + 459, + 385 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "identification of the physical properties. We developed iterative geometry-physics optimization (Algorithm 1) to answer this question. As described above, we first conduct PAC-NeRF optimization ((1) and (2)) and then apply LPO (3). Subsequently, we render the images in the first frame based on the updated $\\sigma^P$ , $\\mathbf{c}^P$ , and $\\mathbf{x}^P(4)$ . We denote them as $\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)$ , where $\\check{\\mathbf{r}} \\in \\check{\\mathcal{R}}$ and $\\check{\\mathcal{R}}$ is designed such that it covers the missing area in $\\hat{\\mathcal{R}}$ in the training data. We retrain PAC-NeRF from scratch using the combination of the original $\\hat{\\mathbf{C}}(\\hat{\\mathbf{r}}, t_0)$ and synthesized $\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)$ as training data. Specifically, to alleviate the negative effect caused by incomplete geometry correction, which can occur at the beginning of the iterative calculation, we only utilize $\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)$ for the Eulerian static voxel grid optimization and do not utilize it to optimize the physical properties and particles.", + "bbox": [ + 75, + 411, + 467, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Another possible solution is to update the voxel grids by applying P2G to the updated $\\sigma^P$ , $\\mathbf{c}^P$ , and $\\mathbf{x}^P$ instead of (4) and (1). However, we found that the repeated utilization of G2P and P2G tends to produce artifacts (such as those typically occurring in the erosion process) owing to their approximate nature (Equation (6)). Therefore, the full recalculation approach described above was adopted.", + "bbox": [ + 75, + 636, + 467, + 737 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 751, + 209, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 776, + 263, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Two experiments were conducted to investigate the effectiveness of the proposed LPO. First, we evaluated the effec", + "bbox": [ + 75, + 799, + 467, + 828 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tiveness of LPO for geometric correction (Section 4.2) and then we investigated the utility of LPO for physical identification (Section 4.3). The main results of these experiments are presented here, and the detailed analyses, extended results, and implementation details are provided in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript. $^{1}$ In this section, we provide the experimental setup common to both experiments and other setups in subsequent sections.", + "bbox": [ + 496, + 90, + 890, + 222 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We investigated the benchmark performance on the dataset provided by the original study on PAC-NeRF [41]. This dataset comprised nine scenes and various continuum materials, including Newtonian fluids (Droplet and Letter with fluid viscosity $\\mu$ and bulk modulus $\\kappa$ ), non-Newtonian fluids (Cream and Toothpaste with shear modulus $\\nu$ , bulk modulus $\\kappa$ , yield stress $\\tau_{Y}$ , and plastic viscosity $\\eta$ ), granular media (Trophy with friction angle $\\theta_{fric}$ ), deformable solid (Torus and Bird with Young's modulus $E$ and Poisson's ratio $\\nu$ ), and plasticine (Cat and Playdoh with $E$ , $\\nu$ , and $\\tau_{Y}$ ). In each scene, the objects fall freely under the influence of gravity and undergo collisions. The ground-truth simulation data were generated using the MLS-MPM framework [31]. A photorealistic simulation engine rendered objects under diverse environmental lighting conditions and ground textures. Each scene was captured from 11 viewpoints with cameras evenly spaced on the upper hemisphere, including the object. To evaluate our method under sparse-view settings, three views were used for training and the remaining eight views were used for testing. To show the robustness to the view settings, we provide the results for the other view settings in Appendix C.", + "bbox": [ + 496, + 224, + 890, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Assumptions and preprocessing. For a fair comparison, we follow the assumptions and preprocessing used in PAC-NeRF [41]. It was assumed that the intrinsic and extrinsic parameters of the set of static cameras were previously known. Moreover, it was assumed that collision objects, such as the ground plane, were previously known. As mentioned in [41], this is not difficult to estimate from the observed images. For preprocessing, a video matting framework [44] was applied to remove static background objects and focus the rendering computation on the target object.", + "bbox": [ + 496, + 547, + 890, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation of geometric correction", + "text_level": 1, + "bbox": [ + 500, + 699, + 802, + 714 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared models. In the first experiment, we investigated the effectiveness of LPO on the geometric correction (i.e., the method described in Section 3.3). Three models were used as the baseline. (I) PAC-NeRF was the same as that in the original [41] and was trained with all views, including the eight views that were used for testing. We examined this model to determine the upper bound of its performance. (II) PAC-NeRF-3v was trained using three views. The training settings were the same as those for (I) except that the", + "bbox": [ + 496, + 724, + 890, + 856 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "A similar phenomenon was observed in the original study on PAC-NeRF [41]. Based on this observation, they rendered an image in the first frame by utilizing the voxel grids obtained after the P2G and G2P conversions, that is, $\\mathcal{F}^G(t_0)$ , instead of the original voxel grids $\\mathcal{F}^{G'}(t_0)$ to make the rendering conditions the same as those in other frames.", + "bbox": [ + 75, + 838, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "Note that although only one dataset was used, this dataset is useful for assessing the versatility because it includes a wide variety of materials, surpassing the scope of previous studies (e.g., elastic objects only in [10]).", + "bbox": [ + 500, + 864, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5475", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b44f0e6550e7b482692c16b24cd335c4d71e542c726ce84fe2165fafd2e4274d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PAC-NeRFPAC-NeRF-3v+LPO+LPO-F+LPO-P+GOPAC-NeRF-3v†+LPO+LPO-F+LPO-P+GO
PSNR↑35.9927.3929.2228.2228.8928.3328.4730.1129.3129.8729.39
SSIM↑0.9890.9780.9800.9790.9800.9790.9800.9820.9810.9810.981
LPIPS↓0.0200.0340.0320.0330.0320.0330.0330.0310.0320.0310.031
", + "bbox": [ + 76, + 89, + 893, + 143 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Comparison of PSNR↑, SSIM↑, and LPIPS↓ on geometric correction. The scores for each scene and qualitative results are provided in Table 5 and Figures 3-7, respectively, in the Supplementary Material.", + "bbox": [ + 75, + 146, + 893, + 175 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "number of views varied. (III) $PAC\\text{-}NeRF-3\\nu^{\\dagger}$ was an improved variant of (II) for sparse-view settings. An interesting question is whether LPO, which is a few-shot learning method for dynamic scenes, can be used with other few-shot learning methods, such as those for static scenes. To answer this question, we adjusted the Eulerian static voxel grid optimization (Figure 2(1)) of PAC-NeRF-3v, such that it became robust to sparse views. Specifically, we scheduled a surface regularizer to reduce unexpected artifacts, introduced a view-invariant pixel-wise loss to compensate for the lack of views, and adjusted the training length to prevent overfitting. Details are provided in Appendix A. $^{8}$ We applied LPO to both (II) and (III) to investigate the effect of the initial Eulerian static voxel grid optimization. Hereafter, we denote these variants by $+LPO$ . Furthermore, three comparative and ablation models were evaluated to determine the importance of each component. (i) $+LPO-F$ and (ii) $+LPO-P$ are variants of LPO, in which only the features and positions of the particles are optimized. (iii) $+GO$ optimized Eulerian voxel grids through the entire video sequence instead of using Lagrangian particles. (i)-(iii) are used as alternatives to $+LPO$ . These variants were applied to both (II) and (III).", + "bbox": [ + 75, + 181, + 472, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation metrics. We evaluated the performance of the geometric correction using metrics commonly used to assess the performance of novel view synthesis in NeRF studies: the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [78], and learned perceptual image patch similarity (LPIPS) [92]. In particular, we calculated the scores using all test data over time.", + "bbox": [ + 75, + 518, + 468, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. The results are summarized in Table 1. Our findings are threefold. (1) $PAC\\text{-}NeRF-3\\nu/3\\nu^{\\dagger}$ vs. $+LPO$ . $+LPO$ improved both baselines in terms of all metrics. In particular, the utility of $+LPO$ for $PAC\\text{-}NeRF-3\\nu^{\\dagger}$ indicates an improvement in the Eulerian static voxel grid optimization and that of LPO are complementary. (2) $+LPO$ vs. $+LPO-F/P$ . We found that $+LPO$ was superior or comparable to $+LPO-F/P$ . This is because the feature and position optimizations are complementary. Intuitively, feature optimization is useful for correcting features of the appearance that are invisible in the first frame but visible after the object has moved. Similarly, position optimization is effective for", + "bbox": [ + 75, + 623, + 472, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the preliminary experiments, we examined the previous representative few-shot learning methods (e.g., DietNeRF [33] and FreeNeRF [85]). However, we found that they were less stable than PAC-NeRF-3v, possibly because in our experimental settings, the number of views was small (three) despite the wide range of the views (upper hemisphere), and explicit voxel representations were more useful than the fully implicit representation in [33, 85]. However, this study and previous studies are complementary. Further investigations will be important in future work.", + "bbox": [ + 75, + 806, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "correcting features of the shape that are invisible in the first frame but visible after the object has moved. In severe (e.g., sparse-view) settings, the utilization of both is important. $(3) + LPO$ vs. $+GO$ . $+LPO$ outperforms $+GO$ , possibly because $+LPO$ can optimize the geometry adequately within the physical constraints of the MPM, whereas $+GO$ cannot because of the absence of an explicit physical constraint.", + "bbox": [ + 496, + 181, + 893, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Evaluation of physical identification", + "text_level": 1, + "bbox": [ + 498, + 295, + 812, + 311 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared models. In the second experiment, we verified the usefulness of LPO for physical identification (i.e., the method described in Section 3.4). In addition to the models described in Section 4.2, we examined +None, for which iterative training (Algorithm 1) was conducted without geometric correction (i.e., step (3) was skipped). This model was used to investigate the importance of geometric correction. For a fair comparison, we set the number of iterations (i.e., $R$ in Algorithm 1) to four for all models. We use the superscript 4 (e.g., $+\\mathrm{LPO}^4$ ) to specify this.", + "bbox": [ + 496, + 323, + 890, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation metrics. To evaluate the performance of the physical identification, we measured the absolute distance between the ground truth and the estimated physical properties. For an easy comparison, we calculated these distances after adjusting the scale (i.e., either a logarithmic scale or a linear scale) following the study of PAC-NeRF [41]. The smaller the values, the better was the performance.", + "bbox": [ + 496, + 474, + 893, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. The results are summarized in Table 2. Our findings are fourfold. (1) $PAC\\text{-} NeRF\\text{-} 3v/3v^{\\dagger}$ vs. $+LPO^{4}$ . $+LPO^{4}$ improved the physical identification of PAC-NeRF- $3v/3v^{\\dagger}$ in most cases. In particular, the effectiveness of $+LPO^{4}$ for PAC-NeRF- $3v^{\\dagger}$ indicates that the improvement in the Eulerian static voxel grid optimization and that of LPO are complementary for physical identification. (2) $+LPO^{4}$ vs. $+LPO\\text{-} F^{4}/P^{4}$ . In some cases, superiority depends on the physical properties because the physical properties interact with each other, and finding the optimal balance is difficult. However, we found that $+LPO\\text{-} F^{4}/P^{4}$ sometimes had obvious difficulties (e.g., PAC-NeRF- $3v\\text{+}LPO\\text{-} F^{4}$ on Bird and PAC-NeRF- $3v^{\\dagger}$ +LPO-P $^{4}$ on Play-doh), whereas $+LPO^{4}$ exhibited good stability. We consider that the joint optimization of the features and positions is useful for tackling difficult situations. (3) $+LPO^{4}$ vs. $+GO^{4}$ . $+GO^{4}$ also experienced apparent difficulties in some cases (e.g., on Bird). $+LPO^{4}$ exhibited a more stable performance. (4) $+LPO^{4}$ vs. $+None^{4}$ . $+None^{4}$ sometimes worsened the performance. The results indicated that simple iterations were insufficient and that geometric correction was essential.", + "bbox": [ + 496, + 580, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5476", + "bbox": [ + 482, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f0d90caff5baffff321651f7f050b8ff15fdf1dc3571dcba31a630ea8875d6b8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PAC-NeRFPAC-NeRF-3v+LPO4+LPO-F4+LPO-P4+GO4+None4PAC-NeRF-3v†+LPO4+LPO-F4+LPO-P4+GO4+None4
Dropletlog10(μ)0.0390.1400.1120.1120.1190.1110.1310.1360.0820.0680.0670.0820.090
log10(κ)0.0171.2851.6281.6381.4661.6751.6841.2630.1061.1390.5201.5201.656
Letterlog10(μ)0.0410.6740.0150.0260.0790.0480.5300.3790.0100.0870.0070.1180.436
log10(κ)0.0396.7720.1740.4111.0400.8656.0835.2290.0600.0270.1270.1385.060
Creamlog10(μ)0.0900.3110.1780.1630.2340.1830.2510.1790.1000.0730.0650.0920.076
log10(κ)0.1320.2150.1580.2490.0270.0280.2440.3360.1210.1970.1420.1930.339
log10(τY)0.0070.0140.0040.0300.0050.0060.0250.0090.0060.0010.0040.0100.008
log10(η)0.0150.2810.1830.2560.0830.0610.2520.1950.0330.0590.0790.0960.051
Toothpastelog10(μ)0.0261.8910.1090.1560.1190.1640.2150.2520.0310.2010.0050.2520.138
log10(κ)0.2471.5800.6011.3560.5970.6480.7291.4360.6730.6300.8990.5900.596
log10(τY)0.0660.2010.1140.1910.0750.2500.0610.1990.0930.0640.1170.1490.054
log10(η)0.0130.3730.0030.2670.0130.0070.0470.2120.0090.0160.0050.0070.042
Toruslog10(E)0.0190.2770.0610.0080.0830.0100.0540.0740.0360.0260.0390.0150.074
ν0.0230.0850.0010.1200.0310.0740.3160.1310.0070.0400.0330.0500.129
Birdlog10(E)0.0130.4490.0670.2400.0740.3130.2460.1230.0270.1860.0390.2310.296
ν0.0290.1020.0010.3720.0750.3650.5810.1410.0470.0720.0080.1320.145
Playdohlog10(E)0.2860.2900.1160.5800.1200.3040.1700.5210.1330.4742.1210.2322.148
log10(τY)0.0380.2830.1650.0270.2140.1960.2370.1100.1730.0791.1790.1970.967
ν0.0760.4950.1110.1730.1090.2480.1280.2120.0630.1330.1100.1270.106
Catlog10(E)0.8551.3010.9731.0681.0711.1271.0661.1920.7060.5340.7120.7830.793
log10(τY)0.0260.1200.1070.1170.1130.0860.1120.0840.0670.0140.0760.0690.072
ν0.0270.0440.0040.0360.0690.1900.0790.1180.0030.0270.0070.0280.063
Trophyθfric [rad]0.0480.0530.0550.0510.0560.0570.0540.0300.0390.0410.0430.0440.039
", + "bbox": [ + 81, + 89, + 890, + 393 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c97d481a447109bfb66322e17f4ef5cd587895fd51beefca0ebc06ea26efce15.jpg", + "table_caption": [ + "Table 2. Comparison of the absolute differences between the ground-truth and the estimated physical properties on physical identification. The smaller the values, the better was the performance. The values of the physical properties (i.e., not the absolute differences) are provided in Tables 6 and 7 in the Supplementary Material. The qualitative comparisons are presented in Figures 3-9 in the Supplementary Material." + ], + "table_footnote": [], + "table_body": "
PAC-NeRF-3v+LPO+LPO4PAC-NeRF-3v†+LPO+LPO4
PSNR↑27.3929.2229.6528.4730.1130.34
SSIM↑0.9780.9800.9820.9800.9820.983
LPIPS↓0.0340.0320.0300.0330.0310.029
", + "bbox": [ + 78, + 454, + 467, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Comparison of PSNR $\\uparrow$ , SSIM $\\uparrow$ , and LPIPS $\\downarrow$ on geometric recorrection. The scores for each scene and the qualitative comparisons are provided in Table 8 and Figures 3-9, respectively, in the Supplementary Material.", + "bbox": [ + 76, + 518, + 468, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Applications. As mentioned above, there is a chicken-and-egg relationship between the geometric structure and physical properties. An interesting question is whether the corrected physical properties can be used to re-estimate the geometry (the opposite problem). To answer this question, we investigated the geometry identification performance after physical re-identification. The results are summarized in Table 3. These results indicate that accurate physical identification is useful for improving the geometry identification performance.", + "bbox": [ + 75, + 585, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 744, + 191, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Based on the above experiments, we demonstrated promising results for geometric correction and physical identification. However, our methods have some limitations. (1) Our methods require a longer training time due to the introduction of LPO (Section 3.3) $^{9}$ and the iterative algorithm (Sec", + "bbox": [ + 76, + 768, + 468, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion 3.4).10 However, it is not trivial to obtain robustness to sparse views only by increasing the training time because overfitting is a typical factor that causes learning to fail. (2) LPO is sensitive to the state before applying LPO (e.g., either PAC-NeRF-3v or $-3\\mathrm{v}^{\\dagger}$ ) because solving geometry-agnostic system identification in sparse-view settings is ill-posed and challenging. We believe that the advancements in previous few-shot learning methods (Section 2) and the newly introduced few-shot learning method with physical constraints will solve this problem.", + "bbox": [ + 500, + 449, + 890, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 608, + 617, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed LPO to improve PAC-NeRF-based geometric-agnostic system identification. Our core idea is to optimize the geometry not in Eulerian space but in Lagrangian space, utilizing the particles to directly reflect the physical constraints of an MPM. The results demonstrate that LPO is useful for both geometric correction and physical identification. Although we focused on PAC-NeRF while prioritizing its high generality, Lagrangian particles are commonly employed in physics-informed models (e.g., several studies discussed in Section 2). We expect that our ideas can be utilized in other models or tasks.", + "bbox": [ + 496, + 632, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "The calculation time of LPO (Figure 2(3)) is almost identical to that of the main process of physical property optimization (Figure 2(2)) because the forward and backward processes are identical with different optimization targets. Similarly, the calculation times for $+\\mathrm{LPO - F}$ , $+\\mathrm{LPO - P}$", + "bbox": [ + 75, + 851, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "and $+\\mathrm{GO}$ were almost identical to those for $+\\mathrm{LPO}$ , indicating that the improvement was attributable to the ingenuity of the algorithm and not to an increase in the calculation cost. The computation times are discussed in detail in Appendix B.2.", + "bbox": [ + 496, + 816, + 890, + 864 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "10The total computation time increases linearly when running Algorithm 1 repeatedly but is adjustable under a quality-and-time trade-off as discussed in Appendix B.3.", + "bbox": [ + 496, + 864, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5477", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Chayan Banerjee, Kien Nguyen, Clinton Fookes, and George Karniadakis. Physics-informed computer vision: A review and perspectives. arXiv preprint arXiv:2305.18035, 2023. 1", + "[2] Jonathan T. 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In CVPR, 2018. 7" + ], + "bbox": [ + 503, + 92, + 890, + 772 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5480", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/4b87738e-8519-4923-9186-4d7b85e26126_model.json b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/4b87738e-8519-4923-9186-4d7b85e26126_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c49557e844bdd5ba9fe1d859c241e13883ede9d9 --- /dev/null +++ b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/4b87738e-8519-4923-9186-4d7b85e26126_model.json @@ -0,0 +1,2587 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.13, + 0.895, + 0.177 + ], + "angle": 0, + "content": "Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization" + }, + { + "type": "text", + "bbox": [ + 0.413, + 0.202, + 0.558, + 0.238 + ], + "angle": 0, + "content": "Takuhiro Kaneko \nNTT Corporation" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.27, + 0.314, + 0.287 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.474, + 0.695 + ], + "angle": 0, + "content": "Geometry-agnostic system identification is a technique for identifying the geometry and physical properties of an object from video sequences without any geometric assumptions. Recently, physics-augmented continuum neural radiance fields (PAC-NeRF) has demonstrated promising results for this technique by utilizing a hybrid Eulerian-Lagrangian representation, in which the geometry is represented by the Eulerian grid representations of NeRF, the physics is described by a material point method (MPM), and they are connected via Lagrangian particles. However, a notable limitation of PAC-NeRF is that its performance is sensitive to the learning of the geometry from the first frames owing to its two-step optimization. First, the grid representations are optimized with the first frames of video sequences, and then the physical properties are optimized through video sequences utilizing the fixed first-frame grid representations. This limitation can be critical when learning of the geometric structure is difficult, for example, in a few-shot (sparse view) setting. To overcome this limitation, we propose Lagrangian particle optimization (LPO), in which the positions and features of particles are optimized through video sequences in Lagrangian space. This method allows for the optimization of the geometric structure across the entire video sequence within the physical constraints imposed by the MPM. The experimental results demonstrate that the LPO is useful for geometric correction and physical identification in sparse-view settings.\\(^{1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.723, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.866 + ], + "angle": 0, + "content": "System identification is a technique used to identify the geometry and physical properties of an object based on visual observations. It has been actively studied in computer vision and physics because of its wide range of applications, including 3D reproduction, environmental understanding, and content creation. To solve this problem in a realistic environment, it is important to adequately address both the extrinsic geometry structure and the intrinsic physical prop" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.269, + 0.62, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.422, + 0.617, + 0.46 + ], + "angle": 0, + "content": "(a) Ground truth \\(E = 1.00\\times 10^{6}\\) \\(\\nu = 0.300\\)" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.269, + 0.752, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.409, + 0.758, + 0.419 + ], + "angle": 0, + "content": "PSNR: 23.99" + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.269, + 0.882, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.409, + 0.886, + 0.419 + ], + "angle": 0, + "content": "PSNR: 30.07" + }, + { + "type": "image_caption", + "bbox": [ + 0.653, + 0.422, + 0.74, + 0.46 + ], + "angle": 0, + "content": "(b) PAC-NeRF \\(E = 1.89\\times 10^{6}\\) \\(\\nu = 0.215\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.422, + 0.884, + 0.461 + ], + "angle": 0, + "content": "(c) +LPO (proposed) \\(E = 1.15\\times 10^{6}\\) \\(\\nu = 0.299\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.465, + 0.895, + 0.613 + ], + "angle": 0, + "content": "Figure 1. Impact of the proposed Lagrangian particle optimization (LPO) in sparse-view geometric-agnostic system identification. We aim to identify the geometry and physical properties of an object from visual observations without any geometric assumptions in severe (e.g., sparse-view) settings. As shown in (b), a standard PAC-NeRF [41] has difficulty learning the geometry in a sparse-view setting (particularly, when the number of viewpoints is three). Consequently, it also fails to estimate the physical properties (Young's modulus \\( E \\) and Poisson's ratio \\( \\mu \\)). As shown in (c), LPO is useful for correcting this failure and succeeds in improving the identification of both geometry and physical properties." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.895, + 0.856 + ], + "angle": 0, + "content": "erties. For example, to identify the geometry and physical properties of an object from the observation that it collides with the ground, it is necessary to understand not only the appearance and shape change in the geometry but also other internal factors in physics which are necessary to explain this phenomenon without any discrepancies over time. Generally, this problem is ill-posed and challenging to resolve. However, the emergence of powerful geometric representations by neural fields [82], 2D-3D connections by neural rendering [74], and trainable physical simulations using differentiable physical simulators [1] provide clues for solving this problem. For instance, previous studies [34, 35, 47] succeeded in estimating physical properties such as velocity, mass, friction, inertia, and elasticity directly from video sequences by combining differentiable physical simulators with differentiable renderers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Although these studies have yielded promising results in terms of physical property estimation, their applicability is restricted by the assumption that the geometric struc" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.468, + 0.903 + ], + "angle": 0, + "content": "1Video samples are available at https://www.kecl.ntt.co.jp/people/kaneko.takuhiro/projects/lpo/." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5470" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.382 + ], + "angle": 0, + "content": "ture of a scene is completely known, which makes it difficult to apply them in practical scenarios. To eliminate this assumption, geometry-agnostic system identification, which is a technique for identifying the geometry and physical properties of an object from visual observations without any geometric assumptions, has been studied. Specifically, a pioneering model involves physics-augmented continuum neural radiance fields (PAC-NeRF) [41], which is an extension of NeRF [50] that is enforced to follow the conservation laws of continuum mechanics. PAC-NeRF obtains this functionality utilizing a hybrid Eulerian-Lagrangian representation, that is, the geometry (volume density and color fields) is represented with the Eulerian grid representations of NeRF [72], which is transformed into a material space via Lagrangian particles, and physical simulation is conducted on the particles using a material point method (MPM) (particularly, differentiable MPM (DiffMPM) [32]). Because all modules are differentiable, PAC-NeRF can be trained directly with multi-view video sequences and can optimize the geometry and physics without explicit supervision." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.385, + 0.473, + 0.544 + ], + "angle": 0, + "content": "Although PAC-NeRF has enabled the tackling of new tasks, its notable limitation is that its performance is sensitive to the learning of the geometry from the first frames of the video sequences owing to its two-step optimization. First, the grid representations were trained with the first frames of the video sequences, and then the physical properties were optimized across the video sequences by utilizing the frozen first-frame grid representations. This limitation makes it difficult to apply it to cases in which geometry learning is difficult, for example, in a few-shot (sparse-view) setting, as shown in Figure 1(b)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.547, + 0.473, + 0.679 + ], + "angle": 0, + "content": "One possible solution is to train the Eulerian grid representations using all video sequences and not just the first frame. However, a critical problem with this approach is that Eulerian grid representations cannot be trained with explicit physical constraints on the particles because they are optimized in Eulerian (i.e., world) space and cannot reflect all physical phenomena occurring in Lagrangian (i.e., material or particle) space; for example, they cannot propagate gradients calculated for particle positions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.68, + 0.473, + 0.812 + ], + "angle": 0, + "content": "To solve this problem, we propose Lagrangian particle optimization (LPO), in which the positions and features (i.e., volume density and color) of the particles are optimized in Lagrangian space and not in Eulerian space. Contrary to the abovementioned possible solution, this method allows for the optimization of the geometric structure across video sequences with explicit physical constraints on the particles imposed by the MPM. Thus, the gradients calculated for the particle positions are reflected." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.814, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Furthermore, LPO is useful not only for geometry correction, but also for corrections to the physical identification because this task is closely related, that is, an accurate geometry is useful for accurately identifying the physical properties, and vice versa. This motivated us to utilize the geometry corrected by LPO to re-identify the phys" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.135 + ], + "angle": 0, + "content": "ical properties and propose iterative geometry-physics optimization for gradually seeking the optimized states. Figure 1(c) shows the effectiveness of this method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.136, + 0.892, + 0.267 + ], + "angle": 0, + "content": "We evaluated the effectiveness of LPO in sparse-view settings. In particular, we first applied LPO to a pretrained PAC-NeRF and demonstrated that LPO is useful for correcting geometric structures through video sequences. Subsequently, we employed LPO in iterative geometry-physics optimization and demonstrated that LPO contributes to improving the performance of physical identification. Ablation and comparative studies were conducted to determine the importance of each component." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.267, + 0.845, + 0.28 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.282, + 0.892, + 0.354 + ], + "angle": 0, + "content": "- To improve the performance of geometry-agnostic system identification, we propose LPO, which optimizes the position and features of the particles in Lagrangian space to optimize the geometrical structures across video sequences within the physical constraints of an MPM." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.355, + 0.892, + 0.397 + ], + "angle": 0, + "content": "- We propose iterative geometry-physics optimization to utilize the geometry corrected by LPO for re-identifying physical properties in an iterative manner." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.397, + 0.892, + 0.485 + ], + "angle": 0, + "content": "- We experimentally demonstrated that LPO is useful for geometric correction and physical identification in sparse-view settings. We also provide detailed analyses and extended results in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.282, + 0.892, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.638, + 0.515 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Neural radiance fields (NeRF). Novel view synthesis is a fundamental problem in computer vision and graphics and has been addressed in a large body of research. Recently, a substantial breakthrough has been achieved with the emergence of neural fields that represent a scene utilizing a coordinate-based network (e.g., a survey paper [82]). NeRF [50] is a representative variant of such neural fields and has attracted significant attention because of its geometrical consistency and high-fidelity novel view synthesis. Various studies have been conducted since the emergence of NeRF. These can be categorized into three topics. (1) Improvements to the image quality and expanding of the applicable settings, such as wild or few-shot settings (e.g., [2-4, 8, 11, 12, 14, 30, 33, 48, 51, 56, 65, 76, 79, 85, 87, 89, 91]), (2) speeding up the training or inference speed (e.g., [4, 6, 9, 18, 20, 26, 29, 30, 38, 40, 45, 46, 52, 53, 58, 63, 64, 72, 80, 81, 86]), and (3) incorporating other models or functionalities, such as generative models [22, 28, 71] (e.g., [5-7, 15, 23, 37, 54, 55, 59, 67, 70, 84]) and dynamics/physics (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). Among these, this study relates to the first in terms of its application to few-shot settings. This study relates to the third in terms of seeking physics-informed models. As studies on NeRF are benefiting from developments in adjacent categories, applying our ideas to other categories and models will be an interesting future research direction." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5471" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.557 + ], + "angle": 0, + "content": "NeRF with dynamics/physics. As mentioned above, NeRFs with dynamics/physics have been actively studied (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). These studies have one characteristic in common: they learned time-varying neural fields from video sequences. These can be roughly categorized into two models: (1) non- (or weak) physics-informed models (e.g., [19, 25, 43, 57, 60, 68, 75, 90]) and (2) physics-informed models (e.g., [13, 24, 41]). The advantage of the first is that it can be applied to scenes or objects that are difficult to describe physically; however, its disadvantage is that it requires a large amount of training data to learn dynamics from scratch, and the learned representations are not necessarily interpretable because they are not based on physics. The advantage of the second is that it can obtain interpretable representations based on physics; however, the disadvantage is that its application is limited to physically describable objects or scenes. In particular, PI-NeRF [13] targets smoke scenes and does not address the boundary conditions; therefore, it cannot handle solid or contact materials. NeuroFluid [24] focuses on fluid dynamics grounding and solves it using an intuitive physics-based approach in which formal instruction in physics is not explicitly defined. In contrast, PAC-NeRF [41] is based on a principled and interpretable physical simulator and can be applied to various materials, including Newtonian/non-Newtonian fluids, granular media, deformable solids, and plasticine. This study focused on the PAC-NeRF and attempted to widen its applicability while prioritizing its interpretability. However, a Lagrangian particle representation is commonly utilized in physics (e.g., NeuroFluid \\([24]^2\\)); therefore, applying our ideas, that is, LPO, to other models is an interesting research topic." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.558, + 0.473, + 0.837 + ], + "angle": 0, + "content": "NeRF for few-shot (sparse-view) settings. In practice, it is often laborious or impractical to collect multi-view images. Recent studies [8, 12-14, 33, 56, 65, 68, 79, 85, 87, 89] addressed this problem by refining NeRF such that it could be applied to few-shot (sparse-view) settings. These methods can be roughly divided into three approaches. (1) Regularization using external models. For example, normalizing flow [16]-based [56], VGG [69]-based [89], depth-based [14, 65, 79], and CLIP [62]-based [33] regularizations have been proposed. (2) Utilization of general and transferable models [8, 12, 68, 87]. They are trained using external datasets, and in several studies, they are finetuned for each scene. (3) Introduction of advanced training methods, such as gradual training to prevent overfitting to sparse views, including frequency regularization [85] and layer-by-layer growing strategies [13]. Among these categories, the proposed LPO is categorized as the third one, that is, optimization is conducted for each scene, and external models/datasets are not required. The main difference between" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.472, + 0.902 + ], + "angle": 0, + "content": "2Note that NeuroFluid optimizes the transition probability of particles under the assumption that the initial particle positions are known, that is, fixed. In contrast, LPO optimizes the initial particle positions to correct the geometry estimation of the first frames. Therefore, NeuroFluid and LPO are complementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.179 + ], + "angle": 0, + "content": "the LPO and previous methods is that LPO attempts to optimize geometric structures through video sequences with the physical constraints of an MPM. However, previous studies have not sufficiently considered these constraints. Owing to this difference in applications, the proposed method is complementary to, rather than competitive with, other methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.182, + 0.893, + 0.634 + ], + "angle": 0, + "content": "System identification of soft bodies. Soft bodies are not only high-dimensional, but also allow large deformations; therefore, it is challenging to identify their geometry and physical properties. Typical methods can be categorized into three types. (1) Gradient-free methods [73, 77], (2) neural network-based methods [42, 66, 83], and (3) differentiable physics-simulation-based methods [10, 17, 21, 27, 35, 41, 47, 61]. The strength of the methods in the first and second categories is that they are flexible; however, they have difficulty achieving a high accuracy owing to their black-box modeling. Methods in the third category require sophisticated modeling to fill the gap between simulations and the real world; however, they have recently demonstrated promising results owing to advancements in differentiable physical simulators. The third category can be further divided into two subcategories. (i) Methods that assume that watertight geometric mesh representations of objects are available [17, 21, 27, 35, 47, 61] and (2) methods that do not assume this [10, 41]. Among these methods, we focused on the final category, PAC-NeRF [41], which prioritizes general and fast characteristics. Specifically, PAC-NeRF adopts an MPM that can be applied to various materials, including elastic objects, sand [39], fluids [36], and foam [88]. In particular, PAC-NeRF utilizes a differentiable MPM (DiffMPM) [32] to construct a fully differentiable simulation rendering system. This study is based on this advancement. In particular, sensitivity to geometry learning from the first frames is one of the bottlenecks of PAC-NeRF. Therefore, this study focused on alleviating this bottleneck and attempted to widen its applicability to severe (e.g., sparse-view) settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.593, + 0.663 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.761 + ], + "angle": 0, + "content": "In this section, we first define the problem statement (Section 3.1) and then briefly review PAC-NeRF [41], upon which our method is built (Section 3.2). Subsequently, we explain the main idea of the proposed method, that is, geometric correction using LPO (Section 3.3), and then introduce its application to physical identification (Section 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.685, + 0.785 + ], + "angle": 0, + "content": "3.1. Problem statement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Given a set of multi-view video sequences, our objectives are as follows: (1) to recover geometric representations3 of the target dynamic object (particularly continuum materials) through video sequences and (2) identify its physical properties. More formally, the training data comprise" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.876, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3Here, both appearance and shape are treated as part of the geometric representation. We attempted to recover both." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5472" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.887, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.183, + 0.644, + 0.198 + ], + "angle": 0, + "content": "(1) Eulerian static voxel grid optimization (PAC-NeRF)" + }, + { + "type": "image", + "bbox": [ + 0.076, + 0.203, + 0.881, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.35, + 0.371, + 0.622, + 0.385 + ], + "angle": 0, + "content": "(2) Physical property optimization (PAC-NeRF)" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.385, + 0.88, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.556, + 0.631, + 0.57 + ], + "angle": 0, + "content": "(3) Lagrangian particle optimization (proposed)" + }, + { + "type": "image_caption", + "bbox": [ + 0.257, + 0.578, + 0.712, + 0.593 + ], + "angle": 0, + "content": "Figure 2. Training pipelines of PAC-NeRF (1)(2) and the proposed LPO (3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.473, + 0.799 + ], + "angle": 0, + "content": "ground truth color observations, that is, \\(\\hat{\\mathbf{C}} (\\mathbf{r},t)\\). Here, \\(\\mathbf{r}(s)\\in \\mathbb{R}^3\\) is a camera ray defined as \\(\\mathbf{r}(s) = \\mathbf{o} + s\\mathbf{d}\\), where \\(\\mathbf{o}\\in \\mathbb{R}^3\\) is the camera origin, \\(\\mathbf{d}\\in \\mathbb{S}^2\\) is the view direction, and \\(s\\in [s_n,s_f]\\) is a distance from the origin. \\(\\mathbf{r}\\) is sampled from a set of ray collections in the training data, that is, \\(\\hat{\\mathcal{R}}\\). \\(t\\in \\mathbb{R}^{+}\\) is a time variable, and during training, it is sampled from \\(\\{t_0,\\dots ,t_{N - 1}\\}\\), where \\(N\\) is the number of frames. Given these training data, we attempt to (1) predict the color observation \\(\\mathbf{C}(\\mathbf{r},t)\\) that can recover \\(\\hat{\\mathbf{C}} (\\mathbf{r},t)\\) from the training data and those for novel views, and (2) identify the physical properties. In particular, to widen its applicability, we addressed a scenario in which input views are sparse, that is, \\(\\hat{\\mathcal{R}}\\) is limited." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.811, + 0.306, + 0.829 + ], + "angle": 0, + "content": "3.2. Preliminary: PAC-NeRF" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.836, + 0.47, + 0.881 + ], + "angle": 0, + "content": "To solve the abovementioned problem, PAC-NeRF employs three core components: a continuum NeRF, particle-grid interconverters, and a Lagrangian field." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Continuum NeRF. PAC-NeRF extends the standard (static)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.722 + ], + "angle": 0, + "content": "NeRF to a continuum NeRF to address the dynamics of continuum materials. To achieve this, a standard NeRF is first extended to a dynamic NeRF [60] for dynamic scenarios. In a dynamic NeRF, the volume density and color fields are defined as \\(\\sigma (\\mathbf{r},t)\\) and \\(\\mathbf{c}(\\mathbf{r},\\mathbf{d},t)\\), respectively, where the time variable \\(t\\) is introduced to represent the dynamics. The color of each pixel \\(\\mathbf{C}(\\mathbf{r},t)\\) is calculated using volume rendering [49]" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.727, + 0.892, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} (\\mathbf {r}, t) = \\int_ {s _ {n}} ^ {s _ {f}} T (s, t) \\sigma (\\mathbf {r} (s), t) \\mathbf {c} (\\mathbf {r}, \\mathbf {d}, t) d s + \\mathbf {c} _ {b g} T (s _ {f}, t), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.779, + 0.892, + 0.814 + ], + "angle": 0, + "content": "\\[\nT (s, t) = \\exp \\left(- \\int_ {s _ {n}} ^ {s} \\sigma (\\mathbf {r} (u), t) d u\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.818, + 0.892, + 0.847 + ], + "angle": 0, + "content": "where \\(\\mathbf{c}_{bg}\\) denotes the background color. The model is trained with pixel-wise loss." + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.853, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p i x e l}} = \\frac {1}{N} \\sum_ {i = 0} ^ {N - 1} \\frac {1}{| \\hat {\\mathcal {R}} |} \\sum_ {\\mathbf {r} \\in \\hat {\\mathcal {R}}} \\| \\mathbf {C} (\\mathbf {r}, t _ {i}) - \\hat {\\mathbf {C}} (\\mathbf {r}, t _ {i}) \\| _ {2} ^ {2}. \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5473" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.15 + ], + "angle": 0, + "content": "Furthermore, dynamic NeRF is extended to a continuum NeRF to represent continuum materials. To achieve this, conservation laws for the velocity field are imposed on the volume density and color fields." + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.157, + 0.47, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\frac {D \\sigma}{D t} = 0, \\frac {D \\mathbf {c}}{D t} = \\mathbf {0}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.193, + 0.469, + 0.252 + ], + "angle": 0, + "content": "whereas the material derivative of an arbitrary time-dependent field \\(\\phi (\\mathbf{x},t)\\) is defined as \\(\\frac{D\\phi}{Dt} = \\frac{\\partial\\phi}{\\partial t} +\\mathbf{v}\\cdot \\nabla \\phi\\) Here, \\(\\mathbf{v}\\) is the velocity field and follows momentum conservation for continuum materials:" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.256, + 0.469, + 0.287 + ], + "angle": 0, + "content": "\\[\n\\rho \\frac {D \\mathbf {v}}{D t} = \\nabla \\cdot \\boldsymbol {T} + \\rho \\mathbf {g}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.469, + 0.337 + ], + "angle": 0, + "content": "where \\(\\rho\\) is the physical density field, \\(T\\) is the internal Cauchy stress tensor, and \\(\\mathbf{g}\\) is the acceleration owing to gravity. This equation is solved using DiffMPM [32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.469, + 0.44 + ], + "angle": 0, + "content": "Particle-grid interconverters. As shown in Figure 2(1)(2), in PAC-NeRF, a physical simulation is conducted in Lagrangian particle space using DiffMPM [32], whereas neural rendering is performed in Eulerian grid space with a discretized voxel-based NeRF [72]. To bridge these two spaces, grid-to-particle (G2P) and particle-to-grid (P2G) conversions are conducted." + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.446, + 0.469, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {p} ^ {P} \\approx \\sum_ {i} w _ {i p} \\mathcal {F} _ {i} ^ {G}, \\mathcal {F} _ {i} ^ {G} \\approx \\frac {\\sum_ {p} w _ {i p} \\mathcal {F} _ {p} ^ {P}}{\\sum_ {p} w _ {i p}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.566 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_*\\) is a field (e.g., volume density or color field); \\(P\\) and \\(G\\) denote particle and grid views, respectively; \\(i\\) and \\(p\\) indicate the index of the grid node and particle, respectively; and \\(w_{ip}\\) is the weight of the trilinear shape function defined on \\(i\\) and evaluated at \\(p\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.469, + 0.817 + ], + "angle": 0, + "content": "Lagrangian field. As shown in Figure 2(1), during training, the Eulerian voxel field \\(\\mathcal{F}^{G^{\\prime}}(t_0)\\) is optimized for the first frames of the video sequences. Subsequently, this field is converted into a Lagrangian particle field \\(\\mathcal{F}^P (t_0)\\) using G2P, in which the positions of the particles are determined by random sampling around voxel grids. The geometric shape is represented in Lagrangian space by removing the particles whose alpha values are small, that is, the remaining particles represent the shape of the object. As shown in Figure 2(2), the particle field in the next step, that is, \\(\\mathcal{F}^P (t_1)\\), where \\(t_1 = t_0 + \\delta t\\) and \\(\\delta t\\) is the duration of the simulation time step, is calculated based on \\(\\mathcal{F}^P (t_0)\\) using DiffMPM [32]. After this process, \\(\\mathcal{F}^P (t_1)\\) is converted to the Eulerian voxel field \\(\\mathcal{F}^G (t_1)\\) using P2G, and pixels are rendered based on this field using voxel-based volume rendering [72], in which the volume density and color of a sample on a ray are rendered as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.824, + 0.468, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\sigma (\\mathbf {x}, t) = \\operatorname {s o f t p l u s} \\left(\\operatorname {i n t e r p} \\left(\\mathbf {x}, \\sigma^ {G}\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.845, + 0.469, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, t) = \\operatorname {M L P} \\left(\\operatorname {i n t e r p} (\\mathbf {x}, \\mathbf {c} ^ {G}), \\mathbf {d}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\sigma^G\\) and \\(\\mathbf{c}^G\\) denote the volume density and color fields, respectively, discretized on fixed voxel grids." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.78, + 0.105 + ], + "angle": 0, + "content": "3.3. Geometric correction with LPO" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.114, + 0.892, + 0.29 + ], + "angle": 0, + "content": "As explained above, in PAC-NeRF, the Eulerian voxel fields \\(\\mathcal{F}^{G^{\\prime}}(t_0)\\) are optimized for the first frames of the video sequences (Figure 2(1)). These are fixed while optimizing the physical properties using video sequences (Figure 2(2)). This approach is problematic when the learning of the Eulerian voxel field from the first frames is difficult, for example, in sparse-view settings, because failure of this learning cannot be corrected after the process. This also means that in dynamic scenes, information over time is useful for covering a lack of information owing to sparse views; however, this approach cannot utilize this information to optimize the volume density and color." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.394 + ], + "angle": 0, + "content": "One possible solution is to train \\(\\mathcal{F}^{G^{\\prime}}(t_0)\\) with the entire video sequence and not just the first frame. However, in this approach, the optimization targets are limited to the volume density and color of the grids; therefore, it is difficult to reflect the physics-based optimization that occurs in Lagrangian particle space. This can cause excessive modification of the geometry beyond physical constraints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Alternatively, we developed Lagrangian particle optimization (LPO), in which the geometric structure is optimized not in Eulerian grid space but in Lagrangian particle space, as shown in Figure 2(3). More formally, in the Eulerian voxel grid optimization, \\(\\sigma^G\\) (Equation (7)) and \\(\\mathbf{c}^G\\) (Equation (8)) are optimized for the fixed voxel grid \\(\\mathbf{x}^G\\). In contrast, in LPO, not only the volume density and color fields of the particles, that is, \\(\\sigma^P\\) and \\(\\mathbf{c}^P\\), but also the particle position, that is \\(\\mathbf{x}^P\\), are optimized. Because \\(\\mathbf{x}^P\\) is defined in Lagrangian space, it can reflect the physical constraints of the MPM. Consequently, we can optimize the geometric structures within the physical allowance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.579, + 0.785, + 0.594 + ], + "angle": 0, + "content": "3.4. Physical identification with LPO" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Identifying both the geometry and physical properties from limited observations is ill-posed and challenging because there is a chicken-and-egg relationship between the geometric structure and the physical properties, that is, accurate geometry estimation is necessary for accurate physical identification and vice versa. Considering that particle-based geometric correction is highly challenging when there is a large gap between the ground truth and the predicted pixels owing to the high-dimensional nature (e.g., in extreme cases, particles can diverge), in practice, we apply LPO after physical property optimization, as shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.763, + 0.892, + 0.793 + ], + "angle": 0, + "content": "However, an interesting question is whether the corrected geometric structures can be utilized to improve the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.804, + 0.892, + 0.865 + ], + "angle": 0, + "content": "4More precisely, as explained in Section 3.2, particles are randomly sampled around equally spaced voxel grids, and the Eulerian voxel fields (precisely, alpha values calculated from them) are only utilized to mask them (with a non-differentiable way). Consequently, gradients calculated for the particle positions cannot propagate to \\(\\mathcal{F}^{G^{\\prime}}(t_0)\\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.865, + 0.892, + 0.901 + ], + "angle": 0, + "content": "5Note that the values of \\(\\sigma^P\\) and \\(\\mathbf{c}^P\\) are changed in training but they are time-invariant, i.e., have the same values across sequences. Therefore, the conservation laws (Equation (4)) are preserved." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.804, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5474" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.079, + 0.092, + 0.435, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Iterative geometry-physics optimization" + }, + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.112, + 0.46, + 0.386 + ], + "angle": 0, + "content": "Input: Ground-truth color observations \\(\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)\\) \\(\\hat{\\mathbf{r}}\\in \\hat{\\mathcal{R}}\\) : Rays from observed viewpoints \\(t\\in \\{t_0,\\dots ,t_{N - 1}\\}\\) : Time \nOutput: Physical properties \n1: for \\(i = 1\\) to \\(R\\) do \n2: // (1) Eulerian static voxel grid optimization \n3: if \\(i = 1\\) then \n4: Optimize voxel grids with \\(\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t_0)\\) \n5: else \n6: Optimize voxel grids with \\(\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t_0)\\) and \\(\\check{\\mathbf{C}} (\\check{\\mathbf{r}},t_0)\\) \n7: end if \n8: // (2) Physical property optimization \n9: Optimize physical properties with \\(\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)\\) \n10: // (3) Lagrangian particle optimization \n11: Optimize particles with \\(\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)\\) \n12: // (4) Color prediction for unobserved views \\(\\check{\\mathbf{r}}\\in \\check{\\mathcal{R}}\\) \n13: Predict \\(\\check{\\mathbf{C}} (\\check{\\mathbf{r}},t_0)\\) \n14: end for" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.468, + 0.636 + ], + "angle": 0, + "content": "identification of the physical properties. We developed iterative geometry-physics optimization (Algorithm 1) to answer this question. As described above, we first conduct PAC-NeRF optimization ((1) and (2)) and then apply LPO (3). Subsequently, we render the images in the first frame based on the updated \\(\\sigma^P\\), \\(\\mathbf{c}^P\\), and \\(\\mathbf{x}^P(4)\\). We denote them as \\(\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)\\), where \\(\\check{\\mathbf{r}} \\in \\check{\\mathcal{R}}\\) and \\(\\check{\\mathcal{R}}\\) is designed such that it covers the missing area in \\(\\hat{\\mathcal{R}}\\) in the training data. We retrain PAC-NeRF from scratch using the combination of the original \\(\\hat{\\mathbf{C}}(\\hat{\\mathbf{r}}, t_0)\\) and synthesized \\(\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)\\) as training data. Specifically, to alleviate the negative effect caused by incomplete geometry correction, which can occur at the beginning of the iterative calculation, we only utilize \\(\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)\\) for the Eulerian static voxel grid optimization and do not utilize it to optimize the physical properties and particles." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.468, + 0.738 + ], + "angle": 0, + "content": "Another possible solution is to update the voxel grids by applying P2G to the updated \\(\\sigma^P\\), \\(\\mathbf{c}^P\\), and \\(\\mathbf{x}^P\\) instead of (4) and (1). However, we found that the repeated utilization of G2P and P2G tends to produce artifacts (such as those typically occurring in the erosion process) owing to their approximate nature (Equation (6)). Therefore, the full recalculation approach described above was adopted." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.752, + 0.21, + 0.769 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.777, + 0.264, + 0.793 + ], + "angle": 0, + "content": "4.1. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.468, + 0.829 + ], + "angle": 0, + "content": "Two experiments were conducted to investigate the effectiveness of the proposed LPO. First, we evaluated the effec" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.839, + 0.468, + 0.9 + ], + "angle": 0, + "content": "A similar phenomenon was observed in the original study on PAC-NeRF [41]. Based on this observation, they rendered an image in the first frame by utilizing the voxel grids obtained after the P2G and G2P conversions, that is, \\(\\mathcal{F}^G(t_0)\\), instead of the original voxel grids \\(\\mathcal{F}^{G'}(t_0)\\) to make the rendering conditions the same as those in other frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.223 + ], + "angle": 0, + "content": "tiveness of LPO for geometric correction (Section 4.2) and then we investigated the utility of LPO for physical identification (Section 4.3). The main results of these experiments are presented here, and the detailed analyses, extended results, and implementation details are provided in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript.\\(^{1}\\) In this section, we provide the experimental setup common to both experiments and other setups in subsequent sections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.225, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Dataset. We investigated the benchmark performance on the dataset provided by the original study on PAC-NeRF [41]. This dataset comprised nine scenes and various continuum materials, including Newtonian fluids (Droplet and Letter with fluid viscosity \\(\\mu\\) and bulk modulus \\(\\kappa\\)), non-Newtonian fluids (Cream and Toothpaste with shear modulus \\(\\nu\\), bulk modulus \\(\\kappa\\), yield stress \\(\\tau_{Y}\\), and plastic viscosity \\(\\eta\\)), granular media (Trophy with friction angle \\(\\theta_{fric}\\)), deformable solid (Torus and Bird with Young's modulus \\(E\\) and Poisson's ratio \\(\\nu\\)), and plasticine (Cat and Playdoh with \\(E\\), \\(\\nu\\), and \\(\\tau_{Y}\\)). In each scene, the objects fall freely under the influence of gravity and undergo collisions. The ground-truth simulation data were generated using the MLS-MPM framework [31]. A photorealistic simulation engine rendered objects under diverse environmental lighting conditions and ground textures. Each scene was captured from 11 viewpoints with cameras evenly spaced on the upper hemisphere, including the object. To evaluate our method under sparse-view settings, three views were used for training and the remaining eight views were used for testing. To show the robustness to the view settings, we provide the results for the other view settings in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.693 + ], + "angle": 0, + "content": "Assumptions and preprocessing. For a fair comparison, we follow the assumptions and preprocessing used in PAC-NeRF [41]. It was assumed that the intrinsic and extrinsic parameters of the set of static cameras were previously known. Moreover, it was assumed that collision objects, such as the ground plane, were previously known. As mentioned in [41], this is not difficult to estimate from the observed images. For preprocessing, a video matting framework [44] was applied to remove static background objects and focus the rendering computation on the target object." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.7, + 0.803, + 0.715 + ], + "angle": 0, + "content": "4.2. Evaluation of geometric correction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.857 + ], + "angle": 0, + "content": "Compared models. In the first experiment, we investigated the effectiveness of LPO on the geometric correction (i.e., the method described in Section 3.3). Three models were used as the baseline. (I) PAC-NeRF was the same as that in the original [41] and was trained with all views, including the eight views that were used for testing. We examined this model to determine the upper bound of its performance. (II) PAC-NeRF-3v was trained using three views. The training settings were the same as those for (I) except that the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.865, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Note that although only one dataset was used, this dataset is useful for assessing the versatility because it includes a wide variety of materials, surpassing the scope of previous studies (e.g., elastic objects only in [10])." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5475" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.09, + 0.895, + 0.145 + ], + "angle": 0, + "content": "
PAC-NeRFPAC-NeRF-3v+LPO+LPO-F+LPO-P+GOPAC-NeRF-3v†+LPO+LPO-F+LPO-P+GO
PSNR↑35.9927.3929.2228.2228.8928.3328.4730.1129.3129.8729.39
SSIM↑0.9890.9780.9800.9790.9800.9790.9800.9820.9810.9810.981
LPIPS↓0.0200.0340.0320.0330.0320.0330.0330.0310.0320.0310.031
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.147, + 0.895, + 0.176 + ], + "angle": 0, + "content": "Table 1. Comparison of PSNR↑, SSIM↑, and LPIPS↓ on geometric correction. The scores for each scene and qualitative results are provided in Table 5 and Figures 3-7, respectively, in the Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.182, + 0.473, + 0.517 + ], + "angle": 0, + "content": "number of views varied. (III) \\(PAC\\text{-}NeRF-3\\nu^{\\dagger}\\) was an improved variant of (II) for sparse-view settings. An interesting question is whether LPO, which is a few-shot learning method for dynamic scenes, can be used with other few-shot learning methods, such as those for static scenes. To answer this question, we adjusted the Eulerian static voxel grid optimization (Figure 2(1)) of PAC-NeRF-3v, such that it became robust to sparse views. Specifically, we scheduled a surface regularizer to reduce unexpected artifacts, introduced a view-invariant pixel-wise loss to compensate for the lack of views, and adjusted the training length to prevent overfitting. Details are provided in Appendix A.\\(^{8}\\) We applied LPO to both (II) and (III) to investigate the effect of the initial Eulerian static voxel grid optimization. Hereafter, we denote these variants by \\(+LPO\\). Furthermore, three comparative and ablation models were evaluated to determine the importance of each component. (i) \\(+LPO-F\\) and (ii) \\(+LPO-P\\) are variants of LPO, in which only the features and positions of the particles are optimized. (iii) \\(+GO\\) optimized Eulerian voxel grids through the entire video sequence instead of using Lagrangian particles. (i)-(iii) are used as alternatives to \\(+LPO\\). These variants were applied to both (II) and (III)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.622 + ], + "angle": 0, + "content": "Evaluation metrics. We evaluated the performance of the geometric correction using metrics commonly used to assess the performance of novel view synthesis in NeRF studies: the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [78], and learned perceptual image patch similarity (LPIPS) [92]. In particular, we calculated the scores using all test data over time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.473, + 0.801 + ], + "angle": 0, + "content": "Results. The results are summarized in Table 1. Our findings are threefold. (1) \\(PAC\\text{-}NeRF-3\\nu/3\\nu^{\\dagger}\\) vs. \\(+LPO\\). \\(+LPO\\) improved both baselines in terms of all metrics. In particular, the utility of \\(+LPO\\) for \\(PAC\\text{-}NeRF-3\\nu^{\\dagger}\\) indicates an improvement in the Eulerian static voxel grid optimization and that of LPO are complementary. (2) \\(+LPO\\) vs. \\(+LPO-F/P\\). We found that \\(+LPO\\) was superior or comparable to \\(+LPO-F/P\\). This is because the feature and position optimizations are complementary. Intuitively, feature optimization is useful for correcting features of the appearance that are invisible in the first frame but visible after the object has moved. Similarly, position optimization is effective for" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.807, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In the preliminary experiments, we examined the previous representative few-shot learning methods (e.g., DietNeRF [33] and FreeNeRF [85]). However, we found that they were less stable than PAC-NeRF-3v, possibly because in our experimental settings, the number of views was small (three) despite the wide range of the views (upper hemisphere), and explicit voxel representations were more useful than the fully implicit representation in [33, 85]. However, this study and previous studies are complementary. Further investigations will be important in future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.182, + 0.895, + 0.288 + ], + "angle": 0, + "content": "correcting features of the shape that are invisible in the first frame but visible after the object has moved. In severe (e.g., sparse-view) settings, the utilization of both is important. \\((3) + LPO\\) vs. \\(+GO\\). \\(+LPO\\) outperforms \\(+GO\\), possibly because \\(+LPO\\) can optimize the geometry adequately within the physical constraints of the MPM, whereas \\(+GO\\) cannot because of the absence of an explicit physical constraint." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.296, + 0.813, + 0.312 + ], + "angle": 0, + "content": "4.3. Evaluation of physical identification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Compared models. In the second experiment, we verified the usefulness of LPO for physical identification (i.e., the method described in Section 3.4). In addition to the models described in Section 4.2, we examined +None, for which iterative training (Algorithm 1) was conducted without geometric correction (i.e., step (3) was skipped). This model was used to investigate the importance of geometric correction. For a fair comparison, we set the number of iterations (i.e., \\( R \\) in Algorithm 1) to four for all models. We use the superscript 4 (e.g., \\( +\\mathrm{LPO}^4 \\)) to specify this." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Evaluation metrics. To evaluate the performance of the physical identification, we measured the absolute distance between the ground truth and the estimated physical properties. For an easy comparison, we calculated these distances after adjusting the scale (i.e., either a logarithmic scale or a linear scale) following the study of PAC-NeRF [41]. The smaller the values, the better was the performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Results. The results are summarized in Table 2. Our findings are fourfold. (1) \\(PAC\\text{-} NeRF\\text{-} 3v/3v^{\\dagger}\\) vs. \\(+LPO^{4}\\). \\(+LPO^{4}\\) improved the physical identification of PAC-NeRF- \\(3v/3v^{\\dagger}\\) in most cases. In particular, the effectiveness of \\(+LPO^{4}\\) for PAC-NeRF- \\(3v^{\\dagger}\\) indicates that the improvement in the Eulerian static voxel grid optimization and that of LPO are complementary for physical identification. (2) \\(+LPO^{4}\\) vs. \\(+LPO\\text{-} F^{4}/P^{4}\\). In some cases, superiority depends on the physical properties because the physical properties interact with each other, and finding the optimal balance is difficult. However, we found that \\(+LPO\\text{-} F^{4}/P^{4}\\) sometimes had obvious difficulties (e.g., PAC-NeRF- \\(3v\\text{+}LPO\\text{-} F^{4}\\) on Bird and PAC-NeRF- \\(3v^{\\dagger}\\) +LPO-P\\(^{4}\\) on Play-doh), whereas \\(+LPO^{4}\\) exhibited good stability. We consider that the joint optimization of the features and positions is useful for tackling difficult situations. (3) \\(+LPO^{4}\\) vs. \\(+GO^{4}\\). \\(+GO^{4}\\) also experienced apparent difficulties in some cases (e.g., on Bird). \\(+LPO^{4}\\) exhibited a more stable performance. (4) \\(+LPO^{4}\\) vs. \\(+None^{4}\\). \\(+None^{4}\\) sometimes worsened the performance. The results indicated that simple iterations were insufficient and that geometric correction was essential." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "5476" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.891, + 0.395 + ], + "angle": 0, + "content": "
PAC-NeRFPAC-NeRF-3v+LPO4+LPO-F4+LPO-P4+GO4+None4PAC-NeRF-3v†+LPO4+LPO-F4+LPO-P4+GO4+None4
Dropletlog10(μ)0.0390.1400.1120.1120.1190.1110.1310.1360.0820.0680.0670.0820.090
log10(κ)0.0171.2851.6281.6381.4661.6751.6841.2630.1061.1390.5201.5201.656
Letterlog10(μ)0.0410.6740.0150.0260.0790.0480.5300.3790.0100.0870.0070.1180.436
log10(κ)0.0396.7720.1740.4111.0400.8656.0835.2290.0600.0270.1270.1385.060
Creamlog10(μ)0.0900.3110.1780.1630.2340.1830.2510.1790.1000.0730.0650.0920.076
log10(κ)0.1320.2150.1580.2490.0270.0280.2440.3360.1210.1970.1420.1930.339
log10(τY)0.0070.0140.0040.0300.0050.0060.0250.0090.0060.0010.0040.0100.008
log10(η)0.0150.2810.1830.2560.0830.0610.2520.1950.0330.0590.0790.0960.051
Toothpastelog10(μ)0.0261.8910.1090.1560.1190.1640.2150.2520.0310.2010.0050.2520.138
log10(κ)0.2471.5800.6011.3560.5970.6480.7291.4360.6730.6300.8990.5900.596
log10(τY)0.0660.2010.1140.1910.0750.2500.0610.1990.0930.0640.1170.1490.054
log10(η)0.0130.3730.0030.2670.0130.0070.0470.2120.0090.0160.0050.0070.042
Toruslog10(E)0.0190.2770.0610.0080.0830.0100.0540.0740.0360.0260.0390.0150.074
ν0.0230.0850.0010.1200.0310.0740.3160.1310.0070.0400.0330.0500.129
Birdlog10(E)0.0130.4490.0670.2400.0740.3130.2460.1230.0270.1860.0390.2310.296
ν0.0290.1020.0010.3720.0750.3650.5810.1410.0470.0720.0080.1320.145
Playdohlog10(E)0.2860.2900.1160.5800.1200.3040.1700.5210.1330.4742.1210.2322.148
log10(τY)0.0380.2830.1650.0270.2140.1960.2370.1100.1730.0791.1790.1970.967
ν0.0760.4950.1110.1730.1090.2480.1280.2120.0630.1330.1100.1270.106
Catlog10(E)0.8551.3010.9731.0681.0711.1271.0661.1920.7060.5340.7120.7830.793
log10(τY)0.0260.1200.1070.1170.1130.0860.1120.0840.0670.0140.0760.0690.072
ν0.0270.0440.0040.0360.0690.1900.0790.1180.0030.0270.0070.0280.063
Trophyθfric [rad]0.0480.0530.0550.0510.0560.0570.0540.0300.0390.0410.0430.0440.039
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.397, + 0.893, + 0.44 + ], + "angle": 0, + "content": "Table 2. Comparison of the absolute differences between the ground-truth and the estimated physical properties on physical identification. The smaller the values, the better was the performance. The values of the physical properties (i.e., not the absolute differences) are provided in Tables 6 and 7 in the Supplementary Material. The qualitative comparisons are presented in Figures 3-9 in the Supplementary Material." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.455, + 0.468, + 0.518 + ], + "angle": 0, + "content": "
PAC-NeRF-3v+LPO+LPO4PAC-NeRF-3v†+LPO+LPO4
PSNR↑27.3929.2229.6528.4730.1130.34
SSIM↑0.9780.9800.9820.9800.9820.983
LPIPS↓0.0340.0320.0300.0330.0310.029
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.52, + 0.47, + 0.576 + ], + "angle": 0, + "content": "Table 3. Comparison of PSNR\\(\\uparrow\\), SSIM\\(\\uparrow\\), and LPIPS\\(\\downarrow\\) on geometric recorrection. The scores for each scene and the qualitative comparisons are provided in Table 8 and Figures 3-9, respectively, in the Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Applications. As mentioned above, there is a chicken-and-egg relationship between the geometric structure and physical properties. An interesting question is whether the corrected physical properties can be used to re-estimate the geometry (the opposite problem). To answer this question, we investigated the geometry identification performance after physical re-identification. The results are summarized in Table 3. These results indicate that accurate physical identification is useful for improving the geometry identification performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.746, + 0.192, + 0.761 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.469, + 0.844 + ], + "angle": 0, + "content": "Based on the above experiments, we demonstrated promising results for geometric correction and physical identification. However, our methods have some limitations. (1) Our methods require a longer training time due to the introduction of LPO (Section 3.3)\\(^{9}\\) and the iterative algorithm (Sec" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.45, + 0.892, + 0.596 + ], + "angle": 0, + "content": "tion 3.4).10 However, it is not trivial to obtain robustness to sparse views only by increasing the training time because overfitting is a typical factor that causes learning to fail. (2) LPO is sensitive to the state before applying LPO (e.g., either PAC-NeRF-3v or \\(-3\\mathrm{v}^{\\dagger}\\)) because solving geometry-agnostic system identification in sparse-view settings is ill-posed and challenging. We believe that the advancements in previous few-shot learning methods (Section 2) and the newly introduced few-shot learning method with physical constraints will solve this problem." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.609, + 0.619, + 0.625 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.793 + ], + "angle": 0, + "content": "We proposed LPO to improve PAC-NeRF-based geometric-agnostic system identification. Our core idea is to optimize the geometry not in Eulerian space but in Lagrangian space, utilizing the particles to directly reflect the physical constraints of an MPM. The results demonstrate that LPO is useful for both geometric correction and physical identification. Although we focused on PAC-NeRF while prioritizing its high generality, Lagrangian particles are commonly employed in physics-informed models (e.g., several studies discussed in Section 2). We expect that our ideas can be utilized in other models or tasks." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.852, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The calculation time of LPO (Figure 2(3)) is almost identical to that of the main process of physical property optimization (Figure 2(2)) because the forward and backward processes are identical with different optimization targets. Similarly, the calculation times for \\(+\\mathrm{LPO - F}\\), \\(+\\mathrm{LPO - P}\\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.818, + 0.892, + 0.865 + ], + "angle": 0, + "content": "and \\(+\\mathrm{GO}\\) were almost identical to those for \\(+\\mathrm{LPO}\\), indicating that the improvement was attributable to the ingenuity of the algorithm and not to an increase in the calculation cost. The computation times are discussed in detail in Appendix B.2." + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.865, + 0.892, + 0.901 + ], + "angle": 0, + "content": "10The total computation time increases linearly when running Algorithm 1 repeatedly but is adjustable under a quality-and-time trade-off as discussed in Appendix B.3." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.818, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5477" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.157 + ], + "angle": 0, + "content": "[1] Chayan Banerjee, Kien Nguyen, Clinton Fookes, and George Karniadakis. 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Recently, physics-augmented continuum neural radiance fields (PAC-NeRF) has demonstrated promising results for this technique by utilizing a hybrid Eulerian-Lagrangian representation, in which the geometry is represented by the Eulerian grid representations of NeRF, the physics is described by a material point method (MPM), and they are connected via Lagrangian particles. However, a notable limitation of PAC-NeRF is that its performance is sensitive to the learning of the geometry from the first frames owing to its two-step optimization. First, the grid representations are optimized with the first frames of video sequences, and then the physical properties are optimized through video sequences utilizing the fixed first-frame grid representations. This limitation can be critical when learning of the geometric structure is difficult, for example, in a few-shot (sparse view) setting. To overcome this limitation, we propose Lagrangian particle optimization (LPO), in which the positions and features of particles are optimized through video sequences in Lagrangian space. This method allows for the optimization of the geometric structure across the entire video sequence within the physical constraints imposed by the MPM. The experimental results demonstrate that the LPO is useful for geometric correction and physical identification in sparse-view settings. $^{1}$ + +# 1. Introduction + +System identification is a technique used to identify the geometry and physical properties of an object based on visual observations. It has been actively studied in computer vision and physics because of its wide range of applications, including 3D reproduction, environmental understanding, and content creation. To solve this problem in a realistic environment, it is important to adequately address both the extrinsic geometry structure and the intrinsic physical prop + +![](images/6a4fee893f99e78038c235f21cd85c6f3dd1520c7c968295981ab9c8ad89f127.jpg) +(a) Ground truth $E = 1.00\times 10^{6}$ $\nu = 0.300$ + +![](images/33e3557af9be976d8466c43f4065c81e8ea3b33d9d1581f7c1bad9a221d0400f.jpg) +PSNR: 23.99 +(c) +LPO (proposed) $E = 1.15\times 10^{6}$ $\nu = 0.299$ +Figure 1. Impact of the proposed Lagrangian particle optimization (LPO) in sparse-view geometric-agnostic system identification. We aim to identify the geometry and physical properties of an object from visual observations without any geometric assumptions in severe (e.g., sparse-view) settings. As shown in (b), a standard PAC-NeRF [41] has difficulty learning the geometry in a sparse-view setting (particularly, when the number of viewpoints is three). Consequently, it also fails to estimate the physical properties (Young's modulus $E$ and Poisson's ratio $\mu$ ). As shown in (c), LPO is useful for correcting this failure and succeeds in improving the identification of both geometry and physical properties. + +![](images/2e32000abb2c1beb17073fdc14762e93a125ef12f9620f38e586baab9d9da3d3.jpg) +PSNR: 30.07 +(b) PAC-NeRF $E = 1.89\times 10^{6}$ $\nu = 0.215$ + +erties. For example, to identify the geometry and physical properties of an object from the observation that it collides with the ground, it is necessary to understand not only the appearance and shape change in the geometry but also other internal factors in physics which are necessary to explain this phenomenon without any discrepancies over time. Generally, this problem is ill-posed and challenging to resolve. However, the emergence of powerful geometric representations by neural fields [82], 2D-3D connections by neural rendering [74], and trainable physical simulations using differentiable physical simulators [1] provide clues for solving this problem. For instance, previous studies [34, 35, 47] succeeded in estimating physical properties such as velocity, mass, friction, inertia, and elasticity directly from video sequences by combining differentiable physical simulators with differentiable renderers. + +Although these studies have yielded promising results in terms of physical property estimation, their applicability is restricted by the assumption that the geometric struc + +ture of a scene is completely known, which makes it difficult to apply them in practical scenarios. To eliminate this assumption, geometry-agnostic system identification, which is a technique for identifying the geometry and physical properties of an object from visual observations without any geometric assumptions, has been studied. Specifically, a pioneering model involves physics-augmented continuum neural radiance fields (PAC-NeRF) [41], which is an extension of NeRF [50] that is enforced to follow the conservation laws of continuum mechanics. PAC-NeRF obtains this functionality utilizing a hybrid Eulerian-Lagrangian representation, that is, the geometry (volume density and color fields) is represented with the Eulerian grid representations of NeRF [72], which is transformed into a material space via Lagrangian particles, and physical simulation is conducted on the particles using a material point method (MPM) (particularly, differentiable MPM (DiffMPM) [32]). Because all modules are differentiable, PAC-NeRF can be trained directly with multi-view video sequences and can optimize the geometry and physics without explicit supervision. + +Although PAC-NeRF has enabled the tackling of new tasks, its notable limitation is that its performance is sensitive to the learning of the geometry from the first frames of the video sequences owing to its two-step optimization. First, the grid representations were trained with the first frames of the video sequences, and then the physical properties were optimized across the video sequences by utilizing the frozen first-frame grid representations. This limitation makes it difficult to apply it to cases in which geometry learning is difficult, for example, in a few-shot (sparse-view) setting, as shown in Figure 1(b). + +One possible solution is to train the Eulerian grid representations using all video sequences and not just the first frame. However, a critical problem with this approach is that Eulerian grid representations cannot be trained with explicit physical constraints on the particles because they are optimized in Eulerian (i.e., world) space and cannot reflect all physical phenomena occurring in Lagrangian (i.e., material or particle) space; for example, they cannot propagate gradients calculated for particle positions. + +To solve this problem, we propose Lagrangian particle optimization (LPO), in which the positions and features (i.e., volume density and color) of the particles are optimized in Lagrangian space and not in Eulerian space. Contrary to the abovementioned possible solution, this method allows for the optimization of the geometric structure across video sequences with explicit physical constraints on the particles imposed by the MPM. Thus, the gradients calculated for the particle positions are reflected. + +Furthermore, LPO is useful not only for geometry correction, but also for corrections to the physical identification because this task is closely related, that is, an accurate geometry is useful for accurately identifying the physical properties, and vice versa. This motivated us to utilize the geometry corrected by LPO to re-identify the phys + +ical properties and propose iterative geometry-physics optimization for gradually seeking the optimized states. Figure 1(c) shows the effectiveness of this method. + +We evaluated the effectiveness of LPO in sparse-view settings. In particular, we first applied LPO to a pretrained PAC-NeRF and demonstrated that LPO is useful for correcting geometric structures through video sequences. Subsequently, we employed LPO in iterative geometry-physics optimization and demonstrated that LPO contributes to improving the performance of physical identification. Ablation and comparative studies were conducted to determine the importance of each component. + +Our contributions can be summarized as follows: + +- To improve the performance of geometry-agnostic system identification, we propose LPO, which optimizes the position and features of the particles in Lagrangian space to optimize the geometrical structures across video sequences within the physical constraints of an MPM. +- We propose iterative geometry-physics optimization to utilize the geometry corrected by LPO for re-identifying physical properties in an iterative manner. +- We experimentally demonstrated that LPO is useful for geometric correction and physical identification in sparse-view settings. We also provide detailed analyses and extended results in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript. + +# 2. Related work + +Neural radiance fields (NeRF). Novel view synthesis is a fundamental problem in computer vision and graphics and has been addressed in a large body of research. Recently, a substantial breakthrough has been achieved with the emergence of neural fields that represent a scene utilizing a coordinate-based network (e.g., a survey paper [82]). NeRF [50] is a representative variant of such neural fields and has attracted significant attention because of its geometrical consistency and high-fidelity novel view synthesis. Various studies have been conducted since the emergence of NeRF. These can be categorized into three topics. (1) Improvements to the image quality and expanding of the applicable settings, such as wild or few-shot settings (e.g., [2-4, 8, 11, 12, 14, 30, 33, 48, 51, 56, 65, 76, 79, 85, 87, 89, 91]), (2) speeding up the training or inference speed (e.g., [4, 6, 9, 18, 20, 26, 29, 30, 38, 40, 45, 46, 52, 53, 58, 63, 64, 72, 80, 81, 86]), and (3) incorporating other models or functionalities, such as generative models [22, 28, 71] (e.g., [5-7, 15, 23, 37, 54, 55, 59, 67, 70, 84]) and dynamics/physics (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). Among these, this study relates to the first in terms of its application to few-shot settings. This study relates to the third in terms of seeking physics-informed models. As studies on NeRF are benefiting from developments in adjacent categories, applying our ideas to other categories and models will be an interesting future research direction. + +NeRF with dynamics/physics. As mentioned above, NeRFs with dynamics/physics have been actively studied (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). These studies have one characteristic in common: they learned time-varying neural fields from video sequences. These can be roughly categorized into two models: (1) non- (or weak) physics-informed models (e.g., [19, 25, 43, 57, 60, 68, 75, 90]) and (2) physics-informed models (e.g., [13, 24, 41]). The advantage of the first is that it can be applied to scenes or objects that are difficult to describe physically; however, its disadvantage is that it requires a large amount of training data to learn dynamics from scratch, and the learned representations are not necessarily interpretable because they are not based on physics. The advantage of the second is that it can obtain interpretable representations based on physics; however, the disadvantage is that its application is limited to physically describable objects or scenes. In particular, PI-NeRF [13] targets smoke scenes and does not address the boundary conditions; therefore, it cannot handle solid or contact materials. NeuroFluid [24] focuses on fluid dynamics grounding and solves it using an intuitive physics-based approach in which formal instruction in physics is not explicitly defined. In contrast, PAC-NeRF [41] is based on a principled and interpretable physical simulator and can be applied to various materials, including Newtonian/non-Newtonian fluids, granular media, deformable solids, and plasticine. This study focused on the PAC-NeRF and attempted to widen its applicability while prioritizing its interpretability. However, a Lagrangian particle representation is commonly utilized in physics (e.g., NeuroFluid $[24]^2$ ); therefore, applying our ideas, that is, LPO, to other models is an interesting research topic. + +NeRF for few-shot (sparse-view) settings. In practice, it is often laborious or impractical to collect multi-view images. Recent studies [8, 12-14, 33, 56, 65, 68, 79, 85, 87, 89] addressed this problem by refining NeRF such that it could be applied to few-shot (sparse-view) settings. These methods can be roughly divided into three approaches. (1) Regularization using external models. For example, normalizing flow [16]-based [56], VGG [69]-based [89], depth-based [14, 65, 79], and CLIP [62]-based [33] regularizations have been proposed. (2) Utilization of general and transferable models [8, 12, 68, 87]. They are trained using external datasets, and in several studies, they are finetuned for each scene. (3) Introduction of advanced training methods, such as gradual training to prevent overfitting to sparse views, including frequency regularization [85] and layer-by-layer growing strategies [13]. Among these categories, the proposed LPO is categorized as the third one, that is, optimization is conducted for each scene, and external models/datasets are not required. The main difference between + +2Note that NeuroFluid optimizes the transition probability of particles under the assumption that the initial particle positions are known, that is, fixed. In contrast, LPO optimizes the initial particle positions to correct the geometry estimation of the first frames. Therefore, NeuroFluid and LPO are complementary. + +the LPO and previous methods is that LPO attempts to optimize geometric structures through video sequences with the physical constraints of an MPM. However, previous studies have not sufficiently considered these constraints. Owing to this difference in applications, the proposed method is complementary to, rather than competitive with, other methods. + +System identification of soft bodies. Soft bodies are not only high-dimensional, but also allow large deformations; therefore, it is challenging to identify their geometry and physical properties. Typical methods can be categorized into three types. (1) Gradient-free methods [73, 77], (2) neural network-based methods [42, 66, 83], and (3) differentiable physics-simulation-based methods [10, 17, 21, 27, 35, 41, 47, 61]. The strength of the methods in the first and second categories is that they are flexible; however, they have difficulty achieving a high accuracy owing to their black-box modeling. Methods in the third category require sophisticated modeling to fill the gap between simulations and the real world; however, they have recently demonstrated promising results owing to advancements in differentiable physical simulators. The third category can be further divided into two subcategories. (i) Methods that assume that watertight geometric mesh representations of objects are available [17, 21, 27, 35, 47, 61] and (2) methods that do not assume this [10, 41]. Among these methods, we focused on the final category, PAC-NeRF [41], which prioritizes general and fast characteristics. Specifically, PAC-NeRF adopts an MPM that can be applied to various materials, including elastic objects, sand [39], fluids [36], and foam [88]. In particular, PAC-NeRF utilizes a differentiable MPM (DiffMPM) [32] to construct a fully differentiable simulation rendering system. This study is based on this advancement. In particular, sensitivity to geometry learning from the first frames is one of the bottlenecks of PAC-NeRF. Therefore, this study focused on alleviating this bottleneck and attempted to widen its applicability to severe (e.g., sparse-view) settings. + +# 3. Method + +In this section, we first define the problem statement (Section 3.1) and then briefly review PAC-NeRF [41], upon which our method is built (Section 3.2). Subsequently, we explain the main idea of the proposed method, that is, geometric correction using LPO (Section 3.3), and then introduce its application to physical identification (Section 3.4). + +# 3.1. Problem statement + +Given a set of multi-view video sequences, our objectives are as follows: (1) to recover geometric representations3 of the target dynamic object (particularly continuum materials) through video sequences and (2) identify its physical properties. More formally, the training data comprise + +![](images/8f181108a197c39887f014830553f1e5fe9f1c3fdfa0407d68255a9268faafb3.jpg) +(1) Eulerian static voxel grid optimization (PAC-NeRF) + +![](images/4e619bb5fa17dc898229f626060a5f9441d5f52513e5193879e12b4afe8b7dd3.jpg) + +![](images/1e63532372324b5738d78e64d7dca11671bb8e8418e924ee538b4f8841fbc615.jpg) +(2) Physical property optimization (PAC-NeRF) +(3) Lagrangian particle optimization (proposed) +Figure 2. Training pipelines of PAC-NeRF (1)(2) and the proposed LPO (3). + +ground truth color observations, that is, $\hat{\mathbf{C}} (\mathbf{r},t)$ . Here, $\mathbf{r}(s)\in \mathbb{R}^3$ is a camera ray defined as $\mathbf{r}(s) = \mathbf{o} + s\mathbf{d}$ , where $\mathbf{o}\in \mathbb{R}^3$ is the camera origin, $\mathbf{d}\in \mathbb{S}^2$ is the view direction, and $s\in [s_n,s_f]$ is a distance from the origin. $\mathbf{r}$ is sampled from a set of ray collections in the training data, that is, $\hat{\mathcal{R}}$ . $t\in \mathbb{R}^{+}$ is a time variable, and during training, it is sampled from $\{t_0,\dots ,t_{N - 1}\}$ , where $N$ is the number of frames. Given these training data, we attempt to (1) predict the color observation $\mathbf{C}(\mathbf{r},t)$ that can recover $\hat{\mathbf{C}} (\mathbf{r},t)$ from the training data and those for novel views, and (2) identify the physical properties. In particular, to widen its applicability, we addressed a scenario in which input views are sparse, that is, $\hat{\mathcal{R}}$ is limited. + +# 3.2. Preliminary: PAC-NeRF + +To solve the abovementioned problem, PAC-NeRF employs three core components: a continuum NeRF, particle-grid interconverters, and a Lagrangian field. + +Continuum NeRF. PAC-NeRF extends the standard (static) + +NeRF to a continuum NeRF to address the dynamics of continuum materials. To achieve this, a standard NeRF is first extended to a dynamic NeRF [60] for dynamic scenarios. In a dynamic NeRF, the volume density and color fields are defined as $\sigma (\mathbf{r},t)$ and $\mathbf{c}(\mathbf{r},\mathbf{d},t)$ , respectively, where the time variable $t$ is introduced to represent the dynamics. The color of each pixel $\mathbf{C}(\mathbf{r},t)$ is calculated using volume rendering [49] + +$$ +\mathbf {C} (\mathbf {r}, t) = \int_ {s _ {n}} ^ {s _ {f}} T (s, t) \sigma (\mathbf {r} (s), t) \mathbf {c} (\mathbf {r}, \mathbf {d}, t) d s + \mathbf {c} _ {b g} T (s _ {f}, t), \tag {1} +$$ + +$$ +T (s, t) = \exp \left(- \int_ {s _ {n}} ^ {s} \sigma (\mathbf {r} (u), t) d u\right), \tag {2} +$$ + +where $\mathbf{c}_{bg}$ denotes the background color. The model is trained with pixel-wise loss. + +$$ +\mathcal {L} _ {\text {p i x e l}} = \frac {1}{N} \sum_ {i = 0} ^ {N - 1} \frac {1}{| \hat {\mathcal {R}} |} \sum_ {\mathbf {r} \in \hat {\mathcal {R}}} \| \mathbf {C} (\mathbf {r}, t _ {i}) - \hat {\mathbf {C}} (\mathbf {r}, t _ {i}) \| _ {2} ^ {2}. \tag {3} +$$ + +Furthermore, dynamic NeRF is extended to a continuum NeRF to represent continuum materials. To achieve this, conservation laws for the velocity field are imposed on the volume density and color fields. + +$$ +\frac {D \sigma}{D t} = 0, \frac {D \mathbf {c}}{D t} = \mathbf {0}, \tag {4} +$$ + +whereas the material derivative of an arbitrary time-dependent field $\phi (\mathbf{x},t)$ is defined as $\frac{D\phi}{Dt} = \frac{\partial\phi}{\partial t} +\mathbf{v}\cdot \nabla \phi$ Here, $\mathbf{v}$ is the velocity field and follows momentum conservation for continuum materials: + +$$ +\rho \frac {D \mathbf {v}}{D t} = \nabla \cdot \boldsymbol {T} + \rho \mathbf {g}, \tag {5} +$$ + +where $\rho$ is the physical density field, $T$ is the internal Cauchy stress tensor, and $\mathbf{g}$ is the acceleration owing to gravity. This equation is solved using DiffMPM [32]. + +Particle-grid interconverters. As shown in Figure 2(1)(2), in PAC-NeRF, a physical simulation is conducted in Lagrangian particle space using DiffMPM [32], whereas neural rendering is performed in Eulerian grid space with a discretized voxel-based NeRF [72]. To bridge these two spaces, grid-to-particle (G2P) and particle-to-grid (P2G) conversions are conducted. + +$$ +\mathcal {F} _ {p} ^ {P} \approx \sum_ {i} w _ {i p} \mathcal {F} _ {i} ^ {G}, \mathcal {F} _ {i} ^ {G} \approx \frac {\sum_ {p} w _ {i p} \mathcal {F} _ {p} ^ {P}}{\sum_ {p} w _ {i p}}, \tag {6} +$$ + +where $\mathcal{F}_*$ is a field (e.g., volume density or color field); $P$ and $G$ denote particle and grid views, respectively; $i$ and $p$ indicate the index of the grid node and particle, respectively; and $w_{ip}$ is the weight of the trilinear shape function defined on $i$ and evaluated at $p$ . + +Lagrangian field. As shown in Figure 2(1), during training, the Eulerian voxel field $\mathcal{F}^{G^{\prime}}(t_0)$ is optimized for the first frames of the video sequences. Subsequently, this field is converted into a Lagrangian particle field $\mathcal{F}^P (t_0)$ using G2P, in which the positions of the particles are determined by random sampling around voxel grids. The geometric shape is represented in Lagrangian space by removing the particles whose alpha values are small, that is, the remaining particles represent the shape of the object. As shown in Figure 2(2), the particle field in the next step, that is, $\mathcal{F}^P (t_1)$ , where $t_1 = t_0 + \delta t$ and $\delta t$ is the duration of the simulation time step, is calculated based on $\mathcal{F}^P (t_0)$ using DiffMPM [32]. After this process, $\mathcal{F}^P (t_1)$ is converted to the Eulerian voxel field $\mathcal{F}^G (t_1)$ using P2G, and pixels are rendered based on this field using voxel-based volume rendering [72], in which the volume density and color of a sample on a ray are rendered as follows: + +$$ +\sigma (\mathbf {x}, t) = \operatorname {s o f t p l u s} \left(\operatorname {i n t e r p} \left(\mathbf {x}, \sigma^ {G}\right)\right), \tag {7} +$$ + +$$ +\mathbf {c} (\mathbf {x}, \mathbf {d}, t) = \operatorname {M L P} \left(\operatorname {i n t e r p} (\mathbf {x}, \mathbf {c} ^ {G}), \mathbf {d}\right), \tag {8} +$$ + +where $\sigma^G$ and $\mathbf{c}^G$ denote the volume density and color fields, respectively, discretized on fixed voxel grids. + +# 3.3. Geometric correction with LPO + +As explained above, in PAC-NeRF, the Eulerian voxel fields $\mathcal{F}^{G^{\prime}}(t_0)$ are optimized for the first frames of the video sequences (Figure 2(1)). These are fixed while optimizing the physical properties using video sequences (Figure 2(2)). This approach is problematic when the learning of the Eulerian voxel field from the first frames is difficult, for example, in sparse-view settings, because failure of this learning cannot be corrected after the process. This also means that in dynamic scenes, information over time is useful for covering a lack of information owing to sparse views; however, this approach cannot utilize this information to optimize the volume density and color. + +One possible solution is to train $\mathcal{F}^{G^{\prime}}(t_0)$ with the entire video sequence and not just the first frame. However, in this approach, the optimization targets are limited to the volume density and color of the grids; therefore, it is difficult to reflect the physics-based optimization that occurs in Lagrangian particle space. This can cause excessive modification of the geometry beyond physical constraints. + +Alternatively, we developed Lagrangian particle optimization (LPO), in which the geometric structure is optimized not in Eulerian grid space but in Lagrangian particle space, as shown in Figure 2(3). More formally, in the Eulerian voxel grid optimization, $\sigma^G$ (Equation (7)) and $\mathbf{c}^G$ (Equation (8)) are optimized for the fixed voxel grid $\mathbf{x}^G$ . In contrast, in LPO, not only the volume density and color fields of the particles, that is, $\sigma^P$ and $\mathbf{c}^P$ , but also the particle position, that is $\mathbf{x}^P$ , are optimized. Because $\mathbf{x}^P$ is defined in Lagrangian space, it can reflect the physical constraints of the MPM. Consequently, we can optimize the geometric structures within the physical allowance. + +# 3.4. Physical identification with LPO + +Identifying both the geometry and physical properties from limited observations is ill-posed and challenging because there is a chicken-and-egg relationship between the geometric structure and the physical properties, that is, accurate geometry estimation is necessary for accurate physical identification and vice versa. Considering that particle-based geometric correction is highly challenging when there is a large gap between the ground truth and the predicted pixels owing to the high-dimensional nature (e.g., in extreme cases, particles can diverge), in practice, we apply LPO after physical property optimization, as shown in Figure 2. + +However, an interesting question is whether the corrected geometric structures can be utilized to improve the + +Algorithm 1 Iterative geometry-physics optimization +Input: Ground-truth color observations $\hat{\mathbf{C}} (\hat{\mathbf{r}},t)$ $\hat{\mathbf{r}}\in \hat{\mathcal{R}}$ : Rays from observed viewpoints $t\in \{t_0,\dots ,t_{N - 1}\}$ : Time +Output: Physical properties +1: for $i = 1$ to $R$ do +2: // (1) Eulerian static voxel grid optimization +3: if $i = 1$ then +4: Optimize voxel grids with $\hat{\mathbf{C}} (\hat{\mathbf{r}},t_0)$ +5: else +6: Optimize voxel grids with $\hat{\mathbf{C}} (\hat{\mathbf{r}},t_0)$ and $\check{\mathbf{C}} (\check{\mathbf{r}},t_0)$ +7: end if +8: // (2) Physical property optimization +9: Optimize physical properties with $\hat{\mathbf{C}} (\hat{\mathbf{r}},t)$ +10: // (3) Lagrangian particle optimization +11: Optimize particles with $\hat{\mathbf{C}} (\hat{\mathbf{r}},t)$ +12: // (4) Color prediction for unobserved views $\check{\mathbf{r}}\in \check{\mathcal{R}}$ +13: Predict $\check{\mathbf{C}} (\check{\mathbf{r}},t_0)$ +14: end for + +identification of the physical properties. We developed iterative geometry-physics optimization (Algorithm 1) to answer this question. As described above, we first conduct PAC-NeRF optimization ((1) and (2)) and then apply LPO (3). Subsequently, we render the images in the first frame based on the updated $\sigma^P$ , $\mathbf{c}^P$ , and $\mathbf{x}^P(4)$ . We denote them as $\check{\mathbf{C}}(\check{\mathbf{r}}, t_0)$ , where $\check{\mathbf{r}} \in \check{\mathcal{R}}$ and $\check{\mathcal{R}}$ is designed such that it covers the missing area in $\hat{\mathcal{R}}$ in the training data. We retrain PAC-NeRF from scratch using the combination of the original $\hat{\mathbf{C}}(\hat{\mathbf{r}}, t_0)$ and synthesized $\check{\mathbf{C}}(\check{\mathbf{r}}, t_0)$ as training data. Specifically, to alleviate the negative effect caused by incomplete geometry correction, which can occur at the beginning of the iterative calculation, we only utilize $\check{\mathbf{C}}(\check{\mathbf{r}}, t_0)$ for the Eulerian static voxel grid optimization and do not utilize it to optimize the physical properties and particles. + +Another possible solution is to update the voxel grids by applying P2G to the updated $\sigma^P$ , $\mathbf{c}^P$ , and $\mathbf{x}^P$ instead of (4) and (1). However, we found that the repeated utilization of G2P and P2G tends to produce artifacts (such as those typically occurring in the erosion process) owing to their approximate nature (Equation (6)). Therefore, the full recalculation approach described above was adopted. + +# 4. Experiments + +# 4.1. Experimental setup + +Two experiments were conducted to investigate the effectiveness of the proposed LPO. First, we evaluated the effec + +tiveness of LPO for geometric correction (Section 4.2) and then we investigated the utility of LPO for physical identification (Section 4.3). The main results of these experiments are presented here, and the detailed analyses, extended results, and implementation details are provided in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript. $^{1}$ In this section, we provide the experimental setup common to both experiments and other setups in subsequent sections. + +Dataset. We investigated the benchmark performance on the dataset provided by the original study on PAC-NeRF [41]. This dataset comprised nine scenes and various continuum materials, including Newtonian fluids (Droplet and Letter with fluid viscosity $\mu$ and bulk modulus $\kappa$ ), non-Newtonian fluids (Cream and Toothpaste with shear modulus $\nu$ , bulk modulus $\kappa$ , yield stress $\tau_{Y}$ , and plastic viscosity $\eta$ ), granular media (Trophy with friction angle $\theta_{fric}$ ), deformable solid (Torus and Bird with Young's modulus $E$ and Poisson's ratio $\nu$ ), and plasticine (Cat and Playdoh with $E$ , $\nu$ , and $\tau_{Y}$ ). In each scene, the objects fall freely under the influence of gravity and undergo collisions. The ground-truth simulation data were generated using the MLS-MPM framework [31]. A photorealistic simulation engine rendered objects under diverse environmental lighting conditions and ground textures. Each scene was captured from 11 viewpoints with cameras evenly spaced on the upper hemisphere, including the object. To evaluate our method under sparse-view settings, three views were used for training and the remaining eight views were used for testing. To show the robustness to the view settings, we provide the results for the other view settings in Appendix C. + +Assumptions and preprocessing. For a fair comparison, we follow the assumptions and preprocessing used in PAC-NeRF [41]. It was assumed that the intrinsic and extrinsic parameters of the set of static cameras were previously known. Moreover, it was assumed that collision objects, such as the ground plane, were previously known. As mentioned in [41], this is not difficult to estimate from the observed images. For preprocessing, a video matting framework [44] was applied to remove static background objects and focus the rendering computation on the target object. + +# 4.2. Evaluation of geometric correction + +Compared models. In the first experiment, we investigated the effectiveness of LPO on the geometric correction (i.e., the method described in Section 3.3). Three models were used as the baseline. (I) PAC-NeRF was the same as that in the original [41] and was trained with all views, including the eight views that were used for testing. We examined this model to determine the upper bound of its performance. (II) PAC-NeRF-3v was trained using three views. The training settings were the same as those for (I) except that the + +
PAC-NeRFPAC-NeRF-3v+LPO+LPO-F+LPO-P+GOPAC-NeRF-3v†+LPO+LPO-F+LPO-P+GO
PSNR↑35.9927.3929.2228.2228.8928.3328.4730.1129.3129.8729.39
SSIM↑0.9890.9780.9800.9790.9800.9790.9800.9820.9810.9810.981
LPIPS↓0.0200.0340.0320.0330.0320.0330.0330.0310.0320.0310.031
+ +Table 1. Comparison of PSNR↑, SSIM↑, and LPIPS↓ on geometric correction. The scores for each scene and qualitative results are provided in Table 5 and Figures 3-7, respectively, in the Supplementary Material. + +number of views varied. (III) $PAC\text{-}NeRF-3\nu^{\dagger}$ was an improved variant of (II) for sparse-view settings. An interesting question is whether LPO, which is a few-shot learning method for dynamic scenes, can be used with other few-shot learning methods, such as those for static scenes. To answer this question, we adjusted the Eulerian static voxel grid optimization (Figure 2(1)) of PAC-NeRF-3v, such that it became robust to sparse views. Specifically, we scheduled a surface regularizer to reduce unexpected artifacts, introduced a view-invariant pixel-wise loss to compensate for the lack of views, and adjusted the training length to prevent overfitting. Details are provided in Appendix A. $^{8}$ We applied LPO to both (II) and (III) to investigate the effect of the initial Eulerian static voxel grid optimization. Hereafter, we denote these variants by $+LPO$ . Furthermore, three comparative and ablation models were evaluated to determine the importance of each component. (i) $+LPO-F$ and (ii) $+LPO-P$ are variants of LPO, in which only the features and positions of the particles are optimized. (iii) $+GO$ optimized Eulerian voxel grids through the entire video sequence instead of using Lagrangian particles. (i)-(iii) are used as alternatives to $+LPO$ . These variants were applied to both (II) and (III). + +Evaluation metrics. We evaluated the performance of the geometric correction using metrics commonly used to assess the performance of novel view synthesis in NeRF studies: the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [78], and learned perceptual image patch similarity (LPIPS) [92]. In particular, we calculated the scores using all test data over time. + +Results. The results are summarized in Table 1. Our findings are threefold. (1) $PAC\text{-}NeRF-3\nu/3\nu^{\dagger}$ vs. $+LPO$ . $+LPO$ improved both baselines in terms of all metrics. In particular, the utility of $+LPO$ for $PAC\text{-}NeRF-3\nu^{\dagger}$ indicates an improvement in the Eulerian static voxel grid optimization and that of LPO are complementary. (2) $+LPO$ vs. $+LPO-F/P$ . We found that $+LPO$ was superior or comparable to $+LPO-F/P$ . This is because the feature and position optimizations are complementary. Intuitively, feature optimization is useful for correcting features of the appearance that are invisible in the first frame but visible after the object has moved. Similarly, position optimization is effective for + +In the preliminary experiments, we examined the previous representative few-shot learning methods (e.g., DietNeRF [33] and FreeNeRF [85]). However, we found that they were less stable than PAC-NeRF-3v, possibly because in our experimental settings, the number of views was small (three) despite the wide range of the views (upper hemisphere), and explicit voxel representations were more useful than the fully implicit representation in [33, 85]. However, this study and previous studies are complementary. Further investigations will be important in future work. + +correcting features of the shape that are invisible in the first frame but visible after the object has moved. In severe (e.g., sparse-view) settings, the utilization of both is important. $(3) + LPO$ vs. $+GO$ . $+LPO$ outperforms $+GO$ , possibly because $+LPO$ can optimize the geometry adequately within the physical constraints of the MPM, whereas $+GO$ cannot because of the absence of an explicit physical constraint. + +# 4.3. Evaluation of physical identification + +Compared models. In the second experiment, we verified the usefulness of LPO for physical identification (i.e., the method described in Section 3.4). In addition to the models described in Section 4.2, we examined +None, for which iterative training (Algorithm 1) was conducted without geometric correction (i.e., step (3) was skipped). This model was used to investigate the importance of geometric correction. For a fair comparison, we set the number of iterations (i.e., $R$ in Algorithm 1) to four for all models. We use the superscript 4 (e.g., $+\mathrm{LPO}^4$ ) to specify this. + +Evaluation metrics. To evaluate the performance of the physical identification, we measured the absolute distance between the ground truth and the estimated physical properties. For an easy comparison, we calculated these distances after adjusting the scale (i.e., either a logarithmic scale or a linear scale) following the study of PAC-NeRF [41]. The smaller the values, the better was the performance. + +Results. The results are summarized in Table 2. Our findings are fourfold. (1) $PAC\text{-} NeRF\text{-} 3v/3v^{\dagger}$ vs. $+LPO^{4}$ . $+LPO^{4}$ improved the physical identification of PAC-NeRF- $3v/3v^{\dagger}$ in most cases. In particular, the effectiveness of $+LPO^{4}$ for PAC-NeRF- $3v^{\dagger}$ indicates that the improvement in the Eulerian static voxel grid optimization and that of LPO are complementary for physical identification. (2) $+LPO^{4}$ vs. $+LPO\text{-} F^{4}/P^{4}$ . In some cases, superiority depends on the physical properties because the physical properties interact with each other, and finding the optimal balance is difficult. However, we found that $+LPO\text{-} F^{4}/P^{4}$ sometimes had obvious difficulties (e.g., PAC-NeRF- $3v\text{+}LPO\text{-} F^{4}$ on Bird and PAC-NeRF- $3v^{\dagger}$ +LPO-P $^{4}$ on Play-doh), whereas $+LPO^{4}$ exhibited good stability. We consider that the joint optimization of the features and positions is useful for tackling difficult situations. (3) $+LPO^{4}$ vs. $+GO^{4}$ . $+GO^{4}$ also experienced apparent difficulties in some cases (e.g., on Bird). $+LPO^{4}$ exhibited a more stable performance. (4) $+LPO^{4}$ vs. $+None^{4}$ . $+None^{4}$ sometimes worsened the performance. The results indicated that simple iterations were insufficient and that geometric correction was essential. + +
PAC-NeRFPAC-NeRF-3v+LPO4+LPO-F4+LPO-P4+GO4+None4PAC-NeRF-3v†+LPO4+LPO-F4+LPO-P4+GO4+None4
Dropletlog10(μ)0.0390.1400.1120.1120.1190.1110.1310.1360.0820.0680.0670.0820.090
log10(κ)0.0171.2851.6281.6381.4661.6751.6841.2630.1061.1390.5201.5201.656
Letterlog10(μ)0.0410.6740.0150.0260.0790.0480.5300.3790.0100.0870.0070.1180.436
log10(κ)0.0396.7720.1740.4111.0400.8656.0835.2290.0600.0270.1270.1385.060
Creamlog10(μ)0.0900.3110.1780.1630.2340.1830.2510.1790.1000.0730.0650.0920.076
log10(κ)0.1320.2150.1580.2490.0270.0280.2440.3360.1210.1970.1420.1930.339
log10(τY)0.0070.0140.0040.0300.0050.0060.0250.0090.0060.0010.0040.0100.008
log10(η)0.0150.2810.1830.2560.0830.0610.2520.1950.0330.0590.0790.0960.051
Toothpastelog10(μ)0.0261.8910.1090.1560.1190.1640.2150.2520.0310.2010.0050.2520.138
log10(κ)0.2471.5800.6011.3560.5970.6480.7291.4360.6730.6300.8990.5900.596
log10(τY)0.0660.2010.1140.1910.0750.2500.0610.1990.0930.0640.1170.1490.054
log10(η)0.0130.3730.0030.2670.0130.0070.0470.2120.0090.0160.0050.0070.042
Toruslog10(E)0.0190.2770.0610.0080.0830.0100.0540.0740.0360.0260.0390.0150.074
ν0.0230.0850.0010.1200.0310.0740.3160.1310.0070.0400.0330.0500.129
Birdlog10(E)0.0130.4490.0670.2400.0740.3130.2460.1230.0270.1860.0390.2310.296
ν0.0290.1020.0010.3720.0750.3650.5810.1410.0470.0720.0080.1320.145
Playdohlog10(E)0.2860.2900.1160.5800.1200.3040.1700.5210.1330.4742.1210.2322.148
log10(τY)0.0380.2830.1650.0270.2140.1960.2370.1100.1730.0791.1790.1970.967
ν0.0760.4950.1110.1730.1090.2480.1280.2120.0630.1330.1100.1270.106
Catlog10(E)0.8551.3010.9731.0681.0711.1271.0661.1920.7060.5340.7120.7830.793
log10(τY)0.0260.1200.1070.1170.1130.0860.1120.0840.0670.0140.0760.0690.072
ν0.0270.0440.0040.0360.0690.1900.0790.1180.0030.0270.0070.0280.063
Trophyθfric [rad]0.0480.0530.0550.0510.0560.0570.0540.0300.0390.0410.0430.0440.039
+ +Table 2. Comparison of the absolute differences between the ground-truth and the estimated physical properties on physical identification. The smaller the values, the better was the performance. The values of the physical properties (i.e., not the absolute differences) are provided in Tables 6 and 7 in the Supplementary Material. The qualitative comparisons are presented in Figures 3-9 in the Supplementary Material. + +
PAC-NeRF-3v+LPO+LPO4PAC-NeRF-3v†+LPO+LPO4
PSNR↑27.3929.2229.6528.4730.1130.34
SSIM↑0.9780.9800.9820.9800.9820.983
LPIPS↓0.0340.0320.0300.0330.0310.029
+ +Table 3. Comparison of PSNR $\uparrow$ , SSIM $\uparrow$ , and LPIPS $\downarrow$ on geometric recorrection. The scores for each scene and the qualitative comparisons are provided in Table 8 and Figures 3-9, respectively, in the Supplementary Material. + +Applications. As mentioned above, there is a chicken-and-egg relationship between the geometric structure and physical properties. An interesting question is whether the corrected physical properties can be used to re-estimate the geometry (the opposite problem). To answer this question, we investigated the geometry identification performance after physical re-identification. The results are summarized in Table 3. These results indicate that accurate physical identification is useful for improving the geometry identification performance. + +# 5. Discussion + +Based on the above experiments, we demonstrated promising results for geometric correction and physical identification. However, our methods have some limitations. (1) Our methods require a longer training time due to the introduction of LPO (Section 3.3) $^{9}$ and the iterative algorithm (Sec + +tion 3.4).10 However, it is not trivial to obtain robustness to sparse views only by increasing the training time because overfitting is a typical factor that causes learning to fail. (2) LPO is sensitive to the state before applying LPO (e.g., either PAC-NeRF-3v or $-3\mathrm{v}^{\dagger}$ ) because solving geometry-agnostic system identification in sparse-view settings is ill-posed and challenging. We believe that the advancements in previous few-shot learning methods (Section 2) and the newly introduced few-shot learning method with physical constraints will solve this problem. + +# 6. Conclusion + +We proposed LPO to improve PAC-NeRF-based geometric-agnostic system identification. Our core idea is to optimize the geometry not in Eulerian space but in Lagrangian space, utilizing the particles to directly reflect the physical constraints of an MPM. The results demonstrate that LPO is useful for both geometric correction and physical identification. Although we focused on PAC-NeRF while prioritizing its high generality, Lagrangian particles are commonly employed in physics-informed models (e.g., several studies discussed in Section 2). We expect that our ideas can be utilized in other models or tasks. + +# References + +[1] Chayan Banerjee, Kien Nguyen, Clinton Fookes, and George Karniadakis. Physics-informed computer vision: A review and perspectives. arXiv preprint arXiv:2305.18035, 2023. 1 +[2] Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. Mip-NeRF: A multiscale representation for antiailiating neural radiance fields. In ICCV, 2021. 2 +[3] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. In CVPR, 2022. +[4] Jonathan T. 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The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, 2018. 7 \ No newline at end of file diff --git a/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/images.zip b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..bb6de692591381d99c790b131caaf4fb2d3cb2d2 --- /dev/null +++ b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:14825a285668e386df6ce03442978b92ed9ff16186ea73758e9fd561ce57c117 +size 387711 diff --git a/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/layout.json b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ddbcd72590ae04abe5f2abd20c146bcdf4c05c1f --- /dev/null +++ b/2024/Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization/layout.json @@ -0,0 +1,10829 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 47, + 102, + 547, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 102, + 547, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 547, + 140 + ], + "type": "text", + "content": "Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 252, + 159, + 341, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 252, + 159, + 341, + 188 + ], + "spans": [ + { + "bbox": [ + 252, + 159, + 341, + 188 + ], + "type": "text", + "content": "Takuhiro Kaneko \nNTT Corporation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 227 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 227 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "text", + "content": "Geometry-agnostic system identification is a technique for identifying the geometry and physical properties of an object from video sequences without any geometric assumptions. Recently, physics-augmented continuum neural radiance fields (PAC-NeRF) has demonstrated promising results for this technique by utilizing a hybrid Eulerian-Lagrangian representation, in which the geometry is represented by the Eulerian grid representations of NeRF, the physics is described by a material point method (MPM), and they are connected via Lagrangian particles. However, a notable limitation of PAC-NeRF is that its performance is sensitive to the learning of the geometry from the first frames owing to its two-step optimization. First, the grid representations are optimized with the first frames of video sequences, and then the physical properties are optimized through video sequences utilizing the fixed first-frame grid representations. This limitation can be critical when learning of the geometric structure is difficult, for example, in a few-shot (sparse view) setting. To overcome this limitation, we propose Lagrangian particle optimization (LPO), in which the positions and features of particles are optimized through video sequences in Lagrangian space. This method allows for the optimization of the geometric structure across the entire video sequence within the physical constraints imposed by the MPM. The experimental results demonstrate that the LPO is useful for geometric correction and physical identification in sparse-view settings." + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 572, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 592, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 685 + ], + "type": "text", + "content": "System identification is a technique used to identify the geometry and physical properties of an object based on visual observations. It has been actively studied in computer vision and physics because of its wide range of applications, including 3D reproduction, environmental understanding, and content creation. To solve this problem in a realistic environment, it is important to adequately address both the extrinsic geometry structure and the intrinsic physical prop" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 213, + 379, + 321 + ], + "blocks": [ + { + "bbox": [ + 316, + 213, + 379, + 321 + ], + "lines": [ + { + "bbox": [ + 316, + 213, + 379, + 321 + ], + "spans": [ + { + "bbox": [ + 316, + 213, + 379, + 321 + ], + "type": "image", + "image_path": "6a4fee893f99e78038c235f21cd85c6f3dd1520c7c968295981ab9c8ad89f127.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 319, + 334, + 377, + 364 + ], + "lines": [ + { + "bbox": [ + 319, + 334, + 377, + 364 + ], + "spans": [ + { + "bbox": [ + 319, + 334, + 377, + 364 + ], + "type": "text", + "content": "(a) Ground truth " + }, + { + "bbox": [ + 319, + 334, + 377, + 364 + ], + "type": "inline_equation", + "content": "E = 1.00\\times 10^{6}" + }, + { + "bbox": [ + 319, + 334, + 377, + 364 + ], + "type": "inline_equation", + "content": "\\nu = 0.300" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 392, + 213, + 460, + 324 + ], + "blocks": [ + { + "bbox": [ + 392, + 213, + 460, + 324 + ], + "lines": [ + { + "bbox": [ + 392, + 213, + 460, + 324 + ], + "spans": [ + { + "bbox": [ + 392, + 213, + 460, + 324 + ], + "type": "image", + "image_path": "33e3557af9be976d8466c43f4065c81e8ea3b33d9d1581f7c1bad9a221d0400f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 420, + 323, + 463, + 331 + ], + "lines": [ + { + "bbox": [ + 420, + 323, + 463, + 331 + ], + "spans": [ + { + "bbox": [ + 420, + 323, + 463, + 331 + ], + "type": "text", + "content": "PSNR: 23.99" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 468, + 334, + 541, + 365 + ], + "lines": [ + { + "bbox": [ + 468, + 334, + 541, + 365 + ], + "spans": [ + { + "bbox": [ + 468, + 334, + 541, + 365 + ], + "type": "text", + "content": "(c) +LPO (proposed) " + }, + { + "bbox": [ + 468, + 334, + 541, + 365 + ], + "type": "inline_equation", + "content": "E = 1.15\\times 10^{6}" + }, + { + "bbox": [ + 468, + 334, + 541, + 365 + ], + "type": "inline_equation", + "content": "\\nu = 0.299" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "lines": [ + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "type": "text", + "content": "Figure 1. Impact of the proposed Lagrangian particle optimization (LPO) in sparse-view geometric-agnostic system identification. We aim to identify the geometry and physical properties of an object from visual observations without any geometric assumptions in severe (e.g., sparse-view) settings. As shown in (b), a standard PAC-NeRF [41] has difficulty learning the geometry in a sparse-view setting (particularly, when the number of viewpoints is three). Consequently, it also fails to estimate the physical properties (Young's modulus " + }, + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "type": "text", + "content": " and Poisson's ratio " + }, + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 368, + 547, + 485 + ], + "type": "text", + "content": "). As shown in (c), LPO is useful for correcting this failure and succeeds in improving the identification of both geometry and physical properties." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 471, + 213, + 539, + 320 + ], + "blocks": [ + { + "bbox": [ + 471, + 213, + 539, + 320 + ], + "lines": [ + { + "bbox": [ + 471, + 213, + 539, + 320 + ], + "spans": [ + { + "bbox": [ + 471, + 213, + 539, + 320 + ], + "type": "image", + "image_path": "2e32000abb2c1beb17073fdc14762e93a125ef12f9620f38e586baab9d9da3d3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 323, + 542, + 331 + ], + "lines": [ + { + "bbox": [ + 501, + 323, + 542, + 331 + ], + "spans": [ + { + "bbox": [ + 501, + 323, + 542, + 331 + ], + "type": "text", + "content": "PSNR: 30.07" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 399, + 334, + 452, + 364 + ], + "lines": [ + { + "bbox": [ + 399, + 334, + 452, + 364 + ], + "spans": [ + { + "bbox": [ + 399, + 334, + 452, + 364 + ], + "type": "text", + "content": "(b) PAC-NeRF " + }, + { + "bbox": [ + 399, + 334, + 452, + 364 + ], + "type": "inline_equation", + "content": "E = 1.89\\times 10^{6}" + }, + { + "bbox": [ + 399, + 334, + 452, + 364 + ], + "type": "inline_equation", + "content": "\\nu = 0.215" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 494, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 547, + 677 + ], + "type": "text", + "content": "erties. For example, to identify the geometry and physical properties of an object from the observation that it collides with the ground, it is necessary to understand not only the appearance and shape change in the geometry but also other internal factors in physics which are necessary to explain this phenomenon without any discrepancies over time. Generally, this problem is ill-posed and challenging to resolve. However, the emergence of powerful geometric representations by neural fields [82], 2D-3D connections by neural rendering [74], and trainable physical simulations using differentiable physical simulators [1] provide clues for solving this problem. For instance, previous studies [34, 35, 47] succeeded in estimating physical properties such as velocity, mass, friction, inertia, and elasticity directly from video sequences by combining differentiable physical simulators with differentiable renderers." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 678, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 547, + 715 + ], + "type": "text", + "content": "Although these studies have yielded promising results in terms of physical property estimation, their applicability is restricted by the assumption that the geometric struc" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 286, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 715 + ], + "type": "text", + "content": "1Video samples are available at https://www.kecl.ntt.co.jp/people/kaneko.takuhiro/projects/lpo/." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5470" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 302 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 302 + ], + "type": "text", + "content": "ture of a scene is completely known, which makes it difficult to apply them in practical scenarios. To eliminate this assumption, geometry-agnostic system identification, which is a technique for identifying the geometry and physical properties of an object from visual observations without any geometric assumptions, has been studied. Specifically, a pioneering model involves physics-augmented continuum neural radiance fields (PAC-NeRF) [41], which is an extension of NeRF [50] that is enforced to follow the conservation laws of continuum mechanics. PAC-NeRF obtains this functionality utilizing a hybrid Eulerian-Lagrangian representation, that is, the geometry (volume density and color fields) is represented with the Eulerian grid representations of NeRF [72], which is transformed into a material space via Lagrangian particles, and physical simulation is conducted on the particles using a material point method (MPM) (particularly, differentiable MPM (DiffMPM) [32]). Because all modules are differentiable, PAC-NeRF can be trained directly with multi-view video sequences and can optimize the geometry and physics without explicit supervision." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 304, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 289, + 430 + ], + "type": "text", + "content": "Although PAC-NeRF has enabled the tackling of new tasks, its notable limitation is that its performance is sensitive to the learning of the geometry from the first frames of the video sequences owing to its two-step optimization. First, the grid representations were trained with the first frames of the video sequences, and then the physical properties were optimized across the video sequences by utilizing the frozen first-frame grid representations. This limitation makes it difficult to apply it to cases in which geometry learning is difficult, for example, in a few-shot (sparse-view) setting, as shown in Figure 1(b)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 433, + 289, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 289, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 289, + 537 + ], + "type": "text", + "content": "One possible solution is to train the Eulerian grid representations using all video sequences and not just the first frame. However, a critical problem with this approach is that Eulerian grid representations cannot be trained with explicit physical constraints on the particles because they are optimized in Eulerian (i.e., world) space and cannot reflect all physical phenomena occurring in Lagrangian (i.e., material or particle) space; for example, they cannot propagate gradients calculated for particle positions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 538, + 289, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 289, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 289, + 643 + ], + "type": "text", + "content": "To solve this problem, we propose Lagrangian particle optimization (LPO), in which the positions and features (i.e., volume density and color) of the particles are optimized in Lagrangian space and not in Eulerian space. Contrary to the abovementioned possible solution, this method allows for the optimization of the geometric structure across video sequences with explicit physical constraints on the particles imposed by the MPM. Thus, the gradients calculated for the particle positions are reflected." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 644, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 289, + 715 + ], + "type": "text", + "content": "Furthermore, LPO is useful not only for geometry correction, but also for corrections to the physical identification because this task is closely related, that is, an accurate geometry is useful for accurately identifying the physical properties, and vice versa. This motivated us to utilize the geometry corrected by LPO to re-identify the phys" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 106 + ], + "type": "text", + "content": "ical properties and propose iterative geometry-physics optimization for gradually seeking the optimized states. Figure 1(c) shows the effectiveness of this method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 107, + 545, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 107, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 304, + 107, + 545, + 211 + ], + "type": "text", + "content": "We evaluated the effectiveness of LPO in sparse-view settings. In particular, we first applied LPO to a pretrained PAC-NeRF and demonstrated that LPO is useful for correcting geometric structures through video sequences. Subsequently, we employed LPO in iterative geometry-physics optimization and demonstrated that LPO contributes to improving the performance of physical identification. Ablation and comparative studies were conducted to determine the importance of each component." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 211, + 517, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 211, + 517, + 221 + ], + "spans": [ + { + "bbox": [ + 317, + 211, + 517, + 221 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 223, + 545, + 384 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 223, + 545, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 223, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 306, + 223, + 545, + 280 + ], + "type": "text", + "content": "- To improve the performance of geometry-agnostic system identification, we propose LPO, which optimizes the position and features of the particles in Lagrangian space to optimize the geometrical structures across video sequences within the physical constraints of an MPM." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "text", + "content": "- We propose iterative geometry-physics optimization to utilize the geometry corrected by LPO for re-identifying physical properties in an iterative manner." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 314, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 545, + 384 + ], + "type": "text", + "content": "- We experimentally demonstrated that LPO is useful for geometric correction and physical identification in sparse-view settings. We also provide detailed analyses and extended results in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 394, + 390, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 390, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 390, + 407 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": "Neural radiance fields (NeRF). Novel view synthesis is a fundamental problem in computer vision and graphics and has been addressed in a large body of research. Recently, a substantial breakthrough has been achieved with the emergence of neural fields that represent a scene utilizing a coordinate-based network (e.g., a survey paper [82]). NeRF [50] is a representative variant of such neural fields and has attracted significant attention because of its geometrical consistency and high-fidelity novel view synthesis. Various studies have been conducted since the emergence of NeRF. These can be categorized into three topics. (1) Improvements to the image quality and expanding of the applicable settings, such as wild or few-shot settings (e.g., [2-4, 8, 11, 12, 14, 30, 33, 48, 51, 56, 65, 76, 79, 85, 87, 89, 91]), (2) speeding up the training or inference speed (e.g., [4, 6, 9, 18, 20, 26, 29, 30, 38, 40, 45, 46, 52, 53, 58, 63, 64, 72, 80, 81, 86]), and (3) incorporating other models or functionalities, such as generative models [22, 28, 71] (e.g., [5-7, 15, 23, 37, 54, 55, 59, 67, 70, 84]) and dynamics/physics (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). Among these, this study relates to the first in terms of its application to few-shot settings. This study relates to the third in terms of seeking physics-informed models. As studies on NeRF are benefiting from developments in adjacent categories, applying our ideas to other categories and models will be an interesting future research direction." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5471" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 441 + ], + "type": "text", + "content": "NeRF with dynamics/physics. As mentioned above, NeRFs with dynamics/physics have been actively studied (e.g., [13, 19, 24, 25, 41, 43, 57, 60, 68, 75, 90]). These studies have one characteristic in common: they learned time-varying neural fields from video sequences. These can be roughly categorized into two models: (1) non- (or weak) physics-informed models (e.g., [19, 25, 43, 57, 60, 68, 75, 90]) and (2) physics-informed models (e.g., [13, 24, 41]). The advantage of the first is that it can be applied to scenes or objects that are difficult to describe physically; however, its disadvantage is that it requires a large amount of training data to learn dynamics from scratch, and the learned representations are not necessarily interpretable because they are not based on physics. The advantage of the second is that it can obtain interpretable representations based on physics; however, the disadvantage is that its application is limited to physically describable objects or scenes. In particular, PI-NeRF [13] targets smoke scenes and does not address the boundary conditions; therefore, it cannot handle solid or contact materials. NeuroFluid [24] focuses on fluid dynamics grounding and solves it using an intuitive physics-based approach in which formal instruction in physics is not explicitly defined. In contrast, PAC-NeRF [41] is based on a principled and interpretable physical simulator and can be applied to various materials, including Newtonian/non-Newtonian fluids, granular media, deformable solids, and plasticine. This study focused on the PAC-NeRF and attempted to widen its applicability while prioritizing its interpretability. However, a Lagrangian particle representation is commonly utilized in physics (e.g., NeuroFluid " + }, + { + "bbox": [ + 47, + 72, + 289, + 441 + ], + "type": "inline_equation", + "content": "[24]^2" + }, + { + "bbox": [ + 47, + 72, + 289, + 441 + ], + "type": "text", + "content": "); therefore, applying our ideas, that is, LPO, to other models is an interesting research topic." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 441, + 289, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 289, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 289, + 662 + ], + "type": "text", + "content": "NeRF for few-shot (sparse-view) settings. In practice, it is often laborious or impractical to collect multi-view images. Recent studies [8, 12-14, 33, 56, 65, 68, 79, 85, 87, 89] addressed this problem by refining NeRF such that it could be applied to few-shot (sparse-view) settings. These methods can be roughly divided into three approaches. (1) Regularization using external models. For example, normalizing flow [16]-based [56], VGG [69]-based [89], depth-based [14, 65, 79], and CLIP [62]-based [33] regularizations have been proposed. (2) Utilization of general and transferable models [8, 12, 68, 87]. They are trained using external datasets, and in several studies, they are finetuned for each scene. (3) Introduction of advanced training methods, such as gradual training to prevent overfitting to sparse views, including frequency regularization [85] and layer-by-layer growing strategies [13]. Among these categories, the proposed LPO is categorized as the third one, that is, optimization is conducted for each scene, and external models/datasets are not required. The main difference between" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "content": "2Note that NeuroFluid optimizes the transition probability of particles under the assumption that the initial particle positions are known, that is, fixed. In contrast, LPO optimizes the initial particle positions to correct the geometry estimation of the first frames. Therefore, NeuroFluid and LPO are complementary." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 141 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 141 + ], + "type": "text", + "content": "the LPO and previous methods is that LPO attempts to optimize geometric structures through video sequences with the physical constraints of an MPM. However, previous studies have not sufficiently considered these constraints. Owing to this difference in applications, the proposed method is complementary to, rather than competitive with, other methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 144, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 502 + ], + "type": "text", + "content": "System identification of soft bodies. Soft bodies are not only high-dimensional, but also allow large deformations; therefore, it is challenging to identify their geometry and physical properties. Typical methods can be categorized into three types. (1) Gradient-free methods [73, 77], (2) neural network-based methods [42, 66, 83], and (3) differentiable physics-simulation-based methods [10, 17, 21, 27, 35, 41, 47, 61]. The strength of the methods in the first and second categories is that they are flexible; however, they have difficulty achieving a high accuracy owing to their black-box modeling. Methods in the third category require sophisticated modeling to fill the gap between simulations and the real world; however, they have recently demonstrated promising results owing to advancements in differentiable physical simulators. The third category can be further divided into two subcategories. (i) Methods that assume that watertight geometric mesh representations of objects are available [17, 21, 27, 35, 47, 61] and (2) methods that do not assume this [10, 41]. Among these methods, we focused on the final category, PAC-NeRF [41], which prioritizes general and fast characteristics. Specifically, PAC-NeRF adopts an MPM that can be applied to various materials, including elastic objects, sand [39], fluids [36], and foam [88]. In particular, PAC-NeRF utilizes a differentiable MPM (DiffMPM) [32] to construct a fully differentiable simulation rendering system. This study is based on this advancement. In particular, sensitivity to geometry learning from the first frames is one of the bottlenecks of PAC-NeRF. Therefore, this study focused on alleviating this bottleneck and attempted to widen its applicability to severe (e.g., sparse-view) settings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 512, + 362, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 362, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 362, + 525 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 532, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 602 + ], + "type": "text", + "content": "In this section, we first define the problem statement (Section 3.1) and then briefly review PAC-NeRF [41], upon which our method is built (Section 3.2). Subsequently, we explain the main idea of the proposed method, that is, geometric correction using LPO (Section 3.3), and then introduce its application to physical identification (Section 3.4)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 609, + 419, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 419, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 419, + 621 + ], + "type": "text", + "content": "3.1. Problem statement" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "text", + "content": "Given a set of multi-view video sequences, our objectives are as follows: (1) to recover geometric representations3 of the target dynamic object (particularly continuum materials) through video sequences and (2) identify its physical properties. More formally, the training data comprise" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "3Here, both appearance and shape are treated as part of the geometric representation. We attempted to recover both." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5472" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 542, + 142 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 542, + 142 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 542, + 142 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 542, + 142 + ], + "type": "image", + "image_path": "8f181108a197c39887f014830553f1e5fe9f1c3fdfa0407d68255a9268faafb3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 200, + 144, + 394, + 156 + ], + "lines": [ + { + "bbox": [ + 200, + 144, + 394, + 156 + ], + "spans": [ + { + "bbox": [ + 200, + 144, + 394, + 156 + ], + "type": "text", + "content": "(1) Eulerian static voxel grid optimization (PAC-NeRF)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 46, + 160, + 539, + 292 + ], + "blocks": [ + { + "bbox": [ + 46, + 160, + 539, + 292 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 539, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 539, + 292 + ], + "type": "image", + "image_path": "4e619bb5fa17dc898229f626060a5f9441d5f52513e5193879e12b4afe8b7dd3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 47, + 304, + 538, + 438 + ], + "blocks": [ + { + "bbox": [ + 214, + 293, + 380, + 304 + ], + "lines": [ + { + "bbox": [ + 214, + 293, + 380, + 304 + ], + "spans": [ + { + "bbox": [ + 214, + 293, + 380, + 304 + ], + "type": "text", + "content": "(2) Physical property optimization (PAC-NeRF)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 304, + 538, + 438 + ], + "lines": [ + { + "bbox": [ + 47, + 304, + 538, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 538, + 438 + ], + "type": "image", + "image_path": "1e63532372324b5738d78e64d7dca11671bb8e8418e924ee538b4f8841fbc615.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 208, + 440, + 386, + 451 + ], + "lines": [ + { + "bbox": [ + 208, + 440, + 386, + 451 + ], + "spans": [ + { + "bbox": [ + 208, + 440, + 386, + 451 + ], + "type": "text", + "content": "(3) Lagrangian particle optimization (proposed)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 157, + 457, + 435, + 469 + ], + "lines": [ + { + "bbox": [ + 157, + 457, + 435, + 469 + ], + "spans": [ + { + "bbox": [ + 157, + 457, + 435, + 469 + ], + "type": "text", + "content": "Figure 2. Training pipelines of PAC-NeRF (1)(2) and the proposed LPO (3)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": "ground truth color observations, that is, " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\mathbf{r},t)" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(s)\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is a camera ray defined as " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(s) = \\mathbf{o} + s\\mathbf{d}" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{o}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is the camera origin, " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{d}\\in \\mathbb{S}^2" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is the view direction, and " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "s\\in [s_n,s_f]" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is a distance from the origin. " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is sampled from a set of ray collections in the training data, that is, " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}}" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "t\\in \\mathbb{R}^{+}" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is a time variable, and during training, it is sampled from " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\{t_0,\\dots ,t_{N - 1}\\}" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is the number of frames. Given these training data, we attempt to (1) predict the color observation " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{r},t)" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " that can recover " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\mathbf{r},t)" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " from the training data and those for novel views, and (2) identify the physical properties. In particular, to widen its applicability, we addressed a scenario in which input views are sparse, that is, " + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}}" + }, + { + "bbox": [ + 46, + 478, + 289, + 632 + ], + "type": "text", + "content": " is limited." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 642, + 187, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 187, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 187, + 656 + ], + "type": "text", + "content": "3.2. Preliminary: PAC-NeRF" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 662, + 287, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 662, + 287, + 697 + ], + "spans": [ + { + "bbox": [ + 46, + 662, + 287, + 697 + ], + "type": "text", + "content": "To solve the abovementioned problem, PAC-NeRF employs three core components: a continuum NeRF, particle-grid interconverters, and a Lagrangian field." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "Continuum NeRF. PAC-NeRF extends the standard (static)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "text", + "content": "NeRF to a continuum NeRF to address the dynamics of continuum materials. To achieve this, a standard NeRF is first extended to a dynamic NeRF [60] for dynamic scenarios. In a dynamic NeRF, the volume density and color fields are defined as " + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\sigma (\\mathbf{r},t)" + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{c}(\\mathbf{r},\\mathbf{d},t)" + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "text", + "content": ", respectively, where the time variable " + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "text", + "content": " is introduced to represent the dynamics. The color of each pixel " + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{r},t)" + }, + { + "bbox": [ + 304, + 479, + 545, + 571 + ], + "type": "text", + "content": " is calculated using volume rendering [49]" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 575, + 545, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 545, + 613 + ], + "type": "interline_equation", + "content": "\\mathbf {C} (\\mathbf {r}, t) = \\int_ {s _ {n}} ^ {s _ {f}} T (s, t) \\sigma (\\mathbf {r} (s), t) \\mathbf {c} (\\mathbf {r}, \\mathbf {d}, t) d s + \\mathbf {c} _ {b g} T (s _ {f}, t), \\tag {1}", + "image_path": "8c571e1a3e224f6e215270fed49b6206f09e1c7b5ddca4f8fac291ceb7bddc8a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 616, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 545, + 644 + ], + "type": "interline_equation", + "content": "T (s, t) = \\exp \\left(- \\int_ {s _ {n}} ^ {s} \\sigma (\\mathbf {r} (u), t) d u\\right), \\tag {2}", + "image_path": "4344bb1fdbbed9f4d7a13e1efca1a0e8906dacfbe24a8ec3c74a167b875aeb8a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 647, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 545, + 670 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 647, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{bg}" + }, + { + "bbox": [ + 306, + 647, + 545, + 670 + ], + "type": "text", + "content": " denotes the background color. The model is trained with pixel-wise loss." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 675, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 675, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 318, + 675, + 545, + 711 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p i x e l}} = \\frac {1}{N} \\sum_ {i = 0} ^ {N - 1} \\frac {1}{| \\hat {\\mathcal {R}} |} \\sum_ {\\mathbf {r} \\in \\hat {\\mathcal {R}}} \\| \\mathbf {C} (\\mathbf {r}, t _ {i}) - \\hat {\\mathbf {C}} (\\mathbf {r}, t _ {i}) \\| _ {2} ^ {2}. \\tag {3}", + "image_path": "b0cf1aea27d6efc2fb8cd5e0ca5604c8991c33c9be9298390d3ad1535e2f088c.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5473" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 118 + ], + "type": "text", + "content": "Furthermore, dynamic NeRF is extended to a continuum NeRF to represent continuum materials. To achieve this, conservation laws for the velocity field are imposed on the volume density and color fields." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 126, + 124, + 287, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 124, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 126, + 124, + 287, + 148 + ], + "type": "interline_equation", + "content": "\\frac {D \\sigma}{D t} = 0, \\frac {D \\mathbf {c}}{D t} = \\mathbf {0}, \\tag {4}", + "image_path": "405e268b70432d210fa79ac54d835ac181adec472c7d0a6542bf2c1ecee170cd.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "text", + "content": "whereas the material derivative of an arbitrary time-dependent field " + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "inline_equation", + "content": "\\phi (\\mathbf{x},t)" + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "inline_equation", + "content": "\\frac{D\\phi}{Dt} = \\frac{\\partial\\phi}{\\partial t} +\\mathbf{v}\\cdot \\nabla \\phi" + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "text", + "content": " Here, " + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 152, + 287, + 199 + ], + "type": "text", + "content": " is the velocity field and follows momentum conservation for continuum materials:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 122, + 202, + 287, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 202, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 122, + 202, + 287, + 227 + ], + "type": "interline_equation", + "content": "\\rho \\frac {D \\mathbf {v}}{D t} = \\nabla \\cdot \\boldsymbol {T} + \\rho \\mathbf {g}, \\tag {5}", + "image_path": "d10193fa76e09f7c23a59ae074b4001e3a705a260e6dbe10cc7ea8be18268a8b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "text", + "content": " is the physical density field, " + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "text", + "content": " is the internal Cauchy stress tensor, and " + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 46, + 231, + 287, + 266 + ], + "type": "text", + "content": " is the acceleration owing to gravity. This equation is solved using DiffMPM [32]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 268, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 287, + 348 + ], + "type": "text", + "content": "Particle-grid interconverters. As shown in Figure 2(1)(2), in PAC-NeRF, a physical simulation is conducted in Lagrangian particle space using DiffMPM [32], whereas neural rendering is performed in Eulerian grid space with a discretized voxel-based NeRF [72]. To bridge these two spaces, grid-to-particle (G2P) and particle-to-grid (P2G) conversions are conducted." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 353, + 287, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 353, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 85, + 353, + 287, + 384 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {p} ^ {P} \\approx \\sum_ {i} w _ {i p} \\mathcal {F} _ {i} ^ {G}, \\mathcal {F} _ {i} ^ {G} \\approx \\frac {\\sum_ {p} w _ {i p} \\mathcal {F} _ {p} ^ {P}}{\\sum_ {p} w _ {i p}}, \\tag {6}", + "image_path": "8c7ec756e3de4d858a558b60822c497e5513ce571fd7ab844d73dc2e9f280d77.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_*" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " is a field (e.g., volume density or color field); " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " denote particle and grid views, respectively; " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " indicate the index of the grid node and particle, respectively; and " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "w_{ip}" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " is the weight of the trilinear shape function defined on " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": " and evaluated at " + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 389, + 287, + 448 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": "Lagrangian field. As shown in Figure 2(1), during training, the Eulerian voxel field " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{G^{\\prime}}(t_0)" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " is optimized for the first frames of the video sequences. Subsequently, this field is converted into a Lagrangian particle field " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^P (t_0)" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " using G2P, in which the positions of the particles are determined by random sampling around voxel grids. The geometric shape is represented in Lagrangian space by removing the particles whose alpha values are small, that is, the remaining particles represent the shape of the object. As shown in Figure 2(2), the particle field in the next step, that is, " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^P (t_1)" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "t_1 = t_0 + \\delta t" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\delta t" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " is the duration of the simulation time step, is calculated based on " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^P (t_0)" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " using DiffMPM [32]. After this process, " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^P (t_1)" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " is converted to the Eulerian voxel field " + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^G (t_1)" + }, + { + "bbox": [ + 46, + 449, + 287, + 647 + ], + "type": "text", + "content": " using P2G, and pixels are rendered based on this field using voxel-based volume rendering [72], in which the volume density and color of a sample on a ray are rendered as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 100, + 652, + 286, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 652, + 286, + 666 + ], + "spans": [ + { + "bbox": [ + 100, + 652, + 286, + 666 + ], + "type": "interline_equation", + "content": "\\sigma (\\mathbf {x}, t) = \\operatorname {s o f t p l u s} \\left(\\operatorname {i n t e r p} \\left(\\mathbf {x}, \\sigma^ {G}\\right)\\right), \\tag {7}", + "image_path": "3651a3d240b3bbaf6f0e9fc4ab054430f4ba3eee0eabf8a3a3055bf39ddbd2f1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 91, + 669, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 669, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 91, + 669, + 287, + 683 + ], + "type": "interline_equation", + "content": "\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, t) = \\operatorname {M L P} \\left(\\operatorname {i n t e r p} (\\mathbf {x}, \\mathbf {c} ^ {G}), \\mathbf {d}\\right), \\tag {8}", + "image_path": "aa4b7e76fcba5123d5b98e881fbd4b162cc2a657a5b42347b045302d83f0bf1b.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\sigma^G" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^G" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " denote the volume density and color fields, respectively, discretized on fixed voxel grids." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 477, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 477, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 477, + 83 + ], + "type": "text", + "content": "3.3. Geometric correction with LPO" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 90, + 545, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 90, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 305, + 90, + 545, + 229 + ], + "type": "text", + "content": "As explained above, in PAC-NeRF, the Eulerian voxel fields " + }, + { + "bbox": [ + 305, + 90, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{G^{\\prime}}(t_0)" + }, + { + "bbox": [ + 305, + 90, + 545, + 229 + ], + "type": "text", + "content": " are optimized for the first frames of the video sequences (Figure 2(1)). These are fixed while optimizing the physical properties using video sequences (Figure 2(2)). This approach is problematic when the learning of the Eulerian voxel field from the first frames is difficult, for example, in sparse-view settings, because failure of this learning cannot be corrected after the process. This also means that in dynamic scenes, information over time is useful for covering a lack of information owing to sparse views; however, this approach cannot utilize this information to optimize the volume density and color." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 230, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 312 + ], + "type": "text", + "content": "One possible solution is to train " + }, + { + "bbox": [ + 304, + 230, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{G^{\\prime}}(t_0)" + }, + { + "bbox": [ + 304, + 230, + 545, + 312 + ], + "type": "text", + "content": " with the entire video sequence and not just the first frame. However, in this approach, the optimization targets are limited to the volume density and color of the grids; therefore, it is difficult to reflect the physics-based optimization that occurs in Lagrangian particle space. This can cause excessive modification of the geometry beyond physical constraints." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": "Alternatively, we developed Lagrangian particle optimization (LPO), in which the geometric structure is optimized not in Eulerian grid space but in Lagrangian particle space, as shown in Figure 2(3). More formally, in the Eulerian voxel grid optimization, " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\sigma^G" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": " (Equation (7)) and " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^G" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": " (Equation (8)) are optimized for the fixed voxel grid " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^G" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": ". In contrast, in LPO, not only the volume density and color fields of the particles, that is, " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\sigma^P" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^P" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": ", but also the particle position, that is " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^P" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": ", are optimized. Because " + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^P" + }, + { + "bbox": [ + 304, + 312, + 545, + 449 + ], + "type": "text", + "content": " is defined in Lagrangian space, it can reflect the physical constraints of the MPM. Consequently, we can optimize the geometric structures within the physical allowance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 458, + 480, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 458, + 480, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 458, + 480, + 470 + ], + "type": "text", + "content": "3.4. Physical identification with LPO" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 476, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 604 + ], + "type": "text", + "content": "Identifying both the geometry and physical properties from limited observations is ill-posed and challenging because there is a chicken-and-egg relationship between the geometric structure and the physical properties, that is, accurate geometry estimation is necessary for accurate physical identification and vice versa. Considering that particle-based geometric correction is highly challenging when there is a large gap between the ground truth and the predicted pixels owing to the high-dimensional nature (e.g., in extreme cases, particles can diverge), in practice, we apply LPO after physical property optimization, as shown in Figure 2." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 604, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 545, + 628 + ], + "type": "text", + "content": "However, an interesting question is whether the corrected geometric structures can be utilized to improve the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 636, + 545, + 685 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 636, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 636, + 545, + 685 + ], + "type": "text", + "content": "4More precisely, as explained in Section 3.2, particles are randomly sampled around equally spaced voxel grids, and the Eulerian voxel fields (precisely, alpha values calculated from them) are only utilized to mask them (with a non-differentiable way). Consequently, gradients calculated for the particle positions cannot propagate to " + }, + { + "bbox": [ + 306, + 636, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{G^{\\prime}}(t_0)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "text", + "content": "5Note that the values of " + }, + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma^P" + }, + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^P" + }, + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "text", + "content": " are changed in training but they are time-invariant, i.e., have the same values across sequences. Therefore, the conservation laws (Equation (4)) are preserved." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5474" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 88, + 281, + 305 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 266, + 84 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 266, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 266, + 84 + ], + "type": "text", + "content": "Algorithm 1 Iterative geometry-physics optimization" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "lines": [ + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "spans": [ + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": "Input: Ground-truth color observations " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{r}}\\in \\hat{\\mathcal{R}}" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " : Rays from observed viewpoints " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "t\\in \\{t_0,\\dots ,t_{N - 1}\\}" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " : Time \nOutput: Physical properties \n1: for " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " do \n2: // (1) Eulerian static voxel grid optimization \n3: if " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " then \n4: Optimize voxel grids with " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t_0)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " \n5: else \n6: Optimize voxel grids with " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t_0)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{C}} (\\check{\\mathbf{r}},t_0)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " \n7: end if \n8: // (2) Physical property optimization \n9: Optimize physical properties with " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " \n10: // (3) Lagrangian particle optimization \n11: Optimize particles with " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\hat{\\mathbf{r}},t)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " \n12: // (4) Color prediction for unobserved views " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{r}}\\in \\check{\\mathcal{R}}" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " \n13: Predict " + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{C}} (\\check{\\mathbf{r}},t_0)" + }, + { + "bbox": [ + 47, + 88, + 281, + 305 + ], + "type": "text", + "content": " \n14: end for" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": "identification of the physical properties. We developed iterative geometry-physics optimization (Algorithm 1) to answer this question. As described above, we first conduct PAC-NeRF optimization ((1) and (2)) and then apply LPO (3). Subsequently, we render the images in the first frame based on the updated " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\sigma^P" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^P" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^P(4)" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": ". We denote them as " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{r}} \\in \\check{\\mathcal{R}}" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\check{\\mathcal{R}}" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": " is designed such that it covers the missing area in " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}}" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": " in the training data. We retrain PAC-NeRF from scratch using the combination of the original " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}(\\hat{\\mathbf{r}}, t_0)" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": " and synthesized " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": " as training data. Specifically, to alleviate the negative effect caused by incomplete geometry correction, which can occur at the beginning of the iterative calculation, we only utilize " + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{C}}(\\check{\\mathbf{r}}, t_0)" + }, + { + "bbox": [ + 46, + 326, + 286, + 503 + ], + "type": "text", + "content": " for the Eulerian static voxel grid optimization and do not utilize it to optimize the physical properties and particles." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "text", + "content": "Another possible solution is to update the voxel grids by applying P2G to the updated " + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "inline_equation", + "content": "\\sigma^P" + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^P" + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^P" + }, + { + "bbox": [ + 46, + 504, + 286, + 584 + ], + "type": "text", + "content": " instead of (4) and (1). However, we found that the repeated utilization of G2P and P2G tends to produce artifacts (such as those typically occurring in the erosion process) owing to their approximate nature (Equation (6)). Therefore, the full recalculation approach described above was adopted." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 595, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 128, + 609 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 615, + 161, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 615, + 161, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 615, + 161, + 628 + ], + "type": "text", + "content": "4.1. Experimental setup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 633, + 286, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 633, + 286, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 633, + 286, + 656 + ], + "type": "text", + "content": "Two experiments were conducted to investigate the effectiveness of the proposed LPO. First, we evaluated the effec" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 176 + ], + "type": "text", + "content": "tiveness of LPO for geometric correction (Section 4.2) and then we investigated the utility of LPO for physical identification (Section 4.3). The main results of these experiments are presented here, and the detailed analyses, extended results, and implementation details are provided in the Supplementary Material. Video samples are available at the link indicated on the first page of this manuscript." + }, + { + "bbox": [ + 304, + 72, + 545, + 176 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 176 + ], + "type": "text", + "content": " In this section, we provide the experimental setup common to both experiments and other setups in subsequent sections." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": "Dataset. We investigated the benchmark performance on the dataset provided by the original study on PAC-NeRF [41]. This dataset comprised nine scenes and various continuum materials, including Newtonian fluids (Droplet and Letter with fluid viscosity " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": " and bulk modulus " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": "), non-Newtonian fluids (Cream and Toothpaste with shear modulus " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": ", bulk modulus " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": ", yield stress " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\tau_{Y}" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": ", and plastic viscosity " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": "), granular media (Trophy with friction angle " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\theta_{fric}" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": "), deformable solid (Torus and Bird with Young's modulus " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": " and Poisson's ratio " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": "), and plasticine (Cat and Playdoh with " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\tau_{Y}" + }, + { + "bbox": [ + 304, + 178, + 545, + 431 + ], + "type": "text", + "content": "). In each scene, the objects fall freely under the influence of gravity and undergo collisions. The ground-truth simulation data were generated using the MLS-MPM framework [31]. A photorealistic simulation engine rendered objects under diverse environmental lighting conditions and ground textures. Each scene was captured from 11 viewpoints with cameras evenly spaced on the upper hemisphere, including the object. To evaluate our method under sparse-view settings, three views were used for training and the remaining eight views were used for testing. To show the robustness to the view settings, we provide the results for the other view settings in Appendix C." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 434, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 548 + ], + "type": "text", + "content": "Assumptions and preprocessing. For a fair comparison, we follow the assumptions and preprocessing used in PAC-NeRF [41]. It was assumed that the intrinsic and extrinsic parameters of the set of static cameras were previously known. Moreover, it was assumed that collision objects, such as the ground plane, were previously known. As mentioned in [41], this is not difficult to estimate from the observed images. For preprocessing, a video matting framework [44] was applied to remove static background objects and focus the rendering computation on the target object." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 554, + 491, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 554, + 491, + 566 + ], + "spans": [ + { + "bbox": [ + 306, + 554, + 491, + 566 + ], + "type": "text", + "content": "4.2. Evaluation of geometric correction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 574, + 545, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 678 + ], + "type": "text", + "content": "Compared models. In the first experiment, we investigated the effectiveness of LPO on the geometric correction (i.e., the method described in Section 3.3). Three models were used as the baseline. (I) PAC-NeRF was the same as that in the original [41] and was trained with all views, including the eight views that were used for testing. We examined this model to determine the upper bound of its performance. (II) PAC-NeRF-3v was trained using three views. The training settings were the same as those for (I) except that the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "type": "text", + "content": "A similar phenomenon was observed in the original study on PAC-NeRF [41]. Based on this observation, they rendered an image in the first frame by utilizing the voxel grids obtained after the P2G and G2P conversions, that is, " + }, + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^G(t_0)" + }, + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "type": "text", + "content": ", instead of the original voxel grids " + }, + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{G'}(t_0)" + }, + { + "bbox": [ + 46, + 664, + 286, + 712 + ], + "type": "text", + "content": " to make the rendering conditions the same as those in other frames." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 685, + 545, + 713 + ], + "type": "text", + "content": "Note that although only one dataset was used, this dataset is useful for assessing the versatility because it includes a wide variety of materials, surpassing the scope of previous studies (e.g., elastic objects only in [10])." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5475" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 71, + 547, + 114 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 547, + 114 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 547, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 547, + 114 + ], + "type": "table", + "html": "
PAC-NeRFPAC-NeRF-3v+LPO+LPO-F+LPO-P+GOPAC-NeRF-3v†+LPO+LPO-F+LPO-P+GO
PSNR↑35.9927.3929.2228.2228.8928.3328.4730.1129.3129.8729.39
SSIM↑0.9890.9780.9800.9790.9800.9790.9800.9820.9810.9810.981
LPIPS↓0.0200.0340.0320.0330.0320.0330.0330.0310.0320.0310.031
", + "image_path": "b44f0e6550e7b482692c16b24cd335c4d71e542c726ce84fe2165fafd2e4274d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 116, + 547, + 139 + ], + "lines": [ + { + "bbox": [ + 46, + 116, + 547, + 139 + ], + "spans": [ + { + "bbox": [ + 46, + 116, + 547, + 139 + ], + "type": "text", + "content": "Table 1. Comparison of PSNR↑, SSIM↑, and LPIPS↓ on geometric correction. The scores for each scene and qualitative results are provided in Table 5 and Figures 3-7, respectively, in the Supplementary Material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": "number of views varied. (III) " + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "PAC\\text{-}NeRF-3\\nu^{\\dagger}" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": " was an improved variant of (II) for sparse-view settings. An interesting question is whether LPO, which is a few-shot learning method for dynamic scenes, can be used with other few-shot learning methods, such as those for static scenes. To answer this question, we adjusted the Eulerian static voxel grid optimization (Figure 2(1)) of PAC-NeRF-3v, such that it became robust to sparse views. Specifically, we scheduled a surface regularizer to reduce unexpected artifacts, introduced a view-invariant pixel-wise loss to compensate for the lack of views, and adjusted the training length to prevent overfitting. Details are provided in Appendix A." + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "^{8}" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": " We applied LPO to both (II) and (III) to investigate the effect of the initial Eulerian static voxel grid optimization. Hereafter, we denote these variants by " + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": ". Furthermore, three comparative and ablation models were evaluated to determine the importance of each component. (i) " + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "+LPO-F" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": " and (ii) " + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "+LPO-P" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": " are variants of LPO, in which only the features and positions of the particles are optimized. (iii) " + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "+GO" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": " optimized Eulerian voxel grids through the entire video sequence instead of using Lagrangian particles. (i)-(iii) are used as alternatives to " + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 144, + 289, + 409 + ], + "type": "text", + "content": ". These variants were applied to both (II) and (III)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 411, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 492 + ], + "type": "text", + "content": "Evaluation metrics. We evaluated the performance of the geometric correction using metrics commonly used to assess the performance of novel view synthesis in NeRF studies: the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [78], and learned perceptual image patch similarity (LPIPS) [92]. In particular, we calculated the scores using all test data over time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": "Results. The results are summarized in Table 1. Our findings are threefold. (1) " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "PAC\\text{-}NeRF-3\\nu/3\\nu^{\\dagger}" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": " improved both baselines in terms of all metrics. In particular, the utility of " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "PAC\\text{-}NeRF-3\\nu^{\\dagger}" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": " indicates an improvement in the Eulerian static voxel grid optimization and that of LPO are complementary. (2) " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO-F/P" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": ". We found that " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": " was superior or comparable to " + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "inline_equation", + "content": "+LPO-F/P" + }, + { + "bbox": [ + 46, + 494, + 289, + 634 + ], + "type": "text", + "content": ". This is because the feature and position optimizations are complementary. Intuitively, feature optimization is useful for correcting features of the appearance that are invisible in the first frame but visible after the object has moved. Similarly, position optimization is effective for" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 639, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 289, + 715 + ], + "type": "text", + "content": "In the preliminary experiments, we examined the previous representative few-shot learning methods (e.g., DietNeRF [33] and FreeNeRF [85]). However, we found that they were less stable than PAC-NeRF-3v, possibly because in our experimental settings, the number of views was small (three) despite the wide range of the views (upper hemisphere), and explicit voxel representations were more useful than the fully implicit representation in [33, 85]. However, this study and previous studies are complementary. Further investigations will be important in future work." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": "correcting features of the shape that are invisible in the first frame but visible after the object has moved. In severe (e.g., sparse-view) settings, the utilization of both is important. " + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "inline_equation", + "content": "(3) + LPO" + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "inline_equation", + "content": "+GO" + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": " outperforms " + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "inline_equation", + "content": "+GO" + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": ", possibly because " + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "inline_equation", + "content": "+LPO" + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": " can optimize the geometry adequately within the physical constraints of the MPM, whereas " + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "inline_equation", + "content": "+GO" + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": " cannot because of the absence of an explicit physical constraint." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 234, + 497, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 234, + 497, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 234, + 497, + 247 + ], + "type": "text", + "content": "4.3. Evaluation of physical identification" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "type": "text", + "content": "Compared models. In the second experiment, we verified the usefulness of LPO for physical identification (i.e., the method described in Section 3.4). In addition to the models described in Section 4.2, we examined +None, for which iterative training (Algorithm 1) was conducted without geometric correction (i.e., step (3) was skipped). This model was used to investigate the importance of geometric correction. For a fair comparison, we set the number of iterations (i.e., " + }, + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "type": "text", + "content": " in Algorithm 1) to four for all models. We use the superscript 4 (e.g., " + }, + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "type": "inline_equation", + "content": "+\\mathrm{LPO}^4" + }, + { + "bbox": [ + 304, + 256, + 545, + 373 + ], + "type": "text", + "content": ") to specify this." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 376, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 456 + ], + "type": "text", + "content": "Evaluation metrics. To evaluate the performance of the physical identification, we measured the absolute distance between the ground truth and the estimated physical properties. For an easy comparison, we calculated these distances after adjusting the scale (i.e., either a logarithmic scale or a linear scale) following the study of PAC-NeRF [41]. The smaller the values, the better was the performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": "Results. The results are summarized in Table 2. Our findings are fourfold. (1) " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "PAC\\text{-} NeRF\\text{-} 3v/3v^{\\dagger}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " improved the physical identification of PAC-NeRF- " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "3v/3v^{\\dagger}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " in most cases. In particular, the effectiveness of " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " for PAC-NeRF- " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "3v^{\\dagger}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " indicates that the improvement in the Eulerian static voxel grid optimization and that of LPO are complementary for physical identification. (2) " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO\\text{-} F^{4}/P^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": ". In some cases, superiority depends on the physical properties because the physical properties interact with each other, and finding the optimal balance is difficult. However, we found that " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO\\text{-} F^{4}/P^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " sometimes had obvious difficulties (e.g., PAC-NeRF- " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "3v\\text{+}LPO\\text{-} F^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " on Bird and PAC-NeRF- " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "3v^{\\dagger}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " +LPO-P" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " on Play-doh), whereas " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " exhibited good stability. We consider that the joint optimization of the features and positions is useful for tackling difficult situations. (3) " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+GO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+GO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " also experienced apparent difficulties in some cases (e.g., on Bird). " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " exhibited a more stable performance. (4) " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+LPO^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+None^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "inline_equation", + "content": "+None^{4}" + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": " sometimes worsened the performance. The results indicated that simple iterations were insufficient and that geometric correction was essential." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 317, + 757 + ], + "type": "text", + "content": "5476" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 545, + 312 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 312 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 312 + ], + "type": "table", + "html": "
PAC-NeRFPAC-NeRF-3v+LPO4+LPO-F4+LPO-P4+GO4+None4PAC-NeRF-3v†+LPO4+LPO-F4+LPO-P4+GO4+None4
Dropletlog10(μ)0.0390.1400.1120.1120.1190.1110.1310.1360.0820.0680.0670.0820.090
log10(κ)0.0171.2851.6281.6381.4661.6751.6841.2630.1061.1390.5201.5201.656
Letterlog10(μ)0.0410.6740.0150.0260.0790.0480.5300.3790.0100.0870.0070.1180.436
log10(κ)0.0396.7720.1740.4111.0400.8656.0835.2290.0600.0270.1270.1385.060
Creamlog10(μ)0.0900.3110.1780.1630.2340.1830.2510.1790.1000.0730.0650.0920.076
log10(κ)0.1320.2150.1580.2490.0270.0280.2440.3360.1210.1970.1420.1930.339
log10(τY)0.0070.0140.0040.0300.0050.0060.0250.0090.0060.0010.0040.0100.008
log10(η)0.0150.2810.1830.2560.0830.0610.2520.1950.0330.0590.0790.0960.051
Toothpastelog10(μ)0.0261.8910.1090.1560.1190.1640.2150.2520.0310.2010.0050.2520.138
log10(κ)0.2471.5800.6011.3560.5970.6480.7291.4360.6730.6300.8990.5900.596
log10(τY)0.0660.2010.1140.1910.0750.2500.0610.1990.0930.0640.1170.1490.054
log10(η)0.0130.3730.0030.2670.0130.0070.0470.2120.0090.0160.0050.0070.042
Toruslog10(E)0.0190.2770.0610.0080.0830.0100.0540.0740.0360.0260.0390.0150.074
ν0.0230.0850.0010.1200.0310.0740.3160.1310.0070.0400.0330.0500.129
Birdlog10(E)0.0130.4490.0670.2400.0740.3130.2460.1230.0270.1860.0390.2310.296
ν0.0290.1020.0010.3720.0750.3650.5810.1410.0470.0720.0080.1320.145
Playdohlog10(E)0.2860.2900.1160.5800.1200.3040.1700.5210.1330.4742.1210.2322.148
log10(τY)0.0380.2830.1650.0270.2140.1960.2370.1100.1730.0791.1790.1970.967
ν0.0760.4950.1110.1730.1090.2480.1280.2120.0630.1330.1100.1270.106
Catlog10(E)0.8551.3010.9731.0681.0711.1271.0661.1920.7060.5340.7120.7830.793
log10(τY)0.0260.1200.1070.1170.1130.0860.1120.0840.0670.0140.0760.0690.072
ν0.0270.0440.0040.0360.0690.1900.0790.1180.0030.0270.0070.0280.063
Trophyθfric [rad]0.0480.0530.0550.0510.0560.0570.0540.0300.0390.0410.0430.0440.039
", + "image_path": "f0d90caff5baffff321651f7f050b8ff15fdf1dc3571dcba31a630ea8875d6b8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 360, + 286, + 410 + ], + "blocks": [ + { + "bbox": [ + 47, + 314, + 546, + 348 + ], + "lines": [ + { + "bbox": [ + 47, + 314, + 546, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 314, + 546, + 348 + ], + "type": "text", + "content": "Table 2. Comparison of the absolute differences between the ground-truth and the estimated physical properties on physical identification. The smaller the values, the better was the performance. The values of the physical properties (i.e., not the absolute differences) are provided in Tables 6 and 7 in the Supplementary Material. The qualitative comparisons are presented in Figures 3-9 in the Supplementary Material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 360, + 286, + 410 + ], + "lines": [ + { + "bbox": [ + 48, + 360, + 286, + 410 + ], + "spans": [ + { + "bbox": [ + 48, + 360, + 286, + 410 + ], + "type": "table", + "html": "
PAC-NeRF-3v+LPO+LPO4PAC-NeRF-3v†+LPO+LPO4
PSNR↑27.3929.2229.6528.4730.1130.34
SSIM↑0.9780.9800.9820.9800.9820.983
LPIPS↓0.0340.0320.0300.0330.0310.029
", + "image_path": "c97d481a447109bfb66322e17f4ef5cd587895fd51beefca0ebc06ea26efce15.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "lines": [ + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "text", + "content": "Table 3. Comparison of PSNR" + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "text", + "content": ", SSIM" + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "text", + "content": ", and LPIPS" + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 47, + 411, + 287, + 456 + ], + "type": "text", + "content": " on geometric recorrection. The scores for each scene and the qualitative comparisons are provided in Table 8 and Figures 3-9, respectively, in the Supplementary Material." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 464, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 581 + ], + "type": "text", + "content": "Applications. As mentioned above, there is a chicken-and-egg relationship between the geometric structure and physical properties. An interesting question is whether the corrected physical properties can be used to re-estimate the geometry (the opposite problem). To answer this question, we investigated the geometry identification performance after physical re-identification. The results are summarized in Table 3. These results indicate that accurate physical identification is useful for improving the geometry identification performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 590, + 117, + 602 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 117, + 602 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 117, + 602 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 609, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 668 + ], + "type": "text", + "content": "Based on the above experiments, we demonstrated promising results for geometric correction and physical identification. However, our methods have some limitations. (1) Our methods require a longer training time due to the introduction of LPO (Section 3.3)" + }, + { + "bbox": [ + 47, + 609, + 287, + 668 + ], + "type": "inline_equation", + "content": "^{9}" + }, + { + "bbox": [ + 47, + 609, + 287, + 668 + ], + "type": "text", + "content": " and the iterative algorithm (Sec" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 356, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 545, + 472 + ], + "type": "text", + "content": "tion 3.4).10 However, it is not trivial to obtain robustness to sparse views only by increasing the training time because overfitting is a typical factor that causes learning to fail. (2) LPO is sensitive to the state before applying LPO (e.g., either PAC-NeRF-3v or " + }, + { + "bbox": [ + 306, + 356, + 545, + 472 + ], + "type": "inline_equation", + "content": "-3\\mathrm{v}^{\\dagger}" + }, + { + "bbox": [ + 306, + 356, + 545, + 472 + ], + "type": "text", + "content": ") because solving geometry-agnostic system identification in sparse-view settings is ill-posed and challenging. We believe that the advancements in previous few-shot learning methods (Section 2) and the newly introduced few-shot learning method with physical constraints will solve this problem." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 482, + 378, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 482, + 378, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 482, + 378, + 495 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 501, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 628 + ], + "type": "text", + "content": "We proposed LPO to improve PAC-NeRF-based geometric-agnostic system identification. Our core idea is to optimize the geometry not in Eulerian space but in Lagrangian space, utilizing the particles to directly reflect the physical constraints of an MPM. The results demonstrate that LPO is useful for both geometric correction and physical identification. Although we focused on PAC-NeRF while prioritizing its high generality, Lagrangian particles are commonly employed in physics-informed models (e.g., several studies discussed in Section 2). We expect that our ideas can be utilized in other models or tasks." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 674, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 674, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 674, + 287, + 713 + ], + "type": "text", + "content": "The calculation time of LPO (Figure 2(3)) is almost identical to that of the main process of physical property optimization (Figure 2(2)) because the forward and backward processes are identical with different optimization targets. Similarly, the calculation times for " + }, + { + "bbox": [ + 46, + 674, + 287, + 713 + ], + "type": "inline_equation", + "content": "+\\mathrm{LPO - F}" + }, + { + "bbox": [ + 46, + 674, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 674, + 287, + 713 + ], + "type": "inline_equation", + "content": "+\\mathrm{LPO - P}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "type": "inline_equation", + "content": "+\\mathrm{GO}" + }, + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "type": "text", + "content": " were almost identical to those for " + }, + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "type": "inline_equation", + "content": "+\\mathrm{LPO}" + }, + { + "bbox": [ + 304, + 647, + 545, + 685 + ], + "type": "text", + "content": ", indicating that the improvement was attributable to the ingenuity of the algorithm and not to an increase in the calculation cost. The computation times are discussed in detail in Appendix B.2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 685, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 685, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 685, + 545, + 713 + ], + "type": "text", + "content": "10The total computation time increases linearly when running Algorithm 1 repeatedly but is adjustable under a quality-and-time trade-off as discussed in Appendix B.3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5477" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Chayan Banerjee, Kien Nguyen, Clinton Fookes, and George Karniadakis. 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Unlike its offline counterpart, in online CL, the training data can only be seen once. Most existing online CL research regards catastrophic forgetting (i.e., model stability) as almost the only challenge. In this paper, we argue that the model's capability to acquire new knowledge (i.e., model plasticity) is another challenge in online CL. While replay-based strategies have been shown to be effective in alleviating catastrophic forgetting, there is a notable gap in research attention toward improving model plasticity. To this end, we propose Collaborative Continual Learning (CCL), a collaborative learning based strategy to improve the model's capability in acquiring new concepts. Additionally, we introduce Distillation Chain (DC), a collaborative learning scheme to boost the training of the models. We adapt CCL-DC to existing representative online CL works. Extensive experiments demonstrate that even if the learners are well-trained with state-of-the-art online CL methods, our strategy can still improve model plasticity dramatically, and thereby improve the overall performance by a large margin. The source code of our work is available at https://github.com/maorong-wang/CCL-DC.", + "bbox": [ + 75, + 304, + 472, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 679, + 209, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continual Learning (CL) [10, 13, 32, 43] aims to incrementally learn a sequence of tasks and enhance the neural network's performance on the current tasks, without forgetting previously learned knowledge. CL can be done in two different manners [4, 43]: offline and online. In offline CL, the learner can have infinite access to all the training data of the current task that it trains on and may go through the data for any epoch. Contrary to offline CL, in online CL, the training data for each task also comes continually in a data stream, and the learner can only see the training data once. Apart from the learning approach, there are also three different CL scenarios [23, 29, 42]: Task-Incremental Learning (TIL), Domain-Incremental Learning (DIL), and Class-", + "bbox": [ + 75, + 703, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Incremental learning (CIL). In this paper, we focus on the CIL setting in online CL.", + "bbox": [ + 498, + 273, + 890, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Various online CL methods [6, 7, 19, 20, 31, 35, 44] have been proposed to help the models learn continually on one-epoch data stream, with alleviated forgetting. Among them, replay-based methods have shown remarkable success, and current state-of-the-art methods rely heavily on memory replay to mitigate catastrophic forgetting [17, 30]. However, while most existing online CL research primarily only focuses on improving model stability (i.e., alleviating catastrophic forgetting) to achieve better overall accuracy, the importance of model plasticity (i.e., the capability to acquire new knowledge) is often overlooked. While in offline CL, it is possible to gain high plasticity by iterating several epochs on the current task before proceeding to the subsequent task, acquiring plasticity in online CL tends to be more challenging because the training data is only available once. As shown in Fig. 1, compared to learning without memory replay, the replay-based methods implicitly alleviate the low plasticity issue to some extent. Also, plasticity can be improved by employing a technique involving multiple updates on incoming samples [3]. However, the combination of memory replay and multiple updates fails to bridge the existing plasticity gap between online and offline CL, and the use of multiple updates can lead to increased catastrophic forgetting. Overall, the plasticity gap adversely affects the performance of online CL methods.", + "bbox": [ + 496, + 306, + 892, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we argue that plasticity is particularly crucial and challenging to acquire in online CL, and even more so than in offline CL. Thus, we shed light on how model plasticity and stability will impact the overall performance. Furthermore, we propose a quantitative link between plasticity, stability, and final accuracy, showing that the plasticity gap between offline and online must be reduced to improve overall performance.", + "bbox": [ + 496, + 686, + 890, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Guided by the quantitative relationship, we focus ourselves on the previously overlooked plasticity perspective. Inspired by the ability of collaborative learning to accelerate the convergence in non-continual scenarios [5], we have incorporated collaborative learning in online CL and observed a similar phenomenon. Consequently, we pro", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23460", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d949bc5c3e3fe341d6a7033f40a99163b0bcddf93c2dffa5ca2489ada7aeeda0.jpg", + "image_caption": [ + "Figure 1. The comparison of plasticity (learning accuracy) and stability (relative forgetting, our metric proposed in Sec. 3) of Experience Replay (ER) [35] under various settings on CIFAR-100. For experiments with memory replay, the size of the memory buffer is set to 2,000. We can witness a plasticity gap between offline CL and online CL, even with memory replay and multiple update trick (memory iteration $>1$ )." + ], + "image_footnote": [], + "bbox": [ + 98, + 90, + 444, + 263 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pose the Collaborative Continual Learning with Distillation Chain (CCL-DC), a collaborative learning scheme that can be adapted to existing online CL methods. CCL-DC consists of two key components: Collaborative Continual Learning (CCL) and Distillation Chain (DC).", + "bbox": [ + 75, + 387, + 467, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CCL involves two peer continual learners to learn from the data stream simultaneously in a peer teaching manner, enhancing optimization parallelism and offering greater flexibility to the continual learners. To the best of our knowledge, CCL is the first method to incorporate collaborative learning techniques in online CL research. Moreover, to fully exploit the potential of collaborative learning in online CL scenarios, we propose DC, an entropy regularization based optimization strategy, specifically designed for online CL.", + "bbox": [ + 75, + 463, + 467, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contribution of this paper can be summarized as follows.", + "bbox": [ + 76, + 614, + 467, + 643 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We establish a quantitative link between plasticity, stability, and final performance. Based on this, we demonstrate that plasticity is an important obstacle in online CL, which was greatly overlooked in the previous research:", + "2. To overcome the plasticity issue, we introduce CCL-DC, a collaborative learning based strategy that can be seamlessly integrated into the existing methods, significantly improving their performance by boosting plasticity;", + "3. Comprehensive experiments show that CCL-DC enhances the performance of existing methods by a large margin." + ], + "bbox": [ + 76, + 647, + 467, + 825 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 844, + 218, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continual Learning. Continual learning can be classified into three different categories: regularization-", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "based, parameter-isolation-based, and replay-based. Regularization-based methods [2, 8, 24, 27, 46] add extra regularization terms to balance the old and new tasks. Parameter-isolation-based methods [1, 16, 36-38] solve the problem explicitly by dynamically allocating task-specific parameters. Replay-based methods [6, 7, 9, 14, 19, 20, 31, 35, 44] maintain a small memory buffer that stores a few old training samples.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Among these methods, replay-based strategies have gained huge success due to their impressive performance and simplicity. ER [35] is the fundamental replay-based method that leverages Cross-Entropy loss for classification and a random replay buffer. DER++ [6] stores the logits in the memory buffer and extends ER with the distillation of old stored logits. ER-ACE [7] extends ER with Asymmetric Cross-Entropy loss for classification to suppress the drift of old class representations. OCM [19] leverages a replay-based strategy by maximizing the mutual information between old and new class representations. GSA [20] solves cross-task class discrimination with replay-based strategy and Gradient Self Adaption. OnPro [44] uses online prototype learning to address shortcut learning and alleviate catastrophic forgetting.", + "bbox": [ + 496, + 212, + 890, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These replay-based methods propose different strategies for alleviating catastrophic forgetting and improving the model stability. However, the importance of the model plasticity is greatly neglected in their research, despite their success in terms of final performance. In our work, these methods serve as the baselines and we adapted our strategy to these baselines to show the effectiveness of our proposed approach.", + "bbox": [ + 496, + 439, + 890, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Collaborative Learning. Collaborative learning [5, 18, 39, 47, 48] originates from online knowledge distillation (KD). Different from the conventional KD methods, online KD involves training a cohort of deep networks from scratch in a peer-teaching manner. During the training process, the models imitate their peers and guides the training of other models simultaneously. Deep Mutual Learning (DML) [47] suggests peer student models learn from each other through the logit distillation between the probability distributions. Codistillation [5] is similar to DML and suggests the ensemble of peer networks can further improve the performance. More importantly, Codistillation shows that online KD can help the model converge faster on non-continual scenarios.", + "bbox": [ + 496, + 568, + 890, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the success of collaborative learning in non-continual scenarios, due to the lack of focus on plasticity, the research on collaborative learning in CL is still limited. To the best of our knowledge, there is no existing research using the collaborative learning technique to boost the training of online CL. Moreover, in our work, we introduce the DC, an entropy regularization based optimization strategy, specifically tailored to fully leverage the potential of collab", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23461", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/453e9be391aaceee9555fc6354adead2b195898fcfb52b5c4e7a27024397fb74.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed CCL-DC framework applied to a baseline online CL method. The proposed CCL-DC framework has two main components. The first one is CCL, which involves two peer continual learners that simultaneously learn from the data stream in a peer teaching manner. The second component, DC, generates a chain of samples with varying levels of difficulty and feeds them into models to produce a chain of logit distribution of different confidence levels. Then, in a collaborative learning approach, DC conducts distillation from less confident predictions to more confident predictions, to serve as a form of learned entropy regularization." + ], + "image_footnote": [], + "bbox": [ + 138, + 88, + 831, + 290 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "orative learning in online CL scenarios.", + "bbox": [ + 76, + 388, + 339, + 405 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Plasticity and Stability in online CL", + "text_level": 1, + "bbox": [ + 76, + 415, + 400, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we revise the metric for model plasticity and propose a novel metric for model stability. In addition, we quantitatively analyze the impact of model plasticity and stability on the final performance.", + "bbox": [ + 75, + 441, + 470, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Model Plasticity", + "text_level": 1, + "bbox": [ + 76, + 508, + 238, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The model plasticity quantifies the learner's ability to learn new knowledge when a new task arrives. Several different metrics have been proposed to measure the model plasticity [8, 28, 34, 43]. In our work, we evaluate the model plasticity with Learning Accuracy (LA) [34]. Formally, the LA for the $j$ -th task is defined as:", + "bbox": [ + 75, + 532, + 468, + 625 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nl _ {j} = a _ {j} ^ {j}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 241, + 631, + 468, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $a_{j}^{i}$ is the accuracy evaluated on the test set of task $j$ after training the network from task 1 to task $i$ . For an overall metric normalized against all tasks, the averaged LA is written as $LA = \\frac{1}{T}\\sum_{j=1}^{T}l_{j}$ , and $T$ is the number of tasks in total.", + "bbox": [ + 75, + 657, + 470, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Model Stability", + "text_level": 1, + "bbox": [ + 76, + 741, + 233, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The stability assesses the extent of knowledge retention or loss within a model in its present state. The most commonly used metric in previous CL research is the Forgetting Measure (FM) [8]. Intuitively, FM for the $j$ -th task, denoted as $f m_{j}^{k}$ , quantifies the decline in performance on a given task $j$ , after the model is trained on task $k$ , relative to its highest past performance on task $j$ :", + "bbox": [ + 75, + 765, + 468, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf m _ {j} ^ {k} = \\max _ {i \\in \\{1, \\dots , k - 1 \\}} \\left(a _ {j} ^ {i} - a _ {j} ^ {k}\\right), \\forall j < k. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 877, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/b6b98e37bfda136f86bf97da3f1fb1aca874c3c7f9e378647cf955fb9187ed44.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
a ijT1T2T3T4T5FMkRFk
T130/15------
T225/12.525/12.5---5/2.58.33/8.33
T320/1020/1020/10--7.5/3.7517.78/17.78
T415/7.515/7.515/7.515/7.5-10/528.75/28.75
T510/510/510/510/510/512.5/6.2542/42
", + "bbox": [ + 503, + 383, + 888, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Forgetting Measure (\\%) and Relative Forgetting (\\%) of two example learners (Learner 1 in teal and Learner 2 in brown) in a continual setting of five tasks with two classes per task. Each element $a_{j}^{i}$ at row $j$ and column $i$ is the per task accuracy evaluated on the test set of task $j$ after training the network from task 1 to task $i$ .", + "bbox": [ + 496, + 460, + 893, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the overall metric obtained across all tasks, FM can be expressed as:", + "bbox": [ + 498, + 555, + 892, + 585 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF M = \\frac {1}{T - 1} \\sum_ {j = 1} ^ {T - 1} f m _ {j} ^ {T}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 597, + 890, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our work, we propose a novel stability metric, termed Relative Forgetting (RF), as an alternative to the traditional Forgetting Measure (FM). RF measures how much proportion of performance the model forgets. Specifically, RF for the $j$ -th task after training on task $k$ is defined as:", + "bbox": [ + 496, + 652, + 893, + 729 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {j} ^ {k} = \\max _ {i \\in \\{1, \\dots , k \\}} \\left(1 - \\frac {a _ {j} ^ {k}}{a _ {j} ^ {i}}\\right), \\forall j \\leq k. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 739, + 890, + 781 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall metric averaged across all tasks can be written as:", + "bbox": [ + 498, + 792, + 890, + 820 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nR F = \\frac {1}{T} \\sum_ {j = 1} ^ {T} f _ {j} ^ {T}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 821, + 890, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are two advantages for shifting from absolute forgetting to relative forgetting:", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23462", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. RF is fairer for methods with higher plasticity. As shown in Table 1, when comparing two continual learners, one with high plasticity and the other with low, using both forgetting metrics, it is observed that despite having identical RF values, the model with lower plasticity shows a lower FM. This indicates that the FM metric might unfairly favor models with poorer initial performance, even when the relative decline in performance is equivalent across models;", + "2. RF facilitates a quantitative analysis of the relationship between model stability and final performance. This enables a more nuanced understanding of how stability influences overall model efficacy, thereby guiding improvements in continual learning strategies." + ], + "bbox": [ + 76, + 90, + 472, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Impact on the Overall Performance", + "text_level": 1, + "bbox": [ + 76, + 311, + 387, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For online CL, the model's final average accuracy (AA) is the most vital metric. In this subsection, we try to show how the model plasticity and stability will impact the final performance quantitatively.", + "bbox": [ + 76, + 334, + 468, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model's final average accuracy can be calculated as:", + "bbox": [ + 96, + 393, + 467, + 410 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA A = \\frac {1}{T} \\sum_ {j = 1} ^ {T} a _ {j} ^ {T}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 420, + 468, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the establishment of our plasticity metric (LA) and stability metric (RF), we can easily find the relationship between learning accuracy, relative forgetting, and accuracy:", + "bbox": [ + 76, + 467, + 468, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na _ {j} ^ {i} \\geq l _ {j} \\times \\left(1 - f _ {j} ^ {i}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 526, + 468, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "assuming equality when $a_{j}^{j} = \\max_{i\\in \\{1,\\dots ,j\\}}a_{j}^{i}$ . When extending the class-specific final accuracy $a_{j}^{T}$ to the final AA, we consider the dot product of the LA vector $[l_1,\\dots,l_T]$ with the RF vector $[f_1^T,\\dots,f_T^T]$ , which simplifies the calculation. More practically, this relationship can be approximated with:", + "bbox": [ + 76, + 551, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA A \\gtrsim L A \\times (1 - R F). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 659, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As indicated by Eq. 8, the lower bound of the final performance is proportional to $LA$ and $1 - RF$ , which suggests that both plasticity (LA) and stability (RF) play a crucial role in the final accuracy. Our findings reveal the importance of the model plasticity which was neglected in the past. And it can serve as a good guide for future online CL research.", + "bbox": [ + 76, + 681, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 800, + 250, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we first justify our motivations. Then, we introduce our proposed strategy: Collaborative Continual Learning and Distillation Chain. Finally, we show how to adapt our proposed strategy to the existing online CL methods and boost their plasticity.", + "bbox": [ + 76, + 824, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eed6f57ff3f3d25573b93d9645df16683c05d16c58b77fe782a34fc94c8d6270.jpg", + "image_caption": [ + "Figure 3. Conceptual diagram of the training framework, when distilling from an untrained network $\\theta^2$ to suppress the confidence of network $\\theta^1$ ." + ], + "image_footnote": [], + "bbox": [ + 526, + 88, + 867, + 268 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/83d1461421d08eccb68f012c4cd192e5f660517dad4ba075083b42cc784439a3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCIFAR-100
Memory Size MM=1000M=2000M=5000
ER24.47±0.7231.89±1.4539.41±1.81
ER + Untrained Distillation27.07±1.2034.84±0.6441.15±1.16
", + "bbox": [ + 521, + 314, + 864, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2. The performance of network $\\theta^1$ when distilling from untrained network $\\theta^2$ on CIFAR-100. All numbers are average over 10 runs.", + "bbox": [ + 500, + 378, + 890, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Motivation Justification", + "text_level": 1, + "bbox": [ + 500, + 430, + 718, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Plasticity matters in Online CL. Online continual learners are designed to continuously adapt to non-stationary data streams, efficiently acquiring new knowledge while retaining previously learned information. In current online CL research, the emphasis has predominantly been on mitigating catastrophic forgetting. Even among state-of-the-art methods such as [19, 44], plasticity is often compromised in the quest for improved stability. However, our finding in Sec. 3 shows that both plasticity and stability are crucial for achieving satisfactory final performance, with plasticity proving particularly difficult to achieve in online CL settings. To this end, we deliberately prioritize the plasticity aspect.", + "bbox": [ + 496, + 453, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The potential of collaborative learning to improve convergence in non-continual scenarios [5] positions it as a promising candidate for enhancing plasticity. With the apparent lack of focus on plasticity, collaborative learning has yet to be leveraged to boost convergence of online continual learners. In our research, we propose to exploit collaborative learning convergence properties for improving plasticity. We find that similar to non-continual scenarios, collaborative learning strategy can boost convergence by allowing more parallelism in the training and more maneuverability of the continual learners.", + "bbox": [ + 496, + 651, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overconfidence hurts Online CL. In conventional supervised learning, it is well established that excessive confidence can harm the generalization ability. To tackle this issue, many methods such as label smoothing [41], knowledge distillation [45], and confidence penalty [33] are pro", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23463", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "posed.", + "bbox": [ + 76, + 92, + 122, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In online CL, we find a counter-intuitive, yet similar phenomenon. As shown in Fig. 3, while we train network $\\theta^1$ with the classification loss, we initiate another network $\\theta^2$ at the beginning of the training. During the continual training, we stagnate the network $\\theta^2$ (i.e., Kaiming initialize and stay untrained) and train the network $\\theta^1$ with both classification loss and the distillation loss (Kullback-Leibler divergence loss) from untrained network $\\theta^2$ . The experimental result in Table 2 shows a decent performance gain compared with independent training. The distillation from the prediction of untrained network $\\theta^2$ to network $\\theta^1$ serves as a regularization to suppress the overall confidence, and the performance gain under this condition makes it evident that, in continual scenarios, overconfidence will also harm the performance.", + "bbox": [ + 75, + 106, + 468, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To tackle the overconfidence problem, we propose Distillation Chain (DC), an entropy regularizer to suppress the overall confidence level.", + "bbox": [ + 75, + 316, + 468, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Collaborative Continual Learning", + "text_level": 1, + "bbox": [ + 76, + 369, + 375, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The introduced Collaborative Continual Learning (CCL) enables more parallelism and flexibility in training online continual learners, and it is the key to improving the model plasticity and the final performance. As shown in Fig. 2, CCL involves two peer continual learners of the same architecture and optimizer setting training in a peer-teaching manner. In the training phase, networks are supervised with both the ground truth label and the predictions of their peers. In the inference phase, models can either make predictions collaboratively with ensemble methods [5] to get a better performance or predict independently for the sake of computation efficiency. If we denote two networks in CCL as $\\theta^1$ and $\\theta^2$ , we formulate our loss to network $\\theta^1$ as:", + "bbox": [ + 75, + 393, + 470, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C C L} ^ {1} = \\lambda_ {1} \\cdot \\mathcal {L} _ {c l s} \\left(\\theta^ {1} (X), y\\right) \\\\ + \\lambda_ {2} \\cdot D _ {K L} \\left(\\theta^ {1} (X) / \\tau , \\theta^ {2} (X) / \\tau\\right), \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 595, + 468, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $(X,y)$ is the data-label pair, $\\mathcal{L}_{cls}(\\cdot)$ is the classification loss in the baseline method CCL adapts to, $D_{KL}(\\cdot)$ is the Kullback-Leibler divergence, $\\lambda_{1}$ and $\\lambda_{2}$ are the balancing hyperparameters and $\\tau$ is the temperature hyperparameter. Note that the network $\\theta^2$ should be trained with $\\mathcal{L}_{CCL}^2$ , respectively.", + "bbox": [ + 75, + 642, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Distillation Chain", + "text_level": 1, + "bbox": [ + 76, + 741, + 250, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To fully take advantage of CCL, we propose Distillation Chain (DC), an entropy regularizaion based strategy explicitly designed for online CL. As illustrated in Fig. 2, DC comprises two steps: (1) generating a chain of samples with different levels of difficulty [40] using data augmentation, and (2) distillation of logit distribution from harder samples to easier samples in a collaborative learning way.", + "bbox": [ + 75, + 763, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 2, we observed that overconfidence will hurt the performance in continual training. To tackle", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 PyTorch-like pseudo-code of CCL-DC to integrate to other baselines." + ], + "code_body": "# model1: student model\n# model2: teacher model\n# optim1: optimizer for student model\n# cls: classification loss in baseline\nfor x, y in dataloader:\n # Baseline loss\n loss基礎 = criterion基礎(model1, x, y)\n # DC Augmentation\n x1 = geometric_distortion(x)\n x2 = RandAugment(x1, N, M)\n x3 = RandAugment(x2, N, M)\n # CCL-DC loss\n ls, ls1, ls2, ls3 = model1(x, x1, x2, x3)\n lt, lt1, lt2, lt3 = model2(x, x1, x2, x3) # no grad\n loss_CLS = cls(ls, y) + cls(ls1, y) + cls(ls2, y) +\n $\\leftrightarrow$ cls(ls3, y)\n loss_ccl = kl_div(ls/t, lt/t) # temperature t\n loss_dC = kl_div(ls/t, lt1/t) + kl_div(ls1/t, lt2/t) +\n $\\leftrightarrow$ kl_div(ls2/t, lt3/t)\n loss_ours = lam1*loss_CLS + lam2*(loss_ccl + loss_dC)\n loss = loss基礎 + loss_ours\n optim1.zero_grad()\n loss.backup()\n optim1.step()", + "bbox": [ + 500, + 122, + 890, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the problem, DC uses data augmentation strategies to generate samples with different levels of difficulty and produces logit distribution with different confidence. The distillation from less confident predictions to more confident predictions weakens the overall confidence of the network and benefits the performance by improving the generalization capability.", + "bbox": [ + 496, + 453, + 890, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our work, we use a geometric distortion comprised of RandomCrop and RandomHorizontalFlip as the first step of DC augmentation. After that, we use RandAugment [12] for the subsequent augmentations and we involve two hyperparameters $N$ and $M$ for RandAugment. We take three augmentation steps and distill the logit distribution from the teacher with harder samples to the student with easier samples. We formulate our loss with DC to network $\\theta^1$ as:", + "bbox": [ + 496, + 559, + 892, + 679 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {D C} ^ {1} = \\lambda_ {1} \\sum_ {i = 1} ^ {3} \\mathcal {L} _ {c l s} \\left(\\theta^ {1} \\left(X _ {i}\\right), y\\right) \\tag {10} \\\\ + \\lambda_ {2} \\sum_ {i = 1} ^ {3} D _ {K L} (\\theta^ {1} (X _ {i - 1}) / \\tau , \\theta^ {2} (X _ {i}) / \\tau), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 689, + 890, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $X_{i}$ is the augmentation of input sample $X$ after $i$ augmentation steps.", + "bbox": [ + 496, + 782, + 890, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Apply CCL-DC to online CL methods", + "text_level": 1, + "bbox": [ + 498, + 820, + 826, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss to network $\\theta^1$ when adapting CCL-DC can be written as:", + "bbox": [ + 496, + 843, + 890, + 871 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {1} = \\mathcal {L} _ {\\text {B a s e l i n e}} + \\mathcal {L} _ {C C L} ^ {1} + \\mathcal {L} _ {D C} ^ {1}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 883, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23464", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/99f71e98e90c5ab3b3a286de78feb2807a3d187b2e4350a280810313a9e148d6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER [35]56.68±1.8962.32±4.1324.47±0.7231.89±1.4539.41±1.8110.82±0.7919.16±1.4224.71±2.5233.30±1.74
ER + Ours66.43±2.4874.10±1.7133.43±1.0644.45±1.0453.81±1.1616.56±1.6329.39±1.2337.73±0.8543.11±1.49
DER++ [6]58.04±2.3064.02±1.9225.09±1.4132.33±2.6638.31±2.288.73±1.5817.95±2.4919.40±3.7134.75±2.23
DER++ + Ours68.79±1.4274.25±1.1034.36±0.8943.52±1.3552.95±0.8610.99±1.3921.68±1.9428.01±2.4645.70±1.32
ER-ACE [7]53.26±3.0459.94±2.4028.36±1.9934.21±1.5339.39±1.3113.56±1.0020.84±0.4325.92±1.0738.37±1.20
ER-ACE + Ours70.08±1.3875.56±1.1437.20±1.1545.14±1.0053.92±0.4818.32±1.4926.22±2.0132.23±1.7045.15±1.94
OCM [19]68.19±1.7573.15±1.0528.02±0.7435.69±1.3642.22±1.0618.36±0.9526.74±1.0231.94±1.1923.67±2.36
OCM + Ours74.14±0.8577.66±1.4635.00±1.1543.34±1.5151.43±1.3723.36±1.1833.17±0.9739.25±0.8843.19±0.98
GSA [20]60.34±1.9766.54±2.2827.72±1.5735.08±1.3741.41±1.6512.44±1.1719.59±1.3025.34±1.4341.03±0.99
GSA + Ours68.91±1.6875.78±1.1635.56±1.3944.74±1.3255.39±1.0916.70±1.6628.11±1.7037.13±1.7544.28±1.16
OnPro [44]70.47±2.1274.70±1.5127.22±0.7733.33±0.9341.59±1.3814.32±1.4021.13±2.1226.38±2.1838.75±1.03
OnPro + Ours74.49±2.1478.64±1.4234.76±1.1241.89±0.8250.01±0.8521.81±1.0232.00±0.7238.18±1.0247.93±1.26
", + "bbox": [ + 81, + 88, + 883, + 323 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8ccdafce771356fd5e6302b4c632ea056d9ae8f6e822b1073dcd9ad38a7225a0.jpg", + "table_caption": [ + "Table 3. Average Accuracy (\\%, higher is better) on four benchmark datasets with difference memory buffer size $M$ , with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + ], + "table_footnote": [], + "table_body": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER83.13±1.6078.15±3.6053.77±1.5151.53±1.6650.79±0.7168.15±1.4764.99±1.2264.44±1.4553.95±1.51
ER + Ours90.60±1.5089.99±1.5072.38±0.6670.86±0.7268.84±1.0585.24±0.5381.75±0.8379.54±0.7468.73±1.21
DER++77.14±2.9678.00±2.1656.13±3.7555.33±3.2656.32±3.4470.01±1.8366.87±1.3070.28±2.4260.65±2.97
DER++ + Ours88.85±1.8889.00±1.6772.85±1.3771.54±1.9969.52±2.3782.83±1.2778.80±1.6277.79±0.8670.16±1.03
ER-ACE57.66±4.1661.59±3.3538.53±1.6139.95±2.0041.56±1.445.60±1.454.83±0.784.92±0.9549.82±1.05
ER-ACE + Ours88.37±1.3988.40±1.1569.47±0.8868.39±1.3266.63±0.9021.91±5.1621.88±4.3918.88±3.1268.52±0.82
OCM78.71±3.6681.33±2.0640.87±1.6042.00±1.4842.43±1.8018.56±2.8715.86±2.0115.03±2.0220.77±1.88
OCM + Ours82.39±2.2384.53±1.6348.89±2.0449.83±2.0149.94±2.1631.69±1.8129.54±2.3528.10±2.2848.20±1.38
GSA79.87±3.2677.09±4.5558.16±1.5855.13±1.8150.34±1.7320.46±1.5915.86±1.2614.50±0.6362.59±1.17
GSA + Ours91.69±1.1190.98±1.3373.73±1.0372.68±0.9870.36±1.0780.36±1.2274.77±1.6670.71±1.1973.71±1.12
OnPro84.23±2.0085.60±1.5641.34±1.6342.59±1.6542.92±1.0020.84±1.4716.73±1.2715.82±1.0439.60±0.86
OnPro + Ours90.39±1.5990.18±1.5846.30±1.1047.13±1.0147.27±1.8125.87±1.9121.40±1.5219.75±1.2252.55±2.18
", + "bbox": [ + 80, + 357, + 883, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Learning Accuracy (%, higher is better) on four benchmark datasets with difference memory buffer size $M$ , with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs.", + "bbox": [ + 75, + 594, + 890, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\text{Baseline}}$ is the loss function of the baseline model CCL-DC adapts to. Note that the model $\\theta^2$ should be trained similarly. In Algorithm 1, we provide a Pytorch-like pseudo-code demonstrating how to incorporate CCLDC into a given baseline. For simplicity, we only show the loss function for model $\\theta^1$ . Also, we omitted the memory buffer in the pseudo-code. However, the training should be consistent with the baseline, using both streaming and memory data.", + "bbox": [ + 75, + 631, + 468, + 767 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 787, + 207, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 814, + 266, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We use four image classification benchmark datasets to evaluate the effectiveness of our method, including CIFAR-10 [25], CIFAR-100 [25], TinyImageNet [26], and ImageNet-100 [11, 15, 22]. More detailed information", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "about the dataset split and task allocation is given in the supplementary material.", + "bbox": [ + 498, + 631, + 890, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. To show the effectiveness of our strategy, we applied CCL-DC to six typical and state-of-the-art online CL methods, including ER [35], DER++ [6], ER-ACE [7], OCM [19], GSA [20], and OnPro [44].", + "bbox": [ + 498, + 667, + 890, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We use full ResNet-18 [21] (not pre-trained) as the backbone for every method. For each baseline method, we perform a hyperparameter search on CIFAR-100, $M = 2\\mathrm{k}$ , and apply the hyperparameter to all of the settings. For fair comparison, we use the same optimizer and hyperparameter setting when adapting CCL-DC to the baselines. For hyperparameters unique to CCL-DC, we conduct another hyperparameter search as stated in the supplementary material. We set the streaming batch size to 10 and the memory batch size to 64. We do not use the multiple update trick as described in [3]. More detailed in", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23465", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/adc897516da34b929a8c3e481f18df748ab934f6dec23688a2eaf01e48b391ed.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER31.63±3.8120.63±8.3255.71±2.2439.11±3.8723.05±3.6985.00±1.3071.62±2.1862.43±3.8339.26±3.21
ER + Ours26.74±3.9917.58±2.7154.34±2.2237.67±2.1621.98±2.5981.13±1.9364.79±1.3253.18±0.9937.78±2.18
DER++23.60±3.6417.71±2.1855.65±4.3641.27±4.9331.72±3.9587.79±2.3573.28±3.8872.51±5.5342.97±5.89
DER++ + Ours22.62±3.0316.43±3.3653.45±1.4039.39±2.7123.71±3.3987.16±1.6073.15±2.1564.48±3.0835.32±2.80
ER-ACE12.25±3.849.92±2.8325.88±4.1017.68±1.9010.62±2.0857.41±2.3844.48±1.9637.83±3.1223.92±2.05
ER-ACE + Ours20.62±2.2614.32±2.5846.78±1.9134.19±2.4019.01±0.9456.56±4.1642.20±3.9431.13±3.5234.43±3.60
OCM13.05±4.3711.00±3.1131.16±2.6917.90±3.736.85±2.2556.66±2.5340.59±1.5530.80±2.294.55±1.60
OCM + Ours10.75±2.528.45±2.6329.65±4.0017.02±3.016.16±1.3551.58±2.8135.58±2.5427.24±1.6015.33±2.28
GSA25.02±2.8316.56±4.0253.42±3.1237.29±2.6020.50±4.3366.87±3.3153.42±3.8443.44±3.8135.44±2.42
GSA + Ours24.96±3.2716.59±2.0952.29±2.0638.76±2.4121.36±2.3680.08±1.9763.85±1.7849.73±2.1040.46±2.54
OnPro16.47±4.2312.93±3.0235.03±4.4524.26±2.3112.04±2.1164.69±3.3650.47±4.2042.81±4.6314.44±2.08
OnPro + Ours17.54±4.1512.90±2.7727.64±3.2917.78±1.398.41±2.6256.03±2.9638.70±1.8829.24±1.3315.72±3.29
", + "bbox": [ + 81, + 88, + 885, + 323 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "formation about data augmentation, hyperparameter search, and hardware environments is given in the supplementary material.", + "bbox": [ + 75, + 375, + 468, + 419 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results and Analysis", + "text_level": 1, + "bbox": [ + 76, + 430, + 272, + 446 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Final average accuracy. Table 3 presents average accuracy (AA) at the end of the training on four datasets. As indicated in Sec. 4, to fully take advantage of collaborative learning, we show the results with the ensemble of two models, with the independent model performance available in the supplementary material. Generally, the ensemble method provides about $1\\%$ additional accuracy compared to independent inference. For all datasets, memory size $M$ , and baseline methods, applying CCL-DC constantly improves the performance by a large margin. Notably, even for state-of-the-art methods such as GSA and OnPro, we can still gain significant performance when incorporating CCL-DC.", + "bbox": [ + 73, + 454, + 468, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "More interestingly, for almost all settings with different memory buffer sizes $M$ , the performance gain tends to be a constant on a relative basis. For example, CCL-DC can boost the performance of ER on Tiny/ImageNet from 10.82 to 16.56 when $M = 2\\mathrm{k}$ , which is a $53.0\\%$ performance gain on a relative basis. The performance gain is $53.4\\%$ and $52.7\\%$ when $M = 5\\mathrm{k}$ and $M = 10\\mathrm{k}$ , respectively. This indicates that we can achieve a decent performance gain regardless of the memory buffer size, and it shows the scalability of our method to different resource conditions.", + "bbox": [ + 75, + 651, + 470, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Plasticity and stability metric. As mentioned in Sec. 3, we evaluate the plasticity and stability of different continual learners with LA and RF, respectively. Table 4 shows the plasticity metric on four datasets. For all settings, CCL-DC constantly improves the model plasticity by a large margin. For model stability, as indicated by RF in Table 5, mod", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ba4f950c0c829a895ab1f7a85bc9a6b89b6d2879f70b24fe444dcff09aba5aa3.jpg", + "table_caption": [ + "Table 5. Relative Forgetting (%, lower is better) on four benchmark datasets with difference memory buffer size $M$ ,with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + ], + "table_footnote": [], + "table_body": "
MethodAcc. ↑LA ↑
ER31.89±1.4551.53±1.66
ER + Multivew38.18±1.4664.02±1.12
ER + Ours (CCL only)41.05±1.2168.76±0.79
ER + Ours44.45±1.0470.86±0.72
ER-ACE34.21±1.5339.95±2.00
ER-ACE + Multivew38.61±1.4847.45±1.88
ER-ACE + Ours (CCL only)40.90±1.0850.91±1.63
ER-ACE + Ours45.14±1.0068.39±1.32
", + "bbox": [ + 552, + 371, + 838, + 493 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation studies on CIFAR-100 (M=2k). We report the ensemble performance for methods incorporating CCL.", + "bbox": [ + 498, + 503, + 890, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "els trained with CCL-DC are comparable with the baselines under most cases. ER-ACE is an exception as its plasticity is unexpectedly low, especially on TinyImagenet. Also, the stability of ER-ACE is compromised when incorporating CCL-DC. We will explain the reason for this unexpected phenomenon in the supplementary material.", + "bbox": [ + 496, + 542, + 893, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 643, + 663, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of multiview learning. As mentioned in Sec. 4, CCL-DC benefits from multiview learning with data augmentation in DC. For fair comparison, we explore how multiview learning will impact the performance of the baselines. We apply the classification loss part of CCL-DC to the baselines. Table 6 demonstrates that multiview learning can improve both AA and LA of baselines. However, those performance gains are still inferior to CCL-DC.", + "bbox": [ + 496, + 667, + 890, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of CCL. We evaluate how CCL alone can improve the baselines. In the experiments, we remove multiview learning and DC, and we train the continual learner pair with the loss illustrated in Eq. 9. Table 6 shows the performance gain for ER and ER-ACE. We can see that CCL alone can provide significant gains in both final accuracy and plasticity. Also, when combining CCL with DC, the", + "bbox": [ + 496, + 794, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23466", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2dc5e8536654b407d7e434f449dc76265a070105e6be1973d55078dee1deca8a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDistillation schemeAcc. ↑LA ↑
EREasy to hard40.95±0.9760.03±0.98
ERSame difficulty43.64±1.0969.49±0.78
ERHard to easy (Ours)44.45±1.0470.86±0.72
ER-ACEEasy to hard38.46±1.5139.00±1.03
ER-ACESame difficulty43.81±1.2855.37±1.54
ER-ACEHard to easy (Ours)45.14±1.0068.39±1.32
", + "bbox": [ + 120, + 88, + 424, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/20eab53c9faa6170476bdcf208a8ed34dc5b45d8343cf74cea83ff3dc424156e.jpg", + "table_caption": [ + "Table 7. Comparison of different distillation schemes in DC on CIFAR-100 (M=2k)." + ], + "table_footnote": [ + "Table 8. Final average accuracy when conducting multiview distillation within the same model on CIFAR-100 (M=2k). All values are averaged over 10 runs." + ], + "table_body": "
MethodDistillation schemeAcc. ↑LA ↑
ER + SDCEasy to hard35.00±1.3156.67±0.84
ER + SDCHard to easy41.31±1.2568.62±0.60
ER + CCL-DCEasy to hard40.95±0.9760.03±0.98
ER + CCL-DCHard to easy (Ours)44.45±1.0470.86±0.72
", + "bbox": [ + 104, + 231, + 439, + 308 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "performance can be further improved.", + "bbox": [ + 76, + 369, + 328, + 386 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Distillation scheme of DC. We also evaluate the effectiveness of DC's strategy of distilling from harder samples to easier samples in collaborative learning manner. As shown in Table 7, we compared it with other distillation strategies. The result shows that the distillation scheme of DC constantly outperforms other schemes.", + "bbox": [ + 75, + 393, + 468, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Self-Distillation Chain in an independent model. While DC was originally designed to incorporate CCL, it is possible to conduct DC's strategy within an independent model. We name such a strategy as the Self-Distillation Chain (SDC). Similar to different schemes of DC, SDC can be implemented in two ways: distillation from easier samples to harder samples, and distillation from harder samples to easier samples. As shown in Table 8, both strategy gives extra final performance and plasticity, while the latter strategy benefits the performance more. Moreover, incorporating DC with CCL (i.e., ours) further improves the accuracy.", + "bbox": [ + 75, + 494, + 468, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussions", + "text_level": 1, + "bbox": [ + 76, + 678, + 197, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we analyze some properties of CCL-DC.", + "bbox": [ + 76, + 704, + 446, + 719 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Improving plasticity. One of the important advantages of CCL-DC is that it can improve the plasticity of continual learners. This can be evident by plasticity metrics like LA. Moreover, we have observed that the plasticity of CCL-DC facilitates the model to converge faster and descend to a deeper loss. Figure 4 illustrates the classification loss (cross-entropy) curve of the model. To obtain the loss curve, we take a snapshot of the model every 10 iterations and compute the cross-entropy over all the training samples on the current task. We plot the curve on the logarithm scale so that it is easy to observe that CCL-DC helps the model descend deeper at the end of each task.", + "bbox": [ + 75, + 729, + 468, + 910 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cc6e78fa9779260185745a5bce5135b3feda206577c5e0ad8bece680652272f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 547, + 90, + 836, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d38af7bf7c93506edc2903772304a3813807ee0ad2100d466180d4e841895a08.jpg", + "image_caption": [ + "Figure 4. Classification loss curve of ER on CIFAR-100 $(\\mathbf{M} = 2\\mathbf{k})$ The curve is calculated on all training samples of the current task. Since there are 10 tasks in total, the curve has 10 peaks.", + "Figure 5. The entropy of prediction produced by ER with and without CCL-DC on CIFAR-100 $(\\mathbf{M} = 2\\mathbf{k})$ . $X_{i}$ represents the sample after $i$ -th augmentation in Eq. 10. The value is calculated at the end of the training and is averaged over all training samples." + ], + "image_footnote": [], + "bbox": [ + 568, + 263, + 820, + 444 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Alleviating overconfidence. To show the effect of DC in alleviating overconfidence, we compared the confidence of models trained with and without CCL-DC. We measure the confidence with the entropy of predictions. Fig. 5 shows the entropy of prediction produced by the ER (baseline) with and without CCL-DC on CIFAR-100 $(\\mathrm{M} = 2\\mathrm{k})$ . The entropy is calculated at the end of training and averaged across all samples in the training set. Moreover, we also calculate the entropy of models trained with CCL-DC, by forwarding images of different difficulties (from $X_0$ to $X_3$ in Eq. 10) in the augmentation chain. The experimental results show the effect of DC in suppressing overall confidence.", + "bbox": [ + 498, + 512, + 890, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 709, + 617, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we highlighted the significance of plasticity in online CL, which has been overlooked in prior research when compared to stability. We also established the quantitative link between plasticity, stability, and final accuracy. The quantitative relationship shed light on the future direction of online CL research. Based on this, we introduced collaborative learning into online CL and proposed CCL-DC, a strategy that can be seamlessly integrated into existing online CL methods. Extensive experiments showed the effectiveness of CCL-DC in boosting plasticity and subsequently improving the final performance.", + "bbox": [ + 498, + 732, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23467", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. Expert gate: Lifelong learning with a network of experts. In CVPR, 2017. 2", + "[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. 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In NeurIPS, 2018. 2" + ], + "bbox": [ + 78, + 92, + 468, + 875 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23469", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/ea24163b-c4cd-4a88-9ea1-8a8c1cf095e0_model.json b/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/ea24163b-c4cd-4a88-9ea1-8a8c1cf095e0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..600c59bc0c4396540a91d6a0d89f98661258b9f8 --- /dev/null +++ b/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/ea24163b-c4cd-4a88-9ea1-8a8c1cf095e0_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.131, + 0.88, + 0.153 + ], + "angle": 0, + "content": "Improving Plasticity in Online Continual Learning via Collaborative Learning" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.18, + 0.777, + 0.201 + ], + "angle": 0, + "content": "Maorong Wang1 Nicolas Michel2 Ling Xiao1 Toshihiko Yamasaki1" + }, + { + "type": "text", + "bbox": [ + 0.292, + 0.204, + 0.7, + 0.221 + ], + "angle": 0, + "content": "The University of Tokyo 2Univ Gustave Eiffel, CNRS, LIGM" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.223, + 0.746, + 0.239 + ], + "angle": 0, + "content": "{ma_wang, ling, yamasaki} @cvm.t.u-tokyo.ac.jp, nicolas.michel@univ-eiffel.fr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.653 + ], + "angle": 0, + "content": "Online Continual Learning (CL) solves the problem of learning the ever-emerging new classification tasks from a continuous data stream. Unlike its offline counterpart, in online CL, the training data can only be seen once. Most existing online CL research regards catastrophic forgetting (i.e., model stability) as almost the only challenge. In this paper, we argue that the model's capability to acquire new knowledge (i.e., model plasticity) is another challenge in online CL. While replay-based strategies have been shown to be effective in alleviating catastrophic forgetting, there is a notable gap in research attention toward improving model plasticity. To this end, we propose Collaborative Continual Learning (CCL), a collaborative learning based strategy to improve the model's capability in acquiring new concepts. Additionally, we introduce Distillation Chain (DC), a collaborative learning scheme to boost the training of the models. We adapt CCL-DC to existing representative online CL works. Extensive experiments demonstrate that even if the learners are well-trained with state-of-the-art online CL methods, our strategy can still improve model plasticity dramatically, and thereby improve the overall performance by a large margin. The source code of our work is available at https://github.com/maorong-wang/CCL-DC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.68, + 0.21, + 0.695 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Continual Learning (CL) [10, 13, 32, 43] aims to incrementally learn a sequence of tasks and enhance the neural network's performance on the current tasks, without forgetting previously learned knowledge. CL can be done in two different manners [4, 43]: offline and online. In offline CL, the learner can have infinite access to all the training data of the current task that it trains on and may go through the data for any epoch. Contrary to offline CL, in online CL, the training data for each task also comes continually in a data stream, and the learner can only see the training data once. Apart from the learning approach, there are also three different CL scenarios [23, 29, 42]: Task-Incremental Learning (TIL), Domain-Incremental Learning (DIL), and Class-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.275, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Incremental learning (CIL). In this paper, we focus on the CIL setting in online CL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.893, + 0.685 + ], + "angle": 0, + "content": "Various online CL methods [6, 7, 19, 20, 31, 35, 44] have been proposed to help the models learn continually on one-epoch data stream, with alleviated forgetting. Among them, replay-based methods have shown remarkable success, and current state-of-the-art methods rely heavily on memory replay to mitigate catastrophic forgetting [17, 30]. However, while most existing online CL research primarily only focuses on improving model stability (i.e., alleviating catastrophic forgetting) to achieve better overall accuracy, the importance of model plasticity (i.e., the capability to acquire new knowledge) is often overlooked. While in offline CL, it is possible to gain high plasticity by iterating several epochs on the current task before proceeding to the subsequent task, acquiring plasticity in online CL tends to be more challenging because the training data is only available once. As shown in Fig. 1, compared to learning without memory replay, the replay-based methods implicitly alleviate the low plasticity issue to some extent. Also, plasticity can be improved by employing a technique involving multiple updates on incoming samples [3]. However, the combination of memory replay and multiple updates fails to bridge the existing plasticity gap between online and offline CL, and the use of multiple updates can lead to increased catastrophic forgetting. Overall, the plasticity gap adversely affects the performance of online CL methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.809 + ], + "angle": 0, + "content": "In this paper, we argue that plasticity is particularly crucial and challenging to acquire in online CL, and even more so than in offline CL. Thus, we shed light on how model plasticity and stability will impact the overall performance. Furthermore, we propose a quantitative link between plasticity, stability, and final accuracy, showing that the plasticity gap between offline and online must be reduced to improve overall performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Guided by the quantitative relationship, we focus ourselves on the previously overlooked plasticity perspective. Inspired by the ability of collaborative learning to accelerate the convergence in non-continual scenarios [5], we have incorporated collaborative learning in online CL and observed a similar phenomenon. Consequently, we pro" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23460" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.091, + 0.445, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.47, + 0.366 + ], + "angle": 0, + "content": "Figure 1. The comparison of plasticity (learning accuracy) and stability (relative forgetting, our metric proposed in Sec. 3) of Experience Replay (ER) [35] under various settings on CIFAR-100. For experiments with memory replay, the size of the memory buffer is set to 2,000. We can witness a plasticity gap between offline CL and online CL, even with memory replay and multiple update trick (memory iteration \\(>1\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.468, + 0.463 + ], + "angle": 0, + "content": "pose the Collaborative Continual Learning with Distillation Chain (CCL-DC), a collaborative learning scheme that can be adapted to existing online CL methods. CCL-DC consists of two key components: Collaborative Continual Learning (CCL) and Distillation Chain (DC)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.468, + 0.612 + ], + "angle": 0, + "content": "CCL involves two peer continual learners to learn from the data stream simultaneously in a peer teaching manner, enhancing optimization parallelism and offering greater flexibility to the continual learners. To the best of our knowledge, CCL is the first method to incorporate collaborative learning techniques in online CL research. Moreover, to fully exploit the potential of collaborative learning in online CL scenarios, we propose DC, an entropy regularization based optimization strategy, specifically designed for online CL." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.615, + 0.468, + 0.645 + ], + "angle": 0, + "content": "The main contribution of this paper can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.648, + 0.468, + 0.72 + ], + "angle": 0, + "content": "1. We establish a quantitative link between plasticity, stability, and final performance. Based on this, we demonstrate that plasticity is an important obstacle in online CL, which was greatly overlooked in the previous research:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.723, + 0.468, + 0.782 + ], + "angle": 0, + "content": "2. To overcome the plasticity issue, we introduce CCL-DC, a collaborative learning based strategy that can be seamlessly integrated into the existing methods, significantly improving their performance by boosting plasticity;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.784, + 0.468, + 0.827 + ], + "angle": 0, + "content": "3. Comprehensive experiments show that CCL-DC enhances the performance of existing methods by a large margin." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.648, + 0.468, + 0.827 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.219, + 0.86 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Continual Learning. Continual learning can be classified into three different categories: regularization-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "based, parameter-isolation-based, and replay-based. Regularization-based methods [2, 8, 24, 27, 46] add extra regularization terms to balance the old and new tasks. Parameter-isolation-based methods [1, 16, 36-38] solve the problem explicitly by dynamically allocating task-specific parameters. Replay-based methods [6, 7, 9, 14, 19, 20, 31, 35, 44] maintain a small memory buffer that stores a few old training samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Among these methods, replay-based strategies have gained huge success due to their impressive performance and simplicity. ER [35] is the fundamental replay-based method that leverages Cross-Entropy loss for classification and a random replay buffer. DER++ [6] stores the logits in the memory buffer and extends ER with the distillation of old stored logits. ER-ACE [7] extends ER with Asymmetric Cross-Entropy loss for classification to suppress the drift of old class representations. OCM [19] leverages a replay-based strategy by maximizing the mutual information between old and new class representations. GSA [20] solves cross-task class discrimination with replay-based strategy and Gradient Self Adaption. OnPro [44] uses online prototype learning to address shortcut learning and alleviate catastrophic forgetting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.56 + ], + "angle": 0, + "content": "These replay-based methods propose different strategies for alleviating catastrophic forgetting and improving the model stability. However, the importance of the model plasticity is greatly neglected in their research, despite their success in terms of final performance. In our work, these methods serve as the baselines and we adapted our strategy to these baselines to show the effectiveness of our proposed approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Collaborative Learning. Collaborative learning [5, 18, 39, 47, 48] originates from online knowledge distillation (KD). Different from the conventional KD methods, online KD involves training a cohort of deep networks from scratch in a peer-teaching manner. During the training process, the models imitate their peers and guides the training of other models simultaneously. Deep Mutual Learning (DML) [47] suggests peer student models learn from each other through the logit distillation between the probability distributions. Codistillation [5] is similar to DML and suggests the ensemble of peer networks can further improve the performance. More importantly, Codistillation shows that online KD can help the model converge faster on non-continual scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Despite the success of collaborative learning in non-continual scenarios, due to the lack of focus on plasticity, the research on collaborative learning in CL is still limited. To the best of our knowledge, there is no existing research using the collaborative learning technique to boost the training of online CL. Moreover, in our work, we introduce the DC, an entropy regularization based optimization strategy, specifically tailored to fully leverage the potential of collab" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23461" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.14, + 0.089, + 0.833, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.895, + 0.377 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed CCL-DC framework applied to a baseline online CL method. The proposed CCL-DC framework has two main components. The first one is CCL, which involves two peer continual learners that simultaneously learn from the data stream in a peer teaching manner. The second component, DC, generates a chain of samples with varying levels of difficulty and feeds them into models to produce a chain of logit distribution of different confidence levels. Then, in a collaborative learning approach, DC conducts distillation from less confident predictions to more confident predictions, to serve as a form of learned entropy regularization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.389, + 0.341, + 0.406 + ], + "angle": 0, + "content": "orative learning in online CL scenarios." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.416, + 0.401, + 0.433 + ], + "angle": 0, + "content": "3. Plasticity and Stability in online CL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.471, + 0.503 + ], + "angle": 0, + "content": "In this section, we revise the metric for model plasticity and propose a novel metric for model stability. In addition, we quantitatively analyze the impact of model plasticity and stability on the final performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.51, + 0.24, + 0.526 + ], + "angle": 0, + "content": "3.1. Model Plasticity" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.625 + ], + "angle": 0, + "content": "The model plasticity quantifies the learner's ability to learn new knowledge when a new task arrives. Several different metrics have been proposed to measure the model plasticity [8, 28, 34, 43]. In our work, we evaluate the model plasticity with Learning Accuracy (LA) [34]. Formally, the LA for the \\( j \\)-th task is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.243, + 0.632, + 0.47, + 0.653 + ], + "angle": 0, + "content": "\\[\nl _ {j} = a _ {j} ^ {j}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.471, + 0.735 + ], + "angle": 0, + "content": "where \\( a_{j}^{i} \\) is the accuracy evaluated on the test set of task \\( j \\) after training the network from task 1 to task \\( i \\). For an overall metric normalized against all tasks, the averaged LA is written as \\( LA = \\frac{1}{T}\\sum_{j=1}^{T}l_{j} \\), and \\( T \\) is the number of tasks in total." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.234, + 0.759 + ], + "angle": 0, + "content": "3.2. Model Stability" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.47, + 0.873 + ], + "angle": 0, + "content": "The stability assesses the extent of knowledge retention or loss within a model in its present state. The most commonly used metric in previous CL research is the Forgetting Measure (FM) [8]. Intuitively, FM for the \\(j\\)-th task, denoted as \\(f m_{j}^{k}\\), quantifies the decline in performance on a given task \\(j\\), after the model is trained on task \\(k\\), relative to its highest past performance on task \\(j\\):" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.878, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\nf m _ {j} ^ {k} = \\max _ {i \\in \\{1, \\dots , k - 1 \\}} \\left(a _ {j} ^ {i} - a _ {j} ^ {k}\\right), \\forall j < k. \\tag {2}\n\\]" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.385, + 0.89, + 0.461 + ], + "angle": 0, + "content": "
a ijT1T2T3T4T5FMkRFk
T130/15------
T225/12.525/12.5---5/2.58.33/8.33
T320/1020/1020/10--7.5/3.7517.78/17.78
T415/7.515/7.515/7.515/7.5-10/528.75/28.75
T510/510/510/510/510/512.5/6.2542/42
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.462, + 0.894, + 0.546 + ], + "angle": 0, + "content": "Table 1. Forgetting Measure (\\%) and Relative Forgetting (\\%) of two example learners (Learner 1 in teal and Learner 2 in brown) in a continual setting of five tasks with two classes per task. Each element \\(a_{j}^{i}\\) at row \\(j\\) and column \\(i\\) is the per task accuracy evaluated on the test set of task \\(j\\) after training the network from task 1 to task \\(i\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.556, + 0.893, + 0.587 + ], + "angle": 0, + "content": "For the overall metric obtained across all tasks, FM can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.598, + 0.892, + 0.642 + ], + "angle": 0, + "content": "\\[\nF M = \\frac {1}{T - 1} \\sum_ {j = 1} ^ {T - 1} f m _ {j} ^ {T}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.894, + 0.73 + ], + "angle": 0, + "content": "In our work, we propose a novel stability metric, termed Relative Forgetting (RF), as an alternative to the traditional Forgetting Measure (FM). RF measures how much proportion of performance the model forgets. Specifically, RF for the \\( j \\)-th task after training on task \\( k \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.74, + 0.892, + 0.782 + ], + "angle": 0, + "content": "\\[\nf _ {j} ^ {k} = \\max _ {i \\in \\{1, \\dots , k \\}} \\left(1 - \\frac {a _ {j} ^ {k}}{a _ {j} ^ {i}}\\right), \\forall j \\leq k. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.793, + 0.892, + 0.821 + ], + "angle": 0, + "content": "The overall metric averaged across all tasks can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.822, + 0.892, + 0.864 + ], + "angle": 0, + "content": "\\[\nR F = \\frac {1}{T} \\sum_ {j = 1} ^ {T} f _ {j} ^ {T}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "There are two advantages for shifting from absolute forgetting to relative forgetting:" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23462" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.079, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "1. RF is fairer for methods with higher plasticity. As shown in Table 1, when comparing two continual learners, one with high plasticity and the other with low, using both forgetting metrics, it is observed that despite having identical RF values, the model with lower plasticity shows a lower FM. This indicates that the FM metric might unfairly favor models with poorer initial performance, even when the relative decline in performance is equivalent across models;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.228, + 0.47, + 0.304 + ], + "angle": 0, + "content": "2. RF facilitates a quantitative analysis of the relationship between model stability and final performance. This enables a more nuanced understanding of how stability influences overall model efficacy, thereby guiding improvements in continual learning strategies." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.312, + 0.388, + 0.329 + ], + "angle": 0, + "content": "3.3. Impact on the Overall Performance" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.47, + 0.395 + ], + "angle": 0, + "content": "For online CL, the model's final average accuracy (AA) is the most vital metric. In this subsection, we try to show how the model plasticity and stability will impact the final performance quantitatively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.395, + 0.468, + 0.411 + ], + "angle": 0, + "content": "The model's final average accuracy can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.213, + 0.421, + 0.47, + 0.464 + ], + "angle": 0, + "content": "\\[\nA A = \\frac {1}{T} \\sum_ {j = 1} ^ {T} a _ {j} ^ {T}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.468, + 0.47, + 0.515 + ], + "angle": 0, + "content": "With the establishment of our plasticity metric (LA) and stability metric (RF), we can easily find the relationship between learning accuracy, relative forgetting, and accuracy:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.527, + 0.47, + 0.547 + ], + "angle": 0, + "content": "\\[\na _ {j} ^ {i} \\geq l _ {j} \\times \\left(1 - f _ {j} ^ {i}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.552, + 0.469, + 0.645 + ], + "angle": 0, + "content": "assuming equality when \\( a_{j}^{j} = \\max_{i\\in \\{1,\\dots ,j\\}}a_{j}^{i} \\). When extending the class-specific final accuracy \\( a_{j}^{T} \\) to the final AA, we consider the dot product of the LA vector \\( [l_1,\\dots,l_T] \\) with the RF vector \\( [f_1^T,\\dots,f_T^T] \\), which simplifies the calculation. More practically, this relationship can be approximated with:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.66, + 0.469, + 0.677 + ], + "angle": 0, + "content": "\\[\nA A \\gtrsim L A \\times (1 - R F). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.682, + 0.47, + 0.788 + ], + "angle": 0, + "content": "As indicated by Eq. 8, the lower bound of the final performance is proportional to \\( LA \\) and \\( 1 - RF \\), which suggests that both plasticity (LA) and stability (RF) play a crucial role in the final accuracy. Our findings reveal the importance of the model plasticity which was neglected in the past. And it can serve as a good guide for future online CL research." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.801, + 0.251, + 0.817 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.902 + ], + "angle": 0, + "content": "In this section, we first justify our motivations. Then, we introduce our proposed strategy: Collaborative Continual Learning and Distillation Chain. Finally, we show how to adapt our proposed strategy to the existing online CL methods and boost their plasticity." + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.089, + 0.868, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.272, + 0.892, + 0.312 + ], + "angle": 0, + "content": "Figure 3. Conceptual diagram of the training framework, when distilling from an untrained network \\(\\theta^2\\) to suppress the confidence of network \\(\\theta^1\\)." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.315, + 0.865, + 0.376 + ], + "angle": 0, + "content": "
DatasetCIFAR-100
Memory Size MM=1000M=2000M=5000
ER24.47±0.7231.89±1.4539.41±1.81
ER + Untrained Distillation27.07±1.2034.84±0.6441.15±1.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.379, + 0.892, + 0.42 + ], + "angle": 0, + "content": "Table 2. The performance of network \\( \\theta^1 \\) when distilling from untrained network \\( \\theta^2 \\) on CIFAR-100. All numbers are average over 10 runs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.431, + 0.72, + 0.446 + ], + "angle": 0, + "content": "4.1. Motivation Justification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.892, + 0.65 + ], + "angle": 0, + "content": "Plasticity matters in Online CL. Online continual learners are designed to continuously adapt to non-stationary data streams, efficiently acquiring new knowledge while retaining previously learned information. In current online CL research, the emphasis has predominantly been on mitigating catastrophic forgetting. Even among state-of-the-art methods such as [19, 44], plasticity is often compromised in the quest for improved stability. However, our finding in Sec. 3 shows that both plasticity and stability are crucial for achieving satisfactory final performance, with plasticity proving particularly difficult to achieve in online CL settings. To this end, we deliberately prioritize the plasticity aspect." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.817 + ], + "angle": 0, + "content": "The potential of collaborative learning to improve convergence in non-continual scenarios [5] positions it as a promising candidate for enhancing plasticity. With the apparent lack of focus on plasticity, collaborative learning has yet to be leveraged to boost convergence of online continual learners. In our research, we propose to exploit collaborative learning convergence properties for improving plasticity. We find that similar to non-continual scenarios, collaborative learning strategy can boost convergence by allowing more parallelism in the training and more maneuverability of the continual learners." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Overconfidence hurts Online CL. In conventional supervised learning, it is well established that excessive confidence can harm the generalization ability. To tackle this issue, many methods such as label smoothing [41], knowledge distillation [45], and confidence penalty [33] are pro" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23463" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.093, + 0.124, + 0.106 + ], + "angle": 0, + "content": "posed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.47, + 0.318 + ], + "angle": 0, + "content": "In online CL, we find a counter-intuitive, yet similar phenomenon. As shown in Fig. 3, while we train network \\(\\theta^1\\) with the classification loss, we initiate another network \\(\\theta^2\\) at the beginning of the training. During the continual training, we stagnate the network \\(\\theta^2\\) (i.e., Kaiming initialize and stay untrained) and train the network \\(\\theta^1\\) with both classification loss and the distillation loss (Kullback-Leibler divergence loss) from untrained network \\(\\theta^2\\). The experimental result in Table 2 shows a decent performance gain compared with independent training. The distillation from the prediction of untrained network \\(\\theta^2\\) to network \\(\\theta^1\\) serves as a regularization to suppress the overall confidence, and the performance gain under this condition makes it evident that, in continual scenarios, overconfidence will also harm the performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.47, + 0.363 + ], + "angle": 0, + "content": "To tackle the overconfidence problem, we propose Distillation Chain (DC), an entropy regularizer to suppress the overall confidence level." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.371, + 0.377, + 0.387 + ], + "angle": 0, + "content": "4.2. Collaborative Continual Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.471, + 0.591 + ], + "angle": 0, + "content": "The introduced Collaborative Continual Learning (CCL) enables more parallelism and flexibility in training online continual learners, and it is the key to improving the model plasticity and the final performance. As shown in Fig. 2, CCL involves two peer continual learners of the same architecture and optimizer setting training in a peer-teaching manner. In the training phase, networks are supervised with both the ground truth label and the predictions of their peers. In the inference phase, models can either make predictions collaboratively with ensemble methods [5] to get a better performance or predict independently for the sake of computation efficiency. If we denote two networks in CCL as \\(\\theta^1\\) and \\(\\theta^2\\), we formulate our loss to network \\(\\theta^1\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.597, + 0.469, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {C C L} ^ {1} = \\lambda_ {1} \\cdot \\mathcal {L} _ {c l s} \\left(\\theta^ {1} (X), y\\right) \\\\ + \\lambda_ {2} \\cdot D _ {K L} \\left(\\theta^ {1} (X) / \\tau , \\theta^ {2} (X) / \\tau\\right), \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.734 + ], + "angle": 0, + "content": "where \\((X,y)\\) is the data-label pair, \\(\\mathcal{L}_{cls}(\\cdot)\\) is the classification loss in the baseline method CCL adapts to, \\(D_{KL}(\\cdot)\\) is the Kullback-Leibler divergence, \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are the balancing hyperparameters and \\(\\tau\\) is the temperature hyperparameter. Note that the network \\(\\theta^2\\) should be trained with \\(\\mathcal{L}_{CCL}^2\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.251, + 0.757 + ], + "angle": 0, + "content": "4.3. Distillation Chain" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.87 + ], + "angle": 0, + "content": "To fully take advantage of CCL, we propose Distillation Chain (DC), an entropy regularizaion based strategy explicitly designed for online CL. As illustrated in Fig. 2, DC comprises two steps: (1) generating a chain of samples with different levels of difficulty [40] using data augmentation, and (2) distillation of logit distribution from harder samples to easier samples in a collaborative learning way." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 2, we observed that overconfidence will hurt the performance in continual training. To tackle" + }, + { + "type": "code_caption", + "bbox": [ + 0.5, + 0.091, + 0.892, + 0.121 + ], + "angle": 0, + "content": "Algorithm 1 PyTorch-like pseudo-code of CCL-DC to integrate to other baselines." + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.123, + 0.892, + 0.429 + ], + "angle": 0, + "content": "# model1: student model\n# model2: teacher model\n# optim1: optimizer for student model\n# cls: classification loss in baseline\nfor x, y in dataloader:\n # Baseline loss\n loss基礎 = criterion基礎(model1, x, y)\n # DC Augmentation\n x1 = geometric_distortion(x)\n x2 = RandAugment(x1, N, M)\n x3 = RandAugment(x2, N, M)\n # CCL-DC loss\n ls, ls1, ls2, ls3 = model1(x, x1, x2, x3)\n lt, lt1, lt2, lt3 = model2(x, x1, x2, x3) # no grad\n loss_CLS = cls(ls, y) + cls(ls1, y) + cls(ls2, y) +\n \\(\\leftrightarrow\\) cls(ls3, y)\n loss_ccl = kl_div(ls/t, lt/t) # temperature t\n loss_dC = kl_div(ls/t, lt1/t) + kl_div(ls1/t, lt2/t) +\n \\(\\leftrightarrow\\) kl_div(ls2/t, lt3/t)\n loss_ours = lam1*loss_CLS + lam2*(loss_ccl + loss_dC)\n loss = loss基礎 + loss_ours\n optim1.zero_grad()\n loss.backup()\n optim1.step()" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.892, + 0.559 + ], + "angle": 0, + "content": "the problem, DC uses data augmentation strategies to generate samples with different levels of difficulty and produces logit distribution with different confidence. The distillation from less confident predictions to more confident predictions weakens the overall confidence of the network and benefits the performance by improving the generalization capability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.893, + 0.68 + ], + "angle": 0, + "content": "In our work, we use a geometric distortion comprised of RandomCrop and RandomHorizontalFlip as the first step of DC augmentation. After that, we use RandAugment [12] for the subsequent augmentations and we involve two hyperparameters \\( N \\) and \\( M \\) for RandAugment. We take three augmentation steps and distill the logit distribution from the teacher with harder samples to the student with easier samples. We formulate our loss with DC to network \\( \\theta^1 \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.69, + 0.892, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {D C} ^ {1} = \\lambda_ {1} \\sum_ {i = 1} ^ {3} \\mathcal {L} _ {c l s} \\left(\\theta^ {1} \\left(X _ {i}\\right), y\\right) \\tag {10} \\\\ + \\lambda_ {2} \\sum_ {i = 1} ^ {3} D _ {K L} (\\theta^ {1} (X _ {i - 1}) / \\tau , \\theta^ {2} (X _ {i}) / \\tau), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.816 + ], + "angle": 0, + "content": "where \\( X_{i} \\) is the augmentation of input sample \\( X \\) after \\( i \\) augmentation steps." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.821, + 0.828, + 0.837 + ], + "angle": 0, + "content": "4.4. Apply CCL-DC to online CL methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.844, + 0.892, + 0.872 + ], + "angle": 0, + "content": "The overall loss to network \\(\\theta^1\\) when adapting CCL-DC can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.884, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {1} = \\mathcal {L} _ {\\text {B a s e l i n e}} + \\mathcal {L} _ {C C L} ^ {1} + \\mathcal {L} _ {D C} ^ {1}, \\tag {11}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23464" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.885, + 0.324 + ], + "angle": 0, + "content": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER [35]56.68±1.8962.32±4.1324.47±0.7231.89±1.4539.41±1.8110.82±0.7919.16±1.4224.71±2.5233.30±1.74
ER + Ours66.43±2.4874.10±1.7133.43±1.0644.45±1.0453.81±1.1616.56±1.6329.39±1.2337.73±0.8543.11±1.49
DER++ [6]58.04±2.3064.02±1.9225.09±1.4132.33±2.6638.31±2.288.73±1.5817.95±2.4919.40±3.7134.75±2.23
DER++ + Ours68.79±1.4274.25±1.1034.36±0.8943.52±1.3552.95±0.8610.99±1.3921.68±1.9428.01±2.4645.70±1.32
ER-ACE [7]53.26±3.0459.94±2.4028.36±1.9934.21±1.5339.39±1.3113.56±1.0020.84±0.4325.92±1.0738.37±1.20
ER-ACE + Ours70.08±1.3875.56±1.1437.20±1.1545.14±1.0053.92±0.4818.32±1.4926.22±2.0132.23±1.7045.15±1.94
OCM [19]68.19±1.7573.15±1.0528.02±0.7435.69±1.3642.22±1.0618.36±0.9526.74±1.0231.94±1.1923.67±2.36
OCM + Ours74.14±0.8577.66±1.4635.00±1.1543.34±1.5151.43±1.3723.36±1.1833.17±0.9739.25±0.8843.19±0.98
GSA [20]60.34±1.9766.54±2.2827.72±1.5735.08±1.3741.41±1.6512.44±1.1719.59±1.3025.34±1.4341.03±0.99
GSA + Ours68.91±1.6875.78±1.1635.56±1.3944.74±1.3255.39±1.0916.70±1.6628.11±1.7037.13±1.7544.28±1.16
OnPro [44]70.47±2.1274.70±1.5127.22±0.7733.33±0.9341.59±1.3814.32±1.4021.13±2.1226.38±2.1838.75±1.03
OnPro + Ours74.49±2.1478.64±1.4234.76±1.1241.89±0.8250.01±0.8521.81±1.0232.00±0.7238.18±1.0247.93±1.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.326, + 0.892, + 0.354 + ], + "angle": 0, + "content": "Table 3. Average Accuracy (\\%, higher is better) on four benchmark datasets with difference memory buffer size \\( M \\), with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.358, + 0.885, + 0.593 + ], + "angle": 0, + "content": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER83.13±1.6078.15±3.6053.77±1.5151.53±1.6650.79±0.7168.15±1.4764.99±1.2264.44±1.4553.95±1.51
ER + Ours90.60±1.5089.99±1.5072.38±0.6670.86±0.7268.84±1.0585.24±0.5381.75±0.8379.54±0.7468.73±1.21
DER++77.14±2.9678.00±2.1656.13±3.7555.33±3.2656.32±3.4470.01±1.8366.87±1.3070.28±2.4260.65±2.97
DER++ + Ours88.85±1.8889.00±1.6772.85±1.3771.54±1.9969.52±2.3782.83±1.2778.80±1.6277.79±0.8670.16±1.03
ER-ACE57.66±4.1661.59±3.3538.53±1.6139.95±2.0041.56±1.445.60±1.454.83±0.784.92±0.9549.82±1.05
ER-ACE + Ours88.37±1.3988.40±1.1569.47±0.8868.39±1.3266.63±0.9021.91±5.1621.88±4.3918.88±3.1268.52±0.82
OCM78.71±3.6681.33±2.0640.87±1.6042.00±1.4842.43±1.8018.56±2.8715.86±2.0115.03±2.0220.77±1.88
OCM + Ours82.39±2.2384.53±1.6348.89±2.0449.83±2.0149.94±2.1631.69±1.8129.54±2.3528.10±2.2848.20±1.38
GSA79.87±3.2677.09±4.5558.16±1.5855.13±1.8150.34±1.7320.46±1.5915.86±1.2614.50±0.6362.59±1.17
GSA + Ours91.69±1.1190.98±1.3373.73±1.0372.68±0.9870.36±1.0780.36±1.2274.77±1.6670.71±1.1973.71±1.12
OnPro84.23±2.0085.60±1.5641.34±1.6342.59±1.6542.92±1.0020.84±1.4716.73±1.2715.82±1.0439.60±0.86
OnPro + Ours90.39±1.5990.18±1.5846.30±1.1047.13±1.0147.27±1.8125.87±1.9121.40±1.5219.75±1.2252.55±2.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.595, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Table 4. Learning Accuracy (%, higher is better) on four benchmark datasets with difference memory buffer size \\(M\\), with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.768 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\text{Baseline}}\\) is the loss function of the baseline model CCL-DC adapts to. Note that the model \\(\\theta^2\\) should be trained similarly. In Algorithm 1, we provide a Pytorch-like pseudo-code demonstrating how to incorporate CCLDC into a given baseline. For simplicity, we only show the loss function for model \\(\\theta^1\\). Also, we omitted the memory buffer in the pseudo-code. However, the training should be consistent with the baseline, using both streaming and memory data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.788, + 0.209, + 0.805 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.267, + 0.832 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Datasets. We use four image classification benchmark datasets to evaluate the effectiveness of our method, including CIFAR-10 [25], CIFAR-100 [25], TinyImageNet [26], and ImageNet-100 [11, 15, 22]. More detailed information" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.632, + 0.892, + 0.663 + ], + "angle": 0, + "content": "about the dataset split and task allocation is given in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.668, + 0.892, + 0.73 + ], + "angle": 0, + "content": "Baselines. To show the effectiveness of our strategy, we applied CCL-DC to six typical and state-of-the-art online CL methods, including ER [35], DER++ [6], ER-ACE [7], OCM [19], GSA [20], and OnPro [44]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. We use full ResNet-18 [21] (not pre-trained) as the backbone for every method. For each baseline method, we perform a hyperparameter search on CIFAR-100, \\( M = 2\\mathrm{k} \\), and apply the hyperparameter to all of the settings. For fair comparison, we use the same optimizer and hyperparameter setting when adapting CCL-DC to the baselines. For hyperparameters unique to CCL-DC, we conduct another hyperparameter search as stated in the supplementary material. We set the streaming batch size to 10 and the memory batch size to 64. We do not use the multiple update trick as described in [3]. More detailed in" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23465" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.887, + 0.324 + ], + "angle": 0, + "content": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER31.63±3.8120.63±8.3255.71±2.2439.11±3.8723.05±3.6985.00±1.3071.62±2.1862.43±3.8339.26±3.21
ER + Ours26.74±3.9917.58±2.7154.34±2.2237.67±2.1621.98±2.5981.13±1.9364.79±1.3253.18±0.9937.78±2.18
DER++23.60±3.6417.71±2.1855.65±4.3641.27±4.9331.72±3.9587.79±2.3573.28±3.8872.51±5.5342.97±5.89
DER++ + Ours22.62±3.0316.43±3.3653.45±1.4039.39±2.7123.71±3.3987.16±1.6073.15±2.1564.48±3.0835.32±2.80
ER-ACE12.25±3.849.92±2.8325.88±4.1017.68±1.9010.62±2.0857.41±2.3844.48±1.9637.83±3.1223.92±2.05
ER-ACE + Ours20.62±2.2614.32±2.5846.78±1.9134.19±2.4019.01±0.9456.56±4.1642.20±3.9431.13±3.5234.43±3.60
OCM13.05±4.3711.00±3.1131.16±2.6917.90±3.736.85±2.2556.66±2.5340.59±1.5530.80±2.294.55±1.60
OCM + Ours10.75±2.528.45±2.6329.65±4.0017.02±3.016.16±1.3551.58±2.8135.58±2.5427.24±1.6015.33±2.28
GSA25.02±2.8316.56±4.0253.42±3.1237.29±2.6020.50±4.3366.87±3.3153.42±3.8443.44±3.8135.44±2.42
GSA + Ours24.96±3.2716.59±2.0952.29±2.0638.76±2.4121.36±2.3680.08±1.9763.85±1.7849.73±2.1040.46±2.54
OnPro16.47±4.2312.93±3.0235.03±4.4524.26±2.3112.04±2.1164.69±3.3650.47±4.2042.81±4.6314.44±2.08
OnPro + Ours17.54±4.1512.90±2.7727.64±3.2917.78±1.398.41±2.6256.03±2.9638.70±1.8829.24±1.3315.72±3.29
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.33, + 0.893, + 0.361 + ], + "angle": 0, + "content": "Table 5. Relative Forgetting (%, lower is better) on four benchmark datasets with difference memory buffer size \\( M \\) ,with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.42 + ], + "angle": 0, + "content": "formation about data augmentation, hyperparameter search, and hardware environments is given in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.431, + 0.273, + 0.448 + ], + "angle": 0, + "content": "5.2. Results and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.455, + 0.47, + 0.65 + ], + "angle": 0, + "content": "Final average accuracy. Table 3 presents average accuracy (AA) at the end of the training on four datasets. As indicated in Sec. 4, to fully take advantage of collaborative learning, we show the results with the ensemble of two models, with the independent model performance available in the supplementary material. Generally, the ensemble method provides about \\(1\\%\\) additional accuracy compared to independent inference. For all datasets, memory size \\(M\\), and baseline methods, applying CCL-DC constantly improves the performance by a large margin. Notably, even for state-of-the-art methods such as GSA and OnPro, we can still gain significant performance when incorporating CCL-DC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.471, + 0.803 + ], + "angle": 0, + "content": "More interestingly, for almost all settings with different memory buffer sizes \\( M \\), the performance gain tends to be a constant on a relative basis. For example, CCL-DC can boost the performance of ER on Tiny/ImageNet from 10.82 to 16.56 when \\( M = 2\\mathrm{k} \\), which is a \\( 53.0\\% \\) performance gain on a relative basis. The performance gain is \\( 53.4\\% \\) and \\( 52.7\\% \\) when \\( M = 5\\mathrm{k} \\) and \\( M = 10\\mathrm{k} \\), respectively. This indicates that we can achieve a decent performance gain regardless of the memory buffer size, and it shows the scalability of our method to different resource conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Plasticity and stability metric. As mentioned in Sec. 3, we evaluate the plasticity and stability of different continual learners with LA and RF, respectively. Table 4 shows the plasticity metric on four datasets. For all settings, CCL-DC constantly improves the model plasticity by a large margin. For model stability, as indicated by RF in Table 5, mod" + }, + { + "type": "table", + "bbox": [ + 0.553, + 0.372, + 0.839, + 0.494 + ], + "angle": 0, + "content": "
MethodAcc. ↑LA ↑
ER31.89±1.4551.53±1.66
ER + Multivew38.18±1.4664.02±1.12
ER + Ours (CCL only)41.05±1.2168.76±0.79
ER + Ours44.45±1.0470.86±0.72
ER-ACE34.21±1.5339.95±2.00
ER-ACE + Multivew38.61±1.4847.45±1.88
ER-ACE + Ours (CCL only)40.90±1.0850.91±1.63
ER-ACE + Ours45.14±1.0068.39±1.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.504, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Table 6. Ablation studies on CIFAR-100 (M=2k). We report the ensemble performance for methods incorporating CCL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.894, + 0.635 + ], + "angle": 0, + "content": "els trained with CCL-DC are comparable with the baselines under most cases. ER-ACE is an exception as its plasticity is unexpectedly low, especially on TinyImagenet. Also, the stability of ER-ACE is compromised when incorporating CCL-DC. We will explain the reason for this unexpected phenomenon in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.644, + 0.665, + 0.659 + ], + "angle": 0, + "content": "5.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Effect of multiview learning. As mentioned in Sec. 4, CCL-DC benefits from multiview learning with data augmentation in DC. For fair comparison, we explore how multiview learning will impact the performance of the baselines. We apply the classification loss part of CCL-DC to the baselines. Table 6 demonstrates that multiview learning can improve both AA and LA of baselines. However, those performance gains are still inferior to CCL-DC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Effect of CCL. We evaluate how CCL alone can improve the baselines. In the experiments, we remove multiview learning and DC, and we train the continual learner pair with the loss illustrated in Eq. 9. Table 6 shows the performance gain for ER and ER-ACE. We can see that CCL alone can provide significant gains in both final accuracy and plasticity. Also, when combining CCL with DC, the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23466" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.426, + 0.188 + ], + "angle": 0, + "content": "
MethodDistillation schemeAcc. ↑LA ↑
EREasy to hard40.95±0.9760.03±0.98
ERSame difficulty43.64±1.0969.49±0.78
ERHard to easy (Ours)44.45±1.0470.86±0.72
ER-ACEEasy to hard38.46±1.5139.00±1.03
ER-ACESame difficulty43.81±1.2855.37±1.54
ER-ACEHard to easy (Ours)45.14±1.0068.39±1.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.199, + 0.47, + 0.226 + ], + "angle": 0, + "content": "Table 7. Comparison of different distillation schemes in DC on CIFAR-100 (M=2k)." + }, + { + "type": "table", + "bbox": [ + 0.105, + 0.232, + 0.44, + 0.309 + ], + "angle": 0, + "content": "
MethodDistillation schemeAcc. ↑LA ↑
ER + SDCEasy to hard35.00±1.3156.67±0.84
ER + SDCHard to easy41.31±1.2568.62±0.60
ER + CCL-DCEasy to hard40.95±0.9760.03±0.98
ER + CCL-DCHard to easy (Ours)44.45±1.0470.86±0.72
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.313, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Table 8. Final average accuracy when conducting multiview distillation within the same model on CIFAR-100 (M=2k). All values are averaged over 10 runs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.371, + 0.33, + 0.387 + ], + "angle": 0, + "content": "performance can be further improved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.47, + 0.487 + ], + "angle": 0, + "content": "Distillation scheme of DC. We also evaluate the effectiveness of DC's strategy of distilling from harder samples to easier samples in collaborative learning manner. As shown in Table 7, we compared it with other distillation strategies. The result shows that the distillation scheme of DC constantly outperforms other schemes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.47, + 0.664 + ], + "angle": 0, + "content": "Self-Distillation Chain in an independent model. While DC was originally designed to incorporate CCL, it is possible to conduct DC's strategy within an independent model. We name such a strategy as the Self-Distillation Chain (SDC). Similar to different schemes of DC, SDC can be implemented in two ways: distillation from easier samples to harder samples, and distillation from harder samples to easier samples. As shown in Table 8, both strategy gives extra final performance and plasticity, while the latter strategy benefits the performance more. Moreover, incorporating DC with CCL (i.e., ours) further improves the accuracy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.199, + 0.695 + ], + "angle": 0, + "content": "6. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.447, + 0.72 + ], + "angle": 0, + "content": "In this section, we analyze some properties of CCL-DC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.911 + ], + "angle": 0, + "content": "Improving plasticity. One of the important advantages of CCL-DC is that it can improve the plasticity of continual learners. This can be evident by plasticity metrics like LA. Moreover, we have observed that the plasticity of CCL-DC facilitates the model to converge faster and descend to a deeper loss. Figure 4 illustrates the classification loss (cross-entropy) curve of the model. To obtain the loss curve, we take a snapshot of the model every 10 iterations and compute the cross-entropy over all the training samples on the current task. We plot the curve on the logarithm scale so that it is easy to observe that CCL-DC helps the model descend deeper at the end of each task." + }, + { + "type": "image", + "bbox": [ + 0.549, + 0.091, + 0.838, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.221, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Figure 4. Classification loss curve of ER on CIFAR-100 \\((\\mathbf{M} = 2\\mathbf{k})\\) The curve is calculated on all training samples of the current task. Since there are 10 tasks in total, the curve has 10 peaks." + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.265, + 0.821, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.448, + 0.892, + 0.504 + ], + "angle": 0, + "content": "Figure 5. The entropy of prediction produced by ER with and without CCL-DC on CIFAR-100 \\((\\mathbf{M} = 2\\mathbf{k})\\). \\(X_{i}\\) represents the sample after \\(i\\)-th augmentation in Eq. 10. The value is calculated at the end of the training and is averaged over all training samples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.513, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Alleviating overconfidence. To show the effect of DC in alleviating overconfidence, we compared the confidence of models trained with and without CCL-DC. We measure the confidence with the entropy of predictions. Fig. 5 shows the entropy of prediction produced by the ER (baseline) with and without CCL-DC on CIFAR-100 \\((\\mathrm{M} = 2\\mathrm{k})\\). The entropy is calculated at the end of training and averaged across all samples in the training set. Moreover, we also calculate the entropy of models trained with CCL-DC, by forwarding images of different difficulties (from \\(X_0\\) to \\(X_3\\) in Eq. 10) in the augmentation chain. The experimental results show the effect of DC in suppressing overall confidence." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.619, + 0.725 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.733, + 0.892, + 0.888 + ], + "angle": 0, + "content": "In this paper, we highlighted the significance of plasticity in online CL, which has been overlooked in prior research when compared to stability. We also established the quantitative link between plasticity, stability, and final accuracy. The quantitative relationship shed light on the future direction of online CL research. Based on this, we introduced collaborative learning into online CL and proposed CCL-DC, a strategy that can be seamlessly integrated into existing online CL methods. Extensive experiments showed the effectiveness of CCL-DC in boosting plasticity and subsequently improving the final performance." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23467" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. Expert gate: Lifelong learning with a network of experts. In CVPR, 2017. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.47, + 0.212 + ], + "angle": 0, + "content": "[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. 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Unlike its offline counterpart, in online CL, the training data can only be seen once. Most existing online CL research regards catastrophic forgetting (i.e., model stability) as almost the only challenge. In this paper, we argue that the model's capability to acquire new knowledge (i.e., model plasticity) is another challenge in online CL. While replay-based strategies have been shown to be effective in alleviating catastrophic forgetting, there is a notable gap in research attention toward improving model plasticity. To this end, we propose Collaborative Continual Learning (CCL), a collaborative learning based strategy to improve the model's capability in acquiring new concepts. Additionally, we introduce Distillation Chain (DC), a collaborative learning scheme to boost the training of the models. We adapt CCL-DC to existing representative online CL works. Extensive experiments demonstrate that even if the learners are well-trained with state-of-the-art online CL methods, our strategy can still improve model plasticity dramatically, and thereby improve the overall performance by a large margin. The source code of our work is available at https://github.com/maorong-wang/CCL-DC. + +# 1. Introduction + +Continual Learning (CL) [10, 13, 32, 43] aims to incrementally learn a sequence of tasks and enhance the neural network's performance on the current tasks, without forgetting previously learned knowledge. CL can be done in two different manners [4, 43]: offline and online. In offline CL, the learner can have infinite access to all the training data of the current task that it trains on and may go through the data for any epoch. Contrary to offline CL, in online CL, the training data for each task also comes continually in a data stream, and the learner can only see the training data once. Apart from the learning approach, there are also three different CL scenarios [23, 29, 42]: Task-Incremental Learning (TIL), Domain-Incremental Learning (DIL), and Class- + +Incremental learning (CIL). In this paper, we focus on the CIL setting in online CL. + +Various online CL methods [6, 7, 19, 20, 31, 35, 44] have been proposed to help the models learn continually on one-epoch data stream, with alleviated forgetting. Among them, replay-based methods have shown remarkable success, and current state-of-the-art methods rely heavily on memory replay to mitigate catastrophic forgetting [17, 30]. However, while most existing online CL research primarily only focuses on improving model stability (i.e., alleviating catastrophic forgetting) to achieve better overall accuracy, the importance of model plasticity (i.e., the capability to acquire new knowledge) is often overlooked. While in offline CL, it is possible to gain high plasticity by iterating several epochs on the current task before proceeding to the subsequent task, acquiring plasticity in online CL tends to be more challenging because the training data is only available once. As shown in Fig. 1, compared to learning without memory replay, the replay-based methods implicitly alleviate the low plasticity issue to some extent. Also, plasticity can be improved by employing a technique involving multiple updates on incoming samples [3]. However, the combination of memory replay and multiple updates fails to bridge the existing plasticity gap between online and offline CL, and the use of multiple updates can lead to increased catastrophic forgetting. Overall, the plasticity gap adversely affects the performance of online CL methods. + +In this paper, we argue that plasticity is particularly crucial and challenging to acquire in online CL, and even more so than in offline CL. Thus, we shed light on how model plasticity and stability will impact the overall performance. Furthermore, we propose a quantitative link between plasticity, stability, and final accuracy, showing that the plasticity gap between offline and online must be reduced to improve overall performance. + +Guided by the quantitative relationship, we focus ourselves on the previously overlooked plasticity perspective. Inspired by the ability of collaborative learning to accelerate the convergence in non-continual scenarios [5], we have incorporated collaborative learning in online CL and observed a similar phenomenon. Consequently, we pro + +![](images/d949bc5c3e3fe341d6a7033f40a99163b0bcddf93c2dffa5ca2489ada7aeeda0.jpg) +Figure 1. The comparison of plasticity (learning accuracy) and stability (relative forgetting, our metric proposed in Sec. 3) of Experience Replay (ER) [35] under various settings on CIFAR-100. For experiments with memory replay, the size of the memory buffer is set to 2,000. We can witness a plasticity gap between offline CL and online CL, even with memory replay and multiple update trick (memory iteration $>1$ ). + +pose the Collaborative Continual Learning with Distillation Chain (CCL-DC), a collaborative learning scheme that can be adapted to existing online CL methods. CCL-DC consists of two key components: Collaborative Continual Learning (CCL) and Distillation Chain (DC). + +CCL involves two peer continual learners to learn from the data stream simultaneously in a peer teaching manner, enhancing optimization parallelism and offering greater flexibility to the continual learners. To the best of our knowledge, CCL is the first method to incorporate collaborative learning techniques in online CL research. Moreover, to fully exploit the potential of collaborative learning in online CL scenarios, we propose DC, an entropy regularization based optimization strategy, specifically designed for online CL. + +The main contribution of this paper can be summarized as follows. + +1. We establish a quantitative link between plasticity, stability, and final performance. Based on this, we demonstrate that plasticity is an important obstacle in online CL, which was greatly overlooked in the previous research: +2. To overcome the plasticity issue, we introduce CCL-DC, a collaborative learning based strategy that can be seamlessly integrated into the existing methods, significantly improving their performance by boosting plasticity; +3. Comprehensive experiments show that CCL-DC enhances the performance of existing methods by a large margin. + +# 2. Related Work + +Continual Learning. Continual learning can be classified into three different categories: regularization- + +based, parameter-isolation-based, and replay-based. Regularization-based methods [2, 8, 24, 27, 46] add extra regularization terms to balance the old and new tasks. Parameter-isolation-based methods [1, 16, 36-38] solve the problem explicitly by dynamically allocating task-specific parameters. Replay-based methods [6, 7, 9, 14, 19, 20, 31, 35, 44] maintain a small memory buffer that stores a few old training samples. + +Among these methods, replay-based strategies have gained huge success due to their impressive performance and simplicity. ER [35] is the fundamental replay-based method that leverages Cross-Entropy loss for classification and a random replay buffer. DER++ [6] stores the logits in the memory buffer and extends ER with the distillation of old stored logits. ER-ACE [7] extends ER with Asymmetric Cross-Entropy loss for classification to suppress the drift of old class representations. OCM [19] leverages a replay-based strategy by maximizing the mutual information between old and new class representations. GSA [20] solves cross-task class discrimination with replay-based strategy and Gradient Self Adaption. OnPro [44] uses online prototype learning to address shortcut learning and alleviate catastrophic forgetting. + +These replay-based methods propose different strategies for alleviating catastrophic forgetting and improving the model stability. However, the importance of the model plasticity is greatly neglected in their research, despite their success in terms of final performance. In our work, these methods serve as the baselines and we adapted our strategy to these baselines to show the effectiveness of our proposed approach. + +Collaborative Learning. Collaborative learning [5, 18, 39, 47, 48] originates from online knowledge distillation (KD). Different from the conventional KD methods, online KD involves training a cohort of deep networks from scratch in a peer-teaching manner. During the training process, the models imitate their peers and guides the training of other models simultaneously. Deep Mutual Learning (DML) [47] suggests peer student models learn from each other through the logit distillation between the probability distributions. Codistillation [5] is similar to DML and suggests the ensemble of peer networks can further improve the performance. More importantly, Codistillation shows that online KD can help the model converge faster on non-continual scenarios. + +Despite the success of collaborative learning in non-continual scenarios, due to the lack of focus on plasticity, the research on collaborative learning in CL is still limited. To the best of our knowledge, there is no existing research using the collaborative learning technique to boost the training of online CL. Moreover, in our work, we introduce the DC, an entropy regularization based optimization strategy, specifically tailored to fully leverage the potential of collab + +![](images/453e9be391aaceee9555fc6354adead2b195898fcfb52b5c4e7a27024397fb74.jpg) +Figure 2. Overview of the proposed CCL-DC framework applied to a baseline online CL method. The proposed CCL-DC framework has two main components. The first one is CCL, which involves two peer continual learners that simultaneously learn from the data stream in a peer teaching manner. The second component, DC, generates a chain of samples with varying levels of difficulty and feeds them into models to produce a chain of logit distribution of different confidence levels. Then, in a collaborative learning approach, DC conducts distillation from less confident predictions to more confident predictions, to serve as a form of learned entropy regularization. + +orative learning in online CL scenarios. + +# 3. Plasticity and Stability in online CL + +In this section, we revise the metric for model plasticity and propose a novel metric for model stability. In addition, we quantitatively analyze the impact of model plasticity and stability on the final performance. + +# 3.1. Model Plasticity + +The model plasticity quantifies the learner's ability to learn new knowledge when a new task arrives. Several different metrics have been proposed to measure the model plasticity [8, 28, 34, 43]. In our work, we evaluate the model plasticity with Learning Accuracy (LA) [34]. Formally, the LA for the $j$ -th task is defined as: + +$$ +l _ {j} = a _ {j} ^ {j}, \tag {1} +$$ + +where $a_{j}^{i}$ is the accuracy evaluated on the test set of task $j$ after training the network from task 1 to task $i$ . For an overall metric normalized against all tasks, the averaged LA is written as $LA = \frac{1}{T}\sum_{j=1}^{T}l_{j}$ , and $T$ is the number of tasks in total. + +# 3.2. Model Stability + +The stability assesses the extent of knowledge retention or loss within a model in its present state. The most commonly used metric in previous CL research is the Forgetting Measure (FM) [8]. Intuitively, FM for the $j$ -th task, denoted as $f m_{j}^{k}$ , quantifies the decline in performance on a given task $j$ , after the model is trained on task $k$ , relative to its highest past performance on task $j$ : + +$$ +f m _ {j} ^ {k} = \max _ {i \in \{1, \dots , k - 1 \}} \left(a _ {j} ^ {i} - a _ {j} ^ {k}\right), \forall j < k. \tag {2} +$$ + +
a ijT1T2T3T4T5FMkRFk
T130/15------
T225/12.525/12.5---5/2.58.33/8.33
T320/1020/1020/10--7.5/3.7517.78/17.78
T415/7.515/7.515/7.515/7.5-10/528.75/28.75
T510/510/510/510/510/512.5/6.2542/42
+ +Table 1. Forgetting Measure (\%) and Relative Forgetting (\%) of two example learners (Learner 1 in teal and Learner 2 in brown) in a continual setting of five tasks with two classes per task. Each element $a_{j}^{i}$ at row $j$ and column $i$ is the per task accuracy evaluated on the test set of task $j$ after training the network from task 1 to task $i$ . + +For the overall metric obtained across all tasks, FM can be expressed as: + +$$ +F M = \frac {1}{T - 1} \sum_ {j = 1} ^ {T - 1} f m _ {j} ^ {T}. \tag {3} +$$ + +In our work, we propose a novel stability metric, termed Relative Forgetting (RF), as an alternative to the traditional Forgetting Measure (FM). RF measures how much proportion of performance the model forgets. Specifically, RF for the $j$ -th task after training on task $k$ is defined as: + +$$ +f _ {j} ^ {k} = \max _ {i \in \{1, \dots , k \}} \left(1 - \frac {a _ {j} ^ {k}}{a _ {j} ^ {i}}\right), \forall j \leq k. \tag {4} +$$ + +The overall metric averaged across all tasks can be written as: + +$$ +R F = \frac {1}{T} \sum_ {j = 1} ^ {T} f _ {j} ^ {T}. \tag {5} +$$ + +There are two advantages for shifting from absolute forgetting to relative forgetting: + +1. RF is fairer for methods with higher plasticity. As shown in Table 1, when comparing two continual learners, one with high plasticity and the other with low, using both forgetting metrics, it is observed that despite having identical RF values, the model with lower plasticity shows a lower FM. This indicates that the FM metric might unfairly favor models with poorer initial performance, even when the relative decline in performance is equivalent across models; +2. RF facilitates a quantitative analysis of the relationship between model stability and final performance. This enables a more nuanced understanding of how stability influences overall model efficacy, thereby guiding improvements in continual learning strategies. + +# 3.3. Impact on the Overall Performance + +For online CL, the model's final average accuracy (AA) is the most vital metric. In this subsection, we try to show how the model plasticity and stability will impact the final performance quantitatively. + +The model's final average accuracy can be calculated as: + +$$ +A A = \frac {1}{T} \sum_ {j = 1} ^ {T} a _ {j} ^ {T}. \tag {6} +$$ + +With the establishment of our plasticity metric (LA) and stability metric (RF), we can easily find the relationship between learning accuracy, relative forgetting, and accuracy: + +$$ +a _ {j} ^ {i} \geq l _ {j} \times \left(1 - f _ {j} ^ {i}\right), \tag {7} +$$ + +assuming equality when $a_{j}^{j} = \max_{i\in \{1,\dots ,j\}}a_{j}^{i}$ . When extending the class-specific final accuracy $a_{j}^{T}$ to the final AA, we consider the dot product of the LA vector $[l_1,\dots,l_T]$ with the RF vector $[f_1^T,\dots,f_T^T]$ , which simplifies the calculation. More practically, this relationship can be approximated with: + +$$ +A A \gtrsim L A \times (1 - R F). \tag {8} +$$ + +As indicated by Eq. 8, the lower bound of the final performance is proportional to $LA$ and $1 - RF$ , which suggests that both plasticity (LA) and stability (RF) play a crucial role in the final accuracy. Our findings reveal the importance of the model plasticity which was neglected in the past. And it can serve as a good guide for future online CL research. + +# 4. Proposed Method + +In this section, we first justify our motivations. Then, we introduce our proposed strategy: Collaborative Continual Learning and Distillation Chain. Finally, we show how to adapt our proposed strategy to the existing online CL methods and boost their plasticity. + +![](images/eed6f57ff3f3d25573b93d9645df16683c05d16c58b77fe782a34fc94c8d6270.jpg) +Figure 3. Conceptual diagram of the training framework, when distilling from an untrained network $\theta^2$ to suppress the confidence of network $\theta^1$ . + +
DatasetCIFAR-100
Memory Size MM=1000M=2000M=5000
ER24.47±0.7231.89±1.4539.41±1.81
ER + Untrained Distillation27.07±1.2034.84±0.6441.15±1.16
+ +Table 2. The performance of network $\theta^1$ when distilling from untrained network $\theta^2$ on CIFAR-100. All numbers are average over 10 runs. + +# 4.1. Motivation Justification + +Plasticity matters in Online CL. Online continual learners are designed to continuously adapt to non-stationary data streams, efficiently acquiring new knowledge while retaining previously learned information. In current online CL research, the emphasis has predominantly been on mitigating catastrophic forgetting. Even among state-of-the-art methods such as [19, 44], plasticity is often compromised in the quest for improved stability. However, our finding in Sec. 3 shows that both plasticity and stability are crucial for achieving satisfactory final performance, with plasticity proving particularly difficult to achieve in online CL settings. To this end, we deliberately prioritize the plasticity aspect. + +The potential of collaborative learning to improve convergence in non-continual scenarios [5] positions it as a promising candidate for enhancing plasticity. With the apparent lack of focus on plasticity, collaborative learning has yet to be leveraged to boost convergence of online continual learners. In our research, we propose to exploit collaborative learning convergence properties for improving plasticity. We find that similar to non-continual scenarios, collaborative learning strategy can boost convergence by allowing more parallelism in the training and more maneuverability of the continual learners. + +Overconfidence hurts Online CL. In conventional supervised learning, it is well established that excessive confidence can harm the generalization ability. To tackle this issue, many methods such as label smoothing [41], knowledge distillation [45], and confidence penalty [33] are pro + +posed. + +In online CL, we find a counter-intuitive, yet similar phenomenon. As shown in Fig. 3, while we train network $\theta^1$ with the classification loss, we initiate another network $\theta^2$ at the beginning of the training. During the continual training, we stagnate the network $\theta^2$ (i.e., Kaiming initialize and stay untrained) and train the network $\theta^1$ with both classification loss and the distillation loss (Kullback-Leibler divergence loss) from untrained network $\theta^2$ . The experimental result in Table 2 shows a decent performance gain compared with independent training. The distillation from the prediction of untrained network $\theta^2$ to network $\theta^1$ serves as a regularization to suppress the overall confidence, and the performance gain under this condition makes it evident that, in continual scenarios, overconfidence will also harm the performance. + +To tackle the overconfidence problem, we propose Distillation Chain (DC), an entropy regularizer to suppress the overall confidence level. + +# 4.2. Collaborative Continual Learning + +The introduced Collaborative Continual Learning (CCL) enables more parallelism and flexibility in training online continual learners, and it is the key to improving the model plasticity and the final performance. As shown in Fig. 2, CCL involves two peer continual learners of the same architecture and optimizer setting training in a peer-teaching manner. In the training phase, networks are supervised with both the ground truth label and the predictions of their peers. In the inference phase, models can either make predictions collaboratively with ensemble methods [5] to get a better performance or predict independently for the sake of computation efficiency. If we denote two networks in CCL as $\theta^1$ and $\theta^2$ , we formulate our loss to network $\theta^1$ as: + +$$ +\begin{array}{l} \mathcal {L} _ {C C L} ^ {1} = \lambda_ {1} \cdot \mathcal {L} _ {c l s} \left(\theta^ {1} (X), y\right) \\ + \lambda_ {2} \cdot D _ {K L} \left(\theta^ {1} (X) / \tau , \theta^ {2} (X) / \tau\right), \tag {9} \\ \end{array} +$$ + +where $(X,y)$ is the data-label pair, $\mathcal{L}_{cls}(\cdot)$ is the classification loss in the baseline method CCL adapts to, $D_{KL}(\cdot)$ is the Kullback-Leibler divergence, $\lambda_{1}$ and $\lambda_{2}$ are the balancing hyperparameters and $\tau$ is the temperature hyperparameter. Note that the network $\theta^2$ should be trained with $\mathcal{L}_{CCL}^2$ , respectively. + +# 4.3. Distillation Chain + +To fully take advantage of CCL, we propose Distillation Chain (DC), an entropy regularizaion based strategy explicitly designed for online CL. As illustrated in Fig. 2, DC comprises two steps: (1) generating a chain of samples with different levels of difficulty [40] using data augmentation, and (2) distillation of logit distribution from harder samples to easier samples in a collaborative learning way. + +As shown in Table 2, we observed that overconfidence will hurt the performance in continual training. To tackle + +Algorithm 1 PyTorch-like pseudo-code of CCL-DC to integrate to other baselines. +# model1: student model +# model2: teacher model +# optim1: optimizer for student model +# cls: classification loss in baseline +for x, y in dataloader: + # Baseline loss + loss基礎 = criterion基礎(model1, x, y) + # DC Augmentation + x1 = geometric_distortion(x) + x2 = RandAugment(x1, N, M) + x3 = RandAugment(x2, N, M) + # CCL-DC loss + ls, ls1, ls2, ls3 = model1(x, x1, x2, x3) + lt, lt1, lt2, lt3 = model2(x, x1, x2, x3) # no grad + loss_CLS = cls(ls, y) + cls(ls1, y) + cls(ls2, y) + + $\leftrightarrow$ cls(ls3, y) + loss_ccl = kl_div(ls/t, lt/t) # temperature t + loss_dC = kl_div(ls/t, lt1/t) + kl_div(ls1/t, lt2/t) + + $\leftrightarrow$ kl_div(ls2/t, lt3/t) + loss_ours = lam1*loss_CLS + lam2*(loss_ccl + loss_dC) + loss = loss基礎 + loss_ours + optim1.zero_grad() + loss.backup() + optim1.step() + +the problem, DC uses data augmentation strategies to generate samples with different levels of difficulty and produces logit distribution with different confidence. The distillation from less confident predictions to more confident predictions weakens the overall confidence of the network and benefits the performance by improving the generalization capability. + +In our work, we use a geometric distortion comprised of RandomCrop and RandomHorizontalFlip as the first step of DC augmentation. After that, we use RandAugment [12] for the subsequent augmentations and we involve two hyperparameters $N$ and $M$ for RandAugment. We take three augmentation steps and distill the logit distribution from the teacher with harder samples to the student with easier samples. We formulate our loss with DC to network $\theta^1$ as: + +$$ +\begin{array}{l} \mathcal {L} _ {D C} ^ {1} = \lambda_ {1} \sum_ {i = 1} ^ {3} \mathcal {L} _ {c l s} \left(\theta^ {1} \left(X _ {i}\right), y\right) \tag {10} \\ + \lambda_ {2} \sum_ {i = 1} ^ {3} D _ {K L} (\theta^ {1} (X _ {i - 1}) / \tau , \theta^ {2} (X _ {i}) / \tau), \\ \end{array} +$$ + +where $X_{i}$ is the augmentation of input sample $X$ after $i$ augmentation steps. + +# 4.4. Apply CCL-DC to online CL methods + +The overall loss to network $\theta^1$ when adapting CCL-DC can be written as: + +$$ +\mathcal {L} ^ {1} = \mathcal {L} _ {\text {B a s e l i n e}} + \mathcal {L} _ {C C L} ^ {1} + \mathcal {L} _ {D C} ^ {1}, \tag {11} +$$ + +
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER [35]56.68±1.8962.32±4.1324.47±0.7231.89±1.4539.41±1.8110.82±0.7919.16±1.4224.71±2.5233.30±1.74
ER + Ours66.43±2.4874.10±1.7133.43±1.0644.45±1.0453.81±1.1616.56±1.6329.39±1.2337.73±0.8543.11±1.49
DER++ [6]58.04±2.3064.02±1.9225.09±1.4132.33±2.6638.31±2.288.73±1.5817.95±2.4919.40±3.7134.75±2.23
DER++ + Ours68.79±1.4274.25±1.1034.36±0.8943.52±1.3552.95±0.8610.99±1.3921.68±1.9428.01±2.4645.70±1.32
ER-ACE [7]53.26±3.0459.94±2.4028.36±1.9934.21±1.5339.39±1.3113.56±1.0020.84±0.4325.92±1.0738.37±1.20
ER-ACE + Ours70.08±1.3875.56±1.1437.20±1.1545.14±1.0053.92±0.4818.32±1.4926.22±2.0132.23±1.7045.15±1.94
OCM [19]68.19±1.7573.15±1.0528.02±0.7435.69±1.3642.22±1.0618.36±0.9526.74±1.0231.94±1.1923.67±2.36
OCM + Ours74.14±0.8577.66±1.4635.00±1.1543.34±1.5151.43±1.3723.36±1.1833.17±0.9739.25±0.8843.19±0.98
GSA [20]60.34±1.9766.54±2.2827.72±1.5735.08±1.3741.41±1.6512.44±1.1719.59±1.3025.34±1.4341.03±0.99
GSA + Ours68.91±1.6875.78±1.1635.56±1.3944.74±1.3255.39±1.0916.70±1.6628.11±1.7037.13±1.7544.28±1.16
OnPro [44]70.47±2.1274.70±1.5127.22±0.7733.33±0.9341.59±1.3814.32±1.4021.13±2.1226.38±2.1838.75±1.03
OnPro + Ours74.49±2.1478.64±1.4234.76±1.1241.89±0.8250.01±0.8521.81±1.0232.00±0.7238.18±1.0247.93±1.26
+ +Table 3. Average Accuracy (\%, higher is better) on four benchmark datasets with difference memory buffer size $M$ , with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs. + +
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER83.13±1.6078.15±3.6053.77±1.5151.53±1.6650.79±0.7168.15±1.4764.99±1.2264.44±1.4553.95±1.51
ER + Ours90.60±1.5089.99±1.5072.38±0.6670.86±0.7268.84±1.0585.24±0.5381.75±0.8379.54±0.7468.73±1.21
DER++77.14±2.9678.00±2.1656.13±3.7555.33±3.2656.32±3.4470.01±1.8366.87±1.3070.28±2.4260.65±2.97
DER++ + Ours88.85±1.8889.00±1.6772.85±1.3771.54±1.9969.52±2.3782.83±1.2778.80±1.6277.79±0.8670.16±1.03
ER-ACE57.66±4.1661.59±3.3538.53±1.6139.95±2.0041.56±1.445.60±1.454.83±0.784.92±0.9549.82±1.05
ER-ACE + Ours88.37±1.3988.40±1.1569.47±0.8868.39±1.3266.63±0.9021.91±5.1621.88±4.3918.88±3.1268.52±0.82
OCM78.71±3.6681.33±2.0640.87±1.6042.00±1.4842.43±1.8018.56±2.8715.86±2.0115.03±2.0220.77±1.88
OCM + Ours82.39±2.2384.53±1.6348.89±2.0449.83±2.0149.94±2.1631.69±1.8129.54±2.3528.10±2.2848.20±1.38
GSA79.87±3.2677.09±4.5558.16±1.5855.13±1.8150.34±1.7320.46±1.5915.86±1.2614.50±0.6362.59±1.17
GSA + Ours91.69±1.1190.98±1.3373.73±1.0372.68±0.9870.36±1.0780.36±1.2274.77±1.6670.71±1.1973.71±1.12
OnPro84.23±2.0085.60±1.5641.34±1.6342.59±1.6542.92±1.0020.84±1.4716.73±1.2715.82±1.0439.60±0.86
OnPro + Ours90.39±1.5990.18±1.5846.30±1.1047.13±1.0147.27±1.8125.87±1.9121.40±1.5219.75±1.2252.55±2.18
+ +Table 4. Learning Accuracy (%, higher is better) on four benchmark datasets with difference memory buffer size $M$ , with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs. + +where $\mathcal{L}_{\text{Baseline}}$ is the loss function of the baseline model CCL-DC adapts to. Note that the model $\theta^2$ should be trained similarly. In Algorithm 1, we provide a Pytorch-like pseudo-code demonstrating how to incorporate CCLDC into a given baseline. For simplicity, we only show the loss function for model $\theta^1$ . Also, we omitted the memory buffer in the pseudo-code. However, the training should be consistent with the baseline, using both streaming and memory data. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. We use four image classification benchmark datasets to evaluate the effectiveness of our method, including CIFAR-10 [25], CIFAR-100 [25], TinyImageNet [26], and ImageNet-100 [11, 15, 22]. More detailed information + +about the dataset split and task allocation is given in the supplementary material. + +Baselines. To show the effectiveness of our strategy, we applied CCL-DC to six typical and state-of-the-art online CL methods, including ER [35], DER++ [6], ER-ACE [7], OCM [19], GSA [20], and OnPro [44]. + +Implementation details. We use full ResNet-18 [21] (not pre-trained) as the backbone for every method. For each baseline method, we perform a hyperparameter search on CIFAR-100, $M = 2\mathrm{k}$ , and apply the hyperparameter to all of the settings. For fair comparison, we use the same optimizer and hyperparameter setting when adapting CCL-DC to the baselines. For hyperparameters unique to CCL-DC, we conduct another hyperparameter search as stated in the supplementary material. We set the streaming batch size to 10 and the memory batch size to 64. We do not use the multiple update trick as described in [3]. More detailed in + +
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER31.63±3.8120.63±8.3255.71±2.2439.11±3.8723.05±3.6985.00±1.3071.62±2.1862.43±3.8339.26±3.21
ER + Ours26.74±3.9917.58±2.7154.34±2.2237.67±2.1621.98±2.5981.13±1.9364.79±1.3253.18±0.9937.78±2.18
DER++23.60±3.6417.71±2.1855.65±4.3641.27±4.9331.72±3.9587.79±2.3573.28±3.8872.51±5.5342.97±5.89
DER++ + Ours22.62±3.0316.43±3.3653.45±1.4039.39±2.7123.71±3.3987.16±1.6073.15±2.1564.48±3.0835.32±2.80
ER-ACE12.25±3.849.92±2.8325.88±4.1017.68±1.9010.62±2.0857.41±2.3844.48±1.9637.83±3.1223.92±2.05
ER-ACE + Ours20.62±2.2614.32±2.5846.78±1.9134.19±2.4019.01±0.9456.56±4.1642.20±3.9431.13±3.5234.43±3.60
OCM13.05±4.3711.00±3.1131.16±2.6917.90±3.736.85±2.2556.66±2.5340.59±1.5530.80±2.294.55±1.60
OCM + Ours10.75±2.528.45±2.6329.65±4.0017.02±3.016.16±1.3551.58±2.8135.58±2.5427.24±1.6015.33±2.28
GSA25.02±2.8316.56±4.0253.42±3.1237.29±2.6020.50±4.3366.87±3.3153.42±3.8443.44±3.8135.44±2.42
GSA + Ours24.96±3.2716.59±2.0952.29±2.0638.76±2.4121.36±2.3680.08±1.9763.85±1.7849.73±2.1040.46±2.54
OnPro16.47±4.2312.93±3.0235.03±4.4524.26±2.3112.04±2.1164.69±3.3650.47±4.2042.81±4.6314.44±2.08
OnPro + Ours17.54±4.1512.90±2.7727.64±3.2917.78±1.398.41±2.6256.03±2.9638.70±1.8829.24±1.3315.72±3.29
+ +formation about data augmentation, hyperparameter search, and hardware environments is given in the supplementary material. + +# 5.2. Results and Analysis + +Final average accuracy. Table 3 presents average accuracy (AA) at the end of the training on four datasets. As indicated in Sec. 4, to fully take advantage of collaborative learning, we show the results with the ensemble of two models, with the independent model performance available in the supplementary material. Generally, the ensemble method provides about $1\%$ additional accuracy compared to independent inference. For all datasets, memory size $M$ , and baseline methods, applying CCL-DC constantly improves the performance by a large margin. Notably, even for state-of-the-art methods such as GSA and OnPro, we can still gain significant performance when incorporating CCL-DC. + +More interestingly, for almost all settings with different memory buffer sizes $M$ , the performance gain tends to be a constant on a relative basis. For example, CCL-DC can boost the performance of ER on Tiny/ImageNet from 10.82 to 16.56 when $M = 2\mathrm{k}$ , which is a $53.0\%$ performance gain on a relative basis. The performance gain is $53.4\%$ and $52.7\%$ when $M = 5\mathrm{k}$ and $M = 10\mathrm{k}$ , respectively. This indicates that we can achieve a decent performance gain regardless of the memory buffer size, and it shows the scalability of our method to different resource conditions. + +Plasticity and stability metric. As mentioned in Sec. 3, we evaluate the plasticity and stability of different continual learners with LA and RF, respectively. Table 4 shows the plasticity metric on four datasets. For all settings, CCL-DC constantly improves the model plasticity by a large margin. For model stability, as indicated by RF in Table 5, mod + +Table 5. Relative Forgetting (%, lower is better) on four benchmark datasets with difference memory buffer size $M$ ,with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs. + +
MethodAcc. ↑LA ↑
ER31.89±1.4551.53±1.66
ER + Multivew38.18±1.4664.02±1.12
ER + Ours (CCL only)41.05±1.2168.76±0.79
ER + Ours44.45±1.0470.86±0.72
ER-ACE34.21±1.5339.95±2.00
ER-ACE + Multivew38.61±1.4847.45±1.88
ER-ACE + Ours (CCL only)40.90±1.0850.91±1.63
ER-ACE + Ours45.14±1.0068.39±1.32
+ +Table 6. Ablation studies on CIFAR-100 (M=2k). We report the ensemble performance for methods incorporating CCL. + +els trained with CCL-DC are comparable with the baselines under most cases. ER-ACE is an exception as its plasticity is unexpectedly low, especially on TinyImagenet. Also, the stability of ER-ACE is compromised when incorporating CCL-DC. We will explain the reason for this unexpected phenomenon in the supplementary material. + +# 5.3. Ablation Studies + +Effect of multiview learning. As mentioned in Sec. 4, CCL-DC benefits from multiview learning with data augmentation in DC. For fair comparison, we explore how multiview learning will impact the performance of the baselines. We apply the classification loss part of CCL-DC to the baselines. Table 6 demonstrates that multiview learning can improve both AA and LA of baselines. However, those performance gains are still inferior to CCL-DC. + +Effect of CCL. We evaluate how CCL alone can improve the baselines. In the experiments, we remove multiview learning and DC, and we train the continual learner pair with the loss illustrated in Eq. 9. Table 6 shows the performance gain for ER and ER-ACE. We can see that CCL alone can provide significant gains in both final accuracy and plasticity. Also, when combining CCL with DC, the + +
MethodDistillation schemeAcc. ↑LA ↑
EREasy to hard40.95±0.9760.03±0.98
ERSame difficulty43.64±1.0969.49±0.78
ERHard to easy (Ours)44.45±1.0470.86±0.72
ER-ACEEasy to hard38.46±1.5139.00±1.03
ER-ACESame difficulty43.81±1.2855.37±1.54
ER-ACEHard to easy (Ours)45.14±1.0068.39±1.32
+ +Table 7. Comparison of different distillation schemes in DC on CIFAR-100 (M=2k). + +
MethodDistillation schemeAcc. ↑LA ↑
ER + SDCEasy to hard35.00±1.3156.67±0.84
ER + SDCHard to easy41.31±1.2568.62±0.60
ER + CCL-DCEasy to hard40.95±0.9760.03±0.98
ER + CCL-DCHard to easy (Ours)44.45±1.0470.86±0.72
+ +Table 8. Final average accuracy when conducting multiview distillation within the same model on CIFAR-100 (M=2k). All values are averaged over 10 runs. + +performance can be further improved. + +Distillation scheme of DC. We also evaluate the effectiveness of DC's strategy of distilling from harder samples to easier samples in collaborative learning manner. As shown in Table 7, we compared it with other distillation strategies. The result shows that the distillation scheme of DC constantly outperforms other schemes. + +Self-Distillation Chain in an independent model. While DC was originally designed to incorporate CCL, it is possible to conduct DC's strategy within an independent model. We name such a strategy as the Self-Distillation Chain (SDC). Similar to different schemes of DC, SDC can be implemented in two ways: distillation from easier samples to harder samples, and distillation from harder samples to easier samples. As shown in Table 8, both strategy gives extra final performance and plasticity, while the latter strategy benefits the performance more. Moreover, incorporating DC with CCL (i.e., ours) further improves the accuracy. + +# 6. Discussions + +In this section, we analyze some properties of CCL-DC. + +Improving plasticity. One of the important advantages of CCL-DC is that it can improve the plasticity of continual learners. This can be evident by plasticity metrics like LA. Moreover, we have observed that the plasticity of CCL-DC facilitates the model to converge faster and descend to a deeper loss. Figure 4 illustrates the classification loss (cross-entropy) curve of the model. To obtain the loss curve, we take a snapshot of the model every 10 iterations and compute the cross-entropy over all the training samples on the current task. We plot the curve on the logarithm scale so that it is easy to observe that CCL-DC helps the model descend deeper at the end of each task. + +![](images/cc6e78fa9779260185745a5bce5135b3feda206577c5e0ad8bece680652272f1.jpg) + +![](images/d38af7bf7c93506edc2903772304a3813807ee0ad2100d466180d4e841895a08.jpg) +Figure 4. Classification loss curve of ER on CIFAR-100 $(\mathbf{M} = 2\mathbf{k})$ The curve is calculated on all training samples of the current task. Since there are 10 tasks in total, the curve has 10 peaks. +Figure 5. The entropy of prediction produced by ER with and without CCL-DC on CIFAR-100 $(\mathbf{M} = 2\mathbf{k})$ . $X_{i}$ represents the sample after $i$ -th augmentation in Eq. 10. The value is calculated at the end of the training and is averaged over all training samples. + +Alleviating overconfidence. To show the effect of DC in alleviating overconfidence, we compared the confidence of models trained with and without CCL-DC. We measure the confidence with the entropy of predictions. Fig. 5 shows the entropy of prediction produced by the ER (baseline) with and without CCL-DC on CIFAR-100 $(\mathrm{M} = 2\mathrm{k})$ . The entropy is calculated at the end of training and averaged across all samples in the training set. Moreover, we also calculate the entropy of models trained with CCL-DC, by forwarding images of different difficulties (from $X_0$ to $X_3$ in Eq. 10) in the augmentation chain. The experimental results show the effect of DC in suppressing overall confidence. + +# 7. Conclusion + +In this paper, we highlighted the significance of plasticity in online CL, which has been overlooked in prior research when compared to stability. We also established the quantitative link between plasticity, stability, and final accuracy. The quantitative relationship shed light on the future direction of online CL research. 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In NeurIPS, 2018. 2 \ No newline at end of file diff --git a/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/images.zip b/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..faa6ef982be1c86a5365332118b082eb3d492380 --- /dev/null +++ b/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f052880b0b1e4122a84d1fa3db2a20663478a8001cd3c682d2052978f2656825 +size 688242 diff --git a/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/layout.json b/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..9ade55fc25e1ce9c01865b1a15bbafa45635da86 --- /dev/null +++ b/2024/Improving Plasticity in Online Continual Learning via Collaborative Learning/layout.json @@ -0,0 +1,8290 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 56, + 103, + 538, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 103, + 538, + 121 + ], + "spans": [ + { + "bbox": [ + 56, + 103, + 538, + 121 + ], + "type": "text", + "content": "Improving Plasticity in Online Continual Learning via Collaborative Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 114, + 142, + 475, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 142, + 475, + 159 + ], + "spans": [ + { + "bbox": [ + 114, + 142, + 475, + 159 + ], + "type": "text", + "content": "Maorong Wang1 Nicolas Michel2 Ling Xiao1 Toshihiko Yamasaki1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 178, + 161, + 428, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 178, + 161, + 428, + 175 + ], + "spans": [ + { + "bbox": [ + 178, + 161, + 428, + 175 + ], + "type": "text", + "content": "The University of Tokyo 2Univ Gustave Eiffel, CNRS, LIGM" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 135, + 176, + 456, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 176, + 456, + 189 + ], + "spans": [ + { + "bbox": [ + 135, + 176, + 456, + 189 + ], + "type": "text", + "content": "{ma_wang, ling, yamasaki} @cvm.t.u-tokyo.ac.jp, nicolas.michel@univ-eiffel.fr" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 217, + 192, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 192, + 228 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 192, + 228 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 241, + 289, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 517 + ], + "type": "text", + "content": "Online Continual Learning (CL) solves the problem of learning the ever-emerging new classification tasks from a continuous data stream. Unlike its offline counterpart, in online CL, the training data can only be seen once. Most existing online CL research regards catastrophic forgetting (i.e., model stability) as almost the only challenge. In this paper, we argue that the model's capability to acquire new knowledge (i.e., model plasticity) is another challenge in online CL. While replay-based strategies have been shown to be effective in alleviating catastrophic forgetting, there is a notable gap in research attention toward improving model plasticity. To this end, we propose Collaborative Continual Learning (CCL), a collaborative learning based strategy to improve the model's capability in acquiring new concepts. Additionally, we introduce Distillation Chain (DC), a collaborative learning scheme to boost the training of the models. We adapt CCL-DC to existing representative online CL works. Extensive experiments demonstrate that even if the learners are well-trained with state-of-the-art online CL methods, our strategy can still improve model plasticity dramatically, and thereby improve the overall performance by a large margin. The source code of our work is available at https://github.com/maorong-wang/CCL-DC." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 538, + 128, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 128, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 128, + 550 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "Continual Learning (CL) [10, 13, 32, 43] aims to incrementally learn a sequence of tasks and enhance the neural network's performance on the current tasks, without forgetting previously learned knowledge. CL can be done in two different manners [4, 43]: offline and online. In offline CL, the learner can have infinite access to all the training data of the current task that it trains on and may go through the data for any epoch. Contrary to offline CL, in online CL, the training data for each task also comes continually in a data stream, and the learner can only see the training data once. Apart from the learning approach, there are also three different CL scenarios [23, 29, 42]: Task-Incremental Learning (TIL), Domain-Incremental Learning (DIL), and Class-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 217, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 217, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 545, + 240 + ], + "type": "text", + "content": "Incremental learning (CIL). In this paper, we focus on the CIL setting in online CL." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 243, + 546, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 546, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 546, + 542 + ], + "type": "text", + "content": "Various online CL methods [6, 7, 19, 20, 31, 35, 44] have been proposed to help the models learn continually on one-epoch data stream, with alleviated forgetting. Among them, replay-based methods have shown remarkable success, and current state-of-the-art methods rely heavily on memory replay to mitigate catastrophic forgetting [17, 30]. However, while most existing online CL research primarily only focuses on improving model stability (i.e., alleviating catastrophic forgetting) to achieve better overall accuracy, the importance of model plasticity (i.e., the capability to acquire new knowledge) is often overlooked. While in offline CL, it is possible to gain high plasticity by iterating several epochs on the current task before proceeding to the subsequent task, acquiring plasticity in online CL tends to be more challenging because the training data is only available once. As shown in Fig. 1, compared to learning without memory replay, the replay-based methods implicitly alleviate the low plasticity issue to some extent. Also, plasticity can be improved by employing a technique involving multiple updates on incoming samples [3]. However, the combination of memory replay and multiple updates fails to bridge the existing plasticity gap between online and offline CL, and the use of multiple updates can lead to increased catastrophic forgetting. Overall, the plasticity gap adversely affects the performance of online CL methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "type": "text", + "content": "In this paper, we argue that plasticity is particularly crucial and challenging to acquire in online CL, and even more so than in offline CL. Thus, we shed light on how model plasticity and stability will impact the overall performance. Furthermore, we propose a quantitative link between plasticity, stability, and final accuracy, showing that the plasticity gap between offline and online must be reduced to improve overall performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "Guided by the quantitative relationship, we focus ourselves on the previously overlooked plasticity perspective. Inspired by the ability of collaborative learning to accelerate the convergence in non-continual scenarios [5], we have incorporated collaborative learning in online CL and observed a similar phenomenon. Consequently, we pro" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23460" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 72, + 272, + 209 + ], + "blocks": [ + { + "bbox": [ + 60, + 72, + 272, + 209 + ], + "lines": [ + { + "bbox": [ + 60, + 72, + 272, + 209 + ], + "spans": [ + { + "bbox": [ + 60, + 72, + 272, + 209 + ], + "type": "image", + "image_path": "d949bc5c3e3fe341d6a7033f40a99163b0bcddf93c2dffa5ca2489ada7aeeda0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 287, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 289 + ], + "type": "text", + "content": "Figure 1. The comparison of plasticity (learning accuracy) and stability (relative forgetting, our metric proposed in Sec. 3) of Experience Replay (ER) [35] under various settings on CIFAR-100. For experiments with memory replay, the size of the memory buffer is set to 2,000. We can witness a plasticity gap between offline CL and online CL, even with memory replay and multiple update trick (memory iteration " + }, + { + "bbox": [ + 46, + 213, + 287, + 289 + ], + "type": "inline_equation", + "content": ">1" + }, + { + "bbox": [ + 46, + 213, + 287, + 289 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 307, + 286, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 286, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 286, + 366 + ], + "type": "text", + "content": "pose the Collaborative Continual Learning with Distillation Chain (CCL-DC), a collaborative learning scheme that can be adapted to existing online CL methods. CCL-DC consists of two key components: Collaborative Continual Learning (CCL) and Distillation Chain (DC)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 367, + 286, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 286, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 286, + 484 + ], + "type": "text", + "content": "CCL involves two peer continual learners to learn from the data stream simultaneously in a peer teaching manner, enhancing optimization parallelism and offering greater flexibility to the continual learners. To the best of our knowledge, CCL is the first method to incorporate collaborative learning techniques in online CL research. Moreover, to fully exploit the potential of collaborative learning in online CL scenarios, we propose DC, an entropy regularization based optimization strategy, specifically designed for online CL." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 487, + 286, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 286, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 286, + 510 + ], + "type": "text", + "content": "The main contribution of this paper can be summarized as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 513, + 286, + 654 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 513, + 286, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 286, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 286, + 570 + ], + "type": "text", + "content": "1. We establish a quantitative link between plasticity, stability, and final performance. Based on this, we demonstrate that plasticity is an important obstacle in online CL, which was greatly overlooked in the previous research:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 572, + 286, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 286, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 286, + 619 + ], + "type": "text", + "content": "2. To overcome the plasticity issue, we introduce CCL-DC, a collaborative learning based strategy that can be seamlessly integrated into the existing methods, significantly improving their performance by boosting plasticity;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 620, + 286, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 286, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 286, + 654 + ], + "type": "text", + "content": "3. Comprehensive experiments show that CCL-DC enhances the performance of existing methods by a large margin." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "Continual Learning. Continual learning can be classified into three different categories: regularization-" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "based, parameter-isolation-based, and replay-based. Regularization-based methods [2, 8, 24, 27, 46] add extra regularization terms to balance the old and new tasks. Parameter-isolation-based methods [1, 16, 36-38] solve the problem explicitly by dynamically allocating task-specific parameters. Replay-based methods [6, 7, 9, 14, 19, 20, 31, 35, 44] maintain a small memory buffer that stores a few old training samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 168, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 347 + ], + "type": "text", + "content": "Among these methods, replay-based strategies have gained huge success due to their impressive performance and simplicity. ER [35] is the fundamental replay-based method that leverages Cross-Entropy loss for classification and a random replay buffer. DER++ [6] stores the logits in the memory buffer and extends ER with the distillation of old stored logits. ER-ACE [7] extends ER with Asymmetric Cross-Entropy loss for classification to suppress the drift of old class representations. OCM [19] leverages a replay-based strategy by maximizing the mutual information between old and new class representations. GSA [20] solves cross-task class discrimination with replay-based strategy and Gradient Self Adaption. OnPro [44] uses online prototype learning to address shortcut learning and alleviate catastrophic forgetting." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 348, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 443 + ], + "type": "text", + "content": "These replay-based methods propose different strategies for alleviating catastrophic forgetting and improving the model stability. However, the importance of the model plasticity is greatly neglected in their research, despite their success in terms of final performance. In our work, these methods serve as the baselines and we adapted our strategy to these baselines to show the effectiveness of our proposed approach." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 450, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 616 + ], + "type": "text", + "content": "Collaborative Learning. Collaborative learning [5, 18, 39, 47, 48] originates from online knowledge distillation (KD). Different from the conventional KD methods, online KD involves training a cohort of deep networks from scratch in a peer-teaching manner. During the training process, the models imitate their peers and guides the training of other models simultaneously. Deep Mutual Learning (DML) [47] suggests peer student models learn from each other through the logit distillation between the probability distributions. Codistillation [5] is similar to DML and suggests the ensemble of peer networks can further improve the performance. More importantly, Codistillation shows that online KD can help the model converge faster on non-continual scenarios." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "Despite the success of collaborative learning in non-continual scenarios, due to the lack of focus on plasticity, the research on collaborative learning in CL is still limited. To the best of our knowledge, there is no existing research using the collaborative learning technique to boost the training of online CL. Moreover, in our work, we introduce the DC, an entropy regularization based optimization strategy, specifically tailored to fully leverage the potential of collab" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23461" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 70, + 509, + 230 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 509, + 230 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 509, + 230 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 509, + 230 + ], + "type": "image", + "image_path": "453e9be391aaceee9555fc6354adead2b195898fcfb52b5c4e7a27024397fb74.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 298 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed CCL-DC framework applied to a baseline online CL method. The proposed CCL-DC framework has two main components. The first one is CCL, which involves two peer continual learners that simultaneously learn from the data stream in a peer teaching manner. The second component, DC, generates a chain of samples with varying levels of difficulty and feeds them into models to produce a chain of logit distribution of different confidence levels. Then, in a collaborative learning approach, DC conducts distillation from less confident predictions to more confident predictions, to serve as a form of learned entropy regularization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 308, + 208, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 208, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 208, + 321 + ], + "type": "text", + "content": "orative learning in online CL scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 329, + 245, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 329, + 245, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 329, + 245, + 342 + ], + "type": "text", + "content": "3. Plasticity and Stability in online CL" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 288, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 288, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 288, + 398 + ], + "type": "text", + "content": "In this section, we revise the metric for model plasticity and propose a novel metric for model stability. In addition, we quantitatively analyze the impact of model plasticity and stability on the final performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 403, + 146, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 146, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 146, + 416 + ], + "type": "text", + "content": "3.1. Model Plasticity" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": "The model plasticity quantifies the learner's ability to learn new knowledge when a new task arrives. Several different metrics have been proposed to measure the model plasticity [8, 28, 34, 43]. In our work, we evaluate the model plasticity with Learning Accuracy (LA) [34]. Formally, the LA for the " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": "-th task is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 148, + 500, + 287, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 500, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 148, + 500, + 287, + 517 + ], + "type": "interline_equation", + "content": "l _ {j} = a _ {j} ^ {j}, \\tag {1}", + "image_path": "f91f02989a1a6dfcb26a1c127eeae37524432e6bfe2ece23bab4f5d6fe04e99e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "inline_equation", + "content": "a_{j}^{i}" + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "content": " is the accuracy evaluated on the test set of task " + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "content": " after training the network from task 1 to task " + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "content": ". For an overall metric normalized against all tasks, the averaged LA is written as " + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "inline_equation", + "content": "LA = \\frac{1}{T}\\sum_{j=1}^{T}l_{j}" + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 521, + 288, + 582 + ], + "type": "text", + "content": " is the number of tasks in total." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 587, + 143, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 143, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 143, + 601 + ], + "type": "text", + "content": "3.2. Model Stability" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "content": "The stability assesses the extent of knowledge retention or loss within a model in its present state. The most commonly used metric in previous CL research is the Forgetting Measure (FM) [8]. Intuitively, FM for the " + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "content": "-th task, denoted as " + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "inline_equation", + "content": "f m_{j}^{k}" + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "content": ", quantifies the decline in performance on a given task " + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "content": ", after the model is trained on task " + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "content": ", relative to its highest past performance on task " + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 606, + 287, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 695, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 695, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 86, + 695, + 287, + 715 + ], + "type": "interline_equation", + "content": "f m _ {j} ^ {k} = \\max _ {i \\in \\{1, \\dots , k - 1 \\}} \\left(a _ {j} ^ {i} - a _ {j} ^ {k}\\right), \\forall j < k. \\tag {2}", + "image_path": "ff2160ab4a44957d7834afb202b908a4fb8efc4f2a1ec39f9ea2649a267240d0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 308, + 304, + 544, + 365 + ], + "blocks": [ + { + "bbox": [ + 308, + 304, + 544, + 365 + ], + "lines": [ + { + "bbox": [ + 308, + 304, + 544, + 365 + ], + "spans": [ + { + "bbox": [ + 308, + 304, + 544, + 365 + ], + "type": "table", + "html": "
a ijT1T2T3T4T5FMkRFk
T130/15------
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", + "image_path": "b6b98e37bfda136f86bf97da3f1fb1aca874c3c7f9e378647cf955fb9187ed44.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "text", + "content": "Table 1. Forgetting Measure (\\%) and Relative Forgetting (\\%) of two example learners (Learner 1 in teal and Learner 2 in brown) in a continual setting of five tasks with two classes per task. Each element " + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "inline_equation", + "content": "a_{j}^{i}" + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "text", + "content": " at row " + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "text", + "content": " and column " + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "text", + "content": " is the per task accuracy evaluated on the test set of task " + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "text", + "content": " after training the network from task 1 to task " + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 365, + 547, + 432 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 440, + 546, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 440, + 546, + 464 + ], + "spans": [ + { + "bbox": [ + 305, + 440, + 546, + 464 + ], + "type": "text", + "content": "For the overall metric obtained across all tasks, FM can be expressed as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 373, + 473, + 545, + 508 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 473, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 373, + 473, + 545, + 508 + ], + "type": "interline_equation", + "content": "F M = \\frac {1}{T - 1} \\sum_ {j = 1} ^ {T - 1} f m _ {j} ^ {T}. \\tag {3}", + "image_path": "03849d18dc2900a926af3158165f98fe48981e914c5ba2e0a0c63a39e98c3877.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "type": "text", + "content": "In our work, we propose a novel stability metric, termed Relative Forgetting (RF), as an alternative to the traditional Forgetting Measure (FM). RF measures how much proportion of performance the model forgets. Specifically, RF for the " + }, + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "type": "text", + "content": "-th task after training on task " + }, + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 517, + 547, + 578 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 349, + 586, + 545, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 586, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 349, + 586, + 545, + 619 + ], + "type": "interline_equation", + "content": "f _ {j} ^ {k} = \\max _ {i \\in \\{1, \\dots , k \\}} \\left(1 - \\frac {a _ {j} ^ {k}}{a _ {j} ^ {i}}\\right), \\forall j \\leq k. \\tag {4}", + "image_path": "6c22c7dba496aac8fe21b3f91d02cf610c92500630a770bda11d6b22ec36ee6a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 628, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 545, + 650 + ], + "type": "text", + "content": "The overall metric averaged across all tasks can be written as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 389, + 651, + 545, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 651, + 545, + 684 + ], + "spans": [ + { + "bbox": [ + 389, + 651, + 545, + 684 + ], + "type": "interline_equation", + "content": "R F = \\frac {1}{T} \\sum_ {j = 1} ^ {T} f _ {j} ^ {T}. \\tag {5}", + "image_path": "658191bd3f607704583b8f40074d0a02e569baadfc57d489d62e7ffff99af2a0.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "There are two advantages for shifting from absolute forgetting to relative forgetting:" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23462" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 240 + ], + "type": "list", + "angle": 0, + "index": 2, + "blocks": [ + { + "bbox": [ + 48, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 289, + 179 + ], + "type": "text", + "content": "1. RF is fairer for methods with higher plasticity. As shown in Table 1, when comparing two continual learners, one with high plasticity and the other with low, using both forgetting metrics, it is observed that despite having identical RF values, the model with lower plasticity shows a lower FM. This indicates that the FM metric might unfairly favor models with poorer initial performance, even when the relative decline in performance is equivalent across models;" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 180, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 180, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 287, + 240 + ], + "type": "text", + "content": "2. RF facilitates a quantitative analysis of the relationship between model stability and final performance. This enables a more nuanced understanding of how stability influences overall model efficacy, thereby guiding improvements in continual learning strategies." + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 247, + 237, + 260 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 237, + 260 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 237, + 260 + ], + "type": "text", + "content": "3.3. Impact on the Overall Performance" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 265, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 287, + 312 + ], + "type": "text", + "content": "For online CL, the model's final average accuracy (AA) is the most vital metric. In this subsection, we try to show how the model plasticity and stability will impact the final performance quantitatively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 312, + 286, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 312, + 286, + 325 + ], + "spans": [ + { + "bbox": [ + 59, + 312, + 286, + 325 + ], + "type": "text", + "content": "The model's final average accuracy can be calculated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 130, + 333, + 287, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 333, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 130, + 333, + 287, + 367 + ], + "type": "interline_equation", + "content": "A A = \\frac {1}{T} \\sum_ {j = 1} ^ {T} a _ {j} ^ {T}. \\tag {6}", + "image_path": "3ac06ff887cce1bd6e66b57413e4ee01050e36cf33b16c80d620ac8a01b0d1cf.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 370, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 287, + 407 + ], + "type": "text", + "content": "With the establishment of our plasticity metric (LA) and stability metric (RF), we can easily find the relationship between learning accuracy, relative forgetting, and accuracy:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 125, + 417, + 287, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 417, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 125, + 417, + 287, + 433 + ], + "type": "interline_equation", + "content": "a _ {j} ^ {i} \\geq l _ {j} \\times \\left(1 - f _ {j} ^ {i}\\right), \\tag {7}", + "image_path": "42e9486b686ebe9f8799ab0dcd9cee401cab5f2fa7cb20164774148e54c6b9c3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "content": "assuming equality when " + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "a_{j}^{j} = \\max_{i\\in \\{1,\\dots ,j\\}}a_{j}^{i}" + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "content": ". When extending the class-specific final accuracy " + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "a_{j}^{T}" + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "content": " to the final AA, we consider the dot product of the LA vector " + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "[l_1,\\dots,l_T]" + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "content": " with the RF vector " + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "[f_1^T,\\dots,f_T^T]" + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "content": ", which simplifies the calculation. More practically, this relationship can be approximated with:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 116, + 522, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 522, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 116, + 522, + 287, + 536 + ], + "type": "interline_equation", + "content": "A A \\gtrsim L A \\times (1 - R F). \\tag {8}", + "image_path": "10e059f6fb6235f9b793ed81747023e44609d1d27f2530340c3145b3f332959c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "type": "text", + "content": "As indicated by Eq. 8, the lower bound of the final performance is proportional to " + }, + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "LA" + }, + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "1 - RF" + }, + { + "bbox": [ + 47, + 540, + 287, + 624 + ], + "type": "text", + "content": ", which suggests that both plasticity (LA) and stability (RF) play a crucial role in the final accuracy. Our findings reveal the importance of the model plasticity which was neglected in the past. And it can serve as a good guide for future online CL research." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 634, + 153, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 153, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 153, + 647 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": "In this section, we first justify our motivations. Then, we introduce our proposed strategy: Collaborative Continual Learning and Distillation Chain. Finally, we show how to adapt our proposed strategy to the existing online CL methods and boost their plasticity." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 322, + 70, + 531, + 213 + ], + "blocks": [ + { + "bbox": [ + 322, + 70, + 531, + 213 + ], + "lines": [ + { + "bbox": [ + 322, + 70, + 531, + 213 + ], + "spans": [ + { + "bbox": [ + 322, + 70, + 531, + 213 + ], + "type": "image", + "image_path": "eed6f57ff3f3d25573b93d9645df16683c05d16c58b77fe782a34fc94c8d6270.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "type": "text", + "content": "Figure 3. Conceptual diagram of the training framework, when distilling from an untrained network " + }, + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "type": "text", + "content": " to suppress the confidence of network " + }, + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 305, + 215, + 545, + 247 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 319, + 249, + 529, + 297 + ], + "blocks": [ + { + "bbox": [ + 319, + 249, + 529, + 297 + ], + "lines": [ + { + "bbox": [ + 319, + 249, + 529, + 297 + ], + "spans": [ + { + "bbox": [ + 319, + 249, + 529, + 297 + ], + "type": "table", + "html": "
DatasetCIFAR-100
Memory Size MM=1000M=2000M=5000
ER24.47±0.7231.89±1.4539.41±1.81
ER + Untrained Distillation27.07±1.2034.84±0.6441.15±1.16
", + "image_path": "83d1461421d08eccb68f012c4cd192e5f660517dad4ba075083b42cc784439a3.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "lines": [ + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "type": "text", + "content": "Table 2. The performance of network " + }, + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "type": "text", + "content": " when distilling from untrained network " + }, + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 306, + 300, + 545, + 332 + ], + "type": "text", + "content": " on CIFAR-100. All numbers are average over 10 runs." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 341, + 440, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 341, + 440, + 353 + ], + "spans": [ + { + "bbox": [ + 306, + 341, + 440, + 353 + ], + "type": "text", + "content": "4.1. Motivation Justification" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 359, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 545, + 514 + ], + "type": "text", + "content": "Plasticity matters in Online CL. Online continual learners are designed to continuously adapt to non-stationary data streams, efficiently acquiring new knowledge while retaining previously learned information. In current online CL research, the emphasis has predominantly been on mitigating catastrophic forgetting. Even among state-of-the-art methods such as [19, 44], plasticity is often compromised in the quest for improved stability. However, our finding in Sec. 3 shows that both plasticity and stability are crucial for achieving satisfactory final performance, with plasticity proving particularly difficult to achieve in online CL settings. To this end, we deliberately prioritize the plasticity aspect." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 516, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 647 + ], + "type": "text", + "content": "The potential of collaborative learning to improve convergence in non-continual scenarios [5] positions it as a promising candidate for enhancing plasticity. With the apparent lack of focus on plasticity, collaborative learning has yet to be leveraged to boost convergence of online continual learners. In our research, we propose to exploit collaborative learning convergence properties for improving plasticity. We find that similar to non-continual scenarios, collaborative learning strategy can boost convergence by allowing more parallelism in the training and more maneuverability of the continual learners." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "Overconfidence hurts Online CL. In conventional supervised learning, it is well established that excessive confidence can harm the generalization ability. To tackle this issue, many methods such as label smoothing [41], knowledge distillation [45], and confidence penalty [33] are pro" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23463" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 73, + 75, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 73, + 75, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 73, + 75, + 83 + ], + "type": "text", + "content": "posed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": "In online CL, we find a counter-intuitive, yet similar phenomenon. As shown in Fig. 3, while we train network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": " with the classification loss, we initiate another network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": " at the beginning of the training. During the continual training, we stagnate the network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": " (i.e., Kaiming initialize and stay untrained) and train the network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": " with both classification loss and the distillation loss (Kullback-Leibler divergence loss) from untrained network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": ". The experimental result in Table 2 shows a decent performance gain compared with independent training. The distillation from the prediction of untrained network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": " to network " + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 46, + 84, + 287, + 251 + ], + "type": "text", + "content": " serves as a regularization to suppress the overall confidence, and the performance gain under this condition makes it evident that, in continual scenarios, overconfidence will also harm the performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 287 + ], + "type": "text", + "content": "To tackle the overconfidence problem, we propose Distillation Chain (DC), an entropy regularizer to suppress the overall confidence level." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 293, + 230, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 230, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 230, + 306 + ], + "type": "text", + "content": "4.2. Collaborative Continual Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "text", + "content": "The introduced Collaborative Continual Learning (CCL) enables more parallelism and flexibility in training online continual learners, and it is the key to improving the model plasticity and the final performance. As shown in Fig. 2, CCL involves two peer continual learners of the same architecture and optimizer setting training in a peer-teaching manner. In the training phase, networks are supervised with both the ground truth label and the predictions of their peers. In the inference phase, models can either make predictions collaboratively with ensemble methods [5] to get a better performance or predict independently for the sake of computation efficiency. If we denote two networks in CCL as " + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "text", + "content": ", we formulate our loss to network " + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 46, + 312, + 288, + 468 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 84, + 472, + 287, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 472, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 84, + 472, + 287, + 503 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {C C L} ^ {1} = \\lambda_ {1} \\cdot \\mathcal {L} _ {c l s} \\left(\\theta^ {1} (X), y\\right) \\\\ + \\lambda_ {2} \\cdot D _ {K L} \\left(\\theta^ {1} (X) / \\tau , \\theta^ {2} (X) / \\tau\\right), \\tag {9} \\\\ \\end{array}", + "image_path": "bcc0af6cf0d6172221d1e3a48d38aa6ab106b2d4aca8c68df1fc8279bd1f3a90.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "(X,y)" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " is the data-label pair, " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}(\\cdot)" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " is the classification loss in the baseline method CCL adapts to, " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "D_{KL}(\\cdot)" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " is the Kullback-Leibler divergence, " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " are the balancing hyperparameters and " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " is the temperature hyperparameter. Note that the network " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": " should be trained with " + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CCL}^2" + }, + { + "bbox": [ + 46, + 509, + 287, + 581 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 153, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 153, + 599 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 153, + 599 + ], + "type": "text", + "content": "4.3. Distillation Chain" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": "To fully take advantage of CCL, we propose Distillation Chain (DC), an entropy regularizaion based strategy explicitly designed for online CL. As illustrated in Fig. 2, DC comprises two steps: (1) generating a chain of samples with different levels of difficulty [40] using data augmentation, and (2) distillation of logit distribution from harder samples to easier samples in a collaborative learning way." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "As shown in Table 2, we observed that overconfidence will hurt the performance in continual training. To tackle" + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 306, + 97, + 545, + 339 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "type": "text", + "content": "Algorithm 1 PyTorch-like pseudo-code of CCL-DC to integrate to other baselines." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "type": "text", + "content": "# model1: student model\n# model2: teacher model\n# optim1: optimizer for student model\n# cls: classification loss in baseline\nfor x, y in dataloader:\n # Baseline loss\n loss基礎 = criterion基礎(model1, x, y)\n # DC Augmentation\n x1 = geometric_distortion(x)\n x2 = RandAugment(x1, N, M)\n x3 = RandAugment(x2, N, M)\n # CCL-DC loss\n ls, ls1, ls2, ls3 = model1(x, x1, x2, x3)\n lt, lt1, lt2, lt3 = model2(x, x1, x2, x3) # no grad\n loss_CLS = cls(ls, y) + cls(ls1, y) + cls(ls2, y) +\n " + }, + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "type": "text", + "content": " cls(ls3, y)\n loss_ccl = kl_div(ls/t, lt/t) # temperature t\n loss_dC = kl_div(ls/t, lt1/t) + kl_div(ls1/t, lt2/t) +\n " + }, + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 306, + 97, + 545, + 339 + ], + "type": "text", + "content": " kl_div(ls2/t, lt3/t)\n loss_ours = lam1*loss_CLS + lam2*(loss_ccl + loss_dC)\n loss = loss基礎 + loss_ours\n optim1.zero_grad()\n loss.backup()\n optim1.step()" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 359, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 545, + 442 + ], + "type": "text", + "content": "the problem, DC uses data augmentation strategies to generate samples with different levels of difficulty and produces logit distribution with different confidence. The distillation from less confident predictions to more confident predictions weakens the overall confidence of the network and benefits the performance by improving the generalization capability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "text", + "content": "In our work, we use a geometric distortion comprised of RandomCrop and RandomHorizontalFlip as the first step of DC augmentation. After that, we use RandAugment [12] for the subsequent augmentations and we involve two hyperparameters " + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "text", + "content": " for RandAugment. We take three augmentation steps and distill the logit distribution from the teacher with harder samples to the student with easier samples. We formulate our loss with DC to network " + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 304, + 443, + 546, + 538 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 324, + 546, + 545, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 546, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 324, + 546, + 545, + 613 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {D C} ^ {1} = \\lambda_ {1} \\sum_ {i = 1} ^ {3} \\mathcal {L} _ {c l s} \\left(\\theta^ {1} \\left(X _ {i}\\right), y\\right) \\tag {10} \\\\ + \\lambda_ {2} \\sum_ {i = 1} ^ {3} D _ {K L} (\\theta^ {1} (X _ {i - 1}) / \\tau , \\theta^ {2} (X _ {i}) / \\tau), \\\\ \\end{array}", + "image_path": "da44e02f5cfadaa2f3fb9c3cf3fd6a7e8cda9d49c12ca9a10157b0ec0461a51d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "text", + "content": " is the augmentation of input sample " + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "text", + "content": " after " + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 620, + 545, + 646 + ], + "type": "text", + "content": " augmentation steps." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 650, + 506, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 650, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 305, + 650, + 506, + 662 + ], + "type": "text", + "content": "4.4. Apply CCL-DC to online CL methods" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 668, + 545, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 668, + 545, + 690 + ], + "spans": [ + { + "bbox": [ + 304, + 668, + 545, + 690 + ], + "type": "text", + "content": "The overall loss to network " + }, + { + "bbox": [ + 304, + 668, + 545, + 690 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 304, + 668, + 545, + 690 + ], + "type": "text", + "content": " when adapting CCL-DC can be written as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 355, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 355, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {1} = \\mathcal {L} _ {\\text {B a s e l i n e}} + \\mathcal {L} _ {C C L} ^ {1} + \\mathcal {L} _ {D C} ^ {1}, \\tag {11}", + "image_path": "1e7453bded2e17757eec8105e51fd44f475a56839a5950c66591e6fd600f1cbf.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23464" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 541, + 256 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 541, + 256 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 541, + 256 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 541, + 256 + ], + "type": "table", + "html": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER [35]56.68±1.8962.32±4.1324.47±0.7231.89±1.4539.41±1.8110.82±0.7919.16±1.4224.71±2.5233.30±1.74
ER + Ours66.43±2.4874.10±1.7133.43±1.0644.45±1.0453.81±1.1616.56±1.6329.39±1.2337.73±0.8543.11±1.49
DER++ [6]58.04±2.3064.02±1.9225.09±1.4132.33±2.6638.31±2.288.73±1.5817.95±2.4919.40±3.7134.75±2.23
DER++ + Ours68.79±1.4274.25±1.1034.36±0.8943.52±1.3552.95±0.8610.99±1.3921.68±1.9428.01±2.4645.70±1.32
ER-ACE [7]53.26±3.0459.94±2.4028.36±1.9934.21±1.5339.39±1.3113.56±1.0020.84±0.4325.92±1.0738.37±1.20
ER-ACE + Ours70.08±1.3875.56±1.1437.20±1.1545.14±1.0053.92±0.4818.32±1.4926.22±2.0132.23±1.7045.15±1.94
OCM [19]68.19±1.7573.15±1.0528.02±0.7435.69±1.3642.22±1.0618.36±0.9526.74±1.0231.94±1.1923.67±2.36
OCM + Ours74.14±0.8577.66±1.4635.00±1.1543.34±1.5151.43±1.3723.36±1.1833.17±0.9739.25±0.8843.19±0.98
GSA [20]60.34±1.9766.54±2.2827.72±1.5735.08±1.3741.41±1.6512.44±1.1719.59±1.3025.34±1.4341.03±0.99
GSA + Ours68.91±1.6875.78±1.1635.56±1.3944.74±1.3255.39±1.0916.70±1.6628.11±1.7037.13±1.7544.28±1.16
OnPro [44]70.47±2.1274.70±1.5127.22±0.7733.33±0.9341.59±1.3814.32±1.4021.13±2.1226.38±2.1838.75±1.03
OnPro + Ours74.49±2.1478.64±1.4234.76±1.1241.89±0.8250.01±0.8521.81±1.0232.00±0.7238.18±1.0247.93±1.26
", + "image_path": "99f71e98e90c5ab3b3a286de78feb2807a3d187b2e4350a280810313a9e148d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 283, + 541, + 469 + ], + "blocks": [ + { + "bbox": [ + 47, + 258, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 47, + 258, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 545, + 280 + ], + "type": "text", + "content": "Table 3. Average Accuracy (\\%, higher is better) on four benchmark datasets with difference memory buffer size " + }, + { + "bbox": [ + 47, + 258, + 545, + 280 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 258, + 545, + 280 + ], + "type": "text", + "content": ", with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 283, + 541, + 469 + ], + "lines": [ + { + "bbox": [ + 49, + 283, + 541, + 469 + ], + "spans": [ + { + "bbox": [ + 49, + 283, + 541, + 469 + ], + "type": "table", + "html": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER83.13±1.6078.15±3.6053.77±1.5151.53±1.6650.79±0.7168.15±1.4764.99±1.2264.44±1.4553.95±1.51
ER + Ours90.60±1.5089.99±1.5072.38±0.6670.86±0.7268.84±1.0585.24±0.5381.75±0.8379.54±0.7468.73±1.21
DER++77.14±2.9678.00±2.1656.13±3.7555.33±3.2656.32±3.4470.01±1.8366.87±1.3070.28±2.4260.65±2.97
DER++ + Ours88.85±1.8889.00±1.6772.85±1.3771.54±1.9969.52±2.3782.83±1.2778.80±1.6277.79±0.8670.16±1.03
ER-ACE57.66±4.1661.59±3.3538.53±1.6139.95±2.0041.56±1.445.60±1.454.83±0.784.92±0.9549.82±1.05
ER-ACE + Ours88.37±1.3988.40±1.1569.47±0.8868.39±1.3266.63±0.9021.91±5.1621.88±4.3918.88±3.1268.52±0.82
OCM78.71±3.6681.33±2.0640.87±1.6042.00±1.4842.43±1.8018.56±2.8715.86±2.0115.03±2.0220.77±1.88
OCM + Ours82.39±2.2384.53±1.6348.89±2.0449.83±2.0149.94±2.1631.69±1.8129.54±2.3528.10±2.2848.20±1.38
GSA79.87±3.2677.09±4.5558.16±1.5855.13±1.8150.34±1.7320.46±1.5915.86±1.2614.50±0.6362.59±1.17
GSA + Ours91.69±1.1190.98±1.3373.73±1.0372.68±0.9870.36±1.0780.36±1.2274.77±1.6670.71±1.1973.71±1.12
OnPro84.23±2.0085.60±1.5641.34±1.6342.59±1.6542.92±1.0020.84±1.4716.73±1.2715.82±1.0439.60±0.86
OnPro + Ours90.39±1.5990.18±1.5846.30±1.1047.13±1.0147.27±1.8125.87±1.9121.40±1.5219.75±1.2252.55±2.18
", + "image_path": "8ccdafce771356fd5e6302b4c632ea056d9ae8f6e822b1073dcd9ad38a7225a0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 471, + 545, + 493 + ], + "lines": [ + { + "bbox": [ + 46, + 471, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 545, + 493 + ], + "type": "text", + "content": "Table 4. Learning Accuracy (%, higher is better) on four benchmark datasets with difference memory buffer size " + }, + { + "bbox": [ + 46, + 471, + 545, + 493 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 471, + 545, + 493 + ], + "type": "text", + "content": ", with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{Baseline}}" + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "text", + "content": " is the loss function of the baseline model CCL-DC adapts to. Note that the model " + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\theta^2" + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "text", + "content": " should be trained similarly. In Algorithm 1, we provide a Pytorch-like pseudo-code demonstrating how to incorporate CCLDC into a given baseline. For simplicity, we only show the loss function for model " + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\theta^1" + }, + { + "bbox": [ + 46, + 500, + 287, + 608 + ], + "type": "text", + "content": ". Also, we omitted the memory buffer in the pseudo-code. However, the training should be consistent with the baseline, using both streaming and memory data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 624, + 127, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 127, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 127, + 637 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 645, + 163, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 163, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 163, + 658 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Datasets. We use four image classification benchmark datasets to evaluate the effectiveness of our method, including CIFAR-10 [25], CIFAR-100 [25], TinyImageNet [26], and ImageNet-100 [11, 15, 22]. More detailed information" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 500, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 500, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 500, + 545, + 525 + ], + "type": "text", + "content": "about the dataset split and task allocation is given in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 529, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 529, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 305, + 529, + 545, + 578 + ], + "type": "text", + "content": "Baselines. To show the effectiveness of our strategy, we applied CCL-DC to six typical and state-of-the-art online CL methods, including ER [35], DER++ [6], ER-ACE [7], OCM [19], GSA [20], and OnPro [44]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. We use full ResNet-18 [21] (not pre-trained) as the backbone for every method. For each baseline method, we perform a hyperparameter search on CIFAR-100, " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "M = 2\\mathrm{k}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ", and apply the hyperparameter to all of the settings. For fair comparison, we use the same optimizer and hyperparameter setting when adapting CCL-DC to the baselines. For hyperparameters unique to CCL-DC, we conduct another hyperparameter search as stated in the supplementary material. We set the streaming batch size to 10 and the memory batch size to 64. We do not use the multiple update trick as described in [3]. More detailed in" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23465" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 542, + 256 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 542, + 256 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 542, + 256 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 542, + 256 + ], + "type": "table", + "html": "
DatasetCIFAR10CIFAR100Tiny-ImageNetImageNet-100
Memory Size M500100010002000500020005000100005000
ER31.63±3.8120.63±8.3255.71±2.2439.11±3.8723.05±3.6985.00±1.3071.62±2.1862.43±3.8339.26±3.21
ER + Ours26.74±3.9917.58±2.7154.34±2.2237.67±2.1621.98±2.5981.13±1.9364.79±1.3253.18±0.9937.78±2.18
DER++23.60±3.6417.71±2.1855.65±4.3641.27±4.9331.72±3.9587.79±2.3573.28±3.8872.51±5.5342.97±5.89
DER++ + Ours22.62±3.0316.43±3.3653.45±1.4039.39±2.7123.71±3.3987.16±1.6073.15±2.1564.48±3.0835.32±2.80
ER-ACE12.25±3.849.92±2.8325.88±4.1017.68±1.9010.62±2.0857.41±2.3844.48±1.9637.83±3.1223.92±2.05
ER-ACE + Ours20.62±2.2614.32±2.5846.78±1.9134.19±2.4019.01±0.9456.56±4.1642.20±3.9431.13±3.5234.43±3.60
OCM13.05±4.3711.00±3.1131.16±2.6917.90±3.736.85±2.2556.66±2.5340.59±1.5530.80±2.294.55±1.60
OCM + Ours10.75±2.528.45±2.6329.65±4.0017.02±3.016.16±1.3551.58±2.8135.58±2.5427.24±1.6015.33±2.28
GSA25.02±2.8316.56±4.0253.42±3.1237.29±2.6020.50±4.3366.87±3.3153.42±3.8443.44±3.8135.44±2.42
GSA + Ours24.96±3.2716.59±2.0952.29±2.0638.76±2.4121.36±2.3680.08±1.9763.85±1.7849.73±2.1040.46±2.54
OnPro16.47±4.2312.93±3.0235.03±4.4524.26±2.3112.04±2.1164.69±3.3650.47±4.2042.81±4.6314.44±2.08
OnPro + Ours17.54±4.1512.90±2.7727.64±3.2917.78±1.398.41±2.6256.03±2.9638.70±1.8829.24±1.3315.72±3.29
", + "image_path": "adc897516da34b929a8c3e481f18df748ab934f6dec23688a2eaf01e48b391ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 332 + ], + "type": "text", + "content": "formation about data augmentation, hyperparameter search, and hardware environments is given in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 341, + 167, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 167, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 167, + 354 + ], + "type": "text", + "content": "5.2. Results and Analysis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "type": "text", + "content": "Final average accuracy. Table 3 presents average accuracy (AA) at the end of the training on four datasets. As indicated in Sec. 4, to fully take advantage of collaborative learning, we show the results with the ensemble of two models, with the independent model performance available in the supplementary material. Generally, the ensemble method provides about " + }, + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "type": "text", + "content": " additional accuracy compared to independent inference. For all datasets, memory size " + }, + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 360, + 287, + 514 + ], + "type": "text", + "content": ", and baseline methods, applying CCL-DC constantly improves the performance by a large margin. Notably, even for state-of-the-art methods such as GSA and OnPro, we can still gain significant performance when incorporating CCL-DC." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": "More interestingly, for almost all settings with different memory buffer sizes " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": ", the performance gain tends to be a constant on a relative basis. For example, CCL-DC can boost the performance of ER on Tiny/ImageNet from 10.82 to 16.56 when " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "M = 2\\mathrm{k}" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": ", which is a " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "53.0\\%" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": " performance gain on a relative basis. The performance gain is " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "53.4\\%" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "52.7\\%" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "M = 5\\mathrm{k}" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "inline_equation", + "content": "M = 10\\mathrm{k}" + }, + { + "bbox": [ + 46, + 516, + 288, + 635 + ], + "type": "text", + "content": ", respectively. This indicates that we can achieve a decent performance gain regardless of the memory buffer size, and it shows the scalability of our method to different resource conditions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "Plasticity and stability metric. As mentioned in Sec. 3, we evaluate the plasticity and stability of different continual learners with LA and RF, respectively. Table 4 shows the plasticity metric on four datasets. For all settings, CCL-DC constantly improves the model plasticity by a large margin. For model stability, as indicated by RF in Table 5, mod" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 338, + 294, + 513, + 391 + ], + "blocks": [ + { + "bbox": [ + 46, + 261, + 546, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 546, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 546, + 285 + ], + "type": "text", + "content": "Table 5. Relative Forgetting (%, lower is better) on four benchmark datasets with difference memory buffer size " + }, + { + "bbox": [ + 46, + 261, + 546, + 285 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 261, + 546, + 285 + ], + "type": "text", + "content": " ,with and without our proposed CCL-DC scheme. The result of our method is given by the ensemble of two peer models. All values are averages of 10 runs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 338, + 294, + 513, + 391 + ], + "lines": [ + { + "bbox": [ + 338, + 294, + 513, + 391 + ], + "spans": [ + { + "bbox": [ + 338, + 294, + 513, + 391 + ], + "type": "table", + "html": "
MethodAcc. ↑LA ↑
ER31.89±1.4551.53±1.66
ER + Multivew38.18±1.4664.02±1.12
ER + Ours (CCL only)41.05±1.2168.76±0.79
ER + Ours44.45±1.0470.86±0.72
ER-ACE34.21±1.5339.95±2.00
ER-ACE + Multivew38.61±1.4847.45±1.88
ER-ACE + Ours (CCL only)40.90±1.0850.91±1.63
ER-ACE + Ours45.14±1.0068.39±1.32
", + "image_path": "ba4f950c0c829a895ab1f7a85bc9a6b89b6d2879f70b24fe444dcff09aba5aa3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 399, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 422 + ], + "type": "text", + "content": "Table 6. Ablation studies on CIFAR-100 (M=2k). We report the ensemble performance for methods incorporating CCL." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 430, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 502 + ], + "type": "text", + "content": "els trained with CCL-DC are comparable with the baselines under most cases. ER-ACE is an exception as its plasticity is unexpectedly low, especially on TinyImagenet. Also, the stability of ER-ACE is compromised when incorporating CCL-DC. We will explain the reason for this unexpected phenomenon in the supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 510, + 406, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 406, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 406, + 521 + ], + "type": "text", + "content": "5.3. Ablation Studies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": "Effect of multiview learning. As mentioned in Sec. 4, CCL-DC benefits from multiview learning with data augmentation in DC. For fair comparison, we explore how multiview learning will impact the performance of the baselines. We apply the classification loss part of CCL-DC to the baselines. Table 6 demonstrates that multiview learning can improve both AA and LA of baselines. However, those performance gains are still inferior to CCL-DC." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": "Effect of CCL. We evaluate how CCL alone can improve the baselines. In the experiments, we remove multiview learning and DC, and we train the continual learner pair with the loss illustrated in Eq. 9. Table 6 shows the performance gain for ER and ER-ACE. We can see that CCL alone can provide significant gains in both final accuracy and plasticity. Also, when combining CCL with DC, the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23466" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 260, + 148 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 260, + 148 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 260, + 148 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 260, + 148 + ], + "type": "table", + "html": "
MethodDistillation schemeAcc. ↑LA ↑
EREasy to hard40.95±0.9760.03±0.98
ERSame difficulty43.64±1.0969.49±0.78
ERHard to easy (Ours)44.45±1.0470.86±0.72
ER-ACEEasy to hard38.46±1.5139.00±1.03
ER-ACESame difficulty43.81±1.2855.37±1.54
ER-ACEHard to easy (Ours)45.14±1.0068.39±1.32
", + "image_path": "2dc5e8536654b407d7e434f449dc76265a070105e6be1973d55078dee1deca8a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 64, + 183, + 269, + 244 + ], + "blocks": [ + { + "bbox": [ + 47, + 157, + 287, + 178 + ], + "lines": [ + { + "bbox": [ + 47, + 157, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 157, + 287, + 178 + ], + "type": "text", + "content": "Table 7. Comparison of different distillation schemes in DC on CIFAR-100 (M=2k)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 64, + 183, + 269, + 244 + ], + "lines": [ + { + "bbox": [ + 64, + 183, + 269, + 244 + ], + "spans": [ + { + "bbox": [ + 64, + 183, + 269, + 244 + ], + "type": "table", + "html": "
MethodDistillation schemeAcc. ↑LA ↑
ER + SDCEasy to hard35.00±1.3156.67±0.84
ER + SDCHard to easy41.31±1.2568.62±0.60
ER + CCL-DCEasy to hard40.95±0.9760.03±0.98
ER + CCL-DCHard to easy (Ours)44.45±1.0470.86±0.72
", + "image_path": "20eab53c9faa6170476bdcf208a8ed34dc5b45d8343cf74cea83ff3dc424156e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "type": "text", + "content": "Table 8. Final average accuracy when conducting multiview distillation within the same model on CIFAR-100 (M=2k). All values are averaged over 10 runs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 293, + 201, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 201, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 201, + 306 + ], + "type": "text", + "content": "performance can be further improved." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 312, + 287, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 385 + ], + "type": "text", + "content": "Distillation scheme of DC. We also evaluate the effectiveness of DC's strategy of distilling from harder samples to easier samples in collaborative learning manner. As shown in Table 7, we compared it with other distillation strategies. The result shows that the distillation scheme of DC constantly outperforms other schemes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 392, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 525 + ], + "type": "text", + "content": "Self-Distillation Chain in an independent model. While DC was originally designed to incorporate CCL, it is possible to conduct DC's strategy within an independent model. We name such a strategy as the Self-Distillation Chain (SDC). Similar to different schemes of DC, SDC can be implemented in two ways: distillation from easier samples to harder samples, and distillation from harder samples to easier samples. As shown in Table 8, both strategy gives extra final performance and plasticity, while the latter strategy benefits the performance more. Moreover, incorporating DC with CCL (i.e., ours) further improves the accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 537, + 121, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 121, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 121, + 550 + ], + "type": "text", + "content": "6. Discussions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "type": "text", + "content": "In this section, we analyze some properties of CCL-DC." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 578, + 287, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 721 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 721 + ], + "type": "text", + "content": "Improving plasticity. One of the important advantages of CCL-DC is that it can improve the plasticity of continual learners. This can be evident by plasticity metrics like LA. Moreover, we have observed that the plasticity of CCL-DC facilitates the model to converge faster and descend to a deeper loss. Figure 4 illustrates the classification loss (cross-entropy) curve of the model. To obtain the loss curve, we take a snapshot of the model every 10 iterations and compute the cross-entropy over all the training samples on the current task. We plot the curve on the logarithm scale so that it is easy to observe that CCL-DC helps the model descend deeper at the end of each task." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 335, + 72, + 512, + 172 + ], + "blocks": [ + { + "bbox": [ + 335, + 72, + 512, + 172 + ], + "lines": [ + { + "bbox": [ + 335, + 72, + 512, + 172 + ], + "spans": [ + { + "bbox": [ + 335, + 72, + 512, + 172 + ], + "type": "image", + "image_path": "cc6e78fa9779260185745a5bce5135b3feda206577c5e0ad8bece680652272f1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 348, + 209, + 502, + 352 + ], + "blocks": [ + { + "bbox": [ + 305, + 175, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 208 + ], + "type": "text", + "content": "Figure 4. Classification loss curve of ER on CIFAR-100 " + }, + { + "bbox": [ + 305, + 175, + 545, + 208 + ], + "type": "inline_equation", + "content": "(\\mathbf{M} = 2\\mathbf{k})" + }, + { + "bbox": [ + 305, + 175, + 545, + 208 + ], + "type": "text", + "content": " The curve is calculated on all training samples of the current task. Since there are 10 tasks in total, the curve has 10 peaks." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 348, + 209, + 502, + 352 + ], + "lines": [ + { + "bbox": [ + 348, + 209, + 502, + 352 + ], + "spans": [ + { + "bbox": [ + 348, + 209, + 502, + 352 + ], + "type": "image", + "image_path": "d38af7bf7c93506edc2903772304a3813807ee0ad2100d466180d4e841895a08.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "text", + "content": "Figure 5. The entropy of prediction produced by ER with and without CCL-DC on CIFAR-100 " + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "inline_equation", + "content": "(\\mathbf{M} = 2\\mathbf{k})" + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "text", + "content": " represents the sample after " + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 354, + 545, + 399 + ], + "type": "text", + "content": "-th augmentation in Eq. 10. The value is calculated at the end of the training and is averaged over all training samples." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "text", + "content": "Alleviating overconfidence. To show the effect of DC in alleviating overconfidence, we compared the confidence of models trained with and without CCL-DC. We measure the confidence with the entropy of predictions. Fig. 5 shows the entropy of prediction produced by the ER (baseline) with and without CCL-DC on CIFAR-100 " + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "inline_equation", + "content": "(\\mathrm{M} = 2\\mathrm{k})" + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "text", + "content": ". The entropy is calculated at the end of training and averaged across all samples in the training set. Moreover, we also calculate the entropy of models trained with CCL-DC, by forwarding images of different difficulties (from " + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "inline_equation", + "content": "X_3" + }, + { + "bbox": [ + 305, + 406, + 545, + 550 + ], + "type": "text", + "content": " in Eq. 10) in the augmentation chain. The experimental results show the effect of DC in suppressing overall confidence." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 562, + 378, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 378, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 378, + 574 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 580, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 580, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 305, + 580, + 545, + 703 + ], + "type": "text", + "content": "In this paper, we highlighted the significance of plasticity in online CL, which has been overlooked in prior research when compared to stability. We also established the quantitative link between plasticity, stability, and final accuracy. The quantitative relationship shed light on the future direction of online CL research. Based on this, we introduced collaborative learning into online CL and proposed CCL-DC, a strategy that can be seamlessly integrated into existing online CL methods. 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In NeurIPS, 2018. 2" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23469" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_content_list.json b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dd896efa395448a2bb32af350f0bbe45f1fea7dc --- /dev/null +++ b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_content_list.json @@ -0,0 +1,1483 @@ +[ + { + "type": "text", + "text": "Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps", + "text_level": 1, + "bbox": [ + 94, + 130, + 875, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Octave Mariotti Oisin Mac Aodha Hakan Bilen", + "bbox": [ + 256, + 180, + 712, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Edinburgh", + "bbox": [ + 387, + 203, + 581, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "groups.inf.ed.ac.uk/vico/research/sphericalmaps", + "bbox": [ + 292, + 220, + 671, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 313, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent self-supervised models produce visual features that are not only effective at encoding image-level, but also pixel-level, semantics. They have been reported to obtain impressive results for dense visual semantic correspondence estimation, even outperforming fully-supervised methods. Nevertheless, these models still fail in the presence of challenging image characteristics such as symmetries and repeated parts. To address these limitations, we propose a new semantic correspondence estimation method that supplements state-of-the-art self-supervised features with 3D understanding via a weak geometric spherical prior. Compared to more involved 3D pipelines, our model provides a simple and effective way of injecting informative geometric priors into the learned representation while requiring only weak viewpoint information. We also propose a new evaluation metric that better accounts for repeated part and symmetry-induced mistakes. We show that our method succeeds in distinguishing between symmetric views and repeated parts across many object categories in the challenging SPair-71k dataset and also in generalizing to previously unseen classes in the AwA dataset.", + "bbox": [ + 75, + 305, + 473, + 623 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 648, + 209, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic correspondence (SC) estimation aims to find local regions that correspond to the same semantic entities across a collection of images, where each image contains a different instance of the same object category [30]. SC has been studied in both supervised [9, 26, 59] and unsupervised [2, 50] settings. Thanks to the recent progress in self-supervised learning (SSL) [6, 40, 60], recent SSL-based approaches have been shown to obtain strong performance on multiple benchmarks [1, 2, 54]. However, they often act as simple part detectors, without having any 3D understanding of object extent, or relative location of object parts. As these SSL methods are typically trained using only 2D-based objectives, they are not able to learn 3D-aware representations, and often converge to similar features for object parts that share appearance but not fine-grained semantics.", + "bbox": [ + 75, + 674, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf42395a54f16cd93a35efc6090b8caacfe541aabb42c3a7daf34fe28a0a3327.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 501, + 285, + 609, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d6a4d5ce187995cd2e41c258ddd2b6758814ec4627c5d5b868eee9a20f7ad27.jpg", + "image_caption": [ + "DINOv2" + ], + "image_footnote": [], + "bbox": [ + 627, + 285, + 738, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c0a9464c0fb9c2526df1b455fd01dba7c10b83171dedd6ae4cdaabb20009d690.jpg", + "image_caption": [ + "Figure 1. Features from self-supervised methods such as DINOv2 [40] have been used to discover parts and regions of objects. However, these features fail to correctly distinguish (i) object symmetries, e.g. the left and right side of the car have the same features and (ii) individual parts, e.g. the wheels are represented by the same features irrespective of their location on the car. Our approach through use of a weak geometric spherical prior addresses these issues. Note, we use the 3D PCA projection of the features for DINOv2 and our learned spherical mapping for our method." + ], + "image_footnote": [], + "bbox": [ + 501, + 388, + 609, + 473 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/769c98ff9096e99c04cdf49df27d6968daba1feec95d907f84fc453281b9125a.jpg", + "image_caption": [ + "collapsed sides", + "collapsed parts" + ], + "image_footnote": [], + "bbox": [ + 630, + 388, + 738, + 474 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1080e5808b8ed0d5af3ebceb47639559b7547eaba36990b500c131073d112a48.jpg", + "image_caption": [ + "Ours", + "distinct sides" + ], + "image_footnote": [], + "bbox": [ + 759, + 285, + 867, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b4bc07b933358b181f02ed7a06323e13289bf045a7817322fde81749635f219b.jpg", + "image_caption": [ + "distinct parts" + ], + "image_footnote": [], + "bbox": [ + 759, + 388, + 867, + 474 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The two main failure modes of current methods are depicted in Fig. 1. First, they are often confused by the symmetries that objects can exhibit (e.g. left vs. right side of a car), producing reflected versions of the feature maps when presented with the two different sides of a symmetric object. Second, they predict similar features for similar looking parts (e.g. the front left vs. back left wheel of a car), and fail to discriminate between part instances. Such symmetries and repeated structures are ubiquitous in both human-made and naturally occurring object categories.", + "bbox": [ + 496, + 628, + 890, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We posit that these shortcomings can be addressed by enforcing an explicit 3D structure into correspondence learning, allowing the model to disambiguate multiple repeated parts, and accounting for the fact that some object parts might not be visible in all images. Indeed, scene-based correspondence pipelines use geometric verification in order to guarantee robustness in their matches [44], while other works have shown that detailed 3D meshes can be used to", + "bbox": [ + 496, + 780, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19521", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "discover category-based correspondences through a render-and-compare pipeline [29, 62]. However, these approaches typically require 3D mesh supervision which is difficult and costly to obtain at scale.", + "bbox": [ + 75, + 90, + 468, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the limitations, and the promise of the recent SSL representations [40], we propose a novel method that incorporates the missing 3D geometry into object representations. We make use of a weak 3D prior by representing object features on the surface of a sphere which encodes both geometry and appearance information. Our method consistently maps features corresponding to the same semantic parts (e.g. left headlight of a car) in images of different object instances to the same spherical coordinates, hence enabling a 3D aware and accurate correspondence. However, learning such a mapping without the ground-truth 3D supervision is nontrivial because of repeated parts and object symmetries. To this end, we propose to use much weaker supervision via coarse camera viewpoint annotations to help separate these confusing features during training. We couple this with geometric constraints to prevent collapsed representations for repeated parts. As a result, our method learns to separate object parts based on their position and spatial configuration in an image.", + "bbox": [ + 75, + 151, + 470, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we point out that the standard evaluation metric for SC, Percentage of Correct Keypoints (PCK), is not able to properly evaluate symmetry-related failures as it only considers keypoints that are simultaneously visible in both the source and target image. For instance, a system predicting high similarity between a front left wheel in the source and front right wheel in the target is unlikely to be penalized for it, as the target image is unlikely to contain both a front left and front right wheel due to self-occlusions. In such cases PCK will simply not evaluate what the nearest neighbor of the source wheel is. Rather than simple accuracy-based metric, we argue that average precision is a more robust scoring mechanism and propose a new metric, Keypoint Average Precision (KAP), to account for potential spurious matches.", + "bbox": [ + 75, + 438, + 468, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are: i) a novel SC approach that learns to separate visually similar parts by mapping them to different location on a sphere, ii) a set of simple geometric constraints that force separation of visually similar parts during training, and iii) a new evaluation protocol that better accounts for the failure cases of current methods.", + "bbox": [ + 75, + 665, + 468, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 761, + 215, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image matching. Visual correspondences were first explored as exact matches between different views of the same scene with applications to stereo vision [24, 38], object detection [14, 33], structure from motion [20, 44, 52], and SLAM [12, 19]. Correspondences can also be computed across pixels in the frames of a video, which is referred to as optical flow [5, 7]. Traditionally they are obtained by computing hand-crafted visual descriptors [11, 32, 43].", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic correspondence (SC). In SC estimation [30], the goal is not only to find matches across different views of the exact same object instance, but also across different instances of the same object category. While earlier work [30] match two images through densely sampled SIFT [32] features, later works extended pairwise correspondence learning to a global matching problem [61] and established region correspondences using object proposals and their geometric relations over dense descriptors [17]. Subsequently, CNNs trained with only image-level supervision have been shown to discover correspondences [31], paving the way for many deep learning correspondence systems [10, 18, 26, 59]. Typical correspondence-specific CNN architectures rely on aggregating features along the depth of a network [35, 53, 59] or use 4D convolutions spanning two images simultaneously [41]. Recently, transformers have been shown to be particularly suited to correspondence discovery thanks to their attention mechanism [9].", + "bbox": [ + 496, + 90, + 890, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While the early works in unsupervised correspondence discovery [2, 27, 50] use on the convolutional representations, recent methods [1, 47, 54, 57] build on the success of transformer-based self-supervised representations [6, 40, 60] to discover salient and robust features, which subsequent works have applied to detect semantic correspondences successfully, often surpassing supervised methods. The features from generative image models have also been used in SC [22, 49, 57]. Two closely related works [16, 39] propose to create category-wide representations by aligning self-supervised feature maps. Unlike our approach, these works are limited to 2D, and find correspondences between images without knowing the underlying 3D structure of the world which renders them incapable of distinguishing different sides of objects (e.g. left vs. right side of a car). A concurrent work [58] also identifies geometry-related issues in SSL-based correspondence but targets a supervised training regime where our approach does not necessitate keypoint supervision.", + "bbox": [ + 496, + 364, + 890, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D priors for correspondence. In literature, 3D priors have been used for SC, mainly in the form of annotated meshes [8, 29, 37, 46, 62], where annotations can either be from image to mesh, or between meshes. [29, 37] in particular use a dense parametrization of the mesh surface similar to our sphere. When no mesh is available, precise camera pose can be used to recover sparse correspondences through constrained geometric optimization [48] or by training a neural field [56]. In comparison, our approach requires no meshes and only very coarse viewpoint supervision.", + "bbox": [ + 496, + 656, + 890, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Alternatively, it is possible to estimate 3D models of object categories from image supervision alone [3, 15, 23, 25, 36, 55], from which correspondences are extracted. However, this is very challenging by itself, requiring complex pipelines capable of modeling accurate mesh deformations, pose, and rendering, which are all failure-prone.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19522", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 89, + 166, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem statement", + "text_level": 1, + "bbox": [ + 76, + 114, + 259, + 128 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "General formulation. Given an unordered monocular image collection, we wish to learn a mapping $f(\\mathbf{I}, x) = z$ that takes in an RGB image $\\mathbf{I} : \\Lambda \\to \\mathbb{R}^3$ , $\\Lambda \\subset \\mathbb{R}^2$ and a pixel location $x \\in \\Lambda$ to an $n$ -dimensional embedding $z \\in \\mathcal{Z} \\subset \\mathbb{R}^n$ . In particular, we would like $f$ to map semantic concepts from different instances of the same category (e.g. center of front-right wheel of a car) to the same point in the embedding space $\\mathcal{Z}$ . Formally, $f(\\mathbf{I}, x) = f(\\mathbf{I}', x')$ , when the pixels $x$ in $\\mathbf{I}$ , and $x'$ in $\\mathbf{I}'$ correspond to the same semantic part and instance. In practice, the corresponding location for $(\\mathbf{I}, x)$ in $\\mathbf{I}'$ can be obtained by finding the nearest neighbor of $f(\\mathbf{I}, x)$ in the embedding space, i.e. $\\arg \\min_{x'} d_{\\mathcal{Z}}(f(\\mathbf{I}, x), f(\\mathbf{I}', x'))$ , where $d_{\\mathcal{Z}}$ is a distance function over $\\mathcal{Z}$ . For simplicity, we will use $f(\\mathbf{I})$ to refer to the feature map obtained by evaluating $f$ on all pixels.", + "bbox": [ + 75, + 138, + 468, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An ideal embedding function should be general enough as to not only match related semantic parts across different object instances (e.g. match the front-left wheel across two different car models) but also specific enough to distinguish between different part instances within the same object instance (e.g. front-left wheel vs. front-right wheel). Learning this from image-based self-supervision alone is a challenging task due to the visual similarity of repeated parts and self-occlusion. As a result, it is quite challenging for correspondence estimators to learn that cars have four distinct wheels from single images without explicit supervision.", + "bbox": [ + 75, + 366, + 468, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spherical mapping. Instead, it is beneficial to endow a correspondence estimator with priors about the underlying 3D structure of objects. To this end, previous methods [29, 62] use detailed 3D meshes via a render-and compare approach. However, they rely on the presence of groundtruth 3D meshes and the precise viewpoint information. Instead, following [50, 51], we use a simplified 3D structure, specifically a sphere $S^2 \\subset \\mathbb{R}^3$ (denoted as $S$ for simplicity) based on the assumption that the object categories of interest are approximately homeomorphic to spheres (i.e. objects without holes). While this may at first appear particularly ill-suited for some categories, e.g. bicycles, the geometric simplicity of $S$ provides a convenient parameterization of an object's surface by allowing easy computation of geometric constraints to separate visual and semantic similarity. In particular, $S$ provides a simple geodesic distance through the dot product, making it straightforward to push different semantic parts apart, which we use to distinguish repeated object features. Formally, we are interested in building a spherical mapping $f_S(\\pmb{I}, x)$ that maps pixels in $\\pmb{I}$ to the surface of $S$ . Unlike an arbitrary $n$ dimensional space, $S$ forms an object-centric specific coordinate system where each region ideally repre", + "bbox": [ + 75, + 551, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sents a distinct semantic part and instance on the surface of the object.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Learning formulation", + "text_level": 1, + "bbox": [ + 498, + 133, + 702, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the absence of ground truth correspondences, ensuring the semantic consistency of our spherical mapping function is very challenging. [50] enforces correspondence between image pairs through synthetically augmenting training images via thinplate splines. Unfortunately, such augmentations do not produce realistic 3D transformations such as 3D rotations which can result in the self-occlusion of parts. Instead, similar to [16, 39], we formulate the learning objective as one of aligning features from a pretrained SSL model $\\phi : \\Lambda \\to \\mathcal{Z}_{\\phi}$ between different instances of an object category. For simplicity, we will refer to the SSL embedding space $\\mathcal{Z}_{\\phi}$ simply as $\\mathcal{Z}$ in the rest of the text.", + "bbox": [ + 496, + 157, + 890, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While those approaches use flat atlases $\\mathbb{R}^2\\to \\mathcal{Z}$ , we build a spherical prototype $S_{\\mathcal{Z}}:S\\to \\mathcal{Z}$ that maps a point on the surface of the sphere $s\\in S^2$ to a feature vector $\\mathbf{z}\\in \\mathcal{Z}$ . This formulation has two important benefits. First, the input domain of $S_{\\mathcal{Z}}$ is simply $S$ , meaning that it does not depend on $I$ , and it is shared across all images, constituting a category-based map. Second, and in contrast to [16, 39], because we chose the output of $f_{S}$ to lie on the surface of a sphere, we can use it to enforce 3D priors during training (Sec. 3.3).", + "bbox": [ + 496, + 340, + 890, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Intuitively, for a given category, the spherical prototype $S_{\\mathcal{Z}}$ should be able to reconstruct any self-supervised feature map $\\phi(\\boldsymbol{I})$ when queried on the coordinates predicted by $f_{S}$ , i.e. $S_{\\mathcal{Z}}(f_{S}(\\boldsymbol{I}, x))$ must closely approximate $\\phi(\\boldsymbol{I}, x)$ for any $\\boldsymbol{I}, x$ . Even if $S_{\\mathcal{Z}}$ encodes a perfect category prototype, it will be unable to encode information about the image background. Hence we use instance masks $M(\\boldsymbol{I})$ at training time to restrict the loss computation to only the pixels on an object's surface. In practice, these can be obtained using pretrained segmentation models [21]. Thus, given a training image $\\boldsymbol{I}$ and a pixel location $x$ , our primary training objective to learn the parameters of $f_{S}$ and $S_{\\mathcal{Z}}$ can be formulated as the minimization of", + "bbox": [ + 496, + 493, + 890, + 689 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\frac {1}{| \\Lambda |} \\sum_ {x \\in \\Lambda} M (\\boldsymbol {I}, x) \\times \\Gamma \\left(\\phi (\\boldsymbol {I}, x), S _ {\\mathcal {Z}} \\left(f _ {S} (\\boldsymbol {I}, x)\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 699, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Gamma$ is the cosine distance between the two inputs. Our spherical prototypes are implemented via a neural network that maps points in $\\mathbb{R}^3$ to $\\mathcal{Z}$ . Importantly, each point $s\\in S^2\\subset \\mathbb{R}^3$ must be mapped independently, meaning that it should correspond to a unique point $\\mathbf{z}\\in \\mathcal{Z}$ , irrespective of which instance it comes from or where in the image this part is located. To model multiple categories, and to encourage information sharing between closely related ones, we use a single network conditioned on a category embedding. In practice, $S_{\\mathcal{Z}}$ is a visual transformer [13] without", + "bbox": [ + 496, + 750, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19523", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b72b9756630e070510f259a7d3984fb574b60b297dfb9a57dd1382a481fa2f4a.jpg", + "image_caption": [ + "Figure 2. Overview of our semantic correspondence estimation approach. We begin by extracting features from a frozen self-supervised backbone, and further use them to predict spherical coordinates via a learned module. Each predicted point is used to query a jointly learned prototype, providing the supervision signal (Sec. 3.2). The sphere is used to enforce weak geometric priors (Sec. 3.3). During inference, SSL features are combined with spherical coordinates (Sec. 3.4). A blue outline indicates a fixed module, while orange indicate learned parameters." + ], + "image_footnote": [], + "bbox": [ + 76, + 102, + 893, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "self-attention, but with cross-attention between image tokens and a single category token $\\mathbf{c}$ which is a one hot embedding of the category. As learning $f_{S}$ from scratch can be challenging, we further leverage the SSL backbone by simply adding a prediction head $f_{S}^{\\prime}$ to it to produce spherical maps, i.e. $f_{S} = f_{S}^{\\prime} \\circ \\phi$ . An overview of our architecture is presented in Fig. 2.", + "bbox": [ + 75, + 300, + 470, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Enforcing geometric priors", + "text_level": 1, + "bbox": [ + 76, + 417, + 321, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above spherical reconstruction formulation alone offers little benefit over matching the self-supervised features from $\\phi$ directly, especially considering the low dimensionality of the intermediate spherical space, which is not guaranteed to be well-behaved. However, this spherical structure enables the computation of simple geometric priors that can be enforced during training.", + "bbox": [ + 75, + 440, + 468, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Viewpoint regularization. Many object categories exhibit some form of symmetry which can make it particularly challenging for image-based models to distinguish between different sides of an object, creating spurious correlations between distinct parts (e.g. see cars in Fig. 1). One potential way of addressing this challenge, without using dense groundtruth correspondence, is to exploit viewpoint information of the object instance.", + "bbox": [ + 75, + 566, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An interesting property of using a spherical prototype to represent an object category is that it can easily be used to infer an object's viewpoint with respect to the camera. We posit that the average coordinate of a spherical map of an image, which we present as $\\mu(f_S(I)) = 1 / |\\Lambda| \\sum_{x \\in \\Lambda} f_S(I, x)$ , can be viewed as a coarse approximation of the camera viewpoint under which the object is seen, e.g. right side views should be approximately mapped to the right side of the sphere, and left side views to the left. Intuitively, thinking of $f_S$ as a mapping from image pixels to the object's surface, the visible parts of an object should roughly be those closest to the camera, while the others should be hidden by self-occlusion.", + "bbox": [ + 75, + 688, + 470, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By using the groundtruth camera viewpoint $v_{I}$ , we en", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "force the average direction of the spherical map $\\mu (f_S(I))$ to align with $v_{I}$ . When this is satisfied, symmetric views must be mapped to different parts of the sphere. While precise viewpoint information is hard to obtain, we observe it is sufficient to use coarse relative viewpoint supervision between images. In practice, viewpoints are discretized into a small number of bins, and $v_{I}$ is represented by the median value of the corresponding bin. Then, we simply enforce that the dot product between viewpoints from two images equals that of their average spherical maps,", + "bbox": [ + 496, + 300, + 893, + 450 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v p} = \\sum_ {\\boldsymbol {I}, \\boldsymbol {I} ^ {\\prime}} | | v _ {\\boldsymbol {I}} \\cdot v _ {\\boldsymbol {I} ^ {\\prime}} - \\mu \\left(f _ {S} (\\boldsymbol {I})\\right) \\cdot \\mu \\left(f _ {S} \\left(\\boldsymbol {I} ^ {\\prime}\\right)\\right) | | ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 457, + 890, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relative distance loss. As noted earlier, current self-supervised extracted features can confuse repeated object repeated parts. Depending on the target goal, this can be desirable, if the parts do indeed belong to the same part category. However, this is detrimental for dense correspondence estimation as the parts may actually be different part instances, e.g. left vs. right leg. It can be hard to distinguish between these based on their appearance alone and additional geometric context is required.", + "bbox": [ + 496, + 507, + 890, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One trivial way of encoding this context is by making the assumption that similar parts that appear in different locations on an image (i.e. not beside each other) are in fact different instances of the same semantic part. Therefore, we would like to enforce the property on our predicted spherical maps that distant pixels in the image should be mapped far apart on the sphere. Due to scale variation, distance on the image plane is hard to link to distances on the surface of the sphere. However, we can reformulate this property as a relative distance comparison using a triplet. Given three points $a$ , $b$ , and $c$ on an image $\\pmb{I}$ , and their corresponding positions $s_a = f_S(\\pmb{I}, a)$ , $s_b$ , and $s_c$ on the sphere, the ordering between distances should be preserved, that is:", + "bbox": [ + 496, + 643, + 892, + 839 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\left| a - b \\right| \\right| \\leq \\left| \\left| a - c \\right| \\right| \\iff \\Gamma \\left(s _ {a}, s _ {b}\\right) \\leq \\Gamma \\left(s _ {a}, s _ {c}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 845, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In reality, this does not hold for distances along an object's surface, which the sphere is supposed to represent, partly", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Feature Reconstruction Loss", + "bbox": [ + 504, + 88, + 676, + 99 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19524", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/32af9dd198c5b9ba01d3c41d465b8c613609eb1f19593e7d2d7e8c73764d482f.jpg", + "image_caption": [ + "Spherical Coordinates" + ], + "image_footnote": [], + "bbox": [ + 78, + 102, + 184, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e014c2f4184defb79360348d7bca1d228a221d638f30ebd71c4496572deca634.jpg", + "image_caption": [ + "Relative Distance Loss $\\mathcal{L}_{rd}$" + ], + "image_footnote": [], + "bbox": [ + 207, + 102, + 316, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/da551187e926cc15d95fb6ad0557ae2c7e29ca97de66847b48b4cdce1475d6d2.jpg", + "image_caption": [ + "Orientation Loss $\\mathcal{L}_o$", + "Figure 3. Illustration of our geometry losses $\\mathcal{L}_{rd}$ and $\\mathcal{L}_o$ . The left image shows a spherical map from which a triplet of points is sampled. $\\mathcal{L}_{rd}$ : as the anchor patch $a$ is closer to the positive $b$ on the image compared with the negative $c$ , its corresponding position $s_a$ on the sphere must also be closer to $s_b$ than $s_c$ . $\\mathcal{L}_o$ : after projecting $s_b$ and $s_c$ to the plane tangent to the sphere at $s_a$ , we ensure orientation is preserved by enforcing positive collinearity between $u_b \\times u_c$ and the normal vector $n$ ." + ], + "image_footnote": [], + "bbox": [ + 349, + 102, + 468, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "due to perspective. For example, in the case of a long train seen from a near frontal view, parts at the back of the train might appear very close to the front in the image, even though they are very far in 3D space. Nevertheless, we find that this is still an effective prior for discouraging repeated part instances from being mapped to the same location.", + "bbox": [ + 75, + 343, + 468, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, point triplets $(a,b,c)$ are randomly sampled among pixels that belong to the object. Among each such triplet, we chose an anchor location $anc = a$ , a positive location $pos = \\arg \\min_{x\\in \\{b,c\\}}||a - x||$ , and a negative location $neg = \\arg \\max_{x\\in \\{b,c\\}}||a - x||$ (see Fig. 3). We can then define a triplet margin loss as:", + "bbox": [ + 75, + 434, + 468, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {r d} = \\max (\\Gamma (f _ {S} (\\boldsymbol {I}, a n c), f _ {S} (\\boldsymbol {I}, p o s)) \\tag {4} \\\\ - \\Gamma (f _ {S} (\\boldsymbol {I}, a n c), f _ {S} (\\boldsymbol {I}, n e g)) + \\delta , 0), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 534, + 468, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\delta$ is a hyperparameter which specifies the margin. A useful side product of this formulation is that it encourages the spherical maps to be smooth, as strong discontinuities would produce a large anchor to positive distance.", + "bbox": [ + 75, + 580, + 468, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Orientation loss. A final advantage of using $S$ as a latent space is that it is an orientable 2D space, just like images. Therefore, enforcing that $f_{S}$ preserves orientation prevents spurious matches between symmetric views. Intuitively, if a point $a$ appears on the right side of $b$ in the image, then $s_a$ must appear in the same side of $s_b$ . Given a point triplet as defined earlier, this can be enforced by making sure that the determinant of the image triplet and sphere triplet positively correlate. Formally, defining $P_a$ as the orthogonal projection to the plane tangent to $S$ at $s_a$ and $u_b$ as $P_a(s_b) - s_a$ , we have $d_I = \\det(b - a, c - a)$ and $d_S = \\det(u_b, u_c)$ , and want $sign(d_I) = sign(d_S)$ (see Fig. 3).", + "bbox": [ + 75, + 659, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As objects can have complex geometry that our model does not have access to, there exists no exact relation linking the two determinants together, as for instance perspective distortions might alter angles. However, we can as-", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sume that image triplets of large determinants should also have large determinant on the sphere, as a change of sign in determinant indicates the relative orientation on the sphere has been inverted. In practice, we randomly sample image triplets $(a,b,c)$ and select those whose image determinant $d_{I}$ is higher than a threshold $d_{\\tau} = 0.7$ while swapping $b$ and $c$ if $d_{I}$ is negative. Then, we enforce the determinant of the corresponding sphere triplet to be at least $d_{\\tau}$ ,", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o} = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} d _ {I} < d _ {\\tau} \\\\ \\max \\left(d _ {\\tau} - d _ {S}, 0\\right) & \\text {i f} d _ {I} \\geq d _ {\\tau}. \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 219, + 890, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Correspondence via combined representations", + "text_level": 1, + "bbox": [ + 498, + 275, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During inference, it is possible to directly query the spherical maps $f_{S}$ of two images to obtain correspondences using the cosine distance. That is, for an image pair $I, I'$ and a query location $q$ on $I$ , its location in $I'$ can be computed as", + "bbox": [ + 496, + 297, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np ^ {*} = \\underset {p} {\\arg \\min } \\Gamma \\left(f _ {S} (\\boldsymbol {I}, q), f _ {S} \\left(\\boldsymbol {I} ^ {\\prime}, p\\right)\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 373, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While this protocol is sound, it comes with two important drawbacks. First, $f_{S}$ produces spherical maps for the whole image, including the background, meaning segmentation masks would be required at inference time to prevent the emergence of spurious matches. Second, the spherical map is designed to be a smooth parameterization of the object surface, making it susceptible to missing fine details. A slightly incorrect mapping $f_{S}(I,q) + \\epsilon$ has a high probability of finding a higher match in a nearby region of the correct match $f_{S}(I^{\\prime},p^{*})$ if both maps are smooth. In comparison, SSL feature maps can exhibit strict feature separation, e.g. wheel features are very different from other nearby non-wheel features, making it unlikely that a wheel pixel finds a nearest neighbor among nearby non-wheel pixels.", + "bbox": [ + 496, + 402, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To mitigate this issue, we make use of the feature maps that are already computed by the self-supervised backbone network $\\phi$ , in a similar way to supervised correspondence approaches that aggregate features from a network [35, 53, 59]. Existing literature has shown that DINO features are particularly effective at differentiating between the foreground and background [1], removing the need for inference-time segmentation. To leverage these DINO features, we reformulate Eq. (6) as the combination of self-supervised features and spherical locations:", + "bbox": [ + 496, + 614, + 890, + 765 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} p ^ {*} = \\arg \\min _ {p} (1 - \\alpha) \\Gamma (\\phi (\\boldsymbol {I}, q), \\phi (\\boldsymbol {I} ^ {\\prime}, p)) & \\\\ + \\alpha \\Gamma (f _ {S} (\\boldsymbol {I}, q), f _ {S} (\\boldsymbol {I} ^ {\\prime}, p)), & \\end{array} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 772, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is a hyperparameter that balances each term.", + "bbox": [ + 500, + 816, + 849, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 844, + 630, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We build our models on DINOv1-B/8 [6] and DINOv2-B/14 [40] backbones. Training masks", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19525", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ff419bee49174526624b759c8748d84105895a7c89c718bf83086da27705c078.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
↑3%4%5%6%7%8%9%10%11%12%13%14%15%16%17%avg
CustomCATS [9]52.034.772.234.349.957.543.666.524.463.256.552.042.641.743.033.672.658.049.9
MMNet+FCN [59]55.937.065.035.450.063.945.762.828.765.054.751.638.534.641.736.377.762.550.4
SCorrSan [26]57.140.378.338.151.857.847.167.925.271.363.949.345.349.848.840.377.769.754.4
DINOv1DINOv1 [6]44.326.857.622.029.332.819.754.014.940.139.329.329.037.020.028.240.621.132.6
ASIC [16]57.925.268.124.735.428.430.954.821.645.047.239.926.248.814.524.549.024.637.0
Ours47.126.070.921.837.534.932.460.023.253.648.542.528.342.721.141.939.741.739.7
SDDIFT [49]63.554.580.834.546.252.748.377.739.076.054.961.353.346.057.857.171.163.457.7
SD [57]63.155.680.233.844.949.347.874.438.470.853.761.154.455.054.853.565.053.356.1
DINOv2DINOv2 [40]72.762.085.241.340.452.351.571.136.267.164.667.661.068.230.762.054.324.256.2
DINOv2 + SD [57]73.064.186.440.752.955.053.878.645.577.364.769.763.369.258.467.666.253.563.3
Ours (sphere only)46.728.866.333.036.566.659.174.925.465.750.152.727.113.715.846.673.536.745.5
Ours76.961.285.942.148.473.367.280.046.380.266.771.266.063.936.268.667.842.263.6
Ours + SD74.864.587.145.652.777.871.482.447.782.067.373.967.660.049.969.878.559.167.3
", + "bbox": [ + 81, + 88, + 890, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Keypoint matching scores on SPair-71k evaluated using PCK@0.1 with macro-averaging for the summary scores. We present our approach using DINOv1 [6] features (middle rows) and DINOv2 [40] features (bottom rows). In both cases, we improve over the DINO only baselines and are superior to fully supervised methods (top rows). Bold entries are best per category and underlined are second-best.", + "bbox": [ + 75, + 275, + 892, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "are obtained using a pretrained Mask R-CNN model [21]. Our spherical mapper consists of a linear dimension reduction layer halving the number of features, a visual transformer block with self-attention, and a final linear layer with an output dimension of three. The resulting feature map is then normalized pixel-wise so that its output values lie on the surface of $S^2$ . The dimensionality reduction layer, while not strictly necessary, is helpful considering the small number of images used during training, while the transformer block helps in disentangling sides and repeated parts by allowing global reasoning between image patches.", + "bbox": [ + 75, + 337, + 470, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The final loss term is computed as $\\mathcal{L} = \\mathcal{L}_{rec} + \\lambda_{rd}\\mathcal{L}_{rd} + \\lambda_o\\mathcal{L}_o + \\lambda_{vp}\\mathcal{L}_{vp}$ . We set $\\lambda_{rd} = \\lambda_o = 0.3$ , while $\\lambda_{vp} = 0.1$ is set slightly lower as it can have the detrimental effect of pulling all predictions towards the average over image pixels - cf. Eq. (2). The relative distance margin is set to $\\delta = 0.5$ to encourage feature separation. To perform matching in Eq. (7), $\\alpha$ is set to 0.2 so that we leverage the highly discriminative DINO features, while using the sphere as a symmetry and repetition-breaking mechanism. Our model is trained for a total of 200 epochs using Adam [28].", + "bbox": [ + 75, + 512, + 468, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Following existing work [16, 26, 57], we evaluate our method primarily on the Spair-71k dataset [34], which contains images from 18 different object categories. The evaluation set contains between 600 and 900 image pairs, each of which are annotated with the keypoints that are visible in both images. We train our model on the Spair-71k training split on all categories simultaneously, without using any keypoint annotations. Additionally, we evaluate on the AwA-pose dataset [4], which contains images from 35 quadruped categories, annotated with keypoints. We also present results by training on the Freiburg cars dataset [45]. This dataset was collected by densely sampling approximately 100 images each around 48 different car instances. The higher image count, coupled with $360^{\\circ}$ dense sampling, enables us to learn a more detailed spherical prototype.", + "bbox": [ + 75, + 672, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Keypoint average precision", + "text_level": 1, + "bbox": [ + 498, + 337, + 743, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While issues with symmetries are clear in Fig. 4, we argue that the PCK metric fails to account for them as it is only computed between keypoints that appear in both the source and target image. Hence, models that predict high similarity between two visually similar but semantically different keypoints might not be penalized for it. PCK can partly account for repetition-related mistakes if the parts appear simultaneously in both images, but it does not penalize symmetry-related issues, like mistaking the left and right side of a car, as the corresponding keypoints do not appear simultaneously. PCK was initially proposed for simpler cases where keypoints were assumed to be always be visible, e.g. faces or different instances in the same pose. However, as benchmarks become more challenging, a more robust protocol should be used. To illustrate how much these failure cases impact SSL models, we propose an alternative evaluation metric, Keypoint Average Precision - $\\mathrm{KAP}@\\kappa$ . It is similar to $\\mathrm{PCK}@\\kappa$ , but accounts for these errors by evaluating average precision instead of accuracy and penalizes methods that predict matches when none exist.", + "bbox": [ + 496, + 364, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When performing evaluation on a pair of images, instead of restricting it to keypoints that simultaneously appear in both images, we consider all keypoints that appear in the source, irrespective of whether they are also visible in the target image. For each such keypoint, if it appears in the target image, we extract the highest similarity value within radius $\\kappa$ of the ground-truth and label it as positive. We also extract the highest similarity value outside the radius and label it as negative, penalizing overly high predictions on wrong, possibly repeated parts. If the source keypoint does not appear on the target image, we simply extract the highest similarity prediction across the whole target image and label it as negative to penalize incorrectly high similarity when none should exist. This effectively reformulates the task as a binary classification problem, where the embed-", + "bbox": [ + 496, + 672, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19526", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d6af9bd0cc6974ca74fc3d532f867971c3de3740bff2e5fc718217f869c09983.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of dense correspondence maps. For DINOv2, SD, and DINO+SD features we perform PCA on the segmented object features independently for each category, then visualize the three main components. Note that the SD and DINO+SD features are not completely equivalent to the ones used to compute matches, but are provided here for illustration. Spherical maps from $f_{S}$ (Sphere) for our approach are visualized directly. Our spherical maps correctly identify the different sides of objects, whereas other features fail to capture these differences." + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 890, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ding of each source keypoint has to be close to, and only to, the corresponding target keypoint. Finally, we compute the average precision over all the extracted pairs, and report mean average precision per-category.", + "bbox": [ + 75, + 426, + 470, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. SPair-71k results", + "text_level": 1, + "bbox": [ + 76, + 498, + 245, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first evaluate on the task of keypoint transfer between pairs of images using Spair-71k [34]. We present quantitative per-category results in Tab. 1, using the standard PCK metric along with macro-averaged scores as the number of per-category pairs varies greatly. We split the models according to their backbone: custom supervised models, DINOv1-based, SD-based, and DINOv2-based. A striking preliminary observation is the effectiveness of DINOv2, surpassing supervised approaches on most categories. While its success can partially be attributed to evaluation biases [2], this demonstrates the effectiveness of large scale learned self-supervised features.", + "bbox": [ + 75, + 522, + 468, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Using a DINOv1 backbone, our model improves over its backbone on most categories, and over ASIC [16] on average. When combined with the DINOv2 backbone, our model provides improvements on all but two categories. A clear pattern can be identified, with strongest improvements being observed over blob-like symmetric objects with repeated parts (+21.0 on bus and +15.7 on car), while spherical mapping hinders performance on highly deformable categories (-4.3 on person), or high-genus objects for which a sphere is a poor surface prior (-0.8 on bicycle). Our model performs slightly better compared to DINO+SD [57], while requiring a fraction of the computational cost at inference time. Finally, following [57] we evaluate adding Stable Diff", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fusion (SD) [42] features to our method at inference time, which yields further improvements. This illustrates that spherical maps and SD features capture different facets of the correspondence problem.", + "bbox": [ + 496, + 426, + 892, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the results of evaluating correspondences with KAP in Tab. 2. We observe particularly large discrepancies between PCK and KAP in highly symmetric objects with repeated parts, e.g. buses and cars, and the ranking between our model and DINOv2 is reversed on humans, possibly due to DINOv2's symmetric predictions on left and right limbs. All models across all categories obtain lower results when using KAP highlight the symmetry issues they are facing. A limitation of KAP is that it might still count correct repeated parts mistakes if their distance in the image is less than $\\kappa$ . Nonetheless, we argue that KAP is more informative than PCK and is just as efficient to evaluate.", + "bbox": [ + 496, + 487, + 892, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The qualitative visualization shown in Fig. 4 illustrates these improved results. Our model correctly maps the two opposite sides of the cars to different sphere regions, while other feature maps look extremely similar, even when looking at two opposite sides of an object, with the notable exception of SD on birds. The fact that such similarities exist between opposite views suggest that the utility of baselines such as DINOv2 would be quite limited in real scenarios.", + "bbox": [ + 496, + 669, + 893, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Additional evaluation", + "text_level": 1, + "bbox": [ + 500, + 801, + 702, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Animals with Attributes (AwA). To further evaluate our model, we also report results on the AwA-pose dataset from [4], which contains images from 35 different categories of quadruped. While our spherical prototype needs category information during training to reconstruct", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19527", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/235c8aed9c71033407841370678a650d0449d211e1b822b7f11305a214f65294.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
↑%avg
DINOv2 [40]53.554.060.235.544.436.331.761.337.454.752.551.548.848.237.844.147.438.246.5
SD [57]44.448.554.531.545.232.730.068.435.855.247.948.144.842.344.539.252.751.245.4
DINOv2 + SD [57]52.055.959.234.749.036.032.570.339.859.853.152.450.650.447.846.253.349.849.6
Ours (sphere only)38.434.253.933.037.949.743.471.729.857.145.842.532.427.029.537.157.436.042.1
Ours60.751.263.138.445.055.945.769.740.463.254.854.351.248.738.847.955.542.251.5
Ours + SD58.954.262.239.646.654.547.176.240.965.357.356.154.247.443.749.462.452.053.8
", + "bbox": [ + 81, + 88, + 888, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "category-specific features, only the sphere mapper is used during inference, meaning it can be readily applied to unseen categories. Five quadruped classes (cat, cow, dog, horse, and sheep) appear in both SPair and AwA-pose, and are therefore seen during training, but the rest are completely new for our sphere mapper. Nonetheless, results shown in Tab. 3 show that the sphere mapper generalizes well to unseen categories. We attribute this to the assistance from the strong category-agnostic features from DINOv2. Once again, the improvement of using our spherical method is much more apparent using KAP, i.e. the PCK improvement over DINOv2 alone is 2.2 when adding SD and 2.6 when adding spheres, while these become 1.8 and 3.9 respectively with KAP.", + "bbox": [ + 75, + 220, + 472, + 431 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/57e5ca2d521273cf80a5375f70b995ae58af2e339e003d3a9c91afa239f8730f.jpg", + "table_caption": [ + "Table 2. Keypoint matching scores on SPair-71k evaluated using KAP@0.1 with macro-averaging for the summary scores." + ], + "table_footnote": [], + "table_body": "
Dv2SDDv2+SDOursOurs+SD
PCK@0.165.956.068.168.769.8
KAP@0.155.050.756.858.960.6
", + "bbox": [ + 98, + 444, + 444, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model ablation. We also analyze the impact of removing each individual loss term when training our model in an ablation study. The results in Tab. 4 indicate that all variants except the no $\\mathcal{L}_{rd}$ one do not significantly improve over the DINOv2 baseline as they also fail to identify opposite sides of objects and repeated parts.", + "bbox": [ + 75, + 549, + 468, + 642 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9d3050d202ecc208ce416d945793ededf19ab754ded0736fb2be144ac06cdfd0.jpg", + "table_caption": [ + "Table 3. Average scores when evaluating on AwA-pose using a random subset of 200 pairs per category. 'Ours' denotes our model trained on SPair-71k with a DINoV2 backbone." + ], + "table_footnote": [], + "table_body": "
DINOv2no Lvpno Lrdno Lofull model
56.258.661.256.063.6
", + "bbox": [ + 98, + 652, + 444, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inference speed. The results in Tab. 1 demonstrate how effective the addition of Stable Diffusion features are. However, computing correspondences through diffusion requires adding noise to images, running iterative diffusion, and performing joint decomposition between the source and target features. As a result, its inference speed is much slower compared to using DINOv2 features. In comparison, our approach only requires a few extra layers on top of DINOv2 and has negligible additional overhead. Timing results in Tab. 5 illustrate that adding diffusion-extracted features reduces throughput by an order of magnitude.", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/718e39410e2825884dd321ff8f8d8e24d038d94a42fdf4ab6c3afd50855f6a2a.jpg", + "table_caption": [ + "Table 4. Average PCK@0.1 scores when training and testing on SPair-71k using different ablated versions of our approach." + ], + "table_footnote": [], + "table_body": "
DINOv2SDDINOv2+SDOursOurs+SD
3.40.380.353.30.34
", + "bbox": [ + 522, + 210, + 867, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Descriptor computation throughput in pairs/second at inference time on a single A5000 GPU, where higher is better.", + "bbox": [ + 498, + 241, + 890, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Limitations", + "text_level": 1, + "bbox": [ + 500, + 297, + 625, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While our approach results in significant improvements over the DINOV2 baseline for many categories (see Tab. 1), there are still some limitations. For example, we do not perform as well on a small number of categories that cannot be well approximated by a sphere (e.g. humans). Furthermore, the very low-dimensional spherical encoding on its own is not as effective at discriminating parts and subparts and thus needs to be combined with self-supervised features. However, as we already densely compute these features at inference time for each test image, there is no additional cost in combining them with our spherical mapping when evaluating correspondence. Finally, our method relies on additional supervision at training time in the form of automatically computed segmentation masks and weak camera pose supervision. However, results in the supplementary material suggest that coarse camera viewpoints are enough to obtain good performance.", + "bbox": [ + 496, + 321, + 890, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 595, + 619, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented a new approach for semantic correspondence estimation that is robust to issues resulting from object symmetries and repeated part instances. In addition, we proposed a new evaluation protocol that is more sensitive to these issues. Our approach leverages recent advances in the self-supervised learning of discriminative image features and combines them with a weak geometric spherical prior. By using weak pose supervision to represent objects categories on the surface of spheres, we are able to enforce simple geometric constraints during training that result in more geometric and semantically consistent representations. Results on the task of semantic keypoint matching between images from different object instances, a fundamental task in 3D computer vision, demonstrate that our approach alone is superior to existing strong baselines and can be combined with existing methods to further boost performance.", + "bbox": [ + 496, + 622, + 890, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This project was supported by the EP-SRC Visual AI grant EP/T028572/1.", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19528", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shir Amir, Yossi Gandelsman, Shai Bagon, and Tali Dekel. Deep vit features as dense visual descriptors. ECCV Workshop - What is Motion For?, 2022. 1, 2, 5", + "[2] Mehmet Aygün and Oisin Mac Aodha. Demystifying unsupervised semantic correspondence estimation. In ECCV, 2022. 1, 2, 7", + "[3] Mehmet Aygün and Oisin Mac Aodha. SAOR: Single-View Articulated Object Reconstruction. In CVPR, 2024. 2", + "[4] Prianka Banik, Lin Li, and Xishuang Dong. 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In CVPR, 2016. 2, 3" + ], + "bbox": [ + 501, + 92, + 890, + 402 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19530", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_model.json b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a9305effe81114f2512613bde08f58266f345cbf --- /dev/null +++ b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_model.json @@ -0,0 +1,2211 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.131, + 0.877, + 0.155 + ], + "angle": 0, + "content": "Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.181, + 0.713, + 0.199 + ], + "angle": 0, + "content": "Octave Mariotti Oisin Mac Aodha Hakan Bilen" + }, + { + "type": "text", + "bbox": [ + 0.388, + 0.204, + 0.582, + 0.222 + ], + "angle": 0, + "content": "University of Edinburgh" + }, + { + "type": "text", + "bbox": [ + 0.294, + 0.222, + 0.673, + 0.24 + ], + "angle": 0, + "content": "groups.inf.ed.ac.uk/vico/research/sphericalmaps" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.474, + 0.624 + ], + "angle": 0, + "content": "Recent self-supervised models produce visual features that are not only effective at encoding image-level, but also pixel-level, semantics. They have been reported to obtain impressive results for dense visual semantic correspondence estimation, even outperforming fully-supervised methods. Nevertheless, these models still fail in the presence of challenging image characteristics such as symmetries and repeated parts. To address these limitations, we propose a new semantic correspondence estimation method that supplements state-of-the-art self-supervised features with 3D understanding via a weak geometric spherical prior. Compared to more involved 3D pipelines, our model provides a simple and effective way of injecting informative geometric priors into the learned representation while requiring only weak viewpoint information. We also propose a new evaluation metric that better accounts for repeated part and symmetry-induced mistakes. We show that our method succeeds in distinguishing between symmetric views and repeated parts across many object categories in the challenging SPair-71k dataset and also in generalizing to previously unseen classes in the AwA dataset." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.649, + 0.21, + 0.665 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Semantic correspondence (SC) estimation aims to find local regions that correspond to the same semantic entities across a collection of images, where each image contains a different instance of the same object category [30]. SC has been studied in both supervised [9, 26, 59] and unsupervised [2, 50] settings. Thanks to the recent progress in self-supervised learning (SSL) [6, 40, 60], recent SSL-based approaches have been shown to obtain strong performance on multiple benchmarks [1, 2, 54]. However, they often act as simple part detectors, without having any 3D understanding of object extent, or relative location of object parts. As these SSL methods are typically trained using only 2D-based objectives, they are not able to learn 3D-aware representations, and often converge to similar features for object parts that share appearance but not fine-grained semantics." + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.272, + 0.574, + 0.285 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.286, + 0.611, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.273, + 0.713, + 0.285 + ], + "angle": 0, + "content": "DINOv2" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.286, + 0.74, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.373, + 0.73, + 0.386 + ], + "angle": 0, + "content": "collapsed sides" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.39, + 0.61, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.39, + 0.739, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.478, + 0.73, + 0.492 + ], + "angle": 0, + "content": "collapsed parts" + }, + { + "type": "image_caption", + "bbox": [ + 0.798, + 0.273, + 0.833, + 0.285 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.286, + 0.869, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.373, + 0.854, + 0.385 + ], + "angle": 0, + "content": "distinct sides" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.39, + 0.869, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.478, + 0.853, + 0.492 + ], + "angle": 0, + "content": "distinct parts" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.495, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Figure 1. Features from self-supervised methods such as DINOv2 [40] have been used to discover parts and regions of objects. However, these features fail to correctly distinguish (i) object symmetries, e.g. the left and right side of the car have the same features and (ii) individual parts, e.g. the wheels are represented by the same features irrespective of their location on the car. Our approach through use of a weak geometric spherical prior addresses these issues. Note, we use the 3D PCA projection of the features for DINOv2 and our learned spherical mapping for our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.78 + ], + "angle": 0, + "content": "The two main failure modes of current methods are depicted in Fig. 1. First, they are often confused by the symmetries that objects can exhibit (e.g. left vs. right side of a car), producing reflected versions of the feature maps when presented with the two different sides of a symmetric object. Second, they predict similar features for similar looking parts (e.g. the front left vs. back left wheel of a car), and fail to discriminate between part instances. Such symmetries and repeated structures are ubiquitous in both human-made and naturally occurring object categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We posit that these shortcomings can be addressed by enforcing an explicit 3D structure into correspondence learning, allowing the model to disambiguate multiple repeated parts, and accounting for the fact that some object parts might not be visible in all images. Indeed, scene-based correspondence pipelines use geometric verification in order to guarantee robustness in their matches [44], while other works have shown that detailed 3D meshes can be used to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19521" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.151 + ], + "angle": 0, + "content": "discover category-based correspondences through a render-and-compare pipeline [29, 62]. However, these approaches typically require 3D mesh supervision which is difficult and costly to obtain at scale." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.438 + ], + "angle": 0, + "content": "Motivated by the limitations, and the promise of the recent SSL representations [40], we propose a novel method that incorporates the missing 3D geometry into object representations. We make use of a weak 3D prior by representing object features on the surface of a sphere which encodes both geometry and appearance information. Our method consistently maps features corresponding to the same semantic parts (e.g. left headlight of a car) in images of different object instances to the same spherical coordinates, hence enabling a 3D aware and accurate correspondence. However, learning such a mapping without the ground-truth 3D supervision is nontrivial because of repeated parts and object symmetries. To this end, we propose to use much weaker supervision via coarse camera viewpoint annotations to help separate these confusing features during training. We couple this with geometric constraints to prevent collapsed representations for repeated parts. As a result, our method learns to separate object parts based on their position and spatial configuration in an image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.664 + ], + "angle": 0, + "content": "Furthermore, we point out that the standard evaluation metric for SC, Percentage of Correct Keypoints (PCK), is not able to properly evaluate symmetry-related failures as it only considers keypoints that are simultaneously visible in both the source and target image. For instance, a system predicting high similarity between a front left wheel in the source and front right wheel in the target is unlikely to be penalized for it, as the target image is unlikely to contain both a front left and front right wheel due to self-occlusions. In such cases PCK will simply not evaluate what the nearest neighbor of the source wheel is. Rather than simple accuracy-based metric, we argue that average precision is a more robust scoring mechanism and propose a new metric, Keypoint Average Precision (KAP), to account for potential spurious matches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.47, + 0.755 + ], + "angle": 0, + "content": "Our contributions are: i) a novel SC approach that learns to separate visually similar parts by mapping them to different location on a sphere, ii) a set of simple geometric constraints that force separation of visually similar parts during training, and iii) a new evaluation protocol that better accounts for the failure cases of current methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.762, + 0.216, + 0.777 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Image matching. Visual correspondences were first explored as exact matches between different views of the same scene with applications to stereo vision [24, 38], object detection [14, 33], structure from motion [20, 44, 52], and SLAM [12, 19]. Correspondences can also be computed across pixels in the frames of a video, which is referred to as optical flow [5, 7]. Traditionally they are obtained by computing hand-crafted visual descriptors [11, 32, 43]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.363 + ], + "angle": 0, + "content": "Semantic correspondence (SC). In SC estimation [30], the goal is not only to find matches across different views of the exact same object instance, but also across different instances of the same object category. While earlier work [30] match two images through densely sampled SIFT [32] features, later works extended pairwise correspondence learning to a global matching problem [61] and established region correspondences using object proposals and their geometric relations over dense descriptors [17]. Subsequently, CNNs trained with only image-level supervision have been shown to discover correspondences [31], paving the way for many deep learning correspondence systems [10, 18, 26, 59]. Typical correspondence-specific CNN architectures rely on aggregating features along the depth of a network [35, 53, 59] or use 4D convolutions spanning two images simultaneously [41]. Recently, transformers have been shown to be particularly suited to correspondence discovery thanks to their attention mechanism [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.653 + ], + "angle": 0, + "content": "While the early works in unsupervised correspondence discovery [2, 27, 50] use on the convolutional representations, recent methods [1, 47, 54, 57] build on the success of transformer-based self-supervised representations [6, 40, 60] to discover salient and robust features, which subsequent works have applied to detect semantic correspondences successfully, often surpassing supervised methods. The features from generative image models have also been used in SC [22, 49, 57]. Two closely related works [16, 39] propose to create category-wide representations by aligning self-supervised feature maps. Unlike our approach, these works are limited to 2D, and find correspondences between images without knowing the underlying 3D structure of the world which renders them incapable of distinguishing different sides of objects (e.g. left vs. right side of a car). A concurrent work [58] also identifies geometry-related issues in SSL-based correspondence but targets a supervised training regime where our approach does not necessitate keypoint supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.807 + ], + "angle": 0, + "content": "3D priors for correspondence. In literature, 3D priors have been used for SC, mainly in the form of annotated meshes [8, 29, 37, 46, 62], where annotations can either be from image to mesh, or between meshes. [29, 37] in particular use a dense parametrization of the mesh surface similar to our sphere. When no mesh is available, precise camera pose can be used to recover sparse correspondences through constrained geometric optimization [48] or by training a neural field [56]. In comparison, our approach requires no meshes and only very coarse viewpoint supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Alternatively, it is possible to estimate 3D models of object categories from image supervision alone [3, 15, 23, 25, 36, 55], from which correspondences are extracted. However, this is very challenging by itself, requiring complex pipelines capable of modeling accurate mesh deformations, pose, and rendering, which are all failure-prone." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19522" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.168, + 0.105 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.26, + 0.13 + ], + "angle": 0, + "content": "3.1. Problem statement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.47, + 0.365 + ], + "angle": 0, + "content": "General formulation. Given an unordered monocular image collection, we wish to learn a mapping \\( f(\\mathbf{I}, x) = z \\) that takes in an RGB image \\( \\mathbf{I} : \\Lambda \\to \\mathbb{R}^3 \\), \\( \\Lambda \\subset \\mathbb{R}^2 \\) and a pixel location \\( x \\in \\Lambda \\) to an \\( n \\)-dimensional embedding \\( z \\in \\mathcal{Z} \\subset \\mathbb{R}^n \\). In particular, we would like \\( f \\) to map semantic concepts from different instances of the same category (e.g. center of front-right wheel of a car) to the same point in the embedding space \\( \\mathcal{Z} \\). Formally, \\( f(\\mathbf{I}, x) = f(\\mathbf{I}', x') \\), when the pixels \\( x \\) in \\( \\mathbf{I} \\), and \\( x' \\) in \\( \\mathbf{I}' \\) correspond to the same semantic part and instance. In practice, the corresponding location for \\( (\\mathbf{I}, x) \\) in \\( \\mathbf{I}' \\) can be obtained by finding the nearest neighbor of \\( f(\\mathbf{I}, x) \\) in the embedding space, i.e. \\( \\arg \\min_{x'} d_{\\mathcal{Z}}(f(\\mathbf{I}, x), f(\\mathbf{I}', x')) \\), where \\( d_{\\mathcal{Z}} \\) is a distance function over \\( \\mathcal{Z} \\). For simplicity, we will use \\( f(\\mathbf{I}) \\) to refer to the feature map obtained by evaluating \\( f \\) on all pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.47, + 0.534 + ], + "angle": 0, + "content": "An ideal embedding function should be general enough as to not only match related semantic parts across different object instances (e.g. match the front-left wheel across two different car models) but also specific enough to distinguish between different part instances within the same object instance (e.g. front-left wheel vs. front-right wheel). Learning this from image-based self-supervision alone is a challenging task due to the visual similarity of repeated parts and self-occlusion. As a result, it is quite challenging for correspondence estimators to learn that cars have four distinct wheels from single images without explicit supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Spherical mapping. Instead, it is beneficial to endow a correspondence estimator with priors about the underlying 3D structure of objects. To this end, previous methods [29, 62] use detailed 3D meshes via a render-and compare approach. However, they rely on the presence of groundtruth 3D meshes and the precise viewpoint information. Instead, following [50, 51], we use a simplified 3D structure, specifically a sphere \\( S^2 \\subset \\mathbb{R}^3 \\) (denoted as \\( S \\) for simplicity) based on the assumption that the object categories of interest are approximately homeomorphic to spheres (i.e. objects without holes). While this may at first appear particularly ill-suited for some categories, e.g. bicycles, the geometric simplicity of \\( S \\) provides a convenient parameterization of an object's surface by allowing easy computation of geometric constraints to separate visual and semantic similarity. In particular, \\( S \\) provides a simple geodesic distance through the dot product, making it straightforward to push different semantic parts apart, which we use to distinguish repeated object features. Formally, we are interested in building a spherical mapping \\( f_S(\\pmb{I}, x) \\) that maps pixels in \\( \\pmb{I} \\) to the surface of \\( S \\). Unlike an arbitrary \\( n \\) dimensional space, \\( S \\) forms an object-centric specific coordinate system where each region ideally repre" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "sents a distinct semantic part and instance on the surface of the object." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.135, + 0.704, + 0.15 + ], + "angle": 0, + "content": "3.2. Learning formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.159, + 0.892, + 0.34 + ], + "angle": 0, + "content": "In the absence of ground truth correspondences, ensuring the semantic consistency of our spherical mapping function is very challenging. [50] enforces correspondence between image pairs through synthetically augmenting training images via thinplate splines. Unfortunately, such augmentations do not produce realistic 3D transformations such as 3D rotations which can result in the self-occlusion of parts. Instead, similar to [16, 39], we formulate the learning objective as one of aligning features from a pretrained SSL model \\(\\phi : \\Lambda \\to \\mathcal{Z}_{\\phi}\\) between different instances of an object category. For simplicity, we will refer to the SSL embedding space \\(\\mathcal{Z}_{\\phi}\\) simply as \\(\\mathcal{Z}\\) in the rest of the text." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.493 + ], + "angle": 0, + "content": "While those approaches use flat atlases \\(\\mathbb{R}^2\\to \\mathcal{Z}\\), we build a spherical prototype \\(S_{\\mathcal{Z}}:S\\to \\mathcal{Z}\\) that maps a point on the surface of the sphere \\(s\\in S^2\\) to a feature vector \\(\\mathbf{z}\\in \\mathcal{Z}\\). This formulation has two important benefits. First, the input domain of \\(S_{\\mathcal{Z}}\\) is simply \\(S\\), meaning that it does not depend on \\(I\\), and it is shared across all images, constituting a category-based map. Second, and in contrast to [16, 39], because we chose the output of \\(f_{S}\\) to lie on the surface of a sphere, we can use it to enforce 3D priors during training (Sec. 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.69 + ], + "angle": 0, + "content": "Intuitively, for a given category, the spherical prototype \\( S_{\\mathcal{Z}} \\) should be able to reconstruct any self-supervised feature map \\( \\phi(\\boldsymbol{I}) \\) when queried on the coordinates predicted by \\( f_{S} \\), i.e. \\( S_{\\mathcal{Z}}(f_{S}(\\boldsymbol{I}, x)) \\) must closely approximate \\( \\phi(\\boldsymbol{I}, x) \\) for any \\( \\boldsymbol{I}, x \\). Even if \\( S_{\\mathcal{Z}} \\) encodes a perfect category prototype, it will be unable to encode information about the image background. Hence we use instance masks \\( M(\\boldsymbol{I}) \\) at training time to restrict the loss computation to only the pixels on an object's surface. In practice, these can be obtained using pretrained segmentation models [21]. Thus, given a training image \\( \\boldsymbol{I} \\) and a pixel location \\( x \\), our primary training objective to learn the parameters of \\( f_{S} \\) and \\( S_{\\mathcal{Z}} \\) can be formulated as the minimization of" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.7, + 0.892, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\frac {1}{| \\Lambda |} \\sum_ {x \\in \\Lambda} M (\\boldsymbol {I}, x) \\times \\Gamma \\left(\\phi (\\boldsymbol {I}, x), S _ {\\mathcal {Z}} \\left(f _ {S} (\\boldsymbol {I}, x)\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\Gamma\\) is the cosine distance between the two inputs. Our spherical prototypes are implemented via a neural network that maps points in \\(\\mathbb{R}^3\\) to \\(\\mathcal{Z}\\). Importantly, each point \\(s\\in S^2\\subset \\mathbb{R}^3\\) must be mapped independently, meaning that it should correspond to a unique point \\(\\mathbf{z}\\in \\mathcal{Z}\\), irrespective of which instance it comes from or where in the image this part is located. To model multiple categories, and to encourage information sharing between closely related ones, we use a single network conditioned on a category embedding. In practice, \\(S_{\\mathcal{Z}}\\) is a visual transformer [13] without" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19523" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.506, + 0.089, + 0.678, + 0.1 + ], + "angle": 0, + "content": "Feature Reconstruction Loss" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.103, + 0.895, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.219, + 0.895, + 0.29 + ], + "angle": 0, + "content": "Figure 2. Overview of our semantic correspondence estimation approach. We begin by extracting features from a frozen self-supervised backbone, and further use them to predict spherical coordinates via a learned module. Each predicted point is used to query a jointly learned prototype, providing the supervision signal (Sec. 3.2). The sphere is used to enforce weak geometric priors (Sec. 3.3). During inference, SSL features are combined with spherical coordinates (Sec. 3.4). A blue outline indicates a fixed module, while orange indicate learned parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.471, + 0.407 + ], + "angle": 0, + "content": "self-attention, but with cross-attention between image tokens and a single category token \\(\\mathbf{c}\\) which is a one hot embedding of the category. As learning \\(f_{S}\\) from scratch can be challenging, we further leverage the SSL backbone by simply adding a prediction head \\(f_{S}^{\\prime}\\) to it to produce spherical maps, i.e. \\(f_{S} = f_{S}^{\\prime} \\circ \\phi\\). An overview of our architecture is presented in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.418, + 0.322, + 0.433 + ], + "angle": 0, + "content": "3.3. Enforcing geometric priors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.47, + 0.548 + ], + "angle": 0, + "content": "The above spherical reconstruction formulation alone offers little benefit over matching the self-supervised features from \\(\\phi\\) directly, especially considering the low dimensionality of the intermediate spherical space, which is not guaranteed to be well-behaved. However, this spherical structure enables the computation of simple geometric priors that can be enforced during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Viewpoint regularization. Many object categories exhibit some form of symmetry which can make it particularly challenging for image-based models to distinguish between different sides of an object, creating spurious correlations between distinct parts (e.g. see cars in Fig. 1). One potential way of addressing this challenge, without using dense groundtruth correspondence, is to exploit viewpoint information of the object instance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.885 + ], + "angle": 0, + "content": "An interesting property of using a spherical prototype to represent an object category is that it can easily be used to infer an object's viewpoint with respect to the camera. We posit that the average coordinate of a spherical map of an image, which we present as \\(\\mu(f_S(I)) = 1 / |\\Lambda| \\sum_{x \\in \\Lambda} f_S(I, x)\\), can be viewed as a coarse approximation of the camera viewpoint under which the object is seen, e.g. right side views should be approximately mapped to the right side of the sphere, and left side views to the left. Intuitively, thinking of \\(f_S\\) as a mapping from image pixels to the object's surface, the visible parts of an object should roughly be those closest to the camera, while the others should be hidden by self-occlusion." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "By using the groundtruth camera viewpoint \\( v_{I} \\), we en" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.895, + 0.452 + ], + "angle": 0, + "content": "force the average direction of the spherical map \\(\\mu (f_S(I))\\) to align with \\(v_{I}\\). When this is satisfied, symmetric views must be mapped to different parts of the sphere. While precise viewpoint information is hard to obtain, we observe it is sufficient to use coarse relative viewpoint supervision between images. In practice, viewpoints are discretized into a small number of bins, and \\(v_{I}\\) is represented by the median value of the corresponding bin. Then, we simply enforce that the dot product between viewpoints from two images equals that of their average spherical maps," + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.458, + 0.892, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v p} = \\sum_ {\\boldsymbol {I}, \\boldsymbol {I} ^ {\\prime}} | | v _ {\\boldsymbol {I}} \\cdot v _ {\\boldsymbol {I} ^ {\\prime}} - \\mu \\left(f _ {S} (\\boldsymbol {I})\\right) \\cdot \\mu \\left(f _ {S} \\left(\\boldsymbol {I} ^ {\\prime}\\right)\\right) | | ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Relative distance loss. As noted earlier, current self-supervised extracted features can confuse repeated object repeated parts. Depending on the target goal, this can be desirable, if the parts do indeed belong to the same part category. However, this is detrimental for dense correspondence estimation as the parts may actually be different part instances, e.g. left vs. right leg. It can be hard to distinguish between these based on their appearance alone and additional geometric context is required." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.84 + ], + "angle": 0, + "content": "One trivial way of encoding this context is by making the assumption that similar parts that appear in different locations on an image (i.e. not beside each other) are in fact different instances of the same semantic part. Therefore, we would like to enforce the property on our predicted spherical maps that distant pixels in the image should be mapped far apart on the sphere. Due to scale variation, distance on the image plane is hard to link to distances on the surface of the sphere. However, we can reformulate this property as a relative distance comparison using a triplet. Given three points \\(a\\), \\(b\\), and \\(c\\) on an image \\(\\pmb{I}\\), and their corresponding positions \\(s_a = f_S(\\pmb{I}, a)\\), \\(s_b\\), and \\(s_c\\) on the sphere, the ordering between distances should be preserved, that is:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.847, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\left| \\left| a - b \\right| \\right| \\leq \\left| \\left| a - c \\right| \\right| \\iff \\Gamma \\left(s _ {a}, s _ {b}\\right) \\leq \\Gamma \\left(s _ {a}, s _ {c}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In reality, this does not hold for distances along an object's surface, which the sphere is supposed to represent, partly" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19524" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.089, + 0.185, + 0.1 + ], + "angle": 0, + "content": "Spherical Coordinates" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.103, + 0.186, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.089, + 0.334, + 0.101 + ], + "angle": 0, + "content": "Relative Distance Loss \\(\\mathcal{L}_{rd}\\)" + }, + { + "type": "image", + "bbox": [ + 0.208, + 0.103, + 0.318, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.089, + 0.451, + 0.1 + ], + "angle": 0, + "content": "Orientation Loss \\(\\mathcal{L}_o\\)" + }, + { + "type": "image", + "bbox": [ + 0.35, + 0.103, + 0.47, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.217, + 0.47, + 0.327 + ], + "angle": 0, + "content": "Figure 3. Illustration of our geometry losses \\(\\mathcal{L}_{rd}\\) and \\(\\mathcal{L}_o\\). The left image shows a spherical map from which a triplet of points is sampled. \\(\\mathcal{L}_{rd}\\): as the anchor patch \\(a\\) is closer to the positive \\(b\\) on the image compared with the negative \\(c\\), its corresponding position \\(s_a\\) on the sphere must also be closer to \\(s_b\\) than \\(s_c\\). \\(\\mathcal{L}_o\\): after projecting \\(s_b\\) and \\(s_c\\) to the plane tangent to the sphere at \\(s_a\\), we ensure orientation is preserved by enforcing positive collinearity between \\(u_b \\times u_c\\) and the normal vector \\(n\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.344, + 0.469, + 0.434 + ], + "angle": 0, + "content": "due to perspective. For example, in the case of a long train seen from a near frontal view, parts at the back of the train might appear very close to the front in the image, even though they are very far in 3D space. Nevertheless, we find that this is still an effective prior for discouraging repeated part instances from being mapped to the same location." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.469, + 0.525 + ], + "angle": 0, + "content": "During training, point triplets \\((a,b,c)\\) are randomly sampled among pixels that belong to the object. Among each such triplet, we chose an anchor location \\(anc = a\\), a positive location \\(pos = \\arg \\min_{x\\in \\{b,c\\}}||a - x||\\), and a negative location \\(neg = \\arg \\max_{x\\in \\{b,c\\}}||a - x||\\) (see Fig. 3). We can then define a triplet margin loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.535, + 0.469, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {r d} = \\max (\\Gamma (f _ {S} (\\boldsymbol {I}, a n c), f _ {S} (\\boldsymbol {I}, p o s)) \\tag {4} \\\\ - \\Gamma (f _ {S} (\\boldsymbol {I}, a n c), f _ {S} (\\boldsymbol {I}, n e g)) + \\delta , 0), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.469, + 0.642 + ], + "angle": 0, + "content": "where \\(\\delta\\) is a hyperparameter which specifies the margin. A useful side product of this formulation is that it encourages the spherical maps to be smooth, as strong discontinuities would produce a large anchor to positive distance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Orientation loss. A final advantage of using \\( S \\) as a latent space is that it is an orientable 2D space, just like images. Therefore, enforcing that \\( f_{S} \\) preserves orientation prevents spurious matches between symmetric views. Intuitively, if a point \\( a \\) appears on the right side of \\( b \\) in the image, then \\( s_a \\) must appear in the same side of \\( s_b \\). Given a point triplet as defined earlier, this can be enforced by making sure that the determinant of the image triplet and sphere triplet positively correlate. Formally, defining \\( P_a \\) as the orthogonal projection to the plane tangent to \\( S \\) at \\( s_a \\) and \\( u_b \\) as \\( P_a(s_b) - s_a \\), we have \\( d_I = \\det(b - a, c - a) \\) and \\( d_S = \\det(u_b, u_c) \\), and want \\( sign(d_I) = sign(d_S) \\) (see Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "As objects can have complex geometry that our model does not have access to, there exists no exact relation linking the two determinants together, as for instance perspective distortions might alter angles. However, we can as-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "sume that image triplets of large determinants should also have large determinant on the sphere, as a change of sign in determinant indicates the relative orientation on the sphere has been inverted. In practice, we randomly sample image triplets \\((a,b,c)\\) and select those whose image determinant \\(d_{I}\\) is higher than a threshold \\(d_{\\tau} = 0.7\\) while swapping \\(b\\) and \\(c\\) if \\(d_{I}\\) is negative. Then, we enforce the determinant of the corresponding sphere triplet to be at least \\(d_{\\tau}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.22, + 0.892, + 0.261 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o} = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} d _ {I} < d _ {\\tau} \\\\ \\max \\left(d _ {\\tau} - d _ {S}, 0\\right) & \\text {i f} d _ {I} \\geq d _ {\\tau}. \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.276, + 0.891, + 0.293 + ], + "angle": 0, + "content": "3.4. Correspondence via combined representations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.36 + ], + "angle": 0, + "content": "During inference, it is possible to directly query the spherical maps \\( f_{S} \\) of two images to obtain correspondences using the cosine distance. That is, for an image pair \\( I, I' \\) and a query location \\( q \\) on \\( I \\), its location in \\( I' \\) can be computed as" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.374, + 0.891, + 0.4 + ], + "angle": 0, + "content": "\\[\np ^ {*} = \\underset {p} {\\arg \\min } \\Gamma \\left(f _ {S} (\\boldsymbol {I}, q), f _ {S} \\left(\\boldsymbol {I} ^ {\\prime}, p\\right)\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.614 + ], + "angle": 0, + "content": "While this protocol is sound, it comes with two important drawbacks. First, \\( f_{S} \\) produces spherical maps for the whole image, including the background, meaning segmentation masks would be required at inference time to prevent the emergence of spurious matches. Second, the spherical map is designed to be a smooth parameterization of the object surface, making it susceptible to missing fine details. A slightly incorrect mapping \\( f_{S}(I,q) + \\epsilon \\) has a high probability of finding a higher match in a nearby region of the correct match \\( f_{S}(I^{\\prime},p^{*}) \\) if both maps are smooth. In comparison, SSL feature maps can exhibit strict feature separation, e.g. wheel features are very different from other nearby non-wheel features, making it unlikely that a wheel pixel finds a nearest neighbor among nearby non-wheel pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.892, + 0.766 + ], + "angle": 0, + "content": "To mitigate this issue, we make use of the feature maps that are already computed by the self-supervised backbone network \\(\\phi\\), in a similar way to supervised correspondence approaches that aggregate features from a network [35, 53, 59]. Existing literature has shown that DINO features are particularly effective at differentiating between the foreground and background [1], removing the need for inference-time segmentation. To leverage these DINO features, we reformulate Eq. (6) as the combination of self-supervised features and spherical locations:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.773, + 0.892, + 0.812 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} p ^ {*} = \\arg \\min _ {p} (1 - \\alpha) \\Gamma (\\phi (\\boldsymbol {I}, q), \\phi (\\boldsymbol {I} ^ {\\prime}, p)) & \\\\ + \\alpha \\Gamma (f _ {S} (\\boldsymbol {I}, q), f _ {S} (\\boldsymbol {I} ^ {\\prime}, p)), & \\end{array} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.818, + 0.851, + 0.833 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a hyperparameter that balances each term." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.632, + 0.862 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. We build our models on DINOv1-B/8 [6] and DINOv2-B/14 [40] backbones. Training masks" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19525" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.27 + ], + "angle": 0, + "content": "
↑3%4%5%6%7%8%9%10%11%12%13%14%15%16%17%avg
CustomCATS [9]52.034.772.234.349.957.543.666.524.463.256.552.042.641.743.033.672.658.049.9
MMNet+FCN [59]55.937.065.035.450.063.945.762.828.765.054.751.638.534.641.736.377.762.550.4
SCorrSan [26]57.140.378.338.151.857.847.167.925.271.363.949.345.349.848.840.377.769.754.4
DINOv1DINOv1 [6]44.326.857.622.029.332.819.754.014.940.139.329.329.037.020.028.240.621.132.6
ASIC [16]57.925.268.124.735.428.430.954.821.645.047.239.926.248.814.524.549.024.637.0
Ours47.126.070.921.837.534.932.460.023.253.648.542.528.342.721.141.939.741.739.7
SDDIFT [49]63.554.580.834.546.252.748.377.739.076.054.961.353.346.057.857.171.163.457.7
SD [57]63.155.680.233.844.949.347.874.438.470.853.761.154.455.054.853.565.053.356.1
DINOv2DINOv2 [40]72.762.085.241.340.452.351.571.136.267.164.667.661.068.230.762.054.324.256.2
DINOv2 + SD [57]73.064.186.440.752.955.053.878.645.577.364.769.763.369.258.467.666.253.563.3
Ours (sphere only)46.728.866.333.036.566.659.174.925.465.750.152.727.113.715.846.673.536.745.5
Ours76.961.285.942.148.473.367.280.046.380.266.771.266.063.936.268.667.842.263.6
Ours + SD74.864.587.145.652.777.871.482.447.782.067.373.967.660.049.969.878.559.167.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.276, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Table 1. Keypoint matching scores on SPair-71k evaluated using PCK@0.1 with macro-averaging for the summary scores. We present our approach using DINOv1 [6] features (middle rows) and DINOv2 [40] features (bottom rows). In both cases, we improve over the DINO only baselines and are superior to fully supervised methods (top rows). Bold entries are best per category and underlined are second-best." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.471, + 0.504 + ], + "angle": 0, + "content": "are obtained using a pretrained Mask R-CNN model [21]. Our spherical mapper consists of a linear dimension reduction layer halving the number of features, a visual transformer block with self-attention, and a final linear layer with an output dimension of three. The resulting feature map is then normalized pixel-wise so that its output values lie on the surface of \\( S^2 \\). The dimensionality reduction layer, while not strictly necessary, is helpful considering the small number of images used during training, while the transformer block helps in disentangling sides and repeated parts by allowing global reasoning between image patches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.665 + ], + "angle": 0, + "content": "The final loss term is computed as \\(\\mathcal{L} = \\mathcal{L}_{rec} + \\lambda_{rd}\\mathcal{L}_{rd} + \\lambda_o\\mathcal{L}_o + \\lambda_{vp}\\mathcal{L}_{vp}\\). We set \\(\\lambda_{rd} = \\lambda_o = 0.3\\), while \\(\\lambda_{vp} = 0.1\\) is set slightly lower as it can have the detrimental effect of pulling all predictions towards the average over image pixels - cf. Eq. (2). The relative distance margin is set to \\(\\delta = 0.5\\) to encourage feature separation. To perform matching in Eq. (7), \\(\\alpha\\) is set to 0.2 so that we leverage the highly discriminative DINO features, while using the sphere as a symmetry and repetition-breaking mechanism. Our model is trained for a total of 200 epochs using Adam [28]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Datasets. Following existing work [16, 26, 57], we evaluate our method primarily on the Spair-71k dataset [34], which contains images from 18 different object categories. The evaluation set contains between 600 and 900 image pairs, each of which are annotated with the keypoints that are visible in both images. We train our model on the Spair-71k training split on all categories simultaneously, without using any keypoint annotations. Additionally, we evaluate on the AwA-pose dataset [4], which contains images from 35 quadruped categories, annotated with keypoints. We also present results by training on the Freiburg cars dataset [45]. This dataset was collected by densely sampling approximately 100 images each around 48 different car instances. The higher image count, coupled with \\(360^{\\circ}\\) dense sampling, enables us to learn a more detailed spherical prototype." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.338, + 0.745, + 0.354 + ], + "angle": 0, + "content": "4.1. Keypoint average precision" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.669 + ], + "angle": 0, + "content": "While issues with symmetries are clear in Fig. 4, we argue that the PCK metric fails to account for them as it is only computed between keypoints that appear in both the source and target image. Hence, models that predict high similarity between two visually similar but semantically different keypoints might not be penalized for it. PCK can partly account for repetition-related mistakes if the parts appear simultaneously in both images, but it does not penalize symmetry-related issues, like mistaking the left and right side of a car, as the corresponding keypoints do not appear simultaneously. PCK was initially proposed for simpler cases where keypoints were assumed to be always be visible, e.g. faces or different instances in the same pose. However, as benchmarks become more challenging, a more robust protocol should be used. To illustrate how much these failure cases impact SSL models, we propose an alternative evaluation metric, Keypoint Average Precision - \\(\\mathrm{KAP}@\\kappa\\). It is similar to \\(\\mathrm{PCK}@\\kappa\\), but accounts for these errors by evaluating average precision instead of accuracy and penalizes methods that predict matches when none exist." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.901 + ], + "angle": 0, + "content": "When performing evaluation on a pair of images, instead of restricting it to keypoints that simultaneously appear in both images, we consider all keypoints that appear in the source, irrespective of whether they are also visible in the target image. For each such keypoint, if it appears in the target image, we extract the highest similarity value within radius \\(\\kappa\\) of the ground-truth and label it as positive. We also extract the highest similarity value outside the radius and label it as negative, penalizing overly high predictions on wrong, possibly repeated parts. If the source keypoint does not appear on the target image, we simply extract the highest similarity prediction across the whole target image and label it as negative to penalize incorrectly high similarity when none should exist. This effectively reformulates the task as a binary classification problem, where the embed-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19526" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.891, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.346, + 0.895, + 0.416 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of dense correspondence maps. For DINOv2, SD, and DINO+SD features we perform PCA on the segmented object features independently for each category, then visualize the three main components. Note that the SD and DINO+SD features are not completely equivalent to the ones used to compute matches, but are provided here for illustration. Spherical maps from \\( f_{S} \\) (Sphere) for our approach are visualized directly. Our spherical maps correctly identify the different sides of objects, whereas other features fail to capture these differences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.471, + 0.489 + ], + "angle": 0, + "content": "ding of each source keypoint has to be close to, and only to, the corresponding target keypoint. Finally, we compute the average precision over all the extracted pairs, and report mean average precision per-category." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.499, + 0.246, + 0.513 + ], + "angle": 0, + "content": "4.2. SPair-71k results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.703 + ], + "angle": 0, + "content": "We first evaluate on the task of keypoint transfer between pairs of images using Spair-71k [34]. We present quantitative per-category results in Tab. 1, using the standard PCK metric along with macro-averaged scores as the number of per-category pairs varies greatly. We split the models according to their backbone: custom supervised models, DINOv1-based, SD-based, and DINOv2-based. A striking preliminary observation is the effectiveness of DINOv2, surpassing supervised approaches on most categories. While its success can partially be attributed to evaluation biases [2], this demonstrates the effectiveness of large scale learned self-supervised features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Using a DINOv1 backbone, our model improves over its backbone on most categories, and over ASIC [16] on average. When combined with the DINOv2 backbone, our model provides improvements on all but two categories. A clear pattern can be identified, with strongest improvements being observed over blob-like symmetric objects with repeated parts (+21.0 on bus and +15.7 on car), while spherical mapping hinders performance on highly deformable categories (-4.3 on person), or high-genus objects for which a sphere is a poor surface prior (-0.8 on bicycle). Our model performs slightly better compared to DINO+SD [57], while requiring a fraction of the computational cost at inference time. Finally, following [57] we evaluate adding Stable Diff" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.893, + 0.488 + ], + "angle": 0, + "content": "fusion (SD) [42] features to our method at inference time, which yields further improvements. This illustrates that spherical maps and SD features capture different facets of the correspondence problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.893, + 0.669 + ], + "angle": 0, + "content": "We show the results of evaluating correspondences with KAP in Tab. 2. We observe particularly large discrepancies between PCK and KAP in highly symmetric objects with repeated parts, e.g. buses and cars, and the ranking between our model and DINOv2 is reversed on humans, possibly due to DINOv2's symmetric predictions on left and right limbs. All models across all categories obtain lower results when using KAP highlight the symmetry issues they are facing. A limitation of KAP is that it might still count correct repeated parts mistakes if their distance in the image is less than \\(\\kappa\\). Nonetheless, we argue that KAP is more informative than PCK and is just as efficient to evaluate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.894, + 0.791 + ], + "angle": 0, + "content": "The qualitative visualization shown in Fig. 4 illustrates these improved results. Our model correctly maps the two opposite sides of the cars to different sphere regions, while other feature maps look extremely similar, even when looking at two opposite sides of an object, with the notable exception of SD on birds. The fact that such similarities exist between opposite views suggest that the utility of baselines such as DINOv2 would be quite limited in real scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.704, + 0.816 + ], + "angle": 0, + "content": "4.3. Additional evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Animals with Attributes (AwA). To further evaluate our model, we also report results on the AwA-pose dataset from [4], which contains images from 35 different categories of quadruped. While our spherical prototype needs category information during training to reconstruct" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19527" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.889, + 0.182 + ], + "angle": 0, + "content": "
↑%avg
DINOv2 [40]53.554.060.235.544.436.331.761.337.454.752.551.548.848.237.844.147.438.246.5
SD [57]44.448.554.531.545.232.730.068.435.855.247.948.144.842.344.539.252.751.245.4
DINOv2 + SD [57]52.055.959.234.749.036.032.570.339.859.853.152.450.650.447.846.253.349.849.6
Ours (sphere only)38.434.253.933.037.949.743.471.729.857.145.842.532.427.029.537.157.436.042.1
Ours60.751.263.138.445.055.945.769.740.463.254.854.351.248.738.847.955.542.251.5
Ours + SD58.954.262.239.646.654.547.176.240.965.357.356.154.247.443.749.462.452.053.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.121, + 0.186, + 0.848, + 0.201 + ], + "angle": 0, + "content": "Table 2. Keypoint matching scores on SPair-71k evaluated using KAP@0.1 with macro-averaging for the summary scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.221, + 0.473, + 0.433 + ], + "angle": 0, + "content": "category-specific features, only the sphere mapper is used during inference, meaning it can be readily applied to unseen categories. Five quadruped classes (cat, cow, dog, horse, and sheep) appear in both SPair and AwA-pose, and are therefore seen during training, but the rest are completely new for our sphere mapper. Nonetheless, results shown in Tab. 3 show that the sphere mapper generalizes well to unseen categories. We attribute this to the assistance from the strong category-agnostic features from DINOv2. Once again, the improvement of using our spherical method is much more apparent using KAP, i.e. the PCK improvement over DINOv2 alone is 2.2 when adding SD and 2.6 when adding spheres, while these become 1.8 and 3.9 respectively with KAP." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.445, + 0.445, + 0.486 + ], + "angle": 0, + "content": "
Dv2SDDv2+SDOursOurs+SD
PCK@0.165.956.068.168.769.8
KAP@0.155.050.756.858.960.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.486, + 0.471, + 0.527 + ], + "angle": 0, + "content": "Table 3. Average scores when evaluating on AwA-pose using a random subset of 200 pairs per category. 'Ours' denotes our model trained on SPair-71k with a DINoV2 backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.643 + ], + "angle": 0, + "content": "Model ablation. We also analyze the impact of removing each individual loss term when training our model in an ablation study. The results in Tab. 4 indicate that all variants except the no \\(\\mathcal{L}_{rd}\\) one do not significantly improve over the DINOv2 baseline as they also fail to identify opposite sides of objects and repeated parts." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.654, + 0.445, + 0.683 + ], + "angle": 0, + "content": "
DINOv2no Lvpno Lrdno Lofull model
56.258.661.256.063.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Table 4. Average PCK@0.1 scores when training and testing on SPair-71k using different ablated versions of our approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Inference speed. The results in Tab. 1 demonstrate how effective the addition of Stable Diffusion features are. However, computing correspondences through diffusion requires adding noise to images, running iterative diffusion, and performing joint decomposition between the source and target features. As a result, its inference speed is much slower compared to using DINOv2 features. In comparison, our approach only requires a few extra layers on top of DINOv2 and has negligible additional overhead. Timing results in Tab. 5 illustrate that adding diffusion-extracted features reduces throughput by an order of magnitude." + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.212, + 0.868, + 0.24 + ], + "angle": 0, + "content": "
DINOv2SDDINOv2+SDOursOurs+SD
3.40.380.353.30.34
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.242, + 0.892, + 0.27 + ], + "angle": 0, + "content": "Table 5. Descriptor computation throughput in pairs/second at inference time on a single A5000 GPU, where higher is better." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.298, + 0.627, + 0.313 + ], + "angle": 0, + "content": "4.4. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.323, + 0.892, + 0.58 + ], + "angle": 0, + "content": "While our approach results in significant improvements over the DINOV2 baseline for many categories (see Tab. 1), there are still some limitations. For example, we do not perform as well on a small number of categories that cannot be well approximated by a sphere (e.g. humans). Furthermore, the very low-dimensional spherical encoding on its own is not as effective at discriminating parts and subparts and thus needs to be combined with self-supervised features. However, as we already densely compute these features at inference time for each test image, there is no additional cost in combining them with our spherical mapping when evaluating correspondence. Finally, our method relies on additional supervision at training time in the form of automatically computed segmentation masks and weak camera pose supervision. However, results in the supplementary material suggest that coarse camera viewpoints are enough to obtain good performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.596, + 0.62, + 0.612 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.866 + ], + "angle": 0, + "content": "We presented a new approach for semantic correspondence estimation that is robust to issues resulting from object symmetries and repeated part instances. In addition, we proposed a new evaluation protocol that is more sensitive to these issues. Our approach leverages recent advances in the self-supervised learning of discriminative image features and combines them with a weak geometric spherical prior. By using weak pose supervision to represent objects categories on the surface of spheres, we are able to enforce simple geometric constraints during training that result in more geometric and semantically consistent representations. Results on the task of semantic keypoint matching between images from different object instances, a fundamental task in 3D computer vision, demonstrate that our approach alone is superior to existing strong baselines and can be combined with existing methods to further boost performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This project was supported by the EP-SRC Visual AI grant EP/T028572/1." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19528" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Shir Amir, Yossi Gandelsman, Shai Bagon, and Tali Dekel. Deep vit features as dense visual descriptors. ECCV Workshop - What is Motion For?, 2022. 1, 2, 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.468, + 0.199 + ], + "angle": 0, + "content": "[2] Mehmet Aygün and Oisin Mac Aodha. Demystifying unsupervised semantic correspondence estimation. In ECCV, 2022. 1, 2, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.089, + 0.202, + 0.468, + 0.228 + ], + "angle": 0, + "content": "[3] Mehmet Aygün and Oisin Mac Aodha. 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In CVPR, 2016. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19530" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_origin.pdf b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..98308c893b8f7b750bb01be6fec03a7d90b5e1c3 --- /dev/null +++ b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/22b6ed4b-b424-4fe5-8f1f-d4f3f6fa485d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:907d4aa69ee89c5a97cfd1cd0a4ff11e7f0a6ecef91f5df16482c14950f6ae46 +size 8819685 diff --git a/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/full.md b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fe07583154a3c2b94348b4f6a7287e3f85311d4b --- /dev/null +++ b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/full.md @@ -0,0 +1,305 @@ +# Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps + +Octave Mariotti Oisin Mac Aodha Hakan Bilen + +University of Edinburgh + +groups.inf.ed.ac.uk/vico/research/sphericalmaps + +# Abstract + +Recent self-supervised models produce visual features that are not only effective at encoding image-level, but also pixel-level, semantics. They have been reported to obtain impressive results for dense visual semantic correspondence estimation, even outperforming fully-supervised methods. Nevertheless, these models still fail in the presence of challenging image characteristics such as symmetries and repeated parts. To address these limitations, we propose a new semantic correspondence estimation method that supplements state-of-the-art self-supervised features with 3D understanding via a weak geometric spherical prior. Compared to more involved 3D pipelines, our model provides a simple and effective way of injecting informative geometric priors into the learned representation while requiring only weak viewpoint information. We also propose a new evaluation metric that better accounts for repeated part and symmetry-induced mistakes. We show that our method succeeds in distinguishing between symmetric views and repeated parts across many object categories in the challenging SPair-71k dataset and also in generalizing to previously unseen classes in the AwA dataset. + +# 1. Introduction + +Semantic correspondence (SC) estimation aims to find local regions that correspond to the same semantic entities across a collection of images, where each image contains a different instance of the same object category [30]. SC has been studied in both supervised [9, 26, 59] and unsupervised [2, 50] settings. Thanks to the recent progress in self-supervised learning (SSL) [6, 40, 60], recent SSL-based approaches have been shown to obtain strong performance on multiple benchmarks [1, 2, 54]. However, they often act as simple part detectors, without having any 3D understanding of object extent, or relative location of object parts. As these SSL methods are typically trained using only 2D-based objectives, they are not able to learn 3D-aware representations, and often converge to similar features for object parts that share appearance but not fine-grained semantics. + +![](images/cf42395a54f16cd93a35efc6090b8caacfe541aabb42c3a7daf34fe28a0a3327.jpg) +Input + +![](images/4d6a4d5ce187995cd2e41c258ddd2b6758814ec4627c5d5b868eee9a20f7ad27.jpg) +DINOv2 + +![](images/c0a9464c0fb9c2526df1b455fd01dba7c10b83171dedd6ae4cdaabb20009d690.jpg) +Figure 1. Features from self-supervised methods such as DINOv2 [40] have been used to discover parts and regions of objects. However, these features fail to correctly distinguish (i) object symmetries, e.g. the left and right side of the car have the same features and (ii) individual parts, e.g. the wheels are represented by the same features irrespective of their location on the car. Our approach through use of a weak geometric spherical prior addresses these issues. Note, we use the 3D PCA projection of the features for DINOv2 and our learned spherical mapping for our method. + +![](images/769c98ff9096e99c04cdf49df27d6968daba1feec95d907f84fc453281b9125a.jpg) +collapsed sides +collapsed parts + +![](images/1080e5808b8ed0d5af3ebceb47639559b7547eaba36990b500c131073d112a48.jpg) +Ours +distinct sides + +![](images/b4bc07b933358b181f02ed7a06323e13289bf045a7817322fde81749635f219b.jpg) +distinct parts + +The two main failure modes of current methods are depicted in Fig. 1. First, they are often confused by the symmetries that objects can exhibit (e.g. left vs. right side of a car), producing reflected versions of the feature maps when presented with the two different sides of a symmetric object. Second, they predict similar features for similar looking parts (e.g. the front left vs. back left wheel of a car), and fail to discriminate between part instances. Such symmetries and repeated structures are ubiquitous in both human-made and naturally occurring object categories. + +We posit that these shortcomings can be addressed by enforcing an explicit 3D structure into correspondence learning, allowing the model to disambiguate multiple repeated parts, and accounting for the fact that some object parts might not be visible in all images. Indeed, scene-based correspondence pipelines use geometric verification in order to guarantee robustness in their matches [44], while other works have shown that detailed 3D meshes can be used to + +discover category-based correspondences through a render-and-compare pipeline [29, 62]. However, these approaches typically require 3D mesh supervision which is difficult and costly to obtain at scale. + +Motivated by the limitations, and the promise of the recent SSL representations [40], we propose a novel method that incorporates the missing 3D geometry into object representations. We make use of a weak 3D prior by representing object features on the surface of a sphere which encodes both geometry and appearance information. Our method consistently maps features corresponding to the same semantic parts (e.g. left headlight of a car) in images of different object instances to the same spherical coordinates, hence enabling a 3D aware and accurate correspondence. However, learning such a mapping without the ground-truth 3D supervision is nontrivial because of repeated parts and object symmetries. To this end, we propose to use much weaker supervision via coarse camera viewpoint annotations to help separate these confusing features during training. We couple this with geometric constraints to prevent collapsed representations for repeated parts. As a result, our method learns to separate object parts based on their position and spatial configuration in an image. + +Furthermore, we point out that the standard evaluation metric for SC, Percentage of Correct Keypoints (PCK), is not able to properly evaluate symmetry-related failures as it only considers keypoints that are simultaneously visible in both the source and target image. For instance, a system predicting high similarity between a front left wheel in the source and front right wheel in the target is unlikely to be penalized for it, as the target image is unlikely to contain both a front left and front right wheel due to self-occlusions. In such cases PCK will simply not evaluate what the nearest neighbor of the source wheel is. Rather than simple accuracy-based metric, we argue that average precision is a more robust scoring mechanism and propose a new metric, Keypoint Average Precision (KAP), to account for potential spurious matches. + +Our contributions are: i) a novel SC approach that learns to separate visually similar parts by mapping them to different location on a sphere, ii) a set of simple geometric constraints that force separation of visually similar parts during training, and iii) a new evaluation protocol that better accounts for the failure cases of current methods. + +# 2. Related work + +Image matching. Visual correspondences were first explored as exact matches between different views of the same scene with applications to stereo vision [24, 38], object detection [14, 33], structure from motion [20, 44, 52], and SLAM [12, 19]. Correspondences can also be computed across pixels in the frames of a video, which is referred to as optical flow [5, 7]. Traditionally they are obtained by computing hand-crafted visual descriptors [11, 32, 43]. + +Semantic correspondence (SC). In SC estimation [30], the goal is not only to find matches across different views of the exact same object instance, but also across different instances of the same object category. While earlier work [30] match two images through densely sampled SIFT [32] features, later works extended pairwise correspondence learning to a global matching problem [61] and established region correspondences using object proposals and their geometric relations over dense descriptors [17]. Subsequently, CNNs trained with only image-level supervision have been shown to discover correspondences [31], paving the way for many deep learning correspondence systems [10, 18, 26, 59]. Typical correspondence-specific CNN architectures rely on aggregating features along the depth of a network [35, 53, 59] or use 4D convolutions spanning two images simultaneously [41]. Recently, transformers have been shown to be particularly suited to correspondence discovery thanks to their attention mechanism [9]. + +While the early works in unsupervised correspondence discovery [2, 27, 50] use on the convolutional representations, recent methods [1, 47, 54, 57] build on the success of transformer-based self-supervised representations [6, 40, 60] to discover salient and robust features, which subsequent works have applied to detect semantic correspondences successfully, often surpassing supervised methods. The features from generative image models have also been used in SC [22, 49, 57]. Two closely related works [16, 39] propose to create category-wide representations by aligning self-supervised feature maps. Unlike our approach, these works are limited to 2D, and find correspondences between images without knowing the underlying 3D structure of the world which renders them incapable of distinguishing different sides of objects (e.g. left vs. right side of a car). A concurrent work [58] also identifies geometry-related issues in SSL-based correspondence but targets a supervised training regime where our approach does not necessitate keypoint supervision. + +3D priors for correspondence. In literature, 3D priors have been used for SC, mainly in the form of annotated meshes [8, 29, 37, 46, 62], where annotations can either be from image to mesh, or between meshes. [29, 37] in particular use a dense parametrization of the mesh surface similar to our sphere. When no mesh is available, precise camera pose can be used to recover sparse correspondences through constrained geometric optimization [48] or by training a neural field [56]. In comparison, our approach requires no meshes and only very coarse viewpoint supervision. + +Alternatively, it is possible to estimate 3D models of object categories from image supervision alone [3, 15, 23, 25, 36, 55], from which correspondences are extracted. However, this is very challenging by itself, requiring complex pipelines capable of modeling accurate mesh deformations, pose, and rendering, which are all failure-prone. + +# 3. Method + +# 3.1. Problem statement + +General formulation. Given an unordered monocular image collection, we wish to learn a mapping $f(\mathbf{I}, x) = z$ that takes in an RGB image $\mathbf{I} : \Lambda \to \mathbb{R}^3$ , $\Lambda \subset \mathbb{R}^2$ and a pixel location $x \in \Lambda$ to an $n$ -dimensional embedding $z \in \mathcal{Z} \subset \mathbb{R}^n$ . In particular, we would like $f$ to map semantic concepts from different instances of the same category (e.g. center of front-right wheel of a car) to the same point in the embedding space $\mathcal{Z}$ . Formally, $f(\mathbf{I}, x) = f(\mathbf{I}', x')$ , when the pixels $x$ in $\mathbf{I}$ , and $x'$ in $\mathbf{I}'$ correspond to the same semantic part and instance. In practice, the corresponding location for $(\mathbf{I}, x)$ in $\mathbf{I}'$ can be obtained by finding the nearest neighbor of $f(\mathbf{I}, x)$ in the embedding space, i.e. $\arg \min_{x'} d_{\mathcal{Z}}(f(\mathbf{I}, x), f(\mathbf{I}', x'))$ , where $d_{\mathcal{Z}}$ is a distance function over $\mathcal{Z}$ . For simplicity, we will use $f(\mathbf{I})$ to refer to the feature map obtained by evaluating $f$ on all pixels. + +An ideal embedding function should be general enough as to not only match related semantic parts across different object instances (e.g. match the front-left wheel across two different car models) but also specific enough to distinguish between different part instances within the same object instance (e.g. front-left wheel vs. front-right wheel). Learning this from image-based self-supervision alone is a challenging task due to the visual similarity of repeated parts and self-occlusion. As a result, it is quite challenging for correspondence estimators to learn that cars have four distinct wheels from single images without explicit supervision. + +Spherical mapping. Instead, it is beneficial to endow a correspondence estimator with priors about the underlying 3D structure of objects. To this end, previous methods [29, 62] use detailed 3D meshes via a render-and compare approach. However, they rely on the presence of groundtruth 3D meshes and the precise viewpoint information. Instead, following [50, 51], we use a simplified 3D structure, specifically a sphere $S^2 \subset \mathbb{R}^3$ (denoted as $S$ for simplicity) based on the assumption that the object categories of interest are approximately homeomorphic to spheres (i.e. objects without holes). While this may at first appear particularly ill-suited for some categories, e.g. bicycles, the geometric simplicity of $S$ provides a convenient parameterization of an object's surface by allowing easy computation of geometric constraints to separate visual and semantic similarity. In particular, $S$ provides a simple geodesic distance through the dot product, making it straightforward to push different semantic parts apart, which we use to distinguish repeated object features. Formally, we are interested in building a spherical mapping $f_S(\pmb{I}, x)$ that maps pixels in $\pmb{I}$ to the surface of $S$ . Unlike an arbitrary $n$ dimensional space, $S$ forms an object-centric specific coordinate system where each region ideally repre + +sents a distinct semantic part and instance on the surface of the object. + +# 3.2. Learning formulation + +In the absence of ground truth correspondences, ensuring the semantic consistency of our spherical mapping function is very challenging. [50] enforces correspondence between image pairs through synthetically augmenting training images via thinplate splines. Unfortunately, such augmentations do not produce realistic 3D transformations such as 3D rotations which can result in the self-occlusion of parts. Instead, similar to [16, 39], we formulate the learning objective as one of aligning features from a pretrained SSL model $\phi : \Lambda \to \mathcal{Z}_{\phi}$ between different instances of an object category. For simplicity, we will refer to the SSL embedding space $\mathcal{Z}_{\phi}$ simply as $\mathcal{Z}$ in the rest of the text. + +While those approaches use flat atlases $\mathbb{R}^2\to \mathcal{Z}$ , we build a spherical prototype $S_{\mathcal{Z}}:S\to \mathcal{Z}$ that maps a point on the surface of the sphere $s\in S^2$ to a feature vector $\mathbf{z}\in \mathcal{Z}$ . This formulation has two important benefits. First, the input domain of $S_{\mathcal{Z}}$ is simply $S$ , meaning that it does not depend on $I$ , and it is shared across all images, constituting a category-based map. Second, and in contrast to [16, 39], because we chose the output of $f_{S}$ to lie on the surface of a sphere, we can use it to enforce 3D priors during training (Sec. 3.3). + +Intuitively, for a given category, the spherical prototype $S_{\mathcal{Z}}$ should be able to reconstruct any self-supervised feature map $\phi(\boldsymbol{I})$ when queried on the coordinates predicted by $f_{S}$ , i.e. $S_{\mathcal{Z}}(f_{S}(\boldsymbol{I}, x))$ must closely approximate $\phi(\boldsymbol{I}, x)$ for any $\boldsymbol{I}, x$ . Even if $S_{\mathcal{Z}}$ encodes a perfect category prototype, it will be unable to encode information about the image background. Hence we use instance masks $M(\boldsymbol{I})$ at training time to restrict the loss computation to only the pixels on an object's surface. In practice, these can be obtained using pretrained segmentation models [21]. Thus, given a training image $\boldsymbol{I}$ and a pixel location $x$ , our primary training objective to learn the parameters of $f_{S}$ and $S_{\mathcal{Z}}$ can be formulated as the minimization of + +$$ +\mathcal {L} _ {r e c} = \frac {1}{| \Lambda |} \sum_ {x \in \Lambda} M (\boldsymbol {I}, x) \times \Gamma \left(\phi (\boldsymbol {I}, x), S _ {\mathcal {Z}} \left(f _ {S} (\boldsymbol {I}, x)\right)\right), \tag {1} +$$ + +where $\Gamma$ is the cosine distance between the two inputs. Our spherical prototypes are implemented via a neural network that maps points in $\mathbb{R}^3$ to $\mathcal{Z}$ . Importantly, each point $s\in S^2\subset \mathbb{R}^3$ must be mapped independently, meaning that it should correspond to a unique point $\mathbf{z}\in \mathcal{Z}$ , irrespective of which instance it comes from or where in the image this part is located. To model multiple categories, and to encourage information sharing between closely related ones, we use a single network conditioned on a category embedding. In practice, $S_{\mathcal{Z}}$ is a visual transformer [13] without + +![](images/b72b9756630e070510f259a7d3984fb574b60b297dfb9a57dd1382a481fa2f4a.jpg) +Figure 2. Overview of our semantic correspondence estimation approach. We begin by extracting features from a frozen self-supervised backbone, and further use them to predict spherical coordinates via a learned module. Each predicted point is used to query a jointly learned prototype, providing the supervision signal (Sec. 3.2). The sphere is used to enforce weak geometric priors (Sec. 3.3). During inference, SSL features are combined with spherical coordinates (Sec. 3.4). A blue outline indicates a fixed module, while orange indicate learned parameters. + +self-attention, but with cross-attention between image tokens and a single category token $\mathbf{c}$ which is a one hot embedding of the category. As learning $f_{S}$ from scratch can be challenging, we further leverage the SSL backbone by simply adding a prediction head $f_{S}^{\prime}$ to it to produce spherical maps, i.e. $f_{S} = f_{S}^{\prime} \circ \phi$ . An overview of our architecture is presented in Fig. 2. + +# 3.3. Enforcing geometric priors + +The above spherical reconstruction formulation alone offers little benefit over matching the self-supervised features from $\phi$ directly, especially considering the low dimensionality of the intermediate spherical space, which is not guaranteed to be well-behaved. However, this spherical structure enables the computation of simple geometric priors that can be enforced during training. + +Viewpoint regularization. Many object categories exhibit some form of symmetry which can make it particularly challenging for image-based models to distinguish between different sides of an object, creating spurious correlations between distinct parts (e.g. see cars in Fig. 1). One potential way of addressing this challenge, without using dense groundtruth correspondence, is to exploit viewpoint information of the object instance. + +An interesting property of using a spherical prototype to represent an object category is that it can easily be used to infer an object's viewpoint with respect to the camera. We posit that the average coordinate of a spherical map of an image, which we present as $\mu(f_S(I)) = 1 / |\Lambda| \sum_{x \in \Lambda} f_S(I, x)$ , can be viewed as a coarse approximation of the camera viewpoint under which the object is seen, e.g. right side views should be approximately mapped to the right side of the sphere, and left side views to the left. Intuitively, thinking of $f_S$ as a mapping from image pixels to the object's surface, the visible parts of an object should roughly be those closest to the camera, while the others should be hidden by self-occlusion. + +By using the groundtruth camera viewpoint $v_{I}$ , we en + +force the average direction of the spherical map $\mu (f_S(I))$ to align with $v_{I}$ . When this is satisfied, symmetric views must be mapped to different parts of the sphere. While precise viewpoint information is hard to obtain, we observe it is sufficient to use coarse relative viewpoint supervision between images. In practice, viewpoints are discretized into a small number of bins, and $v_{I}$ is represented by the median value of the corresponding bin. Then, we simply enforce that the dot product between viewpoints from two images equals that of their average spherical maps, + +$$ +\mathcal {L} _ {v p} = \sum_ {\boldsymbol {I}, \boldsymbol {I} ^ {\prime}} | | v _ {\boldsymbol {I}} \cdot v _ {\boldsymbol {I} ^ {\prime}} - \mu \left(f _ {S} (\boldsymbol {I})\right) \cdot \mu \left(f _ {S} \left(\boldsymbol {I} ^ {\prime}\right)\right) | | ^ {2}. \tag {2} +$$ + +Relative distance loss. As noted earlier, current self-supervised extracted features can confuse repeated object repeated parts. Depending on the target goal, this can be desirable, if the parts do indeed belong to the same part category. However, this is detrimental for dense correspondence estimation as the parts may actually be different part instances, e.g. left vs. right leg. It can be hard to distinguish between these based on their appearance alone and additional geometric context is required. + +One trivial way of encoding this context is by making the assumption that similar parts that appear in different locations on an image (i.e. not beside each other) are in fact different instances of the same semantic part. Therefore, we would like to enforce the property on our predicted spherical maps that distant pixels in the image should be mapped far apart on the sphere. Due to scale variation, distance on the image plane is hard to link to distances on the surface of the sphere. However, we can reformulate this property as a relative distance comparison using a triplet. Given three points $a$ , $b$ , and $c$ on an image $\pmb{I}$ , and their corresponding positions $s_a = f_S(\pmb{I}, a)$ , $s_b$ , and $s_c$ on the sphere, the ordering between distances should be preserved, that is: + +$$ +\left| \left| a - b \right| \right| \leq \left| \left| a - c \right| \right| \iff \Gamma \left(s _ {a}, s _ {b}\right) \leq \Gamma \left(s _ {a}, s _ {c}\right). \tag {3} +$$ + +In reality, this does not hold for distances along an object's surface, which the sphere is supposed to represent, partly + +![](images/32af9dd198c5b9ba01d3c41d465b8c613609eb1f19593e7d2d7e8c73764d482f.jpg) +Spherical Coordinates + +![](images/e014c2f4184defb79360348d7bca1d228a221d638f30ebd71c4496572deca634.jpg) +Relative Distance Loss $\mathcal{L}_{rd}$ + +![](images/da551187e926cc15d95fb6ad0557ae2c7e29ca97de66847b48b4cdce1475d6d2.jpg) +Orientation Loss $\mathcal{L}_o$ +Figure 3. Illustration of our geometry losses $\mathcal{L}_{rd}$ and $\mathcal{L}_o$ . The left image shows a spherical map from which a triplet of points is sampled. $\mathcal{L}_{rd}$ : as the anchor patch $a$ is closer to the positive $b$ on the image compared with the negative $c$ , its corresponding position $s_a$ on the sphere must also be closer to $s_b$ than $s_c$ . $\mathcal{L}_o$ : after projecting $s_b$ and $s_c$ to the plane tangent to the sphere at $s_a$ , we ensure orientation is preserved by enforcing positive collinearity between $u_b \times u_c$ and the normal vector $n$ . + +due to perspective. For example, in the case of a long train seen from a near frontal view, parts at the back of the train might appear very close to the front in the image, even though they are very far in 3D space. Nevertheless, we find that this is still an effective prior for discouraging repeated part instances from being mapped to the same location. + +During training, point triplets $(a,b,c)$ are randomly sampled among pixels that belong to the object. Among each such triplet, we chose an anchor location $anc = a$ , a positive location $pos = \arg \min_{x\in \{b,c\}}||a - x||$ , and a negative location $neg = \arg \max_{x\in \{b,c\}}||a - x||$ (see Fig. 3). We can then define a triplet margin loss as: + +$$ +\begin{array}{l} \mathcal {L} _ {r d} = \max (\Gamma (f _ {S} (\boldsymbol {I}, a n c), f _ {S} (\boldsymbol {I}, p o s)) \tag {4} \\ - \Gamma (f _ {S} (\boldsymbol {I}, a n c), f _ {S} (\boldsymbol {I}, n e g)) + \delta , 0), \\ \end{array} +$$ + +where $\delta$ is a hyperparameter which specifies the margin. A useful side product of this formulation is that it encourages the spherical maps to be smooth, as strong discontinuities would produce a large anchor to positive distance. + +Orientation loss. A final advantage of using $S$ as a latent space is that it is an orientable 2D space, just like images. Therefore, enforcing that $f_{S}$ preserves orientation prevents spurious matches between symmetric views. Intuitively, if a point $a$ appears on the right side of $b$ in the image, then $s_a$ must appear in the same side of $s_b$ . Given a point triplet as defined earlier, this can be enforced by making sure that the determinant of the image triplet and sphere triplet positively correlate. Formally, defining $P_a$ as the orthogonal projection to the plane tangent to $S$ at $s_a$ and $u_b$ as $P_a(s_b) - s_a$ , we have $d_I = \det(b - a, c - a)$ and $d_S = \det(u_b, u_c)$ , and want $sign(d_I) = sign(d_S)$ (see Fig. 3). + +As objects can have complex geometry that our model does not have access to, there exists no exact relation linking the two determinants together, as for instance perspective distortions might alter angles. However, we can as- + +sume that image triplets of large determinants should also have large determinant on the sphere, as a change of sign in determinant indicates the relative orientation on the sphere has been inverted. In practice, we randomly sample image triplets $(a,b,c)$ and select those whose image determinant $d_{I}$ is higher than a threshold $d_{\tau} = 0.7$ while swapping $b$ and $c$ if $d_{I}$ is negative. Then, we enforce the determinant of the corresponding sphere triplet to be at least $d_{\tau}$ , + +$$ +\mathcal {L} _ {o} = \left\{ \begin{array}{l l} 0 & \text {i f} d _ {I} < d _ {\tau} \\ \max \left(d _ {\tau} - d _ {S}, 0\right) & \text {i f} d _ {I} \geq d _ {\tau}. \end{array} \right. \tag {5} +$$ + +# 3.4. Correspondence via combined representations + +During inference, it is possible to directly query the spherical maps $f_{S}$ of two images to obtain correspondences using the cosine distance. That is, for an image pair $I, I'$ and a query location $q$ on $I$ , its location in $I'$ can be computed as + +$$ +p ^ {*} = \underset {p} {\arg \min } \Gamma \left(f _ {S} (\boldsymbol {I}, q), f _ {S} \left(\boldsymbol {I} ^ {\prime}, p\right)\right). \tag {6} +$$ + +While this protocol is sound, it comes with two important drawbacks. First, $f_{S}$ produces spherical maps for the whole image, including the background, meaning segmentation masks would be required at inference time to prevent the emergence of spurious matches. Second, the spherical map is designed to be a smooth parameterization of the object surface, making it susceptible to missing fine details. A slightly incorrect mapping $f_{S}(I,q) + \epsilon$ has a high probability of finding a higher match in a nearby region of the correct match $f_{S}(I^{\prime},p^{*})$ if both maps are smooth. In comparison, SSL feature maps can exhibit strict feature separation, e.g. wheel features are very different from other nearby non-wheel features, making it unlikely that a wheel pixel finds a nearest neighbor among nearby non-wheel pixels. + +To mitigate this issue, we make use of the feature maps that are already computed by the self-supervised backbone network $\phi$ , in a similar way to supervised correspondence approaches that aggregate features from a network [35, 53, 59]. Existing literature has shown that DINO features are particularly effective at differentiating between the foreground and background [1], removing the need for inference-time segmentation. To leverage these DINO features, we reformulate Eq. (6) as the combination of self-supervised features and spherical locations: + +$$ +\begin{array}{r l} p ^ {*} = \arg \min _ {p} (1 - \alpha) \Gamma (\phi (\boldsymbol {I}, q), \phi (\boldsymbol {I} ^ {\prime}, p)) & \\ + \alpha \Gamma (f _ {S} (\boldsymbol {I}, q), f _ {S} (\boldsymbol {I} ^ {\prime}, p)), & \end{array} \tag {7} +$$ + +where $\alpha$ is a hyperparameter that balances each term. + +# 4. Experiments + +Implementation details. We build our models on DINOv1-B/8 [6] and DINOv2-B/14 [40] backbones. Training masks + +
↑3%4%5%6%7%8%9%10%11%12%13%14%15%16%17%avg
CustomCATS [9]52.034.772.234.349.957.543.666.524.463.256.552.042.641.743.033.672.658.049.9
MMNet+FCN [59]55.937.065.035.450.063.945.762.828.765.054.751.638.534.641.736.377.762.550.4
SCorrSan [26]57.140.378.338.151.857.847.167.925.271.363.949.345.349.848.840.377.769.754.4
DINOv1DINOv1 [6]44.326.857.622.029.332.819.754.014.940.139.329.329.037.020.028.240.621.132.6
ASIC [16]57.925.268.124.735.428.430.954.821.645.047.239.926.248.814.524.549.024.637.0
Ours47.126.070.921.837.534.932.460.023.253.648.542.528.342.721.141.939.741.739.7
SDDIFT [49]63.554.580.834.546.252.748.377.739.076.054.961.353.346.057.857.171.163.457.7
SD [57]63.155.680.233.844.949.347.874.438.470.853.761.154.455.054.853.565.053.356.1
DINOv2DINOv2 [40]72.762.085.241.340.452.351.571.136.267.164.667.661.068.230.762.054.324.256.2
DINOv2 + SD [57]73.064.186.440.752.955.053.878.645.577.364.769.763.369.258.467.666.253.563.3
Ours (sphere only)46.728.866.333.036.566.659.174.925.465.750.152.727.113.715.846.673.536.745.5
Ours76.961.285.942.148.473.367.280.046.380.266.771.266.063.936.268.667.842.263.6
Ours + SD74.864.587.145.652.777.871.482.447.782.067.373.967.660.049.969.878.559.167.3
+ +Table 1. Keypoint matching scores on SPair-71k evaluated using PCK@0.1 with macro-averaging for the summary scores. We present our approach using DINOv1 [6] features (middle rows) and DINOv2 [40] features (bottom rows). In both cases, we improve over the DINO only baselines and are superior to fully supervised methods (top rows). Bold entries are best per category and underlined are second-best. + +are obtained using a pretrained Mask R-CNN model [21]. Our spherical mapper consists of a linear dimension reduction layer halving the number of features, a visual transformer block with self-attention, and a final linear layer with an output dimension of three. The resulting feature map is then normalized pixel-wise so that its output values lie on the surface of $S^2$ . The dimensionality reduction layer, while not strictly necessary, is helpful considering the small number of images used during training, while the transformer block helps in disentangling sides and repeated parts by allowing global reasoning between image patches. + +The final loss term is computed as $\mathcal{L} = \mathcal{L}_{rec} + \lambda_{rd}\mathcal{L}_{rd} + \lambda_o\mathcal{L}_o + \lambda_{vp}\mathcal{L}_{vp}$ . We set $\lambda_{rd} = \lambda_o = 0.3$ , while $\lambda_{vp} = 0.1$ is set slightly lower as it can have the detrimental effect of pulling all predictions towards the average over image pixels - cf. Eq. (2). The relative distance margin is set to $\delta = 0.5$ to encourage feature separation. To perform matching in Eq. (7), $\alpha$ is set to 0.2 so that we leverage the highly discriminative DINO features, while using the sphere as a symmetry and repetition-breaking mechanism. Our model is trained for a total of 200 epochs using Adam [28]. + +Datasets. Following existing work [16, 26, 57], we evaluate our method primarily on the Spair-71k dataset [34], which contains images from 18 different object categories. The evaluation set contains between 600 and 900 image pairs, each of which are annotated with the keypoints that are visible in both images. We train our model on the Spair-71k training split on all categories simultaneously, without using any keypoint annotations. Additionally, we evaluate on the AwA-pose dataset [4], which contains images from 35 quadruped categories, annotated with keypoints. We also present results by training on the Freiburg cars dataset [45]. This dataset was collected by densely sampling approximately 100 images each around 48 different car instances. The higher image count, coupled with $360^{\circ}$ dense sampling, enables us to learn a more detailed spherical prototype. + +# 4.1. Keypoint average precision + +While issues with symmetries are clear in Fig. 4, we argue that the PCK metric fails to account for them as it is only computed between keypoints that appear in both the source and target image. Hence, models that predict high similarity between two visually similar but semantically different keypoints might not be penalized for it. PCK can partly account for repetition-related mistakes if the parts appear simultaneously in both images, but it does not penalize symmetry-related issues, like mistaking the left and right side of a car, as the corresponding keypoints do not appear simultaneously. PCK was initially proposed for simpler cases where keypoints were assumed to be always be visible, e.g. faces or different instances in the same pose. However, as benchmarks become more challenging, a more robust protocol should be used. To illustrate how much these failure cases impact SSL models, we propose an alternative evaluation metric, Keypoint Average Precision - $\mathrm{KAP}@\kappa$ . It is similar to $\mathrm{PCK}@\kappa$ , but accounts for these errors by evaluating average precision instead of accuracy and penalizes methods that predict matches when none exist. + +When performing evaluation on a pair of images, instead of restricting it to keypoints that simultaneously appear in both images, we consider all keypoints that appear in the source, irrespective of whether they are also visible in the target image. For each such keypoint, if it appears in the target image, we extract the highest similarity value within radius $\kappa$ of the ground-truth and label it as positive. We also extract the highest similarity value outside the radius and label it as negative, penalizing overly high predictions on wrong, possibly repeated parts. If the source keypoint does not appear on the target image, we simply extract the highest similarity prediction across the whole target image and label it as negative to penalize incorrectly high similarity when none should exist. This effectively reformulates the task as a binary classification problem, where the embed- + +![](images/d6af9bd0cc6974ca74fc3d532f867971c3de3740bff2e5fc718217f869c09983.jpg) +Figure 4. Qualitative comparison of dense correspondence maps. For DINOv2, SD, and DINO+SD features we perform PCA on the segmented object features independently for each category, then visualize the three main components. Note that the SD and DINO+SD features are not completely equivalent to the ones used to compute matches, but are provided here for illustration. Spherical maps from $f_{S}$ (Sphere) for our approach are visualized directly. Our spherical maps correctly identify the different sides of objects, whereas other features fail to capture these differences. + +ding of each source keypoint has to be close to, and only to, the corresponding target keypoint. Finally, we compute the average precision over all the extracted pairs, and report mean average precision per-category. + +# 4.2. SPair-71k results + +We first evaluate on the task of keypoint transfer between pairs of images using Spair-71k [34]. We present quantitative per-category results in Tab. 1, using the standard PCK metric along with macro-averaged scores as the number of per-category pairs varies greatly. We split the models according to their backbone: custom supervised models, DINOv1-based, SD-based, and DINOv2-based. A striking preliminary observation is the effectiveness of DINOv2, surpassing supervised approaches on most categories. While its success can partially be attributed to evaluation biases [2], this demonstrates the effectiveness of large scale learned self-supervised features. + +Using a DINOv1 backbone, our model improves over its backbone on most categories, and over ASIC [16] on average. When combined with the DINOv2 backbone, our model provides improvements on all but two categories. A clear pattern can be identified, with strongest improvements being observed over blob-like symmetric objects with repeated parts (+21.0 on bus and +15.7 on car), while spherical mapping hinders performance on highly deformable categories (-4.3 on person), or high-genus objects for which a sphere is a poor surface prior (-0.8 on bicycle). Our model performs slightly better compared to DINO+SD [57], while requiring a fraction of the computational cost at inference time. Finally, following [57] we evaluate adding Stable Diff + +fusion (SD) [42] features to our method at inference time, which yields further improvements. This illustrates that spherical maps and SD features capture different facets of the correspondence problem. + +We show the results of evaluating correspondences with KAP in Tab. 2. We observe particularly large discrepancies between PCK and KAP in highly symmetric objects with repeated parts, e.g. buses and cars, and the ranking between our model and DINOv2 is reversed on humans, possibly due to DINOv2's symmetric predictions on left and right limbs. All models across all categories obtain lower results when using KAP highlight the symmetry issues they are facing. A limitation of KAP is that it might still count correct repeated parts mistakes if their distance in the image is less than $\kappa$ . Nonetheless, we argue that KAP is more informative than PCK and is just as efficient to evaluate. + +The qualitative visualization shown in Fig. 4 illustrates these improved results. Our model correctly maps the two opposite sides of the cars to different sphere regions, while other feature maps look extremely similar, even when looking at two opposite sides of an object, with the notable exception of SD on birds. The fact that such similarities exist between opposite views suggest that the utility of baselines such as DINOv2 would be quite limited in real scenarios. + +# 4.3. Additional evaluation + +Animals with Attributes (AwA). To further evaluate our model, we also report results on the AwA-pose dataset from [4], which contains images from 35 different categories of quadruped. While our spherical prototype needs category information during training to reconstruct + +
↑%avg
DINOv2 [40]53.554.060.235.544.436.331.761.337.454.752.551.548.848.237.844.147.438.246.5
SD [57]44.448.554.531.545.232.730.068.435.855.247.948.144.842.344.539.252.751.245.4
DINOv2 + SD [57]52.055.959.234.749.036.032.570.339.859.853.152.450.650.447.846.253.349.849.6
Ours (sphere only)38.434.253.933.037.949.743.471.729.857.145.842.532.427.029.537.157.436.042.1
Ours60.751.263.138.445.055.945.769.740.463.254.854.351.248.738.847.955.542.251.5
Ours + SD58.954.262.239.646.654.547.176.240.965.357.356.154.247.443.749.462.452.053.8
+ +category-specific features, only the sphere mapper is used during inference, meaning it can be readily applied to unseen categories. Five quadruped classes (cat, cow, dog, horse, and sheep) appear in both SPair and AwA-pose, and are therefore seen during training, but the rest are completely new for our sphere mapper. Nonetheless, results shown in Tab. 3 show that the sphere mapper generalizes well to unseen categories. We attribute this to the assistance from the strong category-agnostic features from DINOv2. Once again, the improvement of using our spherical method is much more apparent using KAP, i.e. the PCK improvement over DINOv2 alone is 2.2 when adding SD and 2.6 when adding spheres, while these become 1.8 and 3.9 respectively with KAP. + +Table 2. Keypoint matching scores on SPair-71k evaluated using KAP@0.1 with macro-averaging for the summary scores. + +
Dv2SDDv2+SDOursOurs+SD
PCK@0.165.956.068.168.769.8
KAP@0.155.050.756.858.960.6
+ +Model ablation. We also analyze the impact of removing each individual loss term when training our model in an ablation study. The results in Tab. 4 indicate that all variants except the no $\mathcal{L}_{rd}$ one do not significantly improve over the DINOv2 baseline as they also fail to identify opposite sides of objects and repeated parts. + +Table 3. Average scores when evaluating on AwA-pose using a random subset of 200 pairs per category. 'Ours' denotes our model trained on SPair-71k with a DINoV2 backbone. + +
DINOv2no Lvpno Lrdno Lofull model
56.258.661.256.063.6
+ +Inference speed. The results in Tab. 1 demonstrate how effective the addition of Stable Diffusion features are. However, computing correspondences through diffusion requires adding noise to images, running iterative diffusion, and performing joint decomposition between the source and target features. As a result, its inference speed is much slower compared to using DINOv2 features. In comparison, our approach only requires a few extra layers on top of DINOv2 and has negligible additional overhead. Timing results in Tab. 5 illustrate that adding diffusion-extracted features reduces throughput by an order of magnitude. + +Table 4. Average PCK@0.1 scores when training and testing on SPair-71k using different ablated versions of our approach. + +
DINOv2SDDINOv2+SDOursOurs+SD
3.40.380.353.30.34
+ +Table 5. Descriptor computation throughput in pairs/second at inference time on a single A5000 GPU, where higher is better. + +# 4.4. Limitations + +While our approach results in significant improvements over the DINOV2 baseline for many categories (see Tab. 1), there are still some limitations. For example, we do not perform as well on a small number of categories that cannot be well approximated by a sphere (e.g. humans). Furthermore, the very low-dimensional spherical encoding on its own is not as effective at discriminating parts and subparts and thus needs to be combined with self-supervised features. However, as we already densely compute these features at inference time for each test image, there is no additional cost in combining them with our spherical mapping when evaluating correspondence. Finally, our method relies on additional supervision at training time in the form of automatically computed segmentation masks and weak camera pose supervision. However, results in the supplementary material suggest that coarse camera viewpoints are enough to obtain good performance. + +# 5. Conclusion + +We presented a new approach for semantic correspondence estimation that is robust to issues resulting from object symmetries and repeated part instances. In addition, we proposed a new evaluation protocol that is more sensitive to these issues. Our approach leverages recent advances in the self-supervised learning of discriminative image features and combines them with a weak geometric spherical prior. By using weak pose supervision to represent objects categories on the surface of spheres, we are able to enforce simple geometric constraints during training that result in more geometric and semantically consistent representations. 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In CVPR, 2016. 2, 3 \ No newline at end of file diff --git a/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/images.zip b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..db7b6420b298ca8af5c9735cf93cc0232ea57bf4 --- /dev/null +++ b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e8c24f58fdfa563bc6c17a4845a54e20c0ba40b6769f2df1ad4f40ffac3e521e +size 434888 diff --git a/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/layout.json b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..89132a9b5677d029acdb32aa505adef3365aad99 --- /dev/null +++ b/2024/Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps/layout.json @@ -0,0 +1,9651 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 103, + 536, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 103, + 536, + 122 + ], + "spans": [ + { + "bbox": [ + 58, + 103, + 536, + 122 + ], + "type": "text", + "content": "Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 157, + 143, + 436, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 157, + 143, + 436, + 157 + ], + "spans": [ + { + "bbox": [ + 157, + 143, + 436, + 157 + ], + "type": "text", + "content": "Octave Mariotti Oisin Mac Aodha Hakan Bilen" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 237, + 161, + 356, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 237, + 161, + 356, + 175 + ], + "spans": [ + { + "bbox": [ + 237, + 161, + 356, + 175 + ], + "type": "text", + "content": "University of Edinburgh" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 179, + 175, + 411, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 175, + 411, + 190 + ], + "spans": [ + { + "bbox": [ + 179, + 175, + 411, + 190 + ], + "type": "text", + "content": "groups.inf.ed.ac.uk/vico/research/sphericalmaps" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 217, + 192, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 192, + 228 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 192, + 228 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 242, + 290, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 290, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 290, + 494 + ], + "type": "text", + "content": "Recent self-supervised models produce visual features that are not only effective at encoding image-level, but also pixel-level, semantics. They have been reported to obtain impressive results for dense visual semantic correspondence estimation, even outperforming fully-supervised methods. Nevertheless, these models still fail in the presence of challenging image characteristics such as symmetries and repeated parts. To address these limitations, we propose a new semantic correspondence estimation method that supplements state-of-the-art self-supervised features with 3D understanding via a weak geometric spherical prior. Compared to more involved 3D pipelines, our model provides a simple and effective way of injecting informative geometric priors into the learned representation while requiring only weak viewpoint information. We also propose a new evaluation metric that better accounts for repeated part and symmetry-induced mistakes. We show that our method succeeds in distinguishing between symmetric views and repeated parts across many object categories in the challenging SPair-71k dataset and also in generalizing to previously unseen classes in the AwA dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 514, + 128, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 128, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 128, + 526 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "content": "Semantic correspondence (SC) estimation aims to find local regions that correspond to the same semantic entities across a collection of images, where each image contains a different instance of the same object category [30]. SC has been studied in both supervised [9, 26, 59] and unsupervised [2, 50] settings. Thanks to the recent progress in self-supervised learning (SSL) [6, 40, 60], recent SSL-based approaches have been shown to obtain strong performance on multiple benchmarks [1, 2, 54]. However, they often act as simple part detectors, without having any 3D understanding of object extent, or relative location of object parts. As these SSL methods are typically trained using only 2D-based objectives, they are not able to learn 3D-aware representations, and often converge to similar features for object parts that share appearance but not fine-grained semantics." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 226, + 373, + 293 + ], + "blocks": [ + { + "bbox": [ + 329, + 215, + 351, + 225 + ], + "lines": [ + { + "bbox": [ + 329, + 215, + 351, + 225 + ], + "spans": [ + { + "bbox": [ + 329, + 215, + 351, + 225 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 226, + 373, + 293 + ], + "lines": [ + { + "bbox": [ + 307, + 226, + 373, + 293 + ], + "spans": [ + { + "bbox": [ + 307, + 226, + 373, + 293 + ], + "type": "image", + "image_path": "cf42395a54f16cd93a35efc6090b8caacfe541aabb42c3a7daf34fe28a0a3327.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 384, + 226, + 452, + 293 + ], + "blocks": [ + { + "bbox": [ + 403, + 216, + 436, + 225 + ], + "lines": [ + { + "bbox": [ + 403, + 216, + 436, + 225 + ], + "spans": [ + { + "bbox": [ + 403, + 216, + 436, + 225 + ], + "type": "text", + "content": "DINOv2" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 384, + 226, + 452, + 293 + ], + "lines": [ + { + "bbox": [ + 384, + 226, + 452, + 293 + ], + "spans": [ + { + "bbox": [ + 384, + 226, + 452, + 293 + ], + "type": "image", + "image_path": "4d6a4d5ce187995cd2e41c258ddd2b6758814ec4627c5d5b868eee9a20f7ad27.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 308, + 373, + 375 + ], + "blocks": [ + { + "bbox": [ + 307, + 308, + 373, + 375 + ], + "lines": [ + { + "bbox": [ + 307, + 308, + 373, + 375 + ], + "spans": [ + { + "bbox": [ + 307, + 308, + 373, + 375 + ], + "type": "image", + "image_path": "c0a9464c0fb9c2526df1b455fd01dba7c10b83171dedd6ae4cdaabb20009d690.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 392, + 545, + 491 + ], + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 491 + ], + "type": "text", + "content": "Figure 1. Features from self-supervised methods such as DINOv2 [40] have been used to discover parts and regions of objects. However, these features fail to correctly distinguish (i) object symmetries, e.g. the left and right side of the car have the same features and (ii) individual parts, e.g. the wheels are represented by the same features irrespective of their location on the car. Our approach through use of a weak geometric spherical prior addresses these issues. Note, we use the 3D PCA projection of the features for DINOv2 and our learned spherical mapping for our method." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 386, + 308, + 452, + 376 + ], + "blocks": [ + { + "bbox": [ + 392, + 295, + 446, + 305 + ], + "lines": [ + { + "bbox": [ + 392, + 295, + 446, + 305 + ], + "spans": [ + { + "bbox": [ + 392, + 295, + 446, + 305 + ], + "type": "text", + "content": "collapsed sides" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 386, + 308, + 452, + 376 + ], + "lines": [ + { + "bbox": [ + 386, + 308, + 452, + 376 + ], + "spans": [ + { + "bbox": [ + 386, + 308, + 452, + 376 + ], + "type": "image", + "image_path": "769c98ff9096e99c04cdf49df27d6968daba1feec95d907f84fc453281b9125a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 378, + 446, + 389 + ], + "lines": [ + { + "bbox": [ + 392, + 378, + 446, + 389 + ], + "spans": [ + { + "bbox": [ + 392, + 378, + 446, + 389 + ], + "type": "text", + "content": "collapsed parts" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 465, + 226, + 531, + 293 + ], + "blocks": [ + { + "bbox": [ + 488, + 216, + 509, + 225 + ], + "lines": [ + { + "bbox": [ + 488, + 216, + 509, + 225 + ], + "spans": [ + { + "bbox": [ + 488, + 216, + 509, + 225 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 465, + 226, + 531, + 293 + ], + "lines": [ + { + "bbox": [ + 465, + 226, + 531, + 293 + ], + "spans": [ + { + "bbox": [ + 465, + 226, + 531, + 293 + ], + "type": "image", + "image_path": "1080e5808b8ed0d5af3ebceb47639559b7547eaba36990b500c131073d112a48.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 295, + 522, + 304 + ], + "lines": [ + { + "bbox": [ + 474, + 295, + 522, + 304 + ], + "spans": [ + { + "bbox": [ + 474, + 295, + 522, + 304 + ], + "type": "text", + "content": "distinct sides" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 465, + 308, + 531, + 376 + ], + "blocks": [ + { + "bbox": [ + 465, + 308, + 531, + 376 + ], + "lines": [ + { + "bbox": [ + 465, + 308, + 531, + 376 + ], + "spans": [ + { + "bbox": [ + 465, + 308, + 531, + 376 + ], + "type": "image", + "image_path": "b4bc07b933358b181f02ed7a06323e13289bf045a7817322fde81749635f219b.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 378, + 522, + 389 + ], + "lines": [ + { + "bbox": [ + 474, + 378, + 522, + 389 + ], + "spans": [ + { + "bbox": [ + 474, + 378, + 522, + 389 + ], + "type": "text", + "content": "distinct parts" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "type": "text", + "content": "The two main failure modes of current methods are depicted in Fig. 1. First, they are often confused by the symmetries that objects can exhibit (e.g. left vs. right side of a car), producing reflected versions of the feature maps when presented with the two different sides of a symmetric object. Second, they predict similar features for similar looking parts (e.g. the front left vs. back left wheel of a car), and fail to discriminate between part instances. Such symmetries and repeated structures are ubiquitous in both human-made and naturally occurring object categories." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 618, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 712 + ], + "type": "text", + "content": "We posit that these shortcomings can be addressed by enforcing an explicit 3D structure into correspondence learning, allowing the model to disambiguate multiple repeated parts, and accounting for the fact that some object parts might not be visible in all images. Indeed, scene-based correspondence pipelines use geometric verification in order to guarantee robustness in their matches [44], while other works have shown that detailed 3D meshes can be used to" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19521" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "type": "text", + "content": "discover category-based correspondences through a render-and-compare pipeline [29, 62]. However, these approaches typically require 3D mesh supervision which is difficult and costly to obtain at scale." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 346 + ], + "type": "text", + "content": "Motivated by the limitations, and the promise of the recent SSL representations [40], we propose a novel method that incorporates the missing 3D geometry into object representations. We make use of a weak 3D prior by representing object features on the surface of a sphere which encodes both geometry and appearance information. Our method consistently maps features corresponding to the same semantic parts (e.g. left headlight of a car) in images of different object instances to the same spherical coordinates, hence enabling a 3D aware and accurate correspondence. However, learning such a mapping without the ground-truth 3D supervision is nontrivial because of repeated parts and object symmetries. To this end, we propose to use much weaker supervision via coarse camera viewpoint annotations to help separate these confusing features during training. We couple this with geometric constraints to prevent collapsed representations for repeated parts. As a result, our method learns to separate object parts based on their position and spatial configuration in an image." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 347, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 525 + ], + "type": "text", + "content": "Furthermore, we point out that the standard evaluation metric for SC, Percentage of Correct Keypoints (PCK), is not able to properly evaluate symmetry-related failures as it only considers keypoints that are simultaneously visible in both the source and target image. For instance, a system predicting high similarity between a front left wheel in the source and front right wheel in the target is unlikely to be penalized for it, as the target image is unlikely to contain both a front left and front right wheel due to self-occlusions. In such cases PCK will simply not evaluate what the nearest neighbor of the source wheel is. Rather than simple accuracy-based metric, we argue that average precision is a more robust scoring mechanism and propose a new metric, Keypoint Average Precision (KAP), to account for potential spurious matches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 527, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 287, + 597 + ], + "type": "text", + "content": "Our contributions are: i) a novel SC approach that learns to separate visually similar parts by mapping them to different location on a sphere, ii) a set of simple geometric constraints that force separation of visually similar parts during training, and iii) a new evaluation protocol that better accounts for the failure cases of current methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 603, + 132, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 603, + 132, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 603, + 132, + 615 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "Image matching. Visual correspondences were first explored as exact matches between different views of the same scene with applications to stereo vision [24, 38], object detection [14, 33], structure from motion [20, 44, 52], and SLAM [12, 19]. Correspondences can also be computed across pixels in the frames of a video, which is referred to as optical flow [5, 7]. Traditionally they are obtained by computing hand-crafted visual descriptors [11, 32, 43]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": "Semantic correspondence (SC). In SC estimation [30], the goal is not only to find matches across different views of the exact same object instance, but also across different instances of the same object category. While earlier work [30] match two images through densely sampled SIFT [32] features, later works extended pairwise correspondence learning to a global matching problem [61] and established region correspondences using object proposals and their geometric relations over dense descriptors [17]. Subsequently, CNNs trained with only image-level supervision have been shown to discover correspondences [31], paving the way for many deep learning correspondence systems [10, 18, 26, 59]. Typical correspondence-specific CNN architectures rely on aggregating features along the depth of a network [35, 53, 59] or use 4D convolutions spanning two images simultaneously [41]. Recently, transformers have been shown to be particularly suited to correspondence discovery thanks to their attention mechanism [9]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 289, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 517 + ], + "type": "text", + "content": "While the early works in unsupervised correspondence discovery [2, 27, 50] use on the convolutional representations, recent methods [1, 47, 54, 57] build on the success of transformer-based self-supervised representations [6, 40, 60] to discover salient and robust features, which subsequent works have applied to detect semantic correspondences successfully, often surpassing supervised methods. The features from generative image models have also been used in SC [22, 49, 57]. Two closely related works [16, 39] propose to create category-wide representations by aligning self-supervised feature maps. Unlike our approach, these works are limited to 2D, and find correspondences between images without knowing the underlying 3D structure of the world which renders them incapable of distinguishing different sides of objects (e.g. left vs. right side of a car). A concurrent work [58] also identifies geometry-related issues in SSL-based correspondence but targets a supervised training regime where our approach does not necessitate keypoint supervision." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": "3D priors for correspondence. In literature, 3D priors have been used for SC, mainly in the form of annotated meshes [8, 29, 37, 46, 62], where annotations can either be from image to mesh, or between meshes. [29, 37] in particular use a dense parametrization of the mesh surface similar to our sphere. When no mesh is available, precise camera pose can be used to recover sparse correspondences through constrained geometric optimization [48] or by training a neural field [56]. In comparison, our approach requires no meshes and only very coarse viewpoint supervision." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Alternatively, it is possible to estimate 3D models of object categories from image supervision alone [3, 15, 23, 25, 36, 55], from which correspondences are extracted. However, this is very challenging by itself, requiring complex pipelines capable of modeling accurate mesh deformations, pose, and rendering, which are all failure-prone." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19522" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 102, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 102, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 102, + 83 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 159, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 159, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 159, + 102 + ], + "type": "text", + "content": "3.1. Problem statement" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": "General formulation. Given an unordered monocular image collection, we wish to learn a mapping " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "f(\\mathbf{I}, x) = z" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " that takes in an RGB image " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{I} : \\Lambda \\to \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\Lambda \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " and a pixel location " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "x \\in \\Lambda" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " to an " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": "-dimensional embedding " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{Z} \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ". In particular, we would like " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " to map semantic concepts from different instances of the same category (e.g. center of front-right wheel of a car) to the same point in the embedding space " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ". Formally, " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "f(\\mathbf{I}, x) = f(\\mathbf{I}', x')" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ", when the pixels " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "x'" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{I}'" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " correspond to the same semantic part and instance. In practice, the corresponding location for " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "(\\mathbf{I}, x)" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{I}'" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " can be obtained by finding the nearest neighbor of " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "f(\\mathbf{I}, x)" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " in the embedding space, i.e. " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\arg \\min_{x'} d_{\\mathcal{Z}}(f(\\mathbf{I}, x), f(\\mathbf{I}', x'))" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{Z}}" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " is a distance function over " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": ". For simplicity, we will use " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "f(\\mathbf{I})" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " to refer to the feature map obtained by evaluating " + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": " on all pixels." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 290, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 422 + ], + "type": "text", + "content": "An ideal embedding function should be general enough as to not only match related semantic parts across different object instances (e.g. match the front-left wheel across two different car models) but also specific enough to distinguish between different part instances within the same object instance (e.g. front-left wheel vs. front-right wheel). Learning this from image-based self-supervision alone is a challenging task due to the visual similarity of repeated parts and self-occlusion. As a result, it is quite challenging for correspondence estimators to learn that cars have four distinct wheels from single images without explicit supervision." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": "Spherical mapping. Instead, it is beneficial to endow a correspondence estimator with priors about the underlying 3D structure of objects. To this end, previous methods [29, 62] use detailed 3D meshes via a render-and compare approach. However, they rely on the presence of groundtruth 3D meshes and the precise viewpoint information. Instead, following [50, 51], we use a simplified 3D structure, specifically a sphere " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "S^2 \\subset \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " (denoted as " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " for simplicity) based on the assumption that the object categories of interest are approximately homeomorphic to spheres (i.e. objects without holes). While this may at first appear particularly ill-suited for some categories, e.g. bicycles, the geometric simplicity of " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " provides a convenient parameterization of an object's surface by allowing easy computation of geometric constraints to separate visual and semantic similarity. In particular, " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " provides a simple geodesic distance through the dot product, making it straightforward to push different semantic parts apart, which we use to distinguish repeated object features. Formally, we are interested in building a spherical mapping " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "f_S(\\pmb{I}, x)" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " that maps pixels in " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " to the surface of " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": ". Unlike an arbitrary " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " dimensional space, " + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": " forms an object-centric specific coordinate system where each region ideally repre" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "sents a distinct semantic part and instance on the surface of the object." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 106, + 430, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 106, + 430, + 118 + ], + "spans": [ + { + "bbox": [ + 305, + 106, + 430, + 118 + ], + "type": "text", + "content": "3.2. Learning formulation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "text", + "content": "In the absence of ground truth correspondences, ensuring the semantic consistency of our spherical mapping function is very challenging. [50] enforces correspondence between image pairs through synthetically augmenting training images via thinplate splines. Unfortunately, such augmentations do not produce realistic 3D transformations such as 3D rotations which can result in the self-occlusion of parts. Instead, similar to [16, 39], we formulate the learning objective as one of aligning features from a pretrained SSL model " + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\phi : \\Lambda \\to \\mathcal{Z}_{\\phi}" + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "text", + "content": " between different instances of an object category. For simplicity, we will refer to the SSL embedding space " + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\phi}" + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "text", + "content": " simply as " + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 125, + 545, + 269 + ], + "type": "text", + "content": " in the rest of the text." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": "While those approaches use flat atlases " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^2\\to \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": ", we build a spherical prototype " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}:S\\to \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": " that maps a point on the surface of the sphere " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "s\\in S^2" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": " to a feature vector " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\in \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": ". This formulation has two important benefits. First, the input domain of " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": " is simply " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": ", meaning that it does not depend on " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": ", and it is shared across all images, constituting a category-based map. Second, and in contrast to [16, 39], because we chose the output of " + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 270, + 545, + 390 + ], + "type": "text", + "content": " to lie on the surface of a sphere, we can use it to enforce 3D priors during training (Sec. 3.3)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": "Intuitively, for a given category, the spherical prototype " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " should be able to reconstruct any self-supervised feature map " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\phi(\\boldsymbol{I})" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " when queried on the coordinates predicted by " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}(f_{S}(\\boldsymbol{I}, x))" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " must closely approximate " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\phi(\\boldsymbol{I}, x)" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\boldsymbol{I}, x" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": ". Even if " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " encodes a perfect category prototype, it will be unable to encode information about the image background. Hence we use instance masks " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "M(\\boldsymbol{I})" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " at training time to restrict the loss computation to only the pixels on an object's surface. In practice, these can be obtained using pretrained segmentation models [21]. Thus, given a training image " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\boldsymbol{I}" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " and a pixel location " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": ", our primary training objective to learn the parameters of " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}" + }, + { + "bbox": [ + 304, + 391, + 545, + 546 + ], + "type": "text", + "content": " can be formulated as the minimization of" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 554, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 554, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 312, + 554, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\frac {1}{| \\Lambda |} \\sum_ {x \\in \\Lambda} M (\\boldsymbol {I}, x) \\times \\Gamma \\left(\\phi (\\boldsymbol {I}, x), S _ {\\mathcal {Z}} \\left(f _ {S} (\\boldsymbol {I}, x)\\right)\\right), \\tag {1}", + "image_path": "768cbbc75ca4ae7322f77aa23c165d1ea8bbab0e1495ce1dbf5ef46d00f2eed6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " is the cosine distance between the two inputs. Our spherical prototypes are implemented via a neural network that maps points in " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": ". Importantly, each point " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "s\\in S^2\\subset \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " must be mapped independently, meaning that it should correspond to a unique point " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\in \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": ", irrespective of which instance it comes from or where in the image this part is located. To model multiple categories, and to encourage information sharing between closely related ones, we use a single network conditioned on a category embedding. In practice, " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{Z}}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " is a visual transformer [13] without" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19523" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 81, + 547, + 170 + ], + "blocks": [ + { + "bbox": [ + 47, + 81, + 547, + 170 + ], + "lines": [ + { + "bbox": [ + 47, + 81, + 547, + 170 + ], + "spans": [ + { + "bbox": [ + 47, + 81, + 547, + 170 + ], + "type": "image", + "image_path": "b72b9756630e070510f259a7d3984fb574b60b297dfb9a57dd1382a481fa2f4a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 173, + 547, + 229 + ], + "lines": [ + { + "bbox": [ + 46, + 173, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 547, + 229 + ], + "type": "text", + "content": "Figure 2. Overview of our semantic correspondence estimation approach. We begin by extracting features from a frozen self-supervised backbone, and further use them to predict spherical coordinates via a learned module. Each predicted point is used to query a jointly learned prototype, providing the supervision signal (Sec. 3.2). The sphere is used to enforce weak geometric priors (Sec. 3.3). During inference, SSL features are combined with spherical coordinates (Sec. 3.4). A blue outline indicates a fixed module, while orange indicate learned parameters." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "text", + "content": "self-attention, but with cross-attention between image tokens and a single category token " + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "text", + "content": " which is a one hot embedding of the category. As learning " + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "text", + "content": " from scratch can be challenging, we further leverage the SSL backbone by simply adding a prediction head " + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "inline_equation", + "content": "f_{S}^{\\prime}" + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "text", + "content": " to it to produce spherical maps, i.e. " + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "inline_equation", + "content": "f_{S} = f_{S}^{\\prime} \\circ \\phi" + }, + { + "bbox": [ + 46, + 238, + 288, + 322 + ], + "type": "text", + "content": ". An overview of our architecture is presented in Fig. 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 331, + 197, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 197, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 197, + 342 + ], + "type": "text", + "content": "3.3. Enforcing geometric priors" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 349, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 434 + ], + "type": "text", + "content": "The above spherical reconstruction formulation alone offers little benefit over matching the self-supervised features from " + }, + { + "bbox": [ + 46, + 349, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 349, + 287, + 434 + ], + "type": "text", + "content": " directly, especially considering the low dimensionality of the intermediate spherical space, which is not guaranteed to be well-behaved. However, this spherical structure enables the computation of simple geometric priors that can be enforced during training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "content": "Viewpoint regularization. Many object categories exhibit some form of symmetry which can make it particularly challenging for image-based models to distinguish between different sides of an object, creating spurious correlations between distinct parts (e.g. see cars in Fig. 1). One potential way of addressing this challenge, without using dense groundtruth correspondence, is to exploit viewpoint information of the object instance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "type": "text", + "content": "An interesting property of using a spherical prototype to represent an object category is that it can easily be used to infer an object's viewpoint with respect to the camera. We posit that the average coordinate of a spherical map of an image, which we present as " + }, + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "type": "inline_equation", + "content": "\\mu(f_S(I)) = 1 / |\\Lambda| \\sum_{x \\in \\Lambda} f_S(I, x)" + }, + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "type": "text", + "content": ", can be viewed as a coarse approximation of the camera viewpoint under which the object is seen, e.g. right side views should be approximately mapped to the right side of the sphere, and left side views to the left. Intuitively, thinking of " + }, + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "type": "inline_equation", + "content": "f_S" + }, + { + "bbox": [ + 46, + 545, + 288, + 700 + ], + "type": "text", + "content": " as a mapping from image pixels to the object's surface, the visible parts of an object should roughly be those closest to the camera, while the others should be hidden by self-occlusion." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "By using the groundtruth camera viewpoint " + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "v_{I}" + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": ", we en" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "text", + "content": "force the average direction of the spherical map " + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "inline_equation", + "content": "\\mu (f_S(I))" + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "text", + "content": " to align with " + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "inline_equation", + "content": "v_{I}" + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "text", + "content": ". When this is satisfied, symmetric views must be mapped to different parts of the sphere. While precise viewpoint information is hard to obtain, we observe it is sufficient to use coarse relative viewpoint supervision between images. In practice, viewpoints are discretized into a small number of bins, and " + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "inline_equation", + "content": "v_{I}" + }, + { + "bbox": [ + 304, + 238, + 547, + 357 + ], + "type": "text", + "content": " is represented by the median value of the corresponding bin. Then, we simply enforce that the dot product between viewpoints from two images equals that of their average spherical maps," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 322, + 362, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 362, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 322, + 362, + 545, + 389 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v p} = \\sum_ {\\boldsymbol {I}, \\boldsymbol {I} ^ {\\prime}} | | v _ {\\boldsymbol {I}} \\cdot v _ {\\boldsymbol {I} ^ {\\prime}} - \\mu \\left(f _ {S} (\\boldsymbol {I})\\right) \\cdot \\mu \\left(f _ {S} \\left(\\boldsymbol {I} ^ {\\prime}\\right)\\right) | | ^ {2}. \\tag {2}", + "image_path": "c1e98bfe720f6b06a7eae15c3cab8e5ef39065ee48fe5eac484dba4e2d5b315c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 402, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 509 + ], + "type": "text", + "content": "Relative distance loss. As noted earlier, current self-supervised extracted features can confuse repeated object repeated parts. Depending on the target goal, this can be desirable, if the parts do indeed belong to the same part category. However, this is detrimental for dense correspondence estimation as the parts may actually be different part instances, e.g. left vs. right leg. It can be hard to distinguish between these based on their appearance alone and additional geometric context is required." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": "One trivial way of encoding this context is by making the assumption that similar parts that appear in different locations on an image (i.e. not beside each other) are in fact different instances of the same semantic part. Therefore, we would like to enforce the property on our predicted spherical maps that distant pixels in the image should be mapped far apart on the sphere. Due to scale variation, distance on the image plane is hard to link to distances on the surface of the sphere. However, we can reformulate this property as a relative distance comparison using a triplet. Given three points " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": " on an image " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": ", and their corresponding positions " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "s_a = f_S(\\pmb{I}, a)" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "s_b" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "inline_equation", + "content": "s_c" + }, + { + "bbox": [ + 304, + 510, + 546, + 665 + ], + "type": "text", + "content": " on the sphere, the ordering between distances should be preserved, that is:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 319, + 670, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 670, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 319, + 670, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\left| \\left| a - b \\right| \\right| \\leq \\left| \\left| a - c \\right| \\right| \\iff \\Gamma \\left(s _ {a}, s _ {b}\\right) \\leq \\Gamma \\left(s _ {a}, s _ {c}\\right). \\tag {3}", + "image_path": "3f7003d595a20c179165c2bca389d5413507d02d020f6e3097f3265bd5b8678b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "In reality, this does not hold for distances along an object's surface, which the sphere is supposed to represent, partly" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 309, + 70, + 414, + 79 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 70, + 414, + 79 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 414, + 79 + ], + "type": "text", + "content": "Feature Reconstruction Loss" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19524" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 81, + 113, + 146 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 113, + 79 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 113, + 79 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 113, + 79 + ], + "type": "text", + "content": "Spherical Coordinates" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 81, + 113, + 146 + ], + "lines": [ + { + "bbox": [ + 48, + 81, + 113, + 146 + ], + "spans": [ + { + "bbox": [ + 48, + 81, + 113, + 146 + ], + "type": "image", + "image_path": "32af9dd198c5b9ba01d3c41d465b8c613609eb1f19593e7d2d7e8c73764d482f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 127, + 81, + 194, + 146 + ], + "blocks": [ + { + "bbox": [ + 124, + 70, + 204, + 79 + ], + "lines": [ + { + "bbox": [ + 124, + 70, + 204, + 79 + ], + "spans": [ + { + "bbox": [ + 124, + 70, + 204, + 79 + ], + "type": "text", + "content": "Relative Distance Loss " + }, + { + "bbox": [ + 124, + 70, + 204, + 79 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rd}" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 127, + 81, + 194, + 146 + ], + "lines": [ + { + "bbox": [ + 127, + 81, + 194, + 146 + ], + "spans": [ + { + "bbox": [ + 127, + 81, + 194, + 146 + ], + "type": "image", + "image_path": "e014c2f4184defb79360348d7bca1d228a221d638f30ebd71c4496572deca634.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 214, + 81, + 287, + 159 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 276, + 79 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 276, + 79 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 276, + 79 + ], + "type": "text", + "content": "Orientation Loss " + }, + { + "bbox": [ + 216, + 70, + 276, + 79 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_o" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 214, + 81, + 287, + 159 + ], + "lines": [ + { + "bbox": [ + 214, + 81, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 214, + 81, + 287, + 159 + ], + "type": "image", + "image_path": "da551187e926cc15d95fb6ad0557ae2c7e29ca97de66847b48b4cdce1475d6d2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": "Figure 3. Illustration of our geometry losses " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rd}" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_o" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": ". The left image shows a spherical map from which a triplet of points is sampled. " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rd}" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": ": as the anchor patch " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " is closer to the positive " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " on the image compared with the negative " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": ", its corresponding position " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "s_a" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " on the sphere must also be closer to " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "s_b" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " than " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "s_c" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_o" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": ": after projecting " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "s_b" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "s_c" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " to the plane tangent to the sphere at " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "s_a" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": ", we ensure orientation is preserved by enforcing positive collinearity between " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "u_b \\times u_c" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": " and the normal vector " + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 171, + 287, + 258 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 272, + 287, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 272, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 272, + 287, + 343 + ], + "type": "text", + "content": "due to perspective. For example, in the case of a long train seen from a near frontal view, parts at the back of the train might appear very close to the front in the image, even though they are very far in 3D space. Nevertheless, we find that this is still an effective prior for discouraging repeated part instances from being mapped to the same location." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "text", + "content": "During training, point triplets " + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "inline_equation", + "content": "(a,b,c)" + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "text", + "content": " are randomly sampled among pixels that belong to the object. Among each such triplet, we chose an anchor location " + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "inline_equation", + "content": "anc = a" + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "text", + "content": ", a positive location " + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "inline_equation", + "content": "pos = \\arg \\min_{x\\in \\{b,c\\}}||a - x||" + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "text", + "content": ", and a negative location " + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "inline_equation", + "content": "neg = \\arg \\max_{x\\in \\{b,c\\}}||a - x||" + }, + { + "bbox": [ + 46, + 344, + 287, + 415 + ], + "type": "text", + "content": " (see Fig. 3). We can then define a triplet margin loss as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 63, + 423, + 287, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 423, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 63, + 423, + 287, + 452 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {r d} = \\max (\\Gamma (f _ {S} (\\boldsymbol {I}, a n c), f _ {S} (\\boldsymbol {I}, p o s)) \\tag {4} \\\\ - \\Gamma (f _ {S} (\\boldsymbol {I}, a n c), f _ {S} (\\boldsymbol {I}, n e g)) + \\delta , 0), \\\\ \\end{array}", + "image_path": "d23bb5158af99b68045b22341b3507f1e5dad16d8c512e5fe420c92f9a53e166.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 460, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 508 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 460, + 287, + 508 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 460, + 287, + 508 + ], + "type": "text", + "content": " is a hyperparameter which specifies the margin. A useful side product of this formulation is that it encourages the spherical maps to be smooth, as strong discontinuities would produce a large anchor to positive distance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": "Orientation loss. A final advantage of using " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " as a latent space is that it is an orientable 2D space, just like images. Therefore, enforcing that " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " preserves orientation prevents spurious matches between symmetric views. Intuitively, if a point " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " appears on the right side of " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " in the image, then " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "s_a" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " must appear in the same side of " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "s_b" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": ". Given a point triplet as defined earlier, this can be enforced by making sure that the determinant of the image triplet and sphere triplet positively correlate. Formally, defining " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "P_a" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " as the orthogonal projection to the plane tangent to " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "s_a" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "u_b" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "P_a(s_b) - s_a" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "d_I = \\det(b - a, c - a)" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "d_S = \\det(u_b, u_c)" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": ", and want " + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "inline_equation", + "content": "sign(d_I) = sign(d_S)" + }, + { + "bbox": [ + 46, + 522, + 287, + 665 + ], + "type": "text", + "content": " (see Fig. 3)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "As objects can have complex geometry that our model does not have access to, there exists no exact relation linking the two determinants together, as for instance perspective distortions might alter angles. However, we can as-" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "sume that image triplets of large determinants should also have large determinant on the sphere, as a change of sign in determinant indicates the relative orientation on the sphere has been inverted. In practice, we randomly sample image triplets " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "(a,b,c)" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and select those whose image determinant " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "d_{I}" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " is higher than a threshold " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "d_{\\tau} = 0.7" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " while swapping " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "d_{I}" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " is negative. Then, we enforce the determinant of the corresponding sphere triplet to be at least " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "d_{\\tau}" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 344, + 174, + 545, + 206 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 174, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 344, + 174, + 545, + 206 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o} = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} d _ {I} < d _ {\\tau} \\\\ \\max \\left(d _ {\\tau} - d _ {S}, 0\\right) & \\text {i f} d _ {I} \\geq d _ {\\tau}. \\end{array} \\right. \\tag {5}", + "image_path": "683df0f21d6a536c093f3b7e084554be505fd8747c5d31de8daebc5e50bad7bb.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 218, + 545, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 218, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 218, + 545, + 232 + ], + "type": "text", + "content": "3.4. Correspondence via combined representations" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": "During inference, it is possible to directly query the spherical maps " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " of two images to obtain correspondences using the cosine distance. That is, for an image pair " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "I, I'" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " and a query location " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": ", its location in " + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "inline_equation", + "content": "I'" + }, + { + "bbox": [ + 304, + 236, + 545, + 285 + ], + "type": "text", + "content": " can be computed as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 349, + 296, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 296, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 349, + 296, + 545, + 316 + ], + "type": "interline_equation", + "content": "p ^ {*} = \\underset {p} {\\arg \\min } \\Gamma \\left(f _ {S} (\\boldsymbol {I}, q), f _ {S} \\left(\\boldsymbol {I} ^ {\\prime}, p\\right)\\right). \\tag {6}", + "image_path": "0f16eff4273af1e6352273fb1003459a344cd58f6bee7099106a7141880784ef.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "text", + "content": "While this protocol is sound, it comes with two important drawbacks. First, " + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "text", + "content": " produces spherical maps for the whole image, including the background, meaning segmentation masks would be required at inference time to prevent the emergence of spurious matches. Second, the spherical map is designed to be a smooth parameterization of the object surface, making it susceptible to missing fine details. A slightly incorrect mapping " + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "inline_equation", + "content": "f_{S}(I,q) + \\epsilon" + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "text", + "content": " has a high probability of finding a higher match in a nearby region of the correct match " + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "inline_equation", + "content": "f_{S}(I^{\\prime},p^{*})" + }, + { + "bbox": [ + 304, + 319, + 545, + 486 + ], + "type": "text", + "content": " if both maps are smooth. In comparison, SSL feature maps can exhibit strict feature separation, e.g. wheel features are very different from other nearby non-wheel features, making it unlikely that a wheel pixel finds a nearest neighbor among nearby non-wheel pixels." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 487, + 545, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 606 + ], + "type": "text", + "content": "To mitigate this issue, we make use of the feature maps that are already computed by the self-supervised backbone network " + }, + { + "bbox": [ + 304, + 487, + 545, + 606 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 487, + 545, + 606 + ], + "type": "text", + "content": ", in a similar way to supervised correspondence approaches that aggregate features from a network [35, 53, 59]. Existing literature has shown that DINO features are particularly effective at differentiating between the foreground and background [1], removing the need for inference-time segmentation. To leverage these DINO features, we reformulate Eq. (6) as the combination of self-supervised features and spherical locations:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 330, + 612, + 545, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 612, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 330, + 612, + 545, + 643 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} p ^ {*} = \\arg \\min _ {p} (1 - \\alpha) \\Gamma (\\phi (\\boldsymbol {I}, q), \\phi (\\boldsymbol {I} ^ {\\prime}, p)) & \\\\ + \\alpha \\Gamma (f _ {S} (\\boldsymbol {I}, q), f _ {S} (\\boldsymbol {I} ^ {\\prime}, p)), & \\end{array} \\tag {7}", + "image_path": "47a8b05e3838f47f33a0bc753af86096c34fa3e416c3a839230e22d6f561e00e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 647, + 520, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 520, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 520, + 659 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 647, + 520, + 659 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 647, + 520, + 659 + ], + "type": "text", + "content": " is a hyperparameter that balances each term." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 669, + 386, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 386, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 386, + 682 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. We build our models on DINOv1-B/8 [6] and DINOv2-B/14 [40] backbones. Training masks" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19525" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 213 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 213 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 213 + ], + "type": "table", + "html": "
↑3%4%5%6%7%8%9%10%11%12%13%14%15%16%17%avg
CustomCATS [9]52.034.772.234.349.957.543.666.524.463.256.552.042.641.743.033.672.658.049.9
MMNet+FCN [59]55.937.065.035.450.063.945.762.828.765.054.751.638.534.641.736.377.762.550.4
SCorrSan [26]57.140.378.338.151.857.847.167.925.271.363.949.345.349.848.840.377.769.754.4
DINOv1DINOv1 [6]44.326.857.622.029.332.819.754.014.940.139.329.329.037.020.028.240.621.132.6
ASIC [16]57.925.268.124.735.428.430.954.821.645.047.239.926.248.814.524.549.024.637.0
Ours47.126.070.921.837.534.932.460.023.253.648.542.528.342.721.141.939.741.739.7
SDDIFT [49]63.554.580.834.546.252.748.377.739.076.054.961.353.346.057.857.171.163.457.7
SD [57]63.155.680.233.844.949.347.874.438.470.853.761.154.455.054.853.565.053.356.1
DINOv2DINOv2 [40]72.762.085.241.340.452.351.571.136.267.164.667.661.068.230.762.054.324.256.2
DINOv2 + SD [57]73.064.186.440.752.955.053.878.645.577.364.769.763.369.258.467.666.253.563.3
Ours (sphere only)46.728.866.333.036.566.659.174.925.465.750.152.727.113.715.846.673.536.745.5
Ours76.961.285.942.148.473.367.280.046.380.266.771.266.063.936.268.667.842.263.6
Ours + SD74.864.587.145.652.777.871.482.447.782.067.373.967.660.049.969.878.559.167.3
", + "image_path": "ff419bee49174526624b759c8748d84105895a7c89c718bf83086da27705c078.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 218, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 546, + 251 + ], + "type": "text", + "content": "Table 1. Keypoint matching scores on SPair-71k evaluated using PCK@0.1 with macro-averaging for the summary scores. We present our approach using DINOv1 [6] features (middle rows) and DINOv2 [40] features (bottom rows). In both cases, we improve over the DINO only baselines and are superior to fully supervised methods (top rows). Bold entries are best per category and underlined are second-best." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "type": "text", + "content": "are obtained using a pretrained Mask R-CNN model [21]. Our spherical mapper consists of a linear dimension reduction layer halving the number of features, a visual transformer block with self-attention, and a final linear layer with an output dimension of three. The resulting feature map is then normalized pixel-wise so that its output values lie on the surface of " + }, + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "type": "inline_equation", + "content": "S^2" + }, + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "type": "text", + "content": ". The dimensionality reduction layer, while not strictly necessary, is helpful considering the small number of images used during training, while the transformer block helps in disentangling sides and repeated parts by allowing global reasoning between image patches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": "The final loss term is computed as " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_{rec} + \\lambda_{rd}\\mathcal{L}_{rd} + \\lambda_o\\mathcal{L}_o + \\lambda_{vp}\\mathcal{L}_{vp}" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "\\lambda_{rd} = \\lambda_o = 0.3" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "\\lambda_{vp} = 0.1" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": " is set slightly lower as it can have the detrimental effect of pulling all predictions towards the average over image pixels - cf. Eq. (2). The relative distance margin is set to " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "\\delta = 0.5" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": " to encourage feature separation. To perform matching in Eq. (7), " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": " is set to 0.2 so that we leverage the highly discriminative DINO features, while using the sphere as a symmetry and repetition-breaking mechanism. Our model is trained for a total of 200 epochs using Adam [28]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": "Datasets. Following existing work [16, 26, 57], we evaluate our method primarily on the Spair-71k dataset [34], which contains images from 18 different object categories. The evaluation set contains between 600 and 900 image pairs, each of which are annotated with the keypoints that are visible in both images. We train our model on the Spair-71k training split on all categories simultaneously, without using any keypoint annotations. Additionally, we evaluate on the AwA-pose dataset [4], which contains images from 35 quadruped categories, annotated with keypoints. We also present results by training on the Freiburg cars dataset [45]. This dataset was collected by densely sampling approximately 100 images each around 48 different car instances. The higher image count, coupled with " + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": " dense sampling, enables us to learn a more detailed spherical prototype." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 267, + 455, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 455, + 280 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 455, + 280 + ], + "type": "text", + "content": "4.1. Keypoint average precision" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "type": "text", + "content": "While issues with symmetries are clear in Fig. 4, we argue that the PCK metric fails to account for them as it is only computed between keypoints that appear in both the source and target image. Hence, models that predict high similarity between two visually similar but semantically different keypoints might not be penalized for it. PCK can partly account for repetition-related mistakes if the parts appear simultaneously in both images, but it does not penalize symmetry-related issues, like mistaking the left and right side of a car, as the corresponding keypoints do not appear simultaneously. PCK was initially proposed for simpler cases where keypoints were assumed to be always be visible, e.g. faces or different instances in the same pose. However, as benchmarks become more challenging, a more robust protocol should be used. To illustrate how much these failure cases impact SSL models, we propose an alternative evaluation metric, Keypoint Average Precision - " + }, + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathrm{KAP}@\\kappa" + }, + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "type": "text", + "content": ". It is similar to " + }, + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathrm{PCK}@\\kappa" + }, + { + "bbox": [ + 304, + 289, + 545, + 529 + ], + "type": "text", + "content": ", but accounts for these errors by evaluating average precision instead of accuracy and penalizes methods that predict matches when none exist." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": "When performing evaluation on a pair of images, instead of restricting it to keypoints that simultaneously appear in both images, we consider all keypoints that appear in the source, irrespective of whether they are also visible in the target image. For each such keypoint, if it appears in the target image, we extract the highest similarity value within radius " + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": " of the ground-truth and label it as positive. We also extract the highest similarity value outside the radius and label it as negative, penalizing overly high predictions on wrong, possibly repeated parts. If the source keypoint does not appear on the target image, we simply extract the highest similarity prediction across the whole target image and label it as negative to penalize incorrectly high similarity when none should exist. This effectively reformulates the task as a binary classification problem, where the embed-" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "19526" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 545, + 269 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 545, + 269 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 545, + 269 + ], + "type": "image", + "image_path": "d6af9bd0cc6974ca74fc3d532f867971c3de3740bff2e5fc718217f869c09983.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 547, + 329 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 547, + 329 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of dense correspondence maps. For DINOv2, SD, and DINO+SD features we perform PCA on the segmented object features independently for each category, then visualize the three main components. Note that the SD and DINO+SD features are not completely equivalent to the ones used to compute matches, but are provided here for illustration. Spherical maps from " + }, + { + "bbox": [ + 46, + 274, + 547, + 329 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 46, + 274, + 547, + 329 + ], + "type": "text", + "content": " (Sphere) for our approach are visualized directly. Our spherical maps correctly identify the different sides of objects, whereas other features fail to capture these differences." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 338, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 387 + ], + "type": "text", + "content": "ding of each source keypoint has to be close to, and only to, the corresponding target keypoint. Finally, we compute the average precision over all the extracted pairs, and report mean average precision per-category." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 395, + 150, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 150, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 150, + 406 + ], + "type": "text", + "content": "4.2. SPair-71k results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 414, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 556 + ], + "type": "text", + "content": "We first evaluate on the task of keypoint transfer between pairs of images using Spair-71k [34]. We present quantitative per-category results in Tab. 1, using the standard PCK metric along with macro-averaged scores as the number of per-category pairs varies greatly. We split the models according to their backbone: custom supervised models, DINOv1-based, SD-based, and DINOv2-based. A striking preliminary observation is the effectiveness of DINOv2, surpassing supervised approaches on most categories. While its success can partially be attributed to evaluation biases [2], this demonstrates the effectiveness of large scale learned self-supervised features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Using a DINOv1 backbone, our model improves over its backbone on most categories, and over ASIC [16] on average. When combined with the DINOv2 backbone, our model provides improvements on all but two categories. A clear pattern can be identified, with strongest improvements being observed over blob-like symmetric objects with repeated parts (+21.0 on bus and +15.7 on car), while spherical mapping hinders performance on highly deformable categories (-4.3 on person), or high-genus objects for which a sphere is a poor surface prior (-0.8 on bicycle). Our model performs slightly better compared to DINO+SD [57], while requiring a fraction of the computational cost at inference time. Finally, following [57] we evaluate adding Stable Diff" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 338, + 546, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 546, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 546, + 386 + ], + "type": "text", + "content": "fusion (SD) [42] features to our method at inference time, which yields further improvements. This illustrates that spherical maps and SD features capture different facets of the correspondence problem." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 386, + 546, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 546, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 546, + 529 + ], + "type": "text", + "content": "We show the results of evaluating correspondences with KAP in Tab. 2. We observe particularly large discrepancies between PCK and KAP in highly symmetric objects with repeated parts, e.g. buses and cars, and the ranking between our model and DINOv2 is reversed on humans, possibly due to DINOv2's symmetric predictions on left and right limbs. All models across all categories obtain lower results when using KAP highlight the symmetry issues they are facing. A limitation of KAP is that it might still count correct repeated parts mistakes if their distance in the image is less than " + }, + { + "bbox": [ + 304, + 386, + 546, + 529 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 386, + 546, + 529 + ], + "type": "text", + "content": ". Nonetheless, we argue that KAP is more informative than PCK and is just as efficient to evaluate." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 530, + 547, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 547, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 547, + 626 + ], + "type": "text", + "content": "The qualitative visualization shown in Fig. 4 illustrates these improved results. Our model correctly maps the two opposite sides of the cars to different sphere regions, while other feature maps look extremely similar, even when looking at two opposite sides of an object, with the notable exception of SD on birds. The fact that such similarities exist between opposite views suggest that the utility of baselines such as DINOv2 would be quite limited in real scenarios." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 635, + 430, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 430, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 430, + 646 + ], + "type": "text", + "content": "4.3. Additional evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Animals with Attributes (AwA). To further evaluate our model, we also report results on the AwA-pose dataset from [4], which contains images from 35 different categories of quadruped. While our spherical prototype needs category information during training to reconstruct" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19527" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 544, + 144 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 544, + 144 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 544, + 144 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 544, + 144 + ], + "type": "table", + "html": "
↑%avg
DINOv2 [40]53.554.060.235.544.436.331.761.337.454.752.551.548.848.237.844.147.438.246.5
SD [57]44.448.554.531.545.232.730.068.435.855.247.948.144.842.344.539.252.751.245.4
DINOv2 + SD [57]52.055.959.234.749.036.032.570.339.859.853.152.450.650.447.846.253.349.849.6
Ours (sphere only)38.434.253.933.037.949.743.471.729.857.145.842.532.427.029.537.157.436.042.1
Ours60.751.263.138.445.055.945.769.740.463.254.854.351.248.738.847.955.542.251.5
Ours + SD58.954.262.239.646.654.547.176.240.965.357.356.154.247.443.749.462.452.053.8
", + "image_path": "235c8aed9c71033407841370678a650d0449d211e1b822b7f11305a214f65294.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 175, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 289, + 342 + ], + "type": "text", + "content": "category-specific features, only the sphere mapper is used during inference, meaning it can be readily applied to unseen categories. Five quadruped classes (cat, cow, dog, horse, and sheep) appear in both SPair and AwA-pose, and are therefore seen during training, but the rest are completely new for our sphere mapper. Nonetheless, results shown in Tab. 3 show that the sphere mapper generalizes well to unseen categories. We attribute this to the assistance from the strong category-agnostic features from DINOv2. Once again, the improvement of using our spherical method is much more apparent using KAP, i.e. the PCK improvement over DINOv2 alone is 2.2 when adding SD and 2.6 when adding spheres, while these become 1.8 and 3.9 respectively with KAP." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 60, + 352, + 272, + 384 + ], + "blocks": [ + { + "bbox": [ + 74, + 147, + 518, + 159 + ], + "lines": [ + { + "bbox": [ + 74, + 147, + 518, + 159 + ], + "spans": [ + { + "bbox": [ + 74, + 147, + 518, + 159 + ], + "type": "text", + "content": "Table 2. Keypoint matching scores on SPair-71k evaluated using KAP@0.1 with macro-averaging for the summary scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 352, + 272, + 384 + ], + "lines": [ + { + "bbox": [ + 60, + 352, + 272, + 384 + ], + "spans": [ + { + "bbox": [ + 60, + 352, + 272, + 384 + ], + "type": "table", + "html": "
Dv2SDDv2+SDOursOurs+SD
PCK@0.165.956.068.168.769.8
KAP@0.155.050.756.858.960.6
", + "image_path": "57e5ca2d521273cf80a5375f70b995ae58af2e339e003d3a9c91afa239f8730f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 435, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 509 + ], + "type": "text", + "content": "Model ablation. We also analyze the impact of removing each individual loss term when training our model in an ablation study. The results in Tab. 4 indicate that all variants except the no " + }, + { + "bbox": [ + 46, + 435, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rd}" + }, + { + "bbox": [ + 46, + 435, + 287, + 509 + ], + "type": "text", + "content": " one do not significantly improve over the DINOv2 baseline as they also fail to identify opposite sides of objects and repeated parts." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 60, + 517, + 272, + 540 + ], + "blocks": [ + { + "bbox": [ + 46, + 384, + 288, + 417 + ], + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 417 + ], + "type": "text", + "content": "Table 3. Average scores when evaluating on AwA-pose using a random subset of 200 pairs per category. 'Ours' denotes our model trained on SPair-71k with a DINoV2 backbone." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 517, + 272, + 540 + ], + "lines": [ + { + "bbox": [ + 60, + 517, + 272, + 540 + ], + "spans": [ + { + "bbox": [ + 60, + 517, + 272, + 540 + ], + "type": "table", + "html": "
DINOv2no Lvpno Lrdno Lofull model
56.258.661.256.063.6
", + "image_path": "9d3050d202ecc208ce416d945793ededf19ab754ded0736fb2be144ac06cdfd0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Inference speed. The results in Tab. 1 demonstrate how effective the addition of Stable Diffusion features are. However, computing correspondences through diffusion requires adding noise to images, running iterative diffusion, and performing joint decomposition between the source and target features. As a result, its inference speed is much slower compared to using DINOv2 features. In comparison, our approach only requires a few extra layers on top of DINOv2 and has negligible additional overhead. Timing results in Tab. 5 illustrate that adding diffusion-extracted features reduces throughput by an order of magnitude." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 320, + 167, + 531, + 190 + ], + "blocks": [ + { + "bbox": [ + 46, + 541, + 287, + 564 + ], + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 564 + ], + "type": "text", + "content": "Table 4. Average PCK@0.1 scores when training and testing on SPair-71k using different ablated versions of our approach." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 167, + 531, + 190 + ], + "lines": [ + { + "bbox": [ + 320, + 167, + 531, + 190 + ], + "spans": [ + { + "bbox": [ + 320, + 167, + 531, + 190 + ], + "type": "table", + "html": "
DINOv2SDDINOv2+SDOursOurs+SD
3.40.380.353.30.34
", + "image_path": "718e39410e2825884dd321ff8f8d8e24d038d94a42fdf4ab6c3afd50855f6a2a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 191, + 545, + 213 + ], + "lines": [ + { + "bbox": [ + 305, + 191, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 545, + 213 + ], + "type": "text", + "content": "Table 5. Descriptor computation throughput in pairs/second at inference time on a single A5000 GPU, where higher is better." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 236, + 383, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 383, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 383, + 247 + ], + "type": "text", + "content": "4.4. Limitations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 255, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 459 + ], + "type": "text", + "content": "While our approach results in significant improvements over the DINOV2 baseline for many categories (see Tab. 1), there are still some limitations. For example, we do not perform as well on a small number of categories that cannot be well approximated by a sphere (e.g. humans). Furthermore, the very low-dimensional spherical encoding on its own is not as effective at discriminating parts and subparts and thus needs to be combined with self-supervised features. However, as we already densely compute these features at inference time for each test image, there is no additional cost in combining them with our spherical mapping when evaluating correspondence. Finally, our method relies on additional supervision at training time in the form of automatically computed segmentation masks and weak camera pose supervision. However, results in the supplementary material suggest that coarse camera viewpoints are enough to obtain good performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 472, + 379, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 379, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 379, + 484 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 493, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 685 + ], + "type": "text", + "content": "We presented a new approach for semantic correspondence estimation that is robust to issues resulting from object symmetries and repeated part instances. In addition, we proposed a new evaluation protocol that is more sensitive to these issues. Our approach leverages recent advances in the self-supervised learning of discriminative image features and combines them with a weak geometric spherical prior. By using weak pose supervision to represent objects categories on the surface of spheres, we are able to enforce simple geometric constraints during training that result in more geometric and semantically consistent representations. Results on the task of semantic keypoint matching between images from different object instances, a fundamental task in 3D computer vision, demonstrate that our approach alone is superior to existing strong baselines and can be combined with existing methods to further boost performance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. 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Saquib Sarfraz3,4 Mohsen Ali2", + "bbox": [ + 307, + 227, + 661, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Mohamed bin Zayed University of Artificial Intelligence, 2Information Technology University of Punjab,", + "bbox": [ + 169, + 247, + 797, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3Mercedes-Benz Tech Innovation, 4Karlsruhe Institute of Technology", + "bbox": [ + 277, + 265, + 691, + 281 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "muhammad.sohail@mbzuai.ac.ae, muhammad.haris@mbzuai.ac.ae", + "bbox": [ + 223, + 284, + 730, + 297 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 333, + 313, + 349 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we tackle the problem of domain generalization for object detection, specifically focusing on the scenario where only a single source domain is available. We propose an effective approach that involves two key steps: diversifying the source domain and aligning detections based on class prediction confidence and localization. Firstly, we demonstrate that by carefully selecting a set of augmentations, a base detector can outperform existing methods for single domain generalization by a good margin. This highlights the importance of domain diversification in improving the performance of object detectors. Secondly, we introduce a method to align detections from multiple views, considering both classification and localization outputs. This alignment procedure leads to better generalized and well-calibrated object detector models, which are crucial for accurate decision-making in safety-critical applications. Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage detectors. To validate the effectiveness of our proposed methods, we conduct extensive experiments and ablations on challenging domain-shift scenarios. The results consistently demonstrate the superiority of our approach compared to existing methods. Our code and models are available at: https://github.com/msohaildanish/DivAlign.", + "bbox": [ + 75, + 366, + 472, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, we have witnessed remarkable performance improvements in supervised object detection [39, 47, 48, 53]. The success of these methods rely on the assumption that the training and testing data are sampled from the same distribution. However, in many real-world applications, such as autonomous driving, this assumption is often violated and these object detectors usually show degraded performance due to a phenomenon called domain-", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "shift [3, 5, 49]. Shifts in real-world domains are typically caused by environmental alterations, like varying weather and time conditions. These changes manifest in diverse contrasts, brightness levels, and textures among others.", + "bbox": [ + 496, + 335, + 893, + 396 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A prominent line of research that attempts to alleviate the impact of domain-shift is known as unsupervised domain adaptation (UDA) [20, 24, 42, 49, 63, 68, 72]. Given the labeled data from the source domain and unlabelled data from the target domain, the aim of UDA methods is to align the source and target data distributions so that the trained model can generalize well to the target domain [67]. An obvious limitation of UDA methods is that they require pre-collecting data and re-training the model for different target domains. Collecting data, even without annotation, for all possible domain shifts and training the model when shift happens is difficult and sometime not possible.", + "bbox": [ + 496, + 398, + 893, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To cope with the domain-shift problem, a more realistic albeit challenging problem is domain generalization [2, 11, 23, 26, 32, 34, 35, 40, 58]. The goal of domain generalization (DG) is to learn a generalizable model typically from multiple source domains, available during training, that can perform well on the unseen target domain. A dominant class of DG methods attempts to learn domain-invariant feature space across multiple source domains [1, 11, 33, 35]. The performance of these methods is sensitive to the number of available source domains [7, 70]. In many realistic scenarios, acquiring labeled data from multiple source domains is often costly and time-consuming, eventually restricting the potential utilization of such methods. For these reasons, generalizing from a single-source domain is a more practical setting.", + "bbox": [ + 496, + 580, + 895, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent surveys [29, 70] reveal that very little work has been done on DG for object detection [38, 60], despite the fact that object detectors occupy an important position in many safety-critical and security-sensitive applications e.g., autonomous driving. An object detector should be able to provide accurate as well as calibrated detections in different", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17732", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "out-domain scenarios. Towards this end, we study the problem of single-domain generalized object detection (Single-DGOD). In the Single-DGOD setting, a single source domain is available for training, and the goal is to learn an object detector that can generalize well to multiple unseen target domains. Note that, many existing DG methods cannot be applied to solve this task since both multiple source domains and domain-level annotations are unavailable.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We are inspired by the class of DG methods for classification [46, 55, 66] that show that simulating novel domains during model training allows segregating domain-specific and semantics-oriented features. Consequently, the spurious correlations between the input and model predictions are suppressed. We begin by leveraging this idea of augmenting our input examples to realize the simulation of novel domains, thereby increasing the diversity of single-source training domain. In particular, we use the common off-the-shelf visual corruptions coupled with a simple training scheme to build a strong Single-DGOD baseline. The augmentation strategy aims to disrupt surface-level statistical patterns that are specific to a particular domain while preserving high-level semantic concepts that are common across domains. In addition to diversifying the single source domain, we propose a novel approach that aligns detection across different views of the image. The introduced method aligns both the class prediction distributions and predicted bounding box coordinates between augmented views of the image. By ensuring such a consistency of detections, we show that this not only helps in better out-domain detections but importantly also results in better calibrated models.", + "bbox": [ + 75, + 210, + 470, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our work makes two main contributions:", + "bbox": [ + 96, + 545, + 465, + 558 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We show that, using a set of carefully selected augmentations, the base model can surpass the performance of state-of-the-art published single-DGOD methods. To our knowledge, achieving such a strong baseline with known augmentation methods has not been shown before in the single domain object detection generalization.", + "- Our second contribution is an effective classification and localization alignment method that is shown to further improve detections in unseen domain and results in implicitly well calibrated detector model." + ], + "bbox": [ + 76, + 560, + 468, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage object detectors.", + "bbox": [ + 75, + 710, + 468, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 753, + 218, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain adaptive object detection: Several domain adaptive detection methods aim to reduce the pixel-level or feature-level gap between the source and target domain [36, 44]. For instance, the works of [3, 10, 21, 24, 52, 65] utilized the labeled images generated from CycleGAN [71] to achieve pixel-level consistency. Likewise, [3, 5, 10, 19, 49, 51] proposed various mechanisms to progressively obtain a feature-level consistency. A common component", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of these methods is domain adversarial network [15] for achieving feature alignment. The work of [5] performed domain alignment on both global features (backbone features) and local features (Instance-level RoI features). Since then, several methods aimed to further improve these alignments by leveraging multi-scale [19], contextual [3, 49], spatial attention [31], category attention [57], and cross-domain topological relations [4] information. A few methods resorted to pseudo-labelling of instances to include class-level discriminative information. For instance, [24] constructed pseudo-labels by putting a threshold on top-1 accuracy over the predicted class of a detection. Towards refining the noisy pseudo-labels, [27] developed a robust training mechanism coupled with an independent classification module. With a similar goal, [28] proposed a weak self-training method and an adversarial background regularization module. Recently, [42] developed an uncertainty-guided criterion for selecting pseudo-labels in the target domain. We note that almost all of the aforementioned methods require access to both source and (unlabelled) target domain data coupled with an adaptation step to perform well in the target domain. As a consequence, these methods cannot be used to solve single-domain generalized object detection.", + "bbox": [ + 496, + 90, + 890, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single source domain generalization: A more challenging and recently proposed setting in DG is single source domain generalization. It is a more practical setting compared to multi-source DG since the availability of data from multiple different domains is a difficult requirement to fulfill for many real-world applications. The goal is to learn a generalized model using only a single source domain that can perform well on many unseen target domains. An intuitive approach for this setting is to increase the diversity of single source data by proposing different data augmentation techniques. Qiao et al. [46] leveraged adversarial training to construct difficult examples which facilitate model generalization. Earlier attempts involve training a label classifier and a domain classifier in a joint manner by their corresponding perturbations Similarly-[50] proposed to impose Wasserstein constraint in the feature space to generate adversarial samples from synthetic target distribution [56]. Recently, Wu et al. [60] proposed a cyclic-disentangled self-distillation approach for single domaingeneralized object detection. Wang et al. [59] proposed a style-complement module that synthesizes examples from domains complementary to the source domain. Towards exploring the impact of the normalization layer on DG performance, Wang et al. [14] developed a generic normalization approach that learns both the standardization and rescaling statistics by neural networks. The aforementioned methods have shown promising results for the image classification task, however, they are not readily applicable to object detection since it has both classification and localization.", + "bbox": [ + 496, + 443, + 890, + 881 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain diversification for domain generalization: Sev-", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17733", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c166fd0aa20f385609f0b4dd9a85b01c6241757db502612d718811d4ff9ffb5a.jpg", + "image_caption": [ + "Figure 1. Overall architecture of our proposed method. At the core is a baseline detector, Here a two-stage detector Faster-RCNN[48] is depicted, comprising of backbone, region proposal network (RPN), and ROI alignment (RA). To improve the single domain generalization of the baseline detector, we propose to diversify the single source domain and also align the diversified views by minimizing losses at both classification and regression outputs." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 874, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "eral DG methods for object recognition have proposed various data augmentation techniques in an effort to improve the diversity of source domain(s). By using a CNN generator with different losses, Zhou et al. [69] synthesized novel examples from simulated domains. A few methods attempt to suppress the intrinsic style bias of CNNs. For instance, to focus on the contents and styles of images, [43] proposed content-biased and style-biased networks, respectively. To constantly seek diverse styles, [25] proposed a style synthesis process that is formulated as a monotone submodular optimization. Among the more recent methods, [13] explores diversifying source domain by perturbing channel statistics of low-level features for single domain-generalized object detector. In [54] the authors introduced the semantic augmentation of images by utilizing text-prompts relevant to potential target domain concepts in a vision-language model framework to improve the robustness of object detectors in unseen target domains. Along similar lines, [12] adapted the source model using textual descriptions of the target domain in a zero-shot manner to enhance the cross-domain generalizability in object detectors. Note that, both [54] and [12] incorporate the prior target domain knowledge using textual prompts. However, we follow domain generalization settings and leverage no prior knowledge about the target domain. Further, we diversify the source domain in input space and then align the detections in both original and diversified images.", + "bbox": [ + 76, + 330, + 472, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Methodology", + "text_level": 1, + "bbox": [ + 76, + 758, + 294, + 776 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 784, + 218, + 799 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem Settings: Let $\\mathcal{D}_s$ be the single source domain containing $N^s$ labelled training examples $\\{\\left(\\mathbf{x}_i^s,\\mathbf{y}_i^s\\right)\\}_{i = 1}^{N^s}$ , where $\\mathbf{x}_i\\in \\mathbb{R}^{H\\times W\\times C}$ is an image and $\\mathbf{y}_i = \\{k_i,\\mathbf{b}_i\\}$ is the corresponding label with bounding box coordinates $\\mathbf{b}_i\\in \\mathbb{R}^4$ and the associated class category $k_{i}\\in \\{1,\\dots,K\\}$ . $K$ is the number of class categories and $H$ , $W$ and $C$ represent the", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "height, width, and number of channels, respectively. Let $\\{\\mathcal{D}_t\\}_{t=1}^T$ be the set of $T$ (unseen) target domains. Our goal is to learn an object detector using training examples from $\\mathcal{D}_s$ that generalizes well on test examples from $\\mathcal{D}_t$ . We assume that both $\\mathcal{D}_s$ and $\\mathcal{D}_t$ share the same label space.", + "bbox": [ + 498, + 330, + 890, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object Detection: Let $\\mathcal{F}_{det}$ be an object detection model, that takes input image $\\mathbf{x}$ and outputs $Z$ detections $\\{(P(\\hat{k}_n|\\mathbf{x}),\\hat{\\mathbf{b}}_n)\\}_{n = 1}^Z$ , where $\\hat{k}_n$ denotes the class and bounding box $\\hat{\\mathbf{b}}_n$ predictions for $n^{th}$ proposal, respectively. We take the Faster R-CNN [48] model as $\\mathcal{F}_{det}$ to detail our method, but note that our method is detector-agnostic and can be easily applied to other object detection paradigms, as shown in our results. We first overview Faster R-CNN to make the method section self-contained. Faster R-CNN is a popular and widely used two-stage object detector. The first stage comprises of a backbone feature extractor layer which generates a feature map and a region proposal network (RPN) which predicts a set of object proposals or regions of interest (RoIs) from the feature map. The second stage begins with ROI-Alignment, which extracts a fixed-size feature representation for each ROI and then feeds it to a classifier and a regressor to predict class confidence scores and bounding box coordinates, respectively.", + "bbox": [ + 496, + 411, + 892, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Single domain-generalized object detection: In this case, we assume that the object detection $\\mathcal{F}_{det}$ has been trained on the examples taken from the source domain $D_{s}$ and then tested on examples from $\\{\\mathcal{D}_t\\}_{t=1}^T$ . Akin to image classification models, object detection models like Faster-RCNN, which exhibits state-of-the-art performance when testing data and training data are from the same domain (i.e. in-domain scenario), but suffers from performance degradation when domains are different (i.e. out-of-domain scenario) (Figure 4). The presence of multiple domains during training penalizes the object detector in learning shortcuts which are typically domain-specific and instead encourages learning domain-invariant features. Nevertheless, the multi-domain data with the ground truth are difficult requirements", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17734", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to fulfill in several realistic settings and thus we are reduced to a single-domain generalization problem.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Domain invariant object detection: We first re-formulate the definition of the domain invariance for a single source domain-generalized object detector by including a classifier and a regressor. Following [61], let's consider a visual corruption function $\\phi(.)$ as a domain transformation function, in (continuous) domain space $\\mathfrak{D}$ , which takes a source image from $\\mathcal{D}_s$ and transforms it into a different domain $\\mathcal{D}_{\\phi}$ where $\\phi \\sim \\Phi$ (is a set of possible transformations). By making this assumption, we define domain-invariance for single domain- generalized object detector as follows:", + "bbox": [ + 75, + 121, + 467, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 3.1 (Domain Invariance for Object Detection)", + "text_level": 1, + "bbox": [ + 75, + 282, + 467, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Assuming that, for an input image $\\mathbf{x}$ , an object detection model $\\mathcal{F}_{\\text{det}}$ predicts class probability distribution $\\hat{\\mathbf{p}}_n$ and bounding box coordinates $\\hat{\\mathbf{b}}_n \\in \\mathbb{R}^4$ for the $n^{th}$ proposal. Let $\\mathbf{x}^s$ be an image from $\\mathcal{D}_s$ and $\\mathbf{x}^\\phi = \\phi(\\mathbf{x}^s)$ be the transformation of $\\mathbf{x}^s$ , denoted as $\\mathbf{x}^\\phi$ , where $\\phi \\sim \\Phi$ . The model $\\mathcal{F}_{\\text{det}}$ is domain invariant if:", + "bbox": [ + 75, + 299, + 467, + 388 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {p}} _ {n} ^ {s} = \\hat {\\mathbf {p}} _ {n} ^ {\\phi} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 238, + 404, + 467, + 422 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n1 - \\operatorname {I o U} \\left(\\hat {\\mathbf {b}} _ {n} ^ {s}, \\hat {\\mathbf {b}} _ {n} ^ {\\phi}\\right) = 0 \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 443, + 467, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 470, + 248, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through developing realizations of Eq. (1) and Eq. (2), we intend to improve the domain generalization of object detectors, when the training data from only a single source domain is available. So, our method has two main components: 1) diversification of the source domain (sec. 3.2.1) and 2) a detection alignment mechanism for improving generalization and calibration of detectors (sec. 3.2.2). Fig. 1 displays the overall architecture of our proposed method.", + "bbox": [ + 75, + 493, + 467, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Diversifying Single Source Domain", + "text_level": 1, + "bbox": [ + 76, + 633, + 374, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our proposed approach is motivated by various techniques used in diversifying source domains for object classification [26, 50, 56, 69]. Deep convolutional networks often learn shortcuts instead of actual semantics, but diversifying training domains can reduce this problem. Since obtaining multiple domains is difficult, we simulate them through data augmentation. This introduces diversity in the training data and improves the network's ability to learn robust object representations. We achieve this by perturbing the single source domain images using a set of existing visual corruptions $\\Phi$ . During training, we augment every image in minibatch by using image augmentation function $\\phi(.)$ which randomly samples a corruption method from $\\Phi$ and apply to the input image. We then pass both original clean images along with their augmented versions to the model. Specifically, we investigate the visual corruptions set used in image", + "bbox": [ + 75, + 659, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "classification domain [9] that simply combines ImageNet-C with Fourier transform-based corruptions, thereby providing a total of 22 corruptions with 5 severity levels.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We classify image corruptions used for augmentation into five groups: Weather, Noise, Blur, Digital, and Fourier. In the case of Blur corruption, we employ various blur functions such as Gaussian, motion, glass, and defocus to smooth the pixel values in the image. Noise introduces different types of noise, including shot, impulse, speckle, and Gaussian, to perturb the image. Digital corruptions modify the pixel intensities by adjusting brightness, contrast, and saturation, or by changing the image resolution using JPEG compression, pixelation, and elastic transformation. Fig. 2 shows the impact of such augmentations. To ensure a fair comparison, we exclude weather-based transformations from our augmentation pool. Fourier-based corruptions such as phase scaling, constant amplitude, and High Pass Filter exploit the well-known property of Fourier transformation in that the phase component represents high-level semantics of an image, while the amplitude component covers low-level statistics or texture information. Perturbing these components enables us to reconstruct a new transformed image. Phase scaling introduces various artifacts by scaling the phase component in the Fourier spectrum. Constant amplitude replaces the amplitude component with a fixed vector, resulting in the loss of textual information and retaining only high-level semantics. We exclude the constant amplitude augmentation as it destroys the instance-level features. We note that this simple technique of diversifying source domain during object detector training outperforms baselines and competing methods by visible margins in challenging out-of-domain scenarios. As a result, though simple, as it makes minimal modifications to the baseline, it provides a solid baseline in single domain-generalized object detection.", + "bbox": [ + 496, + 138, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Aligning Diversified Domains", + "text_level": 1, + "bbox": [ + 500, + 647, + 756, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the single-source domain diversification approach provides a strong baseline, it does not enforce the main requirement for the Domain invariance (Def. 3.1); that is the predictions on diversified images $x^{\\phi}$ do not align with predictions on original images $x^{s}$ . To quantify this, we measured mAP of the model predictions over original images, and mAP of the same model's predictions on diversified images. Regardless of whichever diversification is performed, there is considerable performance gap, indicating the lack of generalization. This is depicted in Fig. 3. This gap can be explained when considering the following two constraints. (1.) Object Classification Constraint, Eq.(1), states that model's predicted class probability distribution for the object in the source image, $x^{s}$ , should be same for the corresponding object in diversified image $x^{\\phi}$ . (2.) Object Local-", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17735", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/acba897208d7d15c4d048b43d2092e5eccc2b6825bf43eca2de28bff9115447b.jpg", + "image_caption": [ + "Figure 2. Examples of augmentations for domain diversification." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 467, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ization Constraint, Eq.(2), states that is the objects should be predicted at same location (and of same size) on both diversified and original version of the images. Note that here these constraints are not related to the accuracy of the prediction, but that any prediction made should be same.", + "bbox": [ + 76, + 371, + 468, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike the image classification, where there is only one class prediction vector, enforcing such constraints in object detection is more challenging. We propose a strategy to overcome this challenge. Based on definition 3.1, on domain-invariance for object detection, we align the detections from two views i.e. clean and diversified (augmented) images both from the classification and the regression outputs. We take the widely used two-stage object detector as an example i.e. Faster R-CNN. Given $\\mathbf{x}_i^s$ or $\\mathbf{x}_i^\\phi$ as input, we can obtain a feature map $F\\in \\mathbb{R}^{m\\times w\\times h}$ from the backbone, where $m,h$ ,and $w$ denote the number of channels,height and width of the feature map, respectively. This feature map is then passed through region proposal network (RPN) to obtain object proposals $O\\in \\mathbb{R}^{Z\\times 4}$ ,where $Z$ is the number of proposals. Next, RoI-Alignment (RA) is performed using $O$ i.e $A = \\mathrm{RA}(O,F)\\in \\mathbb{R}^{Z\\times m}$ to obtain a fixed length feature representation for each proposal. Detection loss is given by:", + "bbox": [ + 75, + 446, + 468, + 719 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {d e t}} = \\sum_ {n = 1} ^ {Z} L _ {d e t} \\left(\\Psi \\left(A _ {n}\\right), \\mathbf {y} _ {n}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 731, + 467, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $\\Psi$ indicates the classifier and a bounding box regressor and $\\mathbf{y}_n$ ) is the ground truth including class label and bounding box coordinates for the $n^{th}$ proposal. The $L_{det}$ consists of smooth-L1 loss and the negative log-likelihood loss.", + "bbox": [ + 76, + 779, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Aligning classification: To enforce Object Classification constraint for object detector generalization, we propose to measure the Kullback-Leibler (KL) divergence between the classifier output probability vectors $\\hat{\\mathbf{p}}_n^s$ and $\\hat{\\mathbf{p}}_n^\\phi$ correspond", + "bbox": [ + 76, + 839, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3b176797cfb78d3b19c336bdeba5c97f7089ca582cd6cd0139117ad8f90008c0.jpg", + "image_caption": [ + "Figure 3. We augment the validation set from the source domain by one augmentation at a time and report the performance of the strong baseline model trained on all these augmentations. There is noticeable gap between the performance on original and diversified images. Our alignment losses allows reducing the gap between the performance on original and diversified images." + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 885, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ing to $\\mathbf{x}_i^s$ and $\\mathbf{x}_i^\\phi$ . It is likely that RPN will produce a different set of proposals from $\\mathbf{x}_i^s$ and $\\mathbf{x}_i^\\phi$ i.e. $O^s \\neq O^\\phi$ . These proposals might not be spatially consistent. To achieve 1-1 correspondence between the proposals from $\\mathbf{x}_i^s$ and $\\mathbf{x}_i^\\phi$ , we perform predictions using the region proposals from the $\\mathbf{x}_i^s$ and features pooled from the feature map for $\\mathbf{x}_i^\\phi$ . That is, we pass the feature map $F^\\phi$ corresponding to $\\mathbf{x}_i^\\phi$ with proposals from $O^s$ : $A^\\phi' = \\mathrm{RA}(O^s, F^\\phi)$ . $O^s$ : $A^\\phi' = \\mathrm{RA}(O^s, F^\\phi)$ , obtaining $\\hat{\\mathbf{p}}_n^\\phi'$ . The difference between the predictions is minimized using the KL-divergence:", + "bbox": [ + 496, + 402, + 890, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c a l}} = \\sum_ {n = 1} ^ {Z} \\mathrm {K L} \\left(\\hat {\\mathbf {p}} _ {n} ^ {s} \\| \\hat {\\mathbf {p}} _ {n} ^ {\\phi^ {\\prime}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 571, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Aligning localization: To make the Object Localization constraint for generalization part of the training process, we maximize the IoU between $\\hat{\\mathbf{b}}_n^s$ and $\\hat{\\mathbf{b}}_n^{\\phi '}$ . This is realized by minimizing the L2-squared norm between $\\hat{\\mathbf{b}}_n^s$ and $\\hat{\\mathbf{b}}_n^{\\phi '}$ :", + "bbox": [ + 498, + 618, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r a l}} = \\left\\| \\hat {\\mathbf {b}} _ {n} ^ {s} - \\hat {\\mathbf {b}} _ {n} ^ {\\phi^ {\\prime}} \\right\\| _ {2} ^ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 691, + 890, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our overall training objective is given by:", + "bbox": [ + 500, + 717, + 774, + 732 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t}} = \\mathcal {L} _ {\\text {d e t}} + \\alpha \\mathcal {L} _ {\\text {c a l}} + \\beta \\mathcal {L} _ {\\text {r a l}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 743, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are the hyperparameters for balancing the contributions of $\\mathcal{L}_{\\mathrm{cal}}$ and $\\mathcal{L}_{\\mathrm{ral}}$ .", + "bbox": [ + 498, + 771, + 890, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 814, + 632, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets: Real to Artistic consists of four datasets, including the Pascal VOC which contains real images from 20 different object classes and acts as a source domain, and remaining three are Clipart1k, Watercolor2k and Comic2k", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17736", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which offer artistic and comic images and are used as target domains. Clipart1k shares the same 20 classes as Pascal VOC, while Watercolor2k and Comic2k consist of 6 classes each, which are subsets of the Pascal VOC classes. Following [24], we combine Pascal VOC2007 and VOC2012 trainval set resulting in 16551 images for training and 5K images from VOC2007 test for in-domain evaluation. The Clipart1k consists of 1K and Watercolor2k and Comic2k each contain 2K images which are equally split into training and test sets. Following [24], we select all images from Clipart1k and test sets from Watercolor2k and Comic2k for out-domain evaluations. Urban Scene Detection is a self-driving dataset introduced by [60]. It offers images of 5 different weather conditions including Daytime Sunny, Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy. The images are collected from three different datasets: Barkeley Deep Drive 100k (BDD-100k)[64], FoggyCityscapes[8] and Adverse-Weather[17]. Rainy scenes are synthetic images generated by simulating rain on BDD-100k images. Daytime Sunny serves as a source domain consisting 26,518 images out of which 8,313 are used for in-domain evaluation whereas Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy are used as target domains containing 26,158, 2,494, 3,501, and 3,775 images, respectively.", + "bbox": [ + 76, + 90, + 472, + 453 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation and Training Details: For two-stage object detector as a baseline, we use Faster R-CNN[48] with ResNet101[18] as feature backbone, while for single-stage detector, we use FCOS [53] with ResNet50-FPN[37] as feature backbone. In all experiments our models are trained using SGD for 18k iterations with initial learning rate of 0.2 and dropped by a factor of 10 after 12K and 16k iterations. The batch size is set to 16. All results are reported using mean average precision (mAP) at IoU@0.5. For reporting calibration performance, we use the detection expected calibration error (D-ECE) [30] and reliability diagrams [16].", + "bbox": [ + 75, + 454, + 472, + 621 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Real to artistic: We evaluate our method on challenging real to artistic domain-shift where the distribution shift is large i.e. from PASCAL VOC to Clipart1k, Watercolor2k, and Comic2k. Table 1 shows that diversifying the training domain helps the model to generalize quite well by obtaining a significant gain of $8.5\\%$ , $8.5\\%$ , and $5.3\\%$ from the Faster R-CNN baseline in Clipart1k, Watercolor2k, and Comic2k, respectively. With our proposed alignment losses, we are able to boost the overall performance by $13.2\\%$ , $12.9\\%$ , and $14.3\\%$ . We also evaluated Normalization Perturbation (NP) [13] method on this benchmark and found it inferior to our method. Tables 2 and 3 reveal the class-wise results in Watercolor2k and Comic2k shifts. See supplementary for class-wise results on Clipart1k.", + "bbox": [ + 75, + 623, + 472, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Urban scene detection: Table 4 shows the results on different weather conditions manifesting various shifts scenarios. Due to large shifts like Daytime-Foggy and Night Raining the objects become unclear. We note that,", + "bbox": [ + 75, + 839, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/848c93d8e522ffddbc9ced8b8c304eba87afef73d02bed68fc193922bdf1a3cb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodVOCClipartWatercolorComic
Faster R-CNN81.825.744.518.9
NP [13]79.235.453.328.9
Diversification (div.)82.134.253.024.2
div. + Lcal82.136.253.928.7
div. + Lral80.735.053.828.7
div. + Lcal + Lral (Ours)80.138.957.433.2
", + "bbox": [ + 511, + 88, + 883, + 178 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4c3411b83377c6461aa1648e7601debad32512ce7db7d43c2e474bbfe1b47658.jpg", + "table_caption": [ + "Table 1. Performance comparison with baseline and possible ablations, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k." + ], + "table_footnote": [], + "table_body": "
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN85.742.536.429.018.754.544.5
Diversification (div.)87.151.753.635.123.663.652.5
div. + Lcal83.950.448.540.336.563.353.8
div. + Lral83.352.350.739.232.765.253.9
div. + Lcal + Lral (Ours)90.451.851.943.935.970.257.4
", + "bbox": [ + 504, + 243, + 887, + 311 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7972250bce3f75d6ab9d53b9e8328b6346f43cfabe9304ad6c48b36b52599250.jpg", + "table_caption": [ + "Table 2. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Watercolor2k scenario." + ], + "table_footnote": [], + "table_body": "
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN39.79.123.99.19.122.218.9
Diversification (div.)41.712.329.013.220.636.525.5
div. + Lcal49.015.827.020.221.838.428.7
div. + Lral53.313.529.019.120.536.728.7
div. + Lcal + Lral (Ours)54.116.930.125.027.445.933.2
", + "bbox": [ + 504, + 363, + 887, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by only diversifying single domain, we obtain $0.5\\%$ , $7\\%$ , $6.3\\%$ , and $2.5\\%$ on Night Clear (NC), Dusk Rainy (DR), Night Rainy (NR), and Daytime Foggy (DF), respectively. Our method beats all baselines and state-of-the-art method from [54]. Over the baseline, our method delivers the highest gain of $8.4\\%$ on Night Rainy while $8.1\\%$ , $4.1\\%$ and $3.6\\%$ gains on Dusk Rainy, Daytime Foggy and Night Clear respectively.", + "bbox": [ + 496, + 496, + 893, + 618 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c84df7d02bcfeaeb27eaddf524aba037e4b7106d55952d63e41e505b2f15e02b.jpg", + "table_caption": [ + "Table 3. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Comic2k scenario." + ], + "table_footnote": [], + "table_body": "
MethodDSNCDRNRDF
Faster R-CNN51.838.930.015.733.1
SW[45]50.633.426.313.730.8
IBN-Net[62]49.732.126.114.329.6
IterNorm[22]43.929.622.812.628.4
ISW[6]51.333.225.914.131.8
Wu et al. [60]56.136.628.216.633.5
Vidit et al. [54]51.336.932.318.738.5
Diversification50.639.437.022.035.6
Ours52.842.538.124.137.2
", + "bbox": [ + 545, + 642, + 846, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Results, mAP@0.5(%) reported on a multi-weather scenario where the model is trained on Daytime Sunny (DS) and tested on Night-Clear (NC), Night-Rainy (NR), Dusk-Rainy (DR) and Daytime-Foggy (DF). The results for SW, IBN-Net, IterNorm, ISW, S-DGOD are directly taken from [60].", + "bbox": [ + 496, + 781, + 893, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Calibration: Table 5, reports the calibration performance (D-ECE) of the base model and the impact of us", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17737", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ca20dfd3d5f1ed24ef11e401e0484239d4e2396d01706c6d4422bda77cb1590c.jpg", + "image_caption": [ + "Figure 4. Our method (diversification and alignment) results in both considerable improvement in domain generalization and out-of-domain calibration. Diversification with the Label Smoothing (LS) or Temperature Scaling (TS) improves calibration but overall lower mAP indicates lacking in generalization. Note that our method does not have an explicit model calibration mechanism. (left) mAP: higher the better, (right) D-ECE: lower the better." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 465, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ddd1ff4377a03504eee09833cda255ffa47ab28a1ccf876c48dbc81a2149785c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 90, + 883, + 261 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e6f2a5177923ded8f7a5b01742b8671d6febdca652b9ae25b3ab0a209596af9c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 352, + 460, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a28aeaa4da3d4f1c428f8d85f0d39efad69efd197918e956ed1b8c90cb6bccae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 446, + 460, + 537 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc1dbfb54b7236af1916f4a0ee70562a9e461b81700e45ed2e60a2c33e785348.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 537, + 460, + 630 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a8531d8060d8a1a4a013194306da37c162296ea0122fc12cb7d295d9b6c74436.jpg", + "image_caption": [ + "Figure 5. Reliability Diagram for different target domains." + ], + "image_footnote": [], + "bbox": [ + 86, + 631, + 460, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing our diversification and alignment approach under various shift scenarios. As seen, simple diversification of the domain, while improving generalization, negatively affects the calibration for both in-domain and out-domain scenarios. This is to be expected since model is trained using Negative log-likelihood loss in $\\mathcal{L}_{\\mathrm{det}}$ (Eq. 3) which is in general attributed to making models highly confident, resulting in", + "bbox": [ + 75, + 794, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "poor calibration. On the diversified images, where information might have been reduced or content has become noisy (w.r.t original image), high confidence predictions affects the calibration. In contrast, as detailed in (Sec. 3.2.2), our alignment step implicitly reduces the overconfidence in predictions (Fig. 5). Overall, as our results show, we achieve not only better generalization (higher mAP) but also better calibration (lower D-ECE). To further make apparent the the", + "bbox": [ + 496, + 349, + 893, + 470 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8ce91f4ef80597f78e1cc6d7f4378a93d8532f9569b8b55d1af45fe9a1a2ee44.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Artistic ShiftsUrban Scene
MethodClipartWatercolorComicNRDRNCDF
Faster R-CNN11.918.515.431.529.327.925.8
Diversification (div.)14.521.417.433.030.228.925.7
Ours10.714.414.329.324.915.820.6
", + "bbox": [ + 503, + 481, + 893, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Comparison of calibration performance using D-ECE metric (\\%) on Real to artistic shifts and in urban scene detection.", + "bbox": [ + 496, + 547, + 893, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "utility of our alignment approach in achieving better calibration. We also include the impact of using existing simple calibration and generalization techniques such as temperature scaling (TS) [16] or label smoothing (LS) [41] with our diversification approach. Fig. 4 depicts the improvements our presented methods achieve in multiple shift scenarios.", + "bbox": [ + 496, + 583, + 890, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results with single-stage detector: To show the applicability of our proposed method, we instantiate it in one-stage detector, namely FCOS [53] (Table 6). In comparison to FCOS, our method delivers a significant gain of $13.0\\%$ , $10.7\\%$ and $15.8\\%$ on Clipart1k, Watercolor2k, and Comic2k shifts, respectively.", + "bbox": [ + 496, + 674, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with domain-adaptive detection methods: Table 7 compares our method with some unsupervised domain-adaptive object detectors using the same backbone. Note that these methods assume access to target domain and directly train using unlabelled target samples. In contrast even though our method does not have access to the target domain dataset at training time, it still shows better generalization results than many domain-adaptive detection methods. For instance, in watercolor and comic", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17738", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4cedc87cb4c7a2b60ddb4c8eeae153415372aea6b157a8d20aa163a0376ef170.jpg", + "image_caption": [ + "Figure 6. Qualitative results of baseline (Faster-RCNN), only diversifying domain, and our method." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 890, + 292 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7cdd10c96fa208ab59eb031a067b349752b3a5af84d06d5004eecb747d414f3a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodVOCClipartWatercolorComic
FCOS78.124.444.315.4
Diversification (div.)79.631.748.825.2
div. + Lcal80.135.452.629.4
div. + Lral77.529.850.324.0
div. + Lcal + Lral (Ours)77.537.455.031.2
", + "bbox": [ + 89, + 339, + 460, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shifts, our model outperforms all methods by delivering a gain of $3.2\\%$ and $2.5\\%$ , respectively. Results for the existing domain adaptive methods are taken from [4].", + "bbox": [ + 75, + 486, + 468, + 532 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/af7e75bf2b940423c5c66d65baa4fe1032402479463d9e2bc58020a505b76133.jpg", + "table_caption": [ + "Table 6. Performance comparison with single-stage baseline, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k." + ], + "table_footnote": [], + "table_body": "
MethodClipartWatercolorComic
DA-Faster[5]19.846.0-
SWDA[49]38.153.327.4
HTCN[3]40.3--
DBGL[4]41.653.829.7
Our Method38.557.032.2
", + "bbox": [ + 140, + 555, + 406, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results: We sample some results for the qualitative comparison in Fig. 6. Aligning the predicted confidence and predicted localization between the original and diversified image, results in improved generalizability as visible from columns (c & f) where objects missed by baseline, diversification and NP[13] method, were properly localized and classified. Note that diversification actually results in more false positive detections with high confidence than baseline. This is visible in the column g where objects have been falsely classified as chairs and birds.", + "bbox": [ + 75, + 688, + 468, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of different types of augmentations: We analyze the impact of different types of visual corruptions obtained from $\\Phi$ in our method. First, we only diversify VOC-dataset using ImageNet-C corruption and then with Fourier-based", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5692e6204b1a6fb51bb3b86f01ccc62ed9a5f50d691e207c4f6cac017d36bcca.jpg", + "table_caption": [ + "Table 7. Comparison with domain adaptive detectors in mAP@0.5(%)" + ], + "table_footnote": [], + "table_body": "
MethodClipartWatercolorComic
Faster R-CNN25.744.518.9
Ours - w/Fourier-based36.154.829.1
Ours - w/Imagenet-C36.855.530.6
Ours38.957.433.2
", + "bbox": [ + 539, + 340, + 857, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Ablation study with different augmentations used for diversifying source domain in our method, mAP@0.5(%) reported.", + "bbox": [ + 498, + 415, + 890, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "corruption. As reported in Table 8, ImageNet-C corruption has a slight edge over Fourier corruption, however, using both provides the best results. This suggests that obtaining diversity through both types of corruption is complimentary. Aligning Classification vs aligning localization: Not aligning one of the prediction tasks across the diversified domains results in considerable degradation of the results (Table 1). In general, the results indicate that, as expected, the alignment of both these tasks is equally vital for achieving cross-domain generalizable object detectors.", + "bbox": [ + 496, + 468, + 890, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 633, + 619, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a detector-agnostic, simple, and effective approach to improve the generalization and calibration of the object detectors given only a single source domain for training. To this end, we first explored effective image augmentation methods for domain diversification and developed a strong baseline for single-DGOD. Our results show that by carefully selecting a set of augmentations, a base detector can outperform SOTA methods for single domain generalization by a good margin. Secondly, we proposed a novel method to align the detections across the original and diversified images. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 687-696, 2019. 1" + ], + "bbox": [ + 501, + 92, + 890, + 597 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17742", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/8c4702fb-5780-47bb-bdfa-6d2896061b4d_model.json b/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/8c4702fb-5780-47bb-bdfa-6d2896061b4d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a0c76273d88a98453ae728cf38d1598958682d05 --- /dev/null +++ b/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/8c4702fb-5780-47bb-bdfa-6d2896061b4d_model.json @@ -0,0 +1,2257 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.139, + 0.13, + 0.833, + 0.175 + ], + "angle": 0, + "content": "Improving Single Domain-Generalized Object Detection: A Focus on Diversification and Alignment" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.203, + 0.852, + 0.221 + ], + "angle": 0, + "content": "Muhammad Sohail Danish1 Muhammad Haris Khan1 Muhammad Akhtar Munir1,2" + }, + { + "type": "text", + "bbox": [ + 0.308, + 0.228, + 0.662, + 0.246 + ], + "angle": 0, + "content": "M. Saquib Sarfraz3,4 Mohsen Ali2" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.248, + 0.798, + 0.265 + ], + "angle": 0, + "content": "1Mohamed bin Zayed University of Artificial Intelligence, 2Information Technology University of Punjab," + }, + { + "type": "text", + "bbox": [ + 0.278, + 0.266, + 0.692, + 0.282 + ], + "angle": 0, + "content": "3Mercedes-Benz Tech Innovation, 4Karlsruhe Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.285, + 0.732, + 0.299 + ], + "angle": 0, + "content": "muhammad.sohail@mbzuai.ac.ae, muhammad.haris@mbzuai.ac.ae" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.334, + 0.314, + 0.351 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.473, + 0.73 + ], + "angle": 0, + "content": "In this work, we tackle the problem of domain generalization for object detection, specifically focusing on the scenario where only a single source domain is available. We propose an effective approach that involves two key steps: diversifying the source domain and aligning detections based on class prediction confidence and localization. Firstly, we demonstrate that by carefully selecting a set of augmentations, a base detector can outperform existing methods for single domain generalization by a good margin. This highlights the importance of domain diversification in improving the performance of object detectors. Secondly, we introduce a method to align detections from multiple views, considering both classification and localization outputs. This alignment procedure leads to better generalized and well-calibrated object detector models, which are crucial for accurate decision-making in safety-critical applications. Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage detectors. To validate the effectiveness of our proposed methods, we conduct extensive experiments and ablations on challenging domain-shift scenarios. The results consistently demonstrate the superiority of our approach compared to existing methods. Our code and models are available at: https://github.com/msohaildanish/DivAlign." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In recent years, we have witnessed remarkable performance improvements in supervised object detection [39, 47, 48, 53]. The success of these methods rely on the assumption that the training and testing data are sampled from the same distribution. However, in many real-world applications, such as autonomous driving, this assumption is often violated and these object detectors usually show degraded performance due to a phenomenon called domain-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.895, + 0.397 + ], + "angle": 0, + "content": "shift [3, 5, 49]. Shifts in real-world domains are typically caused by environmental alterations, like varying weather and time conditions. These changes manifest in diverse contrasts, brightness levels, and textures among others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.895, + 0.581 + ], + "angle": 0, + "content": "A prominent line of research that attempts to alleviate the impact of domain-shift is known as unsupervised domain adaptation (UDA) [20, 24, 42, 49, 63, 68, 72]. Given the labeled data from the source domain and unlabelled data from the target domain, the aim of UDA methods is to align the source and target data distributions so that the trained model can generalize well to the target domain [67]. An obvious limitation of UDA methods is that they require pre-collecting data and re-training the model for different target domains. Collecting data, even without annotation, for all possible domain shifts and training the model when shift happens is difficult and sometime not possible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.896, + 0.809 + ], + "angle": 0, + "content": "To cope with the domain-shift problem, a more realistic albeit challenging problem is domain generalization [2, 11, 23, 26, 32, 34, 35, 40, 58]. The goal of domain generalization (DG) is to learn a generalizable model typically from multiple source domains, available during training, that can perform well on the unseen target domain. A dominant class of DG methods attempts to learn domain-invariant feature space across multiple source domains [1, 11, 33, 35]. The performance of these methods is sensitive to the number of available source domains [7, 70]. In many realistic scenarios, acquiring labeled data from multiple source domains is often costly and time-consuming, eventually restricting the potential utilization of such methods. For these reasons, generalizing from a single-source domain is a more practical setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recent surveys [29, 70] reveal that very little work has been done on DG for object detection [38, 60], despite the fact that object detectors occupy an important position in many safety-critical and security-sensitive applications e.g., autonomous driving. An object detector should be able to provide accurate as well as calibrated detections in different" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "17732" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.211 + ], + "angle": 0, + "content": "out-domain scenarios. Towards this end, we study the problem of single-domain generalized object detection (Single-DGOD). In the Single-DGOD setting, a single source domain is available for training, and the goal is to learn an object detector that can generalize well to multiple unseen target domains. Note that, many existing DG methods cannot be applied to solve this task since both multiple source domains and domain-level annotations are unavailable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.212, + 0.471, + 0.544 + ], + "angle": 0, + "content": "We are inspired by the class of DG methods for classification [46, 55, 66] that show that simulating novel domains during model training allows segregating domain-specific and semantics-oriented features. Consequently, the spurious correlations between the input and model predictions are suppressed. We begin by leveraging this idea of augmenting our input examples to realize the simulation of novel domains, thereby increasing the diversity of single-source training domain. In particular, we use the common off-the-shelf visual corruptions coupled with a simple training scheme to build a strong Single-DGOD baseline. The augmentation strategy aims to disrupt surface-level statistical patterns that are specific to a particular domain while preserving high-level semantic concepts that are common across domains. In addition to diversifying the single source domain, we propose a novel approach that aligns detection across different views of the image. The introduced method aligns both the class prediction distributions and predicted bounding box coordinates between augmented views of the image. By ensuring such a consistency of detections, we show that this not only helps in better out-domain detections but importantly also results in better calibrated models." + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.546, + 0.466, + 0.559 + ], + "angle": 0, + "content": "To summarize, our work makes two main contributions:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.561, + 0.47, + 0.65 + ], + "angle": 0, + "content": "- We show that, using a set of carefully selected augmentations, the base model can surpass the performance of state-of-the-art published single-DGOD methods. To our knowledge, achieving such a strong baseline with known augmentation methods has not been shown before in the single domain object detection generalization." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.651, + 0.469, + 0.709 + ], + "angle": 0, + "content": "- Our second contribution is an effective classification and localization alignment method that is shown to further improve detections in unseen domain and results in implicitly well calibrated detector model." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.561, + 0.47, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.711, + 0.469, + 0.742 + ], + "angle": 0, + "content": "Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage object detectors." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.22, + 0.77 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Domain adaptive object detection: Several domain adaptive detection methods aim to reduce the pixel-level or feature-level gap between the source and target domain [36, 44]. For instance, the works of [3, 10, 21, 24, 52, 65] utilized the labeled images generated from CycleGAN [71] to achieve pixel-level consistency. Likewise, [3, 5, 10, 19, 49, 51] proposed various mechanisms to progressively obtain a feature-level consistency. A common component" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.439 + ], + "angle": 0, + "content": "of these methods is domain adversarial network [15] for achieving feature alignment. The work of [5] performed domain alignment on both global features (backbone features) and local features (Instance-level RoI features). Since then, several methods aimed to further improve these alignments by leveraging multi-scale [19], contextual [3, 49], spatial attention [31], category attention [57], and cross-domain topological relations [4] information. A few methods resorted to pseudo-labelling of instances to include class-level discriminative information. For instance, [24] constructed pseudo-labels by putting a threshold on top-1 accuracy over the predicted class of a detection. Towards refining the noisy pseudo-labels, [27] developed a robust training mechanism coupled with an independent classification module. With a similar goal, [28] proposed a weak self-training method and an adversarial background regularization module. Recently, [42] developed an uncertainty-guided criterion for selecting pseudo-labels in the target domain. We note that almost all of the aforementioned methods require access to both source and (unlabelled) target domain data coupled with an adaptation step to perform well in the target domain. As a consequence, these methods cannot be used to solve single-domain generalized object detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.882 + ], + "angle": 0, + "content": "Single source domain generalization: A more challenging and recently proposed setting in DG is single source domain generalization. It is a more practical setting compared to multi-source DG since the availability of data from multiple different domains is a difficult requirement to fulfill for many real-world applications. The goal is to learn a generalized model using only a single source domain that can perform well on many unseen target domains. An intuitive approach for this setting is to increase the diversity of single source data by proposing different data augmentation techniques. Qiao et al. [46] leveraged adversarial training to construct difficult examples which facilitate model generalization. Earlier attempts involve training a label classifier and a domain classifier in a joint manner by their corresponding perturbations Similarly-[50] proposed to impose Wasserstein constraint in the feature space to generate adversarial samples from synthetic target distribution [56]. Recently, Wu et al. [60] proposed a cyclic-disentangled self-distillation approach for single domaingeneralized object detection. Wang et al. [59] proposed a style-complement module that synthesizes examples from domains complementary to the source domain. Towards exploring the impact of the normalization layer on DG performance, Wang et al. [14] developed a generic normalization approach that learns both the standardization and rescaling statistics by neural networks. The aforementioned methods have shown promising results for the image classification task, however, they are not readily applicable to object detection since it has both classification and localization." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Domain diversification for domain generalization: Sev-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17733" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.875, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.25, + 0.895, + 0.307 + ], + "angle": 0, + "content": "Figure 1. Overall architecture of our proposed method. At the core is a baseline detector, Here a two-stage detector Faster-RCNN[48] is depicted, comprising of backbone, region proposal network (RPN), and ROI alignment (RA). To improve the single domain generalization of the baseline detector, we propose to diversify the single source domain and also align the diversified views by minimizing losses at both classification and regression outputs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.332, + 0.473, + 0.742 + ], + "angle": 0, + "content": "eral DG methods for object recognition have proposed various data augmentation techniques in an effort to improve the diversity of source domain(s). By using a CNN generator with different losses, Zhou et al. [69] synthesized novel examples from simulated domains. A few methods attempt to suppress the intrinsic style bias of CNNs. For instance, to focus on the contents and styles of images, [43] proposed content-biased and style-biased networks, respectively. To constantly seek diverse styles, [25] proposed a style synthesis process that is formulated as a monotone submodular optimization. Among the more recent methods, [13] explores diversifying source domain by perturbing channel statistics of low-level features for single domain-generalized object detector. In [54] the authors introduced the semantic augmentation of images by utilizing text-prompts relevant to potential target domain concepts in a vision-language model framework to improve the robustness of object detectors in unseen target domains. Along similar lines, [12] adapted the source model using textual descriptions of the target domain in a zero-shot manner to enhance the cross-domain generalizability in object detectors. Note that, both [54] and [12] incorporate the prior target domain knowledge using textual prompts. However, we follow domain generalization settings and leverage no prior knowledge about the target domain. Further, we diversify the source domain in input space and then align the detections in both original and diversified images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.759, + 0.295, + 0.777 + ], + "angle": 0, + "content": "3. Proposed Methodology" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.785, + 0.219, + 0.8 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Problem Settings: Let \\(\\mathcal{D}_s\\) be the single source domain containing \\(N^s\\) labelled training examples \\(\\{\\left(\\mathbf{x}_i^s,\\mathbf{y}_i^s\\right)\\}_{i = 1}^{N^s}\\), where \\(\\mathbf{x}_i\\in \\mathbb{R}^{H\\times W\\times C}\\) is an image and \\(\\mathbf{y}_i = \\{k_i,\\mathbf{b}_i\\}\\) is the corresponding label with bounding box coordinates \\(\\mathbf{b}_i\\in \\mathbb{R}^4\\) and the associated class category \\(k_{i}\\in \\{1,\\dots,K\\}\\). \\(K\\) is the number of class categories and \\(H\\), \\(W\\) and \\(C\\) represent the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.409 + ], + "angle": 0, + "content": "height, width, and number of channels, respectively. Let \\(\\{\\mathcal{D}_t\\}_{t=1}^T\\) be the set of \\(T\\) (unseen) target domains. Our goal is to learn an object detector using training examples from \\(\\mathcal{D}_s\\) that generalizes well on test examples from \\(\\mathcal{D}_t\\). We assume that both \\(\\mathcal{D}_s\\) and \\(\\mathcal{D}_t\\) share the same label space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.893, + 0.686 + ], + "angle": 0, + "content": "Object Detection: Let \\(\\mathcal{F}_{det}\\) be an object detection model, that takes input image \\(\\mathbf{x}\\) and outputs \\(Z\\) detections \\(\\{(P(\\hat{k}_n|\\mathbf{x}),\\hat{\\mathbf{b}}_n)\\}_{n = 1}^Z\\), where \\(\\hat{k}_n\\) denotes the class and bounding box \\(\\hat{\\mathbf{b}}_n\\) predictions for \\(n^{th}\\) proposal, respectively. We take the Faster R-CNN [48] model as \\(\\mathcal{F}_{det}\\) to detail our method, but note that our method is detector-agnostic and can be easily applied to other object detection paradigms, as shown in our results. We first overview Faster R-CNN to make the method section self-contained. Faster R-CNN is a popular and widely used two-stage object detector. The first stage comprises of a backbone feature extractor layer which generates a feature map and a region proposal network (RPN) which predicts a set of object proposals or regions of interest (RoIs) from the feature map. The second stage begins with ROI-Alignment, which extracts a fixed-size feature representation for each ROI and then feeds it to a classifier and a regressor to predict class confidence scores and bounding box coordinates, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Single domain-generalized object detection: In this case, we assume that the object detection \\(\\mathcal{F}_{det}\\) has been trained on the examples taken from the source domain \\(D_{s}\\) and then tested on examples from \\(\\{\\mathcal{D}_t\\}_{t=1}^T\\). Akin to image classification models, object detection models like Faster-RCNN, which exhibits state-of-the-art performance when testing data and training data are from the same domain (i.e. in-domain scenario), but suffers from performance degradation when domains are different (i.e. out-of-domain scenario) (Figure 4). The presence of multiple domains during training penalizes the object detector in learning shortcuts which are typically domain-specific and instead encourages learning domain-invariant features. Nevertheless, the multi-domain data with the ground truth are difficult requirements" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17734" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "to fulfill in several realistic settings and thus we are reduced to a single-domain generalization problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.273 + ], + "angle": 0, + "content": "Domain invariant object detection: We first re-formulate the definition of the domain invariance for a single source domain-generalized object detector by including a classifier and a regressor. Following [61], let's consider a visual corruption function \\(\\phi(.)\\) as a domain transformation function, in (continuous) domain space \\(\\mathfrak{D}\\), which takes a source image from \\(\\mathcal{D}_s\\) and transforms it into a different domain \\(\\mathcal{D}_{\\phi}\\) where \\(\\phi \\sim \\Phi\\) (is a set of possible transformations). By making this assumption, we define domain-invariance for single domain- generalized object detector as follows:" + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.284, + 0.468, + 0.299 + ], + "angle": 0, + "content": "Definition 3.1 (Domain Invariance for Object Detection)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.468, + 0.39 + ], + "angle": 0, + "content": "Assuming that, for an input image \\(\\mathbf{x}\\), an object detection model \\(\\mathcal{F}_{\\text{det}}\\) predicts class probability distribution \\(\\hat{\\mathbf{p}}_n\\) and bounding box coordinates \\(\\hat{\\mathbf{b}}_n \\in \\mathbb{R}^4\\) for the \\(n^{th}\\) proposal. Let \\(\\mathbf{x}^s\\) be an image from \\(\\mathcal{D}_s\\) and \\(\\mathbf{x}^\\phi = \\phi(\\mathbf{x}^s)\\) be the transformation of \\(\\mathbf{x}^s\\), denoted as \\(\\mathbf{x}^\\phi\\), where \\(\\phi \\sim \\Phi\\). The model \\(\\mathcal{F}_{\\text{det}}\\) is domain invariant if:" + }, + { + "type": "equation", + "bbox": [ + 0.24, + 0.405, + 0.468, + 0.423 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {p}} _ {n} ^ {s} = \\hat {\\mathbf {p}} _ {n} ^ {\\phi} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.444, + 0.468, + 0.462 + ], + "angle": 0, + "content": "\\[\n1 - \\operatorname {I o U} \\left(\\hat {\\mathbf {b}} _ {n} ^ {s}, \\hat {\\mathbf {b}} _ {n} ^ {\\phi}\\right) = 0 \\tag {2}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.471, + 0.249, + 0.487 + ], + "angle": 0, + "content": "3.2. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.468, + 0.614 + ], + "angle": 0, + "content": "Through developing realizations of Eq. (1) and Eq. (2), we intend to improve the domain generalization of object detectors, when the training data from only a single source domain is available. So, our method has two main components: 1) diversification of the source domain (sec. 3.2.1) and 2) a detection alignment mechanism for improving generalization and calibration of detectors (sec. 3.2.2). Fig. 1 displays the overall architecture of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.375, + 0.65 + ], + "angle": 0, + "content": "3.2.1 Diversifying Single Source Domain" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Our proposed approach is motivated by various techniques used in diversifying source domains for object classification [26, 50, 56, 69]. Deep convolutional networks often learn shortcuts instead of actual semantics, but diversifying training domains can reduce this problem. Since obtaining multiple domains is difficult, we simulate them through data augmentation. This introduces diversity in the training data and improves the network's ability to learn robust object representations. We achieve this by perturbing the single source domain images using a set of existing visual corruptions \\(\\Phi\\). During training, we augment every image in minibatch by using image augmentation function \\(\\phi(.)\\) which randomly samples a corruption method from \\(\\Phi\\) and apply to the input image. We then pass both original clean images along with their augmented versions to the model. Specifically, we investigate the visual corruptions set used in image" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "classification domain [9] that simply combines ImageNet-C with Fourier transform-based corruptions, thereby providing a total of 22 corruptions with 5 severity levels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.621 + ], + "angle": 0, + "content": "We classify image corruptions used for augmentation into five groups: Weather, Noise, Blur, Digital, and Fourier. In the case of Blur corruption, we employ various blur functions such as Gaussian, motion, glass, and defocus to smooth the pixel values in the image. Noise introduces different types of noise, including shot, impulse, speckle, and Gaussian, to perturb the image. Digital corruptions modify the pixel intensities by adjusting brightness, contrast, and saturation, or by changing the image resolution using JPEG compression, pixelation, and elastic transformation. Fig. 2 shows the impact of such augmentations. To ensure a fair comparison, we exclude weather-based transformations from our augmentation pool. Fourier-based corruptions such as phase scaling, constant amplitude, and High Pass Filter exploit the well-known property of Fourier transformation in that the phase component represents high-level semantics of an image, while the amplitude component covers low-level statistics or texture information. Perturbing these components enables us to reconstruct a new transformed image. Phase scaling introduces various artifacts by scaling the phase component in the Fourier spectrum. Constant amplitude replaces the amplitude component with a fixed vector, resulting in the loss of textual information and retaining only high-level semantics. We exclude the constant amplitude augmentation as it destroys the instance-level features. We note that this simple technique of diversifying source domain during object detector training outperforms baselines and competing methods by visible margins in challenging out-of-domain scenarios. As a result, though simple, as it makes minimal modifications to the baseline, it provides a solid baseline in single domain-generalized object detection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.757, + 0.663 + ], + "angle": 0, + "content": "3.2.2 Aligning Diversified Domains" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "While the single-source domain diversification approach provides a strong baseline, it does not enforce the main requirement for the Domain invariance (Def. 3.1); that is the predictions on diversified images \\( x^{\\phi} \\) do not align with predictions on original images \\( x^{s} \\). To quantify this, we measured mAP of the model predictions over original images, and mAP of the same model's predictions on diversified images. Regardless of whichever diversification is performed, there is considerable performance gap, indicating the lack of generalization. This is depicted in Fig. 3. This gap can be explained when considering the following two constraints. (1.) Object Classification Constraint, Eq.(1), states that model's predicted class probability distribution for the object in the source image, \\( x^{s} \\), should be same for the corresponding object in diversified image \\( x^{\\phi} \\). (2.) Object Local-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17735" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.468, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.352, + 0.462, + 0.366 + ], + "angle": 0, + "content": "Figure 2. Examples of augmentations for domain diversification." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.469, + 0.447 + ], + "angle": 0, + "content": "ization Constraint, Eq.(2), states that is the objects should be predicted at same location (and of same size) on both diversified and original version of the images. Note that here these constraints are not related to the accuracy of the prediction, but that any prediction made should be same." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.72 + ], + "angle": 0, + "content": "Unlike the image classification, where there is only one class prediction vector, enforcing such constraints in object detection is more challenging. We propose a strategy to overcome this challenge. Based on definition 3.1, on domain-invariance for object detection, we align the detections from two views i.e. clean and diversified (augmented) images both from the classification and the regression outputs. We take the widely used two-stage object detector as an example i.e. Faster R-CNN. Given \\(\\mathbf{x}_i^s\\) or \\(\\mathbf{x}_i^\\phi\\) as input, we can obtain a feature map \\(F\\in \\mathbb{R}^{m\\times w\\times h}\\) from the backbone, where \\(m,h\\) ,and \\(w\\) denote the number of channels,height and width of the feature map, respectively. This feature map is then passed through region proposal network (RPN) to obtain object proposals \\(O\\in \\mathbb{R}^{Z\\times 4}\\) ,where \\(Z\\) is the number of proposals. Next, RoI-Alignment (RA) is performed using \\(O\\) i.e \\(A = \\mathrm{RA}(O,F)\\in \\mathbb{R}^{Z\\times m}\\) to obtain a fixed length feature representation for each proposal. Detection loss is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.732, + 0.468, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {d e t}} = \\sum_ {n = 1} ^ {Z} L _ {d e t} \\left(\\Psi \\left(A _ {n}\\right), \\mathbf {y} _ {n}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.78, + 0.469, + 0.841 + ], + "angle": 0, + "content": "Here \\(\\Psi\\) indicates the classifier and a bounding box regressor and \\(\\mathbf{y}_n\\)) is the ground truth including class label and bounding box coordinates for the \\(n^{th}\\) proposal. The \\(L_{det}\\) consists of smooth-L1 loss and the negative log-likelihood loss." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Aligning classification: To enforce Object Classification constraint for object detector generalization, we propose to measure the Kullback-Leibler (KL) divergence between the classifier output probability vectors \\(\\hat{\\mathbf{p}}_n^s\\) and \\(\\hat{\\mathbf{p}}_n^\\phi\\) correspond" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.092, + 0.886, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.301, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Figure 3. We augment the validation set from the source domain by one augmentation at a time and report the performance of the strong baseline model trained on all these augmentations. There is noticeable gap between the performance on original and diversified images. Our alignment losses allows reducing the gap between the performance on original and diversified images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.562 + ], + "angle": 0, + "content": "ing to \\(\\mathbf{x}_i^s\\) and \\(\\mathbf{x}_i^\\phi\\). It is likely that RPN will produce a different set of proposals from \\(\\mathbf{x}_i^s\\) and \\(\\mathbf{x}_i^\\phi\\) i.e. \\(O^s \\neq O^\\phi\\). These proposals might not be spatially consistent. To achieve 1-1 correspondence between the proposals from \\(\\mathbf{x}_i^s\\) and \\(\\mathbf{x}_i^\\phi\\), we perform predictions using the region proposals from the \\(\\mathbf{x}_i^s\\) and features pooled from the feature map for \\(\\mathbf{x}_i^\\phi\\). That is, we pass the feature map \\(F^\\phi\\) corresponding to \\(\\mathbf{x}_i^\\phi\\) with proposals from \\(O^s\\): \\(A^\\phi' = \\mathrm{RA}(O^s, F^\\phi)\\). \\(O^s\\): \\(A^\\phi' = \\mathrm{RA}(O^s, F^\\phi)\\), obtaining \\(\\hat{\\mathbf{p}}_n^\\phi'\\). The difference between the predictions is minimized using the KL-divergence:" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.572, + 0.891, + 0.614 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c a l}} = \\sum_ {n = 1} ^ {Z} \\mathrm {K L} \\left(\\hat {\\mathbf {p}} _ {n} ^ {s} \\| \\hat {\\mathbf {p}} _ {n} ^ {\\phi^ {\\prime}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.619, + 0.892, + 0.682 + ], + "angle": 0, + "content": "Aligning localization: To make the Object Localization constraint for generalization part of the training process, we maximize the IoU between \\(\\hat{\\mathbf{b}}_n^s\\) and \\(\\hat{\\mathbf{b}}_n^{\\phi '}\\). This is realized by minimizing the L2-squared norm between \\(\\hat{\\mathbf{b}}_n^s\\) and \\(\\hat{\\mathbf{b}}_n^{\\phi '}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.692, + 0.891, + 0.712 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r a l}} = \\left\\| \\hat {\\mathbf {b}} _ {n} ^ {s} - \\hat {\\mathbf {b}} _ {n} ^ {\\phi^ {\\prime}} \\right\\| _ {2} ^ {2} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.718, + 0.776, + 0.733 + ], + "angle": 0, + "content": "Our overall training objective is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.744, + 0.891, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t}} = \\mathcal {L} _ {\\text {d e t}} + \\alpha \\mathcal {L} _ {\\text {c a l}} + \\beta \\mathcal {L} _ {\\text {r a l}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.772, + 0.891, + 0.802 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are the hyperparameters for balancing the contributions of \\(\\mathcal{L}_{\\mathrm{cal}}\\) and \\(\\mathcal{L}_{\\mathrm{ral}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.633, + 0.832 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets: Real to Artistic consists of four datasets, including the Pascal VOC which contains real images from 20 different object classes and acts as a source domain, and remaining three are Clipart1k, Watercolor2k and Comic2k" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17736" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.454 + ], + "angle": 0, + "content": "which offer artistic and comic images and are used as target domains. Clipart1k shares the same 20 classes as Pascal VOC, while Watercolor2k and Comic2k consist of 6 classes each, which are subsets of the Pascal VOC classes. Following [24], we combine Pascal VOC2007 and VOC2012 trainval set resulting in 16551 images for training and 5K images from VOC2007 test for in-domain evaluation. The Clipart1k consists of 1K and Watercolor2k and Comic2k each contain 2K images which are equally split into training and test sets. Following [24], we select all images from Clipart1k and test sets from Watercolor2k and Comic2k for out-domain evaluations. Urban Scene Detection is a self-driving dataset introduced by [60]. It offers images of 5 different weather conditions including Daytime Sunny, Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy. The images are collected from three different datasets: Barkeley Deep Drive 100k (BDD-100k)[64], FoggyCityscapes[8] and Adverse-Weather[17]. Rainy scenes are synthetic images generated by simulating rain on BDD-100k images. Daytime Sunny serves as a source domain consisting 26,518 images out of which 8,313 are used for in-domain evaluation whereas Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy are used as target domains containing 26,158, 2,494, 3,501, and 3,775 images, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.473, + 0.622 + ], + "angle": 0, + "content": "Implementation and Training Details: For two-stage object detector as a baseline, we use Faster R-CNN[48] with ResNet101[18] as feature backbone, while for single-stage detector, we use FCOS [53] with ResNet50-FPN[37] as feature backbone. In all experiments our models are trained using SGD for 18k iterations with initial learning rate of 0.2 and dropped by a factor of 10 after 12K and 16k iterations. The batch size is set to 16. All results are reported using mean average precision (mAP) at IoU@0.5. For reporting calibration performance, we use the detection expected calibration error (D-ECE) [30] and reliability diagrams [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.473, + 0.838 + ], + "angle": 0, + "content": "Real to artistic: We evaluate our method on challenging real to artistic domain-shift where the distribution shift is large i.e. from PASCAL VOC to Clipart1k, Watercolor2k, and Comic2k. Table 1 shows that diversifying the training domain helps the model to generalize quite well by obtaining a significant gain of \\(8.5\\%\\), \\(8.5\\%\\), and \\(5.3\\%\\) from the Faster R-CNN baseline in Clipart1k, Watercolor2k, and Comic2k, respectively. With our proposed alignment losses, we are able to boost the overall performance by \\(13.2\\%\\), \\(12.9\\%\\), and \\(14.3\\%\\). We also evaluated Normalization Perturbation (NP) [13] method on this benchmark and found it inferior to our method. Tables 2 and 3 reveal the class-wise results in Watercolor2k and Comic2k shifts. See supplementary for class-wise results on Clipart1k." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Urban scene detection: Table 4 shows the results on different weather conditions manifesting various shifts scenarios. Due to large shifts like Daytime-Foggy and Night Raining the objects become unclear. We note that," + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.089, + 0.885, + 0.179 + ], + "angle": 0, + "content": "
MethodVOCClipartWatercolorComic
Faster R-CNN81.825.744.518.9
NP [13]79.235.453.328.9
Diversification (div.)82.134.253.024.2
div. + Lcal82.136.253.928.7
div. + Lral80.735.053.828.7
div. + Lcal + Lral (Ours)80.138.957.433.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.188, + 0.895, + 0.23 + ], + "angle": 0, + "content": "Table 1. Performance comparison with baseline and possible ablations, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.244, + 0.888, + 0.312 + ], + "angle": 0, + "content": "
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN85.742.536.429.018.754.544.5
Diversification (div.)87.151.753.635.123.663.652.5
div. + Lcal83.950.448.540.336.563.353.8
div. + Lral83.352.350.739.232.765.253.9
div. + Lcal + Lral (Ours)90.451.851.943.935.970.257.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.322, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Table 2. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Watercolor2k scenario." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.364, + 0.888, + 0.432 + ], + "angle": 0, + "content": "
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN39.79.123.99.19.122.218.9
Diversification (div.)41.712.329.013.220.636.525.5
div. + Lcal49.015.827.020.221.838.428.7
div. + Lral53.313.529.019.120.536.728.7
div. + Lcal + Lral (Ours)54.116.930.125.027.445.933.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.442, + 0.895, + 0.47 + ], + "angle": 0, + "content": "Table 3. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Comic2k scenario." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.895, + 0.619 + ], + "angle": 0, + "content": "by only diversifying single domain, we obtain \\(0.5\\%\\), \\(7\\%\\), \\(6.3\\%\\), and \\(2.5\\%\\) on Night Clear (NC), Dusk Rainy (DR), Night Rainy (NR), and Daytime Foggy (DF), respectively. Our method beats all baselines and state-of-the-art method from [54]. Over the baseline, our method delivers the highest gain of \\(8.4\\%\\) on Night Rainy while \\(8.1\\%\\), \\(4.1\\%\\) and \\(3.6\\%\\) gains on Dusk Rainy, Daytime Foggy and Night Clear respectively." + }, + { + "type": "table", + "bbox": [ + 0.546, + 0.643, + 0.848, + 0.772 + ], + "angle": 0, + "content": "
MethodDSNCDRNRDF
Faster R-CNN51.838.930.015.733.1
SW[45]50.633.426.313.730.8
IBN-Net[62]49.732.126.114.329.6
IterNorm[22]43.929.622.812.628.4
ISW[6]51.333.225.914.131.8
Wu et al. [60]56.136.628.216.633.5
Vidit et al. [54]51.336.932.318.738.5
Diversification50.639.437.022.035.6
Ours52.842.538.124.137.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.782, + 0.895, + 0.853 + ], + "angle": 0, + "content": "Table 4. Results, mAP@0.5(%) reported on a multi-weather scenario where the model is trained on Daytime Sunny (DS) and tested on Night-Clear (NC), Night-Rainy (NR), Dusk-Rainy (DR) and Daytime-Foggy (DF). The results for SW, IBN-Net, IterNorm, ISW, S-DGOD are directly taken from [60]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Model Calibration: Table 5, reports the calibration performance (D-ECE) of the base model and the impact of us" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17737" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.092, + 0.466, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.092, + 0.885, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.278, + 0.895, + 0.337 + ], + "angle": 0, + "content": "Figure 4. Our method (diversification and alignment) results in both considerable improvement in domain generalization and out-of-domain calibration. Diversification with the Label Smoothing (LS) or Temperature Scaling (TS) improves calibration but overall lower mAP indicates lacking in generalization. Note that our method does not have an explicit model calibration mechanism. (left) mAP: higher the better, (right) D-ECE: lower the better." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.353, + 0.462, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.447, + 0.462, + 0.538 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.539, + 0.462, + 0.631 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.632, + 0.462, + 0.74 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.755, + 0.449, + 0.77 + ], + "angle": 0, + "content": "Figure 5. Reliability Diagram for different target domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.473, + 0.903 + ], + "angle": 0, + "content": "ing our diversification and alignment approach under various shift scenarios. As seen, simple diversification of the domain, while improving generalization, negatively affects the calibration for both in-domain and out-domain scenarios. This is to be expected since model is trained using Negative log-likelihood loss in \\(\\mathcal{L}_{\\mathrm{det}}\\) (Eq. 3) which is in general attributed to making models highly confident, resulting in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.895, + 0.472 + ], + "angle": 0, + "content": "poor calibration. On the diversified images, where information might have been reduced or content has become noisy (w.r.t original image), high confidence predictions affects the calibration. In contrast, as detailed in (Sec. 3.2.2), our alignment step implicitly reduces the overconfidence in predictions (Fig. 5). Overall, as our results show, we achieve not only better generalization (higher mAP) but also better calibration (lower D-ECE). To further make apparent the the" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.482, + 0.895, + 0.538 + ], + "angle": 0, + "content": "
Artistic ShiftsUrban Scene
MethodClipartWatercolorComicNRDRNCDF
Faster R-CNN11.918.515.431.529.327.925.8
Diversification (div.)14.521.417.433.030.228.925.7
Ours10.714.414.329.324.915.820.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.548, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Table 5. Comparison of calibration performance using D-ECE metric (\\%) on Real to artistic shifts and in urban scene detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.675 + ], + "angle": 0, + "content": "utility of our alignment approach in achieving better calibration. We also include the impact of using existing simple calibration and generalization techniques such as temperature scaling (TS) [16] or label smoothing (LS) [41] with our diversification approach. Fig. 4 depicts the improvements our presented methods achieve in multiple shift scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Results with single-stage detector: To show the applicability of our proposed method, we instantiate it in one-stage detector, namely FCOS [53] (Table 6). In comparison to FCOS, our method delivers a significant gain of \\(13.0\\%\\), \\(10.7\\%\\) and \\(15.8\\%\\) on Clipart1k, Watercolor2k, and Comic2k shifts, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Comparison with domain-adaptive detection methods: Table 7 compares our method with some unsupervised domain-adaptive object detectors using the same backbone. Note that these methods assume access to target domain and directly train using unlabelled target samples. In contrast even though our method does not have access to the target domain dataset at training time, it still shows better generalization results than many domain-adaptive detection methods. For instance, in watercolor and comic" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17738" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.891, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.305, + 0.778, + 0.32 + ], + "angle": 0, + "content": "Figure 6. Qualitative results of baseline (Faster-RCNN), only diversifying domain, and our method." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.34, + 0.462, + 0.418 + ], + "angle": 0, + "content": "
MethodVOCClipartWatercolorComic
FCOS78.124.444.315.4
Diversification (div.)79.631.748.825.2
div. + Lcal80.135.452.629.4
div. + Lral77.529.850.324.0
div. + Lcal + Lral (Ours)77.537.455.031.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.428, + 0.47, + 0.47 + ], + "angle": 0, + "content": "Table 6. Performance comparison with single-stage baseline, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.534 + ], + "angle": 0, + "content": "shifts, our model outperforms all methods by delivering a gain of \\(3.2\\%\\) and \\(2.5\\%\\), respectively. Results for the existing domain adaptive methods are taken from [4]." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.556, + 0.407, + 0.633 + ], + "angle": 0, + "content": "
MethodClipartWatercolorComic
DA-Faster[5]19.846.0-
SWDA[49]38.153.327.4
HTCN[3]40.3--
DBGL[4]41.653.829.7
Our Method38.557.032.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.672 + ], + "angle": 0, + "content": "Table 7. Comparison with domain adaptive detectors in mAP@0.5(%)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Qualitative Results: We sample some results for the qualitative comparison in Fig. 6. Aligning the predicted confidence and predicted localization between the original and diversified image, results in improved generalizability as visible from columns (c & f) where objects missed by baseline, diversification and NP[13] method, were properly localized and classified. Note that diversification actually results in more false positive detections with high confidence than baseline. This is visible in the column g where objects have been falsely classified as chairs and birds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Effect of different types of augmentations: We analyze the impact of different types of visual corruptions obtained from \\(\\Phi\\) in our method. First, we only diversify VOC-dataset using ImageNet-C corruption and then with Fourier-based" + }, + { + "type": "table", + "bbox": [ + 0.54, + 0.341, + 0.858, + 0.406 + ], + "angle": 0, + "content": "
MethodClipartWatercolorComic
Faster R-CNN25.744.518.9
Ours - w/Fourier-based36.154.829.1
Ours - w/Imagenet-C36.855.530.6
Ours38.957.433.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.446 + ], + "angle": 0, + "content": "Table 8. Ablation study with different augmentations used for diversifying source domain in our method, mAP@0.5(%) reported." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.621 + ], + "angle": 0, + "content": "corruption. As reported in Table 8, ImageNet-C corruption has a slight edge over Fourier corruption, however, using both provides the best results. This suggests that obtaining diversity through both types of corruption is complimentary. Aligning Classification vs aligning localization: Not aligning one of the prediction tasks across the diversified domains results in considerable degradation of the results (Table 1). In general, the results indicate that, as expected, the alignment of both these tasks is equally vital for achieving cross-domain generalizable object detectors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.62, + 0.65 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We proposed a detector-agnostic, simple, and effective approach to improve the generalization and calibration of the object detectors given only a single source domain for training. To this end, we first explored effective image augmentation methods for domain diversification and developed a strong baseline for single-DGOD. Our results show that by carefully selecting a set of augmentations, a base detector can outperform SOTA methods for single domain generalization by a good margin. Secondly, we proposed a novel method to align the detections across the original and diversified images. This alignment procedure leads to better generalized and well-calibrated object detectors, which are crucial for accurate decision-making in safety-critical applications. Extensive results on various challenging shift scenarios corroborate the effectiveness and applicability of our approach." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17739" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Yogesh Balaji, Swami Sankaranarayanan, and Rama Chellappa. Metareg: Towards domain generalization using meta regularization. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 687-696, 2019. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "17742" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/8c4702fb-5780-47bb-bdfa-6d2896061b4d_origin.pdf b/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/8c4702fb-5780-47bb-bdfa-6d2896061b4d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a0b3bc6e79ea75c3b2c1b30faca7325bd1033570 --- /dev/null +++ b/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/8c4702fb-5780-47bb-bdfa-6d2896061b4d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:277a5730e6703f485a79587c4e1c663c1fe41c317ed9ed7345a4e64fdfb3ccd3 +size 2992585 diff --git a/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/full.md b/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/full.md new file mode 100644 index 0000000000000000000000000000000000000000..22a030ca8fbffc2c8681f1243c83486d83869529 --- /dev/null +++ b/2024/Improving Single Domain-Generalized Object Detection_ A Focus on Diversification and Alignment/full.md @@ -0,0 +1,303 @@ +# Improving Single Domain-Generalized Object Detection: A Focus on Diversification and Alignment + +Muhammad Sohail Danish1 Muhammad Haris Khan1 Muhammad Akhtar Munir1,2 + +M. Saquib Sarfraz3,4 Mohsen Ali2 + +1Mohamed bin Zayed University of Artificial Intelligence, 2Information Technology University of Punjab, + +3Mercedes-Benz Tech Innovation, 4Karlsruhe Institute of Technology + +muhammad.sohail@mbzuai.ac.ae, muhammad.haris@mbzuai.ac.ae + +# Abstract + +In this work, we tackle the problem of domain generalization for object detection, specifically focusing on the scenario where only a single source domain is available. We propose an effective approach that involves two key steps: diversifying the source domain and aligning detections based on class prediction confidence and localization. Firstly, we demonstrate that by carefully selecting a set of augmentations, a base detector can outperform existing methods for single domain generalization by a good margin. This highlights the importance of domain diversification in improving the performance of object detectors. Secondly, we introduce a method to align detections from multiple views, considering both classification and localization outputs. This alignment procedure leads to better generalized and well-calibrated object detector models, which are crucial for accurate decision-making in safety-critical applications. Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage detectors. To validate the effectiveness of our proposed methods, we conduct extensive experiments and ablations on challenging domain-shift scenarios. The results consistently demonstrate the superiority of our approach compared to existing methods. Our code and models are available at: https://github.com/msohaildanish/DivAlign. + +# 1. Introduction + +In recent years, we have witnessed remarkable performance improvements in supervised object detection [39, 47, 48, 53]. The success of these methods rely on the assumption that the training and testing data are sampled from the same distribution. However, in many real-world applications, such as autonomous driving, this assumption is often violated and these object detectors usually show degraded performance due to a phenomenon called domain- + +shift [3, 5, 49]. Shifts in real-world domains are typically caused by environmental alterations, like varying weather and time conditions. These changes manifest in diverse contrasts, brightness levels, and textures among others. + +A prominent line of research that attempts to alleviate the impact of domain-shift is known as unsupervised domain adaptation (UDA) [20, 24, 42, 49, 63, 68, 72]. Given the labeled data from the source domain and unlabelled data from the target domain, the aim of UDA methods is to align the source and target data distributions so that the trained model can generalize well to the target domain [67]. An obvious limitation of UDA methods is that they require pre-collecting data and re-training the model for different target domains. Collecting data, even without annotation, for all possible domain shifts and training the model when shift happens is difficult and sometime not possible. + +To cope with the domain-shift problem, a more realistic albeit challenging problem is domain generalization [2, 11, 23, 26, 32, 34, 35, 40, 58]. The goal of domain generalization (DG) is to learn a generalizable model typically from multiple source domains, available during training, that can perform well on the unseen target domain. A dominant class of DG methods attempts to learn domain-invariant feature space across multiple source domains [1, 11, 33, 35]. The performance of these methods is sensitive to the number of available source domains [7, 70]. In many realistic scenarios, acquiring labeled data from multiple source domains is often costly and time-consuming, eventually restricting the potential utilization of such methods. For these reasons, generalizing from a single-source domain is a more practical setting. + +Recent surveys [29, 70] reveal that very little work has been done on DG for object detection [38, 60], despite the fact that object detectors occupy an important position in many safety-critical and security-sensitive applications e.g., autonomous driving. An object detector should be able to provide accurate as well as calibrated detections in different + +out-domain scenarios. Towards this end, we study the problem of single-domain generalized object detection (Single-DGOD). In the Single-DGOD setting, a single source domain is available for training, and the goal is to learn an object detector that can generalize well to multiple unseen target domains. Note that, many existing DG methods cannot be applied to solve this task since both multiple source domains and domain-level annotations are unavailable. + +We are inspired by the class of DG methods for classification [46, 55, 66] that show that simulating novel domains during model training allows segregating domain-specific and semantics-oriented features. Consequently, the spurious correlations between the input and model predictions are suppressed. We begin by leveraging this idea of augmenting our input examples to realize the simulation of novel domains, thereby increasing the diversity of single-source training domain. In particular, we use the common off-the-shelf visual corruptions coupled with a simple training scheme to build a strong Single-DGOD baseline. The augmentation strategy aims to disrupt surface-level statistical patterns that are specific to a particular domain while preserving high-level semantic concepts that are common across domains. In addition to diversifying the single source domain, we propose a novel approach that aligns detection across different views of the image. The introduced method aligns both the class prediction distributions and predicted bounding box coordinates between augmented views of the image. By ensuring such a consistency of detections, we show that this not only helps in better out-domain detections but importantly also results in better calibrated models. + +To summarize, our work makes two main contributions: + +- We show that, using a set of carefully selected augmentations, the base model can surpass the performance of state-of-the-art published single-DGOD methods. To our knowledge, achieving such a strong baseline with known augmentation methods has not been shown before in the single domain object detection generalization. +- Our second contribution is an effective classification and localization alignment method that is shown to further improve detections in unseen domain and results in implicitly well calibrated detector model. + +Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage object detectors. + +# 2. Related Work + +Domain adaptive object detection: Several domain adaptive detection methods aim to reduce the pixel-level or feature-level gap between the source and target domain [36, 44]. For instance, the works of [3, 10, 21, 24, 52, 65] utilized the labeled images generated from CycleGAN [71] to achieve pixel-level consistency. Likewise, [3, 5, 10, 19, 49, 51] proposed various mechanisms to progressively obtain a feature-level consistency. A common component + +of these methods is domain adversarial network [15] for achieving feature alignment. The work of [5] performed domain alignment on both global features (backbone features) and local features (Instance-level RoI features). Since then, several methods aimed to further improve these alignments by leveraging multi-scale [19], contextual [3, 49], spatial attention [31], category attention [57], and cross-domain topological relations [4] information. A few methods resorted to pseudo-labelling of instances to include class-level discriminative information. For instance, [24] constructed pseudo-labels by putting a threshold on top-1 accuracy over the predicted class of a detection. Towards refining the noisy pseudo-labels, [27] developed a robust training mechanism coupled with an independent classification module. With a similar goal, [28] proposed a weak self-training method and an adversarial background regularization module. Recently, [42] developed an uncertainty-guided criterion for selecting pseudo-labels in the target domain. We note that almost all of the aforementioned methods require access to both source and (unlabelled) target domain data coupled with an adaptation step to perform well in the target domain. As a consequence, these methods cannot be used to solve single-domain generalized object detection. + +Single source domain generalization: A more challenging and recently proposed setting in DG is single source domain generalization. It is a more practical setting compared to multi-source DG since the availability of data from multiple different domains is a difficult requirement to fulfill for many real-world applications. The goal is to learn a generalized model using only a single source domain that can perform well on many unseen target domains. An intuitive approach for this setting is to increase the diversity of single source data by proposing different data augmentation techniques. Qiao et al. [46] leveraged adversarial training to construct difficult examples which facilitate model generalization. Earlier attempts involve training a label classifier and a domain classifier in a joint manner by their corresponding perturbations Similarly-[50] proposed to impose Wasserstein constraint in the feature space to generate adversarial samples from synthetic target distribution [56]. Recently, Wu et al. [60] proposed a cyclic-disentangled self-distillation approach for single domaingeneralized object detection. Wang et al. [59] proposed a style-complement module that synthesizes examples from domains complementary to the source domain. Towards exploring the impact of the normalization layer on DG performance, Wang et al. [14] developed a generic normalization approach that learns both the standardization and rescaling statistics by neural networks. The aforementioned methods have shown promising results for the image classification task, however, they are not readily applicable to object detection since it has both classification and localization. + +Domain diversification for domain generalization: Sev- + +![](images/c166fd0aa20f385609f0b4dd9a85b01c6241757db502612d718811d4ff9ffb5a.jpg) +Figure 1. Overall architecture of our proposed method. At the core is a baseline detector, Here a two-stage detector Faster-RCNN[48] is depicted, comprising of backbone, region proposal network (RPN), and ROI alignment (RA). To improve the single domain generalization of the baseline detector, we propose to diversify the single source domain and also align the diversified views by minimizing losses at both classification and regression outputs. + +eral DG methods for object recognition have proposed various data augmentation techniques in an effort to improve the diversity of source domain(s). By using a CNN generator with different losses, Zhou et al. [69] synthesized novel examples from simulated domains. A few methods attempt to suppress the intrinsic style bias of CNNs. For instance, to focus on the contents and styles of images, [43] proposed content-biased and style-biased networks, respectively. To constantly seek diverse styles, [25] proposed a style synthesis process that is formulated as a monotone submodular optimization. Among the more recent methods, [13] explores diversifying source domain by perturbing channel statistics of low-level features for single domain-generalized object detector. In [54] the authors introduced the semantic augmentation of images by utilizing text-prompts relevant to potential target domain concepts in a vision-language model framework to improve the robustness of object detectors in unseen target domains. Along similar lines, [12] adapted the source model using textual descriptions of the target domain in a zero-shot manner to enhance the cross-domain generalizability in object detectors. Note that, both [54] and [12] incorporate the prior target domain knowledge using textual prompts. However, we follow domain generalization settings and leverage no prior knowledge about the target domain. Further, we diversify the source domain in input space and then align the detections in both original and diversified images. + +# 3. Proposed Methodology + +# 3.1. Preliminaries + +Problem Settings: Let $\mathcal{D}_s$ be the single source domain containing $N^s$ labelled training examples $\{\left(\mathbf{x}_i^s,\mathbf{y}_i^s\right)\}_{i = 1}^{N^s}$ , where $\mathbf{x}_i\in \mathbb{R}^{H\times W\times C}$ is an image and $\mathbf{y}_i = \{k_i,\mathbf{b}_i\}$ is the corresponding label with bounding box coordinates $\mathbf{b}_i\in \mathbb{R}^4$ and the associated class category $k_{i}\in \{1,\dots,K\}$ . $K$ is the number of class categories and $H$ , $W$ and $C$ represent the + +height, width, and number of channels, respectively. Let $\{\mathcal{D}_t\}_{t=1}^T$ be the set of $T$ (unseen) target domains. Our goal is to learn an object detector using training examples from $\mathcal{D}_s$ that generalizes well on test examples from $\mathcal{D}_t$ . We assume that both $\mathcal{D}_s$ and $\mathcal{D}_t$ share the same label space. + +Object Detection: Let $\mathcal{F}_{det}$ be an object detection model, that takes input image $\mathbf{x}$ and outputs $Z$ detections $\{(P(\hat{k}_n|\mathbf{x}),\hat{\mathbf{b}}_n)\}_{n = 1}^Z$ , where $\hat{k}_n$ denotes the class and bounding box $\hat{\mathbf{b}}_n$ predictions for $n^{th}$ proposal, respectively. We take the Faster R-CNN [48] model as $\mathcal{F}_{det}$ to detail our method, but note that our method is detector-agnostic and can be easily applied to other object detection paradigms, as shown in our results. We first overview Faster R-CNN to make the method section self-contained. Faster R-CNN is a popular and widely used two-stage object detector. The first stage comprises of a backbone feature extractor layer which generates a feature map and a region proposal network (RPN) which predicts a set of object proposals or regions of interest (RoIs) from the feature map. The second stage begins with ROI-Alignment, which extracts a fixed-size feature representation for each ROI and then feeds it to a classifier and a regressor to predict class confidence scores and bounding box coordinates, respectively. + +Single domain-generalized object detection: In this case, we assume that the object detection $\mathcal{F}_{det}$ has been trained on the examples taken from the source domain $D_{s}$ and then tested on examples from $\{\mathcal{D}_t\}_{t=1}^T$ . Akin to image classification models, object detection models like Faster-RCNN, which exhibits state-of-the-art performance when testing data and training data are from the same domain (i.e. in-domain scenario), but suffers from performance degradation when domains are different (i.e. out-of-domain scenario) (Figure 4). The presence of multiple domains during training penalizes the object detector in learning shortcuts which are typically domain-specific and instead encourages learning domain-invariant features. Nevertheless, the multi-domain data with the ground truth are difficult requirements + +to fulfill in several realistic settings and thus we are reduced to a single-domain generalization problem. + +Domain invariant object detection: We first re-formulate the definition of the domain invariance for a single source domain-generalized object detector by including a classifier and a regressor. Following [61], let's consider a visual corruption function $\phi(.)$ as a domain transformation function, in (continuous) domain space $\mathfrak{D}$ , which takes a source image from $\mathcal{D}_s$ and transforms it into a different domain $\mathcal{D}_{\phi}$ where $\phi \sim \Phi$ (is a set of possible transformations). By making this assumption, we define domain-invariance for single domain- generalized object detector as follows: + +# Definition 3.1 (Domain Invariance for Object Detection) + +Assuming that, for an input image $\mathbf{x}$ , an object detection model $\mathcal{F}_{\text{det}}$ predicts class probability distribution $\hat{\mathbf{p}}_n$ and bounding box coordinates $\hat{\mathbf{b}}_n \in \mathbb{R}^4$ for the $n^{th}$ proposal. Let $\mathbf{x}^s$ be an image from $\mathcal{D}_s$ and $\mathbf{x}^\phi = \phi(\mathbf{x}^s)$ be the transformation of $\mathbf{x}^s$ , denoted as $\mathbf{x}^\phi$ , where $\phi \sim \Phi$ . The model $\mathcal{F}_{\text{det}}$ is domain invariant if: + +$$ +\hat {\mathbf {p}} _ {n} ^ {s} = \hat {\mathbf {p}} _ {n} ^ {\phi} \tag {1} +$$ + +$$ +1 - \operatorname {I o U} \left(\hat {\mathbf {b}} _ {n} ^ {s}, \hat {\mathbf {b}} _ {n} ^ {\phi}\right) = 0 \tag {2} +$$ + +# 3.2. Proposed Method + +Through developing realizations of Eq. (1) and Eq. (2), we intend to improve the domain generalization of object detectors, when the training data from only a single source domain is available. So, our method has two main components: 1) diversification of the source domain (sec. 3.2.1) and 2) a detection alignment mechanism for improving generalization and calibration of detectors (sec. 3.2.2). Fig. 1 displays the overall architecture of our proposed method. + +# 3.2.1 Diversifying Single Source Domain + +Our proposed approach is motivated by various techniques used in diversifying source domains for object classification [26, 50, 56, 69]. Deep convolutional networks often learn shortcuts instead of actual semantics, but diversifying training domains can reduce this problem. Since obtaining multiple domains is difficult, we simulate them through data augmentation. This introduces diversity in the training data and improves the network's ability to learn robust object representations. We achieve this by perturbing the single source domain images using a set of existing visual corruptions $\Phi$ . During training, we augment every image in minibatch by using image augmentation function $\phi(.)$ which randomly samples a corruption method from $\Phi$ and apply to the input image. We then pass both original clean images along with their augmented versions to the model. Specifically, we investigate the visual corruptions set used in image + +classification domain [9] that simply combines ImageNet-C with Fourier transform-based corruptions, thereby providing a total of 22 corruptions with 5 severity levels. + +We classify image corruptions used for augmentation into five groups: Weather, Noise, Blur, Digital, and Fourier. In the case of Blur corruption, we employ various blur functions such as Gaussian, motion, glass, and defocus to smooth the pixel values in the image. Noise introduces different types of noise, including shot, impulse, speckle, and Gaussian, to perturb the image. Digital corruptions modify the pixel intensities by adjusting brightness, contrast, and saturation, or by changing the image resolution using JPEG compression, pixelation, and elastic transformation. Fig. 2 shows the impact of such augmentations. To ensure a fair comparison, we exclude weather-based transformations from our augmentation pool. Fourier-based corruptions such as phase scaling, constant amplitude, and High Pass Filter exploit the well-known property of Fourier transformation in that the phase component represents high-level semantics of an image, while the amplitude component covers low-level statistics or texture information. Perturbing these components enables us to reconstruct a new transformed image. Phase scaling introduces various artifacts by scaling the phase component in the Fourier spectrum. Constant amplitude replaces the amplitude component with a fixed vector, resulting in the loss of textual information and retaining only high-level semantics. We exclude the constant amplitude augmentation as it destroys the instance-level features. We note that this simple technique of diversifying source domain during object detector training outperforms baselines and competing methods by visible margins in challenging out-of-domain scenarios. As a result, though simple, as it makes minimal modifications to the baseline, it provides a solid baseline in single domain-generalized object detection. + +# 3.2.2 Aligning Diversified Domains + +While the single-source domain diversification approach provides a strong baseline, it does not enforce the main requirement for the Domain invariance (Def. 3.1); that is the predictions on diversified images $x^{\phi}$ do not align with predictions on original images $x^{s}$ . To quantify this, we measured mAP of the model predictions over original images, and mAP of the same model's predictions on diversified images. Regardless of whichever diversification is performed, there is considerable performance gap, indicating the lack of generalization. This is depicted in Fig. 3. This gap can be explained when considering the following two constraints. (1.) Object Classification Constraint, Eq.(1), states that model's predicted class probability distribution for the object in the source image, $x^{s}$ , should be same for the corresponding object in diversified image $x^{\phi}$ . (2.) Object Local- + +![](images/acba897208d7d15c4d048b43d2092e5eccc2b6825bf43eca2de28bff9115447b.jpg) +Figure 2. Examples of augmentations for domain diversification. + +ization Constraint, Eq.(2), states that is the objects should be predicted at same location (and of same size) on both diversified and original version of the images. Note that here these constraints are not related to the accuracy of the prediction, but that any prediction made should be same. + +Unlike the image classification, where there is only one class prediction vector, enforcing such constraints in object detection is more challenging. We propose a strategy to overcome this challenge. Based on definition 3.1, on domain-invariance for object detection, we align the detections from two views i.e. clean and diversified (augmented) images both from the classification and the regression outputs. We take the widely used two-stage object detector as an example i.e. Faster R-CNN. Given $\mathbf{x}_i^s$ or $\mathbf{x}_i^\phi$ as input, we can obtain a feature map $F\in \mathbb{R}^{m\times w\times h}$ from the backbone, where $m,h$ ,and $w$ denote the number of channels,height and width of the feature map, respectively. This feature map is then passed through region proposal network (RPN) to obtain object proposals $O\in \mathbb{R}^{Z\times 4}$ ,where $Z$ is the number of proposals. Next, RoI-Alignment (RA) is performed using $O$ i.e $A = \mathrm{RA}(O,F)\in \mathbb{R}^{Z\times m}$ to obtain a fixed length feature representation for each proposal. Detection loss is given by: + +$$ +\mathcal {L} _ {\mathrm {d e t}} = \sum_ {n = 1} ^ {Z} L _ {d e t} \left(\Psi \left(A _ {n}\right), \mathbf {y} _ {n}\right). \tag {3} +$$ + +Here $\Psi$ indicates the classifier and a bounding box regressor and $\mathbf{y}_n$ ) is the ground truth including class label and bounding box coordinates for the $n^{th}$ proposal. The $L_{det}$ consists of smooth-L1 loss and the negative log-likelihood loss. + +Aligning classification: To enforce Object Classification constraint for object detector generalization, we propose to measure the Kullback-Leibler (KL) divergence between the classifier output probability vectors $\hat{\mathbf{p}}_n^s$ and $\hat{\mathbf{p}}_n^\phi$ correspond + +![](images/3b176797cfb78d3b19c336bdeba5c97f7089ca582cd6cd0139117ad8f90008c0.jpg) +Figure 3. We augment the validation set from the source domain by one augmentation at a time and report the performance of the strong baseline model trained on all these augmentations. There is noticeable gap between the performance on original and diversified images. Our alignment losses allows reducing the gap between the performance on original and diversified images. + +ing to $\mathbf{x}_i^s$ and $\mathbf{x}_i^\phi$ . It is likely that RPN will produce a different set of proposals from $\mathbf{x}_i^s$ and $\mathbf{x}_i^\phi$ i.e. $O^s \neq O^\phi$ . These proposals might not be spatially consistent. To achieve 1-1 correspondence between the proposals from $\mathbf{x}_i^s$ and $\mathbf{x}_i^\phi$ , we perform predictions using the region proposals from the $\mathbf{x}_i^s$ and features pooled from the feature map for $\mathbf{x}_i^\phi$ . That is, we pass the feature map $F^\phi$ corresponding to $\mathbf{x}_i^\phi$ with proposals from $O^s$ : $A^\phi' = \mathrm{RA}(O^s, F^\phi)$ . $O^s$ : $A^\phi' = \mathrm{RA}(O^s, F^\phi)$ , obtaining $\hat{\mathbf{p}}_n^\phi'$ . The difference between the predictions is minimized using the KL-divergence: + +$$ +\mathcal {L} _ {\mathrm {c a l}} = \sum_ {n = 1} ^ {Z} \mathrm {K L} \left(\hat {\mathbf {p}} _ {n} ^ {s} \| \hat {\mathbf {p}} _ {n} ^ {\phi^ {\prime}}\right). \tag {4} +$$ + +Aligning localization: To make the Object Localization constraint for generalization part of the training process, we maximize the IoU between $\hat{\mathbf{b}}_n^s$ and $\hat{\mathbf{b}}_n^{\phi '}$ . This is realized by minimizing the L2-squared norm between $\hat{\mathbf{b}}_n^s$ and $\hat{\mathbf{b}}_n^{\phi '}$ : + +$$ +\mathcal {L} _ {\mathrm {r a l}} = \left\| \hat {\mathbf {b}} _ {n} ^ {s} - \hat {\mathbf {b}} _ {n} ^ {\phi^ {\prime}} \right\| _ {2} ^ {2} \tag {5} +$$ + +Our overall training objective is given by: + +$$ +\mathcal {L} _ {\text {t o t}} = \mathcal {L} _ {\text {d e t}} + \alpha \mathcal {L} _ {\text {c a l}} + \beta \mathcal {L} _ {\text {r a l}} \tag {6} +$$ + +where $\alpha$ and $\beta$ are the hyperparameters for balancing the contributions of $\mathcal{L}_{\mathrm{cal}}$ and $\mathcal{L}_{\mathrm{ral}}$ . + +# 4. Experiments + +Datasets: Real to Artistic consists of four datasets, including the Pascal VOC which contains real images from 20 different object classes and acts as a source domain, and remaining three are Clipart1k, Watercolor2k and Comic2k + +which offer artistic and comic images and are used as target domains. Clipart1k shares the same 20 classes as Pascal VOC, while Watercolor2k and Comic2k consist of 6 classes each, which are subsets of the Pascal VOC classes. Following [24], we combine Pascal VOC2007 and VOC2012 trainval set resulting in 16551 images for training and 5K images from VOC2007 test for in-domain evaluation. The Clipart1k consists of 1K and Watercolor2k and Comic2k each contain 2K images which are equally split into training and test sets. Following [24], we select all images from Clipart1k and test sets from Watercolor2k and Comic2k for out-domain evaluations. Urban Scene Detection is a self-driving dataset introduced by [60]. It offers images of 5 different weather conditions including Daytime Sunny, Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy. The images are collected from three different datasets: Barkeley Deep Drive 100k (BDD-100k)[64], FoggyCityscapes[8] and Adverse-Weather[17]. Rainy scenes are synthetic images generated by simulating rain on BDD-100k images. Daytime Sunny serves as a source domain consisting 26,518 images out of which 8,313 are used for in-domain evaluation whereas Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy are used as target domains containing 26,158, 2,494, 3,501, and 3,775 images, respectively. + +Implementation and Training Details: For two-stage object detector as a baseline, we use Faster R-CNN[48] with ResNet101[18] as feature backbone, while for single-stage detector, we use FCOS [53] with ResNet50-FPN[37] as feature backbone. In all experiments our models are trained using SGD for 18k iterations with initial learning rate of 0.2 and dropped by a factor of 10 after 12K and 16k iterations. The batch size is set to 16. All results are reported using mean average precision (mAP) at IoU@0.5. For reporting calibration performance, we use the detection expected calibration error (D-ECE) [30] and reliability diagrams [16]. + +Real to artistic: We evaluate our method on challenging real to artistic domain-shift where the distribution shift is large i.e. from PASCAL VOC to Clipart1k, Watercolor2k, and Comic2k. Table 1 shows that diversifying the training domain helps the model to generalize quite well by obtaining a significant gain of $8.5\%$ , $8.5\%$ , and $5.3\%$ from the Faster R-CNN baseline in Clipart1k, Watercolor2k, and Comic2k, respectively. With our proposed alignment losses, we are able to boost the overall performance by $13.2\%$ , $12.9\%$ , and $14.3\%$ . We also evaluated Normalization Perturbation (NP) [13] method on this benchmark and found it inferior to our method. Tables 2 and 3 reveal the class-wise results in Watercolor2k and Comic2k shifts. See supplementary for class-wise results on Clipart1k. + +Urban scene detection: Table 4 shows the results on different weather conditions manifesting various shifts scenarios. Due to large shifts like Daytime-Foggy and Night Raining the objects become unclear. We note that, + +
MethodVOCClipartWatercolorComic
Faster R-CNN81.825.744.518.9
NP [13]79.235.453.328.9
Diversification (div.)82.134.253.024.2
div. + Lcal82.136.253.928.7
div. + Lral80.735.053.828.7
div. + Lcal + Lral (Ours)80.138.957.433.2
+ +Table 1. Performance comparison with baseline and possible ablations, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k. + +
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN85.742.536.429.018.754.544.5
Diversification (div.)87.151.753.635.123.663.652.5
div. + Lcal83.950.448.540.336.563.353.8
div. + Lral83.352.350.739.232.765.253.9
div. + Lcal + Lral (Ours)90.451.851.943.935.970.257.4
+ +Table 2. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Watercolor2k scenario. + +
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN39.79.123.99.19.122.218.9
Diversification (div.)41.712.329.013.220.636.525.5
div. + Lcal49.015.827.020.221.838.428.7
div. + Lral53.313.529.019.120.536.728.7
div. + Lcal + Lral (Ours)54.116.930.125.027.445.933.2
+ +by only diversifying single domain, we obtain $0.5\%$ , $7\%$ , $6.3\%$ , and $2.5\%$ on Night Clear (NC), Dusk Rainy (DR), Night Rainy (NR), and Daytime Foggy (DF), respectively. Our method beats all baselines and state-of-the-art method from [54]. Over the baseline, our method delivers the highest gain of $8.4\%$ on Night Rainy while $8.1\%$ , $4.1\%$ and $3.6\%$ gains on Dusk Rainy, Daytime Foggy and Night Clear respectively. + +Table 3. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Comic2k scenario. + +
MethodDSNCDRNRDF
Faster R-CNN51.838.930.015.733.1
SW[45]50.633.426.313.730.8
IBN-Net[62]49.732.126.114.329.6
IterNorm[22]43.929.622.812.628.4
ISW[6]51.333.225.914.131.8
Wu et al. [60]56.136.628.216.633.5
Vidit et al. [54]51.336.932.318.738.5
Diversification50.639.437.022.035.6
Ours52.842.538.124.137.2
+ +Table 4. Results, mAP@0.5(%) reported on a multi-weather scenario where the model is trained on Daytime Sunny (DS) and tested on Night-Clear (NC), Night-Rainy (NR), Dusk-Rainy (DR) and Daytime-Foggy (DF). The results for SW, IBN-Net, IterNorm, ISW, S-DGOD are directly taken from [60]. + +Model Calibration: Table 5, reports the calibration performance (D-ECE) of the base model and the impact of us + +![](images/ca20dfd3d5f1ed24ef11e401e0484239d4e2396d01706c6d4422bda77cb1590c.jpg) +Figure 4. Our method (diversification and alignment) results in both considerable improvement in domain generalization and out-of-domain calibration. Diversification with the Label Smoothing (LS) or Temperature Scaling (TS) improves calibration but overall lower mAP indicates lacking in generalization. Note that our method does not have an explicit model calibration mechanism. (left) mAP: higher the better, (right) D-ECE: lower the better. + +![](images/ddd1ff4377a03504eee09833cda255ffa47ab28a1ccf876c48dbc81a2149785c.jpg) + +![](images/e6f2a5177923ded8f7a5b01742b8671d6febdca652b9ae25b3ab0a209596af9c.jpg) + +![](images/a28aeaa4da3d4f1c428f8d85f0d39efad69efd197918e956ed1b8c90cb6bccae.jpg) + +![](images/fc1dbfb54b7236af1916f4a0ee70562a9e461b81700e45ed2e60a2c33e785348.jpg) + +![](images/a8531d8060d8a1a4a013194306da37c162296ea0122fc12cb7d295d9b6c74436.jpg) +Figure 5. Reliability Diagram for different target domains. + +ing our diversification and alignment approach under various shift scenarios. As seen, simple diversification of the domain, while improving generalization, negatively affects the calibration for both in-domain and out-domain scenarios. This is to be expected since model is trained using Negative log-likelihood loss in $\mathcal{L}_{\mathrm{det}}$ (Eq. 3) which is in general attributed to making models highly confident, resulting in + +poor calibration. On the diversified images, where information might have been reduced or content has become noisy (w.r.t original image), high confidence predictions affects the calibration. In contrast, as detailed in (Sec. 3.2.2), our alignment step implicitly reduces the overconfidence in predictions (Fig. 5). Overall, as our results show, we achieve not only better generalization (higher mAP) but also better calibration (lower D-ECE). To further make apparent the the + +
Artistic ShiftsUrban Scene
MethodClipartWatercolorComicNRDRNCDF
Faster R-CNN11.918.515.431.529.327.925.8
Diversification (div.)14.521.417.433.030.228.925.7
Ours10.714.414.329.324.915.820.6
+ +Table 5. Comparison of calibration performance using D-ECE metric (\%) on Real to artistic shifts and in urban scene detection. + +utility of our alignment approach in achieving better calibration. We also include the impact of using existing simple calibration and generalization techniques such as temperature scaling (TS) [16] or label smoothing (LS) [41] with our diversification approach. Fig. 4 depicts the improvements our presented methods achieve in multiple shift scenarios. + +Results with single-stage detector: To show the applicability of our proposed method, we instantiate it in one-stage detector, namely FCOS [53] (Table 6). In comparison to FCOS, our method delivers a significant gain of $13.0\%$ , $10.7\%$ and $15.8\%$ on Clipart1k, Watercolor2k, and Comic2k shifts, respectively. + +Comparison with domain-adaptive detection methods: Table 7 compares our method with some unsupervised domain-adaptive object detectors using the same backbone. Note that these methods assume access to target domain and directly train using unlabelled target samples. In contrast even though our method does not have access to the target domain dataset at training time, it still shows better generalization results than many domain-adaptive detection methods. For instance, in watercolor and comic + +![](images/4cedc87cb4c7a2b60ddb4c8eeae153415372aea6b157a8d20aa163a0376ef170.jpg) +Figure 6. Qualitative results of baseline (Faster-RCNN), only diversifying domain, and our method. + +
MethodVOCClipartWatercolorComic
FCOS78.124.444.315.4
Diversification (div.)79.631.748.825.2
div. + Lcal80.135.452.629.4
div. + Lral77.529.850.324.0
div. + Lcal + Lral (Ours)77.537.455.031.2
+ +shifts, our model outperforms all methods by delivering a gain of $3.2\%$ and $2.5\%$ , respectively. Results for the existing domain adaptive methods are taken from [4]. + +Table 6. Performance comparison with single-stage baseline, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k. + +
MethodClipartWatercolorComic
DA-Faster[5]19.846.0-
SWDA[49]38.153.327.4
HTCN[3]40.3--
DBGL[4]41.653.829.7
Our Method38.557.032.2
+ +Qualitative Results: We sample some results for the qualitative comparison in Fig. 6. Aligning the predicted confidence and predicted localization between the original and diversified image, results in improved generalizability as visible from columns (c & f) where objects missed by baseline, diversification and NP[13] method, were properly localized and classified. Note that diversification actually results in more false positive detections with high confidence than baseline. This is visible in the column g where objects have been falsely classified as chairs and birds. + +Effect of different types of augmentations: We analyze the impact of different types of visual corruptions obtained from $\Phi$ in our method. First, we only diversify VOC-dataset using ImageNet-C corruption and then with Fourier-based + +Table 7. Comparison with domain adaptive detectors in mAP@0.5(%) + +
MethodClipartWatercolorComic
Faster R-CNN25.744.518.9
Ours - w/Fourier-based36.154.829.1
Ours - w/Imagenet-C36.855.530.6
Ours38.957.433.2
+ +Table 8. Ablation study with different augmentations used for diversifying source domain in our method, mAP@0.5(%) reported. + +corruption. As reported in Table 8, ImageNet-C corruption has a slight edge over Fourier corruption, however, using both provides the best results. This suggests that obtaining diversity through both types of corruption is complimentary. Aligning Classification vs aligning localization: Not aligning one of the prediction tasks across the diversified domains results in considerable degradation of the results (Table 1). In general, the results indicate that, as expected, the alignment of both these tasks is equally vital for achieving cross-domain generalizable object detectors. + +# 5. Conclusion + +We proposed a detector-agnostic, simple, and effective approach to improve the generalization and calibration of the object detectors given only a single source domain for training. 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We propose an effective approach that involves two key steps: diversifying the source domain and aligning detections based on class prediction confidence and localization. Firstly, we demonstrate that by carefully selecting a set of augmentations, a base detector can outperform existing methods for single domain generalization by a good margin. This highlights the importance of domain diversification in improving the performance of object detectors. Secondly, we introduce a method to align detections from multiple views, considering both classification and localization outputs. This alignment procedure leads to better generalized and well-calibrated object detector models, which are crucial for accurate decision-making in safety-critical applications. Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage detectors. To validate the effectiveness of our proposed methods, we conduct extensive experiments and ablations on challenging domain-shift scenarios. The results consistently demonstrate the superiority of our approach compared to existing methods. Our code and models are available at: https://github.com/msohaildanish/DivAlign." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "In recent years, we have witnessed remarkable performance improvements in supervised object detection [39, 47, 48, 53]. The success of these methods rely on the assumption that the training and testing data are sampled from the same distribution. However, in many real-world applications, such as autonomous driving, this assumption is often violated and these object detectors usually show degraded performance due to a phenomenon called domain-" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 266, + 547, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 314 + ], + "type": "text", + "content": "shift [3, 5, 49]. Shifts in real-world domains are typically caused by environmental alterations, like varying weather and time conditions. These changes manifest in diverse contrasts, brightness levels, and textures among others." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 316, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 460 + ], + "type": "text", + "content": "A prominent line of research that attempts to alleviate the impact of domain-shift is known as unsupervised domain adaptation (UDA) [20, 24, 42, 49, 63, 68, 72]. Given the labeled data from the source domain and unlabelled data from the target domain, the aim of UDA methods is to align the source and target data distributions so that the trained model can generalize well to the target domain [67]. An obvious limitation of UDA methods is that they require pre-collecting data and re-training the model for different target domains. Collecting data, even without annotation, for all possible domain shifts and training the model when shift happens is difficult and sometime not possible." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 460, + 548, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 548, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 548, + 640 + ], + "type": "text", + "content": "To cope with the domain-shift problem, a more realistic albeit challenging problem is domain generalization [2, 11, 23, 26, 32, 34, 35, 40, 58]. The goal of domain generalization (DG) is to learn a generalizable model typically from multiple source domains, available during training, that can perform well on the unseen target domain. A dominant class of DG methods attempts to learn domain-invariant feature space across multiple source domains [1, 11, 33, 35]. The performance of these methods is sensitive to the number of available source domains [7, 70]. In many realistic scenarios, acquiring labeled data from multiple source domains is often costly and time-consuming, eventually restricting the potential utilization of such methods. For these reasons, generalizing from a single-source domain is a more practical setting." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Recent surveys [29, 70] reveal that very little work has been done on DG for object detection [38, 60], despite the fact that object detectors occupy an important position in many safety-critical and security-sensitive applications e.g., autonomous driving. An object detector should be able to provide accurate as well as calibrated detections in different" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "17732" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "out-domain scenarios. Towards this end, we study the problem of single-domain generalized object detection (Single-DGOD). In the Single-DGOD setting, a single source domain is available for training, and the goal is to learn an object detector that can generalize well to multiple unseen target domains. Note that, many existing DG methods cannot be applied to solve this task since both multiple source domains and domain-level annotations are unavailable." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 167, + 288, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 288, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 288, + 430 + ], + "type": "text", + "content": "We are inspired by the class of DG methods for classification [46, 55, 66] that show that simulating novel domains during model training allows segregating domain-specific and semantics-oriented features. Consequently, the spurious correlations between the input and model predictions are suppressed. We begin by leveraging this idea of augmenting our input examples to realize the simulation of novel domains, thereby increasing the diversity of single-source training domain. In particular, we use the common off-the-shelf visual corruptions coupled with a simple training scheme to build a strong Single-DGOD baseline. The augmentation strategy aims to disrupt surface-level statistical patterns that are specific to a particular domain while preserving high-level semantic concepts that are common across domains. In addition to diversifying the single source domain, we propose a novel approach that aligns detection across different views of the image. The introduced method aligns both the class prediction distributions and predicted bounding box coordinates between augmented views of the image. By ensuring such a consistency of detections, we show that this not only helps in better out-domain detections but importantly also results in better calibrated models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 432, + 285, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 432, + 285, + 442 + ], + "spans": [ + { + "bbox": [ + 59, + 432, + 285, + 442 + ], + "type": "text", + "content": "To summarize, our work makes two main contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 444, + 287, + 561 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 444, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 287, + 514 + ], + "type": "text", + "content": "- We show that, using a set of carefully selected augmentations, the base model can surpass the performance of state-of-the-art published single-DGOD methods. To our knowledge, achieving such a strong baseline with known augmentation methods has not been shown before in the single domain object detection generalization." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 515, + 287, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 287, + 561 + ], + "type": "text", + "content": "- Our second contribution is an effective classification and localization alignment method that is shown to further improve detections in unseen domain and results in implicitly well calibrated detector model." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 563, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 587 + ], + "type": "text", + "content": "Our approach is detector-agnostic and can be seamlessly applied to both single-stage and two-stage object detectors." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "Domain adaptive object detection: Several domain adaptive detection methods aim to reduce the pixel-level or feature-level gap between the source and target domain [36, 44]. For instance, the works of [3, 10, 21, 24, 52, 65] utilized the labeled images generated from CycleGAN [71] to achieve pixel-level consistency. Likewise, [3, 5, 10, 19, 49, 51] proposed various mechanisms to progressively obtain a feature-level consistency. A common component" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "text", + "content": "of these methods is domain adversarial network [15] for achieving feature alignment. The work of [5] performed domain alignment on both global features (backbone features) and local features (Instance-level RoI features). Since then, several methods aimed to further improve these alignments by leveraging multi-scale [19], contextual [3, 49], spatial attention [31], category attention [57], and cross-domain topological relations [4] information. A few methods resorted to pseudo-labelling of instances to include class-level discriminative information. For instance, [24] constructed pseudo-labels by putting a threshold on top-1 accuracy over the predicted class of a detection. Towards refining the noisy pseudo-labels, [27] developed a robust training mechanism coupled with an independent classification module. With a similar goal, [28] proposed a weak self-training method and an adversarial background regularization module. Recently, [42] developed an uncertainty-guided criterion for selecting pseudo-labels in the target domain. We note that almost all of the aforementioned methods require access to both source and (unlabelled) target domain data coupled with an adaptation step to perform well in the target domain. As a consequence, these methods cannot be used to solve single-domain generalized object detection." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 351, + 545, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 698 + ], + "type": "text", + "content": "Single source domain generalization: A more challenging and recently proposed setting in DG is single source domain generalization. It is a more practical setting compared to multi-source DG since the availability of data from multiple different domains is a difficult requirement to fulfill for many real-world applications. The goal is to learn a generalized model using only a single source domain that can perform well on many unseen target domains. An intuitive approach for this setting is to increase the diversity of single source data by proposing different data augmentation techniques. Qiao et al. [46] leveraged adversarial training to construct difficult examples which facilitate model generalization. Earlier attempts involve training a label classifier and a domain classifier in a joint manner by their corresponding perturbations Similarly-[50] proposed to impose Wasserstein constraint in the feature space to generate adversarial samples from synthetic target distribution [56]. Recently, Wu et al. [60] proposed a cyclic-disentangled self-distillation approach for single domaingeneralized object detection. Wang et al. [59] proposed a style-complement module that synthesizes examples from domains complementary to the source domain. Towards exploring the impact of the normalization layer on DG performance, Wang et al. [14] developed a generic normalization approach that learns both the standardization and rescaling statistics by neural networks. The aforementioned methods have shown promising results for the image classification task, however, they are not readily applicable to object detection since it has both classification and localization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Domain diversification for domain generalization: Sev-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17733" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 535, + 190 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 535, + 190 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 535, + 190 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 535, + 190 + ], + "type": "image", + "image_path": "c166fd0aa20f385609f0b4dd9a85b01c6241757db502612d718811d4ff9ffb5a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 243 + ], + "type": "text", + "content": "Figure 1. Overall architecture of our proposed method. At the core is a baseline detector, Here a two-stage detector Faster-RCNN[48] is depicted, comprising of backbone, region proposal network (RPN), and ROI alignment (RA). To improve the single domain generalization of the baseline detector, we propose to diversify the single source domain and also align the diversified views by minimizing losses at both classification and regression outputs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 262, + 289, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 289, + 587 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 289, + 587 + ], + "type": "text", + "content": "eral DG methods for object recognition have proposed various data augmentation techniques in an effort to improve the diversity of source domain(s). By using a CNN generator with different losses, Zhou et al. [69] synthesized novel examples from simulated domains. A few methods attempt to suppress the intrinsic style bias of CNNs. For instance, to focus on the contents and styles of images, [43] proposed content-biased and style-biased networks, respectively. To constantly seek diverse styles, [25] proposed a style synthesis process that is formulated as a monotone submodular optimization. Among the more recent methods, [13] explores diversifying source domain by perturbing channel statistics of low-level features for single domain-generalized object detector. In [54] the authors introduced the semantic augmentation of images by utilizing text-prompts relevant to potential target domain concepts in a vision-language model framework to improve the robustness of object detectors in unseen target domains. Along similar lines, [12] adapted the source model using textual descriptions of the target domain in a zero-shot manner to enhance the cross-domain generalizability in object detectors. Note that, both [54] and [12] incorporate the prior target domain knowledge using textual prompts. However, we follow domain generalization settings and leverage no prior knowledge about the target domain. Further, we diversify the source domain in input space and then align the detections in both original and diversified images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 601, + 180, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 180, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 180, + 615 + ], + "type": "text", + "content": "3. Proposed Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 621, + 134, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 134, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 134, + 633 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "Problem Settings: Let " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " be the single source domain containing " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "N^s" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " labelled training examples " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{\\left(\\mathbf{x}_i^s,\\mathbf{y}_i^s\\right)\\}_{i = 1}^{N^s}" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " is an image and " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i = \\{k_i,\\mathbf{b}_i\\}" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " is the corresponding label with bounding box coordinates " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_i\\in \\mathbb{R}^4" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " and the associated class category " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "k_{i}\\in \\{1,\\dots,K\\}" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " is the number of class categories and " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " represent the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": "height, width, and number of channels, respectively. Let " + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{D}_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": " be the set of " + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": " (unseen) target domains. Our goal is to learn an object detector using training examples from " + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": " that generalizes well on test examples from " + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": ". We assume that both " + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 305, + 262, + 545, + 323 + ], + "type": "text", + "content": " share the same label space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": "Object Detection: Let " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{det}" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " be an object detection model, that takes input image " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " and outputs " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " detections " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\{(P(\\hat{k}_n|\\mathbf{x}),\\hat{\\mathbf{b}}_n)\\}_{n = 1}^Z" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\hat{k}_n" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " denotes the class and bounding box " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{b}}_n" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " predictions for " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " proposal, respectively. We take the Faster R-CNN [48] model as " + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{det}" + }, + { + "bbox": [ + 304, + 326, + 546, + 543 + ], + "type": "text", + "content": " to detail our method, but note that our method is detector-agnostic and can be easily applied to other object detection paradigms, as shown in our results. We first overview Faster R-CNN to make the method section self-contained. Faster R-CNN is a popular and widely used two-stage object detector. The first stage comprises of a backbone feature extractor layer which generates a feature map and a region proposal network (RPN) which predicts a set of object proposals or regions of interest (RoIs) from the feature map. The second stage begins with ROI-Alignment, which extracts a fixed-size feature representation for each ROI and then feeds it to a classifier and a regressor to predict class confidence scores and bounding box coordinates, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "Single domain-generalized object detection: In this case, we assume that the object detection " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{det}" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " has been trained on the examples taken from the source domain " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " and then tested on examples from " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{D}_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": ". Akin to image classification models, object detection models like Faster-RCNN, which exhibits state-of-the-art performance when testing data and training data are from the same domain (i.e. in-domain scenario), but suffers from performance degradation when domains are different (i.e. out-of-domain scenario) (Figure 4). The presence of multiple domains during training penalizes the object detector in learning shortcuts which are typically domain-specific and instead encourages learning domain-invariant features. Nevertheless, the multi-domain data with the ground truth are difficult requirements" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17734" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "to fulfill in several realistic settings and thus we are reduced to a single-domain generalization problem." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": "Domain invariant object detection: We first re-formulate the definition of the domain invariance for a single source domain-generalized object detector by including a classifier and a regressor. Following [61], let's consider a visual corruption function " + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "inline_equation", + "content": "\\phi(.)" + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": " as a domain transformation function, in (continuous) domain space " + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "inline_equation", + "content": "\\mathfrak{D}" + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": ", which takes a source image from " + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": " and transforms it into a different domain " + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\phi}" + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "inline_equation", + "content": "\\phi \\sim \\Phi" + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": " (is a set of possible transformations). By making this assumption, we define domain-invariance for single domain- generalized object detector as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 224, + 286, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 286, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 286, + 236 + ], + "type": "text", + "content": "Definition 3.1 (Domain Invariance for Object Detection)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": "Assuming that, for an input image " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": ", an object detection model " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\text{det}}" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " predicts class probability distribution " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_n" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " and bounding box coordinates " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{b}}_n \\in \\mathbb{R}^4" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " proposal. Let " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^s" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " be an image from " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^\\phi = \\phi(\\mathbf{x}^s)" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " be the transformation of " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^s" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^\\phi" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\phi \\sim \\Phi" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": ". The model " + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\text{det}}" + }, + { + "bbox": [ + 46, + 237, + 286, + 308 + ], + "type": "text", + "content": " is domain invariant if:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 146, + 320, + 286, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 320, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 146, + 320, + 286, + 335 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {p}} _ {n} ^ {s} = \\hat {\\mathbf {p}} _ {n} ^ {\\phi} \\tag {1}", + "image_path": "a5a4fc0825faa44bff355078db4a9a0100b6e38248509e8b90a2941e7ea1dfd2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 122, + 351, + 286, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 351, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 122, + 351, + 286, + 365 + ], + "type": "interline_equation", + "content": "1 - \\operatorname {I o U} \\left(\\hat {\\mathbf {b}} _ {n} ^ {s}, \\hat {\\mathbf {b}} _ {n} ^ {\\phi}\\right) = 0 \\tag {2}", + "image_path": "e43bed22ac3f1a7a032d58dadca6413c5b0607f1127c7011c4192dc098f3b530.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 373, + 152, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 152, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 152, + 385 + ], + "type": "text", + "content": "3.2. Proposed Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 391, + 286, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 286, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 286, + 486 + ], + "type": "text", + "content": "Through developing realizations of Eq. (1) and Eq. (2), we intend to improve the domain generalization of object detectors, when the training data from only a single source domain is available. So, our method has two main components: 1) diversification of the source domain (sec. 3.2.1) and 2) a detection alignment mechanism for improving generalization and calibration of detectors (sec. 3.2.2). Fig. 1 displays the overall architecture of our proposed method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 502, + 229, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 229, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 229, + 514 + ], + "type": "text", + "content": "3.2.1 Diversifying Single Source Domain" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": "Our proposed approach is motivated by various techniques used in diversifying source domains for object classification [26, 50, 56, 69]. Deep convolutional networks often learn shortcuts instead of actual semantics, but diversifying training domains can reduce this problem. Since obtaining multiple domains is difficult, we simulate them through data augmentation. This introduces diversity in the training data and improves the network's ability to learn robust object representations. We achieve this by perturbing the single source domain images using a set of existing visual corruptions " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": ". During training, we augment every image in minibatch by using image augmentation function " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\phi(.)" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " which randomly samples a corruption method from " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " and apply to the input image. We then pass both original clean images along with their augmented versions to the model. Specifically, we investigate the visual corruptions set used in image" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "classification domain [9] that simply combines ImageNet-C with Fourier transform-based corruptions, thereby providing a total of 22 corruptions with 5 severity levels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 110, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 491 + ], + "type": "text", + "content": "We classify image corruptions used for augmentation into five groups: Weather, Noise, Blur, Digital, and Fourier. In the case of Blur corruption, we employ various blur functions such as Gaussian, motion, glass, and defocus to smooth the pixel values in the image. Noise introduces different types of noise, including shot, impulse, speckle, and Gaussian, to perturb the image. Digital corruptions modify the pixel intensities by adjusting brightness, contrast, and saturation, or by changing the image resolution using JPEG compression, pixelation, and elastic transformation. Fig. 2 shows the impact of such augmentations. To ensure a fair comparison, we exclude weather-based transformations from our augmentation pool. Fourier-based corruptions such as phase scaling, constant amplitude, and High Pass Filter exploit the well-known property of Fourier transformation in that the phase component represents high-level semantics of an image, while the amplitude component covers low-level statistics or texture information. Perturbing these components enables us to reconstruct a new transformed image. Phase scaling introduces various artifacts by scaling the phase component in the Fourier spectrum. Constant amplitude replaces the amplitude component with a fixed vector, resulting in the loss of textual information and retaining only high-level semantics. We exclude the constant amplitude augmentation as it destroys the instance-level features. We note that this simple technique of diversifying source domain during object detector training outperforms baselines and competing methods by visible margins in challenging out-of-domain scenarios. As a result, though simple, as it makes minimal modifications to the baseline, it provides a solid baseline in single domain-generalized object detection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 513, + 463, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 463, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 463, + 525 + ], + "type": "text", + "content": "3.2.2 Aligning Diversified Domains" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "While the single-source domain diversification approach provides a strong baseline, it does not enforce the main requirement for the Domain invariance (Def. 3.1); that is the predictions on diversified images " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "x^{\\phi}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " do not align with predictions on original images " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "x^{s}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". To quantify this, we measured mAP of the model predictions over original images, and mAP of the same model's predictions on diversified images. Regardless of whichever diversification is performed, there is considerable performance gap, indicating the lack of generalization. This is depicted in Fig. 3. This gap can be explained when considering the following two constraints. (1.) Object Classification Constraint, Eq.(1), states that model's predicted class probability distribution for the object in the source image, " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "x^{s}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", should be same for the corresponding object in diversified image " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "x^{\\phi}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". (2.) Object Local-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17735" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 286, + 264 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 264 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 264 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 264 + ], + "type": "image", + "image_path": "acba897208d7d15c4d048b43d2092e5eccc2b6825bf43eca2de28bff9115447b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 278, + 282, + 289 + ], + "lines": [ + { + "bbox": [ + 47, + 278, + 282, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 282, + 289 + ], + "type": "text", + "content": "Figure 2. Examples of augmentations for domain diversification." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 294, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 287, + 354 + ], + "type": "text", + "content": "ization Constraint, Eq.(2), states that is the objects should be predicted at same location (and of same size) on both diversified and original version of the images. Note that here these constraints are not related to the accuracy of the prediction, but that any prediction made should be same." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": "Unlike the image classification, where there is only one class prediction vector, enforcing such constraints in object detection is more challenging. We propose a strategy to overcome this challenge. Based on definition 3.1, on domain-invariance for object detection, we align the detections from two views i.e. clean and diversified (augmented) images both from the classification and the regression outputs. We take the widely used two-stage object detector as an example i.e. Faster R-CNN. Given " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^s" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^\\phi" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " as input, we can obtain a feature map " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "F\\in \\mathbb{R}^{m\\times w\\times h}" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " from the backbone, where " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "m,h" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " denote the number of channels,height and width of the feature map, respectively. This feature map is then passed through region proposal network (RPN) to obtain object proposals " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "O\\in \\mathbb{R}^{Z\\times 4}" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " ,where " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " is the number of proposals. Next, RoI-Alignment (RA) is performed using " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " i.e " + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "inline_equation", + "content": "A = \\mathrm{RA}(O,F)\\in \\mathbb{R}^{Z\\times m}" + }, + { + "bbox": [ + 46, + 354, + 287, + 570 + ], + "type": "text", + "content": " to obtain a fixed length feature representation for each proposal. Detection loss is given by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 579, + 286, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 579, + 286, + 612 + ], + "spans": [ + { + "bbox": [ + 104, + 579, + 286, + 612 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {d e t}} = \\sum_ {n = 1} ^ {Z} L _ {d e t} \\left(\\Psi \\left(A _ {n}\\right), \\mathbf {y} _ {n}\\right). \\tag {3}", + "image_path": "5f2e86cffb4145fcd61cd018a8106c8a920629cb77fd2b440f5c7a79890336a6.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "text", + "content": " indicates the classifier and a bounding box regressor and " + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_n" + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "text", + "content": ") is the ground truth including class label and bounding box coordinates for the " + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "text", + "content": " proposal. The " + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "inline_equation", + "content": "L_{det}" + }, + { + "bbox": [ + 47, + 617, + 287, + 666 + ], + "type": "text", + "content": " consists of smooth-L1 loss and the negative log-likelihood loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": "Aligning classification: To enforce Object Classification constraint for object detector generalization, we propose to measure the Kullback-Leibler (KL) divergence between the classifier output probability vectors " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_n^s" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_n^\\phi" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " correspond" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 542, + 225 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 542, + 225 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 542, + 225 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 542, + 225 + ], + "type": "image", + "image_path": "3b176797cfb78d3b19c336bdeba5c97f7089ca582cd6cd0139117ad8f90008c0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 238, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 305, + 238, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 305, + 238, + 545, + 304 + ], + "type": "text", + "content": "Figure 3. We augment the validation set from the source domain by one augmentation at a time and report the performance of the strong baseline model trained on all these augmentations. There is noticeable gap between the performance on original and diversified images. Our alignment losses allows reducing the gap between the performance on original and diversified images." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": "ing to " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^s" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ". It is likely that RPN will produce a different set of proposals from " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^s" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " i.e. " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "O^s \\neq O^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ". These proposals might not be spatially consistent. To achieve 1-1 correspondence between the proposals from " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^s" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ", we perform predictions using the region proposals from the " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^s" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " and features pooled from the feature map for " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ". That is, we pass the feature map " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "F^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^\\phi" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": " with proposals from " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "O^s" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "A^\\phi' = \\mathrm{RA}(O^s, F^\\phi)" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "O^s" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "A^\\phi' = \\mathrm{RA}(O^s, F^\\phi)" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ", obtaining " + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_n^\\phi'" + }, + { + "bbox": [ + 304, + 319, + 545, + 445 + ], + "type": "text", + "content": ". The difference between the predictions is minimized using the KL-divergence:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 372, + 453, + 545, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 453, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 372, + 453, + 545, + 486 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c a l}} = \\sum_ {n = 1} ^ {Z} \\mathrm {K L} \\left(\\hat {\\mathbf {p}} _ {n} ^ {s} \\| \\hat {\\mathbf {p}} _ {n} ^ {\\phi^ {\\prime}}\\right). \\tag {4}", + "image_path": "8e7ed5dc2d6205cfd0fa7679abdb4e3355093d97c6272c6f6d7e53cf91ef53a0.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "text", + "content": "Aligning localization: To make the Object Localization constraint for generalization part of the training process, we maximize the IoU between " + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{b}}_n^s" + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{b}}_n^{\\phi '}" + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "text", + "content": ". This is realized by minimizing the L2-squared norm between " + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{b}}_n^s" + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{b}}_n^{\\phi '}" + }, + { + "bbox": [ + 305, + 490, + 545, + 540 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 382, + 548, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 548, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 382, + 548, + 545, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r a l}} = \\left\\| \\hat {\\mathbf {b}} _ {n} ^ {s} - \\hat {\\mathbf {b}} _ {n} ^ {\\phi^ {\\prime}} \\right\\| _ {2} ^ {2} \\tag {5}", + "image_path": "3c3d44a4eb8ce0b4fc2081c5bc355f35d854a6898793ee97cef1e2f882b0c2c3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 568, + 474, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 568, + 474, + 580 + ], + "spans": [ + { + "bbox": [ + 306, + 568, + 474, + 580 + ], + "type": "text", + "content": "Our overall training objective is given by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 364, + 589, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 589, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 364, + 589, + 545, + 601 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t}} = \\mathcal {L} _ {\\text {d e t}} + \\alpha \\mathcal {L} _ {\\text {c a l}} + \\beta \\mathcal {L} _ {\\text {r a l}} \\tag {6}", + "image_path": "7109d3a5ef061932ea62204bfe86d200160831652d7b5efc263c08ceb3870045.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "text", + "content": " are the hyperparameters for balancing the contributions of " + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cal}}" + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ral}}" + }, + { + "bbox": [ + 305, + 611, + 545, + 635 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 645, + 387, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 387, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 387, + 658 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Datasets: Real to Artistic consists of four datasets, including the Pascal VOC which contains real images from 20 different object classes and acts as a source domain, and remaining three are Clipart1k, Watercolor2k and Comic2k" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17736" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 359 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 359 + ], + "type": "text", + "content": "which offer artistic and comic images and are used as target domains. Clipart1k shares the same 20 classes as Pascal VOC, while Watercolor2k and Comic2k consist of 6 classes each, which are subsets of the Pascal VOC classes. Following [24], we combine Pascal VOC2007 and VOC2012 trainval set resulting in 16551 images for training and 5K images from VOC2007 test for in-domain evaluation. The Clipart1k consists of 1K and Watercolor2k and Comic2k each contain 2K images which are equally split into training and test sets. Following [24], we select all images from Clipart1k and test sets from Watercolor2k and Comic2k for out-domain evaluations. Urban Scene Detection is a self-driving dataset introduced by [60]. It offers images of 5 different weather conditions including Daytime Sunny, Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy. The images are collected from three different datasets: Barkeley Deep Drive 100k (BDD-100k)[64], FoggyCityscapes[8] and Adverse-Weather[17]. Rainy scenes are synthetic images generated by simulating rain on BDD-100k images. Daytime Sunny serves as a source domain consisting 26,518 images out of which 8,313 are used for in-domain evaluation whereas Night Clear, Night Rainy, Dusk Rainy and Daytime Foggy are used as target domains containing 26,158, 2,494, 3,501, and 3,775 images, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 360, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 289, + 492 + ], + "type": "text", + "content": "Implementation and Training Details: For two-stage object detector as a baseline, we use Faster R-CNN[48] with ResNet101[18] as feature backbone, while for single-stage detector, we use FCOS [53] with ResNet50-FPN[37] as feature backbone. In all experiments our models are trained using SGD for 18k iterations with initial learning rate of 0.2 and dropped by a factor of 10 after 12K and 16k iterations. The batch size is set to 16. All results are reported using mean average precision (mAP) at IoU@0.5. For reporting calibration performance, we use the detection expected calibration error (D-ECE) [30] and reliability diagrams [16]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": "Real to artistic: We evaluate our method on challenging real to artistic domain-shift where the distribution shift is large i.e. from PASCAL VOC to Clipart1k, Watercolor2k, and Comic2k. Table 1 shows that diversifying the training domain helps the model to generalize quite well by obtaining a significant gain of " + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "inline_equation", + "content": "8.5\\%" + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "inline_equation", + "content": "8.5\\%" + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "inline_equation", + "content": "5.3\\%" + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": " from the Faster R-CNN baseline in Clipart1k, Watercolor2k, and Comic2k, respectively. With our proposed alignment losses, we are able to boost the overall performance by " + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "inline_equation", + "content": "13.2\\%" + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "inline_equation", + "content": "12.9\\%" + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "inline_equation", + "content": "14.3\\%" + }, + { + "bbox": [ + 46, + 494, + 289, + 663 + ], + "type": "text", + "content": ". We also evaluated Normalization Perturbation (NP) [13] method on this benchmark and found it inferior to our method. Tables 2 and 3 reveal the class-wise results in Watercolor2k and Comic2k shifts. See supplementary for class-wise results on Clipart1k." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": "Urban scene detection: Table 4 shows the results on different weather conditions manifesting various shifts scenarios. Due to large shifts like Daytime-Foggy and Night Raining the objects become unclear. We note that," + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 313, + 70, + 541, + 141 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 541, + 141 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 541, + 141 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 541, + 141 + ], + "type": "table", + "html": "
MethodVOCClipartWatercolorComic
Faster R-CNN81.825.744.518.9
NP [13]79.235.453.328.9
Diversification (div.)82.134.253.024.2
div. + Lcal82.136.253.928.7
div. + Lral80.735.053.828.7
div. + Lcal + Lral (Ours)80.138.957.433.2
", + "image_path": "848c93d8e522ffddbc9ced8b8c304eba87afef73d02bed68fc193922bdf1a3cb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 309, + 193, + 543, + 247 + ], + "blocks": [ + { + "bbox": [ + 305, + 148, + 547, + 182 + ], + "lines": [ + { + "bbox": [ + 305, + 148, + 547, + 182 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 547, + 182 + ], + "type": "text", + "content": "Table 1. Performance comparison with baseline and possible ablations, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 193, + 543, + 247 + ], + "lines": [ + { + "bbox": [ + 309, + 193, + 543, + 247 + ], + "spans": [ + { + "bbox": [ + 309, + 193, + 543, + 247 + ], + "type": "table", + "html": "
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN85.742.536.429.018.754.544.5
Diversification (div.)87.151.753.635.123.663.652.5
div. + Lcal83.950.448.540.336.563.353.8
div. + Lral83.352.350.739.232.765.253.9
div. + Lcal + Lral (Ours)90.451.851.943.935.970.257.4
", + "image_path": "4c3411b83377c6461aa1648e7601debad32512ce7db7d43c2e474bbfe1b47658.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 288, + 543, + 342 + ], + "blocks": [ + { + "bbox": [ + 305, + 255, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 305, + 255, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 547, + 277 + ], + "type": "text", + "content": "Table 2. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Watercolor2k scenario." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 288, + 543, + 342 + ], + "lines": [ + { + "bbox": [ + 309, + 288, + 543, + 342 + ], + "spans": [ + { + "bbox": [ + 309, + 288, + 543, + 342 + ], + "type": "table", + "html": "
MethodbikebirdcarcatdogpersonmAP
Faster R-CNN39.79.123.99.19.122.218.9
Diversification (div.)41.712.329.013.220.636.525.5
div. + Lcal49.015.827.020.221.838.428.7
div. + Lral53.313.529.019.120.536.728.7
div. + Lcal + Lral (Ours)54.116.930.125.027.445.933.2
", + "image_path": "7972250bce3f75d6ab9d53b9e8328b6346f43cfabe9304ad6c48b36b52599250.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": "by only diversifying single domain, we obtain " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "6.3\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": " on Night Clear (NC), Dusk Rainy (DR), Night Rainy (NR), and Daytime Foggy (DF), respectively. Our method beats all baselines and state-of-the-art method from [54]. Over the baseline, our method delivers the highest gain of " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "8.4\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": " on Night Rainy while " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "8.1\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 304, + 393, + 547, + 490 + ], + "type": "text", + "content": " gains on Dusk Rainy, Daytime Foggy and Night Clear respectively." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 334, + 509, + 518, + 611 + ], + "blocks": [ + { + "bbox": [ + 305, + 350, + 547, + 372 + ], + "lines": [ + { + "bbox": [ + 305, + 350, + 547, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 547, + 372 + ], + "type": "text", + "content": "Table 3. Class-wise AP(%) comparison of baseline and proposed method on Pascal VOC to Comic2k scenario." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 334, + 509, + 518, + 611 + ], + "lines": [ + { + "bbox": [ + 334, + 509, + 518, + 611 + ], + "spans": [ + { + "bbox": [ + 334, + 509, + 518, + 611 + ], + "type": "table", + "html": "
MethodDSNCDRNRDF
Faster R-CNN51.838.930.015.733.1
SW[45]50.633.426.313.730.8
IBN-Net[62]49.732.126.114.329.6
IterNorm[22]43.929.622.812.628.4
ISW[6]51.333.225.914.131.8
Wu et al. [60]56.136.628.216.633.5
Vidit et al. [54]51.336.932.318.738.5
Diversification50.639.437.022.035.6
Ours52.842.538.124.137.2
", + "image_path": "c84df7d02bcfeaeb27eaddf524aba037e4b7106d55952d63e41e505b2f15e02b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 619, + 547, + 675 + ], + "lines": [ + { + "bbox": [ + 304, + 619, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 619, + 547, + 675 + ], + "type": "text", + "content": "Table 4. Results, mAP@0.5(%) reported on a multi-weather scenario where the model is trained on Daytime Sunny (DS) and tested on Night-Clear (NC), Night-Rainy (NR), Dusk-Rainy (DR) and Daytime-Foggy (DF). The results for SW, IBN-Net, IterNorm, ISW, S-DGOD are directly taken from [60]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Model Calibration: Table 5, reports the calibration performance (D-ECE) of the base model and the impact of us" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17737" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 72, + 285, + 208 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 285, + 208 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 285, + 208 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 285, + 208 + ], + "type": "image", + "image_path": "ca20dfd3d5f1ed24ef11e401e0484239d4e2396d01706c6d4422bda77cb1590c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 547, + 266 + ], + "type": "text", + "content": "Figure 4. Our method (diversification and alignment) results in both considerable improvement in domain generalization and out-of-domain calibration. Diversification with the Label Smoothing (LS) or Temperature Scaling (TS) improves calibration but overall lower mAP indicates lacking in generalization. Note that our method does not have an explicit model calibration mechanism. (left) mAP: higher the better, (right) D-ECE: lower the better." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 319, + 72, + 541, + 207 + ], + "blocks": [ + { + "bbox": [ + 319, + 72, + 541, + 207 + ], + "lines": [ + { + "bbox": [ + 319, + 72, + 541, + 207 + ], + "spans": [ + { + "bbox": [ + 319, + 72, + 541, + 207 + ], + "type": "image", + "image_path": "ddd1ff4377a03504eee09833cda255ffa47ab28a1ccf876c48dbc81a2149785c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 279, + 282, + 353 + ], + "blocks": [ + { + "bbox": [ + 53, + 279, + 282, + 353 + ], + "lines": [ + { + "bbox": [ + 53, + 279, + 282, + 353 + ], + "spans": [ + { + "bbox": [ + 53, + 279, + 282, + 353 + ], + "type": "image", + "image_path": "e6f2a5177923ded8f7a5b01742b8671d6febdca652b9ae25b3ab0a209596af9c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 53, + 354, + 282, + 426 + ], + "blocks": [ + { + "bbox": [ + 53, + 354, + 282, + 426 + ], + "lines": [ + { + "bbox": [ + 53, + 354, + 282, + 426 + ], + "spans": [ + { + "bbox": [ + 53, + 354, + 282, + 426 + ], + "type": "image", + "image_path": "a28aeaa4da3d4f1c428f8d85f0d39efad69efd197918e956ed1b8c90cb6bccae.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 53, + 426, + 282, + 499 + ], + "blocks": [ + { + "bbox": [ + 53, + 426, + 282, + 499 + ], + "lines": [ + { + "bbox": [ + 53, + 426, + 282, + 499 + ], + "spans": [ + { + "bbox": [ + 53, + 426, + 282, + 499 + ], + "type": "image", + "image_path": "fc1dbfb54b7236af1916f4a0ee70562a9e461b81700e45ed2e60a2c33e785348.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 53, + 500, + 282, + 586 + ], + "blocks": [ + { + "bbox": [ + 53, + 500, + 282, + 586 + ], + "lines": [ + { + "bbox": [ + 53, + 500, + 282, + 586 + ], + "spans": [ + { + "bbox": [ + 53, + 500, + 282, + 586 + ], + "type": "image", + "image_path": "a8531d8060d8a1a4a013194306da37c162296ea0122fc12cb7d295d9b6c74436.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 597, + 274, + 609 + ], + "lines": [ + { + "bbox": [ + 60, + 597, + 274, + 609 + ], + "spans": [ + { + "bbox": [ + 60, + 597, + 274, + 609 + ], + "type": "text", + "content": "Figure 5. Reliability Diagram for different target domains." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": "ing our diversification and alignment approach under various shift scenarios. As seen, simple diversification of the domain, while improving generalization, negatively affects the calibration for both in-domain and out-domain scenarios. This is to be expected since model is trained using Negative log-likelihood loss in " + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{det}}" + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": " (Eq. 3) which is in general attributed to making models highly confident, resulting in" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 373 + ], + "type": "text", + "content": "poor calibration. On the diversified images, where information might have been reduced or content has become noisy (w.r.t original image), high confidence predictions affects the calibration. In contrast, as detailed in (Sec. 3.2.2), our alignment step implicitly reduces the overconfidence in predictions (Fig. 5). Overall, as our results show, we achieve not only better generalization (higher mAP) but also better calibration (lower D-ECE). To further make apparent the the" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 308, + 381, + 547, + 426 + ], + "blocks": [ + { + "bbox": [ + 308, + 381, + 547, + 426 + ], + "lines": [ + { + "bbox": [ + 308, + 381, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 308, + 381, + 547, + 426 + ], + "type": "table", + "html": "
Artistic ShiftsUrban Scene
MethodClipartWatercolorComicNRDRNCDF
Faster R-CNN11.918.515.431.529.327.925.8
Diversification (div.)14.521.417.433.030.228.925.7
Ours10.714.414.329.324.915.820.6
", + "image_path": "8ce91f4ef80597f78e1cc6d7f4378a93d8532f9569b8b55d1af45fe9a1a2ee44.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 434, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 456 + ], + "type": "text", + "content": "Table 5. Comparison of calibration performance using D-ECE metric (\\%) on Real to artistic shifts and in urban scene detection." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 462, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 534 + ], + "type": "text", + "content": "utility of our alignment approach in achieving better calibration. We also include the impact of using existing simple calibration and generalization techniques such as temperature scaling (TS) [16] or label smoothing (LS) [41] with our diversification approach. Fig. 4 depicts the improvements our presented methods achieve in multiple shift scenarios." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "text", + "content": "Results with single-stage detector: To show the applicability of our proposed method, we instantiate it in one-stage detector, namely FCOS [53] (Table 6). In comparison to FCOS, our method delivers a significant gain of " + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "13.0\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "10.7\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "15.8\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 605 + ], + "type": "text", + "content": " on Clipart1k, Watercolor2k, and Comic2k shifts, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Comparison with domain-adaptive detection methods: Table 7 compares our method with some unsupervised domain-adaptive object detectors using the same backbone. Note that these methods assume access to target domain and directly train using unlabelled target samples. In contrast even though our method does not have access to the target domain dataset at training time, it still shows better generalization results than many domain-adaptive detection methods. For instance, in watercolor and comic" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17738" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 545, + 232 + ], + "type": "image", + "image_path": "4cedc87cb4c7a2b60ddb4c8eeae153415372aea6b157a8d20aa163a0376ef170.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 116, + 241, + 476, + 253 + ], + "lines": [ + { + "bbox": [ + 116, + 241, + 476, + 253 + ], + "spans": [ + { + "bbox": [ + 116, + 241, + 476, + 253 + ], + "type": "text", + "content": "Figure 6. Qualitative results of baseline (Faster-RCNN), only diversifying domain, and our method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 269, + 282, + 331 + ], + "blocks": [ + { + "bbox": [ + 55, + 269, + 282, + 331 + ], + "lines": [ + { + "bbox": [ + 55, + 269, + 282, + 331 + ], + "spans": [ + { + "bbox": [ + 55, + 269, + 282, + 331 + ], + "type": "table", + "html": "
MethodVOCClipartWatercolorComic
FCOS78.124.444.315.4
Diversification (div.)79.631.748.825.2
div. + Lcal80.135.452.629.4
div. + Lral77.529.850.324.0
div. + Lcal + Lral (Ours)77.537.455.031.2
", + "image_path": "7cdd10c96fa208ab59eb031a067b349752b3a5af84d06d5004eecb747d414f3a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "type": "text", + "content": "shifts, our model outperforms all methods by delivering a gain of " + }, + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 46, + 385, + 287, + 422 + ], + "type": "text", + "content": ", respectively. Results for the existing domain adaptive methods are taken from [4]." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 86, + 440, + 249, + 501 + ], + "blocks": [ + { + "bbox": [ + 46, + 338, + 287, + 372 + ], + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 372 + ], + "type": "text", + "content": "Table 6. Performance comparison with single-stage baseline, mAP@0.5(%) reported. The model is trained on Pascal VOC and tested on Clipart1k, Watercolor2k and Comic2k." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 440, + 249, + 501 + ], + "lines": [ + { + "bbox": [ + 86, + 440, + 249, + 501 + ], + "spans": [ + { + "bbox": [ + 86, + 440, + 249, + 501 + ], + "type": "table", + "html": "
MethodClipartWatercolorComic
DA-Faster[5]19.846.0-
SWDA[49]38.153.327.4
HTCN[3]40.3--
DBGL[4]41.653.829.7
Our Method38.557.032.2
", + "image_path": "af7e75bf2b940423c5c66d65baa4fe1032402479463d9e2bc58020a505b76133.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "content": "Qualitative Results: We sample some results for the qualitative comparison in Fig. 6. Aligning the predicted confidence and predicted localization between the original and diversified image, results in improved generalizability as visible from columns (c & f) where objects missed by baseline, diversification and NP[13] method, were properly localized and classified. Note that diversification actually results in more false positive detections with high confidence than baseline. This is visible in the column g where objects have been falsely classified as chairs and birds." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Effect of different types of augmentations: We analyze the impact of different types of visual corruptions obtained from " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " in our method. First, we only diversify VOC-dataset using ImageNet-C corruption and then with Fourier-based" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 330, + 270, + 525, + 321 + ], + "blocks": [ + { + "bbox": [ + 46, + 509, + 287, + 532 + ], + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 532 + ], + "type": "text", + "content": "Table 7. Comparison with domain adaptive detectors in mAP@0.5(%)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 330, + 270, + 525, + 321 + ], + "lines": [ + { + "bbox": [ + 330, + 270, + 525, + 321 + ], + "spans": [ + { + "bbox": [ + 330, + 270, + 525, + 321 + ], + "type": "table", + "html": "
MethodClipartWatercolorComic
Faster R-CNN25.744.518.9
Ours - w/Fourier-based36.154.829.1
Ours - w/Imagenet-C36.855.530.6
Ours38.957.433.2
", + "image_path": "5692e6204b1a6fb51bb3b86f01ccc62ed9a5f50d691e207c4f6cac017d36bcca.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 329, + 545, + 353 + ], + "lines": [ + { + "bbox": [ + 305, + 329, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 545, + 353 + ], + "type": "text", + "content": "Table 8. Ablation study with different augmentations used for diversifying source domain in our method, mAP@0.5(%) reported." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 371, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 545, + 491 + ], + "type": "text", + "content": "corruption. As reported in Table 8, ImageNet-C corruption has a slight edge over Fourier corruption, however, using both provides the best results. This suggests that obtaining diversity through both types of corruption is complimentary. Aligning Classification vs aligning localization: Not aligning one of the prediction tasks across the diversified domains results in considerable degradation of the results (Table 1). In general, the results indicate that, as expected, the alignment of both these tasks is equally vital for achieving cross-domain generalizable object detectors." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 502, + 379, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 379, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 379, + 514 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "We proposed a detector-agnostic, simple, and effective approach to improve the generalization and calibration of the object detectors given only a single source domain for training. To this end, we first explored effective image augmentation methods for domain diversification and developed a strong baseline for single-DGOD. Our results show that by carefully selecting a set of augmentations, a base detector can outperform SOTA methods for single domain generalization by a good margin. Secondly, we proposed a novel method to align the detections across the original and diversified images. This alignment procedure leads to better generalized and well-calibrated object detectors, which are crucial for accurate decision-making in safety-critical applications. Extensive results on various challenging shift scenarios corroborate the effectiveness and applicability of our approach." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17739" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Yogesh Balaji, Swami Sankaranarayanan, and Rama Chellappa. 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Recently, the spectra-wise transformer has shown great potential in capturing inter-spectra similarities of HSI, but the classic design of the transformer, i.e., multi-head division in the spectral (channel) dimension hinders the modeling of global spectral information and results in mean effect. In addition, previous methods adopt the normal spatial priors without taking imaging processes into account and fail to address the unique spatial degradation in snapshot spectral reconstruction. In this paper, we analyze the influence of multihead division and propose a novel Spectral-Spatial Rectification (SSR) method to enhance the utilization of spectral information and improve spatial degradation. Specifically, SSR includes two core parts: Window-based Spectra-wise Self-Attention (WSSA) and spAtial Rectification Block (ARB). WSSA is proposed to capture global spectral information and account for local differences, whereas ARB aims to mitigate the spatial degradation using a spatial alignment strategy. The experimental results on simulation and real scenes demonstrate the effectiveness of the proposed modules, and we also provide models at multiple scales to demonstrate the superiority of our approach. https://github.com/ZhangJC-2k/SSR", + "bbox": [ + 76, + 284, + 473, + 661 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 694, + 209, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The advent of compressed sensing introduced the coded aperture snapshot spectral compressive imaging (CASSI) system [13, 29, 36], addressing drawbacks in traditional hyperspectral cameras regarding efficiency and cost-effectiveness, gaining significant attention. This system offers the promise of swift and cost-efficient capture of Hyperspectral Images (HSIs). However, the inherent ill-posedness of decoding 3D HSIs from 2D measurements poses a significant challenge for reconstruction algorithm design. Consequently, various model-based [1, 23, 24, 33,", + "bbox": [ + 75, + 720, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f528c9a5e802fd09a1ce2b4158621ecd3da637193eb884e436c5d87cba130440.jpg", + "image_caption": [ + "Figure 1. Comparison of PSNR-FLOPs between our SSR and previous reconstruction methods. Our SSR significantly outperforms other methods over 2dB at the same FLOPs when surpassing the state-of-the-art method over 1dB with fewer FLOPs." + ], + "image_footnote": [], + "bbox": [ + 504, + 256, + 870, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "38, 40] and learning-based [2-6, 17, 18, 28, 37, 42] approaches have emerged to tackle this challenge. Within the realm of reconstruction algorithms, the effective utilization of diverse priors remains a pivotal research challenge.", + "bbox": [ + 496, + 500, + 892, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Model-based methods initially adopt total variation [20, 40], low-rank [24], sparsity [21, 34] and more traditional hand-craft priors [1, 23, 24, 33, 38] to construct the optimization model, which preliminarily shows the practical feasibility of snapshot spectral reconstruction. With the advancement of deep learning, both convolutional neural networks (CNNs) [6, 17, 18, 28, 37, 42] and transformers [3-5, 11] have been successively introduced for learning the spatial and spectral characteristics of HSIs. They serve as end-to-end denoisers [3, 4, 6, 17, 28] or deep image priors [5, 11, 18, 37, 42] in learning-based methods. These advancements have led to significant progress in both real-world and simulated scenario reconstructions. In addition, the effective utilization of spectral and spatial characteristics has also naturally become a research hotspot.", + "bbox": [ + 496, + 564, + 893, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous CNN methods such as TSA-Net [28], HDNet [17], DGSMP [18], and HerosNet [42], along with spatial transformers like Swin Transformer [25] and DAUHST [5], excel in learning spatial representations but do not effectively utilize the distinctive spectral characteristics inherent in HSIs. Conversely, spectra-wise transformers such as MST [3], MST++ [4], and RDLUF [11] show promising", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25817", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "potential in snapshot spectral reconstruction by exploiting inter-spectral similarities. However, their implementations follow the conventional transformer architecture, involving multi-head division in the spectral dimension, which limits the modeling of global spectral similarities and results in mean effect. Furthermore, in spectral snapshot imaging, some spatial degradation occurs in certain bands due to masking, shifting, and compression factors. Unfortunately, existing spatial and spectral networks lack tailored designs to mitigate such degradation effectively.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To optimize the utilization of spectral information and mitigate distinctive spatial degradation, we introduce the Spectral-Spatial Rectification (SSR) method into snapshot spectral reconstruction. Specifically, SSR comprises two key components: Window-based Spectral Self-Attention (WSSA) and spAtial Rectification Blocks (ARB). WSSA divides the features into multiple local windows in the spatial dimension, facilitating global spectral self-attention computations and the local difference consideration. Addressing the interaction gap between windows of WSSA, ARB leverages a Convolution Modulated Block (CMB). This block employs sliding large-kernel convolutions to interact with features between windows and learn effective spatial representation. Subsequently, to mitigate spatial degradation, ARB integrates a novel spatial alignment strategy. It assists low-quality bands in leveraging information from high-quality bands through learning a unified spatial representation and spectral weights, which further optimizes the utilization of spatial information. Overall, our contributions are summarized as follows:", + "bbox": [ + 75, + 242, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We analyze the influence of multi-head division on previous spectra-wise transformers and propose Window-based Spectra-wise Self-Attention to model global spectral information while accounting for local differences.", + "- A Spatial Rectification Block is specially designed to enhance spatial representation and mitigate the spatial degradation in low-quality bands through large-kernel convolutions and a novel spatial alignment strategy.", + "- The qualitative and quantitative results of real and simulation experiments demonstrate that our SSR method significantly improves spectral snapshot reconstruction." + ], + "bbox": [ + 76, + 544, + 468, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 723, + 218, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The model-based methods [1, 20, 21, 23, 24, 33, 34, 38, 40] construct convex optimization models with some specific priors such as total variation [20, 40], low-rankness [24], and sparsity [21, 34] according to the physical schema of CASSI then solve the problem in an iterative manner to obtain reconstructed images. They have good interpretability and low cost, yet lack performance guarantee. Subsequently, the rise of deep learning [14, 15, 22] has facilitated the rapid development of spectral snapshot reconstruction. To improve reconstruction quality, Plug-and-Play", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "methods [41, 44] plug pre-trained deep networks as priors, which make great progress in performance but are still limited by slow reconstruction speed. Along with faster inference and better results, the CNN-based end-to-end denoisers [17, 28, 31] quickly achieved better results by establishing a mapping between measurements and HSIs, but also brought huge memory and computation costs.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, the transformer-based end-to-end denoisers [2-4] which capture data similarity and long-range dependence have shown impressive performance in both simulation and real scenes. These methods adopt self-attention to learn effective spatial and spectral representation, achieving very high parameter and computational efficiency. Following this, the unfolding methods [5, 11] regard transformers as deep priors for optimization formulas and improve iterative frameworks through end-to-end training. In these approaches, CNNs and transformers play a huge role either as end-to-end denoisers or as deep priors. While previous CNNs and spatial transformers fail to effectively utilize the spectral characteristics inherent in HSIs, spectra-wise transformer [3, 4, 11] has shown great potential in spectral tasks and attracted wide attention. However, current spectra-wise transformers follow classic multi-head design [12, 25, 35] and suffer from the loss of global spectral information and the limitation of ignoring local differences.", + "bbox": [ + 496, + 198, + 892, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Spectral Snapshot Imaging Model", + "text_level": 1, + "bbox": [ + 498, + 481, + 808, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Mathematically, we assume a spectral image patch with $\\Lambda$ bands $\\{F_{\\lambda}\\}_{\\lambda = 1}^{\\Lambda}\\in \\mathbb{R}^{H\\times W}$ , where $H$ and $W$ represents the HSI's height and weight. Image frame $F_{\\lambda}$ is modulated by a physical mask with pattern $M\\in \\mathbb{R}^{H\\times W}$ to get modulated image frame $F_{\\lambda}^{\\prime}$ :", + "bbox": [ + 496, + 506, + 890, + 582 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\lambda} ^ {\\prime} = M \\circ F _ {\\lambda}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 582, + 890, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\circ$ denotes Hadamard's (element-wise) product. Then the modulated image frames of different wavelengths $\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}$ are separated to different positions by the disperser. After that, $\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}$ distributed across different bands are shifted spatially and summed element-wise. Thus, $\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}$ are compressed to a coded measurement:", + "bbox": [ + 496, + 609, + 890, + 734 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nG (m, n) = \\sum_ {i = 1} ^ {\\Lambda} F _ {\\lambda} ^ {\\prime} (m, n + D (\\lambda)), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 734, + 890, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $m$ and $n$ index the spatial coordinates, $D(\\lambda) = d(\\lambda - 1)$ , $d$ represents pixels shift between adjacent bands. Note Eq. (2) assumes a dispersion along the vertical dimension, and the derivation is also applicable for horizontal dispersion. The imaging model in Eq. (2) can be rewritten in the matrix-vector form as follows:", + "bbox": [ + 496, + 784, + 890, + 873 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\ng = \\Phi f, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 663, + 885, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25818", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0026dcc841925382e011a1de0924356289c07d3ccfef79ab0a999025a9c99a6d.jpg", + "image_caption": [ + "Figure 2. (a)-(c) The overall architecture of SSR, SSRUnet, and SSRB. LMP is achieved via a formula. (d) Details of WSSA." + ], + "image_footnote": [], + "bbox": [ + 81, + 71, + 408, + 292 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/00643df8bf9708cfa3453ad56d8dacdcb1d322ebe38f70651a8dccf638a2a0b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 71, + 645, + 292 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2c9a1c4047f038f1af3e177cdad9e88b910772e8591ebb54a5c99611ebb7abdc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 71, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $g \\in \\mathbb{R}^{HW}$ , $f \\in \\mathbb{R}^{HW\\Lambda}$ are the vectorized representation of the compressed image $G$ and the original spectral image $F$ respectively, and $\\Phi \\in \\mathbb{R}^{HW \\times HW\\Lambda}$ is the sensing matrix that describes the system imaging model. In spectral snapshot reconstruction, what we need to do is recover 3D HSI $f$ from the compressed 2D measurement $g$ .", + "bbox": [ + 75, + 316, + 470, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 422, + 168, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing spectral and spatial network designs [2-5, 11] are limited by the direct application of traditional multi-head division and unique spatial degradation of snapshot spectral imaging. To address the limitations, we propose the Spectral-Spatial Rectification (SSR) method to better model the spectral information, enhance spatial representation, and improve spatial degradation.", + "bbox": [ + 75, + 446, + 468, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Overall Architecture", + "text_level": 1, + "bbox": [ + 76, + 563, + 272, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of SSR is presented in Fig. 2 (a), we adopt a multistage network including initialization and $N$ cascaded stages, and each stage consists of Linear Manifold Projection (LMP), Spectral-Spatial Rectification Unet (SSRUnet), and spAtial Rectification Block (ARB). First, the compressed measurement $g$ is reversed to the initial shape [3] and the 2D mask is repeated in channel dimension to obtain the 3D mask. Then the two are inputted to a $1 \\times 1$ convolution kernel $(conv1 \\times 1)$ to get the initialization. In each stage, LMP is adopted to assist the reconstruction based on the imaging model. Then the SSRUnet is employed to refine the input through novel spatial and spectral design. Finally, ARB is used to further improve spatial degradation in reconstruction. For the core module SSRUnet, as illustrated in Fig. 2 (b), the $conv3 \\times 3s$ with residual are utilized to embed mask information into input $X$ as follows:", + "bbox": [ + 75, + 585, + 470, + 829 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nX _ {M E} = \\operatorname {C o n v} _ {3 \\times 3} (X) \\circ \\left(T _ {I} + \\operatorname {C o n v} _ {3 \\times 3} (\\text {M a s k})\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 839, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $X_{ME}$ is the features embedded with the mask, $T_{I}$ is an all-one tensor and $Mask$ is the 3D mask obtained in ini", + "bbox": [ + 76, + 869, + 470, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tialization. Then SSRUnet with three layers and $conv3 \\times 3$ are employed to extract the deep feature which is combined with the input as a residual to produce a refined output. The SSRUnet consists of downsampling modules ( $conv4 \\times 4$ ), Spectral-Spatial Rectification Block (SSRB), upsampling modules ( $deconv2 \\times 2$ ), and Fusion modules ( $conv1 \\times 1$ ). Spectral-Spatial Rectification Block (SSRB). SSRB is the basic module of SSRUnet. As shown in Fig. 2 (c), the implicit positional information [10] is firstly embedded in the input for applying self-attention later in SSRB. Each SSRB is the sequential combination of the spEctral Rectification Block (ERB) and ARB. Fig. 2 (c) illustrates the components of ERB and ARB, i.e., a Feed Forward Network(FFN) and a Window-based Spectral Self-Attention (WSSA) for ERB, a Convolution Moudulated Block (CMB) and a Spatial Alignment Block (SAB) for ARB, and same Layer Normalization (LN) and Group Normalization (GN) for ERB and ARB. WSSA is detailed in Fig. 2 (d) and FFN consists of two linear layers sandwiched with depth-wise $conv3 \\times 3$ .", + "bbox": [ + 496, + 318, + 890, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Spectral Rectification Block", + "text_level": 1, + "bbox": [ + 498, + 619, + 750, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spectral self-attention is a promising approach to utilize spectral characteristics for HSI tasks. However, we find that the previous spectra-wise transformer [3, 4, 11] directly considers a band as a token and follows traditional spatial self-attention design, i.e., multi-head division in spectral (channel) dimension, which ignores the local differences in spectral distribution and results in mean effect and nonglobal spectral utilization. To solve the problem, we propose the ERB based on WSSA to consider local differences and model global spectral information.", + "bbox": [ + 496, + 643, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Influence of Multi-Head Division in Spectral (Channel) Dimension. In the classic transformer design [12, 25, 35], the use of multi-head division in the channel dimension is common and brings some gains. Possibly affected by this, the previous spectra-wise transformer in spectral snapshot reconstruction also divides multi-head in spectral dimension as shown in Fig. 3 (a), which results in the sep", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25819", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bccbcbcf1a52e83ff19d2405b07bdef96435b3f648d1c3633542157669025afe.jpg", + "image_caption": [ + "(a) Multi-head Division in Spectral Dimension" + ], + "image_footnote": [], + "bbox": [ + 81, + 71, + 380, + 199 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d7fcda305dd1eadfa1ed0ee606353b104f0450649b1f64beed0aaebd69e7ff01.jpg", + "image_caption": [ + "(b) Mean Effect" + ], + "image_footnote": [], + "bbox": [ + 398, + 79, + 545, + 181 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4f81174c8393974768e401ef4dfe157f8c5c35ef743deeed1c2bb5a5818116a7.jpg", + "image_caption": [ + "Figure 3. (a)-(c) The influence of multi-head attention and mean effect, (d) The illustration of WSSA." + ], + "image_footnote": [], + "bbox": [ + 563, + 88, + 699, + 189 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cbde6d6fd07e5a3e1034d8ae90ad89077fd3c760438945264d970c51b825ffd5.jpg", + "image_caption": [ + "(c) Multi-head Division in Spatial Dimension", + "(d) Window-based Attention" + ], + "image_footnote": [], + "bbox": [ + 725, + 90, + 872, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "aration of spectral information and failure to model global spectral information. It's very easy to get confused because the spectral transformer is in contrast to the spatial transformer, where the characteristic dimension of the former is the spatial dimension, and the characteristic dimension of the latter is the spectral (channel) dimension.", + "bbox": [ + 75, + 250, + 468, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Influence of Mean Effect. In addition, considering that HSIs depict the spectral distribution of scenes, the similarities of different regions should be different but previous multi-head division results in all regions sharing the same similarity. When treating the whole band as a token to calculate spectral self-attention, we obtain the mean of all region similarities in the band and the local differences between regions are lost, which we call the 'Mean Effect'. Define $\\Lambda$ features $\\{f_{\\lambda}\\}_{\\lambda = 1}^{\\Lambda}$ where feature dimension consists of $p$ different patterns (regions), i.e., $f_{\\lambda} = [f_{\\lambda}^{1}, f_{\\lambda}^{2}, \\ldots, f_{\\lambda}^{p}]$ , the influence of mean effect on the similarity calculation can be simply described as follows:", + "bbox": [ + 75, + 340, + 468, + 522 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s i m} \\left(f _ {i} ^ {k}, f _ {j} ^ {k}\\right)\\rightarrow \\frac {1}{p} \\sum_ {m = 1} ^ {p} \\operatorname {s i m} \\left(f _ {i} ^ {m}, f _ {j} ^ {m}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 527, + 468, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the left part denotes the expected similarity of the $k$ th pattern between $f_{i}^{k}$ and $f_{j}^{k}$ , and the right part represents the obtained similarity in previous approaches. We also present an example in Fig. 3 (b), the average similarity and local region similarity between the red band and other bands are marked with red numbers and black numbers respectively. To demonstrate the validity of our theory, we carried out ablation experiments of different region sizes, i.e., window size under the same conditions later. In addition, the mean effect may explain why multi-head attention is more effective than single-head attention.", + "bbox": [ + 75, + 568, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Head Division in Spatial Dimension. When realizing appropriate feature dimension and mean effect, it was natural to treat the entire band frame as a token and then directly divide multi-head [35] in the merged spatial dimension to calculate self-attention, which we call MSSA later for short. However, as shown in Fig. 3 (c), this would split the entire image into (incomplete) strip shapes on each head, which mitigates the mean effect to some extent but breaks the spatial correlation of features. That is, adjacent areas are divided into different heads, while areas that are far apart in space are divided into the same head.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Window-based Spectral Self-Attention (WSSA). To capture the global spectral similarity, solve the mean effect, and maintain spatial correlation, WSSA divides features into a number of windows spatial-wisely, and then the spectrawise self-attention is calculated within windows to avoid the interference of each other, which is shown in Fig. 3 (d). Specifically, define input $X \\in \\mathbb{R}^{H \\times W \\times C}$ , as shown in Fig. 2 (d), $X$ is first linearly projected to $3C$ channels tensor via a $1 \\times 1$ convolution then uniformly divides the tensor channel-wisely into the query $(Q)$ , key $(K)$ , value $(V)$ . Subsequently, $Q, K, V$ are split spatial-wise into $HW / M^2$ windows with size of $\\mathbb{R}^{M \\times M \\times C}$ separately:", + "bbox": [ + 496, + 250, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{Q _ {i}, K _ {i}, V _ {i} \\right\\} _ {i = 1} ^ {H W / M ^ {2}} = Q, K, V, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 439, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Q_{i},K_{i},V_{i}\\in \\mathbb{R}^{M\\times M\\times C}$ and are then reshaped into shape $\\mathbb{R}^{M^2\\times C}$ as tokens to calculate attention as follows:", + "bbox": [ + 498, + 467, + 890, + 501 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {A t t e n t i o n} _ {i} = \\operatorname {S o f t M a x} \\left(Q _ {i} ^ {T} K _ {i} / M\\right) V _ {i}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 508, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{M}$ is used as the scale factor before applying the softmax function. Then the outputs of $HW / M^2$ attention are reshape in $\\mathbb{R}^{M\\times M\\times C}$ and merge together in the original arrangement to undergo a conv1 $\\times 1$ projection:", + "bbox": [ + 498, + 532, + 890, + 594 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {\\prime} = \\left\\{A t t e n t i o n _ {i} \\right\\} _ {i = 1} ^ {H W / M ^ {2}} W _ {1}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 601, + 890, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_{1} \\in \\mathbb{R}^{C \\times C}$ are weight matrices of a $conv1 \\times 1$ and $X'$ is the final output in $\\mathbb{R}^{H \\times W \\times C}$ . Different from multi-head self-attention which implements token embedding and then divides heads, WSSA first implements windows split then reshaping into tokens, which preserves the spatial correlation of each token. Regarding WSSA as a special multi-head self-attention, the number of WSSA heads is more, often hundreds of thousands, far more than the number of multi-head attention.", + "bbox": [ + 496, + 630, + 890, + 766 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Computational Complexity. The computational complexity of WSSA is displayed as follows:", + "bbox": [ + 498, + 768, + 888, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nO (W S S A) = 4 H W C ^ {2} + 2 M ^ {2} C ^ {2} \\frac {H W}{M ^ {2}} = 6 H W C ^ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 804, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The computational complexity of WSSA is linear to the spatial size $HW$ and window size-independent, meaning that there is no additional computation cost when we improve spectral utilization.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25820", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9f74e7384f6bb4a1fca7f1e4b41334c5ab09c7b5617ae32edde3e0a2484a6631.jpg", + "image_caption": [ + "Figure 4. (a) Display of spatial degradation in spectra-wise transformers. (b) The details of CMB. (c) The effect of large kernel convolution in CMB. (d) The details of SAB. (e) Spatial alignment strategy of SAB." + ], + "image_footnote": [], + "bbox": [ + 83, + 71, + 890, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Spatial Rectification Block", + "text_level": 1, + "bbox": [ + 76, + 349, + 316, + 366 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The utilization of WSSA enhances the capability of spectral information capture. However, a limitation arises from the absence of interaction between adjacent windows within WSSA, potentially leading to discontinuous spatial representation and the occurrence of blocking artifacts, as highlighted by [7]. Additionally, unique spatial degradation occurs due to mask, shift, and compression in spectral snapshot imaging. To address these concerns, we propose a spA tial Rectification Block (ARB) comprising a Convolution Modulated Block (CMB) and a Spatial Alignment Block (SAB). This ARB aims to foster interaction between adjacent windows and alleviate spatial degradation in the HSIs. Convolution Modulated Block (CMB). Here, we try to solve two problems: (1) When different windows cannot interfere with each other, WSSA also fails to exchange information, which leads to discrete spatial expression and may lead to blocking artifacts [7]. (2) As shown in the top two rows of Fig .4 (a), over-smoothing demonstrates that the spatial representation ability of a single spectra-wise transformer is not sufficient. To solve these two problems and inspired by the development of large kernel convolution in high-level tasks, we adopted a Convolution Modulated Block (CMB) proposed in [16] to modulate spatial information and make adjacent windows interact with each other through large kernel convolution sliding as shown in Fig. 4 (b). CMB modulates spatial information in a similar manner to self-attention but much more efficiently. Specifically, given the input tokens $X\\in \\mathbb{R}^{H\\times W\\times C}$ , we use a simple depth-wise convolution with kernel size $11\\times 11$ to calculate the modulated attention $A$ as follows:", + "bbox": [ + 75, + 375, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA = D C o n v _ {1 1 \\times 1 1} (X W _ {2}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 840, + 468, + 857 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{2}\\in \\mathbb{R}^{H\\times W\\times C}$ are weight matrices of conv1 x 1s, and $DConv_{11\\times 11}$ denotes a depth-wise convolution with", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "kernal size $11 \\times 11$ . Then we adopt the element-wise product and attention $A$ to modulate the project feature $V'$ to get the output $Z$ :", + "bbox": [ + 498, + 351, + 890, + 395 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nZ = \\left(A \\circ V ^ {\\prime}\\right) W _ {4}, V ^ {\\prime} = X W _ {3}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 396, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{3}$ and $W_{4} \\in \\mathbb{R}^{C \\times C}$ are weight matrices of $conv1 \\times 1s$ . On the one hand, CMB could effectively improve the spatial representation of features through modulation operation. On the other hand, CMB enables the pixels between adjacent windows of WSSA to interact spatial-wisely when depth-wise convolution kernel size $11 \\times 11$ is greater than patch size $8 \\times 8$ , as demonstrated in Fig. 4 (c).", + "bbox": [ + 496, + 421, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatial Alignment Block (SAB). As shown in the bottom two rows of Fig. 4 (a), we observe that the reconstruction results of some bands have more spatial degradation such as distortion and deformation, which is not common in other HSI tasks. Thus, we think this may be related to the unique imaging process. As shown in Fig. 4 (e), shift and compression in the imaging process mix information from different spatial locations, and spatial texture recovery in bands with low spectral density may be difficult, which is neglected by previous methods. Considering that the low-density bands can be obtained by multiplying the high-density bands by weights, we can utilize the high-quality bands to improve the spatial texture of the low-quality bands through a novel spatial alignment strategy, as shown in Fig. 4 (e). To achieve this, a Spatial Alignment Block (SAB) is proposed to improve spatial degradation. As shown in 4 (d), we adopt different convolution kernels to estimate spatial texture distribution which corresponds to the high-density part, and learn spectral weights in SAB when two linear layers are used to mix channel information. Specifically, given the input feature $F \\in \\mathbb{R}^{H \\times W \\times C}$ , we use a convolution with kernel size $3 \\times 3$ and $GELU$ activation function to learn the spatial texture $T$ as follows:", + "bbox": [ + 496, + 527, + 892, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT = \\psi \\left(\\operatorname {C o n v} _ {3 \\times 3} \\left(F W _ {5}\\right)\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25821", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5bb4087632ef293203f4f7f7263a9875c53ef460e54e8578861cbf8f81531ee2.jpg", + "table_caption": [ + "Table 1. The PSNR (upper entry in each cell) in dB and SSIM (lower entry in each cell) results of the test methods on 10 scenes." + ], + "table_footnote": [], + "table_body": "
AlgorithmsReferenceParamsGFLOPsScene1Scene2Scene3Scene4Scene5Scene6Scene7Scene8Scene9Scene10Avg
DIP-HSI [30]ICCV 202133.8564.4232.6827.2631.3040.5429.7930.3928.1829.4434.5128.5131.26
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
TSA-Net [28]ECCV 202044.25110.0632.0331.0032.2539.1929.3931.4430.3229.3530.0129.5931.46
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
DGSMP [18]CVPR 20213.5884.7733.2632.0933.0640.5428.8633.0830.7431.5531.6631.4432.63
0.9150.8980.9250.9640.8820.9370.8860.9230.9110.9250.917
GAP-Net [27]IJCV 20234.2778.5833.7433.2634.2841.0331.4432.4032.2730.4633.5130.2433.26
0.9110.9000.9290.9670.9190.9250.9020.9050.9150.8950.917
HerosNet [42]CVPR 202211.27414.7635.6935.0134.8238.0733.1834.9433.5833.1933.0433.0134.45
0.9730.9680.9670.9850.9690.9760.9620.9680.9640.9650.970
HDNet [17]CVPR 20222.37154.7635.1435.6736.0342.3032.6934.4633.6732.4834.8932.3834.97
0.9350.9400.9430.9690.9460.9520.9260.9410.9420.9370.943
MST [3]CVPR 20222.0328.1535.4035.8736.5142.2732.7734.8033.6632.6735.3932.5035.18
0.9410.9440.9530.9730.9470.9550.9250.9480.9490.9410.948
CST [2]ECCV 20223.040.1035.9636.8438.1642.4433.2535.7234.8634.3436.5133.0936.12
0.9490.9550.9620.9750.9550.9630.9440.9610.9570.9450.957
BIRNAT [8]TPAMI 20234.402122.6636.7937.8940.6146.9435.4235.3036.5833.9639.4732.8037.58
0.9510.9570.9710.9850.9640.9590.9550.9560.9700.9380.960
DAUHST [5]NeurIPS 20226.1579.5037.2539.0241.0546.1535.8037.0837.5735.1040.0234.5938.36
0.9580.9670.9710.9830.9690.9700.9630.9660.9700.9560.967
RDLUF [11]CVPR 20231.81115.3437.9440.9543.2547.8337.1137.4738.5835.5041.8335.2339.57
0.9660.9770.9790.9900.9760.9750.9690.9700.9780.9620.974
SSR-SOurs1.7326.3738.2240.0542.5747.4636.5037.3337.6035.7041.3735.0639.19
0.9630.9720.9750.9860.9720.9710.9640.9680.9750.9590.971
SSR-MOurs3.4552.6538.6141.3543.9448.3237.8038.0738.5436.8242.7235.7940.20
0.9670.9780.9790.9880.9770.9750.9690.9740.9800.9650.975
SSR-LOurs5.1878.9339.0742.0444.4948.8038.6438.5039.1636.9643.1236.0840.69
0.9700.9810.9800.9900.9800.9780.9710.9760.9820.9680.978
SSR-L*Ours1.7378.9338.8141.5143.7648.6238.3237.8538.5036.8542.6435.8240.27
0.9680.9790.9790.9880.9790.9750.9690.9740.9800.9650.976
", + "bbox": [ + 81, + 85, + 883, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $T \\in \\mathbb{R}^{H \\times W \\times 1}$ , $\\psi$ is GELU activation function and $W_5 \\in \\mathbb{R}^{C \\times C}$ are weight matrices of the linear layer. Meanwhile, we use a depth-wise convolution with kernel size $3 \\times 3$ and Sigmoid activation function to learn spectral element-wise weight as follows:", + "bbox": [ + 75, + 436, + 468, + 513 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS W = \\sigma \\left(D C o n v _ {3 \\times 3} \\left(F W _ {5}\\right)\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 526, + 468, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $SW \\in \\mathbb{R}^{H \\times W \\times C}$ , $\\sigma$ is Sigmoid activation function. Finally, we use multiple element-wise products and a conv1 × 1 projection $W_{6}$ to calculate the output $Y$ as follows:", + "bbox": [ + 75, + 553, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nY = \\left\\{T \\circ S W _ {i} \\right\\} _ {i = 1} ^ {C} W _ {6}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 613, + 468, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $Y \\in \\mathbb{R}^{H \\times W \\times C}$ and $SW_{i} \\in \\mathbb{R}^{H \\times W \\times 1}$ .", + "bbox": [ + 76, + 637, + 380, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Linear Manifold Projection (LMP)", + "text_level": 1, + "bbox": [ + 76, + 662, + 382, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Eq. (3) is a key constraint in spectral compression reconstruction. To take advantage of this prior, we introduce a Linear Manifold Projection (LMP) proposed in GAP-Net [27] to assist the reconstruction. We add an additional parameter to control projection intensity and perform the LMP as follows:", + "bbox": [ + 75, + 686, + 468, + 775 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\prime} = f + \\rho \\Phi^ {T} [ (g - \\Phi f) \\cdot / (\\Phi \\Phi^ {T}) ], \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 777, + 468, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\rho$ is the parameter that is estimated through a simple network similar to [5].", + "bbox": [ + 75, + 806, + 468, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 847, + 294, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We change the stage numbers $N$ to establish a series of SSR models with small, medium, and large scales: SSR-S", + "bbox": [ + 75, + 869, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$(N = 3)$ , SSR-M $(N = 6)$ , and SSR-L $(N = 9)$ . The proposed SSR is implemented by PyTorch and the window size in WSSA is empirically set to $8 \\times 8$ . Adam [19] optimizer $(\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999)$ and Cosine Annealing [26] scheduler are adopted to train SSR on a single RTX 3090 GPU. Training samples are patches with spatial sizes of $256 \\times 256$ and $384 \\times 384$ randomly cropped from 3D HSI data cubes for simulation and real experiments separately. The shifting step $d$ of the imaging model is 2. The channels of SSRUnet layers are set to $\\Lambda, 2\\Lambda, 4\\Lambda$ in sequence and basic bands $\\Lambda = 28$ . The training loss function is the root mean square error (RMSE) between reconstructed and ground-truth HSIs and adopts the multi-stage loss setting proposed in [43].", + "bbox": [ + 496, + 438, + 890, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 500, + 652, + 624, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 679, + 705, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following [5, 11, 17, 28, 42], we select 28 wavelengths from $450\\mathrm{nm}$ to $650\\mathrm{nm}$ by using spectral interpolation manipulation to derive HSIs. We conduct experiments on simulation and real datasets.", + "bbox": [ + 496, + 700, + 890, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Simulation and Real Data. Two simulation datasets, CAVE [32] and KAIST [9], and five real HSIs captured by the CASSI system developed in [28] are adopted. The CAVE dataset provides 32 HSIs with a spatial size of $512 \\times 512$ . The KAIST dataset includes 30 HSIs with a spatial size of $2704 \\times 3376$ . We use CAVE for simulation training and select 10 scenes from KAIST for simulation testing.", + "bbox": [ + 496, + 762, + 890, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. We adopt two image quality indexes including peak signal-to-noise ratio (PSNR), and structure", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25822", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c41ff77b099a8ced2ad89208d45437b39c0b325467a55798dc7b11a0eef1dc7.jpg", + "image_caption": [ + "RGB Image Measurement" + ], + "image_footnote": [], + "bbox": [ + 81, + 71, + 145, + 125 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c7233b0e7e76929826cee6c83310d550e72df55815efcb97a9c2c53d9121ecf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 148, + 75, + 223, + 125 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f588e08a219c13433ec2118b2791b3fdf36b762ef2611214c86894765fd50357.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 73, + 290, + 123 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/850ff6c95a21dfdca12a95807cdf7285051438af9b60c7ddeb3dd1dc01e30f7f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 71, + 356, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/65b3e9357ee96c96c5397a65bed73f0f40bf4ac24d7598d2481bf3bb3bbb4ec0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 71, + 421, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c99ca4ebd4ea90ac461e3f7763d541f0122ad22d9562ad1ac3fd3657c008caf4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 424, + 71, + 488, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fb52ba76f747165a02c73d18da3c759ceada24d788e2d3745c9e0142300bcbf9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 71, + 555, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/40e0364957d9ac90023c9d9111166234b65c9061090e1e683d3acedfafab6fb6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 558, + 71, + 622, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eff762c970ab0324414e4281cf740aaef3b54d3976216b57853efb40b22ec710.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 71, + 689, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f15620f9fe5552495a458ddafd176639ff838e7f3bb71aef655f8cc4065dbeb4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 71, + 756, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f29423dcb21d2706591cf03133abc22f367e4cc21fb98b314eb6ec903bc51a72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 71, + 821, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7a5680969a9f69eb01bd38e6c800f4f6d98bdbc3c243058aa0d16eef9bbdcc31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 825, + 71, + 890, + 122 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/213c9131c01798328d13231f0a66f4e85b881241e344dd23be8a7691b90242aa.jpg", + "image_caption": [ + "(a) Wavelength(nm)" + ], + "image_footnote": [], + "bbox": [ + 78, + 136, + 222, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3128e0f1234e93c7ad70edd0381839c5571f751723b04154b308301d38ceaa3b.jpg", + "image_caption": [ + "Figure 5. Reconstructed images of simulation scene1 with 4 out of 28 spectral channels by the state-of-the-art methods. Two regions in scene1 are selected for analyzing the spectra of the reconstructed results. The figure is better viewed in a zoomed-in PDF." + ], + "image_footnote": [], + "bbox": [ + 78, + 205, + 220, + 272 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5733d1f23ea23cc310a059495c9e5fb72ca8a44c033ce18ecd7e16615a54ea1f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 125, + 289, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aa01679e2c464b2e8fe154fec2009bc1f04e8cd95ad9a47b684fbdb4853f77bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 125, + 356, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d11ac4ccd0b43c715b9a3a45a9e38d6912e7871993ae304bdb6b3628dff3847.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 125, + 421, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/40a913d8bdd0597488d33c9eb8c8f4ecc600658a3cb0c9dd6a92d7bd2cfdd168.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ 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"images/2abd000406f68f2cc8265835265a0734536a60e58e1c693a75e02d213193c3d1.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 825, + 223, + 890, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "similarity (SSIM) [39] for quantitative evaluation. Specifically, PSNR measures the visual quality, while SSIM measures the structure similarity. Generally, higher values of PSNR and SSIM mean better reconstruction results.", + "bbox": [ + 75, + 321, + 468, + 382 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Simulation Scene", + "text_level": 1, + "bbox": [ + 76, + 393, + 245, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results. Table. 1 and Fig. 1 show the quantitative comparison of our SSR and the state-of-the-art (SOTA) methods: DIP-HSI [30], TSA-Net [28], DGSMP [18], GAPnet [27], HerosNet [42], HDNet [17], MST [3], CST [2], BIRNAT [8], DAUHST [5], RDLUF [11]. We can see that SSR significantly outperforms the other methods by over 2dB at the same FLOPs and exceeds the leading method RDLUF by more than 1dB with reduced computational demands. Concretely, our best model, SSR-L surpasses SOTA methods RDLUF, DAUHST, and DAUHST by 1.12, 2.33, and 3.11dB while less computational effort is required. Surprisingly, our small model SSR-S surpasses most methods when requiring the least parameters and FLOPs. Moreover, our middle model outperforms the best method RDLUF by 0.63dB when less than 1/2 FLOPs are required. It is worth noting that RDLUF adopts a stage parameter-sharing strategy and we take the same strategy to establish our SSR- $L^*$ , which brings performance degradation but still achieves a clear advantage over other methods with the least parameters. We found that the degradation comes from the stability of the method, that is, as the number of parameters increases, the performance of our SSR steadily increases and RDLUF decreases.", + "bbox": [ + 75, + 416, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual comparison. We provide the visual comparison of simulation scene7 with 4 out of 28 spectral channels in Fig. 5. SSR-L successfully recovers the clear pattern and sharp edge on the cup when the other methods all suffer from blurred or distorted effects. In addition, we plot the spectral curves of two regions in scene1 in the bottom-left of Fig. 5. It's intuitive that SSR-L has a prominent higher correlation with the reference spectra, which demonstrates the effectiveness of our spectra-wise attention.", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/32e2ce8734b1ebcc553df50e2aa933bb7de777127ce0239b47d4ce53aeaec268.jpg", + "table_caption": [ + "Table 2. Ablation study of WSSA and ARB." + ], + "table_footnote": [], + "table_body": "
Baseline-1WSSAARBPSNRSSIMParams (M)FLOPs (G)
✓36.600.9561.0614.43
✓✓37.760.9651.3018.82
✓✓✓39.190.9711.7326.37
", + "bbox": [ + 503, + 334, + 888, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Real Scene Results", + "text_level": 1, + "bbox": [ + 500, + 416, + 679, + 430 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effect of the proposed method on the real scenes, five measurements captured by the CASSI system are utilized for testing and the ground truths of the scenes are unavailable. For fair comparisons, all methods are trained on the CAVE and KAIST datasets jointly using the fixed real mask with 11-bit shot noise injected. The bottom two rows of Fig. 6 plot the visual comparisons of the proposed SSR-S and the existing SOTA methods while the top two rows plot the visual comparisons of different spectra-wise transformers [3, 4]. It is intuitive to see that our SSR-S restores clearer spatial textures and sharper edges than previous spectra-wise transformers in the top two rows, which shows the effect of spatial modulation. Compared with other methods in the bottom two rows, SSR-S obtains clearer results in these two bands when other methods fail to recover these two bands, demonstrating the effectiveness of our spatial alignment strategy.", + "bbox": [ + 496, + 440, + 892, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Experiment", + "text_level": 1, + "bbox": [ + 500, + 709, + 697, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this part, we adopt the CAVE and KAIST datasets to conduct ablation studies.", + "bbox": [ + 496, + 733, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of WSSA and ARB. We first conduct a break-down ablation experiment to investigate the effect of each component towards higher performance. The results are listed in Table. 2. The baseline-1 model is derived by removing our WSSA and ARB from SSR-S and yields $36.60\\mathrm{dB}$ . When we successively apply our WSSA and ARB, the model continuously achieves $1.16\\mathrm{dB}$ and $1.43\\mathrm{dB}$ improvements. These results suggest the effectiveness of WSSA and ARB.", + "bbox": [ + 496, + 763, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25823", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0c7bbf5863d38458a426c15b6df5a6e99b9665515ebbb8df1b48b20f96008698.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 69, + 890, + 349 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e2ce8719680c23d88a00478c790ed07862e7565f5fe4a873b6f782d7e75268b9.jpg", + "table_caption": [ + "Table 3. Ablation study of different self-attention schemes." + ], + "table_footnote": [], + "table_body": "
MetricBaseline-2S-MSA [3]Swin-MSA [25]HS-MSA [5]WSSA*WSSA
PSNR32.0132.8533.0133.0933.1933.30
SSIM0.9080.9160.9180.9190.9220.924
Params (M)1.031.291.291.291.291.29
FLOPs (G)13.8418.1519.0419.0418.1518.65
", + "bbox": [ + 83, + 402, + 467, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Self-Attention Scheme Comparison. We compare WSSA with other self-attention and report the results in Table. 3. We adopt the half operation [5] in Swin-MSA [25] to keep the computation almost the same and use multi-head attention in the spectral dimension of WSSA* to align with S-MSA[3]. Baseline-2 is SSR-S that retains only the ERB and removes attention and yields 32.01dB. WSSA yields the most significant improvement of 1.29dB, which is 0.45dB, 0.29dB, and 0.21dB higher than S-MSA [3], Swin-MSA [25], and HS-MSA [5], which shows the effectiveness of WSSA. In addition, WSSA* and WSSA achieve 0.34dB and 0.45dB gain than S-MSA respectively, which demonstrates the role of considering local differences and modeling global spectral information.", + "bbox": [ + 75, + 488, + 468, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Influence of Multi-head attention and Mean effect. We demonstrate the influence of multi-head attention and mean effect on the spectra-wise self-attention through further experiments on the relationship between performance and token dim (window size) in WSSA and MSSA, which is shown in Fig. 7. Intuitively, the large window size would suffer from limited performance, which illustrates the influence of the mean effect. Performance degradation also occurs when the window size is too small to retain complete feature information. In our experiments, $8 \\times 8$ window size optimally balances retaining feature information while minimizing the mean effect, which produces the highest performance of 33.3dB. When the token dim is small, WSSA", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a6cfbecee2bdd53ef115aa6926374723d641ea5960035cc626a5dd237cde9ae1.jpg", + "image_caption": [ + "Figure 6. Reconstructed images of real scene2 and scene4 with 2 and 4 out of 28 spectral channels separately by the state-of-the-art methods. Compared with other competing methods, our SSR recovers more details and clear content.", + "Figure 7. Influence of token dim in spectra-wise attention." + ], + "image_footnote": [], + "bbox": [ + 517, + 380, + 857, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "clearly performs better than MSSA, which shows the role of maintaining spatial correlation. When the token dim is large, MSSA is slightly better than WSSA, which may be related to the shift in the imaging process and the strip pattern can contain some shift information.", + "bbox": [ + 496, + 498, + 890, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 588, + 617, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we analyze the influence of multi-head attention and mean effect on the spectra-wise transformer, and a novel SSR method is proposed to improve spectral snapshot reconstruction. To model the global spectral information, consider the local difference, and maintain spatial correlation, WSSA is proposed to better utilize spectral similarity. ARB leverages CMB to address the interaction between adjacent windows of WSSA and learn spatial representation when SAB is specially designed to mitigate spatial degradation in low-quality bands through a novel spatial alignment strategy. Extensive experiments on simulation and real scenes show the effectiveness of the proposed modules. Our SSR at different scales also significantly outperforms the state-of-the-art methods with less cost.", + "bbox": [ + 496, + 613, + 890, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62302394 and 62106063, the China Postdoctoral Science Foundation under Grant 317751, and the Natural Science Foundation of Shaanxi under Grant 2023-JC-QN-0757.", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25824", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] José M. Bioucas-Dias and Mário A. T. Figueiredo. A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration. 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Photonics Research, 9(2):B18-B29, 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 372 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "25826", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Spectral Snapshot Reconstruction with Spectral-Spatial Rectification/1d035099-0d94-4bf4-acc9-0b3e57ed6aca_model.json b/2024/Improving Spectral Snapshot Reconstruction with Spectral-Spatial Rectification/1d035099-0d94-4bf4-acc9-0b3e57ed6aca_model.json new file mode 100644 index 0000000000000000000000000000000000000000..232ae9f27e4bbdba5b517f1bc0a2760e8e36de51 --- /dev/null +++ b/2024/Improving Spectral Snapshot Reconstruction with Spectral-Spatial Rectification/1d035099-0d94-4bf4-acc9-0b3e57ed6aca_model.json @@ -0,0 +1,2673 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.89, + 0.153 + ], + "angle": 0, + "content": "Improving Spectral Snapshot Reconstruction with Spectral-Spatial Rectification" + }, + { + "type": "text", + "bbox": [ + 0.154, + 0.18, + 0.835, + 0.199 + ], + "angle": 0, + "content": "Jiancheng Zhang \\(^{1}\\), Haijin Zeng \\(^{2}\\), Yongyong Chen \\(^{3}\\), Dengxiu Yu \\(^{1}\\), Yin-Ping Zhao \\(^{1,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.199, + 0.897, + 0.218 + ], + "angle": 0, + "content": "1 Northwestern Polytechnical University, 2 IMEC-UGent, 3 Harbin Institute of Technology (Shenzhen)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.269 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.285, + 0.474, + 0.662 + ], + "angle": 0, + "content": "How to effectively utilize the spectral and spatial characteristics of Hyperspectral Image (HSI) is always a key problem in spectral snapshot reconstruction. Recently, the spectra-wise transformer has shown great potential in capturing inter-spectra similarities of HSI, but the classic design of the transformer, i.e., multi-head division in the spectral (channel) dimension hinders the modeling of global spectral information and results in mean effect. In addition, previous methods adopt the normal spatial priors without taking imaging processes into account and fail to address the unique spatial degradation in snapshot spectral reconstruction. In this paper, we analyze the influence of multihead division and propose a novel Spectral-Spatial Rectification (SSR) method to enhance the utilization of spectral information and improve spatial degradation. Specifically, SSR includes two core parts: Window-based Spectra-wise Self-Attention (WSSA) and spAtial Rectification Block (ARB). WSSA is proposed to capture global spectral information and account for local differences, whereas ARB aims to mitigate the spatial degradation using a spatial alignment strategy. The experimental results on simulation and real scenes demonstrate the effectiveness of the proposed modules, and we also provide models at multiple scales to demonstrate the superiority of our approach. https://github.com/ZhangJC-2k/SSR" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.695, + 0.21, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.47, + 0.875 + ], + "angle": 0, + "content": "The advent of compressed sensing introduced the coded aperture snapshot spectral compressive imaging (CASSI) system [13, 29, 36], addressing drawbacks in traditional hyperspectral cameras regarding efficiency and cost-effectiveness, gaining significant attention. This system offers the promise of swift and cost-efficient capture of Hyperspectral Images (HSIs). However, the inherent ill-posedness of decoding 3D HSIs from 2D measurements poses a significant challenge for reconstruction algorithm design. Consequently, various model-based [1, 23, 24, 33," + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.257, + 0.872, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.433, + 0.895, + 0.489 + ], + "angle": 0, + "content": "Figure 1. Comparison of PSNR-FLOPs between our SSR and previous reconstruction methods. Our SSR significantly outperforms other methods over 2dB at the same FLOPs when surpassing the state-of-the-art method over 1dB with fewer FLOPs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.893, + 0.563 + ], + "angle": 0, + "content": "38, 40] and learning-based [2-6, 17, 18, 28, 37, 42] approaches have emerged to tackle this challenge. Within the realm of reconstruction algorithms, the effective utilization of diverse priors remains a pivotal research challenge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.895, + 0.793 + ], + "angle": 0, + "content": "Model-based methods initially adopt total variation [20, 40], low-rank [24], sparsity [21, 34] and more traditional hand-craft priors [1, 23, 24, 33, 38] to construct the optimization model, which preliminarily shows the practical feasibility of snapshot spectral reconstruction. With the advancement of deep learning, both convolutional neural networks (CNNs) [6, 17, 18, 28, 37, 42] and transformers [3-5, 11] have been successively introduced for learning the spatial and spectral characteristics of HSIs. They serve as end-to-end denoisers [3, 4, 6, 17, 28] or deep image priors [5, 11, 18, 37, 42] in learning-based methods. These advancements have led to significant progress in both real-world and simulated scenario reconstructions. In addition, the effective utilization of spectral and spatial characteristics has also naturally become a research hotspot." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Previous CNN methods such as TSA-Net [28], HDNet [17], DGSMP [18], and HerosNet [42], along with spatial transformers like Swin Transformer [25] and DAUHST [5], excel in learning spatial representations but do not effectively utilize the distinctive spectral characteristics inherent in HSIs. Conversely, spectra-wise transformers such as MST [3], MST++ [4], and RDLUF [11] show promising" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25817" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "potential in snapshot spectral reconstruction by exploiting inter-spectral similarities. However, their implementations follow the conventional transformer architecture, involving multi-head division in the spectral dimension, which limits the modeling of global spectral similarities and results in mean effect. Furthermore, in spectral snapshot imaging, some spatial degradation occurs in certain bands due to masking, shifting, and compression factors. Unfortunately, existing spatial and spectral networks lack tailored designs to mitigate such degradation effectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.544 + ], + "angle": 0, + "content": "To optimize the utilization of spectral information and mitigate distinctive spatial degradation, we introduce the Spectral-Spatial Rectification (SSR) method into snapshot spectral reconstruction. Specifically, SSR comprises two key components: Window-based Spectral Self-Attention (WSSA) and spAtial Rectification Blocks (ARB). WSSA divides the features into multiple local windows in the spatial dimension, facilitating global spectral self-attention computations and the local difference consideration. Addressing the interaction gap between windows of WSSA, ARB leverages a Convolution Modulated Block (CMB). This block employs sliding large-kernel convolutions to interact with features between windows and learn effective spatial representation. Subsequently, to mitigate spatial degradation, ARB integrates a novel spatial alignment strategy. It assists low-quality bands in leveraging information from high-quality bands through learning a unified spatial representation and spectral weights, which further optimizes the utilization of spatial information. Overall, our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.545, + 0.47, + 0.605 + ], + "angle": 0, + "content": "- We analyze the influence of multi-head division on previous spectra-wise transformers and propose Window-based Spectra-wise Self-Attention to model global spectral information while accounting for local differences." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.606, + 0.47, + 0.667 + ], + "angle": 0, + "content": "- A Spatial Rectification Block is specially designed to enhance spatial representation and mitigate the spatial degradation in low-quality bands through large-kernel convolutions and a novel spatial alignment strategy." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.666, + 0.47, + 0.711 + ], + "angle": 0, + "content": "- The qualitative and quantitative results of real and simulation experiments demonstrate that our SSR method significantly improves spectral snapshot reconstruction." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.545, + 0.47, + 0.711 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.22, + 0.74 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The model-based methods [1, 20, 21, 23, 24, 33, 34, 38, 40] construct convex optimization models with some specific priors such as total variation [20, 40], low-rankness [24], and sparsity [21, 34] according to the physical schema of CASSI then solve the problem in an iterative manner to obtain reconstructed images. They have good interpretability and low cost, yet lack performance guarantee. Subsequently, the rise of deep learning [14, 15, 22] has facilitated the rapid development of spectral snapshot reconstruction. To improve reconstruction quality, Plug-and-Play" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "methods [41, 44] plug pre-trained deep networks as priors, which make great progress in performance but are still limited by slow reconstruction speed. Along with faster inference and better results, the CNN-based end-to-end denoisers [17, 28, 31] quickly achieved better results by establishing a mapping between measurements and HSIs, but also brought huge memory and computation costs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.893, + 0.47 + ], + "angle": 0, + "content": "Recently, the transformer-based end-to-end denoisers [2-4] which capture data similarity and long-range dependence have shown impressive performance in both simulation and real scenes. These methods adopt self-attention to learn effective spatial and spectral representation, achieving very high parameter and computational efficiency. Following this, the unfolding methods [5, 11] regard transformers as deep priors for optimization formulas and improve iterative frameworks through end-to-end training. In these approaches, CNNs and transformers play a huge role either as end-to-end denoisers or as deep priors. While previous CNNs and spatial transformers fail to effectively utilize the spectral characteristics inherent in HSIs, spectra-wise transformer [3, 4, 11] has shown great potential in spectral tasks and attracted wide attention. However, current spectra-wise transformers follow classic multi-head design [12, 25, 35] and suffer from the loss of global spectral information and the limitation of ignoring local differences." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.482, + 0.81, + 0.5 + ], + "angle": 0, + "content": "3. Spectral Snapshot Imaging Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Mathematically, we assume a spectral image patch with \\(\\Lambda\\) bands \\(\\{F_{\\lambda}\\}_{\\lambda = 1}^{\\Lambda}\\in \\mathbb{R}^{H\\times W}\\), where \\(H\\) and \\(W\\) represents the HSI's height and weight. Image frame \\(F_{\\lambda}\\) is modulated by a physical mask with pattern \\(M\\in \\mathbb{R}^{H\\times W}\\) to get modulated image frame \\(F_{\\lambda}^{\\prime}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.583, + 0.891, + 0.601 + ], + "angle": 0, + "content": "\\[\nF _ {\\lambda} ^ {\\prime} = M \\circ F _ {\\lambda}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.735 + ], + "angle": 0, + "content": "where \\(\\circ\\) denotes Hadamard's (element-wise) product. Then the modulated image frames of different wavelengths \\(\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}\\) are separated to different positions by the disperser. After that, \\(\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}\\) distributed across different bands are shifted spatially and summed element-wise. Thus, \\(\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}\\) are compressed to a coded measurement:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.735, + 0.891, + 0.775 + ], + "angle": 0, + "content": "\\[\nG (m, n) = \\sum_ {i = 1} ^ {\\Lambda} F _ {\\lambda} ^ {\\prime} (m, n + D (\\lambda)), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.892, + 0.874 + ], + "angle": 0, + "content": "where \\(m\\) and \\(n\\) index the spatial coordinates, \\(D(\\lambda) = d(\\lambda - 1)\\), \\(d\\) represents pixels shift between adjacent bands. Note Eq. (2) assumes a dispersion along the vertical dimension, and the derivation is also applicable for horizontal dispersion. The imaging model in Eq. (2) can be rewritten in the matrix-vector form as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.665, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "\\[\ng = \\Phi f, \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25818" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.073, + 0.41, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.073, + 0.647, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.073, + 0.891, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.296, + 0.855, + 0.311 + ], + "angle": 0, + "content": "Figure 2. (a)-(c) The overall architecture of SSR, SSRUnet, and SSRB. LMP is achieved via a formula. (d) Details of WSSA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.471, + 0.412 + ], + "angle": 0, + "content": "where \\( g \\in \\mathbb{R}^{HW} \\), \\( f \\in \\mathbb{R}^{HW\\Lambda} \\) are the vectorized representation of the compressed image \\( G \\) and the original spectral image \\( F \\) respectively, and \\( \\Phi \\in \\mathbb{R}^{HW \\times HW\\Lambda} \\) is the sensing matrix that describes the system imaging model. In spectral snapshot reconstruction, what we need to do is recover 3D HSI \\( f \\) from the compressed 2D measurement \\( g \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.169, + 0.438 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.555 + ], + "angle": 0, + "content": "Existing spectral and spatial network designs [2-5, 11] are limited by the direct application of traditional multi-head division and unique spatial degradation of snapshot spectral imaging. To address the limitations, we propose the Spectral-Spatial Rectification (SSR) method to better model the spectral information, enhance spatial representation, and improve spatial degradation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.564, + 0.274, + 0.578 + ], + "angle": 0, + "content": "4.1. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.471, + 0.83 + ], + "angle": 0, + "content": "An overview of SSR is presented in Fig. 2 (a), we adopt a multistage network including initialization and \\(N\\) cascaded stages, and each stage consists of Linear Manifold Projection (LMP), Spectral-Spatial Rectification Unet (SSRUnet), and spAtial Rectification Block (ARB). First, the compressed measurement \\(g\\) is reversed to the initial shape [3] and the 2D mask is repeated in channel dimension to obtain the 3D mask. Then the two are inputted to a \\(1 \\times 1\\) convolution kernel \\((conv1 \\times 1)\\) to get the initialization. In each stage, LMP is adopted to assist the reconstruction based on the imaging model. Then the SSRUnet is employed to refine the input through novel spatial and spectral design. Finally, ARB is used to further improve spatial degradation in reconstruction. For the core module SSRUnet, as illustrated in Fig. 2 (b), the \\(conv3 \\times 3s\\) with residual are utilized to embed mask information into input \\(X\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.84, + 0.47, + 0.871 + ], + "angle": 0, + "content": "\\[\nX _ {M E} = \\operatorname {C o n v} _ {3 \\times 3} (X) \\circ \\left(T _ {I} + \\operatorname {C o n v} _ {3 \\times 3} (\\text {M a s k})\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.9 + ], + "angle": 0, + "content": "where \\(X_{ME}\\) is the features embedded with the mask, \\(T_{I}\\) is an all-one tensor and \\(Mask\\) is the 3D mask obtained in ini" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.608 + ], + "angle": 0, + "content": "tialization. Then SSRUnet with three layers and \\( conv3 \\times 3 \\) are employed to extract the deep feature which is combined with the input as a residual to produce a refined output. The SSRUnet consists of downsampling modules (\\( conv4 \\times 4 \\)), Spectral-Spatial Rectification Block (SSRB), upsampling modules (\\( deconv2 \\times 2 \\)), and Fusion modules (\\( conv1 \\times 1 \\)). Spectral-Spatial Rectification Block (SSRB). SSRB is the basic module of SSRUnet. As shown in Fig. 2 (c), the implicit positional information [10] is firstly embedded in the input for applying self-attention later in SSRB. Each SSRB is the sequential combination of the spEctral Rectification Block (ERB) and ARB. Fig. 2 (c) illustrates the components of ERB and ARB, i.e., a Feed Forward Network(FFN) and a Window-based Spectral Self-Attention (WSSA) for ERB, a Convolution Moudulated Block (CMB) and a Spatial Alignment Block (SAB) for ARB, and same Layer Normalization (LN) and Group Normalization (GN) for ERB and ARB. WSSA is detailed in Fig. 2 (d) and FFN consists of two linear layers sandwiched with depth-wise \\( conv3 \\times 3 \\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.62, + 0.75, + 0.636 + ], + "angle": 0, + "content": "4.2. Spectral Rectification Block" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Spectral self-attention is a promising approach to utilize spectral characteristics for HSI tasks. However, we find that the previous spectra-wise transformer [3, 4, 11] directly considers a band as a token and follows traditional spatial self-attention design, i.e., multi-head division in spectral (channel) dimension, which ignores the local differences in spectral distribution and results in mean effect and nonglobal spectral utilization. To solve the problem, we propose the ERB based on WSSA to consider local differences and model global spectral information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The Influence of Multi-Head Division in Spectral (Channel) Dimension. In the classic transformer design [12, 25, 35], the use of multi-head division in the channel dimension is common and brings some gains. Possibly affected by this, the previous spectra-wise transformer in spectral snapshot reconstruction also divides multi-head in spectral dimension as shown in Fig. 3 (a), which results in the sep" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25819" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.073, + 0.382, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.205, + 0.362, + 0.217 + ], + "angle": 0, + "content": "(a) Multi-head Division in Spectral Dimension" + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.08, + 0.547, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.422, + 0.205, + 0.506, + 0.217 + ], + "angle": 0, + "content": "(b) Mean Effect" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.089, + 0.7, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.2, + 0.7, + 0.222 + ], + "angle": 0, + "content": "(c) Multi-head Division in Spatial Dimension" + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.092, + 0.874, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.205, + 0.877, + 0.217 + ], + "angle": 0, + "content": "(d) Window-based Attention" + }, + { + "type": "image_caption", + "bbox": [ + 0.183, + 0.228, + 0.785, + 0.242 + ], + "angle": 0, + "content": "Figure 3. (a)-(c) The influence of multi-head attention and mean effect, (d) The illustration of WSSA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.251, + 0.47, + 0.341 + ], + "angle": 0, + "content": "aration of spectral information and failure to model global spectral information. It's very easy to get confused because the spectral transformer is in contrast to the spatial transformer, where the characteristic dimension of the former is the spatial dimension, and the characteristic dimension of the latter is the spectral (channel) dimension." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.523 + ], + "angle": 0, + "content": "The Influence of Mean Effect. In addition, considering that HSIs depict the spectral distribution of scenes, the similarities of different regions should be different but previous multi-head division results in all regions sharing the same similarity. When treating the whole band as a token to calculate spectral self-attention, we obtain the mean of all region similarities in the band and the local differences between regions are lost, which we call the 'Mean Effect'. Define \\(\\Lambda\\) features \\(\\{f_{\\lambda}\\}_{\\lambda = 1}^{\\Lambda}\\) where feature dimension consists of \\(p\\) different patterns (regions), i.e., \\(f_{\\lambda} = [f_{\\lambda}^{1}, f_{\\lambda}^{2}, \\ldots, f_{\\lambda}^{p}]\\), the influence of mean effect on the similarity calculation can be simply described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.528, + 0.469, + 0.564 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s i m} \\left(f _ {i} ^ {k}, f _ {j} ^ {k}\\right)\\rightarrow \\frac {1}{p} \\sum_ {m = 1} ^ {p} \\operatorname {s i m} \\left(f _ {i} ^ {m}, f _ {j} ^ {m}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.734 + ], + "angle": 0, + "content": "where the left part denotes the expected similarity of the \\(k\\)th pattern between \\(f_{i}^{k}\\) and \\(f_{j}^{k}\\), and the right part represents the obtained similarity in previous approaches. We also present an example in Fig. 3 (b), the average similarity and local region similarity between the red band and other bands are marked with red numbers and black numbers respectively. To demonstrate the validity of our theory, we carried out ablation experiments of different region sizes, i.e., window size under the same conditions later. In addition, the mean effect may explain why multi-head attention is more effective than single-head attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Multi-Head Division in Spatial Dimension. When realizing appropriate feature dimension and mean effect, it was natural to treat the entire band frame as a token and then directly divide multi-head [35] in the merged spatial dimension to calculate self-attention, which we call MSSA later for short. However, as shown in Fig. 3 (c), this would split the entire image into (incomplete) strip shapes on each head, which mitigates the mean effect to some extent but breaks the spatial correlation of features. That is, adjacent areas are divided into different heads, while areas that are far apart in space are divided into the same head." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.433 + ], + "angle": 0, + "content": "Window-based Spectral Self-Attention (WSSA). To capture the global spectral similarity, solve the mean effect, and maintain spatial correlation, WSSA divides features into a number of windows spatial-wisely, and then the spectrawise self-attention is calculated within windows to avoid the interference of each other, which is shown in Fig. 3 (d). Specifically, define input \\( X \\in \\mathbb{R}^{H \\times W \\times C} \\), as shown in Fig. 2 (d), \\( X \\) is first linearly projected to \\( 3C \\) channels tensor via a \\( 1 \\times 1 \\) convolution then uniformly divides the tensor channel-wisely into the query \\( (Q) \\), key \\( (K) \\), value \\( (V) \\). Subsequently, \\( Q, K, V \\) are split spatial-wise into \\( HW / M^2 \\) windows with size of \\( \\mathbb{R}^{M \\times M \\times C} \\) separately:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.44, + 0.891, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\left\\{Q _ {i}, K _ {i}, V _ {i} \\right\\} _ {i = 1} ^ {H W / M ^ {2}} = Q, K, V, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.468, + 0.891, + 0.502 + ], + "angle": 0, + "content": "where \\(Q_{i},K_{i},V_{i}\\in \\mathbb{R}^{M\\times M\\times C}\\) and are then reshaped into shape \\(\\mathbb{R}^{M^2\\times C}\\) as tokens to calculate attention as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.509, + 0.891, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\text {A t t e n t i o n} _ {i} = \\operatorname {S o f t M a x} \\left(Q _ {i} ^ {T} K _ {i} / M\\right) V _ {i}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.534, + 0.892, + 0.595 + ], + "angle": 0, + "content": "where \\(\\mathbf{M}\\) is used as the scale factor before applying the softmax function. Then the outputs of \\(HW / M^2\\) attention are reshape in \\(\\mathbb{R}^{M\\times M\\times C}\\) and merge together in the original arrangement to undergo a conv1 \\(\\times 1\\) projection:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.602, + 0.891, + 0.623 + ], + "angle": 0, + "content": "\\[\nX ^ {\\prime} = \\left\\{A t t e n t i o n _ {i} \\right\\} _ {i = 1} ^ {H W / M ^ {2}} W _ {1}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.767 + ], + "angle": 0, + "content": "where \\( W_{1} \\in \\mathbb{R}^{C \\times C} \\) are weight matrices of a \\( conv1 \\times 1 \\) and \\( X' \\) is the final output in \\( \\mathbb{R}^{H \\times W \\times C} \\). Different from multi-head self-attention which implements token embedding and then divides heads, WSSA first implements windows split then reshaping into tokens, which preserves the spatial correlation of each token. Regarding WSSA as a special multi-head self-attention, the number of WSSA heads is more, often hundreds of thousands, far more than the number of multi-head attention." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.769, + 0.89, + 0.799 + ], + "angle": 0, + "content": "Computational Complexity. The computational complexity of WSSA is displayed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.805, + 0.891, + 0.833 + ], + "angle": 0, + "content": "\\[\nO (W S S A) = 4 H W C ^ {2} + 2 M ^ {2} C ^ {2} \\frac {H W}{M ^ {2}} = 6 H W C ^ {2}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The computational complexity of WSSA is linear to the spatial size \\( HW \\) and window size-independent, meaning that there is no additional computation cost when we improve spectral utilization." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25820" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.072, + 0.891, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.307, + 0.893, + 0.337 + ], + "angle": 0, + "content": "Figure 4. (a) Display of spatial degradation in spectra-wise transformers. (b) The details of CMB. (c) The effect of large kernel convolution in CMB. (d) The details of SAB. (e) Spatial alignment strategy of SAB." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.351, + 0.318, + 0.367 + ], + "angle": 0, + "content": "4.3. Spatial Rectification Block" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.827 + ], + "angle": 0, + "content": "The utilization of WSSA enhances the capability of spectral information capture. However, a limitation arises from the absence of interaction between adjacent windows within WSSA, potentially leading to discontinuous spatial representation and the occurrence of blocking artifacts, as highlighted by [7]. Additionally, unique spatial degradation occurs due to mask, shift, and compression in spectral snapshot imaging. To address these concerns, we propose a spA tial Rectification Block (ARB) comprising a Convolution Modulated Block (CMB) and a Spatial Alignment Block (SAB). This ARB aims to foster interaction between adjacent windows and alleviate spatial degradation in the HSIs. Convolution Modulated Block (CMB). Here, we try to solve two problems: (1) When different windows cannot interfere with each other, WSSA also fails to exchange information, which leads to discrete spatial expression and may lead to blocking artifacts [7]. (2) As shown in the top two rows of Fig .4 (a), over-smoothing demonstrates that the spatial representation ability of a single spectra-wise transformer is not sufficient. To solve these two problems and inspired by the development of large kernel convolution in high-level tasks, we adopted a Convolution Modulated Block (CMB) proposed in [16] to modulate spatial information and make adjacent windows interact with each other through large kernel convolution sliding as shown in Fig. 4 (b). CMB modulates spatial information in a similar manner to self-attention but much more efficiently. Specifically, given the input tokens \\(X\\in \\mathbb{R}^{H\\times W\\times C}\\), we use a simple depth-wise convolution with kernel size \\(11\\times 11\\) to calculate the modulated attention \\(A\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.842, + 0.469, + 0.858 + ], + "angle": 0, + "content": "\\[\nA = D C o n v _ {1 1 \\times 1 1} (X W _ {2}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(W_{2}\\in \\mathbb{R}^{H\\times W\\times C}\\) are weight matrices of conv1 x 1s, and \\(DConv_{11\\times 11}\\) denotes a depth-wise convolution with" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.892, + 0.396 + ], + "angle": 0, + "content": "kernal size \\(11 \\times 11\\). Then we adopt the element-wise product and attention \\(A\\) to modulate the project feature \\(V'\\) to get the output \\(Z\\):" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.397, + 0.891, + 0.413 + ], + "angle": 0, + "content": "\\[\nZ = \\left(A \\circ V ^ {\\prime}\\right) W _ {4}, V ^ {\\prime} = X W _ {3}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.528 + ], + "angle": 0, + "content": "where \\( W_{3} \\) and \\( W_{4} \\in \\mathbb{R}^{C \\times C} \\) are weight matrices of \\( conv1 \\times 1s \\). On the one hand, CMB could effectively improve the spatial representation of features through modulation operation. On the other hand, CMB enables the pixels between adjacent windows of WSSA to interact spatial-wisely when depth-wise convolution kernel size \\( 11 \\times 11 \\) is greater than patch size \\( 8 \\times 8 \\), as demonstrated in Fig. 4 (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.893, + 0.875 + ], + "angle": 0, + "content": "Spatial Alignment Block (SAB). As shown in the bottom two rows of Fig. 4 (a), we observe that the reconstruction results of some bands have more spatial degradation such as distortion and deformation, which is not common in other HSI tasks. Thus, we think this may be related to the unique imaging process. As shown in Fig. 4 (e), shift and compression in the imaging process mix information from different spatial locations, and spatial texture recovery in bands with low spectral density may be difficult, which is neglected by previous methods. Considering that the low-density bands can be obtained by multiplying the high-density bands by weights, we can utilize the high-quality bands to improve the spatial texture of the low-quality bands through a novel spatial alignment strategy, as shown in Fig. 4 (e). To achieve this, a Spatial Alignment Block (SAB) is proposed to improve spatial degradation. As shown in 4 (d), we adopt different convolution kernels to estimate spatial texture distribution which corresponds to the high-density part, and learn spectral weights in SAB when two linear layers are used to mix channel information. Specifically, given the input feature \\( F \\in \\mathbb{R}^{H \\times W \\times C} \\), we use a convolution with kernel size \\( 3 \\times 3 \\) and \\( GELU \\) activation function to learn the spatial texture \\( T \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "\\[\nT = \\psi \\left(\\operatorname {C o n v} _ {3 \\times 3} \\left(F W _ {5}\\right)\\right), \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25821" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.105, + 0.072, + 0.864, + 0.086 + ], + "angle": 0, + "content": "Table 1. The PSNR (upper entry in each cell) in dB and SSIM (lower entry in each cell) results of the test methods on 10 scenes." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.087, + 0.885, + 0.426 + ], + "angle": 0, + "content": "
AlgorithmsReferenceParamsGFLOPsScene1Scene2Scene3Scene4Scene5Scene6Scene7Scene8Scene9Scene10Avg
DIP-HSI [30]ICCV 202133.8564.4232.6827.2631.3040.5429.7930.3928.1829.4434.5128.5131.26
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
TSA-Net [28]ECCV 202044.25110.0632.0331.0032.2539.1929.3931.4430.3229.3530.0129.5931.46
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
DGSMP [18]CVPR 20213.5884.7733.2632.0933.0640.5428.8633.0830.7431.5531.6631.4432.63
0.9150.8980.9250.9640.8820.9370.8860.9230.9110.9250.917
GAP-Net [27]IJCV 20234.2778.5833.7433.2634.2841.0331.4432.4032.2730.4633.5130.2433.26
0.9110.9000.9290.9670.9190.9250.9020.9050.9150.8950.917
HerosNet [42]CVPR 202211.27414.7635.6935.0134.8238.0733.1834.9433.5833.1933.0433.0134.45
0.9730.9680.9670.9850.9690.9760.9620.9680.9640.9650.970
HDNet [17]CVPR 20222.37154.7635.1435.6736.0342.3032.6934.4633.6732.4834.8932.3834.97
0.9350.9400.9430.9690.9460.9520.9260.9410.9420.9370.943
MST [3]CVPR 20222.0328.1535.4035.8736.5142.2732.7734.8033.6632.6735.3932.5035.18
0.9410.9440.9530.9730.9470.9550.9250.9480.9490.9410.948
CST [2]ECCV 20223.040.1035.9636.8438.1642.4433.2535.7234.8634.3436.5133.0936.12
0.9490.9550.9620.9750.9550.9630.9440.9610.9570.9450.957
BIRNAT [8]TPAMI 20234.402122.6636.7937.8940.6146.9435.4235.3036.5833.9639.4732.8037.58
0.9510.9570.9710.9850.9640.9590.9550.9560.9700.9380.960
DAUHST [5]NeurIPS 20226.1579.5037.2539.0241.0546.1535.8037.0837.5735.1040.0234.5938.36
0.9580.9670.9710.9830.9690.9700.9630.9660.9700.9560.967
RDLUF [11]CVPR 20231.81115.3437.9440.9543.2547.8337.1137.4738.5835.5041.8335.2339.57
0.9660.9770.9790.9900.9760.9750.9690.9700.9780.9620.974
SSR-SOurs1.7326.3738.2240.0542.5747.4636.5037.3337.6035.7041.3735.0639.19
0.9630.9720.9750.9860.9720.9710.9640.9680.9750.9590.971
SSR-MOurs3.4552.6538.6141.3543.9448.3237.8038.0738.5436.8242.7235.7940.20
0.9670.9780.9790.9880.9770.9750.9690.9740.9800.9650.975
SSR-LOurs5.1878.9339.0742.0444.4948.8038.6438.5039.1636.9643.1236.0840.69
0.9700.9810.9800.9900.9800.9780.9710.9760.9820.9680.978
SSR-L*Ours1.7378.9338.8141.5143.7648.6238.3237.8538.5036.8542.6435.8240.27
0.9680.9790.9790.9880.9790.9750.9690.9740.9800.9650.976
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.47, + 0.515 + ], + "angle": 0, + "content": "where \\(T \\in \\mathbb{R}^{H \\times W \\times 1}\\), \\(\\psi\\) is GELU activation function and \\(W_5 \\in \\mathbb{R}^{C \\times C}\\) are weight matrices of the linear layer. Meanwhile, we use a depth-wise convolution with kernel size \\(3 \\times 3\\) and Sigmoid activation function to learn spectral element-wise weight as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.527, + 0.469, + 0.543 + ], + "angle": 0, + "content": "\\[\nS W = \\sigma \\left(D C o n v _ {3 \\times 3} \\left(F W _ {5}\\right)\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.613 + ], + "angle": 0, + "content": "where \\( SW \\in \\mathbb{R}^{H \\times W \\times C} \\), \\( \\sigma \\) is Sigmoid activation function. Finally, we use multiple element-wise products and a conv1 × 1 projection \\( W_{6} \\) to calculate the output \\( Y \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.614, + 0.469, + 0.632 + ], + "angle": 0, + "content": "\\[\nY = \\left\\{T \\circ S W _ {i} \\right\\} _ {i = 1} ^ {C} W _ {6}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.638, + 0.381, + 0.655 + ], + "angle": 0, + "content": "where \\( Y \\in \\mathbb{R}^{H \\times W \\times C} \\) and \\( SW_{i} \\in \\mathbb{R}^{H \\times W \\times 1} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.383, + 0.681 + ], + "angle": 0, + "content": "4.4. Linear Manifold Projection (LMP)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.776 + ], + "angle": 0, + "content": "Eq. (3) is a key constraint in spectral compression reconstruction. To take advantage of this prior, we introduce a Linear Manifold Projection (LMP) proposed in GAP-Net [27] to assist the reconstruction. We add an additional parameter to control projection intensity and perform the LMP as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.778, + 0.469, + 0.797 + ], + "angle": 0, + "content": "\\[\nf ^ {\\prime} = f + \\rho \\Phi^ {T} [ (g - \\Phi f) \\cdot / (\\Phi \\Phi^ {T}) ], \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.808, + 0.47, + 0.839 + ], + "angle": 0, + "content": "where \\(\\rho\\) is the parameter that is estimated through a simple network similar to [5]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.295, + 0.864 + ], + "angle": 0, + "content": "4.5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We change the stage numbers \\(N\\) to establish a series of SSR models with small, medium, and large scales: SSR-S" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.637 + ], + "angle": 0, + "content": "\\((N = 3)\\), SSR-M \\((N = 6)\\), and SSR-L \\((N = 9)\\). The proposed SSR is implemented by PyTorch and the window size in WSSA is empirically set to \\(8 \\times 8\\). Adam [19] optimizer \\((\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999)\\) and Cosine Annealing [26] scheduler are adopted to train SSR on a single RTX 3090 GPU. Training samples are patches with spatial sizes of \\(256 \\times 256\\) and \\(384 \\times 384\\) randomly cropped from 3D HSI data cubes for simulation and real experiments separately. The shifting step \\(d\\) of the imaging model is 2. The channels of SSRUnet layers are set to \\(\\Lambda, 2\\Lambda, 4\\Lambda\\) in sequence and basic bands \\(\\Lambda = 28\\). The training loss function is the root mean square error (RMSE) between reconstructed and ground-truth HSIs and adopts the multi-stage loss setting proposed in [43]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.654, + 0.625, + 0.671 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.707, + 0.696 + ], + "angle": 0, + "content": "5.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Following [5, 11, 17, 28, 42], we select 28 wavelengths from \\(450\\mathrm{nm}\\) to \\(650\\mathrm{nm}\\) by using spectral interpolation manipulation to derive HSIs. We conduct experiments on simulation and real datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Simulation and Real Data. Two simulation datasets, CAVE [32] and KAIST [9], and five real HSIs captured by the CASSI system developed in [28] are adopted. The CAVE dataset provides 32 HSIs with a spatial size of \\(512 \\times 512\\). The KAIST dataset includes 30 HSIs with a spatial size of \\(2704 \\times 3376\\). We use CAVE for simulation training and select 10 scenes from KAIST for simulation testing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. We adopt two image quality indexes including peak signal-to-noise ratio (PSNR), and structure" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "25822" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.073, + 0.147, + 0.125 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.077, + 0.225, + 0.125 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.074, + 0.291, + 0.124 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.073, + 0.357, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.073, + 0.423, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.426, + 0.073, + 0.49, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.073, + 0.557, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.559, + 0.073, + 0.623, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.073, + 0.69, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.073, + 0.757, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.073, + 0.823, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.826, + 0.073, + 0.891, + 0.123 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.126, + 0.222, + 0.136 + ], + "angle": 0, + "content": "RGB Image Measurement" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.137, + 0.223, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.196, + 0.192, + 0.205 + ], + "angle": 0, + "content": "(a) Wavelength(nm)" + }, + { + "type": "image", + "bbox": [ 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0.611, + 0.282 + ], + "angle": 0, + "content": "BIRNAT" + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.274, + 0.681, + 0.282 + ], + "angle": 0, + "content": "DAUHST" + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.274, + 0.745, + 0.281 + ], + "angle": 0, + "content": "RDLUE" + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.274, + 0.807, + 0.281 + ], + "angle": 0, + "content": "SSR-L" + }, + { + "type": "image_caption", + "bbox": [ + 0.825, + 0.274, + 0.889, + 0.281 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.285, + 0.892, + 0.313 + ], + "angle": 0, + "content": "Figure 5. Reconstructed images of simulation scene1 with 4 out of 28 spectral channels by the state-of-the-art methods. Two regions in scene1 are selected for analyzing the spectra of the reconstructed results. The figure is better viewed in a zoomed-in PDF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.47, + 0.383 + ], + "angle": 0, + "content": "similarity (SSIM) [39] for quantitative evaluation. Specifically, PSNR measures the visual quality, while SSIM measures the structure similarity. Generally, higher values of PSNR and SSIM mean better reconstruction results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.394, + 0.246, + 0.409 + ], + "angle": 0, + "content": "5.2. Simulation Scene" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.47, + 0.764 + ], + "angle": 0, + "content": "Quantitative results. Table. 1 and Fig. 1 show the quantitative comparison of our SSR and the state-of-the-art (SOTA) methods: DIP-HSI [30], TSA-Net [28], DGSMP [18], GAPnet [27], HerosNet [42], HDNet [17], MST [3], CST [2], BIRNAT [8], DAUHST [5], RDLUF [11]. We can see that SSR significantly outperforms the other methods by over 2dB at the same FLOPs and exceeds the leading method RDLUF by more than 1dB with reduced computational demands. Concretely, our best model, SSR-L surpasses SOTA methods RDLUF, DAUHST, and DAUHST by 1.12, 2.33, and 3.11dB while less computational effort is required. Surprisingly, our small model SSR-S surpasses most methods when requiring the least parameters and FLOPs. Moreover, our middle model outperforms the best method RDLUF by 0.63dB when less than 1/2 FLOPs are required. It is worth noting that RDLUF adopts a stage parameter-sharing strategy and we take the same strategy to establish our SSR-\\(L^*\\), which brings performance degradation but still achieves a clear advantage over other methods with the least parameters. We found that the degradation comes from the stability of the method, that is, as the number of parameters increases, the performance of our SSR steadily increases and RDLUF decreases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Visual comparison. We provide the visual comparison of simulation scene7 with 4 out of 28 spectral channels in Fig. 5. SSR-L successfully recovers the clear pattern and sharp edge on the cup when the other methods all suffer from blurred or distorted effects. In addition, we plot the spectral curves of two regions in scene1 in the bottom-left of Fig. 5. It's intuitive that SSR-L has a prominent higher correlation with the reference spectra, which demonstrates the effectiveness of our spectra-wise attention." + }, + { + "type": "table_caption", + "bbox": [ + 0.563, + 0.321, + 0.828, + 0.335 + ], + "angle": 0, + "content": "Table 2. Ablation study of WSSA and ARB." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.335, + 0.89, + 0.4 + ], + "angle": 0, + "content": "
Baseline-1WSSAARBPSNRSSIMParams (M)FLOPs (G)
✓36.600.9561.0614.43
✓✓37.760.9651.3018.82
✓✓✓39.190.9711.7326.37
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.417, + 0.681, + 0.431 + ], + "angle": 0, + "content": "5.3. Real Scene Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.893, + 0.699 + ], + "angle": 0, + "content": "To verify the effect of the proposed method on the real scenes, five measurements captured by the CASSI system are utilized for testing and the ground truths of the scenes are unavailable. For fair comparisons, all methods are trained on the CAVE and KAIST datasets jointly using the fixed real mask with 11-bit shot noise injected. The bottom two rows of Fig. 6 plot the visual comparisons of the proposed SSR-S and the existing SOTA methods while the top two rows plot the visual comparisons of different spectra-wise transformers [3, 4]. It is intuitive to see that our SSR-S restores clearer spatial textures and sharper edges than previous spectra-wise transformers in the top two rows, which shows the effect of spatial modulation. Compared with other methods in the bottom two rows, SSR-S obtains clearer results in these two bands when other methods fail to recover these two bands, demonstrating the effectiveness of our spatial alignment strategy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.699, + 0.726 + ], + "angle": 0, + "content": "5.4. Ablation Experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.891, + 0.763 + ], + "angle": 0, + "content": "In this part, we adopt the CAVE and KAIST datasets to conduct ablation studies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Effectiveness of WSSA and ARB. We first conduct a break-down ablation experiment to investigate the effect of each component towards higher performance. The results are listed in Table. 2. The baseline-1 model is derived by removing our WSSA and ARB from SSR-S and yields \\(36.60\\mathrm{dB}\\). When we successively apply our WSSA and ARB, the model continuously achieves \\(1.16\\mathrm{dB}\\) and \\(1.43\\mathrm{dB}\\) improvements. These results suggest the effectiveness of WSSA and ARB." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25823" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.07, + 0.892, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.353, + 0.893, + 0.381 + ], + "angle": 0, + "content": "Figure 6. Reconstructed images of real scene2 and scene4 with 2 and 4 out of 28 spectral channels separately by the state-of-the-art methods. Compared with other competing methods, our SSR recovers more details and clear content." + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.39, + 0.447, + 0.403 + ], + "angle": 0, + "content": "Table 3. Ablation study of different self-attention schemes." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.403, + 0.468, + 0.473 + ], + "angle": 0, + "content": "
MetricBaseline-2S-MSA [3]Swin-MSA [25]HS-MSA [5]WSSA*WSSA
PSNR32.0132.8533.0133.0933.1933.30
SSIM0.9080.9160.9180.9190.9220.924
Params (M)1.031.291.291.291.291.29
FLOPs (G)13.8418.1519.0419.0418.1518.65
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Self-Attention Scheme Comparison. We compare WSSA with other self-attention and report the results in Table. 3. We adopt the half operation [5] in Swin-MSA [25] to keep the computation almost the same and use multi-head attention in the spectral dimension of WSSA* to align with S-MSA[3]. Baseline-2 is SSR-S that retains only the ERB and removes attention and yields 32.01dB. WSSA yields the most significant improvement of 1.29dB, which is 0.45dB, 0.29dB, and 0.21dB higher than S-MSA [3], Swin-MSA [25], and HS-MSA [5], which shows the effectiveness of WSSA. In addition, WSSA* and WSSA achieve 0.34dB and 0.45dB gain than S-MSA respectively, which demonstrates the role of considering local differences and modeling global spectral information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Influence of Multi-head attention and Mean effect. We demonstrate the influence of multi-head attention and mean effect on the spectra-wise self-attention through further experiments on the relationship between performance and token dim (window size) in WSSA and MSSA, which is shown in Fig. 7. Intuitively, the large window size would suffer from limited performance, which illustrates the influence of the mean effect. Performance degradation also occurs when the window size is too small to retain complete feature information. In our experiments, \\(8 \\times 8\\) window size optimally balances retaining feature information while minimizing the mean effect, which produces the highest performance of 33.3dB. When the token dim is small, WSSA" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.381, + 0.858, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.481, + 0.868, + 0.494 + ], + "angle": 0, + "content": "Figure 7. Influence of token dim in spectra-wise attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.575 + ], + "angle": 0, + "content": "clearly performs better than MSSA, which shows the role of maintaining spatial correlation. When the token dim is large, MSSA is slightly better than WSSA, which may be related to the shift in the imaging process and the strip pattern can contain some shift information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.619, + 0.605 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.824 + ], + "angle": 0, + "content": "In this paper, we analyze the influence of multi-head attention and mean effect on the spectra-wise transformer, and a novel SSR method is proposed to improve spectral snapshot reconstruction. To model the global spectral information, consider the local difference, and maintain spatial correlation, WSSA is proposed to better utilize spectral similarity. ARB leverages CMB to address the interaction between adjacent windows of WSSA and learn spatial representation when SAB is specially designed to mitigate spatial degradation in low-quality bands through a novel spatial alignment strategy. Extensive experiments on simulation and real scenes show the effectiveness of the proposed modules. Our SSR at different scales also significantly outperforms the state-of-the-art methods with less cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62302394 and 62106063, the China Postdoctoral Science Foundation under Grant 317751, and the Natural Science Foundation of Shaanxi under Grant 2023-JC-QN-0757." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25824" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] José M. Bioucas-Dias and Mário A. T. Figueiredo. A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration. 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Recently, the spectra-wise transformer has shown great potential in capturing inter-spectra similarities of HSI, but the classic design of the transformer, i.e., multi-head division in the spectral (channel) dimension hinders the modeling of global spectral information and results in mean effect. In addition, previous methods adopt the normal spatial priors without taking imaging processes into account and fail to address the unique spatial degradation in snapshot spectral reconstruction. In this paper, we analyze the influence of multihead division and propose a novel Spectral-Spatial Rectification (SSR) method to enhance the utilization of spectral information and improve spatial degradation. Specifically, SSR includes two core parts: Window-based Spectra-wise Self-Attention (WSSA) and spAtial Rectification Block (ARB). WSSA is proposed to capture global spectral information and account for local differences, whereas ARB aims to mitigate the spatial degradation using a spatial alignment strategy. The experimental results on simulation and real scenes demonstrate the effectiveness of the proposed modules, and we also provide models at multiple scales to demonstrate the superiority of our approach. https://github.com/ZhangJC-2k/SSR + +# 1. Introduction + +The advent of compressed sensing introduced the coded aperture snapshot spectral compressive imaging (CASSI) system [13, 29, 36], addressing drawbacks in traditional hyperspectral cameras regarding efficiency and cost-effectiveness, gaining significant attention. This system offers the promise of swift and cost-efficient capture of Hyperspectral Images (HSIs). However, the inherent ill-posedness of decoding 3D HSIs from 2D measurements poses a significant challenge for reconstruction algorithm design. Consequently, various model-based [1, 23, 24, 33, + +![](images/f528c9a5e802fd09a1ce2b4158621ecd3da637193eb884e436c5d87cba130440.jpg) +Figure 1. Comparison of PSNR-FLOPs between our SSR and previous reconstruction methods. Our SSR significantly outperforms other methods over 2dB at the same FLOPs when surpassing the state-of-the-art method over 1dB with fewer FLOPs. + +38, 40] and learning-based [2-6, 17, 18, 28, 37, 42] approaches have emerged to tackle this challenge. Within the realm of reconstruction algorithms, the effective utilization of diverse priors remains a pivotal research challenge. + +Model-based methods initially adopt total variation [20, 40], low-rank [24], sparsity [21, 34] and more traditional hand-craft priors [1, 23, 24, 33, 38] to construct the optimization model, which preliminarily shows the practical feasibility of snapshot spectral reconstruction. With the advancement of deep learning, both convolutional neural networks (CNNs) [6, 17, 18, 28, 37, 42] and transformers [3-5, 11] have been successively introduced for learning the spatial and spectral characteristics of HSIs. They serve as end-to-end denoisers [3, 4, 6, 17, 28] or deep image priors [5, 11, 18, 37, 42] in learning-based methods. These advancements have led to significant progress in both real-world and simulated scenario reconstructions. In addition, the effective utilization of spectral and spatial characteristics has also naturally become a research hotspot. + +Previous CNN methods such as TSA-Net [28], HDNet [17], DGSMP [18], and HerosNet [42], along with spatial transformers like Swin Transformer [25] and DAUHST [5], excel in learning spatial representations but do not effectively utilize the distinctive spectral characteristics inherent in HSIs. Conversely, spectra-wise transformers such as MST [3], MST++ [4], and RDLUF [11] show promising + +potential in snapshot spectral reconstruction by exploiting inter-spectral similarities. However, their implementations follow the conventional transformer architecture, involving multi-head division in the spectral dimension, which limits the modeling of global spectral similarities and results in mean effect. Furthermore, in spectral snapshot imaging, some spatial degradation occurs in certain bands due to masking, shifting, and compression factors. Unfortunately, existing spatial and spectral networks lack tailored designs to mitigate such degradation effectively. + +To optimize the utilization of spectral information and mitigate distinctive spatial degradation, we introduce the Spectral-Spatial Rectification (SSR) method into snapshot spectral reconstruction. Specifically, SSR comprises two key components: Window-based Spectral Self-Attention (WSSA) and spAtial Rectification Blocks (ARB). WSSA divides the features into multiple local windows in the spatial dimension, facilitating global spectral self-attention computations and the local difference consideration. Addressing the interaction gap between windows of WSSA, ARB leverages a Convolution Modulated Block (CMB). This block employs sliding large-kernel convolutions to interact with features between windows and learn effective spatial representation. Subsequently, to mitigate spatial degradation, ARB integrates a novel spatial alignment strategy. It assists low-quality bands in leveraging information from high-quality bands through learning a unified spatial representation and spectral weights, which further optimizes the utilization of spatial information. Overall, our contributions are summarized as follows: + +- We analyze the influence of multi-head division on previous spectra-wise transformers and propose Window-based Spectra-wise Self-Attention to model global spectral information while accounting for local differences. +- A Spatial Rectification Block is specially designed to enhance spatial representation and mitigate the spatial degradation in low-quality bands through large-kernel convolutions and a novel spatial alignment strategy. +- The qualitative and quantitative results of real and simulation experiments demonstrate that our SSR method significantly improves spectral snapshot reconstruction. + +# 2. Related Work + +The model-based methods [1, 20, 21, 23, 24, 33, 34, 38, 40] construct convex optimization models with some specific priors such as total variation [20, 40], low-rankness [24], and sparsity [21, 34] according to the physical schema of CASSI then solve the problem in an iterative manner to obtain reconstructed images. They have good interpretability and low cost, yet lack performance guarantee. Subsequently, the rise of deep learning [14, 15, 22] has facilitated the rapid development of spectral snapshot reconstruction. To improve reconstruction quality, Plug-and-Play + +methods [41, 44] plug pre-trained deep networks as priors, which make great progress in performance but are still limited by slow reconstruction speed. Along with faster inference and better results, the CNN-based end-to-end denoisers [17, 28, 31] quickly achieved better results by establishing a mapping between measurements and HSIs, but also brought huge memory and computation costs. + +Recently, the transformer-based end-to-end denoisers [2-4] which capture data similarity and long-range dependence have shown impressive performance in both simulation and real scenes. These methods adopt self-attention to learn effective spatial and spectral representation, achieving very high parameter and computational efficiency. Following this, the unfolding methods [5, 11] regard transformers as deep priors for optimization formulas and improve iterative frameworks through end-to-end training. In these approaches, CNNs and transformers play a huge role either as end-to-end denoisers or as deep priors. While previous CNNs and spatial transformers fail to effectively utilize the spectral characteristics inherent in HSIs, spectra-wise transformer [3, 4, 11] has shown great potential in spectral tasks and attracted wide attention. However, current spectra-wise transformers follow classic multi-head design [12, 25, 35] and suffer from the loss of global spectral information and the limitation of ignoring local differences. + +# 3. Spectral Snapshot Imaging Model + +Mathematically, we assume a spectral image patch with $\Lambda$ bands $\{F_{\lambda}\}_{\lambda = 1}^{\Lambda}\in \mathbb{R}^{H\times W}$ , where $H$ and $W$ represents the HSI's height and weight. Image frame $F_{\lambda}$ is modulated by a physical mask with pattern $M\in \mathbb{R}^{H\times W}$ to get modulated image frame $F_{\lambda}^{\prime}$ : + +$$ +F _ {\lambda} ^ {\prime} = M \circ F _ {\lambda}, \tag {1} +$$ + +where $\circ$ denotes Hadamard's (element-wise) product. Then the modulated image frames of different wavelengths $\left\{F_{\lambda}^{\prime}\right\}_{\lambda = 1}^{\Lambda}$ are separated to different positions by the disperser. After that, $\left\{F_{\lambda}^{\prime}\right\}_{\lambda = 1}^{\Lambda}$ distributed across different bands are shifted spatially and summed element-wise. Thus, $\left\{F_{\lambda}^{\prime}\right\}_{\lambda = 1}^{\Lambda}$ are compressed to a coded measurement: + +$$ +G (m, n) = \sum_ {i = 1} ^ {\Lambda} F _ {\lambda} ^ {\prime} (m, n + D (\lambda)), \tag {2} +$$ + +where $m$ and $n$ index the spatial coordinates, $D(\lambda) = d(\lambda - 1)$ , $d$ represents pixels shift between adjacent bands. Note Eq. (2) assumes a dispersion along the vertical dimension, and the derivation is also applicable for horizontal dispersion. The imaging model in Eq. (2) can be rewritten in the matrix-vector form as follows: + +$$ +g = \Phi f, \tag {3} +$$ + +![](images/0026dcc841925382e011a1de0924356289c07d3ccfef79ab0a999025a9c99a6d.jpg) +Figure 2. (a)-(c) The overall architecture of SSR, SSRUnet, and SSRB. LMP is achieved via a formula. (d) Details of WSSA. + +![](images/00643df8bf9708cfa3453ad56d8dacdcb1d322ebe38f70651a8dccf638a2a0b2.jpg) + +![](images/2c9a1c4047f038f1af3e177cdad9e88b910772e8591ebb54a5c99611ebb7abdc.jpg) + +where $g \in \mathbb{R}^{HW}$ , $f \in \mathbb{R}^{HW\Lambda}$ are the vectorized representation of the compressed image $G$ and the original spectral image $F$ respectively, and $\Phi \in \mathbb{R}^{HW \times HW\Lambda}$ is the sensing matrix that describes the system imaging model. In spectral snapshot reconstruction, what we need to do is recover 3D HSI $f$ from the compressed 2D measurement $g$ . + +# 4. Method + +Existing spectral and spatial network designs [2-5, 11] are limited by the direct application of traditional multi-head division and unique spatial degradation of snapshot spectral imaging. To address the limitations, we propose the Spectral-Spatial Rectification (SSR) method to better model the spectral information, enhance spatial representation, and improve spatial degradation. + +# 4.1. Overall Architecture + +An overview of SSR is presented in Fig. 2 (a), we adopt a multistage network including initialization and $N$ cascaded stages, and each stage consists of Linear Manifold Projection (LMP), Spectral-Spatial Rectification Unet (SSRUnet), and spAtial Rectification Block (ARB). First, the compressed measurement $g$ is reversed to the initial shape [3] and the 2D mask is repeated in channel dimension to obtain the 3D mask. Then the two are inputted to a $1 \times 1$ convolution kernel $(conv1 \times 1)$ to get the initialization. In each stage, LMP is adopted to assist the reconstruction based on the imaging model. Then the SSRUnet is employed to refine the input through novel spatial and spectral design. Finally, ARB is used to further improve spatial degradation in reconstruction. For the core module SSRUnet, as illustrated in Fig. 2 (b), the $conv3 \times 3s$ with residual are utilized to embed mask information into input $X$ as follows: + +$$ +X _ {M E} = \operatorname {C o n v} _ {3 \times 3} (X) \circ \left(T _ {I} + \operatorname {C o n v} _ {3 \times 3} (\text {M a s k})\right), \tag {4} +$$ + +where $X_{ME}$ is the features embedded with the mask, $T_{I}$ is an all-one tensor and $Mask$ is the 3D mask obtained in ini + +tialization. Then SSRUnet with three layers and $conv3 \times 3$ are employed to extract the deep feature which is combined with the input as a residual to produce a refined output. The SSRUnet consists of downsampling modules ( $conv4 \times 4$ ), Spectral-Spatial Rectification Block (SSRB), upsampling modules ( $deconv2 \times 2$ ), and Fusion modules ( $conv1 \times 1$ ). Spectral-Spatial Rectification Block (SSRB). SSRB is the basic module of SSRUnet. As shown in Fig. 2 (c), the implicit positional information [10] is firstly embedded in the input for applying self-attention later in SSRB. Each SSRB is the sequential combination of the spEctral Rectification Block (ERB) and ARB. Fig. 2 (c) illustrates the components of ERB and ARB, i.e., a Feed Forward Network(FFN) and a Window-based Spectral Self-Attention (WSSA) for ERB, a Convolution Moudulated Block (CMB) and a Spatial Alignment Block (SAB) for ARB, and same Layer Normalization (LN) and Group Normalization (GN) for ERB and ARB. WSSA is detailed in Fig. 2 (d) and FFN consists of two linear layers sandwiched with depth-wise $conv3 \times 3$ . + +# 4.2. Spectral Rectification Block + +Spectral self-attention is a promising approach to utilize spectral characteristics for HSI tasks. However, we find that the previous spectra-wise transformer [3, 4, 11] directly considers a band as a token and follows traditional spatial self-attention design, i.e., multi-head division in spectral (channel) dimension, which ignores the local differences in spectral distribution and results in mean effect and nonglobal spectral utilization. To solve the problem, we propose the ERB based on WSSA to consider local differences and model global spectral information. + +The Influence of Multi-Head Division in Spectral (Channel) Dimension. In the classic transformer design [12, 25, 35], the use of multi-head division in the channel dimension is common and brings some gains. Possibly affected by this, the previous spectra-wise transformer in spectral snapshot reconstruction also divides multi-head in spectral dimension as shown in Fig. 3 (a), which results in the sep + +![](images/bccbcbcf1a52e83ff19d2405b07bdef96435b3f648d1c3633542157669025afe.jpg) +(a) Multi-head Division in Spectral Dimension + +![](images/d7fcda305dd1eadfa1ed0ee606353b104f0450649b1f64beed0aaebd69e7ff01.jpg) +(b) Mean Effect + +![](images/4f81174c8393974768e401ef4dfe157f8c5c35ef743deeed1c2bb5a5818116a7.jpg) +Figure 3. (a)-(c) The influence of multi-head attention and mean effect, (d) The illustration of WSSA. + +![](images/cbde6d6fd07e5a3e1034d8ae90ad89077fd3c760438945264d970c51b825ffd5.jpg) +(c) Multi-head Division in Spatial Dimension +(d) Window-based Attention + +aration of spectral information and failure to model global spectral information. It's very easy to get confused because the spectral transformer is in contrast to the spatial transformer, where the characteristic dimension of the former is the spatial dimension, and the characteristic dimension of the latter is the spectral (channel) dimension. + +The Influence of Mean Effect. In addition, considering that HSIs depict the spectral distribution of scenes, the similarities of different regions should be different but previous multi-head division results in all regions sharing the same similarity. When treating the whole band as a token to calculate spectral self-attention, we obtain the mean of all region similarities in the band and the local differences between regions are lost, which we call the 'Mean Effect'. Define $\Lambda$ features $\{f_{\lambda}\}_{\lambda = 1}^{\Lambda}$ where feature dimension consists of $p$ different patterns (regions), i.e., $f_{\lambda} = [f_{\lambda}^{1}, f_{\lambda}^{2}, \ldots, f_{\lambda}^{p}]$ , the influence of mean effect on the similarity calculation can be simply described as follows: + +$$ +\operatorname {s i m} \left(f _ {i} ^ {k}, f _ {j} ^ {k}\right)\rightarrow \frac {1}{p} \sum_ {m = 1} ^ {p} \operatorname {s i m} \left(f _ {i} ^ {m}, f _ {j} ^ {m}\right), \tag {5} +$$ + +where the left part denotes the expected similarity of the $k$ th pattern between $f_{i}^{k}$ and $f_{j}^{k}$ , and the right part represents the obtained similarity in previous approaches. We also present an example in Fig. 3 (b), the average similarity and local region similarity between the red band and other bands are marked with red numbers and black numbers respectively. To demonstrate the validity of our theory, we carried out ablation experiments of different region sizes, i.e., window size under the same conditions later. In addition, the mean effect may explain why multi-head attention is more effective than single-head attention. + +Multi-Head Division in Spatial Dimension. When realizing appropriate feature dimension and mean effect, it was natural to treat the entire band frame as a token and then directly divide multi-head [35] in the merged spatial dimension to calculate self-attention, which we call MSSA later for short. However, as shown in Fig. 3 (c), this would split the entire image into (incomplete) strip shapes on each head, which mitigates the mean effect to some extent but breaks the spatial correlation of features. That is, adjacent areas are divided into different heads, while areas that are far apart in space are divided into the same head. + +Window-based Spectral Self-Attention (WSSA). To capture the global spectral similarity, solve the mean effect, and maintain spatial correlation, WSSA divides features into a number of windows spatial-wisely, and then the spectrawise self-attention is calculated within windows to avoid the interference of each other, which is shown in Fig. 3 (d). Specifically, define input $X \in \mathbb{R}^{H \times W \times C}$ , as shown in Fig. 2 (d), $X$ is first linearly projected to $3C$ channels tensor via a $1 \times 1$ convolution then uniformly divides the tensor channel-wisely into the query $(Q)$ , key $(K)$ , value $(V)$ . Subsequently, $Q, K, V$ are split spatial-wise into $HW / M^2$ windows with size of $\mathbb{R}^{M \times M \times C}$ separately: + +$$ +\left\{Q _ {i}, K _ {i}, V _ {i} \right\} _ {i = 1} ^ {H W / M ^ {2}} = Q, K, V, \tag {6} +$$ + +where $Q_{i},K_{i},V_{i}\in \mathbb{R}^{M\times M\times C}$ and are then reshaped into shape $\mathbb{R}^{M^2\times C}$ as tokens to calculate attention as follows: + +$$ +\text {A t t e n t i o n} _ {i} = \operatorname {S o f t M a x} \left(Q _ {i} ^ {T} K _ {i} / M\right) V _ {i}, \tag {7} +$$ + +where $\mathbf{M}$ is used as the scale factor before applying the softmax function. Then the outputs of $HW / M^2$ attention are reshape in $\mathbb{R}^{M\times M\times C}$ and merge together in the original arrangement to undergo a conv1 $\times 1$ projection: + +$$ +X ^ {\prime} = \left\{A t t e n t i o n _ {i} \right\} _ {i = 1} ^ {H W / M ^ {2}} W _ {1}, \tag {8} +$$ + +where $W_{1} \in \mathbb{R}^{C \times C}$ are weight matrices of a $conv1 \times 1$ and $X'$ is the final output in $\mathbb{R}^{H \times W \times C}$ . Different from multi-head self-attention which implements token embedding and then divides heads, WSSA first implements windows split then reshaping into tokens, which preserves the spatial correlation of each token. Regarding WSSA as a special multi-head self-attention, the number of WSSA heads is more, often hundreds of thousands, far more than the number of multi-head attention. + +Computational Complexity. The computational complexity of WSSA is displayed as follows: + +$$ +O (W S S A) = 4 H W C ^ {2} + 2 M ^ {2} C ^ {2} \frac {H W}{M ^ {2}} = 6 H W C ^ {2}. \tag {9} +$$ + +The computational complexity of WSSA is linear to the spatial size $HW$ and window size-independent, meaning that there is no additional computation cost when we improve spectral utilization. + +![](images/9f74e7384f6bb4a1fca7f1e4b41334c5ab09c7b5617ae32edde3e0a2484a6631.jpg) +Figure 4. (a) Display of spatial degradation in spectra-wise transformers. (b) The details of CMB. (c) The effect of large kernel convolution in CMB. (d) The details of SAB. (e) Spatial alignment strategy of SAB. + +# 4.3. Spatial Rectification Block + +The utilization of WSSA enhances the capability of spectral information capture. However, a limitation arises from the absence of interaction between adjacent windows within WSSA, potentially leading to discontinuous spatial representation and the occurrence of blocking artifacts, as highlighted by [7]. Additionally, unique spatial degradation occurs due to mask, shift, and compression in spectral snapshot imaging. To address these concerns, we propose a spA tial Rectification Block (ARB) comprising a Convolution Modulated Block (CMB) and a Spatial Alignment Block (SAB). This ARB aims to foster interaction between adjacent windows and alleviate spatial degradation in the HSIs. Convolution Modulated Block (CMB). Here, we try to solve two problems: (1) When different windows cannot interfere with each other, WSSA also fails to exchange information, which leads to discrete spatial expression and may lead to blocking artifacts [7]. (2) As shown in the top two rows of Fig .4 (a), over-smoothing demonstrates that the spatial representation ability of a single spectra-wise transformer is not sufficient. To solve these two problems and inspired by the development of large kernel convolution in high-level tasks, we adopted a Convolution Modulated Block (CMB) proposed in [16] to modulate spatial information and make adjacent windows interact with each other through large kernel convolution sliding as shown in Fig. 4 (b). CMB modulates spatial information in a similar manner to self-attention but much more efficiently. Specifically, given the input tokens $X\in \mathbb{R}^{H\times W\times C}$ , we use a simple depth-wise convolution with kernel size $11\times 11$ to calculate the modulated attention $A$ as follows: + +$$ +A = D C o n v _ {1 1 \times 1 1} (X W _ {2}), \tag {10} +$$ + +where $W_{2}\in \mathbb{R}^{H\times W\times C}$ are weight matrices of conv1 x 1s, and $DConv_{11\times 11}$ denotes a depth-wise convolution with + +kernal size $11 \times 11$ . Then we adopt the element-wise product and attention $A$ to modulate the project feature $V'$ to get the output $Z$ : + +$$ +Z = \left(A \circ V ^ {\prime}\right) W _ {4}, V ^ {\prime} = X W _ {3}, \tag {11} +$$ + +where $W_{3}$ and $W_{4} \in \mathbb{R}^{C \times C}$ are weight matrices of $conv1 \times 1s$ . On the one hand, CMB could effectively improve the spatial representation of features through modulation operation. On the other hand, CMB enables the pixels between adjacent windows of WSSA to interact spatial-wisely when depth-wise convolution kernel size $11 \times 11$ is greater than patch size $8 \times 8$ , as demonstrated in Fig. 4 (c). + +Spatial Alignment Block (SAB). As shown in the bottom two rows of Fig. 4 (a), we observe that the reconstruction results of some bands have more spatial degradation such as distortion and deformation, which is not common in other HSI tasks. Thus, we think this may be related to the unique imaging process. As shown in Fig. 4 (e), shift and compression in the imaging process mix information from different spatial locations, and spatial texture recovery in bands with low spectral density may be difficult, which is neglected by previous methods. Considering that the low-density bands can be obtained by multiplying the high-density bands by weights, we can utilize the high-quality bands to improve the spatial texture of the low-quality bands through a novel spatial alignment strategy, as shown in Fig. 4 (e). To achieve this, a Spatial Alignment Block (SAB) is proposed to improve spatial degradation. As shown in 4 (d), we adopt different convolution kernels to estimate spatial texture distribution which corresponds to the high-density part, and learn spectral weights in SAB when two linear layers are used to mix channel information. Specifically, given the input feature $F \in \mathbb{R}^{H \times W \times C}$ , we use a convolution with kernel size $3 \times 3$ and $GELU$ activation function to learn the spatial texture $T$ as follows: + +$$ +T = \psi \left(\operatorname {C o n v} _ {3 \times 3} \left(F W _ {5}\right)\right), \tag {12} +$$ + +Table 1. The PSNR (upper entry in each cell) in dB and SSIM (lower entry in each cell) results of the test methods on 10 scenes. + +
AlgorithmsReferenceParamsGFLOPsScene1Scene2Scene3Scene4Scene5Scene6Scene7Scene8Scene9Scene10Avg
DIP-HSI [30]ICCV 202133.8564.4232.6827.2631.3040.5429.7930.3928.1829.4434.5128.5131.26
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
TSA-Net [28]ECCV 202044.25110.0632.0331.0032.2539.1929.3931.4430.3229.3530.0129.5931.46
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
DGSMP [18]CVPR 20213.5884.7733.2632.0933.0640.5428.8633.0830.7431.5531.6631.4432.63
0.9150.8980.9250.9640.8820.9370.8860.9230.9110.9250.917
GAP-Net [27]IJCV 20234.2778.5833.7433.2634.2841.0331.4432.4032.2730.4633.5130.2433.26
0.9110.9000.9290.9670.9190.9250.9020.9050.9150.8950.917
HerosNet [42]CVPR 202211.27414.7635.6935.0134.8238.0733.1834.9433.5833.1933.0433.0134.45
0.9730.9680.9670.9850.9690.9760.9620.9680.9640.9650.970
HDNet [17]CVPR 20222.37154.7635.1435.6736.0342.3032.6934.4633.6732.4834.8932.3834.97
0.9350.9400.9430.9690.9460.9520.9260.9410.9420.9370.943
MST [3]CVPR 20222.0328.1535.4035.8736.5142.2732.7734.8033.6632.6735.3932.5035.18
0.9410.9440.9530.9730.9470.9550.9250.9480.9490.9410.948
CST [2]ECCV 20223.040.1035.9636.8438.1642.4433.2535.7234.8634.3436.5133.0936.12
0.9490.9550.9620.9750.9550.9630.9440.9610.9570.9450.957
BIRNAT [8]TPAMI 20234.402122.6636.7937.8940.6146.9435.4235.3036.5833.9639.4732.8037.58
0.9510.9570.9710.9850.9640.9590.9550.9560.9700.9380.960
DAUHST [5]NeurIPS 20226.1579.5037.2539.0241.0546.1535.8037.0837.5735.1040.0234.5938.36
0.9580.9670.9710.9830.9690.9700.9630.9660.9700.9560.967
RDLUF [11]CVPR 20231.81115.3437.9440.9543.2547.8337.1137.4738.5835.5041.8335.2339.57
0.9660.9770.9790.9900.9760.9750.9690.9700.9780.9620.974
SSR-SOurs1.7326.3738.2240.0542.5747.4636.5037.3337.6035.7041.3735.0639.19
0.9630.9720.9750.9860.9720.9710.9640.9680.9750.9590.971
SSR-MOurs3.4552.6538.6141.3543.9448.3237.8038.0738.5436.8242.7235.7940.20
0.9670.9780.9790.9880.9770.9750.9690.9740.9800.9650.975
SSR-LOurs5.1878.9339.0742.0444.4948.8038.6438.5039.1636.9643.1236.0840.69
0.9700.9810.9800.9900.9800.9780.9710.9760.9820.9680.978
SSR-L*Ours1.7378.9338.8141.5143.7648.6238.3237.8538.5036.8542.6435.8240.27
0.9680.9790.9790.9880.9790.9750.9690.9740.9800.9650.976
+ +where $T \in \mathbb{R}^{H \times W \times 1}$ , $\psi$ is GELU activation function and $W_5 \in \mathbb{R}^{C \times C}$ are weight matrices of the linear layer. Meanwhile, we use a depth-wise convolution with kernel size $3 \times 3$ and Sigmoid activation function to learn spectral element-wise weight as follows: + +$$ +S W = \sigma \left(D C o n v _ {3 \times 3} \left(F W _ {5}\right)\right), \tag {13} +$$ + +where $SW \in \mathbb{R}^{H \times W \times C}$ , $\sigma$ is Sigmoid activation function. Finally, we use multiple element-wise products and a conv1 × 1 projection $W_{6}$ to calculate the output $Y$ as follows: + +$$ +Y = \left\{T \circ S W _ {i} \right\} _ {i = 1} ^ {C} W _ {6}, \tag {14} +$$ + +where $Y \in \mathbb{R}^{H \times W \times C}$ and $SW_{i} \in \mathbb{R}^{H \times W \times 1}$ . + +# 4.4. Linear Manifold Projection (LMP) + +Eq. (3) is a key constraint in spectral compression reconstruction. To take advantage of this prior, we introduce a Linear Manifold Projection (LMP) proposed in GAP-Net [27] to assist the reconstruction. We add an additional parameter to control projection intensity and perform the LMP as follows: + +$$ +f ^ {\prime} = f + \rho \Phi^ {T} [ (g - \Phi f) \cdot / (\Phi \Phi^ {T}) ], \tag {15} +$$ + +where $\rho$ is the parameter that is estimated through a simple network similar to [5]. + +# 4.5. Implementation Details + +We change the stage numbers $N$ to establish a series of SSR models with small, medium, and large scales: SSR-S + +$(N = 3)$ , SSR-M $(N = 6)$ , and SSR-L $(N = 9)$ . The proposed SSR is implemented by PyTorch and the window size in WSSA is empirically set to $8 \times 8$ . Adam [19] optimizer $(\beta_{1} = 0.9$ and $\beta_{2} = 0.999)$ and Cosine Annealing [26] scheduler are adopted to train SSR on a single RTX 3090 GPU. Training samples are patches with spatial sizes of $256 \times 256$ and $384 \times 384$ randomly cropped from 3D HSI data cubes for simulation and real experiments separately. The shifting step $d$ of the imaging model is 2. The channels of SSRUnet layers are set to $\Lambda, 2\Lambda, 4\Lambda$ in sequence and basic bands $\Lambda = 28$ . The training loss function is the root mean square error (RMSE) between reconstructed and ground-truth HSIs and adopts the multi-stage loss setting proposed in [43]. + +# 5. Experiment + +# 5.1. Experimental Settings + +Following [5, 11, 17, 28, 42], we select 28 wavelengths from $450\mathrm{nm}$ to $650\mathrm{nm}$ by using spectral interpolation manipulation to derive HSIs. We conduct experiments on simulation and real datasets. + +Simulation and Real Data. Two simulation datasets, CAVE [32] and KAIST [9], and five real HSIs captured by the CASSI system developed in [28] are adopted. The CAVE dataset provides 32 HSIs with a spatial size of $512 \times 512$ . The KAIST dataset includes 30 HSIs with a spatial size of $2704 \times 3376$ . We use CAVE for simulation training and select 10 scenes from KAIST for simulation testing. + +Evaluation Metrics. We adopt two image quality indexes including peak signal-to-noise ratio (PSNR), and structure + +![](images/0c41ff77b099a8ced2ad89208d45437b39c0b325467a55798dc7b11a0eef1dc7.jpg) +RGB Image Measurement + +![](images/2c7233b0e7e76929826cee6c83310d550e72df55815efcb97a9c2c53d9121ecf.jpg) + +![](images/f588e08a219c13433ec2118b2791b3fdf36b762ef2611214c86894765fd50357.jpg) + +![](images/850ff6c95a21dfdca12a95807cdf7285051438af9b60c7ddeb3dd1dc01e30f7f.jpg) + +![](images/65b3e9357ee96c96c5397a65bed73f0f40bf4ac24d7598d2481bf3bb3bbb4ec0.jpg) + +![](images/c99ca4ebd4ea90ac461e3f7763d541f0122ad22d9562ad1ac3fd3657c008caf4.jpg) + +![](images/fb52ba76f747165a02c73d18da3c759ceada24d788e2d3745c9e0142300bcbf9.jpg) + +![](images/40e0364957d9ac90023c9d9111166234b65c9061090e1e683d3acedfafab6fb6.jpg) + +![](images/eff762c970ab0324414e4281cf740aaef3b54d3976216b57853efb40b22ec710.jpg) + +![](images/f15620f9fe5552495a458ddafd176639ff838e7f3bb71aef655f8cc4065dbeb4.jpg) + +![](images/f29423dcb21d2706591cf03133abc22f367e4cc21fb98b314eb6ec903bc51a72.jpg) + +![](images/7a5680969a9f69eb01bd38e6c800f4f6d98bdbc3c243058aa0d16eef9bbdcc31.jpg) + +![](images/213c9131c01798328d13231f0a66f4e85b881241e344dd23be8a7691b90242aa.jpg) +(a) Wavelength(nm) + +![](images/3128e0f1234e93c7ad70edd0381839c5571f751723b04154b308301d38ceaa3b.jpg) +Figure 5. Reconstructed images of simulation scene1 with 4 out of 28 spectral channels by the state-of-the-art methods. Two regions in scene1 are selected for analyzing the spectra of the reconstructed results. The figure is better viewed in a zoomed-in PDF. + +![](images/5733d1f23ea23cc310a059495c9e5fb72ca8a44c033ce18ecd7e16615a54ea1f.jpg) + +![](images/aa01679e2c464b2e8fe154fec2009bc1f04e8cd95ad9a47b684fbdb4853f77bd.jpg) + +![](images/5d11ac4ccd0b43c715b9a3a45a9e38d6912e7871993ae304bdb6b3628dff3847.jpg) + +![](images/40a913d8bdd0597488d33c9eb8c8f4ecc600658a3cb0c9dd6a92d7bd2cfdd168.jpg) + +![](images/55c324e99e79eb664b35416066e00a111c9a1917ed298ca4191cadedbf264b42.jpg) + +![](images/b7b3732caf06ed42e723d0fbd32c1633208110e89ab325d8f45a7cee9032ca21.jpg) + +![](images/c9e6d82e76ac63c370afa19f28dc3eecde642b7a102938c26d934cfc4c7f5050.jpg) + +![](images/08ed403f862f91b0cfee4be0e71eab108e8adaf453ef107d9efe750ca2685513.jpg) + +![](images/5d5f663bba8c86298f0f948af1fe5de2f65ff7a6de6760f0ac8f6830b6fba235.jpg) + +![](images/d43e8c575bbacb599bfd1a8ae1481ae253f433a36f6a4234ac4e3a02b450ee10.jpg) + +![](images/d7432ab04867893cd31434d7a3bfb5b13afa371112e5fde08b99e935054907ab.jpg) + +![](images/b1bfd62de8e05dececd1bd9dd395714a43032f160edc4962b35efe69ca315f5e.jpg) + +![](images/d5a8fbd49fd9b664e52dc3dc2c8b5da7cf24d6cd652f5173e056632c7ff07d51.jpg) + +![](images/8ff112b19313348660044e556417e8930a3c5b171e43f2625b7d7e470fcd988e.jpg) + +![](images/36def84cae0d16879fa6a260200bc20fe49c2e6556045efd2b82168d6927cc17.jpg) + +![](images/d332f5efc847b58bfbdf677c85368612b33ca5999329bd04613a975749fadec5.jpg) + +![](images/0bc0b7e07bc9eb29277d50d9e1562115025f1a66badbea82512b593fe9ebb4a9.jpg) + +![](images/020e11a5418174a899d7d5d5671510949911033763abc0efa2547ad0ff5e0e93.jpg) + +![](images/f96b7240c30efeab15b3be69e48e521b6b1806c41eab75905f6c0924e823c3de.jpg) + +![](images/5fca745856bb3f239349c6c46559ccfaf279bd883bd167ead046b3707e034e65.jpg) + +![](images/5d2342194d20a6bc3d819a7735cf51ca3b112f9a2946a82d7bf8ac2d84c1fe96.jpg) +DGSMP + +![](images/536379def56c933158c676aa661be3649ad8f87dfd773b8a186f1b13b291f50d.jpg) +HerosNet + +![](images/b6ce8a5276cb3ad0eaafbe0589dcdaaff6b4bcbff4d813cd6f5628a1ad3e8f34.jpg) +HDNet + +![](images/1fb47eb6ad2b816f85904ed668c0d91532bceb3d41d258cbbc7a107a5d9facb1.jpg) +MST + +![](images/4971c631d6ff33dba2f6ff388a4f73b6f193145d47b5d63836e3bd02983ea260.jpg) + +![](images/9e36da2c76faf70aaf40aecf7a243d1baff213d409a2b4e61331cadac3683a1c.jpg) +BIRNAT + +![](images/9c8100d55603f3ee4154c0a367a5587d800df2500a23b5f7275917a9ded9e8ce.jpg) +DAUHST + +![](images/208a082939f0113ee4624cdf2cae1f592af972473b95bbc03c4caeabec5782ee.jpg) +RDLUE + +![](images/9bce46e01f5cd32d7e6c19dc2ef3dc08ddbc59123327f591f1a25ce0c5c1c494.jpg) +SSR-L + +![](images/2abd000406f68f2cc8265835265a0734536a60e58e1c693a75e02d213193c3d1.jpg) +Ground Truth + +similarity (SSIM) [39] for quantitative evaluation. Specifically, PSNR measures the visual quality, while SSIM measures the structure similarity. Generally, higher values of PSNR and SSIM mean better reconstruction results. + +# 5.2. Simulation Scene + +Quantitative results. Table. 1 and Fig. 1 show the quantitative comparison of our SSR and the state-of-the-art (SOTA) methods: DIP-HSI [30], TSA-Net [28], DGSMP [18], GAPnet [27], HerosNet [42], HDNet [17], MST [3], CST [2], BIRNAT [8], DAUHST [5], RDLUF [11]. We can see that SSR significantly outperforms the other methods by over 2dB at the same FLOPs and exceeds the leading method RDLUF by more than 1dB with reduced computational demands. Concretely, our best model, SSR-L surpasses SOTA methods RDLUF, DAUHST, and DAUHST by 1.12, 2.33, and 3.11dB while less computational effort is required. Surprisingly, our small model SSR-S surpasses most methods when requiring the least parameters and FLOPs. Moreover, our middle model outperforms the best method RDLUF by 0.63dB when less than 1/2 FLOPs are required. It is worth noting that RDLUF adopts a stage parameter-sharing strategy and we take the same strategy to establish our SSR- $L^*$ , which brings performance degradation but still achieves a clear advantage over other methods with the least parameters. We found that the degradation comes from the stability of the method, that is, as the number of parameters increases, the performance of our SSR steadily increases and RDLUF decreases. + +Visual comparison. We provide the visual comparison of simulation scene7 with 4 out of 28 spectral channels in Fig. 5. SSR-L successfully recovers the clear pattern and sharp edge on the cup when the other methods all suffer from blurred or distorted effects. In addition, we plot the spectral curves of two regions in scene1 in the bottom-left of Fig. 5. It's intuitive that SSR-L has a prominent higher correlation with the reference spectra, which demonstrates the effectiveness of our spectra-wise attention. + +Table 2. Ablation study of WSSA and ARB. + +
Baseline-1WSSAARBPSNRSSIMParams (M)FLOPs (G)
✓36.600.9561.0614.43
✓✓37.760.9651.3018.82
✓✓✓39.190.9711.7326.37
+ +# 5.3. Real Scene Results + +To verify the effect of the proposed method on the real scenes, five measurements captured by the CASSI system are utilized for testing and the ground truths of the scenes are unavailable. For fair comparisons, all methods are trained on the CAVE and KAIST datasets jointly using the fixed real mask with 11-bit shot noise injected. The bottom two rows of Fig. 6 plot the visual comparisons of the proposed SSR-S and the existing SOTA methods while the top two rows plot the visual comparisons of different spectra-wise transformers [3, 4]. It is intuitive to see that our SSR-S restores clearer spatial textures and sharper edges than previous spectra-wise transformers in the top two rows, which shows the effect of spatial modulation. Compared with other methods in the bottom two rows, SSR-S obtains clearer results in these two bands when other methods fail to recover these two bands, demonstrating the effectiveness of our spatial alignment strategy. + +# 5.4. Ablation Experiment + +In this part, we adopt the CAVE and KAIST datasets to conduct ablation studies. + +Effectiveness of WSSA and ARB. We first conduct a break-down ablation experiment to investigate the effect of each component towards higher performance. The results are listed in Table. 2. The baseline-1 model is derived by removing our WSSA and ARB from SSR-S and yields $36.60\mathrm{dB}$ . When we successively apply our WSSA and ARB, the model continuously achieves $1.16\mathrm{dB}$ and $1.43\mathrm{dB}$ improvements. These results suggest the effectiveness of WSSA and ARB. + +![](images/0c7bbf5863d38458a426c15b6df5a6e99b9665515ebbb8df1b48b20f96008698.jpg) + +Table 3. Ablation study of different self-attention schemes. + +
MetricBaseline-2S-MSA [3]Swin-MSA [25]HS-MSA [5]WSSA*WSSA
PSNR32.0132.8533.0133.0933.1933.30
SSIM0.9080.9160.9180.9190.9220.924
Params (M)1.031.291.291.291.291.29
FLOPs (G)13.8418.1519.0419.0418.1518.65
+ +Self-Attention Scheme Comparison. We compare WSSA with other self-attention and report the results in Table. 3. We adopt the half operation [5] in Swin-MSA [25] to keep the computation almost the same and use multi-head attention in the spectral dimension of WSSA* to align with S-MSA[3]. Baseline-2 is SSR-S that retains only the ERB and removes attention and yields 32.01dB. WSSA yields the most significant improvement of 1.29dB, which is 0.45dB, 0.29dB, and 0.21dB higher than S-MSA [3], Swin-MSA [25], and HS-MSA [5], which shows the effectiveness of WSSA. In addition, WSSA* and WSSA achieve 0.34dB and 0.45dB gain than S-MSA respectively, which demonstrates the role of considering local differences and modeling global spectral information. + +Influence of Multi-head attention and Mean effect. We demonstrate the influence of multi-head attention and mean effect on the spectra-wise self-attention through further experiments on the relationship between performance and token dim (window size) in WSSA and MSSA, which is shown in Fig. 7. Intuitively, the large window size would suffer from limited performance, which illustrates the influence of the mean effect. Performance degradation also occurs when the window size is too small to retain complete feature information. In our experiments, $8 \times 8$ window size optimally balances retaining feature information while minimizing the mean effect, which produces the highest performance of 33.3dB. When the token dim is small, WSSA + +![](images/a6cfbecee2bdd53ef115aa6926374723d641ea5960035cc626a5dd237cde9ae1.jpg) +Figure 6. Reconstructed images of real scene2 and scene4 with 2 and 4 out of 28 spectral channels separately by the state-of-the-art methods. Compared with other competing methods, our SSR recovers more details and clear content. +Figure 7. Influence of token dim in spectra-wise attention. + +clearly performs better than MSSA, which shows the role of maintaining spatial correlation. When the token dim is large, MSSA is slightly better than WSSA, which may be related to the shift in the imaging process and the strip pattern can contain some shift information. + +# 6. Conclusion + +In this paper, we analyze the influence of multi-head attention and mean effect on the spectra-wise transformer, and a novel SSR method is proposed to improve spectral snapshot reconstruction. To model the global spectral information, consider the local difference, and maintain spatial correlation, WSSA is proposed to better utilize spectral similarity. ARB leverages CMB to address the interaction between adjacent windows of WSSA and learn spatial representation when SAB is specially designed to mitigate spatial degradation in low-quality bands through a novel spatial alignment strategy. Extensive experiments on simulation and real scenes show the effectiveness of the proposed modules. Our SSR at different scales also significantly outperforms the state-of-the-art methods with less cost. + +Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62302394 and 62106063, the China Postdoctoral Science Foundation under Grant 317751, and the Natural Science Foundation of Shaanxi under Grant 2023-JC-QN-0757. + +# References + +[1] José M. Bioucas-Dias and Mário A. T. Figueiredo. A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration. 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Recently, the spectra-wise transformer has shown great potential in capturing inter-spectra similarities of HSI, but the classic design of the transformer, i.e., multi-head division in the spectral (channel) dimension hinders the modeling of global spectral information and results in mean effect. In addition, previous methods adopt the normal spatial priors without taking imaging processes into account and fail to address the unique spatial degradation in snapshot spectral reconstruction. In this paper, we analyze the influence of multihead division and propose a novel Spectral-Spatial Rectification (SSR) method to enhance the utilization of spectral information and improve spatial degradation. Specifically, SSR includes two core parts: Window-based Spectra-wise Self-Attention (WSSA) and spAtial Rectification Block (ARB). WSSA is proposed to capture global spectral information and account for local differences, whereas ARB aims to mitigate the spatial degradation using a spatial alignment strategy. The experimental results on simulation and real scenes demonstrate the effectiveness of the proposed modules, and we also provide models at multiple scales to demonstrate the superiority of our approach. https://github.com/ZhangJC-2k/SSR" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 550, + 128, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 128, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 128, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 571, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 693 + ], + "type": "text", + "content": "The advent of compressed sensing introduced the coded aperture snapshot spectral compressive imaging (CASSI) system [13, 29, 36], addressing drawbacks in traditional hyperspectral cameras regarding efficiency and cost-effectiveness, gaining significant attention. This system offers the promise of swift and cost-efficient capture of Hyperspectral Images (HSIs). However, the inherent ill-posedness of decoding 3D HSIs from 2D measurements poses a significant challenge for reconstruction algorithm design. Consequently, various model-based [1, 23, 24, 33," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 203, + 533, + 342 + ], + "blocks": [ + { + "bbox": [ + 309, + 203, + 533, + 342 + ], + "lines": [ + { + "bbox": [ + 309, + 203, + 533, + 342 + ], + "spans": [ + { + "bbox": [ + 309, + 203, + 533, + 342 + ], + "type": "image", + "image_path": "f528c9a5e802fd09a1ce2b4158621ecd3da637193eb884e436c5d87cba130440.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 342, + 547, + 387 + ], + "lines": [ + { + "bbox": [ + 305, + 342, + 547, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 547, + 387 + ], + "type": "text", + "content": "Figure 1. Comparison of PSNR-FLOPs between our SSR and previous reconstruction methods. Our SSR significantly outperforms other methods over 2dB at the same FLOPs when surpassing the state-of-the-art method over 1dB with fewer FLOPs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 396, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 546, + 445 + ], + "type": "text", + "content": "38, 40] and learning-based [2-6, 17, 18, 28, 37, 42] approaches have emerged to tackle this challenge. Within the realm of reconstruction algorithms, the effective utilization of diverse priors remains a pivotal research challenge." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 447, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 547, + 628 + ], + "type": "text", + "content": "Model-based methods initially adopt total variation [20, 40], low-rank [24], sparsity [21, 34] and more traditional hand-craft priors [1, 23, 24, 33, 38] to construct the optimization model, which preliminarily shows the practical feasibility of snapshot spectral reconstruction. With the advancement of deep learning, both convolutional neural networks (CNNs) [6, 17, 18, 28, 37, 42] and transformers [3-5, 11] have been successively introduced for learning the spatial and spectral characteristics of HSIs. They serve as end-to-end denoisers [3, 4, 6, 17, 28] or deep image priors [5, 11, 18, 37, 42] in learning-based methods. These advancements have led to significant progress in both real-world and simulated scenario reconstructions. In addition, the effective utilization of spectral and spatial characteristics has also naturally become a research hotspot." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Previous CNN methods such as TSA-Net [28], HDNet [17], DGSMP [18], and HerosNet [42], along with spatial transformers like Swin Transformer [25] and DAUHST [5], excel in learning spatial representations but do not effectively utilize the distinctive spectral characteristics inherent in HSIs. Conversely, spectra-wise transformers such as MST [3], MST++ [4], and RDLUF [11] show promising" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25817" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "potential in snapshot spectral reconstruction by exploiting inter-spectral similarities. However, their implementations follow the conventional transformer architecture, involving multi-head division in the spectral dimension, which limits the modeling of global spectral similarities and results in mean effect. Furthermore, in spectral snapshot imaging, some spatial degradation occurs in certain bands due to masking, shifting, and compression factors. Unfortunately, existing spatial and spectral networks lack tailored designs to mitigate such degradation effectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 430 + ], + "type": "text", + "content": "To optimize the utilization of spectral information and mitigate distinctive spatial degradation, we introduce the Spectral-Spatial Rectification (SSR) method into snapshot spectral reconstruction. Specifically, SSR comprises two key components: Window-based Spectral Self-Attention (WSSA) and spAtial Rectification Blocks (ARB). WSSA divides the features into multiple local windows in the spatial dimension, facilitating global spectral self-attention computations and the local difference consideration. Addressing the interaction gap between windows of WSSA, ARB leverages a Convolution Modulated Block (CMB). This block employs sliding large-kernel convolutions to interact with features between windows and learn effective spatial representation. Subsequently, to mitigate spatial degradation, ARB integrates a novel spatial alignment strategy. It assists low-quality bands in leveraging information from high-quality bands through learning a unified spatial representation and spectral weights, which further optimizes the utilization of spatial information. Overall, our contributions are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 431, + 287, + 563 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": "- We analyze the influence of multi-head division on previous spectra-wise transformers and propose Window-based Spectra-wise Self-Attention to model global spectral information while accounting for local differences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 479, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 287, + 528 + ], + "type": "text", + "content": "- A Spatial Rectification Block is specially designed to enhance spatial representation and mitigate the spatial degradation in low-quality bands through large-kernel convolutions and a novel spatial alignment strategy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 527, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 287, + 563 + ], + "type": "text", + "content": "- The qualitative and quantitative results of real and simulation experiments demonstrate that our SSR method significantly improves spectral snapshot reconstruction." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "The model-based methods [1, 20, 21, 23, 24, 33, 34, 38, 40] construct convex optimization models with some specific priors such as total variation [20, 40], low-rankness [24], and sparsity [21, 34] according to the physical schema of CASSI then solve the problem in an iterative manner to obtain reconstructed images. They have good interpretability and low cost, yet lack performance guarantee. Subsequently, the rise of deep learning [14, 15, 22] has facilitated the rapid development of spectral snapshot reconstruction. To improve reconstruction quality, Plug-and-Play" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "methods [41, 44] plug pre-trained deep networks as priors, which make great progress in performance but are still limited by slow reconstruction speed. Along with faster inference and better results, the CNN-based end-to-end denoisers [17, 28, 31] quickly achieved better results by establishing a mapping between measurements and HSIs, but also brought huge memory and computation costs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 157, + 546, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 546, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 546, + 372 + ], + "type": "text", + "content": "Recently, the transformer-based end-to-end denoisers [2-4] which capture data similarity and long-range dependence have shown impressive performance in both simulation and real scenes. These methods adopt self-attention to learn effective spatial and spectral representation, achieving very high parameter and computational efficiency. Following this, the unfolding methods [5, 11] regard transformers as deep priors for optimization formulas and improve iterative frameworks through end-to-end training. In these approaches, CNNs and transformers play a huge role either as end-to-end denoisers or as deep priors. While previous CNNs and spatial transformers fail to effectively utilize the spectral characteristics inherent in HSIs, spectra-wise transformer [3, 4, 11] has shown great potential in spectral tasks and attracted wide attention. However, current spectra-wise transformers follow classic multi-head design [12, 25, 35] and suffer from the loss of global spectral information and the limitation of ignoring local differences." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 381, + 495, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 381, + 495, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 381, + 495, + 396 + ], + "type": "text", + "content": "3. Spectral Snapshot Imaging Model" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": "Mathematically, we assume a spectral image patch with " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": " bands " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\{F_{\\lambda}\\}_{\\lambda = 1}^{\\Lambda}\\in \\mathbb{R}^{H\\times W}" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": " represents the HSI's height and weight. Image frame " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "F_{\\lambda}" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": " is modulated by a physical mask with pattern " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "M\\in \\mathbb{R}^{H\\times W}" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": " to get modulated image frame " + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "inline_equation", + "content": "F_{\\lambda}^{\\prime}" + }, + { + "bbox": [ + 304, + 401, + 545, + 461 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 394, + 461, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 461, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 394, + 461, + 545, + 475 + ], + "type": "interline_equation", + "content": "F _ {\\lambda} ^ {\\prime} = M \\circ F _ {\\lambda}, \\tag {1}", + "image_path": "d027e20f417a43ba37f92308170e899f05e31cc859b2909e63ffb0cd98daccb3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "text", + "content": " denotes Hadamard's (element-wise) product. Then the modulated image frames of different wavelengths " + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}" + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "text", + "content": " are separated to different positions by the disperser. After that, " + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}" + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "text", + "content": " distributed across different bands are shifted spatially and summed element-wise. Thus, " + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\left\\{F_{\\lambda}^{\\prime}\\right\\}_{\\lambda = 1}^{\\Lambda}" + }, + { + "bbox": [ + 304, + 483, + 545, + 582 + ], + "type": "text", + "content": " are compressed to a coded measurement:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 351, + 582, + 545, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 582, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 351, + 582, + 545, + 613 + ], + "type": "interline_equation", + "content": "G (m, n) = \\sum_ {i = 1} ^ {\\Lambda} F _ {\\lambda} ^ {\\prime} (m, n + D (\\lambda)), \\tag {2}", + "image_path": "c3e5ef7328155f0e68b3811663d75fb06d197a1486dccd6c87444fe97451751e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "text", + "content": " index the spatial coordinates, " + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "inline_equation", + "content": "D(\\lambda) = d(\\lambda - 1)" + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 621, + 545, + 692 + ], + "type": "text", + "content": " represents pixels shift between adjacent bands. Note Eq. (2) assumes a dispersion along the vertical dimension, and the derivation is also applicable for horizontal dispersion. The imaging model in Eq. (2) can be rewritten in the matrix-vector form as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 406, + 701, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 406, + 701, + 545, + 713 + ], + "type": "interline_equation", + "content": "g = \\Phi f, \\tag {3}", + "image_path": "99cfa661b698b1184f82bca8910287b4cd552ca2f5b13ba368909da9a6112fa1.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25818" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 57, + 250, + 232 + ], + "blocks": [ + { + "bbox": [ + 50, + 57, + 250, + 232 + ], + "lines": [ + { + "bbox": [ + 50, + 57, + 250, + 232 + ], + "spans": [ + { + "bbox": [ + 50, + 57, + 250, + 232 + ], + "type": "image", + "image_path": "0026dcc841925382e011a1de0924356289c07d3ccfef79ab0a999025a9c99a6d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 234, + 523, + 246 + ], + "lines": [ + { + "bbox": [ + 69, + 234, + 523, + 246 + ], + "spans": [ + { + "bbox": [ + 69, + 234, + 523, + 246 + ], + "type": "text", + "content": "Figure 2. (a)-(c) The overall architecture of SSR, SSRUnet, and SSRB. LMP is achieved via a formula. (d) Details of WSSA." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 253, + 57, + 395, + 232 + ], + "blocks": [ + { + "bbox": [ + 253, + 57, + 395, + 232 + ], + "lines": [ + { + "bbox": [ + 253, + 57, + 395, + 232 + ], + "spans": [ + { + "bbox": [ + 253, + 57, + 395, + 232 + ], + "type": "image", + "image_path": "00643df8bf9708cfa3453ad56d8dacdcb1d322ebe38f70651a8dccf638a2a0b2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 399, + 57, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 399, + 57, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 399, + 57, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 399, + 57, + 545, + 232 + ], + "type": "image", + "image_path": "2c9a1c4047f038f1af3e177cdad9e88b910772e8591ebb54a5c99611ebb7abdc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "g \\in \\mathbb{R}^{HW}" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "f \\in \\mathbb{R}^{HW\\Lambda}" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": " are the vectorized representation of the compressed image " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": " and the original spectral image " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": " respectively, and " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "\\Phi \\in \\mathbb{R}^{HW \\times HW\\Lambda}" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": " is the sensing matrix that describes the system imaging model. In spectral snapshot reconstruction, what we need to do is recover 3D HSI " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": " from the compressed 2D measurement " + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 251, + 288, + 326 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 335, + 103, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 103, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 103, + 346 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 354, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 439 + ], + "type": "text", + "content": "Existing spectral and spatial network designs [2-5, 11] are limited by the direct application of traditional multi-head division and unique spatial degradation of snapshot spectral imaging. To address the limitations, we propose the Spectral-Spatial Rectification (SSR) method to better model the spectral information, enhance spatial representation, and improve spatial degradation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 446, + 167, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 167, + 457 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 167, + 457 + ], + "type": "text", + "content": "4.1. Overall Architecture" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": "An overview of SSR is presented in Fig. 2 (a), we adopt a multistage network including initialization and " + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": " cascaded stages, and each stage consists of Linear Manifold Projection (LMP), Spectral-Spatial Rectification Unet (SSRUnet), and spAtial Rectification Block (ARB). First, the compressed measurement " + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": " is reversed to the initial shape [3] and the 2D mask is repeated in channel dimension to obtain the 3D mask. Then the two are inputted to a " + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": " convolution kernel " + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "inline_equation", + "content": "(conv1 \\times 1)" + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": " to get the initialization. In each stage, LMP is adopted to assist the reconstruction based on the imaging model. Then the SSRUnet is employed to refine the input through novel spatial and spectral design. Finally, ARB is used to further improve spatial degradation in reconstruction. For the core module SSRUnet, as illustrated in Fig. 2 (b), the " + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "inline_equation", + "content": "conv3 \\times 3s" + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": " with residual are utilized to embed mask information into input " + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 464, + 288, + 657 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 62, + 665, + 287, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 665, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 62, + 665, + 287, + 689 + ], + "type": "interline_equation", + "content": "X _ {M E} = \\operatorname {C o n v} _ {3 \\times 3} (X) \\circ \\left(T _ {I} + \\operatorname {C o n v} _ {3 \\times 3} (\\text {M a s k})\\right), \\tag {4}", + "image_path": "95471afd82a72c30e34b09f51f9250f00a76a2d826b407e71a22f49e8439a588.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "inline_equation", + "content": "X_{ME}" + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "content": " is the features embedded with the mask, " + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "inline_equation", + "content": "T_{I}" + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "content": " is an all-one tensor and " + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "inline_equation", + "content": "Mask" + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "content": " is the 3D mask obtained in ini" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "content": "tialization. Then SSRUnet with three layers and " + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "inline_equation", + "content": "conv3 \\times 3" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "content": " are employed to extract the deep feature which is combined with the input as a residual to produce a refined output. The SSRUnet consists of downsampling modules (" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "inline_equation", + "content": "conv4 \\times 4" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "content": "), Spectral-Spatial Rectification Block (SSRB), upsampling modules (" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "inline_equation", + "content": "deconv2 \\times 2" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "content": "), and Fusion modules (" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "inline_equation", + "content": "conv1 \\times 1" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "content": "). Spectral-Spatial Rectification Block (SSRB). SSRB is the basic module of SSRUnet. As shown in Fig. 2 (c), the implicit positional information [10] is firstly embedded in the input for applying self-attention later in SSRB. Each SSRB is the sequential combination of the spEctral Rectification Block (ERB) and ARB. Fig. 2 (c) illustrates the components of ERB and ARB, i.e., a Feed Forward Network(FFN) and a Window-based Spectral Self-Attention (WSSA) for ERB, a Convolution Moudulated Block (CMB) and a Spatial Alignment Block (SAB) for ARB, and same Layer Normalization (LN) and Group Normalization (GN) for ERB and ARB. WSSA is detailed in Fig. 2 (d) and FFN consists of two linear layers sandwiched with depth-wise " + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "inline_equation", + "content": "conv3 \\times 3" + }, + { + "bbox": [ + 304, + 252, + 545, + 481 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 491, + 459, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 459, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 459, + 503 + ], + "type": "text", + "content": "4.2. Spectral Rectification Block" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 628 + ], + "type": "text", + "content": "Spectral self-attention is a promising approach to utilize spectral characteristics for HSI tasks. However, we find that the previous spectra-wise transformer [3, 4, 11] directly considers a band as a token and follows traditional spatial self-attention design, i.e., multi-head division in spectral (channel) dimension, which ignores the local differences in spectral distribution and results in mean effect and nonglobal spectral utilization. To solve the problem, we propose the ERB based on WSSA to consider local differences and model global spectral information." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "The Influence of Multi-Head Division in Spectral (Channel) Dimension. In the classic transformer design [12, 25, 35], the use of multi-head division in the channel dimension is common and brings some gains. Possibly affected by this, the previous spectra-wise transformer in spectral snapshot reconstruction also divides multi-head in spectral dimension as shown in Fig. 3 (a), which results in the sep" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25819" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 57, + 233, + 158 + ], + "blocks": [ + { + "bbox": [ + 50, + 57, + 233, + 158 + ], + "lines": [ + { + "bbox": [ + 50, + 57, + 233, + 158 + ], + "spans": [ + { + "bbox": [ + 50, + 57, + 233, + 158 + ], + "type": "image", + "image_path": "bccbcbcf1a52e83ff19d2405b07bdef96435b3f648d1c3633542157669025afe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 162, + 221, + 171 + ], + "lines": [ + { + "bbox": [ + 72, + 162, + 221, + 171 + ], + "spans": [ + { + "bbox": [ + 72, + 162, + 221, + 171 + ], + "type": "text", + "content": "(a) Multi-head Division in Spectral Dimension" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 244, + 63, + 334, + 144 + ], + "blocks": [ + { + "bbox": [ + 244, + 63, + 334, + 144 + ], + "lines": [ + { + "bbox": [ + 244, + 63, + 334, + 144 + ], + "spans": [ + { + "bbox": [ + 244, + 63, + 334, + 144 + ], + "type": "image", + "image_path": "d7fcda305dd1eadfa1ed0ee606353b104f0450649b1f64beed0aaebd69e7ff01.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 258, + 162, + 309, + 171 + ], + "lines": [ + { + "bbox": [ + 258, + 162, + 309, + 171 + ], + "spans": [ + { + "bbox": [ + 258, + 162, + 309, + 171 + ], + "type": "text", + "content": "(b) Mean Effect" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 345, + 70, + 428, + 150 + ], + "blocks": [ + { + "bbox": [ + 345, + 70, + 428, + 150 + ], + "lines": [ + { + "bbox": [ + 345, + 70, + 428, + 150 + ], + "spans": [ + { + "bbox": [ + 345, + 70, + 428, + 150 + ], + "type": "image", + "image_path": "4f81174c8393974768e401ef4dfe157f8c5c35ef743deeed1c2bb5a5818116a7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 180, + 480, + 191 + ], + "lines": [ + { + "bbox": [ + 111, + 180, + 480, + 191 + ], + "spans": [ + { + "bbox": [ + 111, + 180, + 480, + 191 + ], + "type": "text", + "content": "Figure 3. (a)-(c) The influence of multi-head attention and mean effect, (d) The illustration of WSSA." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 444, + 72, + 534, + 149 + ], + "blocks": [ + { + "bbox": [ + 351, + 158, + 428, + 175 + ], + "lines": [ + { + "bbox": [ + 351, + 158, + 428, + 175 + ], + "spans": [ + { + "bbox": [ + 351, + 158, + 428, + 175 + ], + "type": "text", + "content": "(c) Multi-head Division in Spatial Dimension" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 444, + 72, + 534, + 149 + ], + "lines": [ + { + "bbox": [ + 444, + 72, + 534, + 149 + ], + "spans": [ + { + "bbox": [ + 444, + 72, + 534, + 149 + ], + "type": "image", + "image_path": "cbde6d6fd07e5a3e1034d8ae90ad89077fd3c760438945264d970c51b825ffd5.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 162, + 536, + 171 + ], + "lines": [ + { + "bbox": [ + 443, + 162, + 536, + 171 + ], + "spans": [ + { + "bbox": [ + 443, + 162, + 536, + 171 + ], + "type": "text", + "content": "(d) Window-based Attention" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 198, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 270 + ], + "type": "text", + "content": "aration of spectral information and failure to model global spectral information. It's very easy to get confused because the spectral transformer is in contrast to the spatial transformer, where the characteristic dimension of the former is the spatial dimension, and the characteristic dimension of the latter is the spectral (channel) dimension." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "text", + "content": "The Influence of Mean Effect. In addition, considering that HSIs depict the spectral distribution of scenes, the similarities of different regions should be different but previous multi-head division results in all regions sharing the same similarity. When treating the whole band as a token to calculate spectral self-attention, we obtain the mean of all region similarities in the band and the local differences between regions are lost, which we call the 'Mean Effect'. Define " + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "text", + "content": " features " + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "inline_equation", + "content": "\\{f_{\\lambda}\\}_{\\lambda = 1}^{\\Lambda}" + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "text", + "content": " where feature dimension consists of " + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "text", + "content": " different patterns (regions), i.e., " + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "inline_equation", + "content": "f_{\\lambda} = [f_{\\lambda}^{1}, f_{\\lambda}^{2}, \\ldots, f_{\\lambda}^{p}]" + }, + { + "bbox": [ + 46, + 270, + 287, + 414 + ], + "type": "text", + "content": ", the influence of mean effect on the similarity calculation can be simply described as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 96, + 418, + 287, + 446 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 418, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 96, + 418, + 287, + 446 + ], + "type": "interline_equation", + "content": "\\operatorname {s i m} \\left(f _ {i} ^ {k}, f _ {j} ^ {k}\\right)\\rightarrow \\frac {1}{p} \\sum_ {m = 1} ^ {p} \\operatorname {s i m} \\left(f _ {i} ^ {m}, f _ {j} ^ {m}\\right), \\tag {5}", + "image_path": "5a814af1e4253a566a52b14d97ea706e7e3b5b20a25f7bfac3980e2baaae0ca1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "content": "where the left part denotes the expected similarity of the " + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "content": "th pattern between " + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "inline_equation", + "content": "f_{i}^{k}" + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "inline_equation", + "content": "f_{j}^{k}" + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "content": ", and the right part represents the obtained similarity in previous approaches. We also present an example in Fig. 3 (b), the average similarity and local region similarity between the red band and other bands are marked with red numbers and black numbers respectively. To demonstrate the validity of our theory, we carried out ablation experiments of different region sizes, i.e., window size under the same conditions later. In addition, the mean effect may explain why multi-head attention is more effective than single-head attention." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "Multi-Head Division in Spatial Dimension. When realizing appropriate feature dimension and mean effect, it was natural to treat the entire band frame as a token and then directly divide multi-head [35] in the merged spatial dimension to calculate self-attention, which we call MSSA later for short. However, as shown in Fig. 3 (c), this would split the entire image into (incomplete) strip shapes on each head, which mitigates the mean effect to some extent but breaks the spatial correlation of features. That is, adjacent areas are divided into different heads, while areas that are far apart in space are divided into the same head." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": "Window-based Spectral Self-Attention (WSSA). To capture the global spectral similarity, solve the mean effect, and maintain spatial correlation, WSSA divides features into a number of windows spatial-wisely, and then the spectrawise self-attention is calculated within windows to avoid the interference of each other, which is shown in Fig. 3 (d). Specifically, define input " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": ", as shown in Fig. 2 (d), " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": " is first linearly projected to " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "3C" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": " channels tensor via a " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": " convolution then uniformly divides the tensor channel-wisely into the query " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "(Q)" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "(K)" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": ", value " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "(V)" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": ". Subsequently, " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "Q, K, V" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": " are split spatial-wise into " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "HW / M^2" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": " windows with size of " + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{M \\times M \\times C}" + }, + { + "bbox": [ + 304, + 198, + 545, + 342 + ], + "type": "text", + "content": " separately:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 359, + 348, + 545, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 348, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 359, + 348, + 545, + 365 + ], + "type": "interline_equation", + "content": "\\left\\{Q _ {i}, K _ {i}, V _ {i} \\right\\} _ {i = 1} ^ {H W / M ^ {2}} = Q, K, V, \\tag {6}", + "image_path": "a7fdf67d213bc18ed1f20ab18af703fa09f1289c6660046fdd0ac11d7c0d13ae.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "type": "inline_equation", + "content": "Q_{i},K_{i},V_{i}\\in \\mathbb{R}^{M\\times M\\times C}" + }, + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "type": "text", + "content": " and are then reshaped into shape " + }, + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{M^2\\times C}" + }, + { + "bbox": [ + 305, + 370, + 545, + 397 + ], + "type": "text", + "content": " as tokens to calculate attention as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 342, + 403, + 545, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 403, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 342, + 403, + 545, + 417 + ], + "type": "interline_equation", + "content": "\\text {A t t e n t i o n} _ {i} = \\operatorname {S o f t M a x} \\left(Q _ {i} ^ {T} K _ {i} / M\\right) V _ {i}, \\tag {7}", + "image_path": "517449e2f0bb32729459d790603024a90ce5431bec3bd6ab68d4ed5485c057fc.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "text", + "content": " is used as the scale factor before applying the softmax function. Then the outputs of " + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "inline_equation", + "content": "HW / M^2" + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "text", + "content": " attention are reshape in " + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{M\\times M\\times C}" + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "text", + "content": " and merge together in the original arrangement to undergo a conv1 " + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\times 1" + }, + { + "bbox": [ + 305, + 422, + 545, + 471 + ], + "type": "text", + "content": " projection:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 359, + 476, + 545, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 476, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 359, + 476, + 545, + 493 + ], + "type": "interline_equation", + "content": "X ^ {\\prime} = \\left\\{A t t e n t i o n _ {i} \\right\\} _ {i = 1} ^ {H W / M ^ {2}} W _ {1}, \\tag {8}", + "image_path": "43f7c501fc1a04104e70e5d50b8d24aba42b1c21d53568684da4b6dcfa02a39b.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "inline_equation", + "content": "W_{1} \\in \\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "text", + "content": " are weight matrices of a " + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "inline_equation", + "content": "conv1 \\times 1" + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "text", + "content": " is the final output in " + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 499, + 545, + 607 + ], + "type": "text", + "content": ". Different from multi-head self-attention which implements token embedding and then divides heads, WSSA first implements windows split then reshaping into tokens, which preserves the spatial correlation of each token. Regarding WSSA as a special multi-head self-attention, the number of WSSA heads is more, often hundreds of thousands, far more than the number of multi-head attention." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 609, + 544, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 544, + 632 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 544, + 632 + ], + "type": "text", + "content": "Computational Complexity. The computational complexity of WSSA is displayed as follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 637, + 545, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 637, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 317, + 637, + 545, + 659 + ], + "type": "interline_equation", + "content": "O (W S S A) = 4 H W C ^ {2} + 2 M ^ {2} C ^ {2} \\frac {H W}{M ^ {2}} = 6 H W C ^ {2}. \\tag {9}", + "image_path": "ffb6b6167d5375429a24b22dd154927f3ab3d55b87e35a13e39093ea02d78fb1.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "The computational complexity of WSSA is linear to the spatial size " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "HW" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " and window size-independent, meaning that there is no additional computation cost when we improve spectral utilization." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25820" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 57, + 545, + 241 + ], + "blocks": [ + { + "bbox": [ + 51, + 57, + 545, + 241 + ], + "lines": [ + { + "bbox": [ + 51, + 57, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 51, + 57, + 545, + 241 + ], + "type": "image", + "image_path": "9f74e7384f6bb4a1fca7f1e4b41334c5ab09c7b5617ae32edde3e0a2484a6631.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 546, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 546, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 546, + 266 + ], + "type": "text", + "content": "Figure 4. (a) Display of spatial degradation in spectra-wise transformers. (b) The details of CMB. (c) The effect of large kernel convolution in CMB. (d) The details of SAB. (e) Spatial alignment strategy of SAB." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 277, + 194, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 194, + 290 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 194, + 290 + ], + "type": "text", + "content": "4.3. Spatial Rectification Block" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "text", + "content": "The utilization of WSSA enhances the capability of spectral information capture. However, a limitation arises from the absence of interaction between adjacent windows within WSSA, potentially leading to discontinuous spatial representation and the occurrence of blocking artifacts, as highlighted by [7]. Additionally, unique spatial degradation occurs due to mask, shift, and compression in spectral snapshot imaging. To address these concerns, we propose a spA tial Rectification Block (ARB) comprising a Convolution Modulated Block (CMB) and a Spatial Alignment Block (SAB). This ARB aims to foster interaction between adjacent windows and alleviate spatial degradation in the HSIs. Convolution Modulated Block (CMB). Here, we try to solve two problems: (1) When different windows cannot interfere with each other, WSSA also fails to exchange information, which leads to discrete spatial expression and may lead to blocking artifacts [7]. (2) As shown in the top two rows of Fig .4 (a), over-smoothing demonstrates that the spatial representation ability of a single spectra-wise transformer is not sufficient. To solve these two problems and inspired by the development of large kernel convolution in high-level tasks, we adopted a Convolution Modulated Block (CMB) proposed in [16] to modulate spatial information and make adjacent windows interact with each other through large kernel convolution sliding as shown in Fig. 4 (b). CMB modulates spatial information in a similar manner to self-attention but much more efficiently. Specifically, given the input tokens " + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "inline_equation", + "content": "X\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "text", + "content": ", we use a simple depth-wise convolution with kernel size " + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "inline_equation", + "content": "11\\times 11" + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "text", + "content": " to calculate the modulated attention " + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 297, + 287, + 654 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 666, + 287, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 666, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 111, + 666, + 287, + 679 + ], + "type": "interline_equation", + "content": "A = D C o n v _ {1 1 \\times 1 1} (X W _ {2}), \\tag {10}", + "image_path": "5658a2971e0cbd130dcfc88f623138740294a0c4cc1db30a3efa15820856a6c0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "W_{2}\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " are weight matrices of conv1 x 1s, and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "DConv_{11\\times 11}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " denotes a depth-wise convolution with" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "text", + "content": "kernal size " + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "inline_equation", + "content": "11 \\times 11" + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "text", + "content": ". Then we adopt the element-wise product and attention " + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "text", + "content": " to modulate the project feature " + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "inline_equation", + "content": "V'" + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "text", + "content": " to get the output " + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 305, + 278, + 545, + 313 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 362, + 314, + 545, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 314, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 362, + 314, + 545, + 327 + ], + "type": "interline_equation", + "content": "Z = \\left(A \\circ V ^ {\\prime}\\right) W _ {4}, V ^ {\\prime} = X W _ {3}, \\tag {11}", + "image_path": "05f88c1762108622482e3fd9f1fb0776dfd6fbd744d35ab34bd206638a2f71f8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "W_{3}" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "W_{4} \\in \\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": " are weight matrices of " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "conv1 \\times 1s" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": ". On the one hand, CMB could effectively improve the spatial representation of features through modulation operation. On the other hand, CMB enables the pixels between adjacent windows of WSSA to interact spatial-wisely when depth-wise convolution kernel size " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "11 \\times 11" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": " is greater than patch size " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": ", as demonstrated in Fig. 4 (c)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": "Spatial Alignment Block (SAB). As shown in the bottom two rows of Fig. 4 (a), we observe that the reconstruction results of some bands have more spatial degradation such as distortion and deformation, which is not common in other HSI tasks. Thus, we think this may be related to the unique imaging process. As shown in Fig. 4 (e), shift and compression in the imaging process mix information from different spatial locations, and spatial texture recovery in bands with low spectral density may be difficult, which is neglected by previous methods. Considering that the low-density bands can be obtained by multiplying the high-density bands by weights, we can utilize the high-quality bands to improve the spatial texture of the low-quality bands through a novel spatial alignment strategy, as shown in Fig. 4 (e). To achieve this, a Spatial Alignment Block (SAB) is proposed to improve spatial degradation. As shown in 4 (d), we adopt different convolution kernels to estimate spatial texture distribution which corresponds to the high-density part, and learn spectral weights in SAB when two linear layers are used to mix channel information. Specifically, given the input feature " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ", we use a convolution with kernel size " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "GELU" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " activation function to learn the spatial texture " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 371, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 371, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "T = \\psi \\left(\\operatorname {C o n v} _ {3 \\times 3} \\left(F W _ {5}\\right)\\right), \\tag {12}", + "image_path": "56d3f433c7a17ede7ddd8b01068d10a56fa6464b80221b1332f97d6a0b145a0a.jpg" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25821" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 68, + 541, + 337 + ], + "blocks": [ + { + "bbox": [ + 64, + 57, + 528, + 68 + ], + "lines": [ + { + "bbox": [ + 64, + 57, + 528, + 68 + ], + "spans": [ + { + "bbox": [ + 64, + 57, + 528, + 68 + ], + "type": "text", + "content": "Table 1. The PSNR (upper entry in each cell) in dB and SSIM (lower entry in each cell) results of the test methods on 10 scenes." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 68, + 541, + 337 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 541, + 337 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 541, + 337 + ], + "type": "table", + "html": "
AlgorithmsReferenceParamsGFLOPsScene1Scene2Scene3Scene4Scene5Scene6Scene7Scene8Scene9Scene10Avg
DIP-HSI [30]ICCV 202133.8564.4232.6827.2631.3040.5429.7930.3928.1829.4434.5128.5131.26
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
TSA-Net [28]ECCV 202044.25110.0632.0331.0032.2539.1929.3931.4430.3229.3530.0129.5931.46
0.8920.8580.9150.9530.8840.9080.8780.8880.8900.8740.894
DGSMP [18]CVPR 20213.5884.7733.2632.0933.0640.5428.8633.0830.7431.5531.6631.4432.63
0.9150.8980.9250.9640.8820.9370.8860.9230.9110.9250.917
GAP-Net [27]IJCV 20234.2778.5833.7433.2634.2841.0331.4432.4032.2730.4633.5130.2433.26
0.9110.9000.9290.9670.9190.9250.9020.9050.9150.8950.917
HerosNet [42]CVPR 202211.27414.7635.6935.0134.8238.0733.1834.9433.5833.1933.0433.0134.45
0.9730.9680.9670.9850.9690.9760.9620.9680.9640.9650.970
HDNet [17]CVPR 20222.37154.7635.1435.6736.0342.3032.6934.4633.6732.4834.8932.3834.97
0.9350.9400.9430.9690.9460.9520.9260.9410.9420.9370.943
MST [3]CVPR 20222.0328.1535.4035.8736.5142.2732.7734.8033.6632.6735.3932.5035.18
0.9410.9440.9530.9730.9470.9550.9250.9480.9490.9410.948
CST [2]ECCV 20223.040.1035.9636.8438.1642.4433.2535.7234.8634.3436.5133.0936.12
0.9490.9550.9620.9750.9550.9630.9440.9610.9570.9450.957
BIRNAT [8]TPAMI 20234.402122.6636.7937.8940.6146.9435.4235.3036.5833.9639.4732.8037.58
0.9510.9570.9710.9850.9640.9590.9550.9560.9700.9380.960
DAUHST [5]NeurIPS 20226.1579.5037.2539.0241.0546.1535.8037.0837.5735.1040.0234.5938.36
0.9580.9670.9710.9830.9690.9700.9630.9660.9700.9560.967
RDLUF [11]CVPR 20231.81115.3437.9440.9543.2547.8337.1137.4738.5835.5041.8335.2339.57
0.9660.9770.9790.9900.9760.9750.9690.9700.9780.9620.974
SSR-SOurs1.7326.3738.2240.0542.5747.4636.5037.3337.6035.7041.3735.0639.19
0.9630.9720.9750.9860.9720.9710.9640.9680.9750.9590.971
SSR-MOurs3.4552.6538.6141.3543.9448.3237.8038.0738.5436.8242.7235.7940.20
0.9670.9780.9790.9880.9770.9750.9690.9740.9800.9650.975
SSR-LOurs5.1878.9339.0742.0444.4948.8038.6438.5039.1636.9643.1236.0840.69
0.9700.9810.9800.9900.9800.9780.9710.9760.9820.9680.978
SSR-L*Ours1.7378.9338.8141.5143.7648.6238.3237.8538.5036.8542.6435.8240.27
0.9680.9790.9790.9880.9790.9750.9690.9740.9800.9650.976
", + "image_path": "5bb4087632ef293203f4f7f7263a9875c53ef460e54e8578861cbf8f81531ee2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}^{H \\times W \\times 1}" + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "content": " is GELU activation function and " + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "W_5 \\in \\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "content": " are weight matrices of the linear layer. Meanwhile, we use a depth-wise convolution with kernel size " + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "content": " and Sigmoid activation function to learn spectral element-wise weight as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 103, + 417, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 417, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 103, + 417, + 287, + 430 + ], + "type": "interline_equation", + "content": "S W = \\sigma \\left(D C o n v _ {3 \\times 3} \\left(F W _ {5}\\right)\\right), \\tag {13}", + "image_path": "24a3e10a7e42ff9d348cfdf78279e61098c7f39b023b2c65913e07801c21ec84.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "inline_equation", + "content": "SW \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "text", + "content": " is Sigmoid activation function. Finally, we use multiple element-wise products and a conv1 × 1 projection " + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "inline_equation", + "content": "W_{6}" + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "text", + "content": " to calculate the output " + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 438, + 287, + 485 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 486, + 287, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 486, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 116, + 486, + 287, + 500 + ], + "type": "interline_equation", + "content": "Y = \\left\\{T \\circ S W _ {i} \\right\\} _ {i = 1} ^ {C} W _ {6}, \\tag {14}", + "image_path": "a6edd29b7141a718371540f92167f4d49fa58310eae250c1540706e835302bde.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "type": "inline_equation", + "content": "Y \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "type": "inline_equation", + "content": "SW_{i} \\in \\mathbb{R}^{H \\times W \\times 1}" + }, + { + "bbox": [ + 47, + 505, + 233, + 518 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 234, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 234, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 234, + 539 + ], + "type": "text", + "content": "4.4. Linear Manifold Projection (LMP)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 544, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 614 + ], + "type": "text", + "content": "Eq. (3) is a key constraint in spectral compression reconstruction. To take advantage of this prior, we introduce a Linear Manifold Projection (LMP) proposed in GAP-Net [27] to assist the reconstruction. We add an additional parameter to control projection intensity and perform the LMP as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 94, + 616, + 287, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 616, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 94, + 616, + 287, + 631 + ], + "type": "interline_equation", + "content": "f ^ {\\prime} = f + \\rho \\Phi^ {T} [ (g - \\Phi f) \\cdot / (\\Phi \\Phi^ {T}) ], \\tag {15}", + "image_path": "32a0658ca0e95098c8e436f34c7d415208d08e2c248bed42c5743bcbba176cc1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 639, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 287, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 639, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 639, + 287, + 664 + ], + "type": "text", + "content": " is the parameter that is estimated through a simple network similar to [5]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 671, + 180, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 180, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 180, + 684 + ], + "type": "text", + "content": "4.5. Implementation Details" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": "We change the stage numbers " + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": " to establish a series of SSR models with small, medium, and large scales: SSR-S" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "(N = 3)" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": ", SSR-M " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "(N = 6)" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": ", and SSR-L " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "(N = 9)" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": ". The proposed SSR is implemented by PyTorch and the window size in WSSA is empirically set to " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": ". Adam [19] optimizer " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "(\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999)" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": " and Cosine Annealing [26] scheduler are adopted to train SSR on a single RTX 3090 GPU. Training samples are patches with spatial sizes of " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": " randomly cropped from 3D HSI data cubes for simulation and real experiments separately. The shifting step " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": " of the imaging model is 2. The channels of SSRUnet layers are set to " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Lambda, 2\\Lambda, 4\\Lambda" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": " in sequence and basic bands " + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Lambda = 28" + }, + { + "bbox": [ + 304, + 347, + 545, + 504 + ], + "type": "text", + "content": ". The training loss function is the root mean square error (RMSE) between reconstructed and ground-truth HSIs and adopts the multi-stage loss setting proposed in [43]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 517, + 382, + 531 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 382, + 531 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 382, + 531 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 538, + 432, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 432, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 432, + 551 + ], + "type": "text", + "content": "5.1. Experimental Settings" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "text", + "content": "Following [5, 11, 17, 28, 42], we select 28 wavelengths from " + }, + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "inline_equation", + "content": "450\\mathrm{nm}" + }, + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "inline_equation", + "content": "650\\mathrm{nm}" + }, + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "text", + "content": " by using spectral interpolation manipulation to derive HSIs. We conduct experiments on simulation and real datasets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "content": "Simulation and Real Data. Two simulation datasets, CAVE [32] and KAIST [9], and five real HSIs captured by the CASSI system developed in [28] are adopted. The CAVE dataset provides 32 HSIs with a spatial size of " + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "content": ". The KAIST dataset includes 30 HSIs with a spatial size of " + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "inline_equation", + "content": "2704 \\times 3376" + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "content": ". We use CAVE for simulation training and select 10 scenes from KAIST for simulation testing." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. We adopt two image quality indexes including peak signal-to-noise ratio (PSNR), and structure" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "25822" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 57, + 89, + 99 + ], + "blocks": [ + { + "bbox": [ + 50, + 57, + 89, + 99 + ], + "lines": [ + { + "bbox": [ + 50, + 57, + 89, + 99 + ], + "spans": [ + { + "bbox": [ + 50, + 57, + 89, + 99 + ], + "type": "image", + "image_path": "0c41ff77b099a8ced2ad89208d45437b39c0b325467a55798dc7b11a0eef1dc7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 49, + 99, + 135, + 107 + ], + "lines": [ + 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"2abd000406f68f2cc8265835265a0734536a60e58e1c693a75e02d213193c3d1.jpg" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 504, + 217, + 544, + 222 + ], + "lines": [ + { + "bbox": [ + 504, + 217, + 544, + 222 + ], + "spans": [ + { + "bbox": [ + 504, + 217, + 544, + 222 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 54, + "angle": 0, + "type": "image_caption" + } + ], + "index": 45 + }, + { + "bbox": [ + 46, + 255, + 287, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 303 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 303 + ], + "type": "text", + "content": "similarity (SSIM) [39] for quantitative evaluation. Specifically, PSNR measures the visual quality, while SSIM measures the structure similarity. Generally, higher values of PSNR and SSIM mean better reconstruction results." + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 47, + 312, + 150, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 150, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 150, + 323 + ], + "type": "text", + "content": "5.2. Simulation Scene" + } + ] + } + ], + "index": 57 + }, + { + "bbox": [ + 46, + 330, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 287, + 605 + ], + "type": "text", + "content": "Quantitative results. Table. 1 and Fig. 1 show the quantitative comparison of our SSR and the state-of-the-art (SOTA) methods: DIP-HSI [30], TSA-Net [28], DGSMP [18], GAPnet [27], HerosNet [42], HDNet [17], MST [3], CST [2], BIRNAT [8], DAUHST [5], RDLUF [11]. We can see that SSR significantly outperforms the other methods by over 2dB at the same FLOPs and exceeds the leading method RDLUF by more than 1dB with reduced computational demands. Concretely, our best model, SSR-L surpasses SOTA methods RDLUF, DAUHST, and DAUHST by 1.12, 2.33, and 3.11dB while less computational effort is required. Surprisingly, our small model SSR-S surpasses most methods when requiring the least parameters and FLOPs. Moreover, our middle model outperforms the best method RDLUF by 0.63dB when less than 1/2 FLOPs are required. It is worth noting that RDLUF adopts a stage parameter-sharing strategy and we take the same strategy to establish our SSR-" + }, + { + "bbox": [ + 46, + 330, + 287, + 605 + ], + "type": "inline_equation", + "content": "L^*" + }, + { + "bbox": [ + 46, + 330, + 287, + 605 + ], + "type": "text", + "content": ", which brings performance degradation but still achieves a clear advantage over other methods with the least parameters. We found that the degradation comes from the stability of the method, that is, as the number of parameters increases, the performance of our SSR steadily increases and RDLUF decreases." + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "Visual comparison. We provide the visual comparison of simulation scene7 with 4 out of 28 spectral channels in Fig. 5. SSR-L successfully recovers the clear pattern and sharp edge on the cup when the other methods all suffer from blurred or distorted effects. In addition, we plot the spectral curves of two regions in scene1 in the bottom-left of Fig. 5. It's intuitive that SSR-L has a prominent higher correlation with the reference spectra, which demonstrates the effectiveness of our spectra-wise attention." + } + ] + } + ], + "index": 59 + }, + { + "type": "table", + "bbox": [ + 308, + 265, + 544, + 316 + ], + "blocks": [ + { + "bbox": [ + 344, + 254, + 506, + 265 + ], + "lines": [ + { + "bbox": [ + 344, + 254, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 344, + 254, + 506, + 265 + ], + "type": "text", + "content": "Table 2. Ablation study of WSSA and ARB." + } + ] + } + ], + "index": 60, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 265, + 544, + 316 + ], + "lines": [ + { + "bbox": [ + 308, + 265, + 544, + 316 + ], + "spans": [ + { + "bbox": [ + 308, + 265, + 544, + 316 + ], + "type": "table", + "html": "
Baseline-1WSSAARBPSNRSSIMParams (M)FLOPs (G)
✓36.600.9561.0614.43
✓✓37.760.9651.3018.82
✓✓✓39.190.9711.7326.37
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For fair comparisons, all methods are trained on the CAVE and KAIST datasets jointly using the fixed real mask with 11-bit shot noise injected. The bottom two rows of Fig. 6 plot the visual comparisons of the proposed SSR-S and the existing SOTA methods while the top two rows plot the visual comparisons of different spectra-wise transformers [3, 4]. It is intuitive to see that our SSR-S restores clearer spatial textures and sharper edges than previous spectra-wise transformers in the top two rows, which shows the effect of spatial modulation. Compared with other methods in the bottom two rows, SSR-S obtains clearer results in these two bands when other methods fail to recover these two bands, demonstrating the effectiveness of our spatial alignment strategy." + } + ] + } + ], + "index": 63 + }, + { + "bbox": [ + 306, + 562, + 427, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 427, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 427, + 574 + ], + "type": "text", + "content": "5.4. Ablation Experiment" + } + ] + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "type": "text", + "content": "In this part, we adopt the CAVE and KAIST datasets to conduct ablation studies." + } + ] + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": "Effectiveness of WSSA and ARB. We first conduct a break-down ablation experiment to investigate the effect of each component towards higher performance. The results are listed in Table. 2. The baseline-1 model is derived by removing our WSSA and ARB from SSR-S and yields " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "36.60\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": ". When we successively apply our WSSA and ARB, the model continuously achieves " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "1.16\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "1.43\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": " improvements. These results suggest the effectiveness of WSSA and ARB." + } + ] + } + ], + "index": 66 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25823" + } + ] + } + ], + "index": 67 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 55, + 545, + 277 + ], + "blocks": [ + { + "bbox": [ + 50, + 55, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 50, + 55, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 50, + 55, + 545, + 277 + ], + "type": "image", + "image_path": "0c7bbf5863d38458a426c15b6df5a6e99b9665515ebbb8df1b48b20f96008698.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 319, + 286, + 374 + ], + "blocks": [ + { + "bbox": [ + 59, + 308, + 273, + 319 + ], + "lines": [ + { + "bbox": [ + 59, + 308, + 273, + 319 + ], + "spans": [ + { + "bbox": [ + 59, + 308, + 273, + 319 + ], + "type": "text", + "content": "Table 3. Ablation study of different self-attention schemes." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 319, + 286, + 374 + ], + "lines": [ + { + "bbox": [ + 51, + 319, + 286, + 374 + ], + "spans": [ + { + "bbox": [ + 51, + 319, + 286, + 374 + ], + "type": "table", + "html": "
MetricBaseline-2S-MSA [3]Swin-MSA [25]HS-MSA [5]WSSA*WSSA
PSNR32.0132.8533.0133.0933.1933.30
SSIM0.9080.9160.9180.9190.9220.924
Params (M)1.031.291.291.291.291.29
FLOPs (G)13.8418.1519.0419.0418.1518.65
", + "image_path": "e2ce8719680c23d88a00478c790ed07862e7565f5fe4a873b6f782d7e75268b9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 387, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 287, + 555 + ], + "type": "text", + "content": "Self-Attention Scheme Comparison. We compare WSSA with other self-attention and report the results in Table. 3. We adopt the half operation [5] in Swin-MSA [25] to keep the computation almost the same and use multi-head attention in the spectral dimension of WSSA* to align with S-MSA[3]. Baseline-2 is SSR-S that retains only the ERB and removes attention and yields 32.01dB. WSSA yields the most significant improvement of 1.29dB, which is 0.45dB, 0.29dB, and 0.21dB higher than S-MSA [3], Swin-MSA [25], and HS-MSA [5], which shows the effectiveness of WSSA. In addition, WSSA* and WSSA achieve 0.34dB and 0.45dB gain than S-MSA respectively, which demonstrates the role of considering local differences and modeling global spectral information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Influence of Multi-head attention and Mean effect. We demonstrate the influence of multi-head attention and mean effect on the spectra-wise self-attention through further experiments on the relationship between performance and token dim (window size) in WSSA and MSSA, which is shown in Fig. 7. Intuitively, the large window size would suffer from limited performance, which illustrates the influence of the mean effect. Performance degradation also occurs when the window size is too small to retain complete feature information. In our experiments, " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " window size optimally balances retaining feature information while minimizing the mean effect, which produces the highest performance of 33.3dB. When the token dim is small, WSSA" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 301, + 525, + 380 + ], + "blocks": [ + { + "bbox": [ + 46, + 279, + 546, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 279, + 546, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 546, + 301 + ], + "type": "text", + "content": "Figure 6. Reconstructed images of real scene2 and scene4 with 2 and 4 out of 28 spectral channels separately by the state-of-the-art methods. Compared with other competing methods, our SSR recovers more details and clear content." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 301, + 525, + 380 + ], + "lines": [ + { + "bbox": [ + 317, + 301, + 525, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 301, + 525, + 380 + ], + "type": "image", + "image_path": "a6cfbecee2bdd53ef115aa6926374723d641ea5960035cc626a5dd237cde9ae1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 319, + 380, + 531, + 391 + ], + "lines": [ + { + "bbox": [ + 319, + 380, + 531, + 391 + ], + "spans": [ + { + "bbox": [ + 319, + 380, + 531, + 391 + ], + "type": "text", + "content": "Figure 7. Influence of token dim in spectra-wise attention." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 395, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 455 + ], + "type": "text", + "content": "clearly performs better than MSSA, which shows the role of maintaining spatial correlation. When the token dim is large, MSSA is slightly better than WSSA, which may be related to the shift in the imaging process and the strip pattern can contain some shift information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 466, + 378, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 378, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 378, + 479 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 652 + ], + "type": "text", + "content": "In this paper, we analyze the influence of multi-head attention and mean effect on the spectra-wise transformer, and a novel SSR method is proposed to improve spectral snapshot reconstruction. To model the global spectral information, consider the local difference, and maintain spatial correlation, WSSA is proposed to better utilize spectral similarity. ARB leverages CMB to address the interaction between adjacent windows of WSSA and learn spatial representation when SAB is specially designed to mitigate spatial degradation in low-quality bands through a novel spatial alignment strategy. Extensive experiments on simulation and real scenes show the effectiveness of the proposed modules. Our SSR at different scales also significantly outperforms the state-of-the-art methods with less cost." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements: This work was supported by the National Natural Science Foundation of China under Grant 62302394 and 62106063, the China Postdoctoral Science Foundation under Grant 317751, and the Natural Science Foundation of Shaanxi under Grant 2023-JC-QN-0757." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25824" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] José M. 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Deep plug-and-play priors for spectral snapshot compressive imaging. 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Chan", + "bbox": [ + 148, + 180, + 292, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yang Zhao", + "bbox": [ + 313, + 181, + 403, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xuhui Jia", + "bbox": [ + 424, + 181, + 503, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ming-Hsuan Yang", + "bbox": [ + 524, + 181, + 671, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Huisheng Wang", + "bbox": [ + 692, + 181, + 820, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Google", + "bbox": [ + 450, + 215, + 514, + 233 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5de574b835a309c4792c12cdff0d78cb8ff8503a2b81cd62e4ba2c5548d9a570.jpg", + "image_caption": [ + "Reference" + ], + "image_footnote": [], + "bbox": [ + 86, + 255, + 215, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6577426fa01efb34c7abe3b3e2d8cabbb975e20bfd75e153dd753143003ea49f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 256, + 344, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e71e3b64773ae109661485010682c8b842f889b7191f86f7839af51425e5dd8.jpg", + "image_caption": [ + "$S^x$ ; Monet style" + ], + "image_footnote": [], + "bbox": [ + 217, + 358, + 344, + 457 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a00530e609542a4f54c0a95f2bd6abe4ef7526a63f38486ed180db86a820c71c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 346, + 256, + 475, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a1bef649ea5e0ed316f78f3ceb4f2c0748661892d7ee6c21feaaae0055a0c879.jpg", + "image_caption": [ + "S', swimming in frontof Eiffel Tower, VanGogh starry might style", + "Figure 1. Addressing Content Ignorance. Given user-provided subject images, a part of the content specified in the text prompt (highlighted in blue) are overlooked. Our Subject-Agnostic Guidance (SAG) aligns the output more closely with both the target subject and text prompt. Here $S^*$ denotes a pseudo-word, with its text embedding replaced by a learnable subject embedding." + ], + "image_footnote": [], + "bbox": [ + 346, + 359, + 473, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/37637fe9a9571439987d79095c106b8d60e6a23ed45b5fb32c9573cadf65cb47.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 478, + 256, + 604, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/508ad3400fad76a1113f61e472eb80d8c6b41e2dec3c34329612ed884b33c584.jpg", + "image_caption": [ + "$S^k$ in a basket, at a beach" + ], + "image_footnote": [], + "bbox": [ + 478, + 359, + 604, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/88b9fbde61e4804427849a918eddf901728440a2a266e6a42160c21729415456.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 256, + 736, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba1464abb12149bf470d57f59f1e82f49c7df4160405797a4424d2e691d8b462.jpg", + "image_caption": [ + "${S}^{k}$ with a cloudy night" + ], + "image_footnote": [], + "bbox": [ + 609, + 359, + 736, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/53bcbeda8bad4ae26b23eed213b9a4f21dce4274a92fac01a001bbb5fcf309ac.jpg", + "image_caption": [ + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 738, + 256, + 867, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8551f04b4268c2654905f6154ee1f2e53f4284be3f895aff7f7edfcc82c07351.jpg", + "image_caption": [ + "$S^{\\star}$ ,Pixar movie", + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 738, + 359, + 867, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 585, + 313, + 601 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In subject-driven text-to-image synthesis, the synthesis process tends to be heavily influenced by the reference images provided by users, often overlooking crucial attributes detailed in the text prompt. In this work, we propose Subject-Agnostic Guidance (SAG), a simple yet effective solution to remedy the problem. We show that through constructing a subject-agnostic condition and applying our proposed dual classifier-free guidance, one could obtain outputs consistent with both the given subject and input text prompts. We validate the efficacy of our approach through both optimization-based and encoder-based methods. Additionally, we demonstrate its applicability in second-order customization methods, where an encoder-based model is fine-tuned with DreamBooth. Our approach is conceptually simple and requires only minimal code modifications, but leads to substantial quality improvements, as evidenced by our evaluations and user studies.", + "bbox": [ + 73, + 628, + 472, + 885 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 585, + 632, + 602 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Subject-driven text-to-image synthesis focuses on generating diverse image samples, conditioned on user-given text descriptions and subject images. This domain has witnessed a surge of interest and significant advancements in recent years. Optimization-based methods [16, 37, 41] tackle the problem by overfitting pre-trained text-to-image synthesis models [36, 38] and text tokens to the given subject. Recently, encoder-based approaches [10, 24, 49] propose to train auxiliary encoders to generate subject embeddings, bypassing the necessity of per-subject optimization.", + "bbox": [ + 496, + 613, + 890, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the aforementioned approaches, both the embeddings and networks are intentionally tailored to closely fit the target subject. As a consequence, these learnable conditions tend to dominate the synthesis process, often obscuring the attributes specified in the text prompt. For instance, as shown in Fig. 1, when employing $S^{*1}$ alongside the style", + "bbox": [ + 496, + 766, + 890, + 857 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}\\mathbb{S}^{*}$ denotes a pseudo-word, where its embedding is substituted by a learnable subject embedding.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6733", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "description Monet style, the desired style is not appropriately synthesized. Such observations underscore that the network struggles to prioritize key content in the existence of learnable components. To address the content ignorance issue, existing solutions modify the training process through additional regularization [37, 49], leading to improved performance.", + "bbox": [ + 75, + 90, + 468, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present Subject-Agnostic Guidance (SAG), an approach that diverges from traditional methodologies. Our strategy emphasizes attending to subject-agnostic attributes by diminishing the influence of subject-specific attributes, accomplished using classifier-free guidance. Differing from standard classifier-free guidance [19], our method incorporates a subject-agnostic condition2. Subsequently, our proposed Dual Classifier-Free Guidance (DCFG) is employed to enhance attention directed towards subject-agnostic attributes. Crucially, motivated by the observation that structures are constructed during early iterations [12, 22], we temporarily replace the subject-aware condition with a subject-agnostic condition at the beginning of the iteration process. Following the construction of coarse image structures, the original subject-aware condition is reintroduced to refine customized details.", + "bbox": [ + 75, + 196, + 470, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our SAG is elegant in both design and implementation, seamlessly blending with existing methods. We showcase the efficacy of SAG using both optimization-based and encoder-based approaches. Furthermore, we delve into its applicability in second-order customization, with an encoder-based model fine-tuned via DreamBooth [37]. Qualitative and quantitative evaluations as well as user feedback verify our robustness, succinctness, and versatility.", + "bbox": [ + 75, + 438, + 468, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the evolving realm of subject-driven text-to-image synthesis, challenges have emerged due to over-tailored embeddings and networks. These often inherit crucial attributes. While existing solutions modify training to address these issues, our novel Subject-Agnostic Guidance (SAG) provides a distinct approach. Seamlessly integrating with prevalent methods, SAG emphasizes a more balanced synthesis process. Its effectiveness is demonstrated through various methodologies and supported by user feedback.", + "bbox": [ + 75, + 559, + 470, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 705, + 218, + 722 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Model for Text-To-Image Synthesis. Typically, given natural language descriptions, a text encoder such as CLIP [33] or T5 [34] is employed to derive the text embedding. This embedding is then fed into the diffusion model for the generation phase. Earlier approaches [35] operated directly within the high-resolution image space for generation. While these methods yielded promising outcomes, the direct iteration in high-resolution space poses significant computational challenges. In light of these constraints,", + "bbox": [ + 75, + 731, + 468, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "considerable efforts have been devoted to enhancing generation efficiency. For instance, Imagen [38] employs a multistage diffusion model. It starts by synthesizing a $64 \\times 64$ resolution image based on the input text prompt and subsequently employs a series of super-resolution modules to increase the resolution to $1024 \\times 1024$ . Benefiting from optimized architectures in the super-resolution stages, this cascaded approach considerably reduces computational overhead compared to direct high-resolution image synthesis. Latent Diffusion [36] transitions the generation process to a low-resolution feature space to improve efficiency. Initially, a VAE [26] or VQGAN [15, 45] is pre-trained. During training, images are encoded into low-resolution features using the pre-trained encoder, and the diffusion model aims to reconstruct these encoded features. In the inference stage, the trained diffusion model produces a feature which is subsequently decoded using the pre-trained module to render the final output image.", + "bbox": [ + 500, + 90, + 890, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Subject-Driven Image Synthesis. Subject-driven text-to-image synthesis [1, 8, 9, 18, 21, 27-29, 31, 40, 43, 47] is a sub-branch of text-to-image synthesis [3, 6, 14, 25, 36, 38, 50] with an additional requirement that the primary attributes in the output aligns with the subjects provided by the user. Existing research [16, 17, 37, 44] has demonstrated that subject information can be encoded as a subject-aware embedding through test-time optimization, given several reference images. For instance, Textual Inversion [16] leverages pre-trained synthesis networks and optimizes a special token while keeping the network static. DreamBooth [37] shares a similar premise but also fine-tunes the network to enhance subject consistency. To bypass test-time optimization, which restricts instant feedback, recent studies [10, 24] advocate the use of an encoder to encapsulate subject information. However, despite advancements in both quality and speed, the encoded subject information often dominates the synthesis process, resulting in inadequately capture of subject information. In this study, we introduce Subject-Agnostic Guidance (SAG) to rectify this challenge. Our SAG focuses on enhancing subject-agnostic attributes, diminishing the influence of subject-specific elements through our dual classifier-free guidance. We illustrate that SAG not only enhances consistency to the input captions but also maintains fidelity to the subject.", + "bbox": [ + 498, + 378, + 890, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 803, + 633, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we introduce an intuitive and effective method to enhance content alignment. We first provide the background for our approach, followed by the discussion of our method - Subject-Agnostic Guidance.", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "2The construction of this condition varies based on the specific customization approach used.", + "bbox": [ + 75, + 875, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6734", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e0cac1acd78dd4df3e31ea5893bcaa1b258a32d0dcce380cd61de0182d3447cd.jpg", + "image_caption": [ + "Figure 2. Overview of SAG. Given a subject-aware embedding, we first construct a subject-agnostic embedding. These embeddings are subsequently used in our dual classifier-free guidance (DCFG), which consists of weak classifier-free guidance and null-classifier-free guidance. Null CFG adopts a constant weight (Eqn. 2) and Weak CFG adopts a variable weight (Eqn. 3)." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 457, + 236 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 357, + 218, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 380, + 243, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The diffusion process transforms a data distribution to a Gaussian noise distribution by iteratively adding noise. Diffusion model is a class of generative models that invert the diffusion process through iterative denoising. Extended from the original unconditional model [20], recent works demonstrate huge success by conditioning diffusion models on various modalities, including text [7, 23, 39], segmentation [2, 22, 32], and many more [30, 42, 48].", + "bbox": [ + 75, + 405, + 468, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathbf{x}_0$ be the input image, and $\\mathbf{c}$ be the condition. During training, a noisy image $\\mathbf{x}_t$ is obtained by adding Gaussian noise $\\epsilon_t$ to $\\mathbf{x}_0$ . The network is trained to predict the added noise, given the noisy image and condition as input. It is generally optimized with a single denoising objective:", + "bbox": [ + 75, + 526, + 468, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d} = \\left| \\left| \\epsilon \\left(\\mathbf {x} _ {t}, \\mathbf {c}\\right) - \\epsilon_ {t} \\right| \\right| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 614, + 468, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{t}$ the noise added to the input image, and $\\epsilon (\\mathbf{x}_t,\\mathbf{c})$ corresponds to the noise estimated by the network. Here $\\mathbf{x}_t$ and $\\mathbf{c}$ refer to the noisy image and condition, respectively. During inference, the process starts with a pure Gaussian noise $\\mathbf{x}_{T_0}$ , and the trained network is iteratively applied to obtain a series of intermediate outputs $\\{\\mathbf{x}_{T_0 - 1},\\mathbf{x}_{T_0 - 2},\\dots ,\\mathbf{x}_0\\}$ , where $\\mathbf{x}_0$ is the final output.", + "bbox": [ + 75, + 643, + 468, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.2 Classifier-Free Guidance", + "text_level": 1, + "bbox": [ + 76, + 768, + 303, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similar to classifier guidance [13], classifier-free guidance is designed to trade between image quality and diversity, but without the need of a classifier. It is widely adopted in existing works [46, 51].", + "bbox": [ + 75, + 794, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During training, an unconditional diffusion model is jointly trained by randomly replacing the input condition $\\mathbf{c}$ by a null condition $\\phi$ . Once trained, during each iteration", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$t$ , a weighted sum of the conditional output and the unconditional output is computed:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {\\epsilon}} _ {t} = (1 + w) \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\mathbf {c}) - w \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\phi). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 133, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In general, a larger $w$ produces better quality, whereas a smaller $w$ yields greater diversity.", + "bbox": [ + 498, + 164, + 890, + 194 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Subject-Agnostic Guidance", + "text_level": 1, + "bbox": [ + 500, + 204, + 746, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the concept of Subject-Agnostic Guidance (SAG). The essence of SAG is anchored in formulating a subject-agnostic embedding based on the inputs provided by users. The embedding is then used in our dual classifier-free guidance (DCFG) in generating outputs that align with both the subject and text prompt. We delve into the details of constructing subject-agnostic embeddings in Sec. 3.2.1, and discuss our dual classifier-free guidance in Sec. 3.2.2.", + "bbox": [ + 496, + 228, + 890, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Subject-Agnostic Embeddings", + "text_level": 1, + "bbox": [ + 500, + 386, + 764, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The construction of subject-agnostic embeddings depends on the choice of methods. Existing approaches generally fall into two categories: Learnable Text Token and Separate Subject Embedding. In this section, we discuss the construction of subject-agnostic embeddings in these two approaches.", + "bbox": [ + 496, + 410, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learnable Text Token. Given images of a reference subject, the learnable text token approach derives a token embedding that captures the identity of the subject, either through fine-tuning [16, 47] or by using an encoder [1, 49]. The resultant token embedding, combined with the token embedding of the text description, is processed by text encoders such as CLIP [33] and T5 [34] to produce a subject-aware embedding.", + "bbox": [ + 496, + 503, + 890, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To construct a subject-agnostic embedding, we replace the derived token embedding with one from a general description of the subject. This strategy ensures that the synthesis process is not dominated by any adaptable components, thereby allowing the model to focus attention on the attributes specified in the text prompt.", + "bbox": [ + 496, + 626, + 890, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathbf{c}$ be the text condition containing the learnable token $S^*$ . We define a subject-agnostic condition $\\mathbf{c}_0$ by replacing the token $S^*$ by a generic descriptor. For example, assuming the target subject is a dog and", + "bbox": [ + 496, + 717, + 890, + 777 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} = \\mathrm {A} \\text {p e n c i l s k e t c h o f S} ^ {*}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 790, + 813, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "we construct $\\mathbf{c}_0$ as", + "bbox": [ + 500, + 816, + 625, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {0} = \\mathrm {A p e n c i l s k e t c h o f a d o g}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 844, + 834, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The generic descriptor is chosen as a noun describing the subject.", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6735", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Separate Subject Embedding. Instead of encoding the subject identity to a learnable text token, the separate subject embedding approach [10, 24] adopts an independent embedding. This embedding is then integrated into the network via auxiliary operations. For instance, Jia et al. [24] employ the CLIP image encoder to encapsulate the subject information into an embedding, which is then injected to Imagen [38] using cross attention.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To construct the subject-agnostic embedding, we opt for a direct method – setting both the subject embedding and its corresponding attention mask to zero. This disables attention to the subject, directing focus towards subject-agnostic information.", + "bbox": [ + 75, + 212, + 468, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Dual Classifier-Free Guidance", + "text_level": 1, + "bbox": [ + 76, + 305, + 341, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce the Dual Classifier-Free Guidance (DCFG), designed primarily to address the issue of content ignorance by attenuating the subject-aware condition. Our DCFG requires no modifications of the training process. It simply requires the application of an additional classifier-free guidance using the subject-aware condition $\\mathbf{c}$ and the subject-agnostic condition $\\mathbf{c}_0$ . The derived feature is subsequently merged with the null condition $\\phi$ within a conventional classifier-free guidance.", + "bbox": [ + 75, + 329, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Weak Classifier-Free Guidance. Given the subject-aware condition $\\mathbf{c}$ and the subject-agnostic condition $\\mathbf{c}_0$ , we first perform classifier-free guidance using $\\mathbf{c}$ and $\\mathbf{c}_0$ . Incorporating $\\mathbf{c}_0$ into the synthesis process directs the generation towards subject-agnostic content, representing a weaker version of the desired generation. When subject information is absent, the model more effectively creates the correct outline and structure, generating outputs that align with both the subject and text description.", + "bbox": [ + 75, + 468, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Differing from the conventional classifier-free guidance, where the guidance weight $w$ often remains constant during the denoising process, we implement a time-varying scheme to enhance performance. Building on the observation that earlier iterations emphasize structure construction [12, 22], we highlight the subject-agnostic condition during the initial phases. Specifically, we adopt a time-varying weighting strategy, suppressing subject information in the early stages:", + "bbox": [ + 75, + 604, + 468, + 739 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\boldsymbol {\\epsilon}} _ {t} = \\left(1 + w _ {t}\\right) \\cdot \\boldsymbol {\\epsilon} \\left(\\mathbf {x} _ {t}, \\mathbf {c}\\right) - w _ {t} \\cdot \\boldsymbol {\\epsilon} \\left(\\mathbf {x} _ {t}, \\mathbf {c} _ {\\mathbf {0}}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 751, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w_{t}$ denotes the guidance weight, similar to $w$ in Eqn. 2. Since a larger $w_{t}$ corresponds to a larger contribution from $\\mathbf{c}$ , $w_{t}$ is devised as a non-increasing function with respect to the iteration $t$ . In this work, we find that a simple piecewise constant scheme suffices to produce promising results:", + "bbox": [ + 75, + 777, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t} = \\left\\{ \\begin{array}{l l} r & \\text {i f} 0 \\leq t \\leq T, \\\\ - 1 & \\text {i f} T < t \\leq 1. \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 863, + 468, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $0 \\leq T \\leq 1$ and $r \\geq -1$ are pre-determined constants, which will be ablated in Sec. 5. Essentially, in the early stages (i.e., when $t \\approx 1$ ), we use solely the subject-agnostic condition to establish the structure and outline of the output. The subject information is integrated in the subsequent stages.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Null Classifier-Free Guidance. The null classifier-free guidance is identical to the conventional classifier-free guidance, leveraging the null condition to encourage diversity. We adopt a constant guidance weight throughout iterations. Specifically, the output $\\overline{\\epsilon}_t$ of the weak-classifier-free guidance is used in place of $\\epsilon (\\mathbf{x}_t,\\mathbf{c})$ in the conventional classifier-free guidance (Eqn. 2):", + "bbox": [ + 496, + 185, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {\\epsilon}} _ {t} = (1 + w) \\cdot \\bar {\\boldsymbol {\\epsilon}} _ {t} - w \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\phi). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 305, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 349, + 630, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To validate the efficacy of SAG, we conduct experiments across multiple approaches, namely Textual Inversion [16] (optimization-based), ELITE [49] (encoder-based), SuTI [10] (encoder-based), and DreamSuTI [10] (second-order).", + "bbox": [ + 496, + 376, + 890, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. ELITE", + "text_level": 1, + "bbox": [ + 498, + 463, + 591, + 478 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we examine the performance improvement when applying SAG to ELITE [49]. In this study, we simplify its architecture by using only the global mapping branch. The settings are as follows:", + "bbox": [ + 496, + 487, + 890, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training. To promote the learning of subject information, we create a domain-specific (e.g., animals) text-image dataset where the text caption incorporates the specialized token. Specifically, we gather images from a pre-defined category and employ straightforward templates such as A photo of $S^*$ for the corresponding captions. During training, the token corresponding to $S^*$ is substituted with the output of the encoder. The condition is subsequently fed into the text encoder.", + "bbox": [ + 496, + 551, + 890, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As discussed in concurrent work [24], text prompts generated using templates and captioning models [11] have inherent limits to their diversity. Moreover, training within narrow domains may harm generation diversity. To counteract this, we employ a general-domain dataset containing detailed text descriptions for regularization. Training on a broad array of text captions ensures the model retains its text-understanding abilities.", + "bbox": [ + 496, + 688, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the training phase, the domain-specific and general-domain datasets are sampled with probabilities $p \\leq 1$ and $(1 - p)$ , respectively. Given that the general-domain dataset serves primarily for regularization, we allocate a higher value to $p$ , greater than 0.5, emphasizing subject encoding.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6736", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3b19a9e3da2f4e86d8a7964866eb1c916fbb5e84a474219dde3a71a36424f3c2.jpg", + "image_caption": [ + "Figure 3. SAG on ELITE [49]. Our ELITE-SAG produces outputs that are more faithful to text prompts while still preserving subject identity. For Stable Diffusion, we generate pure text-to-image results by substituting \"S*\" with \"A dog\" or \"A cat\"." + ], + "image_footnote": [], + "bbox": [ + 86, + 94, + 877, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the subject-agnostic condition $\\mathbf{c}_0$ is also natural language, no modification to the original denoising objective (Eqn. 1) is needed. Additionally, we adopt a regularization to the learnable token [49] by constraining its $\\ell_2$ -norm. The effective training loss is:", + "bbox": [ + 75, + 631, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {d} + \\| s \\| ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 717, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s$ denotes the output of the subject encoder. The remaining part of the training is identical to the training of conventional text-to-image networks.", + "bbox": [ + 75, + 746, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. For each input image, we use the encoder to map the target subject into a text token. This learnable token is then combined with the text description to form the input condition $\\mathbf{c}$ . The subject-agnostic condition is $\\mathbf{c}_0$ is then constructed following the process discussed in Sec. 3.2.1. Starting from random Gaussian noise $\\mathbf{x}_T$ , the fine-tuned network iteratively denoises the intermediate outputs. In", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "stead of applying the conventional classifier-free guidance, our SAG is employed.", + "bbox": [ + 496, + 631, + 888, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation. We adopt the pre-trained Stable Diffusion [36] as the synthesis network, which uses CLIP [33] as the text encoder. For the subject encoder, we use the CLIP image encoder and a three-layer MLP to obtain the learnable token. During training, only the cross-attention layers in Stable Diffusion and the MLP are trained, all other weights are being fixed.", + "bbox": [ + 496, + 666, + 890, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use an internal text-image dataset for training. To construct the domain-specific dataset, we extract images containing dogs and cats from the meta-dataset. The remaining part is used as our general-domain dataset. The dataset mixing ratio is 0.1. The proposed method is implemented in JAX [4]. The detailed experimental settings will be discussed in the supplementary material.", + "bbox": [ + 496, + 773, + 890, + 880 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison. We compare our modified model, ELITE-", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6737", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/10dfefe73b8075bd91b5d52b3b07e420a2c56644ced31f0378887347dfc0796f.jpg", + "image_caption": [ + "Figure 4. SAG on Textual Inversion [16]. Our SAG improves text alignment without sacrificing the identity of the subject." + ], + "image_footnote": [], + "bbox": [ + 81, + 92, + 883, + 220 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3e6f6408dfeadabb4e3e7933f73184d37cb8b259f37c72ac5b15ac295b2c985f.jpg", + "table_caption": [ + "Table 1. Quantitative Comparison. Our ELITE-SAG yields improved performance in both text and subject alignment." + ], + "table_footnote": [], + "table_body": "
MethodsCLIP-T ↑CLIP-I ↑DINO ↑
DreamBooth [37]0.3150.7850.651
Textual Inversion [16]0.3390.7510.571
ELITE [49]0.3420.7510.586
ELITE-SAG (ours)0.3440.7900.671
", + "bbox": [ + 91, + 310, + 452, + 383 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/17ada6bc1d653d50966ec0c98e150cca4c1d1ef5f90230da9435c21c41d09cbf.jpg", + "table_caption": [ + "Table 2. User Study. Across all three compared methods, the majority of raters favor the results produced by our approach." + ], + "table_footnote": [], + "table_body": "
% Prefer OursSubject Align.Text Align.Quality
DreamBooth [37]52%68%60%
Textual Inversion [16]64%76%84%
ELITE [49]56%80%76%
", + "bbox": [ + 81, + 434, + 478, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SAG, with three existing works: DreamBooth [37], Textual Inversion [16], and ELITE [49]. In this section, we assume the existence of only one reference image. As illustrated in Fig. 3, while Stable Diffusion exhibits high text alignment, the compared methods often fall short in generating results faithful to text prompts in the presence of additional subject images. In contrast, with our SAG, outputs adhering to both text captions and reference subjects are consistently generated.", + "bbox": [ + 75, + 518, + 468, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also conduct a quantitative comparison as presented in Table 1, utilizing CLIP [33] and DINO [5] scores. Specifically, the image feature similarities of CLIP [33] and DINO underscore that SAG enhances subject fidelity, while the text feature similarity indicates that SAG improves text alignment. Furthermore, our user study depicted in Table 2 reveals that more than half of the raters prefer our method when compared to the aforementioned methods, thereby corroborating the effectiveness of SAG.", + "bbox": [ + 75, + 656, + 468, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Textual Inversion", + "text_level": 1, + "bbox": [ + 76, + 801, + 246, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Textual Inversion [16] is an optimization-based method for customization. For each given subject, Textual Inversion learns a text token to represent the subject. As discussed in Sec. 3.2.1, the subject-agnostic embedding is generated by replacing the learned special token by a generic description.", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, the conventional CFG is replaced by our SAG. The remaining generation pipeline remains unchanged.", + "bbox": [ + 498, + 273, + 890, + 304 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As illustrated in Fig. 4, the absence of SAG leads to generation dominated by the optimized text token, resulting in suboptimal text alignment. Conversely, the incorporation of SAG enables the model to produce outputs that align more closely with the text description, while preserving the identity of the subject.", + "bbox": [ + 496, + 308, + 892, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. SuTI", + "text_level": 1, + "bbox": [ + 500, + 421, + 576, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unlike ELITE, which encodes subject information into a text token, SuTI [10] employs an encoder-based approach that leverages a distinct subject embedding. This embedding is then fed to the generation network through independent cross-attention layers. As discussed in Sec. 3.2.1, the subject-agnostic condition, denoted as $\\mathbf{c}_0$ , is simply constructed by setting the subject embedding to zero.", + "bbox": [ + 496, + 448, + 890, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As illustrated in Fig. 5, without SAG, the model successfully preserves the identity of the individual provided in the reference images, yet the text alignment is inadequate. Specifically, the styles are unsatisfactory across all outputs. In contrast, employing SAG and suppressing the subject information during initial iterations significantly enhances text alignment. Consequently, the outputs exhibit both high identity preservation and improved text alignment.", + "bbox": [ + 496, + 559, + 892, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. DreamSuTI", + "text_level": 1, + "bbox": [ + 500, + 702, + 627, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DreamSuTI [10] is a second-order method that fine-tunes SuTI using DreamBooth [37] for compositional customization. In this section, we fine-tune SuTI with a provided style image to achieve simultaneous customization of style and subject. The subject-agnostic embedding is generated using the same method as in SuTI.", + "bbox": [ + 496, + 729, + 890, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As depicted in Fig. 6, in the presence of subject images, the outputs are dominated by the subject, resulting in a lack of style fidelity. In contrast, when applying SAG, the subject is suppressed during the early stages of generation, effectively leading to enhanced style generation.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6738", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A bronze face, looks like bronze statue or bronze figure, fine details.", + "bbox": [ + 81, + 126, + 196, + 161 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/82e14d05437c62bbaaa9e580e72f6ba5dd0a4a6142f9a22f3526187d2a69d5e7.jpg", + "image_caption": [ + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 212, + 90, + 346, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a4424dda0c2032a0d7b8af114bd754acd096eb07d45614567e378f6b2cc39f5.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 348, + 90, + 480, + 193 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Beautiful steampunk face \nwearing mask, \nd & d, fantasy, intricate, \nelegant, digital painting, \nmatte, sharp focus, \nillustration, hearthsfone, \ngradient background, hdr \n8k.", + "bbox": [ + 493, + 98, + 602, + 189 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/df503725ac73ba225bd8e2ab7f5077f5903b53c0e49203368f9a031f425eb33d.jpg", + "image_caption": [ + "Prompt", + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 622, + 90, + 754, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13eadd74403c61ce3132686ec9cbdc1e5ddc6e8f6c2fa638b47cf4010b3e8ba3.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 756, + 90, + 890, + 193 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pixel art of face figures, \nattractive faces, edgy, cool, \nextreme detail, tiny pixels, \nvery coherent, vibrant colors", + "bbox": [ + 83, + 247, + 207, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1d31c7c01323de220f499a5f9cd91b4fb54fd578e1d5fd0730950631721c1f8.jpg", + "image_caption": [ + "Prompt", + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 214, + 217, + 346, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d22270f9c7f00431460899050157cc6215d481c45965a5ca8c3509e6bbb960b1.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 348, + 217, + 480, + 319 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Portrait photography of a face, city, 35mm, night time, blue green, pink and gold, heavy bokeh.", + "bbox": [ + 493, + 247, + 614, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4db3a93f772db0592bdd95bfba218f0becd6ced5824d6da23517a99d4f2b9f06.jpg", + "image_caption": [ + "Prompt", + "w/o SAG", + "Figure 5. SAG on SuTI [10]. When applying SAG on SuTI, the subject is discarded during initial iterations, yielding outputs with markedly improved text alignment. Reference images are not provided to protect privacy." + ], + "image_footnote": [], + "bbox": [ + 624, + 217, + 754, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fdec6b875f8da50d03d06afa50592518c7f47c23e2e07202742b9100b4294899.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 756, + 217, + 890, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/280a71b22bfb6c9b34d1b1bf8a8a7cf7875aa6023af21f2c5e18b359bfd4182d.jpg", + "image_caption": [ + "Prompt", + "References" + ], + "image_footnote": [], + "bbox": [ + 81, + 414, + 147, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/df204c4147ae0b25091f3270e3ec45ecdf513e62a565cb89b157cdc2a5dc0384.jpg", + "image_caption": [ + "A vase in kid line drawing style" + ], + "image_footnote": [], + "bbox": [ + 148, + 414, + 214, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b7fefaf02903319644b5255f9635e37503d2e654a5d6793520925f7027eef15c.jpg", + "image_caption": [ + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 217, + 414, + 346, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e43d4273d7e435795ae1d41397b42ac493fb257a38dcfd0856d81255ada0605.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 348, + 414, + 480, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6f1ac2b20d75577b71f70805a680f4f1c1e5c552ee0d8bb40c92e3c7cc619149.jpg", + "image_caption": [ + "A berry bowl in 3D rendering style", + "References" + ], + "image_footnote": [], + "bbox": [ + 490, + 414, + 620, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a776d4e9c25d3489b5cf2aa325ea80092c1c45c60f5268d329149b771482372d.jpg", + "image_caption": [ + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 624, + 414, + 754, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51141d6986cb8be3bda194acd1dc4a008dfc27c81605adfa07e90ece361e7c58.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 756, + 414, + 888, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3c4fca9c6666a872ff50a9d3bc5f4cc385cadf7dd86206827731add0c45450f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 553, + 147, + 603 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0281a2df482e14397bc8662d2d944ca50b22fdb9d842d561f0e49b4d177cda67.jpg", + "image_caption": [ + "A beer can in watercolor painting style" + ], + "image_footnote": [], + "bbox": [ + 148, + 553, + 212, + 603 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e471d4e90a5ff888e4209765b5d163333f0270b179b75be749d3ad7a96e679d0.jpg", + "image_caption": [ + "References" + ], + "image_footnote": [], + "bbox": [ + 81, + 604, + 147, + 652 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2fd4766314cef28fad99f961f5bb6f0bad69e829e477bfd217a94702322b6937.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 148, + 604, + 212, + 652 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7c58bb6d337894621d6ea9a96a1938c13cfa61acc5bffe5c617d67d22287a6d9.jpg", + "image_caption": [ + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 217, + 553, + 346, + 652 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3bbc53924b1bc0b2ef97695bfee913fc79d2f184ce3d2a2bbf7fe923642b5ad1.jpg", + "image_caption": [ + "w/ SAG", + "Figure 6. SAG on DreamSuTI [10]. Even after fine-tuning with DreamBooth to adapt to the specified style, the generated results tend to be dominated by the subjects, leading to an inadequate style-alignment. Our SAG addresses this issue by diminishing the influence of subjects, thereby ensuring outputs that are well-aligned with both the text, subject, and style." + ], + "image_footnote": [], + "bbox": [ + 348, + 553, + 480, + 654 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1e5fdb8c249c13ddcf3213d233f8d4024e9b6d079419b80d7fbb3128129986c7.jpg", + "image_caption": [ + "A grey sloth plushie in watercolor painting style", + "References" + ], + "image_footnote": [], + "bbox": [ + 490, + 553, + 620, + 654 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/14998945c846965d864f52f0d07a3e379defd76a8ae51405972a47d146481bb8.jpg", + "image_caption": [ + "w/o SAG" + ], + "image_footnote": [], + "bbox": [ + 624, + 553, + 754, + 654 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/da84c935238b876cfa5e0cbd9901cb53781f3ffc4d49f812ed6932bf70ec59de.jpg", + "image_caption": [ + "w/ SAG" + ], + "image_footnote": [], + "bbox": [ + 756, + 553, + 888, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Ablations", + "text_level": 1, + "bbox": [ + 76, + 750, + 181, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Guidance Timing. The hyper-parameter $T$ plays an important role in controlling the contribution of the subject embedding. An illustration employing DreamSuTI is provided in Fig. 7. With $r = 0$ , adopting a smaller $T$ results in a stronger suppression of the subject embedding, thereby promoting a better text-alignment (i.e., style-alignment in this example). A gradual increment in $T$ facilitates a transition from style alignment to subject alignment.", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Guidance Weight. While a default value of $r = 0$ (i.e., employing only the subject-aware condition in later iterations) performs well generally, decreasing $r$ facilitates the utilization of the subject-agnostic condition in subsequent iterations, thereby further enhancing content faithfulness. As depicted in Fig. 8, the inclusion of subject-agnostic conditions significantly improves the style alignment of DreamSuTI. Since no re-training is required, the values of $T$ and $r$ can be dynamically adjusted based on user preference.", + "bbox": [ + 496, + 750, + 890, + 887 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6739", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f88001af69f7fa2c237e6deb1d777291572d5d338f84036d3828b784c3e43e99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 88, + 196, + 175 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fa30c100677187006130f0bb1364ee6037610f2e28134284913b0c590694e651.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 199, + 89, + 313, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/597c4a7090bbe2f2eef7e9dc1a8609ef3e527315fdc921d0e7cf33adc6cc3be5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 316, + 90, + 426, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9e62fefb145c2bca13d48cb51007efbcc4f1f8026f88e9b5a18954b9798f10d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 428, + 90, + 540, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5d6fc2090f49ce87baac529b4e7b4b0536725ed09121ba92b4c6528cb3135561.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 90, + 653, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/384e6564a90a825cd39b69e24f0d37bee66d279191710306485b21be150e5064.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 90, + 766, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0542b05bf5b8bb62abcfe0a2b8ee9c81c7678ba21a428d1cd38cc5e150f0a9b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 90, + 880, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/39e1a8797721570b75cda986fbcb1dfb210445c4500b8cac60719f812d00fcca.jpg", + "image_caption": [ + "References" + ], + "image_footnote": [], + "bbox": [ + 80, + 181, + 194, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/947e5fb298688d68919ba25072c59eb2f7c038a03e92d1ec0898cefe0694c797.jpg", + "image_caption": [ + "$\\mathrm{T} = 1.0$" + ], + "image_footnote": [], + "bbox": [ + 199, + 181, + 312, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/764a4756f046cb4c1f9cc30cd2c3930c535155fa0760c9c0af4086c1819bc889.jpg", + "image_caption": [ + "$\\mathrm{T} = 0.99$" + ], + "image_footnote": [], + "bbox": [ + 315, + 181, + 426, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0193b937970bb5bf6299b74c5424f294294835d7f0a11cc42366332c39fa73fd.jpg", + "image_caption": [ + "$\\mathrm{T} = 0.95$" + ], + "image_footnote": [], + "bbox": [ + 429, + 181, + 540, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f4717edd3cd7307a6aa4d638719dafa57c4114e79be0046f54c337d910c97134.jpg", + "image_caption": [ + "$\\mathrm{T} = 0.9$" + ], + "image_footnote": [], + "bbox": [ + 542, + 181, + 653, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/daab1502d3a2c8907b219d10ff729e84b1b30dbe6d8f0df7968043228d340f20.jpg", + "image_caption": [ + "$\\mathrm{T} = 0.85$" + ], + "image_footnote": [], + "bbox": [ + 656, + 181, + 767, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/57b8030e2647b3c0b6b1e21f7150cc6b1c017a35e94f763424f7f54c180607c0.jpg", + "image_caption": [ + "$\\mathrm{T} = 0.0$", + "Style Alignment" + ], + "image_footnote": [], + "bbox": [ + 769, + 181, + 880, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/218694d004b3823301fcfbb6e84517a7466d8fafd77f21a52acd8a0cd7bdf2c5.jpg", + "image_caption": [ + "Figure 7. Guidance Timing. As an example, when fine-tuning SuTI [10] to a given style using DreamBooth [37], our SAG facilitates a transition from subject-centric alignment to style-centric alignment. Here $r = 0$ is used." + ], + "image_footnote": [], + "bbox": [ + 81, + 371, + 194, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1757d3b8c2fd80a8692bb2cdfbabfac0e6f4ef5ae7a1d848d97f36848550c4c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 200, + 371, + 313, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48edac884f687cd20801345f070093f49f01a85802f5a922ca85c4b4597db397.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 316, + 371, + 426, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd8be653ad444e7aff162b709339e98e0825e5cb6a2a183387a8cc5651d12042.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 429, + 371, + 540, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a7d9f634b164a79908ca00a78b0c710b5f915d7047a417b208fd9b22081e49ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 371, + 653, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ada63259e55901f10c8503dc299bf4614ddfbc1db7bb98e11150ce88eb2e336.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 371, + 767, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d0a95b339e4573e7282060ce839af72a7321ec410c075b5b42b216d0a57467c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 371, + 880, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f15e21927ab750f1e9c2e40c29085bc9a99703ef4ad0ebd6546a594f0338599.jpg", + "image_caption": [ + "References", + "Figure 8. Guidance Weight. The guidance weight $r$ can be leveraged to enhance content faithfulness further. For instance, lowering $r$ results in improved style alignment in DreamSuTI. Here $T = 0.9$ is used." + ], + "image_footnote": [], + "bbox": [ + 81, + 463, + 194, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dcace783335414369d6f83091b5b655ef5fb89148235ec8cbf93d7b69a9b51c6.jpg", + "image_caption": [ + "$\\mathrm{r} = 0.0$", + "Subject", + "Alignment" + ], + "image_footnote": [], + "bbox": [ + 200, + 463, + 312, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6dd1f36b32ae041bbf3768995db356af94089454b6c253fde4026e31d4b2b4b0.jpg", + "image_caption": [ + "$\\mathrm{r} = -0.2$" + ], + "image_footnote": [], + "bbox": [ + 316, + 463, + 426, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/adcb2f93fc06463c5775a7a999f1294d1093c272560ff0a4cc53896d622d0f4a.jpg", + "image_caption": [ + "$\\mathrm{r} = -0.4$" + ], + "image_footnote": [], + "bbox": [ + 429, + 463, + 540, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/945088ad5fa4d7725da4a253d5138894bf3312e102a66328138be8c6bdf0b84f.jpg", + "image_caption": [ + "$\\mathrm{r} = -0.6$" + ], + "image_footnote": [], + "bbox": [ + 542, + 463, + 653, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/182166e82c66f875317db3ffeac6efaab93f97ca4a2567d5253c4e689e1425a9.jpg", + "image_caption": [ + "$\\mathrm{r} = -0.8$" + ], + "image_footnote": [], + "bbox": [ + 656, + 463, + 767, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c609eb99446a59a75301bcbd74ce617f8baffe999c8c07b8c5149170f1293c80.jpg", + "image_caption": [ + "$\\mathrm{r} = -1.0$", + "Style", + "Alignment" + ], + "image_footnote": [], + "bbox": [ + 769, + 463, + 880, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitation and Societal Impact", + "text_level": 1, + "bbox": [ + 75, + 647, + 362, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation. While our SAG significantly enhances content alignment compared to existing methods, the quality of outputs is inherently constrained by the underlying generation model. Hence, it may still exhibit suboptimal performance for uncommon content that challenges the generation model. However, this limitation can be mitigated by incorporating a more robust synthesis network, a direction we aim to explore in our future work.", + "bbox": [ + 75, + 672, + 468, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Societal Impact. This project targets at improving content alignment in customized synthesis, which holds the potential for misuse by malicious entities aiming to mislead the public. Future investigations in this domain should duly consider these ethical implications. Moreover, ensuing efforts to develop mechanisms for detecting images generated by such models emerge as a critical avenue to foster the safe", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "advancement of generative models.", + "bbox": [ + 500, + 648, + 733, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 678, + 617, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Subject-driven text-to-image synthesis has witnessed notable progress in recent years. However, overcoming the problem of content ignorance remains a significant challenge. As shown in this work, this problem significantly limits the diversity of the generation. Rather than introducing complex modules, we propose a straightforward yet effective method to address this issue. Our Subject-Agnostic Guidance demonstrates how a balance between content consistency and subject fidelity can be achieved using a subject-agnostic condition. The proposed method enables users to generate customized and diverse scenes without modifying the training process, making it adaptable across various existing approaches.", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6740", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Moab Arar, Rinon Gal, Yuval Atzmon, Gal Chechik, Daniel Cohen-Or, Ariel Shamir, and Amit H Bermano. Domain-agnostic tuning-encoder for fast personalization of text-to-image models. arXiv preprint arXiv:2307.06925, 2023. 2, 3", + "[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.131, + 0.87, + 0.154 + ], + "angle": 0, + "content": "Improving Subject-Driven Image Synthesis with Subject-Agnostic Guidance" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.181, + 0.294, + 0.198 + ], + "angle": 0, + "content": "Kelvin C.K. 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Addressing Content Ignorance. Given user-provided subject images, a part of the content specified in the text prompt (highlighted in blue) are overlooked. Our Subject-Agnostic Guidance (SAG) aligns the output more closely with both the target subject and text prompt. Here \\( S^* \\) denotes a pseudo-word, with its text embedding replaced by a learnable subject embedding." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.587, + 0.314, + 0.602 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.629, + 0.473, + 0.886 + ], + "angle": 0, + "content": "In subject-driven text-to-image synthesis, the synthesis process tends to be heavily influenced by the reference images provided by users, often overlooking crucial attributes detailed in the text prompt. In this work, we propose Subject-Agnostic Guidance (SAG), a simple yet effective solution to remedy the problem. We show that through constructing a subject-agnostic condition and applying our proposed dual classifier-free guidance, one could obtain outputs consistent with both the given subject and input text prompts. We validate the efficacy of our approach through both optimization-based and encoder-based methods. Additionally, we demonstrate its applicability in second-order customization methods, where an encoder-based model is fine-tuned with DreamBooth. Our approach is conceptually simple and requires only minimal code modifications, but leads to substantial quality improvements, as evidenced by our evaluations and user studies." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.587, + 0.633, + 0.603 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Subject-driven text-to-image synthesis focuses on generating diverse image samples, conditioned on user-given text descriptions and subject images. This domain has witnessed a surge of interest and significant advancements in recent years. Optimization-based methods [16, 37, 41] tackle the problem by overfitting pre-trained text-to-image synthesis models [36, 38] and text tokens to the given subject. Recently, encoder-based approaches [10, 24, 49] propose to train auxiliary encoders to generate subject embeddings, bypassing the necessity of per-subject optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.767, + 0.892, + 0.858 + ], + "angle": 0, + "content": "In the aforementioned approaches, both the embeddings and networks are intentionally tailored to closely fit the target subject. As a consequence, these learnable conditions tend to dominate the synthesis process, often obscuring the attributes specified in the text prompt. For instance, as shown in Fig. 1, when employing \\( S^{*1} \\) alongside the style" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\mathbb{S}^{*}\\) denotes a pseudo-word, where its embedding is substituted by a learnable subject embedding." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6733" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.196 + ], + "angle": 0, + "content": "description Monet style, the desired style is not appropriately synthesized. Such observations underscore that the network struggles to prioritize key content in the existence of learnable components. To address the content ignorance issue, existing solutions modify the training process through additional regularization [37, 49], leading to improved performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.471, + 0.438 + ], + "angle": 0, + "content": "In this work, we present Subject-Agnostic Guidance (SAG), an approach that diverges from traditional methodologies. Our strategy emphasizes attending to subject-agnostic attributes by diminishing the influence of subject-specific attributes, accomplished using classifier-free guidance. Differing from standard classifier-free guidance [19], our method incorporates a subject-agnostic condition2. Subsequently, our proposed Dual Classifier-Free Guidance (DCFG) is employed to enhance attention directed towards subject-agnostic attributes. Crucially, motivated by the observation that structures are constructed during early iterations [12, 22], we temporarily replace the subject-aware condition with a subject-agnostic condition at the beginning of the iteration process. Following the construction of coarse image structures, the original subject-aware condition is reintroduced to refine customized details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Our SAG is elegant in both design and implementation, seamlessly blending with existing methods. We showcase the efficacy of SAG using both optimization-based and encoder-based approaches. Furthermore, we delve into its applicability in second-order customization, with an encoder-based model fine-tuned via DreamBooth [37]. Qualitative and quantitative evaluations as well as user feedback verify our robustness, succinctness, and versatility." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.471, + 0.696 + ], + "angle": 0, + "content": "In the evolving realm of subject-driven text-to-image synthesis, challenges have emerged due to over-tailored embeddings and networks. These often inherit crucial attributes. While existing solutions modify training to address these issues, our novel Subject-Agnostic Guidance (SAG) provides a distinct approach. Seamlessly integrating with prevalent methods, SAG emphasizes a more balanced synthesis process. Its effectiveness is demonstrated through various methodologies and supported by user feedback." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.707, + 0.22, + 0.723 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Diffusion Model for Text-To-Image Synthesis. Typically, given natural language descriptions, a text encoder such as CLIP [33] or T5 [34] is employed to derive the text embedding. This embedding is then fed into the diffusion model for the generation phase. Earlier approaches [35] operated directly within the high-resolution image space for generation. While these methods yielded promising outcomes, the direct iteration in high-resolution space poses significant computational challenges. In light of these constraints," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.364 + ], + "angle": 0, + "content": "considerable efforts have been devoted to enhancing generation efficiency. For instance, Imagen [38] employs a multistage diffusion model. It starts by synthesizing a \\(64 \\times 64\\) resolution image based on the input text prompt and subsequently employs a series of super-resolution modules to increase the resolution to \\(1024 \\times 1024\\). Benefiting from optimized architectures in the super-resolution stages, this cascaded approach considerably reduces computational overhead compared to direct high-resolution image synthesis. Latent Diffusion [36] transitions the generation process to a low-resolution feature space to improve efficiency. Initially, a VAE [26] or VQGAN [15, 45] is pre-trained. During training, images are encoded into low-resolution features using the pre-trained encoder, and the diffusion model aims to reconstruct these encoded features. In the inference stage, the trained diffusion model produces a feature which is subsequently decoded using the pre-trained module to render the final output image." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.758 + ], + "angle": 0, + "content": "Subject-Driven Image Synthesis. Subject-driven text-to-image synthesis [1, 8, 9, 18, 21, 27-29, 31, 40, 43, 47] is a sub-branch of text-to-image synthesis [3, 6, 14, 25, 36, 38, 50] with an additional requirement that the primary attributes in the output aligns with the subjects provided by the user. Existing research [16, 17, 37, 44] has demonstrated that subject information can be encoded as a subject-aware embedding through test-time optimization, given several reference images. For instance, Textual Inversion [16] leverages pre-trained synthesis networks and optimizes a special token while keeping the network static. DreamBooth [37] shares a similar premise but also fine-tunes the network to enhance subject consistency. To bypass test-time optimization, which restricts instant feedback, recent studies [10, 24] advocate the use of an encoder to encapsulate subject information. However, despite advancements in both quality and speed, the encoded subject information often dominates the synthesis process, resulting in inadequately capture of subject information. In this study, we introduce Subject-Agnostic Guidance (SAG) to rectify this challenge. Our SAG focuses on enhancing subject-agnostic attributes, diminishing the influence of subject-specific elements through our dual classifier-free guidance. We illustrate that SAG not only enhances consistency to the input captions but also maintains fidelity to the subject." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.804, + 0.634, + 0.822 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we introduce an intuitive and effective method to enhance content alignment. We first provide the background for our approach, followed by the discussion of our method - Subject-Agnostic Guidance." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "2The construction of this condition varies based on the specific customization approach used." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6734" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.458, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.473, + 0.334 + ], + "angle": 0, + "content": "Figure 2. Overview of SAG. Given a subject-aware embedding, we first construct a subject-agnostic embedding. These embeddings are subsequently used in our dual classifier-free guidance (DCFG), which consists of weak classifier-free guidance and null-classifier-free guidance. Null CFG adopts a constant weight (Eqn. 2) and Weak CFG adopts a variable weight (Eqn. 3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.358, + 0.22, + 0.373 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.381, + 0.245, + 0.397 + ], + "angle": 0, + "content": "3.1.1 Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.47, + 0.527 + ], + "angle": 0, + "content": "The diffusion process transforms a data distribution to a Gaussian noise distribution by iteratively adding noise. Diffusion model is a class of generative models that invert the diffusion process through iterative denoising. Extended from the original unconditional model [20], recent works demonstrate huge success by conditioning diffusion models on various modalities, including text [7, 23, 39], segmentation [2, 22, 32], and many more [30, 42, 48]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Let \\(\\mathbf{x}_0\\) be the input image, and \\(\\mathbf{c}\\) be the condition. During training, a noisy image \\(\\mathbf{x}_t\\) is obtained by adding Gaussian noise \\(\\epsilon_t\\) to \\(\\mathbf{x}_0\\). The network is trained to predict the added noise, given the noisy image and condition as input. It is generally optimized with a single denoising objective:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.615, + 0.47, + 0.633 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d} = \\left| \\left| \\epsilon \\left(\\mathbf {x} _ {t}, \\mathbf {c}\\right) - \\epsilon_ {t} \\right| \\right| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.752 + ], + "angle": 0, + "content": "where \\(\\epsilon_{t}\\) the noise added to the input image, and \\(\\epsilon (\\mathbf{x}_t,\\mathbf{c})\\) corresponds to the noise estimated by the network. Here \\(\\mathbf{x}_t\\) and \\(\\mathbf{c}\\) refer to the noisy image and condition, respectively. During inference, the process starts with a pure Gaussian noise \\(\\mathbf{x}_{T_0}\\), and the trained network is iteratively applied to obtain a series of intermediate outputs \\(\\{\\mathbf{x}_{T_0 - 1},\\mathbf{x}_{T_0 - 2},\\dots ,\\mathbf{x}_0\\}\\), where \\(\\mathbf{x}_0\\) is the final output." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.305, + 0.785 + ], + "angle": 0, + "content": "3.1.2 Classifier-Free Guidance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Similar to classifier guidance [13], classifier-free guidance is designed to trade between image quality and diversity, but without the need of a classifier. It is widely adopted in existing works [46, 51]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "During training, an unconditional diffusion model is jointly trained by randomly replacing the input condition \\(\\mathbf{c}\\) by a null condition \\(\\phi\\). Once trained, during each iteration" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "\\(t\\), a weighted sum of the conditional output and the unconditional output is computed:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.135, + 0.892, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {\\epsilon}} _ {t} = (1 + w) \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\mathbf {c}) - w \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\phi). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.165, + 0.892, + 0.195 + ], + "angle": 0, + "content": "In general, a larger \\( w \\) produces better quality, whereas a smaller \\( w \\) yields greater diversity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.205, + 0.747, + 0.221 + ], + "angle": 0, + "content": "3.2. Subject-Agnostic Guidance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.892, + 0.364 + ], + "angle": 0, + "content": "In this section, we introduce the concept of Subject-Agnostic Guidance (SAG). The essence of SAG is anchored in formulating a subject-agnostic embedding based on the inputs provided by users. The embedding is then used in our dual classifier-free guidance (DCFG) in generating outputs that align with both the subject and text prompt. We delve into the details of constructing subject-agnostic embeddings in Sec. 3.2.1, and discuss our dual classifier-free guidance in Sec. 3.2.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.387, + 0.765, + 0.402 + ], + "angle": 0, + "content": "3.2.1 Subject-Agnostic Embeddings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.501 + ], + "angle": 0, + "content": "The construction of subject-agnostic embeddings depends on the choice of methods. Existing approaches generally fall into two categories: Learnable Text Token and Separate Subject Embedding. In this section, we discuss the construction of subject-agnostic embeddings in these two approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Learnable Text Token. Given images of a reference subject, the learnable text token approach derives a token embedding that captures the identity of the subject, either through fine-tuning [16, 47] or by using an encoder [1, 49]. The resultant token embedding, combined with the token embedding of the text description, is processed by text encoders such as CLIP [33] and T5 [34] to produce a subject-aware embedding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.718 + ], + "angle": 0, + "content": "To construct a subject-agnostic embedding, we replace the derived token embedding with one from a general description of the subject. This strategy ensures that the synthesis process is not dominated by any adaptable components, thereby allowing the model to focus attention on the attributes specified in the text prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Let \\( \\mathbf{c} \\) be the text condition containing the learnable token \\( S^* \\). We define a subject-agnostic condition \\( \\mathbf{c}_0 \\) by replacing the token \\( S^* \\) by a generic descriptor. For example, assuming the target subject is a dog and" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.791, + 0.815, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} = \\mathrm {A} \\text {p e n c i l s k e t c h o f S} ^ {*}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.818, + 0.627, + 0.832 + ], + "angle": 0, + "content": "we construct \\(\\mathbf{c}_0\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.845, + 0.835, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {0} = \\mathrm {A p e n c i l s k e t c h o f a d o g}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The generic descriptor is chosen as a noun describing the subject." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6735" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "Separate Subject Embedding. Instead of encoding the subject identity to a learnable text token, the separate subject embedding approach [10, 24] adopts an independent embedding. This embedding is then integrated into the network via auxiliary operations. For instance, Jia et al. [24] employ the CLIP image encoder to encapsulate the subject information into an embedding, which is then injected to Imagen [38] using cross attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.287 + ], + "angle": 0, + "content": "To construct the subject-agnostic embedding, we opt for a direct method – setting both the subject embedding and its corresponding attention mask to zero. This disables attention to the subject, directing focus towards subject-agnostic information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.306, + 0.342, + 0.32 + ], + "angle": 0, + "content": "3.2.2 Dual Classifier-Free Guidance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.469, + 0.466 + ], + "angle": 0, + "content": "In this section, we introduce the Dual Classifier-Free Guidance (DCFG), designed primarily to address the issue of content ignorance by attenuating the subject-aware condition. Our DCFG requires no modifications of the training process. It simply requires the application of an additional classifier-free guidance using the subject-aware condition \\(\\mathbf{c}\\) and the subject-agnostic condition \\(\\mathbf{c}_0\\). The derived feature is subsequently merged with the null condition \\(\\phi\\) within a conventional classifier-free guidance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.469, + 0.605 + ], + "angle": 0, + "content": "Weak Classifier-Free Guidance. Given the subject-aware condition \\(\\mathbf{c}\\) and the subject-agnostic condition \\(\\mathbf{c}_0\\), we first perform classifier-free guidance using \\(\\mathbf{c}\\) and \\(\\mathbf{c}_0\\). Incorporating \\(\\mathbf{c}_0\\) into the synthesis process directs the generation towards subject-agnostic content, representing a weaker version of the desired generation. When subject information is absent, the model more effectively creates the correct outline and structure, generating outputs that align with both the subject and text description." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.469, + 0.741 + ], + "angle": 0, + "content": "Differing from the conventional classifier-free guidance, where the guidance weight \\( w \\) often remains constant during the denoising process, we implement a time-varying scheme to enhance performance. Building on the observation that earlier iterations emphasize structure construction [12, 22], we highlight the subject-agnostic condition during the initial phases. Specifically, we adopt a time-varying weighting strategy, suppressing subject information in the early stages:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.752, + 0.469, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\bar {\\boldsymbol {\\epsilon}} _ {t} = \\left(1 + w _ {t}\\right) \\cdot \\boldsymbol {\\epsilon} \\left(\\mathbf {x} _ {t}, \\mathbf {c}\\right) - w _ {t} \\cdot \\boldsymbol {\\epsilon} \\left(\\mathbf {x} _ {t}, \\mathbf {c} _ {\\mathbf {0}}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.469, + 0.866 + ], + "angle": 0, + "content": "where \\( w_{t} \\) denotes the guidance weight, similar to \\( w \\) in Eqn. 2. Since a larger \\( w_{t} \\) corresponds to a larger contribution from \\( \\mathbf{c} \\), \\( w_{t} \\) is devised as a non-increasing function with respect to the iteration \\( t \\). In this work, we find that a simple piecewise constant scheme suffices to produce promising results:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.864, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\nw _ {t} = \\left\\{ \\begin{array}{l l} r & \\text {i f} 0 \\leq t \\leq T, \\\\ - 1 & \\text {i f} T < t \\leq 1. \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "Here \\(0 \\leq T \\leq 1\\) and \\(r \\geq -1\\) are pre-determined constants, which will be ablated in Sec. 5. Essentially, in the early stages (i.e., when \\(t \\approx 1\\)), we use solely the subject-agnostic condition to establish the structure and outline of the output. The subject information is integrated in the subsequent stages." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.186, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Null Classifier-Free Guidance. The null classifier-free guidance is identical to the conventional classifier-free guidance, leveraging the null condition to encourage diversity. We adopt a constant guidance weight throughout iterations. Specifically, the output \\(\\overline{\\epsilon}_t\\) of the weak-classifier-free guidance is used in place of \\(\\epsilon (\\mathbf{x}_t,\\mathbf{c})\\) in the conventional classifier-free guidance (Eqn. 2):" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.306, + 0.892, + 0.322 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {\\epsilon}} _ {t} = (1 + w) \\cdot \\bar {\\boldsymbol {\\epsilon}} _ {t} - w \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\phi). \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.351, + 0.632, + 0.368 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.892, + 0.452 + ], + "angle": 0, + "content": "To validate the efficacy of SAG, we conduct experiments across multiple approaches, namely Textual Inversion [16] (optimization-based), ELITE [49] (encoder-based), SuTI [10] (encoder-based), and DreamSuTI [10] (second-order)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.464, + 0.593, + 0.479 + ], + "angle": 0, + "content": "4.1. ELITE" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.548 + ], + "angle": 0, + "content": "First, we examine the performance improvement when applying SAG to ELITE [49]. In this study, we simplify its architecture by using only the global mapping branch. The settings are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Training. To promote the learning of subject information, we create a domain-specific (e.g., animals) text-image dataset where the text caption incorporates the specialized token. Specifically, we gather images from a pre-defined category and employ straightforward templates such as A photo of \\( S^* \\) for the corresponding captions. During training, the token corresponding to \\( S^* \\) is substituted with the output of the encoder. The condition is subsequently fed into the text encoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.809 + ], + "angle": 0, + "content": "As discussed in concurrent work [24], text prompts generated using templates and captioning models [11] have inherent limits to their diversity. Moreover, training within narrow domains may harm generation diversity. To counteract this, we employ a general-domain dataset containing detailed text descriptions for regularization. Training on a broad array of text captions ensures the model retains its text-understanding abilities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "During the training phase, the domain-specific and general-domain datasets are sampled with probabilities \\( p \\leq 1 \\) and \\( (1 - p) \\), respectively. Given that the general-domain dataset serves primarily for regularization, we allocate a higher value to \\( p \\), greater than 0.5, emphasizing subject encoding." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6736" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.095, + 0.878, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.577, + 0.893, + 0.607 + ], + "angle": 0, + "content": "Figure 3. SAG on ELITE [49]. Our ELITE-SAG produces outputs that are more faithful to text prompts while still preserving subject identity. For Stable Diffusion, we generate pure text-to-image results by substituting \"S*\" with \"A dog\" or \"A cat\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.707 + ], + "angle": 0, + "content": "Since the subject-agnostic condition \\(\\mathbf{c}_0\\) is also natural language, no modification to the original denoising objective (Eqn. 1) is needed. Additionally, we adopt a regularization to the learnable token [49] by constraining its \\(\\ell_2\\)-norm. The effective training loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.718, + 0.47, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {d} + \\| s \\| ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.793 + ], + "angle": 0, + "content": "where \\( s \\) denotes the output of the subject encoder. The remaining part of the training is identical to the training of conventional text-to-image networks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Inference. For each input image, we use the encoder to map the target subject into a text token. This learnable token is then combined with the text description to form the input condition \\(\\mathbf{c}\\). The subject-agnostic condition is \\(\\mathbf{c}_0\\) is then constructed following the process discussed in Sec. 3.2.1. Starting from random Gaussian noise \\(\\mathbf{x}_T\\), the fine-tuned network iteratively denoises the intermediate outputs. In" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.89, + 0.663 + ], + "angle": 0, + "content": "stead of applying the conventional classifier-free guidance, our SAG is employed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.773 + ], + "angle": 0, + "content": "Implementation. We adopt the pre-trained Stable Diffusion [36] as the synthesis network, which uses CLIP [33] as the text encoder. For the subject encoder, we use the CLIP image encoder and a three-layer MLP to obtain the learnable token. During training, only the cross-attention layers in Stable Diffusion and the MLP are trained, all other weights are being fixed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.892, + 0.881 + ], + "angle": 0, + "content": "We use an internal text-image dataset for training. To construct the domain-specific dataset, we extract images containing dogs and cats from the meta-dataset. The remaining part is used as our general-domain dataset. The dataset mixing ratio is 0.1. The proposed method is implemented in JAX [4]. The detailed experimental settings will be discussed in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Comparison. We compare our modified model, ELITE-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6737" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.093, + 0.885, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.233, + 0.85, + 0.248 + ], + "angle": 0, + "content": "Figure 4. SAG on Textual Inversion [16]. Our SAG improves text alignment without sacrificing the identity of the subject." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.302 + ], + "angle": 0, + "content": "Table 1. Quantitative Comparison. Our ELITE-SAG yields improved performance in both text and subject alignment." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.311, + 0.454, + 0.384 + ], + "angle": 0, + "content": "
MethodsCLIP-T ↑CLIP-I ↑DINO ↑
DreamBooth [37]0.3150.7850.651
Textual Inversion [16]0.3390.7510.571
ELITE [49]0.3420.7510.586
ELITE-SAG (ours)0.3440.7900.671
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.396, + 0.471, + 0.425 + ], + "angle": 0, + "content": "Table 2. User Study. Across all three compared methods, the majority of raters favor the results produced by our approach." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.435, + 0.48, + 0.495 + ], + "angle": 0, + "content": "
% Prefer OursSubject Align.Text Align.Quality
DreamBooth [37]52%68%60%
Textual Inversion [16]64%76%84%
ELITE [49]56%80%76%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.655 + ], + "angle": 0, + "content": "SAG, with three existing works: DreamBooth [37], Textual Inversion [16], and ELITE [49]. In this section, we assume the existence of only one reference image. As illustrated in Fig. 3, while Stable Diffusion exhibits high text alignment, the compared methods often fall short in generating results faithful to text prompts in the presence of additional subject images. In contrast, with our SAG, outputs adhering to both text captions and reference subjects are consistently generated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.792 + ], + "angle": 0, + "content": "We also conduct a quantitative comparison as presented in Table 1, utilizing CLIP [33] and DINO [5] scores. Specifically, the image feature similarities of CLIP [33] and DINO underscore that SAG enhances subject fidelity, while the text feature similarity indicates that SAG improves text alignment. Furthermore, our user study depicted in Table 2 reveals that more than half of the raters prefer our method when compared to the aforementioned methods, thereby corroborating the effectiveness of SAG." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.248, + 0.817 + ], + "angle": 0, + "content": "4.2. Textual Inversion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Textual Inversion [16] is an optimization-based method for customization. For each given subject, Textual Inversion learns a text token to represent the subject. As discussed in Sec. 3.2.1, the subject-agnostic embedding is generated by replacing the learned special token by a generic description." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.275, + 0.892, + 0.305 + ], + "angle": 0, + "content": "Then, the conventional CFG is replaced by our SAG. The remaining generation pipeline remains unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.893, + 0.4 + ], + "angle": 0, + "content": "As illustrated in Fig. 4, the absence of SAG leads to generation dominated by the optimized text token, resulting in suboptimal text alignment. Conversely, the incorporation of SAG enables the model to produce outputs that align more closely with the text description, while preserving the identity of the subject." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.577, + 0.436 + ], + "angle": 0, + "content": "4.3. SuTI" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Unlike ELITE, which encodes subject information into a text token, SuTI [10] employs an encoder-based approach that leverages a distinct subject embedding. This embedding is then fed to the generation network through independent cross-attention layers. As discussed in Sec. 3.2.1, the subject-agnostic condition, denoted as \\(\\mathbf{c}_0\\), is simply constructed by setting the subject embedding to zero." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.893, + 0.681 + ], + "angle": 0, + "content": "As illustrated in Fig. 5, without SAG, the model successfully preserves the identity of the individual provided in the reference images, yet the text alignment is inadequate. Specifically, the styles are unsatisfactory across all outputs. In contrast, employing SAG and suppressing the subject information during initial iterations significantly enhances text alignment. Consequently, the outputs exhibit both high identity preservation and improved text alignment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.703, + 0.628, + 0.717 + ], + "angle": 0, + "content": "4.4. DreamSuTI" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.892, + 0.82 + ], + "angle": 0, + "content": "DreamSuTI [10] is a second-order method that fine-tunes SuTI using DreamBooth [37] for compositional customization. In this section, we fine-tune SuTI with a provided style image to achieve simultaneous customization of style and subject. The subject-agnostic embedding is generated using the same method as in SuTI." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As depicted in Fig. 6, in the presence of subject images, the outputs are dominated by the subject, resulting in a lack of style fidelity. In contrast, when applying SAG, the subject is suppressed during the early stages of generation, effectively leading to enhanced style generation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6738" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.083, + 0.127, + 0.197, + 0.162 + ], + "angle": 0, + "content": "A bronze face, looks like bronze statue or bronze figure, fine details." + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.196, + 0.171, + 0.209 + ], + "angle": 0, + "content": "Prompt" + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.092, + 0.347, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.197, + 0.307, + 0.207 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.092, + 0.481, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.197, + 0.438, + 0.207 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "text", + "bbox": [ + 0.495, + 0.099, + 0.604, + 0.19 + ], + "angle": 0, + "content": "Beautiful steampunk face \nwearing mask, \nd & d, fantasy, intricate, \nelegant, digital painting, \nmatte, sharp focus, \nillustration, hearthsfone, \ngradient background, hdr \n8k." + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.197, + 0.578, + 0.209 + ], + "angle": 0, + "content": "Prompt" + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.092, + 0.756, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.197, + 0.716, + 0.207 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.092, + 0.891, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.197, + 0.846, + 0.207 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.248, + 0.209, + 0.293 + ], + "angle": 0, + "content": "Pixel art of face figures, \nattractive faces, edgy, cool, \nextreme detail, tiny pixels, \nvery coherent, vibrant colors" + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.322, + 0.169, + 0.334 + ], + "angle": 0, + "content": "Prompt" + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.218, + 0.347, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.322, + 0.306, + 0.333 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.218, + 0.481, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.322, + 0.438, + 0.333 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "text", + "bbox": [ + 0.495, + 0.248, + 0.616, + 0.294 + ], + "angle": 0, + "content": "Portrait photography of a face, city, 35mm, night time, blue green, pink and gold, heavy bokeh." + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.322, + 0.579, + 0.334 + ], + "angle": 0, + "content": "Prompt" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.218, + 0.756, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.322, + 0.716, + 0.333 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.218, + 0.891, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.322, + 0.846, + 0.333 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.349, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Figure 5. SAG on SuTI [10]. When applying SAG on SuTI, the subject is discarded during initial iterations, yielding outputs with markedly improved text alignment. Reference images are not provided to protect privacy." + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.402, + 0.362, + 0.414 + ], + "angle": 0, + "content": "A vase in kid line drawing style" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.415, + 0.148, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.415, + 0.215, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.519, + 0.18, + 0.529 + ], + "angle": 0, + "content": "References" + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.415, + 0.348, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.255, + 0.519, + 0.309, + 0.529 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.415, + 0.482, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.519, + 0.439, + 0.529 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "image_caption", + "bbox": [ + 0.603, + 0.402, + 0.78, + 0.414 + ], + "angle": 0, + "content": "A berry bowl in 3D rendering style" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.415, + 0.622, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.519, + 0.588, + 0.529 + ], + "angle": 0, + "content": "References" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.415, + 0.756, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.519, + 0.717, + 0.529 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.415, + 0.89, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.519, + 0.846, + 0.529 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.54, + 0.382, + 0.553 + ], + "angle": 0, + "content": "A beer can in watercolor painting style" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.554, + 0.148, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.554, + 0.214, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.605, + 0.148, + 0.654 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.605, + 0.214, + 0.654 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.657, + 0.179, + 0.668 + ], + "angle": 0, + "content": "References" + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.554, + 0.348, + 0.654 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.255, + 0.657, + 0.307, + 0.668 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.554, + 0.482, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.393, + 0.657, + 0.438, + 0.668 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "image_caption", + "bbox": [ + 0.57, + 0.54, + 0.81, + 0.553 + ], + "angle": 0, + "content": "A grey sloth plushie in watercolor painting style" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.554, + 0.622, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.657, + 0.587, + 0.668 + ], + "angle": 0, + "content": "References" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.554, + 0.756, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.657, + 0.716, + 0.668 + ], + "angle": 0, + "content": "w/o SAG" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.554, + 0.89, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.657, + 0.845, + 0.668 + ], + "angle": 0, + "content": "w/ SAG" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.683, + 0.892, + 0.725 + ], + "angle": 0, + "content": "Figure 6. SAG on DreamSuTI [10]. Even after fine-tuning with DreamBooth to adapt to the specified style, the generated results tend to be dominated by the subjects, leading to an inadequate style-alignment. Our SAG addresses this issue by diminishing the influence of subjects, thereby ensuring outputs that are well-aligned with both the text, subject, and style." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.75, + 0.182, + 0.765 + ], + "angle": 0, + "content": "5. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Guidance Timing. The hyper-parameter \\( T \\) plays an important role in controlling the contribution of the subject embedding. An illustration employing DreamSuTI is provided in Fig. 7. With \\( r = 0 \\), adopting a smaller \\( T \\) results in a stronger suppression of the subject embedding, thereby promoting a better text-alignment (i.e., style-alignment in this example). A gradual increment in \\( T \\) facilitates a transition from style alignment to subject alignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.888 + ], + "angle": 0, + "content": "Guidance Weight. While a default value of \\( r = 0 \\) (i.e., employing only the subject-aware condition in later iterations) performs well generally, decreasing \\( r \\) facilitates the utilization of the subject-agnostic condition in subsequent iterations, thereby further enhancing content faithfulness. As depicted in Fig. 8, the inclusion of subject-agnostic conditions significantly improves the style alignment of DreamSuTI. Since no re-training is required, the values of \\( T \\) and \\( r \\) can be dynamically adjusted based on user preference." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6739" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.197, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.2, + 0.09, + 0.314, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.091, + 0.427, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.091, + 0.541, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.091, + 0.655, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.091, + 0.767, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.091, + 0.882, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.182, + 0.195, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.271, + 0.171, + 0.282 + ], + "angle": 0, + "content": "References" + }, + { + "type": "image", + "bbox": [ + 0.2, + 0.182, + 0.313, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.271, + 0.278, + 0.283 + ], + "angle": 0, + "content": "\\(\\mathrm{T} = 1.0\\)" + }, + { + "type": "image", + "bbox": [ + 0.316, + 0.182, + 0.428, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.348, + 0.271, + 0.396, + 0.282 + ], + "angle": 0, + "content": "\\(\\mathrm{T} = 0.99\\)" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.182, + 0.541, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.461, + 0.271, + 0.508, + 0.282 + ], + "angle": 0, + "content": "\\(\\mathrm{T} = 0.95\\)" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.182, + 0.655, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.578, + 0.271, + 0.619, + 0.282 + ], + "angle": 0, + "content": "\\(\\mathrm{T} = 0.9\\)" + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.182, + 0.768, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.271, + 0.735, + 0.282 + ], + "angle": 0, + "content": "\\(\\mathrm{T} = 0.85\\)" + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.182, + 0.882, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.805, + 0.271, + 0.845, + 0.281 + ], + "angle": 0, + "content": "\\(\\mathrm{T} = 0.0\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.292, + 0.856, + 0.316 + ], + "angle": 0, + "content": "Style Alignment" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.328, + 0.894, + 0.357 + ], + "angle": 0, + "content": "Figure 7. Guidance Timing. As an example, when fine-tuning SuTI [10] to a given style using DreamBooth [37], our SAG facilitates a transition from subject-centric alignment to style-centric alignment. Here \\( r = 0 \\) is used." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.372, + 0.195, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.372, + 0.314, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.372, + 0.427, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.372, + 0.541, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.372, + 0.655, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.372, + 0.768, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.372, + 0.882, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.464, + 0.195, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.553, + 0.17, + 0.563 + ], + "angle": 0, + "content": "References" + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.464, + 0.313, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.553, + 0.277, + 0.563 + ], + "angle": 0, + "content": "\\(\\mathrm{r} = 0.0\\)" + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.464, + 0.428, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.35, + 0.553, + 0.392, + 0.563 + ], + "angle": 0, + "content": "\\(\\mathrm{r} = -0.2\\)" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.464, + 0.541, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.463, + 0.553, + 0.506, + 0.563 + ], + "angle": 0, + "content": "\\(\\mathrm{r} = -0.4\\)" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.464, + 0.655, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.553, + 0.619, + 0.563 + ], + "angle": 0, + "content": "\\(\\mathrm{r} = -0.6\\)" + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.464, + 0.768, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.553, + 0.732, + 0.563 + ], + "angle": 0, + "content": "\\(\\mathrm{r} = -0.8\\)" + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.464, + 0.882, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.553, + 0.846, + 0.563 + ], + "angle": 0, + "content": "\\(\\mathrm{r} = -1.0\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.23, + 0.573, + 0.279, + 0.585 + ], + "angle": 0, + "content": "Subject" + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.586, + 0.288, + 0.597 + ], + "angle": 0, + "content": "Alignment" + }, + { + "type": "image_caption", + "bbox": [ + 0.809, + 0.573, + 0.84, + 0.585 + ], + "angle": 0, + "content": "Style" + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.586, + 0.855, + 0.598 + ], + "angle": 0, + "content": "Alignment" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.609, + 0.893, + 0.638 + ], + "angle": 0, + "content": "Figure 8. Guidance Weight. The guidance weight \\( r \\) can be leveraged to enhance content faithfulness further. For instance, lowering \\( r \\) results in improved style alignment in DreamSuTI. Here \\( T = 0.9 \\) is used." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.648, + 0.364, + 0.667 + ], + "angle": 0, + "content": "6. Limitation and Societal Impact" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.794 + ], + "angle": 0, + "content": "Limitation. While our SAG significantly enhances content alignment compared to existing methods, the quality of outputs is inherently constrained by the underlying generation model. Hence, it may still exhibit suboptimal performance for uncommon content that challenges the generation model. However, this limitation can be mitigated by incorporating a more robust synthesis network, a direction we aim to explore in our future work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Societal Impact. This project targets at improving content alignment in customized synthesis, which holds the potential for misuse by malicious entities aiming to mislead the public. Future investigations in this domain should duly consider these ethical implications. Moreover, ensuing efforts to develop mechanisms for detecting images generated by such models emerge as a critical avenue to foster the safe" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.65, + 0.735, + 0.665 + ], + "angle": 0, + "content": "advancement of generative models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.619, + 0.695 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Subject-driven text-to-image synthesis has witnessed notable progress in recent years. However, overcoming the problem of content ignorance remains a significant challenge. As shown in this work, this problem significantly limits the diversity of the generation. Rather than introducing complex modules, we propose a straightforward yet effective method to address this issue. Our Subject-Agnostic Guidance demonstrates how a balance between content consistency and subject fidelity can be achieved using a subject-agnostic condition. The proposed method enables users to generate customized and diverse scenes without modifying the training process, making it adaptable across various existing approaches." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6740" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.183 + ], + "angle": 0, + "content": "[1] Moab Arar, Rinon Gal, Yuval Atzmon, Gal Chechik, Daniel Cohen-Or, Ariel Shamir, and Amit H Bermano. Domain-agnostic tuning-encoder for fast personalization of text-to-image models. arXiv preprint arXiv:2307.06925, 2023. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.47, + 0.227 + ], + "angle": 0, + "content": "[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. 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Chan + +Yang Zhao + +Xuhui Jia + +Ming-Hsuan Yang + +Huisheng Wang + +Google + +![](images/5de574b835a309c4792c12cdff0d78cb8ff8503a2b81cd62e4ba2c5548d9a570.jpg) +Reference + +![](images/6577426fa01efb34c7abe3b3e2d8cabbb975e20bfd75e153dd753143003ea49f.jpg) + +![](images/2e71e3b64773ae109661485010682c8b842f889b7191f86f7839af51425e5dd8.jpg) +$S^x$ ; Monet style + +![](images/a00530e609542a4f54c0a95f2bd6abe4ef7526a63f38486ed180db86a820c71c.jpg) + +![](images/a1bef649ea5e0ed316f78f3ceb4f2c0748661892d7ee6c21feaaae0055a0c879.jpg) +S', swimming in frontof Eiffel Tower, VanGogh starry might style +Figure 1. Addressing Content Ignorance. Given user-provided subject images, a part of the content specified in the text prompt (highlighted in blue) are overlooked. Our Subject-Agnostic Guidance (SAG) aligns the output more closely with both the target subject and text prompt. Here $S^*$ denotes a pseudo-word, with its text embedding replaced by a learnable subject embedding. + +![](images/37637fe9a9571439987d79095c106b8d60e6a23ed45b5fb32c9573cadf65cb47.jpg) + +![](images/508ad3400fad76a1113f61e472eb80d8c6b41e2dec3c34329612ed884b33c584.jpg) +$S^k$ in a basket, at a beach + +![](images/88b9fbde61e4804427849a918eddf901728440a2a266e6a42160c21729415456.jpg) + +![](images/ba1464abb12149bf470d57f59f1e82f49c7df4160405797a4424d2e691d8b462.jpg) +${S}^{k}$ with a cloudy night + +![](images/53bcbeda8bad4ae26b23eed213b9a4f21dce4274a92fac01a001bbb5fcf309ac.jpg) +w/o SAG + +![](images/8551f04b4268c2654905f6154ee1f2e53f4284be3f895aff7f7edfcc82c07351.jpg) +$S^{\star}$ ,Pixar movie +w/ SAG + +# Abstract + +In subject-driven text-to-image synthesis, the synthesis process tends to be heavily influenced by the reference images provided by users, often overlooking crucial attributes detailed in the text prompt. In this work, we propose Subject-Agnostic Guidance (SAG), a simple yet effective solution to remedy the problem. We show that through constructing a subject-agnostic condition and applying our proposed dual classifier-free guidance, one could obtain outputs consistent with both the given subject and input text prompts. We validate the efficacy of our approach through both optimization-based and encoder-based methods. Additionally, we demonstrate its applicability in second-order customization methods, where an encoder-based model is fine-tuned with DreamBooth. Our approach is conceptually simple and requires only minimal code modifications, but leads to substantial quality improvements, as evidenced by our evaluations and user studies. + +# 1. Introduction + +Subject-driven text-to-image synthesis focuses on generating diverse image samples, conditioned on user-given text descriptions and subject images. This domain has witnessed a surge of interest and significant advancements in recent years. Optimization-based methods [16, 37, 41] tackle the problem by overfitting pre-trained text-to-image synthesis models [36, 38] and text tokens to the given subject. Recently, encoder-based approaches [10, 24, 49] propose to train auxiliary encoders to generate subject embeddings, bypassing the necessity of per-subject optimization. + +In the aforementioned approaches, both the embeddings and networks are intentionally tailored to closely fit the target subject. As a consequence, these learnable conditions tend to dominate the synthesis process, often obscuring the attributes specified in the text prompt. For instance, as shown in Fig. 1, when employing $S^{*1}$ alongside the style + +description Monet style, the desired style is not appropriately synthesized. Such observations underscore that the network struggles to prioritize key content in the existence of learnable components. To address the content ignorance issue, existing solutions modify the training process through additional regularization [37, 49], leading to improved performance. + +In this work, we present Subject-Agnostic Guidance (SAG), an approach that diverges from traditional methodologies. Our strategy emphasizes attending to subject-agnostic attributes by diminishing the influence of subject-specific attributes, accomplished using classifier-free guidance. Differing from standard classifier-free guidance [19], our method incorporates a subject-agnostic condition2. Subsequently, our proposed Dual Classifier-Free Guidance (DCFG) is employed to enhance attention directed towards subject-agnostic attributes. Crucially, motivated by the observation that structures are constructed during early iterations [12, 22], we temporarily replace the subject-aware condition with a subject-agnostic condition at the beginning of the iteration process. Following the construction of coarse image structures, the original subject-aware condition is reintroduced to refine customized details. + +Our SAG is elegant in both design and implementation, seamlessly blending with existing methods. We showcase the efficacy of SAG using both optimization-based and encoder-based approaches. Furthermore, we delve into its applicability in second-order customization, with an encoder-based model fine-tuned via DreamBooth [37]. Qualitative and quantitative evaluations as well as user feedback verify our robustness, succinctness, and versatility. + +In the evolving realm of subject-driven text-to-image synthesis, challenges have emerged due to over-tailored embeddings and networks. These often inherit crucial attributes. While existing solutions modify training to address these issues, our novel Subject-Agnostic Guidance (SAG) provides a distinct approach. Seamlessly integrating with prevalent methods, SAG emphasizes a more balanced synthesis process. Its effectiveness is demonstrated through various methodologies and supported by user feedback. + +# 2. Related Work + +Diffusion Model for Text-To-Image Synthesis. Typically, given natural language descriptions, a text encoder such as CLIP [33] or T5 [34] is employed to derive the text embedding. This embedding is then fed into the diffusion model for the generation phase. Earlier approaches [35] operated directly within the high-resolution image space for generation. While these methods yielded promising outcomes, the direct iteration in high-resolution space poses significant computational challenges. In light of these constraints, + +considerable efforts have been devoted to enhancing generation efficiency. For instance, Imagen [38] employs a multistage diffusion model. It starts by synthesizing a $64 \times 64$ resolution image based on the input text prompt and subsequently employs a series of super-resolution modules to increase the resolution to $1024 \times 1024$ . Benefiting from optimized architectures in the super-resolution stages, this cascaded approach considerably reduces computational overhead compared to direct high-resolution image synthesis. Latent Diffusion [36] transitions the generation process to a low-resolution feature space to improve efficiency. Initially, a VAE [26] or VQGAN [15, 45] is pre-trained. During training, images are encoded into low-resolution features using the pre-trained encoder, and the diffusion model aims to reconstruct these encoded features. In the inference stage, the trained diffusion model produces a feature which is subsequently decoded using the pre-trained module to render the final output image. + +Subject-Driven Image Synthesis. Subject-driven text-to-image synthesis [1, 8, 9, 18, 21, 27-29, 31, 40, 43, 47] is a sub-branch of text-to-image synthesis [3, 6, 14, 25, 36, 38, 50] with an additional requirement that the primary attributes in the output aligns with the subjects provided by the user. Existing research [16, 17, 37, 44] has demonstrated that subject information can be encoded as a subject-aware embedding through test-time optimization, given several reference images. For instance, Textual Inversion [16] leverages pre-trained synthesis networks and optimizes a special token while keeping the network static. DreamBooth [37] shares a similar premise but also fine-tunes the network to enhance subject consistency. To bypass test-time optimization, which restricts instant feedback, recent studies [10, 24] advocate the use of an encoder to encapsulate subject information. However, despite advancements in both quality and speed, the encoded subject information often dominates the synthesis process, resulting in inadequately capture of subject information. In this study, we introduce Subject-Agnostic Guidance (SAG) to rectify this challenge. Our SAG focuses on enhancing subject-agnostic attributes, diminishing the influence of subject-specific elements through our dual classifier-free guidance. We illustrate that SAG not only enhances consistency to the input captions but also maintains fidelity to the subject. + +# 3. Methodology + +In this work, we introduce an intuitive and effective method to enhance content alignment. We first provide the background for our approach, followed by the discussion of our method - Subject-Agnostic Guidance. + +![](images/e0cac1acd78dd4df3e31ea5893bcaa1b258a32d0dcce380cd61de0182d3447cd.jpg) +Figure 2. Overview of SAG. Given a subject-aware embedding, we first construct a subject-agnostic embedding. These embeddings are subsequently used in our dual classifier-free guidance (DCFG), which consists of weak classifier-free guidance and null-classifier-free guidance. Null CFG adopts a constant weight (Eqn. 2) and Weak CFG adopts a variable weight (Eqn. 3). + +# 3.1. Preliminaries + +# 3.1.1 Diffusion Model + +The diffusion process transforms a data distribution to a Gaussian noise distribution by iteratively adding noise. Diffusion model is a class of generative models that invert the diffusion process through iterative denoising. Extended from the original unconditional model [20], recent works demonstrate huge success by conditioning diffusion models on various modalities, including text [7, 23, 39], segmentation [2, 22, 32], and many more [30, 42, 48]. + +Let $\mathbf{x}_0$ be the input image, and $\mathbf{c}$ be the condition. During training, a noisy image $\mathbf{x}_t$ is obtained by adding Gaussian noise $\epsilon_t$ to $\mathbf{x}_0$ . The network is trained to predict the added noise, given the noisy image and condition as input. It is generally optimized with a single denoising objective: + +$$ +\mathcal {L} _ {d} = \left| \left| \epsilon \left(\mathbf {x} _ {t}, \mathbf {c}\right) - \epsilon_ {t} \right| \right| _ {2} ^ {2}, \tag {1} +$$ + +where $\epsilon_{t}$ the noise added to the input image, and $\epsilon (\mathbf{x}_t,\mathbf{c})$ corresponds to the noise estimated by the network. Here $\mathbf{x}_t$ and $\mathbf{c}$ refer to the noisy image and condition, respectively. During inference, the process starts with a pure Gaussian noise $\mathbf{x}_{T_0}$ , and the trained network is iteratively applied to obtain a series of intermediate outputs $\{\mathbf{x}_{T_0 - 1},\mathbf{x}_{T_0 - 2},\dots ,\mathbf{x}_0\}$ , where $\mathbf{x}_0$ is the final output. + +# 3.1.2 Classifier-Free Guidance + +Similar to classifier guidance [13], classifier-free guidance is designed to trade between image quality and diversity, but without the need of a classifier. It is widely adopted in existing works [46, 51]. + +During training, an unconditional diffusion model is jointly trained by randomly replacing the input condition $\mathbf{c}$ by a null condition $\phi$ . Once trained, during each iteration + +$t$ , a weighted sum of the conditional output and the unconditional output is computed: + +$$ +\tilde {\boldsymbol {\epsilon}} _ {t} = (1 + w) \cdot \boldsymbol {\epsilon} (\mathbf {x} _ {t}, \mathbf {c}) - w \cdot \boldsymbol {\epsilon} (\mathbf {x} _ {t}, \phi). \tag {2} +$$ + +In general, a larger $w$ produces better quality, whereas a smaller $w$ yields greater diversity. + +# 3.2. Subject-Agnostic Guidance + +In this section, we introduce the concept of Subject-Agnostic Guidance (SAG). The essence of SAG is anchored in formulating a subject-agnostic embedding based on the inputs provided by users. The embedding is then used in our dual classifier-free guidance (DCFG) in generating outputs that align with both the subject and text prompt. We delve into the details of constructing subject-agnostic embeddings in Sec. 3.2.1, and discuss our dual classifier-free guidance in Sec. 3.2.2. + +# 3.2.1 Subject-Agnostic Embeddings + +The construction of subject-agnostic embeddings depends on the choice of methods. Existing approaches generally fall into two categories: Learnable Text Token and Separate Subject Embedding. In this section, we discuss the construction of subject-agnostic embeddings in these two approaches. + +Learnable Text Token. Given images of a reference subject, the learnable text token approach derives a token embedding that captures the identity of the subject, either through fine-tuning [16, 47] or by using an encoder [1, 49]. The resultant token embedding, combined with the token embedding of the text description, is processed by text encoders such as CLIP [33] and T5 [34] to produce a subject-aware embedding. + +To construct a subject-agnostic embedding, we replace the derived token embedding with one from a general description of the subject. This strategy ensures that the synthesis process is not dominated by any adaptable components, thereby allowing the model to focus attention on the attributes specified in the text prompt. + +Let $\mathbf{c}$ be the text condition containing the learnable token $S^*$ . We define a subject-agnostic condition $\mathbf{c}_0$ by replacing the token $S^*$ by a generic descriptor. For example, assuming the target subject is a dog and + +$$ +\mathbf {c} = \mathrm {A} \text {p e n c i l s k e t c h o f S} ^ {*} +$$ + +we construct $\mathbf{c}_0$ as + +$$ +\mathbf {c} _ {0} = \mathrm {A p e n c i l s k e t c h o f a d o g} +$$ + +The generic descriptor is chosen as a noun describing the subject. + +Separate Subject Embedding. Instead of encoding the subject identity to a learnable text token, the separate subject embedding approach [10, 24] adopts an independent embedding. This embedding is then integrated into the network via auxiliary operations. For instance, Jia et al. [24] employ the CLIP image encoder to encapsulate the subject information into an embedding, which is then injected to Imagen [38] using cross attention. + +To construct the subject-agnostic embedding, we opt for a direct method – setting both the subject embedding and its corresponding attention mask to zero. This disables attention to the subject, directing focus towards subject-agnostic information. + +# 3.2.2 Dual Classifier-Free Guidance + +In this section, we introduce the Dual Classifier-Free Guidance (DCFG), designed primarily to address the issue of content ignorance by attenuating the subject-aware condition. Our DCFG requires no modifications of the training process. It simply requires the application of an additional classifier-free guidance using the subject-aware condition $\mathbf{c}$ and the subject-agnostic condition $\mathbf{c}_0$ . The derived feature is subsequently merged with the null condition $\phi$ within a conventional classifier-free guidance. + +Weak Classifier-Free Guidance. Given the subject-aware condition $\mathbf{c}$ and the subject-agnostic condition $\mathbf{c}_0$ , we first perform classifier-free guidance using $\mathbf{c}$ and $\mathbf{c}_0$ . Incorporating $\mathbf{c}_0$ into the synthesis process directs the generation towards subject-agnostic content, representing a weaker version of the desired generation. When subject information is absent, the model more effectively creates the correct outline and structure, generating outputs that align with both the subject and text description. + +Differing from the conventional classifier-free guidance, where the guidance weight $w$ often remains constant during the denoising process, we implement a time-varying scheme to enhance performance. Building on the observation that earlier iterations emphasize structure construction [12, 22], we highlight the subject-agnostic condition during the initial phases. Specifically, we adopt a time-varying weighting strategy, suppressing subject information in the early stages: + +$$ +\bar {\boldsymbol {\epsilon}} _ {t} = \left(1 + w _ {t}\right) \cdot \boldsymbol {\epsilon} \left(\mathbf {x} _ {t}, \mathbf {c}\right) - w _ {t} \cdot \boldsymbol {\epsilon} \left(\mathbf {x} _ {t}, \mathbf {c} _ {\mathbf {0}}\right), \tag {3} +$$ + +where $w_{t}$ denotes the guidance weight, similar to $w$ in Eqn. 2. Since a larger $w_{t}$ corresponds to a larger contribution from $\mathbf{c}$ , $w_{t}$ is devised as a non-increasing function with respect to the iteration $t$ . In this work, we find that a simple piecewise constant scheme suffices to produce promising results: + +$$ +w _ {t} = \left\{ \begin{array}{l l} r & \text {i f} 0 \leq t \leq T, \\ - 1 & \text {i f} T < t \leq 1. \end{array} \right. \tag {4} +$$ + +Here $0 \leq T \leq 1$ and $r \geq -1$ are pre-determined constants, which will be ablated in Sec. 5. Essentially, in the early stages (i.e., when $t \approx 1$ ), we use solely the subject-agnostic condition to establish the structure and outline of the output. The subject information is integrated in the subsequent stages. + +Null Classifier-Free Guidance. The null classifier-free guidance is identical to the conventional classifier-free guidance, leveraging the null condition to encourage diversity. We adopt a constant guidance weight throughout iterations. Specifically, the output $\overline{\epsilon}_t$ of the weak-classifier-free guidance is used in place of $\epsilon (\mathbf{x}_t,\mathbf{c})$ in the conventional classifier-free guidance (Eqn. 2): + +$$ +\tilde {\boldsymbol {\epsilon}} _ {t} = (1 + w) \cdot \bar {\boldsymbol {\epsilon}} _ {t} - w \cdot \boldsymbol {\epsilon} (\mathbf {x} _ {t}, \phi). \tag {5} +$$ + +# 4. Experiments + +To validate the efficacy of SAG, we conduct experiments across multiple approaches, namely Textual Inversion [16] (optimization-based), ELITE [49] (encoder-based), SuTI [10] (encoder-based), and DreamSuTI [10] (second-order). + +# 4.1. ELITE + +First, we examine the performance improvement when applying SAG to ELITE [49]. In this study, we simplify its architecture by using only the global mapping branch. The settings are as follows: + +Training. To promote the learning of subject information, we create a domain-specific (e.g., animals) text-image dataset where the text caption incorporates the specialized token. Specifically, we gather images from a pre-defined category and employ straightforward templates such as A photo of $S^*$ for the corresponding captions. During training, the token corresponding to $S^*$ is substituted with the output of the encoder. The condition is subsequently fed into the text encoder. + +As discussed in concurrent work [24], text prompts generated using templates and captioning models [11] have inherent limits to their diversity. Moreover, training within narrow domains may harm generation diversity. To counteract this, we employ a general-domain dataset containing detailed text descriptions for regularization. Training on a broad array of text captions ensures the model retains its text-understanding abilities. + +During the training phase, the domain-specific and general-domain datasets are sampled with probabilities $p \leq 1$ and $(1 - p)$ , respectively. Given that the general-domain dataset serves primarily for regularization, we allocate a higher value to $p$ , greater than 0.5, emphasizing subject encoding. + +![](images/3b19a9e3da2f4e86d8a7964866eb1c916fbb5e84a474219dde3a71a36424f3c2.jpg) +Figure 3. SAG on ELITE [49]. Our ELITE-SAG produces outputs that are more faithful to text prompts while still preserving subject identity. For Stable Diffusion, we generate pure text-to-image results by substituting "S*" with "A dog" or "A cat". + +Since the subject-agnostic condition $\mathbf{c}_0$ is also natural language, no modification to the original denoising objective (Eqn. 1) is needed. Additionally, we adopt a regularization to the learnable token [49] by constraining its $\ell_2$ -norm. The effective training loss is: + +$$ +\mathcal {L} = \mathcal {L} _ {d} + \| s \| ^ {2}, \tag {6} +$$ + +where $s$ denotes the output of the subject encoder. The remaining part of the training is identical to the training of conventional text-to-image networks. + +Inference. For each input image, we use the encoder to map the target subject into a text token. This learnable token is then combined with the text description to form the input condition $\mathbf{c}$ . The subject-agnostic condition is $\mathbf{c}_0$ is then constructed following the process discussed in Sec. 3.2.1. Starting from random Gaussian noise $\mathbf{x}_T$ , the fine-tuned network iteratively denoises the intermediate outputs. In + +stead of applying the conventional classifier-free guidance, our SAG is employed. + +Implementation. We adopt the pre-trained Stable Diffusion [36] as the synthesis network, which uses CLIP [33] as the text encoder. For the subject encoder, we use the CLIP image encoder and a three-layer MLP to obtain the learnable token. During training, only the cross-attention layers in Stable Diffusion and the MLP are trained, all other weights are being fixed. + +We use an internal text-image dataset for training. To construct the domain-specific dataset, we extract images containing dogs and cats from the meta-dataset. The remaining part is used as our general-domain dataset. The dataset mixing ratio is 0.1. The proposed method is implemented in JAX [4]. The detailed experimental settings will be discussed in the supplementary material. + +Comparison. We compare our modified model, ELITE- + +![](images/10dfefe73b8075bd91b5d52b3b07e420a2c56644ced31f0378887347dfc0796f.jpg) +Figure 4. SAG on Textual Inversion [16]. Our SAG improves text alignment without sacrificing the identity of the subject. + +Table 1. Quantitative Comparison. Our ELITE-SAG yields improved performance in both text and subject alignment. + +
MethodsCLIP-T ↑CLIP-I ↑DINO ↑
DreamBooth [37]0.3150.7850.651
Textual Inversion [16]0.3390.7510.571
ELITE [49]0.3420.7510.586
ELITE-SAG (ours)0.3440.7900.671
+ +Table 2. User Study. Across all three compared methods, the majority of raters favor the results produced by our approach. + +
% Prefer OursSubject Align.Text Align.Quality
DreamBooth [37]52%68%60%
Textual Inversion [16]64%76%84%
ELITE [49]56%80%76%
+ +SAG, with three existing works: DreamBooth [37], Textual Inversion [16], and ELITE [49]. In this section, we assume the existence of only one reference image. As illustrated in Fig. 3, while Stable Diffusion exhibits high text alignment, the compared methods often fall short in generating results faithful to text prompts in the presence of additional subject images. In contrast, with our SAG, outputs adhering to both text captions and reference subjects are consistently generated. + +We also conduct a quantitative comparison as presented in Table 1, utilizing CLIP [33] and DINO [5] scores. Specifically, the image feature similarities of CLIP [33] and DINO underscore that SAG enhances subject fidelity, while the text feature similarity indicates that SAG improves text alignment. Furthermore, our user study depicted in Table 2 reveals that more than half of the raters prefer our method when compared to the aforementioned methods, thereby corroborating the effectiveness of SAG. + +# 4.2. Textual Inversion + +Textual Inversion [16] is an optimization-based method for customization. For each given subject, Textual Inversion learns a text token to represent the subject. As discussed in Sec. 3.2.1, the subject-agnostic embedding is generated by replacing the learned special token by a generic description. + +Then, the conventional CFG is replaced by our SAG. The remaining generation pipeline remains unchanged. + +As illustrated in Fig. 4, the absence of SAG leads to generation dominated by the optimized text token, resulting in suboptimal text alignment. Conversely, the incorporation of SAG enables the model to produce outputs that align more closely with the text description, while preserving the identity of the subject. + +# 4.3. SuTI + +Unlike ELITE, which encodes subject information into a text token, SuTI [10] employs an encoder-based approach that leverages a distinct subject embedding. This embedding is then fed to the generation network through independent cross-attention layers. As discussed in Sec. 3.2.1, the subject-agnostic condition, denoted as $\mathbf{c}_0$ , is simply constructed by setting the subject embedding to zero. + +As illustrated in Fig. 5, without SAG, the model successfully preserves the identity of the individual provided in the reference images, yet the text alignment is inadequate. Specifically, the styles are unsatisfactory across all outputs. In contrast, employing SAG and suppressing the subject information during initial iterations significantly enhances text alignment. Consequently, the outputs exhibit both high identity preservation and improved text alignment. + +# 4.4. DreamSuTI + +DreamSuTI [10] is a second-order method that fine-tunes SuTI using DreamBooth [37] for compositional customization. In this section, we fine-tune SuTI with a provided style image to achieve simultaneous customization of style and subject. The subject-agnostic embedding is generated using the same method as in SuTI. + +As depicted in Fig. 6, in the presence of subject images, the outputs are dominated by the subject, resulting in a lack of style fidelity. In contrast, when applying SAG, the subject is suppressed during the early stages of generation, effectively leading to enhanced style generation. + +A bronze face, looks like bronze statue or bronze figure, fine details. + +![](images/82e14d05437c62bbaaa9e580e72f6ba5dd0a4a6142f9a22f3526187d2a69d5e7.jpg) +w/o SAG + +![](images/8a4424dda0c2032a0d7b8af114bd754acd096eb07d45614567e378f6b2cc39f5.jpg) +w/ SAG + +Beautiful steampunk face +wearing mask, +d & d, fantasy, intricate, +elegant, digital painting, +matte, sharp focus, +illustration, hearthsfone, +gradient background, hdr +8k. + +![](images/df503725ac73ba225bd8e2ab7f5077f5903b53c0e49203368f9a031f425eb33d.jpg) +Prompt +w/o SAG + +![](images/13eadd74403c61ce3132686ec9cbdc1e5ddc6e8f6c2fa638b47cf4010b3e8ba3.jpg) +w/ SAG + +Pixel art of face figures, +attractive faces, edgy, cool, +extreme detail, tiny pixels, +very coherent, vibrant colors + +![](images/e1d31c7c01323de220f499a5f9cd91b4fb54fd578e1d5fd0730950631721c1f8.jpg) +Prompt +w/o SAG + +![](images/d22270f9c7f00431460899050157cc6215d481c45965a5ca8c3509e6bbb960b1.jpg) +w/ SAG + +Portrait photography of a face, city, 35mm, night time, blue green, pink and gold, heavy bokeh. + +![](images/4db3a93f772db0592bdd95bfba218f0becd6ced5824d6da23517a99d4f2b9f06.jpg) +Prompt +w/o SAG +Figure 5. SAG on SuTI [10]. When applying SAG on SuTI, the subject is discarded during initial iterations, yielding outputs with markedly improved text alignment. Reference images are not provided to protect privacy. + +![](images/fdec6b875f8da50d03d06afa50592518c7f47c23e2e07202742b9100b4294899.jpg) +w/ SAG + +![](images/280a71b22bfb6c9b34d1b1bf8a8a7cf7875aa6023af21f2c5e18b359bfd4182d.jpg) +Prompt +References + +![](images/df204c4147ae0b25091f3270e3ec45ecdf513e62a565cb89b157cdc2a5dc0384.jpg) +A vase in kid line drawing style + +![](images/b7fefaf02903319644b5255f9635e37503d2e654a5d6793520925f7027eef15c.jpg) +w/o SAG + +![](images/8e43d4273d7e435795ae1d41397b42ac493fb257a38dcfd0856d81255ada0605.jpg) +w/ SAG + +![](images/6f1ac2b20d75577b71f70805a680f4f1c1e5c552ee0d8bb40c92e3c7cc619149.jpg) +A berry bowl in 3D rendering style +References + +![](images/a776d4e9c25d3489b5cf2aa325ea80092c1c45c60f5268d329149b771482372d.jpg) +w/o SAG + +![](images/51141d6986cb8be3bda194acd1dc4a008dfc27c81605adfa07e90ece361e7c58.jpg) +w/ SAG + +![](images/e3c4fca9c6666a872ff50a9d3bc5f4cc385cadf7dd86206827731add0c45450f.jpg) + +![](images/0281a2df482e14397bc8662d2d944ca50b22fdb9d842d561f0e49b4d177cda67.jpg) +A beer can in watercolor painting style + +![](images/e471d4e90a5ff888e4209765b5d163333f0270b179b75be749d3ad7a96e679d0.jpg) +References + +![](images/2fd4766314cef28fad99f961f5bb6f0bad69e829e477bfd217a94702322b6937.jpg) + +![](images/7c58bb6d337894621d6ea9a96a1938c13cfa61acc5bffe5c617d67d22287a6d9.jpg) +w/o SAG + +![](images/3bbc53924b1bc0b2ef97695bfee913fc79d2f184ce3d2a2bbf7fe923642b5ad1.jpg) +w/ SAG +Figure 6. SAG on DreamSuTI [10]. Even after fine-tuning with DreamBooth to adapt to the specified style, the generated results tend to be dominated by the subjects, leading to an inadequate style-alignment. Our SAG addresses this issue by diminishing the influence of subjects, thereby ensuring outputs that are well-aligned with both the text, subject, and style. + +![](images/1e5fdb8c249c13ddcf3213d233f8d4024e9b6d079419b80d7fbb3128129986c7.jpg) +A grey sloth plushie in watercolor painting style +References + +![](images/14998945c846965d864f52f0d07a3e379defd76a8ae51405972a47d146481bb8.jpg) +w/o SAG + +![](images/da84c935238b876cfa5e0cbd9901cb53781f3ffc4d49f812ed6932bf70ec59de.jpg) +w/ SAG + +# 5. Ablations + +Guidance Timing. The hyper-parameter $T$ plays an important role in controlling the contribution of the subject embedding. An illustration employing DreamSuTI is provided in Fig. 7. With $r = 0$ , adopting a smaller $T$ results in a stronger suppression of the subject embedding, thereby promoting a better text-alignment (i.e., style-alignment in this example). A gradual increment in $T$ facilitates a transition from style alignment to subject alignment. + +Guidance Weight. While a default value of $r = 0$ (i.e., employing only the subject-aware condition in later iterations) performs well generally, decreasing $r$ facilitates the utilization of the subject-agnostic condition in subsequent iterations, thereby further enhancing content faithfulness. As depicted in Fig. 8, the inclusion of subject-agnostic conditions significantly improves the style alignment of DreamSuTI. Since no re-training is required, the values of $T$ and $r$ can be dynamically adjusted based on user preference. + +![](images/f88001af69f7fa2c237e6deb1d777291572d5d338f84036d3828b784c3e43e99.jpg) + +![](images/fa30c100677187006130f0bb1364ee6037610f2e28134284913b0c590694e651.jpg) + +![](images/597c4a7090bbe2f2eef7e9dc1a8609ef3e527315fdc921d0e7cf33adc6cc3be5.jpg) + +![](images/9e62fefb145c2bca13d48cb51007efbcc4f1f8026f88e9b5a18954b9798f10d0.jpg) + +![](images/5d6fc2090f49ce87baac529b4e7b4b0536725ed09121ba92b4c6528cb3135561.jpg) + +![](images/384e6564a90a825cd39b69e24f0d37bee66d279191710306485b21be150e5064.jpg) + +![](images/0542b05bf5b8bb62abcfe0a2b8ee9c81c7678ba21a428d1cd38cc5e150f0a9b2.jpg) + +![](images/39e1a8797721570b75cda986fbcb1dfb210445c4500b8cac60719f812d00fcca.jpg) +References + +![](images/947e5fb298688d68919ba25072c59eb2f7c038a03e92d1ec0898cefe0694c797.jpg) +$\mathrm{T} = 1.0$ + +![](images/764a4756f046cb4c1f9cc30cd2c3930c535155fa0760c9c0af4086c1819bc889.jpg) +$\mathrm{T} = 0.99$ + +![](images/0193b937970bb5bf6299b74c5424f294294835d7f0a11cc42366332c39fa73fd.jpg) +$\mathrm{T} = 0.95$ + +![](images/f4717edd3cd7307a6aa4d638719dafa57c4114e79be0046f54c337d910c97134.jpg) +$\mathrm{T} = 0.9$ + +![](images/daab1502d3a2c8907b219d10ff729e84b1b30dbe6d8f0df7968043228d340f20.jpg) +$\mathrm{T} = 0.85$ + +![](images/57b8030e2647b3c0b6b1e21f7150cc6b1c017a35e94f763424f7f54c180607c0.jpg) +$\mathrm{T} = 0.0$ +Style Alignment + +![](images/218694d004b3823301fcfbb6e84517a7466d8fafd77f21a52acd8a0cd7bdf2c5.jpg) +Figure 7. Guidance Timing. As an example, when fine-tuning SuTI [10] to a given style using DreamBooth [37], our SAG facilitates a transition from subject-centric alignment to style-centric alignment. Here $r = 0$ is used. + +![](images/1757d3b8c2fd80a8692bb2cdfbabfac0e6f4ef5ae7a1d848d97f36848550c4c9.jpg) + +![](images/48edac884f687cd20801345f070093f49f01a85802f5a922ca85c4b4597db397.jpg) + +![](images/fd8be653ad444e7aff162b709339e98e0825e5cb6a2a183387a8cc5651d12042.jpg) + +![](images/a7d9f634b164a79908ca00a78b0c710b5f915d7047a417b208fd9b22081e49ed.jpg) + +![](images/8ada63259e55901f10c8503dc299bf4614ddfbc1db7bb98e11150ce88eb2e336.jpg) + +![](images/d0a95b339e4573e7282060ce839af72a7321ec410c075b5b42b216d0a57467c1.jpg) + +![](images/3f15e21927ab750f1e9c2e40c29085bc9a99703ef4ad0ebd6546a594f0338599.jpg) +References +Figure 8. Guidance Weight. The guidance weight $r$ can be leveraged to enhance content faithfulness further. For instance, lowering $r$ results in improved style alignment in DreamSuTI. Here $T = 0.9$ is used. + +![](images/dcace783335414369d6f83091b5b655ef5fb89148235ec8cbf93d7b69a9b51c6.jpg) +$\mathrm{r} = 0.0$ +Subject +Alignment + +![](images/6dd1f36b32ae041bbf3768995db356af94089454b6c253fde4026e31d4b2b4b0.jpg) +$\mathrm{r} = -0.2$ + +![](images/adcb2f93fc06463c5775a7a999f1294d1093c272560ff0a4cc53896d622d0f4a.jpg) +$\mathrm{r} = -0.4$ + +![](images/945088ad5fa4d7725da4a253d5138894bf3312e102a66328138be8c6bdf0b84f.jpg) +$\mathrm{r} = -0.6$ + +![](images/182166e82c66f875317db3ffeac6efaab93f97ca4a2567d5253c4e689e1425a9.jpg) +$\mathrm{r} = -0.8$ + +![](images/c609eb99446a59a75301bcbd74ce617f8baffe999c8c07b8c5149170f1293c80.jpg) +$\mathrm{r} = -1.0$ +Style +Alignment + +# 6. Limitation and Societal Impact + +Limitation. While our SAG significantly enhances content alignment compared to existing methods, the quality of outputs is inherently constrained by the underlying generation model. Hence, it may still exhibit suboptimal performance for uncommon content that challenges the generation model. However, this limitation can be mitigated by incorporating a more robust synthesis network, a direction we aim to explore in our future work. + +Societal Impact. This project targets at improving content alignment in customized synthesis, which holds the potential for misuse by malicious entities aiming to mislead the public. Future investigations in this domain should duly consider these ethical implications. Moreover, ensuing efforts to develop mechanisms for detecting images generated by such models emerge as a critical avenue to foster the safe + +advancement of generative models. + +# 7. Conclusion + +Subject-driven text-to-image synthesis has witnessed notable progress in recent years. However, overcoming the problem of content ignorance remains a significant challenge. As shown in this work, this problem significantly limits the diversity of the generation. Rather than introducing complex modules, we propose a straightforward yet effective method to address this issue. Our Subject-Agnostic Guidance demonstrates how a balance between content consistency and subject fidelity can be achieved using a subject-agnostic condition. The proposed method enables users to generate customized and diverse scenes without modifying the training process, making it adaptable across various existing approaches. + +# References + +[1] Moab Arar, Rinon Gal, Yuval Atzmon, Gal Chechik, Daniel Cohen-Or, Ariel Shamir, and Amit H Bermano. Domain-agnostic tuning-encoder for fast personalization of text-to-image models. arXiv preprint arXiv:2307.06925, 2023. 2, 3 +[2] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. MultiDiffusion: Fusing diffusion paths for controlled image generation. 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In this work, we propose Subject-Agnostic Guidance (SAG), a simple yet effective solution to remedy the problem. We show that through constructing a subject-agnostic condition and applying our proposed dual classifier-free guidance, one could obtain outputs consistent with both the given subject and input text prompts. We validate the efficacy of our approach through both optimization-based and encoder-based methods. Additionally, we demonstrate its applicability in second-order customization methods, where an encoder-based model is fine-tuned with DreamBooth. Our approach is conceptually simple and requires only minimal code modifications, but leads to substantial quality improvements, as evidenced by our evaluations and user studies." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 307, + 464, + 387, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 464, + 387, + 477 + ], + "spans": [ + { + "bbox": [ + 307, + 464, + 387, + 477 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 486, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 605 + ], + "type": "text", + "content": "Subject-driven text-to-image synthesis focuses on generating diverse image samples, conditioned on user-given text descriptions and subject images. This domain has witnessed a surge of interest and significant advancements in recent years. Optimization-based methods [16, 37, 41] tackle the problem by overfitting pre-trained text-to-image synthesis models [36, 38] and text tokens to the given subject. Recently, encoder-based approaches [10, 24, 49] propose to train auxiliary encoders to generate subject embeddings, bypassing the necessity of per-subject optimization." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 607, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 607, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 607, + 545, + 679 + ], + "type": "text", + "content": "In the aforementioned approaches, both the embeddings and networks are intentionally tailored to closely fit the target subject. As a consequence, these learnable conditions tend to dominate the synthesis process, often obscuring the attributes specified in the text prompt. For instance, as shown in Fig. 1, when employing " + }, + { + "bbox": [ + 304, + 607, + 545, + 679 + ], + "type": "inline_equation", + "content": "S^{*1}" + }, + { + "bbox": [ + 304, + 607, + 545, + 679 + ], + "type": "text", + "content": " alongside the style" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "inline_equation", + "content": "^{1}\\mathbb{S}^{*}" + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": " denotes a pseudo-word, where its embedding is substituted by a learnable subject embedding." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6733" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": "description Monet style, the desired style is not appropriately synthesized. Such observations underscore that the network struggles to prioritize key content in the existence of learnable components. To address the content ignorance issue, existing solutions modify the training process through additional regularization [37, 49], leading to improved performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 288, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 288, + 346 + ], + "type": "text", + "content": "In this work, we present Subject-Agnostic Guidance (SAG), an approach that diverges from traditional methodologies. Our strategy emphasizes attending to subject-agnostic attributes by diminishing the influence of subject-specific attributes, accomplished using classifier-free guidance. Differing from standard classifier-free guidance [19], our method incorporates a subject-agnostic condition2. Subsequently, our proposed Dual Classifier-Free Guidance (DCFG) is employed to enhance attention directed towards subject-agnostic attributes. Crucially, motivated by the observation that structures are constructed during early iterations [12, 22], we temporarily replace the subject-aware condition with a subject-agnostic condition at the beginning of the iteration process. Following the construction of coarse image structures, the original subject-aware condition is reintroduced to refine customized details." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 347, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 443 + ], + "type": "text", + "content": "Our SAG is elegant in both design and implementation, seamlessly blending with existing methods. We showcase the efficacy of SAG using both optimization-based and encoder-based approaches. Furthermore, we delve into its applicability in second-order customization, with an encoder-based model fine-tuned via DreamBooth [37]. Qualitative and quantitative evaluations as well as user feedback verify our robustness, succinctness, and versatility." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 443, + 288, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 288, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 288, + 551 + ], + "type": "text", + "content": "In the evolving realm of subject-driven text-to-image synthesis, challenges have emerged due to over-tailored embeddings and networks. These often inherit crucial attributes. While existing solutions modify training to address these issues, our novel Subject-Agnostic Guidance (SAG) provides a distinct approach. Seamlessly integrating with prevalent methods, SAG emphasizes a more balanced synthesis process. Its effectiveness is demonstrated through various methodologies and supported by user feedback." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 559, + 134, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 134, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 134, + 572 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 579, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 287, + 687 + ], + "type": "text", + "content": "Diffusion Model for Text-To-Image Synthesis. Typically, given natural language descriptions, a text encoder such as CLIP [33] or T5 [34] is employed to derive the text embedding. This embedding is then fed into the diffusion model for the generation phase. Earlier approaches [35] operated directly within the high-resolution image space for generation. While these methods yielded promising outcomes, the direct iteration in high-resolution space poses significant computational challenges. In light of these constraints," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "type": "text", + "content": "considerable efforts have been devoted to enhancing generation efficiency. For instance, Imagen [38] employs a multistage diffusion model. It starts by synthesizing a " + }, + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "type": "text", + "content": " resolution image based on the input text prompt and subsequently employs a series of super-resolution modules to increase the resolution to " + }, + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 306, + 72, + 545, + 288 + ], + "type": "text", + "content": ". Benefiting from optimized architectures in the super-resolution stages, this cascaded approach considerably reduces computational overhead compared to direct high-resolution image synthesis. Latent Diffusion [36] transitions the generation process to a low-resolution feature space to improve efficiency. Initially, a VAE [26] or VQGAN [15, 45] is pre-trained. During training, images are encoded into low-resolution features using the pre-trained encoder, and the diffusion model aims to reconstruct these encoded features. In the inference stage, the trained diffusion model produces a feature which is subsequently decoded using the pre-trained module to render the final output image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 300, + 545, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 600 + ], + "type": "text", + "content": "Subject-Driven Image Synthesis. Subject-driven text-to-image synthesis [1, 8, 9, 18, 21, 27-29, 31, 40, 43, 47] is a sub-branch of text-to-image synthesis [3, 6, 14, 25, 36, 38, 50] with an additional requirement that the primary attributes in the output aligns with the subjects provided by the user. Existing research [16, 17, 37, 44] has demonstrated that subject information can be encoded as a subject-aware embedding through test-time optimization, given several reference images. For instance, Textual Inversion [16] leverages pre-trained synthesis networks and optimizes a special token while keeping the network static. DreamBooth [37] shares a similar premise but also fine-tunes the network to enhance subject consistency. To bypass test-time optimization, which restricts instant feedback, recent studies [10, 24] advocate the use of an encoder to encapsulate subject information. However, despite advancements in both quality and speed, the encoded subject information often dominates the synthesis process, resulting in inadequately capture of subject information. In this study, we introduce Subject-Agnostic Guidance (SAG) to rectify this challenge. Our SAG focuses on enhancing subject-agnostic attributes, diminishing the influence of subject-specific elements through our dual classifier-free guidance. We illustrate that SAG not only enhances consistency to the input captions but also maintains fidelity to the subject." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 636, + 388, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 636, + 388, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 636, + 388, + 651 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "In this work, we introduce an intuitive and effective method to enhance content alignment. We first provide the background for our approach, followed by the discussion of our method - Subject-Agnostic Guidance." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": "2The construction of this condition varies based on the specific customization approach used." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6734" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 280, + 187 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 280, + 187 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 280, + 187 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 280, + 187 + ], + "type": "image", + "image_path": "e0cac1acd78dd4df3e31ea5893bcaa1b258a32d0dcce380cd61de0182d3447cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 289, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 289, + 264 + ], + "type": "text", + "content": "Figure 2. Overview of SAG. Given a subject-aware embedding, we first construct a subject-agnostic embedding. These embeddings are subsequently used in our dual classifier-free guidance (DCFG), which consists of weak classifier-free guidance and null-classifier-free guidance. Null CFG adopts a constant weight (Eqn. 2) and Weak CFG adopts a variable weight (Eqn. 3)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 283, + 134, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 283, + 134, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 283, + 134, + 295 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 301, + 149, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 301, + 149, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 301, + 149, + 314 + ], + "type": "text", + "content": "3.1.1 Diffusion Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 321, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 287, + 417 + ], + "type": "text", + "content": "The diffusion process transforms a data distribution to a Gaussian noise distribution by iteratively adding noise. Diffusion model is a class of generative models that invert the diffusion process through iterative denoising. Extended from the original unconditional model [20], recent works demonstrate huge success by conditioning diffusion models on various modalities, including text [7, 23, 39], segmentation [2, 22, 32], and many more [30, 42, 48]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "content": " be the input image, and " + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "content": " be the condition. During training, a noisy image " + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "content": " is obtained by adding Gaussian noise " + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\epsilon_t" + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 417, + 287, + 477 + ], + "type": "text", + "content": ". The network is trained to predict the added noise, given the noisy image and condition as input. It is generally optimized with a single denoising objective:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 117, + 487, + 287, + 501 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 487, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 117, + 487, + 287, + 501 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d} = \\left| \\left| \\epsilon \\left(\\mathbf {x} _ {t}, \\mathbf {c}\\right) - \\epsilon_ {t} \\right| \\right| _ {2} ^ {2}, \\tag {1}", + "image_path": "67cd595328862daf42a4905e61e35eb593ef09bdc32ccaab5fc5a763b69285ed.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": " the noise added to the input image, and " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\epsilon (\\mathbf{x}_t,\\mathbf{c})" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": " corresponds to the noise estimated by the network. Here " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": " refer to the noisy image and condition, respectively. During inference, the process starts with a pure Gaussian noise " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_0}" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": ", and the trained network is iteratively applied to obtain a series of intermediate outputs " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_{T_0 - 1},\\mathbf{x}_{T_0 - 2},\\dots ,\\mathbf{x}_0\\}" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 510, + 287, + 595 + ], + "type": "text", + "content": " is the final output." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 609, + 186, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 186, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 186, + 621 + ], + "type": "text", + "content": "3.1.2 Classifier-Free Guidance" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "type": "text", + "content": "Similar to classifier guidance [13], classifier-free guidance is designed to trade between image quality and diversity, but without the need of a classifier. It is widely adopted in existing works [46, 51]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "During training, an unconditional diffusion model is jointly trained by randomly replacing the input condition " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " by a null condition " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": ". Once trained, during each iteration" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": ", a weighted sum of the conditional output and the unconditional output is computed:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 345, + 106, + 545, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 106, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 345, + 106, + 545, + 120 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {\\epsilon}} _ {t} = (1 + w) \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\mathbf {c}) - w \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\phi). \\tag {2}", + "image_path": "ec5e4cc7a1bda59eef0b5f3fc444df599ca3d7ba77b992d775efe24bd54e2ae0.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "spans": [ + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "type": "text", + "content": "In general, a larger " + }, + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "type": "text", + "content": " produces better quality, whereas a smaller " + }, + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 130, + 545, + 154 + ], + "type": "text", + "content": " yields greater diversity." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 162, + 457, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 162, + 457, + 175 + ], + "spans": [ + { + "bbox": [ + 306, + 162, + 457, + 175 + ], + "type": "text", + "content": "3.2. Subject-Agnostic Guidance" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 181, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 545, + 288 + ], + "type": "text", + "content": "In this section, we introduce the concept of Subject-Agnostic Guidance (SAG). The essence of SAG is anchored in formulating a subject-agnostic embedding based on the inputs provided by users. The embedding is then used in our dual classifier-free guidance (DCFG) in generating outputs that align with both the subject and text prompt. We delve into the details of constructing subject-agnostic embeddings in Sec. 3.2.1, and discuss our dual classifier-free guidance in Sec. 3.2.2." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 306, + 468, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 306, + 468, + 318 + ], + "spans": [ + { + "bbox": [ + 306, + 306, + 468, + 318 + ], + "type": "text", + "content": "3.2.1 Subject-Agnostic Embeddings" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 325, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 396 + ], + "type": "text", + "content": "The construction of subject-agnostic embeddings depends on the choice of methods. Existing approaches generally fall into two categories: Learnable Text Token and Separate Subject Embedding. In this section, we discuss the construction of subject-agnostic embeddings in these two approaches." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 399, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 496 + ], + "type": "text", + "content": "Learnable Text Token. Given images of a reference subject, the learnable text token approach derives a token embedding that captures the identity of the subject, either through fine-tuning [16, 47] or by using an encoder [1, 49]. The resultant token embedding, combined with the token embedding of the text description, is processed by text encoders such as CLIP [33] and T5 [34] to produce a subject-aware embedding." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 496, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 568 + ], + "type": "text", + "content": "To construct a subject-agnostic embedding, we replace the derived token embedding with one from a general description of the subject. This strategy ensures that the synthesis process is not dominated by any adaptable components, thereby allowing the model to focus attention on the attributes specified in the text prompt." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "text", + "content": " be the text condition containing the learnable token " + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "S^*" + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "text", + "content": ". We define a subject-agnostic condition " + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "text", + "content": " by replacing the token " + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "S^*" + }, + { + "bbox": [ + 304, + 568, + 545, + 616 + ], + "type": "text", + "content": " by a generic descriptor. For example, assuming the target subject is a dog and" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 352, + 626, + 498, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 626, + 498, + 637 + ], + "spans": [ + { + "bbox": [ + 352, + 626, + 498, + 637 + ], + "type": "interline_equation", + "content": "\\mathbf {c} = \\mathrm {A} \\text {p e n c i l s k e t c h o f S} ^ {*}", + "image_path": "058ff917d2ba969ffd0bdb7bf2af6f0cd5ed035ad7448c34908ff5bb81837a15.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 647, + 383, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 383, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 383, + 658 + ], + "type": "text", + "content": "we construct " + }, + { + "bbox": [ + 306, + 647, + 383, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 306, + 647, + 383, + 658 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 340, + 669, + 511, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 669, + 511, + 681 + ], + "spans": [ + { + "bbox": [ + 340, + 669, + 511, + 681 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {0} = \\mathrm {A p e n c i l s k e t c h o f a d o g}", + "image_path": "60b50c79e3695e08d233e98b505f8c688c9953a9f22e8b8ece0937ced3d9e92a.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "The generic descriptor is chosen as a noun describing the subject." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6735" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "Separate Subject Embedding. Instead of encoding the subject identity to a learnable text token, the separate subject embedding approach [10, 24] adopts an independent embedding. This embedding is then integrated into the network via auxiliary operations. For instance, Jia et al. [24] employ the CLIP image encoder to encapsulate the subject information into an embedding, which is then injected to Imagen [38] using cross attention." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 227 + ], + "type": "text", + "content": "To construct the subject-agnostic embedding, we opt for a direct method – setting both the subject embedding and its corresponding attention mask to zero. This disables attention to the subject, directing focus towards subject-agnostic information." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 242, + 209, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 242, + 209, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 209, + 253 + ], + "type": "text", + "content": "3.2.2 Dual Classifier-Free Guidance" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "text", + "content": "In this section, we introduce the Dual Classifier-Free Guidance (DCFG), designed primarily to address the issue of content ignorance by attenuating the subject-aware condition. Our DCFG requires no modifications of the training process. It simply requires the application of an additional classifier-free guidance using the subject-aware condition " + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "text", + "content": " and the subject-agnostic condition " + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "text", + "content": ". The derived feature is subsequently merged with the null condition " + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 261, + 287, + 369 + ], + "type": "text", + "content": " within a conventional classifier-free guidance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "content": "Weak Classifier-Free Guidance. Given the subject-aware condition " + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "content": " and the subject-agnostic condition " + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "content": ", we first perform classifier-free guidance using " + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "content": ". Incorporating " + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 371, + 287, + 479 + ], + "type": "text", + "content": " into the synthesis process directs the generation towards subject-agnostic content, representing a weaker version of the desired generation. When subject information is absent, the model more effectively creates the correct outline and structure, generating outputs that align with both the subject and text description." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 479, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 586 + ], + "type": "text", + "content": "Differing from the conventional classifier-free guidance, where the guidance weight " + }, + { + "bbox": [ + 46, + 479, + 287, + 586 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 479, + 287, + 586 + ], + "type": "text", + "content": " often remains constant during the denoising process, we implement a time-varying scheme to enhance performance. Building on the observation that earlier iterations emphasize structure construction [12, 22], we highlight the subject-agnostic condition during the initial phases. Specifically, we adopt a time-varying weighting strategy, suppressing subject information in the early stages:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 595, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 595, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 82, + 595, + 287, + 608 + ], + "type": "interline_equation", + "content": "\\bar {\\boldsymbol {\\epsilon}} _ {t} = \\left(1 + w _ {t}\\right) \\cdot \\boldsymbol {\\epsilon} \\left(\\mathbf {x} _ {t}, \\mathbf {c}\\right) - w _ {t} \\cdot \\boldsymbol {\\epsilon} \\left(\\mathbf {x} _ {t}, \\mathbf {c} _ {\\mathbf {0}}\\right), \\tag {3}", + "image_path": "031c4d6e29a0872bdbbf25a665d7afd21b009eef5a694812203ac19cf890ac29.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": " denotes the guidance weight, similar to " + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": " in Eqn. 2. Since a larger " + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": " corresponds to a larger contribution from " + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": " is devised as a non-increasing function with respect to the iteration " + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 616, + 287, + 685 + ], + "type": "text", + "content": ". In this work, we find that a simple piecewise constant scheme suffices to produce promising results:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 684, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 684, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 105, + 684, + 287, + 716 + ], + "type": "interline_equation", + "content": "w _ {t} = \\left\\{ \\begin{array}{l l} r & \\text {i f} 0 \\leq t \\leq T, \\\\ - 1 & \\text {i f} T < t \\leq 1. \\end{array} \\right. \\tag {4}", + "image_path": "5f0c1a964beaa265847e702ac0e6dd883ff13becbf6efff13682539420688040.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "0 \\leq T \\leq 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "r \\geq -1" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " are pre-determined constants, which will be ablated in Sec. 5. Essentially, in the early stages (i.e., when " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "t \\approx 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "), we use solely the subject-agnostic condition to establish the structure and outline of the output. The subject information is integrated in the subsequent stages." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "type": "text", + "content": "Null Classifier-Free Guidance. The null classifier-free guidance is identical to the conventional classifier-free guidance, leveraging the null condition to encourage diversity. We adopt a constant guidance weight throughout iterations. Specifically, the output " + }, + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\overline{\\epsilon}_t" + }, + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "type": "text", + "content": " of the weak-classifier-free guidance is used in place of " + }, + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\epsilon (\\mathbf{x}_t,\\mathbf{c})" + }, + { + "bbox": [ + 304, + 147, + 545, + 232 + ], + "type": "text", + "content": " in the conventional classifier-free guidance (Eqn. 2):" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 357, + 242, + 545, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 242, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 357, + 242, + 545, + 255 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {\\epsilon}} _ {t} = (1 + w) \\cdot \\bar {\\boldsymbol {\\epsilon}} _ {t} - w \\cdot \\boldsymbol {\\epsilon} (\\mathbf {x} _ {t}, \\phi). \\tag {5}", + "image_path": "3ffe3bbae98712a3d0921924900b0544640c819d918c46d4ddbd30da8ed439a6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 277, + 386, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 386, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 386, + 291 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 298, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 357 + ], + "type": "text", + "content": "To validate the efficacy of SAG, we conduct experiments across multiple approaches, namely Textual Inversion [16] (optimization-based), ELITE [49] (encoder-based), SuTI [10] (encoder-based), and DreamSuTI [10] (second-order)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 367, + 362, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 367, + 362, + 379 + ], + "spans": [ + { + "bbox": [ + 305, + 367, + 362, + 379 + ], + "type": "text", + "content": "4.1. ELITE" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 386, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 434 + ], + "type": "text", + "content": "First, we examine the performance improvement when applying SAG to ELITE [49]. In this study, we simplify its architecture by using only the global mapping branch. The settings are as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": "Training. To promote the learning of subject information, we create a domain-specific (e.g., animals) text-image dataset where the text caption incorporates the specialized token. Specifically, we gather images from a pre-defined category and employ straightforward templates such as A photo of " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "S^*" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " for the corresponding captions. During training, the token corresponding to " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "S^*" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " is substituted with the output of the encoder. The condition is subsequently fed into the text encoder." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "content": "As discussed in concurrent work [24], text prompts generated using templates and captioning models [11] have inherent limits to their diversity. Moreover, training within narrow domains may harm generation diversity. To counteract this, we employ a general-domain dataset containing detailed text descriptions for regularization. Training on a broad array of text captions ensures the model retains its text-understanding abilities." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "During the training phase, the domain-specific and general-domain datasets are sampled with probabilities " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "p \\leq 1" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "(1 - p)" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ", respectively. Given that the general-domain dataset serves primarily for regularization, we allocate a higher value to " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ", greater than 0.5, emphasizing subject encoding." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6736" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 75, + 537, + 443 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 537, + 443 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 537, + 443 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 537, + 443 + ], + "type": "image", + "image_path": "3b19a9e3da2f4e86d8a7964866eb1c916fbb5e84a474219dde3a71a36424f3c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 456, + 546, + 480 + ], + "lines": [ + { + "bbox": [ + 46, + 456, + 546, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 546, + 480 + ], + "type": "text", + "content": "Figure 3. SAG on ELITE [49]. Our ELITE-SAG produces outputs that are more faithful to text prompts while still preserving subject identity. For Stable Diffusion, we generate pure text-to-image results by substituting \"S*\" with \"A dog\" or \"A cat\"." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "type": "text", + "content": "Since the subject-agnostic condition " + }, + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "type": "text", + "content": " is also natural language, no modification to the original denoising objective (Eqn. 1) is needed. Additionally, we adopt a regularization to the learnable token [49] by constraining its " + }, + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 500, + 287, + 559 + ], + "type": "text", + "content": "-norm. The effective training loss is:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 131, + 568, + 287, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 568, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 131, + 568, + 287, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {d} + \\| s \\| ^ {2}, \\tag {6}", + "image_path": "79b54b6242d7e4a09180a9b197168966f0c823f514490d869acba7e445d66be8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 591, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 591, + 287, + 628 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 591, + 287, + 628 + ], + "type": "text", + "content": " denotes the output of the subject encoder. The remaining part of the training is identical to the training of conventional text-to-image networks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Inference. For each input image, we use the encoder to map the target subject into a text token. This learnable token is then combined with the text description to form the input condition " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": ". The subject-agnostic condition is " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " is then constructed following the process discussed in Sec. 3.2.1. Starting from random Gaussian noise " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": ", the fine-tuned network iteratively denoises the intermediate outputs. In" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 500, + 544, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 544, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 544, + 525 + ], + "type": "text", + "content": "stead of applying the conventional classifier-free guidance, our SAG is employed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 528, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 612 + ], + "type": "text", + "content": "Implementation. We adopt the pre-trained Stable Diffusion [36] as the synthesis network, which uses CLIP [33] as the text encoder. For the subject encoder, we use the CLIP image encoder and a three-layer MLP to obtain the learnable token. During training, only the cross-attention layers in Stable Diffusion and the MLP are trained, all other weights are being fixed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 613, + 545, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 697 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 697 + ], + "type": "text", + "content": "We use an internal text-image dataset for training. To construct the domain-specific dataset, we extract images containing dogs and cats from the meta-dataset. The remaining part is used as our general-domain dataset. The dataset mixing ratio is 0.1. The proposed method is implemented in JAX [4]. The detailed experimental settings will be discussed in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Comparison. We compare our modified model, ELITE-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6737" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 73, + 541, + 175 + ], + "blocks": [ + { + "bbox": [ + 50, + 73, + 541, + 175 + ], + "lines": [ + { + "bbox": [ + 50, + 73, + 541, + 175 + ], + "spans": [ + { + "bbox": [ + 50, + 73, + 541, + 175 + ], + "type": "image", + "image_path": "10dfefe73b8075bd91b5d52b3b07e420a2c56644ced31f0378887347dfc0796f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 184, + 520, + 196 + ], + "lines": [ + { + "bbox": [ + 72, + 184, + 520, + 196 + ], + "spans": [ + { + "bbox": [ + 72, + 184, + 520, + 196 + ], + "type": "text", + "content": "Figure 4. SAG on Textual Inversion [16]. Our SAG improves text alignment without sacrificing the identity of the subject." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 246, + 277, + 304 + ], + "blocks": [ + { + "bbox": [ + 46, + 215, + 288, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 239 + ], + "type": "text", + "content": "Table 1. Quantitative Comparison. Our ELITE-SAG yields improved performance in both text and subject alignment." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 246, + 277, + 304 + ], + "lines": [ + { + "bbox": [ + 56, + 246, + 277, + 304 + ], + "spans": [ + { + "bbox": [ + 56, + 246, + 277, + 304 + ], + "type": "table", + "html": "
MethodsCLIP-T ↑CLIP-I ↑DINO ↑
DreamBooth [37]0.3150.7850.651
Textual Inversion [16]0.3390.7510.571
ELITE [49]0.3420.7510.586
ELITE-SAG (ours)0.3440.7900.671
", + "image_path": "3e6f6408dfeadabb4e3e7933f73184d37cb8b259f37c72ac5b15ac295b2c985f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 344, + 293, + 392 + ], + "blocks": [ + { + "bbox": [ + 46, + 313, + 288, + 336 + ], + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 336 + ], + "type": "text", + "content": "Table 2. User Study. Across all three compared methods, the majority of raters favor the results produced by our approach." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 344, + 293, + 392 + ], + "lines": [ + { + "bbox": [ + 50, + 344, + 293, + 392 + ], + "spans": [ + { + "bbox": [ + 50, + 344, + 293, + 392 + ], + "type": "table", + "html": "
% Prefer OursSubject Align.Text Align.Quality
DreamBooth [37]52%68%60%
Textual Inversion [16]64%76%84%
ELITE [49]56%80%76%
", + "image_path": "17ada6bc1d653d50966ec0c98e150cca4c1d1ef5f90230da9435c21c41d09cbf.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 518 + ], + "type": "text", + "content": "SAG, with three existing works: DreamBooth [37], Textual Inversion [16], and ELITE [49]. In this section, we assume the existence of only one reference image. As illustrated in Fig. 3, while Stable Diffusion exhibits high text alignment, the compared methods often fall short in generating results faithful to text prompts in the presence of additional subject images. In contrast, with our SAG, outputs adhering to both text captions and reference subjects are consistently generated." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 520, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 627 + ], + "type": "text", + "content": "We also conduct a quantitative comparison as presented in Table 1, utilizing CLIP [33] and DINO [5] scores. Specifically, the image feature similarities of CLIP [33] and DINO underscore that SAG enhances subject fidelity, while the text feature similarity indicates that SAG improves text alignment. Furthermore, our user study depicted in Table 2 reveals that more than half of the raters prefer our method when compared to the aforementioned methods, thereby corroborating the effectiveness of SAG." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 635, + 151, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 151, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 151, + 647 + ], + "type": "text", + "content": "4.2. Textual Inversion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Textual Inversion [16] is an optimization-based method for customization. For each given subject, Textual Inversion learns a text token to represent the subject. As discussed in Sec. 3.2.1, the subject-agnostic embedding is generated by replacing the learned special token by a generic description." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 217, + 545, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 217, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 545, + 241 + ], + "type": "text", + "content": "Then, the conventional CFG is replaced by our SAG. The remaining generation pipeline remains unchanged." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 244, + 546, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 546, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 546, + 316 + ], + "type": "text", + "content": "As illustrated in Fig. 4, the absence of SAG leads to generation dominated by the optimized text token, resulting in suboptimal text alignment. Conversely, the incorporation of SAG enables the model to produce outputs that align more closely with the text description, while preserving the identity of the subject." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 334, + 353, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 353, + 345 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 353, + 345 + ], + "type": "text", + "content": "4.3. SuTI" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 355, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 440 + ], + "type": "text", + "content": "Unlike ELITE, which encodes subject information into a text token, SuTI [10] employs an encoder-based approach that leverages a distinct subject embedding. This embedding is then fed to the generation network through independent cross-attention layers. As discussed in Sec. 3.2.1, the subject-agnostic condition, denoted as " + }, + { + "bbox": [ + 304, + 355, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 304, + 355, + 545, + 440 + ], + "type": "text", + "content": ", is simply constructed by setting the subject embedding to zero." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 443, + 546, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 546, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 546, + 539 + ], + "type": "text", + "content": "As illustrated in Fig. 5, without SAG, the model successfully preserves the identity of the individual provided in the reference images, yet the text alignment is inadequate. Specifically, the styles are unsatisfactory across all outputs. In contrast, employing SAG and suppressing the subject information during initial iterations significantly enhances text alignment. Consequently, the outputs exhibit both high identity preservation and improved text alignment." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 556, + 384, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 556, + 384, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 556, + 384, + 567 + ], + "type": "text", + "content": "4.4. DreamSuTI" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 578, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 649 + ], + "type": "text", + "content": "DreamSuTI [10] is a second-order method that fine-tunes SuTI using DreamBooth [37] for compositional customization. In this section, we fine-tune SuTI with a provided style image to achieve simultaneous customization of style and subject. The subject-agnostic embedding is generated using the same method as in SuTI." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "As depicted in Fig. 6, in the presence of subject images, the outputs are dominated by the subject, resulting in a lack of style fidelity. In contrast, when applying SAG, the subject is suppressed during the early stages of generation, effectively leading to enhanced style generation." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6738" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 50, + 100, + 120, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 100, + 120, + 128 + ], + "spans": [ + { + "bbox": [ + 50, + 100, + 120, + 128 + ], + "type": "text", + "content": "A bronze face, looks like bronze statue or bronze figure, fine details." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 130, + 72, + 212, + 153 + ], + "blocks": [ + { 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"Alignment" + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_caption" + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 513, + 222, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 222, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 222, + 528 + ], + "type": "text", + "content": "6. Limitation and Societal Impact" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 46, + 533, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 628 + ], + "type": "text", + "content": "Limitation. While our SAG significantly enhances content alignment compared to existing methods, the quality of outputs is inherently constrained by the underlying generation model. Hence, it may still exhibit suboptimal performance for uncommon content that challenges the generation model. However, this limitation can be mitigated by incorporating a more robust synthesis network, a direction we aim to explore in our future work." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Societal Impact. This project targets at improving content alignment in customized synthesis, which holds the potential for misuse by malicious entities aiming to mislead the public. Future investigations in this domain should duly consider these ethical implications. Moreover, ensuing efforts to develop mechanisms for detecting images generated by such models emerge as a critical avenue to foster the safe" + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 306, + 514, + 449, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 449, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 449, + 526 + ], + "type": "text", + "content": "advancement of generative models." + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 306, + 537, + 378, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 378, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 378, + 550 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Subject-driven text-to-image synthesis has witnessed notable progress in recent years. However, overcoming the problem of content ignorance remains a significant challenge. As shown in this work, this problem significantly limits the diversity of the generation. Rather than introducing complex modules, we propose a straightforward yet effective method to address this issue. Our Subject-Agnostic Guidance demonstrates how a balance between content consistency and subject fidelity can be achieved using a subject-agnostic condition. The proposed method enables users to generate customized and diverse scenes without modifying the training process, making it adaptable across various existing approaches." + } + ] + } + ], + "index": 54 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6740" + } + ] + } + ], + "index": 55 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "text", + "content": "[1] Moab Arar, Rinon Gal, Yuval Atzmon, Gal Chechik, Daniel Cohen-Or, Ariel Shamir, and Amit H Bermano. 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In ICCV, 2023. 3" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "6742" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture/ab8cb3ef-8706-4683-ab23-b47ea618549e_content_list.json b/2024/Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture/ab8cb3ef-8706-4683-ab23-b47ea618549e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4f35a813329071443d918768b145620db3181c2b --- /dev/null +++ b/2024/Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture/ab8cb3ef-8706-4683-ab23-b47ea618549e_content_list.json @@ -0,0 +1,1464 @@ +[ + { + "type": "text", + "text": "Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture", + "text_level": 1, + "bbox": [ + 86, + 128, + 883, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Huijie Zhang $^{1}$ * Yifu Lu $^{1}$ * Ismail Alkhouri $^{1,2}$ Saiprasad Ravishankar $^{2,3}$ Dogyoon Song $^{1}$ Qing Qu $^{1}$", + "bbox": [ + 173, + 200, + 795, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Department of Electrical Engineering & Computer Science, University of Michigan $^{2}$ Department of Computational Mathematics, Science & Engineering, Michigan State University $^{3}$ Department of Biomedical Engineering, Michigan State University {huijiezh, yifulu, ismailal, dogyoons, qingqu}@umich.edu ravisha3@msu.edu", + "bbox": [ + 158, + 243, + 810, + 313 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/892d1ddedd1e3b62409e2a1fa38578d3481cc7b8e84f4cfe5550ff0c2f5ba07a.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 135, + 352, + 302, + 515 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/79088b5fbc21d894fd2fa1573865cc3420c2679a854a80c21fea870d14a6027f.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 303, + 349, + 467, + 515 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/76440afb44231cace2814a9a7c2d4fba0964dfb38cadecbe139274cb92bddeec.jpg", + "image_caption": [ + "(c)", + "Figure 1. Overview of three diffusion model architectures: (a) unified, (b) separate, and (c) our proposed multistage architecture. Compared with (a) and (b), our approach improves sampling quality, and significantly enhances training efficiency, as indicated by the FID scores and their corresponding training iterations (d)." + ], + "image_footnote": [], + "bbox": [ + 467, + 349, + 638, + 515 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/62fdc19d83e16c6ea50fe22f2a67f124b0c0d9f8e92467a0db4b28e72868c4e2.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 638, + 349, + 826, + 515 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 584, + 313, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new samples (e.g., images). However, their remarkable generative performance is hindered by slow training and sampling. This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i.e., noise levels). To tackle these challenges, we present a multi-stage framework inspired by our empirical findings. These observations indicate the advantages of employing distinct parameters tailored to each timestep while retaining universal parameters shared across all time steps. Our approach involves segmenting the time interval into multiple stages where we employ custom multi-decoder U-net architecture that blends time-dependent models with a universally shared encoder. Our framework enables the", + "bbox": [ + 75, + 628, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "efficient distribution of computational resources and mitigates inter-stage interference, which substantially improves training efficiency. Extensive numerical experiments affirm the effectiveness of our framework, showcasing significant training and sampling efficiency enhancements on three state-of-the-art diffusion models, including large-scale latent diffusion models. Furthermore, our ablation studies illustrate the impact of two important components in our framework: (i) a novel timestep clustering algorithm for stage division, and (ii) an innovative multi-decoder U-net architecture, seamlessly integrating universal and customized hyperparameters.", + "bbox": [ + 496, + 585, + 893, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 784, + 632, + 800 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, diffusion models have made remarkable progress as powerful deep generative modeling tools, showcasing remarkable performance in various applications, ranging from unconditional image generation [1, 2], conditional image generation [3, 4], image-to-image translation [5-7], text-to-image generation [8-10], inverse problem solving [11-14],", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7372", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "video generation [15, 16], and so on. These models employ a training process involving continuous injection of noise into training samples (\"diffusion\"), which are then utilized to generate new samples, such as images, by transforming random noise instances through a reverse diffusion process guided by the \"score function\" of the data distribution learned by the model. Moreover, recent work demonstrates that those diffusion models enjoy optimization stability and model reproducibility compared with other types of generative models [17]. However, diffusion models suffer from slow training and sampling despite their remarkable generative capabilities, which hinders their use in applications where real-time generation is desired [1, 2]. These drawbacks primarily arise from the necessity of tracking extensive forward and reverse diffusion trajectories, as well as managing a large model with numerous parameters across multiple timesteps (i.e., diffusion noise levels).", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we address these challenges based on two key observations: (i) there exists substantial parameter redundancy in current diffusion models, and (ii) they are trained inefficiently due to dissimilar gradients across different noise levels. Specifically, we find that training diffusion models require fewer parameters to accurately learn the score function at high noise levels, while larger parameters are needed at low noise levels. Furthermore, we also observe that when learning the score function, distinct shapes of distributions at different noise levels result in dissimilar gradients, which appear to slow down the training process driven by gradient descent.", + "bbox": [ + 75, + 352, + 472, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Building on these insights, we propose a multi-stage framework with two key components: (i) a multi-decoder U-net architecture, and (ii) a new partitioning algorithm to cluster timesteps (noise levels) into distinct stages. In terms of our new architecture, we design a multi-decoder U-Net that incorporates one universal encoder shared across all intervals and individual decoders tailored to each time stage; see Figure 1 (c) for an illustration. This approach combines the advantages of both universal and stage-specific architectures, which is much more efficient than the unified architecture for the entire training process [1, 2, 18] (Figure 1 (a)). Moreover, compared to previous approaches that completely separate architectures for each sub-interval [19-22] (Figure 1 (b)), our approach can effectively mitigate overfitting, leading to improved training efficiency. On the other hand, when it comes to partitioning the training stages of our network, we designed an algorithm aimed at grouping the timesteps. This is achieved by minimizing the functional distance within each cluster in the training objective and making use of the optimal denoiser formulation [18]. By integrating these two key components, our framework enables efficient allocation of computational resources (e.g., U-net parameters) and stage-tailored parameterization. Throughout our extensive numerical experi", + "bbox": [ + 75, + 537, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ments (Section 5), we show that out framework effectively improves both training and sampling efficiency. These experiments are performed on diverse benchmark datasets, demonstrating significant acceleration by using our framework when compared to three state-of-the-art (SOTA) diffusion model architectures. As a summary, the major contributions of this work can be highlighted as follows:", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Identifying two key sources of inefficiency. We identified two key sources that cause inefficiencies in training diffusion models across various time steps: (i) a significant variation in the requirement of model capacity, and (ii) the gradient dissimilarity. As such, using a unified network cannot meet with the changing requirement at different time steps.", + "bbox": [ + 500, + 199, + 890, + 304 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- A new multi-stage framework. We introduced a new multi-stage architecture, illustrated in Fig. 1 (c). We tackle these two sources of inefficiency by segmenting the time interval into multiple stages, where we employ customized multi-decoder U-net architectures that blends time-dependent models with a universally shared encoder.", + "bbox": [ + 500, + 305, + 890, + 395 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Improved training and sampling efficiency. With comparable computational resources for unconditional image generation, we demonstrate that our multi-stage approach improves the Fréchet Inception Distance (FID) score for all SOTA methods. For example, on CIFAR-10 dataset [23], our method improves the FID for DPM-Solver [24] from 2.84 to 2.37, and it improves the FID for EDM [18] from 2.05 (our training result) to 1.96. Moreover, on the CelebA dataset [25], while maintaining a similar generation quality, our approach significantly reduces the required training FLOPS of EDM by $82\\%$ and the Latent Diffusion Model (LDM) [8] by $30\\%$ .", + "bbox": [ + 500, + 396, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Organization. In Sec. 2, we provide preliminaries and an overview of related literatures. In Sec. 3, we present our observations and analysis that motivated the proposed multistage framework, justifying its development. In Sec. 4, we describe our proposed multistage framework for diffusion models, outlining the two core components. Finally, in Sec. 5, we provide the results from our numerical experiments that validate the effectiveness of the proposed multistage approach.", + "bbox": [ + 496, + 580, + 890, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Preliminaries & Related Work", + "text_level": 1, + "bbox": [ + 500, + 729, + 779, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we start by reviewing the basic fundamentals of diffusion models [1, 2, 18]. Subsequently, we delve into prior approaches aimed at improving the training and efficiency of diffusion models through the partitioning of the timestep interval. Lastly, we survey prior studies that significantly decrease the number of required sampling iterations.", + "bbox": [ + 496, + 755, + 890, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Background on diffusion models. Let $\\pmb{x}_0 \\in \\mathbb{R}^n$ denote a sample from the data distribution $p_{\\mathrm{data}}(\\pmb{x})$ . Diffu", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7373", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sion models operate within forward and reverse processes. The forward process progressively perturbs data $\\boldsymbol{x}_0$ to a noisy version $\\boldsymbol{x}_{t\\in [0,1]}$ via corrupting with the Gaussian kernel. This process can be formulated as a stochastic differential equation (SDE) [2] of the form $\\mathrm{d}\\boldsymbol {x} = \\boldsymbol {x}_t f(t)\\mathrm{d}t + g(t)\\mathrm{d}\\boldsymbol{w}_t$ , where $f(t)$ and $g(t)$ are the drift and diffusion coefficients, respectively, that correspond to a pre-defined noise schedule. $\\boldsymbol{w}_t\\in \\mathbb{R}^n$ is the standard Wiener process. Under the forward SDE, the perturbation kernel is given by the conditional distribution defined as $p_t(\\boldsymbol {x}_t|\\boldsymbol {x}_0) = \\mathcal{N}(\\boldsymbol {x}_t;s_t\\boldsymbol {x}_0,s_t^2\\sigma_t^2\\mathbf{I})$ , where", + "bbox": [ + 75, + 90, + 472, + 258 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {t} = \\exp \\left(\\int_ {0} ^ {t} f (\\xi) \\mathrm {d} \\xi\\right), \\text {a n d} \\sigma_ {t} = \\sqrt {\\int_ {0} ^ {t} \\frac {g ^ {2} (\\xi)}{s _ {\\xi} ^ {2}} \\mathrm {d} \\xi}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 268, + 468, + 310 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The parameters $s_t$ and $\\sigma_t$ are designed such that: (i) the data distribution is approximately estimated when $t = 0$ , and (ii) a nearly standard Gaussian distribution is obtained when $t = 1$ . The objective of diffusion models is to learn the corresponding reverse SDE, defined as $\\mathrm{d}\\pmb{x} = \\left[f(t)\\pmb{x}_t - g^2(t)\\nabla_{\\pmb{x}_t}\\log p_t(\\pmb{x}_t)\\right]\\mathrm{d}t + g(t)\\mathrm{d}\\bar{\\pmb{w}}$ , where $\\bar{\\pmb{w}} \\in \\mathbb{R}^n$ is the standard Wiener process running backward in time, and $\\nabla_{\\pmb{x}_t}\\log p_t(\\pmb{x}_t)$ is the (Stein) score function. In practice, the score function is approximated using a neural network $\\epsilon_{\\theta}:\\mathbb{R}^n\\times [0,1]\\to \\mathbb{R}^n$ parameterized by $\\pmb{\\theta}$ , which can be trained by the denoising score matching technique [26] as", + "bbox": [ + 75, + 319, + 472, + 501 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {\\theta}} \\mathbb {E} \\left[ \\omega (t) \\| \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, t) + s _ {t} \\sigma_ {t} \\nabla_ {\\boldsymbol {x} _ {t}} \\log p _ {t} (\\boldsymbol {x} _ {t} | \\boldsymbol {x} _ {0}) \\| _ {2} ^ {2} \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 508, + 468, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which can also be written as $\\min_{\\pmb{\\theta}}\\mathbb{E}[\\omega (t)||\\pmb{\\epsilon}_{\\pmb{\\theta}}(\\pmb{x}_t,t) - \\pmb{\\epsilon}||^2 ] + C$ , where the expectation is taken over $t\\sim [0,1]$ , $\\pmb{x}_t\\sim p_t(\\pmb{x}_t|\\pmb{x}_0)$ , $\\pmb{x}_0\\sim p_{\\mathrm{data}}(\\pmb {x})$ , and $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ . Here, $C$ is a constant independent of $\\pmb{\\theta}$ , and $\\omega (t)$ is a scalar representing the weight of the loss as a function of $t$ . In DDPM [1], it is simplified to $\\omega (t) = 1$ . Once the parameterized score function $\\epsilon_{\\theta}$ is trained, it can be utilized to approximate the reverse-time SDE using numerical solvers such as Euler-Maruyama.", + "bbox": [ + 75, + 544, + 472, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Timestep clustering methods. Diffusion models have demonstrated exceptional performance but face efficiency challenges in training and sampling. In response, several studies proposed to cluster the timestep range $t \\in [0,1]$ into multiple intervals (e.g., $[0,t_1),[t_1,t_2),\\ldots ,[t_n,1]$ ). Notably, Choi et al. [19] reconfigured the loss weights for different intervals to enhance performance. Deja et al. [27] divide the entire process into a denoisr and a generator based on their functionalities. Balaji et al. [28] introduced \"expert denoisers\", which proposed using distinct architectures for different time intervals in text-to-image diffusion models. Go et al. [22] further improved the efficiency of these expert denoisers through parameter-efficient fine-tuning and data-free knowledge transfer. Lee et al. [21] designed separate", + "bbox": [ + 75, + 688, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "architectures for each interval based on frequency characteristics. Moreover, Go et al. [20] treated different intervals as distinct tasks and employed multi-task learning strategies for diffusion model training, along with various timestep clustering methods.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach distinguishes itself from the aforementioned methods in two key aspects. The first key component is our tailored U-net architecture using a unified encoder coupled with different decoders for different intervals. Previous models have either adopted a unified architecture, as seen in [19, 20], or employed separate architectures (referred to as expert denoisers) for each interval [21, 22, 28]. In comparison, our multistage architecture surpasses these methodologies, as demonstrated in Sec. 5.3. Second, we developed a new timestep clustering method leveraging a general optimal denoiser (Prop. 1) that showcases superior performance (see Sec. 5.4). In contrast, prior works rely on (i) a simple timestep-based clustering cost function [20-22, 28], (ii) Signal-to-Noise Ratio (SNR) based clustering [20], or (iii) gradients-based partitioning that uses task affinity scores [20].", + "bbox": [ + 496, + 167, + 892, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reducing the sampling iterations methods. Efforts to improve sampling efficiency of diffusion models have led to many recent advancements in SDE and Ordinary Differential Equation (ODE) samplers [2]. For instance, the Denoising Diffusion Implicit Model (DDIM) [29] formulates the forward diffusion as a non-Markovian process with a deterministic generative path, significantly reducing the number of function evaluations (NFE) required for sampling (from thousands to hundreds). Generalized DDIM (gDDIM) [30] further optimized DDIM by modifying the parameterization of the scoring network. Furthermore, the works in [24] and [31], termed the Diffusion Probabilistic Model solver (DPM-solver) and the Diffusion Exponential Integrator Sampler (DEIS), respectively, introduced fast higher-order solvers, employing exponential integrators that require 10s NFE for comparable generation quality. Moreover, the consistency model [32] introduced a novel training loss and parameterization, achieving high-quality generation with merely 1-2 NFE.", + "bbox": [ + 496, + 417, + 892, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We remark that while the aforementioned methods are indirectly related to our work, our experiments in Sec. 5.1 and Sec. 5.2 show that our approach can be easily integrated into these techniques, further improving diffusion models' overall training and sampling efficiency.", + "bbox": [ + 496, + 705, + 890, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Identification of Key Sources of Inefficiency", + "text_level": 1, + "bbox": [ + 498, + 797, + 888, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conventional diffusion model architectures, as exemplified by [1, 2, 18], treat the training of the diffusion model as a unified process across all timesteps. Recent researches, such as [19-22], have highlighted the benefits of recognizing distinctions between different timesteps and the poten", + "bbox": [ + 496, + 824, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7374", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tial efficiency gains from treating them as separate tasks during the training process. However, our experimental results demonstrate that both unified and separate architectures suffer inefficiency for training diffusion models, where the inefficiency comes from (i) overparameterization, (ii) gradient dissimilarity, and (iii) overfitting.", + "bbox": [ + 75, + 90, + 470, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Empirical Observations on the Key Sources of Inefficiency", + "text_level": 1, + "bbox": [ + 76, + 194, + 470, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To illustrate the inefficiency in each interval, we isolate the interval by using a separate architecture from the rest.", + "bbox": [ + 76, + 234, + 468, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Experiment setup. In our experiments, we consider three-stage training and divide the time steps into three intervals: $[0, t_1), [t_1, t_2), [t_2, 1]^1$ . Let $(\\epsilon_{\\theta})_i^{[a,b]}, 0 \\leq a < b \\leq 1$ denote a U-Net architecture with parameter $\\theta$ trained with $i$ iterations and fed with data pairs $(x_t, t)$ , where $t \\in [a,b]$ . We then train models using two different strategies: a unified architecture with 108M network parameters for all intervals, i.e., $(\\epsilon_{\\theta})_i^{[0,1]}$ , and separate architectures with varying network parameters (e.g., 47M, 108M, 169M) for each interval; e.g., $(\\epsilon_{\\theta})_i^{[0,t_1)}$ for the interval $[0,t_1)$ , etc. It is worth noting that, apart from the differences in network parameters, we utilize the same network architecture (e.g., U-Net) for both the unified and the separate approaches. We assessed the training progress of each model by evaluating image generation quality at different training iterations. Notably, because some of the models are only trained on one interval, we need to provide a ground truth score for the other intervals. In Fig. 2, the sampling process is shown top and the experimental results are shown bottom.", + "bbox": [ + 75, + 271, + 470, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inefficiency in unified architectures. From Fig. 2, we observe the following:", + "bbox": [ + 76, + 571, + 468, + 602 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Overparameterization and underfitting emerge simultaneously for unified architectures. In Fig. 2a, we observe that increasing the number of parameters in Interval 0 can improve the image generation quality (as indicated by a lower FID score). In contrast, Fig. 2b reveals that increasing the number of parameters in Interval 2 has minimal impact on the quality of image generation. This implies that using a unified architecture will result in underfitting in Interval 0 and overparameterization in Interval 2. The current unified architecture's parameter redundancy leaves significant room for improving its efficiency. To optimize the computational usage, we should allocate more parameters to Interval 0 while allocating fewer parameters to Interval 2.", + "- Gradient dissimilarity hinders training for unified architecture. Quantitative results from [20] demonstrate dissimilarity in gradients caused by differences within each interval. This can also be observed from our results based" + ], + "bbox": [ + 76, + 604, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "upon both Fig. 2a and Fig. 2b. For the unified and separate architectures using the same number of parameters (108M), separate architecture achieves a significantly lower FID with the same training iterations, implying that dissimilar gradients among intervals may hinder training when using a unified architecture. Here, the only difference between training separate and unified architectures is that the batch gradient for unified architecture is calculated based on all timesteps while the batch gradien2 for separate architecture is calculated only from a specific interval.", + "bbox": [ + 511, + 90, + 890, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inefficiency in existing separate architectures. Although separated architecture [19, 21, 22] better allocates computational resources for each interval, it suffers from overfitting. This can be illustrated based upon training separate architectures (169M) and (108M) in Interval 0 shown in Fig. 2a, where increasing the number of parameters will lead to overfitting. This also happens in Interval 2, when we compare all separate architectures in Fig. 2b. In comparison, the unified networks with 108M parameters are less prone to overfitting for both Interval 0 and Interval 2. This suggests that we can reduce overfitting by training shared weights across different intervals together.", + "bbox": [ + 496, + 273, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Tackling the Inefficiency via Multistage U-Net Architectures", + "text_level": 1, + "bbox": [ + 498, + 468, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a unified architecture applied across all timesteps, there is often a dual challenge: requirements for more parameters (169M) in the interval $[0, t_1)$ but fewer parameters (47M) in the interval $[t_2, 1]$ . This issue is compounded by the gradient dissimilarity across different timesteps, which can impede effective training. Alternatively, employing separate architectures for different intervals might lead to overfitting and a lack of robust early stopping mechanisms. To address these challenges, our proposed multistage architecture in Sec. 4 combines shared parameters to reduce overfitting with interval-specific parameters to mitigate the impact of gradient dissimilarity. This tailored approach for each interval ensures improved adaptability. Furthermore, we conduct an in-depth ablation study in Sec. 5.3 to showcase the effectiveness of our multi-stage architecture over the existing models.", + "bbox": [ + 496, + 508, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Proposed Multistage Framework", + "text_level": 1, + "bbox": [ + 498, + 768, + 802, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce our new multistage framework (as illustrated in Fig. 1 (c)). Specifically, we first introduce the multi-stage U-Net architecture design in Sec. 4.1, following a new clustering method for choosing the optimal interval to partition the entire timestep [0, 1] into intervals in Sec. 4.2., and discuss the rationale of the proposed architecture in Sec. 4.3.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1Details for interval clustering can be found in Appendix B.1.", + "bbox": [ + 94, + 886, + 421, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7375", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a7f05e825ef767cb2e1911201bf99b4652428f823de776cfb9b43dd1dd2029f9.jpg", + "image_caption": [ + "(a) Analysis on interval $[0, t_1)$" + ], + "image_footnote": [], + "bbox": [ + 174, + 88, + 467, + 310 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/92f94ab5b87d8b6dc50c15aa21be981ed618a51747dbcb8c453c0d9e1ea78432.jpg", + "image_caption": [ + "(b) Analysis on interval $[t_2, 1]$", + "Figure 2. Comparison between separate architecture and unified architecture w.r.t. the image generation quality in different intervals: (a) analysis on interval $[0, t_1)$ ; and (b) analysis on interval $[t_2, 1]$ . As illustrated on top of each figure, we only train separate architectures within specific intervals for the sampling process in both (a) and (b). For the remaining period of sampling, we use a well-trained diffusion model $(\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}$ to approximate the ground truth score function. As shown in the above figure of (a), e.g. for the separate architecture on interval 1, sampling utilizes trained model $(\\epsilon_{\\theta'})_i^{[0,t_1)}$ for interval 0 and well-trained model $(\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}$ for interval 1 and 2. Notably, for both $(\\epsilon_{\\theta})_i^{[0,1]}$ and $(\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}$ , we are using the model with 108M parameters. For separate architecture, the number in the parentheses represents the number of parameters of the model $(\\epsilon_{\\theta'})_i^{[a,b]}$ . For example, for separate architecture (169M) in (a), the model $(\\epsilon_{\\theta'})_i^{[0,t_1)}$ has 169M parameters for $\\theta'$ . The bottom figures in (a-b) illustrate the FID of the generation from each architecture under different training iterations." + ], + "image_footnote": [], + "bbox": [ + 486, + 88, + 781, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Proposed Multi-stage U-Net Architectures", + "text_level": 1, + "bbox": [ + 76, + 477, + 434, + 493 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As discussed in Sec. 3, most existing diffusion models either employ a unified architecture across all intervals [1, 2, 18] to share features for all timesteps, or use completely separate architectures for different timestep intervals [21, 22, 28] where the goal is to take advantage of the benign properties within different intervals.", + "bbox": [ + 75, + 502, + 468, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To harness the advantages of both unified and separate architectures employed in prior studies, we introduce a multistage U-Net architecture, as illustrated in Figure 1(c). Specifically, we partition the entire timestep $[0,1]$ into several intervals, e.g., three intervals $[0,t_1),[t_1,t_2),[t_2,1]$ in Fig. 1. For the architecture, we introduce:", + "bbox": [ + 75, + 595, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- One shared encoder across all time intervals. For each timestep interval, we implement a shared encoder architecture (plotted in blue in Fig. 1 (c)), which is similar to the architecture employed in the original U-Net framework [33]. Unlike separate architecture, the shared encoder provides shared information across all timesteps, preventing models from overfitting (see Sec. 5.3 for a discussion).", + "- Separate decoders for different time intervals. Motivated by the multi-head structure introduced in the Mask Region-based Convolutional Neural Networks (MaskRCNN) method [34], we propose to use multiple distinct decoders (plotted in colors for different intervals in Fig. 1(c)), where each decoder is tailored to a spe" + ], + "bbox": [ + 76, + 689, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cific timestep interval. The architecture of each decoder closely resembles the one utilized in [2], with deliberate adjustments made to the embedding dimensions to optimize performance.", + "bbox": [ + 511, + 478, + 890, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we observe, the primary difference in the architecture resides within the decoder structure. Intuitively, we use a decoder with fewer number of parameters for intervals closer to the noise, because the learning task is easier. We use a decoder with a larger number of parameters for intervals closer to the image.", + "bbox": [ + 496, + 540, + 890, + 631 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Optimal Denoiser-based Timestep Clustering", + "text_level": 1, + "bbox": [ + 498, + 645, + 880, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we discuss how we principally choose the interval partition time points in practice. For simplicity, we focus on the case where we partition the time $[0,1]$ into three intervals $[0,t_1],[t_1,t_2],[t_2,1]$ , and we develop a timestep clustering method to choose the optimal $t_1$ and $t_2$ . Of course, our method can be generalized to multi-stage networks with arbitrary interval numbers. However, in practice, we find that the choice of three intervals strikes a good balance between effectiveness and complexity; see our ablation study in Appendix B.6.", + "bbox": [ + 496, + 671, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To partition the time interval, we employ the optimal denoiser established in Proposition 1.", + "bbox": [ + 498, + 824, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 1. Suppose we train a diffusion model denoiser function $\\epsilon_{\\theta}(\\pmb{x},t)$ with parameters $\\pmb{\\theta}$ using dataset", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7376", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Optimal Denoiser based Timestep Clustering", + "text_level": 1, + "bbox": [ + 78, + 90, + 464, + 106 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Input: Total samples $K$ , optimal denoiser function $\\pmb{\\epsilon}_{\\pmb{\\theta}}^{*}(\\pmb{x},t)$ , thresholds $\\alpha, \\eta$ , dataset $p_{\\mathrm{data}}$ , $S_0 = S_1 = \\emptyset$", + "2: Output: Timesteps $t_1, t_2$", + "3: for $k \\in \\{1, \\dots, K\\}$ do", + "4: $\\pmb{y}_k\\sim p_{\\mathrm{data}},\\pmb{\\epsilon}_k\\sim \\mathcal{N}(0,\\mathbf{I}),t_k\\sim [0,1]$", + "5: $\\mathcal{S}_0^k\\gets \\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*,\\pmb{\\epsilon}_0^*,\\pmb {y}_k,\\pmb {\\epsilon}_k),\\mathcal{S}_1^k\\gets \\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*,\\pmb {\\epsilon}_1^*,\\pmb {y}_k,\\pmb {\\epsilon}_k)$", + "6: $\\mathcal{S}_0\\gets \\mathcal{S}_0\\cup \\{\\big(t_k,\\mathcal{S}_0^k\\big)\\} ,\\mathcal{S}_1\\gets \\mathcal{S}_1\\cup \\{\\big(t_k,\\mathcal{S}_1^k\\big)\\}$", + "7: end for", + "8: $t_1 = \\arg \\max_{\\tau}\\left\\{\\tau \\Big|\\frac{\\sum_{(t_k,\\mathcal{S}_0^k)\\in\\mathcal{S}_0}\\big[\\mathcal{S}_0^k\\cdot\\mathbb{1}(t_k\\leq\\tau)\\big]}{\\sum_{(t_k,\\mathcal{S}_0^k)\\in\\mathcal{S}_0}[\\mathbb{1}(t_k\\leq\\tau)]}\\geq\\alpha\\right\\}$", + "9: $t_2 = \\arg \\min_{\\tau}\\left\\{\\tau \\Big|\\frac{\\sum_{(t_k,\\mathcal{S}_1^k)\\in\\mathcal{S}_0}\\big[\\mathcal{S}_1^k\\cdot\\mathbb{1}(t_k\\geq\\tau)\\big]}{\\sum_{(t_k,\\mathcal{S}_1^k)\\in\\mathcal{S}_0}[\\mathbb{1}(t_k\\geq\\tau)]}\\geq\\alpha\\right\\}$" + ], + "bbox": [ + 86, + 109, + 467, + 290 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {y} _ {i} \\in \\mathbb {R} ^ {n} \\right\\} _ {i = 1} ^ {N} b y\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 316, + 196, + 335 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {\\theta}} \\mathcal {L} (\\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}}; t) = \\mathbb {E} _ {\\boldsymbol {x} _ {0}, \\boldsymbol {x} _ {t}, \\epsilon} [ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} ], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 345, + 468, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\pmb{x}_0\\sim p_{data}(\\pmb {x}) = \\frac{1}{N}\\sum_{i = 1}^{N}\\delta (\\pmb {x} - \\pmb {y}_i)$ $\\epsilon \\sim \\mathcal{N}(0,\\pmb {I})$ and $\\pmb{x}_{t}\\sim p_{t}(\\pmb{x}_{t}|\\pmb{x}_{0}) = \\mathcal{N}(\\pmb{x}_{t};s_{t}\\pmb{x}_{0},s_{t}^{2}\\sigma_{t}^{2}\\pmb {I})$ with perturbation parameters $s_t$ and $\\sigma_t$ defined in Eq. (1). Then, the optimal denoiser at $t$ defined as $\\epsilon_{\\theta}^{*}(\\pmb {x};t) = \\arg \\min_{\\epsilon_{\\theta}}\\mathcal{L}(\\epsilon_{\\theta};t)$ is given by", + "bbox": [ + 76, + 378, + 468, + 455 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} ^ {*} (\\boldsymbol {x}; t) = \\frac {1}{s _ {t} \\sigma_ {t}} \\left[ \\boldsymbol {x} - s _ {t} \\frac {\\sum_ {i = 1} ^ {N} \\mathcal {N} (\\boldsymbol {x} ; s _ {t} \\boldsymbol {y} _ {i} , s _ {t} ^ {2} \\sigma_ {t} ^ {2} \\boldsymbol {I}) \\boldsymbol {y} _ {i}}{\\sum_ {i = 1} ^ {N} \\mathcal {N} (\\boldsymbol {x} ; s _ {t} \\boldsymbol {y} _ {i} , s _ {t} ^ {2} \\sigma_ {t} ^ {2} \\boldsymbol {I})} \\right]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 465, + 468, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proof is provided in Appendix A, and the result can be generalized from recent work of Karras et al. [18], extending from a specific kernel $p_t(\\boldsymbol{x}_t|\\boldsymbol{x}_0) = \\mathcal{N}(\\boldsymbol{x}_t; \\boldsymbol{x}_0, \\sigma_t^2\\mathbf{I})$ to encompassing a broader scope of noise perturbation kernels, given by $p_t(\\boldsymbol{x}_t|\\boldsymbol{x}_0) = \\mathcal{N}(\\boldsymbol{x}_t; s_t\\boldsymbol{x}_0, s_t^2\\sigma_t^2\\mathbf{I})$ . For brevity, we simplify the notation of the optimal denoiser $\\epsilon_{\\theta}^{*}(\\boldsymbol{x}, t)$ in Proposition 1 as $\\epsilon_t^*(\\boldsymbol{x})$ .", + "bbox": [ + 76, + 532, + 468, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To obtain the optimal interval, our rationale is to homogenize the regression task as much as possible within each individual time interval. To achieve this goal, given sampled $\\pmb{x}_0, \\pmb{\\epsilon}$ , we define the function distance of the optimal denoiser at any given timestep $t_a, t_b$ as:", + "bbox": [ + 76, + 637, + 468, + 713 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}\\right) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathbb {1} \\left(\\left| \\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*} \\left(\\boldsymbol {x} _ {t _ {a}}\\right) - \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*} \\left(\\boldsymbol {x} _ {t _ {b}}\\right) \\right| _ {i} \\leq \\eta\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 723, + 467, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbb{1}(\\cdot)$ is the indicator function, $\\eta$ is a pre-specified threshold, $\\pmb{x}_{t_a} = s_{t_a}\\pmb{x}_0 + s_{t_a}\\sigma_{t_a}\\pmb{\\epsilon}$ , and $\\pmb{x}_{t_b} = s_{t_b}\\pmb{x}_0 + s_{t_b}\\sigma_{t_b}\\pmb{\\epsilon}$ . Consequently, we define the functional similarity of the optimal denoiser at timesteps $t_a$ and $t_b$ as:", + "bbox": [ + 76, + 771, + 468, + 832 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}\\right) = \\mathbb {E} _ {\\boldsymbol {x} _ {0} \\sim p _ {\\mathrm {d a t a}}} \\mathbb {E} _ {\\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I})} \\left[ \\mathcal {D} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}\\right) \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 843, + 468, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based upon the definition, we design the following optimization problem to find the largest $t_1$ and smallest $t_2$ as:", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt _ {1} \\leftarrow \\underset {\\tau} {\\arg \\max } \\left\\{\\tau \\left| \\mathbb {E} _ {t \\sim [ 0, \\tau)} \\left[ \\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t} ^ {*}, \\boldsymbol {\\epsilon} _ {0} ^ {*}\\right) \\right] \\geq \\alpha \\right. \\right\\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 112, + 890, + 140 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt _ {2} \\leftarrow \\underset {\\tau} {\\arg \\min } \\left\\{\\tau \\left| \\mathbb {E} _ {t \\sim [ \\tau , 1 ]} \\left[ \\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t} ^ {*}, \\boldsymbol {\\epsilon} _ {1} ^ {*}\\right) \\right] \\geq \\alpha \\right. \\right\\}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 143, + 890, + 170 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "such that the average functional similarity of $\\pmb{\\epsilon}_t^*$ (resp. $\\pmb{\\epsilon}_t^*$ ) to $\\pmb{\\epsilon}_0^*$ (resp. $\\pmb{\\epsilon}_1^*$ ) in $[0, t_1)$ (resp. $[t_2, 1]$ ) is larger than or equal to a pre-defined threshold $\\alpha$ . As the above optimization problems are intractable, we propose the procedure outlined in Algorithm 1 to obtain an approximate solution. In particular, the algorithm samples $K$ pairs $(\\pmb{y}_k, \\pmb{\\epsilon}_k, t_k), k \\in \\{1, \\dots, K\\}$ to calculate the distances $\\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*, \\pmb{\\epsilon}_0^*, \\pmb{y}_k, \\pmb{\\epsilon}_k)$ and $\\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*, \\pmb{\\epsilon}_1^*, \\pmb{y}_k, \\pmb{\\epsilon}_k)$ (step 6). Based on those distances, we solve the optimization problems defined in the lines 8 and 9 of Algorithm 1 to obtain $t_1$ and $t_2$ .", + "bbox": [ + 500, + 180, + 890, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Rationales for the proposed architecture", + "text_level": 1, + "bbox": [ + 500, + 340, + 844, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, we summarize the rationales of our proposed architecture based on the empirical observations in Sec. 3 and previous works.", + "bbox": [ + 498, + 363, + 890, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rationales for the shared encoder. (i) Prevent overfitting: If we treat training separate stages of diffusion models as multi-task learning, [35] suggests that shared parameters across tasks in multi-task learning can mitigate overfitting. (ii) Maintain consistency in $h$ -space. The output of the encoder for UNet is named as $h$ -space [36], which has properties for semantic manipulation such as homogeneity, linearity, robustness, and consistency across timesteps. Therefore, sharing the encoder can maintain better consistency of the $h$ -space among all timesteps compared to separate encoders.", + "bbox": [ + 498, + 409, + 890, + 573 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rationales for network parameter design. First, we provide some intuitions as to why the learning task at $t = 0$ is harder than that at $t = 1$ . Suppose diffusion models could converge to the optimal denoiser $\\epsilon_{\\theta}^{*}(\\boldsymbol{x}_t,t)$ given in Eq. (4). Based on this, we observe: (i) when $t \\to 0$ , we have $\\boldsymbol{x}_{t \\to 0} = \\boldsymbol{x}_0$ , $\\epsilon_{\\theta}^{*}|_{t \\to 0} = \\epsilon$ , so that $\\epsilon_{\\theta}^{*}$ is a complicated mapping from training data distribution $p_{\\mathrm{data}}(\\boldsymbol{x})$ to the gaussian distribution; (ii) when $t \\to 1$ , we have $\\boldsymbol{x}_{t \\to 1} = \\epsilon$ , $\\epsilon_{\\theta}^{*}|_{t \\to 1} = \\epsilon$ , so $\\epsilon_{\\theta}^{*}$ is an identity mapping. The two extreme cases reveal that the identity mapping for $t \\to 1$ (close to noise) is easier to learn than that for $t \\to 0$ . Second, our choice of network parameters across different stages share similar spirits with the recent work [37], which employs a high dimensional subspace as $t \\to 0$ and gradually decreases the dimensionality of each subspace until $t = 1$ .", + "bbox": [ + 498, + 575, + 890, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 815, + 632, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we start by providing the experimental setups. Next, we present results in terms of generation quality (Sec. 5.1). Subsequently, results for training and sampling efficiency are presented. Finally, in Sec. 5.3 and", + "bbox": [ + 498, + 839, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7377", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sec. 5.4, comprehensive ablation studies on timestep clustering methods and multistage architectures are given.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multistage architectures. Our multistage architecture, inspired by the U-Net model [33] used in $\\mathrm{DDPM}++$ [1, 2, 18], is modified for interval-specific channel dimensions. The proposed architecture is adopted to three diffusion models: DPM-Solver [24], EDM [18], and LDM [8]. In particular, for the cases of DPM-Solver and EDM, the encoder's channel dimensions are standardized at 128, while the decoders are configured with 192, 128, and 16 channels for intervals $[0, t_1)$ , $[t_1, t_2)$ , and $[t_2, 1]$ , respectively. In the LDM case, we use 224 channels across the encoder for all intervals whereas the decoders are configured with 256, 192, and 128 channels for the respective intervals. To decide the specific number of parameters for each decoder, we apply ablation studies in Appendix B.5. Training details are in Appendix D.", + "bbox": [ + 75, + 131, + 470, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets, evaluation metrics, & baselines. We use CIFAR-10 $(32 \\times 32)$ , CelebA $(32 \\times 32)$ , and CelebA (256 $\\times$ 256) datasets for our experiments. To evaluate the performance of our multistage diffusion model in terms of the generation quality, we use the standard Fréchet Inception Distance (FID) metric [38]. We assess the sampling efficiency using the NFE, and giga-floating point operations (GFLOPs) per function evaluation. For both separate architecture and our multistage architecture, equivalent GFLOPs are computed as a weighted summation of GFLOPs for each interval. Training efficiency is evaluated using total training iterations multiplied by the GFLOPs per function evaluation, measured by peta-floating point operations (PFLOPs). For baselines, we consider DDPM [1], Score SDE [2], Poisson Flow Generative Models (PFGM) [39], DDIM [29], gDDIM [30], DEIS [31], DPM-solver [24], and EDM [18].", + "bbox": [ + 75, + 378, + 468, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Image Generation Quality Results", + "text_level": 1, + "bbox": [ + 76, + 645, + 375, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we demonstrate the effectiveness of our approach by comparing the image generation quality (measured by FID) with comparable training and sampling computations (measured by NFE). Specifically, Tab. 1 presents FID scores to measure the sampling quality, and NFE to measure the number of sampling iterations required using the CIFAR-10 dataset. Our method is compared to 8 baselines. As observed, our multistage DPM-Solver outperforms DPM-Solver in terms of the reported FID values while requiring similar training iterations (both are $4.5 \\times 10^{5}$ ) and model GFLOPs (18.65 for multistage DPM-Solver versus 17.65 for DPM-Solver). A similar observation holds when we compare our multistage EDM and the", + "bbox": [ + 75, + 667, + 467, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "vanilla EDM, where we reduce FID from 2.05 to 1.96 by using the multi-stage architecture. Remarkably, utilizing only 20 NFE, our Multistage DPM-Solver returns the same FID score as the one reported for the PFGM method, which requires 147 NFEs. These results also highlight the adaptability of our framework to higher-order ODE solvers; see the 8th and last row of Tab. 1.", + "bbox": [ + 504, + 89, + 895, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/15db83ff9e87b7787c6b9fcb9c09e0150f545aa3ae9fa93b97e098cd57d6590a.jpg", + "table_caption": [ + "Table 1. Sampling quality on CIFAR-10 Dataset." + ], + "table_footnote": [], + "table_body": "
METHODNFE(↓)FID(↓)
DDPM10003.17
Score SDE20002.20
PFGM1472.35
DDIM1004.16
gDDIM202.97
DEIS202.86
DPM-solver202.73
Multistage DPM-solver (Ours)202.35
EDM352.05
Multistage EDM (Ours)351.96
", + "bbox": [ + 509, + 233, + 888, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Training & Sampling Efficiency Results", + "text_level": 1, + "bbox": [ + 500, + 478, + 841, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we further demonstrate the superiority of our method by comparing the training and sampling efficiency under comparable image generation quality. Specifically, in Tab. 2, we present the number of training iterations, GFLOPs, and total training PFLOPs of our approach, DPM-solver, EDM, and LDM using CIFAR-10 and CelebA datasets. Using the CIFAR-10 dataset, our multistage DPM-solver achieves similar FID scores (2.71 vs 2.73) while requiring nearly half the training iterations when compared to the vanilla DPM-solver. For the case of EDM (resp. LDM), our approach returns an FID score of 1.44 (resp. 8.29), requiring $1.4 \\times 10^{5}$ ( $3.2 \\times 10^{5}$ ) less iterations when compared to vanilla DPM-solver (resp. LDM). For the cases of DPM-solver and EDM, we can achieve a substantial reduction of training iterations, which is demonstrated by a marginal increase in the number of GFLOPs. For the LDM case, we also achieve a significant reduction of both training iterations and GFLOPs. These promising results highlight the significantly improved computational efficiency achieved by using the proposed multistage framework.", + "bbox": [ + 496, + 502, + 890, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparison of Different Architectures", + "text_level": 1, + "bbox": [ + 500, + 816, + 833, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Sec. 3, we highlighted the limitations of both unified and separate diffusion model architectures in terms of training efficiency (see Fig. 2). In this part, we further illustrate these limitations through extensive experiments as shown", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2Here we simplify it by ignoring the FLOPs for backward propagation, which is approximately proportional to FLOPs of forward evaluation.", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7378", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a73b7ef5ce65c5e08d089a21cb457ddc11c0be57ab285511bb94053e64507c78.jpg", + "table_caption": [ + "Table 2. Training and Sampling Efficiency on More Datasets." + ], + "table_footnote": [], + "table_body": "
DatasetMethodTraining Iterations(↓)GFLOPs(↓)Total Training PFLOPs(↓)FID(↓)
CIFAR-10DPM-Solver [18]4.5 × 10517.657.942.73
32 × 32Multistage DPM-Solver (Ours)2.5 × 105(56%)18.65 (106%)4.66 (59%)2.71
CelebAEDM [18]5.7 × 10517.6510.061.55
32 × 32Multistage EDM (Ours)4.3 × 105(75%)19.25 (109%)8.28 (82%)1.44
CelebALDM [8]4.9 × 10588.3943.318.29
256 × 256Multistage LDM (Ours)1.7 × 105(35%)76.19 (86%)12.95 (30.0%)8.38
", + "bbox": [ + 114, + 112, + 854, + 213 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in Tab. 3. Here, we use the U-Net architecture, trained on the CIFAR-10 dataset, and utilize the DPM-Solver for sampling. For the unified case, we use a single U-Net model with 128 channels. For the separate case, three distinct U-Nets with 128 channels are used. For improved performance of the separate architecture, we implement two techniques: early stopping (ES) and tailored parameters (TP) to tackle the overfitting and parameter inefficiency discussed in Sec. 3. Under ES, the criteria is to stop training prior to overfitting. For TP, the three U-Nets are configured with 192, 128, and 16 channels decoders for Intervals 0, 1, and 2, respectively.", + "bbox": [ + 75, + 237, + 468, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our comparison and analysis in Tab. 3 reveal notable insights of our network design. Comparisons between the 2nd and 3rd rows (and between the 4th and 5th rows) on the separate architectures indicate that early stopping effectively mitigates overfitting and enhances generation quality. When comparing the 2nd and 4th rows (as well as the 3rd and 5th rows) on the separate architectures, we observe that optimizing parameter usage can achieve a significant decrease in FID under comparable GFLOPs. Most importantly, our multistage architecture, as shown in the 6th row, benefits from both unified and separate architectures, achieving the best FID (2.35, compared to 2.73 and 2.52). Comparing the 2nd row and the 4th row, the shared encoder not only prevents overfitting but also improves the convergence of the diffusion model as reported by the FID scores.", + "bbox": [ + 75, + 419, + 470, + 647 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c67da0aab71d48873d5481c7fe33804d467d0b1003c03c0f40427b220364b9ac.jpg", + "table_caption": [ + "Table 3. Ablation study on different diffusion model architectures." + ], + "table_footnote": [], + "table_body": "
MethodGFLOPsFID(↓)
Unified17.652.73
Separate17.652.87
Separate (+ ES)17.652.80
Separate (+ TP)18.652.68
Separate (+ ES, TP)18.652.52
Multistage (Ours)18.652.35
", + "bbox": [ + 116, + 685, + 426, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Comparison of Timestep Clustering Methods", + "text_level": 1, + "bbox": [ + 76, + 845, + 459, + 863 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As previously stated in Sec. 2, various timestep clustering methods are proposed including timestep-based, SNR-", + "bbox": [ + 76, + 869, + 467, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "based, and gradient-based clustering approaches [20, 21]. In this subsection, we conduct an experiment to demonstrate the superiority of our clustering method compared to previous arts. Specifically, we apply the clustering methods in [20, 21] to partition the interval along with our proposed multistage UNet architecture. The computed intervals are shown in the Tab. 4. We use the multistage DPM-Solver with these different intervals trained on the CIFAR-10 dataset. As observed, our optimal denoiser-based clustering method achieves the highest FID score, consistently outperforming all other clustering methods.", + "bbox": [ + 496, + 237, + 890, + 404 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0453858cfea0a13d19a2601a611cf0f0e570be20ee1edca8974b8270fd47d282.jpg", + "table_caption": [ + "Table 4. Ablation study on different clustering methods." + ], + "table_footnote": [], + "table_body": "
Clustering Methodt1t2FID(↓)
Timestep [20, 21]0.3300.6703.12
SNR [20]0.3480.7092.72
Gradient [20]0.3600.6602.75
Optimal Denoiser0.4420.6312.35
", + "bbox": [ + 539, + 439, + 849, + 534 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion & Future Work", + "text_level": 1, + "bbox": [ + 500, + 558, + 754, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced a novel multi-stage framework for diffusion models (DM) to improve the training and sampling efficiency. We proposed an algorithm that divides the timestep into several stages. Based on these stages, we designed a stage-specific multi-decoder U-net architecture and a shared encoder across all stages. We conducted thorough numerical experiments with several SOTA diffusion model frameworks and confirmed the effectiveness of our strategy using small scale and large scale datasets.", + "bbox": [ + 496, + 583, + 890, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In future research, it would be interesting to expand our multi-stage approach beyond unconditional diffusion models by considering conditional DMs and DM-based inverse problems solvers. Our experiment in Sec. 5.2 demonstrate that training latent diffusion models within our multi-stage framework requires only $30\\%$ of the computational effort needed for training standard latent diffusion models on the CelebA dataset. Thus, employing a multi-stage strategy could significantly reduce the computational demands for training large-scale stable diffusion models, such as those described in [8], which typically requires significant computations.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7379", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020. 1, 2, 3, 5, 7", + "[2] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 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Version: 0.2.0, DOI: 10.5281/zenodo.3786540.2" + ], + "bbox": [ + 78, + 90, + 468, + 797 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7381", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture/ab8cb3ef-8706-4683-ab23-b47ea618549e_model.json b/2024/Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture/ab8cb3ef-8706-4683-ab23-b47ea618549e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a725c4f93d590ee456e530e4cf58426979bf69ab --- /dev/null +++ b/2024/Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture/ab8cb3ef-8706-4683-ab23-b47ea618549e_model.json @@ -0,0 +1,2090 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.13, + 0.885, + 0.175 + ], + "angle": 0, + "content": "Improving Training Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architecture" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.202, + 0.796, + 0.24 + ], + "angle": 0, + "content": "Huijie Zhang\\(^{1}\\) * Yifu Lu\\(^{1}\\) * Ismail Alkhouri\\(^{1,2}\\) Saiprasad Ravishankar\\(^{2,3}\\) Dogyoon Song\\(^{1}\\) Qing Qu\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.244, + 0.812, + 0.314 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of Electrical Engineering & Computer Science, University of Michigan \\(^{2}\\)Department of Computational Mathematics, Science & Engineering, Michigan State University \\(^{3}\\)Department of Biomedical Engineering, Michigan State University {huijiezh, yifulu, ismailal, dogyoons, qingqu}@umich.edu ravisha3@msu.edu" + }, + { + "type": "image", + "bbox": [ + 0.137, + 0.353, + 0.303, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.52, + 0.23, + 0.53 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.304, + 0.351, + 0.468, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.519, + 0.398, + 0.53 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.468, + 0.351, + 0.64, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.519, + 0.572, + 0.53 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.35, + 0.828, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.517, + 0.751, + 0.529 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.531, + 0.894, + 0.573 + ], + "angle": 0, + "content": "Figure 1. Overview of three diffusion model architectures: (a) unified, (b) separate, and (c) our proposed multistage architecture. Compared with (a) and (b), our approach improves sampling quality, and significantly enhances training efficiency, as indicated by the FID scores and their corresponding training iterations (d)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.585, + 0.314, + 0.601 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.474, + 0.903 + ], + "angle": 0, + "content": "Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new samples (e.g., images). However, their remarkable generative performance is hindered by slow training and sampling. This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i.e., noise levels). To tackle these challenges, we present a multi-stage framework inspired by our empirical findings. These observations indicate the advantages of employing distinct parameters tailored to each timestep while retaining universal parameters shared across all time steps. Our approach involves segmenting the time interval into multiple stages where we employ custom multi-decoder U-net architecture that blends time-dependent models with a universally shared encoder. Our framework enables the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.895, + 0.768 + ], + "angle": 0, + "content": "efficient distribution of computational resources and mitigates inter-stage interference, which substantially improves training efficiency. Extensive numerical experiments affirm the effectiveness of our framework, showcasing significant training and sampling efficiency enhancements on three state-of-the-art diffusion models, including large-scale latent diffusion models. Furthermore, our ablation studies illustrate the impact of two important components in our framework: (i) a novel timestep clustering algorithm for stage division, and (ii) an innovative multi-decoder U-net architecture, seamlessly integrating universal and customized hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.785, + 0.633, + 0.801 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, diffusion models have made remarkable progress as powerful deep generative modeling tools, showcasing remarkable performance in various applications, ranging from unconditional image generation [1, 2], conditional image generation [3, 4], image-to-image translation [5-7], text-to-image generation [8-10], inverse problem solving [11-14]," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7372" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.35 + ], + "angle": 0, + "content": "video generation [15, 16], and so on. These models employ a training process involving continuous injection of noise into training samples (\"diffusion\"), which are then utilized to generate new samples, such as images, by transforming random noise instances through a reverse diffusion process guided by the \"score function\" of the data distribution learned by the model. Moreover, recent work demonstrates that those diffusion models enjoy optimization stability and model reproducibility compared with other types of generative models [17]. However, diffusion models suffer from slow training and sampling despite their remarkable generative capabilities, which hinders their use in applications where real-time generation is desired [1, 2]. These drawbacks primarily arise from the necessity of tracking extensive forward and reverse diffusion trajectories, as well as managing a large model with numerous parameters across multiple timesteps (i.e., diffusion noise levels)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.534 + ], + "angle": 0, + "content": "In this paper, we address these challenges based on two key observations: (i) there exists substantial parameter redundancy in current diffusion models, and (ii) they are trained inefficiently due to dissimilar gradients across different noise levels. Specifically, we find that training diffusion models require fewer parameters to accurately learn the score function at high noise levels, while larger parameters are needed at low noise levels. Furthermore, we also observe that when learning the score function, distinct shapes of distributions at different noise levels result in dissimilar gradients, which appear to slow down the training process driven by gradient descent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Building on these insights, we propose a multi-stage framework with two key components: (i) a multi-decoder U-net architecture, and (ii) a new partitioning algorithm to cluster timesteps (noise levels) into distinct stages. In terms of our new architecture, we design a multi-decoder U-Net that incorporates one universal encoder shared across all intervals and individual decoders tailored to each time stage; see Figure 1 (c) for an illustration. This approach combines the advantages of both universal and stage-specific architectures, which is much more efficient than the unified architecture for the entire training process [1, 2, 18] (Figure 1 (a)). Moreover, compared to previous approaches that completely separate architectures for each sub-interval [19-22] (Figure 1 (b)), our approach can effectively mitigate overfitting, leading to improved training efficiency. On the other hand, when it comes to partitioning the training stages of our network, we designed an algorithm aimed at grouping the timesteps. This is achieved by minimizing the functional distance within each cluster in the training objective and making use of the optimal denoiser formulation [18]. By integrating these two key components, our framework enables efficient allocation of computational resources (e.g., U-net parameters) and stage-tailored parameterization. Throughout our extensive numerical experi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "ments (Section 5), we show that out framework effectively improves both training and sampling efficiency. These experiments are performed on diverse benchmark datasets, demonstrating significant acceleration by using our framework when compared to three state-of-the-art (SOTA) diffusion model architectures. As a summary, the major contributions of this work can be highlighted as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.2, + 0.892, + 0.305 + ], + "angle": 0, + "content": "- Identifying two key sources of inefficiency. We identified two key sources that cause inefficiencies in training diffusion models across various time steps: (i) a significant variation in the requirement of model capacity, and (ii) the gradient dissimilarity. As such, using a unified network cannot meet with the changing requirement at different time steps." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.306, + 0.892, + 0.396 + ], + "angle": 0, + "content": "- A new multi-stage framework. We introduced a new multi-stage architecture, illustrated in Fig. 1 (c). We tackle these two sources of inefficiency by segmenting the time interval into multiple stages, where we employ customized multi-decoder U-net architectures that blends time-dependent models with a universally shared encoder." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.397, + 0.892, + 0.577 + ], + "angle": 0, + "content": "- Improved training and sampling efficiency. With comparable computational resources for unconditional image generation, we demonstrate that our multi-stage approach improves the Fréchet Inception Distance (FID) score for all SOTA methods. For example, on CIFAR-10 dataset [23], our method improves the FID for DPM-Solver [24] from 2.84 to 2.37, and it improves the FID for EDM [18] from 2.05 (our training result) to 1.96. Moreover, on the CelebA dataset [25], while maintaining a similar generation quality, our approach significantly reduces the required training FLOPS of EDM by \\(82\\%\\) and the Latent Diffusion Model (LDM) [8] by \\(30\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Organization. In Sec. 2, we provide preliminaries and an overview of related literatures. In Sec. 3, we present our observations and analysis that motivated the proposed multistage framework, justifying its development. In Sec. 4, we describe our proposed multistage framework for diffusion models, outlining the two core components. Finally, in Sec. 5, we provide the results from our numerical experiments that validate the effectiveness of the proposed multistage approach." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.731, + 0.78, + 0.746 + ], + "angle": 0, + "content": "2. Preliminaries & Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.861 + ], + "angle": 0, + "content": "In this section, we start by reviewing the basic fundamentals of diffusion models [1, 2, 18]. Subsequently, we delve into prior approaches aimed at improving the training and efficiency of diffusion models through the partitioning of the timestep interval. Lastly, we survey prior studies that significantly decrease the number of required sampling iterations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Background on diffusion models. Let \\( \\pmb{x}_0 \\in \\mathbb{R}^n \\) denote a sample from the data distribution \\( p_{\\mathrm{data}}(\\pmb{x}) \\). Diffu" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7373" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.26 + ], + "angle": 0, + "content": "sion models operate within forward and reverse processes. The forward process progressively perturbs data \\( \\boldsymbol{x}_0 \\) to a noisy version \\( \\boldsymbol{x}_{t\\in [0,1]} \\) via corrupting with the Gaussian kernel. This process can be formulated as a stochastic differential equation (SDE) [2] of the form \\( \\mathrm{d}\\boldsymbol {x} = \\boldsymbol {x}_t f(t)\\mathrm{d}t + g(t)\\mathrm{d}\\boldsymbol{w}_t \\), where \\( f(t) \\) and \\( g(t) \\) are the drift and diffusion coefficients, respectively, that correspond to a pre-defined noise schedule. \\( \\boldsymbol{w}_t\\in \\mathbb{R}^n \\) is the standard Wiener process. Under the forward SDE, the perturbation kernel is given by the conditional distribution defined as \\( p_t(\\boldsymbol {x}_t|\\boldsymbol {x}_0) = \\mathcal{N}(\\boldsymbol {x}_t;s_t\\boldsymbol {x}_0,s_t^2\\sigma_t^2\\mathbf{I}) \\), where" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.27, + 0.47, + 0.311 + ], + "angle": 0, + "content": "\\[\ns _ {t} = \\exp \\left(\\int_ {0} ^ {t} f (\\xi) \\mathrm {d} \\xi\\right), \\text {a n d} \\sigma_ {t} = \\sqrt {\\int_ {0} ^ {t} \\frac {g ^ {2} (\\xi)}{s _ {\\xi} ^ {2}} \\mathrm {d} \\xi}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.473, + 0.502 + ], + "angle": 0, + "content": "The parameters \\( s_t \\) and \\( \\sigma_t \\) are designed such that: (i) the data distribution is approximately estimated when \\( t = 0 \\), and (ii) a nearly standard Gaussian distribution is obtained when \\( t = 1 \\). The objective of diffusion models is to learn the corresponding reverse SDE, defined as \\( \\mathrm{d}\\pmb{x} = \\left[f(t)\\pmb{x}_t - g^2(t)\\nabla_{\\pmb{x}_t}\\log p_t(\\pmb{x}_t)\\right]\\mathrm{d}t + g(t)\\mathrm{d}\\bar{\\pmb{w}} \\), where \\( \\bar{\\pmb{w}} \\in \\mathbb{R}^n \\) is the standard Wiener process running backward in time, and \\( \\nabla_{\\pmb{x}_t}\\log p_t(\\pmb{x}_t) \\) is the (Stein) score function. In practice, the score function is approximated using a neural network \\( \\epsilon_{\\theta}:\\mathbb{R}^n\\times [0,1]\\to \\mathbb{R}^n \\) parameterized by \\( \\pmb{\\theta} \\), which can be trained by the denoising score matching technique [26] as" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.51, + 0.47, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {\\theta}} \\mathbb {E} \\left[ \\omega (t) \\| \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, t) + s _ {t} \\sigma_ {t} \\nabla_ {\\boldsymbol {x} _ {t}} \\log p _ {t} (\\boldsymbol {x} _ {t} | \\boldsymbol {x} _ {0}) \\| _ {2} ^ {2} \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.473, + 0.682 + ], + "angle": 0, + "content": "which can also be written as \\(\\min_{\\pmb{\\theta}}\\mathbb{E}[\\omega (t)||\\pmb{\\epsilon}_{\\pmb{\\theta}}(\\pmb{x}_t,t) - \\pmb{\\epsilon}||^2 ] + C\\), where the expectation is taken over \\(t\\sim [0,1]\\), \\(\\pmb{x}_t\\sim p_t(\\pmb{x}_t|\\pmb{x}_0)\\), \\(\\pmb{x}_0\\sim p_{\\mathrm{data}}(\\pmb {x})\\), and \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\). Here, \\(C\\) is a constant independent of \\(\\pmb{\\theta}\\), and \\(\\omega (t)\\) is a scalar representing the weight of the loss as a function of \\(t\\). In DDPM [1], it is simplified to \\(\\omega (t) = 1\\). Once the parameterized score function \\(\\epsilon_{\\theta}\\) is trained, it can be utilized to approximate the reverse-time SDE using numerical solvers such as Euler-Maruyama." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Timestep clustering methods. Diffusion models have demonstrated exceptional performance but face efficiency challenges in training and sampling. In response, several studies proposed to cluster the timestep range \\( t \\in [0,1] \\) into multiple intervals (e.g., \\( [0,t_1),[t_1,t_2),\\ldots ,[t_n,1] \\)). Notably, Choi et al. [19] reconfigured the loss weights for different intervals to enhance performance. Deja et al. [27] divide the entire process into a denoisr and a generator based on their functionalities. Balaji et al. [28] introduced \"expert denoisers\", which proposed using distinct architectures for different time intervals in text-to-image diffusion models. Go et al. [22] further improved the efficiency of these expert denoisers through parameter-efficient fine-tuning and data-free knowledge transfer. Lee et al. [21] designed separate" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "architectures for each interval based on frequency characteristics. Moreover, Go et al. [20] treated different intervals as distinct tasks and employed multi-task learning strategies for diffusion model training, along with various timestep clustering methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.893, + 0.41 + ], + "angle": 0, + "content": "Our approach distinguishes itself from the aforementioned methods in two key aspects. The first key component is our tailored U-net architecture using a unified encoder coupled with different decoders for different intervals. Previous models have either adopted a unified architecture, as seen in [19, 20], or employed separate architectures (referred to as expert denoisers) for each interval [21, 22, 28]. In comparison, our multistage architecture surpasses these methodologies, as demonstrated in Sec. 5.3. Second, we developed a new timestep clustering method leveraging a general optimal denoiser (Prop. 1) that showcases superior performance (see Sec. 5.4). In contrast, prior works rely on (i) a simple timestep-based clustering cost function [20-22, 28], (ii) Signal-to-Noise Ratio (SNR) based clustering [20], or (iii) gradients-based partitioning that uses task affinity scores [20]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.893, + 0.706 + ], + "angle": 0, + "content": "Reducing the sampling iterations methods. Efforts to improve sampling efficiency of diffusion models have led to many recent advancements in SDE and Ordinary Differential Equation (ODE) samplers [2]. For instance, the Denoising Diffusion Implicit Model (DDIM) [29] formulates the forward diffusion as a non-Markovian process with a deterministic generative path, significantly reducing the number of function evaluations (NFE) required for sampling (from thousands to hundreds). Generalized DDIM (gDDIM) [30] further optimized DDIM by modifying the parameterization of the scoring network. Furthermore, the works in [24] and [31], termed the Diffusion Probabilistic Model solver (DPM-solver) and the Diffusion Exponential Integrator Sampler (DEIS), respectively, introduced fast higher-order solvers, employing exponential integrators that require 10s NFE for comparable generation quality. Moreover, the consistency model [32] introduced a novel training loss and parameterization, achieving high-quality generation with merely 1-2 NFE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.785 + ], + "angle": 0, + "content": "We remark that while the aforementioned methods are indirectly related to our work, our experiments in Sec. 5.1 and Sec. 5.2 show that our approach can be easily integrated into these techniques, further improving diffusion models' overall training and sampling efficiency." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.799, + 0.889, + 0.817 + ], + "angle": 0, + "content": "3. Identification of Key Sources of Inefficiency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Conventional diffusion model architectures, as exemplified by [1, 2, 18], treat the training of the diffusion model as a unified process across all timesteps. Recent researches, such as [19-22], have highlighted the benefits of recognizing distinctions between different timesteps and the poten" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7374" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.184 + ], + "angle": 0, + "content": "tial efficiency gains from treating them as separate tasks during the training process. However, our experimental results demonstrate that both unified and separate architectures suffer inefficiency for training diffusion models, where the inefficiency comes from (i) overparameterization, (ii) gradient dissimilarity, and (iii) overfitting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.195, + 0.471, + 0.228 + ], + "angle": 0, + "content": "3.1. Empirical Observations on the Key Sources of Inefficiency" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.235, + 0.47, + 0.266 + ], + "angle": 0, + "content": "To illustrate the inefficiency in each interval, we isolate the interval by using a separate architecture from the rest." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.566 + ], + "angle": 0, + "content": "Experiment setup. In our experiments, we consider three-stage training and divide the time steps into three intervals: \\([0, t_1), [t_1, t_2), [t_2, 1]^1\\). Let \\((\\epsilon_{\\theta})_i^{[a,b]}, 0 \\leq a < b \\leq 1\\) denote a U-Net architecture with parameter \\(\\theta\\) trained with \\(i\\) iterations and fed with data pairs \\((x_t, t)\\), where \\(t \\in [a,b]\\). We then train models using two different strategies: a unified architecture with 108M network parameters for all intervals, i.e., \\((\\epsilon_{\\theta})_i^{[0,1]}\\), and separate architectures with varying network parameters (e.g., 47M, 108M, 169M) for each interval; e.g., \\((\\epsilon_{\\theta})_i^{[0,t_1)}\\) for the interval \\([0,t_1)\\), etc. It is worth noting that, apart from the differences in network parameters, we utilize the same network architecture (e.g., U-Net) for both the unified and the separate approaches. We assessed the training progress of each model by evaluating image generation quality at different training iterations. Notably, because some of the models are only trained on one interval, we need to provide a ground truth score for the other intervals. In Fig. 2, the sampling process is shown top and the experimental results are shown bottom." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.573, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Inefficiency in unified architectures. From Fig. 2, we observe the following:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.605, + 0.47, + 0.814 + ], + "angle": 0, + "content": "- Overparameterization and underfitting emerge simultaneously for unified architectures. In Fig. 2a, we observe that increasing the number of parameters in Interval 0 can improve the image generation quality (as indicated by a lower FID score). In contrast, Fig. 2b reveals that increasing the number of parameters in Interval 2 has minimal impact on the quality of image generation. This implies that using a unified architecture will result in underfitting in Interval 0 and overparameterization in Interval 2. The current unified architecture's parameter redundancy leaves significant room for improving its efficiency. To optimize the computational usage, we should allocate more parameters to Interval 0 while allocating fewer parameters to Interval 2." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.816, + 0.47, + 0.875 + ], + "angle": 0, + "content": "- Gradient dissimilarity hinders training for unified architecture. Quantitative results from [20] demonstrate dissimilarity in gradients caused by differences within each interval. This can also be observed from our results based" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.605, + 0.47, + 0.875 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "upon both Fig. 2a and Fig. 2b. For the unified and separate architectures using the same number of parameters (108M), separate architecture achieves a significantly lower FID with the same training iterations, implying that dissimilar gradients among intervals may hinder training when using a unified architecture. Here, the only difference between training separate and unified architectures is that the batch gradient for unified architecture is calculated based on all timesteps while the batch gradien2 for separate architecture is calculated only from a specific interval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Inefficiency in existing separate architectures. Although separated architecture [19, 21, 22] better allocates computational resources for each interval, it suffers from overfitting. This can be illustrated based upon training separate architectures (169M) and (108M) in Interval 0 shown in Fig. 2a, where increasing the number of parameters will lead to overfitting. This also happens in Interval 2, when we compare all separate architectures in Fig. 2b. In comparison, the unified networks with 108M parameters are less prone to overfitting for both Interval 0 and Interval 2. This suggests that we can reduce overfitting by training shared weights across different intervals together." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.5 + ], + "angle": 0, + "content": "3.2. Tackling the Inefficiency via Multistage U-Net Architectures" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.751 + ], + "angle": 0, + "content": "In a unified architecture applied across all timesteps, there is often a dual challenge: requirements for more parameters (169M) in the interval \\([0, t_1)\\) but fewer parameters (47M) in the interval \\([t_2, 1]\\). This issue is compounded by the gradient dissimilarity across different timesteps, which can impede effective training. Alternatively, employing separate architectures for different intervals might lead to overfitting and a lack of robust early stopping mechanisms. To address these challenges, our proposed multistage architecture in Sec. 4 combines shared parameters to reduce overfitting with interval-specific parameters to mitigate the impact of gradient dissimilarity. This tailored approach for each interval ensures improved adaptability. Furthermore, we conduct an in-depth ablation study in Sec. 5.3 to showcase the effectiveness of our multi-stage architecture over the existing models." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.769, + 0.803, + 0.787 + ], + "angle": 0, + "content": "4. Proposed Multistage Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we introduce our new multistage framework (as illustrated in Fig. 1 (c)). Specifically, we first introduce the multi-stage U-Net architecture design in Sec. 4.1, following a new clustering method for choosing the optimal interval to partition the entire timestep [0, 1] into intervals in Sec. 4.2., and discuss the rationale of the proposed architecture in Sec. 4.3." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.422, + 0.901 + ], + "angle": 0, + "content": "1Details for interval clustering can be found in Appendix B.1." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7375" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.175, + 0.089, + 0.468, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.314, + 0.376, + 0.326 + ], + "angle": 0, + "content": "(a) Analysis on interval \\([0, t_1)\\)" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.089, + 0.782, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.314, + 0.714, + 0.326 + ], + "angle": 0, + "content": "(b) Analysis on interval \\([t_2, 1]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.328, + 0.892, + 0.452 + ], + "angle": 0, + "content": "Figure 2. Comparison between separate architecture and unified architecture w.r.t. the image generation quality in different intervals: (a) analysis on interval \\([0, t_1)\\); and (b) analysis on interval \\([t_2, 1]\\). As illustrated on top of each figure, we only train separate architectures within specific intervals for the sampling process in both (a) and (b). For the remaining period of sampling, we use a well-trained diffusion model \\((\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}\\) to approximate the ground truth score function. As shown in the above figure of (a), e.g. for the separate architecture on interval 1, sampling utilizes trained model \\((\\epsilon_{\\theta'})_i^{[0,t_1)}\\) for interval 0 and well-trained model \\((\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}\\) for interval 1 and 2. Notably, for both \\((\\epsilon_{\\theta})_i^{[0,1]}\\) and \\((\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}\\), we are using the model with 108M parameters. For separate architecture, the number in the parentheses represents the number of parameters of the model \\((\\epsilon_{\\theta'})_i^{[a,b]}\\). For example, for separate architecture (169M) in (a), the model \\((\\epsilon_{\\theta'})_i^{[0,t_1)}\\) has 169M parameters for \\(\\theta'\\). The bottom figures in (a-b) illustrate the FID of the generation from each architecture under different training iterations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.478, + 0.436, + 0.494 + ], + "angle": 0, + "content": "4.1. Proposed Multi-stage U-Net Architectures" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.469, + 0.594 + ], + "angle": 0, + "content": "As discussed in Sec. 3, most existing diffusion models either employ a unified architecture across all intervals [1, 2, 18] to share features for all timesteps, or use completely separate architectures for different timestep intervals [21, 22, 28] where the goal is to take advantage of the benign properties within different intervals." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.687 + ], + "angle": 0, + "content": "To harness the advantages of both unified and separate architectures employed in prior studies, we introduce a multistage U-Net architecture, as illustrated in Figure 1(c). Specifically, we partition the entire timestep \\([0,1]\\) into several intervals, e.g., three intervals \\([0,t_1),[t_1,t_2),[t_2,1]\\) in Fig. 1. For the architecture, we introduce:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.809 + ], + "angle": 0, + "content": "- One shared encoder across all time intervals. For each timestep interval, we implement a shared encoder architecture (plotted in blue in Fig. 1 (c)), which is similar to the architecture employed in the original U-Net framework [33]. Unlike separate architecture, the shared encoder provides shared information across all timesteps, preventing models from overfitting (see Sec. 5.3 for a discussion)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- Separate decoders for different time intervals. Motivated by the multi-head structure introduced in the Mask Region-based Convolutional Neural Networks (MaskRCNN) method [34], we propose to use multiple distinct decoders (plotted in colors for different intervals in Fig. 1(c)), where each decoder is tailored to a spe" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.479, + 0.891, + 0.539 + ], + "angle": 0, + "content": "cific timestep interval. The architecture of each decoder closely resembles the one utilized in [2], with deliberate adjustments made to the embedding dimensions to optimize performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.892, + 0.632 + ], + "angle": 0, + "content": "As we observe, the primary difference in the architecture resides within the decoder structure. Intuitively, we use a decoder with fewer number of parameters for intervals closer to the noise, because the learning task is easier. We use a decoder with a larger number of parameters for intervals closer to the image." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.646, + 0.882, + 0.663 + ], + "angle": 0, + "content": "4.2. Optimal Denoiser-based Timestep Clustering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Next, we discuss how we principally choose the interval partition time points in practice. For simplicity, we focus on the case where we partition the time \\([0,1]\\) into three intervals \\([0,t_1],[t_1,t_2],[t_2,1]\\), and we develop a timestep clustering method to choose the optimal \\(t_1\\) and \\(t_2\\). Of course, our method can be generalized to multi-stage networks with arbitrary interval numbers. However, in practice, we find that the choice of three intervals strikes a good balance between effectiveness and complexity; see our ablation study in Appendix B.6." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.891, + 0.856 + ], + "angle": 0, + "content": "To partition the time interval, we employ the optimal denoiser established in Proposition 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Proposition 1. Suppose we train a diffusion model denoiser function \\(\\epsilon_{\\theta}(\\pmb{x},t)\\) with parameters \\(\\pmb{\\theta}\\) using dataset" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7376" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.092, + 0.465, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Optimal Denoiser based Timestep Clustering" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.111, + 0.468, + 0.139 + ], + "angle": 0, + "content": "1: Input: Total samples \\(K\\), optimal denoiser function \\(\\pmb{\\epsilon}_{\\pmb{\\theta}}^{*}(\\pmb{x},t)\\), thresholds \\(\\alpha, \\eta\\), dataset \\(p_{\\mathrm{data}}\\), \\(S_0 = S_1 = \\emptyset\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.14, + 0.259, + 0.153 + ], + "angle": 0, + "content": "2: Output: Timesteps \\( t_1, t_2 \\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.154, + 0.25, + 0.166 + ], + "angle": 0, + "content": "3: for \\( k \\in \\{1, \\dots, K\\} \\) do" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.167, + 0.351, + 0.18 + ], + "angle": 0, + "content": "4: \\(\\pmb{y}_k\\sim p_{\\mathrm{data}},\\pmb{\\epsilon}_k\\sim \\mathcal{N}(0,\\mathbf{I}),t_k\\sim [0,1]\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.18, + 0.438, + 0.195 + ], + "angle": 0, + "content": "5: \\(\\mathcal{S}_0^k\\gets \\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*,\\pmb{\\epsilon}_0^*,\\pmb {y}_k,\\pmb {\\epsilon}_k),\\mathcal{S}_1^k\\gets \\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*,\\pmb {\\epsilon}_1^*,\\pmb {y}_k,\\pmb {\\epsilon}_k)\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.195, + 0.414, + 0.21 + ], + "angle": 0, + "content": "6: \\(\\mathcal{S}_0\\gets \\mathcal{S}_0\\cup \\{\\big(t_k,\\mathcal{S}_0^k\\big)\\} ,\\mathcal{S}_1\\gets \\mathcal{S}_1\\cup \\{\\big(t_k,\\mathcal{S}_1^k\\big)\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.21, + 0.156, + 0.22 + ], + "angle": 0, + "content": "7: end for" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.22, + 0.417, + 0.254 + ], + "angle": 0, + "content": "8: \\(t_1 = \\arg \\max_{\\tau}\\left\\{\\tau \\Big|\\frac{\\sum_{(t_k,\\mathcal{S}_0^k)\\in\\mathcal{S}_0}\\big[\\mathcal{S}_0^k\\cdot\\mathbb{1}(t_k\\leq\\tau)\\big]}{\\sum_{(t_k,\\mathcal{S}_0^k)\\in\\mathcal{S}_0}[\\mathbb{1}(t_k\\leq\\tau)]}\\geq\\alpha\\right\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.255, + 0.415, + 0.291 + ], + "angle": 0, + "content": "9: \\(t_2 = \\arg \\min_{\\tau}\\left\\{\\tau \\Big|\\frac{\\sum_{(t_k,\\mathcal{S}_1^k)\\in\\mathcal{S}_0}\\big[\\mathcal{S}_1^k\\cdot\\mathbb{1}(t_k\\geq\\tau)\\big]}{\\sum_{(t_k,\\mathcal{S}_1^k)\\in\\mathcal{S}_0}[\\mathbb{1}(t_k\\geq\\tau)]}\\geq\\alpha\\right\\}\\)" + }, + { + "type": "list", + "bbox": [ + 0.088, + 0.111, + 0.468, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.317, + 0.197, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {y} _ {i} \\in \\mathbb {R} ^ {n} \\right\\} _ {i = 1} ^ {N} b y\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.346, + 0.469, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {\\theta}} \\mathcal {L} (\\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}}; t) = \\mathbb {E} _ {\\boldsymbol {x} _ {0}, \\boldsymbol {x} _ {t}, \\epsilon} [ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} ], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.469, + 0.457 + ], + "angle": 0, + "content": "where \\(\\pmb{x}_0\\sim p_{data}(\\pmb {x}) = \\frac{1}{N}\\sum_{i = 1}^{N}\\delta (\\pmb {x} - \\pmb {y}_i)\\) \\(\\epsilon \\sim \\mathcal{N}(0,\\pmb {I})\\) and \\(\\pmb{x}_{t}\\sim p_{t}(\\pmb{x}_{t}|\\pmb{x}_{0}) = \\mathcal{N}(\\pmb{x}_{t};s_{t}\\pmb{x}_{0},s_{t}^{2}\\sigma_{t}^{2}\\pmb {I})\\) with perturbation parameters \\(s_t\\) and \\(\\sigma_t\\) defined in Eq. (1). Then, the optimal denoiser at \\(t\\) defined as \\(\\epsilon_{\\theta}^{*}(\\pmb {x};t) = \\arg \\min_{\\epsilon_{\\theta}}\\mathcal{L}(\\epsilon_{\\theta};t)\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.466, + 0.469, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} ^ {*} (\\boldsymbol {x}; t) = \\frac {1}{s _ {t} \\sigma_ {t}} \\left[ \\boldsymbol {x} - s _ {t} \\frac {\\sum_ {i = 1} ^ {N} \\mathcal {N} (\\boldsymbol {x} ; s _ {t} \\boldsymbol {y} _ {i} , s _ {t} ^ {2} \\sigma_ {t} ^ {2} \\boldsymbol {I}) \\boldsymbol {y} _ {i}}{\\sum_ {i = 1} ^ {N} \\mathcal {N} (\\boldsymbol {x} ; s _ {t} \\boldsymbol {y} _ {i} , s _ {t} ^ {2} \\sigma_ {t} ^ {2} \\boldsymbol {I})} \\right]. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.533, + 0.469, + 0.638 + ], + "angle": 0, + "content": "The proof is provided in Appendix A, and the result can be generalized from recent work of Karras et al. [18], extending from a specific kernel \\( p_t(\\boldsymbol{x}_t|\\boldsymbol{x}_0) = \\mathcal{N}(\\boldsymbol{x}_t; \\boldsymbol{x}_0, \\sigma_t^2\\mathbf{I}) \\) to encompassing a broader scope of noise perturbation kernels, given by \\( p_t(\\boldsymbol{x}_t|\\boldsymbol{x}_0) = \\mathcal{N}(\\boldsymbol{x}_t; s_t\\boldsymbol{x}_0, s_t^2\\sigma_t^2\\mathbf{I}) \\). For brevity, we simplify the notation of the optimal denoiser \\( \\epsilon_{\\theta}^{*}(\\boldsymbol{x}, t) \\) in Proposition 1 as \\( \\epsilon_t^*(\\boldsymbol{x}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.638, + 0.469, + 0.714 + ], + "angle": 0, + "content": "To obtain the optimal interval, our rationale is to homogenize the regression task as much as possible within each individual time interval. To achieve this goal, given sampled \\( \\pmb{x}_0, \\pmb{\\epsilon} \\), we define the function distance of the optimal denoiser at any given timestep \\( t_a, t_b \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.724, + 0.468, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}\\right) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathbb {1} \\left(\\left| \\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*} \\left(\\boldsymbol {x} _ {t _ {a}}\\right) - \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*} \\left(\\boldsymbol {x} _ {t _ {b}}\\right) \\right| _ {i} \\leq \\eta\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.772, + 0.469, + 0.833 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}(\\cdot)\\) is the indicator function, \\(\\eta\\) is a pre-specified threshold, \\(\\pmb{x}_{t_a} = s_{t_a}\\pmb{x}_0 + s_{t_a}\\sigma_{t_a}\\pmb{\\epsilon}\\), and \\(\\pmb{x}_{t_b} = s_{t_b}\\pmb{x}_0 + s_{t_b}\\sigma_{t_b}\\pmb{\\epsilon}\\). Consequently, we define the functional similarity of the optimal denoiser at timesteps \\(t_a\\) and \\(t_b\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.844, + 0.469, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}\\right) = \\mathbb {E} _ {\\boldsymbol {x} _ {0} \\sim p _ {\\mathrm {d a t a}}} \\mathbb {E} _ {\\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I})} \\left[ \\mathcal {D} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}\\right) \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Based upon the definition, we design the following optimization problem to find the largest \\( t_1 \\) and smallest \\( t_2 \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.113, + 0.892, + 0.141 + ], + "angle": 0, + "content": "\\[\nt _ {1} \\leftarrow \\underset {\\tau} {\\arg \\max } \\left\\{\\tau \\left| \\mathbb {E} _ {t \\sim [ 0, \\tau)} \\left[ \\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t} ^ {*}, \\boldsymbol {\\epsilon} _ {0} ^ {*}\\right) \\right] \\geq \\alpha \\right. \\right\\}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.144, + 0.892, + 0.171 + ], + "angle": 0, + "content": "\\[\nt _ {2} \\leftarrow \\underset {\\tau} {\\arg \\min } \\left\\{\\tau \\left| \\mathbb {E} _ {t \\sim [ \\tau , 1 ]} \\left[ \\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t} ^ {*}, \\boldsymbol {\\epsilon} _ {1} ^ {*}\\right) \\right] \\geq \\alpha \\right. \\right\\}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.181, + 0.892, + 0.333 + ], + "angle": 0, + "content": "such that the average functional similarity of \\(\\pmb{\\epsilon}_t^*\\) (resp. \\(\\pmb{\\epsilon}_t^*\\)) to \\(\\pmb{\\epsilon}_0^*\\) (resp. \\(\\pmb{\\epsilon}_1^*\\)) in \\([0, t_1)\\) (resp. \\([t_2, 1]\\)) is larger than or equal to a pre-defined threshold \\(\\alpha\\). As the above optimization problems are intractable, we propose the procedure outlined in Algorithm 1 to obtain an approximate solution. In particular, the algorithm samples \\(K\\) pairs \\((\\pmb{y}_k, \\pmb{\\epsilon}_k, t_k), k \\in \\{1, \\dots, K\\}\\) to calculate the distances \\(\\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*, \\pmb{\\epsilon}_0^*, \\pmb{y}_k, \\pmb{\\epsilon}_k)\\) and \\(\\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*, \\pmb{\\epsilon}_1^*, \\pmb{y}_k, \\pmb{\\epsilon}_k)\\) (step 6). Based on those distances, we solve the optimization problems defined in the lines 8 and 9 of Algorithm 1 to obtain \\(t_1\\) and \\(t_2\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.341, + 0.845, + 0.358 + ], + "angle": 0, + "content": "4.3. Rationales for the proposed architecture" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.364, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Finally, we summarize the rationales of our proposed architecture based on the empirical observations in Sec. 3 and previous works." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.41, + 0.892, + 0.574 + ], + "angle": 0, + "content": "Rationales for the shared encoder. (i) Prevent overfitting: If we treat training separate stages of diffusion models as multi-task learning, [35] suggests that shared parameters across tasks in multi-task learning can mitigate overfitting. (ii) Maintain consistency in \\( h \\)-space. The output of the encoder for UNet is named as \\( h \\)-space [36], which has properties for semantic manipulation such as homogeneity, linearity, robustness, and consistency across timesteps. Therefore, sharing the encoder can maintain better consistency of the \\( h \\)-space among all timesteps compared to separate encoders." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.576, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Rationales for network parameter design. First, we provide some intuitions as to why the learning task at \\( t = 0 \\) is harder than that at \\( t = 1 \\). Suppose diffusion models could converge to the optimal denoiser \\( \\epsilon_{\\theta}^{*}(\\boldsymbol{x}_t,t) \\) given in Eq. (4). Based on this, we observe: (i) when \\( t \\to 0 \\), we have \\( \\boldsymbol{x}_{t \\to 0} = \\boldsymbol{x}_0 \\), \\( \\epsilon_{\\theta}^{*}|_{t \\to 0} = \\epsilon \\), so that \\( \\epsilon_{\\theta}^{*} \\) is a complicated mapping from training data distribution \\( p_{\\mathrm{data}}(\\boldsymbol{x}) \\) to the gaussian distribution; (ii) when \\( t \\to 1 \\), we have \\( \\boldsymbol{x}_{t \\to 1} = \\epsilon \\), \\( \\epsilon_{\\theta}^{*}|_{t \\to 1} = \\epsilon \\), so \\( \\epsilon_{\\theta}^{*} \\) is an identity mapping. The two extreme cases reveal that the identity mapping for \\( t \\to 1 \\) (close to noise) is easier to learn than that for \\( t \\to 0 \\). Second, our choice of network parameters across different stages share similar spirits with the recent work [37], which employs a high dimensional subspace as \\( t \\to 0 \\) and gradually decreases the dimensionality of each subspace until \\( t = 1 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.633, + 0.832 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this section, we start by providing the experimental setups. Next, we present results in terms of generation quality (Sec. 5.1). Subsequently, results for training and sampling efficiency are presented. Finally, in Sec. 5.3 and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7377" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Sec. 5.4, comprehensive ablation studies on timestep clustering methods and multistage architectures are given." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.132, + 0.471, + 0.36 + ], + "angle": 0, + "content": "Multistage architectures. Our multistage architecture, inspired by the U-Net model [33] used in \\(\\mathrm{DDPM}++\\) [1, 2, 18], is modified for interval-specific channel dimensions. The proposed architecture is adopted to three diffusion models: DPM-Solver [24], EDM [18], and LDM [8]. In particular, for the cases of DPM-Solver and EDM, the encoder's channel dimensions are standardized at 128, while the decoders are configured with 192, 128, and 16 channels for intervals \\([0, t_1)\\), \\([t_1, t_2)\\), and \\([t_2, 1]\\), respectively. In the LDM case, we use 224 channels across the encoder for all intervals whereas the decoders are configured with 256, 192, and 128 channels for the respective intervals. To decide the specific number of parameters for each decoder, we apply ablation studies in Appendix B.5. Training details are in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.635 + ], + "angle": 0, + "content": "Datasets, evaluation metrics, & baselines. We use CIFAR-10 \\((32 \\times 32)\\), CelebA \\((32 \\times 32)\\), and CelebA (256 \\(\\times\\) 256) datasets for our experiments. To evaluate the performance of our multistage diffusion model in terms of the generation quality, we use the standard Fréchet Inception Distance (FID) metric [38]. We assess the sampling efficiency using the NFE, and giga-floating point operations (GFLOPs) per function evaluation. For both separate architecture and our multistage architecture, equivalent GFLOPs are computed as a weighted summation of GFLOPs for each interval. Training efficiency is evaluated using total training iterations multiplied by the GFLOPs per function evaluation, measured by peta-floating point operations (PFLOPs). For baselines, we consider DDPM [1], Score SDE [2], Poisson Flow Generative Models (PFGM) [39], DDIM [29], gDDIM [30], DEIS [31], DPM-solver [24], and EDM [18]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.646, + 0.377, + 0.663 + ], + "angle": 0, + "content": "5.1. Image Generation Quality Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.468, + 0.865 + ], + "angle": 0, + "content": "In this subsection, we demonstrate the effectiveness of our approach by comparing the image generation quality (measured by FID) with comparable training and sampling computations (measured by NFE). Specifically, Tab. 1 presents FID scores to measure the sampling quality, and NFE to measure the number of sampling iterations required using the CIFAR-10 dataset. Our method is compared to 8 baselines. As observed, our multistage DPM-Solver outperforms DPM-Solver in terms of the reported FID values while requiring similar training iterations (both are \\(4.5 \\times 10^{5}\\)) and model GFLOPs (18.65 for multistage DPM-Solver versus 17.65 for DPM-Solver). A similar observation holds when we compare our multistage EDM and the" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.09, + 0.897, + 0.196 + ], + "angle": 0, + "content": "vanilla EDM, where we reduce FID from 2.05 to 1.96 by using the multi-stage architecture. Remarkably, utilizing only 20 NFE, our Multistage DPM-Solver returns the same FID score as the one reported for the PFGM method, which requires 147 NFEs. These results also highlight the adaptability of our framework to higher-order ODE solvers; see the 8th and last row of Tab. 1." + }, + { + "type": "table_caption", + "bbox": [ + 0.549, + 0.209, + 0.842, + 0.223 + ], + "angle": 0, + "content": "Table 1. Sampling quality on CIFAR-10 Dataset." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.234, + 0.889, + 0.451 + ], + "angle": 0, + "content": "
METHODNFE(↓)FID(↓)
DDPM10003.17
Score SDE20002.20
PFGM1472.35
DDIM1004.16
gDDIM202.97
DEIS202.86
DPM-solver202.73
Multistage DPM-solver (Ours)202.35
EDM352.05
Multistage EDM (Ours)351.96
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.479, + 0.842, + 0.496 + ], + "angle": 0, + "content": "5.2. Training & Sampling Efficiency Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.806 + ], + "angle": 0, + "content": "In this subsection, we further demonstrate the superiority of our method by comparing the training and sampling efficiency under comparable image generation quality. Specifically, in Tab. 2, we present the number of training iterations, GFLOPs, and total training PFLOPs of our approach, DPM-solver, EDM, and LDM using CIFAR-10 and CelebA datasets. Using the CIFAR-10 dataset, our multistage DPM-solver achieves similar FID scores (2.71 vs 2.73) while requiring nearly half the training iterations when compared to the vanilla DPM-solver. For the case of EDM (resp. LDM), our approach returns an FID score of 1.44 (resp. 8.29), requiring \\(1.4 \\times 10^{5}\\) (\\(3.2 \\times 10^{5}\\)) less iterations when compared to vanilla DPM-solver (resp. LDM). For the cases of DPM-solver and EDM, we can achieve a substantial reduction of training iterations, which is demonstrated by a marginal increase in the number of GFLOPs. For the LDM case, we also achieve a significant reduction of both training iterations and GFLOPs. These promising results highlight the significantly improved computational efficiency achieved by using the proposed multistage framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.834, + 0.833 + ], + "angle": 0, + "content": "5.3. Comparison of Different Architectures" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In Sec. 3, we highlighted the limitations of both unified and separate diffusion model architectures in terms of training efficiency (see Fig. 2). In this part, we further illustrate these limitations through extensive experiments as shown" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "2Here we simplify it by ignoring the FLOPs for backward propagation, which is approximately proportional to FLOPs of forward evaluation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7378" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.302, + 0.09, + 0.668, + 0.104 + ], + "angle": 0, + "content": "Table 2. Training and Sampling Efficiency on More Datasets." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.113, + 0.855, + 0.214 + ], + "angle": 0, + "content": "
DatasetMethodTraining Iterations(↓)GFLOPs(↓)Total Training PFLOPs(↓)FID(↓)
CIFAR-10DPM-Solver [18]4.5 × 10517.657.942.73
32 × 32Multistage DPM-Solver (Ours)2.5 × 105(56%)18.65 (106%)4.66 (59%)2.71
CelebAEDM [18]5.7 × 10517.6510.061.55
32 × 32Multistage EDM (Ours)4.3 × 105(75%)19.25 (109%)8.28 (82%)1.44
CelebALDM [8]4.9 × 10588.3943.318.29
256 × 256Multistage LDM (Ours)1.7 × 105(35%)76.19 (86%)12.95 (30.0%)8.38
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.238, + 0.47, + 0.419 + ], + "angle": 0, + "content": "in Tab. 3. Here, we use the U-Net architecture, trained on the CIFAR-10 dataset, and utilize the DPM-Solver for sampling. For the unified case, we use a single U-Net model with 128 channels. For the separate case, three distinct U-Nets with 128 channels are used. For improved performance of the separate architecture, we implement two techniques: early stopping (ES) and tailored parameters (TP) to tackle the overfitting and parameter inefficiency discussed in Sec. 3. Under ES, the criteria is to stop training prior to overfitting. For TP, the three U-Nets are configured with 192, 128, and 16 channels decoders for Intervals 0, 1, and 2, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.471, + 0.648 + ], + "angle": 0, + "content": "Our comparison and analysis in Tab. 3 reveal notable insights of our network design. Comparisons between the 2nd and 3rd rows (and between the 4th and 5th rows) on the separate architectures indicate that early stopping effectively mitigates overfitting and enhances generation quality. When comparing the 2nd and 4th rows (as well as the 3rd and 5th rows) on the separate architectures, we observe that optimizing parameter usage can achieve a significant decrease in FID under comparable GFLOPs. Most importantly, our multistage architecture, as shown in the 6th row, benefits from both unified and separate architectures, achieving the best FID (2.35, compared to 2.73 and 2.52). Comparing the 2nd row and the 4th row, the shared encoder not only prevents overfitting but also improves the convergence of the diffusion model as reported by the FID scores." + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.66, + 0.468, + 0.675 + ], + "angle": 0, + "content": "Table 3. Ablation study on different diffusion model architectures." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.686, + 0.428, + 0.821 + ], + "angle": 0, + "content": "
MethodGFLOPsFID(↓)
Unified17.652.73
Separate17.652.87
Separate (+ ES)17.652.80
Separate (+ TP)18.652.68
Separate (+ ES, TP)18.652.52
Multistage (Ours)18.652.35
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.46, + 0.864 + ], + "angle": 0, + "content": "5.4. Comparison of Timestep Clustering Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.903 + ], + "angle": 0, + "content": "As previously stated in Sec. 2, various timestep clustering methods are proposed including timestep-based, SNR-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.892, + 0.405 + ], + "angle": 0, + "content": "based, and gradient-based clustering approaches [20, 21]. In this subsection, we conduct an experiment to demonstrate the superiority of our clustering method compared to previous arts. Specifically, we apply the clustering methods in [20, 21] to partition the interval along with our proposed multistage UNet architecture. The computed intervals are shown in the Tab. 4. We use the multistage DPM-Solver with these different intervals trained on the CIFAR-10 dataset. As observed, our optimal denoiser-based clustering method achieves the highest FID score, consistently outperforming all other clustering methods." + }, + { + "type": "table_caption", + "bbox": [ + 0.529, + 0.416, + 0.862, + 0.43 + ], + "angle": 0, + "content": "Table 4. Ablation study on different clustering methods." + }, + { + "type": "table", + "bbox": [ + 0.54, + 0.44, + 0.851, + 0.535 + ], + "angle": 0, + "content": "
Clustering Methodt1t2FID(↓)
Timestep [20, 21]0.3300.6703.12
SNR [20]0.3480.7092.72
Gradient [20]0.3600.6602.75
Optimal Denoiser0.4420.6312.35
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.755, + 0.575 + ], + "angle": 0, + "content": "6. Conclusion & Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.719 + ], + "angle": 0, + "content": "In this paper, we introduced a novel multi-stage framework for diffusion models (DM) to improve the training and sampling efficiency. We proposed an algorithm that divides the timestep into several stages. Based on these stages, we designed a stage-specific multi-decoder U-net architecture and a shared encoder across all stages. We conducted thorough numerical experiments with several SOTA diffusion model frameworks and confirmed the effectiveness of our strategy using small scale and large scale datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In future research, it would be interesting to expand our multi-stage approach beyond unconditional diffusion models by considering conditional DMs and DM-based inverse problems solvers. Our experiment in Sec. 5.2 demonstrate that training latent diffusion models within our multi-stage framework requires only \\(30\\%\\) of the computational effort needed for training standard latent diffusion models on the CelebA dataset. Thus, employing a multi-stage strategy could significantly reduce the computational demands for training large-scale stable diffusion models, such as those described in [8], which typically requires significant computations." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7379" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020. 1, 2, 3, 5, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.225 + ], + "angle": 0, + "content": "[2] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 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Overview of three diffusion model architectures: (a) unified, (b) separate, and (c) our proposed multistage architecture. Compared with (a) and (b), our approach improves sampling quality, and significantly enhances training efficiency, as indicated by the FID scores and their corresponding training iterations (d). + +![](images/62fdc19d83e16c6ea50fe22f2a67f124b0c0d9f8e92467a0db4b28e72868c4e2.jpg) +(d) + +# Abstract + +Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new samples (e.g., images). However, their remarkable generative performance is hindered by slow training and sampling. This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i.e., noise levels). To tackle these challenges, we present a multi-stage framework inspired by our empirical findings. These observations indicate the advantages of employing distinct parameters tailored to each timestep while retaining universal parameters shared across all time steps. Our approach involves segmenting the time interval into multiple stages where we employ custom multi-decoder U-net architecture that blends time-dependent models with a universally shared encoder. Our framework enables the + +efficient distribution of computational resources and mitigates inter-stage interference, which substantially improves training efficiency. Extensive numerical experiments affirm the effectiveness of our framework, showcasing significant training and sampling efficiency enhancements on three state-of-the-art diffusion models, including large-scale latent diffusion models. Furthermore, our ablation studies illustrate the impact of two important components in our framework: (i) a novel timestep clustering algorithm for stage division, and (ii) an innovative multi-decoder U-net architecture, seamlessly integrating universal and customized hyperparameters. + +# 1. Introduction + +Recently, diffusion models have made remarkable progress as powerful deep generative modeling tools, showcasing remarkable performance in various applications, ranging from unconditional image generation [1, 2], conditional image generation [3, 4], image-to-image translation [5-7], text-to-image generation [8-10], inverse problem solving [11-14], + +video generation [15, 16], and so on. These models employ a training process involving continuous injection of noise into training samples ("diffusion"), which are then utilized to generate new samples, such as images, by transforming random noise instances through a reverse diffusion process guided by the "score function" of the data distribution learned by the model. Moreover, recent work demonstrates that those diffusion models enjoy optimization stability and model reproducibility compared with other types of generative models [17]. However, diffusion models suffer from slow training and sampling despite their remarkable generative capabilities, which hinders their use in applications where real-time generation is desired [1, 2]. These drawbacks primarily arise from the necessity of tracking extensive forward and reverse diffusion trajectories, as well as managing a large model with numerous parameters across multiple timesteps (i.e., diffusion noise levels). + +In this paper, we address these challenges based on two key observations: (i) there exists substantial parameter redundancy in current diffusion models, and (ii) they are trained inefficiently due to dissimilar gradients across different noise levels. Specifically, we find that training diffusion models require fewer parameters to accurately learn the score function at high noise levels, while larger parameters are needed at low noise levels. Furthermore, we also observe that when learning the score function, distinct shapes of distributions at different noise levels result in dissimilar gradients, which appear to slow down the training process driven by gradient descent. + +Building on these insights, we propose a multi-stage framework with two key components: (i) a multi-decoder U-net architecture, and (ii) a new partitioning algorithm to cluster timesteps (noise levels) into distinct stages. In terms of our new architecture, we design a multi-decoder U-Net that incorporates one universal encoder shared across all intervals and individual decoders tailored to each time stage; see Figure 1 (c) for an illustration. This approach combines the advantages of both universal and stage-specific architectures, which is much more efficient than the unified architecture for the entire training process [1, 2, 18] (Figure 1 (a)). Moreover, compared to previous approaches that completely separate architectures for each sub-interval [19-22] (Figure 1 (b)), our approach can effectively mitigate overfitting, leading to improved training efficiency. On the other hand, when it comes to partitioning the training stages of our network, we designed an algorithm aimed at grouping the timesteps. This is achieved by minimizing the functional distance within each cluster in the training objective and making use of the optimal denoiser formulation [18]. By integrating these two key components, our framework enables efficient allocation of computational resources (e.g., U-net parameters) and stage-tailored parameterization. Throughout our extensive numerical experi + +ments (Section 5), we show that out framework effectively improves both training and sampling efficiency. These experiments are performed on diverse benchmark datasets, demonstrating significant acceleration by using our framework when compared to three state-of-the-art (SOTA) diffusion model architectures. As a summary, the major contributions of this work can be highlighted as follows: + +- Identifying two key sources of inefficiency. We identified two key sources that cause inefficiencies in training diffusion models across various time steps: (i) a significant variation in the requirement of model capacity, and (ii) the gradient dissimilarity. As such, using a unified network cannot meet with the changing requirement at different time steps. + +- A new multi-stage framework. We introduced a new multi-stage architecture, illustrated in Fig. 1 (c). We tackle these two sources of inefficiency by segmenting the time interval into multiple stages, where we employ customized multi-decoder U-net architectures that blends time-dependent models with a universally shared encoder. + +- Improved training and sampling efficiency. With comparable computational resources for unconditional image generation, we demonstrate that our multi-stage approach improves the Fréchet Inception Distance (FID) score for all SOTA methods. For example, on CIFAR-10 dataset [23], our method improves the FID for DPM-Solver [24] from 2.84 to 2.37, and it improves the FID for EDM [18] from 2.05 (our training result) to 1.96. Moreover, on the CelebA dataset [25], while maintaining a similar generation quality, our approach significantly reduces the required training FLOPS of EDM by $82\%$ and the Latent Diffusion Model (LDM) [8] by $30\%$ . + +Organization. In Sec. 2, we provide preliminaries and an overview of related literatures. In Sec. 3, we present our observations and analysis that motivated the proposed multistage framework, justifying its development. In Sec. 4, we describe our proposed multistage framework for diffusion models, outlining the two core components. Finally, in Sec. 5, we provide the results from our numerical experiments that validate the effectiveness of the proposed multistage approach. + +# 2. Preliminaries & Related Work + +In this section, we start by reviewing the basic fundamentals of diffusion models [1, 2, 18]. Subsequently, we delve into prior approaches aimed at improving the training and efficiency of diffusion models through the partitioning of the timestep interval. Lastly, we survey prior studies that significantly decrease the number of required sampling iterations. + +Background on diffusion models. Let $\pmb{x}_0 \in \mathbb{R}^n$ denote a sample from the data distribution $p_{\mathrm{data}}(\pmb{x})$ . Diffu + +sion models operate within forward and reverse processes. The forward process progressively perturbs data $\boldsymbol{x}_0$ to a noisy version $\boldsymbol{x}_{t\in [0,1]}$ via corrupting with the Gaussian kernel. This process can be formulated as a stochastic differential equation (SDE) [2] of the form $\mathrm{d}\boldsymbol {x} = \boldsymbol {x}_t f(t)\mathrm{d}t + g(t)\mathrm{d}\boldsymbol{w}_t$ , where $f(t)$ and $g(t)$ are the drift and diffusion coefficients, respectively, that correspond to a pre-defined noise schedule. $\boldsymbol{w}_t\in \mathbb{R}^n$ is the standard Wiener process. Under the forward SDE, the perturbation kernel is given by the conditional distribution defined as $p_t(\boldsymbol {x}_t|\boldsymbol {x}_0) = \mathcal{N}(\boldsymbol {x}_t;s_t\boldsymbol {x}_0,s_t^2\sigma_t^2\mathbf{I})$ , where + +$$ +s _ {t} = \exp \left(\int_ {0} ^ {t} f (\xi) \mathrm {d} \xi\right), \text {a n d} \sigma_ {t} = \sqrt {\int_ {0} ^ {t} \frac {g ^ {2} (\xi)}{s _ {\xi} ^ {2}} \mathrm {d} \xi}. \tag {1} +$$ + +The parameters $s_t$ and $\sigma_t$ are designed such that: (i) the data distribution is approximately estimated when $t = 0$ , and (ii) a nearly standard Gaussian distribution is obtained when $t = 1$ . The objective of diffusion models is to learn the corresponding reverse SDE, defined as $\mathrm{d}\pmb{x} = \left[f(t)\pmb{x}_t - g^2(t)\nabla_{\pmb{x}_t}\log p_t(\pmb{x}_t)\right]\mathrm{d}t + g(t)\mathrm{d}\bar{\pmb{w}}$ , where $\bar{\pmb{w}} \in \mathbb{R}^n$ is the standard Wiener process running backward in time, and $\nabla_{\pmb{x}_t}\log p_t(\pmb{x}_t)$ is the (Stein) score function. In practice, the score function is approximated using a neural network $\epsilon_{\theta}:\mathbb{R}^n\times [0,1]\to \mathbb{R}^n$ parameterized by $\pmb{\theta}$ , which can be trained by the denoising score matching technique [26] as + +$$ +\min _ {\boldsymbol {\theta}} \mathbb {E} \left[ \omega (t) \| \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, t) + s _ {t} \sigma_ {t} \nabla_ {\boldsymbol {x} _ {t}} \log p _ {t} (\boldsymbol {x} _ {t} | \boldsymbol {x} _ {0}) \| _ {2} ^ {2} \right], \tag {2} +$$ + +which can also be written as $\min_{\pmb{\theta}}\mathbb{E}[\omega (t)||\pmb{\epsilon}_{\pmb{\theta}}(\pmb{x}_t,t) - \pmb{\epsilon}||^2 ] + C$ , where the expectation is taken over $t\sim [0,1]$ , $\pmb{x}_t\sim p_t(\pmb{x}_t|\pmb{x}_0)$ , $\pmb{x}_0\sim p_{\mathrm{data}}(\pmb {x})$ , and $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ . Here, $C$ is a constant independent of $\pmb{\theta}$ , and $\omega (t)$ is a scalar representing the weight of the loss as a function of $t$ . In DDPM [1], it is simplified to $\omega (t) = 1$ . Once the parameterized score function $\epsilon_{\theta}$ is trained, it can be utilized to approximate the reverse-time SDE using numerical solvers such as Euler-Maruyama. + +Timestep clustering methods. Diffusion models have demonstrated exceptional performance but face efficiency challenges in training and sampling. In response, several studies proposed to cluster the timestep range $t \in [0,1]$ into multiple intervals (e.g., $[0,t_1),[t_1,t_2),\ldots ,[t_n,1]$ ). Notably, Choi et al. [19] reconfigured the loss weights for different intervals to enhance performance. Deja et al. [27] divide the entire process into a denoisr and a generator based on their functionalities. Balaji et al. [28] introduced "expert denoisers", which proposed using distinct architectures for different time intervals in text-to-image diffusion models. Go et al. [22] further improved the efficiency of these expert denoisers through parameter-efficient fine-tuning and data-free knowledge transfer. Lee et al. [21] designed separate + +architectures for each interval based on frequency characteristics. Moreover, Go et al. [20] treated different intervals as distinct tasks and employed multi-task learning strategies for diffusion model training, along with various timestep clustering methods. + +Our approach distinguishes itself from the aforementioned methods in two key aspects. The first key component is our tailored U-net architecture using a unified encoder coupled with different decoders for different intervals. Previous models have either adopted a unified architecture, as seen in [19, 20], or employed separate architectures (referred to as expert denoisers) for each interval [21, 22, 28]. In comparison, our multistage architecture surpasses these methodologies, as demonstrated in Sec. 5.3. Second, we developed a new timestep clustering method leveraging a general optimal denoiser (Prop. 1) that showcases superior performance (see Sec. 5.4). In contrast, prior works rely on (i) a simple timestep-based clustering cost function [20-22, 28], (ii) Signal-to-Noise Ratio (SNR) based clustering [20], or (iii) gradients-based partitioning that uses task affinity scores [20]. + +Reducing the sampling iterations methods. Efforts to improve sampling efficiency of diffusion models have led to many recent advancements in SDE and Ordinary Differential Equation (ODE) samplers [2]. For instance, the Denoising Diffusion Implicit Model (DDIM) [29] formulates the forward diffusion as a non-Markovian process with a deterministic generative path, significantly reducing the number of function evaluations (NFE) required for sampling (from thousands to hundreds). Generalized DDIM (gDDIM) [30] further optimized DDIM by modifying the parameterization of the scoring network. Furthermore, the works in [24] and [31], termed the Diffusion Probabilistic Model solver (DPM-solver) and the Diffusion Exponential Integrator Sampler (DEIS), respectively, introduced fast higher-order solvers, employing exponential integrators that require 10s NFE for comparable generation quality. Moreover, the consistency model [32] introduced a novel training loss and parameterization, achieving high-quality generation with merely 1-2 NFE. + +We remark that while the aforementioned methods are indirectly related to our work, our experiments in Sec. 5.1 and Sec. 5.2 show that our approach can be easily integrated into these techniques, further improving diffusion models' overall training and sampling efficiency. + +# 3. Identification of Key Sources of Inefficiency + +Conventional diffusion model architectures, as exemplified by [1, 2, 18], treat the training of the diffusion model as a unified process across all timesteps. Recent researches, such as [19-22], have highlighted the benefits of recognizing distinctions between different timesteps and the poten + +tial efficiency gains from treating them as separate tasks during the training process. However, our experimental results demonstrate that both unified and separate architectures suffer inefficiency for training diffusion models, where the inefficiency comes from (i) overparameterization, (ii) gradient dissimilarity, and (iii) overfitting. + +# 3.1. Empirical Observations on the Key Sources of Inefficiency + +To illustrate the inefficiency in each interval, we isolate the interval by using a separate architecture from the rest. + +Experiment setup. In our experiments, we consider three-stage training and divide the time steps into three intervals: $[0, t_1), [t_1, t_2), [t_2, 1]^1$ . Let $(\epsilon_{\theta})_i^{[a,b]}, 0 \leq a < b \leq 1$ denote a U-Net architecture with parameter $\theta$ trained with $i$ iterations and fed with data pairs $(x_t, t)$ , where $t \in [a,b]$ . We then train models using two different strategies: a unified architecture with 108M network parameters for all intervals, i.e., $(\epsilon_{\theta})_i^{[0,1]}$ , and separate architectures with varying network parameters (e.g., 47M, 108M, 169M) for each interval; e.g., $(\epsilon_{\theta})_i^{[0,t_1)}$ for the interval $[0,t_1)$ , etc. It is worth noting that, apart from the differences in network parameters, we utilize the same network architecture (e.g., U-Net) for both the unified and the separate approaches. We assessed the training progress of each model by evaluating image generation quality at different training iterations. Notably, because some of the models are only trained on one interval, we need to provide a ground truth score for the other intervals. In Fig. 2, the sampling process is shown top and the experimental results are shown bottom. + +Inefficiency in unified architectures. From Fig. 2, we observe the following: + +- Overparameterization and underfitting emerge simultaneously for unified architectures. In Fig. 2a, we observe that increasing the number of parameters in Interval 0 can improve the image generation quality (as indicated by a lower FID score). In contrast, Fig. 2b reveals that increasing the number of parameters in Interval 2 has minimal impact on the quality of image generation. This implies that using a unified architecture will result in underfitting in Interval 0 and overparameterization in Interval 2. The current unified architecture's parameter redundancy leaves significant room for improving its efficiency. To optimize the computational usage, we should allocate more parameters to Interval 0 while allocating fewer parameters to Interval 2. +- Gradient dissimilarity hinders training for unified architecture. Quantitative results from [20] demonstrate dissimilarity in gradients caused by differences within each interval. This can also be observed from our results based + +upon both Fig. 2a and Fig. 2b. For the unified and separate architectures using the same number of parameters (108M), separate architecture achieves a significantly lower FID with the same training iterations, implying that dissimilar gradients among intervals may hinder training when using a unified architecture. Here, the only difference between training separate and unified architectures is that the batch gradient for unified architecture is calculated based on all timesteps while the batch gradien2 for separate architecture is calculated only from a specific interval. + +Inefficiency in existing separate architectures. Although separated architecture [19, 21, 22] better allocates computational resources for each interval, it suffers from overfitting. This can be illustrated based upon training separate architectures (169M) and (108M) in Interval 0 shown in Fig. 2a, where increasing the number of parameters will lead to overfitting. This also happens in Interval 2, when we compare all separate architectures in Fig. 2b. In comparison, the unified networks with 108M parameters are less prone to overfitting for both Interval 0 and Interval 2. This suggests that we can reduce overfitting by training shared weights across different intervals together. + +# 3.2. Tackling the Inefficiency via Multistage U-Net Architectures + +In a unified architecture applied across all timesteps, there is often a dual challenge: requirements for more parameters (169M) in the interval $[0, t_1)$ but fewer parameters (47M) in the interval $[t_2, 1]$ . This issue is compounded by the gradient dissimilarity across different timesteps, which can impede effective training. Alternatively, employing separate architectures for different intervals might lead to overfitting and a lack of robust early stopping mechanisms. To address these challenges, our proposed multistage architecture in Sec. 4 combines shared parameters to reduce overfitting with interval-specific parameters to mitigate the impact of gradient dissimilarity. This tailored approach for each interval ensures improved adaptability. Furthermore, we conduct an in-depth ablation study in Sec. 5.3 to showcase the effectiveness of our multi-stage architecture over the existing models. + +# 4. Proposed Multistage Framework + +In this section, we introduce our new multistage framework (as illustrated in Fig. 1 (c)). Specifically, we first introduce the multi-stage U-Net architecture design in Sec. 4.1, following a new clustering method for choosing the optimal interval to partition the entire timestep [0, 1] into intervals in Sec. 4.2., and discuss the rationale of the proposed architecture in Sec. 4.3. + +![](images/a7f05e825ef767cb2e1911201bf99b4652428f823de776cfb9b43dd1dd2029f9.jpg) +(a) Analysis on interval $[0, t_1)$ + +![](images/92f94ab5b87d8b6dc50c15aa21be981ed618a51747dbcb8c453c0d9e1ea78432.jpg) +(b) Analysis on interval $[t_2, 1]$ +Figure 2. Comparison between separate architecture and unified architecture w.r.t. the image generation quality in different intervals: (a) analysis on interval $[0, t_1)$ ; and (b) analysis on interval $[t_2, 1]$ . As illustrated on top of each figure, we only train separate architectures within specific intervals for the sampling process in both (a) and (b). For the remaining period of sampling, we use a well-trained diffusion model $(\epsilon_{\theta})_{4 \times 10^5}^{[0,1]}$ to approximate the ground truth score function. As shown in the above figure of (a), e.g. for the separate architecture on interval 1, sampling utilizes trained model $(\epsilon_{\theta'})_i^{[0,t_1)}$ for interval 0 and well-trained model $(\epsilon_{\theta})_{4 \times 10^5}^{[0,1]}$ for interval 1 and 2. Notably, for both $(\epsilon_{\theta})_i^{[0,1]}$ and $(\epsilon_{\theta})_{4 \times 10^5}^{[0,1]}$ , we are using the model with 108M parameters. For separate architecture, the number in the parentheses represents the number of parameters of the model $(\epsilon_{\theta'})_i^{[a,b]}$ . For example, for separate architecture (169M) in (a), the model $(\epsilon_{\theta'})_i^{[0,t_1)}$ has 169M parameters for $\theta'$ . The bottom figures in (a-b) illustrate the FID of the generation from each architecture under different training iterations. + +# 4.1. Proposed Multi-stage U-Net Architectures + +As discussed in Sec. 3, most existing diffusion models either employ a unified architecture across all intervals [1, 2, 18] to share features for all timesteps, or use completely separate architectures for different timestep intervals [21, 22, 28] where the goal is to take advantage of the benign properties within different intervals. + +To harness the advantages of both unified and separate architectures employed in prior studies, we introduce a multistage U-Net architecture, as illustrated in Figure 1(c). Specifically, we partition the entire timestep $[0,1]$ into several intervals, e.g., three intervals $[0,t_1),[t_1,t_2),[t_2,1]$ in Fig. 1. For the architecture, we introduce: + +- One shared encoder across all time intervals. For each timestep interval, we implement a shared encoder architecture (plotted in blue in Fig. 1 (c)), which is similar to the architecture employed in the original U-Net framework [33]. Unlike separate architecture, the shared encoder provides shared information across all timesteps, preventing models from overfitting (see Sec. 5.3 for a discussion). +- Separate decoders for different time intervals. Motivated by the multi-head structure introduced in the Mask Region-based Convolutional Neural Networks (MaskRCNN) method [34], we propose to use multiple distinct decoders (plotted in colors for different intervals in Fig. 1(c)), where each decoder is tailored to a spe + +cific timestep interval. The architecture of each decoder closely resembles the one utilized in [2], with deliberate adjustments made to the embedding dimensions to optimize performance. + +As we observe, the primary difference in the architecture resides within the decoder structure. Intuitively, we use a decoder with fewer number of parameters for intervals closer to the noise, because the learning task is easier. We use a decoder with a larger number of parameters for intervals closer to the image. + +# 4.2. Optimal Denoiser-based Timestep Clustering + +Next, we discuss how we principally choose the interval partition time points in practice. For simplicity, we focus on the case where we partition the time $[0,1]$ into three intervals $[0,t_1],[t_1,t_2],[t_2,1]$ , and we develop a timestep clustering method to choose the optimal $t_1$ and $t_2$ . Of course, our method can be generalized to multi-stage networks with arbitrary interval numbers. However, in practice, we find that the choice of three intervals strikes a good balance between effectiveness and complexity; see our ablation study in Appendix B.6. + +To partition the time interval, we employ the optimal denoiser established in Proposition 1. + +Proposition 1. Suppose we train a diffusion model denoiser function $\epsilon_{\theta}(\pmb{x},t)$ with parameters $\pmb{\theta}$ using dataset + +# Algorithm 1 Optimal Denoiser based Timestep Clustering + +1: Input: Total samples $K$ , optimal denoiser function $\pmb{\epsilon}_{\pmb{\theta}}^{*}(\pmb{x},t)$ , thresholds $\alpha, \eta$ , dataset $p_{\mathrm{data}}$ , $S_0 = S_1 = \emptyset$ +2: Output: Timesteps $t_1, t_2$ +3: for $k \in \{1, \dots, K\}$ do +4: $\pmb{y}_k\sim p_{\mathrm{data}},\pmb{\epsilon}_k\sim \mathcal{N}(0,\mathbf{I}),t_k\sim [0,1]$ +5: $\mathcal{S}_0^k\gets \mathcal{D}(\pmb{\epsilon}_{t_k}^*,\pmb{\epsilon}_0^*,\pmb {y}_k,\pmb {\epsilon}_k),\mathcal{S}_1^k\gets \mathcal{D}(\pmb{\epsilon}_{t_k}^*,\pmb {\epsilon}_1^*,\pmb {y}_k,\pmb {\epsilon}_k)$ +6: $\mathcal{S}_0\gets \mathcal{S}_0\cup \{\big(t_k,\mathcal{S}_0^k\big)\} ,\mathcal{S}_1\gets \mathcal{S}_1\cup \{\big(t_k,\mathcal{S}_1^k\big)\}$ +7: end for +8: $t_1 = \arg \max_{\tau}\left\{\tau \Big|\frac{\sum_{(t_k,\mathcal{S}_0^k)\in\mathcal{S}_0}\big[\mathcal{S}_0^k\cdot\mathbb{1}(t_k\leq\tau)\big]}{\sum_{(t_k,\mathcal{S}_0^k)\in\mathcal{S}_0}[\mathbb{1}(t_k\leq\tau)]}\geq\alpha\right\}$ +9: $t_2 = \arg \min_{\tau}\left\{\tau \Big|\frac{\sum_{(t_k,\mathcal{S}_1^k)\in\mathcal{S}_0}\big[\mathcal{S}_1^k\cdot\mathbb{1}(t_k\geq\tau)\big]}{\sum_{(t_k,\mathcal{S}_1^k)\in\mathcal{S}_0}[\mathbb{1}(t_k\geq\tau)]}\geq\alpha\right\}$ + +$$ +\left\{\boldsymbol {y} _ {i} \in \mathbb {R} ^ {n} \right\} _ {i = 1} ^ {N} b y +$$ + +$$ +\min _ {\boldsymbol {\theta}} \mathcal {L} (\boldsymbol {\epsilon} _ {\boldsymbol {\theta}}; t) = \mathbb {E} _ {\boldsymbol {x} _ {0}, \boldsymbol {x} _ {t}, \epsilon} [ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, t) \| ^ {2} ], \tag {3} +$$ + +where $\pmb{x}_0\sim p_{data}(\pmb {x}) = \frac{1}{N}\sum_{i = 1}^{N}\delta (\pmb {x} - \pmb {y}_i)$ $\epsilon \sim \mathcal{N}(0,\pmb {I})$ and $\pmb{x}_{t}\sim p_{t}(\pmb{x}_{t}|\pmb{x}_{0}) = \mathcal{N}(\pmb{x}_{t};s_{t}\pmb{x}_{0},s_{t}^{2}\sigma_{t}^{2}\pmb {I})$ with perturbation parameters $s_t$ and $\sigma_t$ defined in Eq. (1). Then, the optimal denoiser at $t$ defined as $\epsilon_{\theta}^{*}(\pmb {x};t) = \arg \min_{\epsilon_{\theta}}\mathcal{L}(\epsilon_{\theta};t)$ is given by + +$$ +\boldsymbol {\epsilon} _ {\boldsymbol {\theta}} ^ {*} (\boldsymbol {x}; t) = \frac {1}{s _ {t} \sigma_ {t}} \left[ \boldsymbol {x} - s _ {t} \frac {\sum_ {i = 1} ^ {N} \mathcal {N} (\boldsymbol {x} ; s _ {t} \boldsymbol {y} _ {i} , s _ {t} ^ {2} \sigma_ {t} ^ {2} \boldsymbol {I}) \boldsymbol {y} _ {i}}{\sum_ {i = 1} ^ {N} \mathcal {N} (\boldsymbol {x} ; s _ {t} \boldsymbol {y} _ {i} , s _ {t} ^ {2} \sigma_ {t} ^ {2} \boldsymbol {I})} \right]. \tag {4} +$$ + +The proof is provided in Appendix A, and the result can be generalized from recent work of Karras et al. [18], extending from a specific kernel $p_t(\boldsymbol{x}_t|\boldsymbol{x}_0) = \mathcal{N}(\boldsymbol{x}_t; \boldsymbol{x}_0, \sigma_t^2\mathbf{I})$ to encompassing a broader scope of noise perturbation kernels, given by $p_t(\boldsymbol{x}_t|\boldsymbol{x}_0) = \mathcal{N}(\boldsymbol{x}_t; s_t\boldsymbol{x}_0, s_t^2\sigma_t^2\mathbf{I})$ . For brevity, we simplify the notation of the optimal denoiser $\epsilon_{\theta}^{*}(\boldsymbol{x}, t)$ in Proposition 1 as $\epsilon_t^*(\boldsymbol{x})$ . + +To obtain the optimal interval, our rationale is to homogenize the regression task as much as possible within each individual time interval. To achieve this goal, given sampled $\pmb{x}_0, \pmb{\epsilon}$ , we define the function distance of the optimal denoiser at any given timestep $t_a, t_b$ as: + +$$ +\mathcal {D} \left(\boldsymbol {\epsilon} _ {t _ {a}} ^ {*}, \boldsymbol {\epsilon} _ {t _ {b}} ^ {*}, \boldsymbol {x} _ {0}, \boldsymbol {\epsilon}\right) = \frac {1}{n} \sum_ {i = 1} ^ {n} \mathbb {1} \left(\left| \boldsymbol {\epsilon} _ {t _ {a}} ^ {*} \left(\boldsymbol {x} _ {t _ {a}}\right) - \boldsymbol {\epsilon} _ {t _ {b}} ^ {*} \left(\boldsymbol {x} _ {t _ {b}}\right) \right| _ {i} \leq \eta\right), +$$ + +where $\mathbb{1}(\cdot)$ is the indicator function, $\eta$ is a pre-specified threshold, $\pmb{x}_{t_a} = s_{t_a}\pmb{x}_0 + s_{t_a}\sigma_{t_a}\pmb{\epsilon}$ , and $\pmb{x}_{t_b} = s_{t_b}\pmb{x}_0 + s_{t_b}\sigma_{t_b}\pmb{\epsilon}$ . Consequently, we define the functional similarity of the optimal denoiser at timesteps $t_a$ and $t_b$ as: + +$$ +\mathcal {S} \left(\boldsymbol {\epsilon} _ {t _ {a}} ^ {*}, \boldsymbol {\epsilon} _ {t _ {b}} ^ {*}\right) = \mathbb {E} _ {\boldsymbol {x} _ {0} \sim p _ {\mathrm {d a t a}}} \mathbb {E} _ {\boldsymbol {\epsilon} \sim \mathcal {N} (0, \mathbf {I})} \left[ \mathcal {D} \left(\boldsymbol {\epsilon} _ {t _ {a}} ^ {*}, \boldsymbol {\epsilon} _ {t _ {b}} ^ {*}, \boldsymbol {x} _ {0}, \boldsymbol {\epsilon}\right) \right]. \tag {5} +$$ + +Based upon the definition, we design the following optimization problem to find the largest $t_1$ and smallest $t_2$ as: + +$$ +t _ {1} \leftarrow \underset {\tau} {\arg \max } \left\{\tau \left| \mathbb {E} _ {t \sim [ 0, \tau)} \left[ \mathcal {S} \left(\boldsymbol {\epsilon} _ {t} ^ {*}, \boldsymbol {\epsilon} _ {0} ^ {*}\right) \right] \geq \alpha \right. \right\}, \tag {6} +$$ + +$$ +t _ {2} \leftarrow \underset {\tau} {\arg \min } \left\{\tau \left| \mathbb {E} _ {t \sim [ \tau , 1 ]} \left[ \mathcal {S} \left(\boldsymbol {\epsilon} _ {t} ^ {*}, \boldsymbol {\epsilon} _ {1} ^ {*}\right) \right] \geq \alpha \right. \right\}, \tag {7} +$$ + +such that the average functional similarity of $\pmb{\epsilon}_t^*$ (resp. $\pmb{\epsilon}_t^*$ ) to $\pmb{\epsilon}_0^*$ (resp. $\pmb{\epsilon}_1^*$ ) in $[0, t_1)$ (resp. $[t_2, 1]$ ) is larger than or equal to a pre-defined threshold $\alpha$ . As the above optimization problems are intractable, we propose the procedure outlined in Algorithm 1 to obtain an approximate solution. In particular, the algorithm samples $K$ pairs $(\pmb{y}_k, \pmb{\epsilon}_k, t_k), k \in \{1, \dots, K\}$ to calculate the distances $\mathcal{D}(\pmb{\epsilon}_{t_k}^*, \pmb{\epsilon}_0^*, \pmb{y}_k, \pmb{\epsilon}_k)$ and $\mathcal{D}(\pmb{\epsilon}_{t_k}^*, \pmb{\epsilon}_1^*, \pmb{y}_k, \pmb{\epsilon}_k)$ (step 6). Based on those distances, we solve the optimization problems defined in the lines 8 and 9 of Algorithm 1 to obtain $t_1$ and $t_2$ . + +# 4.3. Rationales for the proposed architecture + +Finally, we summarize the rationales of our proposed architecture based on the empirical observations in Sec. 3 and previous works. + +Rationales for the shared encoder. (i) Prevent overfitting: If we treat training separate stages of diffusion models as multi-task learning, [35] suggests that shared parameters across tasks in multi-task learning can mitigate overfitting. (ii) Maintain consistency in $h$ -space. The output of the encoder for UNet is named as $h$ -space [36], which has properties for semantic manipulation such as homogeneity, linearity, robustness, and consistency across timesteps. Therefore, sharing the encoder can maintain better consistency of the $h$ -space among all timesteps compared to separate encoders. + +Rationales for network parameter design. First, we provide some intuitions as to why the learning task at $t = 0$ is harder than that at $t = 1$ . Suppose diffusion models could converge to the optimal denoiser $\epsilon_{\theta}^{*}(\boldsymbol{x}_t,t)$ given in Eq. (4). Based on this, we observe: (i) when $t \to 0$ , we have $\boldsymbol{x}_{t \to 0} = \boldsymbol{x}_0$ , $\epsilon_{\theta}^{*}|_{t \to 0} = \epsilon$ , so that $\epsilon_{\theta}^{*}$ is a complicated mapping from training data distribution $p_{\mathrm{data}}(\boldsymbol{x})$ to the gaussian distribution; (ii) when $t \to 1$ , we have $\boldsymbol{x}_{t \to 1} = \epsilon$ , $\epsilon_{\theta}^{*}|_{t \to 1} = \epsilon$ , so $\epsilon_{\theta}^{*}$ is an identity mapping. The two extreme cases reveal that the identity mapping for $t \to 1$ (close to noise) is easier to learn than that for $t \to 0$ . Second, our choice of network parameters across different stages share similar spirits with the recent work [37], which employs a high dimensional subspace as $t \to 0$ and gradually decreases the dimensionality of each subspace until $t = 1$ . + +# 5. Experiments + +In this section, we start by providing the experimental setups. Next, we present results in terms of generation quality (Sec. 5.1). Subsequently, results for training and sampling efficiency are presented. Finally, in Sec. 5.3 and + +Sec. 5.4, comprehensive ablation studies on timestep clustering methods and multistage architectures are given. + +Multistage architectures. Our multistage architecture, inspired by the U-Net model [33] used in $\mathrm{DDPM}++$ [1, 2, 18], is modified for interval-specific channel dimensions. The proposed architecture is adopted to three diffusion models: DPM-Solver [24], EDM [18], and LDM [8]. In particular, for the cases of DPM-Solver and EDM, the encoder's channel dimensions are standardized at 128, while the decoders are configured with 192, 128, and 16 channels for intervals $[0, t_1)$ , $[t_1, t_2)$ , and $[t_2, 1]$ , respectively. In the LDM case, we use 224 channels across the encoder for all intervals whereas the decoders are configured with 256, 192, and 128 channels for the respective intervals. To decide the specific number of parameters for each decoder, we apply ablation studies in Appendix B.5. Training details are in Appendix D. + +Datasets, evaluation metrics, & baselines. We use CIFAR-10 $(32 \times 32)$ , CelebA $(32 \times 32)$ , and CelebA (256 $\times$ 256) datasets for our experiments. To evaluate the performance of our multistage diffusion model in terms of the generation quality, we use the standard Fréchet Inception Distance (FID) metric [38]. We assess the sampling efficiency using the NFE, and giga-floating point operations (GFLOPs) per function evaluation. For both separate architecture and our multistage architecture, equivalent GFLOPs are computed as a weighted summation of GFLOPs for each interval. Training efficiency is evaluated using total training iterations multiplied by the GFLOPs per function evaluation, measured by peta-floating point operations (PFLOPs). For baselines, we consider DDPM [1], Score SDE [2], Poisson Flow Generative Models (PFGM) [39], DDIM [29], gDDIM [30], DEIS [31], DPM-solver [24], and EDM [18]. + +# 5.1. Image Generation Quality Results + +In this subsection, we demonstrate the effectiveness of our approach by comparing the image generation quality (measured by FID) with comparable training and sampling computations (measured by NFE). Specifically, Tab. 1 presents FID scores to measure the sampling quality, and NFE to measure the number of sampling iterations required using the CIFAR-10 dataset. Our method is compared to 8 baselines. As observed, our multistage DPM-Solver outperforms DPM-Solver in terms of the reported FID values while requiring similar training iterations (both are $4.5 \times 10^{5}$ ) and model GFLOPs (18.65 for multistage DPM-Solver versus 17.65 for DPM-Solver). A similar observation holds when we compare our multistage EDM and the + +vanilla EDM, where we reduce FID from 2.05 to 1.96 by using the multi-stage architecture. Remarkably, utilizing only 20 NFE, our Multistage DPM-Solver returns the same FID score as the one reported for the PFGM method, which requires 147 NFEs. These results also highlight the adaptability of our framework to higher-order ODE solvers; see the 8th and last row of Tab. 1. + +Table 1. Sampling quality on CIFAR-10 Dataset. + +
METHODNFE(↓)FID(↓)
DDPM10003.17
Score SDE20002.20
PFGM1472.35
DDIM1004.16
gDDIM202.97
DEIS202.86
DPM-solver202.73
Multistage DPM-solver (Ours)202.35
EDM352.05
Multistage EDM (Ours)351.96
+ +# 5.2. Training & Sampling Efficiency Results + +In this subsection, we further demonstrate the superiority of our method by comparing the training and sampling efficiency under comparable image generation quality. Specifically, in Tab. 2, we present the number of training iterations, GFLOPs, and total training PFLOPs of our approach, DPM-solver, EDM, and LDM using CIFAR-10 and CelebA datasets. Using the CIFAR-10 dataset, our multistage DPM-solver achieves similar FID scores (2.71 vs 2.73) while requiring nearly half the training iterations when compared to the vanilla DPM-solver. For the case of EDM (resp. LDM), our approach returns an FID score of 1.44 (resp. 8.29), requiring $1.4 \times 10^{5}$ ( $3.2 \times 10^{5}$ ) less iterations when compared to vanilla DPM-solver (resp. LDM). For the cases of DPM-solver and EDM, we can achieve a substantial reduction of training iterations, which is demonstrated by a marginal increase in the number of GFLOPs. For the LDM case, we also achieve a significant reduction of both training iterations and GFLOPs. These promising results highlight the significantly improved computational efficiency achieved by using the proposed multistage framework. + +# 5.3. Comparison of Different Architectures + +In Sec. 3, we highlighted the limitations of both unified and separate diffusion model architectures in terms of training efficiency (see Fig. 2). In this part, we further illustrate these limitations through extensive experiments as shown + +Table 2. Training and Sampling Efficiency on More Datasets. + +
DatasetMethodTraining Iterations(↓)GFLOPs(↓)Total Training PFLOPs(↓)FID(↓)
CIFAR-10DPM-Solver [18]4.5 × 10517.657.942.73
32 × 32Multistage DPM-Solver (Ours)2.5 × 105(56%)18.65 (106%)4.66 (59%)2.71
CelebAEDM [18]5.7 × 10517.6510.061.55
32 × 32Multistage EDM (Ours)4.3 × 105(75%)19.25 (109%)8.28 (82%)1.44
CelebALDM [8]4.9 × 10588.3943.318.29
256 × 256Multistage LDM (Ours)1.7 × 105(35%)76.19 (86%)12.95 (30.0%)8.38
+ +in Tab. 3. Here, we use the U-Net architecture, trained on the CIFAR-10 dataset, and utilize the DPM-Solver for sampling. For the unified case, we use a single U-Net model with 128 channels. For the separate case, three distinct U-Nets with 128 channels are used. For improved performance of the separate architecture, we implement two techniques: early stopping (ES) and tailored parameters (TP) to tackle the overfitting and parameter inefficiency discussed in Sec. 3. Under ES, the criteria is to stop training prior to overfitting. For TP, the three U-Nets are configured with 192, 128, and 16 channels decoders for Intervals 0, 1, and 2, respectively. + +Our comparison and analysis in Tab. 3 reveal notable insights of our network design. Comparisons between the 2nd and 3rd rows (and between the 4th and 5th rows) on the separate architectures indicate that early stopping effectively mitigates overfitting and enhances generation quality. When comparing the 2nd and 4th rows (as well as the 3rd and 5th rows) on the separate architectures, we observe that optimizing parameter usage can achieve a significant decrease in FID under comparable GFLOPs. Most importantly, our multistage architecture, as shown in the 6th row, benefits from both unified and separate architectures, achieving the best FID (2.35, compared to 2.73 and 2.52). Comparing the 2nd row and the 4th row, the shared encoder not only prevents overfitting but also improves the convergence of the diffusion model as reported by the FID scores. + +Table 3. Ablation study on different diffusion model architectures. + +
MethodGFLOPsFID(↓)
Unified17.652.73
Separate17.652.87
Separate (+ ES)17.652.80
Separate (+ TP)18.652.68
Separate (+ ES, TP)18.652.52
Multistage (Ours)18.652.35
+ +# 5.4. Comparison of Timestep Clustering Methods + +As previously stated in Sec. 2, various timestep clustering methods are proposed including timestep-based, SNR- + +based, and gradient-based clustering approaches [20, 21]. In this subsection, we conduct an experiment to demonstrate the superiority of our clustering method compared to previous arts. Specifically, we apply the clustering methods in [20, 21] to partition the interval along with our proposed multistage UNet architecture. The computed intervals are shown in the Tab. 4. We use the multistage DPM-Solver with these different intervals trained on the CIFAR-10 dataset. As observed, our optimal denoiser-based clustering method achieves the highest FID score, consistently outperforming all other clustering methods. + +Table 4. Ablation study on different clustering methods. + +
Clustering Methodt1t2FID(↓)
Timestep [20, 21]0.3300.6703.12
SNR [20]0.3480.7092.72
Gradient [20]0.3600.6602.75
Optimal Denoiser0.4420.6312.35
+ +# 6. Conclusion & Future Work + +In this paper, we introduced a novel multi-stage framework for diffusion models (DM) to improve the training and sampling efficiency. We proposed an algorithm that divides the timestep into several stages. Based on these stages, we designed a stage-specific multi-decoder U-net architecture and a shared encoder across all stages. We conducted thorough numerical experiments with several SOTA diffusion model frameworks and confirmed the effectiveness of our strategy using small scale and large scale datasets. + +In future research, it would be interesting to expand our multi-stage approach beyond unconditional diffusion models by considering conditional DMs and DM-based inverse problems solvers. Our experiment in Sec. 5.2 demonstrate that training latent diffusion models within our multi-stage framework requires only $30\%$ of the computational effort needed for training standard latent diffusion models on the CelebA dataset. Thus, employing a multi-stage strategy could significantly reduce the computational demands for training large-scale stable diffusion models, such as those described in [8], which typically requires significant computations. + +# References + +[1] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020. 1, 2, 3, 5, 7 +[2] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020. 1, 2, 3, 5, 7 +[3] Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34:8780-8794, 2021. 1 +[4] Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598, 2022. 1 +[5] Xuan Su, Jiaming Song, Chenlin Meng, and Stefano Ermon. 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Overview of three diffusion model architectures: (a) unified, (b) separate, and (c) our proposed multistage architecture. Compared with (a) and (b), our approach improves sampling quality, and significantly enhances training efficiency, as indicated by the FID scores and their corresponding training iterations (d)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 391, + 277, + 506, + 408 + ], + "blocks": [ + { + "bbox": [ + 391, + 277, + 506, + 408 + ], + "lines": [ + { + "bbox": [ + 391, + 277, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 391, + 277, + 506, + 408 + ], + "type": "image", + "image_path": "62fdc19d83e16c6ea50fe22f2a67f124b0c0d9f8e92467a0db4b28e72868c4e2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 409, + 459, + 418 + ], + "lines": [ + { + "bbox": [ + 449, + 409, + 459, + 418 + ], + "spans": [ + { + "bbox": [ + 449, + 409, + 459, + 418 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 143, + 463, + 192, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 463, + 192, + 475 + ], + "spans": [ + { + "bbox": [ + 143, + 463, + 192, + 475 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 498, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 290, + 715 + ], + "type": "text", + "content": "Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new samples (e.g., images). However, their remarkable generative performance is hindered by slow training and sampling. This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i.e., noise levels). To tackle these challenges, we present a multi-stage framework inspired by our empirical findings. These observations indicate the advantages of employing distinct parameters tailored to each timestep while retaining universal parameters shared across all time steps. Our approach involves segmenting the time interval into multiple stages where we employ custom multi-decoder U-net architecture that blends time-dependent models with a universally shared encoder. Our framework enables the" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 464, + 547, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 608 + ], + "type": "text", + "content": "efficient distribution of computational resources and mitigates inter-stage interference, which substantially improves training efficiency. Extensive numerical experiments affirm the effectiveness of our framework, showcasing significant training and sampling efficiency enhancements on three state-of-the-art diffusion models, including large-scale latent diffusion models. Furthermore, our ablation studies illustrate the impact of two important components in our framework: (i) a novel timestep clustering algorithm for stage division, and (ii) an innovative multi-decoder U-net architecture, seamlessly integrating universal and customized hyperparameters." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 621, + 387, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 387, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 387, + 634 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Recently, diffusion models have made remarkable progress as powerful deep generative modeling tools, showcasing remarkable performance in various applications, ranging from unconditional image generation [1, 2], conditional image generation [3, 4], image-to-image translation [5-7], text-to-image generation [8-10], inverse problem solving [11-14]," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7372" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "video generation [15, 16], and so on. These models employ a training process involving continuous injection of noise into training samples (\"diffusion\"), which are then utilized to generate new samples, such as images, by transforming random noise instances through a reverse diffusion process guided by the \"score function\" of the data distribution learned by the model. Moreover, recent work demonstrates that those diffusion models enjoy optimization stability and model reproducibility compared with other types of generative models [17]. However, diffusion models suffer from slow training and sampling despite their remarkable generative capabilities, which hinders their use in applications where real-time generation is desired [1, 2]. These drawbacks primarily arise from the necessity of tracking extensive forward and reverse diffusion trajectories, as well as managing a large model with numerous parameters across multiple timesteps (i.e., diffusion noise levels)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 289, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 422 + ], + "type": "text", + "content": "In this paper, we address these challenges based on two key observations: (i) there exists substantial parameter redundancy in current diffusion models, and (ii) they are trained inefficiently due to dissimilar gradients across different noise levels. Specifically, we find that training diffusion models require fewer parameters to accurately learn the score function at high noise levels, while larger parameters are needed at low noise levels. Furthermore, we also observe that when learning the score function, distinct shapes of distributions at different noise levels result in dissimilar gradients, which appear to slow down the training process driven by gradient descent." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": "Building on these insights, we propose a multi-stage framework with two key components: (i) a multi-decoder U-net architecture, and (ii) a new partitioning algorithm to cluster timesteps (noise levels) into distinct stages. In terms of our new architecture, we design a multi-decoder U-Net that incorporates one universal encoder shared across all intervals and individual decoders tailored to each time stage; see Figure 1 (c) for an illustration. This approach combines the advantages of both universal and stage-specific architectures, which is much more efficient than the unified architecture for the entire training process [1, 2, 18] (Figure 1 (a)). Moreover, compared to previous approaches that completely separate architectures for each sub-interval [19-22] (Figure 1 (b)), our approach can effectively mitigate overfitting, leading to improved training efficiency. On the other hand, when it comes to partitioning the training stages of our network, we designed an algorithm aimed at grouping the timesteps. This is achieved by minimizing the functional distance within each cluster in the training objective and making use of the optimal denoiser formulation [18]. By integrating these two key components, our framework enables efficient allocation of computational resources (e.g., U-net parameters) and stage-tailored parameterization. Throughout our extensive numerical experi" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "ments (Section 5), we show that out framework effectively improves both training and sampling efficiency. These experiments are performed on diverse benchmark datasets, demonstrating significant acceleration by using our framework when compared to three state-of-the-art (SOTA) diffusion model architectures. As a summary, the major contributions of this work can be highlighted as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 158, + 545, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 158, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 306, + 158, + 545, + 241 + ], + "type": "text", + "content": "- Identifying two key sources of inefficiency. We identified two key sources that cause inefficiencies in training diffusion models across various time steps: (i) a significant variation in the requirement of model capacity, and (ii) the gradient dissimilarity. As such, using a unified network cannot meet with the changing requirement at different time steps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 242, + 545, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 242, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 545, + 313 + ], + "type": "text", + "content": "- A new multi-stage framework. We introduced a new multi-stage architecture, illustrated in Fig. 1 (c). We tackle these two sources of inefficiency by segmenting the time interval into multiple stages, where we employ customized multi-decoder U-net architectures that blends time-dependent models with a universally shared encoder." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "type": "text", + "content": "- Improved training and sampling efficiency. With comparable computational resources for unconditional image generation, we demonstrate that our multi-stage approach improves the Fréchet Inception Distance (FID) score for all SOTA methods. For example, on CIFAR-10 dataset [23], our method improves the FID for DPM-Solver [24] from 2.84 to 2.37, and it improves the FID for EDM [18] from 2.05 (our training result) to 1.96. Moreover, on the CelebA dataset [25], while maintaining a similar generation quality, our approach significantly reduces the required training FLOPS of EDM by " + }, + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "type": "inline_equation", + "content": "82\\%" + }, + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "type": "text", + "content": " and the Latent Diffusion Model (LDM) [8] by " + }, + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 306, + 314, + 545, + 456 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "content": "Organization. In Sec. 2, we provide preliminaries and an overview of related literatures. In Sec. 3, we present our observations and analysis that motivated the proposed multistage framework, justifying its development. In Sec. 4, we describe our proposed multistage framework for diffusion models, outlining the two core components. Finally, in Sec. 5, we provide the results from our numerical experiments that validate the effectiveness of the proposed multistage approach." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 578, + 477, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 477, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 477, + 590 + ], + "type": "text", + "content": "2. Preliminaries & Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 598, + 545, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 598, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 598, + 545, + 681 + ], + "type": "text", + "content": "In this section, we start by reviewing the basic fundamentals of diffusion models [1, 2, 18]. Subsequently, we delve into prior approaches aimed at improving the training and efficiency of diffusion models through the partitioning of the timestep interval. Lastly, we survey prior studies that significantly decrease the number of required sampling iterations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Background on diffusion models. Let " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0 \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " denote a sample from the data distribution " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}(\\pmb{x})" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": ". Diffu" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7373" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": "sion models operate within forward and reverse processes. The forward process progressively perturbs data " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_0" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " to a noisy version " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{t\\in [0,1]}" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " via corrupting with the Gaussian kernel. This process can be formulated as a stochastic differential equation (SDE) [2] of the form " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\boldsymbol {x} = \\boldsymbol {x}_t f(t)\\mathrm{d}t + g(t)\\mathrm{d}\\boldsymbol{w}_t" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "f(t)" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "g(t)" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " are the drift and diffusion coefficients, respectively, that correspond to a pre-defined noise schedule. " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_t\\in \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " is the standard Wiener process. Under the forward SDE, the perturbation kernel is given by the conditional distribution defined as " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "p_t(\\boldsymbol {x}_t|\\boldsymbol {x}_0) = \\mathcal{N}(\\boldsymbol {x}_t;s_t\\boldsymbol {x}_0,s_t^2\\sigma_t^2\\mathbf{I})" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 213, + 287, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 213, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 59, + 213, + 287, + 246 + ], + "type": "interline_equation", + "content": "s _ {t} = \\exp \\left(\\int_ {0} ^ {t} f (\\xi) \\mathrm {d} \\xi\\right), \\text {a n d} \\sigma_ {t} = \\sqrt {\\int_ {0} ^ {t} \\frac {g ^ {2} (\\xi)}{s _ {\\xi} ^ {2}} \\mathrm {d} \\xi}. \\tag {1}", + "image_path": "d998b4ed02f88d81a88e819902a968f9cc5706810fc56ff376f1378eb4e7e341.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": "The parameters " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": " are designed such that: (i) the data distribution is approximately estimated when " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": ", and (ii) a nearly standard Gaussian distribution is obtained when " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": ". The objective of diffusion models is to learn the corresponding reverse SDE, defined as " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\pmb{x} = \\left[f(t)\\pmb{x}_t - g^2(t)\\nabla_{\\pmb{x}_t}\\log p_t(\\pmb{x}_t)\\right]\\mathrm{d}t + g(t)\\mathrm{d}\\bar{\\pmb{w}}" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{w}} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": " is the standard Wiener process running backward in time, and " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "\\nabla_{\\pmb{x}_t}\\log p_t(\\pmb{x}_t)" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": " is the (Stein) score function. In practice, the score function is approximated using a neural network " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}:\\mathbb{R}^n\\times [0,1]\\to \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 46, + 253, + 289, + 397 + ], + "type": "text", + "content": ", which can be trained by the denoising score matching technique [26] as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 403, + 287, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 403, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 53, + 403, + 287, + 423 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {\\theta}} \\mathbb {E} \\left[ \\omega (t) \\| \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, t) + s _ {t} \\sigma_ {t} \\nabla_ {\\boldsymbol {x} _ {t}} \\log p _ {t} (\\boldsymbol {x} _ {t} | \\boldsymbol {x} _ {0}) \\| _ {2} ^ {2} \\right], \\tag {2}", + "image_path": "46cf061da9da3ecd73a1e928504f62468efa815f54b21fb217026b112488223a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": "which can also be written as " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\min_{\\pmb{\\theta}}\\mathbb{E}[\\omega (t)||\\pmb{\\epsilon}_{\\pmb{\\theta}}(\\pmb{x}_t,t) - \\pmb{\\epsilon}||^2 ] + C" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ", where the expectation is taken over " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "t\\sim [0,1]" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t\\sim p_t(\\pmb{x}_t|\\pmb{x}_0)" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0\\sim p_{\\mathrm{data}}(\\pmb {x})" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": " is a constant independent of " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\omega (t)" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": " is a scalar representing the weight of the loss as a function of " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ". In DDPM [1], it is simplified to " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\omega (t) = 1" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": ". Once the parameterized score function " + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 431, + 289, + 540 + ], + "type": "text", + "content": " is trained, it can be utilized to approximate the reverse-time SDE using numerical solvers such as Euler-Maruyama." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "Timestep clustering methods. Diffusion models have demonstrated exceptional performance but face efficiency challenges in training and sampling. In response, several studies proposed to cluster the timestep range " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " into multiple intervals (e.g., " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "[0,t_1),[t_1,t_2),\\ldots ,[t_n,1]" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "). Notably, Choi et al. [19] reconfigured the loss weights for different intervals to enhance performance. Deja et al. [27] divide the entire process into a denoisr and a generator based on their functionalities. Balaji et al. [28] introduced \"expert denoisers\", which proposed using distinct architectures for different time intervals in text-to-image diffusion models. Go et al. [22] further improved the efficiency of these expert denoisers through parameter-efficient fine-tuning and data-free knowledge transfer. Lee et al. [21] designed separate" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "architectures for each interval based on frequency characteristics. Moreover, Go et al. [20] treated different intervals as distinct tasks and employed multi-task learning strategies for diffusion model training, along with various timestep clustering methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 133, + 546, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 546, + 324 + ], + "type": "text", + "content": "Our approach distinguishes itself from the aforementioned methods in two key aspects. The first key component is our tailored U-net architecture using a unified encoder coupled with different decoders for different intervals. Previous models have either adopted a unified architecture, as seen in [19, 20], or employed separate architectures (referred to as expert denoisers) for each interval [21, 22, 28]. In comparison, our multistage architecture surpasses these methodologies, as demonstrated in Sec. 5.3. Second, we developed a new timestep clustering method leveraging a general optimal denoiser (Prop. 1) that showcases superior performance (see Sec. 5.4). In contrast, prior works rely on (i) a simple timestep-based clustering cost function [20-22, 28], (ii) Signal-to-Noise Ratio (SNR) based clustering [20], or (iii) gradients-based partitioning that uses task affinity scores [20]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 331, + 546, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 559 + ], + "type": "text", + "content": "Reducing the sampling iterations methods. Efforts to improve sampling efficiency of diffusion models have led to many recent advancements in SDE and Ordinary Differential Equation (ODE) samplers [2]. For instance, the Denoising Diffusion Implicit Model (DDIM) [29] formulates the forward diffusion as a non-Markovian process with a deterministic generative path, significantly reducing the number of function evaluations (NFE) required for sampling (from thousands to hundreds). Generalized DDIM (gDDIM) [30] further optimized DDIM by modifying the parameterization of the scoring network. Furthermore, the works in [24] and [31], termed the Diffusion Probabilistic Model solver (DPM-solver) and the Diffusion Exponential Integrator Sampler (DEIS), respectively, introduced fast higher-order solvers, employing exponential integrators that require 10s NFE for comparable generation quality. Moreover, the consistency model [32] introduced a novel training loss and parameterization, achieving high-quality generation with merely 1-2 NFE." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 559, + 545, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 621 + ], + "type": "text", + "content": "We remark that while the aforementioned methods are indirectly related to our work, our experiments in Sec. 5.1 and Sec. 5.2 show that our approach can be easily integrated into these techniques, further improving diffusion models' overall training and sampling efficiency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 632, + 544, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 632, + 544, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 632, + 544, + 647 + ], + "type": "text", + "content": "3. Identification of Key Sources of Inefficiency" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "Conventional diffusion model architectures, as exemplified by [1, 2, 18], treat the training of the diffusion model as a unified process across all timesteps. Recent researches, such as [19-22], have highlighted the benefits of recognizing distinctions between different timesteps and the poten" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7374" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "content": "tial efficiency gains from treating them as separate tasks during the training process. However, our experimental results demonstrate that both unified and separate architectures suffer inefficiency for training diffusion models, where the inefficiency comes from (i) overparameterization, (ii) gradient dissimilarity, and (iii) overfitting." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 154, + 288, + 180 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 154, + 288, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 154, + 288, + 180 + ], + "type": "text", + "content": "3.1. Empirical Observations on the Key Sources of Inefficiency" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 186, + 287, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 186, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 287, + 210 + ], + "type": "text", + "content": "To illustrate the inefficiency in each interval, we isolate the interval by using a separate architecture from the rest." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": "Experiment setup. In our experiments, we consider three-stage training and divide the time steps into three intervals: " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "[0, t_1), [t_1, t_2), [t_2, 1]^1" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_i^{[a,b]}, 0 \\leq a < b \\leq 1" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": " denote a U-Net architecture with parameter " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": " trained with " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": " iterations and fed with data pairs " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "(x_t, t)" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "t \\in [a,b]" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": ". We then train models using two different strategies: a unified architecture with 108M network parameters for all intervals, i.e., " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_i^{[0,1]}" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": ", and separate architectures with varying network parameters (e.g., 47M, 108M, 169M) for each interval; e.g., " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_i^{[0,t_1)}" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": " for the interval " + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "inline_equation", + "content": "[0,t_1)" + }, + { + "bbox": [ + 46, + 215, + 288, + 448 + ], + "type": "text", + "content": ", etc. It is worth noting that, apart from the differences in network parameters, we utilize the same network architecture (e.g., U-Net) for both the unified and the separate approaches. We assessed the training progress of each model by evaluating image generation quality at different training iterations. Notably, because some of the models are only trained on one interval, we need to provide a ground truth score for the other intervals. In Fig. 2, the sampling process is shown top and the experimental results are shown bottom." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 453, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 287, + 477 + ], + "type": "text", + "content": "Inefficiency in unified architectures. From Fig. 2, we observe the following:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 479, + 287, + 693 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 479, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 287, + 644 + ], + "type": "text", + "content": "- Overparameterization and underfitting emerge simultaneously for unified architectures. In Fig. 2a, we observe that increasing the number of parameters in Interval 0 can improve the image generation quality (as indicated by a lower FID score). In contrast, Fig. 2b reveals that increasing the number of parameters in Interval 2 has minimal impact on the quality of image generation. This implies that using a unified architecture will result in underfitting in Interval 0 and overparameterization in Interval 2. The current unified architecture's parameter redundancy leaves significant room for improving its efficiency. To optimize the computational usage, we should allocate more parameters to Interval 0 while allocating fewer parameters to Interval 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 646, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 287, + 693 + ], + "type": "text", + "content": "- Gradient dissimilarity hinders training for unified architecture. Quantitative results from [20] demonstrate dissimilarity in gradients caused by differences within each interval. This can also be observed from our results based" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 204 + ], + "type": "text", + "content": "upon both Fig. 2a and Fig. 2b. For the unified and separate architectures using the same number of parameters (108M), separate architecture achieves a significantly lower FID with the same training iterations, implying that dissimilar gradients among intervals may hinder training when using a unified architecture. Here, the only difference between training separate and unified architectures is that the batch gradient for unified architecture is calculated based on all timesteps while the batch gradien2 for separate architecture is calculated only from a specific interval." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 217, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 361 + ], + "type": "text", + "content": "Inefficiency in existing separate architectures. Although separated architecture [19, 21, 22] better allocates computational resources for each interval, it suffers from overfitting. This can be illustrated based upon training separate architectures (169M) and (108M) in Interval 0 shown in Fig. 2a, where increasing the number of parameters will lead to overfitting. This also happens in Interval 2, when we compare all separate architectures in Fig. 2b. In comparison, the unified networks with 108M parameters are less prone to overfitting for both Interval 0 and Interval 2. This suggests that we can reduce overfitting by training shared weights across different intervals together." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 371, + 545, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 396 + ], + "type": "text", + "content": "3.2. Tackling the Inefficiency via Multistage U-Net Architectures" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "type": "text", + "content": "In a unified architecture applied across all timesteps, there is often a dual challenge: requirements for more parameters (169M) in the interval " + }, + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "type": "inline_equation", + "content": "[0, t_1)" + }, + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "type": "text", + "content": " but fewer parameters (47M) in the interval " + }, + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "type": "inline_equation", + "content": "[t_2, 1]" + }, + { + "bbox": [ + 304, + 403, + 545, + 594 + ], + "type": "text", + "content": ". This issue is compounded by the gradient dissimilarity across different timesteps, which can impede effective training. Alternatively, employing separate architectures for different intervals might lead to overfitting and a lack of robust early stopping mechanisms. To address these challenges, our proposed multistage architecture in Sec. 4 combines shared parameters to reduce overfitting with interval-specific parameters to mitigate the impact of gradient dissimilarity. This tailored approach for each interval ensures improved adaptability. Furthermore, we conduct an in-depth ablation study in Sec. 5.3 to showcase the effectiveness of our multi-stage architecture over the existing models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 609, + 491, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 491, + 623 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 491, + 623 + ], + "type": "text", + "content": "4. Proposed Multistage Framework" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In this section, we introduce our new multistage framework (as illustrated in Fig. 1 (c)). Specifically, we first introduce the multi-stage U-Net architecture design in Sec. 4.1, following a new clustering method for choosing the optimal interval to partition the entire timestep [0, 1] into intervals in Sec. 4.2., and discuss the rationale of the proposed architecture in Sec. 4.3." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 258, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 258, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 258, + 713 + ], + "type": "text", + "content": "1Details for interval clustering can be found in Appendix B.1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7375" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 70, + 286, + 246 + ], + "blocks": [ + { + "bbox": [ + 107, + 70, + 286, + 246 + ], + "lines": [ + { + "bbox": [ + 107, + 70, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 107, + 70, + 286, + 246 + ], + "type": "image", + "image_path": "a7f05e825ef767cb2e1911201bf99b4652428f823de776cfb9b43dd1dd2029f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 131, + 248, + 230, + 258 + ], + "lines": [ + { + "bbox": [ + 131, + 248, + 230, + 258 + ], + "spans": [ + { + "bbox": [ + 131, + 248, + 230, + 258 + ], + "type": "text", + "content": "(a) Analysis on interval " + }, + { + "bbox": [ + 131, + 248, + 230, + 258 + ], + "type": "inline_equation", + "content": "[0, t_1)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 70, + 478, + 247 + ], + "blocks": [ + { + "bbox": [ + 298, + 70, + 478, + 247 + ], + "lines": [ + { + "bbox": [ + 298, + 70, + 478, + 247 + ], + "spans": [ + { + "bbox": [ + 298, + 70, + 478, + 247 + ], + "type": "image", + "image_path": "92f94ab5b87d8b6dc50c15aa21be981ed618a51747dbcb8c453c0d9e1ea78432.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 248, + 436, + 258 + ], + "lines": [ + { + "bbox": [ + 339, + 248, + 436, + 258 + ], + "spans": [ + { + "bbox": [ + 339, + 248, + 436, + 258 + ], + "type": "text", + "content": "(b) Analysis on interval " + }, + { + "bbox": [ + 339, + 248, + 436, + 258 + ], + "type": "inline_equation", + "content": "[t_2, 1]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": "Figure 2. Comparison between separate architecture and unified architecture w.r.t. the image generation quality in different intervals: (a) analysis on interval " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "[0, t_1)" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": "; and (b) analysis on interval " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "[t_2, 1]" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": ". As illustrated on top of each figure, we only train separate architectures within specific intervals for the sampling process in both (a) and (b). For the remaining period of sampling, we use a well-trained diffusion model " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": " to approximate the ground truth score function. As shown in the above figure of (a), e.g. for the separate architecture on interval 1, sampling utilizes trained model " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta'})_i^{[0,t_1)}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": " for interval 0 and well-trained model " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": " for interval 1 and 2. Notably, for both " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_i^{[0,1]}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta})_{4 \\times 10^5}^{[0,1]}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": ", we are using the model with 108M parameters. For separate architecture, the number in the parentheses represents the number of parameters of the model " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta'})_i^{[a,b]}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": ". For example, for separate architecture (169M) in (a), the model " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\theta'})_i^{[0,t_1)}" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": " has 169M parameters for " + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "inline_equation", + "content": "\\theta'" + }, + { + "bbox": [ + 46, + 259, + 545, + 357 + ], + "type": "text", + "content": ". The bottom figures in (a-b) illustrate the FID of the generation from each architecture under different training iterations." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 378, + 266, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 266, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 266, + 391 + ], + "type": "text", + "content": "4.1. Proposed Multi-stage U-Net Architectures" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 398, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 287, + 470 + ], + "type": "text", + "content": "As discussed in Sec. 3, most existing diffusion models either employ a unified architecture across all intervals [1, 2, 18] to share features for all timesteps, or use completely separate architectures for different timestep intervals [21, 22, 28] where the goal is to take advantage of the benign properties within different intervals." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": "To harness the advantages of both unified and separate architectures employed in prior studies, we introduce a multistage U-Net architecture, as illustrated in Figure 1(c). Specifically, we partition the entire timestep " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " into several intervals, e.g., three intervals " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "[0,t_1),[t_1,t_2),[t_2,1]" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " in Fig. 1. For the architecture, we introduce:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 546, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 546, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 287, + 640 + ], + "type": "text", + "content": "- One shared encoder across all time intervals. For each timestep interval, we implement a shared encoder architecture (plotted in blue in Fig. 1 (c)), which is similar to the architecture employed in the original U-Net framework [33]. Unlike separate architecture, the shared encoder provides shared information across all timesteps, preventing models from overfitting (see Sec. 5.3 for a discussion)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": "- Separate decoders for different time intervals. Motivated by the multi-head structure introduced in the Mask Region-based Convolutional Neural Networks (MaskRCNN) method [34], we propose to use multiple distinct decoders (plotted in colors for different intervals in Fig. 1(c)), where each decoder is tailored to a spe" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 379, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 379, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 313, + 379, + 545, + 426 + ], + "type": "text", + "content": "cific timestep interval. The architecture of each decoder closely resembles the one utilized in [2], with deliberate adjustments made to the embedding dimensions to optimize performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 428, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 545, + 500 + ], + "type": "text", + "content": "As we observe, the primary difference in the architecture resides within the decoder structure. Intuitively, we use a decoder with fewer number of parameters for intervals closer to the noise, because the learning task is easier. We use a decoder with a larger number of parameters for intervals closer to the image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 511, + 539, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 511, + 539, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 511, + 539, + 525 + ], + "type": "text", + "content": "4.2. Optimal Denoiser-based Timestep Clustering" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": "Next, we discuss how we principally choose the interval partition time points in practice. For simplicity, we focus on the case where we partition the time " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": " into three intervals " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "[0,t_1],[t_1,t_2],[t_2,1]" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": ", and we develop a timestep clustering method to choose the optimal " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": ". Of course, our method can be generalized to multi-stage networks with arbitrary interval numbers. However, in practice, we find that the choice of three intervals strikes a good balance between effectiveness and complexity; see our ablation study in Appendix B.6." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 653, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 677 + ], + "type": "text", + "content": "To partition the time interval, we employ the optimal denoiser established in Proposition 1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Proposition 1. Suppose we train a diffusion model denoiser function " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\pmb{x},t)" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " using dataset" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7376" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 284, + 84 + ], + "type": "title", + 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+ 286, + 110 + ], + "type": "text", + "content": ", thresholds " + }, + { + "bbox": [ + 53, + 87, + 286, + 110 + ], + "type": "inline_equation", + "content": "\\alpha, \\eta" + }, + { + "bbox": [ + 53, + 87, + 286, + 110 + ], + "type": "text", + "content": ", dataset " + }, + { + "bbox": [ + 53, + 87, + 286, + 110 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}" + }, + { + "bbox": [ + 53, + 87, + 286, + 110 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 53, + 87, + 286, + 110 + ], + "type": "inline_equation", + "content": "S_0 = S_1 = \\emptyset" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 110, + 158, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 110, + 158, + 121 + ], + "spans": [ + { + "bbox": [ + 53, + 110, + 158, + 121 + ], + "type": "text", + "content": "2: Output: Timesteps " + }, + { + "bbox": [ + 53, + 110, + 158, + 121 + ], + "type": "inline_equation", + "content": "t_1, t_2" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 121, + 153, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 121, + 153, + 131 + ], + "spans": [ + { + "bbox": [ + 53, + 121, + 153, + 131 + ], + "type": "text", + "content": "3: for " + }, + { + "bbox": [ + 53, + 121, + 153, + 131 + ], + "type": "inline_equation", + "content": "k \\in \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 53, + 121, + 153, + 131 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 132, + 214, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 132, + 214, + 142 + ], + "spans": [ + { + "bbox": [ + 53, + 132, + 214, + 142 + ], + "type": "text", + "content": "4: " + }, + { + "bbox": [ + 53, + 132, + 214, + 142 + ], + "type": "inline_equation", + "content": "\\pmb{y}_k\\sim p_{\\mathrm{data}},\\pmb{\\epsilon}_k\\sim \\mathcal{N}(0,\\mathbf{I}),t_k\\sim [0,1]" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 142, + 268, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 142, + 268, + 154 + ], + "spans": [ + { + "bbox": [ + 53, + 142, + 268, + 154 + ], + "type": "text", + "content": "5: " + }, + { + "bbox": [ + 53, + 142, + 268, + 154 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_0^k\\gets \\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*,\\pmb{\\epsilon}_0^*,\\pmb {y}_k,\\pmb {\\epsilon}_k),\\mathcal{S}_1^k\\gets \\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*,\\pmb {\\epsilon}_1^*,\\pmb {y}_k,\\pmb {\\epsilon}_k)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 154, + 253, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 154, + 253, + 166 + ], + "spans": [ + { + "bbox": [ + 53, + 154, + 253, + 166 + ], + "type": "text", + "content": "6: " + }, + { + "bbox": [ + 53, + 154, + 253, + 166 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_0\\gets \\mathcal{S}_0\\cup \\{\\big(t_k,\\mathcal{S}_0^k\\big)\\} ,\\mathcal{S}_1\\gets \\mathcal{S}_1\\cup \\{\\big(t_k,\\mathcal{S}_1^k\\big)\\}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 166, + 95, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 166, + 95, + 174 + ], + "spans": [ + { + "bbox": [ + 53, + 166, + 95, + 174 + ], + "type": "text", + "content": "7: end for" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 174, + 255, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 174, + 255, + 201 + ], + "spans": [ + { + "bbox": [ + 53, + 174, + 255, + 201 + ], + "type": "text", + "content": "8: " + }, + { + "bbox": [ + 53, + 174, + 255, + 201 + ], + "type": "inline_equation", + "content": "t_1 = \\arg \\max_{\\tau}\\left\\{\\tau \\Big|\\frac{\\sum_{(t_k,\\mathcal{S}_0^k)\\in\\mathcal{S}_0}\\big[\\mathcal{S}_0^k\\cdot\\mathbb{1}(t_k\\leq\\tau)\\big]}{\\sum_{(t_k,\\mathcal{S}_0^k)\\in\\mathcal{S}_0}[\\mathbb{1}(t_k\\leq\\tau)]}\\geq\\alpha\\right\\}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 201, + 253, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 201, + 253, + 230 + ], + "spans": [ + { + "bbox": [ + 53, + 201, + 253, + 230 + ], + "type": "text", + "content": "9: " + }, + { + "bbox": [ + 53, + 201, + 253, + 230 + ], + "type": "inline_equation", + "content": "t_2 = \\arg \\min_{\\tau}\\left\\{\\tau \\Big|\\frac{\\sum_{(t_k,\\mathcal{S}_1^k)\\in\\mathcal{S}_0}\\big[\\mathcal{S}_1^k\\cdot\\mathbb{1}(t_k\\geq\\tau)\\big]}{\\sum_{(t_k,\\mathcal{S}_1^k)\\in\\mathcal{S}_0}[\\mathbb{1}(t_k\\geq\\tau)]}\\geq\\alpha\\right\\}" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 48, + 251, + 120, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 251, + 120, + 266 + ], + "spans": [ + { + "bbox": [ + 48, + 251, + 120, + 266 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {y} _ {i} \\in \\mathbb {R} ^ {n} \\right\\} _ {i = 1} ^ {N} b y", + "image_path": "023ebe2eda1fd1533ab76b1f54534af69248c4d68fd534fec382116f7d26a77c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 78, + 274, + 287, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 274, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 78, + 274, + 287, + 291 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {\\theta}} \\mathcal {L} (\\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}}; t) = \\mathbb {E} _ {\\boldsymbol {x} _ {0}, \\boldsymbol {x} _ {t}, \\epsilon} [ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} ], \\tag {3}", + "image_path": "4bd46549e088c25721805f7ee3f01065c5066274691908cfb6c78470bd3bde7b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0\\sim p_{data}(\\pmb {x}) = \\frac{1}{N}\\sum_{i = 1}^{N}\\delta (\\pmb {x} - \\pmb {y}_i)" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,\\pmb {I})" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{t}\\sim p_{t}(\\pmb{x}_{t}|\\pmb{x}_{0}) = \\mathcal{N}(\\pmb{x}_{t};s_{t}\\pmb{x}_{0},s_{t}^{2}\\sigma_{t}^{2}\\pmb {I})" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": " with perturbation parameters " + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": " defined in Eq. (1). Then, the optimal denoiser at " + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": " defined as " + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}(\\pmb {x};t) = \\arg \\min_{\\epsilon_{\\theta}}\\mathcal{L}(\\epsilon_{\\theta};t)" + }, + { + "bbox": [ + 47, + 300, + 287, + 361 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 53, + 369, + 287, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 369, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 53, + 369, + 287, + 413 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} ^ {*} (\\boldsymbol {x}; t) = \\frac {1}{s _ {t} \\sigma_ {t}} \\left[ \\boldsymbol {x} - s _ {t} \\frac {\\sum_ {i = 1} ^ {N} \\mathcal {N} (\\boldsymbol {x} ; s _ {t} \\boldsymbol {y} _ {i} , s _ {t} ^ {2} \\sigma_ {t} ^ {2} \\boldsymbol {I}) \\boldsymbol {y} _ {i}}{\\sum_ {i = 1} ^ {N} \\mathcal {N} (\\boldsymbol {x} ; s _ {t} \\boldsymbol {y} _ {i} , s _ {t} ^ {2} \\sigma_ {t} ^ {2} \\boldsymbol {I})} \\right]. \\tag {4}", + "image_path": "67445f03324f20b370aa2a0315bf5718d47be15b72c5387d56dc2ef903b76ff1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "text", + "content": "The proof is provided in Appendix A, and the result can be generalized from recent work of Karras et al. [18], extending from a specific kernel " + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "inline_equation", + "content": "p_t(\\boldsymbol{x}_t|\\boldsymbol{x}_0) = \\mathcal{N}(\\boldsymbol{x}_t; \\boldsymbol{x}_0, \\sigma_t^2\\mathbf{I})" + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "text", + "content": " to encompassing a broader scope of noise perturbation kernels, given by " + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "inline_equation", + "content": "p_t(\\boldsymbol{x}_t|\\boldsymbol{x}_0) = \\mathcal{N}(\\boldsymbol{x}_t; s_t\\boldsymbol{x}_0, s_t^2\\sigma_t^2\\mathbf{I})" + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "text", + "content": ". For brevity, we simplify the notation of the optimal denoiser " + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}(\\boldsymbol{x}, t)" + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "text", + "content": " in Proposition 1 as " + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "inline_equation", + "content": "\\epsilon_t^*(\\boldsymbol{x})" + }, + { + "bbox": [ + 47, + 422, + 287, + 505 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "type": "text", + "content": "To obtain the optimal interval, our rationale is to homogenize the regression task as much as possible within each individual time interval. To achieve this goal, given sampled " + }, + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0, \\pmb{\\epsilon}" + }, + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "type": "text", + "content": ", we define the function distance of the optimal denoiser at any given timestep " + }, + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "type": "inline_equation", + "content": "t_a, t_b" + }, + { + "bbox": [ + 47, + 505, + 287, + 565 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 573, + 286, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 286, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 286, + 604 + ], + "type": "interline_equation", + "content": "\\mathcal {D} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}\\right) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\mathbb {1} \\left(\\left| \\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*} \\left(\\boldsymbol {x} _ {t _ {a}}\\right) - \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*} \\left(\\boldsymbol {x} _ {t _ {b}}\\right) \\right| _ {i} \\leq \\eta\\right),", + "image_path": "48e9f11e7f58d7db71863f7631a341bf35ee5cad36d9a73690b0af552da66eb8.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\mathbb{1}(\\cdot)" + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": " is the indicator function, " + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": " is a pre-specified threshold, " + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{t_a} = s_{t_a}\\pmb{x}_0 + s_{t_a}\\sigma_{t_a}\\pmb{\\epsilon}" + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{t_b} = s_{t_b}\\pmb{x}_0 + s_{t_b}\\sigma_{t_b}\\pmb{\\epsilon}" + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": ". Consequently, we define the functional similarity of the optimal denoiser at timesteps " + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "inline_equation", + "content": "t_a" + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "inline_equation", + "content": "t_b" + }, + { + "bbox": [ + 47, + 611, + 287, + 659 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 53, + 668, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 668, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 53, + 668, + 287, + 683 + ], + "type": "interline_equation", + "content": "\\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}\\right) = \\mathbb {E} _ {\\boldsymbol {x} _ {0} \\sim p _ {\\mathrm {d a t a}}} \\mathbb {E} _ {\\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I})} \\left[ \\mathcal {D} \\left(\\boldsymbol {\\epsilon} _ {t _ {a}} ^ {*}, \\boldsymbol {\\epsilon} _ {t _ {b}} ^ {*}, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}\\right) \\right]. \\tag {5}", + "image_path": "6e29fd2794186bbb979a3d49f63fd6a755a5f960ccc1b8ce3fef044e63ff4a02.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Based upon the definition, we design the following optimization problem to find the largest " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " and smallest " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 332, + 89, + 545, + 111 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 89, + 545, + 111 + ], + "spans": [ + { + "bbox": [ + 332, + 89, + 545, + 111 + ], + "type": "interline_equation", + "content": "t _ {1} \\leftarrow \\underset {\\tau} {\\arg \\max } \\left\\{\\tau \\left| \\mathbb {E} _ {t \\sim [ 0, \\tau)} \\left[ \\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t} ^ {*}, \\boldsymbol {\\epsilon} _ {0} ^ {*}\\right) \\right] \\geq \\alpha \\right. \\right\\}, \\tag {6}", + "image_path": "5d1d563ca98f28c8dfd37b9afb8c0ab031e32caa3288511b06cd0142f7964be3.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 333, + 114, + 545, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 114, + 545, + 135 + ], + "spans": [ + { + "bbox": [ + 333, + 114, + 545, + 135 + ], + "type": "interline_equation", + "content": "t _ {2} \\leftarrow \\underset {\\tau} {\\arg \\min } \\left\\{\\tau \\left| \\mathbb {E} _ {t \\sim [ \\tau , 1 ]} \\left[ \\mathcal {S} \\left(\\boldsymbol {\\epsilon} _ {t} ^ {*}, \\boldsymbol {\\epsilon} _ {1} ^ {*}\\right) \\right] \\geq \\alpha \\right. \\right\\}, \\tag {7}", + "image_path": "e3bf0ec5a7605f1a2ce333694248bd03482d3f5929c9a84fb0f217e974acd560.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": "such that the average functional similarity of " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_t^*" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " (resp. " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_t^*" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": ") to " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_0^*" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " (resp. " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_1^*" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": ") in " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "[0, t_1)" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " (resp. " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "[t_2, 1]" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": ") is larger than or equal to a pre-defined threshold " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": ". As the above optimization problems are intractable, we propose the procedure outlined in Algorithm 1 to obtain an approximate solution. In particular, the algorithm samples " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " pairs " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "(\\pmb{y}_k, \\pmb{\\epsilon}_k, t_k), k \\in \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " to calculate the distances " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*, \\pmb{\\epsilon}_0^*, \\pmb{y}_k, \\pmb{\\epsilon}_k)" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\pmb{\\epsilon}_{t_k}^*, \\pmb{\\epsilon}_1^*, \\pmb{y}_k, \\pmb{\\epsilon}_k)" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " (step 6). Based on those distances, we solve the optimization problems defined in the lines 8 and 9 of Algorithm 1 to obtain " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 306, + 143, + 545, + 263 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 270, + 517, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 517, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 517, + 283 + ], + "type": "text", + "content": "4.3. Rationales for the proposed architecture" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 288, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 545, + 323 + ], + "type": "text", + "content": "Finally, we summarize the rationales of our proposed architecture based on the empirical observations in Sec. 3 and previous works." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "text", + "content": "Rationales for the shared encoder. (i) Prevent overfitting: If we treat training separate stages of diffusion models as multi-task learning, [35] suggests that shared parameters across tasks in multi-task learning can mitigate overfitting. (ii) Maintain consistency in " + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "text", + "content": "-space. The output of the encoder for UNet is named as " + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "text", + "content": "-space [36], which has properties for semantic manipulation such as homogeneity, linearity, robustness, and consistency across timesteps. Therefore, sharing the encoder can maintain better consistency of the " + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 324, + 545, + 454 + ], + "type": "text", + "content": "-space among all timesteps compared to separate encoders." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": "Rationales for network parameter design. First, we provide some intuitions as to why the learning task at " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " is harder than that at " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ". Suppose diffusion models could converge to the optimal denoiser " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}(\\boldsymbol{x}_t,t)" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " given in Eq. (4). Based on this, we observe: (i) when " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t \\to 0" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{t \\to 0} = \\boldsymbol{x}_0" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}|_{t \\to 0} = \\epsilon" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ", so that " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " is a complicated mapping from training data distribution " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}(\\boldsymbol{x})" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " to the gaussian distribution; (ii) when " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t \\to 1" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{t \\to 1} = \\epsilon" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}|_{t \\to 1} = \\epsilon" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ", so " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{*}" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " is an identity mapping. The two extreme cases reveal that the identity mapping for " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t \\to 1" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " (close to noise) is easier to learn than that for " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t \\to 0" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": ". Second, our choice of network parameters across different stages share similar spirits with the recent work [37], which employs a high dimensional subspace as " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t \\to 0" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": " and gradually decreases the dimensionality of each subspace until " + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 305, + 456, + 545, + 635 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 646, + 387, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 387, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 387, + 658 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": "In this section, we start by providing the experimental setups. Next, we present results in terms of generation quality (Sec. 5.1). Subsequently, results for training and sampling efficiency are presented. Finally, in Sec. 5.3 and" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7377" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "Sec. 5.4, comprehensive ablation studies on timestep clustering methods and multistage architectures are given." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "text", + "content": "Multistage architectures. Our multistage architecture, inspired by the U-Net model [33] used in " + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "inline_equation", + "content": "\\mathrm{DDPM}++" + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "text", + "content": " [1, 2, 18], is modified for interval-specific channel dimensions. The proposed architecture is adopted to three diffusion models: DPM-Solver [24], EDM [18], and LDM [8]. In particular, for the cases of DPM-Solver and EDM, the encoder's channel dimensions are standardized at 128, while the decoders are configured with 192, 128, and 16 channels for intervals " + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "inline_equation", + "content": "[0, t_1)" + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "inline_equation", + "content": "[t_1, t_2)" + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "inline_equation", + "content": "[t_2, 1]" + }, + { + "bbox": [ + 46, + 104, + 288, + 285 + ], + "type": "text", + "content": ", respectively. In the LDM case, we use 224 channels across the encoder for all intervals whereas the decoders are configured with 256, 192, and 128 channels for the respective intervals. To decide the specific number of parameters for each decoder, we apply ablation studies in Appendix B.5. Training details are in Appendix D." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "text", + "content": "Datasets, evaluation metrics, & baselines. We use CIFAR-10 " + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "inline_equation", + "content": "(32 \\times 32)" + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "text", + "content": ", CelebA " + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "inline_equation", + "content": "(32 \\times 32)" + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "text", + "content": ", and CelebA (256 " + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 300, + 287, + 502 + ], + "type": "text", + "content": " 256) datasets for our experiments. To evaluate the performance of our multistage diffusion model in terms of the generation quality, we use the standard Fréchet Inception Distance (FID) metric [38]. We assess the sampling efficiency using the NFE, and giga-floating point operations (GFLOPs) per function evaluation. For both separate architecture and our multistage architecture, equivalent GFLOPs are computed as a weighted summation of GFLOPs for each interval. Training efficiency is evaluated using total training iterations multiplied by the GFLOPs per function evaluation, measured by peta-floating point operations (PFLOPs). For baselines, we consider DDPM [1], Score SDE [2], Poisson Flow Generative Models (PFGM) [39], DDIM [29], gDDIM [30], DEIS [31], DPM-solver [24], and EDM [18]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 511, + 230, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 230, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 230, + 525 + ], + "type": "text", + "content": "5.1. Image Generation Quality Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 529, + 286, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 286, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 286, + 685 + ], + "type": "text", + "content": "In this subsection, we demonstrate the effectiveness of our approach by comparing the image generation quality (measured by FID) with comparable training and sampling computations (measured by NFE). Specifically, Tab. 1 presents FID scores to measure the sampling quality, and NFE to measure the number of sampling iterations required using the CIFAR-10 dataset. Our method is compared to 8 baselines. As observed, our multistage DPM-Solver outperforms DPM-Solver in terms of the reported FID values while requiring similar training iterations (both are " + }, + { + "bbox": [ + 46, + 529, + 286, + 685 + ], + "type": "inline_equation", + "content": "4.5 \\times 10^{5}" + }, + { + "bbox": [ + 46, + 529, + 286, + 685 + ], + "type": "text", + "content": ") and model GFLOPs (18.65 for multistage DPM-Solver versus 17.65 for DPM-Solver). A similar observation holds when we compare our multistage EDM and the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 309, + 71, + 548, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 71, + 548, + 155 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 548, + 155 + ], + "type": "text", + "content": "vanilla EDM, where we reduce FID from 2.05 to 1.96 by using the multi-stage architecture. Remarkably, utilizing only 20 NFE, our Multistage DPM-Solver returns the same FID score as the one reported for the PFGM method, which requires 147 NFEs. These results also highlight the adaptability of our framework to higher-order ODE solvers; see the 8th and last row of Tab. 1." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 312, + 185, + 544, + 357 + ], + "blocks": [ + { + "bbox": [ + 335, + 165, + 515, + 176 + ], + "lines": [ + { + "bbox": [ + 335, + 165, + 515, + 176 + ], + "spans": [ + { + "bbox": [ + 335, + 165, + 515, + 176 + ], + "type": "text", + "content": "Table 1. Sampling quality on CIFAR-10 Dataset." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 185, + 544, + 357 + ], + "lines": [ + { + "bbox": [ + 312, + 185, + 544, + 357 + ], + "spans": [ + { + "bbox": [ + 312, + 185, + 544, + 357 + ], + "type": "table", + "html": "
METHODNFE(↓)FID(↓)
DDPM10003.17
Score SDE20002.20
PFGM1472.35
DDIM1004.16
gDDIM202.97
DEIS202.86
DPM-solver202.73
Multistage DPM-solver (Ours)202.35
EDM352.05
Multistage EDM (Ours)351.96
", + "image_path": "15db83ff9e87b7787c6b9fcb9c09e0150f545aa3ae9fa93b97e098cd57d6590a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 379, + 515, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 379, + 515, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 379, + 515, + 392 + ], + "type": "text", + "content": "5.2. Training & Sampling Efficiency Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "type": "text", + "content": "In this subsection, we further demonstrate the superiority of our method by comparing the training and sampling efficiency under comparable image generation quality. Specifically, in Tab. 2, we present the number of training iterations, GFLOPs, and total training PFLOPs of our approach, DPM-solver, EDM, and LDM using CIFAR-10 and CelebA datasets. Using the CIFAR-10 dataset, our multistage DPM-solver achieves similar FID scores (2.71 vs 2.73) while requiring nearly half the training iterations when compared to the vanilla DPM-solver. For the case of EDM (resp. LDM), our approach returns an FID score of 1.44 (resp. 8.29), requiring " + }, + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "type": "inline_equation", + "content": "1.4 \\times 10^{5}" + }, + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "type": "inline_equation", + "content": "3.2 \\times 10^{5}" + }, + { + "bbox": [ + 304, + 398, + 545, + 638 + ], + "type": "text", + "content": ") less iterations when compared to vanilla DPM-solver (resp. LDM). For the cases of DPM-solver and EDM, we can achieve a substantial reduction of training iterations, which is demonstrated by a marginal increase in the number of GFLOPs. For the LDM case, we also achieve a significant reduction of both training iterations and GFLOPs. These promising results highlight the significantly improved computational efficiency achieved by using the proposed multistage framework." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 647, + 510, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 510, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 510, + 659 + ], + "type": "text", + "content": "5.3. Comparison of Different Architectures" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "In Sec. 3, we highlighted the limitations of both unified and separate diffusion model architectures in terms of training efficiency (see Fig. 2). In this part, we further illustrate these limitations through extensive experiments as shown" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "2Here we simplify it by ignoring the FLOPs for backward propagation, which is approximately proportional to FLOPs of forward evaluation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7378" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 89, + 523, + 169 + ], + "blocks": [ + { + "bbox": [ + 184, + 71, + 408, + 82 + ], + "lines": [ + { + "bbox": [ + 184, + 71, + 408, + 82 + ], + "spans": [ + { + "bbox": [ + 184, + 71, + 408, + 82 + ], + "type": "text", + "content": "Table 2. Training and Sampling Efficiency on More Datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 89, + 523, + 169 + ], + "lines": [ + { + "bbox": [ + 70, + 89, + 523, + 169 + ], + "spans": [ + { + "bbox": [ + 70, + 89, + 523, + 169 + ], + "type": "table", + "html": "
DatasetMethodTraining Iterations(↓)GFLOPs(↓)Total Training PFLOPs(↓)FID(↓)
CIFAR-10DPM-Solver [18]4.5 × 10517.657.942.73
32 × 32Multistage DPM-Solver (Ours)2.5 × 105(56%)18.65 (106%)4.66 (59%)2.71
CelebAEDM [18]5.7 × 10517.6510.061.55
32 × 32Multistage EDM (Ours)4.3 × 105(75%)19.25 (109%)8.28 (82%)1.44
CelebALDM [8]4.9 × 10588.3943.318.29
256 × 256Multistage LDM (Ours)1.7 × 105(35%)76.19 (86%)12.95 (30.0%)8.38
", + "image_path": "a73b7ef5ce65c5e08d089a21cb457ddc11c0be57ab285511bb94053e64507c78.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 188, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 188, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 287, + 331 + ], + "type": "text", + "content": "in Tab. 3. Here, we use the U-Net architecture, trained on the CIFAR-10 dataset, and utilize the DPM-Solver for sampling. For the unified case, we use a single U-Net model with 128 channels. For the separate case, three distinct U-Nets with 128 channels are used. For improved performance of the separate architecture, we implement two techniques: early stopping (ES) and tailored parameters (TP) to tackle the overfitting and parameter inefficiency discussed in Sec. 3. Under ES, the criteria is to stop training prior to overfitting. For TP, the three U-Nets are configured with 192, 128, and 16 channels decoders for Intervals 0, 1, and 2, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 332, + 288, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 288, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 288, + 513 + ], + "type": "text", + "content": "Our comparison and analysis in Tab. 3 reveal notable insights of our network design. Comparisons between the 2nd and 3rd rows (and between the 4th and 5th rows) on the separate architectures indicate that early stopping effectively mitigates overfitting and enhances generation quality. When comparing the 2nd and 4th rows (as well as the 3rd and 5th rows) on the separate architectures, we observe that optimizing parameter usage can achieve a significant decrease in FID under comparable GFLOPs. Most importantly, our multistage architecture, as shown in the 6th row, benefits from both unified and separate architectures, achieving the best FID (2.35, compared to 2.73 and 2.52). Comparing the 2nd row and the 4th row, the shared encoder not only prevents overfitting but also improves the convergence of the diffusion model as reported by the FID scores." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 71, + 543, + 261, + 650 + ], + "blocks": [ + { + "bbox": [ + 47, + 522, + 286, + 534 + ], + "lines": [ + { + "bbox": [ + 47, + 522, + 286, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 286, + 534 + ], + "type": "text", + "content": "Table 3. Ablation study on different diffusion model architectures." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 543, + 261, + 650 + ], + "lines": [ + { + "bbox": [ + 71, + 543, + 261, + 650 + ], + "spans": [ + { + "bbox": [ + 71, + 543, + 261, + 650 + ], + "type": "table", + "html": "
MethodGFLOPsFID(↓)
Unified17.652.73
Separate17.652.87
Separate (+ ES)17.652.80
Separate (+ TP)18.652.68
Separate (+ ES, TP)18.652.52
Multistage (Ours)18.652.35
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Clustering Methodt1t2FID(↓)
Timestep [20, 21]0.3300.6703.12
SNR [20]0.3480.7092.72
Gradient [20]0.3600.6602.75
Optimal Denoiser0.4420.6312.35
", + "image_path": "0453858cfea0a13d19a2601a611cf0f0e570be20ee1edca8974b8270fd47d282.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 442, + 462, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 462, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 462, + 455 + ], + "type": "text", + "content": "6. Conclusion & Future Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 569 + ], + "type": "text", + "content": "In this paper, we introduced a novel multi-stage framework for diffusion models (DM) to improve the training and sampling efficiency. We proposed an algorithm that divides the timestep into several stages. Based on these stages, we designed a stage-specific multi-decoder U-net architecture and a shared encoder across all stages. We conducted thorough numerical experiments with several SOTA diffusion model frameworks and confirmed the effectiveness of our strategy using small scale and large scale datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "In future research, it would be interesting to expand our multi-stage approach beyond unconditional diffusion models by considering conditional DMs and DM-based inverse problems solvers. Our experiment in Sec. 5.2 demonstrate that training latent diffusion models within our multi-stage framework requires only " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " of the computational effort needed for training standard latent diffusion models on the CelebA dataset. Thus, employing a multi-stage strategy could significantly reduce the computational demands for training large-scale stable diffusion models, such as those described in [8], which typically requires significant computations." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7379" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Jonathan Ho, Ajay Jain, and Pieter Abbeel. 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Although manifesting remarkable performance in generating untargeted adversarial perturbations, existing proposals still fail to achieve high targeted transferability. In this work, we discover that the adversarial perturbations' overfitting towards source models of mediocre generalization capability can hurt their targeted transferability. To address this issue, we focus on enhancing the source model's generalization capability to improve its ability to conduct transferable targeted adversarial attacks. In pursuit of this goal, we propose a novel model self-enhancement method that incorporates two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model, which mirrors the source model's structure, into the source model while flattening the source model's loss landscape. WS obtains an approximate ensemble of numerous pruned models to perform model augmentation, which can be conveniently synergized with SASD to elevate the source model's generalization capability and thus improve the resultant targeted perturbations' transferability. Extensive experiments corroborate the effectiveness of the proposed method. Notably, under the black-box setting, our approach can outperform the state-of-the-art baselines by a significant margin of $12.2\\%$ on average in terms of the obtained targeted transferability. Code is available at https://github.com/g4allff/SASD.", + "bbox": [ + 75, + 323, + 473, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 761, + 209, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite their wide range of applications in real-world scenarios, deep neural networks (DNNs) have shown vulnerability in the face of imperceptible adversarial perturbations [41, 43, 49, 50]. In recent years, numerous transfer attack methods have been proposed to evaluate the robustness of", + "bbox": [ + 75, + 787, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a0830ab200275dacf559d6f9e16ab206335a4ac742a4906a1d5aeb7eeffb325c.jpg", + "image_caption": [ + "Figure 1. The motivation of the proposed method that enhances the source model's generalization capability to enable more transferable targeted adversarial attacks." + ], + "image_footnote": [], + "bbox": [ + 504, + 291, + 738, + 411 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef2518e5cf97edaf880567b6f852d75b3f1866592960b1661a0d48e2268e9db5.jpg", + "image_caption": [ + "Source Model" + ], + "image_footnote": [], + "bbox": [ + 741, + 296, + 777, + 313 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5203ca12082f8a9889ee43ae567d087b6edf1517fbb9c01054e003ad720b3150.jpg", + "image_caption": [ + "Enhanced Model" + ], + "image_footnote": [], + "bbox": [ + 743, + 316, + 777, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/42a37a3c77603bac41dce95b7f387159c4b7e3f170ae192a87e8bdf899bf8425.jpg", + "image_caption": [ + "Target Model" + ], + "image_footnote": [], + "bbox": [ + 743, + 340, + 777, + 359 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4964f98c55aabe61b865f251be6d448f2b3ce392553035733e252c88aa2fc874.jpg", + "image_caption": [ + "adv" + ], + "image_footnote": [], + "bbox": [ + 753, + 368, + 777, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/238a9c1481956de0ae93d7aea391c429b5b45f8a7b0c46fca79c4ac5244f886a.jpg", + "image_caption": [ + "adv enhanced" + ], + "image_footnote": [], + "bbox": [ + 753, + 391, + 777, + 407 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "DNNs [1, 42, 44, 48]. Although existing approaches have demonstrated excellent performances on untargeted transfer attacks, it is still challenging to accomplish targeted transfer attacks, which require the attacker to generate perturbations that can mislead the black-box victims to return a target label [22, 30].", + "bbox": [ + 496, + 491, + 890, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adversarial perturbations are prone to overfit the source model and manifest limited targeted transferability when the source model's generalization capability is mediocre. Specifically, neural networks can capture features essential for decision-making, with some features being general while the others being model-specific [16]. Intuitively, adversarial examples that primarily manipulate model-specific features are unlikely to transfer well among different models. Working towards a more generalized source model can alleviate the reliance on model-specific features, thus enhancing the transferability of the synthesized adversarial examples [35].", + "bbox": [ + 496, + 583, + 892, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Therefore, we propose to enhance the source model's generalization capability to enable more transferable targeted adversarial attacks. We conceptually illustrate the motivation of our method in Figure 1. Since different models rely on different features to make decisions, and their loss landscapes are often sharp, the transferable targeted adversarial examples are likely to reside away from the local optima of different models. It is thus challenging to transfer the adversarial examples generated by the vanilla", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 875, + 205, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24615", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f6e62b387ab344c05a3ba6d8630cc7e62b4de7ec03a5d5fad99f191cf333ae22.jpg", + "image_caption": [ + "Figure 2. The overall procedure of SASD-WS." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 457, + 203 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "source model to a different target model. A viable solution is to enhance the source model's generalization capability to capture the general features learned by different models. This can be achieved by learning a flatter loss landscape that covers the transferable targeted adversarial examples in the low-loss region.", + "bbox": [ + 75, + 258, + 468, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a novel model self-enhancement method: SASD-WS, which incorporates Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to promote the source model's generalization capability. Then, we can employ the enhanced source model to produce targeted perturbations with better transferability. The overall procedure of our method is summarized in Figure 2. We explain the two major components of the proposed SASD-WS as follows:", + "bbox": [ + 75, + 352, + 468, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SASD. In the warm-up step of SASD, we employ the technique of Sharpness-Aware Minimization (SAM) [6] to fine-tune an auxiliary model, which mirrors the source model's structure. Specifically, during the fine-tuning of the auxiliary model, we simultaneously minimize its loss of sharpness and the cross-entropy loss between its predictions and ground-truth labels. Given the fine-tuned auxiliary model, we then enhance our source model by distilling the auxiliary model into the source model while minimizing the source model's loss of sharpness. As a result, SASD can effectively endow the source model with a flatter loss landscape and improve the resultant targeted perturbations' transferability.", + "bbox": [ + 75, + 489, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "WS. To further boost the generalization capability of the obtained SASD model, we propose WS for efficient model augmentation. Specifically, we apply random pruning to the obtained SASD model to produce numerous pruned models. The resultant ensemble of randomly pruned SASD models can possess better generalization capability than the original SASD model. However, generating adversarial examples with an ensemble model can be computationally expensive. Motivated by the approximation scheme in [17], we efficiently approximate the ensemble of randomly pruned SASD models by scaling the weights of the SASD model. Therefore, WS can be efficiently synergized with SASD to further boost the targeted transferability of the synthesized adversarial examples.", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, the main contributions of this work are:", + "bbox": [ + 517, + 90, + 857, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel model self-enhancement method incorporating two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model into the source model while flattening its loss landscape. WS then performs model augmentation with an efficient approximation. Their resonance promotes the source model's generalization capability and thus enables more transferable targeted adversarial attacks.", + "- We conduct extensive experiments to validate the superiority of the proposed method. Notably, compared with the state-of-the-art benchmarks, our approach can improve the targeted attack success rate by a significant margin of $12.2\\%$ on average under the black-box setting.", + "- We confirm that our attacks can transfer well to real-world applications, exceeding the state-of-the-art baselines by $8.4\\%$ on average. We also visualize the effectiveness of the proposed method from the perspective of the enhanced model's loss landscape, and validate the efficacy of our approach against defense methods." + ], + "bbox": [ + 500, + 107, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 425, + 640, + 440 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Transferable Adversarial Attack", + "text_level": 1, + "bbox": [ + 500, + 450, + 785, + 465 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the development of transfer attack techniques, there are currently three types of approaches to improve the perturbation's transferability:", + "bbox": [ + 498, + 474, + 890, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Enhancing the source model. As normally trained neural networks perform poorly in targeted attacks, several model enhancement methods have been proposed to improve the source model's capability to conduct targeted transfer attacks. These methods include replacing a single source model with an ensemble of models obtained by random dropout [23] and additional training epochs [9]. Springer et al. [35] instead utilizes adversarial fine-tuning to enhance the source model's ability to synthesize transferable adversarial examples. Our method also attempts to improve adversarial transferability by enhancing the source model. Nevertheless, unlike existing model enhancement-based attacks, we propose to flatten the source model's loss landscape to improve its generalization capability, enabling more transferable targeted attacks.", + "bbox": [ + 496, + 521, + 890, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Augmenting the input data. To boost adversarial transferability, some transfer attacks resort to input augmentation, such as image translation [3], random resizing and padding [46], and mixup [40]. Unlike prior efforts, a recent input augmentation-based attack technique, Spectrum Simulation Attack (SSA), proposes to apply a spectrum transformation to the input [27].", + "bbox": [ + 496, + 748, + 890, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rectifying the optimization procedure. Instead of greedily perturbing the clean images along the gradient of the cross-entropy loss [20], several attempts propose to im", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24616", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prove the optimization procedure to craft more transferable adversarial examples. Straightforward solutions include employing momentum [2] and Nesterov accelerated gradient [25]. Huang et al. [15] instead consider adding the intermediate feature loss into the attack objective to regularize the search of adversarial examples. The state-of-the-art attack of this kind, Reverse Adversarial Perturbation (RAP) [31], seeks adversarial examples located at a region with uniformly low loss values.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our attack can be conveniently combined with other transfer attacks based on input augmentation and optimization procedure rectification to further enhance the transferability of adversarial attacks.", + "bbox": [ + 75, + 227, + 468, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Improving DNNs' Generalization Ability", + "text_level": 1, + "bbox": [ + 76, + 295, + 426, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Foret et al. [6] propose Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness to improve the model's generalization ability. Hinton et al. [13] introduce knowledge distillation to transfer the knowledge of a teacher model to the student model [45]. Intriguingly, Stanton et al. [36] discover that knowledge distillation can enhance the student model's generalization ability. Building upon Sharpness-Aware Minimization and knowledge distillation methodologies, we propose Sharpness-Aware Self-Distillation (SASD) to integrate Sharpness-Aware Minimization with knowledge distillation, which can further improve the source model's generalization capability. Since a more generalized source model can better capture the general features learned by different models, the produced adversarial examples are more likely to possess better targeted transferability [35].", + "bbox": [ + 75, + 318, + 472, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 573, + 212, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 598, + 279, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first formulate the targeted transfer attack. Given a labeled image dataset $D$ and a target classifier $f_{\\mathrm{target}}$ , for an image-label pair $(x,y)\\in D$ , a targeted transfer attack aims to generate an adversarial example $x_{\\mathrm{adv}} = x + \\delta$ to mislead the target classifier $f_{\\mathrm{target}}$ to predict a specific target label $y_{\\mathrm{target}}\\neq y$ . Since the target classifier is black-box, a targeted transfer attack instead derives the adversarial example $x_{\\mathrm{adv}}$ with a white-box source model $f$ . It is usually accomplished by optimizing $x_{\\mathrm{adv}}$ to minimize the source model's cross-entropy loss $L_{\\mathrm{CE}}$ on the target label [8, 51]:", + "bbox": [ + 75, + 621, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {L _ {\\mathrm {C E}} (f (x + \\delta), y _ {\\text {t a r g e t}}),} \\tag {1} \\\\ \\mathrm {s . t .} \\left. | | \\delta | | _ {\\infty} \\leq \\epsilon . \\right. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 781, + 468, + 815 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To ensure that the perturbation $\\delta$ is imperceptible, attackers should also set a small perturbation budget $\\epsilon$ . After generating the adversarial example $x_{\\mathrm{adv}}$ with the source model, a targeted transfer attack directly uses $x_{\\mathrm{adv}}$ to attack the target classifier, with the goal of $f_{\\mathrm{target}}(x_{\\mathrm{adv}}) = y_{\\mathrm{target}}$ . To", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Sharpness-Aware Self-Distillation" + ], + "code_body": "Input: Fine-tuned auxiliary model \n1: Initialization: $n \\gets 0$ \n2: for every batch in the data loader do \n3: $n \\gets n + 1$ \n4: Calculate $L_{\\mathrm{distillation}}$ by Equation (3) \n5: $\\epsilon \\gets \\operatorname{argmax}_{\\| \\epsilon \\|_2 \\leq \\rho} \\epsilon^T \\nabla_{\\omega_s} L_{\\mathrm{distillation}}(\\omega_s)$ \n6: $g = \\nabla_{\\omega_s} L(\\omega_s)|_{\\omega_s + \\epsilon}$ \n7: $\\omega_s \\gets \\omega_s - lr \\cdot g$ \n8: if $n \\geq n_{\\mathrm{max}}$ then \n9: break \n10: end if \n11: end for \nOutput: SASD model", + "bbox": [ + 500, + 108, + 795, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "improve the attack success rate (i.e., the transferability) of the generated targeted perturbations, we propose enhancing the source model's generalization ability, detailed in the following sections.", + "bbox": [ + 496, + 348, + 893, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Sharpness-Aware Self-Distillation", + "text_level": 1, + "bbox": [ + 500, + 417, + 794, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fine-tuning the auxiliary model. We start with a pretrained source model and fine-tune it on its original training dataset to obtain the auxiliary model. The fine-tuning procedure follows Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness [6]. Specifically, in each iteration, we first perform back-propagation based on the cross-entropy loss [7] between the output of the auxiliary model and the ground-truth label. We then modify the auxiliary model's weight $\\omega$ by adding a perturbation $\\epsilon_{m}$ that can maximize the cross-entropy loss:", + "bbox": [ + 496, + 441, + 890, + 609 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {m} = \\underset {\\epsilon_ {m}} {\\arg \\max } L _ {\\mathrm {C E}} (f (\\omega + \\epsilon_ {m}, x), y), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 621, + 890, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f(\\omega, x)$ is the output of a neural network $f$ given the model weight $\\omega$ and the input $x$ . We perform backpropagation again based on the perturbed weight to minimize the auxiliary model's loss of sharpness.", + "bbox": [ + 496, + 657, + 890, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Distilling the auxiliary model. After obtaining a finetuned auxiliary model, we distill it into the source model to enhance its generalization ability. Specifically, we first make the source model's probability output close to the auxiliary model's. Let $q_{1} = \\phi_{1}(l_{\\mathrm{aux}})$ denote the probability output of the auxiliary model, where $\\phi_{1}$ is a differentiable transformation, and $l_{\\mathrm{aux}}$ is the auxiliary model's logit output. In our SASD, we set $\\phi_{1}(l_{\\mathrm{aux}}) = \\mathrm{Softmax}(l_{\\mathrm{aux}} / \\tau)$ , where $\\tau$ is the distillation temperature. The larger the temperature is, the softer the probability distribution will be. Similarly, let $q_{2} = \\phi_{2}(l_{\\mathrm{source}})$ denote the probability output of the source model, where $\\phi_{2}(l_{\\mathrm{source}}) =$", + "bbox": [ + 496, + 719, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24617", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathrm{Softmax}(l_{\\mathrm{source}} / \\tau)$ . To minimize the prediction difference between the auxiliary and source models, we employ the Kullback-Leibler divergence $D_{\\mathrm{KL}}$ [18] between $q_{1}$ and $q_{2}$ as the distillation loss:", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) = \\mathbb {E} _ {(x, y) \\in D} \\left[ D _ {\\mathrm {K L}} \\left(q _ {1} (x, y), q _ {2} (x, y)\\right) \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 162, + 468, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then simultaneously minimize the distillation loss and its sharpness:", + "bbox": [ + 76, + 205, + 468, + 236 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\omega_ {s}} \\mathbb {E} _ {(x, y) \\in D} [ L (\\omega_ {s}) ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 248, + 468, + 270 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 282, + 122, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L \\left(\\omega_ {s}\\right) = \\max _ {\\| \\epsilon \\| _ {2} \\leq \\rho} L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s} + \\epsilon\\right) \\\\ \\approx \\max _ {\\| \\epsilon \\| _ {2} \\leq \\rho} \\left[ L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) + \\epsilon^ {T} \\nabla_ {\\omega_ {s}} L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) \\right]. \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 304, + 468, + 373 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $lr$ be the learning rate, and $n_{\\mathrm{max}}$ be the maximum iteration number. Algorithm 1 summarizes the SASD process.", + "bbox": [ + 76, + 385, + 468, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Weight Scaling", + "text_level": 1, + "bbox": [ + 76, + 440, + 228, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further boost the generalization capability of the obtained SASD model, we apply the network pruning method [47] to generate an ensemble of pruned SASD models. Specifically, we randomly prune the convolutional layers of the obtained SASD model with a probability of $1 - p$ . Then, the weight of a pruned SASD model is:", + "bbox": [ + 76, + 463, + 468, + 554 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\omega_ {\\text {p r u n e d}} = \\omega \\odot (\\mathbf {1} - \\xi (\\omega , 1 - p)), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 566, + 468, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{1}$ denotes the all-ones matrix with the same size as the weight of the SASD model. $\\xi (\\omega ,1 - p)$ indicates the randomly selected weights in the convolutional layers to be pruned. By applying the Hadamard product $\\odot$ that represents element-wise multiplication to the weight, we can obtain the pruned model with some weights in the convolutional layers setting to zero.", + "bbox": [ + 76, + 594, + 468, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by the approximation scheme in [17], we further approximate an ensemble of pruned models with a weight-scaled model. Specifically, let $\\overline{f} = \\frac{1}{n}\\sum_{i=1}^{n}f(\\omega_i)$ be the ensemble of models with the same structure but different weights. Let $\\overline{\\omega} = \\frac{1}{n}\\sum_{i=1}^{n}\\omega_i$ be the average weight of the component networks in the ensemble, and $\\eta_i = \\omega_i - \\overline{\\omega}$ . For $i\\in \\{i|1\\leq i\\leq n,i\\in \\mathbb{N}\\}$ , we have:", + "bbox": [ + 76, + 699, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\eta_ {i} = 0, (7) \\\\ f \\left(\\omega_ {i}, x\\right) = f (\\bar {\\omega} + \\eta_ {i}, x) (8) \\\\ = f (\\bar {\\omega}, x) + \\eta_ {i} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta_ {i} \\| _ {2} ^ {2}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 818, + 468, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, we can derive that:", + "bbox": [ + 519, + 90, + 718, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {f} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} f (\\omega_ {i}, x) \\\\ = \\frac {1}{n} \\sum_ {i = 1} ^ {n} [ f (\\bar {\\omega}, x) + \\eta_ {i} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta_ {i} \\| _ {2} ^ {2}\\right) ] \\tag {9} \\\\ = f (\\bar {\\omega}, x) + \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\eta_ {j} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta \\| _ {2} ^ {2}\\right) \\\\ = f (\\bar {\\omega}, x) + O \\left(\\| \\eta \\| _ {2} ^ {2}\\right) \\approx f (\\bar {\\omega}, x). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 116, + 890, + 260 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It implies that a single model with the average weight of multiple models can replace the ensemble of these models as long as their weight differences are small enough.", + "bbox": [ + 498, + 270, + 892, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, if the pruning probability $1 - p$ is small, the ensemble of infinite pruned SASD models can be approximated by a single SASD model that is weight-scaled by the scaling ratio $p$ (i.e., the SASD-WS model):", + "bbox": [ + 498, + 316, + 890, + 376 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {f} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} f \\left(\\omega_ {i} ^ {\\text {p r u n e d S A S D}}, x\\right) \\tag {10} \\\\ \\approx f (\\bar {\\omega}, x) = f (p \\cdot \\omega^ {\\mathrm {S A S D}}, x) = f _ {\\mathrm {S A S D - W S}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 387, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\omega^{\\mathrm{SASD}}$ is the weight of the SASD model before pruning.", + "bbox": [ + 498, + 458, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Attacking Algorithm", + "text_level": 1, + "bbox": [ + 500, + 500, + 696, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After obtaining the SASD-WS model, we generate targeted adversarial examples with the TI-DI-MI method [2, 3, 46]. Specifically, given the input data $x$ , the source model $f$ , and the target class $y_{target}$ , the perturbation $\\delta_{i+1}$ can be iteratively updated by:", + "bbox": [ + 498, + 522, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {i + 1} = \\operatorname {C l i p} _ {\\delta_ {i}} ^ {\\epsilon_ {\\mathrm {p}}} \\left\\{\\delta_ {i} + \\alpha \\cdot \\operatorname {s i g n} \\left(g _ {i + 1}\\right) \\right\\}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 608, + 890, + 627 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng _ {i + 1} = g _ {i} + W \\cdot \\nabla_ {\\delta} \\frac {\\mathcal {L} (\\mathrm {D I} (x + \\delta_ {i}) , y _ {\\text {t a r g e t}} ; f)}{\\| \\mathcal {L} (\\mathrm {D I} (x _ {i} + \\delta_ {i}) , y _ {\\text {t a r g e t}} ; f) \\| _ {1}}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 628, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\alpha$ is the step size for attacks. $W$ is the Gaussian kernel for image translation. $\\mathcal{L}$ is the attack objective function. DI denotes the input transformation of random resizing and padding. The generated adversarial perturbation is $l_{\\infty}$ -norm bounded by the maximum perturbation budget $\\epsilon_p$ .", + "bbox": [ + 500, + 672, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 762, + 632, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 786, + 689, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We focus on attacking the image classifiers trained on the ImageNet (ILSVRC 2012) dataset [33]. We perform SASD with the standard training and validation splits of the ImageNet dataset. We apply our method to eight models pretrained on ImageNet: Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101", + "bbox": [ + 498, + 810, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24618", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/7a2784597c13542bb14afa3457ef0e1e8932f552678bd314e4954d2d301bcf52.jpg", + "table_caption": [ + "Table 1. Targeted transfer attack success rates (%) with a single source model. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. \"Pre-trained\" means directly using the normally trained model as the source model without modification. \" * \" indicates white-box cases. We run each method five times and show the mean and standard deviation of the results." + ], + "table_footnote": [], + "table_body": "
MethodSource Model: Inc-v3Source Model: Res50
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained99.0 ± 0.0*2.1 ± 0.13.6 ± 0.11.9 ± 0.37.8 ± 0.398.7 ± 0.1*64.3 ± 0.953.8 ± 0.7
RAP93.6 ± 0.0*3.5 ± 0.05.4 ± 0.03.9 ± 0.014.4 ± 0.098.5 ± 0.0*56.2 ± 0.052.6 ± 0.0
GhostNet97.9 ± 0.2*8.1 ± 0.312.8 ± 0.16.6 ± 0.413.2 ± 0.498.0 ± 0.2*75.0 ± 0.368.4 ± 0.6
LGV55.0 ± 0.2*40.5 ± 0.348.3 ± 0.349.5 ± 0.254.5 ± 0.893.2 ± 0.2*90.0 ± 0.184.0 ± 0.2
SASD-WS94.6 ± 0.2*44.4 ± 0.257.6 ± 1.153.8 ± 0.870.3 ± 0.897.2 ± 0.4*93.0 ± 0.288.7 ± 0.4
MethodSource Model: Dense121Source Model: VGG16
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained6.0 ± 0.439.3 ± 0.698.8 ± 0.2*33.6 ± 0.50.9 ± 0.29.8 ± 0.512.2 ± 0.595.4 ± 0.3*
RAP12.0 ± 0.041.2 ± 0.097.8 ± 0.0*37.4 ± 0.02.1 ± 0.09.9 ± 0.09.8 ± 0.085.8 ± 0.0*
GhostNet10.4 ± 0.649.6 ± 0.898.6 ± 0.1*44.0 ± 0.61.1 ± 0.213.0 ± 0.114.9 ± 0.794.9 ± 0.2*
LGV51.3 ± 0.380.8 ± 0.292.9 ± 0.2*75.8 ± 0.2————
SASD-WS61.6 ± 0.687.5 ± 0.297.7 ± 0.1*82.7 ± 0.616.3 ± 0.741.9 ± 0.551.7 ± 0.294.5 ± 0.3*
", + "bbox": [ + 109, + 156, + 867, + 366 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "[11], ResNet-152 [11], DenseNet-121 [14], and VGGNet-16 [34]. All these pre-trained models' weights are publicly accessible1. For SASD, we set the distillation temperature $\\tau = 1$ and the learning rate $lr = 0.05$ for all source models. We set WS's scaling ratio $p$ to 0.93 for each SASD-WS model.", + "bbox": [ + 75, + 388, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare the targeted transfer attack performance of our SASD-WS method with the state-of-the-art model enhancement-based attacks: GhostNet [23] and LGV [9]. Although RAP [31] works by rectifying the optimization procedure and does not modify the source model, its motivation is similar to our method. Therefore, we also compare our approach with RAP. We implement the baseline methods following the default settings in their original papers. For LGV, we additionally train the source model on the ImageNet training set for ten epochs [33]. We then obtain four LGV models in each epoch, leading to 40 LGV models for each source model. We cannot apply LGV to VGGNet-16 since the default settings of LGV are not compatible with VGGNet-16. Notably, since LGV and GhostNet transform a single source model into multiple models to generate adversarial examples, we follow their papers to ensemble these models with the longitudinal ensemble method [23]. In contrast, we only transform a single source model into a single SASD-WS model when generating adversarial examples.", + "bbox": [ + 75, + 482, + 468, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the practice in the literature [2, 23], we set the step size $\\alpha = 2 / 255$ and the maximum perturbation budget $\\epsilon_{p} = 16 / 255$ . We set the maximum iteration number $t_{\\mathrm{max}} = 100$ in the adversarial perturbation generation", + "bbox": [ + 75, + 786, + 468, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "process. We conduct targeted transfer attacks on NIPS17 targeted adversarial attack competition dataset[21]. All experiments are implemented with PyTorch 2.0.1 and conducted with an NVIDIA GeForce RTX 4090 GPU of 24 GB memory.", + "bbox": [ + 500, + 388, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Attacking Performance", + "text_level": 1, + "bbox": [ + 500, + 477, + 718, + 493 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Targeted transfer attacks with a single source model. We first evaluate the performance of our method when only a single source model is available. We use the logit loss $L_{\\mathrm{Logit}} = -l^{(t)}(x + \\delta)$ proposed in [51] as the attack objective function $\\mathcal{L}$ , where $l^{(t)}(\\cdot)$ is the output logit of the source model concerning the target label. Table 1 reports the attack success rate of each method.", + "bbox": [ + 498, + 501, + 890, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 1, our method consistently outperforms the state-of-the-art baselines by a significant margin of $12.2\\%$ on average under the black-box settings. Besides improving the targeted attack success rate under the black-box settings, SASD-WS can also maintain high white-box attack performance.", + "bbox": [ + 496, + 608, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Targeted transfer attacks with an ensemble of source models. We then test the performance of our method when multiple source models are available, including Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. For the target models, due to the widespread application of adversarial training techniques [19, 28, 39], we first consider adversially trained models. We also consider the scenarios where the target and source models are from different structure families. Specifically, we evaluate the effectiveness of the targeted perturbation on Vision", + "bbox": [ + 496, + 699, + 892, + 851 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "https://github.com/Cadene/pretrained-models.pytorch, https://pytorch.org/vision/stable/models.html", + "bbox": [ + 75, + 862, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2https://github.com/cleverhans-lab/cleverhans/ blob/master/cleverhans_v3.1.0/examples/nips17_adversarial_competition/dataset/dev_dataset.csv", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24619", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ad04c565ffc6b903115c30d443d49724179cea2c8c117dd13db56665a2fda08a.jpg", + "table_caption": [ + "Table 2. Targeted transfer attack success rates (%) with an ensemble of six source models: Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. \"Pre-trained\" means directly using the normally trained model as the source model without modification. We run each method five times and show the mean and standard deviation of the results." + ], + "table_footnote": [], + "table_body": "
MethodInc-v3adv ens3Inc-v3adv ens4IncRes-v2adv ensViT-B/16ViT-L/16CLIP (RN50)CLIP (ViT-B/32)CLIP (ViT-L/14)
Pre-trained0.0 ± 0.00.1 ± 0.00.0 ± 0.03.1 ± 0.31.5 ± 0.216.3 ± 0.72.0 ± 0.13.2 ± 0.4
RAP1.7 ± 0.01.5 ± 0.00.1 ± 0.06.0 ± 0.03.0 ± 0.017.7 ± 0.05.1 ± 0.04.8 ± 0.0
GhostNet0.7 ± 0.11.1 ± 0.20.2 ± 0.09.1 ± 0.55.7 ± 0.133.0 ± 0.55.3 ± 0.210.7 ± 0.1
LGV8.1 ± 0.26.7 ± 0.21.7 ± 0.119.6 ± 0.013.0 ± 0.259.4 ± 0.322.4 ± 0.228.4 ± 0.3
SASD-WS16.6 ± 0.213.5 ± 0.35.3 ± 0.134.1 ± 0.225.1 ± 0.258.7 ± 0.524.2 ± 0.234.7 ± 0.2
", + "bbox": [ + 80, + 155, + 893, + 252 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a14d9cfbfb4711b7429d4d959c8eaa7ce8a53d333c4b3eb9c8bbef99ffd780b1.jpg", + "table_caption": [ + "Table 3. Targeted transfer attack success rates (\\%) of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. We run each test five times and show the mean and standard deviation of the results." + ], + "table_footnote": [], + "table_body": "
Method→ Inc-v3→ Dense121→ VGG16
Pre-trained7.7 ± 0.363.7 ± 0.156.2 ± 0.5
WS35.0 ± 0.584.7 ± 0.277.8 ± 0.4
SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
SASD-WS70.3 ± 0.893.0 ± 0.288.7 ± 0.4
", + "bbox": [ + 107, + 354, + 439, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Transformers (ViTs) [4] and CLIP models [32]. ViTs apply the transformer models to visual data and leverage the self-attention mechanism to process data patches. CLIP models utilize both the image and text encoders to encode and calculate the similarity of the image-text pairs. They can produce the similarity score for each label. In our experiments, we use Inc-v3adv ens3 [39], Inc-v3adv ens4 [39], and IncRes-v2adv ens [39] as the target adversarially trained models. We consider ViT-B/16 and ViT-L/16 as the target ViTs. We target CLIP models with ResNet50, ViT-B/32, and ViT-L/14 as the image encoders, respectively. We use the cross-entropy loss as our attack objective function $\\mathcal{L}$ .", + "bbox": [ + 75, + 460, + 468, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report the results in Table 2. It shows that SASDWS can generate more transferable targeted perturbations than the other baseline methods, with a significant improvement of $6.6\\%$ on average. While most baselines can generate perturbations that can manifest a certain degree of targeted transferability, RAP performs poorly under the ensemble source model setting compared with the other baseline methods, with an average attack success rate of only $8.2\\%$ . We believe that the poor targeted attack performance of RAP under the ensemble source model setting is due to the ensemble model's lack of a uniformly low-loss region. Therefore, it highlights the need to enhance the source model to enable more transferable targeted adversarial attacks. Besides, our method's high targeted attack success rates against different target models, including adversarially trained models, reveal the potential security risk of DNNs and call for more effort to improve DNNs' robustness.", + "bbox": [ + 75, + 643, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Targeted transfer attack success rates (\\%) when using different SASD variants: (1) SASD without fine-tuning the auxiliary model (SASD w/o FT Aux), (2) SASD without distilling the auxiliary model (SASD w/o D), (3) SASD via the commonly used knowledge distillation method (SASD w/ KD), and (4) our proposed SASD. We run each test five times and show the mean and standard deviation of the results.", + "bbox": [ + 496, + 272, + 893, + 369 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7f40efca568a321d3c3cbdb935689bd5ea24c01258aa98551e4844f6ca1b18a6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method→ Inc-v3→ Dense121→ VGG16
SASD w/o FT Aux32.2 ± 0.387.1 ± 0.081.3 ± 0.1
SASD w/o D29.6 ± 0.587.7 ± 0.279.5 ± 0.3
SASD w/ KD38.5 ± 0.490.7 ± 0.184.9 ± 0.2
Our SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
", + "bbox": [ + 514, + 381, + 880, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ness against adversarial perturbations.", + "bbox": [ + 500, + 486, + 753, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 512, + 653, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Validating the contribution of SASD and WS. We validate the contribution of two major components in our method: SASD and WS. Specifically, following the setting of Table 1, we compare the targeted attack success rates of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. The results are shown in Table 3. We can see that both SASD and WS can improve the pre-trained source models' capability to launch targeted transfer attacks. Besides, combining SASD and WS can further enhance the source model to generate more transferable targeted adversarial perturbations.", + "bbox": [ + 496, + 536, + 890, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Validating the design of SASD. We validate the design of SASD by examining SASD's two steps: fine-tuning the auxiliary model and distilling the auxiliary model. Specifically, for examining the first step of SASD, we conduct SASD without fine-tuning the auxiliary model. In other words, we conduct the second step of SASD directly with a pre-trained source model. For examining the second step of SASD, we conduct SASD without distilling the auxiliary model. In other words, we directly use the fine-tuned auxiliary model to generate adversarial examples. Besides, we also consider distilling the auxiliary model via the commonly used knowledge distillation method [13]. Specif", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24620", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c3ab4dcb7a815d15b4a55cfc50d83c0d0262f12047e8e3081506ab9e99d2b354.jpg", + "table_caption": [ + "Table 5. Targeted transfer attack success rates (\\%) against different defense methods. All methods are combined with the TI-DI-MI technique to generate adversarial perturbations. We run each test five times and show the mean and standard deviation of the results." + ], + "table_footnote": [], + "table_body": "
MethodJPEGHGDNRPNoisyMixAugMix
Pre-trained99.7 ± 0.01.4 ± 0.13.7 ± 0.00.4 ± 0.00.7 ± 0.0
RAP88.7 ± 0.00.5 ± 0.014.3 ± 0.01.0 ± 0.00.5 ± 0.0
GhostNet99.9 ± 0.01.4 ± 0.012.4 ± 0.62.4 ± 0.00.8 ± 0.0
LGV99.4 ± 0.17.6 ± 0.22.0 ± 0.36.5 ± 0.11.4 ± 0.0
SASD-WS99.8 ± 0.023.5 ± 0.117.9 ± 0.58.0 ± 0.12.0 ± 0.0
", + "bbox": [ + 81, + 155, + 467, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/026c2789f82a5ecfe57a004a751dc60178029ed8237211a2d319bb1109e902c4.jpg", + "image_caption": [ + "Figure 3. Successful targeted adversarial examples on Google Cloud Vision. The target class is tigers." + ], + "image_footnote": [], + "bbox": [ + 117, + 247, + 250, + 349 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4848d76355ba67b797ea6de594536f44156b1b19753db42126f693667b148610.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 256, + 250, + 429, + 349 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ically, the commonly used knowledge distillation method combines the cross-entropy loss with respect to the true label and the Kullback-Leibler divergence with respect to the prediction of the teacher model as the distillation loss. Following the setting of Table 1, we examine the performance of targeted adversarial perturbations generated by the above SASD variants. The results are shown in Table 4. When employing the normal knowledge distillation method, we distill the auxiliary model for ten epochs to maximize the attack performance. Our SASD instead only needs less than one epoch distillation. Nevertheless, our SASD method can still surpass the normal knowledge distillation method. Besides, the SASD model's performance improves when employing a fine-tuned auxiliary model, and distilling the auxiliary model performs better than directly using the fine-tuned auxiliary model. Therefore, the experimental results validate the design of our SASD.", + "bbox": [ + 75, + 414, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Further Analysis", + "text_level": 1, + "bbox": [ + 76, + 681, + 243, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Transfer attacks against defense methods. In this part, we evaluate SASD-WS's targeted attack performance against several adversarial defense methods and common corruption defense methods, including JPEG [10], HGD [24], NRP [29], NoisyMix [5], and AugMix [12]. We use the same experimental settings as those in the ensemble targeted and untargeted attack experiments with an ensemble of source models (Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101 [11], ResNet-152 [11]).", + "bbox": [ + 75, + 703, + 467, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5 presents the results of the targeted transfer attack. We can see that SASD-WS can effectively generate effective perturbations against these defense methods in tar", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8a857046165a1175fa4b60ee5cd69efbf6e09dbc723cb92004621517eda63e66.jpg", + "table_caption": [ + "Table 6. Comparison of the average $l_{2}$ -norm across 100 images for (1) the logit output difference of the ensemble of pruned models and the corresponding WS model, and (2) the standard deviation among the logit outputs of pruned models in the ensemble. Results for the ensemble of 20/50/100 pruned models are reported." + ], + "table_footnote": [], + "table_body": "
2050100
Output Difference30.7129.5429.57
Standard Deviation26.8726.6626.36
", + "bbox": [ + 555, + 169, + 841, + 226 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "geted attack settings. Even though for defense methods like NoisyMix and AugMix, most of the tested adversarial attack methods failed to achieve successful targeted attack, SASD-WS can still generate targeted perturbations with superior transferability compared with other baseline methods and achieves a nearly $100\\%$ attack success rate in attacking JPEG. These results show from another perspective that our approach can generate adversarial perturbations with higher transferability.", + "bbox": [ + 496, + 250, + 890, + 385 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Attacking real-world applications. We launch targeted transfer attacks against Google Cloud Vision to verify the practical applicability of the proposed method. Similar to previous experiments, we use an ensemble of six source models as the source model. We randomly sample 500 images from the NIPS17 targeted adversarial attack competition dataset as the test set to generate adversarial perturbations. Following the experimental settings in [26], when the labels with similar semantic meanings to the target label appear in the predicted labels of Google Cloud Vision, we regard the attack as successful. Although Google Cloud Vision will return the labels with probabilities more than $50.0\\%$ , we only consider the top-5 labels as the predicted labels.", + "bbox": [ + 496, + 386, + 892, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental results show that our method can achieve a targeted transfer attack success rate of $40.2\\%$ . In contrast, the baseline methods, LGV, GhostNet, RAP, and Pretrained, can only attain a targeted transfer attack success rate of $31.8\\%, 17.0\\%, 4.6\\%,$ and $3.6\\%$ , respectively. Figure 3 presents some of the adversarial examples generated by our method.", + "bbox": [ + 496, + 598, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Validating WS. We further validate the effectiveness of our Weight Scaling (WS) method in simulating an ensemble of source models. Intuitively, if the output of the pruned models' ensemble is close to that of the corresponding WS model, the difference between their outputs should be within the standard deviation among the pruned models' outputs in the ensemble. Therefore, we calculate the $l_{2}$ -norm value of the difference between the logit outputs of the pruned models' ensemble and the corresponding WS model. We also compute the $l_{2}$ -norm value of the standard deviation among the pruned models' logit outputs in the ensemble. The results are shown in Table 6. According to the three-sigma rule, we can see that the output difference be", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24621", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad2559f7e7b94a8fe8a3be833761b5386561a43284157b644ea11f714d0b442c.jpg", + "image_caption": [ + "Figure 4. Targeted transfer attack success rates $(\\%)$ of the base model (SASD ResNet-50), the longitudinal ensemble of pruned base models, and the WS version of the base model (SASD-WS ResNet-50)." + ], + "image_footnote": [], + "bbox": [ + 218, + 90, + 401, + 223 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e35000de00261d8ae4ec091024ab3288f6b6c0e8fbd6712269fb69860fe4e648.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 405, + 90, + 575, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/14c8290d1bdec73c5bed48185bd717b9cc318a6d7f4ba5353d667852b781115f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 578, + 90, + 750, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9f281f9513cc24918e41f59e3b9a7c33c87fa6a4aad602d0b229a7e252f01c2b.jpg", + "image_caption": [ + "Figure 5. The change of the loss landscapes with the application of our method. The fine-tuned ResNet-50 is the auxiliary model adopted in our SASD method." + ], + "image_footnote": [], + "bbox": [ + 106, + 285, + 285, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dffdf088adb92789db15bbbcdb38ba1c1ce934398bcb1c551464c229fe2f0824.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 285, + 480, + 411 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/16efc18a6fdaabf5f517c36d12eb4b9fee2bd75e551a246814a8c610c50107ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 285, + 674, + 411 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/82022adcb754f5a2db7760015660c3028fe3a87a6f9322e27485bac925a931cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 285, + 870, + 411 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tween the pruned models' ensemble and the corresponding WS model falls into the three-sigma range of the internal variability of the pruned models in the ensemble. Therefore, the output of the WS model is not an outlier among the pruned models' outputs, which implies that the output of the WS model is close to the ensemble model.", + "bbox": [ + 75, + 478, + 468, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Moreover, we compare the targeted attack performance of a single weight-scaled SASD model and the ensemble of pruned SASD models. Specifically, we generate adversarial perturbations by employing a longitudinal ensemble of pruned SASD models with a pruning rate of $1 - p = 0.07$ . Therefore, we set our WS method's scaling ratio $p = 0.93$ . Figure 4 shows the targeted transfer attack success rates of three types of source models with SASD ResNet-50 as the base model. According to the attack performance, we can see that our WS method can reasonably approximate the ensemble of pruned models.", + "bbox": [ + 75, + 575, + 468, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualizing the effectiveness of SASD-WS. Our SASD-WS attempts to promote the source model's generalization capability to enable more transferable targeted adversarial attacks. To visualize the effectiveness of our SASD-WS on improving the source model's generalization capability, we depict the change of the loss landscapes by applying our method in Figure 5. We can see that with the application of our approach, the loss landscape of the resultant enhanced model becomes flatter, which can help to capture general features learned by different models [6, 16, 35]. Therefore,", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the enhanced model is more likely to cover the transferable targeted adversarial examples in its low-loss region, facilitating more transferable targeted adversarial attacks.", + "bbox": [ + 498, + 478, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 547, + 617, + 563 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work presents a novel model self-enhancement method, incorporating Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to enhance the source model's capability to generate more transferable targeted perturbations. Extensive experiments show that our method can significantly outperform the state-of-the-art approaches. Notably, under the black-box setting, we can surpass the state-of-the-art baselines by a significant margin of $12.2\\%$ on average. We also validate the design of our method by several ablation studies and the practical applicability of the proposed method by attacking a popular real-world application. We believe that our approach can serve as a strong benchmark when evaluating the robustness of DNNs and an effective patch when conducting adversarial training.", + "bbox": [ + 496, + 575, + 890, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 811, + 651, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 62206318).", + "bbox": [ + 498, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24622", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yang Deng, Weibin Wu, Jianping Zhang, and Zibin Zheng. Blurred-dilated method for adversarial attacks. In Advances in Neural Information Processing Systems, pages 58613-58624, 2023. 1", + "[2] Yinpeng Dong, Fangzhou Liao, Tianyu Pang, Hang Su, Jun Zhu, Xiaolin Hu, and Jianguo Li. Boosting adversarial attacks with momentum. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9185-9193, 2018. 3, 4, 5", + "[3] Yinpeng Dong, Tianyu Pang, Hang Su, and Jun Zhu. 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In Advances in Neural Information Processing Systems, pages 6115-6128, 2021. 3, 5" + ], + "bbox": [ + 501, + 92, + 890, + 867 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24624", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/bed83424-cf5b-430d-ae99-b81617d05b70_model.json b/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/bed83424-cf5b-430d-ae99-b81617d05b70_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2a1173db820c9f96322e50e771b5272837fc6b11 --- /dev/null +++ b/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/bed83424-cf5b-430d-ae99-b81617d05b70_model.json @@ -0,0 +1,2343 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.153, + 0.131, + 0.82, + 0.175 + ], + "angle": 0, + "content": "Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.204, + 0.728, + 0.222 + ], + "angle": 0, + "content": "Han Wu* Guanyan Ou* Weibin Wu† Zibin Zheng" + }, + { + "type": "text", + "bbox": [ + 0.262, + 0.223, + 0.709, + 0.24 + ], + "angle": 0, + "content": "School of Software Engineering, Sun Yat-sen University" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.242, + 0.79, + 0.258 + ], + "angle": 0, + "content": "{wuhan36, ougy3}@mail2.sysu.edu.cn, {wuwb36, zhzibin}@mail.sysu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.734 + ], + "angle": 0, + "content": "Various transfer attack methods have been proposed to evaluate the robustness of deep neural networks (DNNs). Although manifesting remarkable performance in generating untargeted adversarial perturbations, existing proposals still fail to achieve high targeted transferability. In this work, we discover that the adversarial perturbations' overfitting towards source models of mediocre generalization capability can hurt their targeted transferability. To address this issue, we focus on enhancing the source model's generalization capability to improve its ability to conduct transferable targeted adversarial attacks. In pursuit of this goal, we propose a novel model self-enhancement method that incorporates two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model, which mirrors the source model's structure, into the source model while flattening the source model's loss landscape. WS obtains an approximate ensemble of numerous pruned models to perform model augmentation, which can be conveniently synergized with SASD to elevate the source model's generalization capability and thus improve the resultant targeted perturbations' transferability. Extensive experiments corroborate the effectiveness of the proposed method. Notably, under the black-box setting, our approach can outperform the state-of-the-art baselines by a significant margin of \\(12.2\\%\\) on average in terms of the obtained targeted transferability. Code is available at https://github.com/g4allff/SASD." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.762, + 0.21, + 0.779 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Despite their wide range of applications in real-world scenarios, deep neural networks (DNNs) have shown vulnerability in the face of imperceptible adversarial perturbations [41, 43, 49, 50]. In recent years, numerous transfer attack methods have been proposed to evaluate the robustness of" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.292, + 0.74, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.297, + 0.778, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.299, + 0.871, + 0.313 + ], + "angle": 0, + "content": "Source Model" + }, + { + "type": "image", + "bbox": [ + 0.744, + 0.318, + 0.779, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.322, + 0.889, + 0.335 + ], + "angle": 0, + "content": "Enhanced Model" + }, + { + "type": "image", + "bbox": [ + 0.744, + 0.341, + 0.779, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.344, + 0.868, + 0.358 + ], + "angle": 0, + "content": "Target Model" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.369, + 0.778, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.369, + 0.858, + 0.387 + ], + "angle": 0, + "content": "adv" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.392, + 0.778, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.391, + 0.842, + 0.41 + ], + "angle": 0, + "content": "adv enhanced" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.423, + 0.895, + 0.465 + ], + "angle": 0, + "content": "Figure 1. The motivation of the proposed method that enhances the source model's generalization capability to enable more transferable targeted adversarial attacks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.583 + ], + "angle": 0, + "content": "DNNs [1, 42, 44, 48]. Although existing approaches have demonstrated excellent performances on untargeted transfer attacks, it is still challenging to accomplish targeted transfer attacks, which require the attacker to generate perturbations that can mislead the black-box victims to return a target label [22, 30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.765 + ], + "angle": 0, + "content": "Adversarial perturbations are prone to overfit the source model and manifest limited targeted transferability when the source model's generalization capability is mediocre. Specifically, neural networks can capture features essential for decision-making, with some features being general while the others being model-specific [16]. Intuitively, adversarial examples that primarily manipulate model-specific features are unlikely to transfer well among different models. Working towards a more generalized source model can alleviate the reliance on model-specific features, thus enhancing the transferability of the synthesized adversarial examples [35]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Therefore, we propose to enhance the source model's generalization capability to enable more transferable targeted adversarial attacks. We conceptually illustrate the motivation of our method in Figure 1. Since different models rely on different features to make decisions, and their loss landscapes are often sharp, the transferable targeted adversarial examples are likely to reside away from the local optima of different models. It is thus challenging to transfer the adversarial examples generated by the vanilla" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.207, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.222, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24615" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.09, + 0.458, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.213, + 0.414, + 0.228 + ], + "angle": 0, + "content": "Figure 2. The overall procedure of SASD-WS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.259, + 0.47, + 0.35 + ], + "angle": 0, + "content": "source model to a different target model. A viable solution is to enhance the source model's generalization capability to capture the general features learned by different models. This can be achieved by learning a flatter loss landscape that covers the transferable targeted adversarial examples in the low-loss region." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.488 + ], + "angle": 0, + "content": "To this end, we propose a novel model self-enhancement method: SASD-WS, which incorporates Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to promote the source model's generalization capability. Then, we can employ the enhanced source model to produce targeted perturbations with better transferability. The overall procedure of our method is summarized in Figure 2. We explain the two major components of the proposed SASD-WS as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.688 + ], + "angle": 0, + "content": "SASD. In the warm-up step of SASD, we employ the technique of Sharpness-Aware Minimization (SAM) [6] to fine-tune an auxiliary model, which mirrors the source model's structure. Specifically, during the fine-tuning of the auxiliary model, we simultaneously minimize its loss of sharpness and the cross-entropy loss between its predictions and ground-truth labels. Given the fine-tuned auxiliary model, we then enhance our source model by distilling the auxiliary model into the source model while minimizing the source model's loss of sharpness. As a result, SASD can effectively endow the source model with a flatter loss landscape and improve the resultant targeted perturbations' transferability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "WS. To further boost the generalization capability of the obtained SASD model, we propose WS for efficient model augmentation. Specifically, we apply random pruning to the obtained SASD model to produce numerous pruned models. The resultant ensemble of randomly pruned SASD models can possess better generalization capability than the original SASD model. However, generating adversarial examples with an ensemble model can be computationally expensive. Motivated by the approximation scheme in [17], we efficiently approximate the ensemble of randomly pruned SASD models by scaling the weights of the SASD model. Therefore, WS can be efficiently synergized with SASD to further boost the targeted transferability of the synthesized adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.859, + 0.106 + ], + "angle": 0, + "content": "To sum up, the main contributions of this work are:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.108, + 0.892, + 0.242 + ], + "angle": 0, + "content": "- We propose a novel model self-enhancement method incorporating two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model into the source model while flattening its loss landscape. WS then performs model augmentation with an efficient approximation. Their resonance promotes the source model's generalization capability and thus enables more transferable targeted adversarial attacks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.244, + 0.892, + 0.318 + ], + "angle": 0, + "content": "- We conduct extensive experiments to validate the superiority of the proposed method. Notably, compared with the state-of-the-art benchmarks, our approach can improve the targeted attack success rate by a significant margin of \\(12.2\\%\\) on average under the black-box setting." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.319, + 0.892, + 0.409 + ], + "angle": 0, + "content": "- We confirm that our attacks can transfer well to real-world applications, exceeding the state-of-the-art baselines by \\(8.4\\%\\) on average. We also visualize the effectiveness of the proposed method from the perspective of the enhanced model's loss landscape, and validate the efficacy of our approach against defense methods." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.108, + 0.892, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.426, + 0.642, + 0.441 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.452, + 0.787, + 0.467 + ], + "angle": 0, + "content": "2.1. Transferable Adversarial Attack" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.475, + 0.892, + 0.521 + ], + "angle": 0, + "content": "With the development of transfer attack techniques, there are currently three types of approaches to improve the perturbation's transferability:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Enhancing the source model. As normally trained neural networks perform poorly in targeted attacks, several model enhancement methods have been proposed to improve the source model's capability to conduct targeted transfer attacks. These methods include replacing a single source model with an ensemble of models obtained by random dropout [23] and additional training epochs [9]. Springer et al. [35] instead utilizes adversarial fine-tuning to enhance the source model's ability to synthesize transferable adversarial examples. Our method also attempts to improve adversarial transferability by enhancing the source model. Nevertheless, unlike existing model enhancement-based attacks, we propose to flatten the source model's loss landscape to improve its generalization capability, enabling more transferable targeted attacks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Augmenting the input data. To boost adversarial transferability, some transfer attacks resort to input augmentation, such as image translation [3], random resizing and padding [46], and mixup [40]. Unlike prior efforts, a recent input augmentation-based attack technique, Spectrum Simulation Attack (SSA), proposes to apply a spectrum transformation to the input [27]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Rectifying the optimization procedure. Instead of greedily perturbing the clean images along the gradient of the cross-entropy loss [20], several attempts propose to im" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24616" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "prove the optimization procedure to craft more transferable adversarial examples. Straightforward solutions include employing momentum [2] and Nesterov accelerated gradient [25]. Huang et al. [15] instead consider adding the intermediate feature loss into the attack objective to regularize the search of adversarial examples. The state-of-the-art attack of this kind, Reverse Adversarial Perturbation (RAP) [31], seeks adversarial examples located at a region with uniformly low loss values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.47, + 0.288 + ], + "angle": 0, + "content": "Our attack can be conveniently combined with other transfer attacks based on input augmentation and optimization procedure rectification to further enhance the transferability of adversarial attacks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.296, + 0.427, + 0.313 + ], + "angle": 0, + "content": "2.2. Improving DNNs' Generalization Ability" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.562 + ], + "angle": 0, + "content": "Foret et al. [6] propose Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness to improve the model's generalization ability. Hinton et al. [13] introduce knowledge distillation to transfer the knowledge of a teacher model to the student model [45]. Intriguingly, Stanton et al. [36] discover that knowledge distillation can enhance the student model's generalization ability. Building upon Sharpness-Aware Minimization and knowledge distillation methodologies, we propose Sharpness-Aware Self-Distillation (SASD) to integrate Sharpness-Aware Minimization with knowledge distillation, which can further improve the source model's generalization capability. Since a more generalized source model can better capture the general features learned by different models, the produced adversarial examples are more likely to possess better targeted transferability [35]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.213, + 0.59 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.599, + 0.28, + 0.613 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.773 + ], + "angle": 0, + "content": "We first formulate the targeted transfer attack. Given a labeled image dataset \\(D\\) and a target classifier \\(f_{\\mathrm{target}}\\), for an image-label pair \\((x,y)\\in D\\), a targeted transfer attack aims to generate an adversarial example \\(x_{\\mathrm{adv}} = x + \\delta\\) to mislead the target classifier \\(f_{\\mathrm{target}}\\) to predict a specific target label \\(y_{\\mathrm{target}}\\neq y\\). Since the target classifier is black-box, a targeted transfer attack instead derives the adversarial example \\(x_{\\mathrm{adv}}\\) with a white-box source model \\(f\\). It is usually accomplished by optimizing \\(x_{\\mathrm{adv}}\\) to minimize the source model's cross-entropy loss \\(L_{\\mathrm{CE}}\\) on the target label [8, 51]:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.782, + 0.47, + 0.816 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {L _ {\\mathrm {C E}} (f (x + \\delta), y _ {\\text {t a r g e t}}),} \\tag {1} \\\\ \\mathrm {s . t .} \\left. | | \\delta | | _ {\\infty} \\leq \\epsilon . \\right. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To ensure that the perturbation \\(\\delta\\) is imperceptible, attackers should also set a small perturbation budget \\(\\epsilon\\). After generating the adversarial example \\(x_{\\mathrm{adv}}\\) with the source model, a targeted transfer attack directly uses \\(x_{\\mathrm{adv}}\\) to attack the target classifier, with the goal of \\(f_{\\mathrm{target}}(x_{\\mathrm{adv}}) = y_{\\mathrm{target}}\\). To" + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.091, + 0.818, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Sharpness-Aware Self-Distillation" + }, + { + "type": "algorithm", + "bbox": [ + 0.5, + 0.109, + 0.797, + 0.319 + ], + "angle": 0, + "content": "Input: Fine-tuned auxiliary model \n1: Initialization: \\( n \\gets 0 \\) \n2: for every batch in the data loader do \n3: \\( n \\gets n + 1 \\) \n4: Calculate \\( L_{\\mathrm{distillation}} \\) by Equation (3) \n5: \\( \\epsilon \\gets \\operatorname{argmax}_{\\| \\epsilon \\|_2 \\leq \\rho} \\epsilon^T \\nabla_{\\omega_s} L_{\\mathrm{distillation}}(\\omega_s) \\) \n6: \\( g = \\nabla_{\\omega_s} L(\\omega_s)|_{\\omega_s + \\epsilon} \\) \n7: \\( \\omega_s \\gets \\omega_s - lr \\cdot g \\) \n8: if \\( n \\geq n_{\\mathrm{max}} \\) then \n9: break \n10: end if \n11: end for \nOutput: SASD model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.894, + 0.409 + ], + "angle": 0, + "content": "improve the attack success rate (i.e., the transferability) of the generated targeted perturbations, we propose enhancing the source model's generalization ability, detailed in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.419, + 0.795, + 0.435 + ], + "angle": 0, + "content": "3.2. Sharpness-Aware Self-Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Fine-tuning the auxiliary model. We start with a pretrained source model and fine-tune it on its original training dataset to obtain the auxiliary model. The fine-tuning procedure follows Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness [6]. Specifically, in each iteration, we first perform back-propagation based on the cross-entropy loss [7] between the output of the auxiliary model and the ground-truth label. We then modify the auxiliary model's weight \\(\\omega\\) by adding a perturbation \\(\\epsilon_{m}\\) that can maximize the cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.622, + 0.892, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {m} = \\underset {\\epsilon_ {m}} {\\arg \\max } L _ {\\mathrm {C E}} (f (\\omega + \\epsilon_ {m}, x), y), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.719 + ], + "angle": 0, + "content": "where \\( f(\\omega, x) \\) is the output of a neural network \\( f \\) given the model weight \\( \\omega \\) and the input \\( x \\). We perform backpropagation again based on the perturbed weight to minimize the auxiliary model's loss of sharpness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Distilling the auxiliary model. After obtaining a finetuned auxiliary model, we distill it into the source model to enhance its generalization ability. Specifically, we first make the source model's probability output close to the auxiliary model's. Let \\( q_{1} = \\phi_{1}(l_{\\mathrm{aux}}) \\) denote the probability output of the auxiliary model, where \\( \\phi_{1} \\) is a differentiable transformation, and \\( l_{\\mathrm{aux}} \\) is the auxiliary model's logit output. In our SASD, we set \\( \\phi_{1}(l_{\\mathrm{aux}}) = \\mathrm{Softmax}(l_{\\mathrm{aux}} / \\tau) \\), where \\( \\tau \\) is the distillation temperature. The larger the temperature is, the softer the probability distribution will be. Similarly, let \\( q_{2} = \\phi_{2}(l_{\\mathrm{source}}) \\) denote the probability output of the source model, where \\( \\phi_{2}(l_{\\mathrm{source}}) = \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24617" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "\\(\\mathrm{Softmax}(l_{\\mathrm{source}} / \\tau)\\). To minimize the prediction difference between the auxiliary and source models, we employ the Kullback-Leibler divergence \\(D_{\\mathrm{KL}}\\) [18] between \\(q_{1}\\) and \\(q_{2}\\) as the distillation loss:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.164, + 0.47, + 0.196 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) = \\mathbb {E} _ {(x, y) \\in D} \\left[ D _ {\\mathrm {K L}} \\left(q _ {1} (x, y), q _ {2} (x, y)\\right) \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.207, + 0.469, + 0.237 + ], + "angle": 0, + "content": "We then simultaneously minimize the distillation loss and its sharpness:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.249, + 0.469, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\omega_ {s}} \\mathbb {E} _ {(x, y) \\in D} [ L (\\omega_ {s}) ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.283, + 0.124, + 0.295 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.305, + 0.469, + 0.374 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L \\left(\\omega_ {s}\\right) = \\max _ {\\| \\epsilon \\| _ {2} \\leq \\rho} L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s} + \\epsilon\\right) \\\\ \\approx \\max _ {\\| \\epsilon \\| _ {2} \\leq \\rho} \\left[ L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) + \\epsilon^ {T} \\nabla_ {\\omega_ {s}} L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) \\right]. \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.386, + 0.469, + 0.43 + ], + "angle": 0, + "content": "Let \\( lr \\) be the learning rate, and \\( n_{\\mathrm{max}} \\) be the maximum iteration number. Algorithm 1 summarizes the SASD process." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.441, + 0.23, + 0.457 + ], + "angle": 0, + "content": "3.3. Weight Scaling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.464, + 0.47, + 0.555 + ], + "angle": 0, + "content": "To further boost the generalization capability of the obtained SASD model, we apply the network pruning method [47] to generate an ensemble of pruned SASD models. Specifically, we randomly prune the convolutional layers of the obtained SASD model with a probability of \\(1 - p\\). Then, the weight of a pruned SASD model is:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.568, + 0.469, + 0.584 + ], + "angle": 0, + "content": "\\[\n\\omega_ {\\text {p r u n e d}} = \\omega \\odot (\\mathbf {1} - \\xi (\\omega , 1 - p)), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.595, + 0.469, + 0.7 + ], + "angle": 0, + "content": "where \\(\\mathbf{1}\\) denotes the all-ones matrix with the same size as the weight of the SASD model. \\(\\xi (\\omega ,1 - p)\\) indicates the randomly selected weights in the convolutional layers to be pruned. By applying the Hadamard product \\(\\odot\\) that represents element-wise multiplication to the weight, we can obtain the pruned model with some weights in the convolutional layers setting to zero." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.7, + 0.469, + 0.807 + ], + "angle": 0, + "content": "Inspired by the approximation scheme in [17], we further approximate an ensemble of pruned models with a weight-scaled model. Specifically, let \\(\\overline{f} = \\frac{1}{n}\\sum_{i=1}^{n}f(\\omega_i)\\) be the ensemble of models with the same structure but different weights. Let \\(\\overline{\\omega} = \\frac{1}{n}\\sum_{i=1}^{n}\\omega_i\\) be the average weight of the component networks in the ensemble, and \\(\\eta_i = \\omega_i - \\overline{\\omega}\\). For \\(i\\in \\{i|1\\leq i\\leq n,i\\in \\mathbb{N}\\}\\), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.819, + 0.469, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\eta_ {i} = 0, (7) \\\\ f \\left(\\omega_ {i}, x\\right) = f (\\bar {\\omega} + \\eta_ {i}, x) (8) \\\\ = f (\\bar {\\omega}, x) + \\eta_ {i} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta_ {i} \\| _ {2} ^ {2}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.092, + 0.72, + 0.106 + ], + "angle": 0, + "content": "Therefore, we can derive that:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.117, + 0.891, + 0.261 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {f} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} f (\\omega_ {i}, x) \\\\ = \\frac {1}{n} \\sum_ {i = 1} ^ {n} [ f (\\bar {\\omega}, x) + \\eta_ {i} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta_ {i} \\| _ {2} ^ {2}\\right) ] \\tag {9} \\\\ = f (\\bar {\\omega}, x) + \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\eta_ {j} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta \\| _ {2} ^ {2}\\right) \\\\ = f (\\bar {\\omega}, x) + O \\left(\\| \\eta \\| _ {2} ^ {2}\\right) \\approx f (\\bar {\\omega}, x). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.271, + 0.893, + 0.316 + ], + "angle": 0, + "content": "It implies that a single model with the average weight of multiple models can replace the ensemble of these models as long as their weight differences are small enough." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.317, + 0.892, + 0.377 + ], + "angle": 0, + "content": "Therefore, if the pruning probability \\( 1 - p \\) is small, the ensemble of infinite pruned SASD models can be approximated by a single SASD model that is weight-scaled by the scaling ratio \\( p \\) (i.e., the SASD-WS model):" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.388, + 0.891, + 0.447 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {f} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} f \\left(\\omega_ {i} ^ {\\text {p r u n e d S A S D}}, x\\right) \\tag {10} \\\\ \\approx f (\\bar {\\omega}, x) = f (p \\cdot \\omega^ {\\mathrm {S A S D}}, x) = f _ {\\mathrm {S A S D - W S}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.459, + 0.891, + 0.49 + ], + "angle": 0, + "content": "where \\(\\omega^{\\mathrm{SASD}}\\) is the weight of the SASD model before pruning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.5, + 0.697, + 0.516 + ], + "angle": 0, + "content": "3.4. Attacking Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.523, + 0.892, + 0.599 + ], + "angle": 0, + "content": "After obtaining the SASD-WS model, we generate targeted adversarial examples with the TI-DI-MI method [2, 3, 46]. Specifically, given the input data \\( x \\), the source model \\( f \\), and the target class \\( y_{target} \\), the perturbation \\( \\delta_{i+1} \\) can be iteratively updated by:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.609, + 0.891, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\delta_ {i + 1} = \\operatorname {C l i p} _ {\\delta_ {i}} ^ {\\epsilon_ {\\mathrm {p}}} \\left\\{\\delta_ {i} + \\alpha \\cdot \\operatorname {s i g n} \\left(g _ {i + 1}\\right) \\right\\}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.63, + 0.891, + 0.664 + ], + "angle": 0, + "content": "\\[\ng _ {i + 1} = g _ {i} + W \\cdot \\nabla_ {\\delta} \\frac {\\mathcal {L} (\\mathrm {D I} (x + \\delta_ {i}) , y _ {\\text {t a r g e t}} ; f)}{\\| \\mathcal {L} (\\mathrm {D I} (x _ {i} + \\delta_ {i}) , y _ {\\text {t a r g e t}} ; f) \\| _ {1}}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.673, + 0.892, + 0.75 + ], + "angle": 0, + "content": "\\(\\alpha\\) is the step size for attacks. \\(W\\) is the Gaussian kernel for image translation. \\(\\mathcal{L}\\) is the attack objective function. DI denotes the input transformation of random resizing and padding. The generated adversarial perturbation is \\(l_{\\infty}\\)-norm bounded by the maximum perturbation budget \\(\\epsilon_p\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.633, + 0.779 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.691, + 0.804 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We focus on attacking the image classifiers trained on the ImageNet (ILSVRC 2012) dataset [33]. We perform SASD with the standard training and validation splits of the ImageNet dataset. We apply our method to eight models pretrained on ImageNet: Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24618" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.145 + ], + "angle": 0, + "content": "Table 1. Targeted transfer attack success rates (%) with a single source model. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. \"Pre-trained\" means directly using the normally trained model as the source model without modification. \" * \" indicates white-box cases. We run each method five times and show the mean and standard deviation of the results." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.157, + 0.868, + 0.367 + ], + "angle": 0, + "content": "
MethodSource Model: Inc-v3Source Model: Res50
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained99.0 ± 0.0*2.1 ± 0.13.6 ± 0.11.9 ± 0.37.8 ± 0.398.7 ± 0.1*64.3 ± 0.953.8 ± 0.7
RAP93.6 ± 0.0*3.5 ± 0.05.4 ± 0.03.9 ± 0.014.4 ± 0.098.5 ± 0.0*56.2 ± 0.052.6 ± 0.0
GhostNet97.9 ± 0.2*8.1 ± 0.312.8 ± 0.16.6 ± 0.413.2 ± 0.498.0 ± 0.2*75.0 ± 0.368.4 ± 0.6
LGV55.0 ± 0.2*40.5 ± 0.348.3 ± 0.349.5 ± 0.254.5 ± 0.893.2 ± 0.2*90.0 ± 0.184.0 ± 0.2
SASD-WS94.6 ± 0.2*44.4 ± 0.257.6 ± 1.153.8 ± 0.870.3 ± 0.897.2 ± 0.4*93.0 ± 0.288.7 ± 0.4
MethodSource Model: Dense121Source Model: VGG16
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained6.0 ± 0.439.3 ± 0.698.8 ± 0.2*33.6 ± 0.50.9 ± 0.29.8 ± 0.512.2 ± 0.595.4 ± 0.3*
RAP12.0 ± 0.041.2 ± 0.097.8 ± 0.0*37.4 ± 0.02.1 ± 0.09.9 ± 0.09.8 ± 0.085.8 ± 0.0*
GhostNet10.4 ± 0.649.6 ± 0.898.6 ± 0.1*44.0 ± 0.61.1 ± 0.213.0 ± 0.114.9 ± 0.794.9 ± 0.2*
LGV51.3 ± 0.380.8 ± 0.292.9 ± 0.2*75.8 ± 0.2————
SASD-WS61.6 ± 0.687.5 ± 0.297.7 ± 0.1*82.7 ± 0.616.3 ± 0.741.9 ± 0.551.7 ± 0.294.5 ± 0.3*
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.48 + ], + "angle": 0, + "content": "[11], ResNet-152 [11], DenseNet-121 [14], and VGGNet-16 [34]. All these pre-trained models' weights are publicly accessible1. For SASD, we set the distillation temperature \\(\\tau = 1\\) and the learning rate \\(lr = 0.05\\) for all source models. We set WS's scaling ratio \\(p\\) to 0.93 for each SASD-WS model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.47, + 0.786 + ], + "angle": 0, + "content": "We compare the targeted transfer attack performance of our SASD-WS method with the state-of-the-art model enhancement-based attacks: GhostNet [23] and LGV [9]. Although RAP [31] works by rectifying the optimization procedure and does not modify the source model, its motivation is similar to our method. Therefore, we also compare our approach with RAP. We implement the baseline methods following the default settings in their original papers. For LGV, we additionally train the source model on the ImageNet training set for ten epochs [33]. We then obtain four LGV models in each epoch, leading to 40 LGV models for each source model. We cannot apply LGV to VGGNet-16 since the default settings of LGV are not compatible with VGGNet-16. Notably, since LGV and GhostNet transform a single source model into multiple models to generate adversarial examples, we follow their papers to ensemble these models with the longitudinal ensemble method [23]. In contrast, we only transform a single source model into a single SASD-WS model when generating adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.47, + 0.849 + ], + "angle": 0, + "content": "Following the practice in the literature [2, 23], we set the step size \\(\\alpha = 2 / 255\\) and the maximum perturbation budget \\(\\epsilon_{p} = 16 / 255\\). We set the maximum iteration number \\(t_{\\mathrm{max}} = 100\\) in the adversarial perturbation generation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.39, + 0.892, + 0.467 + ], + "angle": 0, + "content": "process. We conduct targeted transfer attacks on NIPS17 targeted adversarial attack competition dataset[21]. All experiments are implemented with PyTorch 2.0.1 and conducted with an NVIDIA GeForce RTX 4090 GPU of 24 GB memory." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.478, + 0.719, + 0.494 + ], + "angle": 0, + "content": "4.2. Attacking Performance" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.607 + ], + "angle": 0, + "content": "Targeted transfer attacks with a single source model. We first evaluate the performance of our method when only a single source model is available. We use the logit loss \\( L_{\\mathrm{Logit}} = -l^{(t)}(x + \\delta) \\) proposed in [51] as the attack objective function \\( \\mathcal{L} \\), where \\( l^{(t)}(\\cdot) \\) is the output logit of the source model concerning the target label. Table 1 reports the attack success rate of each method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.699 + ], + "angle": 0, + "content": "As shown in Table 1, our method consistently outperforms the state-of-the-art baselines by a significant margin of \\(12.2\\%\\) on average under the black-box settings. Besides improving the targeted attack success rate under the black-box settings, SASD-WS can also maintain high white-box attack performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.893, + 0.852 + ], + "angle": 0, + "content": "Targeted transfer attacks with an ensemble of source models. We then test the performance of our method when multiple source models are available, including Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. For the target models, due to the widespread application of adversarial training techniques [19, 28, 39], we first consider adversially trained models. We also consider the scenarios where the target and source models are from different structure families. Specifically, we evaluate the effectiveness of the targeted perturbation on Vision" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.468, + 0.9 + ], + "angle": 0, + "content": "https://github.com/Cadene/pretrained-models.pytorch, https://pytorch.org/vision/stable/models.html" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2https://github.com/cleverhans-lab/cleverhans/ blob/master/cleverhans_v3.1.0/examples/nips17_adversarial_competition/dataset/dev_dataset.csv" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24619" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.146 + ], + "angle": 0, + "content": "Table 2. Targeted transfer attack success rates (%) with an ensemble of six source models: Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. \"Pre-trained\" means directly using the normally trained model as the source model without modification. We run each method five times and show the mean and standard deviation of the results." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.156, + 0.894, + 0.253 + ], + "angle": 0, + "content": "
MethodInc-v3adv ens3Inc-v3adv ens4IncRes-v2adv ensViT-B/16ViT-L/16CLIP (RN50)CLIP (ViT-B/32)CLIP (ViT-L/14)
Pre-trained0.0 ± 0.00.1 ± 0.00.0 ± 0.03.1 ± 0.31.5 ± 0.216.3 ± 0.72.0 ± 0.13.2 ± 0.4
RAP1.7 ± 0.01.5 ± 0.00.1 ± 0.06.0 ± 0.03.0 ± 0.017.7 ± 0.05.1 ± 0.04.8 ± 0.0
GhostNet0.7 ± 0.11.1 ± 0.20.2 ± 0.09.1 ± 0.55.7 ± 0.133.0 ± 0.55.3 ± 0.210.7 ± 0.1
LGV8.1 ± 0.26.7 ± 0.21.7 ± 0.119.6 ± 0.013.0 ± 0.259.4 ± 0.322.4 ± 0.228.4 ± 0.3
SASD-WS16.6 ± 0.213.5 ± 0.35.3 ± 0.134.1 ± 0.225.1 ± 0.258.7 ± 0.524.2 ± 0.234.7 ± 0.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.273, + 0.472, + 0.342 + ], + "angle": 0, + "content": "Table 3. Targeted transfer attack success rates (\\%) of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. We run each test five times and show the mean and standard deviation of the results." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.355, + 0.441, + 0.436 + ], + "angle": 0, + "content": "
Method→ Inc-v3→ Dense121→ VGG16
Pre-trained7.7 ± 0.363.7 ± 0.156.2 ± 0.5
WS35.0 ± 0.584.7 ± 0.277.8 ± 0.4
SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
SASD-WS70.3 ± 0.893.0 ± 0.288.7 ± 0.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.643 + ], + "angle": 0, + "content": "Transformers (ViTs) [4] and CLIP models [32]. ViTs apply the transformer models to visual data and leverage the self-attention mechanism to process data patches. CLIP models utilize both the image and text encoders to encode and calculate the similarity of the image-text pairs. They can produce the similarity score for each label. In our experiments, we use Inc-v3adv ens3 [39], Inc-v3adv ens4 [39], and IncRes-v2adv ens [39] as the target adversarially trained models. We consider ViT-B/16 and ViT-L/16 as the target ViTs. We target CLIP models with ResNet50, ViT-B/32, and ViT-L/14 as the image encoders, respectively. We use the cross-entropy loss as our attack objective function \\(\\mathcal{L}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We report the results in Table 2. It shows that SASDWS can generate more transferable targeted perturbations than the other baseline methods, with a significant improvement of \\(6.6\\%\\) on average. While most baselines can generate perturbations that can manifest a certain degree of targeted transferability, RAP performs poorly under the ensemble source model setting compared with the other baseline methods, with an average attack success rate of only \\(8.2\\%\\). We believe that the poor targeted attack performance of RAP under the ensemble source model setting is due to the ensemble model's lack of a uniformly low-loss region. Therefore, it highlights the need to enhance the source model to enable more transferable targeted adversarial attacks. Besides, our method's high targeted attack success rates against different target models, including adversarially trained models, reveal the potential security risk of DNNs and call for more effort to improve DNNs' robustness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Table 4. Targeted transfer attack success rates (\\%) when using different SASD variants: (1) SASD without fine-tuning the auxiliary model (SASD w/o FT Aux), (2) SASD without distilling the auxiliary model (SASD w/o D), (3) SASD via the commonly used knowledge distillation method (SASD w/ KD), and (4) our proposed SASD. We run each test five times and show the mean and standard deviation of the results." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.382, + 0.882, + 0.461 + ], + "angle": 0, + "content": "
Method→ Inc-v3→ Dense121→ VGG16
SASD w/o FT Aux32.2 ± 0.387.1 ± 0.081.3 ± 0.1
SASD w/o D29.6 ± 0.587.7 ± 0.279.5 ± 0.3
SASD w/ KD38.5 ± 0.490.7 ± 0.184.9 ± 0.2
Our SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.487, + 0.754, + 0.503 + ], + "angle": 0, + "content": "ness against adversarial perturbations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.513, + 0.655, + 0.531 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Validating the contribution of SASD and WS. We validate the contribution of two major components in our method: SASD and WS. Specifically, following the setting of Table 1, we compare the targeted attack success rates of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. The results are shown in Table 3. We can see that both SASD and WS can improve the pre-trained source models' capability to launch targeted transfer attacks. Besides, combining SASD and WS can further enhance the source model to generate more transferable targeted adversarial perturbations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Validating the design of SASD. We validate the design of SASD by examining SASD's two steps: fine-tuning the auxiliary model and distilling the auxiliary model. Specifically, for examining the first step of SASD, we conduct SASD without fine-tuning the auxiliary model. In other words, we conduct the second step of SASD directly with a pre-trained source model. For examining the second step of SASD, we conduct SASD without distilling the auxiliary model. In other words, we directly use the fine-tuned auxiliary model to generate adversarial examples. Besides, we also consider distilling the auxiliary model via the commonly used knowledge distillation method [13]. Specif" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24620" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.146 + ], + "angle": 0, + "content": "Table 5. Targeted transfer attack success rates (\\%) against different defense methods. All methods are combined with the TI-DI-MI technique to generate adversarial perturbations. We run each test five times and show the mean and standard deviation of the results." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.156, + 0.468, + 0.235 + ], + "angle": 0, + "content": "
MethodJPEGHGDNRPNoisyMixAugMix
Pre-trained99.7 ± 0.01.4 ± 0.13.7 ± 0.00.4 ± 0.00.7 ± 0.0
RAP88.7 ± 0.00.5 ± 0.014.3 ± 0.01.0 ± 0.00.5 ± 0.0
GhostNet99.9 ± 0.01.4 ± 0.012.4 ± 0.62.4 ± 0.00.8 ± 0.0
LGV99.4 ± 0.17.6 ± 0.22.0 ± 0.36.5 ± 0.11.4 ± 0.0
SASD-WS99.8 ± 0.023.5 ± 0.117.9 ± 0.58.0 ± 0.12.0 ± 0.0
" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.248, + 0.25, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.251, + 0.43, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.361, + 0.47, + 0.39 + ], + "angle": 0, + "content": "Figure 3. Successful targeted adversarial examples on Google Cloud Vision. The target class is tigers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.47, + 0.673 + ], + "angle": 0, + "content": "ically, the commonly used knowledge distillation method combines the cross-entropy loss with respect to the true label and the Kullback-Leibler divergence with respect to the prediction of the teacher model as the distillation loss. Following the setting of Table 1, we examine the performance of targeted adversarial perturbations generated by the above SASD variants. The results are shown in Table 4. When employing the normal knowledge distillation method, we distill the auxiliary model for ten epochs to maximize the attack performance. Our SASD instead only needs less than one epoch distillation. Nevertheless, our SASD method can still surpass the normal knowledge distillation method. Besides, the SASD model's performance improves when employing a fine-tuned auxiliary model, and distilling the auxiliary model performs better than directly using the fine-tuned auxiliary model. Therefore, the experimental results validate the design of our SASD." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.245, + 0.697 + ], + "angle": 0, + "content": "4.4. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.856 + ], + "angle": 0, + "content": "Transfer attacks against defense methods. In this part, we evaluate SASD-WS's targeted attack performance against several adversarial defense methods and common corruption defense methods, including JPEG [10], HGD [24], NRP [29], NoisyMix [5], and AugMix [12]. We use the same experimental settings as those in the ensemble targeted and untargeted attack experiments with an ensemble of source models (Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101 [11], ResNet-152 [11])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Table 5 presents the results of the targeted transfer attack. We can see that SASD-WS can effectively generate effective perturbations against these defense methods in tar" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.16 + ], + "angle": 0, + "content": "Table 6. Comparison of the average \\( l_{2} \\)-norm across 100 images for (1) the logit output difference of the ensemble of pruned models and the corresponding WS model, and (2) the standard deviation among the logit outputs of pruned models in the ensemble. Results for the ensemble of 20/50/100 pruned models are reported." + }, + { + "type": "table", + "bbox": [ + 0.557, + 0.17, + 0.842, + 0.227 + ], + "angle": 0, + "content": "
2050100
Output Difference30.7129.5429.57
Standard Deviation26.8726.6626.36
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.386 + ], + "angle": 0, + "content": "geted attack settings. Even though for defense methods like NoisyMix and AugMix, most of the tested adversarial attack methods failed to achieve successful targeted attack, SASD-WS can still generate targeted perturbations with superior transferability compared with other baseline methods and achieves a nearly \\(100\\%\\) attack success rate in attacking JPEG. These results show from another perspective that our approach can generate adversarial perturbations with higher transferability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.893, + 0.599 + ], + "angle": 0, + "content": "Attacking real-world applications. We launch targeted transfer attacks against Google Cloud Vision to verify the practical applicability of the proposed method. Similar to previous experiments, we use an ensemble of six source models as the source model. We randomly sample 500 images from the NIPS17 targeted adversarial attack competition dataset as the test set to generate adversarial perturbations. Following the experimental settings in [26], when the labels with similar semantic meanings to the target label appear in the predicted labels of Google Cloud Vision, we regard the attack as successful. Although Google Cloud Vision will return the labels with probabilities more than \\(50.0\\%\\), we only consider the top-5 labels as the predicted labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Experimental results show that our method can achieve a targeted transfer attack success rate of \\(40.2\\%\\). In contrast, the baseline methods, LGV, GhostNet, RAP, and Pretrained, can only attain a targeted transfer attack success rate of \\(31.8\\%, 17.0\\%, 4.6\\%,\\) and \\(3.6\\%\\), respectively. Figure 3 presents some of the adversarial examples generated by our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Validating WS. We further validate the effectiveness of our Weight Scaling (WS) method in simulating an ensemble of source models. Intuitively, if the output of the pruned models' ensemble is close to that of the corresponding WS model, the difference between their outputs should be within the standard deviation among the pruned models' outputs in the ensemble. Therefore, we calculate the \\( l_{2} \\)-norm value of the difference between the logit outputs of the pruned models' ensemble and the corresponding WS model. We also compute the \\( l_{2} \\)-norm value of the standard deviation among the pruned models' logit outputs in the ensemble. The results are shown in Table 6. According to the three-sigma rule, we can see that the output difference be" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24621" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.22, + 0.092, + 0.403, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.092, + 0.576, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.092, + 0.75, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.24, + 0.895, + 0.269 + ], + "angle": 0, + "content": "Figure 4. Targeted transfer attack success rates \\((\\%)\\) of the base model (SASD ResNet-50), the longitudinal ensemble of pruned base models, and the WS version of the base model (SASD-WS ResNet-50)." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.286, + 0.287, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.286, + 0.481, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.286, + 0.676, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.286, + 0.871, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.424, + 0.893, + 0.452 + ], + "angle": 0, + "content": "Figure 5. The change of the loss landscapes with the application of our method. The fine-tuned ResNet-50 is the auxiliary model adopted in our SASD method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.569 + ], + "angle": 0, + "content": "tween the pruned models' ensemble and the corresponding WS model falls into the three-sigma range of the internal variability of the pruned models in the ensemble. Therefore, the output of the WS model is not an outlier among the pruned models' outputs, which implies that the output of the WS model is close to the ensemble model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.47, + 0.743 + ], + "angle": 0, + "content": "Moreover, we compare the targeted attack performance of a single weight-scaled SASD model and the ensemble of pruned SASD models. Specifically, we generate adversarial perturbations by employing a longitudinal ensemble of pruned SASD models with a pruning rate of \\(1 - p = 0.07\\). Therefore, we set our WS method's scaling ratio \\(p = 0.93\\). Figure 4 shows the targeted transfer attack success rates of three types of source models with SASD ResNet-50 as the base model. According to the attack performance, we can see that our WS method can reasonably approximate the ensemble of pruned models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Visualizing the effectiveness of SASD-WS. Our SASD-WS attempts to promote the source model's generalization capability to enable more transferable targeted adversarial attacks. To visualize the effectiveness of our SASD-WS on improving the source model's generalization capability, we depict the change of the loss landscapes by applying our method in Figure 5. We can see that with the application of our approach, the loss landscape of the resultant enhanced model becomes flatter, which can help to capture general features learned by different models [6, 16, 35]. Therefore," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.525 + ], + "angle": 0, + "content": "the enhanced model is more likely to cover the transferable targeted adversarial examples in its low-loss region, facilitating more transferable targeted adversarial attacks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.619, + 0.564 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.789 + ], + "angle": 0, + "content": "This work presents a novel model self-enhancement method, incorporating Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to enhance the source model's capability to generate more transferable targeted perturbations. Extensive experiments show that our method can significantly outperform the state-of-the-art approaches. Notably, under the black-box setting, we can surpass the state-of-the-art baselines by a significant margin of \\(12.2\\%\\) on average. We also validate the design of our method by several ablation studies and the practical applicability of the proposed method by attacking a popular real-world application. We believe that our approach can serve as a strong benchmark when evaluating the robustness of DNNs and an effective patch when conducting adversarial training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.812, + 0.652, + 0.829 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 62206318)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24622" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Yang Deng, Weibin Wu, Jianping Zhang, and Zibin Zheng. Blurred-dilated method for adversarial attacks. In Advances in Neural Information Processing Systems, pages 58613-58624, 2023. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.241 + ], + "angle": 0, + "content": "[2] Yinpeng Dong, Fangzhou Liao, Tianyu Pang, Hang Su, Jun Zhu, Xiaolin Hu, and Jianguo Li. Boosting adversarial attacks with momentum. 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Although manifesting remarkable performance in generating untargeted adversarial perturbations, existing proposals still fail to achieve high targeted transferability. In this work, we discover that the adversarial perturbations' overfitting towards source models of mediocre generalization capability can hurt their targeted transferability. To address this issue, we focus on enhancing the source model's generalization capability to improve its ability to conduct transferable targeted adversarial attacks. In pursuit of this goal, we propose a novel model self-enhancement method that incorporates two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model, which mirrors the source model's structure, into the source model while flattening the source model's loss landscape. WS obtains an approximate ensemble of numerous pruned models to perform model augmentation, which can be conveniently synergized with SASD to elevate the source model's generalization capability and thus improve the resultant targeted perturbations' transferability. Extensive experiments corroborate the effectiveness of the proposed method. Notably, under the black-box setting, our approach can outperform the state-of-the-art baselines by a significant margin of $12.2\%$ on average in terms of the obtained targeted transferability. Code is available at https://github.com/g4allff/SASD. + +# 1. Introduction + +Despite their wide range of applications in real-world scenarios, deep neural networks (DNNs) have shown vulnerability in the face of imperceptible adversarial perturbations [41, 43, 49, 50]. In recent years, numerous transfer attack methods have been proposed to evaluate the robustness of + +![](images/a0830ab200275dacf559d6f9e16ab206335a4ac742a4906a1d5aeb7eeffb325c.jpg) +Figure 1. The motivation of the proposed method that enhances the source model's generalization capability to enable more transferable targeted adversarial attacks. + +![](images/ef2518e5cf97edaf880567b6f852d75b3f1866592960b1661a0d48e2268e9db5.jpg) +Source Model + +![](images/5203ca12082f8a9889ee43ae567d087b6edf1517fbb9c01054e003ad720b3150.jpg) +Enhanced Model + +![](images/42a37a3c77603bac41dce95b7f387159c4b7e3f170ae192a87e8bdf899bf8425.jpg) +Target Model + +![](images/4964f98c55aabe61b865f251be6d448f2b3ce392553035733e252c88aa2fc874.jpg) +adv + +![](images/238a9c1481956de0ae93d7aea391c429b5b45f8a7b0c46fca79c4ac5244f886a.jpg) +adv enhanced + +DNNs [1, 42, 44, 48]. Although existing approaches have demonstrated excellent performances on untargeted transfer attacks, it is still challenging to accomplish targeted transfer attacks, which require the attacker to generate perturbations that can mislead the black-box victims to return a target label [22, 30]. + +Adversarial perturbations are prone to overfit the source model and manifest limited targeted transferability when the source model's generalization capability is mediocre. Specifically, neural networks can capture features essential for decision-making, with some features being general while the others being model-specific [16]. Intuitively, adversarial examples that primarily manipulate model-specific features are unlikely to transfer well among different models. Working towards a more generalized source model can alleviate the reliance on model-specific features, thus enhancing the transferability of the synthesized adversarial examples [35]. + +Therefore, we propose to enhance the source model's generalization capability to enable more transferable targeted adversarial attacks. We conceptually illustrate the motivation of our method in Figure 1. Since different models rely on different features to make decisions, and their loss landscapes are often sharp, the transferable targeted adversarial examples are likely to reside away from the local optima of different models. It is thus challenging to transfer the adversarial examples generated by the vanilla + +![](images/f6e62b387ab344c05a3ba6d8630cc7e62b4de7ec03a5d5fad99f191cf333ae22.jpg) +Figure 2. The overall procedure of SASD-WS. + +source model to a different target model. A viable solution is to enhance the source model's generalization capability to capture the general features learned by different models. This can be achieved by learning a flatter loss landscape that covers the transferable targeted adversarial examples in the low-loss region. + +To this end, we propose a novel model self-enhancement method: SASD-WS, which incorporates Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to promote the source model's generalization capability. Then, we can employ the enhanced source model to produce targeted perturbations with better transferability. The overall procedure of our method is summarized in Figure 2. We explain the two major components of the proposed SASD-WS as follows: + +SASD. In the warm-up step of SASD, we employ the technique of Sharpness-Aware Minimization (SAM) [6] to fine-tune an auxiliary model, which mirrors the source model's structure. Specifically, during the fine-tuning of the auxiliary model, we simultaneously minimize its loss of sharpness and the cross-entropy loss between its predictions and ground-truth labels. Given the fine-tuned auxiliary model, we then enhance our source model by distilling the auxiliary model into the source model while minimizing the source model's loss of sharpness. As a result, SASD can effectively endow the source model with a flatter loss landscape and improve the resultant targeted perturbations' transferability. + +WS. To further boost the generalization capability of the obtained SASD model, we propose WS for efficient model augmentation. Specifically, we apply random pruning to the obtained SASD model to produce numerous pruned models. The resultant ensemble of randomly pruned SASD models can possess better generalization capability than the original SASD model. However, generating adversarial examples with an ensemble model can be computationally expensive. Motivated by the approximation scheme in [17], we efficiently approximate the ensemble of randomly pruned SASD models by scaling the weights of the SASD model. Therefore, WS can be efficiently synergized with SASD to further boost the targeted transferability of the synthesized adversarial examples. + +To sum up, the main contributions of this work are: + +- We propose a novel model self-enhancement method incorporating two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model into the source model while flattening its loss landscape. WS then performs model augmentation with an efficient approximation. Their resonance promotes the source model's generalization capability and thus enables more transferable targeted adversarial attacks. +- We conduct extensive experiments to validate the superiority of the proposed method. Notably, compared with the state-of-the-art benchmarks, our approach can improve the targeted attack success rate by a significant margin of $12.2\%$ on average under the black-box setting. +- We confirm that our attacks can transfer well to real-world applications, exceeding the state-of-the-art baselines by $8.4\%$ on average. We also visualize the effectiveness of the proposed method from the perspective of the enhanced model's loss landscape, and validate the efficacy of our approach against defense methods. + +# 2. Related Work + +# 2.1. Transferable Adversarial Attack + +With the development of transfer attack techniques, there are currently three types of approaches to improve the perturbation's transferability: + +Enhancing the source model. As normally trained neural networks perform poorly in targeted attacks, several model enhancement methods have been proposed to improve the source model's capability to conduct targeted transfer attacks. These methods include replacing a single source model with an ensemble of models obtained by random dropout [23] and additional training epochs [9]. Springer et al. [35] instead utilizes adversarial fine-tuning to enhance the source model's ability to synthesize transferable adversarial examples. Our method also attempts to improve adversarial transferability by enhancing the source model. Nevertheless, unlike existing model enhancement-based attacks, we propose to flatten the source model's loss landscape to improve its generalization capability, enabling more transferable targeted attacks. + +Augmenting the input data. To boost adversarial transferability, some transfer attacks resort to input augmentation, such as image translation [3], random resizing and padding [46], and mixup [40]. Unlike prior efforts, a recent input augmentation-based attack technique, Spectrum Simulation Attack (SSA), proposes to apply a spectrum transformation to the input [27]. + +Rectifying the optimization procedure. Instead of greedily perturbing the clean images along the gradient of the cross-entropy loss [20], several attempts propose to im + +prove the optimization procedure to craft more transferable adversarial examples. Straightforward solutions include employing momentum [2] and Nesterov accelerated gradient [25]. Huang et al. [15] instead consider adding the intermediate feature loss into the attack objective to regularize the search of adversarial examples. The state-of-the-art attack of this kind, Reverse Adversarial Perturbation (RAP) [31], seeks adversarial examples located at a region with uniformly low loss values. + +Our attack can be conveniently combined with other transfer attacks based on input augmentation and optimization procedure rectification to further enhance the transferability of adversarial attacks. + +# 2.2. Improving DNNs' Generalization Ability + +Foret et al. [6] propose Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness to improve the model's generalization ability. Hinton et al. [13] introduce knowledge distillation to transfer the knowledge of a teacher model to the student model [45]. Intriguingly, Stanton et al. [36] discover that knowledge distillation can enhance the student model's generalization ability. Building upon Sharpness-Aware Minimization and knowledge distillation methodologies, we propose Sharpness-Aware Self-Distillation (SASD) to integrate Sharpness-Aware Minimization with knowledge distillation, which can further improve the source model's generalization capability. Since a more generalized source model can better capture the general features learned by different models, the produced adversarial examples are more likely to possess better targeted transferability [35]. + +# 3. Methodology + +# 3.1. Problem Formulation + +We first formulate the targeted transfer attack. Given a labeled image dataset $D$ and a target classifier $f_{\mathrm{target}}$ , for an image-label pair $(x,y)\in D$ , a targeted transfer attack aims to generate an adversarial example $x_{\mathrm{adv}} = x + \delta$ to mislead the target classifier $f_{\mathrm{target}}$ to predict a specific target label $y_{\mathrm{target}}\neq y$ . Since the target classifier is black-box, a targeted transfer attack instead derives the adversarial example $x_{\mathrm{adv}}$ with a white-box source model $f$ . It is usually accomplished by optimizing $x_{\mathrm{adv}}$ to minimize the source model's cross-entropy loss $L_{\mathrm{CE}}$ on the target label [8, 51]: + +$$ +\begin{array}{l} \min _ {L _ {\mathrm {C E}} (f (x + \delta), y _ {\text {t a r g e t}}),} \tag {1} \\ \mathrm {s . t .} \left. | | \delta | | _ {\infty} \leq \epsilon . \right. \\ \end{array} +$$ + +To ensure that the perturbation $\delta$ is imperceptible, attackers should also set a small perturbation budget $\epsilon$ . After generating the adversarial example $x_{\mathrm{adv}}$ with the source model, a targeted transfer attack directly uses $x_{\mathrm{adv}}$ to attack the target classifier, with the goal of $f_{\mathrm{target}}(x_{\mathrm{adv}}) = y_{\mathrm{target}}$ . To + +Algorithm 1 Sharpness-Aware Self-Distillation +Input: Fine-tuned auxiliary model +1: Initialization: $n \gets 0$ +2: for every batch in the data loader do +3: $n \gets n + 1$ +4: Calculate $L_{\mathrm{distillation}}$ by Equation (3) +5: $\epsilon \gets \operatorname{argmax}_{\| \epsilon \|_2 \leq \rho} \epsilon^T \nabla_{\omega_s} L_{\mathrm{distillation}}(\omega_s)$ +6: $g = \nabla_{\omega_s} L(\omega_s)|_{\omega_s + \epsilon}$ +7: $\omega_s \gets \omega_s - lr \cdot g$ +8: if $n \geq n_{\mathrm{max}}$ then +9: break +10: end if +11: end for +Output: SASD model + +improve the attack success rate (i.e., the transferability) of the generated targeted perturbations, we propose enhancing the source model's generalization ability, detailed in the following sections. + +# 3.2. Sharpness-Aware Self-Distillation + +Fine-tuning the auxiliary model. We start with a pretrained source model and fine-tune it on its original training dataset to obtain the auxiliary model. The fine-tuning procedure follows Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness [6]. Specifically, in each iteration, we first perform back-propagation based on the cross-entropy loss [7] between the output of the auxiliary model and the ground-truth label. We then modify the auxiliary model's weight $\omega$ by adding a perturbation $\epsilon_{m}$ that can maximize the cross-entropy loss: + +$$ +\epsilon_ {m} = \underset {\epsilon_ {m}} {\arg \max } L _ {\mathrm {C E}} (f (\omega + \epsilon_ {m}, x), y), \tag {2} +$$ + +where $f(\omega, x)$ is the output of a neural network $f$ given the model weight $\omega$ and the input $x$ . We perform backpropagation again based on the perturbed weight to minimize the auxiliary model's loss of sharpness. + +Distilling the auxiliary model. After obtaining a finetuned auxiliary model, we distill it into the source model to enhance its generalization ability. Specifically, we first make the source model's probability output close to the auxiliary model's. Let $q_{1} = \phi_{1}(l_{\mathrm{aux}})$ denote the probability output of the auxiliary model, where $\phi_{1}$ is a differentiable transformation, and $l_{\mathrm{aux}}$ is the auxiliary model's logit output. In our SASD, we set $\phi_{1}(l_{\mathrm{aux}}) = \mathrm{Softmax}(l_{\mathrm{aux}} / \tau)$ , where $\tau$ is the distillation temperature. The larger the temperature is, the softer the probability distribution will be. Similarly, let $q_{2} = \phi_{2}(l_{\mathrm{source}})$ denote the probability output of the source model, where $\phi_{2}(l_{\mathrm{source}}) =$ + +$\mathrm{Softmax}(l_{\mathrm{source}} / \tau)$ . To minimize the prediction difference between the auxiliary and source models, we employ the Kullback-Leibler divergence $D_{\mathrm{KL}}$ [18] between $q_{1}$ and $q_{2}$ as the distillation loss: + +$$ +L _ {\text {d i s t i l l a t i o n}} \left(\omega_ {s}\right) = \mathbb {E} _ {(x, y) \in D} \left[ D _ {\mathrm {K L}} \left(q _ {1} (x, y), q _ {2} (x, y)\right) \right]. \tag {3} +$$ + +We then simultaneously minimize the distillation loss and its sharpness: + +$$ +\min _ {\omega_ {s}} \mathbb {E} _ {(x, y) \in D} [ L (\omega_ {s}) ], \tag {4} +$$ + +where + +$$ +\begin{array}{l} L \left(\omega_ {s}\right) = \max _ {\| \epsilon \| _ {2} \leq \rho} L _ {\text {d i s t i l l a t i o n}} \left(\omega_ {s} + \epsilon\right) \\ \approx \max _ {\| \epsilon \| _ {2} \leq \rho} \left[ L _ {\text {d i s t i l l a t i o n}} \left(\omega_ {s}\right) + \epsilon^ {T} \nabla_ {\omega_ {s}} L _ {\text {d i s t i l l a t i o n}} \left(\omega_ {s}\right) \right]. \tag {5} \\ \end{array} +$$ + +Let $lr$ be the learning rate, and $n_{\mathrm{max}}$ be the maximum iteration number. Algorithm 1 summarizes the SASD process. + +# 3.3. Weight Scaling + +To further boost the generalization capability of the obtained SASD model, we apply the network pruning method [47] to generate an ensemble of pruned SASD models. Specifically, we randomly prune the convolutional layers of the obtained SASD model with a probability of $1 - p$ . Then, the weight of a pruned SASD model is: + +$$ +\omega_ {\text {p r u n e d}} = \omega \odot (\mathbf {1} - \xi (\omega , 1 - p)), \tag {6} +$$ + +where $\mathbf{1}$ denotes the all-ones matrix with the same size as the weight of the SASD model. $\xi (\omega ,1 - p)$ indicates the randomly selected weights in the convolutional layers to be pruned. By applying the Hadamard product $\odot$ that represents element-wise multiplication to the weight, we can obtain the pruned model with some weights in the convolutional layers setting to zero. + +Inspired by the approximation scheme in [17], we further approximate an ensemble of pruned models with a weight-scaled model. Specifically, let $\overline{f} = \frac{1}{n}\sum_{i=1}^{n}f(\omega_i)$ be the ensemble of models with the same structure but different weights. Let $\overline{\omega} = \frac{1}{n}\sum_{i=1}^{n}\omega_i$ be the average weight of the component networks in the ensemble, and $\eta_i = \omega_i - \overline{\omega}$ . For $i\in \{i|1\leq i\leq n,i\in \mathbb{N}\}$ , we have: + +$$ +\begin{array}{l} \frac {1}{n} \sum_ {i = 1} ^ {n} \eta_ {i} = 0, (7) \\ f \left(\omega_ {i}, x\right) = f (\bar {\omega} + \eta_ {i}, x) (8) \\ = f (\bar {\omega}, x) + \eta_ {i} ^ {T} \nabla_ {\bar {\omega}} f (\bar {\omega}, x) + O \left(\| \eta_ {i} \| _ {2} ^ {2}\right). \\ \end{array} +$$ + +Therefore, we can derive that: + +$$ +\begin{array}{l} \bar {f} = \frac {1}{n} \sum_ {i = 1} ^ {n} f (\omega_ {i}, x) \\ = \frac {1}{n} \sum_ {i = 1} ^ {n} [ f (\bar {\omega}, x) + \eta_ {i} ^ {T} \nabla_ {\bar {\omega}} f (\bar {\omega}, x) + O \left(\| \eta_ {i} \| _ {2} ^ {2}\right) ] \tag {9} \\ = f (\bar {\omega}, x) + \frac {1}{n} \sum_ {i = 1} ^ {n} \eta_ {j} ^ {T} \nabla_ {\bar {\omega}} f (\bar {\omega}, x) + O \left(\| \eta \| _ {2} ^ {2}\right) \\ = f (\bar {\omega}, x) + O \left(\| \eta \| _ {2} ^ {2}\right) \approx f (\bar {\omega}, x). \\ \end{array} +$$ + +It implies that a single model with the average weight of multiple models can replace the ensemble of these models as long as their weight differences are small enough. + +Therefore, if the pruning probability $1 - p$ is small, the ensemble of infinite pruned SASD models can be approximated by a single SASD model that is weight-scaled by the scaling ratio $p$ (i.e., the SASD-WS model): + +$$ +\begin{array}{l} \bar {f} = \frac {1}{n} \sum_ {i = 1} ^ {n} f \left(\omega_ {i} ^ {\text {p r u n e d S A S D}}, x\right) \tag {10} \\ \approx f (\bar {\omega}, x) = f (p \cdot \omega^ {\mathrm {S A S D}}, x) = f _ {\mathrm {S A S D - W S}}, \\ \end{array} +$$ + +where $\omega^{\mathrm{SASD}}$ is the weight of the SASD model before pruning. + +# 3.4. Attacking Algorithm + +After obtaining the SASD-WS model, we generate targeted adversarial examples with the TI-DI-MI method [2, 3, 46]. Specifically, given the input data $x$ , the source model $f$ , and the target class $y_{target}$ , the perturbation $\delta_{i+1}$ can be iteratively updated by: + +$$ +\delta_ {i + 1} = \operatorname {C l i p} _ {\delta_ {i}} ^ {\epsilon_ {\mathrm {p}}} \left\{\delta_ {i} + \alpha \cdot \operatorname {s i g n} \left(g _ {i + 1}\right) \right\}, \tag {11} +$$ + +$$ +g _ {i + 1} = g _ {i} + W \cdot \nabla_ {\delta} \frac {\mathcal {L} (\mathrm {D I} (x + \delta_ {i}) , y _ {\text {t a r g e t}} ; f)}{\| \mathcal {L} (\mathrm {D I} (x _ {i} + \delta_ {i}) , y _ {\text {t a r g e t}} ; f) \| _ {1}}. \tag {12} +$$ + +$\alpha$ is the step size for attacks. $W$ is the Gaussian kernel for image translation. $\mathcal{L}$ is the attack objective function. DI denotes the input transformation of random resizing and padding. The generated adversarial perturbation is $l_{\infty}$ -norm bounded by the maximum perturbation budget $\epsilon_p$ . + +# 4. Experiments + +# 4.1. Experimental Setup + +We focus on attacking the image classifiers trained on the ImageNet (ILSVRC 2012) dataset [33]. We perform SASD with the standard training and validation splits of the ImageNet dataset. We apply our method to eight models pretrained on ImageNet: Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101 + +Table 1. Targeted transfer attack success rates (%) with a single source model. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. "Pre-trained" means directly using the normally trained model as the source model without modification. " * " indicates white-box cases. We run each method five times and show the mean and standard deviation of the results. + +
MethodSource Model: Inc-v3Source Model: Res50
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained99.0 ± 0.0*2.1 ± 0.13.6 ± 0.11.9 ± 0.37.8 ± 0.398.7 ± 0.1*64.3 ± 0.953.8 ± 0.7
RAP93.6 ± 0.0*3.5 ± 0.05.4 ± 0.03.9 ± 0.014.4 ± 0.098.5 ± 0.0*56.2 ± 0.052.6 ± 0.0
GhostNet97.9 ± 0.2*8.1 ± 0.312.8 ± 0.16.6 ± 0.413.2 ± 0.498.0 ± 0.2*75.0 ± 0.368.4 ± 0.6
LGV55.0 ± 0.2*40.5 ± 0.348.3 ± 0.349.5 ± 0.254.5 ± 0.893.2 ± 0.2*90.0 ± 0.184.0 ± 0.2
SASD-WS94.6 ± 0.2*44.4 ± 0.257.6 ± 1.153.8 ± 0.870.3 ± 0.897.2 ± 0.4*93.0 ± 0.288.7 ± 0.4
MethodSource Model: Dense121Source Model: VGG16
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained6.0 ± 0.439.3 ± 0.698.8 ± 0.2*33.6 ± 0.50.9 ± 0.29.8 ± 0.512.2 ± 0.595.4 ± 0.3*
RAP12.0 ± 0.041.2 ± 0.097.8 ± 0.0*37.4 ± 0.02.1 ± 0.09.9 ± 0.09.8 ± 0.085.8 ± 0.0*
GhostNet10.4 ± 0.649.6 ± 0.898.6 ± 0.1*44.0 ± 0.61.1 ± 0.213.0 ± 0.114.9 ± 0.794.9 ± 0.2*
LGV51.3 ± 0.380.8 ± 0.292.9 ± 0.2*75.8 ± 0.2————
SASD-WS61.6 ± 0.687.5 ± 0.297.7 ± 0.1*82.7 ± 0.616.3 ± 0.741.9 ± 0.551.7 ± 0.294.5 ± 0.3*
+ +[11], ResNet-152 [11], DenseNet-121 [14], and VGGNet-16 [34]. All these pre-trained models' weights are publicly accessible1. For SASD, we set the distillation temperature $\tau = 1$ and the learning rate $lr = 0.05$ for all source models. We set WS's scaling ratio $p$ to 0.93 for each SASD-WS model. + +We compare the targeted transfer attack performance of our SASD-WS method with the state-of-the-art model enhancement-based attacks: GhostNet [23] and LGV [9]. Although RAP [31] works by rectifying the optimization procedure and does not modify the source model, its motivation is similar to our method. Therefore, we also compare our approach with RAP. We implement the baseline methods following the default settings in their original papers. For LGV, we additionally train the source model on the ImageNet training set for ten epochs [33]. We then obtain four LGV models in each epoch, leading to 40 LGV models for each source model. We cannot apply LGV to VGGNet-16 since the default settings of LGV are not compatible with VGGNet-16. Notably, since LGV and GhostNet transform a single source model into multiple models to generate adversarial examples, we follow their papers to ensemble these models with the longitudinal ensemble method [23]. In contrast, we only transform a single source model into a single SASD-WS model when generating adversarial examples. + +Following the practice in the literature [2, 23], we set the step size $\alpha = 2 / 255$ and the maximum perturbation budget $\epsilon_{p} = 16 / 255$ . We set the maximum iteration number $t_{\mathrm{max}} = 100$ in the adversarial perturbation generation + +process. We conduct targeted transfer attacks on NIPS17 targeted adversarial attack competition dataset[21]. All experiments are implemented with PyTorch 2.0.1 and conducted with an NVIDIA GeForce RTX 4090 GPU of 24 GB memory. + +# 4.2. Attacking Performance + +Targeted transfer attacks with a single source model. We first evaluate the performance of our method when only a single source model is available. We use the logit loss $L_{\mathrm{Logit}} = -l^{(t)}(x + \delta)$ proposed in [51] as the attack objective function $\mathcal{L}$ , where $l^{(t)}(\cdot)$ is the output logit of the source model concerning the target label. Table 1 reports the attack success rate of each method. + +As shown in Table 1, our method consistently outperforms the state-of-the-art baselines by a significant margin of $12.2\%$ on average under the black-box settings. Besides improving the targeted attack success rate under the black-box settings, SASD-WS can also maintain high white-box attack performance. + +Targeted transfer attacks with an ensemble of source models. We then test the performance of our method when multiple source models are available, including Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. For the target models, due to the widespread application of adversarial training techniques [19, 28, 39], we first consider adversially trained models. We also consider the scenarios where the target and source models are from different structure families. Specifically, we evaluate the effectiveness of the targeted perturbation on Vision + +Table 2. Targeted transfer attack success rates (%) with an ensemble of six source models: Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. "Pre-trained" means directly using the normally trained model as the source model without modification. We run each method five times and show the mean and standard deviation of the results. + +
MethodInc-v3adv ens3Inc-v3adv ens4IncRes-v2adv ensViT-B/16ViT-L/16CLIP (RN50)CLIP (ViT-B/32)CLIP (ViT-L/14)
Pre-trained0.0 ± 0.00.1 ± 0.00.0 ± 0.03.1 ± 0.31.5 ± 0.216.3 ± 0.72.0 ± 0.13.2 ± 0.4
RAP1.7 ± 0.01.5 ± 0.00.1 ± 0.06.0 ± 0.03.0 ± 0.017.7 ± 0.05.1 ± 0.04.8 ± 0.0
GhostNet0.7 ± 0.11.1 ± 0.20.2 ± 0.09.1 ± 0.55.7 ± 0.133.0 ± 0.55.3 ± 0.210.7 ± 0.1
LGV8.1 ± 0.26.7 ± 0.21.7 ± 0.119.6 ± 0.013.0 ± 0.259.4 ± 0.322.4 ± 0.228.4 ± 0.3
SASD-WS16.6 ± 0.213.5 ± 0.35.3 ± 0.134.1 ± 0.225.1 ± 0.258.7 ± 0.524.2 ± 0.234.7 ± 0.2
+ +Table 3. Targeted transfer attack success rates (\%) of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. We run each test five times and show the mean and standard deviation of the results. + +
Method→ Inc-v3→ Dense121→ VGG16
Pre-trained7.7 ± 0.363.7 ± 0.156.2 ± 0.5
WS35.0 ± 0.584.7 ± 0.277.8 ± 0.4
SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
SASD-WS70.3 ± 0.893.0 ± 0.288.7 ± 0.4
+ +Transformers (ViTs) [4] and CLIP models [32]. ViTs apply the transformer models to visual data and leverage the self-attention mechanism to process data patches. CLIP models utilize both the image and text encoders to encode and calculate the similarity of the image-text pairs. They can produce the similarity score for each label. In our experiments, we use Inc-v3adv ens3 [39], Inc-v3adv ens4 [39], and IncRes-v2adv ens [39] as the target adversarially trained models. We consider ViT-B/16 and ViT-L/16 as the target ViTs. We target CLIP models with ResNet50, ViT-B/32, and ViT-L/14 as the image encoders, respectively. We use the cross-entropy loss as our attack objective function $\mathcal{L}$ . + +We report the results in Table 2. It shows that SASDWS can generate more transferable targeted perturbations than the other baseline methods, with a significant improvement of $6.6\%$ on average. While most baselines can generate perturbations that can manifest a certain degree of targeted transferability, RAP performs poorly under the ensemble source model setting compared with the other baseline methods, with an average attack success rate of only $8.2\%$ . We believe that the poor targeted attack performance of RAP under the ensemble source model setting is due to the ensemble model's lack of a uniformly low-loss region. Therefore, it highlights the need to enhance the source model to enable more transferable targeted adversarial attacks. Besides, our method's high targeted attack success rates against different target models, including adversarially trained models, reveal the potential security risk of DNNs and call for more effort to improve DNNs' robustness. + +Table 4. Targeted transfer attack success rates (\%) when using different SASD variants: (1) SASD without fine-tuning the auxiliary model (SASD w/o FT Aux), (2) SASD without distilling the auxiliary model (SASD w/o D), (3) SASD via the commonly used knowledge distillation method (SASD w/ KD), and (4) our proposed SASD. We run each test five times and show the mean and standard deviation of the results. + +
Method→ Inc-v3→ Dense121→ VGG16
SASD w/o FT Aux32.2 ± 0.387.1 ± 0.081.3 ± 0.1
SASD w/o D29.6 ± 0.587.7 ± 0.279.5 ± 0.3
SASD w/ KD38.5 ± 0.490.7 ± 0.184.9 ± 0.2
Our SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
+ +ness against adversarial perturbations. + +# 4.3. Ablation Study + +Validating the contribution of SASD and WS. We validate the contribution of two major components in our method: SASD and WS. Specifically, following the setting of Table 1, we compare the targeted attack success rates of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. The results are shown in Table 3. We can see that both SASD and WS can improve the pre-trained source models' capability to launch targeted transfer attacks. Besides, combining SASD and WS can further enhance the source model to generate more transferable targeted adversarial perturbations. + +Validating the design of SASD. We validate the design of SASD by examining SASD's two steps: fine-tuning the auxiliary model and distilling the auxiliary model. Specifically, for examining the first step of SASD, we conduct SASD without fine-tuning the auxiliary model. In other words, we conduct the second step of SASD directly with a pre-trained source model. For examining the second step of SASD, we conduct SASD without distilling the auxiliary model. In other words, we directly use the fine-tuned auxiliary model to generate adversarial examples. Besides, we also consider distilling the auxiliary model via the commonly used knowledge distillation method [13]. Specif + +Table 5. Targeted transfer attack success rates (\%) against different defense methods. All methods are combined with the TI-DI-MI technique to generate adversarial perturbations. We run each test five times and show the mean and standard deviation of the results. + +
MethodJPEGHGDNRPNoisyMixAugMix
Pre-trained99.7 ± 0.01.4 ± 0.13.7 ± 0.00.4 ± 0.00.7 ± 0.0
RAP88.7 ± 0.00.5 ± 0.014.3 ± 0.01.0 ± 0.00.5 ± 0.0
GhostNet99.9 ± 0.01.4 ± 0.012.4 ± 0.62.4 ± 0.00.8 ± 0.0
LGV99.4 ± 0.17.6 ± 0.22.0 ± 0.36.5 ± 0.11.4 ± 0.0
SASD-WS99.8 ± 0.023.5 ± 0.117.9 ± 0.58.0 ± 0.12.0 ± 0.0
+ +![](images/026c2789f82a5ecfe57a004a751dc60178029ed8237211a2d319bb1109e902c4.jpg) +Figure 3. Successful targeted adversarial examples on Google Cloud Vision. The target class is tigers. + +![](images/4848d76355ba67b797ea6de594536f44156b1b19753db42126f693667b148610.jpg) + +ically, the commonly used knowledge distillation method combines the cross-entropy loss with respect to the true label and the Kullback-Leibler divergence with respect to the prediction of the teacher model as the distillation loss. Following the setting of Table 1, we examine the performance of targeted adversarial perturbations generated by the above SASD variants. The results are shown in Table 4. When employing the normal knowledge distillation method, we distill the auxiliary model for ten epochs to maximize the attack performance. Our SASD instead only needs less than one epoch distillation. Nevertheless, our SASD method can still surpass the normal knowledge distillation method. Besides, the SASD model's performance improves when employing a fine-tuned auxiliary model, and distilling the auxiliary model performs better than directly using the fine-tuned auxiliary model. Therefore, the experimental results validate the design of our SASD. + +# 4.4. Further Analysis + +Transfer attacks against defense methods. In this part, we evaluate SASD-WS's targeted attack performance against several adversarial defense methods and common corruption defense methods, including JPEG [10], HGD [24], NRP [29], NoisyMix [5], and AugMix [12]. We use the same experimental settings as those in the ensemble targeted and untargeted attack experiments with an ensemble of source models (Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101 [11], ResNet-152 [11]). + +Table 5 presents the results of the targeted transfer attack. We can see that SASD-WS can effectively generate effective perturbations against these defense methods in tar + +Table 6. Comparison of the average $l_{2}$ -norm across 100 images for (1) the logit output difference of the ensemble of pruned models and the corresponding WS model, and (2) the standard deviation among the logit outputs of pruned models in the ensemble. Results for the ensemble of 20/50/100 pruned models are reported. + +
2050100
Output Difference30.7129.5429.57
Standard Deviation26.8726.6626.36
+ +geted attack settings. Even though for defense methods like NoisyMix and AugMix, most of the tested adversarial attack methods failed to achieve successful targeted attack, SASD-WS can still generate targeted perturbations with superior transferability compared with other baseline methods and achieves a nearly $100\%$ attack success rate in attacking JPEG. These results show from another perspective that our approach can generate adversarial perturbations with higher transferability. + +Attacking real-world applications. We launch targeted transfer attacks against Google Cloud Vision to verify the practical applicability of the proposed method. Similar to previous experiments, we use an ensemble of six source models as the source model. We randomly sample 500 images from the NIPS17 targeted adversarial attack competition dataset as the test set to generate adversarial perturbations. Following the experimental settings in [26], when the labels with similar semantic meanings to the target label appear in the predicted labels of Google Cloud Vision, we regard the attack as successful. Although Google Cloud Vision will return the labels with probabilities more than $50.0\%$ , we only consider the top-5 labels as the predicted labels. + +Experimental results show that our method can achieve a targeted transfer attack success rate of $40.2\%$ . In contrast, the baseline methods, LGV, GhostNet, RAP, and Pretrained, can only attain a targeted transfer attack success rate of $31.8\%, 17.0\%, 4.6\%,$ and $3.6\%$ , respectively. Figure 3 presents some of the adversarial examples generated by our method. + +Validating WS. We further validate the effectiveness of our Weight Scaling (WS) method in simulating an ensemble of source models. Intuitively, if the output of the pruned models' ensemble is close to that of the corresponding WS model, the difference between their outputs should be within the standard deviation among the pruned models' outputs in the ensemble. Therefore, we calculate the $l_{2}$ -norm value of the difference between the logit outputs of the pruned models' ensemble and the corresponding WS model. We also compute the $l_{2}$ -norm value of the standard deviation among the pruned models' logit outputs in the ensemble. The results are shown in Table 6. According to the three-sigma rule, we can see that the output difference be + +![](images/ad2559f7e7b94a8fe8a3be833761b5386561a43284157b644ea11f714d0b442c.jpg) +Figure 4. Targeted transfer attack success rates $(\%)$ of the base model (SASD ResNet-50), the longitudinal ensemble of pruned base models, and the WS version of the base model (SASD-WS ResNet-50). + +![](images/e35000de00261d8ae4ec091024ab3288f6b6c0e8fbd6712269fb69860fe4e648.jpg) + +![](images/14c8290d1bdec73c5bed48185bd717b9cc318a6d7f4ba5353d667852b781115f.jpg) + +![](images/9f281f9513cc24918e41f59e3b9a7c33c87fa6a4aad602d0b229a7e252f01c2b.jpg) +Figure 5. The change of the loss landscapes with the application of our method. The fine-tuned ResNet-50 is the auxiliary model adopted in our SASD method. + +![](images/dffdf088adb92789db15bbbcdb38ba1c1ce934398bcb1c551464c229fe2f0824.jpg) + +![](images/16efc18a6fdaabf5f517c36d12eb4b9fee2bd75e551a246814a8c610c50107ec.jpg) + +![](images/82022adcb754f5a2db7760015660c3028fe3a87a6f9322e27485bac925a931cd.jpg) + +tween the pruned models' ensemble and the corresponding WS model falls into the three-sigma range of the internal variability of the pruned models in the ensemble. Therefore, the output of the WS model is not an outlier among the pruned models' outputs, which implies that the output of the WS model is close to the ensemble model. + +Moreover, we compare the targeted attack performance of a single weight-scaled SASD model and the ensemble of pruned SASD models. Specifically, we generate adversarial perturbations by employing a longitudinal ensemble of pruned SASD models with a pruning rate of $1 - p = 0.07$ . Therefore, we set our WS method's scaling ratio $p = 0.93$ . Figure 4 shows the targeted transfer attack success rates of three types of source models with SASD ResNet-50 as the base model. According to the attack performance, we can see that our WS method can reasonably approximate the ensemble of pruned models. + +Visualizing the effectiveness of SASD-WS. Our SASD-WS attempts to promote the source model's generalization capability to enable more transferable targeted adversarial attacks. To visualize the effectiveness of our SASD-WS on improving the source model's generalization capability, we depict the change of the loss landscapes by applying our method in Figure 5. We can see that with the application of our approach, the loss landscape of the resultant enhanced model becomes flatter, which can help to capture general features learned by different models [6, 16, 35]. Therefore, + +the enhanced model is more likely to cover the transferable targeted adversarial examples in its low-loss region, facilitating more transferable targeted adversarial attacks. + +# 5. Conclusion + +This work presents a novel model self-enhancement method, incorporating Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to enhance the source model's capability to generate more transferable targeted perturbations. Extensive experiments show that our method can significantly outperform the state-of-the-art approaches. Notably, under the black-box setting, we can surpass the state-of-the-art baselines by a significant margin of $12.2\%$ on average. We also validate the design of our method by several ablation studies and the practical applicability of the proposed method by attacking a popular real-world application. We believe that our approach can serve as a strong benchmark when evaluating the robustness of DNNs and an effective patch when conducting adversarial training. + +# Acknowledgment + +We thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 62206318). + +# References + +[1] Yang Deng, Weibin Wu, Jianping Zhang, and Zibin Zheng. Blurred-dilated method for adversarial attacks. In Advances in Neural Information Processing Systems, pages 58613-58624, 2023. 1 +[2] Yinpeng Dong, Fangzhou Liao, Tianyu Pang, Hang Su, Jun Zhu, Xiaolin Hu, and Jianguo Li. Boosting adversarial attacks with momentum. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9185-9193, 2018. 3, 4, 5 +[3] Yinpeng Dong, Tianyu Pang, Hang Su, and Jun Zhu. Evading defenses to transferable adversarial examples by translation-invariant attacks. 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In Advances in Neural Information Processing Systems, pages 6115-6128, 2021. 3, 5 \ No newline at end of file diff --git a/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/images.zip b/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..5c0780982b37b3feb62e2771247d7f3d560f222b --- /dev/null +++ b/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e7af38d2b5e6afeadbf8068f60cda0d856fa48259a1990ec2872e949c74d4b48 +size 487324 diff --git a/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/layout.json b/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4010d531d381c60b552708b494c6b6e58facfea1 --- /dev/null +++ b/2024/Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement/layout.json @@ -0,0 +1,8995 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 93, + 103, + 501, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 103, + 501, + 138 + ], + "spans": [ + { + "bbox": [ + 93, + 103, + 501, + 138 + ], + "type": "text", + "content": "Improving Transferable Targeted Adversarial Attacks with Model Self-Enhancement" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 147, + 161, + 445, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 161, + 445, + 175 + ], + "spans": [ + { + "bbox": [ + 147, + 161, + 445, + 175 + ], + "type": "text", + "content": "Han Wu* Guanyan Ou* Weibin Wu† Zibin Zheng" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 160, + 176, + 433, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 160, + 176, + 433, + 190 + ], + "spans": [ + { + "bbox": [ + 160, + 176, + 433, + 190 + ], + "type": "text", + "content": "School of Software Engineering, Sun Yat-sen University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 191, + 483, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 191, + 483, + 204 + ], + "spans": [ + { + "bbox": [ + 107, + 191, + 483, + 204 + ], + "type": "text", + "content": "{wuhan36, ougy3}@mail2.sysu.edu.cn, {wuwb36, zhzibin}@mail.sysu.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 256, + 290, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 581 + ], + "type": "text", + "content": "Various transfer attack methods have been proposed to evaluate the robustness of deep neural networks (DNNs). Although manifesting remarkable performance in generating untargeted adversarial perturbations, existing proposals still fail to achieve high targeted transferability. In this work, we discover that the adversarial perturbations' overfitting towards source models of mediocre generalization capability can hurt their targeted transferability. To address this issue, we focus on enhancing the source model's generalization capability to improve its ability to conduct transferable targeted adversarial attacks. In pursuit of this goal, we propose a novel model self-enhancement method that incorporates two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model, which mirrors the source model's structure, into the source model while flattening the source model's loss landscape. WS obtains an approximate ensemble of numerous pruned models to perform model augmentation, which can be conveniently synergized with SASD to elevate the source model's generalization capability and thus improve the resultant targeted perturbations' transferability. Extensive experiments corroborate the effectiveness of the proposed method. Notably, under the black-box setting, our approach can outperform the state-of-the-art baselines by a significant margin of " + }, + { + "bbox": [ + 46, + 256, + 290, + 581 + ], + "type": "inline_equation", + "content": "12.2\\%" + }, + { + "bbox": [ + 46, + 256, + 290, + 581 + ], + "type": "text", + "content": " on average in terms of the obtained targeted transferability. 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Although existing approaches have demonstrated excellent performances on untargeted transfer attacks, it is still challenging to accomplish targeted transfer attacks, which require the attacker to generate perturbations that can mislead the black-box victims to return a target label [22, 30]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 462, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 605 + ], + "type": "text", + "content": "Adversarial perturbations are prone to overfit the source model and manifest limited targeted transferability when the source model's generalization capability is mediocre. Specifically, neural networks can capture features essential for decision-making, with some features being general while the others being model-specific [16]. Intuitively, adversarial examples that primarily manipulate model-specific features are unlikely to transfer well among different models. Working towards a more generalized source model can alleviate the reliance on model-specific features, thus enhancing the transferability of the synthesized adversarial examples [35]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "Therefore, we propose to enhance the source model's generalization capability to enable more transferable targeted adversarial attacks. We conceptually illustrate the motivation of our method in Figure 1. Since different models rely on different features to make decisions, and their loss landscapes are often sharp, the transferable targeted adversarial examples are likely to reside away from the local optima of different models. It is thus challenging to transfer the adversarial examples generated by the vanilla" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 126, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 126, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 126, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24615" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 280, + 161 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 280, + 161 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 280, + 161 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 280, + 161 + ], + "type": "image", + "image_path": "f6e62b387ab344c05a3ba6d8630cc7e62b4de7ec03a5d5fad99f191cf333ae22.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 168, + 253, + 180 + ], + "lines": [ + { + "bbox": [ + 81, + 168, + 253, + 180 + ], + "spans": [ + { + "bbox": [ + 81, + 168, + 253, + 180 + ], + "type": "text", + "content": "Figure 2. The overall procedure of SASD-WS." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "type": "text", + "content": "source model to a different target model. A viable solution is to enhance the source model's generalization capability to capture the general features learned by different models. This can be achieved by learning a flatter loss landscape that covers the transferable targeted adversarial examples in the low-loss region." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 279, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 386 + ], + "type": "text", + "content": "To this end, we propose a novel model self-enhancement method: SASD-WS, which incorporates Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to promote the source model's generalization capability. Then, we can employ the enhanced source model to produce targeted perturbations with better transferability. The overall procedure of our method is summarized in Figure 2. We explain the two major components of the proposed SASD-WS as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "type": "text", + "content": "SASD. In the warm-up step of SASD, we employ the technique of Sharpness-Aware Minimization (SAM) [6] to fine-tune an auxiliary model, which mirrors the source model's structure. Specifically, during the fine-tuning of the auxiliary model, we simultaneously minimize its loss of sharpness and the cross-entropy loss between its predictions and ground-truth labels. Given the fine-tuned auxiliary model, we then enhance our source model by distilling the auxiliary model into the source model while minimizing the source model's loss of sharpness. As a result, SASD can effectively endow the source model with a flatter loss landscape and improve the resultant targeted perturbations' transferability." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "WS. To further boost the generalization capability of the obtained SASD model, we propose WS for efficient model augmentation. Specifically, we apply random pruning to the obtained SASD model to produce numerous pruned models. The resultant ensemble of randomly pruned SASD models can possess better generalization capability than the original SASD model. However, generating adversarial examples with an ensemble model can be computationally expensive. Motivated by the approximation scheme in [17], we efficiently approximate the ensemble of randomly pruned SASD models by scaling the weights of the SASD model. Therefore, WS can be efficiently synergized with SASD to further boost the targeted transferability of the synthesized adversarial examples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 72, + 525, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 525, + 83 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 525, + 83 + ], + "type": "text", + "content": "To sum up, the main contributions of this work are:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 85, + 545, + 323 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 85, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 85, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 85, + 545, + 191 + ], + "type": "text", + "content": "- We propose a novel model self-enhancement method incorporating two major components: Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS). Specifically, SASD distills a fine-tuned auxiliary model into the source model while flattening its loss landscape. WS then performs model augmentation with an efficient approximation. Their resonance promotes the source model's generalization capability and thus enables more transferable targeted adversarial attacks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 193, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 193, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 193, + 545, + 251 + ], + "type": "text", + "content": "- We conduct extensive experiments to validate the superiority of the proposed method. Notably, compared with the state-of-the-art benchmarks, our approach can improve the targeted attack success rate by a significant margin of " + }, + { + "bbox": [ + 306, + 193, + 545, + 251 + ], + "type": "inline_equation", + "content": "12.2\\%" + }, + { + "bbox": [ + 306, + 193, + 545, + 251 + ], + "type": "text", + "content": " on average under the black-box setting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 252, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 252, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 252, + 545, + 323 + ], + "type": "text", + "content": "- We confirm that our attacks can transfer well to real-world applications, exceeding the state-of-the-art baselines by " + }, + { + "bbox": [ + 306, + 252, + 545, + 323 + ], + "type": "inline_equation", + "content": "8.4\\%" + }, + { + "bbox": [ + 306, + 252, + 545, + 323 + ], + "type": "text", + "content": " on average. We also visualize the effectiveness of the proposed method from the perspective of the enhanced model's loss landscape, and validate the efficacy of our approach against defense methods." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 337, + 392, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 337, + 392, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 337, + 392, + 349 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 357, + 481, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 481, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 481, + 369 + ], + "type": "text", + "content": "2.1. Transferable Adversarial Attack" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 376, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 412 + ], + "type": "text", + "content": "With the development of transfer attack techniques, there are currently three types of approaches to improve the perturbation's transferability:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": "Enhancing the source model. As normally trained neural networks perform poorly in targeted attacks, several model enhancement methods have been proposed to improve the source model's capability to conduct targeted transfer attacks. These methods include replacing a single source model with an ensemble of models obtained by random dropout [23] and additional training epochs [9]. Springer et al. [35] instead utilizes adversarial fine-tuning to enhance the source model's ability to synthesize transferable adversarial examples. Our method also attempts to improve adversarial transferability by enhancing the source model. Nevertheless, unlike existing model enhancement-based attacks, we propose to flatten the source model's loss landscape to improve its generalization capability, enabling more transferable targeted attacks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 593, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 676 + ], + "type": "text", + "content": "Augmenting the input data. To boost adversarial transferability, some transfer attacks resort to input augmentation, such as image translation [3], random resizing and padding [46], and mixup [40]. Unlike prior efforts, a recent input augmentation-based attack technique, Spectrum Simulation Attack (SSA), proposes to apply a spectrum transformation to the input [27]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Rectifying the optimization procedure. Instead of greedily perturbing the clean images along the gradient of the cross-entropy loss [20], several attempts propose to im" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24616" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "prove the optimization procedure to craft more transferable adversarial examples. Straightforward solutions include employing momentum [2] and Nesterov accelerated gradient [25]. Huang et al. [15] instead consider adding the intermediate feature loss into the attack objective to regularize the search of adversarial examples. The state-of-the-art attack of this kind, Reverse Adversarial Perturbation (RAP) [31], seeks adversarial examples located at a region with uniformly low loss values." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 287, + 228 + ], + "type": "text", + "content": "Our attack can be conveniently combined with other transfer attacks based on input augmentation and optimization procedure rectification to further enhance the transferability of adversarial attacks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 234, + 261, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 234, + 261, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 234, + 261, + 247 + ], + "type": "text", + "content": "2.2. Improving DNNs' Generalization Ability" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 252, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 445 + ], + "type": "text", + "content": "Foret et al. [6] propose Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness to improve the model's generalization ability. Hinton et al. [13] introduce knowledge distillation to transfer the knowledge of a teacher model to the student model [45]. Intriguingly, Stanton et al. [36] discover that knowledge distillation can enhance the student model's generalization ability. Building upon Sharpness-Aware Minimization and knowledge distillation methodologies, we propose Sharpness-Aware Self-Distillation (SASD) to integrate Sharpness-Aware Minimization with knowledge distillation, which can further improve the source model's generalization capability. Since a more generalized source model can better capture the general features learned by different models, the produced adversarial examples are more likely to possess better targeted transferability [35]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 454, + 130, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 130, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 130, + 467 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 474, + 171, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 171, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 171, + 485 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": "We first formulate the targeted transfer attack. Given a labeled image dataset " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": " and a target classifier " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{target}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": ", for an image-label pair " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "(x,y)\\in D" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": ", a targeted transfer attack aims to generate an adversarial example " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}} = x + \\delta" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": " to mislead the target classifier " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{target}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": " to predict a specific target label " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{target}}\\neq y" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": ". Since the target classifier is black-box, a targeted transfer attack instead derives the adversarial example " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": " with a white-box source model " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": ". It is usually accomplished by optimizing " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": " to minimize the source model's cross-entropy loss " + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CE}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": " on the target label [8, 51]:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 619, + 287, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 619, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 287, + 646 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {L _ {\\mathrm {C E}} (f (x + \\delta), y _ {\\text {t a r g e t}}),} \\tag {1} \\\\ \\mathrm {s . t .} \\left. | | \\delta | | _ {\\infty} \\leq \\epsilon . \\right. \\\\ \\end{array}", + "image_path": "e6f0702ba0959081f49ac3d91228389bc15edd48dd5cca713a47a0c181ef9255.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "To ensure that the perturbation " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " is imperceptible, attackers should also set a small perturbation budget " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": ". After generating the adversarial example " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " with the source model, a targeted transfer attack directly uses " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " to attack the target classifier, with the goal of " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{target}}(x_{\\mathrm{adv}}) = y_{\\mathrm{target}}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": ". To" + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 306, + 86, + 487, + 252 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 500, + 84 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 500, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 500, + 84 + ], + "type": "text", + "content": "Algorithm 1 Sharpness-Aware Self-Distillation" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "lines": [ + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": "Input: Fine-tuned auxiliary model \n1: Initialization: " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "n \\gets 0" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " \n2: for every batch in the data loader do \n3: " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "n \\gets n + 1" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " \n4: Calculate " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{distillation}}" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " by Equation (3) \n5: " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "\\epsilon \\gets \\operatorname{argmax}_{\\| \\epsilon \\|_2 \\leq \\rho} \\epsilon^T \\nabla_{\\omega_s} L_{\\mathrm{distillation}}(\\omega_s)" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " \n6: " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "g = \\nabla_{\\omega_s} L(\\omega_s)|_{\\omega_s + \\epsilon}" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " \n7: " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "\\omega_s \\gets \\omega_s - lr \\cdot g" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " \n8: if " + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "inline_equation", + "content": "n \\geq n_{\\mathrm{max}}" + }, + { + "bbox": [ + 306, + 86, + 487, + 252 + ], + "type": "text", + "content": " then \n9: break \n10: end if \n11: end for \nOutput: SASD model" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 276, + 547, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 547, + 323 + ], + "type": "text", + "content": "improve the attack success rate (i.e., the transferability) of the generated targeted perturbations, we propose enhancing the source model's generalization ability, detailed in the following sections." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 331, + 486, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 486, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 486, + 344 + ], + "type": "text", + "content": "3.2. Sharpness-Aware Self-Distillation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "type": "text", + "content": "Fine-tuning the auxiliary model. We start with a pretrained source model and fine-tune it on its original training dataset to obtain the auxiliary model. The fine-tuning procedure follows Sharpness-Aware Minimization (SAM), which simultaneously minimizes loss values and loss sharpness [6]. Specifically, in each iteration, we first perform back-propagation based on the cross-entropy loss [7] between the output of the auxiliary model and the ground-truth label. We then modify the auxiliary model's weight " + }, + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "type": "text", + "content": " by adding a perturbation " + }, + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\epsilon_{m}" + }, + { + "bbox": [ + 304, + 350, + 545, + 483 + ], + "type": "text", + "content": " that can maximize the cross-entropy loss:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 345, + 492, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 492, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 345, + 492, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\epsilon_ {m} = \\underset {\\epsilon_ {m}} {\\arg \\max } L _ {\\mathrm {C E}} (f (\\omega + \\epsilon_ {m}, x), y), \\tag {2}", + "image_path": "d310591f5315fa2df970656196d92545be31c4930b28c5aa8e03d05f54d3f6c7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "f(\\omega, x)" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": " is the output of a neural network " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": " given the model weight " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": " and the input " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": ". We perform backpropagation again based on the perturbed weight to minimize the auxiliary model's loss of sharpness." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": "Distilling the auxiliary model. After obtaining a finetuned auxiliary model, we distill it into the source model to enhance its generalization ability. Specifically, we first make the source model's probability output close to the auxiliary model's. Let " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "q_{1} = \\phi_{1}(l_{\\mathrm{aux}})" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " denote the probability output of the auxiliary model, where " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\phi_{1}" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " is a differentiable transformation, and " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{aux}}" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " is the auxiliary model's logit output. In our SASD, we set " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\phi_{1}(l_{\\mathrm{aux}}) = \\mathrm{Softmax}(l_{\\mathrm{aux}} / \\tau)" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " is the distillation temperature. The larger the temperature is, the softer the probability distribution will be. Similarly, let " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "q_{2} = \\phi_{2}(l_{\\mathrm{source}})" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " denote the probability output of the source model, where " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\phi_{2}(l_{\\mathrm{source}}) =" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24617" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathrm{Softmax}(l_{\\mathrm{source}} / \\tau)" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". To minimize the prediction difference between the auxiliary and source models, we employ the Kullback-Leibler divergence " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " [18] between " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "q_{1}" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "q_{2}" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " as the distillation loss:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 129, + 287, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 129, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 55, + 129, + 287, + 155 + ], + "type": "interline_equation", + "content": "L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) = \\mathbb {E} _ {(x, y) \\in D} \\left[ D _ {\\mathrm {K L}} \\left(q _ {1} (x, y), q _ {2} (x, y)\\right) \\right]. \\tag {3}", + "image_path": "e052e51f8c88927a83c5d65cdf0fce110adf05d4ff1f0d56e7b5f44c608914d5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 163, + 287, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 287, + 187 + ], + "type": "text", + "content": "We then simultaneously minimize the distillation loss and its sharpness:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 120, + 197, + 287, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 197, + 287, + 214 + ], + "spans": [ + { + "bbox": [ + 120, + 197, + 287, + 214 + ], + "type": "interline_equation", + "content": "\\min _ {\\omega_ {s}} \\mathbb {E} _ {(x, y) \\in D} [ L (\\omega_ {s}) ], \\tag {4}", + "image_path": "1393d7956b7110bbda547ebe1d0e2304f2c8cc86dfc21ae535bdcdb67e641569.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 224, + 75, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 75, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 75, + 233 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 241, + 287, + 296 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 241, + 287, + 296 + ], + "spans": [ + { + "bbox": [ + 55, + 241, + 287, + 296 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L \\left(\\omega_ {s}\\right) = \\max _ {\\| \\epsilon \\| _ {2} \\leq \\rho} L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s} + \\epsilon\\right) \\\\ \\approx \\max _ {\\| \\epsilon \\| _ {2} \\leq \\rho} \\left[ L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) + \\epsilon^ {T} \\nabla_ {\\omega_ {s}} L _ {\\text {d i s t i l l a t i o n}} \\left(\\omega_ {s}\\right) \\right]. \\tag {5} \\\\ \\end{array}", + "image_path": "2e5c856ed3327e493abe5bbe9d00e9b6060acbf70c355f9d40075dd1887aa77b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "type": "text", + "content": " be the learning rate, and " + }, + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{max}}" + }, + { + "bbox": [ + 47, + 305, + 287, + 340 + ], + "type": "text", + "content": " be the maximum iteration number. Algorithm 1 summarizes the SASD process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 349, + 140, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 140, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 140, + 361 + ], + "type": "text", + "content": "3.3. Weight Scaling" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 367, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 287, + 439 + ], + "type": "text", + "content": "To further boost the generalization capability of the obtained SASD model, we apply the network pruning method [47] to generate an ensemble of pruned SASD models. Specifically, we randomly prune the convolutional layers of the obtained SASD model with a probability of " + }, + { + "bbox": [ + 47, + 367, + 287, + 439 + ], + "type": "inline_equation", + "content": "1 - p" + }, + { + "bbox": [ + 47, + 367, + 287, + 439 + ], + "type": "text", + "content": ". Then, the weight of a pruned SASD model is:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 96, + 449, + 287, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 449, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 96, + 449, + 287, + 462 + ], + "type": "interline_equation", + "content": "\\omega_ {\\text {p r u n e d}} = \\omega \\odot (\\mathbf {1} - \\xi (\\omega , 1 - p)), \\tag {6}", + "image_path": "e902bd15d3dddd2000b520d196a520d4b908d21f410a78136c783f68dcba287e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{1}" + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "text", + "content": " denotes the all-ones matrix with the same size as the weight of the SASD model. " + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\xi (\\omega ,1 - p)" + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "text", + "content": " indicates the randomly selected weights in the convolutional layers to be pruned. By applying the Hadamard product " + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 471, + 287, + 554 + ], + "type": "text", + "content": " that represents element-wise multiplication to the weight, we can obtain the pruned model with some weights in the convolutional layers setting to zero." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "text", + "content": "Inspired by the approximation scheme in [17], we further approximate an ensemble of pruned models with a weight-scaled model. Specifically, let " + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\overline{f} = \\frac{1}{n}\\sum_{i=1}^{n}f(\\omega_i)" + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "text", + "content": " be the ensemble of models with the same structure but different weights. Let " + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\overline{\\omega} = \\frac{1}{n}\\sum_{i=1}^{n}\\omega_i" + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "text", + "content": " be the average weight of the component networks in the ensemble, and " + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\eta_i = \\omega_i - \\overline{\\omega}" + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "inline_equation", + "content": "i\\in \\{i|1\\leq i\\leq n,i\\in \\mathbb{N}\\}" + }, + { + "bbox": [ + 47, + 554, + 287, + 639 + ], + "type": "text", + "content": ", we have:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 61, + 648, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 648, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 61, + 648, + 287, + 711 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\eta_ {i} = 0, (7) \\\\ f \\left(\\omega_ {i}, x\\right) = f (\\bar {\\omega} + \\eta_ {i}, x) (8) \\\\ = f (\\bar {\\omega}, x) + \\eta_ {i} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta_ {i} \\| _ {2} ^ {2}\\right). \\\\ \\end{array}", + "image_path": "ad59ef22b47384eb09ed6e7634cb834b2f9d3fbcadbd48c99dca3eecb77293cf.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 72, + 440, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 72, + 440, + 83 + ], + "spans": [ + { + "bbox": [ + 318, + 72, + 440, + 83 + ], + "type": "text", + "content": "Therefore, we can derive that:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 92, + 545, + 206 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 92, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 316, + 92, + 545, + 206 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {f} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} f (\\omega_ {i}, x) \\\\ = \\frac {1}{n} \\sum_ {i = 1} ^ {n} [ f (\\bar {\\omega}, x) + \\eta_ {i} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta_ {i} \\| _ {2} ^ {2}\\right) ] \\tag {9} \\\\ = f (\\bar {\\omega}, x) + \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\eta_ {j} ^ {T} \\nabla_ {\\bar {\\omega}} f (\\bar {\\omega}, x) + O \\left(\\| \\eta \\| _ {2} ^ {2}\\right) \\\\ = f (\\bar {\\omega}, x) + O \\left(\\| \\eta \\| _ {2} ^ {2}\\right) \\approx f (\\bar {\\omega}, x). \\\\ \\end{array}", + "image_path": "2084a5ce0a167c41d81764ade87a0ec41c7171c27fa761178404bfd1e4f55f20.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 214, + 546, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 214, + 546, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 214, + 546, + 250 + ], + "type": "text", + "content": "It implies that a single model with the average weight of multiple models can replace the ensemble of these models as long as their weight differences are small enough." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "type": "text", + "content": "Therefore, if the pruning probability " + }, + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "type": "inline_equation", + "content": "1 - p" + }, + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "type": "text", + "content": " is small, the ensemble of infinite pruned SASD models can be approximated by a single SASD model that is weight-scaled by the scaling ratio " + }, + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 251, + 545, + 298 + ], + "type": "text", + "content": " (i.e., the SASD-WS model):" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 321, + 307, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 307, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 321, + 307, + 545, + 354 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {f} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} f \\left(\\omega_ {i} ^ {\\text {p r u n e d S A S D}}, x\\right) \\tag {10} \\\\ \\approx f (\\bar {\\omega}, x) = f (p \\cdot \\omega^ {\\mathrm {S A S D}}, x) = f _ {\\mathrm {S A S D - W S}}, \\\\ \\end{array}", + "image_path": "5cc65a32837d85479a5b5abdd424a1dcb3cbbe1c745e2f2e69f660d720f40e22.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 363, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 545, + 388 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 363, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\omega^{\\mathrm{SASD}}" + }, + { + "bbox": [ + 305, + 363, + 545, + 388 + ], + "type": "text", + "content": " is the weight of the SASD model before pruning." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 396, + 426, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 426, + 408 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 426, + 408 + ], + "type": "text", + "content": "3.4. Attacking Algorithm" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "text", + "content": "After obtaining the SASD-WS model, we generate targeted adversarial examples with the TI-DI-MI method [2, 3, 46]. Specifically, given the input data " + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "text", + "content": ", the source model " + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "text", + "content": ", and the target class " + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "inline_equation", + "content": "y_{target}" + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "text", + "content": ", the perturbation " + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\delta_{i+1}" + }, + { + "bbox": [ + 305, + 414, + 545, + 474 + ], + "type": "text", + "content": " can be iteratively updated by:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 332, + 482, + 545, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 482, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 332, + 482, + 545, + 497 + ], + "type": "interline_equation", + "content": "\\delta_ {i + 1} = \\operatorname {C l i p} _ {\\delta_ {i}} ^ {\\epsilon_ {\\mathrm {p}}} \\left\\{\\delta_ {i} + \\alpha \\cdot \\operatorname {s i g n} \\left(g _ {i + 1}\\right) \\right\\}, \\tag {11}", + "image_path": "2c3986b8535b214174f57381913d3210bda0261bb1640ed1dbc4f8e911f4c4d6.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 311, + 498, + 545, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 498, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 311, + 498, + 545, + 525 + ], + "type": "interline_equation", + "content": "g _ {i + 1} = g _ {i} + W \\cdot \\nabla_ {\\delta} \\frac {\\mathcal {L} (\\mathrm {D I} (x + \\delta_ {i}) , y _ {\\text {t a r g e t}} ; f)}{\\| \\mathcal {L} (\\mathrm {D I} (x _ {i} + \\delta_ {i}) , y _ {\\text {t a r g e t}} ; f) \\| _ {1}}. \\tag {12}", + "image_path": "af66036ca36dca8ac88e7d560c9653d5d6e738ee53422d17209e1c6c0a3b04b0.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "text", + "content": " is the step size for attacks. " + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "text", + "content": " is the Gaussian kernel for image translation. " + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "text", + "content": " is the attack objective function. DI denotes the input transformation of random resizing and padding. The generated adversarial perturbation is " + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "inline_equation", + "content": "l_{\\infty}" + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "text", + "content": "-norm bounded by the maximum perturbation budget " + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\epsilon_p" + }, + { + "bbox": [ + 306, + 533, + 545, + 594 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 604, + 387, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 387, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 387, + 616 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 623, + 422, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 422, + 636 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 422, + 636 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": "We focus on attacking the image classifiers trained on the ImageNet (ILSVRC 2012) dataset [33]. We perform SASD with the standard training and validation splits of the ImageNet dataset. We apply our method to eight models pretrained on ImageNet: Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24618" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 124, + 531, + 290 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 114 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 114 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 114 + ], + "type": "text", + "content": "Table 1. Targeted transfer attack success rates (%) with a single source model. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. \"Pre-trained\" means directly using the normally trained model as the source model without modification. \" * \" indicates white-box cases. We run each method five times and show the mean and standard deviation of the results." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 124, + 531, + 290 + ], + "lines": [ + { + "bbox": [ + 67, + 124, + 531, + 290 + ], + "spans": [ + { + "bbox": [ + 67, + 124, + 531, + 290 + ], + "type": "table", + "html": "
MethodSource Model: Inc-v3Source Model: Res50
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained99.0 ± 0.0*2.1 ± 0.13.6 ± 0.11.9 ± 0.37.8 ± 0.398.7 ± 0.1*64.3 ± 0.953.8 ± 0.7
RAP93.6 ± 0.0*3.5 ± 0.05.4 ± 0.03.9 ± 0.014.4 ± 0.098.5 ± 0.0*56.2 ± 0.052.6 ± 0.0
GhostNet97.9 ± 0.2*8.1 ± 0.312.8 ± 0.16.6 ± 0.413.2 ± 0.498.0 ± 0.2*75.0 ± 0.368.4 ± 0.6
LGV55.0 ± 0.2*40.5 ± 0.348.3 ± 0.349.5 ± 0.254.5 ± 0.893.2 ± 0.2*90.0 ± 0.184.0 ± 0.2
SASD-WS94.6 ± 0.2*44.4 ± 0.257.6 ± 1.153.8 ± 0.870.3 ± 0.897.2 ± 0.4*93.0 ± 0.288.7 ± 0.4
MethodSource Model: Dense121Source Model: VGG16
→ Inc-v3→ Res50→ Dense121→ VGG16→ Inc-v3→ Res50→ Dense121→ VGG16
Pre-trained6.0 ± 0.439.3 ± 0.698.8 ± 0.2*33.6 ± 0.50.9 ± 0.29.8 ± 0.512.2 ± 0.595.4 ± 0.3*
RAP12.0 ± 0.041.2 ± 0.097.8 ± 0.0*37.4 ± 0.02.1 ± 0.09.9 ± 0.09.8 ± 0.085.8 ± 0.0*
GhostNet10.4 ± 0.649.6 ± 0.898.6 ± 0.1*44.0 ± 0.61.1 ± 0.213.0 ± 0.114.9 ± 0.794.9 ± 0.2*
LGV51.3 ± 0.380.8 ± 0.292.9 ± 0.2*75.8 ± 0.2————
SASD-WS61.6 ± 0.687.5 ± 0.297.7 ± 0.1*82.7 ± 0.616.3 ± 0.741.9 ± 0.551.7 ± 0.294.5 ± 0.3*
", + "image_path": "7a2784597c13542bb14afa3457ef0e1e8932f552678bd314e4954d2d301bcf52.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "content": "[11], ResNet-152 [11], DenseNet-121 [14], and VGGNet-16 [34]. All these pre-trained models' weights are publicly accessible1. For SASD, we set the distillation temperature " + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "inline_equation", + "content": "\\tau = 1" + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "content": " and the learning rate " + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "inline_equation", + "content": "lr = 0.05" + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "content": " for all source models. We set WS's scaling ratio " + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "content": " to 0.93 for each SASD-WS model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 382, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 287, + 622 + ], + "type": "text", + "content": "We compare the targeted transfer attack performance of our SASD-WS method with the state-of-the-art model enhancement-based attacks: GhostNet [23] and LGV [9]. Although RAP [31] works by rectifying the optimization procedure and does not modify the source model, its motivation is similar to our method. Therefore, we also compare our approach with RAP. We implement the baseline methods following the default settings in their original papers. For LGV, we additionally train the source model on the ImageNet training set for ten epochs [33]. We then obtain four LGV models in each epoch, leading to 40 LGV models for each source model. We cannot apply LGV to VGGNet-16 since the default settings of LGV are not compatible with VGGNet-16. Notably, since LGV and GhostNet transform a single source model into multiple models to generate adversarial examples, we follow their papers to ensemble these models with the longitudinal ensemble method [23]. In contrast, we only transform a single source model into a single SASD-WS model when generating adversarial examples." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": "Following the practice in the literature [2, 23], we set the step size " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "\\alpha = 2 / 255" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": " and the maximum perturbation budget " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "\\epsilon_{p} = 16 / 255" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": ". We set the maximum iteration number " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{max}} = 100" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": " in the adversarial perturbation generation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 308, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 545, + 369 + ], + "type": "text", + "content": "process. We conduct targeted transfer attacks on NIPS17 targeted adversarial attack competition dataset[21]. All experiments are implemented with PyTorch 2.0.1 and conducted with an NVIDIA GeForce RTX 4090 GPU of 24 GB memory." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 378, + 440, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 440, + 391 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 440, + 391 + ], + "type": "text", + "content": "4.2. Attacking Performance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": "Targeted transfer attacks with a single source model. We first evaluate the performance of our method when only a single source model is available. We use the logit loss " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{Logit}} = -l^{(t)}(x + \\delta)" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " proposed in [51] as the attack objective function " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "l^{(t)}(\\cdot)" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " is the output logit of the source model concerning the target label. Table 1 reports the attack success rate of each method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 482, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 553 + ], + "type": "text", + "content": "As shown in Table 1, our method consistently outperforms the state-of-the-art baselines by a significant margin of " + }, + { + "bbox": [ + 304, + 482, + 545, + 553 + ], + "type": "inline_equation", + "content": "12.2\\%" + }, + { + "bbox": [ + 304, + 482, + 545, + 553 + ], + "type": "text", + "content": " on average under the black-box settings. Besides improving the targeted attack success rate under the black-box settings, SASD-WS can also maintain high white-box attack performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 554, + 546, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 546, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 546, + 674 + ], + "type": "text", + "content": "Targeted transfer attacks with an ensemble of source models. We then test the performance of our method when multiple source models are available, including Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. For the target models, due to the widespread application of adversarial training techniques [19, 28, 39], we first consider adversially trained models. We also consider the scenarios where the target and source models are from different structure families. Specifically, we evaluate the effectiveness of the targeted perturbation on Vision" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 286, + 712 + ], + "type": "text", + "content": "https://github.com/Cadene/pretrained-models.pytorch, https://pytorch.org/vision/stable/models.html" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "2https://github.com/cleverhans-lab/cleverhans/ blob/master/cleverhans_v3.1.0/examples/nips17_adversarial_competition/dataset/dev_dataset.csv" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24619" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 123, + 547, + 200 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 115 + ], + "type": "text", + "content": "Table 2. Targeted transfer attack success rates (%) with an ensemble of six source models: Inception-v3, Inception-v4, Inc-Res-v2, ResNet-50, ResNet-101, and ResNet-152. All methods are combined with the input augmentation technique TI-DI-MI to generate adversarial perturbations. \"Pre-trained\" means directly using the normally trained model as the source model without modification. We run each method five times and show the mean and standard deviation of the results." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 123, + 547, + 200 + ], + "lines": [ + { + "bbox": [ + 49, + 123, + 547, + 200 + ], + "spans": [ + { + "bbox": [ + 49, + 123, + 547, + 200 + ], + "type": "table", + "html": "
MethodInc-v3adv ens3Inc-v3adv ens4IncRes-v2adv ensViT-B/16ViT-L/16CLIP (RN50)CLIP (ViT-B/32)CLIP (ViT-L/14)
Pre-trained0.0 ± 0.00.1 ± 0.00.0 ± 0.03.1 ± 0.31.5 ± 0.216.3 ± 0.72.0 ± 0.13.2 ± 0.4
RAP1.7 ± 0.01.5 ± 0.00.1 ± 0.06.0 ± 0.03.0 ± 0.017.7 ± 0.05.1 ± 0.04.8 ± 0.0
GhostNet0.7 ± 0.11.1 ± 0.20.2 ± 0.09.1 ± 0.55.7 ± 0.133.0 ± 0.55.3 ± 0.210.7 ± 0.1
LGV8.1 ± 0.26.7 ± 0.21.7 ± 0.119.6 ± 0.013.0 ± 0.259.4 ± 0.322.4 ± 0.228.4 ± 0.3
SASD-WS16.6 ± 0.213.5 ± 0.35.3 ± 0.134.1 ± 0.225.1 ± 0.258.7 ± 0.524.2 ± 0.234.7 ± 0.2
", + "image_path": "ad04c565ffc6b903115c30d443d49724179cea2c8c117dd13db56665a2fda08a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 66, + 281, + 269, + 345 + ], + "blocks": [ + { + "bbox": [ + 46, + 216, + 288, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 288, + 270 + ], + "type": "text", + "content": "Table 3. Targeted transfer attack success rates (\\%) of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. We run each test five times and show the mean and standard deviation of the results." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 281, + 269, + 345 + ], + "lines": [ + { + "bbox": [ + 66, + 281, + 269, + 345 + ], + "spans": [ + { + "bbox": [ + 66, + 281, + 269, + 345 + ], + "type": "table", + "html": "
Method→ Inc-v3→ Dense121→ VGG16
Pre-trained7.7 ± 0.363.7 ± 0.156.2 ± 0.5
WS35.0 ± 0.584.7 ± 0.277.8 ± 0.4
SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
SASD-WS70.3 ± 0.893.0 ± 0.288.7 ± 0.4
", + "image_path": "a14d9cfbfb4711b7429d4d959c8eaa7ce8a53d333c4b3eb9c8bbef99ffd780b1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 365, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 509 + ], + "type": "text", + "content": "Transformers (ViTs) [4] and CLIP models [32]. ViTs apply the transformer models to visual data and leverage the self-attention mechanism to process data patches. CLIP models utilize both the image and text encoders to encode and calculate the similarity of the image-text pairs. They can produce the similarity score for each label. In our experiments, we use Inc-v3adv ens3 [39], Inc-v3adv ens4 [39], and IncRes-v2adv ens [39] as the target adversarially trained models. We consider ViT-B/16 and ViT-L/16 as the target ViTs. We target CLIP models with ResNet50, ViT-B/32, and ViT-L/14 as the image encoders, respectively. We use the cross-entropy loss as our attack objective function " + }, + { + "bbox": [ + 46, + 365, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 365, + 287, + 509 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "We report the results in Table 2. It shows that SASDWS can generate more transferable targeted perturbations than the other baseline methods, with a significant improvement of " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "6.6\\%" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " on average. While most baselines can generate perturbations that can manifest a certain degree of targeted transferability, RAP performs poorly under the ensemble source model setting compared with the other baseline methods, with an average attack success rate of only " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "8.2\\%" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ". We believe that the poor targeted attack performance of RAP under the ensemble source model setting is due to the ensemble model's lack of a uniformly low-loss region. Therefore, it highlights the need to enhance the source model to enable more transferable targeted adversarial attacks. Besides, our method's high targeted attack success rates against different target models, including adversarially trained models, reveal the potential security risk of DNNs and call for more effort to improve DNNs' robustness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 216, + 547, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 547, + 293 + ], + "type": "text", + "content": "Table 4. Targeted transfer attack success rates (\\%) when using different SASD variants: (1) SASD without fine-tuning the auxiliary model (SASD w/o FT Aux), (2) SASD without distilling the auxiliary model (SASD w/o D), (3) SASD via the commonly used knowledge distillation method (SASD w/ KD), and (4) our proposed SASD. We run each test five times and show the mean and standard deviation of the results." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 315, + 302, + 539, + 365 + ], + "blocks": [ + { + "bbox": [ + 315, + 302, + 539, + 365 + ], + "lines": [ + { + "bbox": [ + 315, + 302, + 539, + 365 + ], + "spans": [ + { + "bbox": [ + 315, + 302, + 539, + 365 + ], + "type": "table", + "html": "
Method→ Inc-v3→ Dense121→ VGG16
SASD w/o FT Aux32.2 ± 0.387.1 ± 0.081.3 ± 0.1
SASD w/o D29.6 ± 0.587.7 ± 0.279.5 ± 0.3
SASD w/ KD38.5 ± 0.490.7 ± 0.184.9 ± 0.2
Our SASD46.5 ± 0.591.2 ± 0.286.7 ± 0.1
", + "image_path": "7f40efca568a321d3c3cbdb935689bd5ea24c01258aa98551e4844f6ca1b18a6.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 385, + 461, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 461, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 461, + 398 + ], + "type": "text", + "content": "ness against adversarial perturbations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 406, + 400, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 400, + 420 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 400, + 420 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 425, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 569 + ], + "type": "text", + "content": "Validating the contribution of SASD and WS. We validate the contribution of two major components in our method: SASD and WS. Specifically, following the setting of Table 1, we compare the targeted attack success rates of the adversarial examples generated by the normally trained ResNet-50 and that enhanced by our SASD and WS, respectively. The results are shown in Table 3. We can see that both SASD and WS can improve the pre-trained source models' capability to launch targeted transfer attacks. Besides, combining SASD and WS can further enhance the source model to generate more transferable targeted adversarial perturbations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Validating the design of SASD. We validate the design of SASD by examining SASD's two steps: fine-tuning the auxiliary model and distilling the auxiliary model. Specifically, for examining the first step of SASD, we conduct SASD without fine-tuning the auxiliary model. In other words, we conduct the second step of SASD directly with a pre-trained source model. For examining the second step of SASD, we conduct SASD without distilling the auxiliary model. In other words, we directly use the fine-tuned auxiliary model to generate adversarial examples. Besides, we also consider distilling the auxiliary model via the commonly used knowledge distillation method [13]. Specif" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24620" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 123, + 286, + 186 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "text", + "content": "Table 5. Targeted transfer attack success rates (\\%) against different defense methods. All methods are combined with the TI-DI-MI technique to generate adversarial perturbations. We run each test five times and show the mean and standard deviation of the results." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 123, + 286, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 123, + 286, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 123, + 286, + 186 + ], + "type": "table", + "html": "
MethodJPEGHGDNRPNoisyMixAugMix
Pre-trained99.7 ± 0.01.4 ± 0.13.7 ± 0.00.4 ± 0.00.7 ± 0.0
RAP88.7 ± 0.00.5 ± 0.014.3 ± 0.01.0 ± 0.00.5 ± 0.0
GhostNet99.9 ± 0.01.4 ± 0.012.4 ± 0.62.4 ± 0.00.8 ± 0.0
LGV99.4 ± 0.17.6 ± 0.22.0 ± 0.36.5 ± 0.11.4 ± 0.0
SASD-WS99.8 ± 0.023.5 ± 0.117.9 ± 0.58.0 ± 0.12.0 ± 0.0
", + "image_path": "c3ab4dcb7a815d15b4a55cfc50d83c0d0262f12047e8e3081506ab9e99d2b354.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 72, + 196, + 153, + 277 + ], + "blocks": [ + { + "bbox": [ + 72, + 196, + 153, + 277 + ], + "lines": [ + { + "bbox": [ + 72, + 196, + 153, + 277 + ], + "spans": [ + { + "bbox": [ + 72, + 196, + 153, + 277 + ], + "type": "image", + "image_path": "026c2789f82a5ecfe57a004a751dc60178029ed8237211a2d319bb1109e902c4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 285, + 287, + 308 + ], + "lines": [ + { + "bbox": [ + 47, + 285, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 287, + 308 + ], + "type": "text", + "content": "Figure 3. Successful targeted adversarial examples on Google Cloud Vision. The target class is tigers." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 157, + 198, + 263, + 277 + ], + "blocks": [ + { + "bbox": [ + 157, + 198, + 263, + 277 + ], + "lines": [ + { + "bbox": [ + 157, + 198, + 263, + 277 + ], + "spans": [ + { + "bbox": [ + 157, + 198, + 263, + 277 + ], + "type": "image", + "image_path": "4848d76355ba67b797ea6de594536f44156b1b19753db42126f693667b148610.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 328, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 287, + 533 + ], + "type": "text", + "content": "ically, the commonly used knowledge distillation method combines the cross-entropy loss with respect to the true label and the Kullback-Leibler divergence with respect to the prediction of the teacher model as the distillation loss. Following the setting of Table 1, we examine the performance of targeted adversarial perturbations generated by the above SASD variants. The results are shown in Table 4. When employing the normal knowledge distillation method, we distill the auxiliary model for ten epochs to maximize the attack performance. Our SASD instead only needs less than one epoch distillation. Nevertheless, our SASD method can still surpass the normal knowledge distillation method. Besides, the SASD model's performance improves when employing a fine-tuned auxiliary model, and distilling the auxiliary model performs better than directly using the fine-tuned auxiliary model. Therefore, the experimental results validate the design of our SASD." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 540, + 149, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 149, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 149, + 552 + ], + "type": "text", + "content": "4.4. Further Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 677 + ], + "type": "text", + "content": "Transfer attacks against defense methods. In this part, we evaluate SASD-WS's targeted attack performance against several adversarial defense methods and common corruption defense methods, including JPEG [10], HGD [24], NRP [29], NoisyMix [5], and AugMix [12]. We use the same experimental settings as those in the ensemble targeted and untargeted attack experiments with an ensemble of source models (Inception-v3 [37], Inception-v4 [38], Inception-ResNet-v2 [38], ResNet-50 [11], ResNet-101 [11], ResNet-152 [11])." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Table 5 presents the results of the targeted transfer attack. We can see that SASD-WS can effectively generate effective perturbations against these defense methods in tar" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 340, + 134, + 515, + 179 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 126 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 126 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 126 + ], + "type": "text", + "content": "Table 6. Comparison of the average " + }, + { + "bbox": [ + 305, + 70, + 545, + 126 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 305, + 70, + 545, + 126 + ], + "type": "text", + "content": "-norm across 100 images for (1) the logit output difference of the ensemble of pruned models and the corresponding WS model, and (2) the standard deviation among the logit outputs of pruned models in the ensemble. Results for the ensemble of 20/50/100 pruned models are reported." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 340, + 134, + 515, + 179 + ], + "lines": [ + { + "bbox": [ + 340, + 134, + 515, + 179 + ], + "spans": [ + { + "bbox": [ + 340, + 134, + 515, + 179 + ], + "type": "table", + "html": "
2050100
Output Difference30.7129.5429.57
Standard Deviation26.8726.6626.36
", + "image_path": "8a857046165a1175fa4b60ee5cd69efbf6e09dbc723cb92004621517eda63e66.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 198, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 305 + ], + "type": "text", + "content": "geted attack settings. Even though for defense methods like NoisyMix and AugMix, most of the tested adversarial attack methods failed to achieve successful targeted attack, SASD-WS can still generate targeted perturbations with superior transferability compared with other baseline methods and achieves a nearly " + }, + { + "bbox": [ + 304, + 198, + 545, + 305 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 198, + 545, + 305 + ], + "type": "text", + "content": " attack success rate in attacking JPEG. These results show from another perspective that our approach can generate adversarial perturbations with higher transferability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 306, + 546, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 546, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 546, + 474 + ], + "type": "text", + "content": "Attacking real-world applications. We launch targeted transfer attacks against Google Cloud Vision to verify the practical applicability of the proposed method. Similar to previous experiments, we use an ensemble of six source models as the source model. We randomly sample 500 images from the NIPS17 targeted adversarial attack competition dataset as the test set to generate adversarial perturbations. Following the experimental settings in [26], when the labels with similar semantic meanings to the target label appear in the predicted labels of Google Cloud Vision, we regard the attack as successful. Although Google Cloud Vision will return the labels with probabilities more than " + }, + { + "bbox": [ + 304, + 306, + 546, + 474 + ], + "type": "inline_equation", + "content": "50.0\\%" + }, + { + "bbox": [ + 304, + 306, + 546, + 474 + ], + "type": "text", + "content": ", we only consider the top-5 labels as the predicted labels." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "content": "Experimental results show that our method can achieve a targeted transfer attack success rate of " + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "inline_equation", + "content": "40.2\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "content": ". In contrast, the baseline methods, LGV, GhostNet, RAP, and Pretrained, can only attain a targeted transfer attack success rate of " + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "inline_equation", + "content": "31.8\\%, 17.0\\%, 4.6\\%," + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "content": ", respectively. Figure 3 presents some of the adversarial examples generated by our method." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "Validating WS. We further validate the effectiveness of our Weight Scaling (WS) method in simulating an ensemble of source models. Intuitively, if the output of the pruned models' ensemble is close to that of the corresponding WS model, the difference between their outputs should be within the standard deviation among the pruned models' outputs in the ensemble. Therefore, we calculate the " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "-norm value of the difference between the logit outputs of the pruned models' ensemble and the corresponding WS model. We also compute the " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "-norm value of the standard deviation among the pruned models' logit outputs in the ensemble. The results are shown in Table 6. According to the three-sigma rule, we can see that the output difference be" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24621" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 134, + 72, + 246, + 177 + ], + "blocks": [ + { + "bbox": [ + 134, + 72, + 246, + 177 + ], + "lines": [ + { + "bbox": [ + 134, + 72, + 246, + 177 + ], + "spans": [ + { + "bbox": [ + 134, + 72, + 246, + 177 + ], + "type": "image", + "image_path": "ad2559f7e7b94a8fe8a3be833761b5386561a43284157b644ea11f714d0b442c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 190, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 547, + 213 + ], + "type": "text", + "content": "Figure 4. Targeted transfer attack success rates " + }, + { + "bbox": [ + 46, + 190, + 547, + 213 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 190, + 547, + 213 + ], + "type": "text", + "content": " of the base model (SASD ResNet-50), the longitudinal ensemble of pruned base models, and the WS version of the base model (SASD-WS ResNet-50)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 248, + 72, + 352, + 176 + ], + "blocks": [ + { + "bbox": [ + 248, + 72, + 352, + 176 + ], + "lines": [ + { + "bbox": [ + 248, + 72, + 352, + 176 + ], + "spans": [ + { + "bbox": [ + 248, + 72, + 352, + 176 + ], + "type": "image", + "image_path": "e35000de00261d8ae4ec091024ab3288f6b6c0e8fbd6712269fb69860fe4e648.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 354, + 72, + 459, + 176 + ], + "blocks": [ + { + "bbox": [ + 354, + 72, + 459, + 176 + ], + "lines": [ + { + "bbox": [ + 354, + 72, + 459, + 176 + ], + "spans": [ + { + "bbox": [ + 354, + 72, + 459, + 176 + ], + "type": "image", + "image_path": "14c8290d1bdec73c5bed48185bd717b9cc318a6d7f4ba5353d667852b781115f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 65, + 226, + 175, + 327 + ], + "blocks": [ + { + "bbox": [ + 65, + 226, + 175, + 327 + ], + "lines": [ + { + "bbox": [ + 65, + 226, + 175, + 327 + ], + "spans": [ + { + "bbox": [ + 65, + 226, + 175, + 327 + ], + "type": "image", + "image_path": "9f281f9513cc24918e41f59e3b9a7c33c87fa6a4aad602d0b229a7e252f01c2b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 335, + 546, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 546, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 546, + 357 + ], + "type": "text", + "content": "Figure 5. The change of the loss landscapes with the application of our method. The fine-tuned ResNet-50 is the auxiliary model adopted in our SASD method." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 184, + 226, + 294, + 326 + ], + "blocks": [ + { + "bbox": [ + 184, + 226, + 294, + 326 + ], + "lines": [ + { + "bbox": [ + 184, + 226, + 294, + 326 + ], + "spans": [ + { + "bbox": [ + 184, + 226, + 294, + 326 + ], + "type": "image", + "image_path": "dffdf088adb92789db15bbbcdb38ba1c1ce934398bcb1c551464c229fe2f0824.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 304, + 226, + 413, + 326 + ], + "blocks": [ + { + "bbox": [ + 304, + 226, + 413, + 326 + ], + "lines": [ + { + "bbox": [ + 304, + 226, + 413, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 226, + 413, + 326 + ], + "type": "image", + "image_path": "16efc18a6fdaabf5f517c36d12eb4b9fee2bd75e551a246814a8c610c50107ec.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 424, + 226, + 533, + 326 + ], + "blocks": [ + { + "bbox": [ + 424, + 226, + 533, + 326 + ], + "lines": [ + { + "bbox": [ + 424, + 226, + 533, + 326 + ], + "spans": [ + { + "bbox": [ + 424, + 226, + 533, + 326 + ], + "type": "image", + "image_path": "82022adcb754f5a2db7760015660c3028fe3a87a6f9322e27485bac925a931cd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 379, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 450 + ], + "type": "text", + "content": "tween the pruned models' ensemble and the corresponding WS model falls into the three-sigma range of the internal variability of the pruned models in the ensemble. Therefore, the output of the WS model is not an outlier among the pruned models' outputs, which implies that the output of the WS model is close to the ensemble model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "type": "text", + "content": "Moreover, we compare the targeted attack performance of a single weight-scaled SASD model and the ensemble of pruned SASD models. Specifically, we generate adversarial perturbations by employing a longitudinal ensemble of pruned SASD models with a pruning rate of " + }, + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "type": "inline_equation", + "content": "1 - p = 0.07" + }, + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "type": "text", + "content": ". Therefore, we set our WS method's scaling ratio " + }, + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "type": "inline_equation", + "content": "p = 0.93" + }, + { + "bbox": [ + 46, + 456, + 287, + 588 + ], + "type": "text", + "content": ". Figure 4 shows the targeted transfer attack success rates of three types of source models with SASD ResNet-50 as the base model. According to the attack performance, we can see that our WS method can reasonably approximate the ensemble of pruned models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Visualizing the effectiveness of SASD-WS. Our SASD-WS attempts to promote the source model's generalization capability to enable more transferable targeted adversarial attacks. To visualize the effectiveness of our SASD-WS on improving the source model's generalization capability, we depict the change of the loss landscapes by applying our method in Figure 5. We can see that with the application of our approach, the loss landscape of the resultant enhanced model becomes flatter, which can help to capture general features learned by different models [6, 16, 35]. Therefore," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "text", + "content": "the enhanced model is more likely to cover the transferable targeted adversarial examples in its low-loss region, facilitating more transferable targeted adversarial attacks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 434, + 378, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 378, + 446 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 378, + 446 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": "This work presents a novel model self-enhancement method, incorporating Sharpness-Aware Self-Distillation (SASD) and Weight Scaling (WS) to enhance the source model's capability to generate more transferable targeted perturbations. Extensive experiments show that our method can significantly outperform the state-of-the-art approaches. Notably, under the black-box setting, we can surpass the state-of-the-art baselines by a significant margin of " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "12.2\\%" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": " on average. We also validate the design of our method by several ablation studies and the practical applicability of the proposed method by attacking a popular real-world application. We believe that our approach can serve as a strong benchmark when evaluating the robustness of DNNs and an effective patch when conducting adversarial training." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 643, + 399, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 399, + 656 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 399, + 656 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "We thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 62206318)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24622" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Yang Deng, Weibin Wu, Jianping Zhang, and Zibin Zheng. 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The hierarchical structure of explanatory factors hidden in data is such a general representation and could be potentially achieved with a hierarchical VAE. However, training a hierarchical VAE always suffers from the \"posterior collapse\", where the data information is hard to propagate to the higher-level latent variables, hence resulting in a bad hierarchical representation. To address this issue, we first analyze the shortcomings of existing methods for mitigating the posterior collapse from an information theory perspective, then highlight the necessity of regularization for explicitly propagating data information to higher-level latent variables while maintaining the dependency between different levels. This naturally leads to formulating the inference of the hierarchical latent representation as a sequential decision process, which could benefit from applying reinforcement learning (RL). Aligning RL's objective with the regularization, we first introduce a skip-generative path to acquire a reward for evaluating the information content of an inferred latent representation, and then the developed $Q$ -value function based on it could have a consistent optimization direction of the regularization. Finally, policy gradient, one of the typical RL methods, is employed to train a hierarchical VAE without introducing a gradient estimator. Experimental results firmly support our analysis and demonstrate that our proposed method effectively mitigates the posterior collapse issue, learns an informative hierarchy, acquires explainable latent representations, and significantly outperforms other hierarchical VAE-based methods in downstream tasks.", + "bbox": [ + 75, + 353, + 473, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 811, + 209, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deriving meaningful representations of data with minimal supervision is a central challenge in machine learn", + "bbox": [ + 76, + 837, + 470, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f0a0c0dad670a851adee2a7c6dcad7b3dd709e897f20f156b6b1dec325c4e954.jpg", + "image_caption": [ + "Figure 1. Visualization of different levels' latent representations of hierarchical VAEs on FashinMNIST and CelebA [53] to demonstrate the learned hierarchical structure. HVAE fails to learn a 5-level hierarchy, where higher-level latent representations display posterior collapse, collapsing into the same modes of \"clothing\" and \"female faces\" regardless of the input. For IVAE, reconstructions of certain consecutive layers appear highly similar, suggesting a disrupted hierarchy. In contrast, our method preserves detailed information of inputs at low levels and captures increasingly abstract semantics at higher levels, mitigating posterior collapse and establishing an informative hierarchy." + ], + "image_footnote": [], + "bbox": [ + 500, + 324, + 705, + 486 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d0f2e8272e6f37b60b40f429d294b3fbbcb29ad590a5a5207fdb6f2cbb504e27.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 325, + 890, + 486 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing [5], while existing research has predominantly concentrated on the discriminative approach [10] that relies on meticulously crafted preprocessing pipelines like pretext tasks [22, 30, 62, 65, 95] and data augmentations [3, 59]. Methods such as contrastive learning [8, 9, 11, 12, 14-16, 27, 29, 32, 34, 36, 49, 87, 97, 98] exemplify the success of this discriminative approach. However, representations derived from these methods are only limited to tasks invariant to the preprocessing pipelines [24], e.g. representations learned with the random cropping data augmentation cannot be applied to pixel-level localization tasks [83, 84], limiting their broader applicability. To transcend these confines, Bengio et al. [5] advocate for the pursuit of a universal and fundamental understanding of the world-a \"general-purpose prior\"-enabling the direct learning of representations without prior knowledge or assumptions about downstream tasks. Such representations could be learned by generative ap", + "bbox": [ + 496, + 641, + 895, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution, authors listed alphabetically by last name.", + "bbox": [ + 93, + 875, + 426, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding to: Yewen Li .", + "bbox": [ + 98, + 887, + 401, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22946", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bfb37a6f44c78cc518baaabae97d79fc887101545bbd4663c1803d908c0d1b72.jpg", + "image_caption": [ + "Figure 2. Absolute Pearson's correlation between data representations of the inference network of a hierarchical VAE trained on FashionMNIST and another trained on MNIST [48], given the same data point from FashionMNIST. Our method enables the model to learn low-level information shared on different datasets and high-level semantic information in a hierarchical manner." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 467, + 126 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "proaches [47, 79], which utilize a deep generative model [21, 31, 40, 43, 68, 81] to capture the posterior distribution of the underlying explanatory factors in the observed data, i.e., the general-purpose prior, such as the hierarchical structure [76, 85, 86], disentanglement [38], and temporal and spatial coherence [71]. In this work, we focus on one specific aspect of this general-purpose prior, the hierarchical structure of data, which could be potentially achieved by learning a hierarchy of multi-level abstract latent representations with a hierarchical VAE [5, 79].", + "bbox": [ + 75, + 222, + 470, + 375 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, actualizing a meaningful hierarchical structure with a hierarchical VAE faces a considerable issue named \"posterior collapse\" [51, 57, 76], where the data information fails to be propagated to higher-level latent variables. Specifically, their posterior distribution $q_{\\phi}(z|x)$ would be equal to an uninformative prior distribution $p(z)$ [13, 51, 82], undermining hierarchical VAEs' capability to capture meaningful representations. Existing literature proposing mitigation approaches for posterior collapse mainly focuses on two aspects: the limited capacity of the model architecture [19, 20, 57, 67, 76, 80] and the improper training objective [20, 41, 51, 70, 88]. However, our theoretical analysis from the perspective of information theory [18] presented in Section 3.1 suggests that current methodologies focusing on model architectures fail to explicitly enforce regularization on the inference of higher-level latent variables, where posterior collapse may still occur; and approaches targeting training objectives might disrupt the hierarchical dependencies between latent variables, compromising the model's structural integrity. Experimental results for better understanding can be seen in Figs. 1 and 2. These limitations contribute to the significant lag in the quality and performance of learned representation using hierarchical VAEs and have resulted in their limited adoption in representation learning tasks recently [47, 79].", + "bbox": [ + 75, + 380, + 472, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the issue of posterior collapse that hinders acquiring an informative hierarchical latent representation, where different levels' latent representations are inferred sequentially from inputs and high-level latent representations are reliant on the abstraction of low-level ones, it is imperative to consider not only the information content of an inferred single-level latent variable but also its impact on subsequent, higher-level latent variables. This naturally inspires us to formulate the inference of the hierarchical latent", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "representation as a sequential decision process. Inspired by the huge success of reinforcement learning (RL) in learning a high-quality sequence, we tried to apply RL to the learning of a hierarchical VAE for a better hierarchical latent representation. Please note that although some methods have also successfully introduced RL into tasks related to generative models [6, 50, 94], none of these methods can be directly applied to train a hierarchical VAE with a focus on learning informative hierarchical latent presentations. A detailed discussion can be found in Appendix A.3.", + "bbox": [ + 496, + 90, + 893, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, the contribution of this work could be summarized as follows:", + "bbox": [ + 496, + 242, + 893, + 272 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We highlight limitations of existing approaches of addressing posterior collapse for an informative hierarchical latent representation from an information theory perspective and appeal for more effective regularization of the inference process to explicitly propagate data information to higher-level latent variables and maintain the dependency between different levels. To our knowledge, this work is the first to conceptualize the hierarchical VAE's inference as a sequential decision process and employ an RL approach, specifically policy gradient, to regularize this process. Our method is broadly applicable to both primary types of hierarchical VAEs: top-down and bottom-up structures;", + "- Technically, we set up an RL formulation tailored to hierarchical VAEs training, notably with a skip-generative path that skips its lower levels' latent variables by marginalization to acquire a reward assessing the information content of the inferred latent variables without introducing additional networks or modules; then, the Q-value function developed based on it could have a consistent optimization direction of the regularization;", + "- Experiments demonstrate the mitigation of the posterior collapse, learned informative hierarchy, explanation ability of latent representations, and superior performance in VAE-based representation learning tasks." + ], + "bbox": [ + 500, + 273, + 893, + 637 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 652, + 637, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Hierarchical Variational Autoencoder", + "text_level": 1, + "bbox": [ + 500, + 679, + 823, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An $L$ -layer hierarchical VAE is an extension of the vanilla VAE [43, 68], where the generative process is extended to multi-step generation, formulated as $p_{\\theta}(\\boldsymbol{x}, \\boldsymbol{z}_{1:L}) = p_{\\theta}(\\boldsymbol{x} | \\boldsymbol{z}_1) p_{\\theta}(\\boldsymbol{z}_L) \\prod_{l=1}^{L-1} p_{\\theta}(\\boldsymbol{z}_l | \\boldsymbol{z}_{l+1})$ . The $p_{\\theta}(\\boldsymbol{z}_L)$ is typically modeled as a multivariate Gaussian distribution $\\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ and $\\theta$ represents the parameters of the decoder. The inference process of hierarchical VAEs could be implemented in two main approaches, bottom-up (BU) and top-down (TD):", + "bbox": [ + 496, + 703, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {B U}: q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) = q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x}) \\prod_ {l = 2} ^ {L} q _ {\\phi} (\\boldsymbol {z} _ {l} | \\boldsymbol {z} _ {l - 1}, \\boldsymbol {x}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 825, + 890, + 847 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {T D}: q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) = q _ {\\phi} (\\boldsymbol {z} _ {L} | \\boldsymbol {x}) \\prod_ {l = L} ^ {2} q _ {\\phi} (\\boldsymbol {z} _ {l - 1} | \\boldsymbol {z} _ {l}, \\boldsymbol {x}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 849, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\phi$ represents the parameters of the encoder. We provide a demonstration of these processes in Fig. 3. As", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22947", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f67f695941115d423416945506a76c7863b94226535c9aa428582eb4fe8b9100.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 116, + 140, + 230, + 200 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/efac10a82d11aa145427c8c7166ae6374dee01de8fa928c5ecf054e6beec0491.jpg", + "image_caption": [ + "(a) VAE", + "(c) Bottom-up (BU) inference", + "Figure 3. Probabilistic graphical illustration of VAE and hierarchical VAE during inference and generation. Solid lines $(\\rightarrow)$ denote inference while dashed lines $(\\dashrightarrow)$ denote generation." + ], + "image_footnote": [], + "bbox": [ + 112, + 248, + 207, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dad2c9bb4e7a40ab12dfce5edf5341a84fcd3c297eb78dbdd89148b42b93ef6d.jpg", + "image_caption": [ + "(b) Generation" + ], + "image_footnote": [], + "bbox": [ + 339, + 90, + 436, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ec581b4a559da48fb84cc4fd6d08b40caaea7b10c995e206fd7a1fd5b5ed799e.jpg", + "image_caption": [ + "(d) Top-down (TD) inference" + ], + "image_footnote": [], + "bbox": [ + 297, + 248, + 439, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the inference process is to produce a sequence of latent variables step by step, we denote a hierarchy $\\mathbf{z}^{1:T} = \\{ \\mathbf{z}^1, \\dots, \\mathbf{z}^t, \\dots, \\mathbf{z}^T \\}$ , where $T = L$ . In BU inference scheme, $\\mathbf{z}^{1:T} = \\{ \\mathbf{z}_1, \\dots, \\mathbf{z}_t, \\dots, \\mathbf{z}_L \\}$ ; in TD inference scheme, $\\mathbf{z}^{1:T} = \\{ \\mathbf{z}_L, \\dots, \\mathbf{z}_t, \\dots, \\mathbf{z}_1 \\}$ . For brevity, we use $\\mathbf{z}$ to represent $\\mathbf{z}^{1:T}$ in the following parts. Additionally, we introduce $j$ for representing the lower level variable $\\mathbf{z}_j$ w.r.t. $\\mathbf{z}^t$ defined by", + "bbox": [ + 76, + 462, + 470, + 568 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nj = \\left\\{ \\begin{array}{l l} t - 1, & \\text {i n B U h i e r a c h i c a l V A E ,} \\\\ T - t, & \\text {i n T D h i e r a c h i c a l V A E .} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 580, + 468, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The training objective of a hierarchical VAE is to maximize the variational evidence lower bound (ELBO), denoted as $\\mathcal{L}_{\\pmb{x}}$ , of the training data's marginal log-likelihood $\\log p(\\pmb{x})$ by jointly updating the parameters $\\theta$ and $\\phi$ , expressed as:", + "bbox": [ + 75, + 622, + 468, + 683 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\boldsymbol {x}} = \\log p (\\boldsymbol {x}) - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) \\| p _ {\\theta} (\\mathbf {z} | \\boldsymbol {x}) \\right] \\tag {4} \\\\ = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log p _ {\\theta} (\\mathbf {x} | \\mathbf {z}) \\right] - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p (\\mathbf {z}) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 685, + 468, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $D_{\\mathrm{KL}}(\\cdot ||\\cdot)$ refers to the Kullback-Leibler (KL) divergence. Defining $q_{\\phi}(z_1|z_0,x)\\coloneqq q_{\\phi}(z_1|x)$ and $p_{\\theta}(z_L|z_{L + 1})\\coloneqq p_{\\theta}(z_L)$ , for BU and TD hierarchical VAEs, the respective detailed expressions of their ELBOs are:", + "bbox": [ + 75, + 722, + 468, + 781 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathrm {B U}: \\mathcal {L} _ {\\boldsymbol {x}} = \\mathbb {E} _ {q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] \\tag {5} \\\\ - \\sum_ {l = 1} ^ {L} D _ {\\mathrm {K L}} \\left[ \\left(q _ {\\phi} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l - 1}, \\boldsymbol {x}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}\\right)\\right) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 784, + 468, + 825 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathrm {T D}: \\mathcal {L} _ {\\boldsymbol {x}} = \\mathbb {E} _ {q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] \\tag {6} \\\\ - \\sum_ {l = 1} ^ {L} D _ {\\mathrm {K L}} \\left[ \\left(q _ {\\phi} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}, \\boldsymbol {x}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}\\right)\\right) \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 828, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After convergence, we could extract level $l$ 's latent representation by the maximum a posteriori (MAP) estimate", + "bbox": [ + 75, + 869, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion of the learned latent variables $\\mathbf{z}_l$ , defined as $\\mathbf{z}_l^* = \\arg \\max_{\\mathbf{z}_l} q_{\\phi}(\\mathbf{z}_l | \\mathbf{x})$ [5, 43].", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, training hierarchical VAEs often suffers from the issue known as posterior collapse, which can be formally defined as follows.", + "bbox": [ + 498, + 121, + 890, + 165 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1 (posterior collapse [7, 13, 82, 88]). Given a hierarchical VAE $p(\\pmb{x}, \\pmb{z}; \\theta, \\phi)$ , paramters' value $\\phi = \\hat{\\phi}$ , $\\theta = \\hat{\\theta}$ , and for any data $\\pmb{x}$ in a dataset $\\mathcal{D}_{\\pmb{x}} = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_N\\}$ , the posterior of inference step $t$ 's latent variable $\\pmb{z}^t$ collapses if", + "bbox": [ + 498, + 175, + 893, + 237 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} ^ {t - 1}, \\boldsymbol {x}; \\hat {\\phi}\\right) = p _ {\\theta} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} _ {j + 2}; \\hat {\\theta}\\right), \\forall \\boldsymbol {x} \\in \\mathcal {D} _ {\\boldsymbol {x}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 252, + 890, + 270 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The posterior collapse issue mainly occurs in higher-level latent variables of hierarchical VAEs. Stochastic latent variables $\\mathbf{z}$ can be manually divided into lower-level variables, $z_{< k} = \\{z_1,\\dots,z_{k - 1}\\}$ and higher-level ones, $z_{\\geq k} = \\{z_k,\\dots,z_L\\}$ where $k\\in \\{2,\\ldots ,L\\}$ . Though $z_{< k}$ may not suffer from posterior collapse that could encode sufficient information to reconstruct the inputs well, the corresponding high-level stochastic latent variables $\\mathbf{z}_{\\geq k}$ could be inclined to collapse into priors, i.e., $q_{\\phi}(z_{\\geq k}|\\boldsymbol {x})\\approx p_{\\theta}(z_{\\geq k})$ . An illustration can be seen in Fig. 1. Consequently, these higher-level posteriors will hold limited relevance to its input $\\boldsymbol{x}$ , resulting in non-informative representations.", + "bbox": [ + 498, + 277, + 893, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Reinforcement Learning", + "text_level": 1, + "bbox": [ + 500, + 479, + 723, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider a standard RL setup in continuous action space and discrete timesteps, formalized as a Markov decision process (MDP) defined by a tuple $\\langle S, \\mathcal{A}, P, r \\rangle$ [33, 52, 72, 94]. Here, the state space $S$ and action space $\\mathcal{A}$ are continuous, the state transition probability function $P: S \\times \\mathcal{A} \\to \\Delta(S)$ represents the probability density of the next state $s_{t+1} \\in S$ given the current state $s_t \\in S$ and action $a_t \\in \\mathcal{A}$ , and $r: S \\times \\mathcal{A} \\to \\mathbb{R}$ denotes the reward function on each transition.", + "bbox": [ + 496, + 502, + 893, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At each time step $t \\in \\{1, 2, \\dots, T\\}$ , an agent observes a state $s_t \\in S$ , takes an action $a_t \\in \\mathcal{A}$ , and receives a scalar reward $r_t: S \\times \\mathcal{A} \\to \\mathbb{R}$ . The state $s_t$ could be described in various ways, such as the entire history of the observations $s_t = (o_1, \\dots, o_t)$ [94] or only the current observation $s_t = o_t$ [33]. An agent's behavior could be defined by a policy $\\pi(a_t | s_t)$ , which maps states to a probability distribution over actions. The return at time step $t$ is defined as the sum of the discounted future reward $R_t = \\sum_{i=t}^{T} \\gamma^{(i-t)} r(s_i, a_i)$ with a discount factor $\\gamma \\in (0, 1)$ . The expectation of the return could be flexibly formulated by the Q-value function $Q^\\pi(s_t, a_t)$ after taking an action $a_t$ in state $s_t$ and thereafter following policy $\\pi$ :", + "bbox": [ + 496, + 625, + 890, + 819 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {s _ {i > t} \\sim P, a _ {i > t} \\sim \\pi} \\left[ R _ {t} \\mid s _ {t}, a _ {t} \\right] \\tag {8} \\\\ = r \\left(s _ {t}, a _ {t}\\right) + \\gamma \\mathbb {E} _ {s _ {t + 1} \\sim P, a _ {t} \\sim \\pi} \\left[ Q ^ {\\pi} \\left(s _ {t + 1}, a _ {t + 1}\\right) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 821, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which not only considers the reward of the action to be taken on the current state but also its effect on the future decision process. Let us assume that drawing from $a_{t} \\sim \\pi (a_{t}|s_{t})$ can", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22948", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "be realized with reparameterization as $a_{t} = f(s_{t},\\epsilon_{t}),\\epsilon_{t}\\sim p(\\epsilon)$ . We could directly apply the policy gradient method [52, 78, 94] on the model parameters $\\Theta$ with gradient ascent to maximize the $Q^{\\pi}(s_t,a_t)$ at a time step $t$ :", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta \\leftarrow \\Theta + \\nabla_ {\\Theta} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 152, + 468, + 169 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We sum all time step $t$ 's policy gradient together to represent the optimization direction $\\nabla_{\\Theta}\\mathcal{I}$ of the RL, expressed as", + "bbox": [ + 76, + 172, + 468, + 200 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\Theta} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {s _ {t} \\sim P, \\epsilon_ {t} \\sim p (\\epsilon)} \\nabla_ {\\Theta} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right), a _ {t} = f \\left(s _ {t}, \\epsilon_ {t}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 203, + 468, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the discussion on Related Works, we move it to Appendix A.", + "bbox": [ + 76, + 242, + 468, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Improving Unsupervised Hierarchical Representation with RL", + "text_level": 1, + "bbox": [ + 76, + 292, + 419, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first provide an analysis of the existing two major approaches mitigating posterior collapse for learning a hierarchical representation with a hierarchical VAE. However, we found that they either lack regularization for propagating data information to higher-level latent variables or break the dependency between different levels' latent variables. Therefore, to address these drawbacks, a better training objective from the perspective of information theory could naturally lead to an RL scheme with a proper design of the Q-value function as the regularization of latent representations. Finally, we develop an RL training scheme with the policy gradient method to train a hierarchical VAE.", + "bbox": [ + 75, + 339, + 472, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Analysis of Representation Learning with Hierarchical VAEs", + "text_level": 1, + "bbox": [ + 76, + 531, + 431, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The aim of representation learning with a hierarchical VAE is to learn a hierarchy of latent variables $\\mathbf{z}$ that could represent the input data $\\mathbf{x}$ . We begin with rethinking how different approaches are affecting the representation learning with a hierarchical VAE. We first rewrite the ELBO from an information theory standpoint [18]:", + "bbox": [ + 75, + 571, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} [ \\operatorname {E L B O} (\\boldsymbol {x}) ] \\\\ = \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} \\left[ \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} \\left[ D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x}) \\| p (\\boldsymbol {z})\\right) \\right] \\\\ = \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) - \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) - D _ {\\mathrm {K L}} (q (\\boldsymbol {z}) \\| p (\\boldsymbol {z})) - \\mathcal {H} _ {p} (\\boldsymbol {x}), \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 664, + 491, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the mutual information between $x$ and $z$ under different distribution is defined by", + "bbox": [ + 75, + 729, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) = \\mathbb {E} _ {p (\\boldsymbol {x}) q _ {\\phi} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right)} \\left[ \\log \\frac {p (\\boldsymbol {x} , \\boldsymbol {z} _ {1})}{p (\\boldsymbol {x}) q \\left(\\boldsymbol {z} _ {1}\\right)} \\right] \\tag {12} \\\\ = \\mathbb {E} _ {p (\\boldsymbol {x}) q _ {\\phi} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right)} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {p (\\boldsymbol {x})} \\left[ \\log p (\\boldsymbol {x}) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 762, + 485, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) = \\mathbb {E} _ {q (\\boldsymbol {x}) q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x})} \\left[ \\log \\frac {q (\\boldsymbol {x} , \\boldsymbol {z} _ {1})}{q (\\boldsymbol {x}) q (\\boldsymbol {z} _ {1})} \\right] \\tag {13} \\\\ = \\mathbb {E} _ {q (\\boldsymbol {x}) q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x})} \\left[ \\log q _ {\\phi} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {q (\\boldsymbol {x})} \\left[ \\log q (\\boldsymbol {x}) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 816, + 485, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q(x)$ is the training data's distribution and it is assumed to be equal to the true data distribution $p(\\pmb{x})$ ;", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$p_{\\theta}(\\pmb {x}|z_1)$ and $q_{\\phi}(\\pmb {x}|z_{1})$ could be expressed by", + "bbox": [ + 500, + 90, + 807, + 107 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) = \\frac {p _ {\\theta} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right) p (\\boldsymbol {x})}{q \\left(\\boldsymbol {z} _ {1}\\right)} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 108, + 890, + 141 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {\\phi} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) = \\frac {q _ {\\phi} (\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}) q (\\boldsymbol {x})}{q (\\boldsymbol {z} _ {1})} \\simeq \\frac {q _ {\\phi} (\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}) p (\\boldsymbol {x})}{q (\\boldsymbol {z} _ {1})}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 143, + 890, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, the target of the ELBO in Eq. 11 effectively becomes minimizing the gap between the bottom-most latent variable's posterior $q_{\\phi}(\\pmb{z}_1|\\pmb{x})$ and its corresponding true posterior $p_{\\theta}(\\pmb{z}_1|\\pmb{x})$ and meanwhile the posterior of higher-level latent variables $\\{\\pmb{z}_l\\}_{l=1:L}$ are trained to be close to their respective priors by the $D_{\\mathrm{KL}}[q(\\mathbf{z})\\| p(\\mathbf{z})]$ term.", + "bbox": [ + 500, + 176, + 893, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the latent variables above $z_{1}$ do not receive direct regularization to maximize $\\mathcal{I}(x, z_{l}), l > 1$ , it could potentially lead to the posterior collapse phenomenon. Therefore, approaches that only modify the model structure [25, 57, 76, 80] still do not impose additional regularization to higher-level latent variables in the training objective, where the posterior collapse could still occur.", + "bbox": [ + 496, + 271, + 893, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing regularization strategies in the literature aim to refine the posterior distribution in order to cultivate good representations [41, 51, 54]. These methods typically focus on the relationship between observed data $\\mathbf{x}$ and a single-level latent variable $z^t$ , which could be interpreted as an additional regularization on the ELBO expressed as", + "bbox": [ + 496, + 383, + 893, + 473 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z}) \\simeq \\sum_ {t = 1} ^ {T} \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {t}). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 474, + 890, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, by optimizing all latent variables $\\{z^t\\}_{t = 1:T}$ with a shared objective $\\mathcal{I}(\\pmb {x},\\pmb{z}^t)$ simultaneously, these approaches may hurt the hierarchical dependency amongst them. This is due to the implicit incentive for all latent variables to assimilate, potentially undermining the hierarchical structure. Learning to generate a sequence $\\{\\pmb {x},\\pmb {z}^1,\\dots,\\pmb {z}^T\\}$ with only one loss after finishing generating the whole sequence could also bring the imbalance issue, where the concentration of optimization to the mediate items is not clear [94]. These limitations hinder the exploitation of the full capabilities inherent in hierarchical VAEs.", + "bbox": [ + 496, + 496, + 892, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We leave a detailed discussion for the above two approaches in Appendix B.", + "bbox": [ + 500, + 667, + 893, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In summary, an effective training scheme should maximize the information content hidden in latent variables of all layers, while maintaining the dependencies among latent variables. Specifically, the regularization on $z^t$ should account for not only $\\mathcal{I}(\\pmb{x},\\pmb{z}^t)$ , but also the influence on the subsequent latent variables $\\mathcal{I}(\\pmb{x},\\pmb{z}^i|\\pmb{z}^{i - 1})$ , $i > t$ , i.e.,", + "bbox": [ + 496, + 703, + 893, + 794 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t: T}\\right) = \\sum_ {i = t} ^ {T} \\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 795, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By incorporating a discount factor $\\gamma \\in (0,1)$ , which allocates greater weight to the mutual information with proximal latent variables, the regularization for $z^t$ becomes:", + "bbox": [ + 496, + 816, + 890, + 862 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right) = \\sum_ {i = t} ^ {T} \\gamma^ {i - t} \\mathcal {I} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 863, + 890, + 885 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, the optimization direction of learning the se", + "bbox": [ + 500, + 886, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22949", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/987ce437da5c751f31358593159a817e7b4ca1bdc94cb0bb4adf3a287605433e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 104, + 500, + 220 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{r (s _ {t} , a _ {t}) = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} (z ^ {1 : t} | x)} \\log p _ {\\theta} (x | z ^ {t}) - D _ {\\mathrm {K L}} [ q _ {\\phi} (z ^ {1 : t} | x) | | p (z ^ {1 : t}) ]}}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 238, + 462, + 258 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a6a31bb3fcf94a98fa8a5a06d37714ead8fd78c5660cfcb79800373c70ffa8e0.jpg", + "image_caption": [ + "Figure 4. Illustration of modeling the inference process of a hierarchical VAE as a sequential decision process (left) and the details of the elements of RL $s_t$ , $a_t$ , $s_{t+1}$ (right). A reward $r(s_t, a_t)$ is derived with the skip-generative path depicted in the gray box." + ], + "image_footnote": [], + "bbox": [ + 611, + 87, + 846, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "quence $\\{\\pmb {x},\\pmb {z}^1,\\dots,\\pmb {z}^T\\}$ can then be expressed by", + "bbox": [ + 75, + 306, + 398, + 323 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\phi , \\theta} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {p (\\boldsymbol {x}), q _ {\\phi}, p _ {\\theta}} \\nabla_ {\\phi , \\theta} \\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right). \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 323, + 468, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The resemblance of the optimization direction to Eq. 10 naturally leads to formulating the learning of hierarchical VAE as a sequential decision process, prompting the application of RL methods. Particularly, we are driven to develop a proper Q-value function $Q(s_{t},a_{t})$ to play the role of the regularization $\\mathcal{L}_{\\mathcal{I}}(\\boldsymbol {x},\\boldsymbol{z}^t)$ to achieve a consistent expression of the two optimization objectives.", + "bbox": [ + 75, + 345, + 472, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Training Hierarchical VAEs with RL", + "text_level": 1, + "bbox": [ + 76, + 462, + 395, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by the tremendous success of RL methods in stably propagating information along long Markov Decision chains that maximize the cumulative rewards tallied at every step, i.e., the Q-value $Q^{\\pi}(s_t,a_t)$ in Eq. 8, we formulate the progressive inference process of an $L$ -layer hierarchical VAEs as an $L$ -step sequential decision process. Specifically, given an input $\\pmb{x}$ from a training set $\\mathcal{D}_{\\pmb{x}}$ , we need a hierarchical VAE parameterized with $\\{\\theta ,\\phi \\}$ to produce a sequence $Y_{1:T} = \\{\\pmb {x},\\pmb {z}^{1},\\pmb {z}^{2},\\dots,\\pmb{z}^{T}\\} ,T = L$", + "bbox": [ + 75, + 486, + 470, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Now, we can set up the basic elements for training with RL. At each time step $t$ , the state $s_t$ is characterized as a tuple including the observed input and already produced latent variables $z^{1:t-1} = \\{z^1, \\dots, z^{t-1}\\}$ up to the step:", + "bbox": [ + 75, + 623, + 468, + 684 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {t} \\triangleq \\left\\{\\boldsymbol {x}, \\boldsymbol {z} ^ {1: t - 1} \\right\\}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 684, + 468, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s_1 = \\{x\\}$ . After receiving a state $s_t$ , the encoder $q_{\\phi}(\\mathbf{z}|x)$ of the hierarchical model acts as the policy network $\\pi (a_t|s_t)$ to produce the latent variable as an action:", + "bbox": [ + 75, + 703, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {\\phi} \\left(a _ {t} \\mid s _ {t}\\right) \\triangleq q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {x}, \\boldsymbol {z} ^ {1: t - 1}\\right) = q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} ^ {t - 1}, \\boldsymbol {x}\\right), \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 750, + 468, + 767 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\na _ {t} \\triangleq z ^ {t} \\sim q _ {\\phi} \\left(z ^ {t} \\mid z ^ {t - 1}, x\\right). \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 770, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once executing the $a_{t}$ , we will get to the next state according the state transition probability function $P$ , specified as", + "bbox": [ + 75, + 790, + 468, + 820 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(s _ {t + 1} \\mid s _ {t}, a _ {t}\\right) \\triangleq \\left(\\delta_ {\\boldsymbol {x}}, \\delta_ {\\boldsymbol {z} ^ {1: t}}\\right), \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 821, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which is deterministic and reflects the unchanged observed data $\\pmb{x}$ and the inclusion of new inferred latent variables at the successor state. $\\delta_v$ is a Dirac delta distribution that only manifests a non-zero impulse at $v$ .", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reward function design. When getting such a transition $\\{s_t, a_t, s_{t+1}\\}$ , we need to design a reward function $r(s_t, a_t)$ . The principle of the design is to evaluate the information content $\\mathcal{I}(\\boldsymbol{x}, \\boldsymbol{z}^t | \\boldsymbol{z}^{t-1})$ hidden in the latent variable $\\boldsymbol{z}^t$ that represents the inputs, then we could formulate the Q-value function to regularize $\\boldsymbol{z}^t$ by $\\sum_{i=t}^{T} \\mathcal{I}(\\boldsymbol{x}, \\boldsymbol{z}^i | \\boldsymbol{z}^{i-1})$ . We design a reward function $r(s_t, a_t)$ to evaluate the information between $\\boldsymbol{x}$ and $\\boldsymbol{z}^t$ as below:", + "bbox": [ + 498, + 306, + 893, + 421 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} \\left(\\mathbf {z} ^ {1: t} \\mid \\mathbf {x}\\right)} \\log p _ {\\theta} (\\mathbf {x} \\mid \\mathbf {z} ^ {t}) - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} \\left(\\mathbf {z} ^ {1: t} \\mid \\mathbf {x}\\right) \\| p \\left(\\mathbf {z} ^ {1: t}\\right) \\right], \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 428, + 901, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_{\\theta}(\\boldsymbol{x}|\\boldsymbol{z}^t)$ is a skip-generative path, expressed as", + "bbox": [ + 501, + 470, + 866, + 486 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} ^ {t}) = \\int_ {\\boldsymbol {z} _ {1: j}} p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\prod_ {i = j} ^ {1} p _ {\\theta} (\\boldsymbol {z} _ {i} | \\boldsymbol {z} _ {i + 1}), \\boldsymbol {z} ^ {t} \\sim q (\\boldsymbol {z} ^ {t} | \\boldsymbol {z} ^ {< t}, \\boldsymbol {x}),\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 492, + 890, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $z_{1:j}$ are marginalized out by the integral. Kindly note that the skip-generative path $p_{\\theta}(\\pmb{x}|\\pmb{z}^t)$ is different from the generative path in vanilla hierarchical VAEs, where $p_{\\theta}(\\pmb{x}|\\pmb{z}^{1:t}) = p_{\\theta}(\\pmb{x}|\\pmb{z}_1)$ after observing $z^{1:t}$ . The $r(s_t,a_t)$ based on the skip-generative path could empirically force the training on maximizing the mutual information between $\\pmb{x}$ and $z^t$ after observing $z^{t-1}$ , expressed by", + "bbox": [ + 498, + 527, + 890, + 626 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {p (\\boldsymbol {x})} \\left[ r \\left(s _ {t}, a _ {t}\\right) \\right] \\tag {25} \\\\ = \\mathbb {E} _ {p (\\boldsymbol {x}) q (\\boldsymbol {z} ^ {1: t} | \\boldsymbol {x})} \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} ^ {t}) - \\mathbb {E} _ {p (\\boldsymbol {x})} D _ {\\mathrm {K L}} \\left[ q _ {\\phi} \\left(\\boldsymbol {z} ^ {1: t} | \\boldsymbol {x}\\right) \\| p (\\boldsymbol {z} ^ {1: t}) \\right] \\\\ = \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {t}) - \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {1}) - D _ {\\mathrm {K L}} [ q (\\boldsymbol {z} ^ {1: t}) | | p (\\boldsymbol {z} ^ {1: t}) ] - \\mathcal {H} _ {p} (\\boldsymbol {x}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 632, + 890, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, as shown in Eq. 25, the reward function $r(s_{t},a_{t})$ is to evaluate how $\\mathcal{I}(\\pmb {x},\\pmb{z}^t)$ is closer or larger than $\\mathcal{I}(\\pmb {x},\\pmb{z}^{1})$ Thus, the reward function could be an approximate evaluation of $\\mathcal{I}_q(\\pmb {x},\\pmb {z}^t |\\pmb {z}^{t - 1})$ after observing the inferred $\\pmb{z}^{t - 1}$ , i.e., $r(s_{t},a_{t})\\simeq \\mathcal{I}_{q}(\\pmb {x},\\pmb{z}^{t}|\\pmb{z}^{t - 1})$", + "bbox": [ + 498, + 696, + 893, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Q-value function. To explicitly add regularization on a current inferred latent variable $z^{t}$ ,s influence on its following latent variables $z^{>t}$ , we propose to maximize its corresponding Q-value, which considers not only its own reward $r(s_{t},a_{t})$ , but also the future accumulative rewards, i.e.,", + "bbox": [ + 498, + 779, + 893, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = r \\left(s _ {t}, a _ {t}\\right) + \\gamma \\mathbb {E} _ {\\pi} \\left[ Q ^ {\\pi} \\left(s _ {t + 1}, a _ {t + 1}\\right) \\right] \\\\ = r \\left(s _ {t}, a _ {t}\\right) + \\mathbb {E} _ {\\pi} \\left[ \\sum_ {i = t + 1} ^ {T} \\gamma^ {i - t} r \\left(s _ {i}, a _ {i}\\right) \\right]. \\tag {26} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 856, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22950", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the efficient reparameterization trick [43], we could do a single-sample based Monte Carlos (MC) estimation for the expectation of the Q-value function, i.e., $Q^{\\pi}(s_t,a_t)\\simeq \\sum_{i = t}^{T}\\gamma^{i - t}r(s_i,a_i)$ . Please note that the reward function is differentiable to the model's parameters, hence we could directly use gradient descent method [42, 69] to maximize the $Q_{\\pi}(s_t,a_t)$ , where $\\theta$ and $\\phi$ are trained simultaneously.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Therefore, at every time step $t$ , maximizing its corresponding Q-value function is approximately maximizing the mutual information between $x$ and $z^t$ and the influence of the inferred $z^t$ in the following latent variables $z^{t+1:T}$ that depends on it, expressed as:", + "bbox": [ + 75, + 198, + 470, + 273 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nQ ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) \\simeq \\sum_ {i = t} ^ {T} \\gamma^ {i - t} \\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right) = \\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right), \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 273, + 468, + 295 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which is consistent with the expression of Eq. 18 and the analysis in Section 3.1.", + "bbox": [ + 75, + 295, + 468, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, to learn a high-quality sequence $\\{\\pmb{x},\\pmb{z}^1,\\dots,\\pmb{z}^T\\}$ aligning with the optimization direction in Eq. 19, we define the optimization direction on the Q-value function:", + "bbox": [ + 75, + 325, + 468, + 371 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\theta , \\phi} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {s _ {i} \\sim P, a _ {i} \\sim \\pi} \\nabla_ {\\theta , \\phi} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right). \\tag {28}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 372, + 468, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As $a_{t}$ could be obtained by reparameterization and $Q^{\\pi}(s_t, a_t)$ is differentiable to model parameters, we could implement the policy gradient by directly maximizing $Q^{\\pi}(s_t, a_t)$ at every time step $t$ by Eq. 9, thereby eliminating the need for a gradient estimator like REINFORCE [89] and avoiding the high variance associated with these estimators [77]. We summarize the overall training scheme in Algorithm 1.", + "bbox": [ + 75, + 393, + 470, + 515 + ], + "page_idx": 5 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Optimizing a hierarchical VAE with RL." + ], + "code_body": "Input: A training dataset $\\mathcal{D}_{\\pmb{x}}$ training hyperparameters; \nOutput: An $L$ -layer hierarchical VAE parameterized with an encoder $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ and a decoder $p_{\\theta}(\\pmb {x}|\\mathbf{z})$ \nInitialization: Randomly initialize the parameters $\\theta ,\\phi$ \nfor epoch $= 1$ to max_epochs do Sample a batch of $N$ training samples $\\pmb{x}^n$ from $\\mathcal{D}_x$ . for time step $t = 1$ to $L$ do for $i = t$ to $L$ do Follow Eq.22, but with reparameterization, to sample an action $a_i^n\\sim \\pi (a_i^n |s_i^n)$ Get reward $r(s_i^n,a_i^n)$ by Eq.24; end for Get $Q^{\\pi}(s_t^n,a_t^n)\\simeq \\sum_{i = t}^{T}\\gamma^{i - t}r(s_i^n,a_i^n)$ Update $\\theta ,\\phi$ using the policy gradient for the current time step $t$ by Eq.9; end for \nend for", + "bbox": [ + 91, + 542, + 468, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 814, + 209, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our experiments engage in comparisons with several hierarchical VAE variants and various unsupervised methods to assess if our method of training hierarchical VAEs with RL yields superior performance in 1) mitigating posterior", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "collapse at higher latent representations, 2) learning a clear hierarchical representation, 3) attaining an explainable latent representation, and more importantly, 4) offering better representation than other hierarchical VAE-based unsupervised learning methods on downstream tasks. Additionally, we present several ablation studies to further evaluate different settings' influence on our method's performance.", + "bbox": [ + 496, + 90, + 893, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 498, + 207, + 689, + 223 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: Our method is benchmarked on 5 datasets: FashionMNIST [91], CIFAR10 and CIFAR100 [44], TinyImageNet [46], and STL-10 [17]. Each method is trained using standard train splits and assessed on corresponding test splits.", + "bbox": [ + 496, + 229, + 893, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics: For representation evaluation, we follow the commonly adopted downstream linear classification [5, 39, 63], using a linear support vector machine (SVM) [37] classifier on representations from frozen models. Classification accuracy is reported to measure linear separability, acting as a proxy for mutual information of representations with the labels. Additionally, we apply the MINE statistics network [4] to estimate the mutual information $\\widetilde{\\mathcal{I}}(x, z_L)$ , between input $x$ and the top latent variable $z_L$ .", + "bbox": [ + 496, + 306, + 893, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines: We compare our method with two groups of baselines: i) those modifying the inference process without changing the training objective (ELBO); ii) those modifying the training objective to add more regularization on the inference process. For i, we include a BU hierarchical VAE (HVAE) powered with residual connections [35], a TD hierarchical VAE (LVAE) with a ladder inference [76], and a more sophisticated bidirectional structure hierarchical VAE (BIVA) [57]. For ii, to our best knowledge, the most relevant work to our method is informative hierarchical VAE (IVAE) [51], which introduces additional layer-wise regularization on latent representations of a hierarchical VAE. Additionally, we include a vanilla VAE (VAE) [43] and an adversarial autoencoder (AAE) [58] of single-level to assess the performance improvement brought by hierarchical structures.", + "bbox": [ + 496, + 460, + 895, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details: We apply our RL optimization approach to hierarchical VAEs with BU $(\\mathbf{HVAE} + \\mathbf{RL})$ and TD (LVAE+RL) inference schemes. For Fashion-MNIST, hierarchical models use latent dimensions of $\\{128, 64, 32, 16, 8\\}$ , and single-layer models use 8. For other image datasets, hierarchical models' latent dimensions are $\\{128\\text{conv}, 64\\text{conv}, 256, 128, 64\\}$ , and single-layer models have $\\{64\\}$ . The discount factor, $\\gamma$ , is set to 0.9. Run on one NVIDIA A100 GPU with PyTorch [64], models are optimized using Adam optimizer [42] at a learning rate of 3e-4. Training epochs are set to 1000 for baselines and $1000 / L$ for our method, with outcomes averaged over 5 random seeds.", + "bbox": [ + 496, + 703, + 893, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Detailed experimental setup are in Appendix C.", + "bbox": [ + 519, + 885, + 854, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22951", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9bc034c2894af8fdf4c5df6b779945f347b7ca10a538674e757dd2908afd2396.jpg", + "table_caption": [ + "Table 1. Classification acc. and $\\widetilde{\\mathcal{I}}\\left( {\\mathbf{x},{\\mathbf{z}}_{L}}\\right)$ comparisons. Our methods' results are marked in purple. The best two results are in bold." + ], + "table_footnote": [], + "table_body": "
MethodFashionMNISTCIFAR10CIFAR100TinyImageNetSTL-10 (32 × 32-downsampled)
Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{I}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)
AAE [58]72.11±0.274.08±0.6738.36±0.205.91±1.0317.56±0.456.19±0.958.73±0.583.37±0.6736.64±0.176.65±1.10
VAE [43]75.08±0.094.36±0.3539.98±0.056.32±0.6519.05±0.2013.76±1.858.92±0.363.76±1.2137.75±0.076.87±0.75
BIVA [57]28.67±0.643.48±0.4810.40±0.135e-9±0.001.07±0.058e-9±0.000.67±0.069e-8±0.0010.02±0.201.41±0.38
IVAE [51]76.25±0.302.44±0.5239.26±0.256.41±0.6919.49±0.338.91±0.968.07±0.693.92±0.9837.98±0.412.86±0.95
HVAE [35]10.73±0.080.31±0.0810.40±0.053e-8±0.001.21±0.107e-7±0.000.63±0.065e-10±0.0010.24±0.070.97±0.17
HVAE+RL(ours)78.23±0.135.01±0.7046.46±0.1511.39±1.2025.21±0.2117.01±2.4112.76±0.3911.88±2.8743.76±0.1510.93±1.73
LVAE [76]19.70±0.211.73±0.3215.32±0.105e-5±0.0010.38±0.891.04±0.394.77±0.470.54±0.1211.89±0.100.45±0.08
LVAE+RL(ours)78.48±0.154.37±0.5846.35±0.176.91±0.8625.41±0.209.00±1.1913.41±0.444.48±1.7141.86±0.2610.77±1.94
", + "bbox": [ + 81, + 114, + 893, + 234 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c77f039f07879fa50c5db0113faf191579d8128d6d762598d2009d009757596a.jpg", + "table_caption": [ + "Table 2. Density estimation in bits per dimension (bpd) [21] and KL divergence at the topmost level of hierarchical VAEs." + ], + "table_footnote": [], + "table_body": "
ModelFashionMNISTCIFAR10
bpdKLbpdKL
VAE0.306±0.04117.9±0.33.74±0.01263.0±4.0
BIVA0.302±0.0713e-4±0.02.85±0.022e-3±0.0
IVAE0.403±0.09628.9±0.73.48±0.05233.0±7.0
HVAE0.315±0.0676e-5±0.04.55±0.021e-3±0.0
HVAE+RL0.305±0.08941.2±0.44.36±0.03265.0±8.0
LVAE0.313±0.0509e-4±0.02.91±0.032e-3±0.0
LVAE+RL0.335±0.07232.1±0.53.21±0.07181.0±6.0
", + "bbox": [ + 81, + 297, + 465, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Quantitative Results", + "text_level": 1, + "bbox": [ + 76, + 428, + 269, + 443 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Considering the highest-level latent representation $z_{L}$ should ideally encapsulate the most abstract representation, such as categorical distinctions, we use top-level representations for linear classification. Additionally, given that $z_{L}$ could be the most prone to posterior collapse among all levels, we estimate its information content $\\mathcal{I}(x,z_L)$ via MINE. Table 1 reports the classification accuracy on various datasets and estimated mutual information. Applying RL to the hierarchical VAEs (HVAE+RL & LVAE+RL) significantly improves accuracy compared to their counterparts trained on ELBO (HVAE & LVAE), and also outperforms other methods, including IVAE, across all datasets. This demonstrates our approach's superior representation quality. Moreover, $\\widetilde{\\mathcal{I}}(x,z_L)$ generally correlates classification performance, with our methods enabling higher mutual information in the same backbone models than the baselines in most cases, showing that our method extracts rich information from data. Notably, HVAE+RL yields significantly high $\\mathcal{I}(x,z_L)$ on complex datasets like CIFAR100 and TinyImageNet.", + "bbox": [ + 75, + 455, + 470, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 2, we present negative log-likelihood scores in bpd, where a lower bpd indicates better marginal likelihood estimation, along with KL divergences at the highest layer. Intriguingly, we find no direct correlation between the performance in estimating marginal log-likelihood $\\log p(x)$ using ELBO and the representation learning efficacy, as gauged by accuracy and $\\widehat{\\mathcal{I}}(x, z_L)$ in Table 1. For instance, despite BIVA and LVAE's superior marginal likelihood estimation on CIFAR10, their performance in representation learning tasks lags behind IVAE and our methods. This observation", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "lends empirical support to our analysis in Section 3.1 that solely optimizing ELBO does not necessarily enhance hierarchical representation learning. Additionally, we note that a low KL divergence often signals poor downstream performance and reduced $\\widetilde{\\mathcal{I}}(x, z_L)$ , indicative of posterior collapse as defined in Definition 1.", + "bbox": [ + 496, + 260, + 893, + 351 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 498, + 359, + 683, + 376 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To elucidate the efficacy of our method in learning informative hierarchical representations, we first examine the hierarchies learned by different approaches in Fig. 1 by projecting latent representations of different levels to the input space via the skip-generative path. Fig. 1 shows training with RL effectively mitigates posterior collapse, yielding a more informative latent hierarchy. This enhancement in hierarchical representation is further evident in Fig. 2, reinforcing the conclusions drawn in Section 3.1.", + "bbox": [ + 496, + 383, + 893, + 518 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "An interesting property of hierarchical VAEs is their explainable latent space, which we probe using t-SNE and latent traversal at the topmost level for generation, as shown in Fig. 5. The results demonstrate notable improvements achieved by applying RL on mapping inputs to an explainable semantic space, to which the improvement of performance in linear classification (Table 1) can be attributed. Furthermore, our exploration into latent traversal sheds light on the explainability of the latent space, with individual latent dimensions corresponding to specific abstract features like widths and positions of hollow parts, thus underscoring the interpretability of our learned representations.", + "bbox": [ + 496, + 520, + 895, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 710, + 653, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Total number of levels. We investigate the impact of varying $L$ in hierarchical VAEs on downstream task performance using representations from the topmost latent variable in Fig. 6. We observe that all baselines suffer from classification performance degeneracy with increasing latent levels: posterior collapses largely impair downstream task performance. In comparison, our methods are much more stable and achieve superior performance across all level number settings, indicating its robustness. More importantly, these results suggest our approach enables the possibility of learning a higher hierarchy of latent representation.", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22952", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ea7b4fb86aae653602389ce77b874991804951005029081ff8ab0dd9577bd564.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 274, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9143d653fa2cd04affcdac0c3d74936abf0d16fda6bd375c8ab4ae1827f29d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 87, + 460, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dda5b4c17049ff3c632c6ecfd4c9b40e3ea6710aee516c1277a7ba56626a54bd.jpg", + "image_caption": [ + "Figure 5. Panels showing the t-SNE and latent traversal generation on the highest latent variable in FashionMNIST, for vanilla HVAE (top) and HVAE+RL(bottom). The anchor point (original input) for latent traversal is bounded in red in grid center. Traversals are spaced by inverse Gaussian cdf to align with the prior distribution." + ], + "image_footnote": [], + "bbox": [ + 80, + 220, + 274, + 353 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/937cf7f78054e3e590112704c524e14123fc0a33be9429b0aa796604ffb8270b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 220, + 460, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ef4d5830fba17057e7f59d6f669ddd65473704db28c3eb4da53d9571f2a839d3.jpg", + "image_caption": [ + "Figure 6. Classification acc. of hierarchical VAEs of different levels." + ], + "image_footnote": [], + "bbox": [ + 81, + 441, + 277, + 566 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/70656d968635ac0abcf7c965c878bc7fef2280bb4083959894f44bd1bb9502f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 441, + 467, + 566 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ea17bff3408f62fae31ea875691646dab7ecac58be8ab1efca9b63aa74ed4348.jpg", + "table_caption": [ + "Table 3. Classification acc. of different representation source." + ], + "table_footnote": [], + "table_body": "
ObjectiveRepre. sourceFashionMNISTCIFAR10
HVAELVAEHVAELVAE
ELBOzLonly10.73±0.0819.70±0.2110.40±0.0515.32±0.10
full z79.96±0.2380.25±0.2750.09±0.6749.87±0.39
RLzLonly78.23±0.1378.48±0.1546.46±0.1546.35±0.17
full z84.56±0.2584.77±0.3052.87±0.5452.89±0.48
", + "bbox": [ + 81, + 628, + 467, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Latent representation source. The substantial cumulative dimension of all hierarchical latent variables $\\mathbf{z}$ , while potentially having greater representation capacity, may not be practical for all tasks. To explore this, we compare in Table 3 the downstream task performance of representations sourcing from the full $\\mathbf{z}$ versus the most abstract topmost latent representation $z_{L}$ to assess if $z_{L}$ can maintain performance comparable to full $\\mathbf{z}$ . We observe that with RL, models effectively retain comparable classification performance using just $z_{L}$ , showing efficient learning of key abstract information at the topmost layer.", + "bbox": [ + 75, + 703, + 468, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Discount factor $\\gamma$ . Exploring the impact of focusing solely on the current step's reward, we set the discount factor $\\gamma$ to", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "0 in our method. Besides, we ablate two typical settings of $\\gamma$ , 0.9 and 0.98, in the Q-value function to assess robustness. As in Table 4, models using $Q(s_{t},a_{t})$ for step-wise optimization outperform those relying only on $r(s_{t},a_{t})$ , highlighting the benefits in downstream tasks of considering future accumulative rewards, i.e., regularizing dependencies between different levels' latent representations. Moreover, the stable performance across $\\gamma$ confirms our approach's robustness.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ad2f88d3cb604143fb82ec30a2a5d33c95fb0151601bdf8cd503411016ac3bd2.jpg", + "table_caption": [ + "Table 4. Classification acc. of RL using different discount factors $\\gamma$ , where $\\gamma = 0$ means we only maximize $r(s_{t},a_{t})$ at time step $t$ ." + ], + "table_footnote": [], + "table_body": "
ObjectiveγFashionMNISTCIFAR10
HVAELVAEHVAELVAE
r(st, at)075.63±0.1175.52±0.1041.91±0.1542.16±0.13
Q(st, at)0.878.03±0.1677.98±0.2346.45±0.3046.42±0.27
Q(st, at)0.8578.11±0.2478.34±0.1945.89±0.2445.97±0.31
Q(st, at)0.978.23±0.1378.48±0.1546.46±0.1546.35±0.17
Q(st, at)0.9577.95±0.1978.53±0.1646.21±0.2146.25±0.25
Q(st, at)0.9878.01±0.1078.28±0.1746.31±0.2046.37±0.19
", + "bbox": [ + 503, + 250, + 888, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 351, + 748, + 367 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation and Future work. Though the (hierarchical) VAEs have advantages in modeling flexibility and sampling speed compared to other deep generative models [92] and are the most suitable models to demonstrate our idea with a theoretical interpretation, hierarchical VAE-based methods' application on downstream representation tasks could be somewhat outdated recently. Nevertheless, it's noteworthy that our idea of training hierarchical models with RL is not exclusively limited to hierarchical VAEs. Instead, it holds the potential when extended to general hierarchical models like diffusion models [40, 55], which feature more levels of latent representation and employ a fixed, non-trainable encoder for the efficient loss computation as independent terms over the hierarchy [61]. Our approach may be extended to learn a diffusion model with a trainable encoder, which may potentially enhance their representation capacity.", + "bbox": [ + 496, + 376, + 890, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. In this paper, we investigate the unsupervised representation learning with hierarchical VAEs from the perspective of information theory. We identify an urgent need to apply reinforcement learning to learn a high-quality hierarchy. The learned hierarchical representations have shown their superiority in improving the downstream task performance and mitigating the notorious posterior collapse. Additionally, an interesting finding is that learning a better ELBO (original training objective of hierarchical VAEs) is not necessary for learning a better representation, which has been supported by both our theoretical analysis and empirical results. Beyond hierarchical VAEs, our method may inspire future works to apply reinforcement learning to learn a hierarchical representation in time ahead.", + "bbox": [ + 496, + 619, + 893, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This research is supported by the National Research Foundation, Singapore, under its Competitive Research Programme (Grant No. NRF-CRP23-2019-0006).", + "bbox": [ + 496, + 835, + 893, + 895 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22953", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 80, + 90, + 171, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Korbinian Abstreiter, Sarthak Mittal, Stefan Bauer, Bernhard Scholkopf, and Arash Mehrjou. Diffusion-based representation learning. arXiv preprint arXiv:2105.14257, 2021.", + "[2] Alexander A. Alemi, Ian Fischer, Joshua V. Dillon, and Kevin Murphy. Deep variational information bottleneck. In International Conference on Learning Representations, 2017.", + "[3] Philip Bachman, R Devon Hjelm, and William Buchwalter. 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In ICLR, 2022." + ], + "bbox": [ + 501, + 92, + 892, + 503 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22956", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/303e0d84-56db-4046-87a5-f6c50e1e3b69_model.json b/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/303e0d84-56db-4046-87a5-f6c50e1e3b69_model.json new file mode 100644 index 0000000000000000000000000000000000000000..87841f40326b44e86c5c47d808546bf9f8a13102 --- /dev/null +++ b/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/303e0d84-56db-4046-87a5-f6c50e1e3b69_model.json @@ -0,0 +1,3104 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.215, + 0.131, + 0.758, + 0.177 + ], + "angle": 0, + "content": "Improving Unsupervised Hierarchical Representation with Reinforcement Learning" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.203, + 0.849, + 0.277 + ], + "angle": 0, + "content": "Ruyi An\\(^{1*}\\) Yewen Li\\(^{1*†}\\) Xu He\\(^{3}\\) Pengjie Gu\\(^{1}\\) Mengchen Zhao\\(^{4}\\) Dong Li\\(^{3}\\) Jianye Hao\\(^{3}\\) Chaojie Wang\\(^{1,2}\\) Bo An\\(^{1,2}\\) Mingyuan Zhou\\(^{5}\\) \n\\(^{1}\\)Nanyang Technological University \n\\(^{2}\\)Skywork AI, Singapore \n\\(^{3}\\)Huawei Noah's Ark Lab \n\\(^{4}\\)South China University of Technology \n\\(^{5}\\)The University of Texas at Austin" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.278, + 0.678, + 0.293 + ], + "angle": 0, + "content": "https://github.com/ruyianry/rep_hierarchy_r1" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.474, + 0.807 + ], + "angle": 0, + "content": "Learning representations to capture the very fundamental understanding of the world is a key challenge in machine learning. The hierarchical structure of explanatory factors hidden in data is such a general representation and could be potentially achieved with a hierarchical VAE. However, training a hierarchical VAE always suffers from the \"posterior collapse\", where the data information is hard to propagate to the higher-level latent variables, hence resulting in a bad hierarchical representation. To address this issue, we first analyze the shortcomings of existing methods for mitigating the posterior collapse from an information theory perspective, then highlight the necessity of regularization for explicitly propagating data information to higher-level latent variables while maintaining the dependency between different levels. This naturally leads to formulating the inference of the hierarchical latent representation as a sequential decision process, which could benefit from applying reinforcement learning (RL). Aligning RL's objective with the regularization, we first introduce a skip-generative path to acquire a reward for evaluating the information content of an inferred latent representation, and then the developed \\(Q\\)-value function based on it could have a consistent optimization direction of the regularization. Finally, policy gradient, one of the typical RL methods, is employed to train a hierarchical VAE without introducing a gradient estimator. Experimental results firmly support our analysis and demonstrate that our proposed method effectively mitigates the posterior collapse issue, learns an informative hierarchy, acquires explainable latent representations, and significantly outperforms other hierarchical VAE-based methods in downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.813, + 0.21, + 0.829 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.838, + 0.472, + 0.868 + ], + "angle": 0, + "content": "Deriving meaningful representations of data with minimal supervision is a central challenge in machine learn" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.325, + 0.707, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.327, + 0.892, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.488, + 0.895, + 0.639 + ], + "angle": 0, + "content": "Figure 1. Visualization of different levels' latent representations of hierarchical VAEs on FashinMNIST and CelebA [53] to demonstrate the learned hierarchical structure. HVAE fails to learn a 5-level hierarchy, where higher-level latent representations display posterior collapse, collapsing into the same modes of \"clothing\" and \"female faces\" regardless of the input. For IVAE, reconstructions of certain consecutive layers appear highly similar, suggesting a disrupted hierarchy. In contrast, our method preserves detailed information of inputs at low levels and captures increasingly abstract semantics at higher levels, mitigating posterior collapse and establishing an informative hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.897, + 0.9 + ], + "angle": 0, + "content": "ing [5], while existing research has predominantly concentrated on the discriminative approach [10] that relies on meticulously crafted preprocessing pipelines like pretext tasks [22, 30, 62, 65, 95] and data augmentations [3, 59]. Methods such as contrastive learning [8, 9, 11, 12, 14-16, 27, 29, 32, 34, 36, 49, 87, 97, 98] exemplify the success of this discriminative approach. However, representations derived from these methods are only limited to tasks invariant to the preprocessing pipelines [24], e.g. representations learned with the random cropping data augmentation cannot be applied to pixel-level localization tasks [83, 84], limiting their broader applicability. To transcend these confines, Bengio et al. [5] advocate for the pursuit of a universal and fundamental understanding of the world-a \"general-purpose prior\"-enabling the direct learning of representations without prior knowledge or assumptions about downstream tasks. Such representations could be learned by generative ap" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.428, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution, authors listed alphabetically by last name." + }, + { + "type": "page_footnote", + "bbox": [ + 0.099, + 0.888, + 0.402, + 0.9 + ], + "angle": 0, + "content": "† Corresponding to: Yewen Li ." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.428, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22946" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.127 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.137, + 0.47, + 0.22 + ], + "angle": 0, + "content": "Figure 2. Absolute Pearson's correlation between data representations of the inference network of a hierarchical VAE trained on FashionMNIST and another trained on MNIST [48], given the same data point from FashionMNIST. Our method enables the model to learn low-level information shared on different datasets and high-level semantic information in a hierarchical manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.471, + 0.375 + ], + "angle": 0, + "content": "proaches [47, 79], which utilize a deep generative model [21, 31, 40, 43, 68, 81] to capture the posterior distribution of the underlying explanatory factors in the observed data, i.e., the general-purpose prior, such as the hierarchical structure [76, 85, 86], disentanglement [38], and temporal and spatial coherence [71]. In this work, we focus on one specific aspect of this general-purpose prior, the hierarchical structure of data, which could be potentially achieved by learning a hierarchy of multi-level abstract latent representations with a hierarchical VAE [5, 79]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.473, + 0.76 + ], + "angle": 0, + "content": "However, actualizing a meaningful hierarchical structure with a hierarchical VAE faces a considerable issue named \"posterior collapse\" [51, 57, 76], where the data information fails to be propagated to higher-level latent variables. Specifically, their posterior distribution \\( q_{\\phi}(z|x) \\) would be equal to an uninformative prior distribution \\( p(z) \\) [13, 51, 82], undermining hierarchical VAEs' capability to capture meaningful representations. Existing literature proposing mitigation approaches for posterior collapse mainly focuses on two aspects: the limited capacity of the model architecture [19, 20, 57, 67, 76, 80] and the improper training objective [20, 41, 51, 70, 88]. However, our theoretical analysis from the perspective of information theory [18] presented in Section 3.1 suggests that current methodologies focusing on model architectures fail to explicitly enforce regularization on the inference of higher-level latent variables, where posterior collapse may still occur; and approaches targeting training objectives might disrupt the hierarchical dependencies between latent variables, compromising the model's structural integrity. Experimental results for better understanding can be seen in Figs. 1 and 2. These limitations contribute to the significant lag in the quality and performance of learned representation using hierarchical VAEs and have resulted in their limited adoption in representation learning tasks recently [47, 79]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To tackle the issue of posterior collapse that hinders acquiring an informative hierarchical latent representation, where different levels' latent representations are inferred sequentially from inputs and high-level latent representations are reliant on the abstraction of low-level ones, it is imperative to consider not only the information content of an inferred single-level latent variable but also its impact on subsequent, higher-level latent variables. This naturally inspires us to formulate the inference of the hierarchical latent" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.242 + ], + "angle": 0, + "content": "representation as a sequential decision process. Inspired by the huge success of reinforcement learning (RL) in learning a high-quality sequence, we tried to apply RL to the learning of a hierarchical VAE for a better hierarchical latent representation. Please note that although some methods have also successfully introduced RL into tasks related to generative models [6, 50, 94], none of these methods can be directly applied to train a hierarchical VAE with a focus on learning informative hierarchical latent presentations. A detailed discussion can be found in Appendix A.3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.895, + 0.273 + ], + "angle": 0, + "content": "Overall, the contribution of this work could be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.275, + 0.895, + 0.456 + ], + "angle": 0, + "content": "- We highlight limitations of existing approaches of addressing posterior collapse for an informative hierarchical latent representation from an information theory perspective and appeal for more effective regularization of the inference process to explicitly propagate data information to higher-level latent variables and maintain the dependency between different levels. To our knowledge, this work is the first to conceptualize the hierarchical VAE's inference as a sequential decision process and employ an RL approach, specifically policy gradient, to regularize this process. Our method is broadly applicable to both primary types of hierarchical VAEs: top-down and bottom-up structures;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.456, + 0.895, + 0.577 + ], + "angle": 0, + "content": "- Technically, we set up an RL formulation tailored to hierarchical VAEs training, notably with a skip-generative path that skips its lower levels' latent variables by marginalization to acquire a reward assessing the information content of the inferred latent variables without introducing additional networks or modules; then, the Q-value function developed based on it could have a consistent optimization direction of the regularization;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.577, + 0.894, + 0.638 + ], + "angle": 0, + "content": "- Experiments demonstrate the mitigation of the posterior collapse, learned informative hierarchy, explanation ability of latent representations, and superior performance in VAE-based representation learning tasks." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.275, + 0.895, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.654, + 0.638, + 0.669 + ], + "angle": 0, + "content": "2. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.825, + 0.695 + ], + "angle": 0, + "content": "2.1. Hierarchical Variational Autoencoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.825 + ], + "angle": 0, + "content": "An \\(L\\)-layer hierarchical VAE is an extension of the vanilla VAE [43, 68], where the generative process is extended to multi-step generation, formulated as \\(p_{\\theta}(\\boldsymbol{x}, \\boldsymbol{z}_{1:L}) = p_{\\theta}(\\boldsymbol{x} | \\boldsymbol{z}_1) p_{\\theta}(\\boldsymbol{z}_L) \\prod_{l=1}^{L-1} p_{\\theta}(\\boldsymbol{z}_l | \\boldsymbol{z}_{l+1})\\). The \\(p_{\\theta}(\\boldsymbol{z}_L)\\) is typically modeled as a multivariate Gaussian distribution \\(\\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\) and \\(\\theta\\) represents the parameters of the decoder. The inference process of hierarchical VAEs could be implemented in two main approaches, bottom-up (BU) and top-down (TD):" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.827, + 0.892, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathrm {B U}: q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) = q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x}) \\prod_ {l = 2} ^ {L} q _ {\\phi} (\\boldsymbol {z} _ {l} | \\boldsymbol {z} _ {l - 1}, \\boldsymbol {x}), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.85, + 0.892, + 0.871 + ], + "angle": 0, + "content": "\\[\n\\mathrm {T D}: q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) = q _ {\\phi} (\\boldsymbol {z} _ {L} | \\boldsymbol {x}) \\prod_ {l = L} ^ {2} q _ {\\phi} (\\boldsymbol {z} _ {l - 1} | \\boldsymbol {z} _ {l}, \\boldsymbol {x}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\phi\\) represents the parameters of the encoder. We provide a demonstration of these processes in Fig. 3. As" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22947" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.141, + 0.231, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.234, + 0.197, + 0.246 + ], + "angle": 0, + "content": "(a) VAE" + }, + { + "type": "image", + "bbox": [ + 0.113, + 0.249, + 0.208, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.392, + 0.253, + 0.405 + ], + "angle": 0, + "content": "(c) Bottom-up (BU) inference" + }, + { + "type": "image", + "bbox": [ + 0.341, + 0.091, + 0.437, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.234, + 0.414, + 0.246 + ], + "angle": 0, + "content": "(b) Generation" + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.249, + 0.44, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.292, + 0.392, + 0.448, + 0.405 + ], + "angle": 0, + "content": "(d) Top-down (TD) inference" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.417, + 0.471, + 0.459 + ], + "angle": 0, + "content": "Figure 3. Probabilistic graphical illustration of VAE and hierarchical VAE during inference and generation. Solid lines \\((\\rightarrow)\\) denote inference while dashed lines \\((\\dashrightarrow)\\) denote generation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.463, + 0.472, + 0.569 + ], + "angle": 0, + "content": "the inference process is to produce a sequence of latent variables step by step, we denote a hierarchy \\( \\mathbf{z}^{1:T} = \\{ \\mathbf{z}^1, \\dots, \\mathbf{z}^t, \\dots, \\mathbf{z}^T \\} \\), where \\( T = L \\). In BU inference scheme, \\( \\mathbf{z}^{1:T} = \\{ \\mathbf{z}_1, \\dots, \\mathbf{z}_t, \\dots, \\mathbf{z}_L \\} \\); in TD inference scheme, \\( \\mathbf{z}^{1:T} = \\{ \\mathbf{z}_L, \\dots, \\mathbf{z}_t, \\dots, \\mathbf{z}_1 \\} \\). For brevity, we use \\( \\mathbf{z} \\) to represent \\( \\mathbf{z}^{1:T} \\) in the following parts. Additionally, we introduce \\( j \\) for representing the lower level variable \\( \\mathbf{z}_j \\) w.r.t. \\( \\mathbf{z}^t \\) defined by" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.582, + 0.47, + 0.621 + ], + "angle": 0, + "content": "\\[\nj = \\left\\{ \\begin{array}{l l} t - 1, & \\text {i n B U h i e r a c h i c a l V A E ,} \\\\ T - t, & \\text {i n T D h i e r a c h i c a l V A E .} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.684 + ], + "angle": 0, + "content": "The training objective of a hierarchical VAE is to maximize the variational evidence lower bound (ELBO), denoted as \\(\\mathcal{L}_{\\pmb{x}}\\), of the training data's marginal log-likelihood \\(\\log p(\\pmb{x})\\) by jointly updating the parameters \\(\\theta\\) and \\(\\phi\\), expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.686, + 0.47, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\boldsymbol {x}} = \\log p (\\boldsymbol {x}) - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) \\| p _ {\\theta} (\\mathbf {z} | \\boldsymbol {x}) \\right] \\tag {4} \\\\ = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log p _ {\\theta} (\\mathbf {x} | \\mathbf {z}) \\right] - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p (\\mathbf {z}) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.47, + 0.782 + ], + "angle": 0, + "content": "where \\(D_{\\mathrm{KL}}(\\cdot ||\\cdot)\\) refers to the Kullback-Leibler (KL) divergence. Defining \\(q_{\\phi}(z_1|z_0,x)\\coloneqq q_{\\phi}(z_1|x)\\) and \\(p_{\\theta}(z_L|z_{L + 1})\\coloneqq p_{\\theta}(z_L)\\), for BU and TD hierarchical VAEs, the respective detailed expressions of their ELBOs are:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.785, + 0.47, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathrm {B U}: \\mathcal {L} _ {\\boldsymbol {x}} = \\mathbb {E} _ {q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] \\tag {5} \\\\ - \\sum_ {l = 1} ^ {L} D _ {\\mathrm {K L}} \\left[ \\left(q _ {\\phi} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l - 1}, \\boldsymbol {x}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}\\right)\\right) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.829, + 0.47, + 0.871 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathrm {T D}: \\mathcal {L} _ {\\boldsymbol {x}} = \\mathbb {E} _ {q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] \\tag {6} \\\\ - \\sum_ {l = 1} ^ {L} D _ {\\mathrm {K L}} \\left[ \\left(q _ {\\phi} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}, \\boldsymbol {x}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}\\right)\\right) \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.472, + 0.901 + ], + "angle": 0, + "content": "After convergence, we could extract level \\( l \\)'s latent representation by the maximum a posteriori (MAP) estimate" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "tion of the learned latent variables \\( \\mathbf{z}_l \\), defined as \\( \\mathbf{z}_l^* = \\arg \\max_{\\mathbf{z}_l} q_{\\phi}(\\mathbf{z}_l | \\mathbf{x}) \\) [5, 43]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.892, + 0.166 + ], + "angle": 0, + "content": "However, training hierarchical VAEs often suffers from the issue known as posterior collapse, which can be formally defined as follows." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.176, + 0.894, + 0.238 + ], + "angle": 0, + "content": "Definition 1 (posterior collapse [7, 13, 82, 88]). Given a hierarchical VAE \\( p(\\pmb{x}, \\pmb{z}; \\theta, \\phi) \\), paramters' value \\( \\phi = \\hat{\\phi} \\), \\( \\theta = \\hat{\\theta} \\), and for any data \\( \\pmb{x} \\) in a dataset \\( \\mathcal{D}_{\\pmb{x}} = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_N\\} \\), the posterior of inference step \\( t \\)'s latent variable \\( \\pmb{z}^t \\) collapses if" + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.253, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\nq _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} ^ {t - 1}, \\boldsymbol {x}; \\hat {\\phi}\\right) = p _ {\\theta} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} _ {j + 2}; \\hat {\\theta}\\right), \\forall \\boldsymbol {x} \\in \\mathcal {D} _ {\\boldsymbol {x}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.278, + 0.895, + 0.459 + ], + "angle": 0, + "content": "The posterior collapse issue mainly occurs in higher-level latent variables of hierarchical VAEs. Stochastic latent variables \\(\\mathbf{z}\\) can be manually divided into lower-level variables, \\(z_{< k} = \\{z_1,\\dots,z_{k - 1}\\}\\) and higher-level ones, \\(z_{\\geq k} = \\{z_k,\\dots,z_L\\}\\) where \\(k\\in \\{2,\\ldots ,L\\}\\). Though \\(z_{< k}\\) may not suffer from posterior collapse that could encode sufficient information to reconstruct the inputs well, the corresponding high-level stochastic latent variables \\(\\mathbf{z}_{\\geq k}\\) could be inclined to collapse into priors, i.e., \\(q_{\\phi}(z_{\\geq k}|\\boldsymbol {x})\\approx p_{\\theta}(z_{\\geq k})\\). An illustration can be seen in Fig. 1. Consequently, these higher-level posteriors will hold limited relevance to its input \\(\\boldsymbol{x}\\), resulting in non-informative representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.481, + 0.725, + 0.496 + ], + "angle": 0, + "content": "2.2. Reinforcement Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.894, + 0.624 + ], + "angle": 0, + "content": "We consider a standard RL setup in continuous action space and discrete timesteps, formalized as a Markov decision process (MDP) defined by a tuple \\(\\langle S, \\mathcal{A}, P, r \\rangle\\) [33, 52, 72, 94]. Here, the state space \\(S\\) and action space \\(\\mathcal{A}\\) are continuous, the state transition probability function \\(P: S \\times \\mathcal{A} \\to \\Delta(S)\\) represents the probability density of the next state \\(s_{t+1} \\in S\\) given the current state \\(s_t \\in S\\) and action \\(a_t \\in \\mathcal{A}\\), and \\(r: S \\times \\mathcal{A} \\to \\mathbb{R}\\) denotes the reward function on each transition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.82 + ], + "angle": 0, + "content": "At each time step \\(t \\in \\{1, 2, \\dots, T\\}\\), an agent observes a state \\(s_t \\in S\\), takes an action \\(a_t \\in \\mathcal{A}\\), and receives a scalar reward \\(r_t: S \\times \\mathcal{A} \\to \\mathbb{R}\\). The state \\(s_t\\) could be described in various ways, such as the entire history of the observations \\(s_t = (o_1, \\dots, o_t)\\) [94] or only the current observation \\(s_t = o_t\\) [33]. An agent's behavior could be defined by a policy \\(\\pi(a_t | s_t)\\), which maps states to a probability distribution over actions. The return at time step \\(t\\) is defined as the sum of the discounted future reward \\(R_t = \\sum_{i=t}^{T} \\gamma^{(i-t)} r(s_i, a_i)\\) with a discount factor \\(\\gamma \\in (0, 1)\\). The expectation of the return could be flexibly formulated by the Q-value function \\(Q^\\pi(s_t, a_t)\\) after taking an action \\(a_t\\) in state \\(s_t\\) and thereafter following policy \\(\\pi\\):" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.822, + 0.892, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {s _ {i > t} \\sim P, a _ {i > t} \\sim \\pi} \\left[ R _ {t} \\mid s _ {t}, a _ {t} \\right] \\tag {8} \\\\ = r \\left(s _ {t}, a _ {t}\\right) + \\gamma \\mathbb {E} _ {s _ {t + 1} \\sim P, a _ {t} \\sim \\pi} \\left[ Q ^ {\\pi} \\left(s _ {t + 1}, a _ {t + 1}\\right) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "which not only considers the reward of the action to be taken on the current state but also its effect on the future decision process. Let us assume that drawing from \\( a_{t} \\sim \\pi (a_{t}|s_{t}) \\) can" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22948" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "be realized with reparameterization as \\( a_{t} = f(s_{t},\\epsilon_{t}),\\epsilon_{t}\\sim p(\\epsilon) \\). We could directly apply the policy gradient method [52, 78, 94] on the model parameters \\( \\Theta \\) with gradient ascent to maximize the \\( Q^{\\pi}(s_t,a_t) \\) at a time step \\( t \\):" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.154, + 0.47, + 0.17 + ], + "angle": 0, + "content": "\\[\n\\Theta \\leftarrow \\Theta + \\nabla_ {\\Theta} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.173, + 0.469, + 0.202 + ], + "angle": 0, + "content": "We sum all time step \\(t\\) 's policy gradient together to represent the optimization direction \\(\\nabla_{\\Theta}\\mathcal{I}\\) of the RL, expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.204, + 0.47, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\Theta} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {s _ {t} \\sim P, \\epsilon_ {t} \\sim p (\\epsilon)} \\nabla_ {\\Theta} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right), a _ {t} = f \\left(s _ {t}, \\epsilon_ {t}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.243, + 0.469, + 0.273 + ], + "angle": 0, + "content": "For the discussion on Related Works, we move it to Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.294, + 0.42, + 0.328 + ], + "angle": 0, + "content": "3. Improving Unsupervised Hierarchical Representation with RL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.473, + 0.522 + ], + "angle": 0, + "content": "We first provide an analysis of the existing two major approaches mitigating posterior collapse for learning a hierarchical representation with a hierarchical VAE. However, we found that they either lack regularization for propagating data information to higher-level latent variables or break the dependency between different levels' latent variables. Therefore, to address these drawbacks, a better training objective from the perspective of information theory could naturally lead to an RL scheme with a proper design of the Q-value function as the regularization of latent representations. Finally, we develop an RL training scheme with the policy gradient method to train a hierarchical VAE." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.532, + 0.433, + 0.561 + ], + "angle": 0, + "content": "3.1. Analysis of Representation Learning with Hierarchical VAEs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.47, + 0.663 + ], + "angle": 0, + "content": "The aim of representation learning with a hierarchical VAE is to learn a hierarchy of latent variables \\(\\mathbf{z}\\) that could represent the input data \\(\\mathbf{x}\\). We begin with rethinking how different approaches are affecting the representation learning with a hierarchical VAE. We first rewrite the ELBO from an information theory standpoint [18]:" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.665, + 0.492, + 0.73 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} [ \\operatorname {E L B O} (\\boldsymbol {x}) ] \\\\ = \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} \\left[ \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} \\left[ D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x}) \\| p (\\boldsymbol {z})\\right) \\right] \\\\ = \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) - \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) - D _ {\\mathrm {K L}} (q (\\boldsymbol {z}) \\| p (\\boldsymbol {z})) - \\mathcal {H} _ {p} (\\boldsymbol {x}), \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.76 + ], + "angle": 0, + "content": "where the mutual information between \\( x \\) and \\( z \\) under different distribution is defined by" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.763, + 0.486, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) = \\mathbb {E} _ {p (\\boldsymbol {x}) q _ {\\phi} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right)} \\left[ \\log \\frac {p (\\boldsymbol {x} , \\boldsymbol {z} _ {1})}{p (\\boldsymbol {x}) q \\left(\\boldsymbol {z} _ {1}\\right)} \\right] \\tag {12} \\\\ = \\mathbb {E} _ {p (\\boldsymbol {x}) q _ {\\phi} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right)} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {p (\\boldsymbol {x})} \\left[ \\log p (\\boldsymbol {x}) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.818, + 0.486, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) = \\mathbb {E} _ {q (\\boldsymbol {x}) q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x})} \\left[ \\log \\frac {q (\\boldsymbol {x} , \\boldsymbol {z} _ {1})}{q (\\boldsymbol {x}) q (\\boldsymbol {z} _ {1})} \\right] \\tag {13} \\\\ = \\mathbb {E} _ {q (\\boldsymbol {x}) q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x})} \\left[ \\log q _ {\\phi} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {q (\\boldsymbol {x})} \\left[ \\log q (\\boldsymbol {x}) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(q(x)\\) is the training data's distribution and it is assumed to be equal to the true data distribution \\(p(\\pmb{x})\\);" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.808, + 0.108 + ], + "angle": 0, + "content": "\\(p_{\\theta}(\\pmb {x}|z_1)\\) and \\(q_{\\phi}(\\pmb {x}|z_{1})\\) could be expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.109, + 0.892, + 0.142 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) = \\frac {p _ {\\theta} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right) p (\\boldsymbol {x})}{q \\left(\\boldsymbol {z} _ {1}\\right)} \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.144, + 0.892, + 0.177 + ], + "angle": 0, + "content": "\\[\nq _ {\\phi} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) = \\frac {q _ {\\phi} (\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}) q (\\boldsymbol {x})}{q (\\boldsymbol {z} _ {1})} \\simeq \\frac {q _ {\\phi} (\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}) p (\\boldsymbol {x})}{q (\\boldsymbol {z} _ {1})}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.178, + 0.894, + 0.269 + ], + "angle": 0, + "content": "Thus, the target of the ELBO in Eq. 11 effectively becomes minimizing the gap between the bottom-most latent variable's posterior \\(q_{\\phi}(\\pmb{z}_1|\\pmb{x})\\) and its corresponding true posterior \\(p_{\\theta}(\\pmb{z}_1|\\pmb{x})\\) and meanwhile the posterior of higher-level latent variables \\(\\{\\pmb{z}_l\\}_{l=1:L}\\) are trained to be close to their respective priors by the \\(D_{\\mathrm{KL}}[q(\\mathbf{z})\\| p(\\mathbf{z})]\\) term." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.894, + 0.379 + ], + "angle": 0, + "content": "Since the latent variables above \\( z_{1} \\) do not receive direct regularization to maximize \\( \\mathcal{I}(x, z_{l}), l > 1 \\), it could potentially lead to the posterior collapse phenomenon. Therefore, approaches that only modify the model structure [25, 57, 76, 80] still do not impose additional regularization to higher-level latent variables in the training objective, where the posterior collapse could still occur." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.894, + 0.474 + ], + "angle": 0, + "content": "Existing regularization strategies in the literature aim to refine the posterior distribution in order to cultivate good representations [41, 51, 54]. These methods typically focus on the relationship between observed data \\( \\mathbf{x} \\) and a single-level latent variable \\( z^t \\), which could be interpreted as an additional regularization on the ELBO expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.476, + 0.892, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z}) \\simeq \\sum_ {t = 1} ^ {T} \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {t}). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.663 + ], + "angle": 0, + "content": "However, by optimizing all latent variables \\(\\{z^t\\}_{t = 1:T}\\) with a shared objective \\(\\mathcal{I}(\\pmb {x},\\pmb{z}^t)\\) simultaneously, these approaches may hurt the hierarchical dependency amongst them. This is due to the implicit incentive for all latent variables to assimilate, potentially undermining the hierarchical structure. Learning to generate a sequence \\(\\{\\pmb {x},\\pmb {z}^1,\\dots,\\pmb {z}^T\\}\\) with only one loss after finishing generating the whole sequence could also bring the imbalance issue, where the concentration of optimization to the mediate items is not clear [94]. These limitations hinder the exploitation of the full capabilities inherent in hierarchical VAEs." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.669, + 0.894, + 0.699 + ], + "angle": 0, + "content": "We leave a detailed discussion for the above two approaches in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.894, + 0.795 + ], + "angle": 0, + "content": "In summary, an effective training scheme should maximize the information content hidden in latent variables of all layers, while maintaining the dependencies among latent variables. Specifically, the regularization on \\( z^t \\) should account for not only \\( \\mathcal{I}(\\pmb{x},\\pmb{z}^t) \\), but also the influence on the subsequent latent variables \\( \\mathcal{I}(\\pmb{x},\\pmb{z}^i|\\pmb{z}^{i - 1}) \\), \\( i > t \\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.796, + 0.892, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t: T}\\right) = \\sum_ {i = t} ^ {T} \\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.818, + 0.892, + 0.863 + ], + "angle": 0, + "content": "By incorporating a discount factor \\(\\gamma \\in (0,1)\\), which allocates greater weight to the mutual information with proximal latent variables, the regularization for \\(z^t\\) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.864, + 0.892, + 0.886 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right) = \\sum_ {i = t} ^ {T} \\gamma^ {i - t} \\mathcal {I} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.887, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Therefore, the optimization direction of learning the se" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22949" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.105, + 0.501, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.239, + 0.464, + 0.26 + ], + "angle": 0, + "content": "\\[\n\\overline {{r (s _ {t} , a _ {t}) = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} (z ^ {1 : t} | x)} \\log p _ {\\theta} (x | z ^ {t}) - D _ {\\mathrm {K L}} [ q _ {\\phi} (z ^ {1 : t} | x) | | p (z ^ {1 : t}) ]}}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.088, + 0.848, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.893, + 0.302 + ], + "angle": 0, + "content": "Figure 4. Illustration of modeling the inference process of a hierarchical VAE as a sequential decision process (left) and the details of the elements of RL \\( s_t \\), \\( a_t \\), \\( s_{t+1} \\) (right). A reward \\( r(s_t, a_t) \\) is derived with the skip-generative path depicted in the gray box." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.4, + 0.324 + ], + "angle": 0, + "content": "quence \\(\\{\\pmb {x},\\pmb {z}^1,\\dots,\\pmb {z}^T\\}\\) can then be expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.324, + 0.47, + 0.347 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\phi , \\theta} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {p (\\boldsymbol {x}), q _ {\\phi}, p _ {\\theta}} \\nabla_ {\\phi , \\theta} \\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right). \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.473, + 0.455 + ], + "angle": 0, + "content": "The resemblance of the optimization direction to Eq. 10 naturally leads to formulating the learning of hierarchical VAE as a sequential decision process, prompting the application of RL methods. Particularly, we are driven to develop a proper Q-value function \\(Q(s_{t},a_{t})\\) to play the role of the regularization \\(\\mathcal{L}_{\\mathcal{I}}(\\boldsymbol {x},\\boldsymbol{z}^t)\\) to achieve a consistent expression of the two optimization objectives." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.463, + 0.396, + 0.479 + ], + "angle": 0, + "content": "3.2. Training Hierarchical VAEs with RL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.472, + 0.623 + ], + "angle": 0, + "content": "Inspired by the tremendous success of RL methods in stably propagating information along long Markov Decision chains that maximize the cumulative rewards tallied at every step, i.e., the Q-value \\(Q^{\\pi}(s_t,a_t)\\) in Eq. 8, we formulate the progressive inference process of an \\(L\\)-layer hierarchical VAEs as an \\(L\\)-step sequential decision process. Specifically, given an input \\(\\pmb{x}\\) from a training set \\(\\mathcal{D}_{\\pmb{x}}\\), we need a hierarchical VAE parameterized with \\(\\{\\theta ,\\phi \\}\\) to produce a sequence \\(Y_{1:T} = \\{\\pmb {x},\\pmb {z}^{1},\\pmb {z}^{2},\\dots,\\pmb{z}^{T}\\} ,T = L\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.685 + ], + "angle": 0, + "content": "Now, we can set up the basic elements for training with RL. At each time step \\( t \\), the state \\( s_t \\) is characterized as a tuple including the observed input and already produced latent variables \\( z^{1:t-1} = \\{z^1, \\dots, z^{t-1}\\} \\) up to the step:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.685, + 0.47, + 0.703 + ], + "angle": 0, + "content": "\\[\ns _ {t} \\triangleq \\left\\{\\boldsymbol {x}, \\boldsymbol {z} ^ {1: t - 1} \\right\\}, \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.75 + ], + "angle": 0, + "content": "where \\( s_1 = \\{x\\} \\). After receiving a state \\( s_t \\), the encoder \\( q_{\\phi}(\\mathbf{z}|x) \\) of the hierarchical model acts as the policy network \\( \\pi (a_t|s_t) \\) to produce the latent variable as an action:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.75, + 0.47, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\pi_ {\\phi} \\left(a _ {t} \\mid s _ {t}\\right) \\triangleq q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {x}, \\boldsymbol {z} ^ {1: t - 1}\\right) = q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} ^ {t - 1}, \\boldsymbol {x}\\right), \\tag {21}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.771, + 0.47, + 0.789 + ], + "angle": 0, + "content": "\\[\na _ {t} \\triangleq z ^ {t} \\sim q _ {\\phi} \\left(z ^ {t} \\mid z ^ {t - 1}, x\\right). \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.791, + 0.469, + 0.821 + ], + "angle": 0, + "content": "Once executing the \\( a_{t} \\), we will get to the next state according the state transition probability function \\( P \\), specified as" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.822, + 0.47, + 0.839 + ], + "angle": 0, + "content": "\\[\nP \\left(s _ {t + 1} \\mid s _ {t}, a _ {t}\\right) \\triangleq \\left(\\delta_ {\\boldsymbol {x}}, \\delta_ {\\boldsymbol {z} ^ {1: t}}\\right), \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.901 + ], + "angle": 0, + "content": "which is deterministic and reflects the unchanged observed data \\( \\pmb{x} \\) and the inclusion of new inferred latent variables at the successor state. \\( \\delta_v \\) is a Dirac delta distribution that only manifests a non-zero impulse at \\( v \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.308, + 0.895, + 0.422 + ], + "angle": 0, + "content": "Reward function design. When getting such a transition \\(\\{s_t, a_t, s_{t+1}\\}\\), we need to design a reward function \\(r(s_t, a_t)\\). The principle of the design is to evaluate the information content \\(\\mathcal{I}(\\boldsymbol{x}, \\boldsymbol{z}^t | \\boldsymbol{z}^{t-1})\\) hidden in the latent variable \\(\\boldsymbol{z}^t\\) that represents the inputs, then we could formulate the Q-value function to regularize \\(\\boldsymbol{z}^t\\) by \\(\\sum_{i=t}^{T} \\mathcal{I}(\\boldsymbol{x}, \\boldsymbol{z}^i | \\boldsymbol{z}^{i-1})\\). We design a reward function \\(r(s_t, a_t)\\) to evaluate the information between \\(\\boldsymbol{x}\\) and \\(\\boldsymbol{z}^t\\) as below:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.429, + 0.902, + 0.462 + ], + "angle": 0, + "content": "\\[\nr \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} \\left(\\mathbf {z} ^ {1: t} \\mid \\mathbf {x}\\right)} \\log p _ {\\theta} (\\mathbf {x} \\mid \\mathbf {z} ^ {t}) - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} \\left(\\mathbf {z} ^ {1: t} \\mid \\mathbf {x}\\right) \\| p \\left(\\mathbf {z} ^ {1: t}\\right) \\right], \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.471, + 0.867, + 0.487 + ], + "angle": 0, + "content": "where \\(p_{\\theta}(\\boldsymbol{x}|\\boldsymbol{z}^t)\\) is a skip-generative path, expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.493, + 0.892, + 0.521 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} ^ {t}) = \\int_ {\\boldsymbol {z} _ {1: j}} p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\prod_ {i = j} ^ {1} p _ {\\theta} (\\boldsymbol {z} _ {i} | \\boldsymbol {z} _ {i + 1}), \\boldsymbol {z} ^ {t} \\sim q (\\boldsymbol {z} ^ {t} | \\boldsymbol {z} ^ {< t}, \\boldsymbol {x}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.528, + 0.892, + 0.627 + ], + "angle": 0, + "content": "in which \\( z_{1:j} \\) are marginalized out by the integral. Kindly note that the skip-generative path \\( p_{\\theta}(\\pmb{x}|\\pmb{z}^t) \\) is different from the generative path in vanilla hierarchical VAEs, where \\( p_{\\theta}(\\pmb{x}|\\pmb{z}^{1:t}) = p_{\\theta}(\\pmb{x}|\\pmb{z}_1) \\) after observing \\( z^{1:t} \\). The \\( r(s_t,a_t) \\) based on the skip-generative path could empirically force the training on maximizing the mutual information between \\( \\pmb{x} \\) and \\( z^t \\) after observing \\( z^{t-1} \\), expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.633, + 0.892, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {p (\\boldsymbol {x})} \\left[ r \\left(s _ {t}, a _ {t}\\right) \\right] \\tag {25} \\\\ = \\mathbb {E} _ {p (\\boldsymbol {x}) q (\\boldsymbol {z} ^ {1: t} | \\boldsymbol {x})} \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} ^ {t}) - \\mathbb {E} _ {p (\\boldsymbol {x})} D _ {\\mathrm {K L}} \\left[ q _ {\\phi} \\left(\\boldsymbol {z} ^ {1: t} | \\boldsymbol {x}\\right) \\| p (\\boldsymbol {z} ^ {1: t}) \\right] \\\\ = \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {t}) - \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {1}) - D _ {\\mathrm {K L}} [ q (\\boldsymbol {z} ^ {1: t}) | | p (\\boldsymbol {z} ^ {1: t}) ] - \\mathcal {H} _ {p} (\\boldsymbol {x}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.697, + 0.895, + 0.774 + ], + "angle": 0, + "content": "Therefore, as shown in Eq. 25, the reward function \\(r(s_{t},a_{t})\\) is to evaluate how \\(\\mathcal{I}(\\pmb {x},\\pmb{z}^t)\\) is closer or larger than \\(\\mathcal{I}(\\pmb {x},\\pmb{z}^{1})\\) Thus, the reward function could be an approximate evaluation of \\(\\mathcal{I}_q(\\pmb {x},\\pmb {z}^t |\\pmb {z}^{t - 1})\\) after observing the inferred \\(\\pmb{z}^{t - 1}\\), i.e., \\(r(s_{t},a_{t})\\simeq \\mathcal{I}_{q}(\\pmb {x},\\pmb{z}^{t}|\\pmb{z}^{t - 1})\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.895, + 0.855 + ], + "angle": 0, + "content": "Q-value function. To explicitly add regularization on a current inferred latent variable \\( z^{t} \\),s influence on its following latent variables \\( z^{>t} \\), we propose to maximize its corresponding Q-value, which considers not only its own reward \\( r(s_{t},a_{t}) \\), but also the future accumulative rewards, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.857, + 0.892, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = r \\left(s _ {t}, a _ {t}\\right) + \\gamma \\mathbb {E} _ {\\pi} \\left[ Q ^ {\\pi} \\left(s _ {t + 1}, a _ {t + 1}\\right) \\right] \\\\ = r \\left(s _ {t}, a _ {t}\\right) + \\mathbb {E} _ {\\pi} \\left[ \\sum_ {i = t + 1} ^ {T} \\gamma^ {i - t} r \\left(s _ {i}, a _ {i}\\right) \\right]. \\tag {26} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22950" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "With the efficient reparameterization trick [43], we could do a single-sample based Monte Carlos (MC) estimation for the expectation of the Q-value function, i.e., \\(Q^{\\pi}(s_t,a_t)\\simeq \\sum_{i = t}^{T}\\gamma^{i - t}r(s_i,a_i)\\). Please note that the reward function is differentiable to the model's parameters, hence we could directly use gradient descent method [42, 69] to maximize the \\(Q_{\\pi}(s_t,a_t)\\), where \\(\\theta\\) and \\(\\phi\\) are trained simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.274 + ], + "angle": 0, + "content": "Therefore, at every time step \\( t \\), maximizing its corresponding Q-value function is approximately maximizing the mutual information between \\( x \\) and \\( z^t \\) and the influence of the inferred \\( z^t \\) in the following latent variables \\( z^{t+1:T} \\) that depends on it, expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.275, + 0.47, + 0.296 + ], + "angle": 0, + "content": "\\[\nQ ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) \\simeq \\sum_ {i = t} ^ {T} \\gamma^ {i - t} \\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right) = \\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right), \\tag {27}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.469, + 0.326 + ], + "angle": 0, + "content": "which is consistent with the expression of Eq. 18 and the analysis in Section 3.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.469, + 0.372 + ], + "angle": 0, + "content": "Finally, to learn a high-quality sequence \\(\\{\\pmb{x},\\pmb{z}^1,\\dots,\\pmb{z}^T\\}\\) aligning with the optimization direction in Eq. 19, we define the optimization direction on the Q-value function:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.373, + 0.47, + 0.395 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\theta , \\phi} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {s _ {i} \\sim P, a _ {i} \\sim \\pi} \\nabla_ {\\theta , \\phi} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right). \\tag {28}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.472, + 0.516 + ], + "angle": 0, + "content": "As \\( a_{t} \\) could be obtained by reparameterization and \\( Q^{\\pi}(s_t, a_t) \\) is differentiable to model parameters, we could implement the policy gradient by directly maximizing \\( Q^{\\pi}(s_t, a_t) \\) at every time step \\( t \\) by Eq. 9, thereby eliminating the need for a gradient estimator like REINFORCE [89] and avoiding the high variance associated with these estimators [77]. We summarize the overall training scheme in Algorithm 1." + }, + { + "type": "code_caption", + "bbox": [ + 0.079, + 0.524, + 0.434, + 0.54 + ], + "angle": 0, + "content": "Algorithm 1 Optimizing a hierarchical VAE with RL." + }, + { + "type": "algorithm", + "bbox": [ + 0.092, + 0.544, + 0.47, + 0.802 + ], + "angle": 0, + "content": "Input: A training dataset \\(\\mathcal{D}_{\\pmb{x}}\\) training hyperparameters; \nOutput: An \\(L\\) -layer hierarchical VAE parameterized with an encoder \\(q_{\\phi}(\\mathbf{z}|\\mathbf{x})\\) and a decoder \\(p_{\\theta}(\\pmb {x}|\\mathbf{z})\\) \nInitialization: Randomly initialize the parameters \\(\\theta ,\\phi\\) \nfor epoch \\(= 1\\) to max_epochs do Sample a batch of \\(N\\) training samples \\(\\pmb{x}^n\\) from \\(\\mathcal{D}_x\\) . for time step \\(t = 1\\) to \\(L\\) do for \\(i = t\\) to \\(L\\) do Follow Eq.22, but with reparameterization, to sample an action \\(a_i^n\\sim \\pi (a_i^n |s_i^n)\\) Get reward \\(r(s_i^n,a_i^n)\\) by Eq.24; end for Get \\(Q^{\\pi}(s_t^n,a_t^n)\\simeq \\sum_{i = t}^{T}\\gamma^{i - t}r(s_i^n,a_i^n)\\) Update \\(\\theta ,\\phi\\) using the policy gradient for the current time step \\(t\\) by Eq.9; end for \nend for" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.21, + 0.832 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Our experiments engage in comparisons with several hierarchical VAE variants and various unsupervised methods to assess if our method of training hierarchical VAEs with RL yields superior performance in 1) mitigating posterior" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.198 + ], + "angle": 0, + "content": "collapse at higher latent representations, 2) learning a clear hierarchical representation, 3) attaining an explainable latent representation, and more importantly, 4) offering better representation than other hierarchical VAE-based unsupervised learning methods on downstream tasks. Additionally, we present several ablation studies to further evaluate different settings' influence on our method's performance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.208, + 0.691, + 0.224 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.895, + 0.293 + ], + "angle": 0, + "content": "Datasets: Our method is benchmarked on 5 datasets: FashionMNIST [91], CIFAR10 and CIFAR100 [44], TinyImageNet [46], and STL-10 [17]. Each method is trained using standard train splits and assessed on corresponding test splits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.895, + 0.446 + ], + "angle": 0, + "content": "Evaluation metrics: For representation evaluation, we follow the commonly adopted downstream linear classification [5, 39, 63], using a linear support vector machine (SVM) [37] classifier on representations from frozen models. Classification accuracy is reported to measure linear separability, acting as a proxy for mutual information of representations with the labels. Additionally, we apply the MINE statistics network [4] to estimate the mutual information \\(\\widetilde{\\mathcal{I}}(x, z_L)\\), between input \\(x\\) and the top latent variable \\(z_L\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.897, + 0.689 + ], + "angle": 0, + "content": "Baselines: We compare our method with two groups of baselines: i) those modifying the inference process without changing the training objective (ELBO); ii) those modifying the training objective to add more regularization on the inference process. For i, we include a BU hierarchical VAE (HVAE) powered with residual connections [35], a TD hierarchical VAE (LVAE) with a ladder inference [76], and a more sophisticated bidirectional structure hierarchical VAE (BIVA) [57]. For ii, to our best knowledge, the most relevant work to our method is informative hierarchical VAE (IVAE) [51], which introduces additional layer-wise regularization on latent representations of a hierarchical VAE. Additionally, we include a vanilla VAE (VAE) [43] and an adversarial autoencoder (AAE) [58] of single-level to assess the performance improvement brought by hierarchical structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.885 + ], + "angle": 0, + "content": "Implementation details: We apply our RL optimization approach to hierarchical VAEs with BU \\((\\mathbf{HVAE} + \\mathbf{RL})\\) and TD (LVAE+RL) inference schemes. For Fashion-MNIST, hierarchical models use latent dimensions of \\(\\{128, 64, 32, 16, 8\\}\\), and single-layer models use 8. For other image datasets, hierarchical models' latent dimensions are \\(\\{128\\text{conv}, 64\\text{conv}, 256, 128, 64\\}\\), and single-layer models have \\(\\{64\\}\\). The discount factor, \\(\\gamma\\), is set to 0.9. Run on one NVIDIA A100 GPU with PyTorch [64], models are optimized using Adam optimizer [42] at a learning rate of 3e-4. Training epochs are set to 1000 for baselines and \\(1000 / L\\) for our method, with outcomes averaged over 5 random seeds." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.855, + 0.902 + ], + "angle": 0, + "content": "Detailed experimental setup are in Appendix C." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22951" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.09, + 0.873, + 0.105 + ], + "angle": 0, + "content": "Table 1. Classification acc. and \\( \\widetilde{\\mathcal{I}}\\left( {\\mathbf{x},{\\mathbf{z}}_{L}}\\right) \\) comparisons. Our methods' results are marked in purple. The best two results are in bold." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.895, + 0.235 + ], + "angle": 0, + "content": "
MethodFashionMNISTCIFAR10CIFAR100TinyImageNetSTL-10 (32 × 32-downsampled)
Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{I}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)
AAE [58]72.11±0.274.08±0.6738.36±0.205.91±1.0317.56±0.456.19±0.958.73±0.583.37±0.6736.64±0.176.65±1.10
VAE [43]75.08±0.094.36±0.3539.98±0.056.32±0.6519.05±0.2013.76±1.858.92±0.363.76±1.2137.75±0.076.87±0.75
BIVA [57]28.67±0.643.48±0.4810.40±0.135e-9±0.001.07±0.058e-9±0.000.67±0.069e-8±0.0010.02±0.201.41±0.38
IVAE [51]76.25±0.302.44±0.5239.26±0.256.41±0.6919.49±0.338.91±0.968.07±0.693.92±0.9837.98±0.412.86±0.95
HVAE [35]10.73±0.080.31±0.0810.40±0.053e-8±0.001.21±0.107e-7±0.000.63±0.065e-10±0.0010.24±0.070.97±0.17
HVAE+RL(ours)78.23±0.135.01±0.7046.46±0.1511.39±1.2025.21±0.2117.01±2.4112.76±0.3911.88±2.8743.76±0.1510.93±1.73
LVAE [76]19.70±0.211.73±0.3215.32±0.105e-5±0.0010.38±0.891.04±0.394.77±0.470.54±0.1211.89±0.100.45±0.08
LVAE+RL(ours)78.48±0.154.37±0.5846.35±0.176.91±0.8625.41±0.209.00±1.1913.41±0.444.48±1.7141.86±0.2610.77±1.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.259, + 0.471, + 0.287 + ], + "angle": 0, + "content": "Table 2. Density estimation in bits per dimension (bpd) [21] and KL divergence at the topmost level of hierarchical VAEs." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.298, + 0.466, + 0.422 + ], + "angle": 0, + "content": "
ModelFashionMNISTCIFAR10
bpdKLbpdKL
VAE0.306±0.04117.9±0.33.74±0.01263.0±4.0
BIVA0.302±0.0713e-4±0.02.85±0.022e-3±0.0
IVAE0.403±0.09628.9±0.73.48±0.05233.0±7.0
HVAE0.315±0.0676e-5±0.04.55±0.021e-3±0.0
HVAE+RL0.305±0.08941.2±0.44.36±0.03265.0±8.0
LVAE0.313±0.0509e-4±0.02.91±0.032e-3±0.0
LVAE+RL0.335±0.07232.1±0.53.21±0.07181.0±6.0
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.429, + 0.271, + 0.444 + ], + "angle": 0, + "content": "4.2. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.472, + 0.745 + ], + "angle": 0, + "content": "Considering the highest-level latent representation \\( z_{L} \\) should ideally encapsulate the most abstract representation, such as categorical distinctions, we use top-level representations for linear classification. Additionally, given that \\( z_{L} \\) could be the most prone to posterior collapse among all levels, we estimate its information content \\( \\mathcal{I}(x,z_L) \\) via MINE. Table 1 reports the classification accuracy on various datasets and estimated mutual information. Applying RL to the hierarchical VAEs (HVAE+RL & LVAE+RL) significantly improves accuracy compared to their counterparts trained on ELBO (HVAE & LVAE), and also outperforms other methods, including IVAE, across all datasets. This demonstrates our approach's superior representation quality. Moreover, \\( \\widetilde{\\mathcal{I}}(x,z_L) \\) generally correlates classification performance, with our methods enabling higher mutual information in the same backbone models than the baselines in most cases, showing that our method extracts rich information from data. Notably, HVAE+RL yields significantly high \\( \\mathcal{I}(x,z_L) \\) on complex datasets like CIFAR100 and TinyImageNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.472, + 0.902 + ], + "angle": 0, + "content": "In Table 2, we present negative log-likelihood scores in bpd, where a lower bpd indicates better marginal likelihood estimation, along with KL divergences at the highest layer. Intriguingly, we find no direct correlation between the performance in estimating marginal log-likelihood \\(\\log p(x)\\) using ELBO and the representation learning efficacy, as gauged by accuracy and \\(\\widehat{\\mathcal{I}}(x, z_L)\\) in Table 1. For instance, despite BIVA and LVAE's superior marginal likelihood estimation on CIFAR10, their performance in representation learning tasks lags behind IVAE and our methods. This observation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.352 + ], + "angle": 0, + "content": "lends empirical support to our analysis in Section 3.1 that solely optimizing ELBO does not necessarily enhance hierarchical representation learning. Additionally, we note that a low KL divergence often signals poor downstream performance and reduced \\(\\widetilde{\\mathcal{I}}(x, z_L)\\), indicative of posterior collapse as defined in Definition 1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.361, + 0.684, + 0.377 + ], + "angle": 0, + "content": "4.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.895, + 0.52 + ], + "angle": 0, + "content": "To elucidate the efficacy of our method in learning informative hierarchical representations, we first examine the hierarchies learned by different approaches in Fig. 1 by projecting latent representations of different levels to the input space via the skip-generative path. Fig. 1 shows training with RL effectively mitigates posterior collapse, yielding a more informative latent hierarchy. This enhancement in hierarchical representation is further evident in Fig. 2, reinforcing the conclusions drawn in Section 3.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.896, + 0.703 + ], + "angle": 0, + "content": "An interesting property of hierarchical VAEs is their explainable latent space, which we probe using t-SNE and latent traversal at the topmost level for generation, as shown in Fig. 5. The results demonstrate notable improvements achieved by applying RL on mapping inputs to an explainable semantic space, to which the improvement of performance in linear classification (Table 1) can be attributed. Furthermore, our exploration into latent traversal sheds light on the explainability of the latent space, with individual latent dimensions corresponding to specific abstract features like widths and positions of hollow parts, thus underscoring the interpretability of our learned representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.655, + 0.728 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Total number of levels. We investigate the impact of varying \\( L \\) in hierarchical VAEs on downstream task performance using representations from the topmost latent variable in Fig. 6. We observe that all baselines suffer from classification performance degeneracy with increasing latent levels: posterior collapses largely impair downstream task performance. In comparison, our methods are much more stable and achieve superior performance across all level number settings, indicating its robustness. More importantly, these results suggest our approach enables the possibility of learning a higher hierarchy of latent representation." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22952" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.275, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.088, + 0.462, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.222, + 0.275, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.222, + 0.462, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.428 + ], + "angle": 0, + "content": "Figure 5. Panels showing the t-SNE and latent traversal generation on the highest latent variable in FashionMNIST, for vanilla HVAE (top) and HVAE+RL(bottom). The anchor point (original input) for latent traversal is bounded in red in grid center. Traversals are spaced by inverse Gaussian cdf to align with the prior distribution." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.443, + 0.278, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.443, + 0.468, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.58, + 0.468, + 0.594 + ], + "angle": 0, + "content": "Figure 6. Classification acc. of hierarchical VAEs of different levels." + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.612, + 0.454, + 0.626 + ], + "angle": 0, + "content": "Table 3. Classification acc. of different representation source." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.63, + 0.468, + 0.697 + ], + "angle": 0, + "content": "
ObjectiveRepre. sourceFashionMNISTCIFAR10
HVAELVAEHVAELVAE
ELBOzLonly10.73±0.0819.70±0.2110.40±0.0515.32±0.10
full z79.96±0.2380.25±0.2750.09±0.6749.87±0.39
RLzLonly78.23±0.1378.48±0.1546.46±0.1546.35±0.17
full z84.56±0.2584.77±0.3052.87±0.5452.89±0.48
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Latent representation source. The substantial cumulative dimension of all hierarchical latent variables \\(\\mathbf{z}\\), while potentially having greater representation capacity, may not be practical for all tasks. To explore this, we compare in Table 3 the downstream task performance of representations sourcing from the full \\(\\mathbf{z}\\) versus the most abstract topmost latent representation \\(z_{L}\\) to assess if \\(z_{L}\\) can maintain performance comparable to full \\(\\mathbf{z}\\). We observe that with RL, models effectively retain comparable classification performance using just \\(z_{L}\\), showing efficient learning of key abstract information at the topmost layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Discount factor \\(\\gamma\\). Exploring the impact of focusing solely on the current step's reward, we set the discount factor \\(\\gamma\\) to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.213 + ], + "angle": 0, + "content": "0 in our method. Besides, we ablate two typical settings of \\(\\gamma\\), 0.9 and 0.98, in the Q-value function to assess robustness. As in Table 4, models using \\(Q(s_{t},a_{t})\\) for step-wise optimization outperform those relying only on \\(r(s_{t},a_{t})\\), highlighting the benefits in downstream tasks of considering future accumulative rewards, i.e., regularizing dependencies between different levels' latent representations. Moreover, the stable performance across \\(\\gamma\\) confirms our approach's robustness." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.219, + 0.892, + 0.247 + ], + "angle": 0, + "content": "Table 4. Classification acc. of RL using different discount factors \\(\\gamma\\), where \\(\\gamma = 0\\) means we only maximize \\(r(s_{t},a_{t})\\) at time step \\(t\\)." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.25, + 0.89, + 0.346 + ], + "angle": 0, + "content": "
ObjectiveγFashionMNISTCIFAR10
HVAELVAEHVAELVAE
r(st, at)075.63±0.1175.52±0.1041.91±0.1542.16±0.13
Q(st, at)0.878.03±0.1677.98±0.2346.45±0.3046.42±0.27
Q(st, at)0.8578.11±0.2478.34±0.1945.89±0.2445.97±0.31
Q(st, at)0.978.23±0.1378.48±0.1546.46±0.1546.35±0.17
Q(st, at)0.9577.95±0.1978.53±0.1646.21±0.2146.25±0.25
Q(st, at)0.9878.01±0.1078.28±0.1746.31±0.2046.37±0.19
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.352, + 0.749, + 0.368 + ], + "angle": 0, + "content": "5. Limitation and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.892, + 0.619 + ], + "angle": 0, + "content": "Limitation and Future work. Though the (hierarchical) VAEs have advantages in modeling flexibility and sampling speed compared to other deep generative models [92] and are the most suitable models to demonstrate our idea with a theoretical interpretation, hierarchical VAE-based methods' application on downstream representation tasks could be somewhat outdated recently. Nevertheless, it's noteworthy that our idea of training hierarchical models with RL is not exclusively limited to hierarchical VAEs. Instead, it holds the potential when extended to general hierarchical models like diffusion models [40, 55], which feature more levels of latent representation and employ a fixed, non-trainable encoder for the efficient loss computation as independent terms over the hierarchy [61]. Our approach may be extended to learn a diffusion model with a trainable encoder, which may potentially enhance their representation capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.895, + 0.83 + ], + "angle": 0, + "content": "Conclusion. In this paper, we investigate the unsupervised representation learning with hierarchical VAEs from the perspective of information theory. We identify an urgent need to apply reinforcement learning to learn a high-quality hierarchy. The learned hierarchical representations have shown their superiority in improving the downstream task performance and mitigating the notorious posterior collapse. Additionally, an interesting finding is that learning a better ELBO (original training objective of hierarchical VAEs) is not necessary for learning a better representation, which has been supported by both our theoretical analysis and empirical results. Beyond hierarchical VAEs, our method may inspire future works to apply reinforcement learning to learn a hierarchical representation in time ahead." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.836, + 0.894, + 0.896 + ], + "angle": 0, + "content": "Acknowledgment. This research is supported by the National Research Foundation, Singapore, under its Competitive Research Programme (Grant No. NRF-CRP23-2019-0006)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22953" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.091, + 0.173, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Korbinian Abstreiter, Sarthak Mittal, Stefan Bauer, Bernhard Scholkopf, and Arash Mehrjou. Diffusion-based representation learning. arXiv preprint arXiv:2105.14257, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.472, + 0.2 + ], + "angle": 0, + "content": "[2] Alexander A. Alemi, Ian Fischer, Joshua V. Dillon, and Kevin Murphy. Deep variational information bottleneck. 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In ICLR, 2022." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "22956" + } + ] +] \ No newline at end of file diff --git a/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/303e0d84-56db-4046-87a5-f6c50e1e3b69_origin.pdf b/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/303e0d84-56db-4046-87a5-f6c50e1e3b69_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aa84d6533d449c87244fca477ce731ea0479a220 --- /dev/null +++ b/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/303e0d84-56db-4046-87a5-f6c50e1e3b69_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a623f5e66ba65c450a9a74f3bcd80683d119a103612a1c3a8f118bf20e121576 +size 4875148 diff --git a/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/full.md b/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8869f0a173224595fd9910c7766f868ca03b0133 --- /dev/null +++ b/2024/Improving Unsupervised Hierarchical Representation with Reinforcement Learning/full.md @@ -0,0 +1,476 @@ +# Improving Unsupervised Hierarchical Representation with Reinforcement Learning + +Ruyi An $^{1*}$ Yewen Li $^{1*†}$ Xu He $^{3}$ Pengjie Gu $^{1}$ Mengchen Zhao $^{4}$ Dong Li $^{3}$ Jianye Hao $^{3}$ Chaojie Wang $^{1,2}$ Bo An $^{1,2}$ Mingyuan Zhou $^{5}$ $^{1}$ Nanyang Technological University + $^{2}$ Skywork AI, Singapore + $^{3}$ Huawei Noah's Ark Lab + $^{4}$ South China University of Technology + $^{5}$ The University of Texas at Austin + +https://github.com/ruyianry/rep_hierarchy_r1 + +# Abstract + +Learning representations to capture the very fundamental understanding of the world is a key challenge in machine learning. The hierarchical structure of explanatory factors hidden in data is such a general representation and could be potentially achieved with a hierarchical VAE. However, training a hierarchical VAE always suffers from the "posterior collapse", where the data information is hard to propagate to the higher-level latent variables, hence resulting in a bad hierarchical representation. To address this issue, we first analyze the shortcomings of existing methods for mitigating the posterior collapse from an information theory perspective, then highlight the necessity of regularization for explicitly propagating data information to higher-level latent variables while maintaining the dependency between different levels. This naturally leads to formulating the inference of the hierarchical latent representation as a sequential decision process, which could benefit from applying reinforcement learning (RL). Aligning RL's objective with the regularization, we first introduce a skip-generative path to acquire a reward for evaluating the information content of an inferred latent representation, and then the developed $Q$ -value function based on it could have a consistent optimization direction of the regularization. Finally, policy gradient, one of the typical RL methods, is employed to train a hierarchical VAE without introducing a gradient estimator. Experimental results firmly support our analysis and demonstrate that our proposed method effectively mitigates the posterior collapse issue, learns an informative hierarchy, acquires explainable latent representations, and significantly outperforms other hierarchical VAE-based methods in downstream tasks. + +# 1. Introduction + +Deriving meaningful representations of data with minimal supervision is a central challenge in machine learn + +![](images/f0a0c0dad670a851adee2a7c6dcad7b3dd709e897f20f156b6b1dec325c4e954.jpg) +Figure 1. Visualization of different levels' latent representations of hierarchical VAEs on FashinMNIST and CelebA [53] to demonstrate the learned hierarchical structure. HVAE fails to learn a 5-level hierarchy, where higher-level latent representations display posterior collapse, collapsing into the same modes of "clothing" and "female faces" regardless of the input. For IVAE, reconstructions of certain consecutive layers appear highly similar, suggesting a disrupted hierarchy. In contrast, our method preserves detailed information of inputs at low levels and captures increasingly abstract semantics at higher levels, mitigating posterior collapse and establishing an informative hierarchy. + +![](images/d0f2e8272e6f37b60b40f429d294b3fbbcb29ad590a5a5207fdb6f2cbb504e27.jpg) + +ing [5], while existing research has predominantly concentrated on the discriminative approach [10] that relies on meticulously crafted preprocessing pipelines like pretext tasks [22, 30, 62, 65, 95] and data augmentations [3, 59]. Methods such as contrastive learning [8, 9, 11, 12, 14-16, 27, 29, 32, 34, 36, 49, 87, 97, 98] exemplify the success of this discriminative approach. However, representations derived from these methods are only limited to tasks invariant to the preprocessing pipelines [24], e.g. representations learned with the random cropping data augmentation cannot be applied to pixel-level localization tasks [83, 84], limiting their broader applicability. To transcend these confines, Bengio et al. [5] advocate for the pursuit of a universal and fundamental understanding of the world-a "general-purpose prior"-enabling the direct learning of representations without prior knowledge or assumptions about downstream tasks. Such representations could be learned by generative ap + +![](images/bfb37a6f44c78cc518baaabae97d79fc887101545bbd4663c1803d908c0d1b72.jpg) +Figure 2. Absolute Pearson's correlation between data representations of the inference network of a hierarchical VAE trained on FashionMNIST and another trained on MNIST [48], given the same data point from FashionMNIST. Our method enables the model to learn low-level information shared on different datasets and high-level semantic information in a hierarchical manner. + +proaches [47, 79], which utilize a deep generative model [21, 31, 40, 43, 68, 81] to capture the posterior distribution of the underlying explanatory factors in the observed data, i.e., the general-purpose prior, such as the hierarchical structure [76, 85, 86], disentanglement [38], and temporal and spatial coherence [71]. In this work, we focus on one specific aspect of this general-purpose prior, the hierarchical structure of data, which could be potentially achieved by learning a hierarchy of multi-level abstract latent representations with a hierarchical VAE [5, 79]. + +However, actualizing a meaningful hierarchical structure with a hierarchical VAE faces a considerable issue named "posterior collapse" [51, 57, 76], where the data information fails to be propagated to higher-level latent variables. Specifically, their posterior distribution $q_{\phi}(z|x)$ would be equal to an uninformative prior distribution $p(z)$ [13, 51, 82], undermining hierarchical VAEs' capability to capture meaningful representations. Existing literature proposing mitigation approaches for posterior collapse mainly focuses on two aspects: the limited capacity of the model architecture [19, 20, 57, 67, 76, 80] and the improper training objective [20, 41, 51, 70, 88]. However, our theoretical analysis from the perspective of information theory [18] presented in Section 3.1 suggests that current methodologies focusing on model architectures fail to explicitly enforce regularization on the inference of higher-level latent variables, where posterior collapse may still occur; and approaches targeting training objectives might disrupt the hierarchical dependencies between latent variables, compromising the model's structural integrity. Experimental results for better understanding can be seen in Figs. 1 and 2. These limitations contribute to the significant lag in the quality and performance of learned representation using hierarchical VAEs and have resulted in their limited adoption in representation learning tasks recently [47, 79]. + +To tackle the issue of posterior collapse that hinders acquiring an informative hierarchical latent representation, where different levels' latent representations are inferred sequentially from inputs and high-level latent representations are reliant on the abstraction of low-level ones, it is imperative to consider not only the information content of an inferred single-level latent variable but also its impact on subsequent, higher-level latent variables. This naturally inspires us to formulate the inference of the hierarchical latent + +representation as a sequential decision process. Inspired by the huge success of reinforcement learning (RL) in learning a high-quality sequence, we tried to apply RL to the learning of a hierarchical VAE for a better hierarchical latent representation. Please note that although some methods have also successfully introduced RL into tasks related to generative models [6, 50, 94], none of these methods can be directly applied to train a hierarchical VAE with a focus on learning informative hierarchical latent presentations. A detailed discussion can be found in Appendix A.3. + +Overall, the contribution of this work could be summarized as follows: + +- We highlight limitations of existing approaches of addressing posterior collapse for an informative hierarchical latent representation from an information theory perspective and appeal for more effective regularization of the inference process to explicitly propagate data information to higher-level latent variables and maintain the dependency between different levels. To our knowledge, this work is the first to conceptualize the hierarchical VAE's inference as a sequential decision process and employ an RL approach, specifically policy gradient, to regularize this process. Our method is broadly applicable to both primary types of hierarchical VAEs: top-down and bottom-up structures; +- Technically, we set up an RL formulation tailored to hierarchical VAEs training, notably with a skip-generative path that skips its lower levels' latent variables by marginalization to acquire a reward assessing the information content of the inferred latent variables without introducing additional networks or modules; then, the Q-value function developed based on it could have a consistent optimization direction of the regularization; +- Experiments demonstrate the mitigation of the posterior collapse, learned informative hierarchy, explanation ability of latent representations, and superior performance in VAE-based representation learning tasks. + +# 2. Preliminaries + +# 2.1. Hierarchical Variational Autoencoder + +An $L$ -layer hierarchical VAE is an extension of the vanilla VAE [43, 68], where the generative process is extended to multi-step generation, formulated as $p_{\theta}(\boldsymbol{x}, \boldsymbol{z}_{1:L}) = p_{\theta}(\boldsymbol{x} | \boldsymbol{z}_1) p_{\theta}(\boldsymbol{z}_L) \prod_{l=1}^{L-1} p_{\theta}(\boldsymbol{z}_l | \boldsymbol{z}_{l+1})$ . The $p_{\theta}(\boldsymbol{z}_L)$ is typically modeled as a multivariate Gaussian distribution $\mathcal{N}(\mathbf{0}, \mathbf{I})$ and $\theta$ represents the parameters of the decoder. The inference process of hierarchical VAEs could be implemented in two main approaches, bottom-up (BU) and top-down (TD): + +$$ +\mathrm {B U}: q _ {\phi} (\mathbf {z} | \boldsymbol {x}) = q _ {\phi} (\boldsymbol {z} _ {1} | \boldsymbol {x}) \prod_ {l = 2} ^ {L} q _ {\phi} (\boldsymbol {z} _ {l} | \boldsymbol {z} _ {l - 1}, \boldsymbol {x}), \tag {1} +$$ + +$$ +\mathrm {T D}: q _ {\phi} (\mathbf {z} | \boldsymbol {x}) = q _ {\phi} (\boldsymbol {z} _ {L} | \boldsymbol {x}) \prod_ {l = L} ^ {2} q _ {\phi} (\boldsymbol {z} _ {l - 1} | \boldsymbol {z} _ {l}, \boldsymbol {x}), \tag {2} +$$ + +where $\phi$ represents the parameters of the encoder. We provide a demonstration of these processes in Fig. 3. As + +![](images/f67f695941115d423416945506a76c7863b94226535c9aa428582eb4fe8b9100.jpg) + +![](images/efac10a82d11aa145427c8c7166ae6374dee01de8fa928c5ecf054e6beec0491.jpg) +(a) VAE +(c) Bottom-up (BU) inference +Figure 3. Probabilistic graphical illustration of VAE and hierarchical VAE during inference and generation. Solid lines $(\rightarrow)$ denote inference while dashed lines $(\dashrightarrow)$ denote generation. + +![](images/dad2c9bb4e7a40ab12dfce5edf5341a84fcd3c297eb78dbdd89148b42b93ef6d.jpg) +(b) Generation + +![](images/ec581b4a559da48fb84cc4fd6d08b40caaea7b10c995e206fd7a1fd5b5ed799e.jpg) +(d) Top-down (TD) inference + +the inference process is to produce a sequence of latent variables step by step, we denote a hierarchy $\mathbf{z}^{1:T} = \{ \mathbf{z}^1, \dots, \mathbf{z}^t, \dots, \mathbf{z}^T \}$ , where $T = L$ . In BU inference scheme, $\mathbf{z}^{1:T} = \{ \mathbf{z}_1, \dots, \mathbf{z}_t, \dots, \mathbf{z}_L \}$ ; in TD inference scheme, $\mathbf{z}^{1:T} = \{ \mathbf{z}_L, \dots, \mathbf{z}_t, \dots, \mathbf{z}_1 \}$ . For brevity, we use $\mathbf{z}$ to represent $\mathbf{z}^{1:T}$ in the following parts. Additionally, we introduce $j$ for representing the lower level variable $\mathbf{z}_j$ w.r.t. $\mathbf{z}^t$ defined by + +$$ +j = \left\{ \begin{array}{l l} t - 1, & \text {i n B U h i e r a c h i c a l V A E ,} \\ T - t, & \text {i n T D h i e r a c h i c a l V A E .} \end{array} \right. \tag {3} +$$ + +The training objective of a hierarchical VAE is to maximize the variational evidence lower bound (ELBO), denoted as $\mathcal{L}_{\pmb{x}}$ , of the training data's marginal log-likelihood $\log p(\pmb{x})$ by jointly updating the parameters $\theta$ and $\phi$ , expressed as: + +$$ +\begin{array}{l} \mathcal {L} _ {\boldsymbol {x}} = \log p (\boldsymbol {x}) - D _ {\mathrm {K L}} \left[ q _ {\phi} (\mathbf {z} | \boldsymbol {x}) \| p _ {\theta} (\mathbf {z} | \boldsymbol {x}) \right] \tag {4} \\ = \mathbb {E} _ {\mathbf {z} \sim q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log p _ {\theta} (\mathbf {x} | \mathbf {z}) \right] - D _ {\mathrm {K L}} \left[ q _ {\phi} (\mathbf {z} | \mathbf {x}) \| p (\mathbf {z}) \right], \\ \end{array} +$$ + +where $D_{\mathrm{KL}}(\cdot ||\cdot)$ refers to the Kullback-Leibler (KL) divergence. Defining $q_{\phi}(z_1|z_0,x)\coloneqq q_{\phi}(z_1|x)$ and $p_{\theta}(z_L|z_{L + 1})\coloneqq p_{\theta}(z_L)$ , for BU and TD hierarchical VAEs, the respective detailed expressions of their ELBOs are: + +$$ +\begin{array}{l} \mathrm {B U}: \mathcal {L} _ {\boldsymbol {x}} = \mathbb {E} _ {q _ {\phi} (\boldsymbol {z} | \boldsymbol {x})} \left[ \log p _ {\theta} (\boldsymbol {x} | \boldsymbol {z} _ {1}) \right] \tag {5} \\ - \sum_ {l = 1} ^ {L} D _ {\mathrm {K L}} \left[ \left(q _ {\phi} \left(\boldsymbol {z} _ {l} \mid \boldsymbol {z} _ {l - 1}, \boldsymbol {x}\right) \| p _ {\theta} \left(\boldsymbol {z} _ {l} \mid \boldsymbol {z} _ {l + 1}\right)\right) \right], \\ \end{array} +$$ + +$$ +\begin{array}{l} \mathrm {T D}: \mathcal {L} _ {\boldsymbol {x}} = \mathbb {E} _ {q _ {\phi} (\boldsymbol {z} | \boldsymbol {x})} \left[ \log p _ {\theta} (\boldsymbol {x} | \boldsymbol {z} _ {1}) \right] \tag {6} \\ - \sum_ {l = 1} ^ {L} D _ {\mathrm {K L}} \left[ \left(q _ {\phi} \left(\boldsymbol {z} _ {l} \mid \boldsymbol {z} _ {l + 1}, \boldsymbol {x}\right) \| p _ {\theta} \left(\boldsymbol {z} _ {l} \mid \boldsymbol {z} _ {l + 1}\right)\right) \right]. \\ \end{array} +$$ + +After convergence, we could extract level $l$ 's latent representation by the maximum a posteriori (MAP) estimate + +tion of the learned latent variables $\mathbf{z}_l$ , defined as $\mathbf{z}_l^* = \arg \max_{\mathbf{z}_l} q_{\phi}(\mathbf{z}_l | \mathbf{x})$ [5, 43]. + +However, training hierarchical VAEs often suffers from the issue known as posterior collapse, which can be formally defined as follows. + +Definition 1 (posterior collapse [7, 13, 82, 88]). Given a hierarchical VAE $p(\pmb{x}, \pmb{z}; \theta, \phi)$ , paramters' value $\phi = \hat{\phi}$ , $\theta = \hat{\theta}$ , and for any data $\pmb{x}$ in a dataset $\mathcal{D}_{\pmb{x}} = \{\pmb{x}_1, \pmb{x}_2, \dots, \pmb{x}_N\}$ , the posterior of inference step $t$ 's latent variable $\pmb{z}^t$ collapses if + +$$ +q _ {\phi} \left(\boldsymbol {z} ^ {t} \mid \boldsymbol {z} ^ {t - 1}, \boldsymbol {x}; \hat {\phi}\right) = p _ {\theta} \left(\boldsymbol {z} ^ {t} \mid \boldsymbol {z} _ {j + 2}; \hat {\theta}\right), \forall \boldsymbol {x} \in \mathcal {D} _ {\boldsymbol {x}}. \tag {7} +$$ + +The posterior collapse issue mainly occurs in higher-level latent variables of hierarchical VAEs. Stochastic latent variables $\mathbf{z}$ can be manually divided into lower-level variables, $z_{< k} = \{z_1,\dots,z_{k - 1}\}$ and higher-level ones, $z_{\geq k} = \{z_k,\dots,z_L\}$ where $k\in \{2,\ldots ,L\}$ . Though $z_{< k}$ may not suffer from posterior collapse that could encode sufficient information to reconstruct the inputs well, the corresponding high-level stochastic latent variables $\mathbf{z}_{\geq k}$ could be inclined to collapse into priors, i.e., $q_{\phi}(z_{\geq k}|\boldsymbol {x})\approx p_{\theta}(z_{\geq k})$ . An illustration can be seen in Fig. 1. Consequently, these higher-level posteriors will hold limited relevance to its input $\boldsymbol{x}$ , resulting in non-informative representations. + +# 2.2. Reinforcement Learning + +We consider a standard RL setup in continuous action space and discrete timesteps, formalized as a Markov decision process (MDP) defined by a tuple $\langle S, \mathcal{A}, P, r \rangle$ [33, 52, 72, 94]. Here, the state space $S$ and action space $\mathcal{A}$ are continuous, the state transition probability function $P: S \times \mathcal{A} \to \Delta(S)$ represents the probability density of the next state $s_{t+1} \in S$ given the current state $s_t \in S$ and action $a_t \in \mathcal{A}$ , and $r: S \times \mathcal{A} \to \mathbb{R}$ denotes the reward function on each transition. + +At each time step $t \in \{1, 2, \dots, T\}$ , an agent observes a state $s_t \in S$ , takes an action $a_t \in \mathcal{A}$ , and receives a scalar reward $r_t: S \times \mathcal{A} \to \mathbb{R}$ . The state $s_t$ could be described in various ways, such as the entire history of the observations $s_t = (o_1, \dots, o_t)$ [94] or only the current observation $s_t = o_t$ [33]. An agent's behavior could be defined by a policy $\pi(a_t | s_t)$ , which maps states to a probability distribution over actions. The return at time step $t$ is defined as the sum of the discounted future reward $R_t = \sum_{i=t}^{T} \gamma^{(i-t)} r(s_i, a_i)$ with a discount factor $\gamma \in (0, 1)$ . The expectation of the return could be flexibly formulated by the Q-value function $Q^\pi(s_t, a_t)$ after taking an action $a_t$ in state $s_t$ and thereafter following policy $\pi$ : + +$$ +\begin{array}{l} Q ^ {\pi} \left(s _ {t}, a _ {t}\right) = \mathbb {E} _ {s _ {i > t} \sim P, a _ {i > t} \sim \pi} \left[ R _ {t} \mid s _ {t}, a _ {t} \right] \tag {8} \\ = r \left(s _ {t}, a _ {t}\right) + \gamma \mathbb {E} _ {s _ {t + 1} \sim P, a _ {t} \sim \pi} \left[ Q ^ {\pi} \left(s _ {t + 1}, a _ {t + 1}\right) \right], \\ \end{array} +$$ + +which not only considers the reward of the action to be taken on the current state but also its effect on the future decision process. Let us assume that drawing from $a_{t} \sim \pi (a_{t}|s_{t})$ can + +be realized with reparameterization as $a_{t} = f(s_{t},\epsilon_{t}),\epsilon_{t}\sim p(\epsilon)$ . We could directly apply the policy gradient method [52, 78, 94] on the model parameters $\Theta$ with gradient ascent to maximize the $Q^{\pi}(s_t,a_t)$ at a time step $t$ : + +$$ +\Theta \leftarrow \Theta + \nabla_ {\Theta} Q ^ {\pi} \left(s _ {t}, a _ {t}\right). \tag {9} +$$ + +We sum all time step $t$ 's policy gradient together to represent the optimization direction $\nabla_{\Theta}\mathcal{I}$ of the RL, expressed as + +$$ +\nabla_ {\Theta} \mathcal {J} \simeq \sum_ {t = 1} ^ {T} \mathbb {E} _ {s _ {t} \sim P, \epsilon_ {t} \sim p (\epsilon)} \nabla_ {\Theta} Q ^ {\pi} \left(s _ {t}, a _ {t}\right), a _ {t} = f \left(s _ {t}, \epsilon_ {t}\right). \tag {10} +$$ + +For the discussion on Related Works, we move it to Appendix A. + +# 3. Improving Unsupervised Hierarchical Representation with RL + +We first provide an analysis of the existing two major approaches mitigating posterior collapse for learning a hierarchical representation with a hierarchical VAE. However, we found that they either lack regularization for propagating data information to higher-level latent variables or break the dependency between different levels' latent variables. Therefore, to address these drawbacks, a better training objective from the perspective of information theory could naturally lead to an RL scheme with a proper design of the Q-value function as the regularization of latent representations. Finally, we develop an RL training scheme with the policy gradient method to train a hierarchical VAE. + +# 3.1. Analysis of Representation Learning with Hierarchical VAEs + +The aim of representation learning with a hierarchical VAE is to learn a hierarchy of latent variables $\mathbf{z}$ that could represent the input data $\mathbf{x}$ . We begin with rethinking how different approaches are affecting the representation learning with a hierarchical VAE. We first rewrite the ELBO from an information theory standpoint [18]: + +$$ +\begin{array}{l} \mathbb {E} _ {\boldsymbol {x} \sim p (\boldsymbol {x})} [ \operatorname {E L B O} (\boldsymbol {x}) ] \\ = \mathbb {E} _ {\boldsymbol {x} \sim p (\boldsymbol {x})} \left[ \mathbb {E} _ {\boldsymbol {z} \sim q _ {\phi} (\boldsymbol {z} | \boldsymbol {x})} \log p _ {\theta} (\boldsymbol {x} | \boldsymbol {z} _ {1}) \right] - \mathbb {E} _ {\boldsymbol {x} \sim p (\boldsymbol {x})} \left[ D _ {\mathrm {K L}} \left(q _ {\phi} (\boldsymbol {z} | \boldsymbol {x}) \| p (\boldsymbol {z})\right) \right] \\ = \mathcal {I} _ {p, q} (\boldsymbol {x}, \boldsymbol {z} _ {1}) - \mathcal {I} _ {q} (\boldsymbol {x}, \boldsymbol {z} _ {1}) - D _ {\mathrm {K L}} (q (\boldsymbol {z}) \| p (\boldsymbol {z})) - \mathcal {H} _ {p} (\boldsymbol {x}), \tag {11} \\ \end{array} +$$ + +where the mutual information between $x$ and $z$ under different distribution is defined by + +$$ +\begin{array}{l} \mathcal {I} _ {p, q} (\boldsymbol {x}, \boldsymbol {z} _ {1}) = \mathbb {E} _ {p (\boldsymbol {x}) q _ {\phi} \left(\boldsymbol {z} _ {1} \mid \boldsymbol {x}\right)} \left[ \log \frac {p (\boldsymbol {x} , \boldsymbol {z} _ {1})}{p (\boldsymbol {x}) q \left(\boldsymbol {z} _ {1}\right)} \right] \tag {12} \\ = \mathbb {E} _ {p (\boldsymbol {x}) q _ {\phi} \left(\boldsymbol {z} _ {1} \mid \boldsymbol {x}\right)} \left[ \log p _ {\theta} (\boldsymbol {x} \mid \boldsymbol {z} _ {1}) \right] - \mathbb {E} _ {p (\boldsymbol {x})} \left[ \log p (\boldsymbol {x}) \right], \\ \end{array} +$$ + +$$ +\begin{array}{l} \mathcal {I} _ {q} (\boldsymbol {x}, \boldsymbol {z} _ {1}) = \mathbb {E} _ {q (\boldsymbol {x}) q _ {\phi} (\boldsymbol {z} _ {1} | \boldsymbol {x})} \left[ \log \frac {q (\boldsymbol {x} , \boldsymbol {z} _ {1})}{q (\boldsymbol {x}) q (\boldsymbol {z} _ {1})} \right] \tag {13} \\ = \mathbb {E} _ {q (\boldsymbol {x}) q _ {\phi} (\boldsymbol {z} _ {1} | \boldsymbol {x})} \left[ \log q _ {\phi} (\boldsymbol {x} | \boldsymbol {z} _ {1}) \right] - \mathbb {E} _ {q (\boldsymbol {x})} \left[ \log q (\boldsymbol {x}) \right], \\ \end{array} +$$ + +where $q(x)$ is the training data's distribution and it is assumed to be equal to the true data distribution $p(\pmb{x})$ ; + +$p_{\theta}(\pmb {x}|z_1)$ and $q_{\phi}(\pmb {x}|z_{1})$ could be expressed by + +$$ +p _ {\theta} (\boldsymbol {x} \mid \boldsymbol {z} _ {1}) = \frac {p _ {\theta} \left(\boldsymbol {z} _ {1} \mid \boldsymbol {x}\right) p (\boldsymbol {x})}{q \left(\boldsymbol {z} _ {1}\right)} \tag {14} +$$ + +$$ +q _ {\phi} (\boldsymbol {x} \mid \boldsymbol {z} _ {1}) = \frac {q _ {\phi} (\boldsymbol {z} _ {1} \mid \boldsymbol {x}) q (\boldsymbol {x})}{q (\boldsymbol {z} _ {1})} \simeq \frac {q _ {\phi} (\boldsymbol {z} _ {1} \mid \boldsymbol {x}) p (\boldsymbol {x})}{q (\boldsymbol {z} _ {1})}. \tag {15} +$$ + +Thus, the target of the ELBO in Eq. 11 effectively becomes minimizing the gap between the bottom-most latent variable's posterior $q_{\phi}(\pmb{z}_1|\pmb{x})$ and its corresponding true posterior $p_{\theta}(\pmb{z}_1|\pmb{x})$ and meanwhile the posterior of higher-level latent variables $\{\pmb{z}_l\}_{l=1:L}$ are trained to be close to their respective priors by the $D_{\mathrm{KL}}[q(\mathbf{z})\| p(\mathbf{z})]$ term. + +Since the latent variables above $z_{1}$ do not receive direct regularization to maximize $\mathcal{I}(x, z_{l}), l > 1$ , it could potentially lead to the posterior collapse phenomenon. Therefore, approaches that only modify the model structure [25, 57, 76, 80] still do not impose additional regularization to higher-level latent variables in the training objective, where the posterior collapse could still occur. + +Existing regularization strategies in the literature aim to refine the posterior distribution in order to cultivate good representations [41, 51, 54]. These methods typically focus on the relationship between observed data $\mathbf{x}$ and a single-level latent variable $z^t$ , which could be interpreted as an additional regularization on the ELBO expressed as + +$$ +\mathcal {I} _ {q} (\boldsymbol {x}, \boldsymbol {z}) \simeq \sum_ {t = 1} ^ {T} \mathcal {I} _ {q} (\boldsymbol {x}, \boldsymbol {z} ^ {t}). \tag {16} +$$ + +However, by optimizing all latent variables $\{z^t\}_{t = 1:T}$ with a shared objective $\mathcal{I}(\pmb {x},\pmb{z}^t)$ simultaneously, these approaches may hurt the hierarchical dependency amongst them. This is due to the implicit incentive for all latent variables to assimilate, potentially undermining the hierarchical structure. Learning to generate a sequence $\{\pmb {x},\pmb {z}^1,\dots,\pmb {z}^T\}$ with only one loss after finishing generating the whole sequence could also bring the imbalance issue, where the concentration of optimization to the mediate items is not clear [94]. These limitations hinder the exploitation of the full capabilities inherent in hierarchical VAEs. + +We leave a detailed discussion for the above two approaches in Appendix B. + +In summary, an effective training scheme should maximize the information content hidden in latent variables of all layers, while maintaining the dependencies among latent variables. Specifically, the regularization on $z^t$ should account for not only $\mathcal{I}(\pmb{x},\pmb{z}^t)$ , but also the influence on the subsequent latent variables $\mathcal{I}(\pmb{x},\pmb{z}^i|\pmb{z}^{i - 1})$ , $i > t$ , i.e., + +$$ +\mathcal {I} _ {q} \left(\boldsymbol {x}, \boldsymbol {z} ^ {t: T}\right) = \sum_ {i = t} ^ {T} \mathcal {I} _ {q} \left(\boldsymbol {x}, \boldsymbol {z} ^ {i} \mid \boldsymbol {z} ^ {i - 1}\right). \tag {17} +$$ + +By incorporating a discount factor $\gamma \in (0,1)$ , which allocates greater weight to the mutual information with proximal latent variables, the regularization for $z^t$ becomes: + +$$ +\mathcal {L} _ {\mathcal {I}} \left(\boldsymbol {x}, \boldsymbol {z} ^ {t}\right) = \sum_ {i = t} ^ {T} \gamma^ {i - t} \mathcal {I} \left(\boldsymbol {x}, \boldsymbol {z} ^ {i} \mid \boldsymbol {z} ^ {i - 1}\right). \tag {18} +$$ + +Therefore, the optimization direction of learning the se + +![](images/987ce437da5c751f31358593159a817e7b4ca1bdc94cb0bb4adf3a287605433e.jpg) + +$$ +\overline {{r (s _ {t} , a _ {t}) = \mathbb {E} _ {\mathbf {z} \sim q _ {\phi} (z ^ {1 : t} | x)} \log p _ {\theta} (x | z ^ {t}) - D _ {\mathrm {K L}} [ q _ {\phi} (z ^ {1 : t} | x) | | p (z ^ {1 : t}) ]}} +$$ + +![](images/a6a31bb3fcf94a98fa8a5a06d37714ead8fd78c5660cfcb79800373c70ffa8e0.jpg) +Figure 4. Illustration of modeling the inference process of a hierarchical VAE as a sequential decision process (left) and the details of the elements of RL $s_t$ , $a_t$ , $s_{t+1}$ (right). A reward $r(s_t, a_t)$ is derived with the skip-generative path depicted in the gray box. + +quence $\{\pmb {x},\pmb {z}^1,\dots,\pmb {z}^T\}$ can then be expressed by + +$$ +\nabla_ {\phi , \theta} \mathcal {J} \simeq \sum_ {t = 1} ^ {T} \mathbb {E} _ {p (\boldsymbol {x}), q _ {\phi}, p _ {\theta}} \nabla_ {\phi , \theta} \mathcal {L} _ {\mathcal {I}} \left(\boldsymbol {x}, \boldsymbol {z} ^ {t}\right). \tag {19} +$$ + +The resemblance of the optimization direction to Eq. 10 naturally leads to formulating the learning of hierarchical VAE as a sequential decision process, prompting the application of RL methods. Particularly, we are driven to develop a proper Q-value function $Q(s_{t},a_{t})$ to play the role of the regularization $\mathcal{L}_{\mathcal{I}}(\boldsymbol {x},\boldsymbol{z}^t)$ to achieve a consistent expression of the two optimization objectives. + +# 3.2. Training Hierarchical VAEs with RL + +Inspired by the tremendous success of RL methods in stably propagating information along long Markov Decision chains that maximize the cumulative rewards tallied at every step, i.e., the Q-value $Q^{\pi}(s_t,a_t)$ in Eq. 8, we formulate the progressive inference process of an $L$ -layer hierarchical VAEs as an $L$ -step sequential decision process. Specifically, given an input $\pmb{x}$ from a training set $\mathcal{D}_{\pmb{x}}$ , we need a hierarchical VAE parameterized with $\{\theta ,\phi \}$ to produce a sequence $Y_{1:T} = \{\pmb {x},\pmb {z}^{1},\pmb {z}^{2},\dots,\pmb{z}^{T}\} ,T = L$ + +Now, we can set up the basic elements for training with RL. At each time step $t$ , the state $s_t$ is characterized as a tuple including the observed input and already produced latent variables $z^{1:t-1} = \{z^1, \dots, z^{t-1}\}$ up to the step: + +$$ +s _ {t} \triangleq \left\{\boldsymbol {x}, \boldsymbol {z} ^ {1: t - 1} \right\}, \tag {20} +$$ + +where $s_1 = \{x\}$ . After receiving a state $s_t$ , the encoder $q_{\phi}(\mathbf{z}|x)$ of the hierarchical model acts as the policy network $\pi (a_t|s_t)$ to produce the latent variable as an action: + +$$ +\pi_ {\phi} \left(a _ {t} \mid s _ {t}\right) \triangleq q _ {\phi} \left(\boldsymbol {z} ^ {t} \mid \boldsymbol {x}, \boldsymbol {z} ^ {1: t - 1}\right) = q _ {\phi} \left(\boldsymbol {z} ^ {t} \mid \boldsymbol {z} ^ {t - 1}, \boldsymbol {x}\right), \tag {21} +$$ + +$$ +a _ {t} \triangleq z ^ {t} \sim q _ {\phi} \left(z ^ {t} \mid z ^ {t - 1}, x\right). \tag {22} +$$ + +Once executing the $a_{t}$ , we will get to the next state according the state transition probability function $P$ , specified as + +$$ +P \left(s _ {t + 1} \mid s _ {t}, a _ {t}\right) \triangleq \left(\delta_ {\boldsymbol {x}}, \delta_ {\boldsymbol {z} ^ {1: t}}\right), \tag {23} +$$ + +which is deterministic and reflects the unchanged observed data $\pmb{x}$ and the inclusion of new inferred latent variables at the successor state. $\delta_v$ is a Dirac delta distribution that only manifests a non-zero impulse at $v$ . + +Reward function design. When getting such a transition $\{s_t, a_t, s_{t+1}\}$ , we need to design a reward function $r(s_t, a_t)$ . The principle of the design is to evaluate the information content $\mathcal{I}(\boldsymbol{x}, \boldsymbol{z}^t | \boldsymbol{z}^{t-1})$ hidden in the latent variable $\boldsymbol{z}^t$ that represents the inputs, then we could formulate the Q-value function to regularize $\boldsymbol{z}^t$ by $\sum_{i=t}^{T} \mathcal{I}(\boldsymbol{x}, \boldsymbol{z}^i | \boldsymbol{z}^{i-1})$ . We design a reward function $r(s_t, a_t)$ to evaluate the information between $\boldsymbol{x}$ and $\boldsymbol{z}^t$ as below: + +$$ +r \left(s _ {t}, a _ {t}\right) = \mathbb {E} _ {\mathbf {z} \sim q _ {\phi} \left(\mathbf {z} ^ {1: t} \mid \mathbf {x}\right)} \log p _ {\theta} (\mathbf {x} \mid \mathbf {z} ^ {t}) - D _ {\mathrm {K L}} \left[ q _ {\phi} \left(\mathbf {z} ^ {1: t} \mid \mathbf {x}\right) \| p \left(\mathbf {z} ^ {1: t}\right) \right], \tag {24} +$$ + +where $p_{\theta}(\boldsymbol{x}|\boldsymbol{z}^t)$ is a skip-generative path, expressed as + +$$ +p _ {\theta} (\boldsymbol {x} | \boldsymbol {z} ^ {t}) = \int_ {\boldsymbol {z} _ {1: j}} p _ {\theta} (\boldsymbol {x} | \boldsymbol {z} _ {1}) \prod_ {i = j} ^ {1} p _ {\theta} (\boldsymbol {z} _ {i} | \boldsymbol {z} _ {i + 1}), \boldsymbol {z} ^ {t} \sim q (\boldsymbol {z} ^ {t} | \boldsymbol {z} ^ {< t}, \boldsymbol {x}), +$$ + +in which $z_{1:j}$ are marginalized out by the integral. Kindly note that the skip-generative path $p_{\theta}(\pmb{x}|\pmb{z}^t)$ is different from the generative path in vanilla hierarchical VAEs, where $p_{\theta}(\pmb{x}|\pmb{z}^{1:t}) = p_{\theta}(\pmb{x}|\pmb{z}_1)$ after observing $z^{1:t}$ . The $r(s_t,a_t)$ based on the skip-generative path could empirically force the training on maximizing the mutual information between $\pmb{x}$ and $z^t$ after observing $z^{t-1}$ , expressed by + +$$ +\begin{array}{l} \mathbb {E} _ {p (\boldsymbol {x})} \left[ r \left(s _ {t}, a _ {t}\right) \right] \tag {25} \\ = \mathbb {E} _ {p (\boldsymbol {x}) q (\boldsymbol {z} ^ {1: t} | \boldsymbol {x})} \log p _ {\theta} (\boldsymbol {x} | \boldsymbol {z} ^ {t}) - \mathbb {E} _ {p (\boldsymbol {x})} D _ {\mathrm {K L}} \left[ q _ {\phi} \left(\boldsymbol {z} ^ {1: t} | \boldsymbol {x}\right) \| p (\boldsymbol {z} ^ {1: t}) \right] \\ = \mathcal {I} _ {p, q} (\boldsymbol {x}, \boldsymbol {z} ^ {t}) - \mathcal {I} _ {q} (\boldsymbol {x}, \boldsymbol {z} ^ {1}) - D _ {\mathrm {K L}} [ q (\boldsymbol {z} ^ {1: t}) | | p (\boldsymbol {z} ^ {1: t}) ] - \mathcal {H} _ {p} (\boldsymbol {x}) \\ \end{array} +$$ + +Therefore, as shown in Eq. 25, the reward function $r(s_{t},a_{t})$ is to evaluate how $\mathcal{I}(\pmb {x},\pmb{z}^t)$ is closer or larger than $\mathcal{I}(\pmb {x},\pmb{z}^{1})$ Thus, the reward function could be an approximate evaluation of $\mathcal{I}_q(\pmb {x},\pmb {z}^t |\pmb {z}^{t - 1})$ after observing the inferred $\pmb{z}^{t - 1}$ , i.e., $r(s_{t},a_{t})\simeq \mathcal{I}_{q}(\pmb {x},\pmb{z}^{t}|\pmb{z}^{t - 1})$ + +Q-value function. To explicitly add regularization on a current inferred latent variable $z^{t}$ ,s influence on its following latent variables $z^{>t}$ , we propose to maximize its corresponding Q-value, which considers not only its own reward $r(s_{t},a_{t})$ , but also the future accumulative rewards, i.e., + +$$ +\begin{array}{l} Q ^ {\pi} \left(s _ {t}, a _ {t}\right) = r \left(s _ {t}, a _ {t}\right) + \gamma \mathbb {E} _ {\pi} \left[ Q ^ {\pi} \left(s _ {t + 1}, a _ {t + 1}\right) \right] \\ = r \left(s _ {t}, a _ {t}\right) + \mathbb {E} _ {\pi} \left[ \sum_ {i = t + 1} ^ {T} \gamma^ {i - t} r \left(s _ {i}, a _ {i}\right) \right]. \tag {26} \\ \end{array} +$$ + +With the efficient reparameterization trick [43], we could do a single-sample based Monte Carlos (MC) estimation for the expectation of the Q-value function, i.e., $Q^{\pi}(s_t,a_t)\simeq \sum_{i = t}^{T}\gamma^{i - t}r(s_i,a_i)$ . Please note that the reward function is differentiable to the model's parameters, hence we could directly use gradient descent method [42, 69] to maximize the $Q_{\pi}(s_t,a_t)$ , where $\theta$ and $\phi$ are trained simultaneously. + +Therefore, at every time step $t$ , maximizing its corresponding Q-value function is approximately maximizing the mutual information between $x$ and $z^t$ and the influence of the inferred $z^t$ in the following latent variables $z^{t+1:T}$ that depends on it, expressed as: + +$$ +Q ^ {\pi} \left(s _ {t}, a _ {t}\right) \simeq \sum_ {i = t} ^ {T} \gamma^ {i - t} \mathcal {I} _ {q} \left(\boldsymbol {x}, \boldsymbol {z} ^ {i} \mid \boldsymbol {z} ^ {i - 1}\right) = \mathcal {L} _ {\mathcal {I}} \left(\boldsymbol {x}, \boldsymbol {z} ^ {t}\right), \tag {27} +$$ + +which is consistent with the expression of Eq. 18 and the analysis in Section 3.1. + +Finally, to learn a high-quality sequence $\{\pmb{x},\pmb{z}^1,\dots,\pmb{z}^T\}$ aligning with the optimization direction in Eq. 19, we define the optimization direction on the Q-value function: + +$$ +\nabla_ {\theta , \phi} \mathcal {J} \simeq \sum_ {t = 1} ^ {T} \mathbb {E} _ {s _ {i} \sim P, a _ {i} \sim \pi} \nabla_ {\theta , \phi} Q ^ {\pi} \left(s _ {t}, a _ {t}\right). \tag {28} +$$ + +As $a_{t}$ could be obtained by reparameterization and $Q^{\pi}(s_t, a_t)$ is differentiable to model parameters, we could implement the policy gradient by directly maximizing $Q^{\pi}(s_t, a_t)$ at every time step $t$ by Eq. 9, thereby eliminating the need for a gradient estimator like REINFORCE [89] and avoiding the high variance associated with these estimators [77]. We summarize the overall training scheme in Algorithm 1. + +Algorithm 1 Optimizing a hierarchical VAE with RL. +Input: A training dataset $\mathcal{D}_{\pmb{x}}$ training hyperparameters; +Output: An $L$ -layer hierarchical VAE parameterized with an encoder $q_{\phi}(\mathbf{z}|\mathbf{x})$ and a decoder $p_{\theta}(\pmb {x}|\mathbf{z})$ +Initialization: Randomly initialize the parameters $\theta ,\phi$ +for epoch $= 1$ to max_epochs do Sample a batch of $N$ training samples $\pmb{x}^n$ from $\mathcal{D}_x$ . for time step $t = 1$ to $L$ do for $i = t$ to $L$ do Follow Eq.22, but with reparameterization, to sample an action $a_i^n\sim \pi (a_i^n |s_i^n)$ Get reward $r(s_i^n,a_i^n)$ by Eq.24; end for Get $Q^{\pi}(s_t^n,a_t^n)\simeq \sum_{i = t}^{T}\gamma^{i - t}r(s_i^n,a_i^n)$ Update $\theta ,\phi$ using the policy gradient for the current time step $t$ by Eq.9; end for +end for + +# 4. Experiments + +Our experiments engage in comparisons with several hierarchical VAE variants and various unsupervised methods to assess if our method of training hierarchical VAEs with RL yields superior performance in 1) mitigating posterior + +collapse at higher latent representations, 2) learning a clear hierarchical representation, 3) attaining an explainable latent representation, and more importantly, 4) offering better representation than other hierarchical VAE-based unsupervised learning methods on downstream tasks. Additionally, we present several ablation studies to further evaluate different settings' influence on our method's performance. + +# 4.1. Experimental Setup + +Datasets: Our method is benchmarked on 5 datasets: FashionMNIST [91], CIFAR10 and CIFAR100 [44], TinyImageNet [46], and STL-10 [17]. Each method is trained using standard train splits and assessed on corresponding test splits. + +Evaluation metrics: For representation evaluation, we follow the commonly adopted downstream linear classification [5, 39, 63], using a linear support vector machine (SVM) [37] classifier on representations from frozen models. Classification accuracy is reported to measure linear separability, acting as a proxy for mutual information of representations with the labels. Additionally, we apply the MINE statistics network [4] to estimate the mutual information $\widetilde{\mathcal{I}}(x, z_L)$ , between input $x$ and the top latent variable $z_L$ . + +Baselines: We compare our method with two groups of baselines: i) those modifying the inference process without changing the training objective (ELBO); ii) those modifying the training objective to add more regularization on the inference process. For i, we include a BU hierarchical VAE (HVAE) powered with residual connections [35], a TD hierarchical VAE (LVAE) with a ladder inference [76], and a more sophisticated bidirectional structure hierarchical VAE (BIVA) [57]. For ii, to our best knowledge, the most relevant work to our method is informative hierarchical VAE (IVAE) [51], which introduces additional layer-wise regularization on latent representations of a hierarchical VAE. Additionally, we include a vanilla VAE (VAE) [43] and an adversarial autoencoder (AAE) [58] of single-level to assess the performance improvement brought by hierarchical structures. + +Implementation details: We apply our RL optimization approach to hierarchical VAEs with BU $(\mathbf{HVAE} + \mathbf{RL})$ and TD (LVAE+RL) inference schemes. For Fashion-MNIST, hierarchical models use latent dimensions of $\{128, 64, 32, 16, 8\}$ , and single-layer models use 8. For other image datasets, hierarchical models' latent dimensions are $\{128\text{conv}, 64\text{conv}, 256, 128, 64\}$ , and single-layer models have $\{64\}$ . The discount factor, $\gamma$ , is set to 0.9. Run on one NVIDIA A100 GPU with PyTorch [64], models are optimized using Adam optimizer [42] at a learning rate of 3e-4. Training epochs are set to 1000 for baselines and $1000 / L$ for our method, with outcomes averaged over 5 random seeds. + +Detailed experimental setup are in Appendix C. + +Table 1. Classification acc. and $\widetilde{\mathcal{I}}\left( {\mathbf{x},{\mathbf{z}}_{L}}\right)$ comparisons. Our methods' results are marked in purple. The best two results are in bold. + +
MethodFashionMNISTCIFAR10CIFAR100TinyImageNetSTL-10 (32 × 32-downsampled)
Acc.\( \widetilde{\mathcal{I}}(\boldsymbol{x},\boldsymbol{z}_L) \)Acc.\( \widetilde{\mathcal{I}}(\boldsymbol{x},\boldsymbol{z}_L) \)Acc.\( \widetilde{\mathcal{I}}(\boldsymbol{x},\boldsymbol{z}_L) \)Acc.\( \widetilde{\mathcal{I}}(\boldsymbol{x},\boldsymbol{z}_L) \)Acc.\( \widetilde{I}(\boldsymbol{x},\boldsymbol{z}_L) \)
AAE [58]72.11±0.274.08±0.6738.36±0.205.91±1.0317.56±0.456.19±0.958.73±0.583.37±0.6736.64±0.176.65±1.10
VAE [43]75.08±0.094.36±0.3539.98±0.056.32±0.6519.05±0.2013.76±1.858.92±0.363.76±1.2137.75±0.076.87±0.75
BIVA [57]28.67±0.643.48±0.4810.40±0.135e-9±0.001.07±0.058e-9±0.000.67±0.069e-8±0.0010.02±0.201.41±0.38
IVAE [51]76.25±0.302.44±0.5239.26±0.256.41±0.6919.49±0.338.91±0.968.07±0.693.92±0.9837.98±0.412.86±0.95
HVAE [35]10.73±0.080.31±0.0810.40±0.053e-8±0.001.21±0.107e-7±0.000.63±0.065e-10±0.0010.24±0.070.97±0.17
HVAE+RL(ours)78.23±0.135.01±0.7046.46±0.1511.39±1.2025.21±0.2117.01±2.4112.76±0.3911.88±2.8743.76±0.1510.93±1.73
LVAE [76]19.70±0.211.73±0.3215.32±0.105e-5±0.0010.38±0.891.04±0.394.77±0.470.54±0.1211.89±0.100.45±0.08
LVAE+RL(ours)78.48±0.154.37±0.5846.35±0.176.91±0.8625.41±0.209.00±1.1913.41±0.444.48±1.7141.86±0.2610.77±1.94
+ +Table 2. Density estimation in bits per dimension (bpd) [21] and KL divergence at the topmost level of hierarchical VAEs. + +
ModelFashionMNISTCIFAR10
bpdKLbpdKL
VAE0.306±0.04117.9±0.33.74±0.01263.0±4.0
BIVA0.302±0.0713e-4±0.02.85±0.022e-3±0.0
IVAE0.403±0.09628.9±0.73.48±0.05233.0±7.0
HVAE0.315±0.0676e-5±0.04.55±0.021e-3±0.0
HVAE+RL0.305±0.08941.2±0.44.36±0.03265.0±8.0
LVAE0.313±0.0509e-4±0.02.91±0.032e-3±0.0
LVAE+RL0.335±0.07232.1±0.53.21±0.07181.0±6.0
+ +# 4.2. Quantitative Results + +Considering the highest-level latent representation $z_{L}$ should ideally encapsulate the most abstract representation, such as categorical distinctions, we use top-level representations for linear classification. Additionally, given that $z_{L}$ could be the most prone to posterior collapse among all levels, we estimate its information content $\mathcal{I}(x,z_L)$ via MINE. Table 1 reports the classification accuracy on various datasets and estimated mutual information. Applying RL to the hierarchical VAEs (HVAE+RL & LVAE+RL) significantly improves accuracy compared to their counterparts trained on ELBO (HVAE & LVAE), and also outperforms other methods, including IVAE, across all datasets. This demonstrates our approach's superior representation quality. Moreover, $\widetilde{\mathcal{I}}(x,z_L)$ generally correlates classification performance, with our methods enabling higher mutual information in the same backbone models than the baselines in most cases, showing that our method extracts rich information from data. Notably, HVAE+RL yields significantly high $\mathcal{I}(x,z_L)$ on complex datasets like CIFAR100 and TinyImageNet. + +In Table 2, we present negative log-likelihood scores in bpd, where a lower bpd indicates better marginal likelihood estimation, along with KL divergences at the highest layer. Intriguingly, we find no direct correlation between the performance in estimating marginal log-likelihood $\log p(x)$ using ELBO and the representation learning efficacy, as gauged by accuracy and $\widehat{\mathcal{I}}(x, z_L)$ in Table 1. For instance, despite BIVA and LVAE's superior marginal likelihood estimation on CIFAR10, their performance in representation learning tasks lags behind IVAE and our methods. This observation + +lends empirical support to our analysis in Section 3.1 that solely optimizing ELBO does not necessarily enhance hierarchical representation learning. Additionally, we note that a low KL divergence often signals poor downstream performance and reduced $\widetilde{\mathcal{I}}(x, z_L)$ , indicative of posterior collapse as defined in Definition 1. + +# 4.3. Qualitative Results + +To elucidate the efficacy of our method in learning informative hierarchical representations, we first examine the hierarchies learned by different approaches in Fig. 1 by projecting latent representations of different levels to the input space via the skip-generative path. Fig. 1 shows training with RL effectively mitigates posterior collapse, yielding a more informative latent hierarchy. This enhancement in hierarchical representation is further evident in Fig. 2, reinforcing the conclusions drawn in Section 3.1. + +An interesting property of hierarchical VAEs is their explainable latent space, which we probe using t-SNE and latent traversal at the topmost level for generation, as shown in Fig. 5. The results demonstrate notable improvements achieved by applying RL on mapping inputs to an explainable semantic space, to which the improvement of performance in linear classification (Table 1) can be attributed. Furthermore, our exploration into latent traversal sheds light on the explainability of the latent space, with individual latent dimensions corresponding to specific abstract features like widths and positions of hollow parts, thus underscoring the interpretability of our learned representations. + +# 4.4. Ablation Study + +Total number of levels. We investigate the impact of varying $L$ in hierarchical VAEs on downstream task performance using representations from the topmost latent variable in Fig. 6. We observe that all baselines suffer from classification performance degeneracy with increasing latent levels: posterior collapses largely impair downstream task performance. In comparison, our methods are much more stable and achieve superior performance across all level number settings, indicating its robustness. More importantly, these results suggest our approach enables the possibility of learning a higher hierarchy of latent representation. + +![](images/ea7b4fb86aae653602389ce77b874991804951005029081ff8ab0dd9577bd564.jpg) + +![](images/b9143d653fa2cd04affcdac0c3d74936abf0d16fda6bd375c8ab4ae1827f29d4.jpg) + +![](images/dda5b4c17049ff3c632c6ecfd4c9b40e3ea6710aee516c1277a7ba56626a54bd.jpg) +Figure 5. Panels showing the t-SNE and latent traversal generation on the highest latent variable in FashionMNIST, for vanilla HVAE (top) and HVAE+RL(bottom). The anchor point (original input) for latent traversal is bounded in red in grid center. Traversals are spaced by inverse Gaussian cdf to align with the prior distribution. + +![](images/937cf7f78054e3e590112704c524e14123fc0a33be9429b0aa796604ffb8270b.jpg) + +![](images/ef4d5830fba17057e7f59d6f669ddd65473704db28c3eb4da53d9571f2a839d3.jpg) +Figure 6. Classification acc. of hierarchical VAEs of different levels. + +![](images/70656d968635ac0abcf7c965c878bc7fef2280bb4083959894f44bd1bb9502f8.jpg) + +Table 3. Classification acc. of different representation source. + +
ObjectiveRepre. sourceFashionMNISTCIFAR10
HVAELVAEHVAELVAE
ELBOzLonly10.73±0.0819.70±0.2110.40±0.0515.32±0.10
full z79.96±0.2380.25±0.2750.09±0.6749.87±0.39
RLzLonly78.23±0.1378.48±0.1546.46±0.1546.35±0.17
full z84.56±0.2584.77±0.3052.87±0.5452.89±0.48
+ +Latent representation source. The substantial cumulative dimension of all hierarchical latent variables $\mathbf{z}$ , while potentially having greater representation capacity, may not be practical for all tasks. To explore this, we compare in Table 3 the downstream task performance of representations sourcing from the full $\mathbf{z}$ versus the most abstract topmost latent representation $z_{L}$ to assess if $z_{L}$ can maintain performance comparable to full $\mathbf{z}$ . We observe that with RL, models effectively retain comparable classification performance using just $z_{L}$ , showing efficient learning of key abstract information at the topmost layer. + +Discount factor $\gamma$ . Exploring the impact of focusing solely on the current step's reward, we set the discount factor $\gamma$ to + +0 in our method. Besides, we ablate two typical settings of $\gamma$ , 0.9 and 0.98, in the Q-value function to assess robustness. As in Table 4, models using $Q(s_{t},a_{t})$ for step-wise optimization outperform those relying only on $r(s_{t},a_{t})$ , highlighting the benefits in downstream tasks of considering future accumulative rewards, i.e., regularizing dependencies between different levels' latent representations. Moreover, the stable performance across $\gamma$ confirms our approach's robustness. + +Table 4. Classification acc. of RL using different discount factors $\gamma$ , where $\gamma = 0$ means we only maximize $r(s_{t},a_{t})$ at time step $t$ . + +
ObjectiveγFashionMNISTCIFAR10
HVAELVAEHVAELVAE
r(st, at)075.63±0.1175.52±0.1041.91±0.1542.16±0.13
Q(st, at)0.878.03±0.1677.98±0.2346.45±0.3046.42±0.27
Q(st, at)0.8578.11±0.2478.34±0.1945.89±0.2445.97±0.31
Q(st, at)0.978.23±0.1378.48±0.1546.46±0.1546.35±0.17
Q(st, at)0.9577.95±0.1978.53±0.1646.21±0.2146.25±0.25
Q(st, at)0.9878.01±0.1078.28±0.1746.31±0.2046.37±0.19
+ +# 5. Limitation and Conclusion + +Limitation and Future work. Though the (hierarchical) VAEs have advantages in modeling flexibility and sampling speed compared to other deep generative models [92] and are the most suitable models to demonstrate our idea with a theoretical interpretation, hierarchical VAE-based methods' application on downstream representation tasks could be somewhat outdated recently. Nevertheless, it's noteworthy that our idea of training hierarchical models with RL is not exclusively limited to hierarchical VAEs. Instead, it holds the potential when extended to general hierarchical models like diffusion models [40, 55], which feature more levels of latent representation and employ a fixed, non-trainable encoder for the efficient loss computation as independent terms over the hierarchy [61]. Our approach may be extended to learn a diffusion model with a trainable encoder, which may potentially enhance their representation capacity. + +Conclusion. In this paper, we investigate the unsupervised representation learning with hierarchical VAEs from the perspective of information theory. We identify an urgent need to apply reinforcement learning to learn a high-quality hierarchy. The learned hierarchical representations have shown their superiority in improving the downstream task performance and mitigating the notorious posterior collapse. Additionally, an interesting finding is that learning a better ELBO (original training objective of hierarchical VAEs) is not necessary for learning a better representation, which has been supported by both our theoretical analysis and empirical results. Beyond hierarchical VAEs, our method may inspire future works to apply reinforcement learning to learn a hierarchical representation in time ahead. + +Acknowledgment. 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"Skywork AI, Singapore \n" + }, + { + "bbox": [ + 75, + 160, + 519, + 219 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 75, + 160, + 519, + 219 + ], + "type": "text", + "content": "Huawei Noah's Ark Lab \n" + }, + { + "bbox": [ + 75, + 160, + 519, + 219 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 75, + 160, + 519, + 219 + ], + "type": "text", + "content": "South China University of Technology \n" + }, + { + "bbox": [ + 75, + 160, + 519, + 219 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 75, + 160, + 519, + 219 + ], + "type": "text", + "content": "The University of Texas at Austin" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 175, + 220, + 414, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 220, + 414, + 232 + ], + "spans": [ + { + "bbox": [ + 175, + 220, + 414, + 232 + ], + "type": "text", + "content": "https://github.com/ruyianry/rep_hierarchy_r1" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 280, + 290, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 290, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 290, + 639 + ], + "type": "text", + "content": "Learning representations to capture the very fundamental understanding of the world is a key challenge in machine learning. The hierarchical structure of explanatory factors hidden in data is such a general representation and could be potentially achieved with a hierarchical VAE. However, training a hierarchical VAE always suffers from the \"posterior collapse\", where the data information is hard to propagate to the higher-level latent variables, hence resulting in a bad hierarchical representation. To address this issue, we first analyze the shortcomings of existing methods for mitigating the posterior collapse from an information theory perspective, then highlight the necessity of regularization for explicitly propagating data information to higher-level latent variables while maintaining the dependency between different levels. This naturally leads to formulating the inference of the hierarchical latent representation as a sequential decision process, which could benefit from applying reinforcement learning (RL). Aligning RL's objective with the regularization, we first introduce a skip-generative path to acquire a reward for evaluating the information content of an inferred latent representation, and then the developed " + }, + { + "bbox": [ + 46, + 280, + 290, + 639 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 280, + 290, + 639 + ], + "type": "text", + "content": "-value function based on it could have a consistent optimization direction of the regularization. Finally, policy gradient, one of the typical RL methods, is employed to train a hierarchical VAE without introducing a gradient estimator. Experimental results firmly support our analysis and demonstrate that our proposed method effectively mitigates the posterior collapse issue, learns an informative hierarchy, acquires explainable latent representations, and significantly outperforms other hierarchical VAE-based methods in downstream tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 643, + 128, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 128, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 128, + 656 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 663, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 288, + 687 + ], + "type": "text", + "content": "Deriving meaningful representations of data with minimal supervision is a central challenge in machine learn" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 306, + 257, + 432, + 385 + ], + "blocks": [ + { + "bbox": [ + 306, + 257, + 432, + 385 + ], + "lines": [ + { + "bbox": [ + 306, + 257, + 432, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 257, + 432, + 385 + ], + "type": "image", + "image_path": "f0a0c0dad670a851adee2a7c6dcad7b3dd709e897f20f156b6b1dec325c4e954.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 386, + 547, + 506 + ], + "lines": [ + { + "bbox": [ + 304, + 386, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 547, + 506 + ], + "type": "text", + "content": "Figure 1. Visualization of different levels' latent representations of hierarchical VAEs on FashinMNIST and CelebA [53] to demonstrate the learned hierarchical structure. HVAE fails to learn a 5-level hierarchy, where higher-level latent representations display posterior collapse, collapsing into the same modes of \"clothing\" and \"female faces\" regardless of the input. For IVAE, reconstructions of certain consecutive layers appear highly similar, suggesting a disrupted hierarchy. In contrast, our method preserves detailed information of inputs at low levels and captures increasingly abstract semantics at higher levels, mitigating posterior collapse and establishing an informative hierarchy." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 434, + 258, + 545, + 385 + ], + "blocks": [ + { + "bbox": [ + 434, + 258, + 545, + 385 + ], + "lines": [ + { + "bbox": [ + 434, + 258, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 434, + 258, + 545, + 385 + ], + "type": "image", + "image_path": "d0f2e8272e6f37b60b40f429d294b3fbbcb29ad590a5a5207fdb6f2cbb504e27.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 508, + 548, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 548, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 548, + 712 + ], + "type": "text", + "content": "ing [5], while existing research has predominantly concentrated on the discriminative approach [10] that relies on meticulously crafted preprocessing pipelines like pretext tasks [22, 30, 62, 65, 95] and data augmentations [3, 59]. Methods such as contrastive learning [8, 9, 11, 12, 14-16, 27, 29, 32, 34, 36, 49, 87, 97, 98] exemplify the success of this discriminative approach. However, representations derived from these methods are only limited to tasks invariant to the preprocessing pipelines [24], e.g. representations learned with the random cropping data augmentation cannot be applied to pixel-level localization tasks [83, 84], limiting their broader applicability. To transcend these confines, Bengio et al. [5] advocate for the pursuit of a universal and fundamental understanding of the world-a \"general-purpose prior\"-enabling the direct learning of representations without prior knowledge or assumptions about downstream tasks. Such representations could be learned by generative ap" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 261, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 261, + 703 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 261, + 703 + ], + "type": "text", + "content": "*Equal contribution, authors listed alphabetically by last name." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 60, + 703, + 246, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 703, + 246, + 712 + ], + "spans": [ + { + "bbox": [ + 60, + 703, + 246, + 712 + ], + "type": "text", + "content": "† Corresponding to: Yewen Li ." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22946" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 286, + 100 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 100 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 100 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 100 + ], + "type": "image", + "image_path": "bfb37a6f44c78cc518baaabae97d79fc887101545bbd4663c1803d908c0d1b72.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 108, + 287, + 174 + ], + "lines": [ + { + "bbox": [ + 46, + 108, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 287, + 174 + ], + "type": "text", + "content": "Figure 2. Absolute Pearson's correlation between data representations of the inference network of a hierarchical VAE trained on FashionMNIST and another trained on MNIST [48], given the same data point from FashionMNIST. Our method enables the model to learn low-level information shared on different datasets and high-level semantic information in a hierarchical manner." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 176, + 288, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 176, + 288, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 288, + 297 + ], + "type": "text", + "content": "proaches [47, 79], which utilize a deep generative model [21, 31, 40, 43, 68, 81] to capture the posterior distribution of the underlying explanatory factors in the observed data, i.e., the general-purpose prior, such as the hierarchical structure [76, 85, 86], disentanglement [38], and temporal and spatial coherence [71]. In this work, we focus on one specific aspect of this general-purpose prior, the hierarchical structure of data, which could be potentially achieved by learning a hierarchy of multi-level abstract latent representations with a hierarchical VAE [5, 79]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "type": "text", + "content": "However, actualizing a meaningful hierarchical structure with a hierarchical VAE faces a considerable issue named \"posterior collapse\" [51, 57, 76], where the data information fails to be propagated to higher-level latent variables. Specifically, their posterior distribution " + }, + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "type": "inline_equation", + "content": "q_{\\phi}(z|x)" + }, + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "type": "text", + "content": " would be equal to an uninformative prior distribution " + }, + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "type": "inline_equation", + "content": "p(z)" + }, + { + "bbox": [ + 46, + 301, + 289, + 601 + ], + "type": "text", + "content": " [13, 51, 82], undermining hierarchical VAEs' capability to capture meaningful representations. Existing literature proposing mitigation approaches for posterior collapse mainly focuses on two aspects: the limited capacity of the model architecture [19, 20, 57, 67, 76, 80] and the improper training objective [20, 41, 51, 70, 88]. However, our theoretical analysis from the perspective of information theory [18] presented in Section 3.1 suggests that current methodologies focusing on model architectures fail to explicitly enforce regularization on the inference of higher-level latent variables, where posterior collapse may still occur; and approaches targeting training objectives might disrupt the hierarchical dependencies between latent variables, compromising the model's structural integrity. Experimental results for better understanding can be seen in Figs. 1 and 2. These limitations contribute to the significant lag in the quality and performance of learned representation using hierarchical VAEs and have resulted in their limited adoption in representation learning tasks recently [47, 79]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "To tackle the issue of posterior collapse that hinders acquiring an informative hierarchical latent representation, where different levels' latent representations are inferred sequentially from inputs and high-level latent representations are reliant on the abstraction of low-level ones, it is imperative to consider not only the information content of an inferred single-level latent variable but also its impact on subsequent, higher-level latent variables. This naturally inspires us to formulate the inference of the hierarchical latent" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 191 + ], + "type": "text", + "content": "representation as a sequential decision process. Inspired by the huge success of reinforcement learning (RL) in learning a high-quality sequence, we tried to apply RL to the learning of a hierarchical VAE for a better hierarchical latent representation. Please note that although some methods have also successfully introduced RL into tasks related to generative models [6, 50, 94], none of these methods can be directly applied to train a hierarchical VAE with a focus on learning informative hierarchical latent presentations. A detailed discussion can be found in Appendix A.3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 192, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 547, + 216 + ], + "type": "text", + "content": "Overall, the contribution of this work could be summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 217, + 547, + 505 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 217, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 547, + 361 + ], + "type": "text", + "content": "- We highlight limitations of existing approaches of addressing posterior collapse for an informative hierarchical latent representation from an information theory perspective and appeal for more effective regularization of the inference process to explicitly propagate data information to higher-level latent variables and maintain the dependency between different levels. To our knowledge, this work is the first to conceptualize the hierarchical VAE's inference as a sequential decision process and employ an RL approach, specifically policy gradient, to regularize this process. Our method is broadly applicable to both primary types of hierarchical VAEs: top-down and bottom-up structures;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 361, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 547, + 456 + ], + "type": "text", + "content": "- Technically, we set up an RL formulation tailored to hierarchical VAEs training, notably with a skip-generative path that skips its lower levels' latent variables by marginalization to acquire a reward assessing the information content of the inferred latent variables without introducing additional networks or modules; then, the Q-value function developed based on it could have a consistent optimization direction of the regularization;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 456, + 547, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 547, + 505 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 547, + 505 + ], + "type": "text", + "content": "- Experiments demonstrate the mitigation of the posterior collapse, learned informative hierarchy, explanation ability of latent representations, and superior performance in VAE-based representation learning tasks." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 517, + 390, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 390, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 390, + 529 + ], + "type": "text", + "content": "2. Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 538, + 504, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 504, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 504, + 550 + ], + "type": "text", + "content": "2.1. Hierarchical Variational Autoencoder" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": "An " + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": "-layer hierarchical VAE is an extension of the vanilla VAE [43, 68], where the generative process is extended to multi-step generation, formulated as " + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\boldsymbol{x}, \\boldsymbol{z}_{1:L}) = p_{\\theta}(\\boldsymbol{x} | \\boldsymbol{z}_1) p_{\\theta}(\\boldsymbol{z}_L) \\prod_{l=1}^{L-1} p_{\\theta}(\\boldsymbol{z}_l | \\boldsymbol{z}_{l+1})" + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\boldsymbol{z}_L)" + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": " is typically modeled as a multivariate Gaussian distribution " + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0}, \\mathbf{I})" + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": " represents the parameters of the decoder. The inference process of hierarchical VAEs could be implemented in two main approaches, bottom-up (BU) and top-down (TD):" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 654, + 545, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 654, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 330, + 654, + 545, + 671 + ], + "type": "interline_equation", + "content": "\\mathrm {B U}: q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) = q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x}) \\prod_ {l = 2} ^ {L} q _ {\\phi} (\\boldsymbol {z} _ {l} | \\boldsymbol {z} _ {l - 1}, \\boldsymbol {x}), \\tag {1}", + "image_path": "1d5772c499c63ebdabff1f5362b955fa39077eb1d41331e5df5aefa037e1d40e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 330, + 673, + 545, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 673, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 330, + 673, + 545, + 689 + ], + "type": "interline_equation", + "content": "\\mathrm {T D}: q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) = q _ {\\phi} (\\boldsymbol {z} _ {L} | \\boldsymbol {x}) \\prod_ {l = L} ^ {2} q _ {\\phi} (\\boldsymbol {z} _ {l - 1} | \\boldsymbol {z} _ {l}, \\boldsymbol {x}), \\tag {2}", + "image_path": "e71de5b68d0199a12d711a66005b188abb2a9e7176679a9c5a14c000d066aa16.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " represents the parameters of the encoder. We provide a demonstration of these processes in Fig. 3. As" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22947" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 111, + 141, + 159 + ], + "blocks": [ + { + "bbox": [ + 71, + 111, + 141, + 159 + ], + "lines": [ + { + "bbox": [ + 71, + 111, + 141, + 159 + ], + "spans": [ + { + "bbox": [ + 71, + 111, + 141, + 159 + ], + "type": "image", + "image_path": "f67f695941115d423416945506a76c7863b94226535c9aa428582eb4fe8b9100.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 69, + 197, + 127, + 304 + ], + "blocks": [ + { + "bbox": [ + 92, + 185, + 120, + 194 + ], + "lines": [ + { + "bbox": [ + 92, + 185, + 120, + 194 + ], + "spans": [ + { + "bbox": [ + 92, + 185, + 120, + 194 + ], + "type": "text", + "content": "(a) VAE" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 69, + 197, + 127, + 304 + ], + "lines": [ + { + "bbox": [ + 69, + 197, + 127, + 304 + ], + "spans": [ + { + "bbox": [ + 69, + 197, + 127, + 304 + ], + "type": "image", + "image_path": "efac10a82d11aa145427c8c7166ae6374dee01de8fa928c5ecf054e6beec0491.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 57, + 310, + 154, + 320 + ], + "lines": [ + { + "bbox": [ + 57, + 310, + 154, + 320 + ], + "spans": [ + { + "bbox": [ + 57, + 310, + 154, + 320 + ], + "type": "text", + "content": "(c) Bottom-up (BU) inference" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "lines": [ + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "type": "text", + "content": "Figure 3. Probabilistic graphical illustration of VAE and hierarchical VAE during inference and generation. Solid lines " + }, + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "type": "inline_equation", + "content": "(\\rightarrow)" + }, + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "type": "text", + "content": " denote inference while dashed lines " + }, + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "type": "inline_equation", + "content": "(\\dashrightarrow)" + }, + { + "bbox": [ + 46, + 330, + 288, + 363 + ], + "type": "text", + "content": " denote generation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 208, + 72, + 267, + 178 + ], + "blocks": [ + { + "bbox": [ + 208, + 72, + 267, + 178 + ], + "lines": [ + { + "bbox": [ + 208, + 72, + 267, + 178 + ], + "spans": [ + { + "bbox": [ + 208, + 72, + 267, + 178 + ], + "type": "image", + "image_path": "dad2c9bb4e7a40ab12dfce5edf5341a84fcd3c297eb78dbdd89148b42b93ef6d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 205, + 185, + 253, + 194 + ], + "lines": [ + { + "bbox": [ + 205, + 185, + 253, + 194 + ], + "spans": [ + { + "bbox": [ + 205, + 185, + 253, + 194 + ], + "type": "text", + "content": "(b) Generation" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 182, + 197, + 269, + 304 + ], + "blocks": [ + { + "bbox": [ + 182, + 197, + 269, + 304 + ], + "lines": [ + { + "bbox": [ + 182, + 197, + 269, + 304 + ], + "spans": [ + { + "bbox": [ + 182, + 197, + 269, + 304 + ], + "type": "image", + "image_path": "ec581b4a559da48fb84cc4fd6d08b40caaea7b10c995e206fd7a1fd5b5ed799e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 178, + 310, + 274, + 320 + ], + "lines": [ + { + "bbox": [ + 178, + 310, + 274, + 320 + ], + "spans": [ + { + "bbox": [ + 178, + 310, + 274, + 320 + ], + "type": "text", + "content": "(d) Top-down (TD) inference" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": "the inference process is to produce a sequence of latent variables step by step, we denote a hierarchy " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{1:T} = \\{ \\mathbf{z}^1, \\dots, \\mathbf{z}^t, \\dots, \\mathbf{z}^T \\}" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "T = L" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": ". In BU inference scheme, " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{1:T} = \\{ \\mathbf{z}_1, \\dots, \\mathbf{z}_t, \\dots, \\mathbf{z}_L \\}" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": "; in TD inference scheme, " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{1:T} = \\{ \\mathbf{z}_L, \\dots, \\mathbf{z}_t, \\dots, \\mathbf{z}_1 \\}" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": ". For brevity, we use " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": " to represent " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{1:T}" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": " in the following parts. Additionally, we introduce " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": " for representing the lower level variable " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_j" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": " w.r.t. " + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^t" + }, + { + "bbox": [ + 47, + 366, + 288, + 450 + ], + "type": "text", + "content": " defined by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 87, + 460, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 460, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 87, + 460, + 287, + 491 + ], + "type": "interline_equation", + "content": "j = \\left\\{ \\begin{array}{l l} t - 1, & \\text {i n B U h i e r a c h i c a l V A E ,} \\\\ T - t, & \\text {i n T D h i e r a c h i c a l V A E .} \\end{array} \\right. \\tag {3}", + "image_path": "074ceb90671ec8b7d69782465b9c57ebd17e0eb935c7d9406982af9c8a01cbe4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "text", + "content": "The training objective of a hierarchical VAE is to maximize the variational evidence lower bound (ELBO), denoted as " + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\pmb{x}}" + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "text", + "content": ", of the training data's marginal log-likelihood " + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\log p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "text", + "content": " by jointly updating the parameters " + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 493, + 287, + 541 + ], + "type": "text", + "content": ", expressed as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 543, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 543, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 59, + 543, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\boldsymbol {x}} = \\log p (\\boldsymbol {x}) - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} (\\mathbf {z} | \\boldsymbol {x}) \\| p _ {\\theta} (\\mathbf {z} | \\boldsymbol {x}) \\right] \\tag {4} \\\\ = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log p _ {\\theta} (\\mathbf {x} | \\mathbf {z}) \\right] - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p (\\mathbf {z}) \\right], \\\\ \\end{array}", + "image_path": "96c1f18da4f3c22fa7544e5ac1c78237ac72cecc7559943d9d5bc5aab4eab02a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(\\cdot ||\\cdot)" + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "text", + "content": " refers to the Kullback-Leibler (KL) divergence. Defining " + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "inline_equation", + "content": "q_{\\phi}(z_1|z_0,x)\\coloneqq q_{\\phi}(z_1|x)" + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "inline_equation", + "content": "p_{\\theta}(z_L|z_{L + 1})\\coloneqq p_{\\theta}(z_L)" + }, + { + "bbox": [ + 46, + 572, + 287, + 619 + ], + "type": "text", + "content": ", for BU and TD hierarchical VAEs, the respective detailed expressions of their ELBOs are:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 621, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 621, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 621, + 287, + 654 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathrm {B U}: \\mathcal {L} _ {\\boldsymbol {x}} = \\mathbb {E} _ {q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] \\tag {5} \\\\ - \\sum_ {l = 1} ^ {L} D _ {\\mathrm {K L}} \\left[ \\left(q _ {\\phi} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l - 1}, \\boldsymbol {x}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}\\right)\\right) \\right], \\\\ \\end{array}", + "image_path": "1776aca675c123fe492013e69b23ee5208851ffe09460a640b048b4ec5875650.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 56, + 656, + 287, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 656, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 56, + 656, + 287, + 689 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathrm {T D}: \\mathcal {L} _ {\\boldsymbol {x}} = \\mathbb {E} _ {q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] \\tag {6} \\\\ - \\sum_ {l = 1} ^ {L} D _ {\\mathrm {K L}} \\left[ \\left(q _ {\\phi} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}, \\boldsymbol {x}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {z} _ {l} \\mid \\boldsymbol {z} _ {l + 1}\\right)\\right) \\right]. \\\\ \\end{array}", + "image_path": "3927934c742be4397d52277dbda70efc3bd1c3aded578191247a17a729be34f4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": "After convergence, we could extract level " + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": "'s latent representation by the maximum a posteriori (MAP) estimate" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "tion of the learned latent variables " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": ", defined as " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_l^* = \\arg \\max_{\\mathbf{z}_l} q_{\\phi}(\\mathbf{z}_l | \\mathbf{x})" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " [5, 43]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 96, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 545, + 131 + ], + "type": "text", + "content": "However, training hierarchical VAEs often suffers from the issue known as posterior collapse, which can be formally defined as follows." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "spans": [ + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": "Definition 1 (posterior collapse [7, 13, 82, 88]). Given a hierarchical VAE " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "p(\\pmb{x}, \\pmb{z}; \\theta, \\phi)" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": ", paramters' value " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "\\phi = \\hat{\\phi}" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "\\theta = \\hat{\\theta}" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": ", and for any data " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": " in a dataset " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\pmb{x}} = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_N\\}" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": ", the posterior of inference step " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": "'s latent variable " + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "inline_equation", + "content": "\\pmb{z}^t" + }, + { + "bbox": [ + 305, + 139, + 547, + 188 + ], + "type": "text", + "content": " collapses if" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 334, + 200, + 545, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 200, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 334, + 200, + 545, + 214 + ], + "type": "interline_equation", + "content": "q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} ^ {t - 1}, \\boldsymbol {x}; \\hat {\\phi}\\right) = p _ {\\theta} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} _ {j + 2}; \\hat {\\theta}\\right), \\forall \\boldsymbol {x} \\in \\mathcal {D} _ {\\boldsymbol {x}}. \\tag {7}", + "image_path": "62be495e95aae89ebb5b98fbbffa3f97f6b6678baf9ad64c8104562023361c64.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": "The posterior collapse issue mainly occurs in higher-level latent variables of hierarchical VAEs. Stochastic latent variables " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": " can be manually divided into lower-level variables, " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "z_{< k} = \\{z_1,\\dots,z_{k - 1}\\}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": " and higher-level ones, " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "z_{\\geq k} = \\{z_k,\\dots,z_L\\}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "k\\in \\{2,\\ldots ,L\\}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": ". Though " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "z_{< k}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": " may not suffer from posterior collapse that could encode sufficient information to reconstruct the inputs well, the corresponding high-level stochastic latent variables " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\geq k}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": " could be inclined to collapse into priors, i.e., " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "q_{\\phi}(z_{\\geq k}|\\boldsymbol {x})\\approx p_{\\theta}(z_{\\geq k})" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": ". An illustration can be seen in Fig. 1. Consequently, these higher-level posteriors will hold limited relevance to its input " + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 305, + 220, + 547, + 363 + ], + "type": "text", + "content": ", resulting in non-informative representations." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 380, + 443, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 443, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 443, + 392 + ], + "type": "text", + "content": "2.2. Reinforcement Learning" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": "We consider a standard RL setup in continuous action space and discrete timesteps, formalized as a Markov decision process (MDP) defined by a tuple " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "\\langle S, \\mathcal{A}, P, r \\rangle" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " [33, 52, 72, 94]. Here, the state space " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " and action space " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " are continuous, the state transition probability function " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "P: S \\times \\mathcal{A} \\to \\Delta(S)" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " represents the probability density of the next state " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "s_{t+1} \\in S" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " given the current state " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "s_t \\in S" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " and action " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "a_t \\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "inline_equation", + "content": "r: S \\times \\mathcal{A} \\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 398, + 547, + 494 + ], + "type": "text", + "content": " denotes the reward function on each transition." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": "At each time step " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "t \\in \\{1, 2, \\dots, T\\}" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ", an agent observes a state " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "s_t \\in S" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ", takes an action " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "a_t \\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ", and receives a scalar reward " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "r_t: S \\times \\mathcal{A} \\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ". The state " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " could be described in various ways, such as the entire history of the observations " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "s_t = (o_1, \\dots, o_t)" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " [94] or only the current observation " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "s_t = o_t" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " [33]. An agent's behavior could be defined by a policy " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "\\pi(a_t | s_t)" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ", which maps states to a probability distribution over actions. The return at time step " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " is defined as the sum of the discounted future reward " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "R_t = \\sum_{i=t}^{T} \\gamma^{(i-t)} r(s_i, a_i)" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " with a discount factor " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "\\gamma \\in (0, 1)" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ". The expectation of the return could be flexibly formulated by the Q-value function " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "Q^\\pi(s_t, a_t)" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " after taking an action " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " in state " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": " and thereafter following policy " + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 495, + 545, + 649 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 315, + 651, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 651, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 315, + 651, + 545, + 677 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {s _ {i > t} \\sim P, a _ {i > t} \\sim \\pi} \\left[ R _ {t} \\mid s _ {t}, a _ {t} \\right] \\tag {8} \\\\ = r \\left(s _ {t}, a _ {t}\\right) + \\gamma \\mathbb {E} _ {s _ {t + 1} \\sim P, a _ {t} \\sim \\pi} \\left[ Q ^ {\\pi} \\left(s _ {t + 1}, a _ {t + 1}\\right) \\right], \\\\ \\end{array}", + "image_path": "6db5c7e9ccadd6f4c0a519d4fe7718742138e45fc6bd63e4f3666aec84aac9e5.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "which not only considers the reward of the action to be taken on the current state but also its effect on the future decision process. Let us assume that drawing from " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "a_{t} \\sim \\pi (a_{t}|s_{t})" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " can" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22948" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "be realized with reparameterization as " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "a_{t} = f(s_{t},\\epsilon_{t}),\\epsilon_{t}\\sim p(\\epsilon)" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". We could directly apply the policy gradient method [52, 78, 94] on the model parameters " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " with gradient ascent to maximize the " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "Q^{\\pi}(s_t,a_t)" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " at a time step " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 121, + 287, + 134 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 121, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 116, + 121, + 287, + 134 + ], + "type": "interline_equation", + "content": "\\Theta \\leftarrow \\Theta + \\nabla_ {\\Theta} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right). \\tag {9}", + "image_path": "f0d4ce90a7b7467bd2c7f7da7d99754418dc4e3cf73e114acc8300981080e608.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "type": "text", + "content": "We sum all time step " + }, + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "type": "text", + "content": " 's policy gradient together to represent the optimization direction " + }, + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "type": "inline_equation", + "content": "\\nabla_{\\Theta}\\mathcal{I}" + }, + { + "bbox": [ + 47, + 137, + 287, + 159 + ], + "type": "text", + "content": " of the RL, expressed as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 51, + 161, + 287, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 161, + 287, + 188 + ], + "spans": [ + { + "bbox": [ + 51, + 161, + 287, + 188 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\Theta} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {s _ {t} \\sim P, \\epsilon_ {t} \\sim p (\\epsilon)} \\nabla_ {\\Theta} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right), a _ {t} = f \\left(s _ {t}, \\epsilon_ {t}\\right). \\tag {10}", + "image_path": "f87ca146b6aee691d9cb329218b3f428d589f17a4a9d1d282288d5dca5e7c016.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 192, + 287, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 287, + 216 + ], + "type": "text", + "content": "For the discussion on Related Works, we move it to Appendix A." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 232, + 257, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 257, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 257, + 259 + ], + "type": "text", + "content": "3. Improving Unsupervised Hierarchical Representation with RL" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 269, + 289, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 289, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 289, + 413 + ], + "type": "text", + "content": "We first provide an analysis of the existing two major approaches mitigating posterior collapse for learning a hierarchical representation with a hierarchical VAE. However, we found that they either lack regularization for propagating data information to higher-level latent variables or break the dependency between different levels' latent variables. Therefore, to address these drawbacks, a better training objective from the perspective of information theory could naturally lead to an RL scheme with a proper design of the Q-value function as the regularization of latent representations. Finally, we develop an RL training scheme with the policy gradient method to train a hierarchical VAE." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 421, + 264, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 421, + 264, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 421, + 264, + 444 + ], + "type": "text", + "content": "3.1. Analysis of Representation Learning with Hierarchical VAEs" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "text", + "content": "The aim of representation learning with a hierarchical VAE is to learn a hierarchy of latent variables " + }, + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "text", + "content": " that could represent the input data " + }, + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "text", + "content": ". We begin with rethinking how different approaches are affecting the representation learning with a hierarchical VAE. We first rewrite the ELBO from an information theory standpoint [18]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 50, + 526, + 301, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 526, + 301, + 578 + ], + "spans": [ + { + "bbox": [ + 50, + 526, + 301, + 578 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} [ \\operatorname {E L B O} (\\boldsymbol {x}) ] \\\\ = \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} \\left[ \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {\\boldsymbol {x} \\sim p (\\boldsymbol {x})} \\left[ D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x}) \\| p (\\boldsymbol {z})\\right) \\right] \\\\ = \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) - \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) - D _ {\\mathrm {K L}} (q (\\boldsymbol {z}) \\| p (\\boldsymbol {z})) - \\mathcal {H} _ {p} (\\boldsymbol {x}), \\tag {11} \\\\ \\end{array}", + "image_path": "42caea9d044d2c31088eb54252f2cd4c659eabb9f4bd0a182eb147a4e3b8ef63.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "type": "text", + "content": "where the mutual information between " + }, + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 578, + 287, + 601 + ], + "type": "text", + "content": " under different distribution is defined by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 604, + 297, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 297, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 297, + 645 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) = \\mathbb {E} _ {p (\\boldsymbol {x}) q _ {\\phi} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right)} \\left[ \\log \\frac {p (\\boldsymbol {x} , \\boldsymbol {z} _ {1})}{p (\\boldsymbol {x}) q \\left(\\boldsymbol {z} _ {1}\\right)} \\right] \\tag {12} \\\\ = \\mathbb {E} _ {p (\\boldsymbol {x}) q _ {\\phi} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right)} \\left[ \\log p _ {\\theta} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {p (\\boldsymbol {x})} \\left[ \\log p (\\boldsymbol {x}) \\right], \\\\ \\end{array}", + "image_path": "15886449ed0ac1a3ee07c50ee96df679cbf224e1a69008b30b984a17abf0fe54.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 647, + 297, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 647, + 297, + 689 + ], + "spans": [ + { + "bbox": [ + 53, + 647, + 297, + 689 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} _ {1}) = \\mathbb {E} _ {q (\\boldsymbol {x}) q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x})} \\left[ \\log \\frac {q (\\boldsymbol {x} , \\boldsymbol {z} _ {1})}{q (\\boldsymbol {x}) q (\\boldsymbol {z} _ {1})} \\right] \\tag {13} \\\\ = \\mathbb {E} _ {q (\\boldsymbol {x}) q _ {\\phi} (\\boldsymbol {z} _ {1} | \\boldsymbol {x})} \\left[ \\log q _ {\\phi} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\right] - \\mathbb {E} _ {q (\\boldsymbol {x})} \\left[ \\log q (\\boldsymbol {x}) \\right], \\\\ \\end{array}", + "image_path": "649b91614a92672a6d82323b06bf122d4ed379fc78088d1dbc58e288913da3a9.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "q(x)" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " is the training data's distribution and it is assumed to be equal to the true data distribution " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "p(\\pmb{x})" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 72, + 494, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 494, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 494, + 85 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb {x}|z_1)" + }, + { + "bbox": [ + 306, + 72, + 494, + 85 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 72, + 494, + 85 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\pmb {x}|z_{1})" + }, + { + "bbox": [ + 306, + 72, + 494, + 85 + ], + "type": "text", + "content": " could be expressed by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 325, + 86, + 545, + 112 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 86, + 545, + 112 + ], + "spans": [ + { + "bbox": [ + 325, + 86, + 545, + 112 + ], + "type": "interline_equation", + "content": "p _ {\\theta} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) = \\frac {p _ {\\theta} \\left(\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}\\right) p (\\boldsymbol {x})}{q \\left(\\boldsymbol {z} _ {1}\\right)} \\tag {14}", + "image_path": "4b2f2775a5c2d41aa990cb23fd5f3c7255d95ad69214961c4f9659e4ee78c51c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 114, + 545, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 114, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 326, + 114, + 545, + 140 + ], + "type": "interline_equation", + "content": "q _ {\\phi} (\\boldsymbol {x} \\mid \\boldsymbol {z} _ {1}) = \\frac {q _ {\\phi} (\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}) q (\\boldsymbol {x})}{q (\\boldsymbol {z} _ {1})} \\simeq \\frac {q _ {\\phi} (\\boldsymbol {z} _ {1} \\mid \\boldsymbol {x}) p (\\boldsymbol {x})}{q (\\boldsymbol {z} _ {1})}. \\tag {15}", + "image_path": "b3514ddaa4d42732c57a073590b47f23f467859bd81cc5868b6866a363a92fef.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "text", + "content": "Thus, the target of the ELBO in Eq. 11 effectively becomes minimizing the gap between the bottom-most latent variable's posterior " + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\pmb{z}_1|\\pmb{x})" + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "text", + "content": " and its corresponding true posterior " + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{z}_1|\\pmb{x})" + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "text", + "content": " and meanwhile the posterior of higher-level latent variables " + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "inline_equation", + "content": "\\{\\pmb{z}_l\\}_{l=1:L}" + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "text", + "content": " are trained to be close to their respective priors by the " + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}[q(\\mathbf{z})\\| p(\\mathbf{z})]" + }, + { + "bbox": [ + 306, + 140, + 547, + 213 + ], + "type": "text", + "content": " term." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "type": "text", + "content": "Since the latent variables above " + }, + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "type": "inline_equation", + "content": "z_{1}" + }, + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "type": "text", + "content": " do not receive direct regularization to maximize " + }, + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(x, z_{l}), l > 1" + }, + { + "bbox": [ + 304, + 215, + 547, + 300 + ], + "type": "text", + "content": ", it could potentially lead to the posterior collapse phenomenon. Therefore, approaches that only modify the model structure [25, 57, 76, 80] still do not impose additional regularization to higher-level latent variables in the training objective, where the posterior collapse could still occur." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "text", + "content": "Existing regularization strategies in the literature aim to refine the posterior distribution in order to cultivate good representations [41, 51, 54]. These methods typically focus on the relationship between observed data " + }, + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "text", + "content": " and a single-level latent variable " + }, + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "text", + "content": ", which could be interpreted as an additional regularization on the ELBO expressed as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 368, + 376, + 545, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 376, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 368, + 376, + 545, + 393 + ], + "type": "interline_equation", + "content": "\\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z}) \\simeq \\sum_ {t = 1} ^ {T} \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {t}). \\tag {16}", + "image_path": "5b2deb55ee65572e5ade7980fd2baf160ff93e0843f29c71657f715fb2f8d654.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "text", + "content": "However, by optimizing all latent variables " + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "inline_equation", + "content": "\\{z^t\\}_{t = 1:T}" + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "text", + "content": " with a shared objective " + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\pmb {x},\\pmb{z}^t)" + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "text", + "content": " simultaneously, these approaches may hurt the hierarchical dependency amongst them. This is due to the implicit incentive for all latent variables to assimilate, potentially undermining the hierarchical structure. Learning to generate a sequence " + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "inline_equation", + "content": "\\{\\pmb {x},\\pmb {z}^1,\\dots,\\pmb {z}^T\\}" + }, + { + "bbox": [ + 304, + 393, + 546, + 525 + ], + "type": "text", + "content": " with only one loss after finishing generating the whole sequence could also bring the imbalance issue, where the concentration of optimization to the mediate items is not clear [94]. These limitations hinder the exploitation of the full capabilities inherent in hierarchical VAEs." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 529, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 547, + 553 + ], + "type": "text", + "content": "We leave a detailed discussion for the above two approaches in Appendix B." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "text", + "content": "In summary, an effective training scheme should maximize the information content hidden in latent variables of all layers, while maintaining the dependencies among latent variables. Specifically, the regularization on " + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "text", + "content": " should account for not only " + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\pmb{x},\\pmb{z}^t)" + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "text", + "content": ", but also the influence on the subsequent latent variables " + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\pmb{x},\\pmb{z}^i|\\pmb{z}^{i - 1})" + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "inline_equation", + "content": "i > t" + }, + { + "bbox": [ + 304, + 557, + 547, + 629 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 353, + 630, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 630, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 353, + 630, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t: T}\\right) = \\sum_ {i = t} ^ {T} \\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right). \\tag {17}", + "image_path": "06d449723ba2a7305a3788fa68ffd58d03d1cf4b19d3c2f6310bb32a8fd89cfd.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "type": "text", + "content": "By incorporating a discount factor " + }, + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "type": "inline_equation", + "content": "\\gamma \\in (0,1)" + }, + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "type": "text", + "content": ", which allocates greater weight to the mutual information with proximal latent variables, the regularization for " + }, + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 304, + 647, + 545, + 683 + ], + "type": "text", + "content": " becomes:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 350, + 684, + 545, + 701 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 684, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 350, + 684, + 545, + 701 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right) = \\sum_ {i = t} ^ {T} \\gamma^ {i - t} \\mathcal {I} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right). \\tag {18}", + "image_path": "3792c6b440da55692428d9a07b0945eca2c73efd56d6d4e26f436201875d8083.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 702, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 702, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 702, + 547, + 714 + ], + "type": "text", + "content": "Therefore, the optimization direction of learning the se" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22949" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 83, + 306, + 175 + ], + "blocks": [ + { + "bbox": [ + 72, + 83, + 306, + 175 + ], + "lines": [ + { + "bbox": [ + 72, + 83, + 306, + 175 + ], + "spans": [ + { + "bbox": [ + 72, + 83, + 306, + 175 + ], + "type": "image", + "image_path": "987ce437da5c751f31358593159a817e7b4ca1bdc94cb0bb4adf3a287605433e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 189, + 283, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 189, + 283, + 205 + ], + "spans": [ + { + "bbox": [ + 99, + 189, + 283, + 205 + ], + "type": "interline_equation", + "content": "\\overline {{r (s _ {t} , a _ {t}) = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} (z ^ {1 : t} | x)} \\log p _ {\\theta} (x | z ^ {t}) - D _ {\\mathrm {K L}} [ q _ {\\phi} (z ^ {1 : t} | x) | | p (z ^ {1 : t}) ]}}", + "image_path": "7e7a4d558eea90ba6f131499e9ff841344e0aafa0dfbb897d84d91d112e9a68a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 374, + 69, + 518, + 208 + ], + "blocks": [ + { + "bbox": [ + 374, + 69, + 518, + 208 + ], + "lines": [ + { + "bbox": [ + 374, + 69, + 518, + 208 + ], + "spans": [ + { + "bbox": [ + 374, + 69, + 518, + 208 + ], + "type": "image", + "image_path": "a6a31bb3fcf94a98fa8a5a06d37714ead8fd78c5660cfcb79800373c70ffa8e0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "text", + "content": "Figure 4. Illustration of modeling the inference process of a hierarchical VAE as a sequential decision process (left) and the details of the elements of RL " + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "inline_equation", + "content": "s_{t+1}" + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "text", + "content": " (right). A reward " + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "inline_equation", + "content": "r(s_t, a_t)" + }, + { + "bbox": [ + 46, + 215, + 546, + 239 + ], + "type": "text", + "content": " is derived with the skip-generative path depicted in the gray box." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 244, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 244, + 256 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 244, + 256 + ], + "type": "text", + "content": "quence " + }, + { + "bbox": [ + 46, + 243, + 244, + 256 + ], + "type": "inline_equation", + "content": "\\{\\pmb {x},\\pmb {z}^1,\\dots,\\pmb {z}^T\\}" + }, + { + "bbox": [ + 46, + 243, + 244, + 256 + ], + "type": "text", + "content": " can then be expressed by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 256, + 287, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 256, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 80, + 256, + 287, + 274 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\phi , \\theta} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {p (\\boldsymbol {x}), q _ {\\phi}, p _ {\\theta}} \\nabla_ {\\phi , \\theta} \\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right). \\tag {19}", + "image_path": "4e7aefe0fa50ae0b1c0bc73918d155c2651e9f7452c0c54e77def4c5a70473ea.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "text", + "content": "The resemblance of the optimization direction to Eq. 10 naturally leads to formulating the learning of hierarchical VAE as a sequential decision process, prompting the application of RL methods. Particularly, we are driven to develop a proper Q-value function " + }, + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "inline_equation", + "content": "Q(s_{t},a_{t})" + }, + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "text", + "content": " to play the role of the regularization " + }, + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{I}}(\\boldsymbol {x},\\boldsymbol{z}^t)" + }, + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "text", + "content": " to achieve a consistent expression of the two optimization objectives." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 366, + 242, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 242, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 242, + 379 + ], + "type": "text", + "content": "3.2. Training Hierarchical VAEs with RL" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": "Inspired by the tremendous success of RL methods in stably propagating information along long Markov Decision chains that maximize the cumulative rewards tallied at every step, i.e., the Q-value " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "Q^{\\pi}(s_t,a_t)" + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": " in Eq. 8, we formulate the progressive inference process of an " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": "-layer hierarchical VAEs as an " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": "-step sequential decision process. Specifically, given an input " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": " from a training set " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\pmb{x}}" + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": ", we need a hierarchical VAE parameterized with " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\{\\theta ,\\phi \\}" + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "text", + "content": " to produce a sequence " + }, + { + "bbox": [ + 46, + 385, + 288, + 493 + ], + "type": "inline_equation", + "content": "Y_{1:T} = \\{\\pmb {x},\\pmb {z}^{1},\\pmb {z}^{2},\\dots,\\pmb{z}^{T}\\} ,T = L" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "text", + "content": "Now, we can set up the basic elements for training with RL. At each time step " + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "text", + "content": ", the state " + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "text", + "content": " is characterized as a tuple including the observed input and already produced latent variables " + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "inline_equation", + "content": "z^{1:t-1} = \\{z^1, \\dots, z^{t-1}\\}" + }, + { + "bbox": [ + 46, + 494, + 287, + 542 + ], + "type": "text", + "content": " up to the step:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 133, + 542, + 287, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 542, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 133, + 542, + 287, + 556 + ], + "type": "interline_equation", + "content": "s _ {t} \\triangleq \\left\\{\\boldsymbol {x}, \\boldsymbol {z} ^ {1: t - 1} \\right\\}, \\tag {20}", + "image_path": "e73ea2ccf62f8f7216faa27f2fab01248183101d0cf179f5f219ce82337f176c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "inline_equation", + "content": "s_1 = \\{x\\}" + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "text", + "content": ". After receiving a state " + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "text", + "content": ", the encoder " + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|x)" + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "text", + "content": " of the hierarchical model acts as the policy network " + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\pi (a_t|s_t)" + }, + { + "bbox": [ + 46, + 557, + 287, + 594 + ], + "type": "text", + "content": " to produce the latent variable as an action:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 64, + 594, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 594, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 64, + 594, + 287, + 608 + ], + "type": "interline_equation", + "content": "\\pi_ {\\phi} \\left(a _ {t} \\mid s _ {t}\\right) \\triangleq q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {x}, \\boldsymbol {z} ^ {1: t - 1}\\right) = q _ {\\phi} \\left(\\boldsymbol {z} ^ {t} \\mid \\boldsymbol {z} ^ {t - 1}, \\boldsymbol {x}\\right), \\tag {21}", + "image_path": "9edb128ffc7ab4d6d49ffc34a1bcf2d656bd7932c8e04ee759768958fe99101e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 94, + 610, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 610, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 94, + 610, + 287, + 624 + ], + "type": "interline_equation", + "content": "a _ {t} \\triangleq z ^ {t} \\sim q _ {\\phi} \\left(z ^ {t} \\mid z ^ {t - 1}, x\\right). \\tag {22}", + "image_path": "4e2f654f580013752114da2806418cb3ac188069347be47711f34c001867c19f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "type": "text", + "content": "Once executing the " + }, + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "type": "text", + "content": ", we will get to the next state according the state transition probability function " + }, + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 626, + 287, + 650 + ], + "type": "text", + "content": ", specified as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 110, + 651, + 287, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 651, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 110, + 651, + 287, + 664 + ], + "type": "interline_equation", + "content": "P \\left(s _ {t + 1} \\mid s _ {t}, a _ {t}\\right) \\triangleq \\left(\\delta_ {\\boldsymbol {x}}, \\delta_ {\\boldsymbol {z} ^ {1: t}}\\right), \\tag {23}", + "image_path": "e391f396ca4f38409dae74324552747bdbca918b4158c7245bccd5e800700b92.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "which is deterministic and reflects the unchanged observed data " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": " and the inclusion of new inferred latent variables at the successor state. " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\delta_v" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": " is a Dirac delta distribution that only manifests a non-zero impulse at " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": "Reward function design. When getting such a transition " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\{s_t, a_t, s_{t+1}\\}" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": ", we need to design a reward function " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "r(s_t, a_t)" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": ". The principle of the design is to evaluate the information content " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\boldsymbol{x}, \\boldsymbol{z}^t | \\boldsymbol{z}^{t-1})" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": " hidden in the latent variable " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}^t" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": " that represents the inputs, then we could formulate the Q-value function to regularize " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}^t" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\sum_{i=t}^{T} \\mathcal{I}(\\boldsymbol{x}, \\boldsymbol{z}^i | \\boldsymbol{z}^{i-1})" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": ". We design a reward function " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "r(s_t, a_t)" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": " to evaluate the information between " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}^t" + }, + { + "bbox": [ + 305, + 243, + 547, + 334 + ], + "type": "text", + "content": " as below:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 339, + 552, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 339, + 552, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 339, + 552, + 365 + ], + "type": "interline_equation", + "content": "r \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {\\mathbf {z} \\sim q _ {\\phi} \\left(\\mathbf {z} ^ {1: t} \\mid \\mathbf {x}\\right)} \\log p _ {\\theta} (\\mathbf {x} \\mid \\mathbf {z} ^ {t}) - D _ {\\mathrm {K L}} \\left[ q _ {\\phi} \\left(\\mathbf {z} ^ {1: t} \\mid \\mathbf {x}\\right) \\| p \\left(\\mathbf {z} ^ {1: t}\\right) \\right], \\tag {24}", + "image_path": "b862b0625e1e2a3c4fa06b00e44a099248d6783ec4e42d56086d1399ce4ed5a5.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 307, + 373, + 530, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 373, + 530, + 385 + ], + "spans": [ + { + "bbox": [ + 307, + 373, + 530, + 385 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 307, + 373, + 530, + 385 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\boldsymbol{x}|\\boldsymbol{z}^t)" + }, + { + "bbox": [ + 307, + 373, + 530, + 385 + ], + "type": "text", + "content": " is a skip-generative path, expressed as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 390, + 545, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 545, + 412 + ], + "type": "interline_equation", + "content": "p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} ^ {t}) = \\int_ {\\boldsymbol {z} _ {1: j}} p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} _ {1}) \\prod_ {i = j} ^ {1} p _ {\\theta} (\\boldsymbol {z} _ {i} | \\boldsymbol {z} _ {i + 1}), \\boldsymbol {z} ^ {t} \\sim q (\\boldsymbol {z} ^ {t} | \\boldsymbol {z} ^ {< t}, \\boldsymbol {x}),", + "image_path": "188436483721fa75a835bb1ec28b12fa81b22a8ae533c7f5ae80406d00a804f1.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "z_{1:j}" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": " are marginalized out by the integral. Kindly note that the skip-generative path " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{x}|\\pmb{z}^t)" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": " is different from the generative path in vanilla hierarchical VAEs, where " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{x}|\\pmb{z}^{1:t}) = p_{\\theta}(\\pmb{x}|\\pmb{z}_1)" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": " after observing " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "z^{1:t}" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "r(s_t,a_t)" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": " based on the skip-generative path could empirically force the training on maximizing the mutual information between " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": " after observing " + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "inline_equation", + "content": "z^{t-1}" + }, + { + "bbox": [ + 305, + 418, + 545, + 496 + ], + "type": "text", + "content": ", expressed by" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 311, + 501, + 545, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 501, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 311, + 501, + 545, + 545 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {p (\\boldsymbol {x})} \\left[ r \\left(s _ {t}, a _ {t}\\right) \\right] \\tag {25} \\\\ = \\mathbb {E} _ {p (\\boldsymbol {x}) q (\\boldsymbol {z} ^ {1: t} | \\boldsymbol {x})} \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z} ^ {t}) - \\mathbb {E} _ {p (\\boldsymbol {x})} D _ {\\mathrm {K L}} \\left[ q _ {\\phi} \\left(\\boldsymbol {z} ^ {1: t} | \\boldsymbol {x}\\right) \\| p (\\boldsymbol {z} ^ {1: t}) \\right] \\\\ = \\mathcal {I} _ {p, q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {t}) - \\mathcal {I} _ {q} (\\boldsymbol {x}, \\boldsymbol {z} ^ {1}) - D _ {\\mathrm {K L}} [ q (\\boldsymbol {z} ^ {1: t}) | | p (\\boldsymbol {z} ^ {1: t}) ] - \\mathcal {H} _ {p} (\\boldsymbol {x}) \\\\ \\end{array}", + "image_path": "19668f2e7e55dc35a794cb98d7b5394a0f20bc328c669b09ca5ebb40bb355b23.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "content": "Therefore, as shown in Eq. 25, the reward function " + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "inline_equation", + "content": "r(s_{t},a_{t})" + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "content": " is to evaluate how " + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\pmb {x},\\pmb{z}^t)" + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "content": " is closer or larger than " + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\pmb {x},\\pmb{z}^{1})" + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "content": " Thus, the reward function could be an approximate evaluation of " + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_q(\\pmb {x},\\pmb {z}^t |\\pmb {z}^{t - 1})" + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "content": " after observing the inferred " + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\pmb{z}^{t - 1}" + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 305, + 552, + 547, + 613 + ], + "type": "inline_equation", + "content": "r(s_{t},a_{t})\\simeq \\mathcal{I}_{q}(\\pmb {x},\\pmb{z}^{t}|\\pmb{z}^{t - 1})" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "text", + "content": "Q-value function. To explicitly add regularization on a current inferred latent variable " + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "inline_equation", + "content": "z^{t}" + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "text", + "content": ",s influence on its following latent variables " + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "inline_equation", + "content": "z^{>t}" + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "text", + "content": ", we propose to maximize its corresponding Q-value, which considers not only its own reward " + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "inline_equation", + "content": "r(s_{t},a_{t})" + }, + { + "bbox": [ + 305, + 617, + 547, + 677 + ], + "type": "text", + "content": ", but also the future accumulative rewards, i.e.," + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 315, + 678, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 678, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 315, + 678, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = r \\left(s _ {t}, a _ {t}\\right) + \\gamma \\mathbb {E} _ {\\pi} \\left[ Q ^ {\\pi} \\left(s _ {t + 1}, a _ {t + 1}\\right) \\right] \\\\ = r \\left(s _ {t}, a _ {t}\\right) + \\mathbb {E} _ {\\pi} \\left[ \\sum_ {i = t + 1} ^ {T} \\gamma^ {i - t} r \\left(s _ {i}, a _ {i}\\right) \\right]. \\tag {26} \\\\ \\end{array}", + "image_path": "182fd833c25755621fc82be6f5462b443742561182bfdbe7f65ac8610f1815cf.jpg" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22950" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "With the efficient reparameterization trick [43], we could do a single-sample based Monte Carlos (MC) estimation for the expectation of the Q-value function, i.e., " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "Q^{\\pi}(s_t,a_t)\\simeq \\sum_{i = t}^{T}\\gamma^{i - t}r(s_i,a_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ". Please note that the reward function is differentiable to the model's parameters, hence we could directly use gradient descent method [42, 69] to maximize the " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "Q_{\\pi}(s_t,a_t)" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " are trained simultaneously." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "content": "Therefore, at every time step " + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "content": ", maximizing its corresponding Q-value function is approximately maximizing the mutual information between " + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "content": " and the influence of the inferred " + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "content": " in the following latent variables " + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "inline_equation", + "content": "z^{t+1:T}" + }, + { + "bbox": [ + 46, + 157, + 288, + 217 + ], + "type": "text", + "content": " that depends on it, expressed as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 217, + 287, + 234 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 217, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 53, + 217, + 287, + 234 + ], + "type": "interline_equation", + "content": "Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) \\simeq \\sum_ {i = t} ^ {T} \\gamma^ {i - t} \\mathcal {I} _ {q} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {i} \\mid \\boldsymbol {z} ^ {i - 1}\\right) = \\mathcal {L} _ {\\mathcal {I}} \\left(\\boldsymbol {x}, \\boldsymbol {z} ^ {t}\\right), \\tag {27}", + "image_path": "d0c4e644f7c43b36f4b125db347f84e11f106cf86774917bfca15499bbd659cf.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "text", + "content": "which is consistent with the expression of Eq. 18 and the analysis in Section 3.1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 258, + 287, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 294 + ], + "type": "text", + "content": "Finally, to learn a high-quality sequence " + }, + { + "bbox": [ + 46, + 258, + 287, + 294 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x},\\pmb{z}^1,\\dots,\\pmb{z}^T\\}" + }, + { + "bbox": [ + 46, + 258, + 287, + 294 + ], + "type": "text", + "content": " aligning with the optimization direction in Eq. 19, we define the optimization direction on the Q-value function:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 295, + 287, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 295, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 80, + 295, + 287, + 312 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\theta , \\phi} \\mathcal {J} \\simeq \\sum_ {t = 1} ^ {T} \\mathbb {E} _ {s _ {i} \\sim P, a _ {i} \\sim \\pi} \\nabla_ {\\theta , \\phi} Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right). \\tag {28}", + "image_path": "a95b2139398bba784d832378af7f9a94eb6807e3c40d149cdb225fff851ceae2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "text", + "content": "As " + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "text", + "content": " could be obtained by reparameterization and " + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "inline_equation", + "content": "Q^{\\pi}(s_t, a_t)" + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "text", + "content": " is differentiable to model parameters, we could implement the policy gradient by directly maximizing " + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "inline_equation", + "content": "Q^{\\pi}(s_t, a_t)" + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "text", + "content": " at every time step " + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 312, + 288, + 408 + ], + "type": "text", + "content": " by Eq. 9, thereby eliminating the need for a gradient estimator like REINFORCE [89] and avoiding the high variance associated with these estimators [77]. We summarize the overall training scheme in Algorithm 1." + } + ] + } + ], + "index": 6 + }, + { + "type": "code", + "bbox": [ + 56, + 430, + 287, + 635 + ], + "blocks": [ + { + "bbox": [ + 48, + 415, + 265, + 427 + ], + "lines": [ + { + "bbox": [ + 48, + 415, + 265, + 427 + ], + "spans": [ + { + "bbox": [ + 48, + 415, + 265, + 427 + ], + "type": "text", + "content": "Algorithm 1 Optimizing a hierarchical VAE with RL." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "lines": [ + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": "Input: A training dataset " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\pmb{x}}" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " training hyperparameters; \nOutput: An " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " -layer hierarchical VAE parameterized with an encoder " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " and a decoder " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb {x}|\\mathbf{z})" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " \nInitialization: Randomly initialize the parameters " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\theta ,\\phi" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " \nfor epoch " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "= 1" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " to max_epochs do Sample a batch of " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " training samples " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\pmb{x}^n" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_x" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " . for time step " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " do for " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "i = t" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " do Follow Eq.22, but with reparameterization, to sample an action " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "a_i^n\\sim \\pi (a_i^n |s_i^n)" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " Get reward " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "r(s_i^n,a_i^n)" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " by Eq.24; end for Get " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "Q^{\\pi}(s_t^n,a_t^n)\\simeq \\sum_{i = t}^{T}\\gamma^{i - t}r(s_i^n,a_i^n)" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " Update " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\theta ,\\phi" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " using the policy gradient for the current time step " + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 56, + 430, + 287, + 635 + ], + "type": "text", + "content": " by Eq.9; end for \nend for" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_body" + } + ], + "index": 8, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 645, + 128, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 128, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 128, + 658 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Our experiments engage in comparisons with several hierarchical VAE variants and various unsupervised methods to assess if our method of training hierarchical VAEs with RL yields superior performance in 1) mitigating posterior" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": "collapse at higher latent representations, 2) learning a clear hierarchical representation, 3) attaining an explainable latent representation, and more importantly, 4) offering better representation than other hierarchical VAE-based unsupervised learning methods on downstream tasks. Additionally, we present several ablation studies to further evaluate different settings' influence on our method's performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 164, + 422, + 177 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 164, + 422, + 177 + ], + "spans": [ + { + "bbox": [ + 305, + 164, + 422, + 177 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 182, + 547, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 232 + ], + "type": "text", + "content": "Datasets: Our method is benchmarked on 5 datasets: FashionMNIST [91], CIFAR10 and CIFAR100 [44], TinyImageNet [46], and STL-10 [17]. Each method is trained using standard train splits and assessed on corresponding test splits." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "text", + "content": "Evaluation metrics: For representation evaluation, we follow the commonly adopted downstream linear classification [5, 39, 63], using a linear support vector machine (SVM) [37] classifier on representations from frozen models. Classification accuracy is reported to measure linear separability, acting as a proxy for mutual information of representations with the labels. Additionally, we apply the MINE statistics network [4] to estimate the mutual information " + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{I}}(x, z_L)" + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "text", + "content": ", between input " + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "text", + "content": " and the top latent variable " + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "inline_equation", + "content": "z_L" + }, + { + "bbox": [ + 304, + 243, + 547, + 353 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 365, + 548, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 548, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 548, + 545 + ], + "type": "text", + "content": "Baselines: We compare our method with two groups of baselines: i) those modifying the inference process without changing the training objective (ELBO); ii) those modifying the training objective to add more regularization on the inference process. For i, we include a BU hierarchical VAE (HVAE) powered with residual connections [35], a TD hierarchical VAE (LVAE) with a ladder inference [76], and a more sophisticated bidirectional structure hierarchical VAE (BIVA) [57]. For ii, to our best knowledge, the most relevant work to our method is informative hierarchical VAE (IVAE) [51], which introduces additional layer-wise regularization on latent representations of a hierarchical VAE. Additionally, we include a vanilla VAE (VAE) [43] and an adversarial autoencoder (AAE) [58] of single-level to assess the performance improvement brought by hierarchical structures." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": "Implementation details: We apply our RL optimization approach to hierarchical VAEs with BU " + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "inline_equation", + "content": "(\\mathbf{HVAE} + \\mathbf{RL})" + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": " and TD (LVAE+RL) inference schemes. For Fashion-MNIST, hierarchical models use latent dimensions of " + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\{128, 64, 32, 16, 8\\}" + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": ", and single-layer models use 8. For other image datasets, hierarchical models' latent dimensions are " + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\{128\\text{conv}, 64\\text{conv}, 256, 128, 64\\}" + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": ", and single-layer models have " + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\{64\\}" + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": ". The discount factor, " + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": ", is set to 0.9. Run on one NVIDIA A100 GPU with PyTorch [64], models are optimized using Adam optimizer [42] at a learning rate of 3e-4. Training epochs are set to 1000 for baselines and " + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "inline_equation", + "content": "1000 / L" + }, + { + "bbox": [ + 304, + 557, + 547, + 700 + ], + "type": "text", + "content": " for our method, with outcomes averaged over 5 random seeds." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 701, + 523, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 523, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 523, + 714 + ], + "type": "text", + "content": "Detailed experimental setup are in Appendix C." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22951" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 547, + 186 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 534, + 83 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 534, + 83 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 534, + 83 + ], + "type": "text", + "content": "Table 1. Classification acc. and " + }, + { + "bbox": [ + 58, + 71, + 534, + 83 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{I}}\\left( {\\mathbf{x},{\\mathbf{z}}_{L}}\\right)" + }, + { + "bbox": [ + 58, + 71, + 534, + 83 + ], + "type": "text", + "content": " comparisons. Our methods' results are marked in purple. The best two results are in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 547, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 547, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 547, + 186 + ], + "type": "table", + "html": "
MethodFashionMNISTCIFAR10CIFAR100TinyImageNetSTL-10 (32 × 32-downsampled)
Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{\\mathcal{I}}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)Acc.\\( \\widetilde{I}(\\boldsymbol{x},\\boldsymbol{z}_L) \\)
AAE [58]72.11±0.274.08±0.6738.36±0.205.91±1.0317.56±0.456.19±0.958.73±0.583.37±0.6736.64±0.176.65±1.10
VAE [43]75.08±0.094.36±0.3539.98±0.056.32±0.6519.05±0.2013.76±1.858.92±0.363.76±1.2137.75±0.076.87±0.75
BIVA [57]28.67±0.643.48±0.4810.40±0.135e-9±0.001.07±0.058e-9±0.000.67±0.069e-8±0.0010.02±0.201.41±0.38
IVAE [51]76.25±0.302.44±0.5239.26±0.256.41±0.6919.49±0.338.91±0.968.07±0.693.92±0.9837.98±0.412.86±0.95
HVAE [35]10.73±0.080.31±0.0810.40±0.053e-8±0.001.21±0.107e-7±0.000.63±0.065e-10±0.0010.24±0.070.97±0.17
HVAE+RL(ours)78.23±0.135.01±0.7046.46±0.1511.39±1.2025.21±0.2117.01±2.4112.76±0.3911.88±2.8743.76±0.1510.93±1.73
LVAE [76]19.70±0.211.73±0.3215.32±0.105e-5±0.0010.38±0.891.04±0.394.77±0.470.54±0.1211.89±0.100.45±0.08
LVAE+RL(ours)78.48±0.154.37±0.5846.35±0.176.91±0.8625.41±0.209.00±1.1913.41±0.444.48±1.7141.86±0.2610.77±1.94
", + "image_path": "9bc034c2894af8fdf4c5df6b779945f347b7ca10a538674e757dd2908afd2396.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 236, + 285, + 334 + ], + "blocks": [ + { + "bbox": [ + 47, + 205, + 288, + 227 + ], + "lines": [ + { + "bbox": [ + 47, + 205, + 288, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 288, + 227 + ], + "type": "text", + "content": "Table 2. Density estimation in bits per dimension (bpd) [21] and KL divergence at the topmost level of hierarchical VAEs." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 236, + 285, + 334 + ], + "lines": [ + { + "bbox": [ + 50, + 236, + 285, + 334 + ], + "spans": [ + { + "bbox": [ + 50, + 236, + 285, + 334 + ], + "type": "table", + "html": "
ModelFashionMNISTCIFAR10
bpdKLbpdKL
VAE0.306±0.04117.9±0.33.74±0.01263.0±4.0
BIVA0.302±0.0713e-4±0.02.85±0.022e-3±0.0
IVAE0.403±0.09628.9±0.73.48±0.05233.0±7.0
HVAE0.315±0.0676e-5±0.04.55±0.021e-3±0.0
HVAE+RL0.305±0.08941.2±0.44.36±0.03265.0±8.0
LVAE0.313±0.0509e-4±0.02.91±0.032e-3±0.0
LVAE+RL0.335±0.07232.1±0.53.21±0.07181.0±6.0
", + "image_path": "c77f039f07879fa50c5db0113faf191579d8128d6d762598d2009d009757596a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 339, + 165, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 165, + 351 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 165, + 351 + ], + "type": "text", + "content": "4.2. Quantitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "content": "Considering the highest-level latent representation " + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "inline_equation", + "content": "z_{L}" + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "content": " should ideally encapsulate the most abstract representation, such as categorical distinctions, we use top-level representations for linear classification. Additionally, given that " + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "inline_equation", + "content": "z_{L}" + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "content": " could be the most prone to posterior collapse among all levels, we estimate its information content " + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(x,z_L)" + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "content": " via MINE. Table 1 reports the classification accuracy on various datasets and estimated mutual information. Applying RL to the hierarchical VAEs (HVAE+RL & LVAE+RL) significantly improves accuracy compared to their counterparts trained on ELBO (HVAE & LVAE), and also outperforms other methods, including IVAE, across all datasets. This demonstrates our approach's superior representation quality. Moreover, " + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{I}}(x,z_L)" + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "content": " generally correlates classification performance, with our methods enabling higher mutual information in the same backbone models than the baselines in most cases, showing that our method extracts rich information from data. Notably, HVAE+RL yields significantly high " + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(x,z_L)" + }, + { + "bbox": [ + 46, + 361, + 288, + 590 + ], + "type": "text", + "content": " on complex datasets like CIFAR100 and TinyImageNet." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "In Table 2, we present negative log-likelihood scores in bpd, where a lower bpd indicates better marginal likelihood estimation, along with KL divergences at the highest layer. Intriguingly, we find no direct correlation between the performance in estimating marginal log-likelihood " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\log p(x)" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " using ELBO and the representation learning efficacy, as gauged by accuracy and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{I}}(x, z_L)" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " in Table 1. For instance, despite BIVA and LVAE's superior marginal likelihood estimation on CIFAR10, their performance in representation learning tasks lags behind IVAE and our methods. This observation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 206, + 547, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 278 + ], + "type": "text", + "content": "lends empirical support to our analysis in Section 3.1 that solely optimizing ELBO does not necessarily enhance hierarchical representation learning. Additionally, we note that a low KL divergence often signals poor downstream performance and reduced " + }, + { + "bbox": [ + 304, + 206, + 547, + 278 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{I}}(x, z_L)" + }, + { + "bbox": [ + 304, + 206, + 547, + 278 + ], + "type": "text", + "content": ", indicative of posterior collapse as defined in Definition 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 285, + 418, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 285, + 418, + 298 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 418, + 298 + ], + "type": "text", + "content": "4.3. Qualitative Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 304, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 411 + ], + "type": "text", + "content": "To elucidate the efficacy of our method in learning informative hierarchical representations, we first examine the hierarchies learned by different approaches in Fig. 1 by projecting latent representations of different levels to the input space via the skip-generative path. Fig. 1 shows training with RL effectively mitigates posterior collapse, yielding a more informative latent hierarchy. This enhancement in hierarchical representation is further evident in Fig. 2, reinforcing the conclusions drawn in Section 3.1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 412, + 548, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 548, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 548, + 556 + ], + "type": "text", + "content": "An interesting property of hierarchical VAEs is their explainable latent space, which we probe using t-SNE and latent traversal at the topmost level for generation, as shown in Fig. 5. The results demonstrate notable improvements achieved by applying RL on mapping inputs to an explainable semantic space, to which the improvement of performance in linear classification (Table 1) can be attributed. Furthermore, our exploration into latent traversal sheds light on the explainability of the latent space, with individual latent dimensions corresponding to specific abstract features like widths and positions of hollow parts, thus underscoring the interpretability of our learned representations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 563, + 400, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 400, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 400, + 576 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "Total number of levels. We investigate the impact of varying " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " in hierarchical VAEs on downstream task performance using representations from the topmost latent variable in Fig. 6. We observe that all baselines suffer from classification performance degeneracy with increasing latent levels: posterior collapses largely impair downstream task performance. In comparison, our methods are much more stable and achieve superior performance across all level number settings, indicating its robustness. More importantly, these results suggest our approach enables the possibility of learning a higher hierarchy of latent representation." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22952" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 168, + 175 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 168, + 175 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 168, + 175 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 168, + 175 + ], + "type": "image", + "image_path": "ea7b4fb86aae653602389ce77b874991804951005029081ff8ab0dd9577bd564.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 69, + 282, + 175 + ], + "blocks": [ + { + "bbox": [ + 173, + 69, + 282, + 175 + ], + "lines": [ + { + "bbox": [ + 173, + 69, + 282, + 175 + ], + "spans": [ + { + "bbox": [ + 173, + 69, + 282, + 175 + ], + "type": "image", + "image_path": "b9143d653fa2cd04affcdac0c3d74936abf0d16fda6bd375c8ab4ae1827f29d4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 175, + 168, + 280 + ], + "blocks": [ + { + "bbox": [ + 49, + 175, + 168, + 280 + ], + "lines": [ + { + "bbox": [ + 49, + 175, + 168, + 280 + ], + "spans": [ + { + "bbox": [ + 49, + 175, + 168, + 280 + ], + "type": "image", + "image_path": "dda5b4c17049ff3c632c6ecfd4c9b40e3ea6710aee516c1277a7ba56626a54bd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 283, + 287, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 338 + ], + "type": "text", + "content": "Figure 5. Panels showing the t-SNE and latent traversal generation on the highest latent variable in FashionMNIST, for vanilla HVAE (top) and HVAE+RL(bottom). The anchor point (original input) for latent traversal is bounded in red in grid center. Traversals are spaced by inverse Gaussian cdf to align with the prior distribution." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 173, + 175, + 282, + 281 + ], + "blocks": [ + { + "bbox": [ + 173, + 175, + 282, + 281 + ], + "lines": [ + { + "bbox": [ + 173, + 175, + 282, + 281 + ], + "spans": [ + { + "bbox": [ + 173, + 175, + 282, + 281 + ], + "type": "image", + "image_path": "937cf7f78054e3e590112704c524e14123fc0a33be9429b0aa796604ffb8270b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 350, + 170, + 449 + ], + "blocks": [ + { + "bbox": [ + 50, + 350, + 170, + 449 + ], + "lines": [ + { + "bbox": [ + 50, + 350, + 170, + 449 + ], + "spans": [ + { + "bbox": [ + 50, + 350, + 170, + 449 + ], + "type": "image", + "image_path": "ef4d5830fba17057e7f59d6f669ddd65473704db28c3eb4da53d9571f2a839d3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 459, + 286, + 470 + ], + "lines": [ + { + "bbox": [ + 47, + 459, + 286, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 286, + 470 + ], + "type": "text", + "content": "Figure 6. Classification acc. of hierarchical VAEs of different levels." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 171, + 350, + 286, + 449 + ], + "blocks": [ + { + "bbox": [ + 171, + 350, + 286, + 449 + ], + "lines": [ + { + "bbox": [ + 171, + 350, + 286, + 449 + ], + "spans": [ + { + "bbox": [ + 171, + 350, + 286, + 449 + ], + "type": "image", + "image_path": "70656d968635ac0abcf7c965c878bc7fef2280bb4083959894f44bd1bb9502f8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 498, + 286, + 552 + ], + "blocks": [ + { + "bbox": [ + 55, + 484, + 277, + 495 + ], + "lines": [ + { + "bbox": [ + 55, + 484, + 277, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 484, + 277, + 495 + ], + "type": "text", + "content": "Table 3. Classification acc. of different representation source." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 498, + 286, + 552 + ], + "lines": [ + { + "bbox": [ + 50, + 498, + 286, + 552 + ], + "spans": [ + { + "bbox": [ + 50, + 498, + 286, + 552 + ], + "type": "table", + "html": "
ObjectiveRepre. sourceFashionMNISTCIFAR10
HVAELVAEHVAELVAE
ELBOzLonly10.73±0.0819.70±0.2110.40±0.0515.32±0.10
full z79.96±0.2380.25±0.2750.09±0.6749.87±0.39
RLzLonly78.23±0.1378.48±0.1546.46±0.1546.35±0.17
full z84.56±0.2584.77±0.3052.87±0.5452.89±0.48
", + "image_path": "ea17bff3408f62fae31ea875691646dab7ecac58be8ab1efca9b63aa74ed4348.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": "Latent representation source. The substantial cumulative dimension of all hierarchical latent variables " + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": ", while potentially having greater representation capacity, may not be practical for all tasks. To explore this, we compare in Table 3 the downstream task performance of representations sourcing from the full " + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": " versus the most abstract topmost latent representation " + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "inline_equation", + "content": "z_{L}" + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": " to assess if " + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "inline_equation", + "content": "z_{L}" + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": " can maintain performance comparable to full " + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": ". We observe that with RL, models effectively retain comparable classification performance using just " + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "inline_equation", + "content": "z_{L}" + }, + { + "bbox": [ + 46, + 557, + 287, + 688 + ], + "type": "text", + "content": ", showing efficient learning of key abstract information at the topmost layer." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "Discount factor " + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": ". Exploring the impact of focusing solely on the current step's reward, we set the discount factor " + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": " to" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "0 in our method. Besides, we ablate two typical settings of " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": ", 0.9 and 0.98, in the Q-value function to assess robustness. As in Table 4, models using " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "Q(s_{t},a_{t})" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " for step-wise optimization outperform those relying only on " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "r(s_{t},a_{t})" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": ", highlighting the benefits in downstream tasks of considering future accumulative rewards, i.e., regularizing dependencies between different levels' latent representations. Moreover, the stable performance across " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " confirms our approach's robustness." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 308, + 198, + 544, + 274 + ], + "blocks": [ + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "lines": [ + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "text", + "content": "Table 4. Classification acc. of RL using different discount factors " + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "inline_equation", + "content": "\\gamma = 0" + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "text", + "content": " means we only maximize " + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "inline_equation", + "content": "r(s_{t},a_{t})" + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 198, + 544, + 274 + ], + "lines": [ + { + "bbox": [ + 308, + 198, + 544, + 274 + ], + "spans": [ + { + "bbox": [ + 308, + 198, + 544, + 274 + ], + "type": "table", + "html": "
ObjectiveγFashionMNISTCIFAR10
HVAELVAEHVAELVAE
r(st, at)075.63±0.1175.52±0.1041.91±0.1542.16±0.13
Q(st, at)0.878.03±0.1677.98±0.2346.45±0.3046.42±0.27
Q(st, at)0.8578.11±0.2478.34±0.1945.89±0.2445.97±0.31
Q(st, at)0.978.23±0.1378.48±0.1546.46±0.1546.35±0.17
Q(st, at)0.9577.95±0.1978.53±0.1646.21±0.2146.25±0.25
Q(st, at)0.9878.01±0.1078.28±0.1746.31±0.2046.37±0.19
", + "image_path": "ad2f88d3cb604143fb82ec30a2a5d33c95fb0151601bdf8cd503411016ac3bd2.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 278, + 458, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 278, + 458, + 291 + ], + "spans": [ + { + "bbox": [ + 306, + 278, + 458, + 291 + ], + "type": "text", + "content": "5. Limitation and Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 298, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 490 + ], + "type": "text", + "content": "Limitation and Future work. Though the (hierarchical) VAEs have advantages in modeling flexibility and sampling speed compared to other deep generative models [92] and are the most suitable models to demonstrate our idea with a theoretical interpretation, hierarchical VAE-based methods' application on downstream representation tasks could be somewhat outdated recently. Nevertheless, it's noteworthy that our idea of training hierarchical models with RL is not exclusively limited to hierarchical VAEs. Instead, it holds the potential when extended to general hierarchical models like diffusion models [40, 55], which feature more levels of latent representation and employ a fixed, non-trainable encoder for the efficient loss computation as independent terms over the hierarchy [61]. Our approach may be extended to learn a diffusion model with a trainable encoder, which may potentially enhance their representation capacity." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 491, + 547, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 657 + ], + "type": "text", + "content": "Conclusion. In this paper, we investigate the unsupervised representation learning with hierarchical VAEs from the perspective of information theory. We identify an urgent need to apply reinforcement learning to learn a high-quality hierarchy. The learned hierarchical representations have shown their superiority in improving the downstream task performance and mitigating the notorious posterior collapse. Additionally, an interesting finding is that learning a better ELBO (original training objective of hierarchical VAEs) is not necessary for learning a better representation, which has been supported by both our theoretical analysis and empirical results. Beyond hierarchical VAEs, our method may inspire future works to apply reinforcement learning to learn a hierarchical representation in time ahead." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 662, + 547, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 662, + 547, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 547, + 709 + ], + "type": "text", + "content": "Acknowledgment. This research is supported by the National Research Foundation, Singapore, under its Competitive Research Programme (Grant No. NRF-CRP23-2019-0006)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22953" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 105, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 105, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 105, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Korbinian Abstreiter, Sarthak Mittal, Stefan Bauer, Bernhard Scholkopf, and Arash Mehrjou. 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In ICLR, 2022." + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22956" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/9a46de44-a8c1-46de-8924-4659484e6064_content_list.json b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/9a46de44-a8c1-46de-8924-4659484e6064_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7780c925f920f1e8b0f23882f862c4cc6b94defc --- /dev/null +++ b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/9a46de44-a8c1-46de-8924-4659484e6064_content_list.json @@ -0,0 +1,1884 @@ +[ + { + "type": "text", + "text": "Improving Visual Recognition with Hyperbolic Visual Hierarchy Mapping", + "text_level": 1, + "bbox": [ + 101, + 130, + 867, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyeongjun Kwon $^{1}$ Jinhyun Jang $^{1}$ Jin Kim $^{1}$ Kwonyoung Kim $^{1}$ Kwanghoon Sohn $^{1,2*}$ $^{1}$ Yonsei University, $^{2}$ Korea Institute of Science and Technology (KIST)", + "bbox": [ + 119, + 179, + 852, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{kwonjunn01, jr000192, kimjin928, kyk12, khsohn}@yonsei.ac.kr,", + "bbox": [ + 210, + 218, + 756, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 264, + 268, + 339, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual scenes are naturally organized in a hierarchy, where a coarse semantic is recursively comprised of several fine details. Exploring such a visual hierarchy is crucial to recognize the complex relations of visual elements, leading to a comprehensive scene understanding. In this paper, we propose a Visual Hierarchy Mapper (Hi-Mapper), a novel approach for enhancing the structured understanding of the pre-trained Deep Neural Networks (DNNs). Hi-Mapper investigates the hierarchical organization of the visual scene by 1) pre-defining a hierarchy tree through the encapsulation of probability densities; and 2) learning the hierarchical relations in hyperbolic space with a novel hierarchical contrastive loss. The pre-defined hierarchy tree recursively interacts with the visual features of the pre-trained DNNs through hierarchy decomposition and encoding procedures, thereby effectively identifying the visual hierarchy and enhancing the recognition of an entire scene. Extensive experiments demonstrate that Hi-Mapper significantly enhances the representation capability of DNNs, leading to an improved performance on various tasks, including image classification and dense prediction tasks. The code is available at https://github.com/kwonjun01/Hi-Mapper.", + "bbox": [ + 75, + 300, + 473, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 666, + 207, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recognizing and representing the visual scene of any content is the fundamental pursuit of the computer vision field [1-4]. In particular, understanding what constitutes a scene and how each element is comprised of plays a key role in various visual recognition tasks such as image retrieval [1, 2], human-object interaction [3, 5], and dense prediction [6, 7]. This goes beyond merely learning discriminative feature representations, as it requires to reason about the fine details as well as their associations to comprehend the structured nature of the complex visual scene.", + "bbox": [ + 75, + 691, + 470, + 843 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f32b955fa92de7d740ba41d014175e41688c6c697ec1ecbb5598c8e7661e5baa.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 501, + 270, + 684, + 545 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f32f34b1fc22f5cfa7b2d4f0b6414b81d20611fab7b40f57b095208dc2d42203.jpg", + "image_caption": [ + "Hyperbolic Space" + ], + "image_footnote": [], + "bbox": [ + 686, + 268, + 890, + 448 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f5cd311959a724571187fc9c2b1b2f8214b5adff0b2a7c28bfe9f6ae35d08452.jpg", + "image_caption": [ + "(b)", + "Figure 1. (a) A visual scene can be decomposed into a hierarchical structure based on the semantics of each visual element. (b) Euclidean space is suboptimal in representing the hierarchical structure due to its flat nature. The relational distance is inaccurately captured, being unaware of the semantic similarity of visual elements (Red line). Hi-Mapper maps the hierarchical elements in hyperbolic space, which effectively preserves their semantic relations and distances due to its constant negative curvature." + ], + "image_footnote": [], + "bbox": [ + 683, + 469, + 890, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Over the decades, the development of deep neural networks (DNNs) has contributed towards advances in representing the complex visual scene. Notably, convolutional neural networks (CNNs) have achieved capturing fine details through the local convolutional filters while Vision Transformer (ViT) [8] has enabled coarse context modeling with multi-head self-attention mechanisms. Owing to their different desirable properties, hybrid architectures [9-12] and multi-scale variants of ViTs [13-15] have been extensively explored to capitalize on the complementary features of CNNs and ViTs. Subsequent works [16, 17] have further imposed interaction between multi-scale image patches to facilitate information exchange between fine details and coarse semantics.", + "bbox": [ + 496, + 689, + 892, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 851, + 222, + 863 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2021R1A2C2006703).", + "bbox": [ + 76, + 863, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17364", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While they have shown effective in capturing coarse-to-fine information, a structured understanding of the visual scene remains underexplored. Concretely, a scene can be interpreted as a hierarchical composition of visual elements, where the ability to recognize an instance (e.g. a man) at a coarse level arises from the ability to compose its constituents (e.g. body parts) at a finer level, as shown in Fig. 1a. Being aware of such semantic hierarchies furthers the perception of grid-like geometry and enhances the recognition of an entire image. Drawn from the same motivation, the recent variants of ViT [18-20] have constructed the hierarchies between image tokens across the transformer layers. However, their hierarchical relations are defined through the symmetric measurement (i.e., cosine similarity) which lacks the ability to represent the asymmetric property of hierarchical structure (i.e., inclusion of parent-child nodes). In addition, their image tokens are represented in Euclidean space where the hierarchical relations become distorted due to its linear and flat geometry [21-29], as shown in Fig. 1b.", + "bbox": [ + 76, + 90, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel Visual Hierarchy Mapper (Hi-Mapper) that improves the structured understanding of pre-trained DNNs by identifying the visual hierarchy. Hi-Mapper accomplishes this through: 1) Probabilistic modeling of hierarchy nodes, where the mean vector and covariance represent the center and scale of visual-semantic cluster, respectively [30-33]. Accordingly, the asymmetric hierarchical relations are captured through the inclusion of probability densities. Furthermore, 2) Hi-Mapper maps the hierarchy nodes to hyperbolic space, where its constant negative curvature effectively represents the exponential growth of hierarchy nodes. Specifically, Hi-Mapper pre-defines a tree-like structure, with its leaf-level node modeled as a unique Gaussian distribution and the higher-level nodes approximated by a Mixture of Gaussians (MoG) of their corresponding child nodes. The pre-defined hierarchy nodes then interact with the penultimate visual feature map of the pre-trained DNNs to decompose the feature map into the visual hierarchy. Moreover, in order to bypass the difficulties of modeling hierarchy in Euclidean space, Hi-Mapper maps the identified visual hierarchy to hyperbolic space and learns the hierarchical relation with a novel hierarchical contrastive loss. The proposed loss enforces the child-parent nodes to be similar and child-child nodes to be dissimilar in a shared hyperbolic space. The visual hierarchy then interacts with the global visual feature of the pre-trained DNNs such that the hierarchical relations are fully encoded in the global feature representation.", + "bbox": [ + 76, + 397, + 472, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hi-Mapper serves as a plug-and-play module, which generalizes over any type of DNNs and flexibly identifies the hierarchical organization of visual scenes. We conduct extensive experiments with various pre-trained DNNs (i.e., ResNet [34], DeiT [35]) on several benchmarks [36-38] to", + "bbox": [ + 76, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "demonstrate the effectiveness of Hi-Mapper.", + "bbox": [ + 500, + 90, + 792, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our key contributions are as follows:", + "bbox": [ + 517, + 108, + 846, + 122 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel Visual Hierarchy Mapper (Hi-Mapper) that enhances the structured understanding of the pre-trained DNNs by investigating the hierarchical organization of visual scene. The proposed Hi-Mapper is applicable to any type of the pre-trained DNNs without modifying the underlying structures.", + "- Hi-Mapper effectively identifies the visual hierarchy by combining the favorable characteristic of probabilistic modeling and hyperbolic geometry for representing the hierarchical structure.", + "- We conduct extensive experiments to validate the efficacy of the proposed Hi-Mapper, and improves over the state-of-the-art approaches on various visual recognition tasks." + ], + "bbox": [ + 500, + 123, + 893, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 334, + 640, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hierarchy-aware visual recognition. Unsupervised image parsing is a long-standing pursuit in visual recognition tasks from the classical computer vision era [39-43]. In the pre-deep learning era, Zhouwen et al. [42] firstly introduces a framework to parse images with their constituents via a divide-and-conquer strategy. CapsuleNet-based methods have demonstrated substantial enhancements in image parsing, facilitated by dynamic routing, which efficiently capture the compositional relationships among the activities of capsules that represent object parts. Recently, hierarchical semantic segmentation has been extensively researched, including human parser [44, 45] based on human-part hierarchy and unsupervised part segmentations [46-48].", + "bbox": [ + 496, + 361, + 893, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Beyond image parsing, recent researches on deep neural networks (DNNs) have attempted to exploit hierarchical relationships between detail and global representations. CrossViT [16] utilizes a dual-branch transformer for multiscale feature extraction, enriching features through a fusion module that integrates inter-scale patch relationships. Quadtree [18] iteratively and hierarchically selects a subset of crucial finer patches within each coarse patch. DependencyViT [19] inverts the self-attention process to organize patches as parent and child nodes, enabling a hierarchical exploration. More recently, CAST [49] employs superpixel-based patch generation and graph pooling for hierarchical patch merging for improving fine-grained recognition performances. While they define hierarchical relations with token similarities in Euclidean space, we predefine a hierarchical structure with probabilistic modeling and learn the relation in hyperbolic space.", + "bbox": [ + 496, + 558, + 895, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Probabilistic modeling. Probabilistic representation has been extensively explored in the early NLP studies for handling the nuance of word semantics with the probability distribution. For instance, Vilnis et al. [30] first introduced the probability densities for representing", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17365", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "word embeddings. Athiwaratkun et al. [31] discovered that an imbalance in word frequency leads to distortions in word order and mitigated the problem by representing the word orders through the encapsulation of probability densities. Besides word representation, abundant research has demonstrated the effectiveness of probabilistic modeling in visual representation [6, 50-52]. For example, Shi et al. [51] proposed to penalize the low quality face images by measuring the variance of each image distribution. Chun et al. [50] identified the limitations of deterministic modeling in vision-language domains and introduced probabilistic cross-modal embedding for providing the uncertainty estimates.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we deploy probabilistic modeling in defining hierarchical structure, where each distribution represents the inclusive relations of hierarchy nodes.", + "bbox": [ + 75, + 273, + 470, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hyperbolic manifold. Hyperbolic manifolds have gained increasing interest in deep learning area due to their effectiveness in modeling hierarchical structures. Their success in NLP field [24, 26, 27, 53] has inspired approaches to adopt hyperbolic manifolds in computer vision researches such as image retrieval [1, 2], image segmentation [54, 55], and few-shot learning [25]. As a pioneering work, Khrulkov et al. [56] investigated an exponential map from Euclidean space to hyperbolic space for learning hierarchical image embeddings. Ermolov et al. [1] applied pair-wise cross entropy loss in hyperbolic space for ViTs. Kim et al. [2] extended the work by discovering the latent hierarchy of training data with learnable hierarchical proxies in hyperbolic space. Focusing on pixel-level analysis, [55] identified the long-tail objects by embedding masked instance regions into hyperbolic manifolds. More recently, Desai et al. [29] introduced to learn joint image-text embedding space in hyperbolic manifold. While they explore hyperbolic manifold for representing the categorical hierarchies, we identify the hierarchical structure of visual elements without the part-level annotation through a novel hierarchical contrastive loss.", + "bbox": [ + 75, + 338, + 472, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Hyperbolic Geometry", + "text_level": 1, + "bbox": [ + 76, + 691, + 284, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hyperbolic manifold is a smooth Riemannian manifold $\\mathcal{M}$ with negative curvature $c$ equipped with a Riemannian metric $g$ . The manifold consists of five isometric models and we utilize the Lorentz model for developing Hi-Mapper due to its training stability. A hyperbolic manifold of $n$ -dimensions can be represented as a sub-manifold of the Lorentz model $\\mathbb{R}^{n+1}$ as an upper half of a two-sheeted hyperboloid. In the Lorentz space, every point $\\mathbf{x} \\in \\mathbb{R}^{n+1}$ can be denoted as $[\\mathbf{x}_{\\mathrm{space}}, x_{\\mathrm{time}}]$ , where $\\mathbf{x}_{\\mathrm{space}} \\in \\mathbb{R}^n$ and $x_{\\mathrm{time}} \\in \\mathbb{R}$ . Let $\\langle \\mathbf{x}, \\mathbf{y} \\rangle$ be the Euclidean inner product and $\\langle \\mathbf{x}, \\mathbf{y} \\rangle_{\\mathbb{L}}$ denote the Lorentzian inner product which is derived by the Riemannian metric of the Lorentz model $g_{\\mathbb{L}}$ . Given two vectors $\\mathbf{x}, \\mathbf{y} \\in$", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{n + 1}$ , the Lorentzian inner product is computed as follows:", + "bbox": [ + 500, + 90, + 885, + 106 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\langle \\mathbf {x}, \\mathbf {y} \\rangle_ {\\mathbb {L}} = - x _ {\\text {t i m e}} y _ {\\text {t i m e}} + \\left\\langle \\mathbf {x} _ {\\text {s p a c e}}, \\mathbf {y} _ {\\text {s p a c e}} \\right\\rangle . \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 116, + 893, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The $n$ -dimensional Lorentz model $(\\mathbb{L}^n,g_{\\mathbb{L}})$ is defined by the manifold $\\mathbb{L}^n = \\{\\mathbf{x}\\in \\mathbb{R}^{n + 1}:\\langle \\mathbf{x},\\mathbf{x}\\rangle_{\\mathbb{L}} = -1 / c,c > 0\\}$ and Riemannian metric of the Lorentz model $g_{\\mathbb{L}}$ . Thus, all vectors satisfy the following constraints:", + "bbox": [ + 496, + 143, + 893, + 205 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n- x _ {\\text {t i m e}} ^ {2} + \\left\\| \\mathbf {x} _ {\\text {s p a c e}} \\right\\| ^ {2} = - 1 / c. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 213, + 892, + 233 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A geodesic is the shortest path between two vectors on the manifold. The Lorentzian distance on $\\mathbb{L}$ is then defined as:", + "bbox": [ + 496, + 243, + 890, + 272 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\mathbb {L}} (\\mathbf {x}, \\mathbf {y}) = \\operatorname {a r c c o s h} (- \\langle \\mathbf {x}, \\mathbf {y} \\rangle_ {\\mathbb {L}}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 284, + 892, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The exponential map is a way to map vectors from tangent space $\\mathcal{T}_z\\mathbb{L}^n$ onto hyperbolic manifolds $\\mathbb{L}^n$ , where $\\mathcal{T}_z\\mathbb{L}^n$ is a Euclidean space of vectors that are orthogonal to some point $\\mathbf{z}\\in \\mathbb{L}^n$ . We map the tangent vector $\\mathbf{v}\\in \\mathcal{T}_z\\mathbb{L}^n$ from Euclidean space to the Lorentz manifolds, in which the exponential map $\\mathrm{expm}_{\\mathbf{z}}$ is defined as:", + "bbox": [ + 496, + 311, + 892, + 402 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\exp_ {z} (\\mathbf {v}) = \\cosh (\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}}) \\mathbf {z} + \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}})}{\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}}} \\mathbf {v}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 411, + 892, + 457 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The logarithm map $\\log \\mathrm{m}_z$ which transfers $\\mathbf{x}$ on the hyperboloid back to the tangent space $\\mathcal{T}_z\\mathcal{M}$ is defined as:", + "bbox": [ + 496, + 458, + 890, + 488 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} = \\log \\mathrm {m} _ {z} (\\mathbf {x}) = \\frac {\\cosh^ {- 1} (- c \\langle \\mathbf {z} , \\mathbf {x} \\rangle_ {\\mathbb {L}})}{\\sqrt {(c \\langle \\mathbf {z} , \\mathbf {x} \\rangle_ {\\mathbb {L}}) ^ {2} - 1}} \\operatorname {p r o j} _ {\\mathbf {z}} (\\mathbf {x}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 498, + 892, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We set $\\mathbf{z}$ as the origin of the hyperboloid $\\mathbf{O} = \\left[\\mathbf{0},\\sqrt{1 / c}\\right]$ .", + "bbox": [ + 496, + 545, + 883, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 580, + 589, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 604, + 609, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to enhance the structured understanding of pre-trained deep neural networks (DNNs) by investigating the hierarchical organization of visual scenes. To this end, we introduce a Visual Hierarchy Mapper (Hi-Mapper) which serves as a plug-and-play module on any type of pre-trained DNNs. An overview of Hi-Mapper is depicted in Fig. 2a.", + "bbox": [ + 496, + 628, + 893, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an image $\\mathcal{I}$ , we first extract visual features $[\\mathbf{v}_{\\mathrm{map}},\\mathbf{v}_{\\mathrm{cls}}] = \\mathcal{F}(\\mathcal{I})$ from a pre-trained image encoder $\\mathcal{F}$ where $\\mathbf{v}_{\\mathrm{map}}\\in \\mathbb{R}^{hw\\times d}$ is the penultimate visual feature map and $\\mathbf{v}_{\\mathrm{cls}}\\in \\mathbb{R}^d$ is the global visual representation, with $hw$ indicating the size of the visual feature map.", + "bbox": [ + 496, + 719, + 893, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hi-Mapper identifies the visual hierarchy from the visual feature map $\\mathbf{v}_{\\mathrm{map}}$ and encodes the identified visual hierarchy back to the global visual representation $\\mathbf{v}_{\\mathrm{cls}}$ for enhancing the recognition of a whole scene. To this end, we predefine a hierarchy tree with Gaussian distribution, where the relations of the hierarchy nodes are defined through the inclusion of probability densities (Sec. 4.2). The pre-defined", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17366", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/66ccadbd22d4d7d91588a6ef746de4350487e564e7e8a54b330eb4bb4947553e.jpg", + "image_caption": [ + "(a) Overall pipeline" + ], + "image_footnote": [], + "bbox": [ + 84, + 94, + 653, + 253 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/94a153c09532eceb565c18d4cfe3a2f7aea756955c0e73e05ba2061962388fe4.jpg", + "image_caption": [ + "(b) Hierarchical contrastive loss" + ], + "image_footnote": [], + "bbox": [ + 673, + 95, + 875, + 251 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/152e897f97f5ede0f072fd9146304cb66f693066a5ba46c13a62799ac5d987ac.jpg", + "image_caption": [ + "Figure 2. (a) An overview of the proposed Hi-Mapper. Hi-Mapper operates on top of pre-trained image encoder $\\mathcal{F}$ , with probabilistic hierarchy tree $\\mathbf{T} = \\{\\mathbf{C}^l\\}_{l=1}^L$ . The tree interacts with visual feature map $\\mathbf{v}_{\\mathrm{map}}$ through hierarchy decomposition module $\\mathcal{D}$ , thereby identifying visual hierarchy in Euclidean space $\\mathbf{T}_{\\mathbb{E}} = \\{\\mathbf{S}^l\\}_{l=1}^L$ . The visual hierarchy is mapped to hyperbolic space $\\mathbf{T}_{\\mathbb{L}} = \\{\\mathbf{H}^l\\}_{l=1}^L$ and optimized with hierarchical contrastive loss $\\mathcal{L}_{\\mathbb{L}-\\mathrm{cont}}$ . The visual hierarchy is further encoded into global visual representation $\\mathbf{v}_{\\mathrm{cls}}$ via hierarchy encoding module $\\mathcal{G}$ for enhancing the recognition of entire scene. (b) The proposed hierarchical contrastive loss pulls each parent-child node and pushes all the other nodes at the same level." + ], + "image_footnote": [], + "bbox": [ + 94, + 371, + 457, + 448 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/061d512bb38d3a54e0aefeddd20c432d103a1ee1bc15bba92b551adeb8ad72b7.jpg", + "image_caption": [ + "(a) Hierarchy decomposition", + "(b) Hierarchy encoding", + "Figure 3. (a) Hierarchy decomposition module groups semantically-relevant visual features $\\mathbf{v}_{\\mathrm{map}}$ to the closest semantic cluster $\\mathbf{C}^l$ . (b) Hierarchy encoding module progressively updates global representation $\\mathbf{v}_{\\mathrm{cls}}$ by aggregating the visual hierarchy $\\mathbf{S}^l$ ." + ], + "image_footnote": [], + "bbox": [ + 96, + 472, + 449, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The hierarchy tree interacts with $\\mathbf{v}_{\\mathrm{map}}$ through the hierarchy decomposition module $\\mathcal{D}$ such that the feature map is decomposed into the visual hierarchy (Sec. 4.3). Since the zero curvature of Euclidean space is not optimal for representing the hierarchical structure, we map the visual hierarchy to hyperbolic space and optimize the relation with a novel hierarchical contrastive loss (Sec. 4.4). The visual hierarchy is then encoded back to the global visual representation $\\mathbf{v}_{\\mathrm{cls}}$ through the hierarchy encoding module $\\mathcal{G}$ resulting in an enhanced global representation (Sec. 4.5).", + "bbox": [ + 75, + 669, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Probabilistic hierarchy tree", + "text_level": 1, + "bbox": [ + 76, + 830, + 323, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The main problem of the recent hierarchy-aware ViTs [18-20] is that they define the hierarchical relations between the image tokens mainly through the self-attention scores. Such", + "bbox": [ + 75, + 854, + 472, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a symmetric measurement is suboptimal for representing the asymmetric inclusive relation of parent-child nodes. To handle the problem, we propose to define $L$ levels of hierarchy tree $\\mathbf{T}$ by modeling each hierarchy node with a probability distribution.", + "bbox": [ + 496, + 369, + 893, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first parameterize each leaf-level (at the initial level) node as a unique Gaussian distribution and subsequently define the higher-level node as a Mixture-of-Gaussians (MoG) of its corresponding child nodes. Accordingly, the mean vector represents the cluster center of the visual semantic and the covariance captures the scale of each semantic cluster.", + "bbox": [ + 496, + 445, + 893, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initial level. Let $\\mathbf{C}^1 = \\{\\mathbf{c}_n^1\\}_{n=1}^{N_1}$ be a set of $N_1$ initial level nodes. We parameterize each node $\\mathbf{c}_n^1$ as a normal distribution with a mean vector $\\mu_n^1$ and a diagonal covariance matrix $\\sigma_n^1\\mathbf{I}$ in $\\mathbb{R}^d$ as:", + "bbox": [ + 496, + 556, + 893, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\mathbf {c} _ {n} ^ {1}\\right) \\sim \\mathcal {N} \\left(\\mu_ {n} ^ {1}, \\sigma_ {n} ^ {1} \\mathbf {I}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 630, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_n^1$ and $\\sigma_{n}^{1}$ are randomly initialized. We use reparameterization trick [57] for stable sampling, such that:", + "bbox": [ + 496, + 660, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {n} ^ {1} = \\mu_ {n} ^ {1} + \\epsilon * \\sigma_ {n} ^ {1} \\in \\mathbb {R} ^ {d}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 702, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$", + "bbox": [ + 496, + 732, + 632, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequent level. We derive the remaining $(L - 1)$ levels of hierarchy tree by conditioning each level on the preceding hierarchy level. For each $l$ -th level, we formulate a set of $N_{l}$ nodes $\\mathbf{C}^{l} = \\{\\mathbf{c}_{k}^{l}\\}_{k = 1}^{N_{l}}$ . Concretely, the $k$ -th node $\\mathbf{c}_k^l$ at the $l$ -th level is approximated by a MoG of its two corresponding child nodes, $\\mathbf{c}_{2k - 1}^{l - 1}$ and $\\mathbf{c}_{2k}^{l - 1}$ , as:", + "bbox": [ + 496, + 755, + 890, + 849 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\mathbf {c} _ {k} ^ {l}\\right) \\sim \\sum_ {k ^ {\\prime} = 2 k - 1} ^ {2 k} \\mathcal {N} \\left(\\mu_ {k ^ {\\prime}} ^ {l - 1}, \\sigma_ {k ^ {\\prime}} ^ {l - 1} \\mathbf {I}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 861, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17367", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To stabilize the construction of hierarchy tree, we increase the sampling rate as the distribution expands, i.e., we sample $2^{l - 1}$ embeddings from $p(\\mathbf{c}_k^l)$ using the reparameterization trick in Eq. (7) as:", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {c} _ {k} ^ {l} = \\left\\{\\hat {\\mathbf {c}} _ {k, 1} ^ {l}, \\dots , \\hat {\\mathbf {c}} _ {k, 2 ^ {l - 1}} ^ {l} \\right\\} \\stackrel {{\\mathrm {i d}}} {{\\sim}} p \\left(\\mathbf {c} _ {k} ^ {l}\\right), \\quad \\mathbf {c} _ {k} ^ {l} \\in \\mathbb {R} ^ {2 ^ {l - 1} \\times d}, \\tag {9} \\\\ \\mathbf {C} ^ {l} = \\left\\{\\mathbf {c} _ {1} ^ {l}, \\dots , \\mathbf {c} _ {N _ {l}} ^ {l} \\right\\} \\in \\mathbb {R} ^ {2 ^ {l - 1} N _ {l} \\times d}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 161, + 468, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By sequentially conditioning the higher-level nodes on the preceding lower-level nodes, we obtain the hierarchy tree $\\mathbf{T} = \\{\\mathbf{C}^l\\}_{l=1}^L$ , where the lower-level nodes capture fine details with concentrated distribution and the higher-level nodes capture coarse instance-level representations with dispersed distribution.", + "bbox": [ + 75, + 215, + 468, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "KL divergence loss. To prevent the variances from collapsing to zero, we employ KL regularization term between the distributions of $L$ -th level nodes and the unit Gaussian prior $\\mathcal{N}(0,\\mathbf{I})$ following [50]:", + "bbox": [ + 75, + 313, + 468, + 375 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K L}} = \\sum_ {i = 1} ^ {N _ {L}} \\mathrm {K L} \\left(\\mathcal {N} \\left(\\mu_ {i} ^ {L}, \\sigma_ {i} ^ {L}\\right) \\| \\mathcal {N} (0, \\mathbf {I})\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 383, + 468, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Visual hierarchy decomposition", + "text_level": 1, + "bbox": [ + 76, + 436, + 354, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the pre-defined hierarchy tree $\\mathbf{T}$ and the visual feature map $\\mathbf{v}_{\\mathrm{map}}$ , we decompose $\\mathbf{v}_{\\mathrm{map}}$ into $L$ levels of visual hierarchy through hierarchy decomposition module $\\mathcal{D}$ , as shown in Fig. 3a. We instantiate $\\mathcal{D}$ as a stack of two transformer decoder layers.", + "bbox": [ + 75, + 459, + 468, + 534 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To identify the visual hierarchy at the $l$ -th level, the decomposition module $\\mathcal{D}$ treats $\\mathbf{C}^l$ as the query, and $\\mathbf{v}_{\\mathrm{map}}$ as the key and value such that the semantically-relevant visual features are aggregated to the closest semantic cluster:", + "bbox": [ + 75, + 535, + 468, + 594 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} ^ {l} = \\left\\{\\mathbf {s} _ {1} ^ {l}, \\dots , \\mathbf {s} _ {N _ {l}} ^ {l} \\right\\} = \\mathcal {D} \\left(\\mathbf {C} ^ {l}, \\mathbf {v} _ {\\text {m a p}}\\right) \\in \\mathbb {R} ^ {2 ^ {l - 1} N _ {l} \\times d}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 604, + 468, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to the hierarchy nodes $\\mathbf{c}_k^l$ in Eq. (9), the decomposed visual hierarchy nodes $\\mathbf{s}_k^l$ are comprised of $2^{l-1}$ visual representations as $\\mathbf{s}_k^l = \\{\\hat{\\mathbf{s}}_{k,1}^l, \\dots, \\hat{\\mathbf{s}}_{k,2^{l-1}}^l\\}$ . We average the set of $2^{l-1}$ representations for each visual hierarchy node $\\mathbf{s}_k^l$ such that:", + "bbox": [ + 75, + 637, + 468, + 715 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} _ {k} ^ {l} = \\frac {1}{2 ^ {l - 1}} \\sum_ {i = 1} ^ {2 ^ {l - 1}} \\hat {\\mathbf {s}} _ {k, i} ^ {l}, \\quad \\mathbf {s} _ {k} ^ {l} \\in \\mathbb {R} ^ {d} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 724, + 468, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform the same decomposition procedure for $L$ levels, thereby obtaining $L$ levels of visual hierarchy in Euclidean space $\\mathbf{T}_{\\mathbb{E}} = \\{\\mathbf{S}^l\\}_{l=1}^L$ .", + "bbox": [ + 75, + 777, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Learning hierarchy in hyperbolic space", + "text_level": 1, + "bbox": [ + 76, + 832, + 415, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A natural characteristic of the hierarchical structure is that the number of nodes exponentially increases as the depth increases. In practice, representing this property in Euclidean", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "space leads to distortions in the semantic distances due to its flat geometry. We propose to handle the problem by learning the hierarchical relations in hyperbolic space, where its exponentially expanding volume can efficiently represent the visual hierarchy.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first map $\\mathbf{T}_{\\mathbb{E}}$ to the Lorentz hyperboloid to derive the visual hierarchy in hyperbolic space $\\mathbf{T}_{\\mathbb{L}}$ . Following [29], we simplify the mapping computation by parameterizing only the space component of the Lorentz model as $\\mathbf{s} = [\\mathbf{s}_k^l, 0] \\in \\mathbb{R}^{d+1}$ , where $\\mathbf{s}$ belongs to the tangent space at the hyperboloid origin $\\mathbf{O}$ . The visual hierarchy node in hyperbolic space $\\mathbf{h}_k^l = [\\mathbf{h}_{k,\\mathrm{space}}^l, h_{k,\\mathrm{time}}^l]$ is then obtained by transforming $\\mathbf{s}_k^l$ to $\\mathbf{h}_{k,\\mathrm{space}}^l$ using the exponential map in Eq. (13) as:", + "bbox": [ + 496, + 167, + 890, + 305 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {h} _ {k, \\text {s p a c e}} ^ {l} = \\cosh (\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}}) \\mathbf {0} + \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}})}{\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}}} \\mathbf {s} _ {k} ^ {l} \\\\ = \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {s} _ {k} ^ {l} \\|)}{\\sqrt {c} \\| \\mathbf {s} _ {k} ^ {l} \\|} \\mathbf {s} _ {k} ^ {l}, \\tag {13} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 316, + 890, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and computing the corresponding time component $h_{k,\\mathrm{time}}^{l}$ using Eq. (2) as $h_{k,\\mathrm{time}}^{l} = \\sqrt{1 / c + \\|\\mathbf{h}_{k,\\mathrm{space}}^{l}\\|^{2}}$ . The visual hierarchy in hyperbolic space $\\mathbf{T}_{\\mathbb{L}}$ is denoted as:", + "bbox": [ + 496, + 398, + 890, + 454 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {T} _ {\\mathbb {L}} = \\left\\{\\mathbf {H} ^ {l} \\right\\} _ {l = 1} ^ {L}, \\quad \\mathbf {H} ^ {l} = \\left\\{\\mathbf {h} _ {1} ^ {l}, \\dots , \\mathbf {h} _ {N _ {l}} ^ {l} \\right\\} \\in \\mathbb {R} ^ {N _ {l} \\times d _ {\\mathbb {L}}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 464, + 890, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d_{\\mathbb{L}}$ is the embedding dimension in Lorentz manifold.", + "bbox": [ + 496, + 494, + 888, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hierarchical contrastive loss. To guarantee the hierarchy nodes to reflect the hierarchical relations, we optimize the distances of $\\mathbf{T}_{\\mathbb{L}}$ with a novel hierarchical contrastive loss $\\mathcal{L}_{\\mathbb{L}\\text{-cont}}$ . Specifically, we formulate the similarity between the nodes in consideration of the length of the connected branch, i.e., geodesic distance, as shown in Fig. 2b.", + "bbox": [ + 496, + 516, + 890, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Consider a node $\\mathbf{h}_{2k}^{l}$ in $\\mathbf{T}_{\\mathbb{L}}$ , where $\\mathbf{h}_k^{l + 1}$ is its parent node. We encourage $\\mathbf{h}_{2k}^{l}$ to be similar with $\\mathbf{h}_k^{l + 1}$ since the pair of parent-child nodes lie on the same branch. Meanwhile, we encourage the remaining nodes in the same level, i.e., $\\{\\mathbf{h}_i^l |\\mathbf{h}_i^l\\in \\mathbf{H}^l,i\\neq 2k\\}$ , to be dissimilar since they all lie on separate branches. The loss also penalizes the close sibling node $\\mathbf{h}_{2k - 1}^{l}$ as their geodesic traverses the parent node. Formally, the hierarchical contrastive loss incorporates the geometric interpretation of hierarchical structure into the contrastive loss [58] as:", + "bbox": [ + 496, + 607, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathbb {L} - \\text {c o n t}} = - \\log \\underset {\\mathbf {T} _ {\\mathbb {L}}} {\\mathbb {E}} \\left[ \\sum_ {i = 0} ^ {1} \\frac {\\exp \\left(D _ {\\mathbb {L}} \\left(\\mathbf {h} _ {k} ^ {l + 1} , \\mathbf {h} _ {2 k - i} ^ {l}\\right)\\right)}{\\sum_ {j \\neq 2 k - i} \\exp \\left(D _ {\\mathbb {L}} \\left(\\mathbf {h} _ {2 k - i} ^ {l} , \\mathbf {h} _ {j} ^ {l}\\right)\\right)} \\right], \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 770, + 890, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D_{\\mathbb{L}}$ is the Lorentzian distance defined in Eq. (3).", + "bbox": [ + 496, + 825, + 861, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By regarding every pair of parent-child nodes as positive and every pair of nodes at the same level as negative, we are able to represent the logical structure of visual hierarchy without the part-level annotation. In addition, the", + "bbox": [ + 496, + 840, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17368", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "hierarchical relation optimized through $\\mathbf{T}_{\\mathbb{L}}$ in hyperbolic space is well-preserved in $\\mathbf{T}_{\\mathbb{E}}$ in Euclidean space thanks to the mapping computation in Eq. (13).", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Visual hierarchy encoding", + "text_level": 1, + "bbox": [ + 76, + 146, + 313, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We propose to enhance the structured understanding of the global visual representation by encoding the identified visual hierarchy into $\\mathbf{v}_{\\mathrm{cls}}$ . While we optimize the hierarchical relations in hyperbolic space due to its ability of handling relative distances, its complex computations and expansion property make it less suitable for tasks that require absolute criteria. Thus, we exploit the visual hierarchy in Euclidean space $\\mathbf{T}_{\\mathbb{E}}$ for hierarchy encoding.", + "bbox": [ + 75, + 169, + 468, + 290 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Specifically, we progressively encode the hierarchy nodes $\\mathbf{S}^l$ into $\\mathbf{v}_{\\mathrm{cls}}$ , from the initial level to the $L$ -th level, via the hierarchy encoding module $\\mathcal{G}$ such that $\\mathbf{v}_{\\mathrm{cls}}$ is updated as a hierarchy-aware global representation $\\mathbf{v}_{\\mathrm{cls}}^L$ . As shown in Fig. 3b, the module $\\mathcal{G}$ is instantiated as a stack of $L$ transformer decoder layers.", + "bbox": [ + 75, + 290, + 468, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To encode the $l$ -th level hierarchy, the $l$ -th layer of $\\mathcal{G}^l$ takes $\\mathbf{v}_{\\mathrm{cls}}^{l-1}$ as the query, and $\\mathbf{S}^l$ as the key and value:", + "bbox": [ + 76, + 380, + 468, + 412 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {\\mathrm {c l s}} ^ {l} = \\mathcal {G} ^ {l} \\left(\\mathbf {v} _ {\\mathrm {c l s}} ^ {l - 1}, \\mathbf {S} ^ {l}\\right) \\in \\mathbb {R} ^ {d}, \\quad 0 < l \\leq L, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 422, + 468, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where we set $\\mathbf{v}_{\\mathrm{cls}}^{0}$ as $\\mathbf{v}_{\\mathrm{cls}}$ . The enhanced global visual representation is then derived as:", + "bbox": [ + 75, + 453, + 468, + 483 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {v}} _ {\\mathrm {c l s}} = \\mathbf {v} _ {\\mathrm {c l s}} + \\mathbf {v} _ {\\mathrm {c l s}} ^ {L}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 494, + 468, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the final prediction, we feed $\\hat{\\mathbf{v}}_{\\mathrm{cls}}$ into the pre-trained classifier of $\\mathcal{F}$ .", + "bbox": [ + 75, + 523, + 468, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall objectives. The overall objective is defined as:", + "bbox": [ + 76, + 561, + 452, + 575 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\mathrm {C E}} + \\alpha \\mathcal {L} _ {\\mathbb {L} - \\text {c o n t}} + \\beta \\mathcal {L} _ {\\mathrm {K L}}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 588, + 468, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are the balancing parameters.", + "bbox": [ + 75, + 616, + 372, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 645, + 209, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct extensive experiments to show the effectiveness of our proposed Hi-Mapper on image classification (Sec. 5.1), object detection and instance segmentation (Sec. 5.2), and semantic segmentation (Sec. 5.3). We apply our Hi-Mapper on both CNN-based [34, 59] and ViT-based [35, 60] backbone networks and compare the performance with the concurrent hierarchy-aware baselines [16, 19]. Lastly, we provide ablation studies (Sec. 6) to demonstrate the effectiveness of our contributions.", + "bbox": [ + 75, + 671, + 468, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Image classification", + "text_level": 1, + "bbox": [ + 76, + 816, + 264, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We apply our Hi-Mapper on the state-of-the-art backbone networks [34, 35, 59, 60] and benchmark on ImageNet-1k [36] dataset. Following [12, 60, 62-64], we use the identical combinations for data augmentation", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d03ee7314273d2f5622ede3e1a0bb473c260b0cb91ae1bd6fe67bc9489cf305b.jpg", + "table_caption": [ + "Table 1. Performance comparisons for image classification on ImageNet-1K [36] dataset." + ], + "table_footnote": [], + "table_body": "
TypeModelParams (M)FLOPs (G)Top-1 (%)
CNNResNet-50 [34]25.63.876.2
EfficientNet-B4* [59]19.34.282.9
Hi-Mapper(RN50)26.94.078.2
Hi-Mapper(ENB4*)20.54.484.1
ViTDeiT-T [35]5.71.372.2
CrossViT-T [16]6.91.673.4
PVT-T [61]13.21.975.1
DependecnyViT-T [19]6.21.375.4
Hi-Mapper(DeiT-T)6.61.574.8
DeiT-S [35]22.24.579.8
CrossViT-S [16]26.75.681
PVT-S [61]24.53.879.8
Swin-T [60]28.34.681.2
DependencyViT-S [19]24.05.082.1
Hi-Mapper(DeiT-S)23.34.882.6
Hi-Mapper(Swin-T)29.54.983.4
DeiT-B [35]85.617.681.8
Swin-S [60]50.18.783.0
Hi-Mapper(DeiT-B)87.218.183.4
Hi-Mapper(Swin-S)51.89.384.1
", + "bbox": [ + 511, + 128, + 879, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and regularization strategies [35] after excluding repeated augmentation [65]. We train our model with batch size 1024 for 50 epochs using AdamW [66] with weight decay 1e-4. The initial learning rate is set to 1e-4 and a cosine learning rate scheduler is applied following [35].", + "bbox": [ + 498, + 537, + 893, + 614 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Tab. 1 presents classification performance. We report the original performance without the fine-tuning schemes for the plain backbone networks since we observed degradation in performance after fine-tuning the models. Our proposed method consistently achieves better performances than the baseline models with only a slight increase in parameters. Specifically, Hi-Mapper surpasses ResNet-50 [34] and EfficientNet-B4 [59] by margins of $2.0\\%$ and $1.2\\%$ , respectively. Additionally, it achieves improvement on DeiT's performance by $2.6\\%/2.8\\%/1.6\\%$ , and Swin [60] by $2.2\\%/1.1\\%$ across various model sizes. The experiments on image classification demonstrate not only the importance of understanding the structured organization of visual scenes, but also the scalability of our method.", + "bbox": [ + 496, + 623, + 893, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Object detection and Instance segmentation", + "text_level": 1, + "bbox": [ + 500, + 845, + 870, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We experiment on the COCO [37] dataset. We use the Hi-Mapper backbones derived from Sec. 5.1. Then,", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17369", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d1e50d09e693ffa00207420146e791c56934ae0890579dbda0349cbcbfdf81df.jpg", + "table_caption": [ + "Table 2. Performance comparisons for object detection and instance segmentation on COCO [37] dataset. $(^{*})$ Results are reproduced based on [10]." + ], + "table_footnote": [], + "table_body": "
BackboneParams (M)Flops (G)Mask R-CNN 1x
APboxAPbox50APbox75APmaskAPmask50APmask75
PVT-T [61]32.919536.759.239.335.156.737.3
DeiT-T* [35]27.324430.346.232.127.144.428.3
Hi-Mapper(Deit-T)29.524637.161.741.035.759.138.1
PVT-S [61]44.124540.462.943.837.860.140.3
DeiT-S* [35]44.927636.354.139.031.751.333.2
Swin-T [60]47.826743.566.447.339.663.142.3
Hi-Mapper(Deit-S)47.027942.665.846.338.962.741.8
Hi-Mapper(Swin-T)50.427044.067.147.939.963.642.8
", + "bbox": [ + 99, + 122, + 874, + 309 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/95b236e3be0fb4c74e23edcf2b2b3ae6d1fc636d964f01dc9e4ad68aedb0c00c.jpg", + "table_caption": [ + "Table 3. Performance comparisons for semantic segmentation on ADE20k [38] dataset. We conduct the single-scale evaluation. FLOPs are measured with $512 \\times 2048$ input resolution." + ], + "table_footnote": [], + "table_body": "
BackboneMethodParams (M)FLOPs (G)mIoU
PVT-T [61]SemanticFPN [69]17.013235.7
DeiT-T [35]UperNet [70]10.714237.8
DependencyViT-T [19]UperNet [70]11.114540.3
Hi-Mapper(DeiT-T)UperNet [70]11.614439.8
PVT-S [61]SemanticFPN [69]28.271239.8
DeiT-S [35]UperNet [70]41.356643.0
Swin-T [60]UperNet [70]60.094544.5
DependencyVIT-S [19]UperNet [70]43.157445.7
Hi-Mapper(DeiT-S)UperNet [70]42.557046.3
Hi-Mapper(Swin-T)UperNet [70]62.194946.8
", + "bbox": [ + 84, + 366, + 467, + 569 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we deploy our pre-trained backbone into Mask R-CNN [67]. All models are trained on COCO 2017, including 118k train images and 5k validation images. We follow the standard learning protocols [67], $1 \\times$ schedule with 12 epochs. Note that we reproduce DeiT-T with Mask R-CNN based on [68].", + "bbox": [ + 75, + 582, + 470, + 659 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. In Table 2, we present a comparison of our results with baseline models, such as DeiT and Swin, on the COCO dataset, which demands a higher capacity for fine representation recognition. Our Hi-Mapper consistently boosts all baseline models capability with only a small increase in parameters. Notably, Hi-Mapper significantly improves DeiT-T and -S by margins of 6.8 and 8.3 on the object detection task. Meanwhile, in the instance segmentation, it also improves DeiT-T and -S by margins of 8.6 and 7.2, respectively. This result shows that the visual hierarchy facilitates complex visual scene recognition.", + "bbox": [ + 75, + 667, + 470, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Semantic segmentation", + "text_level": 1, + "bbox": [ + 76, + 845, + 290, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Settings. We further experiment on the ADE20K [38] dataset for semantic segmentation. ADE20K contains", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/921db102d0149169b19f4add4ced97e00529697b77759daded91a16ead02e422.jpg", + "table_caption": [ + "Table 4. Performance comparison for classification on ImageNet-1K [36] according to embedding spaces and combinations of learning objectives." + ], + "table_footnote": [], + "table_body": "
Manifold\\( \\mathcal{L}_{\\text{LL-cont}} \\)\\( \\mathcal{L}_{\\text{KL}} \\)Top-1(%)
EuclideanXX79.7
X✓79.6
✓X79.2
✓✓79.3
HyperbolicXX79.7
X✓79.5
✓X82.0
✓✓82.6
", + "bbox": [ + 519, + 366, + 874, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "20k training images, 20K validation images, and 3K test images, covering a total 150 classes. Following common practice [70], we report the mIoU on the validation set.", + "bbox": [ + 498, + 559, + 893, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We present the performance comparisons on ADE20K in Tab. 3. The results show that our Hi-Mapper achieves comparable or better performance than the baseline models, including DeiT-T, -S, and Swin-T, requiring a smaller increase in the number of parameters and GFLOPs. Specifically, Hi-Mapper on DeiT-T, -S, and Swin-T achieves a performance improvement of $2.0\\%$ , $3.3\\%$ , and $2.3\\%$ . Additionally, as model sizes increase, Hi-Mapper fully capitalizes fine-grained representations for semantic segmentation with a slight increase in computation.", + "bbox": [ + 496, + 628, + 893, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Visualization", + "text_level": 1, + "bbox": [ + 500, + 797, + 637, + 813 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Fig. 4, we demonstrate our visual hierarchy on images from ImageNet-1K [36]. This confirms that our approach can successfully uncover the inherent hierarchy among visual components without the need for hierarchy or part-level annotations.", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17370", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/706d8901c2f3ddb439c53d6809f228ea320758ba967103398dddcf8f708037d3.jpg", + "image_caption": [ + "Figure 4. Visualization of visual hierarchy decomposed by Hi-Mapper(Deit-S) trained on ImageNet-1K with classification objective. Each color represents different subtrees. We ignore the nodes of the small region and display only the main subtrees." + ], + "image_footnote": [], + "bbox": [ + 96, + 87, + 285, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d3e4622b6feeb935dcf7e03b28adfe3c66a053387ac3280b906d8e7d8b2d403.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 303, + 85, + 488, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5b927843c88fdec8babf1075bb35042def751bb35382b3e22b1d1728b70befa9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 85, + 684, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1574df897aa2498aa3605236196f6ddcad544b74801731746d15ae60155a38e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 85, + 872, + 287 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/976f5ca0c828a0342658ecbebb66124e7dd800dbbde01a188797e2d04223a644.jpg", + "table_caption": [ + "Table 5. Performance comparison for classification on ImageNet-1K [36] with respect to the relation modeling in hierarchy tree." + ], + "table_footnote": [], + "table_body": "
ModelDeterministicProbabilistic
Hi-Mapper(DeiT-S)81.5%82.6%
", + "bbox": [ + 99, + 369, + 450, + 411 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Ablation studies and discussion", + "text_level": 1, + "bbox": [ + 76, + 422, + 362, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further analyze and validate the components of our method, we conduct ablation studies on image classification.", + "bbox": [ + 75, + 449, + 470, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of hyperbolic manifolds. We first investigate the effectiveness of hyperbolic manifolds in our approach. As shown in Tab. 4, we report the impact according to image classification. In Euclidean space, the distance function between two vectors is the cosine similarity function. The results demonstrate that applying hierarchical contrastive loss in Euclidean space degrades performance. It indicates that hyperbolic space is more suitable for stabilizing hierarchical structures. Additionally, the application of a KL loss term shows further benefits derived from the semantic seed distribution.", + "bbox": [ + 75, + 489, + 468, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of probabilistic modeling. In Tab. 5, we report the performance comparisons between the probabilistic hierarchy tree and the deterministic hierarchy tree. For constructing a hierarchy tree, probabilistic modeling defines every node via MoG of its child node distributions, while the deterministic approach determines each node the mean of its child nodes. The probabilistic hierarchy tree achieves significant improvement in performance compared to the deterministic approach. This result shows that probabilistic modeling is more effective in representing hierarchical structure than deterministic modeling, leading to improvement in recognition.", + "bbox": [ + 75, + 665, + 468, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hierarchy width and depth. As shown in Fig. 5, we analyze the effect of the width $N$ and depth $L$ of the hierarchy tree on ImageNet-1K [36] with Hi-Mapper(DeiT", + "bbox": [ + 75, + 854, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/deabd207a932036fc11de7fcdd8be4de360546c242849cb005fc6c98b8d56d6a.jpg", + "image_caption": [ + "Figure 5. Hyper-parameter analysis on ImageNet-1K." + ], + "image_footnote": [], + "bbox": [ + 504, + 339, + 687, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48bdc2c8229b4c81d86e48120cb8144eb0aef1160f3b011e84ff31316161d762.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 339, + 879, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "S). These factors control the granularity of visual elements to be decomposed. While a small number of $N$ degrades the fine-grained recognition capacity, an excess $N$ hinders the optimization. Meanwhile, a large $L$ may provide diverse granularity, however, it leads to entangled object-level representations. In all the cases, we report the best performance of $82.6\\%$ at $N = 32$ , $L = 4$ .", + "bbox": [ + 496, + 476, + 893, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 598, + 617, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented a novel Visual Hierarchy Mapper (Hi-Mapper) that investigates the hierarchical organization of visual scenes. We have achieved the goal by newly defining tree-like structure with probability distribution and learning the hierarchical relations in hyperbolic space. We have incorporated the hierarchical interpretation into the contrastive loss and efficiently identified the visual hierarchy in a data-efficient manner. Through an effective hierarchy decomposition and encoding procedures, the identified hierarchy has been successfully deployed to the global visual representation, enhancing the structured understanding of an entire scene. Hi-Mapper has consistently improved the performance of the existing DNNs when integrated with them, and also has demonstrated the effectiveness on various dense predictions.", + "bbox": [ + 496, + 625, + 893, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This research was supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002).", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17371", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Aleksandr Ermolov, Leyla Mirvakhabova, Valentin Khrulkov, Nicu Sebe, and Ivan Oseledets. Hyperbolic vision transformers: Combining improvements in metric learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7409-7419, 2022. 1, 3", + "[2] Sungyeon Kim, Boseung Jeong, and Suha Kwak. Hier: Metric learning beyond class labels via hierarchical regularization. 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In Proceedings of the European conference on computer vision (ECCV), pages 418-434, 2018. 7" + ], + "bbox": [ + 501, + 92, + 893, + 345 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17374", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/9a46de44-a8c1-46de-8924-4659484e6064_model.json b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/9a46de44-a8c1-46de-8924-4659484e6064_model.json new file mode 100644 index 0000000000000000000000000000000000000000..36a1a5584581859febd9ab2c8aa004580318ef4d --- /dev/null +++ b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/9a46de44-a8c1-46de-8924-4659484e6064_model.json @@ -0,0 +1,2741 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.131, + 0.868, + 0.153 + ], + "angle": 0, + "content": "Improving Visual Recognition with Hyperbolic Visual Hierarchy Mapping" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.18, + 0.854, + 0.217 + ], + "angle": 0, + "content": "Hyeongjun Kwon\\(^{1}\\) Jinhyun Jang\\(^{1}\\) Jin Kim\\(^{1}\\) Kwonyoung Kim\\(^{1}\\) Kwanghoon Sohn\\(^{1,2*}\\) \n\\(^{1}\\)Yonsei University, \\(^{2}\\)Korea Institute of Science and Technology (KIST)" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.219, + 0.757, + 0.234 + ], + "angle": 0, + "content": "{kwonjunn01, jr000192, kimjin928, kyk12, khsohn}@yonsei.ac.kr," + }, + { + "type": "title", + "bbox": [ + 0.265, + 0.269, + 0.341, + 0.284 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.649 + ], + "angle": 0, + "content": "Visual scenes are naturally organized in a hierarchy, where a coarse semantic is recursively comprised of several fine details. Exploring such a visual hierarchy is crucial to recognize the complex relations of visual elements, leading to a comprehensive scene understanding. In this paper, we propose a Visual Hierarchy Mapper (Hi-Mapper), a novel approach for enhancing the structured understanding of the pre-trained Deep Neural Networks (DNNs). Hi-Mapper investigates the hierarchical organization of the visual scene by 1) pre-defining a hierarchy tree through the encapsulation of probability densities; and 2) learning the hierarchical relations in hyperbolic space with a novel hierarchical contrastive loss. The pre-defined hierarchy tree recursively interacts with the visual features of the pre-trained DNNs through hierarchy decomposition and encoding procedures, thereby effectively identifying the visual hierarchy and enhancing the recognition of an entire scene. Extensive experiments demonstrate that Hi-Mapper significantly enhances the representation capability of DNNs, leading to an improved performance on various tasks, including image classification and dense prediction tasks. The code is available at https://github.com/kwonjun01/Hi-Mapper." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.667, + 0.208, + 0.682 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.471, + 0.844 + ], + "angle": 0, + "content": "Recognizing and representing the visual scene of any content is the fundamental pursuit of the computer vision field [1-4]. In particular, understanding what constitutes a scene and how each element is comprised of plays a key role in various visual recognition tasks such as image retrieval [1, 2], human-object interaction [3, 5], and dense prediction [6, 7]. This goes beyond merely learning discriminative feature representations, as it requires to reason about the fine details as well as their associations to comprehend the structured nature of the complex visual scene." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.271, + 0.685, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.549, + 0.601, + 0.56 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.27, + 0.892, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.72, + 0.453, + 0.854, + 0.467 + ], + "angle": 0, + "content": "Hyperbolic Space" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.47, + 0.892, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.55, + 0.796, + 0.56 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.68 + ], + "angle": 0, + "content": "Figure 1. (a) A visual scene can be decomposed into a hierarchical structure based on the semantics of each visual element. (b) Euclidean space is suboptimal in representing the hierarchical structure due to its flat nature. The relational distance is inaccurately captured, being unaware of the semantic similarity of visual elements (Red line). Hi-Mapper maps the hierarchical elements in hyperbolic space, which effectively preserves their semantic relations and distances due to its constant negative curvature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.9 + ], + "angle": 0, + "content": "Over the decades, the development of deep neural networks (DNNs) has contributed towards advances in representing the complex visual scene. Notably, convolutional neural networks (CNNs) have achieved capturing fine details through the local convolutional filters while Vision Transformer (ViT) [8] has enabled coarse context modeling with multi-head self-attention mechanisms. Owing to their different desirable properties, hybrid architectures [9-12] and multi-scale variants of ViTs [13-15] have been extensively explored to capitalize on the complementary features of CNNs and ViTs. Subsequent works [16, 17] have further imposed interaction between multi-scale image patches to facilitate information exchange between fine details and coarse semantics." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.852, + 0.223, + 0.864 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.864, + 0.469, + 0.9 + ], + "angle": 0, + "content": "This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2021R1A2C2006703)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.852, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17364" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.395 + ], + "angle": 0, + "content": "While they have shown effective in capturing coarse-to-fine information, a structured understanding of the visual scene remains underexplored. Concretely, a scene can be interpreted as a hierarchical composition of visual elements, where the ability to recognize an instance (e.g. a man) at a coarse level arises from the ability to compose its constituents (e.g. body parts) at a finer level, as shown in Fig. 1a. Being aware of such semantic hierarchies furthers the perception of grid-like geometry and enhances the recognition of an entire image. Drawn from the same motivation, the recent variants of ViT [18-20] have constructed the hierarchies between image tokens across the transformer layers. However, their hierarchical relations are defined through the symmetric measurement (i.e., cosine similarity) which lacks the ability to represent the asymmetric property of hierarchical structure (i.e., inclusion of parent-child nodes). In addition, their image tokens are represented in Euclidean space where the hierarchical relations become distorted due to its linear and flat geometry [21-29], as shown in Fig. 1b." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.398, + 0.473, + 0.822 + ], + "angle": 0, + "content": "In this paper, we propose a novel Visual Hierarchy Mapper (Hi-Mapper) that improves the structured understanding of pre-trained DNNs by identifying the visual hierarchy. Hi-Mapper accomplishes this through: 1) Probabilistic modeling of hierarchy nodes, where the mean vector and covariance represent the center and scale of visual-semantic cluster, respectively [30-33]. Accordingly, the asymmetric hierarchical relations are captured through the inclusion of probability densities. Furthermore, 2) Hi-Mapper maps the hierarchy nodes to hyperbolic space, where its constant negative curvature effectively represents the exponential growth of hierarchy nodes. Specifically, Hi-Mapper pre-defines a tree-like structure, with its leaf-level node modeled as a unique Gaussian distribution and the higher-level nodes approximated by a Mixture of Gaussians (MoG) of their corresponding child nodes. The pre-defined hierarchy nodes then interact with the penultimate visual feature map of the pre-trained DNNs to decompose the feature map into the visual hierarchy. Moreover, in order to bypass the difficulties of modeling hierarchy in Euclidean space, Hi-Mapper maps the identified visual hierarchy to hyperbolic space and learns the hierarchical relation with a novel hierarchical contrastive loss. The proposed loss enforces the child-parent nodes to be similar and child-child nodes to be dissimilar in a shared hyperbolic space. The visual hierarchy then interacts with the global visual feature of the pre-trained DNNs such that the hierarchical relations are fully encoded in the global feature representation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Hi-Mapper serves as a plug-and-play module, which generalizes over any type of DNNs and flexibly identifies the hierarchical organization of visual scenes. We conduct extensive experiments with various pre-trained DNNs (i.e., ResNet [34], DeiT [35]) on several benchmarks [36-38] to" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.794, + 0.108 + ], + "angle": 0, + "content": "demonstrate the effectiveness of Hi-Mapper." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.109, + 0.847, + 0.123 + ], + "angle": 0, + "content": "In summary, our key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.124, + 0.894, + 0.214 + ], + "angle": 0, + "content": "- We present a novel Visual Hierarchy Mapper (Hi-Mapper) that enhances the structured understanding of the pre-trained DNNs by investigating the hierarchical organization of visual scene. The proposed Hi-Mapper is applicable to any type of the pre-trained DNNs without modifying the underlying structures." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.215, + 0.892, + 0.273 + ], + "angle": 0, + "content": "- Hi-Mapper effectively identifies the visual hierarchy by combining the favorable characteristic of probabilistic modeling and hyperbolic geometry for representing the hierarchical structure." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.275, + 0.894, + 0.32 + ], + "angle": 0, + "content": "- We conduct extensive experiments to validate the efficacy of the proposed Hi-Mapper, and improves over the state-of-the-art approaches on various visual recognition tasks." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.124, + 0.894, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.335, + 0.642, + 0.352 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.895, + 0.558 + ], + "angle": 0, + "content": "Hierarchy-aware visual recognition. Unsupervised image parsing is a long-standing pursuit in visual recognition tasks from the classical computer vision era [39-43]. In the pre-deep learning era, Zhouwen et al. [42] firstly introduces a framework to parse images with their constituents via a divide-and-conquer strategy. CapsuleNet-based methods have demonstrated substantial enhancements in image parsing, facilitated by dynamic routing, which efficiently capture the compositional relationships among the activities of capsules that represent object parts. Recently, hierarchical semantic segmentation has been extensively researched, including human parser [44, 45] based on human-part hierarchy and unsupervised part segmentations [46-48]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.897, + 0.817 + ], + "angle": 0, + "content": "Beyond image parsing, recent researches on deep neural networks (DNNs) have attempted to exploit hierarchical relationships between detail and global representations. CrossViT [16] utilizes a dual-branch transformer for multiscale feature extraction, enriching features through a fusion module that integrates inter-scale patch relationships. Quadtree [18] iteratively and hierarchically selects a subset of crucial finer patches within each coarse patch. DependencyViT [19] inverts the self-attention process to organize patches as parent and child nodes, enabling a hierarchical exploration. More recently, CAST [49] employs superpixel-based patch generation and graph pooling for hierarchical patch merging for improving fine-grained recognition performances. While they define hierarchical relations with token similarities in Euclidean space, we predefine a hierarchical structure with probabilistic modeling and learn the relation in hyperbolic space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Probabilistic modeling. Probabilistic representation has been extensively explored in the early NLP studies for handling the nuance of word semantics with the probability distribution. For instance, Vilnis et al. [30] first introduced the probability densities for representing" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17365" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "word embeddings. Athiwaratkun et al. [31] discovered that an imbalance in word frequency leads to distortions in word order and mitigated the problem by representing the word orders through the encapsulation of probability densities. Besides word representation, abundant research has demonstrated the effectiveness of probabilistic modeling in visual representation [6, 50-52]. For example, Shi et al. [51] proposed to penalize the low quality face images by measuring the variance of each image distribution. Chun et al. [50] identified the limitations of deterministic modeling in vision-language domains and introduced probabilistic cross-modal embedding for providing the uncertainty estimates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.472, + 0.322 + ], + "angle": 0, + "content": "In this work, we deploy probabilistic modeling in defining hierarchical structure, where each distribution represents the inclusive relations of hierarchy nodes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.473, + 0.673 + ], + "angle": 0, + "content": "Hyperbolic manifold. Hyperbolic manifolds have gained increasing interest in deep learning area due to their effectiveness in modeling hierarchical structures. Their success in NLP field [24, 26, 27, 53] has inspired approaches to adopt hyperbolic manifolds in computer vision researches such as image retrieval [1, 2], image segmentation [54, 55], and few-shot learning [25]. As a pioneering work, Khrulkov et al. [56] investigated an exponential map from Euclidean space to hyperbolic space for learning hierarchical image embeddings. Ermolov et al. [1] applied pair-wise cross entropy loss in hyperbolic space for ViTs. Kim et al. [2] extended the work by discovering the latent hierarchy of training data with learnable hierarchical proxies in hyperbolic space. Focusing on pixel-level analysis, [55] identified the long-tail objects by embedding masked instance regions into hyperbolic manifolds. More recently, Desai et al. [29] introduced to learn joint image-text embedding space in hyperbolic manifold. While they explore hyperbolic manifold for representing the categorical hierarchies, we identify the hierarchical structure of visual elements without the part-level annotation through a novel hierarchical contrastive loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.285, + 0.71 + ], + "angle": 0, + "content": "3. Hyperbolic Geometry" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Hyperbolic manifold is a smooth Riemannian manifold \\(\\mathcal{M}\\) with negative curvature \\(c\\) equipped with a Riemannian metric \\(g\\). The manifold consists of five isometric models and we utilize the Lorentz model for developing Hi-Mapper due to its training stability. A hyperbolic manifold of \\(n\\)-dimensions can be represented as a sub-manifold of the Lorentz model \\(\\mathbb{R}^{n+1}\\) as an upper half of a two-sheeted hyperboloid. In the Lorentz space, every point \\(\\mathbf{x} \\in \\mathbb{R}^{n+1}\\) can be denoted as \\([\\mathbf{x}_{\\mathrm{space}}, x_{\\mathrm{time}}]\\), where \\(\\mathbf{x}_{\\mathrm{space}} \\in \\mathbb{R}^n\\) and \\(x_{\\mathrm{time}} \\in \\mathbb{R}\\). Let \\(\\langle \\mathbf{x}, \\mathbf{y} \\rangle\\) be the Euclidean inner product and \\(\\langle \\mathbf{x}, \\mathbf{y} \\rangle_{\\mathbb{L}}\\) denote the Lorentzian inner product which is derived by the Riemannian metric of the Lorentz model \\(g_{\\mathbb{L}}\\). Given two vectors \\(\\mathbf{x}, \\mathbf{y} \\in\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.091, + 0.887, + 0.107 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{n + 1}\\), the Lorentzian inner product is computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.117, + 0.894, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\langle \\mathbf {x}, \\mathbf {y} \\rangle_ {\\mathbb {L}} = - x _ {\\text {t i m e}} y _ {\\text {t i m e}} + \\left\\langle \\mathbf {x} _ {\\text {s p a c e}}, \\mathbf {y} _ {\\text {s p a c e}} \\right\\rangle . \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.145, + 0.895, + 0.206 + ], + "angle": 0, + "content": "The \\(n\\)-dimensional Lorentz model \\((\\mathbb{L}^n,g_{\\mathbb{L}})\\) is defined by the manifold \\(\\mathbb{L}^n = \\{\\mathbf{x}\\in \\mathbb{R}^{n + 1}:\\langle \\mathbf{x},\\mathbf{x}\\rangle_{\\mathbb{L}} = -1 / c,c > 0\\}\\) and Riemannian metric of the Lorentz model \\(g_{\\mathbb{L}}\\). Thus, all vectors satisfy the following constraints:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.214, + 0.893, + 0.234 + ], + "angle": 0, + "content": "\\[\n- x _ {\\text {t i m e}} ^ {2} + \\left\\| \\mathbf {x} _ {\\text {s p a c e}} \\right\\| ^ {2} = - 1 / c. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.273 + ], + "angle": 0, + "content": "A geodesic is the shortest path between two vectors on the manifold. The Lorentzian distance on \\(\\mathbb{L}\\) is then defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.285, + 0.893, + 0.303 + ], + "angle": 0, + "content": "\\[\nD _ {\\mathbb {L}} (\\mathbf {x}, \\mathbf {y}) = \\operatorname {a r c c o s h} (- \\langle \\mathbf {x}, \\mathbf {y} \\rangle_ {\\mathbb {L}}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.893, + 0.404 + ], + "angle": 0, + "content": "The exponential map is a way to map vectors from tangent space \\(\\mathcal{T}_z\\mathbb{L}^n\\) onto hyperbolic manifolds \\(\\mathbb{L}^n\\), where \\(\\mathcal{T}_z\\mathbb{L}^n\\) is a Euclidean space of vectors that are orthogonal to some point \\(\\mathbf{z}\\in \\mathbb{L}^n\\). We map the tangent vector \\(\\mathbf{v}\\in \\mathcal{T}_z\\mathbb{L}^n\\) from Euclidean space to the Lorentz manifolds, in which the exponential map \\(\\mathrm{expm}_{\\mathbf{z}}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.412, + 0.893, + 0.458 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\exp_ {z} (\\mathbf {v}) = \\cosh (\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}}) \\mathbf {z} + \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}})}{\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}}} \\mathbf {v}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.489 + ], + "angle": 0, + "content": "The logarithm map \\(\\log \\mathrm{m}_z\\) which transfers \\(\\mathbf{x}\\) on the hyperboloid back to the tangent space \\(\\mathcal{T}_z\\mathcal{M}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.499, + 0.893, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} = \\log \\mathrm {m} _ {z} (\\mathbf {x}) = \\frac {\\cosh^ {- 1} (- c \\langle \\mathbf {z} , \\mathbf {x} \\rangle_ {\\mathbb {L}})}{\\sqrt {(c \\langle \\mathbf {z} , \\mathbf {x} \\rangle_ {\\mathbb {L}}) ^ {2} - 1}} \\operatorname {p r o j} _ {\\mathbf {z}} (\\mathbf {x}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.885, + 0.572 + ], + "angle": 0, + "content": "We set \\(\\mathbf{z}\\) as the origin of the hyperboloid \\(\\mathbf{O} = \\left[\\mathbf{0},\\sqrt{1 / c}\\right]\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.591, + 0.597 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.611, + 0.621 + ], + "angle": 0, + "content": "4.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.72 + ], + "angle": 0, + "content": "Our goal is to enhance the structured understanding of pre-trained deep neural networks (DNNs) by investigating the hierarchical organization of visual scenes. To this end, we introduce a Visual Hierarchy Mapper (Hi-Mapper) which serves as a plug-and-play module on any type of pre-trained DNNs. An overview of Hi-Mapper is depicted in Fig. 2a." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.894, + 0.796 + ], + "angle": 0, + "content": "Given an image \\(\\mathcal{I}\\), we first extract visual features \\([\\mathbf{v}_{\\mathrm{map}},\\mathbf{v}_{\\mathrm{cls}}] = \\mathcal{F}(\\mathcal{I})\\) from a pre-trained image encoder \\(\\mathcal{F}\\) where \\(\\mathbf{v}_{\\mathrm{map}}\\in \\mathbb{R}^{hw\\times d}\\) is the penultimate visual feature map and \\(\\mathbf{v}_{\\mathrm{cls}}\\in \\mathbb{R}^d\\) is the global visual representation, with \\(hw\\) indicating the size of the visual feature map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Hi-Mapper identifies the visual hierarchy from the visual feature map \\(\\mathbf{v}_{\\mathrm{map}}\\) and encodes the identified visual hierarchy back to the global visual representation \\(\\mathbf{v}_{\\mathrm{cls}}\\) for enhancing the recognition of a whole scene. To this end, we predefine a hierarchy tree with Gaussian distribution, where the relations of the hierarchy nodes are defined through the inclusion of probability densities (Sec. 4.2). The pre-defined" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17366" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.095, + 0.655, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.316, + 0.259, + 0.421, + 0.271 + ], + "angle": 0, + "content": "(a) Overall pipeline" + }, + { + "type": "image", + "bbox": [ + 0.674, + 0.097, + 0.877, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.258, + 0.86, + 0.269 + ], + "angle": 0, + "content": "(b) Hierarchical contrastive loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.278, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. (a) An overview of the proposed Hi-Mapper. Hi-Mapper operates on top of pre-trained image encoder \\(\\mathcal{F}\\), with probabilistic hierarchy tree \\(\\mathbf{T} = \\{\\mathbf{C}^l\\}_{l=1}^L\\). The tree interacts with visual feature map \\(\\mathbf{v}_{\\mathrm{map}}\\) through hierarchy decomposition module \\(\\mathcal{D}\\), thereby identifying visual hierarchy in Euclidean space \\(\\mathbf{T}_{\\mathbb{E}} = \\{\\mathbf{S}^l\\}_{l=1}^L\\). The visual hierarchy is mapped to hyperbolic space \\(\\mathbf{T}_{\\mathbb{L}} = \\{\\mathbf{H}^l\\}_{l=1}^L\\) and optimized with hierarchical contrastive loss \\(\\mathcal{L}_{\\mathbb{L}-\\mathrm{cont}}\\). The visual hierarchy is further encoded into global visual representation \\(\\mathbf{v}_{\\mathrm{cls}}\\) via hierarchy encoding module \\(\\mathcal{G}\\) for enhancing the recognition of entire scene. (b) The proposed hierarchical contrastive loss pulls each parent-child node and pushes all the other nodes at the same level." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.372, + 0.459, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.456, + 0.351, + 0.469 + ], + "angle": 0, + "content": "(a) Hierarchy decomposition" + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.473, + 0.45, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.211, + 0.58, + 0.336, + 0.593 + ], + "angle": 0, + "content": "(b) Hierarchy encoding" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.599, + 0.471, + 0.656 + ], + "angle": 0, + "content": "Figure 3. (a) Hierarchy decomposition module groups semantically-relevant visual features \\(\\mathbf{v}_{\\mathrm{map}}\\) to the closest semantic cluster \\(\\mathbf{C}^l\\). (b) Hierarchy encoding module progressively updates global representation \\(\\mathbf{v}_{\\mathrm{cls}}\\) by aggregating the visual hierarchy \\(\\mathbf{S}^l\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.47, + 0.822 + ], + "angle": 0, + "content": "The hierarchy tree interacts with \\(\\mathbf{v}_{\\mathrm{map}}\\) through the hierarchy decomposition module \\(\\mathcal{D}\\) such that the feature map is decomposed into the visual hierarchy (Sec. 4.3). Since the zero curvature of Euclidean space is not optimal for representing the hierarchical structure, we map the visual hierarchy to hyperbolic space and optimize the relation with a novel hierarchical contrastive loss (Sec. 4.4). The visual hierarchy is then encoded back to the global visual representation \\(\\mathbf{v}_{\\mathrm{cls}}\\) through the hierarchy encoding module \\(\\mathcal{G}\\) resulting in an enhanced global representation (Sec. 4.5)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.325, + 0.848 + ], + "angle": 0, + "content": "4.2. Probabilistic hierarchy tree" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.901 + ], + "angle": 0, + "content": "The main problem of the recent hierarchy-aware ViTs [18-20] is that they define the hierarchical relations between the image tokens mainly through the self-attention scores. Such" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.895, + 0.445 + ], + "angle": 0, + "content": "a symmetric measurement is suboptimal for representing the asymmetric inclusive relation of parent-child nodes. To handle the problem, we propose to define \\( L \\) levels of hierarchy tree \\( \\mathbf{T} \\) by modeling each hierarchy node with a probability distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.895, + 0.55 + ], + "angle": 0, + "content": "Specifically, we first parameterize each leaf-level (at the initial level) node as a unique Gaussian distribution and subsequently define the higher-level node as a Mixture-of-Gaussians (MoG) of its corresponding child nodes. Accordingly, the mean vector represents the cluster center of the visual semantic and the covariance captures the scale of each semantic cluster." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.894, + 0.621 + ], + "angle": 0, + "content": "Initial level. Let \\(\\mathbf{C}^1 = \\{\\mathbf{c}_n^1\\}_{n=1}^{N_1}\\) be a set of \\(N_1\\) initial level nodes. We parameterize each node \\(\\mathbf{c}_n^1\\) as a normal distribution with a mean vector \\(\\mu_n^1\\) and a diagonal covariance matrix \\(\\sigma_n^1\\mathbf{I}\\) in \\(\\mathbb{R}^d\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.631, + 0.892, + 0.65 + ], + "angle": 0, + "content": "\\[\np \\left(\\mathbf {c} _ {n} ^ {1}\\right) \\sim \\mathcal {N} \\left(\\mu_ {n} ^ {1}, \\sigma_ {n} ^ {1} \\mathbf {I}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.692 + ], + "angle": 0, + "content": "where \\(\\mu_n^1\\) and \\(\\sigma_{n}^{1}\\) are randomly initialized. We use reparameterization trick [57] for stable sampling, such that:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.703, + 0.892, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {n} ^ {1} = \\mu_ {n} ^ {1} + \\epsilon * \\sigma_ {n} ^ {1} \\in \\mathbb {R} ^ {d}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.633, + 0.749 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.85 + ], + "angle": 0, + "content": "Subsequent level. We derive the remaining \\((L - 1)\\) levels of hierarchy tree by conditioning each level on the preceding hierarchy level. For each \\(l\\)-th level, we formulate a set of \\(N_{l}\\) nodes \\(\\mathbf{C}^{l} = \\{\\mathbf{c}_{k}^{l}\\}_{k = 1}^{N_{l}}\\). Concretely, the \\(k\\)-th node \\(\\mathbf{c}_k^l\\) at the \\(l\\)-th level is approximated by a MoG of its two corresponding child nodes, \\(\\mathbf{c}_{2k - 1}^{l - 1}\\) and \\(\\mathbf{c}_{2k}^{l - 1}\\), as:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.862, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\np \\left(\\mathbf {c} _ {k} ^ {l}\\right) \\sim \\sum_ {k ^ {\\prime} = 2 k - 1} ^ {2 k} \\mathcal {N} \\left(\\mu_ {k ^ {\\prime}} ^ {l - 1}, \\sigma_ {k ^ {\\prime}} ^ {l - 1} \\mathbf {I}\\right). \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "To stabilize the construction of hierarchy tree, we increase the sampling rate as the distribution expands, i.e., we sample \\(2^{l - 1}\\) embeddings from \\(p(\\mathbf{c}_k^l)\\) using the reparameterization trick in Eq. (7) as:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.162, + 0.47, + 0.208 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {c} _ {k} ^ {l} = \\left\\{\\hat {\\mathbf {c}} _ {k, 1} ^ {l}, \\dots , \\hat {\\mathbf {c}} _ {k, 2 ^ {l - 1}} ^ {l} \\right\\} \\stackrel {{\\mathrm {i d}}} {{\\sim}} p \\left(\\mathbf {c} _ {k} ^ {l}\\right), \\quad \\mathbf {c} _ {k} ^ {l} \\in \\mathbb {R} ^ {2 ^ {l - 1} \\times d}, \\tag {9} \\\\ \\mathbf {C} ^ {l} = \\left\\{\\mathbf {c} _ {1} ^ {l}, \\dots , \\mathbf {c} _ {N _ {l}} ^ {l} \\right\\} \\in \\mathbb {R} ^ {2 ^ {l - 1} N _ {l} \\times d}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.469, + 0.307 + ], + "angle": 0, + "content": "By sequentially conditioning the higher-level nodes on the preceding lower-level nodes, we obtain the hierarchy tree \\(\\mathbf{T} = \\{\\mathbf{C}^l\\}_{l=1}^L\\), where the lower-level nodes capture fine details with concentrated distribution and the higher-level nodes capture coarse instance-level representations with dispersed distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.469, + 0.375 + ], + "angle": 0, + "content": "KL divergence loss. To prevent the variances from collapsing to zero, we employ KL regularization term between the distributions of \\(L\\)-th level nodes and the unit Gaussian prior \\(\\mathcal{N}(0,\\mathbf{I})\\) following [50]:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.385, + 0.47, + 0.426 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {K L}} = \\sum_ {i = 1} ^ {N _ {L}} \\mathrm {K L} \\left(\\mathcal {N} \\left(\\mu_ {i} ^ {L}, \\sigma_ {i} ^ {L}\\right) \\| \\mathcal {N} (0, \\mathbf {I})\\right). \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.437, + 0.356, + 0.453 + ], + "angle": 0, + "content": "4.3. Visual hierarchy decomposition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.469, + 0.535 + ], + "angle": 0, + "content": "Given the pre-defined hierarchy tree \\(\\mathbf{T}\\) and the visual feature map \\(\\mathbf{v}_{\\mathrm{map}}\\), we decompose \\(\\mathbf{v}_{\\mathrm{map}}\\) into \\(L\\) levels of visual hierarchy through hierarchy decomposition module \\(\\mathcal{D}\\), as shown in Fig. 3a. We instantiate \\(\\mathcal{D}\\) as a stack of two transformer decoder layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.469, + 0.595 + ], + "angle": 0, + "content": "To identify the visual hierarchy at the \\(l\\)-th level, the decomposition module \\(\\mathcal{D}\\) treats \\(\\mathbf{C}^l\\) as the query, and \\(\\mathbf{v}_{\\mathrm{map}}\\) as the key and value such that the semantically-relevant visual features are aggregated to the closest semantic cluster:" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.606, + 0.47, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} ^ {l} = \\left\\{\\mathbf {s} _ {1} ^ {l}, \\dots , \\mathbf {s} _ {N _ {l}} ^ {l} \\right\\} = \\mathcal {D} \\left(\\mathbf {C} ^ {l}, \\mathbf {v} _ {\\text {m a p}}\\right) \\in \\mathbb {R} ^ {2 ^ {l - 1} N _ {l} \\times d}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.469, + 0.716 + ], + "angle": 0, + "content": "Similar to the hierarchy nodes \\(\\mathbf{c}_k^l\\) in Eq. (9), the decomposed visual hierarchy nodes \\(\\mathbf{s}_k^l\\) are comprised of \\(2^{l-1}\\) visual representations as \\(\\mathbf{s}_k^l = \\{\\hat{\\mathbf{s}}_{k,1}^l, \\dots, \\hat{\\mathbf{s}}_{k,2^{l-1}}^l\\}\\). We average the set of \\(2^{l-1}\\) representations for each visual hierarchy node \\(\\mathbf{s}_k^l\\) such that:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.725, + 0.47, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} _ {k} ^ {l} = \\frac {1}{2 ^ {l - 1}} \\sum_ {i = 1} ^ {2 ^ {l - 1}} \\hat {\\mathbf {s}} _ {k, i} ^ {l}, \\quad \\mathbf {s} _ {k} ^ {l} \\in \\mathbb {R} ^ {d} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.47, + 0.826 + ], + "angle": 0, + "content": "We perform the same decomposition procedure for \\(L\\) levels, thereby obtaining \\(L\\) levels of visual hierarchy in Euclidean space \\(\\mathbf{T}_{\\mathbb{E}} = \\{\\mathbf{S}^l\\}_{l=1}^L\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.416, + 0.849 + ], + "angle": 0, + "content": "4.4. Learning hierarchy in hyperbolic space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "A natural characteristic of the hierarchical structure is that the number of nodes exponentially increases as the depth increases. In practice, representing this property in Euclidean" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "space leads to distortions in the semantic distances due to its flat geometry. We propose to handle the problem by learning the hierarchical relations in hyperbolic space, where its exponentially expanding volume can efficiently represent the visual hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.306 + ], + "angle": 0, + "content": "We first map \\(\\mathbf{T}_{\\mathbb{E}}\\) to the Lorentz hyperboloid to derive the visual hierarchy in hyperbolic space \\(\\mathbf{T}_{\\mathbb{L}}\\). Following [29], we simplify the mapping computation by parameterizing only the space component of the Lorentz model as \\(\\mathbf{s} = [\\mathbf{s}_k^l, 0] \\in \\mathbb{R}^{d+1}\\), where \\(\\mathbf{s}\\) belongs to the tangent space at the hyperboloid origin \\(\\mathbf{O}\\). The visual hierarchy node in hyperbolic space \\(\\mathbf{h}_k^l = [\\mathbf{h}_{k,\\mathrm{space}}^l, h_{k,\\mathrm{time}}^l]\\) is then obtained by transforming \\(\\mathbf{s}_k^l\\) to \\(\\mathbf{h}_{k,\\mathrm{space}}^l\\) using the exponential map in Eq. (13) as:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.317, + 0.892, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {h} _ {k, \\text {s p a c e}} ^ {l} = \\cosh (\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}}) \\mathbf {0} + \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}})}{\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}}} \\mathbf {s} _ {k} ^ {l} \\\\ = \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {s} _ {k} ^ {l} \\|)}{\\sqrt {c} \\| \\mathbf {s} _ {k} ^ {l} \\|} \\mathbf {s} _ {k} ^ {l}, \\tag {13} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.891, + 0.455 + ], + "angle": 0, + "content": "and computing the corresponding time component \\( h_{k,\\mathrm{time}}^{l} \\) using Eq. (2) as \\( h_{k,\\mathrm{time}}^{l} = \\sqrt{1 / c + \\|\\mathbf{h}_{k,\\mathrm{space}}^{l}\\|^{2}} \\). The visual hierarchy in hyperbolic space \\( \\mathbf{T}_{\\mathbb{L}} \\) is denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.465, + 0.892, + 0.484 + ], + "angle": 0, + "content": "\\[\n\\mathbf {T} _ {\\mathbb {L}} = \\left\\{\\mathbf {H} ^ {l} \\right\\} _ {l = 1} ^ {L}, \\quad \\mathbf {H} ^ {l} = \\left\\{\\mathbf {h} _ {1} ^ {l}, \\dots , \\mathbf {h} _ {N _ {l}} ^ {l} \\right\\} \\in \\mathbb {R} ^ {N _ {l} \\times d _ {\\mathbb {L}}}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.89, + 0.51 + ], + "angle": 0, + "content": "where \\(d_{\\mathbb{L}}\\) is the embedding dimension in Lorentz manifold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.892, + 0.607 + ], + "angle": 0, + "content": "Hierarchical contrastive loss. To guarantee the hierarchy nodes to reflect the hierarchical relations, we optimize the distances of \\(\\mathbf{T}_{\\mathbb{L}}\\) with a novel hierarchical contrastive loss \\(\\mathcal{L}_{\\mathbb{L}\\text{-cont}}\\). Specifically, we formulate the similarity between the nodes in consideration of the length of the connected branch, i.e., geodesic distance, as shown in Fig. 2b." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.76 + ], + "angle": 0, + "content": "Consider a node \\(\\mathbf{h}_{2k}^{l}\\) in \\(\\mathbf{T}_{\\mathbb{L}}\\), where \\(\\mathbf{h}_k^{l + 1}\\) is its parent node. We encourage \\(\\mathbf{h}_{2k}^{l}\\) to be similar with \\(\\mathbf{h}_k^{l + 1}\\) since the pair of parent-child nodes lie on the same branch. Meanwhile, we encourage the remaining nodes in the same level, i.e., \\(\\{\\mathbf{h}_i^l |\\mathbf{h}_i^l\\in \\mathbf{H}^l,i\\neq 2k\\}\\), to be dissimilar since they all lie on separate branches. The loss also penalizes the close sibling node \\(\\mathbf{h}_{2k - 1}^{l}\\) as their geodesic traverses the parent node. Formally, the hierarchical contrastive loss incorporates the geometric interpretation of hierarchical structure into the contrastive loss [58] as:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.771, + 0.892, + 0.825 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathbb {L} - \\text {c o n t}} = - \\log \\underset {\\mathbf {T} _ {\\mathbb {L}}} {\\mathbb {E}} \\left[ \\sum_ {i = 0} ^ {1} \\frac {\\exp \\left(D _ {\\mathbb {L}} \\left(\\mathbf {h} _ {k} ^ {l + 1} , \\mathbf {h} _ {2 k - i} ^ {l}\\right)\\right)}{\\sum_ {j \\neq 2 k - i} \\exp \\left(D _ {\\mathbb {L}} \\left(\\mathbf {h} _ {2 k - i} ^ {l} , \\mathbf {h} _ {j} ^ {l}\\right)\\right)} \\right], \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.862, + 0.84 + ], + "angle": 0, + "content": "where \\(D_{\\mathbb{L}}\\) is the Lorentzian distance defined in Eq. (3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.9 + ], + "angle": 0, + "content": "By regarding every pair of parent-child nodes as positive and every pair of nodes at the same level as negative, we are able to represent the logical structure of visual hierarchy without the part-level annotation. In addition, the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17368" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.138 + ], + "angle": 0, + "content": "hierarchical relation optimized through \\(\\mathbf{T}_{\\mathbb{L}}\\) in hyperbolic space is well-preserved in \\(\\mathbf{T}_{\\mathbb{E}}\\) in Euclidean space thanks to the mapping computation in Eq. (13)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.147, + 0.315, + 0.163 + ], + "angle": 0, + "content": "4.5. Visual hierarchy encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.469, + 0.291 + ], + "angle": 0, + "content": "We propose to enhance the structured understanding of the global visual representation by encoding the identified visual hierarchy into \\(\\mathbf{v}_{\\mathrm{cls}}\\). While we optimize the hierarchical relations in hyperbolic space due to its ability of handling relative distances, its complex computations and expansion property make it less suitable for tasks that require absolute criteria. Thus, we exploit the visual hierarchy in Euclidean space \\(\\mathbf{T}_{\\mathbb{E}}\\) for hierarchy encoding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.469, + 0.381 + ], + "angle": 0, + "content": "Specifically, we progressively encode the hierarchy nodes \\(\\mathbf{S}^l\\) into \\(\\mathbf{v}_{\\mathrm{cls}}\\), from the initial level to the \\(L\\)-th level, via the hierarchy encoding module \\(\\mathcal{G}\\) such that \\(\\mathbf{v}_{\\mathrm{cls}}\\) is updated as a hierarchy-aware global representation \\(\\mathbf{v}_{\\mathrm{cls}}^L\\). As shown in Fig. 3b, the module \\(\\mathcal{G}\\) is instantiated as a stack of \\(L\\) transformer decoder layers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.381, + 0.469, + 0.413 + ], + "angle": 0, + "content": "To encode the \\(l\\)-th level hierarchy, the \\(l\\)-th layer of \\(\\mathcal{G}^l\\) takes \\(\\mathbf{v}_{\\mathrm{cls}}^{l-1}\\) as the query, and \\(\\mathbf{S}^l\\) as the key and value:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.424, + 0.47, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {\\mathrm {c l s}} ^ {l} = \\mathcal {G} ^ {l} \\left(\\mathbf {v} _ {\\mathrm {c l s}} ^ {l - 1}, \\mathbf {S} ^ {l}\\right) \\in \\mathbb {R} ^ {d}, \\quad 0 < l \\leq L, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.469, + 0.484 + ], + "angle": 0, + "content": "where we set \\(\\mathbf{v}_{\\mathrm{cls}}^{0}\\) as \\(\\mathbf{v}_{\\mathrm{cls}}\\). The enhanced global visual representation is then derived as:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.495, + 0.47, + 0.513 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {v}} _ {\\mathrm {c l s}} = \\mathbf {v} _ {\\mathrm {c l s}} + \\mathbf {v} _ {\\mathrm {c l s}} ^ {L}. \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.469, + 0.554 + ], + "angle": 0, + "content": "For the final prediction, we feed \\(\\hat{\\mathbf{v}}_{\\mathrm{cls}}\\) into the pre-trained classifier of \\(\\mathcal{F}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.562, + 0.454, + 0.576 + ], + "angle": 0, + "content": "Overall objectives. The overall objective is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.589, + 0.47, + 0.605 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\mathrm {C E}} + \\alpha \\mathcal {L} _ {\\mathbb {L} - \\text {c o n t}} + \\beta \\mathcal {L} _ {\\mathrm {K L}}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.373, + 0.633 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are the balancing parameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.646, + 0.21, + 0.663 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.807 + ], + "angle": 0, + "content": "In this section, we conduct extensive experiments to show the effectiveness of our proposed Hi-Mapper on image classification (Sec. 5.1), object detection and instance segmentation (Sec. 5.2), and semantic segmentation (Sec. 5.3). We apply our Hi-Mapper on both CNN-based [34, 59] and ViT-based [35, 60] backbone networks and compare the performance with the concurrent hierarchy-aware baselines [16, 19]. Lastly, we provide ablation studies (Sec. 6) to demonstrate the effectiveness of our contributions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.265, + 0.833 + ], + "angle": 0, + "content": "5.1. Image classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Settings. We apply our Hi-Mapper on the state-of-the-art backbone networks [34, 35, 59, 60] and benchmark on ImageNet-1k [36] dataset. Following [12, 60, 62-64], we use the identical combinations for data augmentation" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Performance comparisons for image classification on ImageNet-1K [36] dataset." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.129, + 0.88, + 0.525 + ], + "angle": 0, + "content": "
TypeModelParams (M)FLOPs (G)Top-1 (%)
CNNResNet-50 [34]25.63.876.2
EfficientNet-B4* [59]19.34.282.9
Hi-Mapper(RN50)26.94.078.2
Hi-Mapper(ENB4*)20.54.484.1
ViTDeiT-T [35]5.71.372.2
CrossViT-T [16]6.91.673.4
PVT-T [61]13.21.975.1
DependecnyViT-T [19]6.21.375.4
Hi-Mapper(DeiT-T)6.61.574.8
DeiT-S [35]22.24.579.8
CrossViT-S [16]26.75.681
PVT-S [61]24.53.879.8
Swin-T [60]28.34.681.2
DependencyViT-S [19]24.05.082.1
Hi-Mapper(DeiT-S)23.34.882.6
Hi-Mapper(Swin-T)29.54.983.4
DeiT-B [35]85.617.681.8
Swin-S [60]50.18.783.0
Hi-Mapper(DeiT-B)87.218.183.4
Hi-Mapper(Swin-S)51.89.384.1
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.539, + 0.894, + 0.615 + ], + "angle": 0, + "content": "and regularization strategies [35] after excluding repeated augmentation [65]. We train our model with batch size 1024 for 50 epochs using AdamW [66] with weight decay 1e-4. The initial learning rate is set to 1e-4 and a cosine learning rate scheduler is applied following [35]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.894, + 0.835 + ], + "angle": 0, + "content": "Results. Tab. 1 presents classification performance. We report the original performance without the fine-tuning schemes for the plain backbone networks since we observed degradation in performance after fine-tuning the models. Our proposed method consistently achieves better performances than the baseline models with only a slight increase in parameters. Specifically, Hi-Mapper surpasses ResNet-50 [34] and EfficientNet-B4 [59] by margins of \\(2.0\\%\\) and \\(1.2\\%\\), respectively. Additionally, it achieves improvement on DeiT's performance by \\(2.6\\%/2.8\\%/1.6\\%\\), and Swin [60] by \\(2.2\\%/1.1\\%\\) across various model sizes. The experiments on image classification demonstrate not only the importance of understanding the structured organization of visual scenes, but also the scalability of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.871, + 0.864 + ], + "angle": 0, + "content": "5.2. Object detection and Instance segmentation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Settings. We experiment on the COCO [37] dataset. We use the Hi-Mapper backbones derived from Sec. 5.1. Then," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17369" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 2. Performance comparisons for object detection and instance segmentation on COCO [37] dataset. \\((^{*})\\) Results are reproduced based on [10]." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.123, + 0.875, + 0.31 + ], + "angle": 0, + "content": "
BackboneParams (M)Flops (G)Mask R-CNN 1x
APboxAPbox50APbox75APmaskAPmask50APmask75
PVT-T [61]32.919536.759.239.335.156.737.3
DeiT-T* [35]27.324430.346.232.127.144.428.3
Hi-Mapper(Deit-T)29.524637.161.741.035.759.138.1
PVT-S [61]44.124540.462.943.837.860.140.3
DeiT-S* [35]44.927636.354.139.031.751.333.2
Swin-T [60]47.826743.566.447.339.663.142.3
Hi-Mapper(Deit-S)47.027942.665.846.338.962.741.8
Hi-Mapper(Swin-T)50.427044.067.147.939.963.642.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.363 + ], + "angle": 0, + "content": "Table 3. Performance comparisons for semantic segmentation on ADE20k [38] dataset. We conduct the single-scale evaluation. FLOPs are measured with \\(512 \\times 2048\\) input resolution." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.367, + 0.468, + 0.57 + ], + "angle": 0, + "content": "
BackboneMethodParams (M)FLOPs (G)mIoU
PVT-T [61]SemanticFPN [69]17.013235.7
DeiT-T [35]UperNet [70]10.714237.8
DependencyViT-T [19]UperNet [70]11.114540.3
Hi-Mapper(DeiT-T)UperNet [70]11.614439.8
PVT-S [61]SemanticFPN [69]28.271239.8
DeiT-S [35]UperNet [70]41.356643.0
Swin-T [60]UperNet [70]60.094544.5
DependencyVIT-S [19]UperNet [70]43.157445.7
Hi-Mapper(DeiT-S)UperNet [70]42.557046.3
Hi-Mapper(Swin-T)UperNet [70]62.194946.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.472, + 0.66 + ], + "angle": 0, + "content": "we deploy our pre-trained backbone into Mask R-CNN [67]. All models are trained on COCO 2017, including 118k train images and 5k validation images. We follow the standard learning protocols [67], \\(1 \\times\\) schedule with 12 epochs. Note that we reproduce DeiT-T with Mask R-CNN based on [68]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.472, + 0.837 + ], + "angle": 0, + "content": "Results. In Table 2, we present a comparison of our results with baseline models, such as DeiT and Swin, on the COCO dataset, which demands a higher capacity for fine representation recognition. Our Hi-Mapper consistently boosts all baseline models capability with only a small increase in parameters. Notably, Hi-Mapper significantly improves DeiT-T and -S by margins of 6.8 and 8.3 on the object detection task. Meanwhile, in the instance segmentation, it also improves DeiT-T and -S by margins of 8.6 and 7.2, respectively. This result shows that the visual hierarchy facilitates complex visual scene recognition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.292, + 0.863 + ], + "angle": 0, + "content": "5.3. Semantic segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Settings. We further experiment on the ADE20K [38] dataset for semantic segmentation. ADE20K contains" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.319, + 0.895, + 0.363 + ], + "angle": 0, + "content": "Table 4. Performance comparison for classification on ImageNet-1K [36] according to embedding spaces and combinations of learning objectives." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.367, + 0.875, + 0.543 + ], + "angle": 0, + "content": "
Manifold\\( \\mathcal{L}_{\\text{LL-cont}} \\)\\( \\mathcal{L}_{\\text{KL}} \\)Top-1(%)
EuclideanXX79.7
X✓79.6
✓X79.2
✓✓79.3
HyperbolicXX79.7
X✓79.5
✓X82.0
✓✓82.6
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.56, + 0.895, + 0.607 + ], + "angle": 0, + "content": "20k training images, 20K validation images, and 3K test images, covering a total 150 classes. Following common practice [70], we report the mIoU on the validation set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.782 + ], + "angle": 0, + "content": "Results. We present the performance comparisons on ADE20K in Tab. 3. The results show that our Hi-Mapper achieves comparable or better performance than the baseline models, including DeiT-T, -S, and Swin-T, requiring a smaller increase in the number of parameters and GFLOPs. Specifically, Hi-Mapper on DeiT-T, -S, and Swin-T achieves a performance improvement of \\(2.0\\%\\), \\(3.3\\%\\), and \\(2.3\\%\\). Additionally, as model sizes increase, Hi-Mapper fully capitalizes fine-grained representations for semantic segmentation with a slight increase in computation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.638, + 0.814 + ], + "angle": 0, + "content": "5.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "As shown in Fig. 4, we demonstrate our visual hierarchy on images from ImageNet-1K [36]. This confirms that our approach can successfully uncover the inherent hierarchy among visual components without the need for hierarchy or part-level annotations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17370" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.088, + 0.287, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.304, + 0.087, + 0.49, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.087, + 0.685, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.087, + 0.873, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.893, + 0.327 + ], + "angle": 0, + "content": "Figure 4. Visualization of visual hierarchy decomposed by Hi-Mapper(Deit-S) trained on ImageNet-1K with classification objective. Each color represents different subtrees. We ignore the nodes of the small region and display only the main subtrees." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.337, + 0.471, + 0.366 + ], + "angle": 0, + "content": "Table 5. Performance comparison for classification on ImageNet-1K [36] with respect to the relation modeling in hierarchy tree." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.37, + 0.451, + 0.412 + ], + "angle": 0, + "content": "
ModelDeterministicProbabilistic
Hi-Mapper(DeiT-S)81.5%82.6%
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.364, + 0.439 + ], + "angle": 0, + "content": "6. Ablation studies and discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.471, + 0.48 + ], + "angle": 0, + "content": "To further analyze and validate the components of our method, we conduct ablation studies on image classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Effectiveness of hyperbolic manifolds. We first investigate the effectiveness of hyperbolic manifolds in our approach. As shown in Tab. 4, we report the impact according to image classification. In Euclidean space, the distance function between two vectors is the cosine similarity function. The results demonstrate that applying hierarchical contrastive loss in Euclidean space degrades performance. It indicates that hyperbolic space is more suitable for stabilizing hierarchical structures. Additionally, the application of a KL loss term shows further benefits derived from the semantic seed distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.47, + 0.846 + ], + "angle": 0, + "content": "Impact of probabilistic modeling. In Tab. 5, we report the performance comparisons between the probabilistic hierarchy tree and the deterministic hierarchy tree. For constructing a hierarchy tree, probabilistic modeling defines every node via MoG of its child node distributions, while the deterministic approach determines each node the mean of its child nodes. The probabilistic hierarchy tree achieves significant improvement in performance compared to the deterministic approach. This result shows that probabilistic modeling is more effective in representing hierarchical structure than deterministic modeling, leading to improvement in recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Hierarchy width and depth. As shown in Fig. 5, we analyze the effect of the width \\(N\\) and depth \\(L\\) of the hierarchy tree on ImageNet-1K [36] with Hi-Mapper(DeiT" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.34, + 0.688, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.34, + 0.88, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.447, + 0.855, + 0.461 + ], + "angle": 0, + "content": "Figure 5. Hyper-parameter analysis on ImageNet-1K." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.895, + 0.583 + ], + "angle": 0, + "content": "S). These factors control the granularity of visual elements to be decomposed. While a small number of \\( N \\) degrades the fine-grained recognition capacity, an excess \\( N \\) hinders the optimization. Meanwhile, a large \\( L \\) may provide diverse granularity, however, it leads to entangled object-level representations. In all the cases, we report the best performance of \\( 82.6\\% \\) at \\( N = 32 \\), \\( L = 4 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.599, + 0.619, + 0.615 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.894, + 0.852 + ], + "angle": 0, + "content": "In this paper, we have presented a novel Visual Hierarchy Mapper (Hi-Mapper) that investigates the hierarchical organization of visual scenes. We have achieved the goal by newly defining tree-like structure with probability distribution and learning the hierarchical relations in hyperbolic space. We have incorporated the hierarchical interpretation into the contrastive loss and efficiently identified the visual hierarchy in a data-efficient manner. Through an effective hierarchy decomposition and encoding procedures, the identified hierarchy has been successfully deployed to the global visual representation, enhancing the structured understanding of an entire scene. Hi-Mapper has consistently improved the performance of the existing DNNs when integrated with them, and also has demonstrated the effectiveness on various dense predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This research was supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17371" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Aleksandr Ermolov, Leyla Mirvakhabova, Valentin Khrulkov, Nicu Sebe, and Ivan Oseledets. Hyperbolic vision transformers: Combining improvements in metric learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7409-7419, 2022. 1, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.253 + ], + "angle": 0, + "content": "[2] Sungyeon Kim, Boseung Jeong, and Suha Kwak. Hier: Metric learning beyond class labels via hierarchical regularization. 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Exploring such a visual hierarchy is crucial to recognize the complex relations of visual elements, leading to a comprehensive scene understanding. In this paper, we propose a Visual Hierarchy Mapper (Hi-Mapper), a novel approach for enhancing the structured understanding of the pre-trained Deep Neural Networks (DNNs). Hi-Mapper investigates the hierarchical organization of the visual scene by 1) pre-defining a hierarchy tree through the encapsulation of probability densities; and 2) learning the hierarchical relations in hyperbolic space with a novel hierarchical contrastive loss. The pre-defined hierarchy tree recursively interacts with the visual features of the pre-trained DNNs through hierarchy decomposition and encoding procedures, thereby effectively identifying the visual hierarchy and enhancing the recognition of an entire scene. Extensive experiments demonstrate that Hi-Mapper significantly enhances the representation capability of DNNs, leading to an improved performance on various tasks, including image classification and dense prediction tasks. The code is available at https://github.com/kwonjun01/Hi-Mapper. + +# 1. Introduction + +Recognizing and representing the visual scene of any content is the fundamental pursuit of the computer vision field [1-4]. In particular, understanding what constitutes a scene and how each element is comprised of plays a key role in various visual recognition tasks such as image retrieval [1, 2], human-object interaction [3, 5], and dense prediction [6, 7]. This goes beyond merely learning discriminative feature representations, as it requires to reason about the fine details as well as their associations to comprehend the structured nature of the complex visual scene. + +![](images/f32b955fa92de7d740ba41d014175e41688c6c697ec1ecbb5598c8e7661e5baa.jpg) +(a) + +![](images/f32f34b1fc22f5cfa7b2d4f0b6414b81d20611fab7b40f57b095208dc2d42203.jpg) +Hyperbolic Space + +![](images/f5cd311959a724571187fc9c2b1b2f8214b5adff0b2a7c28bfe9f6ae35d08452.jpg) +(b) +Figure 1. (a) A visual scene can be decomposed into a hierarchical structure based on the semantics of each visual element. (b) Euclidean space is suboptimal in representing the hierarchical structure due to its flat nature. The relational distance is inaccurately captured, being unaware of the semantic similarity of visual elements (Red line). Hi-Mapper maps the hierarchical elements in hyperbolic space, which effectively preserves their semantic relations and distances due to its constant negative curvature. + +Over the decades, the development of deep neural networks (DNNs) has contributed towards advances in representing the complex visual scene. Notably, convolutional neural networks (CNNs) have achieved capturing fine details through the local convolutional filters while Vision Transformer (ViT) [8] has enabled coarse context modeling with multi-head self-attention mechanisms. Owing to their different desirable properties, hybrid architectures [9-12] and multi-scale variants of ViTs [13-15] have been extensively explored to capitalize on the complementary features of CNNs and ViTs. Subsequent works [16, 17] have further imposed interaction between multi-scale image patches to facilitate information exchange between fine details and coarse semantics. + +While they have shown effective in capturing coarse-to-fine information, a structured understanding of the visual scene remains underexplored. Concretely, a scene can be interpreted as a hierarchical composition of visual elements, where the ability to recognize an instance (e.g. a man) at a coarse level arises from the ability to compose its constituents (e.g. body parts) at a finer level, as shown in Fig. 1a. Being aware of such semantic hierarchies furthers the perception of grid-like geometry and enhances the recognition of an entire image. Drawn from the same motivation, the recent variants of ViT [18-20] have constructed the hierarchies between image tokens across the transformer layers. However, their hierarchical relations are defined through the symmetric measurement (i.e., cosine similarity) which lacks the ability to represent the asymmetric property of hierarchical structure (i.e., inclusion of parent-child nodes). In addition, their image tokens are represented in Euclidean space where the hierarchical relations become distorted due to its linear and flat geometry [21-29], as shown in Fig. 1b. + +In this paper, we propose a novel Visual Hierarchy Mapper (Hi-Mapper) that improves the structured understanding of pre-trained DNNs by identifying the visual hierarchy. Hi-Mapper accomplishes this through: 1) Probabilistic modeling of hierarchy nodes, where the mean vector and covariance represent the center and scale of visual-semantic cluster, respectively [30-33]. Accordingly, the asymmetric hierarchical relations are captured through the inclusion of probability densities. Furthermore, 2) Hi-Mapper maps the hierarchy nodes to hyperbolic space, where its constant negative curvature effectively represents the exponential growth of hierarchy nodes. Specifically, Hi-Mapper pre-defines a tree-like structure, with its leaf-level node modeled as a unique Gaussian distribution and the higher-level nodes approximated by a Mixture of Gaussians (MoG) of their corresponding child nodes. The pre-defined hierarchy nodes then interact with the penultimate visual feature map of the pre-trained DNNs to decompose the feature map into the visual hierarchy. Moreover, in order to bypass the difficulties of modeling hierarchy in Euclidean space, Hi-Mapper maps the identified visual hierarchy to hyperbolic space and learns the hierarchical relation with a novel hierarchical contrastive loss. The proposed loss enforces the child-parent nodes to be similar and child-child nodes to be dissimilar in a shared hyperbolic space. The visual hierarchy then interacts with the global visual feature of the pre-trained DNNs such that the hierarchical relations are fully encoded in the global feature representation. + +Hi-Mapper serves as a plug-and-play module, which generalizes over any type of DNNs and flexibly identifies the hierarchical organization of visual scenes. We conduct extensive experiments with various pre-trained DNNs (i.e., ResNet [34], DeiT [35]) on several benchmarks [36-38] to + +demonstrate the effectiveness of Hi-Mapper. + +In summary, our key contributions are as follows: + +- We present a novel Visual Hierarchy Mapper (Hi-Mapper) that enhances the structured understanding of the pre-trained DNNs by investigating the hierarchical organization of visual scene. The proposed Hi-Mapper is applicable to any type of the pre-trained DNNs without modifying the underlying structures. +- Hi-Mapper effectively identifies the visual hierarchy by combining the favorable characteristic of probabilistic modeling and hyperbolic geometry for representing the hierarchical structure. +- We conduct extensive experiments to validate the efficacy of the proposed Hi-Mapper, and improves over the state-of-the-art approaches on various visual recognition tasks. + +# 2. Related Work + +Hierarchy-aware visual recognition. Unsupervised image parsing is a long-standing pursuit in visual recognition tasks from the classical computer vision era [39-43]. In the pre-deep learning era, Zhouwen et al. [42] firstly introduces a framework to parse images with their constituents via a divide-and-conquer strategy. CapsuleNet-based methods have demonstrated substantial enhancements in image parsing, facilitated by dynamic routing, which efficiently capture the compositional relationships among the activities of capsules that represent object parts. Recently, hierarchical semantic segmentation has been extensively researched, including human parser [44, 45] based on human-part hierarchy and unsupervised part segmentations [46-48]. + +Beyond image parsing, recent researches on deep neural networks (DNNs) have attempted to exploit hierarchical relationships between detail and global representations. CrossViT [16] utilizes a dual-branch transformer for multiscale feature extraction, enriching features through a fusion module that integrates inter-scale patch relationships. Quadtree [18] iteratively and hierarchically selects a subset of crucial finer patches within each coarse patch. DependencyViT [19] inverts the self-attention process to organize patches as parent and child nodes, enabling a hierarchical exploration. More recently, CAST [49] employs superpixel-based patch generation and graph pooling for hierarchical patch merging for improving fine-grained recognition performances. While they define hierarchical relations with token similarities in Euclidean space, we predefine a hierarchical structure with probabilistic modeling and learn the relation in hyperbolic space. + +Probabilistic modeling. Probabilistic representation has been extensively explored in the early NLP studies for handling the nuance of word semantics with the probability distribution. For instance, Vilnis et al. [30] first introduced the probability densities for representing + +word embeddings. Athiwaratkun et al. [31] discovered that an imbalance in word frequency leads to distortions in word order and mitigated the problem by representing the word orders through the encapsulation of probability densities. Besides word representation, abundant research has demonstrated the effectiveness of probabilistic modeling in visual representation [6, 50-52]. For example, Shi et al. [51] proposed to penalize the low quality face images by measuring the variance of each image distribution. Chun et al. [50] identified the limitations of deterministic modeling in vision-language domains and introduced probabilistic cross-modal embedding for providing the uncertainty estimates. + +In this work, we deploy probabilistic modeling in defining hierarchical structure, where each distribution represents the inclusive relations of hierarchy nodes. + +Hyperbolic manifold. Hyperbolic manifolds have gained increasing interest in deep learning area due to their effectiveness in modeling hierarchical structures. Their success in NLP field [24, 26, 27, 53] has inspired approaches to adopt hyperbolic manifolds in computer vision researches such as image retrieval [1, 2], image segmentation [54, 55], and few-shot learning [25]. As a pioneering work, Khrulkov et al. [56] investigated an exponential map from Euclidean space to hyperbolic space for learning hierarchical image embeddings. Ermolov et al. [1] applied pair-wise cross entropy loss in hyperbolic space for ViTs. Kim et al. [2] extended the work by discovering the latent hierarchy of training data with learnable hierarchical proxies in hyperbolic space. Focusing on pixel-level analysis, [55] identified the long-tail objects by embedding masked instance regions into hyperbolic manifolds. More recently, Desai et al. [29] introduced to learn joint image-text embedding space in hyperbolic manifold. While they explore hyperbolic manifold for representing the categorical hierarchies, we identify the hierarchical structure of visual elements without the part-level annotation through a novel hierarchical contrastive loss. + +# 3. Hyperbolic Geometry + +Hyperbolic manifold is a smooth Riemannian manifold $\mathcal{M}$ with negative curvature $c$ equipped with a Riemannian metric $g$ . The manifold consists of five isometric models and we utilize the Lorentz model for developing Hi-Mapper due to its training stability. A hyperbolic manifold of $n$ -dimensions can be represented as a sub-manifold of the Lorentz model $\mathbb{R}^{n+1}$ as an upper half of a two-sheeted hyperboloid. In the Lorentz space, every point $\mathbf{x} \in \mathbb{R}^{n+1}$ can be denoted as $[\mathbf{x}_{\mathrm{space}}, x_{\mathrm{time}}]$ , where $\mathbf{x}_{\mathrm{space}} \in \mathbb{R}^n$ and $x_{\mathrm{time}} \in \mathbb{R}$ . Let $\langle \mathbf{x}, \mathbf{y} \rangle$ be the Euclidean inner product and $\langle \mathbf{x}, \mathbf{y} \rangle_{\mathbb{L}}$ denote the Lorentzian inner product which is derived by the Riemannian metric of the Lorentz model $g_{\mathbb{L}}$ . Given two vectors $\mathbf{x}, \mathbf{y} \in$ + +$\mathbb{R}^{n + 1}$ , the Lorentzian inner product is computed as follows: + +$$ +\langle \mathbf {x}, \mathbf {y} \rangle_ {\mathbb {L}} = - x _ {\text {t i m e}} y _ {\text {t i m e}} + \left\langle \mathbf {x} _ {\text {s p a c e}}, \mathbf {y} _ {\text {s p a c e}} \right\rangle . \tag {1} +$$ + +The $n$ -dimensional Lorentz model $(\mathbb{L}^n,g_{\mathbb{L}})$ is defined by the manifold $\mathbb{L}^n = \{\mathbf{x}\in \mathbb{R}^{n + 1}:\langle \mathbf{x},\mathbf{x}\rangle_{\mathbb{L}} = -1 / c,c > 0\}$ and Riemannian metric of the Lorentz model $g_{\mathbb{L}}$ . Thus, all vectors satisfy the following constraints: + +$$ +- x _ {\text {t i m e}} ^ {2} + \left\| \mathbf {x} _ {\text {s p a c e}} \right\| ^ {2} = - 1 / c. \tag {2} +$$ + +A geodesic is the shortest path between two vectors on the manifold. The Lorentzian distance on $\mathbb{L}$ is then defined as: + +$$ +D _ {\mathbb {L}} (\mathbf {x}, \mathbf {y}) = \operatorname {a r c c o s h} (- \langle \mathbf {x}, \mathbf {y} \rangle_ {\mathbb {L}}). \tag {3} +$$ + +The exponential map is a way to map vectors from tangent space $\mathcal{T}_z\mathbb{L}^n$ onto hyperbolic manifolds $\mathbb{L}^n$ , where $\mathcal{T}_z\mathbb{L}^n$ is a Euclidean space of vectors that are orthogonal to some point $\mathbf{z}\in \mathbb{L}^n$ . We map the tangent vector $\mathbf{v}\in \mathcal{T}_z\mathbb{L}^n$ from Euclidean space to the Lorentz manifolds, in which the exponential map $\mathrm{expm}_{\mathbf{z}}$ is defined as: + +$$ +\mathbf {x} = \exp_ {z} (\mathbf {v}) = \cosh (\sqrt {c} \| \mathbf {v} \| _ {\mathbb {L}}) \mathbf {z} + \frac {\sinh (\sqrt {c} \| \mathbf {v} \| _ {\mathbb {L}})}{\sqrt {c} \| \mathbf {v} \| _ {\mathbb {L}}} \mathbf {v}. \tag {4} +$$ + +The logarithm map $\log \mathrm{m}_z$ which transfers $\mathbf{x}$ on the hyperboloid back to the tangent space $\mathcal{T}_z\mathcal{M}$ is defined as: + +$$ +\mathbf {v} = \log \mathrm {m} _ {z} (\mathbf {x}) = \frac {\cosh^ {- 1} (- c \langle \mathbf {z} , \mathbf {x} \rangle_ {\mathbb {L}})}{\sqrt {(c \langle \mathbf {z} , \mathbf {x} \rangle_ {\mathbb {L}}) ^ {2} - 1}} \operatorname {p r o j} _ {\mathbf {z}} (\mathbf {x}). \tag {5} +$$ + +We set $\mathbf{z}$ as the origin of the hyperboloid $\mathbf{O} = \left[\mathbf{0},\sqrt{1 / c}\right]$ . + +# 4. Method + +# 4.1. Overview + +Our goal is to enhance the structured understanding of pre-trained deep neural networks (DNNs) by investigating the hierarchical organization of visual scenes. To this end, we introduce a Visual Hierarchy Mapper (Hi-Mapper) which serves as a plug-and-play module on any type of pre-trained DNNs. An overview of Hi-Mapper is depicted in Fig. 2a. + +Given an image $\mathcal{I}$ , we first extract visual features $[\mathbf{v}_{\mathrm{map}},\mathbf{v}_{\mathrm{cls}}] = \mathcal{F}(\mathcal{I})$ from a pre-trained image encoder $\mathcal{F}$ where $\mathbf{v}_{\mathrm{map}}\in \mathbb{R}^{hw\times d}$ is the penultimate visual feature map and $\mathbf{v}_{\mathrm{cls}}\in \mathbb{R}^d$ is the global visual representation, with $hw$ indicating the size of the visual feature map. + +Hi-Mapper identifies the visual hierarchy from the visual feature map $\mathbf{v}_{\mathrm{map}}$ and encodes the identified visual hierarchy back to the global visual representation $\mathbf{v}_{\mathrm{cls}}$ for enhancing the recognition of a whole scene. To this end, we predefine a hierarchy tree with Gaussian distribution, where the relations of the hierarchy nodes are defined through the inclusion of probability densities (Sec. 4.2). The pre-defined + +![](images/66ccadbd22d4d7d91588a6ef746de4350487e564e7e8a54b330eb4bb4947553e.jpg) +(a) Overall pipeline + +![](images/94a153c09532eceb565c18d4cfe3a2f7aea756955c0e73e05ba2061962388fe4.jpg) +(b) Hierarchical contrastive loss + +![](images/152e897f97f5ede0f072fd9146304cb66f693066a5ba46c13a62799ac5d987ac.jpg) +Figure 2. (a) An overview of the proposed Hi-Mapper. Hi-Mapper operates on top of pre-trained image encoder $\mathcal{F}$ , with probabilistic hierarchy tree $\mathbf{T} = \{\mathbf{C}^l\}_{l=1}^L$ . The tree interacts with visual feature map $\mathbf{v}_{\mathrm{map}}$ through hierarchy decomposition module $\mathcal{D}$ , thereby identifying visual hierarchy in Euclidean space $\mathbf{T}_{\mathbb{E}} = \{\mathbf{S}^l\}_{l=1}^L$ . The visual hierarchy is mapped to hyperbolic space $\mathbf{T}_{\mathbb{L}} = \{\mathbf{H}^l\}_{l=1}^L$ and optimized with hierarchical contrastive loss $\mathcal{L}_{\mathbb{L}-\mathrm{cont}}$ . The visual hierarchy is further encoded into global visual representation $\mathbf{v}_{\mathrm{cls}}$ via hierarchy encoding module $\mathcal{G}$ for enhancing the recognition of entire scene. (b) The proposed hierarchical contrastive loss pulls each parent-child node and pushes all the other nodes at the same level. + +![](images/061d512bb38d3a54e0aefeddd20c432d103a1ee1bc15bba92b551adeb8ad72b7.jpg) +(a) Hierarchy decomposition +(b) Hierarchy encoding +Figure 3. (a) Hierarchy decomposition module groups semantically-relevant visual features $\mathbf{v}_{\mathrm{map}}$ to the closest semantic cluster $\mathbf{C}^l$ . (b) Hierarchy encoding module progressively updates global representation $\mathbf{v}_{\mathrm{cls}}$ by aggregating the visual hierarchy $\mathbf{S}^l$ . + +The hierarchy tree interacts with $\mathbf{v}_{\mathrm{map}}$ through the hierarchy decomposition module $\mathcal{D}$ such that the feature map is decomposed into the visual hierarchy (Sec. 4.3). Since the zero curvature of Euclidean space is not optimal for representing the hierarchical structure, we map the visual hierarchy to hyperbolic space and optimize the relation with a novel hierarchical contrastive loss (Sec. 4.4). The visual hierarchy is then encoded back to the global visual representation $\mathbf{v}_{\mathrm{cls}}$ through the hierarchy encoding module $\mathcal{G}$ resulting in an enhanced global representation (Sec. 4.5). + +# 4.2. Probabilistic hierarchy tree + +The main problem of the recent hierarchy-aware ViTs [18-20] is that they define the hierarchical relations between the image tokens mainly through the self-attention scores. Such + +a symmetric measurement is suboptimal for representing the asymmetric inclusive relation of parent-child nodes. To handle the problem, we propose to define $L$ levels of hierarchy tree $\mathbf{T}$ by modeling each hierarchy node with a probability distribution. + +Specifically, we first parameterize each leaf-level (at the initial level) node as a unique Gaussian distribution and subsequently define the higher-level node as a Mixture-of-Gaussians (MoG) of its corresponding child nodes. Accordingly, the mean vector represents the cluster center of the visual semantic and the covariance captures the scale of each semantic cluster. + +Initial level. Let $\mathbf{C}^1 = \{\mathbf{c}_n^1\}_{n=1}^{N_1}$ be a set of $N_1$ initial level nodes. We parameterize each node $\mathbf{c}_n^1$ as a normal distribution with a mean vector $\mu_n^1$ and a diagonal covariance matrix $\sigma_n^1\mathbf{I}$ in $\mathbb{R}^d$ as: + +$$ +p \left(\mathbf {c} _ {n} ^ {1}\right) \sim \mathcal {N} \left(\mu_ {n} ^ {1}, \sigma_ {n} ^ {1} \mathbf {I}\right), \tag {6} +$$ + +where $\mu_n^1$ and $\sigma_{n}^{1}$ are randomly initialized. We use reparameterization trick [57] for stable sampling, such that: + +$$ +\mathbf {c} _ {n} ^ {1} = \mu_ {n} ^ {1} + \epsilon * \sigma_ {n} ^ {1} \in \mathbb {R} ^ {d}, \tag {7} +$$ + +where $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ + +Subsequent level. We derive the remaining $(L - 1)$ levels of hierarchy tree by conditioning each level on the preceding hierarchy level. For each $l$ -th level, we formulate a set of $N_{l}$ nodes $\mathbf{C}^{l} = \{\mathbf{c}_{k}^{l}\}_{k = 1}^{N_{l}}$ . Concretely, the $k$ -th node $\mathbf{c}_k^l$ at the $l$ -th level is approximated by a MoG of its two corresponding child nodes, $\mathbf{c}_{2k - 1}^{l - 1}$ and $\mathbf{c}_{2k}^{l - 1}$ , as: + +$$ +p \left(\mathbf {c} _ {k} ^ {l}\right) \sim \sum_ {k ^ {\prime} = 2 k - 1} ^ {2 k} \mathcal {N} \left(\mu_ {k ^ {\prime}} ^ {l - 1}, \sigma_ {k ^ {\prime}} ^ {l - 1} \mathbf {I}\right). \tag {8} +$$ + +To stabilize the construction of hierarchy tree, we increase the sampling rate as the distribution expands, i.e., we sample $2^{l - 1}$ embeddings from $p(\mathbf{c}_k^l)$ using the reparameterization trick in Eq. (7) as: + +$$ +\begin{array}{l} \mathbf {c} _ {k} ^ {l} = \left\{\hat {\mathbf {c}} _ {k, 1} ^ {l}, \dots , \hat {\mathbf {c}} _ {k, 2 ^ {l - 1}} ^ {l} \right\} \stackrel {{\mathrm {i d}}} {{\sim}} p \left(\mathbf {c} _ {k} ^ {l}\right), \quad \mathbf {c} _ {k} ^ {l} \in \mathbb {R} ^ {2 ^ {l - 1} \times d}, \tag {9} \\ \mathbf {C} ^ {l} = \left\{\mathbf {c} _ {1} ^ {l}, \dots , \mathbf {c} _ {N _ {l}} ^ {l} \right\} \in \mathbb {R} ^ {2 ^ {l - 1} N _ {l} \times d}. \\ \end{array} +$$ + +By sequentially conditioning the higher-level nodes on the preceding lower-level nodes, we obtain the hierarchy tree $\mathbf{T} = \{\mathbf{C}^l\}_{l=1}^L$ , where the lower-level nodes capture fine details with concentrated distribution and the higher-level nodes capture coarse instance-level representations with dispersed distribution. + +KL divergence loss. To prevent the variances from collapsing to zero, we employ KL regularization term between the distributions of $L$ -th level nodes and the unit Gaussian prior $\mathcal{N}(0,\mathbf{I})$ following [50]: + +$$ +\mathcal {L} _ {\mathrm {K L}} = \sum_ {i = 1} ^ {N _ {L}} \mathrm {K L} \left(\mathcal {N} \left(\mu_ {i} ^ {L}, \sigma_ {i} ^ {L}\right) \| \mathcal {N} (0, \mathbf {I})\right). \tag {10} +$$ + +# 4.3. Visual hierarchy decomposition + +Given the pre-defined hierarchy tree $\mathbf{T}$ and the visual feature map $\mathbf{v}_{\mathrm{map}}$ , we decompose $\mathbf{v}_{\mathrm{map}}$ into $L$ levels of visual hierarchy through hierarchy decomposition module $\mathcal{D}$ , as shown in Fig. 3a. We instantiate $\mathcal{D}$ as a stack of two transformer decoder layers. + +To identify the visual hierarchy at the $l$ -th level, the decomposition module $\mathcal{D}$ treats $\mathbf{C}^l$ as the query, and $\mathbf{v}_{\mathrm{map}}$ as the key and value such that the semantically-relevant visual features are aggregated to the closest semantic cluster: + +$$ +\mathbf {S} ^ {l} = \left\{\mathbf {s} _ {1} ^ {l}, \dots , \mathbf {s} _ {N _ {l}} ^ {l} \right\} = \mathcal {D} \left(\mathbf {C} ^ {l}, \mathbf {v} _ {\text {m a p}}\right) \in \mathbb {R} ^ {2 ^ {l - 1} N _ {l} \times d}. \tag {11} +$$ + +Similar to the hierarchy nodes $\mathbf{c}_k^l$ in Eq. (9), the decomposed visual hierarchy nodes $\mathbf{s}_k^l$ are comprised of $2^{l-1}$ visual representations as $\mathbf{s}_k^l = \{\hat{\mathbf{s}}_{k,1}^l, \dots, \hat{\mathbf{s}}_{k,2^{l-1}}^l\}$ . We average the set of $2^{l-1}$ representations for each visual hierarchy node $\mathbf{s}_k^l$ such that: + +$$ +\mathbf {s} _ {k} ^ {l} = \frac {1}{2 ^ {l - 1}} \sum_ {i = 1} ^ {2 ^ {l - 1}} \hat {\mathbf {s}} _ {k, i} ^ {l}, \quad \mathbf {s} _ {k} ^ {l} \in \mathbb {R} ^ {d} \tag {12} +$$ + +We perform the same decomposition procedure for $L$ levels, thereby obtaining $L$ levels of visual hierarchy in Euclidean space $\mathbf{T}_{\mathbb{E}} = \{\mathbf{S}^l\}_{l=1}^L$ . + +# 4.4. Learning hierarchy in hyperbolic space + +A natural characteristic of the hierarchical structure is that the number of nodes exponentially increases as the depth increases. In practice, representing this property in Euclidean + +space leads to distortions in the semantic distances due to its flat geometry. We propose to handle the problem by learning the hierarchical relations in hyperbolic space, where its exponentially expanding volume can efficiently represent the visual hierarchy. + +We first map $\mathbf{T}_{\mathbb{E}}$ to the Lorentz hyperboloid to derive the visual hierarchy in hyperbolic space $\mathbf{T}_{\mathbb{L}}$ . Following [29], we simplify the mapping computation by parameterizing only the space component of the Lorentz model as $\mathbf{s} = [\mathbf{s}_k^l, 0] \in \mathbb{R}^{d+1}$ , where $\mathbf{s}$ belongs to the tangent space at the hyperboloid origin $\mathbf{O}$ . The visual hierarchy node in hyperbolic space $\mathbf{h}_k^l = [\mathbf{h}_{k,\mathrm{space}}^l, h_{k,\mathrm{time}}^l]$ is then obtained by transforming $\mathbf{s}_k^l$ to $\mathbf{h}_{k,\mathrm{space}}^l$ using the exponential map in Eq. (13) as: + +$$ +\begin{array}{l} \mathbf {h} _ {k, \text {s p a c e}} ^ {l} = \cosh (\sqrt {c} \| \mathbf {s} \| _ {\mathbb {L}}) \mathbf {0} + \frac {\sinh (\sqrt {c} \| \mathbf {s} \| _ {\mathbb {L}})}{\sqrt {c} \| \mathbf {s} \| _ {\mathbb {L}}} \mathbf {s} _ {k} ^ {l} \\ = \frac {\sinh (\sqrt {c} \| \mathbf {s} _ {k} ^ {l} \|)}{\sqrt {c} \| \mathbf {s} _ {k} ^ {l} \|} \mathbf {s} _ {k} ^ {l}, \tag {13} \\ \end{array} +$$ + +and computing the corresponding time component $h_{k,\mathrm{time}}^{l}$ using Eq. (2) as $h_{k,\mathrm{time}}^{l} = \sqrt{1 / c + \|\mathbf{h}_{k,\mathrm{space}}^{l}\|^{2}}$ . The visual hierarchy in hyperbolic space $\mathbf{T}_{\mathbb{L}}$ is denoted as: + +$$ +\mathbf {T} _ {\mathbb {L}} = \left\{\mathbf {H} ^ {l} \right\} _ {l = 1} ^ {L}, \quad \mathbf {H} ^ {l} = \left\{\mathbf {h} _ {1} ^ {l}, \dots , \mathbf {h} _ {N _ {l}} ^ {l} \right\} \in \mathbb {R} ^ {N _ {l} \times d _ {\mathbb {L}}}, \tag {14} +$$ + +where $d_{\mathbb{L}}$ is the embedding dimension in Lorentz manifold. + +Hierarchical contrastive loss. To guarantee the hierarchy nodes to reflect the hierarchical relations, we optimize the distances of $\mathbf{T}_{\mathbb{L}}$ with a novel hierarchical contrastive loss $\mathcal{L}_{\mathbb{L}\text{-cont}}$ . Specifically, we formulate the similarity between the nodes in consideration of the length of the connected branch, i.e., geodesic distance, as shown in Fig. 2b. + +Consider a node $\mathbf{h}_{2k}^{l}$ in $\mathbf{T}_{\mathbb{L}}$ , where $\mathbf{h}_k^{l + 1}$ is its parent node. We encourage $\mathbf{h}_{2k}^{l}$ to be similar with $\mathbf{h}_k^{l + 1}$ since the pair of parent-child nodes lie on the same branch. Meanwhile, we encourage the remaining nodes in the same level, i.e., $\{\mathbf{h}_i^l |\mathbf{h}_i^l\in \mathbf{H}^l,i\neq 2k\}$ , to be dissimilar since they all lie on separate branches. The loss also penalizes the close sibling node $\mathbf{h}_{2k - 1}^{l}$ as their geodesic traverses the parent node. Formally, the hierarchical contrastive loss incorporates the geometric interpretation of hierarchical structure into the contrastive loss [58] as: + +$$ +\mathcal {L} _ {\mathbb {L} - \text {c o n t}} = - \log \underset {\mathbf {T} _ {\mathbb {L}}} {\mathbb {E}} \left[ \sum_ {i = 0} ^ {1} \frac {\exp \left(D _ {\mathbb {L}} \left(\mathbf {h} _ {k} ^ {l + 1} , \mathbf {h} _ {2 k - i} ^ {l}\right)\right)}{\sum_ {j \neq 2 k - i} \exp \left(D _ {\mathbb {L}} \left(\mathbf {h} _ {2 k - i} ^ {l} , \mathbf {h} _ {j} ^ {l}\right)\right)} \right], \tag {15} +$$ + +where $D_{\mathbb{L}}$ is the Lorentzian distance defined in Eq. (3). + +By regarding every pair of parent-child nodes as positive and every pair of nodes at the same level as negative, we are able to represent the logical structure of visual hierarchy without the part-level annotation. In addition, the + +hierarchical relation optimized through $\mathbf{T}_{\mathbb{L}}$ in hyperbolic space is well-preserved in $\mathbf{T}_{\mathbb{E}}$ in Euclidean space thanks to the mapping computation in Eq. (13). + +# 4.5. Visual hierarchy encoding + +We propose to enhance the structured understanding of the global visual representation by encoding the identified visual hierarchy into $\mathbf{v}_{\mathrm{cls}}$ . While we optimize the hierarchical relations in hyperbolic space due to its ability of handling relative distances, its complex computations and expansion property make it less suitable for tasks that require absolute criteria. Thus, we exploit the visual hierarchy in Euclidean space $\mathbf{T}_{\mathbb{E}}$ for hierarchy encoding. + +Specifically, we progressively encode the hierarchy nodes $\mathbf{S}^l$ into $\mathbf{v}_{\mathrm{cls}}$ , from the initial level to the $L$ -th level, via the hierarchy encoding module $\mathcal{G}$ such that $\mathbf{v}_{\mathrm{cls}}$ is updated as a hierarchy-aware global representation $\mathbf{v}_{\mathrm{cls}}^L$ . As shown in Fig. 3b, the module $\mathcal{G}$ is instantiated as a stack of $L$ transformer decoder layers. + +To encode the $l$ -th level hierarchy, the $l$ -th layer of $\mathcal{G}^l$ takes $\mathbf{v}_{\mathrm{cls}}^{l-1}$ as the query, and $\mathbf{S}^l$ as the key and value: + +$$ +\mathbf {v} _ {\mathrm {c l s}} ^ {l} = \mathcal {G} ^ {l} \left(\mathbf {v} _ {\mathrm {c l s}} ^ {l - 1}, \mathbf {S} ^ {l}\right) \in \mathbb {R} ^ {d}, \quad 0 < l \leq L, \tag {16} +$$ + +where we set $\mathbf{v}_{\mathrm{cls}}^{0}$ as $\mathbf{v}_{\mathrm{cls}}$ . The enhanced global visual representation is then derived as: + +$$ +\hat {\mathbf {v}} _ {\mathrm {c l s}} = \mathbf {v} _ {\mathrm {c l s}} + \mathbf {v} _ {\mathrm {c l s}} ^ {L}. \tag {17} +$$ + +For the final prediction, we feed $\hat{\mathbf{v}}_{\mathrm{cls}}$ into the pre-trained classifier of $\mathcal{F}$ . + +Overall objectives. The overall objective is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\mathrm {C E}} + \alpha \mathcal {L} _ {\mathbb {L} - \text {c o n t}} + \beta \mathcal {L} _ {\mathrm {K L}}, \tag {18} +$$ + +where $\alpha$ and $\beta$ are the balancing parameters. + +# 5. Experiments + +In this section, we conduct extensive experiments to show the effectiveness of our proposed Hi-Mapper on image classification (Sec. 5.1), object detection and instance segmentation (Sec. 5.2), and semantic segmentation (Sec. 5.3). We apply our Hi-Mapper on both CNN-based [34, 59] and ViT-based [35, 60] backbone networks and compare the performance with the concurrent hierarchy-aware baselines [16, 19]. Lastly, we provide ablation studies (Sec. 6) to demonstrate the effectiveness of our contributions. + +# 5.1. Image classification + +Settings. We apply our Hi-Mapper on the state-of-the-art backbone networks [34, 35, 59, 60] and benchmark on ImageNet-1k [36] dataset. Following [12, 60, 62-64], we use the identical combinations for data augmentation + +Table 1. Performance comparisons for image classification on ImageNet-1K [36] dataset. + +
TypeModelParams (M)FLOPs (G)Top-1 (%)
CNNResNet-50 [34]25.63.876.2
EfficientNet-B4* [59]19.34.282.9
Hi-Mapper(RN50)26.94.078.2
Hi-Mapper(ENB4*)20.54.484.1
ViTDeiT-T [35]5.71.372.2
CrossViT-T [16]6.91.673.4
PVT-T [61]13.21.975.1
DependecnyViT-T [19]6.21.375.4
Hi-Mapper(DeiT-T)6.61.574.8
DeiT-S [35]22.24.579.8
CrossViT-S [16]26.75.681
PVT-S [61]24.53.879.8
Swin-T [60]28.34.681.2
DependencyViT-S [19]24.05.082.1
Hi-Mapper(DeiT-S)23.34.882.6
Hi-Mapper(Swin-T)29.54.983.4
DeiT-B [35]85.617.681.8
Swin-S [60]50.18.783.0
Hi-Mapper(DeiT-B)87.218.183.4
Hi-Mapper(Swin-S)51.89.384.1
+ +and regularization strategies [35] after excluding repeated augmentation [65]. We train our model with batch size 1024 for 50 epochs using AdamW [66] with weight decay 1e-4. The initial learning rate is set to 1e-4 and a cosine learning rate scheduler is applied following [35]. + +Results. Tab. 1 presents classification performance. We report the original performance without the fine-tuning schemes for the plain backbone networks since we observed degradation in performance after fine-tuning the models. Our proposed method consistently achieves better performances than the baseline models with only a slight increase in parameters. Specifically, Hi-Mapper surpasses ResNet-50 [34] and EfficientNet-B4 [59] by margins of $2.0\%$ and $1.2\%$ , respectively. Additionally, it achieves improvement on DeiT's performance by $2.6\%/2.8\%/1.6\%$ , and Swin [60] by $2.2\%/1.1\%$ across various model sizes. The experiments on image classification demonstrate not only the importance of understanding the structured organization of visual scenes, but also the scalability of our method. + +# 5.2. Object detection and Instance segmentation + +Settings. We experiment on the COCO [37] dataset. We use the Hi-Mapper backbones derived from Sec. 5.1. Then, + +Table 2. Performance comparisons for object detection and instance segmentation on COCO [37] dataset. $(^{*})$ Results are reproduced based on [10]. + +
BackboneParams (M)Flops (G)Mask R-CNN 1x
APboxAPbox50APbox75APmaskAPmask50APmask75
PVT-T [61]32.919536.759.239.335.156.737.3
DeiT-T* [35]27.324430.346.232.127.144.428.3
Hi-Mapper(Deit-T)29.524637.161.741.035.759.138.1
PVT-S [61]44.124540.462.943.837.860.140.3
DeiT-S* [35]44.927636.354.139.031.751.333.2
Swin-T [60]47.826743.566.447.339.663.142.3
Hi-Mapper(Deit-S)47.027942.665.846.338.962.741.8
Hi-Mapper(Swin-T)50.427044.067.147.939.963.642.8
+ +Table 3. Performance comparisons for semantic segmentation on ADE20k [38] dataset. We conduct the single-scale evaluation. FLOPs are measured with $512 \times 2048$ input resolution. + +
BackboneMethodParams (M)FLOPs (G)mIoU
PVT-T [61]SemanticFPN [69]17.013235.7
DeiT-T [35]UperNet [70]10.714237.8
DependencyViT-T [19]UperNet [70]11.114540.3
Hi-Mapper(DeiT-T)UperNet [70]11.614439.8
PVT-S [61]SemanticFPN [69]28.271239.8
DeiT-S [35]UperNet [70]41.356643.0
Swin-T [60]UperNet [70]60.094544.5
DependencyVIT-S [19]UperNet [70]43.157445.7
Hi-Mapper(DeiT-S)UperNet [70]42.557046.3
Hi-Mapper(Swin-T)UperNet [70]62.194946.8
+ +we deploy our pre-trained backbone into Mask R-CNN [67]. All models are trained on COCO 2017, including 118k train images and 5k validation images. We follow the standard learning protocols [67], $1 \times$ schedule with 12 epochs. Note that we reproduce DeiT-T with Mask R-CNN based on [68]. + +Results. In Table 2, we present a comparison of our results with baseline models, such as DeiT and Swin, on the COCO dataset, which demands a higher capacity for fine representation recognition. Our Hi-Mapper consistently boosts all baseline models capability with only a small increase in parameters. Notably, Hi-Mapper significantly improves DeiT-T and -S by margins of 6.8 and 8.3 on the object detection task. Meanwhile, in the instance segmentation, it also improves DeiT-T and -S by margins of 8.6 and 7.2, respectively. This result shows that the visual hierarchy facilitates complex visual scene recognition. + +# 5.3. Semantic segmentation + +Settings. We further experiment on the ADE20K [38] dataset for semantic segmentation. ADE20K contains + +Table 4. Performance comparison for classification on ImageNet-1K [36] according to embedding spaces and combinations of learning objectives. + +
Manifold\( \mathcal{L}_{\text{LL-cont}} \)\( \mathcal{L}_{\text{KL}} \)Top-1(%)
EuclideanXX79.7
X✓79.6
✓X79.2
✓✓79.3
HyperbolicXX79.7
X✓79.5
✓X82.0
✓✓82.6
+ +20k training images, 20K validation images, and 3K test images, covering a total 150 classes. Following common practice [70], we report the mIoU on the validation set. + +Results. We present the performance comparisons on ADE20K in Tab. 3. The results show that our Hi-Mapper achieves comparable or better performance than the baseline models, including DeiT-T, -S, and Swin-T, requiring a smaller increase in the number of parameters and GFLOPs. Specifically, Hi-Mapper on DeiT-T, -S, and Swin-T achieves a performance improvement of $2.0\%$ , $3.3\%$ , and $2.3\%$ . Additionally, as model sizes increase, Hi-Mapper fully capitalizes fine-grained representations for semantic segmentation with a slight increase in computation. + +# 5.4. Visualization + +As shown in Fig. 4, we demonstrate our visual hierarchy on images from ImageNet-1K [36]. This confirms that our approach can successfully uncover the inherent hierarchy among visual components without the need for hierarchy or part-level annotations. + +![](images/706d8901c2f3ddb439c53d6809f228ea320758ba967103398dddcf8f708037d3.jpg) +Figure 4. Visualization of visual hierarchy decomposed by Hi-Mapper(Deit-S) trained on ImageNet-1K with classification objective. Each color represents different subtrees. We ignore the nodes of the small region and display only the main subtrees. + +![](images/4d3e4622b6feeb935dcf7e03b28adfe3c66a053387ac3280b906d8e7d8b2d403.jpg) + +![](images/5b927843c88fdec8babf1075bb35042def751bb35382b3e22b1d1728b70befa9.jpg) + +![](images/1574df897aa2498aa3605236196f6ddcad544b74801731746d15ae60155a38e1.jpg) + +Table 5. Performance comparison for classification on ImageNet-1K [36] with respect to the relation modeling in hierarchy tree. + +
ModelDeterministicProbabilistic
Hi-Mapper(DeiT-S)81.5%82.6%
+ +# 6. Ablation studies and discussion + +To further analyze and validate the components of our method, we conduct ablation studies on image classification. + +Effectiveness of hyperbolic manifolds. We first investigate the effectiveness of hyperbolic manifolds in our approach. As shown in Tab. 4, we report the impact according to image classification. In Euclidean space, the distance function between two vectors is the cosine similarity function. The results demonstrate that applying hierarchical contrastive loss in Euclidean space degrades performance. It indicates that hyperbolic space is more suitable for stabilizing hierarchical structures. Additionally, the application of a KL loss term shows further benefits derived from the semantic seed distribution. + +Impact of probabilistic modeling. In Tab. 5, we report the performance comparisons between the probabilistic hierarchy tree and the deterministic hierarchy tree. For constructing a hierarchy tree, probabilistic modeling defines every node via MoG of its child node distributions, while the deterministic approach determines each node the mean of its child nodes. The probabilistic hierarchy tree achieves significant improvement in performance compared to the deterministic approach. This result shows that probabilistic modeling is more effective in representing hierarchical structure than deterministic modeling, leading to improvement in recognition. + +Hierarchy width and depth. As shown in Fig. 5, we analyze the effect of the width $N$ and depth $L$ of the hierarchy tree on ImageNet-1K [36] with Hi-Mapper(DeiT + +![](images/deabd207a932036fc11de7fcdd8be4de360546c242849cb005fc6c98b8d56d6a.jpg) +Figure 5. Hyper-parameter analysis on ImageNet-1K. + +![](images/48bdc2c8229b4c81d86e48120cb8144eb0aef1160f3b011e84ff31316161d762.jpg) + +S). These factors control the granularity of visual elements to be decomposed. While a small number of $N$ degrades the fine-grained recognition capacity, an excess $N$ hinders the optimization. Meanwhile, a large $L$ may provide diverse granularity, however, it leads to entangled object-level representations. In all the cases, we report the best performance of $82.6\%$ at $N = 32$ , $L = 4$ . + +# 7. Conclusion + +In this paper, we have presented a novel Visual Hierarchy Mapper (Hi-Mapper) that investigates the hierarchical organization of visual scenes. We have achieved the goal by newly defining tree-like structure with probability distribution and learning the hierarchical relations in hyperbolic space. We have incorporated the hierarchical interpretation into the contrastive loss and efficiently identified the visual hierarchy in a data-efficient manner. Through an effective hierarchy decomposition and encoding procedures, the identified hierarchy has been successfully deployed to the global visual representation, enhancing the structured understanding of an entire scene. Hi-Mapper has consistently improved the performance of the existing DNNs when integrated with them, and also has demonstrated the effectiveness on various dense predictions. + +Acknowledgement. This research was supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002). + +# References + +[1] Aleksandr Ermolov, Leyla Mirvakhabova, Valentin Khrulkov, Nicu Sebe, and Ivan Oseledets. Hyperbolic vision transformers: Combining improvements in metric learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7409-7419, 2022. 1, 3 +[2] Sungyeon Kim, Boseung Jeong, and Suha Kwak. Hier: Metric learning beyond class labels via hierarchical regularization. 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In Proceedings of the European conference on computer vision (ECCV), pages 418-434, 2018. 7 \ No newline at end of file diff --git a/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/images.zip b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a834eedea1fe3b8171b3eb01691f4d9940cd5829 --- /dev/null +++ b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1e50e7d09ca27678e341de2b9aa4a690a7de985f3bc2e334631bbcd23be27b28 +size 580830 diff --git a/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/layout.json b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..26aee29b22cbd1456248ae7994a47c2fc06986b9 --- /dev/null +++ b/2024/Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping/layout.json @@ -0,0 +1,11691 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "spans": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "type": "text", + "content": "Improving Visual Recognition with Hyperbolic Visual Hierarchy Mapping" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "spans": [ + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": "Hyeongjun Kwon" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": " Jinhyun Jang" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": " Jin Kim" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": " Kwonyoung Kim" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": " Kwanghoon Sohn" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": "Yonsei University, " + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 73, + 142, + 522, + 171 + ], + "type": "text", + "content": "Korea Institute of Science and Technology (KIST)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 129, + 173, + 463, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 173, + 463, + 185 + ], + "spans": [ + { + "bbox": [ + 129, + 173, + 463, + 185 + ], + "type": "text", + "content": "{kwonjunn01, jr000192, kimjin928, kyk12, khsohn}@yonsei.ac.kr," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 162, + 213, + 208, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 213, + 208, + 224 + ], + "spans": [ + { + "bbox": [ + 162, + 213, + 208, + 224 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "content": "Visual scenes are naturally organized in a hierarchy, where a coarse semantic is recursively comprised of several fine details. Exploring such a visual hierarchy is crucial to recognize the complex relations of visual elements, leading to a comprehensive scene understanding. In this paper, we propose a Visual Hierarchy Mapper (Hi-Mapper), a novel approach for enhancing the structured understanding of the pre-trained Deep Neural Networks (DNNs). Hi-Mapper investigates the hierarchical organization of the visual scene by 1) pre-defining a hierarchy tree through the encapsulation of probability densities; and 2) learning the hierarchical relations in hyperbolic space with a novel hierarchical contrastive loss. The pre-defined hierarchy tree recursively interacts with the visual features of the pre-trained DNNs through hierarchy decomposition and encoding procedures, thereby effectively identifying the visual hierarchy and enhancing the recognition of an entire scene. Extensive experiments demonstrate that Hi-Mapper significantly enhances the representation capability of DNNs, leading to an improved performance on various tasks, including image classification and dense prediction tasks. The code is available at https://github.com/kwonjun01/Hi-Mapper." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 127, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 127, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 127, + 540 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 288, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 288, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 288, + 668 + ], + "type": "text", + "content": "Recognizing and representing the visual scene of any content is the fundamental pursuit of the computer vision field [1-4]. In particular, understanding what constitutes a scene and how each element is comprised of plays a key role in various visual recognition tasks such as image retrieval [1, 2], human-object interaction [3, 5], and dense prediction [6, 7]. This goes beyond merely learning discriminative feature representations, as it requires to reason about the fine details as well as their associations to comprehend the structured nature of the complex visual scene." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 214, + 419, + 432 + ], + "blocks": [ + { + "bbox": [ + 307, + 214, + 419, + 432 + ], + "lines": [ + { + "bbox": [ + 307, + 214, + 419, + 432 + ], + "spans": [ + { + "bbox": [ + 307, + 214, + 419, + 432 + ], + "type": "image", + "image_path": "f32b955fa92de7d740ba41d014175e41688c6c697ec1ecbb5598c8e7661e5baa.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 434, + 367, + 443 + ], + "lines": [ + { + "bbox": [ + 358, + 434, + 367, + 443 + ], + "spans": [ + { + "bbox": [ + 358, + 434, + 367, + 443 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 420, + 213, + 545, + 355 + ], + "blocks": [ + { + "bbox": [ + 420, + 213, + 545, + 355 + ], + "lines": [ + { + "bbox": [ + 420, + 213, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 420, + 213, + 545, + 355 + ], + "type": "image", + "image_path": "f32f34b1fc22f5cfa7b2d4f0b6414b81d20611fab7b40f57b095208dc2d42203.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 358, + 522, + 369 + ], + "lines": [ + { + "bbox": [ + 440, + 358, + 522, + 369 + ], + "spans": [ + { + "bbox": [ + 440, + 358, + 522, + 369 + ], + "type": "text", + "content": "Hyperbolic Space" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 418, + 372, + 545, + 434 + ], + "blocks": [ + { + "bbox": [ + 418, + 372, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 418, + 372, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 418, + 372, + 545, + 434 + ], + "type": "image", + "image_path": "f5cd311959a724571187fc9c2b1b2f8214b5adff0b2a7c28bfe9f6ae35d08452.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 476, + 435, + 487, + 443 + ], + "lines": [ + { + "bbox": [ + 476, + 435, + 487, + 443 + ], + "spans": [ + { + "bbox": [ + 476, + 435, + 487, + 443 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 450, + 545, + 538 + ], + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 538 + ], + "type": "text", + "content": "Figure 1. (a) A visual scene can be decomposed into a hierarchical structure based on the semantics of each visual element. (b) Euclidean space is suboptimal in representing the hierarchical structure due to its flat nature. The relational distance is inaccurately captured, being unaware of the semantic similarity of visual elements (Red line). Hi-Mapper maps the hierarchical elements in hyperbolic space, which effectively preserves their semantic relations and distances due to its constant negative curvature." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 546, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 712 + ], + "type": "text", + "content": "Over the decades, the development of deep neural networks (DNNs) has contributed towards advances in representing the complex visual scene. Notably, convolutional neural networks (CNNs) have achieved capturing fine details through the local convolutional filters while Vision Transformer (ViT) [8] has enabled coarse context modeling with multi-head self-attention mechanisms. Owing to their different desirable properties, hybrid architectures [9-12] and multi-scale variants of ViTs [13-15] have been extensively explored to capitalize on the complementary features of CNNs and ViTs. Subsequent works [16, 17] have further imposed interaction between multi-scale image patches to facilitate information exchange between fine details and coarse semantics." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 674, + 136, + 684 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 674, + 136, + 684 + ], + "spans": [ + { + "bbox": [ + 58, + 674, + 136, + 684 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 684, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 684, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 684, + 287, + 712 + ], + "type": "text", + "content": "This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2021R1A2C2006703)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17364" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": "While they have shown effective in capturing coarse-to-fine information, a structured understanding of the visual scene remains underexplored. Concretely, a scene can be interpreted as a hierarchical composition of visual elements, where the ability to recognize an instance (e.g. a man) at a coarse level arises from the ability to compose its constituents (e.g. body parts) at a finer level, as shown in Fig. 1a. Being aware of such semantic hierarchies furthers the perception of grid-like geometry and enhances the recognition of an entire image. Drawn from the same motivation, the recent variants of ViT [18-20] have constructed the hierarchies between image tokens across the transformer layers. However, their hierarchical relations are defined through the symmetric measurement (i.e., cosine similarity) which lacks the ability to represent the asymmetric property of hierarchical structure (i.e., inclusion of parent-child nodes). In addition, their image tokens are represented in Euclidean space where the hierarchical relations become distorted due to its linear and flat geometry [21-29], as shown in Fig. 1b." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 315, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 289, + 651 + ], + "type": "text", + "content": "In this paper, we propose a novel Visual Hierarchy Mapper (Hi-Mapper) that improves the structured understanding of pre-trained DNNs by identifying the visual hierarchy. Hi-Mapper accomplishes this through: 1) Probabilistic modeling of hierarchy nodes, where the mean vector and covariance represent the center and scale of visual-semantic cluster, respectively [30-33]. Accordingly, the asymmetric hierarchical relations are captured through the inclusion of probability densities. Furthermore, 2) Hi-Mapper maps the hierarchy nodes to hyperbolic space, where its constant negative curvature effectively represents the exponential growth of hierarchy nodes. Specifically, Hi-Mapper pre-defines a tree-like structure, with its leaf-level node modeled as a unique Gaussian distribution and the higher-level nodes approximated by a Mixture of Gaussians (MoG) of their corresponding child nodes. The pre-defined hierarchy nodes then interact with the penultimate visual feature map of the pre-trained DNNs to decompose the feature map into the visual hierarchy. Moreover, in order to bypass the difficulties of modeling hierarchy in Euclidean space, Hi-Mapper maps the identified visual hierarchy to hyperbolic space and learns the hierarchical relation with a novel hierarchical contrastive loss. The proposed loss enforces the child-parent nodes to be similar and child-child nodes to be dissimilar in a shared hyperbolic space. The visual hierarchy then interacts with the global visual feature of the pre-trained DNNs such that the hierarchical relations are fully encoded in the global feature representation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "content": "Hi-Mapper serves as a plug-and-play module, which generalizes over any type of DNNs and flexibly identifies the hierarchical organization of visual scenes. We conduct extensive experiments with various pre-trained DNNs (i.e., ResNet [34], DeiT [35]) on several benchmarks [36-38] to" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 72, + 485, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 485, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 485, + 85 + ], + "type": "text", + "content": "demonstrate the effectiveness of Hi-Mapper." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 86, + 518, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 86, + 518, + 97 + ], + "spans": [ + { + "bbox": [ + 317, + 86, + 518, + 97 + ], + "type": "text", + "content": "In summary, our key contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 98, + 547, + 253 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 98, + 547, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 98, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 306, + 98, + 547, + 169 + ], + "type": "text", + "content": "- We present a novel Visual Hierarchy Mapper (Hi-Mapper) that enhances the structured understanding of the pre-trained DNNs by investigating the hierarchical organization of visual scene. The proposed Hi-Mapper is applicable to any type of the pre-trained DNNs without modifying the underlying structures." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 170, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 170, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 170, + 545, + 216 + ], + "type": "text", + "content": "- Hi-Mapper effectively identifies the visual hierarchy by combining the favorable characteristic of probabilistic modeling and hyperbolic geometry for representing the hierarchical structure." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 217, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 547, + 253 + ], + "type": "text", + "content": "- We conduct extensive experiments to validate the efficacy of the proposed Hi-Mapper, and improves over the state-of-the-art approaches on various visual recognition tasks." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 265, + 392, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 265, + 392, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 265, + 392, + 278 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 286, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 547, + 441 + ], + "type": "text", + "content": "Hierarchy-aware visual recognition. Unsupervised image parsing is a long-standing pursuit in visual recognition tasks from the classical computer vision era [39-43]. In the pre-deep learning era, Zhouwen et al. [42] firstly introduces a framework to parse images with their constituents via a divide-and-conquer strategy. CapsuleNet-based methods have demonstrated substantial enhancements in image parsing, facilitated by dynamic routing, which efficiently capture the compositional relationships among the activities of capsules that represent object parts. Recently, hierarchical semantic segmentation has been extensively researched, including human parser [44, 45] based on human-part hierarchy and unsupervised part segmentations [46-48]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 442, + 548, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 548, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 548, + 647 + ], + "type": "text", + "content": "Beyond image parsing, recent researches on deep neural networks (DNNs) have attempted to exploit hierarchical relationships between detail and global representations. CrossViT [16] utilizes a dual-branch transformer for multiscale feature extraction, enriching features through a fusion module that integrates inter-scale patch relationships. Quadtree [18] iteratively and hierarchically selects a subset of crucial finer patches within each coarse patch. DependencyViT [19] inverts the self-attention process to organize patches as parent and child nodes, enabling a hierarchical exploration. More recently, CAST [49] employs superpixel-based patch generation and graph pooling for hierarchical patch merging for improving fine-grained recognition performances. While they define hierarchical relations with token similarities in Euclidean space, we predefine a hierarchical structure with probabilistic modeling and learn the relation in hyperbolic space." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Probabilistic modeling. Probabilistic representation has been extensively explored in the early NLP studies for handling the nuance of word semantics with the probability distribution. For instance, Vilnis et al. [30] first introduced the probability densities for representing" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17365" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "word embeddings. Athiwaratkun et al. [31] discovered that an imbalance in word frequency leads to distortions in word order and mitigated the problem by representing the word orders through the encapsulation of probability densities. Besides word representation, abundant research has demonstrated the effectiveness of probabilistic modeling in visual representation [6, 50-52]. For example, Shi et al. [51] proposed to penalize the low quality face images by measuring the variance of each image distribution. Chun et al. [50] identified the limitations of deterministic modeling in vision-language domains and introduced probabilistic cross-modal embedding for providing the uncertainty estimates." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 288, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 288, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 288, + 255 + ], + "type": "text", + "content": "In this work, we deploy probabilistic modeling in defining hierarchical structure, where each distribution represents the inclusive relations of hierarchy nodes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 268, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 289, + 533 + ], + "type": "text", + "content": "Hyperbolic manifold. Hyperbolic manifolds have gained increasing interest in deep learning area due to their effectiveness in modeling hierarchical structures. Their success in NLP field [24, 26, 27, 53] has inspired approaches to adopt hyperbolic manifolds in computer vision researches such as image retrieval [1, 2], image segmentation [54, 55], and few-shot learning [25]. As a pioneering work, Khrulkov et al. [56] investigated an exponential map from Euclidean space to hyperbolic space for learning hierarchical image embeddings. Ermolov et al. [1] applied pair-wise cross entropy loss in hyperbolic space for ViTs. Kim et al. [2] extended the work by discovering the latent hierarchy of training data with learnable hierarchical proxies in hyperbolic space. Focusing on pixel-level analysis, [55] identified the long-tail objects by embedding masked instance regions into hyperbolic manifolds. More recently, Desai et al. [29] introduced to learn joint image-text embedding space in hyperbolic manifold. While they explore hyperbolic manifold for representing the categorical hierarchies, we identify the hierarchical structure of visual elements without the part-level annotation through a novel hierarchical contrastive loss." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 548, + 174, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 174, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 174, + 562 + ], + "type": "text", + "content": "3. Hyperbolic Geometry" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "Hyperbolic manifold is a smooth Riemannian manifold " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " with negative curvature " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " equipped with a Riemannian metric " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ". The manifold consists of five isometric models and we utilize the Lorentz model for developing Hi-Mapper due to its training stability. A hyperbolic manifold of " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "-dimensions can be represented as a sub-manifold of the Lorentz model " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{n+1}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " as an upper half of a two-sheeted hyperboloid. In the Lorentz space, every point " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{n+1}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " can be denoted as " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "[\\mathbf{x}_{\\mathrm{space}}, x_{\\mathrm{time}}]" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{space}} \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{time}} \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{x}, \\mathbf{y} \\rangle" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " be the Euclidean inner product and " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{x}, \\mathbf{y} \\rangle_{\\mathbb{L}}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " denote the Lorentzian inner product which is derived by the Riemannian metric of the Lorentz model " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "g_{\\mathbb{L}}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ". Given two vectors " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}, \\mathbf{y} \\in" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 542, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 542, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 542, + 84 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{n + 1}" + }, + { + "bbox": [ + 306, + 72, + 542, + 84 + ], + "type": "text", + "content": ", the Lorentzian inner product is computed as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 344, + 92, + 547, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 92, + 547, + 107 + ], + "spans": [ + { + "bbox": [ + 344, + 92, + 547, + 107 + ], + "type": "interline_equation", + "content": "\\langle \\mathbf {x}, \\mathbf {y} \\rangle_ {\\mathbb {L}} = - x _ {\\text {t i m e}} y _ {\\text {t i m e}} + \\left\\langle \\mathbf {x} _ {\\text {s p a c e}}, \\mathbf {y} _ {\\text {s p a c e}} \\right\\rangle . \\tag {1}", + "image_path": "a2b917f09432f8e9a7a8aa31a19d13c3f9ff5b31e78b9759b09eaf349966b650.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": "-dimensional Lorentz model " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "(\\mathbb{L}^n,g_{\\mathbb{L}})" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": " is defined by the manifold " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "\\mathbb{L}^n = \\{\\mathbf{x}\\in \\mathbb{R}^{n + 1}:\\langle \\mathbf{x},\\mathbf{x}\\rangle_{\\mathbb{L}} = -1 / c,c > 0\\}" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": " and Riemannian metric of the Lorentz model " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "g_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": ". Thus, all vectors satisfy the following constraints:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 367, + 169, + 546, + 185 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 169, + 546, + 185 + ], + "spans": [ + { + "bbox": [ + 367, + 169, + 546, + 185 + ], + "type": "interline_equation", + "content": "- x _ {\\text {t i m e}} ^ {2} + \\left\\| \\mathbf {x} _ {\\text {s p a c e}} \\right\\| ^ {2} = - 1 / c. \\tag {2}", + "image_path": "99be340ea7bcf0d02164f2e0aa5bb742978cb7b79fd41aa0195b56d1535e1944.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 193, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 216 + ], + "type": "text", + "content": "A geodesic is the shortest path between two vectors on the manifold. The Lorentzian distance on " + }, + { + "bbox": [ + 304, + 193, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 304, + 193, + 545, + 216 + ], + "type": "text", + "content": " is then defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 358, + 225, + 546, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 225, + 546, + 239 + ], + "spans": [ + { + "bbox": [ + 358, + 225, + 546, + 239 + ], + "type": "interline_equation", + "content": "D _ {\\mathbb {L}} (\\mathbf {x}, \\mathbf {y}) = \\operatorname {a r c c o s h} (- \\langle \\mathbf {x}, \\mathbf {y} \\rangle_ {\\mathbb {L}}). \\tag {3}", + "image_path": "3b1d7b53124b1627b4ecc3e244b1a5387b3498510c170b283b8a72ca3b718d29.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": "The exponential map is a way to map vectors from tangent space " + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_z\\mathbb{L}^n" + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": " onto hyperbolic manifolds " + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathbb{L}^n" + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_z\\mathbb{L}^n" + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": " is a Euclidean space of vectors that are orthogonal to some point " + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\in \\mathbb{L}^n" + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": ". We map the tangent vector " + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{v}\\in \\mathcal{T}_z\\mathbb{L}^n" + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": " from Euclidean space to the Lorentz manifolds, in which the exponential map " + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathrm{expm}_{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 247, + 546, + 319 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 311, + 326, + 546, + 362 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 326, + 546, + 362 + ], + "spans": [ + { + "bbox": [ + 311, + 326, + 546, + 362 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\exp_ {z} (\\mathbf {v}) = \\cosh (\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}}) \\mathbf {z} + \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}})}{\\sqrt {c} \\| \\mathbf {v} \\| _ {\\mathbb {L}}} \\mathbf {v}. \\tag {4}", + "image_path": "06ac65441ca6b7b06d0bcbb73f7937cfc4c19a0d80e89ccfdef740830065ca91.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "text", + "content": "The logarithm map " + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\log \\mathrm{m}_z" + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "text", + "content": " which transfers " + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "text", + "content": " on the hyperboloid back to the tangent space " + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_z\\mathcal{M}" + }, + { + "bbox": [ + 304, + 363, + 545, + 387 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 395, + 546, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 395, + 546, + 425 + ], + "spans": [ + { + "bbox": [ + 326, + 395, + 546, + 425 + ], + "type": "interline_equation", + "content": "\\mathbf {v} = \\log \\mathrm {m} _ {z} (\\mathbf {x}) = \\frac {\\cosh^ {- 1} (- c \\langle \\mathbf {z} , \\mathbf {x} \\rangle_ {\\mathbb {L}})}{\\sqrt {(c \\langle \\mathbf {z} , \\mathbf {x} \\rangle_ {\\mathbb {L}}) ^ {2} - 1}} \\operatorname {p r o j} _ {\\mathbf {z}} (\\mathbf {x}). \\tag {5}", + "image_path": "712936a2788e2eb616c0dd9ea80ef980cfb367c20af721e801883da97824dd12.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "type": "text", + "content": "We set " + }, + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "type": "text", + "content": " as the origin of the hyperboloid " + }, + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{O} = \\left[\\mathbf{0},\\sqrt{1 / c}\\right]" + }, + { + "bbox": [ + 304, + 432, + 541, + 453 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 460, + 361, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 361, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 361, + 472 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 479, + 373, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 373, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 373, + 491 + ], + "type": "text", + "content": "4.1. Overview" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 498, + 547, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 570 + ], + "type": "text", + "content": "Our goal is to enhance the structured understanding of pre-trained deep neural networks (DNNs) by investigating the hierarchical organization of visual scenes. To this end, we introduce a Visual Hierarchy Mapper (Hi-Mapper) which serves as a plug-and-play module on any type of pre-trained DNNs. An overview of Hi-Mapper is depicted in Fig. 2a." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": "Given an image " + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": ", we first extract visual features " + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "inline_equation", + "content": "[\\mathbf{v}_{\\mathrm{map}},\\mathbf{v}_{\\mathrm{cls}}] = \\mathcal{F}(\\mathcal{I})" + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": " from a pre-trained image encoder " + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}\\in \\mathbb{R}^{hw\\times d}" + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": " is the penultimate visual feature map and " + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": " is the global visual representation, with " + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "inline_equation", + "content": "hw" + }, + { + "bbox": [ + 304, + 570, + 547, + 630 + ], + "type": "text", + "content": " indicating the size of the visual feature map." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Hi-Mapper identifies the visual hierarchy from the visual feature map " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " and encodes the identified visual hierarchy back to the global visual representation " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " for enhancing the recognition of a whole scene. To this end, we predefine a hierarchy tree with Gaussian distribution, where the relations of the hierarchy nodes are defined through the inclusion of probability densities (Sec. 4.2). 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(a) An overview of the proposed Hi-Mapper. Hi-Mapper operates on top of pre-trained image encoder " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": ", with probabilistic hierarchy tree " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{T} = \\{\\mathbf{C}^l\\}_{l=1}^L" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": ". The tree interacts with visual feature map " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": " through hierarchy decomposition module " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": ", thereby identifying visual hierarchy in Euclidean space " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{E}} = \\{\\mathbf{S}^l\\}_{l=1}^L" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": ". The visual hierarchy is mapped to hyperbolic space " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{L}} = \\{\\mathbf{H}^l\\}_{l=1}^L" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": " and optimized with hierarchical contrastive loss " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathbb{L}-\\mathrm{cont}}" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": ". The visual hierarchy is further encoded into global visual representation " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": " via hierarchy encoding module " + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 220, + 547, + 285 + ], + "type": "text", + "content": " for enhancing the recognition of entire scene. (b) The proposed hierarchical contrastive loss pulls each parent-child node and pushes all the other nodes at the same level." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 294, + 280, + 355 + ], + "lines": [ + { + "bbox": [ + 58, + 294, + 280, + 355 + ], + "spans": [ + { + "bbox": [ + 58, + 294, + 280, + 355 + ], + "type": "image", + "image_path": "152e897f97f5ede0f072fd9146304cb66f693066a5ba46c13a62799ac5d987ac.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 59, + 374, + 275, + 453 + ], + "blocks": [ + { + "bbox": [ + 121, + 361, + 214, + 371 + ], + "lines": [ + { + "bbox": [ + 121, + 361, + 214, + 371 + ], + "spans": [ + { + "bbox": [ + 121, + 361, + 214, + 371 + ], + "type": "text", + "content": "(a) Hierarchy decomposition" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 374, + 275, + 453 + ], + "lines": [ + { + "bbox": [ + 59, + 374, + 275, + 453 + ], + "spans": [ + { + "bbox": [ + 59, + 374, + 275, + 453 + ], + "type": "image", + "image_path": "061d512bb38d3a54e0aefeddd20c432d103a1ee1bc15bba92b551adeb8ad72b7.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 129, + 459, + 205, + 469 + ], + "lines": [ + { + "bbox": [ + 129, + 459, + 205, + 469 + ], + "spans": [ + { + "bbox": [ + 129, + 459, + 205, + 469 + ], + "type": "text", + "content": "(b) Hierarchy encoding" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "lines": [ + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "text", + "content": "Figure 3. (a) Hierarchy decomposition module groups semantically-relevant visual features " + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "text", + "content": " to the closest semantic cluster " + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^l" + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "text", + "content": ". (b) Hierarchy encoding module progressively updates global representation " + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "text", + "content": " by aggregating the visual hierarchy " + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^l" + }, + { + "bbox": [ + 46, + 474, + 288, + 519 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "text", + "content": "The hierarchy tree interacts with " + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "text", + "content": " through the hierarchy decomposition module " + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "text", + "content": " such that the feature map is decomposed into the visual hierarchy (Sec. 4.3). Since the zero curvature of Euclidean space is not optimal for representing the hierarchical structure, we map the visual hierarchy to hyperbolic space and optimize the relation with a novel hierarchical contrastive loss (Sec. 4.4). The visual hierarchy is then encoded back to the global visual representation " + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "text", + "content": " through the hierarchy encoding module " + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 530, + 287, + 651 + ], + "type": "text", + "content": " resulting in an enhanced global representation (Sec. 4.5)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 658, + 198, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 198, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 198, + 671 + ], + "type": "text", + "content": "4.2. Probabilistic hierarchy tree" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "type": "text", + "content": "The main problem of the recent hierarchy-aware ViTs [18-20] is that they define the hierarchical relations between the image tokens mainly through the self-attention scores. Such" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "type": "text", + "content": "a symmetric measurement is suboptimal for representing the asymmetric inclusive relation of parent-child nodes. To handle the problem, we propose to define " + }, + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "type": "text", + "content": " levels of hierarchy tree " + }, + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 304, + 293, + 547, + 352 + ], + "type": "text", + "content": " by modeling each hierarchy node with a probability distribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 353, + 547, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 435 + ], + "type": "text", + "content": "Specifically, we first parameterize each leaf-level (at the initial level) node as a unique Gaussian distribution and subsequently define the higher-level node as a Mixture-of-Gaussians (MoG) of its corresponding child nodes. Accordingly, the mean vector represents the cluster center of the visual semantic and the covariance captures the scale of each semantic cluster." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": "Initial level. Let " + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^1 = \\{\\mathbf{c}_n^1\\}_{n=1}^{N_1}" + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": " be a set of " + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "inline_equation", + "content": "N_1" + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": " initial level nodes. We parameterize each node " + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_n^1" + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": " as a normal distribution with a mean vector " + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "inline_equation", + "content": "\\mu_n^1" + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": " and a diagonal covariance matrix " + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "inline_equation", + "content": "\\sigma_n^1\\mathbf{I}" + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 441, + 547, + 491 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 379, + 499, + 545, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 499, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 379, + 499, + 545, + 514 + ], + "type": "interline_equation", + "content": "p \\left(\\mathbf {c} _ {n} ^ {1}\\right) \\sim \\mathcal {N} \\left(\\mu_ {n} ^ {1}, \\sigma_ {n} ^ {1} \\mathbf {I}\\right), \\tag {6}", + "image_path": "4ea82248424963dc6e45985e8ac58b06e030fae80b179139d5588a9980970b9a.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mu_n^1" + }, + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\sigma_{n}^{1}" + }, + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "text", + "content": " are randomly initialized. We use reparameterization trick [57] for stable sampling, such that:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 374, + 556, + 545, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 556, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 374, + 556, + 545, + 571 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {n} ^ {1} = \\mu_ {n} ^ {1} + \\epsilon * \\sigma_ {n} ^ {1} \\in \\mathbb {R} ^ {d}, \\tag {7}", + "image_path": "25e313093d9476e556325fb38bc0ff0f7189ae46a2ace74929c9b9e0432c8a74.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 580, + 387, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 387, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 387, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 580, + 387, + 593 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": "Subsequent level. We derive the remaining " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "(L - 1)" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": " levels of hierarchy tree by conditioning each level on the preceding hierarchy level. For each " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": "-th level, we formulate a set of " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": " nodes " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{l} = \\{\\mathbf{c}_{k}^{l}\\}_{k = 1}^{N_{l}}" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": ". Concretely, the " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": "-th node " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_k^l" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": "-th level is approximated by a MoG of its two corresponding child nodes, " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{2k - 1}^{l - 1}" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{2k}^{l - 1}" + }, + { + "bbox": [ + 304, + 598, + 545, + 673 + ], + "type": "text", + "content": ", as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 354, + 682, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 682, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 354, + 682, + 545, + 715 + ], + "type": "interline_equation", + "content": "p \\left(\\mathbf {c} _ {k} ^ {l}\\right) \\sim \\sum_ {k ^ {\\prime} = 2 k - 1} ^ {2 k} \\mathcal {N} \\left(\\mu_ {k ^ {\\prime}} ^ {l - 1}, \\sigma_ {k ^ {\\prime}} ^ {l - 1} \\mathbf {I}\\right). \\tag {8}", + "image_path": "8b16a160e7c7947474e56cb66882dccf6155f3a857c24def96ea715cefbd6fc2.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17367" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "To stabilize the construction of hierarchy tree, we increase the sampling rate as the distribution expands, i.e., we sample " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "2^{l - 1}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " embeddings from " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p(\\mathbf{c}_k^l)" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " using the reparameterization trick in Eq. (7) as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 128, + 287, + 164 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 128, + 287, + 164 + ], + "spans": [ + { + "bbox": [ + 58, + 128, + 287, + 164 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {c} _ {k} ^ {l} = \\left\\{\\hat {\\mathbf {c}} _ {k, 1} ^ {l}, \\dots , \\hat {\\mathbf {c}} _ {k, 2 ^ {l - 1}} ^ {l} \\right\\} \\stackrel {{\\mathrm {i d}}} {{\\sim}} p \\left(\\mathbf {c} _ {k} ^ {l}\\right), \\quad \\mathbf {c} _ {k} ^ {l} \\in \\mathbb {R} ^ {2 ^ {l - 1} \\times d}, \\tag {9} \\\\ \\mathbf {C} ^ {l} = \\left\\{\\mathbf {c} _ {1} ^ {l}, \\dots , \\mathbf {c} _ {N _ {l}} ^ {l} \\right\\} \\in \\mathbb {R} ^ {2 ^ {l - 1} N _ {l} \\times d}. \\\\ \\end{array}", + "image_path": "720bdce9d1d0ecb15991b8bec4d04cddb2596df0f59cd92462ac134ea9c00dcf.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 171, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 243 + ], + "type": "text", + "content": "By sequentially conditioning the higher-level nodes on the preceding lower-level nodes, we obtain the hierarchy tree " + }, + { + "bbox": [ + 46, + 171, + 287, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{T} = \\{\\mathbf{C}^l\\}_{l=1}^L" + }, + { + "bbox": [ + 46, + 171, + 287, + 243 + ], + "type": "text", + "content": ", where the lower-level nodes capture fine details with concentrated distribution and the higher-level nodes capture coarse instance-level representations with dispersed distribution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "type": "text", + "content": "KL divergence loss. To prevent the variances from collapsing to zero, we employ KL regularization term between the distributions of " + }, + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "type": "text", + "content": "-th level nodes and the unit Gaussian prior " + }, + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 46, + 248, + 287, + 297 + ], + "type": "text", + "content": " following [50]:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 304, + 287, + 337 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 304, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 86, + 304, + 287, + 337 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {K L}} = \\sum_ {i = 1} ^ {N _ {L}} \\mathrm {K L} \\left(\\mathcal {N} \\left(\\mu_ {i} ^ {L}, \\sigma_ {i} ^ {L}\\right) \\| \\mathcal {N} (0, \\mathbf {I})\\right). \\tag {10}", + "image_path": "b6b36ce8ffeffdb52e7d7a9a465a4ebd11dc7ec6e208e45c40317e763cadc0bc.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 217, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 217, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 217, + 358 + ], + "type": "text", + "content": "4.3. Visual hierarchy decomposition" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": "Given the pre-defined hierarchy tree " + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": " and the visual feature map " + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": ", we decompose " + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": " levels of visual hierarchy through hierarchy decomposition module " + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": ", as shown in Fig. 3a. We instantiate " + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 364, + 287, + 423 + ], + "type": "text", + "content": " as a stack of two transformer decoder layers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "text", + "content": "To identify the visual hierarchy at the " + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "text", + "content": "-th level, the decomposition module " + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "text", + "content": " treats " + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^l" + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "text", + "content": " as the query, and " + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{map}}" + }, + { + "bbox": [ + 46, + 424, + 287, + 471 + ], + "type": "text", + "content": " as the key and value such that the semantically-relevant visual features are aggregated to the closest semantic cluster:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 479, + 287, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 479, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 59, + 479, + 287, + 496 + ], + "type": "interline_equation", + "content": "\\mathbf {S} ^ {l} = \\left\\{\\mathbf {s} _ {1} ^ {l}, \\dots , \\mathbf {s} _ {N _ {l}} ^ {l} \\right\\} = \\mathcal {D} \\left(\\mathbf {C} ^ {l}, \\mathbf {v} _ {\\text {m a p}}\\right) \\in \\mathbb {R} ^ {2 ^ {l - 1} N _ {l} \\times d}. \\tag {11}", + "image_path": "71179e7cb54747c3cf6a0e431b67dd68109405cb873696d5f125a8fd84d3f018.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": "Similar to the hierarchy nodes " + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_k^l" + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": " in Eq. (9), the decomposed visual hierarchy nodes " + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_k^l" + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": " are comprised of " + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "inline_equation", + "content": "2^{l-1}" + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": " visual representations as " + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_k^l = \\{\\hat{\\mathbf{s}}_{k,1}^l, \\dots, \\hat{\\mathbf{s}}_{k,2^{l-1}}^l\\}" + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": ". We average the set of " + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "inline_equation", + "content": "2^{l-1}" + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": " representations for each visual hierarchy node " + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_k^l" + }, + { + "bbox": [ + 46, + 505, + 287, + 567 + ], + "type": "text", + "content": " such that:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 102, + 574, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 574, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 102, + 574, + 287, + 608 + ], + "type": "interline_equation", + "content": "\\mathbf {s} _ {k} ^ {l} = \\frac {1}{2 ^ {l - 1}} \\sum_ {i = 1} ^ {2 ^ {l - 1}} \\hat {\\mathbf {s}} _ {k, i} ^ {l}, \\quad \\mathbf {s} _ {k} ^ {l} \\in \\mathbb {R} ^ {d} \\tag {12}", + "image_path": "51a3bc1aac2804f9aac9771b595a590bdb0aef7ecc7cd9f7e13522abc275f8eb.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "text", + "content": "We perform the same decomposition procedure for " + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "text", + "content": " levels, thereby obtaining " + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "text", + "content": " levels of visual hierarchy in Euclidean space " + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{E}} = \\{\\mathbf{S}^l\\}_{l=1}^L" + }, + { + "bbox": [ + 46, + 616, + 287, + 654 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 659, + 254, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 254, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 254, + 672 + ], + "type": "text", + "content": "4.4. Learning hierarchy in hyperbolic space" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "A natural characteristic of the hierarchical structure is that the number of nodes exponentially increases as the depth increases. In practice, representing this property in Euclidean" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "space leads to distortions in the semantic distances due to its flat geometry. We propose to handle the problem by learning the hierarchical relations in hyperbolic space, where its exponentially expanding volume can efficiently represent the visual hierarchy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": "We first map " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{E}}" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": " to the Lorentz hyperboloid to derive the visual hierarchy in hyperbolic space " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": ". Following [29], we simplify the mapping computation by parameterizing only the space component of the Lorentz model as " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{s} = [\\mathbf{s}_k^l, 0] \\in \\mathbb{R}^{d+1}" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": " belongs to the tangent space at the hyperboloid origin " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": ". The visual hierarchy node in hyperbolic space " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_k^l = [\\mathbf{h}_{k,\\mathrm{space}}^l, h_{k,\\mathrm{time}}^l]" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": " is then obtained by transforming " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_k^l" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{k,\\mathrm{space}}^l" + }, + { + "bbox": [ + 304, + 133, + 545, + 242 + ], + "type": "text", + "content": " using the exponential map in Eq. (13) as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 330, + 251, + 545, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 251, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 330, + 251, + 545, + 306 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {h} _ {k, \\text {s p a c e}} ^ {l} = \\cosh (\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}}) \\mathbf {0} + \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}})}{\\sqrt {c} \\| \\mathbf {s} \\| _ {\\mathbb {L}}} \\mathbf {s} _ {k} ^ {l} \\\\ = \\frac {\\sinh (\\sqrt {c} \\| \\mathbf {s} _ {k} ^ {l} \\|)}{\\sqrt {c} \\| \\mathbf {s} _ {k} ^ {l} \\|} \\mathbf {s} _ {k} ^ {l}, \\tag {13} \\\\ \\end{array}", + "image_path": "52d7e064216d329f4463168a10d31b611409642f1aacb291beb397de31dd6891.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "text", + "content": "and computing the corresponding time component " + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "inline_equation", + "content": "h_{k,\\mathrm{time}}^{l}" + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "text", + "content": " using Eq. (2) as " + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "inline_equation", + "content": "h_{k,\\mathrm{time}}^{l} = \\sqrt{1 / c + \\|\\mathbf{h}_{k,\\mathrm{space}}^{l}\\|^{2}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "text", + "content": ". The visual hierarchy in hyperbolic space " + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 360 + ], + "type": "text", + "content": " is denoted as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 368, + 545, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 368, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 315, + 368, + 545, + 383 + ], + "type": "interline_equation", + "content": "\\mathbf {T} _ {\\mathbb {L}} = \\left\\{\\mathbf {H} ^ {l} \\right\\} _ {l = 1} ^ {L}, \\quad \\mathbf {H} ^ {l} = \\left\\{\\mathbf {h} _ {1} ^ {l}, \\dots , \\mathbf {h} _ {N _ {l}} ^ {l} \\right\\} \\in \\mathbb {R} ^ {N _ {l} \\times d _ {\\mathbb {L}}}, \\tag {14}", + "image_path": "a5dfe3606f2bc61e78f3bebf086e39a8dac857f395fe43e53db2f24acb35601e.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 392, + 544, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 544, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 544, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 392, + 544, + 403 + ], + "type": "inline_equation", + "content": "d_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 392, + 544, + 403 + ], + "type": "text", + "content": " is the embedding dimension in Lorentz manifold." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "type": "text", + "content": "Hierarchical contrastive loss. To guarantee the hierarchy nodes to reflect the hierarchical relations, we optimize the distances of " + }, + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "type": "text", + "content": " with a novel hierarchical contrastive loss " + }, + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathbb{L}\\text{-cont}}" + }, + { + "bbox": [ + 304, + 409, + 545, + 480 + ], + "type": "text", + "content": ". Specifically, we formulate the similarity between the nodes in consideration of the length of the connected branch, i.e., geodesic distance, as shown in Fig. 2b." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": "Consider a node " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{2k}^{l}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_k^{l + 1}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": " is its parent node. We encourage " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{2k}^{l}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": " to be similar with " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_k^{l + 1}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": " since the pair of parent-child nodes lie on the same branch. Meanwhile, we encourage the remaining nodes in the same level, i.e., " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{h}_i^l |\\mathbf{h}_i^l\\in \\mathbf{H}^l,i\\neq 2k\\}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": ", to be dissimilar since they all lie on separate branches. The loss also penalizes the close sibling node " + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{2k - 1}^{l}" + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": " as their geodesic traverses the parent node. Formally, the hierarchical contrastive loss incorporates the geometric interpretation of hierarchical structure into the contrastive loss [58] as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 307, + 610, + 545, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 610, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 307, + 610, + 545, + 653 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathbb {L} - \\text {c o n t}} = - \\log \\underset {\\mathbf {T} _ {\\mathbb {L}}} {\\mathbb {E}} \\left[ \\sum_ {i = 0} ^ {1} \\frac {\\exp \\left(D _ {\\mathbb {L}} \\left(\\mathbf {h} _ {k} ^ {l + 1} , \\mathbf {h} _ {2 k - i} ^ {l}\\right)\\right)}{\\sum_ {j \\neq 2 k - i} \\exp \\left(D _ {\\mathbb {L}} \\left(\\mathbf {h} _ {2 k - i} ^ {l} , \\mathbf {h} _ {j} ^ {l}\\right)\\right)} \\right], \\tag {15}", + "image_path": "30afba62caede9e2a815fe430da2ad414bbf53420bbf4bd6232be68a656251d9.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 654, + 527, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 527, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 527, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 654, + 527, + 665 + ], + "type": "inline_equation", + "content": "D_{\\mathbb{L}}" + }, + { + "bbox": [ + 304, + 654, + 527, + 665 + ], + "type": "text", + "content": " is the Lorentzian distance defined in Eq. (3)." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 666, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 712 + ], + "type": "text", + "content": "By regarding every pair of parent-child nodes as positive and every pair of nodes at the same level as negative, we are able to represent the logical structure of visual hierarchy without the part-level annotation. In addition, the" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17368" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "hierarchical relation optimized through " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{L}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " in hyperbolic space is well-preserved in " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{E}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " in Euclidean space thanks to the mapping computation in Eq. (13)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 116, + 192, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 116, + 192, + 129 + ], + "spans": [ + { + "bbox": [ + 47, + 116, + 192, + 129 + ], + "type": "text", + "content": "4.5. Visual hierarchy encoding" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "type": "text", + "content": "We propose to enhance the structured understanding of the global visual representation by encoding the identified visual hierarchy into " + }, + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "type": "text", + "content": ". While we optimize the hierarchical relations in hyperbolic space due to its ability of handling relative distances, its complex computations and expansion property make it less suitable for tasks that require absolute criteria. Thus, we exploit the visual hierarchy in Euclidean space " + }, + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbb{E}}" + }, + { + "bbox": [ + 46, + 134, + 287, + 230 + ], + "type": "text", + "content": " for hierarchy encoding." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": "Specifically, we progressively encode the hierarchy nodes " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^l" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": ", from the initial level to the " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": "-th level, via the hierarchy encoding module " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": " is updated as a hierarchy-aware global representation " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}^L" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": ". As shown in Fig. 3b, the module " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": " is instantiated as a stack of " + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 230, + 287, + 301 + ], + "type": "text", + "content": " transformer decoder layers." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "content": "To encode the " + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "content": "-th level hierarchy, the " + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "content": "-th layer of " + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^l" + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "content": " takes " + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}^{l-1}" + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "content": " as the query, and " + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^l" + }, + { + "bbox": [ + 47, + 301, + 287, + 327 + ], + "type": "text", + "content": " as the key and value:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 84, + 335, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 335, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 84, + 335, + 287, + 350 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {\\mathrm {c l s}} ^ {l} = \\mathcal {G} ^ {l} \\left(\\mathbf {v} _ {\\mathrm {c l s}} ^ {l - 1}, \\mathbf {S} ^ {l}\\right) \\in \\mathbb {R} ^ {d}, \\quad 0 < l \\leq L, \\tag {16}", + "image_path": "51836b396335abf86823a622715dded2ceee1e45c1a6cca3e1df34f33d83c0ff.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "type": "text", + "content": "where we set " + }, + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}^{0}" + }, + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 359, + 287, + 383 + ], + "type": "text", + "content": ". The enhanced global visual representation is then derived as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 392, + 287, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 392, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 129, + 392, + 287, + 406 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {v}} _ {\\mathrm {c l s}} = \\mathbf {v} _ {\\mathrm {c l s}} + \\mathbf {v} _ {\\mathrm {c l s}} ^ {L}. \\tag {17}", + "image_path": "a536f3a52e156098cb6d63176c681f65bf88b00793b4644179973113ff444031.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "type": "text", + "content": "For the final prediction, we feed " + }, + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "type": "text", + "content": " into the pre-trained classifier of " + }, + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 415, + 287, + 438 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 445, + 277, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 277, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 277, + 456 + ], + "type": "text", + "content": "Overall objectives. The overall objective is defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 99, + 466, + 287, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 466, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 99, + 466, + 287, + 479 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\mathrm {C E}} + \\alpha \\mathcal {L} _ {\\mathbb {L} - \\text {c o n t}} + \\beta \\mathcal {L} _ {\\mathrm {K L}}, \\tag {18}", + "image_path": "d1b3d9ad25f7de31e2a6f18d32dc5b2c55671138eadffb005a7bc6505456ead3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 488, + 228, + 501 + ], + "type": "text", + "content": " are the balancing parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 511, + 128, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 128, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 128, + 525 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 532, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 639 + ], + "type": "text", + "content": "In this section, we conduct extensive experiments to show the effectiveness of our proposed Hi-Mapper on image classification (Sec. 5.1), object detection and instance segmentation (Sec. 5.2), and semantic segmentation (Sec. 5.3). We apply our Hi-Mapper on both CNN-based [34, 59] and ViT-based [35, 60] backbone networks and compare the performance with the concurrent hierarchy-aware baselines [16, 19]. Lastly, we provide ablation studies (Sec. 6) to demonstrate the effectiveness of our contributions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 647, + 162, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 162, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 162, + 659 + ], + "type": "text", + "content": "5.1. Image classification" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Settings. We apply our Hi-Mapper on the state-of-the-art backbone networks [34, 35, 59, 60] and benchmark on ImageNet-1k [36] dataset. Following [12, 60, 62-64], we use the identical combinations for data augmentation" + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 313, + 102, + 538, + 415 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "type": "text", + "content": "Table 1. Performance comparisons for image classification on ImageNet-1K [36] dataset." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 102, + 538, + 415 + ], + "lines": [ + { + "bbox": [ + 313, + 102, + 538, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 538, + 415 + ], + "type": "table", + "html": "
TypeModelParams (M)FLOPs (G)Top-1 (%)
CNNResNet-50 [34]25.63.876.2
EfficientNet-B4* [59]19.34.282.9
Hi-Mapper(RN50)26.94.078.2
Hi-Mapper(ENB4*)20.54.484.1
ViTDeiT-T [35]5.71.372.2
CrossViT-T [16]6.91.673.4
PVT-T [61]13.21.975.1
DependecnyViT-T [19]6.21.375.4
Hi-Mapper(DeiT-T)6.61.574.8
DeiT-S [35]22.24.579.8
CrossViT-S [16]26.75.681
PVT-S [61]24.53.879.8
Swin-T [60]28.34.681.2
DependencyViT-S [19]24.05.082.1
Hi-Mapper(DeiT-S)23.34.882.6
Hi-Mapper(Swin-T)29.54.983.4
DeiT-B [35]85.617.681.8
Swin-S [60]50.18.783.0
Hi-Mapper(DeiT-B)87.218.183.4
Hi-Mapper(Swin-S)51.89.384.1
", + "image_path": "d03ee7314273d2f5622ede3e1a0bb473c260b0cb91ae1bd6fe67bc9489cf305b.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 426, + 547, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 547, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 547, + 487 + ], + "type": "text", + "content": "and regularization strategies [35] after excluding repeated augmentation [65]. We train our model with batch size 1024 for 50 epochs using AdamW [66] with weight decay 1e-4. The initial learning rate is set to 1e-4 and a cosine learning rate scheduler is applied following [35]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "text", + "content": "Results. Tab. 1 presents classification performance. We report the original performance without the fine-tuning schemes for the plain backbone networks since we observed degradation in performance after fine-tuning the models. Our proposed method consistently achieves better performances than the baseline models with only a slight increase in parameters. Specifically, Hi-Mapper surpasses ResNet-50 [34] and EfficientNet-B4 [59] by margins of " + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "text", + "content": ", respectively. Additionally, it achieves improvement on DeiT's performance by " + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "inline_equation", + "content": "2.6\\%/2.8\\%/1.6\\%" + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "text", + "content": ", and Swin [60] by " + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "inline_equation", + "content": "2.2\\%/1.1\\%" + }, + { + "bbox": [ + 304, + 494, + 547, + 661 + ], + "type": "text", + "content": " across various model sizes. The experiments on image classification demonstrate not only the importance of understanding the structured organization of visual scenes, but also the scalability of our method." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 670, + 533, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 533, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 533, + 684 + ], + "type": "text", + "content": "5.2. Object detection and Instance segmentation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "Settings. We experiment on the COCO [37] dataset. We use the Hi-Mapper backbones derived from Sec. 5.1. Then," + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17369" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 97, + 535, + 245 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 2. Performance comparisons for object detection and instance segmentation on COCO [37] dataset. " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "(^{*})" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " Results are reproduced based on [10]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 97, + 535, + 245 + ], + "lines": [ + { + "bbox": [ + 61, + 97, + 535, + 245 + ], + "spans": [ + { + "bbox": [ + 61, + 97, + 535, + 245 + ], + "type": "table", + "html": "
BackboneParams (M)Flops (G)Mask R-CNN 1x
APboxAPbox50APbox75APmaskAPmask50APmask75
PVT-T [61]32.919536.759.239.335.156.737.3
DeiT-T* [35]27.324430.346.232.127.144.428.3
Hi-Mapper(Deit-T)29.524637.161.741.035.759.138.1
PVT-S [61]44.124540.462.943.837.860.140.3
DeiT-S* [35]44.927636.354.139.031.751.333.2
Swin-T [60]47.826743.566.447.339.663.142.3
Hi-Mapper(Deit-S)47.027942.665.846.338.962.741.8
Hi-Mapper(Swin-T)50.427044.067.147.939.963.642.8
", + "image_path": "d1e50d09e693ffa00207420146e791c56934ae0890579dbda0349cbcbfdf81df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 290, + 286, + 451 + ], + "blocks": [ + { + "bbox": [ + 46, + 252, + 289, + 287 + ], + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 287 + ], + "type": "text", + "content": "Table 3. Performance comparisons for semantic segmentation on ADE20k [38] dataset. We conduct the single-scale evaluation. FLOPs are measured with " + }, + { + "bbox": [ + 46, + 252, + 289, + 287 + ], + "type": "inline_equation", + "content": "512 \\times 2048" + }, + { + "bbox": [ + 46, + 252, + 289, + 287 + ], + "type": "text", + "content": " input resolution." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 290, + 286, + 451 + ], + "lines": [ + { + "bbox": [ + 52, + 290, + 286, + 451 + ], + "spans": [ + { + "bbox": [ + 52, + 290, + 286, + 451 + ], + "type": "table", + "html": "
BackboneMethodParams (M)FLOPs (G)mIoU
PVT-T [61]SemanticFPN [69]17.013235.7
DeiT-T [35]UperNet [70]10.714237.8
DependencyViT-T [19]UperNet [70]11.114540.3
Hi-Mapper(DeiT-T)UperNet [70]11.614439.8
PVT-S [61]SemanticFPN [69]28.271239.8
DeiT-S [35]UperNet [70]41.356643.0
Swin-T [60]UperNet [70]60.094544.5
DependencyVIT-S [19]UperNet [70]43.157445.7
Hi-Mapper(DeiT-S)UperNet [70]42.557046.3
Hi-Mapper(Swin-T)UperNet [70]62.194946.8
", + "image_path": "95b236e3be0fb4c74e23edcf2b2b3ae6d1fc636d964f01dc9e4ad68aedb0c00c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 461, + 288, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 288, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 288, + 522 + ], + "type": "text", + "content": "we deploy our pre-trained backbone into Mask R-CNN [67]. All models are trained on COCO 2017, including 118k train images and 5k validation images. We follow the standard learning protocols [67], " + }, + { + "bbox": [ + 46, + 461, + 288, + 522 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 461, + 288, + 522 + ], + "type": "text", + "content": " schedule with 12 epochs. Note that we reproduce DeiT-T with Mask R-CNN based on [68]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 529, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 288, + 662 + ], + "type": "text", + "content": "Results. In Table 2, we present a comparison of our results with baseline models, such as DeiT and Swin, on the COCO dataset, which demands a higher capacity for fine representation recognition. Our Hi-Mapper consistently boosts all baseline models capability with only a small increase in parameters. Notably, Hi-Mapper significantly improves DeiT-T and -S by margins of 6.8 and 8.3 on the object detection task. Meanwhile, in the instance segmentation, it also improves DeiT-T and -S by margins of 8.6 and 7.2, respectively. This result shows that the visual hierarchy facilitates complex visual scene recognition." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 178, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 178, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 178, + 683 + ], + "type": "text", + "content": "5.3. Semantic segmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Settings. We further experiment on the ADE20K [38] dataset for semantic segmentation. ADE20K contains" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 318, + 290, + 535, + 430 + ], + "blocks": [ + { + "bbox": [ + 305, + 252, + 547, + 287 + ], + "lines": [ + { + "bbox": [ + 305, + 252, + 547, + 287 + ], + "spans": [ + { + "bbox": [ + 305, + 252, + 547, + 287 + ], + "type": "text", + "content": "Table 4. Performance comparison for classification on ImageNet-1K [36] according to embedding spaces and combinations of learning objectives." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 290, + 535, + 430 + ], + "lines": [ + { + "bbox": [ + 318, + 290, + 535, + 430 + ], + "spans": [ + { + "bbox": [ + 318, + 290, + 535, + 430 + ], + "type": "table", + "html": "
Manifold\\( \\mathcal{L}_{\\text{LL-cont}} \\)\\( \\mathcal{L}_{\\text{KL}} \\)Top-1(%)
EuclideanXX79.7
X✓79.6
✓X79.2
✓✓79.3
HyperbolicXX79.7
X✓79.5
✓X82.0
✓✓82.6
", + "image_path": "921db102d0149169b19f4add4ced97e00529697b77759daded91a16ead02e422.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 443, + 547, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 547, + 480 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 547, + 480 + ], + "type": "text", + "content": "20k training images, 20K validation images, and 3K test images, covering a total 150 classes. Following common practice [70], we report the mIoU on the validation set." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "text", + "content": "Results. We present the performance comparisons on ADE20K in Tab. 3. The results show that our Hi-Mapper achieves comparable or better performance than the baseline models, including DeiT-T, -S, and Swin-T, requiring a smaller increase in the number of parameters and GFLOPs. Specifically, Hi-Mapper on DeiT-T, -S, and Swin-T achieves a performance improvement of " + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 619 + ], + "type": "text", + "content": ". Additionally, as model sizes increase, Hi-Mapper fully capitalizes fine-grained representations for semantic segmentation with a slight increase in computation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 632, + 390, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 390, + 644 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 390, + 644 + ], + "type": "text", + "content": "5.4. Visualization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "As shown in Fig. 4, we demonstrate our visual hierarchy on images from ImageNet-1K [36]. This confirms that our approach can successfully uncover the inherent hierarchy among visual components without the need for hierarchy or part-level annotations." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17370" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 69, + 175, + 228 + ], + "blocks": [ + { + "bbox": [ + 59, + 69, + 175, + 228 + ], + "lines": [ + { + "bbox": [ + 59, + 69, + 175, + 228 + ], + "spans": [ + { + "bbox": [ + 59, + 69, + 175, + 228 + ], + "type": "image", + "image_path": "706d8901c2f3ddb439c53d6809f228ea320758ba967103398dddcf8f708037d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "type": "text", + "content": "Figure 4. Visualization of visual hierarchy decomposed by Hi-Mapper(Deit-S) trained on ImageNet-1K with classification objective. Each color represents different subtrees. We ignore the nodes of the small region and display only the main subtrees." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 186, + 68, + 299, + 228 + ], + "blocks": [ + { + "bbox": [ + 186, + 68, + 299, + 228 + ], + "lines": [ + { + "bbox": [ + 186, + 68, + 299, + 228 + ], + "spans": [ + { + "bbox": [ + 186, + 68, + 299, + 228 + ], + "type": "image", + "image_path": "4d3e4622b6feeb935dcf7e03b28adfe3c66a053387ac3280b906d8e7d8b2d403.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 302, + 68, + 419, + 228 + ], + "blocks": [ + { + "bbox": [ + 302, + 68, + 419, + 228 + ], + "lines": [ + { + "bbox": [ + 302, + 68, + 419, + 228 + ], + "spans": [ + { + "bbox": [ + 302, + 68, + 419, + 228 + ], + "type": "image", + "image_path": "5b927843c88fdec8babf1075bb35042def751bb35382b3e22b1d1728b70befa9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 421, + 68, + 534, + 228 + ], + "blocks": [ + { + "bbox": [ + 421, + 68, + 534, + 228 + ], + "lines": [ + { + "bbox": [ + 421, + 68, + 534, + 228 + ], + "spans": [ + { + "bbox": [ + 421, + 68, + 534, + 228 + ], + "type": "image", + "image_path": "1574df897aa2498aa3605236196f6ddcad544b74801731746d15ae60155a38e1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 61, + 293, + 276, + 326 + ], + "blocks": [ + { + "bbox": [ + 47, + 266, + 288, + 289 + ], + "lines": [ + { + "bbox": [ + 47, + 266, + 288, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 288, + 289 + ], + "type": "text", + "content": "Table 5. Performance comparison for classification on ImageNet-1K [36] with respect to the relation modeling in hierarchy tree." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 293, + 276, + 326 + ], + "lines": [ + { + "bbox": [ + 61, + 293, + 276, + 326 + ], + "spans": [ + { + "bbox": [ + 61, + 293, + 276, + 326 + ], + "type": "table", + "html": "
ModelDeterministicProbabilistic
Hi-Mapper(DeiT-S)81.5%82.6%
", + "image_path": "976f5ca0c828a0342658ecbebb66124e7dd800dbbde01a188797e2d04223a644.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 335, + 222, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 222, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 222, + 347 + ], + "type": "text", + "content": "6. Ablation studies and discussion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 356, + 288, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 288, + 380 + ], + "type": "text", + "content": "To further analyze and validate the components of our method, we conduct ablation studies on image classification." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": "Effectiveness of hyperbolic manifolds. We first investigate the effectiveness of hyperbolic manifolds in our approach. As shown in Tab. 4, we report the impact according to image classification. In Euclidean space, the distance function between two vectors is the cosine similarity function. The results demonstrate that applying hierarchical contrastive loss in Euclidean space degrades performance. It indicates that hyperbolic space is more suitable for stabilizing hierarchical structures. Additionally, the application of a KL loss term shows further benefits derived from the semantic seed distribution." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 527, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 287, + 670 + ], + "type": "text", + "content": "Impact of probabilistic modeling. In Tab. 5, we report the performance comparisons between the probabilistic hierarchy tree and the deterministic hierarchy tree. For constructing a hierarchy tree, probabilistic modeling defines every node via MoG of its child node distributions, while the deterministic approach determines each node the mean of its child nodes. The probabilistic hierarchy tree achieves significant improvement in performance compared to the deterministic approach. This result shows that probabilistic modeling is more effective in representing hierarchical structure than deterministic modeling, leading to improvement in recognition." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": "Hierarchy width and depth. As shown in Fig. 5, we analyze the effect of the width " + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": " of the hierarchy tree on ImageNet-1K [36] with Hi-Mapper(DeiT" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 269, + 421, + 350 + ], + "blocks": [ + { + "bbox": [ + 309, + 269, + 421, + 350 + ], + "lines": [ + { + "bbox": [ + 309, + 269, + 421, + 350 + ], + "spans": [ + { + "bbox": [ + 309, + 269, + 421, + 350 + ], + "type": "image", + "image_path": "deabd207a932036fc11de7fcdd8be4de360546c242849cb005fc6c98b8d56d6a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 354, + 523, + 365 + ], + "lines": [ + { + "bbox": [ + 328, + 354, + 523, + 365 + ], + "spans": [ + { + "bbox": [ + 328, + 354, + 523, + 365 + ], + "type": "text", + "content": "Figure 5. Hyper-parameter analysis on ImageNet-1K." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 427, + 269, + 538, + 350 + ], + "blocks": [ + { + "bbox": [ + 427, + 269, + 538, + 350 + ], + "lines": [ + { + "bbox": [ + 427, + 269, + 538, + 350 + ], + "spans": [ + { + "bbox": [ + 427, + 269, + 538, + 350 + ], + "type": "image", + "image_path": "48bdc2c8229b4c81d86e48120cb8144eb0aef1160f3b011e84ff31316161d762.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": "S). These factors control the granularity of visual elements to be decomposed. While a small number of " + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": " degrades the fine-grained recognition capacity, an excess " + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": " hinders the optimization. Meanwhile, a large " + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": " may provide diverse granularity, however, it leads to entangled object-level representations. In all the cases, we report the best performance of " + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "inline_equation", + "content": "82.6\\%" + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "inline_equation", + "content": "N = 32" + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "inline_equation", + "content": "L = 4" + }, + { + "bbox": [ + 304, + 377, + 547, + 461 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 474, + 378, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 378, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 378, + 487 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "text", + "content": "In this paper, we have presented a novel Visual Hierarchy Mapper (Hi-Mapper) that investigates the hierarchical organization of visual scenes. We have achieved the goal by newly defining tree-like structure with probability distribution and learning the hierarchical relations in hyperbolic space. We have incorporated the hierarchical interpretation into the contrastive loss and efficiently identified the visual hierarchy in a data-efficient manner. Through an effective hierarchy decomposition and encoding procedures, the identified hierarchy has been successfully deployed to the global visual representation, enhancing the structured understanding of an entire scene. Hi-Mapper has consistently improved the performance of the existing DNNs when integrated with them, and also has demonstrated the effectiveness on various dense predictions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgement. 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In Proceedings of the European conference on computer vision (ECCV), pages 418-434, 2018. 7" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17374" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/0c9a1639-459a-4ab7-b55c-2fff676c9ecb_content_list.json b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/0c9a1639-459a-4ab7-b55c-2fff676c9ecb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..971b05e256bd936f9b76e90eb4b45a5902bdca37 --- /dev/null +++ b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/0c9a1639-459a-4ab7-b55c-2fff676c9ecb_content_list.json @@ -0,0 +1,1424 @@ +[ + { + "type": "text", + "text": "Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation", + "text_level": 1, + "bbox": [ + 122, + 130, + 849, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haojie Zhang $^{1*}$ Yongyi Su $^{1*}$ Xun Xu $^{2\\dagger}$ Kui Jia $^{3}$ $^{1}$ South China University of Technology \n $^{2}$ Institute for Infocomm Research, A\\*STAR \nhool of Data Science, The Chinese University of Hong Kong, Shenz", + "bbox": [ + 218, + 202, + 750, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of large language models has inspired the computer vision community to explore image segmentation foundation model that is able to zero/few-shot generalize through prompt engineering. Segment-Anything (SAM), among others, is the state-of-the-art image segmentation foundation model demonstrating strong zero/few-shot generalization. Despite the success, recent studies reveal the weakness of SAM under strong distribution shift. In particular, SAM performs awkwardly on corrupted natural images, camouflaged images, medical images, etc. Motivated by the observations, we aim to develop a self-training based strategy to adapt SAM to target distribution. Given the unique challenges of large source dataset, high computation cost and incorrect pseudo label, we propose a weakly supervised self-training architecture with anchor regularization and low-rank finetuning to improve the robustness and computation efficiency of adaptation. We validate the effectiveness on 5 types of downstream segmentation tasks including natural clean/corrupted images, medical images, camouflaged images and robotic images. Our proposed method is task-agnostic in nature and outperforms pre-trained SAM and state-of-the-art domain adaptation methods on almost all downstream tasks with the same testing prompt inputs.", + "bbox": [ + 75, + 340, + 473, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 705, + 209, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of large language models is partially attributed to the strong capability of zero-shot generalization. This has called for numerous attention into developing foundation model for computer vision tasks where one of the key concern also lies in the generalization ability [26, 44, 48]. In particular, as a promptable image segmentation foundation model with strong zero-shot generalization, the Segment-Anything model (SAM) [27] was developed by training on billions of annotated masks. Despite the overwhelming size", + "bbox": [ + 75, + 729, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c158a82f0d98d0253c02127379fa4b2711ef95ed0c559ab269b37964643a73b4.jpg", + "image_caption": [ + "Figure 1. Segment Anything Model was pre-trained on a large-scale dataset but exhibits awkward performance on diverse downstream segmentation tasks. We adapt SAM through weak supervision to enhance its generalization capabilities." + ], + "image_footnote": [], + "bbox": [ + 501, + 310, + 897, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of dataset used for training, SAM was found to behave awkwardly on certain out-of-distribution downstream tasks, including camouflaged segmentation, medical segmentation, adversarial attacks, visual corruptions, etc. [5, 21]. This is likely caused by the distribution shift between the training data, i.e. the SA-1B dataset [27], and the challenging testing datasets. These observations motivate us to explore tangible solutions to make SAM more robust against real-world and more diverse downstream tasks.", + "bbox": [ + 496, + 578, + 893, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditional paradigm towards improving model robustness and generalization often involves costly re-training. Methods are frequently customized to combat specific domain shifts. For example, domain randomization was developed to improve generalization across real testing domains [6], while adversarial training is commonly used to enhance robustness against attacks [58]. Applying these techniques to large foundation models is nonetheless impractical due to the enormous computing resources required for training the model on the web-scale training data. Therefore, instead of re-training the model, we opt for a more computation friendly paradigm by adapting or finetuning a", + "bbox": [ + 496, + 719, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution.", + "bbox": [ + 99, + 875, + 214, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Correspondence to Xun Xu: alex.xun.xu@gmail.com.", + "bbox": [ + 99, + 887, + 395, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23385", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pre-trained foundation model to downstream dataset.", + "bbox": [ + 76, + 90, + 426, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We specify three major challenges when adapting pretrained foundation model to a new data distribution. First, traditional unsupervised domain adaptation [15] paradigm requires access to both source and target datasets which may not be feasible due to privacy issue and computation cost [34]. Second, updating all model weights for adaptation is often superior in performance, however, is constrained by the prohibitive memory cost due to the large model size [20]. Finally, unsupervised adaptation could be still very challenging due to the absence of label information on the target domain [60, 72, 75].", + "bbox": [ + 75, + 109, + 468, + 275 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the above challenges, we propose a self-training based adaptation approach to synergize the exploitation of weak supervision and unlabeled data on target domain. Specifically, we first alleviate the dependence on source domain data by adopting a self-training based source-free domain adaptation strategy. The self-training approach first makes segmentation predictions, a.k.a. pseudo labels, on the target domain data. The pseudo labels are used for supervising the update of segmentation model. As self-training is fragile due to incorrect pseudo labels, a.k.a. confirmation bias [2], we introduce a frozen source model as the anchor network to regularize the update of segmentation model. To further mitigate the high computation cost of updating the full model weights, we apply a low-rank weight decomposition to encoder weights and the backpropagation flows through the low-rank shortcut only. Finally, to further improve the effectiveness of source-free domain adaptation, weak supervisions, e.g. sparse pointwise annotation, on the target domain are introduced to provide stronger cues for domain adaptation. We reveal that the weak supervisions are naturally compatible with the prompt encoder within SAM. With the weak supervisions as prompt, we are endowed with more localized and less ambiguous pseudo predictions for self-training. The adapted model has demonstrated much stronger generalization capability on multiple downstream tasks.", + "bbox": [ + 75, + 279, + 472, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize the contributions of this work as follows.", + "bbox": [ + 96, + 676, + 467, + 690 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We are motivated by the generalization issue of segment-anything (SAM) model to diverse downstream segmentation tasks and propose a task-agnostic solution to adapt SAM through self-training with no access to source dataset.", + "- We exploit weak supervisions, including bounding box, point-wise annotation and coarse segmentation masks, to improve the effectiveness of adaptation. The weak supervision are fully compatible with the prompt encoder of SAM.", + "- Extensive experiments on 5 types of downstream instance segmentation tasks demonstrate the effectiveness of the proposed weakly supervised adaptation approach." + ], + "bbox": [ + 76, + 702, + 467, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Segmentation Foundation Model: The success of deep learning is attributed to the increasing size and neural networks and huge amount of training data. Recent successful computer vision models, e.g. image segmentation and object detection, follow a practice of finetuning from encoder network pre-trained on large image dataset, e.g. ImageNet [10]. Despite achieving impressive results on standard benchmark datasets, e.g. Psacal VOC [13] and COCO [37], the zero-shot and few-shot generalization ability is often limited. Inspired by the revolutionizing language/vision-language foundation model pre-trained on web-scale datasets [4, 48, 74], a new opportunity awaits for developing a generalizable vision foundation model. This motivates the emergence of vision foundation model pretrained on huge dataset. SAM [27] and DINO v2 [44], to name a few. Among these foundation models, SAM stands out for its ability to enable zero-shot segmentation using prompt engineering. Therefore, we pay particular attention to SAM in this work. Since the inception of SAM, numerous attempts are made to validate the robustness of SAM under more challenging scenarios, such as medical images [42] [71], camouflaged objects [59], glass (transparent objects and mirrors) [18] and pose estimation [36]. Despite these early attempts to discover the weakness, there are very few matured solutions [5] to improve the generalization of SAM to challenging downstream tasks. In this work, we aim to fill this gap by proposing principled solutions to enhance the robustness of SAM against downstream tasks subject to significant distribution shift.", + "bbox": [ + 496, + 111, + 890, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Source-Free Domain Adaptation: Unsupervised Domain Adaptation (UDA)[15, 24, 41, 61, 73] has emerged as a means to address the domain shift between source training data and target testing data. This enables models to be trained on cost-effective and easily annotated data, facilitating the transfer to more valuable but challenging-to-label datasets. However, UDA methods face limitations when source domain data is inaccessible due to privacy concerns or storage constraints. In response to this, Source-Free Domain Adaptation (SFDA)[28, 33, 34, 39, 65, 68] has been proposed to reduce the reliance on source data in domain adaptation (DA) methods. SHOT [34] represents an early effort to alleviate domain shift without access to source data, achieved through self-training on unlabeled target data. Numerous prior works [1, 7, 11, 26, 35, 47, 50] have explored the effectiveness of a teacher-student like self-training architecture in domain shift mitigation. The similar self-training framework [22] simultaneously trains on multiple sets of augmented data, utilizing teacher-student cycle consistency for mutual learning of the two networks. Other methods generate source-like samples [30, 40, 46], construct intermediate domains [65, 69], or perturb target domains [25, 32, 66, 70] to enhance model generalization.", + "bbox": [ + 496, + 553, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23386", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/297e2a5c5aaea891463d596993ab2ebf3d2edf76f802d7746e26ea8359de1758.jpg", + "image_caption": [ + "Figure 2. The proposed self-training architecture with anchor network regularization and contrastive loss regularization. Red arrows indicates the backpropagation flow." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 843, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent approaches [46, 64] leverage contrast loss between target samples and source domain prototypes. Recent attempts to source-free domain adaptation for image segmentation aims to minimize feature discrepancy between source and target domains [3, 29, 40]. In this work, we aim to adapt SAM to downstream tasks without accessing to the source domain data to avoid the high computation overhead and potential privacy issues for foundation models to be released in the future.", + "bbox": [ + 75, + 324, + 470, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Weakly Supervised Domain Adaptive Segmentation:", + "text_level": 1, + "bbox": [ + 75, + 460, + 468, + 476 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised domain adaptation often follows a self-training paradigm [34], which is limited by the quality of pseudo labels. Instead of relying on the pseudo predictions, weakly supervised domain adaptive semantic segmentation (WDASS) exploits limited weak supervisions in the form of bounding box, points or coarse segmentation masks [8, 9, 45, 63]. Among these works, [45] employs both image and point labels, suggesting an adversarial alignment of features at the pixel level to address WDASS. In contrast, [63] relies on bounding boxes as weak labels and employs adversarial learning to achieve domain-invariant features. Additionally, [9] utilizes self-training and a boundary loss to enhance performance in WDASS with coarse labels. More recently, [8] utilizes weak label for aligning the source-target features and outperforms previous methods to achieve competitive performance compared to supervised learning. We observe that the common weak supervisions are inherently compatible with the SAM model as prompt input. Therefore, we propose to adapt SAM with weak supervisions in a seamless way.", + "bbox": [ + 73, + 477, + 470, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 795, + 210, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first provide an overview of segment-anything model. Then, we introduce the self-training based adaptation framework. We elaborate how weak supervision could help establish correspondence between pseudo predictions for effective self-training. Lastly, we introduce the low memory footprint way of updating model weights.", + "bbox": [ + 75, + 814, + 468, + 905 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview of Segment Anything Model", + "text_level": 1, + "bbox": [ + 498, + 324, + 828, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The segment-anything model consists of three major components, the encoder network $z = f(x; \\Theta)$ , prompt encoder $e = g(p; \\Omega)$ and mask decoder $h(z, e; \\Phi)$ . The image encoder is pre-trained using masked autoencoder (MAE) [19]. The whole SAM model is further fine-tuned on the web-scale labeled training set, SA-1B [27], with 1.1B labeled masks. A combination of focal loss and dice loss are used for training SAM. During inference, the testing image $x$ is first encoded by the image encoder $z = f(x; \\Theta)$ . Given encoded prompts $e$ , a light-weight mask decoder makes three levels of segmentation predictions. In this work, we are motivated by the challenge of deploying SAM on many downstream tasks and propose to adapt SAM to downstream segmentation tasks with weak supervision without requiring access to source domain training data.", + "bbox": [ + 496, + 339, + 890, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Source-Free Adaptation as Self-Training", + "text_level": 1, + "bbox": [ + 498, + 566, + 846, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Provided an unlabeled target domain dataset $\\mathcal{D}_T = \\{x_i\\}$ and the pre-trained encoder network $f(x;\\Theta)$ , we adopt a teacher-student architecture for self-training. As illustrated in Fig. 2, we maintain three encoder networks, namely the anchor network $f(x;\\Theta^a)$ , the student network $f(x;\\Theta^s)$ and the teacher network $f(x;\\Theta^t)$ , where the student and teacher networks share the weights $\\Theta^s = \\Theta^t$ . For each sample $x_i$ , we apply one random weak data augmentation $\\mathcal{A}_w(x_i)$ as the input to anchor and teacher networks, and one random strong data augmentation $\\mathcal{A}_s(x_i)$ as the input to student network. Through the three encoder networks, three feature maps are obtained respectively, as $\\mathcal{F}^a = f(\\mathcal{A}_w(x_i),\\Theta^a)$ , $\\mathcal{F}^s = f(\\mathcal{A}_s(x_i),\\Theta^s)$ and $\\mathcal{F}^t = f(\\mathcal{A}_w(x_i),\\Theta^t)$ , where $\\mathcal{F} \\in \\mathbb{R}^{D \\times H \\times W}$ and $D$ refers to feature dimension. In the decoder network, given a number $N_p$ of prompts, e.g. bounding boxes, points or coarse segmentation masks, a set of foreground masks for the instance segmentation results would be deduced, $\\mathcal{Y}^a = \\{y_j^a\\}_{j=1\\dots N_p}$ , $\\mathcal{Y}^s = \\{y_j^s\\}_{j=1\\dots N_p}$ , $\\mathcal{Y}^t = \\{y_j^t\\}_{j=1\\dots N_p}$ , where each mask is then normalized between 0 and 1 by sigmoid function respectively, i.e. $m_j = \\text{Sigmoid}(y_j)$ , $m_j \\in [0,1]^{H \\times W}$ . We", + "bbox": [ + 496, + 583, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23387", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dc88d42718fa8e1fb35f5f3b8e8e07c6f1b472f838e74e54a698e4af501abea2.jpg", + "image_caption": [ + "Figure 3. Illustration of contrastive loss between two views." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 472, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "further denote a binarized segmentation mask with a threshold of 0.5 as $\\hat{m}_j = \\mathbb{1}(m_j > 0.5),\\hat{m}_j\\in \\{0,1\\}^{H\\times W}$ . Based on these notations, we elaborate three sets of adaptation objectives for self-training purpose.", + "bbox": [ + 75, + 231, + 467, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Teacher-Student Self-Training Loss: We first introduce the Self-Training loss to update student/teacher network. Self-Training is widely used in semi-supervised learning [52] and recently is demonstrated to be very effective for source-free domain adaptation [35]. In this work, we continue the idea of self-training in classification task and perform focal loss [38] and dice loss [43] for the supervision of student's outputs with binarized teacher's predictions as follows, where $\\gamma$ controls the focus on hard training pixels and $\\epsilon$ is a small value to avoid dividing by zero.", + "bbox": [ + 75, + 292, + 467, + 443 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {s t} ^ {f o c a l} = - \\sum_ {j = 1 \\dots N _ {p}} \\frac {1}{H W} \\sum_ {h, w} \\mathbb {1} \\left(\\hat {m} _ {j h w} ^ {t} = 1\\right) \\cdot \\left(1 - m _ {j h w} ^ {s}\\right) ^ {\\gamma} \\log \\left(m _ {j h w} ^ {s}\\right) \\tag {1} \\\\ + \\mathbb {1} (\\hat {m} _ {j h w} ^ {t} = 0) \\cdot m _ {j h w} ^ {s} ^ {\\gamma} \\log (1 - m _ {j h w} ^ {s}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 443, + 467, + 487 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s t} ^ {d i c e} = \\sum_ {j = 1 \\dots N _ {p}} 1 - \\frac {2 \\sum_ {h , w} m _ {j h w} ^ {s} \\cdot \\hat {m} _ {j h w} ^ {t} + \\epsilon}{\\sum_ {h , w} m _ {j h w} ^ {s} + \\sum_ {h , w} \\hat {m} _ {j h w} ^ {t} + \\epsilon}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 497, + 467, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Anchored Loss for Robust Regularization: Training the networks with self-training loss alone is vulnerable to the accumulation of incorrect pseudo labels predicted by teacher network, a.k.a. confirmation bias [2]. Observations are made that the performance will drop after long iterations of self-training alone [56]. Existing source-free domain adaptation approaches often adopt additional constraints to prevent the negative impact of self-training, e.g. uniform distribution over predictions [35]. Without making such explicit assumptions, we propose to introduce the regularization by an anchor loss which minimizes the dice loss between an anchor network, which has frozen source model weights, and student and teacher networks respectively in Eq. 3. The frozen anchor network serves as the knowledge inherited from source domain and too much deviation between the source model and self-training updated model is discouraged to prevent the model from collapsing.", + "bbox": [ + 75, + 549, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a n c h o r}} = \\lambda_ {\\text {s t u}} ^ {\\text {d i c e}} \\mathcal {L} ^ {\\text {d i c e}} \\left(m ^ {s}, \\hat {m} ^ {a}\\right) + \\lambda_ {\\text {t e a}} ^ {\\text {d i c e}} \\mathcal {L} ^ {\\text {d i c e}} \\left(m ^ {t}, \\hat {m} ^ {a}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 821, + 467, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Contrastive Loss for Encoder Output Regularization: The above two training objectives are performed in the output space of the decoder. As we empirically revealed in the", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "experiment section, updating encoder network is the most effective way to adapt SAM, it is necessary to apply regularization directly to the feature map as output from the encoder network. Specifically, as illustrated in Fig. 3, we first crop out each instance's feature $I_{j}$ from the feature map based on its prediction mask in anchor and teacher branches.", + "bbox": [ + 496, + 90, + 890, + 191 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {j} = \\frac {\\sum_ {h , w} \\bar {\\mathcal {F}} _ {h w} \\cdot \\hat {m} _ {j h w}}{\\sum_ {h , w} \\hat {m} _ {j h w}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 185, + 890, + 223 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{\\mathcal{F}}$ is the L2 normalized feature map, i.e. $\\overline{\\mathcal{F}}_{hw} = \\frac{\\mathcal{F}_{hw}}{|\\mathcal{F}_{hw}|}$ . We further define the instance features, which are cropped out by the masks used the same prompt in two branches, as positive pairs, and the instances used different prompts as negative pairs to construct the contrast loss. The final contrastive loss is given as below, where $\\tau$ is the temperature scaling.", + "bbox": [ + 496, + 224, + 890, + 332 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n t r a s t}} = - \\log \\frac {\\sum_ {j} \\exp \\left(I _ {j} ^ {a} \\cdot I _ {j} ^ {t} / \\tau\\right)}{\\sum_ {j} \\sum_ {j ^ {\\prime} \\neq j} \\exp \\left(I _ {j} ^ {a} \\cdot I _ {j ^ {\\prime}} ^ {t} / \\tau\\right)} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 339, + 890, + 377 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Total Loss: We combine the above three loss functions as the final source-free domain adaptation loss.", + "bbox": [ + 496, + 382, + 890, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {s t} ^ {f o c a l} \\mathcal {L} _ {s t} ^ {f o c a l} + \\mathcal {L} _ {s t} ^ {d i c e} + \\mathcal {L} _ {\\text {a n c h o r}} + \\mathcal {L} _ {\\text {c o n t r a s t}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 419, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Prompt Generation for Self-Training", + "text_level": 1, + "bbox": [ + 496, + 446, + 818, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The SAM segmentation requires prompt inputs to disambiguate the granularity of segmentation. The prompt engineering can be implemented in both fully automated way and by human interaction.", + "bbox": [ + 496, + 463, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fully Automated Prompt for Self-Training: We first densely sample grid points with a spatial distance of 16 pixels as point prompt input. Initial stage segmentation masks $\\{\\hat{m}_j\\}_{j = 1\\dots N_{init}}$ are generated by the anchor network with the grid point prompts. We follow the fully automated segmentation introduced by SAM [27] to prune out masks with low IoU score and low stability score, followed by NMS suppression. To enable self-training and regularization between different branches, we further generate a fixed set of prompt $\\{e_j\\}_{j = 1\\dots N_p}$ from $\\{\\hat{m}_j\\}_{j = 1\\dots N_{init}}$ as input to all three branches. As such, the segmentation outputs $\\mathcal{Y}^a$ , $\\mathcal{Y}^s$ and $\\mathcal{Y}^t$ are of the same length with exact one-to-one correspondence.", + "bbox": [ + 496, + 523, + 890, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Weak Supervision as Prompt: Despite automatic segmentation can be enabled by sampling a grid of point prompts over the image and filtering out low quality and duplicated masks, the quality of segmentation is relatively poor and may contain many false positive predictions, making self-training less effective. Therefore, following prior weakly supervised domain adaptation works [9], we propose to use three types of weak supervisions, including bounding box, sparse point annotation and coarse segmentation mask. Fortunately, in the context of SAM, these weak supervisions perfect match with the prompt inputs which allow seamless integration of weak supervision for adapting SAM.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23388", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Low-Rank Weights Update", + "text_level": 1, + "bbox": [ + 76, + 90, + 321, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The enormous size of backbone network prohibits updating all model weights with large batchsize. However, many existing studies suggest the update of encoder network weights is an effective way of adapting pre-trained models [35, 54]. To enable updating the backbone network with larger batchsize, we opt for a computation friendly low-rank updating approach [20]. For each weight in the encoder network $\\theta \\in \\mathbb{R}^{d_i \\times d_o}$ , we use a low-rank approximation $\\omega = AB$ where $A \\in \\mathbb{R}^{d_i \\times r}$ and $A \\in \\mathbb{R}^{r \\times d_o}$ with $r$ indicating the rank. We can achieve a compression rate of $r(d_i + d_o) / d_i \\cdot d_o$ . Only $A$ and $B$ are updated via backpropagation during adaptation to reduce memory footprint. At inference stage, the weight is reconstructed by combining the low rank reconstruction and original weight, $\\theta = \\theta + AB$ .", + "bbox": [ + 75, + 107, + 472, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 333, + 202, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first introduce the experiment settings and downstream tasks for adapting SAM model. We provide detailed comparisons to state-of-the-art methods and qualitative results. Finally, we analyze the effectiveness of individual components and specific designs for the network.", + "bbox": [ + 75, + 359, + 468, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 439, + 179, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The source domain training set, SA-1B, was mainly constructed by collecting from natural environments. In this work, we identified five types of downstream segmentation tasks, some of which feature a drastic distribution shift from SA-1B, for evaluation, covering natural clean images, natural corrupted images, medical images, camouflaged images and robotic images. We present the datasets evaluated for each type of downstream task in Tab. 1.", + "bbox": [ + 75, + 455, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasplit: We divide each downstream dataset into non-overlapping training and testing sets following the ratio established by [8]. The adaptation step is implemented on the training set. After the model is adapted, we evaluate the model on the held-out testing set. For adaptation to the Camouflaged Objects, following the training protocol in [5], we use the dataset COD10K (the training set of camouflaged images) for training, and use the test set of CAMO, COD10K and the entire CHAMELEON dataset for performance evaluation.", + "bbox": [ + 75, + 577, + 468, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Experiment Details", + "text_level": 1, + "bbox": [ + 76, + 732, + 261, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Segment-Anything Model: We adopt ViT-B [12] as the encoder network due to memory constraint. The standard prompt encoder and mask decoder are adopted.", + "bbox": [ + 75, + 750, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prompt Generation: We first provide details for generating prompt at both training stages. All training prompts are calculated from ground-truth segmentation mask, simulating the human interactions as weak supervision. Specifically, we extract the minimal bounding box that covers the whole instance segmentation mask as box prompt. The point prompt is created as randomly selecting 5 positive", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "points within ground-truth instance segmentation mask and 5 negative points outside ground-truth mask. The coarse segmentation mask is simulated by fitting a polygon to the ground-truth mask. We choose the number of vertices as $P / 20$ with $P$ indicating the perimeter of mask. The minimal number of vertices is 3. We use the same way to generate testing prompt on the testing data. This practice guarantees fair evaluation of SAM model which requires prompt input for segmentation.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics: We report the mIoU as evaluation metrics. For each input prompt, the IoU is calculated between the ground-truth segmentation mask and predicted mask. The mIoU averages over the IoU of all instances.", + "bbox": [ + 496, + 229, + 890, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Competing Methods: We evaluate multiple source-free domain adaptation approaches and one state-of-the-art weakly supervised domain adaptive segmentation approach. In specific, direct testing the pre-trained model (Direct) with fixed prompt inputs is prone to the distribution shift and may not perform well on target datasets with significant shift. TENT [62] is a vanilla test-time adaptation method which optimizes an entropy loss for adapting to target domain. SHOT [35] employs pseudo label and applies uniform distribution assumption for source-free domain adaptation. Soft Teacher [67] was originally developed for semi-supervised image segmentation. We adapt Soft Teacher for domain adaptation by keeping the self-training component. TRIBE [55] proposed a strong baseline for generic test-time adaptation on continual and class imbalanced domain shifts. We adapt TRIBE for domain adaptive segmentation by replacing the training losses. DePT [16] inserts visual prompts into a visual Transformer and adjusts these source-initialized prompts solely during the adaptation process without accessing the source data. WDASS [8] developed a weakly supervised domain adaptive segmentation method. We also evaluate the upperbound of adapting SAM by fine-tuning with ground-truth segmentation masks, which is dubbed as Supervised. Finally, we evaluate our weakly supervised domain adaptation method as Ours. All the competing methods use the same backbone, i.e. the ViT-B from SAM.", + "bbox": [ + 496, + 292, + 892, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hyperparameters: We finetune LoRA module of the ViTB image encoder by Adam optimizer for all experiments. We set the batchsize to 4, distributed over four RTX3090 GPUs, and the learning rate to 0.0001 with a weight decay of 0.0001. For Self-Training loss, we set the hyperparameters $\\gamma$ and $\\epsilon$ of $\\mathcal{L}_{st}^{focal}$ and $\\mathcal{L}_{st}^{dice}$ to 2 and 1 respectively. $\\lambda_{st}^{focal}$ is set to 20, which is the coefficients of $\\mathcal{L}_{st}^{focal}$ . For Anchor loss, the coefficients of two dice losses are denoted as $\\lambda_{stu}^{dice}$ and $\\lambda_{tea}^{dice}$ , both of which equal 0.5. For Contrast loss, we set the temperature $\\tau$ to 0.3. We have set the low rank of the LoRA module for the image encoder to 4. We apply strong and weak data augmentations for self-training and choices for augmentation follows [53, 67].", + "bbox": [ + 496, + 702, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23389", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b8f706b43794234a7a5715f0f10f466fa7c51ab07ad2cf63cb118ceecdda2dbe.jpg", + "table_caption": [ + "Table 1. Dataset and datasplit used in this work." + ], + "table_footnote": [], + "table_body": "
Natural ImagesCorrupted ImagesMedical ImagesCamouflaged ObjectsRobotic Images
COCO [37]Pascal VOC [13]COCO-Ckvasir-SEG [23]ISIC [17]CHAMELEON [51]CAMO [31]COD10K [14]OCID [57]OSD [49]
# Training4246249742468349004040197256
# Testing70641670616637974250202632855
", + "bbox": [ + 138, + 103, + 828, + 157 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f00a89ac1e16d2136e3d1e971d3f649330de0709d6da3db4b1f27e816e4ad04a.jpg", + "table_caption": [ + "Table 2. Adaptation results on COCO-C dataset using bounding box prompt." + ], + "table_footnote": [], + "table_body": "
MethodBritContrDefocElastFogFrostGaussGlassImpulJpegMotnPixelShotSnowZoomAvg
Direct72.8357.3464.4769.3672.3970.5067.2064.4367.6568.2362.7268.6067.4469.0258.8066.73
TENT76.0261.5167.4870.8874.8973.8869.0167.1069.2870.2565.4570.8169.9672.3762.5969.43
SHOT73.8459.0965.9169.5773.9872.5168.3066.0968.6169.4564.5670.4868.7771.0360.1768.16
Soft Teacher73.9062.1265.4171.3272.1673.2768.8467.4968.7370.1866.8869.7970.0873.3364.8869.23
TRIBE76.4060.8666.1972.7275.0875.1470.3466.6670.8372.4265.9470.2470.6674.2264.5670.15
DePT69.1557.2659.0866.8058.7366.7566.7862.7465.6566.3961.6666.6567.5766.6258.2164.42
WDASS76.2160.5767.0772.3475.9774.6369.8467.8869.9271.3666.2571.9970.3272.2563.6170.01
OURS78.5061.0566.9973.9377.0976.1072.0268.2171.2972.7766.3370.9070.2875.0765.3371.05
Supervised78.8674.8172.0474.3278.0177.1473.4372.1274.0875.3071.3975.1574.2576.3468.0474.35
", + "bbox": [ + 138, + 175, + 826, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Quantitative Evaluations", + "text_level": 1, + "bbox": [ + 76, + 304, + 305, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we report the quantitative evaluations on the 5 types of target datasets. For each dataset, we also report the adaptation results with weak supervision in the form of bounding box (box), sparse points (point) and coarse segmentation mask (poly).", + "bbox": [ + 75, + 321, + 470, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adaptation to Corrupted Images: Visual corruptions often occur due to sensor fault, bad weather conditions, etc. As seen from Tab. 2, without any adaptation, Direct testing is significantly worse than the upperbound. With weakly supervisions, all methods could improve over direct testing, in particular, our proposed method outperforms all competing adaptation methods on 10 out of 15 types of corruptions.", + "bbox": [ + 75, + 398, + 468, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adaptation to Natural Images: We then present the results of adapting SAM to natural images in Tab. 3. For each type of weak supervision, we use the same type of prompt on the testing set. Despite the distribution gap between SA-1B and the target natural images, we observe significant performance gap between Supervised upperbound and Direct baseline, e.g. with box level supervision, there is $5 - 10\\%$ gap in IoU. When weak supervision is provided, both state-of-the-art generic source-free domain adaptation methods and weakly supervised domain adaptive segmentation method improve the generalization on all three types of weak supervisions. Finally, our proposed weakly supervised method achieves a remarkable improvement over all competing methods. The results with box weak supervision is even approaching the fully supervised upperbound.", + "bbox": [ + 75, + 521, + 468, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adaptation to Medical Images: Segmentation for medical images is a major application of foundation models. Our empirical observations in Tab. 4 on two medical segmentation datasets suggest that direct applying pre-trained SAM is suboptimal. With weakly supervised adaptation, the segmentation accuracy is greatly improved. We observe the improvement to be particularly significant with point and box which are relatively easy to obtain due to the low labeling cost.", + "bbox": [ + 75, + 748, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adaptation to Camouflaged Objects: We further eval", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2ac025818c3dd6d6eb363355eff23f077f220cf57f31b98e7fbb92e0c074010e.jpg", + "table_caption": [ + "Table 3. Adaptation results on natural clean image datasets." + ], + "table_footnote": [], + "table_body": "
MethodCOCO 2017Pascal VOC
boxpointpolyboxpointpoly
Direct74.2955.0665.6469.2169.2160.79
TENT78.2152.9971.5180.2474.9765.03
SHOT75.1858.4669.2679.8074.2663.38
Soft Teacher75.9443.3668.2772.9356.0962.20
TRIBE77.5649.5670.9978.8769.2165.39
DePT71.0037.3563.2774.0942.9959.94
WDASS77.2960.5570.1980.1276.1566.98
OURS80.1262.0972.3380.2774.1566.72
Supervised81.5069.7773.3981.2376.9871.32
", + "bbox": [ + 521, + 319, + 867, + 469 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eab3f1df613c93ac82f38b0804fec3cfa35d182b9413499afb98d070b0764706.jpg", + "table_caption": [ + "Table 4. Adaptation results on medical image segmentation datasets." + ], + "table_footnote": [], + "table_body": "
Methodkvasir-SEGISIC
boxpointpolyboxpointpoly
Direct81.5962.3054.0366.7453.4262.82
TENT82.4761.8462.9771.7653.4667.12
SHOT82.3063.7661.3471.9955.9966.86
Soft Teacher84.1273.5358.1575.7454.9572.29
TRIBE85.0573.0364.6172.6150.3667.99
DePT81.9152.0661.5578.4346.7972.75
WDASS84.0163.7864.7874.2355.6367.84
OURS85.4775.2367.4080.0162.1275.36
Supervised85.8977.5481.6481.6279.8180.26
", + "bbox": [ + 519, + 492, + 867, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "uate on adapting SAM to camouflaged object detection. We evaluate on three camouflaged object detection datasets with results reported in Tab. 5. Preliminary studies revealed that SAM is particularly vulnerable to camouflaged objects [59] due to the low contrast between background and foreground. We make similar observations here that even with the help of prompt inputs at testing stage, Direct inference suffers a lot, achieving less than $66\\%$ mIoU. When weakly labeled data are used for adaptation, we observe very significant improvements, with point prompt only we improved by a staggering $35\\%$ in mIoU on the CHAMELEON dataset. Our proposed method is also consistently better than all competing methods on all types of weak supervisions.", + "bbox": [ + 496, + 656, + 890, + 867 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adaptation to Robotic Images: Finally, we evaluate adapting SAM to image collected from robotic environ", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23390", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/de005986e56c8c83c3154f897d12707b3fb1ae4c060b3d46c513d05c9a3db2e1.jpg", + "table_caption": [ + "Table 5. Adaptation results on camouflaged object datasets." + ], + "table_footnote": [], + "table_body": "
MethodCHAMELEONCAMOCOD10K
boxpointpolyboxpointpolyboxpointpoly
Direct51.3239.3745.7862.7257.4350.8566.3263.6140.04
TENT65.4854.5353.0671.2459.5960.2969.3661.9443.36
SHOT68.6062.4754.3671.6162.7858.7269.0965.2542.38
Soft Teacher65.9244.1746.7262.3048.6451.2666.3250.0432.27
TRIBE71.0052.8054.9966.0061.9760.5467.8463.6242.75
DePT54.4833.4642.4755.4433.0748.6359.3234.0635.51
WDASS71.9162.4056.8071.2563.3962.2971.4265.6143.93
OURS75.9474.0066.8373.4265.5562.9071.9370.5545.87
Supervised78.0585.8668.3879.1777.0167.1278.0678.4464.90
", + "bbox": [ + 98, + 103, + 444, + 213 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ments where segmenting out the spatial extent of individual objects is essential for interactions. As seen from the results in Tab. 6, adapting SAM to robotic images with weak supervision further increase the segmentation accuracy. The improvement is more noticeable with point and polygon weak supervisions.", + "bbox": [ + 75, + 220, + 468, + 310 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fbfb7f69641b110efb8da3e96e2f4d0e08bb8a141854b191fa2e53bf2b8b9787.jpg", + "table_caption": [ + "Table 6. Adaptation results on robotic image datasets." + ], + "table_footnote": [], + "table_body": "
MethodOCIDOSD
boxpointpolyboxpointpoly
Direct86.3571.4172.8187.6278.8680.77
TENT87.7766.6177.5388.1080.5387.85
SHOT88.0674.3976.2588.0980.5287.86
Soft Teacher84.9868.4673.7590.4180.4987.00
TRIBE86.7767.8676.5090.4280.5487.84
DePT82.0056.5270.9281.8469.0682.50
WDASS87.6877.1376.7088.0780.5288.19
OURS88.0980.1477.4192.1180.5189.72
Supervised91.2489.2279.2392.1482.4190.83
", + "bbox": [ + 98, + 327, + 444, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Qualitative Evaluations", + "text_level": 1, + "bbox": [ + 76, + 492, + 294, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present the qualitative comparisons of segmentation results for selected examples in Fig. 4. We make the following observations from the results. Evaluating pre-trained SAM (SAM) on COCO with both box and point prompt exhibits very fine-grained segmentation results. However, the model is overly sensitive to the high contrast regions, e.g. the hair for the girl and the toppings of pizza are missing from the segmentation mask. With the proposed weakly supervised adaptation approach, our method is able to generate more smoothed segmentation mask and the mask better reflects the semantic boundary. Similar observations are made from the medical image segmentation dataset. Without adapting the SAM model, segmentation results are either too conservative with low recall or expanding beyond the semantic boundary. With our weakly supervised adaptation, SAM is able to produce high fidelity results. We further present results on camouflaged segmentation task (CAMO). Without adaptation, SAM fails to segment out the spider's belly and confuses the snow background with the harp seal in the foreground. Our weakly adapted SAM successfully segments out the spider's belly and produces high quality mask for the harp seal. Finally, two examples from OCID dataset suggest that the pre-trained SAM tends to over-segment, e.g. missing the open whole for the tissue box, or confusing adjacent objects, e.g. merging the pen with the folder label. With weakly supervised adaptation SAM picks up the", + "bbox": [ + 75, + 508, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/759311c5721657b0b1deecde9405874c95f88785686d42bb1ecf398b07a3e251.jpg", + "table_caption": [ + "Table 7. Ablation studies of the proposed weakly supervised adaptation method on COCO dataset." + ], + "table_footnote": [], + "table_body": "
Weak Sup.Self-Train.AnchorCont. Lossboxpointpoly
original SAM74.2956.3665.42
✓✓58.8832.5155.03
✓✓✓79.6557.2570.49
✓✓✓62.9522.8756.91
✓✓✓✓80.1262.0972.33
✓✓✓76.1847.6370.44
", + "bbox": [ + 521, + 116, + 867, + 202 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7cae0d6076af688126d2b1bddd3190d36bf796bbbc8296cacc0230e669fcc97d.jpg", + "table_caption": [ + "Table 8. Adaptation results on cross-prompt testing scenarios." + ], + "table_footnote": [], + "table_body": "
Tr. Weak. Sup.boxpointpolygon
Te. Promptboxpointpolyboxpointpolyboxpointpoly
Direct74.2954.7666.7574.2954.6466.7574.2954.7665.64
TENT78.2154.8368.8252.9952.9968.5877.0853.9071.51
WDASS77.2958.7868.9474.6960.5569.1575.2755.2770.19
OURS80.1252.2872.0776.4962.0971.0278.5752.8872.33
", + "bbox": [ + 521, + 220, + 867, + 286 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "semantic meaning and produces segmentation results that better aligns with human intention.", + "bbox": [ + 498, + 292, + 890, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 330, + 651, + 345 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we analyze the effectiveness of individual components on COCO dataset. As presented in Tab. 7, when self-training is applied alone, we observe a significant performance drop (74.29% → 58.88% with box weak supervision), suggesting the severity of confirmation bias. This issue can be well remedied when the anchor loss regularization is applied. Self-training with anchored regularization already improves the performance of SAM after adaptation. Finally, the contrastive loss directly regularizes the encoder network's output and contributes with additional improvement of segmentation accuracy. We also investigate the final self-training architecture without any weak supervision, i.e. the pseudo label masks are generated with grid point prompt. The results after adaptation is slightly worse than with weak supervision but consistently better than without adaptation on both box and coarse mask testing prompts. Nevertheless, the results with point prompt performs even worse than without adaptation, suggesting the necessity of weakly supervised adaptation.", + "bbox": [ + 496, + 347, + 890, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Additional Analysis", + "text_level": 1, + "bbox": [ + 498, + 643, + 687, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Generalization to Cross-Prompt Testing: We further investigate the effectiveness of adaptation by testing with all three types of prompts. Specifically, we compare with the best (WDASS) and second best (TENT) methods with results presented in Tab. 8. Apart from using point as testing prompt, our methods consistently improves the performance even though the testing prompt is different from training weak supervision.", + "bbox": [ + 496, + 659, + 890, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Updating Different Components: There are many options for updating the pre-trained SAM model. Given limited computing resources, choosing the appropriate components of network to update is crucial to optimize the generalization performance. In this section, we investigate several options of network components to update during adaptation. Full finetune means finetuning the whole encoder. MaskDecoder finetune the whole decoder", + "bbox": [ + 496, + 780, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23391", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2bd37e97d82e959a86b26f43c1ff352efd4a3e50f2bf0abe8ed3d7022373dd0a.jpg", + "image_caption": [ + "Figure 4. qualitative results on some selected examples. Three types of prompts at testing stage are visualized for reference." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 848, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of SAM without additional redundant learnable parameters. LayerNorm finetune the all layer norms of the SAM image encoder. LoRA finetunes the encoder network in through low-rank decomposition only. EVP use the Embedding Tune and the HFC Tune to tune the extracted features by image encoder. We present the investigation on the COCO dataset with bounding boxes as weak supervision in Tab. 9. In particular, we have also explored the impact of different combinations of components, e.g. MaskDecoder + LoRA, LoRA + EVP, and so on. The results suggest LoRA finetuning the encoder network alone yields the best performance.", + "bbox": [ + 75, + 560, + 472, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 744, + 194, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We studies the generalization of Segment-Anything model for multiple downstream image segmentation tasks. A tangible solution with no access to source dataset and low memory cost was proposed to adapt SAM to downstream data in a source-free domain adaptation manner. The proposed method is naturally compatible with weak supervisions which could substantially improve the efficacy of adaptation. Extensive evaluations on 10 datasets from 5 types of downstream tasks suggest the proposed adapta", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/abfde0052dd0b70961c6c1f4210065b9213a7664f1718ca2329922d50459c8b3.jpg", + "table_caption": [ + "Table 9. Adaptation results produced by finetuning different modules." + ], + "table_footnote": [], + "table_body": "
Finetuning ModuleIoU
None74.30
Full finetune78.54
MaskDecoder76.81
LayerNorm79.30
Low-Rank Adaptation (LoRA)80.12
Explicit Visual Prompt (EVP)77.38
MaskDecoder + LoRA77.28
MaskDecoder + EVP76.83
LoRA + EVP79.47
LoRA + LayerNorm79.35
MaskDecoder + LoRA + EVP77.31
", + "bbox": [ + 571, + 573, + 821, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion method can significantly improve the generalization of SAM under various degrees of distribution shift.", + "bbox": [ + 498, + 761, + 890, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by National Natural Science Foundation of China (NSFC) (Grant Number: 62106078), and Agency for Science, Technology and Research (Grant Number: C210112059). This work was partially done during Yongyi Su's attachment with Institute for Infocomm Research (I2R), funded by China Scholarship Council (CSC).", + "bbox": [ + 496, + 794, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23392", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Waqar Ahmed, Pietro Morerio, and Vittorio Murino. Cleaning noisy labels by negative ensemble learning for source-free unsupervised domain adaptation. In IEEE/CVF Winter Conference on Applications of Computer Vision, 2022. 2", + "[2] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. Pseudo-labeling and confirmation bias in deep semi-supervised learning. 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In IEEE/CVF International Conference on Computer Vision, 2019. 2" + ], + "bbox": [ + 501, + 92, + 890, + 527 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23395", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/0c9a1639-459a-4ab7-b55c-2fff676c9ecb_model.json b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/0c9a1639-459a-4ab7-b55c-2fff676c9ecb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..542c165a12b50559eadf27176aeeefb0034e5534 --- /dev/null +++ b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/0c9a1639-459a-4ab7-b55c-2fff676c9ecb_model.json @@ -0,0 +1,2290 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.131, + 0.85, + 0.177 + ], + "angle": 0, + "content": "Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.203, + 0.75, + 0.277 + ], + "angle": 0, + "content": "Haojie Zhang\\(^{1*}\\) Yongyi Su\\(^{1*}\\) Xun Xu\\(^{2\\dagger}\\) Kui Jia\\(^{3}\\) \n\\(^{1}\\)South China University of Technology \n\\(^{2}\\)Institute for Infocomm Research, A\\*STAR \nhool of Data Science, The Chinese University of Hong Kong, Shenz" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.474, + 0.691 + ], + "angle": 0, + "content": "The success of large language models has inspired the computer vision community to explore image segmentation foundation model that is able to zero/few-shot generalize through prompt engineering. Segment-Anything (SAM), among others, is the state-of-the-art image segmentation foundation model demonstrating strong zero/few-shot generalization. Despite the success, recent studies reveal the weakness of SAM under strong distribution shift. In particular, SAM performs awkwardly on corrupted natural images, camouflaged images, medical images, etc. Motivated by the observations, we aim to develop a self-training based strategy to adapt SAM to target distribution. Given the unique challenges of large source dataset, high computation cost and incorrect pseudo label, we propose a weakly supervised self-training architecture with anchor regularization and low-rank finetuning to improve the robustness and computation efficiency of adaptation. We validate the effectiveness on 5 types of downstream segmentation tasks including natural clean/corrupted images, medical images, camouflaged images and robotic images. Our proposed method is task-agnostic in nature and outperforms pre-trained SAM and state-of-the-art domain adaptation methods on almost all downstream tasks with the same testing prompt inputs." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.706, + 0.21, + 0.721 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.868 + ], + "angle": 0, + "content": "The success of large language models is partially attributed to the strong capability of zero-shot generalization. This has called for numerous attention into developing foundation model for computer vision tasks where one of the key concern also lies in the generalization ability [26, 44, 48]. In particular, as a promptable image segmentation foundation model with strong zero-shot generalization, the Segment-Anything model (SAM) [27] was developed by training on billions of annotated masks. Despite the overwhelming size" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.311, + 0.898, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.512, + 0.895, + 0.568 + ], + "angle": 0, + "content": "Figure 1. Segment Anything Model was pre-trained on a large-scale dataset but exhibits awkward performance on diverse downstream segmentation tasks. We adapt SAM through weak supervision to enhance its generalization capabilities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.895, + 0.716 + ], + "angle": 0, + "content": "of dataset used for training, SAM was found to behave awkwardly on certain out-of-distribution downstream tasks, including camouflaged segmentation, medical segmentation, adversarial attacks, visual corruptions, etc. [5, 21]. This is likely caused by the distribution shift between the training data, i.e. the SA-1B dataset [27], and the challenging testing datasets. These observations motivate us to explore tangible solutions to make SAM more robust against real-world and more diverse downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Traditional paradigm towards improving model robustness and generalization often involves costly re-training. Methods are frequently customized to combat specific domain shifts. For example, domain randomization was developed to improve generalization across real testing domains [6], while adversarial training is commonly used to enhance robustness against attacks [58]. Applying these techniques to large foundation models is nonetheless impractical due to the enormous computing resources required for training the model on the web-scale training data. Therefore, instead of re-training the model, we opt for a more computation friendly paradigm by adapting or finetuning a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.875, + 0.215, + 0.888 + ], + "angle": 0, + "content": "* Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.888, + 0.396, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\) Correspondence to Xun Xu: alex.xun.xu@gmail.com." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.875, + 0.396, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23385" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.427, + 0.106 + ], + "angle": 0, + "content": "pre-trained foundation model to downstream dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.111, + 0.47, + 0.276 + ], + "angle": 0, + "content": "We specify three major challenges when adapting pretrained foundation model to a new data distribution. First, traditional unsupervised domain adaptation [15] paradigm requires access to both source and target datasets which may not be feasible due to privacy issue and computation cost [34]. Second, updating all model weights for adaptation is often superior in performance, however, is constrained by the prohibitive memory cost due to the large model size [20]. Finally, unsupervised adaptation could be still very challenging due to the absence of label information on the target domain [60, 72, 75]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.473, + 0.673 + ], + "angle": 0, + "content": "To tackle the above challenges, we propose a self-training based adaptation approach to synergize the exploitation of weak supervision and unlabeled data on target domain. Specifically, we first alleviate the dependence on source domain data by adopting a self-training based source-free domain adaptation strategy. The self-training approach first makes segmentation predictions, a.k.a. pseudo labels, on the target domain data. The pseudo labels are used for supervising the update of segmentation model. As self-training is fragile due to incorrect pseudo labels, a.k.a. confirmation bias [2], we introduce a frozen source model as the anchor network to regularize the update of segmentation model. To further mitigate the high computation cost of updating the full model weights, we apply a low-rank weight decomposition to encoder weights and the backpropagation flows through the low-rank shortcut only. Finally, to further improve the effectiveness of source-free domain adaptation, weak supervisions, e.g. sparse pointwise annotation, on the target domain are introduced to provide stronger cues for domain adaptation. We reveal that the weak supervisions are naturally compatible with the prompt encoder within SAM. With the weak supervisions as prompt, we are endowed with more localized and less ambiguous pseudo predictions for self-training. The adapted model has demonstrated much stronger generalization capability on multiple downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.677, + 0.468, + 0.691 + ], + "angle": 0, + "content": "We summarize the contributions of this work as follows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.703, + 0.468, + 0.775 + ], + "angle": 0, + "content": "- We are motivated by the generalization issue of segment-anything (SAM) model to diverse downstream segmentation tasks and propose a task-agnostic solution to adapt SAM through self-training with no access to source dataset." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.778, + 0.468, + 0.85 + ], + "angle": 0, + "content": "- We exploit weak supervisions, including bounding box, point-wise annotation and coarse segmentation masks, to improve the effectiveness of adaptation. The weak supervision are fully compatible with the prompt encoder of SAM." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.853, + 0.468, + 0.898 + ], + "angle": 0, + "content": "- Extensive experiments on 5 types of downstream instance segmentation tasks demonstrate the effectiveness of the proposed weakly supervised adaptation approach." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.703, + 0.468, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.112, + 0.892, + 0.55 + ], + "angle": 0, + "content": "Image Segmentation Foundation Model: The success of deep learning is attributed to the increasing size and neural networks and huge amount of training data. Recent successful computer vision models, e.g. image segmentation and object detection, follow a practice of finetuning from encoder network pre-trained on large image dataset, e.g. ImageNet [10]. Despite achieving impressive results on standard benchmark datasets, e.g. Psacal VOC [13] and COCO [37], the zero-shot and few-shot generalization ability is often limited. Inspired by the revolutionizing language/vision-language foundation model pre-trained on web-scale datasets [4, 48, 74], a new opportunity awaits for developing a generalizable vision foundation model. This motivates the emergence of vision foundation model pretrained on huge dataset. SAM [27] and DINO v2 [44], to name a few. Among these foundation models, SAM stands out for its ability to enable zero-shot segmentation using prompt engineering. Therefore, we pay particular attention to SAM in this work. Since the inception of SAM, numerous attempts are made to validate the robustness of SAM under more challenging scenarios, such as medical images [42] [71], camouflaged objects [59], glass (transparent objects and mirrors) [18] and pose estimation [36]. Despite these early attempts to discover the weakness, there are very few matured solutions [5] to improve the generalization of SAM to challenging downstream tasks. In this work, we aim to fill this gap by proposing principled solutions to enhance the robustness of SAM against downstream tasks subject to significant distribution shift." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Source-Free Domain Adaptation: Unsupervised Domain Adaptation (UDA)[15, 24, 41, 61, 73] has emerged as a means to address the domain shift between source training data and target testing data. This enables models to be trained on cost-effective and easily annotated data, facilitating the transfer to more valuable but challenging-to-label datasets. However, UDA methods face limitations when source domain data is inaccessible due to privacy concerns or storage constraints. In response to this, Source-Free Domain Adaptation (SFDA)[28, 33, 34, 39, 65, 68] has been proposed to reduce the reliance on source data in domain adaptation (DA) methods. SHOT [34] represents an early effort to alleviate domain shift without access to source data, achieved through self-training on unlabeled target data. Numerous prior works [1, 7, 11, 26, 35, 47, 50] have explored the effectiveness of a teacher-student like self-training architecture in domain shift mitigation. The similar self-training framework [22] simultaneously trains on multiple sets of augmented data, utilizing teacher-student cycle consistency for mutual learning of the two networks. Other methods generate source-like samples [30, 40, 46], construct intermediate domains [65, 69], or perturb target domains [25, 32, 66, 70] to enhance model generalization." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23386" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.844, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Figure 2. The proposed self-training architecture with anchor network regularization and contrastive loss regularization. Red arrows indicates the backpropagation flow." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.471, + 0.46 + ], + "angle": 0, + "content": "Recent approaches [46, 64] leverage contrast loss between target samples and source domain prototypes. Recent attempts to source-free domain adaptation for image segmentation aims to minimize feature discrepancy between source and target domains [3, 29, 40]. In this work, we aim to adapt SAM to downstream tasks without accessing to the source domain data to avoid the high computation overhead and potential privacy issues for foundation models to be released in the future." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.477 + ], + "angle": 0, + "content": "Weakly Supervised Domain Adaptive Segmentation:" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.478, + 0.471, + 0.78 + ], + "angle": 0, + "content": "Unsupervised domain adaptation often follows a self-training paradigm [34], which is limited by the quality of pseudo labels. Instead of relying on the pseudo predictions, weakly supervised domain adaptive semantic segmentation (WDASS) exploits limited weak supervisions in the form of bounding box, points or coarse segmentation masks [8, 9, 45, 63]. Among these works, [45] employs both image and point labels, suggesting an adversarial alignment of features at the pixel level to address WDASS. In contrast, [63] relies on bounding boxes as weak labels and employs adversarial learning to achieve domain-invariant features. Additionally, [9] utilizes self-training and a boundary loss to enhance performance in WDASS with coarse labels. More recently, [8] utilizes weak label for aligning the source-target features and outperforms previous methods to achieve competitive performance compared to supervised learning. We observe that the common weak supervisions are inherently compatible with the SAM model as prompt input. Therefore, we propose to adapt SAM with weak supervisions in a seamless way." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.796, + 0.212, + 0.813 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.469, + 0.906 + ], + "angle": 0, + "content": "In this section, we first provide an overview of segment-anything model. Then, we introduce the self-training based adaptation framework. We elaborate how weak supervision could help establish correspondence between pseudo predictions for effective self-training. Lastly, we introduce the low memory footprint way of updating model weights." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.325, + 0.83, + 0.34 + ], + "angle": 0, + "content": "3.1. Overview of Segment Anything Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.892, + 0.567 + ], + "angle": 0, + "content": "The segment-anything model consists of three major components, the encoder network \\( z = f(x; \\Theta) \\), prompt encoder \\( e = g(p; \\Omega) \\) and mask decoder \\( h(z, e; \\Phi) \\). The image encoder is pre-trained using masked autoencoder (MAE) [19]. The whole SAM model is further fine-tuned on the web-scale labeled training set, SA-1B [27], with 1.1B labeled masks. A combination of focal loss and dice loss are used for training SAM. During inference, the testing image \\( x \\) is first encoded by the image encoder \\( z = f(x; \\Theta) \\). Given encoded prompts \\( e \\), a light-weight mask decoder makes three levels of segmentation predictions. In this work, we are motivated by the challenge of deploying SAM on many downstream tasks and propose to adapt SAM to downstream segmentation tasks with weak supervision without requiring access to source domain training data." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.568, + 0.848, + 0.584 + ], + "angle": 0, + "content": "3.2. Source-Free Adaptation as Self-Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Provided an unlabeled target domain dataset \\(\\mathcal{D}_T = \\{x_i\\}\\) and the pre-trained encoder network \\(f(x;\\Theta)\\), we adopt a teacher-student architecture for self-training. As illustrated in Fig. 2, we maintain three encoder networks, namely the anchor network \\(f(x;\\Theta^a)\\), the student network \\(f(x;\\Theta^s)\\) and the teacher network \\(f(x;\\Theta^t)\\), where the student and teacher networks share the weights \\(\\Theta^s = \\Theta^t\\). For each sample \\(x_i\\), we apply one random weak data augmentation \\(\\mathcal{A}_w(x_i)\\) as the input to anchor and teacher networks, and one random strong data augmentation \\(\\mathcal{A}_s(x_i)\\) as the input to student network. Through the three encoder networks, three feature maps are obtained respectively, as \\(\\mathcal{F}^a = f(\\mathcal{A}_w(x_i),\\Theta^a)\\), \\(\\mathcal{F}^s = f(\\mathcal{A}_s(x_i),\\Theta^s)\\) and \\(\\mathcal{F}^t = f(\\mathcal{A}_w(x_i),\\Theta^t)\\), where \\(\\mathcal{F} \\in \\mathbb{R}^{D \\times H \\times W}\\) and \\(D\\) refers to feature dimension. In the decoder network, given a number \\(N_p\\) of prompts, e.g. bounding boxes, points or coarse segmentation masks, a set of foreground masks for the instance segmentation results would be deduced, \\(\\mathcal{Y}^a = \\{y_j^a\\}_{j=1\\dots N_p}\\), \\(\\mathcal{Y}^s = \\{y_j^s\\}_{j=1\\dots N_p}\\), \\(\\mathcal{Y}^t = \\{y_j^t\\}_{j=1\\dots N_p}\\), where each mask is then normalized between 0 and 1 by sigmoid function respectively, i.e. \\(m_j = \\text{Sigmoid}(y_j)\\), \\(m_j \\in [0,1]^{H \\times W}\\). We" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23387" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.473, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.209, + 0.448, + 0.223 + ], + "angle": 0, + "content": "Figure 3. Illustration of contrastive loss between two views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.232, + 0.468, + 0.292 + ], + "angle": 0, + "content": "further denote a binarized segmentation mask with a threshold of 0.5 as \\(\\hat{m}_j = \\mathbb{1}(m_j > 0.5),\\hat{m}_j\\in \\{0,1\\}^{H\\times W}\\). Based on these notations, we elaborate three sets of adaptation objectives for self-training purpose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.468, + 0.444 + ], + "angle": 0, + "content": "Teacher-Student Self-Training Loss: We first introduce the Self-Training loss to update student/teacher network. Self-Training is widely used in semi-supervised learning [52] and recently is demonstrated to be very effective for source-free domain adaptation [35]. In this work, we continue the idea of self-training in classification task and perform focal loss [38] and dice loss [43] for the supervision of student's outputs with binarized teacher's predictions as follows, where \\(\\gamma\\) controls the focus on hard training pixels and \\(\\epsilon\\) is a small value to avoid dividing by zero." + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.444, + 0.468, + 0.488 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {s t} ^ {f o c a l} = - \\sum_ {j = 1 \\dots N _ {p}} \\frac {1}{H W} \\sum_ {h, w} \\mathbb {1} \\left(\\hat {m} _ {j h w} ^ {t} = 1\\right) \\cdot \\left(1 - m _ {j h w} ^ {s}\\right) ^ {\\gamma} \\log \\left(m _ {j h w} ^ {s}\\right) \\tag {1} \\\\ + \\mathbb {1} (\\hat {m} _ {j h w} ^ {t} = 0) \\cdot m _ {j h w} ^ {s} ^ {\\gamma} \\log (1 - m _ {j h w} ^ {s}), \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.498, + 0.468, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s t} ^ {d i c e} = \\sum_ {j = 1 \\dots N _ {p}} 1 - \\frac {2 \\sum_ {h , w} m _ {j h w} ^ {s} \\cdot \\hat {m} _ {j h w} ^ {t} + \\epsilon}{\\sum_ {h , w} m _ {j h w} ^ {s} + \\sum_ {h , w} \\hat {m} _ {j h w} ^ {t} + \\epsilon}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Anchored Loss for Robust Regularization: Training the networks with self-training loss alone is vulnerable to the accumulation of incorrect pseudo labels predicted by teacher network, a.k.a. confirmation bias [2]. Observations are made that the performance will drop after long iterations of self-training alone [56]. Existing source-free domain adaptation approaches often adopt additional constraints to prevent the negative impact of self-training, e.g. uniform distribution over predictions [35]. Without making such explicit assumptions, we propose to introduce the regularization by an anchor loss which minimizes the dice loss between an anchor network, which has frozen source model weights, and student and teacher networks respectively in Eq. 3. The frozen anchor network serves as the knowledge inherited from source domain and too much deviation between the source model and self-training updated model is discouraged to prevent the model from collapsing." + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.823, + 0.468, + 0.84 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a n c h o r}} = \\lambda_ {\\text {s t u}} ^ {\\text {d i c e}} \\mathcal {L} ^ {\\text {d i c e}} \\left(m ^ {s}, \\hat {m} ^ {a}\\right) + \\lambda_ {\\text {t e a}} ^ {\\text {d i c e}} \\mathcal {L} ^ {\\text {d i c e}} \\left(m ^ {t}, \\hat {m} ^ {a}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Contrastive Loss for Encoder Output Regularization: The above two training objectives are performed in the output space of the decoder. As we empirically revealed in the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.193 + ], + "angle": 0, + "content": "experiment section, updating encoder network is the most effective way to adapt SAM, it is necessary to apply regularization directly to the feature map as output from the encoder network. Specifically, as illustrated in Fig. 3, we first crop out each instance's feature \\( I_{j} \\) from the feature map based on its prediction mask in anchor and teacher branches." + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.186, + 0.892, + 0.224 + ], + "angle": 0, + "content": "\\[\nI _ {j} = \\frac {\\sum_ {h , w} \\bar {\\mathcal {F}} _ {h w} \\cdot \\hat {m} _ {j h w}}{\\sum_ {h , w} \\hat {m} _ {j h w}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.226, + 0.892, + 0.333 + ], + "angle": 0, + "content": "where \\(\\overline{\\mathcal{F}}\\) is the L2 normalized feature map, i.e. \\(\\overline{\\mathcal{F}}_{hw} = \\frac{\\mathcal{F}_{hw}}{|\\mathcal{F}_{hw}|}\\). We further define the instance features, which are cropped out by the masks used the same prompt in two branches, as positive pairs, and the instances used different prompts as negative pairs to construct the contrast loss. The final contrastive loss is given as below, where \\(\\tau\\) is the temperature scaling." + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.34, + 0.892, + 0.378 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n t r a s t}} = - \\log \\frac {\\sum_ {j} \\exp \\left(I _ {j} ^ {a} \\cdot I _ {j} ^ {t} / \\tau\\right)}{\\sum_ {j} \\sum_ {j ^ {\\prime} \\neq j} \\exp \\left(I _ {j} ^ {a} \\cdot I _ {j ^ {\\prime}} ^ {t} / \\tau\\right)} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.413 + ], + "angle": 0, + "content": "Total Loss: We combine the above three loss functions as the final source-free domain adaptation loss." + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.42, + 0.892, + 0.44 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {s t} ^ {f o c a l} \\mathcal {L} _ {s t} ^ {f o c a l} + \\mathcal {L} _ {s t} ^ {d i c e} + \\mathcal {L} _ {\\text {a n c h o r}} + \\mathcal {L} _ {\\text {c o n t r a s t}}. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.447, + 0.82, + 0.463 + ], + "angle": 0, + "content": "3.3. Prompt Generation for Self-Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.891, + 0.522 + ], + "angle": 0, + "content": "The SAM segmentation requires prompt inputs to disambiguate the granularity of segmentation. The prompt engineering can be implemented in both fully automated way and by human interaction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Fully Automated Prompt for Self-Training: We first densely sample grid points with a spatial distance of 16 pixels as point prompt input. Initial stage segmentation masks \\(\\{\\hat{m}_j\\}_{j = 1\\dots N_{init}}\\) are generated by the anchor network with the grid point prompts. We follow the fully automated segmentation introduced by SAM [27] to prune out masks with low IoU score and low stability score, followed by NMS suppression. To enable self-training and regularization between different branches, we further generate a fixed set of prompt \\(\\{e_j\\}_{j = 1\\dots N_p}\\) from \\(\\{\\hat{m}_j\\}_{j = 1\\dots N_{init}}\\) as input to all three branches. As such, the segmentation outputs \\(\\mathcal{Y}^a\\), \\(\\mathcal{Y}^s\\) and \\(\\mathcal{Y}^t\\) are of the same length with exact one-to-one correspondence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Weak Supervision as Prompt: Despite automatic segmentation can be enabled by sampling a grid of point prompts over the image and filtering out low quality and duplicated masks, the quality of segmentation is relatively poor and may contain many false positive predictions, making self-training less effective. Therefore, following prior weakly supervised domain adaptation works [9], we propose to use three types of weak supervisions, including bounding box, sparse point annotation and coarse segmentation mask. Fortunately, in the context of SAM, these weak supervisions perfect match with the prompt inputs which allow seamless integration of weak supervision for adapting SAM." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23388" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.323, + 0.107 + ], + "angle": 0, + "content": "3.4. Low-Rank Weights Update" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.473, + 0.32 + ], + "angle": 0, + "content": "The enormous size of backbone network prohibits updating all model weights with large batchsize. However, many existing studies suggest the update of encoder network weights is an effective way of adapting pre-trained models [35, 54]. To enable updating the backbone network with larger batchsize, we opt for a computation friendly low-rank updating approach [20]. For each weight in the encoder network \\(\\theta \\in \\mathbb{R}^{d_i \\times d_o}\\), we use a low-rank approximation \\(\\omega = AB\\) where \\(A \\in \\mathbb{R}^{d_i \\times r}\\) and \\(A \\in \\mathbb{R}^{r \\times d_o}\\) with \\(r\\) indicating the rank. We can achieve a compression rate of \\(r(d_i + d_o) / d_i \\cdot d_o\\). Only \\(A\\) and \\(B\\) are updated via backpropagation during adaptation to reduce memory footprint. At inference stage, the weight is reconstructed by combining the low rank reconstruction and original weight, \\(\\theta = \\theta + AB\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.334, + 0.203, + 0.351 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.47, + 0.437 + ], + "angle": 0, + "content": "In this section, we first introduce the experiment settings and downstream tasks for adapting SAM model. We provide detailed comparisons to state-of-the-art methods and qualitative results. Finally, we analyze the effectiveness of individual components and specific designs for the network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.44, + 0.181, + 0.455 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.47, + 0.577 + ], + "angle": 0, + "content": "The source domain training set, SA-1B, was mainly constructed by collecting from natural environments. In this work, we identified five types of downstream segmentation tasks, some of which feature a drastic distribution shift from SA-1B, for evaluation, covering natural clean images, natural corrupted images, medical images, camouflaged images and robotic images. We present the datasets evaluated for each type of downstream task in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.729 + ], + "angle": 0, + "content": "Datasplit: We divide each downstream dataset into non-overlapping training and testing sets following the ratio established by [8]. The adaptation step is implemented on the training set. After the model is adapted, we evaluate the model on the held-out testing set. For adaptation to the Camouflaged Objects, following the training protocol in [5], we use the dataset COD10K (the training set of camouflaged images) for training, and use the test set of CAMO, COD10K and the entire CHAMELEON dataset for performance evaluation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.733, + 0.263, + 0.749 + ], + "angle": 0, + "content": "4.2. Experiment Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.795 + ], + "angle": 0, + "content": "Segment-Anything Model: We adopt ViT-B [12] as the encoder network due to memory constraint. The standard prompt encoder and mask decoder are adopted." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Prompt Generation: We first provide details for generating prompt at both training stages. All training prompts are calculated from ground-truth segmentation mask, simulating the human interactions as weak supervision. Specifically, we extract the minimal bounding box that covers the whole instance segmentation mask as box prompt. The point prompt is created as randomly selecting 5 positive" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "points within ground-truth instance segmentation mask and 5 negative points outside ground-truth mask. The coarse segmentation mask is simulated by fitting a polygon to the ground-truth mask. We choose the number of vertices as \\( P / 20 \\) with \\( P \\) indicating the perimeter of mask. The minimal number of vertices is 3. We use the same way to generate testing prompt on the testing data. This practice guarantees fair evaluation of SAM model which requires prompt input for segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.291 + ], + "angle": 0, + "content": "Evaluation Metrics: We report the mIoU as evaluation metrics. For each input prompt, the IoU is calculated between the ground-truth segmentation mask and predicted mask. The mIoU averages over the IoU of all instances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.893, + 0.7 + ], + "angle": 0, + "content": "Competing Methods: We evaluate multiple source-free domain adaptation approaches and one state-of-the-art weakly supervised domain adaptive segmentation approach. In specific, direct testing the pre-trained model (Direct) with fixed prompt inputs is prone to the distribution shift and may not perform well on target datasets with significant shift. TENT [62] is a vanilla test-time adaptation method which optimizes an entropy loss for adapting to target domain. SHOT [35] employs pseudo label and applies uniform distribution assumption for source-free domain adaptation. Soft Teacher [67] was originally developed for semi-supervised image segmentation. We adapt Soft Teacher for domain adaptation by keeping the self-training component. TRIBE [55] proposed a strong baseline for generic test-time adaptation on continual and class imbalanced domain shifts. We adapt TRIBE for domain adaptive segmentation by replacing the training losses. DePT [16] inserts visual prompts into a visual Transformer and adjusts these source-initialized prompts solely during the adaptation process without accessing the source data. WDASS [8] developed a weakly supervised domain adaptive segmentation method. We also evaluate the upperbound of adapting SAM by fine-tuning with ground-truth segmentation masks, which is dubbed as Supervised. Finally, we evaluate our weakly supervised domain adaptation method as Ours. All the competing methods use the same backbone, i.e. the ViT-B from SAM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Hyperparameters: We finetune LoRA module of the ViTB image encoder by Adam optimizer for all experiments. We set the batchsize to 4, distributed over four RTX3090 GPUs, and the learning rate to 0.0001 with a weight decay of 0.0001. For Self-Training loss, we set the hyperparameters \\(\\gamma\\) and \\(\\epsilon\\) of \\(\\mathcal{L}_{st}^{focal}\\) and \\(\\mathcal{L}_{st}^{dice}\\) to 2 and 1 respectively. \\(\\lambda_{st}^{focal}\\) is set to 20, which is the coefficients of \\(\\mathcal{L}_{st}^{focal}\\). For Anchor loss, the coefficients of two dice losses are denoted as \\(\\lambda_{stu}^{dice}\\) and \\(\\lambda_{tea}^{dice}\\), both of which equal 0.5. For Contrast loss, we set the temperature \\(\\tau\\) to 0.3. We have set the low rank of the LoRA module for the image encoder to 4. We apply strong and weak data augmentations for self-training and choices for augmentation follows [53, 67]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23389" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.342, + 0.09, + 0.628, + 0.103 + ], + "angle": 0, + "content": "Table 1. Dataset and datasplit used in this work." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.104, + 0.83, + 0.159 + ], + "angle": 0, + "content": "
Natural ImagesCorrupted ImagesMedical ImagesCamouflaged ObjectsRobotic Images
COCO [37]Pascal VOC [13]COCO-Ckvasir-SEG [23]ISIC [17]CHAMELEON [51]CAMO [31]COD10K [14]OCID [57]OSD [49]
# Training4246249742468349004040197256
# Testing70641670616637974250202632855
" + }, + { + "type": "table_caption", + "bbox": [ + 0.28, + 0.163, + 0.689, + 0.175 + ], + "angle": 0, + "content": "Table 2. Adaptation results on COCO-C dataset using bounding box prompt." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.176, + 0.828, + 0.297 + ], + "angle": 0, + "content": "
MethodBritContrDefocElastFogFrostGaussGlassImpulJpegMotnPixelShotSnowZoomAvg
Direct72.8357.3464.4769.3672.3970.5067.2064.4367.6568.2362.7268.6067.4469.0258.8066.73
TENT76.0261.5167.4870.8874.8973.8869.0167.1069.2870.2565.4570.8169.9672.3762.5969.43
SHOT73.8459.0965.9169.5773.9872.5168.3066.0968.6169.4564.5670.4868.7771.0360.1768.16
Soft Teacher73.9062.1265.4171.3272.1673.2768.8467.4968.7370.1866.8869.7970.0873.3364.8869.23
TRIBE76.4060.8666.1972.7275.0875.1470.3466.6670.8372.4265.9470.2470.6674.2264.5670.15
DePT69.1557.2659.0866.8058.7366.7566.7862.7465.6566.3961.6666.6567.5766.6258.2164.42
WDASS76.2160.5767.0772.3475.9774.6369.8467.8869.9271.3666.2571.9970.3272.2563.6170.01
OURS78.5061.0566.9973.9377.0976.1072.0268.2171.2972.7766.3370.9070.2875.0765.3371.05
Supervised78.8674.8172.0474.3278.0177.1473.4372.1274.0875.3071.3975.1574.2576.3468.0474.35
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.305, + 0.307, + 0.321 + ], + "angle": 0, + "content": "4.3. Quantitative Evaluations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.471, + 0.399 + ], + "angle": 0, + "content": "In this section, we report the quantitative evaluations on the 5 types of target datasets. For each dataset, we also report the adaptation results with weak supervision in the form of bounding box (box), sparse points (point) and coarse segmentation mask (poly)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.52 + ], + "angle": 0, + "content": "Adaptation to Corrupted Images: Visual corruptions often occur due to sensor fault, bad weather conditions, etc. As seen from Tab. 2, without any adaptation, Direct testing is significantly worse than the upperbound. With weakly supervisions, all methods could improve over direct testing, in particular, our proposed method outperforms all competing adaptation methods on 10 out of 15 types of corruptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.748 + ], + "angle": 0, + "content": "Adaptation to Natural Images: We then present the results of adapting SAM to natural images in Tab. 3. For each type of weak supervision, we use the same type of prompt on the testing set. Despite the distribution gap between SA-1B and the target natural images, we observe significant performance gap between Supervised upperbound and Direct baseline, e.g. with box level supervision, there is \\(5 - 10\\%\\) gap in IoU. When weak supervision is provided, both state-of-the-art generic source-free domain adaptation methods and weakly supervised domain adaptive segmentation method improve the generalization on all three types of weak supervisions. Finally, our proposed weakly supervised method achieves a remarkable improvement over all competing methods. The results with box weak supervision is even approaching the fully supervised upperbound." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Adaptation to Medical Images: Segmentation for medical images is a major application of foundation models. Our empirical observations in Tab. 4 on two medical segmentation datasets suggest that direct applying pre-trained SAM is suboptimal. With weakly supervised adaptation, the segmentation accuracy is greatly improved. We observe the improvement to be particularly significant with point and box which are relatively easy to obtain due to the low labeling cost." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Adaptation to Camouflaged Objects: We further eval" + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.305, + 0.856, + 0.318 + ], + "angle": 0, + "content": "Table 3. Adaptation results on natural clean image datasets." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.32, + 0.869, + 0.47 + ], + "angle": 0, + "content": "
MethodCOCO 2017Pascal VOC
boxpointpolyboxpointpoly
Direct74.2955.0665.6469.2169.2160.79
TENT78.2152.9971.5180.2474.9765.03
SHOT75.1858.4669.2679.8074.2663.38
Soft Teacher75.9443.3668.2772.9356.0962.20
TRIBE77.5649.5670.9978.8769.2165.39
DePT71.0037.3563.2774.0942.9959.94
WDASS77.2960.5570.1980.1276.1566.98
OURS80.1262.0972.3380.2774.1566.72
Supervised81.5069.7773.3981.2376.9871.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.479, + 0.879, + 0.492 + ], + "angle": 0, + "content": "Table 4. Adaptation results on medical image segmentation datasets." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.493, + 0.869, + 0.645 + ], + "angle": 0, + "content": "
Methodkvasir-SEGISIC
boxpointpolyboxpointpoly
Direct81.5962.3054.0366.7453.4262.82
TENT82.4761.8462.9771.7653.4667.12
SHOT82.3063.7661.3471.9955.9966.86
Soft Teacher84.1273.5358.1575.7454.9572.29
TRIBE85.0573.0364.6172.6150.3667.99
DePT81.9152.0661.5578.4346.7972.75
WDASS84.0163.7864.7874.2355.6367.84
OURS85.4775.2367.4080.0162.1275.36
Supervised85.8977.5481.6481.6279.8180.26
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.868 + ], + "angle": 0, + "content": "uate on adapting SAM to camouflaged object detection. We evaluate on three camouflaged object detection datasets with results reported in Tab. 5. Preliminary studies revealed that SAM is particularly vulnerable to camouflaged objects [59] due to the low contrast between background and foreground. We make similar observations here that even with the help of prompt inputs at testing stage, Direct inference suffers a lot, achieving less than \\(66\\%\\) mIoU. When weakly labeled data are used for adaptation, we observe very significant improvements, with point prompt only we improved by a staggering \\(35\\%\\) in mIoU on the CHAMELEON dataset. Our proposed method is also consistently better than all competing methods on all types of weak supervisions." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Adaptation to Robotic Images: Finally, we evaluate adapting SAM to image collected from robotic environ" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23390" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.09, + 0.432, + 0.103 + ], + "angle": 0, + "content": "Table 5. Adaptation results on camouflaged object datasets." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.104, + 0.445, + 0.214 + ], + "angle": 0, + "content": "
MethodCHAMELEONCAMOCOD10K
boxpointpolyboxpointpolyboxpointpoly
Direct51.3239.3745.7862.7257.4350.8566.3263.6140.04
TENT65.4854.5353.0671.2459.5960.2969.3661.9443.36
SHOT68.6062.4754.3671.6162.7858.7269.0965.2542.38
Soft Teacher65.9244.1746.7262.3048.6451.2666.3250.0432.27
TRIBE71.0052.8054.9966.0061.9760.5467.8463.6242.75
DePT54.4833.4642.4755.4433.0748.6359.3234.0635.51
WDASS71.9162.4056.8071.2563.3962.2971.4265.6143.93
OURS75.9474.0066.8373.4265.5562.9071.9370.5545.87
Supervised78.0585.8668.3879.1777.0167.1278.0678.4464.90
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.222, + 0.47, + 0.311 + ], + "angle": 0, + "content": "ments where segmenting out the spatial extent of individual objects is essential for interactions. As seen from the results in Tab. 6, adapting SAM to robotic images with weak supervision further increase the segmentation accuracy. The improvement is more noticeable with point and polygon weak supervisions." + }, + { + "type": "table_caption", + "bbox": [ + 0.128, + 0.315, + 0.418, + 0.327 + ], + "angle": 0, + "content": "Table 6. Adaptation results on robotic image datasets." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.328, + 0.445, + 0.48 + ], + "angle": 0, + "content": "
MethodOCIDOSD
boxpointpolyboxpointpoly
Direct86.3571.4172.8187.6278.8680.77
TENT87.7766.6177.5388.1080.5387.85
SHOT88.0674.3976.2588.0980.5287.86
Soft Teacher84.9868.4673.7590.4180.4987.00
TRIBE86.7767.8676.5090.4280.5487.84
DePT82.0056.5270.9281.8469.0682.50
WDASS87.6877.1376.7088.0780.5288.19
OURS88.0980.1477.4192.1180.5189.72
Supervised91.2489.2279.2392.1482.4190.83
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.493, + 0.295, + 0.508 + ], + "angle": 0, + "content": "4.4. Qualitative Evaluations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We present the qualitative comparisons of segmentation results for selected examples in Fig. 4. We make the following observations from the results. Evaluating pre-trained SAM (SAM) on COCO with both box and point prompt exhibits very fine-grained segmentation results. However, the model is overly sensitive to the high contrast regions, e.g. the hair for the girl and the toppings of pizza are missing from the segmentation mask. With the proposed weakly supervised adaptation approach, our method is able to generate more smoothed segmentation mask and the mask better reflects the semantic boundary. Similar observations are made from the medical image segmentation dataset. Without adapting the SAM model, segmentation results are either too conservative with low recall or expanding beyond the semantic boundary. With our weakly supervised adaptation, SAM is able to produce high fidelity results. We further present results on camouflaged segmentation task (CAMO). Without adaptation, SAM fails to segment out the spider's belly and confuses the snow background with the harp seal in the foreground. Our weakly adapted SAM successfully segments out the spider's belly and produces high quality mask for the harp seal. Finally, two examples from OCID dataset suggest that the pre-trained SAM tends to over-segment, e.g. missing the open whole for the tissue box, or confusing adjacent objects, e.g. merging the pen with the folder label. With weakly supervised adaptation SAM picks up the" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.114 + ], + "angle": 0, + "content": "Table 7. Ablation studies of the proposed weakly supervised adaptation method on COCO dataset." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.117, + 0.868, + 0.203 + ], + "angle": 0, + "content": "
Weak Sup.Self-Train.AnchorCont. Lossboxpointpoly
original SAM74.2956.3665.42
✓✓58.8832.5155.03
✓✓✓79.6557.2570.49
✓✓✓62.9522.8756.91
✓✓✓✓80.1262.0972.33
✓✓✓76.1847.6370.44
" + }, + { + "type": "table_caption", + "bbox": [ + 0.53, + 0.206, + 0.862, + 0.219 + ], + "angle": 0, + "content": "Table 8. Adaptation results on cross-prompt testing scenarios." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.221, + 0.868, + 0.287 + ], + "angle": 0, + "content": "
Tr. Weak. Sup.boxpointpolygon
Te. Promptboxpointpolyboxpointpolyboxpointpoly
Direct74.2954.7666.7574.2954.6466.7574.2954.7665.64
TENT78.2154.8368.8252.9952.9968.5877.0853.9071.51
WDASS77.2958.7868.9474.6960.5569.1575.2755.2770.19
OURS80.1252.2872.0776.4962.0971.0278.5752.8872.33
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.293, + 0.892, + 0.323 + ], + "angle": 0, + "content": "semantic meaning and produces segmentation results that better aligns with human intention." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.332, + 0.653, + 0.347 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.635 + ], + "angle": 0, + "content": "In this section, we analyze the effectiveness of individual components on COCO dataset. As presented in Tab. 7, when self-training is applied alone, we observe a significant performance drop (74.29% → 58.88% with box weak supervision), suggesting the severity of confirmation bias. This issue can be well remedied when the anchor loss regularization is applied. Self-training with anchored regularization already improves the performance of SAM after adaptation. Finally, the contrastive loss directly regularizes the encoder network's output and contributes with additional improvement of segmentation accuracy. We also investigate the final self-training architecture without any weak supervision, i.e. the pseudo label masks are generated with grid point prompt. The results after adaptation is slightly worse than with weak supervision but consistently better than without adaptation on both box and coarse mask testing prompts. Nevertheless, the results with point prompt performs even worse than without adaptation, suggesting the necessity of weakly supervised adaptation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.644, + 0.689, + 0.659 + ], + "angle": 0, + "content": "4.6. Additional Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Generalization to Cross-Prompt Testing: We further investigate the effectiveness of adaptation by testing with all three types of prompts. Specifically, we compare with the best (WDASS) and second best (TENT) methods with results presented in Tab. 8. Apart from using point as testing prompt, our methods consistently improves the performance even though the testing prompt is different from training weak supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Effectiveness of Updating Different Components: There are many options for updating the pre-trained SAM model. Given limited computing resources, choosing the appropriate components of network to update is crucial to optimize the generalization performance. In this section, we investigate several options of network components to update during adaptation. Full finetune means finetuning the whole encoder. MaskDecoder finetune the whole decoder" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23391" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.849, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.118, + 0.535, + 0.85, + 0.55 + ], + "angle": 0, + "content": "Figure 4. qualitative results on some selected examples. Three types of prompts at testing stage are visualized for reference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.473, + 0.728 + ], + "angle": 0, + "content": "of SAM without additional redundant learnable parameters. LayerNorm finetune the all layer norms of the SAM image encoder. LoRA finetunes the encoder network in through low-rank decomposition only. EVP use the Embedding Tune and the HFC Tune to tune the extracted features by image encoder. We present the investigation on the COCO dataset with bounding boxes as weak supervision in Tab. 9. In particular, we have also explored the impact of different combinations of components, e.g. MaskDecoder + LoRA, LoRA + EVP, and so on. The results suggest LoRA finetuning the encoder network alone yields the best performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.745, + 0.196, + 0.76 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We studies the generalization of Segment-Anything model for multiple downstream image segmentation tasks. A tangible solution with no access to source dataset and low memory cost was proposed to adapt SAM to downstream data in a source-free domain adaptation manner. The proposed method is naturally compatible with weak supervisions which could substantially improve the efficacy of adaptation. Extensive evaluations on 10 datasets from 5 types of downstream tasks suggest the proposed adapta" + }, + { + "type": "table_caption", + "bbox": [ + 0.509, + 0.56, + 0.882, + 0.573 + ], + "angle": 0, + "content": "Table 9. Adaptation results produced by finetuning different modules." + }, + { + "type": "table", + "bbox": [ + 0.572, + 0.574, + 0.822, + 0.748 + ], + "angle": 0, + "content": "
Finetuning ModuleIoU
None74.30
Full finetune78.54
MaskDecoder76.81
LayerNorm79.30
Low-Rank Adaptation (LoRA)80.12
Explicit Visual Prompt (EVP)77.38
MaskDecoder + LoRA77.28
MaskDecoder + EVP76.83
LoRA + EVP79.47
LoRA + LayerNorm79.35
MaskDecoder + LoRA + EVP77.31
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.762, + 0.892, + 0.792 + ], + "angle": 0, + "content": "tion method can significantly improve the generalization of SAM under various degrees of distribution shift." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by National Natural Science Foundation of China (NSFC) (Grant Number: 62106078), and Agency for Science, Technology and Research (Grant Number: C210112059). This work was partially done during Yongyi Su's attachment with Institute for Infocomm Research (I2R), funded by China Scholarship Council (CSC)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23392" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Waqar Ahmed, Pietro Morerio, and Vittorio Murino. Cleaning noisy labels by negative ensemble learning for source-free unsupervised domain adaptation. In IEEE/CVF Winter Conference on Applications of Computer Vision, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. Pseudo-labeling and confirmation bias in deep semi-supervised learning. 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Segment-Anything (SAM), among others, is the state-of-the-art image segmentation foundation model demonstrating strong zero/few-shot generalization. Despite the success, recent studies reveal the weakness of SAM under strong distribution shift. In particular, SAM performs awkwardly on corrupted natural images, camouflaged images, medical images, etc. Motivated by the observations, we aim to develop a self-training based strategy to adapt SAM to target distribution. Given the unique challenges of large source dataset, high computation cost and incorrect pseudo label, we propose a weakly supervised self-training architecture with anchor regularization and low-rank finetuning to improve the robustness and computation efficiency of adaptation. We validate the effectiveness on 5 types of downstream segmentation tasks including natural clean/corrupted images, medical images, camouflaged images and robotic images. Our proposed method is task-agnostic in nature and outperforms pre-trained SAM and state-of-the-art domain adaptation methods on almost all downstream tasks with the same testing prompt inputs. + +# 1. Introduction + +The success of large language models is partially attributed to the strong capability of zero-shot generalization. This has called for numerous attention into developing foundation model for computer vision tasks where one of the key concern also lies in the generalization ability [26, 44, 48]. In particular, as a promptable image segmentation foundation model with strong zero-shot generalization, the Segment-Anything model (SAM) [27] was developed by training on billions of annotated masks. Despite the overwhelming size + +![](images/c158a82f0d98d0253c02127379fa4b2711ef95ed0c559ab269b37964643a73b4.jpg) +Figure 1. Segment Anything Model was pre-trained on a large-scale dataset but exhibits awkward performance on diverse downstream segmentation tasks. We adapt SAM through weak supervision to enhance its generalization capabilities. + +of dataset used for training, SAM was found to behave awkwardly on certain out-of-distribution downstream tasks, including camouflaged segmentation, medical segmentation, adversarial attacks, visual corruptions, etc. [5, 21]. This is likely caused by the distribution shift between the training data, i.e. the SA-1B dataset [27], and the challenging testing datasets. These observations motivate us to explore tangible solutions to make SAM more robust against real-world and more diverse downstream tasks. + +Traditional paradigm towards improving model robustness and generalization often involves costly re-training. Methods are frequently customized to combat specific domain shifts. For example, domain randomization was developed to improve generalization across real testing domains [6], while adversarial training is commonly used to enhance robustness against attacks [58]. Applying these techniques to large foundation models is nonetheless impractical due to the enormous computing resources required for training the model on the web-scale training data. Therefore, instead of re-training the model, we opt for a more computation friendly paradigm by adapting or finetuning a + +pre-trained foundation model to downstream dataset. + +We specify three major challenges when adapting pretrained foundation model to a new data distribution. First, traditional unsupervised domain adaptation [15] paradigm requires access to both source and target datasets which may not be feasible due to privacy issue and computation cost [34]. Second, updating all model weights for adaptation is often superior in performance, however, is constrained by the prohibitive memory cost due to the large model size [20]. Finally, unsupervised adaptation could be still very challenging due to the absence of label information on the target domain [60, 72, 75]. + +To tackle the above challenges, we propose a self-training based adaptation approach to synergize the exploitation of weak supervision and unlabeled data on target domain. Specifically, we first alleviate the dependence on source domain data by adopting a self-training based source-free domain adaptation strategy. The self-training approach first makes segmentation predictions, a.k.a. pseudo labels, on the target domain data. The pseudo labels are used for supervising the update of segmentation model. As self-training is fragile due to incorrect pseudo labels, a.k.a. confirmation bias [2], we introduce a frozen source model as the anchor network to regularize the update of segmentation model. To further mitigate the high computation cost of updating the full model weights, we apply a low-rank weight decomposition to encoder weights and the backpropagation flows through the low-rank shortcut only. Finally, to further improve the effectiveness of source-free domain adaptation, weak supervisions, e.g. sparse pointwise annotation, on the target domain are introduced to provide stronger cues for domain adaptation. We reveal that the weak supervisions are naturally compatible with the prompt encoder within SAM. With the weak supervisions as prompt, we are endowed with more localized and less ambiguous pseudo predictions for self-training. The adapted model has demonstrated much stronger generalization capability on multiple downstream tasks. + +We summarize the contributions of this work as follows. + +- We are motivated by the generalization issue of segment-anything (SAM) model to diverse downstream segmentation tasks and propose a task-agnostic solution to adapt SAM through self-training with no access to source dataset. +- We exploit weak supervisions, including bounding box, point-wise annotation and coarse segmentation masks, to improve the effectiveness of adaptation. The weak supervision are fully compatible with the prompt encoder of SAM. +- Extensive experiments on 5 types of downstream instance segmentation tasks demonstrate the effectiveness of the proposed weakly supervised adaptation approach. + +# 2. Related Work + +Image Segmentation Foundation Model: The success of deep learning is attributed to the increasing size and neural networks and huge amount of training data. Recent successful computer vision models, e.g. image segmentation and object detection, follow a practice of finetuning from encoder network pre-trained on large image dataset, e.g. ImageNet [10]. Despite achieving impressive results on standard benchmark datasets, e.g. Psacal VOC [13] and COCO [37], the zero-shot and few-shot generalization ability is often limited. Inspired by the revolutionizing language/vision-language foundation model pre-trained on web-scale datasets [4, 48, 74], a new opportunity awaits for developing a generalizable vision foundation model. This motivates the emergence of vision foundation model pretrained on huge dataset. SAM [27] and DINO v2 [44], to name a few. Among these foundation models, SAM stands out for its ability to enable zero-shot segmentation using prompt engineering. Therefore, we pay particular attention to SAM in this work. Since the inception of SAM, numerous attempts are made to validate the robustness of SAM under more challenging scenarios, such as medical images [42] [71], camouflaged objects [59], glass (transparent objects and mirrors) [18] and pose estimation [36]. Despite these early attempts to discover the weakness, there are very few matured solutions [5] to improve the generalization of SAM to challenging downstream tasks. In this work, we aim to fill this gap by proposing principled solutions to enhance the robustness of SAM against downstream tasks subject to significant distribution shift. + +Source-Free Domain Adaptation: Unsupervised Domain Adaptation (UDA)[15, 24, 41, 61, 73] has emerged as a means to address the domain shift between source training data and target testing data. This enables models to be trained on cost-effective and easily annotated data, facilitating the transfer to more valuable but challenging-to-label datasets. However, UDA methods face limitations when source domain data is inaccessible due to privacy concerns or storage constraints. In response to this, Source-Free Domain Adaptation (SFDA)[28, 33, 34, 39, 65, 68] has been proposed to reduce the reliance on source data in domain adaptation (DA) methods. SHOT [34] represents an early effort to alleviate domain shift without access to source data, achieved through self-training on unlabeled target data. Numerous prior works [1, 7, 11, 26, 35, 47, 50] have explored the effectiveness of a teacher-student like self-training architecture in domain shift mitigation. The similar self-training framework [22] simultaneously trains on multiple sets of augmented data, utilizing teacher-student cycle consistency for mutual learning of the two networks. Other methods generate source-like samples [30, 40, 46], construct intermediate domains [65, 69], or perturb target domains [25, 32, 66, 70] to enhance model generalization. + +![](images/297e2a5c5aaea891463d596993ab2ebf3d2edf76f802d7746e26ea8359de1758.jpg) +Figure 2. The proposed self-training architecture with anchor network regularization and contrastive loss regularization. Red arrows indicates the backpropagation flow. + +Recent approaches [46, 64] leverage contrast loss between target samples and source domain prototypes. Recent attempts to source-free domain adaptation for image segmentation aims to minimize feature discrepancy between source and target domains [3, 29, 40]. In this work, we aim to adapt SAM to downstream tasks without accessing to the source domain data to avoid the high computation overhead and potential privacy issues for foundation models to be released in the future. + +# Weakly Supervised Domain Adaptive Segmentation: + +Unsupervised domain adaptation often follows a self-training paradigm [34], which is limited by the quality of pseudo labels. Instead of relying on the pseudo predictions, weakly supervised domain adaptive semantic segmentation (WDASS) exploits limited weak supervisions in the form of bounding box, points or coarse segmentation masks [8, 9, 45, 63]. Among these works, [45] employs both image and point labels, suggesting an adversarial alignment of features at the pixel level to address WDASS. In contrast, [63] relies on bounding boxes as weak labels and employs adversarial learning to achieve domain-invariant features. Additionally, [9] utilizes self-training and a boundary loss to enhance performance in WDASS with coarse labels. More recently, [8] utilizes weak label for aligning the source-target features and outperforms previous methods to achieve competitive performance compared to supervised learning. We observe that the common weak supervisions are inherently compatible with the SAM model as prompt input. Therefore, we propose to adapt SAM with weak supervisions in a seamless way. + +# 3. Methodology + +In this section, we first provide an overview of segment-anything model. Then, we introduce the self-training based adaptation framework. We elaborate how weak supervision could help establish correspondence between pseudo predictions for effective self-training. Lastly, we introduce the low memory footprint way of updating model weights. + +# 3.1. Overview of Segment Anything Model + +The segment-anything model consists of three major components, the encoder network $z = f(x; \Theta)$ , prompt encoder $e = g(p; \Omega)$ and mask decoder $h(z, e; \Phi)$ . The image encoder is pre-trained using masked autoencoder (MAE) [19]. The whole SAM model is further fine-tuned on the web-scale labeled training set, SA-1B [27], with 1.1B labeled masks. A combination of focal loss and dice loss are used for training SAM. During inference, the testing image $x$ is first encoded by the image encoder $z = f(x; \Theta)$ . Given encoded prompts $e$ , a light-weight mask decoder makes three levels of segmentation predictions. In this work, we are motivated by the challenge of deploying SAM on many downstream tasks and propose to adapt SAM to downstream segmentation tasks with weak supervision without requiring access to source domain training data. + +# 3.2. Source-Free Adaptation as Self-Training + +Provided an unlabeled target domain dataset $\mathcal{D}_T = \{x_i\}$ and the pre-trained encoder network $f(x;\Theta)$ , we adopt a teacher-student architecture for self-training. As illustrated in Fig. 2, we maintain three encoder networks, namely the anchor network $f(x;\Theta^a)$ , the student network $f(x;\Theta^s)$ and the teacher network $f(x;\Theta^t)$ , where the student and teacher networks share the weights $\Theta^s = \Theta^t$ . For each sample $x_i$ , we apply one random weak data augmentation $\mathcal{A}_w(x_i)$ as the input to anchor and teacher networks, and one random strong data augmentation $\mathcal{A}_s(x_i)$ as the input to student network. Through the three encoder networks, three feature maps are obtained respectively, as $\mathcal{F}^a = f(\mathcal{A}_w(x_i),\Theta^a)$ , $\mathcal{F}^s = f(\mathcal{A}_s(x_i),\Theta^s)$ and $\mathcal{F}^t = f(\mathcal{A}_w(x_i),\Theta^t)$ , where $\mathcal{F} \in \mathbb{R}^{D \times H \times W}$ and $D$ refers to feature dimension. In the decoder network, given a number $N_p$ of prompts, e.g. bounding boxes, points or coarse segmentation masks, a set of foreground masks for the instance segmentation results would be deduced, $\mathcal{Y}^a = \{y_j^a\}_{j=1\dots N_p}$ , $\mathcal{Y}^s = \{y_j^s\}_{j=1\dots N_p}$ , $\mathcal{Y}^t = \{y_j^t\}_{j=1\dots N_p}$ , where each mask is then normalized between 0 and 1 by sigmoid function respectively, i.e. $m_j = \text{Sigmoid}(y_j)$ , $m_j \in [0,1]^{H \times W}$ . We + +![](images/dc88d42718fa8e1fb35f5f3b8e8e07c6f1b472f838e74e54a698e4af501abea2.jpg) +Figure 3. Illustration of contrastive loss between two views. + +further denote a binarized segmentation mask with a threshold of 0.5 as $\hat{m}_j = \mathbb{1}(m_j > 0.5),\hat{m}_j\in \{0,1\}^{H\times W}$ . Based on these notations, we elaborate three sets of adaptation objectives for self-training purpose. + +Teacher-Student Self-Training Loss: We first introduce the Self-Training loss to update student/teacher network. Self-Training is widely used in semi-supervised learning [52] and recently is demonstrated to be very effective for source-free domain adaptation [35]. In this work, we continue the idea of self-training in classification task and perform focal loss [38] and dice loss [43] for the supervision of student's outputs with binarized teacher's predictions as follows, where $\gamma$ controls the focus on hard training pixels and $\epsilon$ is a small value to avoid dividing by zero. + +$$ +\begin{array}{l} \mathcal {L} _ {s t} ^ {f o c a l} = - \sum_ {j = 1 \dots N _ {p}} \frac {1}{H W} \sum_ {h, w} \mathbb {1} \left(\hat {m} _ {j h w} ^ {t} = 1\right) \cdot \left(1 - m _ {j h w} ^ {s}\right) ^ {\gamma} \log \left(m _ {j h w} ^ {s}\right) \tag {1} \\ + \mathbb {1} (\hat {m} _ {j h w} ^ {t} = 0) \cdot m _ {j h w} ^ {s} ^ {\gamma} \log (1 - m _ {j h w} ^ {s}), \\ \end{array} +$$ + +$$ +\mathcal {L} _ {s t} ^ {d i c e} = \sum_ {j = 1 \dots N _ {p}} 1 - \frac {2 \sum_ {h , w} m _ {j h w} ^ {s} \cdot \hat {m} _ {j h w} ^ {t} + \epsilon}{\sum_ {h , w} m _ {j h w} ^ {s} + \sum_ {h , w} \hat {m} _ {j h w} ^ {t} + \epsilon}, \tag {2} +$$ + +Anchored Loss for Robust Regularization: Training the networks with self-training loss alone is vulnerable to the accumulation of incorrect pseudo labels predicted by teacher network, a.k.a. confirmation bias [2]. Observations are made that the performance will drop after long iterations of self-training alone [56]. Existing source-free domain adaptation approaches often adopt additional constraints to prevent the negative impact of self-training, e.g. uniform distribution over predictions [35]. Without making such explicit assumptions, we propose to introduce the regularization by an anchor loss which minimizes the dice loss between an anchor network, which has frozen source model weights, and student and teacher networks respectively in Eq. 3. The frozen anchor network serves as the knowledge inherited from source domain and too much deviation between the source model and self-training updated model is discouraged to prevent the model from collapsing. + +$$ +\mathcal {L} _ {\text {a n c h o r}} = \lambda_ {\text {s t u}} ^ {\text {d i c e}} \mathcal {L} ^ {\text {d i c e}} \left(m ^ {s}, \hat {m} ^ {a}\right) + \lambda_ {\text {t e a}} ^ {\text {d i c e}} \mathcal {L} ^ {\text {d i c e}} \left(m ^ {t}, \hat {m} ^ {a}\right). \tag {3} +$$ + +Contrastive Loss for Encoder Output Regularization: The above two training objectives are performed in the output space of the decoder. As we empirically revealed in the + +experiment section, updating encoder network is the most effective way to adapt SAM, it is necessary to apply regularization directly to the feature map as output from the encoder network. Specifically, as illustrated in Fig. 3, we first crop out each instance's feature $I_{j}$ from the feature map based on its prediction mask in anchor and teacher branches. + +$$ +I _ {j} = \frac {\sum_ {h , w} \bar {\mathcal {F}} _ {h w} \cdot \hat {m} _ {j h w}}{\sum_ {h , w} \hat {m} _ {j h w}}, \tag {4} +$$ + +where $\overline{\mathcal{F}}$ is the L2 normalized feature map, i.e. $\overline{\mathcal{F}}_{hw} = \frac{\mathcal{F}_{hw}}{|\mathcal{F}_{hw}|}$ . We further define the instance features, which are cropped out by the masks used the same prompt in two branches, as positive pairs, and the instances used different prompts as negative pairs to construct the contrast loss. The final contrastive loss is given as below, where $\tau$ is the temperature scaling. + +$$ +\mathcal {L} _ {\text {c o n t r a s t}} = - \log \frac {\sum_ {j} \exp \left(I _ {j} ^ {a} \cdot I _ {j} ^ {t} / \tau\right)}{\sum_ {j} \sum_ {j ^ {\prime} \neq j} \exp \left(I _ {j} ^ {a} \cdot I _ {j ^ {\prime}} ^ {t} / \tau\right)} \tag {5} +$$ + +Total Loss: We combine the above three loss functions as the final source-free domain adaptation loss. + +$$ +\mathcal {L} = \lambda_ {s t} ^ {f o c a l} \mathcal {L} _ {s t} ^ {f o c a l} + \mathcal {L} _ {s t} ^ {d i c e} + \mathcal {L} _ {\text {a n c h o r}} + \mathcal {L} _ {\text {c o n t r a s t}}. \tag {6} +$$ + +# 3.3. Prompt Generation for Self-Training + +The SAM segmentation requires prompt inputs to disambiguate the granularity of segmentation. The prompt engineering can be implemented in both fully automated way and by human interaction. + +Fully Automated Prompt for Self-Training: We first densely sample grid points with a spatial distance of 16 pixels as point prompt input. Initial stage segmentation masks $\{\hat{m}_j\}_{j = 1\dots N_{init}}$ are generated by the anchor network with the grid point prompts. We follow the fully automated segmentation introduced by SAM [27] to prune out masks with low IoU score and low stability score, followed by NMS suppression. To enable self-training and regularization between different branches, we further generate a fixed set of prompt $\{e_j\}_{j = 1\dots N_p}$ from $\{\hat{m}_j\}_{j = 1\dots N_{init}}$ as input to all three branches. As such, the segmentation outputs $\mathcal{Y}^a$ , $\mathcal{Y}^s$ and $\mathcal{Y}^t$ are of the same length with exact one-to-one correspondence. + +Weak Supervision as Prompt: Despite automatic segmentation can be enabled by sampling a grid of point prompts over the image and filtering out low quality and duplicated masks, the quality of segmentation is relatively poor and may contain many false positive predictions, making self-training less effective. Therefore, following prior weakly supervised domain adaptation works [9], we propose to use three types of weak supervisions, including bounding box, sparse point annotation and coarse segmentation mask. Fortunately, in the context of SAM, these weak supervisions perfect match with the prompt inputs which allow seamless integration of weak supervision for adapting SAM. + +# 3.4. Low-Rank Weights Update + +The enormous size of backbone network prohibits updating all model weights with large batchsize. However, many existing studies suggest the update of encoder network weights is an effective way of adapting pre-trained models [35, 54]. To enable updating the backbone network with larger batchsize, we opt for a computation friendly low-rank updating approach [20]. For each weight in the encoder network $\theta \in \mathbb{R}^{d_i \times d_o}$ , we use a low-rank approximation $\omega = AB$ where $A \in \mathbb{R}^{d_i \times r}$ and $A \in \mathbb{R}^{r \times d_o}$ with $r$ indicating the rank. We can achieve a compression rate of $r(d_i + d_o) / d_i \cdot d_o$ . Only $A$ and $B$ are updated via backpropagation during adaptation to reduce memory footprint. At inference stage, the weight is reconstructed by combining the low rank reconstruction and original weight, $\theta = \theta + AB$ . + +# 4. Experiment + +In this section, we first introduce the experiment settings and downstream tasks for adapting SAM model. We provide detailed comparisons to state-of-the-art methods and qualitative results. Finally, we analyze the effectiveness of individual components and specific designs for the network. + +# 4.1. Datasets + +The source domain training set, SA-1B, was mainly constructed by collecting from natural environments. In this work, we identified five types of downstream segmentation tasks, some of which feature a drastic distribution shift from SA-1B, for evaluation, covering natural clean images, natural corrupted images, medical images, camouflaged images and robotic images. We present the datasets evaluated for each type of downstream task in Tab. 1. + +Datasplit: We divide each downstream dataset into non-overlapping training and testing sets following the ratio established by [8]. The adaptation step is implemented on the training set. After the model is adapted, we evaluate the model on the held-out testing set. For adaptation to the Camouflaged Objects, following the training protocol in [5], we use the dataset COD10K (the training set of camouflaged images) for training, and use the test set of CAMO, COD10K and the entire CHAMELEON dataset for performance evaluation. + +# 4.2. Experiment Details + +Segment-Anything Model: We adopt ViT-B [12] as the encoder network due to memory constraint. The standard prompt encoder and mask decoder are adopted. + +Prompt Generation: We first provide details for generating prompt at both training stages. All training prompts are calculated from ground-truth segmentation mask, simulating the human interactions as weak supervision. Specifically, we extract the minimal bounding box that covers the whole instance segmentation mask as box prompt. The point prompt is created as randomly selecting 5 positive + +points within ground-truth instance segmentation mask and 5 negative points outside ground-truth mask. The coarse segmentation mask is simulated by fitting a polygon to the ground-truth mask. We choose the number of vertices as $P / 20$ with $P$ indicating the perimeter of mask. The minimal number of vertices is 3. We use the same way to generate testing prompt on the testing data. This practice guarantees fair evaluation of SAM model which requires prompt input for segmentation. + +Evaluation Metrics: We report the mIoU as evaluation metrics. For each input prompt, the IoU is calculated between the ground-truth segmentation mask and predicted mask. The mIoU averages over the IoU of all instances. + +Competing Methods: We evaluate multiple source-free domain adaptation approaches and one state-of-the-art weakly supervised domain adaptive segmentation approach. In specific, direct testing the pre-trained model (Direct) with fixed prompt inputs is prone to the distribution shift and may not perform well on target datasets with significant shift. TENT [62] is a vanilla test-time adaptation method which optimizes an entropy loss for adapting to target domain. SHOT [35] employs pseudo label and applies uniform distribution assumption for source-free domain adaptation. Soft Teacher [67] was originally developed for semi-supervised image segmentation. We adapt Soft Teacher for domain adaptation by keeping the self-training component. TRIBE [55] proposed a strong baseline for generic test-time adaptation on continual and class imbalanced domain shifts. We adapt TRIBE for domain adaptive segmentation by replacing the training losses. DePT [16] inserts visual prompts into a visual Transformer and adjusts these source-initialized prompts solely during the adaptation process without accessing the source data. WDASS [8] developed a weakly supervised domain adaptive segmentation method. We also evaluate the upperbound of adapting SAM by fine-tuning with ground-truth segmentation masks, which is dubbed as Supervised. Finally, we evaluate our weakly supervised domain adaptation method as Ours. All the competing methods use the same backbone, i.e. the ViT-B from SAM. + +Hyperparameters: We finetune LoRA module of the ViTB image encoder by Adam optimizer for all experiments. We set the batchsize to 4, distributed over four RTX3090 GPUs, and the learning rate to 0.0001 with a weight decay of 0.0001. For Self-Training loss, we set the hyperparameters $\gamma$ and $\epsilon$ of $\mathcal{L}_{st}^{focal}$ and $\mathcal{L}_{st}^{dice}$ to 2 and 1 respectively. $\lambda_{st}^{focal}$ is set to 20, which is the coefficients of $\mathcal{L}_{st}^{focal}$ . For Anchor loss, the coefficients of two dice losses are denoted as $\lambda_{stu}^{dice}$ and $\lambda_{tea}^{dice}$ , both of which equal 0.5. For Contrast loss, we set the temperature $\tau$ to 0.3. We have set the low rank of the LoRA module for the image encoder to 4. We apply strong and weak data augmentations for self-training and choices for augmentation follows [53, 67]. + +Table 1. Dataset and datasplit used in this work. + +
Natural ImagesCorrupted ImagesMedical ImagesCamouflaged ObjectsRobotic Images
COCO [37]Pascal VOC [13]COCO-Ckvasir-SEG [23]ISIC [17]CHAMELEON [51]CAMO [31]COD10K [14]OCID [57]OSD [49]
# Training4246249742468349004040197256
# Testing70641670616637974250202632855
+ +Table 2. Adaptation results on COCO-C dataset using bounding box prompt. + +
MethodBritContrDefocElastFogFrostGaussGlassImpulJpegMotnPixelShotSnowZoomAvg
Direct72.8357.3464.4769.3672.3970.5067.2064.4367.6568.2362.7268.6067.4469.0258.8066.73
TENT76.0261.5167.4870.8874.8973.8869.0167.1069.2870.2565.4570.8169.9672.3762.5969.43
SHOT73.8459.0965.9169.5773.9872.5168.3066.0968.6169.4564.5670.4868.7771.0360.1768.16
Soft Teacher73.9062.1265.4171.3272.1673.2768.8467.4968.7370.1866.8869.7970.0873.3364.8869.23
TRIBE76.4060.8666.1972.7275.0875.1470.3466.6670.8372.4265.9470.2470.6674.2264.5670.15
DePT69.1557.2659.0866.8058.7366.7566.7862.7465.6566.3961.6666.6567.5766.6258.2164.42
WDASS76.2160.5767.0772.3475.9774.6369.8467.8869.9271.3666.2571.9970.3272.2563.6170.01
OURS78.5061.0566.9973.9377.0976.1072.0268.2171.2972.7766.3370.9070.2875.0765.3371.05
Supervised78.8674.8172.0474.3278.0177.1473.4372.1274.0875.3071.3975.1574.2576.3468.0474.35
+ +# 4.3. Quantitative Evaluations + +In this section, we report the quantitative evaluations on the 5 types of target datasets. For each dataset, we also report the adaptation results with weak supervision in the form of bounding box (box), sparse points (point) and coarse segmentation mask (poly). + +Adaptation to Corrupted Images: Visual corruptions often occur due to sensor fault, bad weather conditions, etc. As seen from Tab. 2, without any adaptation, Direct testing is significantly worse than the upperbound. With weakly supervisions, all methods could improve over direct testing, in particular, our proposed method outperforms all competing adaptation methods on 10 out of 15 types of corruptions. + +Adaptation to Natural Images: We then present the results of adapting SAM to natural images in Tab. 3. For each type of weak supervision, we use the same type of prompt on the testing set. Despite the distribution gap between SA-1B and the target natural images, we observe significant performance gap between Supervised upperbound and Direct baseline, e.g. with box level supervision, there is $5 - 10\%$ gap in IoU. When weak supervision is provided, both state-of-the-art generic source-free domain adaptation methods and weakly supervised domain adaptive segmentation method improve the generalization on all three types of weak supervisions. Finally, our proposed weakly supervised method achieves a remarkable improvement over all competing methods. The results with box weak supervision is even approaching the fully supervised upperbound. + +Adaptation to Medical Images: Segmentation for medical images is a major application of foundation models. Our empirical observations in Tab. 4 on two medical segmentation datasets suggest that direct applying pre-trained SAM is suboptimal. With weakly supervised adaptation, the segmentation accuracy is greatly improved. We observe the improvement to be particularly significant with point and box which are relatively easy to obtain due to the low labeling cost. + +Adaptation to Camouflaged Objects: We further eval + +Table 3. Adaptation results on natural clean image datasets. + +
MethodCOCO 2017Pascal VOC
boxpointpolyboxpointpoly
Direct74.2955.0665.6469.2169.2160.79
TENT78.2152.9971.5180.2474.9765.03
SHOT75.1858.4669.2679.8074.2663.38
Soft Teacher75.9443.3668.2772.9356.0962.20
TRIBE77.5649.5670.9978.8769.2165.39
DePT71.0037.3563.2774.0942.9959.94
WDASS77.2960.5570.1980.1276.1566.98
OURS80.1262.0972.3380.2774.1566.72
Supervised81.5069.7773.3981.2376.9871.32
+ +Table 4. Adaptation results on medical image segmentation datasets. + +
Methodkvasir-SEGISIC
boxpointpolyboxpointpoly
Direct81.5962.3054.0366.7453.4262.82
TENT82.4761.8462.9771.7653.4667.12
SHOT82.3063.7661.3471.9955.9966.86
Soft Teacher84.1273.5358.1575.7454.9572.29
TRIBE85.0573.0364.6172.6150.3667.99
DePT81.9152.0661.5578.4346.7972.75
WDASS84.0163.7864.7874.2355.6367.84
OURS85.4775.2367.4080.0162.1275.36
Supervised85.8977.5481.6481.6279.8180.26
+ +uate on adapting SAM to camouflaged object detection. We evaluate on three camouflaged object detection datasets with results reported in Tab. 5. Preliminary studies revealed that SAM is particularly vulnerable to camouflaged objects [59] due to the low contrast between background and foreground. We make similar observations here that even with the help of prompt inputs at testing stage, Direct inference suffers a lot, achieving less than $66\%$ mIoU. When weakly labeled data are used for adaptation, we observe very significant improvements, with point prompt only we improved by a staggering $35\%$ in mIoU on the CHAMELEON dataset. Our proposed method is also consistently better than all competing methods on all types of weak supervisions. + +Adaptation to Robotic Images: Finally, we evaluate adapting SAM to image collected from robotic environ + +Table 5. Adaptation results on camouflaged object datasets. + +
MethodCHAMELEONCAMOCOD10K
boxpointpolyboxpointpolyboxpointpoly
Direct51.3239.3745.7862.7257.4350.8566.3263.6140.04
TENT65.4854.5353.0671.2459.5960.2969.3661.9443.36
SHOT68.6062.4754.3671.6162.7858.7269.0965.2542.38
Soft Teacher65.9244.1746.7262.3048.6451.2666.3250.0432.27
TRIBE71.0052.8054.9966.0061.9760.5467.8463.6242.75
DePT54.4833.4642.4755.4433.0748.6359.3234.0635.51
WDASS71.9162.4056.8071.2563.3962.2971.4265.6143.93
OURS75.9474.0066.8373.4265.5562.9071.9370.5545.87
Supervised78.0585.8668.3879.1777.0167.1278.0678.4464.90
+ +ments where segmenting out the spatial extent of individual objects is essential for interactions. As seen from the results in Tab. 6, adapting SAM to robotic images with weak supervision further increase the segmentation accuracy. The improvement is more noticeable with point and polygon weak supervisions. + +Table 6. Adaptation results on robotic image datasets. + +
MethodOCIDOSD
boxpointpolyboxpointpoly
Direct86.3571.4172.8187.6278.8680.77
TENT87.7766.6177.5388.1080.5387.85
SHOT88.0674.3976.2588.0980.5287.86
Soft Teacher84.9868.4673.7590.4180.4987.00
TRIBE86.7767.8676.5090.4280.5487.84
DePT82.0056.5270.9281.8469.0682.50
WDASS87.6877.1376.7088.0780.5288.19
OURS88.0980.1477.4192.1180.5189.72
Supervised91.2489.2279.2392.1482.4190.83
+ +# 4.4. Qualitative Evaluations + +We present the qualitative comparisons of segmentation results for selected examples in Fig. 4. We make the following observations from the results. Evaluating pre-trained SAM (SAM) on COCO with both box and point prompt exhibits very fine-grained segmentation results. However, the model is overly sensitive to the high contrast regions, e.g. the hair for the girl and the toppings of pizza are missing from the segmentation mask. With the proposed weakly supervised adaptation approach, our method is able to generate more smoothed segmentation mask and the mask better reflects the semantic boundary. Similar observations are made from the medical image segmentation dataset. Without adapting the SAM model, segmentation results are either too conservative with low recall or expanding beyond the semantic boundary. With our weakly supervised adaptation, SAM is able to produce high fidelity results. We further present results on camouflaged segmentation task (CAMO). Without adaptation, SAM fails to segment out the spider's belly and confuses the snow background with the harp seal in the foreground. Our weakly adapted SAM successfully segments out the spider's belly and produces high quality mask for the harp seal. Finally, two examples from OCID dataset suggest that the pre-trained SAM tends to over-segment, e.g. missing the open whole for the tissue box, or confusing adjacent objects, e.g. merging the pen with the folder label. With weakly supervised adaptation SAM picks up the + +Table 7. Ablation studies of the proposed weakly supervised adaptation method on COCO dataset. + +
Weak Sup.Self-Train.AnchorCont. Lossboxpointpoly
original SAM74.2956.3665.42
✓✓58.8832.5155.03
✓✓✓79.6557.2570.49
✓✓✓62.9522.8756.91
✓✓✓✓80.1262.0972.33
✓✓✓76.1847.6370.44
+ +Table 8. Adaptation results on cross-prompt testing scenarios. + +
Tr. Weak. Sup.boxpointpolygon
Te. Promptboxpointpolyboxpointpolyboxpointpoly
Direct74.2954.7666.7574.2954.6466.7574.2954.7665.64
TENT78.2154.8368.8252.9952.9968.5877.0853.9071.51
WDASS77.2958.7868.9474.6960.5569.1575.2755.2770.19
OURS80.1252.2872.0776.4962.0971.0278.5752.8872.33
+ +semantic meaning and produces segmentation results that better aligns with human intention. + +# 4.5. Ablation Study + +In this section, we analyze the effectiveness of individual components on COCO dataset. As presented in Tab. 7, when self-training is applied alone, we observe a significant performance drop (74.29% → 58.88% with box weak supervision), suggesting the severity of confirmation bias. This issue can be well remedied when the anchor loss regularization is applied. Self-training with anchored regularization already improves the performance of SAM after adaptation. Finally, the contrastive loss directly regularizes the encoder network's output and contributes with additional improvement of segmentation accuracy. We also investigate the final self-training architecture without any weak supervision, i.e. the pseudo label masks are generated with grid point prompt. The results after adaptation is slightly worse than with weak supervision but consistently better than without adaptation on both box and coarse mask testing prompts. Nevertheless, the results with point prompt performs even worse than without adaptation, suggesting the necessity of weakly supervised adaptation. + +# 4.6. Additional Analysis + +Generalization to Cross-Prompt Testing: We further investigate the effectiveness of adaptation by testing with all three types of prompts. Specifically, we compare with the best (WDASS) and second best (TENT) methods with results presented in Tab. 8. Apart from using point as testing prompt, our methods consistently improves the performance even though the testing prompt is different from training weak supervision. + +Effectiveness of Updating Different Components: There are many options for updating the pre-trained SAM model. Given limited computing resources, choosing the appropriate components of network to update is crucial to optimize the generalization performance. In this section, we investigate several options of network components to update during adaptation. Full finetune means finetuning the whole encoder. MaskDecoder finetune the whole decoder + +![](images/2bd37e97d82e959a86b26f43c1ff352efd4a3e50f2bf0abe8ed3d7022373dd0a.jpg) +Figure 4. qualitative results on some selected examples. Three types of prompts at testing stage are visualized for reference. + +of SAM without additional redundant learnable parameters. LayerNorm finetune the all layer norms of the SAM image encoder. LoRA finetunes the encoder network in through low-rank decomposition only. EVP use the Embedding Tune and the HFC Tune to tune the extracted features by image encoder. We present the investigation on the COCO dataset with bounding boxes as weak supervision in Tab. 9. In particular, we have also explored the impact of different combinations of components, e.g. MaskDecoder + LoRA, LoRA + EVP, and so on. The results suggest LoRA finetuning the encoder network alone yields the best performance. + +# 5. Conclusion + +We studies the generalization of Segment-Anything model for multiple downstream image segmentation tasks. A tangible solution with no access to source dataset and low memory cost was proposed to adapt SAM to downstream data in a source-free domain adaptation manner. The proposed method is naturally compatible with weak supervisions which could substantially improve the efficacy of adaptation. Extensive evaluations on 10 datasets from 5 types of downstream tasks suggest the proposed adapta + +Table 9. Adaptation results produced by finetuning different modules. + +
Finetuning ModuleIoU
None74.30
Full finetune78.54
MaskDecoder76.81
LayerNorm79.30
Low-Rank Adaptation (LoRA)80.12
Explicit Visual Prompt (EVP)77.38
MaskDecoder + LoRA77.28
MaskDecoder + EVP76.83
LoRA + EVP79.47
LoRA + LayerNorm79.35
MaskDecoder + LoRA + EVP77.31
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In IEEE/CVF International Conference on Computer Vision, 2019. 2 \ No newline at end of file diff --git a/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/images.zip b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..10aa9c4d28f4f99f342a3a52a8dd734e18ae0e42 --- /dev/null +++ b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a1739dd3c1d863843f79f2d97be90764d84129728ee0bea9d2f716ee1c33f3e8 +size 736504 diff --git a/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/layout.json b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..bd54ee44c7fb3ce17033f1bc59475fcb7feb669a --- /dev/null +++ b/2024/Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation/layout.json @@ -0,0 +1,8290 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 75, + 103, + 520, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 103, + 520, + 140 + ], + "spans": [ + { + "bbox": [ + 75, + 103, + 520, + 140 + ], + "type": "text", + "content": "Improving the Generalization of Segmentation Foundation Model under Distribution Shift via Weakly Supervised Adaptation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "spans": [ + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "content": "Haojie Zhang" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "content": " Yongyi Su" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "content": " Xun Xu" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "inline_equation", + "content": "^{2\\dagger}" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "content": " Kui Jia" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "content": "South China University of Technology \n" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 134, + 160, + 459, + 219 + ], + "type": "text", + "content": "Institute for Infocomm Research, A\\*STAR \nhool of Data Science, The Chinese University of Hong Kong, Shenz" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 270, + 290, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 547 + ], + "type": "text", + "content": "The success of large language models has inspired the computer vision community to explore image segmentation foundation model that is able to zero/few-shot generalize through prompt engineering. Segment-Anything (SAM), among others, is the state-of-the-art image segmentation foundation model demonstrating strong zero/few-shot generalization. Despite the success, recent studies reveal the weakness of SAM under strong distribution shift. In particular, SAM performs awkwardly on corrupted natural images, camouflaged images, medical images, etc. Motivated by the observations, we aim to develop a self-training based strategy to adapt SAM to target distribution. Given the unique challenges of large source dataset, high computation cost and incorrect pseudo label, we propose a weakly supervised self-training architecture with anchor regularization and low-rank finetuning to improve the robustness and computation efficiency of adaptation. We validate the effectiveness on 5 types of downstream segmentation tasks including natural clean/corrupted images, medical images, camouflaged images and robotic images. Our proposed method is task-agnostic in nature and outperforms pre-trained SAM and state-of-the-art domain adaptation methods on almost all downstream tasks with the same testing prompt inputs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 559, + 128, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 128, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 128, + 571 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "content": "The success of large language models is partially attributed to the strong capability of zero-shot generalization. This has called for numerous attention into developing foundation model for computer vision tasks where one of the key concern also lies in the generalization ability [26, 44, 48]. In particular, as a promptable image segmentation foundation model with strong zero-shot generalization, the Segment-Anything model (SAM) [27] was developed by training on billions of annotated masks. Despite the overwhelming size" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 246, + 549, + 395 + ], + "blocks": [ + { + "bbox": [ + 307, + 246, + 549, + 395 + ], + "lines": [ + { + "bbox": [ + 307, + 246, + 549, + 395 + ], + "spans": [ + { + "bbox": [ + 307, + 246, + 549, + 395 + ], + "type": "image", + "image_path": "c158a82f0d98d0253c02127379fa4b2711ef95ed0c559ab269b37964643a73b4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 405, + 547, + 449 + ], + "lines": [ + { + "bbox": [ + 305, + 405, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 547, + 449 + ], + "type": "text", + "content": "Figure 1. Segment Anything Model was pre-trained on a large-scale dataset but exhibits awkward performance on diverse downstream segmentation tasks. We adapt SAM through weak supervision to enhance its generalization capabilities." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 458, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 547, + 567 + ], + "type": "text", + "content": "of dataset used for training, SAM was found to behave awkwardly on certain out-of-distribution downstream tasks, including camouflaged segmentation, medical segmentation, adversarial attacks, visual corruptions, etc. [5, 21]. This is likely caused by the distribution shift between the training data, i.e. the SA-1B dataset [27], and the challenging testing datasets. These observations motivate us to explore tangible solutions to make SAM more robust against real-world and more diverse downstream tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "Traditional paradigm towards improving model robustness and generalization often involves costly re-training. Methods are frequently customized to combat specific domain shifts. For example, domain randomization was developed to improve generalization across real testing domains [6], while adversarial training is commonly used to enhance robustness against attacks [58]. Applying these techniques to large foundation models is nonetheless impractical due to the enormous computing resources required for training the model on the web-scale training data. Therefore, instead of re-training the model, we opt for a more computation friendly paradigm by adapting or finetuning a" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 131, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 131, + 703 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 131, + 703 + ], + "type": "text", + "content": "* Equal contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 61, + 703, + 242, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 242, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 242, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 61, + 703, + 242, + 712 + ], + "type": "text", + "content": " Correspondence to Xun Xu: alex.xun.xu@gmail.com." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23385" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 261, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 261, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 261, + 83 + ], + "type": "text", + "content": "pre-trained foundation model to downstream dataset." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 287, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 287, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 287, + 218 + ], + "type": "text", + "content": "We specify three major challenges when adapting pretrained foundation model to a new data distribution. First, traditional unsupervised domain adaptation [15] paradigm requires access to both source and target datasets which may not be feasible due to privacy issue and computation cost [34]. Second, updating all model weights for adaptation is often superior in performance, however, is constrained by the prohibitive memory cost due to the large model size [20]. Finally, unsupervised adaptation could be still very challenging due to the absence of label information on the target domain [60, 72, 75]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 221, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 289, + 533 + ], + "type": "text", + "content": "To tackle the above challenges, we propose a self-training based adaptation approach to synergize the exploitation of weak supervision and unlabeled data on target domain. Specifically, we first alleviate the dependence on source domain data by adopting a self-training based source-free domain adaptation strategy. The self-training approach first makes segmentation predictions, a.k.a. pseudo labels, on the target domain data. The pseudo labels are used for supervising the update of segmentation model. As self-training is fragile due to incorrect pseudo labels, a.k.a. confirmation bias [2], we introduce a frozen source model as the anchor network to regularize the update of segmentation model. To further mitigate the high computation cost of updating the full model weights, we apply a low-rank weight decomposition to encoder weights and the backpropagation flows through the low-rank shortcut only. Finally, to further improve the effectiveness of source-free domain adaptation, weak supervisions, e.g. sparse pointwise annotation, on the target domain are introduced to provide stronger cues for domain adaptation. We reveal that the weak supervisions are naturally compatible with the prompt encoder within SAM. With the weak supervisions as prompt, we are endowed with more localized and less ambiguous pseudo predictions for self-training. The adapted model has demonstrated much stronger generalization capability on multiple downstream tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 536, + 286, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 536, + 286, + 547 + ], + "spans": [ + { + "bbox": [ + 59, + 536, + 286, + 547 + ], + "type": "text", + "content": "We summarize the contributions of this work as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 556, + 286, + 711 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 556, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 556, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 556, + 286, + 613 + ], + "type": "text", + "content": "- We are motivated by the generalization issue of segment-anything (SAM) model to diverse downstream segmentation tasks and propose a task-agnostic solution to adapt SAM through self-training with no access to source dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 616, + 286, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 286, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 286, + 673 + ], + "type": "text", + "content": "- We exploit weak supervisions, including bounding box, point-wise annotation and coarse segmentation masks, to improve the effectiveness of adaptation. The weak supervision are fully compatible with the prompt encoder of SAM." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 675, + 286, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 675, + 286, + 711 + ], + "spans": [ + { + "bbox": [ + 47, + 675, + 286, + 711 + ], + "type": "text", + "content": "- Extensive experiments on 5 types of downstream instance segmentation tasks demonstrate the effectiveness of the proposed weakly supervised adaptation approach." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 88, + 545, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 88, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 88, + 545, + 435 + ], + "type": "text", + "content": "Image Segmentation Foundation Model: The success of deep learning is attributed to the increasing size and neural networks and huge amount of training data. Recent successful computer vision models, e.g. image segmentation and object detection, follow a practice of finetuning from encoder network pre-trained on large image dataset, e.g. ImageNet [10]. Despite achieving impressive results on standard benchmark datasets, e.g. Psacal VOC [13] and COCO [37], the zero-shot and few-shot generalization ability is often limited. Inspired by the revolutionizing language/vision-language foundation model pre-trained on web-scale datasets [4, 48, 74], a new opportunity awaits for developing a generalizable vision foundation model. This motivates the emergence of vision foundation model pretrained on huge dataset. SAM [27] and DINO v2 [44], to name a few. Among these foundation models, SAM stands out for its ability to enable zero-shot segmentation using prompt engineering. Therefore, we pay particular attention to SAM in this work. Since the inception of SAM, numerous attempts are made to validate the robustness of SAM under more challenging scenarios, such as medical images [42] [71], camouflaged objects [59], glass (transparent objects and mirrors) [18] and pose estimation [36]. Despite these early attempts to discover the weakness, there are very few matured solutions [5] to improve the generalization of SAM to challenging downstream tasks. In this work, we aim to fill this gap by proposing principled solutions to enhance the robustness of SAM against downstream tasks subject to significant distribution shift." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "content": "Source-Free Domain Adaptation: Unsupervised Domain Adaptation (UDA)[15, 24, 41, 61, 73] has emerged as a means to address the domain shift between source training data and target testing data. This enables models to be trained on cost-effective and easily annotated data, facilitating the transfer to more valuable but challenging-to-label datasets. However, UDA methods face limitations when source domain data is inaccessible due to privacy concerns or storage constraints. In response to this, Source-Free Domain Adaptation (SFDA)[28, 33, 34, 39, 65, 68] has been proposed to reduce the reliance on source data in domain adaptation (DA) methods. SHOT [34] represents an early effort to alleviate domain shift without access to source data, achieved through self-training on unlabeled target data. Numerous prior works [1, 7, 11, 26, 35, 47, 50] have explored the effectiveness of a teacher-student like self-training architecture in domain shift mitigation. The similar self-training framework [22] simultaneously trains on multiple sets of augmented data, utilizing teacher-student cycle consistency for mutual learning of the two networks. Other methods generate source-like samples [30, 40, 46], construct intermediate domains [65, 69], or perturb target domains [25, 32, 66, 70] to enhance model generalization." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "23386" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 516, + 222 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 516, + 222 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 516, + 222 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 516, + 222 + ], + "type": "image", + "image_path": "297e2a5c5aaea891463d596993ab2ebf3d2edf76f802d7746e26ea8359de1758.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "type": "text", + "content": "Figure 2. The proposed self-training architecture with anchor network regularization and contrastive loss regularization. Red arrows indicates the backpropagation flow." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 257, + 288, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 288, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 288, + 364 + ], + "type": "text", + "content": "Recent approaches [46, 64] leverage contrast loss between target samples and source domain prototypes. Recent attempts to source-free domain adaptation for image segmentation aims to minimize feature discrepancy between source and target domains [3, 29, 40]. In this work, we aim to adapt SAM to downstream tasks without accessing to the source domain data to avoid the high computation overhead and potential privacy issues for foundation models to be released in the future." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 377 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 377 + ], + "type": "text", + "content": "Weakly Supervised Domain Adaptive Segmentation:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 378, + 288, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 378, + 288, + 617 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 288, + 617 + ], + "type": "text", + "content": "Unsupervised domain adaptation often follows a self-training paradigm [34], which is limited by the quality of pseudo labels. Instead of relying on the pseudo predictions, weakly supervised domain adaptive semantic segmentation (WDASS) exploits limited weak supervisions in the form of bounding box, points or coarse segmentation masks [8, 9, 45, 63]. Among these works, [45] employs both image and point labels, suggesting an adversarial alignment of features at the pixel level to address WDASS. In contrast, [63] relies on bounding boxes as weak labels and employs adversarial learning to achieve domain-invariant features. Additionally, [9] utilizes self-training and a boundary loss to enhance performance in WDASS with coarse labels. More recently, [8] utilizes weak label for aligning the source-target features and outperforms previous methods to achieve competitive performance compared to supervised learning. We observe that the common weak supervisions are inherently compatible with the SAM model as prompt input. Therefore, we propose to adapt SAM with weak supervisions in a seamless way." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 630, + 129, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 129, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 129, + 643 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 645, + 287, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 287, + 717 + ], + "type": "text", + "content": "In this section, we first provide an overview of segment-anything model. Then, we introduce the self-training based adaptation framework. We elaborate how weak supervision could help establish correspondence between pseudo predictions for effective self-training. Lastly, we introduce the low memory footprint way of updating model weights." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 257, + 507, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 507, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 507, + 269 + ], + "type": "text", + "content": "3.1. Overview of Segment Anything Model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": "The segment-anything model consists of three major components, the encoder network " + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "inline_equation", + "content": "z = f(x; \\Theta)" + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": ", prompt encoder " + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "inline_equation", + "content": "e = g(p; \\Omega)" + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": " and mask decoder " + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "inline_equation", + "content": "h(z, e; \\Phi)" + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": ". The image encoder is pre-trained using masked autoencoder (MAE) [19]. The whole SAM model is further fine-tuned on the web-scale labeled training set, SA-1B [27], with 1.1B labeled masks. A combination of focal loss and dice loss are used for training SAM. During inference, the testing image " + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": " is first encoded by the image encoder " + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "inline_equation", + "content": "z = f(x; \\Theta)" + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": ". Given encoded prompts " + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 269, + 545, + 449 + ], + "type": "text", + "content": ", a light-weight mask decoder makes three levels of segmentation predictions. In this work, we are motivated by the challenge of deploying SAM on many downstream tasks and propose to adapt SAM to downstream segmentation tasks with weak supervision without requiring access to source domain training data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 449, + 518, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 518, + 462 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 518, + 462 + ], + "type": "text", + "content": "3.2. Source-Free Adaptation as Self-Training" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": "Provided an unlabeled target domain dataset " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T = \\{x_i\\}" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " and the pre-trained encoder network " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "f(x;\\Theta)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", we adopt a teacher-student architecture for self-training. As illustrated in Fig. 2, we maintain three encoder networks, namely the anchor network " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "f(x;\\Theta^a)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", the student network " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "f(x;\\Theta^s)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " and the teacher network " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "f(x;\\Theta^t)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", where the student and teacher networks share the weights " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\Theta^s = \\Theta^t" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ". For each sample " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", we apply one random weak data augmentation " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_w(x_i)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " as the input to anchor and teacher networks, and one random strong data augmentation " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_s(x_i)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " as the input to student network. Through the three encoder networks, three feature maps are obtained respectively, as " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^a = f(\\mathcal{A}_w(x_i),\\Theta^a)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^s = f(\\mathcal{A}_s(x_i),\\Theta^s)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^t = f(\\mathcal{A}_w(x_i),\\Theta^t)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F} \\in \\mathbb{R}^{D \\times H \\times W}" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " refers to feature dimension. In the decoder network, given a number " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "N_p" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": " of prompts, e.g. bounding boxes, points or coarse segmentation masks, a set of foreground masks for the instance segmentation results would be deduced, " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}^a = \\{y_j^a\\}_{j=1\\dots N_p}" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}^s = \\{y_j^s\\}_{j=1\\dots N_p}" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}^t = \\{y_j^t\\}_{j=1\\dots N_p}" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", where each mask is then normalized between 0 and 1 by sigmoid function respectively, i.e. " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "m_j = \\text{Sigmoid}(y_j)" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "inline_equation", + "content": "m_j \\in [0,1]^{H \\times W}" + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": ". We" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23387" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 289, + 159 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 289, + 159 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 289, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 289, + 159 + ], + "type": "image", + "image_path": "dc88d42718fa8e1fb35f5f3b8e8e07c6f1b472f838e74e54a698e4af501abea2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 165, + 274, + 176 + ], + "lines": [ + { + "bbox": [ + 56, + 165, + 274, + 176 + ], + "spans": [ + { + "bbox": [ + 56, + 165, + 274, + 176 + ], + "type": "text", + "content": "Figure 3. Illustration of contrastive loss between two views." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 183, + 286, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 183, + 286, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 286, + 231 + ], + "type": "text", + "content": "further denote a binarized segmentation mask with a threshold of 0.5 as " + }, + { + "bbox": [ + 46, + 183, + 286, + 231 + ], + "type": "inline_equation", + "content": "\\hat{m}_j = \\mathbb{1}(m_j > 0.5),\\hat{m}_j\\in \\{0,1\\}^{H\\times W}" + }, + { + "bbox": [ + 46, + 183, + 286, + 231 + ], + "type": "text", + "content": ". Based on these notations, we elaborate three sets of adaptation objectives for self-training purpose." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "type": "text", + "content": "Teacher-Student Self-Training Loss: We first introduce the Self-Training loss to update student/teacher network. Self-Training is widely used in semi-supervised learning [52] and recently is demonstrated to be very effective for source-free domain adaptation [35]. In this work, we continue the idea of self-training in classification task and perform focal loss [38] and dice loss [43] for the supervision of student's outputs with binarized teacher's predictions as follows, where " + }, + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "type": "text", + "content": " controls the focus on hard training pixels and " + }, + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 232, + 286, + 351 + ], + "type": "text", + "content": " is a small value to avoid dividing by zero." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 351, + 286, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 351, + 286, + 386 + ], + "spans": [ + { + "bbox": [ + 56, + 351, + 286, + 386 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {s t} ^ {f o c a l} = - \\sum_ {j = 1 \\dots N _ {p}} \\frac {1}{H W} \\sum_ {h, w} \\mathbb {1} \\left(\\hat {m} _ {j h w} ^ {t} = 1\\right) \\cdot \\left(1 - m _ {j h w} ^ {s}\\right) ^ {\\gamma} \\log \\left(m _ {j h w} ^ {s}\\right) \\tag {1} \\\\ + \\mathbb {1} (\\hat {m} _ {j h w} ^ {t} = 0) \\cdot m _ {j h w} ^ {s} ^ {\\gamma} \\log (1 - m _ {j h w} ^ {s}), \\\\ \\end{array}", + "image_path": "12dcf59627f718e68bccc62c684ed8238e891326bf15fbb375d67fb16ac67b4c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 394, + 286, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 394, + 286, + 427 + ], + "spans": [ + { + "bbox": [ + 52, + 394, + 286, + 427 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s t} ^ {d i c e} = \\sum_ {j = 1 \\dots N _ {p}} 1 - \\frac {2 \\sum_ {h , w} m _ {j h w} ^ {s} \\cdot \\hat {m} _ {j h w} ^ {t} + \\epsilon}{\\sum_ {h , w} m _ {j h w} ^ {s} + \\sum_ {h , w} \\hat {m} _ {j h w} ^ {t} + \\epsilon}, \\tag {2}", + "image_path": "3a559acf8775fd59322114676a56f44d607d1518998c37ad5842caab1d531f75.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 435, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 639 + ], + "type": "text", + "content": "Anchored Loss for Robust Regularization: Training the networks with self-training loss alone is vulnerable to the accumulation of incorrect pseudo labels predicted by teacher network, a.k.a. confirmation bias [2]. Observations are made that the performance will drop after long iterations of self-training alone [56]. Existing source-free domain adaptation approaches often adopt additional constraints to prevent the negative impact of self-training, e.g. uniform distribution over predictions [35]. Without making such explicit assumptions, we propose to introduce the regularization by an anchor loss which minimizes the dice loss between an anchor network, which has frozen source model weights, and student and teacher networks respectively in Eq. 3. The frozen anchor network serves as the knowledge inherited from source domain and too much deviation between the source model and self-training updated model is discouraged to prevent the model from collapsing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 651, + 286, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 651, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 55, + 651, + 286, + 665 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a n c h o r}} = \\lambda_ {\\text {s t u}} ^ {\\text {d i c e}} \\mathcal {L} ^ {\\text {d i c e}} \\left(m ^ {s}, \\hat {m} ^ {a}\\right) + \\lambda_ {\\text {t e a}} ^ {\\text {d i c e}} \\mathcal {L} ^ {\\text {d i c e}} \\left(m ^ {t}, \\hat {m} ^ {a}\\right). \\tag {3}", + "image_path": "050091780b49c6b32d3d6aaab8bdd58447a1b488c27b27684b9fe51fc6d8bf2f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Contrastive Loss for Encoder Output Regularization: The above two training objectives are performed in the output space of the decoder. As we empirically revealed in the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 152 + ], + "type": "text", + "content": "experiment section, updating encoder network is the most effective way to adapt SAM, it is necessary to apply regularization directly to the feature map as output from the encoder network. Specifically, as illustrated in Fig. 3, we first crop out each instance's feature " + }, + { + "bbox": [ + 304, + 72, + 545, + 152 + ], + "type": "inline_equation", + "content": "I_{j}" + }, + { + "bbox": [ + 304, + 72, + 545, + 152 + ], + "type": "text", + "content": " from the feature map based on its prediction mask in anchor and teacher branches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 373, + 147, + 545, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 147, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 373, + 147, + 545, + 177 + ], + "type": "interline_equation", + "content": "I _ {j} = \\frac {\\sum_ {h , w} \\bar {\\mathcal {F}} _ {h w} \\cdot \\hat {m} _ {j h w}}{\\sum_ {h , w} \\hat {m} _ {j h w}}, \\tag {4}", + "image_path": "a5d3799b79f5d96afcc9dd8068f1195d47556f3c9965933edcfa585a6ddc88ec.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{F}}" + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "text", + "content": " is the L2 normalized feature map, i.e. " + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{F}}_{hw} = \\frac{\\mathcal{F}_{hw}}{|\\mathcal{F}_{hw}|}" + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "text", + "content": ". We further define the instance features, which are cropped out by the masks used the same prompt in two branches, as positive pairs, and the instances used different prompts as negative pairs to construct the contrast loss. The final contrastive loss is given as below, where " + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 178, + 545, + 263 + ], + "type": "text", + "content": " is the temperature scaling." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 333, + 269, + 545, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 269, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 333, + 269, + 545, + 299 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n t r a s t}} = - \\log \\frac {\\sum_ {j} \\exp \\left(I _ {j} ^ {a} \\cdot I _ {j} ^ {t} / \\tau\\right)}{\\sum_ {j} \\sum_ {j ^ {\\prime} \\neq j} \\exp \\left(I _ {j} ^ {a} \\cdot I _ {j ^ {\\prime}} ^ {t} / \\tau\\right)} \\tag {5}", + "image_path": "046b5db410353b38fe777aac20e643c27f3f978400dfed207bc05f21cd9c0b8d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 303, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 327 + ], + "type": "text", + "content": "Total Loss: We combine the above three loss functions as the final source-free domain adaptation loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 332, + 545, + 348 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 332, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 316, + 332, + 545, + 348 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {s t} ^ {f o c a l} \\mathcal {L} _ {s t} ^ {f o c a l} + \\mathcal {L} _ {s t} ^ {d i c e} + \\mathcal {L} _ {\\text {a n c h o r}} + \\mathcal {L} _ {\\text {c o n t r a s t}}. \\tag {6}", + "image_path": "9c55d7f31be9c4593cab73e9a88b7ee3afa9f0b20aa692d6912ac59c95dd74cd.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 354, + 501, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 501, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 501, + 366 + ], + "type": "text", + "content": "3.3. Prompt Generation for Self-Training" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 367, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 413 + ], + "type": "text", + "content": "The SAM segmentation requires prompt inputs to disambiguate the granularity of segmentation. The prompt engineering can be implemented in both fully automated way and by human interaction." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": "Fully Automated Prompt for Self-Training: We first densely sample grid points with a spatial distance of 16 pixels as point prompt input. Initial stage segmentation masks " + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\{\\hat{m}_j\\}_{j = 1\\dots N_{init}}" + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": " are generated by the anchor network with the grid point prompts. We follow the fully automated segmentation introduced by SAM [27] to prune out masks with low IoU score and low stability score, followed by NMS suppression. To enable self-training and regularization between different branches, we further generate a fixed set of prompt " + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\{e_j\\}_{j = 1\\dots N_p}" + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\{\\hat{m}_j\\}_{j = 1\\dots N_{init}}" + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": " as input to all three branches. As such, the segmentation outputs " + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}^a" + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}^s" + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}^t" + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": " are of the same length with exact one-to-one correspondence." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Weak Supervision as Prompt: Despite automatic segmentation can be enabled by sampling a grid of point prompts over the image and filtering out low quality and duplicated masks, the quality of segmentation is relatively poor and may contain many false positive predictions, making self-training less effective. Therefore, following prior weakly supervised domain adaptation works [9], we propose to use three types of weak supervisions, including bounding box, sparse point annotation and coarse segmentation mask. Fortunately, in the context of SAM, these weak supervisions perfect match with the prompt inputs which allow seamless integration of weak supervision for adapting SAM." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23388" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 197, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 197, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 197, + 84 + ], + "type": "text", + "content": "3.4. Low-Rank Weights Update" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": "The enormous size of backbone network prohibits updating all model weights with large batchsize. However, many existing studies suggest the update of encoder network weights is an effective way of adapting pre-trained models [35, 54]. To enable updating the backbone network with larger batchsize, we opt for a computation friendly low-rank updating approach [20]. For each weight in the encoder network " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{d_i \\times d_o}" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": ", we use a low-rank approximation " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "\\omega = AB" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{d_i \\times r}" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{r \\times d_o}" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": " indicating the rank. We can achieve a compression rate of " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "r(d_i + d_o) / d_i \\cdot d_o" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": ". Only " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": " are updated via backpropagation during adaptation to reduce memory footprint. At inference stage, the weight is reconstructed by combining the low rank reconstruction and original weight, " + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "inline_equation", + "content": "\\theta = \\theta + AB" + }, + { + "bbox": [ + 46, + 85, + 289, + 253 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 264, + 124, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 124, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 124, + 277 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 346 + ], + "type": "text", + "content": "In this section, we first introduce the experiment settings and downstream tasks for adapting SAM model. We provide detailed comparisons to state-of-the-art methods and qualitative results. Finally, we analyze the effectiveness of individual components and specific designs for the network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 348, + 110, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 110, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 110, + 360 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "text", + "content": "The source domain training set, SA-1B, was mainly constructed by collecting from natural environments. In this work, we identified five types of downstream segmentation tasks, some of which feature a drastic distribution shift from SA-1B, for evaluation, covering natural clean images, natural corrupted images, medical images, camouflaged images and robotic images. We present the datasets evaluated for each type of downstream task in Tab. 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 457, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 577 + ], + "type": "text", + "content": "Datasplit: We divide each downstream dataset into non-overlapping training and testing sets following the ratio established by [8]. The adaptation step is implemented on the training set. After the model is adapted, we evaluate the model on the held-out testing set. For adaptation to the Camouflaged Objects, following the training protocol in [5], we use the dataset COD10K (the training set of camouflaged images) for training, and use the test set of CAMO, COD10K and the entire CHAMELEON dataset for performance evaluation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 580, + 160, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 160, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 160, + 593 + ], + "type": "text", + "content": "4.2. Experiment Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 629 + ], + "type": "text", + "content": "Segment-Anything Model: We adopt ViT-B [12] as the encoder network due to memory constraint. The standard prompt encoder and mask decoder are adopted." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "Prompt Generation: We first provide details for generating prompt at both training stages. All training prompts are calculated from ground-truth segmentation mask, simulating the human interactions as weak supervision. Specifically, we extract the minimal bounding box that covers the whole instance segmentation mask as box prompt. The point prompt is created as randomly selecting 5 positive" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "points within ground-truth instance segmentation mask and 5 negative points outside ground-truth mask. The coarse segmentation mask is simulated by fitting a polygon to the ground-truth mask. We choose the number of vertices as " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "P / 20" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " indicating the perimeter of mask. The minimal number of vertices is 3. We use the same way to generate testing prompt on the testing data. This practice guarantees fair evaluation of SAM model which requires prompt input for segmentation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 182, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 230 + ], + "type": "text", + "content": "Evaluation Metrics: We report the mIoU as evaluation metrics. For each input prompt, the IoU is calculated between the ground-truth segmentation mask and predicted mask. The mIoU averages over the IoU of all instances." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 232, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 546, + 554 + ], + "type": "text", + "content": "Competing Methods: We evaluate multiple source-free domain adaptation approaches and one state-of-the-art weakly supervised domain adaptive segmentation approach. In specific, direct testing the pre-trained model (Direct) with fixed prompt inputs is prone to the distribution shift and may not perform well on target datasets with significant shift. TENT [62] is a vanilla test-time adaptation method which optimizes an entropy loss for adapting to target domain. SHOT [35] employs pseudo label and applies uniform distribution assumption for source-free domain adaptation. Soft Teacher [67] was originally developed for semi-supervised image segmentation. We adapt Soft Teacher for domain adaptation by keeping the self-training component. TRIBE [55] proposed a strong baseline for generic test-time adaptation on continual and class imbalanced domain shifts. We adapt TRIBE for domain adaptive segmentation by replacing the training losses. DePT [16] inserts visual prompts into a visual Transformer and adjusts these source-initialized prompts solely during the adaptation process without accessing the source data. WDASS [8] developed a weakly supervised domain adaptive segmentation method. We also evaluate the upperbound of adapting SAM by fine-tuning with ground-truth segmentation masks, which is dubbed as Supervised. Finally, we evaluate our weakly supervised domain adaptation method as Ours. All the competing methods use the same backbone, i.e. the ViT-B from SAM." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": "Hyperparameters: We finetune LoRA module of the ViTB image encoder by Adam optimizer for all experiments. We set the batchsize to 4, distributed over four RTX3090 GPUs, and the learning rate to 0.0001 with a weight decay of 0.0001. For Self-Training loss, we set the hyperparameters " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{st}^{focal}" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{st}^{dice}" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " to 2 and 1 respectively. " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{st}^{focal}" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " is set to 20, which is the coefficients of " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{st}^{focal}" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": ". For Anchor loss, the coefficients of two dice losses are denoted as " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{stu}^{dice}" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{tea}^{dice}" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": ", both of which equal 0.5. For Contrast loss, we set the temperature " + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 556, + 546, + 714 + ], + "type": "text", + "content": " to 0.3. We have set the low rank of the LoRA module for the image encoder to 4. We apply strong and weak data augmentations for self-training and choices for augmentation follows [53, 67]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23389" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 82, + 507, + 125 + ], + "blocks": [ + { + "bbox": [ + 209, + 71, + 384, + 81 + ], + "lines": [ + { + "bbox": [ + 209, + 71, + 384, + 81 + ], + "spans": [ + { + "bbox": [ + 209, + 71, + 384, + 81 + ], + "type": "text", + "content": "Table 1. Dataset and datasplit used in this work." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 82, + 507, + 125 + ], + "lines": [ + { + "bbox": [ + 85, + 82, + 507, + 125 + ], + "spans": [ + { + "bbox": [ + 85, + 82, + 507, + 125 + ], + "type": "table", + "html": "
Natural ImagesCorrupted ImagesMedical ImagesCamouflaged ObjectsRobotic Images
COCO [37]Pascal VOC [13]COCO-Ckvasir-SEG [23]ISIC [17]CHAMELEON [51]CAMO [31]COD10K [14]OCID [57]OSD [49]
# Training4246249742468349004040197256
# Testing70641670616637974250202632855
", + "image_path": "b8f706b43794234a7a5715f0f10f466fa7c51ab07ad2cf63cb118ceecdda2dbe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 85, + 139, + 506, + 235 + ], + "blocks": [ + { + "bbox": [ + 171, + 129, + 421, + 138 + ], + "lines": [ + { + "bbox": [ + 171, + 129, + 421, + 138 + ], + "spans": [ + { + "bbox": [ + 171, + 129, + 421, + 138 + ], + "type": "text", + "content": "Table 2. Adaptation results on COCO-C dataset using bounding box prompt." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 139, + 506, + 235 + ], + "lines": [ + { + "bbox": [ + 85, + 139, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 85, + 139, + 506, + 235 + ], + "type": "table", + "html": "
MethodBritContrDefocElastFogFrostGaussGlassImpulJpegMotnPixelShotSnowZoomAvg
Direct72.8357.3464.4769.3672.3970.5067.2064.4367.6568.2362.7268.6067.4469.0258.8066.73
TENT76.0261.5167.4870.8874.8973.8869.0167.1069.2870.2565.4570.8169.9672.3762.5969.43
SHOT73.8459.0965.9169.5773.9872.5168.3066.0968.6169.4564.5670.4868.7771.0360.1768.16
Soft Teacher73.9062.1265.4171.3272.1673.2768.8467.4968.7370.1866.8869.7970.0873.3364.8869.23
TRIBE76.4060.8666.1972.7275.0875.1470.3466.6670.8372.4265.9470.2470.6674.2264.5670.15
DePT69.1557.2659.0866.8058.7366.7566.7862.7465.6566.3961.6666.6567.5766.6258.2164.42
WDASS76.2160.5767.0772.3475.9774.6369.8467.8869.9271.3666.2571.9970.3272.2563.6170.01
OURS78.5061.0566.9973.9377.0976.1072.0268.2171.2972.7766.3370.9070.2875.0765.3371.05
Supervised78.8674.8172.0474.3278.0177.1473.4372.1274.0875.3071.3975.1574.2576.3468.0474.35
", + "image_path": "f00a89ac1e16d2136e3d1e971d3f649330de0709d6da3db4b1f27e816e4ad04a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 241, + 187, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 241, + 187, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 241, + 187, + 254 + ], + "type": "text", + "content": "4.3. Quantitative Evaluations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 255, + 288, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 288, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 288, + 316 + ], + "type": "text", + "content": "In this section, we report the quantitative evaluations on the 5 types of target datasets. For each dataset, we also report the adaptation results with weak supervision in the form of bounding box (box), sparse points (point) and coarse segmentation mask (poly)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 316, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 411 + ], + "type": "text", + "content": "Adaptation to Corrupted Images: Visual corruptions often occur due to sensor fault, bad weather conditions, etc. As seen from Tab. 2, without any adaptation, Direct testing is significantly worse than the upperbound. With weakly supervisions, all methods could improve over direct testing, in particular, our proposed method outperforms all competing adaptation methods on 10 out of 15 types of corruptions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 413, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 592 + ], + "type": "text", + "content": "Adaptation to Natural Images: We then present the results of adapting SAM to natural images in Tab. 3. For each type of weak supervision, we use the same type of prompt on the testing set. Despite the distribution gap between SA-1B and the target natural images, we observe significant performance gap between Supervised upperbound and Direct baseline, e.g. with box level supervision, there is " + }, + { + "bbox": [ + 46, + 413, + 287, + 592 + ], + "type": "inline_equation", + "content": "5 - 10\\%" + }, + { + "bbox": [ + 46, + 413, + 287, + 592 + ], + "type": "text", + "content": " gap in IoU. When weak supervision is provided, both state-of-the-art generic source-free domain adaptation methods and weakly supervised domain adaptive segmentation method improve the generalization on all three types of weak supervisions. Finally, our proposed weakly supervised method achieves a remarkable improvement over all competing methods. The results with box weak supervision is even approaching the fully supervised upperbound." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 593, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 700 + ], + "type": "text", + "content": "Adaptation to Medical Images: Segmentation for medical images is a major application of foundation models. Our empirical observations in Tab. 4 on two medical segmentation datasets suggest that direct applying pre-trained SAM is suboptimal. With weakly supervised adaptation, the segmentation accuracy is greatly improved. We observe the improvement to be particularly significant with point and box which are relatively easy to obtain due to the low labeling cost." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "Adaptation to Camouflaged Objects: We further eval" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 319, + 253, + 531, + 372 + ], + "blocks": [ + { + "bbox": [ + 328, + 241, + 523, + 251 + ], + "lines": [ + { + "bbox": [ + 328, + 241, + 523, + 251 + ], + "spans": [ + { + "bbox": [ + 328, + 241, + 523, + 251 + ], + "type": "text", + "content": "Table 3. Adaptation results on natural clean image datasets." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 253, + 531, + 372 + ], + "lines": [ + { + "bbox": [ + 319, + 253, + 531, + 372 + ], + "spans": [ + { + "bbox": [ + 319, + 253, + 531, + 372 + ], + "type": "table", + "html": "
MethodCOCO 2017Pascal VOC
boxpointpolyboxpointpoly
Direct74.2955.0665.6469.2169.2160.79
TENT78.2152.9971.5180.2474.9765.03
SHOT75.1858.4669.2679.8074.2663.38
Soft Teacher75.9443.3668.2772.9356.0962.20
TRIBE77.5649.5670.9978.8769.2165.39
DePT71.0037.3563.2774.0942.9959.94
WDASS77.2960.5570.1980.1276.1566.98
OURS80.1262.0972.3380.2774.1566.72
Supervised81.5069.7773.3981.2376.9871.32
", + "image_path": "2ac025818c3dd6d6eb363355eff23f077f220cf57f31b98e7fbb92e0c074010e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 318, + 390, + 531, + 510 + ], + "blocks": [ + { + "bbox": [ + 313, + 379, + 537, + 389 + ], + "lines": [ + { + "bbox": [ + 313, + 379, + 537, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 379, + 537, + 389 + ], + "type": "text", + "content": "Table 4. Adaptation results on medical image segmentation datasets." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 390, + 531, + 510 + ], + "lines": [ + { + "bbox": [ + 318, + 390, + 531, + 510 + ], + "spans": [ + { + "bbox": [ + 318, + 390, + 531, + 510 + ], + "type": "table", + "html": "
Methodkvasir-SEGISIC
boxpointpolyboxpointpoly
Direct81.5962.3054.0366.7453.4262.82
TENT82.4761.8462.9771.7653.4667.12
SHOT82.3063.7661.3471.9955.9966.86
Soft Teacher84.1273.5358.1575.7454.9572.29
TRIBE85.0573.0364.6172.6150.3667.99
DePT81.9152.0661.5578.4346.7972.75
WDASS84.0163.7864.7874.2355.6367.84
OURS85.4775.2367.4080.0162.1275.36
Supervised85.8977.5481.6481.6279.8180.26
", + "image_path": "eab3f1df613c93ac82f38b0804fec3cfa35d182b9413499afb98d070b0764706.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "type": "text", + "content": "uate on adapting SAM to camouflaged object detection. We evaluate on three camouflaged object detection datasets with results reported in Tab. 5. Preliminary studies revealed that SAM is particularly vulnerable to camouflaged objects [59] due to the low contrast between background and foreground. We make similar observations here that even with the help of prompt inputs at testing stage, Direct inference suffers a lot, achieving less than " + }, + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "type": "inline_equation", + "content": "66\\%" + }, + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "type": "text", + "content": " mIoU. When weakly labeled data are used for adaptation, we observe very significant improvements, with point prompt only we improved by a staggering " + }, + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 304, + 520, + 545, + 687 + ], + "type": "text", + "content": " in mIoU on the CHAMELEON dataset. Our proposed method is also consistently better than all competing methods on all types of weak supervisions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Adaptation to Robotic Images: Finally, we evaluate adapting SAM to image collected from robotic environ" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23390" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 82, + 272, + 169 + ], + "blocks": [ + { + "bbox": [ + 69, + 71, + 264, + 81 + ], + "lines": [ + { + "bbox": [ + 69, + 71, + 264, + 81 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 264, + 81 + ], + "type": "text", + "content": "Table 5. Adaptation results on camouflaged object datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 82, + 272, + 169 + ], + "lines": [ + { + "bbox": [ + 60, + 82, + 272, + 169 + ], + "spans": [ + { + "bbox": [ + 60, + 82, + 272, + 169 + ], + "type": "table", + "html": "
MethodCHAMELEONCAMOCOD10K
boxpointpolyboxpointpolyboxpointpoly
Direct51.3239.3745.7862.7257.4350.8566.3263.6140.04
TENT65.4854.5353.0671.2459.5960.2969.3661.9443.36
SHOT68.6062.4754.3671.6162.7858.7269.0965.2542.38
Soft Teacher65.9244.1746.7262.3048.6451.2666.3250.0432.27
TRIBE71.0052.8054.9966.0061.9760.5467.8463.6242.75
DePT54.4833.4642.4755.4433.0748.6359.3234.0635.51
WDASS71.9162.4056.8071.2563.3962.2971.4265.6143.93
OURS75.9474.0066.8373.4265.5562.9071.9370.5545.87
Supervised78.0585.8668.3879.1777.0167.1278.0678.4464.90
", + "image_path": "de005986e56c8c83c3154f897d12707b3fb1ae4c060b3d46c513d05c9a3db2e1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 287, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 246 + ], + "type": "text", + "content": "ments where segmenting out the spatial extent of individual objects is essential for interactions. As seen from the results in Tab. 6, adapting SAM to robotic images with weak supervision further increase the segmentation accuracy. The improvement is more noticeable with point and polygon weak supervisions." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 60, + 259, + 272, + 380 + ], + "blocks": [ + { + "bbox": [ + 78, + 249, + 255, + 258 + ], + "lines": [ + { + "bbox": [ + 78, + 249, + 255, + 258 + ], + "spans": [ + { + "bbox": [ + 78, + 249, + 255, + 258 + ], + "type": "text", + "content": "Table 6. Adaptation results on robotic image datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 259, + 272, + 380 + ], + "lines": [ + { + "bbox": [ + 60, + 259, + 272, + 380 + ], + "spans": [ + { + "bbox": [ + 60, + 259, + 272, + 380 + ], + "type": "table", + "html": "
MethodOCIDOSD
boxpointpolyboxpointpoly
Direct86.3571.4172.8187.6278.8680.77
TENT87.7766.6177.5388.1080.5387.85
SHOT88.0674.3976.2588.0980.5287.86
Soft Teacher84.9868.4673.7590.4180.4987.00
TRIBE86.7767.8676.5090.4280.5487.84
DePT82.0056.5270.9281.8469.0682.50
WDASS87.6877.1376.7088.0780.5288.19
OURS88.0980.1477.4192.1180.5189.72
Supervised91.2489.2279.2392.1482.4190.83
", + "image_path": "fbfb7f69641b110efb8da3e96e2f4d0e08bb8a141854b191fa2e53bf2b8b9787.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 390, + 180, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 180, + 402 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 180, + 402 + ], + "type": "text", + "content": "4.4. Qualitative Evaluations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 403, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 715 + ], + "type": "text", + "content": "We present the qualitative comparisons of segmentation results for selected examples in Fig. 4. We make the following observations from the results. Evaluating pre-trained SAM (SAM) on COCO with both box and point prompt exhibits very fine-grained segmentation results. However, the model is overly sensitive to the high contrast regions, e.g. the hair for the girl and the toppings of pizza are missing from the segmentation mask. With the proposed weakly supervised adaptation approach, our method is able to generate more smoothed segmentation mask and the mask better reflects the semantic boundary. Similar observations are made from the medical image segmentation dataset. Without adapting the SAM model, segmentation results are either too conservative with low recall or expanding beyond the semantic boundary. With our weakly supervised adaptation, SAM is able to produce high fidelity results. We further present results on camouflaged segmentation task (CAMO). Without adaptation, SAM fails to segment out the spider's belly and confuses the snow background with the harp seal in the foreground. Our weakly adapted SAM successfully segments out the spider's belly and produces high quality mask for the harp seal. Finally, two examples from OCID dataset suggest that the pre-trained SAM tends to over-segment, e.g. missing the open whole for the tissue box, or confusing adjacent objects, e.g. merging the pen with the folder label. With weakly supervised adaptation SAM picks up the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 319, + 92, + 531, + 160 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 90 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 90 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 90 + ], + "type": "text", + "content": "Table 7. Ablation studies of the proposed weakly supervised adaptation method on COCO dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 92, + 531, + 160 + ], + "lines": [ + { + "bbox": [ + 319, + 92, + 531, + 160 + ], + "spans": [ + { + "bbox": [ + 319, + 92, + 531, + 160 + ], + "type": "table", + "html": "
Weak Sup.Self-Train.AnchorCont. Lossboxpointpoly
original SAM74.2956.3665.42
✓✓58.8832.5155.03
✓✓✓79.6557.2570.49
✓✓✓62.9522.8756.91
✓✓✓✓80.1262.0972.33
✓✓✓76.1847.6370.44
", + "image_path": "759311c5721657b0b1deecde9405874c95f88785686d42bb1ecf398b07a3e251.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 319, + 175, + 531, + 227 + ], + "blocks": [ + { + "bbox": [ + 324, + 163, + 527, + 173 + ], + "lines": [ + { + "bbox": [ + 324, + 163, + 527, + 173 + ], + "spans": [ + { + "bbox": [ + 324, + 163, + 527, + 173 + ], + "type": "text", + "content": "Table 8. Adaptation results on cross-prompt testing scenarios." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 175, + 531, + 227 + ], + "lines": [ + { + "bbox": [ + 319, + 175, + 531, + 227 + ], + "spans": [ + { + "bbox": [ + 319, + 175, + 531, + 227 + ], + "type": "table", + "html": "
Tr. Weak. Sup.boxpointpolygon
Te. Promptboxpointpolyboxpointpolyboxpointpoly
Direct74.2954.7666.7574.2954.6466.7574.2954.7665.64
TENT78.2154.8368.8252.9952.9968.5877.0853.9071.51
WDASS77.2958.7868.9474.6960.5569.1575.2755.2770.19
OURS80.1252.2872.0776.4962.0971.0278.5752.8872.33
", + "image_path": "7cae0d6076af688126d2b1bddd3190d36bf796bbbc8296cacc0230e669fcc97d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 232, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 255 + ], + "type": "text", + "content": "semantic meaning and produces segmentation results that better aligns with human intention." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 262, + 399, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 399, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 399, + 274 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "text", + "content": "In this section, we analyze the effectiveness of individual components on COCO dataset. As presented in Tab. 7, when self-training is applied alone, we observe a significant performance drop (74.29% → 58.88% with box weak supervision), suggesting the severity of confirmation bias. This issue can be well remedied when the anchor loss regularization is applied. Self-training with anchored regularization already improves the performance of SAM after adaptation. Finally, the contrastive loss directly regularizes the encoder network's output and contributes with additional improvement of segmentation accuracy. We also investigate the final self-training architecture without any weak supervision, i.e. the pseudo label masks are generated with grid point prompt. The results after adaptation is slightly worse than with weak supervision but consistently better than without adaptation on both box and coarse mask testing prompts. Nevertheless, the results with point prompt performs even worse than without adaptation, suggesting the necessity of weakly supervised adaptation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 510, + 421, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 510, + 421, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 510, + 421, + 521 + ], + "type": "text", + "content": "4.6. Additional Analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 522, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 617 + ], + "type": "text", + "content": "Generalization to Cross-Prompt Testing: We further investigate the effectiveness of adaptation by testing with all three types of prompts. Specifically, we compare with the best (WDASS) and second best (TENT) methods with results presented in Tab. 8. Apart from using point as testing prompt, our methods consistently improves the performance even though the testing prompt is different from training weak supervision." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 618, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 712 + ], + "type": "text", + "content": "Effectiveness of Updating Different Components: There are many options for updating the pre-trained SAM model. Given limited computing resources, choosing the appropriate components of network to update is crucial to optimize the generalization performance. In this section, we investigate several options of network components to update during adaptation. Full finetune means finetuning the whole encoder. MaskDecoder finetune the whole decoder" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23391" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 519, + 419 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 519, + 419 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 519, + 419 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 519, + 419 + ], + "type": "image", + "image_path": "2bd37e97d82e959a86b26f43c1ff352efd4a3e50f2bf0abe8ed3d7022373dd0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 423, + 520, + 435 + ], + "lines": [ + { + "bbox": [ + 72, + 423, + 520, + 435 + ], + "spans": [ + { + "bbox": [ + 72, + 423, + 520, + 435 + ], + "type": "text", + "content": "Figure 4. qualitative results on some selected examples. Three types of prompts at testing stage are visualized for reference." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 444, + 289, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 289, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 289, + 576 + ], + "type": "text", + "content": "of SAM without additional redundant learnable parameters. LayerNorm finetune the all layer norms of the SAM image encoder. LoRA finetunes the encoder network in through low-rank decomposition only. EVP use the Embedding Tune and the HFC Tune to tune the extracted features by image encoder. We present the investigation on the COCO dataset with bounding boxes as weak supervision in Tab. 9. In particular, we have also explored the impact of different combinations of components, e.g. MaskDecoder + LoRA, LoRA + EVP, and so on. The results suggest LoRA finetuning the encoder network alone yields the best performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 590, + 119, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 119, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 119, + 601 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "We studies the generalization of Segment-Anything model for multiple downstream image segmentation tasks. A tangible solution with no access to source dataset and low memory cost was proposed to adapt SAM to downstream data in a source-free domain adaptation manner. The proposed method is naturally compatible with weak supervisions which could substantially improve the efficacy of adaptation. Extensive evaluations on 10 datasets from 5 types of downstream tasks suggest the proposed adapta" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 350, + 454, + 503, + 592 + ], + "blocks": [ + { + "bbox": [ + 311, + 443, + 539, + 453 + ], + "lines": [ + { + "bbox": [ + 311, + 443, + 539, + 453 + ], + "spans": [ + { + "bbox": [ + 311, + 443, + 539, + 453 + ], + "type": "text", + "content": "Table 9. Adaptation results produced by finetuning different modules." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 350, + 454, + 503, + 592 + ], + "lines": [ + { + "bbox": [ + 350, + 454, + 503, + 592 + ], + "spans": [ + { + "bbox": [ + 350, + 454, + 503, + 592 + ], + "type": "table", + "html": "
Finetuning ModuleIoU
None74.30
Full finetune78.54
MaskDecoder76.81
LayerNorm79.30
Low-Rank Adaptation (LoRA)80.12
Explicit Visual Prompt (EVP)77.38
MaskDecoder + LoRA77.28
MaskDecoder + EVP76.83
LoRA + EVP79.47
LoRA + LayerNorm79.35
MaskDecoder + LoRA + EVP77.31
", + "image_path": "abfde0052dd0b70961c6c1f4210065b9213a7664f1718ca2329922d50459c8b3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 603, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 603, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 305, + 603, + 545, + 627 + ], + "type": "text", + "content": "tion method can significantly improve the generalization of SAM under various degrees of distribution shift." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by National Natural Science Foundation of China (NSFC) (Grant Number: 62106078), and Agency for Science, Technology and Research (Grant Number: C210112059). This work was partially done during Yongyi Su's attachment with Institute for Infocomm Research (I2R), funded by China Scholarship Council (CSC)." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23392" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Waqar Ahmed, Pietro Morerio, and Vittorio Murino. 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A key obstacle that prevents its widespread adoption is the encoding speed—generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal.", + "bbox": [ + 75, + 300, + 473, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 584, + 209, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural field is a form of data representation that parameterizes each target signal as a neural network that maps spatiotemporal coordinates to the signal values [33]. For example, a colored image can be represented by a model that maps (X,Y) pixel coordinates to the corresponding (R,G,B) values. This parameterization enjoys many advantages in faithfully and efficiently representing high-dimensional signals with fine detail, and thus is being widely used for modeling signals of various modalities, such as image [4], video [10], 3D scene [19], or spherical data [8].", + "bbox": [ + 75, + 609, + 468, + 761 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A key obstacle that prevents the widespread adoption of neural fields is their training cost. To represent each datum as a neural field, one must train a neural network using many SGD iterations. For instance, NeRF requires at least 12 hours of training time on GPUs to represent a single 3D scene [19]. Representing a set of data thus requires a considerable amount of computation and time, making it very", + "bbox": [ + 75, + 761, + 470, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "difficult to develop practical applications of neural fields.", + "bbox": [ + 500, + 268, + 877, + 285 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many prior works view the \"optimization bias\" as a major cause behind the long training time of neural fields [29]. In particular, the spectral bias of the SGD-based training is known to bias the neural network to prioritize fitting the low-frequency components of the target signal and leave high-frequency components for the late stage of training [22]. It has been observed that such a tendency greatly hinders the neural fields from expressing natural data (e.g., images) with fine, high-frequency details [29, 37].", + "bbox": [ + 496, + 285, + 892, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The prevailing strategy to mitigate such bias is to introduce a useful prior (or inductive bias) that can help neutralize the negative effects of the bias. One popular approach is to develop new network components that bring a favorable architectural prior, such as the Fourier features [19], sinusoidal activation [27], or spatial encoding [18, 20]. Other works also attempt to introduce the prior in the form of initial parameters that have been meta-learned from a large set of signals [26, 30]. Such meta-learned initializations tend to have rich high-frequency spectra, which can help fitting natural signals within a small number of SGD steps [30].", + "bbox": [ + 496, + 422, + 893, + 588 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we approach the problem from a different angle. In particular, we ask the following question:", + "bbox": [ + 498, + 588, + 893, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"Can we exploit the optimization bias of SGD, instead of fighting against it?\"", + "bbox": [ + 540, + 623, + 849, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Precisely, we ask whether we can transform the datum in a way that the optimization bias acts favorably in fitting the transformed data with a neural field. If there exists such a transformation, and if it admits an efficiently computable inverse, we may be able to use the following strategy to reduce the neural field training cost: we train a neural field that expresses the transformed signal, and the original signal can be recovered from the model by applying an inverse transformation to the signal generated by the model (Fig. 1). Contribution. As a first step to answer this question, we conduct an extensive empirical study on how applying simple data transformations affect the computational cost of training the corresponding neural field. In particular, we compare the number of SGD steps needed to fit the transformed data to a certain fidelity level (e.g., PSNR 50 for images), with the steps to fit the original data. We try to", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1code: https://github.com/effl-lab/DT4Neural-Field", + "bbox": [ + 94, + 887, + 433, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4830", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b57ef16bf1f20f07a2d4fb8d92e86dae8be7749268e75d6013da7153054e2e79.jpg", + "image_caption": [ + "Figure 1. Overall pipeline. We consider a three-step procedure to train neural fields. (1) Apply a data transformation to the target datum. (2) Train a neural field to fit the transformed data. (3) Reconstruct the original data by generating the transformed datum from the neural field, and then applying the inverse of the data transformation. By selecting the data transformation carefully, we can significantly reduce the computational cost required to train a neural field that achieves the desired quality of approximation." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 885, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tal seven different data transformations, from the one that permutes the location of the pixels to the one that scales the intensity values of each pixel.", + "bbox": [ + 75, + 321, + 468, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From the experiment, we make a surprising observation: we find that the random pixel permutation (abbr. RPP) provides a consistent acceleration on a range of datasets and various neural field architectures with sophisticated encoding schemes. The RPP is in fact the only data transformation that provided acceleration on every experimental setups that we considered. We find that the original data requires, on average, $\\sim 30\\%$ greater number of SGD steps to achieve the similar fidelity level than the RPP data. As RPP tends to bias the data toward high-frequency, it is quite counter-intuitive that they can be fit faster than the original signals.", + "bbox": [ + 75, + 367, + 468, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Why does the random pixel permutation accelerate neural field training? To explain this phenomenon, we articulate the following \"blessings of no pattern\" hypothesis:", + "bbox": [ + 75, + 535, + 468, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Original data often have smooth, representative patterns that facilitate easy optimization, particularly in the early phase of learning. However, this smoothness quickly transforms into an obstacle when aiming for a sufficiently high level of fidelity. Random pixel permutation removes these easy-to-fit patterns, which accelerates optimization in the long run. $(\\star)$", + "bbox": [ + 96, + 595, + 450, + 703 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To corroborate our hypothesis $\\star$ , we take an in-depth look into the training dynamics of the original and the RPP data. We find that, indeed the training speed on the RPP data is slower than on the original data during the early training phase (Sec. 4.1). However, after training for a sufficient number of epochs, the neural field trained on RPP data finds a \"linear loss highway\" on which the optimization is very easy; the optimization on original data fails to find one (Sec. 4.2). Furthermore, we find that the errors in the RPP images are more evenly distributed over pixels and lack visually distinguishable structures; errors in original images tend to have periodic or axis-aligned patterns, which might", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "be the artifacts of the encoding scheme (Sec. 4.3).", + "bbox": [ + 498, + 321, + 830, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, our contribution can be summarized as:", + "bbox": [ + 517, + 335, + 857, + 349 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Through systematic study, we find that simple data transformations can dramatically change the training speed of neural field $(\\times 0.1 - \\times 20)$ , even on state-of-the-art neural fields architectures with sophisticated encodings [20].", + "2. We discover that random pixel permutations (RPP) provide consistent acceleration over fitting the original image, providing $\\times 1.08 - \\times 1.50$ speedups.", + "3. We conduct an in-depth analysis which sheds light on how RPP speeds up the training by removing the easy-to-fit patterns that slow down the training eventually." + ], + "bbox": [ + 500, + 354, + 890, + 506 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the limitation of RPP that it may be difficult to be applied for applications where generalization is critical, our study has at least two potential impact areas. First, the RPP itself may be useful in the applications of neural field where a strong training fidelity is the core performance criterion, such as data compression [24]. In fact, one of the core challenges in neural-field-based data compression is the slow encoding speed (see, e.g., COOL-CHIC [12]). Second, our study provides a concrete starting point in developing a new data transformation that strikes the balance between the training speed and the generalizability.", + "bbox": [ + 496, + 510, + 890, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. General framework", + "text_level": 1, + "bbox": [ + 500, + 690, + 689, + 705 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The general framework of finding data transformations that accelerate neural field training can be formalized as an optimization problem, as we describe in this section.", + "bbox": [ + 496, + 715, + 890, + 761 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Formalisms", + "text_level": 1, + "bbox": [ + 500, + 771, + 627, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Suppose that we want to use the neural field parameterization to approximate some signal $\\mathbf{x} \\in \\mathcal{X}$ . Here, the signal space $\\mathcal{X}$ is the space of all signals that have the same data type. For example, we can let $\\mathcal{X}$ be the set of all $256 \\times 256$ RGB images; in such case, we may have $\\mathcal{X} \\subseteq \\mathbb{R}^{256 \\times 256 \\times 3}$ .", + "bbox": [ + 496, + 794, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The data transformation $T: \\mathcal{X} \\to \\mathcal{X}$ maps an element in the signal space to another element. We define the trans-", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4831", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/85647fc8ca51df0d49284e508dc7d0645065f654a763314dba082f9ecac827ee.jpg", + "image_caption": [ + "(a) Original" + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 279, + 165 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f577e86b0e27f415e296b3159e1dbd2ba4220d914da42dce6cdf0011fb428d15.jpg", + "image_caption": [ + "(b) Random pixel permutation" + ], + "image_footnote": [], + "bbox": [ + 290, + 89, + 480, + 165 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/20b5186c293b2d455d7313e40e16e6c124e774a2d15a8c628ab21fce9849b354.jpg", + "image_caption": [ + "(c) Zigzag permutation" + ], + "image_footnote": [], + "bbox": [ + 493, + 90, + 684, + 165 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4af3e429968790b534d0921001f326a46e654b0466793144852b16a3ced45fb2.jpg", + "image_caption": [ + "(d) Inversion" + ], + "image_footnote": [], + "bbox": [ + 696, + 90, + 888, + 165 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d6969e9b606660957c43a8705f4619430c0efc13e65f071218488502578d902c.jpg", + "image_caption": [ + "(e) Standardization" + ], + "image_footnote": [], + "bbox": [ + 84, + 185, + 279, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/42616ac7746630b1ad4a8d7e7957efc8fbfae46977ba12afbaabd18d233698bd.jpg", + "image_caption": [ + "(f) Linear Scaling $(t = 0.5)$" + ], + "image_footnote": [], + "bbox": [ + 290, + 186, + 480, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/082a08b787ffcfd240b748769ec53f9c27ad358d6f70158f12612cad05278567.jpg", + "image_caption": [ + "(g) Centering $(t = 1)$" + ], + "image_footnote": [], + "bbox": [ + 493, + 186, + 684, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/062562cf409166941663423826b33f44bf85333aa553e235dd45f5a134c93974.jpg", + "image_caption": [ + "(h) Gamma correction $(\\gamma = 2.0)$" + ], + "image_footnote": [], + "bbox": [ + 696, + 186, + 888, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6c0de187982dbfb6c5c12c9332845c69d4871929b62127093dd9b1e9745d7743.jpg", + "image_caption": [ + "Figure 2. Data transformations considered. In each subfigure, we visualize the data transformations by illustrating how the transformed image (left) and the intensity histogram (right) looks like on a Kodak image." + ], + "image_footnote": [], + "bbox": [ + 282, + 284, + 683, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "formation space $\\mathcal{T}$ as a set of data transformations on $\\mathcal{X}$ that has an inverse.", + "bbox": [ + 73, + 351, + 468, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to find a data transformation $T$ that minimizes the training cost of fitting the transformed signal $T(\\mathbf{x})$ . To formalize this, we define the training cost", + "bbox": [ + 75, + 381, + 468, + 426 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {c o s t}: \\mathcal {X} \\times \\mathcal {T} \\rightarrow \\mathbb {R} _ {+}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 435, + 468, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, the function $\\mathrm{cost}(\\mathbf{x}, T)$ measures the computational burden required to train a neural field for $T(\\mathbf{x})$ , whenever its outcome is inverted back via $T^{-1}$ , approximates the original signal $\\mathbf{x}$ with the desired level of precision. The burden may be measured in various ways, e.g., the number of SGD steps, FLOPs, or wall-clock time. We note that the training cost of $\\mathbf{x}$ using $T(\\cdot)$ need not be identical to the training cost of fitting $T(\\mathbf{x})$ with the same precision, i.e.,", + "bbox": [ + 75, + 459, + 468, + 580 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {c o s t} (\\mathbf {x}, T) \\neq \\operatorname {c o s t} (T (\\mathbf {x}), \\mathrm {I d}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 589, + 468, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "especially when the transformation involves scaling of the signal. Also, the training cost may heavily depend on the choice of neural field architectures, hardware type, and the batch size—using a larger batch size tends to reduce the number of steps until convergence [25], but it also requires training with a larger memory.", + "bbox": [ + 75, + 614, + 468, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given these tools, we work to consider the optimization", + "bbox": [ + 94, + 705, + 468, + 720 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {m i n i m i z e} \\quad \\operatorname {c o s t} (\\mathbf {x}, T), \\quad \\text {s u b j e c t t o} \\quad T \\in \\mathcal {T} ^ {*}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 724, + 468, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{T}^* \\subseteq \\mathcal{T}$ is a subset of the transformation space that satisfies some desired properties. The set $\\mathcal{T}^*$ can be configured in many different ways, to account for the expected usages of the trained neural fields. This problem can also be extended to a version where we have a probability distribution of the signals $\\mathbf{x}$ , and find a single transformation $T$ that minimizes the expected cost.", + "bbox": [ + 75, + 750, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scope of this paper. While the most general framework is to solve the optimization (3) directly, the problem is intractable unless we have an expressive, well-paramaterized", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "transformation space $\\mathcal{T}^*$ that admits an effective optimization method. In this paper, we focus on the proof-of-concept that there exists some choice of $T$ such that", + "bbox": [ + 498, + 351, + 892, + 395 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {c o s t} (\\mathbf {x}, T) < \\operatorname {c o s t} (\\mathbf {x}, \\operatorname {I d}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 411, + 890, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(Sec. 3), and deepening our understanding on when and why such $T(\\cdot)$ can accelerate the training (Sec. 4).", + "bbox": [ + 498, + 440, + 890, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Example cases", + "text_level": 1, + "bbox": [ + 500, + 483, + 648, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here are some examples desired properties of data transformation, and how they relate to practical applications. We provide a more in-depth discussions in the ??", + "bbox": [ + 498, + 508, + 890, + 553 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Efficient invertibility. The inverse $T^{-1}$ should be able to be computed efficiently, e.g., by performing a linear operation. Ideally, one may wish to be able to combine the inverse transformation into the neural field by modifying the parameters of the trained neural field directly. For instance, if $T(\\mathbf{x}) = -\\mathbf{x}$ , we can incorporate the inverse in the neural field by negating the final layer weights of the neural field. This property is useful whenever we expect many repeated inferences of the neural field, e.g., for real-time interaction.", + "bbox": [ + 498, + 554, + 892, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Retains interpolatability. We want our transform $T$ to admit a principled way to sample the value of interpolated coordinates from the neural field that approximates the transformed signal. In some neural field applications, e.g., superresolution [4], this interpolating capability plays an essential role. On the other hand, some applications like data compression do not involve any interpolation [24].", + "bbox": [ + 498, + 691, + 890, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Data transformations vs. training speed", + "text_level": 1, + "bbox": [ + 500, + 813, + 856, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we compare the training cost of the neural field training on various data transformation schemes. As it turns out, there indeed exists a nice data transformation that satisfies ineq. 4: the random pixel permutation (RPP).", + "bbox": [ + 498, + 839, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4832", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/442f8a8f8f0c890ac07aed205776ad9b117b3e86bd38b0daf6f859b4df0d8231.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ArchitectureDatasetRandom pixel perm.Zigzag perm.InversionStandardizationLinear ScalingCenteringGamma Correction
t=0.5t=2.0t=1.0t=2.0γ=0.5γ=2.0
SIRENKodak1.26×17.90×0.72×2.20×0.79×1.39×0.76×0.97×0.36×0.80×
DIV2K1.30×21.74×0.70×2.36×0.82×1.45×0.97×1.22×0.30×0.90×
CLIC1.08×17.07×0.68×2.18×0.76×1.36×0.87×1.14×0.24×0.82×
Instant-NGPKodak1.50×0.86×0.21×0.45×1.15×0.75×1.24×0.80×0.29×0.38×
DIV2K1.32×0.80×0.20×0.61×1.12×0.64×1.39×0.97×0.14×0.33×
CLIC1.35×0.78×0.07×0.53×1.03×0.68×0.99×0.66×0.12×0.32×
", + "bbox": [ + 76, + 88, + 893, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Acceleration factors of data transformations. We compare the average acceleration factor (eq. 5) of seven data transformations under six different combinations of datasets and models. We take average of cost ratios, instead of ratios of averages, to avoid the statistic being driven by a small number of outliers that require very long training time. The shaded figures denote the speedup.", + "bbox": [ + 75, + 219, + 893, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 276, + 264, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We focus on the task of 2D image regression. This choice reduces the computational burden of fitting each datum, so that we can make experimental validations on multiple datasets and models with extensive hyperparameter tuning.", + "bbox": [ + 75, + 299, + 468, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the training cost, we use the number of SGD steps until we reach the training PSNR over 50dB (a near-perfect reconstruction for 8-bit images). The number of SGD steps is an informative indicator of the total FLOPs and runtime for any fixed choice of hardware, model architecture, and data. Importantly, we tune the learning rate for each (transformed) image, making it close to the scenario where all settings have been optimized to minimize the runtime.", + "bbox": [ + 75, + 361, + 468, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each choice of an image and the data transformation, we measure the acceleration factor, i.e.,", + "bbox": [ + 76, + 481, + 468, + 512 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {a c c} (\\mathbf {x}, T) \\triangleq \\frac {\\operatorname {c o s t} (\\mathbf {x} , \\operatorname {I d})}{\\operatorname {c o s t} (\\mathbf {x} , T)}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 516, + 468, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Other configurations are as follows.", + "bbox": [ + 76, + 553, + 315, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Datasets. We use three different image datasets:", + "bbox": [ + 76, + 568, + 397, + 583 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Kodak. Consists of 24 different images from the Kodak lossless true color image suite [11].", + "- DIV2K. Consists of 100 images in the validation split of the DIV2K image super-resolution challenge (HR) [1].", + "- CLIC. Consists of 100 images from the validation split of the dataset for the Challenge on Learned Image Compression 2020 (CLIC) [31]. There are total 102 images in the validation split, but we removed two images that have a sidelength shorter than 512 pixels." + ], + "bbox": [ + 76, + 583, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We pre-process each image in the datasets as follows. Following BACON [14], we resize each image into $512 \\times 512$ pixels by first center-cropping the image to a square with sidelengths equal to the shorter sidelength of the original image, and then resizing with the Lanczos algorithm. Next, we convert the image to grayscale. Finally, we apply sRGB to Linear RGB operation, as in Instant-NGP [20].", + "bbox": [ + 75, + 719, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The resulting images have $512 \\times 512$ pixels (thus total $2^{18}$ pixels) with intensities lying in the interval $[0, 1]$ .", + "bbox": [ + 76, + 824, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Models. We use two different neural field architectures.", + "bbox": [ + 76, + 854, + 444, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- SIREN. A classical architecture that uses multi-layered perceptrons with sinusoidal activation functions [27]. We", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "configure the model to have three hidden layers with 512 neurons in each layer and output dimension 1. We use the default frequency scaling hyperparameter $\\omega_0 = 30$ .", + "bbox": [ + 509, + 277, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- Instant-NGP. A more recently proposed neural field with multi-resolution hash encodings [20]. We use the default setup for the image regression, with the maximum hash table size and 16-bit parameters.", + "bbox": [ + 500, + 323, + 890, + 382 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training. We use full-batch gradient descent, i.e., the batch size $2^{18}$ . This batch size, in general, minimizes the number of SGD steps required to fit the target image. We note that we sample directly from the coordinate grid, instead of sampling from interpolated coordinates (as in, e.g., [20]).", + "bbox": [ + 498, + 383, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hyperparameters. We tune the learning rate using the grid search. For SIREN, we tune the learning rate in the range $\\{2^{-8},\\ldots ,2^{-16}\\}$ . For Instant-NGP, we tune the learning rate in the range $\\{2^{-4},\\ldots ,2^{-15}\\}$ .", + "bbox": [ + 498, + 459, + 890, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data transformations. We consider total seven elementary data transformations (Fig. 2): Two transformations that only change the location of the pixels (random pixel permutation, zigzag permutation), and five transformations that change the intensity values of each pixels (inversion, standardization, linear scaling, centering, and gamma correction).", + "bbox": [ + 498, + 520, + 890, + 609 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Random pixel permutation (RPP). We randomly permute the location of each pixels. This transformation generally increases the frequency spectrum of the image.", + "- Zigzag permutation. We sort all the pixels in the ascending order of their intensities. Then, we place the sorted pixels in the zigzag order, starting from the upper left corner. This produces a low-frequency image.", + "- Inversion. We invert the intensity of each pixel, i.e., perform $z \\mapsto 1 - z$ on each intensity values.", + "- Standardization. We measure the mean $\\mu$ and standard deviation $\\sigma$ for the intensities of all pixels in the image. Then we standardize the intensities via $z \\mapsto \\frac{z - \\mu}{\\sigma}$ .", + "- Linear scaling. We scale the intensities of each pixel by $t$ without any centering, i.e. $z \\mapsto tz$ .", + "- Centering. We center the interval $[0,1]$ at zero and scale the intensities by $t$ , i.e., $z \\mapsto t(z - 1/2)$ .", + "- Gamma correction. We nonlinearly scale the intensity of each pixels as $z \\mapsto z^{1 / \\gamma}$ . Choosing $\\gamma > 1$ makes images brighter, and $\\gamma < 1$ makes darker." + ], + "bbox": [ + 500, + 611, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4833", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1b1d28105599f8145ef579ba8611f9667e4fb6161eebef7f034ad0ed89a66aea.jpg", + "image_caption": [ + "(a) Original" + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 263, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/87a7b4e41f58817d8606882ba5298d362ea17ecbee43771910cb8a3ca1ecf659.jpg", + "image_caption": [ + "(b) RPP", + "Figure 3. Frequency spectra of original vs. RPP. We compare the average DCT coefficients of the original and RPP Kodak images. Upper left region denotes the low-frequency, and the lower right region denotes the high-frequency." + ], + "image_footnote": [], + "bbox": [ + 279, + 89, + 454, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Results", + "text_level": 1, + "bbox": [ + 76, + 282, + 169, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We report the average acceleration factors in Tab. 1. From the table, we make several observations:", + "bbox": [ + 76, + 306, + 467, + 335 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- RPP provides a consistent acceleration over the original image; see Sec. 4 for an in-depth analysis.", + "- The zigzag permutation works tremendously well on SIREN—speeding up training by over $\\times 17$ —but slows down training Instant-NGP. We hypothesize that this is due to the axis-aligned inductive bias imposed by the spatial grid encoding; see Sec. 4.3 for more discussion.", + "- Inversion consistently slows down the training. This fact, ironically, implies that inversion might have been an effective accelerator if all \"natural images\" looked like the color-inverted images.", + "- Scaling up the intensities tends to have opposite effects on different architectures. Scaling up speeds up training in SIRENs, but slows down in Instant-NGPs.", + "- Gamma correction slows down the training, regardless of taking the power of 2 or $1/2$ . We suspect that this is due to the precision errors from taking powers. In other words, excessive scaling operations may not be helpful in accelerating the training." + ], + "bbox": [ + 76, + 338, + 467, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. A closer look at the random permutation", + "text_level": 1, + "bbox": [ + 76, + 638, + 442, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now focus on a specific type of data transformation: the random pixel permutation (RPP). The RPP relocates each pixel to a new random location, i.e.,", + "bbox": [ + 75, + 662, + 467, + 708 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\operatorname {c o o r d s} _ {i}, \\text {v a l u e s} _ {i}\\right) \\mapsto \\left(\\operatorname {c o o r d s} _ {\\pi (i)}, \\text {v a l u e s} _ {i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 720, + 467, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for some random permutation $\\pi(\\cdot)$ . The marginal distributions of the input coordinates or the output values remain the same. As we have seen in Tab. 1, the RPP transformation accelerates the fitting of the corresponding neural field, which is very unexpected and difficult to explain.", + "bbox": [ + 75, + 750, + 467, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Why is this strange? From the perspective of the spectral bias, the RPP operation should have slowed down the training speed, instead of accelerating it. As demonstrated by Rahaman et al. [22], typical neural networks first rapidly fit the low-frequency components of the target signal, and fit", + "bbox": [ + 75, + 825, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d6a74ce77c8ed3c28cdeac9caa716bd64102a6efdf9f650f3912729470509996.jpg", + "image_caption": [ + "Figure 4. PSNR curves for a single Kodak image. The original image (orange) excels during the early stage of training but the RPP image quickly reaches PSNR 50 in the middle of the training." + ], + "image_footnote": [], + "bbox": [ + 513, + 90, + 870, + 256 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c890d06d8bbc48448c28ff8cf99e6323af60477bcee76c5ec86ecc73b0f49d8e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Target PSNRRatio
30dB50dB
Original105.81371.40.08
Random pixel perm.851.81100.50.79
", + "bbox": [ + 549, + 301, + 834, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. The number of steps to reach PSNR 30dB and 50dB. We measure the average steps to reach moderate and high PSNR levels over Kodak images, and report the average ratio.", + "bbox": [ + 498, + 371, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the high-frequency components much later. The RPP transformation, in this sense, should have been detrimental to the training. In fact, RPP images tend to have more higher-frequency components than the original images. In Fig. 3, we provide the average discrete cosine transform (DCT) coefficients of the original and RPP images; for visualization, we raise the coefficients to the power of 0.03, similar to [35]. We observe that the original image is more biased toward low-frequency than RPP. However, we also observe that RPP images fit faster than the original images.", + "bbox": [ + 496, + 428, + 890, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the remainder of this section, we identify three different aspects that the training dynamics of RPP images are critically different from that of original images. These aspects, when put together, support our \"blessings of no pattern\" hypothesis $(\\star)$ that RPP accelerates training by removing easy-to-fit patterns that can be harmful to reaching a high level of fidelity. In particular, we show that", + "bbox": [ + 496, + 579, + 890, + 684 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- RPP is slow to reach moderate PSNR levels, but is fast to reach high PSNR (Sec. 4.1).", + "- there is a linear path that connects the moderate-to-high PSNR points in the RPP loss landscape (Sec. 4.2).", + "- model trained on RPP images tends to have less structured error, while vanilla training leads to error patterns that reflect the underlying encoding schemes (Sec. 4.3)." + ], + "bbox": [ + 500, + 686, + 888, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. The PSNR curve: Slower to approximate well, but faster to approximate “very well”", + "text_level": 1, + "bbox": [ + 498, + 800, + 888, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we observe that RPP images tend to achieve moderate PSNRs (e.g., 30dB) much later than the original images, but they quickly reach high PSNRs (e.g., 50dB) afterwards.", + "bbox": [ + 496, + 840, + 888, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Fig. 4, we provide an example plot of fitting a SIREN", + "bbox": [ + 517, + 885, + 888, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4834", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "on a natural image from the Kodak dataset. From the figure, we can immediately make the following observations:", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- RPPs are slow starters. The training PSNR of the original image quickly arrives at $\\sim 30\\mathrm{dB}$ the early stage of training, even before taking 300 SGD iterations. On the other hand, the PSNR of the RPP image remains very small, under 15 dB at the similar number of steps.", + "- Explosive surge in later stage. After staying at a low PSNR level (under 20 dB) for a while, the PSNR of RPP images bursts explosively. The PSNR jumps from $\\sim 15\\mathrm{dB}$ to 50dB in less than 100 SGD steps. On the other hand, the PSNR curve of the original image oscillates wildly at 30-35dB level for a long time, and gradually reaches the 50dB at around 1600 steps." + ], + "bbox": [ + 76, + 121, + 467, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These observations are consistent over the choice of the target image; we provide a comprehensive collection of figures in the supplementary materials.", + "bbox": [ + 76, + 303, + 467, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a more quantitative comparison, we compare the average number of SGD steps to arrive the PSNR of 30dB and 50dB for the original and RPP images (Tab. 2). Again, we use the images from the Kodak dataset and fit with SIRENs.", + "bbox": [ + 76, + 347, + 467, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We observe that, for original images, the number of steps to reach 30dB is around 100 steps, while the number of SGD steps to reach the 50dB is over 1300 steps. That is, it takes almost $13 \\times$ more steps to reach the high PSNR than for moderate PSNRs. On the other hand, for RPP images, it takes over 800 steps to reach the moderate PSNR level, while it takes only 300 more steps to reach the high PSNR.", + "bbox": [ + 76, + 407, + 467, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Linear paths in the loss landscape: RPP images find a \"linear expressway\"", + "text_level": 1, + "bbox": [ + 76, + 523, + 467, + 554 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From the previous observation, it seems likely that, for RPP images, there may exist an expressway in the neural field parameter space that connects the moderate-PSNR parameter with the high-PSNR parameter; on this expressway, the SGD may not encounter too many hills to circumvent, and may mostly follow a smooth linear path.", + "bbox": [ + 76, + 561, + 467, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate this intuition, we visualize the loss landscape of the SIREN trained on Kodak images. In particular, we capture two different phases of training.", + "bbox": [ + 76, + 652, + 467, + 696 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Early phase. We plot the linear path from the initialization to 30dB point, i.e., the parameter that first achieves PSNR 30dB during the training (Fig. 5)", + "2. Late phase. We plot the linear path from the 30dB point to the PSNR 50dB point (Fig. 6)." + ], + "bbox": [ + 76, + 696, + 467, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To generate such visualization, we project the parameter space into a two-dimensional space, as in [13]. Unlike [13], we fix one axis to a directional vector between two parameter points that we want to capture (e.g., 30dB point and 50dB point); the other axis has been decided randomly.2", + "bbox": [ + 76, + 773, + 467, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During the early phase (Fig. 5), we observe that the loss landscape of RPP is quite hostile; unlike in original images,", + "bbox": [ + 76, + 848, + 467, + 878 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/214cc116f3cf24270d496b115801b22dcb4a4906c5d1162105819ce4fd441447.jpg", + "image_caption": [ + "(a) Elevated view; original" + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 691, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d2e11adfcd62481c61e914d9da8315ae422e8e982a7b9c9fe710432484d63116.jpg", + "image_caption": [ + "(b) Elevated view; RPP" + ], + "image_footnote": [], + "bbox": [ + 702, + 90, + 888, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0fe069709246fb805756ff39a40c3c7d7066851a7200b564b12089e24ad5570f.jpg", + "image_caption": [ + "(c) Side view; original" + ], + "image_footnote": [], + "bbox": [ + 506, + 222, + 691, + 319 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0daeb6394d4aec17a6612133b8dbb0cfbe4f890a68f44c9f4555dcd5ae111e6b.jpg", + "image_caption": [ + "(d) Side view; RPP" + ], + "image_footnote": [], + "bbox": [ + 702, + 222, + 888, + 319 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/712935ba3947a2adc3cb3ac979f390f183d0b46e9d9ca6bc729da8d42bac533a.jpg", + "image_caption": [ + "Figure 5. SIREN loss landscape: from initial point to 30dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the initial point and the parameter that achieves PSNR 30. For RPP, the minima is much narrower and lacks a clear pathway toward it, unlike in the original image.", + "(a) Original", + "Figure 6. SIREN loss landscape: from 30dB point to 50dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the parameters that first achieve PSNR 30 (■) and PSNR 50 (★), respectively. The loss barriers between two minima are dramatically different; 15.3dB for the original image, and 28.3dB for the RPP (averaged over all Kodak images)." + ], + "image_footnote": [], + "bbox": [ + 506, + 421, + 689, + 532 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a32c7b7c05b5c5bf11cf6ec5d1ab9f3d1fc91531a414db5a4f2cab64c33ab0fa.jpg", + "image_caption": [ + "(b) RPP" + ], + "image_footnote": [], + "bbox": [ + 699, + 425, + 888, + 531 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the minima that 30dB point belongs to is quite narrow and there is no clear pathway toward the 30dB point.", + "bbox": [ + 496, + 656, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During the late phase (Fig. 6), for the RPP image, once the parameter arrives at the minima, there exists a linear path that connects the $30\\mathrm{dB}$ point to the $50\\mathrm{dB}$ point. If we measure the loss barrier, i.e. the maximum loss on the linear path between $30\\mathrm{dB}$ and $50\\mathrm{dB}$ points, it is as low as $28.3\\mathrm{dB}$ for the RPP versions of Kodak images. For original images, the loss barrier is quite high (15.3dB).", + "bbox": [ + 496, + 686, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Patterns in the error: The errors are less structured in RPP images", + "text_level": 1, + "bbox": [ + 500, + 801, + 888, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Another interesting property of RPP is that the errors that the neural field makes are more evenly distributed among the pixels, lacking a clearly distinguishable pattern. It turns out that the whiteness of the RPP error can help generat-", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2A similar method has been considered by Goodfellow et al. [7].", + "bbox": [ + 94, + 886, + 434, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4835", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ac9391826d2d3d69625971feecf263661f4894f079a8ab0ec9a469b742d8865f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 343, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/12aaf41fef2c5eb31f014ba123de8abd5e51ca5c6138b55048f3b572ca7f3f91.jpg", + "image_caption": [ + "(a) Original" + ], + "image_footnote": [], + "bbox": [ + 352, + 88, + 614, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad7903394cdca0610e29f820ac0a97316ef20880a39807d6f00ac89790767fef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 88, + 890, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/017b3678fc9ceeda8164c8ff6693aaf6cb94c8c2779982c65732d658fe819b83.jpg", + "image_caption": [ + "Figure 7. Example reconstructions at a target PSNR value of 30 (SIREN). Random pixel permutation enables the network to prioritize the restoration of high-frequency, fine details, whereas the original representation tends to steer the network toward restoring low-frequency components initially. While this behavior may pose challenges during the early stages of training, it ultimately facilitates achieving visually more plausible reconstructions much earlier than the original representation." + ], + "image_footnote": [], + "bbox": [ + 78, + 227, + 341, + 343 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/55137ca5d21e518594aeb4fdb02b4fefaaa4b5febc7697db64cf297f5b9cdea5.jpg", + "image_caption": [ + "(b) RPP" + ], + "image_footnote": [], + "bbox": [ + 352, + 226, + 614, + 342 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e5d6352037d23b4c5f455fb99a78e3373240a6dc2b43dec53fcae89f4efa5d3a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 227, + 887, + 342 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/eac09e35d0da007e50a8bb31029abad5a57b9b40f72c04b782a131b2c52be04b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Target PSNR
20304050
Original10.51e-0423.68e-0619.46e-085.90e-10
Random pixel perm.5.68e-045.89e-067.59e-085.81e-10
Average ratio2.03×5.20×5.80×1.55×
", + "bbox": [ + 78, + 422, + 460, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Loss variance over pixels. We measure the average pixel loss variance in the SIREN trained on Kodak dataset, measured at various levels of PSNR. The \"average ratio\" denotes the mean of $\\mathrm{Var}(\\mathrm{original}) / \\mathrm{Var}(\\mathrm{RPP})$ . RPP has a lower loss variance at all PSNRs.", + "bbox": [ + 76, + 506, + 468, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing more visually sharp and satisfactory images than neural fields trained on original images.", + "bbox": [ + 76, + 580, + 468, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Tab. 3, we measure the pixel loss variance in both original and RPP images trained to various target PSNR levels. From the table, we observe that the loss variance is up to $5.80 \\times$ larger in the neural fields trained on the original images than on RPP images. This implies that, for original images, some pixels in the original image are fit much faster than other pixels. Putting that differently, the neural field trained on the unpermuted images tends to prioritize learning a specific type of patterns first, while the neural field trained on RPP images does less so.", + "bbox": [ + 75, + 611, + 468, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Exactly what pattern is RPP avoiding to fit? In Figs. 7 and 8, we compare the images generated by the neural fields trained on original and RPP images on SIREN and Instant-NGP, respectively. In Fig. 7, we observe that SIRENs trained on original images have thicker wavy patterns, which is likely to be a consequence of the sinusoidal encoding structure of SIREN. The models trained on RPP images, on the other hand, have much sharper texture with fine-grained noise. A similar phenomenon is observed in", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the case of Instant-NGP (Fig. 8). Here, we observe that the models trained on original images attain axis-aligned artifacts; black (or white) horizontal (or vertical) blocks appear in the rendered images. On the other hand, the error is much less structured in models trained on RPP images.", + "bbox": [ + 498, + 426, + 890, + 502 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Related work", + "text_level": 1, + "bbox": [ + 500, + 523, + 635, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Optimization bias of neural networks. It has been well known, both theoretically and empirically, that SGD-based optimization algorithms are biased toward learning \"simplex solutions,\" for various notions of simplicity. A prominent example is the spectral bias, a tendency to prioritize learning lower-frequency components of the target function [3, 22]. Other types of biases have also been studied in the literature: SGD tends to prefer learning smaller-norm solutions [9, 21] and low-rank solutions [32, 34]. These works mostly focus on explaining how such simplicity biases are advantageous in learning a solution that can generalize well (see, e.g., [23]). Our work, in contrast, describes how such bias can be disadvantageous in terms of the training speed, instead of the generalization performance.", + "bbox": [ + 496, + 550, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Random labels and memorization. The question of how neural nets behave when trained on random labels has been actively studied since its connection to the generalization capability of deep learning has been established [38]. Arpit et al. [2] finds that neural networks tend to learn simple patterns first and then memorize the unexplainable samples—such as random label and data—in the later phase. A more recent study argues that training on randomly labeled data can actually be advantageous [17]; pre-training on random", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4836", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a38514ea60a6a0fefa78c4927b3495da11b34bbddfcffb67498562b44902c270.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 269, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/924c2b7c7a3629655a5f8a7ec8f9ea929ff491ac4924e195a6fe52754661b49e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 88, + 464, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c0858e07a9b311ea25f3bb0a0a5cf226a9c55af18b979cb10b64138617fec971.jpg", + "image_caption": [ + "(a) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 83, + 247, + 267, + 390 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cccaa638c5a0a5e625b76f762801c3861d13e85401ed9891fb686280e818aa19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 247, + 464, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/263dbfefae65ebc89efdbe98b52a920d5b10d01aa4d3844f0e42ff465de9da34.jpg", + "image_caption": [ + "(b) Original", + "Figure 8. Example reconstructions at a target PSNR value of 20 (Instant-NGP). Similarly to the SIREN case, we observe that Instant-NGPs trained on the RPP images have much less visually distinguishable artifacts. The models trained on original images tend to have axis-aligned blocks of error, which is likely to have originated from the spatial grid encoding of the model." + ], + "image_footnote": [], + "bbox": [ + 81, + 405, + 267, + 549 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7ff8359250ed7003e4ff95ae4f2fba08bec7737c0ddc91461b947bf066c424ef.jpg", + "image_caption": [ + "(c) RPP" + ], + "image_footnote": [], + "bbox": [ + 276, + 405, + 460, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "data helps fitting the training data, when eventually fine-tuning on the dataset with correct labels. Different from these works, our work discovers how random label can be beneficial in the neural field context, without any consideration on further fine-tuning.", + "bbox": [ + 75, + 669, + 467, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Faster training of neural fields. Other than the works described in the introduction, there have been many other attempts to accelerate the neural field training by designing better encoding schemes. Positional encodings [5, 19, 27, 29] and spatial grids [6, 16, 18, 20] are the most popular options, and some works also use tree-like structures [28, 36]. Our work is complementary to this line of works, and argues that transforming the data in the original data space can provide auxiliary training speed boosts. We also note that a concurrent work also aims to boost the training speed by", + "bbox": [ + 75, + 750, + 467, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "modifying the given data [15]. In particular, [15] finds that separating the visual signals into many sub-segments can facilitate the convergence of SIRENs and proposes a meta-learning algorithm to speed up training. Our work considers a more general class of data transformations, and focus on understanding how transformations accelerate training.", + "bbox": [ + 498, + 90, + 890, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 202, + 617, + 217 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Learning neural fields poses a unique challenge, as the primary objective is to overfit to the given data—an aim contrary to the typical goals in other problem domains where learning attempts to achieve regularization to prevent overfitting. In our study of this distinctive problem, we discovered that certain data transformations can expedite the network's acquisition of fine details more rapidly than when learning from the original images. Specifically, we demonstrated that random pixel permutations, which explicitly make learning low-frequency details more challenging, guide the network away from fixating on low-frequency components. This resulted in significantly enhanced PSNR within a given computational budget and, furthermore, yielded visually more plausible reconstructions at the same PSNR level. Our insights are substantiated by thorough empirical evaluations.", + "bbox": [ + 496, + 229, + 890, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation & future direction. A notable limitation of our approach is that its direct applicability may be constrained when learning neural networks for other problem domains such as classification and regression, where regularization is crucial. As a future work, we aim to conduct more comprehensive studies to understand how data transformations affect both trainability and generalization of neural fields (and other neural networks). Such exploration may offer new insights on how to modify the given workload to jointly optimize the training cost and the model performance.", + "bbox": [ + 496, + 473, + 890, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Another, more narrowly scoped future direction will be to gain a more concrete, theoretical understanding on the effect of random pixel permutations on the training dynamics of neural fields. Although our empirical analyses provide some insights into how RPP can help accelerate the training, we are yet to fully understand why fitting the easy patterns slows down the later phase of training. Deeper understandings on this matter may lead to impactful lessons applicable to any deep learning domain that involves long training.", + "bbox": [ + 496, + 626, + 890, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was partly supported by the National Research Foundation of Korea (NRF) grant (RS-2023-00213710, Neural Network Optimization with Minimal Optimization Costs), and partly by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2022- 0-00713, Meta-learning applicable to real-world problems, No.2019-0-01906, Artificial Intelligence Graduate School Program (POSTECH)), all funded by the Korea government (MSIT).", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4837", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. NTIRE 2017 challenge on single image super-resolution: Dataset and study. 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In ICLR, 2017. 7" + ], + "bbox": [ + 78, + 90, + 468, + 375 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4839", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/In Search of a Data Transformation That Accelerates Neural Field Training/e8b54a6a-20cf-4428-8c04-7ff202724221_model.json b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/e8b54a6a-20cf-4428-8c04-7ff202724221_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea995a4d271df3baaf5b311e0d42b9258efff2f --- /dev/null +++ b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/e8b54a6a-20cf-4428-8c04-7ff202724221_model.json @@ -0,0 +1,2871 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.131, + 0.868, + 0.154 + ], + "angle": 0, + "content": "In Search of a Data Transformation That Accelerates Neural Field Training" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.182, + 0.731, + 0.218 + ], + "angle": 0, + "content": "Junwon Seo* Sangyoon Lee* Kwang In Kim Jaeho Lee Pohang University of Science and Technology (POSTECH)" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.22, + 0.742, + 0.234 + ], + "angle": 0, + "content": "{junwon.seo, sangyoon.lee, kimkin, jaeho.lee}@postech.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.558 + ], + "angle": 0, + "content": "Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed—generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.585, + 0.21, + 0.601 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.47, + 0.762 + ], + "angle": 0, + "content": "Neural field is a form of data representation that parameterizes each target signal as a neural network that maps spatiotemporal coordinates to the signal values [33]. For example, a colored image can be represented by a model that maps (X,Y) pixel coordinates to the corresponding (R,G,B) values. This parameterization enjoys many advantages in faithfully and efficiently representing high-dimensional signals with fine detail, and thus is being widely used for modeling signals of various modalities, such as image [4], video [10], 3D scene [19], or spherical data [8]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.471, + 0.868 + ], + "angle": 0, + "content": "A key obstacle that prevents the widespread adoption of neural fields is their training cost. To represent each datum as a neural field, one must train a neural network using many SGD iterations. For instance, NeRF requires at least 12 hours of training time on GPUs to represent a single 3D scene [19]. Representing a set of data thus requires a considerable amount of computation and time, making it very" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.27, + 0.878, + 0.286 + ], + "angle": 0, + "content": "difficult to develop practical applications of neural fields." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.286, + 0.893, + 0.422 + ], + "angle": 0, + "content": "Many prior works view the \"optimization bias\" as a major cause behind the long training time of neural fields [29]. In particular, the spectral bias of the SGD-based training is known to bias the neural network to prioritize fitting the low-frequency components of the target signal and leave high-frequency components for the late stage of training [22]. It has been observed that such a tendency greatly hinders the neural fields from expressing natural data (e.g., images) with fine, high-frequency details [29, 37]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.589 + ], + "angle": 0, + "content": "The prevailing strategy to mitigate such bias is to introduce a useful prior (or inductive bias) that can help neutralize the negative effects of the bias. One popular approach is to develop new network components that bring a favorable architectural prior, such as the Fourier features [19], sinusoidal activation [27], or spatial encoding [18, 20]. Other works also attempt to introduce the prior in the form of initial parameters that have been meta-learned from a large set of signals [26, 30]. Such meta-learned initializations tend to have rich high-frequency spectra, which can help fitting natural signals within a small number of SGD steps [30]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.589, + 0.894, + 0.62 + ], + "angle": 0, + "content": "In this paper, we approach the problem from a different angle. In particular, we ask the following question:" + }, + { + "type": "text", + "bbox": [ + 0.542, + 0.624, + 0.851, + 0.655 + ], + "angle": 0, + "content": "\"Can we exploit the optimization bias of SGD, instead of fighting against it?\"" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Precisely, we ask whether we can transform the datum in a way that the optimization bias acts favorably in fitting the transformed data with a neural field. If there exists such a transformation, and if it admits an efficiently computable inverse, we may be able to use the following strategy to reduce the neural field training cost: we train a neural field that expresses the transformed signal, and the original signal can be recovered from the model by applying an inverse transformation to the signal generated by the model (Fig. 1). Contribution. As a first step to answer this question, we conduct an extensive empirical study on how applying simple data transformations affect the computational cost of training the corresponding neural field. In particular, we compare the number of SGD steps needed to fit the transformed data to a certain fidelity level (e.g., PSNR 50 for images), with the steps to fit the original data. We try to" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.203, + 0.888 + ], + "angle": 0, + "content": "*equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.434, + 0.9 + ], + "angle": 0, + "content": "1code: https://github.com/effl-lab/DT4Neural-Field" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.434, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "4830" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.887, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.895, + 0.309 + ], + "angle": 0, + "content": "Figure 1. Overall pipeline. We consider a three-step procedure to train neural fields. (1) Apply a data transformation to the target datum. (2) Train a neural field to fit the transformed data. (3) Reconstruct the original data by generating the transformed datum from the neural field, and then applying the inverse of the data transformation. By selecting the data transformation carefully, we can significantly reduce the computational cost required to train a neural field that achieves the desired quality of approximation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.47, + 0.367 + ], + "angle": 0, + "content": "tal seven different data transformations, from the one that permutes the location of the pixels to the one that scales the intensity values of each pixel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.47, + 0.534 + ], + "angle": 0, + "content": "From the experiment, we make a surprising observation: we find that the random pixel permutation (abbr. RPP) provides a consistent acceleration on a range of datasets and various neural field architectures with sophisticated encoding schemes. The RPP is in fact the only data transformation that provided acceleration on every experimental setups that we considered. We find that the original data requires, on average, \\(\\sim 30\\%\\) greater number of SGD steps to achieve the similar fidelity level than the RPP data. As RPP tends to bias the data toward high-frequency, it is quite counter-intuitive that they can be fit faster than the original signals." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Why does the random pixel permutation accelerate neural field training? To explain this phenomenon, we articulate the following \"blessings of no pattern\" hypothesis:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.597, + 0.452, + 0.704 + ], + "angle": 0, + "content": "Original data often have smooth, representative patterns that facilitate easy optimization, particularly in the early phase of learning. However, this smoothness quickly transforms into an obstacle when aiming for a sufficiently high level of fidelity. Random pixel permutation removes these easy-to-fit patterns, which accelerates optimization in the long run. \\((\\star)\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To corroborate our hypothesis \\(\\star\\), we take an in-depth look into the training dynamics of the original and the RPP data. We find that, indeed the training speed on the RPP data is slower than on the original data during the early training phase (Sec. 4.1). However, after training for a sufficient number of epochs, the neural field trained on RPP data finds a \"linear loss highway\" on which the optimization is very easy; the optimization on original data fails to find one (Sec. 4.2). Furthermore, we find that the errors in the RPP images are more evenly distributed over pixels and lack visually distinguishable structures; errors in original images tend to have periodic or axis-aligned patterns, which might" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.322, + 0.831, + 0.336 + ], + "angle": 0, + "content": "be the artifacts of the encoding scheme (Sec. 4.3)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.337, + 0.858, + 0.351 + ], + "angle": 0, + "content": "To sum up, our contribution can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.356, + 0.892, + 0.416 + ], + "angle": 0, + "content": "1. Through systematic study, we find that simple data transformations can dramatically change the training speed of neural field \\((\\times 0.1 - \\times 20)\\), even on state-of-the-art neural fields architectures with sophisticated encodings [20]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.417, + 0.891, + 0.462 + ], + "angle": 0, + "content": "2. We discover that random pixel permutations (RPP) provide consistent acceleration over fitting the original image, providing \\( \\times 1.08 - \\times 1.50 \\) speedups." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.462, + 0.892, + 0.507 + ], + "angle": 0, + "content": "3. We conduct an in-depth analysis which sheds light on how RPP speeds up the training by removing the easy-to-fit patterns that slow down the training eventually." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.356, + 0.892, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.678 + ], + "angle": 0, + "content": "Despite the limitation of RPP that it may be difficult to be applied for applications where generalization is critical, our study has at least two potential impact areas. First, the RPP itself may be useful in the applications of neural field where a strong training fidelity is the core performance criterion, such as data compression [24]. In fact, one of the core challenges in neural-field-based data compression is the slow encoding speed (see, e.g., COOL-CHIC [12]). Second, our study provides a concrete starting point in developing a new data transformation that strikes the balance between the training speed and the generalizability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.691, + 0.691, + 0.707 + ], + "angle": 0, + "content": "2. General framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.762 + ], + "angle": 0, + "content": "The general framework of finding data transformations that accelerate neural field training can be formalized as an optimization problem, as we describe in this section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.628, + 0.786 + ], + "angle": 0, + "content": "2.1. Formalisms" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Suppose that we want to use the neural field parameterization to approximate some signal \\(\\mathbf{x} \\in \\mathcal{X}\\). Here, the signal space \\(\\mathcal{X}\\) is the space of all signals that have the same data type. For example, we can let \\(\\mathcal{X}\\) be the set of all \\(256 \\times 256\\) RGB images; in such case, we may have \\(\\mathcal{X} \\subseteq \\mathbb{R}^{256 \\times 256 \\times 3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The data transformation \\( T: \\mathcal{X} \\to \\mathcal{X} \\) maps an element in the signal space to another element. We define the trans-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4831" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.089, + 0.28, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.168, + 0.212, + 0.178 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.09, + 0.481, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.305, + 0.168, + 0.464, + 0.179 + ], + "angle": 0, + "content": "(b) Random pixel permutation" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.091, + 0.685, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.168, + 0.648, + 0.179 + ], + "angle": 0, + "content": "(c) Zigzag permutation" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.091, + 0.889, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.168, + 0.825, + 0.178 + ], + "angle": 0, + "content": "(d) Inversion" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.186, + 0.28, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.264, + 0.231, + 0.275 + ], + "angle": 0, + "content": "(e) Standardization" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.187, + 0.481, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.264, + 0.458, + 0.276 + ], + "angle": 0, + "content": "(f) Linear Scaling \\((t = 0.5)\\)" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.187, + 0.685, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.264, + 0.645, + 0.276 + ], + "angle": 0, + "content": "(g) Centering \\((t = 1)\\)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.187, + 0.889, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.702, + 0.264, + 0.877, + 0.276 + ], + "angle": 0, + "content": "(h) Gamma correction \\((\\gamma = 2.0)\\)" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.285, + 0.684, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.31, + 0.893, + 0.338 + ], + "angle": 0, + "content": "Figure 2. Data transformations considered. In each subfigure, we visualize the data transformations by illustrating how the transformed image (left) and the intensity histogram (right) looks like on a Kodak image." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.352, + 0.469, + 0.381 + ], + "angle": 0, + "content": "formation space \\(\\mathcal{T}\\) as a set of data transformations on \\(\\mathcal{X}\\) that has an inverse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.469, + 0.427 + ], + "angle": 0, + "content": "Our goal is to find a data transformation \\( T \\) that minimizes the training cost of fitting the transformed signal \\( T(\\mathbf{x}) \\). To formalize this, we define the training cost" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.436, + 0.469, + 0.452 + ], + "angle": 0, + "content": "\\[\n\\operatorname {c o s t}: \\mathcal {X} \\times \\mathcal {T} \\rightarrow \\mathbb {R} _ {+}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Here, the function \\( \\mathrm{cost}(\\mathbf{x}, T) \\) measures the computational burden required to train a neural field for \\( T(\\mathbf{x}) \\), whenever its outcome is inverted back via \\( T^{-1} \\), approximates the original signal \\( \\mathbf{x} \\) with the desired level of precision. The burden may be measured in various ways, e.g., the number of SGD steps, FLOPs, or wall-clock time. We note that the training cost of \\( \\mathbf{x} \\) using \\( T(\\cdot) \\) need not be identical to the training cost of fitting \\( T(\\mathbf{x}) \\) with the same precision, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.59, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\operatorname {c o s t} (\\mathbf {x}, T) \\neq \\operatorname {c o s t} (T (\\mathbf {x}), \\mathrm {I d}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.469, + 0.705 + ], + "angle": 0, + "content": "especially when the transformation involves scaling of the signal. Also, the training cost may heavily depend on the choice of neural field architectures, hardware type, and the batch size—using a larger batch size tends to reduce the number of steps until convergence [25], but it also requires training with a larger memory." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.706, + 0.469, + 0.721 + ], + "angle": 0, + "content": "Given these tools, we work to consider the optimization" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.726, + 0.469, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\text {m i n i m i z e} \\quad \\operatorname {c o s t} (\\mathbf {x}, T), \\quad \\text {s u b j e c t t o} \\quad T \\in \\mathcal {T} ^ {*}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(\\mathcal{T}^* \\subseteq \\mathcal{T}\\) is a subset of the transformation space that satisfies some desired properties. The set \\(\\mathcal{T}^*\\) can be configured in many different ways, to account for the expected usages of the trained neural fields. This problem can also be extended to a version where we have a probability distribution of the signals \\(\\mathbf{x}\\), and find a single transformation \\(T\\) that minimizes the expected cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Scope of this paper. While the most general framework is to solve the optimization (3) directly, the problem is intractable unless we have an expressive, well-paramaterized" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.893, + 0.396 + ], + "angle": 0, + "content": "transformation space \\(\\mathcal{T}^*\\) that admits an effective optimization method. In this paper, we focus on the proof-of-concept that there exists some choice of \\(T\\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.412, + 0.892, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\operatorname {c o s t} (\\mathbf {x}, T) < \\operatorname {c o s t} (\\mathbf {x}, \\operatorname {I d}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.441, + 0.892, + 0.472 + ], + "angle": 0, + "content": "(Sec. 3), and deepening our understanding on when and why such \\( T(\\cdot) \\) can accelerate the training (Sec. 4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.649, + 0.501 + ], + "angle": 0, + "content": "2.2. Example cases" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.509, + 0.892, + 0.554 + ], + "angle": 0, + "content": "Here are some examples desired properties of data transformation, and how they relate to practical applications. We provide a more in-depth discussions in the ??" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.893, + 0.691 + ], + "angle": 0, + "content": "Efficient invertibility. The inverse \\( T^{-1} \\) should be able to be computed efficiently, e.g., by performing a linear operation. Ideally, one may wish to be able to combine the inverse transformation into the neural field by modifying the parameters of the trained neural field directly. For instance, if \\( T(\\mathbf{x}) = -\\mathbf{x} \\), we can incorporate the inverse in the neural field by negating the final layer weights of the neural field. This property is useful whenever we expect many repeated inferences of the neural field, e.g., for real-time interaction." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.692, + 0.892, + 0.798 + ], + "angle": 0, + "content": "Retains interpolatability. We want our transform \\( T \\) to admit a principled way to sample the value of interpolated coordinates from the neural field that approximates the transformed signal. In some neural field applications, e.g., superresolution [4], this interpolating capability plays an essential role. On the other hand, some applications like data compression do not involve any interpolation [24]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.857, + 0.832 + ], + "angle": 0, + "content": "3. Data transformations vs. training speed" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In this section, we compare the training cost of the neural field training on various data transformation schemes. As it turns out, there indeed exists a nice data transformation that satisfies ineq. 4: the random pixel permutation (RPP)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4832" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.216 + ], + "angle": 0, + "content": "
ArchitectureDatasetRandom pixel perm.Zigzag perm.InversionStandardizationLinear ScalingCenteringGamma Correction
t=0.5t=2.0t=1.0t=2.0γ=0.5γ=2.0
SIRENKodak1.26×17.90×0.72×2.20×0.79×1.39×0.76×0.97×0.36×0.80×
DIV2K1.30×21.74×0.70×2.36×0.82×1.45×0.97×1.22×0.30×0.90×
CLIC1.08×17.07×0.68×2.18×0.76×1.36×0.87×1.14×0.24×0.82×
Instant-NGPKodak1.50×0.86×0.21×0.45×1.15×0.75×1.24×0.80×0.29×0.38×
DIV2K1.32×0.80×0.20×0.61×1.12×0.64×1.39×0.97×0.14×0.33×
CLIC1.35×0.78×0.07×0.53×1.03×0.68×0.99×0.66×0.12×0.32×
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.22, + 0.895, + 0.266 + ], + "angle": 0, + "content": "Table 1. Acceleration factors of data transformations. We compare the average acceleration factor (eq. 5) of seven data transformations under six different combinations of datasets and models. We take average of cost ratios, instead of ratios of averages, to avoid the statistic being driven by a small number of outliers that require very long training time. The shaded figures denote the speedup." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.277, + 0.266, + 0.294 + ], + "angle": 0, + "content": "3.1. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.47, + 0.361 + ], + "angle": 0, + "content": "We focus on the task of 2D image regression. This choice reduces the computational burden of fitting each datum, so that we can make experimental validations on multiple datasets and models with extensive hyperparameter tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.47, + 0.481 + ], + "angle": 0, + "content": "For the training cost, we use the number of SGD steps until we reach the training PSNR over 50dB (a near-perfect reconstruction for 8-bit images). The number of SGD steps is an informative indicator of the total FLOPs and runtime for any fixed choice of hardware, model architecture, and data. Importantly, we tune the learning rate for each (transformed) image, making it close to the scenario where all settings have been optimized to minimize the runtime." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.482, + 0.469, + 0.513 + ], + "angle": 0, + "content": "For each choice of an image and the data transformation, we measure the acceleration factor, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.517, + 0.47, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\operatorname {a c c} (\\mathbf {x}, T) \\triangleq \\frac {\\operatorname {c o s t} (\\mathbf {x} , \\operatorname {I d})}{\\operatorname {c o s t} (\\mathbf {x} , T)}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.316, + 0.568 + ], + "angle": 0, + "content": "Other configurations are as follows." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.569, + 0.398, + 0.584 + ], + "angle": 0, + "content": "Datasets. We use three different image datasets:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.584, + 0.469, + 0.614 + ], + "angle": 0, + "content": "- Kodak. Consists of 24 different images from the Kodak lossless true color image suite [11]." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.614, + 0.47, + 0.644 + ], + "angle": 0, + "content": "- DIV2K. Consists of 100 images in the validation split of the DIV2K image super-resolution challenge (HR) [1]." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.645, + 0.47, + 0.719 + ], + "angle": 0, + "content": "- CLIC. Consists of 100 images from the validation split of the dataset for the Challenge on Learned Image Compression 2020 (CLIC) [31]. There are total 102 images in the validation split, but we removed two images that have a sidelength shorter than 512 pixels." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.584, + 0.47, + 0.719 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.825 + ], + "angle": 0, + "content": "We pre-process each image in the datasets as follows. Following BACON [14], we resize each image into \\(512 \\times 512\\) pixels by first center-cropping the image to a square with sidelengths equal to the shorter sidelength of the original image, and then resizing with the Lanczos algorithm. Next, we convert the image to grayscale. Finally, we apply sRGB to Linear RGB operation, as in Instant-NGP [20]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.856 + ], + "angle": 0, + "content": "The resulting images have \\(512 \\times 512\\) pixels (thus total \\(2^{18}\\) pixels) with intensities lying in the interval \\([0, 1]\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.445, + 0.87 + ], + "angle": 0, + "content": "Models. We use two different neural field architectures." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- SIREN. A classical architecture that uses multi-layered perceptrons with sinusoidal activation functions [27]. We" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.278, + 0.892, + 0.323 + ], + "angle": 0, + "content": "configure the model to have three hidden layers with 512 neurons in each layer and output dimension 1. We use the default frequency scaling hyperparameter \\(\\omega_0 = 30\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.324, + 0.892, + 0.383 + ], + "angle": 0, + "content": "- Instant-NGP. A more recently proposed neural field with multi-resolution hash encodings [20]. We use the default setup for the image regression, with the maximum hash table size and 16-bit parameters." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.892, + 0.459 + ], + "angle": 0, + "content": "Training. We use full-batch gradient descent, i.e., the batch size \\(2^{18}\\). This batch size, in general, minimizes the number of SGD steps required to fit the target image. We note that we sample directly from the coordinate grid, instead of sampling from interpolated coordinates (as in, e.g., [20])." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.46, + 0.892, + 0.521 + ], + "angle": 0, + "content": "Hyperparameters. We tune the learning rate using the grid search. For SIREN, we tune the learning rate in the range \\(\\{2^{-8},\\ldots ,2^{-16}\\}\\). For Instant-NGP, we tune the learning rate in the range \\(\\{2^{-4},\\ldots ,2^{-15}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.521, + 0.892, + 0.611 + ], + "angle": 0, + "content": "Data transformations. We consider total seven elementary data transformations (Fig. 2): Two transformations that only change the location of the pixels (random pixel permutation, zigzag permutation), and five transformations that change the intensity values of each pixels (inversion, standardization, linear scaling, centering, and gamma correction)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.612, + 0.892, + 0.657 + ], + "angle": 0, + "content": "- Random pixel permutation (RPP). We randomly permute the location of each pixels. This transformation generally increases the frequency spectrum of the image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.657, + 0.892, + 0.718 + ], + "angle": 0, + "content": "- Zigzag permutation. We sort all the pixels in the ascending order of their intensities. Then, we place the sorted pixels in the zigzag order, starting from the upper left corner. This produces a low-frequency image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.718, + 0.892, + 0.747 + ], + "angle": 0, + "content": "- Inversion. We invert the intensity of each pixel, i.e., perform \\( z \\mapsto 1 - z \\) on each intensity values." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.748, + 0.892, + 0.793 + ], + "angle": 0, + "content": "- Standardization. We measure the mean \\(\\mu\\) and standard deviation \\(\\sigma\\) for the intensities of all pixels in the image. Then we standardize the intensities via \\(z \\mapsto \\frac{z - \\mu}{\\sigma}\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.794, + 0.892, + 0.822 + ], + "angle": 0, + "content": "- Linear scaling. We scale the intensities of each pixel by \\(t\\) without any centering, i.e. \\(z \\mapsto tz\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.822, + 0.892, + 0.853 + ], + "angle": 0, + "content": "- Centering. We center the interval \\([0,1]\\) at zero and scale the intensities by \\(t\\), i.e., \\(z \\mapsto t(z - 1/2)\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.853, + 0.892, + 0.899 + ], + "angle": 0, + "content": "- Gamma correction. We nonlinearly scale the intensity of each pixels as \\( z \\mapsto z^{1 / \\gamma} \\). Choosing \\( \\gamma > 1 \\) makes images brighter, and \\( \\gamma < 1 \\) makes darker." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.612, + 0.892, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4833" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.264, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.204, + 0.208, + 0.215 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.09, + 0.455, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.348, + 0.204, + 0.389, + 0.214 + ], + "angle": 0, + "content": "(b) RPP" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.216, + 0.468, + 0.271 + ], + "angle": 0, + "content": "Figure 3. Frequency spectra of original vs. RPP. We compare the average DCT coefficients of the original and RPP Kodak images. Upper left region denotes the low-frequency, and the lower right region denotes the high-frequency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.284, + 0.17, + 0.299 + ], + "angle": 0, + "content": "3.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.308, + 0.468, + 0.336 + ], + "angle": 0, + "content": "We report the average acceleration factors in Tab. 1. From the table, we make several observations:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.339, + 0.468, + 0.367 + ], + "angle": 0, + "content": "- RPP provides a consistent acceleration over the original image; see Sec. 4 for an in-depth analysis." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.369, + 0.468, + 0.442 + ], + "angle": 0, + "content": "- The zigzag permutation works tremendously well on SIREN—speeding up training by over \\(\\times 17\\)—but slows down training Instant-NGP. We hypothesize that this is due to the axis-aligned inductive bias imposed by the spatial grid encoding; see Sec. 4.3 for more discussion." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.444, + 0.468, + 0.504 + ], + "angle": 0, + "content": "- Inversion consistently slows down the training. This fact, ironically, implies that inversion might have been an effective accelerator if all \"natural images\" looked like the color-inverted images." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.505, + 0.468, + 0.548 + ], + "angle": 0, + "content": "- Scaling up the intensities tends to have opposite effects on different architectures. Scaling up speeds up training in SIRENs, but slows down in Instant-NGPs." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.55, + 0.468, + 0.625 + ], + "angle": 0, + "content": "- Gamma correction slows down the training, regardless of taking the power of 2 or \\(1/2\\). We suspect that this is due to the precision errors from taking powers. In other words, excessive scaling operations may not be helpful in accelerating the training." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.339, + 0.468, + 0.625 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.639, + 0.443, + 0.656 + ], + "angle": 0, + "content": "4. A closer look at the random permutation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.468, + 0.709 + ], + "angle": 0, + "content": "We now focus on a specific type of data transformation: the random pixel permutation (RPP). The RPP relocates each pixel to a new random location, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.722, + 0.468, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\left(\\operatorname {c o o r d s} _ {i}, \\text {v a l u e s} _ {i}\\right) \\mapsto \\left(\\operatorname {c o o r d s} _ {\\pi (i)}, \\text {v a l u e s} _ {i}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.825 + ], + "angle": 0, + "content": "for some random permutation \\(\\pi(\\cdot)\\). The marginal distributions of the input coordinates or the output values remain the same. As we have seen in Tab. 1, the RPP transformation accelerates the fitting of the corresponding neural field, which is very unexpected and difficult to explain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Why is this strange? From the perspective of the spectral bias, the RPP operation should have slowed down the training speed, instead of accelerating it. As demonstrated by Rahaman et al. [22], typical neural networks first rapidly fit the low-frequency components of the target signal, and fit" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.092, + 0.872, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.26, + 0.892, + 0.302 + ], + "angle": 0, + "content": "Figure 4. PSNR curves for a single Kodak image. The original image (orange) excels during the early stage of training but the RPP image quickly reaches PSNR 50 in the middle of the training." + }, + { + "type": "table", + "bbox": [ + 0.55, + 0.303, + 0.836, + 0.368 + ], + "angle": 0, + "content": "
Target PSNRRatio
30dB50dB
Original105.81371.40.08
Random pixel perm.851.81100.50.79
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.372, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Table 2. The number of steps to reach PSNR 30dB and 50dB. We measure the average steps to reach moderate and high PSNR levels over Kodak images, and report the average ratio." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.579 + ], + "angle": 0, + "content": "the high-frequency components much later. The RPP transformation, in this sense, should have been detrimental to the training. In fact, RPP images tend to have more higher-frequency components than the original images. In Fig. 3, we provide the average discrete cosine transform (DCT) coefficients of the original and RPP images; for visualization, we raise the coefficients to the power of 0.03, similar to [35]. We observe that the original image is more biased toward low-frequency than RPP. However, we also observe that RPP images fit faster than the original images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.685 + ], + "angle": 0, + "content": "In the remainder of this section, we identify three different aspects that the training dynamics of RPP images are critically different from that of original images. These aspects, when put together, support our \"blessings of no pattern\" hypothesis \\((\\star)\\) that RPP accelerates training by removing easy-to-fit patterns that can be harmful to reaching a high level of fidelity. In particular, we show that" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.687, + 0.89, + 0.715 + ], + "angle": 0, + "content": "- RPP is slow to reach moderate PSNR levels, but is fast to reach high PSNR (Sec. 4.1)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.717, + 0.89, + 0.746 + ], + "angle": 0, + "content": "- there is a linear path that connects the moderate-to-high PSNR points in the RPP loss landscape (Sec. 4.2)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.747, + 0.89, + 0.791 + ], + "angle": 0, + "content": "- model trained on RPP images tends to have less structured error, while vanilla training leads to error patterns that reflect the underlying encoding schemes (Sec. 4.3)." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.687, + 0.89, + 0.791 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.801, + 0.89, + 0.833 + ], + "angle": 0, + "content": "4.1. The PSNR curve: Slower to approximate well, but faster to approximate “very well”" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.89, + 0.885 + ], + "angle": 0, + "content": "First, we observe that RPP images tend to achieve moderate PSNRs (e.g., 30dB) much later than the original images, but they quickly reach high PSNRs (e.g., 50dB) afterwards." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.89, + 0.901 + ], + "angle": 0, + "content": "In Fig. 4, we provide an example plot of fitting a SIREN" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4834" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "on a natural image from the Kodak dataset. From the figure, we can immediately make the following observations:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.122, + 0.468, + 0.197 + ], + "angle": 0, + "content": "- RPPs are slow starters. The training PSNR of the original image quickly arrives at \\(\\sim 30\\mathrm{dB}\\) the early stage of training, even before taking 300 SGD iterations. On the other hand, the PSNR of the RPP image remains very small, under 15 dB at the similar number of steps." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.198, + 0.468, + 0.303 + ], + "angle": 0, + "content": "- Explosive surge in later stage. After staying at a low PSNR level (under 20 dB) for a while, the PSNR of RPP images bursts explosively. The PSNR jumps from \\(\\sim 15\\mathrm{dB}\\) to 50dB in less than 100 SGD steps. On the other hand, the PSNR curve of the original image oscillates wildly at 30-35dB level for a long time, and gradually reaches the 50dB at around 1600 steps." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.122, + 0.468, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.304, + 0.468, + 0.348 + ], + "angle": 0, + "content": "These observations are consistent over the choice of the target image; we provide a comprehensive collection of figures in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.468, + 0.408 + ], + "angle": 0, + "content": "For a more quantitative comparison, we compare the average number of SGD steps to arrive the PSNR of 30dB and 50dB for the original and RPP images (Tab. 2). Again, we use the images from the Kodak dataset and fit with SIRENs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.468, + 0.514 + ], + "angle": 0, + "content": "We observe that, for original images, the number of steps to reach 30dB is around 100 steps, while the number of SGD steps to reach the 50dB is over 1300 steps. That is, it takes almost \\(13 \\times\\) more steps to reach the high PSNR than for moderate PSNRs. On the other hand, for RPP images, it takes over 800 steps to reach the moderate PSNR level, while it takes only 300 more steps to reach the high PSNR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.524, + 0.468, + 0.555 + ], + "angle": 0, + "content": "4.2. Linear paths in the loss landscape: RPP images find a \"linear expressway\"" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.562, + 0.468, + 0.652 + ], + "angle": 0, + "content": "From the previous observation, it seems likely that, for RPP images, there may exist an expressway in the neural field parameter space that connects the moderate-PSNR parameter with the high-PSNR parameter; on this expressway, the SGD may not encounter too many hills to circumvent, and may mostly follow a smooth linear path." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.653, + 0.468, + 0.697 + ], + "angle": 0, + "content": "To validate this intuition, we visualize the loss landscape of the SIREN trained on Kodak images. In particular, we capture two different phases of training." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.698, + 0.468, + 0.742 + ], + "angle": 0, + "content": "1. Early phase. We plot the linear path from the initialization to 30dB point, i.e., the parameter that first achieves PSNR 30dB during the training (Fig. 5)" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.743, + 0.468, + 0.772 + ], + "angle": 0, + "content": "2. Late phase. We plot the linear path from the 30dB point to the PSNR 50dB point (Fig. 6)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.698, + 0.468, + 0.772 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.774, + 0.468, + 0.848 + ], + "angle": 0, + "content": "To generate such visualization, we project the parameter space into a two-dimensional space, as in [13]. Unlike [13], we fix one axis to a directional vector between two parameter points that we want to capture (e.g., 30dB point and 50dB point); the other axis has been decided randomly.2" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.468, + 0.879 + ], + "angle": 0, + "content": "During the early phase (Fig. 5), we observe that the loss landscape of RPP is quite hostile; unlike in original images," + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.092, + 0.692, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.206, + 0.669, + 0.218 + ], + "angle": 0, + "content": "(a) Elevated view; original" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.091, + 0.89, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.206, + 0.856, + 0.217 + ], + "angle": 0, + "content": "(b) Elevated view; RPP" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.223, + 0.692, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.324, + 0.658, + 0.337 + ], + "angle": 0, + "content": "(c) Side view; original" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.223, + 0.889, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.324, + 0.845, + 0.336 + ], + "angle": 0, + "content": "(d) Side view; RPP" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.418 + ], + "angle": 0, + "content": "Figure 5. SIREN loss landscape: from initial point to 30dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the initial point and the parameter that achieves PSNR 30. For RPP, the minima is much narrower and lacks a clear pathway toward it, unlike in the original image." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.422, + 0.691, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.536, + 0.63, + 0.548 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.426, + 0.889, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.536, + 0.816, + 0.547 + ], + "angle": 0, + "content": "(b) RPP" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Figure 6. SIREN loss landscape: from 30dB point to 50dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the parameters that first achieve PSNR 30 (■) and PSNR 50 (★), respectively. The loss barriers between two minima are dramatically different; 15.3dB for the original image, and 28.3dB for the RPP (averaged over all Kodak images)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.891, + 0.687 + ], + "angle": 0, + "content": "the minima that 30dB point belongs to is quite narrow and there is no clear pathway toward the 30dB point." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.891, + 0.793 + ], + "angle": 0, + "content": "During the late phase (Fig. 6), for the RPP image, once the parameter arrives at the minima, there exists a linear path that connects the \\(30\\mathrm{dB}\\) point to the \\(50\\mathrm{dB}\\) point. If we measure the loss barrier, i.e. the maximum loss on the linear path between \\(30\\mathrm{dB}\\) and \\(50\\mathrm{dB}\\) points, it is as low as \\(28.3\\mathrm{dB}\\) for the RPP versions of Kodak images. For original images, the loss barrier is quite high (15.3dB)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.89, + 0.833 + ], + "angle": 0, + "content": "4.3. Patterns in the error: The errors are less structured in RPP images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Another interesting property of RPP is that the errors that the neural field makes are more evenly distributed among the pixels, lacking a clearly distinguishable pattern. It turns out that the whiteness of the RPP error can help generat-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.436, + 0.9 + ], + "angle": 0, + "content": "2A similar method has been considered by Goodfellow et al. [7]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "4835" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.344, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.089, + 0.616, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.089, + 0.892, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.455, + 0.207, + 0.518, + 0.219 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.228, + 0.342, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.227, + 0.615, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.228, + 0.888, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.463, + 0.346, + 0.504, + 0.356 + ], + "angle": 0, + "content": "(b) RPP" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.893, + 0.414 + ], + "angle": 0, + "content": "Figure 7. Example reconstructions at a target PSNR value of 30 (SIREN). Random pixel permutation enables the network to prioritize the restoration of high-frequency, fine details, whereas the original representation tends to steer the network toward restoring low-frequency components initially. While this behavior may pose challenges during the early stages of training, it ultimately facilitates achieving visually more plausible reconstructions much earlier than the original representation." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.424, + 0.462, + 0.502 + ], + "angle": 0, + "content": "
Target PSNR
20304050
Original10.51e-0423.68e-0619.46e-085.90e-10
Random pixel perm.5.68e-045.89e-067.59e-085.81e-10
Average ratio2.03×5.20×5.80×1.55×
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.507, + 0.47, + 0.562 + ], + "angle": 0, + "content": "Table 3. Loss variance over pixels. We measure the average pixel loss variance in the SIREN trained on Kodak dataset, measured at various levels of PSNR. The \"average ratio\" denotes the mean of \\(\\mathrm{Var}(\\mathrm{original}) / \\mathrm{Var}(\\mathrm{RPP})\\). RPP has a lower loss variance at all PSNRs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.581, + 0.469, + 0.611 + ], + "angle": 0, + "content": "ing more visually sharp and satisfactory images than neural fields trained on original images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.469, + 0.763 + ], + "angle": 0, + "content": "In Tab. 3, we measure the pixel loss variance in both original and RPP images trained to various target PSNR levels. From the table, we observe that the loss variance is up to \\(5.80 \\times\\) larger in the neural fields trained on the original images than on RPP images. This implies that, for original images, some pixels in the original image are fit much faster than other pixels. Putting that differently, the neural field trained on the unpermuted images tends to prioritize learning a specific type of patterns first, while the neural field trained on RPP images does less so." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Exactly what pattern is RPP avoiding to fit? In Figs. 7 and 8, we compare the images generated by the neural fields trained on original and RPP images on SIREN and Instant-NGP, respectively. In Fig. 7, we observe that SIRENs trained on original images have thicker wavy patterns, which is likely to be a consequence of the sinusoidal encoding structure of SIREN. The models trained on RPP images, on the other hand, have much sharper texture with fine-grained noise. A similar phenomenon is observed in" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.427, + 0.892, + 0.503 + ], + "angle": 0, + "content": "the case of Instant-NGP (Fig. 8). Here, we observe that the models trained on original images attain axis-aligned artifacts; black (or white) horizontal (or vertical) blocks appear in the rendered images. On the other hand, the error is much less structured in models trained on RPP images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.524, + 0.637, + 0.539 + ], + "angle": 0, + "content": "5. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Optimization bias of neural networks. It has been well known, both theoretically and empirically, that SGD-based optimization algorithms are biased toward learning \"simplex solutions,\" for various notions of simplicity. A prominent example is the spectral bias, a tendency to prioritize learning lower-frequency components of the target function [3, 22]. Other types of biases have also been studied in the literature: SGD tends to prefer learning smaller-norm solutions [9, 21] and low-rank solutions [32, 34]. These works mostly focus on explaining how such simplicity biases are advantageous in learning a solution that can generalize well (see, e.g., [23]). Our work, in contrast, describes how such bias can be disadvantageous in terms of the training speed, instead of the generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Random labels and memorization. The question of how neural nets behave when trained on random labels has been actively studied since its connection to the generalization capability of deep learning has been established [38]. Arpit et al. [2] finds that neural networks tend to learn simple patterns first and then memorize the unexplainable samples—such as random label and data—in the later phase. A more recent study argues that training on randomly labeled data can actually be advantageous [17]; pre-training on random" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4836" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.27, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.089, + 0.465, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.235, + 0.321, + 0.247 + ], + "angle": 0, + "content": "(a) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.248, + 0.269, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.248, + 0.465, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.242, + 0.394, + 0.306, + 0.405 + ], + "angle": 0, + "content": "(b) Original" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.406, + 0.268, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.406, + 0.462, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.552, + 0.293, + 0.562 + ], + "angle": 0, + "content": "(c) RPP" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.564, + 0.47, + 0.647 + ], + "angle": 0, + "content": "Figure 8. Example reconstructions at a target PSNR value of 20 (Instant-NGP). Similarly to the SIREN case, we observe that Instant-NGPs trained on the RPP images have much less visually distinguishable artifacts. The models trained on original images tend to have axis-aligned blocks of error, which is likely to have originated from the spatial grid encoding of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.468, + 0.746 + ], + "angle": 0, + "content": "data helps fitting the training data, when eventually fine-tuning on the dataset with correct labels. Different from these works, our work discovers how random label can be beneficial in the neural field context, without any consideration on further fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Faster training of neural fields. Other than the works described in the introduction, there have been many other attempts to accelerate the neural field training by designing better encoding schemes. Positional encodings [5, 19, 27, 29] and spatial grids [6, 16, 18, 20] are the most popular options, and some works also use tree-like structures [28, 36]. Our work is complementary to this line of works, and argues that transforming the data in the original data space can provide auxiliary training speed boosts. We also note that a concurrent work also aims to boost the training speed by" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "modifying the given data [15]. In particular, [15] finds that separating the visual signals into many sub-segments can facilitate the convergence of SIRENs and proposes a meta-learning algorithm to speed up training. Our work considers a more general class of data transformations, and focus on understanding how transformations accelerate training." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.203, + 0.618, + 0.218 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Learning neural fields poses a unique challenge, as the primary objective is to overfit to the given data—an aim contrary to the typical goals in other problem domains where learning attempts to achieve regularization to prevent overfitting. In our study of this distinctive problem, we discovered that certain data transformations can expedite the network's acquisition of fine details more rapidly than when learning from the original images. Specifically, we demonstrated that random pixel permutations, which explicitly make learning low-frequency details more challenging, guide the network away from fixating on low-frequency components. This resulted in significantly enhanced PSNR within a given computational budget and, furthermore, yielded visually more plausible reconstructions at the same PSNR level. Our insights are substantiated by thorough empirical evaluations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Limitation & future direction. A notable limitation of our approach is that its direct applicability may be constrained when learning neural networks for other problem domains such as classification and regression, where regularization is crucial. As a future work, we aim to conduct more comprehensive studies to understand how data transformations affect both trainability and generalization of neural fields (and other neural networks). Such exploration may offer new insights on how to modify the given workload to jointly optimize the training cost and the model performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Another, more narrowly scoped future direction will be to gain a more concrete, theoretical understanding on the effect of random pixel permutations on the training dynamics of neural fields. Although our empirical analyses provide some insights into how RPP can help accelerate the training, we are yet to fully understand why fitting the easy patterns slows down the later phase of training. Deeper understandings on this matter may lead to impactful lessons applicable to any deep learning domain that involves long training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Acknowledgments. This work was partly supported by the National Research Foundation of Korea (NRF) grant (RS-2023-00213710, Neural Network Optimization with Minimal Optimization Costs), and partly by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2022- 0-00713, Meta-learning applicable to real-world problems, No.2019-0-01906, Artificial Intelligence Graduate School Program (POSTECH)), all funded by the Korea government (MSIT)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4837" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson and Radu Timofte. NTIRE 2017 challenge on single image super-resolution: Dataset and study. 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In ICLR, 2017. 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.956 + ], + "angle": 0, + "content": "4839" + } + ] +] \ No newline at end of file diff --git a/2024/In Search of a Data Transformation That Accelerates Neural Field Training/e8b54a6a-20cf-4428-8c04-7ff202724221_origin.pdf b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/e8b54a6a-20cf-4428-8c04-7ff202724221_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..19784d5c0b7a0ad7ba4f46fa1f2959b935b25a42 --- /dev/null +++ b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/e8b54a6a-20cf-4428-8c04-7ff202724221_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e32e574b9704ec76b76205a0b446181e66fe127bdcd6a89fe43b1f5dbc56b911 +size 4800538 diff --git a/2024/In Search of a Data Transformation That Accelerates Neural Field Training/full.md b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a6933a157d72131397133bf706171ebd505bb9a4 --- /dev/null +++ b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/full.md @@ -0,0 +1,394 @@ +# In Search of a Data Transformation That Accelerates Neural Field Training + +Junwon Seo* Sangyoon Lee* Kwang In Kim Jaeho Lee Pohang University of Science and Technology (POSTECH) + +{junwon.seo, sangyoon.lee, kimkin, jaeho.lee}@postech.ac.kr + +# Abstract + +Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed—generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal. + +# 1. Introduction + +Neural field is a form of data representation that parameterizes each target signal as a neural network that maps spatiotemporal coordinates to the signal values [33]. For example, a colored image can be represented by a model that maps (X,Y) pixel coordinates to the corresponding (R,G,B) values. This parameterization enjoys many advantages in faithfully and efficiently representing high-dimensional signals with fine detail, and thus is being widely used for modeling signals of various modalities, such as image [4], video [10], 3D scene [19], or spherical data [8]. + +A key obstacle that prevents the widespread adoption of neural fields is their training cost. To represent each datum as a neural field, one must train a neural network using many SGD iterations. For instance, NeRF requires at least 12 hours of training time on GPUs to represent a single 3D scene [19]. Representing a set of data thus requires a considerable amount of computation and time, making it very + +difficult to develop practical applications of neural fields. + +Many prior works view the "optimization bias" as a major cause behind the long training time of neural fields [29]. In particular, the spectral bias of the SGD-based training is known to bias the neural network to prioritize fitting the low-frequency components of the target signal and leave high-frequency components for the late stage of training [22]. It has been observed that such a tendency greatly hinders the neural fields from expressing natural data (e.g., images) with fine, high-frequency details [29, 37]. + +The prevailing strategy to mitigate such bias is to introduce a useful prior (or inductive bias) that can help neutralize the negative effects of the bias. One popular approach is to develop new network components that bring a favorable architectural prior, such as the Fourier features [19], sinusoidal activation [27], or spatial encoding [18, 20]. Other works also attempt to introduce the prior in the form of initial parameters that have been meta-learned from a large set of signals [26, 30]. Such meta-learned initializations tend to have rich high-frequency spectra, which can help fitting natural signals within a small number of SGD steps [30]. + +In this paper, we approach the problem from a different angle. In particular, we ask the following question: + +"Can we exploit the optimization bias of SGD, instead of fighting against it?" + +Precisely, we ask whether we can transform the datum in a way that the optimization bias acts favorably in fitting the transformed data with a neural field. If there exists such a transformation, and if it admits an efficiently computable inverse, we may be able to use the following strategy to reduce the neural field training cost: we train a neural field that expresses the transformed signal, and the original signal can be recovered from the model by applying an inverse transformation to the signal generated by the model (Fig. 1). Contribution. As a first step to answer this question, we conduct an extensive empirical study on how applying simple data transformations affect the computational cost of training the corresponding neural field. In particular, we compare the number of SGD steps needed to fit the transformed data to a certain fidelity level (e.g., PSNR 50 for images), with the steps to fit the original data. We try to + +![](images/b57ef16bf1f20f07a2d4fb8d92e86dae8be7749268e75d6013da7153054e2e79.jpg) +Figure 1. Overall pipeline. We consider a three-step procedure to train neural fields. (1) Apply a data transformation to the target datum. (2) Train a neural field to fit the transformed data. (3) Reconstruct the original data by generating the transformed datum from the neural field, and then applying the inverse of the data transformation. By selecting the data transformation carefully, we can significantly reduce the computational cost required to train a neural field that achieves the desired quality of approximation. + +tal seven different data transformations, from the one that permutes the location of the pixels to the one that scales the intensity values of each pixel. + +From the experiment, we make a surprising observation: we find that the random pixel permutation (abbr. RPP) provides a consistent acceleration on a range of datasets and various neural field architectures with sophisticated encoding schemes. The RPP is in fact the only data transformation that provided acceleration on every experimental setups that we considered. We find that the original data requires, on average, $\sim 30\%$ greater number of SGD steps to achieve the similar fidelity level than the RPP data. As RPP tends to bias the data toward high-frequency, it is quite counter-intuitive that they can be fit faster than the original signals. + +Why does the random pixel permutation accelerate neural field training? To explain this phenomenon, we articulate the following "blessings of no pattern" hypothesis: + +Original data often have smooth, representative patterns that facilitate easy optimization, particularly in the early phase of learning. However, this smoothness quickly transforms into an obstacle when aiming for a sufficiently high level of fidelity. Random pixel permutation removes these easy-to-fit patterns, which accelerates optimization in the long run. $(\star)$ + +To corroborate our hypothesis $\star$ , we take an in-depth look into the training dynamics of the original and the RPP data. We find that, indeed the training speed on the RPP data is slower than on the original data during the early training phase (Sec. 4.1). However, after training for a sufficient number of epochs, the neural field trained on RPP data finds a "linear loss highway" on which the optimization is very easy; the optimization on original data fails to find one (Sec. 4.2). Furthermore, we find that the errors in the RPP images are more evenly distributed over pixels and lack visually distinguishable structures; errors in original images tend to have periodic or axis-aligned patterns, which might + +be the artifacts of the encoding scheme (Sec. 4.3). + +To sum up, our contribution can be summarized as: + +1. Through systematic study, we find that simple data transformations can dramatically change the training speed of neural field $(\times 0.1 - \times 20)$ , even on state-of-the-art neural fields architectures with sophisticated encodings [20]. +2. We discover that random pixel permutations (RPP) provide consistent acceleration over fitting the original image, providing $\times 1.08 - \times 1.50$ speedups. +3. We conduct an in-depth analysis which sheds light on how RPP speeds up the training by removing the easy-to-fit patterns that slow down the training eventually. + +Despite the limitation of RPP that it may be difficult to be applied for applications where generalization is critical, our study has at least two potential impact areas. First, the RPP itself may be useful in the applications of neural field where a strong training fidelity is the core performance criterion, such as data compression [24]. In fact, one of the core challenges in neural-field-based data compression is the slow encoding speed (see, e.g., COOL-CHIC [12]). Second, our study provides a concrete starting point in developing a new data transformation that strikes the balance between the training speed and the generalizability. + +# 2. General framework + +The general framework of finding data transformations that accelerate neural field training can be formalized as an optimization problem, as we describe in this section. + +# 2.1. Formalisms + +Suppose that we want to use the neural field parameterization to approximate some signal $\mathbf{x} \in \mathcal{X}$ . Here, the signal space $\mathcal{X}$ is the space of all signals that have the same data type. For example, we can let $\mathcal{X}$ be the set of all $256 \times 256$ RGB images; in such case, we may have $\mathcal{X} \subseteq \mathbb{R}^{256 \times 256 \times 3}$ . + +The data transformation $T: \mathcal{X} \to \mathcal{X}$ maps an element in the signal space to another element. We define the trans- + +![](images/85647fc8ca51df0d49284e508dc7d0645065f654a763314dba082f9ecac827ee.jpg) +(a) Original + +![](images/f577e86b0e27f415e296b3159e1dbd2ba4220d914da42dce6cdf0011fb428d15.jpg) +(b) Random pixel permutation + +![](images/20b5186c293b2d455d7313e40e16e6c124e774a2d15a8c628ab21fce9849b354.jpg) +(c) Zigzag permutation + +![](images/4af3e429968790b534d0921001f326a46e654b0466793144852b16a3ced45fb2.jpg) +(d) Inversion + +![](images/d6969e9b606660957c43a8705f4619430c0efc13e65f071218488502578d902c.jpg) +(e) Standardization + +![](images/42616ac7746630b1ad4a8d7e7957efc8fbfae46977ba12afbaabd18d233698bd.jpg) +(f) Linear Scaling $(t = 0.5)$ + +![](images/082a08b787ffcfd240b748769ec53f9c27ad358d6f70158f12612cad05278567.jpg) +(g) Centering $(t = 1)$ + +![](images/062562cf409166941663423826b33f44bf85333aa553e235dd45f5a134c93974.jpg) +(h) Gamma correction $(\gamma = 2.0)$ + +![](images/6c0de187982dbfb6c5c12c9332845c69d4871929b62127093dd9b1e9745d7743.jpg) +Figure 2. Data transformations considered. In each subfigure, we visualize the data transformations by illustrating how the transformed image (left) and the intensity histogram (right) looks like on a Kodak image. + +formation space $\mathcal{T}$ as a set of data transformations on $\mathcal{X}$ that has an inverse. + +Our goal is to find a data transformation $T$ that minimizes the training cost of fitting the transformed signal $T(\mathbf{x})$ . To formalize this, we define the training cost + +$$ +\operatorname {c o s t}: \mathcal {X} \times \mathcal {T} \rightarrow \mathbb {R} _ {+}. \tag {1} +$$ + +Here, the function $\mathrm{cost}(\mathbf{x}, T)$ measures the computational burden required to train a neural field for $T(\mathbf{x})$ , whenever its outcome is inverted back via $T^{-1}$ , approximates the original signal $\mathbf{x}$ with the desired level of precision. The burden may be measured in various ways, e.g., the number of SGD steps, FLOPs, or wall-clock time. We note that the training cost of $\mathbf{x}$ using $T(\cdot)$ need not be identical to the training cost of fitting $T(\mathbf{x})$ with the same precision, i.e., + +$$ +\operatorname {c o s t} (\mathbf {x}, T) \neq \operatorname {c o s t} (T (\mathbf {x}), \mathrm {I d}), \tag {2} +$$ + +especially when the transformation involves scaling of the signal. Also, the training cost may heavily depend on the choice of neural field architectures, hardware type, and the batch size—using a larger batch size tends to reduce the number of steps until convergence [25], but it also requires training with a larger memory. + +Given these tools, we work to consider the optimization + +$$ +\text {m i n i m i z e} \quad \operatorname {c o s t} (\mathbf {x}, T), \quad \text {s u b j e c t t o} \quad T \in \mathcal {T} ^ {*}, \tag {3} +$$ + +where $\mathcal{T}^* \subseteq \mathcal{T}$ is a subset of the transformation space that satisfies some desired properties. The set $\mathcal{T}^*$ can be configured in many different ways, to account for the expected usages of the trained neural fields. This problem can also be extended to a version where we have a probability distribution of the signals $\mathbf{x}$ , and find a single transformation $T$ that minimizes the expected cost. + +Scope of this paper. While the most general framework is to solve the optimization (3) directly, the problem is intractable unless we have an expressive, well-paramaterized + +transformation space $\mathcal{T}^*$ that admits an effective optimization method. In this paper, we focus on the proof-of-concept that there exists some choice of $T$ such that + +$$ +\operatorname {c o s t} (\mathbf {x}, T) < \operatorname {c o s t} (\mathbf {x}, \operatorname {I d}), \tag {4} +$$ + +(Sec. 3), and deepening our understanding on when and why such $T(\cdot)$ can accelerate the training (Sec. 4). + +# 2.2. Example cases + +Here are some examples desired properties of data transformation, and how they relate to practical applications. We provide a more in-depth discussions in the ?? + +Efficient invertibility. The inverse $T^{-1}$ should be able to be computed efficiently, e.g., by performing a linear operation. Ideally, one may wish to be able to combine the inverse transformation into the neural field by modifying the parameters of the trained neural field directly. For instance, if $T(\mathbf{x}) = -\mathbf{x}$ , we can incorporate the inverse in the neural field by negating the final layer weights of the neural field. This property is useful whenever we expect many repeated inferences of the neural field, e.g., for real-time interaction. + +Retains interpolatability. We want our transform $T$ to admit a principled way to sample the value of interpolated coordinates from the neural field that approximates the transformed signal. In some neural field applications, e.g., superresolution [4], this interpolating capability plays an essential role. On the other hand, some applications like data compression do not involve any interpolation [24]. + +# 3. Data transformations vs. training speed + +In this section, we compare the training cost of the neural field training on various data transformation schemes. As it turns out, there indeed exists a nice data transformation that satisfies ineq. 4: the random pixel permutation (RPP). + +
ArchitectureDatasetRandom pixel perm.Zigzag perm.InversionStandardizationLinear ScalingCenteringGamma Correction
t=0.5t=2.0t=1.0t=2.0γ=0.5γ=2.0
SIRENKodak1.26×17.90×0.72×2.20×0.79×1.39×0.76×0.97×0.36×0.80×
DIV2K1.30×21.74×0.70×2.36×0.82×1.45×0.97×1.22×0.30×0.90×
CLIC1.08×17.07×0.68×2.18×0.76×1.36×0.87×1.14×0.24×0.82×
Instant-NGPKodak1.50×0.86×0.21×0.45×1.15×0.75×1.24×0.80×0.29×0.38×
DIV2K1.32×0.80×0.20×0.61×1.12×0.64×1.39×0.97×0.14×0.33×
CLIC1.35×0.78×0.07×0.53×1.03×0.68×0.99×0.66×0.12×0.32×
+ +Table 1. Acceleration factors of data transformations. We compare the average acceleration factor (eq. 5) of seven data transformations under six different combinations of datasets and models. We take average of cost ratios, instead of ratios of averages, to avoid the statistic being driven by a small number of outliers that require very long training time. The shaded figures denote the speedup. + +# 3.1. Experimental setup + +We focus on the task of 2D image regression. This choice reduces the computational burden of fitting each datum, so that we can make experimental validations on multiple datasets and models with extensive hyperparameter tuning. + +For the training cost, we use the number of SGD steps until we reach the training PSNR over 50dB (a near-perfect reconstruction for 8-bit images). The number of SGD steps is an informative indicator of the total FLOPs and runtime for any fixed choice of hardware, model architecture, and data. Importantly, we tune the learning rate for each (transformed) image, making it close to the scenario where all settings have been optimized to minimize the runtime. + +For each choice of an image and the data transformation, we measure the acceleration factor, i.e., + +$$ +\operatorname {a c c} (\mathbf {x}, T) \triangleq \frac {\operatorname {c o s t} (\mathbf {x} , \operatorname {I d})}{\operatorname {c o s t} (\mathbf {x} , T)}. \tag {5} +$$ + +Other configurations are as follows. + +Datasets. We use three different image datasets: + +- Kodak. Consists of 24 different images from the Kodak lossless true color image suite [11]. +- DIV2K. Consists of 100 images in the validation split of the DIV2K image super-resolution challenge (HR) [1]. +- CLIC. Consists of 100 images from the validation split of the dataset for the Challenge on Learned Image Compression 2020 (CLIC) [31]. There are total 102 images in the validation split, but we removed two images that have a sidelength shorter than 512 pixels. + +We pre-process each image in the datasets as follows. Following BACON [14], we resize each image into $512 \times 512$ pixels by first center-cropping the image to a square with sidelengths equal to the shorter sidelength of the original image, and then resizing with the Lanczos algorithm. Next, we convert the image to grayscale. Finally, we apply sRGB to Linear RGB operation, as in Instant-NGP [20]. + +The resulting images have $512 \times 512$ pixels (thus total $2^{18}$ pixels) with intensities lying in the interval $[0, 1]$ . + +Models. We use two different neural field architectures. + +- SIREN. A classical architecture that uses multi-layered perceptrons with sinusoidal activation functions [27]. We + +configure the model to have three hidden layers with 512 neurons in each layer and output dimension 1. We use the default frequency scaling hyperparameter $\omega_0 = 30$ . + +- Instant-NGP. A more recently proposed neural field with multi-resolution hash encodings [20]. We use the default setup for the image regression, with the maximum hash table size and 16-bit parameters. + +Training. We use full-batch gradient descent, i.e., the batch size $2^{18}$ . This batch size, in general, minimizes the number of SGD steps required to fit the target image. We note that we sample directly from the coordinate grid, instead of sampling from interpolated coordinates (as in, e.g., [20]). + +Hyperparameters. We tune the learning rate using the grid search. For SIREN, we tune the learning rate in the range $\{2^{-8},\ldots ,2^{-16}\}$ . For Instant-NGP, we tune the learning rate in the range $\{2^{-4},\ldots ,2^{-15}\}$ . + +Data transformations. We consider total seven elementary data transformations (Fig. 2): Two transformations that only change the location of the pixels (random pixel permutation, zigzag permutation), and five transformations that change the intensity values of each pixels (inversion, standardization, linear scaling, centering, and gamma correction). + +- Random pixel permutation (RPP). We randomly permute the location of each pixels. This transformation generally increases the frequency spectrum of the image. +- Zigzag permutation. We sort all the pixels in the ascending order of their intensities. Then, we place the sorted pixels in the zigzag order, starting from the upper left corner. This produces a low-frequency image. +- Inversion. We invert the intensity of each pixel, i.e., perform $z \mapsto 1 - z$ on each intensity values. +- Standardization. We measure the mean $\mu$ and standard deviation $\sigma$ for the intensities of all pixels in the image. Then we standardize the intensities via $z \mapsto \frac{z - \mu}{\sigma}$ . +- Linear scaling. We scale the intensities of each pixel by $t$ without any centering, i.e. $z \mapsto tz$ . +- Centering. We center the interval $[0,1]$ at zero and scale the intensities by $t$ , i.e., $z \mapsto t(z - 1/2)$ . +- Gamma correction. We nonlinearly scale the intensity of each pixels as $z \mapsto z^{1 / \gamma}$ . Choosing $\gamma > 1$ makes images brighter, and $\gamma < 1$ makes darker. + +![](images/1b1d28105599f8145ef579ba8611f9667e4fb6161eebef7f034ad0ed89a66aea.jpg) +(a) Original + +![](images/87a7b4e41f58817d8606882ba5298d362ea17ecbee43771910cb8a3ca1ecf659.jpg) +(b) RPP +Figure 3. Frequency spectra of original vs. RPP. We compare the average DCT coefficients of the original and RPP Kodak images. Upper left region denotes the low-frequency, and the lower right region denotes the high-frequency. + +# 3.2. Results + +We report the average acceleration factors in Tab. 1. From the table, we make several observations: + +- RPP provides a consistent acceleration over the original image; see Sec. 4 for an in-depth analysis. +- The zigzag permutation works tremendously well on SIREN—speeding up training by over $\times 17$ —but slows down training Instant-NGP. We hypothesize that this is due to the axis-aligned inductive bias imposed by the spatial grid encoding; see Sec. 4.3 for more discussion. +- Inversion consistently slows down the training. This fact, ironically, implies that inversion might have been an effective accelerator if all "natural images" looked like the color-inverted images. +- Scaling up the intensities tends to have opposite effects on different architectures. Scaling up speeds up training in SIRENs, but slows down in Instant-NGPs. +- Gamma correction slows down the training, regardless of taking the power of 2 or $1/2$ . We suspect that this is due to the precision errors from taking powers. In other words, excessive scaling operations may not be helpful in accelerating the training. + +# 4. A closer look at the random permutation + +We now focus on a specific type of data transformation: the random pixel permutation (RPP). The RPP relocates each pixel to a new random location, i.e., + +$$ +\left(\operatorname {c o o r d s} _ {i}, \text {v a l u e s} _ {i}\right) \mapsto \left(\operatorname {c o o r d s} _ {\pi (i)}, \text {v a l u e s} _ {i}\right) \tag {6} +$$ + +for some random permutation $\pi(\cdot)$ . The marginal distributions of the input coordinates or the output values remain the same. As we have seen in Tab. 1, the RPP transformation accelerates the fitting of the corresponding neural field, which is very unexpected and difficult to explain. + +Why is this strange? From the perspective of the spectral bias, the RPP operation should have slowed down the training speed, instead of accelerating it. As demonstrated by Rahaman et al. [22], typical neural networks first rapidly fit the low-frequency components of the target signal, and fit + +![](images/d6a74ce77c8ed3c28cdeac9caa716bd64102a6efdf9f650f3912729470509996.jpg) +Figure 4. PSNR curves for a single Kodak image. The original image (orange) excels during the early stage of training but the RPP image quickly reaches PSNR 50 in the middle of the training. + +
Target PSNRRatio
30dB50dB
Original105.81371.40.08
Random pixel perm.851.81100.50.79
+ +Table 2. The number of steps to reach PSNR 30dB and 50dB. We measure the average steps to reach moderate and high PSNR levels over Kodak images, and report the average ratio. + +the high-frequency components much later. The RPP transformation, in this sense, should have been detrimental to the training. In fact, RPP images tend to have more higher-frequency components than the original images. In Fig. 3, we provide the average discrete cosine transform (DCT) coefficients of the original and RPP images; for visualization, we raise the coefficients to the power of 0.03, similar to [35]. We observe that the original image is more biased toward low-frequency than RPP. However, we also observe that RPP images fit faster than the original images. + +In the remainder of this section, we identify three different aspects that the training dynamics of RPP images are critically different from that of original images. These aspects, when put together, support our "blessings of no pattern" hypothesis $(\star)$ that RPP accelerates training by removing easy-to-fit patterns that can be harmful to reaching a high level of fidelity. In particular, we show that + +- RPP is slow to reach moderate PSNR levels, but is fast to reach high PSNR (Sec. 4.1). +- there is a linear path that connects the moderate-to-high PSNR points in the RPP loss landscape (Sec. 4.2). +- model trained on RPP images tends to have less structured error, while vanilla training leads to error patterns that reflect the underlying encoding schemes (Sec. 4.3). + +# 4.1. The PSNR curve: Slower to approximate well, but faster to approximate “very well” + +First, we observe that RPP images tend to achieve moderate PSNRs (e.g., 30dB) much later than the original images, but they quickly reach high PSNRs (e.g., 50dB) afterwards. + +In Fig. 4, we provide an example plot of fitting a SIREN + +on a natural image from the Kodak dataset. From the figure, we can immediately make the following observations: + +- RPPs are slow starters. The training PSNR of the original image quickly arrives at $\sim 30\mathrm{dB}$ the early stage of training, even before taking 300 SGD iterations. On the other hand, the PSNR of the RPP image remains very small, under 15 dB at the similar number of steps. +- Explosive surge in later stage. After staying at a low PSNR level (under 20 dB) for a while, the PSNR of RPP images bursts explosively. The PSNR jumps from $\sim 15\mathrm{dB}$ to 50dB in less than 100 SGD steps. On the other hand, the PSNR curve of the original image oscillates wildly at 30-35dB level for a long time, and gradually reaches the 50dB at around 1600 steps. + +These observations are consistent over the choice of the target image; we provide a comprehensive collection of figures in the supplementary materials. + +For a more quantitative comparison, we compare the average number of SGD steps to arrive the PSNR of 30dB and 50dB for the original and RPP images (Tab. 2). Again, we use the images from the Kodak dataset and fit with SIRENs. + +We observe that, for original images, the number of steps to reach 30dB is around 100 steps, while the number of SGD steps to reach the 50dB is over 1300 steps. That is, it takes almost $13 \times$ more steps to reach the high PSNR than for moderate PSNRs. On the other hand, for RPP images, it takes over 800 steps to reach the moderate PSNR level, while it takes only 300 more steps to reach the high PSNR. + +# 4.2. Linear paths in the loss landscape: RPP images find a "linear expressway" + +From the previous observation, it seems likely that, for RPP images, there may exist an expressway in the neural field parameter space that connects the moderate-PSNR parameter with the high-PSNR parameter; on this expressway, the SGD may not encounter too many hills to circumvent, and may mostly follow a smooth linear path. + +To validate this intuition, we visualize the loss landscape of the SIREN trained on Kodak images. In particular, we capture two different phases of training. + +1. Early phase. We plot the linear path from the initialization to 30dB point, i.e., the parameter that first achieves PSNR 30dB during the training (Fig. 5) +2. Late phase. We plot the linear path from the 30dB point to the PSNR 50dB point (Fig. 6). + +To generate such visualization, we project the parameter space into a two-dimensional space, as in [13]. Unlike [13], we fix one axis to a directional vector between two parameter points that we want to capture (e.g., 30dB point and 50dB point); the other axis has been decided randomly.2 + +During the early phase (Fig. 5), we observe that the loss landscape of RPP is quite hostile; unlike in original images, + +![](images/214cc116f3cf24270d496b115801b22dcb4a4906c5d1162105819ce4fd441447.jpg) +(a) Elevated view; original + +![](images/d2e11adfcd62481c61e914d9da8315ae422e8e982a7b9c9fe710432484d63116.jpg) +(b) Elevated view; RPP + +![](images/0fe069709246fb805756ff39a40c3c7d7066851a7200b564b12089e24ad5570f.jpg) +(c) Side view; original + +![](images/0daeb6394d4aec17a6612133b8dbb0cfbe4f890a68f44c9f4555dcd5ae111e6b.jpg) +(d) Side view; RPP + +![](images/712935ba3947a2adc3cb3ac979f390f183d0b46e9d9ca6bc729da8d42bac533a.jpg) +Figure 5. SIREN loss landscape: from initial point to 30dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the initial point and the parameter that achieves PSNR 30. For RPP, the minima is much narrower and lacks a clear pathway toward it, unlike in the original image. +(a) Original +Figure 6. SIREN loss landscape: from 30dB point to 50dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the parameters that first achieve PSNR 30 (■) and PSNR 50 (★), respectively. The loss barriers between two minima are dramatically different; 15.3dB for the original image, and 28.3dB for the RPP (averaged over all Kodak images). + +![](images/a32c7b7c05b5c5bf11cf6ec5d1ab9f3d1fc91531a414db5a4f2cab64c33ab0fa.jpg) +(b) RPP + +the minima that 30dB point belongs to is quite narrow and there is no clear pathway toward the 30dB point. + +During the late phase (Fig. 6), for the RPP image, once the parameter arrives at the minima, there exists a linear path that connects the $30\mathrm{dB}$ point to the $50\mathrm{dB}$ point. If we measure the loss barrier, i.e. the maximum loss on the linear path between $30\mathrm{dB}$ and $50\mathrm{dB}$ points, it is as low as $28.3\mathrm{dB}$ for the RPP versions of Kodak images. For original images, the loss barrier is quite high (15.3dB). + +# 4.3. Patterns in the error: The errors are less structured in RPP images + +Another interesting property of RPP is that the errors that the neural field makes are more evenly distributed among the pixels, lacking a clearly distinguishable pattern. It turns out that the whiteness of the RPP error can help generat- + +![](images/ac9391826d2d3d69625971feecf263661f4894f079a8ab0ec9a469b742d8865f.jpg) + +![](images/12aaf41fef2c5eb31f014ba123de8abd5e51ca5c6138b55048f3b572ca7f3f91.jpg) +(a) Original + +![](images/ad7903394cdca0610e29f820ac0a97316ef20880a39807d6f00ac89790767fef.jpg) + +![](images/017b3678fc9ceeda8164c8ff6693aaf6cb94c8c2779982c65732d658fe819b83.jpg) +Figure 7. Example reconstructions at a target PSNR value of 30 (SIREN). Random pixel permutation enables the network to prioritize the restoration of high-frequency, fine details, whereas the original representation tends to steer the network toward restoring low-frequency components initially. While this behavior may pose challenges during the early stages of training, it ultimately facilitates achieving visually more plausible reconstructions much earlier than the original representation. + +![](images/55137ca5d21e518594aeb4fdb02b4fefaaa4b5febc7697db64cf297f5b9cdea5.jpg) +(b) RPP + +![](images/e5d6352037d23b4c5f455fb99a78e3373240a6dc2b43dec53fcae89f4efa5d3a.jpg) + +
Target PSNR
20304050
Original10.51e-0423.68e-0619.46e-085.90e-10
Random pixel perm.5.68e-045.89e-067.59e-085.81e-10
Average ratio2.03×5.20×5.80×1.55×
+ +Table 3. Loss variance over pixels. We measure the average pixel loss variance in the SIREN trained on Kodak dataset, measured at various levels of PSNR. The "average ratio" denotes the mean of $\mathrm{Var}(\mathrm{original}) / \mathrm{Var}(\mathrm{RPP})$ . RPP has a lower loss variance at all PSNRs. + +ing more visually sharp and satisfactory images than neural fields trained on original images. + +In Tab. 3, we measure the pixel loss variance in both original and RPP images trained to various target PSNR levels. From the table, we observe that the loss variance is up to $5.80 \times$ larger in the neural fields trained on the original images than on RPP images. This implies that, for original images, some pixels in the original image are fit much faster than other pixels. Putting that differently, the neural field trained on the unpermuted images tends to prioritize learning a specific type of patterns first, while the neural field trained on RPP images does less so. + +Exactly what pattern is RPP avoiding to fit? In Figs. 7 and 8, we compare the images generated by the neural fields trained on original and RPP images on SIREN and Instant-NGP, respectively. In Fig. 7, we observe that SIRENs trained on original images have thicker wavy patterns, which is likely to be a consequence of the sinusoidal encoding structure of SIREN. The models trained on RPP images, on the other hand, have much sharper texture with fine-grained noise. A similar phenomenon is observed in + +the case of Instant-NGP (Fig. 8). Here, we observe that the models trained on original images attain axis-aligned artifacts; black (or white) horizontal (or vertical) blocks appear in the rendered images. On the other hand, the error is much less structured in models trained on RPP images. + +# 5. Related work + +Optimization bias of neural networks. It has been well known, both theoretically and empirically, that SGD-based optimization algorithms are biased toward learning "simplex solutions," for various notions of simplicity. A prominent example is the spectral bias, a tendency to prioritize learning lower-frequency components of the target function [3, 22]. Other types of biases have also been studied in the literature: SGD tends to prefer learning smaller-norm solutions [9, 21] and low-rank solutions [32, 34]. These works mostly focus on explaining how such simplicity biases are advantageous in learning a solution that can generalize well (see, e.g., [23]). Our work, in contrast, describes how such bias can be disadvantageous in terms of the training speed, instead of the generalization performance. + +Random labels and memorization. The question of how neural nets behave when trained on random labels has been actively studied since its connection to the generalization capability of deep learning has been established [38]. Arpit et al. [2] finds that neural networks tend to learn simple patterns first and then memorize the unexplainable samples—such as random label and data—in the later phase. A more recent study argues that training on randomly labeled data can actually be advantageous [17]; pre-training on random + +![](images/a38514ea60a6a0fefa78c4927b3495da11b34bbddfcffb67498562b44902c270.jpg) + +![](images/924c2b7c7a3629655a5f8a7ec8f9ea929ff491ac4924e195a6fe52754661b49e.jpg) + +![](images/c0858e07a9b311ea25f3bb0a0a5cf226a9c55af18b979cb10b64138617fec971.jpg) +(a) Ground Truth + +![](images/cccaa638c5a0a5e625b76f762801c3861d13e85401ed9891fb686280e818aa19.jpg) + +![](images/263dbfefae65ebc89efdbe98b52a920d5b10d01aa4d3844f0e42ff465de9da34.jpg) +(b) Original +Figure 8. Example reconstructions at a target PSNR value of 20 (Instant-NGP). Similarly to the SIREN case, we observe that Instant-NGPs trained on the RPP images have much less visually distinguishable artifacts. The models trained on original images tend to have axis-aligned blocks of error, which is likely to have originated from the spatial grid encoding of the model. + +![](images/7ff8359250ed7003e4ff95ae4f2fba08bec7737c0ddc91461b947bf066c424ef.jpg) +(c) RPP + +data helps fitting the training data, when eventually fine-tuning on the dataset with correct labels. Different from these works, our work discovers how random label can be beneficial in the neural field context, without any consideration on further fine-tuning. + +Faster training of neural fields. Other than the works described in the introduction, there have been many other attempts to accelerate the neural field training by designing better encoding schemes. Positional encodings [5, 19, 27, 29] and spatial grids [6, 16, 18, 20] are the most popular options, and some works also use tree-like structures [28, 36]. Our work is complementary to this line of works, and argues that transforming the data in the original data space can provide auxiliary training speed boosts. We also note that a concurrent work also aims to boost the training speed by + +modifying the given data [15]. In particular, [15] finds that separating the visual signals into many sub-segments can facilitate the convergence of SIRENs and proposes a meta-learning algorithm to speed up training. Our work considers a more general class of data transformations, and focus on understanding how transformations accelerate training. + +# 6. Conclusion + +Learning neural fields poses a unique challenge, as the primary objective is to overfit to the given data—an aim contrary to the typical goals in other problem domains where learning attempts to achieve regularization to prevent overfitting. In our study of this distinctive problem, we discovered that certain data transformations can expedite the network's acquisition of fine details more rapidly than when learning from the original images. Specifically, we demonstrated that random pixel permutations, which explicitly make learning low-frequency details more challenging, guide the network away from fixating on low-frequency components. This resulted in significantly enhanced PSNR within a given computational budget and, furthermore, yielded visually more plausible reconstructions at the same PSNR level. Our insights are substantiated by thorough empirical evaluations. + +Limitation & future direction. A notable limitation of our approach is that its direct applicability may be constrained when learning neural networks for other problem domains such as classification and regression, where regularization is crucial. As a future work, we aim to conduct more comprehensive studies to understand how data transformations affect both trainability and generalization of neural fields (and other neural networks). Such exploration may offer new insights on how to modify the given workload to jointly optimize the training cost and the model performance. + +Another, more narrowly scoped future direction will be to gain a more concrete, theoretical understanding on the effect of random pixel permutations on the training dynamics of neural fields. Although our empirical analyses provide some insights into how RPP can help accelerate the training, we are yet to fully understand why fitting the easy patterns slows down the later phase of training. Deeper understandings on this matter may lead to impactful lessons applicable to any deep learning domain that involves long training. + +Acknowledgments. This work was partly supported by the National Research Foundation of Korea (NRF) grant (RS-2023-00213710, Neural Network Optimization with Minimal Optimization Costs), and partly by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2022- 0-00713, Meta-learning applicable to real-world problems, No.2019-0-01906, Artificial Intelligence Graduate School Program (POSTECH)), all funded by the Korea government (MSIT). + +# References + +[1] Eirikur Agustsson and Radu Timofte. NTIRE 2017 challenge on single image super-resolution: Dataset and study. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2017. 4 +[2] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S. 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In ICLR, 2017. 7 \ No newline at end of file diff --git a/2024/In Search of a Data Transformation That Accelerates Neural Field Training/images.zip b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c839a19948e334df3e2929dfff63e9210616d113 --- /dev/null +++ b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:afc0b12dfe9998cfb4721084299520e74635213992b52b63a75de5f242eb9292 +size 570639 diff --git a/2024/In Search of a Data Transformation That Accelerates Neural Field Training/layout.json b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ecd463189fe525efbd19792ab4a8544612effe4a --- /dev/null +++ b/2024/In Search of a Data Transformation That Accelerates Neural Field Training/layout.json @@ -0,0 +1,10197 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 64, + 103, + 531, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 103, + 531, + 121 + ], + "spans": [ + { + "bbox": [ + 64, + 103, + 531, + 121 + ], + "type": "text", + "content": "In Search of a Data Transformation That Accelerates Neural Field Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 146, + 144, + 447, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 144, + 447, + 172 + ], + "spans": [ + { + "bbox": [ + 146, + 144, + 447, + 172 + ], + "type": "text", + "content": "Junwon Seo* Sangyoon Lee* Kwang In Kim Jaeho Lee Pohang University of Science and Technology (POSTECH)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 136, + 174, + 454, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 174, + 454, + 185 + ], + "spans": [ + { + "bbox": [ + 136, + 174, + 454, + 185 + ], + "type": "text", + "content": "{junwon.seo, sangyoon.lee, kimkin, jaeho.lee}@postech.ac.kr" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 441 + ], + "type": "text", + "content": "Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed—generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 463, + 128, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 128, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 128, + 475 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 483, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 603 + ], + "type": "text", + "content": "Neural field is a form of data representation that parameterizes each target signal as a neural network that maps spatiotemporal coordinates to the signal values [33]. For example, a colored image can be represented by a model that maps (X,Y) pixel coordinates to the corresponding (R,G,B) values. This parameterization enjoys many advantages in faithfully and efficiently representing high-dimensional signals with fine detail, and thus is being widely used for modeling signals of various modalities, such as image [4], video [10], 3D scene [19], or spherical data [8]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 603, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 603, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 603, + 288, + 687 + ], + "type": "text", + "content": "A key obstacle that prevents the widespread adoption of neural fields is their training cost. To represent each datum as a neural field, one must train a neural network using many SGD iterations. For instance, NeRF requires at least 12 hours of training time on GPUs to represent a single 3D scene [19]. Representing a set of data thus requires a considerable amount of computation and time, making it very" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 213, + 537, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 537, + 226 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 537, + 226 + ], + "type": "text", + "content": "difficult to develop practical applications of neural fields." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 226, + 546, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 226, + 546, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 226, + 546, + 334 + ], + "type": "text", + "content": "Many prior works view the \"optimization bias\" as a major cause behind the long training time of neural fields [29]. In particular, the spectral bias of the SGD-based training is known to bias the neural network to prioritize fitting the low-frequency components of the target signal and leave high-frequency components for the late stage of training [22]. It has been observed that such a tendency greatly hinders the neural fields from expressing natural data (e.g., images) with fine, high-frequency details [29, 37]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 335, + 547, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 466 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 466 + ], + "type": "text", + "content": "The prevailing strategy to mitigate such bias is to introduce a useful prior (or inductive bias) that can help neutralize the negative effects of the bias. One popular approach is to develop new network components that bring a favorable architectural prior, such as the Fourier features [19], sinusoidal activation [27], or spatial encoding [18, 20]. Other works also attempt to introduce the prior in the form of initial parameters that have been meta-learned from a large set of signals [26, 30]. Such meta-learned initializations tend to have rich high-frequency spectra, which can help fitting natural signals within a small number of SGD steps [30]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 466, + 547, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 466, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 466, + 547, + 491 + ], + "type": "text", + "content": "In this paper, we approach the problem from a different angle. In particular, we ask the following question:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 331, + 494, + 520, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 494, + 520, + 518 + ], + "spans": [ + { + "bbox": [ + 331, + 494, + 520, + 518 + ], + "type": "text", + "content": "\"Can we exploit the optimization bias of SGD, instead of fighting against it?\"" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "Precisely, we ask whether we can transform the datum in a way that the optimization bias acts favorably in fitting the transformed data with a neural field. If there exists such a transformation, and if it admits an efficiently computable inverse, we may be able to use the following strategy to reduce the neural field training cost: we train a neural field that expresses the transformed signal, and the original signal can be recovered from the model by applying an inverse transformation to the signal generated by the model (Fig. 1). Contribution. As a first step to answer this question, we conduct an extensive empirical study on how applying simple data transformations affect the computational cost of training the corresponding neural field. In particular, we compare the number of SGD steps needed to fit the transformed data to a certain fidelity level (e.g., PSNR 50 for images), with the steps to fit the original data. We try to" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*equal contribution" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 58, + 703, + 265, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 265, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 265, + 712 + ], + "type": "text", + "content": "1code: https://github.com/effl-lab/DT4Neural-Field" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4830" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 542, + 196 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 542, + 196 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 542, + 196 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 542, + 196 + ], + "type": "image", + "image_path": "b57ef16bf1f20f07a2d4fb8d92e86dae8be7749268e75d6013da7153054e2e79.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 547, + 244 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 244 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 244 + ], + "type": "text", + "content": "Figure 1. Overall pipeline. We consider a three-step procedure to train neural fields. (1) Apply a data transformation to the target datum. (2) Train a neural field to fit the transformed data. (3) Reconstruct the original data by generating the transformed datum from the neural field, and then applying the inverse of the data transformation. By selecting the data transformation carefully, we can significantly reduce the computational cost required to train a neural field that achieves the desired quality of approximation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 255, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 290 + ], + "type": "text", + "content": "tal seven different data transformations, from the one that permutes the location of the pixels to the one that scales the intensity values of each pixel." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 291, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 287, + 422 + ], + "type": "text", + "content": "From the experiment, we make a surprising observation: we find that the random pixel permutation (abbr. RPP) provides a consistent acceleration on a range of datasets and various neural field architectures with sophisticated encoding schemes. The RPP is in fact the only data transformation that provided acceleration on every experimental setups that we considered. We find that the original data requires, on average, " + }, + { + "bbox": [ + 46, + 291, + 287, + 422 + ], + "type": "inline_equation", + "content": "\\sim 30\\%" + }, + { + "bbox": [ + 46, + 291, + 287, + 422 + ], + "type": "text", + "content": " greater number of SGD steps to achieve the similar fidelity level than the RPP data. As RPP tends to bias the data toward high-frequency, it is quite counter-intuitive that they can be fit faster than the original signals." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 424, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 460 + ], + "type": "text", + "content": "Why does the random pixel permutation accelerate neural field training? To explain this phenomenon, we articulate the following \"blessings of no pattern\" hypothesis:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 472, + 276, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 472, + 276, + 557 + ], + "spans": [ + { + "bbox": [ + 59, + 472, + 276, + 557 + ], + "type": "text", + "content": "Original data often have smooth, representative patterns that facilitate easy optimization, particularly in the early phase of learning. However, this smoothness quickly transforms into an obstacle when aiming for a sufficiently high level of fidelity. Random pixel permutation removes these easy-to-fit patterns, which accelerates optimization in the long run. " + }, + { + "bbox": [ + 59, + 472, + 276, + 557 + ], + "type": "inline_equation", + "content": "(\\star)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "To corroborate our hypothesis " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", we take an in-depth look into the training dynamics of the original and the RPP data. We find that, indeed the training speed on the RPP data is slower than on the original data during the early training phase (Sec. 4.1). However, after training for a sufficient number of epochs, the neural field trained on RPP data finds a \"linear loss highway\" on which the optimization is very easy; the optimization on original data fails to find one (Sec. 4.2). Furthermore, we find that the errors in the RPP images are more evenly distributed over pixels and lack visually distinguishable structures; errors in original images tend to have periodic or axis-aligned patterns, which might" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 255, + 508, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 508, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 508, + 266 + ], + "type": "text", + "content": "be the artifacts of the encoding scheme (Sec. 4.3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 266, + 525, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 266, + 525, + 277 + ], + "spans": [ + { + "bbox": [ + 317, + 266, + 525, + 277 + ], + "type": "text", + "content": "To sum up, our contribution can be summarized as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 281, + 545, + 401 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 306, + 281, + 545, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 545, + 329 + ], + "type": "text", + "content": "1. Through systematic study, we find that simple data transformations can dramatically change the training speed of neural field " + }, + { + "bbox": [ + 306, + 281, + 545, + 329 + ], + "type": "inline_equation", + "content": "(\\times 0.1 - \\times 20)" + }, + { + "bbox": [ + 306, + 281, + 545, + 329 + ], + "type": "text", + "content": ", even on state-of-the-art neural fields architectures with sophisticated encodings [20]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 330, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 330, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 330, + 545, + 365 + ], + "type": "text", + "content": "2. We discover that random pixel permutations (RPP) provide consistent acceleration over fitting the original image, providing " + }, + { + "bbox": [ + 306, + 330, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\times 1.08 - \\times 1.50" + }, + { + "bbox": [ + 306, + 330, + 545, + 365 + ], + "type": "text", + "content": " speedups." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 365, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 545, + 401 + ], + "type": "text", + "content": "3. We conduct an in-depth analysis which sheds light on how RPP speeds up the training by removing the easy-to-fit patterns that slow down the training eventually." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 404, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 545, + 536 + ], + "type": "text", + "content": "Despite the limitation of RPP that it may be difficult to be applied for applications where generalization is critical, our study has at least two potential impact areas. First, the RPP itself may be useful in the applications of neural field where a strong training fidelity is the core performance criterion, such as data compression [24]. In fact, one of the core challenges in neural-field-based data compression is the slow encoding speed (see, e.g., COOL-CHIC [12]). Second, our study provides a concrete starting point in developing a new data transformation that strikes the balance between the training speed and the generalizability." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 547, + 422, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 422, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 422, + 559 + ], + "type": "text", + "content": "2. General framework" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 567, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 603 + ], + "type": "text", + "content": "The general framework of finding data transformations that accelerate neural field training can be formalized as an optimization problem, as we describe in this section." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 611, + 384, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 384, + 622 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 384, + 622 + ], + "type": "text", + "content": "2.1. Formalisms" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "content": "Suppose that we want to use the neural field parameterization to approximate some signal " + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "content": ". Here, the signal space " + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "content": " is the space of all signals that have the same data type. For example, we can let " + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "content": " be the set of all " + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "content": " RGB images; in such case, we may have " + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{X} \\subseteq \\mathbb{R}^{256 \\times 256 \\times 3}" + }, + { + "bbox": [ + 304, + 629, + 545, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "The data transformation " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "T: \\mathcal{X} \\to \\mathcal{X}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " maps an element in the signal space to another element. 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"blocks": [ + { + "bbox": [ + 426, + 148, + 544, + 208 + ], + "lines": [ + { + "bbox": [ + 426, + 148, + 544, + 208 + ], + "spans": [ + { + "bbox": [ + 426, + 148, + 544, + 208 + ], + "type": "image", + "image_path": "062562cf409166941663423826b33f44bf85333aa553e235dd45f5a134c93974.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 209, + 536, + 218 + ], + "lines": [ + { + "bbox": [ + 429, + 209, + 536, + 218 + ], + "spans": [ + { + "bbox": [ + 429, + 209, + 536, + 218 + ], + "type": "text", + "content": "(h) Gamma correction " + }, + { + "bbox": [ + 429, + 209, + 536, + 218 + ], + "type": "inline_equation", + "content": "(\\gamma = 2.0)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 173, + 225, + 418, + 239 + ], + "blocks": [ + { + "bbox": [ + 173, + 225, + 418, + 239 + ], + "lines": [ + { + "bbox": [ + 173, + 225, + 418, + 239 + ], + "spans": [ + { + "bbox": [ + 173, + 225, + 418, + 239 + ], + "type": "image", + "image_path": "6c0de187982dbfb6c5c12c9332845c69d4871929b62127093dd9b1e9745d7743.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 245, + 546, + 267 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 546, + 267 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 546, + 267 + ], + "type": "text", + "content": "Figure 2. Data transformations considered. In each subfigure, we visualize the data transformations by illustrating how the transformed image (left) and the intensity histogram (right) looks like on a Kodak image." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "type": "text", + "content": "formation space " + }, + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "type": "text", + "content": " as a set of data transformations on " + }, + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 45, + 278, + 287, + 301 + ], + "type": "text", + "content": " that has an inverse." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "type": "text", + "content": "Our goal is to find a data transformation " + }, + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "type": "text", + "content": " that minimizes the training cost of fitting the transformed signal " + }, + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "type": "inline_equation", + "content": "T(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 302, + 287, + 338 + ], + "type": "text", + "content": ". To formalize this, we define the training cost" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 122, + 345, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 345, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 122, + 345, + 287, + 357 + ], + "type": "interline_equation", + "content": "\\operatorname {c o s t}: \\mathcal {X} \\times \\mathcal {T} \\rightarrow \\mathbb {R} _ {+}. \\tag {1}", + "image_path": "002bbd47be3e39f9a6cc0e7761a0ff528a78ea6a3c0b7c18ab5fb4bd55965880.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": "Here, the function " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathrm{cost}(\\mathbf{x}, T)" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": " measures the computational burden required to train a neural field for " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "T(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": ", whenever its outcome is inverted back via " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "T^{-1}" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": ", approximates the original signal " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": " with the desired level of precision. The burden may be measured in various ways, e.g., the number of SGD steps, FLOPs, or wall-clock time. We note that the training cost of " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": " need not be identical to the training cost of fitting " + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "inline_equation", + "content": "T(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 364, + 287, + 460 + ], + "type": "text", + "content": " with the same precision, i.e.," + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 467, + 287, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 467, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 467, + 287, + 480 + ], + "type": "interline_equation", + "content": "\\operatorname {c o s t} (\\mathbf {x}, T) \\neq \\operatorname {c o s t} (T (\\mathbf {x}), \\mathrm {I d}), \\tag {2}", + "image_path": "d3ab87e51da570723edeae1bc0363191b5c30e299ee071e845e86d12bb72ccf4.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 487, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 558 + ], + "type": "text", + "content": "especially when the transformation involves scaling of the signal. Also, the training cost may heavily depend on the choice of neural field architectures, hardware type, and the batch size—using a larger batch size tends to reduce the number of steps until convergence [25], but it also requires training with a larger memory." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 58, + 559, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 559, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 58, + 559, + 287, + 571 + ], + "type": "text", + "content": "Given these tools, we work to consider the optimization" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 58, + 574, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 574, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 58, + 574, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\text {m i n i m i z e} \\quad \\operatorname {c o s t} (\\mathbf {x}, T), \\quad \\text {s u b j e c t t o} \\quad T \\in \\mathcal {T} ^ {*}, \\tag {3}", + "image_path": "87f0520912051d1c56e915caebfa2c69b70989fcceff5f898f727998ecf7b882.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^* \\subseteq \\mathcal{T}" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": " is a subset of the transformation space that satisfies some desired properties. The set " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^*" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": " can be configured in many different ways, to account for the expected usages of the trained neural fields. This problem can also be extended to a version where we have a probability distribution of the signals " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": ", and find a single transformation " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": " that minimizes the expected cost." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Scope of this paper. While the most general framework is to solve the optimization (3) directly, the problem is intractable unless we have an expressive, well-paramaterized" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "type": "text", + "content": "transformation space " + }, + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^*" + }, + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "type": "text", + "content": " that admits an effective optimization method. In this paper, we focus on the proof-of-concept that there exists some choice of " + }, + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 278, + 546, + 313 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 372, + 326, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 326, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 372, + 326, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\operatorname {c o s t} (\\mathbf {x}, T) < \\operatorname {c o s t} (\\mathbf {x}, \\operatorname {I d}), \\tag {4}", + "image_path": "b3c43db953517759e1bcb69b5bd3dac67bcc6475707cc027e8e77e886b386778.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 349, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 545, + 373 + ], + "type": "text", + "content": "(Sec. 3), and deepening our understanding on when and why such " + }, + { + "bbox": [ + 305, + 349, + 545, + 373 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 305, + 349, + 545, + 373 + ], + "type": "text", + "content": " can accelerate the training (Sec. 4)." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 383, + 397, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 397, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 397, + 396 + ], + "type": "text", + "content": "2.2. Example cases" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "type": "text", + "content": "Here are some examples desired properties of data transformation, and how they relate to practical applications. We provide a more in-depth discussions in the ??" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "type": "text", + "content": "Efficient invertibility. The inverse " + }, + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "type": "inline_equation", + "content": "T^{-1}" + }, + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "type": "text", + "content": " should be able to be computed efficiently, e.g., by performing a linear operation. Ideally, one may wish to be able to combine the inverse transformation into the neural field by modifying the parameters of the trained neural field directly. For instance, if " + }, + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "type": "inline_equation", + "content": "T(\\mathbf{x}) = -\\mathbf{x}" + }, + { + "bbox": [ + 305, + 439, + 546, + 547 + ], + "type": "text", + "content": ", we can incorporate the inverse in the neural field by negating the final layer weights of the neural field. This property is useful whenever we expect many repeated inferences of the neural field, e.g., for real-time interaction." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 305, + 548, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 548, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 305, + 548, + 545, + 632 + ], + "type": "text", + "content": "Retains interpolatability. We want our transform " + }, + { + "bbox": [ + 305, + 548, + 545, + 632 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 548, + 545, + 632 + ], + "type": "text", + "content": " to admit a principled way to sample the value of interpolated coordinates from the neural field that approximates the transformed signal. In some neural field applications, e.g., superresolution [4], this interpolating capability plays an essential role. On the other hand, some applications like data compression do not involve any interpolation [24]." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 644, + 524, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 524, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 524, + 658 + ], + "type": "text", + "content": "3. Data transformations vs. training speed" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 305, + 665, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 546, + 713 + ], + "type": "text", + "content": "In this section, we compare the training cost of the neural field training on various data transformation schemes. As it turns out, there indeed exists a nice data transformation that satisfies ineq. 4: the random pixel permutation (RPP)." + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4832" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 547, + 171 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 171 + ], + "type": "table", + "html": "
ArchitectureDatasetRandom pixel perm.Zigzag perm.InversionStandardizationLinear ScalingCenteringGamma Correction
t=0.5t=2.0t=1.0t=2.0γ=0.5γ=2.0
SIRENKodak1.26×17.90×0.72×2.20×0.79×1.39×0.76×0.97×0.36×0.80×
DIV2K1.30×21.74×0.70×2.36×0.82×1.45×0.97×1.22×0.30×0.90×
CLIC1.08×17.07×0.68×2.18×0.76×1.36×0.87×1.14×0.24×0.82×
Instant-NGPKodak1.50×0.86×0.21×0.45×1.15×0.75×1.24×0.80×0.29×0.38×
DIV2K1.32×0.80×0.20×0.61×1.12×0.64×1.39×0.97×0.14×0.33×
CLIC1.35×0.78×0.07×0.53×1.03×0.68×0.99×0.66×0.12×0.32×
", + "image_path": "442f8a8f8f0c890ac07aed205776ad9b117b3e86bd38b0daf6f859b4df0d8231.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 174, + 547, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 174, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 547, + 210 + ], + "type": "text", + "content": "Table 1. Acceleration factors of data transformations. We compare the average acceleration factor (eq. 5) of seven data transformations under six different combinations of datasets and models. We take average of cost ratios, instead of ratios of averages, to avoid the statistic being driven by a small number of outliers that require very long training time. The shaded figures denote the speedup." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 219, + 162, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 219, + 162, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 219, + 162, + 232 + ], + "type": "text", + "content": "3.1. Experimental setup" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 237, + 287, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 285 + ], + "type": "text", + "content": "We focus on the task of 2D image regression. This choice reduces the computational burden of fitting each datum, so that we can make experimental validations on multiple datasets and models with extensive hyperparameter tuning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 286, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 380 + ], + "type": "text", + "content": "For the training cost, we use the number of SGD steps until we reach the training PSNR over 50dB (a near-perfect reconstruction for 8-bit images). The number of SGD steps is an informative indicator of the total FLOPs and runtime for any fixed choice of hardware, model architecture, and data. Importantly, we tune the learning rate for each (transformed) image, making it close to the scenario where all settings have been optimized to minimize the runtime." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 381, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 287, + 406 + ], + "type": "text", + "content": "For each choice of an image and the data transformation, we measure the acceleration factor, i.e.," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 114, + 409, + 287, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 409, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 114, + 409, + 287, + 435 + ], + "type": "interline_equation", + "content": "\\operatorname {a c c} (\\mathbf {x}, T) \\triangleq \\frac {\\operatorname {c o s t} (\\mathbf {x} , \\operatorname {I d})}{\\operatorname {c o s t} (\\mathbf {x} , T)}. \\tag {5}", + "image_path": "1016d78dd40878d523075c3d655295c3385896c6816318320f1cb41931c8ffbb.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 438, + 193, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 193, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 193, + 449 + ], + "type": "text", + "content": "Other configurations are as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 450, + 243, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 450, + 243, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 450, + 243, + 462 + ], + "type": "text", + "content": "Datasets. We use three different image datasets:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 462, + 287, + 569 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 47, + 462, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 462, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 47, + 462, + 287, + 486 + ], + "type": "text", + "content": "- Kodak. Consists of 24 different images from the Kodak lossless true color image suite [11]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 486, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 287, + 510 + ], + "type": "text", + "content": "- DIV2K. Consists of 100 images in the validation split of the DIV2K image super-resolution challenge (HR) [1]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 510, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 287, + 569 + ], + "type": "text", + "content": "- CLIC. Consists of 100 images from the validation split of the dataset for the Challenge on Learned Image Compression 2020 (CLIC) [31]. There are total 102 images in the validation split, but we removed two images that have a sidelength shorter than 512 pixels." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": "We pre-process each image in the datasets as follows. Following BACON [14], we resize each image into " + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": " pixels by first center-cropping the image to a square with sidelengths equal to the shorter sidelength of the original image, and then resizing with the Lanczos algorithm. Next, we convert the image to grayscale. Finally, we apply sRGB to Linear RGB operation, as in Instant-NGP [20]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "text", + "content": "The resulting images have " + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "text", + "content": " pixels (thus total " + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "2^{18}" + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "text", + "content": " pixels) with intensities lying in the interval " + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "[0, 1]" + }, + { + "bbox": [ + 47, + 653, + 287, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 677, + 272, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 272, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 272, + 689 + ], + "type": "text", + "content": "Models. We use two different neural field architectures." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "- SIREN. A classical architecture that uses multi-layered perceptrons with sinusoidal activation functions [27]. We" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 220, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 220, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 312, + 220, + 545, + 255 + ], + "type": "text", + "content": "configure the model to have three hidden layers with 512 neurons in each layer and output dimension 1. We use the default frequency scaling hyperparameter " + }, + { + "bbox": [ + 312, + 220, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\omega_0 = 30" + }, + { + "bbox": [ + 312, + 220, + 545, + 255 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 256, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 256, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 306, + 256, + 545, + 303 + ], + "type": "text", + "content": "- Instant-NGP. A more recently proposed neural field with multi-resolution hash encodings [20]. We use the default setup for the image regression, with the maximum hash table size and 16-bit parameters." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 304, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 363 + ], + "type": "text", + "content": "Training. We use full-batch gradient descent, i.e., the batch size " + }, + { + "bbox": [ + 305, + 304, + 545, + 363 + ], + "type": "inline_equation", + "content": "2^{18}" + }, + { + "bbox": [ + 305, + 304, + 545, + 363 + ], + "type": "text", + "content": ". This batch size, in general, minimizes the number of SGD steps required to fit the target image. We note that we sample directly from the coordinate grid, instead of sampling from interpolated coordinates (as in, e.g., [20])." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "type": "text", + "content": "Hyperparameters. We tune the learning rate using the grid search. For SIREN, we tune the learning rate in the range " + }, + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\{2^{-8},\\ldots ,2^{-16}\\}" + }, + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "type": "text", + "content": ". For Instant-NGP, we tune the learning rate in the range " + }, + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\{2^{-4},\\ldots ,2^{-15}\\}" + }, + { + "bbox": [ + 305, + 364, + 545, + 412 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 412, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 412, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 412, + 545, + 483 + ], + "type": "text", + "content": "Data transformations. We consider total seven elementary data transformations (Fig. 2): Two transformations that only change the location of the pixels (random pixel permutation, zigzag permutation), and five transformations that change the intensity values of each pixels (inversion, standardization, linear scaling, centering, and gamma correction)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 484, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 29, + "blocks": [ + { + "bbox": [ + 306, + 484, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 484, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 306, + 484, + 545, + 520 + ], + "type": "text", + "content": "- Random pixel permutation (RPP). We randomly permute the location of each pixels. This transformation generally increases the frequency spectrum of the image." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 520, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 545, + 568 + ], + "type": "text", + "content": "- Zigzag permutation. We sort all the pixels in the ascending order of their intensities. Then, we place the sorted pixels in the zigzag order, starting from the upper left corner. This produces a low-frequency image." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "type": "text", + "content": "- Inversion. We invert the intensity of each pixel, i.e., perform " + }, + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "type": "inline_equation", + "content": "z \\mapsto 1 - z" + }, + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "type": "text", + "content": " on each intensity values." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "text", + "content": "- Standardization. We measure the mean " + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "text", + "content": " and standard deviation " + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "text", + "content": " for the intensities of all pixels in the image. Then we standardize the intensities via " + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "inline_equation", + "content": "z \\mapsto \\frac{z - \\mu}{\\sigma}" + }, + { + "bbox": [ + 306, + 592, + 545, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "type": "text", + "content": "- Linear scaling. We scale the intensities of each pixel by " + }, + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "type": "text", + "content": " without any centering, i.e. " + }, + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "type": "inline_equation", + "content": "z \\mapsto tz" + }, + { + "bbox": [ + 306, + 628, + 545, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "text", + "content": "- Centering. We center the interval " + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "text", + "content": " at zero and scale the intensities by " + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "inline_equation", + "content": "z \\mapsto t(z - 1/2)" + }, + { + "bbox": [ + 306, + 651, + 545, + 675 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "content": "- Gamma correction. We nonlinearly scale the intensity of each pixels as " + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "inline_equation", + "content": "z \\mapsto z^{1 / \\gamma}" + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "content": ". Choosing " + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\gamma > 1" + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "content": " makes images brighter, and " + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\gamma < 1" + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "content": " makes darker." + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4833" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 161, + 156 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 161, + 156 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 161, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 161, + 156 + ], + "type": "image", + "image_path": "1b1d28105599f8145ef579ba8611f9667e4fb6161eebef7f034ad0ed89a66aea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 161, + 127, + 170 + ], + "lines": [ + { + "bbox": [ + 88, + 161, + 127, + 170 + ], + "spans": [ + { + "bbox": [ + 88, + 161, + 127, + 170 + ], + "type": "text", + "content": "(a) Original" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 171, + 71, + 278, + 156 + ], + "blocks": [ + { + "bbox": [ + 171, + 71, + 278, + 156 + ], + "lines": [ + { + "bbox": [ + 171, + 71, + 278, + 156 + ], + "spans": [ + { + "bbox": [ + 171, + 71, + 278, + 156 + ], + "type": "image", + "image_path": "87a7b4e41f58817d8606882ba5298d362ea17ecbee43771910cb8a3ca1ecf659.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 212, + 161, + 238, + 169 + ], + "lines": [ + { + "bbox": [ + 212, + 161, + 238, + 169 + ], + "spans": [ + { + "bbox": [ + 212, + 161, + 238, + 169 + ], + "type": "text", + "content": "(b) RPP" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 171, + 286, + 214 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 286, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 286, + 214 + ], + "type": "text", + "content": "Figure 3. Frequency spectra of original vs. RPP. We compare the average DCT coefficients of the original and RPP Kodak images. Upper left region denotes the low-frequency, and the lower right region denotes the high-frequency." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 224, + 104, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 104, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 104, + 236 + ], + "type": "text", + "content": "3.2. Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 243, + 286, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 286, + 266 + ], + "type": "text", + "content": "We report the average acceleration factors in Tab. 1. From the table, we make several observations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 268, + 286, + 495 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 47, + 268, + 286, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 268, + 286, + 290 + ], + "spans": [ + { + "bbox": [ + 47, + 268, + 286, + 290 + ], + "type": "text", + "content": "- RPP provides a consistent acceleration over the original image; see Sec. 4 for an in-depth analysis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 292, + 286, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 286, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 286, + 350 + ], + "type": "text", + "content": "- The zigzag permutation works tremendously well on SIREN—speeding up training by over " + }, + { + "bbox": [ + 47, + 292, + 286, + 350 + ], + "type": "inline_equation", + "content": "\\times 17" + }, + { + "bbox": [ + 47, + 292, + 286, + 350 + ], + "type": "text", + "content": "—but slows down training Instant-NGP. We hypothesize that this is due to the axis-aligned inductive bias imposed by the spatial grid encoding; see Sec. 4.3 for more discussion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 351, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 286, + 399 + ], + "type": "text", + "content": "- Inversion consistently slows down the training. This fact, ironically, implies that inversion might have been an effective accelerator if all \"natural images\" looked like the color-inverted images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 399, + 286, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 286, + 434 + ], + "type": "text", + "content": "- Scaling up the intensities tends to have opposite effects on different architectures. Scaling up speeds up training in SIRENs, but slows down in Instant-NGPs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 435, + 286, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 435, + 286, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 435, + 286, + 495 + ], + "type": "text", + "content": "- Gamma correction slows down the training, regardless of taking the power of 2 or " + }, + { + "bbox": [ + 47, + 435, + 286, + 495 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 47, + 435, + 286, + 495 + ], + "type": "text", + "content": ". We suspect that this is due to the precision errors from taking powers. In other words, excessive scaling operations may not be helpful in accelerating the training." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 506, + 271, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 271, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 271, + 519 + ], + "type": "text", + "content": "4. A closer look at the random permutation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 525, + 286, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 286, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 286, + 561 + ], + "type": "text", + "content": "We now focus on a specific type of data transformation: the random pixel permutation (RPP). The RPP relocates each pixel to a new random location, i.e.," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 70, + 571, + 286, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 571, + 286, + 585 + ], + "spans": [ + { + "bbox": [ + 70, + 571, + 286, + 585 + ], + "type": "interline_equation", + "content": "\\left(\\operatorname {c o o r d s} _ {i}, \\text {v a l u e s} _ {i}\\right) \\mapsto \\left(\\operatorname {c o o r d s} _ {\\pi (i)}, \\text {v a l u e s} _ {i}\\right) \\tag {6}", + "image_path": "7b6110fbdfcbd8d49a68b40a4f07b724c8b2da95b81685568a430b2530edeb9b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 594, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 653 + ], + "type": "text", + "content": "for some random permutation " + }, + { + "bbox": [ + 46, + 594, + 286, + 653 + ], + "type": "inline_equation", + "content": "\\pi(\\cdot)" + }, + { + "bbox": [ + 46, + 594, + 286, + 653 + ], + "type": "text", + "content": ". The marginal distributions of the input coordinates or the output values remain the same. As we have seen in Tab. 1, the RPP transformation accelerates the fitting of the corresponding neural field, which is very unexpected and difficult to explain." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 654, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 712 + ], + "type": "text", + "content": "Why is this strange? From the perspective of the spectral bias, the RPP operation should have slowed down the training speed, instead of accelerating it. As demonstrated by Rahaman et al. [22], typical neural networks first rapidly fit the low-frequency components of the target signal, and fit" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 314, + 72, + 533, + 203 + ], + "blocks": [ + { + "bbox": [ + 314, + 72, + 533, + 203 + ], + "lines": [ + { + "bbox": [ + 314, + 72, + 533, + 203 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 533, + 203 + ], + "type": "image", + "image_path": "d6a74ce77c8ed3c28cdeac9caa716bd64102a6efdf9f650f3912729470509996.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 205, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 239 + ], + "type": "text", + "content": "Figure 4. PSNR curves for a single Kodak image. The original image (orange) excels during the early stage of training but the RPP image quickly reaches PSNR 50 in the middle of the training." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 336, + 239, + 511, + 291 + ], + "blocks": [ + { + "bbox": [ + 336, + 239, + 511, + 291 + ], + "lines": [ + { + "bbox": [ + 336, + 239, + 511, + 291 + ], + "spans": [ + { + "bbox": [ + 336, + 239, + 511, + 291 + ], + "type": "table", + "html": "
Target PSNRRatio
30dB50dB
Original105.81371.40.08
Random pixel perm.851.81100.50.79
", + "image_path": "c890d06d8bbc48448c28ff8cf99e6323af60477bcee76c5ec86ecc73b0f49d8e.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 294, + 545, + 327 + ], + "lines": [ + { + "bbox": [ + 305, + 294, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 294, + 545, + 327 + ], + "type": "text", + "content": "Table 2. The number of steps to reach PSNR 30dB and 50dB. We measure the average steps to reach moderate and high PSNR levels over Kodak images, and report the average ratio." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 339, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 458 + ], + "type": "text", + "content": "the high-frequency components much later. The RPP transformation, in this sense, should have been detrimental to the training. In fact, RPP images tend to have more higher-frequency components than the original images. In Fig. 3, we provide the average discrete cosine transform (DCT) coefficients of the original and RPP images; for visualization, we raise the coefficients to the power of 0.03, similar to [35]. We observe that the original image is more biased toward low-frequency than RPP. However, we also observe that RPP images fit faster than the original images." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 459, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 542 + ], + "type": "text", + "content": "In the remainder of this section, we identify three different aspects that the training dynamics of RPP images are critically different from that of original images. These aspects, when put together, support our \"blessings of no pattern\" hypothesis " + }, + { + "bbox": [ + 304, + 459, + 545, + 542 + ], + "type": "inline_equation", + "content": "(\\star)" + }, + { + "bbox": [ + 304, + 459, + 545, + 542 + ], + "type": "text", + "content": " that RPP accelerates training by removing easy-to-fit patterns that can be harmful to reaching a high level of fidelity. In particular, we show that" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 544, + 544, + 626 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 306, + 544, + 544, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 544, + 566 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 544, + 566 + ], + "type": "text", + "content": "- RPP is slow to reach moderate PSNR levels, but is fast to reach high PSNR (Sec. 4.1)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 567, + 544, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 544, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 544, + 590 + ], + "type": "text", + "content": "- there is a linear path that connects the moderate-to-high PSNR points in the RPP loss landscape (Sec. 4.2)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 591, + 544, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 591, + 544, + 626 + ], + "spans": [ + { + "bbox": [ + 306, + 591, + 544, + 626 + ], + "type": "text", + "content": "- model trained on RPP images tends to have less structured error, while vanilla training leads to error patterns that reflect the underlying encoding schemes (Sec. 4.3)." + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 634, + 544, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 634, + 544, + 659 + ], + "spans": [ + { + "bbox": [ + 305, + 634, + 544, + 659 + ], + "type": "text", + "content": "4.1. The PSNR curve: Slower to approximate well, but faster to approximate “very well”" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 666, + 544, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 544, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 544, + 700 + ], + "type": "text", + "content": "First, we observe that RPP images tend to achieve moderate PSNRs (e.g., 30dB) much later than the original images, but they quickly reach high PSNRs (e.g., 50dB) afterwards." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 317, + 701, + 544, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 544, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 544, + 713 + ], + "type": "text", + "content": "In Fig. 4, we provide an example plot of fitting a SIREN" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4834" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "on a natural image from the Kodak dataset. From the figure, we can immediately make the following observations:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 286, + 239 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 47, + 96, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 286, + 156 + ], + "type": "text", + "content": "- RPPs are slow starters. The training PSNR of the original image quickly arrives at " + }, + { + "bbox": [ + 47, + 96, + 286, + 156 + ], + "type": "inline_equation", + "content": "\\sim 30\\mathrm{dB}" + }, + { + "bbox": [ + 47, + 96, + 286, + 156 + ], + "type": "text", + "content": " the early stage of training, even before taking 300 SGD iterations. On the other hand, the PSNR of the RPP image remains very small, under 15 dB at the similar number of steps." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 286, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 239 + ], + "type": "text", + "content": "- Explosive surge in later stage. After staying at a low PSNR level (under 20 dB) for a while, the PSNR of RPP images bursts explosively. The PSNR jumps from " + }, + { + "bbox": [ + 47, + 156, + 286, + 239 + ], + "type": "inline_equation", + "content": "\\sim 15\\mathrm{dB}" + }, + { + "bbox": [ + 47, + 156, + 286, + 239 + ], + "type": "text", + "content": " to 50dB in less than 100 SGD steps. On the other hand, the PSNR curve of the original image oscillates wildly at 30-35dB level for a long time, and gradually reaches the 50dB at around 1600 steps." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 240, + 286, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 286, + 275 + ], + "type": "text", + "content": "These observations are consistent over the choice of the target image; we provide a comprehensive collection of figures in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 275, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 286, + 323 + ], + "type": "text", + "content": "For a more quantitative comparison, we compare the average number of SGD steps to arrive the PSNR of 30dB and 50dB for the original and RPP images (Tab. 2). Again, we use the images from the Kodak dataset and fit with SIRENs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 323, + 286, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 286, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 286, + 407 + ], + "type": "text", + "content": "We observe that, for original images, the number of steps to reach 30dB is around 100 steps, while the number of SGD steps to reach the 50dB is over 1300 steps. That is, it takes almost " + }, + { + "bbox": [ + 47, + 323, + 286, + 407 + ], + "type": "inline_equation", + "content": "13 \\times" + }, + { + "bbox": [ + 47, + 323, + 286, + 407 + ], + "type": "text", + "content": " more steps to reach the high PSNR than for moderate PSNRs. On the other hand, for RPP images, it takes over 800 steps to reach the moderate PSNR level, while it takes only 300 more steps to reach the high PSNR." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 415, + 286, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 286, + 439 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 286, + 439 + ], + "type": "text", + "content": "4.2. Linear paths in the loss landscape: RPP images find a \"linear expressway\"" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "content": "From the previous observation, it seems likely that, for RPP images, there may exist an expressway in the neural field parameter space that connects the moderate-PSNR parameter with the high-PSNR parameter; on this expressway, the SGD may not encounter too many hills to circumvent, and may mostly follow a smooth linear path." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 517, + 286, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 286, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 286, + 552 + ], + "type": "text", + "content": "To validate this intuition, we visualize the loss landscape of the SIREN trained on Kodak images. In particular, we capture two different phases of training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 552, + 286, + 611 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 48, + 552, + 286, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 552, + 286, + 587 + ], + "spans": [ + { + "bbox": [ + 48, + 552, + 286, + 587 + ], + "type": "text", + "content": "1. Early phase. We plot the linear path from the initialization to 30dB point, i.e., the parameter that first achieves PSNR 30dB during the training (Fig. 5)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 588, + 286, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 286, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 286, + 611 + ], + "type": "text", + "content": "2. Late phase. We plot the linear path from the 30dB point to the PSNR 50dB point (Fig. 6)." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 613, + 286, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 286, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 286, + 671 + ], + "type": "text", + "content": "To generate such visualization, we project the parameter space into a two-dimensional space, as in [13]. Unlike [13], we fix one axis to a directional vector between two parameter points that we want to capture (e.g., 30dB point and 50dB point); the other axis has been decided randomly.2" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 672, + 286, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 286, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 286, + 696 + ], + "type": "text", + "content": "During the early phase (Fig. 5), we observe that the loss landscape of RPP is quite hostile; unlike in original images," + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 423, + 159 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 423, + 159 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 423, + 159 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 423, + 159 + ], + "type": "image", + "image_path": "214cc116f3cf24270d496b115801b22dcb4a4906c5d1162105819ce4fd441447.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 163, + 409, + 172 + ], + "lines": [ + { + "bbox": [ + 323, + 163, + 409, + 172 + ], + "spans": [ + { + "bbox": [ + 323, + 163, + 409, + 172 + ], + "type": "text", + "content": "(a) Elevated view; original" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 430, + 72, + 544, + 159 + ], + "blocks": [ + { + "bbox": [ + 430, + 72, + 544, + 159 + ], + "lines": [ + { + "bbox": [ + 430, + 72, + 544, + 159 + ], + "spans": [ + { + "bbox": [ + 430, + 72, + 544, + 159 + ], + "type": "image", + "image_path": "d2e11adfcd62481c61e914d9da8315ae422e8e982a7b9c9fe710432484d63116.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 163, + 523, + 171 + ], + "lines": [ + { + "bbox": [ + 449, + 163, + 523, + 171 + ], + "spans": [ + { + "bbox": [ + 449, + 163, + 523, + 171 + ], + "type": "text", + "content": "(b) Elevated view; RPP" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 310, + 176, + 423, + 253 + ], + "blocks": [ + { + "bbox": [ + 310, + 176, + 423, + 253 + ], + "lines": [ + { + "bbox": [ + 310, + 176, + 423, + 253 + ], + "spans": [ + { + "bbox": [ + 310, + 176, + 423, + 253 + ], + "type": "image", + "image_path": "0fe069709246fb805756ff39a40c3c7d7066851a7200b564b12089e24ad5570f.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 256, + 402, + 266 + ], + "lines": [ + { + "bbox": [ + 329, + 256, + 402, + 266 + ], + "spans": [ + { + "bbox": [ + 329, + 256, + 402, + 266 + ], + "type": "text", + "content": "(c) Side view; original" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 430, + 176, + 544, + 253 + ], + "blocks": [ + { + "bbox": [ + 430, + 176, + 544, + 253 + ], + "lines": [ + { + "bbox": [ + 430, + 176, + 544, + 253 + ], + "spans": [ + { + "bbox": [ + 430, + 176, + 544, + 253 + ], + "type": "image", + "image_path": "0daeb6394d4aec17a6612133b8dbb0cfbe4f890a68f44c9f4555dcd5ae111e6b.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 456, + 256, + 517, + 266 + ], + "lines": [ + { + "bbox": [ + 456, + 256, + 517, + 266 + ], + "spans": [ + { + "bbox": [ + 456, + 256, + 517, + 266 + ], + "type": "text", + "content": "(d) Side view; RPP" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 310, + 334, + 422, + 422 + ], + "blocks": [ + { + "bbox": [ + 304, + 275, + 545, + 331 + ], + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 331 + ], + "type": "text", + "content": "Figure 5. SIREN loss landscape: from initial point to 30dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the initial point and the parameter that achieves PSNR 30. For RPP, the minima is much narrower and lacks a clear pathway toward it, unlike in the original image." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 334, + 422, + 422 + ], + "lines": [ + { + "bbox": [ + 310, + 334, + 422, + 422 + ], + "spans": [ + { + "bbox": [ + 310, + 334, + 422, + 422 + ], + "type": "image", + "image_path": "712935ba3947a2adc3cb3ac979f390f183d0b46e9d9ca6bc729da8d42bac533a.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 347, + 424, + 385, + 434 + ], + "lines": [ + { + "bbox": [ + 347, + 424, + 385, + 434 + ], + "spans": [ + { + "bbox": [ + 347, + 424, + 385, + 434 + ], + "type": "text", + "content": "(a) Original" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 444, + 545, + 510 + ], + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 510 + ], + "type": "text", + "content": "Figure 6. SIREN loss landscape: from 30dB point to 50dB point. For original and RPP versions of a Kodak image, we plot the loss landscape between the parameters that first achieve PSNR 30 (■) and PSNR 50 (★), respectively. The loss barriers between two minima are dramatically different; 15.3dB for the original image, and 28.3dB for the RPP (averaged over all Kodak images)." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 428, + 337, + 544, + 421 + ], + "blocks": [ + { + "bbox": [ + 428, + 337, + 544, + 421 + ], + "lines": [ + { + "bbox": [ + 428, + 337, + 544, + 421 + ], + "spans": [ + { + "bbox": [ + 428, + 337, + 544, + 421 + ], + "type": "image", + "image_path": "a32c7b7c05b5c5bf11cf6ec5d1ab9f3d1fc91531a414db5a4f2cab64c33ab0fa.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 424, + 499, + 433 + ], + "lines": [ + { + "bbox": [ + 474, + 424, + 499, + 433 + ], + "spans": [ + { + "bbox": [ + 474, + 424, + 499, + 433 + ], + "type": "text", + "content": "(b) RPP" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "content": "the minima that 30dB point belongs to is quite narrow and there is no clear pathway toward the 30dB point." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": "During the late phase (Fig. 6), for the RPP image, once the parameter arrives at the minima, there exists a linear path that connects the " + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "inline_equation", + "content": "30\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": " point to the " + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "inline_equation", + "content": "50\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": " point. If we measure the loss barrier, i.e. the maximum loss on the linear path between " + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "inline_equation", + "content": "30\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "inline_equation", + "content": "50\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": " points, it is as low as " + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "inline_equation", + "content": "28.3\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": " for the RPP versions of Kodak images. For original images, the loss barrier is quite high (15.3dB)." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 635, + 544, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 544, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 544, + 659 + ], + "type": "text", + "content": "4.3. Patterns in the error: The errors are less structured in RPP images" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Another interesting property of RPP is that the errors that the neural field makes are more evenly distributed among the pixels, lacking a clearly distinguishable pattern. It turns out that the whiteness of the RPP error can help generat-" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 266, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 266, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 266, + 712 + ], + "type": "text", + "content": "2A similar method has been considered by Goodfellow et al. [7]." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4835" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 210, + 162 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 210, + 162 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 210, + 162 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 210, + 162 + ], + "type": "image", + "image_path": "ac9391826d2d3d69625971feecf263661f4894f079a8ab0ec9a469b742d8865f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 376, + 162 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 376, + 162 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 376, + 162 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 376, + 162 + ], + "type": "image", + "image_path": "12aaf41fef2c5eb31f014ba123de8abd5e51ca5c6138b55048f3b572ca7f3f91.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 278, + 163, + 317, + 173 + ], + "lines": [ + { + "bbox": [ + 278, + 163, + 317, + 173 + ], + "spans": [ + { + "bbox": [ + 278, + 163, + 317, + 173 + ], + "type": "text", + "content": "(a) Original" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 384, + 70, + 545, + 162 + ], + "blocks": [ + { + "bbox": [ + 384, + 70, + 545, + 162 + ], + "lines": [ + { + "bbox": [ + 384, + 70, + 545, + 162 + ], + "spans": [ + { + "bbox": [ + 384, + 70, + 545, + 162 + ], + "type": "image", + "image_path": "ad7903394cdca0610e29f820ac0a97316ef20880a39807d6f00ac89790767fef.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 180, + 209, + 272 + ], + "blocks": [ + { + "bbox": [ + 48, + 180, + 209, + 272 + ], + "lines": [ + { + "bbox": [ + 48, + 180, + 209, + 272 + ], + "spans": [ + { + "bbox": [ + 48, + 180, + 209, + 272 + ], + "type": "image", + "image_path": "017b3678fc9ceeda8164c8ff6693aaf6cb94c8c2779982c65732d658fe819b83.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 546, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 546, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 546, + 327 + ], + "type": "text", + "content": "Figure 7. Example reconstructions at a target PSNR value of 30 (SIREN). Random pixel permutation enables the network to prioritize the restoration of high-frequency, fine details, whereas the original representation tends to steer the network toward restoring low-frequency components initially. While this behavior may pose challenges during the early stages of training, it ultimately facilitates achieving visually more plausible reconstructions much earlier than the original representation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 216, + 179, + 376, + 271 + ], + "blocks": [ + { + "bbox": [ + 216, + 179, + 376, + 271 + ], + "lines": [ + { + "bbox": [ + 216, + 179, + 376, + 271 + ], + "spans": [ + { + "bbox": [ + 216, + 179, + 376, + 271 + ], + "type": "image", + "image_path": "55137ca5d21e518594aeb4fdb02b4fefaaa4b5febc7697db64cf297f5b9cdea5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 283, + 274, + 308, + 281 + ], + "lines": [ + { + "bbox": [ + 283, + 274, + 308, + 281 + ], + "spans": [ + { + "bbox": [ + 283, + 274, + 308, + 281 + ], + "type": "text", + "content": "(b) RPP" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 383, + 180, + 543, + 271 + ], + "blocks": [ + { + "bbox": [ + 383, + 180, + 543, + 271 + ], + "lines": [ + { + "bbox": [ + 383, + 180, + 543, + 271 + ], + "spans": [ + { + "bbox": [ + 383, + 180, + 543, + 271 + ], + "type": "image", + "image_path": "e5d6352037d23b4c5f455fb99a78e3373240a6dc2b43dec53fcae89f4efa5d3a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 48, + 335, + 282, + 397 + ], + "blocks": [ + { + "bbox": [ + 48, + 335, + 282, + 397 + ], + "lines": [ + { + "bbox": [ + 48, + 335, + 282, + 397 + ], + "spans": [ + { + "bbox": [ + 48, + 335, + 282, + 397 + ], + "type": "table", + "html": "
Target PSNR
20304050
Original10.51e-0423.68e-0619.46e-085.90e-10
Random pixel perm.5.68e-045.89e-067.59e-085.81e-10
Average ratio2.03×5.20×5.80×1.55×
", + "image_path": "eac09e35d0da007e50a8bb31029abad5a57b9b40f72c04b782a131b2c52be04b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 401, + 287, + 445 + ], + "lines": [ + { + "bbox": [ + 47, + 401, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 287, + 445 + ], + "type": "text", + "content": "Table 3. Loss variance over pixels. We measure the average pixel loss variance in the SIREN trained on Kodak dataset, measured at various levels of PSNR. The \"average ratio\" denotes the mean of " + }, + { + "bbox": [ + 47, + 401, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathrm{Var}(\\mathrm{original}) / \\mathrm{Var}(\\mathrm{RPP})" + }, + { + "bbox": [ + 47, + 401, + 287, + 445 + ], + "type": "text", + "content": ". RPP has a lower loss variance at all PSNRs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 460, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 287, + 483 + ], + "type": "text", + "content": "ing more visually sharp and satisfactory images than neural fields trained on original images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": "In Tab. 3, we measure the pixel loss variance in both original and RPP images trained to various target PSNR levels. From the table, we observe that the loss variance is up to " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "5.80 \\times" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " larger in the neural fields trained on the original images than on RPP images. This implies that, for original images, some pixels in the original image are fit much faster than other pixels. Putting that differently, the neural field trained on the unpermuted images tends to prioritize learning a specific type of patterns first, while the neural field trained on RPP images does less so." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Exactly what pattern is RPP avoiding to fit? In Figs. 7 and 8, we compare the images generated by the neural fields trained on original and RPP images on SIREN and Instant-NGP, respectively. In Fig. 7, we observe that SIRENs trained on original images have thicker wavy patterns, which is likely to be a consequence of the sinusoidal encoding structure of SIREN. The models trained on RPP images, on the other hand, have much sharper texture with fine-grained noise. A similar phenomenon is observed in" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 338, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 545, + 398 + ], + "type": "text", + "content": "the case of Instant-NGP (Fig. 8). Here, we observe that the models trained on original images attain axis-aligned artifacts; black (or white) horizontal (or vertical) blocks appear in the rendered images. On the other hand, the error is much less structured in models trained on RPP images." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 415, + 389, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 389, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 389, + 426 + ], + "type": "text", + "content": "5. Related work" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 436, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 604 + ], + "type": "text", + "content": "Optimization bias of neural networks. It has been well known, both theoretically and empirically, that SGD-based optimization algorithms are biased toward learning \"simplex solutions,\" for various notions of simplicity. A prominent example is the spectral bias, a tendency to prioritize learning lower-frequency components of the target function [3, 22]. Other types of biases have also been studied in the literature: SGD tends to prefer learning smaller-norm solutions [9, 21] and low-rank solutions [32, 34]. These works mostly focus on explaining how such simplicity biases are advantageous in learning a solution that can generalize well (see, e.g., [23]). Our work, in contrast, describes how such bias can be disadvantageous in terms of the training speed, instead of the generalization performance." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Random labels and memorization. The question of how neural nets behave when trained on random labels has been actively studied since its connection to the generalization capability of deep learning has been established [38]. Arpit et al. [2] finds that neural networks tend to learn simple patterns first and then memorize the unexplainable samples—such as random label and data—in the later phase. A more recent study argues that training on randomly labeled data can actually be advantageous [17]; pre-training on random" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4836" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 165, + 183 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 165, + 183 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 165, + 183 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 165, + 183 + ], + "type": "image", + "image_path": "a38514ea60a6a0fefa78c4927b3495da11b34bbddfcffb67498562b44902c270.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 70, + 284, + 183 + ], + "blocks": [ + { + "bbox": [ + 170, + 70, + 284, + 183 + ], + "lines": [ + { + "bbox": [ + 170, + 70, + 284, + 183 + ], + "spans": [ + { + "bbox": [ + 170, + 70, + 284, + 183 + ], + "type": "image", + "image_path": "924c2b7c7a3629655a5f8a7ec8f9ea929ff491ac4924e195a6fe52754661b49e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 51, + 196, + 164, + 309 + ], + "blocks": [ + { + "bbox": [ + 139, + 186, + 196, + 195 + ], + "lines": [ + { + "bbox": [ + 139, + 186, + 196, + 195 + ], + "spans": [ + { + "bbox": [ + 139, + 186, + 196, + 195 + ], + "type": "text", + "content": "(a) Ground Truth" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 196, + 164, + 309 + ], + "lines": [ + { + "bbox": [ + 51, + 196, + 164, + 309 + ], + "spans": [ + { + "bbox": [ + 51, + 196, + 164, + 309 + ], + "type": "image", + "image_path": "c0858e07a9b311ea25f3bb0a0a5cf226a9c55af18b979cb10b64138617fec971.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 171, + 196, + 284, + 308 + ], + "blocks": [ + { + "bbox": [ + 171, + 196, + 284, + 308 + ], + "lines": [ + { + "bbox": [ + 171, + 196, + 284, + 308 + ], + "spans": [ + { + "bbox": [ + 171, + 196, + 284, + 308 + ], + "type": "image", + "image_path": "cccaa638c5a0a5e625b76f762801c3861d13e85401ed9891fb686280e818aa19.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 50, + 321, + 164, + 435 + ], + "blocks": [ + { + "bbox": [ + 148, + 312, + 187, + 320 + ], + "lines": [ + { + "bbox": [ + 148, + 312, + 187, + 320 + ], + "spans": [ + { + "bbox": [ + 148, + 312, + 187, + 320 + ], + "type": "text", + "content": "(b) Original" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 321, + 164, + 435 + ], + "lines": [ + { + "bbox": [ + 50, + 321, + 164, + 435 + ], + "spans": [ + { + "bbox": [ + 50, + 321, + 164, + 435 + ], + "type": "image", + "image_path": "263dbfefae65ebc89efdbe98b52a920d5b10d01aa4d3844f0e42ff465de9da34.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 446, + 287, + 512 + ], + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 512 + ], + "type": "text", + "content": "Figure 8. Example reconstructions at a target PSNR value of 20 (Instant-NGP). Similarly to the SIREN case, we observe that Instant-NGPs trained on the RPP images have much less visually distinguishable artifacts. The models trained on original images tend to have axis-aligned blocks of error, which is likely to have originated from the spatial grid encoding of the model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 169, + 321, + 282, + 435 + ], + "blocks": [ + { + "bbox": [ + 169, + 321, + 282, + 435 + ], + "lines": [ + { + "bbox": [ + 169, + 321, + 282, + 435 + ], + "spans": [ + { + "bbox": [ + 169, + 321, + 282, + 435 + ], + "type": "image", + "image_path": "7ff8359250ed7003e4ff95ae4f2fba08bec7737c0ddc91461b947bf066c424ef.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 437, + 179, + 445 + ], + "lines": [ + { + "bbox": [ + 154, + 437, + 179, + 445 + ], + "spans": [ + { + "bbox": [ + 154, + 437, + 179, + 445 + ], + "type": "text", + "content": "(c) RPP" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 530, + 286, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 286, + 590 + ], + "type": "text", + "content": "data helps fitting the training data, when eventually fine-tuning on the dataset with correct labels. Different from these works, our work discovers how random label can be beneficial in the neural field context, without any consideration on further fine-tuning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": "Faster training of neural fields. Other than the works described in the introduction, there have been many other attempts to accelerate the neural field training by designing better encoding schemes. Positional encodings [5, 19, 27, 29] and spatial grids [6, 16, 18, 20] are the most popular options, and some works also use tree-like structures [28, 36]. Our work is complementary to this line of works, and argues that transforming the data in the original data space can provide auxiliary training speed boosts. We also note that a concurrent work also aims to boost the training speed by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": "modifying the given data [15]. In particular, [15] finds that separating the visual signals into many sub-segments can facilitate the convergence of SIRENs and proposes a meta-learning algorithm to speed up training. Our work considers a more general class of data transformations, and focus on understanding how transformations accelerate training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 160, + 378, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 160, + 378, + 172 + ], + "spans": [ + { + "bbox": [ + 306, + 160, + 378, + 172 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 182, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 373 + ], + "type": "text", + "content": "Learning neural fields poses a unique challenge, as the primary objective is to overfit to the given data—an aim contrary to the typical goals in other problem domains where learning attempts to achieve regularization to prevent overfitting. In our study of this distinctive problem, we discovered that certain data transformations can expedite the network's acquisition of fine details more rapidly than when learning from the original images. Specifically, we demonstrated that random pixel permutations, which explicitly make learning low-frequency details more challenging, guide the network away from fixating on low-frequency components. This resulted in significantly enhanced PSNR within a given computational budget and, furthermore, yielded visually more plausible reconstructions at the same PSNR level. Our insights are substantiated by thorough empirical evaluations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 375, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 495 + ], + "type": "text", + "content": "Limitation & future direction. A notable limitation of our approach is that its direct applicability may be constrained when learning neural networks for other problem domains such as classification and regression, where regularization is crucial. As a future work, we aim to conduct more comprehensive studies to understand how data transformations affect both trainability and generalization of neural fields (and other neural networks). Such exploration may offer new insights on how to modify the given workload to jointly optimize the training cost and the model performance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 496, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 605 + ], + "type": "text", + "content": "Another, more narrowly scoped future direction will be to gain a more concrete, theoretical understanding on the effect of random pixel permutations on the training dynamics of neural fields. Although our empirical analyses provide some insights into how RPP can help accelerate the training, we are yet to fully understand why fitting the easy patterns slows down the later phase of training. Deeper understandings on this matter may lead to impactful lessons applicable to any deep learning domain that involves long training." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Acknowledgments. This work was partly supported by the National Research Foundation of Korea (NRF) grant (RS-2023-00213710, Neural Network Optimization with Minimal Optimization Costs), and partly by the Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2022- 0-00713, Meta-learning applicable to real-world problems, No.2019-0-01906, Artificial Intelligence Graduate School Program (POSTECH)), all funded by the Korea government (MSIT)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4837" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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In-Context Matting. This novel task setting for image matting enables automatic natural image matting of target images of a certain object category conditioned on a reference image of the same category, with user-provided priors such as masks and scribbles on the reference image only. Notice that, our approach exhibits remarkable cross-domain matting quality." + ], + "image_footnote": [], + "bbox": [ + 125, + 523, + 179, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/12556a0b3e747d5060cb44f0406e21bd910e6498db913bdc448a2d60d5dcf4c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 214, + 525, + 267, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae2266aefe00c71cc9ac71bafcf7a459ea45df98e923ba566edbf08d68b0bd77.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 525, + 341, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6c74018e3314560b3765d0ee195c8a24e76a0cd8219c0e61ae7c789809825ef5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 392, + 523, + 446, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c03457c353c1269af5548df7c8b797b90d664503806504843faca3e0605a4da8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 523, + 553, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3348d7672035d8a61f9b12cb6df72ec68e00fc81c4e0005a21298c419eb4456d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 555, + 525, + 609, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$\\mathsf{N}^*$ image $+1^{*}$ prompt $+1^{*}$ model $\\rightarrow$ N\\*predictions", + "bbox": [ + 560, + 436, + 864, + 450 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/91a7a71a1a1ac45b533cd301ae5834d30b5eb166f53b70771f1bfa004a8caab5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 523, + 720, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a18b7b290f81d29a6d0cee6b2e7d20f8bcd13b8d9cb0e664be32224ddc28ed33.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 523, + 874, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 641, + 313, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce in-context matting, a novel task setting of image matting. Given a reference image of a certain foreground and guided priors such as points, scribbles, and masks, in-context matting enables automatic alpha estimation on a batch of target images of the same foreground category, without additional auxiliary input. This setting marries good performance in auxiliary input-based matting and ease of use in automatic matting, which finds a good tradeoff between customization and automation. To overcome the key challenge of accurate foreground matching, we introduce IconMatting, an in-context matting model built upon a pre-trained text-to-image diffusion model. Conditioned on inter- and intra-similarity matching, IconMatting can", + "bbox": [ + 75, + 674, + 470, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "make full use of reference context to generate accurate target alpha mattes. To benchmark the task, we also introduce a novel testing dataset ICM-57, covering 57 groups of real-world images. Quantitative and qualitative results on the ICM-57 testing set show that IconMatting rivals the accuracy of trimap-based matting while retaining the automation level akin to automatic matting. Code is available at https://github.com/tiny-smart/in-context-matting.", + "bbox": [ + 500, + 642, + 890, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 805, + 632, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image matting has been a long-standing problem in vision and graphics [3]. It typically requires estimating an accurate alpha matte by solving a so-called matting equation", + "bbox": [ + 500, + 830, + 890, + 877 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\nI = \\alpha F + (1 - \\alpha) B, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 101, + 887, + 225, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3711", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "where $I$ is the 3-channel RGB image, $F$ , $B$ , and $\\alpha$ are the 3-channel foreground, the 3-channel background, and the 1-channel alpha matte. The matting equation, however, is highly ill-posed, due to the need to infer 7 unknowns from 3 observations.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prior art has come up with different ways to reduce uncertainties in matting such as using trimaps [7, 16, 18-20, 32, 38], scribbles [39], or a even known background [17, 29]. These approaches are given the name auxiliary input-based matting [14] in modern matting literature. Indeed, these matting models, particularly trimap-based ones, have achieved remarkable accuracy. They are in some way user-unfriendly as an auxiliary input should be provided with each image in practice, which significantly harms matting efficiency and user experience. Recently another stream of work attempts to abandon any auxiliary input completely and forms a new paradigm called automatic matting [4, 9, 11, 12, 21, 31, 43]. Despite their inherent advantages, these automatic matting models are narrowed to specific object categories, such as humans [4, 9, 21, 31], animals [12], and salient objects [11, 43]. This can render poor generalization in natural scenes, infeasibility to tackle general object categories, and unawareness of foreground of interest.", + "bbox": [ + 75, + 167, + 472, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hence, there seems an obvious gap between accuracy and efficiency and between customization and automation. An interesting question is that: Can the auxiliary input-based matting be optimized to enhance the efficiency, while also maintaining guidance for matting targets with sufficient automation, thereby harmonizing the two existing matting paradigms?", + "bbox": [ + 75, + 458, + 468, + 563 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we introduce in-context matting, a novel task setting of image matting, where a reference input can provide guidance for a batch of target images with similar foregrounds. The alpha matts of the target batch are predicted by leveraging the contextual information from the reference input. Fig. 1 provides an example, where a cat marked in the reference image enables the extraction of cats from all target images, regardless of the background or domain. This novel task setting relieves users from providing auxiliary input for each image. Instead, by specifying the matting target only in a single reference image, the alpha matts of the entire batch images could be predicted. Given the reference guidance, in-context matting can also gather sufficient contextual information, leading to higher accuracy and adaptability than fully automatic matting. This setting therefore combines the most notable features of automatic and auxiliary input-based matting, finding a good trade-off between them.", + "bbox": [ + 75, + 566, + 472, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Technically, we confront a primary challenge inherent to in-context matting, i.e., how to leverage the reference input to accurately identify the corresponding target foreground. While SegGPT [35] has explored image segmentation with", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "contextual information, its in-context coloring framework is not suitable for image matting. In this work, we approach this challenge as a problem of region-to-region matching. In particular, recent advances [22, 26, 30] in generative diffusion models have demonstrated emergent capabilities in discriminative tasks like segmentation [37] and correspondence [33]. Given that our region-to-region matching is an inherent aspect of correspondence, and noting the parallels between image segmentation and image matting, we explore the applicability of pretrained diffusion models for in-context matting.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We therefore introduce IconMatting, a model based on the pre-trained Stable Diffusion model [26], specialized for in-context matting. Given a reference image along with its corresponding foreground of interest as context, the target alpha matte could be inferred by exploiting the feature correspondence from Stable Diffusion such that the target foreground is matched conditioned on the correspondence. However, the matching is often sparse and insufficient to represent the entire target area. To address this, the intra-image similarity, based on the self-attention maps of Stable Diffusion, is additionally used to supplement the missing parts. By leveraging both inter- and intra-image similarities, informative guidance of the matting target would be acquired. Finally, any off-the-shelf matting heads can be used to predict the alpha matte.", + "bbox": [ + 496, + 267, + 892, + 494 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since the task setting is different from existing mating benchmarks, we introduce a new testing dataset named ICM-57 to offer a broad and thorough validation of in-context mating. This dataset encompasses 57 contextually-aligned image groups; each comprising images in the real world and has either the same category or the same instance of different views, thereby encompassing a rich variety of in-context scenarios, which ensures a comprehensive test of a model to tackle various contexts.", + "bbox": [ + 496, + 503, + 893, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through extensive experiments on the ICM-57 and AIM-500 [10] datasets, we showcase the potential of in-context matting and IconMatting. The results indicate that IconMatting, while retaining the automation level akin to automatic matting, rivals the accuracy of trimap-based matting, underscoring the value of in-context matting as a promising direction for image matting.", + "bbox": [ + 496, + 650, + 893, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions include:", + "text_level": 1, + "bbox": [ + 517, + 767, + 696, + 781 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce in-context matting, a novel task setting of image matting that takes advantages of both automatic and auxiliary input-based matting;", + "- IconMatting: an effective in-context matting model based on Stable Diffusion.", + "- ICM-57: a novel dataset and the evaluation framework for in-context matting." + ], + "bbox": [ + 500, + 792, + 890, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3712", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We review work related to image matting and in-context learning in vision.", + "bbox": [ + 76, + 114, + 468, + 145 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image Matting. Image matting approaches can be coarsely categorized into auxiliary input-based matting and automatic matting. Auxiliary input-based matting requires user input. The user input can be in the form of a trimap [7, 16, 18, 19, 32, 38], scribbles [39], a background image [17, 29], a coarse mask [23, 42], or even a text description [15]. Despite their effectiveness, they require significant manual effort to provide the auxiliary inputs. Automatic matting [4, 10, 12, 24, 43] predicts the alpha matte without any user intervention. They typically assume salient or certain foregrounds that are implicitly defined by the training dataset. The network structures used in automatic matting can be divided into two groups: one-stage network with global guidance [24] and parallel multi-task network [10, 31]. Some recent work has also introduced transformer structures into automatic matting [21]. While both auxiliary input-based and automatic matting have been studied comprehensively, a paradigm that combines the efficiency of automatic matting and the precision of auxiliary input-based matting has not yet been explored. We fill this gap with in-context matting.", + "bbox": [ + 75, + 152, + 472, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In-Context Learning in Vision. In-context learning, initially a concept in natural language processing [5], is now made popular in computer vision. It allows models to fast adapt to a variety of tasks with minimal examples.", + "bbox": [ + 76, + 477, + 468, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Bar et al. [2] first proposes an in-context learning framework using inpainting with discrete tokens on figures and infographics from vision articles, demonstrating applications in foreground segmentation, single object detection, and colorization. Painter [34] adopts masked image modeling to perform in-context learning with supervised datasets, achieving highly competitive results on seven diverse tasks. More recently, SegGPT [35], which segments everything in context by unifying different segmentation tasks into an in-context coloring framework. Prompt Diffusion [6] presents a diffusion-based generative framework to enable in-context learning across various tasks. Additionally, Flamingo [1], a family of visual language models, shows rapid adaptation to a variety of image and video tasks with few-shot learning capabilities. These models showcase the potential of in-context learning in addressing diverse vision tasks.", + "bbox": [ + 75, + 537, + 472, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The concept of in-context learning, while being transformative in other areas, has not yet impacted the field of image matting. Although SegGPT achieves in-context image segmentation but is limited to coarse levels, lacking in semitransparency handling. Our IconMatting first introduces in-context learning into image matting, enhancing both the efficiency of auxiliary input-based matting and the precision of automatic matting.", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/9ed872c8dc8fcd0b0782bce8e6929b9c2e7c61868127b88ad53ba046e6484241.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Task settingautoauto with ref-inputreal-world generalization#ref-input
AuxXXgood#images
Auto✓-poorzero
In-contextX✓goodone
", + "bbox": [ + 500, + 88, + 895, + 154 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Comparison between in-context matting and two existing image matting paradigms. \"Aux\" and \"Auto\" are abbreviations for auxiliary input-based matting and automatic matting, respectively. In-context matting requires only a single reference input to achieve the automation of automatic matting and the generalizability of auxiliary input-based matting.", + "bbox": [ + 498, + 162, + 893, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work is also related to image co-segmentation [27]. This task aims to segment common objects within a pair of contextual images. However, unlike in-context matting, where users can specify the matting target, co-segmentation operates without user input, predicting rough binary masks delineating common objects across image pairs.", + "bbox": [ + 498, + 270, + 893, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. In-Context Matting with Diffusion Models", + "text_level": 1, + "bbox": [ + 500, + 373, + 879, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We begin with the problem setup, then present our proposed in-context matting model, i.e., IconMatting.", + "bbox": [ + 498, + 398, + 892, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Setup", + "text_level": 1, + "bbox": [ + 500, + 438, + 651, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The objective of in-context matting is to extract the alpha mattes $\\{\\alpha_{i}\\}^{N}$ of a specified foreground category from a collection of input images $\\{I_i\\}^N$ . Through user interaction, the matting target is indicated by a reference image $I_r$ and a corresponding binary region of interest (RoI) map $M_{\\mathrm{RoI}}$ . The RoI map can take the form of a mask, scribbles, or points as exemplified in Fig. 1. Notably, the reference image can either be a part of the input collection or an entirely separate image. When the input image collection has only a single image, users can treat that image as the reference image. In this case, in-context matting degenerates into image matting guided by user interaction.", + "bbox": [ + 498, + 460, + 893, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given $\\{I_i\\}^N$ and $(I_r, M_{\\mathrm{RoI}})$ , in-context matting is formulated as predicting the alpha matte $\\{\\alpha_i\\}^N$ in $\\{I_i\\}^N$ of the matting targets informed by $(I_r, M_{\\mathrm{RoI}})$ . In the context of in-context matting, when provided with a reference input, it becomes an automatic matting system targeted towards a specific foreground. The comparison between in-context matting and existing task settings for image matting is detailed in Table 1.", + "bbox": [ + 496, + 642, + 893, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overall Architecture", + "text_level": 1, + "bbox": [ + 500, + 771, + 696, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here we first present the overall framework of IconMatting. As shown in Fig. 2, IconMatting is comprised of three components: a feature extractor, an in-context similarity module, and a matting head.", + "bbox": [ + 498, + 794, + 892, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The feature extractor is responsible for obtaining the RoI features from the reference image, the features and self-attention maps from the target image. They are then fed into", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3713", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d7f6f36d94073124bde157b16fba206c76eba61caa56641e46aec0508ab6f60c.jpg", + "image_caption": [ + "Figure 2. IconMatting integrates a Stable Diffusion-derived feature extractor, an in-context similarity module, and a matting head. It processes a target image $I_{t}$ , a reference image $I_{r}$ , and an RoI map $M_{RoI}$ . Both reference and target image features and target self-attention maps are extracted and used. In-context similarity uses the in-context query from the reference image to create a guidance map, which, combined with self-attention maps, assists in locating the target object. The matting head finally generates the target alpha matte." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the in-context similarity module, the core of the framework. The module further consists of inter- and intra-similarity sub-modules: the former leverages the reference RoI features as an in-context query to derive a guidance map from the target features; the latter integrates the guidance map with multi-scale self-attention maps to obtain guidance for the matting head. Finally, the matting head uses this synthesized guiding information and the target features to generate the alpha matte of the target image.", + "bbox": [ + 75, + 417, + 470, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. In-Context Feature Extractor", + "text_level": 1, + "bbox": [ + 76, + 565, + 339, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Backbone Selection. As outlined in Section 1, we conceptualize the core challenge of in-context matting – leveraging the reference context to accurately identify the target foreground – as a region-to-region matching problem. Therefore, if the features derived from a backbone naturally possess correspondence capabilities, referred to as in-context features, they would facilitate the implementation of in-context matting. Tang et al. [33] have found that the text-to-image generative model, Stable Diffusion [26], trained on large-scale text-image paired datasets, exhibit emergent capabilities for both geometric and semantic correspondence. It can perform point-to-point correspondence between images across instances, classes, and even domains with simple cosine similarity. Inspired by this observation, we leverage Stable Diffusion as a feature extractor to implement in-context matting.", + "bbox": [ + 75, + 589, + 468, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Preliminary on Stable Diffusion. Recent advances in diffusion models, e.g., Stable Diffusion [26], have shown impressive results in both generative and discriminative tasks. Being a feature extractor, Stable Diffusion encodes", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "an image $x_0$ into a latent space, denoted by $z_0$ , which, through a noise process defined by $\\{\\alpha_t\\}^T$ , transforms into $z_{t} = \\sqrt{\\alpha_{t}} z_{0} + (\\sqrt{1 - \\alpha_{t}})\\varepsilon$ , where $\\varepsilon \\sim \\mathcal{N}(0,\\mathbf{I})$ is the randomly-sampled noise. The latent representation $z_{t}$ undergoes forward propagation in a U-Net $f_{\\theta}$ , generating multi-scale features $\\{\\mathcal{F}_l\\}^L$ and self-attention maps $\\{\\mathcal{A}_l\\}^L$ , which can later be exploited for downstream tasks. Icon-Matting uses the capabilities of Stable Diffusion and both reference and target images to extract multi-scale features and self-attention maps to enhance feature representation.", + "bbox": [ + 496, + 417, + 892, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. In-Context Similarity", + "text_level": 1, + "bbox": [ + 500, + 580, + 702, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In-context similarity plays a key role in our model, because the quality of inferred alpha mattes highly depends on the output of this module. In particular, the in-context similarity module is designed to identify the potential target foreground taking the reference RoI into account, thereby guiding the prediction of the target alpha matte. According to our observations, both the reference-target similarity and target-target similarity matter for locating the potential target foreground. These correspond to the proposed inter-similarity and intra-similarity sub-modules.", + "bbox": [ + 496, + 604, + 890, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation. The core challenge in in-context matting is a semantic correspondence problem. Given Stable Diffusion being the feature extractor, one can associate points of the foreground areas between the reference and target images using the emergent feature correspondence. However, due to the inherent reference-target foreground difference, a rigorous one-to-one mapping of all points between the two areas is unfeasible. There would always be some unmatched outliers, resulting in holes in the matting target", + "bbox": [ + 496, + 763, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3714", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5cb36e307577021a8ea3a8022752051a5b79a799cd770b3826a4ac9a57128b43.jpg", + "image_caption": [ + "(a) Outliers in point to point correspondence" + ], + "image_footnote": [], + "bbox": [ + 101, + 89, + 454, + 155 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/85b74aa009b87d04cea9fac38b20123341b6f43b8e8cf74f99d221e76a435937.jpg", + "image_caption": [ + "(b) Self-attention of random points", + "Figure 3. Observations on the inter- and intra similarities." + ], + "image_footnote": [], + "bbox": [ + 93, + 181, + 460, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "area of the target image, as illustrated in Fig. 3.", + "bbox": [ + 76, + 340, + 388, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since only a subset of points are matched, the goal is changed to how to expand these matched points to cover the entire target foreground area. To address this, we look for other points sharing similar semantic meaning with this subset of points. Intra-image similarity is therefore considered. Intuitively, the self-attention maps from Stable Diffusion reflect the similarities between different image patches. As shown in Fig. 3, by randomly sampling a small number of points from the target area and simply summing over the corresponding self-attention maps, the whole target foreground can be revealed. Based on this observation, we use the self-attention maps as intra-image information to supplement the inter-image matching results.", + "bbox": [ + 75, + 357, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inter-Similarity. Formally, given features $\\{\\mathcal{F}_l^r\\} ^L$ and $\\{\\mathcal{F}_l^t\\} ^L$ extracted from the reference image $I_{r}$ and the target image $I_{t}$ , respectively, the layer with the best correspondence capability is selected following DIFT [33], denoted by $\\mathcal{F}_{\\mathrm{inter}}^r$ for the reference and $\\mathcal{F}_{\\mathrm{inter}}^t$ for the target. Then, features corresponding to the RoI $M_{\\mathrm{RoI}}$ in $\\mathcal{F}_{\\mathrm{inter}}^r$ are extracted and formulated as the in-context query $\\{Q_k\\} ^K$ , where $K$ is the length of the query. $Q_{k}$ takes the form", + "bbox": [ + 76, + 559, + 468, + 683 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {k} = R (k), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 695, + 468, + 712 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR = \\mathcal {F} _ {\\text {i n t e r}} ^ {r} \\odot M _ {\\mathrm {R o I}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 724, + 468, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ is the element-wise product and $R(k)$ denotes the $k$ -th non-zero element of $R$ . Further, $\\{Q_k\\}^K$ is used to compute similarity with $\\mathcal{F}_{\\mathrm{inter}}^t$ , identifying regions on $I_t$ that correspond to the RoI of $I_r$ , formulated as", + "bbox": [ + 76, + 748, + 468, + 810 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {k} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {k} \\cdot F _ {\\text {i n t e r}} ^ {t}}{\\sqrt {d}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 820, + 468, + 858 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The similarity map is denoted by $\\{S_k\\}^K$ , and the mean of all such similarity maps yields $S$ , which measures the", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "degree of similarity between different locations on $I_{t}$ and the RoI in $I_{r}$ , serving as the first intermediate output of in-context similarity.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Intra-Similarity. As noted in our observations (Fig. 3), $S$ is typically sparse. Although the target matting region on $I_{t}$ is partially covered by $S$ , it is insufficient to guide alpha prediction. Here we further design the intra-similarity sub-module to leverage the internal similarity within $I_{t}$ to propagate $S$ into a more precise representation of the RoI on $I_{t}$ . During feature extraction of $I_{t}$ , self-attention maps $\\{\\mathcal{A}_l\\}^L$ representing its internal similarity are also retained, serving as the input for intra-similarity. This sub-module uses $S$ as a weight to the self-attention maps, thereby generating guiding information that accurately represents the matting target on $I_{t}$ , denoted by $\\{S_l'\\}^L$ . Mathematically, the intra-similarity matching is expressed by", + "bbox": [ + 498, + 141, + 892, + 339 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {l} ^ {\\prime} = \\mathcal {A} _ {l} \\odot \\mathcal {S}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 349, + 890, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Matting Head", + "text_level": 1, + "bbox": [ + 500, + 376, + 643, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The success of ViTMatte [40] implies that the information of original image is important during decoding. Following this practice, in our matting head, the original image is concatenated and decoded with outputs from previous modules.", + "bbox": [ + 498, + 400, + 890, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The guidance map from the in-context similarity module and the intra-features from the backbone are merged and refined using a convolutional feature fusion block, including a series of convolution, normalization, and activation layers. The output multi-scale in-context features are progressively merged using a series of fusion layers which comprise upsampling, concatenation, convolution, normalization, and activation layers. Then, following ViTMatte [40], details from the original image are extracted and combined with the merged feature in a detail decoder, enhancing the details of alpha matte. This matting head effectively melds contextual information with original image details, yielding the generation of a highly precise and refined alpha matte.", + "bbox": [ + 498, + 460, + 892, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Reference-Prompt Extension", + "text_level": 1, + "bbox": [ + 500, + 666, + 756, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to the mask prompts, points and scribbles can also be transformed into RoI masks. However, these prompts yield less comprehensive in-context queries compared with mask prompts. To enhance them, we propose an extension of reference prompt to enrich the in-context queries derived from point and scribble prompts.", + "bbox": [ + 496, + 689, + 890, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the self-attention maps from the backbone reflect the similarities across regions, we leverage the attention maps of the reference images to expand the RoI mask. This is achieved by including regions in the attention maps that are similar to the prompt locations. Specifically, for each prompt point, the top $m$ points with the highest responses in their corresponding attention maps are integrated into the RoI mask additionally, thus enriching the in-context query.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3715", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/009de63291823e756df212ca9c836574bccae0b66181568f26270ae959bd3d98.jpg", + "image_caption": [ + "Figure 4. ICM-57 examples. The dataset encompasses foreground subjects including human, animals, plants, and various common objects. It contains both instances from the same category and the same entity." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 467, + 180 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Results and Discussion", + "text_level": 1, + "bbox": [ + 76, + 275, + 292, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 301, + 179, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To facilitate in-context matting, we establish a hybrid training set, along with a test set, ICM-57. The existing AIM-500 dataset was also reorganized to meet the testing requirements of in-context matting. In particular, in-context matting requires to organize images into groups where the annotated foregrounds share categories or instances. Such organization allows for random selection of reference and target images within groups during training. In the test set, one or more images in each group are designated as reference images.", + "bbox": [ + 75, + 325, + 468, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mixing In-Context Training Sets. We selected the RM1K dataset [36]. However, such a dataset was insufficient for training. Therefore, a subset of the Open Images dataset [8], focusing on image segmentation, was also employed. The two formed a mixed training set tailored to in-context matting. Both datasets were reorganized.", + "bbox": [ + 75, + 489, + 468, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the RM-1K dataset, we divided it into 222 groups. A subset of 14,000 images from the Open Images dataset were chosen as well. In the original dataset, each image came with one or more annotations for image segmentation; each corresponds to an object instance. We aggregated these annotations by category, ensuring that the annotations include all instances of the corresponding category. They subsequently formed context groups that met the requirements of in-context matting. As a result, a mixed training set of 15,000 images and 450 groups was created.", + "bbox": [ + 75, + 580, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ICM-57 Testing Set. To assess the performance of our model, we constructed the first testing dataset for in-context matting, named ICM-57, which comprises 57 image groups that form various real-world contexts. This dataset was created by using the instance-segmented dreambooth dataset [28], to which we supplemented high-precision alpha matte annotations. Additionally, we reviewed the existing AIM-500 dataset, selected a subset, and categorized these into groups according to their classes to supplement the in-category groups. Examples of the testing set are shown in Fig 4.", + "bbox": [ + 75, + 744, + 470, + 911 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AIM-500. We also report performance on the AIM-500 dataset [10]. This enables us to compare our matting model with other public matting results on this dataset.", + "bbox": [ + 498, + 90, + 893, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 148, + 718, + 165 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Architecture. We employ the U-Net architecture from Stable Diffusion v2-1-v [26]. For feature extraction, the time step of the diffusion process is set to $t = 0$ by default, with an empty string used for conditional input. U-Net has 11 decoder blocks; we extract feature maps from the 5-th, 8-th, and 11-th blocks as the intra-features and ones from the 5-th block as the inter-features.", + "bbox": [ + 496, + 171, + 892, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Details. We employ distinct loss functions for matting and segmentation, respectively. For matting, we use a combination of $\\ell_1$ loss, Laplacian loss, and Gradient loss. For segmentation, we only use the $\\ell_1$ loss. To leverage the segmentation dataset while reducing the impact of imprecise edge annotations, we adopt the approach from HIM [31] that only backpropagates the loss from the confident areas.", + "bbox": [ + 496, + 287, + 892, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During training, the learning rate is set to 0.0004 and the batch size is 8. The input images are randomly cropped to a size of $768 \\times 768$ pixels. To prevent deviation from the pretrained model space in modeling real images, no additional data augmentation is used. We train IconMatting for 20,000 iterations using the AdamW optimizer.", + "bbox": [ + 496, + 409, + 893, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation. We employ the four widely used matting metrics: SAD, MSE, Grad and Conn [25]. Lower values imply higher-quality matts. In particular, MSE is scaled by a factor of $1 \\times 10^{-3}$ .", + "bbox": [ + 496, + 510, + 892, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To reduce randomness, each method is tested for three rounds, where the metrics were averaged. For each group of images, the reference inputs were fixed and consistently used. This minimizes the variations in reference inputs, allowing for a more scientific and reliable assessment.", + "bbox": [ + 496, + 571, + 893, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 500, + 657, + 638, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with In-Context Segmentation Models. To explore the effectiveness and superiority of our model, we selected SegGPT [35] and SEEM [45], which also operates under in-context learning, as baselines in the image segmentation domain. From Table 2, on the ICM-57 and AIM-500 datasets, under the same experimental setup (one mask per group of images), our model significantly outperforms the baselines across all metrics.", + "bbox": [ + 496, + 683, + 890, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is important to note that due to their distinct task setting (i.e., segmentation rather than matting), the lack of high-quality annotations (e.g., alpha mattes) and the methods (i.e., mask classification rather than alpha matte regression), most of these models have overlooked pixel-level text-semantic alignment and are unable to produce fine-grained masks, as illustrated in Fig. 5.", + "bbox": [ + 496, + 804, + 893, + 911 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3716", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bcc49c4d552375d67696a7bb13e727bd76e6a3227adeb589c83d58e4a2edcebc.jpg", + "image_caption": [], + 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"type": "image", + "img_path": "images/f149e4b9559c1336946b3a846a1d05334e1e54c8d8d7606dbd63a6f90c779f11.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 586, + 90, + 684, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed7609879900a5f3ecb85bdecc7f0ab92580a907325aa9662bb1d131584f11c4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 90, + 784, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef9cd766445834c5fdb6bc62aa27e6330ef551d2a32240dc7ef3182b7804c1b5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 90, + 885, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e84f9b9dfb2af7b3137700e4736c5cb637bd2ecf351ad4c5f0975c5817c9662e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 167, + 181, + 243 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/004a231b8a419db061f5a2d4102925866337a0273528ac24d086a03de7465f66.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 183, + 167, + 282, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c2c424db19d302b614f9af33dffbd6065c45e800e0de9fd6e4b03f685aa4c9b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 167, + 383, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f74b71c8ef0320fca10656eed98477e17d253a12eb6a3a11d97bdc60fd98f0e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 167, + 483, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/49a28b2e63789525e1900fbd9bdaf0023f5b1e0c6d93537c24584dca42e1abb7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 167, + 584, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2bbe35d290da95a8a09ca1327a17a471c57964ac1094cbda78aeb992b5c3d913.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 586, + 167, + 684, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/18bc63d2cdc96288e46e9e595456abe600e6715b4d652a8c61af049c4aa8e2b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 167, + 784, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e4e70941a7ba354312dc101bb45d971fec05b779f4fad3a1a1256660922d58b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 167, + 885, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ebcf32b306401cff58b03e8ea1c18e3ff743bfd216ddb64bd73b156e2ee6684.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 84, + 247, + 181, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/da307446f6464e0de3798fa308a2d2ef5b2a35168e47751645c1f381f9c7b132.jpg", + "image_caption": [ + "Ref-input" + ], + "image_footnote": [], + "bbox": [ + 183, + 247, + 282, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/424ae3b529c7bae43411eacddd084ae80d8e55717dfe1d6156be591d1f50f775.jpg", + "image_caption": [ + "AIM" + ], + "image_footnote": [], + "bbox": [ + 285, + 247, + 383, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/64ad75b37f7e2f6a86f67a8ae3f2925a934d6336806dce6469a77d58dc510641.jpg", + "image_caption": [ + "MatAny" + ], + "image_footnote": [], + "bbox": [ + 385, + 247, + 483, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ab5f5a00881b88fb9523ac315cd8e3d1a7f39bce2d04bf01c0752779a4f84136.jpg", + "image_caption": [ + "SegGPT", + "Figure 5. Qualitative results of different image matting methods. Our method can predict the alpha matte of the matting target specified by the reference input, offering notable prediction accuracy while avoiding interference from unrelated foreground elements." + ], + "image_footnote": [], + "bbox": [ + 485, + 247, + 583, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a6200361ea877a1c8f55f1481aaf1d13dfeadc1a605d2b1392189cfbfcb02082.jpg", + "image_caption": [ + "ICMP" + ], + "image_footnote": [], + "bbox": [ + 586, + 247, + 684, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d14d6de5cf715b56424073f91f326b8218aa9f007ddf8cef735d45dd77510e55.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 686, + 247, + 784, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f241113253f076e6e1c3919115bad4de95c3df552a8b3be7ce83584bba2cc430.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 785, + 247, + 885, + 358 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c867f43ab16adc4e7a8358bbc38a031c89172972cf43e568b48ea114408397b6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodICM-57AIM
MSESADGRADCONNMSESADGRADCONN
SegGPT0.019838.8128.6118.610.039142.6541.9526.69
SEEM0.029264.2837.5423.640.0425114.2374.5174.32
Ours0.008119.1218.6511.210.006218.6515.5110.98
", + "bbox": [ + 78, + 425, + 467, + 502 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison with in-context segmentation models.", + "bbox": [ + 86, + 506, + 457, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Automatic and Auxiliary Input-Based Matting Models. We further compare the performance of our IconMatting with both automatic and auxiliary input-based matting models on the ICM-57 and AIM-500 datasets. Automatic matting methods such as LF [44] and AIM [10] lack specific auxiliary information about the matting target, often produce poor alpha mattes, showing a significant performance gap compared with our model. MGM [42] and MGMiW [23] use a mask for each image as auxiliary input to specify the matting target. Although our method simplifies this by requiring only one mask per group of images, it still outperforms MGM in various metrics. VitMatte [40], a trimap-based image matting method, necessitates manually annotating a trimap for the foreground of each image, making it the performance upper bound for our in-context matting. Nevertheless, the performance of IconMatting is on par with VitMatte, underscoring its efficacy and competitiveness in image matting.", + "bbox": [ + 75, + 542, + 468, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Interactive Matting Models. Recently, with the advent of SAM, some researchers have designed interactive matting models, such as MatAny [41] and MAM [13], based on this generic image segmentation model. Inspired by this, we also designed an In", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Context Matting Pipeline (ICMP) with three stages: correspondence, segmentation, and matting, serving as one of the baselines. ICMP is a combination of existing models, with details available in supplementary materials.", + "bbox": [ + 496, + 428, + 890, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For MatAny and MAM, we compare them under three types of interactions: points, scribbles, and masks. On the ICM-57 testing dataset, both baselines receive interaction information for each image within a group, whereas IconMatting only receive interaction information from one image in the group to indicate the matting target. Despite reducing the amount of human interaction, IconMatting achieves slightly better performance over the baselines.", + "bbox": [ + 496, + 489, + 890, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Limited by the interaction modalities in ICMP, our model is only compared with it under the point interaction setting. Our end-to-end model outperforms the combined ICMP. In ICMP, the cues for the matting target degrade to points during the correspondence phase of the pipeline, often resulting in sparse information, making our end-to-end approach more effective.", + "bbox": [ + 496, + 609, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 726, + 653, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different Modules. To validate different modules, we conducted ablation studies in Table 5. Among the four components, the presence or absence of inter- and intrasimilarity plays a crucial role in performance. Without intra-similarity, the performance of the model significantly worsens across all four metrics. If both inter- and intrasimilarity are absent, the model degenerates to directly predicting the alpha matte from the image, losing the information source for the specified matting target, and thus the performance markedly deteriorates.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3717", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e41292dbd4b9234e3ef3577a14ebc4b40f719103b84eaf034f5b948b0e51537b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodGuidanceICM-57AIM
MSESADGRADCONNMSESADGRADCONN
MGM1 mask per image0.034184.2561.8430.210.026871.9123.3721.97
VitMatte1 trimap per image0.003016.1614.2811.140.003818.7914.2212.47
MGMiW1 mask per image----0.003016.7214.6812.02
LFauto0.0811205.6869.53195.630.0667191.7464.51181.26
AIMauto0.026565.0755.5625.740.018348.0947.5821.74
Ours1 mask per group of images0.008119.1218.6511.210.006218.6515.5110.98
", + "bbox": [ + 76, + 88, + 893, + 239 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2e11b009d8b834e757f8c981181d90eb57fe9bc96fad69ec46746fd8eda600ab.jpg", + "table_caption": [ + "Table 3. Comparison with automatic and auxiliary input-based matting models." + ], + "table_footnote": [], + "table_body": "
MethodIn-contextPointScribbleMask
MSESADMSESADMSESAD
MatAnyX0.0651129.670.0512115.210.041295.26
MAMX0.014941.230.014140.230.010929.65
ICMP✓0.011239.65----
Ours*X0.006115.280.005915.970.002915.28
Ours✓0.012423.210.010524.560.008119.12
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INTERINTRAMFSDMSESADGRADCONN
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✓X✓✓0.009924.1520.3612.11
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✓✓X✓0.005423.6921.9614.52
✓✓✓X0.007118.5619.5412.61
", + "bbox": [ + 78, + 493, + 470, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Reference Inputs. Intuitively, the more reference inputs there are, the more likely the model is to identify the corresponding matting target. We explored the impact of the number of reference inputs on the performance of our model, as shown in Table 6. On ICM-57 test set, the performance improves as the number of reference inputs increases; however, the improvement almost ceases when the number of reference inputs increases from 3 to 4. Therefore, we can conclude that appropriately increasing the number of reference inputs can enhance model performance, which is consistent with intuition.", + "bbox": [ + 75, + 655, + 468, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Extension to Video Object Matting", + "text_level": 1, + "bbox": [ + 76, + 830, + 382, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The technique of in-context matting is easily extendable to video object matting. The key is to use a frame of the video as a reference. For example, an object is marked in the first", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/79268cb670b29090161520993203ab0df095b59c34686ed8bc4f6cd51b1ed611.jpg", + "table_caption": [ + "Table 5. Ablation study on different modules. INTER, INTRA, MF, and SD respectively stand for inter-similarity, intra-similarity, multi-scale features, and segmentation dataset." + ], + "table_footnote": [], + "table_body": "
#ReferenceMSESADGRADCONN
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", + "bbox": [ + 521, + 282, + 867, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation study on the number of reference inputs.", + "bbox": [ + 511, + 349, + 879, + 364 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/145d452896a228b118346bd663fe9d69594195a370dbfa271c7ab48186638b62.jpg", + "image_caption": [ + "Figure 6. Extension to video object matting." + ], + "image_footnote": [], + "bbox": [ + 511, + 387, + 877, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "frame of a video, which serves as a reference input and all frames of the video are treated as target images. With this setup, the model for in-context matting can predict the alpha matte for each frame of the video, visualized in Fig. 6.", + "bbox": [ + 498, + 597, + 890, + 659 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 681, + 619, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we introduce 'in-context matting', which enables automatic matting of foreground of interest on target images given a reference image and its prompt. We introduce IconMatting as a preliminary solution. Extensive experiments have shown its efficacy and robustness across categories and scenes. Being the first work introducing this task, we believe it opens new possibilities for efficient and accurate image matting while reducing user effort, also enhancing the versatility of image matting techniques.", + "bbox": [ + 496, + 709, + 890, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by the National Natural Science Foundation of China under Grant No. 62106080.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3718", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. Advances in Neural Information Processing Systems, 35:23716-23736, 2022. 3", + "[2] Amir Bar, Yossi Gandelsman, Trevor Darrell, Amir Globerson, and Alexei Efros. Visual prompting via image inpainting. 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Segment everything everywhere all at once. arXiv preprint arXiv:2304.06718, 2023. 6" + ], + "bbox": [ + 501, + 92, + 890, + 189 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3720", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/In-Context Matting/d72f8b5e-8660-4264-a6c3-5f329153b637_model.json b/2024/In-Context Matting/d72f8b5e-8660-4264-a6c3-5f329153b637_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1bb32f3f0cca59ba6918226b68df157827945c2b --- /dev/null +++ b/2024/In-Context Matting/d72f8b5e-8660-4264-a6c3-5f329153b637_model.json @@ -0,0 +1,2904 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. 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[ + 0.561, + 0.438, + 0.866, + 0.451 + ], + "angle": 0, + "content": "\\(\\mathsf{N}^*\\) image \\(+1^{*}\\) prompt \\(+1^{*}\\) model \\(\\rightarrow\\) N\\*predictions" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.525, + 0.722, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.525, + 0.875, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.581, + 0.894, + 0.625 + ], + "angle": 0, + "content": "Figure 1. In-Context Matting. This novel task setting for image matting enables automatic natural image matting of target images of a certain object category conditioned on a reference image of the same category, with user-provided priors such as masks and scribbles on the reference image only. Notice that, our approach exhibits remarkable cross-domain matting quality." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.642, + 0.314, + 0.658 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.472, + 0.871 + ], + "angle": 0, + "content": "We introduce in-context matting, a novel task setting of image matting. Given a reference image of a certain foreground and guided priors such as points, scribbles, and masks, in-context matting enables automatic alpha estimation on a batch of target images of the same foreground category, without additional auxiliary input. This setting marries good performance in auxiliary input-based matting and ease of use in automatic matting, which finds a good tradeoff between customization and automation. To overcome the key challenge of accurate foreground matching, we introduce IconMatting, an in-context matting model built upon a pre-trained text-to-image diffusion model. Conditioned on inter- and intra-similarity matching, IconMatting can" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.643, + 0.892, + 0.78 + ], + "angle": 0, + "content": "make full use of reference context to generate accurate target alpha mattes. To benchmark the task, we also introduce a novel testing dataset ICM-57, covering 57 groups of real-world images. Quantitative and qualitative results on the ICM-57 testing set show that IconMatting rivals the accuracy of trimap-based matting while retaining the automation level akin to automatic matting. Code is available at https://github.com/tiny-smart/in-context-matting." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.806, + 0.633, + 0.822 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.832, + 0.892, + 0.878 + ], + "angle": 0, + "content": "Image matting has been a long-standing problem in vision and graphics [3]. It typically requires estimating an accurate alpha matte by solving a so-called matting equation" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.227, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\nI = \\alpha F + (1 - \\alpha) B, \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3711" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "where \\(I\\) is the 3-channel RGB image, \\(F\\), \\(B\\), and \\(\\alpha\\) are the 3-channel foreground, the 3-channel background, and the 1-channel alpha matte. The matting equation, however, is highly ill-posed, due to the need to infer 7 unknowns from 3 observations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.169, + 0.473, + 0.456 + ], + "angle": 0, + "content": "Prior art has come up with different ways to reduce uncertainties in matting such as using trimaps [7, 16, 18-20, 32, 38], scribbles [39], or a even known background [17, 29]. These approaches are given the name auxiliary input-based matting [14] in modern matting literature. Indeed, these matting models, particularly trimap-based ones, have achieved remarkable accuracy. They are in some way user-unfriendly as an auxiliary input should be provided with each image in practice, which significantly harms matting efficiency and user experience. Recently another stream of work attempts to abandon any auxiliary input completely and forms a new paradigm called automatic matting [4, 9, 11, 12, 21, 31, 43]. Despite their inherent advantages, these automatic matting models are narrowed to specific object categories, such as humans [4, 9, 21, 31], animals [12], and salient objects [11, 43]. This can render poor generalization in natural scenes, infeasibility to tackle general object categories, and unawareness of foreground of interest." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.564 + ], + "angle": 0, + "content": "Hence, there seems an obvious gap between accuracy and efficiency and between customization and automation. An interesting question is that: Can the auxiliary input-based matting be optimized to enhance the efficiency, while also maintaining guidance for matting targets with sufficient automation, thereby harmonizing the two existing matting paradigms?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.473, + 0.838 + ], + "angle": 0, + "content": "In this paper, we introduce in-context matting, a novel task setting of image matting, where a reference input can provide guidance for a batch of target images with similar foregrounds. The alpha matts of the target batch are predicted by leveraging the contextual information from the reference input. Fig. 1 provides an example, where a cat marked in the reference image enables the extraction of cats from all target images, regardless of the background or domain. This novel task setting relieves users from providing auxiliary input for each image. Instead, by specifying the matting target only in a single reference image, the alpha matts of the entire batch images could be predicted. Given the reference guidance, in-context matting can also gather sufficient contextual information, leading to higher accuracy and adaptability than fully automatic matting. This setting therefore combines the most notable features of automatic and auxiliary input-based matting, finding a good trade-off between them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Technically, we confront a primary challenge inherent to in-context matting, i.e., how to leverage the reference input to accurately identify the corresponding target foreground. While SegGPT [35] has explored image segmentation with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "contextual information, its in-context coloring framework is not suitable for image matting. In this work, we approach this challenge as a problem of region-to-region matching. In particular, recent advances [22, 26, 30] in generative diffusion models have demonstrated emergent capabilities in discriminative tasks like segmentation [37] and correspondence [33]. Given that our region-to-region matching is an inherent aspect of correspondence, and noting the parallels between image segmentation and image matting, we explore the applicability of pretrained diffusion models for in-context matting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.893, + 0.495 + ], + "angle": 0, + "content": "We therefore introduce IconMatting, a model based on the pre-trained Stable Diffusion model [26], specialized for in-context matting. Given a reference image along with its corresponding foreground of interest as context, the target alpha matte could be inferred by exploiting the feature correspondence from Stable Diffusion such that the target foreground is matched conditioned on the correspondence. However, the matching is often sparse and insufficient to represent the entire target area. To address this, the intra-image similarity, based on the self-attention maps of Stable Diffusion, is additionally used to supplement the missing parts. By leveraging both inter- and intra-image similarities, informative guidance of the matting target would be acquired. Finally, any off-the-shelf matting heads can be used to predict the alpha matte." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.895, + 0.641 + ], + "angle": 0, + "content": "Since the task setting is different from existing mating benchmarks, we introduce a new testing dataset named ICM-57 to offer a broad and thorough validation of in-context mating. This dataset encompasses 57 contextually-aligned image groups; each comprising images in the real world and has either the same category or the same instance of different views, thereby encompassing a rich variety of in-context scenarios, which ensures a comprehensive test of a model to tackle various contexts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.895, + 0.758 + ], + "angle": 0, + "content": "Through extensive experiments on the ICM-57 and AIM-500 [10] datasets, we showcase the potential of in-context matting and IconMatting. The results indicate that IconMatting, while retaining the automation level akin to automatic matting, rivals the accuracy of trimap-based matting, underscoring the value of in-context matting as a promising direction for image matting." + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.768, + 0.697, + 0.782 + ], + "angle": 0, + "content": "Our contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.793, + 0.892, + 0.837 + ], + "angle": 0, + "content": "- We introduce in-context matting, a novel task setting of image matting that takes advantages of both automatic and auxiliary input-based matting;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.838, + 0.891, + 0.867 + ], + "angle": 0, + "content": "- IconMatting: an effective in-context matting model based on Stable Diffusion." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.868, + 0.891, + 0.898 + ], + "angle": 0, + "content": "- ICM-57: a novel dataset and the evaluation framework for in-context matting." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.793, + 0.892, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3712" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.47, + 0.146 + ], + "angle": 0, + "content": "We review work related to image matting and in-context learning in vision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.154, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Image Matting. Image matting approaches can be coarsely categorized into auxiliary input-based matting and automatic matting. Auxiliary input-based matting requires user input. The user input can be in the form of a trimap [7, 16, 18, 19, 32, 38], scribbles [39], a background image [17, 29], a coarse mask [23, 42], or even a text description [15]. Despite their effectiveness, they require significant manual effort to provide the auxiliary inputs. Automatic matting [4, 10, 12, 24, 43] predicts the alpha matte without any user intervention. They typically assume salient or certain foregrounds that are implicitly defined by the training dataset. The network structures used in automatic matting can be divided into two groups: one-stage network with global guidance [24] and parallel multi-task network [10, 31]. Some recent work has also introduced transformer structures into automatic matting [21]. While both auxiliary input-based and automatic matting have been studied comprehensively, a paradigm that combines the efficiency of automatic matting and the precision of auxiliary input-based matting has not yet been explored. We fill this gap with in-context matting." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.478, + 0.47, + 0.538 + ], + "angle": 0, + "content": "In-Context Learning in Vision. In-context learning, initially a concept in natural language processing [5], is now made popular in computer vision. It allows models to fast adapt to a variety of tasks with minimal examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.78 + ], + "angle": 0, + "content": "Bar et al. [2] first proposes an in-context learning framework using inpainting with discrete tokens on figures and infographics from vision articles, demonstrating applications in foreground segmentation, single object detection, and colorization. Painter [34] adopts masked image modeling to perform in-context learning with supervised datasets, achieving highly competitive results on seven diverse tasks. More recently, SegGPT [35], which segments everything in context by unifying different segmentation tasks into an in-context coloring framework. Prompt Diffusion [6] presents a diffusion-based generative framework to enable in-context learning across various tasks. Additionally, Flamingo [1], a family of visual language models, shows rapid adaptation to a variety of image and video tasks with few-shot learning capabilities. These models showcase the potential of in-context learning in addressing diverse vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.472, + 0.903 + ], + "angle": 0, + "content": "The concept of in-context learning, while being transformative in other areas, has not yet impacted the field of image matting. Although SegGPT achieves in-context image segmentation but is limited to coarse levels, lacking in semitransparency handling. Our IconMatting first introduces in-context learning into image matting, enhancing both the efficiency of auxiliary input-based matting and the precision of automatic matting." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.897, + 0.155 + ], + "angle": 0, + "content": "
Task settingautoauto with ref-inputreal-world generalization#ref-input
AuxXXgood#images
Auto✓-poorzero
In-contextX✓goodone
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.164, + 0.895, + 0.248 + ], + "angle": 0, + "content": "Table 1. Comparison between in-context matting and two existing image matting paradigms. \"Aux\" and \"Auto\" are abbreviations for auxiliary input-based matting and automatic matting, respectively. In-context matting requires only a single reference input to achieve the automation of automatic matting and the generalizability of auxiliary input-based matting." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.271, + 0.895, + 0.364 + ], + "angle": 0, + "content": "Our work is also related to image co-segmentation [27]. This task aims to segment common objects within a pair of contextual images. However, unlike in-context matting, where users can specify the matting target, co-segmentation operates without user input, predicting rough binary masks delineating common objects across image pairs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.374, + 0.88, + 0.391 + ], + "angle": 0, + "content": "3. In-Context Matting with Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.893, + 0.431 + ], + "angle": 0, + "content": "We begin with the problem setup, then present our proposed in-context matting model, i.e., IconMatting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.439, + 0.652, + 0.456 + ], + "angle": 0, + "content": "3.1. Problem Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.462, + 0.895, + 0.643 + ], + "angle": 0, + "content": "The objective of in-context matting is to extract the alpha mattes \\(\\{\\alpha_{i}\\}^{N}\\) of a specified foreground category from a collection of input images \\(\\{I_i\\}^N\\). Through user interaction, the matting target is indicated by a reference image \\(I_r\\) and a corresponding binary region of interest (RoI) map \\(M_{\\mathrm{RoI}}\\). The RoI map can take the form of a mask, scribbles, or points as exemplified in Fig. 1. Notably, the reference image can either be a part of the input collection or an entirely separate image. When the input image collection has only a single image, users can treat that image as the reference image. In this case, in-context matting degenerates into image matting guided by user interaction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.895, + 0.764 + ], + "angle": 0, + "content": "Given \\(\\{I_i\\}^N\\) and \\((I_r, M_{\\mathrm{RoI}})\\), in-context matting is formulated as predicting the alpha matte \\(\\{\\alpha_i\\}^N\\) in \\(\\{I_i\\}^N\\) of the matting targets informed by \\((I_r, M_{\\mathrm{RoI}})\\). In the context of in-context matting, when provided with a reference input, it becomes an automatic matting system targeted towards a specific foreground. The comparison between in-context matting and existing task settings for image matting is detailed in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.697, + 0.787 + ], + "angle": 0, + "content": "3.2. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.893, + 0.856 + ], + "angle": 0, + "content": "Here we first present the overall framework of IconMatting. As shown in Fig. 2, IconMatting is comprised of three components: a feature extractor, an in-context similarity module, and a matting head." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "The feature extractor is responsible for obtaining the RoI features from the reference image, the features and self-attention maps from the target image. They are then fed into" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3713" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.891, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.893, + 0.392 + ], + "angle": 0, + "content": "Figure 2. IconMatting integrates a Stable Diffusion-derived feature extractor, an in-context similarity module, and a matting head. It processes a target image \\( I_{t} \\), a reference image \\( I_{r} \\), and an RoI map \\( M_{RoI} \\). Both reference and target image features and target self-attention maps are extracted and used. In-context similarity uses the in-context query from the reference image to create a guidance map, which, combined with self-attention maps, assists in locating the target object. The matting head finally generates the target alpha matte." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.471, + 0.554 + ], + "angle": 0, + "content": "the in-context similarity module, the core of the framework. The module further consists of inter- and intra-similarity sub-modules: the former leverages the reference RoI features as an in-context query to derive a guidance map from the target features; the latter integrates the guidance map with multi-scale self-attention maps to obtain guidance for the matting head. Finally, the matting head uses this synthesized guiding information and the target features to generate the alpha matte of the target image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.566, + 0.341, + 0.58 + ], + "angle": 0, + "content": "3.3. In-Context Feature Extractor" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.831 + ], + "angle": 0, + "content": "Backbone Selection. As outlined in Section 1, we conceptualize the core challenge of in-context matting – leveraging the reference context to accurately identify the target foreground – as a region-to-region matching problem. Therefore, if the features derived from a backbone naturally possess correspondence capabilities, referred to as in-context features, they would facilitate the implementation of in-context matting. Tang et al. [33] have found that the text-to-image generative model, Stable Diffusion [26], trained on large-scale text-image paired datasets, exhibit emergent capabilities for both geometric and semantic correspondence. It can perform point-to-point correspondence between images across instances, classes, and even domains with simple cosine similarity. Inspired by this observation, we leverage Stable Diffusion as a feature extractor to implement in-context matting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Preliminary on Stable Diffusion. Recent advances in diffusion models, e.g., Stable Diffusion [26], have shown impressive results in both generative and discriminative tasks. Being a feature extractor, Stable Diffusion encodes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.893, + 0.57 + ], + "angle": 0, + "content": "an image \\(x_0\\) into a latent space, denoted by \\(z_0\\), which, through a noise process defined by \\(\\{\\alpha_t\\}^T\\), transforms into \\(z_{t} = \\sqrt{\\alpha_{t}} z_{0} + (\\sqrt{1 - \\alpha_{t}})\\varepsilon\\), where \\(\\varepsilon \\sim \\mathcal{N}(0,\\mathbf{I})\\) is the randomly-sampled noise. The latent representation \\(z_{t}\\) undergoes forward propagation in a U-Net \\(f_{\\theta}\\), generating multi-scale features \\(\\{\\mathcal{F}_l\\}^L\\) and self-attention maps \\(\\{\\mathcal{A}_l\\}^L\\), which can later be exploited for downstream tasks. Icon-Matting uses the capabilities of Stable Diffusion and both reference and target images to extract multi-scale features and self-attention maps to enhance feature representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.704, + 0.597 + ], + "angle": 0, + "content": "3.4. In-Context Similarity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.756 + ], + "angle": 0, + "content": "In-context similarity plays a key role in our model, because the quality of inferred alpha mattes highly depends on the output of this module. In particular, the in-context similarity module is designed to identify the potential target foreground taking the reference RoI into account, thereby guiding the prediction of the target alpha matte. According to our observations, both the reference-target similarity and target-target similarity matter for locating the potential target foreground. These correspond to the proposed inter-similarity and intra-similarity sub-modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Observation. The core challenge in in-context matting is a semantic correspondence problem. Given Stable Diffusion being the feature extractor, one can associate points of the foreground areas between the reference and target images using the emergent feature correspondence. However, due to the inherent reference-target foreground difference, a rigorous one-to-one mapping of all points between the two areas is unfeasible. There would always be some unmatched outliers, resulting in holes in the matting target" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3714" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.09, + 0.455, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.159, + 0.39, + 0.171 + ], + "angle": 0, + "content": "(a) Outliers in point to point correspondence" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.182, + 0.462, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.284, + 0.381, + 0.296 + ], + "angle": 0, + "content": "(b) Self-attention of random points" + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.301, + 0.455, + 0.314 + ], + "angle": 0, + "content": "Figure 3. Observations on the inter- and intra similarities." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.389, + 0.356 + ], + "angle": 0, + "content": "area of the target image, as illustrated in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.553 + ], + "angle": 0, + "content": "Since only a subset of points are matched, the goal is changed to how to expand these matched points to cover the entire target foreground area. To address this, we look for other points sharing similar semantic meaning with this subset of points. Intra-image similarity is therefore considered. Intuitively, the self-attention maps from Stable Diffusion reflect the similarities between different image patches. As shown in Fig. 3, by randomly sampling a small number of points from the target area and simply summing over the corresponding self-attention maps, the whole target foreground can be revealed. Based on this observation, we use the self-attention maps as intra-image information to supplement the inter-image matching results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.56, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Inter-Similarity. Formally, given features \\(\\{\\mathcal{F}_l^r\\} ^L\\) and \\(\\{\\mathcal{F}_l^t\\} ^L\\) extracted from the reference image \\(I_{r}\\) and the target image \\(I_{t}\\), respectively, the layer with the best correspondence capability is selected following DIFT [33], denoted by \\(\\mathcal{F}_{\\mathrm{inter}}^r\\) for the reference and \\(\\mathcal{F}_{\\mathrm{inter}}^t\\) for the target. Then, features corresponding to the RoI \\(M_{\\mathrm{RoI}}\\) in \\(\\mathcal{F}_{\\mathrm{inter}}^r\\) are extracted and formulated as the in-context query \\(\\{Q_k\\} ^K\\), where \\(K\\) is the length of the query. \\(Q_{k}\\) takes the form" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.696, + 0.469, + 0.713 + ], + "angle": 0, + "content": "\\[\nQ _ {k} = R (k), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.725, + 0.469, + 0.742 + ], + "angle": 0, + "content": "\\[\nR = \\mathcal {F} _ {\\text {i n t e r}} ^ {r} \\odot M _ {\\mathrm {R o I}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.749, + 0.469, + 0.811 + ], + "angle": 0, + "content": "where \\(\\odot\\) is the element-wise product and \\(R(k)\\) denotes the \\(k\\)-th non-zero element of \\(R\\). Further, \\(\\{Q_k\\}^K\\) is used to compute similarity with \\(\\mathcal{F}_{\\mathrm{inter}}^t\\), identifying regions on \\(I_t\\) that correspond to the RoI of \\(I_r\\), formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.821, + 0.469, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {k} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {k} \\cdot F _ {\\text {i n t e r}} ^ {t}}{\\sqrt {d}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The similarity map is denoted by \\(\\{S_k\\}^K\\), and the mean of all such similarity maps yields \\(S\\), which measures the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "degree of similarity between different locations on \\( I_{t} \\) and the RoI in \\( I_{r} \\), serving as the first intermediate output of in-context similarity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.142, + 0.893, + 0.34 + ], + "angle": 0, + "content": "Intra-Similarity. As noted in our observations (Fig. 3), \\(S\\) is typically sparse. Although the target matting region on \\(I_{t}\\) is partially covered by \\(S\\), it is insufficient to guide alpha prediction. Here we further design the intra-similarity sub-module to leverage the internal similarity within \\(I_{t}\\) to propagate \\(S\\) into a more precise representation of the RoI on \\(I_{t}\\). During feature extraction of \\(I_{t}\\), self-attention maps \\(\\{\\mathcal{A}_l\\}^L\\) representing its internal similarity are also retained, serving as the input for intra-similarity. This sub-module uses \\(S\\) as a weight to the self-attention maps, thereby generating guiding information that accurately represents the matting target on \\(I_{t}\\), denoted by \\(\\{S_l'\\}^L\\). Mathematically, the intra-similarity matching is expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.35, + 0.892, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {l} ^ {\\prime} = \\mathcal {A} _ {l} \\odot \\mathcal {S}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.377, + 0.644, + 0.394 + ], + "angle": 0, + "content": "3.5. Matting Head" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.401, + 0.892, + 0.461 + ], + "angle": 0, + "content": "The success of ViTMatte [40] implies that the information of original image is important during decoding. Following this practice, in our matting head, the original image is concatenated and decoded with outputs from previous modules." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.462, + 0.893, + 0.658 + ], + "angle": 0, + "content": "The guidance map from the in-context similarity module and the intra-features from the backbone are merged and refined using a convolutional feature fusion block, including a series of convolution, normalization, and activation layers. The output multi-scale in-context features are progressively merged using a series of fusion layers which comprise upsampling, concatenation, convolution, normalization, and activation layers. Then, following ViTMatte [40], details from the original image are extracted and combined with the merged feature in a detail decoder, enhancing the details of alpha matte. This matting head effectively melds contextual information with original image details, yielding the generation of a highly precise and refined alpha matte." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.757, + 0.682 + ], + "angle": 0, + "content": "3.6. Reference-Prompt Extension" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In addition to the mask prompts, points and scribbles can also be transformed into RoI masks. However, these prompts yield less comprehensive in-context queries compared with mask prompts. To enhance them, we propose an extension of reference prompt to enrich the in-context queries derived from point and scribble prompts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since the self-attention maps from the backbone reflect the similarities across regions, we leverage the attention maps of the reference images to expand the RoI mask. This is achieved by including regions in the attention maps that are similar to the prompt locations. Specifically, for each prompt point, the top \\( m \\) points with the highest responses in their corresponding attention maps are integrated into the RoI mask additionally, thus enriching the in-context query." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3715" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.193, + 0.472, + 0.25 + ], + "angle": 0, + "content": "Figure 4. ICM-57 examples. The dataset encompasses foreground subjects including human, animals, plants, and various common objects. It contains both instances from the same category and the same entity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.276, + 0.293, + 0.293 + ], + "angle": 0, + "content": "4. Results and Discussion" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.302, + 0.181, + 0.317 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.47, + 0.478 + ], + "angle": 0, + "content": "To facilitate in-context matting, we establish a hybrid training set, along with a test set, ICM-57. The existing AIM-500 dataset was also reorganized to meet the testing requirements of in-context matting. In particular, in-context matting requires to organize images into groups where the annotated foregrounds share categories or instances. Such organization allows for random selection of reference and target images within groups during training. In the test set, one or more images in each group are designated as reference images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Mixing In-Context Training Sets. We selected the RM1K dataset [36]. However, such a dataset was insufficient for training. Therefore, a subset of the Open Images dataset [8], focusing on image segmentation, was also employed. The two formed a mixed training set tailored to in-context matting. Both datasets were reorganized." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.734 + ], + "angle": 0, + "content": "For the RM-1K dataset, we divided it into 222 groups. A subset of 14,000 images from the Open Images dataset were chosen as well. In the original dataset, each image came with one or more annotations for image segmentation; each corresponds to an object instance. We aggregated these annotations by category, ensuring that the annotations include all instances of the corresponding category. They subsequently formed context groups that met the requirements of in-context matting. As a result, a mixed training set of 15,000 images and 450 groups was created." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.471, + 0.912 + ], + "angle": 0, + "content": "ICM-57 Testing Set. To assess the performance of our model, we constructed the first testing dataset for in-context matting, named ICM-57, which comprises 57 image groups that form various real-world contexts. This dataset was created by using the instance-segmented dreambooth dataset [28], to which we supplemented high-precision alpha matte annotations. Additionally, we reviewed the existing AIM-500 dataset, selected a subset, and categorized these into groups according to their classes to supplement the in-category groups. Examples of the testing set are shown in Fig 4." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.894, + 0.138 + ], + "angle": 0, + "content": "AIM-500. We also report performance on the AIM-500 dataset [10]. This enables us to compare our matting model with other public matting results on this dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.149, + 0.719, + 0.166 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.172, + 0.893, + 0.278 + ], + "angle": 0, + "content": "Architecture. We employ the U-Net architecture from Stable Diffusion v2-1-v [26]. For feature extraction, the time step of the diffusion process is set to \\( t = 0 \\) by default, with an empty string used for conditional input. U-Net has 11 decoder blocks; we extract feature maps from the 5-th, 8-th, and 11-th blocks as the intra-features and ones from the 5-th block as the inter-features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.893, + 0.409 + ], + "angle": 0, + "content": "Training Details. We employ distinct loss functions for matting and segmentation, respectively. For matting, we use a combination of \\(\\ell_1\\) loss, Laplacian loss, and Gradient loss. For segmentation, we only use the \\(\\ell_1\\) loss. To leverage the segmentation dataset while reducing the impact of imprecise edge annotations, we adopt the approach from HIM [31] that only backpropagates the loss from the confident areas." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.894, + 0.502 + ], + "angle": 0, + "content": "During training, the learning rate is set to 0.0004 and the batch size is 8. The input images are randomly cropped to a size of \\(768 \\times 768\\) pixels. To prevent deviation from the pretrained model space in modeling real images, no additional data augmentation is used. We train IconMatting for 20,000 iterations using the AdamW optimizer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.893, + 0.572 + ], + "angle": 0, + "content": "Evaluation. We employ the four widely used matting metrics: SAD, MSE, Grad and Conn [25]. Lower values imply higher-quality matts. In particular, MSE is scaled by a factor of \\(1 \\times 10^{-3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.894, + 0.648 + ], + "angle": 0, + "content": "To reduce randomness, each method is tested for three rounds, where the metrics were averaged. For each group of images, the reference inputs were fixed and consistently used. This minimizes the variations in reference inputs, allowing for a more scientific and reliable assessment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.659, + 0.64, + 0.675 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Comparison with In-Context Segmentation Models. To explore the effectiveness and superiority of our model, we selected SegGPT [35] and SEEM [45], which also operates under in-context learning, as baselines in the image segmentation domain. From Table 2, on the ICM-57 and AIM-500 datasets, under the same experimental setup (one mask per group of images), our model significantly outperforms the baselines across all metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.894, + 0.912 + ], + "angle": 0, + "content": "It is important to note that due to their distinct task setting (i.e., segmentation rather than matting), the lack of high-quality annotations (e.g., alpha mattes) and the methods (i.e., mask classification rather than alpha matte regression), most of these models have overlooked pixel-level text-semantic alignment and are unable to produce fine-grained masks, as illustrated in Fig. 5." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3716" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.182, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.091, + 0.283, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.091, + 0.384, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.091, + 0.483, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.091, + 0.585, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.091, + 0.685, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.091, + 0.785, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.091, + 0.887, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.169, + 0.182, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.169, + 0.283, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.169, + 0.384, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.386, + 0.169, + 0.484, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.169, + 0.585, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.169, + 0.685, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.169, + 0.785, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.169, + 0.887, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.248, + 0.182, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.364, + 0.151, + 0.375 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.248, + 0.283, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.364, + 0.262, + 0.375 + ], + "angle": 0, + "content": "Ref-input" + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.248, + 0.384, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.32, + 0.364, + 0.348, + 0.374 + ], + "angle": 0, + "content": "AIM" + }, + { + "type": "image", + "bbox": [ + 0.386, + 0.248, + 0.484, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.411, + 0.363, + 0.461, + 0.375 + ], + "angle": 0, + "content": "MatAny" + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.248, + 0.584, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.363, + 0.562, + 0.375 + ], + "angle": 0, + "content": "SegGPT" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.248, + 0.685, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.618, + 0.363, + 0.653, + 0.374 + ], + "angle": 0, + "content": "ICMP" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.248, + 0.785, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.363, + 0.748, + 0.374 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.248, + 0.887, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.363, + 0.846, + 0.374 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of different image matting methods. Our method can predict the alpha matte of the matting target specified by the reference input, offering notable prediction accuracy while avoiding interference from unrelated foreground elements." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.426, + 0.468, + 0.503 + ], + "angle": 0, + "content": "
MethodICM-57AIM
MSESADGRADCONNMSESADGRADCONN
SegGPT0.019838.8128.6118.610.039142.6541.9526.69
SEEM0.029264.2837.5423.640.0425114.2374.5174.32
Ours0.008119.1218.6511.210.006218.6515.5110.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.088, + 0.507, + 0.458, + 0.521 + ], + "angle": 0, + "content": "Table 2. Comparison with in-context segmentation models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.816 + ], + "angle": 0, + "content": "Comparison with Automatic and Auxiliary Input-Based Matting Models. We further compare the performance of our IconMatting with both automatic and auxiliary input-based matting models on the ICM-57 and AIM-500 datasets. Automatic matting methods such as LF [44] and AIM [10] lack specific auxiliary information about the matting target, often produce poor alpha mattes, showing a significant performance gap compared with our model. MGM [42] and MGMiW [23] use a mask for each image as auxiliary input to specify the matting target. Although our method simplifies this by requiring only one mask per group of images, it still outperforms MGM in various metrics. VitMatte [40], a trimap-based image matting method, necessitates manually annotating a trimap for the foreground of each image, making it the performance upper bound for our in-context matting. Nevertheless, the performance of IconMatting is on par with VitMatte, underscoring its efficacy and competitiveness in image matting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Comparison with Interactive Matting Models. Recently, with the advent of SAM, some researchers have designed interactive matting models, such as MatAny [41] and MAM [13], based on this generic image segmentation model. Inspired by this, we also designed an In" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Context Matting Pipeline (ICMP) with three stages: correspondence, segmentation, and matting, serving as one of the baselines. ICMP is a combination of existing models, with details available in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.61 + ], + "angle": 0, + "content": "For MatAny and MAM, we compare them under three types of interactions: points, scribbles, and masks. On the ICM-57 testing dataset, both baselines receive interaction information for each image within a group, whereas IconMatting only receive interaction information from one image in the group to indicate the matting target. Despite reducing the amount of human interaction, IconMatting achieves slightly better performance over the baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.716 + ], + "angle": 0, + "content": "Limited by the interaction modalities in ICMP, our model is only compared with it under the point interaction setting. Our end-to-end model outperforms the combined ICMP. In ICMP, the cues for the matting target degrade to points during the correspondence phase of the pipeline, often resulting in sparse information, making our end-to-end approach more effective." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.655, + 0.743 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Different Modules. To validate different modules, we conducted ablation studies in Table 5. Among the four components, the presence or absence of inter- and intrasimilarity plays a crucial role in performance. Without intra-similarity, the performance of the model significantly worsens across all four metrics. If both inter- and intrasimilarity are absent, the model degenerates to directly predicting the alpha matte from the image, losing the information source for the specified matting target, and thus the performance markedly deteriorates." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3717" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.24 + ], + "angle": 0, + "content": "
MethodGuidanceICM-57AIM
MSESADGRADCONNMSESADGRADCONN
MGM1 mask per image0.034184.2561.8430.210.026871.9123.3721.97
VitMatte1 trimap per image0.003016.1614.2811.140.003818.7914.2212.47
MGMiW1 mask per image----0.003016.7214.6812.02
LFauto0.0811205.6869.53195.630.0667191.7464.51181.26
AIMauto0.026565.0755.5625.740.018348.0947.5821.74
Ours1 mask per group of images0.008119.1218.6511.210.006218.6515.5110.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.234, + 0.245, + 0.735, + 0.26 + ], + "angle": 0, + "content": "Table 3. Comparison with automatic and auxiliary input-based matting models." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.284, + 0.468, + 0.391 + ], + "angle": 0, + "content": "
MethodIn-contextPointScribbleMask
MSESADMSESADMSESAD
MatAnyX0.0651129.670.0512115.210.041295.26
MAMX0.014941.230.014140.230.010929.65
ICMP✓0.011239.65----
Ours*X0.006115.280.005915.970.002915.28
Ours✓0.012423.210.010524.560.008119.12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.396, + 0.471, + 0.48 + ], + "angle": 0, + "content": "Table 4. Comparison with interactive matting models. In the penultimate row, our method is provided with guidance information for every image, reducing to an auxiliary input-based method. Our method outperforms automatic methods and some of the auxiliary input-based methods, and its performance is comparable to that of the trimap-based method, VitMatte." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.494, + 0.472, + 0.582 + ], + "angle": 0, + "content": "
INTERINTRAMFSDMSESADGRADCONN
✓✓✓✓0.008119.1218.6511.21
✓X✓✓0.009924.1520.3612.11
XX✓✓0.031540.3231.5619.53
✓✓X✓0.005423.6921.9614.52
✓✓✓X0.007118.5619.5412.61
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Table 5. Ablation study on different modules. INTER, INTRA, MF, and SD respectively stand for inter-similarity, intra-similarity, multi-scale features, and segmentation dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Number of Reference Inputs. Intuitively, the more reference inputs there are, the more likely the model is to identify the corresponding matting target. We explored the impact of the number of reference inputs on the performance of our model, as shown in Table 6. On ICM-57 test set, the performance improves as the number of reference inputs increases; however, the improvement almost ceases when the number of reference inputs increases from 3 to 4. Therefore, we can conclude that appropriately increasing the number of reference inputs can enhance model performance, which is consistent with intuition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.383, + 0.85 + ], + "angle": 0, + "content": "4.5. Extension to Video Object Matting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The technique of in-context matting is easily extendable to video object matting. The key is to use a frame of the video as a reference. For example, an object is marked in the first" + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.283, + 0.869, + 0.348 + ], + "angle": 0, + "content": "
#ReferenceMSESADGRADCONN
10.008519.5819.1412.61
20.007516.5718.5211.15
30.007015.4817.5610.56
40.006815.2317.0210.28
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.351, + 0.88, + 0.366 + ], + "angle": 0, + "content": "Table 6. Ablation study on the number of reference inputs." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.388, + 0.878, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.557, + 0.836, + 0.572 + ], + "angle": 0, + "content": "Figure 6. Extension to video object matting." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.892, + 0.66 + ], + "angle": 0, + "content": "frame of a video, which serves as a reference input and all frames of the video are treated as target images. With this setup, the model for in-context matting can predict the alpha matte for each frame of the video, visualized in Fig. 6." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.62, + 0.698 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.892, + 0.848 + ], + "angle": 0, + "content": "In this work, we introduce 'in-context matting', which enables automatic matting of foreground of interest on target images given a reference image and its prompt. We introduce IconMatting as a preliminary solution. Extensive experiments have shown its efficacy and robustness across categories and scenes. Being the first work introducing this task, we believe it opens new possibilities for efficient and accurate image matting while reducing user effort, also enhancing the versatility of image matting techniques." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by the National Natural Science Foundation of China under Grant No. 62106080." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3718" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. Advances in Neural Information Processing Systems, 35:23716-23736, 2022. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.201, + 0.472, + 0.257 + ], + "angle": 0, + "content": "[2] Amir Bar, Yossi Gandelsman, Trevor Darrell, Amir Globerson, and Alexei Efros. Visual prompting via image inpainting. 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In-Context Matting. This novel task setting for image matting enables automatic natural image matting of target images of a certain object category conditioned on a reference image of the same category, with user-provided priors such as masks and scribbles on the reference image only. Notice that, our approach exhibits remarkable cross-domain matting quality. + +![](images/12556a0b3e747d5060cb44f0406e21bd910e6498db913bdc448a2d60d5dcf4c8.jpg) + +![](images/ae2266aefe00c71cc9ac71bafcf7a459ea45df98e923ba566edbf08d68b0bd77.jpg) + +![](images/6c74018e3314560b3765d0ee195c8a24e76a0cd8219c0e61ae7c789809825ef5.jpg) + +![](images/c03457c353c1269af5548df7c8b797b90d664503806504843faca3e0605a4da8.jpg) + +![](images/3348d7672035d8a61f9b12cb6df72ec68e00fc81c4e0005a21298c419eb4456d.jpg) + +$\mathsf{N}^*$ image $+1^{*}$ prompt $+1^{*}$ model $\rightarrow$ N\*predictions + +![](images/91a7a71a1a1ac45b533cd301ae5834d30b5eb166f53b70771f1bfa004a8caab5.jpg) + +![](images/a18b7b290f81d29a6d0cee6b2e7d20f8bcd13b8d9cb0e664be32224ddc28ed33.jpg) + +# Abstract + +We introduce in-context matting, a novel task setting of image matting. Given a reference image of a certain foreground and guided priors such as points, scribbles, and masks, in-context matting enables automatic alpha estimation on a batch of target images of the same foreground category, without additional auxiliary input. This setting marries good performance in auxiliary input-based matting and ease of use in automatic matting, which finds a good tradeoff between customization and automation. To overcome the key challenge of accurate foreground matching, we introduce IconMatting, an in-context matting model built upon a pre-trained text-to-image diffusion model. Conditioned on inter- and intra-similarity matching, IconMatting can + +make full use of reference context to generate accurate target alpha mattes. To benchmark the task, we also introduce a novel testing dataset ICM-57, covering 57 groups of real-world images. Quantitative and qualitative results on the ICM-57 testing set show that IconMatting rivals the accuracy of trimap-based matting while retaining the automation level akin to automatic matting. Code is available at https://github.com/tiny-smart/in-context-matting. + +# 1. Introduction + +Image matting has been a long-standing problem in vision and graphics [3]. It typically requires estimating an accurate alpha matte by solving a so-called matting equation + +$$ +I = \alpha F + (1 - \alpha) B, \tag {1} +$$ + +where $I$ is the 3-channel RGB image, $F$ , $B$ , and $\alpha$ are the 3-channel foreground, the 3-channel background, and the 1-channel alpha matte. The matting equation, however, is highly ill-posed, due to the need to infer 7 unknowns from 3 observations. + +Prior art has come up with different ways to reduce uncertainties in matting such as using trimaps [7, 16, 18-20, 32, 38], scribbles [39], or a even known background [17, 29]. These approaches are given the name auxiliary input-based matting [14] in modern matting literature. Indeed, these matting models, particularly trimap-based ones, have achieved remarkable accuracy. They are in some way user-unfriendly as an auxiliary input should be provided with each image in practice, which significantly harms matting efficiency and user experience. Recently another stream of work attempts to abandon any auxiliary input completely and forms a new paradigm called automatic matting [4, 9, 11, 12, 21, 31, 43]. Despite their inherent advantages, these automatic matting models are narrowed to specific object categories, such as humans [4, 9, 21, 31], animals [12], and salient objects [11, 43]. This can render poor generalization in natural scenes, infeasibility to tackle general object categories, and unawareness of foreground of interest. + +Hence, there seems an obvious gap between accuracy and efficiency and between customization and automation. An interesting question is that: Can the auxiliary input-based matting be optimized to enhance the efficiency, while also maintaining guidance for matting targets with sufficient automation, thereby harmonizing the two existing matting paradigms? + +In this paper, we introduce in-context matting, a novel task setting of image matting, where a reference input can provide guidance for a batch of target images with similar foregrounds. The alpha matts of the target batch are predicted by leveraging the contextual information from the reference input. Fig. 1 provides an example, where a cat marked in the reference image enables the extraction of cats from all target images, regardless of the background or domain. This novel task setting relieves users from providing auxiliary input for each image. Instead, by specifying the matting target only in a single reference image, the alpha matts of the entire batch images could be predicted. Given the reference guidance, in-context matting can also gather sufficient contextual information, leading to higher accuracy and adaptability than fully automatic matting. This setting therefore combines the most notable features of automatic and auxiliary input-based matting, finding a good trade-off between them. + +Technically, we confront a primary challenge inherent to in-context matting, i.e., how to leverage the reference input to accurately identify the corresponding target foreground. While SegGPT [35] has explored image segmentation with + +contextual information, its in-context coloring framework is not suitable for image matting. In this work, we approach this challenge as a problem of region-to-region matching. In particular, recent advances [22, 26, 30] in generative diffusion models have demonstrated emergent capabilities in discriminative tasks like segmentation [37] and correspondence [33]. Given that our region-to-region matching is an inherent aspect of correspondence, and noting the parallels between image segmentation and image matting, we explore the applicability of pretrained diffusion models for in-context matting. + +We therefore introduce IconMatting, a model based on the pre-trained Stable Diffusion model [26], specialized for in-context matting. Given a reference image along with its corresponding foreground of interest as context, the target alpha matte could be inferred by exploiting the feature correspondence from Stable Diffusion such that the target foreground is matched conditioned on the correspondence. However, the matching is often sparse and insufficient to represent the entire target area. To address this, the intra-image similarity, based on the self-attention maps of Stable Diffusion, is additionally used to supplement the missing parts. By leveraging both inter- and intra-image similarities, informative guidance of the matting target would be acquired. Finally, any off-the-shelf matting heads can be used to predict the alpha matte. + +Since the task setting is different from existing mating benchmarks, we introduce a new testing dataset named ICM-57 to offer a broad and thorough validation of in-context mating. This dataset encompasses 57 contextually-aligned image groups; each comprising images in the real world and has either the same category or the same instance of different views, thereby encompassing a rich variety of in-context scenarios, which ensures a comprehensive test of a model to tackle various contexts. + +Through extensive experiments on the ICM-57 and AIM-500 [10] datasets, we showcase the potential of in-context matting and IconMatting. The results indicate that IconMatting, while retaining the automation level akin to automatic matting, rivals the accuracy of trimap-based matting, underscoring the value of in-context matting as a promising direction for image matting. + +# Our contributions include: + +- We introduce in-context matting, a novel task setting of image matting that takes advantages of both automatic and auxiliary input-based matting; +- IconMatting: an effective in-context matting model based on Stable Diffusion. +- ICM-57: a novel dataset and the evaluation framework for in-context matting. + +# 2. Related Work + +We review work related to image matting and in-context learning in vision. + +Image Matting. Image matting approaches can be coarsely categorized into auxiliary input-based matting and automatic matting. Auxiliary input-based matting requires user input. The user input can be in the form of a trimap [7, 16, 18, 19, 32, 38], scribbles [39], a background image [17, 29], a coarse mask [23, 42], or even a text description [15]. Despite their effectiveness, they require significant manual effort to provide the auxiliary inputs. Automatic matting [4, 10, 12, 24, 43] predicts the alpha matte without any user intervention. They typically assume salient or certain foregrounds that are implicitly defined by the training dataset. The network structures used in automatic matting can be divided into two groups: one-stage network with global guidance [24] and parallel multi-task network [10, 31]. Some recent work has also introduced transformer structures into automatic matting [21]. While both auxiliary input-based and automatic matting have been studied comprehensively, a paradigm that combines the efficiency of automatic matting and the precision of auxiliary input-based matting has not yet been explored. We fill this gap with in-context matting. + +In-Context Learning in Vision. In-context learning, initially a concept in natural language processing [5], is now made popular in computer vision. It allows models to fast adapt to a variety of tasks with minimal examples. + +Bar et al. [2] first proposes an in-context learning framework using inpainting with discrete tokens on figures and infographics from vision articles, demonstrating applications in foreground segmentation, single object detection, and colorization. Painter [34] adopts masked image modeling to perform in-context learning with supervised datasets, achieving highly competitive results on seven diverse tasks. More recently, SegGPT [35], which segments everything in context by unifying different segmentation tasks into an in-context coloring framework. Prompt Diffusion [6] presents a diffusion-based generative framework to enable in-context learning across various tasks. Additionally, Flamingo [1], a family of visual language models, shows rapid adaptation to a variety of image and video tasks with few-shot learning capabilities. These models showcase the potential of in-context learning in addressing diverse vision tasks. + +The concept of in-context learning, while being transformative in other areas, has not yet impacted the field of image matting. Although SegGPT achieves in-context image segmentation but is limited to coarse levels, lacking in semitransparency handling. Our IconMatting first introduces in-context learning into image matting, enhancing both the efficiency of auxiliary input-based matting and the precision of automatic matting. + +
Task settingautoauto with ref-inputreal-world generalization#ref-input
AuxXXgood#images
Auto✓-poorzero
In-contextX✓goodone
+ +Table 1. Comparison between in-context matting and two existing image matting paradigms. "Aux" and "Auto" are abbreviations for auxiliary input-based matting and automatic matting, respectively. In-context matting requires only a single reference input to achieve the automation of automatic matting and the generalizability of auxiliary input-based matting. + +Our work is also related to image co-segmentation [27]. This task aims to segment common objects within a pair of contextual images. However, unlike in-context matting, where users can specify the matting target, co-segmentation operates without user input, predicting rough binary masks delineating common objects across image pairs. + +# 3. In-Context Matting with Diffusion Models + +We begin with the problem setup, then present our proposed in-context matting model, i.e., IconMatting. + +# 3.1. Problem Setup + +The objective of in-context matting is to extract the alpha mattes $\{\alpha_{i}\}^{N}$ of a specified foreground category from a collection of input images $\{I_i\}^N$ . Through user interaction, the matting target is indicated by a reference image $I_r$ and a corresponding binary region of interest (RoI) map $M_{\mathrm{RoI}}$ . The RoI map can take the form of a mask, scribbles, or points as exemplified in Fig. 1. Notably, the reference image can either be a part of the input collection or an entirely separate image. When the input image collection has only a single image, users can treat that image as the reference image. In this case, in-context matting degenerates into image matting guided by user interaction. + +Given $\{I_i\}^N$ and $(I_r, M_{\mathrm{RoI}})$ , in-context matting is formulated as predicting the alpha matte $\{\alpha_i\}^N$ in $\{I_i\}^N$ of the matting targets informed by $(I_r, M_{\mathrm{RoI}})$ . In the context of in-context matting, when provided with a reference input, it becomes an automatic matting system targeted towards a specific foreground. The comparison between in-context matting and existing task settings for image matting is detailed in Table 1. + +# 3.2. Overall Architecture + +Here we first present the overall framework of IconMatting. As shown in Fig. 2, IconMatting is comprised of three components: a feature extractor, an in-context similarity module, and a matting head. + +The feature extractor is responsible for obtaining the RoI features from the reference image, the features and self-attention maps from the target image. They are then fed into + +![](images/d7f6f36d94073124bde157b16fba206c76eba61caa56641e46aec0508ab6f60c.jpg) +Figure 2. IconMatting integrates a Stable Diffusion-derived feature extractor, an in-context similarity module, and a matting head. It processes a target image $I_{t}$ , a reference image $I_{r}$ , and an RoI map $M_{RoI}$ . Both reference and target image features and target self-attention maps are extracted and used. In-context similarity uses the in-context query from the reference image to create a guidance map, which, combined with self-attention maps, assists in locating the target object. The matting head finally generates the target alpha matte. + +the in-context similarity module, the core of the framework. The module further consists of inter- and intra-similarity sub-modules: the former leverages the reference RoI features as an in-context query to derive a guidance map from the target features; the latter integrates the guidance map with multi-scale self-attention maps to obtain guidance for the matting head. Finally, the matting head uses this synthesized guiding information and the target features to generate the alpha matte of the target image. + +# 3.3. In-Context Feature Extractor + +Backbone Selection. As outlined in Section 1, we conceptualize the core challenge of in-context matting – leveraging the reference context to accurately identify the target foreground – as a region-to-region matching problem. Therefore, if the features derived from a backbone naturally possess correspondence capabilities, referred to as in-context features, they would facilitate the implementation of in-context matting. Tang et al. [33] have found that the text-to-image generative model, Stable Diffusion [26], trained on large-scale text-image paired datasets, exhibit emergent capabilities for both geometric and semantic correspondence. It can perform point-to-point correspondence between images across instances, classes, and even domains with simple cosine similarity. Inspired by this observation, we leverage Stable Diffusion as a feature extractor to implement in-context matting. + +Preliminary on Stable Diffusion. Recent advances in diffusion models, e.g., Stable Diffusion [26], have shown impressive results in both generative and discriminative tasks. Being a feature extractor, Stable Diffusion encodes + +an image $x_0$ into a latent space, denoted by $z_0$ , which, through a noise process defined by $\{\alpha_t\}^T$ , transforms into $z_{t} = \sqrt{\alpha_{t}} z_{0} + (\sqrt{1 - \alpha_{t}})\varepsilon$ , where $\varepsilon \sim \mathcal{N}(0,\mathbf{I})$ is the randomly-sampled noise. The latent representation $z_{t}$ undergoes forward propagation in a U-Net $f_{\theta}$ , generating multi-scale features $\{\mathcal{F}_l\}^L$ and self-attention maps $\{\mathcal{A}_l\}^L$ , which can later be exploited for downstream tasks. Icon-Matting uses the capabilities of Stable Diffusion and both reference and target images to extract multi-scale features and self-attention maps to enhance feature representation. + +# 3.4. In-Context Similarity + +In-context similarity plays a key role in our model, because the quality of inferred alpha mattes highly depends on the output of this module. In particular, the in-context similarity module is designed to identify the potential target foreground taking the reference RoI into account, thereby guiding the prediction of the target alpha matte. According to our observations, both the reference-target similarity and target-target similarity matter for locating the potential target foreground. These correspond to the proposed inter-similarity and intra-similarity sub-modules. + +Observation. The core challenge in in-context matting is a semantic correspondence problem. Given Stable Diffusion being the feature extractor, one can associate points of the foreground areas between the reference and target images using the emergent feature correspondence. However, due to the inherent reference-target foreground difference, a rigorous one-to-one mapping of all points between the two areas is unfeasible. There would always be some unmatched outliers, resulting in holes in the matting target + +![](images/5cb36e307577021a8ea3a8022752051a5b79a799cd770b3826a4ac9a57128b43.jpg) +(a) Outliers in point to point correspondence + +![](images/85b74aa009b87d04cea9fac38b20123341b6f43b8e8cf74f99d221e76a435937.jpg) +(b) Self-attention of random points +Figure 3. Observations on the inter- and intra similarities. + +area of the target image, as illustrated in Fig. 3. + +Since only a subset of points are matched, the goal is changed to how to expand these matched points to cover the entire target foreground area. To address this, we look for other points sharing similar semantic meaning with this subset of points. Intra-image similarity is therefore considered. Intuitively, the self-attention maps from Stable Diffusion reflect the similarities between different image patches. As shown in Fig. 3, by randomly sampling a small number of points from the target area and simply summing over the corresponding self-attention maps, the whole target foreground can be revealed. Based on this observation, we use the self-attention maps as intra-image information to supplement the inter-image matching results. + +Inter-Similarity. Formally, given features $\{\mathcal{F}_l^r\} ^L$ and $\{\mathcal{F}_l^t\} ^L$ extracted from the reference image $I_{r}$ and the target image $I_{t}$ , respectively, the layer with the best correspondence capability is selected following DIFT [33], denoted by $\mathcal{F}_{\mathrm{inter}}^r$ for the reference and $\mathcal{F}_{\mathrm{inter}}^t$ for the target. Then, features corresponding to the RoI $M_{\mathrm{RoI}}$ in $\mathcal{F}_{\mathrm{inter}}^r$ are extracted and formulated as the in-context query $\{Q_k\} ^K$ , where $K$ is the length of the query. $Q_{k}$ takes the form + +$$ +Q _ {k} = R (k), \tag {2} +$$ + +$$ +R = \mathcal {F} _ {\text {i n t e r}} ^ {r} \odot M _ {\mathrm {R o I}}, \tag {3} +$$ + +where $\odot$ is the element-wise product and $R(k)$ denotes the $k$ -th non-zero element of $R$ . Further, $\{Q_k\}^K$ is used to compute similarity with $\mathcal{F}_{\mathrm{inter}}^t$ , identifying regions on $I_t$ that correspond to the RoI of $I_r$ , formulated as + +$$ +\mathcal {S} _ {k} = \operatorname {s o f t m a x} \left(\frac {Q _ {k} \cdot F _ {\text {i n t e r}} ^ {t}}{\sqrt {d}}\right). \tag {4} +$$ + +The similarity map is denoted by $\{S_k\}^K$ , and the mean of all such similarity maps yields $S$ , which measures the + +degree of similarity between different locations on $I_{t}$ and the RoI in $I_{r}$ , serving as the first intermediate output of in-context similarity. + +Intra-Similarity. As noted in our observations (Fig. 3), $S$ is typically sparse. Although the target matting region on $I_{t}$ is partially covered by $S$ , it is insufficient to guide alpha prediction. Here we further design the intra-similarity sub-module to leverage the internal similarity within $I_{t}$ to propagate $S$ into a more precise representation of the RoI on $I_{t}$ . During feature extraction of $I_{t}$ , self-attention maps $\{\mathcal{A}_l\}^L$ representing its internal similarity are also retained, serving as the input for intra-similarity. This sub-module uses $S$ as a weight to the self-attention maps, thereby generating guiding information that accurately represents the matting target on $I_{t}$ , denoted by $\{S_l'\}^L$ . Mathematically, the intra-similarity matching is expressed by + +$$ +\mathcal {S} _ {l} ^ {\prime} = \mathcal {A} _ {l} \odot \mathcal {S}. \tag {5} +$$ + +# 3.5. Matting Head + +The success of ViTMatte [40] implies that the information of original image is important during decoding. Following this practice, in our matting head, the original image is concatenated and decoded with outputs from previous modules. + +The guidance map from the in-context similarity module and the intra-features from the backbone are merged and refined using a convolutional feature fusion block, including a series of convolution, normalization, and activation layers. The output multi-scale in-context features are progressively merged using a series of fusion layers which comprise upsampling, concatenation, convolution, normalization, and activation layers. Then, following ViTMatte [40], details from the original image are extracted and combined with the merged feature in a detail decoder, enhancing the details of alpha matte. This matting head effectively melds contextual information with original image details, yielding the generation of a highly precise and refined alpha matte. + +# 3.6. Reference-Prompt Extension + +In addition to the mask prompts, points and scribbles can also be transformed into RoI masks. However, these prompts yield less comprehensive in-context queries compared with mask prompts. To enhance them, we propose an extension of reference prompt to enrich the in-context queries derived from point and scribble prompts. + +Since the self-attention maps from the backbone reflect the similarities across regions, we leverage the attention maps of the reference images to expand the RoI mask. This is achieved by including regions in the attention maps that are similar to the prompt locations. Specifically, for each prompt point, the top $m$ points with the highest responses in their corresponding attention maps are integrated into the RoI mask additionally, thus enriching the in-context query. + +![](images/009de63291823e756df212ca9c836574bccae0b66181568f26270ae959bd3d98.jpg) +Figure 4. ICM-57 examples. The dataset encompasses foreground subjects including human, animals, plants, and various common objects. It contains both instances from the same category and the same entity. + +# 4. Results and Discussion + +# 4.1. Datasets + +To facilitate in-context matting, we establish a hybrid training set, along with a test set, ICM-57. The existing AIM-500 dataset was also reorganized to meet the testing requirements of in-context matting. In particular, in-context matting requires to organize images into groups where the annotated foregrounds share categories or instances. Such organization allows for random selection of reference and target images within groups during training. In the test set, one or more images in each group are designated as reference images. + +Mixing In-Context Training Sets. We selected the RM1K dataset [36]. However, such a dataset was insufficient for training. Therefore, a subset of the Open Images dataset [8], focusing on image segmentation, was also employed. The two formed a mixed training set tailored to in-context matting. Both datasets were reorganized. + +For the RM-1K dataset, we divided it into 222 groups. A subset of 14,000 images from the Open Images dataset were chosen as well. In the original dataset, each image came with one or more annotations for image segmentation; each corresponds to an object instance. We aggregated these annotations by category, ensuring that the annotations include all instances of the corresponding category. They subsequently formed context groups that met the requirements of in-context matting. As a result, a mixed training set of 15,000 images and 450 groups was created. + +ICM-57 Testing Set. To assess the performance of our model, we constructed the first testing dataset for in-context matting, named ICM-57, which comprises 57 image groups that form various real-world contexts. This dataset was created by using the instance-segmented dreambooth dataset [28], to which we supplemented high-precision alpha matte annotations. Additionally, we reviewed the existing AIM-500 dataset, selected a subset, and categorized these into groups according to their classes to supplement the in-category groups. Examples of the testing set are shown in Fig 4. + +AIM-500. We also report performance on the AIM-500 dataset [10]. This enables us to compare our matting model with other public matting results on this dataset. + +# 4.2. Implementation Details + +Architecture. We employ the U-Net architecture from Stable Diffusion v2-1-v [26]. For feature extraction, the time step of the diffusion process is set to $t = 0$ by default, with an empty string used for conditional input. U-Net has 11 decoder blocks; we extract feature maps from the 5-th, 8-th, and 11-th blocks as the intra-features and ones from the 5-th block as the inter-features. + +Training Details. We employ distinct loss functions for matting and segmentation, respectively. For matting, we use a combination of $\ell_1$ loss, Laplacian loss, and Gradient loss. For segmentation, we only use the $\ell_1$ loss. To leverage the segmentation dataset while reducing the impact of imprecise edge annotations, we adopt the approach from HIM [31] that only backpropagates the loss from the confident areas. + +During training, the learning rate is set to 0.0004 and the batch size is 8. The input images are randomly cropped to a size of $768 \times 768$ pixels. To prevent deviation from the pretrained model space in modeling real images, no additional data augmentation is used. We train IconMatting for 20,000 iterations using the AdamW optimizer. + +Evaluation. We employ the four widely used matting metrics: SAD, MSE, Grad and Conn [25]. Lower values imply higher-quality matts. In particular, MSE is scaled by a factor of $1 \times 10^{-3}$ . + +To reduce randomness, each method is tested for three rounds, where the metrics were averaged. For each group of images, the reference inputs were fixed and consistently used. This minimizes the variations in reference inputs, allowing for a more scientific and reliable assessment. + +# 4.3. Main Results + +Comparison with In-Context Segmentation Models. To explore the effectiveness and superiority of our model, we selected SegGPT [35] and SEEM [45], which also operates under in-context learning, as baselines in the image segmentation domain. From Table 2, on the ICM-57 and AIM-500 datasets, under the same experimental setup (one mask per group of images), our model significantly outperforms the baselines across all metrics. + +It is important to note that due to their distinct task setting (i.e., segmentation rather than matting), the lack of high-quality annotations (e.g., alpha mattes) and the methods (i.e., mask classification rather than alpha matte regression), most of these models have overlooked pixel-level text-semantic alignment and are unable to produce fine-grained masks, as illustrated in Fig. 5. + +![](images/bcc49c4d552375d67696a7bb13e727bd76e6a3227adeb589c83d58e4a2edcebc.jpg) + +![](images/447bbbe969d578891ff46b3ab77983d55b2c3f3083e53c1cef58130d9b0d3b0c.jpg) + +![](images/fd828d99121f7208d0e451b90dc52d99fa987de72c8240f50eafa48ed4e61282.jpg) + +![](images/2ffae86391c801dc9ab5f67405374285ad67615a28e88cd33590a1dc4ac2c41c.jpg) + +![](images/7e7e0569192afddfb5f0b0ee4453e36b969fb511ba680e4d3fd6f92030f3b283.jpg) + +![](images/f149e4b9559c1336946b3a846a1d05334e1e54c8d8d7606dbd63a6f90c779f11.jpg) + +![](images/ed7609879900a5f3ecb85bdecc7f0ab92580a907325aa9662bb1d131584f11c4.jpg) + +![](images/ef9cd766445834c5fdb6bc62aa27e6330ef551d2a32240dc7ef3182b7804c1b5.jpg) + +![](images/e84f9b9dfb2af7b3137700e4736c5cb637bd2ecf351ad4c5f0975c5817c9662e.jpg) + +![](images/004a231b8a419db061f5a2d4102925866337a0273528ac24d086a03de7465f66.jpg) + +![](images/8c2c424db19d302b614f9af33dffbd6065c45e800e0de9fd6e4b03f685aa4c9b.jpg) + +![](images/f74b71c8ef0320fca10656eed98477e17d253a12eb6a3a11d97bdc60fd98f0e0.jpg) + +![](images/49a28b2e63789525e1900fbd9bdaf0023f5b1e0c6d93537c24584dca42e1abb7.jpg) + +![](images/2bbe35d290da95a8a09ca1327a17a471c57964ac1094cbda78aeb992b5c3d913.jpg) + +![](images/18bc63d2cdc96288e46e9e595456abe600e6715b4d652a8c61af049c4aa8e2b4.jpg) + +![](images/e4e70941a7ba354312dc101bb45d971fec05b779f4fad3a1a1256660922d58b1.jpg) + +![](images/2ebcf32b306401cff58b03e8ea1c18e3ff743bfd216ddb64bd73b156e2ee6684.jpg) +Image + +![](images/da307446f6464e0de3798fa308a2d2ef5b2a35168e47751645c1f381f9c7b132.jpg) +Ref-input + +![](images/424ae3b529c7bae43411eacddd084ae80d8e55717dfe1d6156be591d1f50f775.jpg) +AIM + +![](images/64ad75b37f7e2f6a86f67a8ae3f2925a934d6336806dce6469a77d58dc510641.jpg) +MatAny + +![](images/ab5f5a00881b88fb9523ac315cd8e3d1a7f39bce2d04bf01c0752779a4f84136.jpg) +SegGPT +Figure 5. Qualitative results of different image matting methods. Our method can predict the alpha matte of the matting target specified by the reference input, offering notable prediction accuracy while avoiding interference from unrelated foreground elements. + +![](images/a6200361ea877a1c8f55f1481aaf1d13dfeadc1a605d2b1392189cfbfcb02082.jpg) +ICMP + +![](images/d14d6de5cf715b56424073f91f326b8218aa9f007ddf8cef735d45dd77510e55.jpg) +Ours + +![](images/f241113253f076e6e1c3919115bad4de95c3df552a8b3be7ce83584bba2cc430.jpg) +GT + +
MethodICM-57AIM
MSESADGRADCONNMSESADGRADCONN
SegGPT0.019838.8128.6118.610.039142.6541.9526.69
SEEM0.029264.2837.5423.640.0425114.2374.5174.32
Ours0.008119.1218.6511.210.006218.6515.5110.98
+ +Table 2. Comparison with in-context segmentation models. + +Comparison with Automatic and Auxiliary Input-Based Matting Models. We further compare the performance of our IconMatting with both automatic and auxiliary input-based matting models on the ICM-57 and AIM-500 datasets. Automatic matting methods such as LF [44] and AIM [10] lack specific auxiliary information about the matting target, often produce poor alpha mattes, showing a significant performance gap compared with our model. MGM [42] and MGMiW [23] use a mask for each image as auxiliary input to specify the matting target. Although our method simplifies this by requiring only one mask per group of images, it still outperforms MGM in various metrics. VitMatte [40], a trimap-based image matting method, necessitates manually annotating a trimap for the foreground of each image, making it the performance upper bound for our in-context matting. Nevertheless, the performance of IconMatting is on par with VitMatte, underscoring its efficacy and competitiveness in image matting. + +Comparison with Interactive Matting Models. Recently, with the advent of SAM, some researchers have designed interactive matting models, such as MatAny [41] and MAM [13], based on this generic image segmentation model. Inspired by this, we also designed an In + +Context Matting Pipeline (ICMP) with three stages: correspondence, segmentation, and matting, serving as one of the baselines. ICMP is a combination of existing models, with details available in supplementary materials. + +For MatAny and MAM, we compare them under three types of interactions: points, scribbles, and masks. On the ICM-57 testing dataset, both baselines receive interaction information for each image within a group, whereas IconMatting only receive interaction information from one image in the group to indicate the matting target. Despite reducing the amount of human interaction, IconMatting achieves slightly better performance over the baselines. + +Limited by the interaction modalities in ICMP, our model is only compared with it under the point interaction setting. Our end-to-end model outperforms the combined ICMP. In ICMP, the cues for the matting target degrade to points during the correspondence phase of the pipeline, often resulting in sparse information, making our end-to-end approach more effective. + +# 4.4. Ablation Study + +Different Modules. To validate different modules, we conducted ablation studies in Table 5. Among the four components, the presence or absence of inter- and intrasimilarity plays a crucial role in performance. Without intra-similarity, the performance of the model significantly worsens across all four metrics. If both inter- and intrasimilarity are absent, the model degenerates to directly predicting the alpha matte from the image, losing the information source for the specified matting target, and thus the performance markedly deteriorates. + +
MethodGuidanceICM-57AIM
MSESADGRADCONNMSESADGRADCONN
MGM1 mask per image0.034184.2561.8430.210.026871.9123.3721.97
VitMatte1 trimap per image0.003016.1614.2811.140.003818.7914.2212.47
MGMiW1 mask per image----0.003016.7214.6812.02
LFauto0.0811205.6869.53195.630.0667191.7464.51181.26
AIMauto0.026565.0755.5625.740.018348.0947.5821.74
Ours1 mask per group of images0.008119.1218.6511.210.006218.6515.5110.98
+ +Table 3. Comparison with automatic and auxiliary input-based matting models. + +
MethodIn-contextPointScribbleMask
MSESADMSESADMSESAD
MatAnyX0.0651129.670.0512115.210.041295.26
MAMX0.014941.230.014140.230.010929.65
ICMP✓0.011239.65----
Ours*X0.006115.280.005915.970.002915.28
Ours✓0.012423.210.010524.560.008119.12
+ +Table 4. Comparison with interactive matting models. In the penultimate row, our method is provided with guidance information for every image, reducing to an auxiliary input-based method. Our method outperforms automatic methods and some of the auxiliary input-based methods, and its performance is comparable to that of the trimap-based method, VitMatte. + +
INTERINTRAMFSDMSESADGRADCONN
✓✓✓✓0.008119.1218.6511.21
✓X✓✓0.009924.1520.3612.11
XX✓✓0.031540.3231.5619.53
✓✓X✓0.005423.6921.9614.52
✓✓✓X0.007118.5619.5412.61
+ +Number of Reference Inputs. Intuitively, the more reference inputs there are, the more likely the model is to identify the corresponding matting target. We explored the impact of the number of reference inputs on the performance of our model, as shown in Table 6. On ICM-57 test set, the performance improves as the number of reference inputs increases; however, the improvement almost ceases when the number of reference inputs increases from 3 to 4. Therefore, we can conclude that appropriately increasing the number of reference inputs can enhance model performance, which is consistent with intuition. + +# 4.5. Extension to Video Object Matting + +The technique of in-context matting is easily extendable to video object matting. The key is to use a frame of the video as a reference. For example, an object is marked in the first + +Table 5. Ablation study on different modules. INTER, INTRA, MF, and SD respectively stand for inter-similarity, intra-similarity, multi-scale features, and segmentation dataset. + +
#ReferenceMSESADGRADCONN
10.008519.5819.1412.61
20.007516.5718.5211.15
30.007015.4817.5610.56
40.006815.2317.0210.28
+ +Table 6. Ablation study on the number of reference inputs. + +![](images/145d452896a228b118346bd663fe9d69594195a370dbfa271c7ab48186638b62.jpg) +Figure 6. Extension to video object matting. + +frame of a video, which serves as a reference input and all frames of the video are treated as target images. With this setup, the model for in-context matting can predict the alpha matte for each frame of the video, visualized in Fig. 6. + +# 5. Conclusion + +In this work, we introduce 'in-context matting', which enables automatic matting of foreground of interest on target images given a reference image and its prompt. We introduce IconMatting as a preliminary solution. Extensive experiments have shown its efficacy and robustness across categories and scenes. Being the first work introducing this task, we believe it opens new possibilities for efficient and accurate image matting while reducing user effort, also enhancing the versatility of image matting techniques. + +Acknowledgement. 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Given a reference image of a certain foreground and guided priors such as points, scribbles, and masks, in-context matting enables automatic alpha estimation on a batch of target images of the same foreground category, without additional auxiliary input. This setting marries good performance in auxiliary input-based matting and ease of use in automatic matting, which finds a good tradeoff between customization and automation. To overcome the key challenge of accurate foreground matching, we introduce IconMatting, an in-context matting model built upon a pre-trained text-to-image diffusion model. Conditioned on inter- and intra-similarity matching, IconMatting can" + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 306, + 509, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 545, + 617 + ], + "type": "text", + "content": "make full use of reference context to generate accurate target alpha mattes. To benchmark the task, we also introduce a novel testing dataset ICM-57, covering 57 groups of real-world images. Quantitative and qualitative results on the ICM-57 testing set show that IconMatting rivals the accuracy of trimap-based matting while retaining the automation level akin to automatic matting. Code is available at https://github.com/tiny-smart/in-context-matting." + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 306, + 638, + 387, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 638, + 387, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 638, + 387, + 651 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 57 + }, + { + "bbox": [ + 306, + 658, + 545, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 545, + 695 + ], + "type": "text", + "content": "Image matting has been a long-standing problem in vision and graphics [3]. It typically requires estimating an accurate alpha matte by solving a so-called matting equation" + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 380, + 701, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 380, + 701, + 545, + 713 + ], + "type": "interline_equation", + "content": "I = \\alpha F + (1 - \\alpha) B, \\tag {1}", + "image_path": "ee3618b2ca7851433c8dfe987cf8b20cc498743fb3df68179f4f93d12c20fdb2.jpg" + } + ] + } + ], + "index": 60 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 138, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 138, + 713 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 138, + 713 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 59 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3711" + } + ] + } + ], + "index": 61 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": " is the 3-channel RGB image, " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": " are the 3-channel foreground, the 3-channel background, and the 1-channel alpha matte. The matting equation, however, is highly ill-posed, due to the need to infer 7 unknowns from 3 observations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 289, + 361 + ], + "type": "text", + "content": "Prior art has come up with different ways to reduce uncertainties in matting such as using trimaps [7, 16, 18-20, 32, 38], scribbles [39], or a even known background [17, 29]. These approaches are given the name auxiliary input-based matting [14] in modern matting literature. Indeed, these matting models, particularly trimap-based ones, have achieved remarkable accuracy. They are in some way user-unfriendly as an auxiliary input should be provided with each image in practice, which significantly harms matting efficiency and user experience. Recently another stream of work attempts to abandon any auxiliary input completely and forms a new paradigm called automatic matting [4, 9, 11, 12, 21, 31, 43]. Despite their inherent advantages, these automatic matting models are narrowed to specific object categories, such as humans [4, 9, 21, 31], animals [12], and salient objects [11, 43]. This can render poor generalization in natural scenes, infeasibility to tackle general object categories, and unawareness of foreground of interest." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 363, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 446 + ], + "type": "text", + "content": "Hence, there seems an obvious gap between accuracy and efficiency and between customization and automation. An interesting question is that: Can the auxiliary input-based matting be optimized to enhance the efficiency, while also maintaining guidance for matting targets with sufficient automation, thereby harmonizing the two existing matting paradigms?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 289, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 663 + ], + "type": "text", + "content": "In this paper, we introduce in-context matting, a novel task setting of image matting, where a reference input can provide guidance for a batch of target images with similar foregrounds. The alpha matts of the target batch are predicted by leveraging the contextual information from the reference input. Fig. 1 provides an example, where a cat marked in the reference image enables the extraction of cats from all target images, regardless of the background or domain. This novel task setting relieves users from providing auxiliary input for each image. Instead, by specifying the matting target only in a single reference image, the alpha matts of the entire batch images could be predicted. Given the reference guidance, in-context matting can also gather sufficient contextual information, leading to higher accuracy and adaptability than fully automatic matting. This setting therefore combines the most notable features of automatic and auxiliary input-based matting, finding a good trade-off between them." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Technically, we confront a primary challenge inherent to in-context matting, i.e., how to leverage the reference input to accurately identify the corresponding target foreground. While SegGPT [35] has explored image segmentation with" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "contextual information, its in-context coloring framework is not suitable for image matting. In this work, we approach this challenge as a problem of region-to-region matching. In particular, recent advances [22, 26, 30] in generative diffusion models have demonstrated emergent capabilities in discriminative tasks like segmentation [37] and correspondence [33]. Given that our region-to-region matching is an inherent aspect of correspondence, and noting the parallels between image segmentation and image matting, we explore the applicability of pretrained diffusion models for in-context matting." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 212, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 546, + 392 + ], + "type": "text", + "content": "We therefore introduce IconMatting, a model based on the pre-trained Stable Diffusion model [26], specialized for in-context matting. Given a reference image along with its corresponding foreground of interest as context, the target alpha matte could be inferred by exploiting the feature correspondence from Stable Diffusion such that the target foreground is matched conditioned on the correspondence. However, the matching is often sparse and insufficient to represent the entire target area. To address this, the intra-image similarity, based on the self-attention maps of Stable Diffusion, is additionally used to supplement the missing parts. By leveraging both inter- and intra-image similarities, informative guidance of the matting target would be acquired. Finally, any off-the-shelf matting heads can be used to predict the alpha matte." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 399, + 547, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 547, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 547, + 507 + ], + "type": "text", + "content": "Since the task setting is different from existing mating benchmarks, we introduce a new testing dataset named ICM-57 to offer a broad and thorough validation of in-context mating. This dataset encompasses 57 contextually-aligned image groups; each comprising images in the real world and has either the same category or the same instance of different views, thereby encompassing a rich variety of in-context scenarios, which ensures a comprehensive test of a model to tackle various contexts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 515, + 547, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 547, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 547, + 600 + ], + "type": "text", + "content": "Through extensive experiments on the ICM-57 and AIM-500 [10] datasets, we showcase the potential of in-context matting and IconMatting. The results indicate that IconMatting, while retaining the automation level akin to automatic matting, rivals the accuracy of trimap-based matting, underscoring the value of in-context matting as a promising direction for image matting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 608, + 426, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 608, + 426, + 619 + ], + "spans": [ + { + "bbox": [ + 317, + 608, + 426, + 619 + ], + "type": "text", + "content": "Our contributions include:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 628, + 545, + 711 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 306, + 628, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 628, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 628, + 545, + 662 + ], + "type": "text", + "content": "- We introduce in-context matting, a novel task setting of image matting that takes advantages of both automatic and auxiliary input-based matting;" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 663, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 663, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 306, + 663, + 545, + 686 + ], + "type": "text", + "content": "- IconMatting: an effective in-context matting model based on Stable Diffusion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "type": "text", + "content": "- ICM-57: a novel dataset and the evaluation framework for in-context matting." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3712" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 115 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 115 + ], + "type": "text", + "content": "We review work related to image matting and in-context learning in vision." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 121, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 289, + 373 + ], + "type": "text", + "content": "Image Matting. Image matting approaches can be coarsely categorized into auxiliary input-based matting and automatic matting. Auxiliary input-based matting requires user input. The user input can be in the form of a trimap [7, 16, 18, 19, 32, 38], scribbles [39], a background image [17, 29], a coarse mask [23, 42], or even a text description [15]. Despite their effectiveness, they require significant manual effort to provide the auxiliary inputs. Automatic matting [4, 10, 12, 24, 43] predicts the alpha matte without any user intervention. They typically assume salient or certain foregrounds that are implicitly defined by the training dataset. The network structures used in automatic matting can be divided into two groups: one-stage network with global guidance [24] and parallel multi-task network [10, 31]. Some recent work has also introduced transformer structures into automatic matting [21]. While both auxiliary input-based and automatic matting have been studied comprehensively, a paradigm that combines the efficiency of automatic matting and the precision of auxiliary input-based matting has not yet been explored. We fill this gap with in-context matting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 378, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 287, + 426 + ], + "type": "text", + "content": "In-Context Learning in Vision. In-context learning, initially a concept in natural language processing [5], is now made popular in computer vision. It allows models to fast adapt to a variety of tasks with minimal examples." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 426, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 617 + ], + "type": "text", + "content": "Bar et al. [2] first proposes an in-context learning framework using inpainting with discrete tokens on figures and infographics from vision articles, demonstrating applications in foreground segmentation, single object detection, and colorization. Painter [34] adopts masked image modeling to perform in-context learning with supervised datasets, achieving highly competitive results on seven diverse tasks. More recently, SegGPT [35], which segments everything in context by unifying different segmentation tasks into an in-context coloring framework. Prompt Diffusion [6] presents a diffusion-based generative framework to enable in-context learning across various tasks. Additionally, Flamingo [1], a family of visual language models, shows rapid adaptation to a variety of image and video tasks with few-shot learning capabilities. These models showcase the potential of in-context learning in addressing diverse vision tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "The concept of in-context learning, while being transformative in other areas, has not yet impacted the field of image matting. Although SegGPT achieves in-context image segmentation but is limited to coarse levels, lacking in semitransparency handling. Our IconMatting first introduces in-context learning into image matting, enhancing both the efficiency of auxiliary input-based matting and the precision of automatic matting." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 548, + 122 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 548, + 122 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 548, + 122 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 548, + 122 + ], + "type": "table", + "html": "
Task settingautoauto with ref-inputreal-world generalization#ref-input
AuxXXgood#images
Auto✓-poorzero
In-contextX✓goodone
", + "image_path": "9ed872c8dc8fcd0b0782bce8e6929b9c2e7c61868127b88ad53ba046e6484241.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 129, + 547, + 196 + ], + "lines": [ + { + "bbox": [ + 305, + 129, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 305, + 129, + 547, + 196 + ], + "type": "text", + "content": "Table 1. Comparison between in-context matting and two existing image matting paradigms. \"Aux\" and \"Auto\" are abbreviations for auxiliary input-based matting and automatic matting, respectively. In-context matting requires only a single reference input to achieve the automation of automatic matting and the generalizability of auxiliary input-based matting." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 214, + 547, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 214, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 305, + 214, + 547, + 288 + ], + "type": "text", + "content": "Our work is also related to image co-segmentation [27]. This task aims to segment common objects within a pair of contextual images. However, unlike in-context matting, where users can specify the matting target, co-segmentation operates without user input, predicting rough binary masks delineating common objects across image pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 296, + 538, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 296, + 538, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 538, + 309 + ], + "type": "text", + "content": "3. In-Context Matting with Diffusion Models" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 316, + 546, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 546, + 341 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 546, + 341 + ], + "type": "text", + "content": "We begin with the problem setup, then present our proposed in-context matting model, i.e., IconMatting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 347, + 399, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 347, + 399, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 347, + 399, + 361 + ], + "type": "text", + "content": "3.1. Problem Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "text", + "content": "The objective of in-context matting is to extract the alpha mattes " + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "inline_equation", + "content": "\\{\\alpha_{i}\\}^{N}" + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "text", + "content": " of a specified foreground category from a collection of input images " + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "inline_equation", + "content": "\\{I_i\\}^N" + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "text", + "content": ". Through user interaction, the matting target is indicated by a reference image " + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "inline_equation", + "content": "I_r" + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "text", + "content": " and a corresponding binary region of interest (RoI) map " + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{RoI}}" + }, + { + "bbox": [ + 305, + 365, + 547, + 509 + ], + "type": "text", + "content": ". The RoI map can take the form of a mask, scribbles, or points as exemplified in Fig. 1. Notably, the reference image can either be a part of the input collection or an entirely separate image. When the input image collection has only a single image, users can treat that image as the reference image. In this case, in-context matting degenerates into image matting guided by user interaction." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\{I_i\\}^N" + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "inline_equation", + "content": "(I_r, M_{\\mathrm{RoI}})" + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "content": ", in-context matting is formulated as predicting the alpha matte " + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\{\\alpha_i\\}^N" + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\{I_i\\}^N" + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "content": " of the matting targets informed by " + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "inline_equation", + "content": "(I_r, M_{\\mathrm{RoI}})" + }, + { + "bbox": [ + 304, + 509, + 547, + 605 + ], + "type": "text", + "content": ". In the context of in-context matting, when provided with a reference input, it becomes an automatic matting system targeted towards a specific foreground. The comparison between in-context matting and existing task settings for image matting is detailed in Table 1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 611, + 426, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 426, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 426, + 623 + ], + "type": "text", + "content": "3.2. Overall Architecture" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 629, + 546, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 546, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 546, + 677 + ], + "type": "text", + "content": "Here we first present the overall framework of IconMatting. As shown in Fig. 2, IconMatting is comprised of three components: a feature extractor, an in-context similarity module, and a matting head." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "The feature extractor is responsible for obtaining the RoI features from the reference image, the features and self-attention maps from the target image. They are then fed into" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3713" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 545, + 255 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 545, + 255 + ], + "type": "image", + "image_path": "d7f6f36d94073124bde157b16fba206c76eba61caa56641e46aec0508ab6f60c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "text", + "content": "Figure 2. IconMatting integrates a Stable Diffusion-derived feature extractor, an in-context similarity module, and a matting head. It processes a target image " + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "text", + "content": ", a reference image " + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "inline_equation", + "content": "I_{r}" + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "text", + "content": ", and an RoI map " + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "inline_equation", + "content": "M_{RoI}" + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "text", + "content": ". Both reference and target image features and target self-attention maps are extracted and used. In-context similarity uses the in-context query from the reference image to create a guidance map, which, combined with self-attention maps, assists in locating the target object. The matting head finally generates the target alpha matte." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 288, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 438 + ], + "type": "text", + "content": "the in-context similarity module, the core of the framework. The module further consists of inter- and intra-similarity sub-modules: the former leverages the reference RoI features as an in-context query to derive a guidance map from the target features; the latter integrates the guidance map with multi-scale self-attention maps to obtain guidance for the matting head. Finally, the matting head uses this synthesized guiding information and the target features to generate the alpha matte of the target image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 448, + 208, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 448, + 208, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 448, + 208, + 459 + ], + "type": "text", + "content": "3.3. In-Context Feature Extractor" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 467, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 658 + ], + "type": "text", + "content": "Backbone Selection. As outlined in Section 1, we conceptualize the core challenge of in-context matting – leveraging the reference context to accurately identify the target foreground – as a region-to-region matching problem. Therefore, if the features derived from a backbone naturally possess correspondence capabilities, referred to as in-context features, they would facilitate the implementation of in-context matting. Tang et al. [33] have found that the text-to-image generative model, Stable Diffusion [26], trained on large-scale text-image paired datasets, exhibit emergent capabilities for both geometric and semantic correspondence. It can perform point-to-point correspondence between images across instances, classes, and even domains with simple cosine similarity. Inspired by this observation, we leverage Stable Diffusion as a feature extractor to implement in-context matting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Preliminary on Stable Diffusion. Recent advances in diffusion models, e.g., Stable Diffusion [26], have shown impressive results in both generative and discriminative tasks. Being a feature extractor, Stable Diffusion encodes" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": "an image " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": " into a latent space, denoted by " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": ", which, through a noise process defined by " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\{\\alpha_t\\}^T" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": ", transforms into " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "z_{t} = \\sqrt{\\alpha_{t}} z_{0} + (\\sqrt{1 - \\alpha_{t}})\\varepsilon" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\varepsilon \\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": " is the randomly-sampled noise. The latent representation " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": " undergoes forward propagation in a U-Net " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": ", generating multi-scale features " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_l\\}^L" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": " and self-attention maps " + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{A}_l\\}^L" + }, + { + "bbox": [ + 304, + 331, + 546, + 451 + ], + "type": "text", + "content": ", which can later be exploited for downstream tasks. Icon-Matting uses the capabilities of Stable Diffusion and both reference and target images to extract multi-scale features and self-attention maps to enhance feature representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 460, + 430, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 430, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 430, + 472 + ], + "type": "text", + "content": "3.4. In-Context Similarity" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 479, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 598 + ], + "type": "text", + "content": "In-context similarity plays a key role in our model, because the quality of inferred alpha mattes highly depends on the output of this module. In particular, the in-context similarity module is designed to identify the potential target foreground taking the reference RoI into account, thereby guiding the prediction of the target alpha matte. According to our observations, both the reference-target similarity and target-target similarity matter for locating the potential target foreground. These correspond to the proposed inter-similarity and intra-similarity sub-modules." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "content": "Observation. The core challenge in in-context matting is a semantic correspondence problem. Given Stable Diffusion being the feature extractor, one can associate points of the foreground areas between the reference and target images using the emergent feature correspondence. However, due to the inherent reference-target foreground difference, a rigorous one-to-one mapping of all points between the two areas is unfeasible. There would always be some unmatched outliers, resulting in holes in the matting target" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3714" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 71, + 278, + 123 + ], + "blocks": [ + { + "bbox": [ + 62, + 71, + 278, + 123 + ], + "lines": [ + { + "bbox": [ + 62, + 71, + 278, + 123 + ], + "spans": [ + { + "bbox": [ + 62, + 71, + 278, + 123 + ], + "type": "image", + "image_path": "5cb36e307577021a8ea3a8022752051a5b79a799cd770b3826a4ac9a57128b43.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 96, + 125, + 238, + 135 + ], + "lines": [ + { + "bbox": [ + 96, + 125, + 238, + 135 + ], + "spans": [ + { + "bbox": [ + 96, + 125, + 238, + 135 + ], + "type": "text", + "content": "(a) Outliers in point to point correspondence" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 57, + 144, + 282, + 219 + ], + "blocks": [ + { + "bbox": [ + 57, + 144, + 282, + 219 + ], + "lines": [ + { + "bbox": [ + 57, + 144, + 282, + 219 + ], + "spans": [ + { + "bbox": [ + 57, + 144, + 282, + 219 + ], + "type": "image", + "image_path": "85b74aa009b87d04cea9fac38b20123341b6f43b8e8cf74f99d221e76a435937.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 224, + 233, + 234 + ], + "lines": [ + { + "bbox": [ + 121, + 224, + 233, + 234 + ], + "spans": [ + { + "bbox": [ + 121, + 224, + 233, + 234 + ], + "type": "text", + "content": "(b) Self-attention of random points" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 238, + 278, + 248 + ], + "lines": [ + { + "bbox": [ + 55, + 238, + 278, + 248 + ], + "spans": [ + { + "bbox": [ + 55, + 238, + 278, + 248 + ], + "type": "text", + "content": "Figure 3. Observations on the inter- and intra similarities." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 270, + 238, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 238, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 238, + 281 + ], + "type": "text", + "content": "area of the target image, as illustrated in Fig. 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 283, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 437 + ], + "type": "text", + "content": "Since only a subset of points are matched, the goal is changed to how to expand these matched points to cover the entire target foreground area. To address this, we look for other points sharing similar semantic meaning with this subset of points. Intra-image similarity is therefore considered. Intuitively, the self-attention maps from Stable Diffusion reflect the similarities between different image patches. As shown in Fig. 3, by randomly sampling a small number of points from the target area and simply summing over the corresponding self-attention maps, the whole target foreground can be revealed. Based on this observation, we use the self-attention maps as intra-image information to supplement the inter-image matching results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": "Inter-Similarity. Formally, given features " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_l^r\\} ^L" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_l^t\\} ^L" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " extracted from the reference image " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "I_{r}" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " and the target image " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": ", respectively, the layer with the best correspondence capability is selected following DIFT [33], denoted by " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{inter}}^r" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " for the reference and " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{inter}}^t" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " for the target. Then, features corresponding to the RoI " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{RoI}}" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{inter}}^r" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " are extracted and formulated as the in-context query " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "\\{Q_k\\} ^K" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " is the length of the query. " + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "inline_equation", + "content": "Q_{k}" + }, + { + "bbox": [ + 47, + 443, + 287, + 541 + ], + "type": "text", + "content": " takes the form" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 137, + 551, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 551, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 137, + 551, + 287, + 564 + ], + "type": "interline_equation", + "content": "Q _ {k} = R (k), \\tag {2}", + "image_path": "402ea06ad22840f54a97d7396d545c36f662ff2a6314823249b0684027110dfb.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 123, + 574, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 574, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 123, + 574, + 287, + 587 + ], + "type": "interline_equation", + "content": "R = \\mathcal {F} _ {\\text {i n t e r}} ^ {r} \\odot M _ {\\mathrm {R o I}}, \\tag {3}", + "image_path": "f96f7a9c493cab9b77d1f79ab1adab50b5c4659be971d71c3814e5ed3e59ff22.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": " is the element-wise product and " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "R(k)" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": "-th non-zero element of " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": ". Further, " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\{Q_k\\}^K" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": " is used to compute similarity with " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{inter}}^t" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": ", identifying regions on " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": " that correspond to the RoI of " + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "inline_equation", + "content": "I_r" + }, + { + "bbox": [ + 47, + 593, + 287, + 642 + ], + "type": "text", + "content": ", formulated as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 100, + 650, + 287, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 650, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 100, + 650, + 287, + 680 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {k} = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {k} \\cdot F _ {\\text {i n t e r}} ^ {t}}{\\sqrt {d}}\\right). \\tag {4}", + "image_path": "bfbe185f862ea619fa2c9f5c1a06ea67d2415b4af49727820486ca3aa31ac29e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The similarity map is denoted by " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\{S_k\\}^K" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": ", and the mean of all such similarity maps yields " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": ", which measures the" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "degree of similarity between different locations on " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " and the RoI in " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "I_{r}" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": ", serving as the first intermediate output of in-context similarity." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": "Intra-Similarity. As noted in our observations (Fig. 3), " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": " is typically sparse. Although the target matting region on " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": " is partially covered by " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": ", it is insufficient to guide alpha prediction. Here we further design the intra-similarity sub-module to leverage the internal similarity within " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": " to propagate " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": " into a more precise representation of the RoI on " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": ". During feature extraction of " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": ", self-attention maps " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{A}_l\\}^L" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": " representing its internal similarity are also retained, serving as the input for intra-similarity. This sub-module uses " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": " as a weight to the self-attention maps, thereby generating guiding information that accurately represents the matting target on " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "inline_equation", + "content": "\\{S_l'\\}^L" + }, + { + "bbox": [ + 305, + 112, + 546, + 269 + ], + "type": "text", + "content": ". Mathematically, the intra-similarity matching is expressed by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 394, + 277, + 545, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 277, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 394, + 277, + 545, + 291 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {l} ^ {\\prime} = \\mathcal {A} _ {l} \\odot \\mathcal {S}. \\tag {5}", + "image_path": "3e34f12aae0aebc0f645f33161352989271b1ec7d7bdb677ab7482ba55e510d2.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 298, + 394, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 394, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 394, + 312 + ], + "type": "text", + "content": "3.5. Matting Head" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 317, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 317, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 317, + 545, + 365 + ], + "type": "text", + "content": "The success of ViTMatte [40] implies that the information of original image is important during decoding. Following this practice, in our matting head, the original image is concatenated and decoded with outputs from previous modules." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 365, + 546, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 546, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 546, + 521 + ], + "type": "text", + "content": "The guidance map from the in-context similarity module and the intra-features from the backbone are merged and refined using a convolutional feature fusion block, including a series of convolution, normalization, and activation layers. The output multi-scale in-context features are progressively merged using a series of fusion layers which comprise upsampling, concatenation, convolution, normalization, and activation layers. Then, following ViTMatte [40], details from the original image are extracted and combined with the merged feature in a detail decoder, enhancing the details of alpha matte. This matting head effectively melds contextual information with original image details, yielding the generation of a highly precise and refined alpha matte." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 528, + 463, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 463, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 463, + 540 + ], + "type": "text", + "content": "3.6. Reference-Prompt Extension" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 546, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 617 + ], + "type": "text", + "content": "In addition to the mask prompts, points and scribbles can also be transformed into RoI masks. However, these prompts yield less comprehensive in-context queries compared with mask prompts. To enhance them, we propose an extension of reference prompt to enrich the in-context queries derived from point and scribble prompts." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Since the self-attention maps from the backbone reflect the similarities across regions, we leverage the attention maps of the reference images to expand the RoI mask. This is achieved by including regions in the attention maps that are similar to the prompt locations. Specifically, for each prompt point, the top " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " points with the highest responses in their corresponding attention maps are integrated into the RoI mask additionally, thus enriching the in-context query." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3715" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 286, + 143 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 143 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 143 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 143 + ], + "type": "image", + "image_path": "009de63291823e756df212ca9c836574bccae0b66181568f26270ae959bd3d98.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 152, + 288, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 152, + 288, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 288, + 198 + ], + "type": "text", + "content": "Figure 4. ICM-57 examples. The dataset encompasses foreground subjects including human, animals, plants, and various common objects. It contains both instances from the same category and the same entity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 218, + 179, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 179, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 179, + 232 + ], + "type": "text", + "content": "4. Results and Discussion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 239, + 110, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 110, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 110, + 251 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 258, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 378 + ], + "type": "text", + "content": "To facilitate in-context matting, we establish a hybrid training set, along with a test set, ICM-57. The existing AIM-500 dataset was also reorganized to meet the testing requirements of in-context matting. In particular, in-context matting requires to organize images into groups where the annotated foregrounds share categories or instances. Such organization allows for random selection of reference and target images within groups during training. In the test set, one or more images in each group are designated as reference images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": "Mixing In-Context Training Sets. We selected the RM1K dataset [36]. However, such a dataset was insufficient for training. Therefore, a subset of the Open Images dataset [8], focusing on image segmentation, was also employed. The two formed a mixed training set tailored to in-context matting. Both datasets were reorganized." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "content": "For the RM-1K dataset, we divided it into 222 groups. A subset of 14,000 images from the Open Images dataset were chosen as well. In the original dataset, each image came with one or more annotations for image segmentation; each corresponds to an object instance. We aggregated these annotations by category, ensuring that the annotations include all instances of the corresponding category. They subsequently formed context groups that met the requirements of in-context matting. As a result, a mixed training set of 15,000 images and 450 groups was created." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 288, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 288, + 722 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 288, + 722 + ], + "type": "text", + "content": "ICM-57 Testing Set. To assess the performance of our model, we constructed the first testing dataset for in-context matting, named ICM-57, which comprises 57 image groups that form various real-world contexts. This dataset was created by using the instance-segmented dreambooth dataset [28], to which we supplemented high-precision alpha matte annotations. Additionally, we reviewed the existing AIM-500 dataset, selected a subset, and categorized these into groups according to their classes to supplement the in-category groups. Examples of the testing set are shown in Fig 4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 547, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 109 + ], + "type": "text", + "content": "AIM-500. We also report performance on the AIM-500 dataset [10]. This enables us to compare our matting model with other public matting results on this dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 118, + 440, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 118, + 440, + 131 + ], + "spans": [ + { + "bbox": [ + 305, + 118, + 440, + 131 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 136, + 546, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 136, + 546, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 136, + 546, + 220 + ], + "type": "text", + "content": "Architecture. We employ the U-Net architecture from Stable Diffusion v2-1-v [26]. For feature extraction, the time step of the diffusion process is set to " + }, + { + "bbox": [ + 304, + 136, + 546, + 220 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 304, + 136, + 546, + 220 + ], + "type": "text", + "content": " by default, with an empty string used for conditional input. U-Net has 11 decoder blocks; we extract feature maps from the 5-th, 8-th, and 11-th blocks as the intra-features and ones from the 5-th block as the inter-features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "type": "text", + "content": "Training Details. We employ distinct loss functions for matting and segmentation, respectively. For matting, we use a combination of " + }, + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "type": "text", + "content": " loss, Laplacian loss, and Gradient loss. For segmentation, we only use the " + }, + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 228, + 546, + 323 + ], + "type": "text", + "content": " loss. To leverage the segmentation dataset while reducing the impact of imprecise edge annotations, we adopt the approach from HIM [31] that only backpropagates the loss from the confident areas." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 324, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 397 + ], + "type": "text", + "content": "During training, the learning rate is set to 0.0004 and the batch size is 8. The input images are randomly cropped to a size of " + }, + { + "bbox": [ + 304, + 324, + 547, + 397 + ], + "type": "inline_equation", + "content": "768 \\times 768" + }, + { + "bbox": [ + 304, + 324, + 547, + 397 + ], + "type": "text", + "content": " pixels. To prevent deviation from the pretrained model space in modeling real images, no additional data augmentation is used. We train IconMatting for 20,000 iterations using the AdamW optimizer." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 404, + 546, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 546, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 546, + 453 + ], + "type": "text", + "content": "Evaluation. We employ the four widely used matting metrics: SAD, MSE, Grad and Conn [25]. Lower values imply higher-quality matts. In particular, MSE is scaled by a factor of " + }, + { + "bbox": [ + 304, + 404, + 546, + 453 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 404, + 546, + 453 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "type": "text", + "content": "To reduce randomness, each method is tested for three rounds, where the metrics were averaged. For each group of images, the reference inputs were fixed and consistently used. This minimizes the variations in reference inputs, allowing for a more scientific and reliable assessment." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 521, + 391, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 391, + 534 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 391, + 534 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 541, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 545, + 635 + ], + "type": "text", + "content": "Comparison with In-Context Segmentation Models. To explore the effectiveness and superiority of our model, we selected SegGPT [35] and SEEM [45], which also operates under in-context learning, as baselines in the image segmentation domain. From Table 2, on the ICM-57 and AIM-500 datasets, under the same experimental setup (one mask per group of images), our model significantly outperforms the baselines across all metrics." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 637, + 547, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 637, + 547, + 722 + ], + "spans": [ + { + "bbox": [ + 304, + 637, + 547, + 722 + ], + "type": "text", + "content": "It is important to note that due to their distinct task setting (i.e., segmentation rather than matting), the lack of high-quality annotations (e.g., alpha mattes) and the methods (i.e., mask classification rather than alpha matte regression), most of these models have overlooked pixel-level text-semantic alignment and are unable to produce fine-grained masks, as illustrated in Fig. 5." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + 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Qualitative results of different image matting methods. 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MethodICM-57AIM
MSESADGRADCONNMSESADGRADCONN
SegGPT0.019838.8128.6118.610.039142.6541.9526.69
SEEM0.029264.2837.5423.640.0425114.2374.5174.32
Ours0.008119.1218.6511.210.006218.6515.5110.98
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Automatic matting methods such as LF [44] and AIM [10] lack specific auxiliary information about the matting target, often produce poor alpha mattes, showing a significant performance gap compared with our model. MGM [42] and MGMiW [23] use a mask for each image as auxiliary input to specify the matting target. Although our method simplifies this by requiring only one mask per group of images, it still outperforms MGM in various metrics. VitMatte [40], a trimap-based image matting method, necessitates manually annotating a trimap for the foreground of each image, making it the performance upper bound for our in-context matting. Nevertheless, the performance of IconMatting is on par with VitMatte, underscoring its efficacy and competitiveness in image matting." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "Comparison with Interactive Matting Models. Recently, with the advent of SAM, some researchers have designed interactive matting models, such as MatAny [41] and MAM [13], based on this generic image segmentation model. Inspired by this, we also designed an In" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "content": "Context Matting Pipeline (ICMP) with three stages: correspondence, segmentation, and matting, serving as one of the baselines. ICMP is a combination of existing models, with details available in supplementary materials." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "content": "For MatAny and MAM, we compare them under three types of interactions: points, scribbles, and masks. On the ICM-57 testing dataset, both baselines receive interaction information for each image within a group, whereas IconMatting only receive interaction information from one image in the group to indicate the matting target. Despite reducing the amount of human interaction, IconMatting achieves slightly better performance over the baselines." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "content": "Limited by the interaction modalities in ICMP, our model is only compared with it under the point interaction setting. Our end-to-end model outperforms the combined ICMP. In ICMP, the cues for the matting target degrade to points during the correspondence phase of the pipeline, often resulting in sparse information, making our end-to-end approach more effective." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 575, + 400, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 400, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 400, + 588 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Different Modules. To validate different modules, we conducted ablation studies in Table 5. Among the four components, the presence or absence of inter- and intrasimilarity plays a crucial role in performance. Without intra-similarity, the performance of the model significantly worsens across all four metrics. If both inter- and intrasimilarity are absent, the model degenerates to directly predicting the alpha matte from the image, losing the information source for the specified matting target, and thus the performance markedly deteriorates." + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3717" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 547, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 190 + ], + "type": "table", + "html": "
MethodGuidanceICM-57AIM
MSESADGRADCONNMSESADGRADCONN
MGM1 mask per image0.034184.2561.8430.210.026871.9123.3721.97
VitMatte1 trimap per image0.003016.1614.2811.140.003818.7914.2212.47
MGMiW1 mask per image----0.003016.7214.6812.02
LFauto0.0811205.6869.53195.630.0667191.7464.51181.26
AIMauto0.026565.0755.5625.740.018348.0947.5821.74
Ours1 mask per group of images0.008119.1218.6511.210.006218.6515.5110.98
", + "image_path": "e41292dbd4b9234e3ef3577a14ebc4b40f719103b84eaf034f5b948b0e51537b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 224, + 286, + 309 + ], + "blocks": [ + { + "bbox": [ + 143, + 194, + 449, + 205 + ], + "lines": [ + { + "bbox": [ + 143, + 194, + 449, + 205 + ], + "spans": [ + { + "bbox": [ + 143, + 194, + 449, + 205 + ], + "type": "text", + "content": "Table 3. Comparison with automatic and auxiliary input-based matting models." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 224, + 286, + 309 + ], + "lines": [ + { + "bbox": [ + 48, + 224, + 286, + 309 + ], + "spans": [ + { + "bbox": [ + 48, + 224, + 286, + 309 + ], + "type": "table", + "html": "
MethodIn-contextPointScribbleMask
MSESADMSESADMSESAD
MatAnyX0.0651129.670.0512115.210.041295.26
MAMX0.014941.230.014140.230.010929.65
ICMP✓0.011239.65----
Ours*X0.006115.280.005915.970.002915.28
Ours✓0.012423.210.010524.560.008119.12
", + "image_path": "2e11b009d8b834e757f8c981181d90eb57fe9bc96fad69ec46746fd8eda600ab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 391, + 288, + 460 + ], + "blocks": [ + { + "bbox": [ + 46, + 313, + 288, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 380 + ], + "type": "text", + "content": "Table 4. Comparison with interactive matting models. In the penultimate row, our method is provided with guidance information for every image, reducing to an auxiliary input-based method. Our method outperforms automatic methods and some of the auxiliary input-based methods, and its performance is comparable to that of the trimap-based method, VitMatte." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 391, + 288, + 460 + ], + "lines": [ + { + "bbox": [ + 48, + 391, + 288, + 460 + ], + "spans": [ + { + "bbox": [ + 48, + 391, + 288, + 460 + ], + "type": "table", + "html": "
INTERINTRAMFSDMSESADGRADCONN
✓✓✓✓0.008119.1218.6511.21
✓X✓✓0.009924.1520.3612.11
XX✓✓0.031540.3231.5619.53
✓✓X✓0.005423.6921.9614.52
✓✓✓X0.007118.5619.5412.61
", + "image_path": "2707e25f2bf44379f710fd907226c5157ff2c83c87305b59384b39ff9af07545.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": "Number of Reference Inputs. Intuitively, the more reference inputs there are, the more likely the model is to identify the corresponding matting target. We explored the impact of the number of reference inputs on the performance of our model, as shown in Table 6. On ICM-57 test set, the performance improves as the number of reference inputs increases; however, the improvement almost ceases when the number of reference inputs increases from 3 to 4. Therefore, we can conclude that appropriately increasing the number of reference inputs can enhance model performance, which is consistent with intuition." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 234, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 234, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 234, + 673 + ], + "type": "text", + "content": "4.5. Extension to Video Object Matting" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "The technique of in-context matting is easily extendable to video object matting. The key is to use a frame of the video as a reference. For example, an object is marked in the first" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 319, + 224, + 531, + 275 + ], + "blocks": [ + { + "bbox": [ + 46, + 464, + 287, + 499 + ], + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 499 + ], + "type": "text", + "content": "Table 5. Ablation study on different modules. INTER, INTRA, MF, and SD respectively stand for inter-similarity, intra-similarity, multi-scale features, and segmentation dataset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 224, + 531, + 275 + ], + "lines": [ + { + "bbox": [ + 319, + 224, + 531, + 275 + ], + "spans": [ + { + "bbox": [ + 319, + 224, + 531, + 275 + ], + "type": "table", + "html": "
#ReferenceMSESADGRADCONN
10.008519.5819.1412.61
20.007516.5718.5211.15
30.007015.4817.5610.56
40.006815.2317.0210.28
", + "image_path": "79268cb670b29090161520993203ab0df095b59c34686ed8bc4f6cd51b1ed611.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 277, + 538, + 289 + ], + "lines": [ + { + "bbox": [ + 313, + 277, + 538, + 289 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 538, + 289 + ], + "type": "text", + "content": "Table 6. Ablation study on the number of reference inputs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 313, + 307, + 537, + 437 + ], + "blocks": [ + { + "bbox": [ + 313, + 307, + 537, + 437 + ], + "lines": [ + { + "bbox": [ + 313, + 307, + 537, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 307, + 537, + 437 + ], + "type": "image", + "image_path": "145d452896a228b118346bd663fe9d69594195a370dbfa271c7ab48186638b62.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 441, + 511, + 453 + ], + "lines": [ + { + "bbox": [ + 341, + 441, + 511, + 453 + ], + "spans": [ + { + "bbox": [ + 341, + 441, + 511, + 453 + ], + "type": "text", + "content": "Figure 6. Extension to video object matting." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 473, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 522 + ], + "type": "text", + "content": "frame of a video, which serves as a reference input and all frames of the video are treated as target images. With this setup, the model for in-context matting can predict the alpha matte for each frame of the video, visualized in Fig. 6." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 540, + 379, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 379, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 379, + 552 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 562, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 545, + 671 + ], + "type": "text", + "content": "In this work, we introduce 'in-context matting', which enables automatic matting of foreground of interest on target images given a reference image and its prompt. We introduce IconMatting as a preliminary solution. Extensive experiments have shown its efficacy and robustness across categories and scenes. Being the first work introducing this task, we believe it opens new possibilities for efficient and accurate image matting while reducing user effort, also enhancing the versatility of image matting techniques." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work is supported by the National Natural Science Foundation of China under Grant No. 62106080." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3718" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. 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"images/eedea0ffbdcbbe8571a4abf174bf927eb27998fdaab89a5b4b6c819c219225a3.jpg", + "image_caption": [ + "Surprised" + ], + "image_footnote": [], + "bbox": [ + 357, + 359, + 480, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a2d085ef7d6771436797adf9b35c632d10c70a87fbaa2f7489df4f080e3be29f.jpg", + "image_caption": [ + "Less smile" + ], + "image_footnote": [], + "bbox": [ + 357, + 465, + 483, + 561 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/87c0a33c5954b7689462a14cd3a34e69e161181612c86934ba72b5259571cd24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 565, + 483, + 662 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f6fcb35947ab3accfafa91c6f54c726dac030b051f6508beda7eee7d8ebd4d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 252, + 612, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b4079fca83051792aaa8ba6779ae9e6f4f5ad3299b016f224854c47351732a41.jpg", + "image_caption": [ + "Younger" + ], + "image_footnote": [], + "bbox": [ + 491, + 359, + 612, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/826eb0ba359be3303f42532643b18d9955f4fd67b238de973bc3515d255eac7d.jpg", + "image_caption": [ + "Blond" + ], + "image_footnote": [], + "bbox": [ + 486, + 465, + 625, + 561 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/94fcbb07595ee65e389e77ef967f2f1b6f925877d6c33e5071506c6b11ceb549.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 564, + 625, + 662 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6fc85c01210241e4b4a55a34dbb7fdb2da84a0d0c37c71bdc52cf790a630cae8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 252, + 746, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cd42b860f870df6042f4c64213a622bec0668c9e582ecf14d498dd20d138af8d.jpg", + "image_caption": [ + "Elsa" + ], + "image_footnote": [], + "bbox": [ + 625, + 359, + 746, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/647e0a7ab53d17b5338f0b169ed842ade59e239b166a81ba1a1974c36fa2e3c2.jpg", + "image_caption": [ + "Elsa" + ], + "image_footnote": [], + "bbox": [ + 630, + 465, + 758, + 561 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4fe9fc65cf277ba1a0a996311f9084b9581e99767913ecce3cb0ba0dc5f13c5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 565, + 759, + 662 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/71771b4f042e34e0979ac2b389a5e27b827d178889c1630d71f1fccdb21d3853.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 252, + 880, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8ec2340437ebd852630fd869039abae6a1c0d6d3f2e13dbbcdc4ee25a9f5b693.jpg", + "image_caption": [ + "OD Removal" + ], + "image_footnote": [], + "bbox": [ + 759, + 359, + 880, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b681712ad578de8daaa68119a055207c6a2a81b309e4f0aa341e621458b3af1b.jpg", + "image_caption": [ + "OOD Removal" + ], + "image_footnote": [], + "bbox": [ + 759, + 465, + 892, + 561 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5bdca1810f7b3a4c2df0a3f012be88dc651770f84c46051cbd5dbb368ded9b8d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 565, + 890, + 662 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/78c7cba190e6e91c39a9deeb798dfb06df31e05734b9340144ff9d6b8719699d.jpg", + "image_caption": [ + "Figure 1. Semantic editing for out-of-distribution data. We present a method for reconstructing and editing an out-of-distribution (OOD) image or video using a pre-trained 3D-aware generative model (EG3D [10]). Our method explicitly models and reconstructs the occluders in 3D, allowing faithful reconstruction of the input while preserving the semantic editing capability. Here we showcase the reconstruction and editing results \"Less smile\", \"Younger\", \"Blond\" [47], \"Elsa\", \"Surprised\" [41]. Our method can also remove the OOD part. Data are from the Internet (Creative Commons)." + ], + "image_footnote": [], + "bbox": [ + 75, + 569, + 218, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 750, + 313, + 766 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D-aware GANs offer new capabilities for view synthesis while preserving the editing functionalities of their 2D counterparts. GAN inversion is a crucial step that seeks the latent code to reconstruct input images or videos, subsequently enabling diverse editing tasks through manipulation of this latent code. However, a model pre-trained on a particular dataset (e.g., $FFHQ$ ) often has difficulty re", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "constructing images with out-of-distribution (OOD) objects such as faces with heavy make-up or occluding objects. We address this issue by explicitly modeling OOD objects from the input in 3D-aware GANs. Our core idea is to represent the image using two individual neural radiance fields: one for the in-distribution content and the other for the out-of-distribution object. The final reconstruction is achieved by optimizing the composition of these two radiance fields with carefully designed regularization. We demonstrate that", + "bbox": [ + 496, + 752, + 893, + 888 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "Single Image Input", + "bbox": [ + 57, + 301, + 76, + 401 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7225", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "our explicit decomposition alleviates the inherent trade-off between reconstruction fidelity and editability. We evaluate reconstruction accuracy and editability of our method on challenging real face images and videos and showcase favorable results against other baselines. More results can be found at https://in-n-out-3d.github.io/.", + "bbox": [ + 73, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 210, + 207, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GAN inversion [3, 44, 55, 61, 70] is a set of techniques that project an input image onto the latent space of a pretrained GAN to obtain a latent code so that the image generator can reconstruct the input. This is particularly useful as one could perform various creative semantic editing tasks [18, 24, 41, 47] for images. Similar techniques have also been applied in the video domain, with which recent methods also achieved temporally consistent editing [57, 63]. However, the majority of these methods are effective primarily with 2D GANs, and they fall short in offering explicit 3D controllability, such as view synthesis capabilities. With the rapid recent advancements in 3D reconstruction, especially in neural radiance fields (NeRFs) [6, 11, 36, 37], high-quality 3D-aware GANs [10, 22, 40, 49] have emerged as a powerful tool for learning 3D generation from 2D images. 3D-aware GANs, equipped with a 3D representations like NeRFs [10, 22] or SDF [40], offer explicit control over camera views and ensure 3D geometric consistency in generation. Additionally, they retain the generative capacity and editability of 2D GANs [26-29]. This enables applications such as novel view synthesis, semantic image editing [31, 48, 51, 62, 66, 67] and video editing [17, 56].", + "bbox": [ + 75, + 237, + 468, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Core challenges. While state-of-the-art 3D GAN inversion methods achieve remarkable advances in both image and video editing for human faces, they face challenges when dealing with images including out-of-distribution (OOD) objects (e.g., heavy make-ups or occlusions). This limitation arises primarily because these models are pre-trained only on natural faces without complex textures or substantial occlusions. As a result, the editability performance deteriorates when a pre-trained GAN is forced to model OOD objects in the GAN inversion process. This is commonly known as the reconstruction-editability trade-off [55]. Existing GAN inversion methods assume that a single latent code corresponding to the input image can be found in the latent space [50, 61] through optimization once the model is trained. Therefore, they aim to reconstruct the indistribution (InD) content (e.g., natural face) and the OOD objects together. However, OOD components often cannot be well modeled in a pre-trained GAN, and consequently cannot be well represented with it using a single latent code, existing methods either cannot reconstruct them faithfully [51] or can reconstruct them (e.g., through fine-tuning the generator) but alters the latent space properties and de", + "bbox": [ + 75, + 571, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/01669d708f68f1831a53337352a79b2f2ddce9310947c2ad34bca065ec97a007.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 87, + 625, + 183 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a850c6ab7d5cf9ec4cd20be724289498d9defe16435b0ba5473ebdb675ec5e3a.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 500, + 183, + 625, + 280 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/42cbb6846d737fca4961c1165290a40830c78466bf8c9be160c010f5ed122de8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 88, + 767, + 183 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1ee3a65bafa226154da39acd8c17bae8362db3336bf8a1a60c763c06465413f1.jpg", + "image_caption": [ + "GOAE [67]" + ], + "image_footnote": [], + "bbox": [ + 625, + 183, + 766, + 280 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f258d29636e5310715e878e0b3dd0d9fa14209dc6e23a3834824e05fee13e771.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 88, + 890, + 183 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/46369bb1b87c2677840dcf3f8b20e9c36456f35a04b7e94e692ca5f3aad3f1a6.jpg", + "image_caption": [ + "PTI [45]", + "Figure 2. Limitations of the previous methods. Existing GAN inversion techniques cannot deal with frames with OOD elements, resulting in a poor reconstruction-editing balance." + ], + "image_footnote": [], + "bbox": [ + 767, + 183, + 890, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GOAE [67] can produce faithful editing, but fails to preserve the identity of the input face. PTI [45] provides higher reconstruction fieldity, but the edibility suffers.", + "bbox": [ + 500, + 345, + 888, + 386 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "teriorates the editability [45] (Figure 2).", + "bbox": [ + 500, + 397, + 764, + 412 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work. We propose a new approach to address this issue by drawing inspiration from recent composite volume rendering works that compose multiple radiance fields during rendering [19, 34, 59, 64]. Our core idea is to decompose the 3D representation of an image with OOD components into an in-distribution (InD) part and an out-of-distribution part, and compose them together to reconstruct the image in a composite volumetric rendering manner. We use EG3D [10] as our 3D-aware GAN backbone and leverage its tri-plane representation to model this composed rendering pipeline. For the InD component (i.e. natural face), we project pixel values onto EG3D's $\\mathcal{W}+$ space for an InD component reconstruction. We further introduce an additional tri-plane to represent the OOD content. After that, we combine these two radiance fields in a composite volumetric rendering to reconstruct the input frames. During the editing stage, we perform the latent code based editing solely on the InD part and leave the OOD component unaltered. This framework would allow the applications of any StyleGAN-based editing approache [41, 47] on the InD component such as changing facial expression, which is often desirable for user experiences. The advantages of our work are three-fold: a) we achieve a higher-fidelity reconstruction by composition of InD and OOD components; b) we retain the editability of pre-trained GANs by editing only the InD content; and c) by leveraging 3D-aware GANs, we can render the face from novel viewpoints.", + "bbox": [ + 496, + 417, + 892, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our method on challenging in-the-wild face images and videos (Creative Commons), demonstrating improvement over previous state-of-the-art GAN inversion work on both reconstruction and editing quality. In addition, we demonstrate the usefulness of our method with", + "bbox": [ + 496, + 825, + 893, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7226", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D-aware editing applications, including semantic editing, novel view synthesis, and OOD object removal.", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We will release the code and data used in the paper.", + "bbox": [ + 96, + 121, + 437, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our contributions. In summary, our contributions are:", + "bbox": [ + 76, + 141, + 447, + 156 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a 3D-aware GAN inversion approach to manipulate single images or monocular videos with out-of-distribution objects (e.g., accessories and heavy makeup). See results in Figure 1.", + "- We incorporate composite volume rendering into 3D-aware GAN inversion.", + "- Our method reconstructs 3D shapes of faces with OOD objects faithfully and demonstrates novel 3D-aware applications." + ], + "bbox": [ + 76, + 157, + 468, + 291 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 306, + 217, + 323 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D-aware GANs. StyleGANs [26-29] have achieved high-quality photorealistic 2D image generation and have been successfully applied to various image editing applications [18, 24, 41, 47]. Significant progresses have also been made to lift 2D image generation to 3D space, using various 3D representations, for both higher quality generation and to enable 3D-aware applications such as view synthesis [9, 10, 16, 20, 22, 38, 40, 46, 49, 51]. These methods usually take a two-stage pipeline that renders a raw image (usually also with feature maps) in low resolution and then upsamples the rendered image to high resolution. We leverage EG3D [10] as our generator architecture in this work.", + "bbox": [ + 75, + 338, + 468, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GAN inversion and editing. GAN inversion has been widely studied for 2D GANs. These techniques can largely be categorized as (a) encoder-based methods [4, 8, 33, 39, 44, 44, 54, 55, 55, 58] in which a neural network encoder is trained to project an input image to the latent space of the generator; (b) optimization-based methods [1, 2, 12, 13, 21, 25, 42, 53] where the latent code is recovered via optimizing loss functions between the generator output and a target image; and (c) hybrid methods [5, 7, 45, 71] which combine both approaches. Some recent works have also investigated 3D-aware GAN inversion from a single image [31, 32, 51, 56, 62, 66, 67] or a video [17, 68]. As our experiments demonstrate, previous approaches have difficulty handling these challenging cases. We propose a new mechanism to allow high-quality 3D-aware GAN inversion of out-of-distribution faces even under significant occlusion. With our GAN inversion, we can modify the latent code to perform high-quality semantic image editing [18, 24, 41, 47] or video editing [57, 63, 65].", + "bbox": [ + 75, + 521, + 468, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GAN inversion for out-of-distribution (OOD) data. There have been attempts to invert out-of-distribution data to the GAN's latent space. Early work [1] proposes to project an image onto extended $\\mathcal{W}^+$ space to achieve more accurate reconstruction. PTI [45] finetunes generator with regularization for a lower distortion error. StyleSpace [60]", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "proposes to invert an image using StyleGAN's internal feature maps and tRGB blocks, which shows better reconstruction and disentanglement. Recently, ChunkyGAN [50] proposes to compose multiple generated images from multiple latent codes, with a set of segmentation masks to reconstruct an input image. With a similar goal in mind, we propose to leverage the radiance field of EG3D [10] and decompose the volumetric representation into an in-distribution part and an out-of-distribution part. In contrast to ChunkyGAN [50] that models an image as a collection of $2D$ segments, we model the OOD and face directly in volumetric 3D representation and merge them with composite rendering.", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Composite neural radiance fields. Neural Radiance Fields (NeRFs) [36] have shown impressive view synthesis results. Recently, it has been shown that 3D scenes can be decomposed into different NeRFs. When multiple radiance fields are built, one can compose them together using a composite rendering manner [19, 34, 59, 64]. EG3D [10] uses the tri-plane representation to generate 3D objects from the latent code. We adopt the idea of composite volume rendering to address the out-of-distribution 3D GAN inversion problem. Specifically, we split the in-distribution and out-of-distribution parts in the tri-plane 3D representation and compose them during volume rendering.", + "bbox": [ + 496, + 273, + 890, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. 3D-aware GAN: EG3D", + "text_level": 1, + "bbox": [ + 498, + 468, + 718, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We choose EG3D [10], which consists of a tri-plane representation and a super-resolution (SR) module, as our 3D-aware GAN.", + "bbox": [ + 496, + 493, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural rendering at low resolution. Given a latent code $z \\in \\mathbb{R}^{512}$ (or $w \\in \\mathbb{R}^{14 \\times 512}$ ) and camera parameters $p$ , EG3D first generates a corresponding tri-plane $\\mathbf{T} \\in \\mathbb{R}^{256 \\times 256 \\times 32 \\times 3}$ . For each pixel, a ray $\\mathbf{r}$ is cast, and points are sampled along the ray. Unlike the positional encoding [34, 52] for each point in NeRFs [34], EG3D projects each point onto tri-plane $\\mathbf{T}$ and retrieves features from three planes via bilinear interpolation. These features are then aggregated by summation, and fed into the decoder $D$ (i.e., an MLP) to predict the color and density. Volume rendering [35] is then performed to compute the final color for each pixel. To this end, a raw RGB image with a 32-channel feature in a low resolution (e.g. $128 \\times 128$ ) is generated.", + "bbox": [ + 496, + 542, + 890, + 737 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Super-Resolution (SR). To gain high-resolution outputs, EG3D later uses an SR module that inputs the raw image and the 32-channel feature as the input and yields a high-resolution RGB image (e.g. $512 \\times 512$ ). We build our approach upon EG3D due to its rendering efficiency compared to other alternatives [22, 40].", + "bbox": [ + 496, + 739, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 844, + 589, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an aligned face input image $\\mathbf{I}$ , or a monocular face video $\\mathbf{V} = [\\mathbf{I}_1, \\dots, \\mathbf{I}_t, \\dots, \\mathbf{I}_N]$ with $N$ frames, we aim", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7227", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3b41f43539eace6b6751cfec2bf3e9ca23ca32d8cc22b3603d5d14e69fffcd64.jpg", + "image_caption": [ + "Figure 3. Overview of our method. Given a potrait image or a monocular portrait video, we use two radiance fields to represent (a) in-distribution $(\\text{InD})$ face, and (b) out-of-distribution $(\\text{OOD})$ item. (a) InD reconstruction is the GAN inversion for the in-distribution natural face. We apply GAN inversion by using pre-trained EG3D model $G$ to the frame, where the pre-trained tri-plane generator and tri-plane decoder $D^{I}$ are kept frozen. (b) For OOD item, we propose to model them with a separate radiance field represented by an additional tri-plane $\\mathbf{T}^O$ . During the training process, we optimize the tri-plane $\\mathbf{T}^O$ , a per-frame latent code $\\phi_t$ , and a new decoder $D^O$ . The decoder takes as input tri-plane features $\\mathbf{T}^O$ and $\\phi_t$ and outputs color $\\mathbf{c}^O$ , density $\\sigma^O$ , and blending weight $b$ . (c) Composite Rendering compose the InD and OOD radiance fields together by using a composite rendering scheme (Section 4.3). (d) Finally, we finetune the Super-Resolution module in $G$ to achieve a better output in the high resolution. After training, we can perform various semantic edits and free-view rendering, while preserving the face identity and the OOD components." + ], + "image_footnote": [], + "bbox": [ + 125, + 88, + 838, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to reconstruct the input with EG3D inversion and perform face editing. For simplicity, we use $\\mathbf{I}_t$ to represent a frame, either from a single input image or a sampled frame from a video. If only one frame exists, then $N = 1$ .", + "bbox": [ + 75, + 666, + 470, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We present the high-level overview in Figure 3. We build two neural radiance fields (NeRFs) [36], one for in-distribution (InD) face (Section 4.1), and the other one for out-of-distribution (OOD) object (Section 4.2), using triplane representations [10]. The OOD object, for example, can be a non-face object with a rigid shape or heavy makeup with a complicated texture. Next, we combine two radiance fields (Section 4.3) to reconstruct the low-resolution frame. Finally, we finetune the super-resolution module of EG3D to get the high-resolution output (Section 4.5). After training the radiance fields, we can edit the face image or video", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(Section 4.6).", + "bbox": [ + 500, + 666, + 594, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. In-distribution GAN inversion", + "text_level": 1, + "bbox": [ + 500, + 690, + 767, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Formulation. Since a pretrained EG3D already has prior knowledge of faces, we directly leverage its latent space and perform a regular 3D GAN inversion [32, 61] for the in-distribution part. For a single frame case, we optimize a latent code $w_{t}$ such that it can reconstruct the input frame $\\mathbf{I}_t$ . For a video, we invert all the frames at the same time. Please refer to the supplementary material for more details. For camera parameters $p_t \\in \\mathbb{R}^{25}$ , we obtain them by using an off-the-shelf pose detector [15], following [10, 32].", + "bbox": [ + 496, + 717, + 890, + 851 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Optimization. To represent the InD faces with $\\mathbf{T}^I$ , our insight is to keep the latent code $w_{t}$ in distribution as much as possible. To this end, we use a regularization term to keep", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7228", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$w_{t}$ within its pre-trained distribution through GAN training.", + "bbox": [ + 76, + 90, + 467, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {w} \\left(w _ {t}\\right) = \\left| \\left| w _ {t} - \\bar {w} \\right| \\right| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 119, + 467, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{w}$ is the mean latent code computed over 10,000 sampled latent codes.", + "bbox": [ + 76, + 143, + 467, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also use a another regularization term adopted from [55] to constrain the variation among style vectors in $w$ : $\\mathcal{L}_{\\Delta}(w_t) = \\sum_{i=1}^{13} ||\\Delta_i||_2^2$ , given a latent code $w = (w_0, w_0 + \\Delta_1, \\dots, w_0 + \\Delta_{13}) \\in \\mathbb{R}^{14 \\times 512}$ . This regularization term preserves the editability of the optimized latent code [55].", + "bbox": [ + 76, + 175, + 468, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Modeling out-of-distribution contents", + "text_level": 1, + "bbox": [ + 76, + 279, + 401, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For an OOD object, a pre-trained EG3D usually cannot model it well with its prior distribution. We therefore use an additional tri-plane $\\mathbf{T}^O$ to represent the out-of-distribution content. One additional challenge is that, while dealing with video, the OOD object may not be static across different frames, therefore could not be well reconstructed with a static radiance field. Therefore, in addition to $\\mathbf{T}^O$ , we use a per-frame latent code $\\phi_t \\in \\mathbb{R}^{32}$ for each frame to represent the out-of-distribution object across the temporal domain. Both $\\mathbf{T}^O$ and $\\phi_t$ are randomly initialized from a normal distribution.", + "bbox": [ + 75, + 304, + 468, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Formulation. The out-of-distribution decoder $D^{O}$ takes a tuple $(\\mathbf{T}^{O}(t_{k}),\\phi_{t})\\in \\mathbb{R}^{64}$ as the input, and outputs color $\\mathbf{c}^O\\in \\mathbb{R}^3$ , density $\\sigma^O\\in \\mathbb{R}$ , and blending weight $b\\in [0,1]$", + "bbox": [ + 76, + 473, + 468, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {c} ^ {O}, \\sigma^ {O}, b\\right) = D ^ {O} \\left(\\mathbf {T} ^ {O} \\left(t _ {k}\\right), \\phi_ {t}; \\theta_ {D ^ {O}}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 529, + 468, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{T}^O (t_k)\\in \\mathbb{R}^{32}$ is the aggregated features obtained by projecting 3D coordinate $t_k$ onto each of the three feature planes via bilinear interpolation, then aggregated via summation [10]. The decoder $D^{O}$ is an MLP with weights of $\\theta_{DO}$ . To compute the color of a pixel at time $t$ , we use the volume rendering integral along the ray $\\mathbf{r}$ :", + "bbox": [ + 76, + 558, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} ^ {O} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T \\left(t _ {k}\\right) \\alpha^ {O} \\left(\\sigma^ {O} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {O} \\left(t _ {k}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 652, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T(t_k) = \\exp(-\\sum_{k'=1}^{k-1} \\sigma(t_{k'}) \\delta_{k'})$ , $\\alpha = 1 - \\exp(-x)$ , and $\\delta_k = t_{k+1} - t_k$ is the distance between two 3D points.", + "bbox": [ + 76, + 705, + 467, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Composite volume rendering", + "text_level": 1, + "bbox": [ + 76, + 753, + 334, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Now, with both InD and OOD radiance fields, we can combine them using the blending weight $b$ from Eqn. 2.", + "bbox": [ + 76, + 777, + 467, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Formulation. We compose two radiance fields together by", + "bbox": [ + 76, + 814, + 467, + 828 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {C} ^ {C} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T ^ {C} \\left(t _ {k}\\right) \\left(b \\alpha^ {O} \\left(\\sigma^ {O} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {O} \\left(t _ {k}\\right) \\right. \\tag {4} \\\\ \\left. + (1 - b) \\alpha^ {I} \\left(\\sigma^ {I} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {I} \\left(t _ {k}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 835, + 467, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T^{C}(t_{k}) = \\exp (-\\sum_{k^{\\prime} = 1}^{k - 1}(\\sigma^{O} + \\sigma^{I})\\delta_{k^{\\prime}})$", + "bbox": [ + 500, + 88, + 813, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization. The goal is", + "bbox": [ + 500, + 109, + 684, + 125 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} w_{t}^{*},\\mathbf{T}^{O^{*}},\\theta_{D O}^{*},\\phi_{t}^{*} = \\operatorname *{argmin}_{w_{t},\\mathbf{T}^{O},\\theta_{D O},\\phi_{t}}\\mathcal{L}_{t}^{C} \\\\ = \\operatorname *{argmin}_{w_{t},\\mathbf{T}^{O},\\theta_{D^{O}},\\phi_{t}}\\sum_{ij}||C^{C}(\\mathbf{r}_{ij}) - C^{GT}(\\mathbf{r}_{ij})||_{2}^{2} \\\\ + \\lambda_ {b} \\mathcal {L} _ {b} \\left(\\mathbf {r} _ {i j}\\right) + \\mathcal {L} _ {L P I P S} \\left(\\mathbf {I} _ {L R} ^ {C}, \\mathbf {I} _ {L R}\\right), \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 133, + 890, + 217 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{LPIPS}$ is the LPIPS loss [69], $\\mathbf{I}_{LR}^{C}$ is the composite rendered image at low resolution $(128\\times 128)$ , $\\mathbf{I}_{LR}$ is the ground truth image also at $128\\times 128$ . The weight regularizer $\\mathcal{L}_b$ is adopted from [59], used to penalize the blending weight $b$ if it is not closer to 0 or 1:", + "bbox": [ + 498, + 229, + 890, + 304 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} H _ {b} (b \\left(t _ {k}\\right)), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 316, + 890, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H_{b}(x) = -(x\\log (x) + (1 - x)\\log (x))$ is binary entropy. The reason behind Eqn. 6 is that objects cannot co-occupy the same spatial location. The entropy loss facilitates a cleaner decomposition: encouraging an object to be either in-distribution (i.e. $b\\to 0$ ) or out-of-distribution (i.e. $b\\rightarrow 1$ ).", + "bbox": [ + 498, + 358, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, it is ill-posed to build its 3D geometry accurately, given only a single-frame input, even with a pretrained 3D-aware generator. Therefore, for a single image only, we also introduce a depth regularization term:", + "bbox": [ + 498, + 449, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {D}} = \\left| \\left| \\mathcal {D} ^ {C} - \\mathcal {D} ^ {R e g} \\right| \\right| _ {1} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 518, + 890, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{D}^C$ is the rendering depth map from composite rendering, and $\\mathcal{D}^{Reg}$ is a rescaled depth map from MiDaS [43].", + "bbox": [ + 498, + 547, + 890, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Low-resolution reconstruction", + "text_level": 1, + "bbox": [ + 500, + 588, + 767, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, we jointly optimize for $w_{t}$ (yielding $\\mathbf{T}^{I}$ ), $\\mathbf{T}^{O}$ , $\\theta_{DO}$ , $\\phi_{t}$ , following Section 4.1 to Section 4.3. Our total loss function is", + "bbox": [ + 498, + 609, + 890, + 654 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {L R} = \\sum_ {t = 1} ^ {N} \\mathcal {L} _ {t} ^ {C} + \\lambda_ {\\Delta} \\mathcal {L} _ {\\Delta} + \\lambda_ {w} \\mathcal {L} _ {w} + (\\lambda_ {\\mathcal {D}} \\mathcal {L} _ {\\mathcal {D}}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 664, + 890, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_t^C$ is from Eqn. 4, latent variation regularizer $\\mathcal{L}_{\\Delta}$ from [55], and $\\mathcal{L}_w$ from Eqn. 1, respectively, $\\lambda_{\\Delta}$ is the weight for $\\mathcal{L}_{\\Delta}$ , $\\lambda_w$ is the weight for $\\mathcal{L}_w$ , and $\\lambda_{\\mathcal{D}}$ is the weight for $\\mathcal{L}_{\\mathcal{D}}$ . We only use $\\mathcal{L}_{\\mathcal{D}}$ for single image input.", + "bbox": [ + 498, + 717, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Super-Resolution", + "text_level": 1, + "bbox": [ + 500, + 787, + 668, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After training in Section 4.1, 4.2, 4.3 and 4.4, we can get reconstruction $\\mathbf{I}_{LR}^{C}$ in low resolution $(128\\times 128)$ . We observe that using the pretrained super-resolution (SR) module cannot generate a satisfying high-resolution output, as shown in Figure 4, due to the new OOD tri-plane $\\mathbf{T}^O$ . Therefore, we finetune only the SR module in $G$ for higher resolution", + "bbox": [ + 498, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7229", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bbd8b66ebb236f2e5108aeeecbec65d900d9d29c99be92a79d3134c0af6f28ab.jpg", + "image_caption": [ + "Recon. Target" + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 205, + 185 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/88dc952a5493125ed24d17a25249102f932133e6ee144694bb81163c35a54147.jpg", + "image_caption": [ + "w/o finetuning SR module" + ], + "image_footnote": [], + "bbox": [ + 210, + 88, + 336, + 184 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c2c98ab2b625de9d54d5295e9ed1f70940be2ae30d1f9b517909e6582420e613.jpg", + "image_caption": [ + "w/ finetuning SR module", + "Figure 4. The effect of finetuning SR module. Without finetuning the SR module, the high-resolution output is blurry." + ], + "image_footnote": [], + "bbox": [ + 343, + 88, + 468, + 184 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "at $512 \\times 512$ .", + "bbox": [ + 76, + 265, + 171, + 279 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Optimization. The loss function is that", + "bbox": [ + 76, + 285, + 346, + 300 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {S R} (\\mathbf {x}, \\hat {\\mathbf {x}}) = \\| \\mathbf {x} - \\hat {\\mathbf {x}} \\| _ {2} ^ {2} + \\mathcal {L} _ {L P I P S} (\\mathbf {x}, \\hat {\\mathbf {x}}), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 309, + 468, + 328 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{x} = \\mathbf{I}_t$ and $\\hat{\\mathbf{x}} = SR(\\mathbf{I}_{LR}^C)$", + "bbox": [ + 76, + 338, + 300, + 356 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.6. Editing", + "text_level": 1, + "bbox": [ + 76, + 366, + 171, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After the reconstruction, we can modify the latent code $w_{t}$ to perform various semantic editing tasks. With explicit decomposition, the OOD contents do not interfere with the semantic editing capability of in-distribution components. Here, any existing GAN-based editing approaches can be used. We use InterfaceGAN [47] and StyleCLIP [41].", + "bbox": [ + 75, + 388, + 468, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 494, + 282, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 520, + 266, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. To evaluate how our approach works on data with out-of-distribution components, we collected a dataset of 20 online videos with challenging and diverse appearances. The OOD content contains heavy make-up and occluding objects (e.g. facial masks and large glasses). For the single-image inversion method, we use the first frame of each video. For video inversion, we use all the frames. For the face alignment, we use 3DDFA-v2 [23] to obtain the 68-point landmarks and smooth them across the frames using a sliding window for stabler cropping. After that, we convert the landmarks to EG3D's 5-point landmarks and crop the face out of the input frame.", + "bbox": [ + 75, + 547, + 468, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyperparameters. We use the Adam optimizer [30] for all our experiments. For in-distribution inversion (Section 4.1), we optimize for 200 epochs with a learning rate of $1 \\times 10^{-3}$ , $\\lambda_{\\Delta} = 1 \\times 10^{-3}$ . For the out-of-distribution and composite rendering (Section 4.2, 4.3), we run the optimization for 10,000 iterations with a learning rate of $5 \\times 10^{-3}$ , $\\lambda_{b} = 1$ , $\\lambda_{w} = 1$ , and $\\lambda_{\\mathcal{D}} = 0.1$ if applicable. For the SR module (Section 4.5), we finetune the module for 100 epochs with a learning rate of $1 \\times 10^{-3}$ .", + "bbox": [ + 75, + 731, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We evaluate our approach from 1) reconstruction accuracy and 2) editability to validate the reconstruction-", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "editability trade-off. For the reconstruction accuracy, we report LPIPS [69], PSNR, SSIM and ID similarity [14]. For editability, we follow [45, 50] and evaluate identity preservation after applying the editing direction. More specifically, we use ArcFace [14] to compute the similarity between the inverted and edited results.", + "bbox": [ + 496, + 90, + 890, + 179 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines for evaluation. We compare our method extensively with several previous arts. For optimization-based methods, we compare with HFGI3D [62], PTI [45], $\\mathcal{W}+$ , and $\\mathcal{W}$ optimization. For videos only, we also include VIVE3D [17]. We compare the encoder-based method with GOAE [67] and IDE-3D [51] encoder. We treat $\\mathcal{W}+$ optimization as an ablated version of our method without OOD triplane. The recent work in [56] showcases encoder-based 3D GAN inversion, focusing on real-time inference. However, their method relies on a frozen EG3D and does not explicitly model the OOD components. We do not compare with it as the code is not publicly available.", + "bbox": [ + 496, + 184, + 892, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Quantitative results", + "text_level": 1, + "bbox": [ + 500, + 368, + 687, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Reconstruction. We compare the reconstruction accuracy of our approach with all baselines and report the results in Table 1. For PTI, we first perform a $\\mathcal{W}+$ inversion with a learning rate of $1 \\times 10^{-3}$ and 200 epochs, and then finetune the generator for 200 epochs with a learning rate of $3 \\times 10^{-5}$ . For $\\mathcal{W}+$ and $\\mathcal{W}$ optimization, we use a learning rate of $1 \\times 10^{-3}$ and optimize for 200 epochs. For GOAE and IDE-3D, we use their encoder directly for the inversion.", + "bbox": [ + 496, + 395, + 890, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our approach outperforms other methods on all the evaluation metrics. This indicates that our method produces a more accurate reconstruction with the OOD components.", + "bbox": [ + 496, + 513, + 890, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Editability. We acquire editing directions from InterfaceGAN [47] (\"younger\", \"smile\") and StyleCLIP mapper [41] (\"eyeglasses\", \"surprised\", \"Elsa\"). Following previous work [45, 50], we measure the ID similarity between the inverted image and the edited image, as the editing should not change a person's identity. We report our results in Table 2. Our method outperforms other baselines in terms of identity preservation in most cases.", + "bbox": [ + 496, + 561, + 892, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Qualitative results", + "text_level": 1, + "bbox": [ + 500, + 690, + 676, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inversion. We visually compare the video reconstruction in Figure 5. Our method provides higher-fidelity reconstruction results than other baselines, particularly for OOD regions (e.g., heavy make-up or earrings). Our method shows better reconstruction than the encoder-based method GOAE [67] and IDE-3D [51]. Compared to optimization-based methods, HFGI3D [62], VIVE3D [17], PTI [45], $\\mathcal{W}$ , and $\\mathcal{W}+$ , our method shows higher-fidelity reconstruction for OOD objects (Refer to our supplementary material for more results).", + "bbox": [ + 496, + 717, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Editing. We show a qualitative comparison regarding the editing in Figure 6. Our method shows faithful editing", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7230", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a1cf8f9267c1f3a239e9caa17ace22c49f0ffa5280cce59e8ec5b0b65869af95.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of the video reconstruction. We compare our approach with $\\mathcal{W}+$ and $\\mathcal{W}$ optimization, IDE-3D [51], GOAE [67], HFGI3D [62], VIVE3D [17], and PTI [45]. Our method shows a better reconstruction accuracy on the OOD videos." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 263, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9db79a933db688b3e73a655455bf34e9666baa9bd3cbdcaffa2ab5a19cd72806.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 263, + 89, + 439, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6b7d4352065a3cbbafb3f6fce136a05468f39340beb2e92e2e158d0909afe003.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 439, + 88, + 710, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/640974a9fe30483e175d7f742504032a4bc2bd79ace51f5d8feb9ac9ee8ce29d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 89, + 895, + 193 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c7f9027f8035412068e1a6d6bceb79838cee613cd132d78028553b2052f44bf2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ImagesVideos
LPIPS↓SSIM↑PSNR↑ID Similarity↑Time↓LPIPS↓SSIM↑PSNR↑ID Similarity↑
Ours0.11060.817519.860.96852.68h0.22370.705216.030.9758
HFGI3D [62]0.39120.552111.370.94637.51h0.39540.558711.550.9388
GOAE [67]0.36190.642414.730.968556s0.36420.647014.970.3642
E3DGE [31]0.17090.773815.280.8632-----
VIVE3D [17]----0.59h0.41720.541710.660.9245
PTI [45]0.31920.617212.930.96761.45h0.31440.632013.450.9658
IDE-3D [51]0.50440.43959.180.845677s0.49990.45129.590.8251
W+0.34330.638714.390.91990.49h0.33800.655714.750.9154
W0.40970.561512.080.87570.47h0.40300.578712.480.8652
", + "bbox": [ + 166, + 238, + 805, + 372 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a9b805b9bc35f8ce2eee345a0d4f655d2f9e5d82827941eb77c7f6f2a1213cc0.jpg", + "table_caption": [ + "Table 1. Reconstruction quality evaluation. For each column, deeper color the better." + ], + "table_footnote": [], + "table_body": "
ImagesVideos
eyeglassessurprisedyoungersmileElsaaverageeyeglassessurprisedyoungersmileElsaaverage
Ours.9532.9888.9495.9525.9116.9511.9158.9360.9347.9094.8927.9177
HFGI3D [62].9484.9795.9453.9223.8641.9319.9112.9109.9290.9155.8622.9058
GOAE [67].9179.9306.9327.9332.8851.9199.9120.9224.9235.9221.8641.9088
E3DGE [31]--.8853.9487-0.9170------
VIVE3D [17]------.9078.9475.9183.9369.8728.9167
PTI [45].9114.9562.9380.9410.7927.9079.9049.9357.9319.9336.7945.9001
IDE-3D [51].8811.9538.8723.8055.8780.8781.8767.9481.8551.8662.7871.8666
W+.9012.9567.9248.9356.7892.9015.8971.9249.9290.9170.7968.8930
W.8808.9567.9177.9290.8008.8970.8793.9537.9068.9208.8113.8944
", + "bbox": [ + 109, + 410, + 859, + 545 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "results. For more qualitative results, please refer to our supplementary material.", + "bbox": [ + 75, + 592, + 468, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Other Applications", + "text_level": 1, + "bbox": [ + 76, + 630, + 261, + 646 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "View synthesis. The use of 3D GANs supports rendering novel views after inversion. We show novel view synthesis results in Figure 7.", + "bbox": [ + 75, + 656, + 468, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Object removal. By setting the blending weights of the OOD objects to 0, we can remove OOD objects. We show results in Figure 1.", + "bbox": [ + 75, + 704, + 468, + 750 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0741996c311cedc8e4fb7a850738e715a5e46ab300347bb30e6495df1f5c08e4.jpg", + "table_caption": [ + "Table 2. Identity preservation evaluation. Higher numbers indicate better identity preservation. $\\mathcal{W} +$ is equivalent to our method without OOD tri-plane." + ], + "table_footnote": [], + "table_body": "
InversionEditing
L2↓LPIPS↓ID similarity↑
w/o Lb0.03220.21910.9070
w/o Lw0.03360.22380.9024
Full method0.03390.22370.9177
", + "bbox": [ + 135, + 761, + 411, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation study. We study the effect of different loss functions on 20 videos. For inversion, we compute the metrics between reconstructed frames and input frames. For editing, we compute the ID similarity between before and after editing.", + "bbox": [ + 75, + 844, + 457, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 590, + 653, + 607 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We introduce two new loss functions, Eqn. 1 and Eqn. 6, to preserve the editability from the impact of the OOD radiance field in Section 4.3. To validate the loss functions' effects, we conduct an ablation study in Table 3. Without the weight regularization, $\\mathcal{L}_b$ , and latent code regularizer $\\mathcal{L}_w$ , the reconstruction accuracy is improved while the editability is reduced. One of the reasons is that GAN-based editing usually also brings unwanted changes to other attributes [47]. In Figure 8, the editing direction \"eyeglasses\" also moves the position of the eyes. At this time, if the blending weight $b$ is closer to 1 for pixels outside the OOD object, i.e. the OOD part has more contributions, the editing tends to keep the pixel values in the reconstruction stage. While the eyes will be moved due to the editing direction, it results in the duplicate eyes in Figure 8(a). In contrast, with regularization (Eqn. 1 and Eqn. 6) on the blending weights, pixels in the in-distribution part contribute more to the output, which better supports the editing since we can only edit the in-distribution part. Similar cases happen to $\\mathcal{L}_w$ . With", + "bbox": [ + 496, + 614, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7231", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/786be30cf6817752286a74b54afcc0080be941283d47bbd629c86ea38a8ad006.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of the editing. We compare our editing results from a single image and a video with other baselines, with different editing latent directions \"Eyeglasses\". Our approach can preserve the original appearance details better, and shows improved editability over other baselines." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 893, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9e3f0cdbbdb73030d7bb333c4d3148c7abe8bf52ed9a99d6b8e872c07d9dd57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 297, + 204, + 393 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a87017d855e9457a69a7897bf724180a7aee84fc4d4640dee0ea43ad8565f5b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 297, + 336, + 393 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/853c8600e474e46316a26f16359759188ff3a9b6a6aaf4612c514deec93098da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 297, + 468, + 393 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0f467511554c4cc97dc8f4f78b24831bf368024a9667100977ef29c581cfcf47.jpg", + "image_caption": [ + "Figure 7. Novel view synthesis. We can synthesize novel views for a fixed frame in a video, which is challenging for 2D GANs. Each column shows different view for the same frame.", + "(a) $\\mathrm{w / o}\\mathcal{L}_b$", + "Figure 8. Ablation study on editing. (a) Without $\\mathcal{L}_b$ , the out-of-distribution component dominates ( $b \\to 1$ ) and weakens the editing. It has \"Duplicate eyes\" artifact because the editing direction \"eyeglasses\" is not disentangled well with other attributes, and changes the positions of the eyes, while the blending weights are the same as the reconstruction, it results in duplicated eyes. (b) Without $\\mathcal{L}_w$ , the eyebrow becomes unnatural." + ], + "image_footnote": [], + "bbox": [ + 78, + 454, + 171, + 526 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dcf76b0b8074b53a3bee430c28d2938aba1454f0c61fb16d623b527fde7560f8.jpg", + "image_caption": [ + "(b) $\\mathrm{w / o}\\mathcal{L}_w$" + ], + "image_footnote": [], + "bbox": [ + 227, + 454, + 320, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04197dd14a1468d0b7af65bd05c58c34a8d1082921db57a6eaf20136afe30d43.jpg", + "image_caption": [ + "(c) Full model", + "Figure 9. Limitations. Our approach has some limitations. (a) Editing on where OOD blending weights dominate is challenging, (b) Adding another eyeglasses to OOD eyeglasses will result in duplicated objects, and (c) extreme poses." + ], + "image_footnote": [], + "bbox": [ + 375, + 454, + 468, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "out $\\mathcal{L}_w$ , the eyebrow becomes unnatural in Figure 8 (b).", + "bbox": [ + 76, + 661, + 444, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Speed", + "text_level": 1, + "bbox": [ + 76, + 685, + 158, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We include a comparison of different baselines in Table 1. We compare the speed on 200 frames using a single NVIDIA RTX A6000 GPU. Our method takes more time for optimization but significantly improves the reconstruction-editability trade-off.", + "bbox": [ + 75, + 708, + 468, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations", + "text_level": 1, + "bbox": [ + 76, + 796, + 197, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method still has several limitations. We visualize (a)-(c) in Figure 9.", + "bbox": [ + 76, + 821, + 467, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(a) Editing on OOD part. When editing on the OOD region, e.g. adding eyeglasses to the heavy makeup region, because the blending weights are closer to 1, the eyeglasses", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/79549fc6f255a983434f3f4b2c11f39eeb2f99cb0865af64bb59f16ea77851e2.jpg", + "image_caption": [ + "(a) OOD dominates" + ], + "image_footnote": [], + "bbox": [ + 501, + 297, + 609, + 381 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be6eadc61a6fe2f459247bf0c7d4d53ed2235c401486ad54eee2c7cbe364e0cf.jpg", + "image_caption": [ + "(b) Double glasses" + ], + "image_footnote": [], + "bbox": [ + 640, + 297, + 750, + 381 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32961f16690f18e6b5aaa6d5d65e54d843ba850fce1e489da1deafa344b797b2.jpg", + "image_caption": [ + "(c) Extreme pose" + ], + "image_footnote": [], + "bbox": [ + 781, + 297, + 890, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in the in-distribution radiance field are hard to be added.", + "bbox": [ + 500, + 474, + 870, + 487 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(b) Duplicate objects. Since our OOD radiance field has no knowledge about the GAN and faces prior, when the OOD object itself is glasses, adding eyeglasses introduces duplicate objects.", + "(c) Extreme poses. Our method fails at editing when the subject undergoes extreme poses (e.g., side view).", + "(d) Objects with limited movement. The radiance field reconstruction suffers when the OOD object has slight movement. This may introduce unwanted artifacts like \"floater\" in the novel views.", + "(e) Temporal inconsistency. Our results on video editing may suffer from temporal inconsistency. Temporal constraints and finetuning used in [57, 63] could further improve this aspect." + ], + "bbox": [ + 500, + 492, + 890, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 724, + 625, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a novel method for face image, and its potential for video inversion and editing. Our method handles OOD objects by isolating them from the InD part. Our method achieves accurate reconstruction by building two radiance fields and then composing them together during the rendering. By modifying the latent code in the InD part, we can obtain faithful editing results. We show that our method achieves a better balance in the reconstruction-editability trade-off than other baselines. Malicious use of our technique may lead to misinformation.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7232", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In ICCV, 2019. 3", + "[2] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan++: How to edit the embedded images? In CVPR, 2020. 3", + "[3] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Styleflow: Attribute-conditioned exploration of stylegan-generated images using conditional continuous normalizing flows. ACM Transactions on Graphics (ToG), 40(3):1-21, 2021. 2", + "[4] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. 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In ICCV, 2021. 3" + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7234", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[66] Fei Yin, Yong Zhang, Xuan Wang, Tengfei Wang, Xiaoyu Li, Yuan Gong, Yanbo Fan, Xiaodong Cun, Ying Shan, Cengiz Oztireli, et al. 3d gan inversion with facial symmetry prior. In CVPR, 2023. 2, 3", + "[67] Ziyang Yuan, Yiming Zhu, Yu Li, Hongyu Liu, and Chun Yuan. Make encoder great again in 3d gan inversion through geometry and occlusion-aware encoding. In ICCV, 2023. 2, 3, 6, 7, 8", + "[68] Jichao Zhang, Aliaksandr Siarohin, Yahui Liu, Hao Tang, Nicu Sebe, and Wei Wang. Training and tuning generative neural radiance fields for attribute-conditional 3d-aware face generation. arXiv preprint arXiv:2208.12550, 2022. 3", + "[69] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, 2018. 5, 6", + "[70] Jiapeng Zhu, Yujun Shen, Deli Zhao, and Bolei Zhou. Indomain gan inversion for real image editing. In European conference on computer vision, 2020. 2", + "[71] Jiapeng Zhu, Yujun Shen, Deli Zhao, and Bolei Zhou. Indomain gan inversion for real image editing. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.13, + 0.885, + 0.177 + ], + "angle": 0, + "content": "In-N-Out: Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.202, + 0.199, + 0.22 + ], + "angle": 0, + "content": "Yiran Xu" + }, + { + "type": "text", + "bbox": [ + 0.238, + 0.203, + 0.339, + 0.22 + ], + "angle": 0, + "content": "Zhixin Shu²" + }, + { + "type": "text", + "bbox": [ + 0.379, + 0.204, + 0.514, + 0.22 + ], + "angle": 0, + "content": "Cameron Smith" + }, + { + "type": "text", + "bbox": [ + 0.554, + 0.203, + 0.695, + 0.222 + ], + "angle": 0, + "content": "Seoung Wug Oh²" + }, + { + "type": "text", + "bbox": [ + 0.735, + 0.203, + 0.86, + 0.222 + ], + "angle": 0, + "content": "Jia-Bin Huang" + }, + { + "type": "text", + "bbox": [ + 0.259, + 0.231, + 0.713, 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"content": "Elsa" + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.36, + 0.748, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.455, + 0.709, + 0.466 + ], + "angle": 0, + "content": "Elsa" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.466, + 0.759, + 0.563 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.634, + 0.566, + 0.76, + 0.663 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.253, + 0.882, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.349, + 0.875, + 0.361 + ], + "angle": 0, + "content": "OD Removal" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.36, + 0.882, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.455, + 0.879, + 0.466 + ], + "angle": 0, + "content": "OOD Removal" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.466, + 0.893, + 0.563 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.566, + 0.892, + 0.663 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.076, + 0.57, + 0.22, + 0.663 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.669, + 0.879, + 0.74 + ], + "angle": 0, + "content": "Figure 1. Semantic editing for out-of-distribution data. We present a method for reconstructing and editing an out-of-distribution (OOD) image or video using a pre-trained 3D-aware generative model (EG3D [10]). Our method explicitly models and reconstructs the occluders in 3D, allowing faithful reconstruction of the input while preserving the semantic editing capability. Here we showcase the reconstruction and editing results \"Less smile\", \"Younger\", \"Blond\" [47], \"Elsa\", \"Surprised\" [41]. Our method can also remove the OOD part. Data are from the Internet (Creative Commons)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.751, + 0.314, + 0.767 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "3D-aware GANs offer new capabilities for view synthesis while preserving the editing functionalities of their 2D counterparts. GAN inversion is a crucial step that seeks the latent code to reconstruct input images or videos, subsequently enabling diverse editing tasks through manipulation of this latent code. However, a model pre-trained on a particular dataset (e.g., \\(FFHQ\\)) often has difficulty re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.895, + 0.89 + ], + "angle": 0, + "content": "constructing images with out-of-distribution (OOD) objects such as faces with heavy make-up or occluding objects. We address this issue by explicitly modeling OOD objects from the input in 3D-aware GANs. Our core idea is to represent the image using two individual neural radiance fields: one for the in-distribution content and the other for the out-of-distribution object. The final reconstruction is achieved by optimizing the composition of these two radiance fields with carefully designed regularization. We demonstrate that" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7225" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.075, + 0.092, + 0.472, + 0.182 + ], + "angle": 0, + "content": "our explicit decomposition alleviates the inherent trade-off between reconstruction fidelity and editability. We evaluate reconstruction accuracy and editability of our method on challenging real face images and videos and showcase favorable results against other baselines. More results can be found at https://in-n-out-3d.github.io/." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.212, + 0.208, + 0.227 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.238, + 0.47, + 0.568 + ], + "angle": 0, + "content": "GAN inversion [3, 44, 55, 61, 70] is a set of techniques that project an input image onto the latent space of a pretrained GAN to obtain a latent code so that the image generator can reconstruct the input. This is particularly useful as one could perform various creative semantic editing tasks [18, 24, 41, 47] for images. Similar techniques have also been applied in the video domain, with which recent methods also achieved temporally consistent editing [57, 63]. However, the majority of these methods are effective primarily with 2D GANs, and they fall short in offering explicit 3D controllability, such as view synthesis capabilities. With the rapid recent advancements in 3D reconstruction, especially in neural radiance fields (NeRFs) [6, 11, 36, 37], high-quality 3D-aware GANs [10, 22, 40, 49] have emerged as a powerful tool for learning 3D generation from 2D images. 3D-aware GANs, equipped with a 3D representations like NeRFs [10, 22] or SDF [40], offer explicit control over camera views and ensure 3D geometric consistency in generation. Additionally, they retain the generative capacity and editability of 2D GANs [26-29]. This enables applications such as novel view synthesis, semantic image editing [31, 48, 51, 62, 66, 67] and video editing [17, 56]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Core challenges. While state-of-the-art 3D GAN inversion methods achieve remarkable advances in both image and video editing for human faces, they face challenges when dealing with images including out-of-distribution (OOD) objects (e.g., heavy make-ups or occlusions). This limitation arises primarily because these models are pre-trained only on natural faces without complex textures or substantial occlusions. As a result, the editability performance deteriorates when a pre-trained GAN is forced to model OOD objects in the GAN inversion process. This is commonly known as the reconstruction-editability trade-off [55]. Existing GAN inversion methods assume that a single latent code corresponding to the input image can be found in the latent space [50, 61] through optimization once the model is trained. Therefore, they aim to reconstruct the indistribution (InD) content (e.g., natural face) and the OOD objects together. However, OOD components often cannot be well modeled in a pre-trained GAN, and consequently cannot be well represented with it using a single latent code, existing methods either cannot reconstruct them faithfully [51] or can reconstruct them (e.g., through fine-tuning the generator) but alters the latent space properties and de" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.088, + 0.627, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.184, + 0.627, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.282, + 0.579, + 0.293 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.089, + 0.768, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.184, + 0.767, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.668, + 0.281, + 0.737, + 0.293 + ], + "angle": 0, + "content": "GOAE [67]" + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.089, + 0.892, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.184, + 0.892, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.812, + 0.281, + 0.863, + 0.293 + ], + "angle": 0, + "content": "PTI [45]" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.304, + 0.889, + 0.346 + ], + "angle": 0, + "content": "Figure 2. Limitations of the previous methods. Existing GAN inversion techniques cannot deal with frames with OOD elements, resulting in a poor reconstruction-editing balance." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.347, + 0.89, + 0.387 + ], + "angle": 0, + "content": "GOAE [67] can produce faithful editing, but fails to preserve the identity of the input face. PTI [45] provides higher reconstruction fieldity, but the edibility suffers." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.398, + 0.765, + 0.413 + ], + "angle": 0, + "content": "teriorates the editability [45] (Figure 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.893, + 0.824 + ], + "angle": 0, + "content": "Our work. We propose a new approach to address this issue by drawing inspiration from recent composite volume rendering works that compose multiple radiance fields during rendering [19, 34, 59, 64]. Our core idea is to decompose the 3D representation of an image with OOD components into an in-distribution (InD) part and an out-of-distribution part, and compose them together to reconstruct the image in a composite volumetric rendering manner. We use EG3D [10] as our 3D-aware GAN backbone and leverage its tri-plane representation to model this composed rendering pipeline. For the InD component (i.e. natural face), we project pixel values onto EG3D's \\(\\mathcal{W}+\\) space for an InD component reconstruction. We further introduce an additional tri-plane to represent the OOD content. After that, we combine these two radiance fields in a composite volumetric rendering to reconstruct the input frames. During the editing stage, we perform the latent code based editing solely on the InD part and leave the OOD component unaltered. This framework would allow the applications of any StyleGAN-based editing approache [41, 47] on the InD component such as changing facial expression, which is often desirable for user experiences. The advantages of our work are three-fold: a) we achieve a higher-fidelity reconstruction by composition of InD and OOD components; b) we retain the editability of pre-trained GANs by editing only the InD content; and c) by leveraging 3D-aware GANs, we can render the face from novel viewpoints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.9 + ], + "angle": 0, + "content": "We evaluate our method on challenging in-the-wild face images and videos (Creative Commons), demonstrating improvement over previous state-of-the-art GAN inversion work on both reconstruction and editing quality. In addition, we demonstrate the usefulness of our method with" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7226" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "3D-aware editing applications, including semantic editing, novel view synthesis, and OOD object removal." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.122, + 0.438, + 0.138 + ], + "angle": 0, + "content": "We will release the code and data used in the paper." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.142, + 0.448, + 0.157 + ], + "angle": 0, + "content": "Our contributions. In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.158, + 0.469, + 0.218 + ], + "angle": 0, + "content": "- We propose a 3D-aware GAN inversion approach to manipulate single images or monocular videos with out-of-distribution objects (e.g., accessories and heavy makeup). See results in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.218, + 0.468, + 0.247 + ], + "angle": 0, + "content": "- We incorporate composite volume rendering into 3D-aware GAN inversion." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.248, + 0.468, + 0.292 + ], + "angle": 0, + "content": "- Our method reconstructs 3D shapes of faces with OOD objects faithfully and demonstrates novel 3D-aware applications." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.158, + 0.469, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.308, + 0.218, + 0.324 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.469, + 0.518 + ], + "angle": 0, + "content": "3D-aware GANs. StyleGANs [26-29] have achieved high-quality photorealistic 2D image generation and have been successfully applied to various image editing applications [18, 24, 41, 47]. Significant progresses have also been made to lift 2D image generation to 3D space, using various 3D representations, for both higher quality generation and to enable 3D-aware applications such as view synthesis [9, 10, 16, 20, 22, 38, 40, 46, 49, 51]. These methods usually take a two-stage pipeline that renders a raw image (usually also with feature maps) in low resolution and then upsamples the rendered image to high resolution. We leverage EG3D [10] as our generator architecture in this work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.807 + ], + "angle": 0, + "content": "GAN inversion and editing. GAN inversion has been widely studied for 2D GANs. These techniques can largely be categorized as (a) encoder-based methods [4, 8, 33, 39, 44, 44, 54, 55, 55, 58] in which a neural network encoder is trained to project an input image to the latent space of the generator; (b) optimization-based methods [1, 2, 12, 13, 21, 25, 42, 53] where the latent code is recovered via optimizing loss functions between the generator output and a target image; and (c) hybrid methods [5, 7, 45, 71] which combine both approaches. Some recent works have also investigated 3D-aware GAN inversion from a single image [31, 32, 51, 56, 62, 66, 67] or a video [17, 68]. As our experiments demonstrate, previous approaches have difficulty handling these challenging cases. We propose a new mechanism to allow high-quality 3D-aware GAN inversion of out-of-distribution faces even under significant occlusion. With our GAN inversion, we can modify the latent code to perform high-quality semantic image editing [18, 24, 41, 47] or video editing [57, 63, 65]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "GAN inversion for out-of-distribution (OOD) data. There have been attempts to invert out-of-distribution data to the GAN's latent space. Early work [1] proposes to project an image onto extended \\(\\mathcal{W}^+\\) space to achieve more accurate reconstruction. PTI [45] finetunes generator with regularization for a lower distortion error. StyleSpace [60]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "proposes to invert an image using StyleGAN's internal feature maps and tRGB blocks, which shows better reconstruction and disentanglement. Recently, ChunkyGAN [50] proposes to compose multiple generated images from multiple latent codes, with a set of segmentation masks to reconstruct an input image. With a similar goal in mind, we propose to leverage the radiance field of EG3D [10] and decompose the volumetric representation into an in-distribution part and an out-of-distribution part. In contrast to ChunkyGAN [50] that models an image as a collection of \\(2D\\) segments, we model the OOD and face directly in volumetric 3D representation and merge them with composite rendering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Composite neural radiance fields. Neural Radiance Fields (NeRFs) [36] have shown impressive view synthesis results. Recently, it has been shown that 3D scenes can be decomposed into different NeRFs. When multiple radiance fields are built, one can compose them together using a composite rendering manner [19, 34, 59, 64]. EG3D [10] uses the tri-plane representation to generate 3D objects from the latent code. We adopt the idea of composite volume rendering to address the out-of-distribution 3D GAN inversion problem. Specifically, we split the in-distribution and out-of-distribution parts in the tri-plane 3D representation and compose them during volume rendering." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.469, + 0.719, + 0.485 + ], + "angle": 0, + "content": "3. 3D-aware GAN: EG3D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.891, + 0.538 + ], + "angle": 0, + "content": "We choose EG3D [10], which consists of a tri-plane representation and a super-resolution (SR) module, as our 3D-aware GAN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.892, + 0.738 + ], + "angle": 0, + "content": "Neural rendering at low resolution. Given a latent code \\( z \\in \\mathbb{R}^{512} \\) (or \\( w \\in \\mathbb{R}^{14 \\times 512} \\)) and camera parameters \\( p \\), EG3D first generates a corresponding tri-plane \\( \\mathbf{T} \\in \\mathbb{R}^{256 \\times 256 \\times 32 \\times 3} \\). For each pixel, a ray \\( \\mathbf{r} \\) is cast, and points are sampled along the ray. Unlike the positional encoding [34, 52] for each point in NeRFs [34], EG3D projects each point onto tri-plane \\( \\mathbf{T} \\) and retrieves features from three planes via bilinear interpolation. These features are then aggregated by summation, and fed into the decoder \\( D \\) (i.e., an MLP) to predict the color and density. Volume rendering [35] is then performed to compute the final color for each pixel. To this end, a raw RGB image with a 32-channel feature in a low resolution (e.g. \\( 128 \\times 128 \\)) is generated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.741, + 0.892, + 0.831 + ], + "angle": 0, + "content": "Super-Resolution (SR). To gain high-resolution outputs, EG3D later uses an SR module that inputs the raw image and the 32-channel feature as the input and yields a high-resolution RGB image (e.g. \\(512 \\times 512\\)). We build our approach upon EG3D due to its rendering efficiency compared to other alternatives [22, 40]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.591, + 0.86 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Given an aligned face input image \\(\\mathbf{I}\\), or a monocular face video \\(\\mathbf{V} = [\\mathbf{I}_1, \\dots, \\mathbf{I}_t, \\dots, \\mathbf{I}_N]\\) with \\(N\\) frames, we aim" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7227" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.089, + 0.839, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.531, + 0.877, + 0.657 + ], + "angle": 0, + "content": "Figure 3. Overview of our method. Given a potrait image or a monocular portrait video, we use two radiance fields to represent (a) in-distribution \\((\\text{InD})\\) face, and (b) out-of-distribution \\((\\text{OOD})\\) item. (a) InD reconstruction is the GAN inversion for the in-distribution natural face. We apply GAN inversion by using pre-trained EG3D model \\(G\\) to the frame, where the pre-trained tri-plane generator and tri-plane decoder \\(D^{I}\\) are kept frozen. (b) For OOD item, we propose to model them with a separate radiance field represented by an additional tri-plane \\(\\mathbf{T}^O\\). During the training process, we optimize the tri-plane \\(\\mathbf{T}^O\\), a per-frame latent code \\(\\phi_t\\), and a new decoder \\(D^O\\). The decoder takes as input tri-plane features \\(\\mathbf{T}^O\\) and \\(\\phi_t\\) and outputs color \\(\\mathbf{c}^O\\), density \\(\\sigma^O\\), and blending weight \\(b\\). (c) Composite Rendering compose the InD and OOD radiance fields together by using a composite rendering scheme (Section 4.3). (d) Finally, we finetune the Super-Resolution module in \\(G\\) to achieve a better output in the high resolution. After training, we can perform various semantic edits and free-view rendering, while preserving the face identity and the OOD components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.471, + 0.726 + ], + "angle": 0, + "content": "to reconstruct the input with EG3D inversion and perform face editing. For simplicity, we use \\(\\mathbf{I}_t\\) to represent a frame, either from a single input image or a sampled frame from a video. If only one frame exists, then \\(N = 1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.736, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We present the high-level overview in Figure 3. We build two neural radiance fields (NeRFs) [36], one for in-distribution (InD) face (Section 4.1), and the other one for out-of-distribution (OOD) object (Section 4.2), using triplane representations [10]. The OOD object, for example, can be a non-face object with a rigid shape or heavy makeup with a complicated texture. Next, we combine two radiance fields (Section 4.3) to reconstruct the low-resolution frame. Finally, we finetune the super-resolution module of EG3D to get the high-resolution output (Section 4.5). After training the radiance fields, we can edit the face image or video" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.667, + 0.595, + 0.682 + ], + "angle": 0, + "content": "(Section 4.6)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.691, + 0.769, + 0.707 + ], + "angle": 0, + "content": "4.1. In-distribution GAN inversion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Formulation. Since a pretrained EG3D already has prior knowledge of faces, we directly leverage its latent space and perform a regular 3D GAN inversion [32, 61] for the in-distribution part. For a single frame case, we optimize a latent code \\( w_{t} \\) such that it can reconstruct the input frame \\( \\mathbf{I}_t \\). For a video, we invert all the frames at the same time. Please refer to the supplementary material for more details. For camera parameters \\( p_t \\in \\mathbb{R}^{25} \\), we obtain them by using an off-the-shelf pose detector [15], following [10, 32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Optimization. To represent the InD faces with \\(\\mathbf{T}^I\\), our insight is to keep the latent code \\(w_{t}\\) in distribution as much as possible. To this end, we use a regularization term to keep" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7228" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.468, + 0.107 + ], + "angle": 0, + "content": "\\(w_{t}\\) within its pre-trained distribution through GAN training." + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.12, + 0.468, + 0.137 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {w} \\left(w _ {t}\\right) = \\left| \\left| w _ {t} - \\bar {w} \\right| \\right| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.144, + 0.468, + 0.173 + ], + "angle": 0, + "content": "where \\(\\bar{w}\\) is the mean latent code computed over 10,000 sampled latent codes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.176, + 0.469, + 0.265 + ], + "angle": 0, + "content": "We also use a another regularization term adopted from [55] to constrain the variation among style vectors in \\( w \\): \\( \\mathcal{L}_{\\Delta}(w_t) = \\sum_{i=1}^{13} ||\\Delta_i||_2^2 \\), given a latent code \\( w = (w_0, w_0 + \\Delta_1, \\dots, w_0 + \\Delta_{13}) \\in \\mathbb{R}^{14 \\times 512} \\). This regularization term preserves the editability of the optimized latent code [55]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.28, + 0.402, + 0.295 + ], + "angle": 0, + "content": "4.2. Modeling out-of-distribution contents" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.469, + 0.468 + ], + "angle": 0, + "content": "For an OOD object, a pre-trained EG3D usually cannot model it well with its prior distribution. We therefore use an additional tri-plane \\(\\mathbf{T}^O\\) to represent the out-of-distribution content. One additional challenge is that, while dealing with video, the OOD object may not be static across different frames, therefore could not be well reconstructed with a static radiance field. Therefore, in addition to \\(\\mathbf{T}^O\\), we use a per-frame latent code \\(\\phi_t \\in \\mathbb{R}^{32}\\) for each frame to represent the out-of-distribution object across the temporal domain. Both \\(\\mathbf{T}^O\\) and \\(\\phi_t\\) are randomly initialized from a normal distribution." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.469, + 0.52 + ], + "angle": 0, + "content": "Formulation. The out-of-distribution decoder \\(D^{O}\\) takes a tuple \\((\\mathbf{T}^{O}(t_{k}),\\phi_{t})\\in \\mathbb{R}^{64}\\) as the input, and outputs color \\(\\mathbf{c}^O\\in \\mathbb{R}^3\\) , density \\(\\sigma^O\\in \\mathbb{R}\\) , and blending weight \\(b\\in [0,1]\\)" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.53, + 0.469, + 0.548 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {c} ^ {O}, \\sigma^ {O}, b\\right) = D ^ {O} \\left(\\mathbf {T} ^ {O} \\left(t _ {k}\\right), \\phi_ {t}; \\theta_ {D ^ {O}}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.559, + 0.469, + 0.649 + ], + "angle": 0, + "content": "where \\(\\mathbf{T}^O (t_k)\\in \\mathbb{R}^{32}\\) is the aggregated features obtained by projecting 3D coordinate \\(t_k\\) onto each of the three feature planes via bilinear interpolation, then aggregated via summation [10]. The decoder \\(D^{O}\\) is an MLP with weights of \\(\\theta_{DO}\\). To compute the color of a pixel at time \\(t\\), we use the volume rendering integral along the ray \\(\\mathbf{r}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.654, + 0.469, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} ^ {O} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T \\left(t _ {k}\\right) \\alpha^ {O} \\left(\\sigma^ {O} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {O} \\left(t _ {k}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.707, + 0.468, + 0.753 + ], + "angle": 0, + "content": "where \\( T(t_k) = \\exp(-\\sum_{k'=1}^{k-1} \\sigma(t_{k'}) \\delta_{k'}) \\), \\( \\alpha = 1 - \\exp(-x) \\), and \\( \\delta_k = t_{k+1} - t_k \\) is the distance between two 3D points." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.336, + 0.77 + ], + "angle": 0, + "content": "4.3. Composite volume rendering" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.779, + 0.468, + 0.809 + ], + "angle": 0, + "content": "Now, with both InD and OOD radiance fields, we can combine them using the blending weight \\( b \\) from Eqn. 2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.815, + 0.468, + 0.829 + ], + "angle": 0, + "content": "Formulation. We compose two radiance fields together by" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.836, + 0.468, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {C} ^ {C} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T ^ {C} \\left(t _ {k}\\right) \\left(b \\alpha^ {O} \\left(\\sigma^ {O} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {O} \\left(t _ {k}\\right) \\right. \\tag {4} \\\\ \\left. + (1 - b) \\alpha^ {I} \\left(\\sigma^ {I} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {I} \\left(t _ {k}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.089, + 0.815, + 0.108 + ], + "angle": 0, + "content": "where \\(T^{C}(t_{k}) = \\exp (-\\sum_{k^{\\prime} = 1}^{k - 1}(\\sigma^{O} + \\sigma^{I})\\delta_{k^{\\prime}})\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.111, + 0.685, + 0.125 + ], + "angle": 0, + "content": "Optimization. The goal is" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.135, + 0.891, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} w_{t}^{*},\\mathbf{T}^{O^{*}},\\theta_{D O}^{*},\\phi_{t}^{*} = \\operatorname *{argmin}_{w_{t},\\mathbf{T}^{O},\\theta_{D O},\\phi_{t}}\\mathcal{L}_{t}^{C} \\\\ = \\operatorname *{argmin}_{w_{t},\\mathbf{T}^{O},\\theta_{D^{O}},\\phi_{t}}\\sum_{ij}||C^{C}(\\mathbf{r}_{ij}) - C^{GT}(\\mathbf{r}_{ij})||_{2}^{2} \\\\ + \\lambda_ {b} \\mathcal {L} _ {b} \\left(\\mathbf {r} _ {i j}\\right) + \\mathcal {L} _ {L P I P S} \\left(\\mathbf {I} _ {L R} ^ {C}, \\mathbf {I} _ {L R}\\right), \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.231, + 0.892, + 0.305 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{LPIPS}\\) is the LPIPS loss [69], \\(\\mathbf{I}_{LR}^{C}\\) is the composite rendered image at low resolution \\((128\\times 128)\\), \\(\\mathbf{I}_{LR}\\) is the ground truth image also at \\(128\\times 128\\). The weight regularizer \\(\\mathcal{L}_b\\) is adopted from [59], used to penalize the blending weight \\(b\\) if it is not closer to 0 or 1:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.318, + 0.891, + 0.347 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} H _ {b} (b \\left(t _ {k}\\right)), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.359, + 0.892, + 0.448 + ], + "angle": 0, + "content": "where \\( H_{b}(x) = -(x\\log (x) + (1 - x)\\log (x)) \\) is binary entropy. The reason behind Eqn. 6 is that objects cannot co-occupy the same spatial location. The entropy loss facilitates a cleaner decomposition: encouraging an object to be either in-distribution (i.e. \\( b\\to 0 \\)) or out-of-distribution (i.e. \\( b\\rightarrow 1 \\))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.45, + 0.892, + 0.509 + ], + "angle": 0, + "content": "However, it is ill-posed to build its 3D geometry accurately, given only a single-frame input, even with a pretrained 3D-aware generator. Therefore, for a single image only, we also introduce a depth regularization term:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.519, + 0.891, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {D}} = \\left| \\left| \\mathcal {D} ^ {C} - \\mathcal {D} ^ {R e g} \\right| \\right| _ {1} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.548, + 0.891, + 0.579 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}^C\\) is the rendering depth map from composite rendering, and \\(\\mathcal{D}^{Reg}\\) is a rescaled depth map from MiDaS [43]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.768, + 0.602 + ], + "angle": 0, + "content": "4.4. Low-resolution reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.61, + 0.891, + 0.655 + ], + "angle": 0, + "content": "In practice, we jointly optimize for \\( w_{t} \\) (yielding \\( \\mathbf{T}^{I} \\)), \\( \\mathbf{T}^{O} \\), \\( \\theta_{DO} \\), \\( \\phi_{t} \\), following Section 4.1 to Section 4.3. Our total loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.665, + 0.891, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {L R} = \\sum_ {t = 1} ^ {N} \\mathcal {L} _ {t} ^ {C} + \\lambda_ {\\Delta} \\mathcal {L} _ {\\Delta} + \\lambda_ {w} \\mathcal {L} _ {w} + (\\lambda_ {\\mathcal {D}} \\mathcal {L} _ {\\mathcal {D}}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.718, + 0.891, + 0.779 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_t^C\\) is from Eqn. 4, latent variation regularizer \\(\\mathcal{L}_{\\Delta}\\) from [55], and \\(\\mathcal{L}_w\\) from Eqn. 1, respectively, \\(\\lambda_{\\Delta}\\) is the weight for \\(\\mathcal{L}_{\\Delta}\\), \\(\\lambda_w\\) is the weight for \\(\\mathcal{L}_w\\), and \\(\\lambda_{\\mathcal{D}}\\) is the weight for \\(\\mathcal{L}_{\\mathcal{D}}\\). We only use \\(\\mathcal{L}_{\\mathcal{D}}\\) for single image input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.788, + 0.669, + 0.803 + ], + "angle": 0, + "content": "4.5. Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "After training in Section 4.1, 4.2, 4.3 and 4.4, we can get reconstruction \\(\\mathbf{I}_{LR}^{C}\\) in low resolution \\((128\\times 128)\\). We observe that using the pretrained super-resolution (SR) module cannot generate a satisfying high-resolution output, as shown in Figure 4, due to the new OOD tri-plane \\(\\mathbf{T}^O\\). Therefore, we finetune only the SR module in \\(G\\) for higher resolution" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.956 + ], + "angle": 0, + "content": "7229" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.088, + 0.207, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.188, + 0.182, + 0.202 + ], + "angle": 0, + "content": "Recon. Target" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.089, + 0.338, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.219, + 0.186, + 0.329, + 0.209 + ], + "angle": 0, + "content": "w/o finetuning SR module" + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.089, + 0.47, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.358, + 0.186, + 0.461, + 0.209 + ], + "angle": 0, + "content": "w/ finetuning SR module" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.219, + 0.449, + 0.247 + ], + "angle": 0, + "content": "Figure 4. The effect of finetuning SR module. Without finetuning the SR module, the high-resolution output is blurry." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.266, + 0.172, + 0.28 + ], + "angle": 0, + "content": "at \\(512 \\times 512\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.286, + 0.347, + 0.301 + ], + "angle": 0, + "content": "Optimization. The loss function is that" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.31, + 0.469, + 0.329 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {S R} (\\mathbf {x}, \\hat {\\mathbf {x}}) = \\| \\mathbf {x} - \\hat {\\mathbf {x}} \\| _ {2} ^ {2} + \\mathcal {L} _ {L P I P S} (\\mathbf {x}, \\hat {\\mathbf {x}}), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.339, + 0.301, + 0.357 + ], + "angle": 0, + "content": "where \\(\\mathbf{x} = \\mathbf{I}_t\\) and \\(\\hat{\\mathbf{x}} = SR(\\mathbf{I}_{LR}^C)\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.367, + 0.172, + 0.383 + ], + "angle": 0, + "content": "4.6. Editing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.469, + 0.48 + ], + "angle": 0, + "content": "After the reconstruction, we can modify the latent code \\( w_{t} \\) to perform various semantic editing tasks. With explicit decomposition, the OOD contents do not interfere with the semantic editing capability of in-distribution components. Here, any existing GAN-based editing approaches can be used. We use InterfaceGAN [47] and StyleCLIP [41]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.496, + 0.283, + 0.513 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.521, + 0.267, + 0.537 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Dataset. To evaluate how our approach works on data with out-of-distribution components, we collected a dataset of 20 online videos with challenging and diverse appearances. The OOD content contains heavy make-up and occluding objects (e.g. facial masks and large glasses). For the single-image inversion method, we use the first frame of each video. For video inversion, we use all the frames. For the face alignment, we use 3DDFA-v2 [23] to obtain the 68-point landmarks and smooth them across the frames using a sliding window for stabler cropping. After that, we convert the landmarks to EG3D's 5-point landmarks and crop the face out of the input frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Hyperparameters. We use the Adam optimizer [30] for all our experiments. For in-distribution inversion (Section 4.1), we optimize for 200 epochs with a learning rate of \\(1 \\times 10^{-3}\\), \\(\\lambda_{\\Delta} = 1 \\times 10^{-3}\\). For the out-of-distribution and composite rendering (Section 4.2, 4.3), we run the optimization for 10,000 iterations with a learning rate of \\(5 \\times 10^{-3}\\), \\(\\lambda_{b} = 1\\), \\(\\lambda_{w} = 1\\), and \\(\\lambda_{\\mathcal{D}} = 0.1\\) if applicable. For the SR module (Section 4.5), we finetune the module for 100 epochs with a learning rate of \\(1 \\times 10^{-3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Metrics. We evaluate our approach from 1) reconstruction accuracy and 2) editability to validate the reconstruction-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.18 + ], + "angle": 0, + "content": "editability trade-off. For the reconstruction accuracy, we report LPIPS [69], PSNR, SSIM and ID similarity [14]. For editability, we follow [45, 50] and evaluate identity preservation after applying the editing direction. More specifically, we use ArcFace [14] to compute the similarity between the inverted and edited results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.185, + 0.893, + 0.365 + ], + "angle": 0, + "content": "Baselines for evaluation. We compare our method extensively with several previous arts. For optimization-based methods, we compare with HFGI3D [62], PTI [45], \\(\\mathcal{W}+\\), and \\(\\mathcal{W}\\) optimization. For videos only, we also include VIVE3D [17]. We compare the encoder-based method with GOAE [67] and IDE-3D [51] encoder. We treat \\(\\mathcal{W}+\\) optimization as an ablated version of our method without OOD triplane. The recent work in [56] showcases encoder-based 3D GAN inversion, focusing on real-time inference. However, their method relies on a frozen EG3D and does not explicitly model the OOD components. We do not compare with it as the code is not publicly available." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.369, + 0.688, + 0.385 + ], + "angle": 0, + "content": "5.2. Quantitative results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.892, + 0.515 + ], + "angle": 0, + "content": "Reconstruction. We compare the reconstruction accuracy of our approach with all baselines and report the results in Table 1. For PTI, we first perform a \\(\\mathcal{W}+\\) inversion with a learning rate of \\(1 \\times 10^{-3}\\) and 200 epochs, and then finetune the generator for 200 epochs with a learning rate of \\(3 \\times 10^{-5}\\). For \\(\\mathcal{W}+\\) and \\(\\mathcal{W}\\) optimization, we use a learning rate of \\(1 \\times 10^{-3}\\) and optimize for 200 epochs. For GOAE and IDE-3D, we use their encoder directly for the inversion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Our approach outperforms other methods on all the evaluation metrics. This indicates that our method produces a more accurate reconstruction with the OOD components." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.893, + 0.683 + ], + "angle": 0, + "content": "Editability. We acquire editing directions from InterfaceGAN [47] (\"younger\", \"smile\") and StyleCLIP mapper [41] (\"eyeglasses\", \"surprised\", \"Elsa\"). Following previous work [45, 50], we measure the ID similarity between the inverted image and the edited image, as the editing should not change a person's identity. We report our results in Table 2. Our method outperforms other baselines in terms of identity preservation in most cases." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.691, + 0.677, + 0.707 + ], + "angle": 0, + "content": "5.3. Qualitative results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Inversion. We visually compare the video reconstruction in Figure 5. Our method provides higher-fidelity reconstruction results than other baselines, particularly for OOD regions (e.g., heavy make-up or earrings). Our method shows better reconstruction than the encoder-based method GOAE [67] and IDE-3D [51]. Compared to optimization-based methods, HFGI3D [62], VIVE3D [17], PTI [45], \\(\\mathcal{W}\\), and \\(\\mathcal{W}+\\), our method shows higher-fidelity reconstruction for OOD objects (Refer to our supplementary material for more results)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Editing. We show a qualitative comparison regarding the editing in Figure 6. Our method shows faithful editing" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7230" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.264, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.09, + 0.44, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.44, + 0.089, + 0.712, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.09, + 0.897, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.206, + 0.89, + 0.234 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of the video reconstruction. We compare our approach with \\(\\mathcal{W}+\\) and \\(\\mathcal{W}\\) optimization, IDE-3D [51], GOAE [67], HFGI3D [62], VIVE3D [17], and PTI [45]. Our method shows a better reconstruction accuracy on the OOD videos." + }, + { + "type": "table", + "bbox": [ + 0.167, + 0.239, + 0.806, + 0.373 + ], + "angle": 0, + "content": "
ImagesVideos
LPIPS↓SSIM↑PSNR↑ID Similarity↑Time↓LPIPS↓SSIM↑PSNR↑ID Similarity↑
Ours0.11060.817519.860.96852.68h0.22370.705216.030.9758
HFGI3D [62]0.39120.552111.370.94637.51h0.39540.558711.550.9388
GOAE [67]0.36190.642414.730.968556s0.36420.647014.970.3642
E3DGE [31]0.17090.773815.280.8632-----
VIVE3D [17]----0.59h0.41720.541710.660.9245
PTI [45]0.31920.617212.930.96761.45h0.31440.632013.450.9658
IDE-3D [51]0.50440.43959.180.845677s0.49990.45129.590.8251
W+0.34330.638714.390.91990.49h0.33800.655714.750.9154
W0.40970.561512.080.87570.47h0.40300.578712.480.8652
" + }, + { + "type": "table_caption", + "bbox": [ + 0.226, + 0.383, + 0.743, + 0.398 + ], + "angle": 0, + "content": "Table 1. Reconstruction quality evaluation. For each column, deeper color the better." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.411, + 0.861, + 0.546 + ], + "angle": 0, + "content": "
ImagesVideos
eyeglassessurprisedyoungersmileElsaaverageeyeglassessurprisedyoungersmileElsaaverage
Ours.9532.9888.9495.9525.9116.9511.9158.9360.9347.9094.8927.9177
HFGI3D [62].9484.9795.9453.9223.8641.9319.9112.9109.9290.9155.8622.9058
GOAE [67].9179.9306.9327.9332.8851.9199.9120.9224.9235.9221.8641.9088
E3DGE [31]--.8853.9487-0.9170------
VIVE3D [17]------.9078.9475.9183.9369.8728.9167
PTI [45].9114.9562.9380.9410.7927.9079.9049.9357.9319.9336.7945.9001
IDE-3D [51].8811.9538.8723.8055.8780.8781.8767.9481.8551.8662.7871.8666
W+.9012.9567.9248.9356.7892.9015.8971.9249.9290.9170.7968.8930
W.8808.9567.9177.9290.8008.8970.8793.9537.9068.9208.8113.8944
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.555, + 0.85, + 0.584 + ], + "angle": 0, + "content": "Table 2. Identity preservation evaluation. Higher numbers indicate better identity preservation. \\( \\mathcal{W} + \\) is equivalent to our method without OOD tri-plane." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.623 + ], + "angle": 0, + "content": "results. For more qualitative results, please refer to our supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.631, + 0.262, + 0.647 + ], + "angle": 0, + "content": "5.4. Other Applications" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.703 + ], + "angle": 0, + "content": "View synthesis. The use of 3D GANs supports rendering novel views after inversion. We show novel view synthesis results in Figure 7." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.751 + ], + "angle": 0, + "content": "Object removal. By setting the blending weights of the OOD objects to 0, we can remove OOD objects. We show results in Figure 1." + }, + { + "type": "table", + "bbox": [ + 0.137, + 0.762, + 0.413, + 0.835 + ], + "angle": 0, + "content": "
InversionEditing
L2↓LPIPS↓ID similarity↑
w/o Lb0.03220.21910.9070
w/o Lw0.03360.22380.9024
Full method0.03390.22370.9177
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.845, + 0.458, + 0.903 + ], + "angle": 0, + "content": "Table 3. Ablation study. We study the effect of different loss functions on 20 videos. For inversion, we compute the metrics between reconstructed frames and input frames. For editing, we compute the ID similarity between before and after editing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.655, + 0.608 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We introduce two new loss functions, Eqn. 1 and Eqn. 6, to preserve the editability from the impact of the OOD radiance field in Section 4.3. To validate the loss functions' effects, we conduct an ablation study in Table 3. Without the weight regularization, \\(\\mathcal{L}_b\\), and latent code regularizer \\(\\mathcal{L}_w\\), the reconstruction accuracy is improved while the editability is reduced. One of the reasons is that GAN-based editing usually also brings unwanted changes to other attributes [47]. In Figure 8, the editing direction \"eyeglasses\" also moves the position of the eyes. At this time, if the blending weight \\(b\\) is closer to 1 for pixels outside the OOD object, i.e. the OOD part has more contributions, the editing tends to keep the pixel values in the reconstruction stage. While the eyes will be moved due to the editing direction, it results in the duplicate eyes in Figure 8(a). In contrast, with regularization (Eqn. 1 and Eqn. 6) on the blending weights, pixels in the in-distribution part contribute more to the output, which better supports the editing since we can only edit the in-distribution part. Similar cases happen to \\(\\mathcal{L}_w\\). With" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7231" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.895, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.88, + 0.29 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison of the editing. We compare our editing results from a single image and a video with other baselines, with different editing latent directions \"Eyeglasses\". Our approach can preserve the original appearance details better, and shows improved editability over other baselines." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.298, + 0.205, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.298, + 0.338, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.298, + 0.47, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.405, + 0.458, + 0.446 + ], + "angle": 0, + "content": "Figure 7. Novel view synthesis. We can synthesize novel views for a fixed frame in a video, which is challenging for 2D GANs. Each column shows different view for the same frame." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.455, + 0.172, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.087, + 0.531, + 0.152, + 0.543 + ], + "angle": 0, + "content": "(a) \\(\\mathrm{w / o}\\mathcal{L}_b\\)" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.455, + 0.321, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.531, + 0.296, + 0.543 + ], + "angle": 0, + "content": "(b) \\(\\mathrm{w / o}\\mathcal{L}_w\\)" + }, + { + "type": "image", + "bbox": [ + 0.376, + 0.455, + 0.469, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.372, + 0.531, + 0.458, + 0.543 + ], + "angle": 0, + "content": "(c) Full model" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.554, + 0.468, + 0.651 + ], + "angle": 0, + "content": "Figure 8. Ablation study on editing. (a) Without \\(\\mathcal{L}_b\\), the out-of-distribution component dominates (\\(b \\to 1\\)) and weakens the editing. It has \"Duplicate eyes\" artifact because the editing direction \"eyeglasses\" is not disentangled well with other attributes, and changes the positions of the eyes, while the blending weights are the same as the reconstruction, it results in duplicated eyes. (b) Without \\(\\mathcal{L}_w\\), the eyebrow becomes unnatural." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.662, + 0.445, + 0.677 + ], + "angle": 0, + "content": "out \\(\\mathcal{L}_w\\), the eyebrow becomes unnatural in Figure 8 (b)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.686, + 0.16, + 0.701 + ], + "angle": 0, + "content": "5.6. Speed" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.469, + 0.784 + ], + "angle": 0, + "content": "We include a comparison of different baselines in Table 1. We compare the speed on 200 frames using a single NVIDIA RTX A6000 GPU. Our method takes more time for optimization but significantly improves the reconstruction-editability trade-off." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.797, + 0.199, + 0.813 + ], + "angle": 0, + "content": "6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.822, + 0.468, + 0.852 + ], + "angle": 0, + "content": "Our method still has several limitations. We visualize (a)-(c) in Figure 9." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "(a) Editing on OOD part. When editing on the OOD region, e.g. adding eyeglasses to the heavy makeup region, because the blending weights are closer to 1, the eyeglasses" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.298, + 0.611, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.385, + 0.62, + 0.398 + ], + "angle": 0, + "content": "(a) OOD dominates" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.298, + 0.751, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.385, + 0.753, + 0.398 + ], + "angle": 0, + "content": "(b) Double glasses" + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.298, + 0.892, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.385, + 0.883, + 0.398 + ], + "angle": 0, + "content": "(c) Extreme pose" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.41, + 0.874, + 0.465 + ], + "angle": 0, + "content": "Figure 9. Limitations. Our approach has some limitations. (a) Editing on where OOD blending weights dominate is challenging, (b) Adding another eyeglasses to OOD eyeglasses will result in duplicated objects, and (c) extreme poses." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.475, + 0.871, + 0.488 + ], + "angle": 0, + "content": "in the in-distribution radiance field are hard to be added." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.493, + 0.891, + 0.553 + ], + "angle": 0, + "content": "(b) Duplicate objects. Since our OOD radiance field has no knowledge about the GAN and faces prior, when the OOD object itself is glasses, adding eyeglasses introduces duplicate objects." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.557, + 0.89, + 0.587 + ], + "angle": 0, + "content": "(c) Extreme poses. Our method fails at editing when the subject undergoes extreme poses (e.g., side view)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.59, + 0.891, + 0.649 + ], + "angle": 0, + "content": "(d) Objects with limited movement. The radiance field reconstruction suffers when the OOD object has slight movement. This may introduce unwanted artifacts like \"floater\" in the novel views." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.653, + 0.891, + 0.713 + ], + "angle": 0, + "content": "(e) Temporal inconsistency. Our results on video editing may suffer from temporal inconsistency. Temporal constraints and finetuning used in [57, 63] could further improve this aspect." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.493, + 0.891, + 0.713 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.627, + 0.741 + ], + "angle": 0, + "content": "7. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We have presented a novel method for face image, and its potential for video inversion and editing. Our method handles OOD objects by isolating them from the InD part. Our method achieves accurate reconstruction by building two radiance fields and then composing them together during the rendering. By modifying the latent code in the InD part, we can obtain faithful editing results. We show that our method achieves a better balance in the reconstruction-editability trade-off than other baselines. Malicious use of our technique may lead to misinformation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7232" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In ICCV, 2019. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[2] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan++: How to edit the embedded images? In CVPR, 2020. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.198, + 0.468, + 0.265 + ], + "angle": 0, + "content": "[3] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. 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In ECCV, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7235" + } + ] +] \ No newline at end of file diff --git a/2024/In-N-Out_ Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing/937da690-a378-4303-a4f6-0fbaa725c37d_origin.pdf b/2024/In-N-Out_ Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing/937da690-a378-4303-a4f6-0fbaa725c37d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3534a783ff9cc8091a6b90e314708634dfe30b5d --- /dev/null +++ b/2024/In-N-Out_ Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing/937da690-a378-4303-a4f6-0fbaa725c37d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0623591c7a7f833e3fc7ac6fb4dce18dc673392aa558ba7720cd66617286d268 +size 4011251 diff --git a/2024/In-N-Out_ Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing/full.md b/2024/In-N-Out_ Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1cd43765e2795d014613df6b95a044a69b5655d5 --- /dev/null +++ b/2024/In-N-Out_ Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing/full.md @@ -0,0 +1,451 @@ +# In-N-Out: Faithful 3D GAN Inversion with Volumetric Decomposition for Face Editing + +Yiran Xu + +Zhixin Shu² + +Cameron Smith + +Seoung Wug Oh² + +Jia-Bin Huang + +1University of Maryland, College Park, 2Adobe Research + +![](images/5750a34f5344f1e53a374dba6dec0bbdb36358d3c5f501f7024450359cc2476f.jpg) + +![](images/2cb48b45520f48d46d1dd142d8deccc90eb7ee2695a1bd490f2e6b665f306a3c.jpg) +Input +Input + +![](images/51a301790e69fff6406bd1a8b61c15b95371ac80528646736c670e7244a074e6.jpg) + +![](images/776b75483b8aa78deaeb45aec84d7cb3b456fbd888342b4cb856f7a7d450a296.jpg) +Recon + +![](images/a003860af655011338a4037d5dcd14c2ce799cc15e522dc9ae6a3bf5aab3b5b9.jpg) +Recon. + +![](images/849c7ba6d51f3e079bfab7422d0b01f7babc3f969507fa9bcc4d1a429fdbb0e6.jpg) + +![](images/695a30965c5a5f7675f66407ebfd132acf65e6d2c78a15e67d337b780f950b77.jpg) + +![](images/eedea0ffbdcbbe8571a4abf174bf927eb27998fdaab89a5b4b6c819c219225a3.jpg) +Surprised + +![](images/a2d085ef7d6771436797adf9b35c632d10c70a87fbaa2f7489df4f080e3be29f.jpg) +Less smile + +![](images/87c0a33c5954b7689462a14cd3a34e69e161181612c86934ba72b5259571cd24.jpg) + +![](images/8f6fcb35947ab3accfafa91c6f54c726dac030b051f6508beda7eee7d8ebd4d5.jpg) + +![](images/b4079fca83051792aaa8ba6779ae9e6f4f5ad3299b016f224854c47351732a41.jpg) +Younger + +![](images/826eb0ba359be3303f42532643b18d9955f4fd67b238de973bc3515d255eac7d.jpg) +Blond + +![](images/94fcbb07595ee65e389e77ef967f2f1b6f925877d6c33e5071506c6b11ceb549.jpg) + +![](images/6fc85c01210241e4b4a55a34dbb7fdb2da84a0d0c37c71bdc52cf790a630cae8.jpg) + +![](images/cd42b860f870df6042f4c64213a622bec0668c9e582ecf14d498dd20d138af8d.jpg) +Elsa + +![](images/647e0a7ab53d17b5338f0b169ed842ade59e239b166a81ba1a1974c36fa2e3c2.jpg) +Elsa + +![](images/4fe9fc65cf277ba1a0a996311f9084b9581e99767913ecce3cb0ba0dc5f13c5e.jpg) + +![](images/71771b4f042e34e0979ac2b389a5e27b827d178889c1630d71f1fccdb21d3853.jpg) + +![](images/8ec2340437ebd852630fd869039abae6a1c0d6d3f2e13dbbcdc4ee25a9f5b693.jpg) +OD Removal + +![](images/b681712ad578de8daaa68119a055207c6a2a81b309e4f0aa341e621458b3af1b.jpg) +OOD Removal + +![](images/5bdca1810f7b3a4c2df0a3f012be88dc651770f84c46051cbd5dbb368ded9b8d.jpg) + +![](images/78c7cba190e6e91c39a9deeb798dfb06df31e05734b9340144ff9d6b8719699d.jpg) +Figure 1. Semantic editing for out-of-distribution data. We present a method for reconstructing and editing an out-of-distribution (OOD) image or video using a pre-trained 3D-aware generative model (EG3D [10]). Our method explicitly models and reconstructs the occluders in 3D, allowing faithful reconstruction of the input while preserving the semantic editing capability. Here we showcase the reconstruction and editing results "Less smile", "Younger", "Blond" [47], "Elsa", "Surprised" [41]. Our method can also remove the OOD part. Data are from the Internet (Creative Commons). + +# Abstract + +3D-aware GANs offer new capabilities for view synthesis while preserving the editing functionalities of their 2D counterparts. GAN inversion is a crucial step that seeks the latent code to reconstruct input images or videos, subsequently enabling diverse editing tasks through manipulation of this latent code. However, a model pre-trained on a particular dataset (e.g., $FFHQ$ ) often has difficulty re + +constructing images with out-of-distribution (OOD) objects such as faces with heavy make-up or occluding objects. We address this issue by explicitly modeling OOD objects from the input in 3D-aware GANs. Our core idea is to represent the image using two individual neural radiance fields: one for the in-distribution content and the other for the out-of-distribution object. The final reconstruction is achieved by optimizing the composition of these two radiance fields with carefully designed regularization. We demonstrate that + +our explicit decomposition alleviates the inherent trade-off between reconstruction fidelity and editability. We evaluate reconstruction accuracy and editability of our method on challenging real face images and videos and showcase favorable results against other baselines. More results can be found at https://in-n-out-3d.github.io/. + +# 1. Introduction + +GAN inversion [3, 44, 55, 61, 70] is a set of techniques that project an input image onto the latent space of a pretrained GAN to obtain a latent code so that the image generator can reconstruct the input. This is particularly useful as one could perform various creative semantic editing tasks [18, 24, 41, 47] for images. Similar techniques have also been applied in the video domain, with which recent methods also achieved temporally consistent editing [57, 63]. However, the majority of these methods are effective primarily with 2D GANs, and they fall short in offering explicit 3D controllability, such as view synthesis capabilities. With the rapid recent advancements in 3D reconstruction, especially in neural radiance fields (NeRFs) [6, 11, 36, 37], high-quality 3D-aware GANs [10, 22, 40, 49] have emerged as a powerful tool for learning 3D generation from 2D images. 3D-aware GANs, equipped with a 3D representations like NeRFs [10, 22] or SDF [40], offer explicit control over camera views and ensure 3D geometric consistency in generation. Additionally, they retain the generative capacity and editability of 2D GANs [26-29]. This enables applications such as novel view synthesis, semantic image editing [31, 48, 51, 62, 66, 67] and video editing [17, 56]. + +Core challenges. While state-of-the-art 3D GAN inversion methods achieve remarkable advances in both image and video editing for human faces, they face challenges when dealing with images including out-of-distribution (OOD) objects (e.g., heavy make-ups or occlusions). This limitation arises primarily because these models are pre-trained only on natural faces without complex textures or substantial occlusions. As a result, the editability performance deteriorates when a pre-trained GAN is forced to model OOD objects in the GAN inversion process. This is commonly known as the reconstruction-editability trade-off [55]. Existing GAN inversion methods assume that a single latent code corresponding to the input image can be found in the latent space [50, 61] through optimization once the model is trained. Therefore, they aim to reconstruct the indistribution (InD) content (e.g., natural face) and the OOD objects together. However, OOD components often cannot be well modeled in a pre-trained GAN, and consequently cannot be well represented with it using a single latent code, existing methods either cannot reconstruct them faithfully [51] or can reconstruct them (e.g., through fine-tuning the generator) but alters the latent space properties and de + +![](images/01669d708f68f1831a53337352a79b2f2ddce9310947c2ad34bca065ec97a007.jpg) + +![](images/a850c6ab7d5cf9ec4cd20be724289498d9defe16435b0ba5473ebdb675ec5e3a.jpg) +Input + +![](images/42cbb6846d737fca4961c1165290a40830c78466bf8c9be160c010f5ed122de8.jpg) + +![](images/1ee3a65bafa226154da39acd8c17bae8362db3336bf8a1a60c763c06465413f1.jpg) +GOAE [67] + +![](images/f258d29636e5310715e878e0b3dd0d9fa14209dc6e23a3834824e05fee13e771.jpg) + +![](images/46369bb1b87c2677840dcf3f8b20e9c36456f35a04b7e94e692ca5f3aad3f1a6.jpg) +PTI [45] +Figure 2. Limitations of the previous methods. Existing GAN inversion techniques cannot deal with frames with OOD elements, resulting in a poor reconstruction-editing balance. + +GOAE [67] can produce faithful editing, but fails to preserve the identity of the input face. PTI [45] provides higher reconstruction fieldity, but the edibility suffers. + +teriorates the editability [45] (Figure 2). + +Our work. We propose a new approach to address this issue by drawing inspiration from recent composite volume rendering works that compose multiple radiance fields during rendering [19, 34, 59, 64]. Our core idea is to decompose the 3D representation of an image with OOD components into an in-distribution (InD) part and an out-of-distribution part, and compose them together to reconstruct the image in a composite volumetric rendering manner. We use EG3D [10] as our 3D-aware GAN backbone and leverage its tri-plane representation to model this composed rendering pipeline. For the InD component (i.e. natural face), we project pixel values onto EG3D's $\mathcal{W}+$ space for an InD component reconstruction. We further introduce an additional tri-plane to represent the OOD content. After that, we combine these two radiance fields in a composite volumetric rendering to reconstruct the input frames. During the editing stage, we perform the latent code based editing solely on the InD part and leave the OOD component unaltered. This framework would allow the applications of any StyleGAN-based editing approache [41, 47] on the InD component such as changing facial expression, which is often desirable for user experiences. The advantages of our work are three-fold: a) we achieve a higher-fidelity reconstruction by composition of InD and OOD components; b) we retain the editability of pre-trained GANs by editing only the InD content; and c) by leveraging 3D-aware GANs, we can render the face from novel viewpoints. + +We evaluate our method on challenging in-the-wild face images and videos (Creative Commons), demonstrating improvement over previous state-of-the-art GAN inversion work on both reconstruction and editing quality. In addition, we demonstrate the usefulness of our method with + +3D-aware editing applications, including semantic editing, novel view synthesis, and OOD object removal. + +We will release the code and data used in the paper. + +Our contributions. In summary, our contributions are: + +- We propose a 3D-aware GAN inversion approach to manipulate single images or monocular videos with out-of-distribution objects (e.g., accessories and heavy makeup). See results in Figure 1. +- We incorporate composite volume rendering into 3D-aware GAN inversion. +- Our method reconstructs 3D shapes of faces with OOD objects faithfully and demonstrates novel 3D-aware applications. + +# 2. Related Work + +3D-aware GANs. StyleGANs [26-29] have achieved high-quality photorealistic 2D image generation and have been successfully applied to various image editing applications [18, 24, 41, 47]. Significant progresses have also been made to lift 2D image generation to 3D space, using various 3D representations, for both higher quality generation and to enable 3D-aware applications such as view synthesis [9, 10, 16, 20, 22, 38, 40, 46, 49, 51]. These methods usually take a two-stage pipeline that renders a raw image (usually also with feature maps) in low resolution and then upsamples the rendered image to high resolution. We leverage EG3D [10] as our generator architecture in this work. + +GAN inversion and editing. GAN inversion has been widely studied for 2D GANs. These techniques can largely be categorized as (a) encoder-based methods [4, 8, 33, 39, 44, 44, 54, 55, 55, 58] in which a neural network encoder is trained to project an input image to the latent space of the generator; (b) optimization-based methods [1, 2, 12, 13, 21, 25, 42, 53] where the latent code is recovered via optimizing loss functions between the generator output and a target image; and (c) hybrid methods [5, 7, 45, 71] which combine both approaches. Some recent works have also investigated 3D-aware GAN inversion from a single image [31, 32, 51, 56, 62, 66, 67] or a video [17, 68]. As our experiments demonstrate, previous approaches have difficulty handling these challenging cases. We propose a new mechanism to allow high-quality 3D-aware GAN inversion of out-of-distribution faces even under significant occlusion. With our GAN inversion, we can modify the latent code to perform high-quality semantic image editing [18, 24, 41, 47] or video editing [57, 63, 65]. + +GAN inversion for out-of-distribution (OOD) data. There have been attempts to invert out-of-distribution data to the GAN's latent space. Early work [1] proposes to project an image onto extended $\mathcal{W}^+$ space to achieve more accurate reconstruction. PTI [45] finetunes generator with regularization for a lower distortion error. StyleSpace [60] + +proposes to invert an image using StyleGAN's internal feature maps and tRGB blocks, which shows better reconstruction and disentanglement. Recently, ChunkyGAN [50] proposes to compose multiple generated images from multiple latent codes, with a set of segmentation masks to reconstruct an input image. With a similar goal in mind, we propose to leverage the radiance field of EG3D [10] and decompose the volumetric representation into an in-distribution part and an out-of-distribution part. In contrast to ChunkyGAN [50] that models an image as a collection of $2D$ segments, we model the OOD and face directly in volumetric 3D representation and merge them with composite rendering. + +Composite neural radiance fields. Neural Radiance Fields (NeRFs) [36] have shown impressive view synthesis results. Recently, it has been shown that 3D scenes can be decomposed into different NeRFs. When multiple radiance fields are built, one can compose them together using a composite rendering manner [19, 34, 59, 64]. EG3D [10] uses the tri-plane representation to generate 3D objects from the latent code. We adopt the idea of composite volume rendering to address the out-of-distribution 3D GAN inversion problem. Specifically, we split the in-distribution and out-of-distribution parts in the tri-plane 3D representation and compose them during volume rendering. + +# 3. 3D-aware GAN: EG3D + +We choose EG3D [10], which consists of a tri-plane representation and a super-resolution (SR) module, as our 3D-aware GAN. + +Neural rendering at low resolution. Given a latent code $z \in \mathbb{R}^{512}$ (or $w \in \mathbb{R}^{14 \times 512}$ ) and camera parameters $p$ , EG3D first generates a corresponding tri-plane $\mathbf{T} \in \mathbb{R}^{256 \times 256 \times 32 \times 3}$ . For each pixel, a ray $\mathbf{r}$ is cast, and points are sampled along the ray. Unlike the positional encoding [34, 52] for each point in NeRFs [34], EG3D projects each point onto tri-plane $\mathbf{T}$ and retrieves features from three planes via bilinear interpolation. These features are then aggregated by summation, and fed into the decoder $D$ (i.e., an MLP) to predict the color and density. Volume rendering [35] is then performed to compute the final color for each pixel. To this end, a raw RGB image with a 32-channel feature in a low resolution (e.g. $128 \times 128$ ) is generated. + +Super-Resolution (SR). To gain high-resolution outputs, EG3D later uses an SR module that inputs the raw image and the 32-channel feature as the input and yields a high-resolution RGB image (e.g. $512 \times 512$ ). We build our approach upon EG3D due to its rendering efficiency compared to other alternatives [22, 40]. + +# 4. Method + +Given an aligned face input image $\mathbf{I}$ , or a monocular face video $\mathbf{V} = [\mathbf{I}_1, \dots, \mathbf{I}_t, \dots, \mathbf{I}_N]$ with $N$ frames, we aim + +![](images/3b41f43539eace6b6751cfec2bf3e9ca23ca32d8cc22b3603d5d14e69fffcd64.jpg) +Figure 3. Overview of our method. Given a potrait image or a monocular portrait video, we use two radiance fields to represent (a) in-distribution $(\text{InD})$ face, and (b) out-of-distribution $(\text{OOD})$ item. (a) InD reconstruction is the GAN inversion for the in-distribution natural face. We apply GAN inversion by using pre-trained EG3D model $G$ to the frame, where the pre-trained tri-plane generator and tri-plane decoder $D^{I}$ are kept frozen. (b) For OOD item, we propose to model them with a separate radiance field represented by an additional tri-plane $\mathbf{T}^O$ . During the training process, we optimize the tri-plane $\mathbf{T}^O$ , a per-frame latent code $\phi_t$ , and a new decoder $D^O$ . The decoder takes as input tri-plane features $\mathbf{T}^O$ and $\phi_t$ and outputs color $\mathbf{c}^O$ , density $\sigma^O$ , and blending weight $b$ . (c) Composite Rendering compose the InD and OOD radiance fields together by using a composite rendering scheme (Section 4.3). (d) Finally, we finetune the Super-Resolution module in $G$ to achieve a better output in the high resolution. After training, we can perform various semantic edits and free-view rendering, while preserving the face identity and the OOD components. + +to reconstruct the input with EG3D inversion and perform face editing. For simplicity, we use $\mathbf{I}_t$ to represent a frame, either from a single input image or a sampled frame from a video. If only one frame exists, then $N = 1$ . + +We present the high-level overview in Figure 3. We build two neural radiance fields (NeRFs) [36], one for in-distribution (InD) face (Section 4.1), and the other one for out-of-distribution (OOD) object (Section 4.2), using triplane representations [10]. The OOD object, for example, can be a non-face object with a rigid shape or heavy makeup with a complicated texture. Next, we combine two radiance fields (Section 4.3) to reconstruct the low-resolution frame. Finally, we finetune the super-resolution module of EG3D to get the high-resolution output (Section 4.5). After training the radiance fields, we can edit the face image or video + +(Section 4.6). + +# 4.1. In-distribution GAN inversion + +Formulation. Since a pretrained EG3D already has prior knowledge of faces, we directly leverage its latent space and perform a regular 3D GAN inversion [32, 61] for the in-distribution part. For a single frame case, we optimize a latent code $w_{t}$ such that it can reconstruct the input frame $\mathbf{I}_t$ . For a video, we invert all the frames at the same time. Please refer to the supplementary material for more details. For camera parameters $p_t \in \mathbb{R}^{25}$ , we obtain them by using an off-the-shelf pose detector [15], following [10, 32]. + +Optimization. To represent the InD faces with $\mathbf{T}^I$ , our insight is to keep the latent code $w_{t}$ in distribution as much as possible. To this end, we use a regularization term to keep + +$w_{t}$ within its pre-trained distribution through GAN training. + +$$ +\mathcal {L} _ {w} \left(w _ {t}\right) = \left| \left| w _ {t} - \bar {w} \right| \right| _ {2} ^ {2}, \tag {1} +$$ + +where $\bar{w}$ is the mean latent code computed over 10,000 sampled latent codes. + +We also use a another regularization term adopted from [55] to constrain the variation among style vectors in $w$ : $\mathcal{L}_{\Delta}(w_t) = \sum_{i=1}^{13} ||\Delta_i||_2^2$ , given a latent code $w = (w_0, w_0 + \Delta_1, \dots, w_0 + \Delta_{13}) \in \mathbb{R}^{14 \times 512}$ . This regularization term preserves the editability of the optimized latent code [55]. + +# 4.2. Modeling out-of-distribution contents + +For an OOD object, a pre-trained EG3D usually cannot model it well with its prior distribution. We therefore use an additional tri-plane $\mathbf{T}^O$ to represent the out-of-distribution content. One additional challenge is that, while dealing with video, the OOD object may not be static across different frames, therefore could not be well reconstructed with a static radiance field. Therefore, in addition to $\mathbf{T}^O$ , we use a per-frame latent code $\phi_t \in \mathbb{R}^{32}$ for each frame to represent the out-of-distribution object across the temporal domain. Both $\mathbf{T}^O$ and $\phi_t$ are randomly initialized from a normal distribution. + +Formulation. The out-of-distribution decoder $D^{O}$ takes a tuple $(\mathbf{T}^{O}(t_{k}),\phi_{t})\in \mathbb{R}^{64}$ as the input, and outputs color $\mathbf{c}^O\in \mathbb{R}^3$ , density $\sigma^O\in \mathbb{R}$ , and blending weight $b\in [0,1]$ + +$$ +\left(\mathbf {c} ^ {O}, \sigma^ {O}, b\right) = D ^ {O} \left(\mathbf {T} ^ {O} \left(t _ {k}\right), \phi_ {t}; \theta_ {D ^ {O}}\right), \tag {2} +$$ + +where $\mathbf{T}^O (t_k)\in \mathbb{R}^{32}$ is the aggregated features obtained by projecting 3D coordinate $t_k$ onto each of the three feature planes via bilinear interpolation, then aggregated via summation [10]. The decoder $D^{O}$ is an MLP with weights of $\theta_{DO}$ . To compute the color of a pixel at time $t$ , we use the volume rendering integral along the ray $\mathbf{r}$ : + +$$ +\mathbf {C} ^ {O} (\mathbf {r}) = \sum_ {k = 1} ^ {K} T \left(t _ {k}\right) \alpha^ {O} \left(\sigma^ {O} \left(t _ {k}\right) \delta_ {k}\right) \mathbf {c} ^ {O} \left(t _ {k}\right), \tag {3} +$$ + +where $T(t_k) = \exp(-\sum_{k'=1}^{k-1} \sigma(t_{k'}) \delta_{k'})$ , $\alpha = 1 - \exp(-x)$ , and $\delta_k = t_{k+1} - t_k$ is the distance between two 3D points. + +# 4.3. Composite volume rendering + +Now, with both InD and OOD radiance fields, we can combine them using the blending weight $b$ from Eqn. 2. + +Formulation. We compose two radiance fields together by + +$$ +\begin{array}{l} \mathbf {C} ^ {C} (\mathbf {r}) = \sum_ {k = 1} ^ {K} T ^ {C} \left(t _ {k}\right) \left(b \alpha^ {O} \left(\sigma^ {O} \left(t _ {k}\right) \delta_ {k}\right) \mathbf {c} ^ {O} \left(t _ {k}\right) \right. \tag {4} \\ \left. + (1 - b) \alpha^ {I} \left(\sigma^ {I} \left(t _ {k}\right) \delta_ {k}\right) \mathbf {c} ^ {I} \left(t _ {k}\right)\right), \\ \end{array} +$$ + +where $T^{C}(t_{k}) = \exp (-\sum_{k^{\prime} = 1}^{k - 1}(\sigma^{O} + \sigma^{I})\delta_{k^{\prime}})$ + +Optimization. The goal is + +$$ +\begin{array}{l} w_{t}^{*},\mathbf{T}^{O^{*}},\theta_{D O}^{*},\phi_{t}^{*} = \operatorname *{argmin}_{w_{t},\mathbf{T}^{O},\theta_{D O},\phi_{t}}\mathcal{L}_{t}^{C} \\ = \operatorname *{argmin}_{w_{t},\mathbf{T}^{O},\theta_{D^{O}},\phi_{t}}\sum_{ij}||C^{C}(\mathbf{r}_{ij}) - C^{GT}(\mathbf{r}_{ij})||_{2}^{2} \\ + \lambda_ {b} \mathcal {L} _ {b} \left(\mathbf {r} _ {i j}\right) + \mathcal {L} _ {L P I P S} \left(\mathbf {I} _ {L R} ^ {C}, \mathbf {I} _ {L R}\right), \tag {5} \\ \end{array} +$$ + +where $\mathcal{L}_{LPIPS}$ is the LPIPS loss [69], $\mathbf{I}_{LR}^{C}$ is the composite rendered image at low resolution $(128\times 128)$ , $\mathbf{I}_{LR}$ is the ground truth image also at $128\times 128$ . The weight regularizer $\mathcal{L}_b$ is adopted from [59], used to penalize the blending weight $b$ if it is not closer to 0 or 1: + +$$ +\mathcal {L} _ {b} (\mathbf {r}) = \sum_ {k = 1} ^ {K} H _ {b} (b \left(t _ {k}\right)), \tag {6} +$$ + +where $H_{b}(x) = -(x\log (x) + (1 - x)\log (x))$ is binary entropy. The reason behind Eqn. 6 is that objects cannot co-occupy the same spatial location. The entropy loss facilitates a cleaner decomposition: encouraging an object to be either in-distribution (i.e. $b\to 0$ ) or out-of-distribution (i.e. $b\rightarrow 1$ ). + +However, it is ill-posed to build its 3D geometry accurately, given only a single-frame input, even with a pretrained 3D-aware generator. Therefore, for a single image only, we also introduce a depth regularization term: + +$$ +\mathcal {L} _ {\mathcal {D}} = \left| \left| \mathcal {D} ^ {C} - \mathcal {D} ^ {R e g} \right| \right| _ {1} \tag {7} +$$ + +where $\mathcal{D}^C$ is the rendering depth map from composite rendering, and $\mathcal{D}^{Reg}$ is a rescaled depth map from MiDaS [43]. + +# 4.4. Low-resolution reconstruction + +In practice, we jointly optimize for $w_{t}$ (yielding $\mathbf{T}^{I}$ ), $\mathbf{T}^{O}$ , $\theta_{DO}$ , $\phi_{t}$ , following Section 4.1 to Section 4.3. Our total loss function is + +$$ +\mathcal {L} ^ {L R} = \sum_ {t = 1} ^ {N} \mathcal {L} _ {t} ^ {C} + \lambda_ {\Delta} \mathcal {L} _ {\Delta} + \lambda_ {w} \mathcal {L} _ {w} + (\lambda_ {\mathcal {D}} \mathcal {L} _ {\mathcal {D}}), \tag {8} +$$ + +where $\mathcal{L}_t^C$ is from Eqn. 4, latent variation regularizer $\mathcal{L}_{\Delta}$ from [55], and $\mathcal{L}_w$ from Eqn. 1, respectively, $\lambda_{\Delta}$ is the weight for $\mathcal{L}_{\Delta}$ , $\lambda_w$ is the weight for $\mathcal{L}_w$ , and $\lambda_{\mathcal{D}}$ is the weight for $\mathcal{L}_{\mathcal{D}}$ . We only use $\mathcal{L}_{\mathcal{D}}$ for single image input. + +# 4.5. Super-Resolution + +After training in Section 4.1, 4.2, 4.3 and 4.4, we can get reconstruction $\mathbf{I}_{LR}^{C}$ in low resolution $(128\times 128)$ . We observe that using the pretrained super-resolution (SR) module cannot generate a satisfying high-resolution output, as shown in Figure 4, due to the new OOD tri-plane $\mathbf{T}^O$ . Therefore, we finetune only the SR module in $G$ for higher resolution + +![](images/bbd8b66ebb236f2e5108aeeecbec65d900d9d29c99be92a79d3134c0af6f28ab.jpg) +Recon. Target + +![](images/88dc952a5493125ed24d17a25249102f932133e6ee144694bb81163c35a54147.jpg) +w/o finetuning SR module + +![](images/c2c98ab2b625de9d54d5295e9ed1f70940be2ae30d1f9b517909e6582420e613.jpg) +w/ finetuning SR module +Figure 4. The effect of finetuning SR module. Without finetuning the SR module, the high-resolution output is blurry. + +at $512 \times 512$ . + +Optimization. The loss function is that + +$$ +\mathcal {L} ^ {S R} (\mathbf {x}, \hat {\mathbf {x}}) = \| \mathbf {x} - \hat {\mathbf {x}} \| _ {2} ^ {2} + \mathcal {L} _ {L P I P S} (\mathbf {x}, \hat {\mathbf {x}}), \tag {9} +$$ + +where $\mathbf{x} = \mathbf{I}_t$ and $\hat{\mathbf{x}} = SR(\mathbf{I}_{LR}^C)$ + +# 4.6. Editing + +After the reconstruction, we can modify the latent code $w_{t}$ to perform various semantic editing tasks. With explicit decomposition, the OOD contents do not interfere with the semantic editing capability of in-distribution components. Here, any existing GAN-based editing approaches can be used. We use InterfaceGAN [47] and StyleCLIP [41]. + +# 5. Experimental Results + +# 5.1. Experimental Setup + +Dataset. To evaluate how our approach works on data with out-of-distribution components, we collected a dataset of 20 online videos with challenging and diverse appearances. The OOD content contains heavy make-up and occluding objects (e.g. facial masks and large glasses). For the single-image inversion method, we use the first frame of each video. For video inversion, we use all the frames. For the face alignment, we use 3DDFA-v2 [23] to obtain the 68-point landmarks and smooth them across the frames using a sliding window for stabler cropping. After that, we convert the landmarks to EG3D's 5-point landmarks and crop the face out of the input frame. + +Hyperparameters. We use the Adam optimizer [30] for all our experiments. For in-distribution inversion (Section 4.1), we optimize for 200 epochs with a learning rate of $1 \times 10^{-3}$ , $\lambda_{\Delta} = 1 \times 10^{-3}$ . For the out-of-distribution and composite rendering (Section 4.2, 4.3), we run the optimization for 10,000 iterations with a learning rate of $5 \times 10^{-3}$ , $\lambda_{b} = 1$ , $\lambda_{w} = 1$ , and $\lambda_{\mathcal{D}} = 0.1$ if applicable. For the SR module (Section 4.5), we finetune the module for 100 epochs with a learning rate of $1 \times 10^{-3}$ . + +Metrics. We evaluate our approach from 1) reconstruction accuracy and 2) editability to validate the reconstruction- + +editability trade-off. For the reconstruction accuracy, we report LPIPS [69], PSNR, SSIM and ID similarity [14]. For editability, we follow [45, 50] and evaluate identity preservation after applying the editing direction. More specifically, we use ArcFace [14] to compute the similarity between the inverted and edited results. + +Baselines for evaluation. We compare our method extensively with several previous arts. For optimization-based methods, we compare with HFGI3D [62], PTI [45], $\mathcal{W}+$ , and $\mathcal{W}$ optimization. For videos only, we also include VIVE3D [17]. We compare the encoder-based method with GOAE [67] and IDE-3D [51] encoder. We treat $\mathcal{W}+$ optimization as an ablated version of our method without OOD triplane. The recent work in [56] showcases encoder-based 3D GAN inversion, focusing on real-time inference. However, their method relies on a frozen EG3D and does not explicitly model the OOD components. We do not compare with it as the code is not publicly available. + +# 5.2. Quantitative results + +Reconstruction. We compare the reconstruction accuracy of our approach with all baselines and report the results in Table 1. For PTI, we first perform a $\mathcal{W}+$ inversion with a learning rate of $1 \times 10^{-3}$ and 200 epochs, and then finetune the generator for 200 epochs with a learning rate of $3 \times 10^{-5}$ . For $\mathcal{W}+$ and $\mathcal{W}$ optimization, we use a learning rate of $1 \times 10^{-3}$ and optimize for 200 epochs. For GOAE and IDE-3D, we use their encoder directly for the inversion. + +Our approach outperforms other methods on all the evaluation metrics. This indicates that our method produces a more accurate reconstruction with the OOD components. + +Editability. We acquire editing directions from InterfaceGAN [47] ("younger", "smile") and StyleCLIP mapper [41] ("eyeglasses", "surprised", "Elsa"). Following previous work [45, 50], we measure the ID similarity between the inverted image and the edited image, as the editing should not change a person's identity. We report our results in Table 2. Our method outperforms other baselines in terms of identity preservation in most cases. + +# 5.3. Qualitative results + +Inversion. We visually compare the video reconstruction in Figure 5. Our method provides higher-fidelity reconstruction results than other baselines, particularly for OOD regions (e.g., heavy make-up or earrings). Our method shows better reconstruction than the encoder-based method GOAE [67] and IDE-3D [51]. Compared to optimization-based methods, HFGI3D [62], VIVE3D [17], PTI [45], $\mathcal{W}$ , and $\mathcal{W}+$ , our method shows higher-fidelity reconstruction for OOD objects (Refer to our supplementary material for more results). + +Editing. We show a qualitative comparison regarding the editing in Figure 6. Our method shows faithful editing + +![](images/a1cf8f9267c1f3a239e9caa17ace22c49f0ffa5280cce59e8ec5b0b65869af95.jpg) +Figure 5. Qualitative comparison of the video reconstruction. We compare our approach with $\mathcal{W}+$ and $\mathcal{W}$ optimization, IDE-3D [51], GOAE [67], HFGI3D [62], VIVE3D [17], and PTI [45]. Our method shows a better reconstruction accuracy on the OOD videos. + +![](images/9db79a933db688b3e73a655455bf34e9666baa9bd3cbdcaffa2ab5a19cd72806.jpg) + +![](images/6b7d4352065a3cbbafb3f6fce136a05468f39340beb2e92e2e158d0909afe003.jpg) + +![](images/640974a9fe30483e175d7f742504032a4bc2bd79ace51f5d8feb9ac9ee8ce29d.jpg) + +
ImagesVideos
LPIPS↓SSIM↑PSNR↑ID Similarity↑Time↓LPIPS↓SSIM↑PSNR↑ID Similarity↑
Ours0.11060.817519.860.96852.68h0.22370.705216.030.9758
HFGI3D [62]0.39120.552111.370.94637.51h0.39540.558711.550.9388
GOAE [67]0.36190.642414.730.968556s0.36420.647014.970.3642
E3DGE [31]0.17090.773815.280.8632-----
VIVE3D [17]----0.59h0.41720.541710.660.9245
PTI [45]0.31920.617212.930.96761.45h0.31440.632013.450.9658
IDE-3D [51]0.50440.43959.180.845677s0.49990.45129.590.8251
W+0.34330.638714.390.91990.49h0.33800.655714.750.9154
W0.40970.561512.080.87570.47h0.40300.578712.480.8652
+ +Table 1. Reconstruction quality evaluation. For each column, deeper color the better. + +
ImagesVideos
eyeglassessurprisedyoungersmileElsaaverageeyeglassessurprisedyoungersmileElsaaverage
Ours.9532.9888.9495.9525.9116.9511.9158.9360.9347.9094.8927.9177
HFGI3D [62].9484.9795.9453.9223.8641.9319.9112.9109.9290.9155.8622.9058
GOAE [67].9179.9306.9327.9332.8851.9199.9120.9224.9235.9221.8641.9088
E3DGE [31]--.8853.9487-0.9170------
VIVE3D [17]------.9078.9475.9183.9369.8728.9167
PTI [45].9114.9562.9380.9410.7927.9079.9049.9357.9319.9336.7945.9001
IDE-3D [51].8811.9538.8723.8055.8780.8781.8767.9481.8551.8662.7871.8666
W+.9012.9567.9248.9356.7892.9015.8971.9249.9290.9170.7968.8930
W.8808.9567.9177.9290.8008.8970.8793.9537.9068.9208.8113.8944
+ +results. For more qualitative results, please refer to our supplementary material. + +# 5.4. Other Applications + +View synthesis. The use of 3D GANs supports rendering novel views after inversion. We show novel view synthesis results in Figure 7. + +Object removal. By setting the blending weights of the OOD objects to 0, we can remove OOD objects. We show results in Figure 1. + +Table 2. Identity preservation evaluation. Higher numbers indicate better identity preservation. $\mathcal{W} +$ is equivalent to our method without OOD tri-plane. + +
InversionEditing
L2↓LPIPS↓ID similarity↑
w/o Lb0.03220.21910.9070
w/o Lw0.03360.22380.9024
Full method0.03390.22370.9177
+ +Table 3. Ablation study. We study the effect of different loss functions on 20 videos. For inversion, we compute the metrics between reconstructed frames and input frames. For editing, we compute the ID similarity between before and after editing. + +# 5.5. Ablation Study + +We introduce two new loss functions, Eqn. 1 and Eqn. 6, to preserve the editability from the impact of the OOD radiance field in Section 4.3. To validate the loss functions' effects, we conduct an ablation study in Table 3. Without the weight regularization, $\mathcal{L}_b$ , and latent code regularizer $\mathcal{L}_w$ , the reconstruction accuracy is improved while the editability is reduced. One of the reasons is that GAN-based editing usually also brings unwanted changes to other attributes [47]. In Figure 8, the editing direction "eyeglasses" also moves the position of the eyes. At this time, if the blending weight $b$ is closer to 1 for pixels outside the OOD object, i.e. the OOD part has more contributions, the editing tends to keep the pixel values in the reconstruction stage. While the eyes will be moved due to the editing direction, it results in the duplicate eyes in Figure 8(a). In contrast, with regularization (Eqn. 1 and Eqn. 6) on the blending weights, pixels in the in-distribution part contribute more to the output, which better supports the editing since we can only edit the in-distribution part. Similar cases happen to $\mathcal{L}_w$ . With + +![](images/786be30cf6817752286a74b54afcc0080be941283d47bbd629c86ea38a8ad006.jpg) +Figure 6. Qualitative comparison of the editing. We compare our editing results from a single image and a video with other baselines, with different editing latent directions "Eyeglasses". Our approach can preserve the original appearance details better, and shows improved editability over other baselines. + +![](images/b9e3f0cdbbdb73030d7bb333c4d3148c7abe8bf52ed9a99d6b8e872c07d9dd57.jpg) + +![](images/a87017d855e9457a69a7897bf724180a7aee84fc4d4640dee0ea43ad8565f5b1.jpg) + +![](images/853c8600e474e46316a26f16359759188ff3a9b6a6aaf4612c514deec93098da.jpg) + +![](images/0f467511554c4cc97dc8f4f78b24831bf368024a9667100977ef29c581cfcf47.jpg) +Figure 7. Novel view synthesis. We can synthesize novel views for a fixed frame in a video, which is challenging for 2D GANs. Each column shows different view for the same frame. +(a) $\mathrm{w / o}\mathcal{L}_b$ +Figure 8. Ablation study on editing. (a) Without $\mathcal{L}_b$ , the out-of-distribution component dominates ( $b \to 1$ ) and weakens the editing. It has "Duplicate eyes" artifact because the editing direction "eyeglasses" is not disentangled well with other attributes, and changes the positions of the eyes, while the blending weights are the same as the reconstruction, it results in duplicated eyes. (b) Without $\mathcal{L}_w$ , the eyebrow becomes unnatural. + +![](images/dcf76b0b8074b53a3bee430c28d2938aba1454f0c61fb16d623b527fde7560f8.jpg) +(b) $\mathrm{w / o}\mathcal{L}_w$ + +![](images/04197dd14a1468d0b7af65bd05c58c34a8d1082921db57a6eaf20136afe30d43.jpg) +(c) Full model +Figure 9. Limitations. Our approach has some limitations. (a) Editing on where OOD blending weights dominate is challenging, (b) Adding another eyeglasses to OOD eyeglasses will result in duplicated objects, and (c) extreme poses. + +out $\mathcal{L}_w$ , the eyebrow becomes unnatural in Figure 8 (b). + +# 5.6. Speed + +We include a comparison of different baselines in Table 1. We compare the speed on 200 frames using a single NVIDIA RTX A6000 GPU. Our method takes more time for optimization but significantly improves the reconstruction-editability trade-off. + +# 6. Limitations + +Our method still has several limitations. We visualize (a)-(c) in Figure 9. + +(a) Editing on OOD part. When editing on the OOD region, e.g. adding eyeglasses to the heavy makeup region, because the blending weights are closer to 1, the eyeglasses + +![](images/79549fc6f255a983434f3f4b2c11f39eeb2f99cb0865af64bb59f16ea77851e2.jpg) +(a) OOD dominates + +![](images/be6eadc61a6fe2f459247bf0c7d4d53ed2235c401486ad54eee2c7cbe364e0cf.jpg) +(b) Double glasses + +![](images/32961f16690f18e6b5aaa6d5d65e54d843ba850fce1e489da1deafa344b797b2.jpg) +(c) Extreme pose + +in the in-distribution radiance field are hard to be added. + +(b) Duplicate objects. Since our OOD radiance field has no knowledge about the GAN and faces prior, when the OOD object itself is glasses, adding eyeglasses introduces duplicate objects. +(c) Extreme poses. Our method fails at editing when the subject undergoes extreme poses (e.g., side view). +(d) Objects with limited movement. The radiance field reconstruction suffers when the OOD object has slight movement. This may introduce unwanted artifacts like "floater" in the novel views. +(e) Temporal inconsistency. Our results on video editing may suffer from temporal inconsistency. Temporal constraints and finetuning used in [57, 63] could further improve this aspect. + +# 7. Conclusions + +We have presented a novel method for face image, and its potential for video inversion and editing. Our method handles OOD objects by isolating them from the InD part. Our method achieves accurate reconstruction by building two radiance fields and then composing them together during the rendering. By modifying the latent code in the InD part, we can obtain faithful editing results. We show that our method achieves a better balance in the reconstruction-editability trade-off than other baselines. 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[ + { + "bbox": [ + 46, + 451, + 134, + 525 + ], + "type": "image", + "image_path": "78c7cba190e6e91c39a9deeb798dfb06df31e05734b9340144ff9d6b8719699d.jpg" + } + ] + } + ], + "index": 44, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 529, + 537, + 586 + ], + "lines": [ + { + "bbox": [ + 46, + 529, + 537, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 537, + 586 + ], + "type": "text", + "content": "Figure 1. Semantic editing for out-of-distribution data. We present a method for reconstructing and editing an out-of-distribution (OOD) image or video using a pre-trained 3D-aware generative model (EG3D [10]). Our method explicitly models and reconstructs the occluders in 3D, allowing faithful reconstruction of the input while preserving the semantic editing capability. Here we showcase the reconstruction and editing results \"Less smile\", \"Younger\", \"Blond\" [47], \"Elsa\", \"Surprised\" [41]. Our method can also remove the OOD part. Data are from the Internet (Creative Commons)." + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_caption" + } + ], + "index": 44 + }, + { + "bbox": [ + 143, + 594, + 192, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 594, + 192, + 607 + ], + "spans": [ + { + "bbox": [ + 143, + 594, + 192, + 607 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "3D-aware GANs offer new capabilities for view synthesis while preserving the editing functionalities of their 2D counterparts. GAN inversion is a crucial step that seeks the latent code to reconstruct input images or videos, subsequently enabling diverse editing tasks through manipulation of this latent code. However, a model pre-trained on a particular dataset (e.g., " + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "FFHQ" + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": ") often has difficulty re" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 596, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 596, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 547, + 704 + ], + "type": "text", + "content": "constructing images with out-of-distribution (OOD) objects such as faces with heavy make-up or occluding objects. We address this issue by explicitly modeling OOD objects from the input in 3D-aware GANs. Our core idea is to represent the image using two individual neural radiance fields: one for the in-distribution content and the other for the out-of-distribution object. The final reconstruction is achieved by optimizing the composition of these two radiance fields with carefully designed regularization. We demonstrate that" + } + ] + } + ], + "index": 48 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 35, + 239, + 47, + 318 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 35, + 239, + 47, + 318 + ], + "spans": [ + { + "bbox": [ + 35, + 239, + 47, + 318 + ], + "type": "text", + "content": "Single Image Input" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7225" + } + ] + } + ], + "index": 49 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 45, + 72, + 288, + 144 + ], + "type": "text", + "content": "our explicit decomposition alleviates the inherent trade-off between reconstruction fidelity and editability. We evaluate reconstruction accuracy and editability of our method on challenging real face images and videos and showcase favorable results against other baselines. More results can be found at https://in-n-out-3d.github.io/." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 167, + 127, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 167, + 127, + 179 + ], + "spans": [ + { + "bbox": [ + 48, + 167, + 127, + 179 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 188, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 188, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 287, + 449 + ], + "type": "text", + "content": "GAN inversion [3, 44, 55, 61, 70] is a set of techniques that project an input image onto the latent space of a pretrained GAN to obtain a latent code so that the image generator can reconstruct the input. This is particularly useful as one could perform various creative semantic editing tasks [18, 24, 41, 47] for images. Similar techniques have also been applied in the video domain, with which recent methods also achieved temporally consistent editing [57, 63]. However, the majority of these methods are effective primarily with 2D GANs, and they fall short in offering explicit 3D controllability, such as view synthesis capabilities. With the rapid recent advancements in 3D reconstruction, especially in neural radiance fields (NeRFs) [6, 11, 36, 37], high-quality 3D-aware GANs [10, 22, 40, 49] have emerged as a powerful tool for learning 3D generation from 2D images. 3D-aware GANs, equipped with a 3D representations like NeRFs [10, 22] or SDF [40], offer explicit control over camera views and ensure 3D geometric consistency in generation. Additionally, they retain the generative capacity and editability of 2D GANs [26-29]. This enables applications such as novel view synthesis, semantic image editing [31, 48, 51, 62, 66, 67] and video editing [17, 56]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 453, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 714 + ], + "type": "text", + "content": "Core challenges. While state-of-the-art 3D GAN inversion methods achieve remarkable advances in both image and video editing for human faces, they face challenges when dealing with images including out-of-distribution (OOD) objects (e.g., heavy make-ups or occlusions). This limitation arises primarily because these models are pre-trained only on natural faces without complex textures or substantial occlusions. As a result, the editability performance deteriorates when a pre-trained GAN is forced to model OOD objects in the GAN inversion process. This is commonly known as the reconstruction-editability trade-off [55]. Existing GAN inversion methods assume that a single latent code corresponding to the input image can be found in the latent space [50, 61] through optimization once the model is trained. Therefore, they aim to reconstruct the indistribution (InD) content (e.g., natural face) and the OOD objects together. However, OOD components often cannot be well modeled in a pre-trained GAN, and consequently cannot be well represented with it using a single latent code, existing methods either cannot reconstruct them faithfully [51] or can reconstruct them (e.g., through fine-tuning the generator) but alters the latent space properties and de" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 306, + 69, + 383, + 145 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 383, + 145 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 383, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 383, + 145 + ], + "type": "image", + "image_path": "01669d708f68f1831a53337352a79b2f2ddce9310947c2ad34bca065ec97a007.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 306, + 145, + 383, + 222 + ], + "blocks": [ + { + "bbox": [ + 306, + 145, + 383, + 222 + ], + "lines": [ + { + "bbox": [ + 306, + 145, + 383, + 222 + ], + "spans": [ + { + "bbox": [ + 306, + 145, + 383, + 222 + ], + "type": "image", + "image_path": "a850c6ab7d5cf9ec4cd20be724289498d9defe16435b0ba5473ebdb675ec5e3a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 223, + 354, + 232 + ], + "lines": [ + { + "bbox": [ + 333, + 223, + 354, + 232 + ], + "spans": [ + { + "bbox": [ + 333, + 223, + 354, + 232 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 383, + 70, + 470, + 145 + ], + "blocks": [ + { + "bbox": [ + 383, + 70, + 470, + 145 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 470, + 145 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 470, + 145 + ], + "type": "image", + "image_path": "42cbb6846d737fca4961c1165290a40830c78466bf8c9be160c010f5ed122de8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 383, + 145, + 469, + 222 + ], + "blocks": [ + { + "bbox": [ + 383, + 145, + 469, + 222 + ], + "lines": [ + { + "bbox": [ + 383, + 145, + 469, + 222 + ], + "spans": [ + { + "bbox": [ + 383, + 145, + 469, + 222 + ], + "type": "image", + "image_path": "1ee3a65bafa226154da39acd8c17bae8362db3336bf8a1a60c763c06465413f1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 222, + 451, + 232 + ], + "lines": [ + { + "bbox": [ + 408, + 222, + 451, + 232 + ], + "spans": [ + { + "bbox": [ + 408, + 222, + 451, + 232 + ], + "type": "text", + "content": "GOAE [67]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 470, + 70, + 545, + 145 + ], + "blocks": [ + { + "bbox": [ + 470, + 70, + 545, + 145 + ], + "lines": [ + { + "bbox": [ + 470, + 70, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 470, + 70, + 545, + 145 + ], + "type": "image", + "image_path": "f258d29636e5310715e878e0b3dd0d9fa14209dc6e23a3834824e05fee13e771.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 470, + 145, + 545, + 222 + ], + "blocks": [ + { + "bbox": [ + 470, + 145, + 545, + 222 + ], + "lines": [ + { + "bbox": [ + 470, + 145, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 470, + 145, + 545, + 222 + ], + "type": "image", + "image_path": "46369bb1b87c2677840dcf3f8b20e9c36456f35a04b7e94e692ca5f3aad3f1a6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 496, + 222, + 528, + 232 + ], + "lines": [ + { + "bbox": [ + 496, + 222, + 528, + 232 + ], + "spans": [ + { + "bbox": [ + 496, + 222, + 528, + 232 + ], + "type": "text", + "content": "PTI [45]" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 240, + 544, + 274 + ], + "lines": [ + { + "bbox": [ + 305, + 240, + 544, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 544, + 274 + ], + "type": "text", + "content": "Figure 2. Limitations of the previous methods. Existing GAN inversion techniques cannot deal with frames with OOD elements, resulting in a poor reconstruction-editing balance." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 274, + 544, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 544, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 544, + 306 + ], + "type": "text", + "content": "GOAE [67] can produce faithful editing, but fails to preserve the identity of the input face. PTI [45] provides higher reconstruction fieldity, but the edibility suffers." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 315, + 468, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 315, + 468, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 468, + 327 + ], + "type": "text", + "content": "teriorates the editability [45] (Figure 2)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 331, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 652 + ], + "type": "text", + "content": "Our work. We propose a new approach to address this issue by drawing inspiration from recent composite volume rendering works that compose multiple radiance fields during rendering [19, 34, 59, 64]. Our core idea is to decompose the 3D representation of an image with OOD components into an in-distribution (InD) part and an out-of-distribution part, and compose them together to reconstruct the image in a composite volumetric rendering manner. We use EG3D [10] as our 3D-aware GAN backbone and leverage its tri-plane representation to model this composed rendering pipeline. For the InD component (i.e. natural face), we project pixel values onto EG3D's " + }, + { + "bbox": [ + 304, + 331, + 546, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 331, + 546, + 652 + ], + "type": "text", + "content": " space for an InD component reconstruction. We further introduce an additional tri-plane to represent the OOD content. After that, we combine these two radiance fields in a composite volumetric rendering to reconstruct the input frames. During the editing stage, we perform the latent code based editing solely on the InD part and leave the OOD component unaltered. This framework would allow the applications of any StyleGAN-based editing approache [41, 47] on the InD component such as changing facial expression, which is often desirable for user experiences. The advantages of our work are three-fold: a) we achieve a higher-fidelity reconstruction by composition of InD and OOD components; b) we retain the editability of pre-trained GANs by editing only the InD content; and c) by leveraging 3D-aware GANs, we can render the face from novel viewpoints." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 654, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 712 + ], + "type": "text", + "content": "We evaluate our method on challenging in-the-wild face images and videos (Creative Commons), demonstrating improvement over previous state-of-the-art GAN inversion work on both reconstruction and editing quality. In addition, we demonstrate the usefulness of our method with" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7226" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "3D-aware editing applications, including semantic editing, novel view synthesis, and OOD object removal." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 96, + 268, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 96, + 268, + 109 + ], + "spans": [ + { + "bbox": [ + 59, + 96, + 268, + 109 + ], + "type": "text", + "content": "We will release the code and data used in the paper." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 112, + 274, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 112, + 274, + 124 + ], + "spans": [ + { + "bbox": [ + 47, + 112, + 274, + 124 + ], + "type": "text", + "content": "Our contributions. In summary, our contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 125, + 287, + 231 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 125, + 287, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 125, + 287, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 287, + 172 + ], + "type": "text", + "content": "- We propose a 3D-aware GAN inversion approach to manipulate single images or monocular videos with out-of-distribution objects (e.g., accessories and heavy makeup). See results in Figure 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 172, + 286, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 286, + 195 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 286, + 195 + ], + "type": "text", + "content": "- We incorporate composite volume rendering into 3D-aware GAN inversion." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 196, + 286, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 196, + 286, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 286, + 231 + ], + "type": "text", + "content": "- Our method reconstructs 3D shapes of faces with OOD objects faithfully and demonstrates novel 3D-aware applications." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 243, + 133, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 133, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 133, + 256 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 268, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 287, + 410 + ], + "type": "text", + "content": "3D-aware GANs. StyleGANs [26-29] have achieved high-quality photorealistic 2D image generation and have been successfully applied to various image editing applications [18, 24, 41, 47]. Significant progresses have also been made to lift 2D image generation to 3D space, using various 3D representations, for both higher quality generation and to enable 3D-aware applications such as view synthesis [9, 10, 16, 20, 22, 38, 40, 46, 49, 51]. These methods usually take a two-stage pipeline that renders a raw image (usually also with feature maps) in low resolution and then upsamples the rendered image to high resolution. We leverage EG3D [10] as our generator architecture in this work." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 413, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 639 + ], + "type": "text", + "content": "GAN inversion and editing. GAN inversion has been widely studied for 2D GANs. These techniques can largely be categorized as (a) encoder-based methods [4, 8, 33, 39, 44, 44, 54, 55, 55, 58] in which a neural network encoder is trained to project an input image to the latent space of the generator; (b) optimization-based methods [1, 2, 12, 13, 21, 25, 42, 53] where the latent code is recovered via optimizing loss functions between the generator output and a target image; and (c) hybrid methods [5, 7, 45, 71] which combine both approaches. Some recent works have also investigated 3D-aware GAN inversion from a single image [31, 32, 51, 56, 62, 66, 67] or a video [17, 68]. As our experiments demonstrate, previous approaches have difficulty handling these challenging cases. We propose a new mechanism to allow high-quality 3D-aware GAN inversion of out-of-distribution faces even under significant occlusion. With our GAN inversion, we can modify the latent code to perform high-quality semantic image editing [18, 24, 41, 47] or video editing [57, 63, 65]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "GAN inversion for out-of-distribution (OOD) data. There have been attempts to invert out-of-distribution data to the GAN's latent space. Early work [1] proposes to project an image onto extended " + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^+" + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": " space to achieve more accurate reconstruction. PTI [45] finetunes generator with regularization for a lower distortion error. StyleSpace [60]" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "proposes to invert an image using StyleGAN's internal feature maps and tRGB blocks, which shows better reconstruction and disentanglement. Recently, ChunkyGAN [50] proposes to compose multiple generated images from multiple latent codes, with a set of segmentation masks to reconstruct an input image. With a similar goal in mind, we propose to leverage the radiance field of EG3D [10] and decompose the volumetric representation into an in-distribution part and an out-of-distribution part. In contrast to ChunkyGAN [50] that models an image as a collection of " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "2D" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " segments, we model the OOD and face directly in volumetric 3D representation and merge them with composite rendering." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 217, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 361 + ], + "type": "text", + "content": "Composite neural radiance fields. Neural Radiance Fields (NeRFs) [36] have shown impressive view synthesis results. Recently, it has been shown that 3D scenes can be decomposed into different NeRFs. When multiple radiance fields are built, one can compose them together using a composite rendering manner [19, 34, 59, 64]. EG3D [10] uses the tri-plane representation to generate 3D objects from the latent code. We adopt the idea of composite volume rendering to address the out-of-distribution 3D GAN inversion problem. Specifically, we split the in-distribution and out-of-distribution parts in the tri-plane 3D representation and compose them during volume rendering." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 371, + 440, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 440, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 440, + 384 + ], + "type": "text", + "content": "3. 3D-aware GAN: EG3D" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 391, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 426 + ], + "type": "text", + "content": "We choose EG3D [10], which consists of a tri-plane representation and a super-resolution (SR) module, as our 3D-aware GAN." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": "Neural rendering at low resolution. Given a latent code " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{R}^{512}" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "w \\in \\mathbb{R}^{14 \\times 512}" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": ") and camera parameters " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": ", EG3D first generates a corresponding tri-plane " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\mathbf{T} \\in \\mathbb{R}^{256 \\times 256 \\times 32 \\times 3}" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": ". For each pixel, a ray " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": " is cast, and points are sampled along the ray. Unlike the positional encoding [34, 52] for each point in NeRFs [34], EG3D projects each point onto tri-plane " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": " and retrieves features from three planes via bilinear interpolation. These features are then aggregated by summation, and fed into the decoder " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": " (i.e., an MLP) to predict the color and density. Volume rendering [35] is then performed to compute the final color for each pixel. To this end, a raw RGB image with a 32-channel feature in a low resolution (e.g. " + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 430, + 545, + 584 + ], + "type": "text", + "content": ") is generated." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "type": "text", + "content": "Super-Resolution (SR). To gain high-resolution outputs, EG3D later uses an SR module that inputs the raw image and the 32-channel feature as the input and yields a high-resolution RGB image (e.g. " + }, + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "type": "text", + "content": "). We build our approach upon EG3D due to its rendering efficiency compared to other alternatives [22, 40]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 669, + 361, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 361, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 361, + 681 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "Given an aligned face input image " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": ", or a monocular face video " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = [\\mathbf{I}_1, \\dots, \\mathbf{I}_t, \\dots, \\mathbf{I}_N]" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " frames, we aim" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7227" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 70, + 513, + 418 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 513, + 418 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 513, + 418 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 513, + 418 + ], + "type": "image", + "image_path": "3b41f43539eace6b6751cfec2bf3e9ca23ca32d8cc22b3603d5d14e69fffcd64.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "lines": [ + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": "Figure 3. Overview of our method. Given a potrait image or a monocular portrait video, we use two radiance fields to represent (a) in-distribution " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "(\\text{InD})" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " face, and (b) out-of-distribution " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "(\\text{OOD})" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " item. (a) InD reconstruction is the GAN inversion for the in-distribution natural face. We apply GAN inversion by using pre-trained EG3D model " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " to the frame, where the pre-trained tri-plane generator and tri-plane decoder " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "D^{I}" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " are kept frozen. (b) For OOD item, we propose to model them with a separate radiance field represented by an additional tri-plane " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ". During the training process, we optimize the tri-plane " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ", a per-frame latent code " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ", and a new decoder " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "D^O" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ". The decoder takes as input tri-plane features " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " and outputs color " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^O" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ", density " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "\\sigma^O" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ", and blending weight " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": ". (c) Composite Rendering compose the InD and OOD radiance fields together by using a composite rendering scheme (Section 4.3). (d) Finally, we finetune the Super-Resolution module in " + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 420, + 536, + 520 + ], + "type": "text", + "content": " to achieve a better output in the high resolution. After training, we can perform various semantic edits and free-view rendering, while preserving the face identity and the OOD components." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "type": "text", + "content": "to reconstruct the input with EG3D inversion and perform face editing. For simplicity, we use " + }, + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "type": "text", + "content": " to represent a frame, either from a single input image or a sampled frame from a video. If only one frame exists, then " + }, + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 46, + 528, + 288, + 574 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "We present the high-level overview in Figure 3. We build two neural radiance fields (NeRFs) [36], one for in-distribution (InD) face (Section 4.1), and the other one for out-of-distribution (OOD) object (Section 4.2), using triplane representations [10]. The OOD object, for example, can be a non-face object with a rigid shape or heavy makeup with a complicated texture. Next, we combine two radiance fields (Section 4.3) to reconstruct the low-resolution frame. Finally, we finetune the super-resolution module of EG3D to get the high-resolution output (Section 4.5). After training the radiance fields, we can edit the face image or video" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 528, + 364, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 364, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 364, + 540 + ], + "type": "text", + "content": "(Section 4.6)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 547, + 470, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 470, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 470, + 559 + ], + "type": "text", + "content": "4.1. In-distribution GAN inversion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "text", + "content": "Formulation. Since a pretrained EG3D already has prior knowledge of faces, we directly leverage its latent space and perform a regular 3D GAN inversion [32, 61] for the in-distribution part. For a single frame case, we optimize a latent code " + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "text", + "content": " such that it can reconstruct the input frame " + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "text", + "content": ". For a video, we invert all the frames at the same time. Please refer to the supplementary material for more details. For camera parameters " + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "inline_equation", + "content": "p_t \\in \\mathbb{R}^{25}" + }, + { + "bbox": [ + 304, + 568, + 545, + 674 + ], + "type": "text", + "content": ", we obtain them by using an off-the-shelf pose detector [15], following [10, 32]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Optimization. To represent the InD faces with " + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^I" + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": ", our insight is to keep the latent code " + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": " in distribution as much as possible. To this end, we use a regularization term to keep" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7228" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 84 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 47, + 72, + 286, + 84 + ], + "type": "text", + "content": " within its pre-trained distribution through GAN training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 117, + 95, + 286, + 108 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 95, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 117, + 95, + 286, + 108 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {w} \\left(w _ {t}\\right) = \\left| \\left| w _ {t} - \\bar {w} \\right| \\right| _ {2} ^ {2}, \\tag {1}", + "image_path": "38bb0e3327218ce485e7b97b7fb82cee1cdbd56a12a6100f12e3c87773738b95.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 114, + 286, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 286, + 137 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 286, + 137 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 114, + 286, + 137 + ], + "type": "inline_equation", + "content": "\\bar{w}" + }, + { + "bbox": [ + 47, + 114, + 286, + 137 + ], + "type": "text", + "content": " is the mean latent code computed over 10,000 sampled latent codes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "text", + "content": "We also use a another regularization term adopted from [55] to constrain the variation among style vectors in " + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\Delta}(w_t) = \\sum_{i=1}^{13} ||\\Delta_i||_2^2" + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "text", + "content": ", given a latent code " + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "inline_equation", + "content": "w = (w_0, w_0 + \\Delta_1, \\dots, w_0 + \\Delta_{13}) \\in \\mathbb{R}^{14 \\times 512}" + }, + { + "bbox": [ + 47, + 139, + 287, + 209 + ], + "type": "text", + "content": ". This regularization term preserves the editability of the optimized latent code [55]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 221, + 246, + 233 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 246, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 246, + 233 + ], + "type": "text", + "content": "4.2. Modeling out-of-distribution contents" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "content": "For an OOD object, a pre-trained EG3D usually cannot model it well with its prior distribution. We therefore use an additional tri-plane " + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "content": " to represent the out-of-distribution content. One additional challenge is that, while dealing with video, the OOD object may not be static across different frames, therefore could not be well reconstructed with a static radiance field. Therefore, in addition to " + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "content": ", we use a per-frame latent code " + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\phi_t \\in \\mathbb{R}^{32}" + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "content": " for each frame to represent the out-of-distribution object across the temporal domain. Both " + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 241, + 287, + 370 + ], + "type": "text", + "content": " are randomly initialized from a normal distribution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "text", + "content": "Formulation. The out-of-distribution decoder " + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "inline_equation", + "content": "D^{O}" + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "text", + "content": " takes a tuple " + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "inline_equation", + "content": "(\\mathbf{T}^{O}(t_{k}),\\phi_{t})\\in \\mathbb{R}^{64}" + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "text", + "content": " as the input, and outputs color " + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^O\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "text", + "content": " , density " + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\sigma^O\\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "text", + "content": " , and blending weight " + }, + { + "bbox": [ + 47, + 375, + 287, + 411 + ], + "type": "inline_equation", + "content": "b\\in [0,1]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 89, + 419, + 287, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 419, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 89, + 419, + 287, + 434 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {c} ^ {O}, \\sigma^ {O}, b\\right) = D ^ {O} \\left(\\mathbf {T} ^ {O} \\left(t _ {k}\\right), \\phi_ {t}; \\theta_ {D ^ {O}}\\right), \\tag {2}", + "image_path": "2555d4470f95de243e1d0a2551a5a93b1aaf3f5be44ce5564e2b248ea453bbb3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O (t_k)\\in \\mathbb{R}^{32}" + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": " is the aggregated features obtained by projecting 3D coordinate " + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": " onto each of the three feature planes via bilinear interpolation, then aggregated via summation [10]. The decoder " + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "inline_equation", + "content": "D^{O}" + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": " is an MLP with weights of " + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\theta_{DO}" + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": ". To compute the color of a pixel at time " + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": ", we use the volume rendering integral along the ray " + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 47, + 442, + 287, + 514 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 79, + 517, + 287, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 517, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 79, + 517, + 287, + 550 + ], + "type": "interline_equation", + "content": "\\mathbf {C} ^ {O} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T \\left(t _ {k}\\right) \\alpha^ {O} \\left(\\sigma^ {O} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {O} \\left(t _ {k}\\right), \\tag {3}", + "image_path": "f3351808b4759f79a5e989483ec79d0ec74d90ae991f55412a060abbe6a28fa2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "inline_equation", + "content": "T(t_k) = \\exp(-\\sum_{k'=1}^{k-1} \\sigma(t_{k'}) \\delta_{k'})" + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "inline_equation", + "content": "\\alpha = 1 - \\exp(-x)" + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "inline_equation", + "content": "\\delta_k = t_{k+1} - t_k" + }, + { + "bbox": [ + 47, + 559, + 286, + 596 + ], + "type": "text", + "content": " is the distance between two 3D points." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 597, + 205, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 205, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 205, + 609 + ], + "type": "text", + "content": "4.3. Composite volume rendering" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 616, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 286, + 640 + ], + "type": "text", + "content": "Now, with both InD and OOD radiance fields, we can combine them using the blending weight " + }, + { + "bbox": [ + 47, + 616, + 286, + 640 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 47, + 616, + 286, + 640 + ], + "type": "text", + "content": " from Eqn. 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 645, + 286, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 286, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 286, + 656 + ], + "type": "text", + "content": "Formulation. We compose two radiance fields together by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 73, + 662, + 286, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 662, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 73, + 662, + 286, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {C} ^ {C} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T ^ {C} \\left(t _ {k}\\right) \\left(b \\alpha^ {O} \\left(\\sigma^ {O} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {O} \\left(t _ {k}\\right) \\right. \\tag {4} \\\\ \\left. + (1 - b) \\alpha^ {I} \\left(\\sigma^ {I} \\left(t _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} ^ {I} \\left(t _ {k}\\right)\\right), \\\\ \\end{array}", + "image_path": "e9d1a6a9b43504c41f08188f2edf503a7c9502125421d16bd6a6858cf4a97442.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 70, + 498, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 70, + 498, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 498, + 85 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 70, + 498, + 85 + ], + "type": "inline_equation", + "content": "T^{C}(t_{k}) = \\exp (-\\sum_{k^{\\prime} = 1}^{k - 1}(\\sigma^{O} + \\sigma^{I})\\delta_{k^{\\prime}})" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 87, + 419, + 99 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 87, + 419, + 99 + ], + "spans": [ + { + "bbox": [ + 306, + 87, + 419, + 99 + ], + "type": "text", + "content": "Optimization. The goal is" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 106, + 545, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 106, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 313, + 106, + 545, + 172 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} w_{t}^{*},\\mathbf{T}^{O^{*}},\\theta_{D O}^{*},\\phi_{t}^{*} = \\operatorname *{argmin}_{w_{t},\\mathbf{T}^{O},\\theta_{D O},\\phi_{t}}\\mathcal{L}_{t}^{C} \\\\ = \\operatorname *{argmin}_{w_{t},\\mathbf{T}^{O},\\theta_{D^{O}},\\phi_{t}}\\sum_{ij}||C^{C}(\\mathbf{r}_{ij}) - C^{GT}(\\mathbf{r}_{ij})||_{2}^{2} \\\\ + \\lambda_ {b} \\mathcal {L} _ {b} \\left(\\mathbf {r} _ {i j}\\right) + \\mathcal {L} _ {L P I P S} \\left(\\mathbf {I} _ {L R} ^ {C}, \\mathbf {I} _ {L R}\\right), \\tag {5} \\\\ \\end{array}", + "image_path": "f4506ee8ac5f46a287f21ab354c3393f8d3a7c62ebdfea1f21bb5f19d9a69fcb.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{LPIPS}" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": " is the LPIPS loss [69], " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{LR}^{C}" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": " is the composite rendered image at low resolution " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "(128\\times 128)" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{LR}" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": " is the ground truth image also at " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "128\\times 128" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": ". The weight regularizer " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": " is adopted from [59], used to penalize the blending weight " + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 182, + 545, + 241 + ], + "type": "text", + "content": " if it is not closer to 0 or 1:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 383, + 251, + 545, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 251, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 383, + 251, + 545, + 274 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} H _ {b} (b \\left(t _ {k}\\right)), \\tag {6}", + "image_path": "3a4f6ad6da0648d64df340be30f3381cfac0c712c19bf8b2caa613d3ada869e8.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "inline_equation", + "content": "H_{b}(x) = -(x\\log (x) + (1 - x)\\log (x))" + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "text", + "content": " is binary entropy. The reason behind Eqn. 6 is that objects cannot co-occupy the same spatial location. The entropy loss facilitates a cleaner decomposition: encouraging an object to be either in-distribution (i.e. " + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "inline_equation", + "content": "b\\to 0" + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "text", + "content": ") or out-of-distribution (i.e. " + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "inline_equation", + "content": "b\\rightarrow 1" + }, + { + "bbox": [ + 305, + 284, + 545, + 354 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 356, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 356, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 545, + 403 + ], + "type": "text", + "content": "However, it is ill-posed to build its 3D geometry accurately, given only a single-frame input, even with a pretrained 3D-aware generator. Therefore, for a single image only, we also introduce a depth regularization term:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 377, + 411, + 545, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 411, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 377, + 411, + 545, + 425 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {D}} = \\left| \\left| \\mathcal {D} ^ {C} - \\mathcal {D} ^ {R e g} \\right| \\right| _ {1} \\tag {7}", + "image_path": "767beb45f81f12f2102e530ca00a111e09a8e2f16053b51187b80912faa2c7a9.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^C" + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": " is the rendering depth map from composite rendering, and " + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^{Reg}" + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": " is a rescaled depth map from MiDaS [43]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 466, + 470, + 476 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 470, + 476 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 470, + 476 + ], + "type": "text", + "content": "4.4. 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Our total loss function is" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 329, + 526, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 526, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 329, + 526, + 545, + 559 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {L R} = \\sum_ {t = 1} ^ {N} \\mathcal {L} _ {t} ^ {C} + \\lambda_ {\\Delta} \\mathcal {L} _ {\\Delta} + \\lambda_ {w} \\mathcal {L} _ {w} + (\\lambda_ {\\mathcal {D}} \\mathcal {L} _ {\\mathcal {D}}), \\tag {8}", + "image_path": "2e2aa33dbbb8b7bb278730bfe0856dd13fc36b09f483d2ae8fcc4d4dd523535d.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_t^C" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " is from Eqn. 4, latent variation regularizer " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\Delta}" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " from [55], and " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " from Eqn. 1, respectively, " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{\\Delta}" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " is the weight for " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\Delta}" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_w" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " is the weight for " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathcal{D}}" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " is the weight for " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": ". We only use " + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 305, + 568, + 545, + 616 + ], + "type": "text", + "content": " for single image input." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 624, + 409, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 409, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 409, + 635 + ], + "type": "text", + "content": "4.5. 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We observe that using the pretrained super-resolution (SR) module cannot generate a satisfying high-resolution output, as shown in Figure 4, due to the new OOD tri-plane " + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^O" + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": ". Therefore, we finetune only the SR module in " + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": " for higher resolution" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7229" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 126, + 147 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 126, + 147 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 126, + 147 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 126, + 147 + ], + "type": "image", + "image_path": "bbd8b66ebb236f2e5108aeeecbec65d900d9d29c99be92a79d3134c0af6f28ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 148, + 111, + 159 + ], + "lines": [ + { + "bbox": [ + 58, + 148, + 111, + 159 + ], + "spans": [ + { + "bbox": [ + 58, + 148, + 111, + 159 + ], + "type": "text", + "content": "Recon. 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The effect of finetuning SR module. Without finetuning the SR module, the high-resolution output is blurry." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 210, + 105, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 105, + 221 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 105, + 221 + ], + "type": "text", + "content": "at " + }, + { + "bbox": [ + 47, + 210, + 105, + 221 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 47, + 210, + 105, + 221 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 226, + 212, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 212, + 238 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 212, + 238 + ], + "type": "text", + "content": "Optimization. The loss function is that" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 80, + 245, + 287, + 260 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 245, + 287, + 260 + ], + "spans": [ + { + "bbox": [ + 80, + 245, + 287, + 260 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {S R} (\\mathbf {x}, \\hat {\\mathbf {x}}) = \\| \\mathbf {x} - \\hat {\\mathbf {x}} \\| _ {2} ^ {2} + \\mathcal {L} _ {L P I P S} (\\mathbf {x}, \\hat {\\mathbf {x}}), \\tag {9}", + "image_path": "ed98fc32a74e1d0412109ebaee0b8273c487833e24a97b46e87526637c0519db.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 268, + 184, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 268, + 184, + 282 + ], + "spans": [ + { + "bbox": [ + 47, + 268, + 184, + 282 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 268, + 184, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = \\mathbf{I}_t" + }, + { + "bbox": [ + 47, + 268, + 184, + 282 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 268, + 184, + 282 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} = SR(\\mathbf{I}_{LR}^C)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 290, + 105, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 290, + 105, + 303 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 105, + 303 + ], + "type": "text", + "content": "4.6. Editing" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "content": "After the reconstruction, we can modify the latent code " + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 308, + 287, + 380 + ], + "type": "text", + "content": " to perform various semantic editing tasks. With explicit decomposition, the OOD contents do not interfere with the semantic editing capability of in-distribution components. Here, any existing GAN-based editing approaches can be used. We use InterfaceGAN [47] and StyleCLIP [41]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 392, + 173, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 173, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 173, + 406 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 412, + 163, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 163, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 163, + 425 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 434, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 576 + ], + "type": "text", + "content": "Dataset. To evaluate how our approach works on data with out-of-distribution components, we collected a dataset of 20 online videos with challenging and diverse appearances. The OOD content contains heavy make-up and occluding objects (e.g. facial masks and large glasses). For the single-image inversion method, we use the first frame of each video. For video inversion, we use all the frames. For the face alignment, we use 3DDFA-v2 [23] to obtain the 68-point landmarks and smooth them across the frames using a sliding window for stabler cropping. After that, we convert the landmarks to EG3D's 5-point landmarks and crop the face out of the input frame." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": "Hyperparameters. We use the Adam optimizer [30] for all our experiments. For in-distribution inversion (Section 4.1), we optimize for 200 epochs with a learning rate of " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\lambda_{\\Delta} = 1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": ". For the out-of-distribution and composite rendering (Section 4.2, 4.3), we run the optimization for 10,000 iterations with a learning rate of " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\lambda_{b} = 1" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\lambda_{w} = 1" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathcal{D}} = 0.1" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": " if applicable. For the SR module (Section 4.5), we finetune the module for 100 epochs with a learning rate of " + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 579, + 287, + 686 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Metrics. We evaluate our approach from 1) reconstruction accuracy and 2) editability to validate the reconstruction-" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "type": "text", + "content": "editability trade-off. For the reconstruction accuracy, we report LPIPS [69], PSNR, SSIM and ID similarity [14]. For editability, we follow [45, 50] and evaluate identity preservation after applying the editing direction. More specifically, we use ArcFace [14] to compute the similarity between the inverted and edited results." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "text", + "content": "Baselines for evaluation. We compare our method extensively with several previous arts. For optimization-based methods, we compare with HFGI3D [62], PTI [45], " + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "text", + "content": " optimization. For videos only, we also include VIVE3D [17]. We compare the encoder-based method with GOAE [67] and IDE-3D [51] encoder. We treat " + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 146, + 546, + 289 + ], + "type": "text", + "content": " optimization as an ablated version of our method without OOD triplane. The recent work in [56] showcases encoder-based 3D GAN inversion, focusing on real-time inference. However, their method relies on a frozen EG3D and does not explicitly model the OOD components. We do not compare with it as the code is not publicly available." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 292, + 421, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 292, + 421, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 292, + 421, + 304 + ], + "type": "text", + "content": "5.2. Quantitative results" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": "Reconstruction. We compare the reconstruction accuracy of our approach with all baselines and report the results in Table 1. For PTI, we first perform a " + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": " inversion with a learning rate of " + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": " and 200 epochs, and then finetune the generator for 200 epochs with a learning rate of " + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "inline_equation", + "content": "3 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": " optimization, we use a learning rate of " + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 313, + 545, + 407 + ], + "type": "text", + "content": " and optimize for 200 epochs. For GOAE and IDE-3D, we use their encoder directly for the inversion." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 407, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 443 + ], + "type": "text", + "content": "Our approach outperforms other methods on all the evaluation metrics. This indicates that our method produces a more accurate reconstruction with the OOD components." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 445, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 546, + 540 + ], + "type": "text", + "content": "Editability. We acquire editing directions from InterfaceGAN [47] (\"younger\", \"smile\") and StyleCLIP mapper [41] (\"eyeglasses\", \"surprised\", \"Elsa\"). Following previous work [45, 50], we measure the ID similarity between the inverted image and the edited image, as the editing should not change a person's identity. We report our results in Table 2. Our method outperforms other baselines in terms of identity preservation in most cases." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 547, + 414, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 414, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 414, + 559 + ], + "type": "text", + "content": "5.3. Qualitative results" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "type": "text", + "content": "Inversion. We visually compare the video reconstruction in Figure 5. Our method provides higher-fidelity reconstruction results than other baselines, particularly for OOD regions (e.g., heavy make-up or earrings). Our method shows better reconstruction than the encoder-based method GOAE [67] and IDE-3D [51]. Compared to optimization-based methods, HFGI3D [62], VIVE3D [17], PTI [45], " + }, + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 568, + 545, + 686 + ], + "type": "text", + "content": ", our method shows higher-fidelity reconstruction for OOD objects (Refer to our supplementary material for more results)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Editing. We show a qualitative comparison regarding the editing in Figure 6. Our method shows faithful editing" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7230" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 161, + 153 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 161, + 153 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 161, + 153 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 161, + 153 + ], + "type": "image", + "image_path": "a1cf8f9267c1f3a239e9caa17ace22c49f0ffa5280cce59e8ec5b0b65869af95.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison of the video reconstruction. We compare our approach with " + }, + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 163, + 544, + 185 + ], + "type": "text", + "content": " optimization, IDE-3D [51], GOAE [67], HFGI3D [62], VIVE3D [17], and PTI [45]. Our method shows a better reconstruction accuracy on the OOD videos." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 161, + 71, + 269, + 152 + ], + "blocks": [ + { + "bbox": [ + 161, + 71, + 269, + 152 + ], + "lines": [ + { + "bbox": [ + 161, + 71, + 269, + 152 + ], + "spans": [ + { + "bbox": [ + 161, + 71, + 269, + 152 + ], + "type": "image", + "image_path": "9db79a933db688b3e73a655455bf34e9666baa9bd3cbdcaffa2ab5a19cd72806.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 269, + 70, + 435, + 153 + ], + "blocks": [ + { + "bbox": [ + 269, + 70, + 435, + 153 + ], + "lines": [ + { + "bbox": [ + 269, + 70, + 435, + 153 + ], + "spans": [ + { + "bbox": [ + 269, + 70, + 435, + 153 + ], + "type": "image", + "image_path": "6b7d4352065a3cbbafb3f6fce136a05468f39340beb2e92e2e158d0909afe003.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 435, + 71, + 548, + 153 + ], + "blocks": [ + { + "bbox": [ + 435, + 71, + 548, + 153 + ], + "lines": [ + { + "bbox": [ + 435, + 71, + 548, + 153 + ], + "spans": [ + { + "bbox": [ + 435, + 71, + 548, + 153 + ], + "type": "image", + "image_path": "640974a9fe30483e175d7f742504032a4bc2bd79ace51f5d8feb9ac9ee8ce29d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 102, + 189, + 493, + 295 + ], + "blocks": [ + { + "bbox": [ + 102, + 189, + 493, + 295 + ], + "lines": [ + { + "bbox": [ + 102, + 189, + 493, + 295 + ], + "spans": [ + { + "bbox": [ + 102, + 189, + 493, + 295 + ], + "type": "table", + "html": "
ImagesVideos
LPIPS↓SSIM↑PSNR↑ID Similarity↑Time↓LPIPS↓SSIM↑PSNR↑ID Similarity↑
Ours0.11060.817519.860.96852.68h0.22370.705216.030.9758
HFGI3D [62]0.39120.552111.370.94637.51h0.39540.558711.550.9388
GOAE [67]0.36190.642414.730.968556s0.36420.647014.970.3642
E3DGE [31]0.17090.773815.280.8632-----
VIVE3D [17]----0.59h0.41720.541710.660.9245
PTI [45]0.31920.617212.930.96761.45h0.31440.632013.450.9658
IDE-3D [51]0.50440.43959.180.845677s0.49990.45129.590.8251
W+0.34330.638714.390.91990.49h0.33800.655714.750.9154
W0.40970.561512.080.87570.47h0.40300.578712.480.8652
", + "image_path": "c7f9027f8035412068e1a6d6bceb79838cee613cd132d78028553b2052f44bf2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 67, + 325, + 526, + 432 + ], + "blocks": [ + { + "bbox": [ + 138, + 303, + 454, + 315 + ], + "lines": [ + { + "bbox": [ + 138, + 303, + 454, + 315 + ], + "spans": [ + { + "bbox": [ + 138, + 303, + 454, + 315 + ], + "type": "text", + "content": "Table 1. Reconstruction quality evaluation. For each column, deeper color the better." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 325, + 526, + 432 + ], + "lines": [ + { + "bbox": [ + 67, + 325, + 526, + 432 + ], + "spans": [ + { + "bbox": [ + 67, + 325, + 526, + 432 + ], + "type": "table", + "html": "
ImagesVideos
eyeglassessurprisedyoungersmileElsaaverageeyeglassessurprisedyoungersmileElsaaverage
Ours.9532.9888.9495.9525.9116.9511.9158.9360.9347.9094.8927.9177
HFGI3D [62].9484.9795.9453.9223.8641.9319.9112.9109.9290.9155.8622.9058
GOAE [67].9179.9306.9327.9332.8851.9199.9120.9224.9235.9221.8641.9088
E3DGE [31]--.8853.9487-0.9170------
VIVE3D [17]------.9078.9475.9183.9369.8728.9167
PTI [45].9114.9562.9380.9410.7927.9079.9049.9357.9319.9336.7945.9001
IDE-3D [51].8811.9538.8723.8055.8780.8781.8767.9481.8551.8662.7871.8666
W+.9012.9567.9248.9356.7892.9015.8971.9249.9290.9170.7968.8930
W.8808.9567.9177.9290.8008.8970.8793.9537.9068.9208.8113.8944
", + "image_path": "a9b805b9bc35f8ce2eee345a0d4f655d2f9e5d82827941eb77c7f6f2a1213cc0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 469, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 493 + ], + "type": "text", + "content": "results. For more qualitative results, please refer to our supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 499, + 160, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 160, + 512 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 160, + 512 + ], + "type": "text", + "content": "5.4. Other Applications" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 520, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 556 + ], + "type": "text", + "content": "View synthesis. The use of 3D GANs supports rendering novel views after inversion. We show novel view synthesis results in Figure 7." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 558, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 594 + ], + "type": "text", + "content": "Object removal. By setting the blending weights of the OOD objects to 0, we can remove OOD objects. We show results in Figure 1." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 83, + 603, + 252, + 661 + ], + "blocks": [ + { + "bbox": [ + 46, + 439, + 520, + 462 + ], + "lines": [ + { + "bbox": [ + 46, + 439, + 520, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 520, + 462 + ], + "type": "text", + "content": "Table 2. Identity preservation evaluation. Higher numbers indicate better identity preservation. " + }, + { + "bbox": [ + 46, + 439, + 520, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{W} +" + }, + { + "bbox": [ + 46, + 439, + 520, + 462 + ], + "type": "text", + "content": " is equivalent to our method without OOD tri-plane." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 603, + 252, + 661 + ], + "lines": [ + { + "bbox": [ + 83, + 603, + 252, + 661 + ], + "spans": [ + { + "bbox": [ + 83, + 603, + 252, + 661 + ], + "type": "table", + "html": "
InversionEditing
L2↓LPIPS↓ID similarity↑
w/o Lb0.03220.21910.9070
w/o Lw0.03360.22380.9024
Full method0.03390.22370.9177
", + "image_path": "0741996c311cedc8e4fb7a850738e715a5e46ab300347bb30e6495df1f5c08e4.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 669, + 280, + 715 + ], + "lines": [ + { + "bbox": [ + 46, + 669, + 280, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 669, + 280, + 715 + ], + "type": "text", + "content": "Table 3. Ablation study. We study the effect of different loss functions on 20 videos. For inversion, we compute the metrics between reconstructed frames and input frames. For editing, we compute the ID similarity between before and after editing." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 468, + 400, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 400, + 481 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 400, + 481 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "text", + "content": "We introduce two new loss functions, Eqn. 1 and Eqn. 6, to preserve the editability from the impact of the OOD radiance field in Section 4.3. To validate the loss functions' effects, we conduct an ablation study in Table 3. Without the weight regularization, " + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "text", + "content": ", and latent code regularizer " + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "text", + "content": ", the reconstruction accuracy is improved while the editability is reduced. One of the reasons is that GAN-based editing usually also brings unwanted changes to other attributes [47]. In Figure 8, the editing direction \"eyeglasses\" also moves the position of the eyes. At this time, if the blending weight " + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "text", + "content": " is closer to 1 for pixels outside the OOD object, i.e. the OOD part has more contributions, the editing tends to keep the pixel values in the reconstruction stage. While the eyes will be moved due to the editing direction, it results in the duplicate eyes in Figure 8(a). In contrast, with regularization (Eqn. 1 and Eqn. 6) on the blending weights, pixels in the in-distribution part contribute more to the output, which better supports the editing since we can only edit the in-distribution part. Similar cases happen to " + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 304, + 487, + 547, + 715 + ], + "type": "text", + "content": ". With" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7231" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 547, + 196 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 547, + 196 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 547, + 196 + ], + "type": "image", + "image_path": "786be30cf6817752286a74b54afcc0080be941283d47bbd629c86ea38a8ad006.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 538, + 229 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 538, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 538, + 229 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison of the editing. We compare our editing results from a single image and a video with other baselines, with different editing latent directions \"Eyeglasses\". Our approach can preserve the original appearance details better, and shows improved editability over other baselines." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 236, + 125, + 312 + ], + "blocks": [ + { + "bbox": [ + 48, + 236, + 125, + 312 + ], + "lines": [ + { + "bbox": [ + 48, + 236, + 125, + 312 + ], + "spans": [ + { + "bbox": [ + 48, + 236, + 125, + 312 + ], + "type": "image", + "image_path": "b9e3f0cdbbdb73030d7bb333c4d3148c7abe8bf52ed9a99d6b8e872c07d9dd57.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 129, + 236, + 206, + 312 + ], + "blocks": [ + { + "bbox": [ + 129, + 236, + 206, + 312 + ], + "lines": [ + { + "bbox": [ + 129, + 236, + 206, + 312 + ], + "spans": [ + { + "bbox": [ + 129, + 236, + 206, + 312 + ], + "type": "image", + "image_path": "a87017d855e9457a69a7897bf724180a7aee84fc4d4640dee0ea43ad8565f5b1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 209, + 236, + 287, + 312 + ], + "blocks": [ + { + "bbox": [ + 209, + 236, + 287, + 312 + ], + "lines": [ + { + "bbox": [ + 209, + 236, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 209, + 236, + 287, + 312 + ], + "type": "image", + "image_path": "853c8600e474e46316a26f16359759188ff3a9b6a6aaf4612c514deec93098da.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 48, + 360, + 105, + 417 + ], + "blocks": [ + { + "bbox": [ + 47, + 320, + 280, + 353 + ], + "lines": [ + { + "bbox": [ + 47, + 320, + 280, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 280, + 353 + ], + "type": "text", + "content": "Figure 7. Novel view synthesis. We can synthesize novel views for a fixed frame in a video, which is challenging for 2D GANs. Each column shows different view for the same frame." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 360, + 105, + 417 + ], + "lines": [ + { + "bbox": [ + 48, + 360, + 105, + 417 + ], + "spans": [ + { + "bbox": [ + 48, + 360, + 105, + 417 + ], + "type": "image", + "image_path": "0f467511554c4cc97dc8f4f78b24831bf368024a9667100977ef29c581cfcf47.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 53, + 420, + 93, + 430 + ], + "lines": [ + { + "bbox": [ + 53, + 420, + 93, + 430 + ], + "spans": [ + { + "bbox": [ + 53, + 420, + 93, + 430 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 53, + 420, + 93, + 430 + ], + "type": "inline_equation", + "content": "\\mathrm{w / o}\\mathcal{L}_b" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "text", + "content": "Figure 8. Ablation study on editing. (a) Without " + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "text", + "content": ", the out-of-distribution component dominates (" + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "inline_equation", + "content": "b \\to 1" + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "text", + "content": ") and weakens the editing. It has \"Duplicate eyes\" artifact because the editing direction \"eyeglasses\" is not disentangled well with other attributes, and changes the positions of the eyes, while the blending weights are the same as the reconstruction, it results in duplicated eyes. (b) Without " + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 46, + 438, + 286, + 515 + ], + "type": "text", + "content": ", the eyebrow becomes unnatural." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 139, + 360, + 196, + 416 + ], + "blocks": [ + { + "bbox": [ + 139, + 360, + 196, + 416 + ], + "lines": [ + { + "bbox": [ + 139, + 360, + 196, + 416 + ], + "spans": [ + { + "bbox": [ + 139, + 360, + 196, + 416 + ], + "type": "image", + "image_path": "dcf76b0b8074b53a3bee430c28d2938aba1454f0c61fb16d623b527fde7560f8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 139, + 420, + 181, + 430 + ], + "lines": [ + { + "bbox": [ + 139, + 420, + 181, + 430 + ], + "spans": [ + { + "bbox": [ + 139, + 420, + 181, + 430 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 139, + 420, + 181, + 430 + ], + "type": "inline_equation", + "content": "\\mathrm{w / o}\\mathcal{L}_w" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 230, + 360, + 287, + 416 + ], + "blocks": [ + { + "bbox": [ + 230, + 360, + 287, + 416 + ], + "lines": [ + { + "bbox": [ + 230, + 360, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 230, + 360, + 287, + 416 + ], + "type": "image", + "image_path": "04197dd14a1468d0b7af65bd05c58c34a8d1082921db57a6eaf20136afe30d43.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 227, + 420, + 280, + 430 + ], + "lines": [ + { + "bbox": [ + 227, + 420, + 280, + 430 + ], + "spans": [ + { + "bbox": [ + 227, + 420, + 280, + 430 + ], + "type": "text", + "content": "(c) Full model" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 324, + 534, + 368 + ], + "lines": [ + { + "bbox": [ + 306, + 324, + 534, + 368 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 534, + 368 + ], + "type": "text", + "content": "Figure 9. Limitations. Our approach has some limitations. (a) Editing on where OOD blending weights dominate is challenging, (b) Adding another eyeglasses to OOD eyeglasses will result in duplicated objects, and (c) extreme poses." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 524, + 272, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 272, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 272, + 536 + ], + "type": "text", + "content": "out " + }, + { + "bbox": [ + 47, + 524, + 272, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 47, + 524, + 272, + 536 + ], + "type": "text", + "content": ", the eyebrow becomes unnatural in Figure 8 (b)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 543, + 97, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 543, + 97, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 543, + 97, + 555 + ], + "type": "text", + "content": "5.6. Speed" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 561, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 620 + ], + "type": "text", + "content": "We include a comparison of different baselines in Table 1. We compare the speed on 200 frames using a single NVIDIA RTX A6000 GPU. Our method takes more time for optimization but significantly improves the reconstruction-editability trade-off." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 631, + 121, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 121, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 121, + 643 + ], + "type": "text", + "content": "6. Limitations" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 651, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 286, + 674 + ], + "type": "text", + "content": "Our method still has several limitations. We visualize (a)-(c) in Figure 9." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "(a) Editing on OOD part. When editing on the OOD region, e.g. adding eyeglasses to the heavy makeup region, because the blending weights are closer to 1, the eyeglasses" + } + ] + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 307, + 236, + 373, + 302 + ], + "blocks": [ + { + "bbox": [ + 307, + 236, + 373, + 302 + ], + "lines": [ + { + "bbox": [ + 307, + 236, + 373, + 302 + ], + "spans": [ + { + "bbox": [ + 307, + 236, + 373, + 302 + ], + "type": "image", + "image_path": "79549fc6f255a983434f3f4b2c11f39eeb2f99cb0865af64bb59f16ea77851e2.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 304, + 379, + 315 + ], + "lines": [ + { + "bbox": [ + 307, + 304, + 379, + 315 + ], + "spans": [ + { + "bbox": [ + 307, + 304, + 379, + 315 + ], + "type": "text", + "content": "(a) OOD dominates" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 392, + 236, + 459, + 302 + ], + "blocks": [ + { + "bbox": [ + 392, + 236, + 459, + 302 + ], + "lines": [ + { + "bbox": [ + 392, + 236, + 459, + 302 + ], + "spans": [ + { + "bbox": [ + 392, + 236, + 459, + 302 + ], + "type": "image", + "image_path": "be6eadc61a6fe2f459247bf0c7d4d53ed2235c401486ad54eee2c7cbe364e0cf.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 304, + 460, + 315 + ], + "lines": [ + { + "bbox": [ + 392, + 304, + 460, + 315 + ], + "spans": [ + { + "bbox": [ + 392, + 304, + 460, + 315 + ], + "type": "text", + "content": "(b) Double glasses" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 478, + 236, + 545, + 302 + ], + "blocks": [ + { + "bbox": [ + 478, + 236, + 545, + 302 + ], + "lines": [ + { + "bbox": [ + 478, + 236, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 478, + 236, + 545, + 302 + ], + "type": "image", + "image_path": "32961f16690f18e6b5aaa6d5d65e54d843ba850fce1e489da1deafa344b797b2.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 478, + 304, + 540, + 315 + ], + "lines": [ + { + "bbox": [ + 478, + 304, + 540, + 315 + ], + "spans": [ + { + "bbox": [ + 478, + 304, + 540, + 315 + ], + "type": "text", + "content": "(c) Extreme pose" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 376, + 533, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 533, + 386 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 533, + 386 + ], + "type": "text", + "content": "in the in-distribution radiance field are hard to be added." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 390, + 545, + 564 + ], + "type": "list", + "angle": 0, + "index": 31, + "blocks": [ + { + "bbox": [ + 306, + 390, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 545, + 437 + ], + "type": "text", + "content": "(b) Duplicate objects. Since our OOD radiance field has no knowledge about the GAN and faces prior, when the OOD object itself is glasses, adding eyeglasses introduces duplicate objects." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 441, + 544, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 544, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 544, + 464 + ], + "type": "text", + "content": "(c) Extreme poses. Our method fails at editing when the subject undergoes extreme poses (e.g., side view)." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 467, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 545, + 514 + ], + "type": "text", + "content": "(d) Objects with limited movement. The radiance field reconstruction suffers when the OOD object has slight movement. This may introduce unwanted artifacts like \"floater\" in the novel views." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 517, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 545, + 564 + ], + "type": "text", + "content": "(e) Temporal inconsistency. Our results on video editing may suffer from temporal inconsistency. Temporal constraints and finetuning used in [57, 63] could further improve this aspect." + } + ] + } + ], + "index": 30 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 574, + 383, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 383, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 383, + 586 + ], + "type": "text", + "content": "7. Conclusions" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We have presented a novel method for face image, and its potential for video inversion and editing. Our method handles OOD objects by isolating them from the InD part. Our method achieves accurate reconstruction by building two radiance fields and then composing them together during the rendering. By modifying the latent code in the InD part, we can obtain faithful editing results. We show that our method achieves a better balance in the reconstruction-editability trade-off than other baselines. Malicious use of our technique may lead to misinformation." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7232" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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Recently, the use of in-distribution public data has been investigated, where tiny subsets of datasets are released publicly. In this paper, we investigate a framework that leverages recent diffusion models to amplify the information of public data. Subsequently, we identify data diversity and generalization gap between public and private data as critical factors addressing the limited public data. While assuming $4\\%$ of training data as public, our method achieves $85.48\\%$ on CIFAR-10 with a privacy budget of $\\varepsilon = 2$ , without employing extra public data for training.", + "bbox": [ + 75, + 323, + 473, + 521 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 549, + 209, + 564 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Differential privacy (DP) [18, 19] establishes a mathematical framework to ensure the privacy of training data. In deep learning, differentially private SGD (DP-SGD) [1] has become the de facto standard method to guarantee the models' privacy. However, differentially private training inevitably degrades performance compared to standard (non-DP) training [6, 45]. As a practical solution, leveraging public pre-trained models or public data has been explored to enhance utility [12, 39, 59, 65-67]. As using public data raises no privacy concerns, fine-tuning pre-trained models on private data can make use of learned features for free. Nevertheless, their effectiveness might be diminished when addressing out-of-distribution (OOD) public data of small shared characteristics with private data [59].", + "bbox": [ + 75, + 574, + 468, + 785 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As an alternative, researchers have investigated the use of in-distribution (ID) public data, indicating that a small portion of in-distribution data is made public [38]. For example, some data owners decide to share their data publicly in exchange for economic incentives or public interest. This setup allows us to leverage public data with a distribution", + "bbox": [ + 75, + 786, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f929fc117142acfc5dc25f0cfc35063d22fe0f1db22930d061e9a02b39128b7.jpg", + "image_caption": [ + "Figure 1. Illustration of (Top) existing optimization-based methods and (Bottom) proposed training procedure for amplifying in-distribution public data and utilizing the synthetic data." + ], + "image_footnote": [], + "bbox": [ + 504, + 291, + 885, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "similar to private data. In contrast to previous approaches, such as utilizing extra OOD data or distribution shift, we need to assume a limited amount of ID public data since the public data might contain more sensitive information. However, the repeated use of limited-sized public data can raise critical issues related to memorization and overfitting [43]. To mitigate the aforementioned problems, previous studies mainly have focused on utilizing side information from the little public data to enhance the optimization of differentially private deep learning [2, 4, 38, 43].", + "bbox": [ + 496, + 510, + 892, + 661 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, Ganesh et al. [21] pointed out that warm-up training with public data plays a crucial in private optimization to find a good basin with a small loss, whereas DP-SGD from a random initial point faces a high loss and poor optimization. From this viewpoint, we suggest that enlarging the public dataset could improve the performance of private learning. By using the recent diffusion models [28, 30], we aim to enrich the contextual information of public data. We further identify that data diversity and generalization gap between public and private data act as critical factors, particularly addressing the limited size of public data.", + "bbox": [ + 496, + 662, + 893, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The proposed framework is illustrated in Figure 1. We summarize our approaches and their performance gains in", + "bbox": [ + 500, + 829, + 893, + 861 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. †Equal contribution.", + "bbox": [ + 94, + 886, + 331, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Our code is available at", + "bbox": [ + 517, + 875, + 651, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "https://github.com/JinseongP/DPTrainer.", + "bbox": [ + 500, + 887, + 805, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12236", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/ade704fcfcfd00e4044719ba2854bb7a3f002b40528bfde571a0ac7be99f2dd2.jpg", + "table_caption": [ + "Table 1. Ablation study on the impact of various techniques, including synthesis, augmentation, and optimization, to enhance classification performance using in-distribution public data from CIFAR-10 under $(2,10^{-5})$ -DP. Refer to Section 3.1 for the details of setups and the relevant sections for the details of each method." + ], + "table_footnote": [], + "table_body": "
SetupTraining SettingsTest Acc
Baselines including previous SOTA methods (Sec. 3.1)
ColdCold Baseline (WRN16-4) [12]64.02%
WarmWarm-up on public data68.09%
WarmSynWarm-up on DDPM synthesis [43]72.0%
WarmSEWarmSyn (DDPM) + DOPE-SGD [43]75.1%
In-distributionpublic data synthesis (Sec. 4.1) & Diversity (Sec. 4.2)
WarmSynWarm-up on EDM synthesis75.13 %
WarmSynEDM synthesis + generation diversity77.66 %
WarmSynEDM synthesis + augmentation diversity84.88%
Generalization for public-private datasets (Sec. 4.3)
WarmSynWell-generalizing minimum during warm-up85.48%
", + "bbox": [ + 76, + 169, + 475, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1, assuming $4\\%$ of public data with a privacy budget of $\\varepsilon = 2$ and $\\delta = 10^{-5}$ . The results outperform the existing state-of-the-art (SOTA) methods, i.e., boosting the accuracy from the previous $75.1\\%$ [43] to $85.48\\%$ on CIFAR-10. We emphasize that our approaches for dissecting warm-up training for DP are distinguishable from transfer tasks in non-DP setups, addressing data scarcity and improving underperforming DP-SGD optimization. Table 2 shows the gain and privacy cost of methods with public data usage compared to the training without public data, as in [21]. The results show higher gain and privacy costs with stronger privacy (lower $\\varepsilon$ ), whereas ours shows the highest gain and smallest costs. Notably, we observe tiny improvements in non-private settings, highlighting the distinctiveness of DP scenarios and the unique strengths of our tailored approach.", + "bbox": [ + 75, + 347, + 472, + 575 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/5398f847da1f6a69259a369ca0716af1dd32427964b484b03ce912ff7864b7be.jpg", + "table_caption": [ + "Table 2. Gain (↑) in performance and the corresponding cost of privacy (↓, in parentheses) for each method compared to not exploiting public data. Refer to Section 3.1 for the details of the setups." + ], + "table_footnote": [], + "table_body": "
MethodsNon-priv.ε = 6ε = 2
Warm [43]0.05% (-)0.10% (18.80%)3.20% (27.80%)
WarmSE [43]0.13% (-)3.00% (15.98%)5.60% (25.48%)
Ours0.13% (-)10.06% (8.92%)20.58% (10.50%)
", + "bbox": [ + 86, + 641, + 454, + 699 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Related Work", + "text_level": 1, + "bbox": [ + 76, + 715, + 364, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Differentially Private Deep Learning", + "text_level": 1, + "bbox": [ + 76, + 742, + 395, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Differential privacy (DP) [19] can guarantee the privacy of training data as follows:", + "bbox": [ + 75, + 766, + 468, + 797 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Definition 2.1 (Differential privacy) For two adjacent inputs $d, d' \\in \\mathcal{D}$ , a randomized mechanism $\\mathcal{M}: \\mathcal{D} \\to \\mathcal{R}$ satisfies $(\\varepsilon, \\delta)$ -differential privacy for any set of possible outputs $S \\subseteq \\mathcal{R}$ if", + "bbox": [ + 73, + 810, + 468, + 869 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nP r \\left[ \\mathcal {M} (d) \\in \\mathcal {S} \\right] \\leq e ^ {\\varepsilon} P r \\left[ \\mathcal {M} \\left(d ^ {\\prime}\\right) \\in \\mathcal {S} \\right] + \\delta . \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 883, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The privacy budget $\\varepsilon \\geq 0$ controls the level of privacy guarantee with the broken probability $\\delta \\geq 0$ . In deep learning, differentially private SGD (DP-SGD) [1] is widely used with the following steps: (i) average the clipped per-sample gradient $\\nabla \\ell_{i}(\\boldsymbol{w}) \\coloneqq \\nabla \\ell(\\boldsymbol{w}; \\boldsymbol{x}_{i})$ for weight $\\boldsymbol{w}$ with respect to each individual private data sample $\\boldsymbol{x}_{i} \\in \\boldsymbol{X}_{t}^{pr}$ and (ii) add Gaussian noise to the averaged gradient as follows:", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {g} _ {t} ^ {p r} = \\frac {1}{| \\boldsymbol {X} _ {t} ^ {p r} |} \\sum_ {\\boldsymbol {x} _ {i} \\in \\boldsymbol {X} _ {t} ^ {p r}} \\operatorname {c l i p} \\left(\\nabla \\ell_ {i} (\\boldsymbol {w} _ {t}), C\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 204, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {g}} _ {t} ^ {p r} = \\boldsymbol {g} _ {t} ^ {p r} + \\mathcal {N} (\\mathbf {0}, C ^ {2} \\sigma^ {2} \\mathbf {I}).\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 243, + 736, + 261 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The weight is updated as $\\boldsymbol{w}_{t + 1} = \\boldsymbol{w}_t - \\eta \\tilde{\\boldsymbol{g}}_t^{pr}$ with a learning rate $\\eta$ and $\\operatorname {clip}(\\boldsymbol {u},C)$ projects $\\pmb{u}$ to the $L_{2}$ -ball of radius $C$ . The noise level $\\sigma$ is determined by the privacy budget $(\\varepsilon ,\\delta)$ , the number of training steps, and the sampling probability (refer to Appendix C for details).", + "bbox": [ + 496, + 268, + 890, + 344 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To guarantee privacy with clipping and noise addition, DP-SGD inevitably degrades the performance during optimization. Therefore, various studies explored DP-friendly properties, including architecture [9, 59], loss and activation functions [44, 54], or smoothness [46, 55, 60]. Notably, De et al. [12] introduced a new era in utilizing large models for DP-SGD tasks by introducing the averaged loss of various augmentations called augmentation multiplicity, weight standardization [49], and optimization tricks. Note that adaptive clipping [3, 8] could improve our results.", + "bbox": [ + 496, + 345, + 890, + 496 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Private Learning with Public Information", + "text_level": 1, + "bbox": [ + 500, + 503, + 856, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The benefits of massive OOD public data have been explored in the context of the pre-trained models in vision [7, 12] and language [39, 65-67] models. Additionally, the transfer learning with similar distribution, such as CIFAR-100 for CIFAR-10, was under investigated [58, 59].", + "bbox": [ + 496, + 526, + 890, + 602 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ID public data $\\mathbf{X}^{pub}$ requires different approaches from the massive OOD public data due to its limited size and similar distributional properties. Hence, prior studies [2, 4, 38, 43], categorized as extended methods in Section 3.1, have focused on mitigating errors in the optimization of DP-SGD by utilizing the gradients of public data as a proxy for true gradients. These methods update the weight with $\\boldsymbol{w}_{t+1} = \\boldsymbol{w}_t - \\eta f_g$ , for $f_g(\\boldsymbol{w}_t; \\boldsymbol{X}_t^{pub}, \\boldsymbol{X}_t^{pr})$ such as normalizing the private gradient with the public gradient norm [38], employing a linear combination of private and public gradients [2], or estimating low-rank approximation with public data (even unlabelled) to reduce noise levels [48, 65].", + "bbox": [ + 496, + 602, + 890, + 782 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Nasr et al. [43] firstly introduced training a generative model as an augmentation technique. However, their primary focus is the optimization called DOPE-SGD, which updates towards the public gradient $\\pmb{g}_t^{pub}$ (without clipping and noise addition) and makes $\\pmb{g}_t^{pub} - \\pmb{g}_t^{pr}$ private as follows:", + "bbox": [ + 496, + 784, + 890, + 862 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {w} _ {t + 1} = \\boldsymbol {w} _ {t} - \\eta \\left(\\boldsymbol {g} _ {t} ^ {\\text {p u b}} + \\operatorname {c l i p} \\left(\\boldsymbol {g} _ {t} ^ {\\text {p u b}} - \\boldsymbol {g} _ {t} ^ {\\text {p r}}, C\\right) + \\mathcal {N}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 883, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12237", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with the same noise level $\\mathcal{N}$ in Equation (2). To the best of our knowledge, none of the prior studies deeply investigated the ID public data as a perspective of the data synthesis.", + "bbox": [ + 75, + 90, + 472, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Diffusion Synthesis", + "text_level": 1, + "bbox": [ + 76, + 146, + 261, + 162 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The integration of generative models in classification tasks has been widely explored to enhance generalization performance without extra data samples [5, 22, 25]. In recent years, diffusion models [28, 56, 57] have shown promising results in image generation. Notably, Xiao et al. [62] argued that diffusion models can generate high-quality and diverse images. Subsequently, various studies have focused on enhancing the quality of generation [30, 32], conditioning sampling [15, 27], and text-to-image generation [50, 52].", + "bbox": [ + 75, + 169, + 467, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the significance of privacy concerns during image synthesis, differentially private diffusion synthesis is one of the actively investigated research topics [17, 41]. Given the effectiveness of private fine-tuning upon pre-trained diffusion models for generation and classification tasks [23], utilizing privacy-preserving diffusion models presents opportunities for our future works.", + "bbox": [ + 75, + 306, + 467, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Measures To measure the quality of generated images, various measures are proposed: Inception Score (IS) [53] and Precision [36] to measure fidelity, Recall [36] to measure diversity, and Fréchet Inception Distance (FID) [26] to measure the distributional quality for mean and variance.", + "bbox": [ + 75, + 430, + 467, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To assess the impact of synthetic data on classification tasks, Ravuri and Vinyals [51] proposed the Classification Accuracy Score (CAS), which evaluates the classification performance on a test set using a model trained on synthetic data. Thus, we use CAS to validate the performance of synthetic public data on test data. However, since our main focus is on improving classification performance including private learning, all of the previous measures cannot be perfectly aligned with our goals.", + "bbox": [ + 75, + 506, + 467, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Framework", + "text_level": 1, + "bbox": [ + 76, + 656, + 200, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Training Procedure", + "text_level": 1, + "bbox": [ + 76, + 680, + 264, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our objective is to investigate the potential of diffusion models with ID public data, departing from conventional approaches that focus on guiding optimization with the public data [2, 4, 38, 43, 48, 64]. Our work aligns closely with [43], but we specifically concentrate on synthesizing data from the public and examining the important properties of private learning. We summarize the training scenarios using ID public data as follows [43]:", + "bbox": [ + 75, + 703, + 467, + 824 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Cold: Conduct DP training (e.g., DP-SGD) on the private dataset without using public data.", + "- Warm: Train models through (i) non-DP warm-up training phase on the public dataset (e.g., SGD) and (ii) private training phase on the private dataset with DP methods." + ], + "bbox": [ + 76, + 825, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/36445e508d74e76e65116fa26d959687486a9dc290e4082ba6dfe89ba0d8bf0a.jpg", + "image_caption": [ + "Figure 2. Toy experiment on diffusion synthesis and its effect on decision boundaries while varying the training sample size." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 887, + 208 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- WarmExt: During the private training (after warm-up training), leverage the public side information, such as gradients [2, 4, 38, 43], or low-rank approximation [48, 64], as extended methods of DP optimization.", + "- WarmSyn (Ours, [43]): Amplify the sparse information of public data using generative models or augmentation methods. Optionally, WarmSE indicates employing extended optimization with synthetic public data." + ], + "bbox": [ + 500, + 263, + 890, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In terms of privacy, since utilizing public data does not pose any privacy concerns to the private data, we can leverage the public data multiple times, e.g., training warm-up classification models, diffusion models, or guiding private training. From now on, we denote in-distribution (ID) public data as public data unless otherwise specified.", + "bbox": [ + 498, + 386, + 890, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Public Data Synthesis with Diffusion Models", + "text_level": 1, + "bbox": [ + 500, + 484, + 875, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For amplifying the sparse information in the WarmSyn setting, we first investigate amplifying the number of data samples using diffusion models. Recent studies [5, 22, 25, 61] have demonstrated the performance gain in complicated classification problems by training diffusion models to expand the size of training data samples within the data manifold, e.g., amplifying 50K CIFAR-10 training data into a 50M synthetic dataset improves adversarial training [61].", + "bbox": [ + 496, + 508, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To analyze public data synthesis with limited data samples, we conduct an experiment using a spiral dataset as a toy example (detailed in Appendix C), as shown in Figure 2. We consider two settings: (a) with a sufficient and (b) with an insufficient number of original data samples. For each setting, we train a simple diffusion model to generate new data samples. Then, we train two-layer classifiers until convergence using the original and synthetic data, respectively.", + "bbox": [ + 496, + 628, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With a large number of samples in (a), both diffusion and classification models demonstrate well-trained results. However, when the original data size is limited as in (b-1), the classification model tends to overfit individual data. Thus, despite correctly classifying almost all data samples, the model fails to discover the proper decision boundary. In contrast, in (b-2) where the diffusion model effectively approximates the data manifold, the classifier achieves a superior decision boundary compared to (b-1). Nevertheless, we should be aware that diffusion models can be apt to over", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12238", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/3eba144522c925449580f2a8eed81d5707fcf1cac9d6a67c472b7cb5c426cd88.jpg", + "table_caption": [ + "Table 3. Quality comparison of synthetic data trained with $4\\%$ of public data on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
SamplingFidelityDiversityQualityCAS (↑) (%)Test Acc (%)
IS (↑)Precision (↑)Recall (↑)FID (↓)
EDM (wd=0)11.0080.9640.1577.79962.8275.13
EDM + DG (wd=3)10.8150.9640.1537.78662.4775.31
EDM + DG (wd=10)10.7960.9460.1708.27464.6175.98
EDM + DG (wd=20)10.1570.8730.19111.49767.6177.66
EDM + DG (wd=30)9.1130.7850.21119.74866.5377.22
", + "bbox": [ + 81, + 114, + 645, + 218 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/32968c2f8d721d30e7d3049c2516e72dd65b0b5e59be0ce80825dd2e1a27da15.jpg", + "image_caption": [ + "Figure 3. Selected synthetic data samples from (Top) EDM and (Bottom) EDM + DG $(w_{d} = 30)$ synthesis." + ], + "image_footnote": [], + "bbox": [ + 661, + 88, + 893, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and underestimate the data distribution, as shown in (b-2).", + "bbox": [ + 75, + 241, + 460, + 255 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To push further, we mathematically analyze how the rate of data samples affects synthesis. The ability of a generative model $\\theta$ to approximate the 'entire' data can be determined by the ratio of 'seen' (observed during training) and the 'unseen' (not observed during training). Specifically, with a limited number of seen data, the model is required to estimate the unseen data to approximate the entire data.", + "bbox": [ + 75, + 256, + 468, + 362 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 3.1 For a finite number of 'entire' data samples $S_{data} = \\{\\pmb{x}_1, \\dots, \\pmb{x}_N\\}$ , split the data samples into 'seen' data $S_s = \\{\\pmb{x}_1, \\dots, \\pmb{x}_n\\}$ , and 'unseen' data $S_u = \\{\\pmb{x}_{n+1}, \\dots, \\pmb{x}_N\\}$ , without loss of generality. Let $p_{data}, p_s$ and $p_u$ be the probability distribution of each corresponding dataset. For any generative model $\\theta$ trained on 'seen' data, $p_\\theta$ represents the data distribution generated by $\\theta$ . Then,", + "bbox": [ + 75, + 372, + 470, + 478 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\log \\frac {1}{r _ {1}} + \\hat {p} _ {\\theta} ^ {u} \\log \\frac {\\hat {p} _ {\\theta} ^ {u}}{r _ {2}} \\leq \\tilde {D} _ {K L} (p _ {\\theta} \\| p _ {d a t a}) - \\tilde {D} _ {K L} (p _ {\\theta} \\| p _ {s}) \\\\ \\leq \\log \\frac {1}{r _ {1}} + \\hat {p} _ {\\theta} ^ {u} \\log \\frac {1}{r _ {2}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 93, + 484, + 449, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{p}_{\\theta}^{u} = \\sum_{\\boldsymbol{x}\\in S_{u}}p_{\\theta}(\\boldsymbol{x})\\leq 1$ indicates the capacity of the model $\\theta$ to generate 'unseen' data. For discrete probability distributions $p$ and $q$ , $\\tilde{D}_{KL}(p\\| q)$ indicates the relaxed Kullback-Leibler (KL) divergence, excluding the case when $q = 0$ . $r_1 = \\frac{n}{N}$ and $r_2 = \\frac{N - n}{n}$ denote the ratios of 'seen' to 'entire', and 'unseen' to 'seen' data, respectively.", + "bbox": [ + 75, + 558, + 468, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed proof is presented in Appendix A. The above theorem indicates that the ratios $r_1$ and $r_2$ affect how the model $\\theta$ can approximate the $p_{data}$ . As $r_1 \\rightarrow 1$ with sufficient seen data, then $r_2 \\rightarrow 0$ and $S_u \\rightarrow \\emptyset$ , so that $\\hat{p}_{\\theta}^{u} \\rightarrow 0$ and the upper and lower bounds converge to zero. Thus, ensuring $p_{\\theta}$ is close to $p_s$ ensures proximity of $p_{\\theta}$ to $p_{data}$ .", + "bbox": [ + 75, + 657, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, when considering a small $r_1$ , which is equivalent to a limited number of public data setups, the bounds depend on $\\hat{p}_{\\theta}^{u}$ . For $r_1 \\leq \\frac{1}{e + 1}$ , the lower and upper bounds are decreasing functions with respect to $\\hat{p}_{\\theta}^{u}$ . This implies that as the model's capacity to generate unseen data increases, the differences in divergences decrease. Thus, approximating the distribution of seen data is not enough to learn the whole data distribution for small $r_1$ . Rather, it is important for the model to learn the data manifold effectively to better approximate the data distribution including the unseen data.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Generated Data for Private Learning", + "text_level": 1, + "bbox": [ + 498, + 239, + 834, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now investigate how the aforementioned diffusion synthesis can be utilized in the context of public data and analyze how it can be further leveraged to enhance performance. For experiments, we primarily focus on the CIFAR-10 dataset with a privacy budget of $(2,10^{-5})$ , utilizing WRN-16-4² with 16 augmentation multiplicity and the techniques proposed in [12]. Within the training set, we randomly select 2K instances $(4\\%)$ for the public samples, as suggested in [43]. These samples are uniformly drawn from each class. All the measures for evaluating the generated data in this section are calculated with the entire training set (50K) as a reference. Additional experimental details are provided in Section 5.1 and Appendix B.", + "bbox": [ + 496, + 265, + 890, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Better Diffusion Synthesis with Public Data", + "text_level": 1, + "bbox": [ + 498, + 473, + 870, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 3.1 demonstrates that well-approximating the distribution of seen public data $p_{s}$ enables the synthetic data distribution $p_{\\theta}$ mimic the entire data distribution $p_{\\mathrm{data}}$ , which is essential to obtain good decision boundary as in Figure 2. Thus, we initially replace the Denoising Diffusion Probabilistic Model (DDPM) [28], previously investigated by Nasr et al. [43] for public synthesis, with the Elucidating Diffusion Model (EDM) [30]. EDM is known to generate better images (e.g., lower FID scores) than DDPM by using a higher-order sampling process. Then, we train EDM on 2K public data samples without using external datasets and employ class-conditional sampling to match the original distribution. With the trained EDM, we calculate various measures in Table 3. The FID of EDM synthesis at 7.80 (correspondingly 7.89 on 40K) outperforms the reported FID of 12.8 of DDPM on 40K images [43], which also improves the classification performance as shown in Table 1.", + "bbox": [ + 496, + 496, + 892, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the generation quality using public data is notably worse than the FID of 1.79 achieved with the entire set [30]. Within a limited public data, the model struggles to capture diversity, resulting in a recall of 0.16, even though precision remains high at 0.96. Note that repeating each public sample 25 times (thus 50K samples) results in a precision of 1.00, recall of 0.04, and FID of 13.64. The generated images and their memorization are illustrated in Ap", + "bbox": [ + 496, + 753, + 893, + 876 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2 WRN-40-4 requires excessive GPU considering its performance [43].", + "bbox": [ + 514, + 886, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12239", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/16216fe39e4898ca88c340af798b1153faeacbb571a02b9ab6a5b8510f36f4d0.jpg", + "table_caption": [ + "Table 4. CAS $(\\%)$ , test accuracy $(\\%)$ , and their difference $(\\%)$ with different augmentation methods during warm-up phase." + ], + "table_footnote": [], + "table_body": "
AugmentationCAS(%)Test Acc (%)Diff (%)
No Aug (EDM)62.8275.1313.31
Common77.9983.975.98
Common + Cutout80.7284.884.16
Common + Cutmix65.7382.2016.47
AutoAugment77.2183.456.24
", + "bbox": [ + 89, + 127, + 454, + 220 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6bc078f5b6630c8af42763c7b9d8ee253fe89d081f5bbbc4c5236d0b0fa98851.jpg", + "table_caption": [ + "Table 5. Geometric measures of the models trained with SGD and SAM after warm-up phase." + ], + "table_footnote": [], + "table_body": "
OptSynthetic DataPrivate Data
λmaxλmax/λ5Tr(∇2ℓ(w))λmaxλmax/λ5Tr(∇2ℓ(w))
SGD1.3810.6271.98112.821.58-2527.78
SAM0.442.6353.2158.321.50333.03
", + "bbox": [ + 78, + 273, + 475, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pendix E. No privacy concern occurs in diffusion synthesis since the diffusion model is solely trained with public data.", + "bbox": [ + 76, + 358, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Data Diversity Matters for Public Data", + "text_level": 1, + "bbox": [ + 76, + 400, + 410, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With limited private data, the model's capacity to generate unseen data is required in Theorem 3.1. The lack of diversity in the generated data can lead to misclassification due to distorted decision boundaries, as described in Figure 2. Given the challenge of DP-SGD in identifying a good basin [21], the key to successful warm-up lies in finding a well-generalizing minimum with a high CAS. As observed in [25, 51], data diversity can play an important role in improving CAS. We hypothesize that the importance of diversity is more pronounced in the warm-up phase of private learning, where the generated images exhibit low recall values.", + "bbox": [ + 75, + 422, + 468, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diversity for generation To validate our hypothesis, we first investigate enforcing data diversity in the generation process. Obtaining diversity in generations solely through a diffusion model is a challenging task. Thus, to enhance the data diversity during generation, we can use variants of diffusion models for guidance [27, 32] or editing [10, 40, 42]. Among them, discriminator guidance (DG) [32] introduces a discriminator to judge whether the sampling is from the true data or synthesis, controlling the trade-off between fidelity and diversity of the generated images by adjusting the weight $w_{d}$ of the discriminator. Higher $w_{d}$ yields diversity. Refer to Appendix C for the details of DG.", + "bbox": [ + 75, + 613, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 3, a higher weight of guidance ensures greater data diversity without any augmentation, but sacristies the fidelity. The best FID score is obtained with $w_{d} = 3$ while the best CAS is obtained at a bigger weight $w_{d} = 20$ . Interestingly, we need a larger weight value to achieve a similar gain of diversity than standard training ( $w_{d} = 1.5$ for best FID [32]). Figure 3 represents selected", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "examples from two extreme cases, with $w_{d} = 0$ and $w_{d} = 30$ to visualize the difference. Despite the quality degradation of detailed features with $w_{d} = 30$ , the CAS is higher due to the increased data diversity in features. Thus, we need to enhance diversity while maintaining quality for better classification. Similar to the EDM model trained with public data, no privacy concerns occur since the discriminator requires only original public and synthetic data from EDM.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diversity with augmentation Nonetheless, training an additional discriminator for DG can pose a bottleneck in terms of time and computational efficiency. Thus, to explicitly enhance the diversity of EDM synthetic data during the warm-up training, we employ various data augmentation techniques designed for classification tasks. Wang et al. [61] argued that utilizing appropriate augmentation in diffusion-based generated images can further improve the classification performance. Common augmentation [24] uses padding and random crop to the original size and horizontal flipping for the images. Cutmix [68] randomly replaces a part of the image with another and Cutout [14] randomly pad images. AutoAugment [11] chooses the best combination of augmentations such as color, rotation, or cutout. We set a baseline with no augmentation for synthetic images of EDM and compare these augmentations.", + "bbox": [ + 496, + 231, + 890, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The results are summarized in Table 4. Adding cutout augmentation to common augmentation demonstrates the best performance in terms of CAS and test accuracy. However, the two measures are not always aligned. Rather, the best performance gain with private data, noted as $Diff(\\%) = Test Acc - CAS$ , is obtained from Cutmix, which is known as one of the most diversified augmentations. This indicates that robust decision boundaries achieved through diversity facilitate easier private learning. Interestingly, the performance gain of augmentation surpasses the benefits of generation diversity, as illustrated in Appendix C.", + "bbox": [ + 496, + 474, + 890, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Optimization with Synthetic Data", + "text_level": 1, + "bbox": [ + 498, + 650, + 794, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As the clipping of DP-SGD significantly lowers the performance, it is known that a smaller gradient norm ensures high performance in private training [44, 46, 54]. In Figure 4a, we illustrate the gradient norms during private training with different training setups. The norm of synthetic data is calculated without clipping, whereas the private data used for DP-SGD is summed over individually clipped gradients, each with a clipping value of $C = 1$ . The results indicate that utilizing a synthetic dataset reduces the gradient norm, even in a private dataset where constraining the gradient norm is crucial to mitigate the effect of clipping.", + "bbox": [ + 496, + 672, + 890, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, even though training with diversified synthetic public data and augmentation, the models face the risk of being overfitted to public data. As public samples are selected from in-distribution data, the problem of the public", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12240", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b81f193cff8ed421a844281af901a8190eae929d9c050f0a7944e65881093d41.jpg", + "image_caption": [ + "(a) Gradient norm." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 269, + 213 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1157ed9d86dac895d7c8fbd47af8499a1be645b4ac5534888becbd8203c67f7d.jpg", + "image_caption": [ + "(b) Accuracy $(-)$ and loss $(-)$ .", + "Figure 4. Learning dynamics of private training with different datasets and optimization methods." + ], + "image_footnote": [], + "bbox": [ + 277, + 93, + 455, + 210 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "private generalization gap is analogous to the training-test generalization gap in standard training. In Figure 4b, we illustrate the accuracy and loss for each public, synthetic, private, and test dataset during private training after the warm-up phase. The model consistently achieves near-zero loss and $100\\%$ accuracy on synthetic data (as well as on public data) but struggles with private data (as well as on test data).", + "bbox": [ + 75, + 294, + 467, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To alleviate the generalization gap in standard training, various studies [16, 31, 33, 34, 37, 47] explored the geometric properties of the loss function in the weight space. The prominent optimization methods are designed to uncover flat minima, such as sharpness-aware minimization (SAM) [20] or stochastic weight averaging (SWA) [29]. Therefore, we apply SAM during the warm-up training and calculate geometric generalization measures, including metrics such as the top Hessian value $\\lambda_{max}$ , the ratio of Hessian $\\lambda_{max} / \\lambda_5$ , and the trace of the Hessian matrix $\\mathrm{Tr}(\\nabla^2\\ell (\\pmb {w}))$ for both synthetic and private data. Table 5 indicates that utilizing SAM results in lower (better) metric values, not only for synthetic data but also for private data. Note that SGD even demonstrates a negative trace value on private data.", + "bbox": [ + 75, + 401, + 467, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Moreover, in Figure 4a, as the flat minimum of SAM leads to a decreased gradient norm on synthetic data, it also maintains similar results concerning private data. These results indicate that relieving overfitting to synthetic data can help the generalization of private data. Thus, the aforementioned approaches find suitable initial point of DP-SGD.", + "bbox": [ + 75, + 611, + 467, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 715, + 209, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 741, + 263, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We assess the effectiveness of our proposed methods using public data primarily in two datasets: CIFAR-10 and CIFAR-100. For the public dataset, we randomly sample $4\\%$ of the training data (2K samples) uniformly drawn from each class, while the remaining data are used as private samples following [43]. We then train the EDM [30] models with the 2K public data samples and build 50K synthetic datasets with EDM sampling. To address the computational burden of training diffusion and sampling, we gen", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "erate datasets once and reuse them for classifiers as in [43].", + "bbox": [ + 498, + 90, + 888, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For classification models, we adopt WRN-16-4, following the techniques in [12] with 16 augmentations, and use pre-trained vision transformer models following [7]. Our experiments are conducted using PyTorch libraries [63] on eight NVIDIA GeForce RTX 3090 GPUs, partially on a cloud server with four NVIDIA A100 40GB GPUs. We report the mean and standard deviation for each experiment. For the detailed settings, refer to Appendix B.", + "bbox": [ + 496, + 106, + 890, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Classification Performance with Public Data", + "text_level": 1, + "bbox": [ + 498, + 236, + 874, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of individual techniques We first revisit Table 1, the ablation study of sequentially employing our approaches, with a privacy budget $(2,10^{-5})$ -DP on CIFAR-10. By only using better EDM synthesis without extra optimization techniques, we achieve the previous SOTA performance of $75.1\\%$ [43]. Additionally, recognizing the significance of diversity in data generation, we employ cutout augmentation techniques for diversity in classification, resulting in a performance of $84.88\\%$ . To mitigate potential overfitting to public information, we make use of generalization techniques. All these efforts collectively lead to an accuracy of $85.48\\%$ under $(2,10^{-5})$ -DP.", + "bbox": [ + 496, + 258, + 890, + 440 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Despite achieving the best performance of $85.93\\%$ when combined with DG, we exclude DG in this section due to its marginal performance enhancement $(0.45\\%)$ considering its extended training time, as detailed in Appendix C.", + "bbox": [ + 496, + 440, + 890, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR-10 with public data We report the performance comparison for our method with various previous approaches on a wide range of $\\varepsilon \\in \\{1,2,3,4,6\\}$ with $\\delta = 10^{-5}$ in Table 6. Our approach, which incorporates EDM synthesis, augmentation, and optimization for the public data, exhibits superior classification performance when compared to existing methods including DDPM-based augmentation and extended optimizations. The accuracies of $\\varepsilon = 0$ (after warm-up, without private data) and $\\varepsilon = \\infty$ (not private, with clipping) are $80.72\\%$ and $88.52\\%$ , respectively.", + "bbox": [ + 496, + 518, + 890, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR-100 with public data We then explore the CIFAR-100 dataset for DP, which is not actively investigated without pre-trained models due to its complexity. We first train the EDM model with 2K images and generate 50K images, similar to CIFAR-10. Given the 100 classes in CIFAR-100, only 20 public samples are available per class, significantly fewer than in CIFAR-10. The FID on 50K images with EDM synthesis is 11.28, which reduces the original FID of 15.58 for replicating each public image 25 times. After the warm-up, the accuracy of synthetic images on $\\varepsilon = 0$ is $38.04\\%$ (46.74% on $\\varepsilon = \\infty$ ), while the test accuracy of using 2K public samples without synthesis on $\\varepsilon = 0$ is only $16.79\\%$ . In Table 7, we report the accuracies by sequentially adopting the aforementioned tech", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12241", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ed8cd3db69071e892dd6df2cc90da2465efa559315191facc10d5c54b76b6f37.jpg", + "table_caption": [ + "Table 6. Test accuracy $(\\%)$ of private training on CIFAR-10 with privacy budgets of $\\varepsilon \\in \\{1,2,3,4,6\\}$ . The public and synthesis columns denote the Warm and WarmSyn setups, respectively. Ours employs all the techniques in Table 1, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**." + ], + "table_footnote": [ + "We note the results reported in [43] to set the architecture same. All other baseline results are adopted from the original paper." + ], + "table_body": "
DatasetsArchitecturePublicSynthesisMethodε = 1ε = 2ε = 3ε = 4ε = 6
CIFAR -10CNN-Tanh (0.55M)XX[44]45.858.363.5--
ScatterNet (0.16M)XX[59]60.367.269.3--
DPNAS [9] (0.53M)XX[46]60.13±0.3467.23±0.1269.86±0.49--
WRN-16-4 (2.74M)XX[12]56.8±0.664.9±0.569.2±0.371.9±0.377.0±0.8
WRN-40-4 (8.94M)XX[12]56.4±0.665.9±0.570.7±0.273.5±0.678.8±0.4
✓X[2]†-68.7-73.177.2
✓X[38]†-68.7-73.577.9
WRN-16-4 (2.74M)✓✓[2]†-70.5-74.578.2
✓✓[38]†-69.1-74.178.1
✓✓[43]†-75.1-77.980.0
✓✓Ours84.30±0.1185.48±0.1286.03±0.0986.49±0.1387.06±0.24
", + "bbox": [ + 86, + 142, + 885, + 309 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b8d1c0f107cdfde5cca06585646792eee000b48f669b12dfcd14e4c4894c5c8.jpg", + "table_caption": [ + "Table 7. Test accuracy $(\\%)$ of private classification on CIFAR-100 on the privacy budget of $\\varepsilon \\in \\{1,2,6,10\\}$ . The public and synthesis columns indicate Warm and WarmSyn settings, respectively. We employ the techniques in Table 1 sequentially, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**." + ], + "table_footnote": [ + "$\\dagger$ Unfortunately, their DP-SGD results are not reproducible, even when using the same hyperparameters as in the original paper." + ], + "table_body": "
DatasetsArchitecturePublicSynthesisMethodsε = 1ε = 2ε = 6ε = 10
CIFAR -100Resnet-9XX[35]†18.124.9-40.8
Resnet-9 (6.62M)XXCold†8.3514.4229.8935.11
WRN-16-4 (2.74M)XXCold9.2818.1933.6139.09
✓XWarm20.8425.1533.4738.89
WRN-16-4 (2.74M)✓✓WarmSyn26.13±0.2031.53±0.0435.53±0.1140.82±0.10
✓✓+Augmentation40.96±0.3044.52±0.0150.47±0.0454.29±0.05
✓✓+Optimization45.93±0.0648.61±0.5954.36±0.5256.56±0.11
", + "bbox": [ + 81, + 388, + 888, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "niques, where each of the approaches matters. As a result, we obtain $48.61\\%$ on $\\varepsilon = 2$ without pre-trained models.", + "bbox": [ + 75, + 541, + 470, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CIFAR-100 with pre-trained on ImageNet To push further, we demonstrate the effectiveness of our procedures when combined with pre-trained models with ID public data. We adopt the vision transformers following [7] pretrained on ImageNet [13]. Upon the pre-trained models, we sequentially perform the warm-up training with ID public data and private learning. The results in Table 8 indicate that the synthesis can boost classification performance. Within a wide range of models and privacy budgets, our methods outperform the warm settings.", + "bbox": [ + 75, + 592, + 472, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Distribution shift (CIFAR-100 $\\rightarrow$ CIFAR-10) The distribution shifts from similar but not ID public data [59] can be combined with our methods. We consider $4\\%$ of CIFAR-100 data as public to enhance the performance of CIFAR-10 as a substitute for CIFAR-10 ID public data. In Table 9, we present the classification results for both the warm and our settings, where both models are trained on the public data and synthetic data from $4\\%$ of CIFAR-100, respectively. The experimental results show that the differences in accu", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "racies exceed $20\\%$ , even though neither model has observed CIFAR-10 datasets before private training with DP-SGD. This indicates that amplifying public information is meaningful in distribution shifts. Additional sensitivity analysis and ablation studies can be found in Appendix D.", + "bbox": [ + 496, + 541, + 893, + 618 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pre-trained diffusion models Our main idea to use synthesis for public data is flexible in practical scenarios and diverse datasets. To mitigate the drawbacks of training diffusion on each dataset, we investigated using the pre-trained diffusion models, which are trained on OOD public data. Specifically, we make use of pre-trained Stable Diffusion (SD) [52] and Boomerang sampling [40]. We fed $4\\%$ of public data to Boomerang editing with SD backbone for generation diversity and generated 20 images per sample for classifier training. The similar experiments are shown in Appendix D. We maintain the other training procedures the same as 'Ours', which we call 'Ours-SD'. Table 10 indicates that our framework is straightforward and effective for real-world data, and generalizable without depending on specific diffusion models. We conclude that data diversity can enhance performance when the model is not trained on specific ID public data.", + "bbox": [ + 496, + 643, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12242", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3e9f2aa13ce0c2b64602cb9253f5adcb7663b060f993f6e8a9e8a85fec27d4d6.jpg", + "table_caption": [ + "Table 8. Test accuracy (%) of private classification on CIFAR-100 using pre-trained models on the privacy budget of $\\varepsilon \\in \\{0.5,2\\}$ . The **bold** indicates results within the standard deviation of the top mean score." + ], + "table_footnote": [], + "table_body": "
DatasetsPrivacy budgetε = 0.5ε = 2
ArchitectureColdWarmOursColdWarmOurs
CIFAR -100CrossViT small 240 (26.3M)60.50±1.7073.17±0.2477.43±0.1371.36±0.5277.00±0.2780.25±0.57
CrossViT 18 240 (42.6M)67.03±0.4677.19±0.4479.96±0.1074.28±0.2280.30±0.0282.85±0.08
DeiT base patch16 224 (85.8M)49.34±1.4979.56±0.7479.28±0.7669.09±0.1082.98±0.0483.06±0.01
CrossViT base 240 (103.9M)66.24±0.4775.59±0.2178.06±0.0575.15±0.0379.25±0.0581.14±0.15
", + "bbox": [ + 81, + 128, + 888, + 227 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cd644eb766bd896df824d8dc4299e08c1cc83f7df856202bec8162a5627ecd66.jpg", + "table_caption": [ + "Table 9. Comparison of distribution shift performance on CIFAR-10 with the warm and our models trained on $4\\%$ of CIFAR-100." + ], + "table_footnote": [], + "table_body": "
CIFAR-100 → CIFAR-10Test Acc (%)
ε = 2ε = 4ε = 6
Warm50.65±0.3756.54±0.2059.49±1.39
Ours73.46±0.2878.60±0.1380.12±0.04
", + "bbox": [ + 83, + 289, + 460, + 359 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f74c630bda9aa8072309a75e7c3f5aea65e1e2fbe8fdd8e0292ec6eea3c190c2.jpg", + "table_caption": [ + "Table 10. Classification results on real-world datasets." + ], + "table_footnote": [], + "table_body": "
DataMethodε = 2ε = 4ε = 6
EuroSATWarm (w/ Aug, Opt)83.6785.5286.07
WarmExt [43]84.3785.7886.07
(Land use)Ours-SD90.3791.7492.52
PathMNISTWarm (w/ Aug, Opt)89.2389.3989.54
WarmExt [43]89.0489.2589.28
(Biomedical)Ours-SD91.6491.9492.10
FairFaceWarm (w/ Aug, Opt)53.0054.5554.83
WarmExt [43]53.3354.7454.84
(w.r.t. Race)Ours-SD54.9056.1956.37
", + "bbox": [ + 78, + 398, + 413, + 523 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/492df6f696f815e01ccb2f4d97175c45c200686b15cadcc8c387a522e1841d19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 410, + 468, + 446 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c2e7a0c077e2abcef06c76f6a4e5d781987358a778e1f615dbd7d1da3817f216.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 446, + 468, + 486 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/acb2eb7c1bfa07640df1317abfd51f9b859e76fe42862d4bd31759715c8fcc11.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 486, + 468, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Revisit Extended Optimization", + "text_level": 1, + "bbox": [ + 76, + 542, + 349, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On top of our method, we reevaluate the effectiveness of existing extended methods (thus WarmSE) in Table 11, particularly mirror GD [2] and DOPE-SGD [43]. These methods are trained after our synthesis, augmentation, and warm-up optimization on $\\varepsilon \\in \\{2, 4, 6\\}$ . Remarkably, the performance of the extended methods falls within the standard deviation range of DP-SGD. This implies that, as the models have already extracted substantial side information from public data before private training, extended optimization does not further improve DP optimization. Note that the computational time of the public batch is marginal to DP-SGD.", + "bbox": [ + 75, + 566, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, extended methods sometimes exhibit poorer training stability than DP-SGD. Due to their reliance on public gradients, these methods are sensitive to the hyperparameter settings and easily encounter exploding gradients. In Figure 5, under the same setting as Figure 4a, we observe a gradual decrease in the private gradient norm, while the public gradient norm consistently increases. When the public norm increases to a certain level, the norm of both public and private data with extended methods may diverge after updating toward public gradients. For further insights about the learning dynamics in terms of the loss function", + "bbox": [ + 75, + 734, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ae40abacdb1d77fbda6ad70cd7321de6531f1089a6441442a3a3bfb65c4d30c2.jpg", + "table_caption": [ + "Table 11. Performance and computational time of different extended optimization methods." + ], + "table_footnote": [], + "table_body": "
Privacy budget ε (δ = 10-5)Optimization
DP-SGDMirror GD [2]DOPE-SGD [43]
MedianMinMedianMin
ε = 285.48±0.1785.5210.0085.5310.00
ε = 486.49±0.1386.3110.0086.6910.00
ε = 687.06±0.2486.7310.0086.8410.00
Time (ms/image)12.7012.8012.86
", + "bbox": [ + 501, + 289, + 898, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ebe73e844794760e9cc646618d56a6b53fe88900f1c86d6a7b5e4978f0a27cb1.jpg", + "image_caption": [ + "Figure 5. The norm of gradients with (Left) synthetic dataset and (Right) private dataset with clipping during private training with different optimization methods." + ], + "image_footnote": [], + "bbox": [ + 509, + 402, + 691, + 513 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2f24f6c3ab8483bbb95aa1200eec5a2ef668bf72b4001c3b0a2e7af00ad8e6c4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 402, + 880, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and private gradient norm without clipping, please refer to Appendix C. However, we believe that undiscovered extended methods can be beneficial for the WarmSyn settings.", + "bbox": [ + 498, + 595, + 890, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 655, + 619, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we investigate the potential of diffusion models for in-distribution public data to enhance private classification performance. We demonstrate the importance of synthetic data diversity, augmentation techniques, and the importance of well-generalizing minima for private optimization. As a limitation, we leave the experiments on more extensive and sensitive datasets and the efficient implementation of our method. We hope that this work helps leverage diffusion models to address utility-privacy trade-offs.", + "bbox": [ + 496, + 680, + 893, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported by NRF (No. 2022R1A5A6000840, No. RS-2023-00272502) and IITP (No. 2022-0-00984, No. 2021-0-01343-004) grants funded by the Korea government (MSIT).", + "bbox": [ + 498, + 835, + 893, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12243", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. Deep learning with differential privacy. 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In Proceedings of the IEEE/CVF international conference on computer vision, pages 6023-6032, 2019. 5" + ], + "bbox": [ + 78, + 90, + 468, + 896 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12246", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/35a6ec9e-03c5-459f-83ad-bafb99a44b46_model.json b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/35a6ec9e-03c5-459f-83ad-bafb99a44b46_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2eb00a1aaa41a66c078d540a0d15a6f762ad4bd8 --- /dev/null +++ b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/35a6ec9e-03c5-459f-83ad-bafb99a44b46_model.json @@ -0,0 +1,2554 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.184, + 0.13, + 0.787, + 0.175 + ], + "angle": 0, + "content": "In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.271, + 0.203, + 0.704, + 0.239 + ], + "angle": 0, + "content": "Jinseong Park\\(^{1\\dagger}\\) Yujin Choi\\(^{1\\dagger}\\) Jaewook Lee\\(^{1*}\\) Seoul National University" + }, + { + "type": "text", + "bbox": [ + 0.31, + 0.242, + 0.655, + 0.256 + ], + "angle": 0, + "content": "{jinseong,uznhigh,jaewook} @snu.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.313, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.522 + ], + "angle": 0, + "content": "To alleviate the utility degradation of deep learning image classification with differential privacy (DP), employing extra public data or pre-trained models has been widely explored. Recently, the use of in-distribution public data has been investigated, where tiny subsets of datasets are released publicly. In this paper, we investigate a framework that leverages recent diffusion models to amplify the information of public data. Subsequently, we identify data diversity and generalization gap between public and private data as critical factors addressing the limited public data. While assuming \\(4\\%\\) of training data as public, our method achieves \\(85.48\\%\\) on CIFAR-10 with a privacy budget of \\(\\varepsilon = 2\\), without employing extra public data for training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.55, + 0.21, + 0.565 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Differential privacy (DP) [18, 19] establishes a mathematical framework to ensure the privacy of training data. In deep learning, differentially private SGD (DP-SGD) [1] has become the de facto standard method to guarantee the models' privacy. However, differentially private training inevitably degrades performance compared to standard (non-DP) training [6, 45]. As a practical solution, leveraging public pre-trained models or public data has been explored to enhance utility [12, 39, 59, 65-67]. As using public data raises no privacy concerns, fine-tuning pre-trained models on private data can make use of learned features for free. Nevertheless, their effectiveness might be diminished when addressing out-of-distribution (OOD) public data of small shared characteristics with private data [59]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.47, + 0.879 + ], + "angle": 0, + "content": "As an alternative, researchers have investigated the use of in-distribution (ID) public data, indicating that a small portion of in-distribution data is made public [38]. For example, some data owners decide to share their data publicly in exchange for economic incentives or public interest. This setup allows us to leverage public data with a distribution" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.292, + 0.887, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.452, + 0.892, + 0.494 + ], + "angle": 0, + "content": "Figure 1. Illustration of (Top) existing optimization-based methods and (Bottom) proposed training procedure for amplifying in-distribution public data and utilizing the synthetic data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.893, + 0.662 + ], + "angle": 0, + "content": "similar to private data. In contrast to previous approaches, such as utilizing extra OOD data or distribution shift, we need to assume a limited amount of ID public data since the public data might contain more sensitive information. However, the repeated use of limited-sized public data can raise critical issues related to memorization and overfitting [43]. To mitigate the aforementioned problems, previous studies mainly have focused on utilizing side information from the little public data to enhance the optimization of differentially private deep learning [2, 4, 38, 43]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.895, + 0.829 + ], + "angle": 0, + "content": "Recently, Ganesh et al. [21] pointed out that warm-up training with public data plays a crucial in private optimization to find a good basin with a small loss, whereas DP-SGD from a random initial point faces a high loss and poor optimization. From this viewpoint, we suggest that enlarging the public dataset could improve the performance of private learning. By using the recent diffusion models [28, 30], we aim to enrich the contextual information of public data. We further identify that data diversity and generalization gap between public and private data act as critical factors, particularly addressing the limited size of public data." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.83, + 0.894, + 0.862 + ], + "angle": 0, + "content": "The proposed framework is illustrated in Figure 1. We summarize our approaches and their performance gains in" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.332, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author. †Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.875, + 0.653, + 0.887 + ], + "angle": 0, + "content": "1Our code is available at" + }, + { + "type": "page_footnote", + "bbox": [ + 0.501, + 0.888, + 0.806, + 0.901 + ], + "angle": 0, + "content": "https://github.com/JinseongP/DPTrainer." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12236" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.473, + 0.16 + ], + "angle": 0, + "content": "Table 1. Ablation study on the impact of various techniques, including synthesis, augmentation, and optimization, to enhance classification performance using in-distribution public data from CIFAR-10 under \\((2,10^{-5})\\)-DP. Refer to Section 3.1 for the details of setups and the relevant sections for the details of each method." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.17, + 0.476, + 0.334 + ], + "angle": 0, + "content": "
SetupTraining SettingsTest Acc
Baselines including previous SOTA methods (Sec. 3.1)
ColdCold Baseline (WRN16-4) [12]64.02%
WarmWarm-up on public data68.09%
WarmSynWarm-up on DDPM synthesis [43]72.0%
WarmSEWarmSyn (DDPM) + DOPE-SGD [43]75.1%
In-distributionpublic data synthesis (Sec. 4.1) & Diversity (Sec. 4.2)
WarmSynWarm-up on EDM synthesis75.13 %
WarmSynEDM synthesis + generation diversity77.66 %
WarmSynEDM synthesis + augmentation diversity84.88%
Generalization for public-private datasets (Sec. 4.3)
WarmSynWell-generalizing minimum during warm-up85.48%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Table 1, assuming \\(4\\%\\) of public data with a privacy budget of \\(\\varepsilon = 2\\) and \\(\\delta = 10^{-5}\\). The results outperform the existing state-of-the-art (SOTA) methods, i.e., boosting the accuracy from the previous \\(75.1\\%\\) [43] to \\(85.48\\%\\) on CIFAR-10. We emphasize that our approaches for dissecting warm-up training for DP are distinguishable from transfer tasks in non-DP setups, addressing data scarcity and improving underperforming DP-SGD optimization. Table 2 shows the gain and privacy cost of methods with public data usage compared to the training without public data, as in [21]. The results show higher gain and privacy costs with stronger privacy (lower \\(\\varepsilon\\)), whereas ours shows the highest gain and smallest costs. Notably, we observe tiny improvements in non-private settings, highlighting the distinctiveness of DP scenarios and the unique strengths of our tailored approach." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.633 + ], + "angle": 0, + "content": "Table 2. Gain (↑) in performance and the corresponding cost of privacy (↓, in parentheses) for each method compared to not exploiting public data. Refer to Section 3.1 for the details of the setups." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.642, + 0.455, + 0.7 + ], + "angle": 0, + "content": "
MethodsNon-priv.ε = 6ε = 2
Warm [43]0.05% (-)0.10% (18.80%)3.20% (27.80%)
WarmSE [43]0.13% (-)3.00% (15.98%)5.60% (25.48%)
Ours0.13% (-)10.06% (8.92%)20.58% (10.50%)
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.717, + 0.365, + 0.734 + ], + "angle": 0, + "content": "2. Background and Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.743, + 0.396, + 0.76 + ], + "angle": 0, + "content": "2.1. Differentially Private Deep Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.767, + 0.47, + 0.798 + ], + "angle": 0, + "content": "Differential privacy (DP) [19] can guarantee the privacy of training data as follows:" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.811, + 0.47, + 0.871 + ], + "angle": 0, + "content": "Definition 2.1 (Differential privacy) For two adjacent inputs \\( d, d' \\in \\mathcal{D} \\), a randomized mechanism \\( \\mathcal{M}: \\mathcal{D} \\to \\mathcal{R} \\) satisfies \\( (\\varepsilon, \\delta) \\)-differential privacy for any set of possible outputs \\( S \\subseteq \\mathcal{R} \\) if" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.884, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\nP r \\left[ \\mathcal {M} (d) \\in \\mathcal {S} \\right] \\leq e ^ {\\varepsilon} P r \\left[ \\mathcal {M} \\left(d ^ {\\prime}\\right) \\in \\mathcal {S} \\right] + \\delta . \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "The privacy budget \\(\\varepsilon \\geq 0\\) controls the level of privacy guarantee with the broken probability \\(\\delta \\geq 0\\). In deep learning, differentially private SGD (DP-SGD) [1] is widely used with the following steps: (i) average the clipped per-sample gradient \\(\\nabla \\ell_{i}(\\boldsymbol{w}) \\coloneqq \\nabla \\ell(\\boldsymbol{w}; \\boldsymbol{x}_{i})\\) for weight \\(\\boldsymbol{w}\\) with respect to each individual private data sample \\(\\boldsymbol{x}_{i} \\in \\boldsymbol{X}_{t}^{pr}\\) and (ii) add Gaussian noise to the averaged gradient as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.205, + 0.892, + 0.242 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {g} _ {t} ^ {p r} = \\frac {1}{| \\boldsymbol {X} _ {t} ^ {p r} |} \\sum_ {\\boldsymbol {x} _ {i} \\in \\boldsymbol {X} _ {t} ^ {p r}} \\operatorname {c l i p} \\left(\\nabla \\ell_ {i} (\\boldsymbol {w} _ {t}), C\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.244, + 0.738, + 0.262 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {g}} _ {t} ^ {p r} = \\boldsymbol {g} _ {t} ^ {p r} + \\mathcal {N} (\\mathbf {0}, C ^ {2} \\sigma^ {2} \\mathbf {I}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.345 + ], + "angle": 0, + "content": "The weight is updated as \\(\\boldsymbol{w}_{t + 1} = \\boldsymbol{w}_t - \\eta \\tilde{\\boldsymbol{g}}_t^{pr}\\) with a learning rate \\(\\eta\\) and \\(\\operatorname {clip}(\\boldsymbol {u},C)\\) projects \\(\\pmb{u}\\) to the \\(L_{2}\\)-ball of radius \\(C\\). The noise level \\(\\sigma\\) is determined by the privacy budget \\((\\varepsilon ,\\delta)\\), the number of training steps, and the sampling probability (refer to Appendix C for details)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.892, + 0.497 + ], + "angle": 0, + "content": "To guarantee privacy with clipping and noise addition, DP-SGD inevitably degrades the performance during optimization. Therefore, various studies explored DP-friendly properties, including architecture [9, 59], loss and activation functions [44, 54], or smoothness [46, 55, 60]. Notably, De et al. [12] introduced a new era in utilizing large models for DP-SGD tasks by introducing the averaged loss of various augmentations called augmentation multiplicity, weight standardization [49], and optimization tricks. Note that adaptive clipping [3, 8] could improve our results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.505, + 0.857, + 0.521 + ], + "angle": 0, + "content": "2.2. Private Learning with Public Information" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.603 + ], + "angle": 0, + "content": "The benefits of massive OOD public data have been explored in the context of the pre-trained models in vision [7, 12] and language [39, 65-67] models. Additionally, the transfer learning with similar distribution, such as CIFAR-100 for CIFAR-10, was under investigated [58, 59]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.784 + ], + "angle": 0, + "content": "ID public data \\( \\mathbf{X}^{pub} \\) requires different approaches from the massive OOD public data due to its limited size and similar distributional properties. Hence, prior studies [2, 4, 38, 43], categorized as extended methods in Section 3.1, have focused on mitigating errors in the optimization of DP-SGD by utilizing the gradients of public data as a proxy for true gradients. These methods update the weight with \\( \\boldsymbol{w}_{t+1} = \\boldsymbol{w}_t - \\eta f_g \\), for \\( f_g(\\boldsymbol{w}_t; \\boldsymbol{X}_t^{pub}, \\boldsymbol{X}_t^{pr}) \\) such as normalizing the private gradient with the public gradient norm [38], employing a linear combination of private and public gradients [2], or estimating low-rank approximation with public data (even unlabelled) to reduce noise levels [48, 65]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.892, + 0.863 + ], + "angle": 0, + "content": "Nasr et al. [43] firstly introduced training a generative model as an augmentation technique. However, their primary focus is the optimization called DOPE-SGD, which updates towards the public gradient \\( \\pmb{g}_t^{pub} \\) (without clipping and noise addition) and makes \\( \\pmb{g}_t^{pub} - \\pmb{g}_t^{pr} \\) private as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.884, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {w} _ {t + 1} = \\boldsymbol {w} _ {t} - \\eta \\left(\\boldsymbol {g} _ {t} ^ {\\text {p u b}} + \\operatorname {c l i p} \\left(\\boldsymbol {g} _ {t} ^ {\\text {p u b}} - \\boldsymbol {g} _ {t} ^ {\\text {p r}}, C\\right) + \\mathcal {N}\\right), \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12237" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.138 + ], + "angle": 0, + "content": "with the same noise level \\(\\mathcal{N}\\) in Equation (2). To the best of our knowledge, none of the prior studies deeply investigated the ID public data as a perspective of the data synthesis." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.147, + 0.262, + 0.163 + ], + "angle": 0, + "content": "2.3. Diffusion Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.468, + 0.306 + ], + "angle": 0, + "content": "The integration of generative models in classification tasks has been widely explored to enhance generalization performance without extra data samples [5, 22, 25]. In recent years, diffusion models [28, 56, 57] have shown promising results in image generation. Notably, Xiao et al. [62] argued that diffusion models can generate high-quality and diverse images. Subsequently, various studies have focused on enhancing the quality of generation [30, 32], conditioning sampling [15, 27], and text-to-image generation [50, 52]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.468, + 0.412 + ], + "angle": 0, + "content": "Due to the significance of privacy concerns during image synthesis, differentially private diffusion synthesis is one of the actively investigated research topics [17, 41]. Given the effectiveness of private fine-tuning upon pre-trained diffusion models for generation and classification tasks [23], utilizing privacy-preserving diffusion models presents opportunities for our future works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.468, + 0.506 + ], + "angle": 0, + "content": "Measures To measure the quality of generated images, various measures are proposed: Inception Score (IS) [53] and Precision [36] to measure fidelity, Recall [36] to measure diversity, and Fréchet Inception Distance (FID) [26] to measure the distributional quality for mean and variance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.468, + 0.643 + ], + "angle": 0, + "content": "To assess the impact of synthetic data on classification tasks, Ravuri and Vinyals [51] proposed the Classification Accuracy Score (CAS), which evaluates the classification performance on a test set using a model trained on synthetic data. Thus, we use CAS to validate the performance of synthetic public data on test data. However, since our main focus is on improving classification performance including private learning, all of the previous measures cannot be perfectly aligned with our goals." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.657, + 0.202, + 0.672 + ], + "angle": 0, + "content": "3. Framework" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.265, + 0.697 + ], + "angle": 0, + "content": "3.1. Training Procedure" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.825 + ], + "angle": 0, + "content": "Our objective is to investigate the potential of diffusion models with ID public data, departing from conventional approaches that focus on guiding optimization with the public data [2, 4, 38, 43, 48, 64]. Our work aligns closely with [43], but we specifically concentrate on synthesizing data from the public and examining the important properties of private learning. We summarize the training scenarios using ID public data as follows [43]:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.826, + 0.468, + 0.855 + ], + "angle": 0, + "content": "- Cold: Conduct DP training (e.g., DP-SGD) on the private dataset without using public data." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- Warm: Train models through (i) non-DP warm-up training phase on the public dataset (e.g., SGD) and (ii) private training phase on the private dataset with DP methods." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.091, + 0.888, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.221, + 0.892, + 0.248 + ], + "angle": 0, + "content": "Figure 2. Toy experiment on diffusion synthesis and its effect on decision boundaries while varying the training sample size." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.265, + 0.892, + 0.325 + ], + "angle": 0, + "content": "- WarmExt: During the private training (after warm-up training), leverage the public side information, such as gradients [2, 4, 38, 43], or low-rank approximation [48, 64], as extended methods of DP optimization." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.325, + 0.892, + 0.386 + ], + "angle": 0, + "content": "- WarmSyn (Ours, [43]): Amplify the sparse information of public data using generative models or augmentation methods. Optionally, WarmSE indicates employing extended optimization with synthetic public data." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.265, + 0.892, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.387, + 0.892, + 0.476 + ], + "angle": 0, + "content": "In terms of privacy, since utilizing public data does not pose any privacy concerns to the private data, we can leverage the public data multiple times, e.g., training warm-up classification models, diffusion models, or guiding private training. From now on, we denote in-distribution (ID) public data as public data unless otherwise specified." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.877, + 0.501 + ], + "angle": 0, + "content": "3.2. Public Data Synthesis with Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.629 + ], + "angle": 0, + "content": "For amplifying the sparse information in the WarmSyn setting, we first investigate amplifying the number of data samples using diffusion models. Recent studies [5, 22, 25, 61] have demonstrated the performance gain in complicated classification problems by training diffusion models to expand the size of training data samples within the data manifold, e.g., amplifying 50K CIFAR-10 training data into a 50M synthetic dataset improves adversarial training [61]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.75 + ], + "angle": 0, + "content": "To analyze public data synthesis with limited data samples, we conduct an experiment using a spiral dataset as a toy example (detailed in Appendix C), as shown in Figure 2. We consider two settings: (a) with a sufficient and (b) with an insufficient number of original data samples. For each setting, we train a simple diffusion model to generate new data samples. Then, we train two-layer classifiers until convergence using the original and synthetic data, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With a large number of samples in (a), both diffusion and classification models demonstrate well-trained results. However, when the original data size is limited as in (b-1), the classification model tends to overfit individual data. Thus, despite correctly classifying almost all data samples, the model fails to discover the proper decision boundary. In contrast, in (b-2) where the diffusion model effectively approximates the data manifold, the classifier achieves a superior decision boundary compared to (b-1). Nevertheless, we should be aware that diffusion models can be apt to over" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12238" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.089, + 0.634, + 0.104 + ], + "angle": 0, + "content": "Table 3. Quality comparison of synthetic data trained with \\(4\\%\\) of public data on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.647, + 0.219 + ], + "angle": 0, + "content": "
SamplingFidelityDiversityQualityCAS (↑) (%)Test Acc (%)
IS (↑)Precision (↑)Recall (↑)FID (↓)
EDM (wd=0)11.0080.9640.1577.79962.8275.13
EDM + DG (wd=3)10.8150.9640.1537.78662.4775.31
EDM + DG (wd=10)10.7960.9460.1708.27464.6175.98
EDM + DG (wd=20)10.1570.8730.19111.49767.6177.66
EDM + DG (wd=30)9.1130.7850.21119.74866.5377.22
" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.089, + 0.895, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.173, + 0.893, + 0.215 + ], + "angle": 0, + "content": "Figure 3. Selected synthetic data samples from (Top) EDM and (Bottom) EDM + DG \\((w_{d} = 30)\\) synthesis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.461, + 0.256 + ], + "angle": 0, + "content": "and underestimate the data distribution, as shown in (b-2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.257, + 0.47, + 0.363 + ], + "angle": 0, + "content": "To push further, we mathematically analyze how the rate of data samples affects synthesis. The ability of a generative model \\(\\theta\\) to approximate the 'entire' data can be determined by the ratio of 'seen' (observed during training) and the 'unseen' (not observed during training). Specifically, with a limited number of seen data, the model is required to estimate the unseen data to approximate the entire data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.471, + 0.479 + ], + "angle": 0, + "content": "Theorem 3.1 For a finite number of 'entire' data samples \\( S_{data} = \\{\\pmb{x}_1, \\dots, \\pmb{x}_N\\} \\), split the data samples into 'seen' data \\( S_s = \\{\\pmb{x}_1, \\dots, \\pmb{x}_n\\} \\), and 'unseen' data \\( S_u = \\{\\pmb{x}_{n+1}, \\dots, \\pmb{x}_N\\} \\), without loss of generality. Let \\( p_{data}, p_s \\) and \\( p_u \\) be the probability distribution of each corresponding dataset. For any generative model \\( \\theta \\) trained on 'seen' data, \\( p_\\theta \\) represents the data distribution generated by \\( \\theta \\). Then," + }, + { + "type": "equation", + "bbox": [ + 0.094, + 0.486, + 0.45, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\log \\frac {1}{r _ {1}} + \\hat {p} _ {\\theta} ^ {u} \\log \\frac {\\hat {p} _ {\\theta} ^ {u}}{r _ {2}} \\leq \\tilde {D} _ {K L} (p _ {\\theta} \\| p _ {d a t a}) - \\tilde {D} _ {K L} (p _ {\\theta} \\| p _ {s}) \\\\ \\leq \\log \\frac {1}{r _ {1}} + \\hat {p} _ {\\theta} ^ {u} \\log \\frac {1}{r _ {2}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.651 + ], + "angle": 0, + "content": "where \\(\\hat{p}_{\\theta}^{u} = \\sum_{\\boldsymbol{x}\\in S_{u}}p_{\\theta}(\\boldsymbol{x})\\leq 1\\) indicates the capacity of the model \\(\\theta\\) to generate 'unseen' data. For discrete probability distributions \\(p\\) and \\(q\\), \\(\\tilde{D}_{KL}(p\\| q)\\) indicates the relaxed Kullback-Leibler (KL) divergence, excluding the case when \\(q = 0\\). \\(r_1 = \\frac{n}{N}\\) and \\(r_2 = \\frac{N - n}{n}\\) denote the ratios of 'seen' to 'entire', and 'unseen' to 'seen' data, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.75 + ], + "angle": 0, + "content": "The detailed proof is presented in Appendix A. The above theorem indicates that the ratios \\( r_1 \\) and \\( r_2 \\) affect how the model \\( \\theta \\) can approximate the \\( p_{data} \\). As \\( r_1 \\rightarrow 1 \\) with sufficient seen data, then \\( r_2 \\rightarrow 0 \\) and \\( S_u \\rightarrow \\emptyset \\), so that \\( \\hat{p}_{\\theta}^{u} \\rightarrow 0 \\) and the upper and lower bounds converge to zero. Thus, ensuring \\( p_{\\theta} \\) is close to \\( p_s \\) ensures proximity of \\( p_{\\theta} \\) to \\( p_{data} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.471, + 0.902 + ], + "angle": 0, + "content": "However, when considering a small \\( r_1 \\), which is equivalent to a limited number of public data setups, the bounds depend on \\( \\hat{p}_{\\theta}^{u} \\). For \\( r_1 \\leq \\frac{1}{e + 1} \\), the lower and upper bounds are decreasing functions with respect to \\( \\hat{p}_{\\theta}^{u} \\). This implies that as the model's capacity to generate unseen data increases, the differences in divergences decrease. Thus, approximating the distribution of seen data is not enough to learn the whole data distribution for small \\( r_1 \\). Rather, it is important for the model to learn the data manifold effectively to better approximate the data distribution including the unseen data." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.24, + 0.836, + 0.259 + ], + "angle": 0, + "content": "4. Generated Data for Private Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.266, + 0.892, + 0.465 + ], + "angle": 0, + "content": "We now investigate how the aforementioned diffusion synthesis can be utilized in the context of public data and analyze how it can be further leveraged to enhance performance. For experiments, we primarily focus on the CIFAR-10 dataset with a privacy budget of \\((2,10^{-5})\\), utilizing WRN-16-4² with 16 augmentation multiplicity and the techniques proposed in [12]. Within the training set, we randomly select 2K instances \\((4\\%)\\) for the public samples, as suggested in [43]. These samples are uniformly drawn from each class. All the measures for evaluating the generated data in this section are calculated with the entire training set (50K) as a reference. Additional experimental details are provided in Section 5.1 and Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.474, + 0.871, + 0.49 + ], + "angle": 0, + "content": "4.1. Better Diffusion Synthesis with Public Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.754 + ], + "angle": 0, + "content": "Theorem 3.1 demonstrates that well-approximating the distribution of seen public data \\( p_{s} \\) enables the synthetic data distribution \\( p_{\\theta} \\) mimic the entire data distribution \\( p_{\\mathrm{data}} \\), which is essential to obtain good decision boundary as in Figure 2. Thus, we initially replace the Denoising Diffusion Probabilistic Model (DDPM) [28], previously investigated by Nasr et al. [43] for public synthesis, with the Elucidating Diffusion Model (EDM) [30]. EDM is known to generate better images (e.g., lower FID scores) than DDPM by using a higher-order sampling process. Then, we train EDM on 2K public data samples without using external datasets and employ class-conditional sampling to match the original distribution. With the trained EDM, we calculate various measures in Table 3. The FID of EDM synthesis at 7.80 (correspondingly 7.89 on 40K) outperforms the reported FID of 12.8 of DDPM on 40K images [43], which also improves the classification performance as shown in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.894, + 0.877 + ], + "angle": 0, + "content": "However, the generation quality using public data is notably worse than the FID of 1.79 achieved with the entire set [30]. Within a limited public data, the model struggles to capture diversity, resulting in a recall of 0.16, even though precision remains high at 0.96. Note that repeating each public sample 25 times (thus 50K samples) results in a precision of 1.00, recall of 0.04, and FID of 13.64. The generated images and their memorization are illustrated in Ap" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.892, + 0.902 + ], + "angle": 0, + "content": "2 WRN-40-4 requires excessive GPU considering its performance [43]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12239" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 4. CAS \\((\\%)\\), test accuracy \\((\\%)\\), and their difference \\((\\%)\\) with different augmentation methods during warm-up phase." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.128, + 0.455, + 0.221 + ], + "angle": 0, + "content": "
AugmentationCAS(%)Test Acc (%)Diff (%)
No Aug (EDM)62.8275.1313.31
Common77.9983.975.98
Common + Cutout80.7284.884.16
Common + Cutmix65.7382.2016.47
AutoAugment77.2183.456.24
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.235, + 0.47, + 0.264 + ], + "angle": 0, + "content": "Table 5. Geometric measures of the models trained with SGD and SAM after warm-up phase." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.275, + 0.476, + 0.333 + ], + "angle": 0, + "content": "
OptSynthetic DataPrivate Data
λmaxλmax/λ5Tr(∇2ℓ(w))λmaxλmax/λ5Tr(∇2ℓ(w))
SGD1.3810.6271.98112.821.58-2527.78
SAM0.442.6353.2158.321.50333.03
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.359, + 0.469, + 0.39 + ], + "angle": 0, + "content": "pendix E. No privacy concern occurs in diffusion synthesis since the diffusion model is solely trained with public data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.401, + 0.411, + 0.416 + ], + "angle": 0, + "content": "4.2. Data Diversity Matters for Public Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.469, + 0.591 + ], + "angle": 0, + "content": "With limited private data, the model's capacity to generate unseen data is required in Theorem 3.1. The lack of diversity in the generated data can lead to misclassification due to distorted decision boundaries, as described in Figure 2. Given the challenge of DP-SGD in identifying a good basin [21], the key to successful warm-up lies in finding a well-generalizing minimum with a high CAS. As observed in [25, 51], data diversity can play an important role in improving CAS. We hypothesize that the importance of diversity is more pronounced in the warm-up phase of private learning, where the generated images exhibit low recall values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.794 + ], + "angle": 0, + "content": "Diversity for generation To validate our hypothesis, we first investigate enforcing data diversity in the generation process. Obtaining diversity in generations solely through a diffusion model is a challenging task. Thus, to enhance the data diversity during generation, we can use variants of diffusion models for guidance [27, 32] or editing [10, 40, 42]. Among them, discriminator guidance (DG) [32] introduces a discriminator to judge whether the sampling is from the true data or synthesis, controlling the trade-off between fidelity and diversity of the generated images by adjusting the weight \\( w_{d} \\) of the discriminator. Higher \\( w_{d} \\) yields diversity. Refer to Appendix C for the details of DG." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 3, a higher weight of guidance ensures greater data diversity without any augmentation, but sacristies the fidelity. The best FID score is obtained with \\( w_{d} = 3 \\) while the best CAS is obtained at a bigger weight \\( w_{d} = 20 \\). Interestingly, we need a larger weight value to achieve a similar gain of diversity than standard training (\\( w_{d} = 1.5 \\) for best FID [32]). Figure 3 represents selected" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "examples from two extreme cases, with \\( w_{d} = 0 \\) and \\( w_{d} = 30 \\) to visualize the difference. Despite the quality degradation of detailed features with \\( w_{d} = 30 \\), the CAS is higher due to the increased data diversity in features. Thus, we need to enhance diversity while maintaining quality for better classification. Similar to the EDM model trained with public data, no privacy concerns occur since the discriminator requires only original public and synthetic data from EDM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.232, + 0.892, + 0.474 + ], + "angle": 0, + "content": "Diversity with augmentation Nonetheless, training an additional discriminator for DG can pose a bottleneck in terms of time and computational efficiency. Thus, to explicitly enhance the diversity of EDM synthetic data during the warm-up training, we employ various data augmentation techniques designed for classification tasks. Wang et al. [61] argued that utilizing appropriate augmentation in diffusion-based generated images can further improve the classification performance. Common augmentation [24] uses padding and random crop to the original size and horizontal flipping for the images. Cutmix [68] randomly replaces a part of the image with another and Cutout [14] randomly pad images. AutoAugment [11] chooses the best combination of augmentations such as color, rotation, or cutout. We set a baseline with no augmentation for synthetic images of EDM and compare these augmentations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.641 + ], + "angle": 0, + "content": "The results are summarized in Table 4. Adding cutout augmentation to common augmentation demonstrates the best performance in terms of CAS and test accuracy. However, the two measures are not always aligned. Rather, the best performance gain with private data, noted as \\( Diff(\\%) = Test Acc - CAS \\), is obtained from Cutmix, which is known as one of the most diversified augmentations. This indicates that robust decision boundaries achieved through diversity facilitate easier private learning. Interestingly, the performance gain of augmentation surpasses the benefits of generation diversity, as illustrated in Appendix C." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.651, + 0.795, + 0.667 + ], + "angle": 0, + "content": "4.3. Optimization with Synthetic Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.84 + ], + "angle": 0, + "content": "As the clipping of DP-SGD significantly lowers the performance, it is known that a smaller gradient norm ensures high performance in private training [44, 46, 54]. In Figure 4a, we illustrate the gradient norms during private training with different training setups. The norm of synthetic data is calculated without clipping, whereas the private data used for DP-SGD is summed over individually clipped gradients, each with a clipping value of \\( C = 1 \\). The results indicate that utilizing a synthetic dataset reduces the gradient norm, even in a private dataset where constraining the gradient norm is crucial to mitigate the effect of clipping." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, even though training with diversified synthetic public data and augmentation, the models face the risk of being overfitted to public data. As public samples are selected from in-distribution data, the problem of the public" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12240" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.092, + 0.27, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.216, + 0.23, + 0.227 + ], + "angle": 0, + "content": "(a) Gradient norm." + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.094, + 0.457, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.216, + 0.45, + 0.228 + ], + "angle": 0, + "content": "(b) Accuracy \\((-)\\) and loss \\((-)\\)." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.24, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 4. Learning dynamics of private training with different datasets and optimization methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.468, + 0.401 + ], + "angle": 0, + "content": "private generalization gap is analogous to the training-test generalization gap in standard training. In Figure 4b, we illustrate the accuracy and loss for each public, synthetic, private, and test dataset during private training after the warm-up phase. The model consistently achieves near-zero loss and \\(100\\%\\) accuracy on synthetic data (as well as on public data) but struggles with private data (as well as on test data)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.468, + 0.612 + ], + "angle": 0, + "content": "To alleviate the generalization gap in standard training, various studies [16, 31, 33, 34, 37, 47] explored the geometric properties of the loss function in the weight space. The prominent optimization methods are designed to uncover flat minima, such as sharpness-aware minimization (SAM) [20] or stochastic weight averaging (SWA) [29]. Therefore, we apply SAM during the warm-up training and calculate geometric generalization measures, including metrics such as the top Hessian value \\(\\lambda_{max}\\), the ratio of Hessian \\(\\lambda_{max} / \\lambda_5\\), and the trace of the Hessian matrix \\(\\mathrm{Tr}(\\nabla^2\\ell (\\pmb {w}))\\) for both synthetic and private data. Table 5 indicates that utilizing SAM results in lower (better) metric values, not only for synthetic data but also for private data. Note that SGD even demonstrates a negative trace value on private data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.703 + ], + "angle": 0, + "content": "Moreover, in Figure 4a, as the flat minimum of SAM leads to a decreased gradient norm on synthetic data, it also maintains similar results concerning private data. These results indicate that relieving overfitting to synthetic data can help the generalization of private data. Thus, the aforementioned approaches find suitable initial point of DP-SGD." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.717, + 0.21, + 0.733 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.264, + 0.758 + ], + "angle": 0, + "content": "5.1. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We assess the effectiveness of our proposed methods using public data primarily in two datasets: CIFAR-10 and CIFAR-100. For the public dataset, we randomly sample \\(4\\%\\) of the training data (2K samples) uniformly drawn from each class, while the remaining data are used as private samples following [43]. We then train the EDM [30] models with the 2K public data samples and build 50K synthetic datasets with EDM sampling. To address the computational burden of training diffusion and sampling, we gen" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.107 + ], + "angle": 0, + "content": "erate datasets once and reuse them for classifiers as in [43]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.228 + ], + "angle": 0, + "content": "For classification models, we adopt WRN-16-4, following the techniques in [12] with 16 augmentations, and use pre-trained vision transformer models following [7]. Our experiments are conducted using PyTorch libraries [63] on eight NVIDIA GeForce RTX 3090 GPUs, partially on a cloud server with four NVIDIA A100 40GB GPUs. We report the mean and standard deviation for each experiment. For the detailed settings, refer to Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.237, + 0.875, + 0.252 + ], + "angle": 0, + "content": "5.2. Classification Performance with Public Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.26, + 0.892, + 0.441 + ], + "angle": 0, + "content": "Effects of individual techniques We first revisit Table 1, the ablation study of sequentially employing our approaches, with a privacy budget \\((2,10^{-5})\\)-DP on CIFAR-10. By only using better EDM synthesis without extra optimization techniques, we achieve the previous SOTA performance of \\(75.1\\%\\) [43]. Additionally, recognizing the significance of diversity in data generation, we employ cutout augmentation techniques for diversity in classification, resulting in a performance of \\(84.88\\%\\). To mitigate potential overfitting to public information, we make use of generalization techniques. All these efforts collectively lead to an accuracy of \\(85.48\\%\\) under \\((2,10^{-5})\\)-DP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.502 + ], + "angle": 0, + "content": "Despite achieving the best performance of \\(85.93\\%\\) when combined with DG, we exclude DG in this section due to its marginal performance enhancement \\((0.45\\%)\\) considering its extended training time, as detailed in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.672 + ], + "angle": 0, + "content": "CIFAR-10 with public data We report the performance comparison for our method with various previous approaches on a wide range of \\(\\varepsilon \\in \\{1,2,3,4,6\\}\\) with \\(\\delta = 10^{-5}\\) in Table 6. Our approach, which incorporates EDM synthesis, augmentation, and optimization for the public data, exhibits superior classification performance when compared to existing methods including DDPM-based augmentation and extended optimizations. The accuracies of \\(\\varepsilon = 0\\) (after warm-up, without private data) and \\(\\varepsilon = \\infty\\) (not private, with clipping) are \\(80.72\\%\\) and \\(88.52\\%\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "CIFAR-100 with public data We then explore the CIFAR-100 dataset for DP, which is not actively investigated without pre-trained models due to its complexity. We first train the EDM model with 2K images and generate 50K images, similar to CIFAR-10. Given the 100 classes in CIFAR-100, only 20 public samples are available per class, significantly fewer than in CIFAR-10. The FID on 50K images with EDM synthesis is 11.28, which reduces the original FID of 15.58 for replicating each public image 25 times. After the warm-up, the accuracy of synthetic images on \\(\\varepsilon = 0\\) is \\(38.04\\%\\) (46.74% on \\(\\varepsilon = \\infty\\)), while the test accuracy of using 2K public samples without synthesis on \\(\\varepsilon = 0\\) is only \\(16.79\\%\\). In Table 7, we report the accuracies by sequentially adopting the aforementioned tech" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12241" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 6. Test accuracy \\((\\%)\\) of private training on CIFAR-10 with privacy budgets of \\(\\varepsilon \\in \\{1,2,3,4,6\\}\\). The public and synthesis columns denote the Warm and WarmSyn setups, respectively. Ours employs all the techniques in Table 1, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.143, + 0.887, + 0.31 + ], + "angle": 0, + "content": "
DatasetsArchitecturePublicSynthesisMethodε = 1ε = 2ε = 3ε = 4ε = 6
CIFAR -10CNN-Tanh (0.55M)XX[44]45.858.363.5--
ScatterNet (0.16M)XX[59]60.367.269.3--
DPNAS [9] (0.53M)XX[46]60.13±0.3467.23±0.1269.86±0.49--
WRN-16-4 (2.74M)XX[12]56.8±0.664.9±0.569.2±0.371.9±0.377.0±0.8
WRN-40-4 (8.94M)XX[12]56.4±0.665.9±0.570.7±0.273.5±0.678.8±0.4
✓X[2]†-68.7-73.177.2
✓X[38]†-68.7-73.577.9
WRN-16-4 (2.74M)✓✓[2]†-70.5-74.578.2
✓✓[38]†-69.1-74.178.1
✓✓[43]†-75.1-77.980.0
✓✓Ours84.30±0.1185.48±0.1286.03±0.0986.49±0.1387.06±0.24
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.094, + 0.31, + 0.678, + 0.323 + ], + "angle": 0, + "content": "We note the results reported in [43] to set the architecture same. All other baseline results are adopted from the original paper." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.337, + 0.895, + 0.381 + ], + "angle": 0, + "content": "Table 7. Test accuracy \\((\\%)\\) of private classification on CIFAR-100 on the privacy budget of \\(\\varepsilon \\in \\{1,2,6,10\\}\\). The public and synthesis columns indicate Warm and WarmSyn settings, respectively. We employ the techniques in Table 1 sequentially, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.39, + 0.889, + 0.513 + ], + "angle": 0, + "content": "
DatasetsArchitecturePublicSynthesisMethodsε = 1ε = 2ε = 6ε = 10
CIFAR -100Resnet-9XX[35]†18.124.9-40.8
Resnet-9 (6.62M)XXCold†8.3514.4229.8935.11
WRN-16-4 (2.74M)XXCold9.2818.1933.6139.09
✓XWarm20.8425.1533.4738.89
WRN-16-4 (2.74M)✓✓WarmSyn26.13±0.2031.53±0.0435.53±0.1140.82±0.10
✓✓+Augmentation40.96±0.3044.52±0.0150.47±0.0454.29±0.05
✓✓+Optimization45.93±0.0648.61±0.5954.36±0.5256.56±0.11
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.091, + 0.513, + 0.707, + 0.526 + ], + "angle": 0, + "content": "\\(\\dagger\\) Unfortunately, their DP-SGD results are not reproducible, even when using the same hyperparameters as in the original paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.471, + 0.573 + ], + "angle": 0, + "content": "niques, where each of the approaches matters. As a result, we obtain \\(48.61\\%\\) on \\(\\varepsilon = 2\\) without pre-trained models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.473, + 0.745 + ], + "angle": 0, + "content": "CIFAR-100 with pre-trained on ImageNet To push further, we demonstrate the effectiveness of our procedures when combined with pre-trained models with ID public data. We adopt the vision transformers following [7] pretrained on ImageNet [13]. Upon the pre-trained models, we sequentially perform the warm-up training with ID public data and private learning. The results in Table 8 indicate that the synthesis can boost classification performance. Within a wide range of models and privacy budgets, our methods outperform the warm settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Distribution shift (CIFAR-100 \\(\\rightarrow\\) CIFAR-10) The distribution shifts from similar but not ID public data [59] can be combined with our methods. We consider \\(4\\%\\) of CIFAR-100 data as public to enhance the performance of CIFAR-10 as a substitute for CIFAR-10 ID public data. In Table 9, we present the classification results for both the warm and our settings, where both models are trained on the public data and synthetic data from \\(4\\%\\) of CIFAR-100, respectively. The experimental results show that the differences in accu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.895, + 0.619 + ], + "angle": 0, + "content": "racies exceed \\(20\\%\\), even though neither model has observed CIFAR-10 datasets before private training with DP-SGD. This indicates that amplifying public information is meaningful in distribution shifts. Additional sensitivity analysis and ablation studies can be found in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Pre-trained diffusion models Our main idea to use synthesis for public data is flexible in practical scenarios and diverse datasets. To mitigate the drawbacks of training diffusion on each dataset, we investigated using the pre-trained diffusion models, which are trained on OOD public data. Specifically, we make use of pre-trained Stable Diffusion (SD) [52] and Boomerang sampling [40]. We fed \\(4\\%\\) of public data to Boomerang editing with SD backbone for generation diversity and generated 20 images per sample for classifier training. The similar experiments are shown in Appendix D. We maintain the other training procedures the same as 'Ours', which we call 'Ours-SD'. Table 10 indicates that our framework is straightforward and effective for real-world data, and generalizable without depending on specific diffusion models. We conclude that data diversity can enhance performance when the model is not trained on specific ID public data." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12242" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 8. Test accuracy (%) of private classification on CIFAR-100 using pre-trained models on the privacy budget of \\(\\varepsilon \\in \\{0.5,2\\}\\). The **bold** indicates results within the standard deviation of the top mean score." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.129, + 0.89, + 0.228 + ], + "angle": 0, + "content": "
DatasetsPrivacy budgetε = 0.5ε = 2
ArchitectureColdWarmOursColdWarmOurs
CIFAR -100CrossViT small 240 (26.3M)60.50±1.7073.17±0.2477.43±0.1371.36±0.5277.00±0.2780.25±0.57
CrossViT 18 240 (42.6M)67.03±0.4677.19±0.4479.96±0.1074.28±0.2280.30±0.0282.85±0.08
DeiT base patch16 224 (85.8M)49.34±1.4979.56±0.7479.28±0.7669.09±0.1082.98±0.0483.06±0.01
CrossViT base 240 (103.9M)66.24±0.4775.59±0.2178.06±0.0575.15±0.0379.25±0.0581.14±0.15
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.25, + 0.47, + 0.278 + ], + "angle": 0, + "content": "Table 9. Comparison of distribution shift performance on CIFAR-10 with the warm and our models trained on \\(4\\%\\) of CIFAR-100." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.29, + 0.462, + 0.36 + ], + "angle": 0, + "content": "
CIFAR-100 → CIFAR-10Test Acc (%)
ε = 2ε = 4ε = 6
Warm50.65±0.3756.54±0.2059.49±1.39
Ours73.46±0.2878.60±0.1380.12±0.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.088, + 0.374, + 0.408, + 0.387 + ], + "angle": 0, + "content": "Table 10. Classification results on real-world datasets." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.399, + 0.415, + 0.525 + ], + "angle": 0, + "content": "
DataMethodε = 2ε = 4ε = 6
EuroSATWarm (w/ Aug, Opt)83.6785.5286.07
WarmExt [43]84.3785.7886.07
(Land use)Ours-SD90.3791.7492.52
PathMNISTWarm (w/ Aug, Opt)89.2389.3989.54
WarmExt [43]89.0489.2589.28
(Biomedical)Ours-SD91.6491.9492.10
FairFaceWarm (w/ Aug, Opt)53.0054.5554.83
WarmExt [43]53.3354.7454.84
(w.r.t. Race)Ours-SD54.9056.1956.37
" + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.411, + 0.469, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.448, + 0.469, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.487, + 0.469, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.351, + 0.56 + ], + "angle": 0, + "content": "5.3. Revisit Extended Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.734 + ], + "angle": 0, + "content": "On top of our method, we reevaluate the effectiveness of existing extended methods (thus WarmSE) in Table 11, particularly mirror GD [2] and DOPE-SGD [43]. These methods are trained after our synthesis, augmentation, and warm-up optimization on \\(\\varepsilon \\in \\{2, 4, 6\\}\\). Remarkably, the performance of the extended methods falls within the standard deviation range of DP-SGD. This implies that, as the models have already extracted substantial side information from public data before private training, extended optimization does not further improve DP optimization. Note that the computational time of the public batch is marginal to DP-SGD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.901 + ], + "angle": 0, + "content": "However, extended methods sometimes exhibit poorer training stability than DP-SGD. Due to their reliance on public gradients, these methods are sensitive to the hyperparameter settings and easily encounter exploding gradients. In Figure 5, under the same setting as Figure 4a, we observe a gradual decrease in the private gradient norm, while the public gradient norm consistently increases. When the public norm increases to a certain level, the norm of both public and private data with extended methods may diverge after updating toward public gradients. For further insights about the learning dynamics in terms of the loss function" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Table 11. Performance and computational time of different extended optimization methods." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.29, + 0.9, + 0.389 + ], + "angle": 0, + "content": "
Privacy budget ε (δ = 10-5)Optimization
DP-SGDMirror GD [2]DOPE-SGD [43]
MedianMinMedianMin
ε = 285.48±0.1785.5210.0085.5310.00
ε = 486.49±0.1386.3110.0086.6910.00
ε = 687.06±0.2486.7310.0086.8410.00
Time (ms/image)12.7012.8012.86
" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.403, + 0.692, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.403, + 0.882, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.528, + 0.894, + 0.571 + ], + "angle": 0, + "content": "Figure 5. The norm of gradients with (Left) synthetic dataset and (Right) private dataset with clipping during private training with different optimization methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.597, + 0.892, + 0.644 + ], + "angle": 0, + "content": "and private gradient norm without clipping, please refer to Appendix C. However, we believe that undiscovered extended methods can be beneficial for the WarmSyn settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.656, + 0.62, + 0.672 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.894, + 0.818 + ], + "angle": 0, + "content": "In this paper, we investigate the potential of diffusion models for in-distribution public data to enhance private classification performance. We demonstrate the importance of synthetic data diversity, augmentation techniques, and the importance of well-generalizing minima for private optimization. As a limitation, we leave the experiments on more extensive and sensitive datasets and the efficient implementation of our method. We hope that this work helps leverage diffusion models to address utility-privacy trade-offs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.836, + 0.894, + 0.898 + ], + "angle": 0, + "content": "Acknowledgements This work was supported by NRF (No. 2022R1A5A6000840, No. RS-2023-00272502) and IITP (No. 2022-0-00984, No. 2021-0-01343-004) grants funded by the Korea government (MSIT)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12243" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. Deep learning with differential privacy. 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In Proceedings of the IEEE/CVF international conference on computer vision, pages 6023-6032, 2019. 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.897 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12246" + } + ] +] \ No newline at end of file diff --git a/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/35a6ec9e-03c5-459f-83ad-bafb99a44b46_origin.pdf b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/35a6ec9e-03c5-459f-83ad-bafb99a44b46_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..37e8d7dda37cbdd7b5b41cd2fd8d75daeeef9a18 --- /dev/null +++ b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/35a6ec9e-03c5-459f-83ad-bafb99a44b46_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:674baf3552c2cb168436857bd1e16be65f979469a50cfb65b0fd2724da5edf16 +size 773993 diff --git a/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/full.md b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ab14b56f2243ce7e233b06c3408c9d5860ae9c58 --- /dev/null +++ b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/full.md @@ -0,0 +1,346 @@ +# In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification + +Jinseong Park $^{1\dagger}$ Yujin Choi $^{1\dagger}$ Jaewook Lee $^{1*}$ Seoul National University + +{jinseong,uznhigh,jaewook} @snu.ac.kr + +# Abstract + +To alleviate the utility degradation of deep learning image classification with differential privacy (DP), employing extra public data or pre-trained models has been widely explored. Recently, the use of in-distribution public data has been investigated, where tiny subsets of datasets are released publicly. In this paper, we investigate a framework that leverages recent diffusion models to amplify the information of public data. Subsequently, we identify data diversity and generalization gap between public and private data as critical factors addressing the limited public data. While assuming $4\%$ of training data as public, our method achieves $85.48\%$ on CIFAR-10 with a privacy budget of $\varepsilon = 2$ , without employing extra public data for training. + +# 1. Introduction + +Differential privacy (DP) [18, 19] establishes a mathematical framework to ensure the privacy of training data. In deep learning, differentially private SGD (DP-SGD) [1] has become the de facto standard method to guarantee the models' privacy. However, differentially private training inevitably degrades performance compared to standard (non-DP) training [6, 45]. As a practical solution, leveraging public pre-trained models or public data has been explored to enhance utility [12, 39, 59, 65-67]. As using public data raises no privacy concerns, fine-tuning pre-trained models on private data can make use of learned features for free. Nevertheless, their effectiveness might be diminished when addressing out-of-distribution (OOD) public data of small shared characteristics with private data [59]. + +As an alternative, researchers have investigated the use of in-distribution (ID) public data, indicating that a small portion of in-distribution data is made public [38]. For example, some data owners decide to share their data publicly in exchange for economic incentives or public interest. This setup allows us to leverage public data with a distribution + +![](images/8f929fc117142acfc5dc25f0cfc35063d22fe0f1db22930d061e9a02b39128b7.jpg) +Figure 1. Illustration of (Top) existing optimization-based methods and (Bottom) proposed training procedure for amplifying in-distribution public data and utilizing the synthetic data. + +similar to private data. In contrast to previous approaches, such as utilizing extra OOD data or distribution shift, we need to assume a limited amount of ID public data since the public data might contain more sensitive information. However, the repeated use of limited-sized public data can raise critical issues related to memorization and overfitting [43]. To mitigate the aforementioned problems, previous studies mainly have focused on utilizing side information from the little public data to enhance the optimization of differentially private deep learning [2, 4, 38, 43]. + +Recently, Ganesh et al. [21] pointed out that warm-up training with public data plays a crucial in private optimization to find a good basin with a small loss, whereas DP-SGD from a random initial point faces a high loss and poor optimization. From this viewpoint, we suggest that enlarging the public dataset could improve the performance of private learning. By using the recent diffusion models [28, 30], we aim to enrich the contextual information of public data. We further identify that data diversity and generalization gap between public and private data act as critical factors, particularly addressing the limited size of public data. + +The proposed framework is illustrated in Figure 1. We summarize our approaches and their performance gains in + +Table 1. Ablation study on the impact of various techniques, including synthesis, augmentation, and optimization, to enhance classification performance using in-distribution public data from CIFAR-10 under $(2,10^{-5})$ -DP. Refer to Section 3.1 for the details of setups and the relevant sections for the details of each method. + +
SetupTraining SettingsTest Acc
Baselines including previous SOTA methods (Sec. 3.1)
ColdCold Baseline (WRN16-4) [12]64.02%
WarmWarm-up on public data68.09%
WarmSynWarm-up on DDPM synthesis [43]72.0%
WarmSEWarmSyn (DDPM) + DOPE-SGD [43]75.1%
In-distributionpublic data synthesis (Sec. 4.1) & Diversity (Sec. 4.2)
WarmSynWarm-up on EDM synthesis75.13 %
WarmSynEDM synthesis + generation diversity77.66 %
WarmSynEDM synthesis + augmentation diversity84.88%
Generalization for public-private datasets (Sec. 4.3)
WarmSynWell-generalizing minimum during warm-up85.48%
+ +Table 1, assuming $4\%$ of public data with a privacy budget of $\varepsilon = 2$ and $\delta = 10^{-5}$ . The results outperform the existing state-of-the-art (SOTA) methods, i.e., boosting the accuracy from the previous $75.1\%$ [43] to $85.48\%$ on CIFAR-10. We emphasize that our approaches for dissecting warm-up training for DP are distinguishable from transfer tasks in non-DP setups, addressing data scarcity and improving underperforming DP-SGD optimization. Table 2 shows the gain and privacy cost of methods with public data usage compared to the training without public data, as in [21]. The results show higher gain and privacy costs with stronger privacy (lower $\varepsilon$ ), whereas ours shows the highest gain and smallest costs. Notably, we observe tiny improvements in non-private settings, highlighting the distinctiveness of DP scenarios and the unique strengths of our tailored approach. + +Table 2. Gain (↑) in performance and the corresponding cost of privacy (↓, in parentheses) for each method compared to not exploiting public data. Refer to Section 3.1 for the details of the setups. + +
MethodsNon-priv.ε = 6ε = 2
Warm [43]0.05% (-)0.10% (18.80%)3.20% (27.80%)
WarmSE [43]0.13% (-)3.00% (15.98%)5.60% (25.48%)
Ours0.13% (-)10.06% (8.92%)20.58% (10.50%)
+ +# 2. Background and Related Work + +# 2.1. Differentially Private Deep Learning + +Differential privacy (DP) [19] can guarantee the privacy of training data as follows: + +Definition 2.1 (Differential privacy) For two adjacent inputs $d, d' \in \mathcal{D}$ , a randomized mechanism $\mathcal{M}: \mathcal{D} \to \mathcal{R}$ satisfies $(\varepsilon, \delta)$ -differential privacy for any set of possible outputs $S \subseteq \mathcal{R}$ if + +$$ +P r \left[ \mathcal {M} (d) \in \mathcal {S} \right] \leq e ^ {\varepsilon} P r \left[ \mathcal {M} \left(d ^ {\prime}\right) \in \mathcal {S} \right] + \delta . \tag {1} +$$ + +The privacy budget $\varepsilon \geq 0$ controls the level of privacy guarantee with the broken probability $\delta \geq 0$ . In deep learning, differentially private SGD (DP-SGD) [1] is widely used with the following steps: (i) average the clipped per-sample gradient $\nabla \ell_{i}(\boldsymbol{w}) \coloneqq \nabla \ell(\boldsymbol{w}; \boldsymbol{x}_{i})$ for weight $\boldsymbol{w}$ with respect to each individual private data sample $\boldsymbol{x}_{i} \in \boldsymbol{X}_{t}^{pr}$ and (ii) add Gaussian noise to the averaged gradient as follows: + +$$ +\boldsymbol {g} _ {t} ^ {p r} = \frac {1}{| \boldsymbol {X} _ {t} ^ {p r} |} \sum_ {\boldsymbol {x} _ {i} \in \boldsymbol {X} _ {t} ^ {p r}} \operatorname {c l i p} \left(\nabla \ell_ {i} (\boldsymbol {w} _ {t}), C\right), \tag {2} +$$ + +$$ +\tilde {\boldsymbol {g}} _ {t} ^ {p r} = \boldsymbol {g} _ {t} ^ {p r} + \mathcal {N} (\mathbf {0}, C ^ {2} \sigma^ {2} \mathbf {I}). +$$ + +The weight is updated as $\boldsymbol{w}_{t + 1} = \boldsymbol{w}_t - \eta \tilde{\boldsymbol{g}}_t^{pr}$ with a learning rate $\eta$ and $\operatorname {clip}(\boldsymbol {u},C)$ projects $\pmb{u}$ to the $L_{2}$ -ball of radius $C$ . The noise level $\sigma$ is determined by the privacy budget $(\varepsilon ,\delta)$ , the number of training steps, and the sampling probability (refer to Appendix C for details). + +To guarantee privacy with clipping and noise addition, DP-SGD inevitably degrades the performance during optimization. Therefore, various studies explored DP-friendly properties, including architecture [9, 59], loss and activation functions [44, 54], or smoothness [46, 55, 60]. Notably, De et al. [12] introduced a new era in utilizing large models for DP-SGD tasks by introducing the averaged loss of various augmentations called augmentation multiplicity, weight standardization [49], and optimization tricks. Note that adaptive clipping [3, 8] could improve our results. + +# 2.2. Private Learning with Public Information + +The benefits of massive OOD public data have been explored in the context of the pre-trained models in vision [7, 12] and language [39, 65-67] models. Additionally, the transfer learning with similar distribution, such as CIFAR-100 for CIFAR-10, was under investigated [58, 59]. + +ID public data $\mathbf{X}^{pub}$ requires different approaches from the massive OOD public data due to its limited size and similar distributional properties. Hence, prior studies [2, 4, 38, 43], categorized as extended methods in Section 3.1, have focused on mitigating errors in the optimization of DP-SGD by utilizing the gradients of public data as a proxy for true gradients. These methods update the weight with $\boldsymbol{w}_{t+1} = \boldsymbol{w}_t - \eta f_g$ , for $f_g(\boldsymbol{w}_t; \boldsymbol{X}_t^{pub}, \boldsymbol{X}_t^{pr})$ such as normalizing the private gradient with the public gradient norm [38], employing a linear combination of private and public gradients [2], or estimating low-rank approximation with public data (even unlabelled) to reduce noise levels [48, 65]. + +Nasr et al. [43] firstly introduced training a generative model as an augmentation technique. However, their primary focus is the optimization called DOPE-SGD, which updates towards the public gradient $\pmb{g}_t^{pub}$ (without clipping and noise addition) and makes $\pmb{g}_t^{pub} - \pmb{g}_t^{pr}$ private as follows: + +$$ +\boldsymbol {w} _ {t + 1} = \boldsymbol {w} _ {t} - \eta \left(\boldsymbol {g} _ {t} ^ {\text {p u b}} + \operatorname {c l i p} \left(\boldsymbol {g} _ {t} ^ {\text {p u b}} - \boldsymbol {g} _ {t} ^ {\text {p r}}, C\right) + \mathcal {N}\right), \tag {3} +$$ + +with the same noise level $\mathcal{N}$ in Equation (2). To the best of our knowledge, none of the prior studies deeply investigated the ID public data as a perspective of the data synthesis. + +# 2.3. Diffusion Synthesis + +The integration of generative models in classification tasks has been widely explored to enhance generalization performance without extra data samples [5, 22, 25]. In recent years, diffusion models [28, 56, 57] have shown promising results in image generation. Notably, Xiao et al. [62] argued that diffusion models can generate high-quality and diverse images. Subsequently, various studies have focused on enhancing the quality of generation [30, 32], conditioning sampling [15, 27], and text-to-image generation [50, 52]. + +Due to the significance of privacy concerns during image synthesis, differentially private diffusion synthesis is one of the actively investigated research topics [17, 41]. Given the effectiveness of private fine-tuning upon pre-trained diffusion models for generation and classification tasks [23], utilizing privacy-preserving diffusion models presents opportunities for our future works. + +Measures To measure the quality of generated images, various measures are proposed: Inception Score (IS) [53] and Precision [36] to measure fidelity, Recall [36] to measure diversity, and Fréchet Inception Distance (FID) [26] to measure the distributional quality for mean and variance. + +To assess the impact of synthetic data on classification tasks, Ravuri and Vinyals [51] proposed the Classification Accuracy Score (CAS), which evaluates the classification performance on a test set using a model trained on synthetic data. Thus, we use CAS to validate the performance of synthetic public data on test data. However, since our main focus is on improving classification performance including private learning, all of the previous measures cannot be perfectly aligned with our goals. + +# 3. Framework + +# 3.1. Training Procedure + +Our objective is to investigate the potential of diffusion models with ID public data, departing from conventional approaches that focus on guiding optimization with the public data [2, 4, 38, 43, 48, 64]. Our work aligns closely with [43], but we specifically concentrate on synthesizing data from the public and examining the important properties of private learning. We summarize the training scenarios using ID public data as follows [43]: + +- Cold: Conduct DP training (e.g., DP-SGD) on the private dataset without using public data. +- Warm: Train models through (i) non-DP warm-up training phase on the public dataset (e.g., SGD) and (ii) private training phase on the private dataset with DP methods. + +![](images/36445e508d74e76e65116fa26d959687486a9dc290e4082ba6dfe89ba0d8bf0a.jpg) +Figure 2. Toy experiment on diffusion synthesis and its effect on decision boundaries while varying the training sample size. + +- WarmExt: During the private training (after warm-up training), leverage the public side information, such as gradients [2, 4, 38, 43], or low-rank approximation [48, 64], as extended methods of DP optimization. +- WarmSyn (Ours, [43]): Amplify the sparse information of public data using generative models or augmentation methods. Optionally, WarmSE indicates employing extended optimization with synthetic public data. + +In terms of privacy, since utilizing public data does not pose any privacy concerns to the private data, we can leverage the public data multiple times, e.g., training warm-up classification models, diffusion models, or guiding private training. From now on, we denote in-distribution (ID) public data as public data unless otherwise specified. + +# 3.2. Public Data Synthesis with Diffusion Models + +For amplifying the sparse information in the WarmSyn setting, we first investigate amplifying the number of data samples using diffusion models. Recent studies [5, 22, 25, 61] have demonstrated the performance gain in complicated classification problems by training diffusion models to expand the size of training data samples within the data manifold, e.g., amplifying 50K CIFAR-10 training data into a 50M synthetic dataset improves adversarial training [61]. + +To analyze public data synthesis with limited data samples, we conduct an experiment using a spiral dataset as a toy example (detailed in Appendix C), as shown in Figure 2. We consider two settings: (a) with a sufficient and (b) with an insufficient number of original data samples. For each setting, we train a simple diffusion model to generate new data samples. Then, we train two-layer classifiers until convergence using the original and synthetic data, respectively. + +With a large number of samples in (a), both diffusion and classification models demonstrate well-trained results. However, when the original data size is limited as in (b-1), the classification model tends to overfit individual data. Thus, despite correctly classifying almost all data samples, the model fails to discover the proper decision boundary. In contrast, in (b-2) where the diffusion model effectively approximates the data manifold, the classifier achieves a superior decision boundary compared to (b-1). Nevertheless, we should be aware that diffusion models can be apt to over + +Table 3. Quality comparison of synthetic data trained with $4\%$ of public data on CIFAR-10. + +
SamplingFidelityDiversityQualityCAS (↑) (%)Test Acc (%)
IS (↑)Precision (↑)Recall (↑)FID (↓)
EDM (wd=0)11.0080.9640.1577.79962.8275.13
EDM + DG (wd=3)10.8150.9640.1537.78662.4775.31
EDM + DG (wd=10)10.7960.9460.1708.27464.6175.98
EDM + DG (wd=20)10.1570.8730.19111.49767.6177.66
EDM + DG (wd=30)9.1130.7850.21119.74866.5377.22
+ +![](images/32968c2f8d721d30e7d3049c2516e72dd65b0b5e59be0ce80825dd2e1a27da15.jpg) +Figure 3. Selected synthetic data samples from (Top) EDM and (Bottom) EDM + DG $(w_{d} = 30)$ synthesis. + +and underestimate the data distribution, as shown in (b-2). + +To push further, we mathematically analyze how the rate of data samples affects synthesis. The ability of a generative model $\theta$ to approximate the 'entire' data can be determined by the ratio of 'seen' (observed during training) and the 'unseen' (not observed during training). Specifically, with a limited number of seen data, the model is required to estimate the unseen data to approximate the entire data. + +Theorem 3.1 For a finite number of 'entire' data samples $S_{data} = \{\pmb{x}_1, \dots, \pmb{x}_N\}$ , split the data samples into 'seen' data $S_s = \{\pmb{x}_1, \dots, \pmb{x}_n\}$ , and 'unseen' data $S_u = \{\pmb{x}_{n+1}, \dots, \pmb{x}_N\}$ , without loss of generality. Let $p_{data}, p_s$ and $p_u$ be the probability distribution of each corresponding dataset. For any generative model $\theta$ trained on 'seen' data, $p_\theta$ represents the data distribution generated by $\theta$ . Then, + +$$ +\begin{array}{l} \log \frac {1}{r _ {1}} + \hat {p} _ {\theta} ^ {u} \log \frac {\hat {p} _ {\theta} ^ {u}}{r _ {2}} \leq \tilde {D} _ {K L} (p _ {\theta} \| p _ {d a t a}) - \tilde {D} _ {K L} (p _ {\theta} \| p _ {s}) \\ \leq \log \frac {1}{r _ {1}} + \hat {p} _ {\theta} ^ {u} \log \frac {1}{r _ {2}}, \\ \end{array} +$$ + +where $\hat{p}_{\theta}^{u} = \sum_{\boldsymbol{x}\in S_{u}}p_{\theta}(\boldsymbol{x})\leq 1$ indicates the capacity of the model $\theta$ to generate 'unseen' data. For discrete probability distributions $p$ and $q$ , $\tilde{D}_{KL}(p\| q)$ indicates the relaxed Kullback-Leibler (KL) divergence, excluding the case when $q = 0$ . $r_1 = \frac{n}{N}$ and $r_2 = \frac{N - n}{n}$ denote the ratios of 'seen' to 'entire', and 'unseen' to 'seen' data, respectively. + +The detailed proof is presented in Appendix A. The above theorem indicates that the ratios $r_1$ and $r_2$ affect how the model $\theta$ can approximate the $p_{data}$ . As $r_1 \rightarrow 1$ with sufficient seen data, then $r_2 \rightarrow 0$ and $S_u \rightarrow \emptyset$ , so that $\hat{p}_{\theta}^{u} \rightarrow 0$ and the upper and lower bounds converge to zero. Thus, ensuring $p_{\theta}$ is close to $p_s$ ensures proximity of $p_{\theta}$ to $p_{data}$ . + +However, when considering a small $r_1$ , which is equivalent to a limited number of public data setups, the bounds depend on $\hat{p}_{\theta}^{u}$ . For $r_1 \leq \frac{1}{e + 1}$ , the lower and upper bounds are decreasing functions with respect to $\hat{p}_{\theta}^{u}$ . This implies that as the model's capacity to generate unseen data increases, the differences in divergences decrease. Thus, approximating the distribution of seen data is not enough to learn the whole data distribution for small $r_1$ . Rather, it is important for the model to learn the data manifold effectively to better approximate the data distribution including the unseen data. + +# 4. Generated Data for Private Learning + +We now investigate how the aforementioned diffusion synthesis can be utilized in the context of public data and analyze how it can be further leveraged to enhance performance. For experiments, we primarily focus on the CIFAR-10 dataset with a privacy budget of $(2,10^{-5})$ , utilizing WRN-16-4² with 16 augmentation multiplicity and the techniques proposed in [12]. Within the training set, we randomly select 2K instances $(4\%)$ for the public samples, as suggested in [43]. These samples are uniformly drawn from each class. All the measures for evaluating the generated data in this section are calculated with the entire training set (50K) as a reference. Additional experimental details are provided in Section 5.1 and Appendix B. + +# 4.1. Better Diffusion Synthesis with Public Data + +Theorem 3.1 demonstrates that well-approximating the distribution of seen public data $p_{s}$ enables the synthetic data distribution $p_{\theta}$ mimic the entire data distribution $p_{\mathrm{data}}$ , which is essential to obtain good decision boundary as in Figure 2. Thus, we initially replace the Denoising Diffusion Probabilistic Model (DDPM) [28], previously investigated by Nasr et al. [43] for public synthesis, with the Elucidating Diffusion Model (EDM) [30]. EDM is known to generate better images (e.g., lower FID scores) than DDPM by using a higher-order sampling process. Then, we train EDM on 2K public data samples without using external datasets and employ class-conditional sampling to match the original distribution. With the trained EDM, we calculate various measures in Table 3. The FID of EDM synthesis at 7.80 (correspondingly 7.89 on 40K) outperforms the reported FID of 12.8 of DDPM on 40K images [43], which also improves the classification performance as shown in Table 1. + +However, the generation quality using public data is notably worse than the FID of 1.79 achieved with the entire set [30]. Within a limited public data, the model struggles to capture diversity, resulting in a recall of 0.16, even though precision remains high at 0.96. Note that repeating each public sample 25 times (thus 50K samples) results in a precision of 1.00, recall of 0.04, and FID of 13.64. The generated images and their memorization are illustrated in Ap + +Table 4. CAS $(\%)$ , test accuracy $(\%)$ , and their difference $(\%)$ with different augmentation methods during warm-up phase. + +
AugmentationCAS(%)Test Acc (%)Diff (%)
No Aug (EDM)62.8275.1313.31
Common77.9983.975.98
Common + Cutout80.7284.884.16
Common + Cutmix65.7382.2016.47
AutoAugment77.2183.456.24
+ +Table 5. Geometric measures of the models trained with SGD and SAM after warm-up phase. + +
OptSynthetic DataPrivate Data
λmaxλmax/λ5Tr(∇2ℓ(w))λmaxλmax/λ5Tr(∇2ℓ(w))
SGD1.3810.6271.98112.821.58-2527.78
SAM0.442.6353.2158.321.50333.03
+ +pendix E. No privacy concern occurs in diffusion synthesis since the diffusion model is solely trained with public data. + +# 4.2. Data Diversity Matters for Public Data + +With limited private data, the model's capacity to generate unseen data is required in Theorem 3.1. The lack of diversity in the generated data can lead to misclassification due to distorted decision boundaries, as described in Figure 2. Given the challenge of DP-SGD in identifying a good basin [21], the key to successful warm-up lies in finding a well-generalizing minimum with a high CAS. As observed in [25, 51], data diversity can play an important role in improving CAS. We hypothesize that the importance of diversity is more pronounced in the warm-up phase of private learning, where the generated images exhibit low recall values. + +Diversity for generation To validate our hypothesis, we first investigate enforcing data diversity in the generation process. Obtaining diversity in generations solely through a diffusion model is a challenging task. Thus, to enhance the data diversity during generation, we can use variants of diffusion models for guidance [27, 32] or editing [10, 40, 42]. Among them, discriminator guidance (DG) [32] introduces a discriminator to judge whether the sampling is from the true data or synthesis, controlling the trade-off between fidelity and diversity of the generated images by adjusting the weight $w_{d}$ of the discriminator. Higher $w_{d}$ yields diversity. Refer to Appendix C for the details of DG. + +As shown in Table 3, a higher weight of guidance ensures greater data diversity without any augmentation, but sacristies the fidelity. The best FID score is obtained with $w_{d} = 3$ while the best CAS is obtained at a bigger weight $w_{d} = 20$ . Interestingly, we need a larger weight value to achieve a similar gain of diversity than standard training ( $w_{d} = 1.5$ for best FID [32]). Figure 3 represents selected + +examples from two extreme cases, with $w_{d} = 0$ and $w_{d} = 30$ to visualize the difference. Despite the quality degradation of detailed features with $w_{d} = 30$ , the CAS is higher due to the increased data diversity in features. Thus, we need to enhance diversity while maintaining quality for better classification. Similar to the EDM model trained with public data, no privacy concerns occur since the discriminator requires only original public and synthetic data from EDM. + +Diversity with augmentation Nonetheless, training an additional discriminator for DG can pose a bottleneck in terms of time and computational efficiency. Thus, to explicitly enhance the diversity of EDM synthetic data during the warm-up training, we employ various data augmentation techniques designed for classification tasks. Wang et al. [61] argued that utilizing appropriate augmentation in diffusion-based generated images can further improve the classification performance. Common augmentation [24] uses padding and random crop to the original size and horizontal flipping for the images. Cutmix [68] randomly replaces a part of the image with another and Cutout [14] randomly pad images. AutoAugment [11] chooses the best combination of augmentations such as color, rotation, or cutout. We set a baseline with no augmentation for synthetic images of EDM and compare these augmentations. + +The results are summarized in Table 4. Adding cutout augmentation to common augmentation demonstrates the best performance in terms of CAS and test accuracy. However, the two measures are not always aligned. Rather, the best performance gain with private data, noted as $Diff(\%) = Test Acc - CAS$ , is obtained from Cutmix, which is known as one of the most diversified augmentations. This indicates that robust decision boundaries achieved through diversity facilitate easier private learning. Interestingly, the performance gain of augmentation surpasses the benefits of generation diversity, as illustrated in Appendix C. + +# 4.3. Optimization with Synthetic Data + +As the clipping of DP-SGD significantly lowers the performance, it is known that a smaller gradient norm ensures high performance in private training [44, 46, 54]. In Figure 4a, we illustrate the gradient norms during private training with different training setups. The norm of synthetic data is calculated without clipping, whereas the private data used for DP-SGD is summed over individually clipped gradients, each with a clipping value of $C = 1$ . The results indicate that utilizing a synthetic dataset reduces the gradient norm, even in a private dataset where constraining the gradient norm is crucial to mitigate the effect of clipping. + +However, even though training with diversified synthetic public data and augmentation, the models face the risk of being overfitted to public data. As public samples are selected from in-distribution data, the problem of the public + +![](images/b81f193cff8ed421a844281af901a8190eae929d9c050f0a7944e65881093d41.jpg) +(a) Gradient norm. + +![](images/1157ed9d86dac895d7c8fbd47af8499a1be645b4ac5534888becbd8203c67f7d.jpg) +(b) Accuracy $(-)$ and loss $(-)$ . +Figure 4. Learning dynamics of private training with different datasets and optimization methods. + +private generalization gap is analogous to the training-test generalization gap in standard training. In Figure 4b, we illustrate the accuracy and loss for each public, synthetic, private, and test dataset during private training after the warm-up phase. The model consistently achieves near-zero loss and $100\%$ accuracy on synthetic data (as well as on public data) but struggles with private data (as well as on test data). + +To alleviate the generalization gap in standard training, various studies [16, 31, 33, 34, 37, 47] explored the geometric properties of the loss function in the weight space. The prominent optimization methods are designed to uncover flat minima, such as sharpness-aware minimization (SAM) [20] or stochastic weight averaging (SWA) [29]. Therefore, we apply SAM during the warm-up training and calculate geometric generalization measures, including metrics such as the top Hessian value $\lambda_{max}$ , the ratio of Hessian $\lambda_{max} / \lambda_5$ , and the trace of the Hessian matrix $\mathrm{Tr}(\nabla^2\ell (\pmb {w}))$ for both synthetic and private data. Table 5 indicates that utilizing SAM results in lower (better) metric values, not only for synthetic data but also for private data. Note that SGD even demonstrates a negative trace value on private data. + +Moreover, in Figure 4a, as the flat minimum of SAM leads to a decreased gradient norm on synthetic data, it also maintains similar results concerning private data. These results indicate that relieving overfitting to synthetic data can help the generalization of private data. Thus, the aforementioned approaches find suitable initial point of DP-SGD. + +# 5. Experiments + +# 5.1. Experimental setup + +We assess the effectiveness of our proposed methods using public data primarily in two datasets: CIFAR-10 and CIFAR-100. For the public dataset, we randomly sample $4\%$ of the training data (2K samples) uniformly drawn from each class, while the remaining data are used as private samples following [43]. We then train the EDM [30] models with the 2K public data samples and build 50K synthetic datasets with EDM sampling. To address the computational burden of training diffusion and sampling, we gen + +erate datasets once and reuse them for classifiers as in [43]. + +For classification models, we adopt WRN-16-4, following the techniques in [12] with 16 augmentations, and use pre-trained vision transformer models following [7]. Our experiments are conducted using PyTorch libraries [63] on eight NVIDIA GeForce RTX 3090 GPUs, partially on a cloud server with four NVIDIA A100 40GB GPUs. We report the mean and standard deviation for each experiment. For the detailed settings, refer to Appendix B. + +# 5.2. Classification Performance with Public Data + +Effects of individual techniques We first revisit Table 1, the ablation study of sequentially employing our approaches, with a privacy budget $(2,10^{-5})$ -DP on CIFAR-10. By only using better EDM synthesis without extra optimization techniques, we achieve the previous SOTA performance of $75.1\%$ [43]. Additionally, recognizing the significance of diversity in data generation, we employ cutout augmentation techniques for diversity in classification, resulting in a performance of $84.88\%$ . To mitigate potential overfitting to public information, we make use of generalization techniques. All these efforts collectively lead to an accuracy of $85.48\%$ under $(2,10^{-5})$ -DP. + +Despite achieving the best performance of $85.93\%$ when combined with DG, we exclude DG in this section due to its marginal performance enhancement $(0.45\%)$ considering its extended training time, as detailed in Appendix C. + +CIFAR-10 with public data We report the performance comparison for our method with various previous approaches on a wide range of $\varepsilon \in \{1,2,3,4,6\}$ with $\delta = 10^{-5}$ in Table 6. Our approach, which incorporates EDM synthesis, augmentation, and optimization for the public data, exhibits superior classification performance when compared to existing methods including DDPM-based augmentation and extended optimizations. The accuracies of $\varepsilon = 0$ (after warm-up, without private data) and $\varepsilon = \infty$ (not private, with clipping) are $80.72\%$ and $88.52\%$ , respectively. + +CIFAR-100 with public data We then explore the CIFAR-100 dataset for DP, which is not actively investigated without pre-trained models due to its complexity. We first train the EDM model with 2K images and generate 50K images, similar to CIFAR-10. Given the 100 classes in CIFAR-100, only 20 public samples are available per class, significantly fewer than in CIFAR-10. The FID on 50K images with EDM synthesis is 11.28, which reduces the original FID of 15.58 for replicating each public image 25 times. After the warm-up, the accuracy of synthetic images on $\varepsilon = 0$ is $38.04\%$ (46.74% on $\varepsilon = \infty$ ), while the test accuracy of using 2K public samples without synthesis on $\varepsilon = 0$ is only $16.79\%$ . In Table 7, we report the accuracies by sequentially adopting the aforementioned tech + +Table 6. Test accuracy $(\%)$ of private training on CIFAR-10 with privacy budgets of $\varepsilon \in \{1,2,3,4,6\}$ . The public and synthesis columns denote the Warm and WarmSyn setups, respectively. Ours employs all the techniques in Table 1, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**. + +
DatasetsArchitecturePublicSynthesisMethodε = 1ε = 2ε = 3ε = 4ε = 6
CIFAR -10CNN-Tanh (0.55M)XX[44]45.858.363.5--
ScatterNet (0.16M)XX[59]60.367.269.3--
DPNAS [9] (0.53M)XX[46]60.13±0.3467.23±0.1269.86±0.49--
WRN-16-4 (2.74M)XX[12]56.8±0.664.9±0.569.2±0.371.9±0.377.0±0.8
WRN-40-4 (8.94M)XX[12]56.4±0.665.9±0.570.7±0.273.5±0.678.8±0.4
✓X[2]†-68.7-73.177.2
✓X[38]†-68.7-73.577.9
WRN-16-4 (2.74M)✓✓[2]†-70.5-74.578.2
✓✓[38]†-69.1-74.178.1
✓✓[43]†-75.1-77.980.0
✓✓Ours84.30±0.1185.48±0.1286.03±0.0986.49±0.1387.06±0.24
+ +We note the results reported in [43] to set the architecture same. All other baseline results are adopted from the original paper. + +Table 7. Test accuracy $(\%)$ of private classification on CIFAR-100 on the privacy budget of $\varepsilon \in \{1,2,6,10\}$ . The public and synthesis columns indicate Warm and WarmSyn settings, respectively. We employ the techniques in Table 1 sequentially, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**. + +
DatasetsArchitecturePublicSynthesisMethodsε = 1ε = 2ε = 6ε = 10
CIFAR -100Resnet-9XX[35]†18.124.9-40.8
Resnet-9 (6.62M)XXCold†8.3514.4229.8935.11
WRN-16-4 (2.74M)XXCold9.2818.1933.6139.09
✓XWarm20.8425.1533.4738.89
WRN-16-4 (2.74M)✓✓WarmSyn26.13±0.2031.53±0.0435.53±0.1140.82±0.10
✓✓+Augmentation40.96±0.3044.52±0.0150.47±0.0454.29±0.05
✓✓+Optimization45.93±0.0648.61±0.5954.36±0.5256.56±0.11
+ +$\dagger$ Unfortunately, their DP-SGD results are not reproducible, even when using the same hyperparameters as in the original paper. + +niques, where each of the approaches matters. As a result, we obtain $48.61\%$ on $\varepsilon = 2$ without pre-trained models. + +CIFAR-100 with pre-trained on ImageNet To push further, we demonstrate the effectiveness of our procedures when combined with pre-trained models with ID public data. We adopt the vision transformers following [7] pretrained on ImageNet [13]. Upon the pre-trained models, we sequentially perform the warm-up training with ID public data and private learning. The results in Table 8 indicate that the synthesis can boost classification performance. Within a wide range of models and privacy budgets, our methods outperform the warm settings. + +Distribution shift (CIFAR-100 $\rightarrow$ CIFAR-10) The distribution shifts from similar but not ID public data [59] can be combined with our methods. We consider $4\%$ of CIFAR-100 data as public to enhance the performance of CIFAR-10 as a substitute for CIFAR-10 ID public data. In Table 9, we present the classification results for both the warm and our settings, where both models are trained on the public data and synthetic data from $4\%$ of CIFAR-100, respectively. The experimental results show that the differences in accu + +racies exceed $20\%$ , even though neither model has observed CIFAR-10 datasets before private training with DP-SGD. This indicates that amplifying public information is meaningful in distribution shifts. Additional sensitivity analysis and ablation studies can be found in Appendix D. + +Pre-trained diffusion models Our main idea to use synthesis for public data is flexible in practical scenarios and diverse datasets. To mitigate the drawbacks of training diffusion on each dataset, we investigated using the pre-trained diffusion models, which are trained on OOD public data. Specifically, we make use of pre-trained Stable Diffusion (SD) [52] and Boomerang sampling [40]. We fed $4\%$ of public data to Boomerang editing with SD backbone for generation diversity and generated 20 images per sample for classifier training. The similar experiments are shown in Appendix D. We maintain the other training procedures the same as 'Ours', which we call 'Ours-SD'. Table 10 indicates that our framework is straightforward and effective for real-world data, and generalizable without depending on specific diffusion models. We conclude that data diversity can enhance performance when the model is not trained on specific ID public data. + +Table 8. Test accuracy (%) of private classification on CIFAR-100 using pre-trained models on the privacy budget of $\varepsilon \in \{0.5,2\}$ . The **bold** indicates results within the standard deviation of the top mean score. + +
DatasetsPrivacy budgetε = 0.5ε = 2
ArchitectureColdWarmOursColdWarmOurs
CIFAR -100CrossViT small 240 (26.3M)60.50±1.7073.17±0.2477.43±0.1371.36±0.5277.00±0.2780.25±0.57
CrossViT 18 240 (42.6M)67.03±0.4677.19±0.4479.96±0.1074.28±0.2280.30±0.0282.85±0.08
DeiT base patch16 224 (85.8M)49.34±1.4979.56±0.7479.28±0.7669.09±0.1082.98±0.0483.06±0.01
CrossViT base 240 (103.9M)66.24±0.4775.59±0.2178.06±0.0575.15±0.0379.25±0.0581.14±0.15
+ +Table 9. Comparison of distribution shift performance on CIFAR-10 with the warm and our models trained on $4\%$ of CIFAR-100. + +
CIFAR-100 → CIFAR-10Test Acc (%)
ε = 2ε = 4ε = 6
Warm50.65±0.3756.54±0.2059.49±1.39
Ours73.46±0.2878.60±0.1380.12±0.04
+ +Table 10. Classification results on real-world datasets. + +
DataMethodε = 2ε = 4ε = 6
EuroSATWarm (w/ Aug, Opt)83.6785.5286.07
WarmExt [43]84.3785.7886.07
(Land use)Ours-SD90.3791.7492.52
PathMNISTWarm (w/ Aug, Opt)89.2389.3989.54
WarmExt [43]89.0489.2589.28
(Biomedical)Ours-SD91.6491.9492.10
FairFaceWarm (w/ Aug, Opt)53.0054.5554.83
WarmExt [43]53.3354.7454.84
(w.r.t. Race)Ours-SD54.9056.1956.37
+ +![](images/492df6f696f815e01ccb2f4d97175c45c200686b15cadcc8c387a522e1841d19.jpg) + +![](images/c2e7a0c077e2abcef06c76f6a4e5d781987358a778e1f615dbd7d1da3817f216.jpg) + +![](images/acb2eb7c1bfa07640df1317abfd51f9b859e76fe42862d4bd31759715c8fcc11.jpg) + +# 5.3. Revisit Extended Optimization + +On top of our method, we reevaluate the effectiveness of existing extended methods (thus WarmSE) in Table 11, particularly mirror GD [2] and DOPE-SGD [43]. These methods are trained after our synthesis, augmentation, and warm-up optimization on $\varepsilon \in \{2, 4, 6\}$ . Remarkably, the performance of the extended methods falls within the standard deviation range of DP-SGD. This implies that, as the models have already extracted substantial side information from public data before private training, extended optimization does not further improve DP optimization. Note that the computational time of the public batch is marginal to DP-SGD. + +However, extended methods sometimes exhibit poorer training stability than DP-SGD. Due to their reliance on public gradients, these methods are sensitive to the hyperparameter settings and easily encounter exploding gradients. In Figure 5, under the same setting as Figure 4a, we observe a gradual decrease in the private gradient norm, while the public gradient norm consistently increases. When the public norm increases to a certain level, the norm of both public and private data with extended methods may diverge after updating toward public gradients. For further insights about the learning dynamics in terms of the loss function + +Table 11. Performance and computational time of different extended optimization methods. + +
Privacy budget ε (δ = 10-5)Optimization
DP-SGDMirror GD [2]DOPE-SGD [43]
MedianMinMedianMin
ε = 285.48±0.1785.5210.0085.5310.00
ε = 486.49±0.1386.3110.0086.6910.00
ε = 687.06±0.2486.7310.0086.8410.00
Time (ms/image)12.7012.8012.86
+ +![](images/ebe73e844794760e9cc646618d56a6b53fe88900f1c86d6a7b5e4978f0a27cb1.jpg) +Figure 5. The norm of gradients with (Left) synthetic dataset and (Right) private dataset with clipping during private training with different optimization methods. + +![](images/2f24f6c3ab8483bbb95aa1200eec5a2ef668bf72b4001c3b0a2e7af00ad8e6c4.jpg) + +and private gradient norm without clipping, please refer to Appendix C. However, we believe that undiscovered extended methods can be beneficial for the WarmSyn settings. + +# 6. Conclusion + +In this paper, we investigate the potential of diffusion models for in-distribution public data to enhance private classification performance. We demonstrate the importance of synthetic data diversity, augmentation techniques, and the importance of well-generalizing minima for private optimization. As a limitation, we leave the experiments on more extensive and sensitive datasets and the efficient implementation of our method. We hope that this work helps leverage diffusion models to address utility-privacy trade-offs. + +Acknowledgements This work was supported by NRF (No. 2022R1A5A6000840, No. RS-2023-00272502) and IITP (No. 2022-0-00984, No. 2021-0-01343-004) grants funded by the Korea government (MSIT). + +# References + +[1] Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. Deep learning with differential privacy. In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security, pages 308-318, 2016. 1, 2 +[2] Ehsan Amid, Arun Ganesh, Rajiv Mathews, Swaroop Ramaswamy, Shuang Song, Thomas Steinke, Vinith M Suriyakumar, Om Thakkar, and Abhradeep Thakurta. Public data-assisted mirror descent for private model training. In International Conference on Machine Learning, pages 517-535. PMLR, 2022. 1, 2, 3, 7, 8 +[3] Galen Andrew, Om Thakkar, Hugh Brendan McMahan, and Swaroop Ramaswamy. 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High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684-10695, 2022. 3, 7 +[53] Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. Advances in neural information processing systems, 29, 2016. 3 +[54] Ali Shahin Shamsabadi and Nicolas Papernot. Losing less: A loss for differentially private deep learning. Proceedings on Privacy Enhancing Technologies, 3:307-320, 2023. 2, 5 +[55] Yifan Shi, Yingqi Liu, Kang Wei, Li Shen, Xueqian Wang, and Dacheng Tao. Make landscape flatter in differentially private federated learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24552-24562, 2023. 2 +[56] Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using + +nonequilibrium thermodynamics. In International conference on machine learning, pages 2256-2265. PMLR, 2015. 3 +[57] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. In International Conference on Learning Representations, 2020. 3 +[58] Lichao Sun and Lingjuan Lyu. Federated model distillation with noise-free differential privacy. Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence (IJCAI-21), 2021. 2 +[59] Florian Tramer and Dan Boneh. Differentially private learning needs better features (or much more data). In International Conference on Learning Representations, 2021. 1, 2, 7 +[60] Wenxiao Wang, Tianhao Wang, Lun Wang, Nanqing Luo, Pan Zhou, Dawn Song, and Ruoxi Jia. Dplus: Boosting utility of differentially private deep learning via randomized smoothing. Proceedings on Privacy Enhancing Technologies, 4:163-183, 2021. 2 +[61] Zekai Wang, Tianyu Pang, Chao Du, Min Lin, Weiwei Liu, and Shuicheng Yan. Better diffusion models further improve adversarial training. In Proceedings of the 40th International Conference on Machine Learning, pages 36246-36263. PMLR, 2023. 3, 5 +[62] Zhisheng Xiao, Karsten Kreis, and Arash Vahdat. Tackling the generative learning trilemma with denoising diffusion gans. In International Conference on Learning Representations, 2021. 3 +[63] Ashkan Yousefpour, Igor Shilov, Alexandre Sablayrolles, Davide Testuggine, Karthik Prasad, Mani Malek, John Nguyen, Sayan Ghosh, Akash Bharadwaj, Jessica Zhao, Graham Cormode, and Ilya Mironov. Opacus: User-friendly differential privacy library in PyTorch. arXiv preprint arXiv:2109.12298, 2021. 6 +[64] Da Yu, Huishuai Zhang, Wei Chen, and Tie-Yan Liu. Do not let privacy overbill utility: Gradient embedding perturbation for private learning. In International Conference on Learning Representations, 2020. 3 +[65] Da Yu, Huishuai Zhang, Wei Chen, and Tie-Yan Liu. Do not let privacy overbill utility: Gradient embedding perturbation for private learning. In International Conference on Learning Representations, 2021. 1, 2 +[66] Da Yu, Huishuai Zhang, Wei Chen, Jian Yin, and Tie-Yan Liu. Large scale private learning via low-rank reparametrization. In International Conference on Machine Learning, pages 12208-12218. PMLR, 2021. +[67] Da Yu, Saurabh Naik, Arturs Backurs, Sivakanth Gopi, Huseyin A Inan, Gautam Kamath, Janardhan Kulkarni, Yin Tat Lee, Andre Manoel, Lukas Wutschitz, Sergey Yekhanin, and Huishuai Zhang. Differentially private finetuning of language models. In International Conference on Learning Representations, 2022. 1, 2 +[68] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF international conference on computer vision, pages 6023-6032, 2019. 5 \ No newline at end of file diff --git a/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/images.zip b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d501c91ae2b375833a9cced2868cba2d44e76cf0 --- /dev/null +++ b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dd840a7e2c1946dd7fd5ca3f2fca70ce4ba56503d048b293fd2c590561843c49 +size 587674 diff --git a/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/layout.json b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1452c6cf7b2b436e3b48ed80aab6e72addf303f2 --- /dev/null +++ b/2024/In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification/layout.json @@ -0,0 +1,10442 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 112, + 102, + 481, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 102, + 481, + 138 + ], + "spans": [ + { + "bbox": [ + 112, + 102, + 481, + 138 + ], + "type": "text", + "content": "In-distribution Public Data Synthesis with Diffusion Models for Differentially Private Image Classification" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "spans": [ + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "text", + "content": "Jinseong Park" + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "text", + "content": " Yujin Choi" + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "text", + "content": " Jaewook Lee" + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 165, + 160, + 430, + 189 + ], + "type": "text", + "content": " Seoul National University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 189, + 191, + 400, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 191, + 400, + 202 + ], + "spans": [ + { + "bbox": [ + 189, + 191, + 400, + 202 + ], + "type": "text", + "content": "{jinseong,uznhigh,jaewook} @snu.ac.kr" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "text", + "content": "To alleviate the utility degradation of deep learning image classification with differential privacy (DP), employing extra public data or pre-trained models has been widely explored. Recently, the use of in-distribution public data has been investigated, where tiny subsets of datasets are released publicly. In this paper, we investigate a framework that leverages recent diffusion models to amplify the information of public data. Subsequently, we identify data diversity and generalization gap between public and private data as critical factors addressing the limited public data. While assuming " + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "text", + "content": " of training data as public, our method achieves " + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "inline_equation", + "content": "85.48\\%" + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "text", + "content": " on CIFAR-10 with a privacy budget of " + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "inline_equation", + "content": "\\varepsilon = 2" + }, + { + "bbox": [ + 46, + 256, + 290, + 413 + ], + "type": "text", + "content": ", without employing extra public data for training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 435, + 128, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 435, + 128, + 447 + ], + "spans": [ + { + "bbox": [ + 47, + 435, + 128, + 447 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 455, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 622 + ], + "type": "text", + "content": "Differential privacy (DP) [18, 19] establishes a mathematical framework to ensure the privacy of training data. In deep learning, differentially private SGD (DP-SGD) [1] has become the de facto standard method to guarantee the models' privacy. However, differentially private training inevitably degrades performance compared to standard (non-DP) training [6, 45]. As a practical solution, leveraging public pre-trained models or public data has been explored to enhance utility [12, 39, 59, 65-67]. As using public data raises no privacy concerns, fine-tuning pre-trained models on private data can make use of learned features for free. Nevertheless, their effectiveness might be diminished when addressing out-of-distribution (OOD) public data of small shared characteristics with private data [59]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 623, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 696 + ], + "type": "text", + "content": "As an alternative, researchers have investigated the use of in-distribution (ID) public data, indicating that a small portion of in-distribution data is made public [38]. For example, some data owners decide to share their data publicly in exchange for economic incentives or public interest. This setup allows us to leverage public data with a distribution" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 231, + 542, + 346 + ], + "blocks": [ + { + "bbox": [ + 309, + 231, + 542, + 346 + ], + "lines": [ + { + "bbox": [ + 309, + 231, + 542, + 346 + ], + "spans": [ + { + "bbox": [ + 309, + 231, + 542, + 346 + ], + "type": "image", + "image_path": "8f929fc117142acfc5dc25f0cfc35063d22fe0f1db22930d061e9a02b39128b7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 357, + 545, + 391 + ], + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 391 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 391 + ], + "type": "text", + "content": "Figure 1. Illustration of (Top) existing optimization-based methods and (Bottom) proposed training procedure for amplifying in-distribution public data and utilizing the synthetic data." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 404, + 546, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 546, + 524 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 546, + 524 + ], + "type": "text", + "content": "similar to private data. In contrast to previous approaches, such as utilizing extra OOD data or distribution shift, we need to assume a limited amount of ID public data since the public data might contain more sensitive information. However, the repeated use of limited-sized public data can raise critical issues related to memorization and overfitting [43]. To mitigate the aforementioned problems, previous studies mainly have focused on utilizing side information from the little public data to enhance the optimization of differentially private deep learning [2, 4, 38, 43]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 525, + 547, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 656 + ], + "type": "text", + "content": "Recently, Ganesh et al. [21] pointed out that warm-up training with public data plays a crucial in private optimization to find a good basin with a small loss, whereas DP-SGD from a random initial point faces a high loss and poor optimization. From this viewpoint, we suggest that enlarging the public dataset could improve the performance of private learning. By using the recent diffusion models [28, 30], we aim to enrich the contextual information of public data. We further identify that data diversity and generalization gap between public and private data act as critical factors, particularly addressing the limited size of public data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 657, + 547, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 547, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 547, + 682 + ], + "type": "text", + "content": "The proposed framework is illustrated in Figure 1. We summarize our approaches and their performance gains in" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 203, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 203, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 203, + 712 + ], + "type": "text", + "content": "*Corresponding author. †Equal contribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 693, + 399, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 693, + 399, + 702 + ], + "spans": [ + { + "bbox": [ + 317, + 693, + 399, + 702 + ], + "type": "text", + "content": "1Our code is available at" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 703, + 493, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 703, + 493, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 703, + 493, + 713 + ], + "type": "text", + "content": "https://github.com/JinseongP/DPTrainer." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12236" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 134, + 291, + 264 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 289, + 126 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 289, + 126 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 289, + 126 + ], + "type": "text", + "content": "Table 1. Ablation study on the impact of various techniques, including synthesis, augmentation, and optimization, to enhance classification performance using in-distribution public data from CIFAR-10 under " + }, + { + "bbox": [ + 46, + 70, + 289, + 126 + ], + "type": "inline_equation", + "content": "(2,10^{-5})" + }, + { + "bbox": [ + 46, + 70, + 289, + 126 + ], + "type": "text", + "content": "-DP. Refer to Section 3.1 for the details of setups and the relevant sections for the details of each method." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 134, + 291, + 264 + ], + "lines": [ + { + "bbox": [ + 47, + 134, + 291, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 134, + 291, + 264 + ], + "type": "table", + "html": "
SetupTraining SettingsTest Acc
Baselines including previous SOTA methods (Sec. 3.1)
ColdCold Baseline (WRN16-4) [12]64.02%
WarmWarm-up on public data68.09%
WarmSynWarm-up on DDPM synthesis [43]72.0%
WarmSEWarmSyn (DDPM) + DOPE-SGD [43]75.1%
In-distributionpublic data synthesis (Sec. 4.1) & Diversity (Sec. 4.2)
WarmSynWarm-up on EDM synthesis75.13 %
WarmSynEDM synthesis + generation diversity77.66 %
WarmSynEDM synthesis + augmentation diversity84.88%
Generalization for public-private datasets (Sec. 4.3)
WarmSynWell-generalizing minimum during warm-up85.48%
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MethodsNon-priv.ε = 6ε = 2
Warm [43]0.05% (-)0.10% (18.80%)3.20% (27.80%)
WarmSE [43]0.13% (-)3.00% (15.98%)5.60% (25.48%)
Ours0.13% (-)10.06% (8.92%)20.58% (10.50%)
", + "image_path": "5398f847da1f6a69259a369ca0716af1dd32427964b484b03ce912ff7864b7be.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 567, + 223, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 223, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 223, + 581 + ], + "type": "text", + "content": "2. Background and Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 588, + 242, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 242, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 242, + 601 + ], + "type": "text", + "content": "2.1. Differentially Private Deep Learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 607, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 607, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 287, + 632 + ], + "type": "text", + "content": "Differential privacy (DP) [19] can guarantee the privacy of training data as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "text", + "content": "Definition 2.1 (Differential privacy) For two adjacent inputs " + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "d, d' \\in \\mathcal{D}" + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "text", + "content": ", a randomized mechanism " + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{M}: \\mathcal{D} \\to \\mathcal{R}" + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "text", + "content": " satisfies " + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "(\\varepsilon, \\delta)" + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "text", + "content": "-differential privacy for any set of possible outputs " + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "S \\subseteq \\mathcal{R}" + }, + { + "bbox": [ + 45, + 642, + 287, + 689 + ], + "type": "text", + "content": " if" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 83, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 83, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "P r \\left[ \\mathcal {M} (d) \\in \\mathcal {S} \\right] \\leq e ^ {\\varepsilon} P r \\left[ \\mathcal {M} \\left(d ^ {\\prime}\\right) \\in \\mathcal {S} \\right] + \\delta . \\tag {1}", + "image_path": "f73124febca74af7225b1e369c7e06e2e1ae8f1a83082d4163d1764d270f8889.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "The privacy budget " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\varepsilon \\geq 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " controls the level of privacy guarantee with the broken probability " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\delta \\geq 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ". In deep learning, differentially private SGD (DP-SGD) [1] is widely used with the following steps: (i) average the clipped per-sample gradient " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\nabla \\ell_{i}(\\boldsymbol{w}) \\coloneqq \\nabla \\ell(\\boldsymbol{w}; \\boldsymbol{x}_{i})" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " for weight " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " with respect to each individual private data sample " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{i} \\in \\boldsymbol{X}_{t}^{pr}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " and (ii) add Gaussian noise to the averaged gradient as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 339, + 162, + 545, + 191 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 162, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 339, + 162, + 545, + 191 + ], + "type": "interline_equation", + "content": "\\boldsymbol {g} _ {t} ^ {p r} = \\frac {1}{| \\boldsymbol {X} _ {t} ^ {p r} |} \\sum_ {\\boldsymbol {x} _ {i} \\in \\boldsymbol {X} _ {t} ^ {p r}} \\operatorname {c l i p} \\left(\\nabla \\ell_ {i} (\\boldsymbol {w} _ {t}), C\\right), \\tag {2}", + "image_path": "865b56d29d3efeb0dd0731cfac50399dd15d276e3b57dddade012a39009254ed.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 340, + 193, + 451, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 193, + 451, + 207 + ], + "spans": [ + { + "bbox": [ + 340, + 193, + 451, + 207 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {g}} _ {t} ^ {p r} = \\boldsymbol {g} _ {t} ^ {p r} + \\mathcal {N} (\\mathbf {0}, C ^ {2} \\sigma^ {2} \\mathbf {I}).", + "image_path": "b951c87fd8a7df874e2feeff30ee7df09872a7eb036d0c7c00188973c8c8178f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": "The weight is updated as " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_{t + 1} = \\boldsymbol{w}_t - \\eta \\tilde{\\boldsymbol{g}}_t^{pr}" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": " with a learning rate " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\operatorname {clip}(\\boldsymbol {u},C)" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": " projects " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\pmb{u}" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": "-ball of radius " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": ". The noise level " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": " is determined by the privacy budget " + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "inline_equation", + "content": "(\\varepsilon ,\\delta)" + }, + { + "bbox": [ + 304, + 213, + 545, + 273 + ], + "type": "text", + "content": ", the number of training steps, and the sampling probability (refer to Appendix C for details)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 274, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 393 + ], + "type": "text", + "content": "To guarantee privacy with clipping and noise addition, DP-SGD inevitably degrades the performance during optimization. Therefore, various studies explored DP-friendly properties, including architecture [9, 59], loss and activation functions [44, 54], or smoothness [46, 55, 60]. Notably, De et al. [12] introduced a new era in utilizing large models for DP-SGD tasks by introducing the averaged loss of various augmentations called augmentation multiplicity, weight standardization [49], and optimization tricks. Note that adaptive clipping [3, 8] could improve our results." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 399, + 524, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 524, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 524, + 412 + ], + "type": "text", + "content": "2.2. Private Learning with Public Information" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 417, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 545, + 477 + ], + "type": "text", + "content": "The benefits of massive OOD public data have been explored in the context of the pre-trained models in vision [7, 12] and language [39, 65-67] models. Additionally, the transfer learning with similar distribution, such as CIFAR-100 for CIFAR-10, was under investigated [58, 59]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "text", + "content": "ID public data " + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^{pub}" + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "text", + "content": " requires different approaches from the massive OOD public data due to its limited size and similar distributional properties. Hence, prior studies [2, 4, 38, 43], categorized as extended methods in Section 3.1, have focused on mitigating errors in the optimization of DP-SGD by utilizing the gradients of public data as a proxy for true gradients. These methods update the weight with " + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_{t+1} = \\boldsymbol{w}_t - \\eta f_g" + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "inline_equation", + "content": "f_g(\\boldsymbol{w}_t; \\boldsymbol{X}_t^{pub}, \\boldsymbol{X}_t^{pr})" + }, + { + "bbox": [ + 304, + 477, + 545, + 620 + ], + "type": "text", + "content": " such as normalizing the private gradient with the public gradient norm [38], employing a linear combination of private and public gradients [2], or estimating low-rank approximation with public data (even unlabelled) to reduce noise levels [48, 65]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "type": "text", + "content": "Nasr et al. [43] firstly introduced training a generative model as an augmentation technique. However, their primary focus is the optimization called DOPE-SGD, which updates towards the public gradient " + }, + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "type": "inline_equation", + "content": "\\pmb{g}_t^{pub}" + }, + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "type": "text", + "content": " (without clipping and noise addition) and makes " + }, + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "type": "inline_equation", + "content": "\\pmb{g}_t^{pub} - \\pmb{g}_t^{pr}" + }, + { + "bbox": [ + 304, + 621, + 545, + 683 + ], + "type": "text", + "content": " private as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 315, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {w} _ {t + 1} = \\boldsymbol {w} _ {t} - \\eta \\left(\\boldsymbol {g} _ {t} ^ {\\text {p u b}} + \\operatorname {c l i p} \\left(\\boldsymbol {g} _ {t} ^ {\\text {p u b}} - \\boldsymbol {g} _ {t} ^ {\\text {p r}}, C\\right) + \\mathcal {N}\\right), \\tag {3}", + "image_path": "489ca4de506efa1924b6e9757748e2cd8478d31d7faa230561292be176103e85.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "12237" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "type": "text", + "content": "with the same noise level " + }, + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "type": "text", + "content": " in Equation (2). To the best of our knowledge, none of the prior studies deeply investigated the ID public data as a perspective of the data synthesis." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 116, + 160, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 116, + 160, + 129 + ], + "spans": [ + { + "bbox": [ + 47, + 116, + 160, + 129 + ], + "type": "text", + "content": "2.3. Diffusion Synthesis" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 134, + 286, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 286, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 286, + 242 + ], + "type": "text", + "content": "The integration of generative models in classification tasks has been widely explored to enhance generalization performance without extra data samples [5, 22, 25]. In recent years, diffusion models [28, 56, 57] have shown promising results in image generation. Notably, Xiao et al. [62] argued that diffusion models can generate high-quality and diverse images. Subsequently, various studies have focused on enhancing the quality of generation [30, 32], conditioning sampling [15, 27], and text-to-image generation [50, 52]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 286, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 286, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 286, + 326 + ], + "type": "text", + "content": "Due to the significance of privacy concerns during image synthesis, differentially private diffusion synthesis is one of the actively investigated research topics [17, 41]. Given the effectiveness of private fine-tuning upon pre-trained diffusion models for generation and classification tasks [23], utilizing privacy-preserving diffusion models presents opportunities for our future works." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 341, + 286, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 286, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 286, + 400 + ], + "type": "text", + "content": "Measures To measure the quality of generated images, various measures are proposed: Inception Score (IS) [53] and Precision [36] to measure fidelity, Recall [36] to measure diversity, and Fréchet Inception Distance (FID) [26] to measure the distributional quality for mean and variance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 286, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 286, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 286, + 509 + ], + "type": "text", + "content": "To assess the impact of synthetic data on classification tasks, Ravuri and Vinyals [51] proposed the Classification Accuracy Score (CAS), which evaluates the classification performance on a test set using a model trained on synthetic data. Thus, we use CAS to validate the performance of synthetic public data on test data. However, since our main focus is on improving classification performance including private learning, all of the previous measures cannot be perfectly aligned with our goals." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 520, + 123, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 520, + 123, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 520, + 123, + 532 + ], + "type": "text", + "content": "3. Framework" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 539, + 162, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 162, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 162, + 552 + ], + "type": "text", + "content": "3.1. Training Procedure" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 557, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 653 + ], + "type": "text", + "content": "Our objective is to investigate the potential of diffusion models with ID public data, departing from conventional approaches that focus on guiding optimization with the public data [2, 4, 38, 43, 48, 64]. Our work aligns closely with [43], but we specifically concentrate on synthesizing data from the public and examining the important properties of private learning. We summarize the training scenarios using ID public data as follows [43]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 47, + 654, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 286, + 677 + ], + "type": "text", + "content": "- Cold: Conduct DP training (e.g., DP-SGD) on the private dataset without using public data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "- Warm: Train models through (i) non-DP warm-up training phase on the public dataset (e.g., SGD) and (ii) private training phase on the private dataset with DP methods." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 543, + 165 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 543, + 165 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 543, + 165 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 543, + 165 + ], + "type": "image", + "image_path": "36445e508d74e76e65116fa26d959687486a9dc290e4082ba6dfe89ba0d8bf0a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "type": "text", + "content": "Figure 2. Toy experiment on diffusion synthesis and its effect on decision boundaries while varying the training sample size." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 209, + 545, + 305 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 306, + 209, + 545, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 545, + 257 + ], + "type": "text", + "content": "- WarmExt: During the private training (after warm-up training), leverage the public side information, such as gradients [2, 4, 38, 43], or low-rank approximation [48, 64], as extended methods of DP optimization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 257, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 257, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 306, + 257, + 545, + 305 + ], + "type": "text", + "content": "- WarmSyn (Ours, [43]): Amplify the sparse information of public data using generative models or augmentation methods. Optionally, WarmSE indicates employing extended optimization with synthetic public data." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 306, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 306, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 306, + 545, + 376 + ], + "type": "text", + "content": "In terms of privacy, since utilizing public data does not pose any privacy concerns to the private data, we can leverage the public data multiple times, e.g., training warm-up classification models, diffusion models, or guiding private training. From now on, we denote in-distribution (ID) public data as public data unless otherwise specified." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 384, + 536, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 536, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 536, + 396 + ], + "type": "text", + "content": "3.2. Public Data Synthesis with Diffusion Models" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": "For amplifying the sparse information in the WarmSyn setting, we first investigate amplifying the number of data samples using diffusion models. Recent studies [5, 22, 25, 61] have demonstrated the performance gain in complicated classification problems by training diffusion models to expand the size of training data samples within the data manifold, e.g., amplifying 50K CIFAR-10 training data into a 50M synthetic dataset improves adversarial training [61]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 498, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 594 + ], + "type": "text", + "content": "To analyze public data synthesis with limited data samples, we conduct an experiment using a spiral dataset as a toy example (detailed in Appendix C), as shown in Figure 2. We consider two settings: (a) with a sufficient and (b) with an insufficient number of original data samples. For each setting, we train a simple diffusion model to generate new data samples. Then, we train two-layer classifiers until convergence using the original and synthetic data, respectively." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "With a large number of samples in (a), both diffusion and classification models demonstrate well-trained results. However, when the original data size is limited as in (b-1), the classification model tends to overfit individual data. Thus, despite correctly classifying almost all data samples, the model fails to discover the proper decision boundary. In contrast, in (b-2) where the diffusion model effectively approximates the data manifold, the classifier achieves a superior decision boundary compared to (b-1). Nevertheless, we should be aware that diffusion models can be apt to over" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12238" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 395, + 173 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 388, + 82 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 388, + 82 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 388, + 82 + ], + "type": "text", + "content": "Table 3. Quality comparison of synthetic data trained with " + }, + { + "bbox": [ + 56, + 70, + 388, + 82 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 56, + 70, + 388, + 82 + ], + "type": "text", + "content": " of public data on CIFAR-10." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 395, + 173 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 395, + 173 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 395, + 173 + ], + "type": "table", + "html": "
SamplingFidelityDiversityQualityCAS (↑) (%)Test Acc (%)
IS (↑)Precision (↑)Recall (↑)FID (↓)
EDM (wd=0)11.0080.9640.1577.79962.8275.13
EDM + DG (wd=3)10.8150.9640.1537.78662.4775.31
EDM + DG (wd=10)10.7960.9460.1708.27464.6175.98
EDM + DG (wd=20)10.1570.8730.19111.49767.6177.66
EDM + DG (wd=30)9.1130.7850.21119.74866.5377.22
", + "image_path": "3eba144522c925449580f2a8eed81d5707fcf1cac9d6a67c472b7cb5c426cd88.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 405, + 70, + 547, + 129 + ], + "blocks": [ + { + "bbox": [ + 405, + 70, + 547, + 129 + ], + "lines": [ + { + "bbox": [ + 405, + 70, + 547, + 129 + ], + "spans": [ + { + "bbox": [ + 405, + 70, + 547, + 129 + ], + "type": "image", + "image_path": "32968c2f8d721d30e7d3049c2516e72dd65b0b5e59be0ce80825dd2e1a27da15.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 403, + 137, + 546, + 170 + ], + "lines": [ + { + "bbox": [ + 403, + 137, + 546, + 170 + ], + "spans": [ + { + "bbox": [ + 403, + 137, + 546, + 170 + ], + "type": "text", + "content": "Figure 3. Selected synthetic data samples from (Top) EDM and (Bottom) EDM + DG " + }, + { + "bbox": [ + 403, + 137, + 546, + 170 + ], + "type": "inline_equation", + "content": "(w_{d} = 30)" + }, + { + "bbox": [ + 403, + 137, + 546, + 170 + ], + "type": "text", + "content": " synthesis." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 191, + 282, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 282, + 202 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 282, + 202 + ], + "type": "text", + "content": "and underestimate the data distribution, as shown in (b-2)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 203, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 203, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 287, + 287 + ], + "type": "text", + "content": "To push further, we mathematically analyze how the rate of data samples affects synthesis. The ability of a generative model " + }, + { + "bbox": [ + 46, + 203, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 203, + 287, + 287 + ], + "type": "text", + "content": " to approximate the 'entire' data can be determined by the ratio of 'seen' (observed during training) and the 'unseen' (not observed during training). Specifically, with a limited number of seen data, the model is required to estimate the unseen data to approximate the entire data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": "Theorem 3.1 For a finite number of 'entire' data samples " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "S_{data} = \\{\\pmb{x}_1, \\dots, \\pmb{x}_N\\}" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": ", split the data samples into 'seen' data " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "S_s = \\{\\pmb{x}_1, \\dots, \\pmb{x}_n\\}" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": ", and 'unseen' data " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "S_u = \\{\\pmb{x}_{n+1}, \\dots, \\pmb{x}_N\\}" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": ", without loss of generality. Let " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "p_{data}, p_s" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "p_u" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": " be the probability distribution of each corresponding dataset. For any generative model " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": " trained on 'seen' data, " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "p_\\theta" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": " represents the data distribution generated by " + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 295, + 288, + 379 + ], + "type": "text", + "content": ". Then," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 57, + 384, + 275, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 384, + 275, + 437 + ], + "spans": [ + { + "bbox": [ + 57, + 384, + 275, + 437 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\log \\frac {1}{r _ {1}} + \\hat {p} _ {\\theta} ^ {u} \\log \\frac {\\hat {p} _ {\\theta} ^ {u}}{r _ {2}} \\leq \\tilde {D} _ {K L} (p _ {\\theta} \\| p _ {d a t a}) - \\tilde {D} _ {K L} (p _ {\\theta} \\| p _ {s}) \\\\ \\leq \\log \\frac {1}{r _ {1}} + \\hat {p} _ {\\theta} ^ {u} \\log \\frac {1}{r _ {2}}, \\\\ \\end{array}", + "image_path": "3418ebd3dcea85a8b7ada08e07c2c623e12daefdd6ee7da616a18fe11564574b.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\hat{p}_{\\theta}^{u} = \\sum_{\\boldsymbol{x}\\in S_{u}}p_{\\theta}(\\boldsymbol{x})\\leq 1" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " indicates the capacity of the model " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " to generate 'unseen' data. For discrete probability distributions " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\tilde{D}_{KL}(p\\| q)" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " indicates the relaxed Kullback-Leibler (KL) divergence, excluding the case when " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "q = 0" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "r_1 = \\frac{n}{N}" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "r_2 = \\frac{N - n}{n}" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " denote the ratios of 'seen' to 'entire', and 'unseen' to 'seen' data, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": "The detailed proof is presented in Appendix A. The above theorem indicates that the ratios " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "r_1" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "r_2" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " affect how the model " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " can approximate the " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "p_{data}" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "r_1 \\rightarrow 1" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " with sufficient seen data, then " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "r_2 \\rightarrow 0" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "S_u \\rightarrow \\emptyset" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": ", so that " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\hat{p}_{\\theta}^{u} \\rightarrow 0" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " and the upper and lower bounds converge to zero. Thus, ensuring " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " is close to " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " ensures proximity of " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "inline_equation", + "content": "p_{data}" + }, + { + "bbox": [ + 46, + 521, + 287, + 594 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "However, when considering a small " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_1" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", which is equivalent to a limited number of public data setups, the bounds depend on " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{p}_{\\theta}^{u}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_1 \\leq \\frac{1}{e + 1}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", the lower and upper bounds are decreasing functions with respect to " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{p}_{\\theta}^{u}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". This implies that as the model's capacity to generate unseen data increases, the differences in divergences decrease. Thus, approximating the distribution of seen data is not enough to learn the whole data distribution for small " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_1" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". Rather, it is important for the model to learn the data manifold effectively to better approximate the data distribution including the unseen data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 190, + 511, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 190, + 511, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 511, + 205 + ], + "type": "text", + "content": "4. Generated Data for Private Learning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "type": "text", + "content": "We now investigate how the aforementioned diffusion synthesis can be utilized in the context of public data and analyze how it can be further leveraged to enhance performance. For experiments, we primarily focus on the CIFAR-10 dataset with a privacy budget of " + }, + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "type": "inline_equation", + "content": "(2,10^{-5})" + }, + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "type": "text", + "content": ", utilizing WRN-16-4² with 16 augmentation multiplicity and the techniques proposed in [12]. Within the training set, we randomly select 2K instances " + }, + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "type": "inline_equation", + "content": "(4\\%)" + }, + { + "bbox": [ + 304, + 210, + 545, + 368 + ], + "type": "text", + "content": " for the public samples, as suggested in [43]. These samples are uniformly drawn from each class. All the measures for evaluating the generated data in this section are calculated with the entire training set (50K) as a reference. Additional experimental details are provided in Section 5.1 and Appendix B." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 375, + 533, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 375, + 533, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 533, + 388 + ], + "type": "text", + "content": "4.1. Better Diffusion Synthesis with Public Data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "text", + "content": "Theorem 3.1 demonstrates that well-approximating the distribution of seen public data " + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "inline_equation", + "content": "p_{s}" + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "text", + "content": " enables the synthetic data distribution " + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "text", + "content": " mimic the entire data distribution " + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}" + }, + { + "bbox": [ + 304, + 393, + 546, + 597 + ], + "type": "text", + "content": ", which is essential to obtain good decision boundary as in Figure 2. Thus, we initially replace the Denoising Diffusion Probabilistic Model (DDPM) [28], previously investigated by Nasr et al. [43] for public synthesis, with the Elucidating Diffusion Model (EDM) [30]. EDM is known to generate better images (e.g., lower FID scores) than DDPM by using a higher-order sampling process. Then, we train EDM on 2K public data samples without using external datasets and employ class-conditional sampling to match the original distribution. With the trained EDM, we calculate various measures in Table 3. The FID of EDM synthesis at 7.80 (correspondingly 7.89 on 40K) outperforms the reported FID of 12.8 of DDPM on 40K images [43], which also improves the classification performance as shown in Table 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 597, + 547, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 547, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 547, + 694 + ], + "type": "text", + "content": "However, the generation quality using public data is notably worse than the FID of 1.79 achieved with the entire set [30]. Within a limited public data, the model struggles to capture diversity, resulting in a recall of 0.16, even though precision remains high at 0.96. Note that repeating each public sample 25 times (thus 50K samples) results in a precision of 1.00, recall of 0.04, and FID of 13.64. The generated images and their memorization are illustrated in Ap" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 545, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 545, + 714 + ], + "type": "text", + "content": "2 WRN-40-4 requires excessive GPU considering its performance [43]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12239" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 101, + 278, + 175 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 4. CAS " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": ", test accuracy " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": ", and their difference " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": " with different augmentation methods during warm-up phase." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 101, + 278, + 175 + ], + "lines": [ + { + "bbox": [ + 55, + 101, + 278, + 175 + ], + "spans": [ + { + "bbox": [ + 55, + 101, + 278, + 175 + ], + "type": "table", + "html": "
AugmentationCAS(%)Test Acc (%)Diff (%)
No Aug (EDM)62.8275.1313.31
Common77.9983.975.98
Common + Cutout80.7284.884.16
Common + Cutmix65.7382.2016.47
AutoAugment77.2183.456.24
", + "image_path": "16216fe39e4898ca88c340af798b1153faeacbb571a02b9ab6a5b8510f36f4d0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 217, + 291, + 263 + ], + "blocks": [ + { + "bbox": [ + 47, + 186, + 287, + 209 + ], + "lines": [ + { + "bbox": [ + 47, + 186, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 287, + 209 + ], + "type": "text", + "content": "Table 5. Geometric measures of the models trained with SGD and SAM after warm-up phase." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 217, + 291, + 263 + ], + "lines": [ + { + "bbox": [ + 48, + 217, + 291, + 263 + ], + "spans": [ + { + "bbox": [ + 48, + 217, + 291, + 263 + ], + "type": "table", + "html": "
OptSynthetic DataPrivate Data
λmaxλmax/λ5Tr(∇2ℓ(w))λmaxλmax/λ5Tr(∇2ℓ(w))
SGD1.3810.6271.98112.821.58-2527.78
SAM0.442.6353.2158.321.50333.03
", + "image_path": "6bc078f5b6630c8af42763c7b9d8ee253fe89d081f5bbbc4c5236d0b0fa98851.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 284, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 284, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 284, + 287, + 308 + ], + "type": "text", + "content": "pendix E. No privacy concern occurs in diffusion synthesis since the diffusion model is solely trained with public data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 317, + 251, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 251, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 251, + 329 + ], + "type": "text", + "content": "4.2. Data Diversity Matters for Public Data" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 335, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 468 + ], + "type": "text", + "content": "With limited private data, the model's capacity to generate unseen data is required in Theorem 3.1. The lack of diversity in the generated data can lead to misclassification due to distorted decision boundaries, as described in Figure 2. Given the challenge of DP-SGD in identifying a good basin [21], the key to successful warm-up lies in finding a well-generalizing minimum with a high CAS. As observed in [25, 51], data diversity can play an important role in improving CAS. We hypothesize that the importance of diversity is more pronounced in the warm-up phase of private learning, where the generated images exhibit low recall values." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "type": "text", + "content": "Diversity for generation To validate our hypothesis, we first investigate enforcing data diversity in the generation process. Obtaining diversity in generations solely through a diffusion model is a challenging task. Thus, to enhance the data diversity during generation, we can use variants of diffusion models for guidance [27, 32] or editing [10, 40, 42]. Among them, discriminator guidance (DG) [32] introduces a discriminator to judge whether the sampling is from the true data or synthesis, controlling the trade-off between fidelity and diversity of the generated images by adjusting the weight " + }, + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "type": "inline_equation", + "content": "w_{d}" + }, + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "type": "text", + "content": " of the discriminator. Higher " + }, + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "type": "inline_equation", + "content": "w_{d}" + }, + { + "bbox": [ + 46, + 486, + 287, + 628 + ], + "type": "text", + "content": " yields diversity. Refer to Appendix C for the details of DG." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "As shown in Table 3, a higher weight of guidance ensures greater data diversity without any augmentation, but sacristies the fidelity. The best FID score is obtained with " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "w_{d} = 3" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " while the best CAS is obtained at a bigger weight " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "w_{d} = 20" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": ". Interestingly, we need a larger weight value to achieve a similar gain of diversity than standard training (" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "w_{d} = 1.5" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " for best FID [32]). Figure 3 represents selected" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "examples from two extreme cases, with " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "w_{d} = 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "w_{d} = 30" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " to visualize the difference. Despite the quality degradation of detailed features with " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "w_{d} = 30" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ", the CAS is higher due to the increased data diversity in features. Thus, we need to enhance diversity while maintaining quality for better classification. Similar to the EDM model trained with public data, no privacy concerns occur since the discriminator requires only original public and synthetic data from EDM." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 183, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 183, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 183, + 545, + 375 + ], + "type": "text", + "content": "Diversity with augmentation Nonetheless, training an additional discriminator for DG can pose a bottleneck in terms of time and computational efficiency. Thus, to explicitly enhance the diversity of EDM synthetic data during the warm-up training, we employ various data augmentation techniques designed for classification tasks. Wang et al. [61] argued that utilizing appropriate augmentation in diffusion-based generated images can further improve the classification performance. Common augmentation [24] uses padding and random crop to the original size and horizontal flipping for the images. Cutmix [68] randomly replaces a part of the image with another and Cutout [14] randomly pad images. AutoAugment [11] chooses the best combination of augmentations such as color, rotation, or cutout. We set a baseline with no augmentation for synthetic images of EDM and compare these augmentations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 376, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 507 + ], + "type": "text", + "content": "The results are summarized in Table 4. Adding cutout augmentation to common augmentation demonstrates the best performance in terms of CAS and test accuracy. However, the two measures are not always aligned. Rather, the best performance gain with private data, noted as " + }, + { + "bbox": [ + 304, + 376, + 545, + 507 + ], + "type": "inline_equation", + "content": "Diff(\\%) = Test Acc - CAS" + }, + { + "bbox": [ + 304, + 376, + 545, + 507 + ], + "type": "text", + "content": ", is obtained from Cutmix, which is known as one of the most diversified augmentations. This indicates that robust decision boundaries achieved through diversity facilitate easier private learning. Interestingly, the performance gain of augmentation surpasses the benefits of generation diversity, as illustrated in Appendix C." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 515, + 486, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 486, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 486, + 528 + ], + "type": "text", + "content": "4.3. Optimization with Synthetic Data" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": "As the clipping of DP-SGD significantly lowers the performance, it is known that a smaller gradient norm ensures high performance in private training [44, 46, 54]. In Figure 4a, we illustrate the gradient norms during private training with different training setups. The norm of synthetic data is calculated without clipping, whereas the private data used for DP-SGD is summed over individually clipped gradients, each with a clipping value of " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "C = 1" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": ". The results indicate that utilizing a synthetic dataset reduces the gradient norm, even in a private dataset where constraining the gradient norm is crucial to mitigate the effect of clipping." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "However, even though training with diversified synthetic public data and augmentation, the models face the risk of being overfitted to public data. As public samples are selected from in-distribution data, the problem of the public" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12240" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 165, + 169 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 165, + 169 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 165, + 169 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 165, + 169 + ], + "type": "image", + "image_path": "b81f193cff8ed421a844281af901a8190eae929d9c050f0a7944e65881093d41.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 171, + 140, + 179 + ], + "lines": [ + { + "bbox": [ + 78, + 171, + 140, + 179 + ], + "spans": [ + { + "bbox": [ + 78, + 171, + 140, + 179 + ], + "type": "text", + "content": "(a) Gradient norm." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 74, + 279, + 167 + ], + "blocks": [ + { + "bbox": [ + 170, + 74, + 279, + 167 + ], + "lines": [ + { + "bbox": [ + 170, + 74, + 279, + 167 + ], + "spans": [ + { + "bbox": [ + 170, + 74, + 279, + 167 + ], + "type": "image", + "image_path": "1157ed9d86dac895d7c8fbd47af8499a1be645b4ac5534888becbd8203c67f7d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "lines": [ + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "spans": [ + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "type": "text", + "content": "(b) Accuracy " + }, + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "type": "inline_equation", + "content": "(-)" + }, + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "type": "text", + "content": " and loss " + }, + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "type": "inline_equation", + "content": "(-)" + }, + { + "bbox": [ + 175, + 171, + 275, + 180 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 190, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 212 + ], + "type": "text", + "content": "Figure 4. Learning dynamics of private training with different datasets and optimization methods." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 233, + 286, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 286, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 286, + 317 + ], + "type": "text", + "content": "private generalization gap is analogous to the training-test generalization gap in standard training. In Figure 4b, we illustrate the accuracy and loss for each public, synthetic, private, and test dataset during private training after the warm-up phase. The model consistently achieves near-zero loss and " + }, + { + "bbox": [ + 46, + 233, + 286, + 317 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 233, + 286, + 317 + ], + "type": "text", + "content": " accuracy on synthetic data (as well as on public data) but struggles with private data (as well as on test data)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "text", + "content": "To alleviate the generalization gap in standard training, various studies [16, 31, 33, 34, 37, 47] explored the geometric properties of the loss function in the weight space. The prominent optimization methods are designed to uncover flat minima, such as sharpness-aware minimization (SAM) [20] or stochastic weight averaging (SWA) [29]. Therefore, we apply SAM during the warm-up training and calculate geometric generalization measures, including metrics such as the top Hessian value " + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "inline_equation", + "content": "\\lambda_{max}" + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "text", + "content": ", the ratio of Hessian " + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "inline_equation", + "content": "\\lambda_{max} / \\lambda_5" + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "text", + "content": ", and the trace of the Hessian matrix " + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "inline_equation", + "content": "\\mathrm{Tr}(\\nabla^2\\ell (\\pmb {w}))" + }, + { + "bbox": [ + 46, + 318, + 286, + 484 + ], + "type": "text", + "content": " for both synthetic and private data. Table 5 indicates that utilizing SAM results in lower (better) metric values, not only for synthetic data but also for private data. Note that SGD even demonstrates a negative trace value on private data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 484, + 286, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 556 + ], + "type": "text", + "content": "Moreover, in Figure 4a, as the flat minimum of SAM leads to a decreased gradient norm on synthetic data, it also maintains similar results concerning private data. These results indicate that relieving overfitting to synthetic data can help the generalization of private data. Thus, the aforementioned approaches find suitable initial point of DP-SGD." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 567, + 128, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 128, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 128, + 580 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 587, + 161, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 161, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 161, + 600 + ], + "type": "text", + "content": "5.1. Experimental setup" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "We assess the effectiveness of our proposed methods using public data primarily in two datasets: CIFAR-10 and CIFAR-100. For the public dataset, we randomly sample " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " of the training data (2K samples) uniformly drawn from each class, while the remaining data are used as private samples following [43]. We then train the EDM [30] models with the 2K public data samples and build 50K synthetic datasets with EDM sampling. To address the computational burden of training diffusion and sampling, we gen" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 544, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 84 + ], + "type": "text", + "content": "erate datasets once and reuse them for classifiers as in [43]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 84, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 180 + ], + "type": "text", + "content": "For classification models, we adopt WRN-16-4, following the techniques in [12] with 16 augmentations, and use pre-trained vision transformer models following [7]. Our experiments are conducted using PyTorch libraries [63] on eight NVIDIA GeForce RTX 3090 GPUs, partially on a cloud server with four NVIDIA A100 40GB GPUs. We report the mean and standard deviation for each experiment. For the detailed settings, refer to Appendix B." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 187, + 535, + 199 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 187, + 535, + 199 + ], + "spans": [ + { + "bbox": [ + 305, + 187, + 535, + 199 + ], + "type": "text", + "content": "5.2. Classification Performance with Public Data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "content": "Effects of individual techniques We first revisit Table 1, the ablation study of sequentially employing our approaches, with a privacy budget " + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "inline_equation", + "content": "(2,10^{-5})" + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "content": "-DP on CIFAR-10. By only using better EDM synthesis without extra optimization techniques, we achieve the previous SOTA performance of " + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "inline_equation", + "content": "75.1\\%" + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "content": " [43]. Additionally, recognizing the significance of diversity in data generation, we employ cutout augmentation techniques for diversity in classification, resulting in a performance of " + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "inline_equation", + "content": "84.88\\%" + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "content": ". To mitigate potential overfitting to public information, we make use of generalization techniques. All these efforts collectively lead to an accuracy of " + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "inline_equation", + "content": "85.48\\%" + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "content": " under " + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "inline_equation", + "content": "(2,10^{-5})" + }, + { + "bbox": [ + 304, + 205, + 545, + 349 + ], + "type": "text", + "content": "-DP." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "type": "text", + "content": "Despite achieving the best performance of " + }, + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "type": "inline_equation", + "content": "85.93\\%" + }, + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "type": "text", + "content": " when combined with DG, we exclude DG in this section due to its marginal performance enhancement " + }, + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "type": "inline_equation", + "content": "(0.45\\%)" + }, + { + "bbox": [ + 304, + 349, + 545, + 397 + ], + "type": "text", + "content": " considering its extended training time, as detailed in Appendix C." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": "CIFAR-10 with public data We report the performance comparison for our method with various previous approaches on a wide range of " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\varepsilon \\in \\{1,2,3,4,6\\}" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\delta = 10^{-5}" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " in Table 6. Our approach, which incorporates EDM synthesis, augmentation, and optimization for the public data, exhibits superior classification performance when compared to existing methods including DDPM-based augmentation and extended optimizations. The accuracies of " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " (after warm-up, without private data) and " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\varepsilon = \\infty" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " (not private, with clipping) are " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "80.72\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "88.52\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "CIFAR-100 with public data We then explore the CIFAR-100 dataset for DP, which is not actively investigated without pre-trained models due to its complexity. We first train the EDM model with 2K images and generate 50K images, similar to CIFAR-10. Given the 100 classes in CIFAR-100, only 20 public samples are available per class, significantly fewer than in CIFAR-10. The FID on 50K images with EDM synthesis is 11.28, which reduces the original FID of 15.58 for replicating each public image 25 times. After the warm-up, the accuracy of synthetic images on " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "38.04\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " (46.74% on " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = \\infty" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "), while the test accuracy of using 2K public samples without synthesis on " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " is only " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "16.79\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". In Table 7, we report the accuracies by sequentially adopting the aforementioned tech" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12241" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 113, + 542, + 245 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 6. Test accuracy " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " of private training on CIFAR-10 with privacy budgets of " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\varepsilon \\in \\{1,2,3,4,6\\}" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ". The public and synthesis columns denote the Warm and WarmSyn setups, respectively. Ours employs all the techniques in Table 1, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 113, + 542, + 245 + ], + "lines": [ + { + "bbox": [ + 53, + 113, + 542, + 245 + ], + "spans": [ + { + "bbox": [ + 53, + 113, + 542, + 245 + ], + "type": "table", + "html": "
DatasetsArchitecturePublicSynthesisMethodε = 1ε = 2ε = 3ε = 4ε = 6
CIFAR -10CNN-Tanh (0.55M)XX[44]45.858.363.5--
ScatterNet (0.16M)XX[59]60.367.269.3--
DPNAS [9] (0.53M)XX[46]60.13±0.3467.23±0.1269.86±0.49--
WRN-16-4 (2.74M)XX[12]56.8±0.664.9±0.569.2±0.371.9±0.377.0±0.8
WRN-40-4 (8.94M)XX[12]56.4±0.665.9±0.570.7±0.273.5±0.678.8±0.4
✓X[2]†-68.7-73.177.2
✓X[38]†-68.7-73.577.9
WRN-16-4 (2.74M)✓✓[2]†-70.5-74.578.2
✓✓[38]†-69.1-74.178.1
✓✓[43]†-75.1-77.980.0
✓✓Ours84.30±0.1185.48±0.1286.03±0.0986.49±0.1387.06±0.24
", + "image_path": "ed8cd3db69071e892dd6df2cc90da2465efa559315191facc10d5c54b76b6f37.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 57, + 245, + 414, + 255 + ], + "lines": [ + { + "bbox": [ + 57, + 245, + 414, + 255 + ], + "spans": [ + { + "bbox": [ + 57, + 245, + 414, + 255 + ], + "type": "text", + "content": "We note the results reported in [43] to set the architecture same. All other baseline results are adopted from the original paper." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 308, + 544, + 406 + ], + "blocks": [ + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "type": "text", + "content": "Table 7. Test accuracy " + }, + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "type": "text", + "content": " of private classification on CIFAR-100 on the privacy budget of " + }, + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "type": "inline_equation", + "content": "\\varepsilon \\in \\{1,2,6,10\\}" + }, + { + "bbox": [ + 46, + 266, + 547, + 301 + ], + "type": "text", + "content": ". The public and synthesis columns indicate Warm and WarmSyn settings, respectively. We employ the techniques in Table 1 sequentially, i.e., synthesis, augmentation, and optimization. We highlight the best accuracy in **bold**." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 308, + 544, + 406 + ], + "lines": [ + { + "bbox": [ + 50, + 308, + 544, + 406 + ], + "spans": [ + { + "bbox": [ + 50, + 308, + 544, + 406 + ], + "type": "table", + "html": "
DatasetsArchitecturePublicSynthesisMethodsε = 1ε = 2ε = 6ε = 10
CIFAR -100Resnet-9XX[35]†18.124.9-40.8
Resnet-9 (6.62M)XXCold†8.3514.4229.8935.11
WRN-16-4 (2.74M)XXCold9.2818.1933.6139.09
✓XWarm20.8425.1533.4738.89
WRN-16-4 (2.74M)✓✓WarmSyn26.13±0.2031.53±0.0435.53±0.1140.82±0.10
✓✓+Augmentation40.96±0.3044.52±0.0150.47±0.0454.29±0.05
✓✓+Optimization45.93±0.0648.61±0.5954.36±0.5256.56±0.11
", + "image_path": "8b8d1c0f107cdfde5cca06585646792eee000b48f669b12dfcd14e4c4894c5c8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 406, + 432, + 416 + ], + "lines": [ + { + "bbox": [ + 55, + 406, + 432, + 416 + ], + "spans": [ + { + "bbox": [ + 55, + 406, + 432, + 416 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 55, + 406, + 432, + 416 + ], + "type": "text", + "content": " Unfortunately, their DP-SGD results are not reproducible, even when using the same hyperparameters as in the original paper." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "type": "text", + "content": "niques, where each of the approaches matters. As a result, we obtain " + }, + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "type": "inline_equation", + "content": "48.61\\%" + }, + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\varepsilon = 2" + }, + { + "bbox": [ + 46, + 429, + 288, + 453 + ], + "type": "text", + "content": " without pre-trained models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 469, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 289, + 590 + ], + "type": "text", + "content": "CIFAR-100 with pre-trained on ImageNet To push further, we demonstrate the effectiveness of our procedures when combined with pre-trained models with ID public data. We adopt the vision transformers following [7] pretrained on ImageNet [13]. Upon the pre-trained models, we sequentially perform the warm-up training with ID public data and private learning. The results in Table 8 indicate that the synthesis can boost classification performance. Within a wide range of models and privacy budgets, our methods outperform the warm settings." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Distribution shift (CIFAR-100 " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " CIFAR-10) The distribution shifts from similar but not ID public data [59] can be combined with our methods. We consider " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " of CIFAR-100 data as public to enhance the performance of CIFAR-10 as a substitute for CIFAR-10 ID public data. In Table 9, we present the classification results for both the warm and our settings, where both models are trained on the public data and synthetic data from " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " of CIFAR-100, respectively. The experimental results show that the differences in accu" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 429, + 547, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 547, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 547, + 490 + ], + "type": "text", + "content": "racies exceed " + }, + { + "bbox": [ + 304, + 429, + 547, + 490 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 429, + 547, + 490 + ], + "type": "text", + "content": ", even though neither model has observed CIFAR-10 datasets before private training with DP-SGD. This indicates that amplifying public information is meaningful in distribution shifts. Additional sensitivity analysis and ablation studies can be found in Appendix D." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": "Pre-trained diffusion models Our main idea to use synthesis for public data is flexible in practical scenarios and diverse datasets. To mitigate the drawbacks of training diffusion on each dataset, we investigated using the pre-trained diffusion models, which are trained on OOD public data. Specifically, we make use of pre-trained Stable Diffusion (SD) [52] and Boomerang sampling [40]. We fed " + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": " of public data to Boomerang editing with SD backbone for generation diversity and generated 20 images per sample for classifier training. The similar experiments are shown in Appendix D. We maintain the other training procedures the same as 'Ours', which we call 'Ours-SD'. Table 10 indicates that our framework is straightforward and effective for real-world data, and generalizable without depending on specific diffusion models. We conclude that data diversity can enhance performance when the model is not trained on specific ID public data." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "12242" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 102, + 544, + 180 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 8. Test accuracy (%) of private classification on CIFAR-100 using pre-trained models on the privacy budget of " + }, + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "\\varepsilon \\in \\{0.5,2\\}" + }, + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": ". The **bold** indicates results within the standard deviation of the top mean score." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 102, + 544, + 180 + ], + "lines": [ + { + "bbox": [ + 50, + 102, + 544, + 180 + ], + "spans": [ + { + "bbox": [ + 50, + 102, + 544, + 180 + ], + "type": "table", + "html": "
DatasetsPrivacy budgetε = 0.5ε = 2
ArchitectureColdWarmOursColdWarmOurs
CIFAR -100CrossViT small 240 (26.3M)60.50±1.7073.17±0.2477.43±0.1371.36±0.5277.00±0.2780.25±0.57
CrossViT 18 240 (42.6M)67.03±0.4677.19±0.4479.96±0.1074.28±0.2280.30±0.0282.85±0.08
DeiT base patch16 224 (85.8M)49.34±1.4979.56±0.7479.28±0.7669.09±0.1082.98±0.0483.06±0.01
CrossViT base 240 (103.9M)66.24±0.4775.59±0.2178.06±0.0575.15±0.0379.25±0.0581.14±0.15
", + "image_path": "3e9f2aa13ce0c2b64602cb9253f5adcb7663b060f993f6e8a9e8a85fec27d4d6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 51, + 229, + 282, + 285 + ], + "blocks": [ + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "lines": [ + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "text", + "content": "Table 9. Comparison of distribution shift performance on CIFAR-10 with the warm and our models trained on " + }, + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "text", + "content": " of CIFAR-100." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 229, + 282, + 285 + ], + "lines": [ + { + "bbox": [ + 51, + 229, + 282, + 285 + ], + "spans": [ + { + "bbox": [ + 51, + 229, + 282, + 285 + ], + "type": "table", + "html": "
CIFAR-100 → CIFAR-10Test Acc (%)
ε = 2ε = 4ε = 6
Warm50.65±0.3756.54±0.2059.49±1.39
Ours73.46±0.2878.60±0.1380.12±0.04
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DataMethodε = 2ε = 4ε = 6
EuroSATWarm (w/ Aug, Opt)83.6785.5286.07
WarmExt [43]84.3785.7886.07
(Land use)Ours-SD90.3791.7492.52
PathMNISTWarm (w/ Aug, Opt)89.2389.3989.54
WarmExt [43]89.0489.2589.28
(Biomedical)Ours-SD91.6491.9492.10
FairFaceWarm (w/ Aug, Opt)53.0054.5554.83
WarmExt [43]53.3354.7454.84
(w.r.t. Race)Ours-SD54.9056.1956.37
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Privacy budget ε (δ = 10-5)Optimization
DP-SGDMirror GD [2]DOPE-SGD [43]
MedianMinMedianMin
ε = 285.48±0.1785.5210.0085.5310.00
ε = 486.49±0.1386.3110.0086.6910.00
ε = 687.06±0.2486.7310.0086.8410.00
Time (ms/image)12.7012.8012.86
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The norm of gradients with (Left) synthetic dataset and (Right) private dataset with clipping during private training with different optimization methods." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 428, + 319, + 539, + 407 + ], + "blocks": [ + { + "bbox": [ + 428, + 319, + 539, + 407 + ], + "lines": [ + { + "bbox": [ + 428, + 319, + 539, + 407 + ], + "spans": [ + { + "bbox": [ + 428, + 319, + 539, + 407 + ], + "type": "image", + "image_path": "2f24f6c3ab8483bbb95aa1200eec5a2ef668bf72b4001c3b0a2e7af00ad8e6c4.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 472, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 510 + ], + "type": "text", + "content": "and private gradient norm without clipping, please refer to Appendix C. However, we believe that undiscovered extended methods can be beneficial for the WarmSyn settings." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 519, + 379, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 519, + 379, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 519, + 379, + 532 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 539, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 547, + 647 + ], + "type": "text", + "content": "In this paper, we investigate the potential of diffusion models for in-distribution public data to enhance private classification performance. We demonstrate the importance of synthetic data diversity, augmentation techniques, and the importance of well-generalizing minima for private optimization. As a limitation, we leave the experiments on more extensive and sensitive datasets and the efficient implementation of our method. We hope that this work helps leverage diffusion models to address utility-privacy trade-offs." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 662, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 662, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 305, + 662, + 547, + 711 + ], + "type": "text", + "content": "Acknowledgements This work was supported by NRF (No. 2022R1A5A6000840, No. RS-2023-00272502) and IITP (No. 2022-0-00984, No. 2021-0-01343-004) grants funded by the Korea government (MSIT)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12243" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. 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In Proceedings of the IEEE/CVF international conference on computer vision, pages 6023-6032, 2019. 5" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12246" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/9683a098-8483-47af-abcf-584b3e2dad43_content_list.json b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/9683a098-8483-47af-abcf-584b3e2dad43_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..098934073c449fbef1aada2886d51f93e4edbd46 --- /dev/null +++ b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/9683a098-8483-47af-abcf-584b3e2dad43_content_list.json @@ -0,0 +1,1965 @@ +[ + { + "type": "text", + "text": "In2SET: Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging", + "text_level": 1, + "bbox": [ + 189, + 130, + 782, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xin Wang1", + "bbox": [ + 86, + 202, + 176, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lizhi Wang $^{1*}$ Xiangtian Ma $^{1}$ $^{1}$ Beijing Institute of Technology", + "bbox": [ + 217, + 202, + 496, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Maoqing Zhang $^{1}$ Lin Zhu $^{1}$ $^{2}$ Beijing Normal University", + "bbox": [ + 519, + 202, + 772, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hua Huang", + "bbox": [ + 813, + 202, + 913, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 313, + 289 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dual-camera compressive hyperspectral imaging (DC-CHI) offers the capability to reconstruct 3D hyperspectral image (HSI) by fusing compressive and panchromatic (PAN) image, which has shown great potential for snapshot hyperspectral imaging in practice. In this paper, we introduce a novel DC-CHI reconstruction network, intra-inter similarity exploiting Transformer (In2SET). Our key insight is to make full use of the PAN image to assist the reconstruction. To this end, we propose to use the intra-similarity within the PAN image as a proxy for approximating the intra-similarity in the original HSI, thereby offering an enhanced content prior for more accurate HSI reconstruction. Furthermore, we propose to use the inter-similarity to align the features between HSI and PAN images, thereby maintaining semantic consistency between the two modalities during the reconstruction process. By integrating In2SET into a PAN-guided deep unrolling (PGDU) framework, our method substantially enhances the spatial-spectral fidelity and detail of the reconstructed images, providing a more comprehensive and accurate depiction of the scene. Experiments conducted on both real and simulated datasets demonstrate that our approach consistently outperforms existing state-of-the-art methods in terms of reconstruction quality and computational complexity. The code is available at https://github.com/2JONAS/In2SET.", + "bbox": [ + 76, + 306, + 473, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 713, + 209, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyperspectral imaging collects and processes scene information by dividing the whole spectrum into tens or hundreds of bands [15, 29, 57]. Owing to the capability of detailed scene representation, this technique has been widely adopted in many fields, e.g., medical diagnosis, health care, remote sensing [5, 11, 28, 37], and various computer vision tasks, e.g., recognition, classification, segmentation [26, 35, 49].", + "bbox": [ + 75, + 739, + 468, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The hyperspectral image (HSI) inherently possesses a", + "bbox": [ + 94, + 861, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c7d72ef2e27da3c06045d8b5628b71f0002bbe78f6aa2119931cdbf0c9e3c118.jpg", + "image_caption": [ + "Figure 1. Illustration of the proposed In2SET method for hyperspectral image reconstruction. (a) Intra-Similarity: extraction and application of spatial attention maps from the PAN image to enhance the spatial resolution of the reconstructed HSI. (b) Inter-Similarity: utilization of semantic features from the HSI and PAN image, scored by their consistency, to inform and refine the reconstruction of HSI." + ], + "image_footnote": [], + "bbox": [ + 506, + 273, + 885, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "three-dimensional (3D) structure, comprising two dimensions of spatial information and one dimension of spectral information. Consequently, existing 2D imaging sensors lack the capability to directly capture this complete 3D signal. With the rapid progress in computational photography, snapshot spectral imagers have been developed to enable hyperspectral imaging in dynamic scenes [12, 25, 53]. The coded aperture snapshot spectral imaging (CASSI) [2, 19, 38], serving as a representative prototype of snapshot spectral imagers, captures one compressive image that encodes the spectral information by leveraging a decorated optical system. Inspired by multi-modal image fusion techniques, dual-camera compressive hyperspectral imaging (DCCHI) [39, 40, 43] upgrades the original CASSI by adding a panchromatic (PAN) camera to supply spatial information lost in CASSI. As a result, DCCHI can achieve more accurate reconstructions of HSI by fusing the compressive and PAN images compared to CASSI, which has shown great potential for snapshot hyperspectral imaging in practice.", + "bbox": [ + 496, + 563, + 893, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The significant challenge of DCCHI lies in the HSI reconstruction method, where the key factor that determines", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author: Lizhi Wang (wanglizhi@bit.edu.cn)", + "bbox": [ + 94, + 886, + 419, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24881", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the reconstruction performance is the ability to model HSI priors. Early methods mainly rely on general image priors such as smoothness[4, 39, 51], sparsity[17, 41, 52], low-rank[18, 30, 56], and non-local similarity[20, 42], which ignore the continuous and complete spatial characteristics of PAN images, a feature that could provide stronger image priors.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, some PAN-guided methods like ANSR [42, 45], PFusion [21], and PIDS [13] have utilized PAN image as prior information to guide the reconstruction of HSI. While these approaches have demonstrated merit, their performance is limited by the following two reasons: firstly, current PAN-guided methods rely on handcrafted prior constraints, which lack a precise depiction of the intrinsic structures of HSI and often require manual parameter tuning. Consequently, when dealing with complex scenes, these methods tend to produce degraded reconstruction quality. Secondly, current PAN-guided methods typically model inter-modality correlations between PAN and HSI images from a single perspective, such as using edge information from the PAN images to constrain the HSI edges [13] or employing PAN image content to enrich HSI spatial detail [21]. However, HSI exhibits multifaceted consistency with PAN images across various aspects such as structure, texture, luminance, contrast, and semantic content. Relying on one constraint may not fully exploit the comprehensive spatial-semantic guidance offered by the PAN image. In summary, accurately leveraging PAN image-guided prior modeling for HSI reconstruction is the key to further improving reconstruction quality.", + "bbox": [ + 75, + 199, + 470, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose an intra-inter similarity exploiting Transformer (In2SET) for DCCHI. The proposed In2SET module is integrated into a PAN-guided deep unrolling (PGDU) framework for reconstruction. The PGDU makes use of a multi-scale feature pyramid extracted from the PAN image as guidance. This feature pyramid provides hierarchical representations of the PAN at different resolutions, allowing the network to capture both global context and fine details, resulting in improved spatial fidelity and detail in the reconstructed images.", + "bbox": [ + 75, + 550, + 468, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our key insight is to make full use of the PAN image to assist the reconstruction. The In2SET is based on two observations: (1) given the large redundancy in both the spatial and the spectral dimensions, intra-similarity exist ubiquitously within HSI. Since the original HSI is not available in practice, intra-similarity needs to be computed based on intermediate reconstruction results. However, relying on these intermediate results for intra-similarity calculations introduces unreliability. Fortunately, the PAN image can be regarded as the integral of all spectral bands and provides a natural reference for estimating the intra-similarity in the original HSI. Thus, we propose to employ the intrasimilarity in the PAN image as an approximation proxy for", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the intra-similarity in the original HSI, which provides an enhanced content prior for HSI reconstruction. (2) Since the HSI and the PAN image describe the same scenes, inter-similarity should exist between the HSI and the PAN image, considering semantic information. Inter-similarity, serving as a scorer, assigns higher weights to features in areas of the HSI that are more similar to the corresponding areas in the PAN image, thereby improving feature representation in those areas and minimizing uncertainty and risk in the reconstruction process. This capability enables the reconstruction of the highly ill-posed inverse problem in a more confidently supervised manner, providing new contextual information for HSI reconstruction.", + "bbox": [ + 496, + 90, + 890, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a nutshell, this work integrates intra-similarity and inter-similarity with the advanced Transformer mechanism, specifically for DCCHI, resulting in high-fidelity HSI reconstruction. The main contributions of this work are as follows:", + "bbox": [ + 496, + 287, + 890, + 362 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the PGDU, which employs the feature pyramid from the PAN image to guide the reconstruction of the HSI.", + "- We propose the In2SET, which employs a novel attention mechanism, specifically designed to concurrently capture both intra-similarity and inter-similarity between spectral and PAN images.", + "- Experiments on real and simulated data demonstrate that our method consistently outperforms state-of-the-art approaches." + ], + "bbox": [ + 517, + 367, + 890, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 532, + 640, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This section provides an overview of the advancements in HSI reconstruction, focusing on three pivotal areas: handcrafted HSI priors modeling, data-driven HSI priors modeling, and PAN-guided HSI reconstruction.", + "bbox": [ + 496, + 559, + 890, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Hand-Crafted HSI Priors Modeling", + "text_level": 1, + "bbox": [ + 498, + 630, + 810, + 647 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early HSI reconstruction relied heavily on hand-crafted priors. Total Variation (TV) regularization [39, 54, 55] utilized the piecewise smoothness of images to constrain TV, albeit at the risk of suppressing important high-frequency structural details. Sparse representation techniques [3, 41, 52] have been employed, focusing on constructing dictionaries to model image sparsity. Low-rank priors [30, 47, 56] have been applied, designed to capture contextual information in high-dimensional data. However, these hand-crafted methods often required extensive manual parameter tuning and struggled to represent complex data scenarios effectively.", + "bbox": [ + 496, + 654, + 890, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Data-Driven HSI Priors Modeling", + "text_level": 1, + "bbox": [ + 500, + 830, + 797, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The advent of deep learning has revolutionized the field of HSI reconstruction. Models such as HyperReconNet [44], $\\lambda$ -net [33], TSA-Net [31], DNU [46], DGSMP [23] and", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24882", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "PnP-DIP-HSI [32] have markedly improved reconstruction quality by modeling HSI data prior knowledge. Furthermore, the introduction of Transformer-based methods like MST [7], CST [6], DAU [9], RDLUF [16], and PADUT [27] has led to even more significant advances in reconstruction performance. Benefiting from the attention mechanism, Transformers can efficiently model both spatial and spectral similarities within HSI data, enabling a more flexible handling of input data and providing a richer feature representation for HSI reconstruction.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. PAN-Guided HSI Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 255, + 369, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The integration of PAN guidance in HSI reconstruction represents a significant stride in addressing the inherent limitations of traditional CASSI. ANSR[42, 45] proposed an adaptive non-local sparse representation model, guided by the PAN image. PFusion[21] leveraged RGB measurements for spatial coefficient estimation and CASSI measurements for spectral basis acquisition. It features a patch processing strategy to enhance the spectral low-rank property, optimizing the model efficiently without iterative methods or a spectral sensing matrix. PIDS[13] utilized the RGB measurement as a prior image to enhance semantic correspondence between HSI and the PAN image. These methods have marked significant advancements in the field. However, they often require manual parameter tuning and fail to leverage the rich spatial context and detailed features embedded within the PAN image, suggesting potential areas for further improvements in reconstruction.", + "bbox": [ + 75, + 279, + 468, + 535 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our motivation is to utilize the spatial semantic information provided by the PAN image to improve the HSI reconstruction result in DCCHI. We aim to develop a method that combines the strengths of PAN guidance to model the intra-inter similarity for more accurate reconstruction.", + "bbox": [ + 75, + 537, + 468, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. PGDU", + "text_level": 1, + "bbox": [ + 76, + 630, + 156, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. DCCHI Forward Model", + "text_level": 1, + "bbox": [ + 76, + 656, + 299, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DCCHI consists of a beam splitter, a CASSI branch, and a PAN camera branch, as shown in Figure 2. The beam splitter divides the incident light from the scene into two equal-intensity parts. One part of the light is captured by CASSI, which undergoes spatial modulation and spectral modulation to form the CASSI measurement. The other part of the light is directly captured by the PAN camera.", + "bbox": [ + 75, + 680, + 468, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal{X} \\in \\mathbb{R}^{H \\times W \\times C}$ represent the spectral image of the target scene, where $H$ , $W$ , and $C$ are the height, width, and number of spectral bands, respectively. The spatial and spectral modulation in CASSI is given by", + "bbox": [ + 75, + 786, + 468, + 848 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} ^ {\\mathbf {c}} = \\sum_ {c = 1} ^ {C} \\operatorname {s h i f t} (\\phi \\odot \\mathcal {X} [:,: c ]) + \\mathbf {V} ^ {\\mathbf {c}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 862, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e538731b52e1f510bc135ce8279593ff0139ac3d56a2704f24cb98c1838c93aa.jpg", + "image_caption": [ + "Figure 2. The dual-camera compressive hyperspectral imaging system." + ], + "image_footnote": [], + "bbox": [ + 526, + 88, + 874, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\phi$ is the transmission intensity of the coded aperture, represented as $\\phi \\in \\mathbb{R}^{H\\times W}$ , shift $(\\cdot)$ indicates the spectral modulation caused by the dispersion prism, $\\mathbf{Y}^{\\mathrm{c}}$ is the image captured by the CASSI branch, and $\\mathbf{V}^{\\mathrm{c}}$ is regarded as Gaussian noise in CASSI.", + "bbox": [ + 498, + 340, + 890, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To simplify to a matrix-vector form, the imaging model of the CASSI branch is represented as", + "bbox": [ + 498, + 416, + 890, + 446 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} ^ {\\mathrm {c}} = \\boldsymbol {\\Phi} ^ {\\mathrm {c}} \\mathbf {x} + \\mathbf {v} ^ {\\mathrm {c}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 453, + 890, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Phi^{\\mathbf{c}}$ denotes the imaging model of the CASSI branch sensing matrix, $\\mathbf{y}^{\\mathbf{c}}$ is the vector form of $\\mathbf{Y}^{\\mathbf{c}}$ , $\\mathbf{x}$ is the vector form of $\\mathcal{X}$ , and $\\mathbf{v}^{\\mathbf{c}}$ is the vector form of $\\mathbf{V}^{\\mathbf{c}}$ .", + "bbox": [ + 498, + 476, + 890, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Correspondingly, the imaging model of the PAN camera branch is described by", + "bbox": [ + 498, + 521, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} ^ {\\mathrm {p}} = \\boldsymbol {\\Phi} ^ {\\mathrm {p}} \\mathbf {x} + \\mathbf {v} ^ {\\mathrm {p}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 558, + 890, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Phi^{\\mathbf{P}}$ denotes the imaging model of the PAN camera branch sensing matrix, determined by the spectral response of the sensor, $\\mathbf{y}^{\\mathrm{c}}$ is the vector form of PAN measurement, and $\\mathbf{v}^{\\mathrm{P}}$ is regarded as Gaussian noise in the PAN measurement. To connect the imaging models to the subsequent discussion, we define $\\mathbf{y}$ , $\\Phi$ , and $\\mathbf{v}$ as", + "bbox": [ + 496, + 580, + 890, + 671 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = \\left[ \\begin{array}{l} \\mathbf {y} ^ {\\mathrm {c}} \\\\ \\mathbf {y} ^ {\\mathrm {p}} \\end{array} \\right], \\quad \\boldsymbol {\\Phi} = \\left[ \\begin{array}{l} \\boldsymbol {\\Phi} ^ {\\mathrm {c}} \\\\ \\boldsymbol {\\Phi} ^ {\\mathrm {p}} \\end{array} \\right], \\quad \\mathbf {v} = \\left[ \\begin{array}{l} \\mathbf {v} ^ {\\mathrm {c}} \\\\ \\mathbf {v} ^ {\\mathrm {p}} \\end{array} \\right]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 676, + 890, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using the above definitions, the imaging model can be expressed as", + "bbox": [ + 498, + 715, + 890, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = \\boldsymbol {\\Phi} \\mathbf {x} + \\mathbf {v}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 744, + 890, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Phi$ is a sensing matrix in $\\mathbb{R}^{M\\times N}$ that encodes the system mapping from the original scene $\\mathbf{x}$ to the measurements $\\mathbf{y}$ . $\\mathbf{y}\\in \\mathbb{R}^{M\\times 1}$ , $\\mathbf{x}\\in \\mathbb{R}^{N\\times 1}$ , and $\\Phi \\in \\mathbb{R}^{M\\times N}$ . The dimensions $M$ and $N$ are defined as follows: $M$ is calculated as $H(W + d(C - 1)) + HW$ and $N$ is calculated as $HWC$ , where $d$ represents the dispersion step size. It is important to note that in the context of HSI reconstruction, $M$ is typically much smaller than $N$ , highlighting that the HSI reconstruction task in DCCHI is an ill-posed problem.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24883", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/aabaf940b7620b995bd7df05727d69f8a09ebc27155e27a02f2534ca7932786f.jpg", + "image_caption": [ + "Figure 3. Overview of PGDU. The InitialNet initiates the process with compressive measurements and sensing matrix, followed by a series of stages each containing a conjugate gradient (CG) block and an In2SET denoiser." + ], + "image_footnote": [], + "bbox": [ + 147, + 89, + 823, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Reconstruction Framework", + "text_level": 1, + "bbox": [ + 76, + 364, + 326, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared to learn a brute-force mapping between HSI x and measurement y, model-based methods have potential in compressive imaging due to fully considering the imaging model. Model-based methods usually formulate HSI reconstruction as a Bayesian inference challenge, solving Eq. (5) under a unified Maximum A Posteriori (MAP) framework. Mathematically, the optimization problem for HSI reconstruction could be expressed as", + "bbox": [ + 75, + 388, + 470, + 508 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = \\arg \\min _ {\\mathbf {x}} \\frac {1}{2} \\| \\mathbf {y} - \\boldsymbol {\\Phi} \\mathbf {x} \\| _ {2} ^ {2} + \\eta J (\\mathbf {x}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 511, + 468, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $J(\\mathbf{x})$ represents regularization. The parameter $\\eta$ is a regularization coefficient, controlling the trade-off between data fidelity and the regularization term imposed by $J(\\mathbf{x})$ .", + "bbox": [ + 75, + 541, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve the optimization problem shown in Eq. (6), we design the PGDU based on the physical structure of DC-CHI, as shown in Figure 3. Utilizing the half quadratic splitting (HQS) method, we decompose the optimization problem into two sub-problems: the data fidelity term, as shown in Eq. (7); and the prior term, as shown in Eq. (8).", + "bbox": [ + 75, + 585, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} ^ {k + 1} = \\arg \\min _ {\\mathbf {x}} \\left\\| \\mathbf {y} - \\boldsymbol {\\Phi} \\mathbf {x} \\right\\| _ {2} ^ {2} + \\mu^ {k + 1} \\left\\| \\mathbf {z} ^ {k} - \\mathbf {x} \\right\\| _ {2} ^ {2}, \\quad (7)\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 679, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} ^ {k + 1} = \\arg \\min _ {\\mathbf {z}} \\frac {1}{2} \\mu^ {k + 1} \\left\\| \\mathbf {z} - \\mathbf {x} ^ {k + 1} \\right\\| _ {2} ^ {2} + \\eta^ {k + 1} J (\\mathbf {z}), (8)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 717, + 468, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the superscript $k$ indicates the stage index number, and $\\mathbf{z}$ is an auxiliary variable introduced to facilitate the optimization. The parameter $\\mu^{k + 1}$ is a relaxation parameter that governs the alignment between the current estimate $\\mathbf{x}$ and the auxiliary variable $\\mathbf{z}$ . The parameter $\\eta^{k + 1}$ is a stage-specific parameter for the regularization coefficient $\\eta$ .", + "bbox": [ + 75, + 750, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The data fidelity term can be directly calculated in closed form, as demonstrated in Eq. (9).", + "bbox": [ + 76, + 840, + 468, + 871 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} ^ {k + 1} = \\left(\\boldsymbol {\\Phi} ^ {\\mathrm {T}} \\boldsymbol {\\Phi} + \\mu \\mathbf {I}\\right) ^ {- 1} \\left(\\boldsymbol {\\Phi} ^ {\\mathrm {T}} \\mathbf {y} + \\mu^ {k + 1} \\mathbf {z} ^ {k}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 875, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in the context of HSI reconstruction in CASSI, the matrix $\\Phi^{\\mathsf{T}}\\Phi$ is strictly diagonal. However, with the addition of the PAN camera branch in DCCHI, the matrix $\\Phi^{\\mathsf{T}}\\Phi$ becomes only diagonally dominant, and thus a closed-form solution cannot be explicitly calculated.", + "bbox": [ + 498, + 364, + 890, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the non-diagonal form of $\\Phi^{\\mathrm{T}}\\Phi$ , we employ the conjugate gradient (CG) method [34] for the efficient resolution of the data fidelity term. The CG method is well suited for this problem due to its effectiveness in solving large-scale, sparse linear systems.", + "bbox": [ + 498, + 441, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To fully explore the guidance of the PAN image $\\mathbf{y}^{\\mathbb{P}}$ on prior term, we design a PAN-guided Gaussian denoiser to estimate $\\mathbf{z}^{k + 1}$ . This is formulated as Eq. (10):", + "bbox": [ + 498, + 527, + 890, + 574 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} ^ {k + 1} = \\operatorname {D e n o i s e r} _ {k + 1} \\left(\\mathbf {x} ^ {k + 1}, \\mathbf {G F E} (\\mathbf {y} ^ {\\mathbf {p}}), \\sigma^ {k + 1}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 595, + 890, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{GFE}(\\mathbf{y}^{\\mathrm{P}})$ serves as structural guidance for the denoising, which incorporates multi-scale spatial details from the high-resolution $\\mathbf{y}^{\\mathrm{P}}$ data into the denoiser, aiming to refine the fidelity of the reconstructed HSI by adding contextual information. The Gaussian noise level of the denoiser, denoted as $\\sigma^{k + 1}$ , is equal to $\\sqrt{\\eta^{k + 1} / \\mu^{k + 1}}$ . The $\\mu^{k + 1}$ and $\\sigma^{k + 1}$ are the elements of vectors $\\pmb{\\mu}$ and $\\pmb{\\sigma}$ , which are inferred by the InitialNet of PGDU.", + "bbox": [ + 498, + 637, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The feature extraction from $\\mathbf{y}^{\\mathrm{P}}$ is delineated as follows: within the unrolling framework, the feature representation of $\\mathbf{y}^{\\mathrm{P}}$ is extracted singularly and iteratively shared across multiple stages. A stack of convolutional blocks is utilized to harvest feature maps at varying resolutions, assembling a guided feature pyramid $[\\mathbf{G}_1,\\mathbf{G}_2,\\mathbf{G}_3]$ . The guided feature pyramid is integral to the subsequent denoising stage, aiding in the preservation of intricate spatial details during the denoising.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24884", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2785e85d7758ada156f21e37d991e91e4a3b4c67dc46b540e515ca69d9aa0926.jpg", + "image_caption": [ + "(a) In2SET" + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 361, + 343 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/405407587229aa573a3aa7b47662399b913c4ebcb6febdf2b82af77ac289e540.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 370, + 89, + 883, + 232 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/19776c7f9b5c51cf5ff1b9ad526c2878024d9c5c9b3ad577010874ebf7b8bf04.jpg", + "image_caption": [ + "Figure 4. Diagram of In2SET architecture. (a) The U-shaped In2SET structure. (b) In2AB, consisting of two normalization layers, an intra-similarity attention module, an inter-similarity attention module, and an FFN layer. (c) The components of NPL. (d) The multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S). (e) The cosine similarity reweighting (CRW) mechanism." + ], + "image_footnote": [], + "bbox": [ + 367, + 237, + 883, + 373 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. In2SET", + "text_level": 1, + "bbox": [ + 76, + 472, + 166, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Overall Architecture", + "text_level": 1, + "bbox": [ + 76, + 497, + 272, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we introduce the denoiser In2SET within the PGDU framework. As shown in Figure 4 (a), the proposed In2SET adopts a U-shaped architecture [36], involving the intra-inter attention block (In2AB) as the foundational units. This architecture employs multi-scale feature extraction coupled with skip connections between the encoder and decoder, enhancing the efficiency in information processing and feature extraction. To be specific, the denoiser initializes feature map $\\mathbf{X}$ from the spectral image $\\mathbf{x}^{k + 1}$ and the noise level $\\sigma^{k + 1}$ , passing through a convolutional layer with a kernel size of $3\\times 3$ . The input fed into each In2AB consists of guided feature $\\mathbf{G_i}$ , feature maps extracted from the PAN image, and HSI feature $\\mathbf{X}$ . The denoised image $\\mathbf{z}^{k + 1}$ is the sum of $\\mathbf{x}^{k + 1}$ and the output of the last In2AB, calculated by a convolutional layer with a kernel size of $3\\times 3$ . The In2AB structure is shown in Figure 4 (b). Our In2AB module includes two normalization layers, one intra-similarity attention module, one intersimilarity attention module, and one feed-forward fully connected (FFN) layer. In the following, we introduce the detail of the intra-similarity and inter-similarity.", + "bbox": [ + 75, + 521, + 472, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Intra-Similarity Attention", + "text_level": 1, + "bbox": [ + 76, + 847, + 313, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our intra-similarity attention module is grounded on two key principles: firstly, for exploring intra-spatial similarity,", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the comprehensive and continuous spatial data provided by the PAN image are invaluable. This allows the spatial similarity in the PAN image to serve as an effective proxy for approximating the spatial similarity of the HSI. Secondly, in addressing intra-spectral similarity, analyzing the reconstructed HSI becomes significantly more effective, given the PAN image's deficiency in spectral color information.", + "bbox": [ + 496, + 474, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Figure 4 (b), our intra-similarity attention module includes two branches: multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S), representing the exploration of spectral and spatial self-similarity, respectively. The MHA-C is based on the work in MST [7], which has been demonstrated to effectively explore spectral self-similarity.", + "bbox": [ + 496, + 580, + 890, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The input features $\\mathbf{X}$ and $\\mathbf{G}$ have dimensions $\\mathbb{R}^{H\\times W\\times C}$ and $\\mathbb{R}^{H\\times W\\times \\hat{C}}$ , respectively, where $\\hat{C} = \\frac{C}{2}$ . After normalization and partitioning, the dimensions become $\\mathbb{R}^{B\\times N\\times C}$ and $\\mathbb{R}^{B\\times N\\times \\hat{C}}$ . In the first and last layers of HSAB within In2SET, $B = \\frac{HW}{M^2}$ and $N = M^2$ . For the remaining layers, dimensions are recalibrated to $B = M^2$ and $N = \\frac{HW}{M^2}$ . Following linear projection as shown in Eq. (11) and Eq. (12).", + "bbox": [ + 496, + 685, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {1}, \\mathbf {K} _ {1}, \\mathbf {V} _ {1}, \\mathbf {V} _ {2} = L _ {Q _ {1}, K _ {1}, V _ {1}, V _ {2}} (\\mathbf {X}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 820, + 890, + 837 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {2}, \\mathbf {K} _ {2} = L _ {Q _ {2}, K _ {2}} (\\mathbf {G}), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 861, + 890, + 877 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{X}$ is projected to $\\mathbf{Q}_1, \\mathbf{K}_1, \\mathbf{V}_1 \\in \\mathbb{R}^{B \\times \\hat{C} \\times N}$ and", + "bbox": [ + 500, + 883, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24885", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6dd93b94fe772ca8c68618a95cdc7dffbe05733efd20ab69d962e91d6b196aeb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodGFLOPsSceneAverage
01020304050607080910
PFusion-RGB [21]-40.0938.8438.7046.6532.0737.1239.7436.7534.5235.5338.00
0.9790.9680.9660.9360.9800.9800.9640.9650.9310.9790.965
PIDS-RGB [13]-42.0940.0841.5048.5540.0539.0036.6337.0238.8238.6440.24
0.9830.9490.9680.9890.9820.9740.9400.9480.9530.9800.967
TV-DC [39]-35.8133.2231.0740.1133.3234.6231.0932.3129.3633.8433.47
0.9470.8850.8790.9470.9440.9430.8850.9160.8620.9530.910
PIDS-DC [13]-39.8237.0737.7246.7837.4537.7432.9031.6634.3538.5837.41
0.9770.9210.9500.9780.9730.9630.8960.9150.9020.9720.945
BiSRNet-DC [10]1.3335.0234.1331.5035.8833.7035.5832.3132.7331.3734.4833.67
0.9450.9140.8830.8950.9350.9250.9000.9030.8990.9360.914
CST-DC [6]25.4037.4438.9136.7942.2736.5738.9136.8735.9135.8737.9337.75
0.9750.9780.9690.9830.9820.9840.9670.9800.9730.9900.978
HDNet-DC [22]144.3138.0639.7938.2142.7937.2239.2637.4136.5136.6437.5238.34
0.9760.9820.9730.9830.9830.9860.9680.9820.9760.9880.980
MST-DC [7]25.7738.3840.4537.6342.8837.7239.6637.5637.4037.8638.1038.76
0.9760.9760.9660.9750.9780.9760.9650.9710.9710.9810.974
MST++-DC [8]17.6938.3840.4737.7043.8837.7539.4237.4837.3838.8239.0439.03
0.9770.9800.9680.9840.9830.9850.9640.9820.9800.9890.980
DAUHST-DC-2stg [9]16.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0440.22
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.983
DAUHST-DC-3stg [9]24.7040.2243.5241.7447.0738.8140.1639.8638.2140.6339.3240.95
0.9830.9890.9810.9930.9850.9870.9780.9810.9830.9900.985
DAUHST-DC-5stg [9]40.5140.7444.0041.5846.8439.6640.8940.2138.7239.9840.1041.27
0.9840.9890.9810.9910.9860.9870.9790.9830.9820.9890.916
DAUHST-DC-9stg [9]72.1141.5945.1943.4748.9240.2741.1740.7340.1143.5041.3342.62
0.9850.9910.9840.9930.9880.9880.9790.9860.9880.9900.987
In2SET-2stg (Ours)14.3540.3342.3040.3447.2439.4240.6139.4638.4240.3739.9640.84
0.9830.9850.9770.9910.9860.9860.9750.9790.9810.9880.983
In2SET-3stg (Ours)20.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0441.35
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.984
In2SET-5stg (Ours)33.6641.1344.4342.7447.2940.3340.9540.4939.1542.0739.4441.80
0.9850.9900.9830.9930.9880.9870.9790.9820.9850.9870.985
In2SET-9stg (Ours)59.4042.5646.4244.5550.6342.0142.4941.5940.5343.8342.3343.69
0.9890.9940.9860.9960.9920.9910.9830.9890.9900.9940.990
", + "bbox": [ + 135, + 88, + 831, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparison of In2SET with SOTA DCCHI methods across 10 simulated scenes, including FLOPS, PSNR (upper entry), and SSIM (lower entry). \"Method-RGB\" indicates the use of RGB observations, while \"Method-DC\" denotes grayscale observations in PAN images. It is noted that \"Method-DC\" is modified from other HSI reconstruction method for the DCCHI reconstruction task.", + "bbox": [ + 75, + 518, + 893, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathbf{V}_2 \\in \\mathbb{R}^{B \\times N \\times \\hat{C}}$ . $\\mathbf{G}$ is projected to $\\mathbf{Q}_2$ , $\\mathbf{K}_2 \\in \\mathbb{R}^{B \\times N \\times \\hat{C}}$ .", + "bbox": [ + 76, + 575, + 454, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The computations of MHA-C and MHA-S can be represented by Eq. (13) and Eq. (14),", + "bbox": [ + 76, + 594, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {1} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {1} \\mathbf {K} _ {1} ^ {T}}{\\sqrt {d _ {h 1}}} + \\mathbf {P} _ {1}\\right) \\mathbf {V} _ {1}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 635, + 468, + 671 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {2} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {2} \\mathbf {K} _ {2} ^ {T}}{\\sqrt {d _ {h 2}}} + \\mathbf {P} _ {2}\\right) \\mathbf {V} _ {2}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 685, + 468, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\sqrt{d_{h1}}$ and $\\sqrt{d_{h2}}$ are scalars as defined in [9], $\\mathbf{P}_1 \\in \\mathbb{R}^{B \\times \\hat{C} \\times \\hat{C}}$ , and $\\mathbf{P}_2 \\in \\mathbb{R}^{B \\times N \\times N}$ denote learnable positional encodings.", + "bbox": [ + 76, + 727, + 468, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The output of intra-attention $\\mathbf{X}_{\\mathrm{intra}}$ can be obtained by Eq. (15).", + "bbox": [ + 76, + 773, + 468, + 805 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {\\text {i n t r a}} = \\operatorname {C o n c a t} \\left(\\mathbf {X} _ {1}, \\mathbf {X} _ {2}\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 806, + 468, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Inter-Similarity Attention", + "text_level": 1, + "bbox": [ + 76, + 830, + 313, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We establish our inter-similarity attention module based on one principle: the shallow semantic features of the PAN image and the corresponding HSI area are similar, including", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "consistency in texture, shape features, and low-level image attributes (brightness and contrast). The credibility of the reconstructed area is directly proportional to this consistency. Inter-similarity attention explores cross-modal similarity using cosine similarity reweighting (CRW).", + "bbox": [ + 496, + 578, + 890, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After exploiting intra-similarity, the output of the intrasimilarity attention module $\\mathbf{X}_{\\mathrm{intra}}$ is projected to obtain $\\mathbf{K}_3$ and $\\mathbf{V}_3$ ,", + "bbox": [ + 496, + 654, + 890, + 699 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {K} _ {3}, \\mathbf {V} _ {3} = L _ {K _ {3}, V _ {3}} \\left(\\mathbf {X} _ {\\text {i n t r a}}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 708, + 890, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{K}_3\\in \\mathbb{R}^{B\\times N\\times \\hat{C}}$ and $\\mathbf{V_3}\\in \\mathbb{R}^{B\\times N\\times C}$", + "bbox": [ + 496, + 732, + 799, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, the computations of CRW can be represented as follows:", + "bbox": [ + 496, + 750, + 890, + 776 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {\\text {i n t e r}} = \\frac {\\mathbf {Q} _ {2} \\cdot \\mathbf {K} _ {3}}{\\| \\mathbf {Q} _ {2} \\| \\| \\mathbf {K} _ {3} \\|} \\odot \\mathbf {V} _ {3}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 773, + 890, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the cosine similarity computed along the last dimension between $\\mathbf{Q}_2$ and $\\mathbf{K}_3$ quantifies the feature alignment in corresponding areas. A higher similarity score reflects a stronger feature correspondence, which, in turn, informs the enhanced weighting of $\\mathbf{V}_3$ , improving the fidelity of the region being reconstructed.", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24886", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we begin by introducing detailing the network training process. Subsequently, we evaluate the performance of In2SET on both simulation and real-world DC-CHI datasets. Then, we validate the effectiveness of the intra-similarity block using statistical simulation data. Finally, we perform an ablation study to demonstrate the effectiveness of our proposed method.", + "bbox": [ + 75, + 114, + 467, + 220 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Simulation Dataset. Two distinct datasets are used: CAVE [50] and KAIST [14]. The CAVE dataset is made up of 32 hyperspectral images with $512 \\times 512$ spatial resolution. The KAIST dataset contains 30 hyperspectral images, each with a larger spatial dimension of $2704 \\times 3376$ . The CAVE dataset is used as the training data, while a subset of 10 scenes crop from the KAIST dataset is used for the evaluation phase, in accordance with the protocols established in references [7, 9, 22, 23, 31].", + "bbox": [ + 75, + 220, + 467, + 356 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation. Our method is implemented with Pytorch and trained with Adam [24] optimizer for 300 epochs. During training, the learning rate is $4 \\times 10^{-4}$ using the cosine annealing scheduler, and the loss function for network training is $L_{1}$ loss. We randomly extract patches from 3D HSI cubes to serve as training samples. The dimensions of these patches are $256 \\times 256 \\times 28$ for the simulation experiment and $350 \\times 260 \\times 26$ for the real-world experiment. In simulation imaging model, we configure a dispersion shift step $d$ of 2, directing the dispersion to the right. In real-word imaging model, the dispersion shift step $d$ is set to 1, with the dispersion oriented upwards.", + "bbox": [ + 75, + 358, + 467, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Simulation Data Results", + "text_level": 1, + "bbox": [ + 76, + 547, + 299, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The reconstruction quality of hyperspectral images are assessed using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) [48] metrics.", + "bbox": [ + 75, + 566, + 467, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Table 1 clearly shows that In2SET excels in all test scenarios, particularly in In2SET-9stg, achieving the best performance across all scenes with an average PSNR of $43.69\\mathrm{dB}$ and a SSIM of 0.990. This significantly surpasses model optimization methods like TV-DC and PIDS-DC. Compared to deep learning-based methods, such as various stages of DAUHST-DC [9], In2SET demonstrates remarkable superiority. In2SET-3stg achieves performance comparable to that of DAUHST-DC-5stg [9], but with only $51.3\\%$ of the cost, amounting to 20.78 GFLOPs compared to 40.50 GFLOPs.", + "bbox": [ + 75, + 613, + 467, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To facilitate a direct visual quality assessment, we analyzed the distinction between Ground Truth (GT) and the reconstructions produced by various open-source methods. Figure 5 presents reconstruction results for selected spectral bands. These results are generated from two model-based approaches, TV-DC [39] and PIDS-DC [13], five end-to-end network algorithms, BiSRNet-DC [10], CST-DC [6], HDNet-DC [22], MST-DC [7], MST++-DC [8], as well as", + "bbox": [ + 75, + 780, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/88d013d1d733f0589fc005af1e57e3bfcc4631347bfb885abc7f651afde57e8c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RMSECorrelationPSNR(dB)
CAVE0.0340.99936.28
KAIST0.0250.99635.74
ICVL0.0760.99731.10
", + "bbox": [ + 500, + 87, + 893, + 148 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e51868774c73fd6ae96a08dd7777c1585fb2fe3a322a679d79e651c80837677f.jpg", + "table_caption": [ + "Table 2. Comparison of correlation maps between HSI and PAN image, including average Root Mean Squared Error (RMSE), average correlation, and PSNR." + ], + "table_footnote": [], + "table_body": "
BaselineCRWMHA-CMHA-SPSNR(dB)SSIMGFLOPs
✓37.230.9449.87
✓✓40.050.98011.19
✓✓✓40.460.98214.06
✓✓✓✓40.840.98314.35
", + "bbox": [ + 501, + 194, + 890, + 268 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ac20894f7adec266b26cd79178ef58289cb986eabf04a2dde55c0f95bd0c2e5b.jpg", + "table_caption": [ + "Table 3. Break-down ablation study on individual components of the proposed method." + ], + "table_footnote": [], + "table_body": "
MethodsCG-1CG-2CG-5CG-10
PSNR(dB)40.4240.6640.8441.05
SSIM0.9820.9830.9830.984
FPS26.4522.7919.1613.99
", + "bbox": [ + 501, + 301, + 887, + 361 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study on iterative performance of conjugate gradient descent for data item.", + "bbox": [ + 500, + 362, + 890, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "from two deep unfolding methods, namely DAUHST-DC9stg [9] and our In2SET-9stg. The comparison underlines the exceptional ability of our In2SET approach to maintain spatial and spectral fidelity.", + "bbox": [ + 498, + 398, + 890, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We suggest that the intra similarity in PAN image can effectively approximates that in HSI. To support this, we experiment with three public datasets: CAVE [50], KAIST [14] and ICVL [1]. We compute spatial correlation maps for each scene, comparing the correlation map of the HSI with that of the corresponding PAN image. The results of this comparison are displayed in Table 2, indicating a high degree of similarity between the intra-spatial correlations in PAN images and HSI. More visual results are presented in the supplementary materials.", + "bbox": [ + 498, + 458, + 890, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Real Data Results", + "text_level": 1, + "bbox": [ + 500, + 614, + 671, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this research, we used a real-world DCCHI measurement Ninja, taken from publicly available data as detailed in reference [42]. Figure 6 illustrates the reconstruction results for four spectral bands in this scene, using various DCCHI reconstruction algorithms. The comparison highlights the superior image restoration quality of our model over other methods, validating its effectiveness and reliability in real-world applications.", + "bbox": [ + 498, + 633, + 890, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 760, + 651, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effectiveness of our proposed method, we conducted ablation studies for the In2SET method. All evaluations are conducted on simulated datasets.", + "bbox": [ + 498, + 780, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Break-down Ablation. The break-down study, as delineated in Table 3, offers a detailed examination of how each component within our proposed method influences reconstruction performance. Starting from a baseline derived by removing all ablated components from In2SET-2stg, the", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24887", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4fdaffba071a3baf544045f37e78355564be9b856be9de6229946c6aa8413306.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 94, + 254, + 156 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e002fb5489c1bb0167f529ae788b666bb9bb7cf9524d3092ff9d9c1f7524ae31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 258, + 94, + 467, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0721a1a5146317997daa72fef98305aa92f0f7c1fbcd17aaa87bb8295a17bc5e.jpg", + "image_caption": [ + "Spectral Density Curves" + ], + "image_footnote": [], + "bbox": [ + 91, + 161, + 279, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2047923affd2c5cd01ac1b182f2cc455df68e777c46ff83eb270fdffa25b2a92.jpg", + "image_caption": [ + "GT", + "In2SET-9stg (Ours)" + ], + "image_footnote": [], + "bbox": [ + 287, + 195, + 467, + 294 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47c5afafa3f83ffcf4a6ba0ad3706f369f67c94e026b1579655df722fb4d0d26.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 468, + 95, + 524, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/18cb43938eabfc758d0c5effa66d806b41a763a274e1d0208ae47b7249dd12aa.jpg", + "image_caption": [ + "MST++-DC" + ], + "image_footnote": [], + "bbox": [ + 467, + 195, + 524, + 295 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c28e373c0541351b9616adc817679e5ff3254639f8fa8b6999d4a40a4b4c8b7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 95, + 642, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/451677b7b22e19d13c77f9df830884f2f5014ea8d385623a863866928d7397a3.jpg", + "image_caption": [ + "MST-DC", + "HDNet-DC" + ], + "image_footnote": [], + "bbox": [ + 524, + 195, + 640, + 294 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 581, + 95, + 640, + 193 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 578, + 195, + 640, + 294 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3581add68cf6859ec79da727922f18409b083ae4298488920506f235807135a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 642, + 95, + 700, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/61e419328c3de8c640b9663e709af9ca569025687ac15af860830212bf33c360.jpg", + "image_caption": [ + "CST-DC" + ], + "image_footnote": [], + "bbox": [ + 642, + 195, + 700, + 294 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/13b79b7d8b92b09035534436b7db17341cad8b981c36e124bb88313f0fc6d5d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 95, + 759, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea99d9b7cc2e71cb79e0c0d799fef86aa0c0dcbdb7067e008014e57727f78a9b.jpg", + "image_caption": [ + "BiSRNet-DC" + ], + "image_footnote": [], + "bbox": [ + 700, + 195, + 759, + 294 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0cfc537ba72809e79e7e571c415a7b74099cd1506cbe3e627323b41c2d8087e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 95, + 820, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d09476c0daff9a96396fe7c8ba60c541c6859ccfa5dd4ecb745e8eccecd6da43.jpg", + "image_caption": [ + "PIDS-DC" + ], + "image_footnote": [], + "bbox": [ + 759, + 195, + 818, + 294 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e961223480e37869136544b84a9ef8359932f2365f38ba1ec1786d28a72ecec5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 820, + 95, + 877, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d582beeb41ac9de4762ff58c98fd71b1b183b58a9a6bb95bf392e88b30206de9.jpg", + "image_caption": [ + "TV-DC" + ], + "image_footnote": [], + "bbox": [ + 820, + 195, + 877, + 294 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f469dbd086c0149eb039d9dc1739035ec207fd622394439b32ef2a8346738538.jpg", + "image_caption": [ + "Figure 5. Comparative reconstruction results of different reconstruction methods for Scene 3 from the KAIST dataset at spectral bands $476.5\\mathrm{nm}$ , $536.5\\mathrm{nm}$ , $584.5\\mathrm{nm}$ , and $625.0\\mathrm{nm}$ . The spectral density curves are plotted from the blue region in the colorchecker.", + "Figure 6. Visualization of reconstruction performance across different spectral bands on real data. The spectral bands selected for comparison are $481.5\\mathrm{nm}$ , $544.0\\mathrm{nm}$ , $594.5\\mathrm{nm}$ , and $614.5\\mathrm{nm}$ ." + ], + "image_footnote": [], + "bbox": [ + 102, + 364, + 442, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model achieves a PSNR of 37.23 dB. The addition of the CRW component leads to a significant increase in PSNR by $+2.82$ dB, albeit at an increased computational cost of $+1.32$ GFLOPs. The subsequent integration of MHA-C further elevates the PSNR by $+0.41$ dB. The final inclusion of MHA-S brings an additional PSNR gain of $+0.38$ dB. These step-by-step enhancements highlight the critical role each component plays in enhancing the overall capability of the model for HSI reconstruction, demonstrating a progressive improvement in performance with each added component.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Study of CG Iterations. Table 4 presents a comparative analysis of PSNR, SSIM, and Frames Per Second (FPS) metrics across varying numbers of CG iterations for HSI reconstruction. The CG-1, which conducts a single iteration, essentially operates as a vanilla gradient descent. These experiments are conducted on a system equipped with a TITAN Xp GPU (12GB) and an Intel (R) Xeon (R) Platinum 8358P CPU @ 2.60GHz.", + "bbox": [ + 498, + 366, + 890, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "There is a clear trend of improvement in PSNR as the number of CG iterations increases from 1 to 10, with values escalating from 40.42 dB to 41.05 dB. However, an increase in iterations from CG-1 to CG-10 leads to a decrease in FPS from 26.45 dB to 13.99 dB, indicating a trade-off between reconstruction quality and computational speed. A notable observation is that CG-5 offers an optimal balance between time efficiency and performance, making it the preferred choice for our In2SET network.", + "bbox": [ + 498, + 488, + 890, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 638, + 617, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose the In2SET for DCCHI reconstruction. Our method maximizes PAN image utility for HSI reconstruction by: (1) approximating HSI intrasimilarity using PAN image, addressing the unreliability of direct computation from intermediate results. (2) Leveraging inter-similarity between HSI and PAN images to accurately reconstruct regions, providing cues for uncertain areas. Integrating In2SET into a PGDU framework allowed us to substantially enhance the spatial-spectral fidelity and detail of reconstructed images. Experiments on real and simulated datasets show that our method consistently outperforms the state-of-the-art while maintaining lower computational complexity.", + "bbox": [ + 496, + 661, + 890, + 857 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work is partially supported by the National Natural Science Foundation of China under grants 62322204, 62131003, 62072038 and 62302041.", + "bbox": [ + 498, + 858, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24888", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 118, + 173, + 133 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Boaz Arad and Ohad Ben-Shahar. Sparse recovery of hyperspectral signal from natural rgb images. 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Nature Communications, 14(1):5043, 2023. 1" + ], + "bbox": [ + 78, + 90, + 468, + 373 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "24891", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/9683a098-8483-47af-abcf-584b3e2dad43_model.json b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/9683a098-8483-47af-abcf-584b3e2dad43_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5ec6f93f3dd355deeff8f8ef1a2c2ea65f20aa55 --- /dev/null +++ b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/9683a098-8483-47af-abcf-584b3e2dad43_model.json @@ -0,0 +1,2664 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.191, + 0.131, + 0.783, + 0.177 + ], + "angle": 0, + "content": "In2SET: Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.203, + 0.178, + 0.223 + ], + "angle": 0, + "content": "Xin Wang1" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.203, + 0.498, + 0.242 + ], + "angle": 0, + "content": "Lizhi Wang\\(^{1*}\\) Xiangtian Ma\\(^{1}\\) \n\\(^{1}\\)Beijing Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.203, + 0.773, + 0.24 + ], + "angle": 0, + "content": "Maoqing Zhang\\(^{1}\\) Lin Zhu\\(^{1}\\) \n\\(^{2}\\) Beijing Normal University" + }, + { + "type": "text", + "bbox": [ + 0.815, + 0.203, + 0.915, + 0.223 + ], + "angle": 0, + "content": "Hua Huang" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.307, + 0.474, + 0.685 + ], + "angle": 0, + "content": "Dual-camera compressive hyperspectral imaging (DC-CHI) offers the capability to reconstruct 3D hyperspectral image (HSI) by fusing compressive and panchromatic (PAN) image, which has shown great potential for snapshot hyperspectral imaging in practice. In this paper, we introduce a novel DC-CHI reconstruction network, intra-inter similarity exploiting Transformer (In2SET). Our key insight is to make full use of the PAN image to assist the reconstruction. To this end, we propose to use the intra-similarity within the PAN image as a proxy for approximating the intra-similarity in the original HSI, thereby offering an enhanced content prior for more accurate HSI reconstruction. Furthermore, we propose to use the inter-similarity to align the features between HSI and PAN images, thereby maintaining semantic consistency between the two modalities during the reconstruction process. By integrating In2SET into a PAN-guided deep unrolling (PGDU) framework, our method substantially enhances the spatial-spectral fidelity and detail of the reconstructed images, providing a more comprehensive and accurate depiction of the scene. Experiments conducted on both real and simulated datasets demonstrate that our approach consistently outperforms existing state-of-the-art methods in terms of reconstruction quality and computational complexity. The code is available at https://github.com/2JONAS/In2SET." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.714, + 0.21, + 0.729 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.74, + 0.47, + 0.861 + ], + "angle": 0, + "content": "Hyperspectral imaging collects and processes scene information by dividing the whole spectrum into tens or hundreds of bands [15, 29, 57]. Owing to the capability of detailed scene representation, this technique has been widely adopted in many fields, e.g., medical diagnosis, health care, remote sensing [5, 11, 28, 37], and various computer vision tasks, e.g., recognition, classification, segmentation [26, 35, 49]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.862, + 0.47, + 0.877 + ], + "angle": 0, + "content": "The hyperspectral image (HSI) inherently possesses a" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.274, + 0.887, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.432, + 0.895, + 0.528 + ], + "angle": 0, + "content": "Figure 1. Illustration of the proposed In2SET method for hyperspectral image reconstruction. (a) Intra-Similarity: extraction and application of spatial attention maps from the PAN image to enhance the spatial resolution of the reconstructed HSI. (b) Inter-Similarity: utilization of semantic features from the HSI and PAN image, scored by their consistency, to inform and refine the reconstruction of HSI." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.895, + 0.867 + ], + "angle": 0, + "content": "three-dimensional (3D) structure, comprising two dimensions of spatial information and one dimension of spectral information. Consequently, existing 2D imaging sensors lack the capability to directly capture this complete 3D signal. With the rapid progress in computational photography, snapshot spectral imagers have been developed to enable hyperspectral imaging in dynamic scenes [12, 25, 53]. The coded aperture snapshot spectral imaging (CASSI) [2, 19, 38], serving as a representative prototype of snapshot spectral imagers, captures one compressive image that encodes the spectral information by leveraging a decorated optical system. Inspired by multi-modal image fusion techniques, dual-camera compressive hyperspectral imaging (DCCHI) [39, 40, 43] upgrades the original CASSI by adding a panchromatic (PAN) camera to supply spatial information lost in CASSI. As a result, DCCHI can achieve more accurate reconstructions of HSI by fusing the compressive and PAN images compared to CASSI, which has shown great potential for snapshot hyperspectral imaging in practice." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.87, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The significant challenge of DCCHI lies in the HSI reconstruction method, where the key factor that determines" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.42, + 0.901 + ], + "angle": 0, + "content": "*Corresponding Author: Lizhi Wang (wanglizhi@bit.edu.cn)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24881" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "the reconstruction performance is the ability to model HSI priors. Early methods mainly rely on general image priors such as smoothness[4, 39, 51], sparsity[17, 41, 52], low-rank[18, 30, 56], and non-local similarity[20, 42], which ignore the continuous and complete spatial characteristics of PAN images, a feature that could provide stronger image priors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.471, + 0.548 + ], + "angle": 0, + "content": "In recent years, some PAN-guided methods like ANSR [42, 45], PFusion [21], and PIDS [13] have utilized PAN image as prior information to guide the reconstruction of HSI. While these approaches have demonstrated merit, their performance is limited by the following two reasons: firstly, current PAN-guided methods rely on handcrafted prior constraints, which lack a precise depiction of the intrinsic structures of HSI and often require manual parameter tuning. Consequently, when dealing with complex scenes, these methods tend to produce degraded reconstruction quality. Secondly, current PAN-guided methods typically model inter-modality correlations between PAN and HSI images from a single perspective, such as using edge information from the PAN images to constrain the HSI edges [13] or employing PAN image content to enrich HSI spatial detail [21]. However, HSI exhibits multifaceted consistency with PAN images across various aspects such as structure, texture, luminance, contrast, and semantic content. Relying on one constraint may not fully exploit the comprehensive spatial-semantic guidance offered by the PAN image. In summary, accurately leveraging PAN image-guided prior modeling for HSI reconstruction is the key to further improving reconstruction quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.702 + ], + "angle": 0, + "content": "In this paper, we propose an intra-inter similarity exploiting Transformer (In2SET) for DCCHI. The proposed In2SET module is integrated into a PAN-guided deep unrolling (PGDU) framework for reconstruction. The PGDU makes use of a multi-scale feature pyramid extracted from the PAN image as guidance. This feature pyramid provides hierarchical representations of the PAN at different resolutions, allowing the network to capture both global context and fine details, resulting in improved spatial fidelity and detail in the reconstructed images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our key insight is to make full use of the PAN image to assist the reconstruction. The In2SET is based on two observations: (1) given the large redundancy in both the spatial and the spectral dimensions, intra-similarity exist ubiquitously within HSI. Since the original HSI is not available in practice, intra-similarity needs to be computed based on intermediate reconstruction results. However, relying on these intermediate results for intra-similarity calculations introduces unreliability. Fortunately, the PAN image can be regarded as the integral of all spectral bands and provides a natural reference for estimating the intra-similarity in the original HSI. Thus, we propose to employ the intrasimilarity in the PAN image as an approximation proxy for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.287 + ], + "angle": 0, + "content": "the intra-similarity in the original HSI, which provides an enhanced content prior for HSI reconstruction. (2) Since the HSI and the PAN image describe the same scenes, inter-similarity should exist between the HSI and the PAN image, considering semantic information. Inter-similarity, serving as a scorer, assigns higher weights to features in areas of the HSI that are more similar to the corresponding areas in the PAN image, thereby improving feature representation in those areas and minimizing uncertainty and risk in the reconstruction process. This capability enables the reconstruction of the highly ill-posed inverse problem in a more confidently supervised manner, providing new contextual information for HSI reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.363 + ], + "angle": 0, + "content": "In a nutshell, this work integrates intra-similarity and inter-similarity with the advanced Transformer mechanism, specifically for DCCHI, resulting in high-fidelity HSI reconstruction. The main contributions of this work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.368, + 0.891, + 0.411 + ], + "angle": 0, + "content": "- We propose the PGDU, which employs the feature pyramid from the PAN image to guide the reconstruction of the HSI." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.413, + 0.891, + 0.473 + ], + "angle": 0, + "content": "- We propose the In2SET, which employs a novel attention mechanism, specifically designed to concurrently capture both intra-similarity and inter-similarity between spectral and PAN images." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.473, + 0.891, + 0.518 + ], + "angle": 0, + "content": "- Experiments on real and simulated data demonstrate that our method consistently outperforms state-of-the-art approaches." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.368, + 0.891, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.534, + 0.642, + 0.55 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.621 + ], + "angle": 0, + "content": "This section provides an overview of the advancements in HSI reconstruction, focusing on three pivotal areas: handcrafted HSI priors modeling, data-driven HSI priors modeling, and PAN-guided HSI reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.631, + 0.812, + 0.648 + ], + "angle": 0, + "content": "2.1. Hand-Crafted HSI Priors Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Early HSI reconstruction relied heavily on hand-crafted priors. Total Variation (TV) regularization [39, 54, 55] utilized the piecewise smoothness of images to constrain TV, albeit at the risk of suppressing important high-frequency structural details. Sparse representation techniques [3, 41, 52] have been employed, focusing on constructing dictionaries to model image sparsity. Low-rank priors [30, 47, 56] have been applied, designed to capture contextual information in high-dimensional data. However, these hand-crafted methods often required extensive manual parameter tuning and struggled to represent complex data scenarios effectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.798, + 0.849 + ], + "angle": 0, + "content": "2.2. Data-Driven HSI Priors Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "The advent of deep learning has revolutionized the field of HSI reconstruction. Models such as HyperReconNet [44], \\(\\lambda\\)-net [33], TSA-Net [31], DNU [46], DGSMP [23] and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24882" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.242 + ], + "angle": 0, + "content": "PnP-DIP-HSI [32] have markedly improved reconstruction quality by modeling HSI data prior knowledge. Furthermore, the introduction of Transformer-based methods like MST [7], CST [6], DAU [9], RDLUF [16], and PADUT [27] has led to even more significant advances in reconstruction performance. Benefiting from the attention mechanism, Transformers can efficiently model both spatial and spectral similarities within HSI data, enabling a more flexible handling of input data and providing a richer feature representation for HSI reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.256, + 0.37, + 0.27 + ], + "angle": 0, + "content": "2.3. PAN-Guided HSI Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.47, + 0.536 + ], + "angle": 0, + "content": "The integration of PAN guidance in HSI reconstruction represents a significant stride in addressing the inherent limitations of traditional CASSI. ANSR[42, 45] proposed an adaptive non-local sparse representation model, guided by the PAN image. PFusion[21] leveraged RGB measurements for spatial coefficient estimation and CASSI measurements for spectral basis acquisition. It features a patch processing strategy to enhance the spectral low-rank property, optimizing the model efficiently without iterative methods or a spectral sensing matrix. PIDS[13] utilized the RGB measurement as a prior image to enhance semantic correspondence between HSI and the PAN image. These methods have marked significant advancements in the field. However, they often require manual parameter tuning and fail to leverage the rich spatial context and detailed features embedded within the PAN image, suggesting potential areas for further improvements in reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Our motivation is to utilize the spatial semantic information provided by the PAN image to improve the HSI reconstruction result in DCCHI. We aim to develop a method that combines the strengths of PAN guidance to model the intra-inter similarity for more accurate reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.631, + 0.158, + 0.646 + ], + "angle": 0, + "content": "3. PGDU" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.657, + 0.3, + 0.672 + ], + "angle": 0, + "content": "3.1. DCCHI Forward Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.469, + 0.787 + ], + "angle": 0, + "content": "DCCHI consists of a beam splitter, a CASSI branch, and a PAN camera branch, as shown in Figure 2. The beam splitter divides the incident light from the scene into two equal-intensity parts. One part of the light is captured by CASSI, which undergoes spatial modulation and spectral modulation to form the CASSI measurement. The other part of the light is directly captured by the PAN camera." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.469, + 0.849 + ], + "angle": 0, + "content": "Let \\(\\mathcal{X} \\in \\mathbb{R}^{H \\times W \\times C}\\) represent the spectral image of the target scene, where \\(H\\), \\(W\\), and \\(C\\) are the height, width, and number of spectral bands, respectively. The spatial and spectral modulation in CASSI is given by" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.863, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} ^ {\\mathbf {c}} = \\sum_ {c = 1} ^ {C} \\operatorname {s h i f t} (\\phi \\odot \\mathcal {X} [:,: c ]) + \\mathbf {V} ^ {\\mathbf {c}}, \\tag {1}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.089, + 0.875, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.307, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Figure 2. The dual-camera compressive hyperspectral imaging system." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.341, + 0.892, + 0.415 + ], + "angle": 0, + "content": "where \\(\\phi\\) is the transmission intensity of the coded aperture, represented as \\(\\phi \\in \\mathbb{R}^{H\\times W}\\), shift \\((\\cdot)\\) indicates the spectral modulation caused by the dispersion prism, \\(\\mathbf{Y}^{\\mathrm{c}}\\) is the image captured by the CASSI branch, and \\(\\mathbf{V}^{\\mathrm{c}}\\) is regarded as Gaussian noise in CASSI." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.417, + 0.892, + 0.447 + ], + "angle": 0, + "content": "To simplify to a matrix-vector form, the imaging model of the CASSI branch is represented as" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.454, + 0.891, + 0.469 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} ^ {\\mathrm {c}} = \\boldsymbol {\\Phi} ^ {\\mathrm {c}} \\mathbf {x} + \\mathbf {v} ^ {\\mathrm {c}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.477, + 0.892, + 0.521 + ], + "angle": 0, + "content": "where \\(\\Phi^{\\mathbf{c}}\\) denotes the imaging model of the CASSI branch sensing matrix, \\(\\mathbf{y}^{\\mathbf{c}}\\) is the vector form of \\(\\mathbf{Y}^{\\mathbf{c}}\\), \\(\\mathbf{x}\\) is the vector form of \\(\\mathcal{X}\\), and \\(\\mathbf{v}^{\\mathbf{c}}\\) is the vector form of \\(\\mathbf{V}^{\\mathbf{c}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.522, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Correspondingly, the imaging model of the PAN camera branch is described by" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.559, + 0.891, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} ^ {\\mathrm {p}} = \\boldsymbol {\\Phi} ^ {\\mathrm {p}} \\mathbf {x} + \\mathbf {v} ^ {\\mathrm {p}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.672 + ], + "angle": 0, + "content": "where \\(\\Phi^{\\mathbf{P}}\\) denotes the imaging model of the PAN camera branch sensing matrix, determined by the spectral response of the sensor, \\(\\mathbf{y}^{\\mathrm{c}}\\) is the vector form of PAN measurement, and \\(\\mathbf{v}^{\\mathrm{P}}\\) is regarded as Gaussian noise in the PAN measurement. To connect the imaging models to the subsequent discussion, we define \\(\\mathbf{y}\\), \\(\\Phi\\), and \\(\\mathbf{v}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.677, + 0.891, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = \\left[ \\begin{array}{l} \\mathbf {y} ^ {\\mathrm {c}} \\\\ \\mathbf {y} ^ {\\mathrm {p}} \\end{array} \\right], \\quad \\boldsymbol {\\Phi} = \\left[ \\begin{array}{l} \\boldsymbol {\\Phi} ^ {\\mathrm {c}} \\\\ \\boldsymbol {\\Phi} ^ {\\mathrm {p}} \\end{array} \\right], \\quad \\mathbf {v} = \\left[ \\begin{array}{l} \\mathbf {v} ^ {\\mathrm {c}} \\\\ \\mathbf {v} ^ {\\mathrm {p}} \\end{array} \\right]. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.716, + 0.892, + 0.745 + ], + "angle": 0, + "content": "Using the above definitions, the imaging model can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.746, + 0.891, + 0.761 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = \\boldsymbol {\\Phi} \\mathbf {x} + \\mathbf {v}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\Phi\\) is a sensing matrix in \\(\\mathbb{R}^{M\\times N}\\) that encodes the system mapping from the original scene \\(\\mathbf{x}\\) to the measurements \\(\\mathbf{y}\\). \\(\\mathbf{y}\\in \\mathbb{R}^{M\\times 1}\\), \\(\\mathbf{x}\\in \\mathbb{R}^{N\\times 1}\\), and \\(\\Phi \\in \\mathbb{R}^{M\\times N}\\). The dimensions \\(M\\) and \\(N\\) are defined as follows: \\(M\\) is calculated as \\(H(W + d(C - 1)) + HW\\) and \\(N\\) is calculated as \\(HWC\\), where \\(d\\) represents the dispersion step size. It is important to note that in the context of HSI reconstruction, \\(M\\) is typically much smaller than \\(N\\), highlighting that the HSI reconstruction task in DCCHI is an ill-posed problem." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24883" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.148, + 0.09, + 0.825, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Figure 3. Overview of PGDU. The InitialNet initiates the process with compressive measurements and sensing matrix, followed by a series of stages each containing a conjugate gradient (CG) block and an In2SET denoiser." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.366, + 0.327, + 0.381 + ], + "angle": 0, + "content": "3.2. Reconstruction Framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.471, + 0.51 + ], + "angle": 0, + "content": "Compared to learn a brute-force mapping between HSI x and measurement y, model-based methods have potential in compressive imaging due to fully considering the imaging model. Model-based methods usually formulate HSI reconstruction as a Bayesian inference challenge, solving Eq. (5) under a unified Maximum A Posteriori (MAP) framework. Mathematically, the optimization problem for HSI reconstruction could be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.512, + 0.47, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = \\arg \\min _ {\\mathbf {x}} \\frac {1}{2} \\| \\mathbf {y} - \\boldsymbol {\\Phi} \\mathbf {x} \\| _ {2} ^ {2} + \\eta J (\\mathbf {x}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.47, + 0.587 + ], + "angle": 0, + "content": "where \\( J(\\mathbf{x}) \\) represents regularization. The parameter \\( \\eta \\) is a regularization coefficient, controlling the trade-off between data fidelity and the regularization term imposed by \\( J(\\mathbf{x}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.678 + ], + "angle": 0, + "content": "To solve the optimization problem shown in Eq. (6), we design the PGDU based on the physical structure of DC-CHI, as shown in Figure 3. Utilizing the half quadratic splitting (HQS) method, we decompose the optimization problem into two sub-problems: the data fidelity term, as shown in Eq. (7); and the prior term, as shown in Eq. (8)." + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.68, + 0.47, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} ^ {k + 1} = \\arg \\min _ {\\mathbf {x}} \\left\\| \\mathbf {y} - \\boldsymbol {\\Phi} \\mathbf {x} \\right\\| _ {2} ^ {2} + \\mu^ {k + 1} \\left\\| \\mathbf {z} ^ {k} - \\mathbf {x} \\right\\| _ {2} ^ {2}, \\quad (7)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.718, + 0.47, + 0.748 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} ^ {k + 1} = \\arg \\min _ {\\mathbf {z}} \\frac {1}{2} \\mu^ {k + 1} \\left\\| \\mathbf {z} - \\mathbf {x} ^ {k + 1} \\right\\| _ {2} ^ {2} + \\eta^ {k + 1} J (\\mathbf {z}), (8)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.469, + 0.841 + ], + "angle": 0, + "content": "the superscript \\(k\\) indicates the stage index number, and \\(\\mathbf{z}\\) is an auxiliary variable introduced to facilitate the optimization. The parameter \\(\\mu^{k + 1}\\) is a relaxation parameter that governs the alignment between the current estimate \\(\\mathbf{x}\\) and the auxiliary variable \\(\\mathbf{z}\\). The parameter \\(\\eta^{k + 1}\\) is a stage-specific parameter for the regularization coefficient \\(\\eta\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.469, + 0.872 + ], + "angle": 0, + "content": "The data fidelity term can be directly calculated in closed form, as demonstrated in Eq. (9)." + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.876, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} ^ {k + 1} = \\left(\\boldsymbol {\\Phi} ^ {\\mathrm {T}} \\boldsymbol {\\Phi} + \\mu \\mathbf {I}\\right) ^ {- 1} \\left(\\boldsymbol {\\Phi} ^ {\\mathrm {T}} \\mathbf {y} + \\mu^ {k + 1} \\mathbf {z} ^ {k}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.366, + 0.892, + 0.442 + ], + "angle": 0, + "content": "in the context of HSI reconstruction in CASSI, the matrix \\(\\Phi^{\\mathsf{T}}\\Phi\\) is strictly diagonal. However, with the addition of the PAN camera branch in DCCHI, the matrix \\(\\Phi^{\\mathsf{T}}\\Phi\\) becomes only diagonally dominant, and thus a closed-form solution cannot be explicitly calculated." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.442, + 0.892, + 0.524 + ], + "angle": 0, + "content": "Given the non-diagonal form of \\(\\Phi^{\\mathrm{T}}\\Phi\\), we employ the conjugate gradient (CG) method [34] for the efficient resolution of the data fidelity term. The CG method is well suited for this problem due to its effectiveness in solving large-scale, sparse linear systems." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.529, + 0.892, + 0.575 + ], + "angle": 0, + "content": "To fully explore the guidance of the PAN image \\(\\mathbf{y}^{\\mathbb{P}}\\) on prior term, we design a PAN-guided Gaussian denoiser to estimate \\(\\mathbf{z}^{k + 1}\\). This is formulated as Eq. (10):" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.596, + 0.892, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} ^ {k + 1} = \\operatorname {D e n o i s e r} _ {k + 1} \\left(\\mathbf {x} ^ {k + 1}, \\mathbf {G F E} (\\mathbf {y} ^ {\\mathbf {p}}), \\sigma^ {k + 1}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.759 + ], + "angle": 0, + "content": "where \\(\\mathbf{GFE}(\\mathbf{y}^{\\mathrm{P}})\\) serves as structural guidance for the denoising, which incorporates multi-scale spatial details from the high-resolution \\(\\mathbf{y}^{\\mathrm{P}}\\) data into the denoiser, aiming to refine the fidelity of the reconstructed HSI by adding contextual information. The Gaussian noise level of the denoiser, denoted as \\(\\sigma^{k + 1}\\), is equal to \\(\\sqrt{\\eta^{k + 1} / \\mu^{k + 1}}\\). The \\(\\mu^{k + 1}\\) and \\(\\sigma^{k + 1}\\) are the elements of vectors \\(\\pmb{\\mu}\\) and \\(\\pmb{\\sigma}\\), which are inferred by the InitialNet of PGDU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The feature extraction from \\(\\mathbf{y}^{\\mathrm{P}}\\) is delineated as follows: within the unrolling framework, the feature representation of \\(\\mathbf{y}^{\\mathrm{P}}\\) is extracted singularly and iteratively shared across multiple stages. A stack of convolutional blocks is utilized to harvest feature maps at varying resolutions, assembling a guided feature pyramid \\([\\mathbf{G}_1,\\mathbf{G}_2,\\mathbf{G}_3]\\). The guided feature pyramid is integral to the subsequent denoising stage, aiding in the preservation of intricate spatial details during the denoising." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24884" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.362, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.187, + 0.352, + 0.268, + 0.368 + ], + "angle": 0, + "content": "(a) In2SET" + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.09, + 0.885, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.238, + 0.885, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.393, + 0.893, + 0.448 + ], + "angle": 0, + "content": "Figure 4. Diagram of In2SET architecture. (a) The U-shaped In2SET structure. (b) In2AB, consisting of two normalization layers, an intra-similarity attention module, an inter-similarity attention module, and an FFN layer. (c) The components of NPL. (d) The multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S). (e) The cosine similarity reweighting (CRW) mechanism." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.473, + 0.168, + 0.489 + ], + "angle": 0, + "content": "4. In2SET" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.273, + 0.513 + ], + "angle": 0, + "content": "4.1. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.473, + 0.84 + ], + "angle": 0, + "content": "In this section, we introduce the denoiser In2SET within the PGDU framework. As shown in Figure 4 (a), the proposed In2SET adopts a U-shaped architecture [36], involving the intra-inter attention block (In2AB) as the foundational units. This architecture employs multi-scale feature extraction coupled with skip connections between the encoder and decoder, enhancing the efficiency in information processing and feature extraction. To be specific, the denoiser initializes feature map \\(\\mathbf{X}\\) from the spectral image \\(\\mathbf{x}^{k + 1}\\) and the noise level \\(\\sigma^{k + 1}\\), passing through a convolutional layer with a kernel size of \\(3\\times 3\\). The input fed into each In2AB consists of guided feature \\(\\mathbf{G_i}\\), feature maps extracted from the PAN image, and HSI feature \\(\\mathbf{X}\\). The denoised image \\(\\mathbf{z}^{k + 1}\\) is the sum of \\(\\mathbf{x}^{k + 1}\\) and the output of the last In2AB, calculated by a convolutional layer with a kernel size of \\(3\\times 3\\). The In2AB structure is shown in Figure 4 (b). Our In2AB module includes two normalization layers, one intra-similarity attention module, one intersimilarity attention module, and one feed-forward fully connected (FFN) layer. In the following, we introduce the detail of the intra-similarity and inter-similarity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.315, + 0.864 + ], + "angle": 0, + "content": "4.2. Intra-Similarity Attention" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Our intra-similarity attention module is grounded on two key principles: firstly, for exploring intra-spatial similarity," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.581 + ], + "angle": 0, + "content": "the comprehensive and continuous spatial data provided by the PAN image are invaluable. This allows the spatial similarity in the PAN image to serve as an effective proxy for approximating the spatial similarity of the HSI. Secondly, in addressing intra-spectral similarity, analyzing the reconstructed HSI becomes significantly more effective, given the PAN image's deficiency in spectral color information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.686 + ], + "angle": 0, + "content": "As shown in Figure 4 (b), our intra-similarity attention module includes two branches: multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S), representing the exploration of spectral and spatial self-similarity, respectively. The MHA-C is based on the work in MST [7], which has been demonstrated to effectively explore spectral self-similarity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.812 + ], + "angle": 0, + "content": "The input features \\(\\mathbf{X}\\) and \\(\\mathbf{G}\\) have dimensions \\(\\mathbb{R}^{H\\times W\\times C}\\) and \\(\\mathbb{R}^{H\\times W\\times \\hat{C}}\\), respectively, where \\(\\hat{C} = \\frac{C}{2}\\). After normalization and partitioning, the dimensions become \\(\\mathbb{R}^{B\\times N\\times C}\\) and \\(\\mathbb{R}^{B\\times N\\times \\hat{C}}\\). In the first and last layers of HSAB within In2SET, \\(B = \\frac{HW}{M^2}\\) and \\(N = M^2\\). For the remaining layers, dimensions are recalibrated to \\(B = M^2\\) and \\(N = \\frac{HW}{M^2}\\). Following linear projection as shown in Eq. (11) and Eq. (12)." + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.821, + 0.891, + 0.838 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {1}, \\mathbf {K} _ {1}, \\mathbf {V} _ {1}, \\mathbf {V} _ {2} = L _ {Q _ {1}, K _ {1}, V _ {1}, V _ {2}} (\\mathbf {X}), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.862, + 0.891, + 0.878 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {2}, \\mathbf {K} _ {2} = L _ {Q _ {2}, K _ {2}} (\\mathbf {G}), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.884, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}\\) is projected to \\(\\mathbf{Q}_1, \\mathbf{K}_1, \\mathbf{V}_1 \\in \\mathbb{R}^{B \\times \\hat{C} \\times N}\\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24885" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.137, + 0.089, + 0.833, + 0.509 + ], + "angle": 0, + "content": "
MethodGFLOPsSceneAverage
01020304050607080910
PFusion-RGB [21]-40.0938.8438.7046.6532.0737.1239.7436.7534.5235.5338.00
0.9790.9680.9660.9360.9800.9800.9640.9650.9310.9790.965
PIDS-RGB [13]-42.0940.0841.5048.5540.0539.0036.6337.0238.8238.6440.24
0.9830.9490.9680.9890.9820.9740.9400.9480.9530.9800.967
TV-DC [39]-35.8133.2231.0740.1133.3234.6231.0932.3129.3633.8433.47
0.9470.8850.8790.9470.9440.9430.8850.9160.8620.9530.910
PIDS-DC [13]-39.8237.0737.7246.7837.4537.7432.9031.6634.3538.5837.41
0.9770.9210.9500.9780.9730.9630.8960.9150.9020.9720.945
BiSRNet-DC [10]1.3335.0234.1331.5035.8833.7035.5832.3132.7331.3734.4833.67
0.9450.9140.8830.8950.9350.9250.9000.9030.8990.9360.914
CST-DC [6]25.4037.4438.9136.7942.2736.5738.9136.8735.9135.8737.9337.75
0.9750.9780.9690.9830.9820.9840.9670.9800.9730.9900.978
HDNet-DC [22]144.3138.0639.7938.2142.7937.2239.2637.4136.5136.6437.5238.34
0.9760.9820.9730.9830.9830.9860.9680.9820.9760.9880.980
MST-DC [7]25.7738.3840.4537.6342.8837.7239.6637.5637.4037.8638.1038.76
0.9760.9760.9660.9750.9780.9760.9650.9710.9710.9810.974
MST++-DC [8]17.6938.3840.4737.7043.8837.7539.4237.4837.3838.8239.0439.03
0.9770.9800.9680.9840.9830.9850.9640.9820.9800.9890.980
DAUHST-DC-2stg [9]16.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0440.22
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.983
DAUHST-DC-3stg [9]24.7040.2243.5241.7447.0738.8140.1639.8638.2140.6339.3240.95
0.9830.9890.9810.9930.9850.9870.9780.9810.9830.9900.985
DAUHST-DC-5stg [9]40.5140.7444.0041.5846.8439.6640.8940.2138.7239.9840.1041.27
0.9840.9890.9810.9910.9860.9870.9790.9830.9820.9890.916
DAUHST-DC-9stg [9]72.1141.5945.1943.4748.9240.2741.1740.7340.1143.5041.3342.62
0.9850.9910.9840.9930.9880.9880.9790.9860.9880.9900.987
In2SET-2stg (Ours)14.3540.3342.3040.3447.2439.4240.6139.4638.4240.3739.9640.84
0.9830.9850.9770.9910.9860.9860.9750.9790.9810.9880.983
In2SET-3stg (Ours)20.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0441.35
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.984
In2SET-5stg (Ours)33.6641.1344.4342.7447.2940.3340.9540.4939.1542.0739.4441.80
0.9850.9900.9830.9930.9880.9870.9790.9820.9850.9870.985
In2SET-9stg (Ours)59.4042.5646.4244.5550.6342.0142.4941.5940.5343.8342.3343.69
0.9890.9940.9860.9960.9920.9910.9830.9890.9900.9940.990
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.519, + 0.895, + 0.562 + ], + "angle": 0, + "content": "Table 1. Comparison of In2SET with SOTA DCCHI methods across 10 simulated scenes, including FLOPS, PSNR (upper entry), and SSIM (lower entry). \"Method-RGB\" indicates the use of RGB observations, while \"Method-DC\" denotes grayscale observations in PAN images. It is noted that \"Method-DC\" is modified from other HSI reconstruction method for the DCCHI reconstruction task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.577, + 0.455, + 0.595 + ], + "angle": 0, + "content": "\\(\\mathbf{V}_2 \\in \\mathbb{R}^{B \\times N \\times \\hat{C}}\\). \\(\\mathbf{G}\\) is projected to \\(\\mathbf{Q}_2\\), \\(\\mathbf{K}_2 \\in \\mathbb{R}^{B \\times N \\times \\hat{C}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.595, + 0.47, + 0.626 + ], + "angle": 0, + "content": "The computations of MHA-C and MHA-S can be represented by Eq. (13) and Eq. (14)," + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.636, + 0.47, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {1} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {1} \\mathbf {K} _ {1} ^ {T}}{\\sqrt {d _ {h 1}}} + \\mathbf {P} _ {1}\\right) \\mathbf {V} _ {1}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.686, + 0.47, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {2} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {2} \\mathbf {K} _ {2} ^ {T}}{\\sqrt {d _ {h 2}}} + \\mathbf {P} _ {2}\\right) \\mathbf {V} _ {2}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.728, + 0.47, + 0.775 + ], + "angle": 0, + "content": "where \\(\\sqrt{d_{h1}}\\) and \\(\\sqrt{d_{h2}}\\) are scalars as defined in [9], \\(\\mathbf{P}_1 \\in \\mathbb{R}^{B \\times \\hat{C} \\times \\hat{C}}\\), and \\(\\mathbf{P}_2 \\in \\mathbb{R}^{B \\times N \\times N}\\) denote learnable positional encodings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.775, + 0.469, + 0.806 + ], + "angle": 0, + "content": "The output of intra-attention \\(\\mathbf{X}_{\\mathrm{intra}}\\) can be obtained by Eq. (15)." + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.807, + 0.469, + 0.824 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {\\text {i n t r a}} = \\operatorname {C o n c a t} \\left(\\mathbf {X} _ {1}, \\mathbf {X} _ {2}\\right). \\tag {15}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.314, + 0.849 + ], + "angle": 0, + "content": "4.3. Inter-Similarity Attention" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We establish our inter-similarity attention module based on one principle: the shallow semantic features of the PAN image and the corresponding HSI area are similar, including" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.655 + ], + "angle": 0, + "content": "consistency in texture, shape features, and low-level image attributes (brightness and contrast). The credibility of the reconstructed area is directly proportional to this consistency. Inter-similarity attention explores cross-modal similarity using cosine similarity reweighting (CRW)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.7 + ], + "angle": 0, + "content": "After exploiting intra-similarity, the output of the intrasimilarity attention module \\(\\mathbf{X}_{\\mathrm{intra}}\\) is projected to obtain \\(\\mathbf{K}_3\\) and \\(\\mathbf{V}_3\\)," + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.709, + 0.892, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\mathbf {K} _ {3}, \\mathbf {V} _ {3} = L _ {K _ {3}, V _ {3}} \\left(\\mathbf {X} _ {\\text {i n t r a}}\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.8, + 0.75 + ], + "angle": 0, + "content": "where \\(\\mathbf{K}_3\\in \\mathbb{R}^{B\\times N\\times \\hat{C}}\\) and \\(\\mathbf{V_3}\\in \\mathbb{R}^{B\\times N\\times C}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.777 + ], + "angle": 0, + "content": "Then, the computations of CRW can be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.775, + 0.892, + 0.809 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {\\text {i n t e r}} = \\frac {\\mathbf {Q} _ {2} \\cdot \\mathbf {K} _ {3}}{\\| \\mathbf {Q} _ {2} \\| \\| \\mathbf {K} _ {3} \\|} \\odot \\mathbf {V} _ {3}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where the cosine similarity computed along the last dimension between \\(\\mathbf{Q}_2\\) and \\(\\mathbf{K}_3\\) quantifies the feature alignment in corresponding areas. A higher similarity score reflects a stronger feature correspondence, which, in turn, informs the enhanced weighting of \\(\\mathbf{V}_3\\), improving the fidelity of the region being reconstructed." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24886" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.468, + 0.221 + ], + "angle": 0, + "content": "In this section, we begin by introducing detailing the network training process. Subsequently, we evaluate the performance of In2SET on both simulation and real-world DC-CHI datasets. Then, we validate the effectiveness of the intra-similarity block using statistical simulation data. Finally, we perform an ablation study to demonstrate the effectiveness of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.222, + 0.468, + 0.357 + ], + "angle": 0, + "content": "Simulation Dataset. Two distinct datasets are used: CAVE [50] and KAIST [14]. The CAVE dataset is made up of 32 hyperspectral images with \\(512 \\times 512\\) spatial resolution. The KAIST dataset contains 30 hyperspectral images, each with a larger spatial dimension of \\(2704 \\times 3376\\). The CAVE dataset is used as the training data, while a subset of 10 scenes crop from the KAIST dataset is used for the evaluation phase, in accordance with the protocols established in references [7, 9, 22, 23, 31]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.468, + 0.54 + ], + "angle": 0, + "content": "Implementation. Our method is implemented with Pytorch and trained with Adam [24] optimizer for 300 epochs. During training, the learning rate is \\(4 \\times 10^{-4}\\) using the cosine annealing scheduler, and the loss function for network training is \\(L_{1}\\) loss. We randomly extract patches from 3D HSI cubes to serve as training samples. The dimensions of these patches are \\(256 \\times 256 \\times 28\\) for the simulation experiment and \\(350 \\times 260 \\times 26\\) for the real-world experiment. In simulation imaging model, we configure a dispersion shift step \\(d\\) of 2, directing the dispersion to the right. In real-word imaging model, the dispersion shift step \\(d\\) is set to 1, with the dispersion oriented upwards." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.548, + 0.3, + 0.563 + ], + "angle": 0, + "content": "5.1. Simulation Data Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.468, + 0.613 + ], + "angle": 0, + "content": "The reconstruction quality of hyperspectral images are assessed using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) [48] metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.468, + 0.779 + ], + "angle": 0, + "content": "The Table 1 clearly shows that In2SET excels in all test scenarios, particularly in In2SET-9stg, achieving the best performance across all scenes with an average PSNR of \\(43.69\\mathrm{dB}\\) and a SSIM of 0.990. This significantly surpasses model optimization methods like TV-DC and PIDS-DC. Compared to deep learning-based methods, such as various stages of DAUHST-DC [9], In2SET demonstrates remarkable superiority. In2SET-3stg achieves performance comparable to that of DAUHST-DC-5stg [9], but with only \\(51.3\\%\\) of the cost, amounting to 20.78 GFLOPs compared to 40.50 GFLOPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To facilitate a direct visual quality assessment, we analyzed the distinction between Ground Truth (GT) and the reconstructions produced by various open-source methods. Figure 5 presents reconstruction results for selected spectral bands. These results are generated from two model-based approaches, TV-DC [39] and PIDS-DC [13], five end-to-end network algorithms, BiSRNet-DC [10], CST-DC [6], HDNet-DC [22], MST-DC [7], MST++-DC [8], as well as" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.088, + 0.894, + 0.149 + ], + "angle": 0, + "content": "
RMSECorrelationPSNR(dB)
CAVE0.0340.99936.28
KAIST0.0250.99635.74
ICVL0.0760.99731.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.15, + 0.892, + 0.192 + ], + "angle": 0, + "content": "Table 2. Comparison of correlation maps between HSI and PAN image, including average Root Mean Squared Error (RMSE), average correlation, and PSNR." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.195, + 0.892, + 0.269 + ], + "angle": 0, + "content": "
BaselineCRWMHA-CMHA-SPSNR(dB)SSIMGFLOPs
✓37.230.9449.87
✓✓40.050.98011.19
✓✓✓40.460.98214.06
✓✓✓✓40.840.98314.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.271, + 0.892, + 0.299 + ], + "angle": 0, + "content": "Table 3. Break-down ablation study on individual components of the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.302, + 0.888, + 0.362 + ], + "angle": 0, + "content": "
MethodsCG-1CG-2CG-5CG-10
PSNR(dB)40.4240.6640.8441.05
SSIM0.9820.9830.9830.984
FPS26.4522.7919.1613.99
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.363, + 0.891, + 0.39 + ], + "angle": 0, + "content": "Table 4. Ablation study on iterative performance of conjugate gradient descent for data item." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.399, + 0.891, + 0.459 + ], + "angle": 0, + "content": "from two deep unfolding methods, namely DAUHST-DC9stg [9] and our In2SET-9stg. The comparison underlines the exceptional ability of our In2SET approach to maintain spatial and spectral fidelity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.459, + 0.892, + 0.61 + ], + "angle": 0, + "content": "We suggest that the intra similarity in PAN image can effectively approximates that in HSI. To support this, we experiment with three public datasets: CAVE [50], KAIST [14] and ICVL [1]. We compute spatial correlation maps for each scene, comparing the correlation map of the HSI with that of the corresponding PAN image. The results of this comparison are displayed in Table 2, indicating a high degree of similarity between the intra-spatial correlations in PAN images and HSI. More visual results are presented in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.673, + 0.63 + ], + "angle": 0, + "content": "5.2. Real Data Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.635, + 0.892, + 0.756 + ], + "angle": 0, + "content": "In this research, we used a real-world DCCHI measurement Ninja, taken from publicly available data as detailed in reference [42]. Figure 6 illustrates the reconstruction results for four spectral bands in this scene, using various DCCHI reconstruction algorithms. The comparison highlights the superior image restoration quality of our model over other methods, validating its effectiveness and reliability in real-world applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.761, + 0.653, + 0.777 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.781, + 0.891, + 0.824 + ], + "angle": 0, + "content": "To verify the effectiveness of our proposed method, we conducted ablation studies for the In2SET method. All evaluations are conducted on simulated datasets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Break-down Ablation. The break-down study, as delineated in Table 3, offers a detailed examination of how each component within our proposed method influences reconstruction performance. Starting from a baseline derived by removing all ablated components from In2SET-2stg, the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24887" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.095, + 0.255, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.259, + 0.095, + 0.468, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.162, + 0.281, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.302, + 0.239, + 0.313 + ], + "angle": 0, + "content": "Spectral Density Curves" + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.196, + 0.468, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.309, + 0.298, + 0.326, + 0.312 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.349, + 0.297, + 0.404, + 0.318 + ], + "angle": 0, + "content": "In2SET-9stg (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.47, + 0.096, + 0.525, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.468, + 0.196, + 0.525, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.472, + 0.298, + 0.521, + 0.317 + ], + "angle": 0, + "content": "MST++-DC" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.096, + 0.643, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.196, + 0.642, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.298, + 0.574, + 0.312 + ], + "angle": 0, + "content": "MST-DC" + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.096, + 0.641, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.196, + 0.641, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.298, + 0.636, + 0.312 + ], + "angle": 0, + "content": "HDNet-DC" + }, + { + "type": "image", + "bbox": [ + 0.643, + 0.096, + 0.701, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.643, + 0.196, + 0.701, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.298, + 0.692, + 0.312 + ], + "angle": 0, + "content": "CST-DC" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.096, + 0.76, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.196, + 0.76, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.298, + 0.762, + 0.312 + ], + "angle": 0, + "content": "BiSRNet-DC" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.096, + 0.821, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.196, + 0.82, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.77, + 0.298, + 0.813, + 0.312 + ], + "angle": 0, + "content": "PIDS-DC" + }, + { + "type": "image", + "bbox": [ + 0.821, + 0.096, + 0.879, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.821, + 0.196, + 0.879, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.298, + 0.864, + 0.312 + ], + "angle": 0, + "content": "TV-DC" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.892, + 0.358 + ], + "angle": 0, + "content": "Figure 5. Comparative reconstruction results of different reconstruction methods for Scene 3 from the KAIST dataset at spectral bands \\(476.5\\mathrm{nm}\\), \\(536.5\\mathrm{nm}\\), \\(584.5\\mathrm{nm}\\), and \\(625.0\\mathrm{nm}\\). The spectral density curves are plotted from the blue region in the colorchecker." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.365, + 0.443, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.695, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Figure 6. Visualization of reconstruction performance across different spectral bands on real data. The spectral bands selected for comparison are \\(481.5\\mathrm{nm}\\), \\(544.0\\mathrm{nm}\\), \\(594.5\\mathrm{nm}\\), and \\(614.5\\mathrm{nm}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "model achieves a PSNR of 37.23 dB. The addition of the CRW component leads to a significant increase in PSNR by \\(+2.82\\) dB, albeit at an increased computational cost of \\(+1.32\\) GFLOPs. The subsequent integration of MHA-C further elevates the PSNR by \\(+0.41\\) dB. The final inclusion of MHA-S brings an additional PSNR gain of \\(+0.38\\) dB. These step-by-step enhancements highlight the critical role each component plays in enhancing the overall capability of the model for HSI reconstruction, demonstrating a progressive improvement in performance with each added component." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.367, + 0.892, + 0.486 + ], + "angle": 0, + "content": "Ablation Study of CG Iterations. Table 4 presents a comparative analysis of PSNR, SSIM, and Frames Per Second (FPS) metrics across varying numbers of CG iterations for HSI reconstruction. The CG-1, which conducts a single iteration, essentially operates as a vanilla gradient descent. These experiments are conducted on a system equipped with a TITAN Xp GPU (12GB) and an Intel (R) Xeon (R) Platinum 8358P CPU @ 2.60GHz." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.489, + 0.892, + 0.624 + ], + "angle": 0, + "content": "There is a clear trend of improvement in PSNR as the number of CG iterations increases from 1 to 10, with values escalating from 40.42 dB to 41.05 dB. However, an increase in iterations from CG-1 to CG-10 leads to a decrease in FPS from 26.45 dB to 13.99 dB, indicating a trade-off between reconstruction quality and computational speed. A notable observation is that CG-5 offers an optimal balance between time efficiency and performance, making it the preferred choice for our In2SET network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.639, + 0.619, + 0.654 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.858 + ], + "angle": 0, + "content": "In this paper, we propose the In2SET for DCCHI reconstruction. Our method maximizes PAN image utility for HSI reconstruction by: (1) approximating HSI intrasimilarity using PAN image, addressing the unreliability of direct computation from intermediate results. (2) Leveraging inter-similarity between HSI and PAN images to accurately reconstruct regions, providing cues for uncertain areas. Integrating In2SET into a PGDU framework allowed us to substantially enhance the spatial-spectral fidelity and detail of reconstructed images. Experiments on real and simulated datasets show that our method consistently outperforms the state-of-the-art while maintaining lower computational complexity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.859, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments This work is partially supported by the National Natural Science Foundation of China under grants 62322204, 62131003, 62072038 and 62302041." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24888" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.119, + 0.174, + 0.135 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.468, + 0.186 + ], + "angle": 0, + "content": "[1] Boaz Arad and Ohad Ben-Shahar. Sparse recovery of hyperspectral signal from natural rgb images. 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In this paper, we introduce a novel DC-CHI reconstruction network, intra-inter similarity exploiting Transformer (In2SET). Our key insight is to make full use of the PAN image to assist the reconstruction. To this end, we propose to use the intra-similarity within the PAN image as a proxy for approximating the intra-similarity in the original HSI, thereby offering an enhanced content prior for more accurate HSI reconstruction. Furthermore, we propose to use the inter-similarity to align the features between HSI and PAN images, thereby maintaining semantic consistency between the two modalities during the reconstruction process. By integrating In2SET into a PAN-guided deep unrolling (PGDU) framework, our method substantially enhances the spatial-spectral fidelity and detail of the reconstructed images, providing a more comprehensive and accurate depiction of the scene. Experiments conducted on both real and simulated datasets demonstrate that our approach consistently outperforms existing state-of-the-art methods in terms of reconstruction quality and computational complexity. The code is available at https://github.com/2JONAS/In2SET. + +# 1. Introduction + +Hyperspectral imaging collects and processes scene information by dividing the whole spectrum into tens or hundreds of bands [15, 29, 57]. Owing to the capability of detailed scene representation, this technique has been widely adopted in many fields, e.g., medical diagnosis, health care, remote sensing [5, 11, 28, 37], and various computer vision tasks, e.g., recognition, classification, segmentation [26, 35, 49]. + +The hyperspectral image (HSI) inherently possesses a + +![](images/c7d72ef2e27da3c06045d8b5628b71f0002bbe78f6aa2119931cdbf0c9e3c118.jpg) +Figure 1. Illustration of the proposed In2SET method for hyperspectral image reconstruction. (a) Intra-Similarity: extraction and application of spatial attention maps from the PAN image to enhance the spatial resolution of the reconstructed HSI. (b) Inter-Similarity: utilization of semantic features from the HSI and PAN image, scored by their consistency, to inform and refine the reconstruction of HSI. + +three-dimensional (3D) structure, comprising two dimensions of spatial information and one dimension of spectral information. Consequently, existing 2D imaging sensors lack the capability to directly capture this complete 3D signal. With the rapid progress in computational photography, snapshot spectral imagers have been developed to enable hyperspectral imaging in dynamic scenes [12, 25, 53]. The coded aperture snapshot spectral imaging (CASSI) [2, 19, 38], serving as a representative prototype of snapshot spectral imagers, captures one compressive image that encodes the spectral information by leveraging a decorated optical system. Inspired by multi-modal image fusion techniques, dual-camera compressive hyperspectral imaging (DCCHI) [39, 40, 43] upgrades the original CASSI by adding a panchromatic (PAN) camera to supply spatial information lost in CASSI. As a result, DCCHI can achieve more accurate reconstructions of HSI by fusing the compressive and PAN images compared to CASSI, which has shown great potential for snapshot hyperspectral imaging in practice. + +The significant challenge of DCCHI lies in the HSI reconstruction method, where the key factor that determines + +the reconstruction performance is the ability to model HSI priors. Early methods mainly rely on general image priors such as smoothness[4, 39, 51], sparsity[17, 41, 52], low-rank[18, 30, 56], and non-local similarity[20, 42], which ignore the continuous and complete spatial characteristics of PAN images, a feature that could provide stronger image priors. + +In recent years, some PAN-guided methods like ANSR [42, 45], PFusion [21], and PIDS [13] have utilized PAN image as prior information to guide the reconstruction of HSI. While these approaches have demonstrated merit, their performance is limited by the following two reasons: firstly, current PAN-guided methods rely on handcrafted prior constraints, which lack a precise depiction of the intrinsic structures of HSI and often require manual parameter tuning. Consequently, when dealing with complex scenes, these methods tend to produce degraded reconstruction quality. Secondly, current PAN-guided methods typically model inter-modality correlations between PAN and HSI images from a single perspective, such as using edge information from the PAN images to constrain the HSI edges [13] or employing PAN image content to enrich HSI spatial detail [21]. However, HSI exhibits multifaceted consistency with PAN images across various aspects such as structure, texture, luminance, contrast, and semantic content. Relying on one constraint may not fully exploit the comprehensive spatial-semantic guidance offered by the PAN image. In summary, accurately leveraging PAN image-guided prior modeling for HSI reconstruction is the key to further improving reconstruction quality. + +In this paper, we propose an intra-inter similarity exploiting Transformer (In2SET) for DCCHI. The proposed In2SET module is integrated into a PAN-guided deep unrolling (PGDU) framework for reconstruction. The PGDU makes use of a multi-scale feature pyramid extracted from the PAN image as guidance. This feature pyramid provides hierarchical representations of the PAN at different resolutions, allowing the network to capture both global context and fine details, resulting in improved spatial fidelity and detail in the reconstructed images. + +Our key insight is to make full use of the PAN image to assist the reconstruction. The In2SET is based on two observations: (1) given the large redundancy in both the spatial and the spectral dimensions, intra-similarity exist ubiquitously within HSI. Since the original HSI is not available in practice, intra-similarity needs to be computed based on intermediate reconstruction results. However, relying on these intermediate results for intra-similarity calculations introduces unreliability. Fortunately, the PAN image can be regarded as the integral of all spectral bands and provides a natural reference for estimating the intra-similarity in the original HSI. Thus, we propose to employ the intrasimilarity in the PAN image as an approximation proxy for + +the intra-similarity in the original HSI, which provides an enhanced content prior for HSI reconstruction. (2) Since the HSI and the PAN image describe the same scenes, inter-similarity should exist between the HSI and the PAN image, considering semantic information. Inter-similarity, serving as a scorer, assigns higher weights to features in areas of the HSI that are more similar to the corresponding areas in the PAN image, thereby improving feature representation in those areas and minimizing uncertainty and risk in the reconstruction process. This capability enables the reconstruction of the highly ill-posed inverse problem in a more confidently supervised manner, providing new contextual information for HSI reconstruction. + +In a nutshell, this work integrates intra-similarity and inter-similarity with the advanced Transformer mechanism, specifically for DCCHI, resulting in high-fidelity HSI reconstruction. The main contributions of this work are as follows: + +- We propose the PGDU, which employs the feature pyramid from the PAN image to guide the reconstruction of the HSI. +- We propose the In2SET, which employs a novel attention mechanism, specifically designed to concurrently capture both intra-similarity and inter-similarity between spectral and PAN images. +- Experiments on real and simulated data demonstrate that our method consistently outperforms state-of-the-art approaches. + +# 2. Related Work + +This section provides an overview of the advancements in HSI reconstruction, focusing on three pivotal areas: handcrafted HSI priors modeling, data-driven HSI priors modeling, and PAN-guided HSI reconstruction. + +# 2.1. Hand-Crafted HSI Priors Modeling + +Early HSI reconstruction relied heavily on hand-crafted priors. Total Variation (TV) regularization [39, 54, 55] utilized the piecewise smoothness of images to constrain TV, albeit at the risk of suppressing important high-frequency structural details. Sparse representation techniques [3, 41, 52] have been employed, focusing on constructing dictionaries to model image sparsity. Low-rank priors [30, 47, 56] have been applied, designed to capture contextual information in high-dimensional data. However, these hand-crafted methods often required extensive manual parameter tuning and struggled to represent complex data scenarios effectively. + +# 2.2. Data-Driven HSI Priors Modeling + +The advent of deep learning has revolutionized the field of HSI reconstruction. Models such as HyperReconNet [44], $\lambda$ -net [33], TSA-Net [31], DNU [46], DGSMP [23] and + +PnP-DIP-HSI [32] have markedly improved reconstruction quality by modeling HSI data prior knowledge. Furthermore, the introduction of Transformer-based methods like MST [7], CST [6], DAU [9], RDLUF [16], and PADUT [27] has led to even more significant advances in reconstruction performance. Benefiting from the attention mechanism, Transformers can efficiently model both spatial and spectral similarities within HSI data, enabling a more flexible handling of input data and providing a richer feature representation for HSI reconstruction. + +# 2.3. PAN-Guided HSI Reconstruction + +The integration of PAN guidance in HSI reconstruction represents a significant stride in addressing the inherent limitations of traditional CASSI. ANSR[42, 45] proposed an adaptive non-local sparse representation model, guided by the PAN image. PFusion[21] leveraged RGB measurements for spatial coefficient estimation and CASSI measurements for spectral basis acquisition. It features a patch processing strategy to enhance the spectral low-rank property, optimizing the model efficiently without iterative methods or a spectral sensing matrix. PIDS[13] utilized the RGB measurement as a prior image to enhance semantic correspondence between HSI and the PAN image. These methods have marked significant advancements in the field. However, they often require manual parameter tuning and fail to leverage the rich spatial context and detailed features embedded within the PAN image, suggesting potential areas for further improvements in reconstruction. + +Our motivation is to utilize the spatial semantic information provided by the PAN image to improve the HSI reconstruction result in DCCHI. We aim to develop a method that combines the strengths of PAN guidance to model the intra-inter similarity for more accurate reconstruction. + +# 3. PGDU + +# 3.1. DCCHI Forward Model + +DCCHI consists of a beam splitter, a CASSI branch, and a PAN camera branch, as shown in Figure 2. The beam splitter divides the incident light from the scene into two equal-intensity parts. One part of the light is captured by CASSI, which undergoes spatial modulation and spectral modulation to form the CASSI measurement. The other part of the light is directly captured by the PAN camera. + +Let $\mathcal{X} \in \mathbb{R}^{H \times W \times C}$ represent the spectral image of the target scene, where $H$ , $W$ , and $C$ are the height, width, and number of spectral bands, respectively. The spatial and spectral modulation in CASSI is given by + +$$ +\mathbf {Y} ^ {\mathbf {c}} = \sum_ {c = 1} ^ {C} \operatorname {s h i f t} (\phi \odot \mathcal {X} [:,: c ]) + \mathbf {V} ^ {\mathbf {c}}, \tag {1} +$$ + +![](images/e538731b52e1f510bc135ce8279593ff0139ac3d56a2704f24cb98c1838c93aa.jpg) +Figure 2. The dual-camera compressive hyperspectral imaging system. + +where $\phi$ is the transmission intensity of the coded aperture, represented as $\phi \in \mathbb{R}^{H\times W}$ , shift $(\cdot)$ indicates the spectral modulation caused by the dispersion prism, $\mathbf{Y}^{\mathrm{c}}$ is the image captured by the CASSI branch, and $\mathbf{V}^{\mathrm{c}}$ is regarded as Gaussian noise in CASSI. + +To simplify to a matrix-vector form, the imaging model of the CASSI branch is represented as + +$$ +\mathbf {y} ^ {\mathrm {c}} = \boldsymbol {\Phi} ^ {\mathrm {c}} \mathbf {x} + \mathbf {v} ^ {\mathrm {c}}, \tag {2} +$$ + +where $\Phi^{\mathbf{c}}$ denotes the imaging model of the CASSI branch sensing matrix, $\mathbf{y}^{\mathbf{c}}$ is the vector form of $\mathbf{Y}^{\mathbf{c}}$ , $\mathbf{x}$ is the vector form of $\mathcal{X}$ , and $\mathbf{v}^{\mathbf{c}}$ is the vector form of $\mathbf{V}^{\mathbf{c}}$ . + +Correspondingly, the imaging model of the PAN camera branch is described by + +$$ +\mathbf {y} ^ {\mathrm {p}} = \boldsymbol {\Phi} ^ {\mathrm {p}} \mathbf {x} + \mathbf {v} ^ {\mathrm {p}}, \tag {3} +$$ + +where $\Phi^{\mathbf{P}}$ denotes the imaging model of the PAN camera branch sensing matrix, determined by the spectral response of the sensor, $\mathbf{y}^{\mathrm{c}}$ is the vector form of PAN measurement, and $\mathbf{v}^{\mathrm{P}}$ is regarded as Gaussian noise in the PAN measurement. To connect the imaging models to the subsequent discussion, we define $\mathbf{y}$ , $\Phi$ , and $\mathbf{v}$ as + +$$ +\mathbf {y} = \left[ \begin{array}{l} \mathbf {y} ^ {\mathrm {c}} \\ \mathbf {y} ^ {\mathrm {p}} \end{array} \right], \quad \boldsymbol {\Phi} = \left[ \begin{array}{l} \boldsymbol {\Phi} ^ {\mathrm {c}} \\ \boldsymbol {\Phi} ^ {\mathrm {p}} \end{array} \right], \quad \mathbf {v} = \left[ \begin{array}{l} \mathbf {v} ^ {\mathrm {c}} \\ \mathbf {v} ^ {\mathrm {p}} \end{array} \right]. \tag {4} +$$ + +Using the above definitions, the imaging model can be expressed as + +$$ +\mathbf {y} = \boldsymbol {\Phi} \mathbf {x} + \mathbf {v}, \tag {5} +$$ + +where $\Phi$ is a sensing matrix in $\mathbb{R}^{M\times N}$ that encodes the system mapping from the original scene $\mathbf{x}$ to the measurements $\mathbf{y}$ . $\mathbf{y}\in \mathbb{R}^{M\times 1}$ , $\mathbf{x}\in \mathbb{R}^{N\times 1}$ , and $\Phi \in \mathbb{R}^{M\times N}$ . The dimensions $M$ and $N$ are defined as follows: $M$ is calculated as $H(W + d(C - 1)) + HW$ and $N$ is calculated as $HWC$ , where $d$ represents the dispersion step size. It is important to note that in the context of HSI reconstruction, $M$ is typically much smaller than $N$ , highlighting that the HSI reconstruction task in DCCHI is an ill-posed problem. + +![](images/aabaf940b7620b995bd7df05727d69f8a09ebc27155e27a02f2534ca7932786f.jpg) +Figure 3. Overview of PGDU. The InitialNet initiates the process with compressive measurements and sensing matrix, followed by a series of stages each containing a conjugate gradient (CG) block and an In2SET denoiser. + +# 3.2. Reconstruction Framework + +Compared to learn a brute-force mapping between HSI x and measurement y, model-based methods have potential in compressive imaging due to fully considering the imaging model. Model-based methods usually formulate HSI reconstruction as a Bayesian inference challenge, solving Eq. (5) under a unified Maximum A Posteriori (MAP) framework. Mathematically, the optimization problem for HSI reconstruction could be expressed as + +$$ +\hat {\mathbf {x}} = \arg \min _ {\mathbf {x}} \frac {1}{2} \| \mathbf {y} - \boldsymbol {\Phi} \mathbf {x} \| _ {2} ^ {2} + \eta J (\mathbf {x}), \tag {6} +$$ + +where $J(\mathbf{x})$ represents regularization. The parameter $\eta$ is a regularization coefficient, controlling the trade-off between data fidelity and the regularization term imposed by $J(\mathbf{x})$ . + +To solve the optimization problem shown in Eq. (6), we design the PGDU based on the physical structure of DC-CHI, as shown in Figure 3. Utilizing the half quadratic splitting (HQS) method, we decompose the optimization problem into two sub-problems: the data fidelity term, as shown in Eq. (7); and the prior term, as shown in Eq. (8). + +$$ +\mathbf {x} ^ {k + 1} = \arg \min _ {\mathbf {x}} \left\| \mathbf {y} - \boldsymbol {\Phi} \mathbf {x} \right\| _ {2} ^ {2} + \mu^ {k + 1} \left\| \mathbf {z} ^ {k} - \mathbf {x} \right\| _ {2} ^ {2}, \quad (7) +$$ + +$$ +\mathbf {z} ^ {k + 1} = \arg \min _ {\mathbf {z}} \frac {1}{2} \mu^ {k + 1} \left\| \mathbf {z} - \mathbf {x} ^ {k + 1} \right\| _ {2} ^ {2} + \eta^ {k + 1} J (\mathbf {z}), (8) +$$ + +the superscript $k$ indicates the stage index number, and $\mathbf{z}$ is an auxiliary variable introduced to facilitate the optimization. The parameter $\mu^{k + 1}$ is a relaxation parameter that governs the alignment between the current estimate $\mathbf{x}$ and the auxiliary variable $\mathbf{z}$ . The parameter $\eta^{k + 1}$ is a stage-specific parameter for the regularization coefficient $\eta$ . + +The data fidelity term can be directly calculated in closed form, as demonstrated in Eq. (9). + +$$ +\mathbf {x} ^ {k + 1} = \left(\boldsymbol {\Phi} ^ {\mathrm {T}} \boldsymbol {\Phi} + \mu \mathbf {I}\right) ^ {- 1} \left(\boldsymbol {\Phi} ^ {\mathrm {T}} \mathbf {y} + \mu^ {k + 1} \mathbf {z} ^ {k}\right), \tag {9} +$$ + +in the context of HSI reconstruction in CASSI, the matrix $\Phi^{\mathsf{T}}\Phi$ is strictly diagonal. However, with the addition of the PAN camera branch in DCCHI, the matrix $\Phi^{\mathsf{T}}\Phi$ becomes only diagonally dominant, and thus a closed-form solution cannot be explicitly calculated. + +Given the non-diagonal form of $\Phi^{\mathrm{T}}\Phi$ , we employ the conjugate gradient (CG) method [34] for the efficient resolution of the data fidelity term. The CG method is well suited for this problem due to its effectiveness in solving large-scale, sparse linear systems. + +To fully explore the guidance of the PAN image $\mathbf{y}^{\mathbb{P}}$ on prior term, we design a PAN-guided Gaussian denoiser to estimate $\mathbf{z}^{k + 1}$ . This is formulated as Eq. (10): + +$$ +\mathbf {z} ^ {k + 1} = \operatorname {D e n o i s e r} _ {k + 1} \left(\mathbf {x} ^ {k + 1}, \mathbf {G F E} (\mathbf {y} ^ {\mathbf {p}}), \sigma^ {k + 1}\right), \tag {10} +$$ + +where $\mathbf{GFE}(\mathbf{y}^{\mathrm{P}})$ serves as structural guidance for the denoising, which incorporates multi-scale spatial details from the high-resolution $\mathbf{y}^{\mathrm{P}}$ data into the denoiser, aiming to refine the fidelity of the reconstructed HSI by adding contextual information. The Gaussian noise level of the denoiser, denoted as $\sigma^{k + 1}$ , is equal to $\sqrt{\eta^{k + 1} / \mu^{k + 1}}$ . The $\mu^{k + 1}$ and $\sigma^{k + 1}$ are the elements of vectors $\pmb{\mu}$ and $\pmb{\sigma}$ , which are inferred by the InitialNet of PGDU. + +The feature extraction from $\mathbf{y}^{\mathrm{P}}$ is delineated as follows: within the unrolling framework, the feature representation of $\mathbf{y}^{\mathrm{P}}$ is extracted singularly and iteratively shared across multiple stages. A stack of convolutional blocks is utilized to harvest feature maps at varying resolutions, assembling a guided feature pyramid $[\mathbf{G}_1,\mathbf{G}_2,\mathbf{G}_3]$ . The guided feature pyramid is integral to the subsequent denoising stage, aiding in the preservation of intricate spatial details during the denoising. + +![](images/2785e85d7758ada156f21e37d991e91e4a3b4c67dc46b540e515ca69d9aa0926.jpg) +(a) In2SET + +![](images/405407587229aa573a3aa7b47662399b913c4ebcb6febdf2b82af77ac289e540.jpg) + +![](images/19776c7f9b5c51cf5ff1b9ad526c2878024d9c5c9b3ad577010874ebf7b8bf04.jpg) +Figure 4. Diagram of In2SET architecture. (a) The U-shaped In2SET structure. (b) In2AB, consisting of two normalization layers, an intra-similarity attention module, an inter-similarity attention module, and an FFN layer. (c) The components of NPL. (d) The multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S). (e) The cosine similarity reweighting (CRW) mechanism. + +# 4. In2SET + +# 4.1. Overall Architecture + +In this section, we introduce the denoiser In2SET within the PGDU framework. As shown in Figure 4 (a), the proposed In2SET adopts a U-shaped architecture [36], involving the intra-inter attention block (In2AB) as the foundational units. This architecture employs multi-scale feature extraction coupled with skip connections between the encoder and decoder, enhancing the efficiency in information processing and feature extraction. To be specific, the denoiser initializes feature map $\mathbf{X}$ from the spectral image $\mathbf{x}^{k + 1}$ and the noise level $\sigma^{k + 1}$ , passing through a convolutional layer with a kernel size of $3\times 3$ . The input fed into each In2AB consists of guided feature $\mathbf{G_i}$ , feature maps extracted from the PAN image, and HSI feature $\mathbf{X}$ . The denoised image $\mathbf{z}^{k + 1}$ is the sum of $\mathbf{x}^{k + 1}$ and the output of the last In2AB, calculated by a convolutional layer with a kernel size of $3\times 3$ . The In2AB structure is shown in Figure 4 (b). Our In2AB module includes two normalization layers, one intra-similarity attention module, one intersimilarity attention module, and one feed-forward fully connected (FFN) layer. In the following, we introduce the detail of the intra-similarity and inter-similarity. + +# 4.2. Intra-Similarity Attention + +Our intra-similarity attention module is grounded on two key principles: firstly, for exploring intra-spatial similarity, + +the comprehensive and continuous spatial data provided by the PAN image are invaluable. This allows the spatial similarity in the PAN image to serve as an effective proxy for approximating the spatial similarity of the HSI. Secondly, in addressing intra-spectral similarity, analyzing the reconstructed HSI becomes significantly more effective, given the PAN image's deficiency in spectral color information. + +As shown in Figure 4 (b), our intra-similarity attention module includes two branches: multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S), representing the exploration of spectral and spatial self-similarity, respectively. The MHA-C is based on the work in MST [7], which has been demonstrated to effectively explore spectral self-similarity. + +The input features $\mathbf{X}$ and $\mathbf{G}$ have dimensions $\mathbb{R}^{H\times W\times C}$ and $\mathbb{R}^{H\times W\times \hat{C}}$ , respectively, where $\hat{C} = \frac{C}{2}$ . After normalization and partitioning, the dimensions become $\mathbb{R}^{B\times N\times C}$ and $\mathbb{R}^{B\times N\times \hat{C}}$ . In the first and last layers of HSAB within In2SET, $B = \frac{HW}{M^2}$ and $N = M^2$ . For the remaining layers, dimensions are recalibrated to $B = M^2$ and $N = \frac{HW}{M^2}$ . Following linear projection as shown in Eq. (11) and Eq. (12). + +$$ +\mathbf {Q} _ {1}, \mathbf {K} _ {1}, \mathbf {V} _ {1}, \mathbf {V} _ {2} = L _ {Q _ {1}, K _ {1}, V _ {1}, V _ {2}} (\mathbf {X}), \tag {11} +$$ + +$$ +\mathbf {Q} _ {2}, \mathbf {K} _ {2} = L _ {Q _ {2}, K _ {2}} (\mathbf {G}), \tag {12} +$$ + +where $\mathbf{X}$ is projected to $\mathbf{Q}_1, \mathbf{K}_1, \mathbf{V}_1 \in \mathbb{R}^{B \times \hat{C} \times N}$ and + +
MethodGFLOPsSceneAverage
01020304050607080910
PFusion-RGB [21]-40.0938.8438.7046.6532.0737.1239.7436.7534.5235.5338.00
0.9790.9680.9660.9360.9800.9800.9640.9650.9310.9790.965
PIDS-RGB [13]-42.0940.0841.5048.5540.0539.0036.6337.0238.8238.6440.24
0.9830.9490.9680.9890.9820.9740.9400.9480.9530.9800.967
TV-DC [39]-35.8133.2231.0740.1133.3234.6231.0932.3129.3633.8433.47
0.9470.8850.8790.9470.9440.9430.8850.9160.8620.9530.910
PIDS-DC [13]-39.8237.0737.7246.7837.4537.7432.9031.6634.3538.5837.41
0.9770.9210.9500.9780.9730.9630.8960.9150.9020.9720.945
BiSRNet-DC [10]1.3335.0234.1331.5035.8833.7035.5832.3132.7331.3734.4833.67
0.9450.9140.8830.8950.9350.9250.9000.9030.8990.9360.914
CST-DC [6]25.4037.4438.9136.7942.2736.5738.9136.8735.9135.8737.9337.75
0.9750.9780.9690.9830.9820.9840.9670.9800.9730.9900.978
HDNet-DC [22]144.3138.0639.7938.2142.7937.2239.2637.4136.5136.6437.5238.34
0.9760.9820.9730.9830.9830.9860.9680.9820.9760.9880.980
MST-DC [7]25.7738.3840.4537.6342.8837.7239.6637.5637.4037.8638.1038.76
0.9760.9760.9660.9750.9780.9760.9650.9710.9710.9810.974
MST++-DC [8]17.6938.3840.4737.7043.8837.7539.4237.4837.3838.8239.0439.03
0.9770.9800.9680.9840.9830.9850.9640.9820.9800.9890.980
DAUHST-DC-2stg [9]16.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0440.22
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.983
DAUHST-DC-3stg [9]24.7040.2243.5241.7447.0738.8140.1639.8638.2140.6339.3240.95
0.9830.9890.9810.9930.9850.9870.9780.9810.9830.9900.985
DAUHST-DC-5stg [9]40.5140.7444.0041.5846.8439.6640.8940.2138.7239.9840.1041.27
0.9840.9890.9810.9910.9860.9870.9790.9830.9820.9890.916
DAUHST-DC-9stg [9]72.1141.5945.1943.4748.9240.2741.1740.7340.1143.5041.3342.62
0.9850.9910.9840.9930.9880.9880.9790.9860.9880.9900.987
In2SET-2stg (Ours)14.3540.3342.3040.3447.2439.4240.6139.4638.4240.3739.9640.84
0.9830.9850.9770.9910.9860.9860.9750.9790.9810.9880.983
In2SET-3stg (Ours)20.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0441.35
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.984
In2SET-5stg (Ours)33.6641.1344.4342.7447.2940.3340.9540.4939.1542.0739.4441.80
0.9850.9900.9830.9930.9880.9870.9790.9820.9850.9870.985
In2SET-9stg (Ours)59.4042.5646.4244.5550.6342.0142.4941.5940.5343.8342.3343.69
0.9890.9940.9860.9960.9920.9910.9830.9890.9900.9940.990
+ +Table 1. Comparison of In2SET with SOTA DCCHI methods across 10 simulated scenes, including FLOPS, PSNR (upper entry), and SSIM (lower entry). "Method-RGB" indicates the use of RGB observations, while "Method-DC" denotes grayscale observations in PAN images. It is noted that "Method-DC" is modified from other HSI reconstruction method for the DCCHI reconstruction task. + +$\mathbf{V}_2 \in \mathbb{R}^{B \times N \times \hat{C}}$ . $\mathbf{G}$ is projected to $\mathbf{Q}_2$ , $\mathbf{K}_2 \in \mathbb{R}^{B \times N \times \hat{C}}$ . + +The computations of MHA-C and MHA-S can be represented by Eq. (13) and Eq. (14), + +$$ +\mathbf {X} _ {1} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} _ {1} \mathbf {K} _ {1} ^ {T}}{\sqrt {d _ {h 1}}} + \mathbf {P} _ {1}\right) \mathbf {V} _ {1}, \tag {13} +$$ + +$$ +\mathbf {X} _ {2} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} _ {2} \mathbf {K} _ {2} ^ {T}}{\sqrt {d _ {h 2}}} + \mathbf {P} _ {2}\right) \mathbf {V} _ {2}, \tag {14} +$$ + +where $\sqrt{d_{h1}}$ and $\sqrt{d_{h2}}$ are scalars as defined in [9], $\mathbf{P}_1 \in \mathbb{R}^{B \times \hat{C} \times \hat{C}}$ , and $\mathbf{P}_2 \in \mathbb{R}^{B \times N \times N}$ denote learnable positional encodings. + +The output of intra-attention $\mathbf{X}_{\mathrm{intra}}$ can be obtained by Eq. (15). + +$$ +\mathbf {X} _ {\text {i n t r a}} = \operatorname {C o n c a t} \left(\mathbf {X} _ {1}, \mathbf {X} _ {2}\right). \tag {15} +$$ + +# 4.3. Inter-Similarity Attention + +We establish our inter-similarity attention module based on one principle: the shallow semantic features of the PAN image and the corresponding HSI area are similar, including + +consistency in texture, shape features, and low-level image attributes (brightness and contrast). The credibility of the reconstructed area is directly proportional to this consistency. Inter-similarity attention explores cross-modal similarity using cosine similarity reweighting (CRW). + +After exploiting intra-similarity, the output of the intrasimilarity attention module $\mathbf{X}_{\mathrm{intra}}$ is projected to obtain $\mathbf{K}_3$ and $\mathbf{V}_3$ , + +$$ +\mathbf {K} _ {3}, \mathbf {V} _ {3} = L _ {K _ {3}, V _ {3}} \left(\mathbf {X} _ {\text {i n t r a}}\right), \tag {16} +$$ + +where $\mathbf{K}_3\in \mathbb{R}^{B\times N\times \hat{C}}$ and $\mathbf{V_3}\in \mathbb{R}^{B\times N\times C}$ + +Then, the computations of CRW can be represented as follows: + +$$ +\mathbf {X} _ {\text {i n t e r}} = \frac {\mathbf {Q} _ {2} \cdot \mathbf {K} _ {3}}{\| \mathbf {Q} _ {2} \| \| \mathbf {K} _ {3} \|} \odot \mathbf {V} _ {3}, \tag {17} +$$ + +where the cosine similarity computed along the last dimension between $\mathbf{Q}_2$ and $\mathbf{K}_3$ quantifies the feature alignment in corresponding areas. A higher similarity score reflects a stronger feature correspondence, which, in turn, informs the enhanced weighting of $\mathbf{V}_3$ , improving the fidelity of the region being reconstructed. + +# 5. Experiments + +In this section, we begin by introducing detailing the network training process. Subsequently, we evaluate the performance of In2SET on both simulation and real-world DC-CHI datasets. Then, we validate the effectiveness of the intra-similarity block using statistical simulation data. Finally, we perform an ablation study to demonstrate the effectiveness of our proposed method. + +Simulation Dataset. Two distinct datasets are used: CAVE [50] and KAIST [14]. The CAVE dataset is made up of 32 hyperspectral images with $512 \times 512$ spatial resolution. The KAIST dataset contains 30 hyperspectral images, each with a larger spatial dimension of $2704 \times 3376$ . The CAVE dataset is used as the training data, while a subset of 10 scenes crop from the KAIST dataset is used for the evaluation phase, in accordance with the protocols established in references [7, 9, 22, 23, 31]. + +Implementation. Our method is implemented with Pytorch and trained with Adam [24] optimizer for 300 epochs. During training, the learning rate is $4 \times 10^{-4}$ using the cosine annealing scheduler, and the loss function for network training is $L_{1}$ loss. We randomly extract patches from 3D HSI cubes to serve as training samples. The dimensions of these patches are $256 \times 256 \times 28$ for the simulation experiment and $350 \times 260 \times 26$ for the real-world experiment. In simulation imaging model, we configure a dispersion shift step $d$ of 2, directing the dispersion to the right. In real-word imaging model, the dispersion shift step $d$ is set to 1, with the dispersion oriented upwards. + +# 5.1. Simulation Data Results + +The reconstruction quality of hyperspectral images are assessed using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) [48] metrics. + +The Table 1 clearly shows that In2SET excels in all test scenarios, particularly in In2SET-9stg, achieving the best performance across all scenes with an average PSNR of $43.69\mathrm{dB}$ and a SSIM of 0.990. This significantly surpasses model optimization methods like TV-DC and PIDS-DC. Compared to deep learning-based methods, such as various stages of DAUHST-DC [9], In2SET demonstrates remarkable superiority. In2SET-3stg achieves performance comparable to that of DAUHST-DC-5stg [9], but with only $51.3\%$ of the cost, amounting to 20.78 GFLOPs compared to 40.50 GFLOPs. + +To facilitate a direct visual quality assessment, we analyzed the distinction between Ground Truth (GT) and the reconstructions produced by various open-source methods. Figure 5 presents reconstruction results for selected spectral bands. These results are generated from two model-based approaches, TV-DC [39] and PIDS-DC [13], five end-to-end network algorithms, BiSRNet-DC [10], CST-DC [6], HDNet-DC [22], MST-DC [7], MST++-DC [8], as well as + +
RMSECorrelationPSNR(dB)
CAVE0.0340.99936.28
KAIST0.0250.99635.74
ICVL0.0760.99731.10
+ +Table 2. Comparison of correlation maps between HSI and PAN image, including average Root Mean Squared Error (RMSE), average correlation, and PSNR. + +
BaselineCRWMHA-CMHA-SPSNR(dB)SSIMGFLOPs
✓37.230.9449.87
✓✓40.050.98011.19
✓✓✓40.460.98214.06
✓✓✓✓40.840.98314.35
+ +Table 3. Break-down ablation study on individual components of the proposed method. + +
MethodsCG-1CG-2CG-5CG-10
PSNR(dB)40.4240.6640.8441.05
SSIM0.9820.9830.9830.984
FPS26.4522.7919.1613.99
+ +Table 4. Ablation study on iterative performance of conjugate gradient descent for data item. + +from two deep unfolding methods, namely DAUHST-DC9stg [9] and our In2SET-9stg. The comparison underlines the exceptional ability of our In2SET approach to maintain spatial and spectral fidelity. + +We suggest that the intra similarity in PAN image can effectively approximates that in HSI. To support this, we experiment with three public datasets: CAVE [50], KAIST [14] and ICVL [1]. We compute spatial correlation maps for each scene, comparing the correlation map of the HSI with that of the corresponding PAN image. The results of this comparison are displayed in Table 2, indicating a high degree of similarity between the intra-spatial correlations in PAN images and HSI. More visual results are presented in the supplementary materials. + +# 5.2. Real Data Results + +In this research, we used a real-world DCCHI measurement Ninja, taken from publicly available data as detailed in reference [42]. Figure 6 illustrates the reconstruction results for four spectral bands in this scene, using various DCCHI reconstruction algorithms. The comparison highlights the superior image restoration quality of our model over other methods, validating its effectiveness and reliability in real-world applications. + +# 5.3. Ablation Study + +To verify the effectiveness of our proposed method, we conducted ablation studies for the In2SET method. All evaluations are conducted on simulated datasets. + +Break-down Ablation. The break-down study, as delineated in Table 3, offers a detailed examination of how each component within our proposed method influences reconstruction performance. Starting from a baseline derived by removing all ablated components from In2SET-2stg, the + +![](images/4fdaffba071a3baf544045f37e78355564be9b856be9de6229946c6aa8413306.jpg) + +![](images/e002fb5489c1bb0167f529ae788b666bb9bb7cf9524d3092ff9d9c1f7524ae31.jpg) + +![](images/0721a1a5146317997daa72fef98305aa92f0f7c1fbcd17aaa87bb8295a17bc5e.jpg) +Spectral Density Curves + +![](images/2047923affd2c5cd01ac1b182f2cc455df68e777c46ff83eb270fdffa25b2a92.jpg) +GT +In2SET-9stg (Ours) + +![](images/47c5afafa3f83ffcf4a6ba0ad3706f369f67c94e026b1579655df722fb4d0d26.jpg) + +![](images/18cb43938eabfc758d0c5effa66d806b41a763a274e1d0208ae47b7249dd12aa.jpg) +MST++-DC + +![](images/c28e373c0541351b9616adc817679e5ff3254639f8fa8b6999d4a40a4b4c8b7d.jpg) + +![](images/451677b7b22e19d13c77f9df830884f2f5014ea8d385623a863866928d7397a3.jpg) +MST-DC +HDNet-DC + +![](images/e3581add68cf6859ec79da727922f18409b083ae4298488920506f235807135a.jpg) + +![](images/61e419328c3de8c640b9663e709af9ca569025687ac15af860830212bf33c360.jpg) +CST-DC + +![](images/13b79b7d8b92b09035534436b7db17341cad8b981c36e124bb88313f0fc6d5d1.jpg) + +![](images/ea99d9b7cc2e71cb79e0c0d799fef86aa0c0dcbdb7067e008014e57727f78a9b.jpg) +BiSRNet-DC + +![](images/0cfc537ba72809e79e7e571c415a7b74099cd1506cbe3e627323b41c2d8087e4.jpg) + +![](images/d09476c0daff9a96396fe7c8ba60c541c6859ccfa5dd4ecb745e8eccecd6da43.jpg) +PIDS-DC + +![](images/e961223480e37869136544b84a9ef8359932f2365f38ba1ec1786d28a72ecec5.jpg) + +![](images/d582beeb41ac9de4762ff58c98fd71b1b183b58a9a6bb95bf392e88b30206de9.jpg) +TV-DC + +![](images/f469dbd086c0149eb039d9dc1739035ec207fd622394439b32ef2a8346738538.jpg) +Figure 5. Comparative reconstruction results of different reconstruction methods for Scene 3 from the KAIST dataset at spectral bands $476.5\mathrm{nm}$ , $536.5\mathrm{nm}$ , $584.5\mathrm{nm}$ , and $625.0\mathrm{nm}$ . The spectral density curves are plotted from the blue region in the colorchecker. +Figure 6. Visualization of reconstruction performance across different spectral bands on real data. The spectral bands selected for comparison are $481.5\mathrm{nm}$ , $544.0\mathrm{nm}$ , $594.5\mathrm{nm}$ , and $614.5\mathrm{nm}$ . + +model achieves a PSNR of 37.23 dB. The addition of the CRW component leads to a significant increase in PSNR by $+2.82$ dB, albeit at an increased computational cost of $+1.32$ GFLOPs. The subsequent integration of MHA-C further elevates the PSNR by $+0.41$ dB. The final inclusion of MHA-S brings an additional PSNR gain of $+0.38$ dB. These step-by-step enhancements highlight the critical role each component plays in enhancing the overall capability of the model for HSI reconstruction, demonstrating a progressive improvement in performance with each added component. + +Ablation Study of CG Iterations. Table 4 presents a comparative analysis of PSNR, SSIM, and Frames Per Second (FPS) metrics across varying numbers of CG iterations for HSI reconstruction. The CG-1, which conducts a single iteration, essentially operates as a vanilla gradient descent. These experiments are conducted on a system equipped with a TITAN Xp GPU (12GB) and an Intel (R) Xeon (R) Platinum 8358P CPU @ 2.60GHz. + +There is a clear trend of improvement in PSNR as the number of CG iterations increases from 1 to 10, with values escalating from 40.42 dB to 41.05 dB. However, an increase in iterations from CG-1 to CG-10 leads to a decrease in FPS from 26.45 dB to 13.99 dB, indicating a trade-off between reconstruction quality and computational speed. A notable observation is that CG-5 offers an optimal balance between time efficiency and performance, making it the preferred choice for our In2SET network. + +# 6. Conclusion + +In this paper, we propose the In2SET for DCCHI reconstruction. Our method maximizes PAN image utility for HSI reconstruction by: (1) approximating HSI intrasimilarity using PAN image, addressing the unreliability of direct computation from intermediate results. (2) Leveraging inter-similarity between HSI and PAN images to accurately reconstruct regions, providing cues for uncertain areas. Integrating In2SET into a PGDU framework allowed us to substantially enhance the spatial-spectral fidelity and detail of reconstructed images. 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Nature Communications, 14(1):5043, 2023. 1 \ No newline at end of file diff --git a/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/images.zip b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..357ab031fd08790a58058798bc87a4dc5f63fb56 --- /dev/null +++ b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:87477f06214f156b5f88be8e08a77ec8465c0ec19abdad16da0ba4a5a000314d +size 838965 diff --git a/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/layout.json b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4e9553ee03c4d4a22861846b32c5058ea68d5abc --- /dev/null +++ b/2024/In2SET_ Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging/layout.json @@ -0,0 +1,10878 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 116, + 103, + 479, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 103, + 479, + 140 + ], + "spans": [ + { + "bbox": [ + 116, + 103, + 479, + 140 + ], + "type": "text", + "content": "In2SET: Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 160, + 108, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 160, + 108, + 176 + ], + "spans": [ + { + "bbox": [ + 53, + 160, + 108, + 176 + ], + "type": "text", + "content": "Xin Wang1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "spans": [ + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "text", + "content": "Lizhi Wang" + }, + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "text", + "content": " Xiangtian Ma" + }, + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 133, + 160, + 304, + 191 + ], + "type": "text", + "content": "Beijing Institute of Technology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "spans": [ + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "text", + "content": "Maoqing Zhang" + }, + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "text", + "content": " Lin Zhu" + }, + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 318, + 160, + 473, + 190 + ], + "type": "text", + "content": " Beijing Normal University" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 498, + 160, + 559, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 498, + 160, + 559, + 176 + ], + "spans": [ + { + "bbox": [ + 498, + 160, + 559, + 176 + ], + "type": "text", + "content": "Hua Huang" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 243, + 290, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 290, + 542 + ], + "type": "text", + "content": "Dual-camera compressive hyperspectral imaging (DC-CHI) offers the capability to reconstruct 3D hyperspectral image (HSI) by fusing compressive and panchromatic (PAN) image, which has shown great potential for snapshot hyperspectral imaging in practice. In this paper, we introduce a novel DC-CHI reconstruction network, intra-inter similarity exploiting Transformer (In2SET). Our key insight is to make full use of the PAN image to assist the reconstruction. To this end, we propose to use the intra-similarity within the PAN image as a proxy for approximating the intra-similarity in the original HSI, thereby offering an enhanced content prior for more accurate HSI reconstruction. Furthermore, we propose to use the inter-similarity to align the features between HSI and PAN images, thereby maintaining semantic consistency between the two modalities during the reconstruction process. By integrating In2SET into a PAN-guided deep unrolling (PGDU) framework, our method substantially enhances the spatial-spectral fidelity and detail of the reconstructed images, providing a more comprehensive and accurate depiction of the scene. Experiments conducted on both real and simulated datasets demonstrate that our approach consistently outperforms existing state-of-the-art methods in terms of reconstruction quality and computational complexity. The code is available at https://github.com/2JONAS/In2SET." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 565, + 128, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 565, + 128, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 128, + 577 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": "Hyperspectral imaging collects and processes scene information by dividing the whole spectrum into tens or hundreds of bands [15, 29, 57]. Owing to the capability of detailed scene representation, this technique has been widely adopted in many fields, e.g., medical diagnosis, health care, remote sensing [5, 11, 28, 37], and various computer vision tasks, e.g., recognition, classification, segmentation [26, 35, 49]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 682, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 682, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 58, + 682, + 287, + 694 + ], + "type": "text", + "content": "The hyperspectral image (HSI) inherently possesses a" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 217, + 542, + 334 + ], + "blocks": [ + { + "bbox": [ + 310, + 217, + 542, + 334 + ], + "lines": [ + { + "bbox": [ + 310, + 217, + 542, + 334 + ], + "spans": [ + { + "bbox": [ + 310, + 217, + 542, + 334 + ], + "type": "image", + "image_path": "c7d72ef2e27da3c06045d8b5628b71f0002bbe78f6aa2119931cdbf0c9e3c118.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 342, + 547, + 418 + ], + "lines": [ + { + "bbox": [ + 305, + 342, + 547, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 547, + 418 + ], + "type": "text", + "content": "Figure 1. Illustration of the proposed In2SET method for hyperspectral image reconstruction. (a) Intra-Similarity: extraction and application of spatial attention maps from the PAN image to enhance the spatial resolution of the reconstructed HSI. (b) Inter-Similarity: utilization of semantic features from the HSI and PAN image, scored by their consistency, to inform and refine the reconstruction of HSI." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 446, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 547, + 686 + ], + "type": "text", + "content": "three-dimensional (3D) structure, comprising two dimensions of spatial information and one dimension of spectral information. Consequently, existing 2D imaging sensors lack the capability to directly capture this complete 3D signal. With the rapid progress in computational photography, snapshot spectral imagers have been developed to enable hyperspectral imaging in dynamic scenes [12, 25, 53]. The coded aperture snapshot spectral imaging (CASSI) [2, 19, 38], serving as a representative prototype of snapshot spectral imagers, captures one compressive image that encodes the spectral information by leveraging a decorated optical system. Inspired by multi-modal image fusion techniques, dual-camera compressive hyperspectral imaging (DCCHI) [39, 40, 43] upgrades the original CASSI by adding a panchromatic (PAN) camera to supply spatial information lost in CASSI. As a result, DCCHI can achieve more accurate reconstructions of HSI by fusing the compressive and PAN images compared to CASSI, which has shown great potential for snapshot hyperspectral imaging in practice." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "The significant challenge of DCCHI lies in the HSI reconstruction method, where the key factor that determines" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "text", + "content": "*Corresponding Author: Lizhi Wang (wanglizhi@bit.edu.cn)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24881" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "the reconstruction performance is the ability to model HSI priors. Early methods mainly rely on general image priors such as smoothness[4, 39, 51], sparsity[17, 41, 52], low-rank[18, 30, 56], and non-local similarity[20, 42], which ignore the continuous and complete spatial characteristics of PAN images, a feature that could provide stronger image priors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 288, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 288, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 288, + 434 + ], + "type": "text", + "content": "In recent years, some PAN-guided methods like ANSR [42, 45], PFusion [21], and PIDS [13] have utilized PAN image as prior information to guide the reconstruction of HSI. While these approaches have demonstrated merit, their performance is limited by the following two reasons: firstly, current PAN-guided methods rely on handcrafted prior constraints, which lack a precise depiction of the intrinsic structures of HSI and often require manual parameter tuning. Consequently, when dealing with complex scenes, these methods tend to produce degraded reconstruction quality. Secondly, current PAN-guided methods typically model inter-modality correlations between PAN and HSI images from a single perspective, such as using edge information from the PAN images to constrain the HSI edges [13] or employing PAN image content to enrich HSI spatial detail [21]. However, HSI exhibits multifaceted consistency with PAN images across various aspects such as structure, texture, luminance, contrast, and semantic content. Relying on one constraint may not fully exploit the comprehensive spatial-semantic guidance offered by the PAN image. In summary, accurately leveraging PAN image-guided prior modeling for HSI reconstruction is the key to further improving reconstruction quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 436, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 555 + ], + "type": "text", + "content": "In this paper, we propose an intra-inter similarity exploiting Transformer (In2SET) for DCCHI. The proposed In2SET module is integrated into a PAN-guided deep unrolling (PGDU) framework for reconstruction. The PGDU makes use of a multi-scale feature pyramid extracted from the PAN image as guidance. This feature pyramid provides hierarchical representations of the PAN at different resolutions, allowing the network to capture both global context and fine details, resulting in improved spatial fidelity and detail in the reconstructed images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Our key insight is to make full use of the PAN image to assist the reconstruction. The In2SET is based on two observations: (1) given the large redundancy in both the spatial and the spectral dimensions, intra-similarity exist ubiquitously within HSI. Since the original HSI is not available in practice, intra-similarity needs to be computed based on intermediate reconstruction results. However, relying on these intermediate results for intra-similarity calculations introduces unreliability. Fortunately, the PAN image can be regarded as the integral of all spectral bands and provides a natural reference for estimating the intra-similarity in the original HSI. Thus, we propose to employ the intrasimilarity in the PAN image as an approximation proxy for" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": "the intra-similarity in the original HSI, which provides an enhanced content prior for HSI reconstruction. (2) Since the HSI and the PAN image describe the same scenes, inter-similarity should exist between the HSI and the PAN image, considering semantic information. Inter-similarity, serving as a scorer, assigns higher weights to features in areas of the HSI that are more similar to the corresponding areas in the PAN image, thereby improving feature representation in those areas and minimizing uncertainty and risk in the reconstruction process. This capability enables the reconstruction of the highly ill-posed inverse problem in a more confidently supervised manner, providing new contextual information for HSI reconstruction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 228, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 287 + ], + "type": "text", + "content": "In a nutshell, this work integrates intra-similarity and inter-similarity with the advanced Transformer mechanism, specifically for DCCHI, resulting in high-fidelity HSI reconstruction. The main contributions of this work are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 291, + 545, + 410 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 291, + 545, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 291, + 545, + 325 + ], + "spans": [ + { + "bbox": [ + 317, + 291, + 545, + 325 + ], + "type": "text", + "content": "- We propose the PGDU, which employs the feature pyramid from the PAN image to guide the reconstruction of the HSI." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 327, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 327, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 317, + 327, + 545, + 374 + ], + "type": "text", + "content": "- We propose the In2SET, which employs a novel attention mechanism, specifically designed to concurrently capture both intra-similarity and inter-similarity between spectral and PAN images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 374, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 374, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 317, + 374, + 545, + 410 + ], + "type": "text", + "content": "- Experiments on real and simulated data demonstrate that our method consistently outperforms state-of-the-art approaches." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 422, + 392, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 392, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 392, + 435 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 443, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 491 + ], + "type": "text", + "content": "This section provides an overview of the advancements in HSI reconstruction, focusing on three pivotal areas: handcrafted HSI priors modeling, data-driven HSI priors modeling, and PAN-guided HSI reconstruction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 499, + 496, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 499, + 496, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 499, + 496, + 513 + ], + "type": "text", + "content": "2.1. Hand-Crafted HSI Priors Modeling" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 518, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 651 + ], + "type": "text", + "content": "Early HSI reconstruction relied heavily on hand-crafted priors. Total Variation (TV) regularization [39, 54, 55] utilized the piecewise smoothness of images to constrain TV, albeit at the risk of suppressing important high-frequency structural details. Sparse representation techniques [3, 41, 52] have been employed, focusing on constructing dictionaries to model image sparsity. Low-rank priors [30, 47, 56] have been applied, designed to capture contextual information in high-dimensional data. However, these hand-crafted methods often required extensive manual parameter tuning and struggled to represent complex data scenarios effectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 658, + 488, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 488, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 488, + 672 + ], + "type": "text", + "content": "2.2. Data-Driven HSI Priors Modeling" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "The advent of deep learning has revolutionized the field of HSI reconstruction. Models such as HyperReconNet [44], " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "-net [33], TSA-Net [31], DNU [46], DGSMP [23] and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24882" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "PnP-DIP-HSI [32] have markedly improved reconstruction quality by modeling HSI data prior knowledge. Furthermore, the introduction of Transformer-based methods like MST [7], CST [6], DAU [9], RDLUF [16], and PADUT [27] has led to even more significant advances in reconstruction performance. Benefiting from the attention mechanism, Transformers can efficiently model both spatial and spectral similarities within HSI data, enabling a more flexible handling of input data and providing a richer feature representation for HSI reconstruction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 202, + 226, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 202, + 226, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 202, + 226, + 213 + ], + "type": "text", + "content": "2.3. PAN-Guided HSI Reconstruction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 221, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 287, + 424 + ], + "type": "text", + "content": "The integration of PAN guidance in HSI reconstruction represents a significant stride in addressing the inherent limitations of traditional CASSI. ANSR[42, 45] proposed an adaptive non-local sparse representation model, guided by the PAN image. PFusion[21] leveraged RGB measurements for spatial coefficient estimation and CASSI measurements for spectral basis acquisition. It features a patch processing strategy to enhance the spectral low-rank property, optimizing the model efficiently without iterative methods or a spectral sensing matrix. PIDS[13] utilized the RGB measurement as a prior image to enhance semantic correspondence between HSI and the PAN image. These methods have marked significant advancements in the field. However, they often require manual parameter tuning and fail to leverage the rich spatial context and detailed features embedded within the PAN image, suggesting potential areas for further improvements in reconstruction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 485 + ], + "type": "text", + "content": "Our motivation is to utilize the spatial semantic information provided by the PAN image to improve the HSI reconstruction result in DCCHI. We aim to develop a method that combines the strengths of PAN guidance to model the intra-inter similarity for more accurate reconstruction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 499, + 96, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 96, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 96, + 511 + ], + "type": "text", + "content": "3. PGDU" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 520, + 183, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 520, + 183, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 520, + 183, + 532 + ], + "type": "text", + "content": "3.1. DCCHI Forward Model" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 539, + 287, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 623 + ], + "type": "text", + "content": "DCCHI consists of a beam splitter, a CASSI branch, and a PAN camera branch, as shown in Figure 2. The beam splitter divides the incident light from the scene into two equal-intensity parts. One part of the light is captured by CASSI, which undergoes spatial modulation and spectral modulation to form the CASSI measurement. The other part of the light is directly captured by the PAN camera." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "\\mathcal{X} \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": " represent the spectral image of the target scene, where " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 623, + 287, + 672 + ], + "type": "text", + "content": " are the height, width, and number of spectral bands, respectively. The spatial and spectral modulation in CASSI is given by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 90, + 683, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 683, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 90, + 683, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} ^ {\\mathbf {c}} = \\sum_ {c = 1} ^ {C} \\operatorname {s h i f t} (\\phi \\odot \\mathcal {X} [:,: c ]) + \\mathbf {V} ^ {\\mathbf {c}}, \\tag {1}", + "image_path": "d3385137bb7a68cfb57aa8f6560d9be1b5643238c63ebb6bd48a30c427e9fa1c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 322, + 70, + 535, + 233 + ], + "blocks": [ + { + "bbox": [ + 322, + 70, + 535, + 233 + ], + "lines": [ + { + "bbox": [ + 322, + 70, + 535, + 233 + ], + "spans": [ + { + "bbox": [ + 322, + 70, + 535, + 233 + ], + "type": "image", + "image_path": "e538731b52e1f510bc135ce8279593ff0139ac3d56a2704f24cb98c1838c93aa.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 243, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 305, + 243, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 545, + 264 + ], + "type": "text", + "content": "Figure 2. The dual-camera compressive hyperspectral imaging system." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "content": " is the transmission intensity of the coded aperture, represented as " + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "inline_equation", + "content": "\\phi \\in \\mathbb{R}^{H\\times W}" + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "content": ", shift " + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "content": " indicates the spectral modulation caused by the dispersion prism, " + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\mathrm{c}}" + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "content": " is the image captured by the CASSI branch, and " + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{\\mathrm{c}}" + }, + { + "bbox": [ + 305, + 270, + 545, + 328 + ], + "type": "text", + "content": " is regarded as Gaussian noise in CASSI." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 330, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 330, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 330, + 545, + 354 + ], + "type": "text", + "content": "To simplify to a matrix-vector form, the imaging model of the CASSI branch is represented as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 389, + 359, + 545, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 359, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 389, + 359, + 545, + 371 + ], + "type": "interline_equation", + "content": "\\mathbf {y} ^ {\\mathrm {c}} = \\boldsymbol {\\Phi} ^ {\\mathrm {c}} \\mathbf {x} + \\mathbf {v} ^ {\\mathrm {c}}, \\tag {2}", + "image_path": "69777805dbfdbc69d904705bd2c623e197084aab4c7b3f029e98aae8596210a0.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\Phi^{\\mathbf{c}}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": " denotes the imaging model of the CASSI branch sensing matrix, " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathbf{c}}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": " is the vector form of " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\mathbf{c}}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": " is the vector form of " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{v}^{\\mathbf{c}}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": " is the vector form of " + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{\\mathbf{c}}" + }, + { + "bbox": [ + 305, + 377, + 545, + 412 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 413, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 413, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 545, + 437 + ], + "type": "text", + "content": "Correspondingly, the imaging model of the PAN camera branch is described by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 388, + 442, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 442, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 388, + 442, + 545, + 455 + ], + "type": "interline_equation", + "content": "\\mathbf {y} ^ {\\mathrm {p}} = \\boldsymbol {\\Phi} ^ {\\mathrm {p}} \\mathbf {x} + \\mathbf {v} ^ {\\mathrm {p}}, \\tag {3}", + "image_path": "83af832159b284716d87cdc84ea05ddf7bcdf8d563e815a2761dbb4f37bbb787.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\Phi^{\\mathbf{P}}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " denotes the imaging model of the PAN camera branch sensing matrix, determined by the spectral response of the sensor, " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{c}}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " is the vector form of PAN measurement, and " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{v}^{\\mathrm{P}}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " is regarded as Gaussian noise in the PAN measurement. To connect the imaging models to the subsequent discussion, we define " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 340, + 536, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 536, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 340, + 536, + 545, + 563 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = \\left[ \\begin{array}{l} \\mathbf {y} ^ {\\mathrm {c}} \\\\ \\mathbf {y} ^ {\\mathrm {p}} \\end{array} \\right], \\quad \\boldsymbol {\\Phi} = \\left[ \\begin{array}{l} \\boldsymbol {\\Phi} ^ {\\mathrm {c}} \\\\ \\boldsymbol {\\Phi} ^ {\\mathrm {p}} \\end{array} \\right], \\quad \\mathbf {v} = \\left[ \\begin{array}{l} \\mathbf {v} ^ {\\mathrm {c}} \\\\ \\mathbf {v} ^ {\\mathrm {p}} \\end{array} \\right]. \\tag {4}", + "image_path": "5be4ada59bcabffe7410a9dc62e50c9f40ac418ff6efe1f70b292125221ab042.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 567, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 545, + 590 + ], + "type": "text", + "content": "Using the above definitions, the imaging model can be expressed as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 395, + 590, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 590, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 395, + 590, + 545, + 602 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = \\boldsymbol {\\Phi} \\mathbf {x} + \\mathbf {v}, \\tag {5}", + "image_path": "86844d0733b703bb40d1a1754de3629e3286a893b3f3bec5086653317d2bd90f.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is a sensing matrix in " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{M\\times N}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " that encodes the system mapping from the original scene " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " to the measurements " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}\\in \\mathbb{R}^{M\\times 1}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}\\in \\mathbb{R}^{N\\times 1}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Phi \\in \\mathbb{R}^{M\\times N}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The dimensions " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " are defined as follows: " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is calculated as " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "H(W + d(C - 1)) + HW" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is calculated as " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "HWC" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " represents the dispersion step size. It is important to note that in the context of HSI reconstruction, " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is typically much smaller than " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", highlighting that the HSI reconstruction task in DCCHI is an ill-posed problem." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24883" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 90, + 71, + 504, + 240 + ], + "blocks": [ + { + "bbox": [ + 90, + 71, + 504, + 240 + ], + "lines": [ + { + "bbox": [ + 90, + 71, + 504, + 240 + ], + "spans": [ + { + "bbox": [ + 90, + 71, + 504, + 240 + ], + "type": "image", + "image_path": "aabaf940b7620b995bd7df05727d69f8a09ebc27155e27a02f2534ca7932786f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 547, + 277 + ], + "type": "text", + "content": "Figure 3. Overview of PGDU. The InitialNet initiates the process with compressive measurements and sensing matrix, followed by a series of stages each containing a conjugate gradient (CG) block and an In2SET denoiser." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 289, + 200, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 200, + 301 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 200, + 301 + ], + "type": "text", + "content": "3.2. Reconstruction Framework" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 288, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 288, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 288, + 403 + ], + "type": "text", + "content": "Compared to learn a brute-force mapping between HSI x and measurement y, model-based methods have potential in compressive imaging due to fully considering the imaging model. Model-based methods usually formulate HSI reconstruction as a Bayesian inference challenge, solving Eq. (5) under a unified Maximum A Posteriori (MAP) framework. Mathematically, the optimization problem for HSI reconstruction could be expressed as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 405, + 287, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 405, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 91, + 405, + 287, + 428 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = \\arg \\min _ {\\mathbf {x}} \\frac {1}{2} \\| \\mathbf {y} - \\boldsymbol {\\Phi} \\mathbf {x} \\| _ {2} ^ {2} + \\eta J (\\mathbf {x}), \\tag {6}", + "image_path": "4027e2e7757733e06f219885c377360877f27dc5b387e37b7c648fbea8d445d1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "inline_equation", + "content": "J(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "text", + "content": " represents regularization. The parameter " + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "text", + "content": " is a regularization coefficient, controlling the trade-off between data fidelity and the regularization term imposed by " + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "inline_equation", + "content": "J(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 429, + 287, + 464 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "type": "text", + "content": "To solve the optimization problem shown in Eq. (6), we design the PGDU based on the physical structure of DC-CHI, as shown in Figure 3. Utilizing the half quadratic splitting (HQS) method, we decompose the optimization problem into two sub-problems: the data fidelity term, as shown in Eq. (7); and the prior term, as shown in Eq. (8)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 538, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 538, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 59, + 538, + 287, + 559 + ], + "type": "interline_equation", + "content": "\\mathbf {x} ^ {k + 1} = \\arg \\min _ {\\mathbf {x}} \\left\\| \\mathbf {y} - \\boldsymbol {\\Phi} \\mathbf {x} \\right\\| _ {2} ^ {2} + \\mu^ {k + 1} \\left\\| \\mathbf {z} ^ {k} - \\mathbf {x} \\right\\| _ {2} ^ {2}, \\quad (7)", + "image_path": "1c27471a5bb9f6d385f04829becee5980fc512fb2cc45bf9227e051ff70aea2a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 568, + 287, + 592 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 568, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 568, + 287, + 592 + ], + "type": "interline_equation", + "content": "\\mathbf {z} ^ {k + 1} = \\arg \\min _ {\\mathbf {z}} \\frac {1}{2} \\mu^ {k + 1} \\left\\| \\mathbf {z} - \\mathbf {x} ^ {k + 1} \\right\\| _ {2} ^ {2} + \\eta^ {k + 1} J (\\mathbf {z}), (8)", + "image_path": "43f34f0c17284e0a2b6ff31ea5a86c18dd0530b0f8a5b1646a233d753114a4b4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": "the superscript " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": " indicates the stage index number, and " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": " is an auxiliary variable introduced to facilitate the optimization. The parameter " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mu^{k + 1}" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": " is a relaxation parameter that governs the alignment between the current estimate " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": " and the auxiliary variable " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": ". The parameter " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\eta^{k + 1}" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": " is a stage-specific parameter for the regularization coefficient " + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 666, + 287, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 690 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 690 + ], + "type": "text", + "content": "The data fidelity term can be directly calculated in closed form, as demonstrated in Eq. (9)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 73, + 693, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 693, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 73, + 693, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {x} ^ {k + 1} = \\left(\\boldsymbol {\\Phi} ^ {\\mathrm {T}} \\boldsymbol {\\Phi} + \\mu \\mathbf {I}\\right) ^ {- 1} \\left(\\boldsymbol {\\Phi} ^ {\\mathrm {T}} \\mathbf {y} + \\mu^ {k + 1} \\mathbf {z} ^ {k}\\right), \\tag {9}", + "image_path": "0d700f9243fb31b445cc5a7333190232d5c61daf4597dd07515ba634be1b425c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "type": "text", + "content": "in the context of HSI reconstruction in CASSI, the matrix " + }, + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\Phi^{\\mathsf{T}}\\Phi" + }, + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "type": "text", + "content": " is strictly diagonal. However, with the addition of the PAN camera branch in DCCHI, the matrix " + }, + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\Phi^{\\mathsf{T}}\\Phi" + }, + { + "bbox": [ + 305, + 289, + 545, + 350 + ], + "type": "text", + "content": " becomes only diagonally dominant, and thus a closed-form solution cannot be explicitly calculated." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 350, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 415 + ], + "type": "text", + "content": "Given the non-diagonal form of " + }, + { + "bbox": [ + 305, + 350, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\Phi^{\\mathrm{T}}\\Phi" + }, + { + "bbox": [ + 305, + 350, + 545, + 415 + ], + "type": "text", + "content": ", we employ the conjugate gradient (CG) method [34] for the efficient resolution of the data fidelity term. The CG method is well suited for this problem due to its effectiveness in solving large-scale, sparse linear systems." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "type": "text", + "content": "To fully explore the guidance of the PAN image " + }, + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathbb{P}}" + }, + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "type": "text", + "content": " on prior term, we design a PAN-guided Gaussian denoiser to estimate " + }, + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{k + 1}" + }, + { + "bbox": [ + 305, + 418, + 545, + 455 + ], + "type": "text", + "content": ". This is formulated as Eq. (10):" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 472, + 545, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 472, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 318, + 472, + 545, + 488 + ], + "type": "interline_equation", + "content": "\\mathbf {z} ^ {k + 1} = \\operatorname {D e n o i s e r} _ {k + 1} \\left(\\mathbf {x} ^ {k + 1}, \\mathbf {G F E} (\\mathbf {y} ^ {\\mathbf {p}}), \\sigma^ {k + 1}\\right), \\tag {10}", + "image_path": "f7993a3d854013ee9564cc2a0ffa4ae21417be0a2e0af24d94c957c4b696ec71.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{GFE}(\\mathbf{y}^{\\mathrm{P}})" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": " serves as structural guidance for the denoising, which incorporates multi-scale spatial details from the high-resolution " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{P}}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": " data into the denoiser, aiming to refine the fidelity of the reconstructed HSI by adding contextual information. The Gaussian noise level of the denoiser, denoted as " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\sigma^{k + 1}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": ", is equal to " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\sqrt{\\eta^{k + 1} / \\mu^{k + 1}}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mu^{k + 1}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\sigma^{k + 1}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": " are the elements of vectors " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\pmb{\\sigma}" + }, + { + "bbox": [ + 305, + 505, + 545, + 601 + ], + "type": "text", + "content": ", which are inferred by the InitialNet of PGDU." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The feature extraction from " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{P}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is delineated as follows: within the unrolling framework, the feature representation of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{P}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is extracted singularly and iteratively shared across multiple stages. A stack of convolutional blocks is utilized to harvest feature maps at varying resolutions, assembling a guided feature pyramid " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "[\\mathbf{G}_1,\\mathbf{G}_2,\\mathbf{G}_3]" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The guided feature pyramid is integral to the subsequent denoising stage, aiding in the preservation of intricate spatial details during the denoising." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24884" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 221, + 272 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 221, + 272 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 221, + 272 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 221, + 272 + ], + "type": "image", + "image_path": "2785e85d7758ada156f21e37d991e91e4a3b4c67dc46b540e515ca69d9aa0926.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 114, + 278, + 164, + 291 + ], + "lines": [ + { + "bbox": [ + 114, + 278, + 164, + 291 + ], + "spans": [ + { + "bbox": [ + 114, + 278, + 164, + 291 + ], + "type": "text", + "content": "(a) In2SET" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 227, + 71, + 541, + 184 + ], + "blocks": [ + { + "bbox": [ + 227, + 71, + 541, + 184 + ], + "lines": [ + { + "bbox": [ + 227, + 71, + 541, + 184 + ], + "spans": [ + { + "bbox": [ + 227, + 71, + 541, + 184 + ], + "type": "image", + "image_path": "405407587229aa573a3aa7b47662399b913c4ebcb6febdf2b82af77ac289e540.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 225, + 188, + 541, + 296 + ], + "blocks": [ + { + "bbox": [ + 225, + 188, + 541, + 296 + ], + "lines": [ + { + "bbox": [ + 225, + 188, + 541, + 296 + ], + "spans": [ + { + "bbox": [ + 225, + 188, + 541, + 296 + ], + "type": "image", + "image_path": "19776c7f9b5c51cf5ff1b9ad526c2878024d9c5c9b3ad577010874ebf7b8bf04.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 311, + 546, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 311, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 546, + 354 + ], + "type": "text", + "content": "Figure 4. Diagram of In2SET architecture. (a) The U-shaped In2SET structure. (b) In2AB, consisting of two normalization layers, an intra-similarity attention module, an inter-similarity attention module, and an FFN layer. (c) The components of NPL. (d) The multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S). (e) The cosine similarity reweighting (CRW) mechanism." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 374, + 102, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 374, + 102, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 374, + 102, + 387 + ], + "type": "text", + "content": "4. In2SET" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 394, + 167, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 167, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 167, + 406 + ], + "type": "text", + "content": "4.1. Overall Architecture" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": "In this section, we introduce the denoiser In2SET within the PGDU framework. As shown in Figure 4 (a), the proposed In2SET adopts a U-shaped architecture [36], involving the intra-inter attention block (In2AB) as the foundational units. This architecture employs multi-scale feature extraction coupled with skip connections between the encoder and decoder, enhancing the efficiency in information processing and feature extraction. To be specific, the denoiser initializes feature map " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": " from the spectral image " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{k + 1}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": " and the noise level " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\sigma^{k + 1}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": ", passing through a convolutional layer with a kernel size of " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": ". The input fed into each In2AB consists of guided feature " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{G_i}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": ", feature maps extracted from the PAN image, and HSI feature " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": ". The denoised image " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{k + 1}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": " is the sum of " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{k + 1}" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": " and the output of the last In2AB, calculated by a convolutional layer with a kernel size of " + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 413, + 289, + 665 + ], + "type": "text", + "content": ". The In2AB structure is shown in Figure 4 (b). Our In2AB module includes two normalization layers, one intra-similarity attention module, one intersimilarity attention module, and one feed-forward fully connected (FFN) layer. In the following, we introduce the detail of the intra-similarity and inter-similarity." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 671, + 192, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 192, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 192, + 684 + ], + "type": "text", + "content": "4.2. Intra-Similarity Attention" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Our intra-similarity attention module is grounded on two key principles: firstly, for exploring intra-spatial similarity," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "content": "the comprehensive and continuous spatial data provided by the PAN image are invaluable. This allows the spatial similarity in the PAN image to serve as an effective proxy for approximating the spatial similarity of the HSI. Secondly, in addressing intra-spectral similarity, analyzing the reconstructed HSI becomes significantly more effective, given the PAN image's deficiency in spectral color information." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 460, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 543 + ], + "type": "text", + "content": "As shown in Figure 4 (b), our intra-similarity attention module includes two branches: multi-head self-attention in channel (MHA-C) and multi-head cross-attention in spatial (MHA-S), representing the exploration of spectral and spatial self-similarity, respectively. The MHA-C is based on the work in MST [7], which has been demonstrated to effectively explore spectral self-similarity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": "The input features " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": " have dimensions " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times \\hat{C}}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": ", respectively, where " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\hat{C} = \\frac{C}{2}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": ". After normalization and partitioning, the dimensions become " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{B\\times N\\times C}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{B\\times N\\times \\hat{C}}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": ". In the first and last layers of HSAB within In2SET, " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "B = \\frac{HW}{M^2}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "N = M^2" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": ". For the remaining layers, dimensions are recalibrated to " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "B = M^2" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "inline_equation", + "content": "N = \\frac{HW}{M^2}" + }, + { + "bbox": [ + 304, + 543, + 545, + 643 + ], + "type": "text", + "content": ". Following linear projection as shown in Eq. (11) and Eq. (12)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 347, + 650, + 545, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 650, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 347, + 650, + 545, + 663 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {1}, \\mathbf {K} _ {1}, \\mathbf {V} _ {1}, \\mathbf {V} _ {2} = L _ {Q _ {1}, K _ {1}, V _ {1}, V _ {2}} (\\mathbf {X}), \\tag {11}", + "image_path": "de9c231c876fae98843f6956ceaa8b76ce8f0db496e5472513858b5b77146b66.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 376, + 682, + 545, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 682, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 376, + 682, + 545, + 695 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {2}, \\mathbf {K} _ {2} = L _ {Q _ {2}, K _ {2}} (\\mathbf {G}), \\tag {12}", + "image_path": "d2ab7cf456f1e10734a9c905f8c32f7b6bcd69206135ae452fcc2df211335440.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "type": "text", + "content": " is projected to " + }, + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_1, \\mathbf{K}_1, \\mathbf{V}_1 \\in \\mathbb{R}^{B \\times \\hat{C} \\times N}" + }, + { + "bbox": [ + 306, + 700, + 545, + 714 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24885" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 70, + 509, + 403 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 509, + 403 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 509, + 403 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 509, + 403 + ], + "type": "table", + "html": "
MethodGFLOPsSceneAverage
01020304050607080910
PFusion-RGB [21]-40.0938.8438.7046.6532.0737.1239.7436.7534.5235.5338.00
0.9790.9680.9660.9360.9800.9800.9640.9650.9310.9790.965
PIDS-RGB [13]-42.0940.0841.5048.5540.0539.0036.6337.0238.8238.6440.24
0.9830.9490.9680.9890.9820.9740.9400.9480.9530.9800.967
TV-DC [39]-35.8133.2231.0740.1133.3234.6231.0932.3129.3633.8433.47
0.9470.8850.8790.9470.9440.9430.8850.9160.8620.9530.910
PIDS-DC [13]-39.8237.0737.7246.7837.4537.7432.9031.6634.3538.5837.41
0.9770.9210.9500.9780.9730.9630.8960.9150.9020.9720.945
BiSRNet-DC [10]1.3335.0234.1331.5035.8833.7035.5832.3132.7331.3734.4833.67
0.9450.9140.8830.8950.9350.9250.9000.9030.8990.9360.914
CST-DC [6]25.4037.4438.9136.7942.2736.5738.9136.8735.9135.8737.9337.75
0.9750.9780.9690.9830.9820.9840.9670.9800.9730.9900.978
HDNet-DC [22]144.3138.0639.7938.2142.7937.2239.2637.4136.5136.6437.5238.34
0.9760.9820.9730.9830.9830.9860.9680.9820.9760.9880.980
MST-DC [7]25.7738.3840.4537.6342.8837.7239.6637.5637.4037.8638.1038.76
0.9760.9760.9660.9750.9780.9760.9650.9710.9710.9810.974
MST++-DC [8]17.6938.3840.4737.7043.8837.7539.4237.4837.3838.8239.0439.03
0.9770.9800.9680.9840.9830.9850.9640.9820.9800.9890.980
DAUHST-DC-2stg [9]16.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0440.22
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.983
DAUHST-DC-3stg [9]24.7040.2243.5241.7447.0738.8140.1639.8638.2140.6339.3240.95
0.9830.9890.9810.9930.9850.9870.9780.9810.9830.9900.985
DAUHST-DC-5stg [9]40.5140.7444.0041.5846.8439.6640.8940.2138.7239.9840.1041.27
0.9840.9890.9810.9910.9860.9870.9790.9830.9820.9890.916
DAUHST-DC-9stg [9]72.1141.5945.1943.4748.9240.2741.1740.7340.1143.5041.3342.62
0.9850.9910.9840.9930.9880.9880.9790.9860.9880.9900.987
In2SET-2stg (Ours)14.3540.3342.3040.3447.2439.4240.6139.4638.4240.3739.9640.84
0.9830.9850.9770.9910.9860.9860.9750.9790.9810.9880.983
In2SET-3stg (Ours)20.7940.7843.1341.7347.0939.8440.9039.7538.9841.2940.0441.35
0.9830.9870.9800.9900.9870.9860.9760.9810.9830.9880.984
In2SET-5stg (Ours)33.6641.1344.4342.7447.2940.3340.9540.4939.1542.0739.4441.80
0.9850.9900.9830.9930.9880.9870.9790.9820.9850.9870.985
In2SET-9stg (Ours)59.4042.5646.4244.5550.6342.0142.4941.5940.5343.8342.3343.69
0.9890.9940.9860.9960.9920.9910.9830.9890.9900.9940.990
", + "image_path": "6dd93b94fe772ca8c68618a95cdc7dffbe05733efd20ab69d962e91d6b196aeb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 411, + 547, + 445 + ], + "lines": [ + { + "bbox": [ + 46, + 411, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 547, + 445 + ], + "type": "text", + "content": "Table 1. Comparison of In2SET with SOTA DCCHI methods across 10 simulated scenes, including FLOPS, PSNR (upper entry), and SSIM (lower entry). \"Method-RGB\" indicates the use of RGB observations, while \"Method-DC\" denotes grayscale observations in PAN images. It is noted that \"Method-DC\" is modified from other HSI reconstruction method for the DCCHI reconstruction task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_2 \\in \\mathbb{R}^{B \\times N \\times \\hat{C}}" + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "text", + "content": " is projected to " + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_2" + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_2 \\in \\mathbb{R}^{B \\times N \\times \\hat{C}}" + }, + { + "bbox": [ + 47, + 456, + 278, + 471 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 471, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 287, + 495 + ], + "type": "text", + "content": "The computations of MHA-C and MHA-S can be represented by Eq. (13) and Eq. (14)," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 503, + 287, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 503, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 88, + 503, + 287, + 532 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {1} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {1} \\mathbf {K} _ {1} ^ {T}}{\\sqrt {d _ {h 1}}} + \\mathbf {P} _ {1}\\right) \\mathbf {V} _ {1}, \\tag {13}", + "image_path": "a6bee573b8dd0d4d762fc0310aca9f1a44782031e4398206f4a3c5ea32771aca.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 89, + 543, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 543, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 89, + 543, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {2} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {2} \\mathbf {K} _ {2} ^ {T}}{\\sqrt {d _ {h 2}}} + \\mathbf {P} _ {2}\\right) \\mathbf {V} _ {2}, \\tag {14}", + "image_path": "4405efd931eadbcbb9757bc3b573f90c89f5cfccd1dca75ddb8c7e34486c6779.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\sqrt{d_{h1}}" + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\sqrt{d_{h2}}" + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "text", + "content": " are scalars as defined in [9], " + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_1 \\in \\mathbb{R}^{B \\times \\hat{C} \\times \\hat{C}}" + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_2 \\in \\mathbb{R}^{B \\times N \\times N}" + }, + { + "bbox": [ + 47, + 576, + 287, + 613 + ], + "type": "text", + "content": " denote learnable positional encodings." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "type": "text", + "content": "The output of intra-attention " + }, + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathrm{intra}}" + }, + { + "bbox": [ + 47, + 613, + 287, + 638 + ], + "type": "text", + "content": " can be obtained by Eq. (15)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 639, + 287, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 639, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 639, + 287, + 652 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {\\text {i n t r a}} = \\operatorname {C o n c a t} \\left(\\mathbf {X} _ {1}, \\mathbf {X} _ {2}\\right). \\tag {15}", + "image_path": "946a42685084863db5dc3d0d4d679e31aa46064c7fda0fede998272063bec6ca.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 192, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 192, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 192, + 672 + ], + "type": "text", + "content": "4.3. Inter-Similarity Attention" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "We establish our inter-similarity attention module based on one principle: the shallow semantic features of the PAN image and the corresponding HSI area are similar, including" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 458, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 518 + ], + "type": "text", + "content": "consistency in texture, shape features, and low-level image attributes (brightness and contrast). The credibility of the reconstructed area is directly proportional to this consistency. Inter-similarity attention explores cross-modal similarity using cosine similarity reweighting (CRW)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "text", + "content": "After exploiting intra-similarity, the output of the intrasimilarity attention module " + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathrm{intra}}" + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "text", + "content": " is projected to obtain " + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_3" + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_3" + }, + { + "bbox": [ + 304, + 518, + 545, + 554 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 367, + 561, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 561, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 367, + 561, + 545, + 574 + ], + "type": "interline_equation", + "content": "\\mathbf {K} _ {3}, \\mathbf {V} _ {3} = L _ {K _ {3}, V _ {3}} \\left(\\mathbf {X} _ {\\text {i n t r a}}\\right), \\tag {16}", + "image_path": "838ef0a9154f22f6d80029fef21312c65eddda249d4a239a7848bb5191232e89.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 580, + 489, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 489, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 489, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 580, + 489, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_3\\in \\mathbb{R}^{B\\times N\\times \\hat{C}}" + }, + { + "bbox": [ + 304, + 580, + 489, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 580, + 489, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{V_3}\\in \\mathbb{R}^{B\\times N\\times C}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 615 + ], + "type": "text", + "content": "Then, the computations of CRW can be represented as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 364, + 613, + 545, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 613, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 364, + 613, + 545, + 640 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {\\text {i n t e r}} = \\frac {\\mathbf {Q} _ {2} \\cdot \\mathbf {K} _ {3}}{\\| \\mathbf {Q} _ {2} \\| \\| \\mathbf {K} _ {3} \\|} \\odot \\mathbf {V} _ {3}, \\tag {17}", + "image_path": "913e18135974b9cd133e4bda86d4328a7d7899115e968b6f12ca2fc4a04cf797.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "where the cosine similarity computed along the last dimension between " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_2" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_3" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " quantifies the feature alignment in corresponding areas. A higher similarity score reflects a stronger feature correspondence, which, in turn, informs the enhanced weighting of " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_3" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": ", improving the fidelity of the region being reconstructed." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24886" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 286, + 175 + ], + "type": "text", + "content": "In this section, we begin by introducing detailing the network training process. Subsequently, we evaluate the performance of In2SET on both simulation and real-world DC-CHI datasets. Then, we validate the effectiveness of the intra-similarity block using statistical simulation data. Finally, we perform an ablation study to demonstrate the effectiveness of our proposed method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "type": "text", + "content": "Simulation Dataset. Two distinct datasets are used: CAVE [50] and KAIST [14]. The CAVE dataset is made up of 32 hyperspectral images with " + }, + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "type": "text", + "content": " spatial resolution. The KAIST dataset contains 30 hyperspectral images, each with a larger spatial dimension of " + }, + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "type": "inline_equation", + "content": "2704 \\times 3376" + }, + { + "bbox": [ + 46, + 175, + 286, + 282 + ], + "type": "text", + "content": ". The CAVE dataset is used as the training data, while a subset of 10 scenes crop from the KAIST dataset is used for the evaluation phase, in accordance with the protocols established in references [7, 9, 22, 23, 31]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": "Implementation. Our method is implemented with Pytorch and trained with Adam [24] optimizer for 300 epochs. During training, the learning rate is " + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "inline_equation", + "content": "4 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": " using the cosine annealing scheduler, and the loss function for network training is " + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": " loss. We randomly extract patches from 3D HSI cubes to serve as training samples. The dimensions of these patches are " + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 28" + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": " for the simulation experiment and " + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "inline_equation", + "content": "350 \\times 260 \\times 26" + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": " for the real-world experiment. In simulation imaging model, we configure a dispersion shift step " + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": " of 2, directing the dispersion to the right. In real-word imaging model, the dispersion shift step " + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 284, + 286, + 427 + ], + "type": "text", + "content": " is set to 1, with the dispersion oriented upwards." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 434, + 183, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 183, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 183, + 445 + ], + "type": "text", + "content": "5.1. Simulation Data Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 286, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 286, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 286, + 485 + ], + "type": "text", + "content": "The reconstruction quality of hyperspectral images are assessed using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) [48] metrics." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "type": "text", + "content": "The Table 1 clearly shows that In2SET excels in all test scenarios, particularly in In2SET-9stg, achieving the best performance across all scenes with an average PSNR of " + }, + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "type": "inline_equation", + "content": "43.69\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "type": "text", + "content": " and a SSIM of 0.990. This significantly surpasses model optimization methods like TV-DC and PIDS-DC. Compared to deep learning-based methods, such as various stages of DAUHST-DC [9], In2SET demonstrates remarkable superiority. In2SET-3stg achieves performance comparable to that of DAUHST-DC-5stg [9], but with only " + }, + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "type": "inline_equation", + "content": "51.3\\%" + }, + { + "bbox": [ + 46, + 486, + 286, + 616 + ], + "type": "text", + "content": " of the cost, amounting to 20.78 GFLOPs compared to 40.50 GFLOPs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 286, + 713 + ], + "type": "text", + "content": "To facilitate a direct visual quality assessment, we analyzed the distinction between Ground Truth (GT) and the reconstructions produced by various open-source methods. Figure 5 presents reconstruction results for selected spectral bands. These results are generated from two model-based approaches, TV-DC [39] and PIDS-DC [13], five end-to-end network algorithms, BiSRNet-DC [10], CST-DC [6], HDNet-DC [22], MST-DC [7], MST++-DC [8], as well as" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 306, + 69, + 547, + 118 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 547, + 118 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 547, + 118 + ], + "type": "table", + "html": "
RMSECorrelationPSNR(dB)
CAVE0.0340.99936.28
KAIST0.0250.99635.74
ICVL0.0760.99731.10
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BaselineCRWMHA-CMHA-SPSNR(dB)SSIMGFLOPs
✓37.230.9449.87
✓✓40.050.98011.19
✓✓✓40.460.98214.06
✓✓✓✓40.840.98314.35
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MethodsCG-1CG-2CG-5CG-10
PSNR(dB)40.4240.6640.8441.05
SSIM0.9820.9830.9830.984
FPS26.4522.7919.1613.99
", + "image_path": "ac20894f7adec266b26cd79178ef58289cb986eabf04a2dde55c0f95bd0c2e5b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 287, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 306, + 287, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 545, + 308 + ], + "type": "text", + "content": "Table 4. Ablation study on iterative performance of conjugate gradient descent for data item." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 316, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 545, + 363 + ], + "type": "text", + "content": "from two deep unfolding methods, namely DAUHST-DC9stg [9] and our In2SET-9stg. The comparison underlines the exceptional ability of our In2SET approach to maintain spatial and spectral fidelity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 363, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 545, + 483 + ], + "type": "text", + "content": "We suggest that the intra similarity in PAN image can effectively approximates that in HSI. To support this, we experiment with three public datasets: CAVE [50], KAIST [14] and ICVL [1]. We compute spatial correlation maps for each scene, comparing the correlation map of the HSI with that of the corresponding PAN image. The results of this comparison are displayed in Table 2, indicating a high degree of similarity between the intra-spatial correlations in PAN images and HSI. More visual results are presented in the supplementary materials." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 487, + 411, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 411, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 411, + 498 + ], + "type": "text", + "content": "5.2. Real Data Results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "content": "In this research, we used a real-world DCCHI measurement Ninja, taken from publicly available data as detailed in reference [42]. Figure 6 illustrates the reconstruction results for four spectral bands in this scene, using various DCCHI reconstruction algorithms. The comparison highlights the superior image restoration quality of our model over other methods, validating its effectiveness and reliability in real-world applications." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 602, + 399, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 602, + 399, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 602, + 399, + 615 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 618, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 618, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 305, + 618, + 545, + 652 + ], + "type": "text", + "content": "To verify the effectiveness of our proposed method, we conducted ablation studies for the In2SET method. All evaluations are conducted on simulated datasets." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": "Break-down Ablation. The break-down study, as delineated in Table 3, offers a detailed examination of how each component within our proposed method influences reconstruction performance. 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Comparative reconstruction results of different reconstruction methods for Scene 3 from the KAIST dataset at spectral bands " + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "inline_equation", + "content": "476.5\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "inline_equation", + "content": "536.5\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "inline_equation", + "content": "584.5\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "inline_equation", + "content": "625.0\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 260, + 545, + 283 + ], + "type": "text", + "content": ". The spectral density curves are plotted from the blue region in the colorchecker." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 63, + 289, + 271, + 542 + ], + "lines": [ + { + "bbox": [ + 63, + 289, + 271, + 542 + ], + "spans": [ + { + "bbox": [ + 63, + 289, + 271, + 542 + ], + "type": "image", + "image_path": "f469dbd086c0149eb039d9dc1739035ec207fd622394439b32ef2a8346738538.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "text", + "content": "Figure 6. Visualization of reconstruction performance across different spectral bands on real data. The spectral bands selected for comparison are " + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "inline_equation", + "content": "481.5\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "inline_equation", + "content": "544.0\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "inline_equation", + "content": "594.5\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "inline_equation", + "content": "614.5\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 550, + 287, + 583 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "model achieves a PSNR of 37.23 dB. The addition of the CRW component leads to a significant increase in PSNR by " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "+2.82" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " dB, albeit at an increased computational cost of " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "+1.32" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " GFLOPs. The subsequent integration of MHA-C further elevates the PSNR by " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "+0.41" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " dB. The final inclusion of MHA-S brings an additional PSNR gain of " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "+0.38" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " dB. These step-by-step enhancements highlight the critical role each component plays in enhancing the overall capability of the model for HSI reconstruction, demonstrating a progressive improvement in performance with each added component." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 290, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 290, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 290, + 545, + 384 + ], + "type": "text", + "content": "Ablation Study of CG Iterations. Table 4 presents a comparative analysis of PSNR, SSIM, and Frames Per Second (FPS) metrics across varying numbers of CG iterations for HSI reconstruction. The CG-1, which conducts a single iteration, essentially operates as a vanilla gradient descent. These experiments are conducted on a system equipped with a TITAN Xp GPU (12GB) and an Intel (R) Xeon (R) Platinum 8358P CPU @ 2.60GHz." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 387, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 387, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 545, + 494 + ], + "type": "text", + "content": "There is a clear trend of improvement in PSNR as the number of CG iterations increases from 1 to 10, with values escalating from 40.42 dB to 41.05 dB. However, an increase in iterations from CG-1 to CG-10 leads to a decrease in FPS from 26.45 dB to 13.99 dB, indicating a trade-off between reconstruction quality and computational speed. A notable observation is that CG-5 offers an optimal balance between time efficiency and performance, making it the preferred choice for our In2SET network." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 506, + 378, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 378, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 378, + 517 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 524, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 679 + ], + "type": "text", + "content": "In this paper, we propose the In2SET for DCCHI reconstruction. Our method maximizes PAN image utility for HSI reconstruction by: (1) approximating HSI intrasimilarity using PAN image, addressing the unreliability of direct computation from intermediate results. (2) Leveraging inter-similarity between HSI and PAN images to accurately reconstruct regions, providing cues for uncertain areas. Integrating In2SET into a PGDU framework allowed us to substantially enhance the spatial-spectral fidelity and detail of reconstructed images. Experiments on real and simulated datasets show that our method consistently outperforms the state-of-the-art while maintaining lower computational complexity." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 305, + 680, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 680, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 680, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments This work is partially supported by the National Natural Science Foundation of China under grants 62322204, 62131003, 62072038 and 62302041." + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24888" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 94, + 106, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 94, + 106, + 106 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 106, + 106 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 114, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 114, + 286, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 286, + 147 + ], + "type": "text", + "content": "[1] Boaz Arad and Ohad Ben-Shahar. 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Nature Communications, 14(1):5043, 2023. 1" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24891" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_content_list.json b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..693b8df434055b67bfd2df8aa0d1a879d381deb6 --- /dev/null +++ b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_content_list.json @@ -0,0 +1,1777 @@ +[ + { + "type": "text", + "text": "InNeRF360: Text-Guided 3D-Consistent Object Inpainting on $360^{\\circ}$ Neural Radiance Fields", + "text_level": 1, + "bbox": [ + 187, + 130, + 782, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dongqing Wang Tong Zhang* Alaa Abboud Sabine Süssstrunk \nSchool of Computer and Communication Sciences, EPFL Lausanne, Switzerland", + "bbox": [ + 214, + 203, + 754, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose InNeRF360, an automatic system that accurately removes text-specified objects from $360^{\\circ}$ Neural Radiance Fields (NeRF). The challenge is to effectively remove objects while inpainting perceptually consistent content for the missing regions, which is particularly demanding for existing NeRF models due to their implicit volumetric representation. Moreover, unbounded scenes are more prone to floater artifacts in the inpainted region than frontal-facing scenes, as the change of object appearance and background across views is more sensitive to inaccurate segmentations and inconsistent inpainting. With a trained NeRF and a text description, our method efficiently removes specified objects and inpaints visually consistent content without artifacts. We apply depth-space warping to enforce consistency across multiview text-encoded segmentations, and then refine the inpainted NeRF model using perceptual priors and 3D diffusion-based geometric priors to ensure visual plausibility. Through extensive experiments in segmentation and inpainting on $360^{\\circ}$ and frontal-facing NeRFs, we show that our approach is effective and enhances NeRF's editability. Project page: https://ivrl.github.io/InNeRF360/.", + "bbox": [ + 73, + 323, + 473, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 672, + 209, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recreating and manipulating real-world scenarios is one of the main focuses of Virtual and Augmented Reality (VR/AR) applications. Neural Radiance Field (NeRF) and its variants [2, 23, 28] can efficiently model $360^{\\circ}$ real-world scenes for photorealistic novel view synthesis. Consequently, they have the potential to become widely accessible tools for representing the 3D world.", + "bbox": [ + 75, + 696, + 468, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A desired feature of such applications is the ability to modify the content of the created scene, including object removal. However, direct inpainting in the NeRF framework is intractable due to the implicit representation of the captured scenes encoded through the weights of multilayer", + "bbox": [ + 75, + 803, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ccfbd38d35fe2c39e6ff871d1e1a66ec81f77255c876c82d660133b2331aa87d.jpg", + "image_caption": [ + "Figure 1. Given a pre-trained NeRF and a text to remove specific objects (e.g. \"Remove the flowerpot and flowers\"), InNeRF360 produces accurate multiview object segmentations, and outputs an inpainted NeRF with visually consistent content." + ], + "image_footnote": [], + "bbox": [ + 540, + 292, + 844, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "perceptrons (MLP), which hinders explicit user control of scene contents. For explicit NeRF variants, the scene representation of radiance fields contains ambiguous surface that is hard to segment with a bounding region.", + "bbox": [ + 496, + 732, + 893, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing works on selecting [35] or removing [18, 26, 43] objects in a trained NeRF tackle the 3D problem by utilizing 2D input. These methods begin with sparse user inputs, then use 2D image/video segmentation [7, 10] for multiview segmentation and inpaint on RGB-D sequence. They are restricted to frontal-facing viewing angles, as the input scribbles or masks cannot extrapolate across differ-", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12677", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ent viewpoints in $360^{\\circ}$ scenes where the shape of the object can change drastically. Moreover, in the case of object occlusions on $360^{\\circ}$ scenes, inpainting 2D depth maps is inadequate for geometric supervision as it leads to inconsistencies in scene geometry.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, InNeRF360 is an inpainting pipeline with a depth-guided segmentation method dedicated to accurate object-level editing on $360^{\\circ}$ scenes. Instead of extrapolating sparse 2D input to 3D, InNeRF360 encodes text input into a promptable segmentation model, Segment Anything Model (SAM) [15], leveraging its accurate semantic segmentation. Our method is driven by the intuition that an object's semantic identity is more consistent over different viewpoints than its geometry. However, text-based 2D semantic segmentations may not always maintain consistency across views. To overcome this, we refine object masks using inverse depth space warping in 3D space across viewpoints, utilizing the consistent 3D positioning of objects.", + "bbox": [ + 75, + 167, + 468, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Using view-consistent masks, we train a NeRF from scratch on the multiview inpainting from a 2D image inpainter [36]. The multiview training images slightly differ in the inpainted regions, accumulating into cloudy artifacts, i.e. floaters [42], in the new NeRF. To eliminate floaters, we finetune the scene guided by 3D diffusion priors trained on extensive geometric shapes [6] to determine whether density should be removed or incremented in a local voxel. The texture for the removed region is optimized by contextual appearance priors [45] from the surrounding regions of the segmentation. This creates a perceptually consistent 3D inpainted region that seamlessly blends into the scene. Extensive experiments show that InNeRF360 can effectively inpaint both $360^{\\circ}$ [2] and front-facing [22] real-world scenes, with the potential to be extended into 3D editing.", + "bbox": [ + 75, + 363, + 468, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions are as follows:", + "bbox": [ + 96, + 589, + 411, + 603 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- InNeRF360 is the first work to achieve text-guided object inpainting in $360^{\\circ}$ NeRF scenes, ensuring visually consistent inpainted regions.", + "- Our approach efficiently generates multiview consistent 2D segmentation for 3D object inpainting through depth-warping refinement on initialized masks.", + "- We incorporate a 3D diffusion network as local geometric priors to remove artifacts in the inpainted region." + ], + "bbox": [ + 86, + 604, + 467, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 739, + 225, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Inpainting. Recent advancements in image inpainting focus on filling in masked regions to create visually consistent images. This primarily involves generative models like Generative Adversarial Networks (GANs) [13, 31, 46] and denoising diffusion models (DDPMs) [29, 36, 37]. These models generate photorealistic predictions for the missing pixels. However, when applied to inpainting multiview renderings of 3D scenes [25, 26], they often generate different inpainted regions for nearby views. This is due to", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "their lack of 3D understanding, presenting a challenge for inpainting 2D observations of 3D scenes. InNeRF360 leverages image inpainting to address inpainting $360^{\\circ}$ scenes, ensuring view consistency across viewpoints.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inpainting Neural Radiance Fields. Using neural radiance fields [23] to represent 3D scenes has achieved high-quality, photo-realistic novel view synthesis. NeRF Facto [39] is an architecture designed to optimize NeRF's performance on real-world data. It incorporates various recent advances in NeRF, including hash encoding [28] and per-image appearance encoding [19], among others.", + "bbox": [ + 496, + 154, + 890, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, object removal presents a challenge in NeRF due to the implicit scene representation by the underlying neural networks. Previous works [24, 40] utilize the supervision of Contrastive Text-Image Pre-Training (CLIP) [34]. They focus on inpainting a single object and cannot generalize to real-world scenes. Methods utilizing depth-based approaches [18, 25, 26, 43] remove objects with user-drawn masks and depth sequences, and inpaint missing regions naively with 2D image inpainter on the training images of NeRF. These approaches are limited to front-facing scenes for two reasons. First, their segmentation relies on the quality of initialize masks by supervised video object segmentation methods [4, 5, 7, 30], which struggle on temporal consistency across frames for challenging cases such as transparent objects. These methods cannot output accurate object masks in $360^{\\circ}$ scenes, where object shapes change drastically across views. Secondly, the chosen 2D inpainting methods output different inpainting across views. Such inconsistency results in floaters in the trained NeRF, and is much more pronounced on $360^{\\circ}$ scenes than on frontal-facing ones. In contrast, InNeRF360 enhances the consistency of multiview segmentation by utilizing semantical identity and object 3D location consistency, thereby producing accurate masks for desired objects. Moreover, InNeRF360 is designed for $360^{\\circ}$ NeRF inpainting by removing floaters (Fig. 4) from the inpainted NeRF with geometric priors, and inpaint with contextual perception guidance.", + "bbox": [ + 496, + 263, + 890, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-Guided 3D Editing. Given the popularity of text-conditioned image generative models, many works focus on generating 3D content with text instructions. Some rely on joint embeddings of CLIP to synthesize 3D meshes [21, 27] or neural radiance fields [14, 16]. Others distill a pretrained diffusion model to optimize NeRF scenes in the latent space [20, 33]. These methods all suffer from having to map the inconsistent 2D diffusion model outputs to a 3D-consistent scene. Instruct-NeRF2NeRF [9] edits renderings of a pre-trained NeRF model to preserve 3D consistency. However, it cannot remove scene objects or perform object-level editing as it operates in latent space for image editing. Our InNeRF360 operates in image space to accurately pinpoint and crop objects and allows removing an arbitrary number of objects from the scene through text instructions,", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12678", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/42e47cee7871c6e45f62ccd4d590f62ffbe1a198ee524191d079600f3b94824b.jpg", + "image_caption": [ + "Figure 2. Overview of InNeRF360 framework. 1. Multiview Consistent Segmentation. We initialize masks using bounding boxes from the object detector, which encodes both the source image and text. With rendered depth from the input NeRF, we apply depth-warping prompt refinement to iteratively update points for the Segment Anything Model (SAM) to output view-consistent 2D segmentations. 2. Inpainting $360^{\\circ}$ NeRF. We obtain edited images through image inpainter with the masks and source images to retrain the inpainted NeRF. We then finetune the new NeRF model using a geometric prior trained from a 3D diffusion model and a masked perceptual prior." + ], + "image_footnote": [], + "bbox": [ + 120, + 90, + 851, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "while using 3D diffusion priors for local geometry finetuning to avoid the global inconsistency prior works exhibit.", + "bbox": [ + 75, + 450, + 470, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 484, + 169, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "InNeRF360 takes as input a trained NeRF with source images which the model trained on, and an instructive text. It outputs the inpainted 3D scene with the desired object(s) removed and filled with a visually consistent background without artifacts. Our pipeline is shown in Fig. 2.", + "bbox": [ + 75, + 511, + 468, + 587 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background: Neural Radiance Fields", + "text_level": 1, + "bbox": [ + 76, + 595, + 400, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A Neural Radiance Field (NeRF) encodes a 3D scene as a function $f_{\\theta}$ parametrized by an MLP with learnable parameters $\\theta$ , which maps a 3D viewing position $\\mathbf{x}$ and its 2D direction $\\mathbf{d}$ to the density $\\sigma$ and a viewing-dependent color $\\mathbf{c}$ : $f_{\\theta}:(\\mathbf{x},\\mathbf{d})\\to (\\sigma ,\\mathbf{c})$ . Rendering a NeRF from a posed camera is done by sampling batches of rays for the camera pose, and rendering corresponding pixel colors for each ray. For each ray $\\mathbf{r} = (\\mathbf{o},\\mathbf{d})$ , we sample an array of 3D points $(\\mathbf{x}_i,t_i)$ , $i = 1,2,\\dots ,K$ , where $\\mathbf{x}_i\\in \\mathbb{R}^2$ and $t_i$ is the depth. We query the MLP with these points along the ray for $\\{\\sigma_i\\}_{i = 1}^K$ and $\\{\\mathbf{c}_i\\}_{i = 1}^K$ .", + "bbox": [ + 75, + 618, + 468, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The estimated RGB of ray $\\hat{\\mathbf{C}} (\\mathbf{r})$ is obtained by alpha compositing [23] the densities and colors along the ray:", + "bbox": [ + 75, + 785, + 468, + 816 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {C}} (\\mathbf {r}) = \\sum_ {i = 1} ^ {K} \\alpha_ {i} T _ {i} \\mathbf {c} _ {i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 819, + 468, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T_{i} = 1 - \\exp (-\\sigma_{i}\\| t_{i} - t_{i - 1}\\|)$ is the ray transmittance between $\\mathbf{x}_i$ and $\\mathbf{x}_{i + 1}$ , and $\\alpha_{i} = \\prod_{j = 1}^{i - 1}T_{i}$ is the attenuation.", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "uation from ray origin to $\\mathbf{x}_i$ . The MLP is optimized through pixel loss for the distance between the estimated pixel value and the ground truth color.", + "bbox": [ + 498, + 450, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Multiview Consistent Segmentation", + "text_level": 1, + "bbox": [ + 500, + 507, + 808, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first stage is to obtain refined multiview segmentation masks for the objects to remove/edit given by the text input. We take as input a pre-trained NeRF model and $N$ source images given by the set of $N$ source camera poses.", + "bbox": [ + 496, + 532, + 890, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We initialize segmentations through the Segment-Anything Model (SAM) [15] with the bounding boxes given by Grounded Language-Image Pre-training (GLIP) from a large-scale dataset of image-text pairs [17]. GLIP: $\\mathcal{D}(\\mathbf{I},\\mathbf{s}) = \\{(B_q,p_q)\\}_{q = 1}^Q$ takes in an RGB image $\\mathbf{I}\\in$ $\\mathbb{R}^{H\\times W\\times 3}$ and a text s, and encodes each through respective image and language encoders. $Q$ is the number of bounding boxes. We then take these bounding boxes $\\{B_q\\}_{q = 1}^Q$ from the model output in which $B_{q} = (l_{q},r_{q},u_{q},d_{q})\\in \\mathbb{R}^{4}$ with corresponding probability $p_q$ . These boxes are sometimes inaccurate and fail to enclose the desired region, see Fig. 3 (b). Hence, we propose our depth-based prompt refinement for consistent segmentation.", + "bbox": [ + 496, + 594, + 892, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Depth-Warping Prompt Refinement. \"Depth Warp\" operates on the sampled points to enhance segmentation accuracy. It leverages the depth information inherited from the input NeRF and projects these points back into the pixel space to align them with other 2D observations within the scene. We thereby establish a cohesive depth constraint across different views. The depth for a sampled ray", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12679", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbf{r} = \\mathbf{o} + t\\mathbf{d}$ with origin $\\mathbf{o}$ and direction $\\mathbf{d}$ in a trained NeRF scene can be estimated via a modification of Eq. (1):", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD (\\mathbf {r}) = \\sum_ {i = 1} ^ {I} \\alpha_ {i} T _ {i} \\cdot t _ {i}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 125, + 468, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each training view, we randomly select $m$ other training views. From each selected view, we sample a fixed number $p$ of rays that correspond to pixels within the mask region. Given a ray $\\mathbf{r}$ and its estimated depth from Eq. (2), we compute the 3D location of the selected point prompt. This information is then mapped back to the current training view. Rays and their corresponding point prompts whose depth is above a certain threshold are discarded, as they may represent background objects misclassified as foreground sections to be removed. If the corresponding pixel on the current view falls outside the masked region in the current view, we add this point prompt to the current view. Subsequently, we pass this view with the new sets of point prompts to SAM for refined segmentation.", + "bbox": [ + 75, + 175, + 470, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By generating these \"out-of-the-box\" point-based prompts for the segmentation model with our NeRF-based depth prior, we ensure that the object is accurately segmented even in cases where the initial bounding box information is insufficient or incomplete from certain viewpoints. This approach greatly increases the segmentation masks' accuracy for desired objects in the scene, see Fig. 3.", + "bbox": [ + 75, + 388, + 468, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "\"Remove the flowerpot and flowers", + "bbox": [ + 192, + 501, + 346, + 511 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0890ac0dcae3a2d681f296d511d13e9c6f2fb82d03d2908b8a2a0bc901d38347.jpg", + "image_caption": [ + "Figure 3. Inconsistent bounding box across different views. (a) and (b) are from the same dataset under the same instruction. However, the generated bounding boxes are different. After applying depth warping refinement (point prompts as red dots), (c) generates accurate segmentation." + ], + "image_footnote": [], + "bbox": [ + 96, + 511, + 447, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Promptable Segmentation After obtaining the refined point-based prompts, we employ SAM to identify and segment all the rendered observations $\\{\\mathbf{I}_n\\}_{n=1}^N$ for refined masks $\\{\\mathbf{M}_n\\}_{n=1}^N$ . Specifically, SAM takes as input an image $\\mathbf{I}$ and a prompt in the form of $j$ points pinpointing the object $o_q$ , and produces an accurate segmentation mask $\\mathbf{M}_{\\mathbf{q}}$ of the same size as $\\mathbf{I}$ : $\\mathbf{M}_q = \\mathrm{SAM}(\\mathbf{I}, o_q)$ . For each image $\\mathbf{I}_i \\in \\{\\mathbf{I}_n\\}_{n=1}^N$ , we get a union binary mask for all the objects to be removed:", + "bbox": [ + 75, + 720, + 470, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {i} = \\bigcup_ {q = 1} ^ {Q} \\mathbf {M} _ {q}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 859, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Inpainting $360^{\\circ}$ NeRF", + "text_level": 1, + "bbox": [ + 500, + 90, + 705, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inpainted NeRF Initialization. With the rendered observations $\\{\\mathbf{I}_n\\}_{n=1}^N$ and corresponding masks $\\{\\mathbf{M}_n\\}_{n=1}^N$ , we adopt a 2D image inpainter [36] to edit each observation as priors for the optimization. We then initialize the inpainted scene with Nerfacto [39]. This architecture is designed to optimize the performance of NeRF on real-world image captures. However, each inpainted image has varying pixel-level content despite being perceptually plausible as a standalone image. Therefore, relying solely on RGB supervision leads to floaters in the NeRF (Fig. 4). To produce clean and perceptually consistent inpainting, we fine-tune the initialized NeRF with both geometry and appearance priors.", + "bbox": [ + 496, + 113, + 893, + 311 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7c539969ec57785174ca153f2af15c03310e8fe5264032a32aef2bad00e7349a.jpg", + "image_caption": [ + "Figure 4. Examples of artifacts in the initialized NeRF. 2D inpaintings contain inconsistent inpainted pixels that accumulate in the 3D inpainted region and appear as floater artifacts." + ], + "image_footnote": [], + "bbox": [ + 501, + 321, + 694, + 450 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/94497a9b364bb2f7ab2d288925baa0612cd2400156e2a430f2ebbf890dfd6ce3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 321, + 890, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hallucinating Density Removal. The density artifacts produced through inconsistent 2D inpainting can be seen as floaters. We train a denoising diffusion probabilistic model (DDPM) [12] on ShapeNet [6] to iteratively denoise a $m^3$ resolution voxel grid of discretized binary occupancy $x$ as a local 3D geometry prior: given a NeRF density $\\sigma$ at timestep $t$ , $x_{t} = 1$ if $\\sigma > \\rho$ else $x_{t} = -1$ , where $\\rho$ is a chosen threshold for whether a voxel is empty. For training, from each ShapeNet mesh we randomly select $N$ cubes that encompass $3\\%$ to $8\\%$ of the object bounding volume, and voxelize them to $m^3$ resolution. The loss function for the diffusion model is given by the MSE loss between the true noise $\\epsilon$ and the predicted noise $\\epsilon_{\\theta}$ where $\\theta$ parameterizes the diffusion model U-Net:", + "bbox": [ + 496, + 508, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {d d p m}} (\\theta) = \\mathbb {E} _ {t, x _ {0}, \\sigma} [ \\| \\epsilon - \\epsilon_ {\\theta} (\\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t) \\| _ {2} ^ {2} ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 718, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t \\in [1, 1000]$ is the number of timesteps in the nois-ing diffusion process, and $\\bar{\\alpha}_t = \\prod_{s=1}^t \\alpha_s$ where $\\alpha_t$ is a function of the timestep $t$ that parameterized transitions from $x_0$ to $x_{1000}$ (i.e. a noise schedule).", + "bbox": [ + 496, + 751, + 890, + 811 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Density Score Distillation Sampling (DSDS) [42] loss is defined to penalize regions with density $\\sigma >\\rho$ that the trained diffusion model deems as empty, and regions that are empty where $x_{t} = 1$ predicted by the model:", + "bbox": [ + 496, + 811, + 890, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D S D S}} = \\sum_ {i} u _ {i} \\sigma_ {i} + (1 - u _ {i}) \\max (w - \\sigma_ {i}, 0), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 873, + 890, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12680", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $u = \\mathbb{1}\\{x_0 < 0\\}$ , and $w$ is a chosen upper limit for density $\\sigma$ in occupied voxels.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The original sampling of the DSDS loss is by sampling a low-resolution density grid stored through ray bundles. During training, the grid selects the center of 3D cubes to be voxelized and enter the diffusion process. The grid gets updated by a visibility field determining what it sees in the NeRF scene. Our aim is to focus on removing floaters within the inpainted region. Therefore, we apply the refined segmentation mask from the image space to limit the visibility field to only look at the inpainted regions, and eliminate sampled rays corresponding to pixels outside the mask:", + "bbox": [ + 75, + 121, + 468, + 272 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g e o m}} = \\sum_ {j} \\left(u _ {j} \\sigma_ {j} + (1 - u _ {j}) \\max (w - \\sigma_ {j}, 0)\\right) \\cdot V _ {j}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 273, + 468, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $V$ is an indicator function whose value is 1 for each voxel cube whose center is located within the current \"visible region\" given by the segmentation masks. Consequently, we sample cubes near the inpainted region. The geometric prior trained on extensive shapes in [6] preserves the original surface (e.g., the table supporting the removed flowerpot) while penalizing the floaters in the inpainted region created through inconsistent 2D inpainting.", + "bbox": [ + 75, + 311, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Perceptually-Consistent Appearance Inpainting. The above method removes floaters created by inconsistent 2D inpainting, however, it does not produce visually consistent textures to fill in the removed region. Therefore, we utilize a patch-based loss [45] as an appearance prior to enhancing the model's robustness and alleviate blurring effects.", + "bbox": [ + 75, + 431, + 468, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we sample all the pixels from the input inpainted images to get $W$ image patches $\\{P_w\\}_{w=1}^W$ with the size of $v^2$ . These patches, $\\{P_w\\}_{w=1}^W$ , can be divided into two non-overlapping groups of patches $P_{w_i}$ and $P_{w_o}$ depending on whether a patch contains pixels within the inpainted region. For patches in $P_{w_o}$ , we apply pixel-wise L1. This pixel loss is obtained by comparing the RGB values of each pixel $p$ in the inpainted patch, denoted as $\\hat{\\mathbf{C}}_p$ , with the corresponding rendered RGB value, denoted as $\\hat{\\mathbf{C}}_p$ ,", + "bbox": [ + 75, + 523, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p i x}} = \\frac {1}{v ^ {2} \\left| P _ {w _ {o}} \\right|} \\sum_ {p _ {\\mathrm {r}} \\in P _ {w _ {o}}} \\left\\| \\hat {\\mathbf {C}} _ {p} - \\tilde {\\mathbf {C}} _ {p} \\right\\| _ {1}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 662, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For patches in $P_{w_i}$ containing the inpainted region, we compute the perceptual similarity using LPIPS between the inpainted image patch $\\tilde{P}_I$ and the corresponding patch $P$ on the rendered image. We denote $\\mathbf{C}_P$ as the set of pixel values in patch $P$ , and define $\\mathcal{L}_{\\mathrm{in}}$ as the inpainting loss.", + "bbox": [ + 75, + 713, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n}} = \\frac {1}{\\left| P _ {w _ {i}} \\right|} \\sum_ {P \\in P _ {w _ {i}}} \\operatorname {L P I P S} \\left(\\mathbf {C} _ {P}, \\mathbf {C} _ {\\tilde {P} _ {I}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 789, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The inpainting loss measures the perceptual difference between the inpainted patch and the target inpainted image, while the pixel loss quantifies the pixel-level discrepancy between the inpainted and rendered RGB values. Together,", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "these losses provide a comprehensive assessment of the reconstruction quality, accounting for both perceptual similarity and pixel-wise accuracy.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Functions. Our optimization is the weighted sum of the geometric prior $\\mathcal{L}_{\\mathrm{geom}}$ (Eq. (6)), pixel loss $\\mathcal{L}_{\\mathrm{pix}}$ (Eq. (7)), appearance prior $\\mathcal{L}_{\\mathrm{in}}$ (Eq. (8)) with $\\lambda_{(\\cdot)}$ as weight terms:", + "bbox": [ + 496, + 137, + 890, + 183 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {\\text {g e o m}} \\cdot \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {i n}} \\cdot \\mathcal {L} _ {\\text {i n}} + \\mathcal {L} _ {\\text {p i x}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 188, + 890, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 219, + 632, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate InNeRF360 on various real-world captured datasets for text-guided inpainting.", + "bbox": [ + 496, + 244, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We take 360-degree datasets from MipNeRF, MipNeRF-360, and NeRFStudio [1, 2, 39]. In addition, due to the absence of ground truth data for $360^{\\circ}$ scene inpainting, we capture new datasets with and without the object removed for quantitative evaluation. Segmentation mask ground truth does not exist for the $360^{\\circ}$ scenes we evaluate. We also compare with front-facing datasets from SPInNeRF [26] and IBRNet [41] to show that our method produces better inpainting over baseline methods. Details of the datasets we used are provided in Tab. 5.", + "bbox": [ + 496, + 275, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baseline. We select baselines based on specific tasks. SPIn-NeRF SPN [26] is the closest work to ours. For segmentation, we compare with the multiview segmentation from SPN and a recent video segmentation method Dino [5]. For the inpainting task, we compare our inpainting quality with our implemented version of SPN that works with 360-degree scenes SPN-360. We also compare with per-frame image inpainting [36] to show that our method generates more consistent inpainting across different viewpoints.", + "bbox": [ + 496, + 426, + 890, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Segmentation Comparison", + "text_level": 1, + "bbox": [ + 500, + 574, + 740, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We qualitatively compare our segmentation results to SPN and Dino. As input, we give the first frame segmentation to both SPN and Dino, and give the corresponding text instructions for InNeRF360. As we are evaluating the extrapolation ability of each segmentation method over drastically different viewpoints, we select the 82nd frame from vasedeck and the 81st image from room. They represent the respective frames of the videos created from the dataset.", + "bbox": [ + 496, + 598, + 890, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 5, Dino produces incomplete segmentation for unseen views in challenging scenes, such as the vasedeck featuring a transparent vase. In such cases, SPN struggles to generate complete segmentation when initialized with Dino's output. While we also initialize with a 2D segmentation model (SAM), it facilitates flexible, promptable input. This can be utilized by our depth-warping refinement to output point prompts specifically in the vase section of the image. These prompts guide SAM towards accurate segmentation, as elaborated in Sec. 3.2. For room, where only a part of the slippers is present in the image, Dino and SPN once again yield incomplete segmentations.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12681", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/177eec8b037b3d6bf7dfa5e8e9798941bf119d961a588d198d61aee6694b0e6a.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison on 3D object segmentation. InNeRF360 outputs accurate masks for complex cases containing transparent (vase) or incomplete objects (partial slippers)." + ], + "image_footnote": [], + "bbox": [ + 101, + 89, + 446, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "InNeRF360 is able to output complete object segmentation.", + "bbox": [ + 76, + 527, + 467, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Inpainting Evaluation", + "text_level": 1, + "bbox": [ + 76, + 556, + 282, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on 360-degree scenes. InNeRF360 can handle a wide range of scenarios for object inpainting in 3D scenes, as depicted in Fig. 7. We encourage the readers to view supplementary videos to inspect the quality of our results.", + "bbox": [ + 76, + 580, + 467, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "InNeRF360 can remove large scene objects against complex backgrounds. In Bear, the background of the bear contains varying trees and branches, and the 2D inpainted images are therefore very noisy, as shown in Fig. 16. However, with our floater removal and appearance prior, InNeRF360 produces a clean stone surface in the final edited NeRF.", + "bbox": [ + 75, + 642, + 467, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Occlusion and geometry deformation across varying viewpoints are major causes of 3D inconsistency in inpainting, and the datasets we use contain both scenarios. In Room, the window, wall, and the piano behind the score can lead to inconsistency. However, we generate view-consistent content to seamlessly fill the missing region.", + "bbox": [ + 76, + 734, + 467, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Moreover, InNeRF360 is capable of inpainting multiple objects located anywhere in the 3D scenes without introducing blurry artifacts in the resulting NeRF scene. When given a text input containing multiple objects (Room: \"slippers\" and \"piano sheet\"; Bulldozer: multiple \"cones\"), In", + "bbox": [ + 76, + 824, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/474e5c7f9ca27a8d76902e88fe6c87a41b442f5a47f4d7d304a02cdb394fa7b5.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison with SPN-360. Text: Remove the vase and the flowers. InNeRF360 inpaints clean and visually plausible regions while better preserving surrounding scenes." + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 867, + 280 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/49e472fc98b766f0eb9eb6e02e82ef6ba5da600b70507be78e8488294880583f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsCupStarbucks
LPIPS ↓FID ↓LPIPS ↓FID ↓
Per-Frame0.6149201.700.5981260.93
SPN-3600.6421252.340.6278215.28
NeRFacto0.7328271.560.6832258.39
+Lin0.7137210.570.6658223.82
+Lgeom0.6197189.570.5795166.45
+Lin + Lgeom (Ours)0.5377159.760.4523153.46
", + "bbox": [ + 503, + 329, + 879, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative evaluation on the inpainting quality. Our method achieves better results than baseline methods and our ablated settings on captured datasets.", + "bbox": [ + 500, + 455, + 890, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NeRF360 produces inpainted regions that seamlessly blend with the surrounding context, yielding visually coherent and high-quality inpainting results.", + "bbox": [ + 500, + 507, + 890, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 6 shows qualitative comparison to SPN-360. Our method not only synthesizes a perceptually-consistent inpainted region, but also preserves the surrounding background closer to the input NeRF scene. We speculate the reason for the background-preserving inpainting to be that SPN inpaints on depth maps with segmentation masks generated from RGB images. We elaborate on our choice not to use 2D depth map inpainting in the supplementary.", + "bbox": [ + 500, + 553, + 890, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation studies on our design choices. Our depth-warping method produces refined point-based prompts for the segmentation model, and outputs complete and consistent multi-view segmentation, as shown in Fig. 3.", + "bbox": [ + 500, + 674, + 890, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 8 qualitatively ablates our choice of loss functions. In Fig. 8a (ii), the vanilla NeRFacto model outputs a concentrated artifact in the inpainted region along with noisy texture in nearby regions which we suspect is due to per-image appearance encoding on inconsistent 2D inpainted images. Fig. 8a (iii) shows NeRFacto $+\\mathcal{L}_{\\mathrm{in}}$ which improves inpainted texture, but cannot reduce the floater artifact. These artifacts have view-dependent appearances from individual views and are therefore difficult to remove from appearance priors. In Fig. 8a (iv) for InNeRF360, we can see a clean and perceptually consistent surface in the edited", + "bbox": [ + 500, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12682", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Bear: \"Remove the rectangular base and the bear\"", + "bbox": [ + 351, + 92, + 640, + 106 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c11edfa7db3eee1c961efc332487d235521bb7c7266681de3c3b5fc82ff282ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 125, + 107, + 849, + 281 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Room: \"Remove the slippers and the piano sheet\"", + "bbox": [ + 349, + 286, + 635, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c5142d98fca609dd79a258000a345ef243efd0e327f4ffb6e1a380cf5f63241b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 124, + 303, + 849, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Bulldozer: \"Remove the traffic cones\"", + "bbox": [ + 403, + 484, + 624, + 497 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d0adbfb57d12498920be67209be56231239bfafe81b208b6df72d33e4689a019.jpg", + "image_caption": [ + "Figure 7. Qualitative inpainting results on 360 scenes. Our method works with various types of NeRF scenes. We can also remove arbitrary numbers of objects given the text input, independent of the complexity of the scene content." + ], + "image_footnote": [], + "bbox": [ + 125, + 498, + 849, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "scene. In Fig. 8b shows InNeRF360 versus trained without $\\mathcal{L}_{\\mathrm{in}}$ . We can see that the LPIPS loss can improve blurry background output due to inconsistent 2D inpainting. The lower part of Tab. 1 shows quantitative ablation on each loss term in InNeRF360. Our complete architecture performs better than without each of the loss terms.", + "bbox": [ + 75, + 726, + 470, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inpainting quality. Due to the lack of baseline and ground truth datasets on inpainting $360^{\\circ}$ NeRF scenes, we captured real-world datasets for quantitative comparison on the quality of inpainted renderings. Since InNeRF360 generates consistent and complete 3D segmentation over baseline", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5106f1e7ede3a601101698d9113e5a46c1b69e99ebe684ab5831502d3fcb944f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsGardenRoomVasedeckBulldozerBear
Ours89%71%81%83%92%
Per-frame11%29%19%17%8%
", + "bbox": [ + 509, + 724, + 879, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. User study comparing with per-frame inpainting on visual consistency between consecutive frames. In each of the scenes, our inpainted NeRF renders higher view consistency than per-frame inpainting. Per-frame editing lacks a 3D understanding of each scene and inpaints each image independently.", + "bbox": [ + 498, + 777, + 890, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "methods, the 2D inpainting initialization is naturally much less noisy than baseline methods.", + "bbox": [ + 498, + 853, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our inpainting quality on each frame of the", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12683", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d8460739ca191d042da0b3a3a0e7ec0b76221f9ff94d3b5b9094f7610157113c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 202, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7f40c4a56b769c420fe6c973e6bb99ef2b999300cab758fd98454b67b55d74d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 88, + 325, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c6ba1f5ee9feaa18906d8d8d8e6e350a9df288a100d3416c9b69ef2f0e6c28a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 88, + 450, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4c13c8f63bbd54484870f5d510be225da9119b7e64b12d2380882db3df59cdc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 88, + 575, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fdff20777458c473429485a71ea167f672bacb842f09b3ba3efbad433b880525.jpg", + "image_caption": [ + "(i) Input Scene" + ], + "image_footnote": [], + "bbox": [ + 80, + 186, + 200, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb9d9bad10bf3b6b4b0c5d3118e3f740e91c30df9d75322d482d5a7240f6efff.jpg", + "image_caption": [ + "(ii) NeRFacto" + ], + "image_footnote": [], + "bbox": [ + 202, + 186, + 325, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f3a73ab995b8492b28d8982562d89fea9df526516e7b058e6a85c2608c568672.jpg", + "image_caption": [ + "(iii) $\\mathsf{NeRFacto} + \\mathcal{L}_{\\mathrm{in}}$" + ], + "image_footnote": [], + "bbox": [ + 326, + 186, + 450, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f67ec7046e9736d1c9fd2e2cb4ff1231665893836843e432ec0ccb22fac512b8.jpg", + "image_caption": [ + "(iv) Ours", + "(a) Qualitative ablation for $\\mathcal{L}_{\\mathrm{geom}}$ on Bear and Garden." + ], + "image_footnote": [], + "bbox": [ + 450, + 186, + 575, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/459c481ca201f8fe5dfccebfa2464e55e8ea84eeb7d355dae082568411423ec2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 88, + 761, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7df8a8c54b8e13cb5029a5a522698a991b90b12d7b9853deaedf392f43bdb3be.jpg", + "image_caption": [ + "(i) NeRFacto + geom", + "(b) Qualitative ablation for $\\mathcal{L}_{\\mathrm{in}}$ on Garden." + ], + "image_footnote": [], + "bbox": [ + 637, + 186, + 761, + 281 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/993dd5008e90f9109d233d9f41f5be8bb99366548de069a7b52b3c0a265811a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 89, + 885, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0e6efdbdd6a158d2dbafb798ab7168375729da15cb8b22754df5377ec8af0f4e.jpg", + "image_caption": [ + "(ii) Ours" + ], + "image_footnote": [], + "bbox": [ + 761, + 186, + 885, + 281 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/399b3524a9e995609b55edaf2d7fab6d7b12afb6374c75e6c7ae7bbe7161951e.jpg", + "image_caption": [ + "Figure 8. Ablation for losses on geometric and appearance priors. The artifact in the inpainted region is not as pronounced if viewed from aside as when viewed from the top. Our method is able to optimize an inpainted NeRF without artifacts and with a consistent and unblurry background." + ], + "image_footnote": [], + "bbox": [ + 101, + 386, + 281, + 458 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8eb80fb0200dfe7399b020085a87f2abf5b8972258c667b5bc7d8b8581e81e80.jpg", + "image_caption": [ + "\"Turn the slippers into red slippers\"" + ], + "image_footnote": [], + "bbox": [ + 282, + 386, + 444, + 458 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93abbd958aa96824c36bd54a2fcbf244c0a45ccf1a3123cbd316221a277ffba1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 460, + 281, + 531 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/948bcf51ed81dcce1559a85544110e63b1a55155907b03f848c7787ad58d6313.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 460, + 444, + 531 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25a0ee44139e37692df62ce4f4f0f2f9123b5f6029e4fc676b0a07ee34bf83f2.jpg", + "image_caption": [ + "Figure 9. Editing comparison with In2n. InNeRF360, combined with appropriate mask-conditioned image editing models, can generate accurate editing on desired objects. In contrast, In2n gives the wrong texture to unwanted regions." + ], + "image_footnote": [], + "bbox": [ + 101, + 532, + 281, + 604 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9ef784bac4b137c9d1624592e95eb15e6f9e08e88fcaa4be74345c4c23f154f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 532, + 444, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "renderings with per-frame inpainting and SPN-360. We report LPIPS [44] and Frechet Inception Distance (FID) [11] metric in Tab. 1 by comparing with the output of the captured empty scene rendered under the same camera trajectory which we use as ground truth. Our method outperforms each baseline method and outputs visually consistent inpainting without visual artifacts.", + "bbox": [ + 75, + 672, + 467, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A quantitative baseline comparison to SPN on frontal scenes is also in the supplementary materials.", + "bbox": [ + 75, + 777, + 467, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3D consistency over per-frame inpainting. A naive approach for 3D scene inpainting is to independently inpaint every rendered image of the scene with a 2D image inpainter. In contrast, InNeRF360 produces inpaintings with higher view consistency across all viewpoints.", + "bbox": [ + 75, + 809, + 467, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We verify such a claim with a user study where partici", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pants were presented with two video clips of each inpainted scene, rendered with sequential camera trajectories. They were then asked to identify which clip appeared more consistent. Additional details about the user study can be found in the supplementary material. The results, presented in Tab. 2, clearly show that our rendered inpaintings exhibit superior temporal consistency compared to per-frame edits.", + "bbox": [ + 498, + 369, + 890, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Editing Accuracy", + "text_level": 1, + "bbox": [ + 500, + 477, + 669, + 493 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown by Fig. 9, our segmentation module can be connected with a mask-conditioned image editor [8] to generate view-consistent editing with object-level control through text instructions, which InstructNeRF2NeRF (In2n) [9] cannot. However, note that editing is not the focus of our work. We show this result simply to demonstrate a possible extension to our method. Details are provided in the supplementary.", + "bbox": [ + 498, + 501, + 890, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 628, + 756, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our method inherits certain constraints of vision-language models. In scenarios where the text instruction cannot be accurately localized within the image, InNeRF360 may struggle in generating segmentation consistently aligned with the views. This issue arises when the initial masks provided by the 2D object detector are inaccurate or too noisy for effective refinement. Addressing this challenge is a focus of our future work.", + "bbox": [ + 498, + 647, + 890, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. In conclusion, we have presented InNeRF360, a unified system to accurately segment and inpaint objects in $360^{\\circ}$ NeRFs with text instructions. We synthesize perceptually consistent inpainting without artifacts and can extend to object-level stylization, improving the controllability of NeRF.", + "bbox": [ + 498, + 768, + 890, + 857 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported in part by the Swiss National Science Foundation via the Sinergia grant CRSII5-180359.", + "bbox": [ + 500, + 858, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12684", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5855–5864, 2021. 5", + "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. 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Large scale image completion via co-modulated generative adversarial networks. arXiv preprint arXiv:2103.10428, 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12686", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_model.json b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..74180583ceb4801cee6d147d77909ae2e56f90ff --- /dev/null +++ b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_model.json @@ -0,0 +1,2376 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.189, + 0.131, + 0.784, + 0.175 + ], + "angle": 0, + "content": "InNeRF360: Text-Guided 3D-Consistent Object Inpainting on \\(360^{\\circ}\\) Neural Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.204, + 0.756, + 0.257 + ], + "angle": 0, + "content": "Dongqing Wang Tong Zhang* Alaa Abboud Sabine Süssstrunk \nSchool of Computer and Communication Sciences, EPFL Lausanne, Switzerland" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.324, + 0.474, + 0.655 + ], + "angle": 0, + "content": "We propose InNeRF360, an automatic system that accurately removes text-specified objects from \\(360^{\\circ}\\) Neural Radiance Fields (NeRF). The challenge is to effectively remove objects while inpainting perceptually consistent content for the missing regions, which is particularly demanding for existing NeRF models due to their implicit volumetric representation. Moreover, unbounded scenes are more prone to floater artifacts in the inpainted region than frontal-facing scenes, as the change of object appearance and background across views is more sensitive to inaccurate segmentations and inconsistent inpainting. With a trained NeRF and a text description, our method efficiently removes specified objects and inpaints visually consistent content without artifacts. We apply depth-space warping to enforce consistency across multiview text-encoded segmentations, and then refine the inpainted NeRF model using perceptual priors and 3D diffusion-based geometric priors to ensure visual plausibility. Through extensive experiments in segmentation and inpainting on \\(360^{\\circ}\\) and frontal-facing NeRFs, we show that our approach is effective and enhances NeRF's editability. Project page: https://ivrl.github.io/InNeRF360/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.673, + 0.21, + 0.688 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.47, + 0.804 + ], + "angle": 0, + "content": "Recreating and manipulating real-world scenarios is one of the main focuses of Virtual and Augmented Reality (VR/AR) applications. Neural Radiance Field (NeRF) and its variants [2, 23, 28] can efficiently model \\(360^{\\circ}\\) real-world scenes for photorealistic novel view synthesis. Consequently, they have the potential to become widely accessible tools for representing the 3D world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.804, + 0.471, + 0.88 + ], + "angle": 0, + "content": "A desired feature of such applications is the ability to modify the content of the created scene, including object removal. However, direct inpainting in the NeRF framework is intractable due to the implicit representation of the captured scenes encoded through the weights of multilayer" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.293, + 0.845, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.669, + 0.895, + 0.726 + ], + "angle": 0, + "content": "Figure 1. Given a pre-trained NeRF and a text to remove specific objects (e.g. \"Remove the flowerpot and flowers\"), InNeRF360 produces accurate multiview object segmentations, and outputs an inpainted NeRF with visually consistent content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.794 + ], + "angle": 0, + "content": "perceptrons (MLP), which hinders explicit user control of scene contents. For explicit NeRF variants, the scene representation of radiance fields contains ambiguous surface that is hard to segment with a bounding region." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Existing works on selecting [35] or removing [18, 26, 43] objects in a trained NeRF tackle the 3D problem by utilizing 2D input. These methods begin with sparse user inputs, then use 2D image/video segmentation [7, 10] for multiview segmentation and inpaint on RGB-D sequence. They are restricted to frontal-facing viewing angles, as the input scribbles or masks cannot extrapolate across differ-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12677" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "ent viewpoints in \\(360^{\\circ}\\) scenes where the shape of the object can change drastically. Moreover, in the case of object occlusions on \\(360^{\\circ}\\) scenes, inpainting 2D depth maps is inadequate for geometric supervision as it leads to inconsistencies in scene geometry." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.47, + 0.363 + ], + "angle": 0, + "content": "In contrast, InNeRF360 is an inpainting pipeline with a depth-guided segmentation method dedicated to accurate object-level editing on \\(360^{\\circ}\\) scenes. Instead of extrapolating sparse 2D input to 3D, InNeRF360 encodes text input into a promptable segmentation model, Segment Anything Model (SAM) [15], leveraging its accurate semantic segmentation. Our method is driven by the intuition that an object's semantic identity is more consistent over different viewpoints than its geometry. However, text-based 2D semantic segmentations may not always maintain consistency across views. To overcome this, we refine object masks using inverse depth space warping in 3D space across viewpoints, utilizing the consistent 3D positioning of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.47, + 0.59 + ], + "angle": 0, + "content": "Using view-consistent masks, we train a NeRF from scratch on the multiview inpainting from a 2D image inpainter [36]. The multiview training images slightly differ in the inpainted regions, accumulating into cloudy artifacts, i.e. floaters [42], in the new NeRF. To eliminate floaters, we finetune the scene guided by 3D diffusion priors trained on extensive geometric shapes [6] to determine whether density should be removed or incremented in a local voxel. The texture for the removed region is optimized by contextual appearance priors [45] from the surrounding regions of the segmentation. This creates a perceptually consistent 3D inpainted region that seamlessly blends into the scene. Extensive experiments show that InNeRF360 can effectively inpaint both \\(360^{\\circ}\\) [2] and front-facing [22] real-world scenes, with the potential to be extended into 3D editing." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.59, + 0.412, + 0.604 + ], + "angle": 0, + "content": "To summarize, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.605, + 0.468, + 0.65 + ], + "angle": 0, + "content": "- InNeRF360 is the first work to achieve text-guided object inpainting in \\(360^{\\circ}\\) NeRF scenes, ensuring visually consistent inpainted regions." + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.651, + 0.468, + 0.695 + ], + "angle": 0, + "content": "- Our approach efficiently generates multiview consistent 2D segmentation for 3D object inpainting through depth-warping refinement on initialized masks." + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.697, + 0.468, + 0.726 + ], + "angle": 0, + "content": "- We incorporate a 3D diffusion network as local geometric priors to remove artifacts in the inpainted region." + }, + { + "type": "list", + "bbox": [ + 0.088, + 0.605, + 0.468, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.227, + 0.755 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Image Inpainting. Recent advancements in image inpainting focus on filling in masked regions to create visually consistent images. This primarily involves generative models like Generative Adversarial Networks (GANs) [13, 31, 46] and denoising diffusion models (DDPMs) [29, 36, 37]. These models generate photorealistic predictions for the missing pixels. However, when applied to inpainting multiview renderings of 3D scenes [25, 26], they often generate different inpainted regions for nearby views. This is due to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "their lack of 3D understanding, presenting a challenge for inpainting 2D observations of 3D scenes. InNeRF360 leverages image inpainting to address inpainting \\(360^{\\circ}\\) scenes, ensuring view consistency across viewpoints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.155, + 0.892, + 0.261 + ], + "angle": 0, + "content": "Inpainting Neural Radiance Fields. Using neural radiance fields [23] to represent 3D scenes has achieved high-quality, photo-realistic novel view synthesis. NeRF Facto [39] is an architecture designed to optimize NeRF's performance on real-world data. It incorporates various recent advances in NeRF, including hash encoding [28] and per-image appearance encoding [19], among others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.672 + ], + "angle": 0, + "content": "However, object removal presents a challenge in NeRF due to the implicit scene representation by the underlying neural networks. Previous works [24, 40] utilize the supervision of Contrastive Text-Image Pre-Training (CLIP) [34]. They focus on inpainting a single object and cannot generalize to real-world scenes. Methods utilizing depth-based approaches [18, 25, 26, 43] remove objects with user-drawn masks and depth sequences, and inpaint missing regions naively with 2D image inpainter on the training images of NeRF. These approaches are limited to front-facing scenes for two reasons. First, their segmentation relies on the quality of initialize masks by supervised video object segmentation methods [4, 5, 7, 30], which struggle on temporal consistency across frames for challenging cases such as transparent objects. These methods cannot output accurate object masks in \\(360^{\\circ}\\) scenes, where object shapes change drastically across views. Secondly, the chosen 2D inpainting methods output different inpainting across views. Such inconsistency results in floaters in the trained NeRF, and is much more pronounced on \\(360^{\\circ}\\) scenes than on frontal-facing ones. In contrast, InNeRF360 enhances the consistency of multiview segmentation by utilizing semantical identity and object 3D location consistency, thereby producing accurate masks for desired objects. Moreover, InNeRF360 is designed for \\(360^{\\circ}\\) NeRF inpainting by removing floaters (Fig. 4) from the inpainted NeRF with geometric priors, and inpaint with contextual perception guidance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Text-Guided 3D Editing. Given the popularity of text-conditioned image generative models, many works focus on generating 3D content with text instructions. Some rely on joint embeddings of CLIP to synthesize 3D meshes [21, 27] or neural radiance fields [14, 16]. Others distill a pretrained diffusion model to optimize NeRF scenes in the latent space [20, 33]. These methods all suffer from having to map the inconsistent 2D diffusion model outputs to a 3D-consistent scene. Instruct-NeRF2NeRF [9] edits renderings of a pre-trained NeRF model to preserve 3D consistency. However, it cannot remove scene objects or perform object-level editing as it operates in latent space for image editing. Our InNeRF360 operates in image space to accurately pinpoint and crop objects and allows removing an arbitrary number of objects from the scene through text instructions," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12678" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.092, + 0.852, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Figure 2. Overview of InNeRF360 framework. 1. Multiview Consistent Segmentation. We initialize masks using bounding boxes from the object detector, which encodes both the source image and text. With rendered depth from the input NeRF, we apply depth-warping prompt refinement to iteratively update points for the Segment Anything Model (SAM) to output view-consistent 2D segmentations. 2. Inpainting \\(360^{\\circ}\\) NeRF. We obtain edited images through image inpainter with the masks and source images to retrain the inpainted NeRF. We then finetune the new NeRF model using a geometric prior trained from a 3D diffusion model and a masked perceptual prior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.471, + 0.481 + ], + "angle": 0, + "content": "while using 3D diffusion priors for local geometry finetuning to avoid the global inconsistency prior works exhibit." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.486, + 0.17, + 0.501 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.588 + ], + "angle": 0, + "content": "InNeRF360 takes as input a trained NeRF with source images which the model trained on, and an instructive text. It outputs the inpainted 3D scene with the desired object(s) removed and filled with a visually consistent background without artifacts. Our pipeline is shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.596, + 0.401, + 0.611 + ], + "angle": 0, + "content": "3.1. Background: Neural Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.786 + ], + "angle": 0, + "content": "A Neural Radiance Field (NeRF) encodes a 3D scene as a function \\( f_{\\theta} \\) parametrized by an MLP with learnable parameters \\( \\theta \\), which maps a 3D viewing position \\( \\mathbf{x} \\) and its 2D direction \\( \\mathbf{d} \\) to the density \\( \\sigma \\) and a viewing-dependent color \\( \\mathbf{c} \\): \\( f_{\\theta}:(\\mathbf{x},\\mathbf{d})\\to (\\sigma ,\\mathbf{c}) \\). Rendering a NeRF from a posed camera is done by sampling batches of rays for the camera pose, and rendering corresponding pixel colors for each ray. For each ray \\( \\mathbf{r} = (\\mathbf{o},\\mathbf{d}) \\), we sample an array of 3D points \\( (\\mathbf{x}_i,t_i) \\), \\( i = 1,2,\\dots ,K \\), where \\( \\mathbf{x}_i\\in \\mathbb{R}^2 \\) and \\( t_i \\) is the depth. We query the MLP with these points along the ray for \\( \\{\\sigma_i\\}_{i = 1}^K \\) and \\( \\{\\mathbf{c}_i\\}_{i = 1}^K \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.47, + 0.817 + ], + "angle": 0, + "content": "The estimated RGB of ray \\(\\hat{\\mathbf{C}} (\\mathbf{r})\\) is obtained by alpha compositing [23] the densities and colors along the ray:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.82, + 0.47, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {C}} (\\mathbf {r}) = \\sum_ {i = 1} ^ {K} \\alpha_ {i} T _ {i} \\mathbf {c} _ {i}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.47, + 0.904 + ], + "angle": 0, + "content": "where \\( T_{i} = 1 - \\exp (-\\sigma_{i}\\| t_{i} - t_{i - 1}\\|) \\) is the ray transmittance between \\( \\mathbf{x}_i \\) and \\( \\mathbf{x}_{i + 1} \\), and \\( \\alpha_{i} = \\prod_{j = 1}^{i - 1}T_{i} \\) is the attenuation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.495 + ], + "angle": 0, + "content": "uation from ray origin to \\(\\mathbf{x}_i\\). The MLP is optimized through pixel loss for the distance between the estimated pixel value and the ground truth color." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.508, + 0.809, + 0.525 + ], + "angle": 0, + "content": "3.2. Multiview Consistent Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.594 + ], + "angle": 0, + "content": "The first stage is to obtain refined multiview segmentation masks for the objects to remove/edit given by the text input. We take as input a pre-trained NeRF model and \\(N\\) source images given by the set of \\(N\\) source camera poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.893, + 0.794 + ], + "angle": 0, + "content": "We initialize segmentations through the Segment-Anything Model (SAM) [15] with the bounding boxes given by Grounded Language-Image Pre-training (GLIP) from a large-scale dataset of image-text pairs [17]. GLIP: \\(\\mathcal{D}(\\mathbf{I},\\mathbf{s}) = \\{(B_q,p_q)\\}_{q = 1}^Q\\) takes in an RGB image \\(\\mathbf{I}\\in\\) \\(\\mathbb{R}^{H\\times W\\times 3}\\) and a text s, and encodes each through respective image and language encoders. \\(Q\\) is the number of bounding boxes. We then take these bounding boxes \\(\\{B_q\\}_{q = 1}^Q\\) from the model output in which \\(B_{q} = (l_{q},r_{q},u_{q},d_{q})\\in \\mathbb{R}^{4}\\) with corresponding probability \\(p_q\\). These boxes are sometimes inaccurate and fail to enclose the desired region, see Fig. 3 (b). Hence, we propose our depth-based prompt refinement for consistent segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Depth-Warping Prompt Refinement. \"Depth Warp\" operates on the sampled points to enhance segmentation accuracy. It leverages the depth information inherited from the input NeRF and projects these points back into the pixel space to align them with other 2D observations within the scene. We thereby establish a cohesive depth constraint across different views. The depth for a sampled ray" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12679" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "\\(\\mathbf{r} = \\mathbf{o} + t\\mathbf{d}\\) with origin \\(\\mathbf{o}\\) and direction \\(\\mathbf{d}\\) in a trained NeRF scene can be estimated via a modification of Eq. (1):" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.125, + 0.47, + 0.166 + ], + "angle": 0, + "content": "\\[\nD (\\mathbf {r}) = \\sum_ {i = 1} ^ {I} \\alpha_ {i} T _ {i} \\cdot t _ {i}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.176, + 0.471, + 0.388 + ], + "angle": 0, + "content": "For each training view, we randomly select \\( m \\) other training views. From each selected view, we sample a fixed number \\( p \\) of rays that correspond to pixels within the mask region. Given a ray \\( \\mathbf{r} \\) and its estimated depth from Eq. (2), we compute the 3D location of the selected point prompt. This information is then mapped back to the current training view. Rays and their corresponding point prompts whose depth is above a certain threshold are discarded, as they may represent background objects misclassified as foreground sections to be removed. If the corresponding pixel on the current view falls outside the masked region in the current view, we add this point prompt to the current view. Subsequently, we pass this view with the new sets of point prompts to SAM for refined segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.47, + 0.495 + ], + "angle": 0, + "content": "By generating these \"out-of-the-box\" point-based prompts for the segmentation model with our NeRF-based depth prior, we ensure that the object is accurately segmented even in cases where the initial bounding box information is insufficient or incomplete from certain viewpoints. This approach greatly increases the segmentation masks' accuracy for desired objects in the scene, see Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.502, + 0.347, + 0.512 + ], + "angle": 0, + "content": "\"Remove the flowerpot and flowers" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.512, + 0.449, + 0.648 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.649, + 0.47, + 0.718 + ], + "angle": 0, + "content": "Figure 3. Inconsistent bounding box across different views. (a) and (b) are from the same dataset under the same instruction. However, the generated bounding boxes are different. After applying depth warping refinement (point prompts as red dots), (c) generates accurate segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.471, + 0.858 + ], + "angle": 0, + "content": "Promptable Segmentation After obtaining the refined point-based prompts, we employ SAM to identify and segment all the rendered observations \\(\\{\\mathbf{I}_n\\}_{n=1}^N\\) for refined masks \\(\\{\\mathbf{M}_n\\}_{n=1}^N\\). Specifically, SAM takes as input an image \\(\\mathbf{I}\\) and a prompt in the form of \\(j\\) points pinpointing the object \\(o_q\\), and produces an accurate segmentation mask \\(\\mathbf{M}_{\\mathbf{q}}\\) of the same size as \\(\\mathbf{I}\\): \\(\\mathbf{M}_q = \\mathrm{SAM}(\\mathbf{I}, o_q)\\). For each image \\(\\mathbf{I}_i \\in \\{\\mathbf{I}_n\\}_{n=1}^N\\), we get a union binary mask for all the objects to be removed:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.861, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {i} = \\bigcup_ {q = 1} ^ {Q} \\mathbf {M} _ {q}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.707, + 0.108 + ], + "angle": 0, + "content": "3.3. Inpainting \\(360^{\\circ}\\) NeRF" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.312 + ], + "angle": 0, + "content": "Inpainted NeRF Initialization. With the rendered observations \\(\\{\\mathbf{I}_n\\}_{n=1}^N\\) and corresponding masks \\(\\{\\mathbf{M}_n\\}_{n=1}^N\\), we adopt a 2D image inpainter [36] to edit each observation as priors for the optimization. We then initialize the inpainted scene with Nerfacto [39]. This architecture is designed to optimize the performance of NeRF on real-world image captures. However, each inpainted image has varying pixel-level content despite being perceptually plausible as a standalone image. Therefore, relying solely on RGB supervision leads to floaters in the NeRF (Fig. 4). To produce clean and perceptually consistent inpainting, we fine-tune the initialized NeRF with both geometry and appearance priors." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.322, + 0.696, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.322, + 0.892, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.502 + ], + "angle": 0, + "content": "Figure 4. Examples of artifacts in the initialized NeRF. 2D inpaintings contain inconsistent inpainted pixels that accumulate in the 3D inpainted region and appear as floater artifacts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Hallucinating Density Removal. The density artifacts produced through inconsistent 2D inpainting can be seen as floaters. We train a denoising diffusion probabilistic model (DDPM) [12] on ShapeNet [6] to iteratively denoise a \\(m^3\\) resolution voxel grid of discretized binary occupancy \\(x\\) as a local 3D geometry prior: given a NeRF density \\(\\sigma\\) at timestep \\(t\\), \\(x_{t} = 1\\) if \\(\\sigma > \\rho\\) else \\(x_{t} = -1\\), where \\(\\rho\\) is a chosen threshold for whether a voxel is empty. For training, from each ShapeNet mesh we randomly select \\(N\\) cubes that encompass \\(3\\%\\) to \\(8\\%\\) of the object bounding volume, and voxelize them to \\(m^3\\) resolution. The loss function for the diffusion model is given by the MSE loss between the true noise \\(\\epsilon\\) and the predicted noise \\(\\epsilon_{\\theta}\\) where \\(\\theta\\) parameterizes the diffusion model U-Net:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.719, + 0.892, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {d d p m}} (\\theta) = \\mathbb {E} _ {t, x _ {0}, \\sigma} [ \\| \\epsilon - \\epsilon_ {\\theta} (\\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t) \\| _ {2} ^ {2} ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.892, + 0.812 + ], + "angle": 0, + "content": "where \\( t \\in [1, 1000] \\) is the number of timesteps in the nois-ing diffusion process, and \\( \\bar{\\alpha}_t = \\prod_{s=1}^t \\alpha_s \\) where \\( \\alpha_t \\) is a function of the timestep \\( t \\) that parameterized transitions from \\( x_0 \\) to \\( x_{1000} \\) (i.e. a noise schedule)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.873 + ], + "angle": 0, + "content": "The Density Score Distillation Sampling (DSDS) [42] loss is defined to penalize regions with density \\(\\sigma >\\rho\\) that the trained diffusion model deems as empty, and regions that are empty where \\(x_{t} = 1\\) predicted by the model:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.874, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {D S D S}} = \\sum_ {i} u _ {i} \\sigma_ {i} + (1 - u _ {i}) \\max (w - \\sigma_ {i}, 0), \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12680" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "where \\( u = \\mathbb{1}\\{x_0 < 0\\} \\), and \\( w \\) is a chosen upper limit for density \\( \\sigma \\) in occupied voxels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.469, + 0.273 + ], + "angle": 0, + "content": "The original sampling of the DSDS loss is by sampling a low-resolution density grid stored through ray bundles. During training, the grid selects the center of 3D cubes to be voxelized and enter the diffusion process. The grid gets updated by a visibility field determining what it sees in the NeRF scene. Our aim is to focus on removing floaters within the inpainted region. Therefore, we apply the refined segmentation mask from the image space to limit the visibility field to only look at the inpainted regions, and eliminate sampled rays corresponding to pixels outside the mask:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.275, + 0.469, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g e o m}} = \\sum_ {j} \\left(u _ {j} \\sigma_ {j} + (1 - u _ {j}) \\max (w - \\sigma_ {j}, 0)\\right) \\cdot V _ {j}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.469, + 0.433 + ], + "angle": 0, + "content": "where \\( V \\) is an indicator function whose value is 1 for each voxel cube whose center is located within the current \"visible region\" given by the segmentation masks. Consequently, we sample cubes near the inpainted region. The geometric prior trained on extensive shapes in [6] preserves the original surface (e.g., the table supporting the removed flowerpot) while penalizing the floaters in the inpainted region created through inconsistent 2D inpainting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.469, + 0.524 + ], + "angle": 0, + "content": "Perceptually-Consistent Appearance Inpainting. The above method removes floaters created by inconsistent 2D inpainting, however, it does not produce visually consistent textures to fill in the removed region. Therefore, we utilize a patch-based loss [45] as an appearance prior to enhancing the model's robustness and alleviate blurring effects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.469, + 0.663 + ], + "angle": 0, + "content": "Specifically, we sample all the pixels from the input inpainted images to get \\( W \\) image patches \\( \\{P_w\\}_{w=1}^W \\) with the size of \\( v^2 \\). These patches, \\( \\{P_w\\}_{w=1}^W \\), can be divided into two non-overlapping groups of patches \\( P_{w_i} \\) and \\( P_{w_o} \\) depending on whether a patch contains pixels within the inpainted region. For patches in \\( P_{w_o} \\), we apply pixel-wise L1. This pixel loss is obtained by comparing the RGB values of each pixel \\( p \\) in the inpainted patch, denoted as \\( \\hat{\\mathbf{C}}_p \\), with the corresponding rendered RGB value, denoted as \\( \\hat{\\mathbf{C}}_p \\)," + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.664, + 0.469, + 0.702 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p i x}} = \\frac {1}{v ^ {2} \\left| P _ {w _ {o}} \\right|} \\sum_ {p _ {\\mathrm {r}} \\in P _ {w _ {o}}} \\left\\| \\hat {\\mathbf {C}} _ {p} - \\tilde {\\mathbf {C}} _ {p} \\right\\| _ {1}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.469, + 0.789 + ], + "angle": 0, + "content": "For patches in \\( P_{w_i} \\) containing the inpainted region, we compute the perceptual similarity using LPIPS between the inpainted image patch \\( \\tilde{P}_I \\) and the corresponding patch \\( P \\) on the rendered image. We denote \\( \\mathbf{C}_P \\) as the set of pixel values in patch \\( P \\), and define \\( \\mathcal{L}_{\\mathrm{in}} \\) as the inpainting loss." + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.79, + 0.469, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n}} = \\frac {1}{\\left| P _ {w _ {i}} \\right|} \\sum_ {P \\in P _ {w _ {i}}} \\operatorname {L P I P S} \\left(\\mathbf {C} _ {P}, \\mathbf {C} _ {\\tilde {P} _ {I}}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The inpainting loss measures the perceptual difference between the inpainted patch and the target inpainted image, while the pixel loss quantifies the pixel-level discrepancy between the inpainted and rendered RGB values. Together," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "these losses provide a comprehensive assessment of the reconstruction quality, accounting for both perceptual similarity and pixel-wise accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.892, + 0.184 + ], + "angle": 0, + "content": "Loss Functions. Our optimization is the weighted sum of the geometric prior \\(\\mathcal{L}_{\\mathrm{geom}}\\) (Eq. (6)), pixel loss \\(\\mathcal{L}_{\\mathrm{pix}}\\) (Eq. (7)), appearance prior \\(\\mathcal{L}_{\\mathrm{in}}\\) (Eq. (8)) with \\(\\lambda_{(\\cdot)}\\) as weight terms:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.189, + 0.892, + 0.206 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {\\text {g e o m}} \\cdot \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {i n}} \\cdot \\mathcal {L} _ {\\text {i n}} + \\mathcal {L} _ {\\text {p i x}}. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.22, + 0.633, + 0.237 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.275 + ], + "angle": 0, + "content": "In this section, we evaluate InNeRF360 on various real-world captured datasets for text-guided inpainting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Datasets. We take 360-degree datasets from MipNeRF, MipNeRF-360, and NeRFStudio [1, 2, 39]. In addition, due to the absence of ground truth data for \\(360^{\\circ}\\) scene inpainting, we capture new datasets with and without the object removed for quantitative evaluation. Segmentation mask ground truth does not exist for the \\(360^{\\circ}\\) scenes we evaluate. We also compare with front-facing datasets from SPInNeRF [26] and IBRNet [41] to show that our method produces better inpainting over baseline methods. Details of the datasets we used are provided in Tab. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.564 + ], + "angle": 0, + "content": "Baseline. We select baselines based on specific tasks. SPIn-NeRF SPN [26] is the closest work to ours. For segmentation, we compare with the multiview segmentation from SPN and a recent video segmentation method Dino [5]. For the inpainting task, we compare our inpainting quality with our implemented version of SPN that works with 360-degree scenes SPN-360. We also compare with per-frame image inpainting [36] to show that our method generates more consistent inpainting across different viewpoints." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.741, + 0.591 + ], + "angle": 0, + "content": "4.1. Segmentation Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.718 + ], + "angle": 0, + "content": "We qualitatively compare our segmentation results to SPN and Dino. As input, we give the first frame segmentation to both SPN and Dino, and give the corresponding text instructions for InNeRF360. As we are evaluating the extrapolation ability of each segmentation method over drastically different viewpoints, we select the 82nd frame from vasedeck and the 81st image from room. They represent the respective frames of the videos created from the dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 5, Dino produces incomplete segmentation for unseen views in challenging scenes, such as the vasedeck featuring a transparent vase. In such cases, SPN struggles to generate complete segmentation when initialized with Dino's output. While we also initialize with a 2D segmentation model (SAM), it facilitates flexible, promptable input. This can be utilized by our depth-warping refinement to output point prompts specifically in the vase section of the image. These prompts guide SAM towards accurate segmentation, as elaborated in Sec. 3.2. For room, where only a part of the slippers is present in the image, Dino and SPN once again yield incomplete segmentations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12681" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.09, + 0.447, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.472, + 0.468, + 0.515 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on 3D object segmentation. InNeRF360 outputs accurate masks for complex cases containing transparent (vase) or incomplete objects (partial slippers)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.529, + 0.468, + 0.545 + ], + "angle": 0, + "content": "InNeRF360 is able to output complete object segmentation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.283, + 0.573 + ], + "angle": 0, + "content": "4.2. Inpainting Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.581, + 0.468, + 0.642 + ], + "angle": 0, + "content": "Results on 360-degree scenes. InNeRF360 can handle a wide range of scenarios for object inpainting in 3D scenes, as depicted in Fig. 7. We encourage the readers to view supplementary videos to inspect the quality of our results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.468, + 0.732 + ], + "angle": 0, + "content": "InNeRF360 can remove large scene objects against complex backgrounds. In Bear, the background of the bear contains varying trees and branches, and the 2D inpainted images are therefore very noisy, as shown in Fig. 16. However, with our floater removal and appearance prior, InNeRF360 produces a clean stone surface in the final edited NeRF." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Occlusion and geometry deformation across varying viewpoints are major causes of 3D inconsistency in inpainting, and the datasets we use contain both scenarios. In Room, the window, wall, and the piano behind the score can lead to inconsistency. However, we generate view-consistent content to seamlessly fill the missing region." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Moreover, InNeRF360 is capable of inpainting multiple objects located anywhere in the 3D scenes without introducing blurry artifacts in the resulting NeRF scene. When given a text input containing multiple objects (Room: \"slippers\" and \"piano sheet\"; Bulldozer: multiple \"cones\"), In" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.089, + 0.869, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.285, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison with SPN-360. Text: Remove the vase and the flowers. InNeRF360 inpaints clean and visually plausible regions while better preserving surrounding scenes." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.33, + 0.88, + 0.456 + ], + "angle": 0, + "content": "
MethodsCupStarbucks
LPIPS ↓FID ↓LPIPS ↓FID ↓
Per-Frame0.6149201.700.5981260.93
SPN-3600.6421252.340.6278215.28
NeRFacto0.7328271.560.6832258.39
+Lin0.7137210.570.6658223.82
+Lgeom0.6197189.570.5795166.45
+Lin + Lgeom (Ours)0.5377159.760.4523153.46
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.457, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation on the inpainting quality. Our method achieves better results than baseline methods and our ablated settings on captured datasets." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.508, + 0.891, + 0.554 + ], + "angle": 0, + "content": "NeRF360 produces inpainted regions that seamlessly blend with the surrounding context, yielding visually coherent and high-quality inpainting results." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.554, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Fig. 6 shows qualitative comparison to SPN-360. Our method not only synthesizes a perceptually-consistent inpainted region, but also preserves the surrounding background closer to the input NeRF scene. We speculate the reason for the background-preserving inpainting to be that SPN inpaints on depth maps with segmentation masks generated from RGB images. We elaborate on our choice not to use 2D depth map inpainting in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.675, + 0.891, + 0.735 + ], + "angle": 0, + "content": "Ablation studies on our design choices. Our depth-warping method produces refined point-based prompts for the segmentation model, and outputs complete and consistent multi-view segmentation, as shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Fig. 8 qualitatively ablates our choice of loss functions. In Fig. 8a (ii), the vanilla NeRFacto model outputs a concentrated artifact in the inpainted region along with noisy texture in nearby regions which we suspect is due to per-image appearance encoding on inconsistent 2D inpainted images. Fig. 8a (iii) shows NeRFacto \\( +\\mathcal{L}_{\\mathrm{in}} \\) which improves inpainted texture, but cannot reduce the floater artifact. These artifacts have view-dependent appearances from individual views and are therefore difficult to remove from appearance priors. In Fig. 8a (iv) for InNeRF360, we can see a clean and perceptually consistent surface in the edited" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12682" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.352, + 0.093, + 0.642, + 0.107 + ], + "angle": 0, + "content": "Bear: \"Remove the rectangular base and the bear\"" + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.108, + 0.85, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.351, + 0.287, + 0.637, + 0.302 + ], + "angle": 0, + "content": "Room: \"Remove the slippers and the piano sheet\"" + }, + { + "type": "image", + "bbox": [ + 0.125, + 0.304, + 0.851, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.404, + 0.485, + 0.625, + 0.498 + ], + "angle": 0, + "content": "Bulldozer: \"Remove the traffic cones\"" + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.499, + 0.851, + 0.672 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.683, + 0.895, + 0.711 + ], + "angle": 0, + "content": "Figure 7. Qualitative inpainting results on 360 scenes. Our method works with various types of NeRF scenes. We can also remove arbitrary numbers of objects given the text input, independent of the complexity of the scene content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.471, + 0.817 + ], + "angle": 0, + "content": "scene. In Fig. 8b shows InNeRF360 versus trained without \\(\\mathcal{L}_{\\mathrm{in}}\\). We can see that the LPIPS loss can improve blurry background output due to inconsistent 2D inpainting. The lower part of Tab. 1 shows quantitative ablation on each loss term in InNeRF360. Our complete architecture performs better than without each of the loss terms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Inpainting quality. Due to the lack of baseline and ground truth datasets on inpainting \\(360^{\\circ}\\) NeRF scenes, we captured real-world datasets for quantitative comparison on the quality of inpainted renderings. Since InNeRF360 generates consistent and complete 3D segmentation over baseline" + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.725, + 0.88, + 0.776 + ], + "angle": 0, + "content": "
DatasetsGardenRoomVasedeckBulldozerBear
Ours89%71%81%83%92%
Per-frame11%29%19%17%8%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.778, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Table 2. User study comparing with per-frame inpainting on visual consistency between consecutive frames. In each of the scenes, our inpainted NeRF renders higher view consistency than per-frame inpainting. Per-frame editing lacks a 3D understanding of each scene and inpaints each image independently." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.854, + 0.892, + 0.884 + ], + "angle": 0, + "content": "methods, the 2D inpainting initialization is naturally much less noisy than baseline methods." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We evaluate our inpainting quality on each frame of the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12683" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.203, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.089, + 0.326, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.328, + 0.089, + 0.451, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.089, + 0.576, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.187, + 0.202, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.103, + 0.283, + 0.182, + 0.295 + ], + "angle": 0, + "content": "(i) Input Scene" + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.187, + 0.326, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.283, + 0.301, + 0.295 + ], + "angle": 0, + "content": "(ii) NeRFacto" + }, + { + "type": "image", + "bbox": [ + 0.328, + 0.187, + 0.451, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.283, + 0.441, + 0.295 + ], + "angle": 0, + "content": "(iii) \\(\\mathsf{NeRFacto} + \\mathcal{L}_{\\mathrm{in}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.187, + 0.576, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.486, + 0.283, + 0.537, + 0.295 + ], + "angle": 0, + "content": "(iv) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.305, + 0.473, + 0.318 + ], + "angle": 0, + "content": "(a) Qualitative ablation for \\(\\mathcal{L}_{\\mathrm{geom}}\\) on Bear and Garden." + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.089, + 0.762, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.187, + 0.762, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.284, + 0.75, + 0.297 + ], + "angle": 0, + "content": "(i) NeRFacto + geom" + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.09, + 0.887, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.187, + 0.887, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.284, + 0.849, + 0.295 + ], + "angle": 0, + "content": "(ii) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.305, + 0.872, + 0.317 + ], + "angle": 0, + "content": "(b) Qualitative ablation for \\(\\mathcal{L}_{\\mathrm{in}}\\) on Garden." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.319, + 0.894, + 0.361 + ], + "angle": 0, + "content": "Figure 8. Ablation for losses on geometric and appearance priors. The artifact in the inpainted region is not as pronounced if viewed from aside as when viewed from the top. Our method is able to optimize an inpainted NeRF without artifacts and with a consistent and unblurry background." + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.373, + 0.378, + 0.385 + ], + "angle": 0, + "content": "\"Turn the slippers into red slippers\"" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.387, + 0.282, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.387, + 0.446, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.461, + 0.282, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.461, + 0.446, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.533, + 0.282, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.533, + 0.446, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.607, + 0.47, + 0.662 + ], + "angle": 0, + "content": "Figure 9. Editing comparison with In2n. InNeRF360, combined with appropriate mask-conditioned image editing models, can generate accurate editing on desired objects. In contrast, In2n gives the wrong texture to unwanted regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.468, + 0.778 + ], + "angle": 0, + "content": "renderings with per-frame inpainting and SPN-360. We report LPIPS [44] and Frechet Inception Distance (FID) [11] metric in Tab. 1 by comparing with the output of the captured empty scene rendered under the same camera trajectory which we use as ground truth. Our method outperforms each baseline method and outputs visually consistent inpainting without visual artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.468, + 0.809 + ], + "angle": 0, + "content": "A quantitative baseline comparison to SPN on frontal scenes is also in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.885 + ], + "angle": 0, + "content": "3D consistency over per-frame inpainting. A naive approach for 3D scene inpainting is to independently inpaint every rendered image of the scene with a 2D image inpainter. In contrast, InNeRF360 produces inpaintings with higher view consistency across all viewpoints." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We verify such a claim with a user study where partici" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.37, + 0.892, + 0.476 + ], + "angle": 0, + "content": "pants were presented with two video clips of each inpainted scene, rendered with sequential camera trajectories. They were then asked to identify which clip appeared more consistent. Additional details about the user study can be found in the supplementary material. The results, presented in Tab. 2, clearly show that our rendered inpaintings exhibit superior temporal consistency compared to per-frame edits." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.478, + 0.671, + 0.494 + ], + "angle": 0, + "content": "4.3. Editing Accuracy" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.623 + ], + "angle": 0, + "content": "As shown by Fig. 9, our segmentation module can be connected with a mask-conditioned image editor [8] to generate view-consistent editing with object-level control through text instructions, which InstructNeRF2NeRF (In2n) [9] cannot. However, note that editing is not the focus of our work. We show this result simply to demonstrate a possible extension to our method. Details are provided in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.63, + 0.757, + 0.644 + ], + "angle": 0, + "content": "5. Limitations and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.648, + 0.892, + 0.768 + ], + "angle": 0, + "content": "Limitations. Our method inherits certain constraints of vision-language models. In scenarios where the text instruction cannot be accurately localized within the image, InNeRF360 may struggle in generating segmentation consistently aligned with the views. This issue arises when the initial masks provided by the 2D object detector are inaccurate or too noisy for effective refinement. Addressing this challenge is a focus of our future work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.769, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Conclusion. In conclusion, we have presented InNeRF360, a unified system to accurately segment and inpaint objects in \\(360^{\\circ}\\) NeRFs with text instructions. We synthesize perceptually consistent inpainting without artifacts and can extend to object-level stylization, improving the controllability of NeRF." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.859, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. 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Large scale image completion via co-modulated generative adversarial networks. arXiv preprint arXiv:2103.10428, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12686" + } + ] +] \ No newline at end of file diff --git a/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_origin.pdf b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..784a1df3f09bf3cc913445163a0bbbd2c3067490 --- /dev/null +++ b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/09378d81-d6b3-4b15-9d8b-0c6cf0d263a0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9177fee742d544d8d6fcd1e41f3b1303186d53d6e9ddd391b4521c46110cc3e5 +size 9442217 diff --git a/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/full.md b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/full.md new file mode 100644 index 0000000000000000000000000000000000000000..40ca957fca9a7d5f6465c832f11e10fcfd819459 --- /dev/null +++ b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/full.md @@ -0,0 +1,346 @@ +# InNeRF360: Text-Guided 3D-Consistent Object Inpainting on $360^{\circ}$ Neural Radiance Fields + +Dongqing Wang Tong Zhang* Alaa Abboud Sabine Süssstrunk +School of Computer and Communication Sciences, EPFL Lausanne, Switzerland + +# Abstract + +We propose InNeRF360, an automatic system that accurately removes text-specified objects from $360^{\circ}$ Neural Radiance Fields (NeRF). The challenge is to effectively remove objects while inpainting perceptually consistent content for the missing regions, which is particularly demanding for existing NeRF models due to their implicit volumetric representation. Moreover, unbounded scenes are more prone to floater artifacts in the inpainted region than frontal-facing scenes, as the change of object appearance and background across views is more sensitive to inaccurate segmentations and inconsistent inpainting. With a trained NeRF and a text description, our method efficiently removes specified objects and inpaints visually consistent content without artifacts. We apply depth-space warping to enforce consistency across multiview text-encoded segmentations, and then refine the inpainted NeRF model using perceptual priors and 3D diffusion-based geometric priors to ensure visual plausibility. Through extensive experiments in segmentation and inpainting on $360^{\circ}$ and frontal-facing NeRFs, we show that our approach is effective and enhances NeRF's editability. Project page: https://ivrl.github.io/InNeRF360/. + +# 1. Introduction + +Recreating and manipulating real-world scenarios is one of the main focuses of Virtual and Augmented Reality (VR/AR) applications. Neural Radiance Field (NeRF) and its variants [2, 23, 28] can efficiently model $360^{\circ}$ real-world scenes for photorealistic novel view synthesis. Consequently, they have the potential to become widely accessible tools for representing the 3D world. + +A desired feature of such applications is the ability to modify the content of the created scene, including object removal. However, direct inpainting in the NeRF framework is intractable due to the implicit representation of the captured scenes encoded through the weights of multilayer + +![](images/ccfbd38d35fe2c39e6ff871d1e1a66ec81f77255c876c82d660133b2331aa87d.jpg) +Figure 1. Given a pre-trained NeRF and a text to remove specific objects (e.g. "Remove the flowerpot and flowers"), InNeRF360 produces accurate multiview object segmentations, and outputs an inpainted NeRF with visually consistent content. + +perceptrons (MLP), which hinders explicit user control of scene contents. For explicit NeRF variants, the scene representation of radiance fields contains ambiguous surface that is hard to segment with a bounding region. + +Existing works on selecting [35] or removing [18, 26, 43] objects in a trained NeRF tackle the 3D problem by utilizing 2D input. These methods begin with sparse user inputs, then use 2D image/video segmentation [7, 10] for multiview segmentation and inpaint on RGB-D sequence. They are restricted to frontal-facing viewing angles, as the input scribbles or masks cannot extrapolate across differ- + +ent viewpoints in $360^{\circ}$ scenes where the shape of the object can change drastically. Moreover, in the case of object occlusions on $360^{\circ}$ scenes, inpainting 2D depth maps is inadequate for geometric supervision as it leads to inconsistencies in scene geometry. + +In contrast, InNeRF360 is an inpainting pipeline with a depth-guided segmentation method dedicated to accurate object-level editing on $360^{\circ}$ scenes. Instead of extrapolating sparse 2D input to 3D, InNeRF360 encodes text input into a promptable segmentation model, Segment Anything Model (SAM) [15], leveraging its accurate semantic segmentation. Our method is driven by the intuition that an object's semantic identity is more consistent over different viewpoints than its geometry. However, text-based 2D semantic segmentations may not always maintain consistency across views. To overcome this, we refine object masks using inverse depth space warping in 3D space across viewpoints, utilizing the consistent 3D positioning of objects. + +Using view-consistent masks, we train a NeRF from scratch on the multiview inpainting from a 2D image inpainter [36]. The multiview training images slightly differ in the inpainted regions, accumulating into cloudy artifacts, i.e. floaters [42], in the new NeRF. To eliminate floaters, we finetune the scene guided by 3D diffusion priors trained on extensive geometric shapes [6] to determine whether density should be removed or incremented in a local voxel. The texture for the removed region is optimized by contextual appearance priors [45] from the surrounding regions of the segmentation. This creates a perceptually consistent 3D inpainted region that seamlessly blends into the scene. Extensive experiments show that InNeRF360 can effectively inpaint both $360^{\circ}$ [2] and front-facing [22] real-world scenes, with the potential to be extended into 3D editing. + +To summarize, our contributions are as follows: + +- InNeRF360 is the first work to achieve text-guided object inpainting in $360^{\circ}$ NeRF scenes, ensuring visually consistent inpainted regions. +- Our approach efficiently generates multiview consistent 2D segmentation for 3D object inpainting through depth-warping refinement on initialized masks. +- We incorporate a 3D diffusion network as local geometric priors to remove artifacts in the inpainted region. + +# 2. Related Works + +Image Inpainting. Recent advancements in image inpainting focus on filling in masked regions to create visually consistent images. This primarily involves generative models like Generative Adversarial Networks (GANs) [13, 31, 46] and denoising diffusion models (DDPMs) [29, 36, 37]. These models generate photorealistic predictions for the missing pixels. However, when applied to inpainting multiview renderings of 3D scenes [25, 26], they often generate different inpainted regions for nearby views. This is due to + +their lack of 3D understanding, presenting a challenge for inpainting 2D observations of 3D scenes. InNeRF360 leverages image inpainting to address inpainting $360^{\circ}$ scenes, ensuring view consistency across viewpoints. + +Inpainting Neural Radiance Fields. Using neural radiance fields [23] to represent 3D scenes has achieved high-quality, photo-realistic novel view synthesis. NeRF Facto [39] is an architecture designed to optimize NeRF's performance on real-world data. It incorporates various recent advances in NeRF, including hash encoding [28] and per-image appearance encoding [19], among others. + +However, object removal presents a challenge in NeRF due to the implicit scene representation by the underlying neural networks. Previous works [24, 40] utilize the supervision of Contrastive Text-Image Pre-Training (CLIP) [34]. They focus on inpainting a single object and cannot generalize to real-world scenes. Methods utilizing depth-based approaches [18, 25, 26, 43] remove objects with user-drawn masks and depth sequences, and inpaint missing regions naively with 2D image inpainter on the training images of NeRF. These approaches are limited to front-facing scenes for two reasons. First, their segmentation relies on the quality of initialize masks by supervised video object segmentation methods [4, 5, 7, 30], which struggle on temporal consistency across frames for challenging cases such as transparent objects. These methods cannot output accurate object masks in $360^{\circ}$ scenes, where object shapes change drastically across views. Secondly, the chosen 2D inpainting methods output different inpainting across views. Such inconsistency results in floaters in the trained NeRF, and is much more pronounced on $360^{\circ}$ scenes than on frontal-facing ones. In contrast, InNeRF360 enhances the consistency of multiview segmentation by utilizing semantical identity and object 3D location consistency, thereby producing accurate masks for desired objects. Moreover, InNeRF360 is designed for $360^{\circ}$ NeRF inpainting by removing floaters (Fig. 4) from the inpainted NeRF with geometric priors, and inpaint with contextual perception guidance. + +Text-Guided 3D Editing. Given the popularity of text-conditioned image generative models, many works focus on generating 3D content with text instructions. Some rely on joint embeddings of CLIP to synthesize 3D meshes [21, 27] or neural radiance fields [14, 16]. Others distill a pretrained diffusion model to optimize NeRF scenes in the latent space [20, 33]. These methods all suffer from having to map the inconsistent 2D diffusion model outputs to a 3D-consistent scene. Instruct-NeRF2NeRF [9] edits renderings of a pre-trained NeRF model to preserve 3D consistency. However, it cannot remove scene objects or perform object-level editing as it operates in latent space for image editing. Our InNeRF360 operates in image space to accurately pinpoint and crop objects and allows removing an arbitrary number of objects from the scene through text instructions, + +![](images/42e47cee7871c6e45f62ccd4d590f62ffbe1a198ee524191d079600f3b94824b.jpg) +Figure 2. Overview of InNeRF360 framework. 1. Multiview Consistent Segmentation. We initialize masks using bounding boxes from the object detector, which encodes both the source image and text. With rendered depth from the input NeRF, we apply depth-warping prompt refinement to iteratively update points for the Segment Anything Model (SAM) to output view-consistent 2D segmentations. 2. Inpainting $360^{\circ}$ NeRF. We obtain edited images through image inpainter with the masks and source images to retrain the inpainted NeRF. We then finetune the new NeRF model using a geometric prior trained from a 3D diffusion model and a masked perceptual prior. + +while using 3D diffusion priors for local geometry finetuning to avoid the global inconsistency prior works exhibit. + +# 3. Method + +InNeRF360 takes as input a trained NeRF with source images which the model trained on, and an instructive text. It outputs the inpainted 3D scene with the desired object(s) removed and filled with a visually consistent background without artifacts. Our pipeline is shown in Fig. 2. + +# 3.1. Background: Neural Radiance Fields + +A Neural Radiance Field (NeRF) encodes a 3D scene as a function $f_{\theta}$ parametrized by an MLP with learnable parameters $\theta$ , which maps a 3D viewing position $\mathbf{x}$ and its 2D direction $\mathbf{d}$ to the density $\sigma$ and a viewing-dependent color $\mathbf{c}$ : $f_{\theta}:(\mathbf{x},\mathbf{d})\to (\sigma ,\mathbf{c})$ . Rendering a NeRF from a posed camera is done by sampling batches of rays for the camera pose, and rendering corresponding pixel colors for each ray. For each ray $\mathbf{r} = (\mathbf{o},\mathbf{d})$ , we sample an array of 3D points $(\mathbf{x}_i,t_i)$ , $i = 1,2,\dots ,K$ , where $\mathbf{x}_i\in \mathbb{R}^2$ and $t_i$ is the depth. We query the MLP with these points along the ray for $\{\sigma_i\}_{i = 1}^K$ and $\{\mathbf{c}_i\}_{i = 1}^K$ . + +The estimated RGB of ray $\hat{\mathbf{C}} (\mathbf{r})$ is obtained by alpha compositing [23] the densities and colors along the ray: + +$$ +\hat {\mathbf {C}} (\mathbf {r}) = \sum_ {i = 1} ^ {K} \alpha_ {i} T _ {i} \mathbf {c} _ {i}, \tag {1} +$$ + +where $T_{i} = 1 - \exp (-\sigma_{i}\| t_{i} - t_{i - 1}\|)$ is the ray transmittance between $\mathbf{x}_i$ and $\mathbf{x}_{i + 1}$ , and $\alpha_{i} = \prod_{j = 1}^{i - 1}T_{i}$ is the attenuation. + +uation from ray origin to $\mathbf{x}_i$ . The MLP is optimized through pixel loss for the distance between the estimated pixel value and the ground truth color. + +# 3.2. Multiview Consistent Segmentation + +The first stage is to obtain refined multiview segmentation masks for the objects to remove/edit given by the text input. We take as input a pre-trained NeRF model and $N$ source images given by the set of $N$ source camera poses. + +We initialize segmentations through the Segment-Anything Model (SAM) [15] with the bounding boxes given by Grounded Language-Image Pre-training (GLIP) from a large-scale dataset of image-text pairs [17]. GLIP: $\mathcal{D}(\mathbf{I},\mathbf{s}) = \{(B_q,p_q)\}_{q = 1}^Q$ takes in an RGB image $\mathbf{I}\in$ $\mathbb{R}^{H\times W\times 3}$ and a text s, and encodes each through respective image and language encoders. $Q$ is the number of bounding boxes. We then take these bounding boxes $\{B_q\}_{q = 1}^Q$ from the model output in which $B_{q} = (l_{q},r_{q},u_{q},d_{q})\in \mathbb{R}^{4}$ with corresponding probability $p_q$ . These boxes are sometimes inaccurate and fail to enclose the desired region, see Fig. 3 (b). Hence, we propose our depth-based prompt refinement for consistent segmentation. + +Depth-Warping Prompt Refinement. "Depth Warp" operates on the sampled points to enhance segmentation accuracy. It leverages the depth information inherited from the input NeRF and projects these points back into the pixel space to align them with other 2D observations within the scene. We thereby establish a cohesive depth constraint across different views. The depth for a sampled ray + +$\mathbf{r} = \mathbf{o} + t\mathbf{d}$ with origin $\mathbf{o}$ and direction $\mathbf{d}$ in a trained NeRF scene can be estimated via a modification of Eq. (1): + +$$ +D (\mathbf {r}) = \sum_ {i = 1} ^ {I} \alpha_ {i} T _ {i} \cdot t _ {i}, \tag {2} +$$ + +For each training view, we randomly select $m$ other training views. From each selected view, we sample a fixed number $p$ of rays that correspond to pixels within the mask region. Given a ray $\mathbf{r}$ and its estimated depth from Eq. (2), we compute the 3D location of the selected point prompt. This information is then mapped back to the current training view. Rays and their corresponding point prompts whose depth is above a certain threshold are discarded, as they may represent background objects misclassified as foreground sections to be removed. If the corresponding pixel on the current view falls outside the masked region in the current view, we add this point prompt to the current view. Subsequently, we pass this view with the new sets of point prompts to SAM for refined segmentation. + +By generating these "out-of-the-box" point-based prompts for the segmentation model with our NeRF-based depth prior, we ensure that the object is accurately segmented even in cases where the initial bounding box information is insufficient or incomplete from certain viewpoints. This approach greatly increases the segmentation masks' accuracy for desired objects in the scene, see Fig. 3. + +"Remove the flowerpot and flowers + +![](images/0890ac0dcae3a2d681f296d511d13e9c6f2fb82d03d2908b8a2a0bc901d38347.jpg) +Figure 3. Inconsistent bounding box across different views. (a) and (b) are from the same dataset under the same instruction. However, the generated bounding boxes are different. After applying depth warping refinement (point prompts as red dots), (c) generates accurate segmentation. + +Promptable Segmentation After obtaining the refined point-based prompts, we employ SAM to identify and segment all the rendered observations $\{\mathbf{I}_n\}_{n=1}^N$ for refined masks $\{\mathbf{M}_n\}_{n=1}^N$ . Specifically, SAM takes as input an image $\mathbf{I}$ and a prompt in the form of $j$ points pinpointing the object $o_q$ , and produces an accurate segmentation mask $\mathbf{M}_{\mathbf{q}}$ of the same size as $\mathbf{I}$ : $\mathbf{M}_q = \mathrm{SAM}(\mathbf{I}, o_q)$ . For each image $\mathbf{I}_i \in \{\mathbf{I}_n\}_{n=1}^N$ , we get a union binary mask for all the objects to be removed: + +$$ +\mathbf {M} _ {i} = \bigcup_ {q = 1} ^ {Q} \mathbf {M} _ {q}. \tag {3} +$$ + +# 3.3. Inpainting $360^{\circ}$ NeRF + +Inpainted NeRF Initialization. With the rendered observations $\{\mathbf{I}_n\}_{n=1}^N$ and corresponding masks $\{\mathbf{M}_n\}_{n=1}^N$ , we adopt a 2D image inpainter [36] to edit each observation as priors for the optimization. We then initialize the inpainted scene with Nerfacto [39]. This architecture is designed to optimize the performance of NeRF on real-world image captures. However, each inpainted image has varying pixel-level content despite being perceptually plausible as a standalone image. Therefore, relying solely on RGB supervision leads to floaters in the NeRF (Fig. 4). To produce clean and perceptually consistent inpainting, we fine-tune the initialized NeRF with both geometry and appearance priors. + +![](images/7c539969ec57785174ca153f2af15c03310e8fe5264032a32aef2bad00e7349a.jpg) +Figure 4. Examples of artifacts in the initialized NeRF. 2D inpaintings contain inconsistent inpainted pixels that accumulate in the 3D inpainted region and appear as floater artifacts. + +![](images/94497a9b364bb2f7ab2d288925baa0612cd2400156e2a430f2ebbf890dfd6ce3.jpg) + +Hallucinating Density Removal. The density artifacts produced through inconsistent 2D inpainting can be seen as floaters. We train a denoising diffusion probabilistic model (DDPM) [12] on ShapeNet [6] to iteratively denoise a $m^3$ resolution voxel grid of discretized binary occupancy $x$ as a local 3D geometry prior: given a NeRF density $\sigma$ at timestep $t$ , $x_{t} = 1$ if $\sigma > \rho$ else $x_{t} = -1$ , where $\rho$ is a chosen threshold for whether a voxel is empty. For training, from each ShapeNet mesh we randomly select $N$ cubes that encompass $3\%$ to $8\%$ of the object bounding volume, and voxelize them to $m^3$ resolution. The loss function for the diffusion model is given by the MSE loss between the true noise $\epsilon$ and the predicted noise $\epsilon_{\theta}$ where $\theta$ parameterizes the diffusion model U-Net: + +$$ +\mathcal {L} _ {\mathrm {d d p m}} (\theta) = \mathbb {E} _ {t, x _ {0}, \sigma} [ \| \epsilon - \epsilon_ {\theta} (\sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t) \| _ {2} ^ {2} ], \tag {4} +$$ + +where $t \in [1, 1000]$ is the number of timesteps in the nois-ing diffusion process, and $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$ where $\alpha_t$ is a function of the timestep $t$ that parameterized transitions from $x_0$ to $x_{1000}$ (i.e. a noise schedule). + +The Density Score Distillation Sampling (DSDS) [42] loss is defined to penalize regions with density $\sigma >\rho$ that the trained diffusion model deems as empty, and regions that are empty where $x_{t} = 1$ predicted by the model: + +$$ +\mathcal {L} _ {\mathrm {D S D S}} = \sum_ {i} u _ {i} \sigma_ {i} + (1 - u _ {i}) \max (w - \sigma_ {i}, 0), \tag {5} +$$ + +where $u = \mathbb{1}\{x_0 < 0\}$ , and $w$ is a chosen upper limit for density $\sigma$ in occupied voxels. + +The original sampling of the DSDS loss is by sampling a low-resolution density grid stored through ray bundles. During training, the grid selects the center of 3D cubes to be voxelized and enter the diffusion process. The grid gets updated by a visibility field determining what it sees in the NeRF scene. Our aim is to focus on removing floaters within the inpainted region. Therefore, we apply the refined segmentation mask from the image space to limit the visibility field to only look at the inpainted regions, and eliminate sampled rays corresponding to pixels outside the mask: + +$$ +\mathcal {L} _ {\text {g e o m}} = \sum_ {j} \left(u _ {j} \sigma_ {j} + (1 - u _ {j}) \max (w - \sigma_ {j}, 0)\right) \cdot V _ {j}, \tag {6} +$$ + +where $V$ is an indicator function whose value is 1 for each voxel cube whose center is located within the current "visible region" given by the segmentation masks. Consequently, we sample cubes near the inpainted region. The geometric prior trained on extensive shapes in [6] preserves the original surface (e.g., the table supporting the removed flowerpot) while penalizing the floaters in the inpainted region created through inconsistent 2D inpainting. + +Perceptually-Consistent Appearance Inpainting. The above method removes floaters created by inconsistent 2D inpainting, however, it does not produce visually consistent textures to fill in the removed region. Therefore, we utilize a patch-based loss [45] as an appearance prior to enhancing the model's robustness and alleviate blurring effects. + +Specifically, we sample all the pixels from the input inpainted images to get $W$ image patches $\{P_w\}_{w=1}^W$ with the size of $v^2$ . These patches, $\{P_w\}_{w=1}^W$ , can be divided into two non-overlapping groups of patches $P_{w_i}$ and $P_{w_o}$ depending on whether a patch contains pixels within the inpainted region. For patches in $P_{w_o}$ , we apply pixel-wise L1. This pixel loss is obtained by comparing the RGB values of each pixel $p$ in the inpainted patch, denoted as $\hat{\mathbf{C}}_p$ , with the corresponding rendered RGB value, denoted as $\hat{\mathbf{C}}_p$ , + +$$ +\mathcal {L} _ {\mathrm {p i x}} = \frac {1}{v ^ {2} \left| P _ {w _ {o}} \right|} \sum_ {p _ {\mathrm {r}} \in P _ {w _ {o}}} \left\| \hat {\mathbf {C}} _ {p} - \tilde {\mathbf {C}} _ {p} \right\| _ {1}. \tag {7} +$$ + +For patches in $P_{w_i}$ containing the inpainted region, we compute the perceptual similarity using LPIPS between the inpainted image patch $\tilde{P}_I$ and the corresponding patch $P$ on the rendered image. We denote $\mathbf{C}_P$ as the set of pixel values in patch $P$ , and define $\mathcal{L}_{\mathrm{in}}$ as the inpainting loss. + +$$ +\mathcal {L} _ {\text {i n}} = \frac {1}{\left| P _ {w _ {i}} \right|} \sum_ {P \in P _ {w _ {i}}} \operatorname {L P I P S} \left(\mathbf {C} _ {P}, \mathbf {C} _ {\tilde {P} _ {I}}\right). \tag {8} +$$ + +The inpainting loss measures the perceptual difference between the inpainted patch and the target inpainted image, while the pixel loss quantifies the pixel-level discrepancy between the inpainted and rendered RGB values. Together, + +these losses provide a comprehensive assessment of the reconstruction quality, accounting for both perceptual similarity and pixel-wise accuracy. + +Loss Functions. Our optimization is the weighted sum of the geometric prior $\mathcal{L}_{\mathrm{geom}}$ (Eq. (6)), pixel loss $\mathcal{L}_{\mathrm{pix}}$ (Eq. (7)), appearance prior $\mathcal{L}_{\mathrm{in}}$ (Eq. (8)) with $\lambda_{(\cdot)}$ as weight terms: + +$$ +\mathcal {L} = \lambda_ {\text {g e o m}} \cdot \mathcal {L} _ {\text {g e o m}} + \lambda_ {\text {i n}} \cdot \mathcal {L} _ {\text {i n}} + \mathcal {L} _ {\text {p i x}}. \tag {9} +$$ + +# 4. Experiments + +In this section, we evaluate InNeRF360 on various real-world captured datasets for text-guided inpainting. + +Datasets. We take 360-degree datasets from MipNeRF, MipNeRF-360, and NeRFStudio [1, 2, 39]. In addition, due to the absence of ground truth data for $360^{\circ}$ scene inpainting, we capture new datasets with and without the object removed for quantitative evaluation. Segmentation mask ground truth does not exist for the $360^{\circ}$ scenes we evaluate. We also compare with front-facing datasets from SPInNeRF [26] and IBRNet [41] to show that our method produces better inpainting over baseline methods. Details of the datasets we used are provided in Tab. 5. + +Baseline. We select baselines based on specific tasks. SPIn-NeRF SPN [26] is the closest work to ours. For segmentation, we compare with the multiview segmentation from SPN and a recent video segmentation method Dino [5]. For the inpainting task, we compare our inpainting quality with our implemented version of SPN that works with 360-degree scenes SPN-360. We also compare with per-frame image inpainting [36] to show that our method generates more consistent inpainting across different viewpoints. + +# 4.1. Segmentation Comparison + +We qualitatively compare our segmentation results to SPN and Dino. As input, we give the first frame segmentation to both SPN and Dino, and give the corresponding text instructions for InNeRF360. As we are evaluating the extrapolation ability of each segmentation method over drastically different viewpoints, we select the 82nd frame from vasedeck and the 81st image from room. They represent the respective frames of the videos created from the dataset. + +As shown in Fig. 5, Dino produces incomplete segmentation for unseen views in challenging scenes, such as the vasedeck featuring a transparent vase. In such cases, SPN struggles to generate complete segmentation when initialized with Dino's output. While we also initialize with a 2D segmentation model (SAM), it facilitates flexible, promptable input. This can be utilized by our depth-warping refinement to output point prompts specifically in the vase section of the image. These prompts guide SAM towards accurate segmentation, as elaborated in Sec. 3.2. For room, where only a part of the slippers is present in the image, Dino and SPN once again yield incomplete segmentations. + +![](images/177eec8b037b3d6bf7dfa5e8e9798941bf119d961a588d198d61aee6694b0e6a.jpg) +Figure 5. Qualitative comparison on 3D object segmentation. InNeRF360 outputs accurate masks for complex cases containing transparent (vase) or incomplete objects (partial slippers). + +InNeRF360 is able to output complete object segmentation. + +# 4.2. Inpainting Evaluation + +Results on 360-degree scenes. InNeRF360 can handle a wide range of scenarios for object inpainting in 3D scenes, as depicted in Fig. 7. We encourage the readers to view supplementary videos to inspect the quality of our results. + +InNeRF360 can remove large scene objects against complex backgrounds. In Bear, the background of the bear contains varying trees and branches, and the 2D inpainted images are therefore very noisy, as shown in Fig. 16. However, with our floater removal and appearance prior, InNeRF360 produces a clean stone surface in the final edited NeRF. + +Occlusion and geometry deformation across varying viewpoints are major causes of 3D inconsistency in inpainting, and the datasets we use contain both scenarios. In Room, the window, wall, and the piano behind the score can lead to inconsistency. However, we generate view-consistent content to seamlessly fill the missing region. + +Moreover, InNeRF360 is capable of inpainting multiple objects located anywhere in the 3D scenes without introducing blurry artifacts in the resulting NeRF scene. When given a text input containing multiple objects (Room: "slippers" and "piano sheet"; Bulldozer: multiple "cones"), In + +![](images/474e5c7f9ca27a8d76902e88fe6c87a41b442f5a47f4d7d304a02cdb394fa7b5.jpg) +Figure 6. Qualitative comparison with SPN-360. Text: Remove the vase and the flowers. InNeRF360 inpaints clean and visually plausible regions while better preserving surrounding scenes. + +
MethodsCupStarbucks
LPIPS ↓FID ↓LPIPS ↓FID ↓
Per-Frame0.6149201.700.5981260.93
SPN-3600.6421252.340.6278215.28
NeRFacto0.7328271.560.6832258.39
+Lin0.7137210.570.6658223.82
+Lgeom0.6197189.570.5795166.45
+Lin + Lgeom (Ours)0.5377159.760.4523153.46
+ +Table 1. Quantitative evaluation on the inpainting quality. Our method achieves better results than baseline methods and our ablated settings on captured datasets. + +NeRF360 produces inpainted regions that seamlessly blend with the surrounding context, yielding visually coherent and high-quality inpainting results. + +Fig. 6 shows qualitative comparison to SPN-360. Our method not only synthesizes a perceptually-consistent inpainted region, but also preserves the surrounding background closer to the input NeRF scene. We speculate the reason for the background-preserving inpainting to be that SPN inpaints on depth maps with segmentation masks generated from RGB images. We elaborate on our choice not to use 2D depth map inpainting in the supplementary. + +Ablation studies on our design choices. Our depth-warping method produces refined point-based prompts for the segmentation model, and outputs complete and consistent multi-view segmentation, as shown in Fig. 3. + +Fig. 8 qualitatively ablates our choice of loss functions. In Fig. 8a (ii), the vanilla NeRFacto model outputs a concentrated artifact in the inpainted region along with noisy texture in nearby regions which we suspect is due to per-image appearance encoding on inconsistent 2D inpainted images. Fig. 8a (iii) shows NeRFacto $+\mathcal{L}_{\mathrm{in}}$ which improves inpainted texture, but cannot reduce the floater artifact. These artifacts have view-dependent appearances from individual views and are therefore difficult to remove from appearance priors. In Fig. 8a (iv) for InNeRF360, we can see a clean and perceptually consistent surface in the edited + +Bear: "Remove the rectangular base and the bear" + +![](images/c11edfa7db3eee1c961efc332487d235521bb7c7266681de3c3b5fc82ff282ab.jpg) + +Room: "Remove the slippers and the piano sheet" + +![](images/c5142d98fca609dd79a258000a345ef243efd0e327f4ffb6e1a380cf5f63241b.jpg) + +Bulldozer: "Remove the traffic cones" + +![](images/d0adbfb57d12498920be67209be56231239bfafe81b208b6df72d33e4689a019.jpg) +Figure 7. Qualitative inpainting results on 360 scenes. Our method works with various types of NeRF scenes. We can also remove arbitrary numbers of objects given the text input, independent of the complexity of the scene content. + +scene. In Fig. 8b shows InNeRF360 versus trained without $\mathcal{L}_{\mathrm{in}}$ . We can see that the LPIPS loss can improve blurry background output due to inconsistent 2D inpainting. The lower part of Tab. 1 shows quantitative ablation on each loss term in InNeRF360. Our complete architecture performs better than without each of the loss terms. + +Inpainting quality. Due to the lack of baseline and ground truth datasets on inpainting $360^{\circ}$ NeRF scenes, we captured real-world datasets for quantitative comparison on the quality of inpainted renderings. Since InNeRF360 generates consistent and complete 3D segmentation over baseline + +
DatasetsGardenRoomVasedeckBulldozerBear
Ours89%71%81%83%92%
Per-frame11%29%19%17%8%
+ +Table 2. User study comparing with per-frame inpainting on visual consistency between consecutive frames. In each of the scenes, our inpainted NeRF renders higher view consistency than per-frame inpainting. Per-frame editing lacks a 3D understanding of each scene and inpaints each image independently. + +methods, the 2D inpainting initialization is naturally much less noisy than baseline methods. + +We evaluate our inpainting quality on each frame of the + +![](images/d8460739ca191d042da0b3a3a0e7ec0b76221f9ff94d3b5b9094f7610157113c.jpg) + +![](images/7f40c4a56b769c420fe6c973e6bb99ef2b999300cab758fd98454b67b55d74d1.jpg) + +![](images/c6ba1f5ee9feaa18906d8d8d8e6e350a9df288a100d3416c9b69ef2f0e6c28a6.jpg) + +![](images/4c13c8f63bbd54484870f5d510be225da9119b7e64b12d2380882db3df59cdc8.jpg) + +![](images/fdff20777458c473429485a71ea167f672bacb842f09b3ba3efbad433b880525.jpg) +(i) Input Scene + +![](images/fb9d9bad10bf3b6b4b0c5d3118e3f740e91c30df9d75322d482d5a7240f6efff.jpg) +(ii) NeRFacto + +![](images/f3a73ab995b8492b28d8982562d89fea9df526516e7b058e6a85c2608c568672.jpg) +(iii) $\mathsf{NeRFacto} + \mathcal{L}_{\mathrm{in}}$ + +![](images/f67ec7046e9736d1c9fd2e2cb4ff1231665893836843e432ec0ccb22fac512b8.jpg) +(iv) Ours +(a) Qualitative ablation for $\mathcal{L}_{\mathrm{geom}}$ on Bear and Garden. + +![](images/459c481ca201f8fe5dfccebfa2464e55e8ea84eeb7d355dae082568411423ec2.jpg) + +![](images/7df8a8c54b8e13cb5029a5a522698a991b90b12d7b9853deaedf392f43bdb3be.jpg) +(i) NeRFacto + geom +(b) Qualitative ablation for $\mathcal{L}_{\mathrm{in}}$ on Garden. + +![](images/993dd5008e90f9109d233d9f41f5be8bb99366548de069a7b52b3c0a265811a5.jpg) + +![](images/0e6efdbdd6a158d2dbafb798ab7168375729da15cb8b22754df5377ec8af0f4e.jpg) +(ii) Ours + +![](images/399b3524a9e995609b55edaf2d7fab6d7b12afb6374c75e6c7ae7bbe7161951e.jpg) +Figure 8. Ablation for losses on geometric and appearance priors. The artifact in the inpainted region is not as pronounced if viewed from aside as when viewed from the top. Our method is able to optimize an inpainted NeRF without artifacts and with a consistent and unblurry background. + +![](images/8eb80fb0200dfe7399b020085a87f2abf5b8972258c667b5bc7d8b8581e81e80.jpg) +"Turn the slippers into red slippers" + +![](images/93abbd958aa96824c36bd54a2fcbf244c0a45ccf1a3123cbd316221a277ffba1.jpg) + +![](images/948bcf51ed81dcce1559a85544110e63b1a55155907b03f848c7787ad58d6313.jpg) + +![](images/25a0ee44139e37692df62ce4f4f0f2f9123b5f6029e4fc676b0a07ee34bf83f2.jpg) +Figure 9. Editing comparison with In2n. InNeRF360, combined with appropriate mask-conditioned image editing models, can generate accurate editing on desired objects. In contrast, In2n gives the wrong texture to unwanted regions. + +![](images/9ef784bac4b137c9d1624592e95eb15e6f9e08e88fcaa4be74345c4c23f154f4.jpg) + +renderings with per-frame inpainting and SPN-360. We report LPIPS [44] and Frechet Inception Distance (FID) [11] metric in Tab. 1 by comparing with the output of the captured empty scene rendered under the same camera trajectory which we use as ground truth. Our method outperforms each baseline method and outputs visually consistent inpainting without visual artifacts. + +A quantitative baseline comparison to SPN on frontal scenes is also in the supplementary materials. + +3D consistency over per-frame inpainting. A naive approach for 3D scene inpainting is to independently inpaint every rendered image of the scene with a 2D image inpainter. In contrast, InNeRF360 produces inpaintings with higher view consistency across all viewpoints. + +We verify such a claim with a user study where partici + +pants were presented with two video clips of each inpainted scene, rendered with sequential camera trajectories. They were then asked to identify which clip appeared more consistent. Additional details about the user study can be found in the supplementary material. The results, presented in Tab. 2, clearly show that our rendered inpaintings exhibit superior temporal consistency compared to per-frame edits. + +# 4.3. Editing Accuracy + +As shown by Fig. 9, our segmentation module can be connected with a mask-conditioned image editor [8] to generate view-consistent editing with object-level control through text instructions, which InstructNeRF2NeRF (In2n) [9] cannot. However, note that editing is not the focus of our work. We show this result simply to demonstrate a possible extension to our method. Details are provided in the supplementary. + +# 5. Limitations and Conclusion + +Limitations. Our method inherits certain constraints of vision-language models. In scenarios where the text instruction cannot be accurately localized within the image, InNeRF360 may struggle in generating segmentation consistently aligned with the views. This issue arises when the initial masks provided by the 2D object detector are inaccurate or too noisy for effective refinement. Addressing this challenge is a focus of our future work. + +Conclusion. In conclusion, we have presented InNeRF360, a unified system to accurately segment and inpaint objects in $360^{\circ}$ NeRFs with text instructions. We synthesize perceptually consistent inpainting without artifacts and can extend to object-level stylization, improving the controllability of NeRF. + +Acknowledgement. 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Large scale image completion via co-modulated generative adversarial networks. arXiv preprint arXiv:2103.10428, 2021. 2 \ No newline at end of file diff --git a/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/images.zip b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6db839649b5b7c256e7ab340c3cf088b99daf1a1 --- /dev/null +++ b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6ca6ab471ad579c1400702fb1ada0fc00588f46df98e9437ba36764d8964780c +size 805868 diff --git a/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/layout.json b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..346dcf5968dcba2b3c3d0dfcaf182e1a0790e320 --- /dev/null +++ b/2024/InNeRF360_ Text-Guided 3D-Consistent Object Inpainting on 360-degree Neural Radiance Fields/layout.json @@ -0,0 +1,9764 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 115, + 103, + 479, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 103, + 479, + 138 + ], + "spans": [ + { + "bbox": [ + 115, + 103, + 479, + 138 + ], + "type": "text", + "content": "InNeRF360: Text-Guided 3D-Consistent Object Inpainting on " + }, + { + "bbox": [ + 115, + 103, + 479, + 138 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 115, + 103, + 479, + 138 + ], + "type": "text", + "content": " Neural Radiance Fields" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 131, + 161, + 462, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 161, + 462, + 203 + ], + "spans": [ + { + "bbox": [ + 131, + 161, + 462, + 203 + ], + "type": "text", + "content": "Dongqing Wang Tong Zhang* Alaa Abboud Sabine Süssstrunk \nSchool of Computer and Communication Sciences, EPFL Lausanne, Switzerland" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "spans": [ + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "type": "text", + "content": "We propose InNeRF360, an automatic system that accurately removes text-specified objects from " + }, + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "type": "text", + "content": " Neural Radiance Fields (NeRF). The challenge is to effectively remove objects while inpainting perceptually consistent content for the missing regions, which is particularly demanding for existing NeRF models due to their implicit volumetric representation. Moreover, unbounded scenes are more prone to floater artifacts in the inpainted region than frontal-facing scenes, as the change of object appearance and background across views is more sensitive to inaccurate segmentations and inconsistent inpainting. With a trained NeRF and a text description, our method efficiently removes specified objects and inpaints visually consistent content without artifacts. We apply depth-space warping to enforce consistency across multiview text-encoded segmentations, and then refine the inpainted NeRF model using perceptual priors and 3D diffusion-based geometric priors to ensure visual plausibility. Through extensive experiments in segmentation and inpainting on " + }, + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 45, + 256, + 290, + 518 + ], + "type": "text", + "content": " and frontal-facing NeRFs, we show that our approach is effective and enhances NeRF's editability. Project page: https://ivrl.github.io/InNeRF360/." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 533, + 128, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 128, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 128, + 544 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "content": "Recreating and manipulating real-world scenarios is one of the main focuses of Virtual and Augmented Reality (VR/AR) applications. Neural Radiance Field (NeRF) and its variants [2, 23, 28] can efficiently model " + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "content": " real-world scenes for photorealistic novel view synthesis. Consequently, they have the potential to become widely accessible tools for representing the 3D world." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": "A desired feature of such applications is the ability to modify the content of the created scene, including object removal. However, direct inpainting in the NeRF framework is intractable due to the implicit representation of the captured scenes encoded through the weights of multilayer" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 331, + 232, + 517, + 521 + ], + "blocks": [ + { + "bbox": [ + 331, + 232, + 517, + 521 + ], + "lines": [ + { + "bbox": [ + 331, + 232, + 517, + 521 + ], + "spans": [ + { + "bbox": [ + 331, + 232, + 517, + 521 + ], + "type": "image", + "image_path": "ccfbd38d35fe2c39e6ff871d1e1a66ec81f77255c876c82d660133b2331aa87d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 529, + 547, + 574 + ], + "lines": [ + { + "bbox": [ + 305, + 529, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 305, + 529, + 547, + 574 + ], + "type": "text", + "content": "Figure 1. Given a pre-trained NeRF and a text to remove specific objects (e.g. \"Remove the flowerpot and flowers\"), InNeRF360 produces accurate multiview object segmentations, and outputs an inpainted NeRF with visually consistent content." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 580, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 628 + ], + "type": "text", + "content": "perceptrons (MLP), which hinders explicit user control of scene contents. For explicit NeRF variants, the scene representation of radiance fields contains ambiguous surface that is hard to segment with a bounding region." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Existing works on selecting [35] or removing [18, 26, 43] objects in a trained NeRF tackle the 3D problem by utilizing 2D input. These methods begin with sparse user inputs, then use 2D image/video segmentation [7, 10] for multiview segmentation and inpaint on RGB-D sequence. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12677" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "ent viewpoints in " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": " scenes where the shape of the object can change drastically. Moreover, in the case of object occlusions on " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": " scenes, inpainting 2D depth maps is inadequate for geometric supervision as it leads to inconsistencies in scene geometry." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 287, + 287 + ], + "type": "text", + "content": "In contrast, InNeRF360 is an inpainting pipeline with a depth-guided segmentation method dedicated to accurate object-level editing on " + }, + { + "bbox": [ + 46, + 133, + 287, + 287 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 133, + 287, + 287 + ], + "type": "text", + "content": " scenes. Instead of extrapolating sparse 2D input to 3D, InNeRF360 encodes text input into a promptable segmentation model, Segment Anything Model (SAM) [15], leveraging its accurate semantic segmentation. Our method is driven by the intuition that an object's semantic identity is more consistent over different viewpoints than its geometry. However, text-based 2D semantic segmentations may not always maintain consistency across views. To overcome this, we refine object masks using inverse depth space warping in 3D space across viewpoints, utilizing the consistent 3D positioning of objects." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 287, + 467 + ], + "type": "text", + "content": "Using view-consistent masks, we train a NeRF from scratch on the multiview inpainting from a 2D image inpainter [36]. The multiview training images slightly differ in the inpainted regions, accumulating into cloudy artifacts, i.e. floaters [42], in the new NeRF. To eliminate floaters, we finetune the scene guided by 3D diffusion priors trained on extensive geometric shapes [6] to determine whether density should be removed or incremented in a local voxel. The texture for the removed region is optimized by contextual appearance priors [45] from the surrounding regions of the segmentation. This creates a perceptually consistent 3D inpainted region that seamlessly blends into the scene. Extensive experiments show that InNeRF360 can effectively inpaint both " + }, + { + "bbox": [ + 46, + 288, + 287, + 467 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 288, + 287, + 467 + ], + "type": "text", + "content": " [2] and front-facing [22] real-world scenes, with the potential to be extended into 3D editing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 467, + 252, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 467, + 252, + 478 + ], + "spans": [ + { + "bbox": [ + 59, + 467, + 252, + 478 + ], + "type": "text", + "content": "To summarize, our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 479, + 286, + 574 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 53, + 479, + 286, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 479, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 53, + 479, + 286, + 514 + ], + "type": "text", + "content": "- InNeRF360 is the first work to achieve text-guided object inpainting in " + }, + { + "bbox": [ + 53, + 479, + 286, + 514 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 53, + 479, + 286, + 514 + ], + "type": "text", + "content": " NeRF scenes, ensuring visually consistent inpainted regions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 515, + 286, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 515, + 286, + 550 + ], + "spans": [ + { + "bbox": [ + 53, + 515, + 286, + 550 + ], + "type": "text", + "content": "- Our approach efficiently generates multiview consistent 2D segmentation for 3D object inpainting through depth-warping refinement on initialized masks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 552, + 286, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 552, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 53, + 552, + 286, + 574 + ], + "type": "text", + "content": "- We incorporate a 3D diffusion network as local geometric priors to remove artifacts in the inpainted region." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 586, + 138, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 138, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 138, + 597 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Image Inpainting. Recent advancements in image inpainting focus on filling in masked regions to create visually consistent images. This primarily involves generative models like Generative Adversarial Networks (GANs) [13, 31, 46] and denoising diffusion models (DDPMs) [29, 36, 37]. These models generate photorealistic predictions for the missing pixels. However, when applied to inpainting multiview renderings of 3D scenes [25, 26], they often generate different inpainted regions for nearby views. This is due to" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "their lack of 3D understanding, presenting a challenge for inpainting 2D observations of 3D scenes. InNeRF360 leverages image inpainting to address inpainting " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " scenes, ensuring view consistency across viewpoints." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 122, + 545, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 122, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 304, + 122, + 545, + 206 + ], + "type": "text", + "content": "Inpainting Neural Radiance Fields. Using neural radiance fields [23] to represent 3D scenes has achieved high-quality, photo-realistic novel view synthesis. NeRF Facto [39] is an architecture designed to optimize NeRF's performance on real-world data. It incorporates various recent advances in NeRF, including hash encoding [28] and per-image appearance encoding [19], among others." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "text", + "content": "However, object removal presents a challenge in NeRF due to the implicit scene representation by the underlying neural networks. Previous works [24, 40] utilize the supervision of Contrastive Text-Image Pre-Training (CLIP) [34]. They focus on inpainting a single object and cannot generalize to real-world scenes. Methods utilizing depth-based approaches [18, 25, 26, 43] remove objects with user-drawn masks and depth sequences, and inpaint missing regions naively with 2D image inpainter on the training images of NeRF. These approaches are limited to front-facing scenes for two reasons. First, their segmentation relies on the quality of initialize masks by supervised video object segmentation methods [4, 5, 7, 30], which struggle on temporal consistency across frames for challenging cases such as transparent objects. These methods cannot output accurate object masks in " + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "text", + "content": " scenes, where object shapes change drastically across views. Secondly, the chosen 2D inpainting methods output different inpainting across views. Such inconsistency results in floaters in the trained NeRF, and is much more pronounced on " + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "text", + "content": " scenes than on frontal-facing ones. In contrast, InNeRF360 enhances the consistency of multiview segmentation by utilizing semantical identity and object 3D location consistency, thereby producing accurate masks for desired objects. Moreover, InNeRF360 is designed for " + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 209, + 545, + 532 + ], + "type": "text", + "content": " NeRF inpainting by removing floaters (Fig. 4) from the inpainted NeRF with geometric priors, and inpaint with contextual perception guidance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Text-Guided 3D Editing. Given the popularity of text-conditioned image generative models, many works focus on generating 3D content with text instructions. Some rely on joint embeddings of CLIP to synthesize 3D meshes [21, 27] or neural radiance fields [14, 16]. Others distill a pretrained diffusion model to optimize NeRF scenes in the latent space [20, 33]. These methods all suffer from having to map the inconsistent 2D diffusion model outputs to a 3D-consistent scene. Instruct-NeRF2NeRF [9] edits renderings of a pre-trained NeRF model to preserve 3D consistency. However, it cannot remove scene objects or perform object-level editing as it operates in latent space for image editing. Our InNeRF360 operates in image space to accurately pinpoint and crop objects and allows removing an arbitrary number of objects from the scene through text instructions," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12678" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 72, + 521, + 286 + ], + "blocks": [ + { + "bbox": [ + 74, + 72, + 521, + 286 + ], + "lines": [ + { + "bbox": [ + 74, + 72, + 521, + 286 + ], + "spans": [ + { + "bbox": [ + 74, + 72, + 521, + 286 + ], + "type": "image", + "image_path": "42e47cee7871c6e45f62ccd4d590f62ffbe1a198ee524191d079600f3b94824b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 292, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 547, + 348 + ], + "type": "text", + "content": "Figure 2. Overview of InNeRF360 framework. 1. Multiview Consistent Segmentation. We initialize masks using bounding boxes from the object detector, which encodes both the source image and text. With rendered depth from the input NeRF, we apply depth-warping prompt refinement to iteratively update points for the Segment Anything Model (SAM) to output view-consistent 2D segmentations. 2. Inpainting " + }, + { + "bbox": [ + 46, + 292, + 547, + 348 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 292, + 547, + 348 + ], + "type": "text", + "content": " NeRF. We obtain edited images through image inpainter with the masks and source images to retrain the inpainted NeRF. We then finetune the new NeRF model using a geometric prior trained from a 3D diffusion model and a masked perceptual prior." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 357, + 288, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 288, + 380 + ], + "type": "text", + "content": "while using 3D diffusion priors for local geometry finetuning to avoid the global inconsistency prior works exhibit." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 384, + 104, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 104, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 104, + 396 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "content": "InNeRF360 takes as input a trained NeRF with source images which the model trained on, and an instructive text. It outputs the inpainted 3D scene with the desired object(s) removed and filled with a visually consistent background without artifacts. Our pipeline is shown in Fig. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 472, + 245, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 245, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 245, + 483 + ], + "type": "text", + "content": "3.1. Background: Neural Radiance Fields" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": "A Neural Radiance Field (NeRF) encodes a 3D scene as a function " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " parametrized by an MLP with learnable parameters " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": ", which maps a 3D viewing position " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " and its 2D direction " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " to the density " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " and a viewing-dependent color " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "f_{\\theta}:(\\mathbf{x},\\mathbf{d})\\to (\\sigma ,\\mathbf{c})" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": ". Rendering a NeRF from a posed camera is done by sampling batches of rays for the camera pose, and rendering corresponding pixel colors for each ray. For each ray " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{r} = (\\mathbf{o},\\mathbf{d})" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": ", we sample an array of 3D points " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i,t_i)" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "i = 1,2,\\dots ,K" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i\\in \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " is the depth. We query the MLP with these points along the ray for " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\{\\sigma_i\\}_{i = 1}^K" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{c}_i\\}_{i = 1}^K" + }, + { + "bbox": [ + 46, + 490, + 287, + 622 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "content": "The estimated RGB of ray " + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}} (\\mathbf{r})" + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "content": " is obtained by alpha compositing [23] the densities and colors along the ray:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 124, + 649, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 649, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 124, + 649, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {C}} (\\mathbf {r}) = \\sum_ {i = 1} ^ {K} \\alpha_ {i} T _ {i} \\mathbf {c} _ {i}, \\tag {1}", + "image_path": "d9f59428b139804de0035bdffb1bc0e3bbfb98077159b67d04a6bf0c9bfdb1c7.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "T_{i} = 1 - \\exp (-\\sigma_{i}\\| t_{i} - t_{i - 1}\\|)" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " is the ray transmittance between " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i + 1}" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{i} = \\prod_{j = 1}^{i - 1}T_{i}" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " is the attenuation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "type": "text", + "content": "uation from ray origin to " + }, + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "type": "text", + "content": ". The MLP is optimized through pixel loss for the distance between the estimated pixel value and the ground truth color." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 402, + 495, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 402, + 495, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 402, + 495, + 415 + ], + "type": "text", + "content": "3.2. Multiview Consistent Segmentation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "type": "text", + "content": "The first stage is to obtain refined multiview segmentation masks for the objects to remove/edit given by the text input. We take as input a pre-trained NeRF model and " + }, + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "type": "text", + "content": " source images given by the set of " + }, + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 422, + 545, + 470 + ], + "type": "text", + "content": " source camera poses." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": "We initialize segmentations through the Segment-Anything Model (SAM) [15] with the bounding boxes given by Grounded Language-Image Pre-training (GLIP) from a large-scale dataset of image-text pairs [17]. GLIP: " + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathbf{I},\\mathbf{s}) = \\{(B_q,p_q)\\}_{q = 1}^Q" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": " takes in an RGB image " + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{I}\\in" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times 3}" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": " and a text s, and encodes each through respective image and language encoders. " + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": " is the number of bounding boxes. We then take these bounding boxes " + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\{B_q\\}_{q = 1}^Q" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": " from the model output in which " + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "B_{q} = (l_{q},r_{q},u_{q},d_{q})\\in \\mathbb{R}^{4}" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": " with corresponding probability " + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "inline_equation", + "content": "p_q" + }, + { + "bbox": [ + 304, + 471, + 546, + 628 + ], + "type": "text", + "content": ". These boxes are sometimes inaccurate and fail to enclose the desired region, see Fig. 3 (b). Hence, we propose our depth-based prompt refinement for consistent segmentation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Depth-Warping Prompt Refinement. \"Depth Warp\" operates on the sampled points to enhance segmentation accuracy. It leverages the depth information inherited from the input NeRF and projects these points back into the pixel space to align them with other 2D observations within the scene. We thereby establish a cohesive depth constraint across different views. The depth for a sampled ray" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12679" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{r} = \\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " with origin " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " and direction " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " in a trained NeRF scene can be estimated via a modification of Eq. (1):" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 122, + 99, + 287, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 99, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 122, + 99, + 287, + 131 + ], + "type": "interline_equation", + "content": "D (\\mathbf {r}) = \\sum_ {i = 1} ^ {I} \\alpha_ {i} T _ {i} \\cdot t _ {i}, \\tag {2}", + "image_path": "c4122b0eca157bce1b3722b3e4ae8a8533bdfc517588cec2e81e9ea160497135.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "text", + "content": "For each training view, we randomly select " + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "text", + "content": " other training views. From each selected view, we sample a fixed number " + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "text", + "content": " of rays that correspond to pixels within the mask region. Given a ray " + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 139, + 288, + 307 + ], + "type": "text", + "content": " and its estimated depth from Eq. (2), we compute the 3D location of the selected point prompt. This information is then mapped back to the current training view. Rays and their corresponding point prompts whose depth is above a certain threshold are discarded, as they may represent background objects misclassified as foreground sections to be removed. If the corresponding pixel on the current view falls outside the masked region in the current view, we add this point prompt to the current view. Subsequently, we pass this view with the new sets of point prompts to SAM for refined segmentation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": "By generating these \"out-of-the-box\" point-based prompts for the segmentation model with our NeRF-based depth prior, we ensure that the object is accurately segmented even in cases where the initial bounding box information is insufficient or incomplete from certain viewpoints. This approach greatly increases the segmentation masks' accuracy for desired objects in the scene, see Fig. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 118, + 397, + 212, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 397, + 212, + 405 + ], + "spans": [ + { + "bbox": [ + 118, + 397, + 212, + 405 + ], + "type": "text", + "content": "\"Remove the flowerpot and flowers" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 59, + 405, + 274, + 513 + ], + "blocks": [ + { + "bbox": [ + 59, + 405, + 274, + 513 + ], + "lines": [ + { + "bbox": [ + 59, + 405, + 274, + 513 + ], + "spans": [ + { + "bbox": [ + 59, + 405, + 274, + 513 + ], + "type": "image", + "image_path": "0890ac0dcae3a2d681f296d511d13e9c6f2fb82d03d2908b8a2a0bc901d38347.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 514, + 287, + 568 + ], + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 568 + ], + "type": "text", + "content": "Figure 3. Inconsistent bounding box across different views. (a) and (b) are from the same dataset under the same instruction. However, the generated bounding boxes are different. After applying depth warping refinement (point prompts as red dots), (c) generates accurate segmentation." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": "Promptable Segmentation After obtaining the refined point-based prompts, we employ SAM to identify and segment all the rendered observations " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": " for refined masks " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{M}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": ". Specifically, SAM takes as input an image " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": " and a prompt in the form of " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": " points pinpointing the object " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "o_q" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": ", and produces an accurate segmentation mask " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\mathbf{q}}" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": " of the same size as " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_q = \\mathrm{SAM}(\\mathbf{I}, o_q)" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": ". For each image " + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i \\in \\{\\mathbf{I}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 571, + 288, + 679 + ], + "type": "text", + "content": ", we get a union binary mask for all the objects to be removed:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 134, + 681, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 681, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 134, + 681, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {i} = \\bigcup_ {q = 1} ^ {Q} \\mathbf {M} _ {q}. \\tag {3}", + "image_path": "67581577370c4a91dd7accf9578b715b1b550173492833895cf5bd61789dc8f6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "text", + "content": "3.3. Inpainting " + }, + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "text", + "content": " NeRF" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "type": "text", + "content": "Inpainted NeRF Initialization. With the rendered observations " + }, + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "type": "text", + "content": " and corresponding masks " + }, + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{M}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 304, + 90, + 547, + 247 + ], + "type": "text", + "content": ", we adopt a 2D image inpainter [36] to edit each observation as priors for the optimization. We then initialize the inpainted scene with Nerfacto [39]. This architecture is designed to optimize the performance of NeRF on real-world image captures. However, each inpainted image has varying pixel-level content despite being perceptually plausible as a standalone image. Therefore, relying solely on RGB supervision leads to floaters in the NeRF (Fig. 4). To produce clean and perceptually consistent inpainting, we fine-tune the initialized NeRF with both geometry and appearance priors." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 255, + 425, + 357 + ], + "blocks": [ + { + "bbox": [ + 307, + 255, + 425, + 357 + ], + "lines": [ + { + "bbox": [ + 307, + 255, + 425, + 357 + ], + "spans": [ + { + "bbox": [ + 307, + 255, + 425, + 357 + ], + "type": "image", + "image_path": "7c539969ec57785174ca153f2af15c03310e8fe5264032a32aef2bad00e7349a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 363, + 546, + 397 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 546, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 546, + 397 + ], + "type": "text", + "content": "Figure 4. Examples of artifacts in the initialized NeRF. 2D inpaintings contain inconsistent inpainted pixels that accumulate in the 3D inpainted region and appear as floater artifacts." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 255, + 545, + 357 + ], + "blocks": [ + { + "bbox": [ + 427, + 255, + 545, + 357 + ], + "lines": [ + { + "bbox": [ + 427, + 255, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 427, + 255, + 545, + 357 + ], + "type": "image", + "image_path": "94497a9b364bb2f7ab2d288925baa0612cd2400156e2a430f2ebbf890dfd6ce3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": "Hallucinating Density Removal. The density artifacts produced through inconsistent 2D inpainting can be seen as floaters. We train a denoising diffusion probabilistic model (DDPM) [12] on ShapeNet [6] to iteratively denoise a " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "m^3" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " resolution voxel grid of discretized binary occupancy " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " as a local 3D geometry prior: given a NeRF density " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "x_{t} = 1" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\sigma > \\rho" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " else " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "x_{t} = -1" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " is a chosen threshold for whether a voxel is empty. For training, from each ShapeNet mesh we randomly select " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " cubes that encompass " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " of the object bounding volume, and voxelize them to " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "m^3" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " resolution. The loss function for the diffusion model is given by the MSE loss between the true noise " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " and the predicted noise " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 403, + 545, + 568 + ], + "type": "text", + "content": " parameterizes the diffusion model U-Net:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 569, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 569, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 312, + 569, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {d d p m}} (\\theta) = \\mathbb {E} _ {t, x _ {0}, \\sigma} [ \\| \\epsilon - \\epsilon_ {\\theta} (\\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , t) \\| _ {2} ^ {2} ], \\tag {4}", + "image_path": "268747e443e491ec3000324c6262cd9b902b66f93ab1bee187346c482d29eeb9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "t \\in [1, 1000]" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " is the number of timesteps in the nois-ing diffusion process, and " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t = \\prod_{s=1}^t \\alpha_s" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\alpha_t" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " is a function of the timestep " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " that parameterized transitions from " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "x_{1000}" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " (i.e. a noise schedule)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "type": "text", + "content": "The Density Score Distillation Sampling (DSDS) [42] loss is defined to penalize regions with density " + }, + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "type": "inline_equation", + "content": "\\sigma >\\rho" + }, + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "type": "text", + "content": " that the trained diffusion model deems as empty, and regions that are empty where " + }, + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "type": "inline_equation", + "content": "x_{t} = 1" + }, + { + "bbox": [ + 304, + 643, + 545, + 691 + ], + "type": "text", + "content": " predicted by the model:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 329, + 692, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 692, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 329, + 692, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {D S D S}} = \\sum_ {i} u _ {i} \\sigma_ {i} + (1 - u _ {i}) \\max (w - \\sigma_ {i}, 0), \\tag {5}", + "image_path": "55e20595f90af784d1e2bbfda12ae997c21036805eb0dfaf330e4266195801f9.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12680" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "u = \\mathbb{1}\\{x_0 < 0\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " is a chosen upper limit for density " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " in occupied voxels." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 216 + ], + "type": "text", + "content": "The original sampling of the DSDS loss is by sampling a low-resolution density grid stored through ray bundles. During training, the grid selects the center of 3D cubes to be voxelized and enter the diffusion process. The grid gets updated by a visibility field determining what it sees in the NeRF scene. Our aim is to focus on removing floaters within the inpainted region. Therefore, we apply the refined segmentation mask from the image space to limit the visibility field to only look at the inpainted regions, and eliminate sampled rays corresponding to pixels outside the mask:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 217, + 287, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 217, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 52, + 217, + 287, + 243 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g e o m}} = \\sum_ {j} \\left(u _ {j} \\sigma_ {j} + (1 - u _ {j}) \\max (w - \\sigma_ {j}, 0)\\right) \\cdot V _ {j}, \\tag {6}", + "image_path": "8d853dbbccaa4dfc9d42a7e40121ed7e320ca0d56418ae2a8fff4f3f6f55acd4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "content": " is an indicator function whose value is 1 for each voxel cube whose center is located within the current \"visible region\" given by the segmentation masks. Consequently, we sample cubes near the inpainted region. The geometric prior trained on extensive shapes in [6] preserves the original surface (e.g., the table supporting the removed flowerpot) while penalizing the floaters in the inpainted region created through inconsistent 2D inpainting." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 415 + ], + "type": "text", + "content": "Perceptually-Consistent Appearance Inpainting. The above method removes floaters created by inconsistent 2D inpainting, however, it does not produce visually consistent textures to fill in the removed region. Therefore, we utilize a patch-based loss [45] as an appearance prior to enhancing the model's robustness and alleviate blurring effects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": "Specifically, we sample all the pixels from the input inpainted images to get " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": " image patches " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\{P_w\\}_{w=1}^W" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": " with the size of " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "v^2" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": ". These patches, " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\{P_w\\}_{w=1}^W" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": ", can be divided into two non-overlapping groups of patches " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "P_{w_i}" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "P_{w_o}" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": " depending on whether a patch contains pixels within the inpainted region. For patches in " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "P_{w_o}" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": ", we apply pixel-wise L1. This pixel loss is obtained by comparing the RGB values of each pixel " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": " in the inpainted patch, denoted as " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_p" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": ", with the corresponding rendered RGB value, denoted as " + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_p" + }, + { + "bbox": [ + 46, + 415, + 287, + 525 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 88, + 525, + 287, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 525, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 88, + 525, + 287, + 555 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p i x}} = \\frac {1}{v ^ {2} \\left| P _ {w _ {o}} \\right|} \\sum_ {p _ {\\mathrm {r}} \\in P _ {w _ {o}}} \\left\\| \\hat {\\mathbf {C}} _ {p} - \\tilde {\\mathbf {C}} _ {p} \\right\\| _ {1}. \\tag {7}", + "image_path": "832a037bae105adb887744e51068a2d627ac5fd996e5199f9ac611fa8f595dfc.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": "For patches in " + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "inline_equation", + "content": "P_{w_i}" + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": " containing the inpainted region, we compute the perceptual similarity using LPIPS between the inpainted image patch " + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\tilde{P}_I" + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": " and the corresponding patch " + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": " on the rendered image. We denote " + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_P" + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": " as the set of pixel values in patch " + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": ", and define " + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 565, + 287, + 624 + ], + "type": "text", + "content": " as the inpainting loss." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 89, + 625, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 625, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 89, + 625, + 287, + 654 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n}} = \\frac {1}{\\left| P _ {w _ {i}} \\right|} \\sum_ {P \\in P _ {w _ {i}}} \\operatorname {L P I P S} \\left(\\mathbf {C} _ {P}, \\mathbf {C} _ {\\tilde {P} _ {I}}\\right). \\tag {8}", + "image_path": "da2c55044124209fc158a602d196bb21fb0c4d0736c28a4401576b2838da8d2a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "The inpainting loss measures the perceptual difference between the inpainted patch and the target inpainted image, while the pixel loss quantifies the pixel-level discrepancy between the inpainted and rendered RGB values. Together," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "these losses provide a comprehensive assessment of the reconstruction quality, accounting for both perceptual similarity and pixel-wise accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "text", + "content": "Loss Functions. Our optimization is the weighted sum of the geometric prior " + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{geom}}" + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "text", + "content": " (Eq. (6)), pixel loss " + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pix}}" + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "text", + "content": " (Eq. (7)), appearance prior " + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "text", + "content": " (Eq. (8)) with " + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\lambda_{(\\cdot)}" + }, + { + "bbox": [ + 304, + 109, + 545, + 145 + ], + "type": "text", + "content": " as weight terms:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 350, + 149, + 545, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 149, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 350, + 149, + 545, + 163 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {\\text {g e o m}} \\cdot \\mathcal {L} _ {\\text {g e o m}} + \\lambda_ {\\text {i n}} \\cdot \\mathcal {L} _ {\\text {i n}} + \\mathcal {L} _ {\\text {p i x}}. \\tag {9}", + "image_path": "08c59f9e8eab3f52a7f3bd9643afe2f346efec75f4edd05ab9fd4bbc227232a5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 174, + 387, + 187 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 174, + 387, + 187 + ], + "spans": [ + { + "bbox": [ + 306, + 174, + 387, + 187 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 194, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 217 + ], + "type": "text", + "content": "In this section, we evaluate InNeRF360 on various real-world captured datasets for text-guided inpainting." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "type": "text", + "content": "Datasets. We take 360-degree datasets from MipNeRF, MipNeRF-360, and NeRFStudio [1, 2, 39]. In addition, due to the absence of ground truth data for " + }, + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "type": "text", + "content": " scene inpainting, we capture new datasets with and without the object removed for quantitative evaluation. Segmentation mask ground truth does not exist for the " + }, + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 218, + 545, + 338 + ], + "type": "text", + "content": " scenes we evaluate. We also compare with front-facing datasets from SPInNeRF [26] and IBRNet [41] to show that our method produces better inpainting over baseline methods. Details of the datasets we used are provided in Tab. 5." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 338, + 545, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 446 + ], + "type": "text", + "content": "Baseline. We select baselines based on specific tasks. SPIn-NeRF SPN [26] is the closest work to ours. For segmentation, we compare with the multiview segmentation from SPN and a recent video segmentation method Dino [5]. For the inpainting task, we compare our inpainting quality with our implemented version of SPN that works with 360-degree scenes SPN-360. We also compare with per-frame image inpainting [36] to show that our method generates more consistent inpainting across different viewpoints." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 455, + 453, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 453, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 453, + 468 + ], + "type": "text", + "content": "4.1. Segmentation Comparison" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 474, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 568 + ], + "type": "text", + "content": "We qualitatively compare our segmentation results to SPN and Dino. As input, we give the first frame segmentation to both SPN and Dino, and give the corresponding text instructions for InNeRF360. As we are evaluating the extrapolation ability of each segmentation method over drastically different viewpoints, we select the 82nd frame from vasedeck and the 81st image from room. They represent the respective frames of the videos created from the dataset." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "As shown in Fig. 5, Dino produces incomplete segmentation for unseen views in challenging scenes, such as the vasedeck featuring a transparent vase. In such cases, SPN struggles to generate complete segmentation when initialized with Dino's output. While we also initialize with a 2D segmentation model (SAM), it facilitates flexible, promptable input. This can be utilized by our depth-warping refinement to output point prompts specifically in the vase section of the image. These prompts guide SAM towards accurate segmentation, as elaborated in Sec. 3.2. For room, where only a part of the slippers is present in the image, Dino and SPN once again yield incomplete segmentations." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12681" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 71, + 273, + 372 + ], + "blocks": [ + { + "bbox": [ + 62, + 71, + 273, + 372 + ], + "lines": [ + { + "bbox": [ + 62, + 71, + 273, + 372 + ], + "spans": [ + { + "bbox": [ + 62, + 71, + 273, + 372 + ], + "type": "image", + "image_path": "177eec8b037b3d6bf7dfa5e8e9798941bf119d961a588d198d61aee6694b0e6a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 373, + 286, + 407 + ], + "lines": [ + { + "bbox": [ + 47, + 373, + 286, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 286, + 407 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison on 3D object segmentation. InNeRF360 outputs accurate masks for complex cases containing transparent (vase) or incomplete objects (partial slippers)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 418, + 286, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 286, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 286, + 431 + ], + "type": "text", + "content": "InNeRF360 is able to output complete object segmentation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 173, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 173, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 173, + 453 + ], + "type": "text", + "content": "4.2. Inpainting Evaluation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 460, + 286, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 286, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 286, + 508 + ], + "type": "text", + "content": "Results on 360-degree scenes. InNeRF360 can handle a wide range of scenarios for object inpainting in 3D scenes, as depicted in Fig. 7. We encourage the readers to view supplementary videos to inspect the quality of our results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 286, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 286, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 286, + 579 + ], + "type": "text", + "content": "InNeRF360 can remove large scene objects against complex backgrounds. In Bear, the background of the bear contains varying trees and branches, and the 2D inpainted images are therefore very noisy, as shown in Fig. 16. However, with our floater removal and appearance prior, InNeRF360 produces a clean stone surface in the final edited NeRF." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 582, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 286, + 652 + ], + "type": "text", + "content": "Occlusion and geometry deformation across varying viewpoints are major causes of 3D inconsistency in inpainting, and the datasets we use contain both scenarios. In Room, the window, wall, and the piano behind the score can lead to inconsistency. However, we generate view-consistent content to seamlessly fill the missing region." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 286, + 713 + ], + "type": "text", + "content": "Moreover, InNeRF360 is capable of inpainting multiple objects located anywhere in the 3D scenes without introducing blurry artifacts in the resulting NeRF scene. When given a text input containing multiple objects (Room: \"slippers\" and \"piano sheet\"; Bulldozer: multiple \"cones\"), In" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 531, + 222 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 531, + 222 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 531, + 222 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 531, + 222 + ], + "type": "image", + "image_path": "474e5c7f9ca27a8d76902e88fe6c87a41b442f5a47f4d7d304a02cdb394fa7b5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 225, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 306, + 225, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 306, + 225, + 545, + 258 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison with SPN-360. Text: Remove the vase and the flowers. InNeRF360 inpaints clean and visually plausible regions while better preserving surrounding scenes." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 261, + 538, + 361 + ], + "blocks": [ + { + "bbox": [ + 308, + 261, + 538, + 361 + ], + "lines": [ + { + "bbox": [ + 308, + 261, + 538, + 361 + ], + "spans": [ + { + "bbox": [ + 308, + 261, + 538, + 361 + ], + "type": "table", + "html": "
MethodsCupStarbucks
LPIPS ↓FID ↓LPIPS ↓FID ↓
Per-Frame0.6149201.700.5981260.93
SPN-3600.6421252.340.6278215.28
NeRFacto0.7328271.560.6832258.39
+Lin0.7137210.570.6658223.82
+Lgeom0.6197189.570.5795166.45
+Lin + Lgeom (Ours)0.5377159.760.4523153.46
", + "image_path": "49e472fc98b766f0eb9eb6e02e82ef6ba5da600b70507be78e8488294880583f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 361, + 545, + 395 + ], + "lines": [ + { + "bbox": [ + 306, + 361, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 545, + 395 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation on the inpainting quality. Our method achieves better results than baseline methods and our ablated settings on captured datasets." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 402, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 402, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 402, + 545, + 438 + ], + "type": "text", + "content": "NeRF360 produces inpainted regions that seamlessly blend with the surrounding context, yielding visually coherent and high-quality inpainting results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 438, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 545, + 533 + ], + "type": "text", + "content": "Fig. 6 shows qualitative comparison to SPN-360. Our method not only synthesizes a perceptually-consistent inpainted region, but also preserves the surrounding background closer to the input NeRF scene. We speculate the reason for the background-preserving inpainting to be that SPN inpaints on depth maps with segmentation masks generated from RGB images. We elaborate on our choice not to use 2D depth map inpainting in the supplementary." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 534, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 545, + 582 + ], + "type": "text", + "content": "Ablation studies on our design choices. Our depth-warping method produces refined point-based prompts for the segmentation model, and outputs complete and consistent multi-view segmentation, as shown in Fig. 3." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 545, + 713 + ], + "type": "text", + "content": "Fig. 8 qualitatively ablates our choice of loss functions. In Fig. 8a (ii), the vanilla NeRFacto model outputs a concentrated artifact in the inpainted region along with noisy texture in nearby regions which we suspect is due to per-image appearance encoding on inconsistent 2D inpainted images. Fig. 8a (iii) shows NeRFacto " + }, + { + "bbox": [ + 306, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "+\\mathcal{L}_{\\mathrm{in}}" + }, + { + "bbox": [ + 306, + 582, + 545, + 713 + ], + "type": "text", + "content": " which improves inpainted texture, but cannot reduce the floater artifact. These artifacts have view-dependent appearances from individual views and are therefore difficult to remove from appearance priors. In Fig. 8a (iv) for InNeRF360, we can see a clean and perceptually consistent surface in the edited" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12682" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 215, + 73, + 392, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 215, + 73, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 215, + 73, + 392, + 84 + ], + "type": "text", + "content": "Bear: \"Remove the rectangular base and the bear\"" + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 77, + 85, + 520, + 223 + ], + "blocks": [ + { + "bbox": [ + 77, + 85, + 520, + 223 + ], + "lines": [ + { + "bbox": [ + 77, + 85, + 520, + 223 + ], + "spans": [ + { + "bbox": [ + 77, + 85, + 520, + 223 + ], + "type": "image", + "image_path": "c11edfa7db3eee1c961efc332487d235521bb7c7266681de3c3b5fc82ff282ab.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 214, + 227, + 389, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 214, + 227, + 389, + 239 + ], + "spans": [ + { + "bbox": [ + 214, + 227, + 389, + 239 + ], + "type": "text", + "content": "Room: \"Remove the slippers and the piano sheet\"" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 76, + 240, + 520, + 378 + ], + "blocks": [ + { + "bbox": [ + 76, + 240, + 520, + 378 + ], + "lines": [ + { + "bbox": [ + 76, + 240, + 520, + 378 + ], + "spans": [ + { + "bbox": [ + 76, + 240, + 520, + 378 + ], + "type": "image", + "image_path": "c5142d98fca609dd79a258000a345ef243efd0e327f4ffb6e1a380cf5f63241b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 247, + 384, + 382, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 247, + 384, + 382, + 394 + ], + "spans": [ + { + "bbox": [ + 247, + 384, + 382, + 394 + ], + "type": "text", + "content": "Bulldozer: \"Remove the traffic cones\"" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 77, + 395, + 520, + 532 + ], + "blocks": [ + { + "bbox": [ + 77, + 395, + 520, + 532 + ], + "lines": [ + { + "bbox": [ + 77, + 395, + 520, + 532 + ], + "spans": [ + { + "bbox": [ + 77, + 395, + 520, + 532 + ], + "type": "image", + "image_path": "d0adbfb57d12498920be67209be56231239bfafe81b208b6df72d33e4689a019.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 540, + 547, + 563 + ], + "lines": [ + { + "bbox": [ + 46, + 540, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 547, + 563 + ], + "type": "text", + "content": "Figure 7. Qualitative inpainting results on 360 scenes. Our method works with various types of NeRF scenes. We can also remove arbitrary numbers of objects given the text input, independent of the complexity of the scene content." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "type": "text", + "content": "scene. In Fig. 8b shows InNeRF360 versus trained without " + }, + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "type": "text", + "content": ". We can see that the LPIPS loss can improve blurry background output due to inconsistent 2D inpainting. The lower part of Tab. 1 shows quantitative ablation on each loss term in InNeRF360. Our complete architecture performs better than without each of the loss terms." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Inpainting quality. Due to the lack of baseline and ground truth datasets on inpainting " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " NeRF scenes, we captured real-world datasets for quantitative comparison on the quality of inpainted renderings. Since InNeRF360 generates consistent and complete 3D segmentation over baseline" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 312, + 574, + 538, + 614 + ], + "blocks": [ + { + "bbox": [ + 312, + 574, + 538, + 614 + ], + "lines": [ + { + "bbox": [ + 312, + 574, + 538, + 614 + ], + "spans": [ + { + "bbox": [ + 312, + 574, + 538, + 614 + ], + "type": "table", + "html": "
DatasetsGardenRoomVasedeckBulldozerBear
Ours89%71%81%83%92%
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Per-frame editing lacks a 3D understanding of each scene and inpaints each image independently." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 676, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 676, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 305, + 676, + 545, + 700 + ], + "type": "text", + "content": "methods, the 2D inpainting initialization is naturally much less noisy than baseline methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "We evaluate our inpainting quality on each frame of the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ 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Ablation for losses on geometric and appearance priors. The artifact in the inpainted region is not as pronounced if viewed from aside as when viewed from the top. Our method is able to optimize an inpainted NeRF without artifacts and with a consistent and unblurry background." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 306, + 172, + 363 + ], + "lines": [ + { + "bbox": [ + 62, + 306, + 172, + 363 + ], + "spans": [ + { + "bbox": [ + 62, + 306, + 172, + 363 + ], + "type": "image", + "image_path": "399b3524a9e995609b55edaf2d7fab6d7b12afb6374c75e6c7ae7bbe7161951e.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 173, + 306, + 272, + 363 + ], + "blocks": [ + { + "bbox": [ + 116, + 295, + 231, + 304 + ], + "lines": [ + { + "bbox": [ + 116, + 295, + 231, + 304 + ], + "spans": [ + { + "bbox": [ + 116, + 295, + 231, + 304 + ], + "type": "text", + "content": "\"Turn the slippers into red slippers\"" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 173, + 306, + 272, + 363 + ], + "lines": [ + { + "bbox": [ + 173, + 306, + 272, + 363 + ], + "spans": [ + { + "bbox": [ + 173, + 306, + 272, + 363 + ], + "type": "image", + "image_path": "8eb80fb0200dfe7399b020085a87f2abf5b8972258c667b5bc7d8b8581e81e80.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 62, + 365, + 172, + 421 + ], + "blocks": [ + { + "bbox": [ + 62, + 365, + 172, + 421 + ], + "lines": [ + { + "bbox": [ + 62, + 365, + 172, + 421 + ], + "spans": [ + { + "bbox": [ + 62, + 365, + 172, + 421 + ], + "type": "image", + "image_path": "93abbd958aa96824c36bd54a2fcbf244c0a45ccf1a3123cbd316221a277ffba1.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 173, + 365, + 272, + 421 + ], + "blocks": [ + { + "bbox": [ + 173, + 365, + 272, + 421 + ], + "lines": [ + { + "bbox": [ + 173, + 365, + 272, + 421 + ], + "spans": [ + { + "bbox": [ + 173, + 365, + 272, + 421 + ], + "type": "image", + "image_path": "948bcf51ed81dcce1559a85544110e63b1a55155907b03f848c7787ad58d6313.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 62, + 422, + 172, + 479 + ], + "blocks": [ + { + "bbox": [ + 62, + 422, + 172, + 479 + ], + "lines": [ + { + "bbox": [ + 62, + 422, + 172, + 479 + ], + "spans": [ + { + "bbox": [ + 62, + 422, + 172, + 479 + ], + "type": "image", + "image_path": "25a0ee44139e37692df62ce4f4f0f2f9123b5f6029e4fc676b0a07ee34bf83f2.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 480, + 287, + 524 + ], + "lines": [ + { + "bbox": [ + 46, + 480, + 287, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 287, + 524 + ], + "type": "text", + "content": "Figure 9. Editing comparison with In2n. InNeRF360, combined with appropriate mask-conditioned image editing models, can generate accurate editing on desired objects. In contrast, In2n gives the wrong texture to unwanted regions." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 173, + 422, + 272, + 479 + ], + "blocks": [ + { + "bbox": [ + 173, + 422, + 272, + 479 + ], + "lines": [ + { + "bbox": [ + 173, + 422, + 272, + 479 + ], + "spans": [ + { + "bbox": [ + 173, + 422, + 272, + 479 + ], + "type": "image", + "image_path": "9ef784bac4b137c9d1624592e95eb15e6f9e08e88fcaa4be74345c4c23f154f4.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 533, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 286, + 616 + ], + "type": "text", + "content": "renderings with per-frame inpainting and SPN-360. We report LPIPS [44] and Frechet Inception Distance (FID) [11] metric in Tab. 1 by comparing with the output of the captured empty scene rendered under the same camera trajectory which we use as ground truth. Our method outperforms each baseline method and outputs visually consistent inpainting without visual artifacts." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 616, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 286, + 640 + ], + "type": "text", + "content": "A quantitative baseline comparison to SPN on frontal scenes is also in the supplementary materials." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 46, + 641, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 700 + ], + "type": "text", + "content": "3D consistency over per-frame inpainting. A naive approach for 3D scene inpainting is to independently inpaint every rendered image of the scene with a 2D image inpainter. In contrast, InNeRF360 produces inpaintings with higher view consistency across all viewpoints." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "We verify such a claim with a user study where partici" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 293, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 376 + ], + "type": "text", + "content": "pants were presented with two video clips of each inpainted scene, rendered with sequential camera trajectories. They were then asked to identify which clip appeared more consistent. Additional details about the user study can be found in the supplementary material. The results, presented in Tab. 2, clearly show that our rendered inpaintings exhibit superior temporal consistency compared to per-frame edits." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 378, + 410, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 410, + 391 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 410, + 391 + ], + "type": "text", + "content": "4.3. Editing Accuracy" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 305, + 397, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 493 + ], + "type": "text", + "content": "As shown by Fig. 9, our segmentation module can be connected with a mask-conditioned image editor [8] to generate view-consistent editing with object-level control through text instructions, which InstructNeRF2NeRF (In2n) [9] cannot. However, note that editing is not the focus of our work. We show this result simply to demonstrate a possible extension to our method. Details are provided in the supplementary." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 498, + 463, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 463, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 463, + 510 + ], + "type": "text", + "content": "5. Limitations and Conclusion" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 513, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 513, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 305, + 513, + 545, + 608 + ], + "type": "text", + "content": "Limitations. Our method inherits certain constraints of vision-language models. In scenarios where the text instruction cannot be accurately localized within the image, InNeRF360 may struggle in generating segmentation consistently aligned with the views. This issue arises when the initial masks provided by the 2D object detector are inaccurate or too noisy for effective refinement. Addressing this challenge is a focus of our future work." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 305, + 609, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 679 + ], + "type": "text", + "content": "Conclusion. In conclusion, we have presented InNeRF360, a unified system to accurately segment and inpaint objects in " + }, + { + "bbox": [ + 305, + 609, + 545, + 679 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 305, + 609, + 545, + 679 + ], + "type": "text", + "content": " NeRFs with text instructions. We synthesize perceptually consistent inpainting without artifacts and can extend to object-level stylization, improving the controllability of NeRF." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 680, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 680, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 680, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work was supported in part by the Swiss National Science Foundation via the Sinergia grant CRSII5-180359." + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12684" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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Large scale image completion via co-modulated generative adversarial networks. arXiv preprint arXiv:2103.10428, 2021. 2" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12686" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/InceptionNeXt_ When Inception Meets ConvNeXt/66d1a177-6c15-49db-8496-bf969a4b7f0e_content_list.json b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/66d1a177-6c15-49db-8496-bf969a4b7f0e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..792be4281d0d67f1d0b90d349578066173306927 --- /dev/null +++ b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/66d1a177-6c15-49db-8496-bf969a4b7f0e_content_list.json @@ -0,0 +1,1432 @@ +[ + { + "type": "text", + "text": "InceptionNeXt: When Inception Meets ConvNeXt", + "text_level": 1, + "bbox": [ + 233, + 130, + 740, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Weihao Yu1 Pan Zhou2,3 Shuicheng Yan4 Xinchao Wang1* \n1National University of Singapore 2Singapore Management University 3Sea AI Lab 4Skywork AI \nweihaoyu@u.nus.edu panzhou@smu.edu.sg shuicheng.yan@kunlun-inc.com xinchao@nus.edu.sg \nCode: https://github.com/sail-sg/inceptionnext", + "bbox": [ + 86, + 179, + 880, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by the long-range modeling ability of ViTs, large-kernel convolutions are widely studied and adopted recently to enlarge the receptive field and improve model performance, like the remarkable work ConvNeXt which employs $7 \\times 7$ depthwise convolution. Although such depth-wise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves $\\sim 60\\%$ throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation, which poses a challenging problem: How to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e., small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely InceptionNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves $1.6 \\times$ higher training throughputs than ConvNeX-T, as well as attains $0.2\\%$ top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint.", + "bbox": [ + 76, + 318, + 473, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 757, + 209, + 772 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reviewing the history of deep learning [35], Convolutional Neural Networks (CNNs) [33, 34] are definitely the most popular models in computer vision. The watershed moment arrived in 2012 when AlexNet [32] claimed victory in the ImageNet contest, ushering in a new era for CNNs in computer vision [11, 32, 54]. Since then, a myriad of influential", + "bbox": [ + 75, + 782, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e9593823df4f4baf048a0deb0bd33c88f053cc8c9d63562a3eaae1fe0f1599f6.jpg", + "image_caption": [ + "Figure 1. Trade-off between accuracy and training throughput. All models are trained under the DeiT training hyperparameters [39, 40, 64, 72]. The training throughput is measured on an A100 GPU with batch size of 128. ConvNeXt-T/kn means variants with depthwise convolution kernel size of $n \\times n$ . InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy." + ], + "image_footnote": [], + "bbox": [ + 506, + 286, + 864, + 487 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CNNs has emerged like Network In Network [37], VGG [56], Inception Nets [58], ResNe(X)t [22, 74], DenseNet [27] and other efficient models [25, 55, 61, 62, 84].", + "bbox": [ + 498, + 590, + 890, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motivated by the great achievement of Transformer in NLP, researchers attempt to integrate its modules or blocks into vision CNN models [2, 4, 28, 70], e.g., the representative works like Non-local Neural Networks [70] and DETR [4], or even make self-attention as stand-alone primitive [50, 85]. Moreover, inspired by the language generative pre-training [46], Image GPT (iGPT) [6] treats pixels as tokens and adopts pure Transformer for visual self-supervised learning. However, iGPT faces limitations in handling high-resolution images due to computational costs [6]. The breakthrough came with Vision Transformer (ViT) [16], which treats image patches as tokens, leverages a pure Transformer as the backbone, and has demonstrated remarkable performance in image classification after large-scale supervised image pre-training.", + "bbox": [ + 496, + 640, + 892, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Apparently, the success of ViT [16] further ignites the enthusiasm for Transformer's application in computer vi", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5672", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5d96a8d1443d26dc2e077572919600dc4f70fadfed9982c167f98d62b8a4d2f1.jpg", + "image_caption": [ + "Figure 2. Block illustration of MetaFormer, MetaNext, ConvNeXt and InceptionNeXt. Similar to MetaFormer block [77], MetaNeXt is a general block abstracted from ConvNeXt [40]. MetaNeXt can be regarded as a simpler version obtained from MetaFormer by merging two residual sub-blocks into one. It is worth noting that the token mixer used in MetaNeXt cannot be too complex (e.g., self-attention [66]) or it may fail to train to converge. By specifying the token mixer as depthwise convolution or Inception depthwise convolution, the model is instantiated as ConvNeXt or InceptionNeXt block. Compared with ConvNeXt, InceptionNeXt is more efficient because it decomposes expensive large-kernel depthwise convolution into four efficient parallel branches." + ], + "image_footnote": [], + "bbox": [ + 204, + 90, + 759, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sion. Many ViT variants [15, 36, 39, 64, 67, 75, 79], like DeiT [64] and Swin [39], are proposed and have achieved remarkable performance across a wide range of vision tasks. The superior performance of ViT-like models over traditional CNNs (e.g., Swin-T's $81.2\\%$ v.s. ResNet-50's $76.1\\%$ on ImageNet [11, 22, 39, 54]) leads many researchers to believe that Transformers will eventually replace CNNs and dominate the field of computer vision.", + "bbox": [ + 75, + 431, + 468, + 553 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "It is time for CNN to fight back. With advanced training techniques in DeiT [64] and Swin [39], the work of \"ResNet strikes back\" [72] shows that the performance of ResNet-50 can rise by $2.3\\%$ , up to $78.4\\%$ . Further, ConvNeXt [40] demonstrates that with modern modules like GELU [23] activation and large kernel size similar to attention window size [39], CNN models can consistently outperform Swin Transformer [39] in various settings and tasks. ConvNeXt is not alone: More and more works have shown similar observations [14, 18, 24, 38, 51, 68, 76, 78], like RepLKNet [14] and SLaK [38]. Among these modern CNN models, the common key feature is the large receptive field that is usually achieved by depthwise convolution [7, 43] with large kernel size (e.g., $7 \\times 7$ ).", + "bbox": [ + 75, + 560, + 468, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, despite its small FLOPs, depthwise convolution is actually an \"expensive\" operator because it brings high memory access costs and can be a bottleneck on powerful computing devices, like GPUs [42]. Moreover, as observed in [14], larger kernel sizes lead to significantly lower speeds. As shown in Figure 1, the ConvNeXt-T with a default $7 \\times 7$ kernel size is $1.4 \\times$ slower than that with small kernel size of $3 \\times 3$ , and is $1.8 \\times$ slower than ResNet-50, al", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "though they have similar FLOPs. However, using a smaller kernel size limits the receptive field, which can result in performance degradation. For example, ConvNeXt-T/k3 suffers a performance drop of $0.6\\%$ top-1 accuracy on the ImageNet-1K dataset when compared to ConvNeXt-T/k7, where $kn$ denotes a kernel size of $n \\times n$ .", + "bbox": [ + 498, + 431, + 890, + 522 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This poses a challenging problem: How to speed up large-kernel CNNs while preserving their performance? In this paper, we aim to address this issue by building upon ConvNeXt as our baseline and improving the depthwise convolution module. Through our preliminary experiments based on ConvNeXt (see Table 1), we find that not all input channels need to undergo the computationally expensive depthwise convolution operation [42]. Accordingly, we propose to leave some channels unaltered and process only a portion of the channels with the depthwise convolution operation. Next, we propose to decompose large kernel of depthwise convolution into several groups of small kernels in Inception style [58-60]. Specifically, for the processing channels, $1/3$ of channels are conducted with kernel of $3 \\times 3$ , another $1/3$ are with $1 \\times k$ , and the remaining $1/3$ are with $k \\times 1$ . With this new simple and cheap operator, termed as \"Inception depthwise convolution\", our built model InceptionNeXt achieves a much better trade-off between accuracy and speed. For example, as shown in Figure 1, InceptionNeXt-T achieves higher accuracy than ConvNeXt-T while enjoying $1.6 \\times$ speedup of training throughput similar to ResNet-50.", + "bbox": [ + 496, + 530, + 892, + 862 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are two-fold. Firstly, we identify the speed bottleneck of ConvNeXt as shown in Fig-", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5673", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ure 1. To solve this speed bottleneck while keeping accuracy, we propose Inception depthwise convolution which decomposes the expensive depthwise convolution into three convolution branches with small kernel sizes as well as a branch of identity mapping. Secondly, extensive experiments on image classification and semantic segmentation show a better speed-accuracy trade-off of our model InceptionNeXt than ConvNeXt. We hope that InceptionNeXt can serve as a new CNN baseline to speed up the research of neural architecture design.", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 253, + 215, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Transformer v.s.CNN", + "text_level": 1, + "bbox": [ + 76, + 275, + 274, + 290 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer [66] was introduced in 2017 for NLP tasks because of its parallel training and also better performance than LSTM. Then many famous NLP models are built on Transformer, including GPT series [3, 44, 46, 47], BERT [12], T5 [49], and OPT [83]. For the application of the Transformer in vision tasks, Vision Transformer (ViT) is definitely the seminal work, showing that Transformer can achieve impressive performance after large-scale supervised training. Follow-up works [20, 52, 53, 64, 67, 69, 79] like Swin [39] continually improve model performance, achieving new state-of-the-art on various vision tasks. These results seem to tell us \"Attention is all you need\" [66].", + "bbox": [ + 75, + 294, + 468, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "But it is not that simple. ViT variants like DeiT usually adopt modern training procedures including various advanced techniques of data augmentation [9, 10, 80, 82, 86], regularization [26, 59] and optimizers [30, 41]. Wightman et al. find that with similar training procedures, the performance of ResNet can be largely improved. Besides, Yu et al. [77] argue that the general architecture instead of attention plays a key role in model performance. Han et al. [21] find by replacing attention in Swin with regular or dynamic depthwise convolution, the model can also obtain comparable performance. ConvNeXt [40], a remarkable work, modernizes ResNet into an advanced version with some designs from ViTs, and the resulting models consistently outperform Swin [39]. Other works like RepLKNet [14], VAN [18], FocalNets [76], HorNet [51], SLKNet [38], ConvFormer [78], Conv2Former [24], and InternImage [68] constantly improve performance of CNNs. Despite the high performance obtained, these models neglect efficiency, exhibiting lower speed than ConvNeXt. Actually, ConvNeXt is also not an efficient model compared with ResNet. We argue that CNN models should keep the original advantage of efficiency. Thus, in this paper, we aim to improve the model efficiency of CNNs while maintaining high performance.", + "bbox": [ + 75, + 491, + 472, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Convolution with large kernels.", + "text_level": 1, + "bbox": [ + 76, + 847, + 354, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Well-known works, like AlexNet [32] and Inception v1 [58] already utilize large kernels up to $11 \\times 11$ and $7 \\times 7$ , respec", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tively. To improve the efficiency of large kernels, VGG [56] proposes to heavily stack $3 \\times 3$ convolutions while Inception v3 [59] factorizes $k \\times k$ convolution into $1 \\times k$ and $k \\times 1$ staking sequentially. For depthwise convolution, MixConv [63] splits kernels into several groups from $3 \\times 3$ to $k \\times k$ . Besides, Peng et al. find that large kernels are important for semantic segmentation and they decompose large kernels similar to Inception v3 [59]. Witnessing the success of Transformer in vision tasks [16, 39, 67], large-kernel convolution is more emphasized since it can offer a large receptive field to imitate attention [21, 40]. For example, ConvNeXt adopts kernel size of $7 \\times 7$ for depthwise convolution by default. To employ larger kernels, RepLKNet [14] proposes to utilize structural re-parameterization techniques [13, 81] to scale up kernel size to $31 \\times 31$ ; VAN [18] sequentially stacks large-kernel depth-wise convolution (DW-Conv) and depthwise dilation convolution to obtain $21 \\times 21$ receptive filed; FocalNets [76] employ a gating mechanism to fuse multilevel features from stacking depthwise convolutions; SegNeXt [17] learns multi-scale features by multiple branches of staking $1 \\times k$ and $k \\times 1$ . Recently, SLaK [38] factorizes large kernel $k \\times k$ into two small non-square kernels ( $k \\times s$ and $s \\times k$ with $s < k$ ). Unlike these works, we do not aim to scale up larger kernels. Instead, we target efficiency and decompose large kernels in a simple and speed-friendly way while keeping comparable performance.", + "bbox": [ + 496, + 90, + 893, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Formulation and Method", + "text_level": 1, + "bbox": [ + 500, + 492, + 736, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.MetaNeXt", + "text_level": 1, + "bbox": [ + 500, + 517, + 617, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formulation of MetaNeXt Block. In ConvNeXt [40], for its each ConvNeXt block, the input $X$ is first processed by a depthwise convolution to propagate information along spatial dimensions. We follow MetaFormer [77] to abstract the depthwise convolution as a token mixer which is responsible for spatial information interaction. Accordingly, as shown in the second subfigure in Figure 2, the ConvNeXt is abstracted as MetaNeXt block. Formally, in a MetaNeXt block, its input $X$ is firstly processed as", + "bbox": [ + 496, + 542, + 893, + 679 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {\\prime} = \\operatorname {T o k e n M i x e r} (X), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 691, + 890, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $X, X' \\in \\mathbb{R}^{B \\times C \\times H \\times W}$ with $B, C, H$ and $W$ respectively denoting batch size, channel number, height and width. Then the output from the token mixer is normalized", + "bbox": [ + 496, + 720, + 893, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nY = \\operatorname {N o r m} \\left(X ^ {\\prime}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 780, + 890, + 796 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After normalization [1, 29], the features are then fed into an MLP module which consists of two fully-connected layers with an activation function between them, the same as feed-forward network in Transformer [66]. The two fully-connected layers can also be implemented by $1 \\times 1$ convolutions. Also, shortcut connection [22, 57] is adopted. This", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5674", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [ + "Algorithm 1 Inception Depthwise Convolution (PyTorch-like Code)" + ], + "code_body": "import torch.nn as nn \nclass InceptionDWConv2d(nnModule): def __init__(self, in_channels, square_kernel_size=3, band_kernel_size=11, branch_ratio=1/8): super().__init_(g) $\\mathrm{gc} =$ int(in_channels * branch_ratio) # channel number of a convolution branch self.dwconv_hw = nn.Conv2d(gc, gc, square_kernel_size, padding= square_kernel_size//2, groups=gc) self.dwconv_w = nn.Conv2d(gc, gc, kernel_size = (1, band_kernel_size), padding=(0, band_kernel_size//2), groups=gc) self.dwconv_h = nn.Conv2d(gc, gc, kernel_size = (band_kernel_size, 1), padding=( band_kernel_size//2, 0), groups=gc) self.split_Indexes = (gc, gc, gc, in_channels -3*gc) def forward(self,x): #B,C,H,W=x.shape x_hw,x_w,x_h,x_id=torch.split(x,self.split.Indexes,dim=1) return torch.cat( (self.dwconv_hw(x_hw), self.dwconv_w(x_w), self.dwconv_h(x_h), x_id), dim=1)", + "guess_lang": "python", + "bbox": [ + 76, + 122, + 467, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "process can be expressed by", + "bbox": [ + 76, + 510, + 264, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY = \\operatorname {C o n v} _ {1 \\times 1} ^ {r C \\rightarrow C} \\left\\{\\sigma \\left[ \\operatorname {C o n v} _ {1 \\times 1} ^ {C \\rightarrow r C} (Y) \\right]\\right\\} + X, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 537, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{Conv}_{k\\times k}^{C_i\\to C_o}$ means convolution with kernel size of $k\\times k$ input channels of $C_i$ and output channels of $C_o$ . $r$ is the expansion ratio and $\\sigma$ denotes activation function.", + "bbox": [ + 76, + 570, + 468, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comparison to MetaFormer block. As shown in Figure 2, it can be found that MetaNeXt block shares similar modules with MetaFormer block [77], e.g., token mixer and MLP. Nevertheless, a critical difference between the two models lies in the number of shortcut connections [22, 57]. MetaNeXt block implements a single shortcut connection, whereas the MetaFormer block incorporates two, one for the token mixer and the other for the MLP. From this aspect, MetaNeXt block can be regarded as a result of merging two residual sub-blocks from MetaFormer, thereby simplifying the overall architecture. As a result, the MetaNeXt architecture exhibits a higher speed compared to MetaFormer. However, this simpler design comes with a limitation: the token mixer component in MetaNeXt cannot be complicated (e.g., Attention) as shown in our experiments (Table 5).", + "bbox": [ + 75, + 622, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instantiation to ConvNeXt. As shown in Figure 2, in ConvNeXt, the token mixer is simply implemented by a depth-", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "wise convolution", + "bbox": [ + 500, + 92, + 614, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {\\prime} = \\operatorname {T o k e n M i x e r} (X) = \\operatorname {D W C o n v} _ {k \\times k} ^ {C \\rightarrow C} (X), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 114, + 890, + 133 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{DWConv}_{k\\times k}^{C\\to C}$ denotes depthwise convolution with kernel size of $k\\times k$ . In ConvNeXt, $k$ is set as 7 by default.", + "bbox": [ + 498, + 143, + 890, + 175 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/6df14c81ff8908e5d0ce2a38d19bd5f296b8228cb772b25237da136a00fb00de.jpg", + "table_caption": [ + "3.2. Inception depthwise convolution" + ], + "table_footnote": [], + "table_body": "
Kernel size of DWConvConvolution ratioParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
7 × 71.028.64.5575241382.1*
5 × 51.028.44.4675270482.0
3 × 31.028.34.4798280281.5
3 × 31/228.34.4818274081.4
3 × 33/828.34.4847276281.4
3 × 31/428.34.4871280881.3
3 × 31/828.34.4901283380.8
3 × 31/1628.34.4916284680.1
", + "bbox": [ + 503, + 210, + 885, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Preliminary experiments based on ConvNeXt-T. Convolution ratio means the ratio of channels to be processed by depthwise convolution while the other channels keep unchanged. Throughputs are measured on an A100 GPU with batch size of 128 and TF32. * The result is reported in ConvNeXt paper [40].", + "bbox": [ + 498, + 337, + 890, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Preliminary experiments on ConvNeXt-T. We first conducted preliminary experiments based on ConvNeXt-T and report the results in Table 1. Firstly, the kernel size of depthwise convolution is reduced from $7 \\times 7$ to $3 \\times 3$ . Compared to the model with kernel size of $7 \\times 7$ , the one with kernel size of $3 \\times 3$ enjoys $1.4 \\times$ higher training throughput, but suffers a significant performance drop from $82.1\\%$ to $81.5\\%$ . Next, inspired by ShuffleNet V2 [42], we only feed partial input channels into depthwise convolution while the remaining ones keep unchanged. The number of processed input channels is controlled by a ratio. It is found that when the ratio is reduced from 1 to $1/4$ , the training throughput can be further improved while the performance almost maintains. In summary, these preliminary experiments convey two findings on ConvNeXt. Finding 1: Large-kernel depthwise convolution is the speed bottleneck. Finding 2: Processing partial channels is good enough in single depthwise convolution layer [42].", + "bbox": [ + 496, + 421, + 892, + 693 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Formulation. Based on the above findings, we propose a new type of convolution to keep both accuracy and effi", + "bbox": [ + 498, + 698, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/44b5c05761469c74555729212b45a83ad68dce0be2f938cb1686205fef29d33b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Conv. typeParamsFLOPs
Conventional conv.k2C22k2C2HW
Depthwise conv.k2C2k2CHW
Inception dep. conv.(2k + 9)C/8(2k + 9)CHW/4
", + "bbox": [ + 504, + 738, + 887, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2. Complexity of different types of convolution. For simplicity, assume input and output channels are the same, and the bias term is omitted. $k$ , $C$ , $H$ and $W$ denote kernel size, channel number, height and width, respectively. The parameters and FLOPs of vanilla convolution and depthwise convolution are quadratic to kernel size $k$ . In contrast, Inception depthwise convolution is linear to $k$ .", + "bbox": [ + 496, + 797, + 890, + 893 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5675", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/70948b99a6a3ed70a3dfe3569c21ebb3546bebdd56acbafa58b85eb1169d7fbd.jpg", + "image_caption": [ + "Figure 3. Comparison of FLOPs between depthwise convolution and Inception depthwise convolution. Inception depthwise convolution is much more efficient than depthwise convolution as kernel size increases." + ], + "image_footnote": [], + "bbox": [ + 122, + 85, + 424, + 255 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/aab91df799e0ed6d5901de0c654b33a2cf587dfe241027bf2669cb78d4017276.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Stage#TokensLayer SpecificationInceptionNeXt
ATSB
1H/4 × W/4Down-samplingKernel Size4 × 4, stride 4
Embed. Dim.4096128
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
2H/8 × W/8Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.90192256
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
3H/16 × W/16Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.180384512
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block6927
4H/32 × W/32Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.3207681024
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio3
# Block23
Global average pooling, MLP
Parameters (M)4.228.149.486.7
MACs (G)0.54.28.414.9
", + "bbox": [ + 81, + 323, + 460, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 3. Configurations of InceptionNeXt models which have similar model configurations to ConvNeXt [40]. \"A\", \"T\", \"S\" and \"B\" represent \"Atto\", \"Tiny\", \"Small\" and \"Base\", respectively.", + "bbox": [ + 76, + 713, + 468, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ciency. According to Fingding 2, we leave partial channels unchanged and denote them as a branch of identity mapping. Motivated by Fingding 1, for the processing channels, we propose to decompose the depthwise operations in Inception style [58-60]. Inception [58] utilizes several branches of small kernels (e.g., $3 \\times 3$ ) and large kernels (e.g., $5 \\times 5$ ). Similarly, we adopt $3 \\times 3$ as one of our branches but get rid of the usage of the large square kernels because of their slow practical speed. Instead, large kernel $k_h \\times k_w$", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is decomposed as $1 \\times k_w$ and $k_h \\times 1$ inspired by Inception v3 [59].", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, for input $X$ , we split it into four groups along the channel dimension,", + "bbox": [ + 498, + 123, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {\\mathrm {h w}}, X _ {\\mathrm {w}}, X _ {\\mathrm {h}}, X _ {\\mathrm {i d}} = \\operatorname {S p l i t} (X) \\tag {5} \\\\ = X _ {:,: g}, X _ {: g: 2 g}, X _ {: 2 g: 3 g}, X _ {: 3 g:}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 167, + 890, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g$ is the channel numbers of convolution branches. We can set a ratio $r_g$ to determine the branch channel numbers by $g = r_g C$ . Next, the splitting inputs are fed into different parallel branches,", + "bbox": [ + 498, + 219, + 890, + 279 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {\\mathrm {h w}} ^ {\\prime} = \\operatorname {D W C o n v} _ {k _ {s} \\times k _ {s}} ^ {g \\rightarrow g} g (X _ {\\mathrm {h w}}), \\\\ \\begin{array}{l}X _ {\\mathrm {w}} ^ {\\prime} = \\operatorname {D W C o n v} _ {1 \\times k _ {b}} ^ {g \\rightarrow g} g \\left(X _ {\\mathrm {w}}\\right),\\\\V ^ {\\prime} = \\operatorname {D W C o n v} _ {1 \\times k _ {b}} ^ {g \\rightarrow g} (X)\\end{array}\\tag {6} \\\\ X _ {\\mathrm {h}} ^ {\\prime} = \\operatorname {D W C o n v} _ {k _ {b} \\times 1} ^ {g \\rightarrow g} g (X _ {\\mathrm {h}}), \\\\ X _ {\\mathrm {i d}} ^ {\\prime} = X _ {\\mathrm {i d}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 294, + 890, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $k_{s}$ denotes the small square kernel size set as 3 by default; $k_{b}$ represents the band kernel size set as 11 by default. Finally, the outputs from each branch are concatenated,", + "bbox": [ + 498, + 388, + 890, + 434 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {\\prime} = \\operatorname {C o n c a t} \\left(X _ {\\mathrm {h w}} ^ {\\prime}, X _ {\\mathrm {w}} ^ {\\prime}, X _ {\\mathrm {h}} ^ {\\prime}, X _ {\\mathrm {i d}} ^ {\\prime}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 449, + 890, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The illustration of InceptionNeXt block is shown in Figure 2. Moreover, its PyTorch [45] code is summarized in Algorithm 1.", + "bbox": [ + 498, + 482, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Complexity. The complexity of three types of convolution, i.e., conventional, depthwise, and Inception depthwise convolution is shown in Table 2. As can be seen, Inception depthwise convolution is much more efficient than the other two types of convolution in terms of parameter numbers of FLOPs. Inception depthwise convolution consumes parameters and FLOPs linear to both channel and kernel size. The comparison of depthwise and Inception depthwise convolutions regarding FLOPs is also clearly shown in Figure 3.", + "bbox": [ + 496, + 535, + 892, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. InceptionNeXt", + "text_level": 1, + "bbox": [ + 500, + 681, + 648, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on InceptionNeXt block, we can build a series of models named InceptionNeXt. Since ConvNeXt [40] is the our main comparing baseline, we mainly follow it to build models with several sizes [71]. Specifically, similar to ResNet [22] and ConvNeXt, InceptionNeXt also adopts 4-stage framework. The same as ConvNeXt, the numbers of 4 stages are [2, 2, 6, 2] for atto size, [3, 3, 9, 3] for small size and [3, 3, 27, 3] for base size. We adopt Batch Normalization since this paper emphasizes speed. Another difference with ConvNeXt is that InceptionNeXt uses an MLP ratio of 3 in stage 4 and moves the saved parameters to the classifier, which can help reduce a few FLOPs (e.g., $3\\%$ for base size). The detailed model configurations are reported in Table 3.", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5676", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f0921cf7b6e3b40c919d18d20f78057a8236e88ab7116d2f4d7bb5ea31aeba31.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. Performance of models trained on ImageNet-1K. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 (TensorFloat-32), and on a 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of \"Channel First\" and \"Channel Last\" memory layouts are reported." + ], + "table_body": "
ModelMixing TypeImage sizeParams (M)MACs (G)Throughput (img/s)Top-1 (%)
A1002080Ti
TrainInferTrainInfer
MobileNetV2 (1.4) [55]Conv22426.10.6010015190471185974.7
EfficientNet-B0 [61]Conv22425.30.409545502464194477.1
GhostNet 1.3× [19]Conv22427.30.249467451589275775.7
ConvNeXt-A [40, 71]Conv22423.70.558354539345156875.7
InceptionNeXt-A (Ours)Conv22424.20.512661+219%9876+118%992+188%3595+129%75.3-0.4
DeiT-S [64]Attn2242224.61227378127678479.8
T2T-ViT-14 [79]Attn2242224.8----81.5
TNT-S [20]Attn2242245.2----81.5
Swin-T [39]Attn2242294.5564176818455481.3
Focal-T [75]Attn2242294.9----82.2
ResNet-50 [22, 72]Conv2242264.1969314927897778.4
RSB-ResNet-50 [22, 72]Conv2242264.1969314927897779.8
RegNetY-4G [48, 72]Conv2242214.0670269422285981.3
FocalNet-T [76]Conv2242294.5----82.3
ConvNeXt-T [40]Conv2242294.5575241317759082.1
InceptionNeXt-T (Ours)Conv2242284.2901+57%2900+20%254+44%822+39%82.3+0.2
T2T-ViT-19 [79]Attn2242398.5----81.9
PVT-Medium [67]Attn2242446.7----81.2
Swin-S [39]Attn2242508.7359113110932883.0
Focal-S [75]Attn2242519.1----83.5
RSB-ResNet-101 [22, 72]Conv2242457.9620205716859281.3
RegNetY-8G [48, 72]Conv2242398.0689132612448082.1
FocalNet-S [76]Conv2242508.7----83.5
ConvNeXt-S [40]Conv2242508.7361153510535383.1
InceptionNeXt-S (Ours)Conv2242498.4521+44%1750+14%130+24%447+27%83.5+0.4
DeiT-B [64]Attn22428617.554116088625981.8
T2T-ViT-24 [79]Attn22426413.8----82.3
TNT-B [20]Attn22426614.1----82.9
PVT-Large [67]Attn2242629.8----81.7
Swin-B [39]Attn22428815.42718437222383.5
Focal-B [75]Attn22429016.0----83.8
RSB-ResNet-152 [22, 72]Conv22426011.6437145711541581.8
RegNetY-16G [48, 72]Conv22428415.932211007629582.2
RepLKNet-31B [14]Conv22427915.3----83.5
FocalNet-B [76]Conv22428915.4----83.9
ConvNeXt-B [40]Conv22428915.426711226823683.8
InceptionNeXt-B (Ours)Conv22428714.9375+40%1244+11%80+18%287+22%84.0+0.2
DeiT-B [64]Attn38428655.4131361257383.1
Swin-B [39]Attn38428847.1104296216584.5
RepLKNet-31B [14]Conv38427945.1----84.8
ConvNeXt-B [40]Conv38428945.095393237985.1
InceptionNeXt-B (Ours)Conv38428743.6139+46%428+9%27+17%97+23%85.2+0.1
", + "bbox": [ + 138, + 87, + 831, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 700, + 202, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Image classification", + "text_level": 1, + "bbox": [ + 76, + 727, + 264, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. For the image classification task, ImageNet-1K [11, 54] is one of the most commonly-used benchmarks, which contains around 1.3 million images in the training set and 50 thousand images in the validation set. To fairly compare with the widely-used baselines, e.g., Swin [39] and ConvNeXt [40], we mainly follow the training hyperparameters from DeiT [64] without distillation. Specifically, the models are trained by AdamW [41] optimizer with a learning rate $lr = 0.001 \\times \\text{batchsize} / 1024$ ( $lr = 4e - 3$ and batchsize $= 4096$ are used in this paper the same as", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ConvNeXt). Following DeiT, data augmentation includes standard random resized crop, horizontal flip, RandAugment [10], Mixup [82], CutMix [80], Random Erasing [86] and color jitter. For regularization, label smoothing [59], stochastic depth [26], and weight decay are adopted. Like ConvNeXt, we also use LayerScale [65], a technique to help train deep models. Our code is based on PyTorch [45] and timm [71].", + "bbox": [ + 496, + 702, + 893, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. We compare InceptionNeXt with various state-of-the-art models, including attention-based and convolution-based models. As can be seen in Table 4, InceptionNeXt achieves highly competitive performance as well as", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5677", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/479f23a1aaf15954e4c27e1843ca59659bd1ac62c8b3b752ecaecee1458ff097.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelParams (M)MACs (G)Throughput (img/s)Top-1 (%)
TrainInfer
DeiT-S [64]224.627678479.8
MetaNeXt-Attn224.62888163.9
ConvNeXt-S (iso.) [40]224.327087979.7
InceptionNeXt-S (iso.)224.231099879.7
", + "bbox": [ + 81, + 88, + 467, + 165 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "enjoys higher speed. InceptionNeXt consistently enjoys better accuracy-speed trade-off than ConvNeXt [40]. For example, InceptionNeXt-T not only surpasses ConvNeXt-T by $0.2\\%$ , but also enjoys $1.6 \\times 1.2 \\times$ training/inference throughputs on A100 than ConvNeXts, similar to those of ResNet-50. That is to say, InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy. Moreover, following Swin and ConvNeXt, we also finetuned the InceptionNeXt-B trained at the resolution of $224 \\times 224$ to $384 \\times 384$ for 30 epochs. We can see that InceptionNeXt-B obtains higher train and inference throughputs than ConvNeXt-B while keeping competitive accuracy.", + "bbox": [ + 75, + 276, + 470, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is observed that the speed improvement is much more significant for the lightweight model size, and the improvement gradually becomes smaller when the model size scales up. The reason is that computation complexity of depthwise and Inception depthwise convolutions are linear to channel number, i.e., $\\mathcal{O}(C)$ where $C$ is channel number. For MLPs, their computation complexity is $\\mathcal{O}(C^2)$ . For larger models (larger $C$ ), its computation is further dominated by MLPs. By only improving depthwise convolution, the speed improvement becomes smaller when the model is larger.", + "bbox": [ + 75, + 460, + 468, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides the 4-stage framework [22, 39, 56], another notable one is ViT-style [16] isotropic architecture which has only one stage. To match the parameters and MACs of DeiT-S, we construct InceptionNeXt-S (iso.) following ConvNeXt-S (iso.) [40]. Specifically, we set the embedding dimension as 384 and the block number as 18. Besides, we build a model called MetaNeXt-Attn which is instantiated from MetaNeXt block by specifying self-attention as token mixer. The aim of this model is to investigate whether it is possible to merge two residual sub-blocks of the Transformer block into a single one. The experiment results are shown in Table 5. It can be seen that InceptionNeXt can also perform well with the isotropic architecture, demonstrating InceptionNeXt exhibits good generalization across different frameworks. It is worth noting that MetaNeXt-Attn could not be trained to converge and only achieved an accuracy of $3.9\\%$ . This result suggests that, unlike the token mixer in MetaFormer, the token mixer in MetaNeXt cannot be too complex. If it is, the model may not be trainable.", + "bbox": [ + 75, + 613, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c8b38bd9e6b128c0cd9957321c0dd3ae8ba3b0526a5aef0dfe5ae046e1370ca6.jpg", + "table_caption": [ + "Table 5. Comparison among ViT, isotropic ConvNeXt and InceptionNeXt. MetaNeXt-Attn is instantiated from MetaNeXt with token mixer of self-attention [66]. The throughputs are measured on 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of \"Channel First\" and \"Channel Last\" memory layouts are reported." + ], + "table_footnote": [], + "table_body": "
BackboneUperNet
Params (M)MACs (G)FPSmIoU (%)
Swin-T [39]6094520.645.8
ConvNeXt-T [40]6093920.646.7
InceptionNeXt-T5693322.747.9
Swin-S [39]81103816.249.5
ConvNeXt-S [40]82102716.849.6
InceptionNeXt-S78102017.650.0
Swin-B [39]121118816.249.7
ConvNeXt-B [40]122117015.749.9
InceptionNeXt-B115115917.550.6
", + "bbox": [ + 501, + 88, + 893, + 224 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b7ded38c1434c03c072fb2d9598c09fa47a8ec200f5ae6dff0fb9f3aed32b1c.jpg", + "table_caption": [ + "Table 6. Performance of semantic segmentation with UperNet [73] on ADE20K [87] validation set. Images are cropped to $512 \\times 512$ for training. The MACs are measured with input size of $512 \\times 2048$ . The FPS are benchmarked on 2080Ti." + ], + "table_footnote": [], + "table_body": "
BackboneSemantic FPN
Params (M)MACs (G)FPSmIoU (%)
ResNet-50 [22]294630.236.7
PVT-Small [67]284527.239.8
PoolFormer-S24 [77]233928.840.3
InceptionNeXt-T284431.443.1
ResNet-101 [22]486522.238.8
ResNeXt-101-32x4d [74]4765-39.7
PVT-Medium [67]486120.041.6
PoolFormer-S36 [77]354821.642.0
PoolFormer-M36 [77]606815.442.4
InceptionNeXt-S506520.745.6
PVT-Large [67]658016.042.1
ResNeXt-101-64x4d [74]86104-40.2
PoolFormer-M48 [77]778212.142.7
InceptionNeXt-B8510020.246.4
", + "bbox": [ + 501, + 287, + 898, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Performance of semantic segmentation with Semantic FPN [31] on ADE20K [87] validation set. Images are cropped to $512 \\times 512$ for training. The MACs are measured with input size of $512 \\times 512$ . The FPS are benchmarked on 2080Ti.", + "bbox": [ + 498, + 487, + 893, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Semantic segmentation", + "text_level": 1, + "bbox": [ + 500, + 550, + 714, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup. ADE20K [87], a commonly used scene parsing benchmark, is used to evaluate our models on semantic segmentation task. ADE20K includes 150 fine-grained semantic categories, containing twenty thousand and two thousand images in the training set and validation set, respectively. The checkpoints trained on ImageNet-1K [11] at the resolution of $224^2$ are utilized to initialize the backbones. Following Swin [39] and ConvNeXt [40], we firstly evaluate InceptionNeXt with UperNet [73]. The models are trained with AdamW [41] optimizer with learning rate of 6e-5 and batch size of 16 for 160K iterations. Following PVT [67] and PoolFormer [77], InceptionNeXt is also evaluated with Semantic FPN [31]. In common practices [5, 31], the batch size is 16 for the setting of 80K iterations. Following PoolFormer [77], we increase the batch size to 32 and decrease the iterations to 40K to speed up training. AdamW [30, 41] is adopted with a learning rate of 2e-4 and a polynomial decay schedule of 0.9 power. Our code is based on PyTorch [45] and mmsegmentation [8].", + "bbox": [ + 496, + 578, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. For segmentation with UpNet [73], the results are shown in Table 6. As can be seen, InceptionNeXt con", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5678", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1bb8a8b38ecdc0c3939e7e496bb6ecac50a5a6dcba99327c4a1e1576d16c21bf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AblationVariantParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
BaselineNone (InceptionNeXt-T)28.14.2901290082.3
BranchRemove horizontal band kernel28.04.2947309381.9
Remove vertical band kernel28.04.2954317381.9
Remove small band kernel28.04.2940300482.0
horizontal and vertical band kernel in parallel → in sequence28.14.2903297182.1
Band kernel sizeBand kernel size 11 → 728.04.2905294682.1
Band kernel size 11 → 928.14.2904291682.1
Band kernel size 11 → 1328.14.2896289582.0
Convolution branch ratioConv. branch ratio 1/8 → 1/428.14.2834249982.2
Conv. branch ratio 1/8 → 1/1628.04.2936309781.8
NormalizationBatch Norm [29] → Layer Norm [1]28.14.2721264682.4
", + "bbox": [ + 89, + 88, + 877, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Ablation for InceptionNeXt on ImageNet-1K classification benchmark. InceptionNeXt-T is utilized as the baseline for the ablation study. Top-1 accuracy on the validation set is reported. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 and batch size of 128.", + "bbox": [ + 75, + 251, + 893, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sistently outperforms Swin [39] and ConvNeXt [40] for different model sizes. In the method of Semantic FPN [31] as shown in Table 7, InceptionNeXt significantly surpasses other backbones, like PVT [67] and PoolFormer [77]. These results show that InceptionNeXt also has a high potential for dense prediction tasks.", + "bbox": [ + 75, + 299, + 470, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation studies", + "text_level": 1, + "bbox": [ + 76, + 404, + 238, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation studies on ImageNet-1K [11, 54] using InceptionNeXt-T as baseline from the following aspects.", + "bbox": [ + 75, + 429, + 470, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Branch. Inception depthwise convolution includes four branches, three convolutional ones, and identity mapping. When removing any branch of horizontal or vertical band kernel, performance significantly drops from $82.3\\%$ to $81.9\\%$ , demonstrating the importance of these two branches. This is because these two branches with band kernels can enlarge the receptive field of the model. For the branch of small square kernel size of $3 \\times 3$ , removing it can still achieve up to $82.0\\%$ top-1 accuracy and bring higher throughput. This inspires us that if we attach more importance to the model speed, the simple version of InceptionNeXt without the square kernel of $3 \\times 3$ can be adopted. For the band kernel, Inception v3 mostly equips them in a sequential way. We find that this assembling method can also obtain similar performance and even a little speed up the model. A possible reason is that PyTorch/CUDA may have optimized sequential convolutions well, and we only implement the parallel branches at a high level (see Algorithm 1). We believe the parallel method will be faster when it is optimized better. Thus, parallel method for the band kernels is adopted by default.", + "bbox": [ + 73, + 465, + 468, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Band kernel size. It is found the performance can be improved from kernel size 7 to 11, but it drops when the band kernel size increases to 13. This phenomenon may result from the optimization and can be solved by methods like structural re-parameterization [13, 14]. For simplicity, we set the kernel size as 11 by default except for atto size.", + "bbox": [ + 75, + 787, + 468, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Convolution branch ratio. When the ratio increases from", + "bbox": [ + 76, + 885, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "1/8 to 1/4, performance improvement can not be observed. Ma et al. [42] also point out that it is not necessary for all channels to conduct convolution. But when the ratio decreases to 1/16, it brings a serious performance drop. This is because a smaller ratio would limit the degree of token mixing, resulting in performance drop. We thus set the convolution branch ratio as 1/8 by default except for atto size.", + "bbox": [ + 496, + 299, + 890, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Normalization. When replacing the Batch Normalization [29] with Layer Normalization [1], the performance improvement improve by $0.1\\%$ but suffer throughput drop in both training and inference. Since this paper focuses on efficiency, we adopt Batch Normalization for InceptionNeXt.", + "bbox": [ + 496, + 410, + 890, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 496, + 617, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose an effective and efficient CNN architecture, InceptionNeXt, which enjoys a better trade-off between the practical speed and the performance than previous network architectures. InceptionNeXt decomposes large-kernel depthwise convolution along channel dimension into four parallel branches, including identity mapping, a small square kernel, and two orthogonal band kernels. All these four branches are much more computationally efficient than a large-kernel depthwise convolution in practice, and can also work together to have a large spatial receptive field for good performance. Extensive experimental results demonstrate the superior performance and the high practical efficiency of InceptionNeXt.", + "bbox": [ + 496, + 518, + 890, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This project is supported by the National Research Foundation Singapore under its Medium Sized Center for Advanced Robotics Technology Innovation, and the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2). Weihao Yu was partly supported by Snap Research Fellowship, Google's TPU Research Cloud (TRC), and Google Cloud Research Credits program. Pan Zhou was supported by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant. We would like to thank Ross Wightman for integrating the model and code into Hugging Face's python-image-models repository.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5679", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016.3,8", + "[2] Irwan Bello, Barret Zoph, Ashish Vaswani, Jonathon Shlens, and Quoc V Le. Attention augmented convolutional networks. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 7" + ], + "bbox": [ + 78, + 90, + 468, + 695 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "5683", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/InceptionNeXt_ When Inception Meets ConvNeXt/66d1a177-6c15-49db-8496-bf969a4b7f0e_model.json b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/66d1a177-6c15-49db-8496-bf969a4b7f0e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..dc098bff258a46997d3b5ce80ef8974ee733573d --- /dev/null +++ b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/66d1a177-6c15-49db-8496-bf969a4b7f0e_model.json @@ -0,0 +1,2369 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.234, + 0.131, + 0.741, + 0.154 + ], + "angle": 0, + "content": "InceptionNeXt: When Inception Meets ConvNeXt" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.18, + 0.882, + 0.252 + ], + "angle": 0, + "content": "Weihao Yu1 Pan Zhou2,3 Shuicheng Yan4 Xinchao Wang1* \n1National University of Singapore 2Singapore Management University 3Sea AI Lab 4Skywork AI \nweihaoyu@u.nus.edu panzhou@smu.edu.sg shuicheng.yan@kunlun-inc.com xinchao@nus.edu.sg \nCode: https://github.com/sail-sg/inceptionnext" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.729 + ], + "angle": 0, + "content": "Inspired by the long-range modeling ability of ViTs, large-kernel convolutions are widely studied and adopted recently to enlarge the receptive field and improve model performance, like the remarkable work ConvNeXt which employs \\(7 \\times 7\\) depthwise convolution. Although such depth-wise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves \\(\\sim 60\\%\\) throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation, which poses a challenging problem: How to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e., small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely InceptionNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves \\(1.6 \\times\\) higher training throughputs than ConvNeX-T, as well as attains \\(0.2\\%\\) top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.758, + 0.21, + 0.773 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Reviewing the history of deep learning [35], Convolutional Neural Networks (CNNs) [33, 34] are definitely the most popular models in computer vision. The watershed moment arrived in 2012 when AlexNet [32] claimed victory in the ImageNet contest, ushering in a new era for CNNs in computer vision [11, 32, 54]. Since then, a myriad of influential" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.287, + 0.865, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.489, + 0.892, + 0.573 + ], + "angle": 0, + "content": "Figure 1. Trade-off between accuracy and training throughput. All models are trained under the DeiT training hyperparameters [39, 40, 64, 72]. The training throughput is measured on an A100 GPU with batch size of 128. ConvNeXt-T/kn means variants with depthwise convolution kernel size of \\( n \\times n \\). InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.592, + 0.892, + 0.637 + ], + "angle": 0, + "content": "CNNs has emerged like Network In Network [37], VGG [56], Inception Nets [58], ResNe(X)t [22, 74], DenseNet [27] and other efficient models [25, 55, 61, 62, 84]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Motivated by the great achievement of Transformer in NLP, researchers attempt to integrate its modules or blocks into vision CNN models [2, 4, 28, 70], e.g., the representative works like Non-local Neural Networks [70] and DETR [4], or even make self-attention as stand-alone primitive [50, 85]. Moreover, inspired by the language generative pre-training [46], Image GPT (iGPT) [6] treats pixels as tokens and adopts pure Transformer for visual self-supervised learning. However, iGPT faces limitations in handling high-resolution images due to computational costs [6]. The breakthrough came with Vision Transformer (ViT) [16], which treats image patches as tokens, leverages a pure Transformer as the backbone, and has demonstrated remarkable performance in image classification after large-scale supervised image pre-training." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Apparently, the success of ViT [16] further ignites the enthusiasm for Transformer's application in computer vi" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5672" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.205, + 0.092, + 0.761, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.341, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Figure 2. Block illustration of MetaFormer, MetaNext, ConvNeXt and InceptionNeXt. Similar to MetaFormer block [77], MetaNeXt is a general block abstracted from ConvNeXt [40]. MetaNeXt can be regarded as a simpler version obtained from MetaFormer by merging two residual sub-blocks into one. It is worth noting that the token mixer used in MetaNeXt cannot be too complex (e.g., self-attention [66]) or it may fail to train to converge. By specifying the token mixer as depthwise convolution or Inception depthwise convolution, the model is instantiated as ConvNeXt or InceptionNeXt block. Compared with ConvNeXt, InceptionNeXt is more efficient because it decomposes expensive large-kernel depthwise convolution into four efficient parallel branches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.554 + ], + "angle": 0, + "content": "sion. Many ViT variants [15, 36, 39, 64, 67, 75, 79], like DeiT [64] and Swin [39], are proposed and have achieved remarkable performance across a wide range of vision tasks. The superior performance of ViT-like models over traditional CNNs (e.g., Swin-T's \\(81.2\\%\\) v.s. ResNet-50's \\(76.1\\%\\) on ImageNet [11, 22, 39, 54]) leads many researchers to believe that Transformers will eventually replace CNNs and dominate the field of computer vision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.773 + ], + "angle": 0, + "content": "It is time for CNN to fight back. With advanced training techniques in DeiT [64] and Swin [39], the work of \"ResNet strikes back\" [72] shows that the performance of ResNet-50 can rise by \\(2.3\\%\\), up to \\(78.4\\%\\). Further, ConvNeXt [40] demonstrates that with modern modules like GELU [23] activation and large kernel size similar to attention window size [39], CNN models can consistently outperform Swin Transformer [39] in various settings and tasks. ConvNeXt is not alone: More and more works have shown similar observations [14, 18, 24, 38, 51, 68, 76, 78], like RepLKNet [14] and SLaK [38]. Among these modern CNN models, the common key feature is the large receptive field that is usually achieved by depthwise convolution [7, 43] with large kernel size (e.g., \\(7 \\times 7\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "However, despite its small FLOPs, depthwise convolution is actually an \"expensive\" operator because it brings high memory access costs and can be a bottleneck on powerful computing devices, like GPUs [42]. Moreover, as observed in [14], larger kernel sizes lead to significantly lower speeds. As shown in Figure 1, the ConvNeXt-T with a default \\(7 \\times 7\\) kernel size is \\(1.4 \\times\\) slower than that with small kernel size of \\(3 \\times 3\\), and is \\(1.8 \\times\\) slower than ResNet-50, al" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.523 + ], + "angle": 0, + "content": "though they have similar FLOPs. However, using a smaller kernel size limits the receptive field, which can result in performance degradation. For example, ConvNeXt-T/k3 suffers a performance drop of \\(0.6\\%\\) top-1 accuracy on the ImageNet-1K dataset when compared to ConvNeXt-T/k7, where \\(kn\\) denotes a kernel size of \\(n \\times n\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.893, + 0.863 + ], + "angle": 0, + "content": "This poses a challenging problem: How to speed up large-kernel CNNs while preserving their performance? In this paper, we aim to address this issue by building upon ConvNeXt as our baseline and improving the depthwise convolution module. Through our preliminary experiments based on ConvNeXt (see Table 1), we find that not all input channels need to undergo the computationally expensive depthwise convolution operation [42]. Accordingly, we propose to leave some channels unaltered and process only a portion of the channels with the depthwise convolution operation. Next, we propose to decompose large kernel of depthwise convolution into several groups of small kernels in Inception style [58-60]. Specifically, for the processing channels, \\(1/3\\) of channels are conducted with kernel of \\(3 \\times 3\\), another \\(1/3\\) are with \\(1 \\times k\\), and the remaining \\(1/3\\) are with \\(k \\times 1\\). With this new simple and cheap operator, termed as \"Inception depthwise convolution\", our built model InceptionNeXt achieves a much better trade-off between accuracy and speed. For example, as shown in Figure 1, InceptionNeXt-T achieves higher accuracy than ConvNeXt-T while enjoying \\(1.6 \\times\\) speedup of training throughput similar to ResNet-50." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The contributions of this paper are two-fold. Firstly, we identify the speed bottleneck of ConvNeXt as shown in Fig-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5673" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "ure 1. To solve this speed bottleneck while keeping accuracy, we propose Inception depthwise convolution which decomposes the expensive depthwise convolution into three convolution branches with small kernel sizes as well as a branch of identity mapping. Secondly, extensive experiments on image classification and semantic segmentation show a better speed-accuracy trade-off of our model InceptionNeXt than ConvNeXt. We hope that InceptionNeXt can serve as a new CNN baseline to speed up the research of neural architecture design." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.255, + 0.216, + 0.27 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.276, + 0.276, + 0.291 + ], + "angle": 0, + "content": "2.1. Transformer v.s.CNN" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.47, + 0.492 + ], + "angle": 0, + "content": "Transformer [66] was introduced in 2017 for NLP tasks because of its parallel training and also better performance than LSTM. Then many famous NLP models are built on Transformer, including GPT series [3, 44, 46, 47], BERT [12], T5 [49], and OPT [83]. For the application of the Transformer in vision tasks, Vision Transformer (ViT) is definitely the seminal work, showing that Transformer can achieve impressive performance after large-scale supervised training. Follow-up works [20, 52, 53, 64, 67, 69, 79] like Swin [39] continually improve model performance, achieving new state-of-the-art on various vision tasks. These results seem to tell us \"Attention is all you need\" [66]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.473, + 0.84 + ], + "angle": 0, + "content": "But it is not that simple. ViT variants like DeiT usually adopt modern training procedures including various advanced techniques of data augmentation [9, 10, 80, 82, 86], regularization [26, 59] and optimizers [30, 41]. Wightman et al. find that with similar training procedures, the performance of ResNet can be largely improved. Besides, Yu et al. [77] argue that the general architecture instead of attention plays a key role in model performance. Han et al. [21] find by replacing attention in Swin with regular or dynamic depthwise convolution, the model can also obtain comparable performance. ConvNeXt [40], a remarkable work, modernizes ResNet into an advanced version with some designs from ViTs, and the resulting models consistently outperform Swin [39]. Other works like RepLKNet [14], VAN [18], FocalNets [76], HorNet [51], SLKNet [38], ConvFormer [78], Conv2Former [24], and InternImage [68] constantly improve performance of CNNs. Despite the high performance obtained, these models neglect efficiency, exhibiting lower speed than ConvNeXt. Actually, ConvNeXt is also not an efficient model compared with ResNet. We argue that CNN models should keep the original advantage of efficiency. Thus, in this paper, we aim to improve the model efficiency of CNNs while maintaining high performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.355, + 0.864 + ], + "angle": 0, + "content": "2.2. Convolution with large kernels." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Well-known works, like AlexNet [32] and Inception v1 [58] already utilize large kernels up to \\( 11 \\times 11 \\) and \\( 7 \\times 7 \\), respec" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.486 + ], + "angle": 0, + "content": "tively. To improve the efficiency of large kernels, VGG [56] proposes to heavily stack \\(3 \\times 3\\) convolutions while Inception v3 [59] factorizes \\(k \\times k\\) convolution into \\(1 \\times k\\) and \\(k \\times 1\\) staking sequentially. For depthwise convolution, MixConv [63] splits kernels into several groups from \\(3 \\times 3\\) to \\(k \\times k\\). Besides, Peng et al. find that large kernels are important for semantic segmentation and they decompose large kernels similar to Inception v3 [59]. Witnessing the success of Transformer in vision tasks [16, 39, 67], large-kernel convolution is more emphasized since it can offer a large receptive field to imitate attention [21, 40]. For example, ConvNeXt adopts kernel size of \\(7 \\times 7\\) for depthwise convolution by default. To employ larger kernels, RepLKNet [14] proposes to utilize structural re-parameterization techniques [13, 81] to scale up kernel size to \\(31 \\times 31\\); VAN [18] sequentially stacks large-kernel depth-wise convolution (DW-Conv) and depthwise dilation convolution to obtain \\(21 \\times 21\\) receptive filed; FocalNets [76] employ a gating mechanism to fuse multilevel features from stacking depthwise convolutions; SegNeXt [17] learns multi-scale features by multiple branches of staking \\(1 \\times k\\) and \\(k \\times 1\\). Recently, SLaK [38] factorizes large kernel \\(k \\times k\\) into two small non-square kernels (\\(k \\times s\\) and \\(s \\times k\\) with \\(s < k\\)). Unlike these works, we do not aim to scale up larger kernels. Instead, we target efficiency and decompose large kernels in a simple and speed-friendly way while keeping comparable performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.493, + 0.738, + 0.508 + ], + "angle": 0, + "content": "3. Formulation and Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.518, + 0.618, + 0.533 + ], + "angle": 0, + "content": "3.1.MetaNeXt" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.894, + 0.68 + ], + "angle": 0, + "content": "Formulation of MetaNeXt Block. In ConvNeXt [40], for its each ConvNeXt block, the input \\( X \\) is first processed by a depthwise convolution to propagate information along spatial dimensions. We follow MetaFormer [77] to abstract the depthwise convolution as a token mixer which is responsible for spatial information interaction. Accordingly, as shown in the second subfigure in Figure 2, the ConvNeXt is abstracted as MetaNeXt block. Formally, in a MetaNeXt block, its input \\( X \\) is firstly processed as" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.693, + 0.892, + 0.71 + ], + "angle": 0, + "content": "\\[\nX ^ {\\prime} = \\operatorname {T o k e n M i x e r} (X), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.721, + 0.894, + 0.768 + ], + "angle": 0, + "content": "where \\(X, X' \\in \\mathbb{R}^{B \\times C \\times H \\times W}\\) with \\(B, C, H\\) and \\(W\\) respectively denoting batch size, channel number, height and width. Then the output from the token mixer is normalized" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.781, + 0.892, + 0.797 + ], + "angle": 0, + "content": "\\[\nY = \\operatorname {N o r m} \\left(X ^ {\\prime}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "After normalization [1, 29], the features are then fed into an MLP module which consists of two fully-connected layers with an activation function between them, the same as feed-forward network in Transformer [66]. The two fully-connected layers can also be implemented by \\(1 \\times 1\\) convolutions. Also, shortcut connection [22, 57] is adopted. This" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5674" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.078, + 0.091, + 0.47, + 0.12 + ], + "angle": 0, + "content": "Algorithm 1 Inception Depthwise Convolution (PyTorch-like Code)" + }, + { + "type": "code", + "bbox": [ + 0.078, + 0.123, + 0.468, + 0.482 + ], + "angle": 0, + "content": "import torch.nn as nn \nclass InceptionDWConv2d(nnModule): def __init__(self, in_channels, square_kernel_size=3, band_kernel_size=11, branch_ratio=1/8): super().__init_(g) \\( \\mathrm{gc} = \\) int(in_channels * branch_ratio) # channel number of a convolution branch self.dwconv_hw = nn.Conv2d(gc, gc, square_kernel_size, padding= square_kernel_size//2, groups=gc) self.dwconv_w = nn.Conv2d(gc, gc, kernel_size = (1, band_kernel_size), padding=(0, band_kernel_size//2), groups=gc) self.dwconv_h = nn.Conv2d(gc, gc, kernel_size = (band_kernel_size, 1), padding=( band_kernel_size//2, 0), groups=gc) self.split_Indexes = (gc, gc, gc, in_channels -3*gc) def forward(self,x): #B,C,H,W=x.shape x_hw,x_w,x_h,x_id=torch.split(x,self.split.Indexes,dim=1) return torch.cat( (self.dwconv_hw(x_hw), self.dwconv_w(x_w), self.dwconv_h(x_h), x_id), dim=1)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.511, + 0.266, + 0.526 + ], + "angle": 0, + "content": "process can be expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.538, + 0.469, + 0.557 + ], + "angle": 0, + "content": "\\[\nY = \\operatorname {C o n v} _ {1 \\times 1} ^ {r C \\rightarrow C} \\left\\{\\sigma \\left[ \\operatorname {C o n v} _ {1 \\times 1} ^ {C \\rightarrow r C} (Y) \\right]\\right\\} + X, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.571, + 0.47, + 0.618 + ], + "angle": 0, + "content": "where \\(\\mathrm{Conv}_{k\\times k}^{C_i\\to C_o}\\) means convolution with kernel size of \\(k\\times k\\) input channels of \\(C_i\\) and output channels of \\(C_o\\) . \\(r\\) is the expansion ratio and \\(\\sigma\\) denotes activation function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.469, + 0.865 + ], + "angle": 0, + "content": "Comparison to MetaFormer block. As shown in Figure 2, it can be found that MetaNeXt block shares similar modules with MetaFormer block [77], e.g., token mixer and MLP. Nevertheless, a critical difference between the two models lies in the number of shortcut connections [22, 57]. MetaNeXt block implements a single shortcut connection, whereas the MetaFormer block incorporates two, one for the token mixer and the other for the MLP. From this aspect, MetaNeXt block can be regarded as a result of merging two residual sub-blocks from MetaFormer, thereby simplifying the overall architecture. As a result, the MetaNeXt architecture exhibits a higher speed compared to MetaFormer. However, this simpler design comes with a limitation: the token mixer component in MetaNeXt cannot be complicated (e.g., Attention) as shown in our experiments (Table 5)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Instantiation to ConvNeXt. As shown in Figure 2, in ConvNeXt, the token mixer is simply implemented by a depth-" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.093, + 0.616, + 0.105 + ], + "angle": 0, + "content": "wise convolution" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.115, + 0.892, + 0.134 + ], + "angle": 0, + "content": "\\[\nX ^ {\\prime} = \\operatorname {T o k e n M i x e r} (X) = \\operatorname {D W C o n v} _ {k \\times k} ^ {C \\rightarrow C} (X), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.144, + 0.892, + 0.176 + ], + "angle": 0, + "content": "where \\(\\mathrm{DWConv}_{k\\times k}^{C\\to C}\\) denotes depthwise convolution with kernel size of \\(k\\times k\\). In ConvNeXt, \\(k\\) is set as 7 by default." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.185, + 0.783, + 0.201 + ], + "angle": 0, + "content": "3.2. Inception depthwise convolution" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.212, + 0.887, + 0.337 + ], + "angle": 0, + "content": "
Kernel size of DWConvConvolution ratioParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
7 × 71.028.64.5575241382.1*
5 × 51.028.44.4675270482.0
3 × 31.028.34.4798280281.5
3 × 31/228.34.4818274081.4
3 × 33/828.34.4847276281.4
3 × 31/428.34.4871280881.3
3 × 31/828.34.4901283380.8
3 × 31/1628.34.4916284680.1
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.338, + 0.892, + 0.407 + ], + "angle": 0, + "content": "Table 1. Preliminary experiments based on ConvNeXt-T. Convolution ratio means the ratio of channels to be processed by depthwise convolution while the other channels keep unchanged. Throughputs are measured on an A100 GPU with batch size of 128 and TF32. * The result is reported in ConvNeXt paper [40]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.893, + 0.694 + ], + "angle": 0, + "content": "Preliminary experiments on ConvNeXt-T. We first conducted preliminary experiments based on ConvNeXt-T and report the results in Table 1. Firstly, the kernel size of depthwise convolution is reduced from \\(7 \\times 7\\) to \\(3 \\times 3\\). Compared to the model with kernel size of \\(7 \\times 7\\), the one with kernel size of \\(3 \\times 3\\) enjoys \\(1.4 \\times\\) higher training throughput, but suffers a significant performance drop from \\(82.1\\%\\) to \\(81.5\\%\\). Next, inspired by ShuffleNet V2 [42], we only feed partial input channels into depthwise convolution while the remaining ones keep unchanged. The number of processed input channels is controlled by a ratio. It is found that when the ratio is reduced from 1 to \\(1/4\\), the training throughput can be further improved while the performance almost maintains. In summary, these preliminary experiments convey two findings on ConvNeXt. Finding 1: Large-kernel depthwise convolution is the speed bottleneck. Finding 2: Processing partial channels is good enough in single depthwise convolution layer [42]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.699, + 0.892, + 0.73 + ], + "angle": 0, + "content": "Formulation. Based on the above findings, we propose a new type of convolution to keep both accuracy and effi" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.739, + 0.888, + 0.793 + ], + "angle": 0, + "content": "
Conv. typeParamsFLOPs
Conventional conv.k2C22k2C2HW
Depthwise conv.k2C2k2CHW
Inception dep. conv.(2k + 9)C/8(2k + 9)CHW/4
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.894 + ], + "angle": 0, + "content": "Table 2. Complexity of different types of convolution. For simplicity, assume input and output channels are the same, and the bias term is omitted. \\( k \\), \\( C \\), \\( H \\) and \\( W \\) denote kernel size, channel number, height and width, respectively. The parameters and FLOPs of vanilla convolution and depthwise convolution are quadratic to kernel size \\( k \\). In contrast, Inception depthwise convolution is linear to \\( k \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5675" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.087, + 0.426, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.258, + 0.47, + 0.313 + ], + "angle": 0, + "content": "Figure 3. Comparison of FLOPs between depthwise convolution and Inception depthwise convolution. Inception depthwise convolution is much more efficient than depthwise convolution as kernel size increases." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.324, + 0.462, + 0.713 + ], + "angle": 0, + "content": "
Stage#TokensLayer SpecificationInceptionNeXt
ATSB
1H/4 × W/4Down-samplingKernel Size4 × 4, stride 4
Embed. Dim.4096128
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
2H/8 × W/8Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.90192256
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
3H/16 × W/16Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.180384512
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block6927
4H/32 × W/32Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.3207681024
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio3
# Block23
Global average pooling, MLP
Parameters (M)4.228.149.486.7
MACs (G)0.54.28.414.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.714, + 0.47, + 0.756 + ], + "angle": 0, + "content": "Table 3. Configurations of InceptionNeXt models which have similar model configurations to ConvNeXt [40]. \"A\", \"T\", \"S\" and \"B\" represent \"Atto\", \"Tiny\", \"Small\" and \"Base\", respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "ciency. According to Fingding 2, we leave partial channels unchanged and denote them as a branch of identity mapping. Motivated by Fingding 1, for the processing channels, we propose to decompose the depthwise operations in Inception style [58-60]. Inception [58] utilizes several branches of small kernels (e.g., \\(3 \\times 3\\)) and large kernels (e.g., \\(5 \\times 5\\)). Similarly, we adopt \\(3 \\times 3\\) as one of our branches but get rid of the usage of the large square kernels because of their slow practical speed. Instead, large kernel \\(k_h \\times k_w\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "is decomposed as \\(1 \\times k_w\\) and \\(k_h \\times 1\\) inspired by Inception v3 [59]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.124, + 0.892, + 0.154 + ], + "angle": 0, + "content": "Specifically, for input \\( X \\), we split it into four groups along the channel dimension," + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.169, + 0.892, + 0.206 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {\\mathrm {h w}}, X _ {\\mathrm {w}}, X _ {\\mathrm {h}}, X _ {\\mathrm {i d}} = \\operatorname {S p l i t} (X) \\tag {5} \\\\ = X _ {:,: g}, X _ {: g: 2 g}, X _ {: 2 g: 3 g}, X _ {: 3 g:}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.22, + 0.892, + 0.28 + ], + "angle": 0, + "content": "where \\( g \\) is the channel numbers of convolution branches. We can set a ratio \\( r_g \\) to determine the branch channel numbers by \\( g = r_g C \\). Next, the splitting inputs are fed into different parallel branches," + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.295, + 0.891, + 0.375 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {\\mathrm {h w}} ^ {\\prime} = \\operatorname {D W C o n v} _ {k _ {s} \\times k _ {s}} ^ {g \\rightarrow g} g (X _ {\\mathrm {h w}}), \\\\ \\begin{array}{l}X _ {\\mathrm {w}} ^ {\\prime} = \\operatorname {D W C o n v} _ {1 \\times k _ {b}} ^ {g \\rightarrow g} g \\left(X _ {\\mathrm {w}}\\right),\\\\V ^ {\\prime} = \\operatorname {D W C o n v} _ {1 \\times k _ {b}} ^ {g \\rightarrow g} (X)\\end{array}\\tag {6} \\\\ X _ {\\mathrm {h}} ^ {\\prime} = \\operatorname {D W C o n v} _ {k _ {b} \\times 1} ^ {g \\rightarrow g} g (X _ {\\mathrm {h}}), \\\\ X _ {\\mathrm {i d}} ^ {\\prime} = X _ {\\mathrm {i d}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.39, + 0.892, + 0.435 + ], + "angle": 0, + "content": "where \\(k_{s}\\) denotes the small square kernel size set as 3 by default; \\(k_{b}\\) represents the band kernel size set as 11 by default. Finally, the outputs from each branch are concatenated," + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.45, + 0.892, + 0.469 + ], + "angle": 0, + "content": "\\[\nX ^ {\\prime} = \\operatorname {C o n c a t} \\left(X _ {\\mathrm {h w}} ^ {\\prime}, X _ {\\mathrm {w}} ^ {\\prime}, X _ {\\mathrm {h}} ^ {\\prime}, X _ {\\mathrm {i d}} ^ {\\prime}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.483, + 0.892, + 0.528 + ], + "angle": 0, + "content": "The illustration of InceptionNeXt block is shown in Figure 2. Moreover, its PyTorch [45] code is summarized in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.893, + 0.672 + ], + "angle": 0, + "content": "Complexity. The complexity of three types of convolution, i.e., conventional, depthwise, and Inception depthwise convolution is shown in Table 2. As can be seen, Inception depthwise convolution is much more efficient than the other two types of convolution in terms of parameter numbers of FLOPs. Inception depthwise convolution consumes parameters and FLOPs linear to both channel and kernel size. The comparison of depthwise and Inception depthwise convolutions regarding FLOPs is also clearly shown in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.683, + 0.65, + 0.699 + ], + "angle": 0, + "content": "3.3. InceptionNeXt" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Based on InceptionNeXt block, we can build a series of models named InceptionNeXt. Since ConvNeXt [40] is the our main comparing baseline, we mainly follow it to build models with several sizes [71]. Specifically, similar to ResNet [22] and ConvNeXt, InceptionNeXt also adopts 4-stage framework. The same as ConvNeXt, the numbers of 4 stages are [2, 2, 6, 2] for atto size, [3, 3, 9, 3] for small size and [3, 3, 27, 3] for base size. We adopt Batch Normalization since this paper emphasizes speed. Another difference with ConvNeXt is that InceptionNeXt uses an MLP ratio of 3 in stage 4 and moves the saved parameters to the classifier, which can help reduce a few FLOPs (e.g., \\(3\\%\\) for base size). The detailed model configurations are reported in Table 3." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5676" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.139, + 0.088, + 0.833, + 0.641 + ], + "angle": 0, + "content": "
ModelMixing TypeImage sizeParams (M)MACs (G)Throughput (img/s)Top-1 (%)
A1002080Ti
TrainInferTrainInfer
MobileNetV2 (1.4) [55]Conv22426.10.6010015190471185974.7
EfficientNet-B0 [61]Conv22425.30.409545502464194477.1
GhostNet 1.3× [19]Conv22427.30.249467451589275775.7
ConvNeXt-A [40, 71]Conv22423.70.558354539345156875.7
InceptionNeXt-A (Ours)Conv22424.20.512661+219%9876+118%992+188%3595+129%75.3-0.4
DeiT-S [64]Attn2242224.61227378127678479.8
T2T-ViT-14 [79]Attn2242224.8----81.5
TNT-S [20]Attn2242245.2----81.5
Swin-T [39]Attn2242294.5564176818455481.3
Focal-T [75]Attn2242294.9----82.2
ResNet-50 [22, 72]Conv2242264.1969314927897778.4
RSB-ResNet-50 [22, 72]Conv2242264.1969314927897779.8
RegNetY-4G [48, 72]Conv2242214.0670269422285981.3
FocalNet-T [76]Conv2242294.5----82.3
ConvNeXt-T [40]Conv2242294.5575241317759082.1
InceptionNeXt-T (Ours)Conv2242284.2901+57%2900+20%254+44%822+39%82.3+0.2
T2T-ViT-19 [79]Attn2242398.5----81.9
PVT-Medium [67]Attn2242446.7----81.2
Swin-S [39]Attn2242508.7359113110932883.0
Focal-S [75]Attn2242519.1----83.5
RSB-ResNet-101 [22, 72]Conv2242457.9620205716859281.3
RegNetY-8G [48, 72]Conv2242398.0689132612448082.1
FocalNet-S [76]Conv2242508.7----83.5
ConvNeXt-S [40]Conv2242508.7361153510535383.1
InceptionNeXt-S (Ours)Conv2242498.4521+44%1750+14%130+24%447+27%83.5+0.4
DeiT-B [64]Attn22428617.554116088625981.8
T2T-ViT-24 [79]Attn22426413.8----82.3
TNT-B [20]Attn22426614.1----82.9
PVT-Large [67]Attn2242629.8----81.7
Swin-B [39]Attn22428815.42718437222383.5
Focal-B [75]Attn22429016.0----83.8
RSB-ResNet-152 [22, 72]Conv22426011.6437145711541581.8
RegNetY-16G [48, 72]Conv22428415.932211007629582.2
RepLKNet-31B [14]Conv22427915.3----83.5
FocalNet-B [76]Conv22428915.4----83.9
ConvNeXt-B [40]Conv22428915.426711226823683.8
InceptionNeXt-B (Ours)Conv22428714.9375+40%1244+11%80+18%287+22%84.0+0.2
DeiT-B [64]Attn38428655.4131361257383.1
Swin-B [39]Attn38428847.1104296216584.5
RepLKNet-31B [14]Conv38427945.1----84.8
ConvNeXt-B [40]Conv38428945.095393237985.1
InceptionNeXt-B (Ours)Conv38428743.6139+46%428+9%27+17%97+23%85.2+0.1
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.641, + 0.894, + 0.698 + ], + "angle": 0, + "content": "Table 4. Performance of models trained on ImageNet-1K. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 (TensorFloat-32), and on a 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of \"Channel First\" and \"Channel Last\" memory layouts are reported." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.702, + 0.204, + 0.72 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.728, + 0.265, + 0.743 + ], + "angle": 0, + "content": "4.1. Image classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Setup. For the image classification task, ImageNet-1K [11, 54] is one of the most commonly-used benchmarks, which contains around 1.3 million images in the training set and 50 thousand images in the validation set. To fairly compare with the widely-used baselines, e.g., Swin [39] and ConvNeXt [40], we mainly follow the training hyperparameters from DeiT [64] without distillation. Specifically, the models are trained by AdamW [41] optimizer with a learning rate \\( lr = 0.001 \\times \\text{batchsize} / 1024 \\) (\\( lr = 4e - 3 \\) and batchsize \\( = 4096 \\) are used in this paper the same as" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.895, + 0.826 + ], + "angle": 0, + "content": "ConvNeXt). Following DeiT, data augmentation includes standard random resized crop, horizontal flip, RandAugment [10], Mixup [82], CutMix [80], Random Erasing [86] and color jitter. For regularization, label smoothing [59], stochastic depth [26], and weight decay are adopted. Like ConvNeXt, we also use LayerScale [65], a technique to help train deep models. Our code is based on PyTorch [45] and timm [71]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results. We compare InceptionNeXt with various state-of-the-art models, including attention-based and convolution-based models. As can be seen in Table 4, InceptionNeXt achieves highly competitive performance as well as" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5677" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.166 + ], + "angle": 0, + "content": "
ModelParams (M)MACs (G)Throughput (img/s)Top-1 (%)
TrainInfer
DeiT-S [64]224.627678479.8
MetaNeXt-Attn224.62888163.9
ConvNeXt-S (iso.) [40]224.327087979.7
InceptionNeXt-S (iso.)224.231099879.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.168, + 0.47, + 0.266 + ], + "angle": 0, + "content": "Table 5. Comparison among ViT, isotropic ConvNeXt and InceptionNeXt. MetaNeXt-Attn is instantiated from MetaNeXt with token mixer of self-attention [66]. The throughputs are measured on 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of \"Channel First\" and \"Channel Last\" memory layouts are reported." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.471, + 0.459 + ], + "angle": 0, + "content": "enjoys higher speed. InceptionNeXt consistently enjoys better accuracy-speed trade-off than ConvNeXt [40]. For example, InceptionNeXt-T not only surpasses ConvNeXt-T by \\(0.2\\%\\), but also enjoys \\(1.6 \\times 1.2 \\times\\) training/inference throughputs on A100 than ConvNeXts, similar to those of ResNet-50. That is to say, InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy. Moreover, following Swin and ConvNeXt, we also finetuned the InceptionNeXt-B trained at the resolution of \\(224 \\times 224\\) to \\(384 \\times 384\\) for 30 epochs. We can see that InceptionNeXt-B obtains higher train and inference throughputs than ConvNeXt-B while keeping competitive accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.611 + ], + "angle": 0, + "content": "It is observed that the speed improvement is much more significant for the lightweight model size, and the improvement gradually becomes smaller when the model size scales up. The reason is that computation complexity of depthwise and Inception depthwise convolutions are linear to channel number, i.e., \\(\\mathcal{O}(C)\\) where \\(C\\) is channel number. For MLPs, their computation complexity is \\(\\mathcal{O}(C^2)\\). For larger models (larger \\(C\\)), its computation is further dominated by MLPs. By only improving depthwise convolution, the speed improvement becomes smaller when the model is larger." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Besides the 4-stage framework [22, 39, 56], another notable one is ViT-style [16] isotropic architecture which has only one stage. To match the parameters and MACs of DeiT-S, we construct InceptionNeXt-S (iso.) following ConvNeXt-S (iso.) [40]. Specifically, we set the embedding dimension as 384 and the block number as 18. Besides, we build a model called MetaNeXt-Attn which is instantiated from MetaNeXt block by specifying self-attention as token mixer. The aim of this model is to investigate whether it is possible to merge two residual sub-blocks of the Transformer block into a single one. The experiment results are shown in Table 5. It can be seen that InceptionNeXt can also perform well with the isotropic architecture, demonstrating InceptionNeXt exhibits good generalization across different frameworks. It is worth noting that MetaNeXt-Attn could not be trained to converge and only achieved an accuracy of \\(3.9\\%\\). This result suggests that, unlike the token mixer in MetaFormer, the token mixer in MetaNeXt cannot be too complex. If it is, the model may not be trainable." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.895, + 0.226 + ], + "angle": 0, + "content": "
BackboneUperNet
Params (M)MACs (G)FPSmIoU (%)
Swin-T [39]6094520.645.8
ConvNeXt-T [40]6093920.646.7
InceptionNeXt-T5693322.747.9
Swin-S [39]81103816.249.5
ConvNeXt-S [40]82102716.849.6
InceptionNeXt-S78102017.650.0
Swin-B [39]121118816.249.7
ConvNeXt-B [40]122117015.749.9
InceptionNeXt-B115115917.550.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.228, + 0.895, + 0.283 + ], + "angle": 0, + "content": "Table 6. Performance of semantic segmentation with UperNet [73] on ADE20K [87] validation set. Images are cropped to \\(512 \\times 512\\) for training. The MACs are measured with input size of \\(512 \\times 2048\\). The FPS are benchmarked on 2080Ti." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.289, + 0.899, + 0.487 + ], + "angle": 0, + "content": "
BackboneSemantic FPN
Params (M)MACs (G)FPSmIoU (%)
ResNet-50 [22]294630.236.7
PVT-Small [67]284527.239.8
PoolFormer-S24 [77]233928.840.3
InceptionNeXt-T284431.443.1
ResNet-101 [22]486522.238.8
ResNeXt-101-32x4d [74]4765-39.7
PVT-Medium [67]486120.041.6
PoolFormer-S36 [77]354821.642.0
PoolFormer-M36 [77]606815.442.4
InceptionNeXt-S506520.745.6
PVT-Large [67]658016.042.1
ResNeXt-101-64x4d [74]86104-40.2
PoolFormer-M48 [77]778212.142.7
InceptionNeXt-B8510020.246.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.488, + 0.894, + 0.543 + ], + "angle": 0, + "content": "Table 7. Performance of semantic segmentation with Semantic FPN [31] on ADE20K [87] validation set. Images are cropped to \\(512 \\times 512\\) for training. The MACs are measured with input size of \\(512 \\times 512\\). The FPS are benchmarked on 2080Ti." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.715, + 0.567 + ], + "angle": 0, + "content": "4.2. Semantic segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Setup. ADE20K [87], a commonly used scene parsing benchmark, is used to evaluate our models on semantic segmentation task. ADE20K includes 150 fine-grained semantic categories, containing twenty thousand and two thousand images in the training set and validation set, respectively. The checkpoints trained on ImageNet-1K [11] at the resolution of \\(224^2\\) are utilized to initialize the backbones. Following Swin [39] and ConvNeXt [40], we firstly evaluate InceptionNeXt with UperNet [73]. The models are trained with AdamW [41] optimizer with learning rate of 6e-5 and batch size of 16 for 160K iterations. Following PVT [67] and PoolFormer [77], InceptionNeXt is also evaluated with Semantic FPN [31]. In common practices [5, 31], the batch size is 16 for the setting of 80K iterations. Following PoolFormer [77], we increase the batch size to 32 and decrease the iterations to 40K to speed up training. AdamW [30, 41] is adopted with a learning rate of 2e-4 and a polynomial decay schedule of 0.9 power. Our code is based on PyTorch [45] and mmsegmentation [8]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Results. For segmentation with UpNet [73], the results are shown in Table 6. As can be seen, InceptionNeXt con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5678" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.091, + 0.089, + 0.878, + 0.251 + ], + "angle": 0, + "content": "
AblationVariantParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
BaselineNone (InceptionNeXt-T)28.14.2901290082.3
BranchRemove horizontal band kernel28.04.2947309381.9
Remove vertical band kernel28.04.2954317381.9
Remove small band kernel28.04.2940300482.0
horizontal and vertical band kernel in parallel → in sequence28.14.2903297182.1
Band kernel sizeBand kernel size 11 → 728.04.2905294682.1
Band kernel size 11 → 928.14.2904291682.1
Band kernel size 11 → 1328.14.2896289582.0
Convolution branch ratioConv. branch ratio 1/8 → 1/428.14.2834249982.2
Conv. branch ratio 1/8 → 1/1628.04.2936309781.8
NormalizationBatch Norm [29] → Layer Norm [1]28.14.2721264682.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.252, + 0.895, + 0.293 + ], + "angle": 0, + "content": "Table 8. Ablation for InceptionNeXt on ImageNet-1K classification benchmark. InceptionNeXt-T is utilized as the baseline for the ablation study. Top-1 accuracy on the validation set is reported. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 and batch size of 128." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.471, + 0.392 + ], + "angle": 0, + "content": "sistently outperforms Swin [39] and ConvNeXt [40] for different model sizes. In the method of Semantic FPN [31] as shown in Table 7, InceptionNeXt significantly surpasses other backbones, like PVT [67] and PoolFormer [77]. These results show that InceptionNeXt also has a high potential for dense prediction tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.405, + 0.24, + 0.42 + ], + "angle": 0, + "content": "4.3. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.471, + 0.461 + ], + "angle": 0, + "content": "We conduct ablation studies on ImageNet-1K [11, 54] using InceptionNeXt-T as baseline from the following aspects." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.466, + 0.47, + 0.784 + ], + "angle": 0, + "content": "Branch. Inception depthwise convolution includes four branches, three convolutional ones, and identity mapping. When removing any branch of horizontal or vertical band kernel, performance significantly drops from \\(82.3\\%\\) to \\(81.9\\%\\), demonstrating the importance of these two branches. This is because these two branches with band kernels can enlarge the receptive field of the model. For the branch of small square kernel size of \\(3 \\times 3\\), removing it can still achieve up to \\(82.0\\%\\) top-1 accuracy and bring higher throughput. This inspires us that if we attach more importance to the model speed, the simple version of InceptionNeXt without the square kernel of \\(3 \\times 3\\) can be adopted. For the band kernel, Inception v3 mostly equips them in a sequential way. We find that this assembling method can also obtain similar performance and even a little speed up the model. A possible reason is that PyTorch/CUDA may have optimized sequential convolutions well, and we only implement the parallel branches at a high level (see Algorithm 1). We believe the parallel method will be faster when it is optimized better. Thus, parallel method for the band kernels is adopted by default." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.789, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Band kernel size. It is found the performance can be improved from kernel size 7 to 11, but it drops when the band kernel size increases to 13. This phenomenon may result from the optimization and can be solved by methods like structural re-parameterization [13, 14]. For simplicity, we set the kernel size as 11 by default except for atto size." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Convolution branch ratio. When the ratio increases from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.3, + 0.892, + 0.407 + ], + "angle": 0, + "content": "1/8 to 1/4, performance improvement can not be observed. Ma et al. [42] also point out that it is not necessary for all channels to conduct convolution. But when the ratio decreases to 1/16, it brings a serious performance drop. This is because a smaller ratio would limit the degree of token mixing, resulting in performance drop. We thus set the convolution branch ratio as 1/8 by default except for atto size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.487 + ], + "angle": 0, + "content": "Normalization. When replacing the Batch Normalization [29] with Layer Normalization [1], the performance improvement improve by \\(0.1\\%\\) but suffer throughput drop in both training and inference. Since this paper focuses on efficiency, we adopt Batch Normalization for InceptionNeXt." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.619, + 0.512 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.716 + ], + "angle": 0, + "content": "In this work, we propose an effective and efficient CNN architecture, InceptionNeXt, which enjoys a better trade-off between the practical speed and the performance than previous network architectures. InceptionNeXt decomposes large-kernel depthwise convolution along channel dimension into four parallel branches, including identity mapping, a small square kernel, and two orthogonal band kernels. All these four branches are much more computationally efficient than a large-kernel depthwise convolution in practice, and can also work together to have a large spatial receptive field for good performance. Extensive experimental results demonstrate the superior performance and the high practical efficiency of InceptionNeXt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This project is supported by the National Research Foundation Singapore under its Medium Sized Center for Advanced Robotics Technology Innovation, and the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2). Weihao Yu was partly supported by Snap Research Fellowship, Google's TPU Research Cloud (TRC), and Google Cloud Research Credits program. Pan Zhou was supported by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant. We would like to thank Ross Wightman for integrating the model and code into Hugging Face's python-image-models repository." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5679" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. 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Although such depth-wise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves $\sim 60\%$ throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation, which poses a challenging problem: How to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e., small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely InceptionNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves $1.6 \times$ higher training throughputs than ConvNeX-T, as well as attains $0.2\%$ top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint. + +# 1. Introduction + +Reviewing the history of deep learning [35], Convolutional Neural Networks (CNNs) [33, 34] are definitely the most popular models in computer vision. The watershed moment arrived in 2012 when AlexNet [32] claimed victory in the ImageNet contest, ushering in a new era for CNNs in computer vision [11, 32, 54]. Since then, a myriad of influential + +![](images/e9593823df4f4baf048a0deb0bd33c88f053cc8c9d63562a3eaae1fe0f1599f6.jpg) +Figure 1. Trade-off between accuracy and training throughput. All models are trained under the DeiT training hyperparameters [39, 40, 64, 72]. The training throughput is measured on an A100 GPU with batch size of 128. ConvNeXt-T/kn means variants with depthwise convolution kernel size of $n \times n$ . InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy. + +CNNs has emerged like Network In Network [37], VGG [56], Inception Nets [58], ResNe(X)t [22, 74], DenseNet [27] and other efficient models [25, 55, 61, 62, 84]. + +Motivated by the great achievement of Transformer in NLP, researchers attempt to integrate its modules or blocks into vision CNN models [2, 4, 28, 70], e.g., the representative works like Non-local Neural Networks [70] and DETR [4], or even make self-attention as stand-alone primitive [50, 85]. Moreover, inspired by the language generative pre-training [46], Image GPT (iGPT) [6] treats pixels as tokens and adopts pure Transformer for visual self-supervised learning. However, iGPT faces limitations in handling high-resolution images due to computational costs [6]. The breakthrough came with Vision Transformer (ViT) [16], which treats image patches as tokens, leverages a pure Transformer as the backbone, and has demonstrated remarkable performance in image classification after large-scale supervised image pre-training. + +Apparently, the success of ViT [16] further ignites the enthusiasm for Transformer's application in computer vi + +![](images/5d96a8d1443d26dc2e077572919600dc4f70fadfed9982c167f98d62b8a4d2f1.jpg) +Figure 2. Block illustration of MetaFormer, MetaNext, ConvNeXt and InceptionNeXt. Similar to MetaFormer block [77], MetaNeXt is a general block abstracted from ConvNeXt [40]. MetaNeXt can be regarded as a simpler version obtained from MetaFormer by merging two residual sub-blocks into one. It is worth noting that the token mixer used in MetaNeXt cannot be too complex (e.g., self-attention [66]) or it may fail to train to converge. By specifying the token mixer as depthwise convolution or Inception depthwise convolution, the model is instantiated as ConvNeXt or InceptionNeXt block. Compared with ConvNeXt, InceptionNeXt is more efficient because it decomposes expensive large-kernel depthwise convolution into four efficient parallel branches. + +sion. Many ViT variants [15, 36, 39, 64, 67, 75, 79], like DeiT [64] and Swin [39], are proposed and have achieved remarkable performance across a wide range of vision tasks. The superior performance of ViT-like models over traditional CNNs (e.g., Swin-T's $81.2\%$ v.s. ResNet-50's $76.1\%$ on ImageNet [11, 22, 39, 54]) leads many researchers to believe that Transformers will eventually replace CNNs and dominate the field of computer vision. + +It is time for CNN to fight back. With advanced training techniques in DeiT [64] and Swin [39], the work of "ResNet strikes back" [72] shows that the performance of ResNet-50 can rise by $2.3\%$ , up to $78.4\%$ . Further, ConvNeXt [40] demonstrates that with modern modules like GELU [23] activation and large kernel size similar to attention window size [39], CNN models can consistently outperform Swin Transformer [39] in various settings and tasks. ConvNeXt is not alone: More and more works have shown similar observations [14, 18, 24, 38, 51, 68, 76, 78], like RepLKNet [14] and SLaK [38]. Among these modern CNN models, the common key feature is the large receptive field that is usually achieved by depthwise convolution [7, 43] with large kernel size (e.g., $7 \times 7$ ). + +However, despite its small FLOPs, depthwise convolution is actually an "expensive" operator because it brings high memory access costs and can be a bottleneck on powerful computing devices, like GPUs [42]. Moreover, as observed in [14], larger kernel sizes lead to significantly lower speeds. As shown in Figure 1, the ConvNeXt-T with a default $7 \times 7$ kernel size is $1.4 \times$ slower than that with small kernel size of $3 \times 3$ , and is $1.8 \times$ slower than ResNet-50, al + +though they have similar FLOPs. However, using a smaller kernel size limits the receptive field, which can result in performance degradation. For example, ConvNeXt-T/k3 suffers a performance drop of $0.6\%$ top-1 accuracy on the ImageNet-1K dataset when compared to ConvNeXt-T/k7, where $kn$ denotes a kernel size of $n \times n$ . + +This poses a challenging problem: How to speed up large-kernel CNNs while preserving their performance? In this paper, we aim to address this issue by building upon ConvNeXt as our baseline and improving the depthwise convolution module. Through our preliminary experiments based on ConvNeXt (see Table 1), we find that not all input channels need to undergo the computationally expensive depthwise convolution operation [42]. Accordingly, we propose to leave some channels unaltered and process only a portion of the channels with the depthwise convolution operation. Next, we propose to decompose large kernel of depthwise convolution into several groups of small kernels in Inception style [58-60]. Specifically, for the processing channels, $1/3$ of channels are conducted with kernel of $3 \times 3$ , another $1/3$ are with $1 \times k$ , and the remaining $1/3$ are with $k \times 1$ . With this new simple and cheap operator, termed as "Inception depthwise convolution", our built model InceptionNeXt achieves a much better trade-off between accuracy and speed. For example, as shown in Figure 1, InceptionNeXt-T achieves higher accuracy than ConvNeXt-T while enjoying $1.6 \times$ speedup of training throughput similar to ResNet-50. + +The contributions of this paper are two-fold. Firstly, we identify the speed bottleneck of ConvNeXt as shown in Fig- + +ure 1. To solve this speed bottleneck while keeping accuracy, we propose Inception depthwise convolution which decomposes the expensive depthwise convolution into three convolution branches with small kernel sizes as well as a branch of identity mapping. Secondly, extensive experiments on image classification and semantic segmentation show a better speed-accuracy trade-off of our model InceptionNeXt than ConvNeXt. We hope that InceptionNeXt can serve as a new CNN baseline to speed up the research of neural architecture design. + +# 2. Related work + +# 2.1. Transformer v.s.CNN + +Transformer [66] was introduced in 2017 for NLP tasks because of its parallel training and also better performance than LSTM. Then many famous NLP models are built on Transformer, including GPT series [3, 44, 46, 47], BERT [12], T5 [49], and OPT [83]. For the application of the Transformer in vision tasks, Vision Transformer (ViT) is definitely the seminal work, showing that Transformer can achieve impressive performance after large-scale supervised training. Follow-up works [20, 52, 53, 64, 67, 69, 79] like Swin [39] continually improve model performance, achieving new state-of-the-art on various vision tasks. These results seem to tell us "Attention is all you need" [66]. + +But it is not that simple. ViT variants like DeiT usually adopt modern training procedures including various advanced techniques of data augmentation [9, 10, 80, 82, 86], regularization [26, 59] and optimizers [30, 41]. Wightman et al. find that with similar training procedures, the performance of ResNet can be largely improved. Besides, Yu et al. [77] argue that the general architecture instead of attention plays a key role in model performance. Han et al. [21] find by replacing attention in Swin with regular or dynamic depthwise convolution, the model can also obtain comparable performance. ConvNeXt [40], a remarkable work, modernizes ResNet into an advanced version with some designs from ViTs, and the resulting models consistently outperform Swin [39]. Other works like RepLKNet [14], VAN [18], FocalNets [76], HorNet [51], SLKNet [38], ConvFormer [78], Conv2Former [24], and InternImage [68] constantly improve performance of CNNs. Despite the high performance obtained, these models neglect efficiency, exhibiting lower speed than ConvNeXt. Actually, ConvNeXt is also not an efficient model compared with ResNet. We argue that CNN models should keep the original advantage of efficiency. Thus, in this paper, we aim to improve the model efficiency of CNNs while maintaining high performance. + +# 2.2. Convolution with large kernels. + +Well-known works, like AlexNet [32] and Inception v1 [58] already utilize large kernels up to $11 \times 11$ and $7 \times 7$ , respec + +tively. To improve the efficiency of large kernels, VGG [56] proposes to heavily stack $3 \times 3$ convolutions while Inception v3 [59] factorizes $k \times k$ convolution into $1 \times k$ and $k \times 1$ staking sequentially. For depthwise convolution, MixConv [63] splits kernels into several groups from $3 \times 3$ to $k \times k$ . Besides, Peng et al. find that large kernels are important for semantic segmentation and they decompose large kernels similar to Inception v3 [59]. Witnessing the success of Transformer in vision tasks [16, 39, 67], large-kernel convolution is more emphasized since it can offer a large receptive field to imitate attention [21, 40]. For example, ConvNeXt adopts kernel size of $7 \times 7$ for depthwise convolution by default. To employ larger kernels, RepLKNet [14] proposes to utilize structural re-parameterization techniques [13, 81] to scale up kernel size to $31 \times 31$ ; VAN [18] sequentially stacks large-kernel depth-wise convolution (DW-Conv) and depthwise dilation convolution to obtain $21 \times 21$ receptive filed; FocalNets [76] employ a gating mechanism to fuse multilevel features from stacking depthwise convolutions; SegNeXt [17] learns multi-scale features by multiple branches of staking $1 \times k$ and $k \times 1$ . Recently, SLaK [38] factorizes large kernel $k \times k$ into two small non-square kernels ( $k \times s$ and $s \times k$ with $s < k$ ). Unlike these works, we do not aim to scale up larger kernels. Instead, we target efficiency and decompose large kernels in a simple and speed-friendly way while keeping comparable performance. + +# 3. Formulation and Method + +# 3.1.MetaNeXt + +Formulation of MetaNeXt Block. In ConvNeXt [40], for its each ConvNeXt block, the input $X$ is first processed by a depthwise convolution to propagate information along spatial dimensions. We follow MetaFormer [77] to abstract the depthwise convolution as a token mixer which is responsible for spatial information interaction. Accordingly, as shown in the second subfigure in Figure 2, the ConvNeXt is abstracted as MetaNeXt block. Formally, in a MetaNeXt block, its input $X$ is firstly processed as + +$$ +X ^ {\prime} = \operatorname {T o k e n M i x e r} (X), \tag {1} +$$ + +where $X, X' \in \mathbb{R}^{B \times C \times H \times W}$ with $B, C, H$ and $W$ respectively denoting batch size, channel number, height and width. Then the output from the token mixer is normalized + +$$ +Y = \operatorname {N o r m} \left(X ^ {\prime}\right). \tag {2} +$$ + +After normalization [1, 29], the features are then fed into an MLP module which consists of two fully-connected layers with an activation function between them, the same as feed-forward network in Transformer [66]. The two fully-connected layers can also be implemented by $1 \times 1$ convolutions. Also, shortcut connection [22, 57] is adopted. This + +Algorithm 1 Inception Depthwise Convolution (PyTorch-like Code) +```python +import torch.nn as nn +class InceptionDWConv2d(nnModule): def __init__(self, in_channels, square_kernel_size=3, band_kernel_size=11, branch_ratio=1/8): super().__init_(g) $\mathrm{gc} =$ int(in_channels * branch_ratio) # channel number of a convolution branch self.dwconv_hw = nn.Conv2d(gc, gc, square_kernel_size, padding= square_kernel_size//2, groups=gc) self.dwconv_w = nn.Conv2d(gc, gc, kernel_size = (1, band_kernel_size), padding=(0, band_kernel_size//2), groups=gc) self.dwconv_h = nn.Conv2d(gc, gc, kernel_size = (band_kernel_size, 1), padding=( band_kernel_size//2, 0), groups=gc) self.split_Indexes = (gc, gc, gc, in_channels -3*gc) def forward(self,x): #B,C,H,W=x.shape x_hw,x_w,x_h,x_id=torch.split(x,self.split.Indexes,dim=1) return torch.cat( (self.dwconv_hw(x_hw), self.dwconv_w(x_w), self.dwconv_h(x_h), x_id), dim=1) +``` + +process can be expressed by + +$$ +Y = \operatorname {C o n v} _ {1 \times 1} ^ {r C \rightarrow C} \left\{\sigma \left[ \operatorname {C o n v} _ {1 \times 1} ^ {C \rightarrow r C} (Y) \right]\right\} + X, \tag {3} +$$ + +where $\mathrm{Conv}_{k\times k}^{C_i\to C_o}$ means convolution with kernel size of $k\times k$ input channels of $C_i$ and output channels of $C_o$ . $r$ is the expansion ratio and $\sigma$ denotes activation function. + +Comparison to MetaFormer block. As shown in Figure 2, it can be found that MetaNeXt block shares similar modules with MetaFormer block [77], e.g., token mixer and MLP. Nevertheless, a critical difference between the two models lies in the number of shortcut connections [22, 57]. MetaNeXt block implements a single shortcut connection, whereas the MetaFormer block incorporates two, one for the token mixer and the other for the MLP. From this aspect, MetaNeXt block can be regarded as a result of merging two residual sub-blocks from MetaFormer, thereby simplifying the overall architecture. As a result, the MetaNeXt architecture exhibits a higher speed compared to MetaFormer. However, this simpler design comes with a limitation: the token mixer component in MetaNeXt cannot be complicated (e.g., Attention) as shown in our experiments (Table 5). + +Instantiation to ConvNeXt. As shown in Figure 2, in ConvNeXt, the token mixer is simply implemented by a depth- + +wise convolution + +$$ +X ^ {\prime} = \operatorname {T o k e n M i x e r} (X) = \operatorname {D W C o n v} _ {k \times k} ^ {C \rightarrow C} (X), \tag {4} +$$ + +where $\mathrm{DWConv}_{k\times k}^{C\to C}$ denotes depthwise convolution with kernel size of $k\times k$ . In ConvNeXt, $k$ is set as 7 by default. + +3.2. Inception depthwise convolution + +
Kernel size of DWConvConvolution ratioParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
7 × 71.028.64.5575241382.1*
5 × 51.028.44.4675270482.0
3 × 31.028.34.4798280281.5
3 × 31/228.34.4818274081.4
3 × 33/828.34.4847276281.4
3 × 31/428.34.4871280881.3
3 × 31/828.34.4901283380.8
3 × 31/1628.34.4916284680.1
+ +Table 1. Preliminary experiments based on ConvNeXt-T. Convolution ratio means the ratio of channels to be processed by depthwise convolution while the other channels keep unchanged. Throughputs are measured on an A100 GPU with batch size of 128 and TF32. * The result is reported in ConvNeXt paper [40]. + +Preliminary experiments on ConvNeXt-T. We first conducted preliminary experiments based on ConvNeXt-T and report the results in Table 1. Firstly, the kernel size of depthwise convolution is reduced from $7 \times 7$ to $3 \times 3$ . Compared to the model with kernel size of $7 \times 7$ , the one with kernel size of $3 \times 3$ enjoys $1.4 \times$ higher training throughput, but suffers a significant performance drop from $82.1\%$ to $81.5\%$ . Next, inspired by ShuffleNet V2 [42], we only feed partial input channels into depthwise convolution while the remaining ones keep unchanged. The number of processed input channels is controlled by a ratio. It is found that when the ratio is reduced from 1 to $1/4$ , the training throughput can be further improved while the performance almost maintains. In summary, these preliminary experiments convey two findings on ConvNeXt. Finding 1: Large-kernel depthwise convolution is the speed bottleneck. Finding 2: Processing partial channels is good enough in single depthwise convolution layer [42]. + +Formulation. Based on the above findings, we propose a new type of convolution to keep both accuracy and effi + +
Conv. typeParamsFLOPs
Conventional conv.k2C22k2C2HW
Depthwise conv.k2C2k2CHW
Inception dep. conv.(2k + 9)C/8(2k + 9)CHW/4
+ +Table 2. Complexity of different types of convolution. For simplicity, assume input and output channels are the same, and the bias term is omitted. $k$ , $C$ , $H$ and $W$ denote kernel size, channel number, height and width, respectively. The parameters and FLOPs of vanilla convolution and depthwise convolution are quadratic to kernel size $k$ . In contrast, Inception depthwise convolution is linear to $k$ . + +![](images/70948b99a6a3ed70a3dfe3569c21ebb3546bebdd56acbafa58b85eb1169d7fbd.jpg) +Figure 3. Comparison of FLOPs between depthwise convolution and Inception depthwise convolution. Inception depthwise convolution is much more efficient than depthwise convolution as kernel size increases. + +
Stage#TokensLayer SpecificationInceptionNeXt
ATSB
1H/4 × W/4Down-samplingKernel Size4 × 4, stride 4
Embed. Dim.4096128
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
2H/8 × W/8Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.90192256
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
3H/16 × W/16Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.180384512
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block6927
4H/32 × W/32Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.3207681024
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio3
# Block23
Global average pooling, MLP
Parameters (M)4.228.149.486.7
MACs (G)0.54.28.414.9
+ +Table 3. Configurations of InceptionNeXt models which have similar model configurations to ConvNeXt [40]. "A", "T", "S" and "B" represent "Atto", "Tiny", "Small" and "Base", respectively. + +ciency. According to Fingding 2, we leave partial channels unchanged and denote them as a branch of identity mapping. Motivated by Fingding 1, for the processing channels, we propose to decompose the depthwise operations in Inception style [58-60]. Inception [58] utilizes several branches of small kernels (e.g., $3 \times 3$ ) and large kernels (e.g., $5 \times 5$ ). Similarly, we adopt $3 \times 3$ as one of our branches but get rid of the usage of the large square kernels because of their slow practical speed. Instead, large kernel $k_h \times k_w$ + +is decomposed as $1 \times k_w$ and $k_h \times 1$ inspired by Inception v3 [59]. + +Specifically, for input $X$ , we split it into four groups along the channel dimension, + +$$ +\begin{array}{l} X _ {\mathrm {h w}}, X _ {\mathrm {w}}, X _ {\mathrm {h}}, X _ {\mathrm {i d}} = \operatorname {S p l i t} (X) \tag {5} \\ = X _ {:,: g}, X _ {: g: 2 g}, X _ {: 2 g: 3 g}, X _ {: 3 g:}, \\ \end{array} +$$ + +where $g$ is the channel numbers of convolution branches. We can set a ratio $r_g$ to determine the branch channel numbers by $g = r_g C$ . Next, the splitting inputs are fed into different parallel branches, + +$$ +\begin{array}{l} X _ {\mathrm {h w}} ^ {\prime} = \operatorname {D W C o n v} _ {k _ {s} \times k _ {s}} ^ {g \rightarrow g} g (X _ {\mathrm {h w}}), \\ \begin{array}{l}X _ {\mathrm {w}} ^ {\prime} = \operatorname {D W C o n v} _ {1 \times k _ {b}} ^ {g \rightarrow g} g \left(X _ {\mathrm {w}}\right),\\V ^ {\prime} = \operatorname {D W C o n v} _ {1 \times k _ {b}} ^ {g \rightarrow g} (X)\end{array}\tag {6} \\ X _ {\mathrm {h}} ^ {\prime} = \operatorname {D W C o n v} _ {k _ {b} \times 1} ^ {g \rightarrow g} g (X _ {\mathrm {h}}), \\ X _ {\mathrm {i d}} ^ {\prime} = X _ {\mathrm {i d}}, \\ \end{array} +$$ + +where $k_{s}$ denotes the small square kernel size set as 3 by default; $k_{b}$ represents the band kernel size set as 11 by default. Finally, the outputs from each branch are concatenated, + +$$ +X ^ {\prime} = \operatorname {C o n c a t} \left(X _ {\mathrm {h w}} ^ {\prime}, X _ {\mathrm {w}} ^ {\prime}, X _ {\mathrm {h}} ^ {\prime}, X _ {\mathrm {i d}} ^ {\prime}\right). \tag {7} +$$ + +The illustration of InceptionNeXt block is shown in Figure 2. Moreover, its PyTorch [45] code is summarized in Algorithm 1. + +Complexity. The complexity of three types of convolution, i.e., conventional, depthwise, and Inception depthwise convolution is shown in Table 2. As can be seen, Inception depthwise convolution is much more efficient than the other two types of convolution in terms of parameter numbers of FLOPs. Inception depthwise convolution consumes parameters and FLOPs linear to both channel and kernel size. The comparison of depthwise and Inception depthwise convolutions regarding FLOPs is also clearly shown in Figure 3. + +# 3.3. InceptionNeXt + +Based on InceptionNeXt block, we can build a series of models named InceptionNeXt. Since ConvNeXt [40] is the our main comparing baseline, we mainly follow it to build models with several sizes [71]. Specifically, similar to ResNet [22] and ConvNeXt, InceptionNeXt also adopts 4-stage framework. The same as ConvNeXt, the numbers of 4 stages are [2, 2, 6, 2] for atto size, [3, 3, 9, 3] for small size and [3, 3, 27, 3] for base size. We adopt Batch Normalization since this paper emphasizes speed. Another difference with ConvNeXt is that InceptionNeXt uses an MLP ratio of 3 in stage 4 and moves the saved parameters to the classifier, which can help reduce a few FLOPs (e.g., $3\%$ for base size). The detailed model configurations are reported in Table 3. + +
ModelMixing TypeImage sizeParams (M)MACs (G)Throughput (img/s)Top-1 (%)
A1002080Ti
TrainInferTrainInfer
MobileNetV2 (1.4) [55]Conv22426.10.6010015190471185974.7
EfficientNet-B0 [61]Conv22425.30.409545502464194477.1
GhostNet 1.3× [19]Conv22427.30.249467451589275775.7
ConvNeXt-A [40, 71]Conv22423.70.558354539345156875.7
InceptionNeXt-A (Ours)Conv22424.20.512661+219%9876+118%992+188%3595+129%75.3-0.4
DeiT-S [64]Attn2242224.61227378127678479.8
T2T-ViT-14 [79]Attn2242224.8----81.5
TNT-S [20]Attn2242245.2----81.5
Swin-T [39]Attn2242294.5564176818455481.3
Focal-T [75]Attn2242294.9----82.2
ResNet-50 [22, 72]Conv2242264.1969314927897778.4
RSB-ResNet-50 [22, 72]Conv2242264.1969314927897779.8
RegNetY-4G [48, 72]Conv2242214.0670269422285981.3
FocalNet-T [76]Conv2242294.5----82.3
ConvNeXt-T [40]Conv2242294.5575241317759082.1
InceptionNeXt-T (Ours)Conv2242284.2901+57%2900+20%254+44%822+39%82.3+0.2
T2T-ViT-19 [79]Attn2242398.5----81.9
PVT-Medium [67]Attn2242446.7----81.2
Swin-S [39]Attn2242508.7359113110932883.0
Focal-S [75]Attn2242519.1----83.5
RSB-ResNet-101 [22, 72]Conv2242457.9620205716859281.3
RegNetY-8G [48, 72]Conv2242398.0689132612448082.1
FocalNet-S [76]Conv2242508.7----83.5
ConvNeXt-S [40]Conv2242508.7361153510535383.1
InceptionNeXt-S (Ours)Conv2242498.4521+44%1750+14%130+24%447+27%83.5+0.4
DeiT-B [64]Attn22428617.554116088625981.8
T2T-ViT-24 [79]Attn22426413.8----82.3
TNT-B [20]Attn22426614.1----82.9
PVT-Large [67]Attn2242629.8----81.7
Swin-B [39]Attn22428815.42718437222383.5
Focal-B [75]Attn22429016.0----83.8
RSB-ResNet-152 [22, 72]Conv22426011.6437145711541581.8
RegNetY-16G [48, 72]Conv22428415.932211007629582.2
RepLKNet-31B [14]Conv22427915.3----83.5
FocalNet-B [76]Conv22428915.4----83.9
ConvNeXt-B [40]Conv22428915.426711226823683.8
InceptionNeXt-B (Ours)Conv22428714.9375+40%1244+11%80+18%287+22%84.0+0.2
DeiT-B [64]Attn38428655.4131361257383.1
Swin-B [39]Attn38428847.1104296216584.5
RepLKNet-31B [14]Conv38427945.1----84.8
ConvNeXt-B [40]Conv38428945.095393237985.1
InceptionNeXt-B (Ours)Conv38428743.6139+46%428+9%27+17%97+23%85.2+0.1
+ +Table 4. Performance of models trained on ImageNet-1K. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 (TensorFloat-32), and on a 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of "Channel First" and "Channel Last" memory layouts are reported. + +# 4. Experiment + +# 4.1. Image classification + +Setup. For the image classification task, ImageNet-1K [11, 54] is one of the most commonly-used benchmarks, which contains around 1.3 million images in the training set and 50 thousand images in the validation set. To fairly compare with the widely-used baselines, e.g., Swin [39] and ConvNeXt [40], we mainly follow the training hyperparameters from DeiT [64] without distillation. Specifically, the models are trained by AdamW [41] optimizer with a learning rate $lr = 0.001 \times \text{batchsize} / 1024$ ( $lr = 4e - 3$ and batchsize $= 4096$ are used in this paper the same as + +ConvNeXt). Following DeiT, data augmentation includes standard random resized crop, horizontal flip, RandAugment [10], Mixup [82], CutMix [80], Random Erasing [86] and color jitter. For regularization, label smoothing [59], stochastic depth [26], and weight decay are adopted. Like ConvNeXt, we also use LayerScale [65], a technique to help train deep models. Our code is based on PyTorch [45] and timm [71]. + +Results. We compare InceptionNeXt with various state-of-the-art models, including attention-based and convolution-based models. As can be seen in Table 4, InceptionNeXt achieves highly competitive performance as well as + +
ModelParams (M)MACs (G)Throughput (img/s)Top-1 (%)
TrainInfer
DeiT-S [64]224.627678479.8
MetaNeXt-Attn224.62888163.9
ConvNeXt-S (iso.) [40]224.327087979.7
InceptionNeXt-S (iso.)224.231099879.7
+ +enjoys higher speed. InceptionNeXt consistently enjoys better accuracy-speed trade-off than ConvNeXt [40]. For example, InceptionNeXt-T not only surpasses ConvNeXt-T by $0.2\%$ , but also enjoys $1.6 \times 1.2 \times$ training/inference throughputs on A100 than ConvNeXts, similar to those of ResNet-50. That is to say, InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy. Moreover, following Swin and ConvNeXt, we also finetuned the InceptionNeXt-B trained at the resolution of $224 \times 224$ to $384 \times 384$ for 30 epochs. We can see that InceptionNeXt-B obtains higher train and inference throughputs than ConvNeXt-B while keeping competitive accuracy. + +It is observed that the speed improvement is much more significant for the lightweight model size, and the improvement gradually becomes smaller when the model size scales up. The reason is that computation complexity of depthwise and Inception depthwise convolutions are linear to channel number, i.e., $\mathcal{O}(C)$ where $C$ is channel number. For MLPs, their computation complexity is $\mathcal{O}(C^2)$ . For larger models (larger $C$ ), its computation is further dominated by MLPs. By only improving depthwise convolution, the speed improvement becomes smaller when the model is larger. + +Besides the 4-stage framework [22, 39, 56], another notable one is ViT-style [16] isotropic architecture which has only one stage. To match the parameters and MACs of DeiT-S, we construct InceptionNeXt-S (iso.) following ConvNeXt-S (iso.) [40]. Specifically, we set the embedding dimension as 384 and the block number as 18. Besides, we build a model called MetaNeXt-Attn which is instantiated from MetaNeXt block by specifying self-attention as token mixer. The aim of this model is to investigate whether it is possible to merge two residual sub-blocks of the Transformer block into a single one. The experiment results are shown in Table 5. It can be seen that InceptionNeXt can also perform well with the isotropic architecture, demonstrating InceptionNeXt exhibits good generalization across different frameworks. It is worth noting that MetaNeXt-Attn could not be trained to converge and only achieved an accuracy of $3.9\%$ . This result suggests that, unlike the token mixer in MetaFormer, the token mixer in MetaNeXt cannot be too complex. If it is, the model may not be trainable. + +Table 5. Comparison among ViT, isotropic ConvNeXt and InceptionNeXt. MetaNeXt-Attn is instantiated from MetaNeXt with token mixer of self-attention [66]. The throughputs are measured on 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of "Channel First" and "Channel Last" memory layouts are reported. + +
BackboneUperNet
Params (M)MACs (G)FPSmIoU (%)
Swin-T [39]6094520.645.8
ConvNeXt-T [40]6093920.646.7
InceptionNeXt-T5693322.747.9
Swin-S [39]81103816.249.5
ConvNeXt-S [40]82102716.849.6
InceptionNeXt-S78102017.650.0
Swin-B [39]121118816.249.7
ConvNeXt-B [40]122117015.749.9
InceptionNeXt-B115115917.550.6
+ +Table 6. Performance of semantic segmentation with UperNet [73] on ADE20K [87] validation set. Images are cropped to $512 \times 512$ for training. The MACs are measured with input size of $512 \times 2048$ . The FPS are benchmarked on 2080Ti. + +
BackboneSemantic FPN
Params (M)MACs (G)FPSmIoU (%)
ResNet-50 [22]294630.236.7
PVT-Small [67]284527.239.8
PoolFormer-S24 [77]233928.840.3
InceptionNeXt-T284431.443.1
ResNet-101 [22]486522.238.8
ResNeXt-101-32x4d [74]4765-39.7
PVT-Medium [67]486120.041.6
PoolFormer-S36 [77]354821.642.0
PoolFormer-M36 [77]606815.442.4
InceptionNeXt-S506520.745.6
PVT-Large [67]658016.042.1
ResNeXt-101-64x4d [74]86104-40.2
PoolFormer-M48 [77]778212.142.7
InceptionNeXt-B8510020.246.4
+ +Table 7. Performance of semantic segmentation with Semantic FPN [31] on ADE20K [87] validation set. Images are cropped to $512 \times 512$ for training. The MACs are measured with input size of $512 \times 512$ . The FPS are benchmarked on 2080Ti. + +# 4.2. Semantic segmentation + +Setup. ADE20K [87], a commonly used scene parsing benchmark, is used to evaluate our models on semantic segmentation task. ADE20K includes 150 fine-grained semantic categories, containing twenty thousand and two thousand images in the training set and validation set, respectively. The checkpoints trained on ImageNet-1K [11] at the resolution of $224^2$ are utilized to initialize the backbones. Following Swin [39] and ConvNeXt [40], we firstly evaluate InceptionNeXt with UperNet [73]. The models are trained with AdamW [41] optimizer with learning rate of 6e-5 and batch size of 16 for 160K iterations. Following PVT [67] and PoolFormer [77], InceptionNeXt is also evaluated with Semantic FPN [31]. In common practices [5, 31], the batch size is 16 for the setting of 80K iterations. Following PoolFormer [77], we increase the batch size to 32 and decrease the iterations to 40K to speed up training. AdamW [30, 41] is adopted with a learning rate of 2e-4 and a polynomial decay schedule of 0.9 power. Our code is based on PyTorch [45] and mmsegmentation [8]. + +Results. For segmentation with UpNet [73], the results are shown in Table 6. As can be seen, InceptionNeXt con + +
AblationVariantParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
BaselineNone (InceptionNeXt-T)28.14.2901290082.3
BranchRemove horizontal band kernel28.04.2947309381.9
Remove vertical band kernel28.04.2954317381.9
Remove small band kernel28.04.2940300482.0
horizontal and vertical band kernel in parallel → in sequence28.14.2903297182.1
Band kernel sizeBand kernel size 11 → 728.04.2905294682.1
Band kernel size 11 → 928.14.2904291682.1
Band kernel size 11 → 1328.14.2896289582.0
Convolution branch ratioConv. branch ratio 1/8 → 1/428.14.2834249982.2
Conv. branch ratio 1/8 → 1/1628.04.2936309781.8
NormalizationBatch Norm [29] → Layer Norm [1]28.14.2721264682.4
+ +Table 8. Ablation for InceptionNeXt on ImageNet-1K classification benchmark. InceptionNeXt-T is utilized as the baseline for the ablation study. Top-1 accuracy on the validation set is reported. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 and batch size of 128. + +sistently outperforms Swin [39] and ConvNeXt [40] for different model sizes. In the method of Semantic FPN [31] as shown in Table 7, InceptionNeXt significantly surpasses other backbones, like PVT [67] and PoolFormer [77]. These results show that InceptionNeXt also has a high potential for dense prediction tasks. + +# 4.3. Ablation studies + +We conduct ablation studies on ImageNet-1K [11, 54] using InceptionNeXt-T as baseline from the following aspects. + +Branch. Inception depthwise convolution includes four branches, three convolutional ones, and identity mapping. When removing any branch of horizontal or vertical band kernel, performance significantly drops from $82.3\%$ to $81.9\%$ , demonstrating the importance of these two branches. This is because these two branches with band kernels can enlarge the receptive field of the model. For the branch of small square kernel size of $3 \times 3$ , removing it can still achieve up to $82.0\%$ top-1 accuracy and bring higher throughput. This inspires us that if we attach more importance to the model speed, the simple version of InceptionNeXt without the square kernel of $3 \times 3$ can be adopted. For the band kernel, Inception v3 mostly equips them in a sequential way. We find that this assembling method can also obtain similar performance and even a little speed up the model. A possible reason is that PyTorch/CUDA may have optimized sequential convolutions well, and we only implement the parallel branches at a high level (see Algorithm 1). We believe the parallel method will be faster when it is optimized better. Thus, parallel method for the band kernels is adopted by default. + +Band kernel size. It is found the performance can be improved from kernel size 7 to 11, but it drops when the band kernel size increases to 13. This phenomenon may result from the optimization and can be solved by methods like structural re-parameterization [13, 14]. For simplicity, we set the kernel size as 11 by default except for atto size. + +Convolution branch ratio. When the ratio increases from + +1/8 to 1/4, performance improvement can not be observed. Ma et al. [42] also point out that it is not necessary for all channels to conduct convolution. But when the ratio decreases to 1/16, it brings a serious performance drop. This is because a smaller ratio would limit the degree of token mixing, resulting in performance drop. We thus set the convolution branch ratio as 1/8 by default except for atto size. + +Normalization. When replacing the Batch Normalization [29] with Layer Normalization [1], the performance improvement improve by $0.1\%$ but suffer throughput drop in both training and inference. Since this paper focuses on efficiency, we adopt Batch Normalization for InceptionNeXt. + +# 5. Conclusion + +In this work, we propose an effective and efficient CNN architecture, InceptionNeXt, which enjoys a better trade-off between the practical speed and the performance than previous network architectures. InceptionNeXt decomposes large-kernel depthwise convolution along channel dimension into four parallel branches, including identity mapping, a small square kernel, and two orthogonal band kernels. All these four branches are much more computationally efficient than a large-kernel depthwise convolution in practice, and can also work together to have a large spatial receptive field for good performance. Extensive experimental results demonstrate the superior performance and the high practical efficiency of InceptionNeXt. + +Acknowledgement. This project is supported by the National Research Foundation Singapore under its Medium Sized Center for Advanced Robotics Technology Innovation, and the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2). Weihao Yu was partly supported by Snap Research Fellowship, Google's TPU Research Cloud (TRC), and Google Cloud Research Credits program. Pan Zhou was supported by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant. We would like to thank Ross Wightman for integrating the model and code into Hugging Face's python-image-models repository. + +# References + +[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 7 \ No newline at end of file diff --git a/2024/InceptionNeXt_ When Inception Meets ConvNeXt/images.zip b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ef053b26dc0e4a62ce635fb4d23e98e760b63b82 --- /dev/null +++ b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4afb848f8e133403eae383f7ce70c7e2c9fe577e3bc73a41e5088bc24c4ccfe5 +size 679937 diff --git a/2024/InceptionNeXt_ When Inception Meets ConvNeXt/layout.json b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5f12b75db4147d8454e533c42e8d1309d4b04cb6 --- /dev/null +++ b/2024/InceptionNeXt_ When Inception Meets ConvNeXt/layout.json @@ -0,0 +1,9325 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 143, + 103, + 453, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 103, + 453, + 121 + ], + "spans": [ + { + "bbox": [ + 143, + 103, + 453, + 121 + ], + "type": "text", + "content": "InceptionNeXt: When Inception Meets ConvNeXt" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 142, + 539, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 142, + 539, + 199 + ], + "spans": [ + { + "bbox": [ + 53, + 142, + 539, + 199 + ], + "type": "text", + "content": "Weihao Yu1 Pan Zhou2,3 Shuicheng Yan4 Xinchao Wang1* \n1National University of Singapore 2Singapore Management University 3Sea AI Lab 4Skywork AI \nweihaoyu@u.nus.edu panzhou@smu.edu.sg shuicheng.yan@kunlun-inc.com xinchao@nus.edu.sg \nCode: https://github.com/sail-sg/inceptionnext" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "text", + "content": "Inspired by the long-range modeling ability of ViTs, large-kernel convolutions are widely studied and adopted recently to enlarge the receptive field and improve model performance, like the remarkable work ConvNeXt which employs " + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "text", + "content": " depthwise convolution. Although such depth-wise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves " + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "inline_equation", + "content": "\\sim 60\\%" + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "text", + "content": " throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation, which poses a challenging problem: How to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e., small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely InceptionNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves " + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "inline_equation", + "content": "1.6 \\times" + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "text", + "content": " higher training throughputs than ConvNeX-T, as well as attains " + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 47, + 252, + 290, + 577 + ], + "type": "text", + "content": " top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 600, + 128, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 600, + 128, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 600, + 128, + 612 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "content": "Reviewing the history of deep learning [35], Convolutional Neural Networks (CNNs) [33, 34] are definitely the most popular models in computer vision. The watershed moment arrived in 2012 when AlexNet [32] claimed victory in the ImageNet contest, ushering in a new era for CNNs in computer vision [11, 32, 54]. Since then, a myriad of influential" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 227, + 529, + 386 + ], + "blocks": [ + { + "bbox": [ + 310, + 227, + 529, + 386 + ], + "lines": [ + { + "bbox": [ + 310, + 227, + 529, + 386 + ], + "spans": [ + { + "bbox": [ + 310, + 227, + 529, + 386 + ], + "type": "image", + "image_path": "e9593823df4f4baf048a0deb0bd33c88f053cc8c9d63562a3eaae1fe0f1599f6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 387, + 545, + 453 + ], + "lines": [ + { + "bbox": [ + 305, + 387, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 545, + 453 + ], + "type": "text", + "content": "Figure 1. Trade-off between accuracy and training throughput. All models are trained under the DeiT training hyperparameters [39, 40, 64, 72]. The training throughput is measured on an A100 GPU with batch size of 128. ConvNeXt-T/kn means variants with depthwise convolution kernel size of " + }, + { + "bbox": [ + 305, + 387, + 545, + 453 + ], + "type": "inline_equation", + "content": "n \\times n" + }, + { + "bbox": [ + 305, + 387, + 545, + 453 + ], + "type": "text", + "content": ". InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 468, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 468, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 468, + 545, + 504 + ], + "type": "text", + "content": "CNNs has emerged like Network In Network [37], VGG [56], Inception Nets [58], ResNe(X)t [22, 74], DenseNet [27] and other efficient models [25, 55, 61, 62, 84]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 507, + 546, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 546, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 546, + 687 + ], + "type": "text", + "content": "Motivated by the great achievement of Transformer in NLP, researchers attempt to integrate its modules or blocks into vision CNN models [2, 4, 28, 70], e.g., the representative works like Non-local Neural Networks [70] and DETR [4], or even make self-attention as stand-alone primitive [50, 85]. Moreover, inspired by the language generative pre-training [46], Image GPT (iGPT) [6] treats pixels as tokens and adopts pure Transformer for visual self-supervised learning. However, iGPT faces limitations in handling high-resolution images due to computational costs [6]. The breakthrough came with Vision Transformer (ViT) [16], which treats image patches as tokens, leverages a pure Transformer as the backbone, and has demonstrated remarkable performance in image classification after large-scale supervised image pre-training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Apparently, the success of ViT [16] further ignites the enthusiasm for Transformer's application in computer vi" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5672" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 125, + 72, + 465, + 265 + ], + "blocks": [ + { + "bbox": [ + 125, + 72, + 465, + 265 + ], + "lines": [ + { + "bbox": [ + 125, + 72, + 465, + 265 + ], + "spans": [ + { + "bbox": [ + 125, + 72, + 465, + 265 + ], + "type": "image", + "image_path": "5d96a8d1443d26dc2e077572919600dc4f70fadfed9982c167f98d62b8a4d2f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 545, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 545, + 335 + ], + "type": "text", + "content": "Figure 2. Block illustration of MetaFormer, MetaNext, ConvNeXt and InceptionNeXt. Similar to MetaFormer block [77], MetaNeXt is a general block abstracted from ConvNeXt [40]. MetaNeXt can be regarded as a simpler version obtained from MetaFormer by merging two residual sub-blocks into one. It is worth noting that the token mixer used in MetaNeXt cannot be too complex (e.g., self-attention [66]) or it may fail to train to converge. By specifying the token mixer as depthwise convolution or Inception depthwise convolution, the model is instantiated as ConvNeXt or InceptionNeXt block. Compared with ConvNeXt, InceptionNeXt is more efficient because it decomposes expensive large-kernel depthwise convolution into four efficient parallel branches." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "type": "text", + "content": "sion. Many ViT variants [15, 36, 39, 64, 67, 75, 79], like DeiT [64] and Swin [39], are proposed and have achieved remarkable performance across a wide range of vision tasks. The superior performance of ViT-like models over traditional CNNs (e.g., Swin-T's " + }, + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "type": "inline_equation", + "content": "81.2\\%" + }, + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "type": "text", + "content": " v.s. ResNet-50's " + }, + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "type": "inline_equation", + "content": "76.1\\%" + }, + { + "bbox": [ + 46, + 342, + 287, + 438 + ], + "type": "text", + "content": " on ImageNet [11, 22, 39, 54]) leads many researchers to believe that Transformers will eventually replace CNNs and dominate the field of computer vision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "text", + "content": "It is time for CNN to fight back. With advanced training techniques in DeiT [64] and Swin [39], the work of \"ResNet strikes back\" [72] shows that the performance of ResNet-50 can rise by " + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "text", + "content": ", up to " + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "inline_equation", + "content": "78.4\\%" + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "text", + "content": ". Further, ConvNeXt [40] demonstrates that with modern modules like GELU [23] activation and large kernel size similar to attention window size [39], CNN models can consistently outperform Swin Transformer [39] in various settings and tasks. ConvNeXt is not alone: More and more works have shown similar observations [14, 18, 24, 38, 51, 68, 76, 78], like RepLKNet [14] and SLaK [38]. Among these modern CNN models, the common key feature is the large receptive field that is usually achieved by depthwise convolution [7, 43] with large kernel size (e.g., " + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 46, + 444, + 287, + 612 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "However, despite its small FLOPs, depthwise convolution is actually an \"expensive\" operator because it brings high memory access costs and can be a bottleneck on powerful computing devices, like GPUs [42]. Moreover, as observed in [14], larger kernel sizes lead to significantly lower speeds. As shown in Figure 1, the ConvNeXt-T with a default " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " kernel size is " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "1.4 \\times" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " slower than that with small kernel size of " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": ", and is " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "1.8 \\times" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " slower than ResNet-50, al" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": "though they have similar FLOPs. However, using a smaller kernel size limits the receptive field, which can result in performance degradation. For example, ConvNeXt-T/k3 suffers a performance drop of " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": " top-1 accuracy on the ImageNet-1K dataset when compared to ConvNeXt-T/k7, where " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "kn" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": " denotes a kernel size of " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "n \\times n" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": "This poses a challenging problem: How to speed up large-kernel CNNs while preserving their performance? In this paper, we aim to address this issue by building upon ConvNeXt as our baseline and improving the depthwise convolution module. Through our preliminary experiments based on ConvNeXt (see Table 1), we find that not all input channels need to undergo the computationally expensive depthwise convolution operation [42]. Accordingly, we propose to leave some channels unaltered and process only a portion of the channels with the depthwise convolution operation. Next, we propose to decompose large kernel of depthwise convolution into several groups of small kernels in Inception style [58-60]. Specifically, for the processing channels, " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "1/3" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": " of channels are conducted with kernel of " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": ", another " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "1/3" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": " are with " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "1 \\times k" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": ", and the remaining " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "1/3" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": " are with " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "k \\times 1" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": ". With this new simple and cheap operator, termed as \"Inception depthwise convolution\", our built model InceptionNeXt achieves a much better trade-off between accuracy and speed. For example, as shown in Figure 1, InceptionNeXt-T achieves higher accuracy than ConvNeXt-T while enjoying " + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "inline_equation", + "content": "1.6 \\times" + }, + { + "bbox": [ + 304, + 420, + 546, + 683 + ], + "type": "text", + "content": " speedup of training throughput similar to ResNet-50." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "The contributions of this paper are two-fold. Firstly, we identify the speed bottleneck of ConvNeXt as shown in Fig-" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5673" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "ure 1. To solve this speed bottleneck while keeping accuracy, we propose Inception depthwise convolution which decomposes the expensive depthwise convolution into three convolution branches with small kernel sizes as well as a branch of identity mapping. Secondly, extensive experiments on image classification and semantic segmentation show a better speed-accuracy trade-off of our model InceptionNeXt than ConvNeXt. We hope that InceptionNeXt can serve as a new CNN baseline to speed up the research of neural architecture design." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 201, + 132, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 201, + 132, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 132, + 213 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 218, + 168, + 230 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 168, + 230 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 168, + 230 + ], + "type": "text", + "content": "2.1. Transformer v.s.CNN" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 233, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 287, + 389 + ], + "type": "text", + "content": "Transformer [66] was introduced in 2017 for NLP tasks because of its parallel training and also better performance than LSTM. Then many famous NLP models are built on Transformer, including GPT series [3, 44, 46, 47], BERT [12], T5 [49], and OPT [83]. For the application of the Transformer in vision tasks, Vision Transformer (ViT) is definitely the seminal work, showing that Transformer can achieve impressive performance after large-scale supervised training. Follow-up works [20, 52, 53, 64, 67, 69, 79] like Swin [39] continually improve model performance, achieving new state-of-the-art on various vision tasks. These results seem to tell us \"Attention is all you need\" [66]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 289, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 289, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 289, + 665 + ], + "type": "text", + "content": "But it is not that simple. ViT variants like DeiT usually adopt modern training procedures including various advanced techniques of data augmentation [9, 10, 80, 82, 86], regularization [26, 59] and optimizers [30, 41]. Wightman et al. find that with similar training procedures, the performance of ResNet can be largely improved. Besides, Yu et al. [77] argue that the general architecture instead of attention plays a key role in model performance. Han et al. [21] find by replacing attention in Swin with regular or dynamic depthwise convolution, the model can also obtain comparable performance. ConvNeXt [40], a remarkable work, modernizes ResNet into an advanced version with some designs from ViTs, and the resulting models consistently outperform Swin [39]. Other works like RepLKNet [14], VAN [18], FocalNets [76], HorNet [51], SLKNet [38], ConvFormer [78], Conv2Former [24], and InternImage [68] constantly improve performance of CNNs. Despite the high performance obtained, these models neglect efficiency, exhibiting lower speed than ConvNeXt. Actually, ConvNeXt is also not an efficient model compared with ResNet. We argue that CNN models should keep the original advantage of efficiency. Thus, in this paper, we aim to improve the model efficiency of CNNs while maintaining high performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 671, + 217, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 217, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 217, + 684 + ], + "type": "text", + "content": "2.2. Convolution with large kernels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Well-known works, like AlexNet [32] and Inception v1 [58] already utilize large kernels up to " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "11 \\times 11" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", respec" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": "tively. To improve the efficiency of large kernels, VGG [56] proposes to heavily stack " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " convolutions while Inception v3 [59] factorizes " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " convolution into " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "1 \\times k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "k \\times 1" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " staking sequentially. For depthwise convolution, MixConv [63] splits kernels into several groups from " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": ". Besides, Peng et al. find that large kernels are important for semantic segmentation and they decompose large kernels similar to Inception v3 [59]. Witnessing the success of Transformer in vision tasks [16, 39, 67], large-kernel convolution is more emphasized since it can offer a large receptive field to imitate attention [21, 40]. For example, ConvNeXt adopts kernel size of " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " for depthwise convolution by default. To employ larger kernels, RepLKNet [14] proposes to utilize structural re-parameterization techniques [13, 81] to scale up kernel size to " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "31 \\times 31" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": "; VAN [18] sequentially stacks large-kernel depth-wise convolution (DW-Conv) and depthwise dilation convolution to obtain " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " receptive filed; FocalNets [76] employ a gating mechanism to fuse multilevel features from stacking depthwise convolutions; SegNeXt [17] learns multi-scale features by multiple branches of staking " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "1 \\times k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "k \\times 1" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": ". Recently, SLaK [38] factorizes large kernel " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " into two small non-square kernels (" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "k \\times s" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "s \\times k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "inline_equation", + "content": "s < k" + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": "). Unlike these works, we do not aim to scale up larger kernels. Instead, we target efficiency and decompose large kernels in a simple and speed-friendly way while keeping comparable performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 390, + 451, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 451, + 402 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 451, + 402 + ], + "type": "text", + "content": "3. Formulation and Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 410, + 378, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 410, + 378, + 422 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 378, + 422 + ], + "type": "text", + "content": "3.1.MetaNeXt" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "type": "text", + "content": "Formulation of MetaNeXt Block. In ConvNeXt [40], for its each ConvNeXt block, the input " + }, + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "type": "text", + "content": " is first processed by a depthwise convolution to propagate information along spatial dimensions. We follow MetaFormer [77] to abstract the depthwise convolution as a token mixer which is responsible for spatial information interaction. Accordingly, as shown in the second subfigure in Figure 2, the ConvNeXt is abstracted as MetaNeXt block. Formally, in a MetaNeXt block, its input " + }, + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 430, + 547, + 538 + ], + "type": "text", + "content": " is firstly processed as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 376, + 548, + 545, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 548, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 376, + 548, + 545, + 562 + ], + "type": "interline_equation", + "content": "X ^ {\\prime} = \\operatorname {T o k e n M i x e r} (X), \\tag {1}", + "image_path": "e3d04049b309d7f1569a9105048bfd69b78c86647861441fe538e379906bfcdc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "inline_equation", + "content": "X, X' \\in \\mathbb{R}^{B \\times C \\times H \\times W}" + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "inline_equation", + "content": "B, C, H" + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 571, + 547, + 608 + ], + "type": "text", + "content": " respectively denoting batch size, channel number, height and width. Then the output from the token mixer is normalized" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 389, + 618, + 545, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 618, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 389, + 618, + 545, + 631 + ], + "type": "interline_equation", + "content": "Y = \\operatorname {N o r m} \\left(X ^ {\\prime}\\right). \\tag {2}", + "image_path": "d6ce2d638202359eb925f223def342da057b7b19318408a55a9622d3b0b1b244.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "After normalization [1, 29], the features are then fed into an MLP module which consists of two fully-connected layers with an activation function between them, the same as feed-forward network in Transformer [66]. The two fully-connected layers can also be implemented by " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " convolutions. Also, shortcut connection [22, 57] is adopted. This" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5674" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 97, + 286, + 381 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "Algorithm 1 Inception Depthwise Convolution (PyTorch-like Code)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 97, + 286, + 381 + ], + "lines": [ + { + "bbox": [ + 47, + 97, + 286, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 286, + 381 + ], + "type": "text", + "content": "import torch.nn as nn \nclass InceptionDWConv2d(nnModule): def __init__(self, in_channels, square_kernel_size=3, band_kernel_size=11, branch_ratio=1/8): super().__init_(g) " + }, + { + "bbox": [ + 47, + 97, + 286, + 381 + ], + "type": "inline_equation", + "content": "\\mathrm{gc} =" + }, + { + "bbox": [ + 47, + 97, + 286, + 381 + ], + "type": "text", + "content": " int(in_channels * branch_ratio) # channel number of a convolution branch self.dwconv_hw = nn.Conv2d(gc, gc, square_kernel_size, padding= square_kernel_size//2, groups=gc) self.dwconv_w = nn.Conv2d(gc, gc, kernel_size = (1, band_kernel_size), padding=(0, band_kernel_size//2), groups=gc) self.dwconv_h = nn.Conv2d(gc, gc, kernel_size = (band_kernel_size, 1), padding=( band_kernel_size//2, 0), groups=gc) self.split_Indexes = (gc, gc, gc, in_channels -3*gc) def forward(self,x): #B,C,H,W=x.shape x_hw,x_w,x_h,x_id=torch.split(x,self.split.Indexes,dim=1) return torch.cat( (self.dwconv_hw(x_hw), self.dwconv_w(x_w), self.dwconv_h(x_h), x_id), dim=1)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "code", + "guess_lang": "python" + }, + { + "bbox": [ + 47, + 404, + 162, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 162, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 162, + 416 + ], + "type": "text", + "content": "process can be expressed by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 76, + 426, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 426, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 76, + 426, + 287, + 441 + ], + "type": "interline_equation", + "content": "Y = \\operatorname {C o n v} _ {1 \\times 1} ^ {r C \\rightarrow C} \\left\\{\\sigma \\left[ \\operatorname {C o n v} _ {1 \\times 1} ^ {C \\rightarrow r C} (Y) \\right]\\right\\} + X, \\tag {3}", + "image_path": "60e95d24685c1288c0c7b953eb8c93e1a1a8f53913f1d69ee2b9d120823e7ce9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{k\\times k}^{C_i\\to C_o}" + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": " means convolution with kernel size of " + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "inline_equation", + "content": "k\\times k" + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": " input channels of " + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": " and output channels of " + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "inline_equation", + "content": "C_o" + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": " is the expansion ratio and " + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 452, + 287, + 489 + ], + "type": "text", + "content": " denotes activation function." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 493, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 685 + ], + "type": "text", + "content": "Comparison to MetaFormer block. As shown in Figure 2, it can be found that MetaNeXt block shares similar modules with MetaFormer block [77], e.g., token mixer and MLP. Nevertheless, a critical difference between the two models lies in the number of shortcut connections [22, 57]. MetaNeXt block implements a single shortcut connection, whereas the MetaFormer block incorporates two, one for the token mixer and the other for the MLP. From this aspect, MetaNeXt block can be regarded as a result of merging two residual sub-blocks from MetaFormer, thereby simplifying the overall architecture. As a result, the MetaNeXt architecture exhibits a higher speed compared to MetaFormer. However, this simpler design comes with a limitation: the token mixer component in MetaNeXt cannot be complicated (e.g., Attention) as shown in our experiments (Table 5)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Instantiation to ConvNeXt. As shown in Figure 2, in ConvNeXt, the token mixer is simply implemented by a depth-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 73, + 376, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 73, + 376, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 73, + 376, + 83 + ], + "type": "text", + "content": "wise convolution" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 330, + 91, + 545, + 106 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 91, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 330, + 91, + 545, + 106 + ], + "type": "interline_equation", + "content": "X ^ {\\prime} = \\operatorname {T o k e n M i x e r} (X) = \\operatorname {D W C o n v} _ {k \\times k} ^ {C \\rightarrow C} (X), \\tag {4}", + "image_path": "5f6c2301cf0c8b454da576d85fada1037bc536cab51ea4d343a4be7b9e4a3c50.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "spans": [ + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "inline_equation", + "content": "\\mathrm{DWConv}_{k\\times k}^{C\\to C}" + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "text", + "content": " denotes depthwise convolution with kernel size of " + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "inline_equation", + "content": "k\\times k" + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "text", + "content": ". In ConvNeXt, " + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 114, + 545, + 139 + ], + "type": "text", + "content": " is set as 7 by default." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 308, + 167, + 542, + 266 + ], + "blocks": [ + { + "bbox": [ + 306, + 146, + 479, + 159 + ], + "lines": [ + { + "bbox": [ + 306, + 146, + 479, + 159 + ], + "spans": [ + { + "bbox": [ + 306, + 146, + 479, + 159 + ], + "type": "text", + "content": "3.2. Inception depthwise convolution" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 167, + 542, + 266 + ], + "lines": [ + { + "bbox": [ + 308, + 167, + 542, + 266 + ], + "spans": [ + { + "bbox": [ + 308, + 167, + 542, + 266 + ], + "type": "table", + "html": "
Kernel size of DWConvConvolution ratioParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
7 × 71.028.64.5575241382.1*
5 × 51.028.44.4675270482.0
3 × 31.028.34.4798280281.5
3 × 31/228.34.4818274081.4
3 × 33/828.34.4847276281.4
3 × 31/428.34.4871280881.3
3 × 31/828.34.4901283380.8
3 × 31/1628.34.4916284680.1
", + "image_path": "6df14c81ff8908e5d0ce2a38d19bd5f296b8228cb772b25237da136a00fb00de.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 267, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 545, + 322 + ], + "type": "text", + "content": "Table 1. Preliminary experiments based on ConvNeXt-T. Convolution ratio means the ratio of channels to be processed by depthwise convolution while the other channels keep unchanged. Throughputs are measured on an A100 GPU with batch size of 128 and TF32. * The result is reported in ConvNeXt paper [40]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": "Preliminary experiments on ConvNeXt-T. We first conducted preliminary experiments based on ConvNeXt-T and report the results in Table 1. Firstly, the kernel size of depthwise convolution is reduced from " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": ". Compared to the model with kernel size of " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": ", the one with kernel size of " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": " enjoys " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "1.4 \\times" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": " higher training throughput, but suffers a significant performance drop from " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "82.1\\%" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "81.5\\%" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": ". Next, inspired by ShuffleNet V2 [42], we only feed partial input channels into depthwise convolution while the remaining ones keep unchanged. The number of processed input channels is controlled by a ratio. It is found that when the ratio is reduced from 1 to " + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 304, + 334, + 546, + 549 + ], + "type": "text", + "content": ", the training throughput can be further improved while the performance almost maintains. In summary, these preliminary experiments convey two findings on ConvNeXt. Finding 1: Large-kernel depthwise convolution is the speed bottleneck. Finding 2: Processing partial channels is good enough in single depthwise convolution layer [42]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 553, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 553, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 305, + 553, + 545, + 578 + ], + "type": "text", + "content": "Formulation. Based on the above findings, we propose a new type of convolution to keep both accuracy and effi" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 309, + 585, + 543, + 628 + ], + "blocks": [ + { + "bbox": [ + 309, + 585, + 543, + 628 + ], + "lines": [ + { + "bbox": [ + 309, + 585, + 543, + 628 + ], + "spans": [ + { + "bbox": [ + 309, + 585, + 543, + 628 + ], + "type": "table", + "html": "
Conv. typeParamsFLOPs
Conventional conv.k2C22k2C2HW
Depthwise conv.k2C2k2CHW
Inception dep. conv.(2k + 9)C/8(2k + 9)CHW/4
", + "image_path": "44b5c05761469c74555729212b45a83ad68dce0be2f938cb1686205fef29d33b.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": "Table 2. Complexity of different types of convolution. For simplicity, assume input and output channels are the same, and the bias term is omitted. " + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": " denote kernel size, channel number, height and width, respectively. The parameters and FLOPs of vanilla convolution and depthwise convolution are quadratic to kernel size " + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": ". In contrast, Inception depthwise convolution is linear to " + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 632, + 545, + 708 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5675" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 68, + 260, + 202 + ], + "blocks": [ + { + "bbox": [ + 75, + 68, + 260, + 202 + ], + "lines": [ + { + "bbox": [ + 75, + 68, + 260, + 202 + ], + "spans": [ + { + "bbox": [ + 75, + 68, + 260, + 202 + ], + "type": "image", + "image_path": "70948b99a6a3ed70a3dfe3569c21ebb3546bebdd56acbafa58b85eb1169d7fbd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 204, + 287, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 204, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 287, + 247 + ], + "type": "text", + "content": "Figure 3. Comparison of FLOPs between depthwise convolution and Inception depthwise convolution. Inception depthwise convolution is much more efficient than depthwise convolution as kernel size increases." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 256, + 282, + 564 + ], + "blocks": [ + { + "bbox": [ + 50, + 256, + 282, + 564 + ], + "lines": [ + { + "bbox": [ + 50, + 256, + 282, + 564 + ], + "spans": [ + { + "bbox": [ + 50, + 256, + 282, + 564 + ], + "type": "table", + "html": "
Stage#TokensLayer SpecificationInceptionNeXt
ATSB
1H/4 × W/4Down-samplingKernel Size4 × 4, stride 4
Embed. Dim.4096128
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
2H/8 × W/8Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.90192256
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block23
3H/16 × W/16Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.180384512
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio4
# Block6927
4H/32 × W/32Down-samplingKernel Size2 × 2, stride 2
Embed. Dim.3207681024
InceptionNeXt BlockBand kernel size911
Conv. group ratio1/41/8
MLP Ratio3
# Block23
Global average pooling, MLP
Parameters (M)4.228.149.486.7
MACs (G)0.54.28.414.9
", + "image_path": "aab91df799e0ed6d5901de0c654b33a2cf587dfe241027bf2669cb78d4017276.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 565, + 287, + 598 + ], + "lines": [ + { + "bbox": [ + 47, + 565, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 287, + 598 + ], + "type": "text", + "content": "Table 3. Configurations of InceptionNeXt models which have similar model configurations to ConvNeXt [40]. \"A\", \"T\", \"S\" and \"B\" represent \"Atto\", \"Tiny\", \"Small\" and \"Base\", respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "ciency. According to Fingding 2, we leave partial channels unchanged and denote them as a branch of identity mapping. Motivated by Fingding 1, for the processing channels, we propose to decompose the depthwise operations in Inception style [58-60]. Inception [58] utilizes several branches of small kernels (e.g., " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ") and large kernels (e.g., " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "). Similarly, we adopt " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " as one of our branches but get rid of the usage of the large square kernels because of their slow practical speed. Instead, large kernel " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "k_h \\times k_w" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "is decomposed as " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "1 \\times k_w" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "k_h \\times 1" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " inspired by Inception v3 [59]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 98, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 98, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 305, + 98, + 545, + 121 + ], + "type": "text", + "content": "Specifically, for input " + }, + { + "bbox": [ + 305, + 98, + 545, + 121 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 98, + 545, + 121 + ], + "type": "text", + "content": ", we split it into four groups along the channel dimension," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 318, + 133, + 545, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 133, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 318, + 133, + 545, + 163 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {\\mathrm {h w}}, X _ {\\mathrm {w}}, X _ {\\mathrm {h}}, X _ {\\mathrm {i d}} = \\operatorname {S p l i t} (X) \\tag {5} \\\\ = X _ {:,: g}, X _ {: g: 2 g}, X _ {: 2 g: 3 g}, X _ {: 3 g:}, \\\\ \\end{array}", + "image_path": "9464d23e2170b083803b7f5c5b8f50b3fcf92700225795a1a934f76aafa7671c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "text", + "content": " is the channel numbers of convolution branches. We can set a ratio " + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "r_g" + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "text", + "content": " to determine the branch channel numbers by " + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "g = r_g C" + }, + { + "bbox": [ + 305, + 174, + 545, + 221 + ], + "type": "text", + "content": ". Next, the splitting inputs are fed into different parallel branches," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 359, + 233, + 545, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 233, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 359, + 233, + 545, + 297 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {\\mathrm {h w}} ^ {\\prime} = \\operatorname {D W C o n v} _ {k _ {s} \\times k _ {s}} ^ {g \\rightarrow g} g (X _ {\\mathrm {h w}}), \\\\ \\begin{array}{l}X _ {\\mathrm {w}} ^ {\\prime} = \\operatorname {D W C o n v} _ {1 \\times k _ {b}} ^ {g \\rightarrow g} g \\left(X _ {\\mathrm {w}}\\right),\\\\V ^ {\\prime} = \\operatorname {D W C o n v} _ {1 \\times k _ {b}} ^ {g \\rightarrow g} (X)\\end{array}\\tag {6} \\\\ X _ {\\mathrm {h}} ^ {\\prime} = \\operatorname {D W C o n v} _ {k _ {b} \\times 1} ^ {g \\rightarrow g} g (X _ {\\mathrm {h}}), \\\\ X _ {\\mathrm {i d}} ^ {\\prime} = X _ {\\mathrm {i d}}, \\\\ \\end{array}", + "image_path": "8e9664e5ea3f088077c90687ecb4c77400eeb49740d3eaf6456c51363fcb656b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "type": "inline_equation", + "content": "k_{s}" + }, + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "type": "text", + "content": " denotes the small square kernel size set as 3 by default; " + }, + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "type": "inline_equation", + "content": "k_{b}" + }, + { + "bbox": [ + 305, + 308, + 545, + 344 + ], + "type": "text", + "content": " represents the band kernel size set as 11 by default. Finally, the outputs from each branch are concatenated," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 353, + 356, + 545, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 356, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 353, + 356, + 545, + 371 + ], + "type": "interline_equation", + "content": "X ^ {\\prime} = \\operatorname {C o n c a t} \\left(X _ {\\mathrm {h w}} ^ {\\prime}, X _ {\\mathrm {w}} ^ {\\prime}, X _ {\\mathrm {h}} ^ {\\prime}, X _ {\\mathrm {i d}} ^ {\\prime}\\right). \\tag {7}", + "image_path": "26902cd7c8ee7fac2ea56efb07785f1d629a1250b5a197c1487f2dcdec019cd3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 382, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 382, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 545, + 418 + ], + "type": "text", + "content": "The illustration of InceptionNeXt block is shown in Figure 2. Moreover, its PyTorch [45] code is summarized in Algorithm 1." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 424, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 546, + 532 + ], + "type": "text", + "content": "Complexity. The complexity of three types of convolution, i.e., conventional, depthwise, and Inception depthwise convolution is shown in Table 2. As can be seen, Inception depthwise convolution is much more efficient than the other two types of convolution in terms of parameter numbers of FLOPs. Inception depthwise convolution consumes parameters and FLOPs linear to both channel and kernel size. The comparison of depthwise and Inception depthwise convolutions regarding FLOPs is also clearly shown in Figure 3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 540, + 397, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 397, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 397, + 553 + ], + "type": "text", + "content": "3.3. InceptionNeXt" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": "Based on InceptionNeXt block, we can build a series of models named InceptionNeXt. Since ConvNeXt [40] is the our main comparing baseline, we mainly follow it to build models with several sizes [71]. Specifically, similar to ResNet [22] and ConvNeXt, InceptionNeXt also adopts 4-stage framework. The same as ConvNeXt, the numbers of 4 stages are [2, 2, 6, 2] for atto size, [3, 3, 9, 3] for small size and [3, 3, 27, 3] for base size. We adopt Batch Normalization since this paper emphasizes speed. Another difference with ConvNeXt is that InceptionNeXt uses an MLP ratio of 3 in stage 4 and moves the saved parameters to the classifier, which can help reduce a few FLOPs (e.g., " + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": " for base size). The detailed model configurations are reported in Table 3." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5676" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 69, + 509, + 507 + ], + "blocks": [ + { + "bbox": [ + 85, + 69, + 509, + 507 + ], + "lines": [ + { + "bbox": [ + 85, + 69, + 509, + 507 + ], + "spans": [ + { + "bbox": [ + 85, + 69, + 509, + 507 + ], + "type": "table", + "html": "
ModelMixing TypeImage sizeParams (M)MACs (G)Throughput (img/s)Top-1 (%)
A1002080Ti
TrainInferTrainInfer
MobileNetV2 (1.4) [55]Conv22426.10.6010015190471185974.7
EfficientNet-B0 [61]Conv22425.30.409545502464194477.1
GhostNet 1.3× [19]Conv22427.30.249467451589275775.7
ConvNeXt-A [40, 71]Conv22423.70.558354539345156875.7
InceptionNeXt-A (Ours)Conv22424.20.512661+219%9876+118%992+188%3595+129%75.3-0.4
DeiT-S [64]Attn2242224.61227378127678479.8
T2T-ViT-14 [79]Attn2242224.8----81.5
TNT-S [20]Attn2242245.2----81.5
Swin-T [39]Attn2242294.5564176818455481.3
Focal-T [75]Attn2242294.9----82.2
ResNet-50 [22, 72]Conv2242264.1969314927897778.4
RSB-ResNet-50 [22, 72]Conv2242264.1969314927897779.8
RegNetY-4G [48, 72]Conv2242214.0670269422285981.3
FocalNet-T [76]Conv2242294.5----82.3
ConvNeXt-T [40]Conv2242294.5575241317759082.1
InceptionNeXt-T (Ours)Conv2242284.2901+57%2900+20%254+44%822+39%82.3+0.2
T2T-ViT-19 [79]Attn2242398.5----81.9
PVT-Medium [67]Attn2242446.7----81.2
Swin-S [39]Attn2242508.7359113110932883.0
Focal-S [75]Attn2242519.1----83.5
RSB-ResNet-101 [22, 72]Conv2242457.9620205716859281.3
RegNetY-8G [48, 72]Conv2242398.0689132612448082.1
FocalNet-S [76]Conv2242508.7----83.5
ConvNeXt-S [40]Conv2242508.7361153510535383.1
InceptionNeXt-S (Ours)Conv2242498.4521+44%1750+14%130+24%447+27%83.5+0.4
DeiT-B [64]Attn22428617.554116088625981.8
T2T-ViT-24 [79]Attn22426413.8----82.3
TNT-B [20]Attn22426614.1----82.9
PVT-Large [67]Attn2242629.8----81.7
Swin-B [39]Attn22428815.42718437222383.5
Focal-B [75]Attn22429016.0----83.8
RSB-ResNet-152 [22, 72]Conv22426011.6437145711541581.8
RegNetY-16G [48, 72]Conv22428415.932211007629582.2
RepLKNet-31B [14]Conv22427915.3----83.5
FocalNet-B [76]Conv22428915.4----83.9
ConvNeXt-B [40]Conv22428915.426711226823683.8
InceptionNeXt-B (Ours)Conv22428714.9375+40%1244+11%80+18%287+22%84.0+0.2
DeiT-B [64]Attn38428655.4131361257383.1
Swin-B [39]Attn38428847.1104296216584.5
RepLKNet-31B [14]Conv38427945.1----84.8
ConvNeXt-B [40]Conv38428945.095393237985.1
InceptionNeXt-B (Ours)Conv38428743.6139+46%428+9%27+17%97+23%85.2+0.1
", + "image_path": "f0921cf7b6e3b40c919d18d20f78057a8236e88ab7116d2f4d7bb5ea31aeba31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 507, + 547, + 552 + ], + "lines": [ + { + "bbox": [ + 46, + 507, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 547, + 552 + ], + "type": "text", + "content": "Table 4. Performance of models trained on ImageNet-1K. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 (TensorFloat-32), and on a 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of \"Channel First\" and \"Channel Last\" memory layouts are reported." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 555, + 124, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 124, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 124, + 570 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 576, + 162, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 162, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 162, + 588 + ], + "type": "text", + "content": "4.1. Image classification" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Setup. For the image classification task, ImageNet-1K [11, 54] is one of the most commonly-used benchmarks, which contains around 1.3 million images in the training set and 50 thousand images in the validation set. To fairly compare with the widely-used baselines, e.g., Swin [39] and ConvNeXt [40], we mainly follow the training hyperparameters from DeiT [64] without distillation. Specifically, the models are trained by AdamW [41] optimizer with a learning rate " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "lr = 0.001 \\times \\text{batchsize} / 1024" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "lr = 4e - 3" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " and batchsize " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "= 4096" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " are used in this paper the same as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 556, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 547, + 654 + ], + "type": "text", + "content": "ConvNeXt). Following DeiT, data augmentation includes standard random resized crop, horizontal flip, RandAugment [10], Mixup [82], CutMix [80], Random Erasing [86] and color jitter. For regularization, label smoothing [59], stochastic depth [26], and weight decay are adopted. Like ConvNeXt, we also use LayerScale [65], a technique to help train deep models. Our code is based on PyTorch [45] and timm [71]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Results. We compare InceptionNeXt with various state-of-the-art models, including attention-based and convolution-based models. As can be seen in Table 4, InceptionNeXt achieves highly competitive performance as well as" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5677" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 131 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 131 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 131 + ], + "type": "table", + "html": "
ModelParams (M)MACs (G)Throughput (img/s)Top-1 (%)
TrainInfer
DeiT-S [64]224.627678479.8
MetaNeXt-Attn224.62888163.9
ConvNeXt-S (iso.) [40]224.327087979.7
InceptionNeXt-S (iso.)224.231099879.7
", + "image_path": "479f23a1aaf15954e4c27e1843ca59659bd1ac62c8b3b752ecaecee1458ff097.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "text", + "content": "enjoys higher speed. InceptionNeXt consistently enjoys better accuracy-speed trade-off than ConvNeXt [40]. For example, InceptionNeXt-T not only surpasses ConvNeXt-T by " + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "text", + "content": ", but also enjoys " + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "inline_equation", + "content": "1.6 \\times 1.2 \\times" + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "text", + "content": " training/inference throughputs on A100 than ConvNeXts, similar to those of ResNet-50. That is to say, InceptionNeXt-T enjoys both ResNet-50's speed and ConvNeXt-T's accuracy. Moreover, following Swin and ConvNeXt, we also finetuned the InceptionNeXt-B trained at the resolution of " + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 46, + 219, + 288, + 363 + ], + "type": "text", + "content": " for 30 epochs. We can see that InceptionNeXt-B obtains higher train and inference throughputs than ConvNeXt-B while keeping competitive accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "text", + "content": "It is observed that the speed improvement is much more significant for the lightweight model size, and the improvement gradually becomes smaller when the model size scales up. The reason is that computation complexity of depthwise and Inception depthwise convolutions are linear to channel number, i.e., " + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(C)" + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "text", + "content": " is channel number. For MLPs, their computation complexity is " + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(C^2)" + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "text", + "content": ". For larger models (larger " + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 365, + 287, + 483 + ], + "type": "text", + "content": "), its computation is further dominated by MLPs. By only improving depthwise convolution, the speed improvement becomes smaller when the model is larger." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": "Besides the 4-stage framework [22, 39, 56], another notable one is ViT-style [16] isotropic architecture which has only one stage. To match the parameters and MACs of DeiT-S, we construct InceptionNeXt-S (iso.) following ConvNeXt-S (iso.) [40]. Specifically, we set the embedding dimension as 384 and the block number as 18. Besides, we build a model called MetaNeXt-Attn which is instantiated from MetaNeXt block by specifying self-attention as token mixer. The aim of this model is to investigate whether it is possible to merge two residual sub-blocks of the Transformer block into a single one. The experiment results are shown in Table 5. It can be seen that InceptionNeXt can also perform well with the isotropic architecture, demonstrating InceptionNeXt exhibits good generalization across different frameworks. It is worth noting that MetaNeXt-Attn could not be trained to converge and only achieved an accuracy of " + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "inline_equation", + "content": "3.9\\%" + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": ". This result suggests that, unlike the token mixer in MetaFormer, the token mixer in MetaNeXt cannot be too complex. If it is, the model may not be trainable." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 547, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 133, + 287, + 210 + ], + "lines": [ + { + "bbox": [ + 47, + 133, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 287, + 210 + ], + "type": "text", + "content": "Table 5. Comparison among ViT, isotropic ConvNeXt and InceptionNeXt. MetaNeXt-Attn is instantiated from MetaNeXt with token mixer of self-attention [66]. The throughputs are measured on 2080Ti (PyTorch 1.8.1 and CUDA 10.2) with FP32. The batch size for throughput benchmarking is initially set as 128 and is reduced until the GPU can host. The better results of \"Channel First\" and \"Channel Last\" memory layouts are reported." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 547, + 178 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 178 + ], + "type": "table", + "html": "
BackboneUperNet
Params (M)MACs (G)FPSmIoU (%)
Swin-T [39]6094520.645.8
ConvNeXt-T [40]6093920.646.7
InceptionNeXt-T5693322.747.9
Swin-S [39]81103816.249.5
ConvNeXt-S [40]82102716.849.6
InceptionNeXt-S78102017.650.0
Swin-B [39]121118816.249.7
ConvNeXt-B [40]122117015.749.9
InceptionNeXt-B115115917.550.6
", + "image_path": "c8b38bd9e6b128c0cd9957321c0dd3ae8ba3b0526a5aef0dfe5ae046e1370ca6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 228, + 550, + 385 + ], + "blocks": [ + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "type": "text", + "content": "Table 6. Performance of semantic segmentation with UperNet [73] on ADE20K [87] validation set. Images are cropped to " + }, + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "type": "text", + "content": " for training. The MACs are measured with input size of " + }, + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "type": "inline_equation", + "content": "512 \\times 2048" + }, + { + "bbox": [ + 305, + 180, + 547, + 224 + ], + "type": "text", + "content": ". The FPS are benchmarked on 2080Ti." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 228, + 550, + 385 + ], + "lines": [ + { + "bbox": [ + 307, + 228, + 550, + 385 + ], + "spans": [ + { + "bbox": [ + 307, + 228, + 550, + 385 + ], + "type": "table", + "html": "
BackboneSemantic FPN
Params (M)MACs (G)FPSmIoU (%)
ResNet-50 [22]294630.236.7
PVT-Small [67]284527.239.8
PoolFormer-S24 [77]233928.840.3
InceptionNeXt-T284431.443.1
ResNet-101 [22]486522.238.8
ResNeXt-101-32x4d [74]4765-39.7
PVT-Medium [67]486120.041.6
PoolFormer-S36 [77]354821.642.0
PoolFormer-M36 [77]606815.442.4
InceptionNeXt-S506520.745.6
PVT-Large [67]658016.042.1
ResNeXt-101-64x4d [74]86104-40.2
PoolFormer-M48 [77]778212.142.7
InceptionNeXt-B8510020.246.4
", + "image_path": "8b7ded38c1434c03c072fb2d9598c09fa47a8ec200f5ae6dff0fb9f3aed32b1c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "lines": [ + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "type": "text", + "content": "Table 7. Performance of semantic segmentation with Semantic FPN [31] on ADE20K [87] validation set. Images are cropped to " + }, + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "type": "text", + "content": " for training. The MACs are measured with input size of " + }, + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 305, + 386, + 547, + 430 + ], + "type": "text", + "content": ". The FPS are benchmarked on 2080Ti." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 436, + 437, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 437, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 437, + 449 + ], + "type": "text", + "content": "4.2. Semantic segmentation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 458, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 686 + ], + "type": "text", + "content": "Setup. ADE20K [87], a commonly used scene parsing benchmark, is used to evaluate our models on semantic segmentation task. ADE20K includes 150 fine-grained semantic categories, containing twenty thousand and two thousand images in the training set and validation set, respectively. The checkpoints trained on ImageNet-1K [11] at the resolution of " + }, + { + "bbox": [ + 304, + 458, + 545, + 686 + ], + "type": "inline_equation", + "content": "224^2" + }, + { + "bbox": [ + 304, + 458, + 545, + 686 + ], + "type": "text", + "content": " are utilized to initialize the backbones. Following Swin [39] and ConvNeXt [40], we firstly evaluate InceptionNeXt with UperNet [73]. The models are trained with AdamW [41] optimizer with learning rate of 6e-5 and batch size of 16 for 160K iterations. Following PVT [67] and PoolFormer [77], InceptionNeXt is also evaluated with Semantic FPN [31]. In common practices [5, 31], the batch size is 16 for the setting of 80K iterations. Following PoolFormer [77], we increase the batch size to 32 and decrease the iterations to 40K to speed up training. AdamW [30, 41] is adopted with a learning rate of 2e-4 and a polynomial decay schedule of 0.9 power. Our code is based on PyTorch [45] and mmsegmentation [8]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "Results. For segmentation with UpNet [73], the results are shown in Table 6. As can be seen, InceptionNeXt con" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5678" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 537, + 198 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 537, + 198 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 537, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 537, + 198 + ], + "type": "table", + "html": "
AblationVariantParams (M)MACs (G)ThroughputTop-1 (%)
TrainInference
BaselineNone (InceptionNeXt-T)28.14.2901290082.3
BranchRemove horizontal band kernel28.04.2947309381.9
Remove vertical band kernel28.04.2954317381.9
Remove small band kernel28.04.2940300482.0
horizontal and vertical band kernel in parallel → in sequence28.14.2903297182.1
Band kernel sizeBand kernel size 11 → 728.04.2905294682.1
Band kernel size 11 → 928.14.2904291682.1
Band kernel size 11 → 1328.14.2896289582.0
Convolution branch ratioConv. branch ratio 1/8 → 1/428.14.2834249982.2
Conv. branch ratio 1/8 → 1/1628.04.2936309781.8
NormalizationBatch Norm [29] → Layer Norm [1]28.14.2721264682.4
", + "image_path": "1bb8a8b38ecdc0c3939e7e496bb6ecac50a5a6dcba99327c4a1e1576d16c21bf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 199, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 547, + 232 + ], + "type": "text", + "content": "Table 8. Ablation for InceptionNeXt on ImageNet-1K classification benchmark. InceptionNeXt-T is utilized as the baseline for the ablation study. Top-1 accuracy on the validation set is reported. The throughputs are measured on an A100 GPU (PyTorch 1.13.0 and CUDA 11.7.1) with TF32 and batch size of 128." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 237, + 288, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 288, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 288, + 310 + ], + "type": "text", + "content": "sistently outperforms Swin [39] and ConvNeXt [40] for different model sizes. In the method of Semantic FPN [31] as shown in Table 7, InceptionNeXt significantly surpasses other backbones, like PVT [67] and PoolFormer [77]. These results show that InceptionNeXt also has a high potential for dense prediction tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 320, + 146, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 146, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 146, + 332 + ], + "type": "text", + "content": "4.3. Ablation studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "text", + "content": "We conduct ablation studies on ImageNet-1K [11, 54] using InceptionNeXt-T as baseline from the following aspects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "content": "Branch. Inception depthwise convolution includes four branches, three convolutional ones, and identity mapping. When removing any branch of horizontal or vertical band kernel, performance significantly drops from " + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "inline_equation", + "content": "82.3\\%" + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "inline_equation", + "content": "81.9\\%" + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "content": ", demonstrating the importance of these two branches. This is because these two branches with band kernels can enlarge the receptive field of the model. For the branch of small square kernel size of " + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "content": ", removing it can still achieve up to " + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "inline_equation", + "content": "82.0\\%" + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "content": " top-1 accuracy and bring higher throughput. This inspires us that if we attach more importance to the model speed, the simple version of InceptionNeXt without the square kernel of " + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 45, + 369, + 287, + 620 + ], + "type": "text", + "content": " can be adopted. For the band kernel, Inception v3 mostly equips them in a sequential way. We find that this assembling method can also obtain similar performance and even a little speed up the model. A possible reason is that PyTorch/CUDA may have optimized sequential convolutions well, and we only implement the parallel branches at a high level (see Algorithm 1). We believe the parallel method will be faster when it is optimized better. Thus, parallel method for the band kernels is adopted by default." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "content": "Band kernel size. It is found the performance can be improved from kernel size 7 to 11, but it drops when the band kernel size increases to 13. This phenomenon may result from the optimization and can be solved by methods like structural re-parameterization [13, 14]. For simplicity, we set the kernel size as 11 by default except for atto size." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 712 + ], + "type": "text", + "content": "Convolution branch ratio. When the ratio increases from" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 237, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 237, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 237, + 545, + 322 + ], + "type": "text", + "content": "1/8 to 1/4, performance improvement can not be observed. Ma et al. [42] also point out that it is not necessary for all channels to conduct convolution. But when the ratio decreases to 1/16, it brings a serious performance drop. This is because a smaller ratio would limit the degree of token mixing, resulting in performance drop. We thus set the convolution branch ratio as 1/8 by default except for atto size." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 325, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 385 + ], + "type": "text", + "content": "Normalization. When replacing the Batch Normalization [29] with Layer Normalization [1], the performance improvement improve by " + }, + { + "bbox": [ + 304, + 325, + 545, + 385 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 304, + 325, + 545, + 385 + ], + "type": "text", + "content": " but suffer throughput drop in both training and inference. Since this paper focuses on efficiency, we adopt Batch Normalization for InceptionNeXt." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 393, + 378, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 378, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 378, + 405 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 411, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 567 + ], + "type": "text", + "content": "In this work, we propose an effective and efficient CNN architecture, InceptionNeXt, which enjoys a better trade-off between the practical speed and the performance than previous network architectures. InceptionNeXt decomposes large-kernel depthwise convolution along channel dimension into four parallel branches, including identity mapping, a small square kernel, and two orthogonal band kernels. All these four branches are much more computationally efficient than a large-kernel depthwise convolution in practice, and can also work together to have a large spatial receptive field for good performance. Extensive experimental results demonstrate the superior performance and the high practical efficiency of InceptionNeXt." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This project is supported by the National Research Foundation Singapore under its Medium Sized Center for Advanced Robotics Technology Innovation, and the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2). Weihao Yu was partly supported by Snap Research Fellowship, Google's TPU Research Cloud (TRC), and Google Cloud Research Credits program. Pan Zhou was supported by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant. 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Class representations need to be adapted to more accurately reflect an object concept under these shifts. In the absence of training data from target geographies, we hypothesize that geographically diverse descriptive knowledge of categories can enhance robustness. For this purpose, we explore the feasibility of probing a large language model for geography-based object knowledge, and we examine the effects of integrating knowledge into zero-shot and learnable soft prompting with CLIP. Within this exploration, we propose geography knowledge regularization to ensure that soft prompts trained on a source set of geographies generalize to an unseen target set. Accuracy gains over prompting baselines on DollarStreet while training only on Europe data are up to $+2.8 / 1.2 / 1.6$ on target data from Africa/Asia/Americas, and $+4.6$ overall on the hardest classes. Competitive performance is shown vs. few-shot target training, and analysis is provided to direct future study of geographical robustness.", + "bbox": [ + 75, + 342, + 473, + 645 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 691, + 209, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The performance of object recognition models degrades when tested in new geographies (e.g., cities, countries, continents) [7, 21, 33, 39, 43]. Numerous factors contribute to the challenging problem of geographical domain shift, such as cross-geography changes in object design/parts, materials, and context. These changes in turn may be due to cultural, climate, or economic differences around the world. Recent work has shown standard adaptation techniques fail when used for geographical domain shifts [21, 33], but there has yet to be significant progress in the creation of techniques that improve geographical robustness. Such progress is necessary to ensure equitable use of AI in the future.", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/713c33555090a3b5a042914109b7f889d86d3485fa58a5c9ee4a09443d665d45.jpg", + "image_caption": [ + "Figure 1. Descriptive knowledge can address concept shifts across geographies. Observe the wide range of object designs and contexts in the DollarStreet [11] category tools around the world. Our work's premise is that textual representations for classes in vision-language models can be enhanced to better suit diverse object representations across geographies. Map made with [16]." + ], + "image_footnote": [], + "bbox": [ + 506, + 310, + 883, + 468 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Overall, models need representations that adequately capture a category's various forms around the world. A natural solution is to collect training data of objects from different regions. However, this approach is expensive, takes significant effort, and is difficult for regions with limited Internet access. Fortunately, geographical shifts have a unique property compared to other common domain shifts (e.g. ones due to artistic style or weather changes)—they can be addressed with descriptive knowledge about concept changes. In other words, it is possible to describe the features of an object in a region and use this information to adapt a model's default representation. For instance, as shown in Fig. 1, for rural areas in Papua New Guinea, tools can be described as being used for \"cooking, hunting, and fishing\", and for rural areas in Malawi, tools may often be \"made of metal and wood, for farming\". Models should account for diverse presentations and contexts of a category and not be limited to biased presentations (e.g. if the model learns tools as just being \"metallic with logos\").", + "bbox": [ + 496, + 582, + 892, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We examine the effects of probing geo-diverse knowledge in two ways. First, we analyze whether a vision", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13515", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "language model (VLM, i.e. CLIP [36]) has encoded categories in a geo-specific manner, such that adding a country's name to a prompt (e.g. \"A photo of a house in China\") elicits knowledge that improves recognition. Second, we probe a large language model (LLM, i.e. GPT-3 davinci003) for geography-specific knowledge to obtain visual feature descriptors for an object in different locations. We analyze results in zero-shot inference on geographically and socioeconomically diverse data (DollarStreet [11]), finding the combination of knowledge to often be complementary.", + "bbox": [ + 75, + 90, + 468, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We further consider a practical scenario where CLIP is optimized with soft prompting, using only a \"source\" geography with easy-to-access data (e.g. Europe), while the model is applied downstream on \"target\" data from other parts of the world (e.g. Africa, Asia, Americas). We propose geography knowledge regularization, which uses knowledge ensembled over countries to enable soft prompts to achieve geographically generalizable class representations. We test our method on the recent DollarStreet and GeoNet [21] datasets. Our regularization boosts performance over baseline soft prompting methods, and has benefits with respect to few-shot target-specific training (a 16-shot-per-class regularized model without any target data outperforms a 12-shot-per-class target-trained model on DollarStreet).", + "bbox": [ + 75, + 242, + 470, + 453 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method is the first to effectively address geo shifts in object recognition. It outperforms zero-shot CLIP (assumed to have some robustness) by $10.3\\%$ on Africa, CoOp [52] by $3.3\\%$ , and the best baseline by $4.6\\%$ on the hardest classes.", + "bbox": [ + 76, + 454, + 468, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we answer the following questions: (1) Does adding geographical context (i.e. country names) to CLIP prompts improve recognition across geographies? (2) Can an LLM provide useful geographical descriptive knowledge to improve recognition? (3) How can we optimize soft prompts for CLIP using an accessible data source with consideration of target geographies not represented in the training set? (4) Where can soft prompts enhanced with geographical knowledge provide the most benefits?", + "bbox": [ + 75, + 513, + 468, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 664, + 218, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Geographical domain shifts occur when the target setting is in a different geography (e.g. continent, country, city) than where the source data was acquired. Shifts involve changes in object design (e.g. differences in house architecture) and context (i.e. background/co-occurring objects vary). Datasets tailored to cross-country/continent object recognition have recently been proposed, e.g. DollarStreet [11], GeoNet [21], GeoDE [37], GeoYFCC [9], and OpenImages-Extended [5]. Interestingly, [21, 33] demonstrate that traditional methods in unsupervised domain adaptation [10, 19, 20, 27, 28, 38, 44, 45, 50] which seek to bridge gaps based on visual features alone, do not effectively address geographical domain shift. They achieve negligible gains (e.g. 0.14 for [10] in [33]) or often drops", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in performance (e.g. all methods tested in [21]), compared to just using the source model. Attempts to specifically address geographical robustness are limited: [43] corrects for differences in the sizes of cars, [9] proposes a discriminative domain embedding from target data, and GiVL [48] pretrains with knowledge from Wikipedia. In contrast, our descriptive knowledge regularization works for different categories (not just cars); we do not require target domain data to achieve gains cross-geography; we explore the strong capabilities of LLMs to gather relevant knowledge; and we propose lightweight adaptation through soft prompting (unlike GiVL's expensive pretraining).", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-language (VL) models [17, 25, 26, 36, 49] excel on a variety of tasks. CLIP [36] shows impressive zero-shot object recognition across different settings. Yet its performance given geographical shift is less apparent. GeoNet [21] only shows finetuned performance, which is expensive given CLIP's large scale. GeoDE [37] only shows zero-shot inference with CLIP's default prompts. Neither work evaluates descriptive knowledge or soft prompting.", + "bbox": [ + 496, + 280, + 890, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning soft textual prompts. Several recent works to adapt CLIP have focused on parameter and data efficiency using linear probing [36] and prompting [18, 23, 52]. Soft textual prompting (e.g. CoOp [52]) is notable as it optimizes class text embeddings (without manual tuning), which we hypothesize is critical to adequately adapt for geographical robustness. As CoOp overfits on base (seen) classes, CoCoOp [51] proposes to condition prompts on the image for better generalizability. KgCoOp [47] alternatively guides learned prompt embeddings towards CLIP's manual prompt embeddings through a distance constraint to avoid degradation on unseen classes. Our approach also uses a distance constraint, but it differs from [47] with the purpose of regularizing learned prompt representations for cross-geography generalization instead of the base-to-new-class setting. We also show novel benefits of regularization when used with an ensemble of CLIP's internal geographical knowledge and external geographical descriptive knowledge. Our approach notably outperforms each of CoOp, CoCoOp, and KgCoOp by at least +2.8 accuracy on target countries in Africa in DollarStreet. External knowledge aids unseen classes in KAPT [22], but not with respect to geographical knowledge. Prompt tuning for adaptation has been tested in [12, 40], but not with descriptive knowledge.", + "bbox": [ + 496, + 409, + 892, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge probed from large language models like [4, 6, 31, 32] has been used for visual reasoning [46], embodied agent planning [15, 41], and to generate additional context for VLM class prompts in object recognition [30, 34]. We uniquely probe LLMs for distinguishable visual descriptions for the same object class across different geographical regions. We are also the first to incorporate geographical knowledge from LLMs into soft prompting.", + "bbox": [ + 496, + 779, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13516", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e5fac3ceb85dba171abc801d8732bfc77254c65ceb8dc213f6409f5e38bcd392.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 93, + 450, + 294 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/776a43bbdcdd29ad0890fd1bb74bbe8e028be5f33f438da2bfd4cdd8036bb74c.jpg", + "image_caption": [ + "(2) Optimize Soft Prompts on Source Data While Regularizing Towards Target Knowledge", + "Figure 2. Geography knowledge regularization. To ensure robustness in soft prompt learning, we (1) incorporate knowledge internal to CLIP and externally obtained from an LLM. (2) This descriptive knowledge regularizes class representations when training on a specific source geography (e.g. Europe), thus (3) increasing robustness when generalizing to target geographies (e.g. Vietnam)." + ], + "image_footnote": [], + "bbox": [ + 465, + 126, + 880, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 364, + 184, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We investigate geographical shift in object recognition with VLMs. We posit that the manner in which classes are described is critical due to cross-geography shifts in design and context. We also hypothesize that CLIP's default class representations elicited through \"a photo of a/an \" prompts may not adequately represent classes around the world. Instead, they may be more aligned to high-resource geographies due to Internet-based training data. Optimizing representations (with soft prompts) on a specific geography (e.g. Europe) may exacerbate a lack of robustness. Our main idea (Fig. 2) is to incorporate object-related geographical knowledge into prompting to ensure model robustness in different regions. We outline our mechanism to obtain geography-specific context by probing CLIP's internal knowledge and an external LLM's descriptive knowledge. We further propose geography knowledge regularization to ensure soft prompts do not overfit when training data is limited to certain geographies.", + "bbox": [ + 75, + 391, + 468, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminaries. We consider object recognition on a dataset $S$ containing a class set $\\mathcal{C}$ (size $N_{c}$ ) over a set of geographies $\\mathcal{G}$ . We consider a geography $g$ to be either a country or continent. Our VLM is CLIP [36], with an image encoder $f$ and language encoder $h$ . We incorporate knowledge of each geography $g$ into prompting using (1) zero-shot inference or (2) soft textual prompting. Prompts are defined as $t$ (each is a set of tokens), and class embeddings $w$ are calculated as $h(t)$ . We refer to CLIP's default prompt \"a photo of a/an \" for a class $c$ as $t_{c}^{\\text{default}}$ .", + "bbox": [ + 75, + 665, + 468, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Geographical Knowledge Probing", + "text_level": 1, + "bbox": [ + 76, + 830, + 375, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Probing CLIP's internal geographical knowledge. Our first strategy of investigation is to augment CLIP's manual prompts to include country names, as we surmise that some", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of the resulting class representations may be better aligned to how categories present in different regions. [3] inspires this hypothesis, showing that adding country names to image generation prompts can achieve gains in geographical representativeness. However, it is an open question whether adding country names in prompts improves recognition. We define the setting CountryInPrompt, using the prompt $t_c^{CountryInPrompt}$ with template \"a photo of a/an in \", e.g. \"a photo of a stove in Burundi.\"", + "bbox": [ + 496, + 366, + 890, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Probing external LLM geographical knowledge. As CLIP may not have sufficient knowledge of objects in some regions, we consider further augmenting prompts with external knowledge. Motivated by probing LLMs for general attribute-based object descriptions [30, 34] (e.g. a tiger with \"stripes and sharp teeth\"), we probe GPT-3 (davinci-003) for geography-specific descriptions of object styles, contexts, and materials.1 We reason that since LLMs are trained on large information sources (e.g. CommonCrawl [1], WebText [35], Wikipedia [2]), they may have knowledge about how an object presents in a region due to climate, economics, and/or cultural factors. For instance, roofs may sometimes be \"thatched\" in tropical and temperate climates, and cutlery may sometimes be made of \"bamboo\" in areas with bamboo forests. Our goal is unique vs. [30, 34] in that we explore descriptive knowledge differences for the same class to address domain shifts across regions.", + "bbox": [ + 496, + 505, + 892, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Acquiring knowledge. We follow [30], but instead of gathering one set of feature descriptors $\\mathcal{D}(c)$ for each $c$ , we collect sets per country. For each class $c$ and geography $g$ , we prompt the LLM to generate descriptor lists $\\mathcal{D}_g(c)$ , using a template consisting of an example question, answer, and format. We use 1-shot prompting to show how to capture geographically representative object designs and contexts.", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1We found ChatGPT to perform worse than GPT-3, also found in [34].", + "bbox": [ + 517, + 886, + 888, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13517", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our prompt exemplifies this below, using the descriptors for Japanese ofuro (お風呂, bathhtub):", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: What are useful features for distinguishing a bathtub in a photo that I took in Japan?", + "bbox": [ + 107, + 133, + 434, + 160 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A: There are several useful visual features to tell there is a bathtub in a photo that I took in Japan:", + "bbox": [ + 109, + 161, + 434, + 189 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- short in length and deep", + "-square shape", + "- wooden, plastic, or steel material", + "- white or brown color", + "-benches on side", + "- next to shower" + ], + "bbox": [ + 109, + 189, + 316, + 270 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Q: What are useful features for distinguishing in a photo that I took in ", + "bbox": [ + 109, + 272, + 434, + 299 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A: There are several useful visual features to tell there is/are $<\\text{category}>$ in a photo that I took in $<\\text{country}>$ :", + "bbox": [ + 109, + 300, + 434, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using knowledge. To convert LLM outputs to CLIP prompts, each descriptor $d$ in $\\mathcal{D}_g(c)$ serves as a prompt $t_{c,d}$ . The format of $t_{c,d}$ is \"a photo of a/an which (is/has/etc.) in which (is/has/etc.) \"). Results on DollarStreet are shown in Table 1.", + "bbox": [ + 496, + 277, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Including country names in prompts can improve object recognition, especially in Africa and Asia. This observation is supported by gains for CountryInPrompt vs. Zero-Shot CLIP, especially in Africa and Asia (up to +5.4 and +2.6 top-1 gains for RN50, resp.). Such differences may occur as country-specific context can align representations closer to these regions, while default prompts do not adequately capture objects around the world (esp. from non-Western regions). In Americas/Europe, adding country names leads to gains with RN50, but slight drops with ViT-B/16 and ViT-B/32. We reason that CLIP's default prompts may be already well-aligned to countries in these regions for those encoders due to overrepresentation in training.", + "bbox": [ + 496, + 400, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prompting with country-specific descriptive knowledge from LLMs outperforms general object knowledge. We observe this from CountryLLM's larger gains over default CLIP than GeneralLLM's for almost all encoders, regions, and metrics. The largest top-1 difference is with ViT-B/32 (in Total, $52.6\\%$ for CountryLLM vs. $51.4\\%$ for GeneralLLM). In top-3 accuracy, the differences for CountryLLM/GeneralLLM in Total are 74.6/73.0 for ViT-B/32, 78.8/77.9 for ViT-B/16, 70.0/68.6 for RN50. These suggest that default non-country-specific knowledge is less adequate for various countries. The gains of CountryLLM vs. Zero-Shot CLIP are generally largest on Africa and Asia, as countries in these regions may have greater shifts vs. the default prompts, but CountryLLM also performs well on Europe. LLM description in general is less effective in Americas, though Americas has a large proportion of USA images, for which default CLIP may be well-aligned.", + "bbox": [ + 496, + 598, + 890, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "There are complementary effects when using CLIP's internal and external LLM geo knowledge. This observation is supported by CountryInPrompt+LLM, the combina", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13519", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b80fcf93084dd217f71b20f4079d5602fb03dd673e67be99ec0b624f3d37256b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
EncoderPrompting MethodTop-1 AccuracyTop-3 Accuracy
EuropeAfricaAsiaAmericasTotalEuropeAfricaAsiaAmericasTotal
Acc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc Δ
ViT-B/32Zero-Shot CLIP [36]59.1 -43.7 -50.8 -55.3 -51.7 -81.1 -64.8 -72.3 -77.4 -73.7 -
GeneralLLM [30]57.3 -1.844.3 +0.650.9 +0.154.6 -0.751.4 -0.378.8 -2.364.5 -0.372.1 -0.275.7 -1.773.0 -0.7
CountryInPrompt57.5 -1.645.2 +1.551.9 +1.155.0 -0.352.1 +0.480.2 -0.965.5 +0.773.3 +1.076.9 -0.573.9 +0.2
CountryLLM59.4 +0.345.2 +1.552.1 +1.355.3 0.052.6 +0.980.9 -0.266.4 +1.673.6 +1.377.4 0.074.6 +0.9
CountryInPrompt+LLM60.8 +1.745.3 +1.652.2 +1.455.0 -0.352.8 +1.181.5 +0.467.4 +2.673.6 +1.376.7 -0.774.7 +1.0
ViT-B/16Zero-Shot CLIP [36]64.3 -46.9 -53.9 -60.1 -55.5 -84.3 -69.3 -75.9 -81.1 -77.2 -
GeneralLLM [30]64.2 -0.148.8 +1.956.0 +2.158.5 -1.656.8 +1.383.9 -0.471.1 +1.876.3 +0.480.4 -0.777.9 +0.7
CountryInPrompt63.9 -0.449.6 +2.755.7 +1.859.3 -0.856.6 +1.184.0 -0.371.3 +2.076.5 +0.680.0 -1.177.7 +0.5
CountryLLM65.2 +0.949.6 +2.755.6 +1.759.7 -0.457.0 +1.584.3 0.071.8 +2.577.5 +1.681.5 +0.478.8 +1.6
CountryInPrompt+LLM65.5 +1.250.8 +3.956.0 +2.159.7 -0.457.4 +1.985.5 +1.272.5 +3.277.0 +1.180.9 -0.278.7 +1.5
RN50Zero-Shot CLIP [36]53.0 -38.0 -44.4 -49.8 -45.7 -76.5 -60.2 -66.4 -72.7 -68.1 -
GeneralLLM [30]55.5 +2.540.9 +2.946.9 +2.550.3 +0.547.9 +2.276.0 -0.561.2 +1.067.7 +1.371.1 -1.668.6 +0.5
CountryInPrompt54.5 +1.543.4 +5.447.0 +2.650.8 +1.048.4 +2.776.0 -0.564.0 +3.868.7 +2.372.7 0.070.0 +1.9
CountryLLM56.2 +3.241.1 +3.147.3 +2.950.4 +0.648.3 +2.677.2 +0.762.5 +2.368.8 +2.472.4 -0.370.0 +1.9
CountryInPrompt+LLM56.4 +3.443.0 +5.048.0 +3.650.9 +1.149.1 +3.476.7 +0.263.1 +2.968.3 +1.971.1 -1.669.4 +1.3
", + "bbox": [ + 98, + 87, + 874, + 325 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/55b8c9edde33a3de4dec99c586dc9b128ea6b014192633c42bceec82ecc60a66.jpg", + "table_caption": [ + "Table 1. Zero-shot CLIP inference with descriptive knowledge prompts, top-1/3 balanced accuracy (Acc) on DollarStreet. Strategies to capture CLIP's internal country knowledge (CountryInPrompt), external LLM country knowledge (CountryLLM), and their combination (CountryInPrompt+LLM), often improve vs. the zero-shot CLIP baseline (prompt \"a photo of a/an \"), especially on Africa and Asia; gains in green, drops in red. CountryLLM notably outperforms the GeneralLLM [30] baseline." + ], + "table_footnote": [], + "table_body": "
EncoderPrompting MethodSource EuropeTarget
AccΔAfricaAsiaAmericasTotal
AccΔAccΔAccΔAcc
ViT-B/16CoOp [52]72.2-53.9-61.5-68.6-61.7
CoCoOp [51]73.2-54.3-61.2-68.3-61.4
KgCoOp [47]73.1-54.4-62.6-68.7-62.4
CountryInPrompt Reg71.8-1.456.8+2.463.0+0.469.8+1.163.5
CountryLLM Reg73.20.055.6+1.263.0+0.470.0+1.363.2
CountryInPrompt+LLM Reg73.6+0.457.2+2.863.8+1.270.3+1.664.0
RN50CoOp [52]64.6-45.2-51.6-59.5-52.2
CoCoOp [51]62.9-44.5-51.0-58.3-51.4
KgCoOp [47]63.5-46.3-53.9-60.5-53.9
CountryInPrompt Reg63.5-1.148.0+1.753.90.060.3-0.254.3
CountryLLM Reg64.5-0.147.4+1.154.2+0.359.9-0.654.3
CountryInPrompt+LLM Reg65.5+0.948.1+1.854.5+0.660.4-0.154.8
", + "bbox": [ + 135, + 398, + 834, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Regularizing soft prompts with geographical knowledge, top-1 bal. acc. on DollarStreet. We emphasize that our regularization aims to improve target performance, rather than source (gray, italicized). Gains/drops are shown vs. the best of soft prompt baselines (shaded). CountryInPrompt+LLM Reg achieves notable gains in target, especially on Africa. Methods use 16 shots per class.", + "bbox": [ + 75, + 602, + 892, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion of CountryInPrompt and CountryLLM, achieving the best Total top-1 performance for every encoder. The Total gains vs. default CLIP are as large as +3.4 (RN50). While CLIP has internal knowledge of country-specific categories, it may be incomplete and imprecise due to limited representation in the image-text training corpus. Adding LLM knowledge, trained on a purely textual corpus, may address some gaps. CountryInPrompt+LLM is notably the top setting in 3/4 regions for each encoder in top-1 accuracy.", + "bbox": [ + 75, + 670, + 470, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Soft Prompting", + "text_level": 1, + "bbox": [ + 76, + 816, + 232, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We next evaluate geography knowledge regularization (Sec. 3.2), our method to improve target performance by ensuring that soft prompts do not overfit class text representations to a source dataset with limited geographical rep", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "resentativeness (e.g. only data from Europe). We compare regularization with ensembles of CountryInPrompt, CountryLLM, and CountryInPrompt+LLM prompts vs. state-of-the-art soft prompting methods in Tables 2/3.", + "bbox": [ + 496, + 670, + 890, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Regularizing soft prompts with target geographical knowledge reduces overfitting to source geographies. Our method effectively improves the ability of CLIP, with prompts trained only on images from Europe, to generalize to target countries. This observation is supported by Total Target gains for CountryInPrompt, CountryLLM, and CountryInPrompt+LLM Reg on DollarStreet (+1.1/0.8/1.6 over the best soft prompt baseline for ViT-B/16). Improvements are notable in Africa: CountryInPrompt+LLM achieves +2.8 for ViT-B/16 and +1.8 for RN50. The effectiveness extends to GeoNet in Table 3: target gains are +1.3", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13520", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0ac535a4285be830b4998e4a2674752702f605ecd65642079d3c8a90ef0a2755.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
EncoderMethodSource USATarget Asia
AccΔAccΔ
ViT-B/16CoOp [52]58.7-51.2-
CoCoOp [51]57.7-52.6-
KgCoOp [47]58.2-52.6-
CIP Reg57.5-1.253.5+0.9
LLM Reg58.5-0.253.1+0.5
CIP+LLM Reg57.6-1.153.9+1.3
RN50CoOp [52]51.4-45.6-
CoCoOp [51]51.1-46.3-
KgCoOp [47]51.8-46.9-
CIPReg50.6-1.247.6+0.7
LLMReg51.80.047.4+0.5
CIP+LLMReg51.1-0.748.3+1.4
", + "bbox": [ + 109, + 88, + 439, + 284 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/af64a739f8d76b1e38bf1a9c84c6931c4a39834b85905a8908af4f4cd125d383.jpg", + "table_caption": [ + "Table 3. Regularizing soft prompts with geographical knowledge, top-1 bal. accuracy on GeoNet. The regularization method accomplishes our goal to increase target performance in GeoNet's USA-to-Asia transfer setting. CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM." + ], + "table_footnote": [], + "table_body": "
MethodThreshold t (# Classes)
<40% (13) Δ<60% (45) Δ<80% (77) Δ≤100% (95) Δ
CoOp [52]31.2-45.6-55.6-61.7
CoCoOp [51]32.8+1.645.4-0.255.2-0.461.4
KgCoOp [47]35.3+4.147.9+2.356.7+1.162.4
CIPReg37.5+6.348.9+3.357.8+2.263.5
LLMReg36.8+5.648.1+2.557.2+1.663.2
CIP+LLMReg39.9+8.749.5+3.958.2+2.664.0
", + "bbox": [ + 102, + 375, + 444, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Performance on DollarStreet classes with less than $t\\%$ recall in CoOp, with ViT-B/16. Gains w.r.t. CoOp of our geography knowledge regularization are especially large for CoOp's difficult classes (+8.7 in <40%), compared to KgCoOp's (+4.1 in <40%, i.e. a 4.6 difference from ours). CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM.", + "bbox": [ + 75, + 500, + 468, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for ViT-B/16 and +1.4 for RN50. The combined strategy works best on target, showing the value of incorporating descriptive knowledge. Since regularization prevents overfitting and potentially optimal source performance, we naturally observe source drops for CountryInPrompt and CountryLLM in Tables 2/3. However, CountryInPrompt+LLM in Table 2 even offers source gains. It is also notable that there are small drops in Americas for RN50, but upon inspection, countries in North America overall have a -0.9 drop, while ones in Central/South America have a +0.8 gain. These results concur with our hypothesis that CLIP is already aligned to countries like the USA. More is in supp., along with experiments varying the source and ensemble.", + "bbox": [ + 75, + 612, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Regularization helps significantly on difficult classes. As certain objects may be especially sensitive to geographical domain shift, we break down classwise performance on DollarStreet in Table 4, using a stratification of class difficulty based on default soft prompting performance (CoOp). The CountryInPrompt+LLM strategy achieves significant", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/137f117ba534aea34faf37626257e927bfa5bf4851ec3fa3139b3a3f67a66c58.jpg", + "image_caption": [ + "Figure 3. Geography knowledge-regularized soft prompts trained on source data (ours, green line) vs. few-shot soft prompts trained on target data (blue curve). (a) Src=Europe, Tgt=Africa, Asia, Amer.; (b) Src=USA, Tgt=Asia. Our 16-shot model trained on only source data (green) outperforms a model with prompts trained on 12 or 4 shots per class of target data (on DollarStreet&GeoNet, resp.), which is 1140&2400 images total." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 694, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f5fa8d183ceb113fc8084085dc751925eaa384b4b68482b543416ada8a1677d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 88, + 885, + 209 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "gains on the classes most difficult with respect to the CoOp baseline. In particular, gains of $+8.7\\%$ in balanced accuracy are achieved for classes with $< 40\\%$ baseline recall, while the highest achieved by $\\mathrm{KgCoOp}$ is $4.1\\%$ . Example classes in this subset are snacks, clothes, and makeup. The DollarStreet classes with greatest improvement, independent of original CoOp accuracy are: piercings, clothes, homes, medication, and refrigerators (all at least $+14\\%$ over CoOp). In GeoNet, dome, goby (fish), eland (antelope), and gloriosa (flower) have $>20$ samples and $>30\\%$ improvement. A total of 64/95 classes in DollarStreet and 209/344 in GeoNet improve vs. CoOp, showing broad coverage.", + "bbox": [ + 496, + 340, + 890, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Regularized source-only prompts outperform few-shot target-trained prompts. Given that soft prompts can show strong performance in few-shot settings, a potential alternative to regularizing soft prompts on source data is to directly acquire a few examples of target data for training. We evaluate this setting by splitting target data into train/test, and training CoOp at varying # of shots of target data for GeoNet and DollarStreet, shown in Fig. 3. Notably, training on 16 shots per class of source data with our regularization method outperforms using 12 & 4 shots per class of target data on DollarStreet & GeoNet. This is a vast amount of target data overall (e.g. 12 shots x 95 classes = 1140 target samples in DollarStreet, 4 shots x 600 classes = 2400 samples in GeoNet). The baseline CoOp trained on 16 shots of source data only outperforms an 8-shot/2-shot target-trained CoOp model (DollarStreet/GeoNet). Our strategy is thus more compelling in the absence of a lot of target data.", + "bbox": [ + 496, + 522, + 892, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance by income. DollarStreet provides estimated monthly income of the household in which an image was captured. We evaluate with the delineation of low, medium, and high-income buckets from [13]. Compared to CoOp/KgCoOp, CountryInPrompt+LLM gains are $+2.5/+3.4$ in low, $+2.4/+1.5$ in medium, and $+2.1/+0.7$ in high. Thus our method especially improves in low-income areas, though it helps across levels. The table is in supp.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13521", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/472f94b47cded8a967066551d0e38e0ac4aa4fe79723bbb21612ea81833d442c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
StatisticCIPCountryLLMCIP+LLM
GDP Per Capita (US $)0.2190.0630.217
Human Devel. Index (HDI)0.4390.3850.451
Land Area (km2)-0.0720.050*-0.046*
Population (#)-0.1310.077-0.123
Population Density (#/km2)0.1030.1580.081
% Agricultural Land0.1390.0700.122
% Forest Area0.1910.0870.201
Avg. Yearly Temp. (°C)0.3800.2560.391
Avg. Yearly Precip. (mm/year)0.2360.1240.230
", + "bbox": [ + 78, + 89, + 470, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Correlation (Pearson's $\\rho$ ) of avg. CLIP class text embedding distance and country statistic difference, e.g. economic (GDP per capita, HDI) and climate factors (temperature, precipitation, forest area). We use the 63 countries in DollarStreet (1,953 pairs). Bold values have $\\rho > 0.2$ , * means not significant ( $\\alpha = 0.01$ ).", + "bbox": [ + 76, + 222, + 468, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f12fa63d81da462d4ff8bc95856453d31beff225d1d17aa4729d63604e18d2ff.jpg", + "image_caption": [ + "Figure 4. Qualitative analysis. We show examples where geography-specific descriptors improve/hurt vs. general descriptors in zero-shot inference. We highlight the prediction's descriptors, bolding the highest activating one. Encoder=RN50." + ], + "image_footnote": [], + "bbox": [ + 86, + 306, + 452, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Further Analysis", + "text_level": 1, + "bbox": [ + 76, + 574, + 243, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Are descriptions correlated with key country statistics? For a pair of countries, we compute two values. We measure the distance between each class embedding and take the average overall distance as one value. We also take the absolute difference between statistics for those countries (from [2, 42], e.g. difference in avg. yearly temperature) as the other value. We compute the correlation between these two values over every unique country pair in DollarStreet, showing results in Table 5. We find that the strongest correlation across each prompt type is with HDI, which summarizes human development. It is notable that factors like yearly temperature and precipitation also show moderate correlations, indicating a potential role of climate. Future work may further explore how object differences present with respect to these factors. It will also be critical to ensure that differences between countries are representative and not exaggerated in embeddings.", + "bbox": [ + 75, + 598, + 467, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Descriptor topics. We show a UMAP [29] visualization comparing CountryLLM text embeddings for the category homes across geographies in Fig. 5. Countries tend to group", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b041f7823e6877bce0aae108097e73d6d42b86c5b29ab7e994725e8fdf5f273.jpg", + "image_caption": [ + "Figure 5. UMAP [29] plot for CountryLLM and the category homes in DollarStreet. Country-specific descriptors are often close to those of other countries intra-continent, likely due to similar weather, environment, and/or economic conditions." + ], + "image_footnote": [], + "bbox": [ + 545, + 90, + 846, + 193 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "by continent, showing the representations may capture similarity in features like climate and/or economics. We examine a few topics mentioned in the CountryLLM descriptors for homes. While “stone” is described across continents, “bright colors” and “mud” are mentioned mostly in Africa, and “balcony” in Europe and Asia. We show more in supp. Success and failure examples. We provide examples of CountryLLM vs. GeneralLLM in Fig. 4 on DollarStreet. The model captures geographical descriptive knowledge like “sandy colored stucco walls” for homes in Jordan, a feature which may be less common for Western homes. Sometimes the model may be too attentive to attributes, leading to confusion (e.g. choosing rug over bed). Future work that enhances alignment in VLMs can likely improve results.", + "bbox": [ + 496, + 287, + 890, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 513, + 617, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we bring attention to how various strategies to prompt CLIP affect recognition performance across geographies. In addition, through soft prompting with descriptive knowledge, we provide a mechanism to achieve a more geo-generalizable set of class representations across regions. Our work is only a first step in this important area.", + "bbox": [ + 496, + 537, + 890, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and ethical considerations. While our method's proof of concept is demonstrated in a positive effort to debias CLIP's default representations through diversity, due to the biased worldview of the Internet, CLIP's representations are likely inadequate, exaggerated, and/or not fully representative for some countries. While we expect quality LLM knowledge to guide better representations, LLM knowledge can also be incorrect (e.g., through hallucination), imprecise, or biased.", + "bbox": [ + 496, + 628, + 890, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future work. For the above reasons, our future efforts aim to ensure more representative VLM/LLM knowledge. We strongly advocate for the community to seek communication with diverse groups within all countries (i.e. to capture areas that range from low to high income) to ensure better representation and fairness in AI technology use. There are notable continent-level disparities to still improve upon.", + "bbox": [ + 496, + 765, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported by National Science Foundation Grants No. 2006885 and 2329992.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13522", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Common Crawl, 2023. https://commoncrawl.org/. 3", + "[2] Wikipedia, 2023. https://en.wikipedia.org/. 3,8", + "[3] Abhipsa Basu, R. Venkatesh Babu, and Danish Pruthi. Inspecting the geographical representativeness of images from text-to-image models. 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International Journal of Computer Vision, 130(9):2337-2348, 2022. 2, 4, 5, 6, 7" + ], + "bbox": [ + 503, + 92, + 890, + 825 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13524", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/a3586110-0f62-4a60-8f39-dd762f0a5105_model.json b/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/a3586110-0f62-4a60-8f39-dd762f0a5105_model.json new file mode 100644 index 0000000000000000000000000000000000000000..10eb2aa3d069fa29bf581f9d66f5ce82a1056485 --- /dev/null +++ b/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/a3586110-0f62-4a60-8f39-dd762f0a5105_model.json @@ -0,0 +1,2112 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.131, + 0.83, + 0.177 + ], + "angle": 0, + "content": "Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.203, + 0.784, + 0.221 + ], + "angle": 0, + "content": "Kyle Buettner1, Sina Malakouti2, Xiang Lorraine Li1,2, Adriana Kovashka1,2" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.222, + 0.882, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\)Intelligent Systems Program, \\(^{2}\\)Department of Computer Science, University of Pittsburgh, PA, USA" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.242, + 0.758, + 0.258 + ], + "angle": 0, + "content": "{buettnerk, sem238}@pitt.edu, {xianglli, kovashka}@cs.pitt.edu" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.26, + 0.702, + 0.275 + ], + "angle": 0, + "content": "https://krbuettner.github.io/GeoKnowledgePrompting" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.474, + 0.646 + ], + "angle": 0, + "content": "Existing object recognition models have been shown to lack robustness in diverse geographical scenarios due to domain shifts in design and context. Class representations need to be adapted to more accurately reflect an object concept under these shifts. In the absence of training data from target geographies, we hypothesize that geographically diverse descriptive knowledge of categories can enhance robustness. For this purpose, we explore the feasibility of probing a large language model for geography-based object knowledge, and we examine the effects of integrating knowledge into zero-shot and learnable soft prompting with CLIP. Within this exploration, we propose geography knowledge regularization to ensure that soft prompts trained on a source set of geographies generalize to an unseen target set. Accuracy gains over prompting baselines on DollarStreet while training only on Europe data are up to \\(+2.8 / 1.2 / 1.6\\) on target data from Africa/Asia/Americas, and \\(+4.6\\) overall on the hardest classes. Competitive performance is shown vs. few-shot target training, and analysis is provided to direct future study of geographical robustness." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.693, + 0.21, + 0.709 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The performance of object recognition models degrades when tested in new geographies (e.g., cities, countries, continents) [7, 21, 33, 39, 43]. Numerous factors contribute to the challenging problem of geographical domain shift, such as cross-geography changes in object design/parts, materials, and context. These changes in turn may be due to cultural, climate, or economic differences around the world. Recent work has shown standard adaptation techniques fail when used for geographical domain shifts [21, 33], but there has yet to be significant progress in the creation of techniques that improve geographical robustness. Such progress is necessary to ensure equitable use of AI in the future." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.311, + 0.885, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.473, + 0.895, + 0.557 + ], + "angle": 0, + "content": "Figure 1. Descriptive knowledge can address concept shifts across geographies. Observe the wide range of object designs and contexts in the DollarStreet [11] category tools around the world. Our work's premise is that textual representations for classes in vision-language models can be enhanced to better suit diverse object representations across geographies. Map made with [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Overall, models need representations that adequately capture a category's various forms around the world. A natural solution is to collect training data of objects from different regions. However, this approach is expensive, takes significant effort, and is difficult for regions with limited Internet access. Fortunately, geographical shifts have a unique property compared to other common domain shifts (e.g. ones due to artistic style or weather changes)—they can be addressed with descriptive knowledge about concept changes. In other words, it is possible to describe the features of an object in a region and use this information to adapt a model's default representation. For instance, as shown in Fig. 1, for rural areas in Papua New Guinea, tools can be described as being used for \"cooking, hunting, and fishing\", and for rural areas in Malawi, tools may often be \"made of metal and wood, for farming\". Models should account for diverse presentations and contexts of a category and not be limited to biased presentations (e.g. if the model learns tools as just being \"metallic with logos\")." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We examine the effects of probing geo-diverse knowledge in two ways. First, we analyze whether a vision" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13515" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.242 + ], + "angle": 0, + "content": "language model (VLM, i.e. CLIP [36]) has encoded categories in a geo-specific manner, such that adding a country's name to a prompt (e.g. \"A photo of a house in China\") elicits knowledge that improves recognition. Second, we probe a large language model (LLM, i.e. GPT-3 davinci003) for geography-specific knowledge to obtain visual feature descriptors for an object in different locations. We analyze results in zero-shot inference on geographically and socioeconomically diverse data (DollarStreet [11]), finding the combination of knowledge to often be complementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.471, + 0.454 + ], + "angle": 0, + "content": "We further consider a practical scenario where CLIP is optimized with soft prompting, using only a \"source\" geography with easy-to-access data (e.g. Europe), while the model is applied downstream on \"target\" data from other parts of the world (e.g. Africa, Asia, Americas). We propose geography knowledge regularization, which uses knowledge ensembled over countries to enable soft prompts to achieve geographically generalizable class representations. We test our method on the recent DollarStreet and GeoNet [21] datasets. Our regularization boosts performance over baseline soft prompting methods, and has benefits with respect to few-shot target-specific training (a 16-shot-per-class regularized model without any target data outperforms a 12-shot-per-class target-trained model on DollarStreet)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.455, + 0.47, + 0.514 + ], + "angle": 0, + "content": "Our method is the first to effectively address geo shifts in object recognition. It outperforms zero-shot CLIP (assumed to have some robustness) by \\(10.3\\%\\) on Africa, CoOp [52] by \\(3.3\\%\\), and the best baseline by \\(4.6\\%\\) on the hardest classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.47, + 0.651 + ], + "angle": 0, + "content": "To summarize, we answer the following questions: (1) Does adding geographical context (i.e. country names) to CLIP prompts improve recognition across geographies? (2) Can an LLM provide useful geographical descriptive knowledge to improve recognition? (3) How can we optimize soft prompts for CLIP using an accessible data source with consideration of target geographies not represented in the training set? (4) Where can soft prompts enhanced with geographical knowledge provide the most benefits?" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.22, + 0.68 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Geographical domain shifts occur when the target setting is in a different geography (e.g. continent, country, city) than where the source data was acquired. Shifts involve changes in object design (e.g. differences in house architecture) and context (i.e. background/co-occurring objects vary). Datasets tailored to cross-country/continent object recognition have recently been proposed, e.g. DollarStreet [11], GeoNet [21], GeoDE [37], GeoYFCC [9], and OpenImages-Extended [5]. Interestingly, [21, 33] demonstrate that traditional methods in unsupervised domain adaptation [10, 19, 20, 27, 28, 38, 44, 45, 50] which seek to bridge gaps based on visual features alone, do not effectively address geographical domain shift. They achieve negligible gains (e.g. 0.14 for [10] in [33]) or often drops" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "in performance (e.g. all methods tested in [21]), compared to just using the source model. Attempts to specifically address geographical robustness are limited: [43] corrects for differences in the sizes of cars, [9] proposes a discriminative domain embedding from target data, and GiVL [48] pretrains with knowledge from Wikipedia. In contrast, our descriptive knowledge regularization works for different categories (not just cars); we do not require target domain data to achieve gains cross-geography; we explore the strong capabilities of LLMs to gather relevant knowledge; and we propose lightweight adaptation through soft prompting (unlike GiVL's expensive pretraining)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.892, + 0.403 + ], + "angle": 0, + "content": "Vision-language (VL) models [17, 25, 26, 36, 49] excel on a variety of tasks. CLIP [36] shows impressive zero-shot object recognition across different settings. Yet its performance given geographical shift is less apparent. GeoNet [21] only shows finetuned performance, which is expensive given CLIP's large scale. GeoDE [37] only shows zero-shot inference with CLIP's default prompts. Neither work evaluates descriptive knowledge or soft prompting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.773 + ], + "angle": 0, + "content": "Learning soft textual prompts. Several recent works to adapt CLIP have focused on parameter and data efficiency using linear probing [36] and prompting [18, 23, 52]. Soft textual prompting (e.g. CoOp [52]) is notable as it optimizes class text embeddings (without manual tuning), which we hypothesize is critical to adequately adapt for geographical robustness. As CoOp overfits on base (seen) classes, CoCoOp [51] proposes to condition prompts on the image for better generalizability. KgCoOp [47] alternatively guides learned prompt embeddings towards CLIP's manual prompt embeddings through a distance constraint to avoid degradation on unseen classes. Our approach also uses a distance constraint, but it differs from [47] with the purpose of regularizing learned prompt representations for cross-geography generalization instead of the base-to-new-class setting. We also show novel benefits of regularization when used with an ensemble of CLIP's internal geographical knowledge and external geographical descriptive knowledge. Our approach notably outperforms each of CoOp, CoCoOp, and KgCoOp by at least +2.8 accuracy on target countries in Africa in DollarStreet. External knowledge aids unseen classes in KAPT [22], but not with respect to geographical knowledge. Prompt tuning for adaptation has been tested in [12, 40], but not with descriptive knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Knowledge probed from large language models like [4, 6, 31, 32] has been used for visual reasoning [46], embodied agent planning [15, 41], and to generate additional context for VLM class prompts in object recognition [30, 34]. We uniquely probe LLMs for distinguishable visual descriptions for the same object class across different geographical regions. We are also the first to incorporate geographical knowledge from LLMs into soft prompting." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13516" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.094, + 0.452, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.468, + 0.098, + 0.75, + 0.123 + ], + "angle": 0, + "content": "(2) Optimize Soft Prompts on Source Data While Regularizing Towards Target Knowledge" + }, + { + "type": "image", + "bbox": [ + 0.467, + 0.127, + 0.882, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.893, + 0.342 + ], + "angle": 0, + "content": "Figure 2. Geography knowledge regularization. To ensure robustness in soft prompt learning, we (1) incorporate knowledge internal to CLIP and externally obtained from an LLM. (2) This descriptive knowledge regularizes class representations when training on a specific source geography (e.g. Europe), thus (3) increasing robustness when generalizing to target geographies (e.g. Vietnam)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.366, + 0.185, + 0.384 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.47, + 0.665 + ], + "angle": 0, + "content": "We investigate geographical shift in object recognition with VLMs. We posit that the manner in which classes are described is critical due to cross-geography shifts in design and context. We also hypothesize that CLIP's default class representations elicited through \"a photo of a/an \" prompts may not adequately represent classes around the world. Instead, they may be more aligned to high-resource geographies due to Internet-based training data. Optimizing representations (with soft prompts) on a specific geography (e.g. Europe) may exacerbate a lack of robustness. Our main idea (Fig. 2) is to incorporate object-related geographical knowledge into prompting to ensure model robustness in different regions. We outline our mechanism to obtain geography-specific context by probing CLIP's internal knowledge and an external LLM's descriptive knowledge. We further propose geography knowledge regularization to ensure soft prompts do not overfit when training data is limited to certain geographies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.47, + 0.817 + ], + "angle": 0, + "content": "Preliminaries. We consider object recognition on a dataset \\( S \\) containing a class set \\( \\mathcal{C} \\) (size \\( N_{c} \\)) over a set of geographies \\( \\mathcal{G} \\). We consider a geography \\( g \\) to be either a country or continent. Our VLM is CLIP [36], with an image encoder \\( f \\) and language encoder \\( h \\). We incorporate knowledge of each geography \\( g \\) into prompting using (1) zero-shot inference or (2) soft textual prompting. Prompts are defined as \\( t \\) (each is a set of tokens), and class embeddings \\( w \\) are calculated as \\( h(t) \\). We refer to CLIP's default prompt \"a photo of a/an \" for a class \\( c \\) as \\( t_{c}^{\\text{default}} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.376, + 0.848 + ], + "angle": 0, + "content": "3.1. Geographical Knowledge Probing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Probing CLIP's internal geographical knowledge. Our first strategy of investigation is to augment CLIP's manual prompts to include country names, as we surmise that some" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.503 + ], + "angle": 0, + "content": "of the resulting class representations may be better aligned to how categories present in different regions. [3] inspires this hypothesis, showing that adding country names to image generation prompts can achieve gains in geographical representativeness. However, it is an open question whether adding country names in prompts improves recognition. We define the setting CountryInPrompt, using the prompt \\( t_c^{CountryInPrompt} \\) with template \"a photo of a/an in \", e.g. \"a photo of a stove in Burundi.\"" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.893, + 0.763 + ], + "angle": 0, + "content": "Probing external LLM geographical knowledge. As CLIP may not have sufficient knowledge of objects in some regions, we consider further augmenting prompts with external knowledge. Motivated by probing LLMs for general attribute-based object descriptions [30, 34] (e.g. a tiger with \"stripes and sharp teeth\"), we probe GPT-3 (davinci-003) for geography-specific descriptions of object styles, contexts, and materials.1 We reason that since LLMs are trained on large information sources (e.g. CommonCrawl [1], WebText [35], Wikipedia [2]), they may have knowledge about how an object presents in a region due to climate, economics, and/or cultural factors. For instance, roofs may sometimes be \"thatched\" in tropical and temperate climates, and cutlery may sometimes be made of \"bamboo\" in areas with bamboo forests. Our goal is unique vs. [30, 34] in that we explore descriptive knowledge differences for the same class to address domain shifts across regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Acquiring knowledge. We follow [30], but instead of gathering one set of feature descriptors \\(\\mathcal{D}(c)\\) for each \\(c\\), we collect sets per country. For each class \\(c\\) and geography \\(g\\), we prompt the LLM to generate descriptor lists \\(\\mathcal{D}_g(c)\\), using a template consisting of an example question, answer, and format. We use 1-shot prompting to show how to capture geographically representative object designs and contexts." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.89, + 0.9 + ], + "angle": 0, + "content": "1We found ChatGPT to perform worse than GPT-3, also found in [34]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13517" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Our prompt exemplifies this below, using the descriptors for Japanese ofuro (お風呂, bathhtub):" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.134, + 0.436, + 0.161 + ], + "angle": 0, + "content": "Q: What are useful features for distinguishing a bathtub in a photo that I took in Japan?" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.162, + 0.436, + 0.19 + ], + "angle": 0, + "content": "A: There are several useful visual features to tell there is a bathtub in a photo that I took in Japan:" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.19, + 0.264, + 0.203 + ], + "angle": 0, + "content": "- short in length and deep" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.205, + 0.199, + 0.217 + ], + "angle": 0, + "content": "-square shape" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.218, + 0.317, + 0.23 + ], + "angle": 0, + "content": "- wooden, plastic, or steel material" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.232, + 0.246, + 0.243 + ], + "angle": 0, + "content": "- white or brown color" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.246, + 0.216, + 0.257 + ], + "angle": 0, + "content": "-benches on side" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.26, + 0.21, + 0.271 + ], + "angle": 0, + "content": "- next to shower" + }, + { + "type": "list", + "bbox": [ + 0.111, + 0.19, + 0.317, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.273, + 0.436, + 0.3 + ], + "angle": 0, + "content": "Q: What are useful features for distinguishing in a photo that I took in " + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.301, + 0.436, + 0.328 + ], + "angle": 0, + "content": "A: There are several useful visual features to tell there is/are \\(<\\text{category}>\\) in a photo that I took in \\(<\\text{country}>\\):" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.34, + 0.47, + 0.493 + ], + "angle": 0, + "content": "Using knowledge. To convert LLM outputs to CLIP prompts, each descriptor \\(d\\) in \\(\\mathcal{D}_g(c)\\) serves as a prompt \\(t_{c,d}\\). The format of \\(t_{c,d}\\) is \"a photo of a/an which (is/has/etc.) in which (is/has/etc.) \"). Results on DollarStreet are shown in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Including country names in prompts can improve object recognition, especially in Africa and Asia. This observation is supported by gains for CountryInPrompt vs. Zero-Shot CLIP, especially in Africa and Asia (up to +5.4 and +2.6 top-1 gains for RN50, resp.). Such differences may occur as country-specific context can align representations closer to these regions, while default prompts do not adequately capture objects around the world (esp. from non-Western regions). In Americas/Europe, adding country names leads to gains with RN50, but slight drops with ViT-B/16 and ViT-B/32. We reason that CLIP's default prompts may be already well-aligned to countries in these regions for those encoders due to overrepresentation in training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Prompting with country-specific descriptive knowledge from LLMs outperforms general object knowledge. We observe this from CountryLLM's larger gains over default CLIP than GeneralLLM's for almost all encoders, regions, and metrics. The largest top-1 difference is with ViT-B/32 (in Total, \\(52.6\\%\\) for CountryLLM vs. \\(51.4\\%\\) for GeneralLLM). In top-3 accuracy, the differences for CountryLLM/GeneralLLM in Total are 74.6/73.0 for ViT-B/32, 78.8/77.9 for ViT-B/16, 70.0/68.6 for RN50. These suggest that default non-country-specific knowledge is less adequate for various countries. The gains of CountryLLM vs. Zero-Shot CLIP are generally largest on Africa and Asia, as countries in these regions may have greater shifts vs. the default prompts, but CountryLLM also performs well on Europe. LLM description in general is less effective in Americas, though Americas has a large proportion of USA images, for which default CLIP may be well-aligned." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "There are complementary effects when using CLIP's internal and external LLM geo knowledge. This observation is supported by CountryInPrompt+LLM, the combina" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13519" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.088, + 0.875, + 0.327 + ], + "angle": 0, + "content": "
EncoderPrompting MethodTop-1 AccuracyTop-3 Accuracy
EuropeAfricaAsiaAmericasTotalEuropeAfricaAsiaAmericasTotal
Acc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc Δ
ViT-B/32Zero-Shot CLIP [36]59.1 -43.7 -50.8 -55.3 -51.7 -81.1 -64.8 -72.3 -77.4 -73.7 -
GeneralLLM [30]57.3 -1.844.3 +0.650.9 +0.154.6 -0.751.4 -0.378.8 -2.364.5 -0.372.1 -0.275.7 -1.773.0 -0.7
CountryInPrompt57.5 -1.645.2 +1.551.9 +1.155.0 -0.352.1 +0.480.2 -0.965.5 +0.773.3 +1.076.9 -0.573.9 +0.2
CountryLLM59.4 +0.345.2 +1.552.1 +1.355.3 0.052.6 +0.980.9 -0.266.4 +1.673.6 +1.377.4 0.074.6 +0.9
CountryInPrompt+LLM60.8 +1.745.3 +1.652.2 +1.455.0 -0.352.8 +1.181.5 +0.467.4 +2.673.6 +1.376.7 -0.774.7 +1.0
ViT-B/16Zero-Shot CLIP [36]64.3 -46.9 -53.9 -60.1 -55.5 -84.3 -69.3 -75.9 -81.1 -77.2 -
GeneralLLM [30]64.2 -0.148.8 +1.956.0 +2.158.5 -1.656.8 +1.383.9 -0.471.1 +1.876.3 +0.480.4 -0.777.9 +0.7
CountryInPrompt63.9 -0.449.6 +2.755.7 +1.859.3 -0.856.6 +1.184.0 -0.371.3 +2.076.5 +0.680.0 -1.177.7 +0.5
CountryLLM65.2 +0.949.6 +2.755.6 +1.759.7 -0.457.0 +1.584.3 0.071.8 +2.577.5 +1.681.5 +0.478.8 +1.6
CountryInPrompt+LLM65.5 +1.250.8 +3.956.0 +2.159.7 -0.457.4 +1.985.5 +1.272.5 +3.277.0 +1.180.9 -0.278.7 +1.5
RN50Zero-Shot CLIP [36]53.0 -38.0 -44.4 -49.8 -45.7 -76.5 -60.2 -66.4 -72.7 -68.1 -
GeneralLLM [30]55.5 +2.540.9 +2.946.9 +2.550.3 +0.547.9 +2.276.0 -0.561.2 +1.067.7 +1.371.1 -1.668.6 +0.5
CountryInPrompt54.5 +1.543.4 +5.447.0 +2.650.8 +1.048.4 +2.776.0 -0.564.0 +3.868.7 +2.372.7 0.070.0 +1.9
CountryLLM56.2 +3.241.1 +3.147.3 +2.950.4 +0.648.3 +2.677.2 +0.762.5 +2.368.8 +2.472.4 -0.370.0 +1.9
CountryInPrompt+LLM56.4 +3.443.0 +5.048.0 +3.650.9 +1.149.1 +3.476.7 +0.263.1 +2.968.3 +1.971.1 -1.669.4 +1.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.331, + 0.895, + 0.388 + ], + "angle": 0, + "content": "Table 1. Zero-shot CLIP inference with descriptive knowledge prompts, top-1/3 balanced accuracy (Acc) on DollarStreet. Strategies to capture CLIP's internal country knowledge (CountryInPrompt), external LLM country knowledge (CountryLLM), and their combination (CountryInPrompt+LLM), often improve vs. the zero-shot CLIP baseline (prompt \"a photo of a/an \"), especially on Africa and Asia; gains in green, drops in red. CountryLLM notably outperforms the GeneralLLM [30] baseline." + }, + { + "type": "table", + "bbox": [ + 0.137, + 0.4, + 0.836, + 0.598 + ], + "angle": 0, + "content": "
EncoderPrompting MethodSource EuropeTarget
AccΔAfricaAsiaAmericasTotal
AccΔAccΔAccΔAcc
ViT-B/16CoOp [52]72.2-53.9-61.5-68.6-61.7
CoCoOp [51]73.2-54.3-61.2-68.3-61.4
KgCoOp [47]73.1-54.4-62.6-68.7-62.4
CountryInPrompt Reg71.8-1.456.8+2.463.0+0.469.8+1.163.5
CountryLLM Reg73.20.055.6+1.263.0+0.470.0+1.363.2
CountryInPrompt+LLM Reg73.6+0.457.2+2.863.8+1.270.3+1.664.0
RN50CoOp [52]64.6-45.2-51.6-59.5-52.2
CoCoOp [51]62.9-44.5-51.0-58.3-51.4
KgCoOp [47]63.5-46.3-53.9-60.5-53.9
CountryInPrompt Reg63.5-1.148.0+1.753.90.060.3-0.254.3
CountryLLM Reg64.5-0.147.4+1.154.2+0.359.9-0.654.3
CountryInPrompt+LLM Reg65.5+0.948.1+1.854.5+0.660.4-0.154.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.603, + 0.893, + 0.646 + ], + "angle": 0, + "content": "Table 2. Regularizing soft prompts with geographical knowledge, top-1 bal. acc. on DollarStreet. We emphasize that our regularization aims to improve target performance, rather than source (gray, italicized). Gains/drops are shown vs. the best of soft prompt baselines (shaded). CountryInPrompt+LLM Reg achieves notable gains in target, especially on Africa. Methods use 16 shots per class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.471, + 0.809 + ], + "angle": 0, + "content": "tion of CountryInPrompt and CountryLLM, achieving the best Total top-1 performance for every encoder. The Total gains vs. default CLIP are as large as +3.4 (RN50). While CLIP has internal knowledge of country-specific categories, it may be incomplete and imprecise due to limited representation in the image-text training corpus. Adding LLM knowledge, trained on a purely textual corpus, may address some gaps. CountryInPrompt+LLM is notably the top setting in 3/4 regions for each encoder in top-1 accuracy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.233, + 0.833 + ], + "angle": 0, + "content": "5.2. Soft Prompting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We next evaluate geography knowledge regularization (Sec. 3.2), our method to improve target performance by ensuring that soft prompts do not overfit class text representations to a source dataset with limited geographical rep" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.732 + ], + "angle": 0, + "content": "resentativeness (e.g. only data from Europe). We compare regularization with ensembles of CountryInPrompt, CountryLLM, and CountryInPrompt+LLM prompts vs. state-of-the-art soft prompting methods in Tables 2/3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Regularizing soft prompts with target geographical knowledge reduces overfitting to source geographies. Our method effectively improves the ability of CLIP, with prompts trained only on images from Europe, to generalize to target countries. This observation is supported by Total Target gains for CountryInPrompt, CountryLLM, and CountryInPrompt+LLM Reg on DollarStreet (+1.1/0.8/1.6 over the best soft prompt baseline for ViT-B/16). Improvements are notable in Africa: CountryInPrompt+LLM achieves +2.8 for ViT-B/16 and +1.8 for RN50. The effectiveness extends to GeoNet in Table 3: target gains are +1.3" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13520" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.44, + 0.285 + ], + "angle": 0, + "content": "
EncoderMethodSource USATarget Asia
AccΔAccΔ
ViT-B/16CoOp [52]58.7-51.2-
CoCoOp [51]57.7-52.6-
KgCoOp [47]58.2-52.6-
CIP Reg57.5-1.253.5+0.9
LLM Reg58.5-0.253.1+0.5
CIP+LLM Reg57.6-1.153.9+1.3
RN50CoOp [52]51.4-45.6-
CoCoOp [51]51.1-46.3-
KgCoOp [47]51.8-46.9-
CIPReg50.6-1.247.6+0.7
LLMReg51.80.047.4+0.5
CIP+LLMReg51.1-0.748.3+1.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.29, + 0.472, + 0.361 + ], + "angle": 0, + "content": "Table 3. Regularizing soft prompts with geographical knowledge, top-1 bal. accuracy on GeoNet. The regularization method accomplishes our goal to increase target performance in GeoNet's USA-to-Asia transfer setting. CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.376, + 0.445, + 0.491 + ], + "angle": 0, + "content": "
MethodThreshold t (# Classes)
<40% (13) Δ<60% (45) Δ<80% (77) Δ≤100% (95) Δ
CoOp [52]31.2-45.6-55.6-61.7
CoCoOp [51]32.8+1.645.4-0.255.2-0.461.4
KgCoOp [47]35.3+4.147.9+2.356.7+1.162.4
CIPReg37.5+6.348.9+3.357.8+2.263.5
LLMReg36.8+5.648.1+2.557.2+1.663.2
CIP+LLMReg39.9+8.749.5+3.958.2+2.664.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.584 + ], + "angle": 0, + "content": "Table 4. Performance on DollarStreet classes with less than \\( t\\% \\) recall in CoOp, with ViT-B/16. Gains w.r.t. CoOp of our geography knowledge regularization are especially large for CoOp's difficult classes (+8.7 in <40%), compared to KgCoOp's (+4.1 in <40%, i.e. a 4.6 difference from ours). CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.809 + ], + "angle": 0, + "content": "for ViT-B/16 and +1.4 for RN50. The combined strategy works best on target, showing the value of incorporating descriptive knowledge. Since regularization prevents overfitting and potentially optimal source performance, we naturally observe source drops for CountryInPrompt and CountryLLM in Tables 2/3. However, CountryInPrompt+LLM in Table 2 even offers source gains. It is also notable that there are small drops in Americas for RN50, but upon inspection, countries in North America overall have a -0.9 drop, while ones in Central/South America have a +0.8 gain. These results concur with our hypothesis that CLIP is already aligned to countries like the USA. More is in supp., along with experiments varying the source and ensemble." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Regularization helps significantly on difficult classes. As certain objects may be especially sensitive to geographical domain shift, we break down classwise performance on DollarStreet in Table 4, using a stratification of class difficulty based on default soft prompting performance (CoOp). The CountryInPrompt+LLM strategy achieves significant" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.695, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.089, + 0.887, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.215, + 0.892, + 0.312 + ], + "angle": 0, + "content": "Figure 3. Geography knowledge-regularized soft prompts trained on source data (ours, green line) vs. few-shot soft prompts trained on target data (blue curve). (a) Src=Europe, Tgt=Africa, Asia, Amer.; (b) Src=USA, Tgt=Asia. Our 16-shot model trained on only source data (green) outperforms a model with prompts trained on 12 or 4 shots per class of target data (on DollarStreet&GeoNet, resp.), which is 1140&2400 images total." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.522 + ], + "angle": 0, + "content": "gains on the classes most difficult with respect to the CoOp baseline. In particular, gains of \\(+8.7\\%\\) in balanced accuracy are achieved for classes with \\(< 40\\%\\) baseline recall, while the highest achieved by \\(\\mathrm{KgCoOp}\\) is \\(4.1\\%\\). Example classes in this subset are snacks, clothes, and makeup. The DollarStreet classes with greatest improvement, independent of original CoOp accuracy are: piercings, clothes, homes, medication, and refrigerators (all at least \\(+14\\%\\) over CoOp). In GeoNet, dome, goby (fish), eland (antelope), and gloriosa (flower) have \\(>20\\) samples and \\(>30\\%\\) improvement. A total of 64/95 classes in DollarStreet and 209/344 in GeoNet improve vs. CoOp, showing broad coverage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Regularized source-only prompts outperform few-shot target-trained prompts. Given that soft prompts can show strong performance in few-shot settings, a potential alternative to regularizing soft prompts on source data is to directly acquire a few examples of target data for training. We evaluate this setting by splitting target data into train/test, and training CoOp at varying # of shots of target data for GeoNet and DollarStreet, shown in Fig. 3. Notably, training on 16 shots per class of source data with our regularization method outperforms using 12 & 4 shots per class of target data on DollarStreet & GeoNet. This is a vast amount of target data overall (e.g. 12 shots x 95 classes = 1140 target samples in DollarStreet, 4 shots x 600 classes = 2400 samples in GeoNet). The baseline CoOp trained on 16 shots of source data only outperforms an 8-shot/2-shot target-trained CoOp model (DollarStreet/GeoNet). Our strategy is thus more compelling in the absence of a lot of target data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Performance by income. DollarStreet provides estimated monthly income of the household in which an image was captured. We evaluate with the delineation of low, medium, and high-income buckets from [13]. Compared to CoOp/KgCoOp, CountryInPrompt+LLM gains are \\(+2.5/+3.4\\) in low, \\(+2.4/+1.5\\) in medium, and \\(+2.1/+0.7\\) in high. Thus our method especially improves in low-income areas, though it helps across levels. The table is in supp." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13521" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.472, + 0.217 + ], + "angle": 0, + "content": "
StatisticCIPCountryLLMCIP+LLM
GDP Per Capita (US $)0.2190.0630.217
Human Devel. Index (HDI)0.4390.3850.451
Land Area (km2)-0.0720.050*-0.046*
Population (#)-0.1310.077-0.123
Population Density (#/km2)0.1030.1580.081
% Agricultural Land0.1390.0700.122
% Forest Area0.1910.0870.201
Avg. Yearly Temp. (°C)0.3800.2560.391
Avg. Yearly Precip. (mm/year)0.2360.1240.230
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.223, + 0.47, + 0.294 + ], + "angle": 0, + "content": "Table 5. Correlation (Pearson's \\( \\rho \\)) of avg. CLIP class text embedding distance and country statistic difference, e.g. economic (GDP per capita, HDI) and climate factors (temperature, precipitation, forest area). We use the 63 countries in DollarStreet (1,953 pairs). Bold values have \\( \\rho > 0.2 \\), * means not significant (\\( \\alpha = 0.01 \\))." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.308, + 0.453, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.548 + ], + "angle": 0, + "content": "Figure 4. Qualitative analysis. We show examples where geography-specific descriptors improve/hurt vs. general descriptors in zero-shot inference. We highlight the prediction's descriptors, bolding the highest activating one. Encoder=RN50." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.575, + 0.245, + 0.59 + ], + "angle": 0, + "content": "5.3. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.468, + 0.854 + ], + "angle": 0, + "content": "Are descriptions correlated with key country statistics? For a pair of countries, we compute two values. We measure the distance between each class embedding and take the average overall distance as one value. We also take the absolute difference between statistics for those countries (from [2, 42], e.g. difference in avg. yearly temperature) as the other value. We compute the correlation between these two values over every unique country pair in DollarStreet, showing results in Table 5. We find that the strongest correlation across each prompt type is with HDI, which summarizes human development. It is notable that factors like yearly temperature and precipitation also show moderate correlations, indicating a potential role of climate. Future work may further explore how object differences present with respect to these factors. It will also be critical to ensure that differences between countries are representative and not exaggerated in embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Descriptor topics. We show a UMAP [29] visualization comparing CountryLLM text embeddings for the category homes across geographies in Fig. 5. Countries tend to group" + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.091, + 0.848, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.206, + 0.892, + 0.261 + ], + "angle": 0, + "content": "Figure 5. UMAP [29] plot for CountryLLM and the category homes in DollarStreet. Country-specific descriptors are often close to those of other countries intra-continent, likely due to similar weather, environment, and/or economic conditions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.501 + ], + "angle": 0, + "content": "by continent, showing the representations may capture similarity in features like climate and/or economics. We examine a few topics mentioned in the CountryLLM descriptors for homes. While “stone” is described across continents, “bright colors” and “mud” are mentioned mostly in Africa, and “balcony” in Europe and Asia. We show more in supp. Success and failure examples. We provide examples of CountryLLM vs. GeneralLLM in Fig. 4 on DollarStreet. The model captures geographical descriptive knowledge like “sandy colored stucco walls” for homes in Jordan, a feature which may be less common for Western homes. Sometimes the model may be too attentive to attributes, leading to confusion (e.g. choosing rug over bed). Future work that enhances alignment in VLMs can likely improve results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.514, + 0.618, + 0.529 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.63 + ], + "angle": 0, + "content": "In this work, we bring attention to how various strategies to prompt CLIP affect recognition performance across geographies. In addition, through soft prompting with descriptive knowledge, we provide a mechanism to achieve a more geo-generalizable set of class representations across regions. Our work is only a first step in this important area." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Limitations and ethical considerations. While our method's proof of concept is demonstrated in a positive effort to debias CLIP's default representations through diversity, due to the biased worldview of the Internet, CLIP's representations are likely inadequate, exaggerated, and/or not fully representative for some countries. While we expect quality LLM knowledge to guide better representations, LLM knowledge can also be incorrect (e.g., through hallucination), imprecise, or biased." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Future work. For the above reasons, our future efforts aim to ensure more representative VLM/LLM knowledge. We strongly advocate for the community to seek communication with diverse groups within all countries (i.e. to capture areas that range from low to high income) to ensure better representation and fairness in AI technology use. There are notable continent-level disparities to still improve upon." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported by National Science Foundation Grants No. 2006885 and 2329992." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13522" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.422, + 0.129 + ], + "angle": 0, + "content": "[1] Common Crawl, 2023. https://commoncrawl.org/. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.13, + 0.397, + 0.144 + ], + "angle": 0, + "content": "[2] Wikipedia, 2023. https://en.wikipedia.org/. 3,8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.469, + 0.213 + ], + "angle": 0, + "content": "[3] Abhipsa Basu, R. 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Class representations need to be adapted to more accurately reflect an object concept under these shifts. In the absence of training data from target geographies, we hypothesize that geographically diverse descriptive knowledge of categories can enhance robustness. For this purpose, we explore the feasibility of probing a large language model for geography-based object knowledge, and we examine the effects of integrating knowledge into zero-shot and learnable soft prompting with CLIP. Within this exploration, we propose geography knowledge regularization to ensure that soft prompts trained on a source set of geographies generalize to an unseen target set. Accuracy gains over prompting baselines on DollarStreet while training only on Europe data are up to $+2.8 / 1.2 / 1.6$ on target data from Africa/Asia/Americas, and $+4.6$ overall on the hardest classes. Competitive performance is shown vs. few-shot target training, and analysis is provided to direct future study of geographical robustness. + +# 1. Introduction + +The performance of object recognition models degrades when tested in new geographies (e.g., cities, countries, continents) [7, 21, 33, 39, 43]. Numerous factors contribute to the challenging problem of geographical domain shift, such as cross-geography changes in object design/parts, materials, and context. These changes in turn may be due to cultural, climate, or economic differences around the world. Recent work has shown standard adaptation techniques fail when used for geographical domain shifts [21, 33], but there has yet to be significant progress in the creation of techniques that improve geographical robustness. Such progress is necessary to ensure equitable use of AI in the future. + +![](images/713c33555090a3b5a042914109b7f889d86d3485fa58a5c9ee4a09443d665d45.jpg) +Figure 1. Descriptive knowledge can address concept shifts across geographies. Observe the wide range of object designs and contexts in the DollarStreet [11] category tools around the world. Our work's premise is that textual representations for classes in vision-language models can be enhanced to better suit diverse object representations across geographies. Map made with [16]. + +Overall, models need representations that adequately capture a category's various forms around the world. A natural solution is to collect training data of objects from different regions. However, this approach is expensive, takes significant effort, and is difficult for regions with limited Internet access. Fortunately, geographical shifts have a unique property compared to other common domain shifts (e.g. ones due to artistic style or weather changes)—they can be addressed with descriptive knowledge about concept changes. In other words, it is possible to describe the features of an object in a region and use this information to adapt a model's default representation. For instance, as shown in Fig. 1, for rural areas in Papua New Guinea, tools can be described as being used for "cooking, hunting, and fishing", and for rural areas in Malawi, tools may often be "made of metal and wood, for farming". Models should account for diverse presentations and contexts of a category and not be limited to biased presentations (e.g. if the model learns tools as just being "metallic with logos"). + +We examine the effects of probing geo-diverse knowledge in two ways. First, we analyze whether a vision + +language model (VLM, i.e. CLIP [36]) has encoded categories in a geo-specific manner, such that adding a country's name to a prompt (e.g. "A photo of a house in China") elicits knowledge that improves recognition. Second, we probe a large language model (LLM, i.e. GPT-3 davinci003) for geography-specific knowledge to obtain visual feature descriptors for an object in different locations. We analyze results in zero-shot inference on geographically and socioeconomically diverse data (DollarStreet [11]), finding the combination of knowledge to often be complementary. + +We further consider a practical scenario where CLIP is optimized with soft prompting, using only a "source" geography with easy-to-access data (e.g. Europe), while the model is applied downstream on "target" data from other parts of the world (e.g. Africa, Asia, Americas). We propose geography knowledge regularization, which uses knowledge ensembled over countries to enable soft prompts to achieve geographically generalizable class representations. We test our method on the recent DollarStreet and GeoNet [21] datasets. Our regularization boosts performance over baseline soft prompting methods, and has benefits with respect to few-shot target-specific training (a 16-shot-per-class regularized model without any target data outperforms a 12-shot-per-class target-trained model on DollarStreet). + +Our method is the first to effectively address geo shifts in object recognition. It outperforms zero-shot CLIP (assumed to have some robustness) by $10.3\%$ on Africa, CoOp [52] by $3.3\%$ , and the best baseline by $4.6\%$ on the hardest classes. + +To summarize, we answer the following questions: (1) Does adding geographical context (i.e. country names) to CLIP prompts improve recognition across geographies? (2) Can an LLM provide useful geographical descriptive knowledge to improve recognition? (3) How can we optimize soft prompts for CLIP using an accessible data source with consideration of target geographies not represented in the training set? (4) Where can soft prompts enhanced with geographical knowledge provide the most benefits? + +# 2. Related Work + +Geographical domain shifts occur when the target setting is in a different geography (e.g. continent, country, city) than where the source data was acquired. Shifts involve changes in object design (e.g. differences in house architecture) and context (i.e. background/co-occurring objects vary). Datasets tailored to cross-country/continent object recognition have recently been proposed, e.g. DollarStreet [11], GeoNet [21], GeoDE [37], GeoYFCC [9], and OpenImages-Extended [5]. Interestingly, [21, 33] demonstrate that traditional methods in unsupervised domain adaptation [10, 19, 20, 27, 28, 38, 44, 45, 50] which seek to bridge gaps based on visual features alone, do not effectively address geographical domain shift. They achieve negligible gains (e.g. 0.14 for [10] in [33]) or often drops + +in performance (e.g. all methods tested in [21]), compared to just using the source model. Attempts to specifically address geographical robustness are limited: [43] corrects for differences in the sizes of cars, [9] proposes a discriminative domain embedding from target data, and GiVL [48] pretrains with knowledge from Wikipedia. In contrast, our descriptive knowledge regularization works for different categories (not just cars); we do not require target domain data to achieve gains cross-geography; we explore the strong capabilities of LLMs to gather relevant knowledge; and we propose lightweight adaptation through soft prompting (unlike GiVL's expensive pretraining). + +Vision-language (VL) models [17, 25, 26, 36, 49] excel on a variety of tasks. CLIP [36] shows impressive zero-shot object recognition across different settings. Yet its performance given geographical shift is less apparent. GeoNet [21] only shows finetuned performance, which is expensive given CLIP's large scale. GeoDE [37] only shows zero-shot inference with CLIP's default prompts. Neither work evaluates descriptive knowledge or soft prompting. + +Learning soft textual prompts. Several recent works to adapt CLIP have focused on parameter and data efficiency using linear probing [36] and prompting [18, 23, 52]. Soft textual prompting (e.g. CoOp [52]) is notable as it optimizes class text embeddings (without manual tuning), which we hypothesize is critical to adequately adapt for geographical robustness. As CoOp overfits on base (seen) classes, CoCoOp [51] proposes to condition prompts on the image for better generalizability. KgCoOp [47] alternatively guides learned prompt embeddings towards CLIP's manual prompt embeddings through a distance constraint to avoid degradation on unseen classes. Our approach also uses a distance constraint, but it differs from [47] with the purpose of regularizing learned prompt representations for cross-geography generalization instead of the base-to-new-class setting. We also show novel benefits of regularization when used with an ensemble of CLIP's internal geographical knowledge and external geographical descriptive knowledge. Our approach notably outperforms each of CoOp, CoCoOp, and KgCoOp by at least +2.8 accuracy on target countries in Africa in DollarStreet. External knowledge aids unseen classes in KAPT [22], but not with respect to geographical knowledge. Prompt tuning for adaptation has been tested in [12, 40], but not with descriptive knowledge. + +Knowledge probed from large language models like [4, 6, 31, 32] has been used for visual reasoning [46], embodied agent planning [15, 41], and to generate additional context for VLM class prompts in object recognition [30, 34]. We uniquely probe LLMs for distinguishable visual descriptions for the same object class across different geographical regions. We are also the first to incorporate geographical knowledge from LLMs into soft prompting. + +![](images/e5fac3ceb85dba171abc801d8732bfc77254c65ceb8dc213f6409f5e38bcd392.jpg) + +![](images/776a43bbdcdd29ad0890fd1bb74bbe8e028be5f33f438da2bfd4cdd8036bb74c.jpg) +(2) Optimize Soft Prompts on Source Data While Regularizing Towards Target Knowledge +Figure 2. Geography knowledge regularization. To ensure robustness in soft prompt learning, we (1) incorporate knowledge internal to CLIP and externally obtained from an LLM. (2) This descriptive knowledge regularizes class representations when training on a specific source geography (e.g. Europe), thus (3) increasing robustness when generalizing to target geographies (e.g. Vietnam). + +# 3. Approach + +We investigate geographical shift in object recognition with VLMs. We posit that the manner in which classes are described is critical due to cross-geography shifts in design and context. We also hypothesize that CLIP's default class representations elicited through "a photo of a/an " prompts may not adequately represent classes around the world. Instead, they may be more aligned to high-resource geographies due to Internet-based training data. Optimizing representations (with soft prompts) on a specific geography (e.g. Europe) may exacerbate a lack of robustness. Our main idea (Fig. 2) is to incorporate object-related geographical knowledge into prompting to ensure model robustness in different regions. We outline our mechanism to obtain geography-specific context by probing CLIP's internal knowledge and an external LLM's descriptive knowledge. We further propose geography knowledge regularization to ensure soft prompts do not overfit when training data is limited to certain geographies. + +Preliminaries. We consider object recognition on a dataset $S$ containing a class set $\mathcal{C}$ (size $N_{c}$ ) over a set of geographies $\mathcal{G}$ . We consider a geography $g$ to be either a country or continent. Our VLM is CLIP [36], with an image encoder $f$ and language encoder $h$ . We incorporate knowledge of each geography $g$ into prompting using (1) zero-shot inference or (2) soft textual prompting. Prompts are defined as $t$ (each is a set of tokens), and class embeddings $w$ are calculated as $h(t)$ . We refer to CLIP's default prompt "a photo of a/an " for a class $c$ as $t_{c}^{\text{default}}$ . + +# 3.1. Geographical Knowledge Probing + +Probing CLIP's internal geographical knowledge. Our first strategy of investigation is to augment CLIP's manual prompts to include country names, as we surmise that some + +of the resulting class representations may be better aligned to how categories present in different regions. [3] inspires this hypothesis, showing that adding country names to image generation prompts can achieve gains in geographical representativeness. However, it is an open question whether adding country names in prompts improves recognition. We define the setting CountryInPrompt, using the prompt $t_c^{CountryInPrompt}$ with template "a photo of a/an in ", e.g. "a photo of a stove in Burundi." + +Probing external LLM geographical knowledge. As CLIP may not have sufficient knowledge of objects in some regions, we consider further augmenting prompts with external knowledge. Motivated by probing LLMs for general attribute-based object descriptions [30, 34] (e.g. a tiger with "stripes and sharp teeth"), we probe GPT-3 (davinci-003) for geography-specific descriptions of object styles, contexts, and materials.1 We reason that since LLMs are trained on large information sources (e.g. CommonCrawl [1], WebText [35], Wikipedia [2]), they may have knowledge about how an object presents in a region due to climate, economics, and/or cultural factors. For instance, roofs may sometimes be "thatched" in tropical and temperate climates, and cutlery may sometimes be made of "bamboo" in areas with bamboo forests. Our goal is unique vs. [30, 34] in that we explore descriptive knowledge differences for the same class to address domain shifts across regions. + +Acquiring knowledge. We follow [30], but instead of gathering one set of feature descriptors $\mathcal{D}(c)$ for each $c$ , we collect sets per country. For each class $c$ and geography $g$ , we prompt the LLM to generate descriptor lists $\mathcal{D}_g(c)$ , using a template consisting of an example question, answer, and format. We use 1-shot prompting to show how to capture geographically representative object designs and contexts. + +Our prompt exemplifies this below, using the descriptors for Japanese ofuro (お風呂, bathhtub): + +Q: What are useful features for distinguishing a bathtub in a photo that I took in Japan? + +A: There are several useful visual features to tell there is a bathtub in a photo that I took in Japan: + +- short in length and deep +-square shape +- wooden, plastic, or steel material +- white or brown color +-benches on side +- next to shower + +Q: What are useful features for distinguishing in a photo that I took in + +A: There are several useful visual features to tell there is/are $<\text{category}>$ in a photo that I took in $<\text{country}>$ : + +Using knowledge. To convert LLM outputs to CLIP prompts, each descriptor $d$ in $\mathcal{D}_g(c)$ serves as a prompt $t_{c,d}$ . The format of $t_{c,d}$ is "a photo of a/an which (is/has/etc.) in which (is/has/etc.) "). Results on DollarStreet are shown in Table 1. + +Including country names in prompts can improve object recognition, especially in Africa and Asia. This observation is supported by gains for CountryInPrompt vs. Zero-Shot CLIP, especially in Africa and Asia (up to +5.4 and +2.6 top-1 gains for RN50, resp.). Such differences may occur as country-specific context can align representations closer to these regions, while default prompts do not adequately capture objects around the world (esp. from non-Western regions). In Americas/Europe, adding country names leads to gains with RN50, but slight drops with ViT-B/16 and ViT-B/32. We reason that CLIP's default prompts may be already well-aligned to countries in these regions for those encoders due to overrepresentation in training. + +Prompting with country-specific descriptive knowledge from LLMs outperforms general object knowledge. We observe this from CountryLLM's larger gains over default CLIP than GeneralLLM's for almost all encoders, regions, and metrics. The largest top-1 difference is with ViT-B/32 (in Total, $52.6\%$ for CountryLLM vs. $51.4\%$ for GeneralLLM). In top-3 accuracy, the differences for CountryLLM/GeneralLLM in Total are 74.6/73.0 for ViT-B/32, 78.8/77.9 for ViT-B/16, 70.0/68.6 for RN50. These suggest that default non-country-specific knowledge is less adequate for various countries. The gains of CountryLLM vs. Zero-Shot CLIP are generally largest on Africa and Asia, as countries in these regions may have greater shifts vs. the default prompts, but CountryLLM also performs well on Europe. LLM description in general is less effective in Americas, though Americas has a large proportion of USA images, for which default CLIP may be well-aligned. + +There are complementary effects when using CLIP's internal and external LLM geo knowledge. This observation is supported by CountryInPrompt+LLM, the combina + +
EncoderPrompting MethodTop-1 AccuracyTop-3 Accuracy
EuropeAfricaAsiaAmericasTotalEuropeAfricaAsiaAmericasTotal
Acc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc Δ
ViT-B/32Zero-Shot CLIP [36]59.1 -43.7 -50.8 -55.3 -51.7 -81.1 -64.8 -72.3 -77.4 -73.7 -
GeneralLLM [30]57.3 -1.844.3 +0.650.9 +0.154.6 -0.751.4 -0.378.8 -2.364.5 -0.372.1 -0.275.7 -1.773.0 -0.7
CountryInPrompt57.5 -1.645.2 +1.551.9 +1.155.0 -0.352.1 +0.480.2 -0.965.5 +0.773.3 +1.076.9 -0.573.9 +0.2
CountryLLM59.4 +0.345.2 +1.552.1 +1.355.3 0.052.6 +0.980.9 -0.266.4 +1.673.6 +1.377.4 0.074.6 +0.9
CountryInPrompt+LLM60.8 +1.745.3 +1.652.2 +1.455.0 -0.352.8 +1.181.5 +0.467.4 +2.673.6 +1.376.7 -0.774.7 +1.0
ViT-B/16Zero-Shot CLIP [36]64.3 -46.9 -53.9 -60.1 -55.5 -84.3 -69.3 -75.9 -81.1 -77.2 -
GeneralLLM [30]64.2 -0.148.8 +1.956.0 +2.158.5 -1.656.8 +1.383.9 -0.471.1 +1.876.3 +0.480.4 -0.777.9 +0.7
CountryInPrompt63.9 -0.449.6 +2.755.7 +1.859.3 -0.856.6 +1.184.0 -0.371.3 +2.076.5 +0.680.0 -1.177.7 +0.5
CountryLLM65.2 +0.949.6 +2.755.6 +1.759.7 -0.457.0 +1.584.3 0.071.8 +2.577.5 +1.681.5 +0.478.8 +1.6
CountryInPrompt+LLM65.5 +1.250.8 +3.956.0 +2.159.7 -0.457.4 +1.985.5 +1.272.5 +3.277.0 +1.180.9 -0.278.7 +1.5
RN50Zero-Shot CLIP [36]53.0 -38.0 -44.4 -49.8 -45.7 -76.5 -60.2 -66.4 -72.7 -68.1 -
GeneralLLM [30]55.5 +2.540.9 +2.946.9 +2.550.3 +0.547.9 +2.276.0 -0.561.2 +1.067.7 +1.371.1 -1.668.6 +0.5
CountryInPrompt54.5 +1.543.4 +5.447.0 +2.650.8 +1.048.4 +2.776.0 -0.564.0 +3.868.7 +2.372.7 0.070.0 +1.9
CountryLLM56.2 +3.241.1 +3.147.3 +2.950.4 +0.648.3 +2.677.2 +0.762.5 +2.368.8 +2.472.4 -0.370.0 +1.9
CountryInPrompt+LLM56.4 +3.443.0 +5.048.0 +3.650.9 +1.149.1 +3.476.7 +0.263.1 +2.968.3 +1.971.1 -1.669.4 +1.3
+ +Table 1. Zero-shot CLIP inference with descriptive knowledge prompts, top-1/3 balanced accuracy (Acc) on DollarStreet. Strategies to capture CLIP's internal country knowledge (CountryInPrompt), external LLM country knowledge (CountryLLM), and their combination (CountryInPrompt+LLM), often improve vs. the zero-shot CLIP baseline (prompt "a photo of a/an "), especially on Africa and Asia; gains in green, drops in red. CountryLLM notably outperforms the GeneralLLM [30] baseline. + +
EncoderPrompting MethodSource EuropeTarget
AccΔAfricaAsiaAmericasTotal
AccΔAccΔAccΔAcc
ViT-B/16CoOp [52]72.2-53.9-61.5-68.6-61.7
CoCoOp [51]73.2-54.3-61.2-68.3-61.4
KgCoOp [47]73.1-54.4-62.6-68.7-62.4
CountryInPrompt Reg71.8-1.456.8+2.463.0+0.469.8+1.163.5
CountryLLM Reg73.20.055.6+1.263.0+0.470.0+1.363.2
CountryInPrompt+LLM Reg73.6+0.457.2+2.863.8+1.270.3+1.664.0
RN50CoOp [52]64.6-45.2-51.6-59.5-52.2
CoCoOp [51]62.9-44.5-51.0-58.3-51.4
KgCoOp [47]63.5-46.3-53.9-60.5-53.9
CountryInPrompt Reg63.5-1.148.0+1.753.90.060.3-0.254.3
CountryLLM Reg64.5-0.147.4+1.154.2+0.359.9-0.654.3
CountryInPrompt+LLM Reg65.5+0.948.1+1.854.5+0.660.4-0.154.8
+ +Table 2. Regularizing soft prompts with geographical knowledge, top-1 bal. acc. on DollarStreet. We emphasize that our regularization aims to improve target performance, rather than source (gray, italicized). Gains/drops are shown vs. the best of soft prompt baselines (shaded). CountryInPrompt+LLM Reg achieves notable gains in target, especially on Africa. Methods use 16 shots per class. + +tion of CountryInPrompt and CountryLLM, achieving the best Total top-1 performance for every encoder. The Total gains vs. default CLIP are as large as +3.4 (RN50). While CLIP has internal knowledge of country-specific categories, it may be incomplete and imprecise due to limited representation in the image-text training corpus. Adding LLM knowledge, trained on a purely textual corpus, may address some gaps. CountryInPrompt+LLM is notably the top setting in 3/4 regions for each encoder in top-1 accuracy. + +# 5.2. Soft Prompting + +We next evaluate geography knowledge regularization (Sec. 3.2), our method to improve target performance by ensuring that soft prompts do not overfit class text representations to a source dataset with limited geographical rep + +resentativeness (e.g. only data from Europe). We compare regularization with ensembles of CountryInPrompt, CountryLLM, and CountryInPrompt+LLM prompts vs. state-of-the-art soft prompting methods in Tables 2/3. + +Regularizing soft prompts with target geographical knowledge reduces overfitting to source geographies. Our method effectively improves the ability of CLIP, with prompts trained only on images from Europe, to generalize to target countries. This observation is supported by Total Target gains for CountryInPrompt, CountryLLM, and CountryInPrompt+LLM Reg on DollarStreet (+1.1/0.8/1.6 over the best soft prompt baseline for ViT-B/16). Improvements are notable in Africa: CountryInPrompt+LLM achieves +2.8 for ViT-B/16 and +1.8 for RN50. The effectiveness extends to GeoNet in Table 3: target gains are +1.3 + +
EncoderMethodSource USATarget Asia
AccΔAccΔ
ViT-B/16CoOp [52]58.7-51.2-
CoCoOp [51]57.7-52.6-
KgCoOp [47]58.2-52.6-
CIP Reg57.5-1.253.5+0.9
LLM Reg58.5-0.253.1+0.5
CIP+LLM Reg57.6-1.153.9+1.3
RN50CoOp [52]51.4-45.6-
CoCoOp [51]51.1-46.3-
KgCoOp [47]51.8-46.9-
CIPReg50.6-1.247.6+0.7
LLMReg51.80.047.4+0.5
CIP+LLMReg51.1-0.748.3+1.4
+ +Table 3. Regularizing soft prompts with geographical knowledge, top-1 bal. accuracy on GeoNet. The regularization method accomplishes our goal to increase target performance in GeoNet's USA-to-Asia transfer setting. CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM. + +
MethodThreshold t (# Classes)
<40% (13) Δ<60% (45) Δ<80% (77) Δ≤100% (95) Δ
CoOp [52]31.2-45.6-55.6-61.7
CoCoOp [51]32.8+1.645.4-0.255.2-0.461.4
KgCoOp [47]35.3+4.147.9+2.356.7+1.162.4
CIPReg37.5+6.348.9+3.357.8+2.263.5
LLMReg36.8+5.648.1+2.557.2+1.663.2
CIP+LLMReg39.9+8.749.5+3.958.2+2.664.0
+ +Table 4. Performance on DollarStreet classes with less than $t\%$ recall in CoOp, with ViT-B/16. Gains w.r.t. CoOp of our geography knowledge regularization are especially large for CoOp's difficult classes (+8.7 in <40%), compared to KgCoOp's (+4.1 in <40%, i.e. a 4.6 difference from ours). CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM. + +for ViT-B/16 and +1.4 for RN50. The combined strategy works best on target, showing the value of incorporating descriptive knowledge. Since regularization prevents overfitting and potentially optimal source performance, we naturally observe source drops for CountryInPrompt and CountryLLM in Tables 2/3. However, CountryInPrompt+LLM in Table 2 even offers source gains. It is also notable that there are small drops in Americas for RN50, but upon inspection, countries in North America overall have a -0.9 drop, while ones in Central/South America have a +0.8 gain. These results concur with our hypothesis that CLIP is already aligned to countries like the USA. More is in supp., along with experiments varying the source and ensemble. + +Regularization helps significantly on difficult classes. As certain objects may be especially sensitive to geographical domain shift, we break down classwise performance on DollarStreet in Table 4, using a stratification of class difficulty based on default soft prompting performance (CoOp). The CountryInPrompt+LLM strategy achieves significant + +![](images/137f117ba534aea34faf37626257e927bfa5bf4851ec3fa3139b3a3f67a66c58.jpg) +Figure 3. Geography knowledge-regularized soft prompts trained on source data (ours, green line) vs. few-shot soft prompts trained on target data (blue curve). (a) Src=Europe, Tgt=Africa, Asia, Amer.; (b) Src=USA, Tgt=Asia. Our 16-shot model trained on only source data (green) outperforms a model with prompts trained on 12 or 4 shots per class of target data (on DollarStreet&GeoNet, resp.), which is 1140&2400 images total. + +![](images/f5fa8d183ceb113fc8084085dc751925eaa384b4b68482b543416ada8a1677d3.jpg) + +gains on the classes most difficult with respect to the CoOp baseline. In particular, gains of $+8.7\%$ in balanced accuracy are achieved for classes with $< 40\%$ baseline recall, while the highest achieved by $\mathrm{KgCoOp}$ is $4.1\%$ . Example classes in this subset are snacks, clothes, and makeup. The DollarStreet classes with greatest improvement, independent of original CoOp accuracy are: piercings, clothes, homes, medication, and refrigerators (all at least $+14\%$ over CoOp). In GeoNet, dome, goby (fish), eland (antelope), and gloriosa (flower) have $>20$ samples and $>30\%$ improvement. A total of 64/95 classes in DollarStreet and 209/344 in GeoNet improve vs. CoOp, showing broad coverage. + +Regularized source-only prompts outperform few-shot target-trained prompts. Given that soft prompts can show strong performance in few-shot settings, a potential alternative to regularizing soft prompts on source data is to directly acquire a few examples of target data for training. We evaluate this setting by splitting target data into train/test, and training CoOp at varying # of shots of target data for GeoNet and DollarStreet, shown in Fig. 3. Notably, training on 16 shots per class of source data with our regularization method outperforms using 12 & 4 shots per class of target data on DollarStreet & GeoNet. This is a vast amount of target data overall (e.g. 12 shots x 95 classes = 1140 target samples in DollarStreet, 4 shots x 600 classes = 2400 samples in GeoNet). The baseline CoOp trained on 16 shots of source data only outperforms an 8-shot/2-shot target-trained CoOp model (DollarStreet/GeoNet). Our strategy is thus more compelling in the absence of a lot of target data. + +Performance by income. DollarStreet provides estimated monthly income of the household in which an image was captured. We evaluate with the delineation of low, medium, and high-income buckets from [13]. Compared to CoOp/KgCoOp, CountryInPrompt+LLM gains are $+2.5/+3.4$ in low, $+2.4/+1.5$ in medium, and $+2.1/+0.7$ in high. Thus our method especially improves in low-income areas, though it helps across levels. The table is in supp. + +
StatisticCIPCountryLLMCIP+LLM
GDP Per Capita (US $)0.2190.0630.217
Human Devel. Index (HDI)0.4390.3850.451
Land Area (km2)-0.0720.050*-0.046*
Population (#)-0.1310.077-0.123
Population Density (#/km2)0.1030.1580.081
% Agricultural Land0.1390.0700.122
% Forest Area0.1910.0870.201
Avg. Yearly Temp. (°C)0.3800.2560.391
Avg. Yearly Precip. (mm/year)0.2360.1240.230
+ +Table 5. Correlation (Pearson's $\rho$ ) of avg. CLIP class text embedding distance and country statistic difference, e.g. economic (GDP per capita, HDI) and climate factors (temperature, precipitation, forest area). We use the 63 countries in DollarStreet (1,953 pairs). Bold values have $\rho > 0.2$ , * means not significant ( $\alpha = 0.01$ ). + +![](images/f12fa63d81da462d4ff8bc95856453d31beff225d1d17aa4729d63604e18d2ff.jpg) +Figure 4. Qualitative analysis. We show examples where geography-specific descriptors improve/hurt vs. general descriptors in zero-shot inference. We highlight the prediction's descriptors, bolding the highest activating one. Encoder=RN50. + +# 5.3. Further Analysis + +Are descriptions correlated with key country statistics? For a pair of countries, we compute two values. We measure the distance between each class embedding and take the average overall distance as one value. We also take the absolute difference between statistics for those countries (from [2, 42], e.g. difference in avg. yearly temperature) as the other value. We compute the correlation between these two values over every unique country pair in DollarStreet, showing results in Table 5. We find that the strongest correlation across each prompt type is with HDI, which summarizes human development. It is notable that factors like yearly temperature and precipitation also show moderate correlations, indicating a potential role of climate. Future work may further explore how object differences present with respect to these factors. It will also be critical to ensure that differences between countries are representative and not exaggerated in embeddings. + +Descriptor topics. We show a UMAP [29] visualization comparing CountryLLM text embeddings for the category homes across geographies in Fig. 5. Countries tend to group + +![](images/8b041f7823e6877bce0aae108097e73d6d42b86c5b29ab7e994725e8fdf5f273.jpg) +Figure 5. UMAP [29] plot for CountryLLM and the category homes in DollarStreet. Country-specific descriptors are often close to those of other countries intra-continent, likely due to similar weather, environment, and/or economic conditions. + +by continent, showing the representations may capture similarity in features like climate and/or economics. We examine a few topics mentioned in the CountryLLM descriptors for homes. While “stone” is described across continents, “bright colors” and “mud” are mentioned mostly in Africa, and “balcony” in Europe and Asia. We show more in supp. Success and failure examples. We provide examples of CountryLLM vs. GeneralLLM in Fig. 4 on DollarStreet. The model captures geographical descriptive knowledge like “sandy colored stucco walls” for homes in Jordan, a feature which may be less common for Western homes. Sometimes the model may be too attentive to attributes, leading to confusion (e.g. choosing rug over bed). Future work that enhances alignment in VLMs can likely improve results. + +# 6. Conclusion + +In this work, we bring attention to how various strategies to prompt CLIP affect recognition performance across geographies. In addition, through soft prompting with descriptive knowledge, we provide a mechanism to achieve a more geo-generalizable set of class representations across regions. Our work is only a first step in this important area. + +Limitations and ethical considerations. While our method's proof of concept is demonstrated in a positive effort to debias CLIP's default representations through diversity, due to the biased worldview of the Internet, CLIP's representations are likely inadequate, exaggerated, and/or not fully representative for some countries. While we expect quality LLM knowledge to guide better representations, LLM knowledge can also be incorrect (e.g., through hallucination), imprecise, or biased. + +Future work. For the above reasons, our future efforts aim to ensure more representative VLM/LLM knowledge. We strongly advocate for the community to seek communication with diverse groups within all countries (i.e. to capture areas that range from low to high income) to ensure better representation and fairness in AI technology use. There are notable continent-level disparities to still improve upon. + +Acknowledgement. This work was supported by National Science Foundation Grants No. 2006885 and 2329992. + +# References + +[1] Common Crawl, 2023. https://commoncrawl.org/. 3 +[2] Wikipedia, 2023. https://en.wikipedia.org/. 3,8 +[3] Abhipsa Basu, R. Venkatesh Babu, and Danish Pruthi. Inspecting the geographical representativeness of images from text-to-image models. 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Test-time prompt tuning for zero-shot generalization in vision-language models. Advances in Neural Information Processing Systems, 35:14274-14289, 2022. 2 +[41] Chan Hee Song, Jiaman Wu, Clayton Washington, Brian M. Sadler, Wei-Lun Chao, and Yu Su. LLM-planner: Few-shot + +grounded planning for embodied agents with large language models. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2023. 2 +[42] The World Bank. World Bank - Indicators, 2023. https://data.worldbank.org/indicator/.8 +[43] Yan Wang, Xiangyu Chen, Yurong You, Li Erran Li, Bharath Hariharan, Mark Campbell, Kilian Q Weinberger, and WeiLun Chao. Train in Germany, test in the USA: Making 3D object detectors generalize. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11713-11723, 2020. 1, 2 +[44] Guoqiang Wei, Cuiling Lan, Wenjun Zeng, Zhizheng Zhang, and Zhibo Chen. Toalign: Task-oriented alignment for unsupervised domain adaptation. Advances in Neural Information Processing Systems, 34:13834-13846, 2021. 2 +[45] Ruijia Xu, Guanbin Li, Jihan Yang, and Liang Lin. Larger norm more transferable: An adaptive feature norm approach for unsupervised domain adaptation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1426-1435, 2019. 2 +[46] Zhengyuan Yang*, Linjie Li*, Jianfeng Wang*, Kevin Lin*, Ehsan Azarnasab*, Faisal Ahmed*, Zicheng Liu, Ce Liu, Michael Zeng, and Lijuan Wang. MM-ReAct: Prompting ChatGPT for multimodal reasoning and action. arXiv preprint arXiv:2303.11381, 2023. 2 +[47] Hantao Yao, Rui Zhang, and Changsheng Xu. Visual-language prompt tuning with knowledge-guided context optimization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6757-6767, 2023. 2, 5, 6, 7 +[48] Da Yin, Feng Gao, Govind Thattai, Michael Johnston, and Kai-Wei Chang. Givl: Improving geographical inclusivity of vision-language models with pre-training methods. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10951-10961, 2023. 2 +[49] Jiahui Yu, Zirui Wang, Vijay Vasudevan, Legg Yeung, Mojtaba Seyedhosseini, and Yonghui Wu. Coca: Contrastive captioners are image-text foundation models. Transactions on Machine Learning Research, 2022. 2 +[50] Yuchen Zhang, Tianle Liu, Mingsheng Long, and Michael Jordan. Bridging theory and algorithm for domain adaptation. In International Conference on Machine Learning, pages 7404-7413. PMLR, 2019. 2 +[51] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Conditional prompt learning for vision-language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 16816-16825, 2022. 2, 5, 6, 7 +[52] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. International Journal of Computer Vision, 130(9):2337-2348, 2022. 2, 4, 5, 6, 7 \ No newline at end of file diff --git a/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/images.zip b/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e31526343d7ca2e8fd9ce5c09d4f8dfd4fd34ff1 --- /dev/null +++ b/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:db83b705f3fb9a991be53a728d5316132241255fd46f79658d9d31f3ca1c549c +size 689072 diff --git a/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/layout.json b/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..29ff681ba259e05c4c9b243f6c5f43630edd9808 --- /dev/null +++ b/2024/Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition/layout.json @@ -0,0 +1,8328 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 86, + 103, + 507, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 103, + 507, + 140 + ], + "spans": [ + { + "bbox": [ + 86, + 103, + 507, + 140 + ], + "type": "text", + "content": "Incorporating Geo-Diverse Knowledge into Prompting for Increased Geographical Robustness in Object Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 160, + 479, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 160, + 479, + 175 + ], + "spans": [ + { + "bbox": [ + 112, + 160, + 479, + 175 + ], + "type": "text", + "content": "Kyle Buettner1, Sina Malakouti2, Xiang Lorraine Li1,2, Adriana Kovashka1,2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 175, + 539, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 175, + 539, + 190 + ], + "spans": [ + { + "bbox": [ + 54, + 175, + 539, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 54, + 175, + 539, + 190 + ], + "type": "text", + "content": "Intelligent Systems Program, " + }, + { + "bbox": [ + 54, + 175, + 539, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 175, + 539, + 190 + ], + "type": "text", + "content": "Department of Computer Science, University of Pittsburgh, PA, USA" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 129, + 191, + 463, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 191, + 463, + 204 + ], + "spans": [ + { + "bbox": [ + 129, + 191, + 463, + 204 + ], + "type": "text", + "content": "{buettnerk, sem238}@pitt.edu, {xianglli, kovashka}@cs.pitt.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 157, + 205, + 429, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 157, + 205, + 429, + 217 + ], + "spans": [ + { + "bbox": [ + 157, + 205, + 429, + 217 + ], + "type": "text", + "content": "https://krbuettner.github.io/GeoKnowledgePrompting" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "type": "text", + "content": "Existing object recognition models have been shown to lack robustness in diverse geographical scenarios due to domain shifts in design and context. Class representations need to be adapted to more accurately reflect an object concept under these shifts. In the absence of training data from target geographies, we hypothesize that geographically diverse descriptive knowledge of categories can enhance robustness. For this purpose, we explore the feasibility of probing a large language model for geography-based object knowledge, and we examine the effects of integrating knowledge into zero-shot and learnable soft prompting with CLIP. Within this exploration, we propose geography knowledge regularization to ensure that soft prompts trained on a source set of geographies generalize to an unseen target set. Accuracy gains over prompting baselines on DollarStreet while training only on Europe data are up to " + }, + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "type": "inline_equation", + "content": "+2.8 / 1.2 / 1.6" + }, + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "type": "text", + "content": " on target data from Africa/Asia/Americas, and " + }, + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "type": "inline_equation", + "content": "+4.6" + }, + { + "bbox": [ + 46, + 271, + 290, + 511 + ], + "type": "text", + "content": " overall on the hardest classes. Competitive performance is shown vs. few-shot target training, and analysis is provided to direct future study of geographical robustness." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 548, + 128, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 128, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 128, + 561 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "The performance of object recognition models degrades when tested in new geographies (e.g., cities, countries, continents) [7, 21, 33, 39, 43]. Numerous factors contribute to the challenging problem of geographical domain shift, such as cross-geography changes in object design/parts, materials, and context. These changes in turn may be due to cultural, climate, or economic differences around the world. Recent work has shown standard adaptation techniques fail when used for geographical domain shifts [21, 33], but there has yet to be significant progress in the creation of techniques that improve geographical robustness. Such progress is necessary to ensure equitable use of AI in the future." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 246, + 541, + 371 + ], + "blocks": [ + { + "bbox": [ + 310, + 246, + 541, + 371 + ], + "lines": [ + { + "bbox": [ + 310, + 246, + 541, + 371 + ], + "spans": [ + { + "bbox": [ + 310, + 246, + 541, + 371 + ], + "type": "image", + "image_path": "713c33555090a3b5a042914109b7f889d86d3485fa58a5c9ee4a09443d665d45.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 374, + 547, + 441 + ], + "lines": [ + { + "bbox": [ + 304, + 374, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 547, + 441 + ], + "type": "text", + "content": "Figure 1. Descriptive knowledge can address concept shifts across geographies. Observe the wide range of object designs and contexts in the DollarStreet [11] category tools around the world. Our work's premise is that textual representations for classes in vision-language models can be enhanced to better suit diverse object representations across geographies. Map made with [16]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 461, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 546, + 689 + ], + "type": "text", + "content": "Overall, models need representations that adequately capture a category's various forms around the world. A natural solution is to collect training data of objects from different regions. However, this approach is expensive, takes significant effort, and is difficult for regions with limited Internet access. Fortunately, geographical shifts have a unique property compared to other common domain shifts (e.g. ones due to artistic style or weather changes)—they can be addressed with descriptive knowledge about concept changes. In other words, it is possible to describe the features of an object in a region and use this information to adapt a model's default representation. For instance, as shown in Fig. 1, for rural areas in Papua New Guinea, tools can be described as being used for \"cooking, hunting, and fishing\", and for rural areas in Malawi, tools may often be \"made of metal and wood, for farming\". Models should account for diverse presentations and contexts of a category and not be limited to biased presentations (e.g. if the model learns tools as just being \"metallic with logos\")." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We examine the effects of probing geo-diverse knowledge in two ways. First, we analyze whether a vision" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13515" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": "language model (VLM, i.e. CLIP [36]) has encoded categories in a geo-specific manner, such that adding a country's name to a prompt (e.g. \"A photo of a house in China\") elicits knowledge that improves recognition. Second, we probe a large language model (LLM, i.e. GPT-3 davinci003) for geography-specific knowledge to obtain visual feature descriptors for an object in different locations. We analyze results in zero-shot inference on geographically and socioeconomically diverse data (DollarStreet [11]), finding the combination of knowledge to often be complementary." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 288, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 288, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 288, + 359 + ], + "type": "text", + "content": "We further consider a practical scenario where CLIP is optimized with soft prompting, using only a \"source\" geography with easy-to-access data (e.g. Europe), while the model is applied downstream on \"target\" data from other parts of the world (e.g. Africa, Asia, Americas). We propose geography knowledge regularization, which uses knowledge ensembled over countries to enable soft prompts to achieve geographically generalizable class representations. We test our method on the recent DollarStreet and GeoNet [21] datasets. Our regularization boosts performance over baseline soft prompting methods, and has benefits with respect to few-shot target-specific training (a 16-shot-per-class regularized model without any target data outperforms a 12-shot-per-class target-trained model on DollarStreet)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "text", + "content": "Our method is the first to effectively address geo shifts in object recognition. It outperforms zero-shot CLIP (assumed to have some robustness) by " + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "inline_equation", + "content": "10.3\\%" + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "text", + "content": " on Africa, CoOp [52] by " + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "text", + "content": ", and the best baseline by " + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "inline_equation", + "content": "4.6\\%" + }, + { + "bbox": [ + 47, + 360, + 287, + 407 + ], + "type": "text", + "content": " on the hardest classes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 407, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 515 + ], + "type": "text", + "content": "To summarize, we answer the following questions: (1) Does adding geographical context (i.e. country names) to CLIP prompts improve recognition across geographies? (2) Can an LLM provide useful geographical descriptive knowledge to improve recognition? (3) How can we optimize soft prompts for CLIP using an accessible data source with consideration of target geographies not represented in the training set? (4) Where can soft prompts enhanced with geographical knowledge provide the most benefits?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 526, + 134, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 134, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 134, + 538 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "Geographical domain shifts occur when the target setting is in a different geography (e.g. continent, country, city) than where the source data was acquired. Shifts involve changes in object design (e.g. differences in house architecture) and context (i.e. background/co-occurring objects vary). Datasets tailored to cross-country/continent object recognition have recently been proposed, e.g. DollarStreet [11], GeoNet [21], GeoDE [37], GeoYFCC [9], and OpenImages-Extended [5]. Interestingly, [21, 33] demonstrate that traditional methods in unsupervised domain adaptation [10, 19, 20, 27, 28, 38, 44, 45, 50] which seek to bridge gaps based on visual features alone, do not effectively address geographical domain shift. They achieve negligible gains (e.g. 0.14 for [10] in [33]) or often drops" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "in performance (e.g. all methods tested in [21]), compared to just using the source model. Attempts to specifically address geographical robustness are limited: [43] corrects for differences in the sizes of cars, [9] proposes a discriminative domain embedding from target data, and GiVL [48] pretrains with knowledge from Wikipedia. In contrast, our descriptive knowledge regularization works for different categories (not just cars); we do not require target domain data to achieve gains cross-geography; we explore the strong capabilities of LLMs to gather relevant knowledge; and we propose lightweight adaptation through soft prompting (unlike GiVL's expensive pretraining)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 222, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 545, + 319 + ], + "type": "text", + "content": "Vision-language (VL) models [17, 25, 26, 36, 49] excel on a variety of tasks. CLIP [36] shows impressive zero-shot object recognition across different settings. Yet its performance given geographical shift is less apparent. GeoNet [21] only shows finetuned performance, which is expensive given CLIP's large scale. GeoDE [37] only shows zero-shot inference with CLIP's default prompts. Neither work evaluates descriptive knowledge or soft prompting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 324, + 546, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 612 + ], + "type": "text", + "content": "Learning soft textual prompts. Several recent works to adapt CLIP have focused on parameter and data efficiency using linear probing [36] and prompting [18, 23, 52]. Soft textual prompting (e.g. CoOp [52]) is notable as it optimizes class text embeddings (without manual tuning), which we hypothesize is critical to adequately adapt for geographical robustness. As CoOp overfits on base (seen) classes, CoCoOp [51] proposes to condition prompts on the image for better generalizability. KgCoOp [47] alternatively guides learned prompt embeddings towards CLIP's manual prompt embeddings through a distance constraint to avoid degradation on unseen classes. Our approach also uses a distance constraint, but it differs from [47] with the purpose of regularizing learned prompt representations for cross-geography generalization instead of the base-to-new-class setting. We also show novel benefits of regularization when used with an ensemble of CLIP's internal geographical knowledge and external geographical descriptive knowledge. Our approach notably outperforms each of CoOp, CoCoOp, and KgCoOp by at least +2.8 accuracy on target countries in Africa in DollarStreet. External knowledge aids unseen classes in KAPT [22], but not with respect to geographical knowledge. Prompt tuning for adaptation has been tested in [12, 40], but not with descriptive knowledge." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": "Knowledge probed from large language models like [4, 6, 31, 32] has been used for visual reasoning [46], embodied agent planning [15, 41], and to generate additional context for VLM class prompts in object recognition [30, 34]. We uniquely probe LLMs for distinguishable visual descriptions for the same object class across different geographical regions. We are also the first to incorporate geographical knowledge from LLMs into soft prompting." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13516" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 74, + 276, + 233 + ], + "blocks": [ + { + "bbox": [ + 52, + 74, + 276, + 233 + ], + "lines": [ + { + "bbox": [ + 52, + 74, + 276, + 233 + ], + "spans": [ + { + "bbox": [ + 52, + 74, + 276, + 233 + ], + "type": "image", + "image_path": "e5fac3ceb85dba171abc801d8732bfc77254c65ceb8dc213f6409f5e38bcd392.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 285, + 100, + 539, + 235 + ], + "blocks": [ + { + "bbox": [ + 286, + 77, + 459, + 97 + ], + "lines": [ + { + "bbox": [ + 286, + 77, + 459, + 97 + ], + "spans": [ + { + "bbox": [ + 286, + 77, + 459, + 97 + ], + "type": "text", + "content": "(2) Optimize Soft Prompts on Source Data While Regularizing Towards Target Knowledge" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 285, + 100, + 539, + 235 + ], + "lines": [ + { + "bbox": [ + 285, + 100, + 539, + 235 + ], + "spans": [ + { + "bbox": [ + 285, + 100, + 539, + 235 + ], + "type": "image", + "image_path": "776a43bbdcdd29ad0890fd1bb74bbe8e028be5f33f438da2bfd4cdd8036bb74c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 546, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 546, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 546, + 270 + ], + "type": "text", + "content": "Figure 2. Geography knowledge regularization. To ensure robustness in soft prompt learning, we (1) incorporate knowledge internal to CLIP and externally obtained from an LLM. (2) This descriptive knowledge regularizes class representations when training on a specific source geography (e.g. Europe), thus (3) increasing robustness when generalizing to target geographies (e.g. Vietnam)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 289, + 113, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 113, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 113, + 304 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 310, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 526 + ], + "type": "text", + "content": "We investigate geographical shift in object recognition with VLMs. We posit that the manner in which classes are described is critical due to cross-geography shifts in design and context. We also hypothesize that CLIP's default class representations elicited through \"a photo of a/an \" prompts may not adequately represent classes around the world. Instead, they may be more aligned to high-resource geographies due to Internet-based training data. Optimizing representations (with soft prompts) on a specific geography (e.g. Europe) may exacerbate a lack of robustness. Our main idea (Fig. 2) is to incorporate object-related geographical knowledge into prompting to ensure model robustness in different regions. We outline our mechanism to obtain geography-specific context by probing CLIP's internal knowledge and an external LLM's descriptive knowledge. We further propose geography knowledge regularization to ensure soft prompts do not overfit when training data is limited to certain geographies." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": "Preliminaries. We consider object recognition on a dataset " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " containing a class set " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " (size " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": ") over a set of geographies " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": ". We consider a geography " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " to be either a country or continent. Our VLM is CLIP [36], with an image encoder " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " and language encoder " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": ". We incorporate knowledge of each geography " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " into prompting using (1) zero-shot inference or (2) soft textual prompting. Prompts are defined as " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " (each is a set of tokens), and class embeddings " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " are calculated as " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "h(t)" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": ". We refer to CLIP's default prompt \"a photo of a/an \" for a class " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "inline_equation", + "content": "t_{c}^{\\text{default}}" + }, + { + "bbox": [ + 46, + 527, + 287, + 647 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 230, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 230, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 230, + 671 + ], + "type": "text", + "content": "3.1. Geographical Knowledge Probing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Probing CLIP's internal geographical knowledge. Our first strategy of investigation is to augment CLIP's manual prompts to include country names, as we surmise that some" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 290, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 398 + ], + "type": "text", + "content": "of the resulting class representations may be better aligned to how categories present in different regions. [3] inspires this hypothesis, showing that adding country names to image generation prompts can achieve gains in geographical representativeness. However, it is an open question whether adding country names in prompts improves recognition. We define the setting CountryInPrompt, using the prompt " + }, + { + "bbox": [ + 304, + 290, + 545, + 398 + ], + "type": "inline_equation", + "content": "t_c^{CountryInPrompt}" + }, + { + "bbox": [ + 304, + 290, + 545, + 398 + ], + "type": "text", + "content": " with template \"a photo of a/an in \", e.g. \"a photo of a stove in Burundi.\"" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 546, + 604 + ], + "type": "text", + "content": "Probing external LLM geographical knowledge. As CLIP may not have sufficient knowledge of objects in some regions, we consider further augmenting prompts with external knowledge. Motivated by probing LLMs for general attribute-based object descriptions [30, 34] (e.g. a tiger with \"stripes and sharp teeth\"), we probe GPT-3 (davinci-003) for geography-specific descriptions of object styles, contexts, and materials.1 We reason that since LLMs are trained on large information sources (e.g. CommonCrawl [1], WebText [35], Wikipedia [2]), they may have knowledge about how an object presents in a region due to climate, economics, and/or cultural factors. For instance, roofs may sometimes be \"thatched\" in tropical and temperate climates, and cutlery may sometimes be made of \"bamboo\" in areas with bamboo forests. Our goal is unique vs. [30, 34] in that we explore descriptive knowledge differences for the same class to address domain shifts across regions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "Acquiring knowledge. We follow [30], but instead of gathering one set of feature descriptors " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(c)" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ", we collect sets per country. For each class " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " and geography " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ", we prompt the LLM to generate descriptor lists " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_g(c)" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ", using a template consisting of an example question, answer, and format. We use 1-shot prompting to show how to capture geographically representative object designs and contexts." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 544, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 544, + 712 + ], + "type": "text", + "content": "1We found ChatGPT to perform worse than GPT-3, also found in [34]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13517" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "Our prompt exemplifies this below, using the descriptors for Japanese ofuro (お風呂, bathhtub):" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 66, + 106, + 266, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 106, + 266, + 127 + ], + "spans": [ + { + "bbox": [ + 66, + 106, + 266, + 127 + ], + "type": "text", + "content": "Q: What are useful features for distinguishing a bathtub in a photo that I took in Japan?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 128, + 266, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 128, + 266, + 150 + ], + "spans": [ + { + "bbox": [ + 67, + 128, + 266, + 150 + ], + "type": "text", + "content": "A: There are several useful visual features to tell there is a bathtub in a photo that I took in Japan:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 150, + 194, + 214 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 67, + 150, + 161, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 150, + 161, + 160 + ], + "spans": [ + { + "bbox": [ + 67, + 150, + 161, + 160 + ], + "type": "text", + "content": "- short in length and deep" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 162, + 121, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 162, + 121, + 171 + ], + "spans": [ + { + "bbox": [ + 67, + 162, + 121, + 171 + ], + "type": "text", + "content": "-square shape" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 172, + 194, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 172, + 194, + 182 + ], + "spans": [ + { + "bbox": [ + 67, + 172, + 194, + 182 + ], + "type": "text", + "content": "- wooden, plastic, or steel material" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 183, + 150, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 183, + 150, + 192 + ], + "spans": [ + { + "bbox": [ + 67, + 183, + 150, + 192 + ], + "type": "text", + "content": "- white or brown color" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 194, + 132, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 194, + 132, + 203 + ], + "spans": [ + { + "bbox": [ + 67, + 194, + 132, + 203 + ], + "type": "text", + "content": "-benches on side" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 205, + 128, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 205, + 128, + 214 + ], + "spans": [ + { + "bbox": [ + 67, + 205, + 128, + 214 + ], + "type": "text", + "content": "- next to shower" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 67, + 216, + 266, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 216, + 266, + 237 + ], + "spans": [ + { + "bbox": [ + 67, + 216, + 266, + 237 + ], + "type": "text", + "content": "Q: What are useful features for distinguishing in a photo that I took in " + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "spans": [ + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "type": "text", + "content": "A: There are several useful visual features to tell there is/are " + }, + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "type": "inline_equation", + "content": "<\\text{category}>" + }, + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "type": "text", + "content": " in a photo that I took in " + }, + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "type": "inline_equation", + "content": "<\\text{country}>" + }, + { + "bbox": [ + 67, + 238, + 266, + 259 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "text", + "content": "Using knowledge. To convert LLM outputs to CLIP prompts, each descriptor " + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_g(c)" + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "text", + "content": " serves as a prompt " + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "inline_equation", + "content": "t_{c,d}" + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "text", + "content": ". The format of " + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "inline_equation", + "content": "t_{c,d}" + }, + { + "bbox": [ + 47, + 269, + 287, + 390 + ], + "type": "text", + "content": " is \"a photo of a/an which (is/has/etc.) in which (is/has/etc.) \"). Results on DollarStreet are shown in Table 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 317, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 472 + ], + "type": "text", + "content": "Including country names in prompts can improve object recognition, especially in Africa and Asia. This observation is supported by gains for CountryInPrompt vs. Zero-Shot CLIP, especially in Africa and Asia (up to +5.4 and +2.6 top-1 gains for RN50, resp.). Such differences may occur as country-specific context can align representations closer to these regions, while default prompts do not adequately capture objects around the world (esp. from non-Western regions). In Americas/Europe, adding country names leads to gains with RN50, but slight drops with ViT-B/16 and ViT-B/32. We reason that CLIP's default prompts may be already well-aligned to countries in these regions for those encoders due to overrepresentation in training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "type": "text", + "content": "Prompting with country-specific descriptive knowledge from LLMs outperforms general object knowledge. We observe this from CountryLLM's larger gains over default CLIP than GeneralLLM's for almost all encoders, regions, and metrics. The largest top-1 difference is with ViT-B/32 (in Total, " + }, + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "type": "inline_equation", + "content": "52.6\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "type": "text", + "content": " for CountryLLM vs. " + }, + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "type": "inline_equation", + "content": "51.4\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 676 + ], + "type": "text", + "content": " for GeneralLLM). In top-3 accuracy, the differences for CountryLLM/GeneralLLM in Total are 74.6/73.0 for ViT-B/32, 78.8/77.9 for ViT-B/16, 70.0/68.6 for RN50. These suggest that default non-country-specific knowledge is less adequate for various countries. The gains of CountryLLM vs. Zero-Shot CLIP are generally largest on Africa and Asia, as countries in these regions may have greater shifts vs. the default prompts, but CountryLLM also performs well on Europe. LLM description in general is less effective in Americas, though Americas has a large proportion of USA images, for which default CLIP may be well-aligned." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "There are complementary effects when using CLIP's internal and external LLM geo knowledge. This observation is supported by CountryInPrompt+LLM, the combina" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13519" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 69, + 535, + 258 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 535, + 258 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 535, + 258 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 535, + 258 + ], + "type": "table", + "html": "
EncoderPrompting MethodTop-1 AccuracyTop-3 Accuracy
EuropeAfricaAsiaAmericasTotalEuropeAfricaAsiaAmericasTotal
Acc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc ΔAcc Δ
ViT-B/32Zero-Shot CLIP [36]59.1 -43.7 -50.8 -55.3 -51.7 -81.1 -64.8 -72.3 -77.4 -73.7 -
GeneralLLM [30]57.3 -1.844.3 +0.650.9 +0.154.6 -0.751.4 -0.378.8 -2.364.5 -0.372.1 -0.275.7 -1.773.0 -0.7
CountryInPrompt57.5 -1.645.2 +1.551.9 +1.155.0 -0.352.1 +0.480.2 -0.965.5 +0.773.3 +1.076.9 -0.573.9 +0.2
CountryLLM59.4 +0.345.2 +1.552.1 +1.355.3 0.052.6 +0.980.9 -0.266.4 +1.673.6 +1.377.4 0.074.6 +0.9
CountryInPrompt+LLM60.8 +1.745.3 +1.652.2 +1.455.0 -0.352.8 +1.181.5 +0.467.4 +2.673.6 +1.376.7 -0.774.7 +1.0
ViT-B/16Zero-Shot CLIP [36]64.3 -46.9 -53.9 -60.1 -55.5 -84.3 -69.3 -75.9 -81.1 -77.2 -
GeneralLLM [30]64.2 -0.148.8 +1.956.0 +2.158.5 -1.656.8 +1.383.9 -0.471.1 +1.876.3 +0.480.4 -0.777.9 +0.7
CountryInPrompt63.9 -0.449.6 +2.755.7 +1.859.3 -0.856.6 +1.184.0 -0.371.3 +2.076.5 +0.680.0 -1.177.7 +0.5
CountryLLM65.2 +0.949.6 +2.755.6 +1.759.7 -0.457.0 +1.584.3 0.071.8 +2.577.5 +1.681.5 +0.478.8 +1.6
CountryInPrompt+LLM65.5 +1.250.8 +3.956.0 +2.159.7 -0.457.4 +1.985.5 +1.272.5 +3.277.0 +1.180.9 -0.278.7 +1.5
RN50Zero-Shot CLIP [36]53.0 -38.0 -44.4 -49.8 -45.7 -76.5 -60.2 -66.4 -72.7 -68.1 -
GeneralLLM [30]55.5 +2.540.9 +2.946.9 +2.550.3 +0.547.9 +2.276.0 -0.561.2 +1.067.7 +1.371.1 -1.668.6 +0.5
CountryInPrompt54.5 +1.543.4 +5.447.0 +2.650.8 +1.048.4 +2.776.0 -0.564.0 +3.868.7 +2.372.7 0.070.0 +1.9
CountryLLM56.2 +3.241.1 +3.147.3 +2.950.4 +0.648.3 +2.677.2 +0.762.5 +2.368.8 +2.472.4 -0.370.0 +1.9
CountryInPrompt+LLM56.4 +3.443.0 +5.048.0 +3.650.9 +1.149.1 +3.476.7 +0.263.1 +2.968.3 +1.971.1 -1.669.4 +1.3
", + "image_path": "b80fcf93084dd217f71b20f4079d5602fb03dd673e67be99ec0b624f3d37256b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 83, + 316, + 511, + 473 + ], + "blocks": [ + { + "bbox": [ + 46, + 262, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 547, + 307 + ], + "type": "text", + "content": "Table 1. Zero-shot CLIP inference with descriptive knowledge prompts, top-1/3 balanced accuracy (Acc) on DollarStreet. Strategies to capture CLIP's internal country knowledge (CountryInPrompt), external LLM country knowledge (CountryLLM), and their combination (CountryInPrompt+LLM), often improve vs. the zero-shot CLIP baseline (prompt \"a photo of a/an \"), especially on Africa and Asia; gains in green, drops in red. CountryLLM notably outperforms the GeneralLLM [30] baseline." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 316, + 511, + 473 + ], + "lines": [ + { + "bbox": [ + 83, + 316, + 511, + 473 + ], + "spans": [ + { + "bbox": [ + 83, + 316, + 511, + 473 + ], + "type": "table", + "html": "
EncoderPrompting MethodSource EuropeTarget
AccΔAfricaAsiaAmericasTotal
AccΔAccΔAccΔAcc
ViT-B/16CoOp [52]72.2-53.9-61.5-68.6-61.7
CoCoOp [51]73.2-54.3-61.2-68.3-61.4
KgCoOp [47]73.1-54.4-62.6-68.7-62.4
CountryInPrompt Reg71.8-1.456.8+2.463.0+0.469.8+1.163.5
CountryLLM Reg73.20.055.6+1.263.0+0.470.0+1.363.2
CountryInPrompt+LLM Reg73.6+0.457.2+2.863.8+1.270.3+1.664.0
RN50CoOp [52]64.6-45.2-51.6-59.5-52.2
CoCoOp [51]62.9-44.5-51.0-58.3-51.4
KgCoOp [47]63.5-46.3-53.9-60.5-53.9
CountryInPrompt Reg63.5-1.148.0+1.753.90.060.3-0.254.3
CountryLLM Reg64.5-0.147.4+1.154.2+0.359.9-0.654.3
CountryInPrompt+LLM Reg65.5+0.948.1+1.854.5+0.660.4-0.154.8
", + "image_path": "55b8c9edde33a3de4dec99c586dc9b128ea6b014192633c42bceec82ecc60a66.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 477, + 546, + 511 + ], + "lines": [ + { + "bbox": [ + 46, + 477, + 546, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 546, + 511 + ], + "type": "text", + "content": "Table 2. Regularizing soft prompts with geographical knowledge, top-1 bal. acc. on DollarStreet. We emphasize that our regularization aims to improve target performance, rather than source (gray, italicized). Gains/drops are shown vs. the best of soft prompt baselines (shaded). CountryInPrompt+LLM Reg achieves notable gains in target, especially on Africa. Methods use 16 shots per class." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 531, + 288, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 288, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 288, + 640 + ], + "type": "text", + "content": "tion of CountryInPrompt and CountryLLM, achieving the best Total top-1 performance for every encoder. The Total gains vs. default CLIP are as large as +3.4 (RN50). While CLIP has internal knowledge of country-specific categories, it may be incomplete and imprecise due to limited representation in the image-text training corpus. Adding LLM knowledge, trained on a purely textual corpus, may address some gaps. CountryInPrompt+LLM is notably the top setting in 3/4 regions for each encoder in top-1 accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 142, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 142, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 142, + 659 + ], + "type": "text", + "content": "5.2. Soft Prompting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We next evaluate geography knowledge regularization (Sec. 3.2), our method to improve target performance by ensuring that soft prompts do not overfit class text representations to a source dataset with limited geographical rep" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 531, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 579 + ], + "type": "text", + "content": "resentativeness (e.g. only data from Europe). We compare regularization with ensembles of CountryInPrompt, CountryLLM, and CountryInPrompt+LLM prompts vs. state-of-the-art soft prompting methods in Tables 2/3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Regularizing soft prompts with target geographical knowledge reduces overfitting to source geographies. Our method effectively improves the ability of CLIP, with prompts trained only on images from Europe, to generalize to target countries. This observation is supported by Total Target gains for CountryInPrompt, CountryLLM, and CountryInPrompt+LLM Reg on DollarStreet (+1.1/0.8/1.6 over the best soft prompt baseline for ViT-B/16). Improvements are notable in Africa: CountryInPrompt+LLM achieves +2.8 for ViT-B/16 and +1.8 for RN50. The effectiveness extends to GeoNet in Table 3: target gains are +1.3" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13520" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 269, + 225 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 269, + 225 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 269, + 225 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 269, + 225 + ], + "type": "table", + "html": "
EncoderMethodSource USATarget Asia
AccΔAccΔ
ViT-B/16CoOp [52]58.7-51.2-
CoCoOp [51]57.7-52.6-
KgCoOp [47]58.2-52.6-
CIP Reg57.5-1.253.5+0.9
LLM Reg58.5-0.253.1+0.5
CIP+LLM Reg57.6-1.153.9+1.3
RN50CoOp [52]51.4-45.6-
CoCoOp [51]51.1-46.3-
KgCoOp [47]51.8-46.9-
CIPReg50.6-1.247.6+0.7
LLMReg51.80.047.4+0.5
CIP+LLMReg51.1-0.748.3+1.4
", + "image_path": "0ac535a4285be830b4998e4a2674752702f605ecd65642079d3c8a90ef0a2755.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 63, + 297, + 272, + 388 + ], + "blocks": [ + { + "bbox": [ + 46, + 229, + 288, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 288, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 288, + 285 + ], + "type": "text", + "content": "Table 3. Regularizing soft prompts with geographical knowledge, top-1 bal. accuracy on GeoNet. The regularization method accomplishes our goal to increase target performance in GeoNet's USA-to-Asia transfer setting. CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 297, + 272, + 388 + ], + "lines": [ + { + "bbox": [ + 63, + 297, + 272, + 388 + ], + "spans": [ + { + "bbox": [ + 63, + 297, + 272, + 388 + ], + "type": "table", + "html": "
MethodThreshold t (# Classes)
<40% (13) Δ<60% (45) Δ<80% (77) Δ≤100% (95) Δ
CoOp [52]31.2-45.6-55.6-61.7
CoCoOp [51]32.8+1.645.4-0.255.2-0.461.4
KgCoOp [47]35.3+4.147.9+2.356.7+1.162.4
CIPReg37.5+6.348.9+3.357.8+2.263.5
LLMReg36.8+5.648.1+2.557.2+1.663.2
CIP+LLMReg39.9+8.749.5+3.958.2+2.664.0
", + "image_path": "af64a739f8d76b1e38bf1a9c84c6931c4a39834b85905a8908af4f4cd125d383.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 287, + 462 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 462 + ], + "type": "text", + "content": "Table 4. Performance on DollarStreet classes with less than " + }, + { + "bbox": [ + 46, + 396, + 287, + 462 + ], + "type": "inline_equation", + "content": "t\\%" + }, + { + "bbox": [ + 46, + 396, + 287, + 462 + ], + "type": "text", + "content": " recall in CoOp, with ViT-B/16. Gains w.r.t. CoOp of our geography knowledge regularization are especially large for CoOp's difficult classes (+8.7 in <40%), compared to KgCoOp's (+4.1 in <40%, i.e. a 4.6 difference from ours). CIP = CountryInPrompt, LLM = CountryLLM, CIP+LLM = CountryInPrompt+LLM." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 485, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 640 + ], + "type": "text", + "content": "for ViT-B/16 and +1.4 for RN50. The combined strategy works best on target, showing the value of incorporating descriptive knowledge. Since regularization prevents overfitting and potentially optimal source performance, we naturally observe source drops for CountryInPrompt and CountryLLM in Tables 2/3. However, CountryInPrompt+LLM in Table 2 even offers source gains. It is also notable that there are small drops in Americas for RN50, but upon inspection, countries in North America overall have a -0.9 drop, while ones in Central/South America have a +0.8 gain. These results concur with our hypothesis that CLIP is already aligned to countries like the USA. More is in supp., along with experiments varying the source and ensemble." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Regularization helps significantly on difficult classes. As certain objects may be especially sensitive to geographical domain shift, we break down classwise performance on DollarStreet in Table 4, using a stratification of class difficulty based on default soft prompting performance (CoOp). The CountryInPrompt+LLM strategy achieves significant" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 425, + 166 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 425, + 166 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 425, + 166 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 425, + 166 + ], + "type": "image", + "image_path": "137f117ba534aea34faf37626257e927bfa5bf4851ec3fa3139b3a3f67a66c58.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 170, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 304, + 170, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 545, + 247 + ], + "type": "text", + "content": "Figure 3. Geography knowledge-regularized soft prompts trained on source data (ours, green line) vs. few-shot soft prompts trained on target data (blue curve). (a) Src=Europe, Tgt=Africa, Asia, Amer.; (b) Src=USA, Tgt=Asia. Our 16-shot model trained on only source data (green) outperforms a model with prompts trained on 12 or 4 shots per class of target data (on DollarStreet&GeoNet, resp.), which is 1140&2400 images total." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 426, + 70, + 542, + 166 + ], + "blocks": [ + { + "bbox": [ + 426, + 70, + 542, + 166 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 542, + 166 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 542, + 166 + ], + "type": "image", + "image_path": "f5fa8d183ceb113fc8084085dc751925eaa384b4b68482b543416ada8a1677d3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": "gains on the classes most difficult with respect to the CoOp baseline. In particular, gains of " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": "+8.7\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": " in balanced accuracy are achieved for classes with " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": "< 40\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": " baseline recall, while the highest achieved by " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathrm{KgCoOp}" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": ". Example classes in this subset are snacks, clothes, and makeup. The DollarStreet classes with greatest improvement, independent of original CoOp accuracy are: piercings, clothes, homes, medication, and refrigerators (all at least " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": "+14\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": " over CoOp). In GeoNet, dome, goby (fish), eland (antelope), and gloriosa (flower) have " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": ">20" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": " samples and " + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "inline_equation", + "content": ">30\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 413 + ], + "type": "text", + "content": " improvement. A total of 64/95 classes in DollarStreet and 209/344 in GeoNet improve vs. CoOp, showing broad coverage." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 414, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 616 + ], + "type": "text", + "content": "Regularized source-only prompts outperform few-shot target-trained prompts. Given that soft prompts can show strong performance in few-shot settings, a potential alternative to regularizing soft prompts on source data is to directly acquire a few examples of target data for training. We evaluate this setting by splitting target data into train/test, and training CoOp at varying # of shots of target data for GeoNet and DollarStreet, shown in Fig. 3. Notably, training on 16 shots per class of source data with our regularization method outperforms using 12 & 4 shots per class of target data on DollarStreet & GeoNet. This is a vast amount of target data overall (e.g. 12 shots x 95 classes = 1140 target samples in DollarStreet, 4 shots x 600 classes = 2400 samples in GeoNet). The baseline CoOp trained on 16 shots of source data only outperforms an 8-shot/2-shot target-trained CoOp model (DollarStreet/GeoNet). Our strategy is thus more compelling in the absence of a lot of target data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Performance by income. DollarStreet provides estimated monthly income of the household in which an image was captured. We evaluate with the delineation of low, medium, and high-income buckets from [13]. Compared to CoOp/KgCoOp, CountryInPrompt+LLM gains are " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "+2.5/+3.4" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " in low, " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "+2.4/+1.5" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " in medium, and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "+2.1/+0.7" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " in high. Thus our method especially improves in low-income areas, though it helps across levels. The table is in supp." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13521" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 288, + 171 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 288, + 171 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 288, + 171 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 288, + 171 + ], + "type": "table", + "html": "
StatisticCIPCountryLLMCIP+LLM
GDP Per Capita (US $)0.2190.0630.217
Human Devel. Index (HDI)0.4390.3850.451
Land Area (km2)-0.0720.050*-0.046*
Population (#)-0.1310.077-0.123
Population Density (#/km2)0.1030.1580.081
% Agricultural Land0.1390.0700.122
% Forest Area0.1910.0870.201
Avg. Yearly Temp. (°C)0.3800.2560.391
Avg. Yearly Precip. (mm/year)0.2360.1240.230
", + "image_path": "472f94b47cded8a967066551d0e38e0ac4aa4fe79723bbb21612ea81833d442c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "text", + "content": "Table 5. Correlation (Pearson's " + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "text", + "content": ") of avg. CLIP class text embedding distance and country statistic difference, e.g. economic (GDP per capita, HDI) and climate factors (temperature, precipitation, forest area). We use the 63 countries in DollarStreet (1,953 pairs). Bold values have " + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\rho > 0.2" + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "text", + "content": ", * means not significant (" + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\alpha = 0.01" + }, + { + "bbox": [ + 47, + 176, + 287, + 232 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 53, + 243, + 277, + 387 + ], + "blocks": [ + { + "bbox": [ + 53, + 243, + 277, + 387 + ], + "lines": [ + { + "bbox": [ + 53, + 243, + 277, + 387 + ], + "spans": [ + { + "bbox": [ + 53, + 243, + 277, + 387 + ], + "type": "image", + "image_path": "f12fa63d81da462d4ff8bc95856453d31beff225d1d17aa4729d63604e18d2ff.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "type": "text", + "content": "Figure 4. Qualitative analysis. We show examples where geography-specific descriptors improve/hurt vs. general descriptors in zero-shot inference. We highlight the prediction's descriptors, bolding the highest activating one. Encoder=RN50." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 455, + 149, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 149, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 149, + 467 + ], + "type": "text", + "content": "5.3. Further Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 286, + 676 + ], + "type": "text", + "content": "Are descriptions correlated with key country statistics? For a pair of countries, we compute two values. We measure the distance between each class embedding and take the average overall distance as one value. We also take the absolute difference between statistics for those countries (from [2, 42], e.g. difference in avg. yearly temperature) as the other value. We compute the correlation between these two values over every unique country pair in DollarStreet, showing results in Table 5. We find that the strongest correlation across each prompt type is with HDI, which summarizes human development. It is notable that factors like yearly temperature and precipitation also show moderate correlations, indicating a potential role of climate. Future work may further explore how object differences present with respect to these factors. It will also be critical to ensure that differences between countries are representative and not exaggerated in embeddings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Descriptor topics. We show a UMAP [29] visualization comparing CountryLLM text embeddings for the category homes across geographies in Fig. 5. Countries tend to group" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 334, + 72, + 518, + 153 + ], + "blocks": [ + { + "bbox": [ + 334, + 72, + 518, + 153 + ], + "lines": [ + { + "bbox": [ + 334, + 72, + 518, + 153 + ], + "spans": [ + { + "bbox": [ + 334, + 72, + 518, + 153 + ], + "type": "image", + "image_path": "8b041f7823e6877bce0aae108097e73d6d42b86c5b29ab7e994725e8fdf5f273.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 163, + 545, + 206 + ], + "lines": [ + { + "bbox": [ + 304, + 163, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 545, + 206 + ], + "type": "text", + "content": "Figure 5. UMAP [29] plot for CountryLLM and the category homes in DollarStreet. Country-specific descriptors are often close to those of other countries intra-continent, likely due to similar weather, environment, and/or economic conditions." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 228, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 396 + ], + "type": "text", + "content": "by continent, showing the representations may capture similarity in features like climate and/or economics. We examine a few topics mentioned in the CountryLLM descriptors for homes. While “stone” is described across continents, “bright colors” and “mud” are mentioned mostly in Africa, and “balcony” in Europe and Asia. We show more in supp. Success and failure examples. We provide examples of CountryLLM vs. GeneralLLM in Fig. 4 on DollarStreet. The model captures geographical descriptive knowledge like “sandy colored stucco walls” for homes in Jordan, a feature which may be less common for Western homes. Sometimes the model may be too attentive to attributes, leading to confusion (e.g. choosing rug over bed). Future work that enhances alignment in VLMs can likely improve results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 407, + 378, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 378, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 378, + 418 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 498 + ], + "type": "text", + "content": "In this work, we bring attention to how various strategies to prompt CLIP affect recognition performance across geographies. In addition, through soft prompting with descriptive knowledge, we provide a mechanism to achieve a more geo-generalizable set of class representations across regions. Our work is only a first step in this important area." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "content": "Limitations and ethical considerations. While our method's proof of concept is demonstrated in a positive effort to debias CLIP's default representations through diversity, due to the biased worldview of the Internet, CLIP's representations are likely inadequate, exaggerated, and/or not fully representative for some countries. While we expect quality LLM knowledge to guide better representations, LLM knowledge can also be incorrect (e.g., through hallucination), imprecise, or biased." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 606, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 545, + 689 + ], + "type": "text", + "content": "Future work. For the above reasons, our future efforts aim to ensure more representative VLM/LLM knowledge. We strongly advocate for the community to seek communication with diverse groups within all countries (i.e. to capture areas that range from low to high income) to ensure better representation and fairness in AI technology use. There are notable continent-level disparities to still improve upon." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work was supported by National Science Foundation Grants No. 2006885 and 2329992." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13522" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 258, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 258, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 258, + 102 + ], + "type": "text", + "content": "[1] Common Crawl, 2023. https://commoncrawl.org/. 3" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 102, + 242, + 114 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 102, + 242, + 114 + ], + "spans": [ + { + "bbox": [ + 53, + 102, + 242, + 114 + ], + "type": "text", + "content": "[2] Wikipedia, 2023. https://en.wikipedia.org/. 3,8" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 114, + 287, + 168 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 287, + 168 + ], + "type": "text", + "content": "[3] Abhipsa Basu, R. 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Yet, it is an indispensable component of computer-aided diagnosis systems. The proposed approach has two key techniques. First, we propose a new future-class awareness mechanism by separating some potential regions for future classes from background based on their similarities to both old and new classes in the representation space. With this mechanism, we can not only reserve more parameter space for future updates but also enhance the representation capability of learned features. We further propose an innovative compatibility-inspired distillation scheme to make our model take full advantage of the knowledge learned by the old model. We conducted extensive experiments on two famous histopathological datasets and the results demonstrate the proposed approach achieves much better performance than state-of-the-art approaches. The code is available at https://github.com/why19991/InSeg.", + "bbox": [ + 75, + 340, + 473, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cellular nuclei segmentation aims to accurately delineate various cell nuclei from histopathological images, which is of great importance for cancer diagnosis, treatment, and prognosis prediction [37]. Recent years, deep learning models have achieved remarkable performance in this task [8, 20, 32, 34, 40], significantly promoting the development of computer-aided diagnosis systems. Despite these progresses, most existing models are incapable of maintaining the performance on previously learned classes when it is required to incrementally learn new classes, which is common in clinical practice [35]. This phenomenon is called", + "bbox": [ + 75, + 710, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/367fcdbd33b9b53ca09cd66f39e070d6167bfcd3358e69feeaf3a548e50a06b6.jpg", + "image_caption": [ + "rrnnnne" + ], + "image_footnote": [], + "bbox": [ + 522, + 308, + 612, + 450 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3ab489b0a909d270f5748d54a042fa219263715bf97c99f828947499a7d50c9b.jpg", + "image_caption": [ + "Figure 1. Pathological images typically contain numerous objects from different categories that have very similar appearances. For instance, epithelia (represented by red objects) and lymphocytes (represented by yellow objects) look quite alike. However, in the 1-1 setting at step 0, epithelia are labeled as new classes, whereas lymphocytes are seen as background. Our approach aims to mine such future classes in an unsupervised way and learn them in advance." + ], + "image_footnote": [], + "bbox": [ + 614, + 308, + 705, + 450 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/138ad2722ec3d01a047a5ac6244483978eb1a7f5d1f7e681669ec24fbe0f2a02.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 308, + 795, + 450 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/95b7b2a62dfba0a7a1eb0421f891f6e7bd8709f431181215fec0411c5769f25c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 799, + 308, + 890, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "catastrophic forgetting [24], which is a long-standing challenge and prohibits these models from being deployed in clinical settings. A common solution is to rebuild the training dataset containing annotations of all classes and retrain the model. However, the cost of collecting histopathological images with pixel-level annotations for segmentation is extremely laborious and time-consuming. Besides, access to previous data is usually limited by patient privacy. In this regard, we often have to incrementally optimize existing models to make them perform well in both old classes and new classes without using training samples of old classes.", + "bbox": [ + 496, + 608, + 892, + 775 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Incremental learning is proposed to solve the problem of catastrophic forgetting, and semantic segmentation based on incremental learning is known as incremental semantic segmentation (ISS). In scenarios where previous data can be reused, some studies [22, 45] select samples to help the model review and reinforce knowledge, greatly alleviating catastrophic forgetting. However, when privacy or storage issues make old data unavailable, which is common", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11408", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in clinical scenarios, most studies turn to employ distillation techniques [4, 13, 23, 25, 26, 30, 36] to constrain the model updating. These methods, while keeping the performance of old classes (stability) well, limit the model's capability in learning new classes (plasticity). In order to improve both stability and plasticity, a few studies [5, 39] propose to learn future classes in advance to prepare for learning new classes. Specifically, SSUL-M [5] applies a salient object detector to detect potential future classes while MicroSeg [39] utilizes mask proposals generated by Mask2Former [9] to detect future classes. Unfortunately, both the salient detector and mask proposals still heavily depend on a number of annotated data, which is, as mentioned, difficult to acquire in clinical practice due to privacy and cost. To the end, it is necessary to aware future classes in an unsupervised manner on the given data.", + "bbox": [ + 75, + 90, + 472, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present a novel ISS method for incremental nuclei segmentation from histopathological images, which has two key components: a new future-class awareness mechanism and an innovative compatibility-inspired distillation scheme. Histopathological images often contain numerous objects belonging to different categories with great similarity in appearance. As illustrated in Figure 1, some nuclei are learned as new classes or old classes, while others (future classes) are treated as background. Thus, we propose to separate some potential regions of future classes from background by calculating their similarities to both old and new classes in the representation space, and then we train the new model with both new and old classes, as well as with the separated regions. To the end, we cannot only reserve more parameter space for future updates but also enhance the representation capability of learned features. Furthermore, we design a compatibility-inspired distillation scheme to further improve both stability and plasticity. As the number of targeting classes of the updated model is always more than that of the old model, directly aligning them poses conflicts and background shifts [4]. In this regard, we propose to expand the old model's prediction range to match that of the new model by harnessing the representation space of the future classes. This scheme not only resolves alignment conflicts and background shifts but also enables the new model to effectively utilize the knowledge of the old model. Our contributions can be summarized as follows.", + "bbox": [ + 75, + 337, + 472, + 760 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel ISS method for incremental nuclei segmentation from histopathological images, which is able to incrementally optimize existing models to make them perform well in both old and new classes without using training samples of old classes.", + "- We propose a new future-class awareness mechanism to reserve more parameter space for incremental learning, and an innovative compatibility-inspired distillation scheme to make our model take full advantage of the" + ], + "bbox": [ + 76, + 763, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "knowledge learned by the old model.", + "bbox": [ + 511, + 90, + 759, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We demonstrate the proposed method achieve a better balance between stability and plasticity than state-of-the-art methods via extensive experiments on two famous public histopathological datasets, MoNuSAC [33] and CoNSeP [14].", + "bbox": [ + 500, + 106, + 893, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 196, + 640, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Nuclei Segmentation", + "text_level": 1, + "bbox": [ + 500, + 220, + 694, + 237 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There have been some preliminary works for nuclei segmentation based on traditional techniques and deep learning methods. Traditional techniques based on background subtraction and color threshold [27, 29] fail to generalize to complex scenarios such as overlap and occlusion in histopathology images. With the development of CNN, deep networks have been widely used in nuclei segmentation [31, 32, 34, 42], significantly improving the segmentation performance in the supervised setting. However, most of these networks are not incrementally designed and tend to forget previously learned classes when learning new types of cell nuclei continually.", + "bbox": [ + 496, + 244, + 893, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Class Incremental Learning", + "text_level": 1, + "bbox": [ + 500, + 435, + 751, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Class incremental learning (CIL) aims to address the problem of catastrophic forgetting when learning knowledge for new classes. Existing CIL techniques can be summarized into regularization-based, replay-based, and architecture-based approaches. Regularization-based approaches utilize consistency constraints between new and old models to prevent significant changes to the knowledge associated with previously learned classes. The constraints can be applied on features [10, 12, 18], the output logits [4, 11, 21], the weights [1, 2, 19], or the gradients [6, 15]. Architecture-based approaches [16, 38, 44] dynamically grow the network to extend model capacity for new tasks. To better retain knowledge of old classes, replay-based approaches store and re-use a subset of previous training data, including raw images [3, 22, 45], features [17, 43] or generated data [7, 28].", + "bbox": [ + 496, + 459, + 893, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Class Incremental Semantic Segmentation", + "text_level": 1, + "bbox": [ + 500, + 710, + 859, + 727 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, several works have extended and combined existing incremental learning methods to semantic segmentation. MiB [4] proposes a novel unbiased function to model background shift. PLOP [13] adopts pseudo label to solve background shift and retain spatial dependencies by local pooling operation. CoNuSeg [35] maintains the relationships between the prototypes of old classes to preserve the semantic information of old classes. EWF [36] propose a weight fusion strategy to fuse parameters from new and old models. SSUL-M [5] and MicroSeg [39] further propose pre-learning future classes to prepare for the future.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11409", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ce59960fb7ec6997c6d9e0bdc295795b05ad7c900f6c7a16eaf983b22124b600.jpg", + "image_caption": [ + "Figure 2. The overall framework. The old $(t - 1)$ and new models $(t)$ consist of the same feature extractor $F$ and segmentation head $H$ . During training, we freeze the old model and update the new model by minimizing the weighted sum of $\\mathcal{L}_{ce}, \\mathcal{L}_{pod}, \\mathcal{L}_{bkd}$ and $\\mathcal{L}_{fkd}$ ." + ], + "image_footnote": [], + "bbox": [ + 166, + 88, + 803, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 411, + 169, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 436, + 279, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Class incremental semantic segmentation involves conducting semantic segmentation in a series of steps, with the underlying assumption that there are a total of $T$ steps. In step $t$ , we have training set $D_{t} = \\{(x,y)\\}$ and label set $\\mathcal{C}_t$ , where $x$ is an RGB image $\\in \\mathbb{R}^{C\\times H\\times W}$ and $y\\in \\mathcal{C}_t$ is the corresponding annotation. The label set $\\mathcal{C}_t$ only contains newly added classes at step $t$ , while previous learned classes $\\mathcal{C}_0\\cup \\mathcal{C}_1\\cup \\ldots \\cup \\mathcal{C}_{t - 1}$ and future classes $\\mathcal{C}_{t + 1:T}$ are considered as background, which can lead to catastrophic forgetting of the previously learned classes. Given a dataset $\\mathcal{D}_t$ , our goal is to achieve a model $M$ with parameter $\\theta_t$ that can perform well on all seen classes $\\mathcal{C}_{0:t}$ . Without loss of generality, $M$ consists of a feature extractor $F$ and a segmentation head $H$ , which makes $M = F\\circ H$ , where $\\circ$ denotes function composition.", + "bbox": [ + 75, + 459, + 473, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Framework Overview", + "text_level": 1, + "bbox": [ + 76, + 696, + 282, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed incremental semantic segmentation framework, depicted in Figure 2, includes an old and new model. Under the incremental setting, both old and future classes are treated as background. To correct pixels of old classes, we adopt the pseudo-labeling strategy to assign them pseudo-labels. For pixels of potential future classes, we propose a new future-class awareness mechanism (detailed in Section. 3.3) to assign them unknown labels. At the feature level, we apply multi-scale local distillation with Local POD (described in Section. 3.5) between the corresponding layers of the two models to avoid a large feature discrepancy. At the output level, we design an innovative", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "compatibility-inspired distillation (depicted in Section. 3.4) between the model's predictions to achieve better stability and plasticity. After training, we fuse the parameters from the two models by using the Endpoints Weight Fusion strategy (EWF) [36]. Specific details about EWF can be found in the supplementary materials.", + "bbox": [ + 496, + 412, + 893, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Future-class Awareness", + "text_level": 1, + "bbox": [ + 498, + 512, + 718, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our future-class awareness mechanism corrects the background pixels that are considered potential future classes, i.e., pixels that are visually similar to a new or old class. We propose to measure the similarity $S$ by utilizing the classcentroids $\\mathcal{V}$ in the representation space of the old model. Subsequently, we assign unknown labels to these pixels for joint learning with both new and old classes. This approach enhances the representation capability of learned features and better prepares the model for the future.", + "bbox": [ + 496, + 536, + 890, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-wise Centroids Aggregation. Class-centroids (prototypes) are representatives of each class in the representation space and serve as an effective tool to measure similarities between classes [30]. Given an image as input, we first generate pseudo-labels $\\hat{y}(i,c)$ for old classes in the background using predictions $O^{t-1}$ of the old model and the ground-truth label $y(i,c)$ at step $t$ :", + "bbox": [ + 496, + 671, + 893, + 779 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} (i, c) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} y (i, c) = 1 \\\\ 1 & \\text {i f} y (i, c) = 0 \\text {a n d} c = \\operatorname {a r g m a x} O ^ {t - 1} (i, c) \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 787, + 890, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This strategy can effectively re-assign labels for old classes in the background but fails to separate potential future classes hidden in the background. Next, we generate class-aware mask $\\mathcal{M}_c$ for class $c$ under the guidance of pseudo", + "bbox": [ + 496, + 840, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11410", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/af6b31687acad4b4d2627304444167624a2e791fa23c55d441854a4b1721c967.jpg", + "image_caption": [ + "Figure 3. Illustration of future-class awareness. Centroids representing both old and new categories are aggregated in representation space, then a class-aware matrix $S$ is computed between all centroids and background features to aware future classes." + ], + "image_footnote": [], + "bbox": [ + 158, + 88, + 816, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "label $\\hat{y} (i,c)$ ..", + "bbox": [ + 76, + 400, + 165, + 416 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {c} (i) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\hat {y} (i, c) = 1 \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 421, + 468, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, for a certain class $k$ , we average the deepest input feature $\\mathcal{F}_d^{t - 1}$ with the class-aware mask to obtain classcentroid $\\nu_{k}$ :", + "bbox": [ + 76, + 465, + 468, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {V} _ {k} = M A P \\left(\\mathcal {M} _ {k}, \\mathcal {F} _ {d} ^ {t - 1}\\right) \\\\ = \\frac {\\sum_ {i} \\mathcal {F} _ {d} ^ {t - 1} (i) \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]}{\\sum_ {i} \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]} \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 515, + 468, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $MAP$ represents the masked average pooling operation. After that, we obtain a centroid set $\\mathcal{V} = \\{\\mathcal{V}_1,\\dots,\\mathcal{V}_{\\mathcal{C}_t}\\}$ containing old and new class-centeroids, which will be utilized to detect future classes.", + "bbox": [ + 76, + 575, + 468, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross Image-wise Centroids Aggregation. Different cell nuclei are typically distributed across different images, which suggests that potential future classes may not coexist in the same image as their similar cell nuclei. Therefore, aggregating class centroids in an image-wise manner may not include centroids of classes that are similar to future classes. To address this issue, we propose to update class centroids using a running average approach. The final class centroids are computed as follows:", + "bbox": [ + 75, + 637, + 468, + 772 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {k} = \\frac {1}{N} \\left(\\mathcal {V} _ {k} ^ {\\prime} \\cdot N _ {k} ^ {\\prime} + \\sum_ {i} \\mathcal {F} _ {d} ^ {t - 1} (i) \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 776, + 468, + 813 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nN = N _ {k} ^ {\\prime} + \\sum_ {i} \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right] \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 815, + 468, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{V}_k^{\\prime}$ and $N_{k}^{\\prime}$ represent the accumulated result and total pixel number of class k from the initial update to the last update, respectively.", + "bbox": [ + 76, + 853, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Awareness & Separation. To aware future classes, we first assemble the background features $\\mathcal{F}_{bg} \\in \\mathbb{R}^{C \\times N_b}$ via the masked multiplication on the deepest feature $\\mathcal{F}_d^{t-1}$ with the background mask $\\mathcal{M}_b$ . We then calculate a pixel-to-centroid affinity matrix $\\mathcal{A}$ between pixels of the reshaped background feature $\\mathcal{F}_{bg}$ and class-centroids $\\mathcal{V}$ via a matrix multiplication operation $Mat$ :", + "bbox": [ + 496, + 400, + 890, + 506 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} = M a t \\left(\\operatorname {N o r m} \\left(\\mathcal {F} _ {b g}\\right) ^ {T}, \\operatorname {N o r m} (\\mathcal {V})\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 513, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Norm$ indicates $l2$ -normalization. The size of $\\mathcal{A}$ is $\\mathbb{R}^{N \\times P}$ and $P = |\\mathcal{V}|$ is the cardinality of class-centroid set. Through the affinity matrix, we construct a semantic graph for each pixel-centroid pair, where each vertex represents the semantic structure and the edge represents the similarity relationship, thus a fine-grained similarity can be measured by utilizing the information in the representation space.", + "bbox": [ + 496, + 541, + 890, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We obtain the final class-aware matrix $\\mathcal{S}$ by taking the average or maximum across the second dimension of affinity matrix $\\mathcal{A}$ . To effectively pre-learn knowledge of future classes, only background pixels that are sufficiently similar are re-assigned unknown labels. The final corrected ground truth $y(i,c)$ of pixel $i$ is defined as:", + "bbox": [ + 496, + 647, + 890, + 738 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny (i, c) = \\left\\{ \\begin{array}{l l} u & \\text {i f} \\mathcal {M} _ {b} (i) = 1 \\text {a n d} \\mathcal {S} (i) < \\tau_ {u} \\\\ \\hat {y} (i, c) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 746, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $u$ represents the unknown label assigned to future classes, and $\\tau_{u}$ is a threshold controlling the confidence of future classes. In other words, for background pixels filtered by Equation 1, we re-label them with an unknown label $u$ on the guidance of the class-aware matrix $S$ . Otherwise, we directly copy their pseudo-labels (for old classes) or true labels (for new classes).", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11411", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Compatibility-inspired Distillation", + "text_level": 1, + "bbox": [ + 76, + 90, + 379, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that the previous model only produces predictions $O^{t-1}$ for $|\\mathcal{C}_{0:t-1}|$ classes, while the new model can produce predictions $O^t$ for $|\\mathcal{C}_{0:t}|(|\\mathcal{C}_{0:t}| > |\\mathcal{C}_{0:t-1}|)$ classes, directly aligning the outputs between the two models is contradictory. Treating the model's predictions as interfaces of software, we introduce new interfaces into the old model to be compatible with the new model (i.e., expanding $O^{t-1}$ to match $O^t$ , and padding the additional channels with 0). The expanded prediction $O^{t-1}$ becomes:", + "bbox": [ + 75, + 113, + 468, + 250 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} _ {t} \\\\ O ^ {t - 1} (i, c) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 255, + 468, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then we enforce constraints to pixels of new class set $\\mathcal{U}_n$ and background set $\\mathcal{U}_b$ from the view of backward compatibility and forward compatibility respectively. It is worth noting that the background here includes old classes, future classes, and true background pixels.", + "bbox": [ + 75, + 301, + 468, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Forward compatibility. For pixels $i$ from the new class set, we transfer the old model's background prediction $O^{t - 1}(i,b)$ to the prediction corresponding to the ground-truth to address background shift [4]. Next, with the future class-aware mechanism, the old model has pre-learned knowledge about the new classes (which are future classes to the old model). Thus we also add the old model's future class prediction $O^{t - 1}(i,u)$ to the prediction corresponding to the ground truth, thereby naturally inheriting the knowledge that the old model has prepared for future learning (forward compatibility). After that, we reset the predictions of background and future classes to 0 while keeping other predictions unchanged. The corrected prediction of the old model is defined as:", + "bbox": [ + 75, + 377, + 468, + 588 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} O ^ {t - 1} (i, u) + O ^ {t - 1} (i, b) & \\text {i f} c \\in \\mathcal {C} _ {t} \\\\ O ^ {t - 1} (i, c) & \\text {i f} c \\in \\mathcal {C} _ {0: t - 1} \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 592, + 468, + 660 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i\\in \\mathcal{U}_n$ and $u$ indicates the future class at step $t - 1$", + "bbox": [ + 76, + 661, + 465, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backward compatibility. For pixels $i \\in \\mathcal{U}_b$ from the background set, similar to regular knowledge distillation, we only need to align the outputs between the two models to ensure that the new model does not deviate significantly from the old model during updates. The complete compatibility-inspired distillation loss is defined as:", + "bbox": [ + 75, + 676, + 468, + 766 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c p d} = \\alpha_ {n} \\cdot \\mathcal {L} _ {f k d} (x, \\mathcal {U} _ {n}) + \\alpha_ {b} \\cdot \\mathcal {L} _ {b k d} (x, \\mathcal {U} _ {b}) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 773, + 468, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{n}$ and $\\alpha_{b}$ control the contribution of the new classes set $\\mathcal{U}_n$ and background set $\\mathcal{U}_b$ , which are discussed in Section 4.3; $\\mathcal{L}(x,\\mathcal{U})$ is a common knowledge distillation loss:", + "bbox": [ + 76, + 797, + 468, + 843 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (x, \\mathcal {U}) = - \\frac {1}{| \\mathcal {U} |} \\sum_ {i \\in \\mathcal {U}} \\sum_ {c} ^ {\\mathcal {C} _ {0: t}} O _ {x} ^ {t - 1} (i, c) \\log O _ {x} ^ {t} (i, c) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 861, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We emphasize that our distillation approach supplements and corrects the contents extended in the interfaces of the old model, thus addressing alignment conflict and background shift, as well as facilitating the new model to effectively leverage the knowledge learned by the old model.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Feature-based Distillation", + "text_level": 1, + "bbox": [ + 500, + 178, + 735, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To prevent catastrophic forgetting in feature space, we also utilize multi-scale local distillation with Local POD [13] to retain knowledge by preserving multi-scale spatial information. The Local POD loss is formulated as:", + "bbox": [ + 496, + 200, + 890, + 261 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p o d} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} | \\phi (\\mathcal {F} _ {l} ^ {t}) - \\phi (\\mathcal {F} _ {l} ^ {t - 1}) | ^ {2} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 272, + 890, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_l^t$ is the feature of the $l$ -th layer and $\\phi(.)$ is a function that captures multi-scale spatial statistics.", + "bbox": [ + 496, + 325, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we train the model with the total loss as follows:", + "bbox": [ + 517, + 357, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a l l} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {c p d} + \\lambda \\cdot \\mathcal {L} _ {p o d} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 388, + 890, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ denotes the weight of LocalPOD, which is set to 0.0001 in our experiments.", + "bbox": [ + 496, + 412, + 890, + 443 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 498, + 459, + 624, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets, Protocols, and Evaluation", + "text_level": 1, + "bbox": [ + 498, + 484, + 805, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We conduct all the experiments on two publicly available nuclei datasets, MoNuSAC and CoNSeP. MoNuSAC contains H&E stained tissue images of four organs, along with annotations for multiple cell types, including epithelial (Epith), lymphocyte (Lymph), macrophage (Macro), and neutrophil (Neutr). We randomly split $20\\%$ of the training set for validation. Besides, all images in the training, testing, and validation sets have been uniformly cropped to a resolution of $320 \\times 320$ . Finally, the MoNuSAC contains 1177 training images, 295 validation images and 651 test images. CoNSeP contains H&E stained image tiles with annotations of 7 cell types, where we divide them into 3 classes: epithelial, spindle-shaped and others. With the same pre-processing, we obtain a training set with 345, a validation set with 87, and a test set with 224 images.", + "bbox": [ + 496, + 508, + 890, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Protocols. There are two common settings in ISS benchmarks: disjoint and overlapped. In the disjoint setting, $D_{t}$ only contains images of new classes and old classes. In the overlapped setting, $D_{t}$ can contain images of all classes, including old classes, new classes, and future classes. Regarding of setting, only new classes are annotated, while others are treated as background. The overlapped setting is considered more realistic since it allows future classes to appear in the current dataset, reflecting real-world scenarios more accurately. In this work, we only focus on the overlapped setting.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11412", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c5dda4dce5ebbb7e3886ac30b27052e93d3f3238c4d26126c7cc583f02dd35c0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method1-1 (4 tasks)2-1 (3 tasks)2-2 (2 tasks)3-1 (2 tasks)
OldNewMeanOldNewMeanOldNewMeanOldNewMean
ILT [25]33.4653.9148.8050.0073.3061.6546.0068.1857.0962.1173.2764.90
MiB [4]59.9564.5763.4152.5174.6763.5957.3376.8767.1063.8575.3866.73
SDR [26]55.5067.3064.3553.4774.3763.9257.0878.0367.5665.7077.3168.60
PLOP [13]60.1465.6064.2356.8575.8766.3656.7475.8866.3166.1677.4368.97
REMARKER [30]62.4166.4965.4756.5775.8966.2359.8976.0367.9668.2277.1870.46
CoNuSeg [35]65.3767.9267.2857.8576.0966.9761.7077.1169.4066.4777.3369.18
IDEC [41]62.1669.4167.5958.6376.0367.3363.2275.4169.3167.3677.1269.80
EWF [36]64.5767.8967.0660.2776.2368.2665.9075.9470.9269.0677.6271.20
Ours68.1169.8669.4463.7976.5370.1665.4377.2171.3270.4678.0372.36
Joint72.0175.2974.4770.3678.5874.4770.3678.5874.4772.6579.9374.47
", + "bbox": [ + 84, + 89, + 888, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Incremental semantic segmentation results (mDice) on MoNuSAC. The best is in bold.", + "bbox": [ + 199, + 324, + 767, + 339 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/18eb1657808d7272ac7e6034b27aa23cbe7fcf14a8e7b0c4a550c75678766333.jpg", + "image_caption": [ + "Figure 4. Visualization of the proposed method and EWF at different incremental steps on two datasets." + ], + "image_footnote": [], + "bbox": [ + 86, + 353, + 524, + 627 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/25c875f2b6b1a66d29a7d029144c353a10c4759a60a29e1e5698040f308c3a61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 352, + 888, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation. The ISS benchmark configurations are represented as $n - m$ where $n$ and $m$ correspond to the number of new classes to be learned during the initial step and each subsequent step, respectively. We set several ISS settings for each dataset, e.g., on MoNuSAC 3-1, 2-1, 2-2, and 1-1 respectively include learning 3 classes then 1 class (2 steps), 2 classes then 1 class (3 steps), 2 classes then 2 classes (2 steps) and 1 class at initial step then 1 class at subsequent step (4 steps). We emphasized that the 1-1 setting is the most challenging task due to its small amount of data and high number of steps. Similarly, on CoNSeP 1-1 (3 steps) and 2-1 (2 steps). After training all steps, we use mean Dice (mDice) to evaluate the performance.", + "bbox": [ + 75, + 678, + 470, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We use the ResNet-101 pre", + "bbox": [ + 76, + 875, + 468, + 891 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "trained on ImageNet as the feature encoder for all experiments. During training, the initial learning rate is set to 0.05 for the first step and 0.01 for subsequent incremental steps. The number of epochs for all steps is set to 100. We employ an SGD optimizer with a batch size of 12, distributed across three 2080Ti GPUs, to train the model.", + "bbox": [ + 496, + 678, + 890, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison Results. To demonstrate the advantages of our method, we employ the state-of-the-art approach (EWF) as our baseline for comparison. Table 1 displays our approach's comparative results against some strong ISS methods on the MoNuSAC dataset. Evidently, the performance of ILT is the worst in all incremental setups, since it lacks the capacity to address background shift. Integrating background correction methods, such as MiB and", + "bbox": [ + 496, + 768, + 892, + 890 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11413", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PLOP, leads to marked improvements for both old and new classes in all settings. By further introducing innovative distillation mechanisms into the background correction method, approaches like REMINDER, CoNuSeg, and IDEC have achieved additional performance gains. EWF receives higher performance after applying the Endpoints Weight Fusion strategy to PLOP.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Despite their great progress, our approach surpasses them by a large margin on all settings. In particular, on the most challenging setup (1-1), our method outperforms the EWF by $3.54\\%$ in old classes and IDEC by $0.45\\%$ in new classes. While the gains in new classes are not that large, we believe that the performance is already quite better compared to that of old classes. As presented in Figure 5, our model achieves all the highest mDice scores from incremental step 1 to step 3. This also indicates that the stability and plasticity of our model are superior to those of other strong models. Experiments in Table 2 further demonstrate the strong generalization ability of our method.", + "bbox": [ + 75, + 198, + 473, + 380 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2fa7f718da9564a20cb7bdf3687b5770c7bad69ae101b5e8b8ec21a82b2e855d.jpg", + "image_caption": [ + "Figure 5. Results of mDice at different incremental steps." + ], + "image_footnote": [], + "bbox": [ + 78, + 391, + 468, + 555 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7f03db8079fa61fb28c0ce9772f876a03e0e810cd2720eadee5896d54c7cb708.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method1-1 (3 tasks)2-1 (2 tasks)
OldNewMeanOldNewMean
ILT [25]35.2363.1944.5540.8263.6148.41
MiB [4]67.0267.0667.0470.9961.9667.98
SDR [26]67.0567.2967.2170.3762.9267.88
PLOP [13]67.0667.7867.5472.5063.1569.38
CoNuSeg [35]67.5268.5968.2372.8063.4169.67
IDEC [41]67.2068.2867.9272.1662.7869.03
EWF [36]67.1870.0369.0874.1663.0070.44
Ours66.6470.8469.4474.2964.6571.08
", + "bbox": [ + 78, + 609, + 475, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual Results. We visualize the segmentation results of our method and EWF on two datasets to highlight the comparative effectiveness. As shown in Figure 4, our method", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "yields segmentation results that are more complete and accurate than those produced by EWF. For example, for the second image (rows 3-4, left), both methods gradually forget class epithelial (the red ones) and macrophage (the green ones) from step 0 to step 2. Nevertheless, our method still yields satisfactory segmentation results after step 3. Similar results can be observed in other images. Figure 6 explicitly presents the Dice score for each class at every step.", + "bbox": [ + 496, + 90, + 890, + 213 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2390ae8b8b006b60ef357598c0390f5f134efc97fa29c56ab96d2bf0cdabfce2.jpg", + "image_caption": [ + "Figure 6. Values of Dice metric for each class at different incremental steps on MoNuSAC 1-1." + ], + "image_footnote": [], + "bbox": [ + 501, + 222, + 890, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 441, + 653, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We verify the effectiveness of the proposed method using 1-1 and 3-1 setups on MoNuSAC. From Table 3, we can find that the performance of PLOP + EWF surpasses that of PLOP. Only adding future-class awareness (FCA) can further boost the performance of EWF across different setups. After applying compatibility-inspired distillation (CID), we obtain the highest performance on MoNuSAC. In particular, the performance of PLOP + EWF + FCA + CID outperforms that of PLOP + EWF in 1-1 settings, with a great improvement of $3.54\\%$ in old classes and $1.97\\%$ in new classes. These results effectively demonstrate that both proposed modules can effectively improve the plasticity and stability of the model, thereby improving the overall performance.", + "bbox": [ + 496, + 464, + 890, + 675 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/48b1b063cbd3b27b9235315efd0689b654868db7621e58189d878c3b2c73d5d9.jpg", + "table_caption": [ + "Table 2. Incremental semantic segmentation results (mDice) on the CoNSeq dataset." + ], + "table_footnote": [], + "table_body": "
Method1-1 (4 tasks)3-1 (2 tasks)
OldNewMeanOldNewMean
PLOP60.1465.6064.2366.1677.4368.97
+ EWF64.5767.8967.0669.0677.6271.20
+FCA67.4269.0068.6070.1177.9372.07
+CID68.1169.8669.4270.4678.0372.36
", + "bbox": [ + 506, + 684, + 888, + 797 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation study results (mDice) on the MoNuSAC dataset.", + "bbox": [ + 500, + 806, + 890, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Further Analysis", + "text_level": 1, + "bbox": [ + 500, + 847, + 668, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Future-class Awareness. To better understand how prelearning of future classes enhances the results, we visual-", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11414", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ize t-SNE distribution of features generated from the baseline and baseline $+$ FCA. As shown in Figure 7, the base", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea0eac70587190c338631bf7f8f256e9e74ad3a046df8c2a83fa53dfb120b347.jpg", + "image_caption": [ + "Figure 7. T-SNE visualization of features learned by Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1." + ], + "image_footnote": [], + "bbox": [ + 81, + 133, + 467, + 275 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "line tends to generate more ambiguous features while the baseline $+\\mathrm{FCA}$ is able to learn more discriminative features. These robust features then help the model to resist catastrophic forgetting better. Similar conclusions can be drawn from the feature map (Figure 8). The baseline model", + "bbox": [ + 75, + 330, + 470, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ae1bb079fb8fa4bda24cea40be98c96e5173ee9b72df904237beddf52fdb7f5.jpg", + "image_caption": [ + "Figure 8. Feature maps of the Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1." + ], + "image_footnote": [], + "bbox": [ + 78, + 419, + 468, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "exhibits a lower response to target features and is prone to generating erroneous high responses in the background, whereas the baseline with FCA generates more accurate and higher responses to target features. This phenomenon further shows that training with FCA can enhance the representation power to alleviate knowledge forgetting and reserve more parameter space to be updated.", + "bbox": [ + 75, + 672, + 467, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compatibility-inspired Distillation. As shown in Table 4, slightly increasing both $\\alpha_{n}$ and $\\alpha_{b}$ to 1 can improve the performance of both new and old classes. However, a large value of $\\alpha_{n}$ , e.g., $\\alpha_{n} = 5$ leads the model to focus excessively on new classes, compromising the performance of old classes and thus negatively affecting overall performance. Similarly, when we set $\\alpha_{b}$ a high value 3, the model tends to overly remember old classes and overlook the new classes.", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In our experiments, we achieve the best performance when $\\alpha_{n}$ and $\\alpha_{b}$ are set to 3 and 1, respectively. For additional ablation studies and detailed analytical experiments, please refer to the supplementary materials.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/533f20239df4367ad17418f829c6770c36ca5ef6b26d8101869f7d9b888a0457.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
αnαbBackgroundOldNewAll
0094.5867.4269.0073.80
1194.5367.7169.3174.03
3194.4368.1169.8674.42
5194.5165.9169.1873.59
3094.7067.6169.2574.01
3294.7468.0869.4174.21
3394.5368.1868.3473.54
", + "bbox": [ + 509, + 166, + 887, + 334 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Effect of the weighted factors ${\\alpha }_{n}$ and ${\\alpha }_{b}$ .", + "bbox": [ + 545, + 345, + 844, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation", + "text_level": 1, + "bbox": [ + 500, + 395, + 612, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We develop our method based on the attributes of histopathological images, where future classes in the dataset exhibit visual similarities to the learned classes. Therefore, our approach may not perform optimally in datasets where future classes significantly differ from the learned classes, which necessitates further research. Nevertheless, considering the vast diversity of cancer cell types, our method shows promise in enhancing computer-aided diagnosis systems with more robust incremental updating capabilities.", + "bbox": [ + 496, + 421, + 890, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 574, + 617, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present a novel method for incremental semantic segmentation from histopathological images, aiming to solve catastrophic forgetting without storing samples of previous data. First, we propose a new future-class awareness approach that detects future classes in an unsupervised way. Second, drawing inspiration from software engineering, we introduce an innovative compatibility-inspired knowledge distillation to make the new model take full advantage of the knowledge learned by the old model. Finally, comparative experiments and ablation studies clearly demonstrate the effectiveness of the proposed method.", + "bbox": [ + 496, + 599, + 890, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 782, + 658, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported partly by National Natural Science Foundation of China (No. 62273241), Natural Science Foundation of Guangdong Province, China (No. 2024A1515011946), and the Theme-based Research Scheme from Hong Kong Research Grants Council (project no. T45-401/22-N).", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11415", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. Expert gate: Lifelong learning with a network of experts. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3366-3375, 2017. 2", + "[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In Proceedings of the European conference on computer vision (ECCV), pages 139-154, 2018. 2", + "[3] Jihwan Bang, Heesu Kim, YoungJoon Yoo, Jung-Woo Ha, and Jonghyun Choi. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 3082-3092, 2023. 1, 2" + ], + "bbox": [ + 501, + 92, + 892, + 795 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11417", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/9fa3bbf9-7154-47a0-a450-b1f92451140e_model.json b/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/9fa3bbf9-7154-47a0-a450-b1f92451140e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d754022275624bc072f7759eccd7493a0a6710af --- /dev/null +++ b/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/9fa3bbf9-7154-47a0-a450-b1f92451140e_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.131, + 0.83, + 0.177 + ], + "angle": 0, + "content": "Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation" + }, + { + "type": "text", + "bbox": [ + 0.334, + 0.203, + 0.636, + 0.222 + ], + "angle": 0, + "content": "Huyong Wang\\(^{1}\\), Huisi Wu\\(^{1*}\\), Jing Qin\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.222, + 0.798, + 0.24 + ], + "angle": 0, + "content": "1 College of Computer Science and Software Engineering, Shenzhen University" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.24, + 0.823, + 0.258 + ], + "angle": 0, + "content": "2 Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.26, + 0.783, + 0.275 + ], + "angle": 0, + "content": "2210273011@email.szu.edu.cn, hswu@szu.edu.cn, harry.qin@polyu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.659 + ], + "angle": 0, + "content": "We present a novel semantic segmentation approach for incremental nuclei segmentation from histopathological images, which is a very challenging task as we have to incrementally optimize existing models to make them perform well in both old and new classes without using training samples of old classes. Yet, it is an indispensable component of computer-aided diagnosis systems. The proposed approach has two key techniques. First, we propose a new future-class awareness mechanism by separating some potential regions for future classes from background based on their similarities to both old and new classes in the representation space. With this mechanism, we can not only reserve more parameter space for future updates but also enhance the representation capability of learned features. We further propose an innovative compatibility-inspired distillation scheme to make our model take full advantage of the knowledge learned by the old model. We conducted extensive experiments on two famous histopathological datasets and the results demonstrate the proposed approach achieves much better performance than state-of-the-art approaches. The code is available at https://github.com/why19991/InSeg." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.687, + 0.21, + 0.703 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Cellular nuclei segmentation aims to accurately delineate various cell nuclei from histopathological images, which is of great importance for cancer diagnosis, treatment, and prognosis prediction [37]. Recent years, deep learning models have achieved remarkable performance in this task [8, 20, 32, 34, 40], significantly promoting the development of computer-aided diagnosis systems. Despite these progresses, most existing models are incapable of maintaining the performance on previously learned classes when it is required to incrementally learn new classes, which is common in clinical practice [35]. This phenomenon is called" + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.339, + 0.521, + 0.434 + ], + "angle": 0, + "content": "rrnnnne" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.309, + 0.614, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.309, + 0.706, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.309, + 0.797, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.8, + 0.309, + 0.892, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.462, + 0.893, + 0.572 + ], + "angle": 0, + "content": "Figure 1. Pathological images typically contain numerous objects from different categories that have very similar appearances. For instance, epithelia (represented by red objects) and lymphocytes (represented by yellow objects) look quite alike. However, in the 1-1 setting at step 0, epithelia are labeled as new classes, whereas lymphocytes are seen as background. Our approach aims to mine such future classes in an unsupervised way and learn them in advance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.893, + 0.776 + ], + "angle": 0, + "content": "catastrophic forgetting [24], which is a long-standing challenge and prohibits these models from being deployed in clinical settings. A common solution is to rebuild the training dataset containing annotations of all classes and retrain the model. However, the cost of collecting histopathological images with pixel-level annotations for segmentation is extremely laborious and time-consuming. Besides, access to previous data is usually limited by patient privacy. In this regard, we often have to incrementally optimize existing models to make them perform well in both old classes and new classes without using training samples of old classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Incremental learning is proposed to solve the problem of catastrophic forgetting, and semantic segmentation based on incremental learning is known as incremental semantic segmentation (ISS). In scenarios where previous data can be reused, some studies [22, 45] select samples to help the model review and reinforce knowledge, greatly alleviating catastrophic forgetting. However, when privacy or storage issues make old data unavailable, which is common" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11408" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.334 + ], + "angle": 0, + "content": "in clinical scenarios, most studies turn to employ distillation techniques [4, 13, 23, 25, 26, 30, 36] to constrain the model updating. These methods, while keeping the performance of old classes (stability) well, limit the model's capability in learning new classes (plasticity). In order to improve both stability and plasticity, a few studies [5, 39] propose to learn future classes in advance to prepare for learning new classes. Specifically, SSUL-M [5] applies a salient object detector to detect potential future classes while MicroSeg [39] utilizes mask proposals generated by Mask2Former [9] to detect future classes. Unfortunately, both the salient detector and mask proposals still heavily depend on a number of annotated data, which is, as mentioned, difficult to acquire in clinical practice due to privacy and cost. To the end, it is necessary to aware future classes in an unsupervised manner on the given data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.473, + 0.761 + ], + "angle": 0, + "content": "In this work, we present a novel ISS method for incremental nuclei segmentation from histopathological images, which has two key components: a new future-class awareness mechanism and an innovative compatibility-inspired distillation scheme. Histopathological images often contain numerous objects belonging to different categories with great similarity in appearance. As illustrated in Figure 1, some nuclei are learned as new classes or old classes, while others (future classes) are treated as background. Thus, we propose to separate some potential regions of future classes from background by calculating their similarities to both old and new classes in the representation space, and then we train the new model with both new and old classes, as well as with the separated regions. To the end, we cannot only reserve more parameter space for future updates but also enhance the representation capability of learned features. Furthermore, we design a compatibility-inspired distillation scheme to further improve both stability and plasticity. As the number of targeting classes of the updated model is always more than that of the old model, directly aligning them poses conflicts and background shifts [4]. In this regard, we propose to expand the old model's prediction range to match that of the new model by harnessing the representation space of the future classes. This scheme not only resolves alignment conflicts and background shifts but also enables the new model to effectively utilize the knowledge of the old model. Our contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.47, + 0.84 + ], + "angle": 0, + "content": "- We propose a novel ISS method for incremental nuclei segmentation from histopathological images, which is able to incrementally optimize existing models to make them perform well in both old and new classes without using training samples of old classes." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.841, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We propose a new future-class awareness mechanism to reserve more parameter space for incremental learning, and an innovative compatibility-inspired distillation scheme to make our model take full advantage of the" + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.76, + 0.106 + ], + "angle": 0, + "content": "knowledge learned by the old model." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.107, + 0.894, + 0.183 + ], + "angle": 0, + "content": "- We demonstrate the proposed method achieve a better balance between stability and plasticity than state-of-the-art methods via extensive experiments on two famous public histopathological datasets, MoNuSAC [33] and CoNSeP [14]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.197, + 0.642, + 0.212 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.222, + 0.695, + 0.238 + ], + "angle": 0, + "content": "2.1. Nuclei Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.895, + 0.427 + ], + "angle": 0, + "content": "There have been some preliminary works for nuclei segmentation based on traditional techniques and deep learning methods. Traditional techniques based on background subtraction and color threshold [27, 29] fail to generalize to complex scenarios such as overlap and occlusion in histopathology images. With the development of CNN, deep networks have been widely used in nuclei segmentation [31, 32, 34, 42], significantly improving the segmentation performance in the supervised setting. However, most of these networks are not incrementally designed and tend to forget previously learned classes when learning new types of cell nuclei continually." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.436, + 0.753, + 0.453 + ], + "angle": 0, + "content": "2.2. Class Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.702 + ], + "angle": 0, + "content": "Class incremental learning (CIL) aims to address the problem of catastrophic forgetting when learning knowledge for new classes. Existing CIL techniques can be summarized into regularization-based, replay-based, and architecture-based approaches. Regularization-based approaches utilize consistency constraints between new and old models to prevent significant changes to the knowledge associated with previously learned classes. The constraints can be applied on features [10, 12, 18], the output logits [4, 11, 21], the weights [1, 2, 19], or the gradients [6, 15]. Architecture-based approaches [16, 38, 44] dynamically grow the network to extend model capacity for new tasks. To better retain knowledge of old classes, replay-based approaches store and re-use a subset of previous training data, including raw images [3, 22, 45], features [17, 43] or generated data [7, 28]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.86, + 0.728 + ], + "angle": 0, + "content": "2.3. Class Incremental Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Recently, several works have extended and combined existing incremental learning methods to semantic segmentation. MiB [4] proposes a novel unbiased function to model background shift. PLOP [13] adopts pseudo label to solve background shift and retain spatial dependencies by local pooling operation. CoNuSeg [35] maintains the relationships between the prototypes of old classes to preserve the semantic information of old classes. EWF [36] propose a weight fusion strategy to fuse parameters from new and old models. SSUL-M [5] and MicroSeg [39] further propose pre-learning future classes to prepare for the future." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11409" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.167, + 0.089, + 0.805, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.359, + 0.895, + 0.391 + ], + "angle": 0, + "content": "Figure 2. The overall framework. The old \\((t - 1)\\) and new models \\((t)\\) consist of the same feature extractor \\(F\\) and segmentation head \\(H\\). During training, we freeze the old model and update the new model by minimizing the weighted sum of \\(\\mathcal{L}_{ce}, \\mathcal{L}_{pod}, \\mathcal{L}_{bkd}\\) and \\(\\mathcal{L}_{fkd}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.412, + 0.17, + 0.428 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.437, + 0.281, + 0.451 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.474, + 0.688 + ], + "angle": 0, + "content": "Class incremental semantic segmentation involves conducting semantic segmentation in a series of steps, with the underlying assumption that there are a total of \\(T\\) steps. In step \\(t\\), we have training set \\(D_{t} = \\{(x,y)\\}\\) and label set \\(\\mathcal{C}_t\\), where \\(x\\) is an RGB image \\(\\in \\mathbb{R}^{C\\times H\\times W}\\) and \\(y\\in \\mathcal{C}_t\\) is the corresponding annotation. The label set \\(\\mathcal{C}_t\\) only contains newly added classes at step \\(t\\), while previous learned classes \\(\\mathcal{C}_0\\cup \\mathcal{C}_1\\cup \\ldots \\cup \\mathcal{C}_{t - 1}\\) and future classes \\(\\mathcal{C}_{t + 1:T}\\) are considered as background, which can lead to catastrophic forgetting of the previously learned classes. Given a dataset \\(\\mathcal{D}_t\\), our goal is to achieve a model \\(M\\) with parameter \\(\\theta_t\\) that can perform well on all seen classes \\(\\mathcal{C}_{0:t}\\). Without loss of generality, \\(M\\) consists of a feature extractor \\(F\\) and a segmentation head \\(H\\), which makes \\(M = F\\circ H\\), where \\(\\circ\\) denotes function composition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.283, + 0.712 + ], + "angle": 0, + "content": "3.2. Framework Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The proposed incremental semantic segmentation framework, depicted in Figure 2, includes an old and new model. Under the incremental setting, both old and future classes are treated as background. To correct pixels of old classes, we adopt the pseudo-labeling strategy to assign them pseudo-labels. For pixels of potential future classes, we propose a new future-class awareness mechanism (detailed in Section. 3.3) to assign them unknown labels. At the feature level, we apply multi-scale local distillation with Local POD (described in Section. 3.5) between the corresponding layers of the two models to avoid a large feature discrepancy. At the output level, we design an innovative" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.895, + 0.506 + ], + "angle": 0, + "content": "compatibility-inspired distillation (depicted in Section. 3.4) between the model's predictions to achieve better stability and plasticity. After training, we fuse the parameters from the two models by using the Endpoints Weight Fusion strategy (EWF) [36]. Specific details about EWF can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.513, + 0.719, + 0.528 + ], + "angle": 0, + "content": "3.3. Future-class Awareness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Our future-class awareness mechanism corrects the background pixels that are considered potential future classes, i.e., pixels that are visually similar to a new or old class. We propose to measure the similarity \\( S \\) by utilizing the classcentroids \\( \\mathcal{V} \\) in the representation space of the old model. Subsequently, we assign unknown labels to these pixels for joint learning with both new and old classes. This approach enhances the representation capability of learned features and better prepares the model for the future." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.895, + 0.78 + ], + "angle": 0, + "content": "Image-wise Centroids Aggregation. Class-centroids (prototypes) are representatives of each class in the representation space and serve as an effective tool to measure similarities between classes [30]. Given an image as input, we first generate pseudo-labels \\(\\hat{y}(i,c)\\) for old classes in the background using predictions \\(O^{t-1}\\) of the old model and the ground-truth label \\(y(i,c)\\) at step \\(t\\):" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.788, + 0.892, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\hat {y} (i, c) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} y (i, c) = 1 \\\\ 1 & \\text {i f} y (i, c) = 0 \\text {a n d} c = \\operatorname {a r g m a x} O ^ {t - 1} (i, c) \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.895, + 0.903 + ], + "angle": 0, + "content": "This strategy can effectively re-assign labels for old classes in the background but fails to separate potential future classes hidden in the background. Next, we generate class-aware mask \\(\\mathcal{M}_c\\) for class \\(c\\) under the guidance of pseudo" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11410" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.089, + 0.817, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.346, + 0.895, + 0.377 + ], + "angle": 0, + "content": "Figure 3. Illustration of future-class awareness. Centroids representing both old and new categories are aggregated in representation space, then a class-aware matrix \\( S \\) is computed between all centroids and background features to aware future classes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.401, + 0.166, + 0.417 + ], + "angle": 0, + "content": "label \\(\\hat{y} (i,c)\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.422, + 0.47, + 0.463 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {c} (i) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\hat {y} (i, c) = 1 \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.467, + 0.47, + 0.512 + ], + "angle": 0, + "content": "Then, for a certain class \\(k\\), we average the deepest input feature \\(\\mathcal{F}_d^{t - 1}\\) with the class-aware mask to obtain classcentroid \\(\\nu_{k}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.516, + 0.47, + 0.574 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {V} _ {k} = M A P \\left(\\mathcal {M} _ {k}, \\mathcal {F} _ {d} ^ {t - 1}\\right) \\\\ = \\frac {\\sum_ {i} \\mathcal {F} _ {d} ^ {t - 1} (i) \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]}{\\sum_ {i} \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]} \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.577, + 0.469, + 0.636 + ], + "angle": 0, + "content": "where \\( MAP \\) represents the masked average pooling operation. After that, we obtain a centroid set \\( \\mathcal{V} = \\{\\mathcal{V}_1,\\dots,\\mathcal{V}_{\\mathcal{C}_t}\\} \\) containing old and new class-centeroids, which will be utilized to detect future classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Cross Image-wise Centroids Aggregation. Different cell nuclei are typically distributed across different images, which suggests that potential future classes may not coexist in the same image as their similar cell nuclei. Therefore, aggregating class centroids in an image-wise manner may not include centroids of classes that are similar to future classes. To address this issue, we propose to update class centroids using a running average approach. The final class centroids are computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.777, + 0.47, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {k} = \\frac {1}{N} \\left(\\mathcal {V} _ {k} ^ {\\prime} \\cdot N _ {k} ^ {\\prime} + \\sum_ {i} \\mathcal {F} _ {d} ^ {t - 1} (i) \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]\\right) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.816, + 0.469, + 0.847 + ], + "angle": 0, + "content": "\\[\nN = N _ {k} ^ {\\prime} + \\sum_ {i} \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right] \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.854, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{V}_k^{\\prime}\\) and \\(N_{k}^{\\prime}\\) represent the accumulated result and total pixel number of class k from the initial update to the last update, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.507 + ], + "angle": 0, + "content": "Awareness & Separation. To aware future classes, we first assemble the background features \\(\\mathcal{F}_{bg} \\in \\mathbb{R}^{C \\times N_b}\\) via the masked multiplication on the deepest feature \\(\\mathcal{F}_d^{t-1}\\) with the background mask \\(\\mathcal{M}_b\\). We then calculate a pixel-to-centroid affinity matrix \\(\\mathcal{A}\\) between pixels of the reshaped background feature \\(\\mathcal{F}_{bg}\\) and class-centroids \\(\\mathcal{V}\\) via a matrix multiplication operation \\(Mat\\):" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.515, + 0.892, + 0.534 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} = M a t \\left(\\operatorname {N o r m} \\left(\\mathcal {F} _ {b g}\\right) ^ {T}, \\operatorname {N o r m} (\\mathcal {V})\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.648 + ], + "angle": 0, + "content": "where \\( Norm \\) indicates \\( l2 \\)-normalization. The size of \\( \\mathcal{A} \\) is \\( \\mathbb{R}^{N \\times P} \\) and \\( P = |\\mathcal{V}| \\) is the cardinality of class-centroid set. Through the affinity matrix, we construct a semantic graph for each pixel-centroid pair, where each vertex represents the semantic structure and the edge represents the similarity relationship, thus a fine-grained similarity can be measured by utilizing the information in the representation space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.739 + ], + "angle": 0, + "content": "We obtain the final class-aware matrix \\(\\mathcal{S}\\) by taking the average or maximum across the second dimension of affinity matrix \\(\\mathcal{A}\\). To effectively pre-learn knowledge of future classes, only background pixels that are sufficiently similar are re-assigned unknown labels. The final corrected ground truth \\(y(i,c)\\) of pixel \\(i\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.747, + 0.892, + 0.789 + ], + "angle": 0, + "content": "\\[\ny (i, c) = \\left\\{ \\begin{array}{l l} u & \\text {i f} \\mathcal {M} _ {b} (i) = 1 \\text {a n d} \\mathcal {S} (i) < \\tau_ {u} \\\\ \\hat {y} (i, c) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( u \\) represents the unknown label assigned to future classes, and \\( \\tau_{u} \\) is a threshold controlling the confidence of future classes. In other words, for background pixels filtered by Equation 1, we re-label them with an unknown label \\( u \\) on the guidance of the class-aware matrix \\( S \\). Otherwise, we directly copy their pseudo-labels (for old classes) or true labels (for new classes)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11411" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.38, + 0.108 + ], + "angle": 0, + "content": "3.4. Compatibility-inspired Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.25 + ], + "angle": 0, + "content": "Considering that the previous model only produces predictions \\( O^{t-1} \\) for \\( |\\mathcal{C}_{0:t-1}| \\) classes, while the new model can produce predictions \\( O^t \\) for \\( |\\mathcal{C}_{0:t}|(|\\mathcal{C}_{0:t}| > |\\mathcal{C}_{0:t-1}|) \\) classes, directly aligning the outputs between the two models is contradictory. Treating the model's predictions as interfaces of software, we introduce new interfaces into the old model to be compatible with the new model (i.e., expanding \\( O^{t-1} \\) to match \\( O^t \\), and padding the additional channels with 0). The expanded prediction \\( O^{t-1} \\) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.256, + 0.47, + 0.297 + ], + "angle": 0, + "content": "\\[\nO ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} _ {t} \\\\ O ^ {t - 1} (i, c) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.469, + 0.377 + ], + "angle": 0, + "content": "Then we enforce constraints to pixels of new class set \\(\\mathcal{U}_n\\) and background set \\(\\mathcal{U}_b\\) from the view of backward compatibility and forward compatibility respectively. It is worth noting that the background here includes old classes, future classes, and true background pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.47, + 0.589 + ], + "angle": 0, + "content": "Forward compatibility. For pixels \\( i \\) from the new class set, we transfer the old model's background prediction \\( O^{t - 1}(i,b) \\) to the prediction corresponding to the ground-truth to address background shift [4]. Next, with the future class-aware mechanism, the old model has pre-learned knowledge about the new classes (which are future classes to the old model). Thus we also add the old model's future class prediction \\( O^{t - 1}(i,u) \\) to the prediction corresponding to the ground truth, thereby naturally inheriting the knowledge that the old model has prepared for future learning (forward compatibility). After that, we reset the predictions of background and future classes to 0 while keeping other predictions unchanged. The corrected prediction of the old model is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.593, + 0.469, + 0.661 + ], + "angle": 0, + "content": "\\[\nO ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} O ^ {t - 1} (i, u) + O ^ {t - 1} (i, b) & \\text {i f} c \\in \\mathcal {C} _ {t} \\\\ O ^ {t - 1} (i, c) & \\text {i f} c \\in \\mathcal {C} _ {0: t - 1} \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.662, + 0.466, + 0.677 + ], + "angle": 0, + "content": "where \\(i\\in \\mathcal{U}_n\\) and \\(u\\) indicates the future class at step \\(t - 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.469, + 0.767 + ], + "angle": 0, + "content": "Backward compatibility. For pixels \\(i \\in \\mathcal{U}_b\\) from the background set, similar to regular knowledge distillation, we only need to align the outputs between the two models to ensure that the new model does not deviate significantly from the old model during updates. The complete compatibility-inspired distillation loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.775, + 0.469, + 0.792 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c p d} = \\alpha_ {n} \\cdot \\mathcal {L} _ {f k d} (x, \\mathcal {U} _ {n}) + \\alpha_ {b} \\cdot \\mathcal {L} _ {b k d} (x, \\mathcal {U} _ {b}) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.798, + 0.469, + 0.844 + ], + "angle": 0, + "content": "where \\(\\alpha_{n}\\) and \\(\\alpha_{b}\\) control the contribution of the new classes set \\(\\mathcal{U}_n\\) and background set \\(\\mathcal{U}_b\\), which are discussed in Section 4.3; \\(\\mathcal{L}(x,\\mathcal{U})\\) is a common knowledge distillation loss:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.862, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (x, \\mathcal {U}) = - \\frac {1}{| \\mathcal {U} |} \\sum_ {i \\in \\mathcal {U}} \\sum_ {c} ^ {\\mathcal {C} _ {0: t}} O _ {x} ^ {t - 1} (i, c) \\log O _ {x} ^ {t} (i, c) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "We emphasize that our distillation approach supplements and corrects the contents extended in the interfaces of the old model, thus addressing alignment conflict and background shift, as well as facilitating the new model to effectively leverage the knowledge learned by the old model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.179, + 0.736, + 0.193 + ], + "angle": 0, + "content": "3.5. Feature-based Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.262 + ], + "angle": 0, + "content": "To prevent catastrophic forgetting in feature space, we also utilize multi-scale local distillation with Local POD [13] to retain knowledge by preserving multi-scale spatial information. The Local POD loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.273, + 0.891, + 0.314 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p o d} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} | \\phi (\\mathcal {F} _ {l} ^ {t}) - \\phi (\\mathcal {F} _ {l} ^ {t - 1}) | ^ {2} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.891, + 0.356 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_l^t\\) is the feature of the \\(l\\)-th layer and \\(\\phi(.)\\) is a function that captures multi-scale spatial statistics." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.358, + 0.891, + 0.373 + ], + "angle": 0, + "content": "Finally, we train the model with the total loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.389, + 0.891, + 0.406 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a l l} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {c p d} + \\lambda \\cdot \\mathcal {L} _ {p o d} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.444 + ], + "angle": 0, + "content": "where \\(\\lambda\\) denotes the weight of LocalPOD, which is set to 0.0001 in our experiments." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.46, + 0.625, + 0.476 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.485, + 0.807, + 0.5 + ], + "angle": 0, + "content": "4.1. Datasets, Protocols, and Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Datasets. We conduct all the experiments on two publicly available nuclei datasets, MoNuSAC and CoNSeP. MoNuSAC contains H&E stained tissue images of four organs, along with annotations for multiple cell types, including epithelial (Epith), lymphocyte (Lymph), macrophage (Macro), and neutrophil (Neutr). We randomly split \\(20\\%\\) of the training set for validation. Besides, all images in the training, testing, and validation sets have been uniformly cropped to a resolution of \\(320 \\times 320\\). Finally, the MoNuSAC contains 1177 training images, 295 validation images and 651 test images. CoNSeP contains H&E stained image tiles with annotations of 7 cell types, where we divide them into 3 classes: epithelial, spindle-shaped and others. With the same pre-processing, we obtain a training set with 345, a validation set with 87, and a test set with 224 images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Protocols. There are two common settings in ISS benchmarks: disjoint and overlapped. In the disjoint setting, \\( D_{t} \\) only contains images of new classes and old classes. In the overlapped setting, \\( D_{t} \\) can contain images of all classes, including old classes, new classes, and future classes. Regarding of setting, only new classes are annotated, while others are treated as background. The overlapped setting is considered more realistic since it allows future classes to appear in the current dataset, reflecting real-world scenarios more accurately. In this work, we only focus on the overlapped setting." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11412" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.09, + 0.89, + 0.316 + ], + "angle": 0, + "content": "
Method1-1 (4 tasks)2-1 (3 tasks)2-2 (2 tasks)3-1 (2 tasks)
OldNewMeanOldNewMeanOldNewMeanOldNewMean
ILT [25]33.4653.9148.8050.0073.3061.6546.0068.1857.0962.1173.2764.90
MiB [4]59.9564.5763.4152.5174.6763.5957.3376.8767.1063.8575.3866.73
SDR [26]55.5067.3064.3553.4774.3763.9257.0878.0367.5665.7077.3168.60
PLOP [13]60.1465.6064.2356.8575.8766.3656.7475.8866.3166.1677.4368.97
REMARKER [30]62.4166.4965.4756.5775.8966.2359.8976.0367.9668.2277.1870.46
CoNuSeg [35]65.3767.9267.2857.8576.0966.9761.7077.1169.4066.4777.3369.18
IDEC [41]62.1669.4167.5958.6376.0367.3363.2275.4169.3167.3677.1269.80
EWF [36]64.5767.8967.0660.2776.2368.2665.9075.9470.9269.0677.6271.20
Ours68.1169.8669.4463.7976.5370.1665.4377.2171.3270.4678.0372.36
Joint72.0175.2974.4770.3678.5874.4770.3678.5874.4772.6579.9374.47
" + }, + { + "type": "table_caption", + "bbox": [ + 0.2, + 0.325, + 0.768, + 0.34 + ], + "angle": 0, + "content": "Table 1. Incremental semantic segmentation results (mDice) on MoNuSAC. The best is in bold." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.354, + 0.526, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.353, + 0.889, + 0.627 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.638, + 0.792, + 0.653 + ], + "angle": 0, + "content": "Figure 4. Visualization of the proposed method and EWF at different incremental steps on two datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Evaluation. The ISS benchmark configurations are represented as \\( n - m \\) where \\( n \\) and \\( m \\) correspond to the number of new classes to be learned during the initial step and each subsequent step, respectively. We set several ISS settings for each dataset, e.g., on MoNuSAC 3-1, 2-1, 2-2, and 1-1 respectively include learning 3 classes then 1 class (2 steps), 2 classes then 1 class (3 steps), 2 classes then 2 classes (2 steps) and 1 class at initial step then 1 class at subsequent step (4 steps). We emphasized that the 1-1 setting is the most challenging task due to its small amount of data and high number of steps. Similarly, on CoNSeP 1-1 (3 steps) and 2-1 (2 steps). After training all steps, we use mean Dice (mDice) to evaluate the performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.876, + 0.469, + 0.892 + ], + "angle": 0, + "content": "Implementation Details. We use the ResNet-101 pre" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.892, + 0.769 + ], + "angle": 0, + "content": "trained on ImageNet as the feature encoder for all experiments. During training, the initial learning rate is set to 0.05 for the first step and 0.01 for subsequent incremental steps. The number of epochs for all steps is set to 100. We employ an SGD optimizer with a batch size of 12, distributed across three 2080Ti GPUs, to train the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.893, + 0.891 + ], + "angle": 0, + "content": "Comparison Results. To demonstrate the advantages of our method, we employ the state-of-the-art approach (EWF) as our baseline for comparison. Table 1 displays our approach's comparative results against some strong ISS methods on the MoNuSAC dataset. Evidently, the performance of ILT is the worst in all incremental setups, since it lacks the capacity to address background shift. Integrating background correction methods, such as MiB and" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11413" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "PLOP, leads to marked improvements for both old and new classes in all settings. By further introducing innovative distillation mechanisms into the background correction method, approaches like REMINDER, CoNuSeg, and IDEC have achieved additional performance gains. EWF receives higher performance after applying the Endpoints Weight Fusion strategy to PLOP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.474, + 0.381 + ], + "angle": 0, + "content": "Despite their great progress, our approach surpasses them by a large margin on all settings. In particular, on the most challenging setup (1-1), our method outperforms the EWF by \\(3.54\\%\\) in old classes and IDEC by \\(0.45\\%\\) in new classes. While the gains in new classes are not that large, we believe that the performance is already quite better compared to that of old classes. As presented in Figure 5, our model achieves all the highest mDice scores from incremental step 1 to step 3. This also indicates that the stability and plasticity of our model are superior to those of other strong models. Experiments in Table 2 further demonstrate the strong generalization ability of our method." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.392, + 0.47, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.566, + 0.444, + 0.58 + ], + "angle": 0, + "content": "Figure 5. Results of mDice at different incremental steps." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.611, + 0.477, + 0.789 + ], + "angle": 0, + "content": "
Method1-1 (3 tasks)2-1 (2 tasks)
OldNewMeanOldNewMean
ILT [25]35.2363.1944.5540.8263.6148.41
MiB [4]67.0267.0667.0470.9961.9667.98
SDR [26]67.0567.2967.2170.3762.9267.88
PLOP [13]67.0667.7867.5472.5063.1569.38
CoNuSeg [35]67.5268.5968.2372.8063.4169.67
IDEC [41]67.2068.2867.9272.1662.7869.03
EWF [36]67.1870.0369.0874.1663.0070.44
Ours66.6470.8469.4474.2964.6571.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Table 2. Incremental semantic segmentation results (mDice) on the CoNSeq dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Visual Results. We visualize the segmentation results of our method and EWF on two datasets to highlight the comparative effectiveness. As shown in Figure 4, our method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.214 + ], + "angle": 0, + "content": "yields segmentation results that are more complete and accurate than those produced by EWF. For example, for the second image (rows 3-4, left), both methods gradually forget class epithelial (the red ones) and macrophage (the green ones) from step 0 to step 2. Nevertheless, our method still yields satisfactory segmentation results after step 3. Similar results can be observed in other images. Figure 6 explicitly presents the Dice score for each class at every step." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.223, + 0.891, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.389, + 0.892, + 0.419 + ], + "angle": 0, + "content": "Figure 6. Values of Dice metric for each class at different incremental steps on MoNuSAC 1-1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.442, + 0.655, + 0.459 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.892, + 0.676 + ], + "angle": 0, + "content": "We verify the effectiveness of the proposed method using 1-1 and 3-1 setups on MoNuSAC. From Table 3, we can find that the performance of PLOP + EWF surpasses that of PLOP. Only adding future-class awareness (FCA) can further boost the performance of EWF across different setups. After applying compatibility-inspired distillation (CID), we obtain the highest performance on MoNuSAC. In particular, the performance of PLOP + EWF + FCA + CID outperforms that of PLOP + EWF in 1-1 settings, with a great improvement of \\(3.54\\%\\) in old classes and \\(1.97\\%\\) in new classes. These results effectively demonstrate that both proposed modules can effectively improve the plasticity and stability of the model, thereby improving the overall performance." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.685, + 0.89, + 0.798 + ], + "angle": 0, + "content": "
Method1-1 (4 tasks)3-1 (2 tasks)
OldNewMeanOldNewMean
PLOP60.1465.6064.2366.1677.4368.97
+ EWF64.5767.8967.0669.0677.6271.20
+FCA67.4269.0068.6070.1177.9372.07
+CID68.1169.8669.4270.4678.0372.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.807, + 0.892, + 0.821 + ], + "angle": 0, + "content": "Table 3. Ablation study results (mDice) on the MoNuSAC dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.669, + 0.864 + ], + "angle": 0, + "content": "4.3. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Future-class Awareness. To better understand how prelearning of future classes enhances the results, we visual-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11414" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "ize t-SNE distribution of features generated from the baseline and baseline \\(+\\) FCA. As shown in Figure 7, the base" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.135, + 0.468, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.285, + 0.47, + 0.315 + ], + "angle": 0, + "content": "Figure 7. T-SNE visualization of features learned by Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.471, + 0.409 + ], + "angle": 0, + "content": "line tends to generate more ambiguous features while the baseline \\(+\\mathrm{FCA}\\) is able to learn more discriminative features. These robust features then help the model to resist catastrophic forgetting better. Similar conclusions can be drawn from the feature map (Figure 8). The baseline model" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.42, + 0.47, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.629, + 0.47, + 0.657 + ], + "angle": 0, + "content": "Figure 8. Feature maps of the Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.468, + 0.78 + ], + "angle": 0, + "content": "exhibits a lower response to target features and is prone to generating erroneous high responses in the background, whereas the baseline with FCA generates more accurate and higher responses to target features. This phenomenon further shows that training with FCA can enhance the representation power to alleviate knowledge forgetting and reserve more parameter space to be updated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Compatibility-inspired Distillation. As shown in Table 4, slightly increasing both \\(\\alpha_{n}\\) and \\(\\alpha_{b}\\) to 1 can improve the performance of both new and old classes. However, a large value of \\(\\alpha_{n}\\), e.g., \\(\\alpha_{n} = 5\\) leads the model to focus excessively on new classes, compromising the performance of old classes and thus negatively affecting overall performance. Similarly, when we set \\(\\alpha_{b}\\) a high value 3, the model tends to overly remember old classes and overlook the new classes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "In our experiments, we achieve the best performance when \\(\\alpha_{n}\\) and \\(\\alpha_{b}\\) are set to 3 and 1, respectively. For additional ablation studies and detailed analytical experiments, please refer to the supplementary materials." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.167, + 0.888, + 0.335 + ], + "angle": 0, + "content": "
αnαbBackgroundOldNewAll
0094.5867.4269.0073.80
1194.5367.7169.3174.03
3194.4368.1169.8674.42
5194.5165.9169.1873.59
3094.7067.6169.2574.01
3294.7468.0869.4174.21
3394.5368.1868.3473.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.546, + 0.346, + 0.846, + 0.361 + ], + "angle": 0, + "content": "Table 4. Effect of the weighted factors \\( {\\alpha }_{n} \\) and \\( {\\alpha }_{b} \\) ." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.396, + 0.614, + 0.411 + ], + "angle": 0, + "content": "5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.558 + ], + "angle": 0, + "content": "We develop our method based on the attributes of histopathological images, where future classes in the dataset exhibit visual similarities to the learned classes. Therefore, our approach may not perform optimally in datasets where future classes significantly differ from the learned classes, which necessitates further research. Nevertheless, considering the vast diversity of cancer cell types, our method shows promise in enhancing computer-aided diagnosis systems with more robust incremental updating capabilities." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.619, + 0.59 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.768 + ], + "angle": 0, + "content": "In this work, we present a novel method for incremental semantic segmentation from histopathological images, aiming to solve catastrophic forgetting without storing samples of previous data. First, we propose a new future-class awareness approach that detects future classes in an unsupervised way. Second, drawing inspiration from software engineering, we introduce an innovative compatibility-inspired knowledge distillation to make the new model take full advantage of the knowledge learned by the old model. Finally, comparative experiments and ablation studies clearly demonstrate the effectiveness of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.784, + 0.659, + 0.801 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was supported partly by National Natural Science Foundation of China (No. 62273241), Natural Science Foundation of Guangdong Province, China (No. 2024A1515011946), and the Theme-based Research Scheme from Hong Kong Research Grants Council (project no. T45-401/22-N)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11415" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. Expert gate: Lifelong learning with a network of experts. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3366-3375, 2017. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 3082-3092, 2023. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11417" + } + ] +] \ No newline at end of file diff --git a/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/9fa3bbf9-7154-47a0-a450-b1f92451140e_origin.pdf b/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/9fa3bbf9-7154-47a0-a450-b1f92451140e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..43de8ceb6476590bf8176baa1f70888ef9c540b4 --- /dev/null +++ b/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/9fa3bbf9-7154-47a0-a450-b1f92451140e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f99caf6b34c93e9ee5aa0e6be494af417508e96e8e0a5bcd4093e8815fa3ee3b +size 4650506 diff --git a/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/full.md b/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d40971bd0dbab2d84f3879b4562df6baa9c0cb5d --- /dev/null +++ b/2024/Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation/full.md @@ -0,0 +1,319 @@ +# Incremental Nuclei Segmentation from Histopathological Images via Future-class Awareness and Compatibility-inspired Distillation + +Huyong Wang $^{1}$ , Huisi Wu $^{1*}$ , Jing Qin $^{2}$ + +1 College of Computer Science and Software Engineering, Shenzhen University + +2 Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University + +2210273011@email.szu.edu.cn, hswu@szu.edu.cn, harry.qin@polyu.edu.hk + +# Abstract + +We present a novel semantic segmentation approach for incremental nuclei segmentation from histopathological images, which is a very challenging task as we have to incrementally optimize existing models to make them perform well in both old and new classes without using training samples of old classes. Yet, it is an indispensable component of computer-aided diagnosis systems. The proposed approach has two key techniques. First, we propose a new future-class awareness mechanism by separating some potential regions for future classes from background based on their similarities to both old and new classes in the representation space. With this mechanism, we can not only reserve more parameter space for future updates but also enhance the representation capability of learned features. We further propose an innovative compatibility-inspired distillation scheme to make our model take full advantage of the knowledge learned by the old model. We conducted extensive experiments on two famous histopathological datasets and the results demonstrate the proposed approach achieves much better performance than state-of-the-art approaches. The code is available at https://github.com/why19991/InSeg. + +# 1. Introduction + +Cellular nuclei segmentation aims to accurately delineate various cell nuclei from histopathological images, which is of great importance for cancer diagnosis, treatment, and prognosis prediction [37]. Recent years, deep learning models have achieved remarkable performance in this task [8, 20, 32, 34, 40], significantly promoting the development of computer-aided diagnosis systems. Despite these progresses, most existing models are incapable of maintaining the performance on previously learned classes when it is required to incrementally learn new classes, which is common in clinical practice [35]. This phenomenon is called + +![](images/367fcdbd33b9b53ca09cd66f39e070d6167bfcd3358e69feeaf3a548e50a06b6.jpg) +rrnnnne + +![](images/3ab489b0a909d270f5748d54a042fa219263715bf97c99f828947499a7d50c9b.jpg) +Figure 1. Pathological images typically contain numerous objects from different categories that have very similar appearances. For instance, epithelia (represented by red objects) and lymphocytes (represented by yellow objects) look quite alike. However, in the 1-1 setting at step 0, epithelia are labeled as new classes, whereas lymphocytes are seen as background. Our approach aims to mine such future classes in an unsupervised way and learn them in advance. + +![](images/138ad2722ec3d01a047a5ac6244483978eb1a7f5d1f7e681669ec24fbe0f2a02.jpg) + +![](images/95b7b2a62dfba0a7a1eb0421f891f6e7bd8709f431181215fec0411c5769f25c.jpg) + +catastrophic forgetting [24], which is a long-standing challenge and prohibits these models from being deployed in clinical settings. A common solution is to rebuild the training dataset containing annotations of all classes and retrain the model. However, the cost of collecting histopathological images with pixel-level annotations for segmentation is extremely laborious and time-consuming. Besides, access to previous data is usually limited by patient privacy. In this regard, we often have to incrementally optimize existing models to make them perform well in both old classes and new classes without using training samples of old classes. + +Incremental learning is proposed to solve the problem of catastrophic forgetting, and semantic segmentation based on incremental learning is known as incremental semantic segmentation (ISS). In scenarios where previous data can be reused, some studies [22, 45] select samples to help the model review and reinforce knowledge, greatly alleviating catastrophic forgetting. However, when privacy or storage issues make old data unavailable, which is common + +in clinical scenarios, most studies turn to employ distillation techniques [4, 13, 23, 25, 26, 30, 36] to constrain the model updating. These methods, while keeping the performance of old classes (stability) well, limit the model's capability in learning new classes (plasticity). In order to improve both stability and plasticity, a few studies [5, 39] propose to learn future classes in advance to prepare for learning new classes. Specifically, SSUL-M [5] applies a salient object detector to detect potential future classes while MicroSeg [39] utilizes mask proposals generated by Mask2Former [9] to detect future classes. Unfortunately, both the salient detector and mask proposals still heavily depend on a number of annotated data, which is, as mentioned, difficult to acquire in clinical practice due to privacy and cost. To the end, it is necessary to aware future classes in an unsupervised manner on the given data. + +In this work, we present a novel ISS method for incremental nuclei segmentation from histopathological images, which has two key components: a new future-class awareness mechanism and an innovative compatibility-inspired distillation scheme. Histopathological images often contain numerous objects belonging to different categories with great similarity in appearance. As illustrated in Figure 1, some nuclei are learned as new classes or old classes, while others (future classes) are treated as background. Thus, we propose to separate some potential regions of future classes from background by calculating their similarities to both old and new classes in the representation space, and then we train the new model with both new and old classes, as well as with the separated regions. To the end, we cannot only reserve more parameter space for future updates but also enhance the representation capability of learned features. Furthermore, we design a compatibility-inspired distillation scheme to further improve both stability and plasticity. As the number of targeting classes of the updated model is always more than that of the old model, directly aligning them poses conflicts and background shifts [4]. In this regard, we propose to expand the old model's prediction range to match that of the new model by harnessing the representation space of the future classes. This scheme not only resolves alignment conflicts and background shifts but also enables the new model to effectively utilize the knowledge of the old model. Our contributions can be summarized as follows. + +- We propose a novel ISS method for incremental nuclei segmentation from histopathological images, which is able to incrementally optimize existing models to make them perform well in both old and new classes without using training samples of old classes. +- We propose a new future-class awareness mechanism to reserve more parameter space for incremental learning, and an innovative compatibility-inspired distillation scheme to make our model take full advantage of the + +knowledge learned by the old model. + +- We demonstrate the proposed method achieve a better balance between stability and plasticity than state-of-the-art methods via extensive experiments on two famous public histopathological datasets, MoNuSAC [33] and CoNSeP [14]. + +# 2. Related Work + +# 2.1. Nuclei Segmentation + +There have been some preliminary works for nuclei segmentation based on traditional techniques and deep learning methods. Traditional techniques based on background subtraction and color threshold [27, 29] fail to generalize to complex scenarios such as overlap and occlusion in histopathology images. With the development of CNN, deep networks have been widely used in nuclei segmentation [31, 32, 34, 42], significantly improving the segmentation performance in the supervised setting. However, most of these networks are not incrementally designed and tend to forget previously learned classes when learning new types of cell nuclei continually. + +# 2.2. Class Incremental Learning + +Class incremental learning (CIL) aims to address the problem of catastrophic forgetting when learning knowledge for new classes. Existing CIL techniques can be summarized into regularization-based, replay-based, and architecture-based approaches. Regularization-based approaches utilize consistency constraints between new and old models to prevent significant changes to the knowledge associated with previously learned classes. The constraints can be applied on features [10, 12, 18], the output logits [4, 11, 21], the weights [1, 2, 19], or the gradients [6, 15]. Architecture-based approaches [16, 38, 44] dynamically grow the network to extend model capacity for new tasks. To better retain knowledge of old classes, replay-based approaches store and re-use a subset of previous training data, including raw images [3, 22, 45], features [17, 43] or generated data [7, 28]. + +# 2.3. Class Incremental Semantic Segmentation + +Recently, several works have extended and combined existing incremental learning methods to semantic segmentation. MiB [4] proposes a novel unbiased function to model background shift. PLOP [13] adopts pseudo label to solve background shift and retain spatial dependencies by local pooling operation. CoNuSeg [35] maintains the relationships between the prototypes of old classes to preserve the semantic information of old classes. EWF [36] propose a weight fusion strategy to fuse parameters from new and old models. SSUL-M [5] and MicroSeg [39] further propose pre-learning future classes to prepare for the future. + +![](images/ce59960fb7ec6997c6d9e0bdc295795b05ad7c900f6c7a16eaf983b22124b600.jpg) +Figure 2. The overall framework. The old $(t - 1)$ and new models $(t)$ consist of the same feature extractor $F$ and segmentation head $H$ . During training, we freeze the old model and update the new model by minimizing the weighted sum of $\mathcal{L}_{ce}, \mathcal{L}_{pod}, \mathcal{L}_{bkd}$ and $\mathcal{L}_{fkd}$ . + +# 3. Method + +# 3.1. Problem Formulation + +Class incremental semantic segmentation involves conducting semantic segmentation in a series of steps, with the underlying assumption that there are a total of $T$ steps. In step $t$ , we have training set $D_{t} = \{(x,y)\}$ and label set $\mathcal{C}_t$ , where $x$ is an RGB image $\in \mathbb{R}^{C\times H\times W}$ and $y\in \mathcal{C}_t$ is the corresponding annotation. The label set $\mathcal{C}_t$ only contains newly added classes at step $t$ , while previous learned classes $\mathcal{C}_0\cup \mathcal{C}_1\cup \ldots \cup \mathcal{C}_{t - 1}$ and future classes $\mathcal{C}_{t + 1:T}$ are considered as background, which can lead to catastrophic forgetting of the previously learned classes. Given a dataset $\mathcal{D}_t$ , our goal is to achieve a model $M$ with parameter $\theta_t$ that can perform well on all seen classes $\mathcal{C}_{0:t}$ . Without loss of generality, $M$ consists of a feature extractor $F$ and a segmentation head $H$ , which makes $M = F\circ H$ , where $\circ$ denotes function composition. + +# 3.2. Framework Overview + +The proposed incremental semantic segmentation framework, depicted in Figure 2, includes an old and new model. Under the incremental setting, both old and future classes are treated as background. To correct pixels of old classes, we adopt the pseudo-labeling strategy to assign them pseudo-labels. For pixels of potential future classes, we propose a new future-class awareness mechanism (detailed in Section. 3.3) to assign them unknown labels. At the feature level, we apply multi-scale local distillation with Local POD (described in Section. 3.5) between the corresponding layers of the two models to avoid a large feature discrepancy. At the output level, we design an innovative + +compatibility-inspired distillation (depicted in Section. 3.4) between the model's predictions to achieve better stability and plasticity. After training, we fuse the parameters from the two models by using the Endpoints Weight Fusion strategy (EWF) [36]. Specific details about EWF can be found in the supplementary materials. + +# 3.3. Future-class Awareness + +Our future-class awareness mechanism corrects the background pixels that are considered potential future classes, i.e., pixels that are visually similar to a new or old class. We propose to measure the similarity $S$ by utilizing the classcentroids $\mathcal{V}$ in the representation space of the old model. Subsequently, we assign unknown labels to these pixels for joint learning with both new and old classes. This approach enhances the representation capability of learned features and better prepares the model for the future. + +Image-wise Centroids Aggregation. Class-centroids (prototypes) are representatives of each class in the representation space and serve as an effective tool to measure similarities between classes [30]. Given an image as input, we first generate pseudo-labels $\hat{y}(i,c)$ for old classes in the background using predictions $O^{t-1}$ of the old model and the ground-truth label $y(i,c)$ at step $t$ : + +$$ +\hat {y} (i, c) = \left\{ \begin{array}{l l} 1 & \text {i f} y (i, c) = 1 \\ 1 & \text {i f} y (i, c) = 0 \text {a n d} c = \operatorname {a r g m a x} O ^ {t - 1} (i, c) \end{array} \right. \tag {1} +$$ + +This strategy can effectively re-assign labels for old classes in the background but fails to separate potential future classes hidden in the background. Next, we generate class-aware mask $\mathcal{M}_c$ for class $c$ under the guidance of pseudo + +![](images/af6b31687acad4b4d2627304444167624a2e791fa23c55d441854a4b1721c967.jpg) +Figure 3. Illustration of future-class awareness. Centroids representing both old and new categories are aggregated in representation space, then a class-aware matrix $S$ is computed between all centroids and background features to aware future classes. + +label $\hat{y} (i,c)$ .. + +$$ +\mathcal {M} _ {c} (i) = \left\{ \begin{array}{l l} 1 & \text {i f} \hat {y} (i, c) = 1 \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {2} +$$ + +Then, for a certain class $k$ , we average the deepest input feature $\mathcal{F}_d^{t - 1}$ with the class-aware mask to obtain classcentroid $\nu_{k}$ : + +$$ +\begin{array}{l} \mathcal {V} _ {k} = M A P \left(\mathcal {M} _ {k}, \mathcal {F} _ {d} ^ {t - 1}\right) \\ = \frac {\sum_ {i} \mathcal {F} _ {d} ^ {t - 1} (i) \mathbb {1} \left[ \mathcal {M} _ {k} (i) = 1 \right]}{\sum_ {i} \mathbb {1} \left[ \mathcal {M} _ {k} (i) = 1 \right]} \tag {3} \\ \end{array} +$$ + +where $MAP$ represents the masked average pooling operation. After that, we obtain a centroid set $\mathcal{V} = \{\mathcal{V}_1,\dots,\mathcal{V}_{\mathcal{C}_t}\}$ containing old and new class-centeroids, which will be utilized to detect future classes. + +Cross Image-wise Centroids Aggregation. Different cell nuclei are typically distributed across different images, which suggests that potential future classes may not coexist in the same image as their similar cell nuclei. Therefore, aggregating class centroids in an image-wise manner may not include centroids of classes that are similar to future classes. To address this issue, we propose to update class centroids using a running average approach. The final class centroids are computed as follows: + +$$ +\mathcal {V} _ {k} = \frac {1}{N} \left(\mathcal {V} _ {k} ^ {\prime} \cdot N _ {k} ^ {\prime} + \sum_ {i} \mathcal {F} _ {d} ^ {t - 1} (i) \mathbb {1} \left[ \mathcal {M} _ {k} (i) = 1 \right]\right) \tag {4} +$$ + +$$ +N = N _ {k} ^ {\prime} + \sum_ {i} \mathbb {1} \left[ \mathcal {M} _ {k} (i) = 1 \right] \tag {5} +$$ + +where $\mathcal{V}_k^{\prime}$ and $N_{k}^{\prime}$ represent the accumulated result and total pixel number of class k from the initial update to the last update, respectively. + +Awareness & Separation. To aware future classes, we first assemble the background features $\mathcal{F}_{bg} \in \mathbb{R}^{C \times N_b}$ via the masked multiplication on the deepest feature $\mathcal{F}_d^{t-1}$ with the background mask $\mathcal{M}_b$ . We then calculate a pixel-to-centroid affinity matrix $\mathcal{A}$ between pixels of the reshaped background feature $\mathcal{F}_{bg}$ and class-centroids $\mathcal{V}$ via a matrix multiplication operation $Mat$ : + +$$ +\mathcal {A} = M a t \left(\operatorname {N o r m} \left(\mathcal {F} _ {b g}\right) ^ {T}, \operatorname {N o r m} (\mathcal {V})\right) \tag {6} +$$ + +where $Norm$ indicates $l2$ -normalization. The size of $\mathcal{A}$ is $\mathbb{R}^{N \times P}$ and $P = |\mathcal{V}|$ is the cardinality of class-centroid set. Through the affinity matrix, we construct a semantic graph for each pixel-centroid pair, where each vertex represents the semantic structure and the edge represents the similarity relationship, thus a fine-grained similarity can be measured by utilizing the information in the representation space. + +We obtain the final class-aware matrix $\mathcal{S}$ by taking the average or maximum across the second dimension of affinity matrix $\mathcal{A}$ . To effectively pre-learn knowledge of future classes, only background pixels that are sufficiently similar are re-assigned unknown labels. The final corrected ground truth $y(i,c)$ of pixel $i$ is defined as: + +$$ +y (i, c) = \left\{ \begin{array}{l l} u & \text {i f} \mathcal {M} _ {b} (i) = 1 \text {a n d} \mathcal {S} (i) < \tau_ {u} \\ \hat {y} (i, c) & \text {o t h e r w i s e} \end{array} \right. \tag {7} +$$ + +where $u$ represents the unknown label assigned to future classes, and $\tau_{u}$ is a threshold controlling the confidence of future classes. In other words, for background pixels filtered by Equation 1, we re-label them with an unknown label $u$ on the guidance of the class-aware matrix $S$ . Otherwise, we directly copy their pseudo-labels (for old classes) or true labels (for new classes). + +# 3.4. Compatibility-inspired Distillation + +Considering that the previous model only produces predictions $O^{t-1}$ for $|\mathcal{C}_{0:t-1}|$ classes, while the new model can produce predictions $O^t$ for $|\mathcal{C}_{0:t}|(|\mathcal{C}_{0:t}| > |\mathcal{C}_{0:t-1}|)$ classes, directly aligning the outputs between the two models is contradictory. Treating the model's predictions as interfaces of software, we introduce new interfaces into the old model to be compatible with the new model (i.e., expanding $O^{t-1}$ to match $O^t$ , and padding the additional channels with 0). The expanded prediction $O^{t-1}$ becomes: + +$$ +O ^ {t - 1} (i, c) = \left\{ \begin{array}{l l} 0 & \text {i f} c \in \mathcal {C} _ {t} \\ O ^ {t - 1} (i, c) & \text {o t h e r w i s e} \end{array} \right. \tag {8} +$$ + +Then we enforce constraints to pixels of new class set $\mathcal{U}_n$ and background set $\mathcal{U}_b$ from the view of backward compatibility and forward compatibility respectively. It is worth noting that the background here includes old classes, future classes, and true background pixels. + +Forward compatibility. For pixels $i$ from the new class set, we transfer the old model's background prediction $O^{t - 1}(i,b)$ to the prediction corresponding to the ground-truth to address background shift [4]. Next, with the future class-aware mechanism, the old model has pre-learned knowledge about the new classes (which are future classes to the old model). Thus we also add the old model's future class prediction $O^{t - 1}(i,u)$ to the prediction corresponding to the ground truth, thereby naturally inheriting the knowledge that the old model has prepared for future learning (forward compatibility). After that, we reset the predictions of background and future classes to 0 while keeping other predictions unchanged. The corrected prediction of the old model is defined as: + +$$ +O ^ {t - 1} (i, c) = \left\{ \begin{array}{l l} O ^ {t - 1} (i, u) + O ^ {t - 1} (i, b) & \text {i f} c \in \mathcal {C} _ {t} \\ O ^ {t - 1} (i, c) & \text {i f} c \in \mathcal {C} _ {0: t - 1} \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {9} +$$ + +where $i\in \mathcal{U}_n$ and $u$ indicates the future class at step $t - 1$ + +Backward compatibility. For pixels $i \in \mathcal{U}_b$ from the background set, similar to regular knowledge distillation, we only need to align the outputs between the two models to ensure that the new model does not deviate significantly from the old model during updates. The complete compatibility-inspired distillation loss is defined as: + +$$ +\mathcal {L} _ {c p d} = \alpha_ {n} \cdot \mathcal {L} _ {f k d} (x, \mathcal {U} _ {n}) + \alpha_ {b} \cdot \mathcal {L} _ {b k d} (x, \mathcal {U} _ {b}) \tag {10} +$$ + +where $\alpha_{n}$ and $\alpha_{b}$ control the contribution of the new classes set $\mathcal{U}_n$ and background set $\mathcal{U}_b$ , which are discussed in Section 4.3; $\mathcal{L}(x,\mathcal{U})$ is a common knowledge distillation loss: + +$$ +\mathcal {L} (x, \mathcal {U}) = - \frac {1}{| \mathcal {U} |} \sum_ {i \in \mathcal {U}} \sum_ {c} ^ {\mathcal {C} _ {0: t}} O _ {x} ^ {t - 1} (i, c) \log O _ {x} ^ {t} (i, c) \tag {11} +$$ + +We emphasize that our distillation approach supplements and corrects the contents extended in the interfaces of the old model, thus addressing alignment conflict and background shift, as well as facilitating the new model to effectively leverage the knowledge learned by the old model. + +# 3.5. Feature-based Distillation + +To prevent catastrophic forgetting in feature space, we also utilize multi-scale local distillation with Local POD [13] to retain knowledge by preserving multi-scale spatial information. The Local POD loss is formulated as: + +$$ +\mathcal {L} _ {p o d} = \frac {1}{L} \sum_ {l = 1} ^ {L} | \phi (\mathcal {F} _ {l} ^ {t}) - \phi (\mathcal {F} _ {l} ^ {t - 1}) | ^ {2} \tag {12} +$$ + +where $\mathcal{F}_l^t$ is the feature of the $l$ -th layer and $\phi(.)$ is a function that captures multi-scale spatial statistics. + +Finally, we train the model with the total loss as follows: + +$$ +\mathcal {L} _ {a l l} = \mathcal {L} _ {c e} + \mathcal {L} _ {c p d} + \lambda \cdot \mathcal {L} _ {p o d} \tag {13} +$$ + +where $\lambda$ denotes the weight of LocalPOD, which is set to 0.0001 in our experiments. + +# 4. Experiment + +# 4.1. Datasets, Protocols, and Evaluation + +Datasets. We conduct all the experiments on two publicly available nuclei datasets, MoNuSAC and CoNSeP. MoNuSAC contains H&E stained tissue images of four organs, along with annotations for multiple cell types, including epithelial (Epith), lymphocyte (Lymph), macrophage (Macro), and neutrophil (Neutr). We randomly split $20\%$ of the training set for validation. Besides, all images in the training, testing, and validation sets have been uniformly cropped to a resolution of $320 \times 320$ . Finally, the MoNuSAC contains 1177 training images, 295 validation images and 651 test images. CoNSeP contains H&E stained image tiles with annotations of 7 cell types, where we divide them into 3 classes: epithelial, spindle-shaped and others. With the same pre-processing, we obtain a training set with 345, a validation set with 87, and a test set with 224 images. + +Protocols. There are two common settings in ISS benchmarks: disjoint and overlapped. In the disjoint setting, $D_{t}$ only contains images of new classes and old classes. In the overlapped setting, $D_{t}$ can contain images of all classes, including old classes, new classes, and future classes. Regarding of setting, only new classes are annotated, while others are treated as background. The overlapped setting is considered more realistic since it allows future classes to appear in the current dataset, reflecting real-world scenarios more accurately. In this work, we only focus on the overlapped setting. + +
Method1-1 (4 tasks)2-1 (3 tasks)2-2 (2 tasks)3-1 (2 tasks)
OldNewMeanOldNewMeanOldNewMeanOldNewMean
ILT [25]33.4653.9148.8050.0073.3061.6546.0068.1857.0962.1173.2764.90
MiB [4]59.9564.5763.4152.5174.6763.5957.3376.8767.1063.8575.3866.73
SDR [26]55.5067.3064.3553.4774.3763.9257.0878.0367.5665.7077.3168.60
PLOP [13]60.1465.6064.2356.8575.8766.3656.7475.8866.3166.1677.4368.97
REMARKER [30]62.4166.4965.4756.5775.8966.2359.8976.0367.9668.2277.1870.46
CoNuSeg [35]65.3767.9267.2857.8576.0966.9761.7077.1169.4066.4777.3369.18
IDEC [41]62.1669.4167.5958.6376.0367.3363.2275.4169.3167.3677.1269.80
EWF [36]64.5767.8967.0660.2776.2368.2665.9075.9470.9269.0677.6271.20
Ours68.1169.8669.4463.7976.5370.1665.4377.2171.3270.4678.0372.36
Joint72.0175.2974.4770.3678.5874.4770.3678.5874.4772.6579.9374.47
+ +Table 1. Incremental semantic segmentation results (mDice) on MoNuSAC. The best is in bold. + +![](images/18eb1657808d7272ac7e6034b27aa23cbe7fcf14a8e7b0c4a550c75678766333.jpg) +Figure 4. Visualization of the proposed method and EWF at different incremental steps on two datasets. + +![](images/25c875f2b6b1a66d29a7d029144c353a10c4759a60a29e1e5698040f308c3a61.jpg) + +Evaluation. The ISS benchmark configurations are represented as $n - m$ where $n$ and $m$ correspond to the number of new classes to be learned during the initial step and each subsequent step, respectively. We set several ISS settings for each dataset, e.g., on MoNuSAC 3-1, 2-1, 2-2, and 1-1 respectively include learning 3 classes then 1 class (2 steps), 2 classes then 1 class (3 steps), 2 classes then 2 classes (2 steps) and 1 class at initial step then 1 class at subsequent step (4 steps). We emphasized that the 1-1 setting is the most challenging task due to its small amount of data and high number of steps. Similarly, on CoNSeP 1-1 (3 steps) and 2-1 (2 steps). After training all steps, we use mean Dice (mDice) to evaluate the performance. + +Implementation Details. We use the ResNet-101 pre + +trained on ImageNet as the feature encoder for all experiments. During training, the initial learning rate is set to 0.05 for the first step and 0.01 for subsequent incremental steps. The number of epochs for all steps is set to 100. We employ an SGD optimizer with a batch size of 12, distributed across three 2080Ti GPUs, to train the model. + +Comparison Results. To demonstrate the advantages of our method, we employ the state-of-the-art approach (EWF) as our baseline for comparison. Table 1 displays our approach's comparative results against some strong ISS methods on the MoNuSAC dataset. Evidently, the performance of ILT is the worst in all incremental setups, since it lacks the capacity to address background shift. Integrating background correction methods, such as MiB and + +PLOP, leads to marked improvements for both old and new classes in all settings. By further introducing innovative distillation mechanisms into the background correction method, approaches like REMINDER, CoNuSeg, and IDEC have achieved additional performance gains. EWF receives higher performance after applying the Endpoints Weight Fusion strategy to PLOP. + +Despite their great progress, our approach surpasses them by a large margin on all settings. In particular, on the most challenging setup (1-1), our method outperforms the EWF by $3.54\%$ in old classes and IDEC by $0.45\%$ in new classes. While the gains in new classes are not that large, we believe that the performance is already quite better compared to that of old classes. As presented in Figure 5, our model achieves all the highest mDice scores from incremental step 1 to step 3. This also indicates that the stability and plasticity of our model are superior to those of other strong models. Experiments in Table 2 further demonstrate the strong generalization ability of our method. + +![](images/2fa7f718da9564a20cb7bdf3687b5770c7bad69ae101b5e8b8ec21a82b2e855d.jpg) +Figure 5. Results of mDice at different incremental steps. + +
Method1-1 (3 tasks)2-1 (2 tasks)
OldNewMeanOldNewMean
ILT [25]35.2363.1944.5540.8263.6148.41
MiB [4]67.0267.0667.0470.9961.9667.98
SDR [26]67.0567.2967.2170.3762.9267.88
PLOP [13]67.0667.7867.5472.5063.1569.38
CoNuSeg [35]67.5268.5968.2372.8063.4169.67
IDEC [41]67.2068.2867.9272.1662.7869.03
EWF [36]67.1870.0369.0874.1663.0070.44
Ours66.6470.8469.4474.2964.6571.08
+ +Visual Results. We visualize the segmentation results of our method and EWF on two datasets to highlight the comparative effectiveness. As shown in Figure 4, our method + +yields segmentation results that are more complete and accurate than those produced by EWF. For example, for the second image (rows 3-4, left), both methods gradually forget class epithelial (the red ones) and macrophage (the green ones) from step 0 to step 2. Nevertheless, our method still yields satisfactory segmentation results after step 3. Similar results can be observed in other images. Figure 6 explicitly presents the Dice score for each class at every step. + +![](images/2390ae8b8b006b60ef357598c0390f5f134efc97fa29c56ab96d2bf0cdabfce2.jpg) +Figure 6. Values of Dice metric for each class at different incremental steps on MoNuSAC 1-1. + +# 4.2. Ablation Study + +We verify the effectiveness of the proposed method using 1-1 and 3-1 setups on MoNuSAC. From Table 3, we can find that the performance of PLOP + EWF surpasses that of PLOP. Only adding future-class awareness (FCA) can further boost the performance of EWF across different setups. After applying compatibility-inspired distillation (CID), we obtain the highest performance on MoNuSAC. In particular, the performance of PLOP + EWF + FCA + CID outperforms that of PLOP + EWF in 1-1 settings, with a great improvement of $3.54\%$ in old classes and $1.97\%$ in new classes. These results effectively demonstrate that both proposed modules can effectively improve the plasticity and stability of the model, thereby improving the overall performance. + +Table 2. Incremental semantic segmentation results (mDice) on the CoNSeq dataset. + +
Method1-1 (4 tasks)3-1 (2 tasks)
OldNewMeanOldNewMean
PLOP60.1465.6064.2366.1677.4368.97
+ EWF64.5767.8967.0669.0677.6271.20
+FCA67.4269.0068.6070.1177.9372.07
+CID68.1169.8669.4270.4678.0372.36
+ +Table 3. Ablation study results (mDice) on the MoNuSAC dataset. + +# 4.3. Further Analysis + +Future-class Awareness. To better understand how prelearning of future classes enhances the results, we visual- + +ize t-SNE distribution of features generated from the baseline and baseline $+$ FCA. As shown in Figure 7, the base + +![](images/ea0eac70587190c338631bf7f8f256e9e74ad3a046df8c2a83fa53dfb120b347.jpg) +Figure 7. T-SNE visualization of features learned by Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1. + +line tends to generate more ambiguous features while the baseline $+\mathrm{FCA}$ is able to learn more discriminative features. These robust features then help the model to resist catastrophic forgetting better. Similar conclusions can be drawn from the feature map (Figure 8). The baseline model + +![](images/1ae1bb079fb8fa4bda24cea40be98c96e5173ee9b72df904237beddf52fdb7f5.jpg) +Figure 8. Feature maps of the Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1. + +exhibits a lower response to target features and is prone to generating erroneous high responses in the background, whereas the baseline with FCA generates more accurate and higher responses to target features. This phenomenon further shows that training with FCA can enhance the representation power to alleviate knowledge forgetting and reserve more parameter space to be updated. + +Compatibility-inspired Distillation. As shown in Table 4, slightly increasing both $\alpha_{n}$ and $\alpha_{b}$ to 1 can improve the performance of both new and old classes. However, a large value of $\alpha_{n}$ , e.g., $\alpha_{n} = 5$ leads the model to focus excessively on new classes, compromising the performance of old classes and thus negatively affecting overall performance. Similarly, when we set $\alpha_{b}$ a high value 3, the model tends to overly remember old classes and overlook the new classes. + +In our experiments, we achieve the best performance when $\alpha_{n}$ and $\alpha_{b}$ are set to 3 and 1, respectively. For additional ablation studies and detailed analytical experiments, please refer to the supplementary materials. + +
αnαbBackgroundOldNewAll
0094.5867.4269.0073.80
1194.5367.7169.3174.03
3194.4368.1169.8674.42
5194.5165.9169.1873.59
3094.7067.6169.2574.01
3294.7468.0869.4174.21
3394.5368.1868.3473.54
+ +Table 4. Effect of the weighted factors ${\alpha }_{n}$ and ${\alpha }_{b}$ . + +# 5. Limitation + +We develop our method based on the attributes of histopathological images, where future classes in the dataset exhibit visual similarities to the learned classes. Therefore, our approach may not perform optimally in datasets where future classes significantly differ from the learned classes, which necessitates further research. Nevertheless, considering the vast diversity of cancer cell types, our method shows promise in enhancing computer-aided diagnosis systems with more robust incremental updating capabilities. + +# 6. Conclusion + +In this work, we present a novel method for incremental semantic segmentation from histopathological images, aiming to solve catastrophic forgetting without storing samples of previous data. First, we propose a new future-class awareness approach that detects future classes in an unsupervised way. Second, drawing inspiration from software engineering, we introduce an innovative compatibility-inspired knowledge distillation to make the new model take full advantage of the knowledge learned by the old model. Finally, comparative experiments and ablation studies clearly demonstrate the effectiveness of the proposed method. + +# Acknowledgments + +This work was supported partly by National Natural Science Foundation of China (No. 62273241), Natural Science Foundation of Guangdong Province, China (No. 2024A1515011946), and the Theme-based Research Scheme from Hong Kong Research Grants Council (project no. T45-401/22-N). + +# References + +[1] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. Expert gate: Lifelong learning with a network of experts. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3366-3375, 2017. 2 +[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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Yet, it is an indispensable component of computer-aided diagnosis systems. The proposed approach has two key techniques. First, we propose a new future-class awareness mechanism by separating some potential regions for future classes from background based on their similarities to both old and new classes in the representation space. With this mechanism, we can not only reserve more parameter space for future updates but also enhance the representation capability of learned features. We further propose an innovative compatibility-inspired distillation scheme to make our model take full advantage of the knowledge learned by the old model. We conducted extensive experiments on two famous histopathological datasets and the results demonstrate the proposed approach achieves much better performance than state-of-the-art approaches. The code is available at https://github.com/why19991/InSeg." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "type": "text", + "content": "Cellular nuclei segmentation aims to accurately delineate various cell nuclei from histopathological images, which is of great importance for cancer diagnosis, treatment, and prognosis prediction [37]. Recent years, deep learning models have achieved remarkable performance in this task [8, 20, 32, 34, 40], significantly promoting the development of computer-aided diagnosis systems. Despite these progresses, most existing models are incapable of maintaining the performance on previously learned classes when it is required to incrementally learn new classes, which is common in clinical practice [35]. This phenomenon is called" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 244, + 375, + 357 + ], + "blocks": [ + { + "bbox": [ + 310, + 268, + 318, + 343 + ], + "lines": [ + { + "bbox": [ + 310, + 268, + 318, + 343 + ], + "spans": [ + { + "bbox": [ + 310, + 268, + 318, + 343 + ], + "type": "text", + "content": "rrnnnne" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 320, + 244, + 375, + 357 + ], + "lines": [ + { + "bbox": [ + 320, + 244, + 375, + 357 + ], + "spans": [ + { + "bbox": [ + 320, + 244, + 375, + 357 + ], + "type": "image", + "image_path": "367fcdbd33b9b53ca09cd66f39e070d6167bfcd3358e69feeaf3a548e50a06b6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 376, + 244, + 432, + 357 + ], + "blocks": [ + { + "bbox": [ + 376, + 244, + 432, + 357 + ], + "lines": [ + { + "bbox": [ + 376, + 244, + 432, + 357 + ], + "spans": [ + { + "bbox": [ + 376, + 244, + 432, + 357 + ], + "type": "image", + "image_path": "3ab489b0a909d270f5748d54a042fa219263715bf97c99f828947499a7d50c9b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 365, + 546, + 453 + ], + "lines": [ + { + "bbox": [ + 306, + 365, + 546, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 546, + 453 + ], + "type": "text", + "content": "Figure 1. Pathological images typically contain numerous objects from different categories that have very similar appearances. For instance, epithelia (represented by red objects) and lymphocytes (represented by yellow objects) look quite alike. However, in the 1-1 setting at step 0, epithelia are labeled as new classes, whereas lymphocytes are seen as background. Our approach aims to mine such future classes in an unsupervised way and learn them in advance." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 433, + 244, + 487, + 357 + ], + "blocks": [ + { + "bbox": [ + 433, + 244, + 487, + 357 + ], + "lines": [ + { + "bbox": [ + 433, + 244, + 487, + 357 + ], + "spans": [ + { + "bbox": [ + 433, + 244, + 487, + 357 + ], + "type": "image", + "image_path": "138ad2722ec3d01a047a5ac6244483978eb1a7f5d1f7e681669ec24fbe0f2a02.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 489, + 244, + 545, + 357 + ], + "blocks": [ + { + "bbox": [ + 489, + 244, + 545, + 357 + ], + "lines": [ + { + "bbox": [ + 489, + 244, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 489, + 244, + 545, + 357 + ], + "type": "image", + "image_path": "95b7b2a62dfba0a7a1eb0421f891f6e7bd8709f431181215fec0411c5769f25c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 482, + 546, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 546, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 546, + 614 + ], + "type": "text", + "content": "catastrophic forgetting [24], which is a long-standing challenge and prohibits these models from being deployed in clinical settings. A common solution is to rebuild the training dataset containing annotations of all classes and retrain the model. However, the cost of collecting histopathological images with pixel-level annotations for segmentation is extremely laborious and time-consuming. Besides, access to previous data is usually limited by patient privacy. In this regard, we often have to incrementally optimize existing models to make them perform well in both old classes and new classes without using training samples of old classes." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Incremental learning is proposed to solve the problem of catastrophic forgetting, and semantic segmentation based on incremental learning is known as incremental semantic segmentation (ISS). In scenarios where previous data can be reused, some studies [22, 45] select samples to help the model review and reinforce knowledge, greatly alleviating catastrophic forgetting. However, when privacy or storage issues make old data unavailable, which is common" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11408" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "content": "in clinical scenarios, most studies turn to employ distillation techniques [4, 13, 23, 25, 26, 30, 36] to constrain the model updating. These methods, while keeping the performance of old classes (stability) well, limit the model's capability in learning new classes (plasticity). In order to improve both stability and plasticity, a few studies [5, 39] propose to learn future classes in advance to prepare for learning new classes. Specifically, SSUL-M [5] applies a salient object detector to detect potential future classes while MicroSeg [39] utilizes mask proposals generated by Mask2Former [9] to detect future classes. Unfortunately, both the salient detector and mask proposals still heavily depend on a number of annotated data, which is, as mentioned, difficult to acquire in clinical practice due to privacy and cost. To the end, it is necessary to aware future classes in an unsupervised manner on the given data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 289, + 602 + ], + "type": "text", + "content": "In this work, we present a novel ISS method for incremental nuclei segmentation from histopathological images, which has two key components: a new future-class awareness mechanism and an innovative compatibility-inspired distillation scheme. Histopathological images often contain numerous objects belonging to different categories with great similarity in appearance. As illustrated in Figure 1, some nuclei are learned as new classes or old classes, while others (future classes) are treated as background. Thus, we propose to separate some potential regions of future classes from background by calculating their similarities to both old and new classes in the representation space, and then we train the new model with both new and old classes, as well as with the separated regions. To the end, we cannot only reserve more parameter space for future updates but also enhance the representation capability of learned features. Furthermore, we design a compatibility-inspired distillation scheme to further improve both stability and plasticity. As the number of targeting classes of the updated model is always more than that of the old model, directly aligning them poses conflicts and background shifts [4]. In this regard, we propose to expand the old model's prediction range to match that of the new model by harnessing the representation space of the future classes. This scheme not only resolves alignment conflicts and background shifts but also enables the new model to effectively utilize the knowledge of the old model. Our contributions can be summarized as follows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 47, + 605, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 665 + ], + "type": "text", + "content": "- We propose a novel ISS method for incremental nuclei segmentation from histopathological images, which is able to incrementally optimize existing models to make them perform well in both old and new classes without using training samples of old classes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "type": "text", + "content": "- We propose a new future-class awareness mechanism to reserve more parameter space for incremental learning, and an innovative compatibility-inspired distillation scheme to make our model take full advantage of the" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 465, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 465, + 83 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 465, + 83 + ], + "type": "text", + "content": "knowledge learned by the old model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 84, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 84, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 84, + 547, + 144 + ], + "type": "text", + "content": "- We demonstrate the proposed method achieve a better balance between stability and plasticity than state-of-the-art methods via extensive experiments on two famous public histopathological datasets, MoNuSAC [33] and CoNSeP [14]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 156, + 392, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 392, + 167 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 392, + 167 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 175, + 425, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 425, + 188 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 425, + 188 + ], + "type": "text", + "content": "2.1. Nuclei Segmentation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 194, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 547, + 338 + ], + "type": "text", + "content": "There have been some preliminary works for nuclei segmentation based on traditional techniques and deep learning methods. Traditional techniques based on background subtraction and color threshold [27, 29] fail to generalize to complex scenarios such as overlap and occlusion in histopathology images. With the development of CNN, deep networks have been widely used in nuclei segmentation [31, 32, 34, 42], significantly improving the segmentation performance in the supervised setting. However, most of these networks are not incrementally designed and tend to forget previously learned classes when learning new types of cell nuclei continually." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 345, + 460, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 345, + 460, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 345, + 460, + 358 + ], + "type": "text", + "content": "2.2. Class Incremental Learning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 364, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 555 + ], + "type": "text", + "content": "Class incremental learning (CIL) aims to address the problem of catastrophic forgetting when learning knowledge for new classes. Existing CIL techniques can be summarized into regularization-based, replay-based, and architecture-based approaches. Regularization-based approaches utilize consistency constraints between new and old models to prevent significant changes to the knowledge associated with previously learned classes. The constraints can be applied on features [10, 12, 18], the output logits [4, 11, 21], the weights [1, 2, 19], or the gradients [6, 15]. Architecture-based approaches [16, 38, 44] dynamically grow the network to extend model capacity for new tasks. To better retain knowledge of old classes, replay-based approaches store and re-use a subset of previous training data, including raw images [3, 22, 45], features [17, 43] or generated data [7, 28]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 563, + 526, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 526, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 526, + 576 + ], + "type": "text", + "content": "2.3. Class Incremental Semantic Segmentation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Recently, several works have extended and combined existing incremental learning methods to semantic segmentation. MiB [4] proposes a novel unbiased function to model background shift. PLOP [13] adopts pseudo label to solve background shift and retain spatial dependencies by local pooling operation. CoNuSeg [35] maintains the relationships between the prototypes of old classes to preserve the semantic information of old classes. EWF [36] propose a weight fusion strategy to fuse parameters from new and old models. SSUL-M [5] and MicroSeg [39] further propose pre-learning future classes to prepare for the future." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11409" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 102, + 70, + 492, + 277 + ], + "blocks": [ + { + "bbox": [ + 102, + 70, + 492, + 277 + ], + "lines": [ + { + "bbox": [ + 102, + 70, + 492, + 277 + ], + "spans": [ + { + "bbox": [ + 102, + 70, + 492, + 277 + ], + "type": "image", + "image_path": "ce59960fb7ec6997c6d9e0bdc295795b05ad7c900f6c7a16eaf983b22124b600.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "text", + "content": "Figure 2. The overall framework. The old " + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "inline_equation", + "content": "(t - 1)" + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "text", + "content": " and new models " + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "inline_equation", + "content": "(t)" + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "text", + "content": " consist of the same feature extractor " + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "text", + "content": " and segmentation head " + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "text", + "content": ". 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Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 346, + 171, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 171, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 171, + 357 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": "Class incremental semantic segmentation involves conducting semantic segmentation in a series of steps, with the underlying assumption that there are a total of " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " steps. 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The label set " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " only contains newly added classes at step " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": ", while previous learned classes " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_0\\cup \\mathcal{C}_1\\cup \\ldots \\cup \\mathcal{C}_{t - 1}" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " and future classes " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{t + 1:T}" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " are considered as background, which can lead to catastrophic forgetting of the previously learned classes. Given a dataset " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": ", our goal is to achieve a model " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " with parameter " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " that can perform well on all seen classes " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{0:t}" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": ". Without loss of generality, " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " consists of a feature extractor " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " and a segmentation head " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": ", which makes " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "M = F\\circ H" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 46, + 364, + 290, + 544 + ], + "type": "text", + "content": " denotes function composition." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 552, + 173, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 173, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 173, + 563 + ], + "type": "text", + "content": "3.2. Framework Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "The proposed incremental semantic segmentation framework, depicted in Figure 2, includes an old and new model. Under the incremental setting, both old and future classes are treated as background. To correct pixels of old classes, we adopt the pseudo-labeling strategy to assign them pseudo-labels. For pixels of potential future classes, we propose a new future-class awareness mechanism (detailed in Section. 3.3) to assign them unknown labels. At the feature level, we apply multi-scale local distillation with Local POD (described in Section. 3.5) between the corresponding layers of the two models to avoid a large feature discrepancy. At the output level, we design an innovative" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 327, + 547, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 547, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 547, + 400 + ], + "type": "text", + "content": "compatibility-inspired distillation (depicted in Section. 3.4) between the model's predictions to achieve better stability and plasticity. After training, we fuse the parameters from the two models by using the Endpoints Weight Fusion strategy (EWF) [36]. Specific details about EWF can be found in the supplementary materials." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 406, + 440, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 406, + 440, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 440, + 418 + ], + "type": "text", + "content": "3.3. Future-class Awareness" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "type": "text", + "content": "Our future-class awareness mechanism corrects the background pixels that are considered potential future classes, i.e., pixels that are visually similar to a new or old class. We propose to measure the similarity " + }, + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "type": "text", + "content": " by utilizing the classcentroids " + }, + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 425, + 545, + 532 + ], + "type": "text", + "content": " in the representation space of the old model. Subsequently, we assign unknown labels to these pixels for joint learning with both new and old classes. This approach enhances the representation capability of learned features and better prepares the model for the future." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "text", + "content": "Image-wise Centroids Aggregation. Class-centroids (prototypes) are representatives of each class in the representation space and serve as an effective tool to measure similarities between classes [30]. Given an image as input, we first generate pseudo-labels " + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "inline_equation", + "content": "\\hat{y}(i,c)" + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "text", + "content": " for old classes in the background using predictions " + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "inline_equation", + "content": "O^{t-1}" + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "text", + "content": " of the old model and the ground-truth label " + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "inline_equation", + "content": "y(i,c)" + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 532, + 547, + 617 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 624, + 545, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 624, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 305, + 624, + 545, + 666 + ], + "type": "interline_equation", + "content": "\\hat {y} (i, c) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} y (i, c) = 1 \\\\ 1 & \\text {i f} y (i, c) = 0 \\text {a n d} c = \\operatorname {a r g m a x} O ^ {t - 1} (i, c) \\end{array} \\right. \\tag {1}", + "image_path": "7f712d2c1cb2e1fa438aa1b7c2c063d4562f9b879d29381fd8c52c595dd8578f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "content": "This strategy can effectively re-assign labels for old classes in the background but fails to separate potential future classes hidden in the background. Next, we generate class-aware mask " + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_c" + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "content": " for class " + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "content": " under the guidance of pseudo" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11410" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 70, + 500, + 266 + ], + "blocks": [ + { + "bbox": [ + 97, + 70, + 500, + 266 + ], + "lines": [ + { + "bbox": [ + 97, + 70, + 500, + 266 + ], + "spans": [ + { + "bbox": [ + 97, + 70, + 500, + 266 + ], + "type": "image", + "image_path": "af6b31687acad4b4d2627304444167624a2e791fa23c55d441854a4b1721c967.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 547, + 298 + ], + "type": "text", + "content": "Figure 3. Illustration of future-class awareness. Centroids representing both old and new categories are aggregated in representation space, then a class-aware matrix " + }, + { + "bbox": [ + 46, + 274, + 547, + 298 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 274, + 547, + 298 + ], + "type": "text", + "content": " is computed between all centroids and background features to aware future classes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 317, + 101, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 101, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 101, + 330 + ], + "type": "text", + "content": "label " + }, + { + "bbox": [ + 47, + 317, + 101, + 330 + ], + "type": "inline_equation", + "content": "\\hat{y} (i,c)" + }, + { + "bbox": [ + 47, + 317, + 101, + 330 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 334, + 287, + 366 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 334, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 101, + 334, + 287, + 366 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {c} (i) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\hat {y} (i, c) = 1 \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}", + "image_path": "53ba02a5bb49bea78220d72a6de204441398fc750fa8d5f0bd0de8fb881ef3d0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "text", + "content": "Then, for a certain class " + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "text", + "content": ", we average the deepest input feature " + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_d^{t - 1}" + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "text", + "content": " with the class-aware mask to obtain classcentroid " + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "inline_equation", + "content": "\\nu_{k}" + }, + { + "bbox": [ + 47, + 369, + 287, + 405 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 98, + 408, + 287, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 408, + 287, + 454 + ], + "spans": [ + { + "bbox": [ + 98, + 408, + 287, + 454 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {V} _ {k} = M A P \\left(\\mathcal {M} _ {k}, \\mathcal {F} _ {d} ^ {t - 1}\\right) \\\\ = \\frac {\\sum_ {i} \\mathcal {F} _ {d} ^ {t - 1} (i) \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]}{\\sum_ {i} \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]} \\tag {3} \\\\ \\end{array}", + "image_path": "e510a026e7f7f03d7ae82bec995b27fd949b5bd622856fe843e7ffe72142eebd.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "type": "inline_equation", + "content": "MAP" + }, + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "type": "text", + "content": " represents the masked average pooling operation. After that, we obtain a centroid set " + }, + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\mathcal{V}_1,\\dots,\\mathcal{V}_{\\mathcal{C}_t}\\}" + }, + { + "bbox": [ + 47, + 456, + 287, + 503 + ], + "type": "text", + "content": " containing old and new class-centeroids, which will be utilized to detect future classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 505, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 612 + ], + "type": "text", + "content": "Cross Image-wise Centroids Aggregation. Different cell nuclei are typically distributed across different images, which suggests that potential future classes may not coexist in the same image as their similar cell nuclei. Therefore, aggregating class centroids in an image-wise manner may not include centroids of classes that are similar to future classes. To address this issue, we propose to update class centroids using a running average approach. The final class centroids are computed as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 615, + 287, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 615, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 62, + 615, + 287, + 644 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {k} = \\frac {1}{N} \\left(\\mathcal {V} _ {k} ^ {\\prime} \\cdot N _ {k} ^ {\\prime} + \\sum_ {i} \\mathcal {F} _ {d} ^ {t - 1} (i) \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right]\\right) \\tag {4}", + "image_path": "62e93fd0347e8c3af95a2bf3d72c446929953a2eece8c777d62ad51231b8ffdd.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 63, + 646, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 646, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 63, + 646, + 287, + 670 + ], + "type": "interline_equation", + "content": "N = N _ {k} ^ {\\prime} + \\sum_ {i} \\mathbb {1} \\left[ \\mathcal {M} _ {k} (i) = 1 \\right] \\tag {5}", + "image_path": "31a666d118978d9b284e39f713bc892d56a2f46a2fcc5e3cc59728b0e7057aea.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_k^{\\prime}" + }, + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "N_{k}^{\\prime}" + }, + { + "bbox": [ + 47, + 676, + 287, + 714 + ], + "type": "text", + "content": " represent the accumulated result and total pixel number of class k from the initial update to the last update, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": "Awareness & Separation. To aware future classes, we first assemble the background features " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{bg} \\in \\mathbb{R}^{C \\times N_b}" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": " via the masked multiplication on the deepest feature " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_d^{t-1}" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": " with the background mask " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": ". We then calculate a pixel-to-centroid affinity matrix " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": " between pixels of the reshaped background feature " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{bg}" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": " and class-centroids " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": " via a matrix multiplication operation " + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "inline_equation", + "content": "Mat" + }, + { + "bbox": [ + 304, + 317, + 545, + 401 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 348, + 407, + 545, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 407, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 348, + 407, + 545, + 422 + ], + "type": "interline_equation", + "content": "\\mathcal {A} = M a t \\left(\\operatorname {N o r m} \\left(\\mathcal {F} _ {b g}\\right) ^ {T}, \\operatorname {N o r m} (\\mathcal {V})\\right) \\tag {6}", + "image_path": "27d6eafd61787ce8733358e58c9fdd8f54d729d4ff9b007b3fbb94e9bb521829.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "inline_equation", + "content": "Norm" + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "content": " indicates " + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "inline_equation", + "content": "l2" + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "content": "-normalization. The size of " + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N \\times P}" + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "inline_equation", + "content": "P = |\\mathcal{V}|" + }, + { + "bbox": [ + 304, + 429, + 545, + 513 + ], + "type": "text", + "content": " is the cardinality of class-centroid set. Through the affinity matrix, we construct a semantic graph for each pixel-centroid pair, where each vertex represents the semantic structure and the edge represents the similarity relationship, thus a fine-grained similarity can be measured by utilizing the information in the representation space." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "text", + "content": "We obtain the final class-aware matrix " + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "text", + "content": " by taking the average or maximum across the second dimension of affinity matrix " + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "text", + "content": ". To effectively pre-learn knowledge of future classes, only background pixels that are sufficiently similar are re-assigned unknown labels. The final corrected ground truth " + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "inline_equation", + "content": "y(i,c)" + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "text", + "content": " of pixel " + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 513, + 545, + 585 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 591, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 591, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 314, + 591, + 545, + 624 + ], + "type": "interline_equation", + "content": "y (i, c) = \\left\\{ \\begin{array}{l l} u & \\text {i f} \\mathcal {M} _ {b} (i) = 1 \\text {a n d} \\mathcal {S} (i) < \\tau_ {u} \\\\ \\hat {y} (i, c) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}", + "image_path": "6dcbf4437f09ccd30c73d5a87363ce3fa57e3a0e5f01ef5e8f8da6c099865681.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " represents the unknown label assigned to future classes, and " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{u}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is a threshold controlling the confidence of future classes. In other words, for background pixels filtered by Equation 1, we re-label them with an unknown label " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " on the guidance of the class-aware matrix " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ". Otherwise, we directly copy their pseudo-labels (for old classes) or true labels (for new classes)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11411" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 232, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 232, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 232, + 85 + ], + "type": "text", + "content": "3.4. Compatibility-inspired Distillation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": "Considering that the previous model only produces predictions " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "O^{t-1}" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "|\\mathcal{C}_{0:t-1}|" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": " classes, while the new model can produce predictions " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "O^t" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "|\\mathcal{C}_{0:t}|(|\\mathcal{C}_{0:t}| > |\\mathcal{C}_{0:t-1}|)" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": " classes, directly aligning the outputs between the two models is contradictory. Treating the model's predictions as interfaces of software, we introduce new interfaces into the old model to be compatible with the new model (i.e., expanding " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "O^{t-1}" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": " to match " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "O^t" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": ", and padding the additional channels with 0). The expanded prediction " + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "inline_equation", + "content": "O^{t-1}" + }, + { + "bbox": [ + 46, + 90, + 287, + 198 + ], + "type": "text", + "content": " becomes:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 83, + 202, + 287, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 202, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 83, + 202, + 287, + 235 + ], + "type": "interline_equation", + "content": "O ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} _ {t} \\\\ O ^ {t - 1} (i, c) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8}", + "image_path": "ecd69e9a8a5e9ceb7afd695ce9f5f6d97762e1615264fc27d63760a274c7debf.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "type": "text", + "content": "Then we enforce constraints to pixels of new class set " + }, + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_n" + }, + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "type": "text", + "content": " and background set " + }, + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_b" + }, + { + "bbox": [ + 46, + 239, + 287, + 298 + ], + "type": "text", + "content": " from the view of backward compatibility and forward compatibility respectively. It is worth noting that the background here includes old classes, future classes, and true background pixels." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "text", + "content": "Forward compatibility. For pixels " + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "text", + "content": " from the new class set, we transfer the old model's background prediction " + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "inline_equation", + "content": "O^{t - 1}(i,b)" + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "text", + "content": " to the prediction corresponding to the ground-truth to address background shift [4]. Next, with the future class-aware mechanism, the old model has pre-learned knowledge about the new classes (which are future classes to the old model). Thus we also add the old model's future class prediction " + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "inline_equation", + "content": "O^{t - 1}(i,u)" + }, + { + "bbox": [ + 46, + 299, + 287, + 466 + ], + "type": "text", + "content": " to the prediction corresponding to the ground truth, thereby naturally inheriting the knowledge that the old model has prepared for future learning (forward compatibility). After that, we reset the predictions of background and future classes to 0 while keeping other predictions unchanged. The corrected prediction of the old model is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 469, + 287, + 523 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 469, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 51, + 469, + 287, + 523 + ], + "type": "interline_equation", + "content": "O ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} O ^ {t - 1} (i, u) + O ^ {t - 1} (i, b) & \\text {i f} c \\in \\mathcal {C} _ {t} \\\\ O ^ {t - 1} (i, c) & \\text {i f} c \\in \\mathcal {C} _ {0: t - 1} \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {9}", + "image_path": "6c493acded9a0005321d37099dd979b8c4b4ec09904508c784dc281cf3304184.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "inline_equation", + "content": "i\\in \\mathcal{U}_n" + }, + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "text", + "content": " indicates the future class at step " + }, + { + "bbox": [ + 47, + 524, + 285, + 536 + ], + "type": "inline_equation", + "content": "t - 1" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 536, + 287, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 607 + ], + "type": "text", + "content": "Backward compatibility. For pixels " + }, + { + "bbox": [ + 46, + 536, + 287, + 607 + ], + "type": "inline_equation", + "content": "i \\in \\mathcal{U}_b" + }, + { + "bbox": [ + 46, + 536, + 287, + 607 + ], + "type": "text", + "content": " from the background set, similar to regular knowledge distillation, we only need to align the outputs between the two models to ensure that the new model does not deviate significantly from the old model during updates. The complete compatibility-inspired distillation loss is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 613, + 287, + 627 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 613, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 67, + 613, + 287, + 627 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c p d} = \\alpha_ {n} \\cdot \\mathcal {L} _ {f k d} (x, \\mathcal {U} _ {n}) + \\alpha_ {b} \\cdot \\mathcal {L} _ {b k d} (x, \\mathcal {U} _ {b}) \\tag {10}", + "image_path": "50777e500cf212dba7d258d763b8a53dcb2e1329de7931c3c8753428dbc61037.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\alpha_{n}" + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\alpha_{b}" + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "content": " control the contribution of the new classes set " + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_n" + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "content": " and background set " + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_b" + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "content": ", which are discussed in Section 4.3; " + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(x,\\mathcal{U})" + }, + { + "bbox": [ + 47, + 632, + 287, + 668 + ], + "type": "text", + "content": " is a common knowledge distillation loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 61, + 682, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 682, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 61, + 682, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (x, \\mathcal {U}) = - \\frac {1}{| \\mathcal {U} |} \\sum_ {i \\in \\mathcal {U}} \\sum_ {c} ^ {\\mathcal {C} _ {0: t}} O _ {x} ^ {t - 1} (i, c) \\log O _ {x} ^ {t} (i, c) \\tag {11}", + "image_path": "77635f77ee6a4b6cdf49e36e280dde041bfe8b3c2a5b23a2ddf3c4e73353d979.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "We emphasize that our distillation approach supplements and corrects the contents extended in the interfaces of the old model, thus addressing alignment conflict and background shift, as well as facilitating the new model to effectively leverage the knowledge learned by the old model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 141, + 450, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 141, + 450, + 152 + ], + "spans": [ + { + "bbox": [ + 306, + 141, + 450, + 152 + ], + "type": "text", + "content": "3.5. Feature-based Distillation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 159, + 545, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 207 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 207 + ], + "type": "text", + "content": "To prevent catastrophic forgetting in feature space, we also utilize multi-scale local distillation with Local POD [13] to retain knowledge by preserving multi-scale spatial information. The Local POD loss is formulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 352, + 216, + 545, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 216, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 352, + 216, + 545, + 248 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p o d} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} | \\phi (\\mathcal {F} _ {l} ^ {t}) - \\phi (\\mathcal {F} _ {l} ^ {t - 1}) | ^ {2} \\tag {12}", + "image_path": "6e9336bab033798db1fb2607aff48311758f9a8b89f315e29b713823934f2495.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_l^t" + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "text", + "content": " is the feature of the " + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "text", + "content": "-th layer and " + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\phi(.)" + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "text", + "content": " is a function that captures multi-scale spatial statistics." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 283, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 283, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 317, + 283, + 545, + 295 + ], + "type": "text", + "content": "Finally, we train the model with the total loss as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 364, + 308, + 545, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 308, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 364, + 308, + 545, + 321 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a l l} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {c p d} + \\lambda \\cdot \\mathcal {L} _ {p o d} \\tag {13}", + "image_path": "5502ae3166ff88d891d7d0c8c64e33709467a14bf3041a044a9104eee811fdac.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 327, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 351 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 327, + 545, + 351 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 327, + 545, + 351 + ], + "type": "text", + "content": " denotes the weight of LocalPOD, which is set to 0.0001 in our experiments." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 364, + 382, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 364, + 382, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 364, + 382, + 376 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 384, + 493, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 493, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 493, + 396 + ], + "type": "text", + "content": "4.1. Datasets, Protocols, and Evaluation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": "Datasets. We conduct all the experiments on two publicly available nuclei datasets, MoNuSAC and CoNSeP. MoNuSAC contains H&E stained tissue images of four organs, along with annotations for multiple cell types, including epithelial (Epith), lymphocyte (Lymph), macrophage (Macro), and neutrophil (Neutr). We randomly split " + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": " of the training set for validation. Besides, all images in the training, testing, and validation sets have been uniformly cropped to a resolution of " + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "inline_equation", + "content": "320 \\times 320" + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": ". Finally, the MoNuSAC contains 1177 training images, 295 validation images and 651 test images. CoNSeP contains H&E stained image tiles with annotations of 7 cell types, where we divide them into 3 classes: epithelial, spindle-shaped and others. With the same pre-processing, we obtain a training set with 345, a validation set with 87, and a test set with 224 images." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Protocols. There are two common settings in ISS benchmarks: disjoint and overlapped. In the disjoint setting, " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " only contains images of new classes and old classes. In the overlapped setting, " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " can contain images of all classes, including old classes, new classes, and future classes. Regarding of setting, only new classes are annotated, while others are treated as background. The overlapped setting is considered more realistic since it allows future classes to appear in the current dataset, reflecting real-world scenarios more accurately. In this work, we only focus on the overlapped setting." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11412" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 71, + 544, + 250 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 544, + 250 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 544, + 250 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 544, + 250 + ], + "type": "table", + "html": "
Method1-1 (4 tasks)2-1 (3 tasks)2-2 (2 tasks)3-1 (2 tasks)
OldNewMeanOldNewMeanOldNewMeanOldNewMean
ILT [25]33.4653.9148.8050.0073.3061.6546.0068.1857.0962.1173.2764.90
MiB [4]59.9564.5763.4152.5174.6763.5957.3376.8767.1063.8575.3866.73
SDR [26]55.5067.3064.3553.4774.3763.9257.0878.0367.5665.7077.3168.60
PLOP [13]60.1465.6064.2356.8575.8766.3656.7475.8866.3166.1677.4368.97
REMARKER [30]62.4166.4965.4756.5775.8966.2359.8976.0367.9668.2277.1870.46
CoNuSeg [35]65.3767.9267.2857.8576.0966.9761.7077.1169.4066.4777.3369.18
IDEC [41]62.1669.4167.5958.6376.0367.3363.2275.4169.3167.3677.1269.80
EWF [36]64.5767.8967.0660.2776.2368.2665.9075.9470.9269.0677.6271.20
Ours68.1169.8669.4463.7976.5370.1665.4377.2171.3270.4678.0372.36
Joint72.0175.2974.4770.3678.5874.4770.3678.5874.4772.6579.9374.47
", + "image_path": "c5dda4dce5ebbb7e3886ac30b27052e93d3f3238c4d26126c7cc583f02dd35c0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 122, + 257, + 470, + 269 + ], + "lines": [ + { + "bbox": [ + 122, + 257, + 470, + 269 + ], + "spans": [ + { + "bbox": [ + 122, + 257, + 470, + 269 + ], + "type": "text", + "content": "Table 1. Incremental semantic segmentation results (mDice) on MoNuSAC. The best is in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 53, + 280, + 321, + 497 + ], + "blocks": [ + { + "bbox": [ + 53, + 280, + 321, + 497 + ], + "lines": [ + { + "bbox": [ + 53, + 280, + 321, + 497 + ], + "spans": [ + { + "bbox": [ + 53, + 280, + 321, + 497 + ], + "type": "image", + "image_path": "18eb1657808d7272ac7e6034b27aa23cbe7fcf14a8e7b0c4a550c75678766333.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 108, + 505, + 484, + 517 + ], + "lines": [ + { + "bbox": [ + 108, + 505, + 484, + 517 + ], + "spans": [ + { + "bbox": [ + 108, + 505, + 484, + 517 + ], + "type": "text", + "content": "Figure 4. Visualization of the proposed method and EWF at different incremental steps on two datasets." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 329, + 279, + 544, + 496 + ], + "blocks": [ + { + "bbox": [ + 329, + 279, + 544, + 496 + ], + "lines": [ + { + "bbox": [ + 329, + 279, + 544, + 496 + ], + "spans": [ + { + "bbox": [ + 329, + 279, + 544, + 496 + ], + "type": "image", + "image_path": "25c875f2b6b1a66d29a7d029144c353a10c4759a60a29e1e5698040f308c3a61.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "text", + "content": "Evaluation. The ISS benchmark configurations are represented as " + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "inline_equation", + "content": "n - m" + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 537, + 288, + 693 + ], + "type": "text", + "content": " correspond to the number of new classes to be learned during the initial step and each subsequent step, respectively. We set several ISS settings for each dataset, e.g., on MoNuSAC 3-1, 2-1, 2-2, and 1-1 respectively include learning 3 classes then 1 class (2 steps), 2 classes then 1 class (3 steps), 2 classes then 2 classes (2 steps) and 1 class at initial step then 1 class at subsequent step (4 steps). We emphasized that the 1-1 setting is the most challenging task due to its small amount of data and high number of steps. Similarly, on CoNSeP 1-1 (3 steps) and 2-1 (2 steps). After training all steps, we use mean Dice (mDice) to evaluate the performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 693, + 287, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 706 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 706 + ], + "type": "text", + "content": "Implementation Details. We use the ResNet-101 pre" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 537, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 545, + 609 + ], + "type": "text", + "content": "trained on ImageNet as the feature encoder for all experiments. During training, the initial learning rate is set to 0.05 for the first step and 0.01 for subsequent incremental steps. The number of epochs for all steps is set to 100. We employ an SGD optimizer with a batch size of 12, distributed across three 2080Ti GPUs, to train the model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 609, + 546, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 546, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 546, + 705 + ], + "type": "text", + "content": "Comparison Results. To demonstrate the advantages of our method, we employ the state-of-the-art approach (EWF) as our baseline for comparison. Table 1 displays our approach's comparative results against some strong ISS methods on the MoNuSAC dataset. Evidently, the performance of ILT is the worst in all incremental setups, since it lacks the capacity to address background shift. Integrating background correction methods, such as MiB and" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11413" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "PLOP, leads to marked improvements for both old and new classes in all settings. By further introducing innovative distillation mechanisms into the background correction method, approaches like REMINDER, CoNuSeg, and IDEC have achieved additional performance gains. EWF receives higher performance after applying the Endpoints Weight Fusion strategy to PLOP." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "type": "text", + "content": "Despite their great progress, our approach surpasses them by a large margin on all settings. In particular, on the most challenging setup (1-1), our method outperforms the EWF by " + }, + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "type": "inline_equation", + "content": "3.54\\%" + }, + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "type": "text", + "content": " in old classes and IDEC by " + }, + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "type": "inline_equation", + "content": "0.45\\%" + }, + { + "bbox": [ + 46, + 157, + 290, + 301 + ], + "type": "text", + "content": " in new classes. While the gains in new classes are not that large, we believe that the performance is already quite better compared to that of old classes. As presented in Figure 5, our model achieves all the highest mDice scores from incremental step 1 to step 3. This also indicates that the stability and plasticity of our model are superior to those of other strong models. Experiments in Table 2 further demonstrate the strong generalization ability of our method." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 310, + 287, + 440 + ], + "blocks": [ + { + "bbox": [ + 48, + 310, + 287, + 440 + ], + "lines": [ + { + "bbox": [ + 48, + 310, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 48, + 310, + 287, + 440 + ], + "type": "image", + "image_path": "2fa7f718da9564a20cb7bdf3687b5770c7bad69ae101b5e8b8ec21a82b2e855d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 448, + 271, + 459 + ], + "lines": [ + { + "bbox": [ + 62, + 448, + 271, + 459 + ], + "spans": [ + { + "bbox": [ + 62, + 448, + 271, + 459 + ], + "type": "text", + "content": "Figure 5. Results of mDice at different incremental steps." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 483, + 291, + 624 + ], + "blocks": [ + { + "bbox": [ + 48, + 483, + 291, + 624 + ], + "lines": [ + { + "bbox": [ + 48, + 483, + 291, + 624 + ], + "spans": [ + { + "bbox": [ + 48, + 483, + 291, + 624 + ], + "type": "table", + "html": "
Method1-1 (3 tasks)2-1 (2 tasks)
OldNewMeanOldNewMean
ILT [25]35.2363.1944.5540.8263.6148.41
MiB [4]67.0267.0667.0470.9961.9667.98
SDR [26]67.0567.2967.2170.3762.9267.88
PLOP [13]67.0667.7867.5472.5063.1569.38
CoNuSeg [35]67.5268.5968.2372.8063.4169.67
IDEC [41]67.2068.2867.9272.1662.7869.03
EWF [36]67.1870.0369.0874.1663.0070.44
Ours66.6470.8469.4474.2964.6571.08
", + "image_path": "7f03db8079fa61fb28c0ce9772f876a03e0e810cd2720eadee5896d54c7cb708.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Visual Results. We visualize the segmentation results of our method and EWF on two datasets to highlight the comparative effectiveness. As shown in Figure 4, our method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 169 + ], + "type": "text", + "content": "yields segmentation results that are more complete and accurate than those produced by EWF. For example, for the second image (rows 3-4, left), both methods gradually forget class epithelial (the red ones) and macrophage (the green ones) from step 0 to step 2. Nevertheless, our method still yields satisfactory segmentation results after step 3. Similar results can be observed in other images. Figure 6 explicitly presents the Dice score for each class at every step." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 176, + 545, + 300 + ], + "blocks": [ + { + "bbox": [ + 307, + 176, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 307, + 176, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 307, + 176, + 545, + 300 + ], + "type": "image", + "image_path": "2390ae8b8b006b60ef357598c0390f5f134efc97fa29c56ab96d2bf0cdabfce2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 308, + 545, + 331 + ], + "lines": [ + { + "bbox": [ + 305, + 308, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 545, + 331 + ], + "type": "text", + "content": "Figure 6. Values of Dice metric for each class at different incremental steps on MoNuSAC 1-1." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 350, + 400, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 400, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 400, + 363 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "type": "text", + "content": "We verify the effectiveness of the proposed method using 1-1 and 3-1 setups on MoNuSAC. From Table 3, we can find that the performance of PLOP + EWF surpasses that of PLOP. Only adding future-class awareness (FCA) can further boost the performance of EWF across different setups. After applying compatibility-inspired distillation (CID), we obtain the highest performance on MoNuSAC. In particular, the performance of PLOP + EWF + FCA + CID outperforms that of PLOP + EWF in 1-1 settings, with a great improvement of " + }, + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "type": "inline_equation", + "content": "3.54\\%" + }, + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "type": "text", + "content": " in old classes and " + }, + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "type": "inline_equation", + "content": "1.97\\%" + }, + { + "bbox": [ + 304, + 368, + 545, + 535 + ], + "type": "text", + "content": " in new classes. These results effectively demonstrate that both proposed modules can effectively improve the plasticity and stability of the model, thereby improving the overall performance." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 310, + 542, + 544, + 632 + ], + "blocks": [ + { + "bbox": [ + 46, + 642, + 287, + 664 + ], + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 664 + ], + "type": "text", + "content": "Table 2. Incremental semantic segmentation results (mDice) on the CoNSeq dataset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 542, + 544, + 632 + ], + "lines": [ + { + "bbox": [ + 310, + 542, + 544, + 632 + ], + "spans": [ + { + "bbox": [ + 310, + 542, + 544, + 632 + ], + "type": "table", + "html": "
Method1-1 (4 tasks)3-1 (2 tasks)
OldNewMeanOldNewMean
PLOP60.1465.6064.2366.1677.4368.97
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", + "image_path": "48b1b063cbd3b27b9235315efd0689b654868db7621e58189d878c3b2c73d5d9.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 639, + 545, + 650 + ], + "lines": [ + { + "bbox": [ + 306, + 639, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 545, + 650 + ], + "type": "text", + "content": "Table 3. Ablation study results (mDice) on the MoNuSAC dataset." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 671, + 409, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 409, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 409, + 684 + ], + "type": "text", + "content": "4.3. Further Analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Future-class Awareness. To better understand how prelearning of future classes enhances the results, we visual-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11414" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "ize t-SNE distribution of features generated from the baseline and baseline " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "+" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " FCA. As shown in Figure 7, the base" + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 106, + 286, + 218 + ], + "blocks": [ + { + "bbox": [ + 50, + 106, + 286, + 218 + ], + "lines": [ + { + "bbox": [ + 50, + 106, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 50, + 106, + 286, + 218 + ], + "type": "image", + "image_path": "ea0eac70587190c338631bf7f8f256e9e74ad3a046df8c2a83fa53dfb120b347.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 225, + 287, + 249 + ], + "lines": [ + { + "bbox": [ + 47, + 225, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 47, + 225, + 287, + 249 + ], + "type": "text", + "content": "Figure 7. T-SNE visualization of features learned by Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 262, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 288, + 323 + ], + "type": "text", + "content": "line tends to generate more ambiguous features while the baseline " + }, + { + "bbox": [ + 46, + 262, + 288, + 323 + ], + "type": "inline_equation", + "content": "+\\mathrm{FCA}" + }, + { + "bbox": [ + 46, + 262, + 288, + 323 + ], + "type": "text", + "content": " is able to learn more discriminative features. These robust features then help the model to resist catastrophic forgetting better. Similar conclusions can be drawn from the feature map (Figure 8). The baseline model" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 48, + 332, + 287, + 488 + ], + "blocks": [ + { + "bbox": [ + 48, + 332, + 287, + 488 + ], + "lines": [ + { + "bbox": [ + 48, + 332, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 48, + 332, + 287, + 488 + ], + "type": "image", + "image_path": "1ae1bb079fb8fa4bda24cea40be98c96e5173ee9b72df904237beddf52fdb7f5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 498, + 287, + 520 + ], + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 520 + ], + "type": "text", + "content": "Figure 8. Feature maps of the Baseline and Baseline + FCA at final incremental step on MoNuSAC 1-1." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 286, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 286, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 286, + 617 + ], + "type": "text", + "content": "exhibits a lower response to target features and is prone to generating erroneous high responses in the background, whereas the baseline with FCA generates more accurate and higher responses to target features. This phenomenon further shows that training with FCA can enhance the representation power to alleviate knowledge forgetting and reserve more parameter space to be updated." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "Compatibility-inspired Distillation. As shown in Table 4, slightly increasing both " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{n}" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{b}" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " to 1 can improve the performance of both new and old classes. However, a large value of " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{n}" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": ", e.g., " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{n} = 5" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " leads the model to focus excessively on new classes, compromising the performance of old classes and thus negatively affecting overall performance. Similarly, when we set " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{b}" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " a high value 3, the model tends to overly remember old classes and overlook the new classes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "In our experiments, we achieve the best performance when " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\alpha_{n}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\alpha_{b}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " are set to 3 and 1, respectively. For additional ablation studies and detailed analytical experiments, please refer to the supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 312, + 132, + 543, + 265 + ], + "blocks": [ + { + "bbox": [ + 312, + 132, + 543, + 265 + ], + "lines": [ + { + "bbox": [ + 312, + 132, + 543, + 265 + ], + "spans": [ + { + "bbox": [ + 312, + 132, + 543, + 265 + ], + "type": "table", + "html": "
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", + "image_path": "533f20239df4367ad17418f829c6770c36ca5ef6b26d8101869f7d9b888a0457.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "lines": [ + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "spans": [ + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "type": "text", + "content": "Table 4. Effect of the weighted factors " + }, + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "type": "inline_equation", + "content": "{\\alpha }_{n}" + }, + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "type": "inline_equation", + "content": "{\\alpha }_{b}" + }, + { + "bbox": [ + 334, + 274, + 517, + 285 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 313, + 375, + 325 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 313, + 375, + 325 + ], + "spans": [ + { + "bbox": [ + 306, + 313, + 375, + 325 + ], + "type": "text", + "content": "5. Limitation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 334, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 441 + ], + "type": "text", + "content": "We develop our method based on the attributes of histopathological images, where future classes in the dataset exhibit visual similarities to the learned classes. Therefore, our approach may not perform optimally in datasets where future classes significantly differ from the learned classes, which necessitates further research. Nevertheless, considering the vast diversity of cancer cell types, our method shows promise in enhancing computer-aided diagnosis systems with more robust incremental updating capabilities." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 455, + 378, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 378, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 378, + 467 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 475, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 608 + ], + "type": "text", + "content": "In this work, we present a novel method for incremental semantic segmentation from histopathological images, aiming to solve catastrophic forgetting without storing samples of previous data. First, we propose a new future-class awareness approach that detects future classes in an unsupervised way. Second, drawing inspiration from software engineering, we introduce an innovative compatibility-inspired knowledge distillation to make the new model take full advantage of the knowledge learned by the old model. Finally, comparative experiments and ablation studies clearly demonstrate the effectiveness of the proposed method." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 620, + 403, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 620, + 403, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 620, + 403, + 634 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "This work was supported partly by National Natural Science Foundation of China (No. 62273241), Natural Science Foundation of Guangdong Province, China (No. 2024A1515011946), and the Theme-based Research Scheme from Hong Kong Research Grants Council (project no. T45-401/22-N)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11415" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 3082-3092, 2023. 1, 2" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11417" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_content_list.json b/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2b66a4b03982171a106cb72d1bc46ca3c69f7fc0 --- /dev/null +++ b/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_content_list.json @@ -0,0 +1,1694 @@ +[ + { + "type": "text", + "text": "Incremental Residual Concept Bottleneck Models", + "text_level": 1, + "bbox": [ + 233, + 130, + 736, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chenming Shang $^{12*}$ Shiji Zhou $^{1}$ Hengyuan Zhang $^{1}$ Xinzhe Ni $^{1}$ Yujiu Yang $^{1\\dagger}$ Yuwang Wang $^{12\\dagger}$ Tsinghua University Shanghai AI Laboratory", + "bbox": [ + 86, + 178, + 916, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{scm22@mails.,zhoushiji@mail.,zhang-hy22@mails.}tsinghua.edu.cn", + "bbox": [ + 220, + 219, + 777, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{nxz22@mails.,yang.yujiu@sz.,wang-yuwang@mail.}tsinghua.edu.cn", + "bbox": [ + 222, + 236, + 769, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Concept Bottleneck Models (CBMs) map the black-box visual representations extracted by deep neural networks onto a set of interpretable concepts and use the concepts to make predictions, enhancing the transparency of the decision-making process. Multimodal pre-trained models can match visual representations with textual concept embeddings, allowing for obtaining the interpretable concept bottleneck without the expertise concept annotations. Recent research has focused on the concept bank establishment and the high-quality concept selection. However, it is challenging to construct a comprehensive concept bank through humans or large language models, which severely limits the performance of CBMs. In this work, we propose the Incremental Residual Concept Bottleneck Model (ResCBM) to address the challenge of concept completeness. Specifically, the residual concept bottleneck model employs a set of estimizable vectors to complete missing concepts, then the incremental concept discovery module converts the complemented vectors with unclear meanings into potential concepts in the candidate concept bank. Our approach can be applied to any user-defined concept bank, as a posthoc processing method to enhance the performance of any CBMs. Furthermore, to measure the descriptive efficiency of CBMs, the Concept Utilization Efficiency (CUE) metric is proposed. Experiments show that the Res-CBM outperforms the current state-of-the-art methods in terms of both accuracy and efficiency and achieves comparable performance to black-box models across multiple datasets.", + "bbox": [ + 76, + 318, + 473, + 743 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 773, + 209, + 789 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks (DNNs) [31, 45] have achieved unprecedented success in a wide range of machine learning tasks, including computer vision [16, 32], natural language processing [14, 59], and speech recognition [34, 41].", + "bbox": [ + 76, + 800, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b584f311df233e268cbea997fc3b4237633a1711c6075fef927fadd07ace8bc.jpg", + "image_caption": [ + "Figure 1. Challenges in CBMs. When a concept contains many atomic attributes, making it too complex for human to comprehend. When a concept is too high-level, DNNs may struggle to provide accurate prediction. Additionally, there is a risk of human-designed concept bank missing some important concepts." + ], + "image_footnote": [], + "bbox": [ + 504, + 284, + 890, + 373 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, due to their complex and deep structures, they are often regarded as black-box models [7, 49], which are too difficult to understand and interpret. In fields that demand high levels of trustworthiness, such as medicine [44], healthcare [21], education [60], and finance [39], model interpretability has become increasingly crucial. It indicates whether we can trust the DNNs' decisions, and how we can rectify the errors when the DNNs make mistakes. Making deep learning models more interpretable is a significant yet challenging research topic.", + "bbox": [ + 496, + 486, + 892, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A promising approach for achieving interpretability in deep learning is through concept-based models [46], which leverage human-generated high-level concepts to explain the black-box features of DNNs. Among these approaches, Concept Bottleneck Models (CBMs) [26] map the visual representations to a set of concept values that are understandable to humans. These interpretable concepts are then used to make the final decision by a linear function, greatly enhancing our understanding of the decision-making process. Of greater significance, humans can repair models' faults by directly editing or intervening on the concept bottleneck [3, 48].", + "bbox": [ + 496, + 640, + 893, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the considerable cost of the fine-grained and precise annotation for each concept in CBMs, multimodal pretrained model-based CBMs [58] have recently emerged as a research hotspot. CLIP [40] demonstrates the capacity to establish correspondences between visual information and", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Shanghai AI Laboratory.", + "bbox": [ + 94, + 875, + 415, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 222, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11030", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "textual descriptions. Accordingly, we can utilize the CLIP text encoder to encode human-understood concepts into concept embeddings and use the visual encoder to encode images into visual representations. By projecting visual representations to each concept embedding, we can obtain the concept bottleneck. The recent innovations have primarily concentrated on comprehensive concept bank establishment and efficient high-quality concept selection. However, these methods face three critical challenges as shown in Fig.1:", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Purity: The essence of concepts is to abstract complex information into a combination of simple foundational elements, which can generalize to unseen data through the infinite combinations of finite concepts, offering an efficient way to describe the world. Long and complex descriptions like small, black insect with six legs or long, thin tool with a wooden handle, can be composed entirely of combinations of simple concepts such as small, black, insect, leg, etc., which may increase the productivity of concept utilization. Since these complicated concepts are excessively detailed, they may not be shared across different classes, which will limit their ability to capture shared knowledge between different categories.", + "- Precision: Each concept should be clearly understandable for both humans and multimodal pre-trained models when annotating concepts. Specifically, concepts should not be markedly more difficult than classes. For example, high-level concepts like amphibians or perennial, are relatively harder for humans to understand and exhibit weaker interpretability. Moreover, we cannot ascertain whether CLIP possesses the capability to understand these high-level concepts, which can potentially lead to errors in concept annotation.", + "- Completeness: Concept bank should strive to include as much relevant visual information that is beneficial for downstream classification tasks as possible. It is essential to avoid losing too much information in the process. However, it is challenging to establish a comprehensive concept bank directly [57]. The exhaustive capability of language descriptions is limited, making it difficult to accomplish a fully thorough concept bank through manual design and selection." + ], + "bbox": [ + 76, + 246, + 472, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose the Incremental Residual Concept Bottleneck Model (Res-CBM) to address the three challenges above. First, we establish a simple and pure base concept bank and candidate concept bank to ensure that the CLIP can accurately recognize each concept. Next, we initialize a set of estimizable vectors as filling concepts and optimize this set of filling concepts through the residual concept bottleneck model, to make up for the inadequacy in the base concept bank. Finally, the incremental concept discovery module is utilized to translate these complemented vectors with unclear meanings into potential concepts in the", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "candidate concept bank, improving the performance while preserving the interpretability of the CBM. Our main contributions can be summarized as follows:", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We systematically reviewed the research on the CLIP-based CBMs, clarifying the importance of the concepts' purity, precision, and completeness.", + "2. We proposed the residual concept bottleneck model to make up for the insufficiency in the base concept bank and converted these complemented unknown vectors into potential concepts in the candidate concept bank through the incremental concept discovery module. It should be emphasized that our approach can be applied to any user-defined concept bank, as a post-hoc processing method to enhance the performance of any CBMs.", + "3. To measure the descriptive efficiency of CBMs, we introduced the metric of the concept utilization efficiency. We performed extensive experiments to validate our methodology and elaborate ablation studies to illustrate the effectiveness of each component." + ], + "bbox": [ + 500, + 137, + 893, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 391, + 640, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep neural networks (DNNs) can be explained through pixels [8, 47], samples [15, 22], weights [54], individual neurons [5, 13], subnetworks [2, 12], representations [4, 19, 20], etc [43]. Concept-based models [23, 33, 52, 53] are representation-level interpretable approaches, whose core idea is to map representations with unknown meanings extracted by the black-box DNNs to a set of concepts that can be comprehended by humans [9, 11, 35, 36]. Concept-based models can be broadly categorized into Concept Bottleneck Models (CBMs) [26], which describe concepts as independent values annotated by experts, and Concept Activation Vectors (CAVs) [24], which represent concepts as normal vectors of the decision boundaries that distinguish positive and negative samples of a concept. CBMs involve the datasets labeled with fine-grained and precise attributes by expert knowledge, such as CUB-200 [18], OAI [10], and LAD [61], whereas CAVs require learning the concept activation vectors on additional probe datasets, and the directions of the concept activation vectors are strictly correlated with the probe datasets [42]. These limitations severely restrict the development of concept-based models.", + "bbox": [ + 496, + 417, + 893, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, there has been a rapid development of multimodal pre-trained models [17], among which CLIP does an excellent job of relating visual information to text through contrastive learning, giving researchers confidence for unsupervised concept labeling with CLIP. PCBM [58] generates a concept bank via ConceptNet [50] and calculates the projection distance between the CLIP textual concept embeddings and the CLIP visual representations of images, analogous to the CAVs, to obtain the concept bottleneck. PCBM-h [58] introduces an uninterpretable residual linear layer to compensate for incomplete concept extraction by", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11031", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e026e67dc6d2b76b6d9dbfa5864e7019d8905c4000defeb73a338bde51f0bd7e.jpg", + "image_caption": [ + "Figure 2. Different CBMs' structures. (a): CLIP linear probing [40]. (b): Original Concept Bottleneck Model (CBM) [26]. (c) Post-hoc Concept Bottleneck Model (PCBM) [38, 56, 58]. (d): Hybrid Post-hoc Concept Bottleneck Model (PCBM-h) [58]." + ], + "image_footnote": [], + "bbox": [ + 163, + 88, + 810, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fitting the difference between the PCBM's result and the ground truth through the original visual representations of CLIP. Label-free CBM [38] only leverages CLIP to concept annotation, maximizing the similarity between the concept bottleneck of the features extracted by arbitrary visual backbone and the concept annotations labeled by CLIP. LaBo [56] generates a set of candidate concepts through large language models and designs a submodular optimization block to select the concepts.", + "bbox": [ + 75, + 412, + 473, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 566, + 171, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 590, + 281, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a dataset of image-label pairs $\\mathcal{D} = \\{(x,y)\\}$ , where $x\\in \\mathcal{X}$ is the image and $y\\in \\mathcal{Y}$ is the label. We have $N$ human-selected concepts to describe the essential information of these images, which can be denoted as discrete tokens $\\mathcal{E} = \\{e_1,e_2,\\dots,e_N\\}$ . Multimodal pre-trained alignment model (e.g., CLIP [40]) has an image encoder $\\Phi_I:\\mathcal{X}\\to \\mathbb{R}^d$ and a text encoder $\\Phi_T$ , which can map images and text into a shared $d$ -dimensional feature space respectively. We encode the discrete tokens with the CLIP text encoder then perform $L_{2}$ normalization to obtain the concept embeddings $\\{w_{1},w_{2},\\ldots ,w_{N}|w_{i} = \\Phi_{T}(e_{i}),i = 1,2,\\ldots ,N\\}$ with the length of 1 and the dimension of $d$ . We concatenate these concept embeddings to a concept projection matrix $W_{N\\times d}:\\mathbb{R}^d\\to \\mathbb{R}^N$ in arbitrary order, also identified as a concept bank.", + "bbox": [ + 75, + 614, + 468, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Correspondingly, we utilize the CLIP image encoder to get the visual representations $f = \\Phi_I(x)$ . Considering that", + "bbox": [ + 76, + 843, + 470, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CLIP has aligned the images with the textual data when pretraining, the visual representations share the feature space with any concept embedding, and the projection length $\\| f\\| _2\\cdot \\cos \\langle w_i,f\\rangle$ can reflect the presence of a particular concept in the image. Since undergoing $L_{2}$ normalization on $w_{i}$ , the concept probability can be directly formulated in terms of the dot product $c = W\\cdot f$", + "bbox": [ + 496, + 412, + 892, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig.2 illustrates the structure of common CBMs. For CLIP Linear Probing [29], an uninterpretable linear classifier $\\Psi : \\mathbb{R}^d \\to \\mathcal{V}$ is trained directly from visual representations:", + "bbox": [ + 496, + 518, + 893, + 578 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\Psi (f) = \\Psi \\left(\\Phi_ {I} (x)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 579, + 890, + 597 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Original CBM [26] first extracts concepts using a concept extractor $\\Psi_{\\mathrm{cpt}}: \\mathbb{R}^d \\to \\mathbb{R}^N$ and then linearly unites the extracted concepts for label prediction by concept classifier $\\Psi_{\\mathrm{cls}}: \\mathbb{R}^N \\to \\mathcal{V}$ .", + "bbox": [ + 496, + 599, + 890, + 660 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\Psi_ {\\mathrm {c l s}} \\left(\\Psi_ {\\mathrm {c p t}} (f)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 667, + 890, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Post-hoc CBM [58] stands for a category of CLIP-based CBMs, including Label-free CBM [38], LaBo [56], etc. They attain concept bottleneck by projecting visual representations $f$ directly to a concept bank $W$ , rather than by learning a concept extractor. After getting concepts, only a linear concept classifier $\\Psi_{c}:\\mathbb{R}^{N}\\to \\mathcal{V}$ needs to be learned.", + "bbox": [ + 496, + 691, + 893, + 782 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\Psi_ {c} (c) = \\Psi_ {c} (W \\cdot f) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 796, + 890, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PCBM-h [58] adds a linear layer $\\Psi_r: \\mathbb{R}^d \\to \\mathcal{Y}$ between the original visual representation and the labels on the basis of PCBM, which is used to predict the difference between the PCBM result and the ground truth.", + "bbox": [ + 496, + 815, + 893, + 878 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\Psi_ {c} (c) + \\Psi_ {r} (f) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (f) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 883, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1The symbol of $L_{2}$ normalization is omitted for writing convenience.", + "bbox": [ + 94, + 886, + 460, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11032", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Concept Bank Establishment", + "text_level": 1, + "bbox": [ + 76, + 90, + 336, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Candidate Concept Bank. To ensure precision, we need to make sure that CLIP is capable of recognizing each concept, and one straightforward way is to construct the concept bank from the CLIP pre-trained dataset. For purity, it is desirable for each concept to be at the atom level rather than the compound level, thus maintaining the clarity and specificity. We find that the scene graph [27] consisting of visual concepts to be an appropriate foundation, in which an atom is defined as a singular visual concept, corresponding to a single scene graph node. Atoms are subtyped into objects, relationships, and attributes. We pick the nouns and adjectives in them as the candidate concept bank $\\mathcal{E}^*$ .", + "bbox": [ + 75, + 114, + 468, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Base Concept Bank. Although our method can recover missing concepts from a diverse base concept bank, a high-quality base concept bank can remarkably improve the efficiency of our approach. A base concept bank is expected to consist of two parts. Firstly, it should include general concepts that are applicable across various scenarios. We select the pre-defined concept library proposed by [24], which has been widely used in various tasks [1, 55], as our general concept bank $\\mathcal{E}_{\\mathrm{ge}}$ . Secondly, it is supposed to include concepts relevant to the specific classification task. Following the PCBM [58], we collect all concepts from ConceptNet [50] that have relations of hasA, isA, partOf, HasProperty, and MadeOf with the classes in each classification task to build the associated concept bank $\\mathcal{E}_{\\mathrm{as}}$ . Both concept banks should be included in the candidate concept bank, from which we can derive the base concept bank:", + "bbox": [ + 75, + 296, + 470, + 537 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} _ {0} = \\left(\\mathcal {E} _ {\\mathrm {g e}} \\cap \\mathcal {E} ^ {*}\\right) \\cup \\left(\\mathcal {E} _ {\\mathrm {a s}} \\cap \\mathcal {E} ^ {*}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 550, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We encode the discrete concept tokens with the CLIP text encoder then perform $L_{2}$ normalization to obtain the base and candidate concept embedding matrices:", + "bbox": [ + 76, + 580, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW _ {0} = \\Phi_ {T} \\left(\\mathcal {E} _ {0}\\right), \\quad W ^ {*} = \\Phi_ {T} \\left(\\mathcal {E} ^ {*}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 638, + 468, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Residual Concept Bottleneck Model", + "text_level": 1, + "bbox": [ + 76, + 679, + 387, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Previous methods have typically involved pre-generating a set of relevant concepts and then deleting some of them to get the final concept bank. However, on the one hand, the pre-generated concepts might be insufficient, as their scale has often limitations. On the other hand, manual filtering without leveraging dataset information may result in the omission of important concepts. Therefore, we propose the residual concept bottleneck model to learn the missing concepts from the dataset content in an incremental approach compared to other decremental methods as shown in Fig.3.", + "bbox": [ + 75, + 703, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first randomly initialize $D$ estimizable vectors $U_{D\\times d} = \\{u_1,u_2,\\dots,u_D\\}$ with dimensions consistent with those of the existing concept embeddings. We likewise", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/318aeaf76579714c5f9a830f5530045deec985f0a5d599033a03548dafcdb562.jpg", + "image_caption": [ + "Figure 3. Incremental Residual Concept Bottleneck Model." + ], + "image_footnote": [], + "bbox": [ + 506, + 92, + 885, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "project the visual representations onto these vectors, resulting in residual concepts $r = U \\cdot f$ with unclear meanings. The prediction result of using the residual concepts to complement the original concepts is as follows:", + "bbox": [ + 498, + 414, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\Psi_ {c} (c) + \\Psi_ {r} (r) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (U \\cdot f) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 484, + 890, + 502 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Psi_c: \\mathbb{R}^N \\to \\mathcal{Y}$ is the original concept linear classifier using existing concepts and $\\Psi_r: \\mathbb{R}^D \\to \\mathcal{Y}$ is the residual concept linear classifier using unknown residual concepts.", + "bbox": [ + 498, + 512, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For one thing, we intend to maximize the accuracy when using only the original concepts, which can be formulated as the following optimization problem:", + "bbox": [ + 498, + 558, + 890, + 603 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Psi_ {c}} \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} \\left[ \\mathcal {L} \\left(\\Psi_ {c} (W \\cdot \\Phi_ {I} (x)), y\\right) \\right] + \\lambda \\cdot \\Omega (\\Psi_ {c}) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 613, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}(\\hat{y}, y)$ is the cross-entropy loss function, $\\Omega(\\Psi_c)$ is a complexity measure to regularize the model, and $\\lambda$ is the regularization strength.", + "bbox": [ + 498, + 652, + 890, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From another perspective, we aim to improve the performance after incorporating the residual concepts, which can be solved by the following optimization problem:", + "bbox": [ + 498, + 699, + 890, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Psi_ {r}, U} \\underset {(x, y) \\in \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} \\left(\\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (U \\cdot f), y\\right) \\right] + \\lambda \\cdot \\Omega (\\Psi_ {r}) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 753, + 890, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f = \\Phi_I(x)$", + "bbox": [ + 500, + 795, + 624, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To simultaneously address these two problems, we perform two forward and backward propagations in each batch to update the parameters. When performing the first propagation, we utilize only the original concepts to optimize the original concept classifier $\\Psi_{c}$ . During the second propagation, we fix the parameters of the original concept classifier", + "bbox": [ + 498, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11033", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\Psi_{c}$ and optimize the residual concept classifier $\\Psi_{r}$ as well as the learnable unknown concept vectors $U$ using both the original and the residual concepts.", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To avoid the influence of extreme values from unknown residual concepts, we employ cosine similarity instead of projection distance as the concept bottleneck and standardize the activations of each concept to have a mean of 0 and a standard deviation of 1 to speed up convergence [38]. These operations are reversible and do not affect the relative order of concepts or introduce additional information.", + "bbox": [ + 75, + 136, + 470, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Incremental Concept Discovery", + "text_level": 1, + "bbox": [ + 76, + 251, + 354, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through the aforementioned steps, the residual concepts effectively compensate for the incompleteness of the original concepts. However, these randomly learned concepts lack human interpretability, so we next translate them into human-understandable concepts.", + "bbox": [ + 75, + 273, + 468, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Parameters Initialization. We first initialize another estimizable vector $v_{d}$ , denoted as the discovered concept vector, whose value is the mean concept embeddings of the base concept bank with added noise. Subsequently, we append the discovered concept vector to the base concept bank and remove one of the learned unknown residual concept vectors, whose residual concept embedding matrix changes to $U_{-v_d} = U_{(D - 1)\\times d}$ and residual classifier changes to $\\Psi_{r - v_d}:\\mathbb{R}^{D - 1}\\to \\mathcal{V}$ . After performing $L_{2}$ normalization and projection, the visual representations will also obtain a similarity score $c_{d} = v_{d}\\cdot f$ to the discovered concept vector, and there will be a corresponding discovered concept linear classifier $\\Phi_d:\\mathbb{R}\\rightarrow \\mathcal{V}$ . We adopt the language priors as the initial weights to ensure stable updating of the discovered concept vector. In particular, the weights of the discovered concept classifier are initialized as the cosine similarity between the discovered concept embedding and the text embeddings for each class name, while other parameters and weights are kept untouched.", + "bbox": [ + 75, + 349, + 468, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Concept Similarity Loss Function. After adding the discovered concept vector to the base concept bank, the prediction under the original and residual strategy is as follows:", + "bbox": [ + 75, + 637, + 468, + 683 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {\\text {o r g}} = \\Psi_ {c} (c) + \\Psi_ {d} \\left(c _ {d}\\right) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {d} \\left(v _ {d} \\cdot f\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 709, + 467, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {\\text {r e s}} = \\hat {y} _ {\\text {o r g}} + \\Psi_ {r - v _ {d}} \\left(U _ {- v _ {d}} \\cdot f\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 728, + 467, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further guarantee that the discovered concept vector is interpretable, we propose the concept similarity loss function $\\mathcal{L}_{\\mathrm{sim}}$ , which utilizes the candidate concept bank $W^{*}$ to constrain the discovered concept embedding:", + "bbox": [ + 76, + 755, + 468, + 816 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i m}} = 1 - \\mathbb {E} \\left[ \\operatorname {R a n k} \\left(W ^ {*} \\cdot \\frac {v _ {d} ^ {T}}{\\| v _ {d} \\| _ {2}}, M\\right) \\right] \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 825, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\operatorname{Rank}(v, M)$ denotes sorting $v$ from largest to smallest and selecting the first $M$ of them.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Referring to the update strategy of the residual concept bottleneck model, we just add the discovered concept with its classifier during the first pass propagation:", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Psi_ {c}, \\Psi_ {d}, v _ {d}} \\mathbb {E} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\text {o r g}}, y\\right) \\right] + \\alpha \\cdot \\mathcal {L} _ {\\text {s i m}} + \\lambda \\cdot \\Omega \\left(\\Psi_ {c}, \\Psi_ {d}\\right) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 141, + 890, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is the weight of the concept similarity loss.", + "bbox": [ + 500, + 170, + 841, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When performing the second propagation, we fix the parameters of the original concept classifier $\\Psi_{c}$ , the discovered concept classifier $\\Psi_{d}$ , and the discovered concept embedding $v_{d}$ , optimizing the residual concept classifier $\\Psi_{r - v_d}$ and the unknown residual concept vectors $U_{-v_d}$ :", + "bbox": [ + 498, + 185, + 890, + 261 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Psi_ {r - v _ {d}}, U - v _ {d}} \\mathbb {E} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\text {r e s}}, y\\right) \\right] + \\lambda \\cdot \\Omega \\left(\\Psi_ {r - v _ {d}}\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 265, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We recover concepts in an incremental way until all the learned unknown residual concept vectors are transformed into pure, accurate, and human-interpretable concepts. At this point, the base concept library is fully updated, and experiments confirm its superior completeness.", + "bbox": [ + 498, + 296, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 383, + 633, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 407, + 689, + 424 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We conduct comprehensive experiments on 7 datasets, including: CIFAR-10, CIFAR-100 [28], TinyImageNet [30], LAD [61], CUB-200 [51], Food-101 [6], Flower-102 [37]. For a fair comparison, we apply CLIPRN50 when comparing with other CBMs and CLIP-ViT-L/14 on few-shot classification tasks as the backbone, and all linear classifiers are optimized with the Adam [25] optimizer. For more detailed information, please refer to the supplementary material.", + "bbox": [ + 498, + 431, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. To evaluate our proposed approach, we compare it with the following baseline methods:", + "bbox": [ + 498, + 566, + 890, + 597 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- CLIP Zero-shot[40]: the cosine similarities between the visual representations and the textual embeddings of each class name are calculated directly without any training. The class with the highest cosine similarity score is selected as the final classification result.", + "- Linear Probing (LP)[40]: We exclusively utilize the CLIP visual encoder and the obtained visual representations are then used to predict the label by training a linear classifier.", + "- Original CBM[26]: The original CBM relies on fine-grained concept annotations, so we compare our method with it only on LAD and CUB with available attribute annotations. In addition, CBMs may suffer from concept leakage, which can only be alleviated by CBMs trained independently [36]. Hence, we choose CBM-independent as the baseline for comparison.", + "- PCBM[58]: PCBM uses the ConceptNet[50], a knowledge graph dataset, to conduct a concept bank. It treats classes as nodes and incorporates surrounding neighboring nodes in the concept bank. More concepts can be included by expanding multiple layers outwards." + ], + "bbox": [ + 500, + 598, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11034", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2bfa2a86977322d1d75f4e3fa4e3f534ca60b75726ed5b1c8f2e346358f45076.jpg", + "table_caption": [ + "Table 1. Comparison with other CLIP-based CBMs. Bold indicates the best interpretable result, underline indicates the 2nd-best result, italic indicates the black-box methods." + ], + "table_footnote": [], + "table_body": "
MethodInterpretabilityLengthCIFAR 10CIFAR 100
AccuracyNumberCUEAccuracyNumberCUE
Zero-shotYesN/A0.6796N/AN/A0.2620N/AN/A
LPNoN/A0.8858N/AN/A0.6995N/AN/A
PCBM-1rYes90.80441755.10730.53794401.3583
PCBM-2rYes90.80743832.34230.545011750.5153
PCBM-3rYes90.820810580.8620N/AN/AN/A
PCBM-hNo90.8757175N/A0.6683440N/A
Lf-CBMYes120.86771435.05650.67458920.6301
LaBo-10cYes270.84891003.14410.661810000.2451
LaBo-20cYes270.86692001.60540.673620000.1247
LaBo-30cYes260.87523001.1221N/AN/AN/A
Res-CBMYes70.8803237+105.09140.6791372+152.5396
", + "bbox": [ + 78, + 128, + 893, + 308 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b6eca2518e5d1af366eee9e48569554b4b5f1dc98499ba93bc363e9f8cd374d8.jpg", + "table_caption": [ + "Table 2. Comparison with CBMs with labeled concept annotations. The labeling significance is consistent with Tab.1." + ], + "table_footnote": [], + "table_body": "
MethodLAD-ALAD-ELAD-FLAD-HLAD-VCUBMean
LP0.94320.86610.73930.49240.86710.72140.7714
Original CBM0.89640.78260.55350.33880.79070.65130.6689
PCBM-annotation0.89340.77110.59820.29820.78140.63630.6631
Res-CBM-before0.78970.77090.43560.14290.75480.59870.5812
Res-CBM-after0.89790.80450.66240.38620.83010.62430.7009
", + "bbox": [ + 132, + 345, + 834, + 436 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- PCBM-h[58]: After training the PCBM, PCBM-h is applied as a post-processing method that connects the visual representation and the class labels result through shortcuts. It utilizes a linear classifier to predict the difference between the result of PCBM and the ground truth.", + "- Lf-CBM[38]: In contrast to PCBM, Lf-CBM generates concepts through a large language model (LLM). It solely utilizes CLIP as the concept annotator, allowing it to act on any visual backbone. We directly select CLIP as the visual backbone, thus omitting the process of computing the similarity matrix.", + "- LaBo[56]: LaBo similarly applies the LLM to generate candidate concepts. However, the quantity of concepts in LaBo is specific to each class. So we generate 10, 20, and 30 concepts per class to compare the performance. In addition, LaBo's linear classifier differs from the above baselines. To evaluate the quality of concepts equitably, we choose the same classifier as the above methods." + ], + "bbox": [ + 76, + 460, + 468, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Besides accuracy, we also concentrate on concepts' efficiency, including both the average length of each concept and quantity of concepts. Specifically, we define the accuracy improvement brought by all concepts' length to measure the Concept Utilization Efficiency (CUE):", + "bbox": [ + 75, + 734, + 470, + 810 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {C U E} = \\frac {1 0 0 0 0 \\times \\mathrm {A c c}}{N \\times \\bar {L}} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 816, + 468, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{Acc}$ is the classification accuracy, $N$ is the quantity of concepts and $\\bar{L}$ is the average number of letters included in each concept. Larger CUE means higher efficiency.", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Accuracy and Efficiency", + "text_level": 1, + "bbox": [ + 498, + 459, + 723, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with other CBMs in terms of accuracy and efficiency. Tab.1 provides the results of our method compared to other CLIP-based CBMs. Res-CBM attains higher accuracy than PCBM by $5.95\\%$ on CIFAR-10 and $13.41\\%$ on CIFAR-100 and even outperforms the inexplicable PCBM-h. Despite Lf-CBM and LaBo being powerful baselines, our methodology still achieves state-of-the-art results. Particularly, it should be noted that our method considerably exceeds both Lf-CBM and LaBo in terms of efficiency, as evidenced by the CUE metric.", + "bbox": [ + 496, + 484, + 893, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On LAD and CUB-200 with attribute annotations, we still use CLIP-50 with frozen parameters as the visual backbone to train Original CBM according to formula (2), as the results are shown in Tab.2. $^{3}$ The close performance of the Original CBM and PCBM-annotation suggests that the CBMs' performance heavily relies on the expert-selected concepts more than the model structure. Although Res-CBM-before performs poorly, a remarkable improvement is observed in Res-CBM-after after applying our unsupervised incremental concept discovery, which even surpasses supervised CBMs with concept annotations on most datasets.", + "bbox": [ + 496, + 638, + 893, + 806 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ PCBM-#r represents expanding outward to include neighboring nodes # times. LaBo-#c represents selecting # concepts per class.", + "bbox": [ + 500, + 825, + 890, + 851 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "${}^{3}$ PCBM-annotation refers to PCBM that utilizes the textual embeddings of the annotated attributes as the concept bank. Res-CBM-before indicates the performance on the initial base concept bank. Res-CBM-after represents the performance after incremental concept discovery.", + "bbox": [ + 500, + 851, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11035", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a80dec07964a41a7194270cbc6a07070c3ca2ab81db8be0df7da7520f4b8d7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 93, + 354, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6453bd78e832b4bc5477907b925a18c8f5a942c20a3465fc37fa81872882a3df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 93, + 607, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/87b000cc3f4823c433e7a1f5de40c28ae0c2ef1717a127a2c0216289b3968fc6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 94, + 864, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d2cffb1373e6c8fc668b82fe71ab55591bca988c2d87c428ccc00a04e81862e3.jpg", + "image_caption": [ + "Figure 4. Test accuracy $(\\%)$ comparison between Res-CBM and LP on 6 datasets. The x-axis represents the number of labeled images." + ], + "image_footnote": [], + "bbox": [ + 102, + 209, + 354, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/db9d49c3f08dfeffa6e9bbdc81bcdcee87a8724fb3aa2fa4259f777441370d82.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 209, + 607, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9996cab42b178f26a64aac5685a427fe3eff1110de64e54686a6f7c887cdf586.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 209, + 864, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/255afeca3b59d4b4887ff40c0fbdb76ff9d54b8a6145dca4553fb0b35bba80f4.jpg", + "image_caption": [ + "Figure 5. Ablation results on residual vector numbers, concept similarity loss weights and candidate concept numbers." + ], + "image_footnote": [], + "bbox": [ + 102, + 369, + 338, + 486 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d9703afb8b9339990d1db65d1de87e1f79e7417cb3a6c1939e14ba154a94bc2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 369, + 609, + 484 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3af79f11e4a84c2fd32f5a96cad420e6e3299cbd24780ebc2d7f0a0cd59f9261.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 369, + 867, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Interpretability", + "text_level": 1, + "bbox": [ + 76, + 539, + 232, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we visualize the mechanism of ResCBM and demonstrate how the newly discovered concepts assist in advancing classification performance. For each image, we display the top 5 concepts with the highest activation scores in the concept bottleneck, as shown in Fig.6. Through a sparse concept classifier, we can obtain predictions, which signifies predicting the class by a linear combination of concepts.", + "bbox": [ + 75, + 566, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "However, due to the incompleteness of the base concept bank, it is challenging to achieve accurate classifications by solely relying on these concepts in several images, e.g., dragonfly and honeybee, peach and hawthorn, both of which possess concepts from the base concept bank. With the help of Res-CBM, we have discovered 2 concepts, nectar and rough, from the candidate concept bank. Unlike dragonflies, honeybees often gather nectar from the center of flowers, thus associating them with the concept of nectar. Moreover, hawthorns have a rougher surface compared to peaches. By incorporating these discovered concepts into the base concept bank, these initially misclassified samples are now correctly categorized, achieving automatic model debugging to a certain extent.", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Few-shot Capability", + "text_level": 1, + "bbox": [ + 500, + 539, + 691, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig.4 illustrates the performance comparison under different data volume settings between Res-CBM and LP. Compared to the end-to-end black-box model, our method achieves superior performance when little data is available, and exhibits a slight performance gap with larger amounts of sample sizes, which indicates that our method has maintained the accuracy without sacrificing interpretability.", + "bbox": [ + 496, + 565, + 890, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For common object datasets, our approach demonstrates excellent performance with 1, 2, 4, and 8 labeled images per category. We credit its success to the incorporation of human concept information, which helps the model extract vital aspects relevant to the categories from the representations of the black-box backbone.", + "bbox": [ + 496, + 672, + 892, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For fine-grained object datasets, our method outperforms the black-box model when the data volume is extremely low. As the data volume increases, the unexplainable black-box model's performance becomes more prominent, especially in expert datasets such as Flower-102 and CUB-200. It might be attributed to common concepts struggling to distinguish the subtle differences between these fine-grained objects. A feasible solution is to enhance the specificity of concepts by a tailored specialized concept candidate bank.", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11036", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e69a11d448879f8439d3257e42204054889ee0a3fe3275996b6fb4ac7d269d41.jpg", + "image_caption": [ + "Figure 6. Concepts applied in Res-CBM on LAD-A (top) and LAD-F (bottom). Solid boxes represent concepts from the base concept bank, dashed boxes indicate the discovered concepts. Heatmaps refer to learned linear concept classifiers, in which the x-axis represents classes, the y-axis represents concepts, and the values represent the contribution of concepts to categories." + ], + "image_footnote": [], + "bbox": [ + 98, + 87, + 450, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 386, + 230, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Residual Vector Number. To investigate the impact of residual vector numbers on performance improvement and demonstrate that our method can be applied as a post-processing approach to any CBMs, we record the results of attaching different residual vector numbers for Lf-CBM on CIFAR-10, as shown in Fig.5-left. As the quantity of vectors increases, the performance of Lf-CBM continuously improves and gradually saturates at around 15 vectors.", + "bbox": [ + 75, + 412, + 468, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Candidate Concept Number. We fix the residual vector number at 10 and set the concept similarity loss weight to 0.1, then record the final accuracy and the average similarity between the discovered concepts and the most similar concepts in the candidate concept bank during the discovery process in Fig.5-middle. When the candidate concept number is small, the model tends to converge to this unique concept, making it difficult to escape local optima. When it is large, the optimizing vectors easily oscillate between different concepts, resulting in lower accuracy and similarity. Overall, setting the candidate concept number to 5 seems to be a good hyperparameter choice.", + "bbox": [ + 75, + 536, + 468, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Concept Similarity Loss Weight. With a fixed candidate concept number at 5, we also record the final accuracy and average similarity for different loss weights as shown in Fig.5-right. When the weight is low, the similarity of the discovered concepts is extremely low, which resembles a random selection strategy, leading to poorer performance. When the weight is large, the model tends to converge to a local optimum only satisfying the concept similarity loss, sacrificing the ability to explore more appropriate concepts. Since Res-CBM has already saturated after the completion of unknown concept vectors, the cross-entropy loss value is small. Therefore, a weight of 0.1 realizes optimal results.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 89, + 750, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Rethinking CBMs. Indeed CBMs are valuable attempts towards transparency of the decision-making process, one important and fundamental problem may be still unclear, which is: how many concepts are good? especially when lacking a well-accepted and rigorous definition of concepts. In this paper, we have tried to explore this problem. Firstly, the number of concepts should not be the larger the better. From the optimization perspective, the operation of CBMs to project visual representations into concept space is a linear transformation. If its rank is greater than or equal to the dimension $d$ of the concept vector, this process is invertible. Therefore, it is straightforward to re-estimate the inverse transformation matrix to preserve classification accuracy in subsequent linear classifiers. The number of concepts larger than $d$ may decrease the efficiency, making the interpretability less effective.", + "bbox": [ + 496, + 114, + 890, + 356 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On the other hand, the concept should be an efficient way to express categories. Humans can describe objects in the world exponentially using a finite set of concepts. Theoretically, from informatics, when each concept weight is binary, the concept quantity needed to distinguish $n$ categories will be enough approximately $\\log_2 n$ . This is the reason for the poor CUE of LaBo [56], which finds concepts for each category in a way that the CUE complexity is $\\mathcal{O}(n)$ rather than $\\mathcal{O}(\\log_2 n)$ . This suggests that the CUE is crucial in CBMs, and a reasonable number of concepts should lie in the interval of $\\left[\\log_2 n\\right]$ , $d$ .", + "bbox": [ + 496, + 358, + 890, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. In this paper, we emphasize the significance of purity, precision, and completeness in CBMs and introduce the CUE metric to evaluate the descriptive efficiency of CBMs. Our proposed Res-CBM complements the missing concepts in any CBM with an incremental concept discovery approach, which achieves optimal accuracy with the best concept utilization efficiency.", + "bbox": [ + 496, + 525, + 890, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation and Future Work. For our proposed ResCBM, the candidate concept bank construction for fine-grained datasets remains a challenge. Additionally, the sequential concept discovery approach increases computational time costs, while more efficient concept similarity calculation and parallel concept discovery techniques are needed to develop. For the CBM structure, existing CBMs represent all concepts into a single bottleneck, disregarding the hierarchical nature of concepts, where simple concepts can be combined to form more complicated ones.", + "bbox": [ + 496, + 631, + 890, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 799, + 668, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partly supported by the National Natural Science Foundation of China (Grant No. 61991451) and the Shenzhen Science and Technology Program (JCYJ20220818101001004). 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0-0, 2019. 2, 5" + ], + "bbox": [ + 78, + 90, + 468, + 388 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11040", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_model.json b/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3120ae1668285a061953d1547ba71471d4379bd3 --- /dev/null +++ b/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_model.json @@ -0,0 +1,2477 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.131, + 0.738, + 0.154 + ], + "angle": 0, + "content": "Incremental Residual Concept Bottleneck Models" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.179, + 0.918, + 0.218 + ], + "angle": 0, + "content": "Chenming Shang\\(^{12*}\\) Shiji Zhou\\(^{1}\\) Hengyuan Zhang\\(^{1}\\) Xinzhe Ni\\(^{1}\\) Yujiu Yang\\(^{1\\dagger}\\) Yuwang Wang\\(^{12\\dagger}\\) Tsinghua University Shanghai AI Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.22, + 0.778, + 0.235 + ], + "angle": 0, + "content": "{scm22@mails.,zhoushiji@mail.,zhang-hy22@mails.}tsinghua.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.237, + 0.771, + 0.252 + ], + "angle": 0, + "content": "{nxz22@mails.,yang.yujiu@sz.,wang-yuwang@mail.}tsinghua.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.744 + ], + "angle": 0, + "content": "Concept Bottleneck Models (CBMs) map the black-box visual representations extracted by deep neural networks onto a set of interpretable concepts and use the concepts to make predictions, enhancing the transparency of the decision-making process. Multimodal pre-trained models can match visual representations with textual concept embeddings, allowing for obtaining the interpretable concept bottleneck without the expertise concept annotations. Recent research has focused on the concept bank establishment and the high-quality concept selection. However, it is challenging to construct a comprehensive concept bank through humans or large language models, which severely limits the performance of CBMs. In this work, we propose the Incremental Residual Concept Bottleneck Model (ResCBM) to address the challenge of concept completeness. Specifically, the residual concept bottleneck model employs a set of estimizable vectors to complete missing concepts, then the incremental concept discovery module converts the complemented vectors with unclear meanings into potential concepts in the candidate concept bank. Our approach can be applied to any user-defined concept bank, as a posthoc processing method to enhance the performance of any CBMs. Furthermore, to measure the descriptive efficiency of CBMs, the Concept Utilization Efficiency (CUE) metric is proposed. Experiments show that the Res-CBM outperforms the current state-of-the-art methods in terms of both accuracy and efficiency and achieves comparable performance to black-box models across multiple datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.774, + 0.21, + 0.79 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.801, + 0.47, + 0.862 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) [31, 45] have achieved unprecedented success in a wide range of machine learning tasks, including computer vision [16, 32], natural language processing [14, 59], and speech recognition [34, 41]." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.285, + 0.892, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.385, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Figure 1. Challenges in CBMs. When a concept contains many atomic attributes, making it too complex for human to comprehend. When a concept is too high-level, DNNs may struggle to provide accurate prediction. Additionally, there is a risk of human-designed concept bank missing some important concepts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.893, + 0.639 + ], + "angle": 0, + "content": "However, due to their complex and deep structures, they are often regarded as black-box models [7, 49], which are too difficult to understand and interpret. In fields that demand high levels of trustworthiness, such as medicine [44], healthcare [21], education [60], and finance [39], model interpretability has become increasingly crucial. It indicates whether we can trust the DNNs' decisions, and how we can rectify the errors when the DNNs make mistakes. Making deep learning models more interpretable is a significant yet challenging research topic." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.895, + 0.822 + ], + "angle": 0, + "content": "A promising approach for achieving interpretability in deep learning is through concept-based models [46], which leverage human-generated high-level concepts to explain the black-box features of DNNs. Among these approaches, Concept Bottleneck Models (CBMs) [26] map the visual representations to a set of concept values that are understandable to humans. These interpretable concepts are then used to make the final decision by a linear function, greatly enhancing our understanding of the decision-making process. Of greater significance, humans can repair models' faults by directly editing or intervening on the concept bottleneck [3, 48]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Due to the considerable cost of the fine-grained and precise annotation for each concept in CBMs, multimodal pretrained model-based CBMs [58] have recently emerged as a research hotspot. CLIP [40] demonstrates the capacity to establish correspondences between visual information and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.416, + 0.888 + ], + "angle": 0, + "content": "*Work done during an internship at Shanghai AI Laboratory." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.223, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.416, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11030" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "textual descriptions. Accordingly, we can utilize the CLIP text encoder to encode human-understood concepts into concept embeddings and use the visual encoder to encode images into visual representations. By projecting visual representations to each concept embedding, we can obtain the concept bottleneck. The recent innovations have primarily concentrated on comprehensive concept bank establishment and efficient high-quality concept selection. However, these methods face three critical challenges as shown in Fig.1:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.247, + 0.473, + 0.444 + ], + "angle": 0, + "content": "- Purity: The essence of concepts is to abstract complex information into a combination of simple foundational elements, which can generalize to unseen data through the infinite combinations of finite concepts, offering an efficient way to describe the world. Long and complex descriptions like small, black insect with six legs or long, thin tool with a wooden handle, can be composed entirely of combinations of simple concepts such as small, black, insect, leg, etc., which may increase the productivity of concept utilization. Since these complicated concepts are excessively detailed, they may not be shared across different classes, which will limit their ability to capture shared knowledge between different categories." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.444, + 0.473, + 0.594 + ], + "angle": 0, + "content": "- Precision: Each concept should be clearly understandable for both humans and multimodal pre-trained models when annotating concepts. Specifically, concepts should not be markedly more difficult than classes. For example, high-level concepts like amphibians or perennial, are relatively harder for humans to understand and exhibit weaker interpretability. Moreover, we cannot ascertain whether CLIP possesses the capability to understand these high-level concepts, which can potentially lead to errors in concept annotation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.595, + 0.473, + 0.731 + ], + "angle": 0, + "content": "- Completeness: Concept bank should strive to include as much relevant visual information that is beneficial for downstream classification tasks as possible. It is essential to avoid losing too much information in the process. However, it is challenging to establish a comprehensive concept bank directly [57]. The exhaustive capability of language descriptions is limited, making it difficult to accomplish a fully thorough concept bank through manual design and selection." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.247, + 0.473, + 0.731 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this work, we propose the Incremental Residual Concept Bottleneck Model (Res-CBM) to address the three challenges above. First, we establish a simple and pure base concept bank and candidate concept bank to ensure that the CLIP can accurately recognize each concept. Next, we initialize a set of estimizable vectors as filling concepts and optimize this set of filling concepts through the residual concept bottleneck model, to make up for the inadequacy in the base concept bank. Finally, the incremental concept discovery module is utilized to translate these complemented vectors with unclear meanings into potential concepts in the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "candidate concept bank, improving the performance while preserving the interpretability of the CBM. Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.138, + 0.892, + 0.184 + ], + "angle": 0, + "content": "1. We systematically reviewed the research on the CLIP-based CBMs, clarifying the importance of the concepts' purity, precision, and completeness." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.184, + 0.894, + 0.305 + ], + "angle": 0, + "content": "2. We proposed the residual concept bottleneck model to make up for the insufficiency in the base concept bank and converted these complemented unknown vectors into potential concepts in the candidate concept bank through the incremental concept discovery module. It should be emphasized that our approach can be applied to any user-defined concept bank, as a post-hoc processing method to enhance the performance of any CBMs." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.305, + 0.894, + 0.382 + ], + "angle": 0, + "content": "3. To measure the descriptive efficiency of CBMs, we introduced the metric of the concept utilization efficiency. We performed extensive experiments to validate our methodology and elaborate ablation studies to illustrate the effectiveness of each component." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.138, + 0.894, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.392, + 0.642, + 0.409 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.895, + 0.735 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) can be explained through pixels [8, 47], samples [15, 22], weights [54], individual neurons [5, 13], subnetworks [2, 12], representations [4, 19, 20], etc [43]. Concept-based models [23, 33, 52, 53] are representation-level interpretable approaches, whose core idea is to map representations with unknown meanings extracted by the black-box DNNs to a set of concepts that can be comprehended by humans [9, 11, 35, 36]. Concept-based models can be broadly categorized into Concept Bottleneck Models (CBMs) [26], which describe concepts as independent values annotated by experts, and Concept Activation Vectors (CAVs) [24], which represent concepts as normal vectors of the decision boundaries that distinguish positive and negative samples of a concept. CBMs involve the datasets labeled with fine-grained and precise attributes by expert knowledge, such as CUB-200 [18], OAI [10], and LAD [61], whereas CAVs require learning the concept activation vectors on additional probe datasets, and the directions of the concept activation vectors are strictly correlated with the probe datasets [42]. These limitations severely restrict the development of concept-based models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, there has been a rapid development of multimodal pre-trained models [17], among which CLIP does an excellent job of relating visual information to text through contrastive learning, giving researchers confidence for unsupervised concept labeling with CLIP. PCBM [58] generates a concept bank via ConceptNet [50] and calculates the projection distance between the CLIP textual concept embeddings and the CLIP visual representations of images, analogous to the CAVs, to obtain the concept bottleneck. PCBM-h [58] introduces an uninterpretable residual linear layer to compensate for incomplete concept extraction by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11031" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.164, + 0.089, + 0.812, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.359, + 0.895, + 0.391 + ], + "angle": 0, + "content": "Figure 2. Different CBMs' structures. (a): CLIP linear probing [40]. (b): Original Concept Bottleneck Model (CBM) [26]. (c) Post-hoc Concept Bottleneck Model (PCBM) [38, 56, 58]. (d): Hybrid Post-hoc Concept Bottleneck Model (PCBM-h) [58]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.475, + 0.552 + ], + "angle": 0, + "content": "fitting the difference between the PCBM's result and the ground truth through the original visual representations of CLIP. Label-free CBM [38] only leverages CLIP to concept annotation, maximizing the similarity between the concept bottleneck of the features extracted by arbitrary visual backbone and the concept annotations labeled by CLIP. LaBo [56] generates a set of candidate concepts through large language models and designs a submodular optimization block to select the concepts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.567, + 0.172, + 0.584 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.592, + 0.282, + 0.608 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.842 + ], + "angle": 0, + "content": "Consider a dataset of image-label pairs \\(\\mathcal{D} = \\{(x,y)\\}\\), where \\(x\\in \\mathcal{X}\\) is the image and \\(y\\in \\mathcal{Y}\\) is the label. We have \\(N\\) human-selected concepts to describe the essential information of these images, which can be denoted as discrete tokens \\(\\mathcal{E} = \\{e_1,e_2,\\dots,e_N\\}\\). Multimodal pre-trained alignment model (e.g., CLIP [40]) has an image encoder \\(\\Phi_I:\\mathcal{X}\\to \\mathbb{R}^d\\) and a text encoder \\(\\Phi_T\\), which can map images and text into a shared \\(d\\)-dimensional feature space respectively. We encode the discrete tokens with the CLIP text encoder then perform \\(L_{2}\\) normalization to obtain the concept embeddings \\(\\{w_{1},w_{2},\\ldots ,w_{N}|w_{i} = \\Phi_{T}(e_{i}),i = 1,2,\\ldots ,N\\}\\) with the length of 1 and the dimension of \\(d\\). We concatenate these concept embeddings to a concept projection matrix \\(W_{N\\times d}:\\mathbb{R}^d\\to \\mathbb{R}^N\\) in arbitrary order, also identified as a concept bank." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.844, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Correspondingly, we utilize the CLIP image encoder to get the visual representations \\( f = \\Phi_I(x) \\). Considering that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.893, + 0.52 + ], + "angle": 0, + "content": "CLIP has aligned the images with the textual data when pretraining, the visual representations share the feature space with any concept embedding, and the projection length \\(\\| f\\| _2\\cdot \\cos \\langle w_i,f\\rangle\\) can reflect the presence of a particular concept in the image. Since undergoing \\(L_{2}\\) normalization on \\(w_{i}\\), the concept probability can be directly formulated in terms of the dot product \\(c = W\\cdot f\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.894, + 0.579 + ], + "angle": 0, + "content": "Fig.2 illustrates the structure of common CBMs. For CLIP Linear Probing [29], an uninterpretable linear classifier \\(\\Psi : \\mathbb{R}^d \\to \\mathcal{V}\\) is trained directly from visual representations:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.58, + 0.892, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\Psi (f) = \\Psi \\left(\\Phi_ {I} (x)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Original CBM [26] first extracts concepts using a concept extractor \\(\\Psi_{\\mathrm{cpt}}: \\mathbb{R}^d \\to \\mathbb{R}^N\\) and then linearly unites the extracted concepts for label prediction by concept classifier \\(\\Psi_{\\mathrm{cls}}: \\mathbb{R}^N \\to \\mathcal{V}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.668, + 0.892, + 0.686 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\Psi_ {\\mathrm {c l s}} \\left(\\Psi_ {\\mathrm {c p t}} (f)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.692, + 0.894, + 0.783 + ], + "angle": 0, + "content": "Post-hoc CBM [58] stands for a category of CLIP-based CBMs, including Label-free CBM [38], LaBo [56], etc. They attain concept bottleneck by projecting visual representations \\(f\\) directly to a concept bank \\(W\\), rather than by learning a concept extractor. After getting concepts, only a linear concept classifier \\(\\Psi_{c}:\\mathbb{R}^{N}\\to \\mathcal{V}\\) needs to be learned." + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.797, + 0.892, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\Psi_ {c} (c) = \\Psi_ {c} (W \\cdot f) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.816, + 0.894, + 0.879 + ], + "angle": 0, + "content": "PCBM-h [58] adds a linear layer \\(\\Psi_r: \\mathbb{R}^d \\to \\mathcal{Y}\\) between the original visual representation and the labels on the basis of PCBM, which is used to predict the difference between the PCBM result and the ground truth." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.462, + 0.902 + ], + "angle": 0, + "content": "1The symbol of \\( L_{2} \\) normalization is omitted for writing convenience." + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\Psi_ {c} (c) + \\Psi_ {r} (f) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (f) \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11032" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.338, + 0.108 + ], + "angle": 0, + "content": "3.2. Concept Bank Establishment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.297 + ], + "angle": 0, + "content": "Candidate Concept Bank. To ensure precision, we need to make sure that CLIP is capable of recognizing each concept, and one straightforward way is to construct the concept bank from the CLIP pre-trained dataset. For purity, it is desirable for each concept to be at the atom level rather than the compound level, thus maintaining the clarity and specificity. We find that the scene graph [27] consisting of visual concepts to be an appropriate foundation, in which an atom is defined as a singular visual concept, corresponding to a single scene graph node. Atoms are subtyped into objects, relationships, and attributes. We pick the nouns and adjectives in them as the candidate concept bank \\(\\mathcal{E}^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.538 + ], + "angle": 0, + "content": "Base Concept Bank. Although our method can recover missing concepts from a diverse base concept bank, a high-quality base concept bank can remarkably improve the efficiency of our approach. A base concept bank is expected to consist of two parts. Firstly, it should include general concepts that are applicable across various scenarios. We select the pre-defined concept library proposed by [24], which has been widely used in various tasks [1, 55], as our general concept bank \\(\\mathcal{E}_{\\mathrm{ge}}\\). Secondly, it is supposed to include concepts relevant to the specific classification task. Following the PCBM [58], we collect all concepts from ConceptNet [50] that have relations of hasA, isA, partOf, HasProperty, and MadeOf with the classes in each classification task to build the associated concept bank \\(\\mathcal{E}_{\\mathrm{as}}\\). Both concept banks should be included in the candidate concept bank, from which we can derive the base concept bank:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.551, + 0.469, + 0.568 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} _ {0} = \\left(\\mathcal {E} _ {\\mathrm {g e}} \\cap \\mathcal {E} ^ {*}\\right) \\cup \\left(\\mathcal {E} _ {\\mathrm {a s}} \\cap \\mathcal {E} ^ {*}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.581, + 0.47, + 0.627 + ], + "angle": 0, + "content": "We encode the discrete concept tokens with the CLIP text encoder then perform \\( L_{2} \\) normalization to obtain the base and candidate concept embedding matrices:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.64, + 0.469, + 0.657 + ], + "angle": 0, + "content": "\\[\nW _ {0} = \\Phi_ {T} \\left(\\mathcal {E} _ {0}\\right), \\quad W ^ {*} = \\Phi_ {T} \\left(\\mathcal {E} ^ {*}\\right) \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.388, + 0.696 + ], + "angle": 0, + "content": "3.3. Residual Concept Bottleneck Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Previous methods have typically involved pre-generating a set of relevant concepts and then deleting some of them to get the final concept bank. However, on the one hand, the pre-generated concepts might be insufficient, as their scale has often limitations. On the other hand, manual filtering without leveraging dataset information may result in the omission of important concepts. Therefore, we propose the residual concept bottleneck model to learn the missing concepts from the dataset content in an incremental approach compared to other decremental methods as shown in Fig.3." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We first randomly initialize \\(D\\) estimizable vectors \\(U_{D\\times d} = \\{u_1,u_2,\\dots,u_D\\}\\) with dimensions consistent with those of the existing concept embeddings. We likewise" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.093, + 0.887, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.375, + 0.871, + 0.389 + ], + "angle": 0, + "content": "Figure 3. Incremental Residual Concept Bottleneck Model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.415, + 0.892, + 0.476 + ], + "angle": 0, + "content": "project the visual representations onto these vectors, resulting in residual concepts \\( r = U \\cdot f \\) with unclear meanings. The prediction result of using the residual concepts to complement the original concepts is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.486, + 0.892, + 0.503 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\Psi_ {c} (c) + \\Psi_ {r} (r) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (U \\cdot f) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.513, + 0.891, + 0.559 + ], + "angle": 0, + "content": "where \\(\\Psi_c: \\mathbb{R}^N \\to \\mathcal{Y}\\) is the original concept linear classifier using existing concepts and \\(\\Psi_r: \\mathbb{R}^D \\to \\mathcal{Y}\\) is the residual concept linear classifier using unknown residual concepts." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.559, + 0.892, + 0.604 + ], + "angle": 0, + "content": "For one thing, we intend to maximize the accuracy when using only the original concepts, which can be formulated as the following optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.614, + 0.892, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Psi_ {c}} \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} \\left[ \\mathcal {L} \\left(\\Psi_ {c} (W \\cdot \\Phi_ {I} (x)), y\\right) \\right] + \\lambda \\cdot \\Omega (\\Psi_ {c}) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.654, + 0.891, + 0.699 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}(\\hat{y}, y)\\) is the cross-entropy loss function, \\(\\Omega(\\Psi_c)\\) is a complexity measure to regularize the model, and \\(\\lambda\\) is the regularization strength." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.7, + 0.891, + 0.745 + ], + "angle": 0, + "content": "From another perspective, we aim to improve the performance after incorporating the residual concepts, which can be solved by the following optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.754, + 0.891, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Psi_ {r}, U} \\underset {(x, y) \\in \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} \\left(\\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (U \\cdot f), y\\right) \\right] + \\lambda \\cdot \\Omega (\\Psi_ {r}) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.796, + 0.625, + 0.81 + ], + "angle": 0, + "content": "where \\(f = \\Phi_I(x)\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To simultaneously address these two problems, we perform two forward and backward propagations in each batch to update the parameters. When performing the first propagation, we utilize only the original concepts to optimize the original concept classifier \\(\\Psi_{c}\\). During the second propagation, we fix the parameters of the original concept classifier" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11033" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\(\\Psi_{c}\\) and optimize the residual concept classifier \\(\\Psi_{r}\\) as well as the learnable unknown concept vectors \\(U\\) using both the original and the residual concepts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.243 + ], + "angle": 0, + "content": "To avoid the influence of extreme values from unknown residual concepts, we employ cosine similarity instead of projection distance as the concept bottleneck and standardize the activations of each concept to have a mean of 0 and a standard deviation of 1 to speed up convergence [38]. These operations are reversible and do not affect the relative order of concepts or introduce additional information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.252, + 0.356, + 0.268 + ], + "angle": 0, + "content": "3.4. Incremental Concept Discovery" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.469, + 0.35 + ], + "angle": 0, + "content": "Through the aforementioned steps, the residual concepts effectively compensate for the incompleteness of the original concepts. However, these randomly learned concepts lack human interpretability, so we next translate them into human-understandable concepts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.636 + ], + "angle": 0, + "content": "Parameters Initialization. We first initialize another estimizable vector \\( v_{d} \\), denoted as the discovered concept vector, whose value is the mean concept embeddings of the base concept bank with added noise. Subsequently, we append the discovered concept vector to the base concept bank and remove one of the learned unknown residual concept vectors, whose residual concept embedding matrix changes to \\( U_{-v_d} = U_{(D - 1)\\times d} \\) and residual classifier changes to \\( \\Psi_{r - v_d}:\\mathbb{R}^{D - 1}\\to \\mathcal{V} \\). After performing \\( L_{2} \\) normalization and projection, the visual representations will also obtain a similarity score \\( c_{d} = v_{d}\\cdot f \\) to the discovered concept vector, and there will be a corresponding discovered concept linear classifier \\( \\Phi_d:\\mathbb{R}\\rightarrow \\mathcal{V} \\). We adopt the language priors as the initial weights to ensure stable updating of the discovered concept vector. In particular, the weights of the discovered concept classifier are initialized as the cosine similarity between the discovered concept embedding and the text embeddings for each class name, while other parameters and weights are kept untouched." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Concept Similarity Loss Function. After adding the discovered concept vector to the base concept bank, the prediction under the original and residual strategy is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.71, + 0.468, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {\\text {o r g}} = \\Psi_ {c} (c) + \\Psi_ {d} \\left(c _ {d}\\right) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {d} \\left(v _ {d} \\cdot f\\right) \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.729, + 0.468, + 0.745 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {\\text {r e s}} = \\hat {y} _ {\\text {o r g}} + \\Psi_ {r - v _ {d}} \\left(U _ {- v _ {d}} \\cdot f\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.756, + 0.469, + 0.817 + ], + "angle": 0, + "content": "To further guarantee that the discovered concept vector is interpretable, we propose the concept similarity loss function \\(\\mathcal{L}_{\\mathrm{sim}}\\), which utilizes the candidate concept bank \\(W^{*}\\) to constrain the discovered concept embedding:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.826, + 0.469, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i m}} = 1 - \\mathbb {E} \\left[ \\operatorname {R a n k} \\left(W ^ {*} \\cdot \\frac {v _ {d} ^ {T}}{\\| v _ {d} \\| _ {2}}, M\\right) \\right] \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\operatorname{Rank}(v, M)\\) denotes sorting \\(v\\) from largest to smallest and selecting the first \\(M\\) of them." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "Referring to the update strategy of the residual concept bottleneck model, we just add the discovered concept with its classifier during the first pass propagation:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.142, + 0.892, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Psi_ {c}, \\Psi_ {d}, v _ {d}} \\mathbb {E} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\text {o r g}}, y\\right) \\right] + \\alpha \\cdot \\mathcal {L} _ {\\text {s i m}} + \\lambda \\cdot \\Omega \\left(\\Psi_ {c}, \\Psi_ {d}\\right) \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.171, + 0.843, + 0.186 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the weight of the concept similarity loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.186, + 0.892, + 0.262 + ], + "angle": 0, + "content": "When performing the second propagation, we fix the parameters of the original concept classifier \\(\\Psi_{c}\\), the discovered concept classifier \\(\\Psi_{d}\\), and the discovered concept embedding \\(v_{d}\\), optimizing the residual concept classifier \\(\\Psi_{r - v_d}\\) and the unknown residual concept vectors \\(U_{-v_d}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.266, + 0.892, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Psi_ {r - v _ {d}}, U - v _ {d}} \\mathbb {E} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\text {r e s}}, y\\right) \\right] + \\lambda \\cdot \\Omega \\left(\\Psi_ {r - v _ {d}}\\right) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.297, + 0.892, + 0.373 + ], + "angle": 0, + "content": "We recover concepts in an incremental way until all the learned unknown residual concept vectors are transformed into pure, accurate, and human-interpretable concepts. At this point, the base concept library is fully updated, and experiments confirm its superior completeness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.384, + 0.634, + 0.401 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.409, + 0.691, + 0.425 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.432, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Datasets. We conduct comprehensive experiments on 7 datasets, including: CIFAR-10, CIFAR-100 [28], TinyImageNet [30], LAD [61], CUB-200 [51], Food-101 [6], Flower-102 [37]. For a fair comparison, we apply CLIPRN50 when comparing with other CBMs and CLIP-ViT-L/14 on few-shot classification tasks as the backbone, and all linear classifiers are optimized with the Adam [25] optimizer. For more detailed information, please refer to the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.568, + 0.892, + 0.598 + ], + "angle": 0, + "content": "Baselines. To evaluate our proposed approach, we compare it with the following baseline methods:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.599, + 0.892, + 0.673 + ], + "angle": 0, + "content": "- CLIP Zero-shot[40]: the cosine similarities between the visual representations and the textual embeddings of each class name are calculated directly without any training. The class with the highest cosine similarity score is selected as the final classification result." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.674, + 0.892, + 0.719 + ], + "angle": 0, + "content": "- Linear Probing (LP)[40]: We exclusively utilize the CLIP visual encoder and the obtained visual representations are then used to predict the label by training a linear classifier." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.72, + 0.892, + 0.825 + ], + "angle": 0, + "content": "- Original CBM[26]: The original CBM relies on fine-grained concept annotations, so we compare our method with it only on LAD and CUB with available attribute annotations. In addition, CBMs may suffer from concept leakage, which can only be alleviated by CBMs trained independently [36]. Hence, we choose CBM-independent as the baseline for comparison." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- PCBM[58]: PCBM uses the ConceptNet[50], a knowledge graph dataset, to conduct a concept bank. It treats classes as nodes and incorporates surrounding neighboring nodes in the concept bank. More concepts can be included by expanding multiple layers outwards." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11034" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 1. Comparison with other CLIP-based CBMs. Bold indicates the best interpretable result, underline indicates the 2nd-best result, italic indicates the black-box methods." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.129, + 0.894, + 0.309 + ], + "angle": 0, + "content": "
MethodInterpretabilityLengthCIFAR 10CIFAR 100
AccuracyNumberCUEAccuracyNumberCUE
Zero-shotYesN/A0.6796N/AN/A0.2620N/AN/A
LPNoN/A0.8858N/AN/A0.6995N/AN/A
PCBM-1rYes90.80441755.10730.53794401.3583
PCBM-2rYes90.80743832.34230.545011750.5153
PCBM-3rYes90.820810580.8620N/AN/AN/A
PCBM-hNo90.8757175N/A0.6683440N/A
Lf-CBMYes120.86771435.05650.67458920.6301
LaBo-10cYes270.84891003.14410.661810000.2451
LaBo-20cYes270.86692001.60540.673620000.1247
LaBo-30cYes260.87523001.1221N/AN/AN/A
Res-CBMYes70.8803237+105.09140.6791372+152.5396
" + }, + { + "type": "table_caption", + "bbox": [ + 0.136, + 0.322, + 0.832, + 0.337 + ], + "angle": 0, + "content": "Table 2. Comparison with CBMs with labeled concept annotations. The labeling significance is consistent with Tab.1." + }, + { + "type": "table", + "bbox": [ + 0.133, + 0.347, + 0.836, + 0.438 + ], + "angle": 0, + "content": "
MethodLAD-ALAD-ELAD-FLAD-HLAD-VCUBMean
LP0.94320.86610.73930.49240.86710.72140.7714
Original CBM0.89640.78260.55350.33880.79070.65130.6689
PCBM-annotation0.89340.77110.59820.29820.78140.63630.6631
Res-CBM-before0.78970.77090.43560.14290.75480.59870.5812
Res-CBM-after0.89790.80450.66240.38620.83010.62430.7009
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.461, + 0.469, + 0.537 + ], + "angle": 0, + "content": "- PCBM-h[58]: After training the PCBM, PCBM-h is applied as a post-processing method that connects the visual representation and the class labels result through shortcuts. It utilizes a linear classifier to predict the difference between the result of PCBM and the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.537, + 0.47, + 0.627 + ], + "angle": 0, + "content": "- Lf-CBM[38]: In contrast to PCBM, Lf-CBM generates concepts through a large language model (LLM). It solely utilizes CLIP as the concept annotator, allowing it to act on any visual backbone. We directly select CLIP as the visual backbone, thus omitting the process of computing the similarity matrix." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.627, + 0.47, + 0.732 + ], + "angle": 0, + "content": "- LaBo[56]: LaBo similarly applies the LLM to generate candidate concepts. However, the quantity of concepts in LaBo is specific to each class. So we generate 10, 20, and 30 concepts per class to compare the performance. In addition, LaBo's linear classifier differs from the above baselines. To evaluate the quality of concepts equitably, we choose the same classifier as the above methods." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.461, + 0.47, + 0.732 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.811 + ], + "angle": 0, + "content": "Metrics. Besides accuracy, we also concentrate on concepts' efficiency, including both the average length of each concept and quantity of concepts. Specifically, we define the accuracy improvement brought by all concepts' length to measure the Concept Utilization Efficiency (CUE):" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.818, + 0.47, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\mathrm {C U E} = \\frac {1 0 0 0 0 \\times \\mathrm {A c c}}{N \\times \\bar {L}} \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathrm{Acc}\\) is the classification accuracy, \\(N\\) is the quantity of concepts and \\(\\bar{L}\\) is the average number of letters included in each concept. Larger CUE means higher efficiency." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.46, + 0.724, + 0.478 + ], + "angle": 0, + "content": "4.2. Accuracy and Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.895, + 0.637 + ], + "angle": 0, + "content": "We compare our method with other CBMs in terms of accuracy and efficiency. Tab.1 provides the results of our method compared to other CLIP-based CBMs. Res-CBM attains higher accuracy than PCBM by \\(5.95\\%\\) on CIFAR-10 and \\(13.41\\%\\) on CIFAR-100 and even outperforms the inexplicable PCBM-h. Despite Lf-CBM and LaBo being powerful baselines, our methodology still achieves state-of-the-art results. Particularly, it should be noted that our method considerably exceeds both Lf-CBM and LaBo in terms of efficiency, as evidenced by the CUE metric." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.895, + 0.807 + ], + "angle": 0, + "content": "On LAD and CUB-200 with attribute annotations, we still use CLIP-50 with frozen parameters as the visual backbone to train Original CBM according to formula (2), as the results are shown in Tab.2.\\(^{3}\\) The close performance of the Original CBM and PCBM-annotation suggests that the CBMs' performance heavily relies on the expert-selected concepts more than the model structure. Although Res-CBM-before performs poorly, a remarkable improvement is observed in Res-CBM-after after applying our unsupervised incremental concept discovery, which even surpasses supervised CBMs with concept annotations on most datasets." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.827, + 0.892, + 0.852 + ], + "angle": 0, + "content": "\\(^{2}\\)PCBM-#r represents expanding outward to include neighboring nodes # times. LaBo-#c represents selecting # concepts per class." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.852, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{3} \\) PCBM-annotation refers to PCBM that utilizes the textual embeddings of the annotated attributes as the concept bank. Res-CBM-before indicates the performance on the initial base concept bank. Res-CBM-after represents the performance after incremental concept discovery." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.827, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11035" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.094, + 0.355, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.094, + 0.608, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.095, + 0.865, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.21, + 0.355, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.21, + 0.609, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.21, + 0.865, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.339, + 0.882, + 0.355 + ], + "angle": 0, + "content": "Figure 4. Test accuracy \\((\\%)\\) comparison between Res-CBM and LP on 6 datasets. The x-axis represents the number of labeled images." + }, + { + "type": "image", + "bbox": [ + 0.103, + 0.371, + 0.339, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.371, + 0.61, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.371, + 0.868, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.5, + 0.833, + 0.515 + ], + "angle": 0, + "content": "Figure 5. Ablation results on residual vector numbers, concept similarity loss weights and candidate concept numbers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.54, + 0.233, + 0.557 + ], + "angle": 0, + "content": "4.3. Interpretability" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.687 + ], + "angle": 0, + "content": "In this subsection, we visualize the mechanism of ResCBM and demonstrate how the newly discovered concepts assist in advancing classification performance. For each image, we display the top 5 concepts with the highest activation scores in the concept bottleneck, as shown in Fig.6. Through a sparse concept classifier, we can obtain predictions, which signifies predicting the class by a linear combination of concepts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "However, due to the incompleteness of the base concept bank, it is challenging to achieve accurate classifications by solely relying on these concepts in several images, e.g., dragonfly and honeybee, peach and hawthorn, both of which possess concepts from the base concept bank. With the help of Res-CBM, we have discovered 2 concepts, nectar and rough, from the candidate concept bank. Unlike dragonflies, honeybees often gather nectar from the center of flowers, thus associating them with the concept of nectar. Moreover, hawthorns have a rougher surface compared to peaches. By incorporating these discovered concepts into the base concept bank, these initially misclassified samples are now correctly categorized, achieving automatic model debugging to a certain extent." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.692, + 0.558 + ], + "angle": 0, + "content": "4.4. Few-shot Capability" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Fig.4 illustrates the performance comparison under different data volume settings between Res-CBM and LP. Compared to the end-to-end black-box model, our method achieves superior performance when little data is available, and exhibits a slight performance gap with larger amounts of sample sizes, which indicates that our method has maintained the accuracy without sacrificing interpretability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.893, + 0.763 + ], + "angle": 0, + "content": "For common object datasets, our approach demonstrates excellent performance with 1, 2, 4, and 8 labeled images per category. We credit its success to the incorporation of human concept information, which helps the model extract vital aspects relevant to the categories from the representations of the black-box backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "For fine-grained object datasets, our method outperforms the black-box model when the data volume is extremely low. As the data volume increases, the unexplainable black-box model's performance becomes more prominent, especially in expert datasets such as Flower-102 and CUB-200. It might be attributed to common concepts struggling to distinguish the subtle differences between these fine-grained objects. A feasible solution is to enhance the specificity of concepts by a tailored specialized concept candidate bank." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11036" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.088, + 0.451, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.473, + 0.357 + ], + "angle": 0, + "content": "Figure 6. Concepts applied in Res-CBM on LAD-A (top) and LAD-F (bottom). Solid boxes represent concepts from the base concept bank, dashed boxes indicate the discovered concepts. Heatmaps refer to learned linear concept classifiers, in which the x-axis represents classes, the y-axis represents concepts, and the values represent the contribution of concepts to categories." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.387, + 0.231, + 0.403 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.534 + ], + "angle": 0, + "content": "Residual Vector Number. To investigate the impact of residual vector numbers on performance improvement and demonstrate that our method can be applied as a post-processing approach to any CBMs, we record the results of attaching different residual vector numbers for Lf-CBM on CIFAR-10, as shown in Fig.5-left. As the quantity of vectors increases, the performance of Lf-CBM continuously improves and gradually saturates at around 15 vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.718 + ], + "angle": 0, + "content": "Candidate Concept Number. We fix the residual vector number at 10 and set the concept similarity loss weight to 0.1, then record the final accuracy and the average similarity between the discovered concepts and the most similar concepts in the candidate concept bank during the discovery process in Fig.5-middle. When the candidate concept number is small, the model tends to converge to this unique concept, making it difficult to escape local optima. When it is large, the optimizing vectors easily oscillate between different concepts, resulting in lower accuracy and similarity. Overall, setting the candidate concept number to 5 seems to be a good hyperparameter choice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Concept Similarity Loss Weight. With a fixed candidate concept number at 5, we also record the final accuracy and average similarity for different loss weights as shown in Fig.5-right. When the weight is low, the similarity of the discovered concepts is extremely low, which resembles a random selection strategy, leading to poorer performance. When the weight is large, the model tends to converge to a local optimum only satisfying the concept similarity loss, sacrificing the ability to explore more appropriate concepts. Since Res-CBM has already saturated after the completion of unknown concept vectors, the cross-entropy loss value is small. Therefore, a weight of 0.1 realizes optimal results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.75, + 0.107 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Rethinking CBMs. Indeed CBMs are valuable attempts towards transparency of the decision-making process, one important and fundamental problem may be still unclear, which is: how many concepts are good? especially when lacking a well-accepted and rigorous definition of concepts. In this paper, we have tried to explore this problem. Firstly, the number of concepts should not be the larger the better. From the optimization perspective, the operation of CBMs to project visual representations into concept space is a linear transformation. If its rank is greater than or equal to the dimension \\( d \\) of the concept vector, this process is invertible. Therefore, it is straightforward to re-estimate the inverse transformation matrix to preserve classification accuracy in subsequent linear classifiers. The number of concepts larger than \\( d \\) may decrease the efficiency, making the interpretability less effective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.526 + ], + "angle": 0, + "content": "On the other hand, the concept should be an efficient way to express categories. Humans can describe objects in the world exponentially using a finite set of concepts. Theoretically, from informatics, when each concept weight is binary, the concept quantity needed to distinguish \\( n \\) categories will be enough approximately \\( \\log_2 n \\). This is the reason for the poor CUE of LaBo [56], which finds concepts for each category in a way that the CUE complexity is \\( \\mathcal{O}(n) \\) rather than \\( \\mathcal{O}(\\log_2 n) \\). This suggests that the CUE is crucial in CBMs, and a reasonable number of concepts should lie in the interval of \\( \\left[\\log_2 n\\right] \\), \\( d \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.526, + 0.892, + 0.632 + ], + "angle": 0, + "content": "Conclusion. In this paper, we emphasize the significance of purity, precision, and completeness in CBMs and introduce the CUE metric to evaluate the descriptive efficiency of CBMs. Our proposed Res-CBM complements the missing concepts in any CBM with an incremental concept discovery approach, which achieves optimal accuracy with the best concept utilization efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.784 + ], + "angle": 0, + "content": "Limitation and Future Work. For our proposed ResCBM, the candidate concept bank construction for fine-grained datasets remains a challenge. Additionally, the sequential concept discovery approach increases computational time costs, while more efficient concept similarity calculation and parallel concept discovery techniques are needed to develop. For the CBM structure, existing CBMs represent all concepts into a single bottleneck, disregarding the hierarchical nature of concepts, where simple concepts can be combined to form more complicated ones." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.669, + 0.817 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was partly supported by the National Natural Science Foundation of China (Grant No. 61991451) and the Shenzhen Science and Technology Program (JCYJ20220818101001004). The first two authors have equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11037" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Abubakar Abid, Mert Yuksekgonul, and James Zou. Meaningfully debugging model mistakes using conceptual counterfactual explanations. In International Conference on Machine Learning, pages 66-88. PMLR, 2022. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.47, + 0.213 + ], + "angle": 0, + "content": "[2] Mohammed Amer and Tomás Maul. A review of modularization techniques in artificial neural networks. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0-0, 2019. 2, 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11040" + } + ] +] \ No newline at end of file diff --git a/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_origin.pdf b/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..757730aabe6ef05db1474be34740f5a118337ff1 --- /dev/null +++ b/2024/Incremental Residual Concept Bottleneck Models/249f4872-e5d6-464e-98af-dc5a4e7c1958_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e19455ee3dbd0366181995b359f643870ce9fbeed5e8acad81b3d7da2367ea31 +size 1004579 diff --git a/2024/Incremental Residual Concept Bottleneck Models/full.md b/2024/Incremental Residual Concept Bottleneck Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..78ef1266e2578c77c30035fe5d2f3d8b84a23944 --- /dev/null +++ b/2024/Incremental Residual Concept Bottleneck Models/full.md @@ -0,0 +1,345 @@ +# Incremental Residual Concept Bottleneck Models + +Chenming Shang $^{12*}$ Shiji Zhou $^{1}$ Hengyuan Zhang $^{1}$ Xinzhe Ni $^{1}$ Yujiu Yang $^{1\dagger}$ Yuwang Wang $^{12\dagger}$ Tsinghua University Shanghai AI Laboratory + +{scm22@mails.,zhoushiji@mail.,zhang-hy22@mails.}tsinghua.edu.cn + +{nxz22@mails.,yang.yujiu@sz.,wang-yuwang@mail.}tsinghua.edu.cn + +# Abstract + +Concept Bottleneck Models (CBMs) map the black-box visual representations extracted by deep neural networks onto a set of interpretable concepts and use the concepts to make predictions, enhancing the transparency of the decision-making process. Multimodal pre-trained models can match visual representations with textual concept embeddings, allowing for obtaining the interpretable concept bottleneck without the expertise concept annotations. Recent research has focused on the concept bank establishment and the high-quality concept selection. However, it is challenging to construct a comprehensive concept bank through humans or large language models, which severely limits the performance of CBMs. In this work, we propose the Incremental Residual Concept Bottleneck Model (ResCBM) to address the challenge of concept completeness. Specifically, the residual concept bottleneck model employs a set of estimizable vectors to complete missing concepts, then the incremental concept discovery module converts the complemented vectors with unclear meanings into potential concepts in the candidate concept bank. Our approach can be applied to any user-defined concept bank, as a posthoc processing method to enhance the performance of any CBMs. Furthermore, to measure the descriptive efficiency of CBMs, the Concept Utilization Efficiency (CUE) metric is proposed. Experiments show that the Res-CBM outperforms the current state-of-the-art methods in terms of both accuracy and efficiency and achieves comparable performance to black-box models across multiple datasets. + +# 1. Introduction + +Deep neural networks (DNNs) [31, 45] have achieved unprecedented success in a wide range of machine learning tasks, including computer vision [16, 32], natural language processing [14, 59], and speech recognition [34, 41]. + +![](images/0b584f311df233e268cbea997fc3b4237633a1711c6075fef927fadd07ace8bc.jpg) +Figure 1. Challenges in CBMs. When a concept contains many atomic attributes, making it too complex for human to comprehend. When a concept is too high-level, DNNs may struggle to provide accurate prediction. Additionally, there is a risk of human-designed concept bank missing some important concepts. + +However, due to their complex and deep structures, they are often regarded as black-box models [7, 49], which are too difficult to understand and interpret. In fields that demand high levels of trustworthiness, such as medicine [44], healthcare [21], education [60], and finance [39], model interpretability has become increasingly crucial. It indicates whether we can trust the DNNs' decisions, and how we can rectify the errors when the DNNs make mistakes. Making deep learning models more interpretable is a significant yet challenging research topic. + +A promising approach for achieving interpretability in deep learning is through concept-based models [46], which leverage human-generated high-level concepts to explain the black-box features of DNNs. Among these approaches, Concept Bottleneck Models (CBMs) [26] map the visual representations to a set of concept values that are understandable to humans. These interpretable concepts are then used to make the final decision by a linear function, greatly enhancing our understanding of the decision-making process. Of greater significance, humans can repair models' faults by directly editing or intervening on the concept bottleneck [3, 48]. + +Due to the considerable cost of the fine-grained and precise annotation for each concept in CBMs, multimodal pretrained model-based CBMs [58] have recently emerged as a research hotspot. CLIP [40] demonstrates the capacity to establish correspondences between visual information and + +textual descriptions. Accordingly, we can utilize the CLIP text encoder to encode human-understood concepts into concept embeddings and use the visual encoder to encode images into visual representations. By projecting visual representations to each concept embedding, we can obtain the concept bottleneck. The recent innovations have primarily concentrated on comprehensive concept bank establishment and efficient high-quality concept selection. However, these methods face three critical challenges as shown in Fig.1: + +- Purity: The essence of concepts is to abstract complex information into a combination of simple foundational elements, which can generalize to unseen data through the infinite combinations of finite concepts, offering an efficient way to describe the world. Long and complex descriptions like small, black insect with six legs or long, thin tool with a wooden handle, can be composed entirely of combinations of simple concepts such as small, black, insect, leg, etc., which may increase the productivity of concept utilization. Since these complicated concepts are excessively detailed, they may not be shared across different classes, which will limit their ability to capture shared knowledge between different categories. +- Precision: Each concept should be clearly understandable for both humans and multimodal pre-trained models when annotating concepts. Specifically, concepts should not be markedly more difficult than classes. For example, high-level concepts like amphibians or perennial, are relatively harder for humans to understand and exhibit weaker interpretability. Moreover, we cannot ascertain whether CLIP possesses the capability to understand these high-level concepts, which can potentially lead to errors in concept annotation. +- Completeness: Concept bank should strive to include as much relevant visual information that is beneficial for downstream classification tasks as possible. It is essential to avoid losing too much information in the process. However, it is challenging to establish a comprehensive concept bank directly [57]. The exhaustive capability of language descriptions is limited, making it difficult to accomplish a fully thorough concept bank through manual design and selection. + +In this work, we propose the Incremental Residual Concept Bottleneck Model (Res-CBM) to address the three challenges above. First, we establish a simple and pure base concept bank and candidate concept bank to ensure that the CLIP can accurately recognize each concept. Next, we initialize a set of estimizable vectors as filling concepts and optimize this set of filling concepts through the residual concept bottleneck model, to make up for the inadequacy in the base concept bank. Finally, the incremental concept discovery module is utilized to translate these complemented vectors with unclear meanings into potential concepts in the + +candidate concept bank, improving the performance while preserving the interpretability of the CBM. Our main contributions can be summarized as follows: + +1. We systematically reviewed the research on the CLIP-based CBMs, clarifying the importance of the concepts' purity, precision, and completeness. +2. We proposed the residual concept bottleneck model to make up for the insufficiency in the base concept bank and converted these complemented unknown vectors into potential concepts in the candidate concept bank through the incremental concept discovery module. It should be emphasized that our approach can be applied to any user-defined concept bank, as a post-hoc processing method to enhance the performance of any CBMs. +3. To measure the descriptive efficiency of CBMs, we introduced the metric of the concept utilization efficiency. We performed extensive experiments to validate our methodology and elaborate ablation studies to illustrate the effectiveness of each component. + +# 2. Related Work + +Deep neural networks (DNNs) can be explained through pixels [8, 47], samples [15, 22], weights [54], individual neurons [5, 13], subnetworks [2, 12], representations [4, 19, 20], etc [43]. Concept-based models [23, 33, 52, 53] are representation-level interpretable approaches, whose core idea is to map representations with unknown meanings extracted by the black-box DNNs to a set of concepts that can be comprehended by humans [9, 11, 35, 36]. Concept-based models can be broadly categorized into Concept Bottleneck Models (CBMs) [26], which describe concepts as independent values annotated by experts, and Concept Activation Vectors (CAVs) [24], which represent concepts as normal vectors of the decision boundaries that distinguish positive and negative samples of a concept. CBMs involve the datasets labeled with fine-grained and precise attributes by expert knowledge, such as CUB-200 [18], OAI [10], and LAD [61], whereas CAVs require learning the concept activation vectors on additional probe datasets, and the directions of the concept activation vectors are strictly correlated with the probe datasets [42]. These limitations severely restrict the development of concept-based models. + +Recently, there has been a rapid development of multimodal pre-trained models [17], among which CLIP does an excellent job of relating visual information to text through contrastive learning, giving researchers confidence for unsupervised concept labeling with CLIP. PCBM [58] generates a concept bank via ConceptNet [50] and calculates the projection distance between the CLIP textual concept embeddings and the CLIP visual representations of images, analogous to the CAVs, to obtain the concept bottleneck. PCBM-h [58] introduces an uninterpretable residual linear layer to compensate for incomplete concept extraction by + +![](images/e026e67dc6d2b76b6d9dbfa5864e7019d8905c4000defeb73a338bde51f0bd7e.jpg) +Figure 2. Different CBMs' structures. (a): CLIP linear probing [40]. (b): Original Concept Bottleneck Model (CBM) [26]. (c) Post-hoc Concept Bottleneck Model (PCBM) [38, 56, 58]. (d): Hybrid Post-hoc Concept Bottleneck Model (PCBM-h) [58]. + +fitting the difference between the PCBM's result and the ground truth through the original visual representations of CLIP. Label-free CBM [38] only leverages CLIP to concept annotation, maximizing the similarity between the concept bottleneck of the features extracted by arbitrary visual backbone and the concept annotations labeled by CLIP. LaBo [56] generates a set of candidate concepts through large language models and designs a submodular optimization block to select the concepts. + +# 3. Method + +# 3.1. Problem Formulation + +Consider a dataset of image-label pairs $\mathcal{D} = \{(x,y)\}$ , where $x\in \mathcal{X}$ is the image and $y\in \mathcal{Y}$ is the label. We have $N$ human-selected concepts to describe the essential information of these images, which can be denoted as discrete tokens $\mathcal{E} = \{e_1,e_2,\dots,e_N\}$ . Multimodal pre-trained alignment model (e.g., CLIP [40]) has an image encoder $\Phi_I:\mathcal{X}\to \mathbb{R}^d$ and a text encoder $\Phi_T$ , which can map images and text into a shared $d$ -dimensional feature space respectively. We encode the discrete tokens with the CLIP text encoder then perform $L_{2}$ normalization to obtain the concept embeddings $\{w_{1},w_{2},\ldots ,w_{N}|w_{i} = \Phi_{T}(e_{i}),i = 1,2,\ldots ,N\}$ with the length of 1 and the dimension of $d$ . We concatenate these concept embeddings to a concept projection matrix $W_{N\times d}:\mathbb{R}^d\to \mathbb{R}^N$ in arbitrary order, also identified as a concept bank. + +Correspondingly, we utilize the CLIP image encoder to get the visual representations $f = \Phi_I(x)$ . Considering that + +CLIP has aligned the images with the textual data when pretraining, the visual representations share the feature space with any concept embedding, and the projection length $\| f\| _2\cdot \cos \langle w_i,f\rangle$ can reflect the presence of a particular concept in the image. Since undergoing $L_{2}$ normalization on $w_{i}$ , the concept probability can be directly formulated in terms of the dot product $c = W\cdot f$ + +Fig.2 illustrates the structure of common CBMs. For CLIP Linear Probing [29], an uninterpretable linear classifier $\Psi : \mathbb{R}^d \to \mathcal{V}$ is trained directly from visual representations: + +$$ +\hat {y} = \Psi (f) = \Psi \left(\Phi_ {I} (x)\right) \tag {1} +$$ + +Original CBM [26] first extracts concepts using a concept extractor $\Psi_{\mathrm{cpt}}: \mathbb{R}^d \to \mathbb{R}^N$ and then linearly unites the extracted concepts for label prediction by concept classifier $\Psi_{\mathrm{cls}}: \mathbb{R}^N \to \mathcal{V}$ . + +$$ +\hat {y} = \Psi_ {\mathrm {c l s}} \left(\Psi_ {\mathrm {c p t}} (f)\right) \tag {2} +$$ + +Post-hoc CBM [58] stands for a category of CLIP-based CBMs, including Label-free CBM [38], LaBo [56], etc. They attain concept bottleneck by projecting visual representations $f$ directly to a concept bank $W$ , rather than by learning a concept extractor. After getting concepts, only a linear concept classifier $\Psi_{c}:\mathbb{R}^{N}\to \mathcal{V}$ needs to be learned. + +$$ +\hat {y} = \Psi_ {c} (c) = \Psi_ {c} (W \cdot f) \tag {3} +$$ + +PCBM-h [58] adds a linear layer $\Psi_r: \mathbb{R}^d \to \mathcal{Y}$ between the original visual representation and the labels on the basis of PCBM, which is used to predict the difference between the PCBM result and the ground truth. + +$$ +\hat {y} = \Psi_ {c} (c) + \Psi_ {r} (f) = \Psi_ {c} (W \cdot f) + \Psi_ {r} (f) \tag {4} +$$ + +# 3.2. Concept Bank Establishment + +Candidate Concept Bank. To ensure precision, we need to make sure that CLIP is capable of recognizing each concept, and one straightforward way is to construct the concept bank from the CLIP pre-trained dataset. For purity, it is desirable for each concept to be at the atom level rather than the compound level, thus maintaining the clarity and specificity. We find that the scene graph [27] consisting of visual concepts to be an appropriate foundation, in which an atom is defined as a singular visual concept, corresponding to a single scene graph node. Atoms are subtyped into objects, relationships, and attributes. We pick the nouns and adjectives in them as the candidate concept bank $\mathcal{E}^*$ . + +Base Concept Bank. Although our method can recover missing concepts from a diverse base concept bank, a high-quality base concept bank can remarkably improve the efficiency of our approach. A base concept bank is expected to consist of two parts. Firstly, it should include general concepts that are applicable across various scenarios. We select the pre-defined concept library proposed by [24], which has been widely used in various tasks [1, 55], as our general concept bank $\mathcal{E}_{\mathrm{ge}}$ . Secondly, it is supposed to include concepts relevant to the specific classification task. Following the PCBM [58], we collect all concepts from ConceptNet [50] that have relations of hasA, isA, partOf, HasProperty, and MadeOf with the classes in each classification task to build the associated concept bank $\mathcal{E}_{\mathrm{as}}$ . Both concept banks should be included in the candidate concept bank, from which we can derive the base concept bank: + +$$ +\mathcal {E} _ {0} = \left(\mathcal {E} _ {\mathrm {g e}} \cap \mathcal {E} ^ {*}\right) \cup \left(\mathcal {E} _ {\mathrm {a s}} \cap \mathcal {E} ^ {*}\right) \tag {5} +$$ + +We encode the discrete concept tokens with the CLIP text encoder then perform $L_{2}$ normalization to obtain the base and candidate concept embedding matrices: + +$$ +W _ {0} = \Phi_ {T} \left(\mathcal {E} _ {0}\right), \quad W ^ {*} = \Phi_ {T} \left(\mathcal {E} ^ {*}\right) \tag {6} +$$ + +# 3.3. Residual Concept Bottleneck Model + +Previous methods have typically involved pre-generating a set of relevant concepts and then deleting some of them to get the final concept bank. However, on the one hand, the pre-generated concepts might be insufficient, as their scale has often limitations. On the other hand, manual filtering without leveraging dataset information may result in the omission of important concepts. Therefore, we propose the residual concept bottleneck model to learn the missing concepts from the dataset content in an incremental approach compared to other decremental methods as shown in Fig.3. + +We first randomly initialize $D$ estimizable vectors $U_{D\times d} = \{u_1,u_2,\dots,u_D\}$ with dimensions consistent with those of the existing concept embeddings. We likewise + +![](images/318aeaf76579714c5f9a830f5530045deec985f0a5d599033a03548dafcdb562.jpg) +Figure 3. Incremental Residual Concept Bottleneck Model. + +project the visual representations onto these vectors, resulting in residual concepts $r = U \cdot f$ with unclear meanings. The prediction result of using the residual concepts to complement the original concepts is as follows: + +$$ +\hat {y} = \Psi_ {c} (c) + \Psi_ {r} (r) = \Psi_ {c} (W \cdot f) + \Psi_ {r} (U \cdot f) \tag {7} +$$ + +where $\Psi_c: \mathbb{R}^N \to \mathcal{Y}$ is the original concept linear classifier using existing concepts and $\Psi_r: \mathbb{R}^D \to \mathcal{Y}$ is the residual concept linear classifier using unknown residual concepts. + +For one thing, we intend to maximize the accuracy when using only the original concepts, which can be formulated as the following optimization problem: + +$$ +\min _ {\Psi_ {c}} \mathbb {E} _ {(x, y) \in \mathcal {D}} \left[ \mathcal {L} \left(\Psi_ {c} (W \cdot \Phi_ {I} (x)), y\right) \right] + \lambda \cdot \Omega (\Psi_ {c}) \tag {8} +$$ + +where $\mathcal{L}(\hat{y}, y)$ is the cross-entropy loss function, $\Omega(\Psi_c)$ is a complexity measure to regularize the model, and $\lambda$ is the regularization strength. + +From another perspective, we aim to improve the performance after incorporating the residual concepts, which can be solved by the following optimization problem: + +$$ +\min _ {\Psi_ {r}, U} \underset {(x, y) \in \mathcal {D}} {\mathbb {E}} \left[ \mathcal {L} \left(\Psi_ {c} (W \cdot f) + \Psi_ {r} (U \cdot f), y\right) \right] + \lambda \cdot \Omega (\Psi_ {r}) \tag {9} +$$ + +where $f = \Phi_I(x)$ + +To simultaneously address these two problems, we perform two forward and backward propagations in each batch to update the parameters. When performing the first propagation, we utilize only the original concepts to optimize the original concept classifier $\Psi_{c}$ . During the second propagation, we fix the parameters of the original concept classifier + +$\Psi_{c}$ and optimize the residual concept classifier $\Psi_{r}$ as well as the learnable unknown concept vectors $U$ using both the original and the residual concepts. + +To avoid the influence of extreme values from unknown residual concepts, we employ cosine similarity instead of projection distance as the concept bottleneck and standardize the activations of each concept to have a mean of 0 and a standard deviation of 1 to speed up convergence [38]. These operations are reversible and do not affect the relative order of concepts or introduce additional information. + +# 3.4. Incremental Concept Discovery + +Through the aforementioned steps, the residual concepts effectively compensate for the incompleteness of the original concepts. However, these randomly learned concepts lack human interpretability, so we next translate them into human-understandable concepts. + +Parameters Initialization. We first initialize another estimizable vector $v_{d}$ , denoted as the discovered concept vector, whose value is the mean concept embeddings of the base concept bank with added noise. Subsequently, we append the discovered concept vector to the base concept bank and remove one of the learned unknown residual concept vectors, whose residual concept embedding matrix changes to $U_{-v_d} = U_{(D - 1)\times d}$ and residual classifier changes to $\Psi_{r - v_d}:\mathbb{R}^{D - 1}\to \mathcal{V}$ . After performing $L_{2}$ normalization and projection, the visual representations will also obtain a similarity score $c_{d} = v_{d}\cdot f$ to the discovered concept vector, and there will be a corresponding discovered concept linear classifier $\Phi_d:\mathbb{R}\rightarrow \mathcal{V}$ . We adopt the language priors as the initial weights to ensure stable updating of the discovered concept vector. In particular, the weights of the discovered concept classifier are initialized as the cosine similarity between the discovered concept embedding and the text embeddings for each class name, while other parameters and weights are kept untouched. + +Concept Similarity Loss Function. After adding the discovered concept vector to the base concept bank, the prediction under the original and residual strategy is as follows: + +$$ +\hat {y} _ {\text {o r g}} = \Psi_ {c} (c) + \Psi_ {d} \left(c _ {d}\right) = \Psi_ {c} (W \cdot f) + \Psi_ {d} \left(v _ {d} \cdot f\right) \tag {10} +$$ + +$$ +\hat {y} _ {\text {r e s}} = \hat {y} _ {\text {o r g}} + \Psi_ {r - v _ {d}} \left(U _ {- v _ {d}} \cdot f\right) \tag {11} +$$ + +To further guarantee that the discovered concept vector is interpretable, we propose the concept similarity loss function $\mathcal{L}_{\mathrm{sim}}$ , which utilizes the candidate concept bank $W^{*}$ to constrain the discovered concept embedding: + +$$ +\mathcal {L} _ {\text {s i m}} = 1 - \mathbb {E} \left[ \operatorname {R a n k} \left(W ^ {*} \cdot \frac {v _ {d} ^ {T}}{\| v _ {d} \| _ {2}}, M\right) \right] \tag {12} +$$ + +where $\operatorname{Rank}(v, M)$ denotes sorting $v$ from largest to smallest and selecting the first $M$ of them. + +Referring to the update strategy of the residual concept bottleneck model, we just add the discovered concept with its classifier during the first pass propagation: + +$$ +\min _ {\Psi_ {c}, \Psi_ {d}, v _ {d}} \mathbb {E} \left[ \mathcal {L} \left(\hat {y} _ {\text {o r g}}, y\right) \right] + \alpha \cdot \mathcal {L} _ {\text {s i m}} + \lambda \cdot \Omega \left(\Psi_ {c}, \Psi_ {d}\right) \tag {13} +$$ + +where $\alpha$ is the weight of the concept similarity loss. + +When performing the second propagation, we fix the parameters of the original concept classifier $\Psi_{c}$ , the discovered concept classifier $\Psi_{d}$ , and the discovered concept embedding $v_{d}$ , optimizing the residual concept classifier $\Psi_{r - v_d}$ and the unknown residual concept vectors $U_{-v_d}$ : + +$$ +\min _ {\Psi_ {r - v _ {d}}, U - v _ {d}} \mathbb {E} \left[ \mathcal {L} \left(\hat {y} _ {\text {r e s}}, y\right) \right] + \lambda \cdot \Omega \left(\Psi_ {r - v _ {d}}\right) \tag {14} +$$ + +We recover concepts in an incremental way until all the learned unknown residual concept vectors are transformed into pure, accurate, and human-interpretable concepts. At this point, the base concept library is fully updated, and experiments confirm its superior completeness. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. We conduct comprehensive experiments on 7 datasets, including: CIFAR-10, CIFAR-100 [28], TinyImageNet [30], LAD [61], CUB-200 [51], Food-101 [6], Flower-102 [37]. For a fair comparison, we apply CLIPRN50 when comparing with other CBMs and CLIP-ViT-L/14 on few-shot classification tasks as the backbone, and all linear classifiers are optimized with the Adam [25] optimizer. For more detailed information, please refer to the supplementary material. + +Baselines. To evaluate our proposed approach, we compare it with the following baseline methods: + +- CLIP Zero-shot[40]: the cosine similarities between the visual representations and the textual embeddings of each class name are calculated directly without any training. The class with the highest cosine similarity score is selected as the final classification result. +- Linear Probing (LP)[40]: We exclusively utilize the CLIP visual encoder and the obtained visual representations are then used to predict the label by training a linear classifier. +- Original CBM[26]: The original CBM relies on fine-grained concept annotations, so we compare our method with it only on LAD and CUB with available attribute annotations. In addition, CBMs may suffer from concept leakage, which can only be alleviated by CBMs trained independently [36]. Hence, we choose CBM-independent as the baseline for comparison. +- PCBM[58]: PCBM uses the ConceptNet[50], a knowledge graph dataset, to conduct a concept bank. It treats classes as nodes and incorporates surrounding neighboring nodes in the concept bank. More concepts can be included by expanding multiple layers outwards. + +Table 1. Comparison with other CLIP-based CBMs. Bold indicates the best interpretable result, underline indicates the 2nd-best result, italic indicates the black-box methods. + +
MethodInterpretabilityLengthCIFAR 10CIFAR 100
AccuracyNumberCUEAccuracyNumberCUE
Zero-shotYesN/A0.6796N/AN/A0.2620N/AN/A
LPNoN/A0.8858N/AN/A0.6995N/AN/A
PCBM-1rYes90.80441755.10730.53794401.3583
PCBM-2rYes90.80743832.34230.545011750.5153
PCBM-3rYes90.820810580.8620N/AN/AN/A
PCBM-hNo90.8757175N/A0.6683440N/A
Lf-CBMYes120.86771435.05650.67458920.6301
LaBo-10cYes270.84891003.14410.661810000.2451
LaBo-20cYes270.86692001.60540.673620000.1247
LaBo-30cYes260.87523001.1221N/AN/AN/A
Res-CBMYes70.8803237+105.09140.6791372+152.5396
+ +Table 2. Comparison with CBMs with labeled concept annotations. The labeling significance is consistent with Tab.1. + +
MethodLAD-ALAD-ELAD-FLAD-HLAD-VCUBMean
LP0.94320.86610.73930.49240.86710.72140.7714
Original CBM0.89640.78260.55350.33880.79070.65130.6689
PCBM-annotation0.89340.77110.59820.29820.78140.63630.6631
Res-CBM-before0.78970.77090.43560.14290.75480.59870.5812
Res-CBM-after0.89790.80450.66240.38620.83010.62430.7009
+ +- PCBM-h[58]: After training the PCBM, PCBM-h is applied as a post-processing method that connects the visual representation and the class labels result through shortcuts. It utilizes a linear classifier to predict the difference between the result of PCBM and the ground truth. +- Lf-CBM[38]: In contrast to PCBM, Lf-CBM generates concepts through a large language model (LLM). It solely utilizes CLIP as the concept annotator, allowing it to act on any visual backbone. We directly select CLIP as the visual backbone, thus omitting the process of computing the similarity matrix. +- LaBo[56]: LaBo similarly applies the LLM to generate candidate concepts. However, the quantity of concepts in LaBo is specific to each class. So we generate 10, 20, and 30 concepts per class to compare the performance. In addition, LaBo's linear classifier differs from the above baselines. To evaluate the quality of concepts equitably, we choose the same classifier as the above methods. + +Metrics. Besides accuracy, we also concentrate on concepts' efficiency, including both the average length of each concept and quantity of concepts. Specifically, we define the accuracy improvement brought by all concepts' length to measure the Concept Utilization Efficiency (CUE): + +$$ +\mathrm {C U E} = \frac {1 0 0 0 0 \times \mathrm {A c c}}{N \times \bar {L}} \tag {15} +$$ + +where $\mathrm{Acc}$ is the classification accuracy, $N$ is the quantity of concepts and $\bar{L}$ is the average number of letters included in each concept. Larger CUE means higher efficiency. + +# 4.2. Accuracy and Efficiency + +We compare our method with other CBMs in terms of accuracy and efficiency. Tab.1 provides the results of our method compared to other CLIP-based CBMs. Res-CBM attains higher accuracy than PCBM by $5.95\%$ on CIFAR-10 and $13.41\%$ on CIFAR-100 and even outperforms the inexplicable PCBM-h. Despite Lf-CBM and LaBo being powerful baselines, our methodology still achieves state-of-the-art results. Particularly, it should be noted that our method considerably exceeds both Lf-CBM and LaBo in terms of efficiency, as evidenced by the CUE metric. + +On LAD and CUB-200 with attribute annotations, we still use CLIP-50 with frozen parameters as the visual backbone to train Original CBM according to formula (2), as the results are shown in Tab.2. $^{3}$ The close performance of the Original CBM and PCBM-annotation suggests that the CBMs' performance heavily relies on the expert-selected concepts more than the model structure. Although Res-CBM-before performs poorly, a remarkable improvement is observed in Res-CBM-after after applying our unsupervised incremental concept discovery, which even surpasses supervised CBMs with concept annotations on most datasets. + +![](images/0a80dec07964a41a7194270cbc6a07070c3ca2ab81db8be0df7da7520f4b8d7c.jpg) + +![](images/6453bd78e832b4bc5477907b925a18c8f5a942c20a3465fc37fa81872882a3df.jpg) + +![](images/87b000cc3f4823c433e7a1f5de40c28ae0c2ef1717a127a2c0216289b3968fc6.jpg) + +![](images/d2cffb1373e6c8fc668b82fe71ab55591bca988c2d87c428ccc00a04e81862e3.jpg) +Figure 4. Test accuracy $(\%)$ comparison between Res-CBM and LP on 6 datasets. The x-axis represents the number of labeled images. + +![](images/db9d49c3f08dfeffa6e9bbdc81bcdcee87a8724fb3aa2fa4259f777441370d82.jpg) + +![](images/9996cab42b178f26a64aac5685a427fe3eff1110de64e54686a6f7c887cdf586.jpg) + +![](images/255afeca3b59d4b4887ff40c0fbdb76ff9d54b8a6145dca4553fb0b35bba80f4.jpg) +Figure 5. Ablation results on residual vector numbers, concept similarity loss weights and candidate concept numbers. + +![](images/8d9703afb8b9339990d1db65d1de87e1f79e7417cb3a6c1939e14ba154a94bc2.jpg) + +![](images/3af79f11e4a84c2fd32f5a96cad420e6e3299cbd24780ebc2d7f0a0cd59f9261.jpg) + +# 4.3. Interpretability + +In this subsection, we visualize the mechanism of ResCBM and demonstrate how the newly discovered concepts assist in advancing classification performance. For each image, we display the top 5 concepts with the highest activation scores in the concept bottleneck, as shown in Fig.6. Through a sparse concept classifier, we can obtain predictions, which signifies predicting the class by a linear combination of concepts. + +However, due to the incompleteness of the base concept bank, it is challenging to achieve accurate classifications by solely relying on these concepts in several images, e.g., dragonfly and honeybee, peach and hawthorn, both of which possess concepts from the base concept bank. With the help of Res-CBM, we have discovered 2 concepts, nectar and rough, from the candidate concept bank. Unlike dragonflies, honeybees often gather nectar from the center of flowers, thus associating them with the concept of nectar. Moreover, hawthorns have a rougher surface compared to peaches. By incorporating these discovered concepts into the base concept bank, these initially misclassified samples are now correctly categorized, achieving automatic model debugging to a certain extent. + +# 4.4. Few-shot Capability + +Fig.4 illustrates the performance comparison under different data volume settings between Res-CBM and LP. Compared to the end-to-end black-box model, our method achieves superior performance when little data is available, and exhibits a slight performance gap with larger amounts of sample sizes, which indicates that our method has maintained the accuracy without sacrificing interpretability. + +For common object datasets, our approach demonstrates excellent performance with 1, 2, 4, and 8 labeled images per category. We credit its success to the incorporation of human concept information, which helps the model extract vital aspects relevant to the categories from the representations of the black-box backbone. + +For fine-grained object datasets, our method outperforms the black-box model when the data volume is extremely low. As the data volume increases, the unexplainable black-box model's performance becomes more prominent, especially in expert datasets such as Flower-102 and CUB-200. It might be attributed to common concepts struggling to distinguish the subtle differences between these fine-grained objects. A feasible solution is to enhance the specificity of concepts by a tailored specialized concept candidate bank. + +![](images/e69a11d448879f8439d3257e42204054889ee0a3fe3275996b6fb4ac7d269d41.jpg) +Figure 6. Concepts applied in Res-CBM on LAD-A (top) and LAD-F (bottom). Solid boxes represent concepts from the base concept bank, dashed boxes indicate the discovered concepts. Heatmaps refer to learned linear concept classifiers, in which the x-axis represents classes, the y-axis represents concepts, and the values represent the contribution of concepts to categories. + +# 4.5. Ablation Study + +Residual Vector Number. To investigate the impact of residual vector numbers on performance improvement and demonstrate that our method can be applied as a post-processing approach to any CBMs, we record the results of attaching different residual vector numbers for Lf-CBM on CIFAR-10, as shown in Fig.5-left. As the quantity of vectors increases, the performance of Lf-CBM continuously improves and gradually saturates at around 15 vectors. + +Candidate Concept Number. We fix the residual vector number at 10 and set the concept similarity loss weight to 0.1, then record the final accuracy and the average similarity between the discovered concepts and the most similar concepts in the candidate concept bank during the discovery process in Fig.5-middle. When the candidate concept number is small, the model tends to converge to this unique concept, making it difficult to escape local optima. When it is large, the optimizing vectors easily oscillate between different concepts, resulting in lower accuracy and similarity. Overall, setting the candidate concept number to 5 seems to be a good hyperparameter choice. + +Concept Similarity Loss Weight. With a fixed candidate concept number at 5, we also record the final accuracy and average similarity for different loss weights as shown in Fig.5-right. When the weight is low, the similarity of the discovered concepts is extremely low, which resembles a random selection strategy, leading to poorer performance. When the weight is large, the model tends to converge to a local optimum only satisfying the concept similarity loss, sacrificing the ability to explore more appropriate concepts. Since Res-CBM has already saturated after the completion of unknown concept vectors, the cross-entropy loss value is small. Therefore, a weight of 0.1 realizes optimal results. + +# 5. Discussion and Conclusion + +Rethinking CBMs. Indeed CBMs are valuable attempts towards transparency of the decision-making process, one important and fundamental problem may be still unclear, which is: how many concepts are good? especially when lacking a well-accepted and rigorous definition of concepts. In this paper, we have tried to explore this problem. Firstly, the number of concepts should not be the larger the better. From the optimization perspective, the operation of CBMs to project visual representations into concept space is a linear transformation. If its rank is greater than or equal to the dimension $d$ of the concept vector, this process is invertible. Therefore, it is straightforward to re-estimate the inverse transformation matrix to preserve classification accuracy in subsequent linear classifiers. The number of concepts larger than $d$ may decrease the efficiency, making the interpretability less effective. + +On the other hand, the concept should be an efficient way to express categories. Humans can describe objects in the world exponentially using a finite set of concepts. Theoretically, from informatics, when each concept weight is binary, the concept quantity needed to distinguish $n$ categories will be enough approximately $\log_2 n$ . This is the reason for the poor CUE of LaBo [56], which finds concepts for each category in a way that the CUE complexity is $\mathcal{O}(n)$ rather than $\mathcal{O}(\log_2 n)$ . This suggests that the CUE is crucial in CBMs, and a reasonable number of concepts should lie in the interval of $\left[\log_2 n\right]$ , $d$ . + +Conclusion. In this paper, we emphasize the significance of purity, precision, and completeness in CBMs and introduce the CUE metric to evaluate the descriptive efficiency of CBMs. Our proposed Res-CBM complements the missing concepts in any CBM with an incremental concept discovery approach, which achieves optimal accuracy with the best concept utilization efficiency. + +Limitation and Future Work. For our proposed ResCBM, the candidate concept bank construction for fine-grained datasets remains a challenge. Additionally, the sequential concept discovery approach increases computational time costs, while more efficient concept similarity calculation and parallel concept discovery techniques are needed to develop. For the CBM structure, existing CBMs represent all concepts into a single bottleneck, disregarding the hierarchical nature of concepts, where simple concepts can be combined to form more complicated ones. + +# Acknowledgements + +This work was partly supported by the National Natural Science Foundation of China (Grant No. 61991451) and the Shenzhen Science and Technology Program (JCYJ20220818101001004). The first two authors have equal contribution. + +# References + +[1] Abubakar Abid, Mert Yuksekgonul, and James Zou. Meaningfully debugging model mistakes using conceptual counterfactual explanations. In International Conference on Machine Learning, pages 66-88. PMLR, 2022. 4 +[2] Mohammed Amer and Tomás Maul. A review of modularization techniques in artificial neural networks. Artificial Intelligence Review, 52:527-561, 2019. 2 +[3] Mohammad Taha Bahadori and David E Heckerman. 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Multimodal pre-trained models can match visual representations with textual concept embeddings, allowing for obtaining the interpretable concept bottleneck without the expertise concept annotations. Recent research has focused on the concept bank establishment and the high-quality concept selection. However, it is challenging to construct a comprehensive concept bank through humans or large language models, which severely limits the performance of CBMs. In this work, we propose the Incremental Residual Concept Bottleneck Model (ResCBM) to address the challenge of concept completeness. Specifically, the residual concept bottleneck model employs a set of estimizable vectors to complete missing concepts, then the incremental concept discovery module converts the complemented vectors with unclear meanings into potential concepts in the candidate concept bank. Our approach can be applied to any user-defined concept bank, as a posthoc processing method to enhance the performance of any CBMs. Furthermore, to measure the descriptive efficiency of CBMs, the Concept Utilization Efficiency (CUE) metric is proposed. Experiments show that the Res-CBM outperforms the current state-of-the-art methods in terms of both accuracy and efficiency and achieves comparable performance to black-box models across multiple datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 613, + 128, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 128, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 128, + 625 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 634, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 287, + 682 + ], + "type": "text", + "content": "Deep neural networks (DNNs) [31, 45] have achieved unprecedented success in a wide range of machine learning tasks, including computer vision [16, 32], natural language processing [14, 59], and speech recognition [34, 41]." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 225, + 545, + 296 + ], + "blocks": [ + { + "bbox": [ + 309, + 225, + 545, + 296 + ], + "lines": [ + { + "bbox": [ + 309, + 225, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 309, + 225, + 545, + 296 + ], + "type": "image", + "image_path": "0b584f311df233e268cbea997fc3b4237633a1711c6075fef927fadd07ace8bc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 304, + 546, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 304, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 546, + 361 + ], + "type": "text", + "content": "Figure 1. Challenges in CBMs. When a concept contains many atomic attributes, making it too complex for human to comprehend. When a concept is too high-level, DNNs may struggle to provide accurate prediction. Additionally, there is a risk of human-designed concept bank missing some important concepts." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 385, + 546, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 546, + 506 + ], + "type": "text", + "content": "However, due to their complex and deep structures, they are often regarded as black-box models [7, 49], which are too difficult to understand and interpret. In fields that demand high levels of trustworthiness, such as medicine [44], healthcare [21], education [60], and finance [39], model interpretability has become increasingly crucial. It indicates whether we can trust the DNNs' decisions, and how we can rectify the errors when the DNNs make mistakes. Making deep learning models more interpretable is a significant yet challenging research topic." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 507, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 651 + ], + "type": "text", + "content": "A promising approach for achieving interpretability in deep learning is through concept-based models [46], which leverage human-generated high-level concepts to explain the black-box features of DNNs. Among these approaches, Concept Bottleneck Models (CBMs) [26] map the visual representations to a set of concept values that are understandable to humans. These interpretable concepts are then used to make the final decision by a linear function, greatly enhancing our understanding of the decision-making process. Of greater significance, humans can repair models' faults by directly editing or intervening on the concept bottleneck [3, 48]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "Due to the considerable cost of the fine-grained and precise annotation for each concept in CBMs, multimodal pretrained model-based CBMs [58] have recently emerged as a research hotspot. CLIP [40] demonstrates the capacity to establish correspondences between visual information and" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 254, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 254, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 254, + 703 + ], + "type": "text", + "content": "*Work done during an internship at Shanghai AI Laboratory." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11030" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "textual descriptions. Accordingly, we can utilize the CLIP text encoder to encode human-understood concepts into concept embeddings and use the visual encoder to encode images into visual representations. By projecting visual representations to each concept embedding, we can obtain the concept bottleneck. The recent innovations have primarily concentrated on comprehensive concept bank establishment and efficient high-quality concept selection. However, these methods face three critical challenges as shown in Fig.1:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 195, + 289, + 578 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 47, + 195, + 289, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 195, + 289, + 351 + ], + "spans": [ + { + "bbox": [ + 47, + 195, + 289, + 351 + ], + "type": "text", + "content": "- Purity: The essence of concepts is to abstract complex information into a combination of simple foundational elements, which can generalize to unseen data through the infinite combinations of finite concepts, offering an efficient way to describe the world. Long and complex descriptions like small, black insect with six legs or long, thin tool with a wooden handle, can be composed entirely of combinations of simple concepts such as small, black, insect, leg, etc., which may increase the productivity of concept utilization. Since these complicated concepts are excessively detailed, they may not be shared across different classes, which will limit their ability to capture shared knowledge between different categories." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 351, + 289, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 289, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 289, + 470 + ], + "type": "text", + "content": "- Precision: Each concept should be clearly understandable for both humans and multimodal pre-trained models when annotating concepts. Specifically, concepts should not be markedly more difficult than classes. For example, high-level concepts like amphibians or perennial, are relatively harder for humans to understand and exhibit weaker interpretability. Moreover, we cannot ascertain whether CLIP possesses the capability to understand these high-level concepts, which can potentially lead to errors in concept annotation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 471, + 289, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 289, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 289, + 578 + ], + "type": "text", + "content": "- Completeness: Concept bank should strive to include as much relevant visual information that is beneficial for downstream classification tasks as possible. It is essential to avoid losing too much information in the process. However, it is challenging to establish a comprehensive concept bank directly [57]. The exhaustive capability of language descriptions is limited, making it difficult to accomplish a fully thorough concept bank through manual design and selection." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "In this work, we propose the Incremental Residual Concept Bottleneck Model (Res-CBM) to address the three challenges above. First, we establish a simple and pure base concept bank and candidate concept bank to ensure that the CLIP can accurately recognize each concept. Next, we initialize a set of estimizable vectors as filling concepts and optimize this set of filling concepts through the residual concept bottleneck model, to make up for the inadequacy in the base concept bank. Finally, the incremental concept discovery module is utilized to translate these complemented vectors with unclear meanings into potential concepts in the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "candidate concept bank, improving the performance while preserving the interpretability of the CBM. Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 109, + 547, + 302 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 109, + 545, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 109, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 109, + 545, + 145 + ], + "type": "text", + "content": "1. We systematically reviewed the research on the CLIP-based CBMs, clarifying the importance of the concepts' purity, precision, and completeness." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 145, + 547, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 145, + 547, + 241 + ], + "spans": [ + { + "bbox": [ + 306, + 145, + 547, + 241 + ], + "type": "text", + "content": "2. We proposed the residual concept bottleneck model to make up for the insufficiency in the base concept bank and converted these complemented unknown vectors into potential concepts in the candidate concept bank through the incremental concept discovery module. It should be emphasized that our approach can be applied to any user-defined concept bank, as a post-hoc processing method to enhance the performance of any CBMs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 241, + 547, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 241, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 547, + 302 + ], + "type": "text", + "content": "3. To measure the descriptive efficiency of CBMs, we introduced the metric of the concept utilization efficiency. We performed extensive experiments to validate our methodology and elaborate ablation studies to illustrate the effectiveness of each component." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 310, + 392, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 310, + 392, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 310, + 392, + 323 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 331, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 582 + ], + "type": "text", + "content": "Deep neural networks (DNNs) can be explained through pixels [8, 47], samples [15, 22], weights [54], individual neurons [5, 13], subnetworks [2, 12], representations [4, 19, 20], etc [43]. Concept-based models [23, 33, 52, 53] are representation-level interpretable approaches, whose core idea is to map representations with unknown meanings extracted by the black-box DNNs to a set of concepts that can be comprehended by humans [9, 11, 35, 36]. Concept-based models can be broadly categorized into Concept Bottleneck Models (CBMs) [26], which describe concepts as independent values annotated by experts, and Concept Activation Vectors (CAVs) [24], which represent concepts as normal vectors of the decision boundaries that distinguish positive and negative samples of a concept. CBMs involve the datasets labeled with fine-grained and precise attributes by expert knowledge, such as CUB-200 [18], OAI [10], and LAD [61], whereas CAVs require learning the concept activation vectors on additional probe datasets, and the directions of the concept activation vectors are strictly correlated with the probe datasets [42]. These limitations severely restrict the development of concept-based models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Recently, there has been a rapid development of multimodal pre-trained models [17], among which CLIP does an excellent job of relating visual information to text through contrastive learning, giving researchers confidence for unsupervised concept labeling with CLIP. PCBM [58] generates a concept bank via ConceptNet [50] and calculates the projection distance between the CLIP textual concept embeddings and the CLIP visual representations of images, analogous to the CAVs, to obtain the concept bottleneck. PCBM-h [58] introduces an uninterpretable residual linear layer to compensate for incomplete concept extraction by" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11031" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 100, + 70, + 496, + 277 + ], + "blocks": [ + { + "bbox": [ + 100, + 70, + 496, + 277 + ], + "lines": [ + { + "bbox": [ + 100, + 70, + 496, + 277 + ], + "spans": [ + { + "bbox": [ + 100, + 70, + 496, + 277 + ], + "type": "image", + "image_path": "e026e67dc6d2b76b6d9dbfa5864e7019d8905c4000defeb73a338bde51f0bd7e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 547, + 309 + ], + "type": "text", + "content": "Figure 2. Different CBMs' structures. (a): CLIP linear probing [40]. (b): Original Concept Bottleneck Model (CBM) [26]. (c) Post-hoc Concept Bottleneck Model (PCBM) [38, 56, 58]. (d): Hybrid Post-hoc Concept Bottleneck Model (PCBM-h) [58]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 327, + 290, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 290, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 290, + 437 + ], + "type": "text", + "content": "fitting the difference between the PCBM's result and the ground truth through the original visual representations of CLIP. Label-free CBM [38] only leverages CLIP to concept annotation, maximizing the similarity between the concept bottleneck of the features extracted by arbitrary visual backbone and the concept annotations labeled by CLIP. LaBo [56] generates a set of candidate concepts through large language models and designs a submodular optimization block to select the concepts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 449, + 105, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 105, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 105, + 462 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 468, + 172, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 172, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 172, + 481 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": "Consider a dataset of image-label pairs " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x,y)\\}" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "x\\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " is the image and " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " is the label. We have " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " human-selected concepts to describe the essential information of these images, which can be denoted as discrete tokens " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{E} = \\{e_1,e_2,\\dots,e_N\\}" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": ". Multimodal pre-trained alignment model (e.g., CLIP [40]) has an image encoder " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\Phi_I:\\mathcal{X}\\to \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\Phi_T" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": ", which can map images and text into a shared " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": "-dimensional feature space respectively. We encode the discrete tokens with the CLIP text encoder then perform " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " normalization to obtain the concept embeddings " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\{w_{1},w_{2},\\ldots ,w_{N}|w_{i} = \\Phi_{T}(e_{i}),i = 1,2,\\ldots ,N\\}" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " with the length of 1 and the dimension of " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": ". We concatenate these concept embeddings to a concept projection matrix " + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "inline_equation", + "content": "W_{N\\times d}:\\mathbb{R}^d\\to \\mathbb{R}^N" + }, + { + "bbox": [ + 46, + 487, + 287, + 666 + ], + "type": "text", + "content": " in arbitrary order, also identified as a concept bank." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 668, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 668, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 668, + 288, + 693 + ], + "type": "text", + "content": "Correspondingly, we utilize the CLIP image encoder to get the visual representations " + }, + { + "bbox": [ + 47, + 668, + 288, + 693 + ], + "type": "inline_equation", + "content": "f = \\Phi_I(x)" + }, + { + "bbox": [ + 47, + 668, + 288, + 693 + ], + "type": "text", + "content": ". Considering that" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "text", + "content": "CLIP has aligned the images with the textual data when pretraining, the visual representations share the feature space with any concept embedding, and the projection length " + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "inline_equation", + "content": "\\| f\\| _2\\cdot \\cos \\langle w_i,f\\rangle" + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "text", + "content": " can reflect the presence of a particular concept in the image. Since undergoing " + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "text", + "content": " normalization on " + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "text", + "content": ", the concept probability can be directly formulated in terms of the dot product " + }, + { + "bbox": [ + 304, + 327, + 546, + 411 + ], + "type": "inline_equation", + "content": "c = W\\cdot f" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 411, + 547, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 458 + ], + "type": "text", + "content": "Fig.2 illustrates the structure of common CBMs. For CLIP Linear Probing [29], an uninterpretable linear classifier " + }, + { + "bbox": [ + 304, + 411, + 547, + 458 + ], + "type": "inline_equation", + "content": "\\Psi : \\mathbb{R}^d \\to \\mathcal{V}" + }, + { + "bbox": [ + 304, + 411, + 547, + 458 + ], + "type": "text", + "content": " is trained directly from visual representations:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 376, + 459, + 545, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 459, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 376, + 459, + 545, + 473 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\Psi (f) = \\Psi \\left(\\Phi_ {I} (x)\\right) \\tag {1}", + "image_path": "1fe7212cde6d4c58b3cbebf1a432ba86a111a95de277c1b474ebe4ef07e53807.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "type": "text", + "content": "Original CBM [26] first extracts concepts using a concept extractor " + }, + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathrm{cpt}}: \\mathbb{R}^d \\to \\mathbb{R}^N" + }, + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "type": "text", + "content": " and then linearly unites the extracted concepts for label prediction by concept classifier " + }, + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathrm{cls}}: \\mathbb{R}^N \\to \\mathcal{V}" + }, + { + "bbox": [ + 304, + 475, + 545, + 523 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 385, + 529, + 545, + 543 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 529, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 385, + 529, + 545, + 543 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\Psi_ {\\mathrm {c l s}} \\left(\\Psi_ {\\mathrm {c p t}} (f)\\right) \\tag {2}", + "image_path": "e8a69b19970c4d1ffd7db9a4baa2e7f56f3dd057078466239167e0cda931517e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "text", + "content": "Post-hoc CBM [58] stands for a category of CLIP-based CBMs, including Label-free CBM [38], LaBo [56], etc. They attain concept bottleneck by projecting visual representations " + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "text", + "content": " directly to a concept bank " + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "text", + "content": ", rather than by learning a concept extractor. After getting concepts, only a linear concept classifier " + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "inline_equation", + "content": "\\Psi_{c}:\\mathbb{R}^{N}\\to \\mathcal{V}" + }, + { + "bbox": [ + 304, + 548, + 547, + 620 + ], + "type": "text", + "content": " needs to be learned." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 374, + 631, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 631, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 374, + 631, + 545, + 644 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\Psi_ {c} (c) = \\Psi_ {c} (W \\cdot f) \\tag {3}", + "image_path": "762384395408f8eed4c054eea2038e2aa2e06e1a9e6037f5dabef9d1fdc99a06.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": "PCBM-h [58] adds a linear layer " + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\Psi_r: \\mathbb{R}^d \\to \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": " between the original visual representation and the labels on the basis of PCBM, which is used to predict the difference between the PCBM result and the ground truth." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 336, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 336, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\Psi_ {c} (c) + \\Psi_ {r} (f) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (f) \\tag {4}", + "image_path": "ff7034cc5909e5a573d30a106706612d90d98dc43be683bf8c7b1e4e1cded62d.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 282, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 282, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 282, + 714 + ], + "type": "text", + "content": "1The symbol of " + }, + { + "bbox": [ + 58, + 702, + 282, + 714 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 58, + 702, + 282, + 714 + ], + "type": "text", + "content": " normalization is omitted for writing convenience." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11032" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 206, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 206, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 206, + 85 + ], + "type": "text", + "content": "3.2. Concept Bank Establishment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "type": "text", + "content": "Candidate Concept Bank. To ensure precision, we need to make sure that CLIP is capable of recognizing each concept, and one straightforward way is to construct the concept bank from the CLIP pre-trained dataset. For purity, it is desirable for each concept to be at the atom level rather than the compound level, thus maintaining the clarity and specificity. We find that the scene graph [27] consisting of visual concepts to be an appropriate foundation, in which an atom is defined as a singular visual concept, corresponding to a single scene graph node. Atoms are subtyped into objects, relationships, and attributes. We pick the nouns and adjectives in them as the candidate concept bank " + }, + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{E}^*" + }, + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "type": "text", + "content": "Base Concept Bank. Although our method can recover missing concepts from a diverse base concept bank, a high-quality base concept bank can remarkably improve the efficiency of our approach. A base concept bank is expected to consist of two parts. Firstly, it should include general concepts that are applicable across various scenarios. We select the pre-defined concept library proposed by [24], which has been widely used in various tasks [1, 55], as our general concept bank " + }, + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{ge}}" + }, + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "type": "text", + "content": ". Secondly, it is supposed to include concepts relevant to the specific classification task. Following the PCBM [58], we collect all concepts from ConceptNet [50] that have relations of hasA, isA, partOf, HasProperty, and MadeOf with the classes in each classification task to build the associated concept bank " + }, + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{as}}" + }, + { + "bbox": [ + 46, + 235, + 288, + 426 + ], + "type": "text", + "content": ". Both concept banks should be included in the candidate concept bank, from which we can derive the base concept bank:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 436, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 436, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {E} _ {0} = \\left(\\mathcal {E} _ {\\mathrm {g e}} \\cap \\mathcal {E} ^ {*}\\right) \\cup \\left(\\mathcal {E} _ {\\mathrm {a s}} \\cap \\mathcal {E} ^ {*}\\right) \\tag {5}", + "image_path": "d3fb1848b757f886e3a3b83453f33f3326394b02bcbaf2800b7c234aafc0f384.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 460, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 287, + 496 + ], + "type": "text", + "content": "We encode the discrete concept tokens with the CLIP text encoder then perform " + }, + { + "bbox": [ + 47, + 460, + 287, + 496 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 47, + 460, + 287, + 496 + ], + "type": "text", + "content": " normalization to obtain the base and candidate concept embedding matrices:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 506, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 506, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 99, + 506, + 287, + 520 + ], + "type": "interline_equation", + "content": "W _ {0} = \\Phi_ {T} \\left(\\mathcal {E} _ {0}\\right), \\quad W ^ {*} = \\Phi_ {T} \\left(\\mathcal {E} ^ {*}\\right) \\tag {6}", + "image_path": "cb5ad1c0b6de91f248ed4c2609b894336bdbd2d4a146c24276a31010fdac208e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 538, + 237, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 237, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 237, + 551 + ], + "type": "text", + "content": "3.3. Residual Concept Bottleneck Model" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 677 + ], + "type": "text", + "content": "Previous methods have typically involved pre-generating a set of relevant concepts and then deleting some of them to get the final concept bank. However, on the one hand, the pre-generated concepts might be insufficient, as their scale has often limitations. On the other hand, manual filtering without leveraging dataset information may result in the omission of important concepts. Therefore, we propose the residual concept bottleneck model to learn the missing concepts from the dataset content in an incremental approach compared to other decremental methods as shown in Fig.3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "We first randomly initialize " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " estimizable vectors " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "U_{D\\times d} = \\{u_1,u_2,\\dots,u_D\\}" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " with dimensions consistent with those of the existing concept embeddings. We likewise" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 73, + 542, + 286 + ], + "blocks": [ + { + "bbox": [ + 310, + 73, + 542, + 286 + ], + "lines": [ + { + "bbox": [ + 310, + 73, + 542, + 286 + ], + "spans": [ + { + "bbox": [ + 310, + 73, + 542, + 286 + ], + "type": "image", + "image_path": "318aeaf76579714c5f9a830f5530045deec985f0a5d599033a03548dafcdb562.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 297, + 533, + 308 + ], + "lines": [ + { + "bbox": [ + 317, + 297, + 533, + 308 + ], + "spans": [ + { + "bbox": [ + 317, + 297, + 533, + 308 + ], + "type": "text", + "content": "Figure 3. Incremental Residual Concept Bottleneck Model." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 328, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 328, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 328, + 545, + 376 + ], + "type": "text", + "content": "project the visual representations onto these vectors, resulting in residual concepts " + }, + { + "bbox": [ + 305, + 328, + 545, + 376 + ], + "type": "inline_equation", + "content": "r = U \\cdot f" + }, + { + "bbox": [ + 305, + 328, + 545, + 376 + ], + "type": "text", + "content": " with unclear meanings. The prediction result of using the residual concepts to complement the original concepts is as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 384, + 545, + 398 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 384, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 329, + 384, + 545, + 398 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\Psi_ {c} (c) + \\Psi_ {r} (r) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (U \\cdot f) \\tag {7}", + "image_path": "283f5eedb293a089abeee922ce423bb6e3059bf6c7aebea69f4b50ce4d44149e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\Psi_c: \\mathbb{R}^N \\to \\mathcal{Y}" + }, + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "type": "text", + "content": " is the original concept linear classifier using existing concepts and " + }, + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\Psi_r: \\mathbb{R}^D \\to \\mathcal{Y}" + }, + { + "bbox": [ + 305, + 406, + 545, + 442 + ], + "type": "text", + "content": " is the residual concept linear classifier using unknown residual concepts." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 442, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 442, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 305, + 442, + 545, + 478 + ], + "type": "text", + "content": "For one thing, we intend to maximize the accuracy when using only the original concepts, which can be formulated as the following optimization problem:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 486, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 486, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 318, + 486, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\min _ {\\Psi_ {c}} \\mathbb {E} _ {(x, y) \\in \\mathcal {D}} \\left[ \\mathcal {L} \\left(\\Psi_ {c} (W \\cdot \\Phi_ {I} (x)), y\\right) \\right] + \\lambda \\cdot \\Omega (\\Psi_ {c}) \\tag {8}", + "image_path": "aabda536b2d84a9be9820f313ee3fd26bd6bbd33bcb4cd1caec68b73bc3484ba.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\hat{y}, y)" + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "text", + "content": " is the cross-entropy loss function, " + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\Omega(\\Psi_c)" + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "text", + "content": " is a complexity measure to regularize the model, and " + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 517, + 545, + 553 + ], + "type": "text", + "content": " is the regularization strength." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 554, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 554, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 554, + 545, + 590 + ], + "type": "text", + "content": "From another perspective, we aim to improve the performance after incorporating the residual concepts, which can be solved by the following optimization problem:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 310, + 597, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 597, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 310, + 597, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\min _ {\\Psi_ {r}, U} \\underset {(x, y) \\in \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} \\left(\\Psi_ {c} (W \\cdot f) + \\Psi_ {r} (U \\cdot f), y\\right) \\right] + \\lambda \\cdot \\Omega (\\Psi_ {r}) \\tag {9}", + "image_path": "b1e3e02b9cfda45f0745a53d5b3383c57cf14045325a5d6e9496b40a8649f380.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 630, + 382, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 382, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 382, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 630, + 382, + 641 + ], + "type": "inline_equation", + "content": "f = \\Phi_I(x)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": "To simultaneously address these two problems, we perform two forward and backward propagations in each batch to update the parameters. When performing the first propagation, we utilize only the original concepts to optimize the original concept classifier " + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Psi_{c}" + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": ". During the second propagation, we fix the parameters of the original concept classifier" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11033" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\Psi_{c}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " and optimize the residual concept classifier " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\Psi_{r}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " as well as the learnable unknown concept vectors " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " using both the original and the residual concepts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 192 + ], + "type": "text", + "content": "To avoid the influence of extreme values from unknown residual concepts, we employ cosine similarity instead of projection distance as the concept bottleneck and standardize the activations of each concept to have a mean of 0 and a standard deviation of 1 to speed up convergence [38]. These operations are reversible and do not affect the relative order of concepts or introduce additional information." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 199, + 217, + 212 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 199, + 217, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 217, + 212 + ], + "type": "text", + "content": "3.4. Incremental Concept Discovery" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 217, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 287, + 277 + ], + "type": "text", + "content": "Through the aforementioned steps, the residual concepts effectively compensate for the incompleteness of the original concepts. However, these randomly learned concepts lack human interpretability, so we next translate them into human-understandable concepts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": "Parameters Initialization. We first initialize another estimizable vector " + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "inline_equation", + "content": "v_{d}" + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": ", denoted as the discovered concept vector, whose value is the mean concept embeddings of the base concept bank with added noise. Subsequently, we append the discovered concept vector to the base concept bank and remove one of the learned unknown residual concept vectors, whose residual concept embedding matrix changes to " + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "inline_equation", + "content": "U_{-v_d} = U_{(D - 1)\\times d}" + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": " and residual classifier changes to " + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\Psi_{r - v_d}:\\mathbb{R}^{D - 1}\\to \\mathcal{V}" + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": ". After performing " + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": " normalization and projection, the visual representations will also obtain a similarity score " + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "inline_equation", + "content": "c_{d} = v_{d}\\cdot f" + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": " to the discovered concept vector, and there will be a corresponding discovered concept linear classifier " + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\Phi_d:\\mathbb{R}\\rightarrow \\mathcal{V}" + }, + { + "bbox": [ + 46, + 277, + 287, + 503 + ], + "type": "text", + "content": ". We adopt the language priors as the initial weights to ensure stable updating of the discovered concept vector. In particular, the weights of the discovered concept classifier are initialized as the cosine similarity between the discovered concept embedding and the text embeddings for each class name, while other parameters and weights are kept untouched." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 505, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 541 + ], + "type": "text", + "content": "Concept Similarity Loss Function. After adding the discovered concept vector to the base concept bank, the prediction under the original and residual strategy is as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 562, + 286, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 562, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 53, + 562, + 286, + 574 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {\\text {o r g}} = \\Psi_ {c} (c) + \\Psi_ {d} \\left(c _ {d}\\right) = \\Psi_ {c} (W \\cdot f) + \\Psi_ {d} \\left(v _ {d} \\cdot f\\right) \\tag {10}", + "image_path": "fabe16115e860e90c46086b4d175815ab63ca6494ba278ba71ddd9804d455e61.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 577, + 286, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 577, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 102, + 577, + 286, + 590 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {\\text {r e s}} = \\hat {y} _ {\\text {o r g}} + \\Psi_ {r - v _ {d}} \\left(U _ {- v _ {d}} \\cdot f\\right) \\tag {11}", + "image_path": "c26da7d57c60f32e6a6b4ca67503a4dd63658e0954efbb420f282ae8bcfc99e0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "type": "text", + "content": "To further guarantee that the discovered concept vector is interpretable, we propose the concept similarity loss function " + }, + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sim}}" + }, + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "type": "text", + "content": ", which utilizes the candidate concept bank " + }, + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "type": "inline_equation", + "content": "W^{*}" + }, + { + "bbox": [ + 47, + 598, + 287, + 647 + ], + "type": "text", + "content": " to constrain the discovered concept embedding:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 84, + 654, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 654, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 84, + 654, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i m}} = 1 - \\mathbb {E} \\left[ \\operatorname {R a n k} \\left(W ^ {*} \\cdot \\frac {v _ {d} ^ {T}}{\\| v _ {d} \\| _ {2}}, M\\right) \\right] \\tag {12}", + "image_path": "d7dc249e8f44fbc4d0e3c82c82a5ae91c94ea2cb8ed16bd784848f0b30253405.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\operatorname{Rank}(v, M)" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " denotes sorting " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " from largest to smallest and selecting the first " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " of them." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "Referring to the update strategy of the residual concept bottleneck model, we just add the discovered concept with its classifier during the first pass propagation:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 112, + 545, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 112, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 313, + 112, + 545, + 131 + ], + "type": "interline_equation", + "content": "\\min _ {\\Psi_ {c}, \\Psi_ {d}, v _ {d}} \\mathbb {E} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\text {o r g}}, y\\right) \\right] + \\alpha \\cdot \\mathcal {L} _ {\\text {s i m}} + \\lambda \\cdot \\Omega \\left(\\Psi_ {c}, \\Psi_ {d}\\right) \\tag {13}", + "image_path": "9e9bec1c08916634ec2c549e6bd4c75846ca6fcddde3e103e66e7c9a84aac267.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 135, + 515, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 135, + 515, + 147 + ], + "spans": [ + { + "bbox": [ + 306, + 135, + 515, + 147 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 135, + 515, + 147 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 135, + 515, + 147 + ], + "type": "text", + "content": " is the weight of the concept similarity loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "spans": [ + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "content": "When performing the second propagation, we fix the parameters of the original concept classifier " + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "inline_equation", + "content": "\\Psi_{c}" + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "content": ", the discovered concept classifier " + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "inline_equation", + "content": "\\Psi_{d}" + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "content": ", and the discovered concept embedding " + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "inline_equation", + "content": "v_{d}" + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "content": ", optimizing the residual concept classifier " + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "inline_equation", + "content": "\\Psi_{r - v_d}" + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "content": " and the unknown residual concept vectors " + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "inline_equation", + "content": "U_{-v_d}" + }, + { + "bbox": [ + 305, + 147, + 545, + 207 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 210, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 210, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 340, + 210, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\min _ {\\Psi_ {r - v _ {d}}, U - v _ {d}} \\mathbb {E} \\left[ \\mathcal {L} \\left(\\hat {y} _ {\\text {r e s}}, y\\right) \\right] + \\lambda \\cdot \\Omega \\left(\\Psi_ {r - v _ {d}}\\right) \\tag {14}", + "image_path": "76be3820ed56f21dcfc181506e719cfe214e40531a2671117f7b9f68db66f56c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 235, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 235, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 235, + 545, + 295 + ], + "type": "text", + "content": "We recover concepts in an incremental way until all the learned unknown residual concept vectors are transformed into pure, accurate, and human-interpretable concepts. At this point, the base concept library is fully updated, and experiments confirm its superior completeness." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 304, + 388, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 388, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 388, + 317 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 323, + 422, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 422, + 336 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 422, + 336 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 342, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 449 + ], + "type": "text", + "content": "Datasets. We conduct comprehensive experiments on 7 datasets, including: CIFAR-10, CIFAR-100 [28], TinyImageNet [30], LAD [61], CUB-200 [51], Food-101 [6], Flower-102 [37]. For a fair comparison, we apply CLIPRN50 when comparing with other CBMs and CLIP-ViT-L/14 on few-shot classification tasks as the backbone, and all linear classifiers are optimized with the Adam [25] optimizer. For more detailed information, please refer to the supplementary material." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 449, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 545, + 473 + ], + "type": "text", + "content": "Baselines. To evaluate our proposed approach, we compare it with the following baseline methods:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 474, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 306, + 474, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 545, + 533 + ], + "type": "text", + "content": "- CLIP Zero-shot[40]: the cosine similarities between the visual representations and the textual embeddings of each class name are calculated directly without any training. The class with the highest cosine similarity score is selected as the final classification result." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 533, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 545, + 569 + ], + "type": "text", + "content": "- Linear Probing (LP)[40]: We exclusively utilize the CLIP visual encoder and the obtained visual representations are then used to predict the label by training a linear classifier." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 570, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 570, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 570, + 545, + 653 + ], + "type": "text", + "content": "- Original CBM[26]: The original CBM relies on fine-grained concept annotations, so we compare our method with it only on LAD and CUB with available attribute annotations. In addition, CBMs may suffer from concept leakage, which can only be alleviated by CBMs trained independently [36]. Hence, we choose CBM-independent as the baseline for comparison." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 653, + 545, + 713 + ], + "type": "text", + "content": "- PCBM[58]: PCBM uses the ConceptNet[50], a knowledge graph dataset, to conduct a concept bank. It treats classes as nodes and incorporates surrounding neighboring nodes in the concept bank. More concepts can be included by expanding multiple layers outwards." + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11034" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 102, + 547, + 244 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 1. Comparison with other CLIP-based CBMs. Bold indicates the best interpretable result, underline indicates the 2nd-best result, italic indicates the black-box methods." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 102, + 547, + 244 + ], + "lines": [ + { + "bbox": [ + 48, + 102, + 547, + 244 + ], + "spans": [ + { + "bbox": [ + 48, + 102, + 547, + 244 + ], + "type": "table", + "html": "
MethodInterpretabilityLengthCIFAR 10CIFAR 100
AccuracyNumberCUEAccuracyNumberCUE
Zero-shotYesN/A0.6796N/AN/A0.2620N/AN/A
LPNoN/A0.8858N/AN/A0.6995N/AN/A
PCBM-1rYes90.80441755.10730.53794401.3583
PCBM-2rYes90.80743832.34230.545011750.5153
PCBM-3rYes90.820810580.8620N/AN/AN/A
PCBM-hNo90.8757175N/A0.6683440N/A
Lf-CBMYes120.86771435.05650.67458920.6301
LaBo-10cYes270.84891003.14410.661810000.2451
LaBo-20cYes270.86692001.60540.673620000.1247
LaBo-30cYes260.87523001.1221N/AN/AN/A
Res-CBMYes70.8803237+105.09140.6791372+152.5396
", + "image_path": "2bfa2a86977322d1d75f4e3fa4e3f534ca60b75726ed5b1c8f2e346358f45076.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 81, + 274, + 511, + 346 + ], + "blocks": [ + { + "bbox": [ + 83, + 255, + 509, + 266 + ], + "lines": [ + { + "bbox": [ + 83, + 255, + 509, + 266 + ], + "spans": [ + { + "bbox": [ + 83, + 255, + 509, + 266 + ], + "type": "text", + "content": "Table 2. Comparison with CBMs with labeled concept annotations. The labeling significance is consistent with Tab.1." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 81, + 274, + 511, + 346 + ], + "lines": [ + { + "bbox": [ + 81, + 274, + 511, + 346 + ], + "spans": [ + { + "bbox": [ + 81, + 274, + 511, + 346 + ], + "type": "table", + "html": "
MethodLAD-ALAD-ELAD-FLAD-HLAD-VCUBMean
LP0.94320.86610.73930.49240.86710.72140.7714
Original CBM0.89640.78260.55350.33880.79070.65130.6689
PCBM-annotation0.89340.77110.59820.29820.78140.63630.6631
Res-CBM-before0.78970.77090.43560.14290.75480.59870.5812
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", + "image_path": "b6eca2518e5d1af366eee9e48569554b4b5f1dc98499ba93bc363e9f8cd374d8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 365, + 287, + 579 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": "- PCBM-h[58]: After training the PCBM, PCBM-h is applied as a post-processing method that connects the visual representation and the class labels result through shortcuts. It utilizes a linear classifier to predict the difference between the result of PCBM and the ground truth." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 425, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 425, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 287, + 496 + ], + "type": "text", + "content": "- Lf-CBM[38]: In contrast to PCBM, Lf-CBM generates concepts through a large language model (LLM). It solely utilizes CLIP as the concept annotator, allowing it to act on any visual backbone. We directly select CLIP as the visual backbone, thus omitting the process of computing the similarity matrix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 496, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 496, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 47, + 496, + 287, + 579 + ], + "type": "text", + "content": "- LaBo[56]: LaBo similarly applies the LLM to generate candidate concepts. However, the quantity of concepts in LaBo is specific to each class. So we generate 10, 20, and 30 concepts per class to compare the performance. In addition, LaBo's linear classifier differs from the above baselines. To evaluate the quality of concepts equitably, we choose the same classifier as the above methods." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 582, + 288, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 642 + ], + "type": "text", + "content": "Metrics. Besides accuracy, we also concentrate on concepts' efficiency, including both the average length of each concept and quantity of concepts. Specifically, we define the accuracy improvement brought by all concepts' length to measure the Concept Utilization Efficiency (CUE):" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 119, + 647, + 287, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 647, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 119, + 647, + 287, + 672 + ], + "type": "interline_equation", + "content": "\\mathrm {C U E} = \\frac {1 0 0 0 0 \\times \\mathrm {A c c}}{N \\times \\bar {L}} \\tag {15}", + "image_path": "1bdb463e8947708423dad8e3d232cb7c35f1b3735e603269fcc09c673d396842.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Acc}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " is the classification accuracy, " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " is the quantity of concepts and " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\bar{L}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " is the average number of letters included in each concept. Larger CUE means higher efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 364, + 443, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 364, + 443, + 378 + ], + "spans": [ + { + "bbox": [ + 305, + 364, + 443, + 378 + ], + "type": "text", + "content": "4.2. Accuracy and Efficiency" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "type": "text", + "content": "We compare our method with other CBMs in terms of accuracy and efficiency. Tab.1 provides the results of our method compared to other CLIP-based CBMs. Res-CBM attains higher accuracy than PCBM by " + }, + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "type": "inline_equation", + "content": "5.95\\%" + }, + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "type": "text", + "content": " on CIFAR-10 and " + }, + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "type": "inline_equation", + "content": "13.41\\%" + }, + { + "bbox": [ + 304, + 384, + 547, + 504 + ], + "type": "text", + "content": " on CIFAR-100 and even outperforms the inexplicable PCBM-h. Despite Lf-CBM and LaBo being powerful baselines, our methodology still achieves state-of-the-art results. Particularly, it should be noted that our method considerably exceeds both Lf-CBM and LaBo in terms of efficiency, as evidenced by the CUE metric." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": "On LAD and CUB-200 with attribute annotations, we still use CLIP-50 with frozen parameters as the visual backbone to train Original CBM according to formula (2), as the results are shown in Tab.2." + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " The close performance of the Original CBM and PCBM-annotation suggests that the CBMs' performance heavily relies on the expert-selected concepts more than the model structure. Although Res-CBM-before performs poorly, a remarkable improvement is observed in Res-CBM-after after applying our unsupervised incremental concept discovery, which even surpasses supervised CBMs with concept annotations on most datasets." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 654, + 545, + 674 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 654, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 306, + 654, + 545, + 674 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 306, + 654, + 545, + 674 + ], + "type": "text", + "content": "PCBM-#r represents expanding outward to include neighboring nodes # times. LaBo-#c represents selecting # concepts per class." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 674, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 674, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 674, + 545, + 713 + ], + "type": "inline_equation", + "content": "{}^{3}" + }, + { + "bbox": [ + 306, + 674, + 545, + 713 + ], + "type": "text", + "content": " PCBM-annotation refers to PCBM that utilizes the textual embeddings of the annotated attributes as the concept bank. Res-CBM-before indicates the performance on the initial base concept bank. Res-CBM-after represents the performance after incremental concept discovery." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11035" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 74, + 217, + 163 + ], + "blocks": [ + { + "bbox": [ + 65, + 74, + 217, + 163 + ], + "lines": [ + { + "bbox": [ + 65, + 74, + 217, + 163 + ], + "spans": [ + { + "bbox": [ + 65, + 74, + 217, + 163 + ], + "type": "image", + "image_path": "0a80dec07964a41a7194270cbc6a07070c3ca2ab81db8be0df7da7520f4b8d7c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 220, + 74, + 372, + 163 + ], + "blocks": [ + { + "bbox": [ + 220, + 74, + 372, + 163 + ], + "lines": [ + { + "bbox": [ + 220, + 74, + 372, + 163 + ], + "spans": [ + { + "bbox": [ + 220, + 74, + 372, + 163 + ], + "type": "image", + "image_path": "6453bd78e832b4bc5477907b925a18c8f5a942c20a3465fc37fa81872882a3df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 377, + 75, + 529, + 163 + ], + "blocks": [ + { + "bbox": [ + 377, + 75, + 529, + 163 + ], + "lines": [ + { + "bbox": [ + 377, + 75, + 529, + 163 + ], + "spans": [ + { + "bbox": [ + 377, + 75, + 529, + 163 + ], + "type": "image", + "image_path": "87b000cc3f4823c433e7a1f5de40c28ae0c2ef1717a127a2c0216289b3968fc6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 63, + 166, + 217, + 255 + ], + "blocks": [ + { + "bbox": [ + 63, + 166, + 217, + 255 + ], + "lines": [ + { + "bbox": [ + 63, + 166, + 217, + 255 + ], + "spans": [ + { + "bbox": [ + 63, + 166, + 217, + 255 + ], + "type": "image", + "image_path": "d2cffb1373e6c8fc668b82fe71ab55591bca988c2d87c428ccc00a04e81862e3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 268, + 539, + 281 + ], + "lines": [ + { + "bbox": [ + 52, + 268, + 539, + 281 + ], + "spans": [ + { + "bbox": [ + 52, + 268, + 539, + 281 + ], + "type": "text", + "content": "Figure 4. Test accuracy " + }, + { + "bbox": [ + 52, + 268, + 539, + 281 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 52, + 268, + 539, + 281 + ], + "type": "text", + "content": " comparison between Res-CBM and LP on 6 datasets. The x-axis represents the number of labeled images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 217, + 166, + 372, + 255 + ], + "blocks": [ + { + "bbox": [ + 217, + 166, + 372, + 255 + ], + "lines": [ + { + "bbox": [ + 217, + 166, + 372, + 255 + ], + "spans": [ + { + "bbox": [ + 217, + 166, + 372, + 255 + ], + "type": "image", + "image_path": "db9d49c3f08dfeffa6e9bbdc81bcdcee87a8724fb3aa2fa4259f777441370d82.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 377, + 166, + 529, + 255 + ], + "blocks": [ + { + "bbox": [ + 377, + 166, + 529, + 255 + ], + "lines": [ + { + "bbox": [ + 377, + 166, + 529, + 255 + ], + "spans": [ + { + "bbox": [ + 377, + 166, + 529, + 255 + ], + "type": "image", + "image_path": "9996cab42b178f26a64aac5685a427fe3eff1110de64e54686a6f7c887cdf586.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 63, + 293, + 207, + 385 + ], + "blocks": [ + { + "bbox": [ + 63, + 293, + 207, + 385 + ], + "lines": [ + { + "bbox": [ + 63, + 293, + 207, + 385 + ], + "spans": [ + { + "bbox": [ + 63, + 293, + 207, + 385 + ], + "type": "image", + "image_path": "255afeca3b59d4b4887ff40c0fbdb76ff9d54b8a6145dca4553fb0b35bba80f4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 82, + 396, + 509, + 407 + ], + "lines": [ + { + "bbox": [ + 82, + 396, + 509, + 407 + ], + "spans": [ + { + "bbox": [ + 82, + 396, + 509, + 407 + ], + "type": "text", + "content": "Figure 5. Ablation results on residual vector numbers, concept similarity loss weights and candidate concept numbers." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 221, + 293, + 373, + 384 + ], + "blocks": [ + { + "bbox": [ + 221, + 293, + 373, + 384 + ], + "lines": [ + { + "bbox": [ + 221, + 293, + 373, + 384 + ], + "spans": [ + { + "bbox": [ + 221, + 293, + 373, + 384 + ], + "type": "image", + "image_path": "8d9703afb8b9339990d1db65d1de87e1f79e7417cb3a6c1939e14ba154a94bc2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 373, + 293, + 531, + 384 + ], + "blocks": [ + { + "bbox": [ + 373, + 293, + 531, + 384 + ], + "lines": [ + { + "bbox": [ + 373, + 293, + 531, + 384 + ], + "spans": [ + { + "bbox": [ + 373, + 293, + 531, + 384 + ], + "type": "image", + "image_path": "3af79f11e4a84c2fd32f5a96cad420e6e3299cbd24780ebc2d7f0a0cd59f9261.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 427, + 142, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 427, + 142, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 142, + 441 + ], + "type": "text", + "content": "4.3. Interpretability" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "content": "In this subsection, we visualize the mechanism of ResCBM and demonstrate how the newly discovered concepts assist in advancing classification performance. For each image, we display the top 5 concepts with the highest activation scores in the concept bottleneck, as shown in Fig.6. Through a sparse concept classifier, we can obtain predictions, which signifies predicting the class by a linear combination of concepts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "However, due to the incompleteness of the base concept bank, it is challenging to achieve accurate classifications by solely relying on these concepts in several images, e.g., dragonfly and honeybee, peach and hawthorn, both of which possess concepts from the base concept bank. With the help of Res-CBM, we have discovered 2 concepts, nectar and rough, from the candidate concept bank. Unlike dragonflies, honeybees often gather nectar from the center of flowers, thus associating them with the concept of nectar. Moreover, hawthorns have a rougher surface compared to peaches. By incorporating these discovered concepts into the base concept bank, these initially misclassified samples are now correctly categorized, achieving automatic model debugging to a certain extent." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 427, + 423, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 423, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 423, + 441 + ], + "type": "text", + "content": "4.4. Few-shot Capability" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 448, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 532 + ], + "type": "text", + "content": "Fig.4 illustrates the performance comparison under different data volume settings between Res-CBM and LP. Compared to the end-to-end black-box model, our method achieves superior performance when little data is available, and exhibits a slight performance gap with larger amounts of sample sizes, which indicates that our method has maintained the accuracy without sacrificing interpretability." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 533, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 604 + ], + "type": "text", + "content": "For common object datasets, our approach demonstrates excellent performance with 1, 2, 4, and 8 labeled images per category. We credit its success to the incorporation of human concept information, which helps the model extract vital aspects relevant to the categories from the representations of the black-box backbone." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "For fine-grained object datasets, our method outperforms the black-box model when the data volume is extremely low. As the data volume increases, the unexplainable black-box model's performance becomes more prominent, especially in expert datasets such as Flower-102 and CUB-200. It might be attributed to common concepts struggling to distinguish the subtle differences between these fine-grained objects. A feasible solution is to enhance the specificity of concepts by a tailored specialized concept candidate bank." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11036" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 69, + 276, + 208 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 276, + 208 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 276, + 208 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 276, + 208 + ], + "type": "image", + "image_path": "e69a11d448879f8439d3257e42204054889ee0a3fe3275996b6fb4ac7d269d41.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 289, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 289, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 289, + 282 + ], + "type": "text", + "content": "Figure 6. Concepts applied in Res-CBM on LAD-A (top) and LAD-F (bottom). Solid boxes represent concepts from the base concept bank, dashed boxes indicate the discovered concepts. Heatmaps refer to learned linear concept classifiers, in which the x-axis represents classes, the y-axis represents concepts, and the values represent the contribution of concepts to categories." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 306, + 141, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 141, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 141, + 319 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 327, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 422 + ], + "type": "text", + "content": "Residual Vector Number. To investigate the impact of residual vector numbers on performance improvement and demonstrate that our method can be applied as a post-processing approach to any CBMs, we record the results of attaching different residual vector numbers for Lf-CBM on CIFAR-10, as shown in Fig.5-left. As the quantity of vectors increases, the performance of Lf-CBM continuously improves and gradually saturates at around 15 vectors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 568 + ], + "type": "text", + "content": "Candidate Concept Number. We fix the residual vector number at 10 and set the concept similarity loss weight to 0.1, then record the final accuracy and the average similarity between the discovered concepts and the most similar concepts in the candidate concept bank during the discovery process in Fig.5-middle. When the candidate concept number is small, the model tends to converge to this unique concept, making it difficult to escape local optima. When it is large, the optimizing vectors easily oscillate between different concepts, resulting in lower accuracy and similarity. Overall, setting the candidate concept number to 5 seems to be a good hyperparameter choice." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Concept Similarity Loss Weight. With a fixed candidate concept number at 5, we also record the final accuracy and average similarity for different loss weights as shown in Fig.5-right. When the weight is low, the similarity of the discovered concepts is extremely low, which resembles a random selection strategy, leading to poorer performance. When the weight is large, the model tends to converge to a local optimum only satisfying the concept similarity loss, sacrificing the ability to explore more appropriate concepts. Since Res-CBM has already saturated after the completion of unknown concept vectors, the cross-entropy loss value is small. Therefore, a weight of 0.1 realizes optimal results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 71, + 459, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 459, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 459, + 84 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "type": "text", + "content": "Rethinking CBMs. Indeed CBMs are valuable attempts towards transparency of the decision-making process, one important and fundamental problem may be still unclear, which is: how many concepts are good? especially when lacking a well-accepted and rigorous definition of concepts. In this paper, we have tried to explore this problem. Firstly, the number of concepts should not be the larger the better. From the optimization perspective, the operation of CBMs to project visual representations into concept space is a linear transformation. If its rank is greater than or equal to the dimension " + }, + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "type": "text", + "content": " of the concept vector, this process is invertible. Therefore, it is straightforward to re-estimate the inverse transformation matrix to preserve classification accuracy in subsequent linear classifiers. The number of concepts larger than " + }, + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 91, + 545, + 282 + ], + "type": "text", + "content": " may decrease the efficiency, making the interpretability less effective." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": "On the other hand, the concept should be an efficient way to express categories. Humans can describe objects in the world exponentially using a finite set of concepts. Theoretically, from informatics, when each concept weight is binary, the concept quantity needed to distinguish " + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": " categories will be enough approximately " + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "inline_equation", + "content": "\\log_2 n" + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": ". This is the reason for the poor CUE of LaBo [56], which finds concepts for each category in a way that the CUE complexity is " + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(n)" + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": " rather than " + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\log_2 n)" + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": ". This suggests that the CUE is crucial in CBMs, and a reasonable number of concepts should lie in the interval of " + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "inline_equation", + "content": "\\left[\\log_2 n\\right]" + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 284, + 545, + 416 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 416, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 416, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 416, + 545, + 500 + ], + "type": "text", + "content": "Conclusion. In this paper, we emphasize the significance of purity, precision, and completeness in CBMs and introduce the CUE metric to evaluate the descriptive efficiency of CBMs. Our proposed Res-CBM complements the missing concepts in any CBM with an incremental concept discovery approach, which achieves optimal accuracy with the best concept utilization efficiency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": "Limitation and Future Work. For our proposed ResCBM, the candidate concept bank construction for fine-grained datasets remains a challenge. Additionally, the sequential concept discovery approach increases computational time costs, while more efficient concept similarity calculation and parallel concept discovery techniques are needed to develop. For the CBM structure, existing CBMs represent all concepts into a single bottleneck, disregarding the hierarchical nature of concepts, where simple concepts can be combined to form more complicated ones." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 633, + 409, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 409, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 409, + 647 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "This work was partly supported by the National Natural Science Foundation of China (Grant No. 61991451) and the Shenzhen Science and Technology Program (JCYJ20220818101001004). 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R. China", + "bbox": [ + 158, + 217, + 810, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "liangys@smail.nju.edu.cn, liwujun@nju.edu.cn", + "bbox": [ + 285, + 236, + 671, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continual learning requires the model to learn multiple tasks sequentially. In continual learning, the model should possess the ability to maintain its performance on old tasks (stability) and the ability to adapt to new tasks continuously (plasticity). Recently, parameter-efficient fine-tuning (PEFT), which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning. Although existing continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT, most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets. Code is available at https://github.com/liangyanshuo/InfLoRA.", + "bbox": [ + 75, + 318, + 472, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 757, + 209, + 772 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continual learning requires the model to learn multiple tasks sequentially [33]. To achieve continual learning, the model should possess two essential abilities, including the ability to keep its performance on the old tasks (stability) and the ability to adapt to the new tasks continuously (plasticity) [33]. Furthermore, two different scenar", + "bbox": [ + 75, + 782, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ios are often considered in continual learning, including task-incremental scenario [32] and class-incremental scenario [41]. Task-incremental scenario allows the model to get task identities during inference. On the contrary, class-incremental scenario does not allow the model to get task identities during inference, making the model learn to distinguish all the classes across all the tasks.", + "bbox": [ + 500, + 287, + 890, + 393 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, parameter-efficient fine-tuning (PEFT) [15, 16, 18], which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning [12, 38, 44], especially in the class-incremental scenario. More specifically, existing continual learning methods based on PEFT [21, 43] inject the learnable parameters into a pre-trained model using some popular PEFT methods such as prompt-tuning [25] or low-rank adaptation (LoRA) [16]. Subsequently, these methods freeze the pre-trained weights and sequentially fine-tune the injected parameters on multiple tasks throughout the continual learning process.", + "bbox": [ + 498, + 396, + 892, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT [44], most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. Specifically, when learning a new task, existing continual learning methods based on PEFT either reuse the previously learned parameters to adapt to the new task [12, 44] or randomly expand some parameters first and then adapt to the new task [38, 42, 43]. During this process, the interference of the new task on the old tasks exists due to the shared parameters between new and old tasks, which means fine-tuning a pre-trained model on a new task may interfere with the model's performance on the old tasks. As a result, it is hard for the model to make a good trade-off between stability and plasticity.", + "bbox": [ + 496, + 595, + 893, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. The contributions of this work are listed as follows:", + "bbox": [ + 498, + 839, + 893, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Wu-Jun Li is the corresponding author.", + "bbox": [ + 94, + 886, + 308, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23638", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that finetuning these injected parameters is equivalent to finetuning the pre-trained weights within a subspace.", + "- InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity.", + "- Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets." + ], + "bbox": [ + 76, + 90, + 467, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work and Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 258, + 370, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Related Work", + "text_level": 1, + "bbox": [ + 76, + 285, + 220, + 299 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Parameter-Efficient Fine-Tuning Parameter-efficient fine-tuning (PEFT) methods freeze a pre-trained model and inject a small number of learnable parameters to adapt to downstream tasks. In this way, PEFT methods reduce the inefficiency of full fine-tuning methods which fine-tune all the parameters of a pre-trained model to learn downstream tasks. For example, Adapter [15] adds small modules in different layers of Transformers and only tunes these added modules to adapt to downstream tasks. Prompt-tuning [25] and Prefix-tuning [27] insert a set of learnable tokens into the input of the Transformer layers and only tune these tokens to adapt to downstream tasks. Low-rank adaptation (LoRA) [16] reparameterizes the pre-trained weights with low-rank branches and only tunes these branches to adapt to the downstream tasks. Although these methods tune much fewer learnable parameters than full fine-tuning, they always show comparable or even superior performance compared with full fine-tuning [11, 16, 31, 45]. Early PEFT methods focus on natural language processing (NLP). Recently, PEFT methods have also been proposed for computer vision (CV). For example, visual prompt tuning (VPT) [18] and AdapterFormer [6] apply prompt-tuning and Adapter techniques to CV tasks, respectively. Both of them exhibit comparable performance to full fine-tuning.", + "bbox": [ + 76, + 309, + 468, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continual Learning Early continual learning was usually considered in the context of learning from scratch. Three types of continual learning methods are proposed, including regularization-based methods [1, 20, 23, 46], memory-based methods [2, 3, 7, 28, 39], and expansion-based methods [17, 26, 35]. Regularization-based methods employ a penalty loss (regularization) to prevent important parameters of old tasks from changing too much. Memory-based methods maintain a memory buffer to store information about old tasks. Expansion-based methods dynamically expand the model's architecture for each new task.", + "bbox": [ + 75, + 672, + 467, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, with the advancements of pre-trained models [9, 10, 13], using pre-trained models for continual learning has gained increasing popularity. Some continual learning methods fully fine-tune the pre-trained models [4, 48],", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which has been shown to be inefficient. Other methods explore PEFT methods in continual learning. For instance, some existing continual learning methods [21, 38, 43, 44] introduce prompt-tuning in continual learning, achieving much higher performance than previous methods that learn from scratch, especially in the class-incremental scenario. The method in [12] introduces a framework in continual learning that can be combined with many existing PEFT methods, such as prompt-tuning, LoRA and Adapter. However, all these methods do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 299, + 638, + 314 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first introduce low-rank adaptation (LoRA) [16], a popular PEFT method related to our method. Then, we give the problem definition for continual learning.", + "bbox": [ + 496, + 323, + 890, + 369 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Low-Rank Adaptation LoRA [16] is one of the most popular PEFT methods. It assumes that the changes of parameters lie in a low-rank space when the model is fully fine-tuned on a downstream task. Specifically, for a linear layer with the input dimension $d_{I}$ and the output dimension $d_{O}$ , we represent its weight with $W^{d_O\\times d_I}$ . Then, LoRA reparametrizes the pre-trained weight $W$ by expanding a branch with two matrices, $A\\in \\mathbb{R}^{d_O\\times r}$ and $B\\in \\mathbb{R}^{r\\times d_I}$ . Typically, $r$ is much smaller than the input dimension $d_{I}$ and output dimension $d_{O}$ , making $A$ a dimensionality increasing matrix and $B$ a dimensionality reduction matrix. Finally, LoRA modifies the forward propagation in this linear layer as $e = Wh + ABh$ . Here, $h$ and $e$ denote the input and output of this layer, respectively. LoRA initializes $A$ as 0 and initializes $B$ using Gaussian distribution. During the learning of the downstream tasks, LoRA freezes the pre-trained weight $W$ and only fine-tunes the parameters $A$ and $B$ .", + "bbox": [ + 496, + 369, + 890, + 641 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Problem Definition In continual learning, there is a sequence of tasks with different distributions. We define the task sequence as $\\mathcal{D} = \\{\\mathcal{D}_1,\\dots,\\mathcal{D}_T\\}$ , where the $t$ -th task $\\mathcal{D}_t = \\{(x_{i,t},y_{i,t})\\}_{i = 1}^{n_t}$ . Here, $x_{i,t}$ denotes an input sample and $y_{i,t}$ denotes its label. The objective of continual learning is to train a model sequentially on these tasks and ensure that the model performs well on all of them.", + "bbox": [ + 496, + 643, + 890, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We follow existing continual learning methods [43, 44] based on PEFT and assume the model is a pre-trained Vision Transformer (ViT) [10]. Specifically, assume the model is $h_{\\Phi}(f_{\\Theta}(\\cdot))$ where $h_{\\Phi}(\\cdot)$ is the classifier with parameters $\\Phi$ and $f_{\\Theta}(\\cdot)$ is the pre-trained ViT backbone with pre-trained parameters $\\Theta$ . Similar to existing work [43], our focus is primarily on the class-incremental scenario, where task identities are unknown during inference. Furthermore, we concentrate on the exemplar-free setting [43, 50], where no historical data can be fetched for rehearsal.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23639", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f80b43ac204c7bffd4f5085e0499ca8c8fad11396ecd907691a5d2bbfdf62394.jpg", + "image_caption": [ + "(a) Architecture" + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 428, + 297 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e66e2ea897b11b01e524b09785e3c48dd147fcd2a0130a1ec8654247e357d348.jpg", + "image_caption": [ + "(b) Designing Dimensionality Reduction Matrix $B_{t}$", + "Figure 1. (a) The architecture of our InfLoRA in a certain linear layer of a Transformer. During the learning of the $t$ -th task, the pre-trained weight and all the old branches are frozen, and only $\\mathbf{A}_t$ is fine-tuned. (b) The pipeline of designing dimensionality reduction matrix $\\mathbf{B}_t$ ." + ], + "image_footnote": [], + "bbox": [ + 433, + 89, + 875, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 356, + 210, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 1 (a) illustrates the architecture of our InfLoRA within a linear layer. Before learning the $t$ -th new task, our InfLoRA expands a LoRA-like branch, which includes a dimensionality reduction matrix $\\pmb{B}_t \\in \\mathbb{R}^{r \\times d_I}$ and a dimensionality increasing matrix $\\pmb{A}_t \\in \\mathbb{R}^{d_O \\times r}$ . Then, the forward propagation of this linear layer is modified as", + "bbox": [ + 75, + 381, + 468, + 472 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ne = W h + \\sum_ {j = 1} ^ {t} A _ {j} B _ {j} h = W _ {t - 1} h + A _ {t} B _ {t} h = W _ {t} h. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 482, + 468, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $W_{t} = W_{t - 1} + A_{t}B_{t} = W + \\sum_{i = 1}^{t}A_{i}B_{i}$ . Similar to LoRA, our InfLoRA also initializes dimensionality increasing matrix $A_{t}$ as 0. However, different from LoRA, which employs Gaussian distribution to initialize the dimensionality reduction matrix $B$ , our InfLoRA designs the dimensionality reduction matrix $B_{t}$ before learning the $t$ -th task. During the learning of the $t$ -th task, InfLoRA fine-tunes $A_{t}$ to learn the new task while keeping the pre-trained weight $W$ , all the old branches and the matrix $B_{t}$ frozen. After learning the $t$ -th tasks, for any given test sample belonging to the learned tasks, the model uses $W_{t}$ and (1) to infer its label. This design ensures that our method is compatible with the class-incremental scenario where task identities are unknown during inference.", + "bbox": [ + 75, + 551, + 468, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following subsections, we first build the relationship between our InfLoRA and the method that fine-tunes the pre-trained weight. Specifically, we show that finetuning parameters $\\mathbf{A}_t$ is equivalent to fine-tuning the pretrained weights $\\mathbf{W}$ within a subspace spanned by the rows of $\\mathbf{B}_t$ . Note that $\\mathbf{B}_t$ is designed before learning the $t$ -th task, making this subspace pre-designed. Then, building upon this relationship, we introduce how our InfLoRA designs this subspace to eliminate the interference of the new", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "task on the old tasks and make a good trade-off between stability and plasticity.", + "bbox": [ + 498, + 358, + 890, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Relationship between InfLoRA and Fine-Tuning the Pre-Trained Weight", + "text_level": 1, + "bbox": [ + 498, + 401, + 890, + 433 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When the $t$ -th task arrives and our method has expanded a new branch, the forward propagation in this layer can be represented by (1). At this time, we can prove the following proposition:", + "bbox": [ + 498, + 441, + 890, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proposition 1. When learning the $t$ -th task with forward propagation represented by (1), fine-tuning $\\mathbf{A}_t$ is equivalent to fine-tuning the pre-trained weight $\\mathbf{W}$ within the subspace $\\operatorname{span}\\{\\pmb{b}_1^t, \\dots, \\pmb{b}_r^t\\}$ . Here, $\\pmb{b}_i^t$ ( $1 \\leq i \\leq r$ ) denotes the $i$ -th row vector of $\\pmb{B}_t$ .", + "bbox": [ + 498, + 516, + 890, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proof. When tuning the pre-trained weight $\\mathbf{W}$ to learn the $t$ -th task, we can compute the gradient of $\\mathbf{W}$ based on the chain rule:", + "bbox": [ + 498, + 606, + 890, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {W}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {e}} \\frac {\\partial \\boldsymbol {e}}{\\partial \\boldsymbol {W}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {e}} \\boldsymbol {h} ^ {T}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 661, + 890, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $\\mathcal{L}$ denotes the loss function. At this time, the change of $\\pmb{W}$ can be denoted as $\\Delta W = -\\alpha \\frac{\\partial\\mathcal{L}}{\\partial W}$ , where $\\alpha$ is the learning rate. Then, we can compute the change of the composed matrix $\\pmb{W}_t = \\pmb {W} + \\sum_{j = 1}^t\\pmb {A}_j\\pmb {B}_j$ :", + "bbox": [ + 498, + 704, + 890, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Delta_ {\\boldsymbol {W}} \\boldsymbol {W} _ {t} = [ \\boldsymbol {W} + \\Delta \\boldsymbol {W} + \\sum_ {j = 1} ^ {t} \\boldsymbol {A} _ {j} \\boldsymbol {B} _ {j} ] - (\\boldsymbol {W} + \\sum_ {j = 1} ^ {t} \\boldsymbol {A} _ {j} \\boldsymbol {B} _ {j}) \\\\ = \\Delta \\boldsymbol {W} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {W} _ {t}} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 781, + 890, + 857 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we use $\\Delta_{\\mathbf{W}}\\mathbf{W}_t$ to denote the change of the composed matrix $\\mathbf{W}_t$ causing by the change of $\\mathbf{W}$ .", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23640", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similarly, when tuning the expanded weight $\\mathbf{A}_t$ , we can get the gradient of $\\mathbf{A}_t$ based on the chain rule:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {A} _ {t}} = \\frac {\\partial \\mathcal {L}}{\\partial e} \\frac {\\partial \\boldsymbol {e}}{\\partial \\boldsymbol {A} _ {t}} = \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\boldsymbol {B} _ {t} ^ {T}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 128, + 468, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At this time, the change of $\\mathbf{A}_t$ can be denoted as $\\Delta \\mathbf{A}_t = -\\alpha \\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{A}_t}$ . Then, we can compute the change of the composed matrix $\\mathbf{W}_t = \\mathbf{W}_{t-1} + \\mathbf{A}_t \\mathbf{B}_t$ :", + "bbox": [ + 76, + 169, + 468, + 214 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Delta_ {\\boldsymbol {A} _ {t}} \\boldsymbol {W} _ {t} = \\left[ \\boldsymbol {W} _ {t - 1} + \\left(\\boldsymbol {A} _ {t} + \\Delta \\boldsymbol {A} _ {t}\\right) \\boldsymbol {B} _ {t} \\right] - \\left(\\boldsymbol {W} _ {t - 1} + \\boldsymbol {A} _ {t} \\boldsymbol {B} _ {t}\\right) \\\\ = \\Delta \\boldsymbol {A} _ {t} \\boldsymbol {B} _ {t} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {A} _ {t}} \\boldsymbol {B} _ {t} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\boldsymbol {B} _ {t} ^ {T} \\boldsymbol {B} _ {t} \\\\ = \\Delta_ {W} W _ {t} B _ {t} ^ {T} B _ {t} \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 223, + 468, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we use $\\Delta_{\\mathbf{A}_t}\\mathbf{W}_t$ to denote the change of the composed matrix $\\mathbf{W}_t$ causing by the change of $\\mathbf{A}_t$ . The fourth equation in (5) holds because of (4). The fifth equation in (5) holds because of (2). (5) shows that $\\Delta_{\\mathbf{A}_t}\\mathbf{W}_t$ is equal to $\\Delta_{\\mathbf{W}}\\mathbf{W}_t$ multiplying a projection matrix $\\mathbf{B}_t^T\\mathbf{B}_t$ . Since $\\mathbf{B}_t^T\\mathbf{B}_t$ projects each row vector of $\\Delta_{\\mathbf{W}}\\mathbf{W}_t$ into the subspace span $\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}$ , Proposition 1 holds.", + "bbox": [ + 76, + 303, + 468, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 1 has demonstrated that using our InfLoRA to train the model is equivalent to directly finetuning the pre-trained weight $W$ within the subspace $\\operatorname{span}\\{b_1^t, \\dots, b_r^t\\}$ . Therefore, before learning the $t$ -th task, we can design matrix $B_t$ such that learning the $t$ -th task in the subspace $\\operatorname{span}\\{b_1^t, \\dots, b_r^t\\}$ will not interfere with the performance of the model on the old tasks.", + "bbox": [ + 76, + 419, + 468, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Eliminating the Interference of the New Task on the Old Tasks", + "text_level": 1, + "bbox": [ + 76, + 534, + 468, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first introduce the desired characteristics that InfLoRA aims to let the subspace $\\mathrm{span}\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}$ have. With these characteristics, InfLoRA can eliminate the interference of the new task on the old tasks and make a good trade-off between stability and plasticity. Then, we introduce how to design dimensionality reduction matrix $B_{t}$ so that subspace $\\mathrm{span}\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}$ has these characteristics.", + "bbox": [ + 76, + 571, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Desired Characteristics", + "text_level": 1, + "bbox": [ + 76, + 696, + 294, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, InfLoRA aims to make the subspace $\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}$ orthogonal to the gradients of all the old tasks. In this way, according to Proposition 1, the update of InfLoRA, which can be represented as $\\Delta_{A_t}W_t$ will also be orthogonal to the gradient of the old tasks. Note that the idea of making the update for the new task orthogonal to the gradient of the old tasks to eliminate the interference of the new task on the old tasks has been proposed in many existing continual learning methods [30, 36]. However, all these existing methods are designed for continual learning from scratch, involving updating all parameters of the model, which is incompatible with the setting in PEFT. On the contrary, our", + "bbox": [ + 76, + 719, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "method is a PEFT method, which only tunes the parameters in $A_{t}$ .", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides eliminating the interference of new tasks on old tasks, our InfLoRA further makes the subspace $\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}$ lie in a subspace that the gradient of the new task lies in to make a good trade-off between stability and plasticity. Specifically, existing work [19] has shown that during fine-tuning, the weight increments of pre-trained ViT exhibit redundancy in terms of weight rank. Therefore, the gradients of the new task lie in a low-dimensional subspace. Our method makes $\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}$ not only orthogonal to the gradient of the old tasks but also lie in the subspace in which the gradients of the new task $t$ lie. By doing so, our method makes the model's focus on the new task when eliminating the interference of the new task on the old tasks, thereby making a good trade-off between stability and plasticity. Section 4.2 verifies the effectiveness of these two characteristics.", + "bbox": [ + 496, + 122, + 890, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Designing Dimensionality Reduction Matrix", + "text_level": 1, + "bbox": [ + 500, + 388, + 859, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "InfLoRA first approximates the gradient space of the new task and old tasks. Here, we use $\\mathcal{N}_t$ to represent the gradient space of the new task approximated by InfLoRA. Similarly, we use $\\mathcal{M}_t$ to represent the gradient space of previous $t - 1$ old tasks approximated by InfLoRA. We also use $\\mathcal{M}_t^\\perp$ to denote the residual gradient space, which is orthogonal to the space $\\mathcal{M}_t$ . Then, in order to meet the characteristics described in Section 3.2.1, InfLoRA ensures that each row of $\\boldsymbol{B}_t$ lies in $\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp$ . In other words, InfLoRA makes $\\mathrm{span}\\{\\boldsymbol{b}_1^t,\\dots,\\boldsymbol{b}_r^t\\} \\subseteq \\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp$ .", + "bbox": [ + 496, + 414, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing works [29, 36] have shown that the gradient update of the linear layer lies in the span of the inputs. Please refer to supplementary material for a detailed explanation of this proposition. Therefore, InfLoRA uses the input matrix of the new task $t$ to approximate the gradient space of the new task. Specifically, InfLoRA computes the input matrix $H_{t} = [h_{1}^{t},\\dots,h_{n}^{t}]$ , with each column of $H_{t}$ representing an input vector of the $t$ -th task. Then, InfLoRA considers $\\mathcal{N}_t$ as the subspace spanned by the columns of matrix $H_{t}$ .", + "bbox": [ + 496, + 566, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, InfLoRA cannot use the input matrix of the old tasks to approximate the gradient space of the old tasks since the data from the old tasks is not available when the model learns the new tasks. Instead, existing methods such as gradient projection memory (GPM) [36] and dual gradient projection memory (DualGPM) [29] can learn a matrix to preserve information about the gradients of the old tasks. InfLoRA incorporates DualGPM to preserve gradient information. With the assistance of DualGPM, the model can learn either a matrix $M_t \\in \\mathbb{R}^{d_I \\times k_t}$ or a matrix $M_t^\\perp \\in \\mathbb{R}^{d_I \\times (d_I - k_t)}$ . Here, the columns of $M_t$ contribute to the orthonormal bases of $M_t$ and the columns of $M_t^\\perp$ contribute to the orthonormal bases of $M_t^\\perp$ . $k_t$ denotes the", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23641", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dimension of $\\mathcal{M}_t$ . For detailed information of how Dual-GPM maintains orthonormal bases $M_t$ or $M_t^\\perp$ , please refer to supplementary material or the original paper [29].", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After approximating the gradient space of the new task and old tasks, InfLoRA gets the component of $\\mathcal{N}_t$ which lies in $\\mathcal{M}_t^\\perp$ . Specifically, when the model maintains $\\mathcal{M}_t$ , InfLoRA performs the operation", + "bbox": [ + 75, + 136, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {H}} _ {t} = \\boldsymbol {H} _ {t} - \\boldsymbol {M} _ {t} \\boldsymbol {M} _ {t} ^ {T} \\boldsymbol {H} _ {t}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 203, + 468, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, when the model maintains $\\mathcal{M}_t^\\perp$ , InfLoRA performs the operation", + "bbox": [ + 75, + 228, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {H}} _ {t} = \\boldsymbol {M} _ {t} ^ {\\perp} \\left(\\boldsymbol {M} _ {t} ^ {\\perp}\\right) ^ {T} \\boldsymbol {H} _ {t}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 263, + 468, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that when $t = 1$ , $\\mathcal{M}_t$ is a null space and $\\hat{H}_t = H_t$ . Obviously, each column of $\\hat{H}_t$ lies in $\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp$ . However, since $(\\hat{H}_t)^T \\in \\mathbb{R}^{n \\times d_I}$ and $B_t \\in \\mathbb{R}^{r \\times d_I}$ have different shapes, InfLoRA can not directly define $B_t$ as $(\\hat{H}_t)^T$ . Note that $n \\gg r$ , InfLoRA uses the principal components of $(\\hat{H}_t)^T$ to set $B_t$ . Specifically, singular value decomposition (SVD) is performed on $(\\hat{H}_t)^T = V_t \\Sigma_t U_t$ . Then, InfLoRA designs $B_t$ by", + "bbox": [ + 75, + 292, + 468, + 416 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {B} _ {t} = \\left(\\boldsymbol {U} _ {t}\\right) _ {r}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 422, + 468, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $(\\boldsymbol{U}_t)_r$ denotes the rows of $\\boldsymbol{U}_t$ corresponding to the top- $r$ singular values. Figure 1 (b) illustrates the pipeline of designing matrix $\\boldsymbol{B}_t$ .", + "bbox": [ + 75, + 446, + 468, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that DualGPM expands subspace $\\mathcal{M}_t$ and reduces subspace $\\mathcal{M}_t^\\perp$ when the number of tasks increases. Since InfLoRA constrains the update of the model within the subspace $\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp \\subseteq \\mathcal{M}_t^\\perp$ , the space for learning the new task reduces when the number of tasks increases. However, by adjusting the approximation error of the gradient for the old tasks, DualGPM can expand $\\mathcal{M}_t$ slowly and reduce $\\mathcal{M}_t^\\perp$ slowly. Therefore, the constraints imposed by InfLoRA do not excessively affect the model's learning of new tasks. Please refer to supplementary material for a detailed explanation.", + "bbox": [ + 75, + 492, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Whole Process of InfLoRA", + "text_level": 1, + "bbox": [ + 76, + 665, + 318, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 outlines the whole process of InfLoRA in continual learning. When the $t$ -th new task arrives, InfLoRA first designs $B_{t}$ through (8) and expands a new branch. Then, InfLoRA learns the $t$ -th task by fine-tuning the newly expanded branch. Please note that, based on empirical findings from existing methods [12, 38], we employ the local cross-entropy (CE) loss as the learning objective, as it usually performs better than the global CE loss in continual learning methods based on PEFT. The local CE is the CE loss constrained to the classes of the current new task, which can be denoted as", + "bbox": [ + 75, + 689, + 468, + 853 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {D} _ {t}\\right) = \\frac {1}{\\left| \\mathcal {D} _ {t} \\right|} \\sum_ {\\left(\\boldsymbol {x}, y\\right) \\in \\mathcal {D} _ {t}} \\mathcal {L} _ {c e} \\left(\\operatorname {m a s k} \\left(h _ {\\boldsymbol {\\Phi}} \\left(f _ {\\boldsymbol {\\Theta}} (\\boldsymbol {x})\\right)\\right), y\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 858, + 468, + 896 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 InfLoRA for Continual Learning", + "text_level": 1, + "bbox": [ + 501, + 90, + 808, + 106 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "1: Input: The data of different tasks $\\{\\mathcal{D}_t\\}_{t=1}^T$ , a pre-trained ViT model $f_{\\Theta}(\\cdot)$ .", + "2: Output: Network $f_{\\Theta}(\\cdot)$ with learned parameters $W_{t}$ .", + "3: for $t$ in $1:T$ do", + "4: Design $\\pmb{B}_{t}$ through (8);", + "5: Expand a new branch for the $t$ -th task;", + "6: for $\\mathcal{B}_t$ sampled from $\\mathcal{D}_t$ do", + "7: Compute the loss $\\mathcal{L}(f_{\\Theta}(\\mathcal{B}_t))$ through (9) and update the parameters;", + "8: end for", + "9: Preserve the information about the gradient of the $t$ -th task through DualGPM;", + "10: end for" + ], + "bbox": [ + 504, + 111, + 890, + 291 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\mathrm{mask}(\\cdot)$ is a function that filters out the logits of the old classes and $\\mathcal{L}_{ce}$ denotes the standard CE loss. After learning the $t$ -th new task, InfLoRA follows the DualGPM to preserve the information about the gradient of the $t$ -th task.", + "bbox": [ + 496, + 321, + 890, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that the branch corresponding to the $t$ -th task will be frozen once the model has learned the $t$ -th task. Since the expanded branches are linear transformations, we can integrate the old branches into the pre-trained weight to reduce the expanded parameters. Specifically, after learning the first task, InfLoRA integrates the first branch into the pre-trained weight and obtains the weight $W_{1} = W + A_{1}B_{1}$ . Before learning the $t$ -th new task ( $t > 1$ ), InfLoRA maintains the weight $W_{t-1}$ . After learning the $t$ -th task, InfLoRA integrates the $t$ -th branch into $W_{t-1}$ and obtains $W_{t} = W_{t-1} + A_{t}B_{t}$ . In this way, the parameters in $A_{t}$ and $B_{t}$ do not need to be maintained in the learning of subsequent tasks. Therefore, during the whole learning process, the number of parameters expanded by InfLoRA equals the number of parameters in a single branch. Since a single branch contains $(d_{I} + d_{O})r$ parameters, the number of parameters expanded by InfLoRA is $(d_{I} + d_{O})r$ all the time.", + "bbox": [ + 496, + 397, + 892, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 670, + 633, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 695, + 705, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Evaluation Metric Similar to existing continual learning methods [12, 44] based on PEFT, we use ImageNet-R [14], CIFAR100 [24], and DomainNet [34] to train and evaluate the models. Imagenet-R is generated through artistic processing of 200 classes from ImageNet [8]. This dataset is introduced to continual learning by existing work [43] and has become a standard benchmark for continual learning methods based on PEFT. CIFAR100 is a dataset commonly used in existing continual learning works. DomainNet contains 345 classes and is introduced by some existing works [38, 42] for continual learning. Following existing continual learning work [38],", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23642", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d122a9363e01ffb13bdcad44dec93d9025808c931087fa46d3c71773e799b103.jpg", + "table_caption": [ + "Table 1. Results (%) on ImageNet-R. Results are included for 5 tasks, 10 tasks, and 20 tasks. We report results averaged over 5 trials." + ], + "table_footnote": [], + "table_body": "
Tasks51020
Method\\(ACC_5 (↑)\\)\\(\\overline{ACC_5} (↑)\\)\\(ACC_{10} (↑)\\)\\(\\overline{ACC_{10}} (↑)\\)\\(ACC_{20} (↑)\\)\\(\\overline{ACC_{20}} (↑)\\)
joint81.14 ± 0.34-81.14 ± 0.34-81.14 ± 0.34-
sequential58.74 ± 1.2872.91 ± 0.2846.07 ± 1.1562.91 ± 0.6834.62 ± 0.8551.15 ± 1.50
L2P [44]64.13 ± 0.7868.66 ± 0.4162.54 ± 0.2467.98 ± 0.2757.92 ± 0.2864.57 ± 0.29
DualPrompt [43]67.88 ± 0.1771.16 ± 0.3165.41 ± 0.5269.39 ± 0.4361.00 ± 0.7265.80 ± 0.67
CODA-P [38]73.09 ± 0.2176.91 ± 0.2171.47 ± 0.3575.82 ± 0.2967.28 ± 0.3072.34 ± 0.17
C-LoRA [37]75.85 ± 0.3178.85 ± 0.3471.89 ± 0.4575.33 ± 0.2865.71 ± 0.6070.63 ± 0.85
LAE [12]73.84 ± 0.1477.29 ± 0.4571.70 ± 0.3976.71 ± 0.1066.98 ± 0.3573.72 ± 0.05
InfLoRA-b575.28 ± 0.0178.95 ± 0.0874.13 ± 0.1878.54 ± 0.1468.41 ± 0.2974.00 ± 0.50
InfLoRA77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
", + "bbox": [ + 96, + 113, + 875, + 289 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we split ImageNet-R into 5, 10, and 20 tasks, with each task containing 40, 20, and 10 classes. We split CIFAR100 into 10 tasks, and each task constrains 10 classes. We split DomainNet into 5 tasks, and each task contains 69 classes.", + "bbox": [ + 75, + 303, + 468, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following existing continual learning methods [12, 44], we evaluate the performance of the model through two popular metrics, including the final accuracy $ACC_{T}$ and the averaged accuracy $\\overline{ACC}_{T} = \\frac{1}{T}\\sum_{i=1}^{T}ACC_{i}$ , where $T$ denotes the total number of tasks and $ACC_{i}$ is defined as", + "bbox": [ + 75, + 364, + 468, + 441 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nA C C _ {i} = \\frac {1}{i} \\sum_ {j = 1} ^ {i} a _ {i, j}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 452, + 468, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $a_{i,j}$ denotes the accuracy of the $j$ -th task once the model has learned the $i$ -th task.", + "bbox": [ + 75, + 506, + 468, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines We compare our InfLoRA with state-of-the-art continual learning methods based on PEFT, including learn to prompt (L2P) [44], DualPrompt [43], continual decomposed attention-based prompt (CODA-P) [38], learning accumulation ensemble (LAE) [12], continual low-rank adaptation (C-LoRA) [37]. For LAE, we implement it with LoRA [16]. Following existing works [12, 38], we also include two methods without continual learning, joint and sequential, in the comparison. Here, joint denotes the method that learns all the tasks jointly, while sequential denotes the method that learns all the tasks sequentially without any operation to overcome the forgetting of the model. The accuracy of joint can be treated as the accuracy upper-bound and the accuracy of sequential can be treated as the accuracy lower-bound.", + "bbox": [ + 75, + 537, + 470, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Architecture and Training Details We follow existing works [12, 43] to perform experiments. Specifically, we use the ViT-B/16 backbone [10] supervised pre-trained on ImageNet 21K as the pre-trained model.", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For all the methods, we follow existing works [12, 38, 44] and use the Adam [22] optimizer with running averages of gradient and its square $(\\beta_{1} = 0.9, \\beta_{2} = 0.999)$ . Each task is trained for 50 epochs on ImageNet-R, 20 epochs on CIFAR100 and 5 epochs on DomainNet. The batch size", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is set to 128 for all the experiments. Since our InfLoRA shares a similar architecture to LoRA, we follow existing work [12] and insert the architecture of our InfLoRA in the key and value of the attention module. Furthermore, existing method DualPrompt [43] treats the inserted blocks as hyperparameters and searches for the best positions for their prompts. On the contrary, we insert the architecture of InfLoRA for all the Transformer blocks to avoid searching. We also implement a variant of our method, which inserts the bottom 5 Transformer blocks like existing methods DualPrompt and CODA-P. We call this variant InfLoRA-b5. As for the hyperparameter $r$ , we determine its value through a grid search on a validation dataset.", + "bbox": [ + 496, + 303, + 893, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 498, + 512, + 702, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accuracy Table 1 shows the results of different methods on ImageNet-R with a different number of tasks. Table 2 shows the results of different methods on CIFAR100 and DomainNet. We can find that our methods InfLoRA and InfLoRA-b5 outperform existing continual learning methods.", + "bbox": [ + 496, + 536, + 893, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 2 shows the variation of the accuracy of different continual learning methods on ImageNet-R and CIFAR100. We can find that our method outperforms existing methods not only at the end of the learning but also throughout the whole learning process. This indicates that our InfLoRA eliminates the interference of the new task on the old tasks and thus the accuracy of our method decreases slower compared to other methods.", + "bbox": [ + 496, + 628, + 893, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis of Expanded Parameters Figure 3 shows the number of expanded parameters and the accuracy of different methods on ImageNet-R and CIFAR100. For L2P, DualPrompt and CODA-P, their expanded parameters are included in the added prompts and corresponding key. For LAE, its expanded parameters are the inserted LoRA modules and an additional copy. For C-LoRA, its expanded parameters are inserted LoRA modules. For our method, the expanded parameters are $B_{t}$ and $A_{t}$ . The details of computing the number of expanded parameters for different meth", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23643", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/644e410ef0cfb211e67873b83027e36775f058d787288685d12b24144ddc06d3.jpg", + "table_caption": [ + "Table 2. Results (%) on CIFAR100 and DomainNet. We report results over 5 trials." + ], + "table_footnote": [], + "table_body": "
TasksCIFAR100DomainNet
Method\\(ACC_{10} (↑)\\)\\(\\overline{ACC}_{10} (↑)\\)\\(ACC_5 (↑)\\)\\(\\overline{ACC}_5 (↑)\\)
joint91.92 ± 0.05-77.72 ± 0.04-
sequential62.18 ± 3.5980.42 ± 0.2353.44 ± 1.2169.09 ± 0.33
L2P [44]82.48 ± 0.2087.64 ± 0.2570.16 ± 0.0575.60 ± 0.03
DualPrompt [43]84.42 ± 0.3090.06 ± 0.0772.14 ± 0.0577.71 ± 0.06
CODA-P [38]86.62 ± 0.1191.08 ± 0.2873.23 ± 0.1378.72 ± 0.07
C-LoRA [37]82.97 ± 0.4788.81 ± 0.3469.34 ± 0.1375.25 ± 0.11
LAE [12]84.15 ± 0.1089.84 ± 0.0366.85 ± 0.4075.01 ± 0.17
InfLoRA-b587.06 ± 0.2591.59 ± 0.1373.26 ± 0.5078.82 ± 0.34
InfLoRA86.51 ± 0.7391.70 ± 0.3274.53 ± 0.2379.57 ± 0.57
", + "bbox": [ + 171, + 114, + 802, + 287 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/671b6d499863a87a8ff6494ae93b5d94e0d338912e348d1c76595f991d50f7ad.jpg", + "image_caption": [ + "(a) ImageNet-R (5 Tasks)" + ], + "image_footnote": [], + "bbox": [ + 107, + 292, + 290, + 414 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7da4d83f881abb800617eb6f7824c0b1200808ec34233e84bce522c4866c62c4.jpg", + "image_caption": [ + "(b) ImageNet-R (10 Tasks)" + ], + "image_footnote": [], + "bbox": [ + 292, + 291, + 482, + 414 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d8a59ab5471815ece96819868d0c44191a497c6e18f6a482dbc6a5794f66976.jpg", + "image_caption": [ + "(c) ImageNet-R (20 Tasks)" + ], + "image_footnote": [], + "bbox": [ + 486, + 291, + 674, + 414 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7f7843b71b6836c5fd769b12cc136143e371a3b4474c77e4218b387ad91a3ee5.jpg", + "image_caption": [ + "(d) CIFAR100" + ], + "image_footnote": [], + "bbox": [ + 676, + 292, + 864, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ods are given in supplementary material. We can find that CODA-P and C-LoRA expand much more parameters than other methods. Furthermore, our methods InfLoRA and InfLoRA-b5 expand comparable parameters to L2P, DualPrompt and LAE but perform better than these methods.", + "bbox": [ + 75, + 450, + 468, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study We perform experiment to verify the effectiveness of designing dimensionality reduction matrix $B_{t}$ by (8). Specifically, we explore three different variants for designing $B_{t}$ . The first variant designs $B_{t}$ randomly using Gaussian distribution. We call this variant 'Random $\\rightarrow B_{t}$ '. The second variant discards the operation in (6) or (7) and directly sets $\\hat{H}_{t} = H_{t}$ . Through this way, this variant ensures that each row of $B_{t}$ lies in $\\mathcal{N}_{t}$ while ignoring $\\mathcal{M}_{t}^{\\perp}$ . We call this variant $\\mathcal{N}_{t} \\rightarrow B_{t}$ . The third variant does not compute the input matrix but initializes $H_{t}$ using a Gaussian distribution before applying the operation in (6) or (7). In this way, this variant ensures that each row of $B_{t}$ lies in $\\mathcal{M}_{t}^{\\perp}$ while ignoring $\\mathcal{N}_{t}$ . We call this variant $\\mathcal{M}_{t}^{\\perp} \\rightarrow B_{t}$ . Since our method focuses both $\\mathcal{M}_{t}^{\\perp}$ and $\\mathcal{N}_{t}$ , we use $\\mathcal{N}_{t} \\cap \\mathcal{M}_{t}^{\\perp} \\rightarrow B_{t}$ to represent our method.", + "bbox": [ + 75, + 532, + 468, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 shows the results of our method and its variants. We can find that all these variants fail to perform as well as our method. To further demonstrate the performance of different variants, we show the relative accuracy of different tasks after the model learns them all in Figure 4. Here, relative accuracy is the accuracy of different variants minus the accuracy of our InfLoRA. Note that the last task is the new task, and the other tasks are old tasks in Figure 4. As we can see, 'Random $\\rightarrow$ $B_{t}$ ' and $\\mathcal{N}_t\\to B_t$ outper", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/48972fa574349124ba18659a6057b7caa35fabdca79fea69a03edbe125c3db97.jpg", + "image_caption": [ + "Figure 2. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100.", + "(a) ImageNet-R (10 Tasks)", + "Figure 3. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100." + ], + "image_footnote": [], + "bbox": [ + 509, + 452, + 691, + 579 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d063d5500dfd2c4615eedacfd6068945ce61ff2be36bc115f2ce0881472fe13a.jpg", + "image_caption": [ + "(b) CIFAR100" + ], + "image_footnote": [], + "bbox": [ + 700, + 452, + 882, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "form $\\mathcal{M}_t^\\perp \\to B_t$ on the new task but shows much lower accuracy than $\\mathcal{M}_t^\\perp \\to B_t$ and our InfLoRA on the old tasks. This means these two variants fail to eliminate the inference of the new task on the old tasks, making the model suffer from low stability. On the contrary, $\\mathcal{M}_t^\\perp \\to B_t$ shows the lowest performance on the new task. This means $\\mathcal{M}_t^\\perp \\to B_t$ ignores the plasticity of the model. Our method outperforms all the variants on most of the tasks. This shows that our method can eliminate the interference of the new task on the old tasks and make a better trade-off between stability and plasticity than these variants.", + "bbox": [ + 496, + 638, + 893, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Varying the Pre-Trained Model We also follow the existing method [40] and perform experiments using a ViT-B/16 pre-trained with two different self-supervised methods, including DINO [5] and iBOT [49]. All experimental settings, except for the choice of the pre-trained model, are kept consistent with the details outlined in Section 4.1.", + "bbox": [ + 496, + 809, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23644", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f5a5fac7949e2d46b5bb7f7b505c47fbb383050799112b69b41ce23bc4f4f7f5.jpg", + "table_caption": [ + "Table 3. Results of different variants on ImageNet-R with a different number of tasks." + ], + "table_footnote": [], + "table_body": "
Tasks51020
\\(ACC_{5} (↑)\\)\\(\\overline{ACC_{5}}\\) (↑)\\(ACC_{10} (↑)\\)\\(\\overline{ACC_{10}}\\) (↑)\\(ACC_{20} (↑)\\)\\(\\overline{ACC_{20}}\\) (↑)
Random → \\(B_{t}\\)72.49 ± 0.3879.40 ± 0.2967.38 ± 0.4176.62 ± 0.0656.17 ± 0.2969.24 ± 0.35
\\(\\mathcal{N}_{t} \\rightarrow \\mathcal{B}_{t}\\)67.01 ± 0.1176.09 ± 0.0457.91 ± 0.3070.23 ± 0.5940.73 ± 0.2959.68 ± 0.52
\\(\\mathcal{M}_{t}^{\\perp} \\rightarrow \\mathcal{B}_{t}\\)75.94 ± 0.5380.69 ± 0.2774.61 ± 0.6279.67 ± 0.2768.79 ± 0.4275.74 ± 0.26
\\(\\mathcal{N}_{t} \\cap \\mathcal{M}_{t}^{\\perp} \\rightarrow \\mathcal{B}_{t} (\\text{InfLoRA})\\)77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
", + "bbox": [ + 86, + 114, + 885, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8989e2019c8e99ca493416992f51649ac0c938d10b86436ec5d133ea721bd9d2.jpg", + "image_caption": [ + "(a) ImageNet-R (10 Tasks)", + "Figure 4. Relative accuracy of different tasks. Relative accuracy is the accuracy of different variants minus the accuracy of InfLoRA." + ], + "image_footnote": [], + "bbox": [ + 81, + 223, + 267, + 345 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b14e4873e8f092a497c93d7f713faf6a45cf1b18fe241f86245b10978ac1a405.jpg", + "image_caption": [ + "(b) ImageNet-R (20 Tasks)" + ], + "image_footnote": [], + "bbox": [ + 272, + 224, + 459, + 345 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7007d15c051c769b0b6ddf018116f120f0ce49e32c7f88c902e242ca9e18dab9.jpg", + "table_caption": [ + "Table 4. Results (\\%) of different methods on ImageNet-R (10 tasks) using various self-supervised pre-trained models. Here, DINO-1k and iBOT-1k indicate that the ViT is pre-trained on ImageNet-1k using these respective methods." + ], + "table_footnote": [], + "table_body": "
Method\\(ACC_{10} \\left(↑\\right)\\)\\(ACC_{10} \\left(↑\\right)\\)
DINO-1kL2P [44]56.71 ± 0.1263.59 ± 0.21
DualPrompt [43]60.23 ± 0.4266.57 ± 0.25
CODA-P [38]64.02 ± 0.6871.50 ± 0.42
C-LoRA [37]63.07 ± 0.3668.09 ± 0.41
LAE [12]61.03 ± 0.2769.89 ± 0.15
InfLoRA-b566.16 ± 0.1473.01 ± 0.17
InfLoRA68.31 ± 0.2876.15 ± 0.05
iBOT-1kL2P [44]60.80 ± 0.3566.58 ± 0.28
DualPrompt [43]63.78 ± 0.3868.88 ± 0.16
CODA-P [38]68.02 ± 0.4874.28 ± 0.47
C-LoRA [37]68.60 ± 0.0773.47 ± 0.28
LAE [12]64.14 ± 0.2972.59 ± 0.22
InfLoRA-b569.72 ± 0.4476.11 ± 0.13
InfLoRA71.84 ± 0.0978.29 ± 0.09
", + "bbox": [ + 78, + 460, + 468, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4 shows the results of different methods on ImageNet-R when using various pre-trained models. Comparing these results to those in Table 1, we can find that the performance of all methods utilizing self-supervised pretrained models is lower than the performance of the corresponding methods using supervised pre-trained models. However, our methods still outperform all other methods.", + "bbox": [ + 75, + 703, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Combining with Classifier Alignment Slow learner with classifier alignment (SLCA) [47] utilizes feature statistics to align classifiers, demonstrating superior performance compared to methods without aligned classifiers. Our InfLoRA can be combined with classifier alignment (CA) to get better performance. Specifically, after learning the $t$ -th task", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6324a0c2ba22d5d4b9f1736b76ff93727cd2302608a262bd1d0aec4ef6e46eb4.jpg", + "table_caption": [ + "Table 5. Results $(\\%)$ of different methods on ImageNet-R (10 tasks) and CIFAR100 using classifier alignment (CA) technique." + ], + "table_footnote": [], + "table_body": "
MethodACC10(↑)ACC10(↑)
CIFAR100SLCA [47]91.06 ± 0.2493.65 ± 0.19
InfLoRA+CA91.59 ± 0.0894.39 ± 0.05
ImageNet-RSLCA [47]77.34 ± 0.2581.35 ± 0.16
InfLoRA+CA79.78 ± 0.2583.38 ± 0.19
", + "bbox": [ + 501, + 261, + 890, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "with parameters $\\mathbf{A}_t$ and $\\mathbf{B}_t$ and loss (9), we collect features $\\mathbf{F}_t = \\{\\mathbf{r}_{i,t}\\}_{i=1}^{n_t}$ of the $t$ -th task. Here, $\\mathbf{r}_{i,t} = f(\\mathbf{x}_{i,t})$ denotes the features extracted by backbone $f_{\\Theta}(\\cdot)$ . Then, mean and covariance of features for each class are computed and saved. After that, for each class $c$ the model has seen during continual learning, $S$ samples are sampled from Gaussian distribution $\\mathcal{N}(\\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c)$ . Here, $\\boldsymbol{\\mu}_c$ and covariance $\\boldsymbol{\\Sigma}_c$ denote the mean and covariance of the class $c$ . Finally, we align the classifier using standard cross-entropy and these samples. The details of this experiment are given in supplementary material.", + "bbox": [ + 496, + 354, + 890, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 shows that our method InfLoRA+CA outperforms SLCA. Note that SLCA tunes all the parameters of the model while our method InfLoRA only tunes the parameters in $\\mathbf{A}_t$ . Therefore, our InfLoRA+CA is much more efficient than SLCA.", + "bbox": [ + 496, + 520, + 890, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 609, + 617, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose a new method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets.", + "bbox": [ + 496, + 635, + 890, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 815, + 650, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by NSFC (No.62192783), National Key R&D Program of China (No.2020YFA0713901), and Fundamental Research Funds for the Central Universities (No.020214380108).", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23645", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5871-5880, 2021. 2" + ], + "bbox": [ + 503, + 92, + 890, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23647", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/318c0ec9-6df7-445c-afc8-eff054c0abb4_model.json b/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/318c0ec9-6df7-445c-afc8-eff054c0abb4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7d61971a866a664f519f69f75505a7dd838f6119 --- /dev/null +++ b/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/318c0ec9-6df7-445c-afc8-eff054c0abb4_model.json @@ -0,0 +1,2387 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.13, + 0.865, + 0.154 + ], + "angle": 0, + "content": "InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning" + }, + { + "type": "text", + "bbox": [ + 0.358, + 0.182, + 0.619, + 0.199 + ], + "angle": 0, + "content": "Yan-Shuo Liang and Wu-Jun Li*" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.2, + 0.713, + 0.218 + ], + "angle": 0, + "content": "National Key Laboratory for Novel Software Technology," + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.218, + 0.812, + 0.235 + ], + "angle": 0, + "content": "Department of Computer Science and Technology, Nanjing University, P. R. China" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.237, + 0.672, + 0.252 + ], + "angle": 0, + "content": "liangys@smail.nju.edu.cn, liwujun@nju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.726 + ], + "angle": 0, + "content": "Continual learning requires the model to learn multiple tasks sequentially. In continual learning, the model should possess the ability to maintain its performance on old tasks (stability) and the ability to adapt to new tasks continuously (plasticity). Recently, parameter-efficient fine-tuning (PEFT), which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning. Although existing continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT, most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets. Code is available at https://github.com/liangyanshuo/InfLoRA." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.758, + 0.21, + 0.773 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Continual learning requires the model to learn multiple tasks sequentially [33]. To achieve continual learning, the model should possess two essential abilities, including the ability to keep its performance on the old tasks (stability) and the ability to adapt to the new tasks continuously (plasticity) [33]. Furthermore, two different scenar" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.892, + 0.394 + ], + "angle": 0, + "content": "ios are often considered in continual learning, including task-incremental scenario [32] and class-incremental scenario [41]. Task-incremental scenario allows the model to get task identities during inference. On the contrary, class-incremental scenario does not allow the model to get task identities during inference, making the model learn to distinguish all the classes across all the tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.397, + 0.893, + 0.593 + ], + "angle": 0, + "content": "Recently, parameter-efficient fine-tuning (PEFT) [15, 16, 18], which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning [12, 38, 44], especially in the class-incremental scenario. More specifically, existing continual learning methods based on PEFT [21, 43] inject the learnable parameters into a pre-trained model using some popular PEFT methods such as prompt-tuning [25] or low-rank adaptation (LoRA) [16]. Subsequently, these methods freeze the pre-trained weights and sequentially fine-tune the injected parameters on multiple tasks throughout the continual learning process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.895, + 0.838 + ], + "angle": 0, + "content": "Although continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT [44], most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. Specifically, when learning a new task, existing continual learning methods based on PEFT either reuse the previously learned parameters to adapt to the new task [12, 44] or randomly expand some parameters first and then adapt to the new task [38, 42, 43]. During this process, the interference of the new task on the old tasks exists due to the shared parameters between new and old tasks, which means fine-tuning a pre-trained model on a new task may interfere with the model's performance on the old tasks. As a result, it is hard for the model to make a good trade-off between stability and plasticity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.895, + 0.9 + ], + "angle": 0, + "content": "In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. The contributions of this work are listed as follows:" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.31, + 0.901 + ], + "angle": 0, + "content": "*Wu-Jun Li is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23638" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.152 + ], + "angle": 0, + "content": "- InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that finetuning these injected parameters is equivalent to finetuning the pre-trained weights within a subspace." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.153, + 0.468, + 0.197 + ], + "angle": 0, + "content": "- InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.198, + 0.468, + 0.243 + ], + "angle": 0, + "content": "- Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.26, + 0.372, + 0.275 + ], + "angle": 0, + "content": "2. Related Work and Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.286, + 0.221, + 0.3 + ], + "angle": 0, + "content": "2.1. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.31, + 0.47, + 0.673 + ], + "angle": 0, + "content": "Parameter-Efficient Fine-Tuning Parameter-efficient fine-tuning (PEFT) methods freeze a pre-trained model and inject a small number of learnable parameters to adapt to downstream tasks. In this way, PEFT methods reduce the inefficiency of full fine-tuning methods which fine-tune all the parameters of a pre-trained model to learn downstream tasks. For example, Adapter [15] adds small modules in different layers of Transformers and only tunes these added modules to adapt to downstream tasks. Prompt-tuning [25] and Prefix-tuning [27] insert a set of learnable tokens into the input of the Transformer layers and only tune these tokens to adapt to downstream tasks. Low-rank adaptation (LoRA) [16] reparameterizes the pre-trained weights with low-rank branches and only tunes these branches to adapt to the downstream tasks. Although these methods tune much fewer learnable parameters than full fine-tuning, they always show comparable or even superior performance compared with full fine-tuning [11, 16, 31, 45]. Early PEFT methods focus on natural language processing (NLP). Recently, PEFT methods have also been proposed for computer vision (CV). For example, visual prompt tuning (VPT) [18] and AdapterFormer [6] apply prompt-tuning and Adapter techniques to CV tasks, respectively. Both of them exhibit comparable performance to full fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.468, + 0.839 + ], + "angle": 0, + "content": "Continual Learning Early continual learning was usually considered in the context of learning from scratch. Three types of continual learning methods are proposed, including regularization-based methods [1, 20, 23, 46], memory-based methods [2, 3, 7, 28, 39], and expansion-based methods [17, 26, 35]. Regularization-based methods employ a penalty loss (regularization) to prevent important parameters of old tasks from changing too much. Memory-based methods maintain a memory buffer to store information about old tasks. Expansion-based methods dynamically expand the model's architecture for each new task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Recently, with the advancements of pre-trained models [9, 10, 13], using pre-trained models for continual learning has gained increasing popularity. Some continual learning methods fully fine-tune the pre-trained models [4, 48]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "which has been shown to be inefficient. Other methods explore PEFT methods in continual learning. For instance, some existing continual learning methods [21, 38, 43, 44] introduce prompt-tuning in continual learning, achieving much higher performance than previous methods that learn from scratch, especially in the class-incremental scenario. The method in [12] introduces a framework in continual learning that can be combined with many existing PEFT methods, such as prompt-tuning, LoRA and Adapter. However, all these methods do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.64, + 0.315 + ], + "angle": 0, + "content": "2.2. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.37 + ], + "angle": 0, + "content": "We first introduce low-rank adaptation (LoRA) [16], a popular PEFT method related to our method. Then, we give the problem definition for continual learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.642 + ], + "angle": 0, + "content": "Low-Rank Adaptation LoRA [16] is one of the most popular PEFT methods. It assumes that the changes of parameters lie in a low-rank space when the model is fully fine-tuned on a downstream task. Specifically, for a linear layer with the input dimension \\( d_{I} \\) and the output dimension \\( d_{O} \\), we represent its weight with \\( W^{d_O\\times d_I} \\). Then, LoRA reparametrizes the pre-trained weight \\( W \\) by expanding a branch with two matrices, \\( A\\in \\mathbb{R}^{d_O\\times r} \\) and \\( B\\in \\mathbb{R}^{r\\times d_I} \\). Typically, \\( r \\) is much smaller than the input dimension \\( d_{I} \\) and output dimension \\( d_{O} \\), making \\( A \\) a dimensionality increasing matrix and \\( B \\) a dimensionality reduction matrix. Finally, LoRA modifies the forward propagation in this linear layer as \\( e = Wh + ABh \\). Here, \\( h \\) and \\( e \\) denote the input and output of this layer, respectively. LoRA initializes \\( A \\) as 0 and initializes \\( B \\) using Gaussian distribution. During the learning of the downstream tasks, LoRA freezes the pre-trained weight \\( W \\) and only fine-tunes the parameters \\( A \\) and \\( B \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Problem Definition In continual learning, there is a sequence of tasks with different distributions. We define the task sequence as \\(\\mathcal{D} = \\{\\mathcal{D}_1,\\dots,\\mathcal{D}_T\\}\\), where the \\(t\\)-th task \\(\\mathcal{D}_t = \\{(x_{i,t},y_{i,t})\\}_{i = 1}^{n_t}\\). Here, \\(x_{i,t}\\) denotes an input sample and \\(y_{i,t}\\) denotes its label. The objective of continual learning is to train a model sequentially on these tasks and ensure that the model performs well on all of them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We follow existing continual learning methods [43, 44] based on PEFT and assume the model is a pre-trained Vision Transformer (ViT) [10]. Specifically, assume the model is \\( h_{\\Phi}(f_{\\Theta}(\\cdot)) \\) where \\( h_{\\Phi}(\\cdot) \\) is the classifier with parameters \\( \\Phi \\) and \\( f_{\\Theta}(\\cdot) \\) is the pre-trained ViT backbone with pre-trained parameters \\( \\Theta \\). Similar to existing work [43], our focus is primarily on the class-incremental scenario, where task identities are unknown during inference. Furthermore, we concentrate on the exemplar-free setting [43, 50], where no historical data can be fetched for rehearsal." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23639" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.429, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.303, + 0.293, + 0.315 + ], + "angle": 0, + "content": "(a) Architecture" + }, + { + "type": "image", + "bbox": [ + 0.434, + 0.09, + 0.876, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.303, + 0.793, + 0.316 + ], + "angle": 0, + "content": "(b) Designing Dimensionality Reduction Matrix \\(B_{t}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.322, + 0.893, + 0.351 + ], + "angle": 0, + "content": "Figure 1. (a) The architecture of our InfLoRA in a certain linear layer of a Transformer. During the learning of the \\(t\\)-th task, the pre-trained weight and all the old branches are frozen, and only \\(\\mathbf{A}_t\\) is fine-tuned. (b) The pipeline of designing dimensionality reduction matrix \\(\\mathbf{B}_t\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.357, + 0.212, + 0.374 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.473 + ], + "angle": 0, + "content": "Figure 1 (a) illustrates the architecture of our InfLoRA within a linear layer. Before learning the \\(t\\)-th new task, our InfLoRA expands a LoRA-like branch, which includes a dimensionality reduction matrix \\(\\pmb{B}_t \\in \\mathbb{R}^{r \\times d_I}\\) and a dimensionality increasing matrix \\(\\pmb{A}_t \\in \\mathbb{R}^{d_O \\times r}\\). Then, the forward propagation of this linear layer is modified as" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.483, + 0.469, + 0.54 + ], + "angle": 0, + "content": "\\[\ne = W h + \\sum_ {j = 1} ^ {t} A _ {j} B _ {j} h = W _ {t - 1} h + A _ {t} B _ {t} h = W _ {t} h. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.765 + ], + "angle": 0, + "content": "Here, \\(W_{t} = W_{t - 1} + A_{t}B_{t} = W + \\sum_{i = 1}^{t}A_{i}B_{i}\\). Similar to LoRA, our InfLoRA also initializes dimensionality increasing matrix \\(A_{t}\\) as 0. However, different from LoRA, which employs Gaussian distribution to initialize the dimensionality reduction matrix \\(B\\), our InfLoRA designs the dimensionality reduction matrix \\(B_{t}\\) before learning the \\(t\\)-th task. During the learning of the \\(t\\)-th task, InfLoRA fine-tunes \\(A_{t}\\) to learn the new task while keeping the pre-trained weight \\(W\\), all the old branches and the matrix \\(B_{t}\\) frozen. After learning the \\(t\\)-th tasks, for any given test sample belonging to the learned tasks, the model uses \\(W_{t}\\) and (1) to infer its label. This design ensures that our method is compatible with the class-incremental scenario where task identities are unknown during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In the following subsections, we first build the relationship between our InfLoRA and the method that fine-tunes the pre-trained weight. Specifically, we show that finetuning parameters \\( \\mathbf{A}_t \\) is equivalent to fine-tuning the pretrained weights \\( \\mathbf{W} \\) within a subspace spanned by the rows of \\( \\mathbf{B}_t \\). Note that \\( \\mathbf{B}_t \\) is designed before learning the \\( t \\)-th task, making this subspace pre-designed. Then, building upon this relationship, we introduce how our InfLoRA designs this subspace to eliminate the interference of the new" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.359, + 0.892, + 0.39 + ], + "angle": 0, + "content": "task on the old tasks and make a good trade-off between stability and plasticity." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.402, + 0.891, + 0.434 + ], + "angle": 0, + "content": "3.1. Relationship between InfLoRA and Fine-Tuning the Pre-Trained Weight" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.442, + 0.892, + 0.503 + ], + "angle": 0, + "content": "When the \\( t \\)-th task arrives and our method has expanded a new branch, the forward propagation in this layer can be represented by (1). At this time, we can prove the following proposition:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.517, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Proposition 1. When learning the \\(t\\)-th task with forward propagation represented by (1), fine-tuning \\(\\mathbf{A}_t\\) is equivalent to fine-tuning the pre-trained weight \\(\\mathbf{W}\\) within the subspace \\(\\operatorname{span}\\{\\pmb{b}_1^t, \\dots, \\pmb{b}_r^t\\}\\). Here, \\(\\pmb{b}_i^t\\) (\\(1 \\leq i \\leq r\\)) denotes the \\(i\\)-th row vector of \\(\\pmb{B}_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.607, + 0.891, + 0.651 + ], + "angle": 0, + "content": "Proof. When tuning the pre-trained weight \\( \\mathbf{W} \\) to learn the \\( t \\)-th task, we can compute the gradient of \\( \\mathbf{W} \\) based on the chain rule:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.662, + 0.891, + 0.693 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {W}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {e}} \\frac {\\partial \\boldsymbol {e}}{\\partial \\boldsymbol {W}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {e}} \\boldsymbol {h} ^ {T}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.891, + 0.768 + ], + "angle": 0, + "content": "Here, \\(\\mathcal{L}\\) denotes the loss function. At this time, the change of \\(\\pmb{W}\\) can be denoted as \\(\\Delta W = -\\alpha \\frac{\\partial\\mathcal{L}}{\\partial W}\\), where \\(\\alpha\\) is the learning rate. Then, we can compute the change of the composed matrix \\(\\pmb{W}_t = \\pmb {W} + \\sum_{j = 1}^t\\pmb {A}_j\\pmb {B}_j\\):" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.782, + 0.891, + 0.858 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Delta_ {\\boldsymbol {W}} \\boldsymbol {W} _ {t} = [ \\boldsymbol {W} + \\Delta \\boldsymbol {W} + \\sum_ {j = 1} ^ {t} \\boldsymbol {A} _ {j} \\boldsymbol {B} _ {j} ] - (\\boldsymbol {W} + \\sum_ {j = 1} ^ {t} \\boldsymbol {A} _ {j} \\boldsymbol {B} _ {j}) \\\\ = \\Delta \\boldsymbol {W} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {W} _ {t}} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Here, we use \\(\\Delta_{\\mathbf{W}}\\mathbf{W}_t\\) to denote the change of the composed matrix \\(\\mathbf{W}_t\\) causing by the change of \\(\\mathbf{W}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23640" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Similarly, when tuning the expanded weight \\( \\mathbf{A}_t \\), we can get the gradient of \\( \\mathbf{A}_t \\) based on the chain rule:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.129, + 0.469, + 0.162 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {A} _ {t}} = \\frac {\\partial \\mathcal {L}}{\\partial e} \\frac {\\partial \\boldsymbol {e}}{\\partial \\boldsymbol {A} _ {t}} = \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\boldsymbol {B} _ {t} ^ {T}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.17, + 0.47, + 0.215 + ], + "angle": 0, + "content": "At this time, the change of \\( \\mathbf{A}_t \\) can be denoted as \\( \\Delta \\mathbf{A}_t = -\\alpha \\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{A}_t} \\). Then, we can compute the change of the composed matrix \\( \\mathbf{W}_t = \\mathbf{W}_{t-1} + \\mathbf{A}_t \\mathbf{B}_t \\):" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.224, + 0.469, + 0.295 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Delta_ {\\boldsymbol {A} _ {t}} \\boldsymbol {W} _ {t} = \\left[ \\boldsymbol {W} _ {t - 1} + \\left(\\boldsymbol {A} _ {t} + \\Delta \\boldsymbol {A} _ {t}\\right) \\boldsymbol {B} _ {t} \\right] - \\left(\\boldsymbol {W} _ {t - 1} + \\boldsymbol {A} _ {t} \\boldsymbol {B} _ {t}\\right) \\\\ = \\Delta \\boldsymbol {A} _ {t} \\boldsymbol {B} _ {t} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {A} _ {t}} \\boldsymbol {B} _ {t} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\boldsymbol {B} _ {t} ^ {T} \\boldsymbol {B} _ {t} \\\\ = \\Delta_ {W} W _ {t} B _ {t} ^ {T} B _ {t} \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.304, + 0.469, + 0.412 + ], + "angle": 0, + "content": "Here, we use \\(\\Delta_{\\mathbf{A}_t}\\mathbf{W}_t\\) to denote the change of the composed matrix \\(\\mathbf{W}_t\\) causing by the change of \\(\\mathbf{A}_t\\). The fourth equation in (5) holds because of (4). The fifth equation in (5) holds because of (2). (5) shows that \\(\\Delta_{\\mathbf{A}_t}\\mathbf{W}_t\\) is equal to \\(\\Delta_{\\mathbf{W}}\\mathbf{W}_t\\) multiplying a projection matrix \\(\\mathbf{B}_t^T\\mathbf{B}_t\\). Since \\(\\mathbf{B}_t^T\\mathbf{B}_t\\) projects each row vector of \\(\\Delta_{\\mathbf{W}}\\mathbf{W}_t\\) into the subspace span \\(\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}\\), Proposition 1 holds." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.42, + 0.469, + 0.526 + ], + "angle": 0, + "content": "Proposition 1 has demonstrated that using our InfLoRA to train the model is equivalent to directly finetuning the pre-trained weight \\( W \\) within the subspace \\( \\operatorname{span}\\{b_1^t, \\dots, b_r^t\\} \\). Therefore, before learning the \\( t \\)-th task, we can design matrix \\( B_t \\) such that learning the \\( t \\)-th task in the subspace \\( \\operatorname{span}\\{b_1^t, \\dots, b_r^t\\} \\) will not interfere with the performance of the model on the old tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.535, + 0.469, + 0.565 + ], + "angle": 0, + "content": "3.2. Eliminating the Interference of the New Task on the Old Tasks" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.573, + 0.469, + 0.68 + ], + "angle": 0, + "content": "We first introduce the desired characteristics that InfLoRA aims to let the subspace \\(\\mathrm{span}\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}\\) have. With these characteristics, InfLoRA can eliminate the interference of the new task on the old tasks and make a good trade-off between stability and plasticity. Then, we introduce how to design dimensionality reduction matrix \\(B_{t}\\) so that subspace \\(\\mathrm{span}\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}\\) has these characteristics." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.697, + 0.295, + 0.71 + ], + "angle": 0, + "content": "3.2.1 Desired Characteristics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.469, + 0.901 + ], + "angle": 0, + "content": "First, InfLoRA aims to make the subspace \\(\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}\\) orthogonal to the gradients of all the old tasks. In this way, according to Proposition 1, the update of InfLoRA, which can be represented as \\(\\Delta_{A_t}W_t\\) will also be orthogonal to the gradient of the old tasks. Note that the idea of making the update for the new task orthogonal to the gradient of the old tasks to eliminate the interference of the new task on the old tasks has been proposed in many existing continual learning methods [30, 36]. However, all these existing methods are designed for continual learning from scratch, involving updating all parameters of the model, which is incompatible with the setting in PEFT. On the contrary, our" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "method is a PEFT method, which only tunes the parameters in \\(A_{t}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Besides eliminating the interference of new tasks on old tasks, our InfLoRA further makes the subspace \\(\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}\\) lie in a subspace that the gradient of the new task lies in to make a good trade-off between stability and plasticity. Specifically, existing work [19] has shown that during fine-tuning, the weight increments of pre-trained ViT exhibit redundancy in terms of weight rank. Therefore, the gradients of the new task lie in a low-dimensional subspace. Our method makes \\(\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}\\) not only orthogonal to the gradient of the old tasks but also lie in the subspace in which the gradients of the new task \\(t\\) lie. By doing so, our method makes the model's focus on the new task when eliminating the interference of the new task on the old tasks, thereby making a good trade-off between stability and plasticity. Section 4.2 verifies the effectiveness of these two characteristics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.39, + 0.86, + 0.405 + ], + "angle": 0, + "content": "3.2.2 Designing Dimensionality Reduction Matrix" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.568 + ], + "angle": 0, + "content": "InfLoRA first approximates the gradient space of the new task and old tasks. Here, we use \\(\\mathcal{N}_t\\) to represent the gradient space of the new task approximated by InfLoRA. Similarly, we use \\(\\mathcal{M}_t\\) to represent the gradient space of previous \\(t - 1\\) old tasks approximated by InfLoRA. We also use \\(\\mathcal{M}_t^\\perp\\) to denote the residual gradient space, which is orthogonal to the space \\(\\mathcal{M}_t\\). Then, in order to meet the characteristics described in Section 3.2.1, InfLoRA ensures that each row of \\(\\boldsymbol{B}_t\\) lies in \\(\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp\\). In other words, InfLoRA makes \\(\\mathrm{span}\\{\\boldsymbol{b}_1^t,\\dots,\\boldsymbol{b}_r^t\\} \\subseteq \\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Existing works [29, 36] have shown that the gradient update of the linear layer lies in the span of the inputs. Please refer to supplementary material for a detailed explanation of this proposition. Therefore, InfLoRA uses the input matrix of the new task \\( t \\) to approximate the gradient space of the new task. Specifically, InfLoRA computes the input matrix \\( H_{t} = [h_{1}^{t},\\dots,h_{n}^{t}] \\), with each column of \\( H_{t} \\) representing an input vector of the \\( t \\)-th task. Then, InfLoRA considers \\( \\mathcal{N}_t \\) as the subspace spanned by the columns of matrix \\( H_{t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, InfLoRA cannot use the input matrix of the old tasks to approximate the gradient space of the old tasks since the data from the old tasks is not available when the model learns the new tasks. Instead, existing methods such as gradient projection memory (GPM) [36] and dual gradient projection memory (DualGPM) [29] can learn a matrix to preserve information about the gradients of the old tasks. InfLoRA incorporates DualGPM to preserve gradient information. With the assistance of DualGPM, the model can learn either a matrix \\( M_t \\in \\mathbb{R}^{d_I \\times k_t} \\) or a matrix \\( M_t^\\perp \\in \\mathbb{R}^{d_I \\times (d_I - k_t)} \\). Here, the columns of \\( M_t \\) contribute to the orthonormal bases of \\( M_t \\) and the columns of \\( M_t^\\perp \\) contribute to the orthonormal bases of \\( M_t^\\perp \\). \\( k_t \\) denotes the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23641" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.137 + ], + "angle": 0, + "content": "dimension of \\(\\mathcal{M}_t\\). For detailed information of how Dual-GPM maintains orthonormal bases \\(M_t\\) or \\(M_t^\\perp\\), please refer to supplementary material or the original paper [29]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.468, + 0.197 + ], + "angle": 0, + "content": "After approximating the gradient space of the new task and old tasks, InfLoRA gets the component of \\(\\mathcal{N}_t\\) which lies in \\(\\mathcal{M}_t^\\perp\\). Specifically, when the model maintains \\(\\mathcal{M}_t\\), InfLoRA performs the operation" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.204, + 0.469, + 0.222 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {H}} _ {t} = \\boldsymbol {H} _ {t} - \\boldsymbol {M} _ {t} \\boldsymbol {M} _ {t} ^ {T} \\boldsymbol {H} _ {t}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.469, + 0.26 + ], + "angle": 0, + "content": "Similarly, when the model maintains \\(\\mathcal{M}_t^\\perp\\), InfLoRA performs the operation" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.265, + 0.469, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {H}} _ {t} = \\boldsymbol {M} _ {t} ^ {\\perp} \\left(\\boldsymbol {M} _ {t} ^ {\\perp}\\right) ^ {T} \\boldsymbol {H} _ {t}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.469, + 0.417 + ], + "angle": 0, + "content": "Note that when \\(t = 1\\), \\(\\mathcal{M}_t\\) is a null space and \\(\\hat{H}_t = H_t\\). Obviously, each column of \\(\\hat{H}_t\\) lies in \\(\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp\\). However, since \\((\\hat{H}_t)^T \\in \\mathbb{R}^{n \\times d_I}\\) and \\(B_t \\in \\mathbb{R}^{r \\times d_I}\\) have different shapes, InfLoRA can not directly define \\(B_t\\) as \\((\\hat{H}_t)^T\\). Note that \\(n \\gg r\\), InfLoRA uses the principal components of \\((\\hat{H}_t)^T\\) to set \\(B_t\\). Specifically, singular value decomposition (SVD) is performed on \\((\\hat{H}_t)^T = V_t \\Sigma_t U_t\\). Then, InfLoRA designs \\(B_t\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.229, + 0.424, + 0.469, + 0.441 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {B} _ {t} = \\left(\\boldsymbol {U} _ {t}\\right) _ {r}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.492 + ], + "angle": 0, + "content": "Here, \\((\\boldsymbol{U}_t)_r\\) denotes the rows of \\(\\boldsymbol{U}_t\\) corresponding to the top-\\(r\\) singular values. Figure 1 (b) illustrates the pipeline of designing matrix \\(\\boldsymbol{B}_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.469, + 0.659 + ], + "angle": 0, + "content": "Note that DualGPM expands subspace \\(\\mathcal{M}_t\\) and reduces subspace \\(\\mathcal{M}_t^\\perp\\) when the number of tasks increases. Since InfLoRA constrains the update of the model within the subspace \\(\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp \\subseteq \\mathcal{M}_t^\\perp\\), the space for learning the new task reduces when the number of tasks increases. However, by adjusting the approximation error of the gradient for the old tasks, DualGPM can expand \\(\\mathcal{M}_t\\) slowly and reduce \\(\\mathcal{M}_t^\\perp\\) slowly. Therefore, the constraints imposed by InfLoRA do not excessively affect the model's learning of new tasks. Please refer to supplementary material for a detailed explanation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.319, + 0.682 + ], + "angle": 0, + "content": "3.3. Whole Process of InfLoRA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Algorithm 1 outlines the whole process of InfLoRA in continual learning. When the \\( t \\)-th new task arrives, InfLoRA first designs \\( B_{t} \\) through (8) and expands a new branch. Then, InfLoRA learns the \\( t \\)-th task by fine-tuning the newly expanded branch. Please note that, based on empirical findings from existing methods [12, 38], we employ the local cross-entropy (CE) loss as the learning objective, as it usually performs better than the global CE loss in continual learning methods based on PEFT. The local CE is the CE loss constrained to the classes of the current new task, which can be denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.859, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathcal {D} _ {t}\\right) = \\frac {1}{\\left| \\mathcal {D} _ {t} \\right|} \\sum_ {\\left(\\boldsymbol {x}, y\\right) \\in \\mathcal {D} _ {t}} \\mathcal {L} _ {c e} \\left(\\operatorname {m a s k} \\left(h _ {\\boldsymbol {\\Phi}} \\left(f _ {\\boldsymbol {\\Theta}} (\\boldsymbol {x})\\right)\\right), y\\right). \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.091, + 0.809, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 InfLoRA for Continual Learning" + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.112, + 0.892, + 0.141 + ], + "angle": 0, + "content": "1: Input: The data of different tasks \\(\\{\\mathcal{D}_t\\}_{t=1}^T\\), a pre-trained ViT model \\(f_{\\Theta}(\\cdot)\\)." + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.142, + 0.85, + 0.154 + ], + "angle": 0, + "content": "2: Output: Network \\( f_{\\Theta}(\\cdot) \\) with learned parameters \\( W_{t} \\)." + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.156, + 0.63, + 0.167 + ], + "angle": 0, + "content": "3: for \\( t \\) in \\( 1:T \\) do" + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.169, + 0.687, + 0.182 + ], + "angle": 0, + "content": "4: Design \\( \\pmb{B}_{t} \\) through (8);" + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.183, + 0.774, + 0.196 + ], + "angle": 0, + "content": "5: Expand a new branch for the \\(t\\)-th task;" + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.197, + 0.713, + 0.209 + ], + "angle": 0, + "content": "6: for \\(\\mathcal{B}_t\\) sampled from \\(\\mathcal{D}_t\\) do" + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.211, + 0.891, + 0.237 + ], + "angle": 0, + "content": "7: Compute the loss \\(\\mathcal{L}(f_{\\Theta}(\\mathcal{B}_t))\\) through (9) and update the parameters;" + }, + { + "type": "ref_text", + "bbox": [ + 0.511, + 0.239, + 0.594, + 0.25 + ], + "angle": 0, + "content": "8: end for" + }, + { + "type": "ref_text", + "bbox": [ + 0.51, + 0.252, + 0.891, + 0.278 + ], + "angle": 0, + "content": "9: Preserve the information about the gradient of the \\( t \\)-th task through DualGPM;" + }, + { + "type": "ref_text", + "bbox": [ + 0.506, + 0.28, + 0.578, + 0.292 + ], + "angle": 0, + "content": "10: end for" + }, + { + "type": "list", + "bbox": [ + 0.506, + 0.112, + 0.892, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Here, \\(\\mathrm{mask}(\\cdot)\\) is a function that filters out the logits of the old classes and \\(\\mathcal{L}_{ce}\\) denotes the standard CE loss. After learning the \\(t\\)-th new task, InfLoRA follows the DualGPM to preserve the information about the gradient of the \\(t\\)-th task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.893, + 0.656 + ], + "angle": 0, + "content": "Note that the branch corresponding to the \\(t\\)-th task will be frozen once the model has learned the \\(t\\)-th task. Since the expanded branches are linear transformations, we can integrate the old branches into the pre-trained weight to reduce the expanded parameters. Specifically, after learning the first task, InfLoRA integrates the first branch into the pre-trained weight and obtains the weight \\(W_{1} = W + A_{1}B_{1}\\). Before learning the \\(t\\)-th new task (\\(t > 1\\)), InfLoRA maintains the weight \\(W_{t-1}\\). After learning the \\(t\\)-th task, InfLoRA integrates the \\(t\\)-th branch into \\(W_{t-1}\\) and obtains \\(W_{t} = W_{t-1} + A_{t}B_{t}\\). In this way, the parameters in \\(A_{t}\\) and \\(B_{t}\\) do not need to be maintained in the learning of subsequent tasks. Therefore, during the whole learning process, the number of parameters expanded by InfLoRA equals the number of parameters in a single branch. Since a single branch contains \\((d_{I} + d_{O})r\\) parameters, the number of parameters expanded by InfLoRA is \\((d_{I} + d_{O})r\\) all the time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.671, + 0.634, + 0.687 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.707, + 0.712 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets and Evaluation Metric Similar to existing continual learning methods [12, 44] based on PEFT, we use ImageNet-R [14], CIFAR100 [24], and DomainNet [34] to train and evaluate the models. Imagenet-R is generated through artistic processing of 200 classes from ImageNet [8]. This dataset is introduced to continual learning by existing work [43] and has become a standard benchmark for continual learning methods based on PEFT. CIFAR100 is a dataset commonly used in existing continual learning works. DomainNet contains 345 classes and is introduced by some existing works [38, 42] for continual learning. Following existing continual learning work [38]," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23642" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.089, + 0.877, + 0.104 + ], + "angle": 0, + "content": "Table 1. Results (%) on ImageNet-R. Results are included for 5 tasks, 10 tasks, and 20 tasks. We report results averaged over 5 trials." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.114, + 0.877, + 0.29 + ], + "angle": 0, + "content": "
Tasks51020
Method\\(ACC_5 (↑)\\)\\(\\overline{ACC_5} (↑)\\)\\(ACC_{10} (↑)\\)\\(\\overline{ACC_{10}} (↑)\\)\\(ACC_{20} (↑)\\)\\(\\overline{ACC_{20}} (↑)\\)
joint81.14 ± 0.34-81.14 ± 0.34-81.14 ± 0.34-
sequential58.74 ± 1.2872.91 ± 0.2846.07 ± 1.1562.91 ± 0.6834.62 ± 0.8551.15 ± 1.50
L2P [44]64.13 ± 0.7868.66 ± 0.4162.54 ± 0.2467.98 ± 0.2757.92 ± 0.2864.57 ± 0.29
DualPrompt [43]67.88 ± 0.1771.16 ± 0.3165.41 ± 0.5269.39 ± 0.4361.00 ± 0.7265.80 ± 0.67
CODA-P [38]73.09 ± 0.2176.91 ± 0.2171.47 ± 0.3575.82 ± 0.2967.28 ± 0.3072.34 ± 0.17
C-LoRA [37]75.85 ± 0.3178.85 ± 0.3471.89 ± 0.4575.33 ± 0.2865.71 ± 0.6070.63 ± 0.85
LAE [12]73.84 ± 0.1477.29 ± 0.4571.70 ± 0.3976.71 ± 0.1066.98 ± 0.3573.72 ± 0.05
InfLoRA-b575.28 ± 0.0178.95 ± 0.0874.13 ± 0.1878.54 ± 0.1468.41 ± 0.2974.00 ± 0.50
InfLoRA77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.47, + 0.365 + ], + "angle": 0, + "content": "we split ImageNet-R into 5, 10, and 20 tasks, with each task containing 40, 20, and 10 classes. We split CIFAR100 into 10 tasks, and each task constrains 10 classes. We split DomainNet into 5 tasks, and each task contains 69 classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Following existing continual learning methods [12, 44], we evaluate the performance of the model through two popular metrics, including the final accuracy \\( ACC_{T} \\) and the averaged accuracy \\( \\overline{ACC}_{T} = \\frac{1}{T}\\sum_{i=1}^{T}ACC_{i} \\), where \\( T \\) denotes the total number of tasks and \\( ACC_{i} \\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.453, + 0.47, + 0.495 + ], + "angle": 0, + "content": "\\[\nA C C _ {i} = \\frac {1}{i} \\sum_ {j = 1} ^ {i} a _ {i, j}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.537 + ], + "angle": 0, + "content": "Here, \\( a_{i,j} \\) denotes the accuracy of the \\( j \\)-th task once the model has learned the \\( i \\)-th task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.471, + 0.763 + ], + "angle": 0, + "content": "Baselines We compare our InfLoRA with state-of-the-art continual learning methods based on PEFT, including learn to prompt (L2P) [44], DualPrompt [43], continual decomposed attention-based prompt (CODA-P) [38], learning accumulation ensemble (LAE) [12], continual low-rank adaptation (C-LoRA) [37]. For LAE, we implement it with LoRA [16]. Following existing works [12, 38], we also include two methods without continual learning, joint and sequential, in the comparison. Here, joint denotes the method that learns all the tasks jointly, while sequential denotes the method that learns all the tasks sequentially without any operation to overcome the forgetting of the model. The accuracy of joint can be treated as the accuracy upper-bound and the accuracy of sequential can be treated as the accuracy lower-bound." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Architecture and Training Details We follow existing works [12, 43] to perform experiments. Specifically, we use the ViT-B/16 backbone [10] supervised pre-trained on ImageNet 21K as the pre-trained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "For all the methods, we follow existing works [12, 38, 44] and use the Adam [22] optimizer with running averages of gradient and its square \\((\\beta_{1} = 0.9, \\beta_{2} = 0.999)\\). Each task is trained for 50 epochs on ImageNet-R, 20 epochs on CIFAR100 and 5 epochs on DomainNet. The batch size" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.895, + 0.502 + ], + "angle": 0, + "content": "is set to 128 for all the experiments. Since our InfLoRA shares a similar architecture to LoRA, we follow existing work [12] and insert the architecture of our InfLoRA in the key and value of the attention module. Furthermore, existing method DualPrompt [43] treats the inserted blocks as hyperparameters and searches for the best positions for their prompts. On the contrary, we insert the architecture of InfLoRA for all the Transformer blocks to avoid searching. We also implement a variant of our method, which inserts the bottom 5 Transformer blocks like existing methods DualPrompt and CODA-P. We call this variant InfLoRA-b5. As for the hyperparameter \\( r \\), we determine its value through a grid search on a validation dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.513, + 0.704, + 0.53 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.894, + 0.627 + ], + "angle": 0, + "content": "Accuracy Table 1 shows the results of different methods on ImageNet-R with a different number of tasks. Table 2 shows the results of different methods on CIFAR100 and DomainNet. We can find that our methods InfLoRA and InfLoRA-b5 outperform existing continual learning methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.749 + ], + "angle": 0, + "content": "Figure 2 shows the variation of the accuracy of different continual learning methods on ImageNet-R and CIFAR100. We can find that our method outperforms existing methods not only at the end of the learning but also throughout the whole learning process. This indicates that our InfLoRA eliminates the interference of the new task on the old tasks and thus the accuracy of our method decreases slower compared to other methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Analysis of Expanded Parameters Figure 3 shows the number of expanded parameters and the accuracy of different methods on ImageNet-R and CIFAR100. For L2P, DualPrompt and CODA-P, their expanded parameters are included in the added prompts and corresponding key. For LAE, its expanded parameters are the inserted LoRA modules and an additional copy. For C-LoRA, its expanded parameters are inserted LoRA modules. For our method, the expanded parameters are \\( B_{t} \\) and \\( A_{t} \\). The details of computing the number of expanded parameters for different meth" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23643" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.238, + 0.089, + 0.731, + 0.104 + ], + "angle": 0, + "content": "Table 2. Results (%) on CIFAR100 and DomainNet. We report results over 5 trials." + }, + { + "type": "table", + "bbox": [ + 0.172, + 0.115, + 0.803, + 0.289 + ], + "angle": 0, + "content": "
TasksCIFAR100DomainNet
Method\\(ACC_{10} (↑)\\)\\(\\overline{ACC}_{10} (↑)\\)\\(ACC_5 (↑)\\)\\(\\overline{ACC}_5 (↑)\\)
joint91.92 ± 0.05-77.72 ± 0.04-
sequential62.18 ± 3.5980.42 ± 0.2353.44 ± 1.2169.09 ± 0.33
L2P [44]82.48 ± 0.2087.64 ± 0.2570.16 ± 0.0575.60 ± 0.03
DualPrompt [43]84.42 ± 0.3090.06 ± 0.0772.14 ± 0.0577.71 ± 0.06
CODA-P [38]86.62 ± 0.1191.08 ± 0.2873.23 ± 0.1378.72 ± 0.07
C-LoRA [37]82.97 ± 0.4788.81 ± 0.3469.34 ± 0.1375.25 ± 0.11
LAE [12]84.15 ± 0.1089.84 ± 0.0366.85 ± 0.4075.01 ± 0.17
InfLoRA-b587.06 ± 0.2591.59 ± 0.1373.26 ± 0.5078.82 ± 0.34
InfLoRA86.51 ± 0.7391.70 ± 0.3274.53 ± 0.2379.57 ± 0.57
" + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.293, + 0.291, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.416, + 0.291, + 0.428 + ], + "angle": 0, + "content": "(a) ImageNet-R (5 Tasks)" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.292, + 0.483, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.416, + 0.487, + 0.428 + ], + "angle": 0, + "content": "(b) ImageNet-R (10 Tasks)" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.292, + 0.675, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.416, + 0.678, + 0.428 + ], + "angle": 0, + "content": "(c) ImageNet-R (20 Tasks)" + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.293, + 0.865, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.416, + 0.834, + 0.428 + ], + "angle": 0, + "content": "(d) CIFAR100" + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.429, + 0.813, + 0.443 + ], + "angle": 0, + "content": "Figure 2. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.528 + ], + "angle": 0, + "content": "ods are given in supplementary material. We can find that CODA-P and C-LoRA expand much more parameters than other methods. Furthermore, our methods InfLoRA and InfLoRA-b5 expand comparable parameters to L2P, DualPrompt and LAE but perform better than these methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.761 + ], + "angle": 0, + "content": "Ablation Study We perform experiment to verify the effectiveness of designing dimensionality reduction matrix \\( B_{t} \\) by (8). Specifically, we explore three different variants for designing \\( B_{t} \\). The first variant designs \\( B_{t} \\) randomly using Gaussian distribution. We call this variant 'Random \\( \\rightarrow B_{t} \\)'. The second variant discards the operation in (6) or (7) and directly sets \\( \\hat{H}_{t} = H_{t} \\). Through this way, this variant ensures that each row of \\( B_{t} \\) lies in \\( \\mathcal{N}_{t} \\) while ignoring \\( \\mathcal{M}_{t}^{\\perp} \\). We call this variant \\( \\mathcal{N}_{t} \\rightarrow B_{t} \\). The third variant does not compute the input matrix but initializes \\( H_{t} \\) using a Gaussian distribution before applying the operation in (6) or (7). In this way, this variant ensures that each row of \\( B_{t} \\) lies in \\( \\mathcal{M}_{t}^{\\perp} \\) while ignoring \\( \\mathcal{N}_{t} \\). We call this variant \\( \\mathcal{M}_{t}^{\\perp} \\rightarrow B_{t} \\). Since our method focuses both \\( \\mathcal{M}_{t}^{\\perp} \\) and \\( \\mathcal{N}_{t} \\), we use \\( \\mathcal{N}_{t} \\cap \\mathcal{M}_{t}^{\\perp} \\rightarrow B_{t} \\) to represent our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Table 3 shows the results of our method and its variants. We can find that all these variants fail to perform as well as our method. To further demonstrate the performance of different variants, we show the relative accuracy of different tasks after the model learns them all in Figure 4. Here, relative accuracy is the accuracy of different variants minus the accuracy of our InfLoRA. Note that the last task is the new task, and the other tasks are old tasks in Figure 4. As we can see, 'Random \\(\\rightarrow\\) \\(B_{t}\\) ' and \\(\\mathcal{N}_t\\to B_t\\) outper" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.453, + 0.692, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.58, + 0.691, + 0.59 + ], + "angle": 0, + "content": "(a) ImageNet-R (10 Tasks)" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.453, + 0.883, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.77, + 0.579, + 0.85, + 0.59 + ], + "angle": 0, + "content": "(b) CIFAR100" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.597, + 0.892, + 0.625 + ], + "angle": 0, + "content": "Figure 3. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.894, + 0.807 + ], + "angle": 0, + "content": "form \\( \\mathcal{M}_t^\\perp \\to B_t \\) on the new task but shows much lower accuracy than \\( \\mathcal{M}_t^\\perp \\to B_t \\) and our InfLoRA on the old tasks. This means these two variants fail to eliminate the inference of the new task on the old tasks, making the model suffer from low stability. On the contrary, \\( \\mathcal{M}_t^\\perp \\to B_t \\) shows the lowest performance on the new task. This means \\( \\mathcal{M}_t^\\perp \\to B_t \\) ignores the plasticity of the model. Our method outperforms all the variants on most of the tasks. This shows that our method can eliminate the interference of the new task on the old tasks and make a better trade-off between stability and plasticity than these variants." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.9 + ], + "angle": 0, + "content": "Varying the Pre-Trained Model We also follow the existing method [40] and perform experiments using a ViT-B/16 pre-trained with two different self-supervised methods, including DINO [5] and iBOT [49]. All experimental settings, except for the choice of the pre-trained model, are kept consistent with the details outlined in Section 4.1." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23644" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.231, + 0.09, + 0.738, + 0.104 + ], + "angle": 0, + "content": "Table 3. Results of different variants on ImageNet-R with a different number of tasks." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.115, + 0.887, + 0.214 + ], + "angle": 0, + "content": "
Tasks51020
\\(ACC_{5} (↑)\\)\\(\\overline{ACC_{5}}\\) (↑)\\(ACC_{10} (↑)\\)\\(\\overline{ACC_{10}}\\) (↑)\\(ACC_{20} (↑)\\)\\(\\overline{ACC_{20}}\\) (↑)
Random → \\(B_{t}\\)72.49 ± 0.3879.40 ± 0.2967.38 ± 0.4176.62 ± 0.0656.17 ± 0.2969.24 ± 0.35
\\(\\mathcal{N}_{t} \\rightarrow \\mathcal{B}_{t}\\)67.01 ± 0.1176.09 ± 0.0457.91 ± 0.3070.23 ± 0.5940.73 ± 0.2959.68 ± 0.52
\\(\\mathcal{M}_{t}^{\\perp} \\rightarrow \\mathcal{B}_{t}\\)75.94 ± 0.5380.69 ± 0.2774.61 ± 0.6279.67 ± 0.2768.79 ± 0.4275.74 ± 0.26
\\(\\mathcal{N}_{t} \\cap \\mathcal{M}_{t}^{\\perp} \\rightarrow \\mathcal{B}_{t} (\\text{InfLoRA})\\)77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.224, + 0.268, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.347, + 0.268, + 0.358 + ], + "angle": 0, + "content": "(a) ImageNet-R (10 Tasks)" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.226, + 0.46, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.347, + 0.46, + 0.358 + ], + "angle": 0, + "content": "(b) ImageNet-R (20 Tasks)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.36, + 0.468, + 0.387 + ], + "angle": 0, + "content": "Figure 4. Relative accuracy of different tasks. Relative accuracy is the accuracy of different variants minus the accuracy of InfLoRA." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.394, + 0.469, + 0.451 + ], + "angle": 0, + "content": "Table 4. Results (\\%) of different methods on ImageNet-R (10 tasks) using various self-supervised pre-trained models. Here, DINO-1k and iBOT-1k indicate that the ViT is pre-trained on ImageNet-1k using these respective methods." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.462, + 0.47, + 0.696 + ], + "angle": 0, + "content": "
Method\\(ACC_{10} \\left(↑\\right)\\)\\(ACC_{10} \\left(↑\\right)\\)
DINO-1kL2P [44]56.71 ± 0.1263.59 ± 0.21
DualPrompt [43]60.23 ± 0.4266.57 ± 0.25
CODA-P [38]64.02 ± 0.6871.50 ± 0.42
C-LoRA [37]63.07 ± 0.3668.09 ± 0.41
LAE [12]61.03 ± 0.2769.89 ± 0.15
InfLoRA-b566.16 ± 0.1473.01 ± 0.17
InfLoRA68.31 ± 0.2876.15 ± 0.05
iBOT-1kL2P [44]60.80 ± 0.3566.58 ± 0.28
DualPrompt [43]63.78 ± 0.3868.88 ± 0.16
CODA-P [38]68.02 ± 0.4874.28 ± 0.47
C-LoRA [37]68.60 ± 0.0773.47 ± 0.28
LAE [12]64.14 ± 0.2972.59 ± 0.22
InfLoRA-b569.72 ± 0.4476.11 ± 0.13
InfLoRA71.84 ± 0.0978.29 ± 0.09
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.469, + 0.809 + ], + "angle": 0, + "content": "Table 4 shows the results of different methods on ImageNet-R when using various pre-trained models. Comparing these results to those in Table 1, we can find that the performance of all methods utilizing self-supervised pretrained models is lower than the performance of the corresponding methods using supervised pre-trained models. However, our methods still outperform all other methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Combining with Classifier Alignment Slow learner with classifier alignment (SLCA) [47] utilizes feature statistics to align classifiers, demonstrating superior performance compared to methods without aligned classifiers. Our InfLoRA can be combined with classifier alignment (CA) to get better performance. Specifically, after learning the \\(t\\)-th task" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.222, + 0.892, + 0.251 + ], + "angle": 0, + "content": "Table 5. Results \\((\\%)\\) of different methods on ImageNet-R (10 tasks) and CIFAR100 using classifier alignment (CA) technique." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.262, + 0.892, + 0.344 + ], + "angle": 0, + "content": "
MethodACC10(↑)ACC10(↑)
CIFAR100SLCA [47]91.06 ± 0.2493.65 ± 0.19
InfLoRA+CA91.59 ± 0.0894.39 ± 0.05
ImageNet-RSLCA [47]77.34 ± 0.2581.35 ± 0.16
InfLoRA+CA79.78 ± 0.2583.38 ± 0.19
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.521 + ], + "angle": 0, + "content": "with parameters \\( \\mathbf{A}_t \\) and \\( \\mathbf{B}_t \\) and loss (9), we collect features \\( \\mathbf{F}_t = \\{\\mathbf{r}_{i,t}\\}_{i=1}^{n_t} \\) of the \\( t \\)-th task. Here, \\( \\mathbf{r}_{i,t} = f(\\mathbf{x}_{i,t}) \\) denotes the features extracted by backbone \\( f_{\\Theta}(\\cdot) \\). Then, mean and covariance of features for each class are computed and saved. After that, for each class \\( c \\) the model has seen during continual learning, \\( S \\) samples are sampled from Gaussian distribution \\( \\mathcal{N}(\\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c) \\). Here, \\( \\boldsymbol{\\mu}_c \\) and covariance \\( \\boldsymbol{\\Sigma}_c \\) denote the mean and covariance of the class \\( c \\). Finally, we align the classifier using standard cross-entropy and these samples. The details of this experiment are given in supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.596 + ], + "angle": 0, + "content": "Table 5 shows that our method InfLoRA+CA outperforms SLCA. Note that SLCA tunes all the parameters of the model while our method InfLoRA only tunes the parameters in \\( \\mathbf{A}_t \\). Therefore, our InfLoRA+CA is much more efficient than SLCA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.619, + 0.626 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.802 + ], + "angle": 0, + "content": "In this work, we propose a new method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.651, + 0.832 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work is supported by NSFC (No.62192783), National Key R&D Program of China (No.2020YFA0713901), and Fundamental Research Funds for the Central Universities (No.020214380108)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23645" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5871-5880, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23647" + } + ] +] \ No newline at end of file diff --git a/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/318c0ec9-6df7-445c-afc8-eff054c0abb4_origin.pdf b/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/318c0ec9-6df7-445c-afc8-eff054c0abb4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..43c29e525f03d319acea9839d61e842aaee966c5 --- /dev/null +++ b/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/318c0ec9-6df7-445c-afc8-eff054c0abb4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a8ba5ba6526399aa3a81c8033e667025393ab916b611c985134bf3b54a3d56cc +size 566580 diff --git a/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/full.md b/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..21d8a753e2fc8589618b995b50087c736195d9be --- /dev/null +++ b/2024/InfLoRA_ Interference-Free Low-Rank Adaptation for Continual Learning/full.md @@ -0,0 +1,339 @@ +# InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning + +Yan-Shuo Liang and Wu-Jun Li* + +National Key Laboratory for Novel Software Technology, + +Department of Computer Science and Technology, Nanjing University, P. R. China + +liangys@smail.nju.edu.cn, liwujun@nju.edu.cn + +# Abstract + +Continual learning requires the model to learn multiple tasks sequentially. In continual learning, the model should possess the ability to maintain its performance on old tasks (stability) and the ability to adapt to new tasks continuously (plasticity). Recently, parameter-efficient fine-tuning (PEFT), which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning. Although existing continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT, most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets. Code is available at https://github.com/liangyanshuo/InfLoRA. + +# 1. Introduction + +Continual learning requires the model to learn multiple tasks sequentially [33]. To achieve continual learning, the model should possess two essential abilities, including the ability to keep its performance on the old tasks (stability) and the ability to adapt to the new tasks continuously (plasticity) [33]. Furthermore, two different scenar + +ios are often considered in continual learning, including task-incremental scenario [32] and class-incremental scenario [41]. Task-incremental scenario allows the model to get task identities during inference. On the contrary, class-incremental scenario does not allow the model to get task identities during inference, making the model learn to distinguish all the classes across all the tasks. + +Recently, parameter-efficient fine-tuning (PEFT) [15, 16, 18], which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning [12, 38, 44], especially in the class-incremental scenario. More specifically, existing continual learning methods based on PEFT [21, 43] inject the learnable parameters into a pre-trained model using some popular PEFT methods such as prompt-tuning [25] or low-rank adaptation (LoRA) [16]. Subsequently, these methods freeze the pre-trained weights and sequentially fine-tune the injected parameters on multiple tasks throughout the continual learning process. + +Although continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT [44], most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. Specifically, when learning a new task, existing continual learning methods based on PEFT either reuse the previously learned parameters to adapt to the new task [12, 44] or randomly expand some parameters first and then adapt to the new task [38, 42, 43]. During this process, the interference of the new task on the old tasks exists due to the shared parameters between new and old tasks, which means fine-tuning a pre-trained model on a new task may interfere with the model's performance on the old tasks. As a result, it is hard for the model to make a good trade-off between stability and plasticity. + +In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. The contributions of this work are listed as follows: + +- InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that finetuning these injected parameters is equivalent to finetuning the pre-trained weights within a subspace. +- InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. +- Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets. + +# 2. Related Work and Preliminaries + +# 2.1. Related Work + +Parameter-Efficient Fine-Tuning Parameter-efficient fine-tuning (PEFT) methods freeze a pre-trained model and inject a small number of learnable parameters to adapt to downstream tasks. In this way, PEFT methods reduce the inefficiency of full fine-tuning methods which fine-tune all the parameters of a pre-trained model to learn downstream tasks. For example, Adapter [15] adds small modules in different layers of Transformers and only tunes these added modules to adapt to downstream tasks. Prompt-tuning [25] and Prefix-tuning [27] insert a set of learnable tokens into the input of the Transformer layers and only tune these tokens to adapt to downstream tasks. Low-rank adaptation (LoRA) [16] reparameterizes the pre-trained weights with low-rank branches and only tunes these branches to adapt to the downstream tasks. Although these methods tune much fewer learnable parameters than full fine-tuning, they always show comparable or even superior performance compared with full fine-tuning [11, 16, 31, 45]. Early PEFT methods focus on natural language processing (NLP). Recently, PEFT methods have also been proposed for computer vision (CV). For example, visual prompt tuning (VPT) [18] and AdapterFormer [6] apply prompt-tuning and Adapter techniques to CV tasks, respectively. Both of them exhibit comparable performance to full fine-tuning. + +Continual Learning Early continual learning was usually considered in the context of learning from scratch. Three types of continual learning methods are proposed, including regularization-based methods [1, 20, 23, 46], memory-based methods [2, 3, 7, 28, 39], and expansion-based methods [17, 26, 35]. Regularization-based methods employ a penalty loss (regularization) to prevent important parameters of old tasks from changing too much. Memory-based methods maintain a memory buffer to store information about old tasks. Expansion-based methods dynamically expand the model's architecture for each new task. + +Recently, with the advancements of pre-trained models [9, 10, 13], using pre-trained models for continual learning has gained increasing popularity. Some continual learning methods fully fine-tune the pre-trained models [4, 48], + +which has been shown to be inefficient. Other methods explore PEFT methods in continual learning. For instance, some existing continual learning methods [21, 38, 43, 44] introduce prompt-tuning in continual learning, achieving much higher performance than previous methods that learn from scratch, especially in the class-incremental scenario. The method in [12] introduces a framework in continual learning that can be combined with many existing PEFT methods, such as prompt-tuning, LoRA and Adapter. However, all these methods do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. + +# 2.2. Preliminaries + +We first introduce low-rank adaptation (LoRA) [16], a popular PEFT method related to our method. Then, we give the problem definition for continual learning. + +Low-Rank Adaptation LoRA [16] is one of the most popular PEFT methods. It assumes that the changes of parameters lie in a low-rank space when the model is fully fine-tuned on a downstream task. Specifically, for a linear layer with the input dimension $d_{I}$ and the output dimension $d_{O}$ , we represent its weight with $W^{d_O\times d_I}$ . Then, LoRA reparametrizes the pre-trained weight $W$ by expanding a branch with two matrices, $A\in \mathbb{R}^{d_O\times r}$ and $B\in \mathbb{R}^{r\times d_I}$ . Typically, $r$ is much smaller than the input dimension $d_{I}$ and output dimension $d_{O}$ , making $A$ a dimensionality increasing matrix and $B$ a dimensionality reduction matrix. Finally, LoRA modifies the forward propagation in this linear layer as $e = Wh + ABh$ . Here, $h$ and $e$ denote the input and output of this layer, respectively. LoRA initializes $A$ as 0 and initializes $B$ using Gaussian distribution. During the learning of the downstream tasks, LoRA freezes the pre-trained weight $W$ and only fine-tunes the parameters $A$ and $B$ . + +Problem Definition In continual learning, there is a sequence of tasks with different distributions. We define the task sequence as $\mathcal{D} = \{\mathcal{D}_1,\dots,\mathcal{D}_T\}$ , where the $t$ -th task $\mathcal{D}_t = \{(x_{i,t},y_{i,t})\}_{i = 1}^{n_t}$ . Here, $x_{i,t}$ denotes an input sample and $y_{i,t}$ denotes its label. The objective of continual learning is to train a model sequentially on these tasks and ensure that the model performs well on all of them. + +We follow existing continual learning methods [43, 44] based on PEFT and assume the model is a pre-trained Vision Transformer (ViT) [10]. Specifically, assume the model is $h_{\Phi}(f_{\Theta}(\cdot))$ where $h_{\Phi}(\cdot)$ is the classifier with parameters $\Phi$ and $f_{\Theta}(\cdot)$ is the pre-trained ViT backbone with pre-trained parameters $\Theta$ . Similar to existing work [43], our focus is primarily on the class-incremental scenario, where task identities are unknown during inference. Furthermore, we concentrate on the exemplar-free setting [43, 50], where no historical data can be fetched for rehearsal. + +![](images/f80b43ac204c7bffd4f5085e0499ca8c8fad11396ecd907691a5d2bbfdf62394.jpg) +(a) Architecture + +![](images/e66e2ea897b11b01e524b09785e3c48dd147fcd2a0130a1ec8654247e357d348.jpg) +(b) Designing Dimensionality Reduction Matrix $B_{t}$ +Figure 1. (a) The architecture of our InfLoRA in a certain linear layer of a Transformer. During the learning of the $t$ -th task, the pre-trained weight and all the old branches are frozen, and only $\mathbf{A}_t$ is fine-tuned. (b) The pipeline of designing dimensionality reduction matrix $\mathbf{B}_t$ . + +# 3. Methodology + +Figure 1 (a) illustrates the architecture of our InfLoRA within a linear layer. Before learning the $t$ -th new task, our InfLoRA expands a LoRA-like branch, which includes a dimensionality reduction matrix $\pmb{B}_t \in \mathbb{R}^{r \times d_I}$ and a dimensionality increasing matrix $\pmb{A}_t \in \mathbb{R}^{d_O \times r}$ . Then, the forward propagation of this linear layer is modified as + +$$ +e = W h + \sum_ {j = 1} ^ {t} A _ {j} B _ {j} h = W _ {t - 1} h + A _ {t} B _ {t} h = W _ {t} h. \tag {1} +$$ + +Here, $W_{t} = W_{t - 1} + A_{t}B_{t} = W + \sum_{i = 1}^{t}A_{i}B_{i}$ . Similar to LoRA, our InfLoRA also initializes dimensionality increasing matrix $A_{t}$ as 0. However, different from LoRA, which employs Gaussian distribution to initialize the dimensionality reduction matrix $B$ , our InfLoRA designs the dimensionality reduction matrix $B_{t}$ before learning the $t$ -th task. During the learning of the $t$ -th task, InfLoRA fine-tunes $A_{t}$ to learn the new task while keeping the pre-trained weight $W$ , all the old branches and the matrix $B_{t}$ frozen. After learning the $t$ -th tasks, for any given test sample belonging to the learned tasks, the model uses $W_{t}$ and (1) to infer its label. This design ensures that our method is compatible with the class-incremental scenario where task identities are unknown during inference. + +In the following subsections, we first build the relationship between our InfLoRA and the method that fine-tunes the pre-trained weight. Specifically, we show that finetuning parameters $\mathbf{A}_t$ is equivalent to fine-tuning the pretrained weights $\mathbf{W}$ within a subspace spanned by the rows of $\mathbf{B}_t$ . Note that $\mathbf{B}_t$ is designed before learning the $t$ -th task, making this subspace pre-designed. Then, building upon this relationship, we introduce how our InfLoRA designs this subspace to eliminate the interference of the new + +task on the old tasks and make a good trade-off between stability and plasticity. + +# 3.1. Relationship between InfLoRA and Fine-Tuning the Pre-Trained Weight + +When the $t$ -th task arrives and our method has expanded a new branch, the forward propagation in this layer can be represented by (1). At this time, we can prove the following proposition: + +Proposition 1. When learning the $t$ -th task with forward propagation represented by (1), fine-tuning $\mathbf{A}_t$ is equivalent to fine-tuning the pre-trained weight $\mathbf{W}$ within the subspace $\operatorname{span}\{\pmb{b}_1^t, \dots, \pmb{b}_r^t\}$ . Here, $\pmb{b}_i^t$ ( $1 \leq i \leq r$ ) denotes the $i$ -th row vector of $\pmb{B}_t$ . + +Proof. When tuning the pre-trained weight $\mathbf{W}$ to learn the $t$ -th task, we can compute the gradient of $\mathbf{W}$ based on the chain rule: + +$$ +\frac {\partial \mathcal {L}}{\partial \boldsymbol {W}} = \frac {\partial \mathcal {L}}{\partial \boldsymbol {e}} \frac {\partial \boldsymbol {e}}{\partial \boldsymbol {W}} = \frac {\partial \mathcal {L}}{\partial \boldsymbol {e}} \boldsymbol {h} ^ {T}. \tag {2} +$$ + +Here, $\mathcal{L}$ denotes the loss function. At this time, the change of $\pmb{W}$ can be denoted as $\Delta W = -\alpha \frac{\partial\mathcal{L}}{\partial W}$ , where $\alpha$ is the learning rate. Then, we can compute the change of the composed matrix $\pmb{W}_t = \pmb {W} + \sum_{j = 1}^t\pmb {A}_j\pmb {B}_j$ : + +$$ +\begin{array}{l} \Delta_ {\boldsymbol {W}} \boldsymbol {W} _ {t} = [ \boldsymbol {W} + \Delta \boldsymbol {W} + \sum_ {j = 1} ^ {t} \boldsymbol {A} _ {j} \boldsymbol {B} _ {j} ] - (\boldsymbol {W} + \sum_ {j = 1} ^ {t} \boldsymbol {A} _ {j} \boldsymbol {B} _ {j}) \\ = \Delta \boldsymbol {W} = - \alpha \frac {\partial \mathcal {L}}{\partial \boldsymbol {W} _ {t}} = - \alpha \frac {\partial \mathcal {L}}{\partial e} \boldsymbol {h} ^ {T} \tag {3} \\ \end{array} +$$ + +Here, we use $\Delta_{\mathbf{W}}\mathbf{W}_t$ to denote the change of the composed matrix $\mathbf{W}_t$ causing by the change of $\mathbf{W}$ . + +Similarly, when tuning the expanded weight $\mathbf{A}_t$ , we can get the gradient of $\mathbf{A}_t$ based on the chain rule: + +$$ +\frac {\partial \mathcal {L}}{\partial \boldsymbol {A} _ {t}} = \frac {\partial \mathcal {L}}{\partial e} \frac {\partial \boldsymbol {e}}{\partial \boldsymbol {A} _ {t}} = \frac {\partial \mathcal {L}}{\partial e} \boldsymbol {h} ^ {T} \boldsymbol {B} _ {t} ^ {T}. \tag {4} +$$ + +At this time, the change of $\mathbf{A}_t$ can be denoted as $\Delta \mathbf{A}_t = -\alpha \frac{\partial \mathcal{L}}{\partial \mathbf{A}_t}$ . Then, we can compute the change of the composed matrix $\mathbf{W}_t = \mathbf{W}_{t-1} + \mathbf{A}_t \mathbf{B}_t$ : + +$$ +\begin{array}{l} \Delta_ {\boldsymbol {A} _ {t}} \boldsymbol {W} _ {t} = \left[ \boldsymbol {W} _ {t - 1} + \left(\boldsymbol {A} _ {t} + \Delta \boldsymbol {A} _ {t}\right) \boldsymbol {B} _ {t} \right] - \left(\boldsymbol {W} _ {t - 1} + \boldsymbol {A} _ {t} \boldsymbol {B} _ {t}\right) \\ = \Delta \boldsymbol {A} _ {t} \boldsymbol {B} _ {t} = - \alpha \frac {\partial \mathcal {L}}{\partial \boldsymbol {A} _ {t}} \boldsymbol {B} _ {t} = - \alpha \frac {\partial \mathcal {L}}{\partial e} \boldsymbol {h} ^ {T} \boldsymbol {B} _ {t} ^ {T} \boldsymbol {B} _ {t} \\ = \Delta_ {W} W _ {t} B _ {t} ^ {T} B _ {t} \tag {5} \\ \end{array} +$$ + +Here, we use $\Delta_{\mathbf{A}_t}\mathbf{W}_t$ to denote the change of the composed matrix $\mathbf{W}_t$ causing by the change of $\mathbf{A}_t$ . The fourth equation in (5) holds because of (4). The fifth equation in (5) holds because of (2). (5) shows that $\Delta_{\mathbf{A}_t}\mathbf{W}_t$ is equal to $\Delta_{\mathbf{W}}\mathbf{W}_t$ multiplying a projection matrix $\mathbf{B}_t^T\mathbf{B}_t$ . Since $\mathbf{B}_t^T\mathbf{B}_t$ projects each row vector of $\Delta_{\mathbf{W}}\mathbf{W}_t$ into the subspace span $\{\pmb {b}_1^t,\dots,\pmb {b}_r^t\}$ , Proposition 1 holds. + +Proposition 1 has demonstrated that using our InfLoRA to train the model is equivalent to directly finetuning the pre-trained weight $W$ within the subspace $\operatorname{span}\{b_1^t, \dots, b_r^t\}$ . Therefore, before learning the $t$ -th task, we can design matrix $B_t$ such that learning the $t$ -th task in the subspace $\operatorname{span}\{b_1^t, \dots, b_r^t\}$ will not interfere with the performance of the model on the old tasks. + +# 3.2. Eliminating the Interference of the New Task on the Old Tasks + +We first introduce the desired characteristics that InfLoRA aims to let the subspace $\mathrm{span}\{\pmb {b}_1^t,\dots,\pmb {b}_r^t\}$ have. With these characteristics, InfLoRA can eliminate the interference of the new task on the old tasks and make a good trade-off between stability and plasticity. Then, we introduce how to design dimensionality reduction matrix $B_{t}$ so that subspace $\mathrm{span}\{\pmb {b}_1^t,\dots,\pmb {b}_r^t\}$ has these characteristics. + +# 3.2.1 Desired Characteristics + +First, InfLoRA aims to make the subspace $\mathrm{span}\{b_1^t,\dots,b_r^t\}$ orthogonal to the gradients of all the old tasks. In this way, according to Proposition 1, the update of InfLoRA, which can be represented as $\Delta_{A_t}W_t$ will also be orthogonal to the gradient of the old tasks. Note that the idea of making the update for the new task orthogonal to the gradient of the old tasks to eliminate the interference of the new task on the old tasks has been proposed in many existing continual learning methods [30, 36]. However, all these existing methods are designed for continual learning from scratch, involving updating all parameters of the model, which is incompatible with the setting in PEFT. On the contrary, our + +method is a PEFT method, which only tunes the parameters in $A_{t}$ . + +Besides eliminating the interference of new tasks on old tasks, our InfLoRA further makes the subspace $\mathrm{span}\{b_1^t,\dots,b_r^t\}$ lie in a subspace that the gradient of the new task lies in to make a good trade-off between stability and plasticity. Specifically, existing work [19] has shown that during fine-tuning, the weight increments of pre-trained ViT exhibit redundancy in terms of weight rank. Therefore, the gradients of the new task lie in a low-dimensional subspace. Our method makes $\mathrm{span}\{b_1^t,\dots,b_r^t\}$ not only orthogonal to the gradient of the old tasks but also lie in the subspace in which the gradients of the new task $t$ lie. By doing so, our method makes the model's focus on the new task when eliminating the interference of the new task on the old tasks, thereby making a good trade-off between stability and plasticity. Section 4.2 verifies the effectiveness of these two characteristics. + +# 3.2.2 Designing Dimensionality Reduction Matrix + +InfLoRA first approximates the gradient space of the new task and old tasks. Here, we use $\mathcal{N}_t$ to represent the gradient space of the new task approximated by InfLoRA. Similarly, we use $\mathcal{M}_t$ to represent the gradient space of previous $t - 1$ old tasks approximated by InfLoRA. We also use $\mathcal{M}_t^\perp$ to denote the residual gradient space, which is orthogonal to the space $\mathcal{M}_t$ . Then, in order to meet the characteristics described in Section 3.2.1, InfLoRA ensures that each row of $\boldsymbol{B}_t$ lies in $\mathcal{N}_t \cap \mathcal{M}_t^\perp$ . In other words, InfLoRA makes $\mathrm{span}\{\boldsymbol{b}_1^t,\dots,\boldsymbol{b}_r^t\} \subseteq \mathcal{N}_t \cap \mathcal{M}_t^\perp$ . + +Existing works [29, 36] have shown that the gradient update of the linear layer lies in the span of the inputs. Please refer to supplementary material for a detailed explanation of this proposition. Therefore, InfLoRA uses the input matrix of the new task $t$ to approximate the gradient space of the new task. Specifically, InfLoRA computes the input matrix $H_{t} = [h_{1}^{t},\dots,h_{n}^{t}]$ , with each column of $H_{t}$ representing an input vector of the $t$ -th task. Then, InfLoRA considers $\mathcal{N}_t$ as the subspace spanned by the columns of matrix $H_{t}$ . + +However, InfLoRA cannot use the input matrix of the old tasks to approximate the gradient space of the old tasks since the data from the old tasks is not available when the model learns the new tasks. Instead, existing methods such as gradient projection memory (GPM) [36] and dual gradient projection memory (DualGPM) [29] can learn a matrix to preserve information about the gradients of the old tasks. InfLoRA incorporates DualGPM to preserve gradient information. With the assistance of DualGPM, the model can learn either a matrix $M_t \in \mathbb{R}^{d_I \times k_t}$ or a matrix $M_t^\perp \in \mathbb{R}^{d_I \times (d_I - k_t)}$ . Here, the columns of $M_t$ contribute to the orthonormal bases of $M_t$ and the columns of $M_t^\perp$ contribute to the orthonormal bases of $M_t^\perp$ . $k_t$ denotes the + +dimension of $\mathcal{M}_t$ . For detailed information of how Dual-GPM maintains orthonormal bases $M_t$ or $M_t^\perp$ , please refer to supplementary material or the original paper [29]. + +After approximating the gradient space of the new task and old tasks, InfLoRA gets the component of $\mathcal{N}_t$ which lies in $\mathcal{M}_t^\perp$ . Specifically, when the model maintains $\mathcal{M}_t$ , InfLoRA performs the operation + +$$ +\hat {\boldsymbol {H}} _ {t} = \boldsymbol {H} _ {t} - \boldsymbol {M} _ {t} \boldsymbol {M} _ {t} ^ {T} \boldsymbol {H} _ {t}. \tag {6} +$$ + +Similarly, when the model maintains $\mathcal{M}_t^\perp$ , InfLoRA performs the operation + +$$ +\hat {\boldsymbol {H}} _ {t} = \boldsymbol {M} _ {t} ^ {\perp} \left(\boldsymbol {M} _ {t} ^ {\perp}\right) ^ {T} \boldsymbol {H} _ {t}. \tag {7} +$$ + +Note that when $t = 1$ , $\mathcal{M}_t$ is a null space and $\hat{H}_t = H_t$ . Obviously, each column of $\hat{H}_t$ lies in $\mathcal{N}_t \cap \mathcal{M}_t^\perp$ . However, since $(\hat{H}_t)^T \in \mathbb{R}^{n \times d_I}$ and $B_t \in \mathbb{R}^{r \times d_I}$ have different shapes, InfLoRA can not directly define $B_t$ as $(\hat{H}_t)^T$ . Note that $n \gg r$ , InfLoRA uses the principal components of $(\hat{H}_t)^T$ to set $B_t$ . Specifically, singular value decomposition (SVD) is performed on $(\hat{H}_t)^T = V_t \Sigma_t U_t$ . Then, InfLoRA designs $B_t$ by + +$$ +\boldsymbol {B} _ {t} = \left(\boldsymbol {U} _ {t}\right) _ {r}. \tag {8} +$$ + +Here, $(\boldsymbol{U}_t)_r$ denotes the rows of $\boldsymbol{U}_t$ corresponding to the top- $r$ singular values. Figure 1 (b) illustrates the pipeline of designing matrix $\boldsymbol{B}_t$ . + +Note that DualGPM expands subspace $\mathcal{M}_t$ and reduces subspace $\mathcal{M}_t^\perp$ when the number of tasks increases. Since InfLoRA constrains the update of the model within the subspace $\mathcal{N}_t \cap \mathcal{M}_t^\perp \subseteq \mathcal{M}_t^\perp$ , the space for learning the new task reduces when the number of tasks increases. However, by adjusting the approximation error of the gradient for the old tasks, DualGPM can expand $\mathcal{M}_t$ slowly and reduce $\mathcal{M}_t^\perp$ slowly. Therefore, the constraints imposed by InfLoRA do not excessively affect the model's learning of new tasks. Please refer to supplementary material for a detailed explanation. + +# 3.3. Whole Process of InfLoRA + +Algorithm 1 outlines the whole process of InfLoRA in continual learning. When the $t$ -th new task arrives, InfLoRA first designs $B_{t}$ through (8) and expands a new branch. Then, InfLoRA learns the $t$ -th task by fine-tuning the newly expanded branch. Please note that, based on empirical findings from existing methods [12, 38], we employ the local cross-entropy (CE) loss as the learning objective, as it usually performs better than the global CE loss in continual learning methods based on PEFT. The local CE is the CE loss constrained to the classes of the current new task, which can be denoted as + +$$ +\mathcal {L} \left(\mathcal {D} _ {t}\right) = \frac {1}{\left| \mathcal {D} _ {t} \right|} \sum_ {\left(\boldsymbol {x}, y\right) \in \mathcal {D} _ {t}} \mathcal {L} _ {c e} \left(\operatorname {m a s k} \left(h _ {\boldsymbol {\Phi}} \left(f _ {\boldsymbol {\Theta}} (\boldsymbol {x})\right)\right), y\right). \tag {9} +$$ + +# Algorithm 1 InfLoRA for Continual Learning + +1: Input: The data of different tasks $\{\mathcal{D}_t\}_{t=1}^T$ , a pre-trained ViT model $f_{\Theta}(\cdot)$ . +2: Output: Network $f_{\Theta}(\cdot)$ with learned parameters $W_{t}$ . +3: for $t$ in $1:T$ do +4: Design $\pmb{B}_{t}$ through (8); +5: Expand a new branch for the $t$ -th task; +6: for $\mathcal{B}_t$ sampled from $\mathcal{D}_t$ do +7: Compute the loss $\mathcal{L}(f_{\Theta}(\mathcal{B}_t))$ through (9) and update the parameters; +8: end for +9: Preserve the information about the gradient of the $t$ -th task through DualGPM; +10: end for + +Here, $\mathrm{mask}(\cdot)$ is a function that filters out the logits of the old classes and $\mathcal{L}_{ce}$ denotes the standard CE loss. After learning the $t$ -th new task, InfLoRA follows the DualGPM to preserve the information about the gradient of the $t$ -th task. + +Note that the branch corresponding to the $t$ -th task will be frozen once the model has learned the $t$ -th task. Since the expanded branches are linear transformations, we can integrate the old branches into the pre-trained weight to reduce the expanded parameters. Specifically, after learning the first task, InfLoRA integrates the first branch into the pre-trained weight and obtains the weight $W_{1} = W + A_{1}B_{1}$ . Before learning the $t$ -th new task ( $t > 1$ ), InfLoRA maintains the weight $W_{t-1}$ . After learning the $t$ -th task, InfLoRA integrates the $t$ -th branch into $W_{t-1}$ and obtains $W_{t} = W_{t-1} + A_{t}B_{t}$ . In this way, the parameters in $A_{t}$ and $B_{t}$ do not need to be maintained in the learning of subsequent tasks. Therefore, during the whole learning process, the number of parameters expanded by InfLoRA equals the number of parameters in a single branch. Since a single branch contains $(d_{I} + d_{O})r$ parameters, the number of parameters expanded by InfLoRA is $(d_{I} + d_{O})r$ all the time. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets and Evaluation Metric Similar to existing continual learning methods [12, 44] based on PEFT, we use ImageNet-R [14], CIFAR100 [24], and DomainNet [34] to train and evaluate the models. Imagenet-R is generated through artistic processing of 200 classes from ImageNet [8]. This dataset is introduced to continual learning by existing work [43] and has become a standard benchmark for continual learning methods based on PEFT. CIFAR100 is a dataset commonly used in existing continual learning works. DomainNet contains 345 classes and is introduced by some existing works [38, 42] for continual learning. Following existing continual learning work [38], + +Table 1. Results (%) on ImageNet-R. Results are included for 5 tasks, 10 tasks, and 20 tasks. We report results averaged over 5 trials. + +
Tasks51020
Method\(ACC_5 (↑)\)\(\overline{ACC_5} (↑)\)\(ACC_{10} (↑)\)\(\overline{ACC_{10}} (↑)\)\(ACC_{20} (↑)\)\(\overline{ACC_{20}} (↑)\)
joint81.14 ± 0.34-81.14 ± 0.34-81.14 ± 0.34-
sequential58.74 ± 1.2872.91 ± 0.2846.07 ± 1.1562.91 ± 0.6834.62 ± 0.8551.15 ± 1.50
L2P [44]64.13 ± 0.7868.66 ± 0.4162.54 ± 0.2467.98 ± 0.2757.92 ± 0.2864.57 ± 0.29
DualPrompt [43]67.88 ± 0.1771.16 ± 0.3165.41 ± 0.5269.39 ± 0.4361.00 ± 0.7265.80 ± 0.67
CODA-P [38]73.09 ± 0.2176.91 ± 0.2171.47 ± 0.3575.82 ± 0.2967.28 ± 0.3072.34 ± 0.17
C-LoRA [37]75.85 ± 0.3178.85 ± 0.3471.89 ± 0.4575.33 ± 0.2865.71 ± 0.6070.63 ± 0.85
LAE [12]73.84 ± 0.1477.29 ± 0.4571.70 ± 0.3976.71 ± 0.1066.98 ± 0.3573.72 ± 0.05
InfLoRA-b575.28 ± 0.0178.95 ± 0.0874.13 ± 0.1878.54 ± 0.1468.41 ± 0.2974.00 ± 0.50
InfLoRA77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
+ +we split ImageNet-R into 5, 10, and 20 tasks, with each task containing 40, 20, and 10 classes. We split CIFAR100 into 10 tasks, and each task constrains 10 classes. We split DomainNet into 5 tasks, and each task contains 69 classes. + +Following existing continual learning methods [12, 44], we evaluate the performance of the model through two popular metrics, including the final accuracy $ACC_{T}$ and the averaged accuracy $\overline{ACC}_{T} = \frac{1}{T}\sum_{i=1}^{T}ACC_{i}$ , where $T$ denotes the total number of tasks and $ACC_{i}$ is defined as + +$$ +A C C _ {i} = \frac {1}{i} \sum_ {j = 1} ^ {i} a _ {i, j}. \tag {10} +$$ + +Here, $a_{i,j}$ denotes the accuracy of the $j$ -th task once the model has learned the $i$ -th task. + +Baselines We compare our InfLoRA with state-of-the-art continual learning methods based on PEFT, including learn to prompt (L2P) [44], DualPrompt [43], continual decomposed attention-based prompt (CODA-P) [38], learning accumulation ensemble (LAE) [12], continual low-rank adaptation (C-LoRA) [37]. For LAE, we implement it with LoRA [16]. Following existing works [12, 38], we also include two methods without continual learning, joint and sequential, in the comparison. Here, joint denotes the method that learns all the tasks jointly, while sequential denotes the method that learns all the tasks sequentially without any operation to overcome the forgetting of the model. The accuracy of joint can be treated as the accuracy upper-bound and the accuracy of sequential can be treated as the accuracy lower-bound. + +Architecture and Training Details We follow existing works [12, 43] to perform experiments. Specifically, we use the ViT-B/16 backbone [10] supervised pre-trained on ImageNet 21K as the pre-trained model. + +For all the methods, we follow existing works [12, 38, 44] and use the Adam [22] optimizer with running averages of gradient and its square $(\beta_{1} = 0.9, \beta_{2} = 0.999)$ . Each task is trained for 50 epochs on ImageNet-R, 20 epochs on CIFAR100 and 5 epochs on DomainNet. The batch size + +is set to 128 for all the experiments. Since our InfLoRA shares a similar architecture to LoRA, we follow existing work [12] and insert the architecture of our InfLoRA in the key and value of the attention module. Furthermore, existing method DualPrompt [43] treats the inserted blocks as hyperparameters and searches for the best positions for their prompts. On the contrary, we insert the architecture of InfLoRA for all the Transformer blocks to avoid searching. We also implement a variant of our method, which inserts the bottom 5 Transformer blocks like existing methods DualPrompt and CODA-P. We call this variant InfLoRA-b5. As for the hyperparameter $r$ , we determine its value through a grid search on a validation dataset. + +# 4.2. Experimental Results + +Accuracy Table 1 shows the results of different methods on ImageNet-R with a different number of tasks. Table 2 shows the results of different methods on CIFAR100 and DomainNet. We can find that our methods InfLoRA and InfLoRA-b5 outperform existing continual learning methods. + +Figure 2 shows the variation of the accuracy of different continual learning methods on ImageNet-R and CIFAR100. We can find that our method outperforms existing methods not only at the end of the learning but also throughout the whole learning process. This indicates that our InfLoRA eliminates the interference of the new task on the old tasks and thus the accuracy of our method decreases slower compared to other methods. + +Analysis of Expanded Parameters Figure 3 shows the number of expanded parameters and the accuracy of different methods on ImageNet-R and CIFAR100. For L2P, DualPrompt and CODA-P, their expanded parameters are included in the added prompts and corresponding key. For LAE, its expanded parameters are the inserted LoRA modules and an additional copy. For C-LoRA, its expanded parameters are inserted LoRA modules. For our method, the expanded parameters are $B_{t}$ and $A_{t}$ . The details of computing the number of expanded parameters for different meth + +Table 2. Results (%) on CIFAR100 and DomainNet. We report results over 5 trials. + +
TasksCIFAR100DomainNet
Method\(ACC_{10} (↑)\)\(\overline{ACC}_{10} (↑)\)\(ACC_5 (↑)\)\(\overline{ACC}_5 (↑)\)
joint91.92 ± 0.05-77.72 ± 0.04-
sequential62.18 ± 3.5980.42 ± 0.2353.44 ± 1.2169.09 ± 0.33
L2P [44]82.48 ± 0.2087.64 ± 0.2570.16 ± 0.0575.60 ± 0.03
DualPrompt [43]84.42 ± 0.3090.06 ± 0.0772.14 ± 0.0577.71 ± 0.06
CODA-P [38]86.62 ± 0.1191.08 ± 0.2873.23 ± 0.1378.72 ± 0.07
C-LoRA [37]82.97 ± 0.4788.81 ± 0.3469.34 ± 0.1375.25 ± 0.11
LAE [12]84.15 ± 0.1089.84 ± 0.0366.85 ± 0.4075.01 ± 0.17
InfLoRA-b587.06 ± 0.2591.59 ± 0.1373.26 ± 0.5078.82 ± 0.34
InfLoRA86.51 ± 0.7391.70 ± 0.3274.53 ± 0.2379.57 ± 0.57
+ +![](images/671b6d499863a87a8ff6494ae93b5d94e0d338912e348d1c76595f991d50f7ad.jpg) +(a) ImageNet-R (5 Tasks) + +![](images/7da4d83f881abb800617eb6f7824c0b1200808ec34233e84bce522c4866c62c4.jpg) +(b) ImageNet-R (10 Tasks) + +![](images/6d8a59ab5471815ece96819868d0c44191a497c6e18f6a482dbc6a5794f66976.jpg) +(c) ImageNet-R (20 Tasks) + +![](images/7f7843b71b6836c5fd769b12cc136143e371a3b4474c77e4218b387ad91a3ee5.jpg) +(d) CIFAR100 + +ods are given in supplementary material. We can find that CODA-P and C-LoRA expand much more parameters than other methods. Furthermore, our methods InfLoRA and InfLoRA-b5 expand comparable parameters to L2P, DualPrompt and LAE but perform better than these methods. + +Ablation Study We perform experiment to verify the effectiveness of designing dimensionality reduction matrix $B_{t}$ by (8). Specifically, we explore three different variants for designing $B_{t}$ . The first variant designs $B_{t}$ randomly using Gaussian distribution. We call this variant 'Random $\rightarrow B_{t}$ '. The second variant discards the operation in (6) or (7) and directly sets $\hat{H}_{t} = H_{t}$ . Through this way, this variant ensures that each row of $B_{t}$ lies in $\mathcal{N}_{t}$ while ignoring $\mathcal{M}_{t}^{\perp}$ . We call this variant $\mathcal{N}_{t} \rightarrow B_{t}$ . The third variant does not compute the input matrix but initializes $H_{t}$ using a Gaussian distribution before applying the operation in (6) or (7). In this way, this variant ensures that each row of $B_{t}$ lies in $\mathcal{M}_{t}^{\perp}$ while ignoring $\mathcal{N}_{t}$ . We call this variant $\mathcal{M}_{t}^{\perp} \rightarrow B_{t}$ . Since our method focuses both $\mathcal{M}_{t}^{\perp}$ and $\mathcal{N}_{t}$ , we use $\mathcal{N}_{t} \cap \mathcal{M}_{t}^{\perp} \rightarrow B_{t}$ to represent our method. + +Table 3 shows the results of our method and its variants. We can find that all these variants fail to perform as well as our method. To further demonstrate the performance of different variants, we show the relative accuracy of different tasks after the model learns them all in Figure 4. Here, relative accuracy is the accuracy of different variants minus the accuracy of our InfLoRA. Note that the last task is the new task, and the other tasks are old tasks in Figure 4. As we can see, 'Random $\rightarrow$ $B_{t}$ ' and $\mathcal{N}_t\to B_t$ outper + +![](images/48972fa574349124ba18659a6057b7caa35fabdca79fea69a03edbe125c3db97.jpg) +Figure 2. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100. +(a) ImageNet-R (10 Tasks) +Figure 3. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100. + +![](images/d063d5500dfd2c4615eedacfd6068945ce61ff2be36bc115f2ce0881472fe13a.jpg) +(b) CIFAR100 + +form $\mathcal{M}_t^\perp \to B_t$ on the new task but shows much lower accuracy than $\mathcal{M}_t^\perp \to B_t$ and our InfLoRA on the old tasks. This means these two variants fail to eliminate the inference of the new task on the old tasks, making the model suffer from low stability. On the contrary, $\mathcal{M}_t^\perp \to B_t$ shows the lowest performance on the new task. This means $\mathcal{M}_t^\perp \to B_t$ ignores the plasticity of the model. Our method outperforms all the variants on most of the tasks. This shows that our method can eliminate the interference of the new task on the old tasks and make a better trade-off between stability and plasticity than these variants. + +Varying the Pre-Trained Model We also follow the existing method [40] and perform experiments using a ViT-B/16 pre-trained with two different self-supervised methods, including DINO [5] and iBOT [49]. All experimental settings, except for the choice of the pre-trained model, are kept consistent with the details outlined in Section 4.1. + +Table 3. Results of different variants on ImageNet-R with a different number of tasks. + +
Tasks51020
\(ACC_{5} (↑)\)\(\overline{ACC_{5}}\) (↑)\(ACC_{10} (↑)\)\(\overline{ACC_{10}}\) (↑)\(ACC_{20} (↑)\)\(\overline{ACC_{20}}\) (↑)
Random → \(B_{t}\)72.49 ± 0.3879.40 ± 0.2967.38 ± 0.4176.62 ± 0.0656.17 ± 0.2969.24 ± 0.35
\(\mathcal{N}_{t} \rightarrow \mathcal{B}_{t}\)67.01 ± 0.1176.09 ± 0.0457.91 ± 0.3070.23 ± 0.5940.73 ± 0.2959.68 ± 0.52
\(\mathcal{M}_{t}^{\perp} \rightarrow \mathcal{B}_{t}\)75.94 ± 0.5380.69 ± 0.2774.61 ± 0.6279.67 ± 0.2768.79 ± 0.4275.74 ± 0.26
\(\mathcal{N}_{t} \cap \mathcal{M}_{t}^{\perp} \rightarrow \mathcal{B}_{t} (\text{InfLoRA})\)77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
+ +![](images/8989e2019c8e99ca493416992f51649ac0c938d10b86436ec5d133ea721bd9d2.jpg) +(a) ImageNet-R (10 Tasks) +Figure 4. Relative accuracy of different tasks. Relative accuracy is the accuracy of different variants minus the accuracy of InfLoRA. + +![](images/b14e4873e8f092a497c93d7f713faf6a45cf1b18fe241f86245b10978ac1a405.jpg) +(b) ImageNet-R (20 Tasks) + +Table 4. Results (\%) of different methods on ImageNet-R (10 tasks) using various self-supervised pre-trained models. Here, DINO-1k and iBOT-1k indicate that the ViT is pre-trained on ImageNet-1k using these respective methods. + +
Method\(ACC_{10} \left(↑\right)\)\(ACC_{10} \left(↑\right)\)
DINO-1kL2P [44]56.71 ± 0.1263.59 ± 0.21
DualPrompt [43]60.23 ± 0.4266.57 ± 0.25
CODA-P [38]64.02 ± 0.6871.50 ± 0.42
C-LoRA [37]63.07 ± 0.3668.09 ± 0.41
LAE [12]61.03 ± 0.2769.89 ± 0.15
InfLoRA-b566.16 ± 0.1473.01 ± 0.17
InfLoRA68.31 ± 0.2876.15 ± 0.05
iBOT-1kL2P [44]60.80 ± 0.3566.58 ± 0.28
DualPrompt [43]63.78 ± 0.3868.88 ± 0.16
CODA-P [38]68.02 ± 0.4874.28 ± 0.47
C-LoRA [37]68.60 ± 0.0773.47 ± 0.28
LAE [12]64.14 ± 0.2972.59 ± 0.22
InfLoRA-b569.72 ± 0.4476.11 ± 0.13
InfLoRA71.84 ± 0.0978.29 ± 0.09
+ +Table 4 shows the results of different methods on ImageNet-R when using various pre-trained models. Comparing these results to those in Table 1, we can find that the performance of all methods utilizing self-supervised pretrained models is lower than the performance of the corresponding methods using supervised pre-trained models. However, our methods still outperform all other methods. + +Combining with Classifier Alignment Slow learner with classifier alignment (SLCA) [47] utilizes feature statistics to align classifiers, demonstrating superior performance compared to methods without aligned classifiers. Our InfLoRA can be combined with classifier alignment (CA) to get better performance. Specifically, after learning the $t$ -th task + +Table 5. Results $(\%)$ of different methods on ImageNet-R (10 tasks) and CIFAR100 using classifier alignment (CA) technique. + +
MethodACC10(↑)ACC10(↑)
CIFAR100SLCA [47]91.06 ± 0.2493.65 ± 0.19
InfLoRA+CA91.59 ± 0.0894.39 ± 0.05
ImageNet-RSLCA [47]77.34 ± 0.2581.35 ± 0.16
InfLoRA+CA79.78 ± 0.2583.38 ± 0.19
+ +with parameters $\mathbf{A}_t$ and $\mathbf{B}_t$ and loss (9), we collect features $\mathbf{F}_t = \{\mathbf{r}_{i,t}\}_{i=1}^{n_t}$ of the $t$ -th task. Here, $\mathbf{r}_{i,t} = f(\mathbf{x}_{i,t})$ denotes the features extracted by backbone $f_{\Theta}(\cdot)$ . Then, mean and covariance of features for each class are computed and saved. After that, for each class $c$ the model has seen during continual learning, $S$ samples are sampled from Gaussian distribution $\mathcal{N}(\boldsymbol{\mu}_c, \boldsymbol{\Sigma}_c)$ . Here, $\boldsymbol{\mu}_c$ and covariance $\boldsymbol{\Sigma}_c$ denote the mean and covariance of the class $c$ . Finally, we align the classifier using standard cross-entropy and these samples. The details of this experiment are given in supplementary material. + +Table 5 shows that our method InfLoRA+CA outperforms SLCA. Note that SLCA tunes all the parameters of the model while our method InfLoRA only tunes the parameters in $\mathbf{A}_t$ . Therefore, our InfLoRA+CA is much more efficient than SLCA. + +# 5. Conclusion + +In this work, we propose a new method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets. + +# Acknowledgment + +This work is supported by NSFC (No.62192783), National Key R&D Program of China (No.2020YFA0713901), and Fundamental Research Funds for the Central Universities (No.020214380108). + +# References + +[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In Proceedings of the European Conference on Computer Vision, pages 139-154, 2018. 2 +[2] Rahaf Aljundi, Eugene Belilovsky, Tinne Tuytelaars, Laurent Charlin, Massimo Caccia, Min Lin, and Lucas Page-Caccia. Online continual learning with maximal interfered retrieval. In Advances in Neural Information Processing Systems, pages 11849-11860, 2019. 2 +[3] Rahaf Aljundi, Min Lin, Baptiste Goujaud, and Yoshua Bengio. Gradient based sample selection for online continual learning. 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In continual learning, the model should possess the ability to maintain its performance on old tasks (stability) and the ability to adapt to new tasks continuously (plasticity). Recently, parameter-efficient fine-tuning (PEFT), which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning. Although existing continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT, most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. 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Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "content": "Continual learning requires the model to learn multiple tasks sequentially [33]. To achieve continual learning, the model should possess two essential abilities, including the ability to keep its performance on the old tasks (stability) and the ability to adapt to the new tasks continuously (plasticity) [33]. Furthermore, two different scenar" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 228, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 545, + 312 + ], + "type": "text", + "content": "ios are often considered in continual learning, including task-incremental scenario [32] and class-incremental scenario [41]. Task-incremental scenario allows the model to get task identities during inference. On the contrary, class-incremental scenario does not allow the model to get task identities during inference, making the model learn to distinguish all the classes across all the tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 314, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 314, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 314, + 546, + 469 + ], + "type": "text", + "content": "Recently, parameter-efficient fine-tuning (PEFT) [15, 16, 18], which involves freezing a pre-trained model and injecting a small number of learnable parameters to adapt to downstream tasks, has gained increasing popularity in continual learning [12, 38, 44], especially in the class-incremental scenario. More specifically, existing continual learning methods based on PEFT [21, 43] inject the learnable parameters into a pre-trained model using some popular PEFT methods such as prompt-tuning [25] or low-rank adaptation (LoRA) [16]. Subsequently, these methods freeze the pre-trained weights and sequentially fine-tune the injected parameters on multiple tasks throughout the continual learning process." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 472, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 663 + ], + "type": "text", + "content": "Although continual learning methods based on PEFT have demonstrated superior performance compared to those not based on PEFT [44], most of them do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity. 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As a result, it is hard for the model to make a good trade-off between stability and plasticity." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 712 + ], + "type": "text", + "content": "In this work, we propose a new PEFT method, called interference-free low-rank adaptation (InfLoRA), for continual learning. The contributions of this work are listed as follows:" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 189, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 189, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 189, + 713 + ], + "type": "text", + "content": "*Wu-Jun Li is the corresponding author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23638" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 192 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": "- InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that finetuning these injected parameters is equivalent to finetuning the pre-trained weights within a subspace." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 121, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 286, + 156 + ], + "type": "text", + "content": "- InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 286, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 192 + ], + "type": "text", + "content": "- Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 205, + 227, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 205, + 227, + 217 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 227, + 217 + ], + "type": "text", + "content": "2. Related Work and Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 226, + 135, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 135, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 135, + 237 + ], + "type": "text", + "content": "2.1. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 245, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 245, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 287, + 533 + ], + "type": "text", + "content": "Parameter-Efficient Fine-Tuning Parameter-efficient fine-tuning (PEFT) methods freeze a pre-trained model and inject a small number of learnable parameters to adapt to downstream tasks. In this way, PEFT methods reduce the inefficiency of full fine-tuning methods which fine-tune all the parameters of a pre-trained model to learn downstream tasks. For example, Adapter [15] adds small modules in different layers of Transformers and only tunes these added modules to adapt to downstream tasks. Prompt-tuning [25] and Prefix-tuning [27] insert a set of learnable tokens into the input of the Transformer layers and only tune these tokens to adapt to downstream tasks. Low-rank adaptation (LoRA) [16] reparameterizes the pre-trained weights with low-rank branches and only tunes these branches to adapt to the downstream tasks. Although these methods tune much fewer learnable parameters than full fine-tuning, they always show comparable or even superior performance compared with full fine-tuning [11, 16, 31, 45]. Early PEFT methods focus on natural language processing (NLP). Recently, PEFT methods have also been proposed for computer vision (CV). For example, visual prompt tuning (VPT) [18] and AdapterFormer [6] apply prompt-tuning and Adapter techniques to CV tasks, respectively. Both of them exhibit comparable performance to full fine-tuning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 533, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 286, + 664 + ], + "type": "text", + "content": "Continual Learning Early continual learning was usually considered in the context of learning from scratch. Three types of continual learning methods are proposed, including regularization-based methods [1, 20, 23, 46], memory-based methods [2, 3, 7, 28, 39], and expansion-based methods [17, 26, 35]. Regularization-based methods employ a penalty loss (regularization) to prevent important parameters of old tasks from changing too much. Memory-based methods maintain a memory buffer to store information about old tasks. Expansion-based methods dynamically expand the model's architecture for each new task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Recently, with the advancements of pre-trained models [9, 10, 13], using pre-trained models for continual learning has gained increasing popularity. Some continual learning methods fully fine-tune the pre-trained models [4, 48]," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "which has been shown to be inefficient. Other methods explore PEFT methods in continual learning. For instance, some existing continual learning methods [21, 38, 43, 44] introduce prompt-tuning in continual learning, achieving much higher performance than previous methods that learn from scratch, especially in the class-incremental scenario. The method in [12] introduces a framework in continual learning that can be combined with many existing PEFT methods, such as prompt-tuning, LoRA and Adapter. However, all these methods do not consider how to eliminate the interference of the new task on the old tasks, which inhibits the model from making a good trade-off between stability and plasticity." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 237, + 391, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 391, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 391, + 249 + ], + "type": "text", + "content": "2.2. Preliminaries" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 256, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 293 + ], + "type": "text", + "content": "We first introduce low-rank adaptation (LoRA) [16], a popular PEFT method related to our method. Then, we give the problem definition for continual learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": "Low-Rank Adaptation LoRA [16] is one of the most popular PEFT methods. It assumes that the changes of parameters lie in a low-rank space when the model is fully fine-tuned on a downstream task. Specifically, for a linear layer with the input dimension " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "d_{I}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " and the output dimension " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "d_{O}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": ", we represent its weight with " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "W^{d_O\\times d_I}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": ". Then, LoRA reparametrizes the pre-trained weight " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " by expanding a branch with two matrices, " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "A\\in \\mathbb{R}^{d_O\\times r}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "B\\in \\mathbb{R}^{r\\times d_I}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": ". Typically, " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " is much smaller than the input dimension " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "d_{I}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " and output dimension " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "d_{O}" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": ", making " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " a dimensionality increasing matrix and " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " a dimensionality reduction matrix. Finally, LoRA modifies the forward propagation in this linear layer as " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "e = Wh + ABh" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " denote the input and output of this layer, respectively. LoRA initializes " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " as 0 and initializes " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " using Gaussian distribution. During the learning of the downstream tasks, LoRA freezes the pre-trained weight " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " and only fine-tunes the parameters " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 293, + 545, + 508 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "content": "Problem Definition In continual learning, there is a sequence of tasks with different distributions. We define the task sequence as " + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathcal{D}_1,\\dots,\\mathcal{D}_T\\}" + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "content": ", where the " + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "content": "-th task " + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t = \\{(x_{i,t},y_{i,t})\\}_{i = 1}^{n_t}" + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "inline_equation", + "content": "x_{i,t}" + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "content": " denotes an input sample and " + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "inline_equation", + "content": "y_{i,t}" + }, + { + "bbox": [ + 304, + 510, + 545, + 593 + ], + "type": "text", + "content": " denotes its label. The objective of continual learning is to train a model sequentially on these tasks and ensure that the model performs well on all of them." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We follow existing continual learning methods [43, 44] based on PEFT and assume the model is a pre-trained Vision Transformer (ViT) [10]. Specifically, assume the model is " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "h_{\\Phi}(f_{\\Theta}(\\cdot))" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "h_{\\Phi}(\\cdot)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " is the classifier with parameters " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\Theta}(\\cdot)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " is the pre-trained ViT backbone with pre-trained parameters " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". Similar to existing work [43], our focus is primarily on the class-incremental scenario, where task identities are unknown during inference. Furthermore, we concentrate on the exemplar-free setting [43, 50], where no historical data can be fetched for rehearsal." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23639" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 262, + 236 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 262, + 236 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 262, + 236 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 262, + 236 + ], + "type": "image", + "image_path": "f80b43ac204c7bffd4f5085e0499ca8c8fad11396ecd907691a5d2bbfdf62394.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 123, + 239, + 179, + 249 + ], + "lines": [ + { + "bbox": [ + 123, + 239, + 179, + 249 + ], + "spans": [ + { + "bbox": [ + 123, + 239, + 179, + 249 + ], + "type": "text", + "content": "(a) Architecture" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 265, + 71, + 536, + 233 + ], + "blocks": [ + { + "bbox": [ + 265, + 71, + 536, + 233 + ], + "lines": [ + { + "bbox": [ + 265, + 71, + 536, + 233 + ], + "spans": [ + { + "bbox": [ + 265, + 71, + 536, + 233 + ], + "type": "image", + "image_path": "e66e2ea897b11b01e524b09785e3c48dd147fcd2a0130a1ec8654247e357d348.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 239, + 485, + 250 + ], + "lines": [ + { + "bbox": [ + 310, + 239, + 485, + 250 + ], + "spans": [ + { + "bbox": [ + 310, + 239, + 485, + 250 + ], + "type": "text", + "content": "(b) Designing Dimensionality Reduction Matrix " + }, + { + "bbox": [ + 310, + 239, + 485, + 250 + ], + "type": "inline_equation", + "content": "B_{t}" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "text", + "content": "Figure 1. (a) The architecture of our InfLoRA in a certain linear layer of a Transformer. During the learning of the " + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "text", + "content": "-th task, the pre-trained weight and all the old branches are frozen, and only " + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "text", + "content": " is fine-tuned. (b) The pipeline of designing dimensionality reduction matrix " + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t" + }, + { + "bbox": [ + 46, + 255, + 546, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 282, + 129, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 282, + 129, + 296 + ], + "spans": [ + { + "bbox": [ + 47, + 282, + 129, + 296 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "text", + "content": "Figure 1 (a) illustrates the architecture of our InfLoRA within a linear layer. Before learning the " + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "text", + "content": "-th new task, our InfLoRA expands a LoRA-like branch, which includes a dimensionality reduction matrix " + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\pmb{B}_t \\in \\mathbb{R}^{r \\times d_I}" + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "text", + "content": " and a dimensionality increasing matrix " + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\pmb{A}_t \\in \\mathbb{R}^{d_O \\times r}" + }, + { + "bbox": [ + 46, + 302, + 287, + 374 + ], + "type": "text", + "content": ". Then, the forward propagation of this linear layer is modified as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 382, + 287, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 382, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 54, + 382, + 287, + 427 + ], + "type": "interline_equation", + "content": "e = W h + \\sum_ {j = 1} ^ {t} A _ {j} B _ {j} h = W _ {t - 1} h + A _ {t} B _ {t} h = W _ {t} h. \\tag {1}", + "image_path": "b35cfa6a8abebd98b3376cae0dee05b9819f99133a66384d5b0505d6577397e4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "W_{t} = W_{t - 1} + A_{t}B_{t} = W + \\sum_{i = 1}^{t}A_{i}B_{i}" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": ". Similar to LoRA, our InfLoRA also initializes dimensionality increasing matrix " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "A_{t}" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": " as 0. However, different from LoRA, which employs Gaussian distribution to initialize the dimensionality reduction matrix " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": ", our InfLoRA designs the dimensionality reduction matrix " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": " before learning the " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": "-th task. During the learning of the " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": "-th task, InfLoRA fine-tunes " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "A_{t}" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": " to learn the new task while keeping the pre-trained weight " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": ", all the old branches and the matrix " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": " frozen. After learning the " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": "-th tasks, for any given test sample belonging to the learned tasks, the model uses " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "W_{t}" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": " and (1) to infer its label. This design ensures that our method is compatible with the class-incremental scenario where task identities are unknown during inference." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "In the following subsections, we first build the relationship between our InfLoRA and the method that fine-tunes the pre-trained weight. Specifically, we show that finetuning parameters " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " is equivalent to fine-tuning the pretrained weights " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " within a subspace spanned by the rows of " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " is designed before learning the " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "-th task, making this subspace pre-designed. Then, building upon this relationship, we introduce how our InfLoRA designs this subspace to eliminate the interference of the new" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 284, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 284, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 545, + 308 + ], + "type": "text", + "content": "task on the old tasks and make a good trade-off between stability and plasticity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 318, + 545, + 343 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 318, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 305, + 318, + 545, + 343 + ], + "type": "text", + "content": "3.1. Relationship between InfLoRA and Fine-Tuning the Pre-Trained Weight" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 350, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 398 + ], + "type": "text", + "content": "When the " + }, + { + "bbox": [ + 305, + 350, + 545, + 398 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 350, + 545, + 398 + ], + "type": "text", + "content": "-th task arrives and our method has expanded a new branch, the forward propagation in this layer can be represented by (1). At this time, we can prove the following proposition:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": "Proposition 1. When learning the " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": "-th task with forward propagation represented by (1), fine-tuning " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": " is equivalent to fine-tuning the pre-trained weight " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": " within the subspace " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\operatorname{span}\\{\\pmb{b}_1^t, \\dots, \\pmb{b}_r^t\\}" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\pmb{b}_i^t" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "1 \\leq i \\leq r" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": ") denotes the " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": "-th row vector of " + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\pmb{B}_t" + }, + { + "bbox": [ + 305, + 409, + 545, + 469 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "text", + "content": "Proof. When tuning the pre-trained weight " + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "text", + "content": " to learn the " + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "text", + "content": "-th task, we can compute the gradient of " + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 305, + 480, + 545, + 515 + ], + "type": "text", + "content": " based on the chain rule:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 367, + 524, + 545, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 524, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 367, + 524, + 545, + 548 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {W}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {e}} \\frac {\\partial \\boldsymbol {e}}{\\partial \\boldsymbol {W}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {e}} \\boldsymbol {h} ^ {T}. \\tag {2}", + "image_path": "fc96128de74c298ea4952ed9afe9f139a287456f1219b669f5333b852c75e76c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "content": " denotes the loss function. At this time, the change of " + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\pmb{W}" + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "content": " can be denoted as " + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\Delta W = -\\alpha \\frac{\\partial\\mathcal{L}}{\\partial W}" + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "content": " is the learning rate. Then, we can compute the change of the composed matrix " + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\pmb{W}_t = \\pmb {W} + \\sum_{j = 1}^t\\pmb {A}_j\\pmb {B}_j" + }, + { + "bbox": [ + 305, + 558, + 545, + 608 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 619, + 545, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 619, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 306, + 619, + 545, + 679 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Delta_ {\\boldsymbol {W}} \\boldsymbol {W} _ {t} = [ \\boldsymbol {W} + \\Delta \\boldsymbol {W} + \\sum_ {j = 1} ^ {t} \\boldsymbol {A} _ {j} \\boldsymbol {B} _ {j} ] - (\\boldsymbol {W} + \\sum_ {j = 1} ^ {t} \\boldsymbol {A} _ {j} \\boldsymbol {B} _ {j}) \\\\ = \\Delta \\boldsymbol {W} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {W} _ {t}} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\tag {3} \\\\ \\end{array}", + "image_path": "75e702428630ca55c7de07399395f782ea55de8d3aaf1663d066c63029c6a013.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Here, we use " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathbf{W}}\\mathbf{W}_t" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " to denote the change of the composed matrix " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " causing by the change of " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23640" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "Similarly, when tuning the expanded weight " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ", we can get the gradient of " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " based on the chain rule:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 101, + 102, + 287, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 102, + 287, + 128 + ], + "spans": [ + { + "bbox": [ + 101, + 102, + 287, + 128 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {A} _ {t}} = \\frac {\\partial \\mathcal {L}}{\\partial e} \\frac {\\partial \\boldsymbol {e}}{\\partial \\boldsymbol {A} _ {t}} = \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\boldsymbol {B} _ {t} ^ {T}. \\tag {4}", + "image_path": "58356d32c7426d1038a4e91c2cf173354b13d2722db6bbbd77f763e37e81310b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "spans": [ + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "text", + "content": "At this time, the change of " + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "text", + "content": " can be denoted as " + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{A}_t = -\\alpha \\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{A}_t}" + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "text", + "content": ". Then, we can compute the change of the composed matrix " + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t = \\mathbf{W}_{t-1} + \\mathbf{A}_t \\mathbf{B}_t" + }, + { + "bbox": [ + 47, + 134, + 287, + 170 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 177, + 287, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 177, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 48, + 177, + 287, + 233 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Delta_ {\\boldsymbol {A} _ {t}} \\boldsymbol {W} _ {t} = \\left[ \\boldsymbol {W} _ {t - 1} + \\left(\\boldsymbol {A} _ {t} + \\Delta \\boldsymbol {A} _ {t}\\right) \\boldsymbol {B} _ {t} \\right] - \\left(\\boldsymbol {W} _ {t - 1} + \\boldsymbol {A} _ {t} \\boldsymbol {B} _ {t}\\right) \\\\ = \\Delta \\boldsymbol {A} _ {t} \\boldsymbol {B} _ {t} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {A} _ {t}} \\boldsymbol {B} _ {t} = - \\alpha \\frac {\\partial \\mathcal {L}}{\\partial e} \\boldsymbol {h} ^ {T} \\boldsymbol {B} _ {t} ^ {T} \\boldsymbol {B} _ {t} \\\\ = \\Delta_ {W} W _ {t} B _ {t} ^ {T} B _ {t} \\tag {5} \\\\ \\end{array}", + "image_path": "9980ad86e14c9f012158bba20c0f37662fcc00d36320b0da5efe348fdcf9bd7e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": "Here, we use " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathbf{A}_t}\\mathbf{W}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": " to denote the change of the composed matrix " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": " causing by the change of " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": ". The fourth equation in (5) holds because of (4). The fifth equation in (5) holds because of (2). (5) shows that " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathbf{A}_t}\\mathbf{W}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": " is equal to " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathbf{W}}\\mathbf{W}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": " multiplying a projection matrix " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t^T\\mathbf{B}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t^T\\mathbf{B}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": " projects each row vector of " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathbf{W}}\\mathbf{W}_t" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": " into the subspace span " + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}" + }, + { + "bbox": [ + 47, + 240, + 287, + 326 + ], + "type": "text", + "content": ", Proposition 1 holds." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": "Proposition 1 has demonstrated that using our InfLoRA to train the model is equivalent to directly finetuning the pre-trained weight " + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": " within the subspace " + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\operatorname{span}\\{b_1^t, \\dots, b_r^t\\}" + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": ". Therefore, before learning the " + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": "-th task, we can design matrix " + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "inline_equation", + "content": "B_t" + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": " such that learning the " + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": "-th task in the subspace " + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\operatorname{span}\\{b_1^t, \\dots, b_r^t\\}" + }, + { + "bbox": [ + 47, + 332, + 287, + 416 + ], + "type": "text", + "content": " will not interfere with the performance of the model on the old tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 423, + 287, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 287, + 447 + ], + "type": "text", + "content": "3.2. Eliminating the Interference of the New Task on the Old Tasks" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "text", + "content": "We first introduce the desired characteristics that InfLoRA aims to let the subspace " + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathrm{span}\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}" + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "text", + "content": " have. With these characteristics, InfLoRA can eliminate the interference of the new task on the old tasks and make a good trade-off between stability and plasticity. Then, we introduce how to design dimensionality reduction matrix " + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "text", + "content": " so that subspace " + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathrm{span}\\{\\pmb {b}_1^t,\\dots,\\pmb {b}_r^t\\}" + }, + { + "bbox": [ + 47, + 453, + 287, + 538 + ], + "type": "text", + "content": " has these characteristics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 180, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 180, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 180, + 562 + ], + "type": "text", + "content": "3.2.1 Desired Characteristics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": "First, InfLoRA aims to make the subspace " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " orthogonal to the gradients of all the old tasks. In this way, according to Proposition 1, the update of InfLoRA, which can be represented as " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Delta_{A_t}W_t" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " will also be orthogonal to the gradient of the old tasks. Note that the idea of making the update for the new task orthogonal to the gradient of the old tasks to eliminate the interference of the new task on the old tasks has been proposed in many existing continual learning methods [30, 36]. However, all these existing methods are designed for continual learning from scratch, involving updating all parameters of the model, which is incompatible with the setting in PEFT. On the contrary, our" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "method is a PEFT method, which only tunes the parameters in " + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "inline_equation", + "content": "A_{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "text", + "content": "Besides eliminating the interference of new tasks on old tasks, our InfLoRA further makes the subspace " + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}" + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "text", + "content": " lie in a subspace that the gradient of the new task lies in to make a good trade-off between stability and plasticity. Specifically, existing work [19] has shown that during fine-tuning, the weight increments of pre-trained ViT exhibit redundancy in terms of weight rank. Therefore, the gradients of the new task lie in a low-dimensional subspace. Our method makes " + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\mathrm{span}\\{b_1^t,\\dots,b_r^t\\}" + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "text", + "content": " not only orthogonal to the gradient of the old tasks but also lie in the subspace in which the gradients of the new task " + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 97, + 545, + 288 + ], + "type": "text", + "content": " lie. By doing so, our method makes the model's focus on the new task when eliminating the interference of the new task on the old tasks, thereby making a good trade-off between stability and plasticity. Section 4.2 verifies the effectiveness of these two characteristics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 308, + 526, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 526, + 320 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 526, + 320 + ], + "type": "text", + "content": "3.2.2 Designing Dimensionality Reduction Matrix" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": "InfLoRA first approximates the gradient space of the new task and old tasks. Here, we use " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": " to represent the gradient space of the new task approximated by InfLoRA. Similarly, we use " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": " to represent the gradient space of previous " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": " old tasks approximated by InfLoRA. We also use " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": " to denote the residual gradient space, which is orthogonal to the space " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": ". Then, in order to meet the characteristics described in Section 3.2.1, InfLoRA ensures that each row of " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\boldsymbol{B}_t" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": " lies in " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": ". In other words, InfLoRA makes " + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathrm{span}\\{\\boldsymbol{b}_1^t,\\dots,\\boldsymbol{b}_r^t\\} \\subseteq \\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 304, + 328, + 545, + 449 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": "Existing works [29, 36] have shown that the gradient update of the linear layer lies in the span of the inputs. Please refer to supplementary material for a detailed explanation of this proposition. Therefore, InfLoRA uses the input matrix of the new task " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": " to approximate the gradient space of the new task. Specifically, InfLoRA computes the input matrix " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "H_{t} = [h_{1}^{t},\\dots,h_{n}^{t}]" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": ", with each column of " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "H_{t}" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": " representing an input vector of the " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": "-th task. Then, InfLoRA considers " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": " as the subspace spanned by the columns of matrix " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "H_{t}" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "However, InfLoRA cannot use the input matrix of the old tasks to approximate the gradient space of the old tasks since the data from the old tasks is not available when the model learns the new tasks. Instead, existing methods such as gradient projection memory (GPM) [36] and dual gradient projection memory (DualGPM) [29] can learn a matrix to preserve information about the gradients of the old tasks. InfLoRA incorporates DualGPM to preserve gradient information. With the assistance of DualGPM, the model can learn either a matrix " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_t \\in \\mathbb{R}^{d_I \\times k_t}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " or a matrix " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_t^\\perp \\in \\mathbb{R}^{d_I \\times (d_I - k_t)}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ". Here, the columns of " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_t" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " contribute to the orthonormal bases of " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_t" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " and the columns of " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_t^\\perp" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " contribute to the orthonormal bases of " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_t^\\perp" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "k_t" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " denotes the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23641" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "dimension of " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": ". For detailed information of how Dual-GPM maintains orthonormal bases " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "M_t" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "M_t^\\perp" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": ", please refer to supplementary material or the original paper [29]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": "After approximating the gradient space of the new task and old tasks, InfLoRA gets the component of " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": " which lies in " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": ". Specifically, when the model maintains " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": ", InfLoRA performs the operation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 161, + 287, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 161, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 115, + 161, + 287, + 175 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {H}} _ {t} = \\boldsymbol {H} _ {t} - \\boldsymbol {M} _ {t} \\boldsymbol {M} _ {t} ^ {T} \\boldsymbol {H} _ {t}. \\tag {6}", + "image_path": "94b42125854adbd82979cbde9b862b838ae07ea826767719717824a4dae656c4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 181, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 205 + ], + "type": "text", + "content": "Similarly, when the model maintains " + }, + { + "bbox": [ + 46, + 181, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 46, + 181, + 287, + 205 + ], + "type": "text", + "content": ", InfLoRA performs the operation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 118, + 209, + 287, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 209, + 287, + 225 + ], + "spans": [ + { + "bbox": [ + 118, + 209, + 287, + 225 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {H}} _ {t} = \\boldsymbol {M} _ {t} ^ {\\perp} \\left(\\boldsymbol {M} _ {t} ^ {\\perp}\\right) ^ {T} \\boldsymbol {H} _ {t}. \\tag {7}", + "image_path": "4b00cce23e927fc60f89dcb4e96ed24ae47ccbe279e524f820085da0fc43274d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": "Note that when " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " is a null space and " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\hat{H}_t = H_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ". Obviously, each column of " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\hat{H}_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " lies in " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ". However, since " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "(\\hat{H}_t)^T \\in \\mathbb{R}^{n \\times d_I}" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "B_t \\in \\mathbb{R}^{r \\times d_I}" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " have different shapes, InfLoRA can not directly define " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "B_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "(\\hat{H}_t)^T" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "n \\gg r" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ", InfLoRA uses the principal components of " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "(\\hat{H}_t)^T" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " to set " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "B_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ". Specifically, singular value decomposition (SVD) is performed on " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "(\\hat{H}_t)^T = V_t \\Sigma_t U_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": ". Then, InfLoRA designs " + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "inline_equation", + "content": "B_t" + }, + { + "bbox": [ + 46, + 232, + 287, + 330 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 140, + 335, + 287, + 349 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 335, + 287, + 349 + ], + "spans": [ + { + "bbox": [ + 140, + 335, + 287, + 349 + ], + "type": "interline_equation", + "content": "\\boldsymbol {B} _ {t} = \\left(\\boldsymbol {U} _ {t}\\right) _ {r}. \\tag {8}", + "image_path": "d987c4e4f7e73d7d1fb75ffbab809056bb337901bfb49bc48216ad9a85535a7b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "inline_equation", + "content": "(\\boldsymbol{U}_t)_r" + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "text", + "content": " denotes the rows of " + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\boldsymbol{U}_t" + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "text", + "content": " corresponding to the top-" + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "text", + "content": " singular values. Figure 1 (b) illustrates the pipeline of designing matrix " + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\boldsymbol{B}_t" + }, + { + "bbox": [ + 46, + 354, + 287, + 389 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "content": "Note that DualGPM expands subspace " + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "content": " and reduces subspace " + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "content": " when the number of tasks increases. Since InfLoRA constrains the update of the model within the subspace " + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t \\cap \\mathcal{M}_t^\\perp \\subseteq \\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "content": ", the space for learning the new task reduces when the number of tasks increases. However, by adjusting the approximation error of the gradient for the old tasks, DualGPM can expand " + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "content": " slowly and reduce " + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp" + }, + { + "bbox": [ + 46, + 390, + 287, + 521 + ], + "type": "text", + "content": " slowly. Therefore, the constraints imposed by InfLoRA do not excessively affect the model's learning of new tasks. Please refer to supplementary material for a detailed explanation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 527, + 195, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 195, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 195, + 540 + ], + "type": "text", + "content": "3.3. Whole Process of InfLoRA" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "text", + "content": "Algorithm 1 outlines the whole process of InfLoRA in continual learning. When the " + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "text", + "content": "-th new task arrives, InfLoRA first designs " + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "text", + "content": " through (8) and expands a new branch. Then, InfLoRA learns the " + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 546, + 287, + 676 + ], + "type": "text", + "content": "-th task by fine-tuning the newly expanded branch. Please note that, based on empirical findings from existing methods [12, 38], we employ the local cross-entropy (CE) loss as the learning objective, as it usually performs better than the global CE loss in continual learning methods based on PEFT. The local CE is the CE loss constrained to the classes of the current new task, which can be denoted as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 56, + 680, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 680, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 56, + 680, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathcal {D} _ {t}\\right) = \\frac {1}{\\left| \\mathcal {D} _ {t} \\right|} \\sum_ {\\left(\\boldsymbol {x}, y\\right) \\in \\mathcal {D} _ {t}} \\mathcal {L} _ {c e} \\left(\\operatorname {m a s k} \\left(h _ {\\boldsymbol {\\Phi}} \\left(f _ {\\boldsymbol {\\Theta}} (\\boldsymbol {x})\\right)\\right), y\\right). \\tag {9}", + "image_path": "fec154f516e4a2178bc8c767a97d1e99803f645bc7069cebca5c5088504662d6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 72, + 495, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 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"\\mathcal{D}_t" + }, + { + "bbox": [ + 312, + 156, + 436, + 165 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 312, + 167, + 545, + 187 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 167, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 312, + 167, + 545, + 187 + ], + "type": "text", + "content": "7: Compute the loss " + }, + { + "bbox": [ + 312, + 167, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\Theta}(\\mathcal{B}_t))" + }, + { + "bbox": [ + 312, + 167, + 545, + 187 + ], + "type": "text", + "content": " through (9) and update the parameters;" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 189, + 363, + 198 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 189, + 363, + 198 + ], + "spans": [ + { + "bbox": [ + 312, + 189, + 363, + 198 + ], + "type": "text", + "content": "8: end for" + } + ] + } + ], + "index": 20 + }, + { + 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After learning the " + }, + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "type": "text", + "content": "-th new task, InfLoRA follows the DualGPM to preserve the information about the gradient of the " + }, + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "type": "text", + "content": "-th task." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "Note that the branch corresponding to the " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "-th task will be frozen once the model has learned the " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "-th task. Since the expanded branches are linear transformations, we can integrate the old branches into the pre-trained weight to reduce the expanded parameters. Specifically, after learning the first task, InfLoRA integrates the first branch into the pre-trained weight and obtains the weight " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "W_{1} = W + A_{1}B_{1}" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": ". Before learning the " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "-th new task (" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "t > 1" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "), InfLoRA maintains the weight " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "W_{t-1}" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": ". After learning the " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "-th task, InfLoRA integrates the " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": "-th branch into " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "W_{t-1}" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": " and obtains " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "W_{t} = W_{t-1} + A_{t}B_{t}" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": ". In this way, the parameters in " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "A_{t}" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": " do not need to be maintained in the learning of subsequent tasks. Therefore, during the whole learning process, the number of parameters expanded by InfLoRA equals the number of parameters in a single branch. Since a single branch contains " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "(d_{I} + d_{O})r" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": " parameters, the number of parameters expanded by InfLoRA is " + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "inline_equation", + "content": "(d_{I} + d_{O})r" + }, + { + "bbox": [ + 304, + 315, + 546, + 519 + ], + "type": "text", + "content": " all the time." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 531, + 388, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 531, + 388, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 531, + 388, + 544 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 551, + 432, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 432, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 432, + 563 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Datasets and Evaluation Metric Similar to existing continual learning methods [12, 44] based on PEFT, we use ImageNet-R [14], CIFAR100 [24], and DomainNet [34] to train and evaluate the models. Imagenet-R is generated through artistic processing of 200 classes from ImageNet [8]. This dataset is introduced to continual learning by existing work [43] and has become a standard benchmark for continual learning methods based on PEFT. CIFAR100 is a dataset commonly used in existing continual learning works. DomainNet contains 345 classes and is introduced by some existing works [38, 42] for continual learning. Following existing continual learning work [38]," + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23642" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 90, + 536, + 229 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 536, + 82 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 536, + 82 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 536, + 82 + ], + "type": "text", + "content": "Table 1. Results (%) on ImageNet-R. Results are included for 5 tasks, 10 tasks, and 20 tasks. We report results averaged over 5 trials." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 90, + 536, + 229 + ], + "lines": [ + { + "bbox": [ + 59, + 90, + 536, + 229 + ], + "spans": [ + { + "bbox": [ + 59, + 90, + 536, + 229 + ], + "type": "table", + "html": "
Tasks51020
Method\\(ACC_5 (↑)\\)\\(\\overline{ACC_5} (↑)\\)\\(ACC_{10} (↑)\\)\\(\\overline{ACC_{10}} (↑)\\)\\(ACC_{20} (↑)\\)\\(\\overline{ACC_{20}} (↑)\\)
joint81.14 ± 0.34-81.14 ± 0.34-81.14 ± 0.34-
sequential58.74 ± 1.2872.91 ± 0.2846.07 ± 1.1562.91 ± 0.6834.62 ± 0.8551.15 ± 1.50
L2P [44]64.13 ± 0.7868.66 ± 0.4162.54 ± 0.2467.98 ± 0.2757.92 ± 0.2864.57 ± 0.29
DualPrompt [43]67.88 ± 0.1771.16 ± 0.3165.41 ± 0.5269.39 ± 0.4361.00 ± 0.7265.80 ± 0.67
CODA-P [38]73.09 ± 0.2176.91 ± 0.2171.47 ± 0.3575.82 ± 0.2967.28 ± 0.3072.34 ± 0.17
C-LoRA [37]75.85 ± 0.3178.85 ± 0.3471.89 ± 0.4575.33 ± 0.2865.71 ± 0.6070.63 ± 0.85
LAE [12]73.84 ± 0.1477.29 ± 0.4571.70 ± 0.3976.71 ± 0.1066.98 ± 0.3573.72 ± 0.05
InfLoRA-b575.28 ± 0.0178.95 ± 0.0874.13 ± 0.1878.54 ± 0.1468.41 ± 0.2974.00 ± 0.50
InfLoRA77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
", + "image_path": "d122a9363e01ffb13bdcad44dec93d9025808c931087fa46d3c71773e799b103.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 287, + 289 + ], + "type": "text", + "content": "we split ImageNet-R into 5, 10, and 20 tasks, with each task containing 40, 20, and 10 classes. We split CIFAR100 into 10 tasks, and each task constrains 10 classes. We split DomainNet into 5 tasks, and each task contains 69 classes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": "Following existing continual learning methods [12, 44], we evaluate the performance of the model through two popular metrics, including the final accuracy " + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "ACC_{T}" + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": " and the averaged accuracy " + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\overline{ACC}_{T} = \\frac{1}{T}\\sum_{i=1}^{T}ACC_{i}" + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": " denotes the total number of tasks and " + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "ACC_{i}" + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 124, + 358, + 287, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 358, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 124, + 358, + 287, + 392 + ], + "type": "interline_equation", + "content": "A C C _ {i} = \\frac {1}{i} \\sum_ {j = 1} ^ {i} a _ {i, j}. \\tag {10}", + "image_path": "a0a65e47c802457dcb57b549cf92f5a006cb42b1239fc512b7876b984e6aa9b2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "inline_equation", + "content": "a_{i,j}" + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "content": " denotes the accuracy of the " + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "content": "-th task once the model has learned the " + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "content": "-th task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 604 + ], + "type": "text", + "content": "Baselines We compare our InfLoRA with state-of-the-art continual learning methods based on PEFT, including learn to prompt (L2P) [44], DualPrompt [43], continual decomposed attention-based prompt (CODA-P) [38], learning accumulation ensemble (LAE) [12], continual low-rank adaptation (C-LoRA) [37]. For LAE, we implement it with LoRA [16]. Following existing works [12, 38], we also include two methods without continual learning, joint and sequential, in the comparison. Here, joint denotes the method that learns all the tasks jointly, while sequential denotes the method that learns all the tasks sequentially without any operation to overcome the forgetting of the model. The accuracy of joint can be treated as the accuracy upper-bound and the accuracy of sequential can be treated as the accuracy lower-bound." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "Architecture and Training Details We follow existing works [12, 43] to perform experiments. Specifically, we use the ViT-B/16 backbone [10] supervised pre-trained on ImageNet 21K as the pre-trained model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "For all the methods, we follow existing works [12, 38, 44] and use the Adam [22] optimizer with running averages of gradient and its square " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\beta_{1} = 0.9, \\beta_{2} = 0.999)" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": ". Each task is trained for 50 epochs on ImageNet-R, 20 epochs on CIFAR100 and 5 epochs on DomainNet. The batch size" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 240, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 547, + 397 + ], + "type": "text", + "content": "is set to 128 for all the experiments. Since our InfLoRA shares a similar architecture to LoRA, we follow existing work [12] and insert the architecture of our InfLoRA in the key and value of the attention module. Furthermore, existing method DualPrompt [43] treats the inserted blocks as hyperparameters and searches for the best positions for their prompts. On the contrary, we insert the architecture of InfLoRA for all the Transformer blocks to avoid searching. We also implement a variant of our method, which inserts the bottom 5 Transformer blocks like existing methods DualPrompt and CODA-P. We call this variant InfLoRA-b5. As for the hyperparameter " + }, + { + "bbox": [ + 304, + 240, + 547, + 397 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 240, + 547, + 397 + ], + "type": "text", + "content": ", we determine its value through a grid search on a validation dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 406, + 430, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 406, + 430, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 430, + 419 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 425, + 547, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 547, + 496 + ], + "type": "text", + "content": "Accuracy Table 1 shows the results of different methods on ImageNet-R with a different number of tasks. Table 2 shows the results of different methods on CIFAR100 and DomainNet. We can find that our methods InfLoRA and InfLoRA-b5 outperform existing continual learning methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 593 + ], + "type": "text", + "content": "Figure 2 shows the variation of the accuracy of different continual learning methods on ImageNet-R and CIFAR100. We can find that our method outperforms existing methods not only at the end of the learning but also throughout the whole learning process. This indicates that our InfLoRA eliminates the interference of the new task on the old tasks and thus the accuracy of our method decreases slower compared to other methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Analysis of Expanded Parameters Figure 3 shows the number of expanded parameters and the accuracy of different methods on ImageNet-R and CIFAR100. For L2P, DualPrompt and CODA-P, their expanded parameters are included in the added prompts and corresponding key. For LAE, its expanded parameters are the inserted LoRA modules and an additional copy. For C-LoRA, its expanded parameters are inserted LoRA modules. For our method, the expanded parameters are " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "A_{t}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": ". The details of computing the number of expanded parameters for different meth" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23643" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 105, + 91, + 491, + 228 + ], + "blocks": [ + { + "bbox": [ + 145, + 70, + 447, + 82 + ], + "lines": [ + { + "bbox": [ + 145, + 70, + 447, + 82 + ], + "spans": [ + { + "bbox": [ + 145, + 70, + 447, + 82 + ], + "type": "text", + "content": "Table 2. Results (%) on CIFAR100 and DomainNet. We report results over 5 trials." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 105, + 91, + 491, + 228 + ], + "lines": [ + { + "bbox": [ + 105, + 91, + 491, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 491, + 228 + ], + "type": "table", + "html": "
TasksCIFAR100DomainNet
Method\\(ACC_{10} (↑)\\)\\(\\overline{ACC}_{10} (↑)\\)\\(ACC_5 (↑)\\)\\(\\overline{ACC}_5 (↑)\\)
joint91.92 ± 0.05-77.72 ± 0.04-
sequential62.18 ± 3.5980.42 ± 0.2353.44 ± 1.2169.09 ± 0.33
L2P [44]82.48 ± 0.2087.64 ± 0.2570.16 ± 0.0575.60 ± 0.03
DualPrompt [43]84.42 ± 0.3090.06 ± 0.0772.14 ± 0.0577.71 ± 0.06
CODA-P [38]86.62 ± 0.1191.08 ± 0.2873.23 ± 0.1378.72 ± 0.07
C-LoRA [37]82.97 ± 0.4788.81 ± 0.3469.34 ± 0.1375.25 ± 0.11
LAE [12]84.15 ± 0.1089.84 ± 0.0366.85 ± 0.4075.01 ± 0.17
InfLoRA-b587.06 ± 0.2591.59 ± 0.1373.26 ± 0.5078.82 ± 0.34
InfLoRA86.51 ± 0.7391.70 ± 0.3274.53 ± 0.2379.57 ± 0.57
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We can find that CODA-P and C-LoRA expand much more parameters than other methods. Furthermore, our methods InfLoRA and InfLoRA-b5 expand comparable parameters to L2P, DualPrompt and LAE but perform better than these methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": "Ablation Study We perform experiment to verify the effectiveness of designing dimensionality reduction matrix " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " by (8). Specifically, we explore three different variants for designing " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ". The first variant designs " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " randomly using Gaussian distribution. We call this variant 'Random " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\rightarrow B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": "'. The second variant discards the operation in (6) or (7) and directly sets " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\hat{H}_{t} = H_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ". Through this way, this variant ensures that each row of " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " lies in " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " while ignoring " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t}^{\\perp}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ". We call this variant " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{t} \\rightarrow B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ". The third variant does not compute the input matrix but initializes " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "H_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " using a Gaussian distribution before applying the operation in (6) or (7). In this way, this variant ensures that each row of " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " lies in " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t}^{\\perp}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " while ignoring " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ". We call this variant " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t}^{\\perp} \\rightarrow B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ". Since our method focuses both " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t}^{\\perp}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": ", we use " + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{t} \\cap \\mathcal{M}_{t}^{\\perp} \\rightarrow B_{t}" + }, + { + "bbox": [ + 46, + 422, + 287, + 602 + ], + "type": "text", + "content": " to represent our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Table 3 shows the results of our method and its variants. We can find that all these variants fail to perform as well as our method. To further demonstrate the performance of different variants, we show the relative accuracy of different tasks after the model learns them all in Figure 4. Here, relative accuracy is the accuracy of different variants minus the accuracy of our InfLoRA. Note that the last task is the new task, and the other tasks are old tasks in Figure 4. As we can see, 'Random " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "B_{t}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " ' and " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t\\to B_t" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " outper" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 312, + 358, + 423, + 459 + ], + "blocks": [ + { + "bbox": [ + 94, + 339, + 497, + 350 + ], + "lines": [ + { + "bbox": [ + 94, + 339, + 497, + 350 + ], + "spans": [ + { + "bbox": [ + 94, + 339, + 497, + 350 + ], + "type": "text", + "content": "Figure 2. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 358, + 423, + 459 + ], + "lines": [ + { + "bbox": [ + 312, + 358, + 423, + 459 + ], + "spans": [ + { + "bbox": [ + 312, + 358, + 423, + 459 + ], + "type": "image", + "image_path": "48972fa574349124ba18659a6057b7caa35fabdca79fea69a03edbe125c3db97.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 459, + 422, + 467 + ], + "lines": [ + { + "bbox": [ + 333, + 459, + 422, + 467 + ], + "spans": [ + { + "bbox": [ + 333, + 459, + 422, + 467 + ], + "type": "text", + "content": "(a) ImageNet-R (10 Tasks)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 472, + 545, + 495 + ], + "lines": [ + { + "bbox": [ + 306, + 472, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 545, + 495 + ], + "type": "text", + "content": "Figure 3. Variation of the performance of different methods during the learning of ImageNet-R and CIFAR100." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 429, + 358, + 540, + 458 + ], + "blocks": [ + { + "bbox": [ + 429, + 358, + 540, + 458 + ], + "lines": [ + { + "bbox": [ + 429, + 358, + 540, + 458 + ], + "spans": [ + { + "bbox": [ + 429, + 358, + 540, + 458 + ], + "type": "image", + "image_path": "d063d5500dfd2c4615eedacfd6068945ce61ff2be36bc115f2ce0881472fe13a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 471, + 458, + 520, + 467 + ], + "lines": [ + { + "bbox": [ + 471, + 458, + 520, + 467 + ], + "spans": [ + { + "bbox": [ + 471, + 458, + 520, + 467 + ], + "type": "text", + "content": "(b) CIFAR100" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": "form " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp \\to B_t" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " on the new task but shows much lower accuracy than " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp \\to B_t" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " and our InfLoRA on the old tasks. This means these two variants fail to eliminate the inference of the new task on the old tasks, making the model suffer from low stability. On the contrary, " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp \\to B_t" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " shows the lowest performance on the new task. This means " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t^\\perp \\to B_t" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " ignores the plasticity of the model. Our method outperforms all the variants on most of the tasks. This shows that our method can eliminate the interference of the new task on the old tasks and make a better trade-off between stability and plasticity than these variants." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 641, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 712 + ], + "type": "text", + "content": "Varying the Pre-Trained Model We also follow the existing method [40] and perform experiments using a ViT-B/16 pre-trained with two different self-supervised methods, including DINO [5] and iBOT [49]. All experimental settings, except for the choice of the pre-trained model, are kept consistent with the details outlined in Section 4.1." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23644" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 91, + 542, + 169 + ], + "blocks": [ + { + "bbox": [ + 141, + 71, + 451, + 82 + ], + "lines": [ + { + "bbox": [ + 141, + 71, + 451, + 82 + ], + "spans": [ + { + "bbox": [ + 141, + 71, + 451, + 82 + ], + "type": "text", + "content": "Table 3. Results of different variants on ImageNet-R with a different number of tasks." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 91, + 542, + 169 + ], + "lines": [ + { + "bbox": [ + 53, + 91, + 542, + 169 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 542, + 169 + ], + "type": "table", + "html": "
Tasks51020
\\(ACC_{5} (↑)\\)\\(\\overline{ACC_{5}}\\) (↑)\\(ACC_{10} (↑)\\)\\(\\overline{ACC_{10}}\\) (↑)\\(ACC_{20} (↑)\\)\\(\\overline{ACC_{20}}\\) (↑)
Random → \\(B_{t}\\)72.49 ± 0.3879.40 ± 0.2967.38 ± 0.4176.62 ± 0.0656.17 ± 0.2969.24 ± 0.35
\\(\\mathcal{N}_{t} \\rightarrow \\mathcal{B}_{t}\\)67.01 ± 0.1176.09 ± 0.0457.91 ± 0.3070.23 ± 0.5940.73 ± 0.2959.68 ± 0.52
\\(\\mathcal{M}_{t}^{\\perp} \\rightarrow \\mathcal{B}_{t}\\)75.94 ± 0.5380.69 ± 0.2774.61 ± 0.6279.67 ± 0.2768.79 ± 0.4275.74 ± 0.26
\\(\\mathcal{N}_{t} \\cap \\mathcal{M}_{t}^{\\perp} \\rightarrow \\mathcal{B}_{t} (\\text{InfLoRA})\\)77.52 ± 0.3782.01 ± 0.1275.65 ± 0.1480.82 ± 0.2471.01 ± 0.4577.28 ± 0.45
", + "image_path": "f5a5fac7949e2d46b5bb7f7b505c47fbb383050799112b69b41ce23bc4f4f7f5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 177, + 164, + 274 + ], + "blocks": [ + { + "bbox": [ + 50, + 177, + 164, + 274 + ], + "lines": [ + { + "bbox": [ + 50, + 177, + 164, + 274 + ], + "spans": [ + { + "bbox": [ + 50, + 177, + 164, + 274 + ], + "type": "image", + "image_path": "8989e2019c8e99ca493416992f51649ac0c938d10b86436ec5d133ea721bd9d2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 274, + 164, + 283 + ], + "lines": [ + { + "bbox": [ + 75, + 274, + 164, + 283 + ], + "spans": [ + { + "bbox": [ + 75, + 274, + 164, + 283 + ], + "type": "text", + "content": "(a) ImageNet-R (10 Tasks)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 285, + 286, + 306 + ], + "lines": [ + { + "bbox": [ + 47, + 285, + 286, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 286, + 306 + ], + "type": "text", + "content": "Figure 4. Relative accuracy of different tasks. Relative accuracy is the accuracy of different variants minus the accuracy of InfLoRA." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 178, + 281, + 274 + ], + "blocks": [ + { + "bbox": [ + 167, + 178, + 281, + 274 + ], + "lines": [ + { + "bbox": [ + 167, + 178, + 281, + 274 + ], + "spans": [ + { + "bbox": [ + 167, + 178, + 281, + 274 + ], + "type": "image", + "image_path": "b14e4873e8f092a497c93d7f713faf6a45cf1b18fe241f86245b10978ac1a405.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 192, + 274, + 281, + 283 + ], + "lines": [ + { + "bbox": [ + 192, + 274, + 281, + 283 + ], + "spans": [ + { + "bbox": [ + 192, + 274, + 281, + 283 + ], + "type": "text", + "content": "(b) ImageNet-R (20 Tasks)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 365, + 287, + 551 + ], + "blocks": [ + { + "bbox": [ + 47, + 312, + 287, + 357 + ], + "lines": [ + { + "bbox": [ + 47, + 312, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 287, + 357 + ], + "type": "text", + "content": "Table 4. Results (\\%) of different methods on ImageNet-R (10 tasks) using various self-supervised pre-trained models. Here, DINO-1k and iBOT-1k indicate that the ViT is pre-trained on ImageNet-1k using these respective methods." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 365, + 287, + 551 + ], + "lines": [ + { + "bbox": [ + 48, + 365, + 287, + 551 + ], + "spans": [ + { + "bbox": [ + 48, + 365, + 287, + 551 + ], + "type": "table", + "html": "
Method\\(ACC_{10} \\left(↑\\right)\\)\\(ACC_{10} \\left(↑\\right)\\)
DINO-1kL2P [44]56.71 ± 0.1263.59 ± 0.21
DualPrompt [43]60.23 ± 0.4266.57 ± 0.25
CODA-P [38]64.02 ± 0.6871.50 ± 0.42
C-LoRA [37]63.07 ± 0.3668.09 ± 0.41
LAE [12]61.03 ± 0.2769.89 ± 0.15
InfLoRA-b566.16 ± 0.1473.01 ± 0.17
InfLoRA68.31 ± 0.2876.15 ± 0.05
iBOT-1kL2P [44]60.80 ± 0.3566.58 ± 0.28
DualPrompt [43]63.78 ± 0.3868.88 ± 0.16
CODA-P [38]68.02 ± 0.4874.28 ± 0.47
C-LoRA [37]68.60 ± 0.0773.47 ± 0.28
LAE [12]64.14 ± 0.2972.59 ± 0.22
InfLoRA-b569.72 ± 0.4476.11 ± 0.13
InfLoRA71.84 ± 0.0978.29 ± 0.09
", + "image_path": "7007d15c051c769b0b6ddf018116f120f0ce49e32c7f88c902e242ca9e18dab9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "text", + "content": "Table 4 shows the results of different methods on ImageNet-R when using various pre-trained models. Comparing these results to those in Table 1, we can find that the performance of all methods utilizing self-supervised pretrained models is lower than the performance of the corresponding methods using supervised pre-trained models. However, our methods still outperform all other methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "Combining with Classifier Alignment Slow learner with classifier alignment (SLCA) [47] utilizes feature statistics to align classifiers, demonstrating superior performance compared to methods without aligned classifiers. Our InfLoRA can be combined with classifier alignment (CA) to get better performance. Specifically, after learning the " + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "-th task" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 207, + 545, + 272 + ], + "blocks": [ + { + "bbox": [ + 305, + 175, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 198 + ], + "type": "text", + "content": "Table 5. Results " + }, + { + "bbox": [ + 305, + 175, + 545, + 198 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 175, + 545, + 198 + ], + "type": "text", + "content": " of different methods on ImageNet-R (10 tasks) and CIFAR100 using classifier alignment (CA) technique." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 207, + 545, + 272 + ], + "lines": [ + { + "bbox": [ + 307, + 207, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 307, + 207, + 545, + 272 + ], + "type": "table", + "html": "
MethodACC10(↑)ACC10(↑)
CIFAR100SLCA [47]91.06 ± 0.2493.65 ± 0.19
InfLoRA+CA91.59 ± 0.0894.39 ± 0.05
ImageNet-RSLCA [47]77.34 ± 0.2581.35 ± 0.16
InfLoRA+CA79.78 ± 0.2583.38 ± 0.19
", + "image_path": "6324a0c2ba22d5d4b9f1736b76ff93727cd2302608a262bd1d0aec4ef6e46eb4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": "with parameters " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " and loss (9), we collect features " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t = \\{\\mathbf{r}_{i,t}\\}_{i=1}^{n_t}" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": "-th task. Here, " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i,t} = f(\\mathbf{x}_{i,t})" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " denotes the features extracted by backbone " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "f_{\\Theta}(\\cdot)" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": ". Then, mean and covariance of features for each class are computed and saved. After that, for each class " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " the model has seen during continual learning, " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " samples are sampled from Gaussian distribution " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\boldsymbol{\\mu}_c, \\boldsymbol{\\Sigma}_c)" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\mu}_c" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " and covariance " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma}_c" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": " denote the mean and covariance of the class " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": ". Finally, we align the classifier using standard cross-entropy and these samples. The details of this experiment are given in supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "type": "text", + "content": "Table 5 shows that our method InfLoRA+CA outperforms SLCA. Note that SLCA tunes all the parameters of the model while our method InfLoRA only tunes the parameters in " + }, + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t" + }, + { + "bbox": [ + 304, + 412, + 545, + 472 + ], + "type": "text", + "content": ". Therefore, our InfLoRA+CA is much more efficient than SLCA." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "content": "In this work, we propose a new method, called interference-free low-rank adaptation (InfLoRA), for continual learning. InfLoRA injects a small number of parameters to reparameterize the pre-trained weights and shows that fine-tuning these injected parameters is equivalent to fine-tuning the pre-trained weights within a subspace. Furthermore, InfLoRA designs this subspace to eliminate the interference of the new task on the old tasks, making a good trade-off between stability and plasticity. Experimental results show that InfLoRA outperforms existing state-of-the-art continual learning methods on multiple datasets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 646, + 398, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 398, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 398, + 658 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "This work is supported by NSFC (No.62192783), National Key R&D Program of China (No.2020YFA0713901), and Fundamental Research Funds for the Central Universities (No.020214380108)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23645" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5871-5880, 2021. 2" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23647" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_content_list.json b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..079ab4ff9dc1a0df4947f671c0a29b125fa59a12 --- /dev/null +++ b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_content_list.json @@ -0,0 +1,1701 @@ +[ + { + "type": "text", + "text": "Infer from What You Have Seen Before: Temporally-dependent Classifier for Semi-supervised Video Segmentation", + "text_level": 1, + "bbox": [ + 112, + 130, + 857, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiafan Zhuang Shantou University jfzhuang@stu.edu.cn", + "bbox": [ + 99, + 203, + 269, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zilei Wang* Yixin Zhang \nUniversity of Science and Technology of China \n{zlwang, zhyx12}@ustc.edu.cn", + "bbox": [ + 305, + 203, + 679, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhun Fan Shantou University zfan@stu.edu.cn", + "bbox": [ + 717, + 203, + 872, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to high expense of human labor, one major challenge for semantic segmentation in real-world scenarios is the lack of sufficient pixel-level labels, which is more serious when processing video data. To exploit unlabeled data for model training, semi-supervised learning methods attempt to construct pseudo labels or various auxiliary constraints as supervision signals. However, most of them just process video data as a set of independent images in a per-frame manner. The rich temporal relationships are ignored, which can serve as valuable clues for representation learning. Besides, this per-frame recognition paradigm is quite different from that of humans. Actually, benefited from the internal temporal relevance of video data, human would wisely use the distinguished semantic concepts in historical frames to aid the recognition of the current frame. Motivated by this observation, we propose a novel temporally-dependent classifier (TDC) to mimic the human-like recognition procedure. Comparing to the conventional classifier, TDC can guide the model to learn a group of temporally-consistent semantic concepts across frames, which essentially provides an implicit and effective constraint. We conduct extensive experiments on Cityscapes and CamVid, and the results demonstrate the superiority of our proposed method to previous state-of-the-art methods. The code is available at https://github.com/jfzhuang/TDC.", + "bbox": [ + 76, + 323, + 473, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 729, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As a fundamental tool, semantic segmentation has profited many downstream applications, and deep learning further boosts this area with remarkable progress. However, training a promising segmentation network relies on sufficient finely annotated data. And pixel-wise labeling is time-consuming, e.g., the annotation process costs more than 1.5 hours on average for a single image in Cityscapes [6].", + "bbox": [ + 75, + 755, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In real-world scenarios, we can usually collect unlabeled", + "bbox": [ + 96, + 862, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/05b2067f4f3aa1df644374ba58d9ef0d650526b5cfb89b95a04dd87b4f4c6945.jpg", + "image_caption": [ + "(a) SSIS Methods" + ], + "image_footnote": [], + "bbox": [ + 521, + 290, + 870, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cbb4157b08d6125ea4bcf9f5284aec7b36f61ac1d42c634383b63a2849967adf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 362, + 870, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9fbc1fdbe26251796d8befe5279bae60d68733882dd8eea0543468c0cb0ce350.jpg", + "image_caption": [ + "(b) IFR", + "(c) Ours", + "Classifier" + ], + "image_footnote": [], + "bbox": [ + 522, + 446, + 870, + 521 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a28ab5e76c07907b68355d5dc662348930e9adc0c69d1a3aa19065c40f060a04.jpg", + "image_caption": [ + "Feature Extractor", + "Figure 1. Comparison between previous methods and ours. To exploit unlabeled frames, SSIS methods attempted to construct different supervision signals. IFR [42] proposed to optimize feature extractor by inter-frame feature reconstruction. Differently, in this work, we propose to improve the recognition procedure by designing a temporal-dependent classifier." + ], + "image_footnote": [], + "bbox": [ + 542, + 532, + 570, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "data conveniently and economically, especially video data. Therefore, to alleviate the label-hungry problem, a growing attention is drawn on semi-supervised learning to take advantage of unlabeled data to aid model training. Besides regular supervised learning on limited labeled images, semi-supervised image segmentation (SSIS) methods proposed to construct extra supervision signals for unlabeled images, e.g., consistency constraint [21, 28] and pseudo label [4, 43]. It is shown that they can bring considerable performance improvement on the challenging datasets, e.g., PASCAL VOC [10] and Cityscapes [6].", + "bbox": [ + 496, + 671, + 892, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, when unlabeled data is scaled up by adding video data, SSIS methods can not obtain further improvement [42]. The primary reason is the homogenization of video data, i.e., the contents of different frames within a", + "bbox": [ + 496, + 839, + 893, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3575", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "video are often similar, which contributes less information increment. Since SSIS methods are designed for image data and do not consider for video characteristics, they just regard videos as a set of independent images and thus fail to exploit unlabeled video data. To tackle this issue, as the first semi-supervised video segmentation (SSVS) method, IFR [42] proposed to optimize the feature extractor by interframe feature reconstruction. Specifically, by reconstructing the representation on labeled frame by features from other frames, the single label can indirectly provide accurate supervision for unlabeled frames within the same video. IFR essentially utilizes the content-relevance characteristic of video data and achieve a promising improvement.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In general, existing methods focus on designing supervision signals for unlabeled data and improving feature extraction, as shown in Figure 1. However, another critical component is ignored, i.e., the classifier. Since video segmentation is derived from image segmentation, the final recognition process is naturally inherited in a per-frame manner. Specifically, after extracting the feature sequence for a video, the classifier is independently adopted on the features of each frame for recognition. However, we found that per-frame classification is quite different from human's recognition procedure, as shown in Figure 2. Specifically, when receiving a video stream, the recognition of the first frame is identical to image recognition. Since no prior information can be used, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. After that, the situation becomes different. The distinguished objects and semantic concepts of historical frames are not immediately forgotten, but stored in the memory as context semantic concepts in a short period of time. Therefore, when recognizing the current frame, human would wisely retrieve both global concepts and updated context concepts. This is fundamentally different from per-frame classification. Actually, this temporally-dependent recognition procedure essentially utilizes the content relevance characteristic of video data.", + "bbox": [ + 75, + 290, + 472, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by human's manner, we propose to design a novel temporal-dependent classifier (TDC), which is more suitable for video perception. Specifically, TDC contains two types of prototypes, i.e., global and context prototypes. The former learns global semantic concepts during model training and fixed during inference, which is identical to the conventional classifier. Differently, the context prototypes are calculated on-the-fly based on the last processed frame. When recognizing the current frame, two types of prototypes are collaborated together to calculate similarity with the extracted feature. In this way, the distinguished context concepts from historical frames can assist the classification.", + "bbox": [ + 75, + 670, + 472, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From experimental results, we surprisingly found that TDC can achieve significant performance improvement by equipping a simple pseudo label supervision [11] in semi-", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5222d701efdf88302edf69a6cb4d93d7900c66e9ca91400a00203d76c9573e6e.jpg", + "image_caption": [ + "Figure 2. Illustration of human-like recognition procedure. When recognizing image data, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. When recognizing the current frame of video data, besides global concepts, human would also retrieve distinguished objects from historical frames as temporal contexts." + ], + "image_footnote": [], + "bbox": [ + 553, + 90, + 841, + 481 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "supervised video segmentation task. The primary cause is that the temporal-dependent recognition paradigm implicitly imposes a temporal consistency constraint. Specifically, TDC actually requires the context prototypes calculated from historical frames to accurately represent the content of the current frame. In this way, the feature extractor would be guided to learn a group of temporally-consistent semantic concepts across frames, which indirectly introduces the content-relevance prior into the feature extraction procedure. This guidance effectively optimizes model training on unlabeled data and improve generalization ability.", + "bbox": [ + 496, + 595, + 890, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We experimentally evaluate the proposed method on the Cityscapes and CamVid datasets. The results validate the effectiveness of TDC, and it can bring a significant improvement for mainstream video semantic segmentation methods. The contributions of this work are summarized as follows.", + "bbox": [ + 496, + 763, + 890, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We find that the commonly adopted per-frame classification paradigm is quite different from human's manner and sub-optimal for video perception task, which is ignored in previous studies.", + "bbox": [ + 500, + 839, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3576", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel temporal-dependent classifier (TDC) for semi-supervised video segmentation, which can implicitly impose a temporal consistency constraint for unsupervised learning. TDC essentially utilizes the internal relevance of different frames within a video.", + "- We experimentally evaluate the effectiveness of our proposed methods, and the results on Cityscapes and CamVid demonstrate the superiority of our method to previous state-of-the-art methods." + ], + "bbox": [ + 76, + 90, + 467, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 241, + 217, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Image Semantic Segmentation", + "text_level": 1, + "bbox": [ + 76, + 266, + 344, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image semantic segmentation aims to assign a class label to every pixel in an image, which is a fundamental yet rather challenging task. Modern deep learning methods for semantic segmentation are mainly based on fully convolutional network (FCN) [25]. To further enhance segmentation results, the dilation convolution [2], pyramid pooling [37], attention mechanism [12, 17, 38], gating mechanism [7, 13, 22], and high-resolution architecture design [34] are proposed to model object relationships and aggregate context information. Recently, some transformer-based models [5, 24, 35] are proposed and exhibit promising performance. Despite the success of these models, they are often impeded in practical deployment due to requiring sufficient pixel-wise annotations for learning.", + "bbox": [ + 75, + 290, + 467, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Video Semantic Segmentation", + "text_level": 1, + "bbox": [ + 76, + 511, + 341, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video semantic segmentation aims to predict pixel-level semantics for each video frame. Different from static images, videos embody rich temporal information that can be exploited to improve segmentation performance. DFF [39] firstly proposes feature propagation to reuse key frame features under the guidance of estimated optical flows, which reduces the average computational cost. Inspired by DFF, Accel [19] proposes an adaptive fusion policy to effectively integrate the predictions from the key and current frames. DAVSS [41] proposes to correct the distorted features caused by inaccurate optical flow when propagating features. Besides the feature propagation paradigm, some recent works propose to improve the performance of lightweight models with temporal constraints [8, 23] and attention mechanism [16, 32, 33].", + "bbox": [ + 75, + 534, + 467, + 761 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Semi-supervised Semantic Segmentation", + "text_level": 1, + "bbox": [ + 76, + 771, + 421, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve good representation learning with limited annotations, semi-supervised image segmentation (SSIS) is studied by exploring unlabeled data. Existing methods can be roughly divided into three families. The adversarial based methods, e.g., AdvSemiSeg [18] and S4GAN [26], utilize a discriminator to distinguish the confidence maps from labeled and unlabeled data predictions. The consistency", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "based methods enforce the consistency of the predictions or intermediate features with various perturbations. The perturbations can be conducted on input images, e.g., CutMix [11], ClassMix [27], and CAC [21], and feature space, e.g., CCT [28]. The self-learning based methods generate pseudo segmentation maps on unlabeled data. [3, 14, 36] propose to generate pseudo labels in an offline manner and retrain the model iteratively. While PseudoSeg [43] and CPS [4] follow the FixMatch [31] scheme and design an online pseudo labeling mechanism.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, SSIS methods are not designed for video data, which only regards videos as a collection of independent images. To tackle this issue, IFR [42] proposed to reconstruct feature on the labeled frame by that on other frames, which can provide accurate supervision signals from the single label for unlabeled frames. IFR essentially utilizes the content-relevance characteristic of video data.", + "bbox": [ + 496, + 243, + 890, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generally, existing methods mainly focus on supervision signal construction and improving feature extraction. Differently, in this work, we concentrate on the classifier design. We find that the per-frame recognition paradigm used in previous works is different from human's manner and thus propose a temporal-dependent classifier.", + "bbox": [ + 496, + 349, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 455, + 589, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 481, + 609, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following IFR [42], in semi-supervised video segmentation task, we are provided with a small set of labeled videos with one frame annotated and a larger set of unlabeled videos. Let $V = \\{x_{1},\\dots ,x_{T}\\}$ represents $T$ frames in a video with $x_{i}$ as the $i^{th}$ frame with spatial resolution of $H\\times W$ . Let $\\mathcal{D}_L = \\{(V_1^L,\\hat{x}_1,y_1),\\dots ,(V_{n_L}^L,\\hat{x}_{n_L},y_{n_L})\\}$ represent the $n_L$ labeled videos, where $\\hat{x}_i$ is the annotated frame of the $i^{th}$ video, $y_{i}\\in \\mathbb{R}^{C\\times H\\times W}$ corresponds to the pixel-level one-hot label, and $C$ is the number of classes. Let $\\mathcal{D}_U = \\{V_1^U,\\dots ,V_{n_U}^U\\}$ represents the $n_U$ unlabeled videos. Besides, another set of labeled videos $\\mathcal{D}_V = \\{(\\mathcal{V}_1^V,\\hat{x}_1,y_1),\\dots ,(\\mathcal{V}_{n_V}^V,\\hat{x}_{n_V},y_{n_V})\\}$ is used for performance evaluation.", + "bbox": [ + 496, + 506, + 890, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 3, our framework consists of three components, i.e., a feature extractor $\\mathsf{Net}_B$ , a conventional classifier $\\mathsf{Net}_C$ and the proposed temporal-dependent classifier $\\mathsf{Net}_{TDC}$ . Two adopted classifiers are used in supervised and unsupervised learning branches, respectively. The reason for retaining the conventional classifier is to keep consistent with existing works [4, 11, 21, 28, 42] for fair comparison. In this way, the effectiveness of our TDC for optimizing unsupervised learning can be clearly revealed.", + "bbox": [ + 496, + 703, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work aims to learn a segmentation model from $\\mathcal{D}_L$ and $\\mathcal{D}_U$ , and generalize to $\\mathcal{D}_V$ . Following previous works, the objective of semi-supervised learning can generally be summarized as two loss functions. The first one is a regular", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3577", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5f65289b7014fe92c48943a8307ab8f36535176d818784f51e31f3974e1e5468.jpg", + "image_caption": [ + "Figure 3. Illustration of our SSVS framework. Our framework consists of two learning branches. For supervised learning, we randomly sample an image $I$ and its corresponding ground-truth $GT$ for model training. For unsupervised learning, we randomly sample a video clip with several consecutive frames $V^U$ . Following the previous work [11], we calculate pseudo labels $PL^U$ for $V^U$ , which is used as supervision signals for predictions $P_S^U$ from the augmented video $V_S^U$ ." + ], + "image_footnote": [], + "bbox": [ + 200, + 88, + 769, + 260 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cross-entropy loss on the labeled data:", + "bbox": [ + 76, + 343, + 331, + 357 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP = \\operatorname {N e t} _ {C} (\\operatorname {N e t} _ {B} (I)), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 369, + 468, + 386 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s u p} = \\text {C r o s s E n t r o p y} (P, G T), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 412, + 468, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where image $I$ and its corresponding ground-truth $GT$ are randomly sampled from $D_{L}$ . The second loss aims to train model on unlabeled data with some constructed supervision signals, which is denoted by $L_{unsup}$ . In our framework, we adopt a simple pseudo label strategy similar to FixMatch [11, 31] scheme:", + "bbox": [ + 75, + 435, + 468, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {S} ^ {U} = T _ {s} \\left(V ^ {U}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 536, + 468, + 554 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {S} ^ {U} = \\operatorname {N e t} _ {T D C} \\left(\\operatorname {N e t} _ {B} \\left(V _ {S} ^ {U}\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 578, + 468, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP L ^ {U} = \\operatorname {a r g m a x} \\left(\\operatorname {N e t} _ {C} \\left(\\operatorname {N e t} _ {B} \\left(V ^ {U}\\right)\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 614, + 468, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {u n s u p} = \\text {C r o s s E n t r o p y} \\left(P _ {S} ^ {U}, P L ^ {U}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 654, + 468, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V^{U}$ is randomly sampled from $D_{U}$ and $T_{s}$ represents the strong data augmentation like color jitter. Specifically, we calculate per-frame pseudo labels $PL^{U}$ for $V^{U}$ , which is used as supervision signals for predictions $P_{S}^{U}$ from the augmented video $V_{S}^{U}$ . Then the overall training objective can be presented as follows", + "bbox": [ + 75, + 676, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {s u p} + \\lambda L _ {u n s u p}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 780, + 468, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a trade-off parameter.", + "bbox": [ + 76, + 806, + 294, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Conventional Classifier", + "text_level": 1, + "bbox": [ + 76, + 832, + 290, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To make it clear, we first elaborate on the process of conventional classifier, and then explain the core mechanism of our TDC.", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A conventional classifier typically consists of a fully connected layer and a softmax layer. We use $\\mathbf{w}_i\\in \\mathbb{R}^n$ to denote the weight parameters for category $i$ in the fully connected layer and use $\\mathsf{f}\\in \\mathbb{R}^n$ to denote the feature for classification. Guided by the cross-entropy loss, the classifier is encouraged to produce a larger inner product between $\\mathsf{f}$ and $\\mathsf{w}_y$ , where $y$ is the corresponding ground-truth category. After model training, the learned weight parameters would automatically align with the feature cluster centers, which is experimentally verified and visualized in previous works [9, 30]. Here, the cluster center is the mean of features belonging to the same category, which is usually denoted as prototype.", + "bbox": [ + 496, + 343, + 890, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This tight relationship among features, prototypes and weight parameters is the basic of our TDC, which provides a solution for utilizing distinguished semantic concepts to aid recognition.", + "bbox": [ + 496, + 539, + 890, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Temporal-dependent Classifier", + "text_level": 1, + "bbox": [ + 500, + 609, + 772, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we mainly focus on designing a classifier to mimic the temporal-dependent recognition paradigm on video data like human's manner. To this end, we optimize conventional classifier by introducing distinguished results from historical frames and then propose a novel classifier, i.e., the temporal-dependent classifier (TDC).", + "bbox": [ + 496, + 632, + 890, + 723 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Prototypes Construction", + "text_level": 1, + "bbox": [ + 500, + 739, + 723, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 4, when recognizing $t + 1^{th}$ frame, TDC would simultaneously utilize two types of prototypes, i.e., global prototypes $PT^G$ and context prototypes $PT_t^C$ that calculated based on the prediction of $t^{th}$ frame. Here, similar to the conventional classifier, $PT^G = \\{\\mathbf{w}_i \\in \\mathbb{R}^n | i = 0, 1, \\dots, C - 1\\}$ is implemented as a set of learnable weight parameters, where $C$ is the number of classes and $n$ is the feature dimension. $PT^G$ is updated by back-propagation during training and keeps fixed during inference. The key", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3578", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eebb6cbe92988fa70f19bfd22ac68c9a78d37465e39d5432aa5920770efe420f.jpg", + "image_caption": [ + "Figure 4. Illustration of temporal-dependent recognition procedure. The critical process is the update of context prototypes $PT^C$ based on the last frame prediction. In the classifier, context prototypes $PT^C$ and global prototypes $PT^G$ are utilized together for recognition." + ], + "image_footnote": [], + "bbox": [ + 107, + 88, + 444, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of TDC is the design of context prototypes, which is calculated on-the-fly based on the prediction of last frame. Here, $PT_{t}^{C} = \\{\\mathsf{w}_{k}^{c}\\in \\mathbb{R}^{n}|k = 0,1,\\dots ,K - 1\\}$ represents $K$ prototypes calculated from the $t^{\\text{th}}$ frame. Specifically, we calculate the pseudo label $PL_{t}$ of the extracted feature $F_{t}$ of the $t^{\\text{th}}$ frame as", + "bbox": [ + 75, + 362, + 472, + 454 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP L _ {t} = \\operatorname {a r g m a x} \\left(\\operatorname {N e t} _ {C} \\left(F _ {t}\\right)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 465, + 468, + 482 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we group the pixel-wise features in $F_{t}$ belonging to the same class $k$ according to $PL_{t}$ , i.e.,", + "bbox": [ + 76, + 492, + 468, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} _ {k} ^ {c} = \\frac {\\sum_ {i} F _ {t} ^ {(i)} * \\mathbb {1} \\left(P L _ {t} ^ {(i , k)} = = 1\\right)}{\\sum_ {i} \\mathbb {1} \\left(P L _ {t} ^ {(i , k)} = = 1\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 532, + 468, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{1}$ is an indicator function and $PL_{t}^{(i,k)}$ represents the one-hot pseudo label of pixel $i$ belonging to the $k^{th}$ class. In this way, context prototypes would be adaptively updated based on the last frame prediction.", + "bbox": [ + 75, + 585, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Recognition Procedure", + "text_level": 1, + "bbox": [ + 76, + 665, + 290, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After constructing the global and context prototypes, here we introduce how to conduct recognition based on theses prototypes. The core process of recognition is to calculate similarity between the input feature and prototypes with known categories. After that, the category corresponding to the prototype that generates the maximum similarity will be regarded as the semantic prediction. Therefore, a naive solution is to calculate similarity with global and context prototypes simultaneously.", + "bbox": [ + 75, + 688, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, the input feature would naturally be similar to context prototypes since they are calculated from consecutive frames and thus global prototypes are always ignored, especially in the early stage of model training. This shortcut behavior would make the model only learning to capture", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "similarity across frames and not being able to learn semantic concepts on unlabeled data. The cause of this issue is that two types of prototypes are updated in different mechanism and contains diverse statistical distribution like magnitudes. Therefore, we first conduct normalization on each prototype and the input feature respectively before classification, which can effectively narrow their the distribution discrepancy and achieve a fair learning process. Thus, the predicted probability of the $i^{th}$ category is computed as follows:", + "bbox": [ + 496, + 90, + 890, + 238 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {i} = \\frac {e ^ {\\eta \\cdot \\langle \\overline {{P T}} _ {i} , \\overline {{F}} _ {t} \\rangle}}{\\sum_ {j} e ^ {\\eta \\cdot \\langle \\overline {{P T}} _ {j} , \\overline {{F}} _ {t} \\rangle}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 238, + 890, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\overline{v} = v / ||v||_2$ denotes the L2 normalized vector, and $\\langle \\overline{v}_1,\\overline{v}_2\\rangle = \\overline{v}_1^T\\overline{v}_2$ measures the cosine similarity between two normalized vectors. Here, $PT = \\{PT^{G},PT_{t}^{C}\\}$ is the combination of two types of prototypes. Inspired by a previous work [15], since the range of $\\langle \\overline{v}_1,\\overline{v}_2\\rangle$ is restricted to $[-1,1]$ , a learnable scalar $\\eta$ is introduced to control the peakiness of softmax distribution. Differently, we set two independent scalars, i.e., $\\eta_G$ and $\\eta_C$ , for global prototypes $PT^{G}$ and context prototypes $PT_{t}^{C}$ respectively.", + "bbox": [ + 498, + 281, + 892, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Joint-prototypes Label Relaxation", + "text_level": 1, + "bbox": [ + 500, + 436, + 792, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After calculating the probability of input feature based on constructed prototypes, a cross-entropy loss is applied according to a pseudo label, as described in Section 3.1. However, there is a mismatch between the probability vector $p \\in \\mathbb{R}^{C + K}$ and the one-hot label $y \\in \\mathbb{R}^C$ , where $C$ and $K$ are the number of categories and prototypes predicted in the last frame. Intuitively, for a specific category $i$ , its corresponding context prototype $PT_{t,i}^{C}$ and global prototype $PT_{i}^{G}$ are different descriptions for an identical semantic concept. Therefore, for a feature belonging to category $i$ , it should not be penalized by loss function regardless of which prototype it is more similar to.", + "bbox": [ + 496, + 459, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on this consideration, we propose a joint-prototypes label relaxation, which is also inspired by a previous work [40]. Suppose we are classifying a feature belonging to class $i$ and class $i$ is related to two prototypes $PT_{i}^{G}$ and $PT_{t,i}^{C}$ . To achieve label relaxation, we propose to maximize the likelihood of both prototypes together instead of any single one. Since two prototypes are mutually exclusive in cross-entropy loss, we aim to maximize the union of them:", + "bbox": [ + 496, + 642, + 892, + 777 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(P T _ {i} ^ {G} \\cup P T _ {t, i} ^ {C}\\right) = P \\left(P T _ {i} ^ {G}\\right) + P \\left(P T _ {t, i} ^ {C}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 785, + 890, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P$ is the softmax probability of each prototype. Therefore, for each pixel $i$ in the $t^{th}$ frame in the video clip, the loss function is as follows:", + "bbox": [ + 496, + 811, + 890, + 856 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {T D C} = \\frac {1}{H * W} \\frac {1}{T} \\sum_ {i} ^ {H * W} \\sum_ {t} ^ {T} L _ {T D C} (i, t), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 862, + 890, + 904 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3579", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5154cd7e06660700d27f1d3b903fa0071b511d29843ee09789be5764376ee0cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 88, + 442, + 190 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5888fae6173ac548fbcb3d23d24316229324f8849dd0b3f82ffb2c61326d057f.jpg", + "image_caption": [ + "Figure 5. Illustration of bidirectional prediction. We simultaneously considering forward $(t\\to t + 1)$ and backward $(t + 1\\rightarrow t)$ directions when constructing context prototypes." + ], + "image_footnote": [], + "bbox": [ + 106, + 196, + 442, + 297 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {T D C} (i, t) = - \\log P \\left(P T _ {y _ {i, t}} ^ {G} \\cup \\mathcal {X} \\left(P T _ {t - 1, y _ {i, t}} ^ {C}\\right)\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 371, + 468, + 392 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {X} (x) = \\left\\{ \\begin{array}{l l} x, & \\text {i f} x \\text {e x i s t s} \\\\ 0, & \\text {e l s e} \\end{array} \\right. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 409, + 468, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To be noticed, when recognizing the first frame, only global prototypes are adopted since context prototypes has not been constructed. This is reasonable and similar to human's manner. When obtaining the first frame of a video, human can only conduct image recognition by recalling learned experience, i.e., global prototypes, since there is no prior information about this video.", + "bbox": [ + 75, + 454, + 468, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3.4 Bidirectional Constraint", + "text_level": 1, + "bbox": [ + 76, + 577, + 302, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Actually, TDC works in a RNN-like manner, where the output from the previous step can affect the prediction on the current step. In TDC, the continuously updated prototypes serve like the hidden state vectors in RNN structure. According to successfully practices [20, 29] in NLP field, comparing to unidirectional RNN, bidirectional RNN can help the model to better exploit contextual information and effectively improve the model performance.", + "bbox": [ + 75, + 601, + 468, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Therefore, in this work, we further propose a bidirectional constraint, i.e., simultaneously considering forward $(t\\to t + 1)$ and backward $(t + 1\\rightarrow t)$ directions, as shown in Figure 5. Specifically, context prototypes are calculated based on the $t + 1^{th}$ frame to aid the current frame recognition:", + "bbox": [ + 75, + 722, + 468, + 810 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {B i - T D C} = \\frac {1}{H * W} \\frac {1}{T} \\sum_ {i} ^ {H * W} \\sum_ {t} ^ {T} L _ {B i - T D C} (i, t), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 819, + 468, + 859 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {B i - T D C} (i, t) = - \\log P \\left(P T _ {y _ {i, t}} ^ {G} \\cup \\mathcal {X} \\left(P T _ {t + 1, y _ {i, t}} ^ {C}\\right)\\right). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 883, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Actually, the primary cause behind the effectiveness of TDC on semi-supervised learning is that TDC can implicitly impose a temporal consistency constraint across frames. Intuitively, the bidirectional calculation can further enhance the constraint by simultaneously considering both forward and backward consistency. Finally, in this work, the adopted unsupervised learning loss is as follows:", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {u n s u p} = L _ {T D C} + L _ {B i - T D C}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 205, + 890, + 223 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 232, + 630, + 248 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 500, + 257, + 594, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cityscapes [6] is a representative dataset in semantic segmentation and autonomous driving domain. It focuses on semantic understanding to urban street scenes. The training and validation subsets contain 2,975 and 500 videos, respectively, and each video contains 30 frames at a resolution of $1024 \\times 2048$ . The $20^{th}$ frame in each is annotated by pixel-level semantic labels with 19 categories.", + "bbox": [ + 496, + 280, + 890, + 385 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CamVid [1] also focuses on the semantic understanding to urban street scenes, but it contains less data than Cityscapes. It has four driving videos and each video contains frames ranging from 3,600 to 11,000 at a resolution of $720 \\times 960$ . Every $30^{th}$ frame of videos is annotated with 11 semantic classes, which results in a total of 701 samples. Similar to Cityscapes, we split videos into 701 videos and each video contains 30 frames. All videos are divided into the trainval set with 468 videos and test set with 233 videos.", + "bbox": [ + 496, + 386, + 890, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow the partition protocols of IFR [42] and divide the whole training set via randomly sub-sampling $1/2$ , $1/4$ , $1/8$ , $1/16$ , and $1/30$ of all training videos, i.e., 2975 videos in Cityscapes and 468 videos in CamVid, as the labeled set and regard the remaining videos as the unlabeled set. Following previous work [11, 18, 26-28, 42], we apply bilinear interpolation to resize every video frame in Cityscapes and CamVid to $512 * 1024$ and $360 * 480$ for the efficiency of training and inference.", + "bbox": [ + 496, + 521, + 890, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 666, + 715, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following IFR [42], we adopt Accel [19] as video semantic segmentation architecture due to its good performance. It consists of two segmentation branches, i.e., a heavy reference branch and a light-weight update branch, an optical flow network, and a score fusion layer. Similar to IFR, we adopt semi-supervised methods for two segmentation branches to improve representation learning with limited annotations. The segmentation model is trained using a SGD optimizer with a momentum of 0.9 and a weight decay of $10^{-4}$ . The learning rate is set at $10^{-3}$ for the backbone parameters and $10^{-2}$ for others, which is annealed following the poly learning rate policy.", + "bbox": [ + 496, + 688, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the segmentation performance on the validation videos, i.e., validation subset in Cityscapes and test", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3580", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b84297e4f53a22aece8cf677ace2e3931fc6d4f29dc46e5f91bf82ba3cdf78ca.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method1/30 (100)1/16 (186)1/8 (372)1/4 (744)1/2 (1488)
Accel45.7352.1057.1260.5562.83
+CCT [28]48.05 (+2.32)53.25 (+1.15)58.88 (+1.76)62.00 (+1.45)64.02 (+1.19)
+CAC [21]48.83 (+3.10)54.56 (+2.46)58.55 (+1.43)62.78 (+2.23)63.87 (+1.04)
+ CPS [4]48.97 (+3.24)54.69 (+2.59)58.97 (+1.85)62.43 (+1.88)63.74 (+0.91)
+ IFR [42]52.86 (+7.13)56.39 (+4.29)60.08 (+2.96)63.45 (+2.90)64.53 (+1.70)
+ Ours55.81 (+10.08)60.97 (+8.87)63.12 (+6.00)65.83 (+5.28)66.67 (+3.84)
", + "bbox": [ + 124, + 88, + 843, + 207 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bd142cade061d643655ffd09654955511c7773e817b8ce2f604c7081af17cc27.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art methods on the Cityscapes validation subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data." + ], + "table_footnote": [], + "table_body": "
Method1/30 (15)1/16 (29)1/8 (58)1/4 (117)1/2 (234)
Accel42.3747.5750.7856.4059.37
+CCT [28]47.09 (+4.72)52.45 (+4.88)54.50 (+3.72)58.69 (+2.29)61.58 (+2.21)
+CAC [21]46.85 (+4.48)52.16 (+4.59)54.03 (+3.25)59.67 (+3.27)63.17 (+3.80)
+CPS [4]46.05 (+3.68)52.04 (+4.47)55.30 (+4.52)59.02 (+2.62)62.49 (+3.12)
+IFR [42]49.50 (+7.13)53.71 (+6.14)57.37 (+6.59)61.27 (+4.87)63.86 (+4.49)
+Ours50.95 (+8.58)55.36 (+7.79)59.88 (+9.10)62.63 (+6.23)64.59 (+5.22)
", + "bbox": [ + 127, + 246, + 839, + 366 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "set in CamVid. Following Accel, for each test video, we conduct the reference branch on a selected key frame and update branch on the annotated frame. The segmentation results are predicted via the feature propagation and score fusion. To be notice, for fair comparison, we adopt the conventional classifier for semantic prediction while TDC is only involved in the training period, since in this work we mainly investigate the effectiveness of TDC on representation learning. We evaluate different methods with mean Intersection-over-Union (mIoU) as metric. The key frame interval is set as 5 throughout the experiments. For our TDC, there is a trade-off parameter $\\lambda$ in Eq. 7, which is set $\\lambda = 0.2$ for all experiments.", + "bbox": [ + 75, + 417, + 472, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Performance Comparison", + "text_level": 1, + "bbox": [ + 76, + 630, + 312, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the superiority of our method, we make a comparison with recent state-of-the-art methods, i.e., three SSIS methods including CCT [28], CAC [21] and CPS [4], and a SSVS method IFR [42]. Following IFR, for fair comparison, all critical components are keep consistent among different methods, including base segmentation model, data splits, data augmentation and training settings (i.e., optimizer and hyperparameters). In this way, we can fairly compare the improvement brought by different methods on the basis of the same supervised learning baseline.", + "bbox": [ + 75, + 656, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The comparison on Cityscapes and CamVid is shown in Table 1 and Table 2. From the results, we have the following two observations. First, our TDC can bring significant improvement under all partition protocols comparing to the supervised learning baseline. A larger gain is achieved for the cases with less labeled data, e.g., $10.08\\%$ mIoU gain with", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7e2a0d92835707293756218071fbfa012728393aa1937e4375d1da579ba94b5d.jpg", + "table_caption": [ + "Table 2. Comparison with state-of-the-art methods on the CamVid test subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data." + ], + "table_footnote": [], + "table_body": "
LsupLTDCLBi-TDCmIoU (%)
PTGPTCt
✓43.68
✓✓46.78 (+3.10)
✓✓✓50.14 (+6.46)
✓✓✓✓51.29 (+7.61)
", + "bbox": [ + 524, + 415, + 864, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation study on our proposed components. Each component can bring performance improvement compared to the baseline, and their combination performs best.", + "bbox": [ + 498, + 535, + 892, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "100 samples in Cityscapes. Such experimental results well verify that TDC can effectively improve the generalization of models. Second, our method surpasses other state-of-the-art methods by a large margin. For example, it outperforms IFR by $4.58\\%$ under 1/16 partition protocol on Cityscapes and $2.51\\%$ under 1/8 partition protocol on CamVid, respectively. It shows that TDC can better utilize the unlabeled video data for training model.", + "bbox": [ + 498, + 583, + 893, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 715, + 653, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we conduct experiments to reveal the effectiveness of our proposed method. All experiments are particularly conducted with 1/30 labeled data on Cityscapes. For efficient training, we adopt PSPNet with ResNet18 as the segmentation network by default.", + "bbox": [ + 498, + 741, + 893, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Components. To reveal the contribution of our proposed components, i.e., global prototypes $PT^G$ , context prototypes $PT_t^C$ and bidirectional constraint $L_{Bi-TDC}$ , we conduct an extensive study by evaluating their combina", + "bbox": [ + 498, + 839, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3581", + "bbox": [ + 482, + 944, + 513, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8f209aabfe4280b7134335435fc1ec1f4a89e42d93e2ba0b98bc00cf92395bff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
λ0.00.050.10.20.51.0
mIoU (%)43.6846.8749.6251.2950.7448.54
", + "bbox": [ + 89, + 89, + 452, + 130 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/126c2e4593d93698587928002879307e8e4517fa83c1fc9fa785f0f5a922ae7f.jpg", + "table_caption": [ + "Table 4. Effect of trade-off parameter $\\lambda$ . Based on the results, we set $\\lambda = 0.2$ for all experiments." + ], + "table_footnote": [], + "table_body": "
T01235710
mIoU (%)43.6846.8749.2450.1851.2950.9350.64
", + "bbox": [ + 84, + 170, + 457, + 213 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tions, and the results are shown in Table 3. It can be seen that each component can bring performance improvement compared with the baseline. In particular, based on the supervised learning baseline, TDC equipped with only global prototypes serves like a pseudo-label scheme similar to previous works [4, 43]. After introducing context prototypes, TDC can obtain significant improvement. Finally, TDC performs best with bidirectional constraint.", + "bbox": [ + 75, + 257, + 467, + 377 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Trade-off Parameter $\\lambda$ . We investigate the influence of trade-off parameter $\\lambda$ used to control the unsupervised learning loss in Eq 7, as shown in Table 4. Here, $\\lambda = 0.0$ represents the supervised learning baseline. The results show that: with the increase of $\\lambda$ , the unsupervised loss help model training on unlabeled data and effectively overcome the overfitting issue due to limited labeled training data, which performs best when $\\lambda = 0.2$ . When $\\lambda$ continuously increases, the performance degrades since the supervised learning branch is interfered. Therefore, based on the results, we set $\\lambda = 0.2$ for all experiments.", + "bbox": [ + 75, + 396, + 467, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the Number of frames. In our framework, we randomly sample a unlabeled video clip with $T$ frames for unsupervised learning. Here, we investigate the influence of number of frames, which relates to the temporal modeling in our proposed TDC. Table 5 shows the results. Here, $T = 0$ represents the supervised learning baseline and $T = 1$ represents using TDC with only global prototypes. From the results we can see that: as $T$ increases, TDC can impose a stronger temporal consistency constraint and improve model training on unlabeled video data. However, if $T$ gets too large, TDC would suffer from training instability and lead to a slight performance degradation. Therefore, based on the results, we set $T = 5$ for all experiments.", + "bbox": [ + 75, + 580, + 467, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Performance with Different VSS Architectures. To study the generalization ability of our method, We apply it to different video semantic segmentation architectures. We particularly adopt three widely adopted video segmentation architectures, i.e., DFF [39], Accel [19] and DAVSS [41]. As shown in Table 6, our proposed method can bring significant performance improvement consistently.", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7f192613636bcf14d2da1fe2f72d5146a6fccf4add1c457535e0af12ec226897.jpg", + "table_caption": [ + "Table 5. Effect of Number of frames. Based on the results, we sample 5 frames per unlabeled video clip for all experiments." + ], + "table_footnote": [], + "table_body": "
MethodBaseline+IFR+ Ours
DFF [39]44.1949.97 (+5.78)52.63 (+8.44)
Accel [19]45.7352.86 (+7.13)55.81 (+10.08)
DAVSS [41]46.5151.97 (+5.46)55.25 (+8.74)
", + "bbox": [ + 516, + 89, + 875, + 162 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bfca2c1b5ca22c05bb00b4ef69b2e031192955ff5a6cf6e41ed72a4ae24ff551.jpg", + "table_caption": [ + "Table 6. Performance on different VSS architectures. Our method can bring significant improvement for different video semantic segmentation architectures consistently." + ], + "table_footnote": [], + "table_body": "
MethodAccel+ CCT+ CAC+ CPS+ IFR+ Ours
TC (%)70.0471.4371.4770.7473.8875.38
", + "bbox": [ + 509, + 226, + 879, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Comparison on Temporal Consistency. We evaluate different methods with temporal consistency (TC) score [23]. Our proposed method can bring a significantly improvement.", + "bbox": [ + 500, + 280, + 890, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness on Temporal Consistency. It is important for VSS methods to produce temporally stable predictions. Thus, we further verify the effectiveness of our method on improving temporal consistency. Particularly, we follow previous works [23, 42] and adopt temporal consistency (TC) score as the evaluation metric. As shown in Table 7, our method can bring a significant improvement, since consistent predictions among different frames can be achieved.", + "bbox": [ + 498, + 338, + 890, + 459 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 479, + 617, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we focus on the semi-supervised video semantic segmentation problem, and propose a novel temporal-dependent classifier (TDC). Motivated by the observation of human's behavior, TDC is designed to utilize distinguished semantic concepts of historical frames when recognizing the current frame, which is more suitable for video data. We found that TDC can achieve significant performance improvement in semi-supervised learning since its recognition mechanism implicitly imposes a temporal-consistency constraint across frame, which is valuable especially in labelscarcce scenarios. To further enhance the effect of TDC, we propose a bidirectional constraint by simultaneously considering both forward and backward calculation. Extensive experiments on Cityscapes and CamVid validated the effectiveness of our method, which outperforms previous state-of-the-art methods.", + "bbox": [ + 496, + 506, + 890, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledge", + "text_level": 1, + "bbox": [ + 500, + 767, + 616, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported in part by the National Key R&D Program of China (grant numbers 2021ZD0111501, 2021ZD0111502), the National Natural Science Foundation of China (grant number 62176246), the Anhui Province Key Research and Development Plan (grant number 202304a05020045), and the STU Scientific Research Foundation for Talents (grant number NTF22030).", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3582", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gabriel J Brostow, Julien Fauqueur, and Roberto Cipolla. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 1, 3, 8" + ], + "bbox": [ + 78, + 90, + 467, + 587 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3584", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_model.json b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4123290d0d98c62dd1d92eac666441b2470793f6 --- /dev/null +++ b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.131, + 0.858, + 0.177 + ], + "angle": 0, + "content": "Infer from What You Have Seen Before: Temporally-dependent Classifier for Semi-supervised Video Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.204, + 0.27, + 0.258 + ], + "angle": 0, + "content": "Jiafan Zhuang Shantou University jfzhuang@stu.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.306, + 0.204, + 0.681, + 0.258 + ], + "angle": 0, + "content": "Zilei Wang* Yixin Zhang \nUniversity of Science and Technology of China \n{zlwang, zhyx12}@ustc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.718, + 0.204, + 0.874, + 0.257 + ], + "angle": 0, + "content": "Zhun Fan Shantou University zfan@stu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.474, + 0.702 + ], + "angle": 0, + "content": "Due to high expense of human labor, one major challenge for semantic segmentation in real-world scenarios is the lack of sufficient pixel-level labels, which is more serious when processing video data. To exploit unlabeled data for model training, semi-supervised learning methods attempt to construct pseudo labels or various auxiliary constraints as supervision signals. However, most of them just process video data as a set of independent images in a per-frame manner. The rich temporal relationships are ignored, which can serve as valuable clues for representation learning. Besides, this per-frame recognition paradigm is quite different from that of humans. Actually, benefited from the internal temporal relevance of video data, human would wisely use the distinguished semantic concepts in historical frames to aid the recognition of the current frame. Motivated by this observation, we propose a novel temporally-dependent classifier (TDC) to mimic the human-like recognition procedure. Comparing to the conventional classifier, TDC can guide the model to learn a group of temporally-consistent semantic concepts across frames, which essentially provides an implicit and effective constraint. We conduct extensive experiments on Cityscapes and CamVid, and the results demonstrate the superiority of our proposed method to previous state-of-the-art methods. The code is available at https://github.com/jfzhuang/TDC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.731, + 0.21, + 0.746 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.862 + ], + "angle": 0, + "content": "As a fundamental tool, semantic segmentation has profited many downstream applications, and deep learning further boosts this area with remarkable progress. However, training a promising segmentation network relies on sufficient finely annotated data. And pixel-wise labeling is time-consuming, e.g., the annotation process costs more than 1.5 hours on average for a single image in Cityscapes [6]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.863, + 0.47, + 0.877 + ], + "angle": 0, + "content": "In real-world scenarios, we can usually collect unlabeled" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.291, + 0.871, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.35, + 0.746, + 0.361 + ], + "angle": 0, + "content": "(a) SSIS Methods" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.363, + 0.871, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.436, + 0.718, + 0.447 + ], + "angle": 0, + "content": "(b) IFR" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.448, + 0.871, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.522, + 0.72, + 0.533 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.534, + 0.571, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.578, + 0.54, + 0.662, + 0.549 + ], + "angle": 0, + "content": "Feature Extractor" + }, + { + "type": "image_caption", + "bbox": [ + 0.699, + 0.54, + 0.747, + 0.55 + ], + "angle": 0, + "content": "Classifier" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.572, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Figure 1. Comparison between previous methods and ours. To exploit unlabeled frames, SSIS methods attempted to construct different supervision signals. IFR [42] proposed to optimize feature extractor by inter-frame feature reconstruction. Differently, in this work, we propose to improve the recognition procedure by designing a temporal-dependent classifier." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.893, + 0.838 + ], + "angle": 0, + "content": "data conveniently and economically, especially video data. Therefore, to alleviate the label-hungry problem, a growing attention is drawn on semi-supervised learning to take advantage of unlabeled data to aid model training. Besides regular supervised learning on limited labeled images, semi-supervised image segmentation (SSIS) methods proposed to construct extra supervision signals for unlabeled images, e.g., consistency constraint [21, 28] and pseudo label [4, 43]. It is shown that they can bring considerable performance improvement on the challenging datasets, e.g., PASCAL VOC [10] and Cityscapes [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.9 + ], + "angle": 0, + "content": "However, when unlabeled data is scaled up by adding video data, SSIS methods can not obtain further improvement [42]. The primary reason is the homogenization of video data, i.e., the contents of different frames within a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3575" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "video are often similar, which contributes less information increment. Since SSIS methods are designed for image data and do not consider for video characteristics, they just regard videos as a set of independent images and thus fail to exploit unlabeled video data. To tackle this issue, as the first semi-supervised video segmentation (SSVS) method, IFR [42] proposed to optimize the feature extractor by interframe feature reconstruction. Specifically, by reconstructing the representation on labeled frame by features from other frames, the single label can indirectly provide accurate supervision for unlabeled frames within the same video. IFR essentially utilizes the content-relevance characteristic of video data and achieve a promising improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.669 + ], + "angle": 0, + "content": "In general, existing methods focus on designing supervision signals for unlabeled data and improving feature extraction, as shown in Figure 1. However, another critical component is ignored, i.e., the classifier. Since video segmentation is derived from image segmentation, the final recognition process is naturally inherited in a per-frame manner. Specifically, after extracting the feature sequence for a video, the classifier is independently adopted on the features of each frame for recognition. However, we found that per-frame classification is quite different from human's recognition procedure, as shown in Figure 2. Specifically, when receiving a video stream, the recognition of the first frame is identical to image recognition. Since no prior information can be used, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. After that, the situation becomes different. The distinguished objects and semantic concepts of historical frames are not immediately forgotten, but stored in the memory as context semantic concepts in a short period of time. Therefore, when recognizing the current frame, human would wisely retrieve both global concepts and updated context concepts. This is fundamentally different from per-frame classification. Actually, this temporally-dependent recognition procedure essentially utilizes the content relevance characteristic of video data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.473, + 0.854 + ], + "angle": 0, + "content": "Inspired by human's manner, we propose to design a novel temporal-dependent classifier (TDC), which is more suitable for video perception. Specifically, TDC contains two types of prototypes, i.e., global and context prototypes. The former learns global semantic concepts during model training and fixed during inference, which is identical to the conventional classifier. Differently, the context prototypes are calculated on-the-fly based on the last processed frame. When recognizing the current frame, two types of prototypes are collaborated together to calculate similarity with the extracted feature. In this way, the distinguished context concepts from historical frames can assist the classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "From experimental results, we surprisingly found that TDC can achieve significant performance improvement by equipping a simple pseudo label supervision [11] in semi-" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.091, + 0.843, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Figure 2. Illustration of human-like recognition procedure. When recognizing image data, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. When recognizing the current frame of video data, besides global concepts, human would also retrieve distinguished objects from historical frames as temporal contexts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.763 + ], + "angle": 0, + "content": "supervised video segmentation task. The primary cause is that the temporal-dependent recognition paradigm implicitly imposes a temporal consistency constraint. Specifically, TDC actually requires the context prototypes calculated from historical frames to accurately represent the content of the current frame. In this way, the feature extractor would be guided to learn a group of temporally-consistent semantic concepts across frames, which indirectly introduces the content-relevance prior into the feature extraction procedure. This guidance effectively optimizes model training on unlabeled data and improve generalization ability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.839 + ], + "angle": 0, + "content": "We experimentally evaluate the proposed method on the Cityscapes and CamVid datasets. The results validate the effectiveness of TDC, and it can bring a significant improvement for mainstream video semantic segmentation methods. The contributions of this work are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "- We find that the commonly adopted per-frame classification paradigm is quite different from human's manner and sub-optimal for video perception task, which is ignored in previous studies." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3576" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.166 + ], + "angle": 0, + "content": "- We propose a novel temporal-dependent classifier (TDC) for semi-supervised video segmentation, which can implicitly impose a temporal consistency constraint for unsupervised learning. TDC essentially utilizes the internal relevance of different frames within a video." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.168, + 0.468, + 0.226 + ], + "angle": 0, + "content": "- We experimentally evaluate the effectiveness of our proposed methods, and the results on Cityscapes and CamVid demonstrate the superiority of our method to previous state-of-the-art methods." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.242, + 0.218, + 0.258 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.267, + 0.345, + 0.283 + ], + "angle": 0, + "content": "2.1. Image Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.468, + 0.501 + ], + "angle": 0, + "content": "Image semantic segmentation aims to assign a class label to every pixel in an image, which is a fundamental yet rather challenging task. Modern deep learning methods for semantic segmentation are mainly based on fully convolutional network (FCN) [25]. To further enhance segmentation results, the dilation convolution [2], pyramid pooling [37], attention mechanism [12, 17, 38], gating mechanism [7, 13, 22], and high-resolution architecture design [34] are proposed to model object relationships and aggregate context information. Recently, some transformer-based models [5, 24, 35] are proposed and exhibit promising performance. Despite the success of these models, they are often impeded in practical deployment due to requiring sufficient pixel-wise annotations for learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.512, + 0.342, + 0.527 + ], + "angle": 0, + "content": "2.2. Video Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.468, + 0.762 + ], + "angle": 0, + "content": "Video semantic segmentation aims to predict pixel-level semantics for each video frame. Different from static images, videos embody rich temporal information that can be exploited to improve segmentation performance. DFF [39] firstly proposes feature propagation to reuse key frame features under the guidance of estimated optical flows, which reduces the average computational cost. Inspired by DFF, Accel [19] proposes an adaptive fusion policy to effectively integrate the predictions from the key and current frames. DAVSS [41] proposes to correct the distorted features caused by inaccurate optical flow when propagating features. Besides the feature propagation paradigm, some recent works propose to improve the performance of lightweight models with temporal constraints [8, 23] and attention mechanism [16, 32, 33]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.423, + 0.788 + ], + "angle": 0, + "content": "2.3. Semi-supervised Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To achieve good representation learning with limited annotations, semi-supervised image segmentation (SSIS) is studied by exploring unlabeled data. Existing methods can be roughly divided into three families. The adversarial based methods, e.g., AdvSemiSeg [18] and S4GAN [26], utilize a discriminator to distinguish the confidence maps from labeled and unlabeled data predictions. The consistency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "based methods enforce the consistency of the predictions or intermediate features with various perturbations. The perturbations can be conducted on input images, e.g., CutMix [11], ClassMix [27], and CAC [21], and feature space, e.g., CCT [28]. The self-learning based methods generate pseudo segmentation maps on unlabeled data. [3, 14, 36] propose to generate pseudo labels in an offline manner and retrain the model iteratively. While PseudoSeg [43] and CPS [4] follow the FixMatch [31] scheme and design an online pseudo labeling mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.348 + ], + "angle": 0, + "content": "However, SSIS methods are not designed for video data, which only regards videos as a collection of independent images. To tackle this issue, IFR [42] proposed to reconstruct feature on the labeled frame by that on other frames, which can provide accurate supervision signals from the single label for unlabeled frames. IFR essentially utilizes the content-relevance characteristic of video data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Generally, existing methods mainly focus on supervision signal construction and improving feature extraction. Differently, in this work, we concentrate on the classifier design. We find that the per-frame recognition paradigm used in previous works is different from human's manner and thus propose a temporal-dependent classifier." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.457, + 0.59, + 0.472 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.482, + 0.61, + 0.497 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Following IFR [42], in semi-supervised video segmentation task, we are provided with a small set of labeled videos with one frame annotated and a larger set of unlabeled videos. Let \\( V = \\{x_{1},\\dots ,x_{T}\\} \\) represents \\( T \\) frames in a video with \\( x_{i} \\) as the \\( i^{th} \\) frame with spatial resolution of \\( H\\times W \\). Let \\( \\mathcal{D}_L = \\{(V_1^L,\\hat{x}_1,y_1),\\dots ,(V_{n_L}^L,\\hat{x}_{n_L},y_{n_L})\\} \\) represent the \\( n_L \\) labeled videos, where \\( \\hat{x}_i \\) is the annotated frame of the \\( i^{th} \\) video, \\( y_{i}\\in \\mathbb{R}^{C\\times H\\times W} \\) corresponds to the pixel-level one-hot label, and \\( C \\) is the number of classes. Let \\( \\mathcal{D}_U = \\{V_1^U,\\dots ,V_{n_U}^U\\} \\) represents the \\( n_U \\) unlabeled videos. Besides, another set of labeled videos \\( \\mathcal{D}_V = \\{(\\mathcal{V}_1^V,\\hat{x}_1,y_1),\\dots ,(\\mathcal{V}_{n_V}^V,\\hat{x}_{n_V},y_{n_V})\\} \\) is used for performance evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.84 + ], + "angle": 0, + "content": "As shown in Figure 3, our framework consists of three components, i.e., a feature extractor \\(\\mathsf{Net}_B\\), a conventional classifier \\(\\mathsf{Net}_C\\) and the proposed temporal-dependent classifier \\(\\mathsf{Net}_{TDC}\\). Two adopted classifiers are used in supervised and unsupervised learning branches, respectively. The reason for retaining the conventional classifier is to keep consistent with existing works [4, 11, 21, 28, 42] for fair comparison. In this way, the effectiveness of our TDC for optimizing unsupervised learning can be clearly revealed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our work aims to learn a segmentation model from \\(\\mathcal{D}_L\\) and \\(\\mathcal{D}_U\\), and generalize to \\(\\mathcal{D}_V\\). Following previous works, the objective of semi-supervised learning can generally be summarized as two loss functions. The first one is a regular" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3577" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.202, + 0.089, + 0.77, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.895, + 0.331 + ], + "angle": 0, + "content": "Figure 3. Illustration of our SSVS framework. Our framework consists of two learning branches. For supervised learning, we randomly sample an image \\( I \\) and its corresponding ground-truth \\( GT \\) for model training. For unsupervised learning, we randomly sample a video clip with several consecutive frames \\( V^U \\). Following the previous work [11], we calculate pseudo labels \\( PL^U \\) for \\( V^U \\), which is used as supervision signals for predictions \\( P_S^U \\) from the augmented video \\( V_S^U \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.344, + 0.332, + 0.358 + ], + "angle": 0, + "content": "cross-entropy loss on the labeled data:" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.371, + 0.47, + 0.387 + ], + "angle": 0, + "content": "\\[\nP = \\operatorname {N e t} _ {C} (\\operatorname {N e t} _ {B} (I)), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.413, + 0.469, + 0.43 + ], + "angle": 0, + "content": "\\[\nL _ {s u p} = \\text {C r o s s E n t r o p y} (P, G T), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.526 + ], + "angle": 0, + "content": "where image \\(I\\) and its corresponding ground-truth \\(GT\\) are randomly sampled from \\(D_{L}\\). The second loss aims to train model on unlabeled data with some constructed supervision signals, which is denoted by \\(L_{unsup}\\). In our framework, we adopt a simple pseudo label strategy similar to FixMatch [11, 31] scheme:" + }, + { + "type": "equation", + "bbox": [ + 0.219, + 0.537, + 0.469, + 0.555 + ], + "angle": 0, + "content": "\\[\nV _ {S} ^ {U} = T _ {s} \\left(V ^ {U}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.579, + 0.469, + 0.597 + ], + "angle": 0, + "content": "\\[\nP _ {S} ^ {U} = \\operatorname {N e t} _ {T D C} \\left(\\operatorname {N e t} _ {B} \\left(V _ {S} ^ {U}\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.616, + 0.469, + 0.635 + ], + "angle": 0, + "content": "\\[\nP L ^ {U} = \\operatorname {a r g m a x} \\left(\\operatorname {N e t} _ {C} \\left(\\operatorname {N e t} _ {B} \\left(V ^ {U}\\right)\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.655, + 0.469, + 0.672 + ], + "angle": 0, + "content": "\\[\nL _ {u n s u p} = \\text {C r o s s E n t r o p y} \\left(P _ {S} ^ {U}, P L ^ {U}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.469, + 0.768 + ], + "angle": 0, + "content": "where \\( V^{U} \\) is randomly sampled from \\( D_{U} \\) and \\( T_{s} \\) represents the strong data augmentation like color jitter. Specifically, we calculate per-frame pseudo labels \\( PL^{U} \\) for \\( V^{U} \\), which is used as supervision signals for predictions \\( P_{S}^{U} \\) from the augmented video \\( V_{S}^{U} \\). Then the overall training objective can be presented as follows" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.781, + 0.469, + 0.798 + ], + "angle": 0, + "content": "\\[\nL = L _ {s u p} + \\lambda L _ {u n s u p}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.808, + 0.295, + 0.823 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a trade-off parameter." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.292, + 0.847 + ], + "angle": 0, + "content": "3.2. Conventional Classifier" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.9 + ], + "angle": 0, + "content": "To make it clear, we first elaborate on the process of conventional classifier, and then explain the core mechanism of our TDC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.54 + ], + "angle": 0, + "content": "A conventional classifier typically consists of a fully connected layer and a softmax layer. We use \\(\\mathbf{w}_i\\in \\mathbb{R}^n\\) to denote the weight parameters for category \\(i\\) in the fully connected layer and use \\(\\mathsf{f}\\in \\mathbb{R}^n\\) to denote the feature for classification. Guided by the cross-entropy loss, the classifier is encouraged to produce a larger inner product between \\(\\mathsf{f}\\) and \\(\\mathsf{w}_y\\), where \\(y\\) is the corresponding ground-truth category. After model training, the learned weight parameters would automatically align with the feature cluster centers, which is experimentally verified and visualized in previous works [9, 30]. Here, the cluster center is the mean of features belonging to the same category, which is usually denoted as prototype." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.892, + 0.601 + ], + "angle": 0, + "content": "This tight relationship among features, prototypes and weight parameters is the basic of our TDC, which provides a solution for utilizing distinguished semantic concepts to aid recognition." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.774, + 0.626 + ], + "angle": 0, + "content": "3.3. Temporal-dependent Classifier" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.724 + ], + "angle": 0, + "content": "In this work, we mainly focus on designing a classifier to mimic the temporal-dependent recognition paradigm on video data like human's manner. To this end, we optimize conventional classifier by introducing distinguished results from historical frames and then propose a novel classifier, i.e., the temporal-dependent classifier (TDC)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.724, + 0.757 + ], + "angle": 0, + "content": "3.3.1 Prototypes Construction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As shown in Figure 4, when recognizing \\( t + 1^{th} \\) frame, TDC would simultaneously utilize two types of prototypes, i.e., global prototypes \\( PT^G \\) and context prototypes \\( PT_t^C \\) that calculated based on the prediction of \\( t^{th} \\) frame. Here, similar to the conventional classifier, \\( PT^G = \\{\\mathbf{w}_i \\in \\mathbb{R}^n | i = 0, 1, \\dots, C - 1\\} \\) is implemented as a set of learnable weight parameters, where \\( C \\) is the number of classes and \\( n \\) is the feature dimension. \\( PT^G \\) is updated by back-propagation during training and keeps fixed during inference. The key" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3578" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.089, + 0.446, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.36 + ], + "angle": 0, + "content": "Figure 4. Illustration of temporal-dependent recognition procedure. The critical process is the update of context prototypes \\( PT^C \\) based on the last frame prediction. In the classifier, context prototypes \\( PT^C \\) and global prototypes \\( PT^G \\) are utilized together for recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.473, + 0.455 + ], + "angle": 0, + "content": "of TDC is the design of context prototypes, which is calculated on-the-fly based on the prediction of last frame. Here, \\( PT_{t}^{C} = \\{\\mathsf{w}_{k}^{c}\\in \\mathbb{R}^{n}|k = 0,1,\\dots ,K - 1\\} \\) represents \\( K \\) prototypes calculated from the \\( t^{\\text{th}} \\) frame. Specifically, we calculate the pseudo label \\( PL_{t} \\) of the extracted feature \\( F_{t} \\) of the \\( t^{\\text{th}} \\) frame as" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.466, + 0.47, + 0.483 + ], + "angle": 0, + "content": "\\[\nP L _ {t} = \\operatorname {a r g m a x} \\left(\\operatorname {N e t} _ {C} \\left(F _ {t}\\right)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.493, + 0.47, + 0.524 + ], + "angle": 0, + "content": "Then, we group the pixel-wise features in \\(F_{t}\\) belonging to the same class \\(k\\) according to \\(PL_{t}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.533, + 0.47, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} _ {k} ^ {c} = \\frac {\\sum_ {i} F _ {t} ^ {(i)} * \\mathbb {1} \\left(P L _ {t} ^ {(i , k)} = = 1\\right)}{\\sum_ {i} \\mathbb {1} \\left(P L _ {t} ^ {(i , k)} = = 1\\right)}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.649 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}\\) is an indicator function and \\(PL_{t}^{(i,k)}\\) represents the one-hot pseudo label of pixel \\(i\\) belonging to the \\(k^{th}\\) class. In this way, context prototypes would be adaptively updated based on the last frame prediction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.292, + 0.681 + ], + "angle": 0, + "content": "3.3.2 Recognition Procedure" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.825 + ], + "angle": 0, + "content": "After constructing the global and context prototypes, here we introduce how to conduct recognition based on theses prototypes. The core process of recognition is to calculate similarity between the input feature and prototypes with known categories. After that, the category corresponding to the prototype that generates the maximum similarity will be regarded as the semantic prediction. Therefore, a naive solution is to calculate similarity with global and context prototypes simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "However, the input feature would naturally be similar to context prototypes since they are calculated from consecutive frames and thus global prototypes are always ignored, especially in the early stage of model training. This shortcut behavior would make the model only learning to capture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.239 + ], + "angle": 0, + "content": "similarity across frames and not being able to learn semantic concepts on unlabeled data. The cause of this issue is that two types of prototypes are updated in different mechanism and contains diverse statistical distribution like magnitudes. Therefore, we first conduct normalization on each prototype and the input feature respectively before classification, which can effectively narrow their the distribution discrepancy and achieve a fair learning process. Thus, the predicted probability of the \\( i^{th} \\) category is computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.239, + 0.892, + 0.28 + ], + "angle": 0, + "content": "\\[\np _ {i} = \\frac {e ^ {\\eta \\cdot \\langle \\overline {{P T}} _ {i} , \\overline {{F}} _ {t} \\rangle}}{\\sum_ {j} e ^ {\\eta \\cdot \\langle \\overline {{P T}} _ {j} , \\overline {{F}} _ {t} \\rangle}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.282, + 0.893, + 0.42 + ], + "angle": 0, + "content": "where \\(\\overline{v} = v / ||v||_2\\) denotes the L2 normalized vector, and \\(\\langle \\overline{v}_1,\\overline{v}_2\\rangle = \\overline{v}_1^T\\overline{v}_2\\) measures the cosine similarity between two normalized vectors. Here, \\(PT = \\{PT^{G},PT_{t}^{C}\\}\\) is the combination of two types of prototypes. Inspired by a previous work [15], since the range of \\(\\langle \\overline{v}_1,\\overline{v}_2\\rangle\\) is restricted to \\([-1,1]\\), a learnable scalar \\(\\eta\\) is introduced to control the peakiness of softmax distribution. Differently, we set two independent scalars, i.e., \\(\\eta_G\\) and \\(\\eta_C\\), for global prototypes \\(PT^{G}\\) and context prototypes \\(PT_{t}^{C}\\) respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.794, + 0.452 + ], + "angle": 0, + "content": "3.3.3 Joint-prototypes Label Relaxation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.643 + ], + "angle": 0, + "content": "After calculating the probability of input feature based on constructed prototypes, a cross-entropy loss is applied according to a pseudo label, as described in Section 3.1. However, there is a mismatch between the probability vector \\( p \\in \\mathbb{R}^{C + K} \\) and the one-hot label \\( y \\in \\mathbb{R}^C \\), where \\( C \\) and \\( K \\) are the number of categories and prototypes predicted in the last frame. Intuitively, for a specific category \\( i \\), its corresponding context prototype \\( PT_{t,i}^{C} \\) and global prototype \\( PT_{i}^{G} \\) are different descriptions for an identical semantic concept. Therefore, for a feature belonging to category \\( i \\), it should not be penalized by loss function regardless of which prototype it is more similar to." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Based on this consideration, we propose a joint-prototypes label relaxation, which is also inspired by a previous work [40]. Suppose we are classifying a feature belonging to class \\( i \\) and class \\( i \\) is related to two prototypes \\( PT_{i}^{G} \\) and \\( PT_{t,i}^{C} \\). To achieve label relaxation, we propose to maximize the likelihood of both prototypes together instead of any single one. Since two prototypes are mutually exclusive in cross-entropy loss, we aim to maximize the union of them:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.786, + 0.892, + 0.806 + ], + "angle": 0, + "content": "\\[\nP \\left(P T _ {i} ^ {G} \\cup P T _ {t, i} ^ {C}\\right) = P \\left(P T _ {i} ^ {G}\\right) + P \\left(P T _ {t, i} ^ {C}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.857 + ], + "angle": 0, + "content": "where \\(P\\) is the softmax probability of each prototype. Therefore, for each pixel \\(i\\) in the \\(t^{th}\\) frame in the video clip, the loss function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.863, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\nL _ {T D C} = \\frac {1}{H * W} \\frac {1}{T} \\sum_ {i} ^ {H * W} \\sum_ {t} ^ {T} L _ {T D C} (i, t), \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3579" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.443, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.197, + 0.443, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.311, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Figure 5. Illustration of bidirectional prediction. We simultaneously considering forward \\((t\\to t + 1)\\) and backward \\((t + 1\\rightarrow t)\\) directions when constructing context prototypes." + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.372, + 0.47, + 0.393 + ], + "angle": 0, + "content": "\\[\nL _ {T D C} (i, t) = - \\log P \\left(P T _ {y _ {i, t}} ^ {G} \\cup \\mathcal {X} \\left(P T _ {t - 1, y _ {i, t}} ^ {C}\\right)\\right), \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.41, + 0.469, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\mathcal {X} (x) = \\left\\{ \\begin{array}{l l} x, & \\text {i f} x \\text {e x i s t s} \\\\ 0, & \\text {e l s e} \\end{array} \\right. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.469, + 0.561 + ], + "angle": 0, + "content": "To be noticed, when recognizing the first frame, only global prototypes are adopted since context prototypes has not been constructed. This is reasonable and similar to human's manner. When obtaining the first frame of a video, human can only conduct image recognition by recalling learned experience, i.e., global prototypes, since there is no prior information about this video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.578, + 0.303, + 0.592 + ], + "angle": 0, + "content": "3.3.4 Bidirectional Constraint" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.469, + 0.722 + ], + "angle": 0, + "content": "Actually, TDC works in a RNN-like manner, where the output from the previous step can affect the prediction on the current step. In TDC, the continuously updated prototypes serve like the hidden state vectors in RNN structure. According to successfully practices [20, 29] in NLP field, comparing to unidirectional RNN, bidirectional RNN can help the model to better exploit contextual information and effectively improve the model performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.469, + 0.811 + ], + "angle": 0, + "content": "Therefore, in this work, we further propose a bidirectional constraint, i.e., simultaneously considering forward \\((t\\to t + 1)\\) and backward \\((t + 1\\rightarrow t)\\) directions, as shown in Figure 5. Specifically, context prototypes are calculated based on the \\(t + 1^{th}\\) frame to aid the current frame recognition:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.82, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\nL _ {B i - T D C} = \\frac {1}{H * W} \\frac {1}{T} \\sum_ {i} ^ {H * W} \\sum_ {t} ^ {T} L _ {B i - T D C} (i, t), \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.884, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\nL _ {B i - T D C} (i, t) = - \\log P \\left(P T _ {y _ {i, t}} ^ {G} \\cup \\mathcal {X} \\left(P T _ {t + 1, y _ {i, t}} ^ {C}\\right)\\right). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Actually, the primary cause behind the effectiveness of TDC on semi-supervised learning is that TDC can implicitly impose a temporal consistency constraint across frames. Intuitively, the bidirectional calculation can further enhance the constraint by simultaneously considering both forward and backward consistency. Finally, in this work, the adopted unsupervised learning loss is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.207, + 0.892, + 0.224 + ], + "angle": 0, + "content": "\\[\nL _ {u n s u p} = L _ {T D C} + L _ {B i - T D C}. \\tag {17}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.233, + 0.632, + 0.249 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.258, + 0.596, + 0.272 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.892, + 0.386 + ], + "angle": 0, + "content": "Cityscapes [6] is a representative dataset in semantic segmentation and autonomous driving domain. It focuses on semantic understanding to urban street scenes. The training and validation subsets contain 2,975 and 500 videos, respectively, and each video contains 30 frames at a resolution of \\(1024 \\times 2048\\). The \\(20^{th}\\) frame in each is annotated by pixel-level semantic labels with 19 categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.521 + ], + "angle": 0, + "content": "CamVid [1] also focuses on the semantic understanding to urban street scenes, but it contains less data than Cityscapes. It has four driving videos and each video contains frames ranging from 3,600 to 11,000 at a resolution of \\(720 \\times 960\\). Every \\(30^{th}\\) frame of videos is annotated with 11 semantic classes, which results in a total of 701 samples. Similar to Cityscapes, we split videos into 701 videos and each video contains 30 frames. All videos are divided into the trainval set with 468 videos and test set with 233 videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.658 + ], + "angle": 0, + "content": "We follow the partition protocols of IFR [42] and divide the whole training set via randomly sub-sampling \\(1/2\\), \\(1/4\\), \\(1/8\\), \\(1/16\\), and \\(1/30\\) of all training videos, i.e., 2975 videos in Cityscapes and 468 videos in CamVid, as the labeled set and regard the remaining videos as the unlabeled set. Following previous work [11, 18, 26-28, 42], we apply bilinear interpolation to resize every video frame in Cityscapes and CamVid to \\(512 * 1024\\) and \\(360 * 480\\) for the efficiency of training and inference." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.667, + 0.717, + 0.682 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Following IFR [42], we adopt Accel [19] as video semantic segmentation architecture due to its good performance. It consists of two segmentation branches, i.e., a heavy reference branch and a light-weight update branch, an optical flow network, and a score fusion layer. Similar to IFR, we adopt semi-supervised methods for two segmentation branches to improve representation learning with limited annotations. The segmentation model is trained using a SGD optimizer with a momentum of 0.9 and a weight decay of \\(10^{-4}\\). The learning rate is set at \\(10^{-3}\\) for the backbone parameters and \\(10^{-2}\\) for others, which is annealed following the poly learning rate policy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate the segmentation performance on the validation videos, i.e., validation subset in Cityscapes and test" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3580" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.125, + 0.089, + 0.844, + 0.208 + ], + "angle": 0, + "content": "
Method1/30 (100)1/16 (186)1/8 (372)1/4 (744)1/2 (1488)
Accel45.7352.1057.1260.5562.83
+CCT [28]48.05 (+2.32)53.25 (+1.15)58.88 (+1.76)62.00 (+1.45)64.02 (+1.19)
+CAC [21]48.83 (+3.10)54.56 (+2.46)58.55 (+1.43)62.78 (+2.23)63.87 (+1.04)
+ CPS [4]48.97 (+3.24)54.69 (+2.59)58.97 (+1.85)62.43 (+1.88)63.74 (+0.91)
+ IFR [42]52.86 (+7.13)56.39 (+4.29)60.08 (+2.96)63.45 (+2.90)64.53 (+1.70)
+ Ours55.81 (+10.08)60.97 (+8.87)63.12 (+6.00)65.83 (+5.28)66.67 (+3.84)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.212, + 0.895, + 0.242 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art methods on the Cityscapes validation subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data." + }, + { + "type": "table", + "bbox": [ + 0.128, + 0.247, + 0.84, + 0.367 + ], + "angle": 0, + "content": "
Method1/30 (15)1/16 (29)1/8 (58)1/4 (117)1/2 (234)
Accel42.3747.5750.7856.4059.37
+CCT [28]47.09 (+4.72)52.45 (+4.88)54.50 (+3.72)58.69 (+2.29)61.58 (+2.21)
+CAC [21]46.85 (+4.48)52.16 (+4.59)54.03 (+3.25)59.67 (+3.27)63.17 (+3.80)
+CPS [4]46.05 (+3.68)52.04 (+4.47)55.30 (+4.52)59.02 (+2.62)62.49 (+3.12)
+IFR [42]49.50 (+7.13)53.71 (+6.14)57.37 (+6.59)61.27 (+4.87)63.86 (+4.49)
+Ours50.95 (+8.58)55.36 (+7.79)59.88 (+9.10)62.63 (+6.23)64.59 (+5.22)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.37, + 0.893, + 0.4 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art methods on the CamVid test subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.473, + 0.614 + ], + "angle": 0, + "content": "set in CamVid. Following Accel, for each test video, we conduct the reference branch on a selected key frame and update branch on the annotated frame. The segmentation results are predicted via the feature propagation and score fusion. To be notice, for fair comparison, we adopt the conventional classifier for semantic prediction while TDC is only involved in the training period, since in this work we mainly investigate the effectiveness of TDC on representation learning. We evaluate different methods with mean Intersection-over-Union (mIoU) as metric. The key frame interval is set as 5 throughout the experiments. For our TDC, there is a trade-off parameter \\(\\lambda\\) in Eq. 7, which is set \\(\\lambda = 0.2\\) for all experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.631, + 0.313, + 0.648 + ], + "angle": 0, + "content": "4.3. Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.809 + ], + "angle": 0, + "content": "To demonstrate the superiority of our method, we make a comparison with recent state-of-the-art methods, i.e., three SSIS methods including CCT [28], CAC [21] and CPS [4], and a SSVS method IFR [42]. Following IFR, for fair comparison, all critical components are keep consistent among different methods, including base segmentation model, data splits, data augmentation and training settings (i.e., optimizer and hyperparameters). In this way, we can fairly compare the improvement brought by different methods on the basis of the same supervised learning baseline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The comparison on Cityscapes and CamVid is shown in Table 1 and Table 2. From the results, we have the following two observations. First, our TDC can bring significant improvement under all partition protocols comparing to the supervised learning baseline. A larger gain is achieved for the cases with less labeled data, e.g., \\(10.08\\%\\) mIoU gain with" + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.416, + 0.866, + 0.528 + ], + "angle": 0, + "content": "
LsupLTDCLBi-TDCmIoU (%)
PTGPTCt
✓43.68
✓✓46.78 (+3.10)
✓✓✓50.14 (+6.46)
✓✓✓✓51.29 (+7.61)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.536, + 0.893, + 0.579 + ], + "angle": 0, + "content": "Table 3. Ablation study on our proposed components. Each component can bring performance improvement compared to the baseline, and their combination performs best." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.584, + 0.894, + 0.706 + ], + "angle": 0, + "content": "100 samples in Cityscapes. Such experimental results well verify that TDC can effectively improve the generalization of models. Second, our method surpasses other state-of-the-art methods by a large margin. For example, it outperforms IFR by \\(4.58\\%\\) under 1/16 partition protocol on Cityscapes and \\(2.51\\%\\) under 1/8 partition protocol on CamVid, respectively. It shows that TDC can better utilize the unlabeled video data for training model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.717, + 0.655, + 0.734 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.742, + 0.894, + 0.817 + ], + "angle": 0, + "content": "In this subsection, we conduct experiments to reveal the effectiveness of our proposed method. All experiments are particularly conducted with 1/30 labeled data on Cityscapes. For efficient training, we adopt PSPNet with ResNet18 as the segmentation network by default." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Effect of Components. To reveal the contribution of our proposed components, i.e., global prototypes \\( PT^G \\), context prototypes \\( PT_t^C \\) and bidirectional constraint \\( L_{Bi-TDC} \\), we conduct an extensive study by evaluating their combina" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "3581" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.09, + 0.454, + 0.131 + ], + "angle": 0, + "content": "
λ0.00.050.10.20.51.0
mIoU (%)43.6846.8749.6251.2950.7448.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.136, + 0.468, + 0.164 + ], + "angle": 0, + "content": "Table 4. Effect of trade-off parameter \\( \\lambda \\). Based on the results, we set \\( \\lambda = 0.2 \\) for all experiments." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.171, + 0.458, + 0.214 + ], + "angle": 0, + "content": "
T01235710
mIoU (%)43.6846.8749.2450.1851.2950.9350.64
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.218, + 0.468, + 0.247 + ], + "angle": 0, + "content": "Table 5. Effect of Number of frames. Based on the results, we sample 5 frames per unlabeled video clip for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.468, + 0.378 + ], + "angle": 0, + "content": "tions, and the results are shown in Table 3. It can be seen that each component can bring performance improvement compared with the baseline. In particular, based on the supervised learning baseline, TDC equipped with only global prototypes serves like a pseudo-label scheme similar to previous works [4, 43]. After introducing context prototypes, TDC can obtain significant improvement. Finally, TDC performs best with bidirectional constraint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.468, + 0.563 + ], + "angle": 0, + "content": "Effect of Trade-off Parameter \\(\\lambda\\). We investigate the influence of trade-off parameter \\(\\lambda\\) used to control the unsupervised learning loss in Eq 7, as shown in Table 4. Here, \\(\\lambda = 0.0\\) represents the supervised learning baseline. The results show that: with the increase of \\(\\lambda\\), the unsupervised loss help model training on unlabeled data and effectively overcome the overfitting issue due to limited labeled training data, which performs best when \\(\\lambda = 0.2\\). When \\(\\lambda\\) continuously increases, the performance degrades since the supervised learning branch is interfered. Therefore, based on the results, we set \\(\\lambda = 0.2\\) for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.468, + 0.777 + ], + "angle": 0, + "content": "Effect of the Number of frames. In our framework, we randomly sample a unlabeled video clip with \\( T \\) frames for unsupervised learning. Here, we investigate the influence of number of frames, which relates to the temporal modeling in our proposed TDC. Table 5 shows the results. Here, \\( T = 0 \\) represents the supervised learning baseline and \\( T = 1 \\) represents using TDC with only global prototypes. From the results we can see that: as \\( T \\) increases, TDC can impose a stronger temporal consistency constraint and improve model training on unlabeled video data. However, if \\( T \\) gets too large, TDC would suffer from training instability and lead to a slight performance degradation. Therefore, based on the results, we set \\( T = 5 \\) for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Performance with Different VSS Architectures. To study the generalization ability of our method, We apply it to different video semantic segmentation architectures. We particularly adopt three widely adopted video segmentation architectures, i.e., DFF [39], Accel [19] and DAVSS [41]. As shown in Table 6, our proposed method can bring significant performance improvement consistently." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.09, + 0.876, + 0.163 + ], + "angle": 0, + "content": "
MethodBaseline+IFR+ Ours
DFF [39]44.1949.97 (+5.78)52.63 (+8.44)
Accel [19]45.7352.86 (+7.13)55.81 (+10.08)
DAVSS [41]46.5151.97 (+5.46)55.25 (+8.74)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.174, + 0.892, + 0.216 + ], + "angle": 0, + "content": "Table 6. Performance on different VSS architectures. Our method can bring significant improvement for different video semantic segmentation architectures consistently." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.227, + 0.88, + 0.273 + ], + "angle": 0, + "content": "
MethodAccel+ CCT+ CAC+ CPS+ IFR+ Ours
TC (%)70.0471.4371.4770.7473.8875.38
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.281, + 0.892, + 0.323 + ], + "angle": 0, + "content": "Table 7. Comparison on Temporal Consistency. We evaluate different methods with temporal consistency (TC) score [23]. Our proposed method can bring a significantly improvement." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.339, + 0.892, + 0.46 + ], + "angle": 0, + "content": "Effectiveness on Temporal Consistency. It is important for VSS methods to produce temporally stable predictions. Thus, we further verify the effectiveness of our method on improving temporal consistency. Particularly, we follow previous works [23, 42] and adopt temporal consistency (TC) score as the evaluation metric. As shown in Table 7, our method can bring a significant improvement, since consistent predictions among different frames can be achieved." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.48, + 0.618, + 0.495 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.747 + ], + "angle": 0, + "content": "In this paper, we focus on the semi-supervised video semantic segmentation problem, and propose a novel temporal-dependent classifier (TDC). Motivated by the observation of human's behavior, TDC is designed to utilize distinguished semantic concepts of historical frames when recognizing the current frame, which is more suitable for video data. We found that TDC can achieve significant performance improvement in semi-supervised learning since its recognition mechanism implicitly imposes a temporal-consistency constraint across frame, which is valuable especially in labelscarcce scenarios. To further enhance the effect of TDC, we propose a bidirectional constraint by simultaneously considering both forward and backward calculation. Extensive experiments on Cityscapes and CamVid validated the effectiveness of our method, which outperforms previous state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.768, + 0.617, + 0.785 + ], + "angle": 0, + "content": "Acknowledge" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work is supported in part by the National Key R&D Program of China (grant numbers 2021ZD0111501, 2021ZD0111502), the National Natural Science Foundation of China (grant number 62176246), the Anhui Province Key Research and Development Plan (grant number 202304a05020045), and the STU Scientific Research Foundation for Talents (grant number NTF22030)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3582" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Gabriel J Brostow, Julien Fauqueur, and Roberto Cipolla. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 1, 3, 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.588 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3584" + } + ] +] \ No newline at end of file diff --git a/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_origin.pdf b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0331ad8fe2981fc5b0fb059f47a2ce850dee2c96 --- /dev/null +++ b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/b88320a5-3d99-4155-a16b-84fc816465a0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:168ace219e101ec40a83fd0f5032df6cc133c696de22a146e52afc25a5878875 +size 831635 diff --git a/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/full.md b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4cf473f7ba6a53dbaf44820a3f0ac8f2e38174b7 --- /dev/null +++ b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/full.md @@ -0,0 +1,350 @@ +# Infer from What You Have Seen Before: Temporally-dependent Classifier for Semi-supervised Video Segmentation + +Jiafan Zhuang Shantou University jfzhuang@stu.edu.cn + +Zilei Wang* Yixin Zhang +University of Science and Technology of China +{zlwang, zhyx12}@ustc.edu.cn + +Zhun Fan Shantou University zfan@stu.edu.cn + +# Abstract + +Due to high expense of human labor, one major challenge for semantic segmentation in real-world scenarios is the lack of sufficient pixel-level labels, which is more serious when processing video data. To exploit unlabeled data for model training, semi-supervised learning methods attempt to construct pseudo labels or various auxiliary constraints as supervision signals. However, most of them just process video data as a set of independent images in a per-frame manner. The rich temporal relationships are ignored, which can serve as valuable clues for representation learning. Besides, this per-frame recognition paradigm is quite different from that of humans. Actually, benefited from the internal temporal relevance of video data, human would wisely use the distinguished semantic concepts in historical frames to aid the recognition of the current frame. Motivated by this observation, we propose a novel temporally-dependent classifier (TDC) to mimic the human-like recognition procedure. Comparing to the conventional classifier, TDC can guide the model to learn a group of temporally-consistent semantic concepts across frames, which essentially provides an implicit and effective constraint. We conduct extensive experiments on Cityscapes and CamVid, and the results demonstrate the superiority of our proposed method to previous state-of-the-art methods. The code is available at https://github.com/jfzhuang/TDC. + +# 1. Introduction + +As a fundamental tool, semantic segmentation has profited many downstream applications, and deep learning further boosts this area with remarkable progress. However, training a promising segmentation network relies on sufficient finely annotated data. And pixel-wise labeling is time-consuming, e.g., the annotation process costs more than 1.5 hours on average for a single image in Cityscapes [6]. + +In real-world scenarios, we can usually collect unlabeled + +![](images/05b2067f4f3aa1df644374ba58d9ef0d650526b5cfb89b95a04dd87b4f4c6945.jpg) +(a) SSIS Methods + +![](images/cbb4157b08d6125ea4bcf9f5284aec7b36f61ac1d42c634383b63a2849967adf.jpg) + +![](images/9fbc1fdbe26251796d8befe5279bae60d68733882dd8eea0543468c0cb0ce350.jpg) +(b) IFR +(c) Ours +Classifier + +![](images/a28ab5e76c07907b68355d5dc662348930e9adc0c69d1a3aa19065c40f060a04.jpg) +Feature Extractor +Figure 1. Comparison between previous methods and ours. To exploit unlabeled frames, SSIS methods attempted to construct different supervision signals. IFR [42] proposed to optimize feature extractor by inter-frame feature reconstruction. Differently, in this work, we propose to improve the recognition procedure by designing a temporal-dependent classifier. + +data conveniently and economically, especially video data. Therefore, to alleviate the label-hungry problem, a growing attention is drawn on semi-supervised learning to take advantage of unlabeled data to aid model training. Besides regular supervised learning on limited labeled images, semi-supervised image segmentation (SSIS) methods proposed to construct extra supervision signals for unlabeled images, e.g., consistency constraint [21, 28] and pseudo label [4, 43]. It is shown that they can bring considerable performance improvement on the challenging datasets, e.g., PASCAL VOC [10] and Cityscapes [6]. + +However, when unlabeled data is scaled up by adding video data, SSIS methods can not obtain further improvement [42]. The primary reason is the homogenization of video data, i.e., the contents of different frames within a + +video are often similar, which contributes less information increment. Since SSIS methods are designed for image data and do not consider for video characteristics, they just regard videos as a set of independent images and thus fail to exploit unlabeled video data. To tackle this issue, as the first semi-supervised video segmentation (SSVS) method, IFR [42] proposed to optimize the feature extractor by interframe feature reconstruction. Specifically, by reconstructing the representation on labeled frame by features from other frames, the single label can indirectly provide accurate supervision for unlabeled frames within the same video. IFR essentially utilizes the content-relevance characteristic of video data and achieve a promising improvement. + +In general, existing methods focus on designing supervision signals for unlabeled data and improving feature extraction, as shown in Figure 1. However, another critical component is ignored, i.e., the classifier. Since video segmentation is derived from image segmentation, the final recognition process is naturally inherited in a per-frame manner. Specifically, after extracting the feature sequence for a video, the classifier is independently adopted on the features of each frame for recognition. However, we found that per-frame classification is quite different from human's recognition procedure, as shown in Figure 2. Specifically, when receiving a video stream, the recognition of the first frame is identical to image recognition. Since no prior information can be used, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. After that, the situation becomes different. The distinguished objects and semantic concepts of historical frames are not immediately forgotten, but stored in the memory as context semantic concepts in a short period of time. Therefore, when recognizing the current frame, human would wisely retrieve both global concepts and updated context concepts. This is fundamentally different from per-frame classification. Actually, this temporally-dependent recognition procedure essentially utilizes the content relevance characteristic of video data. + +Inspired by human's manner, we propose to design a novel temporal-dependent classifier (TDC), which is more suitable for video perception. Specifically, TDC contains two types of prototypes, i.e., global and context prototypes. The former learns global semantic concepts during model training and fixed during inference, which is identical to the conventional classifier. Differently, the context prototypes are calculated on-the-fly based on the last processed frame. When recognizing the current frame, two types of prototypes are collaborated together to calculate similarity with the extracted feature. In this way, the distinguished context concepts from historical frames can assist the classification. + +From experimental results, we surprisingly found that TDC can achieve significant performance improvement by equipping a simple pseudo label supervision [11] in semi- + +![](images/5222d701efdf88302edf69a6cb4d93d7900c66e9ca91400a00203d76c9573e6e.jpg) +Figure 2. Illustration of human-like recognition procedure. When recognizing image data, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. When recognizing the current frame of video data, besides global concepts, human would also retrieve distinguished objects from historical frames as temporal contexts. + +supervised video segmentation task. The primary cause is that the temporal-dependent recognition paradigm implicitly imposes a temporal consistency constraint. Specifically, TDC actually requires the context prototypes calculated from historical frames to accurately represent the content of the current frame. In this way, the feature extractor would be guided to learn a group of temporally-consistent semantic concepts across frames, which indirectly introduces the content-relevance prior into the feature extraction procedure. This guidance effectively optimizes model training on unlabeled data and improve generalization ability. + +We experimentally evaluate the proposed method on the Cityscapes and CamVid datasets. The results validate the effectiveness of TDC, and it can bring a significant improvement for mainstream video semantic segmentation methods. The contributions of this work are summarized as follows. + +- We find that the commonly adopted per-frame classification paradigm is quite different from human's manner and sub-optimal for video perception task, which is ignored in previous studies. + +- We propose a novel temporal-dependent classifier (TDC) for semi-supervised video segmentation, which can implicitly impose a temporal consistency constraint for unsupervised learning. TDC essentially utilizes the internal relevance of different frames within a video. +- We experimentally evaluate the effectiveness of our proposed methods, and the results on Cityscapes and CamVid demonstrate the superiority of our method to previous state-of-the-art methods. + +# 2. Related Work + +# 2.1. Image Semantic Segmentation + +Image semantic segmentation aims to assign a class label to every pixel in an image, which is a fundamental yet rather challenging task. Modern deep learning methods for semantic segmentation are mainly based on fully convolutional network (FCN) [25]. To further enhance segmentation results, the dilation convolution [2], pyramid pooling [37], attention mechanism [12, 17, 38], gating mechanism [7, 13, 22], and high-resolution architecture design [34] are proposed to model object relationships and aggregate context information. Recently, some transformer-based models [5, 24, 35] are proposed and exhibit promising performance. Despite the success of these models, they are often impeded in practical deployment due to requiring sufficient pixel-wise annotations for learning. + +# 2.2. Video Semantic Segmentation + +Video semantic segmentation aims to predict pixel-level semantics for each video frame. Different from static images, videos embody rich temporal information that can be exploited to improve segmentation performance. DFF [39] firstly proposes feature propagation to reuse key frame features under the guidance of estimated optical flows, which reduces the average computational cost. Inspired by DFF, Accel [19] proposes an adaptive fusion policy to effectively integrate the predictions from the key and current frames. DAVSS [41] proposes to correct the distorted features caused by inaccurate optical flow when propagating features. Besides the feature propagation paradigm, some recent works propose to improve the performance of lightweight models with temporal constraints [8, 23] and attention mechanism [16, 32, 33]. + +# 2.3. Semi-supervised Semantic Segmentation + +To achieve good representation learning with limited annotations, semi-supervised image segmentation (SSIS) is studied by exploring unlabeled data. Existing methods can be roughly divided into three families. The adversarial based methods, e.g., AdvSemiSeg [18] and S4GAN [26], utilize a discriminator to distinguish the confidence maps from labeled and unlabeled data predictions. The consistency + +based methods enforce the consistency of the predictions or intermediate features with various perturbations. The perturbations can be conducted on input images, e.g., CutMix [11], ClassMix [27], and CAC [21], and feature space, e.g., CCT [28]. The self-learning based methods generate pseudo segmentation maps on unlabeled data. [3, 14, 36] propose to generate pseudo labels in an offline manner and retrain the model iteratively. While PseudoSeg [43] and CPS [4] follow the FixMatch [31] scheme and design an online pseudo labeling mechanism. + +However, SSIS methods are not designed for video data, which only regards videos as a collection of independent images. To tackle this issue, IFR [42] proposed to reconstruct feature on the labeled frame by that on other frames, which can provide accurate supervision signals from the single label for unlabeled frames. IFR essentially utilizes the content-relevance characteristic of video data. + +Generally, existing methods mainly focus on supervision signal construction and improving feature extraction. Differently, in this work, we concentrate on the classifier design. We find that the per-frame recognition paradigm used in previous works is different from human's manner and thus propose a temporal-dependent classifier. + +# 3. Method + +# 3.1. Overview + +Following IFR [42], in semi-supervised video segmentation task, we are provided with a small set of labeled videos with one frame annotated and a larger set of unlabeled videos. Let $V = \{x_{1},\dots ,x_{T}\}$ represents $T$ frames in a video with $x_{i}$ as the $i^{th}$ frame with spatial resolution of $H\times W$ . Let $\mathcal{D}_L = \{(V_1^L,\hat{x}_1,y_1),\dots ,(V_{n_L}^L,\hat{x}_{n_L},y_{n_L})\}$ represent the $n_L$ labeled videos, where $\hat{x}_i$ is the annotated frame of the $i^{th}$ video, $y_{i}\in \mathbb{R}^{C\times H\times W}$ corresponds to the pixel-level one-hot label, and $C$ is the number of classes. Let $\mathcal{D}_U = \{V_1^U,\dots ,V_{n_U}^U\}$ represents the $n_U$ unlabeled videos. Besides, another set of labeled videos $\mathcal{D}_V = \{(\mathcal{V}_1^V,\hat{x}_1,y_1),\dots ,(\mathcal{V}_{n_V}^V,\hat{x}_{n_V},y_{n_V})\}$ is used for performance evaluation. + +As shown in Figure 3, our framework consists of three components, i.e., a feature extractor $\mathsf{Net}_B$ , a conventional classifier $\mathsf{Net}_C$ and the proposed temporal-dependent classifier $\mathsf{Net}_{TDC}$ . Two adopted classifiers are used in supervised and unsupervised learning branches, respectively. The reason for retaining the conventional classifier is to keep consistent with existing works [4, 11, 21, 28, 42] for fair comparison. In this way, the effectiveness of our TDC for optimizing unsupervised learning can be clearly revealed. + +Our work aims to learn a segmentation model from $\mathcal{D}_L$ and $\mathcal{D}_U$ , and generalize to $\mathcal{D}_V$ . Following previous works, the objective of semi-supervised learning can generally be summarized as two loss functions. The first one is a regular + +![](images/5f65289b7014fe92c48943a8307ab8f36535176d818784f51e31f3974e1e5468.jpg) +Figure 3. Illustration of our SSVS framework. Our framework consists of two learning branches. For supervised learning, we randomly sample an image $I$ and its corresponding ground-truth $GT$ for model training. For unsupervised learning, we randomly sample a video clip with several consecutive frames $V^U$ . Following the previous work [11], we calculate pseudo labels $PL^U$ for $V^U$ , which is used as supervision signals for predictions $P_S^U$ from the augmented video $V_S^U$ . + +cross-entropy loss on the labeled data: + +$$ +P = \operatorname {N e t} _ {C} (\operatorname {N e t} _ {B} (I)), \tag {1} +$$ + +$$ +L _ {s u p} = \text {C r o s s E n t r o p y} (P, G T), \tag {2} +$$ + +where image $I$ and its corresponding ground-truth $GT$ are randomly sampled from $D_{L}$ . The second loss aims to train model on unlabeled data with some constructed supervision signals, which is denoted by $L_{unsup}$ . In our framework, we adopt a simple pseudo label strategy similar to FixMatch [11, 31] scheme: + +$$ +V _ {S} ^ {U} = T _ {s} \left(V ^ {U}\right), \tag {3} +$$ + +$$ +P _ {S} ^ {U} = \operatorname {N e t} _ {T D C} \left(\operatorname {N e t} _ {B} \left(V _ {S} ^ {U}\right)\right), \tag {4} +$$ + +$$ +P L ^ {U} = \operatorname {a r g m a x} \left(\operatorname {N e t} _ {C} \left(\operatorname {N e t} _ {B} \left(V ^ {U}\right)\right)\right), \tag {5} +$$ + +$$ +L _ {u n s u p} = \text {C r o s s E n t r o p y} \left(P _ {S} ^ {U}, P L ^ {U}\right), \tag {6} +$$ + +where $V^{U}$ is randomly sampled from $D_{U}$ and $T_{s}$ represents the strong data augmentation like color jitter. Specifically, we calculate per-frame pseudo labels $PL^{U}$ for $V^{U}$ , which is used as supervision signals for predictions $P_{S}^{U}$ from the augmented video $V_{S}^{U}$ . Then the overall training objective can be presented as follows + +$$ +L = L _ {s u p} + \lambda L _ {u n s u p}, \tag {7} +$$ + +where $\lambda$ is a trade-off parameter. + +# 3.2. Conventional Classifier + +To make it clear, we first elaborate on the process of conventional classifier, and then explain the core mechanism of our TDC. + +A conventional classifier typically consists of a fully connected layer and a softmax layer. We use $\mathbf{w}_i\in \mathbb{R}^n$ to denote the weight parameters for category $i$ in the fully connected layer and use $\mathsf{f}\in \mathbb{R}^n$ to denote the feature for classification. Guided by the cross-entropy loss, the classifier is encouraged to produce a larger inner product between $\mathsf{f}$ and $\mathsf{w}_y$ , where $y$ is the corresponding ground-truth category. After model training, the learned weight parameters would automatically align with the feature cluster centers, which is experimentally verified and visualized in previous works [9, 30]. Here, the cluster center is the mean of features belonging to the same category, which is usually denoted as prototype. + +This tight relationship among features, prototypes and weight parameters is the basic of our TDC, which provides a solution for utilizing distinguished semantic concepts to aid recognition. + +# 3.3. Temporal-dependent Classifier + +In this work, we mainly focus on designing a classifier to mimic the temporal-dependent recognition paradigm on video data like human's manner. To this end, we optimize conventional classifier by introducing distinguished results from historical frames and then propose a novel classifier, i.e., the temporal-dependent classifier (TDC). + +# 3.3.1 Prototypes Construction + +As shown in Figure 4, when recognizing $t + 1^{th}$ frame, TDC would simultaneously utilize two types of prototypes, i.e., global prototypes $PT^G$ and context prototypes $PT_t^C$ that calculated based on the prediction of $t^{th}$ frame. Here, similar to the conventional classifier, $PT^G = \{\mathbf{w}_i \in \mathbb{R}^n | i = 0, 1, \dots, C - 1\}$ is implemented as a set of learnable weight parameters, where $C$ is the number of classes and $n$ is the feature dimension. $PT^G$ is updated by back-propagation during training and keeps fixed during inference. The key + +![](images/eebb6cbe92988fa70f19bfd22ac68c9a78d37465e39d5432aa5920770efe420f.jpg) +Figure 4. Illustration of temporal-dependent recognition procedure. The critical process is the update of context prototypes $PT^C$ based on the last frame prediction. In the classifier, context prototypes $PT^C$ and global prototypes $PT^G$ are utilized together for recognition. + +of TDC is the design of context prototypes, which is calculated on-the-fly based on the prediction of last frame. Here, $PT_{t}^{C} = \{\mathsf{w}_{k}^{c}\in \mathbb{R}^{n}|k = 0,1,\dots ,K - 1\}$ represents $K$ prototypes calculated from the $t^{\text{th}}$ frame. Specifically, we calculate the pseudo label $PL_{t}$ of the extracted feature $F_{t}$ of the $t^{\text{th}}$ frame as + +$$ +P L _ {t} = \operatorname {a r g m a x} \left(\operatorname {N e t} _ {C} \left(F _ {t}\right)\right). \tag {8} +$$ + +Then, we group the pixel-wise features in $F_{t}$ belonging to the same class $k$ according to $PL_{t}$ , i.e., + +$$ +\mathbf {w} _ {k} ^ {c} = \frac {\sum_ {i} F _ {t} ^ {(i)} * \mathbb {1} \left(P L _ {t} ^ {(i , k)} = = 1\right)}{\sum_ {i} \mathbb {1} \left(P L _ {t} ^ {(i , k)} = = 1\right)}, \tag {9} +$$ + +where $\mathbb{1}$ is an indicator function and $PL_{t}^{(i,k)}$ represents the one-hot pseudo label of pixel $i$ belonging to the $k^{th}$ class. In this way, context prototypes would be adaptively updated based on the last frame prediction. + +# 3.3.2 Recognition Procedure + +After constructing the global and context prototypes, here we introduce how to conduct recognition based on theses prototypes. The core process of recognition is to calculate similarity between the input feature and prototypes with known categories. After that, the category corresponding to the prototype that generates the maximum similarity will be regarded as the semantic prediction. Therefore, a naive solution is to calculate similarity with global and context prototypes simultaneously. + +However, the input feature would naturally be similar to context prototypes since they are calculated from consecutive frames and thus global prototypes are always ignored, especially in the early stage of model training. This shortcut behavior would make the model only learning to capture + +similarity across frames and not being able to learn semantic concepts on unlabeled data. The cause of this issue is that two types of prototypes are updated in different mechanism and contains diverse statistical distribution like magnitudes. Therefore, we first conduct normalization on each prototype and the input feature respectively before classification, which can effectively narrow their the distribution discrepancy and achieve a fair learning process. Thus, the predicted probability of the $i^{th}$ category is computed as follows: + +$$ +p _ {i} = \frac {e ^ {\eta \cdot \langle \overline {{P T}} _ {i} , \overline {{F}} _ {t} \rangle}}{\sum_ {j} e ^ {\eta \cdot \langle \overline {{P T}} _ {j} , \overline {{F}} _ {t} \rangle}}, \tag {10} +$$ + +where $\overline{v} = v / ||v||_2$ denotes the L2 normalized vector, and $\langle \overline{v}_1,\overline{v}_2\rangle = \overline{v}_1^T\overline{v}_2$ measures the cosine similarity between two normalized vectors. Here, $PT = \{PT^{G},PT_{t}^{C}\}$ is the combination of two types of prototypes. Inspired by a previous work [15], since the range of $\langle \overline{v}_1,\overline{v}_2\rangle$ is restricted to $[-1,1]$ , a learnable scalar $\eta$ is introduced to control the peakiness of softmax distribution. Differently, we set two independent scalars, i.e., $\eta_G$ and $\eta_C$ , for global prototypes $PT^{G}$ and context prototypes $PT_{t}^{C}$ respectively. + +# 3.3.3 Joint-prototypes Label Relaxation + +After calculating the probability of input feature based on constructed prototypes, a cross-entropy loss is applied according to a pseudo label, as described in Section 3.1. However, there is a mismatch between the probability vector $p \in \mathbb{R}^{C + K}$ and the one-hot label $y \in \mathbb{R}^C$ , where $C$ and $K$ are the number of categories and prototypes predicted in the last frame. Intuitively, for a specific category $i$ , its corresponding context prototype $PT_{t,i}^{C}$ and global prototype $PT_{i}^{G}$ are different descriptions for an identical semantic concept. Therefore, for a feature belonging to category $i$ , it should not be penalized by loss function regardless of which prototype it is more similar to. + +Based on this consideration, we propose a joint-prototypes label relaxation, which is also inspired by a previous work [40]. Suppose we are classifying a feature belonging to class $i$ and class $i$ is related to two prototypes $PT_{i}^{G}$ and $PT_{t,i}^{C}$ . To achieve label relaxation, we propose to maximize the likelihood of both prototypes together instead of any single one. Since two prototypes are mutually exclusive in cross-entropy loss, we aim to maximize the union of them: + +$$ +P \left(P T _ {i} ^ {G} \cup P T _ {t, i} ^ {C}\right) = P \left(P T _ {i} ^ {G}\right) + P \left(P T _ {t, i} ^ {C}\right), \tag {11} +$$ + +where $P$ is the softmax probability of each prototype. Therefore, for each pixel $i$ in the $t^{th}$ frame in the video clip, the loss function is as follows: + +$$ +L _ {T D C} = \frac {1}{H * W} \frac {1}{T} \sum_ {i} ^ {H * W} \sum_ {t} ^ {T} L _ {T D C} (i, t), \tag {12} +$$ + +![](images/5154cd7e06660700d27f1d3b903fa0071b511d29843ee09789be5764376ee0cd.jpg) + +![](images/5888fae6173ac548fbcb3d23d24316229324f8849dd0b3f82ffb2c61326d057f.jpg) +Figure 5. Illustration of bidirectional prediction. We simultaneously considering forward $(t\to t + 1)$ and backward $(t + 1\rightarrow t)$ directions when constructing context prototypes. + +$$ +L _ {T D C} (i, t) = - \log P \left(P T _ {y _ {i, t}} ^ {G} \cup \mathcal {X} \left(P T _ {t - 1, y _ {i, t}} ^ {C}\right)\right), \tag {13} +$$ + +$$ +\mathcal {X} (x) = \left\{ \begin{array}{l l} x, & \text {i f} x \text {e x i s t s} \\ 0, & \text {e l s e} \end{array} \right. \tag {14} +$$ + +To be noticed, when recognizing the first frame, only global prototypes are adopted since context prototypes has not been constructed. This is reasonable and similar to human's manner. When obtaining the first frame of a video, human can only conduct image recognition by recalling learned experience, i.e., global prototypes, since there is no prior information about this video. + +# 3.3.4 Bidirectional Constraint + +Actually, TDC works in a RNN-like manner, where the output from the previous step can affect the prediction on the current step. In TDC, the continuously updated prototypes serve like the hidden state vectors in RNN structure. According to successfully practices [20, 29] in NLP field, comparing to unidirectional RNN, bidirectional RNN can help the model to better exploit contextual information and effectively improve the model performance. + +Therefore, in this work, we further propose a bidirectional constraint, i.e., simultaneously considering forward $(t\to t + 1)$ and backward $(t + 1\rightarrow t)$ directions, as shown in Figure 5. Specifically, context prototypes are calculated based on the $t + 1^{th}$ frame to aid the current frame recognition: + +$$ +L _ {B i - T D C} = \frac {1}{H * W} \frac {1}{T} \sum_ {i} ^ {H * W} \sum_ {t} ^ {T} L _ {B i - T D C} (i, t), \tag {15} +$$ + +$$ +L _ {B i - T D C} (i, t) = - \log P \left(P T _ {y _ {i, t}} ^ {G} \cup \mathcal {X} \left(P T _ {t + 1, y _ {i, t}} ^ {C}\right)\right). \tag {16} +$$ + +Actually, the primary cause behind the effectiveness of TDC on semi-supervised learning is that TDC can implicitly impose a temporal consistency constraint across frames. Intuitively, the bidirectional calculation can further enhance the constraint by simultaneously considering both forward and backward consistency. Finally, in this work, the adopted unsupervised learning loss is as follows: + +$$ +L _ {u n s u p} = L _ {T D C} + L _ {B i - T D C}. \tag {17} +$$ + +# 4. Experiments + +# 4.1. Dataset + +Cityscapes [6] is a representative dataset in semantic segmentation and autonomous driving domain. It focuses on semantic understanding to urban street scenes. The training and validation subsets contain 2,975 and 500 videos, respectively, and each video contains 30 frames at a resolution of $1024 \times 2048$ . The $20^{th}$ frame in each is annotated by pixel-level semantic labels with 19 categories. + +CamVid [1] also focuses on the semantic understanding to urban street scenes, but it contains less data than Cityscapes. It has four driving videos and each video contains frames ranging from 3,600 to 11,000 at a resolution of $720 \times 960$ . Every $30^{th}$ frame of videos is annotated with 11 semantic classes, which results in a total of 701 samples. Similar to Cityscapes, we split videos into 701 videos and each video contains 30 frames. All videos are divided into the trainval set with 468 videos and test set with 233 videos. + +We follow the partition protocols of IFR [42] and divide the whole training set via randomly sub-sampling $1/2$ , $1/4$ , $1/8$ , $1/16$ , and $1/30$ of all training videos, i.e., 2975 videos in Cityscapes and 468 videos in CamVid, as the labeled set and regard the remaining videos as the unlabeled set. Following previous work [11, 18, 26-28, 42], we apply bilinear interpolation to resize every video frame in Cityscapes and CamVid to $512 * 1024$ and $360 * 480$ for the efficiency of training and inference. + +# 4.2. Implementation Details + +Following IFR [42], we adopt Accel [19] as video semantic segmentation architecture due to its good performance. It consists of two segmentation branches, i.e., a heavy reference branch and a light-weight update branch, an optical flow network, and a score fusion layer. Similar to IFR, we adopt semi-supervised methods for two segmentation branches to improve representation learning with limited annotations. The segmentation model is trained using a SGD optimizer with a momentum of 0.9 and a weight decay of $10^{-4}$ . The learning rate is set at $10^{-3}$ for the backbone parameters and $10^{-2}$ for others, which is annealed following the poly learning rate policy. + +We evaluate the segmentation performance on the validation videos, i.e., validation subset in Cityscapes and test + +
Method1/30 (100)1/16 (186)1/8 (372)1/4 (744)1/2 (1488)
Accel45.7352.1057.1260.5562.83
+CCT [28]48.05 (+2.32)53.25 (+1.15)58.88 (+1.76)62.00 (+1.45)64.02 (+1.19)
+CAC [21]48.83 (+3.10)54.56 (+2.46)58.55 (+1.43)62.78 (+2.23)63.87 (+1.04)
+ CPS [4]48.97 (+3.24)54.69 (+2.59)58.97 (+1.85)62.43 (+1.88)63.74 (+0.91)
+ IFR [42]52.86 (+7.13)56.39 (+4.29)60.08 (+2.96)63.45 (+2.90)64.53 (+1.70)
+ Ours55.81 (+10.08)60.97 (+8.87)63.12 (+6.00)65.83 (+5.28)66.67 (+3.84)
+ +Table 1. Comparison with state-of-the-art methods on the Cityscapes validation subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data. + +
Method1/30 (15)1/16 (29)1/8 (58)1/4 (117)1/2 (234)
Accel42.3747.5750.7856.4059.37
+CCT [28]47.09 (+4.72)52.45 (+4.88)54.50 (+3.72)58.69 (+2.29)61.58 (+2.21)
+CAC [21]46.85 (+4.48)52.16 (+4.59)54.03 (+3.25)59.67 (+3.27)63.17 (+3.80)
+CPS [4]46.05 (+3.68)52.04 (+4.47)55.30 (+4.52)59.02 (+2.62)62.49 (+3.12)
+IFR [42]49.50 (+7.13)53.71 (+6.14)57.37 (+6.59)61.27 (+4.87)63.86 (+4.49)
+Ours50.95 (+8.58)55.36 (+7.79)59.88 (+9.10)62.63 (+6.23)64.59 (+5.22)
+ +set in CamVid. Following Accel, for each test video, we conduct the reference branch on a selected key frame and update branch on the annotated frame. The segmentation results are predicted via the feature propagation and score fusion. To be notice, for fair comparison, we adopt the conventional classifier for semantic prediction while TDC is only involved in the training period, since in this work we mainly investigate the effectiveness of TDC on representation learning. We evaluate different methods with mean Intersection-over-Union (mIoU) as metric. The key frame interval is set as 5 throughout the experiments. For our TDC, there is a trade-off parameter $\lambda$ in Eq. 7, which is set $\lambda = 0.2$ for all experiments. + +# 4.3. Performance Comparison + +To demonstrate the superiority of our method, we make a comparison with recent state-of-the-art methods, i.e., three SSIS methods including CCT [28], CAC [21] and CPS [4], and a SSVS method IFR [42]. Following IFR, for fair comparison, all critical components are keep consistent among different methods, including base segmentation model, data splits, data augmentation and training settings (i.e., optimizer and hyperparameters). In this way, we can fairly compare the improvement brought by different methods on the basis of the same supervised learning baseline. + +The comparison on Cityscapes and CamVid is shown in Table 1 and Table 2. From the results, we have the following two observations. First, our TDC can bring significant improvement under all partition protocols comparing to the supervised learning baseline. A larger gain is achieved for the cases with less labeled data, e.g., $10.08\%$ mIoU gain with + +Table 2. Comparison with state-of-the-art methods on the CamVid test subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data. + +
LsupLTDCLBi-TDCmIoU (%)
PTGPTCt
✓43.68
✓✓46.78 (+3.10)
✓✓✓50.14 (+6.46)
✓✓✓✓51.29 (+7.61)
+ +Table 3. Ablation study on our proposed components. Each component can bring performance improvement compared to the baseline, and their combination performs best. + +100 samples in Cityscapes. Such experimental results well verify that TDC can effectively improve the generalization of models. Second, our method surpasses other state-of-the-art methods by a large margin. For example, it outperforms IFR by $4.58\%$ under 1/16 partition protocol on Cityscapes and $2.51\%$ under 1/8 partition protocol on CamVid, respectively. It shows that TDC can better utilize the unlabeled video data for training model. + +# 4.4. Ablation Study + +In this subsection, we conduct experiments to reveal the effectiveness of our proposed method. All experiments are particularly conducted with 1/30 labeled data on Cityscapes. For efficient training, we adopt PSPNet with ResNet18 as the segmentation network by default. + +Effect of Components. To reveal the contribution of our proposed components, i.e., global prototypes $PT^G$ , context prototypes $PT_t^C$ and bidirectional constraint $L_{Bi-TDC}$ , we conduct an extensive study by evaluating their combina + +
λ0.00.050.10.20.51.0
mIoU (%)43.6846.8749.6251.2950.7448.54
+ +Table 4. Effect of trade-off parameter $\lambda$ . Based on the results, we set $\lambda = 0.2$ for all experiments. + +
T01235710
mIoU (%)43.6846.8749.2450.1851.2950.9350.64
+ +tions, and the results are shown in Table 3. It can be seen that each component can bring performance improvement compared with the baseline. In particular, based on the supervised learning baseline, TDC equipped with only global prototypes serves like a pseudo-label scheme similar to previous works [4, 43]. After introducing context prototypes, TDC can obtain significant improvement. Finally, TDC performs best with bidirectional constraint. + +Effect of Trade-off Parameter $\lambda$ . We investigate the influence of trade-off parameter $\lambda$ used to control the unsupervised learning loss in Eq 7, as shown in Table 4. Here, $\lambda = 0.0$ represents the supervised learning baseline. The results show that: with the increase of $\lambda$ , the unsupervised loss help model training on unlabeled data and effectively overcome the overfitting issue due to limited labeled training data, which performs best when $\lambda = 0.2$ . When $\lambda$ continuously increases, the performance degrades since the supervised learning branch is interfered. Therefore, based on the results, we set $\lambda = 0.2$ for all experiments. + +Effect of the Number of frames. In our framework, we randomly sample a unlabeled video clip with $T$ frames for unsupervised learning. Here, we investigate the influence of number of frames, which relates to the temporal modeling in our proposed TDC. Table 5 shows the results. Here, $T = 0$ represents the supervised learning baseline and $T = 1$ represents using TDC with only global prototypes. From the results we can see that: as $T$ increases, TDC can impose a stronger temporal consistency constraint and improve model training on unlabeled video data. However, if $T$ gets too large, TDC would suffer from training instability and lead to a slight performance degradation. Therefore, based on the results, we set $T = 5$ for all experiments. + +Performance with Different VSS Architectures. To study the generalization ability of our method, We apply it to different video semantic segmentation architectures. We particularly adopt three widely adopted video segmentation architectures, i.e., DFF [39], Accel [19] and DAVSS [41]. As shown in Table 6, our proposed method can bring significant performance improvement consistently. + +Table 5. Effect of Number of frames. Based on the results, we sample 5 frames per unlabeled video clip for all experiments. + +
MethodBaseline+IFR+ Ours
DFF [39]44.1949.97 (+5.78)52.63 (+8.44)
Accel [19]45.7352.86 (+7.13)55.81 (+10.08)
DAVSS [41]46.5151.97 (+5.46)55.25 (+8.74)
+ +Table 6. Performance on different VSS architectures. Our method can bring significant improvement for different video semantic segmentation architectures consistently. + +
MethodAccel+ CCT+ CAC+ CPS+ IFR+ Ours
TC (%)70.0471.4371.4770.7473.8875.38
+ +Table 7. Comparison on Temporal Consistency. We evaluate different methods with temporal consistency (TC) score [23]. Our proposed method can bring a significantly improvement. + +Effectiveness on Temporal Consistency. It is important for VSS methods to produce temporally stable predictions. Thus, we further verify the effectiveness of our method on improving temporal consistency. Particularly, we follow previous works [23, 42] and adopt temporal consistency (TC) score as the evaluation metric. As shown in Table 7, our method can bring a significant improvement, since consistent predictions among different frames can be achieved. + +# 5. Conclusion + +In this paper, we focus on the semi-supervised video semantic segmentation problem, and propose a novel temporal-dependent classifier (TDC). Motivated by the observation of human's behavior, TDC is designed to utilize distinguished semantic concepts of historical frames when recognizing the current frame, which is more suitable for video data. We found that TDC can achieve significant performance improvement in semi-supervised learning since its recognition mechanism implicitly imposes a temporal-consistency constraint across frame, which is valuable especially in labelscarcce scenarios. To further enhance the effect of TDC, we propose a bidirectional constraint by simultaneously considering both forward and backward calculation. Extensive experiments on Cityscapes and CamVid validated the effectiveness of our method, which outperforms previous state-of-the-art methods. + +# Acknowledge + +This work is supported in part by the National Key R&D Program of China (grant numbers 2021ZD0111501, 2021ZD0111502), the National Natural Science Foundation of China (grant number 62176246), the Anhui Province Key Research and Development Plan (grant number 202304a05020045), and the STU Scientific Research Foundation for Talents (grant number NTF22030). + +# References + +[1] Gabriel J Brostow, Julien Fauqueur, and Roberto Cipolla. Semantic object classes in video: A high-definition ground truth database. Pattern Recognition Letters, 2009. 6 +[2] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 1, 3, 8 \ No newline at end of file diff --git a/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/images.zip b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..0519e4bac701515813989bffc5630fca65142f64 --- /dev/null +++ b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7b2ac0760222768e01096bb76c4aa463aad1d3c4dd33ab5d8f0598c7b9cf7def +size 480807 diff --git a/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/layout.json b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..df1151ef9d8295c6a3a0272f440e10ea5156ac85 --- /dev/null +++ b/2024/Infer from What You Have Seen Before_ Temporally-dependent Classifier for Semi-supervised Video Segmentation/layout.json @@ -0,0 +1,9596 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 69, + 103, + 525, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 103, + 525, + 140 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 525, + 140 + ], + "type": "text", + "content": "Infer from What You Have Seen Before: Temporally-dependent Classifier for Semi-supervised Video Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 161, + 165, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 161, + 165, + 204 + ], + "spans": [ + { + "bbox": [ + 61, + 161, + 165, + 204 + ], + "type": "text", + "content": "Jiafan Zhuang Shantou University jfzhuang@stu.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 187, + 161, + 416, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 161, + 416, + 204 + ], + "spans": [ + { + "bbox": [ + 187, + 161, + 416, + 204 + ], + "type": "text", + "content": "Zilei Wang* Yixin Zhang \nUniversity of Science and Technology of China \n{zlwang, zhyx12}@ustc.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 439, + 161, + 534, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 439, + 161, + 534, + 203 + ], + "spans": [ + { + "bbox": [ + 439, + 161, + 534, + 203 + ], + "type": "text", + "content": "Zhun Fan Shantou University zfan@stu.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 256, + 290, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 290, + 555 + ], + "type": "text", + "content": "Due to high expense of human labor, one major challenge for semantic segmentation in real-world scenarios is the lack of sufficient pixel-level labels, which is more serious when processing video data. To exploit unlabeled data for model training, semi-supervised learning methods attempt to construct pseudo labels or various auxiliary constraints as supervision signals. However, most of them just process video data as a set of independent images in a per-frame manner. The rich temporal relationships are ignored, which can serve as valuable clues for representation learning. Besides, this per-frame recognition paradigm is quite different from that of humans. Actually, benefited from the internal temporal relevance of video data, human would wisely use the distinguished semantic concepts in historical frames to aid the recognition of the current frame. Motivated by this observation, we propose a novel temporally-dependent classifier (TDC) to mimic the human-like recognition procedure. Comparing to the conventional classifier, TDC can guide the model to learn a group of temporally-consistent semantic concepts across frames, which essentially provides an implicit and effective constraint. We conduct extensive experiments on Cityscapes and CamVid, and the results demonstrate the superiority of our proposed method to previous state-of-the-art methods. The code is available at https://github.com/jfzhuang/TDC." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 598, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 682 + ], + "type": "text", + "content": "As a fundamental tool, semantic segmentation has profited many downstream applications, and deep learning further boosts this area with remarkable progress. However, training a promising segmentation network relies on sufficient finely annotated data. And pixel-wise labeling is time-consuming, e.g., the annotation process costs more than 1.5 hours on average for a single image in Cityscapes [6]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 683, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 683, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 59, + 683, + 287, + 694 + ], + "type": "text", + "content": "In real-world scenarios, we can usually collect unlabeled" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 319, + 230, + 533, + 275 + ], + "blocks": [ + { + "bbox": [ + 319, + 230, + 533, + 275 + ], + "lines": [ + { + "bbox": [ + 319, + 230, + 533, + 275 + ], + "spans": [ + { + "bbox": [ + 319, + 230, + 533, + 275 + ], + "type": "image", + "image_path": "05b2067f4f3aa1df644374ba58d9ef0d650526b5cfb89b95a04dd87b4f4c6945.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 277, + 456, + 285 + ], + "lines": [ + { + "bbox": [ + 397, + 277, + 456, + 285 + ], + "spans": [ + { + "bbox": [ + 397, + 277, + 456, + 285 + ], + "type": "text", + "content": "(a) SSIS Methods" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 320, + 287, + 533, + 343 + ], + "blocks": [ + { + "bbox": [ + 320, + 287, + 533, + 343 + ], + "lines": [ + { + "bbox": [ + 320, + 287, + 533, + 343 + ], + "spans": [ + { + "bbox": [ + 320, + 287, + 533, + 343 + ], + "type": "image", + "image_path": "cbb4157b08d6125ea4bcf9f5284aec7b36f61ac1d42c634383b63a2849967adf.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 320, + 354, + 533, + 413 + ], + "blocks": [ + { + "bbox": [ + 413, + 345, + 439, + 354 + ], + "lines": [ + { + "bbox": [ + 413, + 345, + 439, + 354 + ], + "spans": [ + { + "bbox": [ + 413, + 345, + 439, + 354 + ], + "type": "text", + "content": "(b) IFR" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 320, + 354, + 533, + 413 + ], + "lines": [ + { + "bbox": [ + 320, + 354, + 533, + 413 + ], + "spans": [ + { + "bbox": [ + 320, + 354, + 533, + 413 + ], + "type": "image", + "image_path": "9fbc1fdbe26251796d8befe5279bae60d68733882dd8eea0543468c0cb0ce350.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 413, + 413, + 440, + 422 + ], + "lines": [ + { + "bbox": [ + 413, + 413, + 440, + 422 + ], + "spans": [ + { + "bbox": [ + 413, + 413, + 440, + 422 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 427, + 457, + 435 + ], + "lines": [ + { + "bbox": [ + 427, + 427, + 457, + 435 + ], + "spans": [ + { + "bbox": [ + 427, + 427, + 457, + 435 + ], + "type": "text", + "content": "Classifier" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 332, + 422, + 349, + 439 + ], + "blocks": [ + { + "bbox": [ + 332, + 422, + 349, + 439 + ], + "lines": [ + { + "bbox": [ + 332, + 422, + 349, + 439 + ], + "spans": [ + { + "bbox": [ + 332, + 422, + 349, + 439 + ], + "type": "image", + "image_path": "a28ab5e76c07907b68355d5dc662348930e9adc0c69d1a3aa19065c40f060a04.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 427, + 405, + 434 + ], + "lines": [ + { + "bbox": [ + 353, + 427, + 405, + 434 + ], + "spans": [ + { + "bbox": [ + 353, + 427, + 405, + 434 + ], + "type": "text", + "content": "Feature Extractor" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 453, + 545, + 519 + ], + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 519 + ], + "type": "text", + "content": "Figure 1. Comparison between previous methods and ours. To exploit unlabeled frames, SSIS methods attempted to construct different supervision signals. IFR [42] proposed to optimize feature extractor by inter-frame feature reconstruction. Differently, in this work, we propose to improve the recognition procedure by designing a temporal-dependent classifier." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "type": "text", + "content": "data conveniently and economically, especially video data. Therefore, to alleviate the label-hungry problem, a growing attention is drawn on semi-supervised learning to take advantage of unlabeled data to aid model training. Besides regular supervised learning on limited labeled images, semi-supervised image segmentation (SSIS) methods proposed to construct extra supervision signals for unlabeled images, e.g., consistency constraint [21, 28] and pseudo label [4, 43]. It is shown that they can bring considerable performance improvement on the challenging datasets, e.g., PASCAL VOC [10] and Cityscapes [6]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "content": "However, when unlabeled data is scaled up by adding video data, SSIS methods can not obtain further improvement [42]. The primary reason is the homogenization of video data, i.e., the contents of different frames within a" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3575" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "video are often similar, which contributes less information increment. Since SSIS methods are designed for image data and do not consider for video characteristics, they just regard videos as a set of independent images and thus fail to exploit unlabeled video data. To tackle this issue, as the first semi-supervised video segmentation (SSVS) method, IFR [42] proposed to optimize the feature extractor by interframe feature reconstruction. Specifically, by reconstructing the representation on labeled frame by features from other frames, the single label can indirectly provide accurate supervision for unlabeled frames within the same video. IFR essentially utilizes the content-relevance characteristic of video data and achieve a promising improvement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 529 + ], + "type": "text", + "content": "In general, existing methods focus on designing supervision signals for unlabeled data and improving feature extraction, as shown in Figure 1. However, another critical component is ignored, i.e., the classifier. Since video segmentation is derived from image segmentation, the final recognition process is naturally inherited in a per-frame manner. Specifically, after extracting the feature sequence for a video, the classifier is independently adopted on the features of each frame for recognition. However, we found that per-frame classification is quite different from human's recognition procedure, as shown in Figure 2. Specifically, when receiving a video stream, the recognition of the first frame is identical to image recognition. Since no prior information can be used, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. After that, the situation becomes different. The distinguished objects and semantic concepts of historical frames are not immediately forgotten, but stored in the memory as context semantic concepts in a short period of time. Therefore, when recognizing the current frame, human would wisely retrieve both global concepts and updated context concepts. This is fundamentally different from per-frame classification. Actually, this temporally-dependent recognition procedure essentially utilizes the content relevance characteristic of video data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 531, + 289, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 289, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 289, + 676 + ], + "type": "text", + "content": "Inspired by human's manner, we propose to design a novel temporal-dependent classifier (TDC), which is more suitable for video perception. Specifically, TDC contains two types of prototypes, i.e., global and context prototypes. The former learns global semantic concepts during model training and fixed during inference, which is identical to the conventional classifier. Differently, the context prototypes are calculated on-the-fly based on the last processed frame. When recognizing the current frame, two types of prototypes are collaborated together to calculate similarity with the extracted feature. In this way, the distinguished context concepts from historical frames can assist the classification." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "From experimental results, we surprisingly found that TDC can achieve significant performance improvement by equipping a simple pseudo label supervision [11] in semi-" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 339, + 72, + 515, + 381 + ], + "blocks": [ + { + "bbox": [ + 339, + 72, + 515, + 381 + ], + "lines": [ + { + "bbox": [ + 339, + 72, + 515, + 381 + ], + "spans": [ + { + "bbox": [ + 339, + 72, + 515, + 381 + ], + "type": "image", + "image_path": "5222d701efdf88302edf69a6cb4d93d7900c66e9ca91400a00203d76c9573e6e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 392, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 460 + ], + "type": "text", + "content": "Figure 2. Illustration of human-like recognition procedure. When recognizing image data, human would retrieve the global semantic concepts for classification, which is obtained from past learning experiences. When recognizing the current frame of video data, besides global concepts, human would also retrieve distinguished objects from historical frames as temporal contexts." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 472, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 604 + ], + "type": "text", + "content": "supervised video segmentation task. The primary cause is that the temporal-dependent recognition paradigm implicitly imposes a temporal consistency constraint. Specifically, TDC actually requires the context prototypes calculated from historical frames to accurately represent the content of the current frame. In this way, the feature extractor would be guided to learn a group of temporally-consistent semantic concepts across frames, which indirectly introduces the content-relevance prior into the feature extraction procedure. This guidance effectively optimizes model training on unlabeled data and improve generalization ability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 605, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 664 + ], + "type": "text", + "content": "We experimentally evaluate the proposed method on the Cityscapes and CamVid datasets. The results validate the effectiveness of TDC, and it can bring a significant improvement for mainstream video semantic segmentation methods. The contributions of this work are summarized as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 665, + 547, + 713 + ], + "type": "text", + "content": "- We find that the commonly adopted per-frame classification paradigm is quite different from human's manner and sub-optimal for video perception task, which is ignored in previous studies." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3576" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 178 + ], + "type": "list", + "angle": 0, + "index": 2, + "blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 131 + ], + "type": "text", + "content": "- We propose a novel temporal-dependent classifier (TDC) for semi-supervised video segmentation, which can implicitly impose a temporal consistency constraint for unsupervised learning. TDC essentially utilizes the internal relevance of different frames within a video." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 133, + 286, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 286, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 286, + 178 + ], + "type": "text", + "content": "- We experimentally evaluate the effectiveness of our proposed methods, and the results on Cityscapes and CamVid demonstrate the superiority of our method to previous state-of-the-art methods." + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 191, + 133, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 191, + 133, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 133, + 204 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 211, + 211, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 211, + 211, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 211, + 211, + 224 + ], + "type": "text", + "content": "2.1. Image Semantic Segmentation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 230, + 286, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 286, + 396 + ], + "type": "text", + "content": "Image semantic segmentation aims to assign a class label to every pixel in an image, which is a fundamental yet rather challenging task. Modern deep learning methods for semantic segmentation are mainly based on fully convolutional network (FCN) [25]. To further enhance segmentation results, the dilation convolution [2], pyramid pooling [37], attention mechanism [12, 17, 38], gating mechanism [7, 13, 22], and high-resolution architecture design [34] are proposed to model object relationships and aggregate context information. Recently, some transformer-based models [5, 24, 35] are proposed and exhibit promising performance. Despite the success of these models, they are often impeded in practical deployment due to requiring sufficient pixel-wise annotations for learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 405, + 209, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 209, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 209, + 417 + ], + "type": "text", + "content": "2.2. Video Semantic Segmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 423, + 286, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 286, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 286, + 603 + ], + "type": "text", + "content": "Video semantic segmentation aims to predict pixel-level semantics for each video frame. Different from static images, videos embody rich temporal information that can be exploited to improve segmentation performance. DFF [39] firstly proposes feature propagation to reuse key frame features under the guidance of estimated optical flows, which reduces the average computational cost. Inspired by DFF, Accel [19] proposes an adaptive fusion policy to effectively integrate the predictions from the key and current frames. DAVSS [41] proposes to correct the distorted features caused by inaccurate optical flow when propagating features. Besides the feature propagation paradigm, some recent works propose to improve the performance of lightweight models with temporal constraints [8, 23] and attention mechanism [16, 32, 33]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 611, + 258, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 258, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 258, + 624 + ], + "type": "text", + "content": "2.3. Semi-supervised Semantic Segmentation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "To achieve good representation learning with limited annotations, semi-supervised image segmentation (SSIS) is studied by exploring unlabeled data. Existing methods can be roughly divided into three families. The adversarial based methods, e.g., AdvSemiSeg [18] and S4GAN [26], utilize a discriminator to distinguish the confidence maps from labeled and unlabeled data predictions. The consistency" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "based methods enforce the consistency of the predictions or intermediate features with various perturbations. The perturbations can be conducted on input images, e.g., CutMix [11], ClassMix [27], and CAC [21], and feature space, e.g., CCT [28]. The self-learning based methods generate pseudo segmentation maps on unlabeled data. [3, 14, 36] propose to generate pseudo labels in an offline manner and retrain the model iteratively. While PseudoSeg [43] and CPS [4] follow the FixMatch [31] scheme and design an online pseudo labeling mechanism." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 193, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 275 + ], + "type": "text", + "content": "However, SSIS methods are not designed for video data, which only regards videos as a collection of independent images. To tackle this issue, IFR [42] proposed to reconstruct feature on the labeled frame by that on other frames, which can provide accurate supervision signals from the single label for unlabeled frames. IFR essentially utilizes the content-relevance characteristic of video data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "content": "Generally, existing methods mainly focus on supervision signal construction and improving feature extraction. Differently, in this work, we concentrate on the classifier design. We find that the per-frame recognition paradigm used in previous works is different from human's manner and thus propose a temporal-dependent classifier." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 361, + 361, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 361, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 361, + 373 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 381, + 373, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 373, + 393 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 373, + 393 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": "Following IFR [42], in semi-supervised video segmentation task, we are provided with a small set of labeled videos with one frame annotated and a larger set of unlabeled videos. Let " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "V = \\{x_{1},\\dots ,x_{T}\\}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " frames in a video with " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " as the " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " frame with spatial resolution of " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_L = \\{(V_1^L,\\hat{x}_1,y_1),\\dots ,(V_{n_L}^L,\\hat{x}_{n_L},y_{n_L})\\}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " represent the " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "n_L" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " labeled videos, where " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\hat{x}_i" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " is the annotated frame of the " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " video, " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "y_{i}\\in \\mathbb{R}^{C\\times H\\times W}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " corresponds to the pixel-level one-hot label, and " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " is the number of classes. Let " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_U = \\{V_1^U,\\dots ,V_{n_U}^U\\}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "n_U" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " unlabeled videos. Besides, another set of labeled videos " + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_V = \\{(\\mathcal{V}_1^V,\\hat{x}_1,y_1),\\dots ,(\\mathcal{V}_{n_V}^V,\\hat{x}_{n_V},y_{n_V})\\}" + }, + { + "bbox": [ + 304, + 401, + 545, + 555 + ], + "type": "text", + "content": " is used for performance evaluation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": "As shown in Figure 3, our framework consists of three components, i.e., a feature extractor " + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathsf{Net}_B" + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": ", a conventional classifier " + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathsf{Net}_C" + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": " and the proposed temporal-dependent classifier " + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathsf{Net}_{TDC}" + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": ". Two adopted classifiers are used in supervised and unsupervised learning branches, respectively. The reason for retaining the conventional classifier is to keep consistent with existing works [4, 11, 21, 28, 42] for fair comparison. In this way, the effectiveness of our TDC for optimizing unsupervised learning can be clearly revealed." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Our work aims to learn a segmentation model from " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_L" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_U" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": ", and generalize to " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_V" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": ". Following previous works, the objective of semi-supervised learning can generally be summarized as two loss functions. The first one is a regular" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3577" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 70, + 471, + 206 + ], + "blocks": [ + { + "bbox": [ + 123, + 70, + 471, + 206 + ], + "lines": [ + { + "bbox": [ + 123, + 70, + 471, + 206 + ], + "spans": [ + { + "bbox": [ + 123, + 70, + 471, + 206 + ], + "type": "image", + "image_path": "5f65289b7014fe92c48943a8307ab8f36535176d818784f51e31f3974e1e5468.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": "Figure 3. Illustration of our SSVS framework. Our framework consists of two learning branches. For supervised learning, we randomly sample an image " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": " and its corresponding ground-truth " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "GT" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": " for model training. For unsupervised learning, we randomly sample a video clip with several consecutive frames " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "V^U" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": ". Following the previous work [11], we calculate pseudo labels " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "PL^U" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "V^U" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": ", which is used as supervision signals for predictions " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "P_S^U" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": " from the augmented video " + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "inline_equation", + "content": "V_S^U" + }, + { + "bbox": [ + 46, + 215, + 547, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 272, + 203, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 203, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 203, + 283 + ], + "type": "text", + "content": "cross-entropy loss on the labeled data:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 121, + 293, + 287, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 293, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 121, + 293, + 287, + 306 + ], + "type": "interline_equation", + "content": "P = \\operatorname {N e t} _ {C} (\\operatorname {N e t} _ {B} (I)), \\tag {1}", + "image_path": "25f69f398b957844b7097997ccf42a3fb3b2d63cd4d63d99e0f78e759646e0c2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 327, + 287, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 327, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 99, + 327, + 287, + 340 + ], + "type": "interline_equation", + "content": "L _ {s u p} = \\text {C r o s s E n t r o p y} (P, G T), \\tag {2}", + "image_path": "423708d5b2e90c64810ba8003dc117a5d25f66543fc7b2eefcde3c99f601d454.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "text", + "content": "where image " + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "text", + "content": " and its corresponding ground-truth " + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "inline_equation", + "content": "GT" + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "text", + "content": " are randomly sampled from " + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "inline_equation", + "content": "D_{L}" + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "text", + "content": ". The second loss aims to train model on unlabeled data with some constructed supervision signals, which is denoted by " + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "inline_equation", + "content": "L_{unsup}" + }, + { + "bbox": [ + 46, + 345, + 287, + 416 + ], + "type": "text", + "content": ". In our framework, we adopt a simple pseudo label strategy similar to FixMatch [11, 31] scheme:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 134, + 425, + 287, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 425, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 134, + 425, + 287, + 439 + ], + "type": "interline_equation", + "content": "V _ {S} ^ {U} = T _ {s} \\left(V ^ {U}\\right), \\tag {3}", + "image_path": "798b1ec9a52947d9eeccff98493864c33d60fb2609c490914012d7fb3e9c5846.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 458, + 287, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 458, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 107, + 458, + 287, + 472 + ], + "type": "interline_equation", + "content": "P _ {S} ^ {U} = \\operatorname {N e t} _ {T D C} \\left(\\operatorname {N e t} _ {B} \\left(V _ {S} ^ {U}\\right)\\right), \\tag {4}", + "image_path": "1e0a28d1726f5cd5772bb1bd66d4133ffa184642ec6b93cd98874e693a063f2c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 89, + 487, + 287, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 487, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 89, + 487, + 287, + 502 + ], + "type": "interline_equation", + "content": "P L ^ {U} = \\operatorname {a r g m a x} \\left(\\operatorname {N e t} _ {C} \\left(\\operatorname {N e t} _ {B} \\left(V ^ {U}\\right)\\right)\\right), \\tag {5}", + "image_path": "a83e57c9418f5c1e85073cc7320a5098af29afb39fbbf6e809be120bd7f1cae4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 518, + 287, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 518, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 86, + 518, + 287, + 532 + ], + "type": "interline_equation", + "content": "L _ {u n s u p} = \\text {C r o s s E n t r o p y} \\left(P _ {S} ^ {U}, P L ^ {U}\\right), \\tag {6}", + "image_path": "f8cccdddeab5581ef43fe908fbc5a3a6bf2a5fa28d94a4178d953d2c796eba5b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "V^{U}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " is randomly sampled from " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "D_{U}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " represents the strong data augmentation like color jitter. Specifically, we calculate per-frame pseudo labels " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "PL^{U}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "V^{U}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": ", which is used as supervision signals for predictions " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "P_{S}^{U}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " from the augmented video " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "V_{S}^{U}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": ". Then the overall training objective can be presented as follows" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 120, + 618, + 287, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 618, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 120, + 618, + 287, + 632 + ], + "type": "interline_equation", + "content": "L = L _ {s u p} + \\lambda L _ {u n s u p}, \\tag {7}", + "image_path": "a38d8b8c855b4b7310342a27c019ebca8c6dd0d68c0da9e964f8858be5a72de3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 639, + 180, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 180, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 180, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 639, + 180, + 651 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 639, + 180, + 651 + ], + "type": "text", + "content": " is a trade-off parameter." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 659, + 178, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 178, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 178, + 670 + ], + "type": "text", + "content": "3.2. Conventional Classifier" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": "To make it clear, we first elaborate on the process of conventional classifier, and then explain the core mechanism of our TDC." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": "A conventional classifier typically consists of a fully connected layer and a softmax layer. We use " + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i\\in \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": " to denote the weight parameters for category " + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": " in the fully connected layer and use " + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathsf{f}\\in \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": " to denote the feature for classification. Guided by the cross-entropy loss, the classifier is encouraged to produce a larger inner product between " + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathsf{f}" + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathsf{w}_y" + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 272, + 545, + 427 + ], + "type": "text", + "content": " is the corresponding ground-truth category. After model training, the learned weight parameters would automatically align with the feature cluster centers, which is experimentally verified and visualized in previous works [9, 30]. Here, the cluster center is the mean of features belonging to the same category, which is usually denoted as prototype." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 427, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 545, + 475 + ], + "type": "text", + "content": "This tight relationship among features, prototypes and weight parameters is the basic of our TDC, which provides a solution for utilizing distinguished semantic concepts to aid recognition." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 483, + 473, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 473, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 473, + 495 + ], + "type": "text", + "content": "3.3. Temporal-dependent Classifier" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 501, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 573 + ], + "type": "text", + "content": "In this work, we mainly focus on designing a classifier to mimic the temporal-dependent recognition paradigm on video data like human's manner. To this end, we optimize conventional classifier by introducing distinguished results from historical frames and then propose a novel classifier, i.e., the temporal-dependent classifier (TDC)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 586, + 443, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 443, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 443, + 599 + ], + "type": "text", + "content": "3.3.1 Prototypes Construction" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "As shown in Figure 4, when recognizing " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "t + 1^{th}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " frame, TDC would simultaneously utilize two types of prototypes, i.e., global prototypes " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "PT^G" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " and context prototypes " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "PT_t^C" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " that calculated based on the prediction of " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "t^{th}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " frame. Here, similar to the conventional classifier, " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "PT^G = \\{\\mathbf{w}_i \\in \\mathbb{R}^n | i = 0, 1, \\dots, C - 1\\}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " is implemented as a set of learnable weight parameters, where " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " is the number of classes and " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " is the feature dimension. " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "PT^G" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " is updated by back-propagation during training and keeps fixed during inference. The key" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3578" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 272, + 219 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 272, + 219 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 272, + 219 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 272, + 219 + ], + "type": "image", + "image_path": "eebb6cbe92988fa70f19bfd22ac68c9a78d37465e39d5432aa5920770efe420f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "text", + "content": "Figure 4. Illustration of temporal-dependent recognition procedure. The critical process is the update of context prototypes " + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "inline_equation", + "content": "PT^C" + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "text", + "content": " based on the last frame prediction. In the classifier, context prototypes " + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "inline_equation", + "content": "PT^C" + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "text", + "content": " and global prototypes " + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "inline_equation", + "content": "PT^G" + }, + { + "bbox": [ + 46, + 228, + 289, + 285 + ], + "type": "text", + "content": " are utilized together for recognition." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": "of TDC is the design of context prototypes, which is calculated on-the-fly based on the prediction of last frame. Here, " + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "inline_equation", + "content": "PT_{t}^{C} = \\{\\mathsf{w}_{k}^{c}\\in \\mathbb{R}^{n}|k = 0,1,\\dots ,K - 1\\}" + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": " prototypes calculated from the " + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "inline_equation", + "content": "t^{\\text{th}}" + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": " frame. Specifically, we calculate the pseudo label " + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "inline_equation", + "content": "PL_{t}" + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": " of the extracted feature " + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "inline_equation", + "content": "F_{t}" + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "inline_equation", + "content": "t^{\\text{th}}" + }, + { + "bbox": [ + 46, + 287, + 289, + 360 + ], + "type": "text", + "content": " frame as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 109, + 369, + 287, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 369, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 109, + 369, + 287, + 382 + ], + "type": "interline_equation", + "content": "P L _ {t} = \\operatorname {a r g m a x} \\left(\\operatorname {N e t} _ {C} \\left(F _ {t}\\right)\\right). \\tag {8}", + "image_path": "08e365d90a6bb5570ef5de85d47eaf06f280386043256f2786b53ec8c2e619ea.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "text", + "content": "Then, we group the pixel-wise features in " + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "inline_equation", + "content": "F_{t}" + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "text", + "content": " belonging to the same class " + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "text", + "content": " according to " + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "inline_equation", + "content": "PL_{t}" + }, + { + "bbox": [ + 47, + 390, + 287, + 415 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 94, + 422, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 422, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 94, + 422, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\mathbf {w} _ {k} ^ {c} = \\frac {\\sum_ {i} F _ {t} ^ {(i)} * \\mathbb {1} \\left(P L _ {t} ^ {(i , k)} = = 1\\right)}{\\sum_ {i} \\mathbb {1} \\left(P L _ {t} ^ {(i , k)} = = 1\\right)}, \\tag {9}", + "image_path": "d343b8729a42d66c5823a106d290263cc50093933184da5b6c7638111b3204e1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathbb{1}" + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "text", + "content": " is an indicator function and " + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "inline_equation", + "content": "PL_{t}^{(i,k)}" + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "text", + "content": " represents the one-hot pseudo label of pixel " + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "text", + "content": " belonging to the " + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 464, + 287, + 514 + ], + "type": "text", + "content": " class. In this way, context prototypes would be adaptively updated based on the last frame prediction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 527, + 178, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 178, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 178, + 539 + ], + "type": "text", + "content": "3.3.2 Recognition Procedure" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": "After constructing the global and context prototypes, here we introduce how to conduct recognition based on theses prototypes. The core process of recognition is to calculate similarity between the input feature and prototypes with known categories. After that, the category corresponding to the prototype that generates the maximum similarity will be regarded as the semantic prediction. Therefore, a naive solution is to calculate similarity with global and context prototypes simultaneously." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "However, the input feature would naturally be similar to context prototypes since they are calculated from consecutive frames and thus global prototypes are always ignored, especially in the early stage of model training. This shortcut behavior would make the model only learning to capture" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 189 + ], + "type": "text", + "content": "similarity across frames and not being able to learn semantic concepts on unlabeled data. The cause of this issue is that two types of prototypes are updated in different mechanism and contains diverse statistical distribution like magnitudes. Therefore, we first conduct normalization on each prototype and the input feature respectively before classification, which can effectively narrow their the distribution discrepancy and achieve a fair learning process. Thus, the predicted probability of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 189 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 72, + 545, + 189 + ], + "type": "text", + "content": " category is computed as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 378, + 189, + 545, + 221 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 189, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 378, + 189, + 545, + 221 + ], + "type": "interline_equation", + "content": "p _ {i} = \\frac {e ^ {\\eta \\cdot \\langle \\overline {{P T}} _ {i} , \\overline {{F}} _ {t} \\rangle}}{\\sum_ {j} e ^ {\\eta \\cdot \\langle \\overline {{P T}} _ {j} , \\overline {{F}} _ {t} \\rangle}}, \\tag {10}", + "image_path": "637392dcbb2410eeef2ec9a190dd9eded36ae8dc719750d948896408ee0a4fd2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "spans": [ + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "\\overline{v} = v / ||v||_2" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " denotes the L2 normalized vector, and " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "\\langle \\overline{v}_1,\\overline{v}_2\\rangle = \\overline{v}_1^T\\overline{v}_2" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " measures the cosine similarity between two normalized vectors. Here, " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "PT = \\{PT^{G},PT_{t}^{C}\\}" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " is the combination of two types of prototypes. Inspired by a previous work [15], since the range of " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "\\langle \\overline{v}_1,\\overline{v}_2\\rangle" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " is restricted to " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": ", a learnable scalar " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " is introduced to control the peakiness of softmax distribution. Differently, we set two independent scalars, i.e., " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "\\eta_G" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "\\eta_C" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": ", for global prototypes " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "PT^{G}" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " and context prototypes " + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "inline_equation", + "content": "PT_{t}^{C}" + }, + { + "bbox": [ + 305, + 223, + 546, + 332 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 346, + 485, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 485, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 485, + 357 + ], + "type": "text", + "content": "3.3.3 Joint-prototypes Label Relaxation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": "After calculating the probability of input feature based on constructed prototypes, a cross-entropy loss is applied according to a pseudo label, as described in Section 3.1. However, there is a mismatch between the probability vector " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "p \\in \\mathbb{R}^{C + K}" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": " and the one-hot label " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": " are the number of categories and prototypes predicted in the last frame. Intuitively, for a specific category " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": ", its corresponding context prototype " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "PT_{t,i}^{C}" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": " and global prototype " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "PT_{i}^{G}" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": " are different descriptions for an identical semantic concept. Therefore, for a feature belonging to category " + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 364, + 545, + 509 + ], + "type": "text", + "content": ", it should not be penalized by loss function regardless of which prototype it is more similar to." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "content": "Based on this consideration, we propose a joint-prototypes label relaxation, which is also inspired by a previous work [40]. Suppose we are classifying a feature belonging to class " + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "content": " and class " + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "content": " is related to two prototypes " + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "inline_equation", + "content": "PT_{i}^{G}" + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "inline_equation", + "content": "PT_{t,i}^{C}" + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "content": ". To achieve label relaxation, we propose to maximize the likelihood of both prototypes together instead of any single one. Since two prototypes are mutually exclusive in cross-entropy loss, we aim to maximize the union of them:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 329, + 622, + 545, + 638 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 622, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 329, + 622, + 545, + 638 + ], + "type": "interline_equation", + "content": "P \\left(P T _ {i} ^ {G} \\cup P T _ {t, i} ^ {C}\\right) = P \\left(P T _ {i} ^ {G}\\right) + P \\left(P T _ {t, i} ^ {C}\\right), \\tag {11}", + "image_path": "9aa63c2ba78c7861a99c672de69e875cd10c4be9e44a4a7dc8a16d65fa249b64.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "content": " is the softmax probability of each prototype. Therefore, for each pixel " + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "inline_equation", + "content": "t^{th}" + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "content": " frame in the video clip, the loss function is as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 339, + 683, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 683, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 339, + 683, + 545, + 716 + ], + "type": "interline_equation", + "content": "L _ {T D C} = \\frac {1}{H * W} \\frac {1}{T} \\sum_ {i} ^ {H * W} \\sum_ {t} ^ {T} L _ {T D C} (i, t), \\tag {12}", + "image_path": "ee49daa7fc7ebe6d6f010c23d93c7f9facedc746a328741a078079a07c2cb4ff.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3579" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 271, + 151 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 271, + 151 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 271, + 151 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 271, + 151 + ], + "type": "image", + "image_path": "5154cd7e06660700d27f1d3b903fa0071b511d29843ee09789be5764376ee0cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 156, + 271, + 236 + ], + "blocks": [ + { + "bbox": [ + 65, + 156, + 271, + 236 + ], + "lines": [ + { + "bbox": [ + 65, + 156, + 271, + 236 + ], + "spans": [ + { + "bbox": [ + 65, + 156, + 271, + 236 + ], + "type": "image", + "image_path": "5888fae6173ac548fbcb3d23d24316229324f8849dd0b3f82ffb2c61326d057f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "type": "text", + "content": "Figure 5. Illustration of bidirectional prediction. We simultaneously considering forward " + }, + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "type": "inline_equation", + "content": "(t\\to t + 1)" + }, + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "type": "text", + "content": " and backward " + }, + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "type": "inline_equation", + "content": "(t + 1\\rightarrow t)" + }, + { + "bbox": [ + 46, + 246, + 287, + 280 + ], + "type": "text", + "content": " directions when constructing context prototypes." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 294, + 287, + 311 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 294, + 287, + 311 + ], + "spans": [ + { + "bbox": [ + 61, + 294, + 287, + 311 + ], + "type": "interline_equation", + "content": "L _ {T D C} (i, t) = - \\log P \\left(P T _ {y _ {i, t}} ^ {G} \\cup \\mathcal {X} \\left(P T _ {t - 1, y _ {i, t}} ^ {C}\\right)\\right), \\tag {13}", + "image_path": "1b50756624f6e8b39b6b090c8bf4ca04757e3bc0e0c41b1bc2bd176c06cf2ec6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 324, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 324, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 110, + 324, + 287, + 357 + ], + "type": "interline_equation", + "content": "\\mathcal {X} (x) = \\left\\{ \\begin{array}{l l} x, & \\text {i f} x \\text {e x i s t s} \\\\ 0, & \\text {e l s e} \\end{array} \\right. \\tag {14}", + "image_path": "db760de1637329ca391b743ce804addf227ce58bebe640ca62b34616b75bf296.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 360, + 287, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 444 + ], + "type": "text", + "content": "To be noticed, when recognizing the first frame, only global prototypes are adopted since context prototypes has not been constructed. This is reasonable and similar to human's manner. When obtaining the first frame of a video, human can only conduct image recognition by recalling learned experience, i.e., global prototypes, since there is no prior information about this video." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 457, + 185, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 185, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 185, + 468 + ], + "type": "text", + "content": "3.3.4 Bidirectional Constraint" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 476, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 571 + ], + "type": "text", + "content": "Actually, TDC works in a RNN-like manner, where the output from the previous step can affect the prediction on the current step. In TDC, the continuously updated prototypes serve like the hidden state vectors in RNN structure. According to successfully practices [20, 29] in NLP field, comparing to unidirectional RNN, bidirectional RNN can help the model to better exploit contextual information and effectively improve the model performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "text", + "content": "Therefore, in this work, we further propose a bidirectional constraint, i.e., simultaneously considering forward " + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "inline_equation", + "content": "(t\\to t + 1)" + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "text", + "content": " and backward " + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "inline_equation", + "content": "(t + 1\\rightarrow t)" + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "text", + "content": " directions, as shown in Figure 5. Specifically, context prototypes are calculated based on the " + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "inline_equation", + "content": "t + 1^{th}" + }, + { + "bbox": [ + 46, + 572, + 287, + 642 + ], + "type": "text", + "content": " frame to aid the current frame recognition:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 649, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 649, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 58, + 649, + 287, + 681 + ], + "type": "interline_equation", + "content": "L _ {B i - T D C} = \\frac {1}{H * W} \\frac {1}{T} \\sum_ {i} ^ {H * W} \\sum_ {t} ^ {T} L _ {B i - T D C} (i, t), \\tag {15}", + "image_path": "4b8e84a54364213a7fed8e5ea0bce5957a46d89d869cc46a719301de7c077a2f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 53, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 53, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "L _ {B i - T D C} (i, t) = - \\log P \\left(P T _ {y _ {i, t}} ^ {G} \\cup \\mathcal {X} \\left(P T _ {t + 1, y _ {i, t}} ^ {C}\\right)\\right). \\tag {16}", + "image_path": "b90a1d10837038d889e5616c1a902504935174feafcc826229957269c20035ff.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "Actually, the primary cause behind the effectiveness of TDC on semi-supervised learning is that TDC can implicitly impose a temporal consistency constraint across frames. Intuitively, the bidirectional calculation can further enhance the constraint by simultaneously considering both forward and backward consistency. Finally, in this work, the adopted unsupervised learning loss is as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 361, + 163, + 545, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 163, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 361, + 163, + 545, + 177 + ], + "type": "interline_equation", + "content": "L _ {u n s u p} = L _ {T D C} + L _ {B i - T D C}. \\tag {17}", + "image_path": "1feaa4c51e0156899008c18532ff95ab655bb2e0b749dd49b9ebff704439edee.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 184, + 386, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 184, + 386, + 197 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 386, + 197 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 204, + 364, + 215 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 204, + 364, + 215 + ], + "spans": [ + { + "bbox": [ + 306, + 204, + 364, + 215 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "type": "text", + "content": "Cityscapes [6] is a representative dataset in semantic segmentation and autonomous driving domain. It focuses on semantic understanding to urban street scenes. The training and validation subsets contain 2,975 and 500 videos, respectively, and each video contains 30 frames at a resolution of " + }, + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "type": "inline_equation", + "content": "1024 \\times 2048" + }, + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "type": "inline_equation", + "content": "20^{th}" + }, + { + "bbox": [ + 304, + 222, + 545, + 305 + ], + "type": "text", + "content": " frame in each is annotated by pixel-level semantic labels with 19 categories." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "type": "text", + "content": "CamVid [1] also focuses on the semantic understanding to urban street scenes, but it contains less data than Cityscapes. It has four driving videos and each video contains frames ranging from 3,600 to 11,000 at a resolution of " + }, + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "type": "inline_equation", + "content": "720 \\times 960" + }, + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "type": "text", + "content": ". Every " + }, + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "type": "inline_equation", + "content": "30^{th}" + }, + { + "bbox": [ + 304, + 306, + 545, + 412 + ], + "type": "text", + "content": " frame of videos is annotated with 11 semantic classes, which results in a total of 701 samples. Similar to Cityscapes, we split videos into 701 videos and each video contains 30 frames. All videos are divided into the trainval set with 468 videos and test set with 233 videos." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": "We follow the partition protocols of IFR [42] and divide the whole training set via randomly sub-sampling " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1/8" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1/16" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1/30" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": " of all training videos, i.e., 2975 videos in Cityscapes and 468 videos in CamVid, as the labeled set and regard the remaining videos as the unlabeled set. Following previous work [11, 18, 26-28, 42], we apply bilinear interpolation to resize every video frame in Cityscapes and CamVid to " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "512 * 1024" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "360 * 480" + }, + { + "bbox": [ + 304, + 413, + 545, + 521 + ], + "type": "text", + "content": " for the efficiency of training and inference." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 528, + 438, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 528, + 438, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 528, + 438, + 540 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": "Following IFR [42], we adopt Accel [19] as video semantic segmentation architecture due to its good performance. It consists of two segmentation branches, i.e., a heavy reference branch and a light-weight update branch, an optical flow network, and a score fusion layer. Similar to IFR, we adopt semi-supervised methods for two segmentation branches to improve representation learning with limited annotations. The segmentation model is trained using a SGD optimizer with a momentum of 0.9 and a weight decay of " + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": ". The learning rate is set at " + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": " for the backbone parameters and " + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "inline_equation", + "content": "10^{-2}" + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": " for others, which is annealed following the poly learning rate policy." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We evaluate the segmentation performance on the validation videos, i.e., validation subset in Cityscapes and test" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3580" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 76, + 70, + 516, + 164 + ], + "blocks": [ + { + "bbox": [ + 76, + 70, + 516, + 164 + ], + "lines": [ + { + "bbox": [ + 76, + 70, + 516, + 164 + ], + "spans": [ + { + "bbox": [ + 76, + 70, + 516, + 164 + ], + "type": "table", + "html": "
Method1/30 (100)1/16 (186)1/8 (372)1/4 (744)1/2 (1488)
Accel45.7352.1057.1260.5562.83
+CCT [28]48.05 (+2.32)53.25 (+1.15)58.88 (+1.76)62.00 (+1.45)64.02 (+1.19)
+CAC [21]48.83 (+3.10)54.56 (+2.46)58.55 (+1.43)62.78 (+2.23)63.87 (+1.04)
+ CPS [4]48.97 (+3.24)54.69 (+2.59)58.97 (+1.85)62.43 (+1.88)63.74 (+0.91)
+ IFR [42]52.86 (+7.13)56.39 (+4.29)60.08 (+2.96)63.45 (+2.90)64.53 (+1.70)
+ Ours55.81 (+10.08)60.97 (+8.87)63.12 (+6.00)65.83 (+5.28)66.67 (+3.84)
", + "image_path": "b84297e4f53a22aece8cf677ace2e3931fc6d4f29dc46e5f91bf82ba3cdf78ca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 78, + 195, + 514, + 290 + ], + "blocks": [ + { + "bbox": [ + 46, + 167, + 547, + 191 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 547, + 191 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art methods on the Cityscapes validation subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 195, + 514, + 290 + ], + "lines": [ + { + "bbox": [ + 78, + 195, + 514, + 290 + ], + "spans": [ + { + "bbox": [ + 78, + 195, + 514, + 290 + ], + "type": "table", + "html": "
Method1/30 (15)1/16 (29)1/8 (58)1/4 (117)1/2 (234)
Accel42.3747.5750.7856.4059.37
+CCT [28]47.09 (+4.72)52.45 (+4.88)54.50 (+3.72)58.69 (+2.29)61.58 (+2.21)
+CAC [21]46.85 (+4.48)52.16 (+4.59)54.03 (+3.25)59.67 (+3.27)63.17 (+3.80)
+CPS [4]46.05 (+3.68)52.04 (+4.47)55.30 (+4.52)59.02 (+2.62)62.49 (+3.12)
+IFR [42]49.50 (+7.13)53.71 (+6.14)57.37 (+6.59)61.27 (+4.87)63.86 (+4.49)
+Ours50.95 (+8.58)55.36 (+7.79)59.88 (+9.10)62.63 (+6.23)64.59 (+5.22)
", + "image_path": "bd142cade061d643655ffd09654955511c7773e817b8ce2f604c7081af17cc27.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "type": "text", + "content": "set in CamVid. Following Accel, for each test video, we conduct the reference branch on a selected key frame and update branch on the annotated frame. The segmentation results are predicted via the feature propagation and score fusion. To be notice, for fair comparison, we adopt the conventional classifier for semantic prediction while TDC is only involved in the training period, since in this work we mainly investigate the effectiveness of TDC on representation learning. We evaluate different methods with mean Intersection-over-Union (mIoU) as metric. The key frame interval is set as 5 throughout the experiments. For our TDC, there is a trade-off parameter " + }, + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "type": "text", + "content": " in Eq. 7, which is set " + }, + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 46, + 331, + 289, + 486 + ], + "type": "text", + "content": " for all experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 499, + 191, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 191, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 191, + 513 + ], + "type": "text", + "content": "4.3. Performance Comparison" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 520, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 640 + ], + "type": "text", + "content": "To demonstrate the superiority of our method, we make a comparison with recent state-of-the-art methods, i.e., three SSIS methods including CCT [28], CAC [21] and CPS [4], and a SSVS method IFR [42]. Following IFR, for fair comparison, all critical components are keep consistent among different methods, including base segmentation model, data splits, data augmentation and training settings (i.e., optimizer and hyperparameters). In this way, we can fairly compare the improvement brought by different methods on the basis of the same supervised learning baseline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "The comparison on Cityscapes and CamVid is shown in Table 1 and Table 2. From the results, we have the following two observations. First, our TDC can bring significant improvement under all partition protocols comparing to the supervised learning baseline. A larger gain is achieved for the cases with less labeled data, e.g., " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "10.08\\%" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " mIoU gain with" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 321, + 329, + 529, + 418 + ], + "blocks": [ + { + "bbox": [ + 46, + 293, + 546, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 293, + 546, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 546, + 316 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art methods on the CamVid test subset under different partition protocols. Accel is adopted as the supervised baseline that is only trained on labeled data. Our method gets more gains especially for few labeled training data." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 329, + 529, + 418 + ], + "lines": [ + { + "bbox": [ + 321, + 329, + 529, + 418 + ], + "spans": [ + { + "bbox": [ + 321, + 329, + 529, + 418 + ], + "type": "table", + "html": "
LsupLTDCLBi-TDCmIoU (%)
PTGPTCt
✓43.68
✓✓46.78 (+3.10)
✓✓✓50.14 (+6.46)
✓✓✓✓51.29 (+7.61)
", + "image_path": "7e2a0d92835707293756218071fbfa012728393aa1937e4375d1da579ba94b5d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 424, + 546, + 458 + ], + "lines": [ + { + "bbox": [ + 305, + 424, + 546, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 424, + 546, + 458 + ], + "type": "text", + "content": "Table 3. Ablation study on our proposed components. Each component can bring performance improvement compared to the baseline, and their combination performs best." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "type": "text", + "content": "100 samples in Cityscapes. Such experimental results well verify that TDC can effectively improve the generalization of models. Second, our method surpasses other state-of-the-art methods by a large margin. For example, it outperforms IFR by " + }, + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "type": "inline_equation", + "content": "4.58\\%" + }, + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "type": "text", + "content": " under 1/16 partition protocol on Cityscapes and " + }, + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "type": "inline_equation", + "content": "2.51\\%" + }, + { + "bbox": [ + 305, + 462, + 547, + 559 + ], + "type": "text", + "content": " under 1/8 partition protocol on CamVid, respectively. It shows that TDC can better utilize the unlabeled video data for training model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 567, + 400, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 400, + 581 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 400, + 581 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 587, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 587, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 587, + 547, + 647 + ], + "type": "text", + "content": "In this subsection, we conduct experiments to reveal the effectiveness of our proposed method. All experiments are particularly conducted with 1/30 labeled data on Cityscapes. For efficient training, we adopt PSPNet with ResNet18 as the segmentation network by default." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "content": "Effect of Components. To reveal the contribution of our proposed components, i.e., global prototypes " + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "PT^G" + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "content": ", context prototypes " + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "PT_t^C" + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "content": " and bidirectional constraint " + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "L_{Bi-TDC}" + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "content": ", we conduct an extensive study by evaluating their combina" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "text", + "content": "3581" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 71, + 277, + 103 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 277, + 103 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 277, + 103 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 277, + 103 + ], + "type": "table", + "html": "
λ0.00.050.10.20.51.0
mIoU (%)43.6846.8749.6251.2950.7448.54
", + "image_path": "8f209aabfe4280b7134335435fc1ec1f4a89e42d93e2ba0b98bc00cf92395bff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 135, + 280, + 169 + ], + "blocks": [ + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "lines": [ + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "spans": [ + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "type": "text", + "content": "Table 4. Effect of trade-off parameter " + }, + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "type": "text", + "content": ". Based on the results, we set " + }, + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 47, + 107, + 286, + 129 + ], + "type": "text", + "content": " for all experiments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 135, + 280, + 169 + ], + "lines": [ + { + "bbox": [ + 52, + 135, + 280, + 169 + ], + "spans": [ + { + "bbox": [ + 52, + 135, + 280, + 169 + ], + "type": "table", + "html": "
T01235710
mIoU (%)43.6846.8749.2450.1851.2950.9350.64
", + "image_path": "126c2e4593d93698587928002879307e8e4517fa83c1fc9fa785f0f5a922ae7f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 204, + 286, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 286, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 286, + 299 + ], + "type": "text", + "content": "tions, and the results are shown in Table 3. It can be seen that each component can bring performance improvement compared with the baseline. In particular, based on the supervised learning baseline, TDC equipped with only global prototypes serves like a pseudo-label scheme similar to previous works [4, 43]. After introducing context prototypes, TDC can obtain significant improvement. Finally, TDC performs best with bidirectional constraint." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": "Effect of Trade-off Parameter " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": ". We investigate the influence of trade-off parameter " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": " used to control the unsupervised learning loss in Eq 7, as shown in Table 4. Here, " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda = 0.0" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": " represents the supervised learning baseline. The results show that: with the increase of " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": ", the unsupervised loss help model training on unlabeled data and effectively overcome the overfitting issue due to limited labeled training data, which performs best when " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": " continuously increases, the performance degrades since the supervised learning branch is interfered. Therefore, based on the results, we set " + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 46, + 314, + 286, + 445 + ], + "type": "text", + "content": " for all experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": "Effect of the Number of frames. In our framework, we randomly sample a unlabeled video clip with " + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": " frames for unsupervised learning. Here, we investigate the influence of number of frames, which relates to the temporal modeling in our proposed TDC. Table 5 shows the results. Here, " + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "inline_equation", + "content": "T = 0" + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": " represents the supervised learning baseline and " + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "inline_equation", + "content": "T = 1" + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": " represents using TDC with only global prototypes. From the results we can see that: as " + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": " increases, TDC can impose a stronger temporal consistency constraint and improve model training on unlabeled video data. However, if " + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": " gets too large, TDC would suffer from training instability and lead to a slight performance degradation. Therefore, based on the results, we set " + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "inline_equation", + "content": "T = 5" + }, + { + "bbox": [ + 46, + 460, + 286, + 615 + ], + "type": "text", + "content": " for all experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Performance with Different VSS Architectures. To study the generalization ability of our method, We apply it to different video semantic segmentation architectures. We particularly adopt three widely adopted video segmentation architectures, i.e., DFF [39], Accel [19] and DAVSS [41]. As shown in Table 6, our proposed method can bring significant performance improvement consistently." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 316, + 71, + 536, + 129 + ], + "blocks": [ + { + "bbox": [ + 47, + 172, + 286, + 195 + ], + "lines": [ + { + "bbox": [ + 47, + 172, + 286, + 195 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 286, + 195 + ], + "type": "text", + "content": "Table 5. Effect of Number of frames. Based on the results, we sample 5 frames per unlabeled video clip for all experiments." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 71, + 536, + 129 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 536, + 129 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 536, + 129 + ], + "type": "table", + "html": "
MethodBaseline+IFR+ Ours
DFF [39]44.1949.97 (+5.78)52.63 (+8.44)
Accel [19]45.7352.86 (+7.13)55.81 (+10.08)
DAVSS [41]46.5151.97 (+5.46)55.25 (+8.74)
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MethodAccel+ CCT+ CAC+ CPS+ IFR+ Ours
TC (%)70.0471.4371.4770.7473.8875.38
", + "image_path": "bfca2c1b5ca22c05bb00b4ef69b2e031192955ff5a6cf6e41ed72a4ae24ff551.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 222, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 306, + 222, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 222, + 545, + 255 + ], + "type": "text", + "content": "Table 7. Comparison on Temporal Consistency. We evaluate different methods with temporal consistency (TC) score [23]. Our proposed method can bring a significantly improvement." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 268, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 268, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 268, + 545, + 364 + ], + "type": "text", + "content": "Effectiveness on Temporal Consistency. It is important for VSS methods to produce temporally stable predictions. Thus, we further verify the effectiveness of our method on improving temporal consistency. Particularly, we follow previous works [23, 42] and adopt temporal consistency (TC) score as the evaluation metric. As shown in Table 7, our method can bring a significant improvement, since consistent predictions among different frames can be achieved." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 380, + 378, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 378, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 378, + 392 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 401, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 591 + ], + "type": "text", + "content": "In this paper, we focus on the semi-supervised video semantic segmentation problem, and propose a novel temporal-dependent classifier (TDC). Motivated by the observation of human's behavior, TDC is designed to utilize distinguished semantic concepts of historical frames when recognizing the current frame, which is more suitable for video data. We found that TDC can achieve significant performance improvement in semi-supervised learning since its recognition mechanism implicitly imposes a temporal-consistency constraint across frame, which is valuable especially in labelscarcce scenarios. To further enhance the effect of TDC, we propose a bidirectional constraint by simultaneously considering both forward and backward calculation. Extensive experiments on Cityscapes and CamVid validated the effectiveness of our method, which outperforms previous state-of-the-art methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 608, + 377, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 377, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 377, + 621 + ], + "type": "text", + "content": "Acknowledge" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "This work is supported in part by the National Key R&D Program of China (grant numbers 2021ZD0111501, 2021ZD0111502), the National Natural Science Foundation of China (grant number 62176246), the Anhui Province Key Research and Development Plan (grant number 202304a05020045), and the STU Scientific Research Foundation for Talents (grant number NTF22030)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3582" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Gabriel J Brostow, Julien Fauqueur, and Roberto Cipolla. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 1, 3, 8" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "3584" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/6d8274a0-6d1c-4618-99cc-d4d3f62a5569_content_list.json b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/6d8274a0-6d1c-4618-99cc-d4d3f62a5569_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6800b613f2fdb2443f2e5549c800d0311bbe06 --- /dev/null +++ b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/6d8274a0-6d1c-4618-99cc-d4d3f62a5569_content_list.json @@ -0,0 +1,1838 @@ +[ + { + "type": "text", + "text": "Infinigen Indoors: Photorealistic Indoor Scenes using Procedural Generation", + "text_level": 1, + "bbox": [ + 98, + 130, + 870, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Alexander Raistrick*, Lingjie Mei*, Karhan Kayan*, (*equal contribution; random order) David Yan, Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Lahav Lipson, Zeyu Ma, Jia Deng Department of Computer Science, Princeton University", + "bbox": [ + 165, + 181, + 803, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce Infinigen Indoors, a Blender-based procedural generator of photorealistic indoor scenes. It builds upon the existing Infinigen system, which focuses on natural scenes, but expands its coverage to indoor scenes by introducing a diverse library of procedural indoor assets, including furniture, architecture elements, appliances, and other day-to-day objects. It also introduces a constraint-based arrangement system, which consists of a domain-specific language for expressing diverse constraints on scene composition, and a solver that generates scene compositions that maximally satisfy the constraints. We provide an export tool that allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse and Unreal. Infinigen Indoors is open-sourced under the BSD license. Please visit infinigen.org for code and videos.", + "bbox": [ + 75, + 316, + 473, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 588, + 209, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Synthetic data rendered by conventional computer graphics has seen increasing adoption in computer vision[10, 38, 41, 42, 46, 48, 61] and AI research[20, 28, 76], especially for 3D vision[26, 45, 71, 73-75, 83] and embodied AI[12, 32, 36, 68, 70, 87]. Synthetic data can be rendered in unlimited quantities and can automatically provide high-quality 3D ground truth, enabling large-scale training of computer vision models and embodied agents. Notably, many state-of-the-art 3D vision systems[72, 75] and robotic systems [33, 39] have been trained purely in simulation yet perform surprisingly well in the real world zero-shot.", + "bbox": [ + 75, + 613, + 470, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A promising direction for creating synthetic data is procedural generation, which uses mathematical rules to create 3D objects and scenes, as opposed to manual sculpting or real-world scanning. These mathematical rules can have parameters that are randomized to allow infinite variations. For example, trees can be generated through a recursive set of rules that randomly branch off. Compared to reusing a fixed, static set of 3D assets, procedural generation can greatly", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "improve the diversity of the synthetic data and the simulated environments.", + "bbox": [ + 498, + 287, + 890, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Infinigen [60] is a recent work that pushed the idea of procedural generation to the limit. Infinigen is an open-source system that generates photorealistic 3D scenes fully procedurally, meaning that every 3D asset, from shape to material, from large structures to small details, is completely procedural, without using any external static asset. Being fully procedural means that every aspect of the 3D scene, from the details of individual objects to their arrangements in a scene, can be customized and controlled by simply modifying the underlying mathematical rules. As a result, a 3D scene can be randomized at all levels down to the smallest details, as opposed to only at the level of object arrangement, which was common in earlier work that used procedural generation.", + "bbox": [ + 496, + 320, + 893, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the current Infinigen system is limited to natural scenes and objects (terrains, animals, plants, etc.). Although natural scenes could be sufficient for training foundation models as evidenced by natural evolution [60], this hypothesis remains unproven and may require additional advances in learning algorithms and architecture designs. Evidence from the current literature suggests that synthetic training data that more closely approximates the application domain is still likely to lead to better downstream performance.", + "bbox": [ + 496, + 532, + 893, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome this limitation, we introduce Infinigen Indoors, a procedural generator of photorealistic indoor scenes. It expands the coverage of Infinigen to indoor scenes, which are relevant for many high-impact applications including robotics and augmented reality. Infinigen Indoors generates diverse indoor objects, including furniture, appliances, cookware, dining utensils, architectural elements, and other common day-to-day objects. It also generates full indoor scenes, including the interior of multi-room, multi-floor buildings, with object arrangements that are physically and semantically plausible. Fig. 1 shows random samples of generated scenes, and Fig. 2 shows some automatic annotations.", + "bbox": [ + 496, + 671, + 895, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Like the original Infinigen, Infinigen Indoors is not a fixed set of 3D models or scenes; instead, it is an open-source generator that can create unlimited variations both", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21783", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a607697bebb42081480417d13f24f1ce2795aa7b1a6de2f2a3b7a006a5fbbd49.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 90, + 482, + 250 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/143c90dcba74eff289a20392e68b47b6b1b96c24ea29385c4d6530ad023173c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 888, + 250 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7bd2fcd30f45b9bc0f297533789fa027f35ba55bd84ab25de6b374610bdf09df.jpg", + "image_caption": [ + "Figure 1. Random, non cherry-picked sample of images generated by our system. From top left to bottom right, we show images from dining rooms, bathrooms, living rooms and kitchens. Please see the supplement for an extended random sample." + ], + "image_footnote": [], + "bbox": [ + 80, + 252, + 482, + 412 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c8959a435e72759fbc7560d6e0ccc0c798e3baf7b3f1ffea5156c0133755f981.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 252, + 888, + 412 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "at the object level and at the scene level. Infinigen Indoors is also $100\\%$ procedural, using no external assets and using only mathematical rules to generate everything from scratch.", + "bbox": [ + 75, + 460, + 468, + 506 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Infinigen Indoors builds upon the original Infinigen and Blender [8] but makes significant new contributions. The main contributions include (1) a library of procedural generators of indoor assets, (2) a constraint-based arrangement system, (3) a tool to export the generated scenes to real-time simulators such as NVIDIA Omniverse [54] and Unreal Engine[13].", + "bbox": [ + 75, + 507, + 468, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our second contribution—a constraint-based arrangement system—offers a new capability specifically targeting indoor settings. Indoor scenes are artificial, and object arrangement exhibits a greater degree of regularity than natural scenes: for example, furniture usually does not block the entrance of a room. We thus develop a system that lets the user specify scene arrangement constraints through a domain-specific language using a set of Python APIs. The constraints cover many types of common arrangement, including symmetry (\"Place chairs symmetrically around the table\"), spatial relation (\"Place plant pots close to windows\"), quantity (\"An equal number of knives and forks\"), physics (\"Ensure vases do not overhang\"), and accessibility (\"Ensure there is free-space in-front of all appliances\"). The constraints can be understood as a type of declarative procedural rules, which express what the user desires but not how to achieve it. Like other procedural rules, the constraints can be randomized and can be customized by the user.", + "bbox": [ + 75, + 613, + 470, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to constraint specification, our arrangement", + "bbox": [ + 96, + 886, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "system also includes a constraint solver, which searches for an arrangement that maximally satisfies a set of given constraints. Our solver greedily performs simulated annealing on whole-house floor plans, followed by large furniture layouts and then small objects. Compared to existing approaches for scene arrangement, our solver is highly expressive, supporting complex compositional constraints that are challenging or infeasible for existing approaches. In addition, it is the first solver integrated with an open-source and fully procedural generator.", + "bbox": [ + 496, + 460, + 893, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our constraint-based arrangement system is a significant contribution because it vastly improves the generation system's usability and customizability. Because it separates constraint specification from constraint solving, a user can conveniently express the objectives of procedural generation without worrying about implementation. This capability is not available in the original Infinigen, where the user has to customize the procedure rules at the implementation level.", + "bbox": [ + 496, + 613, + 893, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our third contribution—exporting to real-time simulators—is also noteworthy because it allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse. Thus, Infinigen Indoors can supply diverse 3D assets for simulation environments and enhance their domain randomization.", + "bbox": [ + 496, + 734, + 893, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To validate the effectiveness of the generated data and demonstrate our system's unique customizability, we use Infinigen Indoors to generate synthetic data for shadow removal and occlusion boundary detection, two tasks that lack", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21784", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/ef11e2cf1bd160715d9509ee464745d39f0608b8b9ead72895c648f6c781be0a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetArrangement MethodProcedural AssetsProvides Procedural Code# Scenes in Total# Assets in TotalFree AssetsExternal Asset Source
3DSSG [78]Real-world scansNoN/A1.5K48KYesNone
Matterport3D [6]Real-world scansNoN/A2K-YesNone
Stanford 2D-3D-S [2]Real-world scansNoN/A270-YesNone
ScanNet [9]Real-world scansNoN/A1.5K-YesNone
SceneNN [27]Real-world scansNoN/A100-YesNone
OpenRooms [44]Real-world scansNoNo1.3K3KNo ($500)ShapeNet [7], Scan2CAD [3], Adobe Stock [30]
Replica [69]Artist layoutsNoN/A18-YesAI Habitat [49]
Structured3D [3]Artist layoutsNoN/A22K472KNoProfessional Designers
Hypersim [63]Artist layoutsNoN/A46159KNo ($6000)Evermotion Architectures [14]
InteriorNet [43]Artist layoutsNoN/A22M1MNoManufactures / Kujiale [37]
Habitat 3.0 [34]Artist layoutsNoN/A21118.7KYesFloorplanner [15], Professional Designers
3D-FRONT [17]Artist layoutsNoN/A19K13KYes3D-FUTURE [18]
Robotrix [19]Artist layoutsNoN/A16-NoUE4Arch [77], UnrealEngine Marketplace [31]
DeepFurniture [47]Artist layoutsNoN/A20K-NoAdobe Mixamo [29]
SceneNetRGBD [94]Obj. Cat. Dist.NoN/A∞5.1KYesSceneNet [23], ShapeNet [7]
LUMINOUS [93]OptimizerNoYes∞2KYesAI2-THOR [36]
SceneNet [24]OptimizerNoNo∞3.7KYes3DModelFree [16], ModelNet [86], Archive3D [1], Stanford database
ProcTHOR [10]HeuristicsNoYes∞1.6KYesAI2-THOR [36], Professional Designers
Aria [52]--No100K8K--
Infinigen Indoors (Ours)Constraint LanguageYesYes∞∞YesNone
", + "bbox": [ + 76, + 88, + 893, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Comparisons to existing datasets and generators. Many existing datasets/generators use external, static asset libraries and have limited number of scenes. Ours is fully procedural, without using any external source. Dashes represent numbers we could not acquire or estimate.", + "bbox": [ + 75, + 324, + 893, + 364 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fd9ea204324e101a3c27304f47741832956441fa60a265e62df73b004c4a81a0.jpg", + "image_caption": [ + "Figure 2. Each image (a) is rendered from a mesh (b), from which we can also extract Depth (c), Surface Normals (d), Occlusion Boundaries (e), Segmentation (f), Bounding Boxes (e) and Optical Flow (h), with Albedo (i) from rendering metadata." + ], + "image_footnote": [], + "bbox": [ + 80, + 371, + 468, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "abundant existing training data. Our experiments show that data from our system improves generalization performance on indoor scenes.", + "bbox": [ + 75, + 616, + 468, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Like the original Infinigen, Infinigen Indoors will be open-sourced under the BSD license to enable free and unlimited use by everyone, and to enable community contributions of additional procedural generators.", + "bbox": [ + 75, + 662, + 470, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 738, + 218, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We provide a detailed comparison of Infinigen Indoors with existing datasets and generators in Tab. 1.", + "bbox": [ + 75, + 763, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Real-world datasets. Various real-world datasets have been introduced for indoor scene understanding [2, 6, 9, 27, 66, 67, 78], including the earlier and widely used NYUv2 [66] and Sun RGB-D [67], as well as more recent datasets [2, 4, 9, 78]. However, real-world datasets are labor intensive to collect and limited in size. In addition, real-world 3D ground truth can be difficult to acquire due to the limitations of depth", + "bbox": [ + 75, + 794, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sensors which include limited resolution and range, errors with transparent/reflective surfaces, and artifacts at object edges.", + "bbox": [ + 496, + 375, + 893, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Synthetic Indoor Datasets. There are many existing synthetic datasets for indoor scenes [3, 17, 19, 24, 34, 36, 43, 47, 63, 69]. However, the underlying 3D assets of many datasets are not freely accessible, limiting their utility. In addition, most use a static library of 3D assets, limiting their diversity. Recent work [10, 93] has incorporated procedural generation for scene layout and floor plan generation, but still relies on static libraries of objects and materials. In contrast, Infinigen Indoors is $100\\%$ procedural, with all assets from shape to texture generated from scratch with unlimited variation.", + "bbox": [ + 496, + 422, + 895, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object arrangement and layout generation. Constraints are potent tools to describe the layout of a scene. Early works like [88] represent constraints as hard-coded programs, and [50] represent them as physical relations. Data-driven works like [40, 56, 57, 62, 82, 84] learn constraints implicitly from data. Such implicit constraints are less customizable, interpretable, and controllable than Infinigen Indoors. Recently, modeling constraints using probabilistic graphs have become more popular: [89] uses pairwise grouping, while [11, 91] further extends it to spatial and hierarchical constraints. [90] uses factor graphs to parse the constraints, while [51] models them with Bayesian network. [58, 92] formulates constraints as potentials Markov Random Fields on a fixed graph, which capture only non-compositional and associative constraints for rooms and objects.", + "bbox": [ + 496, + 594, + 893, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compared to existing systems, ours is the first to integrate directly with procedural object generators, and our constraint language is higher level and more easily extendable than existing systems. Our system specifies high level goals for abstract classes of objects (e.g. 'furniture', 'stor", + "bbox": [ + 496, + 824, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21785", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/87f6c23f565177829a704e61e9019b4c18514c166384f73396cd7faa32a09534.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 85, + 472, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2c089284852a24c4cedf8f203f2c42860dfa40c84e3c4df475dd428160982ecd.jpg", + "image_caption": [ + "Figure 3. Random samples of procedurally generated doors (top), staircases (middle/bottom) and windows/warehouse shelving (bottom-right)." + ], + "image_footnote": [], + "bbox": [ + 81, + 253, + 468, + 366 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c130c862e36ee5096dcd9d888737d23958763153e248ffb657978951dc27bcb6.jpg", + "image_caption": [ + "Figure 4. Random samples of procedurally generated ovens, dishwasher and sinks (top/middle), living-room furniture (middle) and bathroom fixtures (bottom).", + "Figure 5. Random samples of procedurally generated furniture, including sofa, chairs and beds (top), tables (middle/bottom), and shelves (bottom)." + ], + "image_footnote": [], + "bbox": [ + 81, + 416, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "age'), rather than exhaustive distance/angle distributions for specific objects [91] which must be fitted to example scenes. Our language also supports compositional constraints such as \"place glassware only on shelves against a diningroom wall.\" These features allow users to write new constraints for their specific needs, including domains without existing artist-made scenes. Our constraint solver uses simulated annealing, following prior work [91], but involves moves that are unique to our constraint language, including updates to object-object relations or changing the parameters of procedural objects (e.g. the size of a table).", + "bbox": [ + 75, + 609, + 470, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 790, + 166, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Procedural Asset Generation", + "text_level": 1, + "bbox": [ + 76, + 816, + 334, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "All assets used in Infinigen Indoors are generated from scratch by compact probabilistic programs. These programs have many human-controllable parameters, which are randomized by default, or can be manually overridden by the", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9d2ef22b14a7fc9ba6b69f4d05292998b4540d6f491c3c44671ef1921a2b10f1.jpg", + "image_caption": [ + "Figure 6. Random samples of procedurally generated tableware, including dinnerware (Row 1-2), cookware (Row 2), food containers (Row 3) and dining utensils (Row 4)." + ], + "image_footnote": [], + "bbox": [ + 509, + 87, + 890, + 238 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1bc91cc0ef7e1d876705ce96035e61b34d0b43fa7b547fab359dfd7e949c29d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 306, + 890, + 385 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eb2fa7a5be9e8a27ef67411c5c38b3f722aa522ff0c549911391ef6db32a42a3.jpg", + "image_caption": [ + "Figure 7. Random samples of procedurally generated home decorations, including lamps, hardware, balloons, wall decor (top), rugs, book stacks, vases and plants (bottom). Small assets for decoration purposes, usually attached to the ground or walls.", + "Figure 8. A collection of materials generated in Infinigen Indoors. The first figure shows one material per generator, with columns (1-3) used on assets of various sizes, (4-5) used on assets and rooms, and (6) for abstract art and text. The second figure shows multiple materials from the same generator with different parameters." + ], + "image_footnote": [], + "bbox": [ + 504, + 452, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "user. These parameters are used along with additional low-level random noise to generate meshes via geometry nodes, modifiers, or mesh manipulations in Blender. We provide a total of 79 randomized procedural object generators. By category, we cover Appliances (10 generators, 112 params), Windows/Doors/Staircases (14 generators, 127 params), Furniture (17 generators, 216 params), Decorations (15 generators, 92 params), and Small Objects (19 generators, 194 params). See the supplement for a list.", + "bbox": [ + 496, + 732, + 893, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Architectural elements shown in Fig. 3 are integrated into room as fixtures. We use array repetition of atomic compo", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21786", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "tables = scene.with_semantics(Tag.Chair)\nchairs = scene.with_semantics(Tag.Table)\non_fLOOR = cl.StableAgainst(Tag Bottom, Tag.Floor)\nconstraints = clforall(rooms[Tag.DiningRoom],\nr,\n(tablets Related_to(r, on_fLOOR).count() == 1,\nchairs related_to(r, on_fLOOR).count().in_range(2, 10)),)\nscore = (\n chairs related_toRooms[Tag.DiningRoom], on_fLOOR)\n .mean(c, cl.reflection_symmetry(c, tables) + \\cl.min_distance(t, tables) * (-1))\n .maximize(weight=2)\n)", + "guess_lang": "txt", + "bbox": [ + 81, + 87, + 468, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 9. Example usage of our constraint specification API, specifying the quantity and aesthetic constraints for a dining table and chairs.", + "bbox": [ + 75, + 244, + 470, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "nents to build staircases, and mesh booleaning to cut out the panels of doors and windows.", + "bbox": [ + 75, + 316, + 468, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Large objects shown in Fig. 4 and 5 provide assets related to cooking, seating and storage. We use soft-body collision simulation to model soft blankets, clothing, and stuffed pillows when they are put on a supporting surface.", + "bbox": [ + 75, + 347, + 468, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Small objects shown in Fig. 6 and 7 can be attached to support surfaces, walls, or ceilings. We also devised a combined text-and-shape logo generator that produces procedural texture for fabrics, food packaging, and art decor. We use cloth simulation to inflate balloons and food packaging with air.", + "bbox": [ + 75, + 409, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Materials are all procedurally created with Blender's Shader nodes, as shown in Fig. 8. We provide 30 material generators with 120 controllable parameters total, split approximately evenly between types of Wood, Ceramic, Fabric, Metal, and others. We cover $78\\%$ of OpenSurfaces'[5] material categories, up from $21\\%$ for Infinigen.", + "bbox": [ + 75, + 484, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Constraint Specification API", + "text_level": 1, + "bbox": [ + 76, + 588, + 334, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Indoor scene layouts are highly regular, and follow complex rules governing ergonomics, aesthetics and functionality. Moreover, the rules that apply to a particular object depend on context - for example, tables are placed against walls when used as desks in study rooms, but must be far from walls and surrounded by chairs when used in a dining room. To capture this, we provide a high-level Constraint Specification API, which allows the user to write complex geometric scoring functions of sets of objects in the scene. This score is optimized by the solver to find a satisfactory layout. An example of the Constraint Specification API is shown in 9.", + "bbox": [ + 75, + 612, + 470, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each constraint in the specification API can be expressed as a composition of geometric operators. Geometric operators are designed to compute spatial and geometric properties, including minimum distance, rotational and reflection symmetry, angle alignment, 2D free-space, accessibility and volume or area of objects. By composing these operators with nested filtering by semantics and relations, the user can create scoped constraints that apply only to objects attached", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to specific surfaces or rooms. Additionally, these geometry terms are affected by the parameters (length, width, etc.) of the procedurally generated assets, meaning that optimizers can automatically discover optimal furniture parameters given available space and constraints. Our system features common scalar arithmetic operations, comparisons, and forall / sum operators to gather results over sets of objects. Please see the supplement for the full API and more constraint specification examples.", + "bbox": [ + 496, + 90, + 893, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A more concrete example of our constraint language can be found in Fig. 9, where the constraint program specifies common-sense human ergonomics and semantic relations found in residential homes. This constraint graph has a total of 1058 nodes, which compute 11 hard constraints and 25 score terms (soft constraints). We provide example constraint specifications for living rooms, bathrooms, dining rooms, kitchens, and warehouses. See the supplement for the full constraint program and example constraints.", + "bbox": [ + 496, + 227, + 890, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For generating training data, we believe many users will consider creating custom constraints tailored to particular applications. Our constraint system is designed to allow easy customization. Our initial spec. has avg. 15 constraints specific to each room: approx. 15 lines of Python. We believe this cost is very tractable when users need customization.", + "bbox": [ + 496, + 363, + 890, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Arrangement Solver", + "text_level": 1, + "bbox": [ + 500, + 462, + 692, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Because our Constraint Specification API is flexible, the solver needs to search a prohibitively large space in which finding an exact minimum is impossible. To deal with this, it uses Simulated Annealing[35] with Metropolis-Hastings criterion [25, 53]. The solver first takes the current state $s$ and randomly chooses a move category. It then uses the constraint graph to generate a proposed state $s'$ that can be reached using the move. The current and proposed states are evaluated on the graph specified by the provided constraints and score terms, yielding loss terms $l(s)$ and $l(s')$ . Then, the solver calculates transition probability between the $s$ and $s'$ as", + "bbox": [ + 496, + 484, + 890, + 664 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(s ^ {\\prime} \\mid s\\right) = \\min \\left[ \\exp \\left(l (s) - l \\left(s ^ {\\prime}\\right)\\right) / \\tau , 1 \\right]\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 666, + 821, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is the temperature of the solver, which cools exponentially from $\\tau = 0.25$ to $\\tau = 0.001$ .", + "bbox": [ + 496, + 688, + 893, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our solver allows both discrete and continuous moves: Addition - Adds a procedural object to the scene.", + "bbox": [ + 496, + 719, + 879, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Deletion - Deletes an object from the scene.", + "bbox": [ + 500, + 750, + 792, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relation Plane Change - Assigns an object to another plane. Resample - Regenerates an object with new parameters.", + "bbox": [ + 500, + 763, + 893, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reinitialize Pose - Samples a new random pose for an object. Translate - Translates the object within its DOF plane.", + "bbox": [ + 500, + 795, + 893, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rotate - Rotates the object around its DOF axis.", + "bbox": [ + 500, + 825, + 820, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We observe that not all moves are equally significant at each point in the optimization. In an empty scene, object addition and relation change allow for higher loss reduction, whereas in a cluttered scene, continuous object movement", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21787", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f9167d8340b1de69bfdfa65989d2e36667186ab3e706203f27ab4d00524e099d.jpg", + "image_caption": [ + "a)" + ], + "image_footnote": [], + "bbox": [ + 76, + 107, + 303, + 165 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4bcf509760a5fab1bf457cc7e9386a85f5e0baef1f810bc61c7600526e918797.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 308, + 90, + 410, + 179 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5f1bbfcddf8f046b949a9a5c21e6b04c603550f70c0ce079419ca816fd0698f3.jpg", + "image_caption": [ + "b)" + ], + "image_footnote": [], + "bbox": [ + 424, + 104, + 532, + 160 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a7e21cbc91fb78c6d923da5493deeea47ecf4e59f5004af782e4ca5a24d5ef0.jpg", + "image_caption": [ + "Figure 10. In Fig. a), we show ten randomly generated single-story floor plans with a diverse set of room combinations, connectedness, and overall contours. In Fig. b), we show results for the generation of multistory floor plans. Floors 0,1,2 are displayed separately. Staircases connect adjacent floors. We remove exterior walls and ceilings for visibility." + ], + "image_footnote": [], + "bbox": [ + 96, + 179, + 305, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/97204a480dcad206601a96285e160215da2a962d4769f747ae971bd35ed4af40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 328, + 179, + 419, + 263 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/345163aead45353d1ad4459cdf57dff9960e5e83fb998513f69489f7b760d15f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 176, + 516, + 267 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2103d2f63f6abc0ea6573a4a0eca0e54245607c13be5f80b616d0469095a4dc2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 540, + 109, + 658, + 176 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e53f2aee5acd224629e3daa19866037d413365ad5f7cf08217c1563a3bd714f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 90, + 776, + 176 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/22200ec601807dd4c191a3f6da957c7278e9b6e991059db92375077e343b6a0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 90, + 892, + 176 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e93e78a86712e8a8b35e0c23e492b18f4a3bb082bbd221c430b8c63a6673d31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 199, + 653, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/25d59dff288a008de0ac69189f254107ff2e45115a97f7587d33a1c5cc092831.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 195, + 769, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e5b967d64ad3c51ec20901c71ffb994a0b42efbd8ffdcf77fc86bc1efe64fb0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 189, + 885, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a0edaca90b3d090e3f46e2a777144b02ea2a4be489796b37b3c51645daa62b92.jpg", + "image_caption": [ + "Figure 11. Qualitative room arrangement results, grouped by room type. From left to right, we show bathrooms, dining rooms, living rooms and kitchens." + ], + "image_footnote": [], + "bbox": [ + 81, + 335, + 890, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "allows for higher loss reduction. Thus, we provide a schedule for moves so that probabilities for discrete moves decay gradually and probabilities for continuous moves increase.", + "bbox": [ + 75, + 539, + 468, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The objects in an indoor scene are interdependent on each other, which makes it unfeasible to optimize over all of them simultaneously. However, they usually depend on each other hierarchically (e.g., a cup is on the table, which is on the floor). To exploit this hierarchy, we divide our optimization into three stages: large object optimization, medium object optimization, and small object optimization.", + "bbox": [ + 75, + 585, + 468, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Each object is constrained in its movement due to the constraints specified by the user and the discrete moves proposed by the solver. For instance, a bookshelf that is stable against a wall is only allowed to move along the 1D line between the wall and the floor. Consequently, an object's degrees of freedom (DoFs) for rotation and translation are determined based on its relations to other objects. When the solver samples a continuous move, it restricts the object's motion to these DoFs. When the solver samples a discrete move, it places the object in the constrained subspace.", + "bbox": [ + 75, + 691, + 470, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Floorplan-specific solver and constraints Our floorplan generator creates realistic full-house room meshes as shown in Fig. 10. First, we procedurally generate a room adjacency", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "graph specifying the number, type, and connectedness of individual rooms required in the floor plan. This graph is produced by inference on a probabilistic context-free grammar on room types, or can be wholly or partially derived from user input. We define our objective function as a weighted combination of the terms below, and optimize it using simulated annealing subject to constraints from the room adjacency graph. See the supplement for full definitions.", + "bbox": [ + 496, + 539, + 893, + 659 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Shortest path to entrance", + "Typical room area", + "- Room aspect ratio", + "- Room convexity", + "- Room wall conciseness", + "- Functional room area", + "- Room collinearity", + "- Narrow passages", + "- Exterior length by room", + "- Exterior corners by room", + "- Staircase occupancies", + "- Staircase IOU with rooms" + ], + "bbox": [ + 509, + 660, + 883, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We initialize our floorplan solver by generating a random house outline, and subdividing it using a Mondrian Process [65] until it produces sufficient spaces for each room. We extrude a wall segment inwards or outwards at each step, or swap the assignment subject to the room adjacency graph. Either action will lead to a change in loss, which we convert to an acceptance probability using Metropolis-Hasting as in Sec 3.3. Once solving is complete, we add floor, wall, and ceiling materials, doors, windows, and staircases, all subject to constraints based on room type and adjacency. Fig", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21788", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/af7b6cba50d663146d8192e16443cea07307a5f05a46aaf5ab85882d1bf8a9f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 89, + 464, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d40cb8630077d8fa4399018ef414b47c66d74e4947eb58c9747cc88d0a234f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 256, + 464, + 421 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/82d7adb74bd039385fd8fdd705b7aca97e4b373e2f794148114788194b6c52a0.jpg", + "image_caption": [ + "Figure 12. A single scene from two different viewpoints in Unreal Engine 5 (above) and Omniverse Isaac Sim (below). Unreal Engine runs at 60 FPS and Isaac Sim with physics simulation enabled runs at 45 FPS, both on RTX 3090s. Differences in lighting are caused by the variations in simulator import systems.", + "Figure 13. Qualitative zero-shot results on SRD [59] test dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 515, + 467, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "11 shows the solutions to room arrangements with objects placed inside.", + "bbox": [ + 76, + 675, + 468, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.4. Data Export", + "text_level": 1, + "bbox": [ + 76, + 717, + 209, + 733 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/758b1e8afa14d5b37ac1abfdc8f307e1bc0984aa0e6fec36dadab265be82ef72.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
All ImageShadow RegionNon-Sh Region
Test SetModelPSNR↑RMSE↓PSNR↑RMSE↓PSNR↑RMSE↓
ISTD [81]R31.964.2738.046.5834.133.85
R+S31.724.3037.417.0633.803.85
SRD [59]R22.8310.8425.5918.7527.937.68
R+S24.569.5427.3916.6329.376.67
", + "bbox": [ + 81, + 753, + 467, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Shadow removal task quantitative performance on ISTD, ISTD+ and SRD dataset across the three variations of the model.", + "bbox": [ + 76, + 845, + 468, + 873 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We develop a one-click tool to export assets from Infini", + "bbox": [ + 96, + 885, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dfd1743aaad4d6f80c3bf809cf9cc3550399ae4bdecc766a94692e7a06680d9b.jpg", + "image_caption": [ + "Figure 14. Qualitative results on synthetic artistic scenes [21]." + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 887, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "gen Indoors to real-time simulators, using Universal Scene Description (USD) or other formats. As seen in Fig. 12, indoor scenes can be exported to Omniverse Isaac Sim and Unreal Engine 5 and can be run at interactive frame rates. This exporting capability allows Infinigen Indoors to help train embodied agents in virtual environments.", + "bbox": [ + 498, + 212, + 893, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Infinigen Indoors uses Blender's procedural material system, which is by default not portable to other simulators or scene editors. To resolve this, we provide tools to automatically post-process and UV-map entire indoor scenes, and use texture baking to create standard texture maps for material color, roughness, metallicity and more. We also provide export code to convert single objects to textured OBJ, FBX or STL meshes, and automatically generate collision and articulation information as Universal Robot Description Format (URDF) files.", + "bbox": [ + 498, + 304, + 893, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 470, + 632, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Solver Performance", + "text_level": 1, + "bbox": [ + 500, + 497, + 687, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To efficiently solve large numbers of constraints in cluttered scenes, we optimized our solver with various features for faster convergence. Plane hashing enables faster access to bounding planes during discrete optimization. BVH caching enables faster mesh distance and collision calculations by reusing Bounding-Volume-Hierarchies except when mutated by a state update. Evaluation caching maintains a cache of results in the evaluation graph. Move filtering narrows down the search space in continuous optimization by selectively pruning candidates to those that can reduce the loss. Place-holder optimization only generates full meshes when other objects are assigned to them; otherwise it keeps bounding boxes. See the supplement for more details.", + "bbox": [ + 498, + 522, + 893, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To analyze the importance of these features, we conducted an ablation in Tab. 3 and Fig. 15, which shows solver performance with each feature removed. All results are averaged over 20 random scenes with $5\\mathrm{k}$ solver steps. Our full system provides a $\\approx 3\\mathrm{x}$ speedup compared to the non-optimized version. Most of the performance gains come from BVH caching and Plane Hashing. We observe that discrete changes such as pose re-initialization, relation changes, and object resampling are necessary for compelling visuals, but decrease the quantitative score and increase the runtime. When we run our fully optimized system as long as the non-optimized version we get a $28\\%$ score increase.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21789", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ab1e66874dd014e90e62ae98718f19d336305031993cd2f69c5e49148450276.jpg", + "image_caption": [ + "Figure 15. Qualitative Ablation. From left to right, we show scenes generated by our system with 10K solving steps (a), 1K solving steps (b), with collision checking removed (c) and with symmetry terms disabled (d)" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 277, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/655a90473f39d29b9f04b258962241b8ddb81e157285740046f8113ebd78c711.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 88, + 483, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4078a12df63c48086f4e7f1f34012e1935bfeda1cd642032d36564b53aacee3f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 88, + 687, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9f451b90a77ca48ddbeeac019502494ac622f946f893c6c28d864d17eaf3a50a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 691, + 88, + 890, + 176 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/057092ae2646936f636ad3fe062fa12e690f6e44fe906cc063e5c94850629743.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRuntime ↓Avg. Score (s) ↑#Objects ↑
Full System2280.6880.8428.94
w/o Discrete change1872.6086.2030.82
w/o Eval. cache2242.7980.8428.94
w/o Move Filter2633.9584.7545.06
w/o Placeholder optim.2665.1880.4627.71
w/o Plane Hashing3522.8692.6534.12
w/o BVH cache4740.4880.8429.06
Full System 100 min.6080.84114.7249.65
w/o Optimization6308.9289.4347.76
", + "bbox": [ + 81, + 239, + 467, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Perceptual Study We recruited human subjects following [57] to evaluate the realism of the scenes and the realism of the layouts. Subjects preferred Infinigen Indoors over [11, 57, 62, 84] in terms of both realism, layout realism, and the lack of errors (caveat: \"realism\" may be influenced by asset and lighting quality). See the supp. for more details.", + "bbox": [ + 75, + 412, + 468, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Shadow Removal", + "text_level": 1, + "bbox": [ + 76, + 512, + 246, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To demonstrate its flexibility in data generation, we used Infinigen-Indoors to create a dataset consisting of 2k image pairs of shadow and shadow-free variants. These pairs were generated by toggling the shadow property of lighting within Blender. For each pair, shadow masks were produced using Otsu's thresholding [55] method. We use ShadowFormer [22] model for the experiments and consider two variations: only trained on ISTD [81] real dataset (R), and trained on combination of ISTD and 2k Infinigen Indoors synthetic dataset $(\\mathbb{R} + \\mathbb{S})$ . The results are shown in Tab. 2. While using synthetic data leads to slightly worse performance on ISTD dataset, the zero-shot application on SRD [59] dataset shows clear improvement for generalization to new test datasets. Qualitative results are shown in Fig. 13.", + "bbox": [ + 75, + 536, + 472, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Occlusion Boundary Estimation", + "text_level": 1, + "bbox": [ + 76, + 756, + 359, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate the effectiveness of Infinigen Indoors, we also evaluate on the task of occlusion boundary estimation, a task with limited available data. We produce 1464 images annotated with ground truth. We train three U-Net [64] models from scratch separately on these images, on images generated from Infinigen [60] and Hypersim [63]. We then compare their performance on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c72371119d8ba6056868dea8d94a2a6c02a37cf0631a63353b582a1f82eb7d55.jpg", + "table_caption": [ + "Table 3. Ablation of solver performance optimizations." + ], + "table_footnote": [], + "table_body": "
Training DatasetODSOISmAP
Infinigen-Nature [60]14.3819.4310.80
Hypersim [63]26.0219.4415.69
Infinigen Indoors (Ours)29.4730.2919.09
", + "bbox": [ + 511, + 239, + 880, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Occlusion boundary quantitative results on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture visualization [21].", + "bbox": [ + 498, + 327, + 893, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "visualization [21], since no existing photorealistic indoor dataset provides such annotations. See the supplement for more details.", + "bbox": [ + 496, + 398, + 890, + 444 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We report the following three metrics [79, 80, 85]: (i) optimal dataset scale $F$ -score (ODS), representing the best F-score achieved on the dataset using a uniform threshold across all test images; (ii) optimal image scale $F$ -score (OIS) indicating the cumulative F-score on the dataset obtained with thresholds dependent on individual images; and (iii) mean average precision (mAP) denoting the mean precision across the complete recall range.", + "bbox": [ + 496, + 446, + 893, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As we can see in Tab. 4, our Infinigen Indoors-trained model generalizes better. The model achieves higher performance across all metrics. These findings underscore the usefulness of Infinigen Indoors as a valuable training resource. Qualitative results are depicted in Fig. 14.", + "bbox": [ + 496, + 568, + 893, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Contributions & Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 662, + 830, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Alexander Raistrick, Lingjie Mei and Karhan Kayan contributed equally and are ordered randomly. Each has the right to list their name first in their CV. Alexander Raistrick performed team coordination and developed the constraint language and object graph solver. Lingjie Mei developed the room solver and many procedural assets. Karhan Kayan developed the geometric constraints and object pose solver. David Yan developed the scene exporter and other utilities. Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Zeyu Ma and Lahav Lipson developed procedural assets and utilities. Jia Deng conceptualized and led the project, and set directions. This work was partially supported by the National Science Foundation and Amazon.", + "bbox": [ + 496, + 688, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21790", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Archive 3D. Archive 3d. https://archive3d.net/. 3", + "[2] I. Armeni, A. Sax, A. R. Zamir, and S. Savarese. Joint 2D-3D-Semantic Data for Indoor Scene Understanding. ArXiv e-prints, 2017. 3", + "[3] Armen Avetisyan, Manuel Dahnert, Angela Dai, Manolis Savva, Angel X Chang, and Matthias Nießner. Scan2cad: Learning cad model alignment in rgb-d scans. 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Luminous: Indoor scene generation for embodied ai challenges. arXiv preprint arXiv:2111.05527, 2021. 3", + "[94] Jia Zheng, Junfei Zhang, Jing Li, Rui Tang, Shenghua Gao, and Zihan Zhou. Structured3d: A large photo-realistic dataset for structured 3d modeling. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part IX 16, pages 519-535. Springer, 2020. 3" + ], + "bbox": [ + 78, + 92, + 470, + 641 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "21794", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/6d8274a0-6d1c-4618-99cc-d4d3f62a5569_model.json b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/6d8274a0-6d1c-4618-99cc-d4d3f62a5569_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ea5b65480299d32544e3140fd9b42ea607f49921 --- /dev/null +++ b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/6d8274a0-6d1c-4618-99cc-d4d3f62a5569_model.json @@ -0,0 +1,3007 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.131, + 0.872, + 0.152 + ], + "angle": 0, + "content": "Infinigen Indoors: Photorealistic Indoor Scenes using Procedural Generation" + }, + { + "type": "text", + "bbox": [ + 0.166, + 0.182, + 0.804, + 0.253 + ], + "angle": 0, + "content": "Alexander Raistrick*, Lingjie Mei*, Karhan Kayan*, (*equal contribution; random order) David Yan, Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Lahav Lipson, Zeyu Ma, Jia Deng Department of Computer Science, Princeton University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.56 + ], + "angle": 0, + "content": "We introduce Infinigen Indoors, a Blender-based procedural generator of photorealistic indoor scenes. It builds upon the existing Infinigen system, which focuses on natural scenes, but expands its coverage to indoor scenes by introducing a diverse library of procedural indoor assets, including furniture, architecture elements, appliances, and other day-to-day objects. It also introduces a constraint-based arrangement system, which consists of a domain-specific language for expressing diverse constraints on scene composition, and a solver that generates scene compositions that maximally satisfy the constraints. We provide an export tool that allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse and Unreal. Infinigen Indoors is open-sourced under the BSD license. Please visit infinigen.org for code and videos." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.589, + 0.21, + 0.605 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.78 + ], + "angle": 0, + "content": "Synthetic data rendered by conventional computer graphics has seen increasing adoption in computer vision[10, 38, 41, 42, 46, 48, 61] and AI research[20, 28, 76], especially for 3D vision[26, 45, 71, 73-75, 83] and embodied AI[12, 32, 36, 68, 70, 87]. Synthetic data can be rendered in unlimited quantities and can automatically provide high-quality 3D ground truth, enabling large-scale training of computer vision models and embodied agents. Notably, many state-of-the-art 3D vision systems[72, 75] and robotic systems [33, 39] have been trained purely in simulation yet perform surprisingly well in the real world zero-shot." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.472, + 0.904 + ], + "angle": 0, + "content": "A promising direction for creating synthetic data is procedural generation, which uses mathematical rules to create 3D objects and scenes, as opposed to manual sculpting or real-world scanning. These mathematical rules can have parameters that are randomized to allow infinite variations. For example, trees can be generated through a recursive set of rules that randomly branch off. Compared to reusing a fixed, static set of 3D assets, procedural generation can greatly" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.288, + 0.892, + 0.317 + ], + "angle": 0, + "content": "improve the diversity of the synthetic data and the simulated environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.895, + 0.532 + ], + "angle": 0, + "content": "Infinigen [60] is a recent work that pushed the idea of procedural generation to the limit. Infinigen is an open-source system that generates photorealistic 3D scenes fully procedurally, meaning that every 3D asset, from shape to material, from large structures to small details, is completely procedural, without using any external static asset. Being fully procedural means that every aspect of the 3D scene, from the details of individual objects to their arrangements in a scene, can be customized and controlled by simply modifying the underlying mathematical rules. As a result, a 3D scene can be randomized at all levels down to the smallest details, as opposed to only at the level of object arrangement, which was common in earlier work that used procedural generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.895, + 0.67 + ], + "angle": 0, + "content": "However, the current Infinigen system is limited to natural scenes and objects (terrains, animals, plants, etc.). Although natural scenes could be sufficient for training foundation models as evidenced by natural evolution [60], this hypothesis remains unproven and may require additional advances in learning algorithms and architecture designs. Evidence from the current literature suggests that synthetic training data that more closely approximates the application domain is still likely to lead to better downstream performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.896, + 0.853 + ], + "angle": 0, + "content": "To overcome this limitation, we introduce Infinigen Indoors, a procedural generator of photorealistic indoor scenes. It expands the coverage of Infinigen to indoor scenes, which are relevant for many high-impact applications including robotics and augmented reality. Infinigen Indoors generates diverse indoor objects, including furniture, appliances, cookware, dining utensils, architectural elements, and other common day-to-day objects. It also generates full indoor scenes, including the interior of multi-room, multi-floor buildings, with object arrangements that are physically and semantically plausible. Fig. 1 shows random samples of generated scenes, and Fig. 2 shows some automatic annotations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Like the original Infinigen, Infinigen Indoors is not a fixed set of 3D models or scenes; instead, it is an open-source generator that can create unlimited variations both" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21783" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.483, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.091, + 0.89, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.253, + 0.483, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.253, + 0.89, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.425, + 0.893, + 0.454 + ], + "angle": 0, + "content": "Figure 1. Random, non cherry-picked sample of images generated by our system. From top left to bottom right, we show images from dining rooms, bathrooms, living rooms and kitchens. Please see the supplement for an extended random sample." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.507 + ], + "angle": 0, + "content": "at the object level and at the scene level. Infinigen Indoors is also \\(100\\%\\) procedural, using no external assets and using only mathematical rules to generate everything from scratch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Infinigen Indoors builds upon the original Infinigen and Blender [8] but makes significant new contributions. The main contributions include (1) a library of procedural generators of indoor assets, (2) a constraint-based arrangement system, (3) a tool to export the generated scenes to real-time simulators such as NVIDIA Omniverse [54] and Unreal Engine[13]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.884 + ], + "angle": 0, + "content": "Our second contribution—a constraint-based arrangement system—offers a new capability specifically targeting indoor settings. Indoor scenes are artificial, and object arrangement exhibits a greater degree of regularity than natural scenes: for example, furniture usually does not block the entrance of a room. We thus develop a system that lets the user specify scene arrangement constraints through a domain-specific language using a set of Python APIs. The constraints cover many types of common arrangement, including symmetry (\"Place chairs symmetrically around the table\"), spatial relation (\"Place plant pots close to windows\"), quantity (\"An equal number of knives and forks\"), physics (\"Ensure vases do not overhang\"), and accessibility (\"Ensure there is free-space in-front of all appliances\"). The constraints can be understood as a type of declarative procedural rules, which express what the user desires but not how to achieve it. Like other procedural rules, the constraints can be randomized and can be customized by the user." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.887, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In addition to constraint specification, our arrangement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.895, + 0.612 + ], + "angle": 0, + "content": "system also includes a constraint solver, which searches for an arrangement that maximally satisfies a set of given constraints. Our solver greedily performs simulated annealing on whole-house floor plans, followed by large furniture layouts and then small objects. Compared to existing approaches for scene arrangement, our solver is highly expressive, supporting complex compositional constraints that are challenging or infeasible for existing approaches. In addition, it is the first solver integrated with an open-source and fully procedural generator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Our constraint-based arrangement system is a significant contribution because it vastly improves the generation system's usability and customizability. Because it separates constraint specification from constraint solving, a user can conveniently express the objectives of procedural generation without worrying about implementation. This capability is not available in the original Infinigen, where the user has to customize the procedure rules at the implementation level." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.839 + ], + "angle": 0, + "content": "Our third contribution—exporting to real-time simulators—is also noteworthy because it allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse. Thus, Infinigen Indoors can supply diverse 3D assets for simulation environments and enhance their domain randomization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To validate the effectiveness of the generated data and demonstrate our system's unique customizability, we use Infinigen Indoors to generate synthetic data for shadow removal and occlusion boundary detection, two tasks that lack" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21784" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.316 + ], + "angle": 0, + "content": "
DatasetArrangement MethodProcedural AssetsProvides Procedural Code# Scenes in Total# Assets in TotalFree AssetsExternal Asset Source
3DSSG [78]Real-world scansNoN/A1.5K48KYesNone
Matterport3D [6]Real-world scansNoN/A2K-YesNone
Stanford 2D-3D-S [2]Real-world scansNoN/A270-YesNone
ScanNet [9]Real-world scansNoN/A1.5K-YesNone
SceneNN [27]Real-world scansNoN/A100-YesNone
OpenRooms [44]Real-world scansNoNo1.3K3KNo ($500)ShapeNet [7], Scan2CAD [3], Adobe Stock [30]
Replica [69]Artist layoutsNoN/A18-YesAI Habitat [49]
Structured3D [3]Artist layoutsNoN/A22K472KNoProfessional Designers
Hypersim [63]Artist layoutsNoN/A46159KNo ($6000)Evermotion Architectures [14]
InteriorNet [43]Artist layoutsNoN/A22M1MNoManufactures / Kujiale [37]
Habitat 3.0 [34]Artist layoutsNoN/A21118.7KYesFloorplanner [15], Professional Designers
3D-FRONT [17]Artist layoutsNoN/A19K13KYes3D-FUTURE [18]
Robotrix [19]Artist layoutsNoN/A16-NoUE4Arch [77], UnrealEngine Marketplace [31]
DeepFurniture [47]Artist layoutsNoN/A20K-NoAdobe Mixamo [29]
SceneNetRGBD [94]Obj. Cat. Dist.NoN/A∞5.1KYesSceneNet [23], ShapeNet [7]
LUMINOUS [93]OptimizerNoYes∞2KYesAI2-THOR [36]
SceneNet [24]OptimizerNoNo∞3.7KYes3DModelFree [16], ModelNet [86], Archive3D [1], Stanford database
ProcTHOR [10]HeuristicsNoYes∞1.6KYesAI2-THOR [36], Professional Designers
Aria [52]--No100K8K--
Infinigen Indoors (Ours)Constraint LanguageYesYes∞∞YesNone
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.325, + 0.895, + 0.366 + ], + "angle": 0, + "content": "Table 1. Comparisons to existing datasets and generators. Many existing datasets/generators use external, static asset libraries and have limited number of scenes. Ours is fully procedural, without using any external source. Dashes represent numbers we could not acquire or estimate." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.372, + 0.47, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.61 + ], + "angle": 0, + "content": "Figure 2. Each image (a) is rendered from a mesh (b), from which we can also extract Depth (c), Surface Normals (d), Occlusion Boundaries (e), Segmentation (f), Bounding Boxes (e) and Optical Flow (h), with Albedo (i) from rendering metadata." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.47, + 0.661 + ], + "angle": 0, + "content": "abundant existing training data. Our experiments show that data from our system improves generalization performance on indoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.471, + 0.724 + ], + "angle": 0, + "content": "Like the original Infinigen, Infinigen Indoors will be open-sourced under the BSD license to enable free and unlimited use by everyone, and to enable community contributions of additional procedural generators." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.22, + 0.755 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.794 + ], + "angle": 0, + "content": "We provide a detailed comparison of Infinigen Indoors with existing datasets and generators in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Real-world datasets. Various real-world datasets have been introduced for indoor scene understanding [2, 6, 9, 27, 66, 67, 78], including the earlier and widely used NYUv2 [66] and Sun RGB-D [67], as well as more recent datasets [2, 4, 9, 78]. However, real-world datasets are labor intensive to collect and limited in size. In addition, real-world 3D ground truth can be difficult to acquire due to the limitations of depth" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.895, + 0.422 + ], + "angle": 0, + "content": "sensors which include limited resolution and range, errors with transparent/reflective surfaces, and artifacts at object edges." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.897, + 0.59 + ], + "angle": 0, + "content": "Synthetic Indoor Datasets. There are many existing synthetic datasets for indoor scenes [3, 17, 19, 24, 34, 36, 43, 47, 63, 69]. However, the underlying 3D assets of many datasets are not freely accessible, limiting their utility. In addition, most use a static library of 3D assets, limiting their diversity. Recent work [10, 93] has incorporated procedural generation for scene layout and floor plan generation, but still relies on static libraries of objects and materials. In contrast, Infinigen Indoors is \\(100\\%\\) procedural, with all assets from shape to texture generated from scratch with unlimited variation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.895, + 0.822 + ], + "angle": 0, + "content": "Object arrangement and layout generation. Constraints are potent tools to describe the layout of a scene. Early works like [88] represent constraints as hard-coded programs, and [50] represent them as physical relations. Data-driven works like [40, 56, 57, 62, 82, 84] learn constraints implicitly from data. Such implicit constraints are less customizable, interpretable, and controllable than Infinigen Indoors. Recently, modeling constraints using probabilistic graphs have become more popular: [89] uses pairwise grouping, while [11, 91] further extends it to spatial and hierarchical constraints. [90] uses factor graphs to parse the constraints, while [51] models them with Bayesian network. [58, 92] formulates constraints as potentials Markov Random Fields on a fixed graph, which capture only non-compositional and associative constraints for rooms and objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Compared to existing systems, ours is the first to integrate directly with procedural object generators, and our constraint language is higher level and more easily extendable than existing systems. Our system specifies high level goals for abstract classes of objects (e.g. 'furniture', 'stor" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21785" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.087, + 0.473, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.213, + 0.47, + 0.255 + ], + "angle": 0, + "content": "Figure 3. Random samples of procedurally generated doors (top), staircases (middle/bottom) and windows/warehouse shelving (bottom-right)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.255, + 0.47, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.376, + 0.471, + 0.417 + ], + "angle": 0, + "content": "Figure 4. Random samples of procedurally generated ovens, dishwasher and sinks (top/middle), living-room furniture (middle) and bathroom fixtures (bottom)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.417, + 0.469, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.54, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Figure 5. Random samples of procedurally generated furniture, including sofa, chairs and beds (top), tables (middle/bottom), and shelves (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.471, + 0.776 + ], + "angle": 0, + "content": "age'), rather than exhaustive distance/angle distributions for specific objects [91] which must be fitted to example scenes. Our language also supports compositional constraints such as \"place glassware only on shelves against a diningroom wall.\" These features allow users to write new constraints for their specific needs, including domains without existing artist-made scenes. Our constraint solver uses simulated annealing, following prior work [91], but involves moves that are unique to our constraint language, including updates to object-object relations or changing the parameters of procedural objects (e.g. the size of a table)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.791, + 0.168, + 0.807 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.336, + 0.832 + ], + "angle": 0, + "content": "3.1. Procedural Asset Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "All assets used in Infinigen Indoors are generated from scratch by compact probabilistic programs. These programs have many human-controllable parameters, which are randomized by default, or can be manually overridden by the" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.088, + 0.891, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.251, + 0.894, + 0.294 + ], + "angle": 0, + "content": "Figure 6. Random samples of procedurally generated tableware, including dinnerware (Row 1-2), cookware (Row 2), food containers (Row 3) and dining utensils (Row 4)." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.308, + 0.891, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.397, + 0.894, + 0.453 + ], + "angle": 0, + "content": "Figure 7. Random samples of procedurally generated home decorations, including lamps, hardware, balloons, wall decor (top), rugs, book stacks, vases and plants (bottom). Small assets for decoration purposes, usually attached to the ground or walls." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.453, + 0.892, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.635, + 0.894, + 0.705 + ], + "angle": 0, + "content": "Figure 8. A collection of materials generated in Infinigen Indoors. The first figure shows one material per generator, with columns (1-3) used on assets of various sizes, (4-5) used on assets and rooms, and (6) for abstract art and text. The second figure shows multiple materials from the same generator with different parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.87 + ], + "angle": 0, + "content": "user. These parameters are used along with additional low-level random noise to generate meshes via geometry nodes, modifiers, or mesh manipulations in Blender. We provide a total of 79 randomized procedural object generators. By category, we cover Appliances (10 generators, 112 params), Windows/Doors/Staircases (14 generators, 127 params), Furniture (17 generators, 216 params), Decorations (15 generators, 92 params), and Small Objects (19 generators, 194 params). See the supplement for a list." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Architectural elements shown in Fig. 3 are integrated into room as fixtures. We use array repetition of atomic compo" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21786" + } + ], + [ + { + "type": "code", + "bbox": [ + 0.082, + 0.088, + 0.47, + 0.235 + ], + "angle": 0, + "content": "```cpp\ntables = scene.with_semantics(Tag.Chair)\nchairs = scene.with_semantics(Tag.Table)\non_fLOOR = cl.StableAgainst(Tag Bottom, Tag.Floor)\nconstraints = clforall(rooms[Tag.DiningRoom],\nr,\n(tablets Related_to(r, on_fLOOR).count() == 1,\nchairs related_to(r, on_fLOOR).count().in_range(2, 10)),)\nscore = (\n chairs related_toRooms[Tag.DiningRoom], on_fLOOR)\n .mean(c, cl.reflection_symmetry(c, tables) + \\cl.min_distance(t, tables) * (-1))\n .maximize(weight=2)\n)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.246, + 0.471, + 0.287 + ], + "angle": 0, + "content": "Figure 9. Example usage of our constraint specification API, specifying the quantity and aesthetic constraints for a dining table and chairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.469, + 0.347 + ], + "angle": 0, + "content": "nents to build staircases, and mesh booleaning to cut out the panels of doors and windows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.409 + ], + "angle": 0, + "content": "Large objects shown in Fig. 4 and 5 provide assets related to cooking, seating and storage. We use soft-body collision simulation to model soft blankets, clothing, and stuffed pillows when they are put on a supporting surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Small objects shown in Fig. 6 and 7 can be attached to support surfaces, walls, or ceilings. We also devised a combined text-and-shape logo generator that produces procedural texture for fabrics, food packaging, and art decor. We use cloth simulation to inflate balloons and food packaging with air." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Materials are all procedurally created with Blender's Shader nodes, as shown in Fig. 8. We provide 30 material generators with 120 controllable parameters total, split approximately evenly between types of Wood, Ceramic, Fabric, Metal, and others. We cover \\(78\\%\\) of OpenSurfaces'[5] material categories, up from \\(21\\%\\) for Infinigen." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.589, + 0.336, + 0.605 + ], + "angle": 0, + "content": "3.2. Constraint Specification API" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.471, + 0.779 + ], + "angle": 0, + "content": "Indoor scene layouts are highly regular, and follow complex rules governing ergonomics, aesthetics and functionality. Moreover, the rules that apply to a particular object depend on context - for example, tables are placed against walls when used as desks in study rooms, but must be far from walls and surrounded by chairs when used in a dining room. To capture this, we provide a high-level Constraint Specification API, which allows the user to write complex geometric scoring functions of sets of objects in the scene. This score is optimized by the solver to find a satisfactory layout. An example of the Constraint Specification API is shown in 9." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Each constraint in the specification API can be expressed as a composition of geometric operators. Geometric operators are designed to compute spatial and geometric properties, including minimum distance, rotational and reflection symmetry, angle alignment, 2D free-space, accessibility and volume or area of objects. By composing these operators with nested filtering by semantics and relations, the user can create scoped constraints that apply only to objects attached" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.227 + ], + "angle": 0, + "content": "to specific surfaces or rooms. Additionally, these geometry terms are affected by the parameters (length, width, etc.) of the procedurally generated assets, meaning that optimizers can automatically discover optimal furniture parameters given available space and constraints. Our system features common scalar arithmetic operations, comparisons, and forall / sum operators to gather results over sets of objects. Please see the supplement for the full API and more constraint specification examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.363 + ], + "angle": 0, + "content": "A more concrete example of our constraint language can be found in Fig. 9, where the constraint program specifies common-sense human ergonomics and semantic relations found in residential homes. This constraint graph has a total of 1058 nodes, which compute 11 hard constraints and 25 score terms (soft constraints). We provide example constraint specifications for living rooms, bathrooms, dining rooms, kitchens, and warehouses. See the supplement for the full constraint program and example constraints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.454 + ], + "angle": 0, + "content": "For generating training data, we believe many users will consider creating custom constraints tailored to particular applications. Our constraint system is designed to allow easy customization. Our initial spec. has avg. 15 constraints specific to each room: approx. 15 lines of Python. We believe this cost is very tractable when users need customization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.463, + 0.694, + 0.479 + ], + "angle": 0, + "content": "3.3. Arrangement Solver" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Because our Constraint Specification API is flexible, the solver needs to search a prohibitively large space in which finding an exact minimum is impossible. To deal with this, it uses Simulated Annealing[35] with Metropolis-Hastings criterion [25, 53]. The solver first takes the current state \\( s \\) and randomly chooses a move category. It then uses the constraint graph to generate a proposed state \\( s' \\) that can be reached using the move. The current and proposed states are evaluated on the graph specified by the provided constraints and score terms, yielding loss terms \\( l(s) \\) and \\( l(s') \\). Then, the solver calculates transition probability between the \\( s \\) and \\( s' \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.667, + 0.822, + 0.684 + ], + "angle": 0, + "content": "\\[\np \\left(s ^ {\\prime} \\mid s\\right) = \\min \\left[ \\exp \\left(l (s) - l \\left(s ^ {\\prime}\\right)\\right) / \\tau , 1 \\right]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.894, + 0.718 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the temperature of the solver, which cools exponentially from \\(\\tau = 0.25\\) to \\(\\tau = 0.001\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.88, + 0.75 + ], + "angle": 0, + "content": "Our solver allows both discrete and continuous moves: Addition - Adds a procedural object to the scene." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.751, + 0.794, + 0.764 + ], + "angle": 0, + "content": "Deletion - Deletes an object from the scene." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.765, + 0.894, + 0.795 + ], + "angle": 0, + "content": "Relation Plane Change - Assigns an object to another plane. Resample - Regenerates an object with new parameters." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.796, + 0.894, + 0.825 + ], + "angle": 0, + "content": "Reinitialize Pose - Samples a new random pose for an object. Translate - Translates the object within its DOF plane." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.826, + 0.821, + 0.84 + ], + "angle": 0, + "content": "Rotate - Rotates the object around its DOF axis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We observe that not all moves are equally significant at each point in the optimization. In an empty scene, object addition and relation change allow for higher loss reduction, whereas in a cluttered scene, continuous object movement" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21787" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.092, + 0.095, + 0.103 + ], + "angle": 0, + "content": "a)" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.108, + 0.305, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.092, + 0.411, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.425, + 0.105, + 0.534, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.18, + 0.307, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.329, + 0.18, + 0.42, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.451, + 0.178, + 0.517, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.091, + 0.553, + 0.103 + ], + "angle": 0, + "content": "b)" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.111, + 0.66, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.092, + 0.777, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.092, + 0.893, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.2, + 0.655, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.196, + 0.77, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.19, + 0.886, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.893, + 0.322 + ], + "angle": 0, + "content": "Figure 10. In Fig. a), we show ten randomly generated single-story floor plans with a diverse set of room combinations, connectedness, and overall contours. In Fig. b), we show results for the generation of multistory floor plans. Floors 0,1,2 are displayed separately. Staircases connect adjacent floors. We remove exterior walls and ceilings for visibility." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.336, + 0.891, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.504, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 11. Qualitative room arrangement results, grouped by room type. From left to right, we show bathrooms, dining rooms, living rooms and kitchens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.47, + 0.584 + ], + "angle": 0, + "content": "allows for higher loss reduction. Thus, we provide a schedule for moves so that probabilities for discrete moves decay gradually and probabilities for continuous moves increase." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.691 + ], + "angle": 0, + "content": "The objects in an indoor scene are interdependent on each other, which makes it unfeasible to optimize over all of them simultaneously. However, they usually depend on each other hierarchically (e.g., a cup is on the table, which is on the floor). To exploit this hierarchy, we divide our optimization into three stages: large object optimization, medium object optimization, and small object optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.471, + 0.844 + ], + "angle": 0, + "content": "Each object is constrained in its movement due to the constraints specified by the user and the discrete moves proposed by the solver. For instance, a bookshelf that is stable against a wall is only allowed to move along the 1D line between the wall and the floor. Consequently, an object's degrees of freedom (DoFs) for rotation and translation are determined based on its relations to other objects. When the solver samples a continuous move, it restricts the object's motion to these DoFs. When the solver samples a discrete move, it places the object in the constrained subspace." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Floorplan-specific solver and constraints Our floorplan generator creates realistic full-house room meshes as shown in Fig. 10. First, we procedurally generate a room adjacency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.895, + 0.66 + ], + "angle": 0, + "content": "graph specifying the number, type, and connectedness of individual rooms required in the floor plan. This graph is produced by inference on a probabilistic context-free grammar on room types, or can be wholly or partially derived from user input. We define our objective function as a weighted combination of the terms below, and optimize it using simulated annealing subject to constraints from the room adjacency graph. See the supplement for full definitions." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.661, + 0.687, + 0.675 + ], + "angle": 0, + "content": "- Shortest path to entrance" + }, + { + "type": "text", + "bbox": [ + 0.699, + 0.661, + 0.834, + 0.675 + ], + "angle": 0, + "content": "Typical room area" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.676, + 0.643, + 0.689 + ], + "angle": 0, + "content": "- Room aspect ratio" + }, + { + "type": "text", + "bbox": [ + 0.703, + 0.676, + 0.822, + 0.689 + ], + "angle": 0, + "content": "- Room convexity" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.691, + 0.677, + 0.704 + ], + "angle": 0, + "content": "- Room wall conciseness" + }, + { + "type": "text", + "bbox": [ + 0.703, + 0.691, + 0.855, + 0.704 + ], + "angle": 0, + "content": "- Functional room area" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.706, + 0.643, + 0.72 + ], + "angle": 0, + "content": "- Room collinearity" + }, + { + "type": "text", + "bbox": [ + 0.703, + 0.706, + 0.826, + 0.72 + ], + "angle": 0, + "content": "- Narrow passages" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.721, + 0.682, + 0.735 + ], + "angle": 0, + "content": "- Exterior length by room" + }, + { + "type": "text", + "bbox": [ + 0.703, + 0.721, + 0.88, + 0.735 + ], + "angle": 0, + "content": "- Exterior corners by room" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.736, + 0.667, + 0.75 + ], + "angle": 0, + "content": "- Staircase occupancies" + }, + { + "type": "text", + "bbox": [ + 0.703, + 0.736, + 0.885, + 0.749 + ], + "angle": 0, + "content": "- Staircase IOU with rooms" + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.661, + 0.885, + 0.75 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We initialize our floorplan solver by generating a random house outline, and subdividing it using a Mondrian Process [65] until it produces sufficient spaces for each room. We extrude a wall segment inwards or outwards at each step, or swap the assignment subject to the room adjacency graph. Either action will lead to a change in loss, which we convert to an acceptance probability using Metropolis-Hasting as in Sec 3.3. Once solving is complete, we add floor, wall, and ceiling materials, doors, windows, and staircases, all subject to constraints based on room type and adjacency. Fig" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21788" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.09, + 0.465, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.257, + 0.465, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.442, + 0.47, + 0.512 + ], + "angle": 0, + "content": "Figure 12. A single scene from two different viewpoints in Unreal Engine 5 (above) and Omniverse Isaac Sim (below). Unreal Engine runs at 60 FPS and Isaac Sim with physics simulation enabled runs at 45 FPS, both on RTX 3090s. Differences in lighting are caused by the variations in simulator import systems." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.516, + 0.468, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.635, + 0.466, + 0.649 + ], + "angle": 0, + "content": "Figure 13. Qualitative zero-shot results on SRD [59] test dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.676, + 0.469, + 0.707 + ], + "angle": 0, + "content": "11 shows the solutions to room arrangements with objects placed inside." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.718, + 0.21, + 0.734 + ], + "angle": 0, + "content": "3.4. Data Export" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.755, + 0.468, + 0.837 + ], + "angle": 0, + "content": "
All ImageShadow RegionNon-Sh Region
Test SetModelPSNR↑RMSE↓PSNR↑RMSE↓PSNR↑RMSE↓
ISTD [81]R31.964.2738.046.5834.133.85
R+S31.724.3037.417.0633.803.85
SRD [59]R22.8310.8425.5918.7527.937.68
R+S24.569.5427.3916.6329.376.67
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.847, + 0.47, + 0.874 + ], + "angle": 0, + "content": "Table 2. Shadow removal task quantitative performance on ISTD, ISTD+ and SRD dataset across the three variations of the model." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We develop a one-click tool to export assets from Infini" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.091, + 0.888, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.189, + 0.88, + 0.203 + ], + "angle": 0, + "content": "Figure 14. Qualitative results on synthetic artistic scenes [21]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.213, + 0.894, + 0.303 + ], + "angle": 0, + "content": "gen Indoors to real-time simulators, using Universal Scene Description (USD) or other formats. As seen in Fig. 12, indoor scenes can be exported to Omniverse Isaac Sim and Unreal Engine 5 and can be run at interactive frame rates. This exporting capability allows Infinigen Indoors to help train embodied agents in virtual environments." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.305, + 0.895, + 0.456 + ], + "angle": 0, + "content": "Infinigen Indoors uses Blender's procedural material system, which is by default not portable to other simulators or scene editors. To resolve this, we provide tools to automatically post-process and UV-map entire indoor scenes, and use texture baking to create standard texture maps for material color, roughness, metallicity and more. We also provide export code to convert single objects to textured OBJ, FBX or STL meshes, and automatically generate collision and articulation information as Universal Robot Description Format (URDF) files." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.472, + 0.633, + 0.489 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.689, + 0.512 + ], + "angle": 0, + "content": "4.1. Solver Performance" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.523, + 0.894, + 0.718 + ], + "angle": 0, + "content": "To efficiently solve large numbers of constraints in cluttered scenes, we optimized our solver with various features for faster convergence. Plane hashing enables faster access to bounding planes during discrete optimization. BVH caching enables faster mesh distance and collision calculations by reusing Bounding-Volume-Hierarchies except when mutated by a state update. Evaluation caching maintains a cache of results in the evaluation graph. Move filtering narrows down the search space in continuous optimization by selectively pruning candidates to those that can reduce the loss. Place-holder optimization only generates full meshes when other objects are assigned to them; otherwise it keeps bounding boxes. See the supplement for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To analyze the importance of these features, we conducted an ablation in Tab. 3 and Fig. 15, which shows solver performance with each feature removed. All results are averaged over 20 random scenes with \\(5\\mathrm{k}\\) solver steps. Our full system provides a \\(\\approx 3\\mathrm{x}\\) speedup compared to the non-optimized version. Most of the performance gains come from BVH caching and Plane Hashing. We observe that discrete changes such as pose re-initialization, relation changes, and object resampling are necessary for compelling visuals, but decrease the quantitative score and increase the runtime. When we run our fully optimized system as long as the non-optimized version we get a \\(28\\%\\) score increase." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21789" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.279, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.484, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.089, + 0.688, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.089, + 0.892, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.188, + 0.894, + 0.217 + ], + "angle": 0, + "content": "Figure 15. Qualitative Ablation. From left to right, we show scenes generated by our system with 10K solving steps (a), 1K solving steps (b), with collision checking removed (c) and with symmetry terms disabled (d)" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.24, + 0.468, + 0.376 + ], + "angle": 0, + "content": "
MethodRuntime ↓Avg. Score (s) ↑#Objects ↑
Full System2280.6880.8428.94
w/o Discrete change1872.6086.2030.82
w/o Eval. cache2242.7980.8428.94
w/o Move Filter2633.9584.7545.06
w/o Placeholder optim.2665.1880.4627.71
w/o Plane Hashing3522.8692.6534.12
w/o BVH cache4740.4880.8429.06
Full System 100 min.6080.84114.7249.65
w/o Optimization6308.9289.4347.76
" + }, + { + "type": "table_caption", + "bbox": [ + 0.109, + 0.386, + 0.436, + 0.4 + ], + "angle": 0, + "content": "Table 3. Ablation of solver performance optimizations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Perceptual Study We recruited human subjects following [57] to evaluate the realism of the scenes and the realism of the layouts. Subjects preferred Infinigen Indoors over [11, 57, 62, 84] in terms of both realism, layout realism, and the lack of errors (caveat: \"realism\" may be influenced by asset and lighting quality). See the supp. for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.248, + 0.528 + ], + "angle": 0, + "content": "4.2. Shadow Removal" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.75 + ], + "angle": 0, + "content": "To demonstrate its flexibility in data generation, we used Infinigen-Indoors to create a dataset consisting of 2k image pairs of shadow and shadow-free variants. These pairs were generated by toggling the shadow property of lighting within Blender. For each pair, shadow masks were produced using Otsu's thresholding [55] method. We use ShadowFormer [22] model for the experiments and consider two variations: only trained on ISTD [81] real dataset (R), and trained on combination of ISTD and 2k Infinigen Indoors synthetic dataset \\((\\mathbb{R} + \\mathbb{S})\\). The results are shown in Tab. 2. While using synthetic data leads to slightly worse performance on ISTD dataset, the zero-shot application on SRD [59] dataset shows clear improvement for generalization to new test datasets. Qualitative results are shown in Fig. 13." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.36, + 0.773 + ], + "angle": 0, + "content": "4.3. Occlusion Boundary Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.472, + 0.901 + ], + "angle": 0, + "content": "To validate the effectiveness of Infinigen Indoors, we also evaluate on the task of occlusion boundary estimation, a task with limited available data. We produce 1464 images annotated with ground truth. We train three U-Net [64] models from scratch separately on these images, on images generated from Infinigen [60] and Hypersim [63]. We then compare their performance on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture" + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.24, + 0.882, + 0.318 + ], + "angle": 0, + "content": "
Training DatasetODSOISmAP
Infinigen-Nature [60]14.3819.4310.80
Hypersim [63]26.0219.4415.69
Infinigen Indoors (Ours)29.4730.2919.09
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.328, + 0.894, + 0.371 + ], + "angle": 0, + "content": "Table 4. Occlusion boundary quantitative results on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture visualization [21]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.445 + ], + "angle": 0, + "content": "visualization [21], since no existing photorealistic indoor dataset provides such annotations. See the supplement for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.895, + 0.568 + ], + "angle": 0, + "content": "We report the following three metrics [79, 80, 85]: (i) optimal dataset scale \\( F \\)-score (ODS), representing the best F-score achieved on the dataset using a uniform threshold across all test images; (ii) optimal image scale \\( F \\)-score (OIS) indicating the cumulative F-score on the dataset obtained with thresholds dependent on individual images; and (iii) mean average precision (mAP) denoting the mean precision across the complete recall range." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.895, + 0.645 + ], + "angle": 0, + "content": "As we can see in Tab. 4, our Infinigen Indoors-trained model generalizes better. The model achieves higher performance across all metrics. These findings underscore the usefulness of Infinigen Indoors as a valuable training resource. Qualitative results are depicted in Fig. 14." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.663, + 0.831, + 0.68 + ], + "angle": 0, + "content": "5. Contributions & Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.9 + ], + "angle": 0, + "content": "Alexander Raistrick, Lingjie Mei and Karhan Kayan contributed equally and are ordered randomly. Each has the right to list their name first in their CV. Alexander Raistrick performed team coordination and developed the constraint language and object graph solver. Lingjie Mei developed the room solver and many procedural assets. Karhan Kayan developed the geometric constraints and object pose solver. David Yan developed the scene exporter and other utilities. Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Zeyu Ma and Lahav Lipson developed procedural assets and utilities. Jia Deng conceptualized and led the project, and set directions. 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It builds upon the existing Infinigen system, which focuses on natural scenes, but expands its coverage to indoor scenes by introducing a diverse library of procedural indoor assets, including furniture, architecture elements, appliances, and other day-to-day objects. It also introduces a constraint-based arrangement system, which consists of a domain-specific language for expressing diverse constraints on scene composition, and a solver that generates scene compositions that maximally satisfy the constraints. We provide an export tool that allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse and Unreal. Infinigen Indoors is open-sourced under the BSD license. Please visit infinigen.org for code and videos. + +# 1. Introduction + +Synthetic data rendered by conventional computer graphics has seen increasing adoption in computer vision[10, 38, 41, 42, 46, 48, 61] and AI research[20, 28, 76], especially for 3D vision[26, 45, 71, 73-75, 83] and embodied AI[12, 32, 36, 68, 70, 87]. Synthetic data can be rendered in unlimited quantities and can automatically provide high-quality 3D ground truth, enabling large-scale training of computer vision models and embodied agents. Notably, many state-of-the-art 3D vision systems[72, 75] and robotic systems [33, 39] have been trained purely in simulation yet perform surprisingly well in the real world zero-shot. + +A promising direction for creating synthetic data is procedural generation, which uses mathematical rules to create 3D objects and scenes, as opposed to manual sculpting or real-world scanning. These mathematical rules can have parameters that are randomized to allow infinite variations. For example, trees can be generated through a recursive set of rules that randomly branch off. Compared to reusing a fixed, static set of 3D assets, procedural generation can greatly + +improve the diversity of the synthetic data and the simulated environments. + +Infinigen [60] is a recent work that pushed the idea of procedural generation to the limit. Infinigen is an open-source system that generates photorealistic 3D scenes fully procedurally, meaning that every 3D asset, from shape to material, from large structures to small details, is completely procedural, without using any external static asset. Being fully procedural means that every aspect of the 3D scene, from the details of individual objects to their arrangements in a scene, can be customized and controlled by simply modifying the underlying mathematical rules. As a result, a 3D scene can be randomized at all levels down to the smallest details, as opposed to only at the level of object arrangement, which was common in earlier work that used procedural generation. + +However, the current Infinigen system is limited to natural scenes and objects (terrains, animals, plants, etc.). Although natural scenes could be sufficient for training foundation models as evidenced by natural evolution [60], this hypothesis remains unproven and may require additional advances in learning algorithms and architecture designs. Evidence from the current literature suggests that synthetic training data that more closely approximates the application domain is still likely to lead to better downstream performance. + +To overcome this limitation, we introduce Infinigen Indoors, a procedural generator of photorealistic indoor scenes. It expands the coverage of Infinigen to indoor scenes, which are relevant for many high-impact applications including robotics and augmented reality. Infinigen Indoors generates diverse indoor objects, including furniture, appliances, cookware, dining utensils, architectural elements, and other common day-to-day objects. It also generates full indoor scenes, including the interior of multi-room, multi-floor buildings, with object arrangements that are physically and semantically plausible. Fig. 1 shows random samples of generated scenes, and Fig. 2 shows some automatic annotations. + +Like the original Infinigen, Infinigen Indoors is not a fixed set of 3D models or scenes; instead, it is an open-source generator that can create unlimited variations both + +![](images/a607697bebb42081480417d13f24f1ce2795aa7b1a6de2f2a3b7a006a5fbbd49.jpg) + +![](images/143c90dcba74eff289a20392e68b47b6b1b96c24ea29385c4d6530ad023173c0.jpg) + +![](images/7bd2fcd30f45b9bc0f297533789fa027f35ba55bd84ab25de6b374610bdf09df.jpg) +Figure 1. Random, non cherry-picked sample of images generated by our system. From top left to bottom right, we show images from dining rooms, bathrooms, living rooms and kitchens. Please see the supplement for an extended random sample. + +![](images/c8959a435e72759fbc7560d6e0ccc0c798e3baf7b3f1ffea5156c0133755f981.jpg) + +at the object level and at the scene level. Infinigen Indoors is also $100\%$ procedural, using no external assets and using only mathematical rules to generate everything from scratch. + +Infinigen Indoors builds upon the original Infinigen and Blender [8] but makes significant new contributions. The main contributions include (1) a library of procedural generators of indoor assets, (2) a constraint-based arrangement system, (3) a tool to export the generated scenes to real-time simulators such as NVIDIA Omniverse [54] and Unreal Engine[13]. + +Our second contribution—a constraint-based arrangement system—offers a new capability specifically targeting indoor settings. Indoor scenes are artificial, and object arrangement exhibits a greater degree of regularity than natural scenes: for example, furniture usually does not block the entrance of a room. We thus develop a system that lets the user specify scene arrangement constraints through a domain-specific language using a set of Python APIs. The constraints cover many types of common arrangement, including symmetry ("Place chairs symmetrically around the table"), spatial relation ("Place plant pots close to windows"), quantity ("An equal number of knives and forks"), physics ("Ensure vases do not overhang"), and accessibility ("Ensure there is free-space in-front of all appliances"). The constraints can be understood as a type of declarative procedural rules, which express what the user desires but not how to achieve it. Like other procedural rules, the constraints can be randomized and can be customized by the user. + +In addition to constraint specification, our arrangement + +system also includes a constraint solver, which searches for an arrangement that maximally satisfies a set of given constraints. Our solver greedily performs simulated annealing on whole-house floor plans, followed by large furniture layouts and then small objects. Compared to existing approaches for scene arrangement, our solver is highly expressive, supporting complex compositional constraints that are challenging or infeasible for existing approaches. In addition, it is the first solver integrated with an open-source and fully procedural generator. + +Our constraint-based arrangement system is a significant contribution because it vastly improves the generation system's usability and customizability. Because it separates constraint specification from constraint solving, a user can conveniently express the objectives of procedural generation without worrying about implementation. This capability is not available in the original Infinigen, where the user has to customize the procedure rules at the implementation level. + +Our third contribution—exporting to real-time simulators—is also noteworthy because it allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse. Thus, Infinigen Indoors can supply diverse 3D assets for simulation environments and enhance their domain randomization. + +To validate the effectiveness of the generated data and demonstrate our system's unique customizability, we use Infinigen Indoors to generate synthetic data for shadow removal and occlusion boundary detection, two tasks that lack + +
DatasetArrangement MethodProcedural AssetsProvides Procedural Code# Scenes in Total# Assets in TotalFree AssetsExternal Asset Source
3DSSG [78]Real-world scansNoN/A1.5K48KYesNone
Matterport3D [6]Real-world scansNoN/A2K-YesNone
Stanford 2D-3D-S [2]Real-world scansNoN/A270-YesNone
ScanNet [9]Real-world scansNoN/A1.5K-YesNone
SceneNN [27]Real-world scansNoN/A100-YesNone
OpenRooms [44]Real-world scansNoNo1.3K3KNo ($500)ShapeNet [7], Scan2CAD [3], Adobe Stock [30]
Replica [69]Artist layoutsNoN/A18-YesAI Habitat [49]
Structured3D [3]Artist layoutsNoN/A22K472KNoProfessional Designers
Hypersim [63]Artist layoutsNoN/A46159KNo ($6000)Evermotion Architectures [14]
InteriorNet [43]Artist layoutsNoN/A22M1MNoManufactures / Kujiale [37]
Habitat 3.0 [34]Artist layoutsNoN/A21118.7KYesFloorplanner [15], Professional Designers
3D-FRONT [17]Artist layoutsNoN/A19K13KYes3D-FUTURE [18]
Robotrix [19]Artist layoutsNoN/A16-NoUE4Arch [77], UnrealEngine Marketplace [31]
DeepFurniture [47]Artist layoutsNoN/A20K-NoAdobe Mixamo [29]
SceneNetRGBD [94]Obj. Cat. Dist.NoN/A∞5.1KYesSceneNet [23], ShapeNet [7]
LUMINOUS [93]OptimizerNoYes∞2KYesAI2-THOR [36]
SceneNet [24]OptimizerNoNo∞3.7KYes3DModelFree [16], ModelNet [86], Archive3D [1], Stanford database
ProcTHOR [10]HeuristicsNoYes∞1.6KYesAI2-THOR [36], Professional Designers
Aria [52]--No100K8K--
Infinigen Indoors (Ours)Constraint LanguageYesYes∞∞YesNone
+ +Table 1. Comparisons to existing datasets and generators. Many existing datasets/generators use external, static asset libraries and have limited number of scenes. Ours is fully procedural, without using any external source. Dashes represent numbers we could not acquire or estimate. + +![](images/fd9ea204324e101a3c27304f47741832956441fa60a265e62df73b004c4a81a0.jpg) +Figure 2. Each image (a) is rendered from a mesh (b), from which we can also extract Depth (c), Surface Normals (d), Occlusion Boundaries (e), Segmentation (f), Bounding Boxes (e) and Optical Flow (h), with Albedo (i) from rendering metadata. + +abundant existing training data. Our experiments show that data from our system improves generalization performance on indoor scenes. + +Like the original Infinigen, Infinigen Indoors will be open-sourced under the BSD license to enable free and unlimited use by everyone, and to enable community contributions of additional procedural generators. + +# 2. Related Work + +We provide a detailed comparison of Infinigen Indoors with existing datasets and generators in Tab. 1. + +Real-world datasets. Various real-world datasets have been introduced for indoor scene understanding [2, 6, 9, 27, 66, 67, 78], including the earlier and widely used NYUv2 [66] and Sun RGB-D [67], as well as more recent datasets [2, 4, 9, 78]. However, real-world datasets are labor intensive to collect and limited in size. In addition, real-world 3D ground truth can be difficult to acquire due to the limitations of depth + +sensors which include limited resolution and range, errors with transparent/reflective surfaces, and artifacts at object edges. + +Synthetic Indoor Datasets. There are many existing synthetic datasets for indoor scenes [3, 17, 19, 24, 34, 36, 43, 47, 63, 69]. However, the underlying 3D assets of many datasets are not freely accessible, limiting their utility. In addition, most use a static library of 3D assets, limiting their diversity. Recent work [10, 93] has incorporated procedural generation for scene layout and floor plan generation, but still relies on static libraries of objects and materials. In contrast, Infinigen Indoors is $100\%$ procedural, with all assets from shape to texture generated from scratch with unlimited variation. + +Object arrangement and layout generation. Constraints are potent tools to describe the layout of a scene. Early works like [88] represent constraints as hard-coded programs, and [50] represent them as physical relations. Data-driven works like [40, 56, 57, 62, 82, 84] learn constraints implicitly from data. Such implicit constraints are less customizable, interpretable, and controllable than Infinigen Indoors. Recently, modeling constraints using probabilistic graphs have become more popular: [89] uses pairwise grouping, while [11, 91] further extends it to spatial and hierarchical constraints. [90] uses factor graphs to parse the constraints, while [51] models them with Bayesian network. [58, 92] formulates constraints as potentials Markov Random Fields on a fixed graph, which capture only non-compositional and associative constraints for rooms and objects. + +Compared to existing systems, ours is the first to integrate directly with procedural object generators, and our constraint language is higher level and more easily extendable than existing systems. Our system specifies high level goals for abstract classes of objects (e.g. 'furniture', 'stor + +![](images/87f6c23f565177829a704e61e9019b4c18514c166384f73396cd7faa32a09534.jpg) + +![](images/2c089284852a24c4cedf8f203f2c42860dfa40c84e3c4df475dd428160982ecd.jpg) +Figure 3. Random samples of procedurally generated doors (top), staircases (middle/bottom) and windows/warehouse shelving (bottom-right). + +![](images/c130c862e36ee5096dcd9d888737d23958763153e248ffb657978951dc27bcb6.jpg) +Figure 4. Random samples of procedurally generated ovens, dishwasher and sinks (top/middle), living-room furniture (middle) and bathroom fixtures (bottom). +Figure 5. Random samples of procedurally generated furniture, including sofa, chairs and beds (top), tables (middle/bottom), and shelves (bottom). + +age'), rather than exhaustive distance/angle distributions for specific objects [91] which must be fitted to example scenes. Our language also supports compositional constraints such as "place glassware only on shelves against a diningroom wall." These features allow users to write new constraints for their specific needs, including domains without existing artist-made scenes. Our constraint solver uses simulated annealing, following prior work [91], but involves moves that are unique to our constraint language, including updates to object-object relations or changing the parameters of procedural objects (e.g. the size of a table). + +# 3. Method + +# 3.1. Procedural Asset Generation + +All assets used in Infinigen Indoors are generated from scratch by compact probabilistic programs. These programs have many human-controllable parameters, which are randomized by default, or can be manually overridden by the + +![](images/9d2ef22b14a7fc9ba6b69f4d05292998b4540d6f491c3c44671ef1921a2b10f1.jpg) +Figure 6. Random samples of procedurally generated tableware, including dinnerware (Row 1-2), cookware (Row 2), food containers (Row 3) and dining utensils (Row 4). + +![](images/1bc91cc0ef7e1d876705ce96035e61b34d0b43fa7b547fab359dfd7e949c29d4.jpg) + +![](images/eb2fa7a5be9e8a27ef67411c5c38b3f722aa522ff0c549911391ef6db32a42a3.jpg) +Figure 7. Random samples of procedurally generated home decorations, including lamps, hardware, balloons, wall decor (top), rugs, book stacks, vases and plants (bottom). Small assets for decoration purposes, usually attached to the ground or walls. +Figure 8. A collection of materials generated in Infinigen Indoors. The first figure shows one material per generator, with columns (1-3) used on assets of various sizes, (4-5) used on assets and rooms, and (6) for abstract art and text. The second figure shows multiple materials from the same generator with different parameters. + +user. These parameters are used along with additional low-level random noise to generate meshes via geometry nodes, modifiers, or mesh manipulations in Blender. We provide a total of 79 randomized procedural object generators. By category, we cover Appliances (10 generators, 112 params), Windows/Doors/Staircases (14 generators, 127 params), Furniture (17 generators, 216 params), Decorations (15 generators, 92 params), and Small Objects (19 generators, 194 params). See the supplement for a list. + +Architectural elements shown in Fig. 3 are integrated into room as fixtures. We use array repetition of atomic compo + +```txt +tables = scene.with_semantics(Tag.Chair) +chairs = scene.with_semantics(Tag.Table) +on_fLOOR = cl.StableAgainst(Tag Bottom, Tag.Floor) +constraints = clforall(rooms[Tag.DiningRoom], +r, +(tablets Related_to(r, on_fLOOR).count() == 1, +chairs related_to(r, on_fLOOR).count().in_range(2, 10)),) +score = ( + chairs related_toRooms[Tag.DiningRoom], on_fLOOR) + .mean(c, cl.reflection_symmetry(c, tables) + \cl.min_distance(t, tables) * (-1)) + .maximize(weight=2) +) +``` + +Figure 9. Example usage of our constraint specification API, specifying the quantity and aesthetic constraints for a dining table and chairs. + +nents to build staircases, and mesh booleaning to cut out the panels of doors and windows. + +Large objects shown in Fig. 4 and 5 provide assets related to cooking, seating and storage. We use soft-body collision simulation to model soft blankets, clothing, and stuffed pillows when they are put on a supporting surface. + +Small objects shown in Fig. 6 and 7 can be attached to support surfaces, walls, or ceilings. We also devised a combined text-and-shape logo generator that produces procedural texture for fabrics, food packaging, and art decor. We use cloth simulation to inflate balloons and food packaging with air. + +Materials are all procedurally created with Blender's Shader nodes, as shown in Fig. 8. We provide 30 material generators with 120 controllable parameters total, split approximately evenly between types of Wood, Ceramic, Fabric, Metal, and others. We cover $78\%$ of OpenSurfaces'[5] material categories, up from $21\%$ for Infinigen. + +# 3.2. Constraint Specification API + +Indoor scene layouts are highly regular, and follow complex rules governing ergonomics, aesthetics and functionality. Moreover, the rules that apply to a particular object depend on context - for example, tables are placed against walls when used as desks in study rooms, but must be far from walls and surrounded by chairs when used in a dining room. To capture this, we provide a high-level Constraint Specification API, which allows the user to write complex geometric scoring functions of sets of objects in the scene. This score is optimized by the solver to find a satisfactory layout. An example of the Constraint Specification API is shown in 9. + +Each constraint in the specification API can be expressed as a composition of geometric operators. Geometric operators are designed to compute spatial and geometric properties, including minimum distance, rotational and reflection symmetry, angle alignment, 2D free-space, accessibility and volume or area of objects. By composing these operators with nested filtering by semantics and relations, the user can create scoped constraints that apply only to objects attached + +to specific surfaces or rooms. Additionally, these geometry terms are affected by the parameters (length, width, etc.) of the procedurally generated assets, meaning that optimizers can automatically discover optimal furniture parameters given available space and constraints. Our system features common scalar arithmetic operations, comparisons, and forall / sum operators to gather results over sets of objects. Please see the supplement for the full API and more constraint specification examples. + +A more concrete example of our constraint language can be found in Fig. 9, where the constraint program specifies common-sense human ergonomics and semantic relations found in residential homes. This constraint graph has a total of 1058 nodes, which compute 11 hard constraints and 25 score terms (soft constraints). We provide example constraint specifications for living rooms, bathrooms, dining rooms, kitchens, and warehouses. See the supplement for the full constraint program and example constraints. + +For generating training data, we believe many users will consider creating custom constraints tailored to particular applications. Our constraint system is designed to allow easy customization. Our initial spec. has avg. 15 constraints specific to each room: approx. 15 lines of Python. We believe this cost is very tractable when users need customization. + +# 3.3. Arrangement Solver + +Because our Constraint Specification API is flexible, the solver needs to search a prohibitively large space in which finding an exact minimum is impossible. To deal with this, it uses Simulated Annealing[35] with Metropolis-Hastings criterion [25, 53]. The solver first takes the current state $s$ and randomly chooses a move category. It then uses the constraint graph to generate a proposed state $s'$ that can be reached using the move. The current and proposed states are evaluated on the graph specified by the provided constraints and score terms, yielding loss terms $l(s)$ and $l(s')$ . Then, the solver calculates transition probability between the $s$ and $s'$ as + +$$ +p \left(s ^ {\prime} \mid s\right) = \min \left[ \exp \left(l (s) - l \left(s ^ {\prime}\right)\right) / \tau , 1 \right] +$$ + +where $\tau$ is the temperature of the solver, which cools exponentially from $\tau = 0.25$ to $\tau = 0.001$ . + +Our solver allows both discrete and continuous moves: Addition - Adds a procedural object to the scene. + +Deletion - Deletes an object from the scene. + +Relation Plane Change - Assigns an object to another plane. Resample - Regenerates an object with new parameters. + +Reinitialize Pose - Samples a new random pose for an object. Translate - Translates the object within its DOF plane. + +Rotate - Rotates the object around its DOF axis. + +We observe that not all moves are equally significant at each point in the optimization. In an empty scene, object addition and relation change allow for higher loss reduction, whereas in a cluttered scene, continuous object movement + +![](images/f9167d8340b1de69bfdfa65989d2e36667186ab3e706203f27ab4d00524e099d.jpg) +a) + +![](images/4bcf509760a5fab1bf457cc7e9386a85f5e0baef1f810bc61c7600526e918797.jpg) + +![](images/5f1bbfcddf8f046b949a9a5c21e6b04c603550f70c0ce079419ca816fd0698f3.jpg) +b) + +![](images/1a7e21cbc91fb78c6d923da5493deeea47ecf4e59f5004af782e4ca5a24d5ef0.jpg) +Figure 10. In Fig. a), we show ten randomly generated single-story floor plans with a diverse set of room combinations, connectedness, and overall contours. In Fig. b), we show results for the generation of multistory floor plans. Floors 0,1,2 are displayed separately. Staircases connect adjacent floors. We remove exterior walls and ceilings for visibility. + +![](images/97204a480dcad206601a96285e160215da2a962d4769f747ae971bd35ed4af40.jpg) + +![](images/345163aead45353d1ad4459cdf57dff9960e5e83fb998513f69489f7b760d15f.jpg) + +![](images/2103d2f63f6abc0ea6573a4a0eca0e54245607c13be5f80b616d0469095a4dc2.jpg) + +![](images/2e53f2aee5acd224629e3daa19866037d413365ad5f7cf08217c1563a3bd714f.jpg) + +![](images/22200ec601807dd4c191a3f6da957c7278e9b6e991059db92375077e343b6a0d.jpg) + +![](images/2e93e78a86712e8a8b35e0c23e492b18f4a3bb082bbd221c430b8c63a6673d31.jpg) + +![](images/25d59dff288a008de0ac69189f254107ff2e45115a97f7587d33a1c5cc092831.jpg) + +![](images/e5b967d64ad3c51ec20901c71ffb994a0b42efbd8ffdcf77fc86bc1efe64fb0d.jpg) + +![](images/a0edaca90b3d090e3f46e2a777144b02ea2a4be489796b37b3c51645daa62b92.jpg) +Figure 11. Qualitative room arrangement results, grouped by room type. From left to right, we show bathrooms, dining rooms, living rooms and kitchens. + +allows for higher loss reduction. Thus, we provide a schedule for moves so that probabilities for discrete moves decay gradually and probabilities for continuous moves increase. + +The objects in an indoor scene are interdependent on each other, which makes it unfeasible to optimize over all of them simultaneously. However, they usually depend on each other hierarchically (e.g., a cup is on the table, which is on the floor). To exploit this hierarchy, we divide our optimization into three stages: large object optimization, medium object optimization, and small object optimization. + +Each object is constrained in its movement due to the constraints specified by the user and the discrete moves proposed by the solver. For instance, a bookshelf that is stable against a wall is only allowed to move along the 1D line between the wall and the floor. Consequently, an object's degrees of freedom (DoFs) for rotation and translation are determined based on its relations to other objects. When the solver samples a continuous move, it restricts the object's motion to these DoFs. When the solver samples a discrete move, it places the object in the constrained subspace. + +Floorplan-specific solver and constraints Our floorplan generator creates realistic full-house room meshes as shown in Fig. 10. First, we procedurally generate a room adjacency + +graph specifying the number, type, and connectedness of individual rooms required in the floor plan. This graph is produced by inference on a probabilistic context-free grammar on room types, or can be wholly or partially derived from user input. We define our objective function as a weighted combination of the terms below, and optimize it using simulated annealing subject to constraints from the room adjacency graph. See the supplement for full definitions. + +- Shortest path to entrance +Typical room area +- Room aspect ratio +- Room convexity +- Room wall conciseness +- Functional room area +- Room collinearity +- Narrow passages +- Exterior length by room +- Exterior corners by room +- Staircase occupancies +- Staircase IOU with rooms + +We initialize our floorplan solver by generating a random house outline, and subdividing it using a Mondrian Process [65] until it produces sufficient spaces for each room. We extrude a wall segment inwards or outwards at each step, or swap the assignment subject to the room adjacency graph. Either action will lead to a change in loss, which we convert to an acceptance probability using Metropolis-Hasting as in Sec 3.3. Once solving is complete, we add floor, wall, and ceiling materials, doors, windows, and staircases, all subject to constraints based on room type and adjacency. Fig + +![](images/af7b6cba50d663146d8192e16443cea07307a5f05a46aaf5ab85882d1bf8a9f1.jpg) + +![](images/8d40cb8630077d8fa4399018ef414b47c66d74e4947eb58c9747cc88d0a234f7.jpg) + +![](images/82d7adb74bd039385fd8fdd705b7aca97e4b373e2f794148114788194b6c52a0.jpg) +Figure 12. A single scene from two different viewpoints in Unreal Engine 5 (above) and Omniverse Isaac Sim (below). Unreal Engine runs at 60 FPS and Isaac Sim with physics simulation enabled runs at 45 FPS, both on RTX 3090s. Differences in lighting are caused by the variations in simulator import systems. +Figure 13. Qualitative zero-shot results on SRD [59] test dataset. + +11 shows the solutions to room arrangements with objects placed inside. + +# 3.4. Data Export + +
All ImageShadow RegionNon-Sh Region
Test SetModelPSNR↑RMSE↓PSNR↑RMSE↓PSNR↑RMSE↓
ISTD [81]R31.964.2738.046.5834.133.85
R+S31.724.3037.417.0633.803.85
SRD [59]R22.8310.8425.5918.7527.937.68
R+S24.569.5427.3916.6329.376.67
+ +Table 2. Shadow removal task quantitative performance on ISTD, ISTD+ and SRD dataset across the three variations of the model. + +We develop a one-click tool to export assets from Infini + +![](images/dfd1743aaad4d6f80c3bf809cf9cc3550399ae4bdecc766a94692e7a06680d9b.jpg) +Figure 14. Qualitative results on synthetic artistic scenes [21]. + +gen Indoors to real-time simulators, using Universal Scene Description (USD) or other formats. As seen in Fig. 12, indoor scenes can be exported to Omniverse Isaac Sim and Unreal Engine 5 and can be run at interactive frame rates. This exporting capability allows Infinigen Indoors to help train embodied agents in virtual environments. + +Infinigen Indoors uses Blender's procedural material system, which is by default not portable to other simulators or scene editors. To resolve this, we provide tools to automatically post-process and UV-map entire indoor scenes, and use texture baking to create standard texture maps for material color, roughness, metallicity and more. We also provide export code to convert single objects to textured OBJ, FBX or STL meshes, and automatically generate collision and articulation information as Universal Robot Description Format (URDF) files. + +# 4. Experiments + +# 4.1. Solver Performance + +To efficiently solve large numbers of constraints in cluttered scenes, we optimized our solver with various features for faster convergence. Plane hashing enables faster access to bounding planes during discrete optimization. BVH caching enables faster mesh distance and collision calculations by reusing Bounding-Volume-Hierarchies except when mutated by a state update. Evaluation caching maintains a cache of results in the evaluation graph. Move filtering narrows down the search space in continuous optimization by selectively pruning candidates to those that can reduce the loss. Place-holder optimization only generates full meshes when other objects are assigned to them; otherwise it keeps bounding boxes. See the supplement for more details. + +To analyze the importance of these features, we conducted an ablation in Tab. 3 and Fig. 15, which shows solver performance with each feature removed. All results are averaged over 20 random scenes with $5\mathrm{k}$ solver steps. Our full system provides a $\approx 3\mathrm{x}$ speedup compared to the non-optimized version. Most of the performance gains come from BVH caching and Plane Hashing. We observe that discrete changes such as pose re-initialization, relation changes, and object resampling are necessary for compelling visuals, but decrease the quantitative score and increase the runtime. When we run our fully optimized system as long as the non-optimized version we get a $28\%$ score increase. + +![](images/8ab1e66874dd014e90e62ae98718f19d336305031993cd2f69c5e49148450276.jpg) +Figure 15. Qualitative Ablation. From left to right, we show scenes generated by our system with 10K solving steps (a), 1K solving steps (b), with collision checking removed (c) and with symmetry terms disabled (d) + +![](images/655a90473f39d29b9f04b258962241b8ddb81e157285740046f8113ebd78c711.jpg) + +![](images/4078a12df63c48086f4e7f1f34012e1935bfeda1cd642032d36564b53aacee3f.jpg) + +![](images/9f451b90a77ca48ddbeeac019502494ac622f946f893c6c28d864d17eaf3a50a.jpg) + +
MethodRuntime ↓Avg. Score (s) ↑#Objects ↑
Full System2280.6880.8428.94
w/o Discrete change1872.6086.2030.82
w/o Eval. cache2242.7980.8428.94
w/o Move Filter2633.9584.7545.06
w/o Placeholder optim.2665.1880.4627.71
w/o Plane Hashing3522.8692.6534.12
w/o BVH cache4740.4880.8429.06
Full System 100 min.6080.84114.7249.65
w/o Optimization6308.9289.4347.76
+ +Perceptual Study We recruited human subjects following [57] to evaluate the realism of the scenes and the realism of the layouts. Subjects preferred Infinigen Indoors over [11, 57, 62, 84] in terms of both realism, layout realism, and the lack of errors (caveat: "realism" may be influenced by asset and lighting quality). See the supp. for more details. + +# 4.2. Shadow Removal + +To demonstrate its flexibility in data generation, we used Infinigen-Indoors to create a dataset consisting of 2k image pairs of shadow and shadow-free variants. These pairs were generated by toggling the shadow property of lighting within Blender. For each pair, shadow masks were produced using Otsu's thresholding [55] method. We use ShadowFormer [22] model for the experiments and consider two variations: only trained on ISTD [81] real dataset (R), and trained on combination of ISTD and 2k Infinigen Indoors synthetic dataset $(\mathbb{R} + \mathbb{S})$ . The results are shown in Tab. 2. While using synthetic data leads to slightly worse performance on ISTD dataset, the zero-shot application on SRD [59] dataset shows clear improvement for generalization to new test datasets. Qualitative results are shown in Fig. 13. + +# 4.3. Occlusion Boundary Estimation + +To validate the effectiveness of Infinigen Indoors, we also evaluate on the task of occlusion boundary estimation, a task with limited available data. We produce 1464 images annotated with ground truth. We train three U-Net [64] models from scratch separately on these images, on images generated from Infinigen [60] and Hypersim [63]. We then compare their performance on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture + +Table 3. Ablation of solver performance optimizations. + +
Training DatasetODSOISmAP
Infinigen-Nature [60]14.3819.4310.80
Hypersim [63]26.0219.4415.69
Infinigen Indoors (Ours)29.4730.2919.09
+ +Table 4. Occlusion boundary quantitative results on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture visualization [21]. + +visualization [21], since no existing photorealistic indoor dataset provides such annotations. See the supplement for more details. + +We report the following three metrics [79, 80, 85]: (i) optimal dataset scale $F$ -score (ODS), representing the best F-score achieved on the dataset using a uniform threshold across all test images; (ii) optimal image scale $F$ -score (OIS) indicating the cumulative F-score on the dataset obtained with thresholds dependent on individual images; and (iii) mean average precision (mAP) denoting the mean precision across the complete recall range. + +As we can see in Tab. 4, our Infinigen Indoors-trained model generalizes better. The model achieves higher performance across all metrics. These findings underscore the usefulness of Infinigen Indoors as a valuable training resource. Qualitative results are depicted in Fig. 14. + +# 5. Contributions & Acknowledgements + +Alexander Raistrick, Lingjie Mei and Karhan Kayan contributed equally and are ordered randomly. Each has the right to list their name first in their CV. Alexander Raistrick performed team coordination and developed the constraint language and object graph solver. Lingjie Mei developed the room solver and many procedural assets. Karhan Kayan developed the geometric constraints and object pose solver. David Yan developed the scene exporter and other utilities. Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Zeyu Ma and Lahav Lipson developed procedural assets and utilities. Jia Deng conceptualized and led the project, and set directions. This work was partially supported by the National Science Foundation and Amazon. + +# References + +[1] Archive 3D. Archive 3d. https://archive3d.net/. 3 +[2] I. Armeni, A. Sax, A. R. Zamir, and S. Savarese. 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Springer, 2020. 3 \ No newline at end of file diff --git a/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/images.zip b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4f1ed66d3a6904b207d5f2a6ad9d1fbc102c6d4c --- /dev/null +++ b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c6a4a67b4ae5d01a57db09df52e5dd1b3760888531ac357b20710c2eb514cf5b +size 884160 diff --git a/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/layout.json b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..8402f6fb70185465a1b974c2c8a6b49a92d335b4 --- /dev/null +++ b/2024/Infinigen Indoors_ Photorealistic Indoor Scenes using Procedural Generation/layout.json @@ -0,0 +1,9760 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 60, + 103, + 533, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 103, + 533, + 120 + ], + "spans": [ + { + "bbox": [ + 60, + 103, + 533, + 120 + ], + "type": "text", + "content": "Infinigen Indoors: Photorealistic Indoor Scenes using Procedural Generation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 144, + 492, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 144, + 492, + 200 + ], + "spans": [ + { + "bbox": [ + 101, + 144, + 492, + 200 + ], + "type": "text", + "content": "Alexander Raistrick*, Lingjie Mei*, Karhan Kayan*, (*equal contribution; random order) David Yan, Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Lahav Lipson, Zeyu Ma, Jia Deng Department of Computer Science, Princeton University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 251, + 290, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 290, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 290, + 443 + ], + "type": "text", + "content": "We introduce Infinigen Indoors, a Blender-based procedural generator of photorealistic indoor scenes. It builds upon the existing Infinigen system, which focuses on natural scenes, but expands its coverage to indoor scenes by introducing a diverse library of procedural indoor assets, including furniture, architecture elements, appliances, and other day-to-day objects. It also introduces a constraint-based arrangement system, which consists of a domain-specific language for expressing diverse constraints on scene composition, and a solver that generates scene compositions that maximally satisfy the constraints. We provide an export tool that allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse and Unreal. Infinigen Indoors is open-sourced under the BSD license. Please visit infinigen.org for code and videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 466, + 128, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 128, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 128, + 479 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 288, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 617 + ], + "type": "text", + "content": "Synthetic data rendered by conventional computer graphics has seen increasing adoption in computer vision[10, 38, 41, 42, 46, 48, 61] and AI research[20, 28, 76], especially for 3D vision[26, 45, 71, 73-75, 83] and embodied AI[12, 32, 36, 68, 70, 87]. Synthetic data can be rendered in unlimited quantities and can automatically provide high-quality 3D ground truth, enabling large-scale training of computer vision models and embodied agents. Notably, many state-of-the-art 3D vision systems[72, 75] and robotic systems [33, 39] have been trained purely in simulation yet perform surprisingly well in the real world zero-shot." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "A promising direction for creating synthetic data is procedural generation, which uses mathematical rules to create 3D objects and scenes, as opposed to manual sculpting or real-world scanning. These mathematical rules can have parameters that are randomized to allow infinite variations. For example, trees can be generated through a recursive set of rules that randomly branch off. Compared to reusing a fixed, static set of 3D assets, procedural generation can greatly" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 228, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 251 + ], + "type": "text", + "content": "improve the diversity of the synthetic data and the simulated environments." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 254, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 547, + 421 + ], + "type": "text", + "content": "Infinigen [60] is a recent work that pushed the idea of procedural generation to the limit. Infinigen is an open-source system that generates photorealistic 3D scenes fully procedurally, meaning that every 3D asset, from shape to material, from large structures to small details, is completely procedural, without using any external static asset. Being fully procedural means that every aspect of the 3D scene, from the details of individual objects to their arrangements in a scene, can be customized and controlled by simply modifying the underlying mathematical rules. As a result, a 3D scene can be randomized at all levels down to the smallest details, as opposed to only at the level of object arrangement, which was common in earlier work that used procedural generation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 422, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 530 + ], + "type": "text", + "content": "However, the current Infinigen system is limited to natural scenes and objects (terrains, animals, plants, etc.). Although natural scenes could be sufficient for training foundation models as evidenced by natural evolution [60], this hypothesis remains unproven and may require additional advances in learning algorithms and architecture designs. Evidence from the current literature suggests that synthetic training data that more closely approximates the application domain is still likely to lead to better downstream performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 532, + 548, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 548, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 548, + 675 + ], + "type": "text", + "content": "To overcome this limitation, we introduce Infinigen Indoors, a procedural generator of photorealistic indoor scenes. It expands the coverage of Infinigen to indoor scenes, which are relevant for many high-impact applications including robotics and augmented reality. Infinigen Indoors generates diverse indoor objects, including furniture, appliances, cookware, dining utensils, architectural elements, and other common day-to-day objects. It also generates full indoor scenes, including the interior of multi-room, multi-floor buildings, with object arrangements that are physically and semantically plausible. Fig. 1 shows random samples of generated scenes, and Fig. 2 shows some automatic annotations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Like the original Infinigen, Infinigen Indoors is not a fixed set of 3D models or scenes; instead, it is an open-source generator that can create unlimited variations both" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21783" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 295, + 198 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 295, + 198 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 295, + 198 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 295, + 198 + ], + "type": "image", + "image_path": "a607697bebb42081480417d13f24f1ce2795aa7b1a6de2f2a3b7a006a5fbbd49.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 72, + 544, + 198 + ], + "blocks": [ + { + "bbox": [ + 298, + 72, + 544, + 198 + ], + "lines": [ + { + "bbox": [ + 298, + 72, + 544, + 198 + ], + "spans": [ + { + "bbox": [ + 298, + 72, + 544, + 198 + ], + "type": "image", + "image_path": "143c90dcba74eff289a20392e68b47b6b1b96c24ea29385c4d6530ad023173c0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 200, + 295, + 327 + ], + "blocks": [ + { + "bbox": [ + 49, + 200, + 295, + 327 + ], + "lines": [ + { + "bbox": [ + 49, + 200, + 295, + 327 + ], + "spans": [ + { + "bbox": [ + 49, + 200, + 295, + 327 + ], + "type": "image", + "image_path": "7bd2fcd30f45b9bc0f297533789fa027f35ba55bd84ab25de6b374610bdf09df.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 336, + 546, + 359 + ], + "lines": [ + { + "bbox": [ + 46, + 336, + 546, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 546, + 359 + ], + "type": "text", + "content": "Figure 1. Random, non cherry-picked sample of images generated by our system. From top left to bottom right, we show images from dining rooms, bathrooms, living rooms and kitchens. Please see the supplement for an extended random sample." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 200, + 544, + 327 + ], + "blocks": [ + { + "bbox": [ + 298, + 200, + 544, + 327 + ], + "lines": [ + { + "bbox": [ + 298, + 200, + 544, + 327 + ], + "spans": [ + { + "bbox": [ + 298, + 200, + 544, + 327 + ], + "type": "image", + "image_path": "c8959a435e72759fbc7560d6e0ccc0c798e3baf7b3f1ffea5156c0133755f981.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "type": "text", + "content": "at the object level and at the scene level. Infinigen Indoors is also " + }, + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "type": "text", + "content": " procedural, using no external assets and using only mathematical rules to generate everything from scratch." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 484 + ], + "type": "text", + "content": "Infinigen Indoors builds upon the original Infinigen and Blender [8] but makes significant new contributions. The main contributions include (1) a library of procedural generators of indoor assets, (2) a constraint-based arrangement system, (3) a tool to export the generated scenes to real-time simulators such as NVIDIA Omniverse [54] and Unreal Engine[13]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "type": "text", + "content": "Our second contribution—a constraint-based arrangement system—offers a new capability specifically targeting indoor settings. Indoor scenes are artificial, and object arrangement exhibits a greater degree of regularity than natural scenes: for example, furniture usually does not block the entrance of a room. We thus develop a system that lets the user specify scene arrangement constraints through a domain-specific language using a set of Python APIs. The constraints cover many types of common arrangement, including symmetry (\"Place chairs symmetrically around the table\"), spatial relation (\"Place plant pots close to windows\"), quantity (\"An equal number of knives and forks\"), physics (\"Ensure vases do not overhang\"), and accessibility (\"Ensure there is free-space in-front of all appliances\"). The constraints can be understood as a type of declarative procedural rules, which express what the user desires but not how to achieve it. Like other procedural rules, the constraints can be randomized and can be customized by the user." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 702, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 702, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 702, + 287, + 714 + ], + "type": "text", + "content": "In addition to constraint specification, our arrangement" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 547, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 484 + ], + "type": "text", + "content": "system also includes a constraint solver, which searches for an arrangement that maximally satisfies a set of given constraints. Our solver greedily performs simulated annealing on whole-house floor plans, followed by large furniture layouts and then small objects. Compared to existing approaches for scene arrangement, our solver is highly expressive, supporting complex compositional constraints that are challenging or infeasible for existing approaches. In addition, it is the first solver integrated with an open-source and fully procedural generator." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 581 + ], + "type": "text", + "content": "Our constraint-based arrangement system is a significant contribution because it vastly improves the generation system's usability and customizability. Because it separates constraint specification from constraint solving, a user can conveniently express the objectives of procedural generation without worrying about implementation. This capability is not available in the original Infinigen, where the user has to customize the procedure rules at the implementation level." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 664 + ], + "type": "text", + "content": "Our third contribution—exporting to real-time simulators—is also noteworthy because it allows the generated 3D objects and scenes to be directly used for training embodied agents in real-time simulators such as Omniverse. Thus, Infinigen Indoors can supply diverse 3D assets for simulation environments and enhance their domain randomization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "To validate the effectiveness of the generated data and demonstrate our system's unique customizability, we use Infinigen Indoors to generate synthetic data for shadow removal and occlusion boundary detection, two tasks that lack" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21784" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 547, + 250 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 250 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 250 + ], + "type": "table", + "html": "
DatasetArrangement MethodProcedural AssetsProvides Procedural Code# Scenes in Total# Assets in TotalFree AssetsExternal Asset Source
3DSSG [78]Real-world scansNoN/A1.5K48KYesNone
Matterport3D [6]Real-world scansNoN/A2K-YesNone
Stanford 2D-3D-S [2]Real-world scansNoN/A270-YesNone
ScanNet [9]Real-world scansNoN/A1.5K-YesNone
SceneNN [27]Real-world scansNoN/A100-YesNone
OpenRooms [44]Real-world scansNoNo1.3K3KNo ($500)ShapeNet [7], Scan2CAD [3], Adobe Stock [30]
Replica [69]Artist layoutsNoN/A18-YesAI Habitat [49]
Structured3D [3]Artist layoutsNoN/A22K472KNoProfessional Designers
Hypersim [63]Artist layoutsNoN/A46159KNo ($6000)Evermotion Architectures [14]
InteriorNet [43]Artist layoutsNoN/A22M1MNoManufactures / Kujiale [37]
Habitat 3.0 [34]Artist layoutsNoN/A21118.7KYesFloorplanner [15], Professional Designers
3D-FRONT [17]Artist layoutsNoN/A19K13KYes3D-FUTURE [18]
Robotrix [19]Artist layoutsNoN/A16-NoUE4Arch [77], UnrealEngine Marketplace [31]
DeepFurniture [47]Artist layoutsNoN/A20K-NoAdobe Mixamo [29]
SceneNetRGBD [94]Obj. Cat. Dist.NoN/A∞5.1KYesSceneNet [23], ShapeNet [7]
LUMINOUS [93]OptimizerNoYes∞2KYesAI2-THOR [36]
SceneNet [24]OptimizerNoNo∞3.7KYes3DModelFree [16], ModelNet [86], Archive3D [1], Stanford database
ProcTHOR [10]HeuristicsNoYes∞1.6KYesAI2-THOR [36], Professional Designers
Aria [52]--No100K8K--
Infinigen Indoors (Ours)Constraint LanguageYesYes∞∞YesNone
", + "image_path": "ef11e2cf1bd160715d9509ee464745d39f0608b8b9ead72895c648f6c781be0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 257, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 547, + 289 + ], + "type": "text", + "content": "Table 1. Comparisons to existing datasets and generators. Many existing datasets/generators use external, static asset libraries and have limited number of scenes. Ours is fully procedural, without using any external source. Dashes represent numbers we could not acquire or estimate." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 49, + 294, + 287, + 430 + ], + "blocks": [ + { + "bbox": [ + 49, + 294, + 287, + 430 + ], + "lines": [ + { + "bbox": [ + 49, + 294, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 49, + 294, + 287, + 430 + ], + "type": "image", + "image_path": "fd9ea204324e101a3c27304f47741832956441fa60a265e62df73b004c4a81a0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 437, + 287, + 483 + ], + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 483 + ], + "type": "text", + "content": "Figure 2. Each image (a) is rendered from a mesh (b), from which we can also extract Depth (c), Surface Normals (d), Occlusion Boundaries (e), Segmentation (f), Bounding Boxes (e) and Optical Flow (h), with Albedo (i) from rendering metadata." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 488, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 287, + 523 + ], + "type": "text", + "content": "abundant existing training data. Our experiments show that data from our system improves generalization performance on indoor scenes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 525, + 288, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 288, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 288, + 573 + ], + "type": "text", + "content": "Like the original Infinigen, Infinigen Indoors will be open-sourced under the BSD license to enable free and unlimited use by everyone, and to enable community contributions of additional procedural generators." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 585, + 134, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 134, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 134, + 597 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "content": "We provide a detailed comparison of Infinigen Indoors with existing datasets and generators in Tab. 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "content": "Real-world datasets. Various real-world datasets have been introduced for indoor scene understanding [2, 6, 9, 27, 66, 67, 78], including the earlier and widely used NYUv2 [66] and Sun RGB-D [67], as well as more recent datasets [2, 4, 9, 78]. However, real-world datasets are labor intensive to collect and limited in size. In addition, real-world 3D ground truth can be difficult to acquire due to the limitations of depth" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 297, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 334 + ], + "type": "text", + "content": "sensors which include limited resolution and range, errors with transparent/reflective surfaces, and artifacts at object edges." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 335, + 548, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 548, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 548, + 467 + ], + "type": "text", + "content": "Synthetic Indoor Datasets. There are many existing synthetic datasets for indoor scenes [3, 17, 19, 24, 34, 36, 43, 47, 63, 69]. However, the underlying 3D assets of many datasets are not freely accessible, limiting their utility. In addition, most use a static library of 3D assets, limiting their diversity. Recent work [10, 93] has incorporated procedural generation for scene layout and floor plan generation, but still relies on static libraries of objects and materials. In contrast, Infinigen Indoors is " + }, + { + "bbox": [ + 304, + 335, + 548, + 467 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 335, + 548, + 467 + ], + "type": "text", + "content": " procedural, with all assets from shape to texture generated from scratch with unlimited variation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 471, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 547, + 651 + ], + "type": "text", + "content": "Object arrangement and layout generation. Constraints are potent tools to describe the layout of a scene. Early works like [88] represent constraints as hard-coded programs, and [50] represent them as physical relations. Data-driven works like [40, 56, 57, 62, 82, 84] learn constraints implicitly from data. Such implicit constraints are less customizable, interpretable, and controllable than Infinigen Indoors. Recently, modeling constraints using probabilistic graphs have become more popular: [89] uses pairwise grouping, while [11, 91] further extends it to spatial and hierarchical constraints. [90] uses factor graphs to parse the constraints, while [51] models them with Bayesian network. [58, 92] formulates constraints as potentials Markov Random Fields on a fixed graph, which capture only non-compositional and associative constraints for rooms and objects." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 548, + 715 + ], + "type": "text", + "content": "Compared to existing systems, ours is the first to integrate directly with procedural object generators, and our constraint language is higher level and more easily extendable than existing systems. Our system specifies high level goals for abstract classes of objects (e.g. 'furniture', 'stor" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21785" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 68, + 289, + 162 + ], + "blocks": [ + { + "bbox": [ + 51, + 68, + 289, + 162 + ], + "lines": [ + { + "bbox": [ + 51, + 68, + 289, + 162 + ], + "spans": [ + { + "bbox": [ + 51, + 68, + 289, + 162 + ], + "type": "image", + "image_path": "87f6c23f565177829a704e61e9019b4c18514c166384f73396cd7faa32a09534.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 201, + 287, + 290 + ], + "blocks": [ + { + "bbox": [ + 47, + 168, + 287, + 201 + ], + "lines": [ + { + "bbox": [ + 47, + 168, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 287, + 201 + ], + "type": "text", + "content": "Figure 3. Random samples of procedurally generated doors (top), staircases (middle/bottom) and windows/warehouse shelving (bottom-right)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 201, + 287, + 290 + ], + "lines": [ + { + "bbox": [ + 50, + 201, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 50, + 201, + 287, + 290 + ], + "type": "image", + "image_path": "2c089284852a24c4cedf8f203f2c42860dfa40c84e3c4df475dd428160982ecd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 330, + 287, + 419 + ], + "blocks": [ + { + "bbox": [ + 47, + 297, + 288, + 330 + ], + "lines": [ + { + "bbox": [ + 47, + 297, + 288, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 288, + 330 + ], + "type": "text", + "content": "Figure 4. Random samples of procedurally generated ovens, dishwasher and sinks (top/middle), living-room furniture (middle) and bathroom fixtures (bottom)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 330, + 287, + 419 + ], + "lines": [ + { + "bbox": [ + 50, + 330, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 50, + 330, + 287, + 419 + ], + "type": "image", + "image_path": "c130c862e36ee5096dcd9d888737d23958763153e248ffb657978951dc27bcb6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 427, + 287, + 460 + ], + "lines": [ + { + "bbox": [ + 47, + 427, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 287, + 460 + ], + "type": "text", + "content": "Figure 5. Random samples of procedurally generated furniture, including sofa, chairs and beds (top), tables (middle/bottom), and shelves (bottom)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "content": "age'), rather than exhaustive distance/angle distributions for specific objects [91] which must be fitted to example scenes. Our language also supports compositional constraints such as \"place glassware only on shelves against a diningroom wall.\" These features allow users to write new constraints for their specific needs, including domains without existing artist-made scenes. Our constraint solver uses simulated annealing, following prior work [91], but involves moves that are unique to our constraint language, including updates to object-object relations or changing the parameters of procedural objects (e.g. the size of a table)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 626, + 102, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 102, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 102, + 639 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 647, + 205, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 205, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 205, + 658 + ], + "type": "text", + "content": "3.1. Procedural Asset Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "All assets used in Infinigen Indoors are generated from scratch by compact probabilistic programs. These programs have many human-controllable parameters, which are randomized by default, or can be manually overridden by the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 69, + 545, + 189 + ], + "blocks": [ + { + "bbox": [ + 312, + 69, + 545, + 189 + ], + "lines": [ + { + "bbox": [ + 312, + 69, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 312, + 69, + 545, + 189 + ], + "type": "image", + "image_path": "9d2ef22b14a7fc9ba6b69f4d05292998b4540d6f491c3c44671ef1921a2b10f1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 198, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 198, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 547, + 232 + ], + "type": "text", + "content": "Figure 6. Random samples of procedurally generated tableware, including dinnerware (Row 1-2), cookware (Row 2), food containers (Row 3) and dining utensils (Row 4)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 312, + 243, + 545, + 305 + ], + "blocks": [ + { + "bbox": [ + 312, + 243, + 545, + 305 + ], + "lines": [ + { + "bbox": [ + 312, + 243, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 312, + 243, + 545, + 305 + ], + "type": "image", + "image_path": "1bc91cc0ef7e1d876705ce96035e61b34d0b43fa7b547fab359dfd7e949c29d4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 358, + 545, + 495 + ], + "blocks": [ + { + "bbox": [ + 306, + 314, + 547, + 358 + ], + "lines": [ + { + "bbox": [ + 306, + 314, + 547, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 547, + 358 + ], + "type": "text", + "content": "Figure 7. Random samples of procedurally generated home decorations, including lamps, hardware, balloons, wall decor (top), rugs, book stacks, vases and plants (bottom). Small assets for decoration purposes, usually attached to the ground or walls." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 358, + 545, + 495 + ], + "lines": [ + { + "bbox": [ + 309, + 358, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 309, + 358, + 545, + 495 + ], + "type": "image", + "image_path": "eb2fa7a5be9e8a27ef67411c5c38b3f722aa522ff0c549911391ef6db32a42a3.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 502, + 547, + 558 + ], + "lines": [ + { + "bbox": [ + 305, + 502, + 547, + 558 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 547, + 558 + ], + "type": "text", + "content": "Figure 8. A collection of materials generated in Infinigen Indoors. The first figure shows one material per generator, with columns (1-3) used on assets of various sizes, (4-5) used on assets and rooms, and (6) for abstract art and text. The second figure shows multiple materials from the same generator with different parameters." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 580, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 689 + ], + "type": "text", + "content": "user. These parameters are used along with additional low-level random noise to generate meshes via geometry nodes, modifiers, or mesh manipulations in Blender. We provide a total of 79 randomized procedural object generators. By category, we cover Appliances (10 generators, 112 params), Windows/Doors/Staircases (14 generators, 127 params), Furniture (17 generators, 216 params), Decorations (15 generators, 92 params), and Small Objects (19 generators, 194 params). See the supplement for a list." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Architectural elements shown in Fig. 3 are integrated into room as fixtures. We use array repetition of atomic compo" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21786" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 50, + 69, + 287, + 186 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 287, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 287, + 186 + ], + "type": "text", + "content": "tables = scene.with_semantics(Tag.Chair)\nchairs = scene.with_semantics(Tag.Table)\non_fLOOR = cl.StableAgainst(Tag Bottom, Tag.Floor)\nconstraints = clforall(rooms[Tag.DiningRoom],\nr,\n(tablets Related_to(r, on_fLOOR).count() == 1,\nchairs related_to(r, on_fLOOR).count().in_range(2, 10)),)\nscore = (\n chairs related_toRooms[Tag.DiningRoom], on_fLOOR)\n .mean(c, cl.reflection_symmetry(c, tables) + \\cl.min_distance(t, tables) * (-1))\n .maximize(weight=2)\n)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + } + ], + "index": 0, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 46, + 194, + 288, + 227 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 288, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 288, + 227 + ], + "type": "text", + "content": "Figure 9. Example usage of our constraint specification API, specifying the quantity and aesthetic constraints for a dining table and chairs." + } + ] + } + ], + "index": 1, + "type": "text" + }, + { + "bbox": [ + 46, + 251, + 287, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 274 + ], + "type": "text", + "content": "nents to build staircases, and mesh booleaning to cut out the panels of doors and windows." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 275, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 323 + ], + "type": "text", + "content": "Large objects shown in Fig. 4 and 5 provide assets related to cooking, seating and storage. We use soft-body collision simulation to model soft blankets, clothing, and stuffed pillows when they are put on a supporting surface." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 324, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 384 + ], + "type": "text", + "content": "Small objects shown in Fig. 6 and 7 can be attached to support surfaces, walls, or ceilings. We also devised a combined text-and-shape logo generator that produces procedural texture for fabrics, food packaging, and art decor. We use cloth simulation to inflate balloons and food packaging with air." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "type": "text", + "content": "Materials are all procedurally created with Blender's Shader nodes, as shown in Fig. 8. We provide 30 material generators with 120 controllable parameters total, split approximately evenly between types of Wood, Ceramic, Fabric, Metal, and others. We cover " + }, + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "type": "inline_equation", + "content": "78\\%" + }, + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "type": "text", + "content": " of OpenSurfaces'[5] material categories, up from " + }, + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "type": "inline_equation", + "content": "21\\%" + }, + { + "bbox": [ + 46, + 384, + 287, + 456 + ], + "type": "text", + "content": " for Infinigen." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 466, + 205, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 205, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 205, + 479 + ], + "type": "text", + "content": "3.2. Constraint Specification API" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 485, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 616 + ], + "type": "text", + "content": "Indoor scene layouts are highly regular, and follow complex rules governing ergonomics, aesthetics and functionality. Moreover, the rules that apply to a particular object depend on context - for example, tables are placed against walls when used as desks in study rooms, but must be far from walls and surrounded by chairs when used in a dining room. To capture this, we provide a high-level Constraint Specification API, which allows the user to write complex geometric scoring functions of sets of objects in the scene. This score is optimized by the solver to find a satisfactory layout. An example of the Constraint Specification API is shown in 9." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Each constraint in the specification API can be expressed as a composition of geometric operators. Geometric operators are designed to compute spatial and geometric properties, including minimum distance, rotational and reflection symmetry, angle alignment, 2D free-space, accessibility and volume or area of objects. By composing these operators with nested filtering by semantics and relations, the user can create scoped constraints that apply only to objects attached" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": "to specific surfaces or rooms. Additionally, these geometry terms are affected by the parameters (length, width, etc.) of the procedurally generated assets, meaning that optimizers can automatically discover optimal furniture parameters given available space and constraints. Our system features common scalar arithmetic operations, comparisons, and forall / sum operators to gather results over sets of objects. Please see the supplement for the full API and more constraint specification examples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 180, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 287 + ], + "type": "text", + "content": "A more concrete example of our constraint language can be found in Fig. 9, where the constraint program specifies common-sense human ergonomics and semantic relations found in residential homes. This constraint graph has a total of 1058 nodes, which compute 11 hard constraints and 25 score terms (soft constraints). We provide example constraint specifications for living rooms, bathrooms, dining rooms, kitchens, and warehouses. See the supplement for the full constraint program and example constraints." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 288, + 545, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 359 + ], + "type": "text", + "content": "For generating training data, we believe many users will consider creating custom constraints tailored to particular applications. Our constraint system is designed to allow easy customization. Our initial spec. has avg. 15 constraints specific to each room: approx. 15 lines of Python. We believe this cost is very tractable when users need customization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 366, + 424, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 366, + 424, + 379 + ], + "spans": [ + { + "bbox": [ + 306, + 366, + 424, + 379 + ], + "type": "text", + "content": "3.3. Arrangement Solver" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": "Because our Constraint Specification API is flexible, the solver needs to search a prohibitively large space in which finding an exact minimum is impossible. To deal with this, it uses Simulated Annealing[35] with Metropolis-Hastings criterion [25, 53]. The solver first takes the current state " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " and randomly chooses a move category. It then uses the constraint graph to generate a proposed state " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " that can be reached using the move. The current and proposed states are evaluated on the graph specified by the provided constraints and score terms, yielding loss terms " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "l(s)" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "l(s')" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": ". Then, the solver calculates transition probability between the " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 347, + 528, + 503, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 528, + 503, + 541 + ], + "spans": [ + { + "bbox": [ + 347, + 528, + 503, + 541 + ], + "type": "interline_equation", + "content": "p \\left(s ^ {\\prime} \\mid s\\right) = \\min \\left[ \\exp \\left(l (s) - l \\left(s ^ {\\prime}\\right)\\right) / \\tau , 1 \\right]", + "image_path": "cf485e50a0575083cbe2e5bce3eae10c3a60a082ca3105211d7e1fa6c2b48ce0.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "text", + "content": " is the temperature of the solver, which cools exponentially from " + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\tau = 0.25" + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\tau = 0.001" + }, + { + "bbox": [ + 304, + 545, + 547, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 538, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 538, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 538, + 594 + ], + "type": "text", + "content": "Our solver allows both discrete and continuous moves: Addition - Adds a procedural object to the scene." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 594, + 485, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 485, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 485, + 605 + ], + "type": "text", + "content": "Deletion - Deletes an object from the scene." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 605, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 605, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 306, + 605, + 547, + 629 + ], + "type": "text", + "content": "Relation Plane Change - Assigns an object to another plane. Resample - Regenerates an object with new parameters." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 630, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 547, + 653 + ], + "type": "text", + "content": "Reinitialize Pose - Samples a new random pose for an object. Translate - Translates the object within its DOF plane." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 654, + 502, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 654, + 502, + 665 + ], + "spans": [ + { + "bbox": [ + 306, + 654, + 502, + 665 + ], + "type": "text", + "content": "Rotate - Rotates the object around its DOF axis." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "We observe that not all moves are equally significant at each point in the optimization. In an empty scene, object addition and relation change allow for higher loss reduction, whereas in a cluttered scene, continuous object movement" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21787" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 85, + 186, + 131 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 58, + 81 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 58, + 81 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 58, + 81 + ], + "type": "text", + "content": "a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 85, + 186, + 131 + ], + "lines": [ + { + "bbox": [ + 47, + 85, + 186, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 85, + 186, + 131 + ], + "type": "image", + "image_path": "f9167d8340b1de69bfdfa65989d2e36667186ab3e706203f27ab4d00524e099d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 189, + 72, + 251, + 142 + ], + "blocks": [ + { + "bbox": [ + 189, + 72, + 251, + 142 + ], + "lines": [ + { + "bbox": [ + 189, + 72, + 251, + 142 + ], + "spans": [ + { + "bbox": [ + 189, + 72, + 251, + 142 + ], + "type": "image", + "image_path": "4bcf509760a5fab1bf457cc7e9386a85f5e0baef1f810bc61c7600526e918797.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 260, + 83, + 326, + 127 + ], + "blocks": [ + { + "bbox": [ + 260, + 83, + 326, + 127 + ], + "lines": [ + { + "bbox": [ + 260, + 83, + 326, + 127 + ], + "spans": [ + { + "bbox": [ + 260, + 83, + 326, + 127 + ], + "type": "image", + "image_path": "5f1bbfcddf8f046b949a9a5c21e6b04c603550f70c0ce079419ca816fd0698f3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 72, + 338, + 81 + ], + "lines": [ + { + "bbox": [ + 329, + 72, + 338, + 81 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 338, + 81 + ], + "type": "text", + "content": "b)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 59, + 142, + 187, + 204 + ], + "blocks": [ + { + "bbox": [ + 59, + 142, + 187, + 204 + ], + "lines": [ + { + "bbox": [ + 59, + 142, + 187, + 204 + ], + "spans": [ + { + "bbox": [ + 59, + 142, + 187, + 204 + ], + "type": "image", + "image_path": "1a7e21cbc91fb78c6d923da5493deeea47ecf4e59f5004af782e4ca5a24d5ef0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 546, + 255 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 546, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 546, + 255 + ], + "type": "text", + "content": "Figure 10. In Fig. a), we show ten randomly generated single-story floor plans with a diverse set of room combinations, connectedness, and overall contours. In Fig. b), we show results for the generation of multistory floor plans. Floors 0,1,2 are displayed separately. Staircases connect adjacent floors. We remove exterior walls and ceilings for visibility." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 201, + 142, + 257, + 209 + ], + "blocks": [ + { + "bbox": [ + 201, + 142, + 257, + 209 + ], + "lines": [ + { + "bbox": [ + 201, + 142, + 257, + 209 + ], + "spans": [ + { + "bbox": [ + 201, + 142, + 257, + 209 + ], + "type": "image", + "image_path": "97204a480dcad206601a96285e160215da2a962d4769f747ae971bd35ed4af40.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 276, + 140, + 316, + 212 + ], + "blocks": [ + { + "bbox": [ + 276, + 140, + 316, + 212 + ], + "lines": [ + { + "bbox": [ + 276, + 140, + 316, + 212 + ], + "spans": [ + { + "bbox": [ + 276, + 140, + 316, + 212 + ], + "type": "image", + "image_path": "345163aead45353d1ad4459cdf57dff9960e5e83fb998513f69489f7b760d15f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 331, + 87, + 403, + 140 + ], + "blocks": [ + { + "bbox": [ + 331, + 87, + 403, + 140 + ], + "lines": [ + { + "bbox": [ + 331, + 87, + 403, + 140 + ], + "spans": [ + { + "bbox": [ + 331, + 87, + 403, + 140 + ], + "type": "image", + "image_path": "2103d2f63f6abc0ea6573a4a0eca0e54245607c13be5f80b616d0469095a4dc2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 403, + 72, + 475, + 140 + ], + "blocks": [ + { + "bbox": [ + 403, + 72, + 475, + 140 + ], + "lines": [ + { + "bbox": [ + 403, + 72, + 475, + 140 + ], + "spans": [ + { + "bbox": [ + 403, + 72, + 475, + 140 + ], + "type": "image", + "image_path": "2e53f2aee5acd224629e3daa19866037d413365ad5f7cf08217c1563a3bd714f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 476, + 72, + 546, + 140 + ], + "blocks": [ + { + "bbox": [ + 476, + 72, + 546, + 140 + ], + "lines": [ + { + "bbox": [ + 476, + 72, + 546, + 140 + ], + "spans": [ + { + "bbox": [ + 476, + 72, + 546, + 140 + ], + "type": "image", + "image_path": "22200ec601807dd4c191a3f6da957c7278e9b6e991059db92375077e343b6a0d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 332, + 158, + 400, + 213 + ], + "blocks": [ + { + "bbox": [ + 332, + 158, + 400, + 213 + ], + "lines": [ + { + "bbox": [ + 332, + 158, + 400, + 213 + ], + "spans": [ + { + "bbox": [ + 332, + 158, + 400, + 213 + ], + "type": "image", + "image_path": "2e93e78a86712e8a8b35e0c23e492b18f4a3bb082bbd221c430b8c63a6673d31.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 403, + 155, + 471, + 213 + ], + "blocks": [ + { + "bbox": [ + 403, + 155, + 471, + 213 + ], + "lines": [ + { + "bbox": [ + 403, + 155, + 471, + 213 + ], + "spans": [ + { + "bbox": [ + 403, + 155, + 471, + 213 + ], + "type": "image", + "image_path": "25d59dff288a008de0ac69189f254107ff2e45115a97f7587d33a1c5cc092831.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 476, + 150, + 542, + 213 + ], + "blocks": [ + { + "bbox": [ + 476, + 150, + 542, + 213 + ], + "lines": [ + { + "bbox": [ + 476, + 150, + 542, + 213 + ], + "spans": [ + { + "bbox": [ + 476, + 150, + 542, + 213 + ], + "type": "image", + "image_path": "e5b967d64ad3c51ec20901c71ffb994a0b42efbd8ffdcf77fc86bc1efe64fb0d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 50, + 266, + 545, + 390 + ], + "blocks": [ + { + "bbox": [ + 50, + 266, + 545, + 390 + ], + "lines": [ + { + "bbox": [ + 50, + 266, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 50, + 266, + 545, + 390 + ], + "type": "image", + "image_path": "a0edaca90b3d090e3f46e2a777144b02ea2a4be489796b37b3c51645daa62b92.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 399, + 546, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 399, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 546, + 420 + ], + "type": "text", + "content": "Figure 11. Qualitative room arrangement results, grouped by room type. From left to right, we show bathrooms, dining rooms, living rooms and kitchens." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 427, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 287, + 462 + ], + "type": "text", + "content": "allows for higher loss reduction. Thus, we provide a schedule for moves so that probabilities for discrete moves decay gradually and probabilities for continuous moves increase." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 464, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 547 + ], + "type": "text", + "content": "The objects in an indoor scene are interdependent on each other, which makes it unfeasible to optimize over all of them simultaneously. However, they usually depend on each other hierarchically (e.g., a cup is on the table, which is on the floor). To exploit this hierarchy, we divide our optimization into three stages: large object optimization, medium object optimization, and small object optimization." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 548, + 288, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 288, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 288, + 668 + ], + "type": "text", + "content": "Each object is constrained in its movement due to the constraints specified by the user and the discrete moves proposed by the solver. For instance, a bookshelf that is stable against a wall is only allowed to move along the 1D line between the wall and the floor. Consequently, an object's degrees of freedom (DoFs) for rotation and translation are determined based on its relations to other objects. When the solver samples a continuous move, it restricts the object's motion to these DoFs. When the solver samples a discrete move, it places the object in the constrained subspace." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Floorplan-specific solver and constraints Our floorplan generator creates realistic full-house room meshes as shown in Fig. 10. First, we procedurally generate a room adjacency" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 427, + 547, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 547, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 547, + 522 + ], + "type": "text", + "content": "graph specifying the number, type, and connectedness of individual rooms required in the floor plan. This graph is produced by inference on a probabilistic context-free grammar on room types, or can be wholly or partially derived from user input. We define our objective function as a weighted combination of the terms below, and optimize it using simulated annealing subject to constraints from the room adjacency graph. See the supplement for full definitions." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 312, + 523, + 541, + 594 + ], + "type": "list", + "angle": 0, + "index": 34, + "blocks": [ + { + "bbox": [ + 312, + 523, + 420, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 523, + 420, + 534 + ], + "spans": [ + { + "bbox": [ + 312, + 523, + 420, + 534 + ], + "type": "text", + "content": "- Shortest path to entrance" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 427, + 523, + 510, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 427, + 523, + 510, + 534 + ], + "spans": [ + { + "bbox": [ + 427, + 523, + 510, + 534 + ], + "type": "text", + "content": "Typical room area" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 312, + 535, + 393, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 535, + 393, + 545 + ], + "spans": [ + { + "bbox": [ + 312, + 535, + 393, + 545 + ], + "type": "text", + "content": "- Room aspect ratio" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 430, + 535, + 503, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 430, + 535, + 503, + 545 + ], + "spans": [ + { + "bbox": [ + 430, + 535, + 503, + 545 + ], + "type": "text", + "content": "- Room convexity" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 312, + 547, + 414, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 547, + 414, + 557 + ], + "spans": [ + { + "bbox": [ + 312, + 547, + 414, + 557 + ], + "type": "text", + "content": "- Room wall conciseness" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 430, + 547, + 523, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 430, + 547, + 523, + 557 + ], + "spans": [ + { + "bbox": [ + 430, + 547, + 523, + 557 + ], + "type": "text", + "content": "- Functional room area" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 312, + 559, + 393, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 559, + 393, + 570 + ], + "spans": [ + { + "bbox": [ + 312, + 559, + 393, + 570 + ], + "type": "text", + "content": "- Room collinearity" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 430, + 559, + 505, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 430, + 559, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 430, + 559, + 505, + 570 + ], + "type": "text", + "content": "- Narrow passages" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 312, + 571, + 417, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 571, + 417, + 582 + ], + "spans": [ + { + "bbox": [ + 312, + 571, + 417, + 582 + ], + "type": "text", + "content": "- Exterior length by room" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 430, + 571, + 538, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 430, + 571, + 538, + 582 + ], + "spans": [ + { + "bbox": [ + 430, + 571, + 538, + 582 + ], + "type": "text", + "content": "- Exterior corners by room" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 312, + 582, + 408, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 582, + 408, + 594 + ], + "spans": [ + { + "bbox": [ + 312, + 582, + 408, + 594 + ], + "type": "text", + "content": "- Staircase occupancies" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 430, + 582, + 541, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 430, + 582, + 541, + 593 + ], + "spans": [ + { + "bbox": [ + 430, + 582, + 541, + 593 + ], + "type": "text", + "content": "- Staircase IOU with rooms" + } + ] + } + ], + "index": 33 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "We initialize our floorplan solver by generating a random house outline, and subdividing it using a Mondrian Process [65] until it produces sufficient spaces for each room. We extrude a wall segment inwards or outwards at each step, or swap the assignment subject to the room adjacency graph. Either action will lead to a change in loss, which we convert to an acceptance probability using Metropolis-Hasting as in Sec 3.3. Once solving is complete, we add floor, wall, and ceiling materials, doors, windows, and staircases, all subject to constraints based on room type and adjacency. Fig" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21788" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 284, + 202 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 284, + 202 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 284, + 202 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 284, + 202 + ], + "type": "image", + "image_path": "af7b6cba50d663146d8192e16443cea07307a5f05a46aaf5ab85882d1bf8a9f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 203, + 284, + 334 + ], + "blocks": [ + { + "bbox": [ + 52, + 203, + 284, + 334 + ], + "lines": [ + { + "bbox": [ + 52, + 203, + 284, + 334 + ], + "spans": [ + { + "bbox": [ + 52, + 203, + 284, + 334 + ], + "type": "image", + "image_path": "8d40cb8630077d8fa4399018ef414b47c66d74e4947eb58c9747cc88d0a234f7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 408, + 286, + 498 + ], + "blocks": [ + { + "bbox": [ + 47, + 350, + 287, + 405 + ], + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 405 + ], + "type": "text", + "content": "Figure 12. A single scene from two different viewpoints in Unreal Engine 5 (above) and Omniverse Isaac Sim (below). Unreal Engine runs at 60 FPS and Isaac Sim with physics simulation enabled runs at 45 FPS, both on RTX 3090s. Differences in lighting are caused by the variations in simulator import systems." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 408, + 286, + 498 + ], + "lines": [ + { + "bbox": [ + 50, + 408, + 286, + 498 + ], + "spans": [ + { + "bbox": [ + 50, + 408, + 286, + 498 + ], + "type": "image", + "image_path": "82d7adb74bd039385fd8fdd705b7aca97e4b373e2f794148114788194b6c52a0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 49, + 502, + 285, + 514 + ], + "lines": [ + { + "bbox": [ + 49, + 502, + 285, + 514 + ], + "spans": [ + { + "bbox": [ + 49, + 502, + 285, + 514 + ], + "type": "text", + "content": "Figure 13. Qualitative zero-shot results on SRD [59] test dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 535, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 535, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 535, + 287, + 559 + ], + "type": "text", + "content": "11 shows the solutions to room arrangements with objects placed inside." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "type": "text", + "content": "3.4. Data Export" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 597, + 286, + 662 + ], + "blocks": [ + { + "bbox": [ + 50, + 597, + 286, + 662 + ], + "lines": [ + { + "bbox": [ + 50, + 597, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 50, + 597, + 286, + 662 + ], + "type": "table", + "html": "
All ImageShadow RegionNon-Sh Region
Test SetModelPSNR↑RMSE↓PSNR↑RMSE↓PSNR↑RMSE↓
ISTD [81]R31.964.2738.046.5834.133.85
R+S31.724.3037.417.0633.803.85
SRD [59]R22.8310.8425.5918.7527.937.68
R+S24.569.5427.3916.6329.376.67
", + "image_path": "758b1e8afa14d5b37ac1abfdc8f307e1bc0984aa0e6fec36dadab265be82ef72.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 670, + 287, + 692 + ], + "lines": [ + { + "bbox": [ + 47, + 670, + 287, + 692 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 287, + 692 + ], + "type": "text", + "content": "Table 2. Shadow removal task quantitative performance on ISTD, ISTD+ and SRD dataset across the three variations of the model." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "content": "We develop a one-click tool to export assets from Infini" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 543, + 144 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 543, + 144 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 543, + 144 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 543, + 144 + ], + "type": "image", + "image_path": "dfd1743aaad4d6f80c3bf809cf9cc3550399ae4bdecc766a94692e7a06680d9b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 149, + 538, + 160 + ], + "lines": [ + { + "bbox": [ + 312, + 149, + 538, + 160 + ], + "spans": [ + { + "bbox": [ + 312, + 149, + 538, + 160 + ], + "type": "text", + "content": "Figure 14. Qualitative results on synthetic artistic scenes [21]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 168, + 547, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 168, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 547, + 239 + ], + "type": "text", + "content": "gen Indoors to real-time simulators, using Universal Scene Description (USD) or other formats. As seen in Fig. 12, indoor scenes can be exported to Omniverse Isaac Sim and Unreal Engine 5 and can be run at interactive frame rates. This exporting capability allows Infinigen Indoors to help train embodied agents in virtual environments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 241, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 241, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 241, + 547, + 361 + ], + "type": "text", + "content": "Infinigen Indoors uses Blender's procedural material system, which is by default not portable to other simulators or scene editors. To resolve this, we provide tools to automatically post-process and UV-map entire indoor scenes, and use texture baking to create standard texture maps for material color, roughness, metallicity and more. We also provide export code to convert single objects to textured OBJ, FBX or STL meshes, and automatically generate collision and articulation information as Universal Robot Description Format (URDF) files." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 373, + 387, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 387, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 387, + 387 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 394, + 421, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 421, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 421, + 405 + ], + "type": "text", + "content": "4.1. Solver Performance" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 414, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 414, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 414, + 547, + 568 + ], + "type": "text", + "content": "To efficiently solve large numbers of constraints in cluttered scenes, we optimized our solver with various features for faster convergence. Plane hashing enables faster access to bounding planes during discrete optimization. BVH caching enables faster mesh distance and collision calculations by reusing Bounding-Volume-Hierarchies except when mutated by a state update. Evaluation caching maintains a cache of results in the evaluation graph. Move filtering narrows down the search space in continuous optimization by selectively pruning candidates to those that can reduce the loss. Place-holder optimization only generates full meshes when other objects are assigned to them; otherwise it keeps bounding boxes. See the supplement for more details." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "To analyze the importance of these features, we conducted an ablation in Tab. 3 and Fig. 15, which shows solver performance with each feature removed. All results are averaged over 20 random scenes with " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "5\\mathrm{k}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " solver steps. Our full system provides a " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\approx 3\\mathrm{x}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " speedup compared to the non-optimized version. Most of the performance gains come from BVH caching and Plane Hashing. We observe that discrete changes such as pose re-initialization, relation changes, and object resampling are necessary for compelling visuals, but decrease the quantitative score and increase the runtime. When we run our fully optimized system as long as the non-optimized version we get a " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "28\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " score increase." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21789" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 170, + 140 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 170, + 140 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 170, + 140 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 170, + 140 + ], + "type": "image", + "image_path": "8ab1e66874dd014e90e62ae98718f19d336305031993cd2f69c5e49148450276.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 148, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 46, + 148, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 547, + 171 + ], + "type": "text", + "content": "Figure 15. Qualitative Ablation. From left to right, we show scenes generated by our system with 10K solving steps (a), 1K solving steps (b), with collision checking removed (c) and with symmetry terms disabled (d)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 296, + 140 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 296, + 140 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 296, + 140 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 296, + 140 + ], + "type": "image", + "image_path": "655a90473f39d29b9f04b258962241b8ddb81e157285740046f8113ebd78c711.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 298, + 70, + 421, + 140 + ], + "blocks": [ + { + "bbox": [ + 298, + 70, + 421, + 140 + ], + "lines": [ + { + "bbox": [ + 298, + 70, + 421, + 140 + ], + "spans": [ + { + "bbox": [ + 298, + 70, + 421, + 140 + ], + "type": "image", + "image_path": "4078a12df63c48086f4e7f1f34012e1935bfeda1cd642032d36564b53aacee3f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 423, + 70, + 545, + 140 + ], + "blocks": [ + { + "bbox": [ + 423, + 70, + 545, + 140 + ], + "lines": [ + { + "bbox": [ + 423, + 70, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 423, + 70, + 545, + 140 + ], + "type": "image", + "image_path": "9f451b90a77ca48ddbeeac019502494ac622f946f893c6c28d864d17eaf3a50a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 190, + 286, + 297 + ], + "blocks": [ + { + "bbox": [ + 50, + 190, + 286, + 297 + ], + "lines": [ + { + "bbox": [ + 50, + 190, + 286, + 297 + ], + "spans": [ + { + "bbox": [ + 50, + 190, + 286, + 297 + ], + "type": "table", + "html": "
MethodRuntime ↓Avg. Score (s) ↑#Objects ↑
Full System2280.6880.8428.94
w/o Discrete change1872.6086.2030.82
w/o Eval. cache2242.7980.8428.94
w/o Move Filter2633.9584.7545.06
w/o Placeholder optim.2665.1880.4627.71
w/o Plane Hashing3522.8692.6534.12
w/o BVH cache4740.4880.8429.06
Full System 100 min.6080.84114.7249.65
w/o Optimization6308.9289.4347.76
", + "image_path": "057092ae2646936f636ad3fe062fa12e690f6e44fe906cc063e5c94850629743.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 327, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 400 + ], + "type": "text", + "content": "Perceptual Study We recruited human subjects following [57] to evaluate the realism of the scenes and the realism of the layouts. Subjects preferred Infinigen Indoors over [11, 57, 62, 84] in terms of both realism, layout realism, and the lack of errors (caveat: \"realism\" may be influenced by asset and lighting quality). See the supp. for more details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 406, + 151, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 151, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 151, + 418 + ], + "type": "text", + "content": "4.2. Shadow Removal" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 425, + 289, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 594 + ], + "type": "text", + "content": "To demonstrate its flexibility in data generation, we used Infinigen-Indoors to create a dataset consisting of 2k image pairs of shadow and shadow-free variants. These pairs were generated by toggling the shadow property of lighting within Blender. For each pair, shadow masks were produced using Otsu's thresholding [55] method. We use ShadowFormer [22] model for the experiments and consider two variations: only trained on ISTD [81] real dataset (R), and trained on combination of ISTD and 2k Infinigen Indoors synthetic dataset " + }, + { + "bbox": [ + 46, + 425, + 289, + 594 + ], + "type": "inline_equation", + "content": "(\\mathbb{R} + \\mathbb{S})" + }, + { + "bbox": [ + 46, + 425, + 289, + 594 + ], + "type": "text", + "content": ". The results are shown in Tab. 2. While using synthetic data leads to slightly worse performance on ISTD dataset, the zero-shot application on SRD [59] dataset shows clear improvement for generalization to new test datasets. Qualitative results are shown in Fig. 13." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 599, + 220, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 220, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 220, + 612 + ], + "type": "text", + "content": "4.3. Occlusion Boundary Estimation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "To validate the effectiveness of Infinigen Indoors, we also evaluate on the task of occlusion boundary estimation, a task with limited available data. We produce 1464 images annotated with ground truth. We train three U-Net [64] models from scratch separately on these images, on images generated from Infinigen [60] and Hypersim [63]. We then compare their performance on a curated test set of photorealistic artist-designed synthetic 3D scenes for architecture" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 313, + 190, + 539, + 251 + ], + "blocks": [ + { + "bbox": [ + 66, + 305, + 266, + 316 + ], + "lines": [ + { + "bbox": [ + 66, + 305, + 266, + 316 + ], + "spans": [ + { + "bbox": [ + 66, + 305, + 266, + 316 + ], + "type": "text", + "content": "Table 3. Ablation of solver performance optimizations." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 190, + 539, + 251 + ], + "lines": [ + { + "bbox": [ + 313, + 190, + 539, + 251 + ], + "spans": [ + { + "bbox": [ + 313, + 190, + 539, + 251 + ], + "type": "table", + "html": "
Training DatasetODSOISmAP
Infinigen-Nature [60]14.3819.4310.80
Hypersim [63]26.0219.4415.69
Infinigen Indoors (Ours)29.4730.2919.09
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See the supplement for more details." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "text", + "content": "We report the following three metrics [79, 80, 85]: (i) optimal dataset scale " + }, + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "text", + "content": "-score (ODS), representing the best F-score achieved on the dataset using a uniform threshold across all test images; (ii) optimal image scale " + }, + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "text", + "content": "-score (OIS) indicating the cumulative F-score on the dataset obtained with thresholds dependent on individual images; and (iii) mean average precision (mAP) denoting the mean precision across the complete recall range." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 450, + 547, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 547, + 510 + ], + "type": "text", + "content": "As we can see in Tab. 4, our Infinigen Indoors-trained model generalizes better. The model achieves higher performance across all metrics. These findings underscore the usefulness of Infinigen Indoors as a valuable training resource. Qualitative results are depicted in Fig. 14." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 525, + 508, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 508, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 508, + 538 + ], + "type": "text", + "content": "5. Contributions & Acknowledgements" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 545, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 712 + ], + "type": "text", + "content": "Alexander Raistrick, Lingjie Mei and Karhan Kayan contributed equally and are ordered randomly. Each has the right to list their name first in their CV. Alexander Raistrick performed team coordination and developed the constraint language and object graph solver. Lingjie Mei developed the room solver and many procedural assets. Karhan Kayan developed the geometric constraints and object pose solver. David Yan developed the scene exporter and other utilities. Yiming Zuo, Beining Han, Hongyu Wen, Meenal Parakh, Stamatis Alexandropoulos, Zeyu Ma and Lahav Lipson developed procedural assets and utilities. Jia Deng conceptualized and led the project, and set directions. This work was partially supported by the National Science Foundation and Amazon." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21790" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "type": "text", + "content": "[1] Archive 3D. 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Springer, 2020. 3" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21794" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Infrared Adversarial Car Stickers/1b21f991-5369-4064-a439-e126cdaa2289_content_list.json b/2024/Infrared Adversarial Car Stickers/1b21f991-5369-4064-a439-e126cdaa2289_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..944e1f7e1f94a2e9e099d5ea686c984dfe5da045 --- /dev/null +++ b/2024/Infrared Adversarial Car Stickers/1b21f991-5369-4064-a439-e126cdaa2289_content_list.json @@ -0,0 +1,1708 @@ +[ + { + "type": "text", + "text": "Infrared Adversarial Car Stickers", + "text_level": 1, + "bbox": [ + 310, + 130, + 656, + 150 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaopei Zhu $^{1}$ Yuqiu Liu $^{2}$ Zhanhao Hu $^{3}$ Jianmin Li $^{4}$ Xiaolin Hu $^{4,5,6*}$ $^{1}$ School of Integrated Circuits, Tsinghua University, Beijing, China \n $^{2}$ Department of Technology, Beijing Forestry University, Beijing, China \n $^{3}$ Department of Electrical Engineering and Computer Sciences, UC Berkeley, California, USA \n $^{4}$ Department of Computer Science and Technology, Institute for Artificial Intelligence, BNRist, Tsinghua University, Beijing, China \n $^{5}$ THBI, IDG/McGovern Institute for Brain Research, Tsinghua University, Beijing, China \n $^{6}$ Chinese Institute for Brain Research (CIBR), Beijing, China \n{zxp18}@mail.tsinghua.edu.cn \n{liuyuqiu99, zhanhaohu.cs}@gmail.com \n{lijianmin, xlhu}@mail.tsinghua.edu.cn", + "bbox": [ + 112, + 178, + 854, + 375 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 409, + 312, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Infrared physical adversarial examples are of great significance for studying the security of infrared AI systems that are widely used in our lives such as autonomous driving. Previous infrared physical attacks mainly focused on 2D infrared pedestrian detection which may not fully manifest its destructiveness to AI systems. In this work, we propose a physical attack method against infrared detectors based on 3D modeling, which is applied to a real car. The goal is to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles, distances, and scenes. We build a 3D infrared car model with real infrared characteristics and propose an infrared adversarial pattern generation method based on 3D mesh shadow. We propose a 3D control points-based mesh smoothing algorithm and use a set of smoothness loss functions to enhance the smoothness of adversarial meshes and facilitate the sticker implementation. Besides, We designed the aluminum stickers and conducted physical experiments on two real Mercedes-Benz A200L cars. Our adversarial stickers hid the cars from Faster RCNN, an object detector, at various viewing angles, distances, and scenes. The attack success rate (ASR) was $91.49\\%$ for real cars. In comparison, the ASRs of random stickers and no sticker were only $6.21\\%$ and $0.66\\%$ , respectively. In addition, the ASRs of the designed stickers against six unseen object detectors such as YOLOv3 and Deformable DETR were between $73.35\\% - 95.80\\%$ , showing good transferability of the attack performance across detectors.", + "bbox": [ + 75, + 441, + 472, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7ee1c75177d4e6b83179ad7c365e6faf0e2ac30d31230988e3d04da0226aeee7.jpg", + "image_caption": [ + "Figure 1. Infrared attack effect on real cars. (a) Visible light view of real cars. (b) Infrared view of real cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers. The numbers above the bounding boxes are object confidence scores (\\%) with 0.6 threshold. Our adversarial stickers hid the car from Faster RCNN at various viewing angles, distances and scenes. In comparison, the clean car and the car with random shape stickers were detected at the same situation." + ], + "image_footnote": [], + "bbox": [ + 501, + 409, + 694, + 664 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b9accba057be4dfcdf360fe56174fd42e44ee65a4987cd2bdd7bbaae20236a7e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 409, + 888, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 813, + 630, + 829 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It is well known that deep learning models can be misled by carefully designed perturbations to the input which is called adversarial example, and the perturbation process is called adversarial attack. Adversarial attacks can be di", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24284", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vided into two categories, digital attacks [4, 8, 9, 16, 24, 26] which assume that the attackers can directly modify the model input in the digital world, and physical attacks [11, 12, 27, 28, 35, 37] which assume that the attackers can only modify the object or scene in the physical world. Physical attacks have attracted much attention because of their importance of assessing the security of real-world AI systems.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One type of physical attack is called infrared physical attack [30-32, 35, 37]. Infrared imaging is widely used in our daily lives, such as body temperature monitoring and autonomous driving. Since infrared cameras can function normally at night, they are becoming more and more important in autonomous driving systems; so is their safety.", + "bbox": [ + 75, + 212, + 468, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous infrared physical attacks [30-32, 35, 37] mainly focused on infrared pedestrians, and only two works [31, 32] conducted experiments on model cars. There is currently a lack of infrared attack research on real cars. The reasons might be as follows. Compared with pedestrians with constant body temperature, the temperature distributions of real cars are more uneven (e.g., the temperature of the engine is much higher than that of other places), so their infrared characteristics are more complex than pedestrians. Compared with model cars without engines, real cars' structures and materials are very different from those of model cars, so their infrared characteristics are also quite different. Besides, real car attacks require designing and manufacturing adversarial patterns on the entire 3D car surface, which poses a great challenge to physical experiments. But we believe that for the safety of autonomous driving cars, physical real car attack is worth in-depth investigation.", + "bbox": [ + 75, + 303, + 472, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The aforementioned two infrared model car attacks [31, 32] are only effective within limited viewing angles (e.g., horizontal angles $-30^{\\circ} - 30^{\\circ}$ and pitch angle $0^{\\circ}$ ). But we want to implement a full-angle attack (the horizontal angles $0^{\\circ} - 360^{\\circ}$ , and pitch angle $0^{\\circ} - 90^{\\circ}$ ), so the attack angles cover an entire hemisphere surface, which is a challenging task. We also notice that these methods [31, 32] are both case-by-case attacks, which needs to optimize an adversarial pattern for each image1, while our goal is to achieve a universal attack which uses the same adversarial pattern to attack detectors at various viewing angles, distances and scenes.", + "bbox": [ + 75, + 560, + 472, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Towards this goal, we propose an infrared physical attack method applied to a real car based on 3D modeling. We aim to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles (full-angle), distances and scenes. Since most current 3D car models are visible-light models, and there is a lack of 3D infrared car models, we build a 3D infrared car model with real infrared characteristics at various viewing angles. For the generation of infrared adversarial pattern for stick-", + "bbox": [ + 75, + 741, + 472, + 878 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ers, we propose to optimize a 3D adversarial mesh at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern, and finally attach the 2D adversarial pattern to the car surface. The motivation of this mesh shadow attack (MSA) method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. To improve the smoothness of adversarial patterns and facilitate sticker implementation, we propose a 3D control points-based mesh smoothing algorithm and use a set of smoothing loss functions.", + "bbox": [ + 496, + 90, + 893, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the physical implementation of infrared adversarial patterns, we use an aluminum film which modifies the surface emissivity of the object instead of altering the surface temperature used by previous works [30-32, 35, 37]. Like many car stickers, the adversarial car stickers can be easily attached on the car surface. The stickers are only $0.08\\mathrm{mm}$ thick and take up almost no space.", + "bbox": [ + 496, + 257, + 893, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To assess the safety of infrared detection in real autonomous driving scenes, we used two real Mercedes-Benz A200L cars. Physical experiments show that our infrared adversarial stickers made the real cars hide from the infrared detector Faster RCNN at various viewing angles, various distances, and multiple scenes, with an attack success rate (ASR) of $91.49\\%$ . To the best our knowledge, this is the first 3D multi-view physical infrared vehicle attack, and also the first infrared attack conducted on real cars.", + "bbox": [ + 496, + 364, + 893, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 513, + 640, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Visible Light Physical Adversarial Attacks", + "text_level": 1, + "bbox": [ + 500, + 540, + 861, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Huang et al. [13] proposed a universal physical camouflage (UPC) attack for object detectors. Zhang et al. [34] proposed a vehicle camouflage for physical adversarial attack on object detectors in the wild. Wang et al. [29] proposed the Dual attention suppression (DAS) attack to generate adversarial vehicle camouflage in the physical world. Suryanto et al. [25] generated the physical adversarial camouflage by using a differentiable transformation network. Wang et al. [28] proposed a 3D full-coverage vehicle camouflage for physical adversarial attack (FCA). It is worth noting that all above works are proposed for visible light images.", + "bbox": [ + 496, + 564, + 890, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Infrared Physical Adversarial Attacks", + "text_level": 1, + "bbox": [ + 500, + 756, + 828, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Zhu et al. [35] proposed a bulb-based board to fool infrared pedestrian detectors in the physical world. Zhu et al. [37] proposed an infrared invisible clothing to hide from infrared pedestrian detectors in the physical world. Wei et al. [30] proposed the HotCold blocks to attack the infrared pedestrian detectors. Wei et al. [32] proposed a physical adversarial infrared patch (AIP) based on a points-clustering algorithm. Wei et al. [31] proposed a unified adversar", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1We found this by checking and running their official codes.", + "bbox": [ + 94, + 886, + 415, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24285", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/45dca83f8fdd2c7d96de099d455b0d45fcb6429ce2221a87981a91b0e7516001.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 124, + 87, + 328, + 193 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/65907a968717533b5674c2bd7db7731cec0d671ff3d2a33e255b9476b3ff6170.jpg", + "image_caption": [ + "(b)", + "Figure 2. Construction and optimization of real infrared car texture mapping. (a) Car mesh model. (b) Reorganized faces map. (c) Infrared car texture map collected from real world. (d) Rendered infrared car model." + ], + "image_footnote": [], + "bbox": [ + 331, + 87, + 468, + 193 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5e995316c8a5d71f4e40b9ad5ee42e127b5ceffbcbeab401afd72710e0ff1f97.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 475, + 88, + 609, + 193 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e339de33fdd50f8ce70720db392201d69e766d95a2c8ac9f9bc71228eb4ceaf2.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 614, + 88, + 846, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ial patch (UAP) for physical attacks based on a boundary-limited shape optimization algorithm. It is worth noting that all above methods are proposed for infrared pedestrian or model car attacks. There is currently a lack of research on infrared real vehicle attacks in the physical world.", + "bbox": [ + 75, + 282, + 470, + 358 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Car Sticker Attack Method", + "text_level": 1, + "bbox": [ + 76, + 375, + 330, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method consists of several steps. First, we build a 3D infrared car model based on real infrared characteristics. Next, we use the infrared adversarial pattern generation method based on 3D mesh shadow. To make the 3D adversarial mesh smoother, we use a 3D control points-based mesh smoothing algorithm and use a set of smoothness losses. Then we apply adversarial patterns to 3D infrared car model and optimize the adversarial patterns. Finally, we introduce the physical implementation method of infrared adversarial car stickers.", + "bbox": [ + 75, + 398, + 470, + 550 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Building a 3D Infrared Car Model", + "text_level": 1, + "bbox": [ + 76, + 561, + 377, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To simulate the infrared car attack realistically, we build a 3D model based on the infrared characteristics of a real car. It is worth noting that our method can be applied to any target car, and we chose Mercedes-Benz A200L in our experiments, simply because one of the authors have this car. Figure 2(a) shows the car mesh model $M_{\\mathrm{car}}$ . Next, we need", + "bbox": [ + 75, + 585, + 468, + 676 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a8450625883b13bb5adbbcb32316b20cf947691fd56ed48a51a68fddb6abb8ee.jpg", + "image_caption": [ + "Figure 3. Schematic diagram of mesh shadow method." + ], + "image_footnote": [], + "bbox": [ + 133, + 700, + 410, + 872 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to create a \"skin\" for the car model based on infrared photos taken by an infrared camera FLIR T560. However, the infrared photos captured by the camera are all 2D images, and the challenge is how to \"paste\" these 2D infrared images onto the 3D car mesh model. First, we flatten all the faces of 3D car mesh onto a 2D plane called faces map. After that, we use MAYA software to rearrange these faces to divide different areas, such as roof, doors, etc., as shown in Figure 2(b). This process facilitates the alignment of real infrared car images with the 3D car mesh.", + "bbox": [ + 496, + 282, + 890, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Subsequently, we crop the infrared images into different parts based on the faces map (Figure 2(b)) and paste the cropped images onto the 2D faces map, and then we get the infrared texture map of the car, as shown in Figure 2(c). See Supplementary Material (SM) for how these infrared photos are taken, cropped and pasted. This process establishes a correspondence between the real infrared car images and the 3D car mesh. The rendered infrared car model is shown in Figure 2(d), which is built for a real car with engine running.", + "bbox": [ + 496, + 436, + 892, + 587 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Generation of 2D Shadow Based on 3D Mesh", + "text_level": 1, + "bbox": [ + 498, + 602, + 879, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to design infrared stickers with adversarial patterns to hide the cars from infrared detectors at various viewing angles (full-angle), distances, and scenes. We propose a 3D adversarial mesh shadow attack (MSA) method to generate the 2D infrared adversarial patterns for stickers. The motivation of MSA method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. The core of MSA method is to optimize a 3D adversarial mesh $M_{\\mathrm{adv}}$ at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern $S_{\\mathrm{adv}}$ , and finally attach the 2D adversarial pattern $S_{\\mathrm{adv}}$ to the car surface. Note that the 3D adversarial mesh $M_{\\mathrm{adv}}$ is different from the 3D car mesh $M_{\\mathrm{car}}$ in Section 3.1. The optimization variables include the 3D mesh vertices coordinates $V$ , the mesh shadowing angle $\\varphi$ , and the center point position $P$ when pasting the 2D pattern onto the car's texture map $T_{\\mathrm{origin}}$ (Figure 3).", + "bbox": [ + 496, + 627, + 890, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The shadowing operation refers to rendering the mesh", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24286", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/253b64bfcfa536d811401f908a95f74536c6ac41a1af84ea690f9ec382032a49.jpg", + "image_caption": [ + "Figure 4. The overall pipeline of the proposed method." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 903, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$M_{\\mathrm{adv}}$ to a dark area while retaining the mesh contour (Figure 3), and the dark area has a uniform grayscale value within the contour. The grayscale value is consistent with the infrared characteristics of the sticker we use. Let $\\Omega$ denote this operation. If we want the car to have adversarial effect at various viewing angles, we need to optimize $N$ adversarial meshes to generate $N$ adversarial shadows on different places of the car (Figure 4):", + "bbox": [ + 75, + 407, + 470, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\mathrm {a d v}} ^ {(i)} = \\Omega \\left(M _ {\\mathrm {a d v}} ^ {(i)}, \\varphi^ {(i)}\\right), i = 1, 2, \\dots N. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 542, + 468, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. 3D Control Points-Based Mesh Smoothing", + "text_level": 1, + "bbox": [ + 76, + 580, + 437, + 597 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If we directly optimize the vertices coordinates $V$ of the mesh $M_{\\mathrm{adv}}$ , many \"peaks\" will appear on the mesh surface, which will make the shadow shape very complex and will be difficult for the physical implementation of the adversarial shadow $S_{\\mathrm{adv}}$ . Inspired by the Gaussian smoothing kernel and spline interpolation method, we propose a smoothing control algorithm for 3D mesh vertices. Its core idea is to use some 3D control points $C$ as anchor points, and the coordinate offsets of mesh vertices $V$ are expressed as the weighted average of the coordinate offsets of $C$ . The calculation details are described in SM.", + "bbox": [ + 75, + 604, + 468, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use $\\Theta$ to denote the above transformation, and $C^{(i)}$ to denote the control points set of $M_{\\mathrm{adv}}^{(i)}$ , then", + "bbox": [ + 76, + 773, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV ^ {(i)} = \\Theta (C ^ {(i)}), i = 1, 2, \\dots N. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 820, + 468, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the control points $C^{(i)}$ determine the vertices coordinates $V^{(i)}$ , the optimization variables changes from $\\left(V^{(i)}, P^{(i)}, \\varphi^{(i)}\\right)$ to $\\left(C^{(i)}, P^{(i)}, \\varphi^{(i)}\\right)$ , $i = 1, 2, \\ldots N$ .", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Mesh Smoothness Loss Functions", + "text_level": 1, + "bbox": [ + 500, + 407, + 792, + 420 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further enhance the smoothness of 3D adversarial mesh $M_{\\mathrm{adv}}$ and 2D adversarial pattern $S_{\\mathrm{adv}}$ , we use a set of loss functions including: mesh normal consistency loss, mesh edge loss, chamfer distance loss, and Laplacian smoothing loss. During the optimization process of 3D mesh $M_{\\mathrm{adv}}$ , these functions guide the generation of a smoother adversarial mesh. A smoother 3D mesh $M_{\\mathrm{adv}}$ results in a smoother 2D shadow pattern $S_{\\mathrm{adv}}$ , which is beneficial for manufacturing physical stickers based on the 2D shadow pattern.", + "bbox": [ + 498, + 429, + 890, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mesh normal consistency loss computes the normal consistency for each pair of neighboring faces, and minimizing it encourages the mesh surface to be smoother. We suppose that mesh $M_{\\mathrm{adv}}$ has a total of $F$ faces. Let $n_i, n_j$ ( $1 \\leq i, j \\leq F$ ) represent the normal vector of any two adjacent faces, then this loss function is described as:", + "bbox": [ + 498, + 566, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {n o r m}} = \\text {A v e r a g e} (1 - \\cos \\left(n _ {i}, n _ {j}\\right)). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 666, + 890, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Average is calculated between any pair of adjacent faces.", + "bbox": [ + 500, + 691, + 879, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mesh edge loss computes mesh edge length regularization loss, and minimizing it encourages a reduction in the average edge length of the adversarial mesh. Suppose $M_{\\mathrm{adv}}$ has a total of $M$ edges, $l_{k}$ ( $k = 1,2,\\dots,M$ ) represents the length of each edge, and this loss function is described as", + "bbox": [ + 498, + 707, + 890, + 781 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {e d g e}} = \\left(\\sum_ {k = 1} ^ {M} l _ {k}\\right) / M. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 790, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The chamfer distance loss computes chamfer distance [6] between the sampling points of adversarial mesh and a standard sphere. Reducing chamfer distance loss encourages the adversarial mesh $M_{\\mathrm{adv}}$ to approximate a sphere.", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24287", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We denote the point clouds sampled by adversarial mesh $M_{\\mathrm{adv}}$ and the standard spherical mesh $M_{\\mathrm{sphere}}$ by $S_{1}$ and $S_{2}$ , respectively. The chamfer distance loss is described as", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {c h a m f e r}} = \\sum_ {p \\in S _ {1}} \\min _ {q \\in S _ {2}} \\| p - q \\| _ {2} ^ {2} + \\sum_ {q \\in S _ {2}} \\min _ {p \\in S _ {1}} \\| q - p \\| _ {2} ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 148, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Laplacian smoothing loss $L_{\\mathrm{Laplace}}$ computes the Laplacian smoothing objective for the adversarial mesh. We define this function as Laplace, and its calculation details are introduced in [18], so", + "bbox": [ + 76, + 198, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {L a p l a c e}} = \\text {L a p l a c e} \\left(M _ {\\text {a d v}}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 273, + 468, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Applying the 2D Shadow to 3D Car Model", + "text_level": 1, + "bbox": [ + 76, + 305, + 437, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We apply the adversarial shadow $S_{\\mathrm{adv}}$ to 3D infrared car model by changing its texture map $T_{\\mathrm{origin}}$ . This simulates the process we paste the adversarial stickers to the car surface in the physical world. To facilitate physical implementation, we simulate to paste the stickers onto the door, roof, front hood and rear of the car, which have wide ranges of flat area and are easy to paste. In each area, we paste one or two adversarial shadow patterns (Figure 4). To simulate real-world perturbations, such as errors in cutting the adversarial stickers, variations in surface temperature on the adversarial stickers, and errors in the pasting positions, we introduce random perturbations to the vertex coordinates $V$ of the adversarial mesh $M_{\\mathrm{adv}}$ , random noise to the pattern $S_{\\mathrm{adv}}$ , random changes in grayscale values of $S_{\\mathrm{adv}}$ , and random perturbations in the position $P$ during the pasting of $S_{\\mathrm{adv}}$ . This approach, known as the Expectation Over Transformation (EOT) algorithm [2], enhances the robustness of our algorithm in real-world scenes.", + "bbox": [ + 75, + 329, + 468, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we need to paste the adversarial patterns $S_{\\mathrm{adv}}$ onto the original car texture map $T_{\\mathrm{origin}}$ . Let $\\Gamma$ denote the pasting operation. We establish a Cartesian coordinate system with the center point of $T_{\\mathrm{origin}}$ as the origin. We use $P^{(i)}$ to represent the coordinates of the pasting positions for $N$ adversarial shadows $S_{\\mathrm{adv}}^{(i)}, i = 1,2,\\dots N$ . The texture map after pasting the adversarial shadows is", + "bbox": [ + 75, + 603, + 468, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT _ {\\mathrm {a d v}} = \\Gamma \\left(S _ {\\mathrm {a d v}} ^ {(i)}, P ^ {(i)}, T _ {\\text {o r i g i n}}\\right), i = 1, 2, \\dots N. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 724, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the differentiable renderer Pytorch3D [20] to render the adversarial texture map $T_{\\mathrm{adv}}$ onto the surface of the car mesh $M_{\\mathrm{car}}$ , resulting in the rendered infrared car images with adversarial patterns, denoted as $I_{\\mathrm{adv}}$ . Let $\\Psi$ denote the rendering operation with parameters $\\theta$ which include the rendering distances and angles. Mathematically, this process can be expressed as:", + "bbox": [ + 75, + 763, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {\\mathrm {a d v}} = \\Psi \\left(M _ {\\mathrm {c a r}}, T _ {\\mathrm {a d v}}, \\theta\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Optimization of 3D Mesh Shadow Attack", + "text_level": 1, + "bbox": [ + 500, + 90, + 851, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After we get the rendered infrared adversarial images $I_{\\mathrm{adv}}$ , we input them into the target detector $f$ . The output of the target detector typically includes object confidence $f_{\\mathrm{obj}}$ , class confidence $f_{\\mathrm{cls}}$ , and bounding box $f_{\\mathrm{bbox}}$ . Since our goal is to create a stealthy attack, meaning that our adversarial texture $T_{\\mathrm{adv}}$ should make the infrared car hide from the detector, we try to lower the object confidence $f_{\\mathrm{obj}}(I_{\\mathrm{adv}})$ as much as possible. Therefore, the detection loss is defined as:", + "bbox": [ + 496, + 113, + 890, + 247 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {d e t}} = f _ {\\text {o b j}} \\left(I _ {\\text {a d v}}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 250, + 890, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function is defined as follows:", + "bbox": [ + 517, + 271, + 828, + 285 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = L _ {\\text {d e t}} + w _ {1} \\cdot L _ {\\text {n o r m}} + w _ {2} \\cdot L _ {\\text {e d g e}} \\tag {10} \\\\ + w _ {3} \\cdot L _ {\\mathrm {c h a m f e r}} + w _ {4} \\cdot L _ {\\mathrm {L a p l a c e}}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 292, + 890, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $w_{1}, w_{2}, w_{3}$ , and $w_{4}$ are weights of different losses, which are determined empirically. We use the backpropagation algorithm according to the loss function $L$ to update the optimization variables $C^{(i)}, P^{(i)}, \\varphi^{(i)}, i = 1, 2, \\ldots, N$ . The overall pipeline is illustrated in Figure 4.", + "bbox": [ + 496, + 338, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.7. Physical Implementation Method", + "text_level": 1, + "bbox": [ + 500, + 422, + 790, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use aluminum films to make adversarial car stickers. Instead of altering the surface temperature of an object, this approach focuses on modifying the surface emissivity of the object, which is different from previous works [30-32, 35, 37]. Aluminum typically has an emissivity around 0.1, while the surface of a car, typically made of steel, has an emissivity around 0.8, resulting in different infrared characteristics. We utilize an ultra-thin (only $0.08\\mathrm{mm}$ ) aluminum film, which can be easily attached on the surface of a car like many car stickers. We only need around 13 mins to make a sticker, and the cost of a sticker is only around 0.2 USD. The implementation process of adversarial stickers is shown in Supplementary Video 1.", + "bbox": [ + 496, + 445, + 890, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 654, + 630, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 500, + 679, + 594, + 693 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We used the FLIR_ADAS_1_3 [7] infrared dataset released by FLIR company for infrared autonomous driving scenes. It contains 10,228 real infrared photos collected in streets and highways of Santa Barbara, USA. The infrared camera is FLIR Tau2. The training set contains 7160 images, and the test set contains 3068 images. We used this dataset to finetune the target detector.", + "bbox": [ + 496, + 702, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Target Detectors", + "text_level": 1, + "bbox": [ + 500, + 816, + 663, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We initially chose the classic two-stage object detector: Faster R-CNN [22], as our primary target detector. We used the pre-trained Faster RCNN model provided by the torchvision library [17] and then finetuned it on the", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24288", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1442227b6ff03203731bd9c3841d495847ffe7bd7697a4ed4ab672662f71ddb1.jpg", + "table_caption": [ + "Table 1. ASRs (%) of cars with different textures against different detectors." + ], + "table_footnote": [], + "table_body": "
Detector TextureFasterRetinaNetCascadeLibraSSDYOLOv3Deformable
Origin2.104.4918.8616.4715.2725.1512.28
Random shape18.2617.0723.9528.7445.8150.0023.65
AIP14.9715.2732.9327.5423.6538.3227.54
UAP20.0631.4438.0233.2336.8339.8224.25
Ours96.3186.8373.3579.0495.8086.5283.83
", + "bbox": [ + 151, + 114, + 818, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FLIR_ADAS_1_3 dataset. The average precision (AP) for car class of the finetuned model on the training set was 0.96, and the AP on the test set was 0.92. After attacking Faster RCNN in a white-box setting, we transferred our attack method to other unseen detectors such as YOLOv3 [21], Deformable DETR [36], etc. which were provided by mmdetection library [5] in a black-box setting.", + "bbox": [ + 75, + 262, + 468, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 378, + 261, + 392 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In our experiments, we used the attack success rate (ASR) as the evaluation metrics of the attack methods. The ASR was defined as the ratio of the number of cars which were not detected to the total number of cars. We set the confidence threshold of target detectors to 0.6 and the IOU threshold between the prediction box and ground truth to 0.5, similar to previous works [31, 32, 35, 37]. The ASR was calculated based on the average value of sample points collected from various distances, horizontal angles, and pitch angles with the sampling method described in Section 4.4.", + "bbox": [ + 75, + 401, + 468, + 565 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Attack Faster RCNN in the Digital World", + "text_level": 1, + "bbox": [ + 76, + 577, + 431, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We optimized $N = 5$ adversarial shadow patterns to simulate 5 adversarial stickers to be pasted on the car surface.", + "bbox": [ + 76, + 599, + 468, + 630 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/37025c724ba623d71180afce0a70ba3380b8932e72eb459628eeb2d6adde00e5.jpg", + "image_caption": [ + "Figure 5. Examples of detection results of different detectors for target cars with different textures. The numbers above the red bounding boxes are the object confidence scores, with a threshold of 0.6. The results of other detectors are shown in SM." + ], + "image_footnote": [], + "bbox": [ + 81, + 654, + 467, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The hyper-parameters are detailed in SM. After optimization, we obtained the adversarial shadow patterns ( $T_{\\mathrm{adv}}$ in Figure 4), and the rendered car with adversarial shadow patterns ( $I_{\\mathrm{adv}}$ in Figure 4).", + "bbox": [ + 496, + 262, + 890, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After that, we evaluated the attack effectiveness of the adversarial shadow patterns. For a fair comparison, we employed the original car pattern (without any sticker) and random shape pattern as control patterns. The figures of these patterns are shown in SM. These patterns were rendered onto the same car model, and the resulting images were input into Faster R-CNN. The results, as shown in Table 1, indicate that our adversarial shadow patterns achieved an ASR of $96.31\\%$ for Faster R-CNN in the digital world. In comparison, the ASRs for the original car pattern and random shape pattern were only $2.10\\%$ and $18.26\\%$ , respectively. This demonstrates the effectiveness of our attack method. Figure 5 shows typical examples.", + "bbox": [ + 496, + 324, + 892, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then analyze the ASR of our method at various (full-angle) viewing angles and distances. The horizontal angle azimuth ranged from 0 to 360 degrees, and we sampled it every 20 degrees. The pitch angle elev ranged from 0 to 90 degrees, and we sampled it every 6 degrees. The distance dist ranged from 1 to 8 meters, and we sampled it every 1 meter. Figure 6(b-d) show the ASRs with respect to one variable (e.g., dist) by taking the average of ASRs over all combinations of values of the other two variables (e.g., elev and azimuth). The results indicate that our approach achieves successful attacks at various (full-angle) viewing angles and various distances. In contrast, many previous works [30-32, 35] were effective only within limited viewing angles (e.g., horizontal angle from -30 to 30 degrees and pitch angle 0 degree) and shorter distances (e.g. 3 to 6 meters). Note that there is a decrease in ASR at 2 meters and 0(or 180)-degree horizontal angle. This suggests that Faster RCNN is more robust in these specific scenes, potentially due to the distribution of training images. Nevertheless, for the majority of viewing angles and distances, the ASRs of our method consistently exceeded $80\\%$ .", + "bbox": [ + 496, + 520, + 892, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 847, + 651, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the effectiveness of the 3D control points-based mesh smoothing algorithm (CMS) and a set of smoothing", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24289", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e0b6b9b57a75f5da399713849c47c7090dff7915203dc674f54c1386155618f7.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 106, + 93, + 308, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/034cea65b171e06c58fdad1c682494c2b1abbf2b3af99b7e5127deb39f2751b7.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 316, + 88, + 509, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27d747eb3ac065d6feac71802a53ac319dd055ca87aca7361be6e14d0811dec5.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 524, + 88, + 681, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/10be2295814f8d363a7a4f4afde244cba95b09d002ef6ee0b292caf60724f35b.jpg", + "image_caption": [ + "(d)", + "Figure 6. Full-angle ASRs at different (a) parameters including (b) distances, (c) pitch angles, and (d) horizontal angles. See text for details." + ], + "image_footnote": [], + "bbox": [ + 699, + 88, + 859, + 209 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "losses (SMLS), we performed ablation experiments. We conducted a subjective evaluation on the smoothness score of the 3D adversarial mesh and 2D adversarial pattern and we also evaluated the physical implementation time of 2D adversarial patterns under different settings. The experimental settings and results are detailed in SM. The results indicate that both CMS and SMLS improved the smoothness of adversarial meshes and patterns, and their combination was better. Besides, these methods effectively reduced the physical implementation time of adversarial patterns.", + "bbox": [ + 75, + 290, + 472, + 443 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Exploring the Interpretability of the Attack", + "text_level": 1, + "bbox": [ + 76, + 450, + 447, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To gain deeper insights into our attack methods, we utilized the GradCAM [23] technique to analyze the changes in network attention maps before and after the attack. See SM for more details.", + "bbox": [ + 75, + 474, + 470, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.7. Comparison with 2D Optimization Methods", + "text_level": 1, + "bbox": [ + 76, + 544, + 450, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We extended the previous 2D infrared model car attack methods [31, 32] to our 3D car model. We generated adversarial car textures on our car model based on their papers and codes, which are shown in SM. Following the settings in Section 4.4, we evaluated the attack performance of the different methods. The statistics of ASRs are presented in Table 1, with typical examples shown in Figure 5.", + "bbox": [ + 75, + 568, + 468, + 675 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9b36a7883b49c5e57f4a3517f69963159d73b0272a326d2ac54943c43edd73fa.jpg", + "image_caption": [ + "(a)", + "Figure 7. Infrared attack effect on model cars. (a) Visible light view of model cars. (b) Infrared view of model cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers." + ], + "image_footnote": [], + "bbox": [ + 78, + 696, + 264, + 833 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b5458f470d8c2c89a18811bc996c4baadcdaf1099ad0cc8bba224071f23fd9b0.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 266, + 696, + 468, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results indicated that the ASR of our method $(96.31\\%)$ outperformed the ASRs of two alternative methods $(14.97\\%$ and $20.06\\%)$ for Faster RCNN in the digital world. The reasons may be as follows. The two 2D optimization methods based on boundary optimization [31] or points clustering [32] are subject to various constraints. These constraints are used to ensure that, for example, the boundary curves do not have overlaps [31], and the adversarial patterns do not split into multiple pieces [32]. With more constraints, the feasible solution space becomes smaller. However, our 3D mesh shadow approach does not have such constraints, and we can explore a larger solution space, leading to better results.", + "bbox": [ + 496, + 290, + 893, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.8. Attack Transferability", + "text_level": 1, + "bbox": [ + 500, + 496, + 707, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We tested the effectiveness of our adversarial car texture $(T_{\\mathrm{adv}}$ in Figure 4) optimized for Faster RCNN against other unseen detectors, including RetinaNet [14], Cascade RCNN [3], Libra RCNN [19], SSD [15], YOLOv3 [21] and Deformable DETR [36]. It is worth noting that these experiments were performed in a black-box setting, which is a more challenging but practically significant scene for real-world applications. The results are shown in Table 1. The ASRs of our method against unseen models reached $73.35\\% - 95.80\\%$ . It indicates that our method performed well in a black-box setting and had good attack transferability to unseen models including not only CNN-based models but also transformer-based models. Besides, the transferability of our method is stronger than not only two simple baselines but also two infrared attack methods [31, 32].", + "bbox": [ + 496, + 518, + 890, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.9. Physical Attacks on Model Cars", + "text_level": 1, + "bbox": [ + 498, + 756, + 782, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We initially conducted physical experiments on three same 1:24 scale Mercedes-Benz model cars (Figure 7(a)). We crafted the adversarial aluminum stickers according to the optimized patterns, scaled to match the size of the model car, and applied them to the model car. In addition, we created randomly cut-shaped stickers as a control. We heated the model cars with hot water to simulate the real car with engine running. We used a rotating turntable to conve", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24290", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/667023f967c1f65b7b5ff5de6d4d020dea067f35f785269cb965b62c78af2156.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 107, + 88, + 295, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1995226415bce4756f76de724cca6189d4d18314060000ec9d137c56780de227.jpg", + "image_caption": [ + "Figure 8. Examples of infrared real car attacks. C: clean car. R: car with random shape stickers. A: car with adversarial stickers." + ], + "image_footnote": [], + "bbox": [ + 107, + 199, + 294, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22a663343b352eef6f33bb50c456bc7b16f2c32391a90bd62c88960347ea571b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 88, + 482, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8197d6903789d7ae4b97dc2b24ef0a563adebd1d444f5c1143ebd5e8fc0b9455.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 199, + 480, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3c0aadfb3ba751be96db1bc78ff03c66dbb42f5ef81b6ee39b74f99e4e214e8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 671, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/389a0362e661fdb7d641cbb91050df4a052513707401863ca3ac4d49990d5743.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 199, + 671, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/34c59ff63e1aedc20f9066320f8dc0984e6b8b031b730c9d7578712612d0ba49.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 674, + 88, + 859, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbd9118d9b1999cdf3e741572256a42a55dcf64c0827200b4fa309b5d9ac0c71.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 674, + 199, + 861, + 305 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "niently assess the attack effectiveness over the entire 0-360 horizontal degree and 0-90 pitch angle range. The infrared camera was FLIR T560. We utilized the same Faster RCNN detector as in Section 4.4. The detection results indicated that our adversarial stickers achieved an ASR of $84.86\\%$ on the 1:24 scale car model in the physical world. In comparison, the clean car and the car with random patterns had ASRs of only $19.08\\%$ and $35.37\\%$ , respectively. Figure 7 provides specific examples from the physical world experiments. A demo video for physical model car attacks is shown in Supplementary Video 2.", + "bbox": [ + 75, + 358, + 472, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.10. Physical Attacks on Real Cars", + "text_level": 1, + "bbox": [ + 76, + 540, + 354, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conducted physical experiments on two real Mercedes-Benz A200L cars (one black one white). It was a sunny day with a temperature of about $25^{\\circ}\\mathrm{C}$ . For a fair comparison, we pasted the adversarial stickers, randomly cut-shaped stickers or nothing on the same car successively. We recorded 30 videos (each video is around 2 minutes) and sampled 3688 infrared images of these cars from various angles and distances in both ground and underground parking lots using a FLIR T560 camera. The height of the camera tripod can be adjusted from $1\\mathrm{m}$ to $2\\mathrm{m}$ . We sent these images to Faster RCNN.", + "bbox": [ + 75, + 566, + 468, + 732 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results indicated that our adversarial stickers achieved an ASR of $91.49\\%$ on the real cars with the engines running, while the random shape stickers and no sticker had ASRs of only $6.21\\%$ and $0.66\\%$ , respectively. When the engines were off for one hour, the ASR of adversarial stickers dropped a little to $88.42\\%$ . The reason might be that the infrared patterns of adversarial stickers with engines off were not as clear as the patterns with engines running. However, the ASR of adversarial stickers were still better than ASR of random shape stickers $(5.72\\%)$ and no sticker $(1.86\\%)$ when the engines were off. Figure 1", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and Figure 8 show some examples. There were a few other cars that passed by or were parked when we were recording videos and therefore appeared in our photos, which were also detected. See Supplementary Video 3 for the demo video.", + "bbox": [ + 496, + 358, + 890, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.11. Adversarial Defense", + "text_level": 1, + "bbox": [ + 498, + 441, + 700, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We tested five adversarial defense methods to defend our attack methods in the digital world, including adversarial training [8], PixelMask [1], Bit squeezing [33], JPEG compression [10] and Total variation minimization [10]. Experiment details for these methods are in SM. The results show that although these methods had a certain defense effect, the ASR of our method still reached $88.83\\% - 94.81\\%$ after adding defense, which shows that our method is a powerful attack method.", + "bbox": [ + 496, + 464, + 892, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 611, + 619, + 627 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose infrared adversarial stickers to hide a real car from infrared detectors at various viewing angles, distances, and scenes in the physical world. We build a 3D infrared car model with real infrared characteristics and propose a 3D mesh shadow method for the generation of infrared adversarial pattern. To make the 3D adversarial mesh smoother, we propose a 3D control points-based smoothing algorithm and use a set of smoothness loss functions. Our adversarial stickers enabled two real cars to evade Faster RCNN at various viewing angles, distances and scenes. Besides, our method has strong attack transferability against multiple unseen detectors in a black-box setting.", + "bbox": [ + 496, + 637, + 893, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 498, + 830, + 687, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China (Nos. 61734004, U2341228, U19B2034).", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24291", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Akshay Agarwal, Mayank Vatsa, Richa Singh, and Nalini Ratha. Cognitive data augmentation for adversarial defense via pixel masking. Pattern Recognition Letters, 146:244-251, 2021. 8", + "[2] Anish Athalye, Logan Engstrom, Andrew Ilyas, and Kevin Kwok. Synthesizing robust adversarial examples. 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Pattern Recog., 2022. 2, 5, 6" + ], + "bbox": [ + 78, + 90, + 468, + 753 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24293", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Infrared Adversarial Car Stickers/1b21f991-5369-4064-a439-e126cdaa2289_model.json b/2024/Infrared Adversarial Car Stickers/1b21f991-5369-4064-a439-e126cdaa2289_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ed143076fca8bb4f679b16382755edc42b66ff28 --- /dev/null +++ b/2024/Infrared Adversarial Car Stickers/1b21f991-5369-4064-a439-e126cdaa2289_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.312, + 0.131, + 0.658, + 0.151 + ], + "angle": 0, + "content": "Infrared Adversarial Car Stickers" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.179, + 0.856, + 0.375 + ], + "angle": 0, + "content": "Xiaopei Zhu\\(^{1}\\) Yuqiu Liu\\(^{2}\\) Zhanhao Hu\\(^{3}\\) Jianmin Li\\(^{4}\\) Xiaolin Hu\\(^{4,5,6*}\\) \n\\(^{1}\\)School of Integrated Circuits, Tsinghua University, Beijing, China \n\\(^{2}\\)Department of Technology, Beijing Forestry University, Beijing, China \n\\(^{3}\\)Department of Electrical Engineering and Computer Sciences, UC Berkeley, California, USA \n\\(^{4}\\)Department of Computer Science and Technology, Institute for Artificial Intelligence, BNRist, Tsinghua University, Beijing, China \n\\(^{5}\\)THBI, IDG/McGovern Institute for Brain Research, Tsinghua University, Beijing, China \n\\(^{6}\\)Chinese Institute for Brain Research (CIBR), Beijing, China \n{zxp18}@mail.tsinghua.edu.cn \n{liuyuqiu99, zhanhaohu.cs}@gmail.com \n{lijianmin, xlhu}@mail.tsinghua.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.41, + 0.313, + 0.426 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.473, + 0.865 + ], + "angle": 0, + "content": "Infrared physical adversarial examples are of great significance for studying the security of infrared AI systems that are widely used in our lives such as autonomous driving. Previous infrared physical attacks mainly focused on 2D infrared pedestrian detection which may not fully manifest its destructiveness to AI systems. In this work, we propose a physical attack method against infrared detectors based on 3D modeling, which is applied to a real car. The goal is to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles, distances, and scenes. We build a 3D infrared car model with real infrared characteristics and propose an infrared adversarial pattern generation method based on 3D mesh shadow. We propose a 3D control points-based mesh smoothing algorithm and use a set of smoothness loss functions to enhance the smoothness of adversarial meshes and facilitate the sticker implementation. Besides, We designed the aluminum stickers and conducted physical experiments on two real Mercedes-Benz A200L cars. Our adversarial stickers hid the cars from Faster RCNN, an object detector, at various viewing angles, distances, and scenes. The attack success rate (ASR) was \\(91.49\\%\\) for real cars. In comparison, the ASRs of random stickers and no sticker were only \\(6.21\\%\\) and \\(0.66\\%\\), respectively. In addition, the ASRs of the designed stickers against six unseen object detectors such as YOLOv3 and Deformable DETR were between \\(73.35\\% - 95.80\\%\\), showing good transferability of the attack performance across detectors." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.41, + 0.695, + 0.665 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.41, + 0.89, + 0.665 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.785 + ], + "angle": 0, + "content": "Figure 1. Infrared attack effect on real cars. (a) Visible light view of real cars. (b) Infrared view of real cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers. The numbers above the bounding boxes are object confidence scores (\\%) with 0.6 threshold. Our adversarial stickers hid the car from Faster RCNN at various viewing angles, distances and scenes. In comparison, the clean car and the car with random shape stickers were detected at the same situation." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.814, + 0.631, + 0.83 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "It is well known that deep learning models can be misled by carefully designed perturbations to the input which is called adversarial example, and the perturbation process is called adversarial attack. Adversarial attacks can be di" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24284" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "vided into two categories, digital attacks [4, 8, 9, 16, 24, 26] which assume that the attackers can directly modify the model input in the digital world, and physical attacks [11, 12, 27, 28, 35, 37] which assume that the attackers can only modify the object or scene in the physical world. Physical attacks have attracted much attention because of their importance of assessing the security of real-world AI systems." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.304 + ], + "angle": 0, + "content": "One type of physical attack is called infrared physical attack [30-32, 35, 37]. Infrared imaging is widely used in our daily lives, such as body temperature monitoring and autonomous driving. Since infrared cameras can function normally at night, they are becoming more and more important in autonomous driving systems; so is their safety." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Previous infrared physical attacks [30-32, 35, 37] mainly focused on infrared pedestrians, and only two works [31, 32] conducted experiments on model cars. There is currently a lack of infrared attack research on real cars. The reasons might be as follows. Compared with pedestrians with constant body temperature, the temperature distributions of real cars are more uneven (e.g., the temperature of the engine is much higher than that of other places), so their infrared characteristics are more complex than pedestrians. Compared with model cars without engines, real cars' structures and materials are very different from those of model cars, so their infrared characteristics are also quite different. Besides, real car attacks require designing and manufacturing adversarial patterns on the entire 3D car surface, which poses a great challenge to physical experiments. But we believe that for the safety of autonomous driving cars, physical real car attack is worth in-depth investigation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.473, + 0.741 + ], + "angle": 0, + "content": "The aforementioned two infrared model car attacks [31, 32] are only effective within limited viewing angles (e.g., horizontal angles \\(-30^{\\circ} - 30^{\\circ}\\) and pitch angle \\(0^{\\circ}\\)). But we want to implement a full-angle attack (the horizontal angles \\(0^{\\circ} - 360^{\\circ}\\), and pitch angle \\(0^{\\circ} - 90^{\\circ}\\)), so the attack angles cover an entire hemisphere surface, which is a challenging task. We also notice that these methods [31, 32] are both case-by-case attacks, which needs to optimize an adversarial pattern for each image1, while our goal is to achieve a universal attack which uses the same adversarial pattern to attack detectors at various viewing angles, distances and scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.473, + 0.879 + ], + "angle": 0, + "content": "Towards this goal, we propose an infrared physical attack method applied to a real car based on 3D modeling. We aim to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles (full-angle), distances and scenes. Since most current 3D car models are visible-light models, and there is a lack of 3D infrared car models, we build a 3D infrared car model with real infrared characteristics at various viewing angles. For the generation of infrared adversarial pattern for stick-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.257 + ], + "angle": 0, + "content": "ers, we propose to optimize a 3D adversarial mesh at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern, and finally attach the 2D adversarial pattern to the car surface. The motivation of this mesh shadow attack (MSA) method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. To improve the smoothness of adversarial patterns and facilitate sticker implementation, we propose a 3D control points-based mesh smoothing algorithm and use a set of smoothing loss functions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.895, + 0.365 + ], + "angle": 0, + "content": "For the physical implementation of infrared adversarial patterns, we use an aluminum film which modifies the surface emissivity of the object instead of altering the surface temperature used by previous works [30-32, 35, 37]. Like many car stickers, the adversarial car stickers can be easily attached on the car surface. The stickers are only \\(0.08\\mathrm{mm}\\) thick and take up almost no space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.895, + 0.502 + ], + "angle": 0, + "content": "To assess the safety of infrared detection in real autonomous driving scenes, we used two real Mercedes-Benz A200L cars. Physical experiments show that our infrared adversarial stickers made the real cars hide from the infrared detector Faster RCNN at various viewing angles, various distances, and multiple scenes, with an attack success rate (ASR) of \\(91.49\\%\\). To the best our knowledge, this is the first 3D multi-view physical infrared vehicle attack, and also the first infrared attack conducted on real cars." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.515, + 0.642, + 0.531 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.541, + 0.862, + 0.557 + ], + "angle": 0, + "content": "2.1. Visible Light Physical Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.746 + ], + "angle": 0, + "content": "Huang et al. [13] proposed a universal physical camouflage (UPC) attack for object detectors. Zhang et al. [34] proposed a vehicle camouflage for physical adversarial attack on object detectors in the wild. Wang et al. [29] proposed the Dual attention suppression (DAS) attack to generate adversarial vehicle camouflage in the physical world. Suryanto et al. [25] generated the physical adversarial camouflage by using a differentiable transformation network. Wang et al. [28] proposed a 3D full-coverage vehicle camouflage for physical adversarial attack (FCA). It is worth noting that all above works are proposed for visible light images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.83, + 0.773 + ], + "angle": 0, + "content": "2.2. Infrared Physical Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Zhu et al. [35] proposed a bulb-based board to fool infrared pedestrian detectors in the physical world. Zhu et al. [37] proposed an infrared invisible clothing to hide from infrared pedestrian detectors in the physical world. Wei et al. [30] proposed the HotCold blocks to attack the infrared pedestrian detectors. Wei et al. [32] proposed a physical adversarial infrared patch (AIP) based on a points-clustering algorithm. Wei et al. [31] proposed a unified adversar" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.416, + 0.902 + ], + "angle": 0, + "content": "1We found this by checking and running their official codes." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24285" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.088, + 0.329, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.199, + 0.244, + 0.212 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.088, + 0.47, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.399, + 0.198, + 0.42, + 0.212 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.089, + 0.611, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.198, + 0.555, + 0.212 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.089, + 0.848, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.722, + 0.199, + 0.743, + 0.213 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.229, + 0.894, + 0.258 + ], + "angle": 0, + "content": "Figure 2. Construction and optimization of real infrared car texture mapping. (a) Car mesh model. (b) Reorganized faces map. (c) Infrared car texture map collected from real world. (d) Rendered infrared car model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.471, + 0.359 + ], + "angle": 0, + "content": "ial patch (UAP) for physical attacks based on a boundary-limited shape optimization algorithm. It is worth noting that all above methods are proposed for infrared pedestrian or model car attacks. There is currently a lack of research on infrared real vehicle attacks in the physical world." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.375, + 0.331, + 0.39 + ], + "angle": 0, + "content": "3. Car Sticker Attack Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.471, + 0.551 + ], + "angle": 0, + "content": "Our method consists of several steps. First, we build a 3D infrared car model based on real infrared characteristics. Next, we use the infrared adversarial pattern generation method based on 3D mesh shadow. To make the 3D adversarial mesh smoother, we use a 3D control points-based mesh smoothing algorithm and use a set of smoothness losses. Then we apply adversarial patterns to 3D infrared car model and optimize the adversarial patterns. Finally, we introduce the physical implementation method of infrared adversarial car stickers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.563, + 0.379, + 0.579 + ], + "angle": 0, + "content": "3.1. Building a 3D Infrared Car Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.678 + ], + "angle": 0, + "content": "To simulate the infrared car attack realistically, we build a 3D model based on the infrared characteristics of a real car. It is worth noting that our method can be applied to any target car, and we chose Mercedes-Benz A200L in our experiments, simply because one of the authors have this car. Figure 2(a) shows the car mesh model \\( M_{\\mathrm{car}} \\). Next, we need" + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.701, + 0.411, + 0.873 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.883, + 0.436, + 0.897 + ], + "angle": 0, + "content": "Figure 3. Schematic diagram of mesh shadow method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.435 + ], + "angle": 0, + "content": "to create a \"skin\" for the car model based on infrared photos taken by an infrared camera FLIR T560. However, the infrared photos captured by the camera are all 2D images, and the challenge is how to \"paste\" these 2D infrared images onto the 3D car mesh model. First, we flatten all the faces of 3D car mesh onto a 2D plane called faces map. After that, we use MAYA software to rearrange these faces to divide different areas, such as roof, doors, etc., as shown in Figure 2(b). This process facilitates the alignment of real infrared car images with the 3D car mesh." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.893, + 0.588 + ], + "angle": 0, + "content": "Subsequently, we crop the infrared images into different parts based on the faces map (Figure 2(b)) and paste the cropped images onto the 2D faces map, and then we get the infrared texture map of the car, as shown in Figure 2(c). See Supplementary Material (SM) for how these infrared photos are taken, cropped and pasted. This process establishes a correspondence between the real infrared car images and the 3D car mesh. The rendered infrared car model is shown in Figure 2(d), which is built for a real car with engine running." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.603, + 0.88, + 0.618 + ], + "angle": 0, + "content": "3.2. Generation of 2D Shadow Based on 3D Mesh" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.884 + ], + "angle": 0, + "content": "We aim to design infrared stickers with adversarial patterns to hide the cars from infrared detectors at various viewing angles (full-angle), distances, and scenes. We propose a 3D adversarial mesh shadow attack (MSA) method to generate the 2D infrared adversarial patterns for stickers. The motivation of MSA method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. The core of MSA method is to optimize a 3D adversarial mesh \\(M_{\\mathrm{adv}}\\) at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern \\(S_{\\mathrm{adv}}\\), and finally attach the 2D adversarial pattern \\(S_{\\mathrm{adv}}\\) to the car surface. Note that the 3D adversarial mesh \\(M_{\\mathrm{adv}}\\) is different from the 3D car mesh \\(M_{\\mathrm{car}}\\) in Section 3.1. The optimization variables include the 3D mesh vertices coordinates \\(V\\), the mesh shadowing angle \\(\\varphi\\), and the center point position \\(P\\) when pasting the 2D pattern onto the car's texture map \\(T_{\\mathrm{origin}}\\) (Figure 3)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The shadowing operation refers to rendering the mesh" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24286" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.905, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.367, + 0.647, + 0.382 + ], + "angle": 0, + "content": "Figure 4. The overall pipeline of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.471, + 0.528 + ], + "angle": 0, + "content": "\\(M_{\\mathrm{adv}}\\) to a dark area while retaining the mesh contour (Figure 3), and the dark area has a uniform grayscale value within the contour. The grayscale value is consistent with the infrared characteristics of the sticker we use. Let \\(\\Omega\\) denote this operation. If we want the car to have adversarial effect at various viewing angles, we need to optimize \\(N\\) adversarial meshes to generate \\(N\\) adversarial shadows on different places of the car (Figure 4):" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.543, + 0.47, + 0.565 + ], + "angle": 0, + "content": "\\[\nS _ {\\mathrm {a d v}} ^ {(i)} = \\Omega \\left(M _ {\\mathrm {a d v}} ^ {(i)}, \\varphi^ {(i)}\\right), i = 1, 2, \\dots N. \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.439, + 0.598 + ], + "angle": 0, + "content": "3.3. 3D Control Points-Based Mesh Smoothing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.47, + 0.771 + ], + "angle": 0, + "content": "If we directly optimize the vertices coordinates \\(V\\) of the mesh \\(M_{\\mathrm{adv}}\\), many \"peaks\" will appear on the mesh surface, which will make the shadow shape very complex and will be difficult for the physical implementation of the adversarial shadow \\(S_{\\mathrm{adv}}\\). Inspired by the Gaussian smoothing kernel and spline interpolation method, we propose a smoothing control algorithm for 3D mesh vertices. Its core idea is to use some 3D control points \\(C\\) as anchor points, and the coordinate offsets of mesh vertices \\(V\\) are expressed as the weighted average of the coordinate offsets of \\(C\\). The calculation details are described in SM." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.774, + 0.469, + 0.807 + ], + "angle": 0, + "content": "We use \\(\\Theta\\) to denote the above transformation, and \\(C^{(i)}\\) to denote the control points set of \\(M_{\\mathrm{adv}}^{(i)}\\), then" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.821, + 0.469, + 0.839 + ], + "angle": 0, + "content": "\\[\nV ^ {(i)} = \\Theta (C ^ {(i)}), i = 1, 2, \\dots N. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Since the control points \\(C^{(i)}\\) determine the vertices coordinates \\(V^{(i)}\\), the optimization variables changes from \\(\\left(V^{(i)}, P^{(i)}, \\varphi^{(i)}\\right)\\) to \\(\\left(C^{(i)}, P^{(i)}, \\varphi^{(i)}\\right)\\), \\(i = 1, 2, \\ldots N\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.408, + 0.794, + 0.421 + ], + "angle": 0, + "content": "3.4. Mesh Smoothness Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.892, + 0.566 + ], + "angle": 0, + "content": "To further enhance the smoothness of 3D adversarial mesh \\( M_{\\mathrm{adv}} \\) and 2D adversarial pattern \\( S_{\\mathrm{adv}} \\), we use a set of loss functions including: mesh normal consistency loss, mesh edge loss, chamfer distance loss, and Laplacian smoothing loss. During the optimization process of 3D mesh \\( M_{\\mathrm{adv}} \\), these functions guide the generation of a smoother adversarial mesh. A smoother 3D mesh \\( M_{\\mathrm{adv}} \\) results in a smoother 2D shadow pattern \\( S_{\\mathrm{adv}} \\), which is beneficial for manufacturing physical stickers based on the 2D shadow pattern." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.567, + 0.892, + 0.656 + ], + "angle": 0, + "content": "The mesh normal consistency loss computes the normal consistency for each pair of neighboring faces, and minimizing it encourages the mesh surface to be smoother. We suppose that mesh \\( M_{\\mathrm{adv}} \\) has a total of \\( F \\) faces. Let \\( n_i, n_j \\) (\\( 1 \\leq i, j \\leq F \\)) represent the normal vector of any two adjacent faces, then this loss function is described as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.667, + 0.891, + 0.684 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {n o r m}} = \\text {A v e r a g e} (1 - \\cos \\left(n _ {i}, n _ {j}\\right)). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.692, + 0.88, + 0.707 + ], + "angle": 0, + "content": "Average is calculated between any pair of adjacent faces." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.708, + 0.892, + 0.782 + ], + "angle": 0, + "content": "The mesh edge loss computes mesh edge length regularization loss, and minimizing it encourages a reduction in the average edge length of the adversarial mesh. Suppose \\( M_{\\mathrm{adv}} \\) has a total of \\( M \\) edges, \\( l_{k} \\) (\\( k = 1,2,\\dots,M \\)) represents the length of each edge, and this loss function is described as" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.791, + 0.892, + 0.833 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {e d g e}} = \\left(\\sum_ {k = 1} ^ {M} l _ {k}\\right) / M. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The chamfer distance loss computes chamfer distance [6] between the sampling points of adversarial mesh and a standard sphere. Reducing chamfer distance loss encourages the adversarial mesh \\( M_{\\mathrm{adv}} \\) to approximate a sphere." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24287" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "We denote the point clouds sampled by adversarial mesh \\( M_{\\mathrm{adv}} \\) and the standard spherical mesh \\( M_{\\mathrm{sphere}} \\) by \\( S_{1} \\) and \\( S_{2} \\), respectively. The chamfer distance loss is described as" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.15, + 0.468, + 0.197 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {c h a m f e r}} = \\sum_ {p \\in S _ {1}} \\min _ {q \\in S _ {2}} \\| p - q \\| _ {2} ^ {2} + \\sum_ {q \\in S _ {2}} \\min _ {p \\in S _ {1}} \\| q - p \\| _ {2} ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.199, + 0.469, + 0.259 + ], + "angle": 0, + "content": "The Laplacian smoothing loss \\( L_{\\mathrm{Laplace}} \\) computes the Laplacian smoothing objective for the adversarial mesh. We define this function as Laplace, and its calculation details are introduced in [18], so" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.274, + 0.469, + 0.291 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {L a p l a c e}} = \\text {L a p l a c e} \\left(M _ {\\text {a d v}}\\right). \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.306, + 0.438, + 0.322 + ], + "angle": 0, + "content": "3.5. Applying the 2D Shadow to 3D Car Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.602 + ], + "angle": 0, + "content": "We apply the adversarial shadow \\( S_{\\mathrm{adv}} \\) to 3D infrared car model by changing its texture map \\( T_{\\mathrm{origin}} \\). This simulates the process we paste the adversarial stickers to the car surface in the physical world. To facilitate physical implementation, we simulate to paste the stickers onto the door, roof, front hood and rear of the car, which have wide ranges of flat area and are easy to paste. In each area, we paste one or two adversarial shadow patterns (Figure 4). To simulate real-world perturbations, such as errors in cutting the adversarial stickers, variations in surface temperature on the adversarial stickers, and errors in the pasting positions, we introduce random perturbations to the vertex coordinates \\( V \\) of the adversarial mesh \\( M_{\\mathrm{adv}} \\), random noise to the pattern \\( S_{\\mathrm{adv}} \\), random changes in grayscale values of \\( S_{\\mathrm{adv}} \\), and random perturbations in the position \\( P \\) during the pasting of \\( S_{\\mathrm{adv}} \\). This approach, known as the Expectation Over Transformation (EOT) algorithm [2], enhances the robustness of our algorithm in real-world scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.469, + 0.711 + ], + "angle": 0, + "content": "Next, we need to paste the adversarial patterns \\( S_{\\mathrm{adv}} \\) onto the original car texture map \\( T_{\\mathrm{origin}} \\). Let \\( \\Gamma \\) denote the pasting operation. We establish a Cartesian coordinate system with the center point of \\( T_{\\mathrm{origin}} \\) as the origin. We use \\( P^{(i)} \\) to represent the coordinates of the pasting positions for \\( N \\) adversarial shadows \\( S_{\\mathrm{adv}}^{(i)}, i = 1,2,\\dots N \\). The texture map after pasting the adversarial shadows is" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.725, + 0.469, + 0.751 + ], + "angle": 0, + "content": "\\[\nT _ {\\mathrm {a d v}} = \\Gamma \\left(S _ {\\mathrm {a d v}} ^ {(i)}, P ^ {(i)}, T _ {\\text {o r i g i n}}\\right), i = 1, 2, \\dots N. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.87 + ], + "angle": 0, + "content": "We use the differentiable renderer Pytorch3D [20] to render the adversarial texture map \\( T_{\\mathrm{adv}} \\) onto the surface of the car mesh \\( M_{\\mathrm{car}} \\), resulting in the rendered infrared car images with adversarial patterns, denoted as \\( I_{\\mathrm{adv}} \\). Let \\( \\Psi \\) denote the rendering operation with parameters \\( \\theta \\) which include the rendering distances and angles. Mathematically, this process can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\nI _ {\\mathrm {a d v}} = \\Psi \\left(M _ {\\mathrm {c a r}}, T _ {\\mathrm {a d v}}, \\theta\\right). \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.852, + 0.107 + ], + "angle": 0, + "content": "3.6. Optimization of 3D Mesh Shadow Attack" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.248 + ], + "angle": 0, + "content": "After we get the rendered infrared adversarial images \\( I_{\\mathrm{adv}} \\), we input them into the target detector \\( f \\). The output of the target detector typically includes object confidence \\( f_{\\mathrm{obj}} \\), class confidence \\( f_{\\mathrm{cls}} \\), and bounding box \\( f_{\\mathrm{bbox}} \\). Since our goal is to create a stealthy attack, meaning that our adversarial texture \\( T_{\\mathrm{adv}} \\) should make the infrared car hide from the detector, we try to lower the object confidence \\( f_{\\mathrm{obj}}(I_{\\mathrm{adv}}) \\) as much as possible. Therefore, the detection loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.25, + 0.892, + 0.267 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {d e t}} = f _ {\\text {o b j}} \\left(I _ {\\text {a d v}}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.272, + 0.829, + 0.286 + ], + "angle": 0, + "content": "The overall loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.294, + 0.892, + 0.33 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = L _ {\\text {d e t}} + w _ {1} \\cdot L _ {\\text {n o r m}} + w _ {2} \\cdot L _ {\\text {e d g e}} \\tag {10} \\\\ + w _ {3} \\cdot L _ {\\mathrm {c h a m f e r}} + w _ {4} \\cdot L _ {\\mathrm {L a p l a c e}}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Here, \\(w_{1}, w_{2}, w_{3}\\), and \\(w_{4}\\) are weights of different losses, which are determined empirically. We use the backpropagation algorithm according to the loss function \\(L\\) to update the optimization variables \\(C^{(i)}, P^{(i)}, \\varphi^{(i)}, i = 1, 2, \\ldots, N\\). The overall pipeline is illustrated in Figure 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.423, + 0.792, + 0.438 + ], + "angle": 0, + "content": "3.7. Physical Implementation Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.642 + ], + "angle": 0, + "content": "We use aluminum films to make adversarial car stickers. Instead of altering the surface temperature of an object, this approach focuses on modifying the surface emissivity of the object, which is different from previous works [30-32, 35, 37]. Aluminum typically has an emissivity around 0.1, while the surface of a car, typically made of steel, has an emissivity around 0.8, resulting in different infrared characteristics. We utilize an ultra-thin (only \\(0.08\\mathrm{mm}\\)) aluminum film, which can be easily attached on the surface of a car like many car stickers. We only need around 13 mins to make a sticker, and the cost of a sticker is only around 0.2 USD. The implementation process of adversarial stickers is shown in Supplementary Video 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.632, + 0.672 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.596, + 0.694 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.809 + ], + "angle": 0, + "content": "We used the FLIR_ADAS_1_3 [7] infrared dataset released by FLIR company for infrared autonomous driving scenes. It contains 10,228 real infrared photos collected in streets and highways of Santa Barbara, USA. The infrared camera is FLIR Tau2. The training set contains 7160 images, and the test set contains 3068 images. We used this dataset to finetune the target detector." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.665, + 0.833 + ], + "angle": 0, + "content": "4.2. Target Detectors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We initially chose the classic two-stage object detector: Faster R-CNN [22], as our primary target detector. We used the pre-trained Faster RCNN model provided by the torchvision library [17] and then finetuned it on the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24288" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.259, + 0.089, + 0.711, + 0.104 + ], + "angle": 0, + "content": "Table 1. ASRs (%) of cars with different textures against different detectors." + }, + { + "type": "table", + "bbox": [ + 0.153, + 0.115, + 0.82, + 0.24 + ], + "angle": 0, + "content": "
Detector TextureFasterRetinaNetCascadeLibraSSDYOLOv3Deformable
Origin2.104.4918.8616.4715.2725.1512.28
Random shape18.2617.0723.9528.7445.8150.0023.65
AIP14.9715.2732.9327.5423.6538.3227.54
UAP20.0631.4438.0233.2336.8339.8224.25
Ours96.3186.8373.3579.0495.8086.5283.83
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.263, + 0.47, + 0.369 + ], + "angle": 0, + "content": "FLIR_ADAS_1_3 dataset. The average precision (AP) for car class of the finetuned model on the training set was 0.96, and the AP on the test set was 0.92. After attacking Faster RCNN in a white-box setting, we transferred our attack method to other unseen detectors such as YOLOv3 [21], Deformable DETR [36], etc. which were provided by mmdetection library [5] in a black-box setting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.379, + 0.262, + 0.393 + ], + "angle": 0, + "content": "4.3. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.47, + 0.566 + ], + "angle": 0, + "content": "In our experiments, we used the attack success rate (ASR) as the evaluation metrics of the attack methods. The ASR was defined as the ratio of the number of cars which were not detected to the total number of cars. We set the confidence threshold of target detectors to 0.6 and the IOU threshold between the prediction box and ground truth to 0.5, similar to previous works [31, 32, 35, 37]. The ASR was calculated based on the average value of sample points collected from various distances, horizontal angles, and pitch angles with the sampling method described in Section 4.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.578, + 0.433, + 0.594 + ], + "angle": 0, + "content": "4.4. Attack Faster RCNN in the Digital World" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.601, + 0.469, + 0.631 + ], + "angle": 0, + "content": "We optimized \\(N = 5\\) adversarial shadow patterns to simulate 5 adversarial stickers to be pasted on the car surface." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.655, + 0.468, + 0.827 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.842, + 0.47, + 0.896 + ], + "angle": 0, + "content": "Figure 5. Examples of detection results of different detectors for target cars with different textures. The numbers above the red bounding boxes are the object confidence scores, with a threshold of 0.6. The results of other detectors are shown in SM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.263, + 0.892, + 0.324 + ], + "angle": 0, + "content": "The hyper-parameters are detailed in SM. After optimization, we obtained the adversarial shadow patterns (\\(T_{\\mathrm{adv}}\\) in Figure 4), and the rendered car with adversarial shadow patterns (\\(I_{\\mathrm{adv}}\\) in Figure 4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.893, + 0.52 + ], + "angle": 0, + "content": "After that, we evaluated the attack effectiveness of the adversarial shadow patterns. For a fair comparison, we employed the original car pattern (without any sticker) and random shape pattern as control patterns. The figures of these patterns are shown in SM. These patterns were rendered onto the same car model, and the resulting images were input into Faster R-CNN. The results, as shown in Table 1, indicate that our adversarial shadow patterns achieved an ASR of \\(96.31\\%\\) for Faster R-CNN in the digital world. In comparison, the ASRs for the original car pattern and random shape pattern were only \\(2.10\\%\\) and \\(18.26\\%\\), respectively. This demonstrates the effectiveness of our attack method. Figure 5 shows typical examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.893, + 0.837 + ], + "angle": 0, + "content": "We then analyze the ASR of our method at various (full-angle) viewing angles and distances. The horizontal angle azimuth ranged from 0 to 360 degrees, and we sampled it every 20 degrees. The pitch angle elev ranged from 0 to 90 degrees, and we sampled it every 6 degrees. The distance dist ranged from 1 to 8 meters, and we sampled it every 1 meter. Figure 6(b-d) show the ASRs with respect to one variable (e.g., dist) by taking the average of ASRs over all combinations of values of the other two variables (e.g., elev and azimuth). The results indicate that our approach achieves successful attacks at various (full-angle) viewing angles and various distances. In contrast, many previous works [30-32, 35] were effective only within limited viewing angles (e.g., horizontal angle from -30 to 30 degrees and pitch angle 0 degree) and shorter distances (e.g. 3 to 6 meters). Note that there is a decrease in ASR at 2 meters and 0(or 180)-degree horizontal angle. This suggests that Faster RCNN is more robust in these specific scenes, potentially due to the distribution of training images. Nevertheless, for the majority of viewing angles and distances, the ASRs of our method consistently exceeded \\(80\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.653, + 0.864 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To evaluate the effectiveness of the 3D control points-based mesh smoothing algorithm (CMS) and a set of smoothing" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24289" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.094, + 0.309, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.213, + 0.218, + 0.229 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.089, + 0.51, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.398, + 0.215, + 0.424, + 0.232 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.089, + 0.682, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.216, + 0.611, + 0.232 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.089, + 0.86, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.215, + 0.789, + 0.232 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.25, + 0.892, + 0.266 + ], + "angle": 0, + "content": "Figure 6. Full-angle ASRs at different (a) parameters including (b) distances, (c) pitch angles, and (d) horizontal angles. See text for details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.444 + ], + "angle": 0, + "content": "losses (SMLS), we performed ablation experiments. We conducted a subjective evaluation on the smoothness score of the 3D adversarial mesh and 2D adversarial pattern and we also evaluated the physical implementation time of 2D adversarial patterns under different settings. The experimental settings and results are detailed in SM. The results indicate that both CMS and SMLS improved the smoothness of adversarial meshes and patterns, and their combination was better. Besides, these methods effectively reduced the physical implementation time of adversarial patterns." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.452, + 0.449, + 0.468 + ], + "angle": 0, + "content": "4.6. Exploring the Interpretability of the Attack" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.471, + 0.535 + ], + "angle": 0, + "content": "To gain deeper insights into our attack methods, we utilized the GradCAM [23] technique to analyze the changes in network attention maps before and after the attack. See SM for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.452, + 0.562 + ], + "angle": 0, + "content": "4.7. Comparison with 2D Optimization Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.676 + ], + "angle": 0, + "content": "We extended the previous 2D infrared model car attack methods [31, 32] to our 3D car model. We generated adversarial car textures on our car model based on their papers and codes, which are shown in SM. Following the settings in Section 4.4, we evaluated the attack performance of the different methods. The statistics of ASRs are presented in Table 1, with typical examples shown in Figure 5." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.697, + 0.266, + 0.834 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.835, + 0.19, + 0.844 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.697, + 0.469, + 0.834 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.352, + 0.835, + 0.367, + 0.844 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.855, + 0.471, + 0.897 + ], + "angle": 0, + "content": "Figure 7. Infrared attack effect on model cars. (a) Visible light view of model cars. (b) Infrared view of model cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.895, + 0.488 + ], + "angle": 0, + "content": "The results indicated that the ASR of our method \\((96.31\\%)\\) outperformed the ASRs of two alternative methods \\((14.97\\%\\) and \\(20.06\\%)\\) for Faster RCNN in the digital world. The reasons may be as follows. The two 2D optimization methods based on boundary optimization [31] or points clustering [32] are subject to various constraints. These constraints are used to ensure that, for example, the boundary curves do not have overlaps [31], and the adversarial patterns do not split into multiple pieces [32]. With more constraints, the feasible solution space becomes smaller. However, our 3D mesh shadow approach does not have such constraints, and we can explore a larger solution space, leading to better results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.708, + 0.513 + ], + "angle": 0, + "content": "4.8. Attack Transferability" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.747 + ], + "angle": 0, + "content": "We tested the effectiveness of our adversarial car texture \\((T_{\\mathrm{adv}}\\) in Figure 4) optimized for Faster RCNN against other unseen detectors, including RetinaNet [14], Cascade RCNN [3], Libra RCNN [19], SSD [15], YOLOv3 [21] and Deformable DETR [36]. It is worth noting that these experiments were performed in a black-box setting, which is a more challenging but practically significant scene for real-world applications. The results are shown in Table 1. The ASRs of our method against unseen models reached \\(73.35\\% - 95.80\\%\\). It indicates that our method performed well in a black-box setting and had good attack transferability to unseen models including not only CNN-based models but also transformer-based models. Besides, the transferability of our method is stronger than not only two simple baselines but also two infrared attack methods [31, 32]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.783, + 0.773 + ], + "angle": 0, + "content": "4.9. Physical Attacks on Model Cars" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We initially conducted physical experiments on three same 1:24 scale Mercedes-Benz model cars (Figure 7(a)). We crafted the adversarial aluminum stickers according to the optimized patterns, scaled to match the size of the model car, and applied them to the model car. In addition, we created randomly cut-shaped stickers as a control. We heated the model cars with hot water to simulate the real car with engine running. We used a rotating turntable to conve" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24290" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.089, + 0.296, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.109, + 0.2, + 0.295, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.089, + 0.483, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.2, + 0.482, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.089, + 0.672, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.2, + 0.672, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.089, + 0.86, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.2, + 0.862, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.318, + 0.862, + 0.332 + ], + "angle": 0, + "content": "Figure 8. Examples of infrared real car attacks. C: clean car. R: car with random shape stickers. A: car with adversarial stickers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.473, + 0.526 + ], + "angle": 0, + "content": "niently assess the attack effectiveness over the entire 0-360 horizontal degree and 0-90 pitch angle range. The infrared camera was FLIR T560. We utilized the same Faster RCNN detector as in Section 4.4. The detection results indicated that our adversarial stickers achieved an ASR of \\(84.86\\%\\) on the 1:24 scale car model in the physical world. In comparison, the clean car and the car with random patterns had ASRs of only \\(19.08\\%\\) and \\(35.37\\%\\), respectively. Figure 7 provides specific examples from the physical world experiments. A demo video for physical model car attacks is shown in Supplementary Video 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.541, + 0.355, + 0.557 + ], + "angle": 0, + "content": "4.10. Physical Attacks on Real Cars" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.733 + ], + "angle": 0, + "content": "We conducted physical experiments on two real Mercedes-Benz A200L cars (one black one white). It was a sunny day with a temperature of about \\(25^{\\circ}\\mathrm{C}\\). For a fair comparison, we pasted the adversarial stickers, randomly cut-shaped stickers or nothing on the same car successively. We recorded 30 videos (each video is around 2 minutes) and sampled 3688 infrared images of these cars from various angles and distances in both ground and underground parking lots using a FLIR T560 camera. The height of the camera tripod can be adjusted from \\(1\\mathrm{m}\\) to \\(2\\mathrm{m}\\). We sent these images to Faster RCNN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The results indicated that our adversarial stickers achieved an ASR of \\(91.49\\%\\) on the real cars with the engines running, while the random shape stickers and no sticker had ASRs of only \\(6.21\\%\\) and \\(0.66\\%\\), respectively. When the engines were off for one hour, the ASR of adversarial stickers dropped a little to \\(88.42\\%\\). The reason might be that the infrared patterns of adversarial stickers with engines off were not as clear as the patterns with engines running. However, the ASR of adversarial stickers were still better than ASR of random shape stickers \\((5.72\\%)\\) and no sticker \\((1.86\\%)\\) when the engines were off. Figure 1" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.435 + ], + "angle": 0, + "content": "and Figure 8 show some examples. There were a few other cars that passed by or were parked when we were recording videos and therefore appeared in our photos, which were also detected. See Supplementary Video 3 for the demo video." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.442, + 0.702, + 0.456 + ], + "angle": 0, + "content": "4.11. Adversarial Defense" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.893, + 0.6 + ], + "angle": 0, + "content": "We tested five adversarial defense methods to defend our attack methods in the digital world, including adversarial training [8], PixelMask [1], Bit squeezing [33], JPEG compression [10] and Total variation minimization [10]. Experiment details for these methods are in SM. The results show that although these methods had a certain defense effect, the ASR of our method still reached \\(88.83\\% - 94.81\\%\\) after adding defense, which shows that our method is a powerful attack method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.612, + 0.62, + 0.628 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.894, + 0.82 + ], + "angle": 0, + "content": "We propose infrared adversarial stickers to hide a real car from infrared detectors at various viewing angles, distances, and scenes in the physical world. We build a 3D infrared car model with real infrared characteristics and propose a 3D mesh shadow method for the generation of infrared adversarial pattern. To make the 3D adversarial mesh smoother, we propose a 3D control points-based smoothing algorithm and use a set of smoothness loss functions. Our adversarial stickers enabled two real cars to evade Faster RCNN at various viewing angles, distances and scenes. Besides, our method has strong attack transferability against multiple unseen detectors in a black-box setting." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.831, + 0.688, + 0.848 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China (Nos. 61734004, U2341228, U19B2034)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24291" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Akshay Agarwal, Mayank Vatsa, Richa Singh, and Nalini Ratha. Cognitive data augmentation for adversarial defense via pixel masking. Pattern Recognition Letters, 146:244-251, 2021. 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Anish Athalye, Logan Engstrom, Andrew Ilyas, and Kevin Kwok. 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Previous infrared physical attacks mainly focused on 2D infrared pedestrian detection which may not fully manifest its destructiveness to AI systems. In this work, we propose a physical attack method against infrared detectors based on 3D modeling, which is applied to a real car. The goal is to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles, distances, and scenes. We build a 3D infrared car model with real infrared characteristics and propose an infrared adversarial pattern generation method based on 3D mesh shadow. We propose a 3D control points-based mesh smoothing algorithm and use a set of smoothness loss functions to enhance the smoothness of adversarial meshes and facilitate the sticker implementation. Besides, We designed the aluminum stickers and conducted physical experiments on two real Mercedes-Benz A200L cars. Our adversarial stickers hid the cars from Faster RCNN, an object detector, at various viewing angles, distances, and scenes. The attack success rate (ASR) was $91.49\%$ for real cars. In comparison, the ASRs of random stickers and no sticker were only $6.21\%$ and $0.66\%$ , respectively. In addition, the ASRs of the designed stickers against six unseen object detectors such as YOLOv3 and Deformable DETR were between $73.35\% - 95.80\%$ , showing good transferability of the attack performance across detectors. + +![](images/7ee1c75177d4e6b83179ad7c365e6faf0e2ac30d31230988e3d04da0226aeee7.jpg) +Figure 1. Infrared attack effect on real cars. (a) Visible light view of real cars. (b) Infrared view of real cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers. The numbers above the bounding boxes are object confidence scores (\%) with 0.6 threshold. Our adversarial stickers hid the car from Faster RCNN at various viewing angles, distances and scenes. In comparison, the clean car and the car with random shape stickers were detected at the same situation. + +![](images/b9accba057be4dfcdf360fe56174fd42e44ee65a4987cd2bdd7bbaae20236a7e.jpg) + +# 1. Introduction + +It is well known that deep learning models can be misled by carefully designed perturbations to the input which is called adversarial example, and the perturbation process is called adversarial attack. Adversarial attacks can be di + +vided into two categories, digital attacks [4, 8, 9, 16, 24, 26] which assume that the attackers can directly modify the model input in the digital world, and physical attacks [11, 12, 27, 28, 35, 37] which assume that the attackers can only modify the object or scene in the physical world. Physical attacks have attracted much attention because of their importance of assessing the security of real-world AI systems. + +One type of physical attack is called infrared physical attack [30-32, 35, 37]. Infrared imaging is widely used in our daily lives, such as body temperature monitoring and autonomous driving. Since infrared cameras can function normally at night, they are becoming more and more important in autonomous driving systems; so is their safety. + +Previous infrared physical attacks [30-32, 35, 37] mainly focused on infrared pedestrians, and only two works [31, 32] conducted experiments on model cars. There is currently a lack of infrared attack research on real cars. The reasons might be as follows. Compared with pedestrians with constant body temperature, the temperature distributions of real cars are more uneven (e.g., the temperature of the engine is much higher than that of other places), so their infrared characteristics are more complex than pedestrians. Compared with model cars without engines, real cars' structures and materials are very different from those of model cars, so their infrared characteristics are also quite different. Besides, real car attacks require designing and manufacturing adversarial patterns on the entire 3D car surface, which poses a great challenge to physical experiments. But we believe that for the safety of autonomous driving cars, physical real car attack is worth in-depth investigation. + +The aforementioned two infrared model car attacks [31, 32] are only effective within limited viewing angles (e.g., horizontal angles $-30^{\circ} - 30^{\circ}$ and pitch angle $0^{\circ}$ ). But we want to implement a full-angle attack (the horizontal angles $0^{\circ} - 360^{\circ}$ , and pitch angle $0^{\circ} - 90^{\circ}$ ), so the attack angles cover an entire hemisphere surface, which is a challenging task. We also notice that these methods [31, 32] are both case-by-case attacks, which needs to optimize an adversarial pattern for each image1, while our goal is to achieve a universal attack which uses the same adversarial pattern to attack detectors at various viewing angles, distances and scenes. + +Towards this goal, we propose an infrared physical attack method applied to a real car based on 3D modeling. We aim to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles (full-angle), distances and scenes. Since most current 3D car models are visible-light models, and there is a lack of 3D infrared car models, we build a 3D infrared car model with real infrared characteristics at various viewing angles. For the generation of infrared adversarial pattern for stick- + +ers, we propose to optimize a 3D adversarial mesh at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern, and finally attach the 2D adversarial pattern to the car surface. The motivation of this mesh shadow attack (MSA) method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. To improve the smoothness of adversarial patterns and facilitate sticker implementation, we propose a 3D control points-based mesh smoothing algorithm and use a set of smoothing loss functions. + +For the physical implementation of infrared adversarial patterns, we use an aluminum film which modifies the surface emissivity of the object instead of altering the surface temperature used by previous works [30-32, 35, 37]. Like many car stickers, the adversarial car stickers can be easily attached on the car surface. The stickers are only $0.08\mathrm{mm}$ thick and take up almost no space. + +To assess the safety of infrared detection in real autonomous driving scenes, we used two real Mercedes-Benz A200L cars. Physical experiments show that our infrared adversarial stickers made the real cars hide from the infrared detector Faster RCNN at various viewing angles, various distances, and multiple scenes, with an attack success rate (ASR) of $91.49\%$ . To the best our knowledge, this is the first 3D multi-view physical infrared vehicle attack, and also the first infrared attack conducted on real cars. + +# 2. Related Work + +# 2.1. Visible Light Physical Adversarial Attacks + +Huang et al. [13] proposed a universal physical camouflage (UPC) attack for object detectors. Zhang et al. [34] proposed a vehicle camouflage for physical adversarial attack on object detectors in the wild. Wang et al. [29] proposed the Dual attention suppression (DAS) attack to generate adversarial vehicle camouflage in the physical world. Suryanto et al. [25] generated the physical adversarial camouflage by using a differentiable transformation network. Wang et al. [28] proposed a 3D full-coverage vehicle camouflage for physical adversarial attack (FCA). It is worth noting that all above works are proposed for visible light images. + +# 2.2. Infrared Physical Adversarial Attacks + +Zhu et al. [35] proposed a bulb-based board to fool infrared pedestrian detectors in the physical world. Zhu et al. [37] proposed an infrared invisible clothing to hide from infrared pedestrian detectors in the physical world. Wei et al. [30] proposed the HotCold blocks to attack the infrared pedestrian detectors. Wei et al. [32] proposed a physical adversarial infrared patch (AIP) based on a points-clustering algorithm. Wei et al. [31] proposed a unified adversar + +![](images/45dca83f8fdd2c7d96de099d455b0d45fcb6429ce2221a87981a91b0e7516001.jpg) +(a) + +![](images/65907a968717533b5674c2bd7db7731cec0d671ff3d2a33e255b9476b3ff6170.jpg) +(b) +Figure 2. Construction and optimization of real infrared car texture mapping. (a) Car mesh model. (b) Reorganized faces map. (c) Infrared car texture map collected from real world. (d) Rendered infrared car model. + +![](images/5e995316c8a5d71f4e40b9ad5ee42e127b5ceffbcbeab401afd72710e0ff1f97.jpg) +(c) + +![](images/e339de33fdd50f8ce70720db392201d69e766d95a2c8ac9f9bc71228eb4ceaf2.jpg) +(d) + +ial patch (UAP) for physical attacks based on a boundary-limited shape optimization algorithm. It is worth noting that all above methods are proposed for infrared pedestrian or model car attacks. There is currently a lack of research on infrared real vehicle attacks in the physical world. + +# 3. Car Sticker Attack Method + +Our method consists of several steps. First, we build a 3D infrared car model based on real infrared characteristics. Next, we use the infrared adversarial pattern generation method based on 3D mesh shadow. To make the 3D adversarial mesh smoother, we use a 3D control points-based mesh smoothing algorithm and use a set of smoothness losses. Then we apply adversarial patterns to 3D infrared car model and optimize the adversarial patterns. Finally, we introduce the physical implementation method of infrared adversarial car stickers. + +# 3.1. Building a 3D Infrared Car Model + +To simulate the infrared car attack realistically, we build a 3D model based on the infrared characteristics of a real car. It is worth noting that our method can be applied to any target car, and we chose Mercedes-Benz A200L in our experiments, simply because one of the authors have this car. Figure 2(a) shows the car mesh model $M_{\mathrm{car}}$ . Next, we need + +![](images/a8450625883b13bb5adbbcb32316b20cf947691fd56ed48a51a68fddb6abb8ee.jpg) +Figure 3. Schematic diagram of mesh shadow method. + +to create a "skin" for the car model based on infrared photos taken by an infrared camera FLIR T560. However, the infrared photos captured by the camera are all 2D images, and the challenge is how to "paste" these 2D infrared images onto the 3D car mesh model. First, we flatten all the faces of 3D car mesh onto a 2D plane called faces map. After that, we use MAYA software to rearrange these faces to divide different areas, such as roof, doors, etc., as shown in Figure 2(b). This process facilitates the alignment of real infrared car images with the 3D car mesh. + +Subsequently, we crop the infrared images into different parts based on the faces map (Figure 2(b)) and paste the cropped images onto the 2D faces map, and then we get the infrared texture map of the car, as shown in Figure 2(c). See Supplementary Material (SM) for how these infrared photos are taken, cropped and pasted. This process establishes a correspondence between the real infrared car images and the 3D car mesh. The rendered infrared car model is shown in Figure 2(d), which is built for a real car with engine running. + +# 3.2. Generation of 2D Shadow Based on 3D Mesh + +We aim to design infrared stickers with adversarial patterns to hide the cars from infrared detectors at various viewing angles (full-angle), distances, and scenes. We propose a 3D adversarial mesh shadow attack (MSA) method to generate the 2D infrared adversarial patterns for stickers. The motivation of MSA method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. The core of MSA method is to optimize a 3D adversarial mesh $M_{\mathrm{adv}}$ at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern $S_{\mathrm{adv}}$ , and finally attach the 2D adversarial pattern $S_{\mathrm{adv}}$ to the car surface. Note that the 3D adversarial mesh $M_{\mathrm{adv}}$ is different from the 3D car mesh $M_{\mathrm{car}}$ in Section 3.1. The optimization variables include the 3D mesh vertices coordinates $V$ , the mesh shadowing angle $\varphi$ , and the center point position $P$ when pasting the 2D pattern onto the car's texture map $T_{\mathrm{origin}}$ (Figure 3). + +The shadowing operation refers to rendering the mesh + +![](images/253b64bfcfa536d811401f908a95f74536c6ac41a1af84ea690f9ec382032a49.jpg) +Figure 4. The overall pipeline of the proposed method. + +$M_{\mathrm{adv}}$ to a dark area while retaining the mesh contour (Figure 3), and the dark area has a uniform grayscale value within the contour. The grayscale value is consistent with the infrared characteristics of the sticker we use. Let $\Omega$ denote this operation. If we want the car to have adversarial effect at various viewing angles, we need to optimize $N$ adversarial meshes to generate $N$ adversarial shadows on different places of the car (Figure 4): + +$$ +S _ {\mathrm {a d v}} ^ {(i)} = \Omega \left(M _ {\mathrm {a d v}} ^ {(i)}, \varphi^ {(i)}\right), i = 1, 2, \dots N. \tag {1} +$$ + +# 3.3. 3D Control Points-Based Mesh Smoothing + +If we directly optimize the vertices coordinates $V$ of the mesh $M_{\mathrm{adv}}$ , many "peaks" will appear on the mesh surface, which will make the shadow shape very complex and will be difficult for the physical implementation of the adversarial shadow $S_{\mathrm{adv}}$ . Inspired by the Gaussian smoothing kernel and spline interpolation method, we propose a smoothing control algorithm for 3D mesh vertices. Its core idea is to use some 3D control points $C$ as anchor points, and the coordinate offsets of mesh vertices $V$ are expressed as the weighted average of the coordinate offsets of $C$ . The calculation details are described in SM. + +We use $\Theta$ to denote the above transformation, and $C^{(i)}$ to denote the control points set of $M_{\mathrm{adv}}^{(i)}$ , then + +$$ +V ^ {(i)} = \Theta (C ^ {(i)}), i = 1, 2, \dots N. \tag {2} +$$ + +Since the control points $C^{(i)}$ determine the vertices coordinates $V^{(i)}$ , the optimization variables changes from $\left(V^{(i)}, P^{(i)}, \varphi^{(i)}\right)$ to $\left(C^{(i)}, P^{(i)}, \varphi^{(i)}\right)$ , $i = 1, 2, \ldots N$ . + +# 3.4. Mesh Smoothness Loss Functions + +To further enhance the smoothness of 3D adversarial mesh $M_{\mathrm{adv}}$ and 2D adversarial pattern $S_{\mathrm{adv}}$ , we use a set of loss functions including: mesh normal consistency loss, mesh edge loss, chamfer distance loss, and Laplacian smoothing loss. During the optimization process of 3D mesh $M_{\mathrm{adv}}$ , these functions guide the generation of a smoother adversarial mesh. A smoother 3D mesh $M_{\mathrm{adv}}$ results in a smoother 2D shadow pattern $S_{\mathrm{adv}}$ , which is beneficial for manufacturing physical stickers based on the 2D shadow pattern. + +The mesh normal consistency loss computes the normal consistency for each pair of neighboring faces, and minimizing it encourages the mesh surface to be smoother. We suppose that mesh $M_{\mathrm{adv}}$ has a total of $F$ faces. Let $n_i, n_j$ ( $1 \leq i, j \leq F$ ) represent the normal vector of any two adjacent faces, then this loss function is described as: + +$$ +L _ {\text {n o r m}} = \text {A v e r a g e} (1 - \cos \left(n _ {i}, n _ {j}\right)). \tag {3} +$$ + +Average is calculated between any pair of adjacent faces. + +The mesh edge loss computes mesh edge length regularization loss, and minimizing it encourages a reduction in the average edge length of the adversarial mesh. Suppose $M_{\mathrm{adv}}$ has a total of $M$ edges, $l_{k}$ ( $k = 1,2,\dots,M$ ) represents the length of each edge, and this loss function is described as + +$$ +L _ {\text {e d g e}} = \left(\sum_ {k = 1} ^ {M} l _ {k}\right) / M. \tag {4} +$$ + +The chamfer distance loss computes chamfer distance [6] between the sampling points of adversarial mesh and a standard sphere. Reducing chamfer distance loss encourages the adversarial mesh $M_{\mathrm{adv}}$ to approximate a sphere. + +We denote the point clouds sampled by adversarial mesh $M_{\mathrm{adv}}$ and the standard spherical mesh $M_{\mathrm{sphere}}$ by $S_{1}$ and $S_{2}$ , respectively. The chamfer distance loss is described as + +$$ +L _ {\text {c h a m f e r}} = \sum_ {p \in S _ {1}} \min _ {q \in S _ {2}} \| p - q \| _ {2} ^ {2} + \sum_ {q \in S _ {2}} \min _ {p \in S _ {1}} \| q - p \| _ {2} ^ {2}. \tag {5} +$$ + +The Laplacian smoothing loss $L_{\mathrm{Laplace}}$ computes the Laplacian smoothing objective for the adversarial mesh. We define this function as Laplace, and its calculation details are introduced in [18], so + +$$ +L _ {\text {L a p l a c e}} = \text {L a p l a c e} \left(M _ {\text {a d v}}\right). \tag {6} +$$ + +# 3.5. Applying the 2D Shadow to 3D Car Model + +We apply the adversarial shadow $S_{\mathrm{adv}}$ to 3D infrared car model by changing its texture map $T_{\mathrm{origin}}$ . This simulates the process we paste the adversarial stickers to the car surface in the physical world. To facilitate physical implementation, we simulate to paste the stickers onto the door, roof, front hood and rear of the car, which have wide ranges of flat area and are easy to paste. In each area, we paste one or two adversarial shadow patterns (Figure 4). To simulate real-world perturbations, such as errors in cutting the adversarial stickers, variations in surface temperature on the adversarial stickers, and errors in the pasting positions, we introduce random perturbations to the vertex coordinates $V$ of the adversarial mesh $M_{\mathrm{adv}}$ , random noise to the pattern $S_{\mathrm{adv}}$ , random changes in grayscale values of $S_{\mathrm{adv}}$ , and random perturbations in the position $P$ during the pasting of $S_{\mathrm{adv}}$ . This approach, known as the Expectation Over Transformation (EOT) algorithm [2], enhances the robustness of our algorithm in real-world scenes. + +Next, we need to paste the adversarial patterns $S_{\mathrm{adv}}$ onto the original car texture map $T_{\mathrm{origin}}$ . Let $\Gamma$ denote the pasting operation. We establish a Cartesian coordinate system with the center point of $T_{\mathrm{origin}}$ as the origin. We use $P^{(i)}$ to represent the coordinates of the pasting positions for $N$ adversarial shadows $S_{\mathrm{adv}}^{(i)}, i = 1,2,\dots N$ . The texture map after pasting the adversarial shadows is + +$$ +T _ {\mathrm {a d v}} = \Gamma \left(S _ {\mathrm {a d v}} ^ {(i)}, P ^ {(i)}, T _ {\text {o r i g i n}}\right), i = 1, 2, \dots N. \tag {7} +$$ + +We use the differentiable renderer Pytorch3D [20] to render the adversarial texture map $T_{\mathrm{adv}}$ onto the surface of the car mesh $M_{\mathrm{car}}$ , resulting in the rendered infrared car images with adversarial patterns, denoted as $I_{\mathrm{adv}}$ . Let $\Psi$ denote the rendering operation with parameters $\theta$ which include the rendering distances and angles. Mathematically, this process can be expressed as: + +$$ +I _ {\mathrm {a d v}} = \Psi \left(M _ {\mathrm {c a r}}, T _ {\mathrm {a d v}}, \theta\right). \tag {8} +$$ + +# 3.6. Optimization of 3D Mesh Shadow Attack + +After we get the rendered infrared adversarial images $I_{\mathrm{adv}}$ , we input them into the target detector $f$ . The output of the target detector typically includes object confidence $f_{\mathrm{obj}}$ , class confidence $f_{\mathrm{cls}}$ , and bounding box $f_{\mathrm{bbox}}$ . Since our goal is to create a stealthy attack, meaning that our adversarial texture $T_{\mathrm{adv}}$ should make the infrared car hide from the detector, we try to lower the object confidence $f_{\mathrm{obj}}(I_{\mathrm{adv}})$ as much as possible. Therefore, the detection loss is defined as: + +$$ +L _ {\text {d e t}} = f _ {\text {o b j}} \left(I _ {\text {a d v}}\right). \tag {9} +$$ + +The overall loss function is defined as follows: + +$$ +\begin{array}{l} L = L _ {\text {d e t}} + w _ {1} \cdot L _ {\text {n o r m}} + w _ {2} \cdot L _ {\text {e d g e}} \tag {10} \\ + w _ {3} \cdot L _ {\mathrm {c h a m f e r}} + w _ {4} \cdot L _ {\mathrm {L a p l a c e}}. \\ \end{array} +$$ + +Here, $w_{1}, w_{2}, w_{3}$ , and $w_{4}$ are weights of different losses, which are determined empirically. We use the backpropagation algorithm according to the loss function $L$ to update the optimization variables $C^{(i)}, P^{(i)}, \varphi^{(i)}, i = 1, 2, \ldots, N$ . The overall pipeline is illustrated in Figure 4. + +# 3.7. Physical Implementation Method + +We use aluminum films to make adversarial car stickers. Instead of altering the surface temperature of an object, this approach focuses on modifying the surface emissivity of the object, which is different from previous works [30-32, 35, 37]. Aluminum typically has an emissivity around 0.1, while the surface of a car, typically made of steel, has an emissivity around 0.8, resulting in different infrared characteristics. We utilize an ultra-thin (only $0.08\mathrm{mm}$ ) aluminum film, which can be easily attached on the surface of a car like many car stickers. We only need around 13 mins to make a sticker, and the cost of a sticker is only around 0.2 USD. The implementation process of adversarial stickers is shown in Supplementary Video 1. + +# 4. Experiments + +# 4.1. Dataset + +We used the FLIR_ADAS_1_3 [7] infrared dataset released by FLIR company for infrared autonomous driving scenes. It contains 10,228 real infrared photos collected in streets and highways of Santa Barbara, USA. The infrared camera is FLIR Tau2. The training set contains 7160 images, and the test set contains 3068 images. We used this dataset to finetune the target detector. + +# 4.2. Target Detectors + +We initially chose the classic two-stage object detector: Faster R-CNN [22], as our primary target detector. We used the pre-trained Faster RCNN model provided by the torchvision library [17] and then finetuned it on the + +Table 1. ASRs (%) of cars with different textures against different detectors. + +
Detector TextureFasterRetinaNetCascadeLibraSSDYOLOv3Deformable
Origin2.104.4918.8616.4715.2725.1512.28
Random shape18.2617.0723.9528.7445.8150.0023.65
AIP14.9715.2732.9327.5423.6538.3227.54
UAP20.0631.4438.0233.2336.8339.8224.25
Ours96.3186.8373.3579.0495.8086.5283.83
+ +FLIR_ADAS_1_3 dataset. The average precision (AP) for car class of the finetuned model on the training set was 0.96, and the AP on the test set was 0.92. After attacking Faster RCNN in a white-box setting, we transferred our attack method to other unseen detectors such as YOLOv3 [21], Deformable DETR [36], etc. which were provided by mmdetection library [5] in a black-box setting. + +# 4.3. Evaluation Metrics + +In our experiments, we used the attack success rate (ASR) as the evaluation metrics of the attack methods. The ASR was defined as the ratio of the number of cars which were not detected to the total number of cars. We set the confidence threshold of target detectors to 0.6 and the IOU threshold between the prediction box and ground truth to 0.5, similar to previous works [31, 32, 35, 37]. The ASR was calculated based on the average value of sample points collected from various distances, horizontal angles, and pitch angles with the sampling method described in Section 4.4. + +# 4.4. Attack Faster RCNN in the Digital World + +We optimized $N = 5$ adversarial shadow patterns to simulate 5 adversarial stickers to be pasted on the car surface. + +![](images/37025c724ba623d71180afce0a70ba3380b8932e72eb459628eeb2d6adde00e5.jpg) +Figure 5. Examples of detection results of different detectors for target cars with different textures. The numbers above the red bounding boxes are the object confidence scores, with a threshold of 0.6. The results of other detectors are shown in SM. + +The hyper-parameters are detailed in SM. After optimization, we obtained the adversarial shadow patterns ( $T_{\mathrm{adv}}$ in Figure 4), and the rendered car with adversarial shadow patterns ( $I_{\mathrm{adv}}$ in Figure 4). + +After that, we evaluated the attack effectiveness of the adversarial shadow patterns. For a fair comparison, we employed the original car pattern (without any sticker) and random shape pattern as control patterns. The figures of these patterns are shown in SM. These patterns were rendered onto the same car model, and the resulting images were input into Faster R-CNN. The results, as shown in Table 1, indicate that our adversarial shadow patterns achieved an ASR of $96.31\%$ for Faster R-CNN in the digital world. In comparison, the ASRs for the original car pattern and random shape pattern were only $2.10\%$ and $18.26\%$ , respectively. This demonstrates the effectiveness of our attack method. Figure 5 shows typical examples. + +We then analyze the ASR of our method at various (full-angle) viewing angles and distances. The horizontal angle azimuth ranged from 0 to 360 degrees, and we sampled it every 20 degrees. The pitch angle elev ranged from 0 to 90 degrees, and we sampled it every 6 degrees. The distance dist ranged from 1 to 8 meters, and we sampled it every 1 meter. Figure 6(b-d) show the ASRs with respect to one variable (e.g., dist) by taking the average of ASRs over all combinations of values of the other two variables (e.g., elev and azimuth). The results indicate that our approach achieves successful attacks at various (full-angle) viewing angles and various distances. In contrast, many previous works [30-32, 35] were effective only within limited viewing angles (e.g., horizontal angle from -30 to 30 degrees and pitch angle 0 degree) and shorter distances (e.g. 3 to 6 meters). Note that there is a decrease in ASR at 2 meters and 0(or 180)-degree horizontal angle. This suggests that Faster RCNN is more robust in these specific scenes, potentially due to the distribution of training images. Nevertheless, for the majority of viewing angles and distances, the ASRs of our method consistently exceeded $80\%$ . + +# 4.5. Ablation Study + +To evaluate the effectiveness of the 3D control points-based mesh smoothing algorithm (CMS) and a set of smoothing + +![](images/e0b6b9b57a75f5da399713849c47c7090dff7915203dc674f54c1386155618f7.jpg) +(a) + +![](images/034cea65b171e06c58fdad1c682494c2b1abbf2b3af99b7e5127deb39f2751b7.jpg) +(b) + +![](images/27d747eb3ac065d6feac71802a53ac319dd055ca87aca7361be6e14d0811dec5.jpg) +(c) + +![](images/10be2295814f8d363a7a4f4afde244cba95b09d002ef6ee0b292caf60724f35b.jpg) +(d) +Figure 6. Full-angle ASRs at different (a) parameters including (b) distances, (c) pitch angles, and (d) horizontal angles. See text for details. + +losses (SMLS), we performed ablation experiments. We conducted a subjective evaluation on the smoothness score of the 3D adversarial mesh and 2D adversarial pattern and we also evaluated the physical implementation time of 2D adversarial patterns under different settings. The experimental settings and results are detailed in SM. The results indicate that both CMS and SMLS improved the smoothness of adversarial meshes and patterns, and their combination was better. Besides, these methods effectively reduced the physical implementation time of adversarial patterns. + +# 4.6. Exploring the Interpretability of the Attack + +To gain deeper insights into our attack methods, we utilized the GradCAM [23] technique to analyze the changes in network attention maps before and after the attack. See SM for more details. + +# 4.7. Comparison with 2D Optimization Methods + +We extended the previous 2D infrared model car attack methods [31, 32] to our 3D car model. We generated adversarial car textures on our car model based on their papers and codes, which are shown in SM. Following the settings in Section 4.4, we evaluated the attack performance of the different methods. The statistics of ASRs are presented in Table 1, with typical examples shown in Figure 5. + +![](images/9b36a7883b49c5e57f4a3517f69963159d73b0272a326d2ac54943c43edd73fa.jpg) +(a) +Figure 7. Infrared attack effect on model cars. (a) Visible light view of model cars. (b) Infrared view of model cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers. + +![](images/b5458f470d8c2c89a18811bc996c4baadcdaf1099ad0cc8bba224071f23fd9b0.jpg) +(b) + +The results indicated that the ASR of our method $(96.31\%)$ outperformed the ASRs of two alternative methods $(14.97\%$ and $20.06\%)$ for Faster RCNN in the digital world. The reasons may be as follows. The two 2D optimization methods based on boundary optimization [31] or points clustering [32] are subject to various constraints. These constraints are used to ensure that, for example, the boundary curves do not have overlaps [31], and the adversarial patterns do not split into multiple pieces [32]. With more constraints, the feasible solution space becomes smaller. However, our 3D mesh shadow approach does not have such constraints, and we can explore a larger solution space, leading to better results. + +# 4.8. Attack Transferability + +We tested the effectiveness of our adversarial car texture $(T_{\mathrm{adv}}$ in Figure 4) optimized for Faster RCNN against other unseen detectors, including RetinaNet [14], Cascade RCNN [3], Libra RCNN [19], SSD [15], YOLOv3 [21] and Deformable DETR [36]. It is worth noting that these experiments were performed in a black-box setting, which is a more challenging but practically significant scene for real-world applications. The results are shown in Table 1. The ASRs of our method against unseen models reached $73.35\% - 95.80\%$ . It indicates that our method performed well in a black-box setting and had good attack transferability to unseen models including not only CNN-based models but also transformer-based models. Besides, the transferability of our method is stronger than not only two simple baselines but also two infrared attack methods [31, 32]. + +# 4.9. Physical Attacks on Model Cars + +We initially conducted physical experiments on three same 1:24 scale Mercedes-Benz model cars (Figure 7(a)). We crafted the adversarial aluminum stickers according to the optimized patterns, scaled to match the size of the model car, and applied them to the model car. In addition, we created randomly cut-shaped stickers as a control. We heated the model cars with hot water to simulate the real car with engine running. We used a rotating turntable to conve + +![](images/667023f967c1f65b7b5ff5de6d4d020dea067f35f785269cb965b62c78af2156.jpg) + +![](images/1995226415bce4756f76de724cca6189d4d18314060000ec9d137c56780de227.jpg) +Figure 8. Examples of infrared real car attacks. C: clean car. R: car with random shape stickers. A: car with adversarial stickers. + +![](images/22a663343b352eef6f33bb50c456bc7b16f2c32391a90bd62c88960347ea571b.jpg) + +![](images/8197d6903789d7ae4b97dc2b24ef0a563adebd1d444f5c1143ebd5e8fc0b9455.jpg) + +![](images/3c0aadfb3ba751be96db1bc78ff03c66dbb42f5ef81b6ee39b74f99e4e214e8b.jpg) + +![](images/389a0362e661fdb7d641cbb91050df4a052513707401863ca3ac4d49990d5743.jpg) + +![](images/34c59ff63e1aedc20f9066320f8dc0984e6b8b031b730c9d7578712612d0ba49.jpg) + +![](images/bbd9118d9b1999cdf3e741572256a42a55dcf64c0827200b4fa309b5d9ac0c71.jpg) + +niently assess the attack effectiveness over the entire 0-360 horizontal degree and 0-90 pitch angle range. The infrared camera was FLIR T560. We utilized the same Faster RCNN detector as in Section 4.4. The detection results indicated that our adversarial stickers achieved an ASR of $84.86\%$ on the 1:24 scale car model in the physical world. In comparison, the clean car and the car with random patterns had ASRs of only $19.08\%$ and $35.37\%$ , respectively. Figure 7 provides specific examples from the physical world experiments. A demo video for physical model car attacks is shown in Supplementary Video 2. + +# 4.10. Physical Attacks on Real Cars + +We conducted physical experiments on two real Mercedes-Benz A200L cars (one black one white). It was a sunny day with a temperature of about $25^{\circ}\mathrm{C}$ . For a fair comparison, we pasted the adversarial stickers, randomly cut-shaped stickers or nothing on the same car successively. We recorded 30 videos (each video is around 2 minutes) and sampled 3688 infrared images of these cars from various angles and distances in both ground and underground parking lots using a FLIR T560 camera. The height of the camera tripod can be adjusted from $1\mathrm{m}$ to $2\mathrm{m}$ . We sent these images to Faster RCNN. + +The results indicated that our adversarial stickers achieved an ASR of $91.49\%$ on the real cars with the engines running, while the random shape stickers and no sticker had ASRs of only $6.21\%$ and $0.66\%$ , respectively. When the engines were off for one hour, the ASR of adversarial stickers dropped a little to $88.42\%$ . The reason might be that the infrared patterns of adversarial stickers with engines off were not as clear as the patterns with engines running. However, the ASR of adversarial stickers were still better than ASR of random shape stickers $(5.72\%)$ and no sticker $(1.86\%)$ when the engines were off. Figure 1 + +and Figure 8 show some examples. There were a few other cars that passed by or were parked when we were recording videos and therefore appeared in our photos, which were also detected. See Supplementary Video 3 for the demo video. + +# 4.11. Adversarial Defense + +We tested five adversarial defense methods to defend our attack methods in the digital world, including adversarial training [8], PixelMask [1], Bit squeezing [33], JPEG compression [10] and Total variation minimization [10]. Experiment details for these methods are in SM. The results show that although these methods had a certain defense effect, the ASR of our method still reached $88.83\% - 94.81\%$ after adding defense, which shows that our method is a powerful attack method. + +# 5. Conclusion + +We propose infrared adversarial stickers to hide a real car from infrared detectors at various viewing angles, distances, and scenes in the physical world. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15305-15314, 2022. 2 +[26] Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus. Intriguing properties of neural networks. In Int. Conf. Learn. Represent., 2014. 2 +[27] Simen Thys, Wiebe Van Ranst, and Toon Goedemé. Fooling automated surveillance cameras: Adversarial patches to attack person detection. In IEEE Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops, 2019. 2 + +[28] Donghua Wang, Tingsong Jiang, Jialiang Sun, Weien Zhou, Zhiqiang Gong, Xiaoya Zhang, Wen Yao, and Xiaoqian Chen. Fca: Learning a 3d full-coverage vehicle camouflage for multi-view physical adversarial attack. In Proceedings of the AAAI conference on artificial intelligence, pages 2414–2422, 2022. 2 +[29] Jiakai Wang, Aishan Liu, Zixin Yin, Shunchang Liu, Shiyu Tang, and Xianglong Liu. Dual attention suppression attack: Generate adversarial camouflage in physical world. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8565-8574, 2021. 2 +[30] Hui Wei, Zhixiang Wang, Xuemei Jia, Yinqiang Zheng, Hao Tang, Shin'ichi Satoh, and Zheng Wang. Hotcold block: Fooling thermal infrared detectors with a novel wearable design. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 15233-15241, 2023. 2, 5, 6 +[31] Xingxing Wei, Yao Huang, Yitong Sun, and Jie Yu. Unified adversarial patch for cross-modal attacks in the physical world. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4445-4454, 2023. 2, 6, 7 +[32] Xingxing Wei, Jie Yu, and Yao Huang. Physically adversarial infrared patches with learnable shapes and locations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12334-12342, 2023. 2, 5, 6, 7 +[33] Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. In 25th Annual Network and Distributed System Security Symposium, NDSS, 2018. 8 +[34] Yang Zhang, PD Hassan Foroosh, and Boqing Gong. Camou: Learning a vehicle camouflage for physical adversarial attack on object detections in the wild. ICLR, 2019. 2 +[35] Xiaopei Zhu, Xiao Li, Jianmin Li, Zheyao Wang, and Xiaolin Hu. Fooling thermal infrared pedestrian detectors in real world using small bulbs. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 3616-3624, 2021. 2, 5, 6 +[36] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable DETR: deformable transformers for end-to-end object detection. In Int. Conf. Learn. Represent., 2021. 6, 7 +[37] Xiaopei Zhu, Zhanhao Hu, Siyuan Huang, Jianmin Li, and Xiaolin Hu. Infrared invisible clothing: Hiding from infrared detectors at multiple angles in real world. In IEEE Conf. Comput. Vis. Pattern Recog., 2022. 2, 5, 6 \ No newline at end of file diff --git a/2024/Infrared Adversarial Car Stickers/images.zip b/2024/Infrared Adversarial Car Stickers/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..0f3f4938ba4cc13bfc2da17daef9f503738fa3a3 --- /dev/null +++ b/2024/Infrared Adversarial Car Stickers/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:390041d75c49c7bb515c845a6be183bb87256175038bab54ab07400ab0edc3cc +size 536330 diff --git a/2024/Infrared Adversarial Car Stickers/layout.json b/2024/Infrared Adversarial Car Stickers/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..31b59b63d54e822116cfb75e895f4e337a544dc9 --- /dev/null +++ b/2024/Infrared Adversarial Car Stickers/layout.json @@ -0,0 +1,9306 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 190, + 103, + 402, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 103, + 402, + 119 + ], + "spans": [ + { + "bbox": [ + 190, + 103, + 402, + 119 + ], + "type": "text", + "content": "Infrared Adversarial Car Stickers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "spans": [ + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "Xiaopei Zhu" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": " Yuqiu Liu" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": " Zhanhao Hu" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": " Jianmin Li" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": " Xiaolin Hu" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{4,5,6*}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "School of Integrated Circuits, Tsinghua University, Beijing, China \n" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "Department of Technology, Beijing Forestry University, Beijing, China \n" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "Department of Electrical Engineering and Computer Sciences, UC Berkeley, California, USA \n" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "Department of Computer Science and Technology, Institute for Artificial Intelligence, BNRist, Tsinghua University, Beijing, China \n" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "THBI, IDG/McGovern Institute for Brain Research, Tsinghua University, Beijing, China \n" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "inline_equation", + "content": "^{6}" + }, + { + "bbox": [ + 69, + 141, + 523, + 297 + ], + "type": "text", + "content": "Chinese Institute for Brain Research (CIBR), Beijing, China \n{zxp18}@mail.tsinghua.edu.cn \n{liuyuqiu99, zhanhaohu.cs}@gmail.com \n{lijianmin, xlhu}@mail.tsinghua.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 324, + 191, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 324, + 191, + 337 + ], + "spans": [ + { + "bbox": [ + 143, + 324, + 191, + 337 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "text", + "content": "Infrared physical adversarial examples are of great significance for studying the security of infrared AI systems that are widely used in our lives such as autonomous driving. Previous infrared physical attacks mainly focused on 2D infrared pedestrian detection which may not fully manifest its destructiveness to AI systems. In this work, we propose a physical attack method against infrared detectors based on 3D modeling, which is applied to a real car. The goal is to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles, distances, and scenes. We build a 3D infrared car model with real infrared characteristics and propose an infrared adversarial pattern generation method based on 3D mesh shadow. We propose a 3D control points-based mesh smoothing algorithm and use a set of smoothness loss functions to enhance the smoothness of adversarial meshes and facilitate the sticker implementation. Besides, We designed the aluminum stickers and conducted physical experiments on two real Mercedes-Benz A200L cars. Our adversarial stickers hid the cars from Faster RCNN, an object detector, at various viewing angles, distances, and scenes. The attack success rate (ASR) was " + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "inline_equation", + "content": "91.49\\%" + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "text", + "content": " for real cars. In comparison, the ASRs of random stickers and no sticker were only " + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "inline_equation", + "content": "6.21\\%" + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "inline_equation", + "content": "0.66\\%" + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "text", + "content": ", respectively. In addition, the ASRs of the designed stickers against six unseen object detectors such as YOLOv3 and Deformable DETR were between " + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "inline_equation", + "content": "73.35\\% - 95.80\\%" + }, + { + "bbox": [ + 46, + 350, + 289, + 685 + ], + "type": "text", + "content": ", showing good transferability of the attack performance across detectors." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 324, + 425, + 526 + ], + "blocks": [ + { + "bbox": [ + 307, + 324, + 425, + 526 + ], + "lines": [ + { + "bbox": [ + 307, + 324, + 425, + 526 + ], + "spans": [ + { + "bbox": [ + 307, + 324, + 425, + 526 + ], + "type": "image", + "image_path": "7ee1c75177d4e6b83179ad7c365e6faf0e2ac30d31230988e3d04da0226aeee7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 533, + 545, + 621 + ], + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 621 + ], + "type": "text", + "content": "Figure 1. Infrared attack effect on real cars. (a) Visible light view of real cars. (b) Infrared view of real cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers. The numbers above the bounding boxes are object confidence scores (\\%) with 0.6 threshold. Our adversarial stickers hid the car from Faster RCNN at various viewing angles, distances and scenes. In comparison, the clean car and the car with random shape stickers were detected at the same situation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 425, + 324, + 544, + 526 + ], + "blocks": [ + { + "bbox": [ + 425, + 324, + 544, + 526 + ], + "lines": [ + { + "bbox": [ + 425, + 324, + 544, + 526 + ], + "spans": [ + { + "bbox": [ + 425, + 324, + 544, + 526 + ], + "type": "image", + "image_path": "b9accba057be4dfcdf360fe56174fd42e44ee65a4987cd2bdd7bbaae20236a7e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 644, + 386, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 386, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 386, + 657 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "It is well known that deep learning models can be misled by carefully designed perturbations to the input which is called adversarial example, and the perturbation process is called adversarial attack. Adversarial attacks can be di" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24284" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "vided into two categories, digital attacks [4, 8, 9, 16, 24, 26] which assume that the attackers can directly modify the model input in the digital world, and physical attacks [11, 12, 27, 28, 35, 37] which assume that the attackers can only modify the object or scene in the physical world. Physical attacks have attracted much attention because of their importance of assessing the security of real-world AI systems." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 240 + ], + "type": "text", + "content": "One type of physical attack is called infrared physical attack [30-32, 35, 37]. Infrared imaging is widely used in our daily lives, such as body temperature monitoring and autonomous driving. Since infrared cameras can function normally at night, they are becoming more and more important in autonomous driving systems; so is their safety." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 289, + 443 + ], + "type": "text", + "content": "Previous infrared physical attacks [30-32, 35, 37] mainly focused on infrared pedestrians, and only two works [31, 32] conducted experiments on model cars. There is currently a lack of infrared attack research on real cars. The reasons might be as follows. Compared with pedestrians with constant body temperature, the temperature distributions of real cars are more uneven (e.g., the temperature of the engine is much higher than that of other places), so their infrared characteristics are more complex than pedestrians. Compared with model cars without engines, real cars' structures and materials are very different from those of model cars, so their infrared characteristics are also quite different. Besides, real car attacks require designing and manufacturing adversarial patterns on the entire 3D car surface, which poses a great challenge to physical experiments. But we believe that for the safety of autonomous driving cars, physical real car attack is worth in-depth investigation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "text", + "content": "The aforementioned two infrared model car attacks [31, 32] are only effective within limited viewing angles (e.g., horizontal angles " + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "inline_equation", + "content": "-30^{\\circ} - 30^{\\circ}" + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "text", + "content": " and pitch angle " + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "text", + "content": "). But we want to implement a full-angle attack (the horizontal angles " + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "inline_equation", + "content": "0^{\\circ} - 360^{\\circ}" + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "text", + "content": ", and pitch angle " + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "inline_equation", + "content": "0^{\\circ} - 90^{\\circ}" + }, + { + "bbox": [ + 46, + 444, + 289, + 586 + ], + "type": "text", + "content": "), so the attack angles cover an entire hemisphere surface, which is a challenging task. We also notice that these methods [31, 32] are both case-by-case attacks, which needs to optimize an adversarial pattern for each image1, while our goal is to achieve a universal attack which uses the same adversarial pattern to attack detectors at various viewing angles, distances and scenes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 587, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 289, + 696 + ], + "type": "text", + "content": "Towards this goal, we propose an infrared physical attack method applied to a real car based on 3D modeling. We aim to design a set of infrared adversarial stickers to make cars invisible to infrared detectors at various viewing angles (full-angle), distances and scenes. Since most current 3D car models are visible-light models, and there is a lack of 3D infrared car models, we build a 3D infrared car model with real infrared characteristics at various viewing angles. For the generation of infrared adversarial pattern for stick-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 203 + ], + "type": "text", + "content": "ers, we propose to optimize a 3D adversarial mesh at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern, and finally attach the 2D adversarial pattern to the car surface. The motivation of this mesh shadow attack (MSA) method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. To improve the smoothness of adversarial patterns and facilitate sticker implementation, we propose a 3D control points-based mesh smoothing algorithm and use a set of smoothing loss functions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 204, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 289 + ], + "type": "text", + "content": "For the physical implementation of infrared adversarial patterns, we use an aluminum film which modifies the surface emissivity of the object instead of altering the surface temperature used by previous works [30-32, 35, 37]. Like many car stickers, the adversarial car stickers can be easily attached on the car surface. The stickers are only " + }, + { + "bbox": [ + 304, + 204, + 547, + 289 + ], + "type": "inline_equation", + "content": "0.08\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 204, + 547, + 289 + ], + "type": "text", + "content": " thick and take up almost no space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 289, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 397 + ], + "type": "text", + "content": "To assess the safety of infrared detection in real autonomous driving scenes, we used two real Mercedes-Benz A200L cars. Physical experiments show that our infrared adversarial stickers made the real cars hide from the infrared detector Faster RCNN at various viewing angles, various distances, and multiple scenes, with an attack success rate (ASR) of " + }, + { + "bbox": [ + 304, + 289, + 547, + 397 + ], + "type": "inline_equation", + "content": "91.49\\%" + }, + { + "bbox": [ + 304, + 289, + 547, + 397 + ], + "type": "text", + "content": ". To the best our knowledge, this is the first 3D multi-view physical infrared vehicle attack, and also the first infrared attack conducted on real cars." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 407, + 392, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 392, + 420 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 392, + 420 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 428, + 527, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 428, + 527, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 428, + 527, + 441 + ], + "type": "text", + "content": "2.1. Visible Light Physical Adversarial Attacks" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 447, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 590 + ], + "type": "text", + "content": "Huang et al. [13] proposed a universal physical camouflage (UPC) attack for object detectors. Zhang et al. [34] proposed a vehicle camouflage for physical adversarial attack on object detectors in the wild. Wang et al. [29] proposed the Dual attention suppression (DAS) attack to generate adversarial vehicle camouflage in the physical world. Suryanto et al. [25] generated the physical adversarial camouflage by using a differentiable transformation network. Wang et al. [28] proposed a 3D full-coverage vehicle camouflage for physical adversarial attack (FCA). It is worth noting that all above works are proposed for visible light images." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 599, + 507, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 507, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 507, + 612 + ], + "type": "text", + "content": "2.2. Infrared Physical Adversarial Attacks" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Zhu et al. [35] proposed a bulb-based board to fool infrared pedestrian detectors in the physical world. Zhu et al. [37] proposed an infrared invisible clothing to hide from infrared pedestrian detectors in the physical world. Wei et al. [30] proposed the HotCold blocks to attack the infrared pedestrian detectors. Wei et al. [32] proposed a physical adversarial infrared patch (AIP) based on a points-clustering algorithm. Wei et al. [31] proposed a unified adversar" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 254, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 254, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 254, + 714 + ], + "type": "text", + "content": "1We found this by checking and running their official codes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24285" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 69, + 201, + 153 + ], + "blocks": [ + { + "bbox": [ + 76, + 69, + 201, + 153 + ], + "lines": [ + { + "bbox": [ + 76, + 69, + 201, + 153 + ], + "spans": [ + { + "bbox": [ + 76, + 69, + 201, + 153 + ], + "type": "image", + "image_path": "45dca83f8fdd2c7d96de099d455b0d45fcb6429ce2221a87981a91b0e7516001.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 136, + 157, + 149, + 167 + ], + "lines": [ + { + "bbox": [ + 136, + 157, + 149, + 167 + ], + "spans": [ + { + "bbox": [ + 136, + 157, + 149, + 167 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 203, + 69, + 287, + 153 + ], + "blocks": [ + { + "bbox": [ + 203, + 69, + 287, + 153 + ], + "lines": [ + { + "bbox": [ + 203, + 69, + 287, + 153 + ], + "spans": [ + { + "bbox": [ + 203, + 69, + 287, + 153 + ], + "type": "image", + "image_path": "65907a968717533b5674c2bd7db7731cec0d671ff3d2a33e255b9476b3ff6170.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 244, + 156, + 257, + 167 + ], + "lines": [ + { + "bbox": [ + 244, + 156, + 257, + 167 + ], + "spans": [ + { + "bbox": [ + 244, + 156, + 257, + 167 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 181, + 547, + 204 + ], + "lines": [ + { + "bbox": [ + 46, + 181, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 547, + 204 + ], + "type": "text", + "content": "Figure 2. Construction and optimization of real infrared car texture mapping. (a) Car mesh model. (b) Reorganized faces map. (c) Infrared car texture map collected from real world. (d) Rendered infrared car model." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 291, + 70, + 373, + 153 + ], + "blocks": [ + { + "bbox": [ + 291, + 70, + 373, + 153 + ], + "lines": [ + { + "bbox": [ + 291, + 70, + 373, + 153 + ], + "spans": [ + { + "bbox": [ + 291, + 70, + 373, + 153 + ], + "type": "image", + "image_path": "5e995316c8a5d71f4e40b9ad5ee42e127b5ceffbcbeab401afd72710e0ff1f97.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 327, + 156, + 339, + 167 + ], + "lines": [ + { + "bbox": [ + 327, + 156, + 339, + 167 + ], + "spans": [ + { + "bbox": [ + 327, + 156, + 339, + 167 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 376, + 70, + 518, + 153 + ], + "blocks": [ + { + "bbox": [ + 376, + 70, + 518, + 153 + ], + "lines": [ + { + "bbox": [ + 376, + 70, + 518, + 153 + ], + "spans": [ + { + "bbox": [ + 376, + 70, + 518, + 153 + ], + "type": "image", + "image_path": "e339de33fdd50f8ce70720db392201d69e766d95a2c8ac9f9bc71228eb4ceaf2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 441, + 157, + 454, + 168 + ], + "lines": [ + { + "bbox": [ + 441, + 157, + 454, + 168 + ], + "spans": [ + { + "bbox": [ + 441, + 157, + 454, + 168 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 224, + 288, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 288, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 288, + 284 + ], + "type": "text", + "content": "ial patch (UAP) for physical attacks based on a boundary-limited shape optimization algorithm. It is worth noting that all above methods are proposed for infrared pedestrian or model car attacks. There is currently a lack of research on infrared real vehicle attacks in the physical world." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 297, + 202, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 202, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 202, + 308 + ], + "type": "text", + "content": "3. Car Sticker Attack Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 316, + 288, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 436 + ], + "type": "text", + "content": "Our method consists of several steps. First, we build a 3D infrared car model based on real infrared characteristics. Next, we use the infrared adversarial pattern generation method based on 3D mesh shadow. To make the 3D adversarial mesh smoother, we use a 3D control points-based mesh smoothing algorithm and use a set of smoothness losses. Then we apply adversarial patterns to 3D infrared car model and optimize the adversarial patterns. Finally, we introduce the physical implementation method of infrared adversarial car stickers." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 445, + 231, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 231, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 231, + 458 + ], + "type": "text", + "content": "3.1. Building a 3D Infrared Car Model" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "type": "text", + "content": "To simulate the infrared car attack realistically, we build a 3D model based on the infrared characteristics of a real car. It is worth noting that our method can be applied to any target car, and we chose Mercedes-Benz A200L in our experiments, simply because one of the authors have this car. Figure 2(a) shows the car mesh model " + }, + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{car}}" + }, + { + "bbox": [ + 46, + 464, + 287, + 536 + ], + "type": "text", + "content": ". Next, we need" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 82, + 555, + 251, + 691 + ], + "blocks": [ + { + "bbox": [ + 82, + 555, + 251, + 691 + ], + "lines": [ + { + "bbox": [ + 82, + 555, + 251, + 691 + ], + "spans": [ + { + "bbox": [ + 82, + 555, + 251, + 691 + ], + "type": "image", + "image_path": "a8450625883b13bb5adbbcb32316b20cf947691fd56ed48a51a68fddb6abb8ee.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 699, + 266, + 710 + ], + "lines": [ + { + "bbox": [ + 67, + 699, + 266, + 710 + ], + "spans": [ + { + "bbox": [ + 67, + 699, + 266, + 710 + ], + "type": "text", + "content": "Figure 3. Schematic diagram of mesh shadow method." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 224, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 344 + ], + "type": "text", + "content": "to create a \"skin\" for the car model based on infrared photos taken by an infrared camera FLIR T560. However, the infrared photos captured by the camera are all 2D images, and the challenge is how to \"paste\" these 2D infrared images onto the 3D car mesh model. First, we flatten all the faces of 3D car mesh onto a 2D plane called faces map. After that, we use MAYA software to rearrange these faces to divide different areas, such as roof, doors, etc., as shown in Figure 2(b). This process facilitates the alignment of real infrared car images with the 3D car mesh." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 346, + 546, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 546, + 465 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 546, + 465 + ], + "type": "text", + "content": "Subsequently, we crop the infrared images into different parts based on the faces map (Figure 2(b)) and paste the cropped images onto the 2D faces map, and then we get the infrared texture map of the car, as shown in Figure 2(c). See Supplementary Material (SM) for how these infrared photos are taken, cropped and pasted. This process establishes a correspondence between the real infrared car images and the 3D car mesh. The rendered infrared car model is shown in Figure 2(d), which is built for a real car with engine running." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 477, + 538, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 477, + 538, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 477, + 538, + 489 + ], + "type": "text", + "content": "3.2. Generation of 2D Shadow Based on 3D Mesh" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": "We aim to design infrared stickers with adversarial patterns to hide the cars from infrared detectors at various viewing angles (full-angle), distances, and scenes. We propose a 3D adversarial mesh shadow attack (MSA) method to generate the 2D infrared adversarial patterns for stickers. The motivation of MSA method is that we hope to find a better solution in a higher-dimensional 3D space instead of directly optimizing the 2D adversarial pattern. The core of MSA method is to optimize a 3D adversarial mesh " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": " at first, then project the shadow of 3D adversarial mesh to obtain a 2D adversarial pattern " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": ", and finally attach the 2D adversarial pattern " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": " to the car surface. Note that the 3D adversarial mesh " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": " is different from the 3D car mesh " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{car}}" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": " in Section 3.1. The optimization variables include the 3D mesh vertices coordinates " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": ", the mesh shadowing angle " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": ", and the center point position " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": " when pasting the 2D pattern onto the car's texture map " + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{origin}}" + }, + { + "bbox": [ + 304, + 497, + 545, + 700 + ], + "type": "text", + "content": " (Figure 3)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "The shadowing operation refers to rendering the mesh" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "24286" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 553, + 281 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 553, + 281 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 553, + 281 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 553, + 281 + ], + "type": "image", + "image_path": "253b64bfcfa536d811401f908a95f74536c6ac41a1af84ea690f9ec382032a49.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 196, + 290, + 395, + 302 + ], + "lines": [ + { + "bbox": [ + 196, + 290, + 395, + 302 + ], + "spans": [ + { + "bbox": [ + 196, + 290, + 395, + 302 + ], + "type": "text", + "content": "Figure 4. The overall pipeline of the proposed method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "text", + "content": " to a dark area while retaining the mesh contour (Figure 3), and the dark area has a uniform grayscale value within the contour. The grayscale value is consistent with the infrared characteristics of the sticker we use. Let " + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "text", + "content": " denote this operation. If we want the car to have adversarial effect at various viewing angles, we need to optimize " + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "text", + "content": " adversarial meshes to generate " + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 323, + 288, + 418 + ], + "type": "text", + "content": " adversarial shadows on different places of the car (Figure 4):" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 430, + 287, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 430, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 89, + 430, + 287, + 447 + ], + "type": "interline_equation", + "content": "S _ {\\mathrm {a d v}} ^ {(i)} = \\Omega \\left(M _ {\\mathrm {a d v}} ^ {(i)}, \\varphi^ {(i)}\\right), i = 1, 2, \\dots N. \\tag {1}", + "image_path": "aa842edb52ab1b662395093e4fe72ad33a40eead74845d293ea19bd004e57ee0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "text", + "content": "3.3. 3D Control Points-Based Mesh Smoothing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": "If we directly optimize the vertices coordinates " + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": " of the mesh " + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": ", many \"peaks\" will appear on the mesh surface, which will make the shadow shape very complex and will be difficult for the physical implementation of the adversarial shadow " + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": ". Inspired by the Gaussian smoothing kernel and spline interpolation method, we propose a smoothing control algorithm for 3D mesh vertices. Its core idea is to use some 3D control points " + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": " as anchor points, and the coordinate offsets of mesh vertices " + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": " are expressed as the weighted average of the coordinate offsets of " + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 479, + 287, + 610 + ], + "type": "text", + "content": ". The calculation details are described in SM." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "text", + "content": "We use " + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "text", + "content": " to denote the above transformation, and " + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "inline_equation", + "content": "C^{(i)}" + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "text", + "content": " to denote the control points set of " + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}^{(i)}" + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "text", + "content": ", then" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 650, + 287, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 650, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 104, + 650, + 287, + 664 + ], + "type": "interline_equation", + "content": "V ^ {(i)} = \\Theta (C ^ {(i)}), i = 1, 2, \\dots N. \\tag {2}", + "image_path": "ec63cd9fc1ec2fbc6813d7d1d74c37968ed9272cf33eefc84a705ab84e249056.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Since the control points " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "C^{(i)}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " determine the vertices coordinates " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "V^{(i)}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": ", the optimization variables changes from " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\left(V^{(i)}, P^{(i)}, \\varphi^{(i)}\\right)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\left(C^{(i)}, P^{(i)}, \\varphi^{(i)}\\right)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "i = 1, 2, \\ldots N" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 323, + 485, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 485, + 333 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 485, + 333 + ], + "type": "text", + "content": "3.4. Mesh Smoothness Loss Functions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "content": "To further enhance the smoothness of 3D adversarial mesh " + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "content": " and 2D adversarial pattern " + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "content": ", we use a set of loss functions including: mesh normal consistency loss, mesh edge loss, chamfer distance loss, and Laplacian smoothing loss. During the optimization process of 3D mesh " + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "content": ", these functions guide the generation of a smoother adversarial mesh. A smoother 3D mesh " + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "content": " results in a smoother 2D shadow pattern " + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 340, + 545, + 448 + ], + "type": "text", + "content": ", which is beneficial for manufacturing physical stickers based on the 2D shadow pattern." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "text", + "content": "The mesh normal consistency loss computes the normal consistency for each pair of neighboring faces, and minimizing it encourages the mesh surface to be smoother. We suppose that mesh " + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "text", + "content": " has a total of " + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "text", + "content": " faces. Let " + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "inline_equation", + "content": "n_i, n_j" + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "inline_equation", + "content": "1 \\leq i, j \\leq F" + }, + { + "bbox": [ + 305, + 449, + 545, + 519 + ], + "type": "text", + "content": ") represent the normal vector of any two adjacent faces, then this loss function is described as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 349, + 528, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 528, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 349, + 528, + 545, + 541 + ], + "type": "interline_equation", + "content": "L _ {\\text {n o r m}} = \\text {A v e r a g e} (1 - \\cos \\left(n _ {i}, n _ {j}\\right)). \\tag {3}", + "image_path": "c208000a7c59eb28d06139968232416ca18441c682aaf4014f8bfdec027dd3a8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 548, + 538, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 538, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 538, + 559 + ], + "type": "text", + "content": "Average is calculated between any pair of adjacent faces." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "text", + "content": "The mesh edge loss computes mesh edge length regularization loss, and minimizing it encourages a reduction in the average edge length of the adversarial mesh. Suppose " + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "text", + "content": " has a total of " + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "text", + "content": " edges, " + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "inline_equation", + "content": "l_{k}" + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "inline_equation", + "content": "k = 1,2,\\dots,M" + }, + { + "bbox": [ + 305, + 560, + 545, + 619 + ], + "type": "text", + "content": ") represents the length of each edge, and this loss function is described as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 377, + 626, + 545, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 626, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 377, + 626, + 545, + 659 + ], + "type": "interline_equation", + "content": "L _ {\\text {e d g e}} = \\left(\\sum_ {k = 1} ^ {M} l _ {k}\\right) / M. \\tag {4}", + "image_path": "c51335e3abeef6473376f27ade294119cf715a05bf111737625842690c219f6b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "The chamfer distance loss computes chamfer distance [6] between the sampling points of adversarial mesh and a standard sphere. Reducing chamfer distance loss encourages the adversarial mesh " + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": " to approximate a sphere." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24287" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "We denote the point clouds sampled by adversarial mesh " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " and the standard spherical mesh " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{sphere}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": ", respectively. The chamfer distance loss is described as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 118, + 286, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 118, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 118, + 286, + 156 + ], + "type": "interline_equation", + "content": "L _ {\\text {c h a m f e r}} = \\sum_ {p \\in S _ {1}} \\min _ {q \\in S _ {2}} \\| p - q \\| _ {2} ^ {2} + \\sum_ {q \\in S _ {2}} \\min _ {p \\in S _ {1}} \\| q - p \\| _ {2} ^ {2}. \\tag {5}", + "image_path": "f3732a8e118e552d38292d6b612cbc8c3eb68cea945910316aa52199fc080a9c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 157, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 157, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 157, + 287, + 205 + ], + "type": "text", + "content": "The Laplacian smoothing loss " + }, + { + "bbox": [ + 47, + 157, + 287, + 205 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{Laplace}}" + }, + { + "bbox": [ + 47, + 157, + 287, + 205 + ], + "type": "text", + "content": " computes the Laplacian smoothing objective for the adversarial mesh. We define this function as Laplace, and its calculation details are introduced in [18], so" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 217, + 287, + 230 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 217, + 287, + 230 + ], + "spans": [ + { + "bbox": [ + 107, + 217, + 287, + 230 + ], + "type": "interline_equation", + "content": "L _ {\\text {L a p l a c e}} = \\text {L a p l a c e} \\left(M _ {\\text {a d v}}\\right). \\tag {6}", + "image_path": "69a1ff41e295c8cb6ce0c63a5b19cbff6a2843f3131ddae3a6ceb7f798a6bd2f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 242, + 268, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 242, + 268, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 268, + 255 + ], + "type": "text", + "content": "3.5. Applying the 2D Shadow to 3D Car Model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": "We apply the adversarial shadow " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": " to 3D infrared car model by changing its texture map " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{origin}}" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": ". This simulates the process we paste the adversarial stickers to the car surface in the physical world. To facilitate physical implementation, we simulate to paste the stickers onto the door, roof, front hood and rear of the car, which have wide ranges of flat area and are easy to paste. In each area, we paste one or two adversarial shadow patterns (Figure 4). To simulate real-world perturbations, such as errors in cutting the adversarial stickers, variations in surface temperature on the adversarial stickers, and errors in the pasting positions, we introduce random perturbations to the vertex coordinates " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": " of the adversarial mesh " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": ", random noise to the pattern " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": ", random changes in grayscale values of " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": ", and random perturbations in the position " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": " during the pasting of " + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 261, + 287, + 476 + ], + "type": "text", + "content": ". This approach, known as the Expectation Over Transformation (EOT) algorithm [2], enhances the robustness of our algorithm in real-world scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": "Next, we need to paste the adversarial patterns " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": " onto the original car texture map " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{origin}}" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": " denote the pasting operation. We establish a Cartesian coordinate system with the center point of " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{origin}}" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": " as the origin. We use " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "P^{(i)}" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": " to represent the coordinates of the pasting positions for " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": " adversarial shadows " + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{adv}}^{(i)}, i = 1,2,\\dots N" + }, + { + "bbox": [ + 46, + 478, + 287, + 563 + ], + "type": "text", + "content": ". The texture map after pasting the adversarial shadows is" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 72, + 574, + 287, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 574, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 72, + 574, + 287, + 594 + ], + "type": "interline_equation", + "content": "T _ {\\mathrm {a d v}} = \\Gamma \\left(S _ {\\mathrm {a d v}} ^ {(i)}, P ^ {(i)}, T _ {\\text {o r i g i n}}\\right), i = 1, 2, \\dots N. \\tag {7}", + "image_path": "23be73c22489e2c7bccbdcc9150522cf919f2f621439c924cfb2f30350114ba3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": "We use the differentiable renderer Pytorch3D [20] to render the adversarial texture map " + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": " onto the surface of the car mesh " + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{car}}" + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": ", resulting in the rendered infrared car images with adversarial patterns, denoted as " + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{adv}}" + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": " denote the rendering operation with parameters " + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": " which include the rendering distances and angles. Mathematically, this process can be expressed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 112, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 112, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "I _ {\\mathrm {a d v}} = \\Psi \\left(M _ {\\mathrm {c a r}}, T _ {\\mathrm {a d v}}, \\theta\\right). \\tag {8}", + "image_path": "752e6fb8c6fe675e3f3b11212fcb15f5e41407469a19e704ca336f47bd6ca5fe.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 521, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 521, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 521, + 84 + ], + "type": "text", + "content": "3.6. Optimization of 3D Mesh Shadow Attack" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": "After we get the rendered infrared adversarial images " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": ", we input them into the target detector " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": ". The output of the target detector typically includes object confidence " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{obj}}" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": ", class confidence " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": ", and bounding box " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{bbox}}" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": ". Since our goal is to create a stealthy attack, meaning that our adversarial texture " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": " should make the infrared car hide from the detector, we try to lower the object confidence " + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{obj}}(I_{\\mathrm{adv}})" + }, + { + "bbox": [ + 304, + 90, + 545, + 196 + ], + "type": "text", + "content": " as much as possible. Therefore, the detection loss is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 384, + 198, + 545, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 198, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 384, + 198, + 545, + 211 + ], + "type": "interline_equation", + "content": "L _ {\\text {d e t}} = f _ {\\text {o b j}} \\left(I _ {\\text {a d v}}\\right). \\tag {9}", + "image_path": "73b4eeb6cc8a1a4823eaa583697913740d6ef06c204b165344ebd9b0786c3f95.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 215, + 507, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 215, + 507, + 226 + ], + "spans": [ + { + "bbox": [ + 317, + 215, + 507, + 226 + ], + "type": "text", + "content": "The overall loss function is defined as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 232, + 545, + 261 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 232, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 349, + 232, + 545, + 261 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = L _ {\\text {d e t}} + w _ {1} \\cdot L _ {\\text {n o r m}} + w _ {2} \\cdot L _ {\\text {e d g e}} \\tag {10} \\\\ + w _ {3} \\cdot L _ {\\mathrm {c h a m f e r}} + w _ {4} \\cdot L _ {\\mathrm {L a p l a c e}}. \\\\ \\end{array}", + "image_path": "6626abf8c470bab1d7a09416b732dd8a8eff3e123e22f5f69a1b380bd06abaf2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "inline_equation", + "content": "w_{1}, w_{2}, w_{3}" + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "inline_equation", + "content": "w_{4}" + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "content": " are weights of different losses, which are determined empirically. We use the backpropagation algorithm according to the loss function " + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "content": " to update the optimization variables " + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "inline_equation", + "content": "C^{(i)}, P^{(i)}, \\varphi^{(i)}, i = 1, 2, \\ldots, N" + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "content": ". The overall pipeline is illustrated in Figure 4." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 335, + 484, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 484, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 484, + 346 + ], + "type": "text", + "content": "3.7. Physical Implementation Method" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 353, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 508 + ], + "type": "text", + "content": "We use aluminum films to make adversarial car stickers. Instead of altering the surface temperature of an object, this approach focuses on modifying the surface emissivity of the object, which is different from previous works [30-32, 35, 37]. Aluminum typically has an emissivity around 0.1, while the surface of a car, typically made of steel, has an emissivity around 0.8, resulting in different infrared characteristics. We utilize an ultra-thin (only " + }, + { + "bbox": [ + 304, + 353, + 545, + 508 + ], + "type": "inline_equation", + "content": "0.08\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 353, + 545, + 508 + ], + "type": "text", + "content": ") aluminum film, which can be easily attached on the surface of a car like many car stickers. We only need around 13 mins to make a sticker, and the cost of a sticker is only around 0.2 USD. The implementation process of adversarial stickers is shown in Supplementary Video 1." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 518, + 386, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 386, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 386, + 532 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 538, + 364, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 364, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 364, + 549 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 556, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 640 + ], + "type": "text", + "content": "We used the FLIR_ADAS_1_3 [7] infrared dataset released by FLIR company for infrared autonomous driving scenes. It contains 10,228 real infrared photos collected in streets and highways of Santa Barbara, USA. The infrared camera is FLIR Tau2. The training set contains 7160 images, and the test set contains 3068 images. We used this dataset to finetune the target detector." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 647, + 406, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 406, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 406, + 659 + ], + "type": "text", + "content": "4.2. Target Detectors" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We initially chose the classic two-stage object detector: Faster R-CNN [22], as our primary target detector. We used the pre-trained Faster RCNN model provided by the torchvision library [17] and then finetuned it on the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24288" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 93, + 91, + 501, + 190 + ], + "blocks": [ + { + "bbox": [ + 158, + 70, + 435, + 82 + ], + "lines": [ + { + "bbox": [ + 158, + 70, + 435, + 82 + ], + "spans": [ + { + "bbox": [ + 158, + 70, + 435, + 82 + ], + "type": "text", + "content": "Table 1. ASRs (%) of cars with different textures against different detectors." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 93, + 91, + 501, + 190 + ], + "lines": [ + { + "bbox": [ + 93, + 91, + 501, + 190 + ], + "spans": [ + { + "bbox": [ + 93, + 91, + 501, + 190 + ], + "type": "table", + "html": "
Detector TextureFasterRetinaNetCascadeLibraSSDYOLOv3Deformable
Origin2.104.4918.8616.4715.2725.1512.28
Random shape18.2617.0723.9528.7445.8150.0023.65
AIP14.9715.2732.9327.5423.6538.3227.54
UAP20.0631.4438.0233.2336.8339.8224.25
Ours96.3186.8373.3579.0495.8086.5283.83
", + "image_path": "1442227b6ff03203731bd9c3841d495847ffe7bd7697a4ed4ab672662f71ddb1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 208, + 287, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 208, + 287, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 287, + 292 + ], + "type": "text", + "content": "FLIR_ADAS_1_3 dataset. The average precision (AP) for car class of the finetuned model on the training set was 0.96, and the AP on the test set was 0.92. After attacking Faster RCNN in a white-box setting, we transferred our attack method to other unseen detectors such as YOLOv3 [21], Deformable DETR [36], etc. which were provided by mmdetection library [5] in a black-box setting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 300, + 160, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 160, + 311 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 160, + 311 + ], + "type": "text", + "content": "4.3. Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 318, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 448 + ], + "type": "text", + "content": "In our experiments, we used the attack success rate (ASR) as the evaluation metrics of the attack methods. The ASR was defined as the ratio of the number of cars which were not detected to the total number of cars. We set the confidence threshold of target detectors to 0.6 and the IOU threshold between the prediction box and ground truth to 0.5, similar to previous works [31, 32, 35, 37]. The ASR was calculated based on the average value of sample points collected from various distances, horizontal angles, and pitch angles with the sampling method described in Section 4.4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 457, + 264, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 264, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 264, + 470 + ], + "type": "text", + "content": "4.4. Attack Faster RCNN in the Digital World" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "content": "We optimized " + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "content": " adversarial shadow patterns to simulate 5 adversarial stickers to be pasted on the car surface." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 50, + 518, + 286, + 654 + ], + "blocks": [ + { + "bbox": [ + 50, + 518, + 286, + 654 + ], + "lines": [ + { + "bbox": [ + 50, + 518, + 286, + 654 + ], + "spans": [ + { + "bbox": [ + 50, + 518, + 286, + 654 + ], + "type": "image", + "image_path": "37025c724ba623d71180afce0a70ba3380b8932e72eb459628eeb2d6adde00e5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 666, + 287, + 709 + ], + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 709 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 709 + ], + "type": "text", + "content": "Figure 5. Examples of detection results of different detectors for target cars with different textures. The numbers above the red bounding boxes are the object confidence scores, with a threshold of 0.6. The results of other detectors are shown in SM." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "type": "text", + "content": "The hyper-parameters are detailed in SM. After optimization, we obtained the adversarial shadow patterns (" + }, + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "type": "text", + "content": " in Figure 4), and the rendered car with adversarial shadow patterns (" + }, + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 208, + 545, + 256 + ], + "type": "text", + "content": " in Figure 4)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "text", + "content": "After that, we evaluated the attack effectiveness of the adversarial shadow patterns. For a fair comparison, we employed the original car pattern (without any sticker) and random shape pattern as control patterns. The figures of these patterns are shown in SM. These patterns were rendered onto the same car model, and the resulting images were input into Faster R-CNN. The results, as shown in Table 1, indicate that our adversarial shadow patterns achieved an ASR of " + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "inline_equation", + "content": "96.31\\%" + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "text", + "content": " for Faster R-CNN in the digital world. In comparison, the ASRs for the original car pattern and random shape pattern were only " + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "inline_equation", + "content": "2.10\\%" + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "inline_equation", + "content": "18.26\\%" + }, + { + "bbox": [ + 304, + 257, + 546, + 411 + ], + "type": "text", + "content": ", respectively. This demonstrates the effectiveness of our attack method. Figure 5 shows typical examples." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 412, + 546, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 546, + 662 + ], + "type": "text", + "content": "We then analyze the ASR of our method at various (full-angle) viewing angles and distances. The horizontal angle azimuth ranged from 0 to 360 degrees, and we sampled it every 20 degrees. The pitch angle elev ranged from 0 to 90 degrees, and we sampled it every 6 degrees. The distance dist ranged from 1 to 8 meters, and we sampled it every 1 meter. Figure 6(b-d) show the ASRs with respect to one variable (e.g., dist) by taking the average of ASRs over all combinations of values of the other two variables (e.g., elev and azimuth). The results indicate that our approach achieves successful attacks at various (full-angle) viewing angles and various distances. In contrast, many previous works [30-32, 35] were effective only within limited viewing angles (e.g., horizontal angle from -30 to 30 degrees and pitch angle 0 degree) and shorter distances (e.g. 3 to 6 meters). Note that there is a decrease in ASR at 2 meters and 0(or 180)-degree horizontal angle. This suggests that Faster RCNN is more robust in these specific scenes, potentially due to the distribution of training images. Nevertheless, for the majority of viewing angles and distances, the ASRs of our method consistently exceeded " + }, + { + "bbox": [ + 304, + 412, + 546, + 662 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 412, + 546, + 662 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 671, + 399, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 399, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 399, + 684 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "To evaluate the effectiveness of the 3D control points-based mesh smoothing algorithm (CMS) and a set of smoothing" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24289" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 74, + 189, + 162 + ], + "blocks": [ + { + "bbox": [ + 65, + 74, + 189, + 162 + ], + "lines": [ + { + "bbox": [ + 65, + 74, + 189, + 162 + ], + "spans": [ + { + "bbox": [ + 65, + 74, + 189, + 162 + ], + "type": "image", + "image_path": "e0b6b9b57a75f5da399713849c47c7090dff7915203dc674f54c1386155618f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 117, + 168, + 133, + 181 + ], + "lines": [ + { + "bbox": [ + 117, + 168, + 133, + 181 + ], + "spans": [ + { + "bbox": [ + 117, + 168, + 133, + 181 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 194, + 70, + 312, + 165 + ], + "blocks": [ + { + "bbox": [ + 194, + 70, + 312, + 165 + ], + "lines": [ + { + "bbox": [ + 194, + 70, + 312, + 165 + ], + "spans": [ + { + "bbox": [ + 194, + 70, + 312, + 165 + ], + "type": "image", + "image_path": "034cea65b171e06c58fdad1c682494c2b1abbf2b3af99b7e5127deb39f2751b7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 243, + 170, + 259, + 183 + ], + "lines": [ + { + "bbox": [ + 243, + 170, + 259, + 183 + ], + "spans": [ + { + "bbox": [ + 243, + 170, + 259, + 183 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 321, + 70, + 417, + 165 + ], + "blocks": [ + { + "bbox": [ + 321, + 70, + 417, + 165 + ], + "lines": [ + { + "bbox": [ + 321, + 70, + 417, + 165 + ], + "spans": [ + { + "bbox": [ + 321, + 70, + 417, + 165 + ], + "type": "image", + "image_path": "27d747eb3ac065d6feac71802a53ac319dd055ca87aca7361be6e14d0811dec5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 359, + 171, + 373, + 183 + ], + "lines": [ + { + "bbox": [ + 359, + 171, + 373, + 183 + ], + "spans": [ + { + "bbox": [ + 359, + 171, + 373, + 183 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 428, + 70, + 526, + 166 + ], + "blocks": [ + { + "bbox": [ + 428, + 70, + 526, + 166 + ], + "lines": [ + { + "bbox": [ + 428, + 70, + 526, + 166 + ], + "spans": [ + { + "bbox": [ + 428, + 70, + 526, + 166 + ], + "type": "image", + "image_path": "10be2295814f8d363a7a4f4afde244cba95b09d002ef6ee0b292caf60724f35b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 466, + 170, + 482, + 183 + ], + "lines": [ + { + "bbox": [ + 466, + 170, + 482, + 183 + ], + "spans": [ + { + "bbox": [ + 466, + 170, + 482, + 183 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 198, + 545, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 545, + 210 + ], + "type": "text", + "content": "Figure 6. Full-angle ASRs at different (a) parameters including (b) distances, (c) pitch angles, and (d) horizontal angles. See text for details." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 230, + 289, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 351 + ], + "type": "text", + "content": "losses (SMLS), we performed ablation experiments. We conducted a subjective evaluation on the smoothness score of the 3D adversarial mesh and 2D adversarial pattern and we also evaluated the physical implementation time of 2D adversarial patterns under different settings. The experimental settings and results are detailed in SM. The results indicate that both CMS and SMLS improved the smoothness of adversarial meshes and patterns, and their combination was better. Besides, these methods effectively reduced the physical implementation time of adversarial patterns." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 357, + 274, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 274, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 274, + 370 + ], + "type": "text", + "content": "4.6. Exploring the Interpretability of the Attack" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 376, + 288, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 423 + ], + "type": "text", + "content": "To gain deeper insights into our attack methods, we utilized the GradCAM [23] technique to analyze the changes in network attention maps before and after the attack. See SM for more details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 431, + 276, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 276, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 276, + 445 + ], + "type": "text", + "content": "4.7. Comparison with 2D Optimization Methods" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 450, + 287, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 535 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 535 + ], + "type": "text", + "content": "We extended the previous 2D infrared model car attack methods [31, 32] to our 3D car model. We generated adversarial car textures on our car model based on their papers and codes, which are shown in SM. Following the settings in Section 4.4, we evaluated the attack performance of the different methods. The statistics of ASRs are presented in Table 1, with typical examples shown in Figure 5." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 48, + 552, + 162, + 660 + ], + "blocks": [ + { + "bbox": [ + 48, + 552, + 162, + 660 + ], + "lines": [ + { + "bbox": [ + 48, + 552, + 162, + 660 + ], + "spans": [ + { + "bbox": [ + 48, + 552, + 162, + 660 + ], + "type": "image", + "image_path": "9b36a7883b49c5e57f4a3517f69963159d73b0272a326d2ac54943c43edd73fa.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 661, + 116, + 668 + ], + "lines": [ + { + "bbox": [ + 107, + 661, + 116, + 668 + ], + "spans": [ + { + "bbox": [ + 107, + 661, + 116, + 668 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 677, + 288, + 710 + ], + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 710 + ], + "type": "text", + "content": "Figure 7. Infrared attack effect on model cars. (a) Visible light view of model cars. (b) Infrared view of model cars. C: clean car. R: car with random shape stickers. A: car with adversarial stickers." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 163, + 552, + 287, + 660 + ], + "blocks": [ + { + "bbox": [ + 163, + 552, + 287, + 660 + ], + "lines": [ + { + "bbox": [ + 163, + 552, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 163, + 552, + 287, + 660 + ], + "type": "image", + "image_path": "b5458f470d8c2c89a18811bc996c4baadcdaf1099ad0cc8bba224071f23fd9b0.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 215, + 661, + 224, + 668 + ], + "lines": [ + { + "bbox": [ + 215, + 661, + 224, + 668 + ], + "spans": [ + { + "bbox": [ + 215, + 661, + 224, + 668 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "text", + "content": "The results indicated that the ASR of our method " + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "inline_equation", + "content": "(96.31\\%)" + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "text", + "content": " outperformed the ASRs of two alternative methods " + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "inline_equation", + "content": "(14.97\\%" + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "inline_equation", + "content": "20.06\\%)" + }, + { + "bbox": [ + 304, + 230, + 547, + 386 + ], + "type": "text", + "content": " for Faster RCNN in the digital world. The reasons may be as follows. The two 2D optimization methods based on boundary optimization [31] or points clustering [32] are subject to various constraints. These constraints are used to ensure that, for example, the boundary curves do not have overlaps [31], and the adversarial patterns do not split into multiple pieces [32]. With more constraints, the feasible solution space becomes smaller. However, our 3D mesh shadow approach does not have such constraints, and we can explore a larger solution space, leading to better results." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 393, + 433, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 433, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 433, + 406 + ], + "type": "text", + "content": "4.8. Attack Transferability" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "type": "text", + "content": "We tested the effectiveness of our adversarial car texture " + }, + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "type": "inline_equation", + "content": "(T_{\\mathrm{adv}}" + }, + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "type": "text", + "content": " in Figure 4) optimized for Faster RCNN against other unseen detectors, including RetinaNet [14], Cascade RCNN [3], Libra RCNN [19], SSD [15], YOLOv3 [21] and Deformable DETR [36]. It is worth noting that these experiments were performed in a black-box setting, which is a more challenging but practically significant scene for real-world applications. The results are shown in Table 1. The ASRs of our method against unseen models reached " + }, + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "type": "inline_equation", + "content": "73.35\\% - 95.80\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 591 + ], + "type": "text", + "content": ". It indicates that our method performed well in a black-box setting and had good attack transferability to unseen models including not only CNN-based models but also transformer-based models. Besides, the transferability of our method is stronger than not only two simple baselines but also two infrared attack methods [31, 32]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 599, + 479, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 479, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 479, + 612 + ], + "type": "text", + "content": "4.9. 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We used a rotating turntable to conve" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24290" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 181, + 156 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 181, + 156 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 181, + 156 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 181, + 156 + ], + "type": "image", + "image_path": "667023f967c1f65b7b5ff5de6d4d020dea067f35f785269cb965b62c78af2156.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 66, + 158, + 180, + 243 + ], + "blocks": [ + { + "bbox": [ + 66, + 158, + 180, + 243 + ], + "lines": [ + { + "bbox": [ + 66, + 158, + 180, + 243 + ], + "spans": [ + { + "bbox": [ + 66, + 158, + 180, + 243 + ], + "type": "image", + "image_path": "1995226415bce4756f76de724cca6189d4d18314060000ec9d137c56780de227.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 251, + 527, + 262 + ], + "lines": [ + { + "bbox": [ + 64, + 251, + 527, + 262 + ], + "spans": [ + { + "bbox": [ + 64, + 251, + 527, + 262 + ], + "type": "text", + "content": "Figure 8. Examples of infrared real car attacks. C: clean car. R: car with random shape stickers. 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The infrared camera was FLIR T560. We utilized the same Faster RCNN detector as in Section 4.4. The detection results indicated that our adversarial stickers achieved an ASR of " + }, + { + "bbox": [ + 46, + 284, + 289, + 416 + ], + "type": "inline_equation", + "content": "84.86\\%" + }, + { + "bbox": [ + 46, + 284, + 289, + 416 + ], + "type": "text", + "content": " on the 1:24 scale car model in the physical world. In comparison, the clean car and the car with random patterns had ASRs of only " + }, + { + "bbox": [ + 46, + 284, + 289, + 416 + ], + "type": "inline_equation", + "content": "19.08\\%" + }, + { + "bbox": [ + 46, + 284, + 289, + 416 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 284, + 289, + 416 + ], + "type": "inline_equation", + "content": "35.37\\%" + }, + { + "bbox": [ + 46, + 284, + 289, + 416 + ], + "type": "text", + "content": ", respectively. Figure 7 provides specific examples from the physical world experiments. A demo video for physical model car attacks is shown in Supplementary Video 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 428, + 217, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 428, + 217, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 428, + 217, + 441 + ], + "type": "text", + "content": "4.10. Physical Attacks on Real Cars" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "text", + "content": "We conducted physical experiments on two real Mercedes-Benz A200L cars (one black one white). It was a sunny day with a temperature of about " + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "inline_equation", + "content": "25^{\\circ}\\mathrm{C}" + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "text", + "content": ". For a fair comparison, we pasted the adversarial stickers, randomly cut-shaped stickers or nothing on the same car successively. We recorded 30 videos (each video is around 2 minutes) and sampled 3688 infrared images of these cars from various angles and distances in both ground and underground parking lots using a FLIR T560 camera. The height of the camera tripod can be adjusted from " + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "inline_equation", + "content": "1\\mathrm{m}" + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "inline_equation", + "content": "2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 449, + 287, + 580 + ], + "type": "text", + "content": ". We sent these images to Faster RCNN." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "The results indicated that our adversarial stickers achieved an ASR of " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "91.49\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " on the real cars with the engines running, while the random shape stickers and no sticker had ASRs of only " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "6.21\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "0.66\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ", respectively. When the engines were off for one hour, the ASR of adversarial stickers dropped a little to " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "88.42\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ". The reason might be that the infrared patterns of adversarial stickers with engines off were not as clear as the patterns with engines running. However, the ASR of adversarial stickers were still better than ASR of random shape stickers " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "(5.72\\%)" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " and no sticker " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "(1.86\\%)" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " when the engines were off. Figure 1" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 284, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 344 + ], + "type": "text", + "content": "and Figure 8 show some examples. There were a few other cars that passed by or were parked when we were recording videos and therefore appeared in our photos, which were also detected. See Supplementary Video 3 for the demo video." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 350, + 429, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 429, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 429, + 361 + ], + "type": "text", + "content": "4.11. Adversarial Defense" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 368, + 546, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 546, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 546, + 475 + ], + "type": "text", + "content": "We tested five adversarial defense methods to defend our attack methods in the digital world, including adversarial training [8], PixelMask [1], Bit squeezing [33], JPEG compression [10] and Total variation minimization [10]. Experiment details for these methods are in SM. The results show that although these methods had a certain defense effect, the ASR of our method still reached " + }, + { + "bbox": [ + 304, + 368, + 546, + 475 + ], + "type": "inline_equation", + "content": "88.83\\% - 94.81\\%" + }, + { + "bbox": [ + 304, + 368, + 546, + 475 + ], + "type": "text", + "content": " after adding defense, which shows that our method is a powerful attack method." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 484, + 379, + 497 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 484, + 379, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 484, + 379, + 497 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 505, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 649 + ], + "type": "text", + "content": "We propose infrared adversarial stickers to hide a real car from infrared detectors at various viewing angles, distances, and scenes in the physical world. We build a 3D infrared car model with real infrared characteristics and propose a 3D mesh shadow method for the generation of infrared adversarial pattern. To make the 3D adversarial mesh smoother, we propose a 3D control points-based smoothing algorithm and use a set of smoothness loss functions. Our adversarial stickers enabled two real cars to evade Faster RCNN at various viewing angles, distances and scenes. Besides, our method has strong attack transferability against multiple unseen detectors in a black-box setting." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 658, + 421, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 658, + 421, + 671 + ], + "spans": [ + { + "bbox": [ + 305, + 658, + 421, + 671 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China (Nos. 61734004, U2341228, U19B2034)." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24291" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Akshay Agarwal, Mayank Vatsa, Richa Singh, and Nalini Ratha. 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Pattern Recog., 2022. 2, 5, 6" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24293" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_content_list.json b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..28866e2405f571bc4f0b28089424d3c0185fed28 --- /dev/null +++ b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_content_list.json @@ -0,0 +1,1624 @@ +[ + { + "type": "text", + "text": "Infrared Small Target Detection with Scale and Location Sensitivity", + "text_level": 1, + "bbox": [ + 143, + 130, + 825, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qiankun Liu $^{1}$ Rui Liu $^{1,2}$ Bolun Zheng $^{3}$ Hongkui Wang $^{3}$ Ying Fu $^{1,2*}$ $^{1}$ Beijing Institute of Technology $^{2}$ Yangtze Delta Region Academy of Beijing Institute of Technology $^{3}$ Hangzhou Dianzi University", + "bbox": [ + 86, + 178, + 893, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{liuqk3, liurui20}@bit.edu.cn, {blzheng, wanghk}@hdu.edu.cn, fuying@bit.edu.cn", + "bbox": [ + 143, + 234, + 830, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, infrared small target detection (IRSTD) has been dominated by deep-learning-based methods. However, these methods mainly focus on the design of complex model structures to extract discriminative features, leaving the loss functions for IRSTD under-explored. For example, the widely used Intersection over Union (IoU) and Dice losses lack sensitivity to the scales and locations of targets, limiting the detection performance of detectors. In this paper, we focus on boosting detection performance with a more effective loss but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses: 1) for scale sensitivity, we compute a weight for the IoU loss based on target scales to help the detector distinguish targets with different scales; 2) for location sensitivity, we introduce a penalty term based on the center points of targets to help the detector localize targets more precisely. Then, we design a simple Multi-Scale Head to the plain U-Net (MSHNet). By applying SLS loss to each scale of the predictions, our MSHNet outperforms existing state-of-the-art methods by a large margin. In addition, the detection performance of existing detectors can be further improved when trained with our SLS loss, demonstrating the effectiveness and generalization of our SLS loss. The code is available at https://github.com/ying-fu/MSHNet.", + "bbox": [ + 76, + 318, + 473, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Infrared small target detection (IRSTD) is an important computer vision task, which has a wide range of applications, such as maritime surveillance [20, 34], traffic management [26, 27, 30] and so on. However, due to the long-distance camera capture, and the noise and clutter interference, infrared targets are often small and dim, making it difficult to detect infrared small targets effectively.", + "bbox": [ + 75, + 753, + 468, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enhance the detection performance of infrared small", + "bbox": [ + 96, + 859, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3e20815e9c661f3c3b80f9e0351b6946e7ffe434f9f3f28dcd02fd9dc1356aeb.jpg", + "image_caption": [ + "Figure 1. Visualization of the detection performance (IoU), inference time consumption (Images/second) as well as the number of floating point of operations (area of circles) of some deep-learning-based methods. It can be seen that our MSHNet achieves a better balance between these three metrics than other methods. Results are evaluated on IRSTD-1k [30]." + ], + "image_footnote": [], + "bbox": [ + 501, + 285, + 893, + 457 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "targets, numerous methods have been proposed. Early traditional methods can be divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10], and low-rank-based methods [2, 28, 29, 31]. However, these traditional methods rely on manually designed features, and thus can not generalize well to environment changes. Recently, with the development of Deep Learning (DL), IRSTD has been dominated by DL-based methods [1, 15, 21, 24]. Different from traditional methods, DL-based methods can automatically learn useful features through a gradient descent algorithm with the constraints of loss functions, making them more robust to various scenarios.", + "bbox": [ + 496, + 580, + 893, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, existing DL-based methods primarily focus on designing complex model structures for feature extraction, leaving the loss functions for IRSTD under-explored. For instance, Li et.al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion, and Wu et.al. [25] nest the U-Net structure to achieve feature aggregation. Although discriminative features can be extracted by the complex model structures, the detection performance is still limited by the under-explored loss functions. For ex", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 1, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17490", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ample, the widely used Intersection over Union (IoU) loss and Dice loss [18] lack sensitivity to the scales and locations of targets. As shown in Fig. 2, targets with different scales (top row) and locations (bottom row) may share the same IoU loss or Dice loss. This insensitivity to scales and locations makes it challenging for detectors to distinguish targets of different scales and locations, which ultimately limits the detection performance.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we focus on boosting detection performance with a more effective loss function but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses. The merits of the proposed SLS loss include: (1) Scale sensitivity. We compute a weight for the IoU loss based on the predicted and ground-truth scales of targets. The larger the gap between predicted and ground-truth scales is, the more attention will be paid by the detector. (2) Location Sensitivity. We design a location penalty based on the predicted and ground-truth center points of targets. Compared with traditional L1 and L2 distances, the designed location penalty produces the same value for fewer different location errors, making the detector locate targets more precisely. Then, we introduce a simple Multi-Scale Head to the plain U-Net (MSHNet), which produces multiscale predictions for each input. Through leveraging SLS loss at different scales, our MSHNet outperforms existing state-of-the-art (SOTA) methods by a large margin. With the absence of complex structures, our detector achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption, as shown in Fig. 1. Moreover, we further train different existing detectors with our SLS loss and achieve better detection performance, demonstrating the effectiveness and generalization of our SLS loss.", + "bbox": [ + 75, + 218, + 472, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are:", + "bbox": [ + 96, + 618, + 364, + 632 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel scale and location sensitive loss for infrared small target detection, which helps detectors distinguish objects with different scales and locations.", + "- We propose a simple but effective detector by introducing a multi-scale head to the plain U-Net, which achieves SOTA performance without bells and whistles.", + "- We apply our loss to existing detectors and show that the detection performance can be further boosted, demonstrating the effectiveness and generalization of our loss." + ], + "bbox": [ + 76, + 638, + 468, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 806, + 218, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we first make a brief introduction to existing methods for IRSTD. Then we provide a review of related works from the perspectives of loss functions and model structures for IRSTD.", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a8cee4a84ad70e1e7b862bc3d824ff324e5da3c662db7cd91382b951ad3a9fc8.jpg", + "image_caption": [ + "$\\mathcal{L}_{SLS} = 0.94$" + ], + "image_footnote": [], + "bbox": [ + 514, + 90, + 602, + 143 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c432f4f31bb60deeacd71c532f50ac3ecf7ea86a35b89106d5aa0f7fd301ad80.jpg", + "image_caption": [ + "$\\mathcal{L}_{SLS} = 0.97$" + ], + "image_footnote": [], + "bbox": [ + 669, + 99, + 723, + 133 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/21c6c2487c900d1f6fad41fe0169d1ebed21acfdc0e94911cf1e837479b298a0.jpg", + "image_caption": [ + "$\\mathcal{L}_{SLS} = 0.92$" + ], + "image_footnote": [], + "bbox": [ + 794, + 90, + 875, + 143 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/493150219f3d330f1ecbb562442f2710b5d0f93efe4c7936da7d2210cbd5b633.jpg", + "image_caption": [ + "$\\mathcal{L}_{SLS} = 0.62$" + ], + "image_footnote": [], + "bbox": [ + 514, + 180, + 611, + 217 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c0ce9e9aefbd1d43777652542cfbb149d3220dd7d225f41eab89e15bc8edade4.jpg", + "image_caption": [ + "$\\mathcal{L}_{SLS} = 0.64$" + ], + "image_footnote": [], + "bbox": [ + 653, + 176, + 741, + 222 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b1fc21b97ec3cd3475c18b0ca174e6848308516ba6b7c83db3826a206ff9c335.jpg", + "image_caption": [ + "$\\mathcal{L}_{SLS} = 0.59$", + "Figure 2. Top row: our SLS loss for the targets of different scales, where IoU loss $(=0.4)$ and Dice loss $(=0.57)$ have the same values for different cases. Bottom row: our SLS loss for the targets of different locations, where IoU loss $(=0.3)$ and Dice loss $(=0.43)$ have the same values for different cases." + ], + "image_footnote": [], + "bbox": [ + 784, + 176, + 874, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Infrared Small Target Detection", + "text_level": 1, + "bbox": [ + 500, + 342, + 782, + 358 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing IRSTD methods can be roughly divided into traditional methods and Deep-Learning-based (DL-based) methods. Among them, traditional methods depend on the hand-crafted priors and can be further divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10, 12], and low-rank-based methods [2, 6, 8, 19, 28, 29, 32]. To get useful features with such hand-crafted priors, lots of hyperparameters need to be manually fine-tuned, making them less robust to the interference of noises and clutters. Differently, DL-based methods [3, 7, 14, 15, 21, 25, 30, 33] can automatically learn useful features with the help of loss functions and gradient descent algorithms. Though impressive detection performance has been achieved, existing DL-based methods mainly focus on the design of model structures for the pursuit of more effective features, leaving the loss functions for IRSTD under-explored.", + "bbox": [ + 496, + 366, + 890, + 608 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from existing DL-based methods, we focus on boosting detection performance with a more effective loss function but a simpler model structure. A better balance between detection performance, FLOPs and inference time consumption can be achieved.", + "bbox": [ + 496, + 609, + 890, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Loss Functions for IRSTD", + "text_level": 1, + "bbox": [ + 500, + 695, + 736, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As one of the components in DL-based methods, the loss function plays a critical role in the learning process of deep models by quantifying the disparity between predictions and ground-truths. The commonly adopted IoU loss and Dice loss [18] suffer from insensitivity to the scales and locations of targets, rendering the detectors for distinguishing the targets of different scales and locations accurately.", + "bbox": [ + 496, + 719, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to achieve better detection performance, researchers have developed several loss functions. For example, the loss for adversarial training [21], edge loss for the detecting of target edges [30] and the likelihood loss between target and background maps [11]. However, these", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17491", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a3900cf293ec5a3ced48697cc45d67611670668830188763afb50eb84a6f8629.jpg", + "image_caption": [ + "Figure 3. Left: the value of weight $w$ in scale sensitive loss with respect to the number of predicted pixels and ground-truth pixels (i.e., predicted and ground-truth scales). Right: the normalized location sensitive loss with respect to the location error between the predicted center point and ground-truth center point. The range of [0, 100] pixels is shown for illustration." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 467, + 205 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "losses are tailored for specific network architectures, limiting their broader utility. Different from these dedicated losses, the generalized IoU (GIoU) [16] and complete IoU (CIoU) [35] losses have been adopted for box-level IRSTD [13, 23]. However, these IoU variant losses still lack the sensitivity of scales and locations.", + "bbox": [ + 75, + 330, + 468, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to these losses, we formulate a general loss function that is better suitable for IRSTD. It can distinguish targets of different scales and locations, enabling different detectors to achieve better detection performance.", + "bbox": [ + 75, + 421, + 470, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Model Structures for IRSTD", + "text_level": 1, + "bbox": [ + 76, + 491, + 334, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The deep model is another key component in DL-based methods. Liu et al. [15] pioneer the application of deep learning to IRSTD. The adopted five-layer Multi-Layer Perceptron (MLP) network demonstrates the superiority of DL-based methods in IRSTD. Recently, lots of works have focused on the design of model structures to get more effective features. Li et al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion. Zhang et al. [30] utilize Taylor finite difference and orientation attention strategy to extract edge information of targets. However, such complex model structures not only bring more computational cost but still suffer from moderate detection performance due to the lack of effective loss functions.", + "bbox": [ + 75, + 513, + 468, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Differently we introduce a simple multi-scale head to the plain U-Net, rather than designing complex structures. By applying our SLS loss to different scales, SOTA performance is achieved with less time consumption.", + "bbox": [ + 75, + 710, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Scale and Location Sensitive Loss", + "text_level": 1, + "bbox": [ + 76, + 786, + 382, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The scale and location sensitive (SLS) loss, denoted as $\\mathcal{L}_{\\text{SLS}}$ , is designed to handle the insensitivity of scales and locations in existing losses. It consists of a scale sensitive loss and a location sensitive loss. Formally,", + "bbox": [ + 76, + 811, + 470, + 873 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S L S} = \\mathcal {L} _ {S} + \\mathcal {L} _ {L}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 885, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_S$ and $\\mathcal{L}_L$ present the scale sensitive loss and location sensitive loss, respectively. In the following, we introduce the SLS loss in detail starting from the scale sensitive loss, which is based on the commonly used IoU loss.", + "bbox": [ + 496, + 90, + 892, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Scale Sensitive Loss", + "text_level": 1, + "bbox": [ + 498, + 160, + 689, + 174 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $A_{p}$ and $A_{gt}$ be the set of predicted pixels and ground-truth pixels of targets, the IoU loss between them can be formulated as:", + "bbox": [ + 496, + 183, + 892, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I o U} = 1 - \\frac {\\left| A _ {p} \\cap A _ {g t} \\right|}{\\left| A _ {p} \\cup A _ {g t} \\right|}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 234, + 892, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Though having been widely used in IRSTD, the IoU loss is insensitive to the scales and locations of targets, as shown in Fig. 2. The scale sensitive loss is implemented by providing a weight to the IoU loss:", + "bbox": [ + 496, + 276, + 890, + 337 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S} = 1 - w \\frac {\\left| A _ {p} \\cap A _ {g t} \\right|}{\\left| A _ {p} \\cup A _ {g t} \\right|}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 345, + 890, + 386 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {s . t .} \\quad w = \\frac {\\operatorname* {m i n} (| A _ {p} | , | A _ {g t} |) + \\operatorname {V a r} (| A _ {p} | , | A _ {g t} |)}{\\operatorname* {m a x} (| A _ {p} | , | A _ {g t} |) + \\operatorname {V a r} (| A _ {p} | , | A _ {g t} |)},\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 380, + 846, + 415 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\operatorname{Var}(\\cdot, \\cdot)$ is the function that gets the variance of provided scalars.", + "bbox": [ + 496, + 422, + 890, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the left of Fig. 3, we visualize the values of $w$ with respect to the number of pixels in $A_{p}$ and $A_{gt}$ . It can be observed that the larger the gap between $|A_{p}|$ and $|A_{gt}|$ is, the smaller the $w$ is, which results in a larger scale sensitive loss (on the assumption that the IoU between $A_{p}$ and $A_{gt}$ is fixed). The intuition behind the design of $w$ is that the detector should pay more attention to the target with a larger loss if the predicted and ground-truth scales (i.e., the numbers of pixels in $A_{p}$ and $A_{gt}$ ) are quite different.", + "bbox": [ + 496, + 453, + 892, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Location Sensitive Loss", + "text_level": 1, + "bbox": [ + 500, + 598, + 715, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The location sensitive loss is calculated based on the predicted and ground-truth center points of targets. Given the sets of predicted pixels $A_{p}$ and ground-truth pixels $A_{gt}$ , the corresponding center points for $A_{p}$ and $A_{gt}$ are obtained by averaging the coordinates of all pixels, which are denoted as $\\mathbf{c}_p = (x_p,y_p)$ and $\\mathbf{c}_{gt} = (x_{gt},y_{gt})$ , respectively. Then, we convert the coordinates of these two center points into the polar coordinate system. Take $\\mathbf{c}_p$ for example, the corresponding distance $d_{p}$ and angle $\\theta_{p}$ in the polar coordinate system are:", + "bbox": [ + 496, + 621, + 890, + 772 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd _ {p} = \\sqrt {x _ {p} ^ {2} + y _ {p} ^ {2}},\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 782, + 750, + 806 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {p} = \\arctan \\left(\\frac {y _ {p}}{x _ {p}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 803, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The location sensitive loss can be obtained by:", + "bbox": [ + 500, + 847, + 807, + 861 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L} = \\left(1 - \\frac {\\operatorname* {m i n} \\left(d _ {p} , d _ {g t}\\right)}{\\operatorname* {m a x} \\left(d _ {p} , d _ {g t}\\right)}\\right) + \\frac {4}{\\pi^ {2}} \\left(\\theta_ {p} - \\theta_ {g t}\\right) ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 869, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17492", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2a36d453dc002d6f42daed267c38909b1106ea87c71b51ca635a7c654aea35f8.jpg", + "image_caption": [ + "Figure 4. Overview of the proposed MSHNet. Our MSHNet is implemented based on a plain U-Net without bells and whistles. Only a simple multi-scale head is introduced. For each scale, the feature map is fed into a dedicated head, producing a prediction with the same spatial shape as the feature map. Different scales of predictions are upsampled (if needed) and concatenated together to get the final prediction. In the training stage, our SLS loss is applied to each of these predictions since it is scale sensitive." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 224 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d_{gt}$ and $\\theta_{gt}$ are the distance and angle of $\\mathbf{c}_{gt}$ in the polar coordinate system, respectively.", + "bbox": [ + 75, + 316, + 468, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "On the right of Fig. 3, we show how the location loss changes with respect to different location errors between $\\mathbf{c}_p$ and $\\mathbf{c}_{gt}$ . As we can see, though some different location errors share the same loss value (these location errors still can be distinguished with their gradients), the location loss distinguishes most of the different location errors effectively, making the detector sensitive to different types of location errors and locate the targets more accurately.", + "bbox": [ + 75, + 348, + 470, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. MSHNet Detector", + "text_level": 1, + "bbox": [ + 76, + 482, + 261, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce our MSHNet detector, which is implemented by introducing a simple but effective multiscale head to the plain U-Net. The overview of MSHNet is shown in Fig. 4. We take the commonly used U-Net as the backbone network. The feature maps that have different scales in the decoder are fed into different prediction heads to get different scales of predictions. All the predictions from different feature maps are finally concatenated (upsampling before concatenation is adopted if needed) to get the final prediction. In the training stage, our SLS loss is applied to each of the predictions. In the following, the multi-scale head is first described in detail. Then we introduce the utilization of SLS loss in MSHNet.", + "bbox": [ + 75, + 507, + 468, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Multi-Scale Head", + "text_level": 1, + "bbox": [ + 76, + 713, + 246, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{x}_i\\in \\mathbb{R}^{H_i\\times W_i\\times C_i}$ be the feature map at the $i$ -th scale in the decoder of U-Net, where $H_{i}\\times W_{i}$ is the spatial size and $C_i$ is the number of channels. Following the common settings within existing works, there are 4 scales in U-Net, which means that $i\\in \\{1,2,3,4\\}$ . Supposing the input spatial size is $H\\times W$ , then $H_{i} = \\frac{H}{2^{4 - i}}$ and $W_{i} = \\frac{W}{2^{4 - i}}$ .", + "bbox": [ + 75, + 734, + 468, + 827 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $i$ -th prediction $\\mathbf{p}_i \\in \\mathbb{R}^{\\bar{H}_i \\times W_i \\times 1}$ is obtained by the corresponding prediction head, which is implemented by a convolution layer and a sigmoid activation function:", + "bbox": [ + 75, + 827, + 468, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {i} = \\operatorname {S i g m o i d} \\left(\\operatorname {C o n v} \\left(\\mathbf {x} _ {i}\\right)\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that different prediction heads have their own dedicated parameters. The final prediction $\\mathbf{p} \\in \\mathbb{R}^{H \\times W \\times 1}$ is obtained based on all the 4 predictions:", + "bbox": [ + 496, + 316, + 890, + 363 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} = \\operatorname {S i g m o i d} \\left(\\operatorname {C o n v} \\left(\\left[ \\uparrow \\left(\\mathbf {p} _ {1}, 8\\right), \\uparrow \\left(\\mathbf {p} _ {2}, 4\\right), \\uparrow \\left(\\mathbf {p} _ {3}, 2\\right), \\mathbf {p} _ {4} \\right]\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 375, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Uparrow (\\cdot ,\\cdot)$ is the operation that spatially upsamples the first argument with the second argument as the factor, and $[\\cdot ,\\dots ,\\cdot ]$ concatenates all the provided arguments along the channel dimensionality.", + "bbox": [ + 498, + 405, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Training MSHNet with SLS Loss", + "text_level": 1, + "bbox": [ + 500, + 474, + 790, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since our SLS loss is scale sensitive and there are several scales in the predictions of MSHNet, we apply SLS loss to all of the predictions. The inspiration is that our SLS loss produces different loss values for different scales even if they share the same spatial layout (refer to the first two cases in the top row, Fig. 2). We hypothesize that by applying our SLS loss to different scales, the targets that are with different scales can attract different attention from the detector, resulting in an overall better detection performance.", + "bbox": [ + 496, + 497, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{p}_{gt} \\in \\{0,1\\}^{H \\times W \\times 1}$ be the ground-truth label. The final loss for MSHNet is:", + "bbox": [ + 500, + 633, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{5} \\left(\\sum_ {i = 1} ^ {4} \\mathcal {L} _ {S L S} \\left(\\mathbf {p} _ {i}, \\Downarrow \\left(\\mathbf {p} _ {g t}, 2 ^ {4 - i}\\right)\\right) + \\mathcal {L} _ {S L S} \\left(\\mathbf {p}, \\mathbf {p} _ {g t}\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 672, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Downarrow (\\cdot ,\\cdot)$ is the operation (i.e., max-pooling) that spatially downsamples the first argument with the second argument as the factor, and $\\mathcal{L}_{SLS}(\\cdot ,\\cdot)$ is our SLS loss.", + "bbox": [ + 498, + 726, + 890, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 784, + 632, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, the adopted datasets and metrics are firstly introduced, followed by the implementation details. Then, we compare the proposed method MSHNet with existing IRSTD detectors. Finally, discussions are provided to show the effectiveness of our Scale and Location Sensitive loss and MHSNet detector.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17493", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/4ba563bc9cb3383fdf0039c75cedf98a885526c5fa81239571a52bf0e34868d8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDescriptionIRSTD-1kNUDT-SIRST
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
Top-Hat [17]Filtering10.0675.11143220.7278.41166.7
Max-Median [5]6.99865.2159.734.19758.4136.89
WSLCM [10]Local Contrast3.45272.4466192.28356.821309
TLLCM [9]3.31177.3967382.17662.011608
IPI [8]Low Rank27.9281.3716.1817.7674.4941.23
NRAM [29]15.2570.6816.936.92756.4019.27
RIPT [2]14.1177.5528.3129.4491.85344.3
PSTNN [28]24.5771.9935.2614.8566.1344.17
MSLSTIPT [19]11.4379.0315248.34247.40888.1
MDvsFA [21]Deep Learning37.3483.7188.5235.8685.2295.37
ALCNet [4]65.6889.2527.7172.8996.1930.40
ISNet [30]62.8892.5927.9267.8692.5934.65
DNANet [14]65.7191.8417.6179.9896.9312.78
MSHNet (Ours)67.1693.8815.0380.5597.9911.77
", + "bbox": [ + 81, + 88, + 890, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative results of different methods. Results for the metrics of IoU(%, Pd(%) and Fa(10-6) are presented. The best values are highlighted with bold. It can be seen that our MSHNet achieves the best results on different metrics and datasets.", + "bbox": [ + 75, + 325, + 892, + 356 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 76, + 392, + 274, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. The experiments are conducted on two datasets i.e., IRSD-1k [30] and NUDT-SIRST [14]. There are 1,001 and 1,327 infrared images in IRSTD-1k and NUDT-SIRST, respectively. Following existing works [14, 30], the images in IRSTD-1k are divided into the training and testing splits with a ratio of 4:1, while the images in NUDT-SIRST are equally divided into the training and testing splits.", + "bbox": [ + 75, + 416, + 470, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We use IoU and false alarm rate $(\\mathrm{F_a})$ as the pixel-level evaluation metric and assess target-level performance using the probability of detection $(\\mathrm{P_d})$ . Different metrics reveal the performance of the detector from different aspects. $\\mathrm{F_a}$ and $\\mathrm{P_d}$ focus on recall and false alarms, while IoU takes both into consideration.", + "bbox": [ + 75, + 540, + 468, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Formally, The false alarm rate is:", + "bbox": [ + 96, + 631, + 318, + 645 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {F} _ {\\mathrm {a}} = \\frac {P _ {\\text {f a l s e}}}{P _ {\\text {a l l}}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 655, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{false}$ is the number of false positive pixels and $P_{all}$ is the number of all pixels in the image.", + "bbox": [ + 76, + 696, + 468, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The probability of detection is:", + "bbox": [ + 96, + 727, + 305, + 742 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {d} = \\frac {N _ {p r e d}}{N _ {a l l}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 751, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{pred}$ is the number of correctly predicted targets and $N_{all}$ is the number of all targets.", + "bbox": [ + 76, + 792, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 830, + 294, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed method is implemented with PyTorch framework. Following existing works, the input size of the detector is set to $256 \\times 256$ . We train different models using", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "AdaGrad on 2 RTX3090 GPUs. The batch size is set to 4 and the learning rate is set to 0.05.", + "bbox": [ + 498, + 392, + 892, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Comparison to Existing Methods", + "text_level": 1, + "bbox": [ + 498, + 433, + 790, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first compare the proposed MSHNet with existing methods. Different types of methods are evaluated, including traditional methods and deep-learning-based methods. The evaluated traditional methods are the filtering-based Top-Hat [17] and Max-Median [5], local-contrast-based WSLCM [10] and TLLCM [9], low-rank-based IPI [8], NRAM [29], RIPT [2], PSTNN [28] and MSLSTIPT [19]. The deep-learning-based methods are MDvsFA [21], ALCNet [4], ISNet [30], and DNANet [14]. For a fair comparison, all the evaluated deep-learning-based models are retrained with their official codes to their convergence on NUDT-SIRST [14] and IRSTD-1k [30] datasets.", + "bbox": [ + 496, + 457, + 892, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative Results. The quantitative results of different methods are presented in Tab. 1. Overall, our MSHNet performs the best on all metrics and all datasets.", + "bbox": [ + 496, + 657, + 890, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As expected, traditional methods perform poorly on these challenging datasets due to the limitations of manually designed priors for feature extraction. In contrast, DL-based methods can automatically learn useful features and yield better results than traditional methods. Nevertheless, existing DL-based methods lack the consideration of different scales and locations of targets in the training stage. The predictions of existing DL-based methods suffer from the incomplete shape and missed detection of valid pixels, e.g., lower IoU and $\\mathrm{P_d}$ . Compared with DNANet, which is one of the existing SOTA DL-based methods, our MSHNet achieves $1.45\\%$ and $0.57\\%$ higher IoU, $2.04\\%$ and $1.06\\%$ higher $\\mathrm{P_d}$ on IRSTD-1k and NUAA-SIRST datasets, re", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17494", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5620e2067139fb0ccbc6da094279699e7a8d1783fa8b2e40ffe72108d5016c75.jpg", + "image_caption": [ + "Figure 5. Visual comparison of detection results on several infrared images. Correctly detected targets, missed targets, and false alarms are framed by red, blue, and yellow boxes, respectively. A close-up view of the target is shown in image corners." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 893, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "spectively. In addition, the false alarm $(\\mathrm{F_a})$ on both datasets are all reduced by a large margin, demonstrating the superiority of our method.", + "bbox": [ + 75, + 579, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As mentioned before, there are no complex model structures in MSHNet, which achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption. The results of DL-based methods are presented in Fig. 1. It can be observed that MSHNet has the best detection performance and the least inference time consumption. It also has the least number of FLOPs except for ALCNet. We own the less inference time consumption of MSHNet to the smaller number of FLOPs and the simple architectures (complex structures in deep models bring more inference time consumption [22]). The better detection performance demonstrates the effectiveness of the proposed multi-scale head and the scale and location sensitive loss.", + "bbox": [ + 75, + 625, + 470, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. For different kinds of methods, we visualize the detection results of the representative methods in Fig. 5 and Fig. 6. It can be observed that our method has", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "better capability for the detection of challenging small targets. Traditional methods are susceptible to noise interference, resulting in a large number of false alarms. Moreover, due to the small scale and low contrast of the target, traditional methods and other DL-based methods struggle to effectively extract feature information of small targets from challenging scenarios, resulting in a considerable number of missed targets. In contrast, our methods can accurately distinguish small targets from these low-contrast infrared images. Take the case in the 5-th row in Fig. 5 for example, except for MSHNet and WLSLCM, other methods fail to detect the target. Moreover, from the peaks and the area under the peaks in Fig. 6, it can be observed that our method predicts targets with higher confidence and obtains a closer number of peaks with ground-truth. We attribute the superiority of MSHNet to the scale and location sensitivity brought by our SLS loss and multi-scale head.", + "bbox": [ + 496, + 579, + 890, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Discussions", + "text_level": 1, + "bbox": [ + 500, + 845, + 624, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide some discussions to show the effectiveness of our method. Experiments are conducted on IRSTD-1k dataset.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17495", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c2d05797e53f5c4ec37fce171c25e7a1cafba1b66f3e081738c156dcb5ae11d6.jpg", + "image_caption": [ + "Figure 6. 3D visualization results corresponding to those in Fig. 5. Different colors represent distinct grayscale values, ranging from blue to yellow, with values gradually increasing. Please zoom in for better viewing." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 883, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Detection Results for Different Scales of Targets. Since our SLS loss and MSHNet both are scale sensitive, we show how the detection performance changes with respect to different scales of targets. To do this, we split the targets into three different scale levels according to the number of pixels: (0,10], (10, 40] and $(40,\\infty]$ . Results are shown in Tab. 2. Due to the limited space, only several DL-based methods are evaluated (specifically, ISNet, DNANet and our MSHNet). Compared with DNANet, MSHNet performs better for all scale levels of targets. Compared with ISNet, MSHNet achieves comparable performance with ISNet for (0,10] and (10,40] scales but much better performance for $(40,\\infty]$ scale. The conclusion is that MSHNet can pay attention to different scale levels of targets, resulting in an overall better performance.", + "bbox": [ + 75, + 455, + 472, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of Scale and Location Sensitive Loss. We compare our SLS loss with the commonly used IoU loss and Dice loss. The results of several DL-based methods trained with different losses are presented in Tab. 3. Overall, the detection performance of different detectors is all improved by our SLS loss in terms of IoU metric, demonstrating the effectiveness and generalization of SLS loss. However, it is hard to tell which loss performs the best on the metric of $\\mathrm{P_d}$ . Interestingly, adopting our SLS loss results in a poorer performance on $\\mathrm{F_a}$ metric. The reason is that more false alarm pixels may be treated as positive targets since our SLS loss tries to distinguish the targets of all different scales.", + "bbox": [ + 75, + 703, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we show the effectiveness of scale sensitive loss", + "bbox": [ + 96, + 885, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ca056dca5d9b84cd682c3993a9707105a2e6ab47b1d37fc2f2d5f7c61ea52c61.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ScaleMethodIoU↑Pd↑Fa↓
(0,10]DNANet [3]47.2691.2722.53
ISNet [14]50.9494.5330.91
MSHNet (Ours)49.5195.2420.68
(10,40]DNANet [3]63.1491.8513.25
ISNet [14]65.4191.9116.60
MSHNet (Ours)64.7991.858.03
(40,∞]DNANet [3]78.4693.946.78
ISNet [14]66.4587.8758.80
MSHNet (Ours)79.2096.9711.02
", + "bbox": [ + 532, + 452, + 859, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparisons of different methods in terms of different scales of targets. Results for the metrics of IoU(\\%), $\\mathrm{P_d}(\\%)$ and $\\mathrm{F_a}(10^{-6})$ are presented. Our MSHNet achieves overall the best performance.", + "bbox": [ + 498, + 607, + 893, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$(\\mathcal{L}_S)$ and location sensitive loss $(\\mathcal{L}_L)$ separately. To do this, we train MSHNet with different losses. The results are presented in Tab. 4. Note that the difference between $\\mathcal{L}_S$ and $\\mathcal{L}_{IoU}$ lies in the newly introduced weight $w$ (refer to Sec. 3.1). By comparing the results in the first two rows, we can find that the introduction of $w$ (refer to Eq. (3)) is positive to the metrics of IoU and $\\mathrm{F_a}$ , indicating that the detector produces more accurate shapes for targets as well as less false alarms. While comparing the results in the last two rows, it can be observed that more false alarms will be produced when the location sensitive loss is introduced. However, both IoU and $\\mathrm{P_d}$ are greatly improved.", + "bbox": [ + 496, + 686, + 890, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we make a study on different types of location sensitive loss. As mentioned in Sec. 3.2, our location sen", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17496", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8774fc0041d4de17055bbb0302639431aec5c82dc4bde2454fad6cd3459f4f65.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LossDNANet [3]ISNet [14]MSHNet (Ours)
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
L IoU65.7191.8417.6162.8892.5927.9264.8391.165.28
L Dice65.5892.1712.7562.9490.9119.2665.3692.1814.12
L SLS (Ours)67.0992.1535.1564.4292.2615.1467.1693.8815.03
", + "bbox": [ + 81, + 88, + 890, + 162 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/28f7254ae1bddb26c46e8ce47b2372e7e6f12d58fabd799c9932a3fc06538bcf.jpg", + "table_caption": [ + "Table 3. Comparisons of different losses and detectors. Results for the metrics of IoU(\\%), $\\mathrm{P_d}(\\%)$ and $\\mathrm{F_a}(10^{-6})$ are presented. The main IoU metrics of different detectors are consistently boosted by our scale and location sensitive loss." + ], + "table_footnote": [], + "table_body": "
LossIoU↑Pd↑Fa↓
LS w/o. w64.8391.165.28
LS65.8289.464.06
LS + LL67.1693.8815.03
", + "bbox": [ + 83, + 224, + 464, + 287 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/40186dd0b292fcc25b6ae977770ae5cfb5643a500246ee575de17fb7ff9470af.jpg", + "table_caption": [ + "Table 4. Ablation study of the scale sensitive loss $(\\mathcal{L}_S)$ and location sensitive loss $(\\mathcal{L}_L)$ . Results are obtained by MSHNet. The metrics of IoU(\\%), $\\mathrm{P_d}(\\%)$ and $\\mathrm{F_a}$ $(10^{-6})$ are adopted. Note that $\\mathcal{L}_S$ without $w$ is equivalent to $\\mathcal{L}_{IoU}$ ." + ], + "table_footnote": [], + "table_body": "
LossIoU↑Pd↑Fa↓
LS+L264.8992.867.29
LS+L164.7593.546.18
LS+L67.1693.8815.03
", + "bbox": [ + 78, + 371, + 468, + 433 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sitive loss can distinguish different location errors more effectively. To show the effectiveness of such distinguishability, we use the $L_{2}$ and $L_{1}$ distances between $\\mathbf{c}_p$ and $\\mathbf{c}_{gt}$ as the location sensitive loss (denoted as $\\mathcal{L}_{L_2}$ and $\\mathcal{L}_{L_1}$ , respectively). Results are shown in Tab. 5. As we can see, the distinguishability of different location errors is effective in getting better IoU and $\\mathrm{P_d}$ metrics. However, more false alarms are produced (higher $\\mathrm{F_a}$ ). Such phenomenon is also observed from Tab. 4. The reason may be that the distinguishability of different location errors makes the detector more sensitive to small targets, resulting in the potential of treating some noises to targets.", + "bbox": [ + 75, + 511, + 472, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Multi-Scale Heads. Now we ablate the number of scales in our multi-scale head. Results are shown in Tab. 6. As we can see, different predictions achieve different detection performance. Overall, the more scales adopted, the better the detection performance is achieved. For example, the IoU is improved from $63.10\\%$ to $67.16\\%$ when the number of scales is increased from 1 to 4. We use 4 scales by default.", + "bbox": [ + 75, + 710, + 468, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 845, + 194, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we focus on boosting the performance of infrared small target detection with an effective loss function", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/41bc64b3d16b3dc4c6f4928b45ecf664822e3db36eadfed7d10671a7f39ee7e8.jpg", + "table_caption": [ + "Table 5. Ablation study of different types of location sensitive loss. Results are obtained by MSHNet. The metrics of IoU(%, $\\mathrm{P_d}(\\%)$ and $\\mathrm{F_a}(10^{-6})$ are adopted." + ], + "table_footnote": [], + "table_body": "
Num. of ScalesSupervised PredictionsIoU↑Pd↑Fa↓
1p63.1086.7319.21
1p4,p64.6993.8736.74
2p3,p4,p64.3594.8935.38
3p2,p3,p4,p65.9093.5424.37
4p1,p2,p3,p4,p67.1693.8815.03
", + "bbox": [ + 500, + 224, + 897, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation study of the number of scales in MSHNet. While reducing the number of adopted scales, the remaining smallest scale is removed. Results for the metrics of IoU(\\%), $\\mathrm{P_d}(\\%)$ and $\\mathrm{F_a} (10^{-6})$ are presented.", + "bbox": [ + 498, + 325, + 892, + 382 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "but a simpler model structure. To do this, a Scale and Location Sensitive (SLS) loss is first proposed. The merits of SLS loss include: (1) it pays more attention to the targets that have large gaps between the predicted and ground-truth scales; (2) it distinguishes different types of location errors between the predicted and ground-truth center points of targets. Then a simple Multi-Scale Head is introduced to the plain U-Net (MSHNet), which produces multi-scale predictions for each input. Through applying SLS loss to different scales of predictions, different scales of targets can attract different attention from the detector, resulting in an overall better detection performance. Experimental results show that MSHNet achieves SOTA detection performance with the better balance of inference time and the number of floating point of operations. While applying our SLS loss to other existing detectors, the overall detection performance can be boosted. However, more false alarms may be introduced. Through the analysis in Sec. 5.4, we find that such a phenomenon is brought by the location sensitive loss in SLS loss which potentially treats some noises as targets. In future works, we try to handle this by designing more suitable location sensitive loss.", + "bbox": [ + 496, + 414, + 893, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 762, + 638, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (62331006,62171038, 62088101, and 62371175), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), the Key R&D Program of Zhejiang (2023C01044), the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK239909299001-013), and the Fundamental Research Funds for the Central Universities.", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17497", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Linwei Chen, Ying Fu, Kaixuan Wei, Dezhi Zheng, and Felix Heide. 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In Proceedings of the AAAI Conference on Artificial Intelligence, pages 12993-13000, 2020. 3" + ], + "bbox": [ + 78, + 90, + 470, + 698 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17499", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_model.json b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..eff2d07f6970f3fedb5322e24914151938966ebd --- /dev/null +++ b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_model.json @@ -0,0 +1,2079 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.144, + 0.131, + 0.826, + 0.154 + ], + "angle": 0, + "content": "Infrared Small Target Detection with Scale and Location Sensitivity" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.179, + 0.894, + 0.234 + ], + "angle": 0, + "content": "Qiankun Liu\\(^{1}\\) Rui Liu\\(^{1,2}\\) Bolun Zheng\\(^{3}\\) Hongkui Wang\\(^{3}\\) Ying Fu\\(^{1,2*}\\) \n\\(^{1}\\)Beijing Institute of Technology \\(^{2}\\)Yangtze Delta Region Academy of Beijing Institute of Technology \\(^{3}\\)Hangzhou Dianzi University" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.236, + 0.831, + 0.252 + ], + "angle": 0, + "content": "{liuqk3, liurui20}@bit.edu.cn, {blzheng, wanghk}@hdu.edu.cn, fuying@bit.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.698 + ], + "angle": 0, + "content": "Recently, infrared small target detection (IRSTD) has been dominated by deep-learning-based methods. However, these methods mainly focus on the design of complex model structures to extract discriminative features, leaving the loss functions for IRSTD under-explored. For example, the widely used Intersection over Union (IoU) and Dice losses lack sensitivity to the scales and locations of targets, limiting the detection performance of detectors. In this paper, we focus on boosting detection performance with a more effective loss but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses: 1) for scale sensitivity, we compute a weight for the IoU loss based on target scales to help the detector distinguish targets with different scales; 2) for location sensitivity, we introduce a penalty term based on the center points of targets to help the detector localize targets more precisely. Then, we design a simple Multi-Scale Head to the plain U-Net (MSHNet). By applying SLS loss to each scale of the predictions, our MSHNet outperforms existing state-of-the-art methods by a large margin. In addition, the detection performance of existing detectors can be further improved when trained with our SLS loss, demonstrating the effectiveness and generalization of our SLS loss. The code is available at https://github.com/ying-fu/MSHNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.86 + ], + "angle": 0, + "content": "Infrared small target detection (IRSTD) is an important computer vision task, which has a wide range of applications, such as maritime surveillance [20, 34], traffic management [26, 27, 30] and so on. However, due to the long-distance camera capture, and the noise and clutter interference, infrared targets are often small and dim, making it difficult to detect infrared small targets effectively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.861, + 0.47, + 0.875 + ], + "angle": 0, + "content": "To enhance the detection performance of infrared small" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.286, + 0.895, + 0.458 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.468, + 0.895, + 0.552 + ], + "angle": 0, + "content": "Figure 1. Visualization of the detection performance (IoU), inference time consumption (Images/second) as well as the number of floating point of operations (area of circles) of some deep-learning-based methods. It can be seen that our MSHNet achieves a better balance between these three metrics than other methods. Results are evaluated on IRSTD-1k [30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.763 + ], + "angle": 0, + "content": "targets, numerous methods have been proposed. Early traditional methods can be divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10], and low-rank-based methods [2, 28, 29, 31]. However, these traditional methods rely on manually designed features, and thus can not generalize well to environment changes. Recently, with the development of Deep Learning (DL), IRSTD has been dominated by DL-based methods [1, 15, 21, 24]. Different from traditional methods, DL-based methods can automatically learn useful features through a gradient descent algorithm with the constraints of loss functions, making them more robust to various scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "However, existing DL-based methods primarily focus on designing complex model structures for feature extraction, leaving the loss functions for IRSTD under-explored. For instance, Li et.al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion, and Wu et.al. [25] nest the U-Net structure to achieve feature aggregation. Although discriminative features can be extracted by the complex model structures, the detection performance is still limited by the under-explored loss functions. For ex" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17490" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "ample, the widely used Intersection over Union (IoU) loss and Dice loss [18] lack sensitivity to the scales and locations of targets. As shown in Fig. 2, targets with different scales (top row) and locations (bottom row) may share the same IoU loss or Dice loss. This insensitivity to scales and locations makes it challenging for detectors to distinguish targets of different scales and locations, which ultimately limits the detection performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.219, + 0.473, + 0.611 + ], + "angle": 0, + "content": "In this paper, we focus on boosting detection performance with a more effective loss function but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses. The merits of the proposed SLS loss include: (1) Scale sensitivity. We compute a weight for the IoU loss based on the predicted and ground-truth scales of targets. The larger the gap between predicted and ground-truth scales is, the more attention will be paid by the detector. (2) Location Sensitivity. We design a location penalty based on the predicted and ground-truth center points of targets. Compared with traditional L1 and L2 distances, the designed location penalty produces the same value for fewer different location errors, making the detector locate targets more precisely. Then, we introduce a simple Multi-Scale Head to the plain U-Net (MSHNet), which produces multiscale predictions for each input. Through leveraging SLS loss at different scales, our MSHNet outperforms existing state-of-the-art (SOTA) methods by a large margin. With the absence of complex structures, our detector achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption, as shown in Fig. 1. Moreover, we further train different existing detectors with our SLS loss and achieve better detection performance, demonstrating the effectiveness and generalization of our SLS loss." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.619, + 0.365, + 0.633 + ], + "angle": 0, + "content": "In summary, our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.64, + 0.47, + 0.685 + ], + "angle": 0, + "content": "- We propose a novel scale and location sensitive loss for infrared small target detection, which helps detectors distinguish objects with different scales and locations." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.686, + 0.47, + 0.729 + ], + "angle": 0, + "content": "- We propose a simple but effective detector by introducing a multi-scale head to the plain U-Net, which achieves SOTA performance without bells and whistles." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.731, + 0.469, + 0.775 + ], + "angle": 0, + "content": "- We apply our loss to existing detectors and show that the detection performance can be further boosted, demonstrating the effectiveness and generalization of our loss." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.64, + 0.47, + 0.775 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.808, + 0.22, + 0.824 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.9 + ], + "angle": 0, + "content": "In this section, we first make a brief introduction to existing methods for IRSTD. Then we provide a review of related works from the perspectives of loss functions and model structures for IRSTD." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.091, + 0.604, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.149, + 0.59, + 0.161 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SLS} = 0.94\\)" + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.101, + 0.724, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.149, + 0.735, + 0.161 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SLS} = 0.97\\)" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.091, + 0.876, + 0.144 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.805, + 0.149, + 0.866, + 0.161 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SLS} = 0.92\\)" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.181, + 0.612, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.228, + 0.589, + 0.239 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SLS} = 0.62\\)" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.177, + 0.743, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.228, + 0.735, + 0.239 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SLS} = 0.64\\)" + }, + { + "type": "image", + "bbox": [ + 0.785, + 0.177, + 0.875, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.81, + 0.228, + 0.871, + 0.239 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SLS} = 0.59\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.247, + 0.895, + 0.316 + ], + "angle": 0, + "content": "Figure 2. Top row: our SLS loss for the targets of different scales, where IoU loss \\((=0.4)\\) and Dice loss \\((=0.57)\\) have the same values for different cases. Bottom row: our SLS loss for the targets of different locations, where IoU loss \\((=0.3)\\) and Dice loss \\((=0.43)\\) have the same values for different cases." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.343, + 0.783, + 0.359 + ], + "angle": 0, + "content": "2.1. Infrared Small Target Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.609 + ], + "angle": 0, + "content": "Existing IRSTD methods can be roughly divided into traditional methods and Deep-Learning-based (DL-based) methods. Among them, traditional methods depend on the hand-crafted priors and can be further divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10, 12], and low-rank-based methods [2, 6, 8, 19, 28, 29, 32]. To get useful features with such hand-crafted priors, lots of hyperparameters need to be manually fine-tuned, making them less robust to the interference of noises and clutters. Differently, DL-based methods [3, 7, 14, 15, 21, 25, 30, 33] can automatically learn useful features with the help of loss functions and gradient descent algorithms. Though impressive detection performance has been achieved, existing DL-based methods mainly focus on the design of model structures for the pursuit of more effective features, leaving the loss functions for IRSTD under-explored." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.685 + ], + "angle": 0, + "content": "Different from existing DL-based methods, we focus on boosting detection performance with a more effective loss function but a simpler model structure. A better balance between detection performance, FLOPs and inference time consumption can be achieved." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.738, + 0.71 + ], + "angle": 0, + "content": "2.2. Loss Functions for IRSTD" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.825 + ], + "angle": 0, + "content": "As one of the components in DL-based methods, the loss function plays a critical role in the learning process of deep models by quantifying the disparity between predictions and ground-truths. The commonly adopted IoU loss and Dice loss [18] suffer from insensitivity to the scales and locations of targets, rendering the detectors for distinguishing the targets of different scales and locations accurately." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In order to achieve better detection performance, researchers have developed several loss functions. For example, the loss for adversarial training [21], edge loss for the detecting of target edges [30] and the likelihood loss between target and background maps [11]. However, these" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17491" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.22, + 0.473, + 0.306 + ], + "angle": 0, + "content": "Figure 3. Left: the value of weight \\( w \\) in scale sensitive loss with respect to the number of predicted pixels and ground-truth pixels (i.e., predicted and ground-truth scales). Right: the normalized location sensitive loss with respect to the location error between the predicted center point and ground-truth center point. The range of [0, 100] pixels is shown for illustration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.331, + 0.47, + 0.42 + ], + "angle": 0, + "content": "losses are tailored for specific network architectures, limiting their broader utility. Different from these dedicated losses, the generalized IoU (GIoU) [16] and complete IoU (CIoU) [35] losses have been adopted for box-level IRSTD [13, 23]. However, these IoU variant losses still lack the sensitivity of scales and locations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.472, + 0.482 + ], + "angle": 0, + "content": "In contrast to these losses, we formulate a general loss function that is better suitable for IRSTD. It can distinguish targets of different scales and locations, enabling different detectors to achieve better detection performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.492, + 0.336, + 0.507 + ], + "angle": 0, + "content": "2.3. Model Structures for IRSTD" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.47, + 0.711 + ], + "angle": 0, + "content": "The deep model is another key component in DL-based methods. Liu et al. [15] pioneer the application of deep learning to IRSTD. The adopted five-layer Multi-Layer Perceptron (MLP) network demonstrates the superiority of DL-based methods in IRSTD. Recently, lots of works have focused on the design of model structures to get more effective features. Li et al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion. Zhang et al. [30] utilize Taylor finite difference and orientation attention strategy to extract edge information of targets. However, such complex model structures not only bring more computational cost but still suffer from moderate detection performance due to the lack of effective loss functions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Differently we introduce a simple multi-scale head to the plain U-Net, rather than designing complex structures. By applying our SLS loss to different scales, SOTA performance is achieved with less time consumption." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.383, + 0.803 + ], + "angle": 0, + "content": "3. Scale and Location Sensitive Loss" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.471, + 0.874 + ], + "angle": 0, + "content": "The scale and location sensitive (SLS) loss, denoted as \\(\\mathcal{L}_{\\text{SLS}}\\), is designed to handle the insensitivity of scales and locations in existing losses. It consists of a scale sensitive loss and a location sensitive loss. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S L S} = \\mathcal {L} _ {S} + \\mathcal {L} _ {L}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.152 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_S\\) and \\(\\mathcal{L}_L\\) present the scale sensitive loss and location sensitive loss, respectively. In the following, we introduce the SLS loss in detail starting from the scale sensitive loss, which is based on the commonly used IoU loss." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.161, + 0.691, + 0.175 + ], + "angle": 0, + "content": "3.1. Scale Sensitive Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.184, + 0.893, + 0.228 + ], + "angle": 0, + "content": "Let \\( A_{p} \\) and \\( A_{gt} \\) be the set of predicted pixels and ground-truth pixels of targets, the IoU loss between them can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.235, + 0.893, + 0.27 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I o U} = 1 - \\frac {\\left| A _ {p} \\cap A _ {g t} \\right|}{\\left| A _ {p} \\cup A _ {g t} \\right|}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.892, + 0.338 + ], + "angle": 0, + "content": "Though having been widely used in IRSTD, the IoU loss is insensitive to the scales and locations of targets, as shown in Fig. 2. The scale sensitive loss is implemented by providing a weight to the IoU loss:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.346, + 0.892, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S} = 1 - w \\frac {\\left| A _ {p} \\cap A _ {g t} \\right|}{\\left| A _ {p} \\cup A _ {g t} \\right|}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.381, + 0.847, + 0.416 + ], + "angle": 0, + "content": "\\[\n\\mathrm {s . t .} \\quad w = \\frac {\\operatorname* {m i n} (| A _ {p} | , | A _ {g t} |) + \\operatorname {V a r} (| A _ {p} | , | A _ {g t} |)}{\\operatorname* {m a x} (| A _ {p} | , | A _ {g t} |) + \\operatorname {V a r} (| A _ {p} | , | A _ {g t} |)},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.453 + ], + "angle": 0, + "content": "where \\(\\operatorname{Var}(\\cdot, \\cdot)\\) is the function that gets the variance of provided scalars." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.893, + 0.591 + ], + "angle": 0, + "content": "On the left of Fig. 3, we visualize the values of \\( w \\) with respect to the number of pixels in \\( A_{p} \\) and \\( A_{gt} \\). It can be observed that the larger the gap between \\( |A_{p}| \\) and \\( |A_{gt}| \\) is, the smaller the \\( w \\) is, which results in a larger scale sensitive loss (on the assumption that the IoU between \\( A_{p} \\) and \\( A_{gt} \\) is fixed). The intuition behind the design of \\( w \\) is that the detector should pay more attention to the target with a larger loss if the predicted and ground-truth scales (i.e., the numbers of pixels in \\( A_{p} \\) and \\( A_{gt} \\)) are quite different." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.599, + 0.717, + 0.613 + ], + "angle": 0, + "content": "3.2. Location Sensitive Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.773 + ], + "angle": 0, + "content": "The location sensitive loss is calculated based on the predicted and ground-truth center points of targets. Given the sets of predicted pixels \\( A_{p} \\) and ground-truth pixels \\( A_{gt} \\), the corresponding center points for \\( A_{p} \\) and \\( A_{gt} \\) are obtained by averaging the coordinates of all pixels, which are denoted as \\( \\mathbf{c}_p = (x_p,y_p) \\) and \\( \\mathbf{c}_{gt} = (x_{gt},y_{gt}) \\), respectively. Then, we convert the coordinates of these two center points into the polar coordinate system. Take \\( \\mathbf{c}_p \\) for example, the corresponding distance \\( d_{p} \\) and angle \\( \\theta_{p} \\) in the polar coordinate system are:" + }, + { + "type": "equation", + "bbox": [ + 0.632, + 0.783, + 0.75, + 0.808 + ], + "angle": 0, + "content": "\\[\nd _ {p} = \\sqrt {x _ {p} ^ {2} + y _ {p} ^ {2}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.804, + 0.891, + 0.84 + ], + "angle": 0, + "content": "\\[\n\\theta_ {p} = \\arctan \\left(\\frac {y _ {p}}{x _ {p}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.848, + 0.808, + 0.862 + ], + "angle": 0, + "content": "The location sensitive loss can be obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.871, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L} = \\left(1 - \\frac {\\operatorname* {m i n} \\left(d _ {p} , d _ {g t}\\right)}{\\operatorname* {m a x} \\left(d _ {p} , d _ {g t}\\right)}\\right) + \\frac {4}{\\pi^ {2}} \\left(\\theta_ {p} - \\theta_ {g t}\\right) ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17492" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.891, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.894, + 0.294 + ], + "angle": 0, + "content": "Figure 4. Overview of the proposed MSHNet. Our MSHNet is implemented based on a plain U-Net without bells and whistles. Only a simple multi-scale head is introduced. For each scale, the feature map is fed into a dedicated head, producing a prediction with the same spatial shape as the feature map. Different scales of predictions are upsampled (if needed) and concatenated together to get the final prediction. In the training stage, our SLS loss is applied to each of these predictions since it is scale sensitive." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.47, + 0.348 + ], + "angle": 0, + "content": "where \\(d_{gt}\\) and \\(\\theta_{gt}\\) are the distance and angle of \\(\\mathbf{c}_{gt}\\) in the polar coordinate system, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.471, + 0.471 + ], + "angle": 0, + "content": "On the right of Fig. 3, we show how the location loss changes with respect to different location errors between \\(\\mathbf{c}_p\\) and \\(\\mathbf{c}_{gt}\\). As we can see, though some different location errors share the same loss value (these location errors still can be distinguished with their gradients), the location loss distinguishes most of the different location errors effectively, making the detector sensitive to different types of location errors and locate the targets more accurately." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.262, + 0.499 + ], + "angle": 0, + "content": "4. MSHNet Detector" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.705 + ], + "angle": 0, + "content": "In this section, we introduce our MSHNet detector, which is implemented by introducing a simple but effective multiscale head to the plain U-Net. The overview of MSHNet is shown in Fig. 4. We take the commonly used U-Net as the backbone network. The feature maps that have different scales in the decoder are fed into different prediction heads to get different scales of predictions. All the predictions from different feature maps are finally concatenated (upsampling before concatenation is adopted if needed) to get the final prediction. In the training stage, our SLS loss is applied to each of the predictions. In the following, the multi-scale head is first described in detail. Then we introduce the utilization of SLS loss in MSHNet." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.714, + 0.248, + 0.729 + ], + "angle": 0, + "content": "4.1. Multi-Scale Head" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.736, + 0.469, + 0.828 + ], + "angle": 0, + "content": "Let \\(\\mathbf{x}_i\\in \\mathbb{R}^{H_i\\times W_i\\times C_i}\\) be the feature map at the \\(i\\) -th scale in the decoder of U-Net, where \\(H_{i}\\times W_{i}\\) is the spatial size and \\(C_i\\) is the number of channels. Following the common settings within existing works, there are 4 scales in U-Net, which means that \\(i\\in \\{1,2,3,4\\}\\). Supposing the input spatial size is \\(H\\times W\\), then \\(H_{i} = \\frac{H}{2^{4 - i}}\\) and \\(W_{i} = \\frac{W}{2^{4 - i}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.828, + 0.469, + 0.873 + ], + "angle": 0, + "content": "The \\(i\\)-th prediction \\(\\mathbf{p}_i \\in \\mathbb{R}^{\\bar{H}_i \\times W_i \\times 1}\\) is obtained by the corresponding prediction head, which is implemented by a convolution layer and a sigmoid activation function:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {i} = \\operatorname {S i g m o i d} \\left(\\operatorname {C o n v} \\left(\\mathbf {x} _ {i}\\right)\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Note that different prediction heads have their own dedicated parameters. The final prediction \\(\\mathbf{p} \\in \\mathbb{R}^{H \\times W \\times 1}\\) is obtained based on all the 4 predictions:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.375, + 0.892, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} = \\operatorname {S i g m o i d} \\left(\\operatorname {C o n v} \\left(\\left[ \\uparrow \\left(\\mathbf {p} _ {1}, 8\\right), \\uparrow \\left(\\mathbf {p} _ {2}, 4\\right), \\uparrow \\left(\\mathbf {p} _ {3}, 2\\right), \\mathbf {p} _ {4} \\right]\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.406, + 0.892, + 0.466 + ], + "angle": 0, + "content": "where \\(\\Uparrow (\\cdot ,\\cdot)\\) is the operation that spatially upsamples the first argument with the second argument as the factor, and \\([\\cdot ,\\dots ,\\cdot ]\\) concatenates all the provided arguments along the channel dimensionality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.475, + 0.791, + 0.491 + ], + "angle": 0, + "content": "4.2. Training MSHNet with SLS Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.634 + ], + "angle": 0, + "content": "Since our SLS loss is scale sensitive and there are several scales in the predictions of MSHNet, we apply SLS loss to all of the predictions. The inspiration is that our SLS loss produces different loss values for different scales even if they share the same spatial layout (refer to the first two cases in the top row, Fig. 2). We hypothesize that by applying our SLS loss to different scales, the targets that are with different scales can attract different attention from the detector, resulting in an overall better detection performance." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.634, + 0.891, + 0.664 + ], + "angle": 0, + "content": "Let \\(\\mathbf{p}_{gt} \\in \\{0,1\\}^{H \\times W \\times 1}\\) be the ground-truth label. The final loss for MSHNet is:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.673, + 0.892, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{5} \\left(\\sum_ {i = 1} ^ {4} \\mathcal {L} _ {S L S} \\left(\\mathbf {p} _ {i}, \\Downarrow \\left(\\mathbf {p} _ {g t}, 2 ^ {4 - i}\\right)\\right) + \\mathcal {L} _ {S L S} \\left(\\mathbf {p}, \\mathbf {p} _ {g t}\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.727, + 0.892, + 0.773 + ], + "angle": 0, + "content": "where \\(\\Downarrow (\\cdot ,\\cdot)\\) is the operation (i.e., max-pooling) that spatially downsamples the first argument with the second argument as the factor, and \\(\\mathcal{L}_{SLS}(\\cdot ,\\cdot)\\) is our SLS loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.633, + 0.802 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this section, the adopted datasets and metrics are firstly introduced, followed by the implementation details. Then, we compare the proposed method MSHNet with existing IRSTD detectors. Finally, discussions are provided to show the effectiveness of our Scale and Location Sensitive loss and MHSNet detector." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17493" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.316 + ], + "angle": 0, + "content": "
MethodDescriptionIRSTD-1kNUDT-SIRST
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
Top-Hat [17]Filtering10.0675.11143220.7278.41166.7
Max-Median [5]6.99865.2159.734.19758.4136.89
WSLCM [10]Local Contrast3.45272.4466192.28356.821309
TLLCM [9]3.31177.3967382.17662.011608
IPI [8]Low Rank27.9281.3716.1817.7674.4941.23
NRAM [29]15.2570.6816.936.92756.4019.27
RIPT [2]14.1177.5528.3129.4491.85344.3
PSTNN [28]24.5771.9935.2614.8566.1344.17
MSLSTIPT [19]11.4379.0315248.34247.40888.1
MDvsFA [21]Deep Learning37.3483.7188.5235.8685.2295.37
ALCNet [4]65.6889.2527.7172.8996.1930.40
ISNet [30]62.8892.5927.9267.8692.5934.65
DNANet [14]65.7191.8417.6179.9896.9312.78
MSHNet (Ours)67.1693.8815.0380.5597.9911.77
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.326, + 0.893, + 0.357 + ], + "angle": 0, + "content": "Table 1. Quantitative results of different methods. Results for the metrics of IoU(%, Pd(%) and Fa(10-6) are presented. The best values are highlighted with bold. It can be seen that our MSHNet achieves the best results on different metrics and datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.393, + 0.276, + 0.409 + ], + "angle": 0, + "content": "5.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.471, + 0.524 + ], + "angle": 0, + "content": "Datasets. The experiments are conducted on two datasets i.e., IRSD-1k [30] and NUDT-SIRST [14]. There are 1,001 and 1,327 infrared images in IRSTD-1k and NUDT-SIRST, respectively. Following existing works [14, 30], the images in IRSTD-1k are divided into the training and testing splits with a ratio of 4:1, while the images in NUDT-SIRST are equally divided into the training and testing splits." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Evaluation Metrics. We use IoU and false alarm rate \\((\\mathrm{F_a})\\) as the pixel-level evaluation metric and assess target-level performance using the probability of detection \\((\\mathrm{P_d})\\). Different metrics reveal the performance of the detector from different aspects. \\(\\mathrm{F_a}\\) and \\(\\mathrm{P_d}\\) focus on recall and false alarms, while IoU takes both into consideration." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.632, + 0.319, + 0.646 + ], + "angle": 0, + "content": "Formally, The false alarm rate is:" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.656, + 0.47, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\mathrm {F} _ {\\mathrm {a}} = \\frac {P _ {\\text {f a l s e}}}{P _ {\\text {a l l}}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.697, + 0.469, + 0.728 + ], + "angle": 0, + "content": "where \\( P_{false} \\) is the number of false positive pixels and \\( P_{all} \\) is the number of all pixels in the image." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.728, + 0.306, + 0.743 + ], + "angle": 0, + "content": "The probability of detection is:" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.752, + 0.47, + 0.784 + ], + "angle": 0, + "content": "\\[\nP _ {d} = \\frac {N _ {p r e d}}{N _ {a l l}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.793, + 0.47, + 0.825 + ], + "angle": 0, + "content": "where \\( N_{pred} \\) is the number of correctly predicted targets and \\( N_{all} \\) is the number of all targets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.295, + 0.849 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The proposed method is implemented with PyTorch framework. Following existing works, the input size of the detector is set to \\(256 \\times 256\\). We train different models using" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.393, + 0.893, + 0.424 + ], + "angle": 0, + "content": "AdaGrad on 2 RTX3090 GPUs. The batch size is set to 4 and the learning rate is set to 0.05." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.434, + 0.792, + 0.451 + ], + "angle": 0, + "content": "5.3. Comparison to Existing Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.893, + 0.64 + ], + "angle": 0, + "content": "We first compare the proposed MSHNet with existing methods. Different types of methods are evaluated, including traditional methods and deep-learning-based methods. The evaluated traditional methods are the filtering-based Top-Hat [17] and Max-Median [5], local-contrast-based WSLCM [10] and TLLCM [9], low-rank-based IPI [8], NRAM [29], RIPT [2], PSTNN [28] and MSLSTIPT [19]. The deep-learning-based methods are MDvsFA [21], ALCNet [4], ISNet [30], and DNANet [14]. For a fair comparison, all the evaluated deep-learning-based models are retrained with their official codes to their convergence on NUDT-SIRST [14] and IRSTD-1k [30] datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Quantitative Results. The quantitative results of different methods are presented in Tab. 1. Overall, our MSHNet performs the best on all metrics and all datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "As expected, traditional methods perform poorly on these challenging datasets due to the limitations of manually designed priors for feature extraction. In contrast, DL-based methods can automatically learn useful features and yield better results than traditional methods. Nevertheless, existing DL-based methods lack the consideration of different scales and locations of targets in the training stage. The predictions of existing DL-based methods suffer from the incomplete shape and missed detection of valid pixels, e.g., lower IoU and \\(\\mathrm{P_d}\\). Compared with DNANet, which is one of the existing SOTA DL-based methods, our MSHNet achieves \\(1.45\\%\\) and \\(0.57\\%\\) higher IoU, \\(2.04\\%\\) and \\(1.06\\%\\) higher \\(\\mathrm{P_d}\\) on IRSTD-1k and NUAA-SIRST datasets, re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17494" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.895, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.525, + 0.893, + 0.555 + ], + "angle": 0, + "content": "Figure 5. Visual comparison of detection results on several infrared images. Correctly detected targets, missed targets, and false alarms are framed by red, blue, and yellow boxes, respectively. A close-up view of the target is shown in image corners." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.625 + ], + "angle": 0, + "content": "spectively. In addition, the false alarm \\((\\mathrm{F_a})\\) on both datasets are all reduced by a large margin, demonstrating the superiority of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.471, + 0.837 + ], + "angle": 0, + "content": "As mentioned before, there are no complex model structures in MSHNet, which achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption. The results of DL-based methods are presented in Fig. 1. It can be observed that MSHNet has the best detection performance and the least inference time consumption. It also has the least number of FLOPs except for ALCNet. We own the less inference time consumption of MSHNet to the smaller number of FLOPs and the simple architectures (complex structures in deep models bring more inference time consumption [22]). The better detection performance demonstrates the effectiveness of the proposed multi-scale head and the scale and location sensitive loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results. For different kinds of methods, we visualize the detection results of the representative methods in Fig. 5 and Fig. 6. It can be observed that our method has" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.837 + ], + "angle": 0, + "content": "better capability for the detection of challenging small targets. Traditional methods are susceptible to noise interference, resulting in a large number of false alarms. Moreover, due to the small scale and low contrast of the target, traditional methods and other DL-based methods struggle to effectively extract feature information of small targets from challenging scenarios, resulting in a considerable number of missed targets. In contrast, our methods can accurately distinguish small targets from these low-contrast infrared images. Take the case in the 5-th row in Fig. 5 for example, except for MSHNet and WLSLCM, other methods fail to detect the target. Moreover, from the peaks and the area under the peaks in Fig. 6, it can be observed that our method predicts targets with higher confidence and obtains a closer number of peaks with ground-truth. We attribute the superiority of MSHNet to the scale and location sensitivity brought by our SLS loss and multi-scale head." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.625, + 0.862 + ], + "angle": 0, + "content": "5.4. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We provide some discussions to show the effectiveness of our method. Experiments are conducted on IRSTD-1k dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17495" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.086, + 0.885, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.402, + 0.893, + 0.43 + ], + "angle": 0, + "content": "Figure 6. 3D visualization results corresponding to those in Fig. 5. Different colors represent distinct grayscale values, ranging from blue to yellow, with values gradually increasing. Please zoom in for better viewing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.473, + 0.683 + ], + "angle": 0, + "content": "Detection Results for Different Scales of Targets. Since our SLS loss and MSHNet both are scale sensitive, we show how the detection performance changes with respect to different scales of targets. To do this, we split the targets into three different scale levels according to the number of pixels: (0,10], (10, 40] and \\((40,\\infty]\\). Results are shown in Tab. 2. Due to the limited space, only several DL-based methods are evaluated (specifically, ISNet, DNANet and our MSHNet). Compared with DNANet, MSHNet performs better for all scale levels of targets. Compared with ISNet, MSHNet achieves comparable performance with ISNet for (0,10] and (10,40] scales but much better performance for \\((40,\\infty]\\) scale. The conclusion is that MSHNet can pay attention to different scale levels of targets, resulting in an overall better performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Impact of Scale and Location Sensitive Loss. We compare our SLS loss with the commonly used IoU loss and Dice loss. The results of several DL-based methods trained with different losses are presented in Tab. 3. Overall, the detection performance of different detectors is all improved by our SLS loss in terms of IoU metric, demonstrating the effectiveness and generalization of SLS loss. However, it is hard to tell which loss performs the best on the metric of \\(\\mathrm{P_d}\\). Interestingly, adopting our SLS loss results in a poorer performance on \\(\\mathrm{F_a}\\) metric. The reason is that more false alarm pixels may be treated as positive targets since our SLS loss tries to distinguish the targets of all different scales." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Next, we show the effectiveness of scale sensitive loss" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.453, + 0.86, + 0.598 + ], + "angle": 0, + "content": "
ScaleMethodIoU↑Pd↑Fa↓
(0,10]DNANet [3]47.2691.2722.53
ISNet [14]50.9494.5330.91
MSHNet (Ours)49.5195.2420.68
(10,40]DNANet [3]63.1491.8513.25
ISNet [14]65.4191.9116.60
MSHNet (Ours)64.7991.858.03
(40,∞]DNANet [3]78.4693.946.78
ISNet [14]66.4587.8758.80
MSHNet (Ours)79.2096.9711.02
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.608, + 0.895, + 0.664 + ], + "angle": 0, + "content": "Table 2. Comparisons of different methods in terms of different scales of targets. Results for the metrics of IoU(\\%), \\( \\mathrm{P_d}(\\%) \\) and \\( \\mathrm{F_a}(10^{-6}) \\) are presented. Our MSHNet achieves overall the best performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.869 + ], + "angle": 0, + "content": "\\((\\mathcal{L}_S)\\) and location sensitive loss \\((\\mathcal{L}_L)\\) separately. To do this, we train MSHNet with different losses. The results are presented in Tab. 4. Note that the difference between \\(\\mathcal{L}_S\\) and \\(\\mathcal{L}_{IoU}\\) lies in the newly introduced weight \\(w\\) (refer to Sec. 3.1). By comparing the results in the first two rows, we can find that the introduction of \\(w\\) (refer to Eq. (3)) is positive to the metrics of IoU and \\(\\mathrm{F_a}\\), indicating that the detector produces more accurate shapes for targets as well as less false alarms. While comparing the results in the last two rows, it can be observed that more false alarms will be produced when the location sensitive loss is introduced. However, both IoU and \\(\\mathrm{P_d}\\) are greatly improved." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Finally, we make a study on different types of location sensitive loss. As mentioned in Sec. 3.2, our location sen" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17496" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.164 + ], + "angle": 0, + "content": "
LossDNANet [3]ISNet [14]MSHNet (Ours)
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
L IoU65.7191.8417.6162.8892.5927.9264.8391.165.28
L Dice65.5892.1712.7562.9490.9119.2665.3692.1814.12
L SLS (Ours)67.0992.1535.1564.4292.2615.1467.1693.8815.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.174, + 0.893, + 0.203 + ], + "angle": 0, + "content": "Table 3. Comparisons of different losses and detectors. Results for the metrics of IoU(\\%), \\( \\mathrm{P_d}(\\%) \\) and \\( \\mathrm{F_a}(10^{-6}) \\) are presented. The main IoU metrics of different detectors are consistently boosted by our scale and location sensitive loss." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.225, + 0.465, + 0.288 + ], + "angle": 0, + "content": "
LossIoU↑Pd↑Fa↓
LS w/o. w64.8391.165.28
LS65.8289.464.06
LS + LL67.1693.8815.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.297, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Table 4. Ablation study of the scale sensitive loss \\((\\mathcal{L}_S)\\) and location sensitive loss \\((\\mathcal{L}_L)\\). Results are obtained by MSHNet. The metrics of IoU(\\%), \\(\\mathrm{P_d}(\\%)\\) and \\(\\mathrm{F_a}\\) \\((10^{-6})\\) are adopted. Note that \\(\\mathcal{L}_S\\) without \\(w\\) is equivalent to \\(\\mathcal{L}_{IoU}\\)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.372, + 0.469, + 0.434 + ], + "angle": 0, + "content": "
LossIoU↑Pd↑Fa↓
LS+L264.8992.867.29
LS+L164.7593.546.18
LS+L67.1693.8815.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.444, + 0.47, + 0.487 + ], + "angle": 0, + "content": "Table 5. Ablation study of different types of location sensitive loss. Results are obtained by MSHNet. The metrics of IoU(%, \\( \\mathrm{P_d}(\\%) \\) and \\( \\mathrm{F_a}(10^{-6}) \\) are adopted." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.473, + 0.695 + ], + "angle": 0, + "content": "sitive loss can distinguish different location errors more effectively. To show the effectiveness of such distinguishability, we use the \\( L_{2} \\) and \\( L_{1} \\) distances between \\( \\mathbf{c}_p \\) and \\( \\mathbf{c}_{gt} \\) as the location sensitive loss (denoted as \\( \\mathcal{L}_{L_2} \\) and \\( \\mathcal{L}_{L_1} \\), respectively). Results are shown in Tab. 5. As we can see, the distinguishability of different location errors is effective in getting better IoU and \\( \\mathrm{P_d} \\) metrics. However, more false alarms are produced (higher \\( \\mathrm{F_a} \\)). Such phenomenon is also observed from Tab. 4. The reason may be that the distinguishability of different location errors makes the detector more sensitive to small targets, resulting in the potential of treating some noises to targets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.711, + 0.47, + 0.833 + ], + "angle": 0, + "content": "Impact of Multi-Scale Heads. Now we ablate the number of scales in our multi-scale head. Results are shown in Tab. 6. As we can see, different predictions achieve different detection performance. Overall, the more scales adopted, the better the detection performance is achieved. For example, the IoU is improved from \\(63.10\\%\\) to \\(67.16\\%\\) when the number of scales is increased from 1 to 4. We use 4 scales by default." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.196, + 0.861 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this paper, we focus on boosting the performance of infrared small target detection with an effective loss function" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.226, + 0.898, + 0.317 + ], + "angle": 0, + "content": "
Num. of ScalesSupervised PredictionsIoU↑Pd↑Fa↓
1p63.1086.7319.21
1p4,p64.6993.8736.74
2p3,p4,p64.3594.8935.38
3p2,p3,p4,p65.9093.5424.37
4p1,p2,p3,p4,p67.1693.8815.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.327, + 0.893, + 0.383 + ], + "angle": 0, + "content": "Table 6. Ablation study of the number of scales in MSHNet. While reducing the number of adopted scales, the remaining smallest scale is removed. Results for the metrics of IoU(\\%), \\( \\mathrm{P_d}(\\%) \\) and \\( \\mathrm{F_a} (10^{-6}) \\) are presented." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.747 + ], + "angle": 0, + "content": "but a simpler model structure. To do this, a Scale and Location Sensitive (SLS) loss is first proposed. The merits of SLS loss include: (1) it pays more attention to the targets that have large gaps between the predicted and ground-truth scales; (2) it distinguishes different types of location errors between the predicted and ground-truth center points of targets. Then a simple Multi-Scale Head is introduced to the plain U-Net (MSHNet), which produces multi-scale predictions for each input. Through applying SLS loss to different scales of predictions, different scales of targets can attract different attention from the detector, resulting in an overall better detection performance. Experimental results show that MSHNet achieves SOTA detection performance with the better balance of inference time and the number of floating point of operations. While applying our SLS loss to other existing detectors, the overall detection performance can be boosted. However, more false alarms may be introduced. Through the analysis in Sec. 5.4, we find that such a phenomenon is brought by the location sensitive loss in SLS loss which potentially treats some noises as targets. In future works, we try to handle this by designing more suitable location sensitive loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.64, + 0.777 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.901 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (62331006,62171038, 62088101, and 62371175), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), the Key R&D Program of Zhejiang (2023C01044), the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK239909299001-013), and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17497" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Linwei Chen, Ying Fu, Kaixuan Wei, Dezhi Zheng, and Felix Heide. 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In Proceedings of the AAAI Conference on Artificial Intelligence, pages 12993-13000, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17499" + } + ] +] \ No newline at end of file diff --git a/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_origin.pdf b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e8b53e6847449e25910ece9095f4899a626656c5 --- /dev/null +++ b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/cc1c597c-b63f-4045-ac03-6fa4f61276e6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e493f947a5017fddbc05c01649f530bb45bda121e4b569ba25dc24c05a7bc561 +size 2293956 diff --git a/2024/Infrared Small Target Detection with Scale and Location Sensitivity/full.md b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c16f955618a2788fe4a8e46a981edde8302489ad --- /dev/null +++ b/2024/Infrared Small Target Detection with Scale and Location Sensitivity/full.md @@ -0,0 +1,317 @@ +# Infrared Small Target Detection with Scale and Location Sensitivity + +Qiankun Liu $^{1}$ Rui Liu $^{1,2}$ Bolun Zheng $^{3}$ Hongkui Wang $^{3}$ Ying Fu $^{1,2*}$ $^{1}$ Beijing Institute of Technology $^{2}$ Yangtze Delta Region Academy of Beijing Institute of Technology $^{3}$ Hangzhou Dianzi University + +{liuqk3, liurui20}@bit.edu.cn, {blzheng, wanghk}@hdu.edu.cn, fuying@bit.edu.cn + +# Abstract + +Recently, infrared small target detection (IRSTD) has been dominated by deep-learning-based methods. However, these methods mainly focus on the design of complex model structures to extract discriminative features, leaving the loss functions for IRSTD under-explored. For example, the widely used Intersection over Union (IoU) and Dice losses lack sensitivity to the scales and locations of targets, limiting the detection performance of detectors. In this paper, we focus on boosting detection performance with a more effective loss but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses: 1) for scale sensitivity, we compute a weight for the IoU loss based on target scales to help the detector distinguish targets with different scales; 2) for location sensitivity, we introduce a penalty term based on the center points of targets to help the detector localize targets more precisely. Then, we design a simple Multi-Scale Head to the plain U-Net (MSHNet). By applying SLS loss to each scale of the predictions, our MSHNet outperforms existing state-of-the-art methods by a large margin. In addition, the detection performance of existing detectors can be further improved when trained with our SLS loss, demonstrating the effectiveness and generalization of our SLS loss. The code is available at https://github.com/ying-fu/MSHNet. + +# 1. Introduction + +Infrared small target detection (IRSTD) is an important computer vision task, which has a wide range of applications, such as maritime surveillance [20, 34], traffic management [26, 27, 30] and so on. However, due to the long-distance camera capture, and the noise and clutter interference, infrared targets are often small and dim, making it difficult to detect infrared small targets effectively. + +To enhance the detection performance of infrared small + +![](images/3e20815e9c661f3c3b80f9e0351b6946e7ffe434f9f3f28dcd02fd9dc1356aeb.jpg) +Figure 1. Visualization of the detection performance (IoU), inference time consumption (Images/second) as well as the number of floating point of operations (area of circles) of some deep-learning-based methods. It can be seen that our MSHNet achieves a better balance between these three metrics than other methods. Results are evaluated on IRSTD-1k [30]. + +targets, numerous methods have been proposed. Early traditional methods can be divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10], and low-rank-based methods [2, 28, 29, 31]. However, these traditional methods rely on manually designed features, and thus can not generalize well to environment changes. Recently, with the development of Deep Learning (DL), IRSTD has been dominated by DL-based methods [1, 15, 21, 24]. Different from traditional methods, DL-based methods can automatically learn useful features through a gradient descent algorithm with the constraints of loss functions, making them more robust to various scenarios. + +However, existing DL-based methods primarily focus on designing complex model structures for feature extraction, leaving the loss functions for IRSTD under-explored. For instance, Li et.al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion, and Wu et.al. [25] nest the U-Net structure to achieve feature aggregation. Although discriminative features can be extracted by the complex model structures, the detection performance is still limited by the under-explored loss functions. For ex + +ample, the widely used Intersection over Union (IoU) loss and Dice loss [18] lack sensitivity to the scales and locations of targets. As shown in Fig. 2, targets with different scales (top row) and locations (bottom row) may share the same IoU loss or Dice loss. This insensitivity to scales and locations makes it challenging for detectors to distinguish targets of different scales and locations, which ultimately limits the detection performance. + +In this paper, we focus on boosting detection performance with a more effective loss function but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses. The merits of the proposed SLS loss include: (1) Scale sensitivity. We compute a weight for the IoU loss based on the predicted and ground-truth scales of targets. The larger the gap between predicted and ground-truth scales is, the more attention will be paid by the detector. (2) Location Sensitivity. We design a location penalty based on the predicted and ground-truth center points of targets. Compared with traditional L1 and L2 distances, the designed location penalty produces the same value for fewer different location errors, making the detector locate targets more precisely. Then, we introduce a simple Multi-Scale Head to the plain U-Net (MSHNet), which produces multiscale predictions for each input. Through leveraging SLS loss at different scales, our MSHNet outperforms existing state-of-the-art (SOTA) methods by a large margin. With the absence of complex structures, our detector achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption, as shown in Fig. 1. Moreover, we further train different existing detectors with our SLS loss and achieve better detection performance, demonstrating the effectiveness and generalization of our SLS loss. + +In summary, our main contributions are: + +- We propose a novel scale and location sensitive loss for infrared small target detection, which helps detectors distinguish objects with different scales and locations. +- We propose a simple but effective detector by introducing a multi-scale head to the plain U-Net, which achieves SOTA performance without bells and whistles. +- We apply our loss to existing detectors and show that the detection performance can be further boosted, demonstrating the effectiveness and generalization of our loss. + +# 2. Related Work + +In this section, we first make a brief introduction to existing methods for IRSTD. Then we provide a review of related works from the perspectives of loss functions and model structures for IRSTD. + +![](images/a8cee4a84ad70e1e7b862bc3d824ff324e5da3c662db7cd91382b951ad3a9fc8.jpg) +$\mathcal{L}_{SLS} = 0.94$ + +![](images/c432f4f31bb60deeacd71c532f50ac3ecf7ea86a35b89106d5aa0f7fd301ad80.jpg) +$\mathcal{L}_{SLS} = 0.97$ + +![](images/21c6c2487c900d1f6fad41fe0169d1ebed21acfdc0e94911cf1e837479b298a0.jpg) +$\mathcal{L}_{SLS} = 0.92$ + +![](images/493150219f3d330f1ecbb562442f2710b5d0f93efe4c7936da7d2210cbd5b633.jpg) +$\mathcal{L}_{SLS} = 0.62$ + +![](images/c0ce9e9aefbd1d43777652542cfbb149d3220dd7d225f41eab89e15bc8edade4.jpg) +$\mathcal{L}_{SLS} = 0.64$ + +![](images/b1fc21b97ec3cd3475c18b0ca174e6848308516ba6b7c83db3826a206ff9c335.jpg) +$\mathcal{L}_{SLS} = 0.59$ +Figure 2. Top row: our SLS loss for the targets of different scales, where IoU loss $(=0.4)$ and Dice loss $(=0.57)$ have the same values for different cases. Bottom row: our SLS loss for the targets of different locations, where IoU loss $(=0.3)$ and Dice loss $(=0.43)$ have the same values for different cases. + +# 2.1. Infrared Small Target Detection + +Existing IRSTD methods can be roughly divided into traditional methods and Deep-Learning-based (DL-based) methods. Among them, traditional methods depend on the hand-crafted priors and can be further divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10, 12], and low-rank-based methods [2, 6, 8, 19, 28, 29, 32]. To get useful features with such hand-crafted priors, lots of hyperparameters need to be manually fine-tuned, making them less robust to the interference of noises and clutters. Differently, DL-based methods [3, 7, 14, 15, 21, 25, 30, 33] can automatically learn useful features with the help of loss functions and gradient descent algorithms. Though impressive detection performance has been achieved, existing DL-based methods mainly focus on the design of model structures for the pursuit of more effective features, leaving the loss functions for IRSTD under-explored. + +Different from existing DL-based methods, we focus on boosting detection performance with a more effective loss function but a simpler model structure. A better balance between detection performance, FLOPs and inference time consumption can be achieved. + +# 2.2. Loss Functions for IRSTD + +As one of the components in DL-based methods, the loss function plays a critical role in the learning process of deep models by quantifying the disparity between predictions and ground-truths. The commonly adopted IoU loss and Dice loss [18] suffer from insensitivity to the scales and locations of targets, rendering the detectors for distinguishing the targets of different scales and locations accurately. + +In order to achieve better detection performance, researchers have developed several loss functions. For example, the loss for adversarial training [21], edge loss for the detecting of target edges [30] and the likelihood loss between target and background maps [11]. However, these + +![](images/a3900cf293ec5a3ced48697cc45d67611670668830188763afb50eb84a6f8629.jpg) +Figure 3. Left: the value of weight $w$ in scale sensitive loss with respect to the number of predicted pixels and ground-truth pixels (i.e., predicted and ground-truth scales). Right: the normalized location sensitive loss with respect to the location error between the predicted center point and ground-truth center point. The range of [0, 100] pixels is shown for illustration. + +losses are tailored for specific network architectures, limiting their broader utility. Different from these dedicated losses, the generalized IoU (GIoU) [16] and complete IoU (CIoU) [35] losses have been adopted for box-level IRSTD [13, 23]. However, these IoU variant losses still lack the sensitivity of scales and locations. + +In contrast to these losses, we formulate a general loss function that is better suitable for IRSTD. It can distinguish targets of different scales and locations, enabling different detectors to achieve better detection performance. + +# 2.3. Model Structures for IRSTD + +The deep model is another key component in DL-based methods. Liu et al. [15] pioneer the application of deep learning to IRSTD. The adopted five-layer Multi-Layer Perceptron (MLP) network demonstrates the superiority of DL-based methods in IRSTD. Recently, lots of works have focused on the design of model structures to get more effective features. Li et al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion. Zhang et al. [30] utilize Taylor finite difference and orientation attention strategy to extract edge information of targets. However, such complex model structures not only bring more computational cost but still suffer from moderate detection performance due to the lack of effective loss functions. + +Differently we introduce a simple multi-scale head to the plain U-Net, rather than designing complex structures. By applying our SLS loss to different scales, SOTA performance is achieved with less time consumption. + +# 3. Scale and Location Sensitive Loss + +The scale and location sensitive (SLS) loss, denoted as $\mathcal{L}_{\text{SLS}}$ , is designed to handle the insensitivity of scales and locations in existing losses. It consists of a scale sensitive loss and a location sensitive loss. Formally, + +$$ +\mathcal {L} _ {S L S} = \mathcal {L} _ {S} + \mathcal {L} _ {L}, \tag {1} +$$ + +where $\mathcal{L}_S$ and $\mathcal{L}_L$ present the scale sensitive loss and location sensitive loss, respectively. In the following, we introduce the SLS loss in detail starting from the scale sensitive loss, which is based on the commonly used IoU loss. + +# 3.1. Scale Sensitive Loss + +Let $A_{p}$ and $A_{gt}$ be the set of predicted pixels and ground-truth pixels of targets, the IoU loss between them can be formulated as: + +$$ +\mathcal {L} _ {I o U} = 1 - \frac {\left| A _ {p} \cap A _ {g t} \right|}{\left| A _ {p} \cup A _ {g t} \right|}. \tag {2} +$$ + +Though having been widely used in IRSTD, the IoU loss is insensitive to the scales and locations of targets, as shown in Fig. 2. The scale sensitive loss is implemented by providing a weight to the IoU loss: + +$$ +\mathcal {L} _ {S} = 1 - w \frac {\left| A _ {p} \cap A _ {g t} \right|}{\left| A _ {p} \cup A _ {g t} \right|}, \tag {3} +$$ + +$$ +\mathrm {s . t .} \quad w = \frac {\operatorname* {m i n} (| A _ {p} | , | A _ {g t} |) + \operatorname {V a r} (| A _ {p} | , | A _ {g t} |)}{\operatorname* {m a x} (| A _ {p} | , | A _ {g t} |) + \operatorname {V a r} (| A _ {p} | , | A _ {g t} |)}, +$$ + +where $\operatorname{Var}(\cdot, \cdot)$ is the function that gets the variance of provided scalars. + +On the left of Fig. 3, we visualize the values of $w$ with respect to the number of pixels in $A_{p}$ and $A_{gt}$ . It can be observed that the larger the gap between $|A_{p}|$ and $|A_{gt}|$ is, the smaller the $w$ is, which results in a larger scale sensitive loss (on the assumption that the IoU between $A_{p}$ and $A_{gt}$ is fixed). The intuition behind the design of $w$ is that the detector should pay more attention to the target with a larger loss if the predicted and ground-truth scales (i.e., the numbers of pixels in $A_{p}$ and $A_{gt}$ ) are quite different. + +# 3.2. Location Sensitive Loss + +The location sensitive loss is calculated based on the predicted and ground-truth center points of targets. Given the sets of predicted pixels $A_{p}$ and ground-truth pixels $A_{gt}$ , the corresponding center points for $A_{p}$ and $A_{gt}$ are obtained by averaging the coordinates of all pixels, which are denoted as $\mathbf{c}_p = (x_p,y_p)$ and $\mathbf{c}_{gt} = (x_{gt},y_{gt})$ , respectively. Then, we convert the coordinates of these two center points into the polar coordinate system. Take $\mathbf{c}_p$ for example, the corresponding distance $d_{p}$ and angle $\theta_{p}$ in the polar coordinate system are: + +$$ +d _ {p} = \sqrt {x _ {p} ^ {2} + y _ {p} ^ {2}}, +$$ + +$$ +\theta_ {p} = \arctan \left(\frac {y _ {p}}{x _ {p}}\right). \tag {4} +$$ + +The location sensitive loss can be obtained by: + +$$ +\mathcal {L} _ {L} = \left(1 - \frac {\operatorname* {m i n} \left(d _ {p} , d _ {g t}\right)}{\operatorname* {m a x} \left(d _ {p} , d _ {g t}\right)}\right) + \frac {4}{\pi^ {2}} \left(\theta_ {p} - \theta_ {g t}\right) ^ {2}, \tag {5} +$$ + +![](images/2a36d453dc002d6f42daed267c38909b1106ea87c71b51ca635a7c654aea35f8.jpg) +Figure 4. Overview of the proposed MSHNet. Our MSHNet is implemented based on a plain U-Net without bells and whistles. Only a simple multi-scale head is introduced. For each scale, the feature map is fed into a dedicated head, producing a prediction with the same spatial shape as the feature map. Different scales of predictions are upsampled (if needed) and concatenated together to get the final prediction. In the training stage, our SLS loss is applied to each of these predictions since it is scale sensitive. + +where $d_{gt}$ and $\theta_{gt}$ are the distance and angle of $\mathbf{c}_{gt}$ in the polar coordinate system, respectively. + +On the right of Fig. 3, we show how the location loss changes with respect to different location errors between $\mathbf{c}_p$ and $\mathbf{c}_{gt}$ . As we can see, though some different location errors share the same loss value (these location errors still can be distinguished with their gradients), the location loss distinguishes most of the different location errors effectively, making the detector sensitive to different types of location errors and locate the targets more accurately. + +# 4. MSHNet Detector + +In this section, we introduce our MSHNet detector, which is implemented by introducing a simple but effective multiscale head to the plain U-Net. The overview of MSHNet is shown in Fig. 4. We take the commonly used U-Net as the backbone network. The feature maps that have different scales in the decoder are fed into different prediction heads to get different scales of predictions. All the predictions from different feature maps are finally concatenated (upsampling before concatenation is adopted if needed) to get the final prediction. In the training stage, our SLS loss is applied to each of the predictions. In the following, the multi-scale head is first described in detail. Then we introduce the utilization of SLS loss in MSHNet. + +# 4.1. Multi-Scale Head + +Let $\mathbf{x}_i\in \mathbb{R}^{H_i\times W_i\times C_i}$ be the feature map at the $i$ -th scale in the decoder of U-Net, where $H_{i}\times W_{i}$ is the spatial size and $C_i$ is the number of channels. Following the common settings within existing works, there are 4 scales in U-Net, which means that $i\in \{1,2,3,4\}$ . Supposing the input spatial size is $H\times W$ , then $H_{i} = \frac{H}{2^{4 - i}}$ and $W_{i} = \frac{W}{2^{4 - i}}$ . + +The $i$ -th prediction $\mathbf{p}_i \in \mathbb{R}^{\bar{H}_i \times W_i \times 1}$ is obtained by the corresponding prediction head, which is implemented by a convolution layer and a sigmoid activation function: + +$$ +\mathbf {p} _ {i} = \operatorname {S i g m o i d} \left(\operatorname {C o n v} \left(\mathbf {x} _ {i}\right)\right). \tag {6} +$$ + +Note that different prediction heads have their own dedicated parameters. The final prediction $\mathbf{p} \in \mathbb{R}^{H \times W \times 1}$ is obtained based on all the 4 predictions: + +$$ +\mathbf {p} = \operatorname {S i g m o i d} \left(\operatorname {C o n v} \left(\left[ \uparrow \left(\mathbf {p} _ {1}, 8\right), \uparrow \left(\mathbf {p} _ {2}, 4\right), \uparrow \left(\mathbf {p} _ {3}, 2\right), \mathbf {p} _ {4} \right]\right)\right), \tag {7} +$$ + +where $\Uparrow (\cdot ,\cdot)$ is the operation that spatially upsamples the first argument with the second argument as the factor, and $[\cdot ,\dots ,\cdot ]$ concatenates all the provided arguments along the channel dimensionality. + +# 4.2. Training MSHNet with SLS Loss + +Since our SLS loss is scale sensitive and there are several scales in the predictions of MSHNet, we apply SLS loss to all of the predictions. The inspiration is that our SLS loss produces different loss values for different scales even if they share the same spatial layout (refer to the first two cases in the top row, Fig. 2). We hypothesize that by applying our SLS loss to different scales, the targets that are with different scales can attract different attention from the detector, resulting in an overall better detection performance. + +Let $\mathbf{p}_{gt} \in \{0,1\}^{H \times W \times 1}$ be the ground-truth label. The final loss for MSHNet is: + +$$ +\mathcal {L} = \frac {1}{5} \left(\sum_ {i = 1} ^ {4} \mathcal {L} _ {S L S} \left(\mathbf {p} _ {i}, \Downarrow \left(\mathbf {p} _ {g t}, 2 ^ {4 - i}\right)\right) + \mathcal {L} _ {S L S} \left(\mathbf {p}, \mathbf {p} _ {g t}\right)\right), \tag {8} +$$ + +where $\Downarrow (\cdot ,\cdot)$ is the operation (i.e., max-pooling) that spatially downsamples the first argument with the second argument as the factor, and $\mathcal{L}_{SLS}(\cdot ,\cdot)$ is our SLS loss. + +# 5. Experiments + +In this section, the adopted datasets and metrics are firstly introduced, followed by the implementation details. Then, we compare the proposed method MSHNet with existing IRSTD detectors. Finally, discussions are provided to show the effectiveness of our Scale and Location Sensitive loss and MHSNet detector. + +
MethodDescriptionIRSTD-1kNUDT-SIRST
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
Top-Hat [17]Filtering10.0675.11143220.7278.41166.7
Max-Median [5]6.99865.2159.734.19758.4136.89
WSLCM [10]Local Contrast3.45272.4466192.28356.821309
TLLCM [9]3.31177.3967382.17662.011608
IPI [8]Low Rank27.9281.3716.1817.7674.4941.23
NRAM [29]15.2570.6816.936.92756.4019.27
RIPT [2]14.1177.5528.3129.4491.85344.3
PSTNN [28]24.5771.9935.2614.8566.1344.17
MSLSTIPT [19]11.4379.0315248.34247.40888.1
MDvsFA [21]Deep Learning37.3483.7188.5235.8685.2295.37
ALCNet [4]65.6889.2527.7172.8996.1930.40
ISNet [30]62.8892.5927.9267.8692.5934.65
DNANet [14]65.7191.8417.6179.9896.9312.78
MSHNet (Ours)67.1693.8815.0380.5597.9911.77
+ +Table 1. Quantitative results of different methods. Results for the metrics of IoU(%, Pd(%) and Fa(10-6) are presented. The best values are highlighted with bold. It can be seen that our MSHNet achieves the best results on different metrics and datasets. + +# 5.1. Datasets and Metrics + +Datasets. The experiments are conducted on two datasets i.e., IRSD-1k [30] and NUDT-SIRST [14]. There are 1,001 and 1,327 infrared images in IRSTD-1k and NUDT-SIRST, respectively. Following existing works [14, 30], the images in IRSTD-1k are divided into the training and testing splits with a ratio of 4:1, while the images in NUDT-SIRST are equally divided into the training and testing splits. + +Evaluation Metrics. We use IoU and false alarm rate $(\mathrm{F_a})$ as the pixel-level evaluation metric and assess target-level performance using the probability of detection $(\mathrm{P_d})$ . Different metrics reveal the performance of the detector from different aspects. $\mathrm{F_a}$ and $\mathrm{P_d}$ focus on recall and false alarms, while IoU takes both into consideration. + +Formally, The false alarm rate is: + +$$ +\mathrm {F} _ {\mathrm {a}} = \frac {P _ {\text {f a l s e}}}{P _ {\text {a l l}}}, \tag {9} +$$ + +where $P_{false}$ is the number of false positive pixels and $P_{all}$ is the number of all pixels in the image. + +The probability of detection is: + +$$ +P _ {d} = \frac {N _ {p r e d}}{N _ {a l l}}, \tag {10} +$$ + +where $N_{pred}$ is the number of correctly predicted targets and $N_{all}$ is the number of all targets. + +# 5.2. Implementation Details + +The proposed method is implemented with PyTorch framework. Following existing works, the input size of the detector is set to $256 \times 256$ . We train different models using + +AdaGrad on 2 RTX3090 GPUs. The batch size is set to 4 and the learning rate is set to 0.05. + +# 5.3. Comparison to Existing Methods + +We first compare the proposed MSHNet with existing methods. Different types of methods are evaluated, including traditional methods and deep-learning-based methods. The evaluated traditional methods are the filtering-based Top-Hat [17] and Max-Median [5], local-contrast-based WSLCM [10] and TLLCM [9], low-rank-based IPI [8], NRAM [29], RIPT [2], PSTNN [28] and MSLSTIPT [19]. The deep-learning-based methods are MDvsFA [21], ALCNet [4], ISNet [30], and DNANet [14]. For a fair comparison, all the evaluated deep-learning-based models are retrained with their official codes to their convergence on NUDT-SIRST [14] and IRSTD-1k [30] datasets. + +Quantitative Results. The quantitative results of different methods are presented in Tab. 1. Overall, our MSHNet performs the best on all metrics and all datasets. + +As expected, traditional methods perform poorly on these challenging datasets due to the limitations of manually designed priors for feature extraction. In contrast, DL-based methods can automatically learn useful features and yield better results than traditional methods. Nevertheless, existing DL-based methods lack the consideration of different scales and locations of targets in the training stage. The predictions of existing DL-based methods suffer from the incomplete shape and missed detection of valid pixels, e.g., lower IoU and $\mathrm{P_d}$ . Compared with DNANet, which is one of the existing SOTA DL-based methods, our MSHNet achieves $1.45\%$ and $0.57\%$ higher IoU, $2.04\%$ and $1.06\%$ higher $\mathrm{P_d}$ on IRSTD-1k and NUAA-SIRST datasets, re + +![](images/5620e2067139fb0ccbc6da094279699e7a8d1783fa8b2e40ffe72108d5016c75.jpg) +Figure 5. Visual comparison of detection results on several infrared images. Correctly detected targets, missed targets, and false alarms are framed by red, blue, and yellow boxes, respectively. A close-up view of the target is shown in image corners. + +spectively. In addition, the false alarm $(\mathrm{F_a})$ on both datasets are all reduced by a large margin, demonstrating the superiority of our method. + +As mentioned before, there are no complex model structures in MSHNet, which achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption. The results of DL-based methods are presented in Fig. 1. It can be observed that MSHNet has the best detection performance and the least inference time consumption. It also has the least number of FLOPs except for ALCNet. We own the less inference time consumption of MSHNet to the smaller number of FLOPs and the simple architectures (complex structures in deep models bring more inference time consumption [22]). The better detection performance demonstrates the effectiveness of the proposed multi-scale head and the scale and location sensitive loss. + +Qualitative Results. For different kinds of methods, we visualize the detection results of the representative methods in Fig. 5 and Fig. 6. It can be observed that our method has + +better capability for the detection of challenging small targets. Traditional methods are susceptible to noise interference, resulting in a large number of false alarms. Moreover, due to the small scale and low contrast of the target, traditional methods and other DL-based methods struggle to effectively extract feature information of small targets from challenging scenarios, resulting in a considerable number of missed targets. In contrast, our methods can accurately distinguish small targets from these low-contrast infrared images. Take the case in the 5-th row in Fig. 5 for example, except for MSHNet and WLSLCM, other methods fail to detect the target. Moreover, from the peaks and the area under the peaks in Fig. 6, it can be observed that our method predicts targets with higher confidence and obtains a closer number of peaks with ground-truth. We attribute the superiority of MSHNet to the scale and location sensitivity brought by our SLS loss and multi-scale head. + +# 5.4. Discussions + +We provide some discussions to show the effectiveness of our method. Experiments are conducted on IRSTD-1k dataset. + +![](images/c2d05797e53f5c4ec37fce171c25e7a1cafba1b66f3e081738c156dcb5ae11d6.jpg) +Figure 6. 3D visualization results corresponding to those in Fig. 5. Different colors represent distinct grayscale values, ranging from blue to yellow, with values gradually increasing. Please zoom in for better viewing. + +Detection Results for Different Scales of Targets. Since our SLS loss and MSHNet both are scale sensitive, we show how the detection performance changes with respect to different scales of targets. To do this, we split the targets into three different scale levels according to the number of pixels: (0,10], (10, 40] and $(40,\infty]$ . Results are shown in Tab. 2. Due to the limited space, only several DL-based methods are evaluated (specifically, ISNet, DNANet and our MSHNet). Compared with DNANet, MSHNet performs better for all scale levels of targets. Compared with ISNet, MSHNet achieves comparable performance with ISNet for (0,10] and (10,40] scales but much better performance for $(40,\infty]$ scale. The conclusion is that MSHNet can pay attention to different scale levels of targets, resulting in an overall better performance. + +Impact of Scale and Location Sensitive Loss. We compare our SLS loss with the commonly used IoU loss and Dice loss. The results of several DL-based methods trained with different losses are presented in Tab. 3. Overall, the detection performance of different detectors is all improved by our SLS loss in terms of IoU metric, demonstrating the effectiveness and generalization of SLS loss. However, it is hard to tell which loss performs the best on the metric of $\mathrm{P_d}$ . Interestingly, adopting our SLS loss results in a poorer performance on $\mathrm{F_a}$ metric. The reason is that more false alarm pixels may be treated as positive targets since our SLS loss tries to distinguish the targets of all different scales. + +Next, we show the effectiveness of scale sensitive loss + +
ScaleMethodIoU↑Pd↑Fa↓
(0,10]DNANet [3]47.2691.2722.53
ISNet [14]50.9494.5330.91
MSHNet (Ours)49.5195.2420.68
(10,40]DNANet [3]63.1491.8513.25
ISNet [14]65.4191.9116.60
MSHNet (Ours)64.7991.858.03
(40,∞]DNANet [3]78.4693.946.78
ISNet [14]66.4587.8758.80
MSHNet (Ours)79.2096.9711.02
+ +Table 2. Comparisons of different methods in terms of different scales of targets. Results for the metrics of IoU(\%), $\mathrm{P_d}(\%)$ and $\mathrm{F_a}(10^{-6})$ are presented. Our MSHNet achieves overall the best performance. + +$(\mathcal{L}_S)$ and location sensitive loss $(\mathcal{L}_L)$ separately. To do this, we train MSHNet with different losses. The results are presented in Tab. 4. Note that the difference between $\mathcal{L}_S$ and $\mathcal{L}_{IoU}$ lies in the newly introduced weight $w$ (refer to Sec. 3.1). By comparing the results in the first two rows, we can find that the introduction of $w$ (refer to Eq. (3)) is positive to the metrics of IoU and $\mathrm{F_a}$ , indicating that the detector produces more accurate shapes for targets as well as less false alarms. While comparing the results in the last two rows, it can be observed that more false alarms will be produced when the location sensitive loss is introduced. However, both IoU and $\mathrm{P_d}$ are greatly improved. + +Finally, we make a study on different types of location sensitive loss. As mentioned in Sec. 3.2, our location sen + +
LossDNANet [3]ISNet [14]MSHNet (Ours)
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
L IoU65.7191.8417.6162.8892.5927.9264.8391.165.28
L Dice65.5892.1712.7562.9490.9119.2665.3692.1814.12
L SLS (Ours)67.0992.1535.1564.4292.2615.1467.1693.8815.03
+ +Table 3. Comparisons of different losses and detectors. Results for the metrics of IoU(\%), $\mathrm{P_d}(\%)$ and $\mathrm{F_a}(10^{-6})$ are presented. The main IoU metrics of different detectors are consistently boosted by our scale and location sensitive loss. + +
LossIoU↑Pd↑Fa↓
LS w/o. w64.8391.165.28
LS65.8289.464.06
LS + LL67.1693.8815.03
+ +Table 4. Ablation study of the scale sensitive loss $(\mathcal{L}_S)$ and location sensitive loss $(\mathcal{L}_L)$ . Results are obtained by MSHNet. The metrics of IoU(\%), $\mathrm{P_d}(\%)$ and $\mathrm{F_a}$ $(10^{-6})$ are adopted. Note that $\mathcal{L}_S$ without $w$ is equivalent to $\mathcal{L}_{IoU}$ . + +
LossIoU↑Pd↑Fa↓
LS+L264.8992.867.29
LS+L164.7593.546.18
LS+L67.1693.8815.03
+ +sitive loss can distinguish different location errors more effectively. To show the effectiveness of such distinguishability, we use the $L_{2}$ and $L_{1}$ distances between $\mathbf{c}_p$ and $\mathbf{c}_{gt}$ as the location sensitive loss (denoted as $\mathcal{L}_{L_2}$ and $\mathcal{L}_{L_1}$ , respectively). Results are shown in Tab. 5. As we can see, the distinguishability of different location errors is effective in getting better IoU and $\mathrm{P_d}$ metrics. However, more false alarms are produced (higher $\mathrm{F_a}$ ). Such phenomenon is also observed from Tab. 4. The reason may be that the distinguishability of different location errors makes the detector more sensitive to small targets, resulting in the potential of treating some noises to targets. + +Impact of Multi-Scale Heads. Now we ablate the number of scales in our multi-scale head. Results are shown in Tab. 6. As we can see, different predictions achieve different detection performance. Overall, the more scales adopted, the better the detection performance is achieved. For example, the IoU is improved from $63.10\%$ to $67.16\%$ when the number of scales is increased from 1 to 4. We use 4 scales by default. + +# 6. Conclusion + +In this paper, we focus on boosting the performance of infrared small target detection with an effective loss function + +Table 5. Ablation study of different types of location sensitive loss. Results are obtained by MSHNet. The metrics of IoU(%, $\mathrm{P_d}(\%)$ and $\mathrm{F_a}(10^{-6})$ are adopted. + +
Num. of ScalesSupervised PredictionsIoU↑Pd↑Fa↓
1p63.1086.7319.21
1p4,p64.6993.8736.74
2p3,p4,p64.3594.8935.38
3p2,p3,p4,p65.9093.5424.37
4p1,p2,p3,p4,p67.1693.8815.03
+ +Table 6. Ablation study of the number of scales in MSHNet. While reducing the number of adopted scales, the remaining smallest scale is removed. Results for the metrics of IoU(\%), $\mathrm{P_d}(\%)$ and $\mathrm{F_a} (10^{-6})$ are presented. + +but a simpler model structure. To do this, a Scale and Location Sensitive (SLS) loss is first proposed. The merits of SLS loss include: (1) it pays more attention to the targets that have large gaps between the predicted and ground-truth scales; (2) it distinguishes different types of location errors between the predicted and ground-truth center points of targets. Then a simple Multi-Scale Head is introduced to the plain U-Net (MSHNet), which produces multi-scale predictions for each input. Through applying SLS loss to different scales of predictions, different scales of targets can attract different attention from the detector, resulting in an overall better detection performance. Experimental results show that MSHNet achieves SOTA detection performance with the better balance of inference time and the number of floating point of operations. While applying our SLS loss to other existing detectors, the overall detection performance can be boosted. However, more false alarms may be introduced. Through the analysis in Sec. 5.4, we find that such a phenomenon is brought by the location sensitive loss in SLS loss which potentially treats some noises as targets. In future works, we try to handle this by designing more suitable location sensitive loss. + +# Acknowledgements + +This work was supported by the National Natural Science Foundation of China (62331006,62171038, 62088101, and 62371175), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), the Key R&D Program of Zhejiang (2023C01044), the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK239909299001-013), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Linwei Chen, Ying Fu, Kaixuan Wei, Dezhi Zheng, and Felix Heide. Instance segmentation in the dark. International Journal of Computer Vision, 131(8):2198-2218, 2023. 1 +[2] Yimian Dai and Yiquan Wu. Reweighted infrared patch-tensor model with both nonlocal and local priors for single-frame small target detection. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14443-14452, 2023. 6 +[23] Kewei Wang, Shuaiyuan Du, Chengxin Liu, and Zhiguo Cao. Interior attention-aware network for infrared small target detection. IEEE Transactions on Geoscience and Remote Sensing, 60:1-13, 2022. 3 +[24] Kaixuan Wei, Angelica I Aviles-Rivero, Jingwei Liang, Ying Fu, Hua Huang, and Carola-Bibiane Schonlieb. Tfnpp: Tuning-free plug-and-play proximal algorithms with applications to inverse imaging problems. J. Mach. Learn. Res., 23(16):1-48, 2022. 1 +[25] Xin Wu, Danfeng Hong, and Jocelyn Chanussot. Uiu-net: U-net in u-net for infrared small object detection. IEEE Transactions on Image Processing, 32:364-376, 2022. 1, 2 + +[26] Xinyi Ying, Li Liu, Yingqian Wang, Ruojing Li, Nuo Chen, Zaiping Lin, Weidong Sheng, and Shilin Zhou. Mapping degeneration meets label evolution: Learning infrared small target detection with single point supervision. 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Distance-iou loss: Faster and better learning for bounding box regression. 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However, these methods mainly focus on the design of complex model structures to extract discriminative features, leaving the loss functions for IRSTD under-explored. For example, the widely used Intersection over Union (IoU) and Dice losses lack sensitivity to the scales and locations of targets, limiting the detection performance of detectors. In this paper, we focus on boosting detection performance with a more effective loss but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses: 1) for scale sensitivity, we compute a weight for the IoU loss based on target scales to help the detector distinguish targets with different scales; 2) for location sensitivity, we introduce a penalty term based on the center points of targets to help the detector localize targets more precisely. Then, we design a simple Multi-Scale Head to the plain U-Net (MSHNet). By applying SLS loss to each scale of the predictions, our MSHNet outperforms existing state-of-the-art methods by a large margin. In addition, the detection performance of existing detectors can be further improved when trained with our SLS loss, demonstrating the effectiveness and generalization of our SLS loss. The code is available at https://github.com/ying-fu/MSHNet." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 597, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 681 + ], + "type": "text", + "content": "Infrared small target detection (IRSTD) is an important computer vision task, which has a wide range of applications, such as maritime surveillance [20, 34], traffic management [26, 27, 30] and so on. However, due to the long-distance camera capture, and the noise and clutter interference, infrared targets are often small and dim, making it difficult to detect infrared small targets effectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 681, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 681, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 59, + 681, + 287, + 693 + ], + "type": "text", + "content": "To enhance the detection performance of infrared small" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 226, + 547, + 362 + ], + "blocks": [ + { + "bbox": [ + 307, + 226, + 547, + 362 + ], + "lines": [ + { + "bbox": [ + 307, + 226, + 547, + 362 + ], + "spans": [ + { + "bbox": [ + 307, + 226, + 547, + 362 + ], + "type": "image", + "image_path": "3e20815e9c661f3c3b80f9e0351b6946e7ffe434f9f3f28dcd02fd9dc1356aeb.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 370, + 547, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 370, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 547, + 437 + ], + "type": "text", + "content": "Figure 1. Visualization of the detection performance (IoU), inference time consumption (Images/second) as well as the number of floating point of operations (area of circles) of some deep-learning-based methods. It can be seen that our MSHNet achieves a better balance between these three metrics than other methods. Results are evaluated on IRSTD-1k [30]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "content": "targets, numerous methods have been proposed. Early traditional methods can be divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10], and low-rank-based methods [2, 28, 29, 31]. However, these traditional methods rely on manually designed features, and thus can not generalize well to environment changes. Recently, with the development of Deep Learning (DL), IRSTD has been dominated by DL-based methods [1, 15, 21, 24]. Different from traditional methods, DL-based methods can automatically learn useful features through a gradient descent algorithm with the constraints of loss functions, making them more robust to various scenarios." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "However, existing DL-based methods primarily focus on designing complex model structures for feature extraction, leaving the loss functions for IRSTD under-explored. For instance, Li et.al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion, and Wu et.al. [25] nest the U-Net structure to achieve feature aggregation. Although discriminative features can be extracted by the complex model structures, the detection performance is still limited by the under-explored loss functions. For ex" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17490" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "ample, the widely used Intersection over Union (IoU) loss and Dice loss [18] lack sensitivity to the scales and locations of targets. As shown in Fig. 2, targets with different scales (top row) and locations (bottom row) may share the same IoU loss or Dice loss. This insensitivity to scales and locations makes it challenging for detectors to distinguish targets of different scales and locations, which ultimately limits the detection performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 173, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 173, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 289, + 483 + ], + "type": "text", + "content": "In this paper, we focus on boosting detection performance with a more effective loss function but a simpler model structure. Specifically, we first propose a novel Scale and Location Sensitive (SLS) loss to handle the limitations of existing losses. The merits of the proposed SLS loss include: (1) Scale sensitivity. We compute a weight for the IoU loss based on the predicted and ground-truth scales of targets. The larger the gap between predicted and ground-truth scales is, the more attention will be paid by the detector. (2) Location Sensitivity. We design a location penalty based on the predicted and ground-truth center points of targets. Compared with traditional L1 and L2 distances, the designed location penalty produces the same value for fewer different location errors, making the detector locate targets more precisely. Then, we introduce a simple Multi-Scale Head to the plain U-Net (MSHNet), which produces multiscale predictions for each input. Through leveraging SLS loss at different scales, our MSHNet outperforms existing state-of-the-art (SOTA) methods by a large margin. With the absence of complex structures, our detector achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption, as shown in Fig. 1. Moreover, we further train different existing detectors with our SLS loss and achieve better detection performance, demonstrating the effectiveness and generalization of our SLS loss." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 490, + 223, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 490, + 223, + 501 + ], + "spans": [ + { + "bbox": [ + 59, + 490, + 223, + 501 + ], + "type": "text", + "content": "In summary, our main contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 506, + 287, + 613 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 506, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 287, + 542 + ], + "type": "text", + "content": "- We propose a novel scale and location sensitive loss for infrared small target detection, which helps detectors distinguish objects with different scales and locations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 543, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 543, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 543, + 287, + 577 + ], + "type": "text", + "content": "- We propose a simple but effective detector by introducing a multi-scale head to the plain U-Net, which achieves SOTA performance without bells and whistles." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 578, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 287, + 613 + ], + "type": "text", + "content": "- We apply our loss to existing detectors and show that the detection performance can be further boosted, demonstrating the effectiveness and generalization of our loss." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 639, + 134, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 134, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 134, + 652 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "In this section, we first make a brief introduction to existing methods for IRSTD. Then we provide a review of related works from the perspectives of loss functions and model structures for IRSTD." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 72, + 369, + 114 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 369, + 114 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 369, + 114 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 369, + 114 + ], + "type": "image", + "image_path": "a8cee4a84ad70e1e7b862bc3d824ff324e5da3c662db7cd91382b951ad3a9fc8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 322, + 118, + 361, + 127 + ], + "lines": [ + { + "bbox": [ + 322, + 118, + 361, + 127 + ], + "spans": [ + { + "bbox": [ + 322, + 118, + 361, + 127 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS} = 0.94" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 410, + 79, + 443, + 106 + ], + "blocks": [ + { + "bbox": [ + 410, + 79, + 443, + 106 + ], + "lines": [ + { + "bbox": [ + 410, + 79, + 443, + 106 + ], + "spans": [ + { + "bbox": [ + 410, + 79, + 443, + 106 + ], + "type": "image", + "image_path": "c432f4f31bb60deeacd71c532f50ac3ecf7ea86a35b89106d5aa0f7fd301ad80.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 118, + 449, + 127 + ], + "lines": [ + { + "bbox": [ + 411, + 118, + 449, + 127 + ], + "spans": [ + { + "bbox": [ + 411, + 118, + 449, + 127 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS} = 0.97" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 486, + 72, + 536, + 114 + ], + "blocks": [ + { + "bbox": [ + 486, + 72, + 536, + 114 + ], + "lines": [ + { + "bbox": [ + 486, + 72, + 536, + 114 + ], + "spans": [ + { + "bbox": [ + 486, + 72, + 536, + 114 + ], + "type": "image", + "image_path": "21c6c2487c900d1f6fad41fe0169d1ebed21acfdc0e94911cf1e837479b298a0.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 492, + 118, + 529, + 127 + ], + "lines": [ + { + "bbox": [ + 492, + 118, + 529, + 127 + ], + "spans": [ + { + "bbox": [ + 492, + 118, + 529, + 127 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS} = 0.92" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 315, + 143, + 374, + 172 + ], + "blocks": [ + { + "bbox": [ + 315, + 143, + 374, + 172 + ], + "lines": [ + { + "bbox": [ + 315, + 143, + 374, + 172 + ], + "spans": [ + { + "bbox": [ + 315, + 143, + 374, + 172 + ], + "type": "image", + "image_path": "493150219f3d330f1ecbb562442f2710b5d0f93efe4c7936da7d2210cbd5b633.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 322, + 180, + 360, + 189 + ], + "lines": [ + { + "bbox": [ + 322, + 180, + 360, + 189 + ], + "spans": [ + { + "bbox": [ + 322, + 180, + 360, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS} = 0.62" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 400, + 140, + 454, + 176 + ], + "blocks": [ + { + "bbox": [ + 400, + 140, + 454, + 176 + ], + "lines": [ + { + "bbox": [ + 400, + 140, + 454, + 176 + ], + "spans": [ + { + "bbox": [ + 400, + 140, + 454, + 176 + ], + "type": "image", + "image_path": "c0ce9e9aefbd1d43777652542cfbb149d3220dd7d225f41eab89e15bc8edade4.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 180, + 449, + 189 + ], + "lines": [ + { + "bbox": [ + 411, + 180, + 449, + 189 + ], + "spans": [ + { + "bbox": [ + 411, + 180, + 449, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS} = 0.64" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 480, + 140, + 535, + 176 + ], + "blocks": [ + { + "bbox": [ + 480, + 140, + 535, + 176 + ], + "lines": [ + { + "bbox": [ + 480, + 140, + 535, + 176 + ], + "spans": [ + { + "bbox": [ + 480, + 140, + 535, + 176 + ], + "type": "image", + "image_path": "b1fc21b97ec3cd3475c18b0ca174e6848308516ba6b7c83db3826a206ff9c335.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 495, + 180, + 533, + 189 + ], + "lines": [ + { + "bbox": [ + 495, + 180, + 533, + 189 + ], + "spans": [ + { + "bbox": [ + 495, + 180, + 533, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS} = 0.59" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "lines": [ + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "text", + "content": "Figure 2. Top row: our SLS loss for the targets of different scales, where IoU loss " + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "inline_equation", + "content": "(=0.4)" + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "text", + "content": " and Dice loss " + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "inline_equation", + "content": "(=0.57)" + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "text", + "content": " have the same values for different cases. Bottom row: our SLS loss for the targets of different locations, where IoU loss " + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "inline_equation", + "content": "(=0.3)" + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "text", + "content": " and Dice loss " + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "inline_equation", + "content": "(=0.43)" + }, + { + "bbox": [ + 304, + 195, + 547, + 250 + ], + "type": "text", + "content": " have the same values for different cases." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 271, + 479, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 271, + 479, + 284 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 479, + 284 + ], + "type": "text", + "content": "2.1. Infrared Small Target Detection" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 290, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 482 + ], + "type": "text", + "content": "Existing IRSTD methods can be roughly divided into traditional methods and Deep-Learning-based (DL-based) methods. Among them, traditional methods depend on the hand-crafted priors and can be further divided into filtering-based methods [5, 17], local-contrast-based methods [9, 10, 12], and low-rank-based methods [2, 6, 8, 19, 28, 29, 32]. To get useful features with such hand-crafted priors, lots of hyperparameters need to be manually fine-tuned, making them less robust to the interference of noises and clutters. Differently, DL-based methods [3, 7, 14, 15, 21, 25, 30, 33] can automatically learn useful features with the help of loss functions and gradient descent algorithms. Though impressive detection performance has been achieved, existing DL-based methods mainly focus on the design of model structures for the pursuit of more effective features, leaving the loss functions for IRSTD under-explored." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 483, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 542 + ], + "type": "text", + "content": "Different from existing DL-based methods, we focus on boosting detection performance with a more effective loss function but a simpler model structure. A better balance between detection performance, FLOPs and inference time consumption can be achieved." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 551, + 451, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 451, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 451, + 562 + ], + "type": "text", + "content": "2.2. Loss Functions for IRSTD" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "content": "As one of the components in DL-based methods, the loss function plays a critical role in the learning process of deep models by quantifying the disparity between predictions and ground-truths. The commonly adopted IoU loss and Dice loss [18] suffer from insensitivity to the scales and locations of targets, rendering the detectors for distinguishing the targets of different scales and locations accurately." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "In order to achieve better detection performance, researchers have developed several loss functions. For example, the loss for adversarial training [21], edge loss for the detecting of target edges [30] and the likelihood loss between target and background maps [11]. However, these" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17491" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 286, + 163 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 163 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 163 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 163 + ], + "type": "image", + "image_path": "a3900cf293ec5a3ced48697cc45d67611670668830188763afb50eb84a6f8629.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 174, + 289, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 174, + 289, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 289, + 242 + ], + "type": "text", + "content": "Figure 3. Left: the value of weight " + }, + { + "bbox": [ + 46, + 174, + 289, + 242 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 174, + 289, + 242 + ], + "type": "text", + "content": " in scale sensitive loss with respect to the number of predicted pixels and ground-truth pixels (i.e., predicted and ground-truth scales). Right: the normalized location sensitive loss with respect to the location error between the predicted center point and ground-truth center point. The range of [0, 100] pixels is shown for illustration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 262, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 332 + ], + "type": "text", + "content": "losses are tailored for specific network architectures, limiting their broader utility. Different from these dedicated losses, the generalized IoU (GIoU) [16] and complete IoU (CIoU) [35] losses have been adopted for box-level IRSTD [13, 23]. However, these IoU variant losses still lack the sensitivity of scales and locations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 334, + 288, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 288, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 288, + 381 + ], + "type": "text", + "content": "In contrast to these losses, we formulate a general loss function that is better suitable for IRSTD. It can distinguish targets of different scales and locations, enabling different detectors to achieve better detection performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 389, + 205, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 205, + 401 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 205, + 401 + ], + "type": "text", + "content": "2.3. Model Structures for IRSTD" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 407, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 563 + ], + "type": "text", + "content": "The deep model is another key component in DL-based methods. Liu et al. [15] pioneer the application of deep learning to IRSTD. The adopted five-layer Multi-Layer Perceptron (MLP) network demonstrates the superiority of DL-based methods in IRSTD. Recently, lots of works have focused on the design of model structures to get more effective features. Li et al. [14] customize a dense nested interactive module to achieve multi-layer feature fusion. Zhang et al. [30] utilize Taylor finite difference and orientation attention strategy to extract edge information of targets. However, such complex model structures not only bring more computational cost but still suffer from moderate detection performance due to the lack of effective loss functions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 563, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 612 + ], + "type": "text", + "content": "Differently we introduce a simple multi-scale head to the plain U-Net, rather than designing complex structures. By applying our SLS loss to different scales, SOTA performance is achieved with less time consumption." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 623, + 234, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 234, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 234, + 635 + ], + "type": "text", + "content": "3. Scale and Location Sensitive Loss" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 643, + 288, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 288, + 692 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 288, + 692 + ], + "type": "text", + "content": "The scale and location sensitive (SLS) loss, denoted as " + }, + { + "bbox": [ + 47, + 643, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{SLS}}" + }, + { + "bbox": [ + 47, + 643, + 288, + 692 + ], + "type": "text", + "content": ", is designed to handle the insensitivity of scales and locations in existing losses. It consists of a scale sensitive loss and a location sensitive loss. Formally," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 126, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S L S} = \\mathcal {L} _ {S} + \\mathcal {L} _ {L}, \\tag {1}", + "image_path": "89f1bec5872eab7f81b55c6b0d8199de3b2001dae3a9a8e622149917af31cbdc.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_L" + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "content": " present the scale sensitive loss and location sensitive loss, respectively. In the following, we introduce the SLS loss in detail starting from the scale sensitive loss, which is based on the commonly used IoU loss." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 127, + 422, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 127, + 422, + 138 + ], + "spans": [ + { + "bbox": [ + 305, + 127, + 422, + 138 + ], + "type": "text", + "content": "3.1. Scale Sensitive Loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "type": "inline_equation", + "content": "A_{p}" + }, + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "type": "inline_equation", + "content": "A_{gt}" + }, + { + "bbox": [ + 304, + 145, + 546, + 180 + ], + "type": "text", + "content": " be the set of predicted pixels and ground-truth pixels of targets, the IoU loss between them can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 373, + 186, + 546, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 186, + 546, + 213 + ], + "spans": [ + { + "bbox": [ + 373, + 186, + 546, + 213 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I o U} = 1 - \\frac {\\left| A _ {p} \\cap A _ {g t} \\right|}{\\left| A _ {p} \\cup A _ {g t} \\right|}. \\tag {2}", + "image_path": "27f42bf6396ae6600f2b614ff5cbed7c71440f6e5f47acc7c2b3e77c94a12340.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 219, + 545, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 545, + 267 + ], + "type": "text", + "content": "Though having been widely used in IRSTD, the IoU loss is insensitive to the scales and locations of targets, as shown in Fig. 2. The scale sensitive loss is implemented by providing a weight to the IoU loss:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 363, + 274, + 545, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 274, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 363, + 274, + 545, + 306 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S} = 1 - w \\frac {\\left| A _ {p} \\cap A _ {g t} \\right|}{\\left| A _ {p} \\cup A _ {g t} \\right|}, \\tag {3}", + "image_path": "2dde3d84076398bda0b87fb7d1e60c824821cc6ab46ae93c784a6a28556ca745.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 322, + 301, + 518, + 329 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 301, + 518, + 329 + ], + "spans": [ + { + "bbox": [ + 322, + 301, + 518, + 329 + ], + "type": "interline_equation", + "content": "\\mathrm {s . t .} \\quad w = \\frac {\\operatorname* {m i n} (| A _ {p} | , | A _ {g t} |) + \\operatorname {V a r} (| A _ {p} | , | A _ {g t} |)}{\\operatorname* {m a x} (| A _ {p} | , | A _ {g t} |) + \\operatorname {V a r} (| A _ {p} | , | A _ {g t} |)},", + "image_path": "00e877d389955f688bc595a429a5a7a604067a4454dd9232e26b4cb8fc4ce559.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 335, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 358 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 335, + 545, + 358 + ], + "type": "inline_equation", + "content": "\\operatorname{Var}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 335, + 545, + 358 + ], + "type": "text", + "content": " is the function that gets the variance of provided scalars." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": "On the left of Fig. 3, we visualize the values of " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " with respect to the number of pixels in " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "A_{p}" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "A_{gt}" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": ". It can be observed that the larger the gap between " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "|A_{p}|" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "|A_{gt}|" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " is, the smaller the " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " is, which results in a larger scale sensitive loss (on the assumption that the IoU between " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "A_{p}" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "A_{gt}" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " is fixed). The intuition behind the design of " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " is that the detector should pay more attention to the target with a larger loss if the predicted and ground-truth scales (i.e., the numbers of pixels in " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "A_{p}" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "inline_equation", + "content": "A_{gt}" + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": ") are quite different." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 474, + 438, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 438, + 485 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 438, + 485 + ], + "type": "text", + "content": "3.2. Location Sensitive Loss" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": "The location sensitive loss is calculated based on the predicted and ground-truth center points of targets. Given the sets of predicted pixels " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "A_{p}" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " and ground-truth pixels " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "A_{gt}" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": ", the corresponding center points for " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "A_{p}" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "A_{gt}" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " are obtained by averaging the coordinates of all pixels, which are denoted as " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_p = (x_p,y_p)" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{gt} = (x_{gt},y_{gt})" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": ", respectively. Then, we convert the coordinates of these two center points into the polar coordinate system. Take " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_p" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " for example, the corresponding distance " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "d_{p}" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " and angle " + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\theta_{p}" + }, + { + "bbox": [ + 304, + 492, + 545, + 612 + ], + "type": "text", + "content": " in the polar coordinate system are:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 386, + 620, + 459, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 620, + 459, + 639 + ], + "spans": [ + { + "bbox": [ + 386, + 620, + 459, + 639 + ], + "type": "interline_equation", + "content": "d _ {p} = \\sqrt {x _ {p} ^ {2} + y _ {p} ^ {2}},", + "image_path": "4b70f45d7aac55c8fd8888578092709d455173c6cb1ebcd05903037fdc6b35b4.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 388, + 636, + 545, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 636, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 388, + 636, + 545, + 665 + ], + "type": "interline_equation", + "content": "\\theta_ {p} = \\arctan \\left(\\frac {y _ {p}}{x _ {p}}\\right). \\tag {4}", + "image_path": "7b009422e9a731f7c8ce5931edea056818a557f243512dc16ddcd3940d319488.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 671, + 494, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 494, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 494, + 682 + ], + "type": "text", + "content": "The location sensitive loss can be obtained by:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 333, + 689, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 689, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 333, + 689, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L} = \\left(1 - \\frac {\\operatorname* {m i n} \\left(d _ {p} , d _ {g t}\\right)}{\\operatorname* {m a x} \\left(d _ {p} , d _ {g t}\\right)}\\right) + \\frac {4}{\\pi^ {2}} \\left(\\theta_ {p} - \\theta_ {g t}\\right) ^ {2}, \\tag {5}", + "image_path": "b434e1479463b49a2d80cd5f8ae8b77e9237a39fa2d281229ce425a898a45b74.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17492" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 178 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 178 + ], + "type": "image", + "image_path": "2a36d453dc002d6f42daed267c38909b1106ea87c71b51ca635a7c654aea35f8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 232 + ], + "type": "text", + "content": "Figure 4. Overview of the proposed MSHNet. Our MSHNet is implemented based on a plain U-Net without bells and whistles. Only a simple multi-scale head is introduced. For each scale, the feature map is fed into a dedicated head, producing a prediction with the same spatial shape as the feature map. Different scales of predictions are upsampled (if needed) and concatenated together to get the final prediction. In the training stage, our SLS loss is applied to each of these predictions since it is scale sensitive." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "inline_equation", + "content": "d_{gt}" + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\theta_{gt}" + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "content": " are the distance and angle of " + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{gt}" + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "content": " in the polar coordinate system, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "type": "text", + "content": "On the right of Fig. 3, we show how the location loss changes with respect to different location errors between " + }, + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_p" + }, + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{gt}" + }, + { + "bbox": [ + 46, + 276, + 288, + 373 + ], + "type": "text", + "content": ". As we can see, though some different location errors share the same loss value (these location errors still can be distinguished with their gradients), the location loss distinguishes most of the different location errors effectively, making the detector sensitive to different types of location errors and locate the targets more accurately." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 382, + 160, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 160, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 160, + 395 + ], + "type": "text", + "content": "4. MSHNet Detector" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 402, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 558 + ], + "type": "text", + "content": "In this section, we introduce our MSHNet detector, which is implemented by introducing a simple but effective multiscale head to the plain U-Net. The overview of MSHNet is shown in Fig. 4. We take the commonly used U-Net as the backbone network. The feature maps that have different scales in the decoder are fed into different prediction heads to get different scales of predictions. All the predictions from different feature maps are finally concatenated (upsampling before concatenation is adopted if needed) to get the final prediction. In the training stage, our SLS loss is applied to each of the predictions. In the following, the multi-scale head is first described in detail. Then we introduce the utilization of SLS loss in MSHNet." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 565, + 151, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 565, + 151, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 151, + 577 + ], + "type": "text", + "content": "4.1. Multi-Scale Head" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i\\in \\mathbb{R}^{H_i\\times W_i\\times C_i}" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": " be the feature map at the " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": " -th scale in the decoder of U-Net, where " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "H_{i}\\times W_{i}" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": " is the spatial size and " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": " is the number of channels. Following the common settings within existing works, there are 4 scales in U-Net, which means that " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "i\\in \\{1,2,3,4\\}" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": ". Supposing the input spatial size is " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "H_{i} = \\frac{H}{2^{4 - i}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "inline_equation", + "content": "W_{i} = \\frac{W}{2^{4 - i}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 655 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "type": "text", + "content": "-th prediction " + }, + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i \\in \\mathbb{R}^{\\bar{H}_i \\times W_i \\times 1}" + }, + { + "bbox": [ + 46, + 655, + 287, + 691 + ], + "type": "text", + "content": " is obtained by the corresponding prediction head, which is implemented by a convolution layer and a sigmoid activation function:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 110, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 110, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {i} = \\operatorname {S i g m o i d} \\left(\\operatorname {C o n v} \\left(\\mathbf {x} _ {i}\\right)\\right). \\tag {6}", + "image_path": "40dc823008626aa698d0acdc043f1f0520b0b233d695785de95c4abea0c507af.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 251, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 288 + ], + "type": "text", + "content": "Note that different prediction heads have their own dedicated parameters. The final prediction " + }, + { + "bbox": [ + 304, + 251, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{R}^{H \\times W \\times 1}" + }, + { + "bbox": [ + 304, + 251, + 545, + 288 + ], + "type": "text", + "content": " is obtained based on all the 4 predictions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 297, + 545, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 297, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 306, + 297, + 545, + 320 + ], + "type": "interline_equation", + "content": "\\mathbf {p} = \\operatorname {S i g m o i d} \\left(\\operatorname {C o n v} \\left(\\left[ \\uparrow \\left(\\mathbf {p} _ {1}, 8\\right), \\uparrow \\left(\\mathbf {p} _ {2}, 4\\right), \\uparrow \\left(\\mathbf {p} _ {3}, 2\\right), \\mathbf {p} _ {4} \\right]\\right)\\right), \\tag {7}", + "image_path": "d0504032bee805e85c2549543772c4a34f8cca26a3084a4b706bcc12cdbe31f7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\Uparrow (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "type": "text", + "content": " is the operation that spatially upsamples the first argument with the second argument as the factor, and " + }, + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "type": "inline_equation", + "content": "[\\cdot ,\\dots ,\\cdot ]" + }, + { + "bbox": [ + 305, + 321, + 545, + 369 + ], + "type": "text", + "content": " concatenates all the provided arguments along the channel dimensionality." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 376, + 484, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 484, + 388 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 484, + 388 + ], + "type": "text", + "content": "4.2. Training MSHNet with SLS Loss" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 394, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 502 + ], + "type": "text", + "content": "Since our SLS loss is scale sensitive and there are several scales in the predictions of MSHNet, we apply SLS loss to all of the predictions. The inspiration is that our SLS loss produces different loss values for different scales even if they share the same spatial layout (refer to the first two cases in the top row, Fig. 2). We hypothesize that by applying our SLS loss to different scales, the targets that are with different scales can attract different attention from the detector, resulting in an overall better detection performance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 502, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 545, + 525 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 306, + 502, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{gt} \\in \\{0,1\\}^{H \\times W \\times 1}" + }, + { + "bbox": [ + 306, + 502, + 545, + 525 + ], + "type": "text", + "content": " be the ground-truth label. The final loss for MSHNet is:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 533, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 545, + 574 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {1}{5} \\left(\\sum_ {i = 1} ^ {4} \\mathcal {L} _ {S L S} \\left(\\mathbf {p} _ {i}, \\Downarrow \\left(\\mathbf {p} _ {g t}, 2 ^ {4 - i}\\right)\\right) + \\mathcal {L} _ {S L S} \\left(\\mathbf {p}, \\mathbf {p} _ {g t}\\right)\\right), \\tag {8}", + "image_path": "e7cc7e0fd40db442ab05386cfb14ff3ed6eb89339de7351ff821b92ee3bb2b1f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\Downarrow (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "type": "text", + "content": " is the operation (i.e., max-pooling) that spatially downsamples the first argument with the second argument as the factor, and " + }, + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SLS}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 575, + 545, + 612 + ], + "type": "text", + "content": " is our SLS loss." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 621, + 387, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 387, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 387, + 635 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "In this section, the adopted datasets and metrics are firstly introduced, followed by the implementation details. Then, we compare the proposed method MSHNet with existing IRSTD detectors. Finally, discussions are provided to show the effectiveness of our Scale and Location Sensitive loss and MHSNet detector." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17493" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 250 + ], + "type": "table", + "html": "
MethodDescriptionIRSTD-1kNUDT-SIRST
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
Top-Hat [17]Filtering10.0675.11143220.7278.41166.7
Max-Median [5]6.99865.2159.734.19758.4136.89
WSLCM [10]Local Contrast3.45272.4466192.28356.821309
TLLCM [9]3.31177.3967382.17662.011608
IPI [8]Low Rank27.9281.3716.1817.7674.4941.23
NRAM [29]15.2570.6816.936.92756.4019.27
RIPT [2]14.1177.5528.3129.4491.85344.3
PSTNN [28]24.5771.9935.2614.8566.1344.17
MSLSTIPT [19]11.4379.0315248.34247.40888.1
MDvsFA [21]Deep Learning37.3483.7188.5235.8685.2295.37
ALCNet [4]65.6889.2527.7172.8996.1930.40
ISNet [30]62.8892.5927.9267.8692.5934.65
DNANet [14]65.7191.8417.6179.9896.9312.78
MSHNet (Ours)67.1693.8815.0380.5597.9911.77
", + "image_path": "4ba563bc9cb3383fdf0039c75cedf98a885526c5fa81239571a52bf0e34868d8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 546, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 546, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 546, + 282 + ], + "type": "text", + "content": "Table 1. Quantitative results of different methods. Results for the metrics of IoU(%, Pd(%) and Fa(10-6) are presented. The best values are highlighted with bold. It can be seen that our MSHNet achieves the best results on different metrics and datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 311, + 168, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 311, + 168, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 311, + 168, + 323 + ], + "type": "text", + "content": "5.1. Datasets and Metrics" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 288, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 288, + 415 + ], + "type": "text", + "content": "Datasets. The experiments are conducted on two datasets i.e., IRSD-1k [30] and NUDT-SIRST [14]. There are 1,001 and 1,327 infrared images in IRSTD-1k and NUDT-SIRST, respectively. Following existing works [14, 30], the images in IRSTD-1k are divided into the training and testing splits with a ratio of 4:1, while the images in NUDT-SIRST are equally divided into the training and testing splits." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "text", + "content": "Evaluation Metrics. We use IoU and false alarm rate " + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "inline_equation", + "content": "(\\mathrm{F_a})" + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "text", + "content": " as the pixel-level evaluation metric and assess target-level performance using the probability of detection " + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "inline_equation", + "content": "(\\mathrm{P_d})" + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "text", + "content": ". Different metrics reveal the performance of the detector from different aspects. " + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}" + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}" + }, + { + "bbox": [ + 46, + 428, + 287, + 499 + ], + "type": "text", + "content": " focus on recall and false alarms, while IoU takes both into consideration." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 500, + 195, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 500, + 195, + 511 + ], + "spans": [ + { + "bbox": [ + 59, + 500, + 195, + 511 + ], + "type": "text", + "content": "Formally, The false alarm rate is:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 137, + 519, + 287, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 519, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 137, + 519, + 287, + 545 + ], + "type": "interline_equation", + "content": "\\mathrm {F} _ {\\mathrm {a}} = \\frac {P _ {\\text {f a l s e}}}{P _ {\\text {a l l}}}, \\tag {9}", + "image_path": "d5ed25477ed616d6c80bb15d5d79f0df9304b77d8e3e8aab66a8f2f37944ee39.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "type": "inline_equation", + "content": "P_{false}" + }, + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "type": "text", + "content": " is the number of false positive pixels and " + }, + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "type": "inline_equation", + "content": "P_{all}" + }, + { + "bbox": [ + 47, + 552, + 287, + 576 + ], + "type": "text", + "content": " is the number of all pixels in the image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 576, + 187, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 576, + 187, + 588 + ], + "spans": [ + { + "bbox": [ + 59, + 576, + 187, + 588 + ], + "type": "text", + "content": "The probability of detection is:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 137, + 595, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 595, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 137, + 595, + 287, + 620 + ], + "type": "interline_equation", + "content": "P _ {d} = \\frac {N _ {p r e d}}{N _ {a l l}}, \\tag {10}", + "image_path": "f9f449a1541a3f4a89083d8a977cd89ad3359be1b2955265496f4b6e48f8a6b4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "type": "inline_equation", + "content": "N_{pred}" + }, + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "type": "text", + "content": " is the number of correctly predicted targets and " + }, + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "type": "inline_equation", + "content": "N_{all}" + }, + { + "bbox": [ + 47, + 628, + 287, + 653 + ], + "type": "text", + "content": " is the number of all targets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 658, + 180, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 180, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 180, + 672 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "The proposed method is implemented with PyTorch framework. Following existing works, the input size of the detector is set to " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": ". We train different models using" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 311, + 546, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 311, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 311, + 546, + 335 + ], + "type": "text", + "content": "AdaGrad on 2 RTX3090 GPUs. The batch size is set to 4 and the learning rate is set to 0.05." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 343, + 484, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 343, + 484, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 343, + 484, + 357 + ], + "type": "text", + "content": "5.3. Comparison to Existing Methods" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 362, + 546, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 546, + 506 + ], + "type": "text", + "content": "We first compare the proposed MSHNet with existing methods. Different types of methods are evaluated, including traditional methods and deep-learning-based methods. The evaluated traditional methods are the filtering-based Top-Hat [17] and Max-Median [5], local-contrast-based WSLCM [10] and TLLCM [9], low-rank-based IPI [8], NRAM [29], RIPT [2], PSTNN [28] and MSLSTIPT [19]. The deep-learning-based methods are MDvsFA [21], ALCNet [4], ISNet [30], and DNANet [14]. For a fair comparison, all the evaluated deep-learning-based models are retrained with their official codes to their convergence on NUDT-SIRST [14] and IRSTD-1k [30] datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "type": "text", + "content": "Quantitative Results. The quantitative results of different methods are presented in Tab. 1. Overall, our MSHNet performs the best on all metrics and all datasets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "As expected, traditional methods perform poorly on these challenging datasets due to the limitations of manually designed priors for feature extraction. In contrast, DL-based methods can automatically learn useful features and yield better results than traditional methods. Nevertheless, existing DL-based methods lack the consideration of different scales and locations of targets in the training stage. The predictions of existing DL-based methods suffer from the incomplete shape and missed detection of valid pixels, e.g., lower IoU and " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": ". Compared with DNANet, which is one of the existing SOTA DL-based methods, our MSHNet achieves " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.45\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "0.57\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " higher IoU, " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "2.04\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.06\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " higher " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " on IRSTD-1k and NUAA-SIRST datasets, re" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17494" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 547, + 404 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 547, + 404 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 547, + 404 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 547, + 404 + ], + "type": "image", + "image_path": "5620e2067139fb0ccbc6da094279699e7a8d1783fa8b2e40ffe72108d5016c75.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 415, + 546, + 439 + ], + "lines": [ + { + "bbox": [ + 46, + 415, + 546, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 546, + 439 + ], + "type": "text", + "content": "Figure 5. Visual comparison of detection results on several infrared images. Correctly detected targets, missed targets, and false alarms are framed by red, blue, and yellow boxes, respectively. A close-up view of the target is shown in image corners." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "content": "spectively. In addition, the false alarm " + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "inline_equation", + "content": "(\\mathrm{F_a})" + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "content": " on both datasets are all reduced by a large margin, demonstrating the superiority of our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 495, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 288, + 662 + ], + "type": "text", + "content": "As mentioned before, there are no complex model structures in MSHNet, which achieves a better balance between detection performance, floating point of operations (FLOPs) and inference time consumption. The results of DL-based methods are presented in Fig. 1. It can be observed that MSHNet has the best detection performance and the least inference time consumption. It also has the least number of FLOPs except for ALCNet. We own the less inference time consumption of MSHNet to the smaller number of FLOPs and the simple architectures (complex structures in deep models bring more inference time consumption [22]). The better detection performance demonstrates the effectiveness of the proposed multi-scale head and the scale and location sensitive loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Qualitative Results. For different kinds of methods, we visualize the detection results of the representative methods in Fig. 5 and Fig. 6. It can be observed that our method has" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 459, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 662 + ], + "type": "text", + "content": "better capability for the detection of challenging small targets. Traditional methods are susceptible to noise interference, resulting in a large number of false alarms. Moreover, due to the small scale and low contrast of the target, traditional methods and other DL-based methods struggle to effectively extract feature information of small targets from challenging scenarios, resulting in a considerable number of missed targets. In contrast, our methods can accurately distinguish small targets from these low-contrast infrared images. Take the case in the 5-th row in Fig. 5 for example, except for MSHNet and WLSLCM, other methods fail to detect the target. Moreover, from the peaks and the area under the peaks in Fig. 6, it can be observed that our method predicts targets with higher confidence and obtains a closer number of peaks with ground-truth. We attribute the superiority of MSHNet to the scale and location sensitivity brought by our SLS loss and multi-scale head." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 670, + 382, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 382, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 382, + 682 + ], + "type": "text", + "content": "5.4. Discussions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We provide some discussions to show the effectiveness of our method. Experiments are conducted on IRSTD-1k dataset." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17495" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 541, + 306 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 541, + 306 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 541, + 306 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 541, + 306 + ], + "type": "image", + "image_path": "c2d05797e53f5c4ec37fce171c25e7a1cafba1b66f3e081738c156dcb5ae11d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 318, + 546, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 318, + 546, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 546, + 340 + ], + "type": "text", + "content": "Figure 6. 3D visualization results corresponding to those in Fig. 5. Different colors represent distinct grayscale values, ranging from blue to yellow, with values gradually increasing. Please zoom in for better viewing." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "type": "text", + "content": "Detection Results for Different Scales of Targets. Since our SLS loss and MSHNet both are scale sensitive, we show how the detection performance changes with respect to different scales of targets. To do this, we split the targets into three different scale levels according to the number of pixels: (0,10], (10, 40] and " + }, + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "type": "inline_equation", + "content": "(40,\\infty]" + }, + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "type": "text", + "content": ". Results are shown in Tab. 2. Due to the limited space, only several DL-based methods are evaluated (specifically, ISNet, DNANet and our MSHNet). Compared with DNANet, MSHNet performs better for all scale levels of targets. Compared with ISNet, MSHNet achieves comparable performance with ISNet for (0,10] and (10,40] scales but much better performance for " + }, + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "type": "inline_equation", + "content": "(40,\\infty]" + }, + { + "bbox": [ + 46, + 361, + 289, + 540 + ], + "type": "text", + "content": " scale. The conclusion is that MSHNet can pay attention to different scale levels of targets, resulting in an overall better performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "type": "text", + "content": "Impact of Scale and Location Sensitive Loss. We compare our SLS loss with the commonly used IoU loss and Dice loss. The results of several DL-based methods trained with different losses are presented in Tab. 3. Overall, the detection performance of different detectors is all improved by our SLS loss in terms of IoU metric, demonstrating the effectiveness and generalization of SLS loss. However, it is hard to tell which loss performs the best on the metric of " + }, + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}" + }, + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "type": "text", + "content": ". Interestingly, adopting our SLS loss results in a poorer performance on " + }, + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}" + }, + { + "bbox": [ + 46, + 557, + 287, + 700 + ], + "type": "text", + "content": " metric. The reason is that more false alarm pixels may be treated as positive targets since our SLS loss tries to distinguish the targets of all different scales." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "content": "Next, we show the effectiveness of scale sensitive loss" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 326, + 358, + 526, + 473 + ], + "blocks": [ + { + "bbox": [ + 326, + 358, + 526, + 473 + ], + "lines": [ + { + "bbox": [ + 326, + 358, + 526, + 473 + ], + "spans": [ + { + "bbox": [ + 326, + 358, + 526, + 473 + ], + "type": "table", + "html": "
ScaleMethodIoU↑Pd↑Fa↓
(0,10]DNANet [3]47.2691.2722.53
ISNet [14]50.9494.5330.91
MSHNet (Ours)49.5195.2420.68
(10,40]DNANet [3]63.1491.8513.25
ISNet [14]65.4191.9116.60
MSHNet (Ours)64.7991.858.03
(40,∞]DNANet [3]78.4693.946.78
ISNet [14]66.4587.8758.80
MSHNet (Ours)79.2096.9711.02
", + "image_path": "ca056dca5d9b84cd682c3993a9707105a2e6ab47b1d37fc2f2d5f7c61ea52c61.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "lines": [ + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "type": "text", + "content": "Table 2. Comparisons of different methods in terms of different scales of targets. Results for the metrics of IoU(\\%), " + }, + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}(\\%)" + }, + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}(10^{-6})" + }, + { + "bbox": [ + 305, + 481, + 547, + 525 + ], + "type": "text", + "content": " are presented. Our MSHNet achieves overall the best performance." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_S)" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " and location sensitive loss " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_L)" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " separately. To do this, we train MSHNet with different losses. The results are presented in Tab. 4. Note that the difference between " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{IoU}" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " lies in the newly introduced weight " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " (refer to Sec. 3.1). By comparing the results in the first two rows, we can find that the introduction of " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " (refer to Eq. (3)) is positive to the metrics of IoU and " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": ", indicating that the detector produces more accurate shapes for targets as well as less false alarms. While comparing the results in the last two rows, it can be observed that more false alarms will be produced when the location sensitive loss is introduced. However, both IoU and " + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}" + }, + { + "bbox": [ + 304, + 544, + 545, + 688 + ], + "type": "text", + "content": " are greatly improved." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "Finally, we make a study on different types of location sensitive loss. As mentioned in Sec. 3.2, our location sen" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17496" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 129 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 129 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 129 + ], + "type": "table", + "html": "
LossDNANet [3]ISNet [14]MSHNet (Ours)
IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓IoU↑Pd↑Fa↓
L IoU65.7191.8417.6162.8892.5927.9264.8391.165.28
L Dice65.5892.1712.7562.9490.9119.2665.3692.1814.12
L SLS (Ours)67.0992.1535.1564.4292.2615.1467.1693.8815.03
", + "image_path": "8774fc0041d4de17055bbb0302639431aec5c82dc4bde2454fad6cd3459f4f65.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 178, + 284, + 228 + ], + "blocks": [ + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "lines": [ + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "spans": [ + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "type": "text", + "content": "Table 3. Comparisons of different losses and detectors. Results for the metrics of IoU(\\%), " + }, + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}(\\%)" + }, + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}(10^{-6})" + }, + { + "bbox": [ + 46, + 137, + 546, + 160 + ], + "type": "text", + "content": " are presented. The main IoU metrics of different detectors are consistently boosted by our scale and location sensitive loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 178, + 284, + 228 + ], + "lines": [ + { + "bbox": [ + 51, + 178, + 284, + 228 + ], + "spans": [ + { + "bbox": [ + 51, + 178, + 284, + 228 + ], + "type": "table", + "html": "
LossIoU↑Pd↑Fa↓
LS w/o. w64.8391.165.28
LS65.8289.464.06
LS + LL67.1693.8815.03
", + "image_path": "28f7254ae1bddb26c46e8ce47b2372e7e6f12d58fabd799c9932a3fc06538bcf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 294, + 287, + 343 + ], + "blocks": [ + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": "Table 4. Ablation study of the scale sensitive loss " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_S)" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": " and location sensitive loss " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_L)" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": ". Results are obtained by MSHNet. The metrics of IoU(\\%), " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}(\\%)" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "(10^{-6})" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": " are adopted. Note that " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": " without " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": " is equivalent to " + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{IoU}" + }, + { + "bbox": [ + 46, + 235, + 287, + 280 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 294, + 287, + 343 + ], + "lines": [ + { + "bbox": [ + 48, + 294, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 48, + 294, + 287, + 343 + ], + "type": "table", + "html": "
LossIoU↑Pd↑Fa↓
LS+L264.8992.867.29
LS+L164.7593.546.18
LS+L67.1693.8815.03
", + "image_path": "40186dd0b292fcc25b6ae977770ae5cfb5643a500246ee575de17fb7ff9470af.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": "sitive loss can distinguish different location errors more effectively. To show the effectiveness of such distinguishability, we use the " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": " distances between " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_p" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{gt}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": " as the location sensitive loss (denoted as " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{L_2}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{L_1}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": ", respectively). Results are shown in Tab. 5. As we can see, the distinguishability of different location errors is effective in getting better IoU and " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": " metrics. However, more false alarms are produced (higher " + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}" + }, + { + "bbox": [ + 46, + 405, + 289, + 550 + ], + "type": "text", + "content": "). Such phenomenon is also observed from Tab. 4. The reason may be that the distinguishability of different location errors makes the detector more sensitive to small targets, resulting in the potential of treating some noises to targets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "type": "text", + "content": "Impact of Multi-Scale Heads. Now we ablate the number of scales in our multi-scale head. Results are shown in Tab. 6. As we can see, different predictions achieve different detection performance. Overall, the more scales adopted, the better the detection performance is achieved. For example, the IoU is improved from " + }, + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "type": "inline_equation", + "content": "63.10\\%" + }, + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "type": "inline_equation", + "content": "67.16\\%" + }, + { + "bbox": [ + 46, + 563, + 287, + 659 + ], + "type": "text", + "content": " when the number of scales is increased from 1 to 4. We use 4 scales by default." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 670, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 119, + 681 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "In this paper, we focus on boosting the performance of infrared small target detection with an effective loss function" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 306, + 178, + 549, + 251 + ], + "blocks": [ + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "type": "text", + "content": "Table 5. Ablation study of different types of location sensitive loss. Results are obtained by MSHNet. The metrics of IoU(%, " + }, + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}(\\%)" + }, + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a}(10^{-6})" + }, + { + "bbox": [ + 46, + 351, + 287, + 385 + ], + "type": "text", + "content": " are adopted." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 178, + 549, + 251 + ], + "lines": [ + { + "bbox": [ + 306, + 178, + 549, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 549, + 251 + ], + "type": "table", + "html": "
Num. of ScalesSupervised PredictionsIoU↑Pd↑Fa↓
1p63.1086.7319.21
1p4,p64.6993.8736.74
2p3,p4,p64.3594.8935.38
3p2,p3,p4,p65.9093.5424.37
4p1,p2,p3,p4,p67.1693.8815.03
", + "image_path": "41bc64b3d16b3dc4c6f4928b45ecf664822e3db36eadfed7d10671a7f39ee7e8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "lines": [ + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "type": "text", + "content": "Table 6. Ablation study of the number of scales in MSHNet. While reducing the number of adopted scales, the remaining smallest scale is removed. Results for the metrics of IoU(\\%), " + }, + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "type": "inline_equation", + "content": "\\mathrm{P_d}(\\%)" + }, + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "type": "inline_equation", + "content": "\\mathrm{F_a} (10^{-6})" + }, + { + "bbox": [ + 305, + 258, + 546, + 303 + ], + "type": "text", + "content": " are presented." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 328, + 547, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 547, + 591 + ], + "type": "text", + "content": "but a simpler model structure. To do this, a Scale and Location Sensitive (SLS) loss is first proposed. The merits of SLS loss include: (1) it pays more attention to the targets that have large gaps between the predicted and ground-truth scales; (2) it distinguishes different types of location errors between the predicted and ground-truth center points of targets. Then a simple Multi-Scale Head is introduced to the plain U-Net (MSHNet), which produces multi-scale predictions for each input. Through applying SLS loss to different scales of predictions, different scales of targets can attract different attention from the detector, resulting in an overall better detection performance. Experimental results show that MSHNet achieves SOTA detection performance with the better balance of inference time and the number of floating point of operations. While applying our SLS loss to other existing detectors, the overall detection performance can be boosted. However, more false alarms may be introduced. Through the analysis in Sec. 5.4, we find that such a phenomenon is brought by the location sensitive loss in SLS loss which potentially treats some noises as targets. In future works, we try to handle this by designing more suitable location sensitive loss." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 604, + 391, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 391, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 391, + 615 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China (62331006,62171038, 62088101, and 62371175), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), the Key R&D Program of Zhejiang (2023C01044), the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK239909299001-013), and the Fundamental Research Funds for the Central Universities." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17497" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Linwei Chen, Ying Fu, Kaixuan Wei, Dezhi Zheng, and Felix Heide. 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However, the imperative of achieving a seamless alignment between the generated image and the provided prompt persists as a formidable challenge. This paper traces the root of these difficulties to invalid initial noise, and proposes a solution in the form of Initial Noise Optimization (INITNO), a paradigm that refines this noise. Considering text prompts, not all random noises are effective in synthesizing semantically-faithful images. We design the cross-attention response score and the self-attention conflict score to evaluate the initial noise, bifurcating the initial latent space into valid and invalid sectors. A strategically crafted noise optimization pipeline is developed to guide the initial noise towards valid regions. Our method, validated through rigorous experimentation, shows a commendable proficiency in generating images in strict accordance with text prompts. Our code is available at https://github.com/xiefan-guo/initno.", + "bbox": [ + 76, + 359, + 473, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 695, + 209, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-Image Synthesis (T2I) stands at the forefront of cutting-edge research, dedicated to the generation of authentic and visually cohesive images from text prompts. In the domain of generative models, including generative adversarial networks [13, 18-21], variational autoencoders [22], and autoregressive models [7, 10, 36, 37], diffusion models [8, 16] have ascended as a predominant solution. The integration of large-scale vision-language models [2, 11, 14, 17, 30-32, 40, 41] has propelled noteworthy advancements in the text-to-image domain.", + "bbox": [ + 76, + 720, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/66b9cac488f6839ebe12d9ab5f38cdadfdbc57682d55c0c506c42a3bea147603.jpg", + "image_caption": [ + "Figure 1. Example results synthesized by SD and ours." + ], + "image_footnote": [], + "bbox": [ + 501, + 325, + 890, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the training of state-of-the-art T2I diffusion models on large-scale text-image datasets, synthesizing images precisely aligned with given text prompts remains a considerable challenge. Well-documented issues, i.e., subject neglect, subject mixing, and incorrect attribute binding, as illustrated in Fig. 1, persist. We attribute these challenges to the presence of invalid initial noise.", + "bbox": [ + 496, + 608, + 893, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When different noise inputs are introduced to the T2I diffusion model with identical text prompts, a substantial discrepancy is observed in the alignment between images and the provided text, as depicted in Fig. 2. This observation signifies that not all randomly sampled noise can produce visually-consistent images. Depending on the consistency between the generated image and the target text, the initial latent space can be divided into valid and invalid regions. Noise sourced from valid regions, when input into the T2I diffusion model, results in semantically-reasonable image. Consequently, our aim is to direct any initial noise towards the valid region, thereby facilitating the generation", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9380", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c3026d5f652db31bf74f0414c7167212bfa7c2ab8710b564f6a28311ef1d36f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 103, + 148, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5436210f03989983c98e11858f4d217b2c49b570daeaf7c6c077471ace92b803.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 151, + 103, + 220, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/75c2aa07cbbd651c5960534988cf5d9859cf283a52b5a696d4b46c8e576f3efd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 103, + 310, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/585e7c11e77658dde601ec7b0738719e93a33e2b165e24c33173ff2849cc4a3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 312, + 103, + 377, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f677a3dc9a6fa8cdd6b45ffae181c77fccea1b17919e7b2fb872afac63994359.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 103, + 447, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5ae96fef33b9afb73f4ea393e50ea0bb6b8b116ef4092b408036ca93979251a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 103, + 519, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8573e67a5beefc5173aae9b0817307ea2166f331061aec370b43d19d4d91b597.jpg", + "image_caption": [ + "Figure 2. INITNO. Our investigation dives into the exploration of various random noise configurations and their subsequent influence on the generated results. Notably, when different noises are input into SD under identical text prompts, there are marked discrepancy in the alignment between the generated image and the given text. Unsuccessful cases are delineated by gray contours, while successful instances are indicated by yellow contours. This observation underscores the pivotal role of initial noise in determining the success of the generation process. Based on this insight, we divide the initial noise space into valid and invalid regions. Introducing Initial Noise Optimization (INITNO), identified as orange arrow, our method is capable of guiding any initial noise into the valid region, thereby synthesizing high-fidelity results (orange contours) that precisely correspond to the given prompt. The same location employs the same random seed." + ], + "image_footnote": [ + "INITNO(Ours)" + ], + "bbox": [ + 81, + 176, + 147, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/71bf8b6a6ee598a88b5de9e16f920b3271c64c795fb178bc7b0b0872a2814617.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 151, + 176, + 220, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/970914c5fa3de4014fdd57c34934ac7ed2e0fa450887f18f96c2c45449109597.jpg", + "image_caption": [], + "image_footnote": [ + "Stable Diffusion (Invalid)" + ], + "bbox": [ + 223, + 176, + 310, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/967c2984c44aeb9b57d8878845d4fd9d87db15cdcfa541c06cc778cd163579ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 312, + 176, + 377, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8e5e28c6b1e166ca728bfb4be8378c04442366d536991678b65a88bc6ef762c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 176, + 447, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c8427be4ca25a646745bb7f20f727ae33069010b97cae8fa9270fd327875248f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 176, + 519, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4f8f8be1daf7fd0d817178802836655b20c0e677110b17c12b8963824cee5daa.jpg", + "image_caption": [ + "Initial latent space" + ], + "image_footnote": [], + "bbox": [ + 527, + 103, + 671, + 214 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1e145a42057d5c71ffc6d0072cf23ee29b90e9527cfdab5f2e994e9b4b3bc2b5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 103, + 746, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e5567a7ce7bd250462d1d0578509576e8c0ef3fd61ea2bd87f5ec292f37ded95.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 103, + 818, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/16d119fcc48888a2d5868c801e54255d24d925cfe92831aa27d5c2eb7e96cf8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 821, + 103, + 890, + 156 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/78b273fda02b39a3b9825ff816b45befa2a3c4e8c4408230bce9b8ca12479e6a.jpg", + "image_caption": [], + "image_footnote": [ + "Stable Diffusion (Valid)" + ], + "bbox": [ + 679, + 176, + 750, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dd79f5ba0e2c6f949663c8ecc4674de6d139ad91c3c4da0dc16137b8c2ee5fe7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 751, + 176, + 818, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c540329de03022e30599b090576f74aba338dc3730141f3706b97a492787487d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 821, + 176, + 888, + 229 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of visually-coherent image that faithfully aligns with the input prompt.", + "bbox": [ + 75, + 367, + 468, + 397 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The core of this paper lies in the concept of Initial Noise Optimization (INITNO), which encompasses initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and directing initial noise navigation, respectively.", + "bbox": [ + 75, + 398, + 468, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our study thoroughly examines attention layers in the diffusion model, specifically the cross-attention map and the self-attention map. The former captures the correlation between text and image features, while the latter captures the correlation among different spatial positions within the image features. These maps effectively measure subject neglect and subject mixing, respectively (see Fig. 3). With these maps, we design the cross-attention response score and the self-attention conflict score. By setting score thresholds, we achieve further partitioning of the initial latent space. Interestingly, we find that accurate rendering of the subject fosters correct attribute binding.", + "bbox": [ + 75, + 474, + 468, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The primary challenge in initial noise navigation is to balance under-optimization and over-optimization of noise. While under-optimization is still plagued by misalignment, over-optimization risks deviating from the initial distribution, i.e., standard Gaussian distribution, resulting in distorted images (see Fig. 9). To address this challenge, we introduce a carefully-crafted noise optimization pipeline. With the explicit modeling of the initial latent space, a novel distribution alignment loss is incorporated to ensure the optimized noise adheres to the initial distribution.", + "bbox": [ + 75, + 657, + 468, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We establish the superiority of the proposed method over state-of-the-art approaches in generating semantically accurate images. Furthermore, our method is plug-and-play and seamlessly integrates into existing diffusion models, enabling training-free controllable generation and improving alignment with specific conditions, such as layout-to-image", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "generation (see Sec. 5.5).", + "bbox": [ + 500, + 367, + 668, + 382 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 401, + 640, + 416 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-image synthesis strives to generate visually-realistic image that reflects given text. Early research mainly focused on GANs [34, 39, 42-44] and autoregressive models [5, 9, 29, 41]. Recently, diffusion models [8, 16] have taken over the mainstream, achieving impressive results. The incorporation of large-scale vision-language models [14, 17, 31, 32, 41] has fostered significant advancements in the text-to-image domain. Despite synthesizing highquality images, it remains challenging to produce results that properly comply with the given text prompt.", + "bbox": [ + 496, + 429, + 890, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To deal with this problem, some works [2, 30, 32, 33, 40] expand the network architecture and introduce large language models [28] to better hint embeddings. However, these works require training new text-to-image models and are not applicable to existing widely used models. Another line of work explores training-free improvement strategies, consistent with our approach.", + "bbox": [ + 496, + 580, + 890, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, Liu et al. [25] propose to use multiple diffusion models for different concepts and then composite the outputs to obtain the final result. This method solves the mentioned problem to some extent, but still suffers from subject mixing. Feng et al. [12] propose to split the input text prompt and process the cross attention layers to align the tokens and the outputs. Chefer et al. [6] introduce the concept of Generative Semantic Nursing (GSN), and slightly shifts the noisy image at each timestep of the denoising process, where the semantic information from the text prompt is better considered. Agarwal et al. [1] and Li et al. [24] further improve the optimization objective on this paradigm for better update direction. However, updating the noisy image at each denoising step requires carefully", + "bbox": [ + 496, + 688, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "Prompt: \"A cat and a dog.\"", + "bbox": [ + 81, + 88, + 254, + 101 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "Prompt: \"An elephant with a crown.\"", + "bbox": [ + 81, + 161, + 313, + 174 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9381", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/88225e67125b10913b6d508a68edf137af5ec5cdb8a8a82d0a80c1ce33a200c6.jpg", + "image_caption": [ + "Figure 3. Visualization of the attention maps." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 467, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "designed optimization parameters, posing a delicate balance between under-optimization and over-optimization.", + "bbox": [ + 75, + 325, + 467, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from previous methods, we explore a novel path by adjusting the sampled noise in the initial latent space, where full optimization is performed. It cleverly avoids the trade-off between under-optimization and over-optimization, is proven to be efficient and orthogonal to existing methods.", + "bbox": [ + 75, + 354, + 468, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 459, + 215, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stable Diffusion Model. This study focuses on the state-of-the-art Stable Diffusion model (SD) [31], belonging to the category of latent diffusion models (LDMs). Unlike traditional diffusion-based approaches operating directly in the image domain, SD functions within the latent space of an autoencoder. Specifically, an encoder $\\mathcal{E}(\\cdot)$ learns the mapping from an input image $\\mathbf{x} \\in \\mathcal{X}$ to a latent code $\\mathbf{z} = \\mathcal{E}(\\mathbf{x})$ . Subsequently, a decoder $\\mathcal{D}(\\cdot)$ reconstructs the input image, aiming for $\\mathcal{D}(\\mathcal{E}(\\mathbf{x})) \\approx \\mathbf{x}$ .", + "bbox": [ + 75, + 484, + 468, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Once the autoencoder is trained, a Denoising Diffusion Probabilistic Model (DDPM) [16] operates within the acquired latent space to generate a denoised version of an input latent $\\mathbf{z}_t$ at each timestep $t$ . During denoising, the diffusion model can be conditioned on additional inputs. In the case of SD, this condition typically takes the form of a text embedding generated by a pre-trained CLIP text encoder [27]. The conditioning embedding for the given prompt $\\mathbf{y}$ is denoted as $\\mathbf{c} = f_{\\mathrm{CLIP}}(\\mathbf{y})$ . The DDPM model $\\epsilon_{\\theta}(\\cdot)$ , parametrized by $\\theta$ , optimizes the following loss:", + "bbox": [ + 75, + 619, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathcal {E} (\\mathbf {x}), \\mathbf {c}, \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {1}), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c}, t) \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 781, + 468, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During inference, a latent variable $\\mathbf{z}_T$ is sampled from the standard Gaussian distribution $\\mathcal{N}(\\mathbf{0},\\mathbf{1})$ and subjected to sequential denoising procedures of DDPM to derive a refined latent representation $\\mathbf{z}_0$ . This denoised latent $\\mathbf{z}_0$ is then fed into the decoder $\\mathcal{D}(\\cdot)$ to synthesize the corresponding image $\\mathcal{D}(\\mathbf{z}_0)$ .", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Cross-attention layer. Text-image correspondence in SD is achieved through the cross-attention layer, enabling text condition guidance. Specifically, the pre-trained CLIP text encoder [27] embeds the text prompt $\\mathbf{y} = \\{\\mathbf{y}_1,\\mathbf{y}_2,\\dots ,\\mathbf{y}_n\\}$ into a sequential embedding, serving as the condition $\\mathbf{c} = f_{\\mathrm{CLIP}}(\\mathbf{y})$ . Linear projections are then employed to extract the key $\\mathbf{K}$ and value $\\mathbf{V}$ from $\\mathbf{c}$ , while the query $\\mathbf{Q}$ is mapped from the intermediate features of UNet. The cross-attention map $\\mathbf{A}^c$ is computed via:", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} ^ {c} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {T}}{\\sqrt {d}}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 238, + 890, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $d$ is the channel dimension. For ease of representation, we omit the denoising timestep $t$ . We denote the attention map that corresponds to the $i$ -th text token as $\\mathbf{A}_{\\mathbf{y}_i}^c$ , and $\\mathbf{A}_{\\mathbf{y}_i}^c[x,y]$ is the probability assigned to text token $\\mathbf{y}_i$ for the $(x,y)$ -th spatial patch of the intermediate feature map.", + "bbox": [ + 496, + 282, + 890, + 358 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-attention layer. In the self-attention layer, intermediate features serve as the key $\\mathbf{K}$ and value $\\mathbf{V}$ instead of the text condition $\\mathbf{c}$ , allowing synthesis of globally coherent structures by correlating image tokens across diverse regions. The self-attention map $\\mathbf{A}^s$ is computed using the same formula as Eq. 2, and $\\mathbf{A}_{x,y}^s$ denotes the attention map that corresponds to the $(x,y)$ -th spatial patch.", + "bbox": [ + 496, + 359, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. INITNO", + "text_level": 1, + "bbox": [ + 500, + 479, + 594, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The core of our method is the Initial Noise Optimization (INITNO), which comprises the initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. This section provides detailed explanations of both components in Sec. 4.1 and 4.2.", + "bbox": [ + 496, + 503, + 890, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Initial latent space partitioning", + "text_level": 1, + "bbox": [ + 498, + 604, + 774, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prevailing studies [4, 6, 15, 26, 35] demonstrate the informativeness of cross-attention maps, elucidating their capability to partially quantify the alignment between generated image and provided text. In this work, we extend these findings by thoroughly investigating the self-attention maps, which capture inter-spatial correlations within image features. We argue that cross-attention maps and self-attention maps can inherently gauge subject neglect and subject mixing, respectively. Leveraging these maps, we formulate the cross-attention response score and the self-attention conflict score. By establishing the score threshold, we achieve the partitioning of the initial latent space.", + "bbox": [ + 496, + 628, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Cross-attention response score. We follow [6] and derive the final cross-attention map by averaging the cross-attention maps in all layers and heads with a resolution of $16 \\times 16$ pixels. The aggregated map $\\mathbf{A}^c \\in \\mathbb{R}^{16 \\times 16 \\times n}$ contains $n$ spatial attention maps, each corresponding to a token of the text prompt. We also re-weight the attention values", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9382", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e3aba0a3b2532841a6692f3517eb96486a4a87e2a4590e9b6966ae32808a8b31.jpg", + "image_caption": [ + "Figure 4. Comparison of Attend-and-Excite with our method. Attend-and-Excite suffers from the trade-off between under-optimization and over-optimization. Under-optimization (lower path) remains confined to invalid regions, while over-optimization (upper path) carries the risk of deviating from the distribution of diffusion model. Our approach (middle path) skillfully addresses this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate optimization." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 890, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prompt: \"A cat and an dog.\"", + "text_level": 1, + "bbox": [ + 80, + 279, + 274, + 294 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/488b741c25f3c716271dc6bd0c6a45025edd1e357386468f5a96bcf162f3a1b3.jpg", + "image_caption": [ + "Figure 5. Effect of the scale factor of Attend-and-Excite. Given the same text prompt, we adjust the scale factor of Attend-and-Excite [6], 20 is used in the original work. Images of varying quality are synthesized, and the red box indicates the highest quality image. Images on the same row share an identical random seed." + ], + "image_footnote": [], + "bbox": [ + 81, + 296, + 467, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by ignoring the attention of the specialized token sot and performing a softmax operation on the remaining tokens. Fig. 3 shows the cross-attention map for each subject token, reflecting the spatial layout information corresponding to the generated image. Notably, a proficient denoising process can assign sufficiently high cross-attention responses to each subject during the early stages.", + "bbox": [ + 75, + 553, + 468, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conversely, a low attention response can lead to the absence of the target subject, i.e., subject neglect. As depicted in the red box in Fig. 3, the token crown registers a significantly lower response than rabbit in the initial denoising step, and crown is missing from the generated image. Building upon the insights from [6], we define the cross-attention response score as:", + "bbox": [ + 75, + 660, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\text {C r o s s A t t n}} = 1 - \\min _ {\\mathbf {y} _ {i} \\in \\mathcal {Y}} \\max \\left(\\mathbf {A} _ {\\mathbf {y} _ {i}} ^ {c}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 776, + 468, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{V}$ denotes the set of target tokens. Specifically, in this work, $S_{\\mathrm{CrossAttn}}$ is calculated over the initial noise and the first denoising step. We further define the cross-attention response score threshold $\\tau_{c}$ , empirically set to 0.2 in our experiments, where scores below this threshold are classified as valid, and those above are deemed invalid.", + "bbox": [ + 75, + 809, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Self-attention conflict score. Consistent with the cross-attention map extraction strategy, we extract the final self-attention map $\\mathbf{A}^s\\in \\mathbb{R}^{16\\times 16\\times (16\\times 16)}$ . For the subject token $\\mathbf{y}_i$ of interest, we first query the spatial coordinates $(x_{i},y_{i})$ corresponding to its maximum cross-attention value:", + "bbox": [ + 498, + 282, + 890, + 357 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {i}, y _ {i} = \\underset {x, y} {\\arg \\max } \\mathbf {A} _ {\\mathbf {y} _ {i}} ^ {c} [ x, y ]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 369, + 890, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, we obtain its corresponding self-attention map $\\mathbf{A}_{x_i,y_i}^s$ , as shown in Fig. 3. For an exemplary denoising process, the self-attention maps of different subject tokens can be distinctly partitioned in the spatial domain. However, existing diffusion models, e.g., SD, suffer from self-attention map overlap, leading to a failure case of subject mixing. As indicated in the blue box in Fig. 3, the self-attention maps of apple and pear significantly overlap, resulting in a combination of both. To quantify this phenomenon, we introduce the self-attention conflict score:", + "bbox": [ + 498, + 406, + 892, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal{S}_{\\text{SelfAttn}} = \\sum_{\\substack{\\mathbf{y}_{i},\\mathbf{y}_{j}\\in \\mathcal{Y},\\forall i < j}}\\frac{\\mathrm{f}(\\mathbf{y}_{i},\\mathbf{y}_{j})}{N}, \\\\ \\mathrm {f} \\left(\\mathbf {y} _ {i}, \\mathbf {y} _ {j}\\right) = \\frac {\\sum_ {x , y} \\min \\left(\\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] , \\mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\\right)}{\\sum_ {x , y} \\left(\\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] + \\mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\\right)}, \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 566, + 890, + 661 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ is the number of pairs of $\\mathbf{y}_i$ and $\\mathbf{y}_j$ . $S_{\\mathrm{SelfAttn}}$ is also calculated based on the initial noise and the first denoising step. We further define the self-attention conflict score threshold $\\tau_s$ , set to 0.3 in our experiments. Scores below $\\tau_s$ are classified as valid, and those above as invalid.", + "bbox": [ + 498, + 671, + 890, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we define the initial noise that passes both the cross-attention response score test and the self-attention conflict test as valid noise, and vice versa as invalid.", + "bbox": [ + 498, + 746, + 890, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Noise optimization pipeline", + "text_level": 1, + "bbox": [ + 500, + 801, + 745, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Fig. 4, existing methods most relevant to ours, represented by Attend-and-Excite [6], modify the noisy image at each denoising step, and encourage it to better encapsulate the semantic information from text. However, they necessitate meticulously calibrated optimization", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9383", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "parameters. As shown in Fig. 5, different optimization parameter settings directly affect the final generated image. Under-optimization leads to subpar quality, while over-optimization skews the noisy image away from the distribution of SD, resulting in an out-of-domain image. Moreover, even with the same text prompt, optimal parameters vary with noise, making case-specific tuning a laborious task.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We bypass this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate adjustment. Specifically, INITNO is exclusively dedicated to navigating within the initial latent space, moving randomly sampled initial noise into the valid region. Unlike denoising processes that implicitly model the noisy image distribution, the initial latent space typically adheres to a standard Gaussian distribution, providing an avenue to restrict the optimized noise to the domain.", + "bbox": [ + 75, + 198, + 470, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Noise update strategy. Given a noise $\\epsilon \\in \\mathcal{N}(\\mathbf{0},\\mathbf{1})$ , as opposed to the commonly used incremental update: $\\epsilon^{\\prime}\\gets$ $\\epsilon +\\Delta \\epsilon$ , we adopt a distribution optimization strategy to update the noise:", + "bbox": [ + 76, + 332, + 470, + 391 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mu^ {\\prime} \\leftarrow \\mu + \\Delta \\mu , \\quad \\sigma^ {\\prime} \\leftarrow \\sigma + \\Delta \\sigma , \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 402, + 468, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu$ and $\\sigma$ are the mean and standard deviation of the Gaussian distribution, initialized to 0 and 1, respectively. Thus, we have: $\\epsilon' \\gets \\mu' + \\sigma'\\epsilon$ , and $\\epsilon' \\sim \\mathcal{N}(\\mu', \\sigma'^2)$ .", + "bbox": [ + 76, + 431, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss functions. We employ a joint loss for optimizing initial noise, comprising cross-attention response loss, self-attention conflict loss, and distribution alignment loss. Intuitively, the first two are formulated as:", + "bbox": [ + 76, + 484, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {C r o s s A t t n}} = \\mathcal {S} _ {\\text {C r o s s A t t n}}, \\quad \\mathcal {L} _ {\\text {S e l f A t t n}} = \\mathcal {S} _ {\\text {S e l f A t t n}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 555, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The distribution alignment loss utilizes Kullback-Leibler divergence [22] to constrain the consistency between the target Gaussian distribution $\\mathcal{N}(\\mu, \\sigma^2)$ and the standard Gaussian distribution $\\mathcal{N}(\\mathbf{0}, \\mathbf{1})$ :", + "bbox": [ + 76, + 582, + 468, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K L}} = \\mathsf {K L} \\left(\\mathcal {N} (\\mu , \\sigma^ {2}) \\| \\mathcal {N} (\\mathbf {0}, \\mathbf {1})\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 652, + 468, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, the joint loss is written as:", + "bbox": [ + 96, + 681, + 357, + 695 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {j o i n t}} = \\lambda_ {1} \\mathcal {L} _ {\\text {C r o s s A t t n}} + \\lambda_ {2} \\mathcal {L} _ {\\text {S e l f A t t n}} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {K L}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 707, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we empirically set $\\lambda 1 = 1$ , $\\lambda_{2} = 1$ , and $\\lambda_{3} = 500$ .", + "bbox": [ + 76, + 734, + 441, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Noise optimization procedure. The outlined noise optimization procedure is encapsulated in Algorithm 1. Sampling the initial noise $\\mathbf{z}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{1})$ , we initialize the learnable parameters $\\mu$ to $\\mathbf{0}$ and $\\sigma$ to $\\mathbf{1}$ . We optimize these parameters using the joint loss, ensuring that the optimized noise $\\mu +\\sigma \\mathbf{z}^T$ resides within the valid initial latent space. The optimization employs the Adam optimizer with a learning rate of $1\\times 10^{-2}$ .", + "bbox": [ + 75, + 750, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To mitigate computational inefficiency due to excessively challenging samples, we impose a maximum limit", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: INITNO" + ], + "code_body": "Input: A pre-trained T2I diffusion model SD $(\\cdot)$ , a text prompt y, a noise $z_{T}$ , threshold: $\\tau_{c}, \\tau_{s}, \\tau_{\\text{MaxStep}}$ , and $\\tau_{\\text{MaxRound}}$ . Output: Generated image x. \n1 Noise pool $\\mathcal{P} \\gets \\{\\}$ \n2 for i = 1 to $\\tau_{\\text{MaxRound}}$ do \n3 Initialize $\\mathbf{z}_{T} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{1})$ , $\\mu \\gets \\mathbf{0}$ , $\\sigma \\gets \\mathbf{1}$ \n4 for j = 1 to $\\tau_{\\text{MaxStep}}$ do \n5 $\\mathbf{A}^{c}, \\mathbf{A}^{s} \\gets \\text{SD}(\\mu + \\sigma \\mathbf{z}^{T}, \\mathbf{y})$ \n6 Calculate $S_{\\text{CrossAttn}}$ (Eq. 3), $S_{\\text{SelfAttn}}$ (Eq. 5) \n7 if $S_{\\text{CrossAttn}} < \\tau_{c}$ and $S_{\\text{SelfAttn}} < \\tau_{s}$ then \n8 $\\hat{\\mathbf{z}}^{T} \\gets \\mu + \\sigma \\mathbf{z}^{T}$ \n9 Go to step 15 ▷ valid noise \n10 else \n11 Calculate $\\mathcal{L}_{\\text{joint}}$ (Eq. 9) \n12 $\\mu, \\sigma \\gets \\text{Adam}(\\mu, \\sigma, \\mathcal{L}_{\\text{joint}})$ \n13 Add $\\mu + \\sigma \\mathbf{z}^{T}$ to $\\mathcal{P}$ \n14 $\\hat{\\mathbf{z}}^{T} \\gets \\arg \\min_{\\mathbf{z}^{T} \\in \\mathcal{P}} S_{\\text{CrossAttn}} + S_{\\text{SelfAttn}}$ \n15 x, -, - ← SD ( $\\hat{\\mathbf{z}}^{T}, \\mathbf{y}$ ) or AE ( $\\hat{\\mathbf{z}}^{T}, \\mathbf{y}$ ) \n16 return x", + "bbox": [ + 500, + 111, + 890, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "on optimization iterations, denoted as $\\tau_{\\mathrm{MaxStep}}$ . If we fail to reach the valid region after $\\tau_{\\mathrm{MaxStep}}$ updates, we resample $\\mathbf{z}_T$ , reset $\\mu$ and $\\sigma$ , and commence a new round of the optimization process. We also define a maximum limit on optimization rounds, denoted as $\\tau_{\\mathrm{MaxRound}}$ . In our experiments, we set $\\tau_{\\mathrm{MaxStep}}$ and $\\tau_{\\mathrm{MaxRound}}$ as 50 and 5, respectively. For a minority of intricate texts where effective noise cannot be found within affordable optimization rounds, we opt for the noise that minimizes the sum of $S_{\\mathrm{CrossAttn}}$ and $S_{\\mathrm{SelfAttn}}$ from the existing noise pool $\\mathcal{P}$ .", + "bbox": [ + 496, + 474, + 890, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 641, + 633, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental settings", + "text_level": 1, + "bbox": [ + 500, + 666, + 702, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Following [6], we utilize the official Stable Diffusion v1.4 text-to-image model. A fixed guidance level of 7.5 is employed. We apply a Gaussian filter with a kernel size of 3 and a standard deviation of 0.5 to smooth the cross-attention map $\\mathbf{A}^c$ and the self-attention map $\\mathbf{A}^s$ . For the denoising process, $T$ is set to 50. The target token identification process can be performed either manually or automatically with the assistance of GPT [3].", + "bbox": [ + 496, + 688, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We assess our method using the Animal-Animal, Animal-Object, and Object-Object datasets [6], which comprise two subjects and selectively assign a color to each subject. It is noteworthy that our method is not constrained to this scenario, and it can be applied to complex prompts containing any number or type of subjects and attributes, as", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9384", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5405766aab0071df04318c45739506ee2b407ebfd8f4f5a0d0e609a1f00c7707.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline. Our method shows excellent alignment with text prompts while maintaining a high level of realism." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 890, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "discussed in Sec. 5.6 and supplementary material.", + "bbox": [ + 76, + 550, + 406, + 565 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Qualitative comparison", + "text_level": 1, + "bbox": [ + 76, + 575, + 292, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 6 presents a comparative analysis of our results against state-of-the-art counterparts, under the same text prompts and random seeds. It can be seen that existing methods commonly suffer from serious problems of subject mixing. For instance, in the case of a cat and a rabbit, conventional methods frequently yield erroneous outputs characterized by the fusion of cat faces and rabbit ears. Leveraging the self-attention conflict mechanism, our method can effectively decouple the two concepts of $\\underline{\\text{cat}}$ and $\\underline{\\text{rabbit}}$ and render them realistically and separately. Concurrently, Stable Diffusion [31], Composable Diffusion [25], and Structure Diffusion [12] suffer from the issue of subject neglect. Attend-and-Excite [6], Divide-and-Bind [24], and A-STAR [1] adhere to the pattern of adjusting noisy images at each denoising step. Given the same text prompt, using the same adjustment strategy, the quality of results generated by sampling different noises vary significantly. For instance, for the prompt a dog and a turtle, only the first example produced by Divide-and-Bind [24] is successful. In contrast, our method exhibits better generalization and", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "adapts to diverse prompts. Furthermore, our approach also demonstrates more faithful binding of properties, e.g., yellow clock.", + "bbox": [ + 498, + 550, + 890, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3.Quantitative comparison", + "text_level": 1, + "bbox": [ + 500, + 604, + 725, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Objective Evaluation. Following to the protocol in [6], we quantitatively evaluate the proposed method using CLIP Image-Text Similarity and CLIP Text-Text Similarity. For each prompt, 64 images are generated, and the average CLIP cosine similarity is computed, maintaining consistent random seeds across all methods. Specifically, for CLIP Image-Text Similarity, we report full prompt similarity (cosine similarity between the full prompt and generated image) and minimum object similarity (minimum of the similarities between the generated image and each of the two subject prompts). For CLIP Text-Text Similarity, text-text similarities are computed by captioning the generated images with BLIP [23] and comparing them with the input prompt. As shown in Fig. 7, the proposed method outperforms other approaches.", + "bbox": [ + 496, + 628, + 893, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "User study. We also conduct a subjective user study involving 12 volunteers with expertise in image processing. Participants were asked to select the most visuallyappealing", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9385", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/02a974bfd3db89a3beef5246894250bb5ba7d31c8e34d8ae357afa857b3ea99c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 90, + 238, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc59dc02f9fbd14860a1c8d074f0eda6ed4bad39005941b5edbae246f7829464.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 90, + 401, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7eb2304f0c31692f7ce8a647b90cfe5eea2b0116def47c43ac3415b77cb89a13.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 90, + 563, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7f289cc65a01b447e58d5b5e0b3f6e4cf12014639a2f87e03c2837921b071255.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 90, + 725, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1c28bcd79568180def8f0fbe7833a1ea06f056af60cbe897ce26ed79e355c9a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 90, + 888, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ae756167bd5179f8551445ee151c7b49aba40746db159ab2785fae7ea0b1b419.jpg", + "image_caption": [ + "Figure 7. Objective evaluation. Average CLIP Image-Text Similarity, including Full Prompt Similarity and Minimum Object Similarity, and Average CLIP Text-Text Similarity are reported for the quantitative measurement. Higher is better." + ], + "image_footnote": [], + "bbox": [ + 80, + 186, + 236, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5178974c9af6f15797a9924cdbbb895e12d895c9f663f17d70bf0f372a1d6ade.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 186, + 401, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/448f69d61779cbee8628fb14b4a383be0680096907454c6b812de09c63f76cdf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 186, + 563, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce0299b23dc18e3573ec455bf2aa34f8383b011277e2d35ed72fe655fa2a3fcb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 186, + 725, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1eaffb86f0b4f9fc6177eb414fe5471524ad45d0307c9aa7a1286793f268605c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 196, + 885, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f47dbf42bc4c88a4a890dae6105f50861c27186093303825c2e65c04ca400c53.jpg", + "image_caption": [ + "Attend- & Excite" + ], + "image_footnote": [], + "bbox": [ + 81, + 327, + 176, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/728d33e0274018001133f050eb590f9c4ff32ffd36b69b302065527b8c72a99e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 179, + 327, + 274, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d18f9fa442092cf078db40b5d27bc7ed258642d3ea14bd9d8226c659ca852973.jpg", + "image_caption": [ + "Attend- & Excite w/ LCrossConflict" + ], + "image_footnote": [], + "bbox": [ + 276, + 327, + 370, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f65b8eecc8b7822ad8eed55d3f44e1582f01c4571e6a5a94986fc63bd313e27e.jpg", + "image_caption": [ + "Attend- & Excite w/ $\\mathcal{L}_{\\mathrm{SelfAttn}}$" + ], + "image_footnote": [], + "bbox": [ + 372, + 327, + 467, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/10b0cd487c06267b940f01e99715eaf057b674d3f5f7e0fd6f82fe92d5334f4a.jpg", + "image_caption": [ + "Stable Diffusion" + ], + "image_footnote": [], + "bbox": [ + 80, + 425, + 176, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/577c63f5e02530d6fd383de2c64c0dd78596f5937d246558d8fbf9cadd4bdb19.jpg", + "image_caption": [ + "Ours w/o $\\mathcal{L}_{\\mathrm{SelfAttn}}$", + "Ours w/ $\\mathcal{L}_{\\mathrm{CrossConflict}}$" + ], + "image_footnote": [], + "bbox": [ + 179, + 425, + 274, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/552ebbeb299984cd822735b247a40313db1990efcd4e2c0b71429b36cf3ebe43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 425, + 370, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/901676f4843312752ec8e4cffbf708e82a7c41ff18dde4bb8d884362467c9f3d.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 372, + 425, + 467, + 500 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/66456342280591f0e7764c4c31bf9bb2f2e257d457104857ae5772fdd8f85495.jpg", + "table_caption": [ + "Figure 8. Visualization of effects of $\\mathcal{L}_{\\mathrm{SelfAttn}}$" + ], + "table_footnote": [], + "table_body": "
MethodUser study
Stable Diffusion [31]4.17%
Composable Diffusion [25]2.50%
Structure Diffusion [12]3.33%
Attend-and-Excite [6]14.17%
Divide-and-Bind [24]6.67%
A-STAR [1]5.83%
INITNO (Ours)63.33%
", + "bbox": [ + 140, + 537, + 408, + 675 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. User study. INITNO performs over other counterparts.", + "bbox": [ + 81, + 680, + 464, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and semantically-faithful image from those generated by our proposed method and the state-of-the-art approaches. Specifically, each participant has 20 questions. We tally the votes and show the statistics in Table 1. Our method performs favorably against the other methods.", + "bbox": [ + 75, + 702, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inference time. Evaluated on a single Tesla V100 (32GB), 100 images with a resolution of $512 \\times 512$ pixels are randomly generated, SD synthesizes an image in an average of 8.34 seconds, while our method takes 18.93 seconds.", + "bbox": [ + 75, + 777, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 847, + 227, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On self-attention conflict loss. The self-attention conflict loss is designed to address the subject mixing issue arising", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8101627ad0d643fd3be378340a4c4a8482cbfdf246ad6ac13e859a2a98ae65b1.jpg", + "image_caption": [ + "W/ $\\mathcal{L}_{\\mathrm{KL}}$", + "Figure 9. Visualization of effects of $\\mathcal{L}_{\\mathrm{KL}}$" + ], + "image_footnote": [], + "bbox": [ + 503, + 327, + 596, + 470 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a98f24f4f38c6b4e82c10dbf8d5c37886a2bfc9e6874741c866dbb1b966fe095.jpg", + "image_caption": [ + "\"A bird and a orange dog.\"" + ], + "image_footnote": [], + "bbox": [ + 596, + 327, + 794, + 469 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3a671904dda5ca63888cb591e1fb04ed6709525d6cf39f0efccccdf98c386b9a.jpg", + "image_caption": [ + "w/o $\\mathcal{L}_{\\mathrm{KL}}$" + ], + "image_footnote": [], + "bbox": [ + 795, + 328, + 890, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "from self-attention map overlap, and it can be effortlessly incorporated into existing methods. As depicted in Fig. 8, the self-attention conflict loss effectively addresses the mixing issue between apple and pear. We also experiment with a cross-attention conflict loss [1], which replaces the self-attention map with cross-attention ones, but it did not produce satisfactory results. We surmise this is due to the inaccurate text embedding extracted by CLIP. Conversely, the self-attention map offers a more intuitive solution.", + "bbox": [ + 496, + 527, + 890, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On distribution alignment loss. The distribution alignment loss is introduced to ensure that the optimized noise $\\hat{\\mathbf{z}}_T$ adheres to the standard Gaussian distribution. As visualized in the t-SNE plot of initial noise in Fig. 9, without constraints, the optimized noise may deviate from the standard Gaussian distribution, resulting in distorted results.", + "bbox": [ + 496, + 665, + 892, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Grounded Text-to-Image", + "text_level": 1, + "bbox": [ + 500, + 770, + 728, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "INITNO is a plug-and-play approach that can be effortlessly integrated with existing diffusion models to enable training-free controllable generation, such as layout-to-image, mask-to-image generation, etc. As demonstrated in Fig. 11, we incorporate INITNO into BoxDiff [38], where modifications to the intermediate noisy image are transferred to the initial latent space, resulting in the synthesis", + "bbox": [ + 496, + 794, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9386", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/76f736042b85fa20397edaea0fd7dfec200dfc7cf31894558880f1050e8b2863.jpg", + "image_caption": [ + "Figure 10. Qualitative comparison with complex text prompts. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/343c2520596c293900357cbf03bc7ae5c99eca91394fa791d60b389fab18c551.jpg", + "image_caption": [ + "Figure 11. Grounded Text-to-Image. Due to sufficient adjustments, INITNO generates more accurately location-aware $\\underline{cat}$ ." + ], + "image_footnote": [], + "bbox": [ + 76, + 329, + 467, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of faithful and location-aware images.", + "bbox": [ + 76, + 628, + 328, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. More results", + "text_level": 1, + "bbox": [ + 76, + 652, + 210, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Complex prompts. Fig. 10 presents examples of complex prompts, inclusive of prompts with three or more subjects and intricate attributes. The synthesis of high-fidelity images is demonstrated, underscoring the capacity of our method to manage complex semantic scenes.", + "bbox": [ + 75, + 676, + 468, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of the attention maps. Following [6], we also provide a visualization of the final cross-attention map for each subject token after denoising process in Fig. 12. Our method achieves reasonable attention allocation, leading to semantically-consistent results.", + "bbox": [ + 75, + 753, + 468, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The core of our method is the Initial Noise Optimization (INITNO), which consists of the initial latent space parti", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1dd51affe6e44ea76fbd8635a9b44d922eda8052d0e693f81aa6c4b9ea923150.jpg", + "image_caption": [ + "Figure 12. Visualization of the final cross-attention maps." + ], + "image_footnote": [], + "bbox": [ + 501, + 329, + 890, + 473 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. Specifically, we investigate the utility of attention maps in the diffusion model, harnessing them to formulate the cross-attention response score and the self-attention conflict score, both instrumental to the partitioning of the initial latent space. Moreover, we bypass the complex balance between under-optimization and over-optimization of noise via a meticulously crafted pipeline that introduces a novel distribution alignment loss. We further demonstrate the superiority of our approach over existing state-of-the-art methods in generating semantically-faithful images, providing a versatile plug-and-play solution that effectively integrates into existing diffusion models for training-free controllable generation", + "bbox": [ + 496, + 513, + 892, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 753, + 651, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is partly supported by the National Key R&D Program of China (2022ZD0161902), the National Natural Science Foundation of China (62022011, 62202031), the Research Program of State Key Laboratory of Software Development Environment (SKLSDE-2023ZX-14), and the Fundamental Research Funds for the Central Universities. We also give special thanks to Alibaba Group for their contribution to this paper.", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9387", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Aishwarya Agarwal, Srikrishna Karanam, KJ Joseph, Apoorv Saxena, Koustava Goswami, and Balaji Vasan Srinivasan. A-star: Test-time attention segregation and retention for text-to-image synthesis. 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In CVPR, 2019. 2" + ], + "bbox": [ + 78, + 90, + 468, + 771 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9389", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/ee9f1a65-ba75-4383-9c8b-786fd3d7ea61_model.json b/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/ee9f1a65-ba75-4383-9c8b-786fd3d7ea61_model.json new file mode 100644 index 0000000000000000000000000000000000000000..910b76ccccaf0b271f1ee332cd2671701e10ad47 --- /dev/null +++ b/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/ee9f1a65-ba75-4383-9c8b-786fd3d7ea61_model.json @@ -0,0 +1,2596 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.131, + 0.895, + 0.155 + ], + "angle": 0, + "content": "INITNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.18, + 0.852, + 0.2 + ], + "angle": 0, + "content": "Xiefan Guo\\(^{1,2}\\) Jinlin Liu Miaomiao Cui Jiankai Li\\(^{1,2}\\) Hongyu Yang\\(^{3,4}\\) Di Huang\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.205, + 0.873, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\)State Key Laboratory of Software Development Environment, Beihang University, Beijing, China \\(^{2}\\)School of Computer Science and Engineering, Beihang University, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.24, + 0.764, + 0.277 + ], + "angle": 0, + "content": "\\(^{3}\\)Institute of Artificial Intelligence, Beihang University, Beijing, China \\(^{4}\\)Shanghai Artificial Intelligence Laboratory, Shanghai, China" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.279, + 0.692, + 0.294 + ], + "angle": 0, + "content": "{xfguo, lijiankai, hongyuyang, dhuang}@buaa.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.328, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.361, + 0.474, + 0.664 + ], + "angle": 0, + "content": "Recent strides in the development of diffusion models, exemplified by advancements such as Stable Diffusion, have underscored their remarkable prowess in generating visually compelling images. However, the imperative of achieving a seamless alignment between the generated image and the provided prompt persists as a formidable challenge. This paper traces the root of these difficulties to invalid initial noise, and proposes a solution in the form of Initial Noise Optimization (INITNO), a paradigm that refines this noise. Considering text prompts, not all random noises are effective in synthesizing semantically-faithful images. We design the cross-attention response score and the self-attention conflict score to evaluate the initial noise, bifurcating the initial latent space into valid and invalid sectors. A strategically crafted noise optimization pipeline is developed to guide the initial noise towards valid regions. Our method, validated through rigorous experimentation, shows a commendable proficiency in generating images in strict accordance with text prompts. Our code is available at https://github.com/xiefan-guo/initno." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.696, + 0.21, + 0.712 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.722, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Text-to-Image Synthesis (T2I) stands at the forefront of cutting-edge research, dedicated to the generation of authentic and visually cohesive images from text prompts. In the domain of generative models, including generative adversarial networks [13, 18-21], variational autoencoders [22], and autoregressive models [7, 10, 36, 37], diffusion models [8, 16] have ascended as a predominant solution. The integration of large-scale vision-language models [2, 11, 14, 17, 30-32, 40, 41] has propelled noteworthy advancements in the text-to-image domain." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.327, + 0.891, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.566, + 0.868, + 0.58 + ], + "angle": 0, + "content": "Figure 1. Example results synthesized by SD and ours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.895, + 0.716 + ], + "angle": 0, + "content": "Despite the training of state-of-the-art T2I diffusion models on large-scale text-image datasets, synthesizing images precisely aligned with given text prompts remains a considerable challenge. Well-documented issues, i.e., subject neglect, subject mixing, and incorrect attribute binding, as illustrated in Fig. 1, persist. We attribute these challenges to the presence of invalid initial noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "When different noise inputs are introduced to the T2I diffusion model with identical text prompts, a substantial discrepancy is observed in the alignment between images and the provided text, as depicted in Fig. 2. This observation signifies that not all randomly sampled noise can produce visually-consistent images. Depending on the consistency between the generated image and the target text, the initial latent space can be divided into valid and invalid regions. Noise sourced from valid regions, when input into the T2I diffusion model, results in semantically-reasonable image. Consequently, our aim is to direct any initial noise towards the valid region, thereby facilitating the generation" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9380" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.082, + 0.089, + 0.255, + 0.102 + ], + "angle": 0, + "content": "Prompt: \"A cat and a dog.\"" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.104, + 0.149, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.104, + 0.221, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.104, + 0.311, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.104, + 0.379, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.104, + 0.449, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.104, + 0.521, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "header", + "bbox": [ + 0.082, + 0.162, + 0.314, + 0.175 + ], + "angle": 0, + "content": "Prompt: \"An elephant with a crown.\"" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.177, + 0.148, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.177, + 0.221, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.177, + 0.311, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.177, + 0.378, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.177, + 0.448, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.177, + 0.521, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.082, + 0.233, + 0.293, + 0.245 + ], + "angle": 0, + "content": "INITNO(Ours)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.313, + 0.233, + 0.521, + 0.245 + ], + "angle": 0, + "content": "Stable Diffusion (Invalid)" + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.104, + 0.672, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.218, + 0.65, + 0.229 + ], + "angle": 0, + "content": "Initial latent space" + }, + { + "type": "image", + "bbox": [ + 0.681, + 0.104, + 0.747, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.104, + 0.819, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.822, + 0.104, + 0.891, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.681, + 0.177, + 0.75, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.752, + 0.177, + 0.82, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.823, + 0.177, + 0.89, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.68, + 0.233, + 0.891, + 0.245 + ], + "angle": 0, + "content": "Stable Diffusion (Valid)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.894, + 0.349 + ], + "angle": 0, + "content": "Figure 2. INITNO. Our investigation dives into the exploration of various random noise configurations and their subsequent influence on the generated results. Notably, when different noises are input into SD under identical text prompts, there are marked discrepancy in the alignment between the generated image and the given text. Unsuccessful cases are delineated by gray contours, while successful instances are indicated by yellow contours. This observation underscores the pivotal role of initial noise in determining the success of the generation process. Based on this insight, we divide the initial noise space into valid and invalid regions. Introducing Initial Noise Optimization (INITNO), identified as orange arrow, our method is capable of guiding any initial noise into the valid region, thereby synthesizing high-fidelity results (orange contours) that precisely correspond to the given prompt. The same location employs the same random seed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.469, + 0.398 + ], + "angle": 0, + "content": "of visually-coherent image that faithfully aligns with the input prompt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.469, + 0.475 + ], + "angle": 0, + "content": "The core of this paper lies in the concept of Initial Noise Optimization (INITNO), which encompasses initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and directing initial noise navigation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.469, + 0.656 + ], + "angle": 0, + "content": "Our study thoroughly examines attention layers in the diffusion model, specifically the cross-attention map and the self-attention map. The former captures the correlation between text and image features, while the latter captures the correlation among different spatial positions within the image features. These maps effectively measure subject neglect and subject mixing, respectively (see Fig. 3). With these maps, we design the cross-attention response score and the self-attention conflict score. By setting score thresholds, we achieve further partitioning of the initial latent space. Interestingly, we find that accurate rendering of the subject fosters correct attribute binding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.809 + ], + "angle": 0, + "content": "The primary challenge in initial noise navigation is to balance under-optimization and over-optimization of noise. While under-optimization is still plagued by misalignment, over-optimization risks deviating from the initial distribution, i.e., standard Gaussian distribution, resulting in distorted images (see Fig. 9). To address this challenge, we introduce a carefully-crafted noise optimization pipeline. With the explicit modeling of the initial latent space, a novel distribution alignment loss is incorporated to ensure the optimized noise adheres to the initial distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.902 + ], + "angle": 0, + "content": "We establish the superiority of the proposed method over state-of-the-art approaches in generating semantically accurate images. Furthermore, our method is plug-and-play and seamlessly integrates into existing diffusion models, enabling training-free controllable generation and improving alignment with specific conditions, such as layout-to-image" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.368, + 0.669, + 0.383 + ], + "angle": 0, + "content": "generation (see Sec. 5.5)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.402, + 0.642, + 0.417 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Text-to-image synthesis strives to generate visually-realistic image that reflects given text. Early research mainly focused on GANs [34, 39, 42-44] and autoregressive models [5, 9, 29, 41]. Recently, diffusion models [8, 16] have taken over the mainstream, achieving impressive results. The incorporation of large-scale vision-language models [14, 17, 31, 32, 41] has fostered significant advancements in the text-to-image domain. Despite synthesizing highquality images, it remains challenging to produce results that properly comply with the given text prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.688 + ], + "angle": 0, + "content": "To deal with this problem, some works [2, 30, 32, 33, 40] expand the network architecture and introduce large language models [28] to better hint embeddings. However, these works require training new text-to-image models and are not applicable to existing widely used models. Another line of work explores training-free improvement strategies, consistent with our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Specifically, Liu et al. [25] propose to use multiple diffusion models for different concepts and then composite the outputs to obtain the final result. This method solves the mentioned problem to some extent, but still suffers from subject mixing. Feng et al. [12] propose to split the input text prompt and process the cross attention layers to align the tokens and the outputs. Chefer et al. [6] introduce the concept of Generative Semantic Nursing (GSN), and slightly shifts the noisy image at each timestep of the denoising process, where the semantic information from the text prompt is better considered. Agarwal et al. [1] and Li et al. [24] further improve the optimization objective on this paradigm for better update direction. However, updating the noisy image at each denoising step requires carefully" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9381" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.3, + 0.414, + 0.314 + ], + "angle": 0, + "content": "Figure 3. Visualization of the attention maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.468, + 0.355 + ], + "angle": 0, + "content": "designed optimization parameters, posing a delicate balance between under-optimization and over-optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.469, + 0.446 + ], + "angle": 0, + "content": "Different from previous methods, we explore a novel path by adjusting the sampled noise in the initial latent space, where full optimization is performed. It cleverly avoids the trade-off between under-optimization and over-optimization, is proven to be efficient and orthogonal to existing methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.46, + 0.216, + 0.475 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.469, + 0.62 + ], + "angle": 0, + "content": "Stable Diffusion Model. This study focuses on the state-of-the-art Stable Diffusion model (SD) [31], belonging to the category of latent diffusion models (LDMs). Unlike traditional diffusion-based approaches operating directly in the image domain, SD functions within the latent space of an autoencoder. Specifically, an encoder \\(\\mathcal{E}(\\cdot)\\) learns the mapping from an input image \\(\\mathbf{x} \\in \\mathcal{X}\\) to a latent code \\(\\mathbf{z} = \\mathcal{E}(\\mathbf{x})\\). Subsequently, a decoder \\(\\mathcal{D}(\\cdot)\\) reconstructs the input image, aiming for \\(\\mathcal{D}(\\mathcal{E}(\\mathbf{x})) \\approx \\mathbf{x}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.469, + 0.773 + ], + "angle": 0, + "content": "Once the autoencoder is trained, a Denoising Diffusion Probabilistic Model (DDPM) [16] operates within the acquired latent space to generate a denoised version of an input latent \\(\\mathbf{z}_t\\) at each timestep \\(t\\). During denoising, the diffusion model can be conditioned on additional inputs. In the case of SD, this condition typically takes the form of a text embedding generated by a pre-trained CLIP text encoder [27]. The conditioning embedding for the given prompt \\(\\mathbf{y}\\) is denoted as \\(\\mathbf{c} = f_{\\mathrm{CLIP}}(\\mathbf{y})\\). The DDPM model \\(\\epsilon_{\\theta}(\\cdot)\\), parametrized by \\(\\theta\\), optimizes the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.782, + 0.469, + 0.801 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathcal {E} (\\mathbf {x}), \\mathbf {c}, \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {1}), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c}, t) \\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.902 + ], + "angle": 0, + "content": "During inference, a latent variable \\(\\mathbf{z}_T\\) is sampled from the standard Gaussian distribution \\(\\mathcal{N}(\\mathbf{0},\\mathbf{1})\\) and subjected to sequential denoising procedures of DDPM to derive a refined latent representation \\(\\mathbf{z}_0\\). This denoised latent \\(\\mathbf{z}_0\\) is then fed into the decoder \\(\\mathcal{D}(\\cdot)\\) to synthesize the corresponding image \\(\\mathcal{D}(\\mathbf{z}_0)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Cross-attention layer. Text-image correspondence in SD is achieved through the cross-attention layer, enabling text condition guidance. Specifically, the pre-trained CLIP text encoder [27] embeds the text prompt \\(\\mathbf{y} = \\{\\mathbf{y}_1,\\mathbf{y}_2,\\dots ,\\mathbf{y}_n\\}\\) into a sequential embedding, serving as the condition \\(\\mathbf{c} = f_{\\mathrm{CLIP}}(\\mathbf{y})\\). Linear projections are then employed to extract the key \\(\\mathbf{K}\\) and value \\(\\mathbf{V}\\) from \\(\\mathbf{c}\\), while the query \\(\\mathbf{Q}\\) is mapped from the intermediate features of UNet. The cross-attention map \\(\\mathbf{A}^c\\) is computed via:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.239, + 0.892, + 0.274 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} ^ {c} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {T}}{\\sqrt {d}}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.359 + ], + "angle": 0, + "content": "where \\(d\\) is the channel dimension. For ease of representation, we omit the denoising timestep \\(t\\). We denote the attention map that corresponds to the \\(i\\)-th text token as \\(\\mathbf{A}_{\\mathbf{y}_i}^c\\), and \\(\\mathbf{A}_{\\mathbf{y}_i}^c[x,y]\\) is the probability assigned to text token \\(\\mathbf{y}_i\\) for the \\((x,y)\\)-th spatial patch of the intermediate feature map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.466 + ], + "angle": 0, + "content": "Self-attention layer. In the self-attention layer, intermediate features serve as the key \\(\\mathbf{K}\\) and value \\(\\mathbf{V}\\) instead of the text condition \\(\\mathbf{c}\\), allowing synthesis of globally coherent structures by correlating image tokens across diverse regions. The self-attention map \\(\\mathbf{A}^s\\) is computed using the same formula as Eq. 2, and \\(\\mathbf{A}_{x,y}^s\\) denotes the attention map that corresponds to the \\((x,y)\\)-th spatial patch." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.48, + 0.596, + 0.495 + ], + "angle": 0, + "content": "4. INITNO" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.595 + ], + "angle": 0, + "content": "The core of our method is the Initial Noise Optimization (INITNO), which comprises the initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. This section provides detailed explanations of both components in Sec. 4.1 and 4.2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.606, + 0.776, + 0.622 + ], + "angle": 0, + "content": "4.1. Initial latent space partitioning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Prevailing studies [4, 6, 15, 26, 35] demonstrate the informativeness of cross-attention maps, elucidating their capability to partially quantify the alignment between generated image and provided text. In this work, we extend these findings by thoroughly investigating the self-attention maps, which capture inter-spatial correlations within image features. We argue that cross-attention maps and self-attention maps can inherently gauge subject neglect and subject mixing, respectively. Leveraging these maps, we formulate the cross-attention response score and the self-attention conflict score. By establishing the score threshold, we achieve the partitioning of the initial latent space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Cross-attention response score. We follow [6] and derive the final cross-attention map by averaging the cross-attention maps in all layers and heads with a resolution of \\(16 \\times 16\\) pixels. The aggregated map \\(\\mathbf{A}^c \\in \\mathbb{R}^{16 \\times 16 \\times n}\\) contains \\(n\\) spatial attention maps, each corresponding to a token of the text prompt. We also re-weight the attention values" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9382" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.892, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.207, + 0.894, + 0.264 + ], + "angle": 0, + "content": "Figure 4. Comparison of Attend-and-Excite with our method. Attend-and-Excite suffers from the trade-off between under-optimization and over-optimization. Under-optimization (lower path) remains confined to invalid regions, while over-optimization (upper path) carries the risk of deviating from the distribution of diffusion model. Our approach (middle path) skillfully addresses this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate optimization." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.28, + 0.276, + 0.295 + ], + "angle": 0, + "content": "Prompt: \"A cat and an dog.\"" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.297, + 0.468, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Figure 5. Effect of the scale factor of Attend-and-Excite. Given the same text prompt, we adjust the scale factor of Attend-and-Excite [6], 20 is used in the original work. Images of varying quality are synthesized, and the red box indicates the highest quality image. Images on the same row share an identical random seed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.469, + 0.66 + ], + "angle": 0, + "content": "by ignoring the attention of the specialized token sot and performing a softmax operation on the remaining tokens. Fig. 3 shows the cross-attention map for each subject token, reflecting the spatial layout information corresponding to the generated image. Notably, a proficient denoising process can assign sufficiently high cross-attention responses to each subject during the early stages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.661, + 0.469, + 0.766 + ], + "angle": 0, + "content": "Conversely, a low attention response can lead to the absence of the target subject, i.e., subject neglect. As depicted in the red box in Fig. 3, the token crown registers a significantly lower response than rabbit in the initial denoising step, and crown is missing from the generated image. Building upon the insights from [6], we define the cross-attention response score as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.777, + 0.469, + 0.801 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\text {C r o s s A t t n}} = 1 - \\min _ {\\mathbf {y} _ {i} \\in \\mathcal {Y}} \\max \\left(\\mathbf {A} _ {\\mathbf {y} _ {i}} ^ {c}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.9 + ], + "angle": 0, + "content": "where \\(\\mathcal{V}\\) denotes the set of target tokens. Specifically, in this work, \\(S_{\\mathrm{CrossAttn}}\\) is calculated over the initial noise and the first denoising step. We further define the cross-attention response score threshold \\(\\tau_{c}\\), empirically set to 0.2 in our experiments, where scores below this threshold are classified as valid, and those above are deemed invalid." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.358 + ], + "angle": 0, + "content": "Self-attention conflict score. Consistent with the cross-attention map extraction strategy, we extract the final self-attention map \\(\\mathbf{A}^s\\in \\mathbb{R}^{16\\times 16\\times (16\\times 16)}\\). For the subject token \\(\\mathbf{y}_i\\) of interest, we first query the spatial coordinates \\((x_{i},y_{i})\\) corresponding to its maximum cross-attention value:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.37, + 0.892, + 0.396 + ], + "angle": 0, + "content": "\\[\nx _ {i}, y _ {i} = \\underset {x, y} {\\arg \\max } \\mathbf {A} _ {\\mathbf {y} _ {i}} ^ {c} [ x, y ]. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.407, + 0.893, + 0.557 + ], + "angle": 0, + "content": "Subsequently, we obtain its corresponding self-attention map \\(\\mathbf{A}_{x_i,y_i}^s\\), as shown in Fig. 3. For an exemplary denoising process, the self-attention maps of different subject tokens can be distinctly partitioned in the spatial domain. However, existing diffusion models, e.g., SD, suffer from self-attention map overlap, leading to a failure case of subject mixing. As indicated in the blue box in Fig. 3, the self-attention maps of apple and pear significantly overlap, resulting in a combination of both. To quantify this phenomenon, we introduce the self-attention conflict score:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.567, + 0.891, + 0.662 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal{S}_{\\text{SelfAttn}} = \\sum_{\\substack{\\mathbf{y}_{i},\\mathbf{y}_{j}\\in \\mathcal{Y},\\forall i < j}}\\frac{\\mathrm{f}(\\mathbf{y}_{i},\\mathbf{y}_{j})}{N}, \\\\ \\mathrm {f} \\left(\\mathbf {y} _ {i}, \\mathbf {y} _ {j}\\right) = \\frac {\\sum_ {x , y} \\min \\left(\\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] , \\mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\\right)}{\\sum_ {x , y} \\left(\\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] + \\mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\\right)}, \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.672, + 0.892, + 0.746 + ], + "angle": 0, + "content": "where \\(N\\) is the number of pairs of \\(\\mathbf{y}_i\\) and \\(\\mathbf{y}_j\\). \\(S_{\\mathrm{SelfAttn}}\\) is also calculated based on the initial noise and the first denoising step. We further define the self-attention conflict score threshold \\(\\tau_s\\), set to 0.3 in our experiments. Scores below \\(\\tau_s\\) are classified as valid, and those above as invalid." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.747, + 0.892, + 0.791 + ], + "angle": 0, + "content": "Finally, we define the initial noise that passes both the cross-attention response score test and the self-attention conflict test as valid noise, and vice versa as invalid." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.746, + 0.818 + ], + "angle": 0, + "content": "4.2. Noise optimization pipeline" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As illustrated in Fig. 4, existing methods most relevant to ours, represented by Attend-and-Excite [6], modify the noisy image at each denoising step, and encourage it to better encapsulate the semantic information from text. However, they necessitate meticulously calibrated optimization" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9383" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "parameters. As shown in Fig. 5, different optimization parameter settings directly affect the final generated image. Under-optimization leads to subpar quality, while over-optimization skews the noisy image away from the distribution of SD, resulting in an out-of-domain image. Moreover, even with the same text prompt, optimal parameters vary with noise, making case-specific tuning a laborious task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.332 + ], + "angle": 0, + "content": "We bypass this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate adjustment. Specifically, INITNO is exclusively dedicated to navigating within the initial latent space, moving randomly sampled initial noise into the valid region. Unlike denoising processes that implicitly model the noisy image distribution, the initial latent space typically adheres to a standard Gaussian distribution, providing an avenue to restrict the optimized noise to the domain." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.333, + 0.471, + 0.392 + ], + "angle": 0, + "content": "Noise update strategy. Given a noise \\(\\epsilon \\in \\mathcal{N}(\\mathbf{0},\\mathbf{1})\\) , as opposed to the commonly used incremental update: \\(\\epsilon^{\\prime}\\gets\\) \\(\\epsilon +\\Delta \\epsilon\\) , we adopt a distribution optimization strategy to update the noise:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.404, + 0.47, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\mu^ {\\prime} \\leftarrow \\mu + \\Delta \\mu , \\quad \\sigma^ {\\prime} \\leftarrow \\sigma + \\Delta \\sigma , \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.432, + 0.469, + 0.485 + ], + "angle": 0, + "content": "where \\(\\mu\\) and \\(\\sigma\\) are the mean and standard deviation of the Gaussian distribution, initialized to 0 and 1, respectively. Thus, we have: \\(\\epsilon' \\gets \\mu' + \\sigma'\\epsilon\\), and \\(\\epsilon' \\sim \\mathcal{N}(\\mu', \\sigma'^2)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.485, + 0.469, + 0.543 + ], + "angle": 0, + "content": "Loss functions. We employ a joint loss for optimizing initial noise, comprising cross-attention response loss, self-attention conflict loss, and distribution alignment loss. Intuitively, the first two are formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.556, + 0.469, + 0.572 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {C r o s s A t t n}} = \\mathcal {S} _ {\\text {C r o s s A t t n}}, \\quad \\mathcal {L} _ {\\text {S e l f A t t n}} = \\mathcal {S} _ {\\text {S e l f A t t n}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.583, + 0.47, + 0.643 + ], + "angle": 0, + "content": "The distribution alignment loss utilizes Kullback-Leibler divergence [22] to constrain the consistency between the target Gaussian distribution \\(\\mathcal{N}(\\mu, \\sigma^2)\\) and the standard Gaussian distribution \\(\\mathcal{N}(\\mathbf{0}, \\mathbf{1})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.653, + 0.469, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {K L}} = \\mathsf {K L} \\left(\\mathcal {N} (\\mu , \\sigma^ {2}) \\| \\mathcal {N} (\\mathbf {0}, \\mathbf {1})\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.682, + 0.358, + 0.696 + ], + "angle": 0, + "content": "In summary, the joint loss is written as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.708, + 0.469, + 0.725 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {j o i n t}} = \\lambda_ {1} \\mathcal {L} _ {\\text {C r o s s A t t n}} + \\lambda_ {2} \\mathcal {L} _ {\\text {S e l f A t t n}} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {K L}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.442, + 0.749 + ], + "angle": 0, + "content": "where we empirically set \\(\\lambda 1 = 1\\), \\(\\lambda_{2} = 1\\), and \\(\\lambda_{3} = 500\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.87 + ], + "angle": 0, + "content": "Noise optimization procedure. The outlined noise optimization procedure is encapsulated in Algorithm 1. Sampling the initial noise \\(\\mathbf{z}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{1})\\), we initialize the learnable parameters \\(\\mu\\) to \\(\\mathbf{0}\\) and \\(\\sigma\\) to \\(\\mathbf{1}\\). We optimize these parameters using the joint loss, ensuring that the optimized noise \\(\\mu +\\sigma \\mathbf{z}^T\\) resides within the valid initial latent space. The optimization employs the Adam optimizer with a learning rate of \\(1\\times 10^{-2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To mitigate computational inefficiency due to excessively challenging samples, we impose a maximum limit" + }, + { + "type": "code_caption", + "bbox": [ + 0.511, + 0.095, + 0.669, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: INITNO" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.112, + 0.892, + 0.445 + ], + "angle": 0, + "content": "Input: A pre-trained T2I diffusion model SD \\((\\cdot)\\), a text prompt y, a noise \\(z_{T}\\), threshold: \\(\\tau_{c}, \\tau_{s}, \\tau_{\\text{MaxStep}}\\), and \\(\\tau_{\\text{MaxRound}}\\). Output: Generated image x. \n1 Noise pool \\(\\mathcal{P} \\gets \\{\\}\\) \n2 for i = 1 to \\(\\tau_{\\text{MaxRound}}\\) do \n3 Initialize \\(\\mathbf{z}_{T} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{1})\\), \\(\\mu \\gets \\mathbf{0}\\), \\(\\sigma \\gets \\mathbf{1}\\) \n4 for j = 1 to \\(\\tau_{\\text{MaxStep}}\\) do \n5 \\(\\mathbf{A}^{c}, \\mathbf{A}^{s} \\gets \\text{SD}(\\mu + \\sigma \\mathbf{z}^{T}, \\mathbf{y})\\) \n6 Calculate \\(S_{\\text{CrossAttn}}\\) (Eq. 3), \\(S_{\\text{SelfAttn}}\\) (Eq. 5) \n7 if \\(S_{\\text{CrossAttn}} < \\tau_{c}\\) and \\(S_{\\text{SelfAttn}} < \\tau_{s}\\) then \n8 \\(\\hat{\\mathbf{z}}^{T} \\gets \\mu + \\sigma \\mathbf{z}^{T}\\) \n9 Go to step 15 ▷ valid noise \n10 else \n11 Calculate \\(\\mathcal{L}_{\\text{joint}}\\) (Eq. 9) \n12 \\(\\mu, \\sigma \\gets \\text{Adam}(\\mu, \\sigma, \\mathcal{L}_{\\text{joint}})\\) \n13 Add \\(\\mu + \\sigma \\mathbf{z}^{T}\\) to \\(\\mathcal{P}\\) \n14 \\(\\hat{\\mathbf{z}}^{T} \\gets \\arg \\min_{\\mathbf{z}^{T} \\in \\mathcal{P}} S_{\\text{CrossAttn}} + S_{\\text{SelfAttn}}\\) \n15 x, -, - ← SD (\\(\\hat{\\mathbf{z}}^{T}, \\mathbf{y}\\)) or AE (\\(\\hat{\\mathbf{z}}^{T}, \\mathbf{y}\\)) \n16 return x" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.628 + ], + "angle": 0, + "content": "on optimization iterations, denoted as \\(\\tau_{\\mathrm{MaxStep}}\\). If we fail to reach the valid region after \\(\\tau_{\\mathrm{MaxStep}}\\) updates, we resample \\(\\mathbf{z}_T\\), reset \\(\\mu\\) and \\(\\sigma\\), and commence a new round of the optimization process. We also define a maximum limit on optimization rounds, denoted as \\(\\tau_{\\mathrm{MaxRound}}\\). In our experiments, we set \\(\\tau_{\\mathrm{MaxStep}}\\) and \\(\\tau_{\\mathrm{MaxRound}}\\) as 50 and 5, respectively. For a minority of intricate texts where effective noise cannot be found within affordable optimization rounds, we opt for the noise that minimizes the sum of \\(S_{\\mathrm{CrossAttn}}\\) and \\(S_{\\mathrm{SelfAttn}}\\) from the existing noise pool \\(\\mathcal{P}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.634, + 0.658 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.704, + 0.683 + ], + "angle": 0, + "content": "5.1. Experimental settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Implementation Details. Following [6], we utilize the official Stable Diffusion v1.4 text-to-image model. A fixed guidance level of 7.5 is employed. We apply a Gaussian filter with a kernel size of 3 and a standard deviation of 0.5 to smooth the cross-attention map \\(\\mathbf{A}^c\\) and the self-attention map \\(\\mathbf{A}^s\\). For the denoising process, \\(T\\) is set to 50. The target token identification process can be performed either manually or automatically with the assistance of GPT [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. We assess our method using the Animal-Animal, Animal-Object, and Object-Object datasets [6], which comprise two subjects and selectively assign a color to each subject. It is noteworthy that our method is not constrained to this scenario, and it can be applied to complex prompts containing any number or type of subjects and attributes, as" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9384" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.892, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.503, + 0.893, + 0.534 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline. Our method shows excellent alignment with text prompts while maintaining a high level of realism." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.551, + 0.407, + 0.566 + ], + "angle": 0, + "content": "discussed in Sec. 5.6 and supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.294, + 0.592 + ], + "angle": 0, + "content": "5.2. Qualitative comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Fig. 6 presents a comparative analysis of our results against state-of-the-art counterparts, under the same text prompts and random seeds. It can be seen that existing methods commonly suffer from serious problems of subject mixing. For instance, in the case of a cat and a rabbit, conventional methods frequently yield erroneous outputs characterized by the fusion of cat faces and rabbit ears. Leveraging the self-attention conflict mechanism, our method can effectively decouple the two concepts of \\( \\underline{\\text{cat}} \\) and \\( \\underline{\\text{rabbit}} \\) and render them realistically and separately. Concurrently, Stable Diffusion [31], Composable Diffusion [25], and Structure Diffusion [12] suffer from the issue of subject neglect. Attend-and-Excite [6], Divide-and-Bind [24], and A-STAR [1] adhere to the pattern of adjusting noisy images at each denoising step. Given the same text prompt, using the same adjustment strategy, the quality of results generated by sampling different noises vary significantly. For instance, for the prompt a dog and a turtle, only the first example produced by Divide-and-Bind [24] is successful. In contrast, our method exhibits better generalization and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.551, + 0.892, + 0.596 + ], + "angle": 0, + "content": "adapts to diverse prompts. Furthermore, our approach also demonstrates more faithful binding of properties, e.g., yellow clock." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.727, + 0.623 + ], + "angle": 0, + "content": "5.3.Quantitative comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.854 + ], + "angle": 0, + "content": "Objective Evaluation. Following to the protocol in [6], we quantitatively evaluate the proposed method using CLIP Image-Text Similarity and CLIP Text-Text Similarity. For each prompt, 64 images are generated, and the average CLIP cosine similarity is computed, maintaining consistent random seeds across all methods. Specifically, for CLIP Image-Text Similarity, we report full prompt similarity (cosine similarity between the full prompt and generated image) and minimum object similarity (minimum of the similarities between the generated image and each of the two subject prompts). For CLIP Text-Text Similarity, text-text similarities are computed by captioning the generated images with BLIP [23] and comparing them with the input prompt. As shown in Fig. 7, the proposed method outperforms other approaches." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "User study. We also conduct a subjective user study involving 12 volunteers with expertise in image processing. Participants were asked to select the most visuallyappealing" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9385" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.239, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.092, + 0.402, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.092, + 0.565, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.092, + 0.727, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.092, + 0.89, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.187, + 0.238, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.187, + 0.402, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.187, + 0.565, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.187, + 0.727, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.197, + 0.887, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.893, + 0.311 + ], + "angle": 0, + "content": "Figure 7. Objective evaluation. Average CLIP Image-Text Similarity, including Full Prompt Similarity and Minimum Object Similarity, and Average CLIP Text-Text Similarity are reported for the quantitative measurement. Higher is better." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.328, + 0.177, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.328, + 0.275, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.328, + 0.371, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.328, + 0.468, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.186, + 0.408, + 0.269, + 0.418 + ], + "angle": 0, + "content": "Attend- & Excite" + }, + { + "type": "image_caption", + "bbox": [ + 0.279, + 0.404, + 0.365, + 0.425 + ], + "angle": 0, + "content": "Attend- & Excite w/ LCrossConflict" + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.403, + 0.468, + 0.425 + ], + "angle": 0, + "content": "Attend- & Excite w/ \\(\\mathcal{L}_{\\mathrm{SelfAttn}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.426, + 0.177, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.501, + 0.17, + 0.511 + ], + "angle": 0, + "content": "Stable Diffusion" + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.426, + 0.275, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.183, + 0.501, + 0.272, + 0.512 + ], + "angle": 0, + "content": "Ours w/o \\(\\mathcal{L}_{\\mathrm{SelfAttn}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.426, + 0.372, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.501, + 0.375, + 0.513 + ], + "angle": 0, + "content": "Ours w/ \\(\\mathcal{L}_{\\mathrm{CrossConflict}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.426, + 0.468, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.501, + 0.433, + 0.511 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "table_caption", + "bbox": [ + 0.137, + 0.518, + 0.411, + 0.533 + ], + "angle": 0, + "content": "Figure 8. Visualization of effects of \\(\\mathcal{L}_{\\mathrm{SelfAttn}}\\)" + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.538, + 0.409, + 0.676 + ], + "angle": 0, + "content": "
MethodUser study
Stable Diffusion [31]4.17%
Composable Diffusion [25]2.50%
Structure Diffusion [12]3.33%
Attend-and-Excite [6]14.17%
Divide-and-Bind [24]6.67%
A-STAR [1]5.83%
INITNO (Ours)63.33%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.082, + 0.681, + 0.465, + 0.696 + ], + "angle": 0, + "content": "Table 1. User study. INITNO performs over other counterparts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.778 + ], + "angle": 0, + "content": "and semantically-faithful image from those generated by our proposed method and the state-of-the-art approaches. Specifically, each participant has 20 questions. We tally the votes and show the statistics in Table 1. Our method performs favorably against the other methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Inference time. Evaluated on a single Tesla V100 (32GB), 100 images with a resolution of \\(512 \\times 512\\) pixels are randomly generated, SD synthesizes an image in an average of 8.34 seconds, while our method takes 18.93 seconds." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.228, + 0.864 + ], + "angle": 0, + "content": "5.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "On self-attention conflict loss. The self-attention conflict loss is designed to address the subject mixing issue arising" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.328, + 0.597, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.473, + 0.57, + 0.486 + ], + "angle": 0, + "content": "W/ \\(\\mathcal{L}_{\\mathrm{KL}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.598, + 0.328, + 0.795, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.615, + 0.472, + 0.778, + 0.487 + ], + "angle": 0, + "content": "\"A bird and a orange dog.\"" + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.329, + 0.891, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.473, + 0.867, + 0.486 + ], + "angle": 0, + "content": "w/o \\(\\mathcal{L}_{\\mathrm{KL}}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.57, + 0.492, + 0.822, + 0.507 + ], + "angle": 0, + "content": "Figure 9. Visualization of effects of \\(\\mathcal{L}_{\\mathrm{KL}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.665 + ], + "angle": 0, + "content": "from self-attention map overlap, and it can be effortlessly incorporated into existing methods. As depicted in Fig. 8, the self-attention conflict loss effectively addresses the mixing issue between apple and pear. We also experiment with a cross-attention conflict loss [1], which replaces the self-attention map with cross-attention ones, but it did not produce satisfactory results. We surmise this is due to the inaccurate text embedding extracted by CLIP. Conversely, the self-attention map offers a more intuitive solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.893, + 0.757 + ], + "angle": 0, + "content": "On distribution alignment loss. The distribution alignment loss is introduced to ensure that the optimized noise \\(\\hat{\\mathbf{z}}_T\\) adheres to the standard Gaussian distribution. As visualized in the t-SNE plot of initial noise in Fig. 9, without constraints, the optimized noise may deviate from the standard Gaussian distribution, resulting in distorted results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.729, + 0.788 + ], + "angle": 0, + "content": "5.5. Grounded Text-to-Image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.902 + ], + "angle": 0, + "content": "INITNO is a plug-and-play approach that can be effortlessly integrated with existing diffusion models to enable training-free controllable generation, such as layout-to-image, mask-to-image generation, etc. As demonstrated in Fig. 11, we incorporate INITNO into BoxDiff [38], where modifications to the intermediate noisy image are transferred to the initial latent space, resulting in the synthesis" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9386" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.29, + 0.893, + 0.319 + ], + "angle": 0, + "content": "Figure 10. Qualitative comparison with complex text prompts. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.33, + 0.468, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.576, + 0.47, + 0.606 + ], + "angle": 0, + "content": "Figure 11. Grounded Text-to-Image. Due to sufficient adjustments, INITNO generates more accurately location-aware \\( \\underline{cat} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.629, + 0.33, + 0.644 + ], + "angle": 0, + "content": "of faithful and location-aware images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.654, + 0.212, + 0.669 + ], + "angle": 0, + "content": "5.6. More results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.47, + 0.754 + ], + "angle": 0, + "content": "Complex prompts. Fig. 10 presents examples of complex prompts, inclusive of prompts with three or more subjects and intricate attributes. The synthesis of high-fidelity images is demonstrated, underscoring the capacity of our method to manage complex semantic scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.47, + 0.83 + ], + "angle": 0, + "content": "Visualization of the attention maps. Following [6], we also provide a visualization of the final cross-attention map for each subject token after denoising process in Fig. 12. Our method achieves reasonable attention allocation, leading to semantically-consistent results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.196, + 0.86 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The core of our method is the Initial Noise Optimization (INITNO), which consists of the initial latent space parti" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.33, + 0.892, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.479, + 0.876, + 0.493 + ], + "angle": 0, + "content": "Figure 12. Visualization of the final cross-attention maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.893, + 0.743 + ], + "angle": 0, + "content": "tioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. Specifically, we investigate the utility of attention maps in the diffusion model, harnessing them to formulate the cross-attention response score and the self-attention conflict score, both instrumental to the partitioning of the initial latent space. Moreover, we bypass the complex balance between under-optimization and over-optimization of noise via a meticulously crafted pipeline that introduces a novel distribution alignment loss. We further demonstrate the superiority of our approach over existing state-of-the-art methods in generating semantically-faithful images, providing a versatile plug-and-play solution that effectively integrates into existing diffusion models for training-free controllable generation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.652, + 0.772 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "This work is partly supported by the National Key R&D Program of China (2022ZD0161902), the National Natural Science Foundation of China (62022011, 62202031), the Research Program of State Key Laboratory of Software Development Environment (SKLSDE-2023ZX-14), and the Fundamental Research Funds for the Central Universities. We also give special thanks to Alibaba Group for their contribution to this paper." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9387" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Aishwarya Agarwal, Srikrishna Karanam, KJ Joseph, Apoorv Saxena, Koustava Goswami, and Balaji Vasan Srinivasan. A-star: Test-time attention segregation and retention for text-to-image synthesis. 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However, the imperative of achieving a seamless alignment between the generated image and the provided prompt persists as a formidable challenge. This paper traces the root of these difficulties to invalid initial noise, and proposes a solution in the form of Initial Noise Optimization (INITNO), a paradigm that refines this noise. Considering text prompts, not all random noises are effective in synthesizing semantically-faithful images. We design the cross-attention response score and the self-attention conflict score to evaluate the initial noise, bifurcating the initial latent space into valid and invalid sectors. A strategically crafted noise optimization pipeline is developed to guide the initial noise towards valid regions. Our method, validated through rigorous experimentation, shows a commendable proficiency in generating images in strict accordance with text prompts. Our code is available at https://github.com/xiefan-guo/initno. + +# 1. Introduction + +Text-to-Image Synthesis (T2I) stands at the forefront of cutting-edge research, dedicated to the generation of authentic and visually cohesive images from text prompts. In the domain of generative models, including generative adversarial networks [13, 18-21], variational autoencoders [22], and autoregressive models [7, 10, 36, 37], diffusion models [8, 16] have ascended as a predominant solution. The integration of large-scale vision-language models [2, 11, 14, 17, 30-32, 40, 41] has propelled noteworthy advancements in the text-to-image domain. + +![](images/66b9cac488f6839ebe12d9ab5f38cdadfdbc57682d55c0c506c42a3bea147603.jpg) +Figure 1. Example results synthesized by SD and ours. + +Despite the training of state-of-the-art T2I diffusion models on large-scale text-image datasets, synthesizing images precisely aligned with given text prompts remains a considerable challenge. Well-documented issues, i.e., subject neglect, subject mixing, and incorrect attribute binding, as illustrated in Fig. 1, persist. We attribute these challenges to the presence of invalid initial noise. + +When different noise inputs are introduced to the T2I diffusion model with identical text prompts, a substantial discrepancy is observed in the alignment between images and the provided text, as depicted in Fig. 2. This observation signifies that not all randomly sampled noise can produce visually-consistent images. Depending on the consistency between the generated image and the target text, the initial latent space can be divided into valid and invalid regions. Noise sourced from valid regions, when input into the T2I diffusion model, results in semantically-reasonable image. Consequently, our aim is to direct any initial noise towards the valid region, thereby facilitating the generation + +![](images/c3026d5f652db31bf74f0414c7167212bfa7c2ab8710b564f6a28311ef1d36f2.jpg) + +![](images/5436210f03989983c98e11858f4d217b2c49b570daeaf7c6c077471ace92b803.jpg) + +![](images/75c2aa07cbbd651c5960534988cf5d9859cf283a52b5a696d4b46c8e576f3efd.jpg) + +![](images/585e7c11e77658dde601ec7b0738719e93a33e2b165e24c33173ff2849cc4a3b.jpg) + +![](images/f677a3dc9a6fa8cdd6b45ffae181c77fccea1b17919e7b2fb872afac63994359.jpg) + +![](images/5ae96fef33b9afb73f4ea393e50ea0bb6b8b116ef4092b408036ca93979251a4.jpg) + +Figure 2. INITNO. Our investigation dives into the exploration of various random noise configurations and their subsequent influence on the generated results. Notably, when different noises are input into SD under identical text prompts, there are marked discrepancy in the alignment between the generated image and the given text. Unsuccessful cases are delineated by gray contours, while successful instances are indicated by yellow contours. This observation underscores the pivotal role of initial noise in determining the success of the generation process. Based on this insight, we divide the initial noise space into valid and invalid regions. Introducing Initial Noise Optimization (INITNO), identified as orange arrow, our method is capable of guiding any initial noise into the valid region, thereby synthesizing high-fidelity results (orange contours) that precisely correspond to the given prompt. The same location employs the same random seed. +![](images/8573e67a5beefc5173aae9b0817307ea2166f331061aec370b43d19d4d91b597.jpg) +INITNO(Ours) + +![](images/71bf8b6a6ee598a88b5de9e16f920b3271c64c795fb178bc7b0b0872a2814617.jpg) + +![](images/970914c5fa3de4014fdd57c34934ac7ed2e0fa450887f18f96c2c45449109597.jpg) +Stable Diffusion (Invalid) + +![](images/967c2984c44aeb9b57d8878845d4fd9d87db15cdcfa541c06cc778cd163579ba.jpg) + +![](images/8e5e28c6b1e166ca728bfb4be8378c04442366d536991678b65a88bc6ef762c8.jpg) + +![](images/c8427be4ca25a646745bb7f20f727ae33069010b97cae8fa9270fd327875248f.jpg) + +![](images/4f8f8be1daf7fd0d817178802836655b20c0e677110b17c12b8963824cee5daa.jpg) +Initial latent space + +![](images/1e145a42057d5c71ffc6d0072cf23ee29b90e9527cfdab5f2e994e9b4b3bc2b5.jpg) + +![](images/e5567a7ce7bd250462d1d0578509576e8c0ef3fd61ea2bd87f5ec292f37ded95.jpg) + +![](images/16d119fcc48888a2d5868c801e54255d24d925cfe92831aa27d5c2eb7e96cf8b.jpg) + +![](images/78b273fda02b39a3b9825ff816b45befa2a3c4e8c4408230bce9b8ca12479e6a.jpg) +Stable Diffusion (Valid) + +![](images/dd79f5ba0e2c6f949663c8ecc4674de6d139ad91c3c4da0dc16137b8c2ee5fe7.jpg) + +![](images/c540329de03022e30599b090576f74aba338dc3730141f3706b97a492787487d.jpg) + +of visually-coherent image that faithfully aligns with the input prompt. + +The core of this paper lies in the concept of Initial Noise Optimization (INITNO), which encompasses initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and directing initial noise navigation, respectively. + +Our study thoroughly examines attention layers in the diffusion model, specifically the cross-attention map and the self-attention map. The former captures the correlation between text and image features, while the latter captures the correlation among different spatial positions within the image features. These maps effectively measure subject neglect and subject mixing, respectively (see Fig. 3). With these maps, we design the cross-attention response score and the self-attention conflict score. By setting score thresholds, we achieve further partitioning of the initial latent space. Interestingly, we find that accurate rendering of the subject fosters correct attribute binding. + +The primary challenge in initial noise navigation is to balance under-optimization and over-optimization of noise. While under-optimization is still plagued by misalignment, over-optimization risks deviating from the initial distribution, i.e., standard Gaussian distribution, resulting in distorted images (see Fig. 9). To address this challenge, we introduce a carefully-crafted noise optimization pipeline. With the explicit modeling of the initial latent space, a novel distribution alignment loss is incorporated to ensure the optimized noise adheres to the initial distribution. + +We establish the superiority of the proposed method over state-of-the-art approaches in generating semantically accurate images. Furthermore, our method is plug-and-play and seamlessly integrates into existing diffusion models, enabling training-free controllable generation and improving alignment with specific conditions, such as layout-to-image + +generation (see Sec. 5.5). + +# 2. Related Work + +Text-to-image synthesis strives to generate visually-realistic image that reflects given text. Early research mainly focused on GANs [34, 39, 42-44] and autoregressive models [5, 9, 29, 41]. Recently, diffusion models [8, 16] have taken over the mainstream, achieving impressive results. The incorporation of large-scale vision-language models [14, 17, 31, 32, 41] has fostered significant advancements in the text-to-image domain. Despite synthesizing highquality images, it remains challenging to produce results that properly comply with the given text prompt. + +To deal with this problem, some works [2, 30, 32, 33, 40] expand the network architecture and introduce large language models [28] to better hint embeddings. However, these works require training new text-to-image models and are not applicable to existing widely used models. Another line of work explores training-free improvement strategies, consistent with our approach. + +Specifically, Liu et al. [25] propose to use multiple diffusion models for different concepts and then composite the outputs to obtain the final result. This method solves the mentioned problem to some extent, but still suffers from subject mixing. Feng et al. [12] propose to split the input text prompt and process the cross attention layers to align the tokens and the outputs. Chefer et al. [6] introduce the concept of Generative Semantic Nursing (GSN), and slightly shifts the noisy image at each timestep of the denoising process, where the semantic information from the text prompt is better considered. Agarwal et al. [1] and Li et al. [24] further improve the optimization objective on this paradigm for better update direction. However, updating the noisy image at each denoising step requires carefully + +![](images/88225e67125b10913b6d508a68edf137af5ec5cdb8a8a82d0a80c1ce33a200c6.jpg) +Figure 3. Visualization of the attention maps. + +designed optimization parameters, posing a delicate balance between under-optimization and over-optimization. + +Different from previous methods, we explore a novel path by adjusting the sampled noise in the initial latent space, where full optimization is performed. It cleverly avoids the trade-off between under-optimization and over-optimization, is proven to be efficient and orthogonal to existing methods. + +# 3. Preliminaries + +Stable Diffusion Model. This study focuses on the state-of-the-art Stable Diffusion model (SD) [31], belonging to the category of latent diffusion models (LDMs). Unlike traditional diffusion-based approaches operating directly in the image domain, SD functions within the latent space of an autoencoder. Specifically, an encoder $\mathcal{E}(\cdot)$ learns the mapping from an input image $\mathbf{x} \in \mathcal{X}$ to a latent code $\mathbf{z} = \mathcal{E}(\mathbf{x})$ . Subsequently, a decoder $\mathcal{D}(\cdot)$ reconstructs the input image, aiming for $\mathcal{D}(\mathcal{E}(\mathbf{x})) \approx \mathbf{x}$ . + +Once the autoencoder is trained, a Denoising Diffusion Probabilistic Model (DDPM) [16] operates within the acquired latent space to generate a denoised version of an input latent $\mathbf{z}_t$ at each timestep $t$ . During denoising, the diffusion model can be conditioned on additional inputs. In the case of SD, this condition typically takes the form of a text embedding generated by a pre-trained CLIP text encoder [27]. The conditioning embedding for the given prompt $\mathbf{y}$ is denoted as $\mathbf{c} = f_{\mathrm{CLIP}}(\mathbf{y})$ . The DDPM model $\epsilon_{\theta}(\cdot)$ , parametrized by $\theta$ , optimizes the following loss: + +$$ +\mathcal {L} = \mathbb {E} _ {\mathbf {z} \sim \mathcal {E} (\mathbf {x}), \mathbf {c}, \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {1}), t} \left[ \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, \mathbf {c}, t) \| _ {2} ^ {2} \right], \tag {1} +$$ + +During inference, a latent variable $\mathbf{z}_T$ is sampled from the standard Gaussian distribution $\mathcal{N}(\mathbf{0},\mathbf{1})$ and subjected to sequential denoising procedures of DDPM to derive a refined latent representation $\mathbf{z}_0$ . This denoised latent $\mathbf{z}_0$ is then fed into the decoder $\mathcal{D}(\cdot)$ to synthesize the corresponding image $\mathcal{D}(\mathbf{z}_0)$ . + +Cross-attention layer. Text-image correspondence in SD is achieved through the cross-attention layer, enabling text condition guidance. Specifically, the pre-trained CLIP text encoder [27] embeds the text prompt $\mathbf{y} = \{\mathbf{y}_1,\mathbf{y}_2,\dots ,\mathbf{y}_n\}$ into a sequential embedding, serving as the condition $\mathbf{c} = f_{\mathrm{CLIP}}(\mathbf{y})$ . Linear projections are then employed to extract the key $\mathbf{K}$ and value $\mathbf{V}$ from $\mathbf{c}$ , while the query $\mathbf{Q}$ is mapped from the intermediate features of UNet. The cross-attention map $\mathbf{A}^c$ is computed via: + +$$ +\mathbf {A} ^ {c} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {T}}{\sqrt {d}}\right), \tag {2} +$$ + +where $d$ is the channel dimension. For ease of representation, we omit the denoising timestep $t$ . We denote the attention map that corresponds to the $i$ -th text token as $\mathbf{A}_{\mathbf{y}_i}^c$ , and $\mathbf{A}_{\mathbf{y}_i}^c[x,y]$ is the probability assigned to text token $\mathbf{y}_i$ for the $(x,y)$ -th spatial patch of the intermediate feature map. + +Self-attention layer. In the self-attention layer, intermediate features serve as the key $\mathbf{K}$ and value $\mathbf{V}$ instead of the text condition $\mathbf{c}$ , allowing synthesis of globally coherent structures by correlating image tokens across diverse regions. The self-attention map $\mathbf{A}^s$ is computed using the same formula as Eq. 2, and $\mathbf{A}_{x,y}^s$ denotes the attention map that corresponds to the $(x,y)$ -th spatial patch. + +# 4. INITNO + +The core of our method is the Initial Noise Optimization (INITNO), which comprises the initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. This section provides detailed explanations of both components in Sec. 4.1 and 4.2. + +# 4.1. Initial latent space partitioning + +Prevailing studies [4, 6, 15, 26, 35] demonstrate the informativeness of cross-attention maps, elucidating their capability to partially quantify the alignment between generated image and provided text. In this work, we extend these findings by thoroughly investigating the self-attention maps, which capture inter-spatial correlations within image features. We argue that cross-attention maps and self-attention maps can inherently gauge subject neglect and subject mixing, respectively. Leveraging these maps, we formulate the cross-attention response score and the self-attention conflict score. By establishing the score threshold, we achieve the partitioning of the initial latent space. + +Cross-attention response score. We follow [6] and derive the final cross-attention map by averaging the cross-attention maps in all layers and heads with a resolution of $16 \times 16$ pixels. The aggregated map $\mathbf{A}^c \in \mathbb{R}^{16 \times 16 \times n}$ contains $n$ spatial attention maps, each corresponding to a token of the text prompt. We also re-weight the attention values + +![](images/e3aba0a3b2532841a6692f3517eb96486a4a87e2a4590e9b6966ae32808a8b31.jpg) +Figure 4. Comparison of Attend-and-Excite with our method. Attend-and-Excite suffers from the trade-off between under-optimization and over-optimization. Under-optimization (lower path) remains confined to invalid regions, while over-optimization (upper path) carries the risk of deviating from the distribution of diffusion model. Our approach (middle path) skillfully addresses this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate optimization. + +# Prompt: "A cat and an dog." + +![](images/488b741c25f3c716271dc6bd0c6a45025edd1e357386468f5a96bcf162f3a1b3.jpg) +Figure 5. Effect of the scale factor of Attend-and-Excite. Given the same text prompt, we adjust the scale factor of Attend-and-Excite [6], 20 is used in the original work. Images of varying quality are synthesized, and the red box indicates the highest quality image. Images on the same row share an identical random seed. + +by ignoring the attention of the specialized token sot and performing a softmax operation on the remaining tokens. Fig. 3 shows the cross-attention map for each subject token, reflecting the spatial layout information corresponding to the generated image. Notably, a proficient denoising process can assign sufficiently high cross-attention responses to each subject during the early stages. + +Conversely, a low attention response can lead to the absence of the target subject, i.e., subject neglect. As depicted in the red box in Fig. 3, the token crown registers a significantly lower response than rabbit in the initial denoising step, and crown is missing from the generated image. Building upon the insights from [6], we define the cross-attention response score as: + +$$ +\mathcal {S} _ {\text {C r o s s A t t n}} = 1 - \min _ {\mathbf {y} _ {i} \in \mathcal {Y}} \max \left(\mathbf {A} _ {\mathbf {y} _ {i}} ^ {c}\right), \tag {3} +$$ + +where $\mathcal{V}$ denotes the set of target tokens. Specifically, in this work, $S_{\mathrm{CrossAttn}}$ is calculated over the initial noise and the first denoising step. We further define the cross-attention response score threshold $\tau_{c}$ , empirically set to 0.2 in our experiments, where scores below this threshold are classified as valid, and those above are deemed invalid. + +Self-attention conflict score. Consistent with the cross-attention map extraction strategy, we extract the final self-attention map $\mathbf{A}^s\in \mathbb{R}^{16\times 16\times (16\times 16)}$ . For the subject token $\mathbf{y}_i$ of interest, we first query the spatial coordinates $(x_{i},y_{i})$ corresponding to its maximum cross-attention value: + +$$ +x _ {i}, y _ {i} = \underset {x, y} {\arg \max } \mathbf {A} _ {\mathbf {y} _ {i}} ^ {c} [ x, y ]. \tag {4} +$$ + +Subsequently, we obtain its corresponding self-attention map $\mathbf{A}_{x_i,y_i}^s$ , as shown in Fig. 3. For an exemplary denoising process, the self-attention maps of different subject tokens can be distinctly partitioned in the spatial domain. However, existing diffusion models, e.g., SD, suffer from self-attention map overlap, leading to a failure case of subject mixing. As indicated in the blue box in Fig. 3, the self-attention maps of apple and pear significantly overlap, resulting in a combination of both. To quantify this phenomenon, we introduce the self-attention conflict score: + +$$ +\begin{array}{l} \mathcal{S}_{\text{SelfAttn}} = \sum_{\substack{\mathbf{y}_{i},\mathbf{y}_{j}\in \mathcal{Y},\forall i < j}}\frac{\mathrm{f}(\mathbf{y}_{i},\mathbf{y}_{j})}{N}, \\ \mathrm {f} \left(\mathbf {y} _ {i}, \mathbf {y} _ {j}\right) = \frac {\sum_ {x , y} \min \left(\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] , \mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\right)}{\sum_ {x , y} \left(\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] + \mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\right)}, \tag {5} \\ \end{array} +$$ + +where $N$ is the number of pairs of $\mathbf{y}_i$ and $\mathbf{y}_j$ . $S_{\mathrm{SelfAttn}}$ is also calculated based on the initial noise and the first denoising step. We further define the self-attention conflict score threshold $\tau_s$ , set to 0.3 in our experiments. Scores below $\tau_s$ are classified as valid, and those above as invalid. + +Finally, we define the initial noise that passes both the cross-attention response score test and the self-attention conflict test as valid noise, and vice versa as invalid. + +# 4.2. Noise optimization pipeline + +As illustrated in Fig. 4, existing methods most relevant to ours, represented by Attend-and-Excite [6], modify the noisy image at each denoising step, and encourage it to better encapsulate the semantic information from text. However, they necessitate meticulously calibrated optimization + +parameters. As shown in Fig. 5, different optimization parameter settings directly affect the final generated image. Under-optimization leads to subpar quality, while over-optimization skews the noisy image away from the distribution of SD, resulting in an out-of-domain image. Moreover, even with the same text prompt, optimal parameters vary with noise, making case-specific tuning a laborious task. + +We bypass this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate adjustment. Specifically, INITNO is exclusively dedicated to navigating within the initial latent space, moving randomly sampled initial noise into the valid region. Unlike denoising processes that implicitly model the noisy image distribution, the initial latent space typically adheres to a standard Gaussian distribution, providing an avenue to restrict the optimized noise to the domain. + +Noise update strategy. Given a noise $\epsilon \in \mathcal{N}(\mathbf{0},\mathbf{1})$ , as opposed to the commonly used incremental update: $\epsilon^{\prime}\gets$ $\epsilon +\Delta \epsilon$ , we adopt a distribution optimization strategy to update the noise: + +$$ +\mu^ {\prime} \leftarrow \mu + \Delta \mu , \quad \sigma^ {\prime} \leftarrow \sigma + \Delta \sigma , \tag {6} +$$ + +where $\mu$ and $\sigma$ are the mean and standard deviation of the Gaussian distribution, initialized to 0 and 1, respectively. Thus, we have: $\epsilon' \gets \mu' + \sigma'\epsilon$ , and $\epsilon' \sim \mathcal{N}(\mu', \sigma'^2)$ . + +Loss functions. We employ a joint loss for optimizing initial noise, comprising cross-attention response loss, self-attention conflict loss, and distribution alignment loss. Intuitively, the first two are formulated as: + +$$ +\mathcal {L} _ {\text {C r o s s A t t n}} = \mathcal {S} _ {\text {C r o s s A t t n}}, \quad \mathcal {L} _ {\text {S e l f A t t n}} = \mathcal {S} _ {\text {S e l f A t t n}}. \tag {7} +$$ + +The distribution alignment loss utilizes Kullback-Leibler divergence [22] to constrain the consistency between the target Gaussian distribution $\mathcal{N}(\mu, \sigma^2)$ and the standard Gaussian distribution $\mathcal{N}(\mathbf{0}, \mathbf{1})$ : + +$$ +\mathcal {L} _ {\mathrm {K L}} = \mathsf {K L} \left(\mathcal {N} (\mu , \sigma^ {2}) \| \mathcal {N} (\mathbf {0}, \mathbf {1})\right). \tag {8} +$$ + +In summary, the joint loss is written as: + +$$ +\mathcal {L} _ {\text {j o i n t}} = \lambda_ {1} \mathcal {L} _ {\text {C r o s s A t t n}} + \lambda_ {2} \mathcal {L} _ {\text {S e l f A t t n}} + \lambda_ {3} \mathcal {L} _ {\mathrm {K L}}, \tag {9} +$$ + +where we empirically set $\lambda 1 = 1$ , $\lambda_{2} = 1$ , and $\lambda_{3} = 500$ . + +Noise optimization procedure. The outlined noise optimization procedure is encapsulated in Algorithm 1. Sampling the initial noise $\mathbf{z}_T\sim \mathcal{N}(\mathbf{0},\mathbf{1})$ , we initialize the learnable parameters $\mu$ to $\mathbf{0}$ and $\sigma$ to $\mathbf{1}$ . We optimize these parameters using the joint loss, ensuring that the optimized noise $\mu +\sigma \mathbf{z}^T$ resides within the valid initial latent space. The optimization employs the Adam optimizer with a learning rate of $1\times 10^{-2}$ . + +To mitigate computational inefficiency due to excessively challenging samples, we impose a maximum limit + +Algorithm 1: INITNO +Input: A pre-trained T2I diffusion model SD $(\cdot)$ , a text prompt y, a noise $z_{T}$ , threshold: $\tau_{c}, \tau_{s}, \tau_{\text{MaxStep}}$ , and $\tau_{\text{MaxRound}}$ . Output: Generated image x. +1 Noise pool $\mathcal{P} \gets \{\}$ +2 for i = 1 to $\tau_{\text{MaxRound}}$ do +3 Initialize $\mathbf{z}_{T} \sim \mathcal{N}(\mathbf{0}, \mathbf{1})$ , $\mu \gets \mathbf{0}$ , $\sigma \gets \mathbf{1}$ +4 for j = 1 to $\tau_{\text{MaxStep}}$ do +5 $\mathbf{A}^{c}, \mathbf{A}^{s} \gets \text{SD}(\mu + \sigma \mathbf{z}^{T}, \mathbf{y})$ +6 Calculate $S_{\text{CrossAttn}}$ (Eq. 3), $S_{\text{SelfAttn}}$ (Eq. 5) +7 if $S_{\text{CrossAttn}} < \tau_{c}$ and $S_{\text{SelfAttn}} < \tau_{s}$ then +8 $\hat{\mathbf{z}}^{T} \gets \mu + \sigma \mathbf{z}^{T}$ +9 Go to step 15 ▷ valid noise +10 else +11 Calculate $\mathcal{L}_{\text{joint}}$ (Eq. 9) +12 $\mu, \sigma \gets \text{Adam}(\mu, \sigma, \mathcal{L}_{\text{joint}})$ +13 Add $\mu + \sigma \mathbf{z}^{T}$ to $\mathcal{P}$ +14 $\hat{\mathbf{z}}^{T} \gets \arg \min_{\mathbf{z}^{T} \in \mathcal{P}} S_{\text{CrossAttn}} + S_{\text{SelfAttn}}$ +15 x, -, - ← SD ( $\hat{\mathbf{z}}^{T}, \mathbf{y}$ ) or AE ( $\hat{\mathbf{z}}^{T}, \mathbf{y}$ ) +16 return x + +on optimization iterations, denoted as $\tau_{\mathrm{MaxStep}}$ . If we fail to reach the valid region after $\tau_{\mathrm{MaxStep}}$ updates, we resample $\mathbf{z}_T$ , reset $\mu$ and $\sigma$ , and commence a new round of the optimization process. We also define a maximum limit on optimization rounds, denoted as $\tau_{\mathrm{MaxRound}}$ . In our experiments, we set $\tau_{\mathrm{MaxStep}}$ and $\tau_{\mathrm{MaxRound}}$ as 50 and 5, respectively. For a minority of intricate texts where effective noise cannot be found within affordable optimization rounds, we opt for the noise that minimizes the sum of $S_{\mathrm{CrossAttn}}$ and $S_{\mathrm{SelfAttn}}$ from the existing noise pool $\mathcal{P}$ . + +# 5. Experiments + +# 5.1. Experimental settings + +Implementation Details. Following [6], we utilize the official Stable Diffusion v1.4 text-to-image model. A fixed guidance level of 7.5 is employed. We apply a Gaussian filter with a kernel size of 3 and a standard deviation of 0.5 to smooth the cross-attention map $\mathbf{A}^c$ and the self-attention map $\mathbf{A}^s$ . For the denoising process, $T$ is set to 50. The target token identification process can be performed either manually or automatically with the assistance of GPT [3]. + +Datasets. We assess our method using the Animal-Animal, Animal-Object, and Object-Object datasets [6], which comprise two subjects and selectively assign a color to each subject. It is noteworthy that our method is not constrained to this scenario, and it can be applied to complex prompts containing any number or type of subjects and attributes, as + +![](images/5405766aab0071df04318c45739506ee2b407ebfd8f4f5a0d0e609a1f00c7707.jpg) +Figure 6. Qualitative comparison. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline. Our method shows excellent alignment with text prompts while maintaining a high level of realism. + +discussed in Sec. 5.6 and supplementary material. + +# 5.2. Qualitative comparison + +Fig. 6 presents a comparative analysis of our results against state-of-the-art counterparts, under the same text prompts and random seeds. It can be seen that existing methods commonly suffer from serious problems of subject mixing. For instance, in the case of a cat and a rabbit, conventional methods frequently yield erroneous outputs characterized by the fusion of cat faces and rabbit ears. Leveraging the self-attention conflict mechanism, our method can effectively decouple the two concepts of $\underline{\text{cat}}$ and $\underline{\text{rabbit}}$ and render them realistically and separately. Concurrently, Stable Diffusion [31], Composable Diffusion [25], and Structure Diffusion [12] suffer from the issue of subject neglect. Attend-and-Excite [6], Divide-and-Bind [24], and A-STAR [1] adhere to the pattern of adjusting noisy images at each denoising step. Given the same text prompt, using the same adjustment strategy, the quality of results generated by sampling different noises vary significantly. For instance, for the prompt a dog and a turtle, only the first example produced by Divide-and-Bind [24] is successful. In contrast, our method exhibits better generalization and + +adapts to diverse prompts. Furthermore, our approach also demonstrates more faithful binding of properties, e.g., yellow clock. + +# 5.3.Quantitative comparison + +Objective Evaluation. Following to the protocol in [6], we quantitatively evaluate the proposed method using CLIP Image-Text Similarity and CLIP Text-Text Similarity. For each prompt, 64 images are generated, and the average CLIP cosine similarity is computed, maintaining consistent random seeds across all methods. Specifically, for CLIP Image-Text Similarity, we report full prompt similarity (cosine similarity between the full prompt and generated image) and minimum object similarity (minimum of the similarities between the generated image and each of the two subject prompts). For CLIP Text-Text Similarity, text-text similarities are computed by captioning the generated images with BLIP [23] and comparing them with the input prompt. As shown in Fig. 7, the proposed method outperforms other approaches. + +User study. We also conduct a subjective user study involving 12 volunteers with expertise in image processing. Participants were asked to select the most visuallyappealing + +![](images/02a974bfd3db89a3beef5246894250bb5ba7d31c8e34d8ae357afa857b3ea99c.jpg) + +![](images/fc59dc02f9fbd14860a1c8d074f0eda6ed4bad39005941b5edbae246f7829464.jpg) + +![](images/7eb2304f0c31692f7ce8a647b90cfe5eea2b0116def47c43ac3415b77cb89a13.jpg) + +![](images/7f289cc65a01b447e58d5b5e0b3f6e4cf12014639a2f87e03c2837921b071255.jpg) + +![](images/1c28bcd79568180def8f0fbe7833a1ea06f056af60cbe897ce26ed79e355c9a3.jpg) + +![](images/ae756167bd5179f8551445ee151c7b49aba40746db159ab2785fae7ea0b1b419.jpg) +Figure 7. Objective evaluation. Average CLIP Image-Text Similarity, including Full Prompt Similarity and Minimum Object Similarity, and Average CLIP Text-Text Similarity are reported for the quantitative measurement. Higher is better. + +![](images/5178974c9af6f15797a9924cdbbb895e12d895c9f663f17d70bf0f372a1d6ade.jpg) + +![](images/448f69d61779cbee8628fb14b4a383be0680096907454c6b812de09c63f76cdf.jpg) + +![](images/ce0299b23dc18e3573ec455bf2aa34f8383b011277e2d35ed72fe655fa2a3fcb.jpg) + +![](images/1eaffb86f0b4f9fc6177eb414fe5471524ad45d0307c9aa7a1286793f268605c.jpg) + +![](images/f47dbf42bc4c88a4a890dae6105f50861c27186093303825c2e65c04ca400c53.jpg) +Attend- & Excite + +![](images/728d33e0274018001133f050eb590f9c4ff32ffd36b69b302065527b8c72a99e.jpg) + +![](images/d18f9fa442092cf078db40b5d27bc7ed258642d3ea14bd9d8226c659ca852973.jpg) +Attend- & Excite w/ LCrossConflict + +![](images/f65b8eecc8b7822ad8eed55d3f44e1582f01c4571e6a5a94986fc63bd313e27e.jpg) +Attend- & Excite w/ $\mathcal{L}_{\mathrm{SelfAttn}}$ + +![](images/10b0cd487c06267b940f01e99715eaf057b674d3f5f7e0fd6f82fe92d5334f4a.jpg) +Stable Diffusion + +![](images/577c63f5e02530d6fd383de2c64c0dd78596f5937d246558d8fbf9cadd4bdb19.jpg) +Ours w/o $\mathcal{L}_{\mathrm{SelfAttn}}$ +Ours w/ $\mathcal{L}_{\mathrm{CrossConflict}}$ + +![](images/552ebbeb299984cd822735b247a40313db1990efcd4e2c0b71429b36cf3ebe43.jpg) + +![](images/901676f4843312752ec8e4cffbf708e82a7c41ff18dde4bb8d884362467c9f3d.jpg) +Ours + +Figure 8. Visualization of effects of $\mathcal{L}_{\mathrm{SelfAttn}}$ + +
MethodUser study
Stable Diffusion [31]4.17%
Composable Diffusion [25]2.50%
Structure Diffusion [12]3.33%
Attend-and-Excite [6]14.17%
Divide-and-Bind [24]6.67%
A-STAR [1]5.83%
INITNO (Ours)63.33%
+ +Table 1. User study. INITNO performs over other counterparts. + +and semantically-faithful image from those generated by our proposed method and the state-of-the-art approaches. Specifically, each participant has 20 questions. We tally the votes and show the statistics in Table 1. Our method performs favorably against the other methods. + +Inference time. Evaluated on a single Tesla V100 (32GB), 100 images with a resolution of $512 \times 512$ pixels are randomly generated, SD synthesizes an image in an average of 8.34 seconds, while our method takes 18.93 seconds. + +# 5.4. Ablation study + +On self-attention conflict loss. The self-attention conflict loss is designed to address the subject mixing issue arising + +![](images/8101627ad0d643fd3be378340a4c4a8482cbfdf246ad6ac13e859a2a98ae65b1.jpg) +W/ $\mathcal{L}_{\mathrm{KL}}$ +Figure 9. Visualization of effects of $\mathcal{L}_{\mathrm{KL}}$ + +![](images/a98f24f4f38c6b4e82c10dbf8d5c37886a2bfc9e6874741c866dbb1b966fe095.jpg) +"A bird and a orange dog." + +![](images/3a671904dda5ca63888cb591e1fb04ed6709525d6cf39f0efccccdf98c386b9a.jpg) +w/o $\mathcal{L}_{\mathrm{KL}}$ + +from self-attention map overlap, and it can be effortlessly incorporated into existing methods. As depicted in Fig. 8, the self-attention conflict loss effectively addresses the mixing issue between apple and pear. We also experiment with a cross-attention conflict loss [1], which replaces the self-attention map with cross-attention ones, but it did not produce satisfactory results. We surmise this is due to the inaccurate text embedding extracted by CLIP. Conversely, the self-attention map offers a more intuitive solution. + +On distribution alignment loss. The distribution alignment loss is introduced to ensure that the optimized noise $\hat{\mathbf{z}}_T$ adheres to the standard Gaussian distribution. As visualized in the t-SNE plot of initial noise in Fig. 9, without constraints, the optimized noise may deviate from the standard Gaussian distribution, resulting in distorted results. + +# 5.5. Grounded Text-to-Image + +INITNO is a plug-and-play approach that can be effortlessly integrated with existing diffusion models to enable training-free controllable generation, such as layout-to-image, mask-to-image generation, etc. As demonstrated in Fig. 11, we incorporate INITNO into BoxDiff [38], where modifications to the intermediate noisy image are transferred to the initial latent space, resulting in the synthesis + +![](images/76f736042b85fa20397edaea0fd7dfec200dfc7cf31894558880f1050e8b2863.jpg) +Figure 10. Qualitative comparison with complex text prompts. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline. + +![](images/343c2520596c293900357cbf03bc7ae5c99eca91394fa791d60b389fab18c551.jpg) +Figure 11. Grounded Text-to-Image. Due to sufficient adjustments, INITNO generates more accurately location-aware $\underline{cat}$ . + +of faithful and location-aware images. + +# 5.6. More results + +Complex prompts. Fig. 10 presents examples of complex prompts, inclusive of prompts with three or more subjects and intricate attributes. The synthesis of high-fidelity images is demonstrated, underscoring the capacity of our method to manage complex semantic scenes. + +Visualization of the attention maps. Following [6], we also provide a visualization of the final cross-attention map for each subject token after denoising process in Fig. 12. Our method achieves reasonable attention allocation, leading to semantically-consistent results. + +# 6. Conclusion + +The core of our method is the Initial Noise Optimization (INITNO), which consists of the initial latent space parti + +![](images/1dd51affe6e44ea76fbd8635a9b44d922eda8052d0e693f81aa6c4b9ea923150.jpg) +Figure 12. Visualization of the final cross-attention maps. + +tioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. Specifically, we investigate the utility of attention maps in the diffusion model, harnessing them to formulate the cross-attention response score and the self-attention conflict score, both instrumental to the partitioning of the initial latent space. Moreover, we bypass the complex balance between under-optimization and over-optimization of noise via a meticulously crafted pipeline that introduces a novel distribution alignment loss. We further demonstrate the superiority of our approach over existing state-of-the-art methods in generating semantically-faithful images, providing a versatile plug-and-play solution that effectively integrates into existing diffusion models for training-free controllable generation + +# Acknowledgment + +This work is partly supported by the National Key R&D Program of China (2022ZD0161902), the National Natural Science Foundation of China (62022011, 62202031), the Research Program of State Key Laboratory of Software Development Environment (SKLSDE-2023ZX-14), and the Fundamental Research Funds for the Central Universities. We also give special thanks to Alibaba Group for their contribution to this paper. + +# References + +[1] Aishwarya Agarwal, Srikrishna Karanam, KJ Joseph, Apoorv Saxena, Koustava Goswami, and Balaji Vasan Srinivasan. A-star: Test-time attention segregation and retention for text-to-image synthesis. 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Scaling autoregressive models for content-rich text-to-image generation. TMLR, 2022. 1, 2 +[42] Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. In ICCV, 2017. 2 +[43] Han Zhang, Jing Yu Koh, Jason Baldridge, Honglak Lee, and Yinfei Yang. Cross-modal contrastive learning for text-to-image generation. In CVPR, 2021. +[44] Minfeng Zhu, Pingbo Pan, Wei Chen, and Yi Yang. Dmagan: Dynamic memory generative adversarial networks for text-to-image synthesis. In CVPR, 2019. 2 \ No newline at end of file diff --git a/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/images.zip b/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fbde7f1373ea78e116fe41622bf272b25438ead2 --- /dev/null +++ b/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:77d10bdc3e08e7aeb0536a0aa3e77c324beb17efb89ba79c8ed62c82d9d2c283 +size 1086955 diff --git a/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/layout.json b/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..52e29fbc7a0fed7efd6db8a0ee096b28ffd2c8aa --- /dev/null +++ b/2024/InitNO_ Boosting Text-to-Image Diffusion Models via Initial Noise Optimization/layout.json @@ -0,0 +1,10862 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 48, + 103, + 547, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 103, + 547, + 122 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 547, + 122 + ], + "type": "text", + "content": "INITNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "spans": [ + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "text", + "content": "Xiefan Guo" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "text", + "content": " Jinlin Liu Miaomiao Cui Jiankai Li" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "text", + "content": " Hongyu Yang" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "inline_equation", + "content": "^{3,4}" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "text", + "content": " Di Huang" + }, + { + "bbox": [ + 75, + 142, + 521, + 158 + ], + "type": "inline_equation", + "content": "^{1,2*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 162, + 534, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 162, + 534, + 190 + ], + "spans": [ + { + "bbox": [ + 59, + 162, + 534, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 59, + 162, + 534, + 190 + ], + "type": "text", + "content": "State Key Laboratory of Software Development Environment, Beihang University, Beijing, China " + }, + { + "bbox": [ + 59, + 162, + 534, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 59, + 162, + 534, + 190 + ], + "type": "text", + "content": "School of Computer Science and Engineering, Beihang University, Beijing, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 127, + 190, + 467, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 190, + 467, + 219 + ], + "spans": [ + { + "bbox": [ + 127, + 190, + 467, + 219 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 127, + 190, + 467, + 219 + ], + "type": "text", + "content": "Institute of Artificial Intelligence, Beihang University, Beijing, China " + }, + { + "bbox": [ + 127, + 190, + 467, + 219 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 127, + 190, + 467, + 219 + ], + "type": "text", + "content": "Shanghai Artificial Intelligence Laboratory, Shanghai, China" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 168, + 220, + 423, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 220, + 423, + 232 + ], + "spans": [ + { + "bbox": [ + 168, + 220, + 423, + 232 + ], + "type": "text", + "content": "{xfguo, lijiankai, hongyuyang, dhuang}@buaa.edu.cn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 259, + 192, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 259, + 192, + 272 + ], + "spans": [ + { + "bbox": [ + 143, + 259, + 192, + 272 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 285, + 290, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 290, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 290, + 525 + ], + "type": "text", + "content": "Recent strides in the development of diffusion models, exemplified by advancements such as Stable Diffusion, have underscored their remarkable prowess in generating visually compelling images. However, the imperative of achieving a seamless alignment between the generated image and the provided prompt persists as a formidable challenge. This paper traces the root of these difficulties to invalid initial noise, and proposes a solution in the form of Initial Noise Optimization (INITNO), a paradigm that refines this noise. Considering text prompts, not all random noises are effective in synthesizing semantically-faithful images. We design the cross-attention response score and the self-attention conflict score to evaluate the initial noise, bifurcating the initial latent space into valid and invalid sectors. A strategically crafted noise optimization pipeline is developed to guide the initial noise towards valid regions. Our method, validated through rigorous experimentation, shows a commendable proficiency in generating images in strict accordance with text prompts. Our code is available at https://github.com/xiefan-guo/initno." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 571, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 287, + 693 + ], + "type": "text", + "content": "Text-to-Image Synthesis (T2I) stands at the forefront of cutting-edge research, dedicated to the generation of authentic and visually cohesive images from text prompts. In the domain of generative models, including generative adversarial networks [13, 18-21], variational autoencoders [22], and autoregressive models [7, 10, 36, 37], diffusion models [8, 16] have ascended as a predominant solution. The integration of large-scale vision-language models [2, 11, 14, 17, 30-32, 40, 41] has propelled noteworthy advancements in the text-to-image domain." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 258, + 545, + 443 + ], + "blocks": [ + { + "bbox": [ + 307, + 258, + 545, + 443 + ], + "lines": [ + { + "bbox": [ + 307, + 258, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 307, + 258, + 545, + 443 + ], + "type": "image", + "image_path": "66b9cac488f6839ebe12d9ab5f38cdadfdbc57682d55c0c506c42a3bea147603.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 448, + 531, + 459 + ], + "lines": [ + { + "bbox": [ + 321, + 448, + 531, + 459 + ], + "spans": [ + { + "bbox": [ + 321, + 448, + 531, + 459 + ], + "type": "text", + "content": "Figure 1. Example results synthesized by SD and ours." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 482, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 547, + 567 + ], + "type": "text", + "content": "Despite the training of state-of-the-art T2I diffusion models on large-scale text-image datasets, synthesizing images precisely aligned with given text prompts remains a considerable challenge. Well-documented issues, i.e., subject neglect, subject mixing, and incorrect attribute binding, as illustrated in Fig. 1, persist. We attribute these challenges to the presence of invalid initial noise." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "When different noise inputs are introduced to the T2I diffusion model with identical text prompts, a substantial discrepancy is observed in the alignment between images and the provided text, as depicted in Fig. 2. This observation signifies that not all randomly sampled noise can produce visually-consistent images. Depending on the consistency between the generated image and the target text, the initial latent space can be divided into valid and invalid regions. Noise sourced from valid regions, when input into the T2I diffusion model, results in semantically-reasonable image. Consequently, our aim is to direct any initial noise towards the valid region, thereby facilitating the generation" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9380" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 82, + 91, + 124 + ], + "blocks": [ + { + "bbox": [ + 50, + 82, + 91, + 124 + ], + "lines": [ + { + "bbox": [ + 50, + 82, + 91, + 124 + ], + "spans": [ + { + "bbox": [ + 50, + 82, + 91, + 124 + ], + "type": "image", + "image_path": "c3026d5f652db31bf74f0414c7167212bfa7c2ab8710b564f6a28311ef1d36f2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 93, + 82, + 135, + 124 + ], + "blocks": [ + { + "bbox": [ + 93, + 82, + 135, + 124 + ], + "lines": [ + { + "bbox": [ + 93, + 82, + 135, + 124 + ], + "spans": [ + { + "bbox": [ + 93, + 82, + 135, + 124 + ], + "type": "image", + "image_path": "5436210f03989983c98e11858f4d217b2c49b570daeaf7c6c077471ace92b803.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 137, + 82, + 190, + 124 + ], + "blocks": [ + { + "bbox": [ + 137, + 82, + 190, + 124 + ], + "lines": [ + { + "bbox": [ + 137, + 82, + 190, + 124 + ], + "spans": [ + { + "bbox": [ + 137, + 82, + 190, + 124 + ], + "type": "image", + "image_path": "75c2aa07cbbd651c5960534988cf5d9859cf283a52b5a696d4b46c8e576f3efd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 191, + 82, + 231, + 124 + ], + "blocks": [ + { + "bbox": [ + 191, + 82, + 231, + 124 + ], + "lines": [ + { + "bbox": [ + 191, + 82, + 231, + 124 + ], + "spans": [ + { + "bbox": [ + 191, + 82, + 231, + 124 + ], + "type": "image", + "image_path": "585e7c11e77658dde601ec7b0738719e93a33e2b165e24c33173ff2849cc4a3b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 233, + 82, + 274, + 124 + ], + "blocks": [ + { + "bbox": [ + 233, + 82, + 274, + 124 + ], + "lines": [ + { + "bbox": [ + 233, + 82, + 274, + 124 + ], + "spans": [ + { + "bbox": [ + 233, + 82, + 274, + 124 + ], + "type": "image", + "image_path": "f677a3dc9a6fa8cdd6b45ffae181c77fccea1b17919e7b2fb872afac63994359.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 276, + 82, + 318, + 124 + ], + "blocks": [ + { + "bbox": [ + 276, + 82, + 318, + 124 + ], + "lines": [ + { + "bbox": [ + 276, + 82, + 318, + 124 + ], + "spans": [ + { + "bbox": [ + 276, + 82, + 318, + 124 + ], + "type": "image", + "image_path": "5ae96fef33b9afb73f4ea393e50ea0bb6b8b116ef4092b408036ca93979251a4.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 50, + 140, + 90, + 182 + ], + "blocks": [ + { + "bbox": [ + 50, + 140, + 90, + 182 + ], + "lines": [ + { + "bbox": [ + 50, + 140, + 90, + 182 + ], + "spans": [ + { + "bbox": [ + 50, + 140, + 90, + 182 + ], + "type": "image", + "image_path": "8573e67a5beefc5173aae9b0817307ea2166f331061aec370b43d19d4d91b597.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 184, + 179, + 194 + ], + "lines": [ + { + "bbox": [ + 50, + 184, + 179, + 194 + ], + "spans": [ + { + "bbox": [ + 50, + 184, + 179, + 194 + ], + "type": "text", + "content": "INITNO(Ours)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 198, + 547, + 276 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 276 + ], + "type": "text", + "content": "Figure 2. INITNO. Our investigation dives into the exploration of various random noise configurations and their subsequent influence on the generated results. Notably, when different noises are input into SD under identical text prompts, there are marked discrepancy in the alignment between the generated image and the given text. Unsuccessful cases are delineated by gray contours, while successful instances are indicated by yellow contours. This observation underscores the pivotal role of initial noise in determining the success of the generation process. Based on this insight, we divide the initial noise space into valid and invalid regions. Introducing Initial Noise Optimization (INITNO), identified as orange arrow, our method is capable of guiding any initial noise into the valid region, thereby synthesizing high-fidelity results (orange contours) that precisely correspond to the given prompt. 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"bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "text", + "content": "The core of this paper lies in the concept of Initial Noise Optimization (INITNO), which encompasses initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and directing initial noise navigation, respectively." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 376, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 519 + ], + "type": "text", + "content": "Our study thoroughly examines attention layers in the diffusion model, specifically the cross-attention map and the self-attention map. The former captures the correlation between text and image features, while the latter captures the correlation among different spatial positions within the image features. These maps effectively measure subject neglect and subject mixing, respectively (see Fig. 3). With these maps, we design the cross-attention response score and the self-attention conflict score. By setting score thresholds, we achieve further partitioning of the initial latent space. Interestingly, we find that accurate rendering of the subject fosters correct attribute binding." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 521, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 640 + ], + "type": "text", + "content": "The primary challenge in initial noise navigation is to balance under-optimization and over-optimization of noise. While under-optimization is still plagued by misalignment, over-optimization risks deviating from the initial distribution, i.e., standard Gaussian distribution, resulting in distorted images (see Fig. 9). To address this challenge, we introduce a carefully-crafted noise optimization pipeline. With the explicit modeling of the initial latent space, a novel distribution alignment loss is incorporated to ensure the optimized noise adheres to the initial distribution." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "We establish the superiority of the proposed method over state-of-the-art approaches in generating semantically accurate images. Furthermore, our method is plug-and-play and seamlessly integrates into existing diffusion models, enabling training-free controllable generation and improving alignment with specific conditions, such as layout-to-image" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 291, + 409, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 291, + 409, + 303 + ], + "spans": [ + { + "bbox": [ + 306, + 291, + 409, + 303 + ], + "type": "text", + "content": "generation (see Sec. 5.5)." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 318, + 392, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 392, + 330 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 392, + 330 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 340, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 545, + 460 + ], + "type": "text", + "content": "Text-to-image synthesis strives to generate visually-realistic image that reflects given text. Early research mainly focused on GANs [34, 39, 42-44] and autoregressive models [5, 9, 29, 41]. Recently, diffusion models [8, 16] have taken over the mainstream, achieving impressive results. The incorporation of large-scale vision-language models [14, 17, 31, 32, 41] has fostered significant advancements in the text-to-image domain. Despite synthesizing highquality images, it remains challenging to produce results that properly comply with the given text prompt." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": "To deal with this problem, some works [2, 30, 32, 33, 40] expand the network architecture and introduce large language models [28] to better hint embeddings. However, these works require training new text-to-image models and are not applicable to existing widely used models. Another line of work explores training-free improvement strategies, consistent with our approach." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": "Specifically, Liu et al. [25] propose to use multiple diffusion models for different concepts and then composite the outputs to obtain the final result. This method solves the mentioned problem to some extent, but still suffers from subject mixing. Feng et al. [12] propose to split the input text prompt and process the cross attention layers to align the tokens and the outputs. Chefer et al. [6] introduce the concept of Generative Semantic Nursing (GSN), and slightly shifts the noisy image at each timestep of the denoising process, where the semantic information from the text prompt is better considered. Agarwal et al. [1] and Li et al. [24] further improve the optimization objective on this paradigm for better update direction. However, updating the noisy image at each denoising step requires carefully" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 50, + 70, + 156, + 80 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 70, + 156, + 80 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 156, + 80 + ], + "type": "text", + "content": "Prompt: \"A cat and a dog.\"" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 50, + 128, + 192, + 138 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 128, + 192, + 138 + ], + "spans": [ + { + "bbox": [ + 50, + 128, + 192, + 138 + ], + "type": "text", + "content": "Prompt: \"An elephant with a crown.\"" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "9381" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 286, + 232 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 232 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 232 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 232 + ], + "type": "image", + "image_path": "88225e67125b10913b6d508a68edf137af5ec5cdb8a8a82d0a80c1ce33a200c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 237, + 253, + 248 + ], + "lines": [ + { + "bbox": [ + 80, + 237, + 253, + 248 + ], + "spans": [ + { + "bbox": [ + 80, + 237, + 253, + 248 + ], + "type": "text", + "content": "Figure 3. Visualization of the attention maps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 286, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 286, + 281 + ], + "type": "text", + "content": "designed optimization parameters, posing a delicate balance between under-optimization and over-optimization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 353 + ], + "type": "text", + "content": "Different from previous methods, we explore a novel path by adjusting the sampled noise in the initial latent space, where full optimization is performed. It cleverly avoids the trade-off between under-optimization and over-optimization, is proven to be efficient and orthogonal to existing methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 364, + 132, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 364, + 132, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 364, + 132, + 376 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "content": "Stable Diffusion Model. This study focuses on the state-of-the-art Stable Diffusion model (SD) [31], belonging to the category of latent diffusion models (LDMs). Unlike traditional diffusion-based approaches operating directly in the image domain, SD functions within the latent space of an autoencoder. Specifically, an encoder " + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\cdot)" + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "content": " learns the mapping from an input image " + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "content": " to a latent code " + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{E}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "content": ". Subsequently, a decoder " + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot)" + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "content": " reconstructs the input image, aiming for " + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathcal{E}(\\mathbf{x})) \\approx \\mathbf{x}" + }, + { + "bbox": [ + 46, + 384, + 287, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": "Once the autoencoder is trained, a Denoising Diffusion Probabilistic Model (DDPM) [16] operates within the acquired latent space to generate a denoised version of an input latent " + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": " at each timestep " + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": ". During denoising, the diffusion model can be conditioned on additional inputs. In the case of SD, this condition typically takes the form of a text embedding generated by a pre-trained CLIP text encoder [27]. The conditioning embedding for the given prompt " + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = f_{\\mathrm{CLIP}}(\\mathbf{y})" + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": ". The DDPM model " + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": ", parametrized by " + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 491, + 287, + 612 + ], + "type": "text", + "content": ", optimizes the following loss:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 619, + 287, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 619, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 63, + 619, + 287, + 634 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathbb {E} _ {\\mathbf {z} \\sim \\mathcal {E} (\\mathbf {x}), \\mathbf {c}, \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {1}), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c}, t) \\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "ed266a9d81a5bc14711e2a83340d14763757235b19d8f4229c737fed489f07fc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "During inference, a latent variable " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " is sampled from the standard Gaussian distribution " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0},\\mathbf{1})" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " and subjected to sequential denoising procedures of DDPM to derive a refined latent representation " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": ". This denoised latent " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " is then fed into the decoder " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot)" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " to synthesize the corresponding image " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\mathbf{z}_0)" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "Cross-attention layer. Text-image correspondence in SD is achieved through the cross-attention layer, enabling text condition guidance. Specifically, the pre-trained CLIP text encoder [27] embeds the text prompt " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{y} = \\{\\mathbf{y}_1,\\mathbf{y}_2,\\dots ,\\mathbf{y}_n\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " into a sequential embedding, serving as the condition " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = f_{\\mathrm{CLIP}}(\\mathbf{y})" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": ". Linear projections are then employed to extract the key " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": ", while the query " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " is mapped from the intermediate features of UNet. The cross-attention map " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^c" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " is computed via:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 372, + 189, + 545, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 189, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 372, + 189, + 545, + 217 + ], + "type": "interline_equation", + "content": "\\mathbf {A} ^ {c} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {T}}{\\sqrt {d}}\\right), \\tag {2}", + "image_path": "883f8687e7befe1d9ac6df227568791778660133b6c685b2a5c456181ce6e6c2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": " is the channel dimension. For ease of representation, we omit the denoising timestep " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": ". We denote the attention map that corresponds to the " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": "-th text token as " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\mathbf{y}_i}^c" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\mathbf{y}_i}^c[x,y]" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": " is the probability assigned to text token " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 304, + 224, + 545, + 284 + ], + "type": "text", + "content": "-th spatial patch of the intermediate feature map." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": "Self-attention layer. In the self-attention layer, intermediate features serve as the key " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " instead of the text condition " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": ", allowing synthesis of globally coherent structures by correlating image tokens across diverse regions. The self-attention map " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^s" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " is computed using the same formula as Eq. 2, and " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{x,y}^s" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " denotes the attention map that corresponds to the " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": "-th spatial patch." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 380, + 364, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 364, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 364, + 392 + ], + "type": "text", + "content": "4. INITNO" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 399, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 471 + ], + "type": "text", + "content": "The core of our method is the Initial Noise Optimization (INITNO), which comprises the initial latent space partitioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. This section provides detailed explanations of both components in Sec. 4.1 and 4.2." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 479, + 474, + 492 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 474, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 474, + 492 + ], + "type": "text", + "content": "4.1. Initial latent space partitioning" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 641 + ], + "type": "text", + "content": "Prevailing studies [4, 6, 15, 26, 35] demonstrate the informativeness of cross-attention maps, elucidating their capability to partially quantify the alignment between generated image and provided text. In this work, we extend these findings by thoroughly investigating the self-attention maps, which capture inter-spatial correlations within image features. We argue that cross-attention maps and self-attention maps can inherently gauge subject neglect and subject mixing, respectively. Leveraging these maps, we formulate the cross-attention response score and the self-attention conflict score. By establishing the score threshold, we achieve the partitioning of the initial latent space." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Cross-attention response score. We follow [6] and derive the final cross-attention map by averaging the cross-attention maps in all layers and heads with a resolution of " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " pixels. The aggregated map " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^c \\in \\mathbb{R}^{16 \\times 16 \\times n}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " contains " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " spatial attention maps, each corresponding to a token of the text prompt. We also re-weight the attention values" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9382" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 545, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 159 + ], + "type": "image", + "image_path": "e3aba0a3b2532841a6692f3517eb96486a4a87e2a4590e9b6966ae32808a8b31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 547, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 547, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 547, + 209 + ], + "type": "text", + "content": "Figure 4. Comparison of Attend-and-Excite with our method. Attend-and-Excite suffers from the trade-off between under-optimization and over-optimization. Under-optimization (lower path) remains confined to invalid regions, while over-optimization (upper path) carries the risk of deviating from the distribution of diffusion model. Our approach (middle path) skillfully addresses this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate optimization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 221, + 168, + 233 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 221, + 168, + 233 + ], + "spans": [ + { + "bbox": [ + 49, + 221, + 168, + 233 + ], + "type": "text", + "content": "Prompt: \"A cat and an dog.\"" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 235, + 286, + 365 + ], + "blocks": [ + { + "bbox": [ + 50, + 235, + 286, + 365 + ], + "lines": [ + { + "bbox": [ + 50, + 235, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 50, + 235, + 286, + 365 + ], + "type": "image", + "image_path": "488b741c25f3c716271dc6bd0c6a45025edd1e357386468f5a96bcf162f3a1b3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 369, + 287, + 424 + ], + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 424 + ], + "type": "text", + "content": "Figure 5. Effect of the scale factor of Attend-and-Excite. Given the same text prompt, we adjust the scale factor of Attend-and-Excite [6], 20 is used in the original work. Images of varying quality are synthesized, and the red box indicates the highest quality image. Images on the same row share an identical random seed." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 287, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 522 + ], + "type": "text", + "content": "by ignoring the attention of the specialized token sot and performing a softmax operation on the remaining tokens. Fig. 3 shows the cross-attention map for each subject token, reflecting the spatial layout information corresponding to the generated image. Notably, a proficient denoising process can assign sufficiently high cross-attention responses to each subject during the early stages." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 523, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 523, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 287, + 606 + ], + "type": "text", + "content": "Conversely, a low attention response can lead to the absence of the target subject, i.e., subject neglect. As depicted in the red box in Fig. 3, the token crown registers a significantly lower response than rabbit in the initial denoising step, and crown is missing from the generated image. Building upon the insights from [6], we define the cross-attention response score as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 96, + 615, + 287, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 615, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 96, + 615, + 287, + 634 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\text {C r o s s A t t n}} = 1 - \\min _ {\\mathbf {y} _ {i} \\in \\mathcal {Y}} \\max \\left(\\mathbf {A} _ {\\mathbf {y} _ {i}} ^ {c}\\right), \\tag {3}", + "image_path": "e26d55afb4f702dd36df6c786881160684c2ea808c34f871a19ec622975a12f8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "content": " denotes the set of target tokens. Specifically, in this work, " + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{CrossAttn}}" + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "content": " is calculated over the initial noise and the first denoising step. We further define the cross-attention response score threshold " + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\tau_{c}" + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "content": ", empirically set to 0.2 in our experiments, where scores below this threshold are classified as valid, and those above are deemed invalid." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "text", + "content": "Self-attention conflict score. Consistent with the cross-attention map extraction strategy, we extract the final self-attention map " + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^s\\in \\mathbb{R}^{16\\times 16\\times (16\\times 16)}" + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "text", + "content": ". For the subject token " + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "text", + "content": " of interest, we first query the spatial coordinates " + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "inline_equation", + "content": "(x_{i},y_{i})" + }, + { + "bbox": [ + 305, + 224, + 545, + 283 + ], + "type": "text", + "content": " corresponding to its maximum cross-attention value:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 365, + 293, + 545, + 313 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 293, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 365, + 293, + 545, + 313 + ], + "type": "interline_equation", + "content": "x _ {i}, y _ {i} = \\underset {x, y} {\\arg \\max } \\mathbf {A} _ {\\mathbf {y} _ {i}} ^ {c} [ x, y ]. \\tag {4}", + "image_path": "c69cf7b3474d7153fbadd7e39d00e6e2cbbf6ac4e0a393a032ab478e8107e44d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 322, + 546, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 322, + 546, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 322, + 546, + 441 + ], + "type": "text", + "content": "Subsequently, we obtain its corresponding self-attention map " + }, + { + "bbox": [ + 305, + 322, + 546, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{x_i,y_i}^s" + }, + { + "bbox": [ + 305, + 322, + 546, + 441 + ], + "type": "text", + "content": ", as shown in Fig. 3. For an exemplary denoising process, the self-attention maps of different subject tokens can be distinctly partitioned in the spatial domain. However, existing diffusion models, e.g., SD, suffer from self-attention map overlap, leading to a failure case of subject mixing. As indicated in the blue box in Fig. 3, the self-attention maps of apple and pear significantly overlap, resulting in a combination of both. To quantify this phenomenon, we introduce the self-attention conflict score:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 310, + 449, + 545, + 524 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 449, + 545, + 524 + ], + "spans": [ + { + "bbox": [ + 310, + 449, + 545, + 524 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal{S}_{\\text{SelfAttn}} = \\sum_{\\substack{\\mathbf{y}_{i},\\mathbf{y}_{j}\\in \\mathcal{Y},\\forall i < j}}\\frac{\\mathrm{f}(\\mathbf{y}_{i},\\mathbf{y}_{j})}{N}, \\\\ \\mathrm {f} \\left(\\mathbf {y} _ {i}, \\mathbf {y} _ {j}\\right) = \\frac {\\sum_ {x , y} \\min \\left(\\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] , \\mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\\right)}{\\sum_ {x , y} \\left(\\mathbf {A} _ {x _ {i} , y _ {i}} ^ {s} [ x , y ] + \\mathbf {A} _ {x _ {j} , y _ {j}} ^ {s} [ x , y ]\\right)}, \\tag {5} \\\\ \\end{array}", + "image_path": "34473fc0cff7cb58d77ab78b79ea79cc1d6cc2e99558d2748ee4d2ac67e37068.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": " is the number of pairs of " + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_j" + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{SelfAttn}}" + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": " is also calculated based on the initial noise and the first denoising step. We further define the self-attention conflict score threshold " + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\tau_s" + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": ", set to 0.3 in our experiments. Scores below " + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\tau_s" + }, + { + "bbox": [ + 305, + 532, + 545, + 590 + ], + "type": "text", + "content": " are classified as valid, and those above as invalid." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 591, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 591, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 305, + 591, + 545, + 626 + ], + "type": "text", + "content": "Finally, we define the initial noise that passes both the cross-attention response score test and the self-attention conflict test as valid noise, and vice versa as invalid." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 635, + 456, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 456, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 456, + 647 + ], + "type": "text", + "content": "4.2. Noise optimization pipeline" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "As illustrated in Fig. 4, existing methods most relevant to ours, represented by Attend-and-Excite [6], modify the noisy image at each denoising step, and encourage it to better encapsulate the semantic information from text. However, they necessitate meticulously calibrated optimization" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9383" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "parameters. As shown in Fig. 5, different optimization parameter settings directly affect the final generated image. Under-optimization leads to subpar quality, while over-optimization skews the noisy image away from the distribution of SD, resulting in an out-of-domain image. Moreover, even with the same text prompt, optimal parameters vary with noise, making case-specific tuning a laborious task." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 262 + ], + "type": "text", + "content": "We bypass this challenge by prioritizing noise optimization in the initial latent space, ensuring sufficient and appropriate adjustment. Specifically, INITNO is exclusively dedicated to navigating within the initial latent space, moving randomly sampled initial noise into the valid region. Unlike denoising processes that implicitly model the noisy image distribution, the initial latent space typically adheres to a standard Gaussian distribution, providing an avenue to restrict the optimized noise to the domain." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "text", + "content": "Noise update strategy. Given a noise " + }, + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "inline_equation", + "content": "\\epsilon \\in \\mathcal{N}(\\mathbf{0},\\mathbf{1})" + }, + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "text", + "content": " , as opposed to the commonly used incremental update: " + }, + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "inline_equation", + "content": "\\epsilon^{\\prime}\\gets" + }, + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "inline_equation", + "content": "\\epsilon +\\Delta \\epsilon" + }, + { + "bbox": [ + 47, + 263, + 288, + 310 + ], + "type": "text", + "content": " , we adopt a distribution optimization strategy to update the noise:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 319, + 287, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 319, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 94, + 319, + 287, + 334 + ], + "type": "interline_equation", + "content": "\\mu^ {\\prime} \\leftarrow \\mu + \\Delta \\mu , \\quad \\sigma^ {\\prime} \\leftarrow \\sigma + \\Delta \\sigma , \\tag {6}", + "image_path": "f040bacb54dabf771e090ba4e1cb9f95e431834b19479da5e9da17106c59f943.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "text", + "content": " are the mean and standard deviation of the Gaussian distribution, initialized to 0 and 1, respectively. Thus, we have: " + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\epsilon' \\gets \\mu' + \\sigma'\\epsilon" + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\epsilon' \\sim \\mathcal{N}(\\mu', \\sigma'^2)" + }, + { + "bbox": [ + 47, + 342, + 287, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 384, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 287, + 430 + ], + "type": "text", + "content": "Loss functions. We employ a joint loss for optimizing initial noise, comprising cross-attention response loss, self-attention conflict loss, and distribution alignment loss. Intuitively, the first two are formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 72, + 440, + 287, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 440, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 72, + 440, + 287, + 453 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {C r o s s A t t n}} = \\mathcal {S} _ {\\text {C r o s s A t t n}}, \\quad \\mathcal {L} _ {\\text {S e l f A t t n}} = \\mathcal {S} _ {\\text {S e l f A t t n}}. \\tag {7}", + "image_path": "fbbf48189f91f1c813563145f73fa310bfe0ebe45964202a2f21806b92909963.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "type": "text", + "content": "The distribution alignment loss utilizes Kullback-Leibler divergence [22] to constrain the consistency between the target Gaussian distribution " + }, + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "type": "text", + "content": " and the standard Gaussian distribution " + }, + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0}, \\mathbf{1})" + }, + { + "bbox": [ + 47, + 461, + 287, + 509 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 88, + 517, + 287, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 517, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 88, + 517, + 287, + 532 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {K L}} = \\mathsf {K L} \\left(\\mathcal {N} (\\mu , \\sigma^ {2}) \\| \\mathcal {N} (\\mathbf {0}, \\mathbf {1})\\right). \\tag {8}", + "image_path": "e138e2e60eb7478a6238b234dc00439e246b5b8dc09a0d751ec1cb3d7c51b873.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 540, + 219, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 540, + 219, + 551 + ], + "spans": [ + { + "bbox": [ + 59, + 540, + 219, + 551 + ], + "type": "text", + "content": "In summary, the joint loss is written as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 73, + 560, + 287, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 560, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 73, + 560, + 287, + 574 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {j o i n t}} = \\lambda_ {1} \\mathcal {L} _ {\\text {C r o s s A t t n}} + \\lambda_ {2} \\mathcal {L} _ {\\text {S e l f A t t n}} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {K L}}, \\tag {9}", + "image_path": "a39e99395ab9ab8a67a9817b873d8335e7ba6ce6ef208d2445cf78deeba6c177.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "text", + "content": "where we empirically set " + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "inline_equation", + "content": "\\lambda 1 = 1" + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 1" + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "inline_equation", + "content": "\\lambda_{3} = 500" + }, + { + "bbox": [ + 47, + 582, + 270, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": "Noise optimization procedure. The outlined noise optimization procedure is encapsulated in Algorithm 1. Sampling the initial noise " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{1})" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": ", we initialize the learnable parameters " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{0}" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{1}" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": ". We optimize these parameters using the joint loss, ensuring that the optimized noise " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mu +\\sigma \\mathbf{z}^T" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": " resides within the valid initial latent space. The optimization employs the Adam optimizer with a learning rate of " + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "inline_equation", + "content": "1\\times 10^{-2}" + }, + { + "bbox": [ + 46, + 594, + 287, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To mitigate computational inefficiency due to excessively challenging samples, we impose a maximum limit" + } + ] + } + ], + "index": 13 + }, + { + "type": "code", + "bbox": [ + 306, + 88, + 545, + 352 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 409, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 409, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 409, + 87 + ], + "type": "text", + "content": "Algorithm 1: INITNO" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "lines": [ + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": "Input: A pre-trained T2I diffusion model SD " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ", a text prompt y, a noise " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "z_{T}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ", threshold: " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\tau_{c}, \\tau_{s}, \\tau_{\\text{MaxStep}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\tau_{\\text{MaxRound}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ". Output: Generated image x. \n1 Noise pool " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathcal{P} \\gets \\{\\}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n2 for i = 1 to " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\tau_{\\text{MaxRound}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " do \n3 Initialize " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{T} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{1})" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mu \\gets \\mathbf{0}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\sigma \\gets \\mathbf{1}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n4 for j = 1 to " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\tau_{\\text{MaxStep}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " do \n5 " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{c}, \\mathbf{A}^{s} \\gets \\text{SD}(\\mu + \\sigma \\mathbf{z}^{T}, \\mathbf{y})" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n6 Calculate " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "S_{\\text{CrossAttn}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " (Eq. 3), " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "S_{\\text{SelfAttn}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " (Eq. 5) \n7 if " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "S_{\\text{CrossAttn}} < \\tau_{c}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "S_{\\text{SelfAttn}} < \\tau_{s}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " then \n8 " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{T} \\gets \\mu + \\sigma \\mathbf{z}^{T}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n9 Go to step 15 ▷ valid noise \n10 else \n11 Calculate " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{joint}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " (Eq. 9) \n12 " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mu, \\sigma \\gets \\text{Adam}(\\mu, \\sigma, \\mathcal{L}_{\\text{joint}})" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n13 Add " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mu + \\sigma \\mathbf{z}^{T}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n14 " + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{T} \\gets \\arg \\min_{\\mathbf{z}^{T} \\in \\mathcal{P}} S_{\\text{CrossAttn}} + S_{\\text{SelfAttn}}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": " \n15 x, -, - ← SD (" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{T}, \\mathbf{y}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ") or AE (" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{T}, \\mathbf{y}" + }, + { + "bbox": [ + 306, + 88, + 545, + 352 + ], + "type": "text", + "content": ") \n16 return x" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_body" + } + ], + "index": 15, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": "on optimization iterations, denoted as " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{MaxStep}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": ". If we fail to reach the valid region after " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{MaxStep}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": " updates, we resample " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": ", reset " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": ", and commence a new round of the optimization process. We also define a maximum limit on optimization rounds, denoted as " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{MaxRound}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": ". In our experiments, we set " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{MaxStep}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{MaxRound}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": " as 50 and 5, respectively. For a minority of intricate texts where effective noise cannot be found within affordable optimization rounds, we opt for the noise that minimizes the sum of " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{CrossAttn}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{SelfAttn}}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": " from the existing noise pool " + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 376, + 545, + 497 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 528, + 430, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 430, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 430, + 540 + ], + "type": "text", + "content": "5.1. Experimental settings" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": "Implementation Details. Following [6], we utilize the official Stable Diffusion v1.4 text-to-image model. A fixed guidance level of 7.5 is employed. We apply a Gaussian filter with a kernel size of 3 and a standard deviation of 0.5 to smooth the cross-attention map " + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^c" + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": " and the self-attention map " + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^s" + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": ". For the denoising process, " + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": " is set to 50. The target token identification process can be performed either manually or automatically with the assistance of GPT [3]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Datasets. We assess our method using the Animal-Animal, Animal-Object, and Object-Object datasets [6], which comprise two subjects and selectively assign a color to each subject. It is noteworthy that our method is not constrained to this scenario, and it can be applied to complex prompts containing any number or type of subjects and attributes, as" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9384" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 545, + 393 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 393 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 393 + ], + "type": "image", + "image_path": "5405766aab0071df04318c45739506ee2b407ebfd8f4f5a0d0e609a1f00c7707.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 398, + 546, + 422 + ], + "lines": [ + { + "bbox": [ + 46, + 398, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 546, + 422 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline. Our method shows excellent alignment with text prompts while maintaining a high level of realism." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 436, + 249, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 249, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 249, + 448 + ], + "type": "text", + "content": "discussed in Sec. 5.6 and supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 456, + 179, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 179, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 179, + 468 + ], + "type": "text", + "content": "5.2. Qualitative comparison" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "Fig. 6 presents a comparative analysis of our results against state-of-the-art counterparts, under the same text prompts and random seeds. It can be seen that existing methods commonly suffer from serious problems of subject mixing. For instance, in the case of a cat and a rabbit, conventional methods frequently yield erroneous outputs characterized by the fusion of cat faces and rabbit ears. Leveraging the self-attention conflict mechanism, our method can effectively decouple the two concepts of " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\underline{\\text{cat}}" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\underline{\\text{rabbit}}" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " and render them realistically and separately. Concurrently, Stable Diffusion [31], Composable Diffusion [25], and Structure Diffusion [12] suffer from the issue of subject neglect. Attend-and-Excite [6], Divide-and-Bind [24], and A-STAR [1] adhere to the pattern of adjusting noisy images at each denoising step. Given the same text prompt, using the same adjustment strategy, the quality of results generated by sampling different noises vary significantly. For instance, for the prompt a dog and a turtle, only the first example produced by Divide-and-Bind [24] is successful. In contrast, our method exhibits better generalization and" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 436, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 436, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 436, + 545, + 472 + ], + "type": "text", + "content": "adapts to diverse prompts. Furthermore, our approach also demonstrates more faithful binding of properties, e.g., yellow clock." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 479, + 444, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 444, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 444, + 493 + ], + "type": "text", + "content": "5.3.Quantitative comparison" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 498, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 676 + ], + "type": "text", + "content": "Objective Evaluation. Following to the protocol in [6], we quantitatively evaluate the proposed method using CLIP Image-Text Similarity and CLIP Text-Text Similarity. For each prompt, 64 images are generated, and the average CLIP cosine similarity is computed, maintaining consistent random seeds across all methods. Specifically, for CLIP Image-Text Similarity, we report full prompt similarity (cosine similarity between the full prompt and generated image) and minimum object similarity (minimum of the similarities between the generated image and each of the two subject prompts). For CLIP Text-Text Similarity, text-text similarities are computed by captioning the generated images with BLIP [23] and comparing them with the input prompt. As shown in Fig. 7, the proposed method outperforms other approaches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "User study. We also conduct a subjective user study involving 12 volunteers with expertise in image processing. 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Objective evaluation. Average CLIP Image-Text Similarity, including Full Prompt Similarity and Minimum Object Similarity, and Average CLIP Text-Text Similarity are reported for the quantitative measurement. 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MethodUser study
Stable Diffusion [31]4.17%
Composable Diffusion [25]2.50%
Structure Diffusion [12]3.33%
Attend-and-Excite [6]14.17%
Divide-and-Bind [24]6.67%
A-STAR [1]5.83%
INITNO (Ours)63.33%
", + "image_path": "66456342280591f0e7764c4c31bf9bb2f2e257d457104857ae5772fdd8f85495.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "table_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 50, + 539, + 284, + 551 + ], + "lines": [ + { + "bbox": [ + 50, + 539, + 284, + 551 + ], + "spans": [ + { + "bbox": [ + 50, + 539, + 284, + 551 + ], + "type": "text", + "content": "Table 1. User study. INITNO performs over other counterparts." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": "and semantically-faithful image from those generated by our proposed method and the state-of-the-art approaches. Specifically, each participant has 20 questions. We tally the votes and show the statistics in Table 1. Our method performs favorably against the other methods." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 616, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 664 + ], + "type": "text", + "content": "Inference time. Evaluated on a single Tesla V100 (32GB), 100 images with a resolution of " + }, + { + "bbox": [ + 46, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 616, + 287, + 664 + ], + "type": "text", + "content": " pixels are randomly generated, SD synthesizes an image in an average of 8.34 seconds, while our method takes 18.93 seconds." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 671, + 139, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 139, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 139, + 684 + ], + "type": "text", + "content": "5.4. Ablation study" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "On self-attention conflict loss. The self-attention conflict loss is designed to address the subject mixing issue arising" + } + ] + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 308, + 259, + 365, + 373 + ], + "blocks": [ + { + "bbox": [ + 308, + 259, + 365, + 373 + ], + "lines": [ + { + "bbox": [ + 308, + 259, + 365, + 373 + ], + "spans": [ + { + "bbox": [ + 308, + 259, + 365, + 373 + ], + "type": "image", + "image_path": "8101627ad0d643fd3be378340a4c4a8482cbfdf246ad6ac13e859a2a98ae65b1.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 374, + 348, + 384 + ], + "lines": [ + { + "bbox": [ + 324, + 374, + 348, + 384 + ], + "spans": [ + { + "bbox": [ + 324, + 374, + 348, + 384 + ], + "type": "text", + "content": "W/ " + }, + { + "bbox": [ + 324, + 374, + 348, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 348, + 389, + 503, + 401 + ], + "lines": [ + { + "bbox": [ + 348, + 389, + 503, + 401 + ], + "spans": [ + { + "bbox": [ + 348, + 389, + 503, + 401 + ], + "type": "text", + "content": "Figure 9. Visualization of effects of " + }, + { + "bbox": [ + 348, + 389, + 503, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_caption" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 365, + 259, + 486, + 372 + ], + "blocks": [ + { + "bbox": [ + 365, + 259, + 486, + 372 + ], + "lines": [ + { + "bbox": [ + 365, + 259, + 486, + 372 + ], + "spans": [ + { + "bbox": [ + 365, + 259, + 486, + 372 + ], + "type": "image", + "image_path": "a98f24f4f38c6b4e82c10dbf8d5c37886a2bfc9e6874741c866dbb1b966fe095.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 376, + 373, + 476, + 385 + ], + "lines": [ + { + "bbox": [ + 376, + 373, + 476, + 385 + ], + "spans": [ + { + "bbox": [ + 376, + 373, + 476, + 385 + ], + "type": "text", + "content": "\"A bird and a orange dog.\"" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 487, + 260, + 545, + 373 + ], + "blocks": [ + { + "bbox": [ + 487, + 260, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 487, + 260, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 487, + 260, + 545, + 373 + ], + "type": "image", + "image_path": "3a671904dda5ca63888cb591e1fb04ed6709525d6cf39f0efccccdf98c386b9a.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 374, + 530, + 384 + ], + "lines": [ + { + "bbox": [ + 501, + 374, + 530, + 384 + ], + "spans": [ + { + "bbox": [ + 501, + 374, + 530, + 384 + ], + "type": "text", + "content": "w/o " + }, + { + "bbox": [ + 501, + 374, + 530, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 418, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 526 + ], + "type": "text", + "content": "from self-attention map overlap, and it can be effortlessly incorporated into existing methods. As depicted in Fig. 8, the self-attention conflict loss effectively addresses the mixing issue between apple and pear. We also experiment with a cross-attention conflict loss [1], which replaces the self-attention map with cross-attention ones, but it did not produce satisfactory results. We surmise this is due to the inaccurate text embedding extracted by CLIP. Conversely, the self-attention map offers a more intuitive solution." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 527, + 546, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 546, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 546, + 599 + ], + "type": "text", + "content": "On distribution alignment loss. The distribution alignment loss is introduced to ensure that the optimized noise " + }, + { + "bbox": [ + 304, + 527, + 546, + 599 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_T" + }, + { + "bbox": [ + 304, + 527, + 546, + 599 + ], + "type": "text", + "content": " adheres to the standard Gaussian distribution. As visualized in the t-SNE plot of initial noise in Fig. 9, without constraints, the optimized noise may deviate from the standard Gaussian distribution, resulting in distorted results." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 306, + 610, + 446, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 446, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 446, + 624 + ], + "type": "text", + "content": "5.5. Grounded Text-to-Image" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 629, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 714 + ], + "type": "text", + "content": "INITNO is a plug-and-play approach that can be effortlessly integrated with existing diffusion models to enable training-free controllable generation, such as layout-to-image, mask-to-image generation, etc. As demonstrated in Fig. 11, we incorporate INITNO into BoxDiff [38], where modifications to the intermediate noisy image are transferred to the initial latent space, resulting in the synthesis" + } + ] + } + ], + "index": 43 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9386" + } + ] + } + ], + "index": 44 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 224 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 224 + ], + "type": "image", + "image_path": "76f736042b85fa20397edaea0fd7dfec200dfc7cf31894558880f1050e8b2863.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 229, + 546, + 252 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 546, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 546, + 252 + ], + "type": "text", + "content": "Figure 10. Qualitative comparison with complex text prompts. Each image is generated with the same text prompt and random seed for all methods. The subject tokens are highlighted in underline." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 261, + 286, + 452 + ], + "blocks": [ + { + "bbox": [ + 47, + 261, + 286, + 452 + ], + "lines": [ + { + "bbox": [ + 47, + 261, + 286, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 286, + 452 + ], + "type": "image", + "image_path": "343c2520596c293900357cbf03bc7ae5c99eca91394fa791d60b389fab18c551.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 456, + 287, + 479 + ], + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 479 + ], + "type": "text", + "content": "Figure 11. Grounded Text-to-Image. Due to sufficient adjustments, INITNO generates more accurately location-aware " + }, + { + "bbox": [ + 47, + 456, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\underline{cat}" + }, + { + "bbox": [ + 47, + 456, + 287, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 498, + 201, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 201, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 201, + 510 + ], + "type": "text", + "content": "of faithful and location-aware images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 517, + 129, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 129, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 129, + 529 + ], + "type": "text", + "content": "5.6. More results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "content": "Complex prompts. Fig. 10 presents examples of complex prompts, inclusive of prompts with three or more subjects and intricate attributes. The synthesis of high-fidelity images is demonstrated, underscoring the capacity of our method to manage complex semantic scenes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 597, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 657 + ], + "type": "text", + "content": "Visualization of the attention maps. Following [6], we also provide a visualization of the final cross-attention map for each subject token after denoising process in Fig. 12. Our method achieves reasonable attention allocation, leading to semantically-consistent results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "The core of our method is the Initial Noise Optimization (INITNO), which consists of the initial latent space parti" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 261, + 545, + 375 + ], + "blocks": [ + { + "bbox": [ + 307, + 261, + 545, + 375 + ], + "lines": [ + { + "bbox": [ + 307, + 261, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 307, + 261, + 545, + 375 + ], + "type": "image", + "image_path": "1dd51affe6e44ea76fbd8635a9b44d922eda8052d0e693f81aa6c4b9ea923150.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 379, + 536, + 390 + ], + "lines": [ + { + "bbox": [ + 315, + 379, + 536, + 390 + ], + "spans": [ + { + "bbox": [ + 315, + 379, + 536, + 390 + ], + "type": "text", + "content": "Figure 12. Visualization of the final cross-attention maps." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 407, + 546, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 546, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 546, + 588 + ], + "type": "text", + "content": "tioning and the noise optimization pipeline, responsible for defining valid regions and steering noise navigation, respectively. Specifically, we investigate the utility of attention maps in the diffusion model, harnessing them to formulate the cross-attention response score and the self-attention conflict score, both instrumental to the partitioning of the initial latent space. Moreover, we bypass the complex balance between under-optimization and over-optimization of noise via a meticulously crafted pipeline that introduces a novel distribution alignment loss. We further demonstrate the superiority of our approach over existing state-of-the-art methods in generating semantically-faithful images, providing a versatile plug-and-play solution that effectively integrates into existing diffusion models for training-free controllable generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 597, + 399, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 399, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 399, + 611 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "This work is partly supported by the National Key R&D Program of China (2022ZD0161902), the National Natural Science Foundation of China (62022011, 62202031), the Research Program of State Key Laboratory of Software Development Environment (SKLSDE-2023ZX-14), and the Fundamental Research Funds for the Central Universities. 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In CVPR, 2019. 2" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9389" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_content_list.json b/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f25d1e31c8ec9f8173c7de18cc6ae9bc1fb043ae --- /dev/null +++ b/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_content_list.json @@ -0,0 +1,1362 @@ +[ + { + "type": "text", + "text": "Initialization Matters for Adversarial Transfer Learning", + "text_level": 1, + "bbox": [ + 200, + 130, + 772, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Andong Hua1 Jindong Gu2 Zhiyu Xue1 Nicholas Carlini3 Eric Wong4 Yao Qin1,3 \n1University of California, Santa Barbara 2University of Oxford \n3Google 4University of Pennsylvania", + "bbox": [ + 109, + 178, + 857, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the prevalence of the Pretraining-Finetuning paradigm in transfer learning, the robustness of downstream tasks has become a critical concern. In this work, we delve into adversarial robustness in transfer learning and reveal the critical role of initialization, including both the pretrained model and the linear head. First, we discover the necessity of an adversially robust pretrained model. Specifically, we reveal that with a standard pretrained model, Parameter-Efficient Finetuning (PEFT) methods either fail to be adversially robust or continue to exhibit significantly degraded adversarial robustness on downstream tasks, even with adversarial training during finetuning. Leveraging a robust pretrained model, surprisingly, we observe that a simple linear probing can outperform full finetuning and other PEFT methods with random initialization on certain datasets. We further identify that linear probing excels in preserving robustness from the robust pretraining. Based on this, we propose Robust Linear Initialization (RoLI) for adversarial finetuning, which initializes the linear head with the weights obtained by adversarial linear probing to maximally inherit the robustness from pretraining. Across five different image classification datasets, we demonstrate the effectiveness of RoLI and achieve new state-of-the-art results. Our code is available at https://github.com/DongXzz/RoLI.", + "bbox": [ + 75, + 300, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 708, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the advancement of large-scale deep learning models, the Pretraining-Finetuning paradigm takes a more dominant role compared to training from scratch across various tasks [2], including computer vision [12, 15, 22, 28], natural language processing [20, 36, 41], and speech recognition [35]. Under the paradigm of Pretraining-Finetuning, advanced parameter-efficient finetuning (PEFT) methods [4, 16-18, 27, 48] have emerged. Compared to full finetuning, PEFT methods either introduce small modules into a fixed pretrained model or optimize only part of the pretrained model, demonstrating exceptional performance while keep", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bdb995711b372ec4a843644134648080b6bacdb8e06d66f82a6449d0925a238d.jpg", + "image_caption": [ + "Figure 1. Robust Linear Initialization (RoLI), significantly improves adversarial robustness. RoLI, denoted in red, achieves an average $3.88\\%$ increase in clean accuracy and a $2.44\\%$ increase in robust accuracy compared to Random Linear Initialization (RanLI) of the linear head during adversarial finetuning, averaged across five downstream datasets. Our best-performing RoLI - Full-FT, which represents adversarial full finetuning with robust linear initialization, achieves a new state-of-the-art performance. We include six popular finetuning methods with Swin Transformer [28] and two existing state-of-the-art techniques for adversarial transfer learning: TWINS-AT [29] and AutoLoRA [43]." + ], + "image_footnote": [], + "bbox": [ + 529, + 268, + 870, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing storage usage low.", + "text_level": 1, + "bbox": [ + 500, + 656, + 651, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While the success of transfer learning is evident, the robustness of downstream models has become a critical concern in real-world applications. For example, as suggested by previous studies, full finetuning will distort the pretrained features, leading to compromised robustness in terms of image corruptions and out-of-distribution (OOD) performance [26, 44]. In addition, adversarial robustness poses another significant challenge to real-world deployment, as a non-robust model demonstrates nearly zero accuracy under adversarial attacks [40]. Many approaches have been proposed to enhance adversarial robustness in transfer learning, including improving the robustness of pretraining through self-supervised techniques [7, 19] and preserving robustness from pretrained models during finetuning [29, 43]. However, most previous works [29, 43] apply", + "bbox": [ + 496, + 674, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24831", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef16f8535229e585afe9d4bb6e0d45a2df09d73369404356bca7632c1b1826c5.jpg", + "image_caption": [ + "Figure 2. Illustration of six different finetuning techniques, arranged in descending order according to the number of tunable parameters." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 888, + 296 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "full finetuning for adversarial transfer learning, overlooking the significance of different finetuning methods.", + "bbox": [ + 76, + 333, + 468, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we comprehensively study six popular finetuning methods in adversarial transfer learning, as shown in Fig. 2. We discover that initialization, which includes 1) the backbone initialization (i.e., a pretrained model), and 2) the initialization of the linear head that adapts features to the target domain, plays a critical role in adversarial transfer learning. We start by comparing the performance of adversarial finetuning when initialized with either a robust or a standard pretrained model. Surprisingly, all PEFT methods fail or exhibit significantly inferior performance when initialized with a standard pretrained model compared to being initialized with a robust pretrained model. Furthermore, we observe that a large-scale pretrained model, such as CLIP [34], cannot alleviate this phenomenon, highlighting the critical role of robust pretraining in adversarial transfer learning.", + "bbox": [ + 75, + 364, + 468, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a robust pretrained model, surprisingly, we discover that adversarial linear probing outperforms other methods on certain datasets, e.g., Caltech256 [13] and Stanford Dogs [21]. We further demonstrate that this is mainly because linear probing excels in inheriting robustness from pretraining. Moreover, we identify the ability to adapt features to the specific target domain as a key factor influencing linear probing's success, supported by a strong correlation between transferred accuracy and robustness. Based on these insights, we introduce Robust Linear Initialization (RoLI), which initializes the model's linear head with the weights obtained from adversarial linear probing. With RoLI followed by adversarial finetuning methods, we maximize the inherited robustness along with a strong feature adaptation ability, resulting in improved performance. In summary, our contributions are as follows:", + "bbox": [ + 75, + 608, + 468, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We comprehensively study six popular finetuning techniques for adversarial transfer learning. We discover that PEFT methods fail or exhibit significantly inferior perfor", + "bbox": [ + 76, + 854, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mance when initialized with a standard pretrained model, even with adversarial finetuning on downstream data.", + "bbox": [ + 511, + 333, + 888, + 363 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We demonstrate that adversarial linear probing excels in preserving robustness from a robust pretrained model. Building upon this insight, we propose Robust Linear Initialization (RoLI) for adversarial finetuning to maximally inherit robustness from pretraining and effectively adapt features through adversarial finetuning.", + "- We demonstrate the effectiveness of RoLI across five downstream datasets. On average, RoLI improves the clean and robust accuracy by $3.88\\%$ and $2.44\\%$ compared with random initialization. This establishes a new state-of-the-art benchmark for adversarial transfer learning." + ], + "bbox": [ + 500, + 364, + 890, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 554, + 648, + 569 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finetuning in Transfer Learning. Transfer learning aims to finetune a pretrained model on downstream tasks to gain better performance [23, 45, 47]. Linear probing and full finetuning are often applied in the finetuning process. Given the increasing size of pretrained models, various Parameter Efficient Finetuning (PEFT) methods have been proposed. PEFT methods can effectively reduce the finetuning cost and alleviate overfitting since only a small number of parameters are updated [16, 17]. Specifically, Bias [3, 46] only updates the bias term, while Scaling & Shifting [27] performs the linear transformation to adapt the features. Different from both of them, Adapter [16, 32, 33], LoRA [17], and VPT [18] introduce extra learnable modules into the pretrained models in the finetuning stage. Although there are various finetuning methods proposed to improve the accuracy, it is still unclear what matters to the robustness on the downstream tasks. [25] points out that feature distortion in finetuning hurts the out-of-distribution robustness on downstream tasks, while we discover initialization plays a critical role in adversarial robustness on downstream tasks.", + "bbox": [ + 496, + 583, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24832", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial Robustness in Transfer Learning. The research on adversarial robustness in transfer learning has been studied from two perspectives, namely, robust pretraining and robust finetuning. Concretely, robust pertaining aims to achieve adversarial robustness in the pertaining stage and finetune pretrained models on the downstream tasks without adversarial training [5, 7, 19, 39]. Besides, [38] demonstrates that the adversially pertaining also benefits standard performance on downstream tasks. In contrast, robust finetuning [29, 43] focuses on preserving the robustness of the pretrained model during the finetuning stage. For example, TWINS [29] incorporates a dual batch normalization in the model to keep the statistics of pretrained and finetuned datasets separately. And AutoLoRA [43] introduces a low-rank (LoRA) branch to disentangle clean and adversarial objectives. Existing works design various strategies to preserve the robustness from the pretrained model, but they simply apply full finetuning on downstream tasks. In this work, we study six different finetuning methods and introduce Robust Linear Initialization (RoLI) to enhance the adversarial robustness for different finetuning methods.", + "bbox": [ + 76, + 90, + 472, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 76, + 440, + 205, + 457 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we provide an overview of existing finetuning techniques, including full finetuning as well as five different PEFT methods, as illustrated in Fig. 2. Additionally, we introduce adversarial finetuning which integrates adversarial training during the finetuning stage.", + "bbox": [ + 76, + 465, + 468, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Existing Finetuning Methods", + "text_level": 1, + "bbox": [ + 76, + 554, + 336, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In transfer learning, finetuning adapts the features from the pretrained domain to the target domain. In this section, we introduce six finetuning methods in descending order according to the number of tunable parameters.", + "bbox": [ + 76, + 579, + 468, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Full Finetune (Full-FT): We initialize the model from a pretrained model and finetune all its parameters on the downstream tasks.", + "bbox": [ + 76, + 640, + 468, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adapter [16, 32, 33]: Adapter introduces a module after the MLP block in every layer. The adapter module consists of a down-sampling layer and an up-sampling layer, with a non-linear activation. During finetuning, we will update the adapter modules as well as the linear head.", + "bbox": [ + 76, + 686, + 468, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Low-Rank Adaptation (LoRA) [17]: LoRA proposes to learn a residual from pretrained weight represented by two low-rank metrics. Specifically, we apply the LoRA branch on the query and value projection in the self-attention block. During finetuning, the pretrained model remains frozen while updates are applied to the LoRA branch and head.", + "bbox": [ + 76, + 763, + 468, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Bias [3, 46]: We update the bias term and keep other parameters unchanged. Additionally, We also update the classification head (including weights and bias).", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Prompt Tuning (VPT) [18]: VPT appends additional learnable tokens (embeddings), called prompts, into the input space of each attention layer in vision transformers. Specifically, we use the structure of VPT-Deep, where every layer introduces a fixed number of trainable prompts independently. During the finetuning stage, we will tune both the prompts and the linear head on downstream tasks while freezing the entire pretrained backbone. We refer readers to [18] for more details.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Linear Probing (Linear): We only finetune the classification head on the downstream tasks.", + "bbox": [ + 496, + 227, + 890, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Adversarial Finetuning", + "text_level": 1, + "bbox": [ + 500, + 266, + 718, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial training corresponds to a min-max optimization problem [31]. In the context of adversarial finetuning, we can formulate the optimization problem as follows:", + "bbox": [ + 496, + 290, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\hat {\\theta}} \\mathbb {E} _ {(x, y) \\sim D} \\left[ \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\varepsilon} \\mathcal {L} (x + \\delta , y; \\theta \\cup \\hat {\\theta}) \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 345, + 890, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\theta$ and $\\hat{\\theta}$ represent the frozen parameters and tunable parameters in model parameters respectively. For example, in adversarial full finetuning, $\\hat{\\theta}$ stands for all the model parameters as we update all of them during the finetuning stage. In contrast, in adversarial VPT, $\\hat{\\theta}$ denotes the extra prompts and linear head while $\\theta$ represents the frozen parameters in the backbone architecture. In addition, $\\delta$ represents adversarial perturbation, whose $\\| \\cdot \\|_{\\infty}$ is bounded by $\\varepsilon$ . During adversarial finetuning, we use the pretrained model together with additional modules introduced by PEFT methods to generate adversarial examples, while only updating the tunable parameters $\\hat{\\theta}$ for each method. If not otherwise specified, we use PGD-7 with $\\varepsilon = 8 / 255$ and step size $\\alpha = 2 / 255$ to generate adversarial attacks during adversarial finetuning.", + "bbox": [ + 496, + 392, + 892, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Robust Pretrained Model Matters", + "text_level": 1, + "bbox": [ + 498, + 633, + 808, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous research [29, 39] suggests that although standard pretraining results in performance inferior to that of adversarially robust pretraining, it can still yield an adversarially robust model with adversarial finetuning. In this section, our goal is to investigate the significance of pretraining in PEFT methods. Specifically, we seek to address the question: Is an adversarially robust model necessary for PEFT methods?", + "bbox": [ + 496, + 659, + 890, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To answer this question, we initialize model parameters using two different pretrained models. One is a standard pretrained model on ImageNet-1k [11] while the other is adversarially pretrained with PGD [31] attacks. These pretrained models are off-the-shelf and their specifics are outlined in the supplementary material. Following initialization, we perform adversarial finetuning on downstream tasks. As shown in Fig. 3, we evaluate six adversarial", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24833", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0e7de21a1b187b3c71bacf61101acf483ab1c7606705b8dce46124561689b9c2.jpg", + "image_caption": [ + "Figure 3. PEFT methods fail or exhibit significantly degraded performance with a standard pretrained model (in blue and gray). Models finetuned from a robust pretrained model (in red) exhibit high accuracy and robustness, as they are consistently positioned in the top-right corner. Among six finetuning techniques, Full-FT outperforms others when starting with a standard pretrained model; however, it falls short of other methods when starting with a robust pretrained model. The specific numerical results are provided in the supplementary." + ], + "image_footnote": [], + "bbox": [ + 81, + 97, + 486, + 291 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6ff51eddecf176ca2dfc47249b7b1ad2e0e099dd86e9eff9607366d92bce1ca6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 98, + 684, + 287 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a13371822d61a5af672f864e7bb0a16f8705676a4b2d4fd7f95f014f4c26603c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 98, + 880, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "finetuning techniques across two model architectures (ViT-B [12] and Swin-B [28]) on the CIFAR10 [24] and Caltech256 [13]. The adversarial robustness is measured with PGD-10 bounded with $\\varepsilon = 8 / 255$ .", + "bbox": [ + 75, + 375, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we find that initializing the model with an adversarially robust pretrained model can significantly improve adversarial robustness on downstream tasks. This consistently holds across all the experimental settings we have evaluated, e.g., 6 adversarial finetuning techniques across 2 model architectures on 2 different datasets. More surprisingly, we discover that a robust pretrained model is especially important for PEFT methods, as they struggle to achieve satisfactory adversarial robustness when initialized with a standard pretrained model. For example, all the PEFT methods fail to achieve adversarial robustness higher than $20\\%$ on the Caltech256 dataset. In addition, adversarial linear probing can only achieve $< 5\\%$ adversarial robustness on both datasets when initiated with a standard pretrained model. This strongly suggests that adversarial PEFT can not sufficiently infuse adversarial robustness in the finetuning stage if the model starts with a non-robust pretrained model. Finally, we observe that Full-FT consistently outperforms other finetuning methods with a non-robust pretraining, indicating the preference for using full finetuning in the absence of robust pretraining.", + "bbox": [ + 75, + 436, + 470, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Does Pretraining on a Larger Dataset Help Adversarial Finetuning? Due to the high computational cost of adversarial pretraining, we aim to investigate whether a model pretrained on a larger dataset could substitute for the necessity of an adversially robust pretrained model. To this end, we initialize the model with an off-the-shelf large-scale pretrained model, CLIP [34], and perform the same adversarial finetuning techniques on downstream tasks. Fig. 3 demonstrates that a standard pretrained model on a larger dataset,", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/a61b0cf7a44ed7de52150feb4e3e8d68b1df6a3d864ed488945fbcd3d2b21951.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsViTSwin
CleanPGDCleanPGD
RanLI - Full-FT80.1744.1585.1954.13
RanLI - Adapter83.1449.5785.2454.22
RanLI - LoRa82.6350.7283.5253.57
RanLI - Bias82.6950.0784.8854.69
RanLI - VPT82.0950.5284.9955.23
RanLI - Linear81.8942.0282.9845.89
", + "bbox": [ + 509, + 372, + 883, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. PEFT methods, excluding Linear, demonstrate strong performance on average across CIFAR10 and Caltech256 datasets. With adversarial finetuning, PEFT methods outperform Full-FT and Linear with RanLI. Full results are available in ??", + "bbox": [ + 498, + 508, + 892, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "like CLIP, does not yield higher robustness compared to the non-robust ImageNet-1k pretrained model. It notably lags far behind the robustness achieved by a smaller-scale robust pretrained model, such as one trained on ImageNet-1k. This observation implies that opting for a smaller yet robust pretrained model proves to be a more effective strategy for attaining adversarial robustness in downstream tasks compared to using a larger, non-robust pretrained model.", + "bbox": [ + 496, + 573, + 890, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Initialization Matters For Finetuning", + "text_level": 1, + "bbox": [ + 500, + 707, + 834, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the previous section, we understand the necessity of initializing a model with an adversarially robust pretrained model. We now ask: given a robust pretrained model, what matters for adversarial finetuning?", + "bbox": [ + 498, + 732, + 893, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Random Linear Initialization", + "text_level": 1, + "bbox": [ + 500, + 801, + 761, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To answer this question, we first evaluate the adversarial robustness of six adversarial finetuning techniques. To adapt the robust pretrained model to the downstream tasks, we initialize the linear head with Random Linear Initialization (RanLI) following [39]. We perform adversarial finetuning", + "bbox": [ + 496, + 824, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24834", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0af4a33a0ae425c8fdc662e2b9b9cce25c2c999b46b8629a351568a83b5b45f3.jpg", + "image_caption": [ + "Figure 4. Linear probing with adversarial finetuning surpasses other methods on Caltech256. With standard finetuning, the PEFT methods exhibit inherited robustness (Robustness $>0$ ) from the pretraining. Notably, linear probing surpasses the other methods by a substantial margin in robustness while maintaining similar clean data accuracy on Caltech256. Additionally, adversarial training during finetuning is effective in enhancing all methods' robustness." + ], + "image_footnote": [], + "bbox": [ + 81, + 98, + 888, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "across two model architectures, e.g., ViT and Swin, on the CIFAR10 and Caltech256 datasets. Additional details regarding the training process can be found in Sec. 5.4 and in supplementary ??", + "bbox": [ + 75, + 364, + 468, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Tab. 1, PEFT methods except Linear consistently demonstrate strong average results with adversarial finetuning. In particular, LoRA achieves the highest average robustness at $50.72\\%$ for ViT, while VPT performs exceptionally well with $55.23\\%$ on Swin.", + "bbox": [ + 75, + 425, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Looking more closely at the performance on each individual dataset in Fig. 4, we observe that adversarial linear probing achieves the strongest robustness on Caltech256. This is rather surprising, given that linear probing has the lowest computational cost compared to others and never outperforms other finetuning methods on any single dataset in standard transfer learning [4, 6, 18].", + "bbox": [ + 75, + 500, + 468, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Why does Adversarial Linear Probing Work?", + "text_level": 1, + "bbox": [ + 76, + 613, + 460, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To understand the remarkable robustness achieved by adversarial linear probing, we then ask: what contributes to adversarial robustness on the downstream tasks given a robust pretrained model? We hypothesize that there are two confounding factors: 1) the robustness inherited from pretrained models, and 2) the robustness achieved by adversarial finetuning. To validate our hypothesis, we conduct a comparative analysis of adversarial robustness in downstream tasks while using standard finetuning versus adversarial finetuning, given the same robust pretrained model.", + "bbox": [ + 75, + 637, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Robustness Inherited from Pretrained Models. In this section, we focus on standard finetuning as it does not bring in additional adversarial robustness to downstream tasks. Therefore, the adversarial robustness achieved during standard finetuning primarily arises from the robust pretrained model, representing the capability of each method to preserve robustness from the pretrained model. As shown in", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 4, all standard finetuning methods (colored in blue) achieve non-zero robustness under PGD-10 attacks. This supports our hypothesis that robustness inherited from the pretrained model contributes to the robustness in downstream tasks. In addition, linear probing significantly outperforms all other standard finetuning methods in preserving robustness from the pretrained model. For example, linear probing exhibits significantly stronger robustness (at least $20\\%$ higher) compared to other methods while maintaining similar accuracy on Caltech256. We explain this as linear probing avoids distorting the robust features inherited from the pretrained model by only updating the linear head. However, on CIFAR10, linear probing does not exhibit a significant advantage over robustness and displays lower clean accuracy compared to others. This is likely due to its limited capability to adapt features from the pretrained source domain to the downstream target domain.", + "bbox": [ + 496, + 364, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Robustness Achieved by Adversarial Finetuning. By comparing adversarial robustness achieved by standard finetuning (colored in blue) and adversarial finetuning (colored in red) in Fig. 4, we can see the extra robustness gain achieved by adversarial training during the finetuning stage. Except for Linear, adversarial finetuning contributes a significant portion of their robustness to the final robustness. For example, Full-FT on Swin, achieving a $99\\%$ final robustness on Caltech256 through adversarial finetuning. Even VPT, which has the fewest tunable parameters after Linear, demonstrates a $78\\%$ final robustness from adversarial finetuning. On the contrary, Linear only achieved a final robustness of $13\\%$ from this stage, with the primal robustness originating from the pretraining model.", + "bbox": [ + 496, + 628, + 890, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Taken together, we validate our hypothesis that both robustness inherited from the pretrained model and achieved through adversarial finetuning contribute to adversarial robustness on downstream tasks. In addition, we conclude", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24835", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "that the exceptional robustness exhibited by adversarial linear probing is mainly because linear probing excels in preserving robustness from pretrained models compared to others, which primarily obtain their robustness from adversarial training during finetuning stage.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Transferred Robustness Correlates with Transferred Accuracy.", + "text_level": 1, + "bbox": [ + 76, + 176, + 468, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As we have seen in Fig. 4, adversarial linear probing achieves the highest adversarial robustness on Caltech256 but falls far behind other methods on CIFAR10. This performance discrepancy across different datasets raises a question: how can we estimate if adversarial linear probing achieves the best robustness? Based on our analysis in Sec. 5.2, where the robustness of adversarial linear probing primarily arises from preserving the robustness in the pretrained model, we hypothesize that the transferred robustness of adversarial linear probing is highly correlated with the transferred accuracy of standard linear probing. This suggests that if standard linear probing successfully adapts the features from the pretrained source domain to the downstream target domain, adversarial linear probing will similarly preserve the robustness in the pretrained model.", + "bbox": [ + 75, + 217, + 468, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate this, we define transferred accuracy of standard linear probing $(\\mathrm{acc}_{std}^T)$ and transferred robustness of adversarial linear probing $(\\mathrm{rob}_{adv}^T)$ as follows, using full finetune as a baseline to normalize the performance across different datasets:", + "bbox": [ + 75, + 444, + 468, + 518 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {a c c} _ {s t d} ^ {T} = \\frac {\\operatorname {a c c} \\left(L P _ {s t d}\\right) - \\operatorname {a c c} \\left(F T _ {s t d}\\right)}{\\operatorname {a c c} \\left(F T _ {s t d}\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 532, + 468, + 566 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {r o b} _ {a d v} ^ {T} = \\frac {\\operatorname {r o b} \\left(L P _ {a d v}\\right) - \\operatorname {r o b} \\left(F T _ {a d v}\\right)}{\\operatorname {r o b} \\left(F T _ {a d v}\\right)} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 575, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{acc}(\\cdot)$ and $\\mathrm{rob}(\\cdot)$ denote the accuracy and robustness of each method, respectively. $FT_{std}$ and $LP_{std}$ represent standard full finetune and standard linear probing whereas $FT_{adv}$ and $LP_{adv}$ stand for their respective adversarial counterparts. We trained 51 models with different hyper-parameter settings across five datasets and present transferred accuracy and robustness in Fig. 5.", + "bbox": [ + 75, + 616, + 468, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Fig. 5, the transferred robustness of adversarial linear probing is strongly correlated with the transferred accuracy of standard linear probing, with a high Pearson correlation coefficient (0.896). When the transferred accuracy approaches or surpasses 0, the transferred robustness becomes positive, indicating the improved performance of adversarial linear probing over adversarial fully finetuning. This strong correlation validates our hypothesis that if standard linear probing successfully adapts features from the pretrained to the target domain, its adversarial counterpart is capable of effectively achieving adversarial robustness on downstream tasks.", + "bbox": [ + 75, + 722, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/be36f60c6e98e83de1994da02953e42dab6719051a828354a4287321abb4cd23.jpg", + "image_caption": [ + "Figure 5. Transferred robustness of adversarial linear probing strongly correlates with transferred accuracy of standard linear probing." + ], + "image_footnote": [], + "bbox": [ + 526, + 90, + 864, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Robust Linear Initialization (RoLI)", + "text_level": 1, + "bbox": [ + 500, + 356, + 805, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on our observation that linear probing can outperform other methods when it effectively adapts features to the target domain, we propose Robust Linear Initialization (denoted as RoLI) for adversarial finetuning. Specifically, we initialize the linear head of a robust pretrained model with weights obtained through adversarial linear probing instead of random initialization. Then, we perform adversarial finetuning, using either full finetune or PEFT methods. Since adversarial linear probing excels in preserving robustness from a pretrained model, RoLI provides a more robust initialization for subsequent adversarial finetuning, maximizing the robustness inherited from a robust pretrained model. In addition, the following adversarial finetuning can further enhance robustness by introducing additional robustness through adversarial training. In the following sections, we will evaluate the effectiveness of RoLI applied to four different adversarial finetuning methods across five different datasets and demonstrate it achieves new state-of-the-art robustness in adversarial transfer learning.", + "bbox": [ + 496, + 380, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. In our experiments, we use five datasets: CIFAR10 [24], CIFAR100 [24], Caltech256 [13], CaltechUCSD Birds-200-2011 (CUB200) [42], and Stanford Dogs (Dogs) [21]. For low-resolution image datasets like CIFAR10 and CIFAR100, we resize the image to match the model input shape. For high-resolution image datasets, we apply random resizing and cropping in training and center crop in testing. It's important to note that we integrate the resizing and normalization process directly into the model since the attacker does not have access to pre-processed images. Additional details are provided in the supplementary ??", + "bbox": [ + 496, + 678, + 890, + 858 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Methods. We provide the results from TWINS-AT [29] AutoLoRa [43] as baselines. We proceed to assess six fine", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24836", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/213306e0669328430cae0df6f74e6c8ca90fa32704409b2197ba027be05dd0d2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
CleanPGDCleanPGDCleanPGDCleanPGDCleanPGDCleanPGD
TWINS-AT [29]91.2452.7370.7231.0876.8648.4068.0929.2464.9820.5874.3836.41
AutoLoRa [43]86.9357.1666.2035.2569.8547.8262.7831.0762.3325.3269.6239.32
RanLI - Full-FT93.0259.1274.3635.6277.3549.1370.8331.5565.8524.7976.2840.04
RanLI - Adapter90.2355.7071.5734.7480.2452.7359.6726.7387.9842.2477.9442.43
RanLI - LoRA90.0256.8871.9834.8377.0250.2564.7429.6584.6339.2477.6842.17
RanLI - Bias90.2556.9471.5036.7279.5052.4366.6929.8887.4142.7579.0743.74
RanLI - VPT90.2457.3872.3735.6079.7453.0761.9426.4686.3443.1078.1343.12
RanLI - Linear84.1637.3067.6525.4681.7954.4769.8824.5691.5545.4579.0137.45
RoLI - Full-FT94.1860.8576.2537.3883.7855.4274.2832.0391.5545.5784.0146.25
RoLI - Adapter90.3155.6971.7534.3381.7454.3264.2025.2292.0247.1280.0043.34
RoLI - LoRA92.2358.6272.8735.1881.7954.5068.8826.7791.2046.7681.3944.37
RoLI - Bias91.8358.3972.1735.1781.7854.4968.1425.7091.5247.2781.0944.20
", + "bbox": [ + 81, + 88, + 888, + 311 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9f81739f4163bebb6728df64503f6b33cf1a128c28c9399cf692b6563b97fac6.jpg", + "table_caption": [ + "Table 2. RoLI significantly improves the performance and achieves SOTA across five image classification tasks. Robust Linear Initialization (RoLI) enhances robustness by $3.88\\%$ and clean accuracy by $2.44\\%$ on average compared to Random Initialization (RanLI). Notably, RoLI - Full-FT achieves the best overall performance, with an accuracy of $84.01\\%$ and $46.25\\%$ robustness." + ], + "table_footnote": [], + "table_body": "
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
RanLI - Full-FT54.931.862.649.742.548.3
RanLI - Adapter50.829.266.740.368.551.1
RanLI - LoRa53.029.062.844.763.350.6
RanLI - Bias52.331.065.846.267.352.5
RanLI - VPT52.329.766.340.367.351.2
RanLI - Linear26.618.465.740.473.544.9
RoLI - Full-FT56.332.770.452.173.557.0
RoLI - Adapter51.129.165.840.675.252.4
RoLI - LoRa53.930.065.744.674.353.7
RoLI - Bias53.929.865.743.574.853.5
", + "bbox": [ + 78, + 369, + 470, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tuning techniques introduced in Sec. 3.1 with random initialization. We use Swin Transformer [28] as a backbone architecture for our experiments, whereas TWINS and AutoLoRa use ResNet50 [14]. We apply RoLI to Full-FT, Bias, Adapter, and LoRa. We initialize the newly introduced modules in Adapter and LoRA with zero to ensure that they start with robust linear probing without distorting the robust features preserved in the pretrained model.", + "bbox": [ + 75, + 643, + 468, + 765 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Details. We use the same optimizer, AdamW [30], and a cosine scheduler with warm-up for all finetuning methods. To determine the optimal learning rate and weight decay values, we conduct a grid search, and the ranges of hyper-parameters along with the optimal combinations can be found in the supplementary ??. We keep method-specific hyper-parameters constant across all datasets. For instance, we set the prompt", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/59445c55ed997810f1cbad78dc34ad2247ffbe429a9fee99178b73edcb17cbc7.jpg", + "table_caption": [ + "Table 3. RoLI consistently outperforms RanLI under AutoAttack. Note, we use $\\varepsilon = 8 / 255$ attack for CIFAR10, CIFAR100, and $\\varepsilon = 4 / 255$ for Caltech256, CUB200 and Stanford Dogs. RoLI shows an average 3.53 AA gain compared with RanLI, and notably, RoLI - Full-FT surpasses other methods by achieving a robustness of 57.0 under AutoAttack. The clean accuracy is illustrated in Tab. 2." + ], + "table_footnote": [], + "table_body": "
Methodsε = 8/255ε = 4/255
RanLI - Full-FT20.1042.50
RanLI - Adapter36.3068.50
RanLI - LoRa32.4063.30
RanLI - Bias35.9067.30
RanLI - VPT34.4067.30
RanLI - Linear30.9073.50
RoLI - Full-FT30.9073.50
RoLI - Adapter37.0075.20
RoLI - LoRa38.4074.30
RoLI - Bias38.2074.80
", + "bbox": [ + 503, + 369, + 890, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. RoLI consistently improves adversarial robustness even against $\\varepsilon = 8 / 255$ AutoAttack. RanLI - Linear performs well under $\\varepsilon = 4 / 255$ AutoAttack, but poorly under $\\varepsilon = 8 / 255$ AutoAttack on Stanford Dogs. This discrepancy demonstrates that adversarial linear probing obtains its robustness mainly from the pretrained model, whereas other methods obtain robustness mainly from adversarial finetuning.", + "bbox": [ + 496, + 535, + 892, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "length to 10 for the VPT method. To avoid adversarial overfitting [37], we apply early stopping with the epoch that has the best performance on the validation set. During adversarial finetuning, we utilize the PGD-7 attack with $\\varepsilon = 8 / 255$ and a step size of $\\alpha = 2 / 255$ . When reporting test accuracy and robustness, we evaluate the models under a PGD-10 attack with $\\varepsilon = 8 / 255$ . Additionally, we report the performance under AutoAttack (AA), which is an ensemble attack and provides a more reliable approach to evaluate the adversarial robustness. We follow the standard AutoAttack setting, i.e., untargeted APGDCE, targeted APGD-DLR, targeted FAB [8], and Square Attack [1].", + "bbox": [ + 496, + 643, + 893, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PGD-10 Results. Looking at Random Initialization (RanLI) in Tab. 2, the same trend holds as in Sec. 5.1: 1) PEFT methods except linear probing exhibit strong average results across five different datasets, with Bias achiev", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24837", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/98bc546f3e75bf3c58c246214c9f8c0712c081b3f8c7dee55eae953d85c82daa.jpg", + "image_caption": [ + "Figure 6. Trade-off between speed and robustness. We conduct the speed test on Stanford Dogs with random linear initialization (RanLI), logistic regression linear initialization (RegLI), standard linear initialization (StdLI), and robust linear initialization (RoLI). RoLI achieves the best performance at the cost of increased training time. Meanwhile, both RegLI and StdLI can improve their performance without incurring substantial time costs." + ], + "image_footnote": [], + "bbox": [ + 109, + 75, + 433, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing the best performance (79.25% accuracy and 43.58% robustness). 2) Linear probing achieves the highest robustness on Caltech256 and Stanford Dogs, although it falls behind others on the remaining three datasets.", + "bbox": [ + 75, + 372, + 468, + 433 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compared to RandLI, we can observe from Tab. 2 that RoLI significantly enhances the robustness on Caltech256 and Stanford Dogs for all finetuning methods. In particular, RoLI - Full-FT achieves a robustness improvement of $6.29\\%$ on Caltech256 and $20.78\\%$ on Stanford Dogs. On other datasets where adversarial linear probing with RanLI does not outperform others, RoLI performs comparable or even better than RanLI. This strongly supports that a robust initialization of the linear head is critical in adversarial transfer learning. Lastly, our RoLI - Full-FT achieves the highest performance across five datasets and sets a new state-of-the-art benchmark.", + "bbox": [ + 75, + 434, + 470, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "AutoAttack Results. We extend our evaluation to Stanford Dogs using $\\varepsilon = 8 / 255$ and $\\varepsilon = 4 / 255$ , as illustrated in Tab. 4. Interestingly, we observe that adversarial linear probing outperforms other methods under $\\varepsilon = 4 / 255$ attack but underperforms when tested against $\\varepsilon = 8 / 255$ adversarial attacks. We conjecture that the pretrained model lacks robustness against $\\varepsilon = 8 / 255$ attacks as it is trained using $\\varepsilon = 4 / 255$ adversarial attacks.", + "bbox": [ + 75, + 627, + 468, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This performance disparity confirms that adversarial linear probing inherently derives robustness from pretraining, whereas other methods predominantly achieve robustness from adversarial finetuning. Notably, RoLI consistently improves adversarial robustness even against $\\varepsilon = 8 / 255$ attacks, further validating the importance of a robust linear initialization for adversarial transfer learning.", + "bbox": [ + 75, + 748, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To maintain consistency with the pre-training, we follow the conventional settings [9, 10] to set $\\varepsilon = 8 / 255$ attack for low-resolution datasets (CIFAR10, CIFAR100) and", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/806767e87ff0aa58b72830b1209cd1eec110c1e6c56e03a8e80033f130070185.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
StdLI -CIFAR-10Caltech-256
CleanPGDCleanPGD
Full-FT93.34(-0.84)59.34(-1.51)83.23(-0.55)52.85(-2.57)
Bias93.34(-0.04)58.12(-0.27)82.93(+1.15)52.93(-1.56)
Adapter90.08(-0.23)55.19(-0.50)82.72(+0.98)53.01(-1.31)
LoRa90.71(-1.52)58.17(-0.45)82.87(+1.08)51.47(-3.03)
", + "bbox": [ + 519, + 89, + 870, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. StdLI is less robust than RoLI. The values in parentheses denote the performance gap (StdLI - RoLI).", + "bbox": [ + 500, + 180, + 888, + 208 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$\\varepsilon = 4 / 255$ attack for high-resolution datasets (Caltech256, CUB200, Stanford Dogs). Tab. 3 demonstrates the robustness under AutoAttack and the clean accuracy is illustrated in Tab. 2. RoLI exhibits higher robustness over RanLI, demonstrating an average 3.53 AA gain. Notably, RoLI - Full-FT achieves a robustness of 57.0, surpassing other methods.", + "bbox": [ + 498, + 217, + 890, + 323 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 500, + 338, + 612, + 353 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison between RoLI and StdLI. Standard Linear Initialization (StdLI) refers to the use of a simple linear probing to initialize the head, while RoLI uses adversarial linear probing. In Tab. 5, we compare the performance of RoLI and StdLI on CIFAR-10 and Caltech-256. We observe that StdLI exhibits lower performance compared to RoLI, with a robustness decrease of 2.48 across three datasets, highlighting the effectiveness of RoLI.", + "bbox": [ + 498, + 363, + 890, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness vs. Speed. Since robust linear initialization involves a two-step adversarial training process, it tends to be considerably slower than adversarial fine-tuning with random initialization. In this section, we show a trade-off between robustness and speed by obtaining the initialization from four different approaches: adversarial linear probing (RoLI), standard linear probing (StdLI), logistic regression (RegLI), and randomization (RanLI). From Fig. 6, it's evident that both RegLI and StdLI enhance robustness compared to random linear initialization within an acceptable time cost. In addition, RoLI achieves the highest performance but at the expense of slower speed.", + "bbox": [ + 498, + 486, + 890, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 681, + 617, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper systematically investigates how to achieve adversarial robustness in downstream tasks. We highlight the necessity of an adversially robust pretraining. Given a robust pretrained model, we propose to use robust linear initialization (RoLI) followed by adversarial full finetuning or PEFT methods to achieve the best performance. We demonstrate that RoLI outperforms random linear initialization across five image classification tasks. We hope the insights from this study greatly advance research aimed at enhancing adversarial robustness in downstream tasks.", + "bbox": [ + 498, + 707, + 890, + 857 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. We thank Chenhe Gu and Xuan Yang for the valuable discussion and insightful feedback.", + "bbox": [ + 500, + 858, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24838", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In European conference on computer vision, pages 484-501. 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Neural prompt search. arXiv preprint arXiv:2206.04673, 2022. 1" + ], + "bbox": [ + 501, + 92, + 890, + 614 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24840", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_model.json b/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_model.json new file mode 100644 index 0000000000000000000000000000000000000000..828b2746d193dba94435f8a9e418d7a41e80306c --- /dev/null +++ b/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_model.json @@ -0,0 +1,1903 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.201, + 0.131, + 0.773, + 0.154 + ], + "angle": 0, + "content": "Initialization Matters for Adversarial Transfer Learning" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.179, + 0.859, + 0.235 + ], + "angle": 0, + "content": "Andong Hua1 Jindong Gu2 Zhiyu Xue1 Nicholas Carlini3 Eric Wong4 Yao Qin1,3 \n1University of California, Santa Barbara 2University of Oxford \n3Google 4University of Pennsylvania" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.681 + ], + "angle": 0, + "content": "With the prevalence of the Pretraining-Finetuning paradigm in transfer learning, the robustness of downstream tasks has become a critical concern. In this work, we delve into adversarial robustness in transfer learning and reveal the critical role of initialization, including both the pretrained model and the linear head. First, we discover the necessity of an adversially robust pretrained model. Specifically, we reveal that with a standard pretrained model, Parameter-Efficient Finetuning (PEFT) methods either fail to be adversially robust or continue to exhibit significantly degraded adversarial robustness on downstream tasks, even with adversarial training during finetuning. Leveraging a robust pretrained model, surprisingly, we observe that a simple linear probing can outperform full finetuning and other PEFT methods with random initialization on certain datasets. We further identify that linear probing excels in preserving robustness from the robust pretraining. Based on this, we propose Robust Linear Initialization (RoLI) for adversarial finetuning, which initializes the linear head with the weights obtained by adversarial linear probing to maximally inherit the robustness from pretraining. Across five different image classification datasets, we demonstrate the effectiveness of RoLI and achieve new state-of-the-art results. Our code is available at https://github.com/DongXzz/RoLI." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.709, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "With the advancement of large-scale deep learning models, the Pretraining-Finetuning paradigm takes a more dominant role compared to training from scratch across various tasks [2], including computer vision [12, 15, 22, 28], natural language processing [20, 36, 41], and speech recognition [35]. Under the paradigm of Pretraining-Finetuning, advanced parameter-efficient finetuning (PEFT) methods [4, 16-18, 27, 48] have emerged. Compared to full finetuning, PEFT methods either introduce small modules into a fixed pretrained model or optimize only part of the pretrained model, demonstrating exceptional performance while keep" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.269, + 0.871, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.643 + ], + "angle": 0, + "content": "Figure 1. Robust Linear Initialization (RoLI), significantly improves adversarial robustness. RoLI, denoted in red, achieves an average \\(3.88\\%\\) increase in clean accuracy and a \\(2.44\\%\\) increase in robust accuracy compared to Random Linear Initialization (RanLI) of the linear head during adversarial finetuning, averaged across five downstream datasets. Our best-performing RoLI - Full-FT, which represents adversarial full finetuning with robust linear initialization, achieves a new state-of-the-art performance. We include six popular finetuning methods with Swin Transformer [28] and two existing state-of-the-art techniques for adversarial transfer learning: TWINS-AT [29] and AutoLoRA [43]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.657, + 0.652, + 0.672 + ], + "angle": 0, + "content": "ing storage usage low." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.903 + ], + "angle": 0, + "content": "While the success of transfer learning is evident, the robustness of downstream models has become a critical concern in real-world applications. For example, as suggested by previous studies, full finetuning will distort the pretrained features, leading to compromised robustness in terms of image corruptions and out-of-distribution (OOD) performance [26, 44]. In addition, adversarial robustness poses another significant challenge to real-world deployment, as a non-robust model demonstrates nearly zero accuracy under adversarial attacks [40]. Many approaches have been proposed to enhance adversarial robustness in transfer learning, including improving the robustness of pretraining through self-supervised techniques [7, 19] and preserving robustness from pretrained models during finetuning [29, 43]. However, most previous works [29, 43] apply" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24831" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.889, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.311, + 0.888, + 0.326 + ], + "angle": 0, + "content": "Figure 2. Illustration of six different finetuning techniques, arranged in descending order according to the number of tunable parameters." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.47, + 0.364 + ], + "angle": 0, + "content": "full finetuning for adversarial transfer learning, overlooking the significance of different finetuning methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.606 + ], + "angle": 0, + "content": "In this work, we comprehensively study six popular finetuning methods in adversarial transfer learning, as shown in Fig. 2. We discover that initialization, which includes 1) the backbone initialization (i.e., a pretrained model), and 2) the initialization of the linear head that adapts features to the target domain, plays a critical role in adversarial transfer learning. We start by comparing the performance of adversarial finetuning when initialized with either a robust or a standard pretrained model. Surprisingly, all PEFT methods fail or exhibit significantly inferior performance when initialized with a standard pretrained model compared to being initialized with a robust pretrained model. Furthermore, we observe that a large-scale pretrained model, such as CLIP [34], cannot alleviate this phenomenon, highlighting the critical role of robust pretraining in adversarial transfer learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.47, + 0.851 + ], + "angle": 0, + "content": "Given a robust pretrained model, surprisingly, we discover that adversarial linear probing outperforms other methods on certain datasets, e.g., Caltech256 [13] and Stanford Dogs [21]. We further demonstrate that this is mainly because linear probing excels in inheriting robustness from pretraining. Moreover, we identify the ability to adapt features to the specific target domain as a key factor influencing linear probing's success, supported by a strong correlation between transferred accuracy and robustness. Based on these insights, we introduce Robust Linear Initialization (RoLI), which initializes the model's linear head with the weights obtained from adversarial linear probing. With RoLI followed by adversarial finetuning methods, we maximize the inherited robustness along with a strong feature adaptation ability, resulting in improved performance. In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We comprehensively study six popular finetuning techniques for adversarial transfer learning. We discover that PEFT methods fail or exhibit significantly inferior perfor" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.334, + 0.89, + 0.364 + ], + "angle": 0, + "content": "mance when initialized with a standard pretrained model, even with adversarial finetuning on downstream data." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.365, + 0.892, + 0.454 + ], + "angle": 0, + "content": "- We demonstrate that adversarial linear probing excels in preserving robustness from a robust pretrained model. Building upon this insight, we propose Robust Linear Initialization (RoLI) for adversarial finetuning to maximally inherit robustness from pretraining and effectively adapt features through adversarial finetuning." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.455, + 0.892, + 0.53 + ], + "angle": 0, + "content": "- We demonstrate the effectiveness of RoLI across five downstream datasets. On average, RoLI improves the clean and robust accuracy by \\(3.88\\%\\) and \\(2.44\\%\\) compared with random initialization. This establishes a new state-of-the-art benchmark for adversarial transfer learning." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.365, + 0.892, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.555, + 0.65, + 0.57 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Finetuning in Transfer Learning. Transfer learning aims to finetune a pretrained model on downstream tasks to gain better performance [23, 45, 47]. Linear probing and full finetuning are often applied in the finetuning process. Given the increasing size of pretrained models, various Parameter Efficient Finetuning (PEFT) methods have been proposed. PEFT methods can effectively reduce the finetuning cost and alleviate overfitting since only a small number of parameters are updated [16, 17]. Specifically, Bias [3, 46] only updates the bias term, while Scaling & Shifting [27] performs the linear transformation to adapt the features. Different from both of them, Adapter [16, 32, 33], LoRA [17], and VPT [18] introduce extra learnable modules into the pretrained models in the finetuning stage. Although there are various finetuning methods proposed to improve the accuracy, it is still unclear what matters to the robustness on the downstream tasks. [25] points out that feature distortion in finetuning hurts the out-of-distribution robustness on downstream tasks, while we discover initialization plays a critical role in adversarial robustness on downstream tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24832" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.425 + ], + "angle": 0, + "content": "Adversarial Robustness in Transfer Learning. The research on adversarial robustness in transfer learning has been studied from two perspectives, namely, robust pretraining and robust finetuning. Concretely, robust pertaining aims to achieve adversarial robustness in the pertaining stage and finetune pretrained models on the downstream tasks without adversarial training [5, 7, 19, 39]. Besides, [38] demonstrates that the adversially pertaining also benefits standard performance on downstream tasks. In contrast, robust finetuning [29, 43] focuses on preserving the robustness of the pretrained model during the finetuning stage. For example, TWINS [29] incorporates a dual batch normalization in the model to keep the statistics of pretrained and finetuned datasets separately. And AutoLoRA [43] introduces a low-rank (LoRA) branch to disentangle clean and adversarial objectives. Existing works design various strategies to preserve the robustness from the pretrained model, but they simply apply full finetuning on downstream tasks. In this work, we study six different finetuning methods and introduce Robust Linear Initialization (RoLI) to enhance the adversarial robustness for different finetuning methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.441, + 0.206, + 0.458 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.467, + 0.47, + 0.543 + ], + "angle": 0, + "content": "In this section, we provide an overview of existing finetuning techniques, including full finetuning as well as five different PEFT methods, as illustrated in Fig. 2. Additionally, we introduce adversarial finetuning which integrates adversarial training during the finetuning stage." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.555, + 0.338, + 0.571 + ], + "angle": 0, + "content": "3.1. Existing Finetuning Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.58, + 0.469, + 0.64 + ], + "angle": 0, + "content": "In transfer learning, finetuning adapts the features from the pretrained domain to the target domain. In this section, we introduce six finetuning methods in descending order according to the number of tunable parameters." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.641, + 0.47, + 0.685 + ], + "angle": 0, + "content": "Full Finetune (Full-FT): We initialize the model from a pretrained model and finetune all its parameters on the downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.687, + 0.469, + 0.763 + ], + "angle": 0, + "content": "Adapter [16, 32, 33]: Adapter introduces a module after the MLP block in every layer. The adapter module consists of a down-sampling layer and an up-sampling layer, with a non-linear activation. During finetuning, we will update the adapter modules as well as the linear head." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.764, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Low-Rank Adaptation (LoRA) [17]: LoRA proposes to learn a residual from pretrained weight represented by two low-rank metrics. Specifically, we apply the LoRA branch on the query and value projection in the self-attention block. During finetuning, the pretrained model remains frozen while updates are applied to the LoRA branch and head." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Bias [3, 46]: We update the bias term and keep other parameters unchanged. Additionally, We also update the classification head (including weights and bias)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "Visual Prompt Tuning (VPT) [18]: VPT appends additional learnable tokens (embeddings), called prompts, into the input space of each attention layer in vision transformers. Specifically, we use the structure of VPT-Deep, where every layer introduces a fixed number of trainable prompts independently. During the finetuning stage, we will tune both the prompts and the linear head on downstream tasks while freezing the entire pretrained backbone. We refer readers to [18] for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.257 + ], + "angle": 0, + "content": "Linear Probing (Linear): We only finetune the classification head on the downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.267, + 0.719, + 0.284 + ], + "angle": 0, + "content": "3.2. Adversarial Finetuning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Adversarial training corresponds to a min-max optimization problem [31]. In the context of adversarial finetuning, we can formulate the optimization problem as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.347, + 0.892, + 0.381 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\hat {\\theta}} \\mathbb {E} _ {(x, y) \\sim D} \\left[ \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\varepsilon} \\mathcal {L} (x + \\delta , y; \\theta \\cup \\hat {\\theta}) \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.893, + 0.621 + ], + "angle": 0, + "content": "where \\(\\theta\\) and \\(\\hat{\\theta}\\) represent the frozen parameters and tunable parameters in model parameters respectively. For example, in adversarial full finetuning, \\(\\hat{\\theta}\\) stands for all the model parameters as we update all of them during the finetuning stage. In contrast, in adversarial VPT, \\(\\hat{\\theta}\\) denotes the extra prompts and linear head while \\(\\theta\\) represents the frozen parameters in the backbone architecture. In addition, \\(\\delta\\) represents adversarial perturbation, whose \\(\\| \\cdot \\|_{\\infty}\\) is bounded by \\(\\varepsilon\\). During adversarial finetuning, we use the pretrained model together with additional modules introduced by PEFT methods to generate adversarial examples, while only updating the tunable parameters \\(\\hat{\\theta}\\) for each method. If not otherwise specified, we use PGD-7 with \\(\\varepsilon = 8 / 255\\) and step size \\(\\alpha = 2 / 255\\) to generate adversarial attacks during adversarial finetuning." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.634, + 0.809, + 0.65 + ], + "angle": 0, + "content": "4. Robust Pretrained Model Matters" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Previous research [29, 39] suggests that although standard pretraining results in performance inferior to that of adversarially robust pretraining, it can still yield an adversarially robust model with adversarial finetuning. In this section, our goal is to investigate the significance of pretraining in PEFT methods. Specifically, we seek to address the question: Is an adversarially robust model necessary for PEFT methods?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To answer this question, we initialize model parameters using two different pretrained models. One is a standard pretrained model on ImageNet-1k [11] while the other is adversarially pretrained with PGD [31] attacks. These pretrained models are off-the-shelf and their specifics are outlined in the supplementary material. Following initialization, we perform adversarial finetuning on downstream tasks. As shown in Fig. 3, we evaluate six adversarial" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24833" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.098, + 0.487, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.099, + 0.685, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.099, + 0.882, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.31, + 0.894, + 0.368 + ], + "angle": 0, + "content": "Figure 3. PEFT methods fail or exhibit significantly degraded performance with a standard pretrained model (in blue and gray). Models finetuned from a robust pretrained model (in red) exhibit high accuracy and robustness, as they are consistently positioned in the top-right corner. Among six finetuning techniques, Full-FT outperforms others when starting with a standard pretrained model; however, it falls short of other methods when starting with a robust pretrained model. The specific numerical results are provided in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.435 + ], + "angle": 0, + "content": "finetuning techniques across two model architectures (ViT-B [12] and Swin-B [28]) on the CIFAR10 [24] and Caltech256 [13]. The adversarial robustness is measured with PGD-10 bounded with \\(\\varepsilon = 8 / 255\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.471, + 0.754 + ], + "angle": 0, + "content": "First, we find that initializing the model with an adversarially robust pretrained model can significantly improve adversarial robustness on downstream tasks. This consistently holds across all the experimental settings we have evaluated, e.g., 6 adversarial finetuning techniques across 2 model architectures on 2 different datasets. More surprisingly, we discover that a robust pretrained model is especially important for PEFT methods, as they struggle to achieve satisfactory adversarial robustness when initialized with a standard pretrained model. For example, all the PEFT methods fail to achieve adversarial robustness higher than \\(20\\%\\) on the Caltech256 dataset. In addition, adversarial linear probing can only achieve \\(< 5\\%\\) adversarial robustness on both datasets when initiated with a standard pretrained model. This strongly suggests that adversarial PEFT can not sufficiently infuse adversarial robustness in the finetuning stage if the model starts with a non-robust pretrained model. Finally, we observe that Full-FT consistently outperforms other finetuning methods with a non-robust pretraining, indicating the preference for using full finetuning in the absence of robust pretraining." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Does Pretraining on a Larger Dataset Help Adversarial Finetuning? Due to the high computational cost of adversarial pretraining, we aim to investigate whether a model pretrained on a larger dataset could substitute for the necessity of an adversially robust pretrained model. To this end, we initialize the model with an off-the-shelf large-scale pretrained model, CLIP [34], and perform the same adversarial finetuning techniques on downstream tasks. Fig. 3 demonstrates that a standard pretrained model on a larger dataset," + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.373, + 0.885, + 0.5 + ], + "angle": 0, + "content": "
MethodsViTSwin
CleanPGDCleanPGD
RanLI - Full-FT80.1744.1585.1954.13
RanLI - Adapter83.1449.5785.2454.22
RanLI - LoRa82.6350.7283.5253.57
RanLI - Bias82.6950.0784.8854.69
RanLI - VPT82.0950.5284.9955.23
RanLI - Linear81.8942.0282.9845.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.51, + 0.893, + 0.566 + ], + "angle": 0, + "content": "Table 1. PEFT methods, excluding Linear, demonstrate strong performance on average across CIFAR10 and Caltech256 datasets. With adversarial finetuning, PEFT methods outperform Full-FT and Linear with RanLI. Full results are available in ??" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.696 + ], + "angle": 0, + "content": "like CLIP, does not yield higher robustness compared to the non-robust ImageNet-1k pretrained model. It notably lags far behind the robustness achieved by a smaller-scale robust pretrained model, such as one trained on ImageNet-1k. This observation implies that opting for a smaller yet robust pretrained model proves to be a more effective strategy for attaining adversarial robustness in downstream tasks compared to using a larger, non-robust pretrained model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.708, + 0.836, + 0.725 + ], + "angle": 0, + "content": "5. Initialization Matters For Finetuning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.733, + 0.894, + 0.794 + ], + "angle": 0, + "content": "In the previous section, we understand the necessity of initializing a model with an adversarially robust pretrained model. We now ask: given a robust pretrained model, what matters for adversarial finetuning?" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.762, + 0.817 + ], + "angle": 0, + "content": "5.1. Random Linear Initialization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To answer this question, we first evaluate the adversarial robustness of six adversarial finetuning techniques. To adapt the robust pretrained model to the downstream tasks, we initialize the linear head with Random Linear Initialization (RanLI) following [39]. We perform adversarial finetuning" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24834" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.099, + 0.889, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.893, + 0.357 + ], + "angle": 0, + "content": "Figure 4. Linear probing with adversarial finetuning surpasses other methods on Caltech256. With standard finetuning, the PEFT methods exhibit inherited robustness (Robustness \\(>0\\)) from the pretraining. Notably, linear probing surpasses the other methods by a substantial margin in robustness while maintaining similar clean data accuracy on Caltech256. Additionally, adversarial training during finetuning is effective in enhancing all methods' robustness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.469, + 0.426 + ], + "angle": 0, + "content": "across two model architectures, e.g., ViT and Swin, on the CIFAR10 and Caltech256 datasets. Additional details regarding the training process can be found in Sec. 5.4 and in supplementary ??" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.469, + 0.501 + ], + "angle": 0, + "content": "As shown in Tab. 1, PEFT methods except Linear consistently demonstrate strong average results with adversarial finetuning. In particular, LoRA achieves the highest average robustness at \\(50.72\\%\\) for ViT, while VPT performs exceptionally well with \\(55.23\\%\\) on Swin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.469, + 0.607 + ], + "angle": 0, + "content": "Looking more closely at the performance on each individual dataset in Fig. 4, we observe that adversarial linear probing achieves the strongest robustness on Caltech256. This is rather surprising, given that linear probing has the lowest computational cost compared to others and never outperforms other finetuning methods on any single dataset in standard transfer learning [4, 6, 18]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.614, + 0.462, + 0.631 + ], + "angle": 0, + "content": "5.2. Why does Adversarial Linear Probing Work?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.469, + 0.789 + ], + "angle": 0, + "content": "To understand the remarkable robustness achieved by adversarial linear probing, we then ask: what contributes to adversarial robustness on the downstream tasks given a robust pretrained model? We hypothesize that there are two confounding factors: 1) the robustness inherited from pretrained models, and 2) the robustness achieved by adversarial finetuning. To validate our hypothesis, we conduct a comparative analysis of adversarial robustness in downstream tasks while using standard finetuning versus adversarial finetuning, given the same robust pretrained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Robustness Inherited from Pretrained Models. In this section, we focus on standard finetuning as it does not bring in additional adversarial robustness to downstream tasks. Therefore, the adversarial robustness achieved during standard finetuning primarily arises from the robust pretrained model, representing the capability of each method to preserve robustness from the pretrained model. As shown in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Fig. 4, all standard finetuning methods (colored in blue) achieve non-zero robustness under PGD-10 attacks. This supports our hypothesis that robustness inherited from the pretrained model contributes to the robustness in downstream tasks. In addition, linear probing significantly outperforms all other standard finetuning methods in preserving robustness from the pretrained model. For example, linear probing exhibits significantly stronger robustness (at least \\(20\\%\\) higher) compared to other methods while maintaining similar accuracy on Caltech256. We explain this as linear probing avoids distorting the robust features inherited from the pretrained model by only updating the linear head. However, on CIFAR10, linear probing does not exhibit a significant advantage over robustness and displays lower clean accuracy compared to others. This is likely due to its limited capability to adapt features from the pretrained source domain to the downstream target domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Robustness Achieved by Adversarial Finetuning. By comparing adversarial robustness achieved by standard finetuning (colored in blue) and adversarial finetuning (colored in red) in Fig. 4, we can see the extra robustness gain achieved by adversarial training during the finetuning stage. Except for Linear, adversarial finetuning contributes a significant portion of their robustness to the final robustness. For example, Full-FT on Swin, achieving a \\(99\\%\\) final robustness on Caltech256 through adversarial finetuning. Even VPT, which has the fewest tunable parameters after Linear, demonstrates a \\(78\\%\\) final robustness from adversarial finetuning. On the contrary, Linear only achieved a final robustness of \\(13\\%\\) from this stage, with the primal robustness originating from the pretraining model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Taken together, we validate our hypothesis that both robustness inherited from the pretrained model and achieved through adversarial finetuning contribute to adversarial robustness on downstream tasks. In addition, we conclude" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24835" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "that the exceptional robustness exhibited by adversarial linear probing is mainly because linear probing excels in preserving robustness from pretrained models compared to others, which primarily obtain their robustness from adversarial training during finetuning stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.178, + 0.469, + 0.21 + ], + "angle": 0, + "content": "5.3. Transferred Robustness Correlates with Transferred Accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.469, + 0.444 + ], + "angle": 0, + "content": "As we have seen in Fig. 4, adversarial linear probing achieves the highest adversarial robustness on Caltech256 but falls far behind other methods on CIFAR10. This performance discrepancy across different datasets raises a question: how can we estimate if adversarial linear probing achieves the best robustness? Based on our analysis in Sec. 5.2, where the robustness of adversarial linear probing primarily arises from preserving the robustness in the pretrained model, we hypothesize that the transferred robustness of adversarial linear probing is highly correlated with the transferred accuracy of standard linear probing. This suggests that if standard linear probing successfully adapts the features from the pretrained source domain to the downstream target domain, adversarial linear probing will similarly preserve the robustness in the pretrained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.52 + ], + "angle": 0, + "content": "To validate this, we define transferred accuracy of standard linear probing \\((\\mathrm{acc}_{std}^T)\\) and transferred robustness of adversarial linear probing \\((\\mathrm{rob}_{adv}^T)\\) as follows, using full finetune as a baseline to normalize the performance across different datasets:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.533, + 0.469, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\operatorname {a c c} _ {s t d} ^ {T} = \\frac {\\operatorname {a c c} \\left(L P _ {s t d}\\right) - \\operatorname {a c c} \\left(F T _ {s t d}\\right)}{\\operatorname {a c c} \\left(F T _ {s t d}\\right)} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.576, + 0.469, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\operatorname {r o b} _ {a d v} ^ {T} = \\frac {\\operatorname {r o b} \\left(L P _ {a d v}\\right) - \\operatorname {r o b} \\left(F T _ {a d v}\\right)}{\\operatorname {r o b} \\left(F T _ {a d v}\\right)} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.469, + 0.722 + ], + "angle": 0, + "content": "where \\(\\mathrm{acc}(\\cdot)\\) and \\(\\mathrm{rob}(\\cdot)\\) denote the accuracy and robustness of each method, respectively. \\(FT_{std}\\) and \\(LP_{std}\\) represent standard full finetune and standard linear probing whereas \\(FT_{adv}\\) and \\(LP_{adv}\\) stand for their respective adversarial counterparts. We trained 51 models with different hyper-parameter settings across five datasets and present transferred accuracy and robustness in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.469, + 0.904 + ], + "angle": 0, + "content": "In Fig. 5, the transferred robustness of adversarial linear probing is strongly correlated with the transferred accuracy of standard linear probing, with a high Pearson correlation coefficient (0.896). When the transferred accuracy approaches or surpasses 0, the transferred robustness becomes positive, indicating the improved performance of adversarial linear probing over adversarial fully finetuning. This strong correlation validates our hypothesis that if standard linear probing successfully adapts features from the pretrained to the target domain, its adversarial counterpart is capable of effectively achieving adversarial robustness on downstream tasks." + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.091, + 0.865, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.306, + 0.892, + 0.349 + ], + "angle": 0, + "content": "Figure 5. Transferred robustness of adversarial linear probing strongly correlates with transferred accuracy of standard linear probing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.357, + 0.807, + 0.373 + ], + "angle": 0, + "content": "5.4. Robust Linear Initialization (RoLI)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Based on our observation that linear probing can outperform other methods when it effectively adapts features to the target domain, we propose Robust Linear Initialization (denoted as RoLI) for adversarial finetuning. Specifically, we initialize the linear head of a robust pretrained model with weights obtained through adversarial linear probing instead of random initialization. Then, we perform adversarial finetuning, using either full finetune or PEFT methods. Since adversarial linear probing excels in preserving robustness from a pretrained model, RoLI provides a more robust initialization for subsequent adversarial finetuning, maximizing the robustness inherited from a robust pretrained model. In addition, the following adversarial finetuning can further enhance robustness by introducing additional robustness through adversarial training. In the following sections, we will evaluate the effectiveness of RoLI applied to four different adversarial finetuning methods across five different datasets and demonstrate it achieves new state-of-the-art robustness in adversarial transfer learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.892, + 0.859 + ], + "angle": 0, + "content": "Datasets. In our experiments, we use five datasets: CIFAR10 [24], CIFAR100 [24], Caltech256 [13], CaltechUCSD Birds-200-2011 (CUB200) [42], and Stanford Dogs (Dogs) [21]. For low-resolution image datasets like CIFAR10 and CIFAR100, we resize the image to match the model input shape. For high-resolution image datasets, we apply random resizing and cropping in training and center crop in testing. It's important to note that we integrate the resizing and normalization process directly into the model since the attacker does not have access to pre-processed images. Additional details are provided in the supplementary ??" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Methods. We provide the results from TWINS-AT [29] AutoLoRa [43] as baselines. We proceed to assess six fine" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24836" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.89, + 0.313 + ], + "angle": 0, + "content": "
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
CleanPGDCleanPGDCleanPGDCleanPGDCleanPGDCleanPGD
TWINS-AT [29]91.2452.7370.7231.0876.8648.4068.0929.2464.9820.5874.3836.41
AutoLoRa [43]86.9357.1666.2035.2569.8547.8262.7831.0762.3325.3269.6239.32
RanLI - Full-FT93.0259.1274.3635.6277.3549.1370.8331.5565.8524.7976.2840.04
RanLI - Adapter90.2355.7071.5734.7480.2452.7359.6726.7387.9842.2477.9442.43
RanLI - LoRA90.0256.8871.9834.8377.0250.2564.7429.6584.6339.2477.6842.17
RanLI - Bias90.2556.9471.5036.7279.5052.4366.6929.8887.4142.7579.0743.74
RanLI - VPT90.2457.3872.3735.6079.7453.0761.9426.4686.3443.1078.1343.12
RanLI - Linear84.1637.3067.6525.4681.7954.4769.8824.5691.5545.4579.0137.45
RoLI - Full-FT94.1860.8576.2537.3883.7855.4274.2832.0391.5545.5784.0146.25
RoLI - Adapter90.3155.6971.7534.3381.7454.3264.2025.2292.0247.1280.0043.34
RoLI - LoRA92.2358.6272.8735.1881.7954.5068.8826.7791.2046.7681.3944.37
RoLI - Bias91.8358.3972.1735.1781.7854.4968.1425.7091.5247.2781.0944.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.323, + 0.893, + 0.365 + ], + "angle": 0, + "content": "Table 2. RoLI significantly improves the performance and achieves SOTA across five image classification tasks. Robust Linear Initialization (RoLI) enhances robustness by \\(3.88\\%\\) and clean accuracy by \\(2.44\\%\\) on average compared to Random Initialization (RanLI). Notably, RoLI - Full-FT achieves the best overall performance, with an accuracy of \\(84.01\\%\\) and \\(46.25\\%\\) robustness." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.371, + 0.472, + 0.525 + ], + "angle": 0, + "content": "
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
RanLI - Full-FT54.931.862.649.742.548.3
RanLI - Adapter50.829.266.740.368.551.1
RanLI - LoRa53.029.062.844.763.350.6
RanLI - Bias52.331.065.846.267.352.5
RanLI - VPT52.329.766.340.367.351.2
RanLI - Linear26.618.465.740.473.544.9
RoLI - Full-FT56.332.770.452.173.557.0
RoLI - Adapter51.129.165.840.675.252.4
RoLI - LoRa53.930.065.744.674.353.7
RoLI - Bias53.929.865.743.574.853.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.632 + ], + "angle": 0, + "content": "Table 3. RoLI consistently outperforms RanLI under AutoAttack. Note, we use \\(\\varepsilon = 8 / 255\\) attack for CIFAR10, CIFAR100, and \\(\\varepsilon = 4 / 255\\) for Caltech256, CUB200 and Stanford Dogs. RoLI shows an average 3.53 AA gain compared with RanLI, and notably, RoLI - Full-FT surpasses other methods by achieving a robustness of 57.0 under AutoAttack. The clean accuracy is illustrated in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.766 + ], + "angle": 0, + "content": "tuning techniques introduced in Sec. 3.1 with random initialization. We use Swin Transformer [28] as a backbone architecture for our experiments, whereas TWINS and AutoLoRa use ResNet50 [14]. We apply RoLI to Full-FT, Bias, Adapter, and LoRa. We initialize the newly introduced modules in Adapter and LoRA with zero to ensure that they start with robust linear probing without distorting the robust features preserved in the pretrained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Training Details. We use the same optimizer, AdamW [30], and a cosine scheduler with warm-up for all finetuning methods. To determine the optimal learning rate and weight decay values, we conduct a grid search, and the ranges of hyper-parameters along with the optimal combinations can be found in the supplementary ??. We keep method-specific hyper-parameters constant across all datasets. For instance, we set the prompt" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.37, + 0.891, + 0.525 + ], + "angle": 0, + "content": "
Methodsε = 8/255ε = 4/255
RanLI - Full-FT20.1042.50
RanLI - Adapter36.3068.50
RanLI - LoRa32.4063.30
RanLI - Bias35.9067.30
RanLI - VPT34.4067.30
RanLI - Linear30.9073.50
RoLI - Full-FT30.9073.50
RoLI - Adapter37.0075.20
RoLI - LoRa38.4074.30
RoLI - Bias38.2074.80
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.536, + 0.893, + 0.634 + ], + "angle": 0, + "content": "Table 4. RoLI consistently improves adversarial robustness even against \\(\\varepsilon = 8 / 255\\) AutoAttack. RanLI - Linear performs well under \\(\\varepsilon = 4 / 255\\) AutoAttack, but poorly under \\(\\varepsilon = 8 / 255\\) AutoAttack on Stanford Dogs. This discrepancy demonstrates that adversarial linear probing obtains its robustness mainly from the pretrained model, whereas other methods obtain robustness mainly from adversarial finetuning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.894, + 0.827 + ], + "angle": 0, + "content": "length to 10 for the VPT method. To avoid adversarial overfitting [37], we apply early stopping with the epoch that has the best performance on the validation set. During adversarial finetuning, we utilize the PGD-7 attack with \\(\\varepsilon = 8 / 255\\) and a step size of \\(\\alpha = 2 / 255\\). When reporting test accuracy and robustness, we evaluate the models under a PGD-10 attack with \\(\\varepsilon = 8 / 255\\). Additionally, we report the performance under AutoAttack (AA), which is an ensemble attack and provides a more reliable approach to evaluate the adversarial robustness. We follow the standard AutoAttack setting, i.e., untargeted APGDCE, targeted APGD-DLR, targeted FAB [8], and Square Attack [1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "PGD-10 Results. Looking at Random Initialization (RanLI) in Tab. 2, the same trend holds as in Sec. 5.1: 1) PEFT methods except linear probing exhibit strong average results across five different datasets, with Bias achiev" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24837" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.077, + 0.434, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.266, + 0.47, + 0.364 + ], + "angle": 0, + "content": "Figure 6. Trade-off between speed and robustness. We conduct the speed test on Stanford Dogs with random linear initialization (RanLI), logistic regression linear initialization (RegLI), standard linear initialization (StdLI), and robust linear initialization (RoLI). RoLI achieves the best performance at the cost of increased training time. Meanwhile, both RegLI and StdLI can improve their performance without incurring substantial time costs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.47, + 0.434 + ], + "angle": 0, + "content": "ing the best performance (79.25% accuracy and 43.58% robustness). 2) Linear probing achieves the highest robustness on Caltech256 and Stanford Dogs, although it falls behind others on the remaining three datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.471, + 0.614 + ], + "angle": 0, + "content": "Compared to RandLI, we can observe from Tab. 2 that RoLI significantly enhances the robustness on Caltech256 and Stanford Dogs for all finetuning methods. In particular, RoLI - Full-FT achieves a robustness improvement of \\(6.29\\%\\) on Caltech256 and \\(20.78\\%\\) on Stanford Dogs. On other datasets where adversarial linear probing with RanLI does not outperform others, RoLI performs comparable or even better than RanLI. This strongly supports that a robust initialization of the linear head is critical in adversarial transfer learning. Lastly, our RoLI - Full-FT achieves the highest performance across five datasets and sets a new state-of-the-art benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.748 + ], + "angle": 0, + "content": "AutoAttack Results. We extend our evaluation to Stanford Dogs using \\(\\varepsilon = 8 / 255\\) and \\(\\varepsilon = 4 / 255\\), as illustrated in Tab. 4. Interestingly, we observe that adversarial linear probing outperforms other methods under \\(\\varepsilon = 4 / 255\\) attack but underperforms when tested against \\(\\varepsilon = 8 / 255\\) adversarial attacks. We conjecture that the pretrained model lacks robustness against \\(\\varepsilon = 8 / 255\\) attacks as it is trained using \\(\\varepsilon = 4 / 255\\) adversarial attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.856 + ], + "angle": 0, + "content": "This performance disparity confirms that adversarial linear probing inherently derives robustness from pretraining, whereas other methods predominantly achieve robustness from adversarial finetuning. Notably, RoLI consistently improves adversarial robustness even against \\(\\varepsilon = 8 / 255\\) attacks, further validating the importance of a robust linear initialization for adversarial transfer learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To maintain consistency with the pre-training, we follow the conventional settings [9, 10] to set \\(\\varepsilon = 8 / 255\\) attack for low-resolution datasets (CIFAR10, CIFAR100) and" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.09, + 0.871, + 0.178 + ], + "angle": 0, + "content": "
StdLI -CIFAR-10Caltech-256
CleanPGDCleanPGD
Full-FT93.34(-0.84)59.34(-1.51)83.23(-0.55)52.85(-2.57)
Bias93.34(-0.04)58.12(-0.27)82.93(+1.15)52.93(-1.56)
Adapter90.08(-0.23)55.19(-0.50)82.72(+0.98)53.01(-1.31)
LoRa90.71(-1.52)58.17(-0.45)82.87(+1.08)51.47(-3.03)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.181, + 0.89, + 0.209 + ], + "angle": 0, + "content": "Table 5. StdLI is less robust than RoLI. The values in parentheses denote the performance gap (StdLI - RoLI)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.218, + 0.892, + 0.324 + ], + "angle": 0, + "content": "\\(\\varepsilon = 4 / 255\\) attack for high-resolution datasets (Caltech256, CUB200, Stanford Dogs). Tab. 3 demonstrates the robustness under AutoAttack and the clean accuracy is illustrated in Tab. 2. RoLI exhibits higher robustness over RanLI, demonstrating an average 3.53 AA gain. Notably, RoLI - Full-FT achieves a robustness of 57.0, surpassing other methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.339, + 0.613, + 0.354 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.364, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Comparison between RoLI and StdLI. Standard Linear Initialization (StdLI) refers to the use of a simple linear probing to initialize the head, while RoLI uses adversarial linear probing. In Tab. 5, we compare the performance of RoLI and StdLI on CIFAR-10 and Caltech-256. We observe that StdLI exhibits lower performance compared to RoLI, with a robustness decrease of 2.48 across three datasets, highlighting the effectiveness of RoLI." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.487, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Robustness vs. Speed. Since robust linear initialization involves a two-step adversarial training process, it tends to be considerably slower than adversarial fine-tuning with random initialization. In this section, we show a trade-off between robustness and speed by obtaining the initialization from four different approaches: adversarial linear probing (RoLI), standard linear probing (StdLI), logistic regression (RegLI), and randomization (RanLI). From Fig. 6, it's evident that both RegLI and StdLI enhance robustness compared to random linear initialization within an acceptable time cost. In addition, RoLI achieves the highest performance but at the expense of slower speed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.683, + 0.619, + 0.699 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.708, + 0.892, + 0.858 + ], + "angle": 0, + "content": "This paper systematically investigates how to achieve adversarial robustness in downstream tasks. We highlight the necessity of an adversially robust pretraining. Given a robust pretrained model, we propose to use robust linear initialization (RoLI) followed by adversarial full finetuning or PEFT methods to achieve the best performance. We demonstrate that RoLI outperforms random linear initialization across five image classification tasks. We hope the insights from this study greatly advance research aimed at enhancing adversarial robustness in downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.859, + 0.892, + 0.888 + ], + "angle": 0, + "content": "Acknowledgment. We thank Chenhe Gu and Xuan Yang for the valuable discussion and insightful feedback." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24838" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.183 + ], + "angle": 0, + "content": "[1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In European conference on computer vision, pages 484-501. 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Neural prompt search. arXiv preprint arXiv:2206.04673, 2022. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24840" + } + ] +] \ No newline at end of file diff --git a/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_origin.pdf b/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e375fb07ace64026208ded6a7dce64f7a118f7e3 --- /dev/null +++ b/2024/Initialization Matters for Adversarial Transfer Learning/22e1735b-5de4-4162-9aa3-d030e26b0bff_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:58d67b4306447f86e46ca172b85b287aff2fbef334e7de7280d3ef40fd26ea09 +size 445370 diff --git a/2024/Initialization Matters for Adversarial Transfer Learning/full.md b/2024/Initialization Matters for Adversarial Transfer Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e5139fc8609743c322ce2bdcba82aaf059c2e9f4 --- /dev/null +++ b/2024/Initialization Matters for Adversarial Transfer Learning/full.md @@ -0,0 +1,263 @@ +# Initialization Matters for Adversarial Transfer Learning + +Andong Hua1 Jindong Gu2 Zhiyu Xue1 Nicholas Carlini3 Eric Wong4 Yao Qin1,3 +1University of California, Santa Barbara 2University of Oxford +3Google 4University of Pennsylvania + +# Abstract + +With the prevalence of the Pretraining-Finetuning paradigm in transfer learning, the robustness of downstream tasks has become a critical concern. In this work, we delve into adversarial robustness in transfer learning and reveal the critical role of initialization, including both the pretrained model and the linear head. First, we discover the necessity of an adversially robust pretrained model. Specifically, we reveal that with a standard pretrained model, Parameter-Efficient Finetuning (PEFT) methods either fail to be adversially robust or continue to exhibit significantly degraded adversarial robustness on downstream tasks, even with adversarial training during finetuning. Leveraging a robust pretrained model, surprisingly, we observe that a simple linear probing can outperform full finetuning and other PEFT methods with random initialization on certain datasets. We further identify that linear probing excels in preserving robustness from the robust pretraining. Based on this, we propose Robust Linear Initialization (RoLI) for adversarial finetuning, which initializes the linear head with the weights obtained by adversarial linear probing to maximally inherit the robustness from pretraining. Across five different image classification datasets, we demonstrate the effectiveness of RoLI and achieve new state-of-the-art results. Our code is available at https://github.com/DongXzz/RoLI. + +# 1. Introduction + +With the advancement of large-scale deep learning models, the Pretraining-Finetuning paradigm takes a more dominant role compared to training from scratch across various tasks [2], including computer vision [12, 15, 22, 28], natural language processing [20, 36, 41], and speech recognition [35]. Under the paradigm of Pretraining-Finetuning, advanced parameter-efficient finetuning (PEFT) methods [4, 16-18, 27, 48] have emerged. Compared to full finetuning, PEFT methods either introduce small modules into a fixed pretrained model or optimize only part of the pretrained model, demonstrating exceptional performance while keep + +![](images/bdb995711b372ec4a843644134648080b6bacdb8e06d66f82a6449d0925a238d.jpg) +Figure 1. Robust Linear Initialization (RoLI), significantly improves adversarial robustness. RoLI, denoted in red, achieves an average $3.88\%$ increase in clean accuracy and a $2.44\%$ increase in robust accuracy compared to Random Linear Initialization (RanLI) of the linear head during adversarial finetuning, averaged across five downstream datasets. Our best-performing RoLI - Full-FT, which represents adversarial full finetuning with robust linear initialization, achieves a new state-of-the-art performance. We include six popular finetuning methods with Swin Transformer [28] and two existing state-of-the-art techniques for adversarial transfer learning: TWINS-AT [29] and AutoLoRA [43]. + +# ing storage usage low. + +While the success of transfer learning is evident, the robustness of downstream models has become a critical concern in real-world applications. For example, as suggested by previous studies, full finetuning will distort the pretrained features, leading to compromised robustness in terms of image corruptions and out-of-distribution (OOD) performance [26, 44]. In addition, adversarial robustness poses another significant challenge to real-world deployment, as a non-robust model demonstrates nearly zero accuracy under adversarial attacks [40]. Many approaches have been proposed to enhance adversarial robustness in transfer learning, including improving the robustness of pretraining through self-supervised techniques [7, 19] and preserving robustness from pretrained models during finetuning [29, 43]. However, most previous works [29, 43] apply + +![](images/ef16f8535229e585afe9d4bb6e0d45a2df09d73369404356bca7632c1b1826c5.jpg) +Figure 2. Illustration of six different finetuning techniques, arranged in descending order according to the number of tunable parameters. + +full finetuning for adversarial transfer learning, overlooking the significance of different finetuning methods. + +In this work, we comprehensively study six popular finetuning methods in adversarial transfer learning, as shown in Fig. 2. We discover that initialization, which includes 1) the backbone initialization (i.e., a pretrained model), and 2) the initialization of the linear head that adapts features to the target domain, plays a critical role in adversarial transfer learning. We start by comparing the performance of adversarial finetuning when initialized with either a robust or a standard pretrained model. Surprisingly, all PEFT methods fail or exhibit significantly inferior performance when initialized with a standard pretrained model compared to being initialized with a robust pretrained model. Furthermore, we observe that a large-scale pretrained model, such as CLIP [34], cannot alleviate this phenomenon, highlighting the critical role of robust pretraining in adversarial transfer learning. + +Given a robust pretrained model, surprisingly, we discover that adversarial linear probing outperforms other methods on certain datasets, e.g., Caltech256 [13] and Stanford Dogs [21]. We further demonstrate that this is mainly because linear probing excels in inheriting robustness from pretraining. Moreover, we identify the ability to adapt features to the specific target domain as a key factor influencing linear probing's success, supported by a strong correlation between transferred accuracy and robustness. Based on these insights, we introduce Robust Linear Initialization (RoLI), which initializes the model's linear head with the weights obtained from adversarial linear probing. With RoLI followed by adversarial finetuning methods, we maximize the inherited robustness along with a strong feature adaptation ability, resulting in improved performance. In summary, our contributions are as follows: + +- We comprehensively study six popular finetuning techniques for adversarial transfer learning. We discover that PEFT methods fail or exhibit significantly inferior perfor + +mance when initialized with a standard pretrained model, even with adversarial finetuning on downstream data. + +- We demonstrate that adversarial linear probing excels in preserving robustness from a robust pretrained model. Building upon this insight, we propose Robust Linear Initialization (RoLI) for adversarial finetuning to maximally inherit robustness from pretraining and effectively adapt features through adversarial finetuning. +- We demonstrate the effectiveness of RoLI across five downstream datasets. On average, RoLI improves the clean and robust accuracy by $3.88\%$ and $2.44\%$ compared with random initialization. This establishes a new state-of-the-art benchmark for adversarial transfer learning. + +# 2. Related Works + +Finetuning in Transfer Learning. Transfer learning aims to finetune a pretrained model on downstream tasks to gain better performance [23, 45, 47]. Linear probing and full finetuning are often applied in the finetuning process. Given the increasing size of pretrained models, various Parameter Efficient Finetuning (PEFT) methods have been proposed. PEFT methods can effectively reduce the finetuning cost and alleviate overfitting since only a small number of parameters are updated [16, 17]. Specifically, Bias [3, 46] only updates the bias term, while Scaling & Shifting [27] performs the linear transformation to adapt the features. Different from both of them, Adapter [16, 32, 33], LoRA [17], and VPT [18] introduce extra learnable modules into the pretrained models in the finetuning stage. Although there are various finetuning methods proposed to improve the accuracy, it is still unclear what matters to the robustness on the downstream tasks. [25] points out that feature distortion in finetuning hurts the out-of-distribution robustness on downstream tasks, while we discover initialization plays a critical role in adversarial robustness on downstream tasks. + +Adversarial Robustness in Transfer Learning. The research on adversarial robustness in transfer learning has been studied from two perspectives, namely, robust pretraining and robust finetuning. Concretely, robust pertaining aims to achieve adversarial robustness in the pertaining stage and finetune pretrained models on the downstream tasks without adversarial training [5, 7, 19, 39]. Besides, [38] demonstrates that the adversially pertaining also benefits standard performance on downstream tasks. In contrast, robust finetuning [29, 43] focuses on preserving the robustness of the pretrained model during the finetuning stage. For example, TWINS [29] incorporates a dual batch normalization in the model to keep the statistics of pretrained and finetuned datasets separately. And AutoLoRA [43] introduces a low-rank (LoRA) branch to disentangle clean and adversarial objectives. Existing works design various strategies to preserve the robustness from the pretrained model, but they simply apply full finetuning on downstream tasks. In this work, we study six different finetuning methods and introduce Robust Linear Initialization (RoLI) to enhance the adversarial robustness for different finetuning methods. + +# 3. Background + +In this section, we provide an overview of existing finetuning techniques, including full finetuning as well as five different PEFT methods, as illustrated in Fig. 2. Additionally, we introduce adversarial finetuning which integrates adversarial training during the finetuning stage. + +# 3.1. Existing Finetuning Methods + +In transfer learning, finetuning adapts the features from the pretrained domain to the target domain. In this section, we introduce six finetuning methods in descending order according to the number of tunable parameters. + +Full Finetune (Full-FT): We initialize the model from a pretrained model and finetune all its parameters on the downstream tasks. + +Adapter [16, 32, 33]: Adapter introduces a module after the MLP block in every layer. The adapter module consists of a down-sampling layer and an up-sampling layer, with a non-linear activation. During finetuning, we will update the adapter modules as well as the linear head. + +Low-Rank Adaptation (LoRA) [17]: LoRA proposes to learn a residual from pretrained weight represented by two low-rank metrics. Specifically, we apply the LoRA branch on the query and value projection in the self-attention block. During finetuning, the pretrained model remains frozen while updates are applied to the LoRA branch and head. + +Bias [3, 46]: We update the bias term and keep other parameters unchanged. Additionally, We also update the classification head (including weights and bias). + +Visual Prompt Tuning (VPT) [18]: VPT appends additional learnable tokens (embeddings), called prompts, into the input space of each attention layer in vision transformers. Specifically, we use the structure of VPT-Deep, where every layer introduces a fixed number of trainable prompts independently. During the finetuning stage, we will tune both the prompts and the linear head on downstream tasks while freezing the entire pretrained backbone. We refer readers to [18] for more details. + +Linear Probing (Linear): We only finetune the classification head on the downstream tasks. + +# 3.2. Adversarial Finetuning + +Adversarial training corresponds to a min-max optimization problem [31]. In the context of adversarial finetuning, we can formulate the optimization problem as follows: + +$$ +\min _ {\hat {\theta}} \mathbb {E} _ {(x, y) \sim D} \left[ \max _ {\| \delta \| _ {\infty} \leq \varepsilon} \mathcal {L} (x + \delta , y; \theta \cup \hat {\theta}) \right] \tag {1} +$$ + +where $\theta$ and $\hat{\theta}$ represent the frozen parameters and tunable parameters in model parameters respectively. For example, in adversarial full finetuning, $\hat{\theta}$ stands for all the model parameters as we update all of them during the finetuning stage. In contrast, in adversarial VPT, $\hat{\theta}$ denotes the extra prompts and linear head while $\theta$ represents the frozen parameters in the backbone architecture. In addition, $\delta$ represents adversarial perturbation, whose $\| \cdot \|_{\infty}$ is bounded by $\varepsilon$ . During adversarial finetuning, we use the pretrained model together with additional modules introduced by PEFT methods to generate adversarial examples, while only updating the tunable parameters $\hat{\theta}$ for each method. If not otherwise specified, we use PGD-7 with $\varepsilon = 8 / 255$ and step size $\alpha = 2 / 255$ to generate adversarial attacks during adversarial finetuning. + +# 4. Robust Pretrained Model Matters + +Previous research [29, 39] suggests that although standard pretraining results in performance inferior to that of adversarially robust pretraining, it can still yield an adversarially robust model with adversarial finetuning. In this section, our goal is to investigate the significance of pretraining in PEFT methods. Specifically, we seek to address the question: Is an adversarially robust model necessary for PEFT methods? + +To answer this question, we initialize model parameters using two different pretrained models. One is a standard pretrained model on ImageNet-1k [11] while the other is adversarially pretrained with PGD [31] attacks. These pretrained models are off-the-shelf and their specifics are outlined in the supplementary material. Following initialization, we perform adversarial finetuning on downstream tasks. As shown in Fig. 3, we evaluate six adversarial + +![](images/0e7de21a1b187b3c71bacf61101acf483ab1c7606705b8dce46124561689b9c2.jpg) +Figure 3. PEFT methods fail or exhibit significantly degraded performance with a standard pretrained model (in blue and gray). Models finetuned from a robust pretrained model (in red) exhibit high accuracy and robustness, as they are consistently positioned in the top-right corner. Among six finetuning techniques, Full-FT outperforms others when starting with a standard pretrained model; however, it falls short of other methods when starting with a robust pretrained model. The specific numerical results are provided in the supplementary. + +![](images/6ff51eddecf176ca2dfc47249b7b1ad2e0e099dd86e9eff9607366d92bce1ca6.jpg) + +![](images/a13371822d61a5af672f864e7bb0a16f8705676a4b2d4fd7f95f014f4c26603c.jpg) + +finetuning techniques across two model architectures (ViT-B [12] and Swin-B [28]) on the CIFAR10 [24] and Caltech256 [13]. The adversarial robustness is measured with PGD-10 bounded with $\varepsilon = 8 / 255$ . + +First, we find that initializing the model with an adversarially robust pretrained model can significantly improve adversarial robustness on downstream tasks. This consistently holds across all the experimental settings we have evaluated, e.g., 6 adversarial finetuning techniques across 2 model architectures on 2 different datasets. More surprisingly, we discover that a robust pretrained model is especially important for PEFT methods, as they struggle to achieve satisfactory adversarial robustness when initialized with a standard pretrained model. For example, all the PEFT methods fail to achieve adversarial robustness higher than $20\%$ on the Caltech256 dataset. In addition, adversarial linear probing can only achieve $< 5\%$ adversarial robustness on both datasets when initiated with a standard pretrained model. This strongly suggests that adversarial PEFT can not sufficiently infuse adversarial robustness in the finetuning stage if the model starts with a non-robust pretrained model. Finally, we observe that Full-FT consistently outperforms other finetuning methods with a non-robust pretraining, indicating the preference for using full finetuning in the absence of robust pretraining. + +Does Pretraining on a Larger Dataset Help Adversarial Finetuning? Due to the high computational cost of adversarial pretraining, we aim to investigate whether a model pretrained on a larger dataset could substitute for the necessity of an adversially robust pretrained model. To this end, we initialize the model with an off-the-shelf large-scale pretrained model, CLIP [34], and perform the same adversarial finetuning techniques on downstream tasks. Fig. 3 demonstrates that a standard pretrained model on a larger dataset, + +
MethodsViTSwin
CleanPGDCleanPGD
RanLI - Full-FT80.1744.1585.1954.13
RanLI - Adapter83.1449.5785.2454.22
RanLI - LoRa82.6350.7283.5253.57
RanLI - Bias82.6950.0784.8854.69
RanLI - VPT82.0950.5284.9955.23
RanLI - Linear81.8942.0282.9845.89
+ +Table 1. PEFT methods, excluding Linear, demonstrate strong performance on average across CIFAR10 and Caltech256 datasets. With adversarial finetuning, PEFT methods outperform Full-FT and Linear with RanLI. Full results are available in ?? + +like CLIP, does not yield higher robustness compared to the non-robust ImageNet-1k pretrained model. It notably lags far behind the robustness achieved by a smaller-scale robust pretrained model, such as one trained on ImageNet-1k. This observation implies that opting for a smaller yet robust pretrained model proves to be a more effective strategy for attaining adversarial robustness in downstream tasks compared to using a larger, non-robust pretrained model. + +# 5. Initialization Matters For Finetuning + +In the previous section, we understand the necessity of initializing a model with an adversarially robust pretrained model. We now ask: given a robust pretrained model, what matters for adversarial finetuning? + +# 5.1. Random Linear Initialization + +To answer this question, we first evaluate the adversarial robustness of six adversarial finetuning techniques. To adapt the robust pretrained model to the downstream tasks, we initialize the linear head with Random Linear Initialization (RanLI) following [39]. We perform adversarial finetuning + +![](images/0af4a33a0ae425c8fdc662e2b9b9cce25c2c999b46b8629a351568a83b5b45f3.jpg) +Figure 4. Linear probing with adversarial finetuning surpasses other methods on Caltech256. With standard finetuning, the PEFT methods exhibit inherited robustness (Robustness $>0$ ) from the pretraining. Notably, linear probing surpasses the other methods by a substantial margin in robustness while maintaining similar clean data accuracy on Caltech256. Additionally, adversarial training during finetuning is effective in enhancing all methods' robustness. + +across two model architectures, e.g., ViT and Swin, on the CIFAR10 and Caltech256 datasets. Additional details regarding the training process can be found in Sec. 5.4 and in supplementary ?? + +As shown in Tab. 1, PEFT methods except Linear consistently demonstrate strong average results with adversarial finetuning. In particular, LoRA achieves the highest average robustness at $50.72\%$ for ViT, while VPT performs exceptionally well with $55.23\%$ on Swin. + +Looking more closely at the performance on each individual dataset in Fig. 4, we observe that adversarial linear probing achieves the strongest robustness on Caltech256. This is rather surprising, given that linear probing has the lowest computational cost compared to others and never outperforms other finetuning methods on any single dataset in standard transfer learning [4, 6, 18]. + +# 5.2. Why does Adversarial Linear Probing Work? + +To understand the remarkable robustness achieved by adversarial linear probing, we then ask: what contributes to adversarial robustness on the downstream tasks given a robust pretrained model? We hypothesize that there are two confounding factors: 1) the robustness inherited from pretrained models, and 2) the robustness achieved by adversarial finetuning. To validate our hypothesis, we conduct a comparative analysis of adversarial robustness in downstream tasks while using standard finetuning versus adversarial finetuning, given the same robust pretrained model. + +Robustness Inherited from Pretrained Models. In this section, we focus on standard finetuning as it does not bring in additional adversarial robustness to downstream tasks. Therefore, the adversarial robustness achieved during standard finetuning primarily arises from the robust pretrained model, representing the capability of each method to preserve robustness from the pretrained model. As shown in + +Fig. 4, all standard finetuning methods (colored in blue) achieve non-zero robustness under PGD-10 attacks. This supports our hypothesis that robustness inherited from the pretrained model contributes to the robustness in downstream tasks. In addition, linear probing significantly outperforms all other standard finetuning methods in preserving robustness from the pretrained model. For example, linear probing exhibits significantly stronger robustness (at least $20\%$ higher) compared to other methods while maintaining similar accuracy on Caltech256. We explain this as linear probing avoids distorting the robust features inherited from the pretrained model by only updating the linear head. However, on CIFAR10, linear probing does not exhibit a significant advantage over robustness and displays lower clean accuracy compared to others. This is likely due to its limited capability to adapt features from the pretrained source domain to the downstream target domain. + +Robustness Achieved by Adversarial Finetuning. By comparing adversarial robustness achieved by standard finetuning (colored in blue) and adversarial finetuning (colored in red) in Fig. 4, we can see the extra robustness gain achieved by adversarial training during the finetuning stage. Except for Linear, adversarial finetuning contributes a significant portion of their robustness to the final robustness. For example, Full-FT on Swin, achieving a $99\%$ final robustness on Caltech256 through adversarial finetuning. Even VPT, which has the fewest tunable parameters after Linear, demonstrates a $78\%$ final robustness from adversarial finetuning. On the contrary, Linear only achieved a final robustness of $13\%$ from this stage, with the primal robustness originating from the pretraining model. + +Taken together, we validate our hypothesis that both robustness inherited from the pretrained model and achieved through adversarial finetuning contribute to adversarial robustness on downstream tasks. In addition, we conclude + +that the exceptional robustness exhibited by adversarial linear probing is mainly because linear probing excels in preserving robustness from pretrained models compared to others, which primarily obtain their robustness from adversarial training during finetuning stage. + +# 5.3. Transferred Robustness Correlates with Transferred Accuracy. + +As we have seen in Fig. 4, adversarial linear probing achieves the highest adversarial robustness on Caltech256 but falls far behind other methods on CIFAR10. This performance discrepancy across different datasets raises a question: how can we estimate if adversarial linear probing achieves the best robustness? Based on our analysis in Sec. 5.2, where the robustness of adversarial linear probing primarily arises from preserving the robustness in the pretrained model, we hypothesize that the transferred robustness of adversarial linear probing is highly correlated with the transferred accuracy of standard linear probing. This suggests that if standard linear probing successfully adapts the features from the pretrained source domain to the downstream target domain, adversarial linear probing will similarly preserve the robustness in the pretrained model. + +To validate this, we define transferred accuracy of standard linear probing $(\mathrm{acc}_{std}^T)$ and transferred robustness of adversarial linear probing $(\mathrm{rob}_{adv}^T)$ as follows, using full finetune as a baseline to normalize the performance across different datasets: + +$$ +\operatorname {a c c} _ {s t d} ^ {T} = \frac {\operatorname {a c c} \left(L P _ {s t d}\right) - \operatorname {a c c} \left(F T _ {s t d}\right)}{\operatorname {a c c} \left(F T _ {s t d}\right)} \tag {2} +$$ + +$$ +\operatorname {r o b} _ {a d v} ^ {T} = \frac {\operatorname {r o b} \left(L P _ {a d v}\right) - \operatorname {r o b} \left(F T _ {a d v}\right)}{\operatorname {r o b} \left(F T _ {a d v}\right)} \tag {3} +$$ + +where $\mathrm{acc}(\cdot)$ and $\mathrm{rob}(\cdot)$ denote the accuracy and robustness of each method, respectively. $FT_{std}$ and $LP_{std}$ represent standard full finetune and standard linear probing whereas $FT_{adv}$ and $LP_{adv}$ stand for their respective adversarial counterparts. We trained 51 models with different hyper-parameter settings across five datasets and present transferred accuracy and robustness in Fig. 5. + +In Fig. 5, the transferred robustness of adversarial linear probing is strongly correlated with the transferred accuracy of standard linear probing, with a high Pearson correlation coefficient (0.896). When the transferred accuracy approaches or surpasses 0, the transferred robustness becomes positive, indicating the improved performance of adversarial linear probing over adversarial fully finetuning. This strong correlation validates our hypothesis that if standard linear probing successfully adapts features from the pretrained to the target domain, its adversarial counterpart is capable of effectively achieving adversarial robustness on downstream tasks. + +![](images/be36f60c6e98e83de1994da02953e42dab6719051a828354a4287321abb4cd23.jpg) +Figure 5. Transferred robustness of adversarial linear probing strongly correlates with transferred accuracy of standard linear probing. + +# 5.4. Robust Linear Initialization (RoLI) + +Based on our observation that linear probing can outperform other methods when it effectively adapts features to the target domain, we propose Robust Linear Initialization (denoted as RoLI) for adversarial finetuning. Specifically, we initialize the linear head of a robust pretrained model with weights obtained through adversarial linear probing instead of random initialization. Then, we perform adversarial finetuning, using either full finetune or PEFT methods. Since adversarial linear probing excels in preserving robustness from a pretrained model, RoLI provides a more robust initialization for subsequent adversarial finetuning, maximizing the robustness inherited from a robust pretrained model. In addition, the following adversarial finetuning can further enhance robustness by introducing additional robustness through adversarial training. In the following sections, we will evaluate the effectiveness of RoLI applied to four different adversarial finetuning methods across five different datasets and demonstrate it achieves new state-of-the-art robustness in adversarial transfer learning. + +Datasets. In our experiments, we use five datasets: CIFAR10 [24], CIFAR100 [24], Caltech256 [13], CaltechUCSD Birds-200-2011 (CUB200) [42], and Stanford Dogs (Dogs) [21]. For low-resolution image datasets like CIFAR10 and CIFAR100, we resize the image to match the model input shape. For high-resolution image datasets, we apply random resizing and cropping in training and center crop in testing. It's important to note that we integrate the resizing and normalization process directly into the model since the attacker does not have access to pre-processed images. Additional details are provided in the supplementary ?? + +Methods. We provide the results from TWINS-AT [29] AutoLoRa [43] as baselines. We proceed to assess six fine + +
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
CleanPGDCleanPGDCleanPGDCleanPGDCleanPGDCleanPGD
TWINS-AT [29]91.2452.7370.7231.0876.8648.4068.0929.2464.9820.5874.3836.41
AutoLoRa [43]86.9357.1666.2035.2569.8547.8262.7831.0762.3325.3269.6239.32
RanLI - Full-FT93.0259.1274.3635.6277.3549.1370.8331.5565.8524.7976.2840.04
RanLI - Adapter90.2355.7071.5734.7480.2452.7359.6726.7387.9842.2477.9442.43
RanLI - LoRA90.0256.8871.9834.8377.0250.2564.7429.6584.6339.2477.6842.17
RanLI - Bias90.2556.9471.5036.7279.5052.4366.6929.8887.4142.7579.0743.74
RanLI - VPT90.2457.3872.3735.6079.7453.0761.9426.4686.3443.1078.1343.12
RanLI - Linear84.1637.3067.6525.4681.7954.4769.8824.5691.5545.4579.0137.45
RoLI - Full-FT94.1860.8576.2537.3883.7855.4274.2832.0391.5545.5784.0146.25
RoLI - Adapter90.3155.6971.7534.3381.7454.3264.2025.2292.0247.1280.0043.34
RoLI - LoRA92.2358.6272.8735.1881.7954.5068.8826.7791.2046.7681.3944.37
RoLI - Bias91.8358.3972.1735.1781.7854.4968.1425.7091.5247.2781.0944.20
+ +Table 2. RoLI significantly improves the performance and achieves SOTA across five image classification tasks. Robust Linear Initialization (RoLI) enhances robustness by $3.88\%$ and clean accuracy by $2.44\%$ on average compared to Random Initialization (RanLI). Notably, RoLI - Full-FT achieves the best overall performance, with an accuracy of $84.01\%$ and $46.25\%$ robustness. + +
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
RanLI - Full-FT54.931.862.649.742.548.3
RanLI - Adapter50.829.266.740.368.551.1
RanLI - LoRa53.029.062.844.763.350.6
RanLI - Bias52.331.065.846.267.352.5
RanLI - VPT52.329.766.340.367.351.2
RanLI - Linear26.618.465.740.473.544.9
RoLI - Full-FT56.332.770.452.173.557.0
RoLI - Adapter51.129.165.840.675.252.4
RoLI - LoRa53.930.065.744.674.353.7
RoLI - Bias53.929.865.743.574.853.5
+ +tuning techniques introduced in Sec. 3.1 with random initialization. We use Swin Transformer [28] as a backbone architecture for our experiments, whereas TWINS and AutoLoRa use ResNet50 [14]. We apply RoLI to Full-FT, Bias, Adapter, and LoRa. We initialize the newly introduced modules in Adapter and LoRA with zero to ensure that they start with robust linear probing without distorting the robust features preserved in the pretrained model. + +Training Details. We use the same optimizer, AdamW [30], and a cosine scheduler with warm-up for all finetuning methods. To determine the optimal learning rate and weight decay values, we conduct a grid search, and the ranges of hyper-parameters along with the optimal combinations can be found in the supplementary ??. We keep method-specific hyper-parameters constant across all datasets. For instance, we set the prompt + +Table 3. RoLI consistently outperforms RanLI under AutoAttack. Note, we use $\varepsilon = 8 / 255$ attack for CIFAR10, CIFAR100, and $\varepsilon = 4 / 255$ for Caltech256, CUB200 and Stanford Dogs. RoLI shows an average 3.53 AA gain compared with RanLI, and notably, RoLI - Full-FT surpasses other methods by achieving a robustness of 57.0 under AutoAttack. The clean accuracy is illustrated in Tab. 2. + +
Methodsε = 8/255ε = 4/255
RanLI - Full-FT20.1042.50
RanLI - Adapter36.3068.50
RanLI - LoRa32.4063.30
RanLI - Bias35.9067.30
RanLI - VPT34.4067.30
RanLI - Linear30.9073.50
RoLI - Full-FT30.9073.50
RoLI - Adapter37.0075.20
RoLI - LoRa38.4074.30
RoLI - Bias38.2074.80
+ +Table 4. RoLI consistently improves adversarial robustness even against $\varepsilon = 8 / 255$ AutoAttack. RanLI - Linear performs well under $\varepsilon = 4 / 255$ AutoAttack, but poorly under $\varepsilon = 8 / 255$ AutoAttack on Stanford Dogs. This discrepancy demonstrates that adversarial linear probing obtains its robustness mainly from the pretrained model, whereas other methods obtain robustness mainly from adversarial finetuning. + +length to 10 for the VPT method. To avoid adversarial overfitting [37], we apply early stopping with the epoch that has the best performance on the validation set. During adversarial finetuning, we utilize the PGD-7 attack with $\varepsilon = 8 / 255$ and a step size of $\alpha = 2 / 255$ . When reporting test accuracy and robustness, we evaluate the models under a PGD-10 attack with $\varepsilon = 8 / 255$ . Additionally, we report the performance under AutoAttack (AA), which is an ensemble attack and provides a more reliable approach to evaluate the adversarial robustness. We follow the standard AutoAttack setting, i.e., untargeted APGDCE, targeted APGD-DLR, targeted FAB [8], and Square Attack [1]. + +PGD-10 Results. Looking at Random Initialization (RanLI) in Tab. 2, the same trend holds as in Sec. 5.1: 1) PEFT methods except linear probing exhibit strong average results across five different datasets, with Bias achiev + +![](images/98bc546f3e75bf3c58c246214c9f8c0712c081b3f8c7dee55eae953d85c82daa.jpg) +Figure 6. Trade-off between speed and robustness. We conduct the speed test on Stanford Dogs with random linear initialization (RanLI), logistic regression linear initialization (RegLI), standard linear initialization (StdLI), and robust linear initialization (RoLI). RoLI achieves the best performance at the cost of increased training time. Meanwhile, both RegLI and StdLI can improve their performance without incurring substantial time costs. + +ing the best performance (79.25% accuracy and 43.58% robustness). 2) Linear probing achieves the highest robustness on Caltech256 and Stanford Dogs, although it falls behind others on the remaining three datasets. + +Compared to RandLI, we can observe from Tab. 2 that RoLI significantly enhances the robustness on Caltech256 and Stanford Dogs for all finetuning methods. In particular, RoLI - Full-FT achieves a robustness improvement of $6.29\%$ on Caltech256 and $20.78\%$ on Stanford Dogs. On other datasets where adversarial linear probing with RanLI does not outperform others, RoLI performs comparable or even better than RanLI. This strongly supports that a robust initialization of the linear head is critical in adversarial transfer learning. Lastly, our RoLI - Full-FT achieves the highest performance across five datasets and sets a new state-of-the-art benchmark. + +AutoAttack Results. We extend our evaluation to Stanford Dogs using $\varepsilon = 8 / 255$ and $\varepsilon = 4 / 255$ , as illustrated in Tab. 4. Interestingly, we observe that adversarial linear probing outperforms other methods under $\varepsilon = 4 / 255$ attack but underperforms when tested against $\varepsilon = 8 / 255$ adversarial attacks. We conjecture that the pretrained model lacks robustness against $\varepsilon = 8 / 255$ attacks as it is trained using $\varepsilon = 4 / 255$ adversarial attacks. + +This performance disparity confirms that adversarial linear probing inherently derives robustness from pretraining, whereas other methods predominantly achieve robustness from adversarial finetuning. Notably, RoLI consistently improves adversarial robustness even against $\varepsilon = 8 / 255$ attacks, further validating the importance of a robust linear initialization for adversarial transfer learning. + +To maintain consistency with the pre-training, we follow the conventional settings [9, 10] to set $\varepsilon = 8 / 255$ attack for low-resolution datasets (CIFAR10, CIFAR100) and + +
StdLI -CIFAR-10Caltech-256
CleanPGDCleanPGD
Full-FT93.34(-0.84)59.34(-1.51)83.23(-0.55)52.85(-2.57)
Bias93.34(-0.04)58.12(-0.27)82.93(+1.15)52.93(-1.56)
Adapter90.08(-0.23)55.19(-0.50)82.72(+0.98)53.01(-1.31)
LoRa90.71(-1.52)58.17(-0.45)82.87(+1.08)51.47(-3.03)
+ +Table 5. StdLI is less robust than RoLI. The values in parentheses denote the performance gap (StdLI - RoLI). + +$\varepsilon = 4 / 255$ attack for high-resolution datasets (Caltech256, CUB200, Stanford Dogs). Tab. 3 demonstrates the robustness under AutoAttack and the clean accuracy is illustrated in Tab. 2. RoLI exhibits higher robustness over RanLI, demonstrating an average 3.53 AA gain. Notably, RoLI - Full-FT achieves a robustness of 57.0, surpassing other methods. + +# 6. Discussion + +Comparison between RoLI and StdLI. Standard Linear Initialization (StdLI) refers to the use of a simple linear probing to initialize the head, while RoLI uses adversarial linear probing. In Tab. 5, we compare the performance of RoLI and StdLI on CIFAR-10 and Caltech-256. We observe that StdLI exhibits lower performance compared to RoLI, with a robustness decrease of 2.48 across three datasets, highlighting the effectiveness of RoLI. + +Robustness vs. Speed. Since robust linear initialization involves a two-step adversarial training process, it tends to be considerably slower than adversarial fine-tuning with random initialization. In this section, we show a trade-off between robustness and speed by obtaining the initialization from four different approaches: adversarial linear probing (RoLI), standard linear probing (StdLI), logistic regression (RegLI), and randomization (RanLI). From Fig. 6, it's evident that both RegLI and StdLI enhance robustness compared to random linear initialization within an acceptable time cost. In addition, RoLI achieves the highest performance but at the expense of slower speed. + +# 7. Conclusion + +This paper systematically investigates how to achieve adversarial robustness in downstream tasks. We highlight the necessity of an adversially robust pretraining. Given a robust pretrained model, we propose to use robust linear initialization (RoLI) followed by adversarial full finetuning or PEFT methods to achieve the best performance. We demonstrate that RoLI outperforms random linear initialization across five image classification tasks. We hope the insights from this study greatly advance research aimed at enhancing adversarial robustness in downstream tasks. + +Acknowledgment. We thank Chenhe Gu and Xuan Yang for the valuable discussion and insightful feedback. + +# References + +[1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In European conference on computer vision, pages 484-501. Springer, 2020. 7 +[2] Rishi Bommasani, Drew A Hudson, Ehsan Adeli, Russ Altman, Simran Arora, Sydney von Arx, Michael S Bernstein, Jeannette Bohg, Antoine Bosselut, Emma Brunskill, et al. 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Neural prompt search. arXiv preprint arXiv:2206.04673, 2022. 1 \ No newline at end of file diff --git a/2024/Initialization Matters for Adversarial Transfer Learning/images.zip b/2024/Initialization Matters for Adversarial Transfer Learning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..810d64962c14382f55e4e31068170f6e16c46b5c --- /dev/null +++ b/2024/Initialization Matters for Adversarial Transfer Learning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:426fdccd40c9afd577316bd90052119d20d0319cf27de514b2e9812342ad3ce6 +size 539286 diff --git a/2024/Initialization Matters for Adversarial Transfer Learning/layout.json b/2024/Initialization Matters for Adversarial Transfer Learning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..24701156209e3547441c7e6a52fcbd5190d7a8e2 --- /dev/null +++ b/2024/Initialization Matters for Adversarial Transfer Learning/layout.json @@ -0,0 +1,6938 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 123, + 103, + 473, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 103, + 473, + 121 + ], + "spans": [ + { + "bbox": [ + 123, + 103, + 473, + 121 + ], + "type": "text", + "content": "Initialization Matters for Adversarial Transfer Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 141, + 525, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 141, + 525, + 186 + ], + "spans": [ + { + "bbox": [ + 67, + 141, + 525, + 186 + ], + "type": "text", + "content": "Andong Hua1 Jindong Gu2 Zhiyu Xue1 Nicholas Carlini3 Eric Wong4 Yao Qin1,3 \n1University of California, Santa Barbara 2University of Oxford \n3Google 4University of Pennsylvania" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": "With the prevalence of the Pretraining-Finetuning paradigm in transfer learning, the robustness of downstream tasks has become a critical concern. In this work, we delve into adversarial robustness in transfer learning and reveal the critical role of initialization, including both the pretrained model and the linear head. First, we discover the necessity of an adversially robust pretrained model. Specifically, we reveal that with a standard pretrained model, Parameter-Efficient Finetuning (PEFT) methods either fail to be adversially robust or continue to exhibit significantly degraded adversarial robustness on downstream tasks, even with adversarial training during finetuning. Leveraging a robust pretrained model, surprisingly, we observe that a simple linear probing can outperform full finetuning and other PEFT methods with random initialization on certain datasets. We further identify that linear probing excels in preserving robustness from the robust pretraining. Based on this, we propose Robust Linear Initialization (RoLI) for adversarial finetuning, which initializes the linear head with the weights obtained by adversarial linear probing to maximally inherit the robustness from pretraining. Across five different image classification datasets, we demonstrate the effectiveness of RoLI and achieve new state-of-the-art results. Our code is available at https://github.com/DongXzz/RoLI." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "With the advancement of large-scale deep learning models, the Pretraining-Finetuning paradigm takes a more dominant role compared to training from scratch across various tasks [2], including computer vision [12, 15, 22, 28], natural language processing [20, 36, 41], and speech recognition [35]. Under the paradigm of Pretraining-Finetuning, advanced parameter-efficient finetuning (PEFT) methods [4, 16-18, 27, 48] have emerged. Compared to full finetuning, PEFT methods either introduce small modules into a fixed pretrained model or optimize only part of the pretrained model, demonstrating exceptional performance while keep" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 324, + 213, + 533, + 383 + ], + "blocks": [ + { + "bbox": [ + 324, + 213, + 533, + 383 + ], + "lines": [ + { + "bbox": [ + 324, + 213, + 533, + 383 + ], + "spans": [ + { + "bbox": [ + 324, + 213, + 533, + 383 + ], + "type": "image", + "image_path": "bdb995711b372ec4a843644134648080b6bacdb8e06d66f82a6449d0925a238d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "type": "text", + "content": "Figure 1. Robust Linear Initialization (RoLI), significantly improves adversarial robustness. RoLI, denoted in red, achieves an average " + }, + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "type": "inline_equation", + "content": "3.88\\%" + }, + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "type": "text", + "content": " increase in clean accuracy and a " + }, + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "type": "inline_equation", + "content": "2.44\\%" + }, + { + "bbox": [ + 304, + 387, + 547, + 509 + ], + "type": "text", + "content": " increase in robust accuracy compared to Random Linear Initialization (RanLI) of the linear head during adversarial finetuning, averaged across five downstream datasets. Our best-performing RoLI - Full-FT, which represents adversarial full finetuning with robust linear initialization, achieves a new state-of-the-art performance. We include six popular finetuning methods with Swin Transformer [28] and two existing state-of-the-art techniques for adversarial transfer learning: TWINS-AT [29] and AutoLoRA [43]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 520, + 399, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 399, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 399, + 532 + ], + "type": "text", + "content": "ing storage usage low." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "content": "While the success of transfer learning is evident, the robustness of downstream models has become a critical concern in real-world applications. For example, as suggested by previous studies, full finetuning will distort the pretrained features, leading to compromised robustness in terms of image corruptions and out-of-distribution (OOD) performance [26, 44]. In addition, adversarial robustness poses another significant challenge to real-world deployment, as a non-robust model demonstrates nearly zero accuracy under adversarial attacks [40]. Many approaches have been proposed to enhance adversarial robustness in transfer learning, including improving the robustness of pretraining through self-supervised techniques [7, 19] and preserving robustness from pretrained models during finetuning [29, 43]. However, most previous works [29, 43] apply" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24831" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 544, + 235 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 544, + 235 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 544, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 544, + 235 + ], + "type": "image", + "image_path": "ef16f8535229e585afe9d4bb6e0d45a2df09d73369404356bca7632c1b1826c5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 246, + 543, + 258 + ], + "lines": [ + { + "bbox": [ + 48, + 246, + 543, + 258 + ], + "spans": [ + { + "bbox": [ + 48, + 246, + 543, + 258 + ], + "type": "text", + "content": "Figure 2. Illustration of six different finetuning techniques, arranged in descending order according to the number of tunable parameters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 264, + 287, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 287, + 288 + ], + "type": "text", + "content": "full finetuning for adversarial transfer learning, overlooking the significance of different finetuning methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 479 + ], + "type": "text", + "content": "In this work, we comprehensively study six popular finetuning methods in adversarial transfer learning, as shown in Fig. 2. We discover that initialization, which includes 1) the backbone initialization (i.e., a pretrained model), and 2) the initialization of the linear head that adapts features to the target domain, plays a critical role in adversarial transfer learning. We start by comparing the performance of adversarial finetuning when initialized with either a robust or a standard pretrained model. Surprisingly, all PEFT methods fail or exhibit significantly inferior performance when initialized with a standard pretrained model compared to being initialized with a robust pretrained model. Furthermore, we observe that a large-scale pretrained model, such as CLIP [34], cannot alleviate this phenomenon, highlighting the critical role of robust pretraining in adversarial transfer learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 482, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 673 + ], + "type": "text", + "content": "Given a robust pretrained model, surprisingly, we discover that adversarial linear probing outperforms other methods on certain datasets, e.g., Caltech256 [13] and Stanford Dogs [21]. We further demonstrate that this is mainly because linear probing excels in inheriting robustness from pretraining. Moreover, we identify the ability to adapt features to the specific target domain as a key factor influencing linear probing's success, supported by a strong correlation between transferred accuracy and robustness. Based on these insights, we introduce Robust Linear Initialization (RoLI), which initializes the model's linear head with the weights obtained from adversarial linear probing. With RoLI followed by adversarial finetuning methods, we maximize the inherited robustness along with a strong feature adaptation ability, resulting in improved performance. In summary, our contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": "- We comprehensively study six popular finetuning techniques for adversarial transfer learning. We discover that PEFT methods fail or exhibit significantly inferior perfor" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 264, + 544, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 264, + 544, + 288 + ], + "spans": [ + { + "bbox": [ + 313, + 264, + 544, + 288 + ], + "type": "text", + "content": "mance when initialized with a standard pretrained model, even with adversarial finetuning on downstream data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 289, + 545, + 419 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 306, + 289, + 545, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 545, + 359 + ], + "type": "text", + "content": "- We demonstrate that adversarial linear probing excels in preserving robustness from a robust pretrained model. Building upon this insight, we propose Robust Linear Initialization (RoLI) for adversarial finetuning to maximally inherit robustness from pretraining and effectively adapt features through adversarial finetuning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "type": "text", + "content": "- We demonstrate the effectiveness of RoLI across five downstream datasets. On average, RoLI improves the clean and robust accuracy by " + }, + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "type": "inline_equation", + "content": "3.88\\%" + }, + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "type": "inline_equation", + "content": "2.44\\%" + }, + { + "bbox": [ + 306, + 360, + 545, + 419 + ], + "type": "text", + "content": " compared with random initialization. This establishes a new state-of-the-art benchmark for adversarial transfer learning." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 439, + 397, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 439, + 397, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 439, + 397, + 451 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "type": "text", + "content": "Finetuning in Transfer Learning. Transfer learning aims to finetune a pretrained model on downstream tasks to gain better performance [23, 45, 47]. Linear probing and full finetuning are often applied in the finetuning process. Given the increasing size of pretrained models, various Parameter Efficient Finetuning (PEFT) methods have been proposed. PEFT methods can effectively reduce the finetuning cost and alleviate overfitting since only a small number of parameters are updated [16, 17]. Specifically, Bias [3, 46] only updates the bias term, while Scaling & Shifting [27] performs the linear transformation to adapt the features. Different from both of them, Adapter [16, 32, 33], LoRA [17], and VPT [18] introduce extra learnable modules into the pretrained models in the finetuning stage. Although there are various finetuning methods proposed to improve the accuracy, it is still unclear what matters to the robustness on the downstream tasks. [25] points out that feature distortion in finetuning hurts the out-of-distribution robustness on downstream tasks, while we discover initialization plays a critical role in adversarial robustness on downstream tasks." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "24832" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 336 + ], + "type": "text", + "content": "Adversarial Robustness in Transfer Learning. The research on adversarial robustness in transfer learning has been studied from two perspectives, namely, robust pretraining and robust finetuning. Concretely, robust pertaining aims to achieve adversarial robustness in the pertaining stage and finetune pretrained models on the downstream tasks without adversarial training [5, 7, 19, 39]. Besides, [38] demonstrates that the adversially pertaining also benefits standard performance on downstream tasks. In contrast, robust finetuning [29, 43] focuses on preserving the robustness of the pretrained model during the finetuning stage. For example, TWINS [29] incorporates a dual batch normalization in the model to keep the statistics of pretrained and finetuned datasets separately. And AutoLoRA [43] introduces a low-rank (LoRA) branch to disentangle clean and adversarial objectives. Existing works design various strategies to preserve the robustness from the pretrained model, but they simply apply full finetuning on downstream tasks. In this work, we study six different finetuning methods and introduce Robust Linear Initialization (RoLI) to enhance the adversarial robustness for different finetuning methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 349, + 126, + 362 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 126, + 362 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 126, + 362 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 369, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 430 + ], + "type": "text", + "content": "In this section, we provide an overview of existing finetuning techniques, including full finetuning as well as five different PEFT methods, as illustrated in Fig. 2. Additionally, we introduce adversarial finetuning which integrates adversarial training during the finetuning stage." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 439, + 206, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 206, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 206, + 452 + ], + "type": "text", + "content": "3.1. Existing Finetuning Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 459, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 459, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 287, + 506 + ], + "type": "text", + "content": "In transfer learning, finetuning adapts the features from the pretrained domain to the target domain. In this section, we introduce six finetuning methods in descending order according to the number of tunable parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 507, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 507, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 507, + 287, + 542 + ], + "type": "text", + "content": "Full Finetune (Full-FT): We initialize the model from a pretrained model and finetune all its parameters on the downstream tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 544, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 287, + 604 + ], + "type": "text", + "content": "Adapter [16, 32, 33]: Adapter introduces a module after the MLP block in every layer. The adapter module consists of a down-sampling layer and an up-sampling layer, with a non-linear activation. During finetuning, we will update the adapter modules as well as the linear head." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 605, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 676 + ], + "type": "text", + "content": "Low-Rank Adaptation (LoRA) [17]: LoRA proposes to learn a residual from pretrained weight represented by two low-rank metrics. Specifically, we apply the LoRA branch on the query and value projection in the self-attention block. During finetuning, the pretrained model remains frozen while updates are applied to the LoRA branch and head." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Bias [3, 46]: We update the bias term and keep other parameters unchanged. Additionally, We also update the classification head (including weights and bias)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "Visual Prompt Tuning (VPT) [18]: VPT appends additional learnable tokens (embeddings), called prompts, into the input space of each attention layer in vision transformers. Specifically, we use the structure of VPT-Deep, where every layer introduces a fixed number of trainable prompts independently. During the finetuning stage, we will tune both the prompts and the linear head on downstream tasks while freezing the entire pretrained backbone. We refer readers to [18] for more details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 180, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 203 + ], + "type": "text", + "content": "Linear Probing (Linear): We only finetune the classification head on the downstream tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 211, + 440, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 211, + 440, + 224 + ], + "spans": [ + { + "bbox": [ + 306, + 211, + 440, + 224 + ], + "type": "text", + "content": "3.2. Adversarial Finetuning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 230, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 266 + ], + "type": "text", + "content": "Adversarial training corresponds to a min-max optimization problem [31]. In the context of adversarial finetuning, we can formulate the optimization problem as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 337, + 274, + 545, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 274, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 337, + 274, + 545, + 301 + ], + "type": "interline_equation", + "content": "\\min _ {\\hat {\\theta}} \\mathbb {E} _ {(x, y) \\sim D} \\left[ \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\varepsilon} \\mathcal {L} (x + \\delta , y; \\theta \\cup \\hat {\\theta}) \\right] \\tag {1}", + "image_path": "b40646539764224de292fd010653f72a9768ca7ae9a161c33c3f9a3b36e32ad9.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " represent the frozen parameters and tunable parameters in model parameters respectively. For example, in adversarial full finetuning, " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " stands for all the model parameters as we update all of them during the finetuning stage. In contrast, in adversarial VPT, " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " denotes the extra prompts and linear head while " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " represents the frozen parameters in the backbone architecture. In addition, " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " represents adversarial perturbation, whose " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_{\\infty}" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " is bounded by " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": ". During adversarial finetuning, we use the pretrained model together with additional modules introduced by PEFT methods to generate adversarial examples, while only updating the tunable parameters " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " for each method. If not otherwise specified, we use PGD-7 with " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " and step size " + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "inline_equation", + "content": "\\alpha = 2 / 255" + }, + { + "bbox": [ + 304, + 311, + 546, + 491 + ], + "type": "text", + "content": " to generate adversarial attacks during adversarial finetuning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 502, + 495, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 495, + 514 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 495, + 514 + ], + "type": "text", + "content": "4. Robust Pretrained Model Matters" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 522, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 616 + ], + "type": "text", + "content": "Previous research [29, 39] suggests that although standard pretraining results in performance inferior to that of adversarially robust pretraining, it can still yield an adversarially robust model with adversarial finetuning. In this section, our goal is to investigate the significance of pretraining in PEFT methods. Specifically, we seek to address the question: Is an adversarially robust model necessary for PEFT methods?" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "To answer this question, we initialize model parameters using two different pretrained models. One is a standard pretrained model on ImageNet-1k [11] while the other is adversarially pretrained with PGD [31] attacks. These pretrained models are off-the-shelf and their specifics are outlined in the supplementary material. Following initialization, we perform adversarial finetuning on downstream tasks. As shown in Fig. 3, we evaluate six adversarial" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24833" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 77, + 298, + 231 + ], + "blocks": [ + { + "bbox": [ + 50, + 77, + 298, + 231 + ], + "lines": [ + { + "bbox": [ + 50, + 77, + 298, + 231 + ], + "spans": [ + { + "bbox": [ + 50, + 77, + 298, + 231 + ], + "type": "image", + "image_path": "0e7de21a1b187b3c71bacf61101acf483ab1c7606705b8dce46124561689b9c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 245, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 547, + 291 + ], + "type": "text", + "content": "Figure 3. PEFT methods fail or exhibit significantly degraded performance with a standard pretrained model (in blue and gray). Models finetuned from a robust pretrained model (in red) exhibit high accuracy and robustness, as they are consistently positioned in the top-right corner. Among six finetuning techniques, Full-FT outperforms others when starting with a standard pretrained model; however, it falls short of other methods when starting with a robust pretrained model. The specific numerical results are provided in the supplementary." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 78, + 419, + 228 + ], + "blocks": [ + { + "bbox": [ + 296, + 78, + 419, + 228 + ], + "lines": [ + { + "bbox": [ + 296, + 78, + 419, + 228 + ], + "spans": [ + { + "bbox": [ + 296, + 78, + 419, + 228 + ], + "type": "image", + "image_path": "6ff51eddecf176ca2dfc47249b7b1ad2e0e099dd86e9eff9607366d92bce1ca6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 419, + 78, + 539, + 230 + ], + "blocks": [ + { + "bbox": [ + 419, + 78, + 539, + 230 + ], + "lines": [ + { + "bbox": [ + 419, + 78, + 539, + 230 + ], + "spans": [ + { + "bbox": [ + 419, + 78, + 539, + 230 + ], + "type": "image", + "image_path": "a13371822d61a5af672f864e7bb0a16f8705676a4b2d4fd7f95f014f4c26603c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 344 + ], + "type": "text", + "content": "finetuning techniques across two model architectures (ViT-B [12] and Swin-B [28]) on the CIFAR10 [24] and Caltech256 [13]. The adversarial robustness is measured with PGD-10 bounded with " + }, + { + "bbox": [ + 46, + 297, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 297, + 287, + 344 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "type": "text", + "content": "First, we find that initializing the model with an adversarially robust pretrained model can significantly improve adversarial robustness on downstream tasks. This consistently holds across all the experimental settings we have evaluated, e.g., 6 adversarial finetuning techniques across 2 model architectures on 2 different datasets. More surprisingly, we discover that a robust pretrained model is especially important for PEFT methods, as they struggle to achieve satisfactory adversarial robustness when initialized with a standard pretrained model. For example, all the PEFT methods fail to achieve adversarial robustness higher than " + }, + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "type": "text", + "content": " on the Caltech256 dataset. In addition, adversarial linear probing can only achieve " + }, + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "type": "inline_equation", + "content": "< 5\\%" + }, + { + "bbox": [ + 46, + 346, + 288, + 597 + ], + "type": "text", + "content": " adversarial robustness on both datasets when initiated with a standard pretrained model. This strongly suggests that adversarial PEFT can not sufficiently infuse adversarial robustness in the finetuning stage if the model starts with a non-robust pretrained model. Finally, we observe that Full-FT consistently outperforms other finetuning methods with a non-robust pretraining, indicating the preference for using full finetuning in the absence of robust pretraining." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Does Pretraining on a Larger Dataset Help Adversarial Finetuning? Due to the high computational cost of adversarial pretraining, we aim to investigate whether a model pretrained on a larger dataset could substitute for the necessity of an adversially robust pretrained model. To this end, we initialize the model with an off-the-shelf large-scale pretrained model, CLIP [34], and perform the same adversarial finetuning techniques on downstream tasks. Fig. 3 demonstrates that a standard pretrained model on a larger dataset," + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 312, + 295, + 541, + 396 + ], + "blocks": [ + { + "bbox": [ + 312, + 295, + 541, + 396 + ], + "lines": [ + { + "bbox": [ + 312, + 295, + 541, + 396 + ], + "spans": [ + { + "bbox": [ + 312, + 295, + 541, + 396 + ], + "type": "table", + "html": "
MethodsViTSwin
CleanPGDCleanPGD
RanLI - Full-FT80.1744.1585.1954.13
RanLI - Adapter83.1449.5785.2454.22
RanLI - LoRa82.6350.7283.5253.57
RanLI - Bias82.6950.0784.8854.69
RanLI - VPT82.0950.5284.9955.23
RanLI - Linear81.8942.0282.9845.89
", + "image_path": "a61b0cf7a44ed7de52150feb4e3e8d68b1df6a3d864ed488945fbcd3d2b21951.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 403, + 546, + 448 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 546, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 546, + 448 + ], + "type": "text", + "content": "Table 1. PEFT methods, excluding Linear, demonstrate strong performance on average across CIFAR10 and Caltech256 datasets. With adversarial finetuning, PEFT methods outperform Full-FT and Linear with RanLI. Full results are available in ??" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 454, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 551 + ], + "type": "text", + "content": "like CLIP, does not yield higher robustness compared to the non-robust ImageNet-1k pretrained model. It notably lags far behind the robustness achieved by a smaller-scale robust pretrained model, such as one trained on ImageNet-1k. This observation implies that opting for a smaller yet robust pretrained model proves to be a more effective strategy for attaining adversarial robustness in downstream tasks compared to using a larger, non-robust pretrained model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 560, + 511, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 511, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 511, + 574 + ], + "type": "text", + "content": "5. Initialization Matters For Finetuning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 580, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 580, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 580, + 547, + 628 + ], + "type": "text", + "content": "In the previous section, we understand the necessity of initializing a model with an adversarially robust pretrained model. We now ask: given a robust pretrained model, what matters for adversarial finetuning?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 635, + 466, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 466, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 466, + 647 + ], + "type": "text", + "content": "5.1. Random Linear Initialization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "content": "To answer this question, we first evaluate the adversarial robustness of six adversarial finetuning techniques. To adapt the robust pretrained model to the downstream tasks, we initialize the linear head with Random Linear Initialization (RanLI) following [39]. We perform adversarial finetuning" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24834" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 78, + 544, + 225 + ], + "blocks": [ + { + "bbox": [ + 50, + 78, + 544, + 225 + ], + "lines": [ + { + "bbox": [ + 50, + 78, + 544, + 225 + ], + "spans": [ + { + "bbox": [ + 50, + 78, + 544, + 225 + ], + "type": "image", + "image_path": "0af4a33a0ae425c8fdc662e2b9b9cce25c2c999b46b8629a351568a83b5b45f3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 238, + 546, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 546, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 546, + 282 + ], + "type": "text", + "content": "Figure 4. Linear probing with adversarial finetuning surpasses other methods on Caltech256. With standard finetuning, the PEFT methods exhibit inherited robustness (Robustness " + }, + { + "bbox": [ + 46, + 238, + 546, + 282 + ], + "type": "inline_equation", + "content": ">0" + }, + { + "bbox": [ + 46, + 238, + 546, + 282 + ], + "type": "text", + "content": ") from the pretraining. Notably, linear probing surpasses the other methods by a substantial margin in robustness while maintaining similar clean data accuracy on Caltech256. Additionally, adversarial training during finetuning is effective in enhancing all methods' robustness." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 289, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 337 + ], + "type": "text", + "content": "across two model architectures, e.g., ViT and Swin, on the CIFAR10 and Caltech256 datasets. Additional details regarding the training process can be found in Sec. 5.4 and in supplementary ??" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "type": "text", + "content": "As shown in Tab. 1, PEFT methods except Linear consistently demonstrate strong average results with adversarial finetuning. In particular, LoRA achieves the highest average robustness at " + }, + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "type": "inline_equation", + "content": "50.72\\%" + }, + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "type": "text", + "content": " for ViT, while VPT performs exceptionally well with " + }, + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "type": "inline_equation", + "content": "55.23\\%" + }, + { + "bbox": [ + 46, + 337, + 287, + 396 + ], + "type": "text", + "content": " on Swin." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 396, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 480 + ], + "type": "text", + "content": "Looking more closely at the performance on each individual dataset in Fig. 4, we observe that adversarial linear probing achieves the strongest robustness on Caltech256. This is rather surprising, given that linear probing has the lowest computational cost compared to others and never outperforms other finetuning methods on any single dataset in standard transfer learning [4, 6, 18]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 486, + 282, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 282, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 282, + 499 + ], + "type": "text", + "content": "5.2. Why does Adversarial Linear Probing Work?" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": "To understand the remarkable robustness achieved by adversarial linear probing, we then ask: what contributes to adversarial robustness on the downstream tasks given a robust pretrained model? We hypothesize that there are two confounding factors: 1) the robustness inherited from pretrained models, and 2) the robustness achieved by adversarial finetuning. To validate our hypothesis, we conduct a comparative analysis of adversarial robustness in downstream tasks while using standard finetuning versus adversarial finetuning, given the same robust pretrained model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Robustness Inherited from Pretrained Models. In this section, we focus on standard finetuning as it does not bring in additional adversarial robustness to downstream tasks. Therefore, the adversarial robustness achieved during standard finetuning primarily arises from the robust pretrained model, representing the capability of each method to preserve robustness from the pretrained model. As shown in" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 289, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 492 + ], + "type": "text", + "content": "Fig. 4, all standard finetuning methods (colored in blue) achieve non-zero robustness under PGD-10 attacks. This supports our hypothesis that robustness inherited from the pretrained model contributes to the robustness in downstream tasks. In addition, linear probing significantly outperforms all other standard finetuning methods in preserving robustness from the pretrained model. For example, linear probing exhibits significantly stronger robustness (at least " + }, + { + "bbox": [ + 304, + 289, + 545, + 492 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 492 + ], + "type": "text", + "content": " higher) compared to other methods while maintaining similar accuracy on Caltech256. We explain this as linear probing avoids distorting the robust features inherited from the pretrained model by only updating the linear head. However, on CIFAR10, linear probing does not exhibit a significant advantage over robustness and displays lower clean accuracy compared to others. This is likely due to its limited capability to adapt features from the pretrained source domain to the downstream target domain." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": "Robustness Achieved by Adversarial Finetuning. By comparing adversarial robustness achieved by standard finetuning (colored in blue) and adversarial finetuning (colored in red) in Fig. 4, we can see the extra robustness gain achieved by adversarial training during the finetuning stage. Except for Linear, adversarial finetuning contributes a significant portion of their robustness to the final robustness. For example, Full-FT on Swin, achieving a " + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": " final robustness on Caltech256 through adversarial finetuning. Even VPT, which has the fewest tunable parameters after Linear, demonstrates a " + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "inline_equation", + "content": "78\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": " final robustness from adversarial finetuning. On the contrary, Linear only achieved a final robustness of " + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": " from this stage, with the primal robustness originating from the pretraining model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Taken together, we validate our hypothesis that both robustness inherited from the pretrained model and achieved through adversarial finetuning contribute to adversarial robustness on downstream tasks. In addition, we conclude" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24835" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "that the exceptional robustness exhibited by adversarial linear probing is mainly because linear probing excels in preserving robustness from pretrained models compared to others, which primarily obtain their robustness from adversarial training during finetuning stage." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 140, + 287, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 166 + ], + "type": "text", + "content": "5.3. Transferred Robustness Correlates with Transferred Accuracy." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 172, + 287, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 172, + 287, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 287, + 351 + ], + "type": "text", + "content": "As we have seen in Fig. 4, adversarial linear probing achieves the highest adversarial robustness on Caltech256 but falls far behind other methods on CIFAR10. This performance discrepancy across different datasets raises a question: how can we estimate if adversarial linear probing achieves the best robustness? Based on our analysis in Sec. 5.2, where the robustness of adversarial linear probing primarily arises from preserving the robustness in the pretrained model, we hypothesize that the transferred robustness of adversarial linear probing is highly correlated with the transferred accuracy of standard linear probing. This suggests that if standard linear probing successfully adapts the features from the pretrained source domain to the downstream target domain, adversarial linear probing will similarly preserve the robustness in the pretrained model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "content": "To validate this, we define transferred accuracy of standard linear probing " + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "inline_equation", + "content": "(\\mathrm{acc}_{std}^T)" + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "content": " and transferred robustness of adversarial linear probing " + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "inline_equation", + "content": "(\\mathrm{rob}_{adv}^T)" + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "content": " as follows, using full finetune as a baseline to normalize the performance across different datasets:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 422, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 422, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 92, + 422, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\operatorname {a c c} _ {s t d} ^ {T} = \\frac {\\operatorname {a c c} \\left(L P _ {s t d}\\right) - \\operatorname {a c c} \\left(F T _ {s t d}\\right)}{\\operatorname {a c c} \\left(F T _ {s t d}\\right)} \\tag {2}", + "image_path": "9d087e348e33eff16e90a63c781b9bed976c7429b338fcd15c1e0b63d569e646.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 90, + 456, + 287, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 456, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 90, + 456, + 287, + 483 + ], + "type": "interline_equation", + "content": "\\operatorname {r o b} _ {a d v} ^ {T} = \\frac {\\operatorname {r o b} \\left(L P _ {a d v}\\right) - \\operatorname {r o b} \\left(F T _ {a d v}\\right)}{\\operatorname {r o b} \\left(F T _ {a d v}\\right)} \\tag {3}", + "image_path": "dfc9e43d12050342d7bab51a5bc5f24eae6b53d41738ca2f3de0dc35c2d9ef52.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "inline_equation", + "content": "\\mathrm{acc}(\\cdot)" + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "inline_equation", + "content": "\\mathrm{rob}(\\cdot)" + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": " denote the accuracy and robustness of each method, respectively. " + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "inline_equation", + "content": "FT_{std}" + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "inline_equation", + "content": "LP_{std}" + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": " represent standard full finetune and standard linear probing whereas " + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "inline_equation", + "content": "FT_{adv}" + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "inline_equation", + "content": "LP_{adv}" + }, + { + "bbox": [ + 46, + 488, + 287, + 571 + ], + "type": "text", + "content": " stand for their respective adversarial counterparts. We trained 51 models with different hyper-parameter settings across five datasets and present transferred accuracy and robustness in Fig. 5." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 572, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 715 + ], + "type": "text", + "content": "In Fig. 5, the transferred robustness of adversarial linear probing is strongly correlated with the transferred accuracy of standard linear probing, with a high Pearson correlation coefficient (0.896). When the transferred accuracy approaches or surpasses 0, the transferred robustness becomes positive, indicating the improved performance of adversarial linear probing over adversarial fully finetuning. This strong correlation validates our hypothesis that if standard linear probing successfully adapts features from the pretrained to the target domain, its adversarial counterpart is capable of effectively achieving adversarial robustness on downstream tasks." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 322, + 72, + 529, + 240 + ], + "blocks": [ + { + "bbox": [ + 322, + 72, + 529, + 240 + ], + "lines": [ + { + "bbox": [ + 322, + 72, + 529, + 240 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 529, + 240 + ], + "type": "image", + "image_path": "be36f60c6e98e83de1994da02953e42dab6719051a828354a4287321abb4cd23.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 242, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 305, + 242, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 545, + 276 + ], + "type": "text", + "content": "Figure 5. Transferred robustness of adversarial linear probing strongly correlates with transferred accuracy of standard linear probing." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 282, + 493, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 282, + 493, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 282, + 493, + 295 + ], + "type": "text", + "content": "5.4. Robust Linear Initialization (RoLI)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": "Based on our observation that linear probing can outperform other methods when it effectively adapts features to the target domain, we propose Robust Linear Initialization (denoted as RoLI) for adversarial finetuning. Specifically, we initialize the linear head of a robust pretrained model with weights obtained through adversarial linear probing instead of random initialization. Then, we perform adversarial finetuning, using either full finetune or PEFT methods. Since adversarial linear probing excels in preserving robustness from a pretrained model, RoLI provides a more robust initialization for subsequent adversarial finetuning, maximizing the robustness inherited from a robust pretrained model. In addition, the following adversarial finetuning can further enhance robustness by introducing additional robustness through adversarial training. In the following sections, we will evaluate the effectiveness of RoLI applied to four different adversarial finetuning methods across five different datasets and demonstrate it achieves new state-of-the-art robustness in adversarial transfer learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 537, + 545, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 545, + 680 + ], + "type": "text", + "content": "Datasets. In our experiments, we use five datasets: CIFAR10 [24], CIFAR100 [24], Caltech256 [13], CaltechUCSD Birds-200-2011 (CUB200) [42], and Stanford Dogs (Dogs) [21]. For low-resolution image datasets like CIFAR10 and CIFAR100, we resize the image to match the model input shape. For high-resolution image datasets, we apply random resizing and cropping in training and center crop in testing. It's important to note that we integrate the resizing and normalization process directly into the model since the attacker does not have access to pre-processed images. Additional details are provided in the supplementary ??" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Methods. We provide the results from TWINS-AT [29] AutoLoRa [43] as baselines. We proceed to assess six fine" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24836" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 544, + 247 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 544, + 247 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 544, + 247 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 544, + 247 + ], + "type": "table", + "html": "
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
CleanPGDCleanPGDCleanPGDCleanPGDCleanPGDCleanPGD
TWINS-AT [29]91.2452.7370.7231.0876.8648.4068.0929.2464.9820.5874.3836.41
AutoLoRa [43]86.9357.1666.2035.2569.8547.8262.7831.0762.3325.3269.6239.32
RanLI - Full-FT93.0259.1274.3635.6277.3549.1370.8331.5565.8524.7976.2840.04
RanLI - Adapter90.2355.7071.5734.7480.2452.7359.6726.7387.9842.2477.9442.43
RanLI - LoRA90.0256.8871.9834.8377.0250.2564.7429.6584.6339.2477.6842.17
RanLI - Bias90.2556.9471.5036.7279.5052.4366.6929.8887.4142.7579.0743.74
RanLI - VPT90.2457.3872.3735.6079.7453.0761.9426.4686.3443.1078.1343.12
RanLI - Linear84.1637.3067.6525.4681.7954.4769.8824.5691.5545.4579.0137.45
RoLI - Full-FT94.1860.8576.2537.3883.7855.4274.2832.0391.5545.5784.0146.25
RoLI - Adapter90.3155.6971.7534.3381.7454.3264.2025.2292.0247.1280.0043.34
RoLI - LoRA92.2358.6272.8735.1881.7954.5068.8826.7791.2046.7681.3944.37
RoLI - Bias91.8358.3972.1735.1781.7854.4968.1425.7091.5247.2781.0944.20
", + "image_path": "213306e0669328430cae0df6f74e6c8ca90fa32704409b2197ba027be05dd0d2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 293, + 288, + 415 + ], + "blocks": [ + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "text", + "content": "Table 2. RoLI significantly improves the performance and achieves SOTA across five image classification tasks. Robust Linear Initialization (RoLI) enhances robustness by " + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "inline_equation", + "content": "3.88\\%" + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "text", + "content": " and clean accuracy by " + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "inline_equation", + "content": "2.44\\%" + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "text", + "content": " on average compared to Random Initialization (RanLI). Notably, RoLI - Full-FT achieves the best overall performance, with an accuracy of " + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "inline_equation", + "content": "84.01\\%" + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "inline_equation", + "content": "46.25\\%" + }, + { + "bbox": [ + 46, + 255, + 546, + 289 + ], + "type": "text", + "content": " robustness." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 293, + 288, + 415 + ], + "lines": [ + { + "bbox": [ + 48, + 293, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 48, + 293, + 288, + 415 + ], + "type": "table", + "html": "
MethodsCIFAR10CIFAR100Caltech256CUB200DogsAvg
RanLI - Full-FT54.931.862.649.742.548.3
RanLI - Adapter50.829.266.740.368.551.1
RanLI - LoRa53.029.062.844.763.350.6
RanLI - Bias52.331.065.846.267.352.5
RanLI - VPT52.329.766.340.367.351.2
RanLI - Linear26.618.465.740.473.544.9
RoLI - Full-FT56.332.770.452.173.557.0
RoLI - Adapter51.129.165.840.675.252.4
RoLI - LoRa53.930.065.744.674.353.7
RoLI - Bias53.929.865.743.574.853.5
", + "image_path": "9f81739f4163bebb6728df64503f6b33cf1a128c28c9399cf692b6563b97fac6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 510, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 606 + ], + "type": "text", + "content": "tuning techniques introduced in Sec. 3.1 with random initialization. We use Swin Transformer [28] as a backbone architecture for our experiments, whereas TWINS and AutoLoRa use ResNet50 [14]. We apply RoLI to Full-FT, Bias, Adapter, and LoRa. We initialize the newly introduced modules in Adapter and LoRA with zero to ensure that they start with robust linear probing without distorting the robust features preserved in the pretrained model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "Training Details. We use the same optimizer, AdamW [30], and a cosine scheduler with warm-up for all finetuning methods. To determine the optimal learning rate and weight decay values, we conduct a grid search, and the ranges of hyper-parameters along with the optimal combinations can be found in the supplementary ??. We keep method-specific hyper-parameters constant across all datasets. For instance, we set the prompt" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 293, + 545, + 415 + ], + "blocks": [ + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "type": "text", + "content": "Table 3. RoLI consistently outperforms RanLI under AutoAttack. Note, we use " + }, + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "type": "text", + "content": " attack for CIFAR10, CIFAR100, and " + }, + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4 / 255" + }, + { + "bbox": [ + 46, + 424, + 287, + 500 + ], + "type": "text", + "content": " for Caltech256, CUB200 and Stanford Dogs. RoLI shows an average 3.53 AA gain compared with RanLI, and notably, RoLI - Full-FT surpasses other methods by achieving a robustness of 57.0 under AutoAttack. The clean accuracy is illustrated in Tab. 2." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 293, + 545, + 415 + ], + "lines": [ + { + "bbox": [ + 308, + 293, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 308, + 293, + 545, + 415 + ], + "type": "table", + "html": "
Methodsε = 8/255ε = 4/255
RanLI - Full-FT20.1042.50
RanLI - Adapter36.3068.50
RanLI - LoRa32.4063.30
RanLI - Bias35.9067.30
RanLI - VPT34.4067.30
RanLI - Linear30.9073.50
RoLI - Full-FT30.9073.50
RoLI - Adapter37.0075.20
RoLI - LoRa38.4074.30
RoLI - Bias38.2074.80
", + "image_path": "59445c55ed997810f1cbad78dc34ad2247ffbe429a9fee99178b73edcb17cbc7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "lines": [ + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "text", + "content": "Table 4. RoLI consistently improves adversarial robustness even against " + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "text", + "content": " AutoAttack. RanLI - Linear performs well under " + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4 / 255" + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "text", + "content": " AutoAttack, but poorly under " + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 424, + 546, + 502 + ], + "type": "text", + "content": " AutoAttack on Stanford Dogs. This discrepancy demonstrates that adversarial linear probing obtains its robustness mainly from the pretrained model, whereas other methods obtain robustness mainly from adversarial finetuning." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "text", + "content": "length to 10 for the VPT method. To avoid adversarial overfitting [37], we apply early stopping with the epoch that has the best performance on the validation set. During adversarial finetuning, we utilize the PGD-7 attack with " + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "text", + "content": " and a step size of " + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "inline_equation", + "content": "\\alpha = 2 / 255" + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "text", + "content": ". When reporting test accuracy and robustness, we evaluate the models under a PGD-10 attack with " + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 510, + 547, + 654 + ], + "type": "text", + "content": ". Additionally, we report the performance under AutoAttack (AA), which is an ensemble attack and provides a more reliable approach to evaluate the adversarial robustness. We follow the standard AutoAttack setting, i.e., untargeted APGDCE, targeted APGD-DLR, targeted FAB [8], and Square Attack [1]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "PGD-10 Results. Looking at Random Initialization (RanLI) in Tab. 2, the same trend holds as in Sec. 5.1: 1) PEFT methods except linear probing exhibit strong average results across five different datasets, with Bias achiev" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24837" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 60, + 265, + 208 + ], + "blocks": [ + { + "bbox": [ + 67, + 60, + 265, + 208 + ], + "lines": [ + { + "bbox": [ + 67, + 60, + 265, + 208 + ], + "spans": [ + { + "bbox": [ + 67, + 60, + 265, + 208 + ], + "type": "image", + "image_path": "98bc546f3e75bf3c58c246214c9f8c0712c081b3f8c7dee55eae953d85c82daa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 210, + 287, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 210, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 287, + 288 + ], + "type": "text", + "content": "Figure 6. Trade-off between speed and robustness. We conduct the speed test on Stanford Dogs with random linear initialization (RanLI), logistic regression linear initialization (RegLI), standard linear initialization (StdLI), and robust linear initialization (RoLI). RoLI achieves the best performance at the cost of increased training time. Meanwhile, both RegLI and StdLI can improve their performance without incurring substantial time costs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 295, + 287, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 343 + ], + "type": "text", + "content": "ing the best performance (79.25% accuracy and 43.58% robustness). 2) Linear probing achieves the highest robustness on Caltech256 and Stanford Dogs, although it falls behind others on the remaining three datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "type": "text", + "content": "Compared to RandLI, we can observe from Tab. 2 that RoLI significantly enhances the robustness on Caltech256 and Stanford Dogs for all finetuning methods. In particular, RoLI - Full-FT achieves a robustness improvement of " + }, + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "type": "inline_equation", + "content": "6.29\\%" + }, + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "type": "text", + "content": " on Caltech256 and " + }, + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "type": "inline_equation", + "content": "20.78\\%" + }, + { + "bbox": [ + 46, + 344, + 288, + 486 + ], + "type": "text", + "content": " on Stanford Dogs. On other datasets where adversarial linear probing with RanLI does not outperform others, RoLI performs comparable or even better than RanLI. This strongly supports that a robust initialization of the linear head is critical in adversarial transfer learning. Lastly, our RoLI - Full-FT achieves the highest performance across five datasets and sets a new state-of-the-art benchmark." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": "AutoAttack Results. We extend our evaluation to Stanford Dogs using " + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4 / 255" + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": ", as illustrated in Tab. 4. Interestingly, we observe that adversarial linear probing outperforms other methods under " + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4 / 255" + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": " attack but underperforms when tested against " + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": " adversarial attacks. We conjecture that the pretrained model lacks robustness against " + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": " attacks as it is trained using " + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4 / 255" + }, + { + "bbox": [ + 46, + 497, + 287, + 592 + ], + "type": "text", + "content": " adversarial attacks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 593, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 677 + ], + "type": "text", + "content": "This performance disparity confirms that adversarial linear probing inherently derives robustness from pretraining, whereas other methods predominantly achieve robustness from adversarial finetuning. Notably, RoLI consistently improves adversarial robustness even against " + }, + { + "bbox": [ + 46, + 593, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 593, + 287, + 677 + ], + "type": "text", + "content": " attacks, further validating the importance of a robust linear initialization for adversarial transfer learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "To maintain consistency with the pre-training, we follow the conventional settings [9, 10] to set " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " attack for low-resolution datasets (CIFAR10, CIFAR100) and" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 318, + 71, + 533, + 140 + ], + "blocks": [ + { + "bbox": [ + 318, + 71, + 533, + 140 + ], + "lines": [ + { + "bbox": [ + 318, + 71, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 318, + 71, + 533, + 140 + ], + "type": "table", + "html": "
StdLI -CIFAR-10Caltech-256
CleanPGDCleanPGD
Full-FT93.34(-0.84)59.34(-1.51)83.23(-0.55)52.85(-2.57)
Bias93.34(-0.04)58.12(-0.27)82.93(+1.15)52.93(-1.56)
Adapter90.08(-0.23)55.19(-0.50)82.72(+0.98)53.01(-1.31)
LoRa90.71(-1.52)58.17(-0.45)82.87(+1.08)51.47(-3.03)
", + "image_path": "806767e87ff0aa58b72830b1209cd1eec110c1e6c56e03a8e80033f130070185.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 143, + 544, + 165 + ], + "lines": [ + { + "bbox": [ + 306, + 143, + 544, + 165 + ], + "spans": [ + { + "bbox": [ + 306, + 143, + 544, + 165 + ], + "type": "text", + "content": "Table 5. StdLI is less robust than RoLI. The values in parentheses denote the performance gap (StdLI - RoLI)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 172, + 545, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 172, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 305, + 172, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4 / 255" + }, + { + "bbox": [ + 305, + 172, + 545, + 256 + ], + "type": "text", + "content": " attack for high-resolution datasets (Caltech256, CUB200, Stanford Dogs). Tab. 3 demonstrates the robustness under AutoAttack and the clean accuracy is illustrated in Tab. 2. RoLI exhibits higher robustness over RanLI, demonstrating an average 3.53 AA gain. Notably, RoLI - Full-FT achieves a robustness of 57.0, surpassing other methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 268, + 375, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 268, + 375, + 280 + ], + "spans": [ + { + "bbox": [ + 306, + 268, + 375, + 280 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 288, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 545, + 384 + ], + "type": "text", + "content": "Comparison between RoLI and StdLI. Standard Linear Initialization (StdLI) refers to the use of a simple linear probing to initialize the head, while RoLI uses adversarial linear probing. In Tab. 5, we compare the performance of RoLI and StdLI on CIFAR-10 and Caltech-256. We observe that StdLI exhibits lower performance compared to RoLI, with a robustness decrease of 2.48 across three datasets, highlighting the effectiveness of RoLI." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 385, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 385, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 545, + 529 + ], + "type": "text", + "content": "Robustness vs. Speed. Since robust linear initialization involves a two-step adversarial training process, it tends to be considerably slower than adversarial fine-tuning with random initialization. In this section, we show a trade-off between robustness and speed by obtaining the initialization from four different approaches: adversarial linear probing (RoLI), standard linear probing (StdLI), logistic regression (RegLI), and randomization (RanLI). From Fig. 6, it's evident that both RegLI and StdLI enhance robustness compared to random linear initialization within an acceptable time cost. In addition, RoLI achieves the highest performance but at the expense of slower speed." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 540, + 378, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 378, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 378, + 553 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 560, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 560, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 305, + 560, + 545, + 679 + ], + "type": "text", + "content": "This paper systematically investigates how to achieve adversarial robustness in downstream tasks. We highlight the necessity of an adversially robust pretraining. Given a robust pretrained model, we propose to use robust linear initialization (RoLI) followed by adversarial full finetuning or PEFT methods to achieve the best performance. We demonstrate that RoLI outperforms random linear initialization across five image classification tasks. We hope the insights from this study greatly advance research aimed at enhancing adversarial robustness in downstream tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 680, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 680, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 306, + 680, + 545, + 703 + ], + "type": "text", + "content": "Acknowledgment. We thank Chenhe Gu and Xuan Yang for the valuable discussion and insightful feedback." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24838" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "text", + "content": "[1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. 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Illustration of halftones generated by our proposed ink dot-oriented differentiable neural halftoning method and several previous methods [12, 26, 35]. Images are from the DIV2K dataset [2]." + ], + "image_footnote": [], + "bbox": [ + 81, + 271, + 686, + 534 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4f9ad381643712b581c72e65779355fd576899d1ebb7e35748e22aedcb24f8cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 268, + 779, + 532 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b05e07671263afdd5e234349c1b63be3a2c6693579d4c5f977146d09a4f59743.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 268, + 890, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 585, + 313, + 602 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Halftoning is a time-honored printing technique that simulates continuous tones using ink dots (halftone dots). The resurgence of deep learning has catalyzed the emergence of innovative technologies in the printing industry, fostering the advancement of data-driven halftoning methods. Nevertheless, current deep learning-based approaches produce halfstones through image-to-image black box transformations, lacking direct control over the movement of individual halftone dots. In this paper, we propose an innovative halftoning method termed \"neural dot-controllable halftoning\". This method allows dot-level image dithering by providing direct control over the motion of each ink dot. We conceptualize halftoning as the process of sprinkling dots on a canvas. Initially, a specific quantity of dots are randomly dispersed on the canvas and subsequently adjusted based on the surrounding grayscale and gradient. To establish differentiable transformations between", + "bbox": [ + 73, + 618, + 473, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "discrete ink dot positions and halftone matrices, we devise a lightweight dot encoding network to spread dense gradients to sparse dots. Dot control offers several advantages to our approach, including the capability to regulate the quantity of halftone dots and enhance specific areas with artifacts in the generated halftones by adjusting the placement of the dots. Our proposed method exhibits superior performance than previous approaches in extensive quantitative and qualitative experiments.", + "bbox": [ + 496, + 588, + 893, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 753, + 632, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the late 1800s, pioneers such as William Henry Fox Talbot, Georg Meisenbach, Frederic Ives, and Max Levy [32] made significant strides in halftone printing techniques, enabling photographs to be printed on paper using ink. Halftoning is a technique of replicating the color and shading of continuous tone images by employing ink dots (halftone dots) of different sizes and frequencies. It remains a crucial and enduring component in the modern printing", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27528", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/186efc2606451bc23b81d48725eac75a0f97c2751d6dc4be8e9effc8c4951d1f.jpg", + "image_caption": [ + "Figure 2. Prior deep networks-based halftoning methods (top) map an image to a halftone-like continuous-tone image before applying a binarization operation. In contrast, our proposed method (bottom) differs from previous halftoning techniques in that it achieves dot-level halftones through direct control over the movement of each dot." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "industry. A successful halftone can closely reproduce the original image with high quality, leveraging the low-pass filtering characteristics of the human visual system to attain near-optimal visual effects.", + "bbox": [ + 75, + 321, + 468, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Halftone technology can be broadly divided into two categories: traditional or deep learning-based methods. The former can be further cast into three groups based on implementations of dithering process: amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [6, 20, 22, 34], and hybrid modulation [14, 39]. Recently, the renaissance of deep learning as a black-box approximation for high-dimensional functions has catalyzed the emergence of several data-driven methods in the field of halftoning [15, 16, 18, 23, 35], demonstrating superior performance.", + "bbox": [ + 75, + 383, + 468, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we argue that current deep learning methods for halftoning, face some weaknesses that impede their deployment in the printing industry. Notably, these methods treat halftones as binary images and heavily rely on a black box encoder-decoder to convert between the original continuous-tone image and the halftone-induced binary image. However, they operate as image-level transforms rather than directly manipulating the halftone dots, leading to a loss of direct control over the desired properties of the resultant halftones. As observed in Figure 1, purely image-level transformations [12, 26, 35] tend to produce undesired artifacts, and they struggle to directly manipulate local dot arrangements to eliminate these artifacts. In addition, traditional methods do not allow for control over the number of halftone dots. In practical applications, opting for halftone techniques that utilize fewer ink dots can be advantageous for consumable savings. For prints with low detail requirements, like halftone cartoon stickers, a modest quantity of dots suffice to faithfully convey the information present in the continuous tone image.", + "bbox": [ + 75, + 536, + 470, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above issues, we propose ink dot-oriented neural image halftoning for the first time in the literature, which directly controls the motion of each ink dot, enabling dot-level differentiable optimization. Nonetheless, a piv", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "otal challenge in achieving this lies in the discrete nature of ink dot positions, while the objective functions piloting the halftone generation are continuous. Directly propagating the gradient flow from halftone pixels to ink dot positions is unfeasible, rendering gradient back-propagation a challenging endeavor. A key contribution of this paper is the presentation of a novel approach to integrate discrete ink dots into continuous halftone optimization in a fully differentiable manner.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach considers halftoning as the process of optimizing dot placements on a blank canvas using halftone quality-related guidance. We commence by randomly spreading a flexible number of dots on the canvas and then progressively move them. To facilitate smooth gradient backpropagation from the objective function to each discrete ink dot, we introduce a dot encoding module that maps dot coordinates to the product of sparse vectors, creating a structure conducive to differentiable optimization. We also develop a motion-estimating module to predict the motion of each ink dot. Our method offers direct control over the quantity of ink dots in the generated halftones, a feat challenging to attain in prior work, owing to the flexibility and scalability of the proposed dot manipulations.", + "bbox": [ + 496, + 227, + 892, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, this paper introduces ink dot-oriented neural image halftoning, the first approach of its kind to achieve dot-level image dithering by controlling the movement of ink dots. Our proposed model showcases superior performance over previous methods in extensive qualitative and quantitative experiments. Furthermore, the method can be easily extended to arbitrary scale and color images.", + "bbox": [ + 496, + 439, + 890, + 545 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 560, + 640, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Traditional Halftoning", + "text_level": 1, + "bbox": [ + 500, + 585, + 710, + 602 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional halftone methods can be categorized into amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [7, 8, 25, 38], and hybrid approaches [14, 39]. AM methods use dot clusters of varying sizes and frequencies to represent different shades of gray and reproduce the original continuous tone image. FM is represented by the error diffusion algorithm, which distributes the quantization error generated by pixel thresholding to adjacent pixels, achieving superior results. For example, Ostromoukhov [26] proposed an improved error-diffusion algorithm based on the deliberately restricted choice of the distribution coefficients. Unlike these traditional methods, which rely on some prior or handcrafted designs, our approach is data-driven, enabling halftone optimization with greater fitting ability and model capacity.", + "bbox": [ + 496, + 608, + 890, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Deep Learning Based Halftoning", + "text_level": 1, + "bbox": [ + 500, + 845, + 787, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the emergence of deep learning techniques, researchers have explored the use of neural networks to gen", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27529", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/84a5a9ab9a101e3b21f852e9c93572eef2ceae6613ddc148796def38e1a90d62.jpg", + "image_caption": [ + "Figure 3. Schematic illustration of the proposed method. The proposed method takes a set of random dots as input. O-Net differentiably transforms discrete ink dot positions into a halftone matrix, effectively spreading dense gradients over sparse dots. P-Net predicts the motion of each halftone dot." + ], + "image_footnote": [], + "bbox": [ + 122, + 89, + 851, + 218 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "erate halftones [16, 17, 23, 35]. For example, Xia et al. [35] utilized stacked convolutional networks to learn reversible halftones capable of concealing color information. However, most of prior methods treat the entire image as a whole and cannot achieve fine control of halftone dots. In contrast, our approach facilitates dot-level controllable halftones, offering greater interpretability and maneuverability.", + "bbox": [ + 75, + 284, + 472, + 391 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 409, + 168, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. O-Net: Spreading Dense Gradients onto Sparse Ink Dots", + "text_level": 1, + "bbox": [ + 76, + 435, + 468, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Halftone images consist solely of black and white pixels, with the arrangement of black pixels determining the brightness and visual structure of each area in the image. A straightforward approach to generate halftone images is to first learn a mapping from a continuous-tone image to an almost binary image, which is then rounded to produce binary halftone dots, as demonstrated in prior work [15-18, 23, 35]. Nevertheless, this approach is subject to several limitations. Primarily, it lacks direct control over individual halftone dots. In the event of defects in some generated halftone areas, the entire halftone have to be regenerated, posing escalating challenges, particularly for larger images. Additionally, previous image-level halftoning methods lack the capability to regulate the quantity of ink dots in halftones. In scenarios where printing equipment features limited or costly consumables, this lack of flexibility hinders the generation of halftones with varying consumable levels.", + "bbox": [ + 75, + 474, + 472, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Figure 3, we present a novel approach for dot-centric halftoning. The process begins by initializing a set of dots at random. Denote the dot set as $\\mathcal{Q} = \\{\\pmb{q}_0,\\pmb{q}_1,\\dots,\\pmb{q}_{k - 1}\\}$ , where $k$ represents the number of dots. Each dot $\\pmb{q}_i$ is represented by its two-dimensional coordinates within the image, i.e., $\\pmb{q}_i = \\{\\pmb{x}_i,\\pmb{y}_i\\}$ , where $i\\in [0,k - 1],\\pmb{x}_i\\in [0,L_1 - 1],\\pmb{y}_i\\in [0,L_2 - 1]$ , with $L_{1}$ and $L_{2}$ being the height and width of the image, respectively. The coordinates of these dots can be used to index their corresponding positions on a \"white canvas\" $\\mathbf{H}$ , which serves as a layout", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for the ink dots. $\\mathbf{H}$ consists solely of elements that are either 0 or 1 (after normalization). A value of 1 in $\\mathbf{H}$ indicates the presence of an ink dot at the corresponding position, while an element 0 indicates the absence of a dot. To pin the dots in set $\\mathcal{Q}$ onto the white canvas $\\mathbf{H}$ , a straightforward approach is to directly fill these halftone dots into the matrix $\\mathbf{H}$ :", + "bbox": [ + 496, + 284, + 893, + 388 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} \\left[ \\left\\lfloor \\boldsymbol {x} _ {i} \\right\\rfloor , \\left\\lfloor \\boldsymbol {y} _ {i} \\right\\rfloor \\right] = 1, \\quad \\forall \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {y} _ {i}\\right) \\in \\mathcal {Q}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 391, + 890, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Performing such an operation is challenging to optimize in an end-to-end neural network due to the discreteness of ink dot coordinates $\\mathbf{q}_i$ , and the continuity of $\\mathbf{H}$ . Directly passing the gradient flow between matrix coordinates $\\mathbf{x}_i, \\mathbf{y}_i$ and $\\mathbf{H}$ is not feasible, and backpropagation is difficult to conduct. While reinforcement learning ideas [10] suggest that decision-making agents can help networks execute decisions under reward functions for discrete action spaces, these approaches are relatively complicated. Instead, we aim to design a simple, differentiable transformation between $\\mathcal{Q}$ and $\\mathbf{H}$ to enable end-to-end training of the network.", + "bbox": [ + 496, + 417, + 893, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our key observation is that the halftone $\\mathbf{H}$ can be generated through the Hadamard product of multiple sparse binary matrices, and these sparse binary matrices can be expressed as the product of one-hot encodings of dot coordinates. For a halftone $\\mathbf{H}$ with $k$ dots, we decompose it into the Hadamard product of $k$ independent matrices $\\mathbf{H}_0,\\mathbf{H}_1,\\dots,\\mathbf{H}_{k - 1}$ :", + "bbox": [ + 496, + 599, + 893, + 705 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} = \\mathbf {I} - \\left(\\mathbf {I} - \\mathbf {H} _ {0}\\right) \\odot \\left(\\mathbf {I} - \\mathbf {H} _ {1}\\right) \\odot \\dots \\odot \\left(\\mathbf {I} - \\mathbf {H} _ {k - 1}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 719, + 890, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\odot$ is the Hadamard product, and $\\mathbf{I}$ stands for an all-one matrix. $\\mathbf{H}_0,\\mathbf{H}_1,\\dots ,\\mathbf{H}_{k - 1}$ have the property that each matrix contains only one element equal to 1, while the rest are 0. Intuitively, $\\mathbf{H}_0,\\mathbf{H}_1,\\ldots ,\\mathbf{H}_{k - 1}$ represent halftones formed by printing dots $q_{0},q_{1},\\ldots ,q_{k - 1}$ , respectively. For a dot $q_{i} = \\{\\pmb {x}_{i},\\pmb {y}_{i}\\}$ , we can get its one-hot encoding from $\\pmb{x}_i$ and $\\pmb{y}_i$ :", + "bbox": [ + 496, + 748, + 893, + 854 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {o} \\left(\\boldsymbol {x} _ {i}\\right) = \\operatorname {O n e H o t E n c o d i n g} \\left(\\boldsymbol {x} _ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 867, + 890, + 891 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\pmb {o} (\\pmb {y} _ {i}) = \\mathrm {O n e H o t E n c o d i n g} (\\pmb {y} _ {i}).\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 888, + 807, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27530", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Assuming $\\pmb{o}(\\pmb{x}_i)$ and $\\pmb{o}(\\pmb{y}_i)$ have been obtained, $\\mathbf{H}_i$ can be calculated according to $\\pmb{o}(\\pmb{x}_i)$ and $\\pmb{o}(\\pmb{y}_i)$ via $\\mathbf{H}_i = \\pmb{o}(\\pmb{x}_i)^\\top \\cdot \\pmb{o}(\\pmb{y}_i)$ .", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Substituting the calculated $\\mathbf{H}_i$ into Equation 2, the halftone $\\mathbf{H}$ can be obtained. The only non-differentiable step occurs in Equation 3 (i.e., OneHotEncoding). The non-differentiable problem of converting discrete ink dots to continuous halftone matrices is transformed into the non-differentiable problem of one-hot encodings, resulting in a simplified problem. We learn a model O-Net ('O' stands for \"one-hot encoding\") to perform the mapping from discrete coordinates $\\boldsymbol{x}_i$ , $\\boldsymbol{y}_i$ to one-hot encoding $\\boldsymbol{o}(\\boldsymbol{x}_i)$ , $\\boldsymbol{o}(\\boldsymbol{y}_i)$ . Denote O-Net as O for brevity, which consists of fully connected layers in our implementation. ReLU activation function is used between each layer. During the optimization of O-Net, the potential coordinate values $\\tilde{\\boldsymbol{x}}$ and $\\tilde{\\boldsymbol{y}}$ are fed into O, and the gradient is computed utilizing the following loss function $\\mathcal{L}_{\\mathrm{O - Net}}$ :", + "bbox": [ + 75, + 137, + 473, + 364 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {O - N e t}} =\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 378, + 153, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{\\max (L _ {1} , L _ {2}) / s} \\sum_ {l = 0} ^ {\\max (L _ {1}, L _ {2}) - 1} | \\mathbf {O} (\\tilde {\\boldsymbol {x}} _ {l}) - \\mathrm {O n e H o t E n c} (\\tilde {\\boldsymbol {x}} _ {l}) | +\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 398, + 473, + 443 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{\\max \\left(L _ {1} , L _ {2}\\right) / s} \\sum_ {l = 0} ^ {\\max \\left(L _ {1}, L _ {2}\\right) - 1} | \\mathbf {O} (\\tilde {\\boldsymbol {y}} _ {l}) - \\operatorname {O n e H o t E n c} (\\tilde {\\boldsymbol {y}} _ {l}) |, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 445, + 468, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where OneHotEncoding $(\\tilde{\\boldsymbol{x}}_l)$ and OneHotEncoding $(\\tilde{\\boldsymbol{y}}_l)$ denote the one-hot vector determined by $\\tilde{\\boldsymbol{x}}_l$ and $\\tilde{\\boldsymbol{y}}_l$ , respectively. $s$ represents the sampling step. It is worth noting that the dot coordinates $\\boldsymbol{x}_i$ and $\\boldsymbol{y}_i$ are decimal numbers. Therefore, to ensure that the network O can accurately handle different coordinate values, it is necessary to densely sample the interval $[0, \\max(L_1, L_2) - 1]$ . In our experiments, we use a sampling step of 0.01 for this interval. The architecture of O-Net is illustrated in Figure 4.", + "bbox": [ + 75, + 500, + 468, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The precision $\\mathcal{P}(\\mathbf{O})$ is calculated as follows:", + "bbox": [ + 96, + 637, + 395, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} (\\mathbf {O}) = \\frac {1}{\\max (L _ {1} , L _ {2}) / s} \\sum_ {l = 0} ^ {\\max (L _ {1}, L _ {2}) - 1} \\mathbb {1} \\left\\{\\arg \\max (\\mathbf {O} (\\tilde {\\boldsymbol {x}} _ {l})) \\right.,\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 666, + 468, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\arg \\max (\\mathrm{OneHotEncoding}(\\tilde{\\boldsymbol{x}}_l))\\} +$", + "bbox": [ + 137, + 713, + 383, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{\\max \\left(L _ {1} , L _ {2}\\right) / s} \\sum_ {l = 0} ^ {\\max \\left(L _ {1}, L _ {2}\\right) - 1} \\mathbb {1} \\left\\{\\arg \\max \\left(\\mathbf {O} \\left(\\tilde {\\boldsymbol {y}} _ {l}\\right)\\right), \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 733, + 468, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\arg \\max (\\mathrm{OneHotEncoding}(\\tilde{\\mathbf{y}}_l)))\\}$ (5)", + "bbox": [ + 137, + 777, + 468, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}\\{a,b\\}$ is 1 when $a$ and $b$ are equal, and 0 otherwise. In the experiments, O-Net is first trained to convergence and its parameters are fixed during halftone generation.", + "bbox": [ + 75, + 808, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discussion. We eschew the use of embedding matrix lookups to establish the mapping between dot coordinates and one-hot encodings due to their non-differentiability.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9d95e883099e2e704951724a1dc8c41abee4199183350e7376b9bf91ed4f8a51.jpg", + "image_caption": [ + "Figure 4. Illustration of O-Net for differentiable transformation from discrete dots to continuous vector-based halftone representations." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 893, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This characteristic disrupts gradients and impedes the process of backpropagation.", + "bbox": [ + 496, + 284, + 890, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. P-Net: Ink Dot Motion Prediction", + "text_level": 1, + "bbox": [ + 498, + 324, + 797, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A primary contribution of this work is the achievement of dot controllable halftones, with the prediction of the ink dot motion playing a crucial role in this realization. While some deep learning methods have introduced techniques for point motion control and prediction, exemplified in point cloud generation [1, 4, 24, 28, 33, 36], applying these methods directly to halftoning is not feasible for the following reasons: (1) Point clouds typically consist of a small number of points, for instance, the 2,048 points utilized in [24] to generate point clouds of various shapes. In contrast, halftones comprise a substantial number of ink dots, with $20,000 \\sim 30,000$ ink dots in a $256 \\times 256$ resolution image. As the dot count escalates, optimizing the model becomes progressively more challenging. (2) Point cloud generation methods are primarily employed to create point cloud shapes with a coarse level of detail. In contrast, halftones incorporate intricate details and textures, demanding precise and meticulous control over the movement of each ink dot to achieve a fine-grained result.", + "bbox": [ + 496, + 347, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To tackle the aforementioned challenges, we propose P-Net, a network that employs image gray levels as guidance to achieve ink dot motion prediction, as shown in Figure 5. Inspired by recent diffusion generative models [9, 29-31], we explore the efficacy of simple and lightweight convolutional blocks for dot motion prediction. P-Net takes the halftone $\\mathbf{H}$ formed by ink dots (Equation 2) and the continuous tone image $\\mathbf{C}$ as input. Each element in the matrix $\\mathbf{C}$ represents the gray level of the image at the corresponding position. The approach employed by P-Net to integrate information from $\\mathbf{H}$ and $\\mathbf{C}$ is relatively straightforward, involving concatenation of the two matrices along the channel dimension:", + "bbox": [ + 496, + 635, + 890, + 829 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {\\text {i n}} = \\operatorname {C o n v 2 D} (\\mathbf {H} | | \\mathbf {C}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 830, + 890, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where Conv2D means two-dimensional convolution, $||$ means the concatenation operation. While alternative approaches, including post-smooth concatenation and density-", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "27531", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Algorithm for Dot Controllable Halftoning", + "bbox": [ + 78, + 90, + 449, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input:", + "text_level": 1, + "bbox": [ + 81, + 111, + 130, + 125 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The set of random dots, $\\mathcal{Q} = \\{\\pmb {q}_0,\\pmb {q}_1,\\dots ,\\pmb {q}_{k - 1}\\}$", + "bbox": [ + 106, + 125, + 426, + 140 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The number of dots in the set $\\mathcal{Q}, k$ ;", + "bbox": [ + 106, + 141, + 339, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Continuous tone image, C;", + "bbox": [ + 106, + 156, + 287, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The number of iterations, $\\tau$", + "bbox": [ + 106, + 171, + 292, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output:", + "text_level": 1, + "bbox": [ + 83, + 186, + 140, + 199 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Generated halftone, $\\mathbf{H}_{\\mathrm{out}}$", + "1: Transform the dots in the set $\\mathcal{Q}$ into halftone $\\mathbf{H}^{(0)}$ using O-Net; /* Equation 2 */", + "2: for $i = 0$ to $\\tau - 1$ do", + "3: Feed $\\mathbf{H}^{(i)}$ and $\\mathbf{C}$ into P-Net as input; /* Equation 6*/", + "4: Obtain motion predictions of each dot in $\\mathcal{Q}$ : $\\mathbf{P}_{\\mathrm{out}}^{(i)} \\gets \\mathbb{P} - \\mathrm{Net}(\\mathbf{H}^{(i)}, \\mathbf{C})$ ; /* Equation 8 */", + "5: Update the position of ink dot $\\forall \\pmb{q}_i \\in \\mathcal{Q}$ , and update the set $\\mathcal{Q}$ ; /* Equation 9*/", + "6: Transform the dots in the set $\\mathcal{Q}$ into halftone $\\mathbf{H}^{(i + 1)}$ using O-Net; /* Equation 2 */", + "7: Calculate $\\mathcal{L}_{\\mathrm{P}}$ and update the model parameters of P-Net; /\\*Equation 13\\*/", + "8: end for", + "9: return $\\mathbf{H}_{\\mathrm{out}}\\gets \\mathbf{H}^{\\tau}$" + ], + "bbox": [ + 86, + 200, + 468, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "integral map-based methods, have been explored in the experiments, they demand greater computation and do not yield substantial performance enhancements. P-Net utilizes a sequence of convolution modules to acquire the fusion representation of matrices $\\mathbf{H}$ and $\\mathbf{C}$ , followed by several downsampling modules to reduce the image resolution:", + "bbox": [ + 75, + 472, + 468, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {P}} = \\operatorname {D o w n S a m p l e} (\\operatorname {S t a c k e d C o n v 2 D} \\left(\\mathbf {P} _ {\\text {i n}}\\right)), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 571, + 468, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\widetilde{\\mathbf{P}}$ represents the feature matrix of high-level gray scale information, which coarsely expresses the overall movement trend of the ink dots within adjacent image blocks. Next, a prediction head composed of convolutions is used on the upsampled $\\widetilde{\\mathbf{P}}$ matrix to make the output dot motion $\\mathbf{P}_{\\mathrm{out}}$ consistent with the resolutions of the halftone matrix $\\mathbf{H}$ :", + "bbox": [ + 75, + 599, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {\\text {o u t}} = \\operatorname {S t a c k e d C o n v 2 D} (\\operatorname {U p S a m p l e} (\\tilde {\\mathbf {P}})). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 715, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each element in $\\mathbf{P}_{\\mathrm{out}}$ represents the displacement vector of the ink dot at the corresponding position, and it has two channels representing the motion prediction along $x$ and $y$ directions, respectively. For $\\forall \\pmb {q}_i\\in \\mathcal{Q},\\pmb {q}_i = \\{\\pmb {x}_i,\\pmb {y}_i\\}$ , its new position can be derived as:", + "bbox": [ + 75, + 742, + 468, + 816 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\hat {\\boldsymbol {x}} _ {i}, \\hat {\\boldsymbol {y}} _ {i}\\right) = \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {y} _ {i}\\right) + \\mathbf {P} _ {\\text {o u t}} \\left[ \\left\\lfloor \\boldsymbol {x} _ {i} \\right\\rfloor , \\left\\lfloor \\boldsymbol {y} _ {i} \\right\\rfloor \\right]. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 827, + 468, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The ink dot coordinates $\\hat{\\pmb{q}}_i = \\{\\hat{x}_i,\\hat{y}_i\\}$ after the motion can be differentiated to form a new halftone matrix $\\widehat{\\mathbf{H}}$ through O-Net, and the iteration is completed.", + "bbox": [ + 75, + 853, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/39cb4c56660063f093c69c8d449f644835a7f4db7d67434b0d033c723188dd9e.jpg", + "image_caption": [ + "Figure 5. Schematic diagram of the proposed P-Net, which is used to predict the motion of each ink dot." + ], + "image_footnote": [], + "bbox": [ + 506, + 92, + 890, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training Scheduling and Optimization", + "text_level": 1, + "bbox": [ + 500, + 244, + 830, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To optimize our model, following [27, 35], we use the tone loss $\\mathcal{L}_T$ , which computes the dissimilarity between halftone predictions $\\mathbf{H}_{\\mathrm{out}}$ and continuous tone images $\\mathbf{C}$ :", + "bbox": [ + 498, + 268, + 890, + 314 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {T} = \\mathbb {E} _ {\\mathbf {H}} \\| \\text {G a u S m o o t h} (\\mathbf {H} _ {\\text {o u t}}) - \\text {G a u S m o o t h} (\\mathbf {C}) \\| _ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 323, + 890, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\| \\cdot \\| _2$ represents the L2 norm. To improve the structural similarity of the generated halftones, the structural loss $\\mathcal{L}_S$ is employed:", + "bbox": [ + 498, + 354, + 890, + 400 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S} = \\mathbb {E} _ {\\mathbf {H}} \\| \\operatorname {S t r u c} \\text {- M e a s u r e} (\\mathbf {H} _ {\\text {o u t}}, \\mathbf {C}) \\| _ {1}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 409, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Additionally, the pixel loss $\\mathcal{L}_R$ is adopted to measure the difference between the generated halftone after inverse halftoning transformation and the continuous tone image:", + "bbox": [ + 498, + 435, + 890, + 481 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R} = \\mathbb {E} _ {\\mathbf {H}} \\| \\mathcal {R} \\left(\\mathbf {H} _ {\\text {o u t}}\\right) - \\mathbf {C} \\| _ {2}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 491, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{R}$ represents the frozen inverse halftoning network [35]. The total loss $\\mathcal{L}_P$ is as follows:", + "bbox": [ + 498, + 517, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {P} = \\mathcal {L} _ {T} + \\gamma_ {S} \\mathcal {L} _ {S} + \\gamma_ {R} \\mathcal {L} _ {R}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 556, + 890, + 573 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma_{S}$ and $\\gamma_{R}$ are hyperparameters to trade-off each loss term. We detail the training process in Algorithm 1.", + "bbox": [ + 498, + 583, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 626, + 632, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets, Baselines, and Evaluation Protocols", + "text_level": 1, + "bbox": [ + 500, + 650, + 880, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Baselines. Following previous research [13, 35], we curate a halftoning dataset by selecting images from UTKFace [37] and DIV2K [2]. The dataset comprises 4000, 1000, and 400 images in the training, validation, and test sets, respectively. We select baseline models from two categories: traditional halftoning methods [12, 21, 26] and deep learning-based halftoning methods [35]. The traditional methods include amplitude modulation techniques (such as Ordered Dithering), frequency modulation techniques (such as Floyd-Steinberg Error Diffusion, Simpler Floyd-Steinberg Error Diffusion, Jarvis, Judice, and Ninke Dithering, Stucki Dithering, Atkinson Dithering, Burkes Dithering, Sierra Dithering, Two Row Sierra Dithering, and Sierra Lite Dithering), and improvements of Floyd-Steinberg error diffusion algorithm (such as Ostromoukhov's Method).", + "bbox": [ + 498, + 672, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27532", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6c0a68b7369da5cd36fd6ef1804600b8a292ff020e9ef4b9f7fbacb0193d36d3.jpg", + "image_caption": [ + "(a) training iteration $= 1000$" + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 277, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/29effad5bb89312958b237c71e72bcdff28d64750b75faa016047a33ab25dc7c.jpg", + "image_caption": [ + "(b) training iteration $= 3000$", + "Figure 6. O-Net robustness test experiment. The figure shows the variation trend of the halftone quality obtained by O-Net with the noise intensity. a, b, c, and d represent 1000, 3000, 6000, and 9000 model iterations $(\\times 10^{4})$ , respectively." + ], + "image_footnote": [], + "bbox": [ + 285, + 90, + 475, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/80e942c4c366fd9384bec6463e3e1910f7933283037a06b8d387338946e7f7a3.jpg", + "image_caption": [ + "(c) training iteration $= 6000$" + ], + "image_footnote": [], + "bbox": [ + 482, + 90, + 669, + 194 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2bd068e964e91eb7c905938d2ef23eedd8b19e2edb31b84c5e7823a10b4cb410.jpg", + "image_caption": [ + "(d) training iteration $= 9000$" + ], + "image_footnote": [], + "bbox": [ + 678, + 90, + 866, + 195 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3413eff1b5d0b910578bfdb03bb22f880462836d801564f9d576ce6a61935391.jpg", + "table_caption": [ + "Table 1. Performance comparison of different halftoning methods on test images in terms of peak signal to noise ratio." + ], + "table_footnote": [], + "table_body": "
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]29.6936.491.1433.04
Floyd-S. [12]35.3144.401.7239.52
Simpler Floyd-S. [21]32.5241.611.6436.81
Jarvis, J., and N. [21]27.7038.291.8532.67
Stucki [21]28.5739.101.8533.40
Atkinson [21]21.7831.771.8226.36
Burkes [21]31.7441.581.7535.62
Sierra [21]28.2338.511.8733.25
Two Row Sierra [21]30.8241.211.7334.86
Sierra Lite [21]35.9545.581.6540.90
Ostromoukhov [26]36.0445.901.7641.18
Xia's Method [35]29.8935.940.8133.83
Our Proposed Method34.7446.642.1843.04
", + "bbox": [ + 84, + 286, + 460, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Regarding deep learning methods, we select [35] as the baseline, which is a recently proposed deep learning-based halftoning approach.", + "bbox": [ + 75, + 506, + 468, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Protocols and Implementation Details. Following previous work [35], we use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) to measure the quality of the generated halftones. Before computing PSNR, we first smooth both the halftone and continuous tone image with an $11 \\times 11$ Gaussian filter, and then use the smoothed images to calculate the metrics. In addition, we also use qualitative experiments to evaluate the performance of different methods. The quantity of initial dots $k$ is determined through a linear transformation based on the grayscale of the continuous tone. In P-Net, the number of channels is 64, the convolution kernel size is set to $3 \\times 3$ . O-Net consists of 4 fully connected layers, and the activation function between layers is ReLU. $\\gamma_{S}$ and $\\gamma_{R}$ are set to 0.04 and 0.08 respectively. Adam optimizer [19] is used to optimize the model, and the learning rate is set to 0.0001.", + "bbox": [ + 75, + 551, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Performance Comparison", + "text_level": 1, + "bbox": [ + 76, + 801, + 310, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct quantitative experiments on images with $64 \\times 64$ resolutions, and the experimental results are shown in Table 1. It can be observed that our proposed method achieves superior performance than previous methods. Traditional methods (e.g., Ordered Dithering, Floyd-Steinberg", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Error Diffusion, Ostromoukhov's Method) usually predefine some dithering matrices or diffusion coefficients, which achieve relatively good results. However, these traditional methods apply a hand-crafted halftoning criterion to all images indiscriminately, and thus have limited flexibility compared to data-driven approaches like [35]. Besides, previous methods perform halftone generation on the global image and cannot adaptively control the motion of each ink dot, which makes it difficult to flexibly remove some undesired artifacts in the generated halftones. In contrast, our method can flexibly control the motion of each ink dot on the halftone, thus achieving better experimental results.", + "bbox": [ + 496, + 255, + 890, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Study on the Effectiveness of O-Net", + "text_level": 1, + "bbox": [ + 498, + 450, + 807, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A well-performing O-Net should be able to handle various coordinate values produced by model predictions. Although we sample the $[0, \\max(L_1, L_2) - 1]$ interval as densely as possible during training, it is still not enough to cover various float coordinate values that may be encountered during model training. In light of this, we design some experiments to verify the robustness of O-Net to numerical noise of float numbers, as shown in Figure 6. The main process of the experiment is that we randomly add noises of different intensities to the correct coordinates of ink dots, and observe the prediction precision of O-Net after adding noises. The magnitude of the noise is constrained between $[0, 1]$ , which is to ensure that the original position of the ink dot will not be changed when the noise is added to the coordinates. The intensity of the noise is defined by its coverage percentage of the coordinate value. As illustrated in Figure 6, during the initial stages of training, noise interference adversely impacts the quality of the halftones generated by the model. However, as training advances towards convergence, the model becomes less sensitive to noise interference, affirming the robustness of O-Net.", + "bbox": [ + 496, + 476, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition, we visualize the heat maps of O-Net prediction results at different stages of training, as shown in Figure 7. We first randomly initialize 64 ink dot coordinates on a $64 \\times 64$ resolution image, then feed these 64 dot coordinates into O-Net, and visualize the model prediction results. As depicted in Figure 7, prior to the convergence of O-Net, the predicted image exhibits numerous non-binarized gray", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27533", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c6ab0862b593f66381d8106f81554a3e3bdd75c1ec4a42d415faef347b8459a.jpg", + "image_caption": [ + "(a) random initialized" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 246, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aa74e95b3353ca56192e7d99303c808726c9f06a1e817351955f7ccfe26a31b7.jpg", + "image_caption": [ + "(b) training iteration $= 10$" + ], + "image_footnote": [], + "bbox": [ + 254, + 90, + 455, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f9670b92e8c8f79181a3ee931bcacf559461b0b305f7409b663515e0cee65bf.jpg", + "image_caption": [ + "(c) training iteration=6000" + ], + "image_footnote": [], + "bbox": [ + 464, + 90, + 656, + 217 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/24b19fe4754260c45de449713cfe095c7ff843f564b1788efdd7ed47597d923b.jpg", + "image_caption": [ + "(d) training iteration $= 9000$" + ], + "image_footnote": [], + "bbox": [ + 663, + 90, + 856, + 217 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b51b5cade0ed58a2221b0c8f61b6225c307ce09ecee050df234454f4e8ea7c92.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 861, + 90, + 885, + 212 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/901009823ea8982d69bee154005d70284a288e823a12e79081e0d12c92c9dead.jpg", + "image_caption": [ + "Figure 7. Visualization of model predictions at different stages of O-Net training. a, b, c, and d represent 0, 10, 6000, and 9000 model iterations $(\\times 10^{4})$ , respectively. The effectiveness of O-Net increases as the image transitions towards a binary representation.", + "(a) continuous tone" + ], + "image_footnote": [], + "bbox": [ + 86, + 280, + 218, + 385 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba615fafe11f44aaff548626466567280301643e32f90ff69c9378736cbe2c93.jpg", + "image_caption": [ + "(b) iteration #1" + ], + "image_footnote": [], + "bbox": [ + 220, + 280, + 354, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3636afd32fd7572cc9918d3ddadc6b10f68fb6653911dc34282d038c644f5b8.jpg", + "image_caption": [ + "(c) iteration #2" + ], + "image_footnote": [], + "bbox": [ + 361, + 280, + 517, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86146f3eb8ad72546c80e0c6d8d3b4f54df843b0dad1ba313ce706a1b94ea322.jpg", + "image_caption": [ + "(d) iteration #3" + ], + "image_footnote": [], + "bbox": [ + 524, + 281, + 683, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f5e29f41d2dfdd799ef56eabefe4c0f28fe39f5ac256a8aa98ce33ed558a7cf1.jpg", + "image_caption": [ + "(e) iteration #4" + ], + "image_footnote": [], + "bbox": [ + 689, + 281, + 851, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7cf657eda71856b3bbf7cf171394f4a9373709fb02a099565f288fa62f8f2b91.jpg", + "image_caption": [ + "Figure 8. Visualization of ink dot motion predictions over several iterations. Here we visualize the motions on x-axis, normalized to 0 to 1.", + "(a) quantity level 1", + "Figure 9. Illustration of the resulting halftones with different numbers of ink dots. Number of ink dots: (a): 10K; (b): 14K; (c): 18K. More ink dots enrich the texture details of the image." + ], + "image_footnote": [], + "bbox": [ + 88, + 434, + 210, + 529 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fbe7e7a46e5f5095d46781a043d12a320879d216955d94801bfd8851abc2869e.jpg", + "image_caption": [ + "(b) quantity level 2" + ], + "image_footnote": [], + "bbox": [ + 212, + 434, + 334, + 529 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/92ed0c7984f06810b1a5113b7b7521d633645fe91dc600b207a04fb3b02db18d.jpg", + "image_caption": [ + "(c) quantity level 3" + ], + "image_footnote": [], + "bbox": [ + 334, + 434, + 459, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pixels, indicating that the one-hot encoding at this stage is not fully optimized. In contrast, upon O-Net convergence, the generated halftone comprises solely black and white pixels, affirming the capability of O-Net in producing binary halftones.", + "bbox": [ + 75, + 619, + 468, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison of Structural Quality", + "text_level": 1, + "bbox": [ + 76, + 705, + 374, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The structural quality of halftones is also an important indicator for evaluating the performance of an algorithm. We compare the structural similarity with methods that generate halftones with higher PSNR, as shown in Table 2. It can be observed that our proposed method achieves better structural similarity than the baseline methods.", + "bbox": [ + 75, + 729, + 468, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Visualization of Motion Predictions", + "text_level": 1, + "bbox": [ + 76, + 830, + 383, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We depict the dot motion predictions generated by P-Net across multiple iterations, as illustrated in Figure 8. Notably, the model rapidly shifts the ink dots from regions with", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1666227016905ebad5fc68cf364a8cf1fb1643b8b05ebdfccaab9aa1916b86b4.jpg", + "table_caption": [ + "Table 2. Performance comparison of different halftoning methods on test images in terms of structural similarity." + ], + "table_footnote": [], + "table_body": "
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]0.02540.30700.04860.1384
Floyd-S. [12]0.02960.43350.06040.1687
Simpler Floyd.-S. [21]0.02950.46100.06290.1664
Sierra Lite [21]0.02840.41100.05960.1660
Ostromoukhov [26]0.02650.41850.05900.1628
Our Proposed Method0.03050.41590.06280.1709
", + "bbox": [ + 501, + 474, + 890, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "elevated grayscale to those with lower grayscale in the initial stage. This observation substantiates that the motion predictions of P-Net are grounded in a keen awareness of image grayscale. With the progression of iterations, the motions converge towards zero across the majority of the image, leading the model to confine ink dot movements to a limited local area.", + "bbox": [ + 496, + 603, + 890, + 708 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Qualitative Experiments", + "text_level": 1, + "bbox": [ + 500, + 724, + 723, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 10 presents qualitative experimental results of different halftone methods, which focus on generating halftones on flat textures with subtle variations in image tone (e.g., light and shadow on clouds). Earlier efforts yield halftones with either undesirable white holes or repetitive streaks of ink dots, compromising the overall quality of the output. Additionally, deep learning methods (Figure $10\\mathrm{m}$ ) introduce visual artifacts and struggle to faithfully reproduce subtle variations in light and shade. In contrast, our method better preserves tonal details in flat regions and achieves su", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27534", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1f9f2f3e70313faf8a44ae248cf9749b82ee19396631c0611a44570019411a83.jpg", + "image_caption": [ + "(a) Contone" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 196, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19ce8d847670b691e2ed68075e98c887199b832a771fb6be1658d39e2b44c26b.jpg", + "image_caption": [ + "(b) Simpler F.-S." + ], + "image_footnote": [], + "bbox": [ + 197, + 88, + 312, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5958c5bdc2effc542b658f99fe0e1ac351abf2809bb8d428db042cb5c395394b.jpg", + "image_caption": [ + "(c) J. J., and Ninke" + ], + "image_footnote": [], + "bbox": [ + 313, + 88, + 424, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/43ec3b426e97a9ade10c38d6be42619d80d0ba6c6b649df66e5e89ac95d932f1.jpg", + "image_caption": [ + "(d) Stucki" + ], + "image_footnote": [], + "bbox": [ + 426, + 88, + 542, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aeacf5f0dc300a6cc1edaf9124497475524b18c77450b5c67f63870d670b1d41.jpg", + "image_caption": [ + "(e) Atkinson" + ], + "image_footnote": [], + "bbox": [ + 544, + 88, + 656, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/748a64f6d168842e65099dab52c1d2fd25c120a28a1e2b49cd685e58361eabd1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 88, + 772, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7bb6ac269a4ed56ef1f2f325ab11df55b67efd9e0fb29d8d52b8776ee199348a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 88, + 890, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01bac461886d9abdd7a23a67b3277ba6208a1bc6d644e4bc872483c1df8efa54.jpg", + "image_caption": [ + "(h) Two Row Sierra" + ], + "image_footnote": [], + "bbox": [ + 81, + 191, + 196, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1c5f36f9ea7e7d689527cc0db8fe00e1ac7b117de83f71fd6ad77027f26f0fa0.jpg", + "image_caption": [ + "(i) Sierra Lite" + ], + "image_footnote": [], + "bbox": [ + 197, + 191, + 310, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e045686601350a670b9b66019cbcbfbfcdabd70cf18c72d535db5480ee7593e3.jpg", + "image_caption": [ + "(j) Ordered Dither" + ], + "image_footnote": [], + "bbox": [ + 312, + 191, + 424, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5166ad0746a05b9a7682e94b25818f3df91929b9a5affc6f8ac4473c1b4deea8.jpg", + "image_caption": [ + "(k) Floyd-Steinberg" + ], + "image_footnote": [], + "bbox": [ + 426, + 191, + 542, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/029e834e57be122910caf292608271a09cf885399ee1d413cfbf9a30fcc85337.jpg", + "image_caption": [ + "(1) Ostromoukhov" + ], + "image_footnote": [], + "bbox": [ + 542, + 191, + 656, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71d1721c6a79da91ec77c15441793e166dc1a7a4b34bb40eaa9fce87aea3dd96.jpg", + "image_caption": [ + "(f)Burkes", + "(m) Xia" + ], + "image_footnote": [], + "bbox": [ + 658, + 191, + 772, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/adfe75e6c6ec6ee2207ddca9eef85b5c8ceaddf94a6c3cb800393f72a4a969f5.jpg", + "image_caption": [ + "(g) Sierra", + "(n) Ours" + ], + "image_footnote": [], + "bbox": [ + 774, + 191, + 890, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8bc396ace471dca3950f7a9898e1afd0fa9a8f05333fa1739a6b617bae0e223a.jpg", + "image_caption": [ + "Figure 10. Qualitative experimental results. Baseline methods yields halftones with some imperfections, including holes (e, m), striped dot distribution (b, f, g, h, l), or other regular visual artifacts (c, d, i, j, k). Images are from the DIV2K dataset [2].", + "(a) continuous tone", + "Figure 11. Experimental results of refining areas with artifacts in generated halftones by manipulating local ink dots. PSNR: (c): 37.24; (d): 44.10; (e): 44.43. SSIM: (c): 0.00756; (d): 0.00772; (e): 0.00776." + ], + "image_footnote": [], + "bbox": [ + 84, + 344, + 267, + 487 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/99c1c0e3d29c856c4788d57e4e3803e9776a62ae2be915cc4cee48957b69bc98.jpg", + "image_caption": [ + "(b) zoom in" + ], + "image_footnote": [], + "bbox": [ + 277, + 345, + 359, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/355fca39702364843a8c8f8b31e50cae5df85a649337354d608ce8837e48cb2b.jpg", + "image_caption": [ + "(c) init. pred." + ], + "image_footnote": [], + "bbox": [ + 279, + 422, + 361, + 484 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/44748e6c2fec3b68517f462e9bad759703f417a45897acb0334fa20b303ca511.jpg", + "image_caption": [ + "(d) 1st. refine" + ], + "image_footnote": [], + "bbox": [ + 374, + 344, + 457, + 409 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/92015db6be7d2b84f21ed3ed9a056e2458a98c9b9c858dbb5a934796f0265822.jpg", + "image_caption": [ + "(e) 2nd. refine" + ], + "image_footnote": [], + "bbox": [ + 375, + 422, + 457, + 484 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/216232aabd7f738fc907fe2a6d9ca8003284fbd3a18d88f6c66b57baf7c39990.jpg", + "table_caption": [ + "Table 3. Statistical results of collisions during ink dot movement." + ], + "table_footnote": [], + "table_body": "
Iteration (τ)48121620
Reduction Ratio0.03140.02490.02960.03160.0287
", + "bbox": [ + 84, + 601, + 454, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "perior visual results. Additional qualitative experimental results, encompassing high-resolution and color images, are presented in the supplementary material.", + "bbox": [ + 75, + 656, + 468, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Study on the Collision Rate of Ink Dots", + "text_level": 1, + "bbox": [ + 75, + 710, + 413, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ink dots may experience collisions during their movement. We compute the reduction ratio in the number of ink dots resulting from these collisions and overlaps, as outlined in Table 3. It can be observed that the reduction in the number of ink dots due to collisions is minimal, constituting approximately $2\\%$ to $3\\%$ of the total ink dot count. This observation suggests that collisions have a negligible impact on both the overall quantity of ink dots and the dithering process in halftones. We will investigate methods to further minimize ink dot collisions and develop strategies for managing colliding ink dots in our future work.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.8. Dot Control Helps Remove Local Artifacts", + "text_level": 1, + "bbox": [ + 500, + 345, + 862, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We explore an advantage of controllable ink dots: the capability to enhance specific areas within generated halftones through precise manipulation of the ink dots. As illustrated in Figure 11, the initially generated halftone may exhibit artifacts in local regions (Figure 11c). To address this, we refine the halftone by readjusting the ink dots in these areas, resulting in a further enhancement of the generated halftone's quality and the elimination of artifacts (Figure 11d, 11e). This process serves as validation for the efficacy of our proposed concept of controllable ink dots.", + "bbox": [ + 496, + 372, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.9. Study on Ink Dot Quantity Control", + "text_level": 1, + "bbox": [ + 498, + 537, + 805, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We investigate another advantage of dot control: the capacity to regulate the quantity of ink dots. In Figure 9, we present some examples of halftones with a gradual increase in the quantity of ink dots, from level 1 (Figure 9a) to level 3 (Figure 9c). Notably, even with a smaller number of ink dots, the halftones still maintain visually pleasing levels of detail. The experimental results verify that the proposed method can control the number of ink dots and generate visually pleasing halftones, making it more flexibly applicable to halftone prints of different consumable levels.", + "bbox": [ + 496, + 564, + 890, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 734, + 617, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce ink dot-oriented neural halftoning in this work. O-Net propagates dense gradients to sparse halftone dots, and completes the differentiable transformation between dot coordinates and halftone matrices. P-Net achieves direct control of halftone dots through dot motion predictions. Extensive quantitative and qualitative experiments verify the effectiveness of our proposed method.", + "bbox": [ + 496, + 762, + 890, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement: This work is supported by National Key R&D Program of China (2022ZD0160300).", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "27535", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. PMLR, 2018. 4", + "[2] Eirikur Agustsson and Radu Timofte. 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In Proceedings of the International MultiConference of Engineers and Computer Scientists, 2008. 2" + ], + "bbox": [ + 78, + 90, + 468, + 486 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "27537", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/1f12ac3c-71f4-433c-8965-472dc5121501_model.json b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/1f12ac3c-71f4-433c-8965-472dc5121501_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0a625875a43b397b7ab5d7b446d7253efeee387e --- /dev/null +++ b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/1f12ac3c-71f4-433c-8965-472dc5121501_model.json @@ -0,0 +1,2970 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.13, + 0.865, + 0.155 + ], + "angle": 0, + "content": "Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.182, + 0.39, + 0.236 + ], + "angle": 0, + "content": "Hao Jiang \nPeking University \njianghao@stu.pku.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.44, + 0.182, + 0.586, + 0.236 + ], + "angle": 0, + "content": "Bingfeng Zhou \nPeking University \nzbf@pku.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.637, + 0.182, + 0.783, + 0.236 + ], + "angle": 0, + "content": "Yadong Mu* Peking University myd@pku.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.272, + 0.687, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.27, + 0.781, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.27, + 0.891, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.546, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Figure 1. Illustration of halftones generated by our proposed ink dot-oriented differentiable neural halftoning method and several previous methods [12, 26, 35]. Images are from the DIV2K dataset [2]." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.587, + 0.314, + 0.603 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.619, + 0.474, + 0.877 + ], + "angle": 0, + "content": "Halftoning is a time-honored printing technique that simulates continuous tones using ink dots (halftone dots). The resurgence of deep learning has catalyzed the emergence of innovative technologies in the printing industry, fostering the advancement of data-driven halftoning methods. Nevertheless, current deep learning-based approaches produce halfstones through image-to-image black box transformations, lacking direct control over the movement of individual halftone dots. In this paper, we propose an innovative halftoning method termed \"neural dot-controllable halftoning\". This method allows dot-level image dithering by providing direct control over the motion of each ink dot. We conceptualize halftoning as the process of sprinkling dots on a canvas. Initially, a specific quantity of dots are randomly dispersed on the canvas and subsequently adjusted based on the surrounding grayscale and gradient. To establish differentiable transformations between" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.895, + 0.726 + ], + "angle": 0, + "content": "discrete ink dot positions and halftone matrices, we devise a lightweight dot encoding network to spread dense gradients to sparse dots. Dot control offers several advantages to our approach, including the capability to regulate the quantity of halftone dots and enhance specific areas with artifacts in the generated halftones by adjusting the placement of the dots. Our proposed method exhibits superior performance than previous approaches in extensive quantitative and qualitative experiments." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.754, + 0.633, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In the late 1800s, pioneers such as William Henry Fox Talbot, Georg Meisenbach, Frederic Ives, and Max Levy [32] made significant strides in halftone printing techniques, enabling photographs to be printed on paper using ink. Halftoning is a technique of replicating the color and shading of continuous tone images by employing ink dots (halftone dots) of different sizes and frequencies. It remains a crucial and enduring component in the modern printing" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27528" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.47, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.223, + 0.471, + 0.306 + ], + "angle": 0, + "content": "Figure 2. Prior deep networks-based halftoning methods (top) map an image to a halftone-like continuous-tone image before applying a binarization operation. In contrast, our proposed method (bottom) differs from previous halftoning techniques in that it achieves dot-level halftones through direct control over the movement of each dot." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.47, + 0.382 + ], + "angle": 0, + "content": "industry. A successful halftone can closely reproduce the original image with high quality, leveraging the low-pass filtering characteristics of the human visual system to attain near-optimal visual effects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Halftone technology can be broadly divided into two categories: traditional or deep learning-based methods. The former can be further cast into three groups based on implementations of dithering process: amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [6, 20, 22, 34], and hybrid modulation [14, 39]. Recently, the renaissance of deep learning as a black-box approximation for high-dimensional functions has catalyzed the emergence of several data-driven methods in the field of halftoning [15, 16, 18, 23, 35], demonstrating superior performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.471, + 0.839 + ], + "angle": 0, + "content": "In this paper, we argue that current deep learning methods for halftoning, face some weaknesses that impede their deployment in the printing industry. Notably, these methods treat halftones as binary images and heavily rely on a black box encoder-decoder to convert between the original continuous-tone image and the halftone-induced binary image. However, they operate as image-level transforms rather than directly manipulating the halftone dots, leading to a loss of direct control over the desired properties of the resultant halftones. As observed in Figure 1, purely image-level transformations [12, 26, 35] tend to produce undesired artifacts, and they struggle to directly manipulate local dot arrangements to eliminate these artifacts. In addition, traditional methods do not allow for control over the number of halftone dots. In practical applications, opting for halftone techniques that utilize fewer ink dots can be advantageous for consumable savings. For prints with low detail requirements, like halftone cartoon stickers, a modest quantity of dots suffice to faithfully convey the information present in the continuous tone image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To address the above issues, we propose ink dot-oriented neural image halftoning for the first time in the literature, which directly controls the motion of each ink dot, enabling dot-level differentiable optimization. Nonetheless, a piv" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "otal challenge in achieving this lies in the discrete nature of ink dot positions, while the objective functions piloting the halftone generation are continuous. Directly propagating the gradient flow from halftone pixels to ink dot positions is unfeasible, rendering gradient back-propagation a challenging endeavor. A key contribution of this paper is the presentation of a novel approach to integrate discrete ink dots into continuous halftone optimization in a fully differentiable manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.893, + 0.44 + ], + "angle": 0, + "content": "Our approach considers halftoning as the process of optimizing dot placements on a blank canvas using halftone quality-related guidance. We commence by randomly spreading a flexible number of dots on the canvas and then progressively move them. To facilitate smooth gradient backpropagation from the objective function to each discrete ink dot, we introduce a dot encoding module that maps dot coordinates to the product of sparse vectors, creating a structure conducive to differentiable optimization. We also develop a motion-estimating module to predict the motion of each ink dot. Our method offers direct control over the quantity of ink dots in the generated halftones, a feat challenging to attain in prior work, owing to the flexibility and scalability of the proposed dot manipulations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.546 + ], + "angle": 0, + "content": "To sum up, this paper introduces ink dot-oriented neural image halftoning, the first approach of its kind to achieve dot-level image dithering by controlling the movement of ink dots. Our proposed model showcases superior performance over previous methods in extensive qualitative and quantitative experiments. Furthermore, the method can be easily extended to arbitrary scale and color images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.642, + 0.577 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.586, + 0.712, + 0.603 + ], + "angle": 0, + "content": "2.1. Traditional Halftoning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Traditional halftone methods can be categorized into amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [7, 8, 25, 38], and hybrid approaches [14, 39]. AM methods use dot clusters of varying sizes and frequencies to represent different shades of gray and reproduce the original continuous tone image. FM is represented by the error diffusion algorithm, which distributes the quantization error generated by pixel thresholding to adjacent pixels, achieving superior results. For example, Ostromoukhov [26] proposed an improved error-diffusion algorithm based on the deliberately restricted choice of the distribution coefficients. Unlike these traditional methods, which rely on some prior or handcrafted designs, our approach is data-driven, enabling halftone optimization with greater fitting ability and model capacity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.788, + 0.864 + ], + "angle": 0, + "content": "2.2. Deep Learning Based Halftoning" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "With the emergence of deep learning techniques, researchers have explored the use of neural networks to gen" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27529" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.09, + 0.852, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.234, + 0.895, + 0.276 + ], + "angle": 0, + "content": "Figure 3. Schematic illustration of the proposed method. The proposed method takes a set of random dots as input. O-Net differentiably transforms discrete ink dot positions into a halftone matrix, effectively spreading dense gradients over sparse dots. P-Net predicts the motion of each halftone dot." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.473, + 0.392 + ], + "angle": 0, + "content": "erate halftones [16, 17, 23, 35]. For example, Xia et al. [35] utilized stacked convolutional networks to learn reversible halftones capable of concealing color information. However, most of prior methods treat the entire image as a whole and cannot achieve fine control of halftone dots. In contrast, our approach facilitates dot-level controllable halftones, offering greater interpretability and maneuverability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.41, + 0.169, + 0.424 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.47, + 0.466 + ], + "angle": 0, + "content": "3.1. O-Net: Spreading Dense Gradients onto Sparse Ink Dots" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.473, + 0.748 + ], + "angle": 0, + "content": "Halftone images consist solely of black and white pixels, with the arrangement of black pixels determining the brightness and visual structure of each area in the image. A straightforward approach to generate halftone images is to first learn a mapping from a continuous-tone image to an almost binary image, which is then rounded to produce binary halftone dots, as demonstrated in prior work [15-18, 23, 35]. Nevertheless, this approach is subject to several limitations. Primarily, it lacks direct control over individual halftone dots. In the event of defects in some generated halftone areas, the entire halftone have to be regenerated, posing escalating challenges, particularly for larger images. Additionally, previous image-level halftoning methods lack the capability to regulate the quantity of ink dots in halftones. In scenarios where printing equipment features limited or costly consumables, this lack of flexibility hinders the generation of halftones with varying consumable levels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In Figure 3, we present a novel approach for dot-centric halftoning. The process begins by initializing a set of dots at random. Denote the dot set as \\(\\mathcal{Q} = \\{\\pmb{q}_0,\\pmb{q}_1,\\dots,\\pmb{q}_{k - 1}\\}\\), where \\(k\\) represents the number of dots. Each dot \\(\\pmb{q}_i\\) is represented by its two-dimensional coordinates within the image, i.e., \\(\\pmb{q}_i = \\{\\pmb{x}_i,\\pmb{y}_i\\}\\), where \\(i\\in [0,k - 1],\\pmb{x}_i\\in [0,L_1 - 1],\\pmb{y}_i\\in [0,L_2 - 1]\\), with \\(L_{1}\\) and \\(L_{2}\\) being the height and width of the image, respectively. The coordinates of these dots can be used to index their corresponding positions on a \"white canvas\" \\(\\mathbf{H}\\), which serves as a layout" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.285, + 0.895, + 0.389 + ], + "angle": 0, + "content": "for the ink dots. \\(\\mathbf{H}\\) consists solely of elements that are either 0 or 1 (after normalization). A value of 1 in \\(\\mathbf{H}\\) indicates the presence of an ink dot at the corresponding position, while an element 0 indicates the absence of a dot. To pin the dots in set \\(\\mathcal{Q}\\) onto the white canvas \\(\\mathbf{H}\\), a straightforward approach is to directly fill these halftone dots into the matrix \\(\\mathbf{H}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.392, + 0.892, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} \\left[ \\left\\lfloor \\boldsymbol {x} _ {i} \\right\\rfloor , \\left\\lfloor \\boldsymbol {y} _ {i} \\right\\rfloor \\right] = 1, \\quad \\forall \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {y} _ {i}\\right) \\in \\mathcal {Q}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.895, + 0.599 + ], + "angle": 0, + "content": "Performing such an operation is challenging to optimize in an end-to-end neural network due to the discreteness of ink dot coordinates \\( \\mathbf{q}_i \\), and the continuity of \\( \\mathbf{H} \\). Directly passing the gradient flow between matrix coordinates \\( \\mathbf{x}_i, \\mathbf{y}_i \\) and \\( \\mathbf{H} \\) is not feasible, and backpropagation is difficult to conduct. While reinforcement learning ideas [10] suggest that decision-making agents can help networks execute decisions under reward functions for discrete action spaces, these approaches are relatively complicated. Instead, we aim to design a simple, differentiable transformation between \\( \\mathcal{Q} \\) and \\( \\mathbf{H} \\) to enable end-to-end training of the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.895, + 0.707 + ], + "angle": 0, + "content": "Our key observation is that the halftone \\(\\mathbf{H}\\) can be generated through the Hadamard product of multiple sparse binary matrices, and these sparse binary matrices can be expressed as the product of one-hot encodings of dot coordinates. For a halftone \\(\\mathbf{H}\\) with \\(k\\) dots, we decompose it into the Hadamard product of \\(k\\) independent matrices \\(\\mathbf{H}_0,\\mathbf{H}_1,\\dots,\\mathbf{H}_{k - 1}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.72, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} = \\mathbf {I} - \\left(\\mathbf {I} - \\mathbf {H} _ {0}\\right) \\odot \\left(\\mathbf {I} - \\mathbf {H} _ {1}\\right) \\odot \\dots \\odot \\left(\\mathbf {I} - \\mathbf {H} _ {k - 1}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.895, + 0.856 + ], + "angle": 0, + "content": "where \\(\\odot\\) is the Hadamard product, and \\(\\mathbf{I}\\) stands for an all-one matrix. \\(\\mathbf{H}_0,\\mathbf{H}_1,\\dots ,\\mathbf{H}_{k - 1}\\) have the property that each matrix contains only one element equal to 1, while the rest are 0. Intuitively, \\(\\mathbf{H}_0,\\mathbf{H}_1,\\ldots ,\\mathbf{H}_{k - 1}\\) represent halftones formed by printing dots \\(q_{0},q_{1},\\ldots ,q_{k - 1}\\), respectively. For a dot \\(q_{i} = \\{\\pmb {x}_{i},\\pmb {y}_{i}\\}\\), we can get its one-hot encoding from \\(\\pmb{x}_i\\) and \\(\\pmb{y}_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.868, + 0.892, + 0.892 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {o} \\left(\\boldsymbol {x} _ {i}\\right) = \\operatorname {O n e H o t E n c o d i n g} \\left(\\boldsymbol {x} _ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.89, + 0.808, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\pmb {o} (\\pmb {y} _ {i}) = \\mathrm {O n e H o t E n c o d i n g} (\\pmb {y} _ {i}).\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "27530" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.137 + ], + "angle": 0, + "content": "Assuming \\( \\pmb{o}(\\pmb{x}_i) \\) and \\( \\pmb{o}(\\pmb{y}_i) \\) have been obtained, \\( \\mathbf{H}_i \\) can be calculated according to \\( \\pmb{o}(\\pmb{x}_i) \\) and \\( \\pmb{o}(\\pmb{y}_i) \\) via \\( \\mathbf{H}_i = \\pmb{o}(\\pmb{x}_i)^\\top \\cdot \\pmb{o}(\\pmb{y}_i) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.474, + 0.366 + ], + "angle": 0, + "content": "Substituting the calculated \\(\\mathbf{H}_i\\) into Equation 2, the halftone \\(\\mathbf{H}\\) can be obtained. The only non-differentiable step occurs in Equation 3 (i.e., OneHotEncoding). The non-differentiable problem of converting discrete ink dots to continuous halftone matrices is transformed into the non-differentiable problem of one-hot encodings, resulting in a simplified problem. We learn a model O-Net ('O' stands for \"one-hot encoding\") to perform the mapping from discrete coordinates \\(\\boldsymbol{x}_i\\), \\(\\boldsymbol{y}_i\\) to one-hot encoding \\(\\boldsymbol{o}(\\boldsymbol{x}_i)\\), \\(\\boldsymbol{o}(\\boldsymbol{y}_i)\\). Denote O-Net as O for brevity, which consists of fully connected layers in our implementation. ReLU activation function is used between each layer. During the optimization of O-Net, the potential coordinate values \\(\\tilde{\\boldsymbol{x}}\\) and \\(\\tilde{\\boldsymbol{y}}\\) are fed into O, and the gradient is computed utilizing the following loss function \\(\\mathcal{L}_{\\mathrm{O - Net}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.379, + 0.154, + 0.395 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {O - N e t}} =\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.399, + 0.475, + 0.444 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{\\max (L _ {1} , L _ {2}) / s} \\sum_ {l = 0} ^ {\\max (L _ {1}, L _ {2}) - 1} | \\mathbf {O} (\\tilde {\\boldsymbol {x}} _ {l}) - \\mathrm {O n e H o t E n c} (\\tilde {\\boldsymbol {x}} _ {l}) | +\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.446, + 0.47, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{\\max \\left(L _ {1} , L _ {2}\\right) / s} \\sum_ {l = 0} ^ {\\max \\left(L _ {1}, L _ {2}\\right) - 1} | \\mathbf {O} (\\tilde {\\boldsymbol {y}} _ {l}) - \\operatorname {O n e H o t E n c} (\\tilde {\\boldsymbol {y}} _ {l}) |, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.636 + ], + "angle": 0, + "content": "where OneHotEncoding \\((\\tilde{\\boldsymbol{x}}_l)\\) and OneHotEncoding \\((\\tilde{\\boldsymbol{y}}_l)\\) denote the one-hot vector determined by \\(\\tilde{\\boldsymbol{x}}_l\\) and \\(\\tilde{\\boldsymbol{y}}_l\\), respectively. \\(s\\) represents the sampling step. It is worth noting that the dot coordinates \\(\\boldsymbol{x}_i\\) and \\(\\boldsymbol{y}_i\\) are decimal numbers. Therefore, to ensure that the network O can accurately handle different coordinate values, it is necessary to densely sample the interval \\([0, \\max(L_1, L_2) - 1]\\). In our experiments, we use a sampling step of 0.01 for this interval. The architecture of O-Net is illustrated in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.638, + 0.396, + 0.653 + ], + "angle": 0, + "content": "The precision \\(\\mathcal{P}(\\mathbf{O})\\) is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.667, + 0.47, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} (\\mathbf {O}) = \\frac {1}{\\max (L _ {1} , L _ {2}) / s} \\sum_ {l = 0} ^ {\\max (L _ {1}, L _ {2}) - 1} \\mathbb {1} \\left\\{\\arg \\max (\\mathbf {O} (\\tilde {\\boldsymbol {x}} _ {l})) \\right.,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.714, + 0.384, + 0.73 + ], + "angle": 0, + "content": "\\(\\arg \\max (\\mathrm{OneHotEncoding}(\\tilde{\\boldsymbol{x}}_l))\\} +\\)" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.734, + 0.469, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{\\max \\left(L _ {1} , L _ {2}\\right) / s} \\sum_ {l = 0} ^ {\\max \\left(L _ {1}, L _ {2}\\right) - 1} \\mathbb {1} \\left\\{\\arg \\max \\left(\\mathbf {O} \\left(\\tilde {\\boldsymbol {y}} _ {l}\\right)\\right), \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.779, + 0.47, + 0.809 + ], + "angle": 0, + "content": "\\(\\arg \\max (\\mathrm{OneHotEncoding}(\\tilde{\\mathbf{y}}_l)))\\}\\) (5)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.47, + 0.855 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}\\{a,b\\}\\) is 1 when \\(a\\) and \\(b\\) are equal, and 0 otherwise. In the experiments, O-Net is first trained to convergence and its parameters are fixed during halftone generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Discussion. We eschew the use of embedding matrix lookups to establish the mapping between dot coordinates and one-hot encodings due to their non-differentiability." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.091, + 0.895, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.23, + 0.894, + 0.271 + ], + "angle": 0, + "content": "Figure 4. Illustration of O-Net for differentiable transformation from discrete dots to continuous vector-based halftone representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.285, + 0.892, + 0.316 + ], + "angle": 0, + "content": "This characteristic disrupts gradients and impedes the process of backpropagation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.325, + 0.798, + 0.34 + ], + "angle": 0, + "content": "3.2. P-Net: Ink Dot Motion Prediction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.635 + ], + "angle": 0, + "content": "A primary contribution of this work is the achievement of dot controllable halftones, with the prediction of the ink dot motion playing a crucial role in this realization. While some deep learning methods have introduced techniques for point motion control and prediction, exemplified in point cloud generation [1, 4, 24, 28, 33, 36], applying these methods directly to halftoning is not feasible for the following reasons: (1) Point clouds typically consist of a small number of points, for instance, the 2,048 points utilized in [24] to generate point clouds of various shapes. In contrast, halftones comprise a substantial number of ink dots, with \\(20,000 \\sim 30,000\\) ink dots in a \\(256 \\times 256\\) resolution image. As the dot count escalates, optimizing the model becomes progressively more challenging. (2) Point cloud generation methods are primarily employed to create point cloud shapes with a coarse level of detail. In contrast, halftones incorporate intricate details and textures, demanding precise and meticulous control over the movement of each ink dot to achieve a fine-grained result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.83 + ], + "angle": 0, + "content": "To tackle the aforementioned challenges, we propose P-Net, a network that employs image gray levels as guidance to achieve ink dot motion prediction, as shown in Figure 5. Inspired by recent diffusion generative models [9, 29-31], we explore the efficacy of simple and lightweight convolutional blocks for dot motion prediction. P-Net takes the halftone \\(\\mathbf{H}\\) formed by ink dots (Equation 2) and the continuous tone image \\(\\mathbf{C}\\) as input. Each element in the matrix \\(\\mathbf{C}\\) represents the gray level of the image at the corresponding position. The approach employed by P-Net to integrate information from \\(\\mathbf{H}\\) and \\(\\mathbf{C}\\) is relatively straightforward, involving concatenation of the two matrices along the channel dimension:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.832, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {\\text {i n}} = \\operatorname {C o n v 2 D} (\\mathbf {H} | | \\mathbf {C}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where Conv2D means two-dimensional convolution, \\(||\\) means the concatenation operation. While alternative approaches, including post-smooth concatenation and density-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27531" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.08, + 0.092, + 0.45, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Algorithm for Dot Controllable Halftoning" + }, + { + "type": "title", + "bbox": [ + 0.083, + 0.112, + 0.131, + 0.125 + ], + "angle": 0, + "content": "Input:" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.126, + 0.427, + 0.141 + ], + "angle": 0, + "content": "The set of random dots, \\(\\mathcal{Q} = \\{\\pmb {q}_0,\\pmb {q}_1,\\dots ,\\pmb {q}_{k - 1}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.142, + 0.34, + 0.155 + ], + "angle": 0, + "content": "The number of dots in the set \\(\\mathcal{Q}, k\\);" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.157, + 0.288, + 0.171 + ], + "angle": 0, + "content": "Continuous tone image, C;" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.172, + 0.293, + 0.185 + ], + "angle": 0, + "content": "The number of iterations, \\(\\tau\\)" + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.187, + 0.142, + 0.2 + ], + "angle": 0, + "content": "Output:" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.202, + 0.281, + 0.216 + ], + "angle": 0, + "content": "Generated halftone, \\(\\mathbf{H}_{\\mathrm{out}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.217, + 0.469, + 0.247 + ], + "angle": 0, + "content": "1: Transform the dots in the set \\(\\mathcal{Q}\\) into halftone \\(\\mathbf{H}^{(0)}\\) using O-Net; /* Equation 2 */" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.248, + 0.249, + 0.26 + ], + "angle": 0, + "content": "2: for \\( i = 0 \\) to \\( \\tau - 1 \\) do" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.261, + 0.469, + 0.292 + ], + "angle": 0, + "content": "3: Feed \\(\\mathbf{H}^{(i)}\\) and \\(\\mathbf{C}\\) into P-Net as input; /* Equation 6*/" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.293, + 0.468, + 0.324 + ], + "angle": 0, + "content": "4: Obtain motion predictions of each dot in \\(\\mathcal{Q}\\): \\(\\mathbf{P}_{\\mathrm{out}}^{(i)} \\gets \\mathbb{P} - \\mathrm{Net}(\\mathbf{H}^{(i)}, \\mathbf{C})\\); /* Equation 8 */" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.325, + 0.468, + 0.354 + ], + "angle": 0, + "content": "5: Update the position of ink dot \\(\\forall \\pmb{q}_i \\in \\mathcal{Q}\\), and update the set \\(\\mathcal{Q}\\); /* Equation 9*/" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.355, + 0.467, + 0.385 + ], + "angle": 0, + "content": "6: Transform the dots in the set \\(\\mathcal{Q}\\) into halftone \\(\\mathbf{H}^{(i + 1)}\\) using O-Net; /* Equation 2 */" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.386, + 0.469, + 0.415 + ], + "angle": 0, + "content": "7: Calculate \\(\\mathcal{L}_{\\mathrm{P}}\\) and update the model parameters of P-Net; /\\*Equation 13\\*/" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.416, + 0.16, + 0.429 + ], + "angle": 0, + "content": "8: end for" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.431, + 0.25, + 0.445 + ], + "angle": 0, + "content": "9: return \\(\\mathbf{H}_{\\mathrm{out}}\\gets \\mathbf{H}^{\\tau}\\)" + }, + { + "type": "list", + "bbox": [ + 0.088, + 0.202, + 0.469, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.469, + 0.565 + ], + "angle": 0, + "content": "integral map-based methods, have been explored in the experiments, they demand greater computation and do not yield substantial performance enhancements. P-Net utilizes a sequence of convolution modules to acquire the fusion representation of matrices \\(\\mathbf{H}\\) and \\(\\mathbf{C}\\), followed by several downsampling modules to reduce the image resolution:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.572, + 0.469, + 0.591 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {P}} = \\operatorname {D o w n S a m p l e} (\\operatorname {S t a c k e d C o n v 2 D} \\left(\\mathbf {P} _ {\\text {i n}}\\right)), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.469, + 0.706 + ], + "angle": 0, + "content": "where \\(\\widetilde{\\mathbf{P}}\\) represents the feature matrix of high-level gray scale information, which coarsely expresses the overall movement trend of the ink dots within adjacent image blocks. Next, a prediction head composed of convolutions is used on the upsampled \\(\\widetilde{\\mathbf{P}}\\) matrix to make the output dot motion \\(\\mathbf{P}_{\\mathrm{out}}\\) consistent with the resolutions of the halftone matrix \\(\\mathbf{H}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.716, + 0.469, + 0.734 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {\\text {o u t}} = \\operatorname {S t a c k e d C o n v 2 D} (\\operatorname {U p S a m p l e} (\\tilde {\\mathbf {P}})). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.469, + 0.818 + ], + "angle": 0, + "content": "Each element in \\(\\mathbf{P}_{\\mathrm{out}}\\) represents the displacement vector of the ink dot at the corresponding position, and it has two channels representing the motion prediction along \\(x\\) and \\(y\\) directions, respectively. For \\(\\forall \\pmb {q}_i\\in \\mathcal{Q},\\pmb {q}_i = \\{\\pmb {x}_i,\\pmb {y}_i\\}\\), its new position can be derived as:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.828, + 0.469, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\left(\\hat {\\boldsymbol {x}} _ {i}, \\hat {\\boldsymbol {y}} _ {i}\\right) = \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {y} _ {i}\\right) + \\mathbf {P} _ {\\text {o u t}} \\left[ \\left\\lfloor \\boldsymbol {x} _ {i} \\right\\rfloor , \\left\\lfloor \\boldsymbol {y} _ {i} \\right\\rfloor \\right]. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.854, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The ink dot coordinates \\(\\hat{\\pmb{q}}_i = \\{\\hat{x}_i,\\hat{y}_i\\}\\) after the motion can be differentiated to form a new halftone matrix \\(\\widehat{\\mathbf{H}}\\) through O-Net, and the iteration is completed." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.093, + 0.891, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.208, + 0.892, + 0.236 + ], + "angle": 0, + "content": "Figure 5. Schematic diagram of the proposed P-Net, which is used to predict the motion of each ink dot." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.246, + 0.831, + 0.263 + ], + "angle": 0, + "content": "3.3. Training Scheduling and Optimization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.269, + 0.892, + 0.315 + ], + "angle": 0, + "content": "To optimize our model, following [27, 35], we use the tone loss \\(\\mathcal{L}_T\\), which computes the dissimilarity between halftone predictions \\(\\mathbf{H}_{\\mathrm{out}}\\) and continuous tone images \\(\\mathbf{C}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.324, + 0.892, + 0.354 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {T} = \\mathbb {E} _ {\\mathbf {H}} \\| \\text {G a u S m o o t h} (\\mathbf {H} _ {\\text {o u t}}) - \\text {G a u S m o o t h} (\\mathbf {C}) \\| _ {2}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.355, + 0.892, + 0.401 + ], + "angle": 0, + "content": "where \\(\\| \\cdot \\| _2\\) represents the L2 norm. To improve the structural similarity of the generated halftones, the structural loss \\(\\mathcal{L}_S\\) is employed:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.41, + 0.891, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S} = \\mathbb {E} _ {\\mathbf {H}} \\| \\operatorname {S t r u c} \\text {- M e a s u r e} (\\mathbf {H} _ {\\text {o u t}}, \\mathbf {C}) \\| _ {1}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.436, + 0.892, + 0.482 + ], + "angle": 0, + "content": "Additionally, the pixel loss \\(\\mathcal{L}_R\\) is adopted to measure the difference between the generated halftone after inverse halftoning transformation and the continuous tone image:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.492, + 0.891, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R} = \\mathbb {E} _ {\\mathbf {H}} \\| \\mathcal {R} \\left(\\mathbf {H} _ {\\text {o u t}}\\right) - \\mathbf {C} \\| _ {2}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.518, + 0.891, + 0.548 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}\\) represents the frozen inverse halftoning network [35]. The total loss \\(\\mathcal{L}_P\\) is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.558, + 0.891, + 0.574 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {P} = \\mathcal {L} _ {T} + \\gamma_ {S} \\mathcal {L} _ {S} + \\gamma_ {R} \\mathcal {L} _ {R}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.584, + 0.891, + 0.614 + ], + "angle": 0, + "content": "where \\(\\gamma_{S}\\) and \\(\\gamma_{R}\\) are hyperparameters to trade-off each loss term. We detail the training process in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.627, + 0.633, + 0.644 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.882, + 0.667 + ], + "angle": 0, + "content": "4.1. Datasets, Baselines, and Evaluation Protocols" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.674, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets and Baselines. Following previous research [13, 35], we curate a halftoning dataset by selecting images from UTKFace [37] and DIV2K [2]. The dataset comprises 4000, 1000, and 400 images in the training, validation, and test sets, respectively. We select baseline models from two categories: traditional halftoning methods [12, 21, 26] and deep learning-based halftoning methods [35]. The traditional methods include amplitude modulation techniques (such as Ordered Dithering), frequency modulation techniques (such as Floyd-Steinberg Error Diffusion, Simpler Floyd-Steinberg Error Diffusion, Jarvis, Judice, and Ninke Dithering, Stucki Dithering, Atkinson Dithering, Burkes Dithering, Sierra Dithering, Two Row Sierra Dithering, and Sierra Lite Dithering), and improvements of Floyd-Steinberg error diffusion algorithm (such as Ostromoukhov's Method)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27532" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.09, + 0.278, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.199, + 0.262, + 0.21 + ], + "angle": 0, + "content": "(a) training iteration \\(= 1000\\)" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.091, + 0.477, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.199, + 0.458, + 0.21 + ], + "angle": 0, + "content": "(b) training iteration \\(= 3000\\)" + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.091, + 0.671, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.199, + 0.652, + 0.21 + ], + "angle": 0, + "content": "(c) training iteration \\(= 6000\\)" + }, + { + "type": "image", + "bbox": [ + 0.679, + 0.091, + 0.867, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.199, + 0.848, + 0.21 + ], + "angle": 0, + "content": "(d) training iteration \\(= 9000\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.216, + 0.892, + 0.245 + ], + "angle": 0, + "content": "Figure 6. O-Net robustness test experiment. The figure shows the variation trend of the halftone quality obtained by O-Net with the noise intensity. a, b, c, and d represent 1000, 3000, 6000, and 9000 model iterations \\((\\times 10^{4})\\), respectively." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.254, + 0.468, + 0.282 + ], + "angle": 0, + "content": "Table 1. Performance comparison of different halftoning methods on test images in terms of peak signal to noise ratio." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.287, + 0.462, + 0.497 + ], + "angle": 0, + "content": "
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]29.6936.491.1433.04
Floyd-S. [12]35.3144.401.7239.52
Simpler Floyd-S. [21]32.5241.611.6436.81
Jarvis, J., and N. [21]27.7038.291.8532.67
Stucki [21]28.5739.101.8533.40
Atkinson [21]21.7831.771.8226.36
Burkes [21]31.7441.581.7535.62
Sierra [21]28.2338.511.8733.25
Two Row Sierra [21]30.8241.211.7334.86
Sierra Lite [21]35.9545.581.6540.90
Ostromoukhov [26]36.0445.901.7641.18
Xia's Method [35]29.8935.940.8133.83
Our Proposed Method34.7446.642.1843.04
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.552 + ], + "angle": 0, + "content": "Regarding deep learning methods, we select [35] as the baseline, which is a recently proposed deep learning-based halftoning approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Evaluation Protocols and Implementation Details. Following previous work [35], we use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) to measure the quality of the generated halftones. Before computing PSNR, we first smooth both the halftone and continuous tone image with an \\(11 \\times 11\\) Gaussian filter, and then use the smoothed images to calculate the metrics. In addition, we also use qualitative experiments to evaluate the performance of different methods. The quantity of initial dots \\(k\\) is determined through a linear transformation based on the grayscale of the continuous tone. In P-Net, the number of channels is 64, the convolution kernel size is set to \\(3 \\times 3\\). O-Net consists of 4 fully connected layers, and the activation function between layers is ReLU. \\(\\gamma_{S}\\) and \\(\\gamma_{R}\\) are set to 0.04 and 0.08 respectively. Adam optimizer [19] is used to optimize the model, and the learning rate is set to 0.0001." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.312, + 0.818 + ], + "angle": 0, + "content": "4.2. Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We conduct quantitative experiments on images with \\(64 \\times 64\\) resolutions, and the experimental results are shown in Table 1. It can be observed that our proposed method achieves superior performance than previous methods. Traditional methods (e.g., Ordered Dithering, Floyd-Steinberg" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.438 + ], + "angle": 0, + "content": "Error Diffusion, Ostromoukhov's Method) usually predefine some dithering matrices or diffusion coefficients, which achieve relatively good results. However, these traditional methods apply a hand-crafted halftoning criterion to all images indiscriminately, and thus have limited flexibility compared to data-driven approaches like [35]. Besides, previous methods perform halftone generation on the global image and cannot adaptively control the motion of each ink dot, which makes it difficult to flexibly remove some undesired artifacts in the generated halftones. In contrast, our method can flexibly control the motion of each ink dot on the halftone, thus achieving better experimental results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.452, + 0.808, + 0.467 + ], + "angle": 0, + "content": "4.3. Study on the Effectiveness of O-Net" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.793 + ], + "angle": 0, + "content": "A well-performing O-Net should be able to handle various coordinate values produced by model predictions. Although we sample the \\([0, \\max(L_1, L_2) - 1]\\) interval as densely as possible during training, it is still not enough to cover various float coordinate values that may be encountered during model training. In light of this, we design some experiments to verify the robustness of O-Net to numerical noise of float numbers, as shown in Figure 6. The main process of the experiment is that we randomly add noises of different intensities to the correct coordinates of ink dots, and observe the prediction precision of O-Net after adding noises. The magnitude of the noise is constrained between \\([0, 1]\\), which is to ensure that the original position of the ink dot will not be changed when the noise is added to the coordinates. The intensity of the noise is defined by its coverage percentage of the coordinate value. As illustrated in Figure 6, during the initial stages of training, noise interference adversely impacts the quality of the halftones generated by the model. However, as training advances towards convergence, the model becomes less sensitive to noise interference, affirming the robustness of O-Net." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In addition, we visualize the heat maps of O-Net prediction results at different stages of training, as shown in Figure 7. We first randomly initialize 64 ink dot coordinates on a \\(64 \\times 64\\) resolution image, then feed these 64 dot coordinates into O-Net, and visualize the model prediction results. As depicted in Figure 7, prior to the convergence of O-Net, the predicted image exhibits numerous non-binarized gray" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "27533" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.248, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.221, + 0.246, + 0.233 + ], + "angle": 0, + "content": "(a) random initialized" + }, + { + "type": "image", + "bbox": [ + 0.256, + 0.092, + 0.457, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.327, + 0.221, + 0.456, + 0.233 + ], + "angle": 0, + "content": "(b) training iteration \\(= 10\\)" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.092, + 0.657, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.221, + 0.661, + 0.234 + ], + "angle": 0, + "content": "(c) training iteration=6000" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.092, + 0.857, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.716, + 0.221, + 0.859, + 0.234 + ], + "angle": 0, + "content": "(d) training iteration \\(= 9000\\)" + }, + { + "type": "image", + "bbox": [ + 0.862, + 0.092, + 0.887, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.892, + 0.274 + ], + "angle": 0, + "content": "Figure 7. Visualization of model predictions at different stages of O-Net training. a, b, c, and d represent 0, 10, 6000, and 9000 model iterations \\((\\times 10^{4})\\), respectively. The effectiveness of O-Net increases as the image transitions towards a binary representation." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.281, + 0.22, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.387, + 0.205, + 0.397 + ], + "angle": 0, + "content": "(a) continuous tone" + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.281, + 0.355, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.387, + 0.342, + 0.397 + ], + "angle": 0, + "content": "(b) iteration #1" + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.281, + 0.519, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.429, + 0.387, + 0.51, + 0.397 + ], + "angle": 0, + "content": "(c) iteration #2" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.282, + 0.684, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.595, + 0.387, + 0.675, + 0.397 + ], + "angle": 0, + "content": "(d) iteration #3" + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.282, + 0.852, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.387, + 0.841, + 0.397 + ], + "angle": 0, + "content": "(e) iteration #4" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.411, + 0.892, + 0.425 + ], + "angle": 0, + "content": "Figure 8. Visualization of ink dot motion predictions over several iterations. Here we visualize the motions on x-axis, normalized to 0 to 1." + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.435, + 0.211, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.532, + 0.199, + 0.544 + ], + "angle": 0, + "content": "(a) quantity level 1" + }, + { + "type": "image", + "bbox": [ + 0.213, + 0.435, + 0.335, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.224, + 0.532, + 0.326, + 0.544 + ], + "angle": 0, + "content": "(b) quantity level 2" + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.435, + 0.46, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.348, + 0.533, + 0.448, + 0.545 + ], + "angle": 0, + "content": "(c) quantity level 3" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.557, + 0.47, + 0.599 + ], + "angle": 0, + "content": "Figure 9. Illustration of the resulting halftones with different numbers of ink dots. Number of ink dots: (a): 10K; (b): 14K; (c): 18K. More ink dots enrich the texture details of the image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.47, + 0.695 + ], + "angle": 0, + "content": "pixels, indicating that the one-hot encoding at this stage is not fully optimized. In contrast, upon O-Net convergence, the generated halftone comprises solely black and white pixels, affirming the capability of O-Net in producing binary halftones." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.375, + 0.723 + ], + "angle": 0, + "content": "4.4. Comparison of Structural Quality" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.82 + ], + "angle": 0, + "content": "The structural quality of halftones is also an important indicator for evaluating the performance of an algorithm. We compare the structural similarity with methods that generate halftones with higher PSNR, as shown in Table 2. It can be observed that our proposed method achieves better structural similarity than the baseline methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.385, + 0.847 + ], + "angle": 0, + "content": "4.5. Visualization of Motion Predictions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We depict the dot motion predictions generated by P-Net across multiple iterations, as illustrated in Figure 8. Notably, the model rapidly shifts the ink dots from regions with" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.435, + 0.892, + 0.464 + ], + "angle": 0, + "content": "Table 2. Performance comparison of different halftoning methods on test images in terms of structural similarity." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.475, + 0.892, + 0.589 + ], + "angle": 0, + "content": "
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]0.02540.30700.04860.1384
Floyd-S. [12]0.02960.43350.06040.1687
Simpler Floyd.-S. [21]0.02950.46100.06290.1664
Sierra Lite [21]0.02840.41100.05960.1660
Ostromoukhov [26]0.02650.41850.05900.1628
Our Proposed Method0.03050.41590.06280.1709
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.892, + 0.709 + ], + "angle": 0, + "content": "elevated grayscale to those with lower grayscale in the initial stage. This observation substantiates that the motion predictions of P-Net are grounded in a keen awareness of image grayscale. With the progression of iterations, the motions converge towards zero across the majority of the image, leading the model to confine ink dot movements to a limited local area." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.725, + 0.741 + ], + "angle": 0, + "content": "4.6. Qualitative Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 10 presents qualitative experimental results of different halftone methods, which focus on generating halftones on flat textures with subtle variations in image tone (e.g., light and shadow on clouds). Earlier efforts yield halftones with either undesirable white holes or repetitive streaks of ink dots, compromising the overall quality of the output. Additionally, deep learning methods (Figure \\(10\\mathrm{m}\\)) introduce visual artifacts and struggle to faithfully reproduce subtle variations in light and shade. In contrast, our method better preserves tonal details in flat regions and achieves su" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "27534" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.197, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.18, + 0.171, + 0.191 + ], + "angle": 0, + "content": "(a) Contone" + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.089, + 0.313, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.21, + 0.18, + 0.297, + 0.191 + ], + "angle": 0, + "content": "(b) Simpler F.-S." + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.089, + 0.426, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.18, + 0.42, + 0.191 + ], + "angle": 0, + "content": "(c) J. J., and Ninke" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.089, + 0.544, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.18, + 0.512, + 0.191 + ], + "angle": 0, + "content": "(d) Stucki" + }, + { + "type": "image", + "bbox": [ + 0.545, + 0.089, + 0.658, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.18, + 0.635, + 0.191 + ], + "angle": 0, + "content": "(e) Atkinson" + }, + { + "type": "image", + "bbox": [ + 0.659, + 0.089, + 0.774, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.18, + 0.745, + 0.191 + ], + "angle": 0, + "content": "(f)Burkes" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.089, + 0.891, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.807, + 0.18, + 0.858, + 0.192 + ], + "angle": 0, + "content": "(g) Sierra" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.192, + 0.197, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.283, + 0.192, + 0.295 + ], + "angle": 0, + "content": "(h) Two Row Sierra" + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.192, + 0.312, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.283, + 0.291, + 0.295 + ], + "angle": 0, + "content": "(i) Sierra Lite" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.192, + 0.426, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.322, + 0.283, + 0.419, + 0.295 + ], + "angle": 0, + "content": "(j) Ordered Dither" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.192, + 0.543, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.434, + 0.283, + 0.538, + 0.295 + ], + "angle": 0, + "content": "(k) Floyd-Steinberg" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.192, + 0.658, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.553, + 0.283, + 0.649, + 0.295 + ], + "angle": 0, + "content": "(1) Ostromoukhov" + }, + { + "type": "image", + "bbox": [ + 0.659, + 0.192, + 0.774, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.696, + 0.283, + 0.738, + 0.295 + ], + "angle": 0, + "content": "(m) Xia" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.192, + 0.891, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.81, + 0.283, + 0.856, + 0.295 + ], + "angle": 0, + "content": "(n) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.307, + 0.893, + 0.336 + ], + "angle": 0, + "content": "Figure 10. Qualitative experimental results. Baseline methods yields halftones with some imperfections, including holes (e, m), striped dot distribution (b, f, g, h, l), or other regular visual artifacts (c, d, i, j, k). Images are from the DIV2K dataset [2]." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.345, + 0.269, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.489, + 0.229, + 0.5 + ], + "angle": 0, + "content": "(a) continuous tone" + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.346, + 0.361, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.412, + 0.352, + 0.421 + ], + "angle": 0, + "content": "(b) zoom in" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.423, + 0.362, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.489, + 0.355, + 0.501 + ], + "angle": 0, + "content": "(c) init. pred." + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.345, + 0.458, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.412, + 0.454, + 0.422 + ], + "angle": 0, + "content": "(d) 1st. refine" + }, + { + "type": "image", + "bbox": [ + 0.376, + 0.423, + 0.458, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.379, + 0.489, + 0.455, + 0.5 + ], + "angle": 0, + "content": "(e) 2nd. refine" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.569 + ], + "angle": 0, + "content": "Figure 11. Experimental results of refining areas with artifacts in generated halftones by manipulating local ink dots. PSNR: (c): 37.24; (d): 44.10; (e): 44.43. SSIM: (c): 0.00756; (d): 0.00772; (e): 0.00776." + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.576, + 0.467, + 0.591 + ], + "angle": 0, + "content": "Table 3. Statistical results of collisions during ink dot movement." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.602, + 0.455, + 0.647 + ], + "angle": 0, + "content": "
Iteration (τ)48121620
Reduction Ratio0.03140.02490.02960.03160.0287
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.703 + ], + "angle": 0, + "content": "perior visual results. Additional qualitative experimental results, encompassing high-resolution and color images, are presented in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.711, + 0.414, + 0.727 + ], + "angle": 0, + "content": "4.7. Study on the Collision Rate of Ink Dots" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Ink dots may experience collisions during their movement. We compute the reduction ratio in the number of ink dots resulting from these collisions and overlaps, as outlined in Table 3. It can be observed that the reduction in the number of ink dots due to collisions is minimal, constituting approximately \\(2\\%\\) to \\(3\\%\\) of the total ink dot count. This observation suggests that collisions have a negligible impact on both the overall quantity of ink dots and the dithering process in halftones. We will investigate methods to further minimize ink dot collisions and develop strategies for managing colliding ink dots in our future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.863, + 0.364 + ], + "angle": 0, + "content": "4.8. Dot Control Helps Remove Local Artifacts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.892, + 0.525 + ], + "angle": 0, + "content": "We explore an advantage of controllable ink dots: the capability to enhance specific areas within generated halftones through precise manipulation of the ink dots. As illustrated in Figure 11, the initially generated halftone may exhibit artifacts in local regions (Figure 11c). To address this, we refine the halftone by readjusting the ink dots in these areas, resulting in a further enhancement of the generated halftone's quality and the elimination of artifacts (Figure 11d, 11e). This process serves as validation for the efficacy of our proposed concept of controllable ink dots." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.539, + 0.807, + 0.556 + ], + "angle": 0, + "content": "4.9. Study on Ink Dot Quantity Control" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.716 + ], + "angle": 0, + "content": "We investigate another advantage of dot control: the capacity to regulate the quantity of ink dots. In Figure 9, we present some examples of halftones with a gradual increase in the quantity of ink dots, from level 1 (Figure 9a) to level 3 (Figure 9c). Notably, even with a smaller number of ink dots, the halftones still maintain visually pleasing levels of detail. The experimental results verify that the proposed method can control the number of ink dots and generate visually pleasing halftones, making it more flexibly applicable to halftone prints of different consumable levels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.736, + 0.619, + 0.751 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.869 + ], + "angle": 0, + "content": "We introduce ink dot-oriented neural halftoning in this work. O-Net propagates dense gradients to sparse halftone dots, and completes the differentiable transformation between dot coordinates and halftone matrices. P-Net achieves direct control of halftone dots through dot motion predictions. Extensive quantitative and qualitative experiments verify the effectiveness of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement: This work is supported by National Key R&D Program of China (2022ZD0160300)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27535" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. 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In Proceedings of the International MultiConference of Engineers and Computer Scientists, 2008. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "27537" + } + ] +] \ No newline at end of file diff --git a/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/1f12ac3c-71f4-433c-8965-472dc5121501_origin.pdf b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/1f12ac3c-71f4-433c-8965-472dc5121501_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..be73c79fb7f8f8bff4b81b0292a86f6728e4f793 --- /dev/null +++ b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/1f12ac3c-71f4-433c-8965-472dc5121501_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:faf8a0a986ea1485ac00a7acdf5b655f8b05ec0ce5768ec23954c927a623d2cb +size 5326462 diff --git a/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/full.md b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a42f09755d354d5a64ed3f7b0ca92d3a4ce61fa0 --- /dev/null +++ b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/full.md @@ -0,0 +1,448 @@ +# Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning + +Hao Jiang +Peking University +jianghao@stu.pku.edu.cn + +Bingfeng Zhou +Peking University +zbf@pku.edu.cn + +Yadong Mu* Peking University myd@pku.edu.cn + +![](images/688e8a0ed5f8d690ed91554623de846df118315656ad49b6e9d865b7237c6583.jpg) +Figure 1. Illustration of halftones generated by our proposed ink dot-oriented differentiable neural halftoning method and several previous methods [12, 26, 35]. Images are from the DIV2K dataset [2]. + +![](images/4f9ad381643712b581c72e65779355fd576899d1ebb7e35748e22aedcb24f8cb.jpg) + +![](images/b05e07671263afdd5e234349c1b63be3a2c6693579d4c5f977146d09a4f59743.jpg) + +# Abstract + +Halftoning is a time-honored printing technique that simulates continuous tones using ink dots (halftone dots). The resurgence of deep learning has catalyzed the emergence of innovative technologies in the printing industry, fostering the advancement of data-driven halftoning methods. Nevertheless, current deep learning-based approaches produce halfstones through image-to-image black box transformations, lacking direct control over the movement of individual halftone dots. In this paper, we propose an innovative halftoning method termed "neural dot-controllable halftoning". This method allows dot-level image dithering by providing direct control over the motion of each ink dot. We conceptualize halftoning as the process of sprinkling dots on a canvas. Initially, a specific quantity of dots are randomly dispersed on the canvas and subsequently adjusted based on the surrounding grayscale and gradient. To establish differentiable transformations between + +discrete ink dot positions and halftone matrices, we devise a lightweight dot encoding network to spread dense gradients to sparse dots. Dot control offers several advantages to our approach, including the capability to regulate the quantity of halftone dots and enhance specific areas with artifacts in the generated halftones by adjusting the placement of the dots. Our proposed method exhibits superior performance than previous approaches in extensive quantitative and qualitative experiments. + +# 1. Introduction + +In the late 1800s, pioneers such as William Henry Fox Talbot, Georg Meisenbach, Frederic Ives, and Max Levy [32] made significant strides in halftone printing techniques, enabling photographs to be printed on paper using ink. Halftoning is a technique of replicating the color and shading of continuous tone images by employing ink dots (halftone dots) of different sizes and frequencies. It remains a crucial and enduring component in the modern printing + +![](images/186efc2606451bc23b81d48725eac75a0f97c2751d6dc4be8e9effc8c4951d1f.jpg) +Figure 2. Prior deep networks-based halftoning methods (top) map an image to a halftone-like continuous-tone image before applying a binarization operation. In contrast, our proposed method (bottom) differs from previous halftoning techniques in that it achieves dot-level halftones through direct control over the movement of each dot. + +industry. A successful halftone can closely reproduce the original image with high quality, leveraging the low-pass filtering characteristics of the human visual system to attain near-optimal visual effects. + +Halftone technology can be broadly divided into two categories: traditional or deep learning-based methods. The former can be further cast into three groups based on implementations of dithering process: amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [6, 20, 22, 34], and hybrid modulation [14, 39]. Recently, the renaissance of deep learning as a black-box approximation for high-dimensional functions has catalyzed the emergence of several data-driven methods in the field of halftoning [15, 16, 18, 23, 35], demonstrating superior performance. + +In this paper, we argue that current deep learning methods for halftoning, face some weaknesses that impede their deployment in the printing industry. Notably, these methods treat halftones as binary images and heavily rely on a black box encoder-decoder to convert between the original continuous-tone image and the halftone-induced binary image. However, they operate as image-level transforms rather than directly manipulating the halftone dots, leading to a loss of direct control over the desired properties of the resultant halftones. As observed in Figure 1, purely image-level transformations [12, 26, 35] tend to produce undesired artifacts, and they struggle to directly manipulate local dot arrangements to eliminate these artifacts. In addition, traditional methods do not allow for control over the number of halftone dots. In practical applications, opting for halftone techniques that utilize fewer ink dots can be advantageous for consumable savings. For prints with low detail requirements, like halftone cartoon stickers, a modest quantity of dots suffice to faithfully convey the information present in the continuous tone image. + +To address the above issues, we propose ink dot-oriented neural image halftoning for the first time in the literature, which directly controls the motion of each ink dot, enabling dot-level differentiable optimization. Nonetheless, a piv + +otal challenge in achieving this lies in the discrete nature of ink dot positions, while the objective functions piloting the halftone generation are continuous. Directly propagating the gradient flow from halftone pixels to ink dot positions is unfeasible, rendering gradient back-propagation a challenging endeavor. A key contribution of this paper is the presentation of a novel approach to integrate discrete ink dots into continuous halftone optimization in a fully differentiable manner. + +Our approach considers halftoning as the process of optimizing dot placements on a blank canvas using halftone quality-related guidance. We commence by randomly spreading a flexible number of dots on the canvas and then progressively move them. To facilitate smooth gradient backpropagation from the objective function to each discrete ink dot, we introduce a dot encoding module that maps dot coordinates to the product of sparse vectors, creating a structure conducive to differentiable optimization. We also develop a motion-estimating module to predict the motion of each ink dot. Our method offers direct control over the quantity of ink dots in the generated halftones, a feat challenging to attain in prior work, owing to the flexibility and scalability of the proposed dot manipulations. + +To sum up, this paper introduces ink dot-oriented neural image halftoning, the first approach of its kind to achieve dot-level image dithering by controlling the movement of ink dots. Our proposed model showcases superior performance over previous methods in extensive qualitative and quantitative experiments. Furthermore, the method can be easily extended to arbitrary scale and color images. + +# 2. Related Work + +# 2.1. Traditional Halftoning + +Traditional halftone methods can be categorized into amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [7, 8, 25, 38], and hybrid approaches [14, 39]. AM methods use dot clusters of varying sizes and frequencies to represent different shades of gray and reproduce the original continuous tone image. FM is represented by the error diffusion algorithm, which distributes the quantization error generated by pixel thresholding to adjacent pixels, achieving superior results. For example, Ostromoukhov [26] proposed an improved error-diffusion algorithm based on the deliberately restricted choice of the distribution coefficients. Unlike these traditional methods, which rely on some prior or handcrafted designs, our approach is data-driven, enabling halftone optimization with greater fitting ability and model capacity. + +# 2.2. Deep Learning Based Halftoning + +With the emergence of deep learning techniques, researchers have explored the use of neural networks to gen + +![](images/84a5a9ab9a101e3b21f852e9c93572eef2ceae6613ddc148796def38e1a90d62.jpg) +Figure 3. Schematic illustration of the proposed method. The proposed method takes a set of random dots as input. O-Net differentiably transforms discrete ink dot positions into a halftone matrix, effectively spreading dense gradients over sparse dots. P-Net predicts the motion of each halftone dot. + +erate halftones [16, 17, 23, 35]. For example, Xia et al. [35] utilized stacked convolutional networks to learn reversible halftones capable of concealing color information. However, most of prior methods treat the entire image as a whole and cannot achieve fine control of halftone dots. In contrast, our approach facilitates dot-level controllable halftones, offering greater interpretability and maneuverability. + +# 3. Method + +# 3.1. O-Net: Spreading Dense Gradients onto Sparse Ink Dots + +Halftone images consist solely of black and white pixels, with the arrangement of black pixels determining the brightness and visual structure of each area in the image. A straightforward approach to generate halftone images is to first learn a mapping from a continuous-tone image to an almost binary image, which is then rounded to produce binary halftone dots, as demonstrated in prior work [15-18, 23, 35]. Nevertheless, this approach is subject to several limitations. Primarily, it lacks direct control over individual halftone dots. In the event of defects in some generated halftone areas, the entire halftone have to be regenerated, posing escalating challenges, particularly for larger images. Additionally, previous image-level halftoning methods lack the capability to regulate the quantity of ink dots in halftones. In scenarios where printing equipment features limited or costly consumables, this lack of flexibility hinders the generation of halftones with varying consumable levels. + +In Figure 3, we present a novel approach for dot-centric halftoning. The process begins by initializing a set of dots at random. Denote the dot set as $\mathcal{Q} = \{\pmb{q}_0,\pmb{q}_1,\dots,\pmb{q}_{k - 1}\}$ , where $k$ represents the number of dots. Each dot $\pmb{q}_i$ is represented by its two-dimensional coordinates within the image, i.e., $\pmb{q}_i = \{\pmb{x}_i,\pmb{y}_i\}$ , where $i\in [0,k - 1],\pmb{x}_i\in [0,L_1 - 1],\pmb{y}_i\in [0,L_2 - 1]$ , with $L_{1}$ and $L_{2}$ being the height and width of the image, respectively. The coordinates of these dots can be used to index their corresponding positions on a "white canvas" $\mathbf{H}$ , which serves as a layout + +for the ink dots. $\mathbf{H}$ consists solely of elements that are either 0 or 1 (after normalization). A value of 1 in $\mathbf{H}$ indicates the presence of an ink dot at the corresponding position, while an element 0 indicates the absence of a dot. To pin the dots in set $\mathcal{Q}$ onto the white canvas $\mathbf{H}$ , a straightforward approach is to directly fill these halftone dots into the matrix $\mathbf{H}$ : + +$$ +\mathbf {H} \left[ \left\lfloor \boldsymbol {x} _ {i} \right\rfloor , \left\lfloor \boldsymbol {y} _ {i} \right\rfloor \right] = 1, \quad \forall \left(\boldsymbol {x} _ {i}, \boldsymbol {y} _ {i}\right) \in \mathcal {Q}. \tag {1} +$$ + +Performing such an operation is challenging to optimize in an end-to-end neural network due to the discreteness of ink dot coordinates $\mathbf{q}_i$ , and the continuity of $\mathbf{H}$ . Directly passing the gradient flow between matrix coordinates $\mathbf{x}_i, \mathbf{y}_i$ and $\mathbf{H}$ is not feasible, and backpropagation is difficult to conduct. While reinforcement learning ideas [10] suggest that decision-making agents can help networks execute decisions under reward functions for discrete action spaces, these approaches are relatively complicated. Instead, we aim to design a simple, differentiable transformation between $\mathcal{Q}$ and $\mathbf{H}$ to enable end-to-end training of the network. + +Our key observation is that the halftone $\mathbf{H}$ can be generated through the Hadamard product of multiple sparse binary matrices, and these sparse binary matrices can be expressed as the product of one-hot encodings of dot coordinates. For a halftone $\mathbf{H}$ with $k$ dots, we decompose it into the Hadamard product of $k$ independent matrices $\mathbf{H}_0,\mathbf{H}_1,\dots,\mathbf{H}_{k - 1}$ : + +$$ +\mathbf {H} = \mathbf {I} - \left(\mathbf {I} - \mathbf {H} _ {0}\right) \odot \left(\mathbf {I} - \mathbf {H} _ {1}\right) \odot \dots \odot \left(\mathbf {I} - \mathbf {H} _ {k - 1}\right), \tag {2} +$$ + +where $\odot$ is the Hadamard product, and $\mathbf{I}$ stands for an all-one matrix. $\mathbf{H}_0,\mathbf{H}_1,\dots ,\mathbf{H}_{k - 1}$ have the property that each matrix contains only one element equal to 1, while the rest are 0. Intuitively, $\mathbf{H}_0,\mathbf{H}_1,\ldots ,\mathbf{H}_{k - 1}$ represent halftones formed by printing dots $q_{0},q_{1},\ldots ,q_{k - 1}$ , respectively. For a dot $q_{i} = \{\pmb {x}_{i},\pmb {y}_{i}\}$ , we can get its one-hot encoding from $\pmb{x}_i$ and $\pmb{y}_i$ : + +$$ +\boldsymbol {o} \left(\boldsymbol {x} _ {i}\right) = \operatorname {O n e H o t E n c o d i n g} \left(\boldsymbol {x} _ {i}\right), \tag {3} +$$ + +$$ +\pmb {o} (\pmb {y} _ {i}) = \mathrm {O n e H o t E n c o d i n g} (\pmb {y} _ {i}). +$$ + +Assuming $\pmb{o}(\pmb{x}_i)$ and $\pmb{o}(\pmb{y}_i)$ have been obtained, $\mathbf{H}_i$ can be calculated according to $\pmb{o}(\pmb{x}_i)$ and $\pmb{o}(\pmb{y}_i)$ via $\mathbf{H}_i = \pmb{o}(\pmb{x}_i)^\top \cdot \pmb{o}(\pmb{y}_i)$ . + +Substituting the calculated $\mathbf{H}_i$ into Equation 2, the halftone $\mathbf{H}$ can be obtained. The only non-differentiable step occurs in Equation 3 (i.e., OneHotEncoding). The non-differentiable problem of converting discrete ink dots to continuous halftone matrices is transformed into the non-differentiable problem of one-hot encodings, resulting in a simplified problem. We learn a model O-Net ('O' stands for "one-hot encoding") to perform the mapping from discrete coordinates $\boldsymbol{x}_i$ , $\boldsymbol{y}_i$ to one-hot encoding $\boldsymbol{o}(\boldsymbol{x}_i)$ , $\boldsymbol{o}(\boldsymbol{y}_i)$ . Denote O-Net as O for brevity, which consists of fully connected layers in our implementation. ReLU activation function is used between each layer. During the optimization of O-Net, the potential coordinate values $\tilde{\boldsymbol{x}}$ and $\tilde{\boldsymbol{y}}$ are fed into O, and the gradient is computed utilizing the following loss function $\mathcal{L}_{\mathrm{O - Net}}$ : + +$$ +\mathcal {L} _ {\mathrm {O - N e t}} = +$$ + +$$ +\frac {1}{\max (L _ {1} , L _ {2}) / s} \sum_ {l = 0} ^ {\max (L _ {1}, L _ {2}) - 1} | \mathbf {O} (\tilde {\boldsymbol {x}} _ {l}) - \mathrm {O n e H o t E n c} (\tilde {\boldsymbol {x}} _ {l}) | + +$$ + +$$ +\frac {1}{\max \left(L _ {1} , L _ {2}\right) / s} \sum_ {l = 0} ^ {\max \left(L _ {1}, L _ {2}\right) - 1} | \mathbf {O} (\tilde {\boldsymbol {y}} _ {l}) - \operatorname {O n e H o t E n c} (\tilde {\boldsymbol {y}} _ {l}) |, \tag {4} +$$ + +where OneHotEncoding $(\tilde{\boldsymbol{x}}_l)$ and OneHotEncoding $(\tilde{\boldsymbol{y}}_l)$ denote the one-hot vector determined by $\tilde{\boldsymbol{x}}_l$ and $\tilde{\boldsymbol{y}}_l$ , respectively. $s$ represents the sampling step. It is worth noting that the dot coordinates $\boldsymbol{x}_i$ and $\boldsymbol{y}_i$ are decimal numbers. Therefore, to ensure that the network O can accurately handle different coordinate values, it is necessary to densely sample the interval $[0, \max(L_1, L_2) - 1]$ . In our experiments, we use a sampling step of 0.01 for this interval. The architecture of O-Net is illustrated in Figure 4. + +The precision $\mathcal{P}(\mathbf{O})$ is calculated as follows: + +$$ +\mathcal {P} (\mathbf {O}) = \frac {1}{\max (L _ {1} , L _ {2}) / s} \sum_ {l = 0} ^ {\max (L _ {1}, L _ {2}) - 1} \mathbb {1} \left\{\arg \max (\mathbf {O} (\tilde {\boldsymbol {x}} _ {l})) \right., +$$ + +$\arg \max (\mathrm{OneHotEncoding}(\tilde{\boldsymbol{x}}_l))\} +$ + +$$ +\frac {1}{\max \left(L _ {1} , L _ {2}\right) / s} \sum_ {l = 0} ^ {\max \left(L _ {1}, L _ {2}\right) - 1} \mathbb {1} \left\{\arg \max \left(\mathbf {O} \left(\tilde {\boldsymbol {y}} _ {l}\right)\right), \right. +$$ + +$\arg \max (\mathrm{OneHotEncoding}(\tilde{\mathbf{y}}_l)))\}$ (5) + +where $\mathbb{1}\{a,b\}$ is 1 when $a$ and $b$ are equal, and 0 otherwise. In the experiments, O-Net is first trained to convergence and its parameters are fixed during halftone generation. + +Discussion. We eschew the use of embedding matrix lookups to establish the mapping between dot coordinates and one-hot encodings due to their non-differentiability. + +![](images/9d95e883099e2e704951724a1dc8c41abee4199183350e7376b9bf91ed4f8a51.jpg) +Figure 4. Illustration of O-Net for differentiable transformation from discrete dots to continuous vector-based halftone representations. + +This characteristic disrupts gradients and impedes the process of backpropagation. + +# 3.2. P-Net: Ink Dot Motion Prediction + +A primary contribution of this work is the achievement of dot controllable halftones, with the prediction of the ink dot motion playing a crucial role in this realization. While some deep learning methods have introduced techniques for point motion control and prediction, exemplified in point cloud generation [1, 4, 24, 28, 33, 36], applying these methods directly to halftoning is not feasible for the following reasons: (1) Point clouds typically consist of a small number of points, for instance, the 2,048 points utilized in [24] to generate point clouds of various shapes. In contrast, halftones comprise a substantial number of ink dots, with $20,000 \sim 30,000$ ink dots in a $256 \times 256$ resolution image. As the dot count escalates, optimizing the model becomes progressively more challenging. (2) Point cloud generation methods are primarily employed to create point cloud shapes with a coarse level of detail. In contrast, halftones incorporate intricate details and textures, demanding precise and meticulous control over the movement of each ink dot to achieve a fine-grained result. + +To tackle the aforementioned challenges, we propose P-Net, a network that employs image gray levels as guidance to achieve ink dot motion prediction, as shown in Figure 5. Inspired by recent diffusion generative models [9, 29-31], we explore the efficacy of simple and lightweight convolutional blocks for dot motion prediction. P-Net takes the halftone $\mathbf{H}$ formed by ink dots (Equation 2) and the continuous tone image $\mathbf{C}$ as input. Each element in the matrix $\mathbf{C}$ represents the gray level of the image at the corresponding position. The approach employed by P-Net to integrate information from $\mathbf{H}$ and $\mathbf{C}$ is relatively straightforward, involving concatenation of the two matrices along the channel dimension: + +$$ +\mathbf {P} _ {\text {i n}} = \operatorname {C o n v 2 D} (\mathbf {H} | | \mathbf {C}), \tag {6} +$$ + +where Conv2D means two-dimensional convolution, $||$ means the concatenation operation. While alternative approaches, including post-smooth concatenation and density- + +Algorithm 1 Algorithm for Dot Controllable Halftoning + +# Input: + +The set of random dots, $\mathcal{Q} = \{\pmb {q}_0,\pmb {q}_1,\dots ,\pmb {q}_{k - 1}\}$ + +The number of dots in the set $\mathcal{Q}, k$ ; + +Continuous tone image, C; + +The number of iterations, $\tau$ + +# Output: + +Generated halftone, $\mathbf{H}_{\mathrm{out}}$ +1: Transform the dots in the set $\mathcal{Q}$ into halftone $\mathbf{H}^{(0)}$ using O-Net; /* Equation 2 */ +2: for $i = 0$ to $\tau - 1$ do +3: Feed $\mathbf{H}^{(i)}$ and $\mathbf{C}$ into P-Net as input; /* Equation 6*/ +4: Obtain motion predictions of each dot in $\mathcal{Q}$ : $\mathbf{P}_{\mathrm{out}}^{(i)} \gets \mathbb{P} - \mathrm{Net}(\mathbf{H}^{(i)}, \mathbf{C})$ ; /* Equation 8 */ +5: Update the position of ink dot $\forall \pmb{q}_i \in \mathcal{Q}$ , and update the set $\mathcal{Q}$ ; /* Equation 9*/ +6: Transform the dots in the set $\mathcal{Q}$ into halftone $\mathbf{H}^{(i + 1)}$ using O-Net; /* Equation 2 */ +7: Calculate $\mathcal{L}_{\mathrm{P}}$ and update the model parameters of P-Net; /\*Equation 13\*/ +8: end for +9: return $\mathbf{H}_{\mathrm{out}}\gets \mathbf{H}^{\tau}$ + +integral map-based methods, have been explored in the experiments, they demand greater computation and do not yield substantial performance enhancements. P-Net utilizes a sequence of convolution modules to acquire the fusion representation of matrices $\mathbf{H}$ and $\mathbf{C}$ , followed by several downsampling modules to reduce the image resolution: + +$$ +\widetilde {\mathbf {P}} = \operatorname {D o w n S a m p l e} (\operatorname {S t a c k e d C o n v 2 D} \left(\mathbf {P} _ {\text {i n}}\right)), \tag {7} +$$ + +where $\widetilde{\mathbf{P}}$ represents the feature matrix of high-level gray scale information, which coarsely expresses the overall movement trend of the ink dots within adjacent image blocks. Next, a prediction head composed of convolutions is used on the upsampled $\widetilde{\mathbf{P}}$ matrix to make the output dot motion $\mathbf{P}_{\mathrm{out}}$ consistent with the resolutions of the halftone matrix $\mathbf{H}$ : + +$$ +\mathbf {P} _ {\text {o u t}} = \operatorname {S t a c k e d C o n v 2 D} (\operatorname {U p S a m p l e} (\tilde {\mathbf {P}})). \tag {8} +$$ + +Each element in $\mathbf{P}_{\mathrm{out}}$ represents the displacement vector of the ink dot at the corresponding position, and it has two channels representing the motion prediction along $x$ and $y$ directions, respectively. For $\forall \pmb {q}_i\in \mathcal{Q},\pmb {q}_i = \{\pmb {x}_i,\pmb {y}_i\}$ , its new position can be derived as: + +$$ +\left(\hat {\boldsymbol {x}} _ {i}, \hat {\boldsymbol {y}} _ {i}\right) = \left(\boldsymbol {x} _ {i}, \boldsymbol {y} _ {i}\right) + \mathbf {P} _ {\text {o u t}} \left[ \left\lfloor \boldsymbol {x} _ {i} \right\rfloor , \left\lfloor \boldsymbol {y} _ {i} \right\rfloor \right]. \tag {9} +$$ + +The ink dot coordinates $\hat{\pmb{q}}_i = \{\hat{x}_i,\hat{y}_i\}$ after the motion can be differentiated to form a new halftone matrix $\widehat{\mathbf{H}}$ through O-Net, and the iteration is completed. + +![](images/39cb4c56660063f093c69c8d449f644835a7f4db7d67434b0d033c723188dd9e.jpg) +Figure 5. Schematic diagram of the proposed P-Net, which is used to predict the motion of each ink dot. + +# 3.3. Training Scheduling and Optimization + +To optimize our model, following [27, 35], we use the tone loss $\mathcal{L}_T$ , which computes the dissimilarity between halftone predictions $\mathbf{H}_{\mathrm{out}}$ and continuous tone images $\mathbf{C}$ : + +$$ +\mathcal {L} _ {T} = \mathbb {E} _ {\mathbf {H}} \| \text {G a u S m o o t h} (\mathbf {H} _ {\text {o u t}}) - \text {G a u S m o o t h} (\mathbf {C}) \| _ {2}, \tag {10} +$$ + +where $\| \cdot \| _2$ represents the L2 norm. To improve the structural similarity of the generated halftones, the structural loss $\mathcal{L}_S$ is employed: + +$$ +\mathcal {L} _ {S} = \mathbb {E} _ {\mathbf {H}} \| \operatorname {S t r u c} \text {- M e a s u r e} (\mathbf {H} _ {\text {o u t}}, \mathbf {C}) \| _ {1}. \tag {11} +$$ + +Additionally, the pixel loss $\mathcal{L}_R$ is adopted to measure the difference between the generated halftone after inverse halftoning transformation and the continuous tone image: + +$$ +\mathcal {L} _ {R} = \mathbb {E} _ {\mathbf {H}} \| \mathcal {R} \left(\mathbf {H} _ {\text {o u t}}\right) - \mathbf {C} \| _ {2}, \tag {12} +$$ + +where $\mathcal{R}$ represents the frozen inverse halftoning network [35]. The total loss $\mathcal{L}_P$ is as follows: + +$$ +\mathcal {L} _ {P} = \mathcal {L} _ {T} + \gamma_ {S} \mathcal {L} _ {S} + \gamma_ {R} \mathcal {L} _ {R}, \tag {13} +$$ + +where $\gamma_{S}$ and $\gamma_{R}$ are hyperparameters to trade-off each loss term. We detail the training process in Algorithm 1. + +# 4. Experiments + +# 4.1. Datasets, Baselines, and Evaluation Protocols + +Datasets and Baselines. Following previous research [13, 35], we curate a halftoning dataset by selecting images from UTKFace [37] and DIV2K [2]. The dataset comprises 4000, 1000, and 400 images in the training, validation, and test sets, respectively. We select baseline models from two categories: traditional halftoning methods [12, 21, 26] and deep learning-based halftoning methods [35]. The traditional methods include amplitude modulation techniques (such as Ordered Dithering), frequency modulation techniques (such as Floyd-Steinberg Error Diffusion, Simpler Floyd-Steinberg Error Diffusion, Jarvis, Judice, and Ninke Dithering, Stucki Dithering, Atkinson Dithering, Burkes Dithering, Sierra Dithering, Two Row Sierra Dithering, and Sierra Lite Dithering), and improvements of Floyd-Steinberg error diffusion algorithm (such as Ostromoukhov's Method). + +![](images/6c0a68b7369da5cd36fd6ef1804600b8a292ff020e9ef4b9f7fbacb0193d36d3.jpg) +(a) training iteration $= 1000$ + +![](images/29effad5bb89312958b237c71e72bcdff28d64750b75faa016047a33ab25dc7c.jpg) +(b) training iteration $= 3000$ +Figure 6. O-Net robustness test experiment. The figure shows the variation trend of the halftone quality obtained by O-Net with the noise intensity. a, b, c, and d represent 1000, 3000, 6000, and 9000 model iterations $(\times 10^{4})$ , respectively. + +![](images/80e942c4c366fd9384bec6463e3e1910f7933283037a06b8d387338946e7f7a3.jpg) +(c) training iteration $= 6000$ + +![](images/2bd068e964e91eb7c905938d2ef23eedd8b19e2edb31b84c5e7823a10b4cb410.jpg) +(d) training iteration $= 9000$ + +Table 1. Performance comparison of different halftoning methods on test images in terms of peak signal to noise ratio. + +
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]29.6936.491.1433.04
Floyd-S. [12]35.3144.401.7239.52
Simpler Floyd-S. [21]32.5241.611.6436.81
Jarvis, J., and N. [21]27.7038.291.8532.67
Stucki [21]28.5739.101.8533.40
Atkinson [21]21.7831.771.8226.36
Burkes [21]31.7441.581.7535.62
Sierra [21]28.2338.511.8733.25
Two Row Sierra [21]30.8241.211.7334.86
Sierra Lite [21]35.9545.581.6540.90
Ostromoukhov [26]36.0445.901.7641.18
Xia's Method [35]29.8935.940.8133.83
Our Proposed Method34.7446.642.1843.04
+ +Regarding deep learning methods, we select [35] as the baseline, which is a recently proposed deep learning-based halftoning approach. + +Evaluation Protocols and Implementation Details. Following previous work [35], we use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) to measure the quality of the generated halftones. Before computing PSNR, we first smooth both the halftone and continuous tone image with an $11 \times 11$ Gaussian filter, and then use the smoothed images to calculate the metrics. In addition, we also use qualitative experiments to evaluate the performance of different methods. The quantity of initial dots $k$ is determined through a linear transformation based on the grayscale of the continuous tone. In P-Net, the number of channels is 64, the convolution kernel size is set to $3 \times 3$ . O-Net consists of 4 fully connected layers, and the activation function between layers is ReLU. $\gamma_{S}$ and $\gamma_{R}$ are set to 0.04 and 0.08 respectively. Adam optimizer [19] is used to optimize the model, and the learning rate is set to 0.0001. + +# 4.2. Performance Comparison + +We conduct quantitative experiments on images with $64 \times 64$ resolutions, and the experimental results are shown in Table 1. It can be observed that our proposed method achieves superior performance than previous methods. Traditional methods (e.g., Ordered Dithering, Floyd-Steinberg + +Error Diffusion, Ostromoukhov's Method) usually predefine some dithering matrices or diffusion coefficients, which achieve relatively good results. However, these traditional methods apply a hand-crafted halftoning criterion to all images indiscriminately, and thus have limited flexibility compared to data-driven approaches like [35]. Besides, previous methods perform halftone generation on the global image and cannot adaptively control the motion of each ink dot, which makes it difficult to flexibly remove some undesired artifacts in the generated halftones. In contrast, our method can flexibly control the motion of each ink dot on the halftone, thus achieving better experimental results. + +# 4.3. Study on the Effectiveness of O-Net + +A well-performing O-Net should be able to handle various coordinate values produced by model predictions. Although we sample the $[0, \max(L_1, L_2) - 1]$ interval as densely as possible during training, it is still not enough to cover various float coordinate values that may be encountered during model training. In light of this, we design some experiments to verify the robustness of O-Net to numerical noise of float numbers, as shown in Figure 6. The main process of the experiment is that we randomly add noises of different intensities to the correct coordinates of ink dots, and observe the prediction precision of O-Net after adding noises. The magnitude of the noise is constrained between $[0, 1]$ , which is to ensure that the original position of the ink dot will not be changed when the noise is added to the coordinates. The intensity of the noise is defined by its coverage percentage of the coordinate value. As illustrated in Figure 6, during the initial stages of training, noise interference adversely impacts the quality of the halftones generated by the model. However, as training advances towards convergence, the model becomes less sensitive to noise interference, affirming the robustness of O-Net. + +In addition, we visualize the heat maps of O-Net prediction results at different stages of training, as shown in Figure 7. We first randomly initialize 64 ink dot coordinates on a $64 \times 64$ resolution image, then feed these 64 dot coordinates into O-Net, and visualize the model prediction results. As depicted in Figure 7, prior to the convergence of O-Net, the predicted image exhibits numerous non-binarized gray + +![](images/0c6ab0862b593f66381d8106f81554a3e3bdd75c1ec4a42d415faef347b8459a.jpg) +(a) random initialized + +![](images/aa74e95b3353ca56192e7d99303c808726c9f06a1e817351955f7ccfe26a31b7.jpg) +(b) training iteration $= 10$ + +![](images/0f9670b92e8c8f79181a3ee931bcacf559461b0b305f7409b663515e0cee65bf.jpg) +(c) training iteration=6000 + +![](images/24b19fe4754260c45de449713cfe095c7ff843f564b1788efdd7ed47597d923b.jpg) +(d) training iteration $= 9000$ + +![](images/b51b5cade0ed58a2221b0c8f61b6225c307ce09ecee050df234454f4e8ea7c92.jpg) + +![](images/901009823ea8982d69bee154005d70284a288e823a12e79081e0d12c92c9dead.jpg) +Figure 7. Visualization of model predictions at different stages of O-Net training. a, b, c, and d represent 0, 10, 6000, and 9000 model iterations $(\times 10^{4})$ , respectively. The effectiveness of O-Net increases as the image transitions towards a binary representation. +(a) continuous tone + +![](images/ba615fafe11f44aaff548626466567280301643e32f90ff69c9378736cbe2c93.jpg) +(b) iteration #1 + +![](images/e3636afd32fd7572cc9918d3ddadc6b10f68fb6653911dc34282d038c644f5b8.jpg) +(c) iteration #2 + +![](images/86146f3eb8ad72546c80e0c6d8d3b4f54df843b0dad1ba313ce706a1b94ea322.jpg) +(d) iteration #3 + +![](images/f5e29f41d2dfdd799ef56eabefe4c0f28fe39f5ac256a8aa98ce33ed558a7cf1.jpg) +(e) iteration #4 + +![](images/7cf657eda71856b3bbf7cf171394f4a9373709fb02a099565f288fa62f8f2b91.jpg) +Figure 8. Visualization of ink dot motion predictions over several iterations. Here we visualize the motions on x-axis, normalized to 0 to 1. +(a) quantity level 1 +Figure 9. Illustration of the resulting halftones with different numbers of ink dots. Number of ink dots: (a): 10K; (b): 14K; (c): 18K. More ink dots enrich the texture details of the image. + +![](images/fbe7e7a46e5f5095d46781a043d12a320879d216955d94801bfd8851abc2869e.jpg) +(b) quantity level 2 + +![](images/92ed0c7984f06810b1a5113b7b7521d633645fe91dc600b207a04fb3b02db18d.jpg) +(c) quantity level 3 + +pixels, indicating that the one-hot encoding at this stage is not fully optimized. In contrast, upon O-Net convergence, the generated halftone comprises solely black and white pixels, affirming the capability of O-Net in producing binary halftones. + +# 4.4. Comparison of Structural Quality + +The structural quality of halftones is also an important indicator for evaluating the performance of an algorithm. We compare the structural similarity with methods that generate halftones with higher PSNR, as shown in Table 2. It can be observed that our proposed method achieves better structural similarity than the baseline methods. + +# 4.5. Visualization of Motion Predictions + +We depict the dot motion predictions generated by P-Net across multiple iterations, as illustrated in Figure 8. Notably, the model rapidly shifts the ink dots from regions with + +Table 2. Performance comparison of different halftoning methods on test images in terms of structural similarity. + +
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]0.02540.30700.04860.1384
Floyd-S. [12]0.02960.43350.06040.1687
Simpler Floyd.-S. [21]0.02950.46100.06290.1664
Sierra Lite [21]0.02840.41100.05960.1660
Ostromoukhov [26]0.02650.41850.05900.1628
Our Proposed Method0.03050.41590.06280.1709
+ +elevated grayscale to those with lower grayscale in the initial stage. This observation substantiates that the motion predictions of P-Net are grounded in a keen awareness of image grayscale. With the progression of iterations, the motions converge towards zero across the majority of the image, leading the model to confine ink dot movements to a limited local area. + +# 4.6. Qualitative Experiments + +Figure 10 presents qualitative experimental results of different halftone methods, which focus on generating halftones on flat textures with subtle variations in image tone (e.g., light and shadow on clouds). Earlier efforts yield halftones with either undesirable white holes or repetitive streaks of ink dots, compromising the overall quality of the output. Additionally, deep learning methods (Figure $10\mathrm{m}$ ) introduce visual artifacts and struggle to faithfully reproduce subtle variations in light and shade. In contrast, our method better preserves tonal details in flat regions and achieves su + +![](images/1f9f2f3e70313faf8a44ae248cf9749b82ee19396631c0611a44570019411a83.jpg) +(a) Contone + +![](images/19ce8d847670b691e2ed68075e98c887199b832a771fb6be1658d39e2b44c26b.jpg) +(b) Simpler F.-S. + +![](images/5958c5bdc2effc542b658f99fe0e1ac351abf2809bb8d428db042cb5c395394b.jpg) +(c) J. J., and Ninke + +![](images/43ec3b426e97a9ade10c38d6be42619d80d0ba6c6b649df66e5e89ac95d932f1.jpg) +(d) Stucki + +![](images/aeacf5f0dc300a6cc1edaf9124497475524b18c77450b5c67f63870d670b1d41.jpg) +(e) Atkinson + +![](images/748a64f6d168842e65099dab52c1d2fd25c120a28a1e2b49cd685e58361eabd1.jpg) + +![](images/7bb6ac269a4ed56ef1f2f325ab11df55b67efd9e0fb29d8d52b8776ee199348a.jpg) + +![](images/01bac461886d9abdd7a23a67b3277ba6208a1bc6d644e4bc872483c1df8efa54.jpg) +(h) Two Row Sierra + +![](images/1c5f36f9ea7e7d689527cc0db8fe00e1ac7b117de83f71fd6ad77027f26f0fa0.jpg) +(i) Sierra Lite + +![](images/e045686601350a670b9b66019cbcbfbfcdabd70cf18c72d535db5480ee7593e3.jpg) +(j) Ordered Dither + +![](images/5166ad0746a05b9a7682e94b25818f3df91929b9a5affc6f8ac4473c1b4deea8.jpg) +(k) Floyd-Steinberg + +![](images/029e834e57be122910caf292608271a09cf885399ee1d413cfbf9a30fcc85337.jpg) +(1) Ostromoukhov + +![](images/71d1721c6a79da91ec77c15441793e166dc1a7a4b34bb40eaa9fce87aea3dd96.jpg) +(f)Burkes +(m) Xia + +![](images/adfe75e6c6ec6ee2207ddca9eef85b5c8ceaddf94a6c3cb800393f72a4a969f5.jpg) +(g) Sierra +(n) Ours + +![](images/8bc396ace471dca3950f7a9898e1afd0fa9a8f05333fa1739a6b617bae0e223a.jpg) +Figure 10. Qualitative experimental results. Baseline methods yields halftones with some imperfections, including holes (e, m), striped dot distribution (b, f, g, h, l), or other regular visual artifacts (c, d, i, j, k). Images are from the DIV2K dataset [2]. +(a) continuous tone +Figure 11. Experimental results of refining areas with artifacts in generated halftones by manipulating local ink dots. PSNR: (c): 37.24; (d): 44.10; (e): 44.43. SSIM: (c): 0.00756; (d): 0.00772; (e): 0.00776. + +![](images/99c1c0e3d29c856c4788d57e4e3803e9776a62ae2be915cc4cee48957b69bc98.jpg) +(b) zoom in + +![](images/355fca39702364843a8c8f8b31e50cae5df85a649337354d608ce8837e48cb2b.jpg) +(c) init. pred. + +![](images/44748e6c2fec3b68517f462e9bad759703f417a45897acb0334fa20b303ca511.jpg) +(d) 1st. refine + +![](images/92015db6be7d2b84f21ed3ed9a056e2458a98c9b9c858dbb5a934796f0265822.jpg) +(e) 2nd. refine + +Table 3. Statistical results of collisions during ink dot movement. + +
Iteration (τ)48121620
Reduction Ratio0.03140.02490.02960.03160.0287
+ +perior visual results. Additional qualitative experimental results, encompassing high-resolution and color images, are presented in the supplementary material. + +# 4.7. Study on the Collision Rate of Ink Dots + +Ink dots may experience collisions during their movement. We compute the reduction ratio in the number of ink dots resulting from these collisions and overlaps, as outlined in Table 3. It can be observed that the reduction in the number of ink dots due to collisions is minimal, constituting approximately $2\%$ to $3\%$ of the total ink dot count. This observation suggests that collisions have a negligible impact on both the overall quantity of ink dots and the dithering process in halftones. We will investigate methods to further minimize ink dot collisions and develop strategies for managing colliding ink dots in our future work. + +# 4.8. Dot Control Helps Remove Local Artifacts + +We explore an advantage of controllable ink dots: the capability to enhance specific areas within generated halftones through precise manipulation of the ink dots. As illustrated in Figure 11, the initially generated halftone may exhibit artifacts in local regions (Figure 11c). To address this, we refine the halftone by readjusting the ink dots in these areas, resulting in a further enhancement of the generated halftone's quality and the elimination of artifacts (Figure 11d, 11e). This process serves as validation for the efficacy of our proposed concept of controllable ink dots. + +# 4.9. Study on Ink Dot Quantity Control + +We investigate another advantage of dot control: the capacity to regulate the quantity of ink dots. In Figure 9, we present some examples of halftones with a gradual increase in the quantity of ink dots, from level 1 (Figure 9a) to level 3 (Figure 9c). Notably, even with a smaller number of ink dots, the halftones still maintain visually pleasing levels of detail. The experimental results verify that the proposed method can control the number of ink dots and generate visually pleasing halftones, making it more flexibly applicable to halftone prints of different consumable levels. + +# 5. Conclusion + +We introduce ink dot-oriented neural halftoning in this work. O-Net propagates dense gradients to sparse halftone dots, and completes the differentiable transformation between dot coordinates and halftone matrices. P-Net achieves direct control of halftone dots through dot motion predictions. Extensive quantitative and qualitative experiments verify the effectiveness of our proposed method. + +Acknowledgement: This work is supported by National Key R&D Program of China (2022ZD0160300). + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In ACM SIGGRAPH 2008 papers, pages 1-8. 2008. 5 +[28] Dong Wook Shu, Sung Woo Park, and Junseok Kwon. 3d point cloud generative adversarial network based on tree structured graph convolutions. In Proceedings of the IEEE/CVF international conference on computer vision, pages 3859-3868, 2019. 4 +[29] Yang Song and Stefano Ermon. Improved techniques for training score-based generative models. Advances in neural information processing systems, 33:12438-12448, 2020. 4 +[30] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021. +[31] Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. In International Conference on Machine Learning, 2023. 4 +[32] Dusan C Stulik and Art Kaplan. Halftone. The Atlas of Analytical Signatures of Photographic Processes, 2013. 1 + +[33] Lyne P Tchapmi, Vineet Kosaraju, Hamid Rezatofighi, Ian Reid, and Silvio Savarese. Topnet: Structural point cloud decoder. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 383-392, 2019. 4 +[34] Ping Wah Wong. Adaptive error diffusion and its application in multiresolution rendering. IEEE Transactions on image Processing, 5(7):1184-1196, 1996. 2 +[35] Menghan Xia, Wenbo Hu, Xueting Liu, and Tien-Tsin Wong. Deep halftoning with reversible binary pattern. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14000-14009, 2021. 1, 2, 3, 5, 6 +[36] Guandao Yang, Xun Huang, Zekun Hao, Ming-Yu Liu, Serge Belongie, and Bharath Hariharan. Pointflow: 3d point cloud generation with continuous normalizing flows. In Proceedings of the IEEE/CVF international conference on computer vision, pages 4541-4550, 2019. 4 +[37] Zhifei Zhang, Yang Song, and Hairong Qi. Age progression/regression by conditional adversarial autoencoder. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5810-5818, 2017. 5 +[38] Bingfeng Zhou and Xifeng Fang. Improving mid-tone quality of variable-coefficient error diffusion using threshold modulation. In ACM SIGGRAPH, pages 437-444. 2003. 2 +[39] Xia Zhuge, Yuki Hirano, and Koji Nakano. A new hybrid multitoning based on the direct binary search. In Proceedings of the International MultiConference of Engineers and Computer Scientists, 2008. 2 \ No newline at end of file diff --git a/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/images.zip b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d717c89390bfe8f36f57568344d7c2fe44a1a520 --- /dev/null +++ b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8158f55cb708432bff83d18c778302b029e2cd90cc5bb4eececf99d83d877d92 +size 945063 diff --git a/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/layout.json b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f987c36b2eb2cabcf39b4ce2314ca5cd62d15c63 --- /dev/null +++ b/2024/Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning/layout.json @@ -0,0 +1,11906 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 65, + 102, + 529, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 102, + 529, + 122 + ], + "spans": [ + { + "bbox": [ + 65, + 102, + 529, + 122 + ], + "type": "text", + "content": "Ink Dot-Oriented Differentiable Optimization for Neural Image Halftoning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 144, + 238, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 144, + 238, + 186 + ], + "spans": [ + { + "bbox": [ + 112, + 144, + 238, + 186 + ], + "type": "text", + "content": "Hao Jiang \nPeking University \njianghao@stu.pku.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 269, + 144, + 358, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 269, + 144, + 358, + 186 + ], + "spans": [ + { + "bbox": [ + 269, + 144, + 358, + 186 + ], + "type": "text", + "content": "Bingfeng Zhou \nPeking University \nzbf@pku.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 389, + 144, + 479, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 144, + 479, + 186 + ], + "spans": [ + { + "bbox": [ + 389, + 144, + 479, + 186 + ], + "type": "text", + "content": "Yadong Mu* Peking University myd@pku.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 50, + 215, + 420, + 423 + ], + "blocks": [ + { + "bbox": [ + 50, + 215, + 420, + 423 + ], + "lines": [ + { + "bbox": [ + 50, + 215, + 420, + 423 + ], + "spans": [ + { + "bbox": [ + 50, + 215, + 420, + 423 + ], + "type": "image", + "image_path": "688e8a0ed5f8d690ed91554623de846df118315656ad49b6e9d865b7237c6583.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 432, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 46, + 432, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 547, + 456 + ], + "type": "text", + "content": "Figure 1. Illustration of halftones generated by our proposed ink dot-oriented differentiable neural halftoning method and several previous methods [12, 26, 35]. Images are from the DIV2K dataset [2]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 422, + 213, + 477, + 422 + ], + "blocks": [ + { + "bbox": [ + 422, + 213, + 477, + 422 + ], + "lines": [ + { + "bbox": [ + 422, + 213, + 477, + 422 + ], + "spans": [ + { + "bbox": [ + 422, + 213, + 477, + 422 + ], + "type": "image", + "image_path": "4f9ad381643712b581c72e65779355fd576899d1ebb7e35748e22aedcb24f8cb.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 477, + 213, + 545, + 422 + ], + "blocks": [ + { + "bbox": [ + 477, + 213, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 477, + 213, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 477, + 213, + 545, + 422 + ], + "type": "image", + "image_path": "b05e07671263afdd5e234349c1b63be3a2c6693579d4c5f977146d09a4f59743.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 464, + 192, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 464, + 192, + 477 + ], + "spans": [ + { + "bbox": [ + 143, + 464, + 192, + 477 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 490, + 290, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 490, + 290, + 694 + ], + "spans": [ + { + "bbox": [ + 45, + 490, + 290, + 694 + ], + "type": "text", + "content": "Halftoning is a time-honored printing technique that simulates continuous tones using ink dots (halftone dots). The resurgence of deep learning has catalyzed the emergence of innovative technologies in the printing industry, fostering the advancement of data-driven halftoning methods. Nevertheless, current deep learning-based approaches produce halfstones through image-to-image black box transformations, lacking direct control over the movement of individual halftone dots. In this paper, we propose an innovative halftoning method termed \"neural dot-controllable halftoning\". This method allows dot-level image dithering by providing direct control over the motion of each ink dot. We conceptualize halftoning as the process of sprinkling dots on a canvas. Initially, a specific quantity of dots are randomly dispersed on the canvas and subsequently adjusted based on the surrounding grayscale and gradient. To establish differentiable transformations between" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "type": "text", + "content": "discrete ink dot positions and halftone matrices, we devise a lightweight dot encoding network to spread dense gradients to sparse dots. Dot control offers several advantages to our approach, including the capability to regulate the quantity of halftone dots and enhance specific areas with artifacts in the generated halftones by adjusting the placement of the dots. Our proposed method exhibits superior performance than previous approaches in extensive quantitative and qualitative experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 597, + 387, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 387, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 387, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "In the late 1800s, pioneers such as William Henry Fox Talbot, Georg Meisenbach, Frederic Ives, and Max Levy [32] made significant strides in halftone printing techniques, enabling photographs to be printed on paper using ink. Halftoning is a technique of replicating the color and shading of continuous tone images by employing ink dots (halftone dots) of different sizes and frequencies. It remains a crucial and enduring component in the modern printing" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27528" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 287, + 167 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 287, + 167 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 287, + 167 + ], + "type": "image", + "image_path": "186efc2606451bc23b81d48725eac75a0f97c2751d6dc4be8e9effc8c4951d1f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 176, + 288, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 176, + 288, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 288, + 242 + ], + "type": "text", + "content": "Figure 2. Prior deep networks-based halftoning methods (top) map an image to a halftone-like continuous-tone image before applying a binarization operation. In contrast, our proposed method (bottom) differs from previous halftoning techniques in that it achieves dot-level halftones through direct control over the movement of each dot." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 255, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 302 + ], + "type": "text", + "content": "industry. A successful halftone can closely reproduce the original image with high quality, leveraging the low-pass filtering characteristics of the human visual system to attain near-optimal visual effects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 424 + ], + "type": "text", + "content": "Halftone technology can be broadly divided into two categories: traditional or deep learning-based methods. The former can be further cast into three groups based on implementations of dithering process: amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [6, 20, 22, 34], and hybrid modulation [14, 39]. Recently, the renaissance of deep learning as a black-box approximation for high-dimensional functions has catalyzed the emergence of several data-driven methods in the field of halftoning [15, 16, 18, 23, 35], demonstrating superior performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 288, + 664 + ], + "type": "text", + "content": "In this paper, we argue that current deep learning methods for halftoning, face some weaknesses that impede their deployment in the printing industry. Notably, these methods treat halftones as binary images and heavily rely on a black box encoder-decoder to convert between the original continuous-tone image and the halftone-induced binary image. However, they operate as image-level transforms rather than directly manipulating the halftone dots, leading to a loss of direct control over the desired properties of the resultant halftones. As observed in Figure 1, purely image-level transformations [12, 26, 35] tend to produce undesired artifacts, and they struggle to directly manipulate local dot arrangements to eliminate these artifacts. In addition, traditional methods do not allow for control over the number of halftone dots. In practical applications, opting for halftone techniques that utilize fewer ink dots can be advantageous for consumable savings. For prints with low detail requirements, like halftone cartoon stickers, a modest quantity of dots suffice to faithfully convey the information present in the continuous tone image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "To address the above issues, we propose ink dot-oriented neural image halftoning for the first time in the literature, which directly controls the motion of each ink dot, enabling dot-level differentiable optimization. Nonetheless, a piv" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "otal challenge in achieving this lies in the discrete nature of ink dot positions, while the objective functions piloting the halftone generation are continuous. Directly propagating the gradient flow from halftone pixels to ink dot positions is unfeasible, rendering gradient back-propagation a challenging endeavor. A key contribution of this paper is the presentation of a novel approach to integrate discrete ink dots into continuous halftone optimization in a fully differentiable manner." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 180, + 546, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 546, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 546, + 348 + ], + "type": "text", + "content": "Our approach considers halftoning as the process of optimizing dot placements on a blank canvas using halftone quality-related guidance. We commence by randomly spreading a flexible number of dots on the canvas and then progressively move them. To facilitate smooth gradient backpropagation from the objective function to each discrete ink dot, we introduce a dot encoding module that maps dot coordinates to the product of sparse vectors, creating a structure conducive to differentiable optimization. We also develop a motion-estimating module to predict the motion of each ink dot. Our method offers direct control over the quantity of ink dots in the generated halftones, a feat challenging to attain in prior work, owing to the flexibility and scalability of the proposed dot manipulations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "content": "To sum up, this paper introduces ink dot-oriented neural image halftoning, the first approach of its kind to achieve dot-level image dithering by controlling the movement of ink dots. Our proposed model showcases superior performance over previous methods in extensive qualitative and quantitative experiments. Furthermore, the method can be easily extended to arbitrary scale and color images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 444, + 392, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 392, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 392, + 456 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 464, + 435, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 435, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 435, + 477 + ], + "type": "text", + "content": "2.1. Traditional Halftoning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 482, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 662 + ], + "type": "text", + "content": "Traditional halftone methods can be categorized into amplitude modulation (AM) [3, 5, 11], frequency modulation (FM) [7, 8, 25, 38], and hybrid approaches [14, 39]. AM methods use dot clusters of varying sizes and frequencies to represent different shades of gray and reproduce the original continuous tone image. FM is represented by the error diffusion algorithm, which distributes the quantization error generated by pixel thresholding to adjacent pixels, achieving superior results. For example, Ostromoukhov [26] proposed an improved error-diffusion algorithm based on the deliberately restricted choice of the distribution coefficients. Unlike these traditional methods, which rely on some prior or handcrafted designs, our approach is data-driven, enabling halftone optimization with greater fitting ability and model capacity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 670, + 482, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 482, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 482, + 684 + ], + "type": "text", + "content": "2.2. Deep Learning Based Halftoning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "With the emergence of deep learning techniques, researchers have explored the use of neural networks to gen" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27529" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 71, + 521, + 173 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 521, + 173 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 521, + 173 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 521, + 173 + ], + "type": "image", + "image_path": "84a5a9ab9a101e3b21f852e9c93572eef2ceae6613ddc148796def38e1a90d62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 185, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 46, + 185, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 547, + 218 + ], + "type": "text", + "content": "Figure 3. Schematic illustration of the proposed method. The proposed method takes a set of random dots as input. O-Net differentiably transforms discrete ink dot positions into a halftone matrix, effectively spreading dense gradients over sparse dots. P-Net predicts the motion of each halftone dot." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 225, + 289, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 289, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 289, + 310 + ], + "type": "text", + "content": "erate halftones [16, 17, 23, 35]. For example, Xia et al. [35] utilized stacked convolutional networks to learn reversible halftones capable of concealing color information. However, most of prior methods treat the entire image as a whole and cannot achieve fine control of halftone dots. In contrast, our approach facilitates dot-level controllable halftones, offering greater interpretability and maneuverability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 324, + 103, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 103, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 103, + 335 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 345, + 287, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 287, + 369 + ], + "type": "text", + "content": "3.1. O-Net: Spreading Dense Gradients onto Sparse Ink Dots" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 376, + 289, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 289, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 289, + 592 + ], + "type": "text", + "content": "Halftone images consist solely of black and white pixels, with the arrangement of black pixels determining the brightness and visual structure of each area in the image. A straightforward approach to generate halftone images is to first learn a mapping from a continuous-tone image to an almost binary image, which is then rounded to produce binary halftone dots, as demonstrated in prior work [15-18, 23, 35]. Nevertheless, this approach is subject to several limitations. Primarily, it lacks direct control over individual halftone dots. In the event of defects in some generated halftone areas, the entire halftone have to be regenerated, posing escalating challenges, particularly for larger images. Additionally, previous image-level halftoning methods lack the capability to regulate the quantity of ink dots in halftones. In scenarios where printing equipment features limited or costly consumables, this lack of flexibility hinders the generation of halftones with varying consumable levels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "In Figure 3, we present a novel approach for dot-centric halftoning. The process begins by initializing a set of dots at random. Denote the dot set as " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = \\{\\pmb{q}_0,\\pmb{q}_1,\\dots,\\pmb{q}_{k - 1}\\}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " represents the number of dots. Each dot " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{q}_i" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is represented by its two-dimensional coordinates within the image, i.e., " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{q}_i = \\{\\pmb{x}_i,\\pmb{y}_i\\}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "i\\in [0,k - 1],\\pmb{x}_i\\in [0,L_1 - 1],\\pmb{y}_i\\in [0,L_2 - 1]" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " being the height and width of the image, respectively. The coordinates of these dots can be used to index their corresponding positions on a \"white canvas\" " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", which serves as a layout" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "content": "for the ink dots. " + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "content": " consists solely of elements that are either 0 or 1 (after normalization). A value of 1 in " + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "content": " indicates the presence of an ink dot at the corresponding position, while an element 0 indicates the absence of a dot. To pin the dots in set " + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "content": " onto the white canvas " + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "content": ", a straightforward approach is to directly fill these halftone dots into the matrix " + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 225, + 547, + 308 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 348, + 310, + 545, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 310, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 348, + 310, + 545, + 326 + ], + "type": "interline_equation", + "content": "\\mathbf {H} \\left[ \\left\\lfloor \\boldsymbol {x} _ {i} \\right\\rfloor , \\left\\lfloor \\boldsymbol {y} _ {i} \\right\\rfloor \\right] = 1, \\quad \\forall \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {y} _ {i}\\right) \\in \\mathcal {Q}. \\tag {1}", + "image_path": "3c2db65aff5951c32f9d8145bf7eab20a7778980524e1b8e9e73eaef85495fa5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": "Performing such an operation is challenging to optimize in an end-to-end neural network due to the discreteness of ink dot coordinates " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": ", and the continuity of " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": ". Directly passing the gradient flow between matrix coordinates " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i, \\mathbf{y}_i" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": " is not feasible, and backpropagation is difficult to conduct. While reinforcement learning ideas [10] suggest that decision-making agents can help networks execute decisions under reward functions for discrete action spaces, these approaches are relatively complicated. Instead, we aim to design a simple, differentiable transformation between " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": " to enable end-to-end training of the network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "content": "Our key observation is that the halftone " + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "content": " can be generated through the Hadamard product of multiple sparse binary matrices, and these sparse binary matrices can be expressed as the product of one-hot encodings of dot coordinates. For a halftone " + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "content": " dots, we decompose it into the Hadamard product of " + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "content": " independent matrices " + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_0,\\mathbf{H}_1,\\dots,\\mathbf{H}_{k - 1}" + }, + { + "bbox": [ + 304, + 475, + 547, + 559 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 570, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 570, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 312, + 570, + 545, + 583 + ], + "type": "interline_equation", + "content": "\\mathbf {H} = \\mathbf {I} - \\left(\\mathbf {I} - \\mathbf {H} _ {0}\\right) \\odot \\left(\\mathbf {I} - \\mathbf {H} _ {1}\\right) \\odot \\dots \\odot \\left(\\mathbf {I} - \\mathbf {H} _ {k - 1}\\right), \\tag {2}", + "image_path": "d9f086c634deff6cfec68249c5bd046c225fdf4b5b98dde5c48cf9b68cf9b1f8.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": " is the Hadamard product, and " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": " stands for an all-one matrix. " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_0,\\mathbf{H}_1,\\dots ,\\mathbf{H}_{k - 1}" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": " have the property that each matrix contains only one element equal to 1, while the rest are 0. Intuitively, " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_0,\\mathbf{H}_1,\\ldots ,\\mathbf{H}_{k - 1}" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": " represent halftones formed by printing dots " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "q_{0},q_{1},\\ldots ,q_{k - 1}" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": ", respectively. For a dot " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "q_{i} = \\{\\pmb {x}_{i},\\pmb {y}_{i}\\}" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": ", we can get its one-hot encoding from " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{y}_i" + }, + { + "bbox": [ + 304, + 593, + 547, + 677 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 357, + 687, + 545, + 706 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 687, + 545, + 706 + ], + "spans": [ + { + "bbox": [ + 357, + 687, + 545, + 706 + ], + "type": "interline_equation", + "content": "\\boldsymbol {o} \\left(\\boldsymbol {x} _ {i}\\right) = \\operatorname {O n e H o t E n c o d i n g} \\left(\\boldsymbol {x} _ {i}\\right), \\tag {3}", + "image_path": "d26c5e83ad817e871e8d1a12c16488714e679e5d2d8938eb46e3d9bf0594b87e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 704, + 494, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 704, + 494, + 715 + ], + "spans": [ + { + "bbox": [ + 359, + 704, + 494, + 715 + ], + "type": "interline_equation", + "content": "\\pmb {o} (\\pmb {y} _ {i}) = \\mathrm {O n e H o t E n c o d i n g} (\\pmb {y} _ {i}).", + "image_path": "f5877e0d4f94652e5d84004480fb3470887606b7759f3b6c82b50365a479a460.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "27530" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "Assuming " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\pmb{o}(\\pmb{x}_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\pmb{o}(\\pmb{y}_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " have been obtained, " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_i" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " can be calculated according to " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\pmb{o}(\\pmb{x}_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\pmb{o}(\\pmb{y}_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_i = \\pmb{o}(\\pmb{x}_i)^\\top \\cdot \\pmb{o}(\\pmb{y}_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": "Substituting the calculated " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_i" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": " into Equation 2, the halftone " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": " can be obtained. The only non-differentiable step occurs in Equation 3 (i.e., OneHotEncoding). The non-differentiable problem of converting discrete ink dots to continuous halftone matrices is transformed into the non-differentiable problem of one-hot encodings, resulting in a simplified problem. We learn a model O-Net ('O' stands for \"one-hot encoding\") to perform the mapping from discrete coordinates " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\boldsymbol{y}_i" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": " to one-hot encoding " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\boldsymbol{o}(\\boldsymbol{x}_i)" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\boldsymbol{o}(\\boldsymbol{y}_i)" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": ". Denote O-Net as O for brevity, which consists of fully connected layers in our implementation. ReLU activation function is used between each layer. During the optimization of O-Net, the potential coordinate values " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{x}}" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{y}}" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": " are fed into O, and the gradient is computed utilizing the following loss function " + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{O - Net}}" + }, + { + "bbox": [ + 46, + 109, + 290, + 289 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 300, + 94, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 94, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 94, + 312 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {O - N e t}} =", + "image_path": "de5ed1edbb790ba1478d7bed8a7d3967be49d3d2414c36eaf5d7c69a84d598c1.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 290, + 351 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 290, + 351 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 290, + 351 + ], + "type": "interline_equation", + "content": "\\frac {1}{\\max (L _ {1} , L _ {2}) / s} \\sum_ {l = 0} ^ {\\max (L _ {1}, L _ {2}) - 1} | \\mathbf {O} (\\tilde {\\boldsymbol {x}} _ {l}) - \\mathrm {O n e H o t E n c} (\\tilde {\\boldsymbol {x}} _ {l}) | +", + "image_path": "43ad45ed5b78f271616719d6897535cd6e64aa77ef5d0ed1cf2b50ab409a9186.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 353, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 353, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 287, + 396 + ], + "type": "interline_equation", + "content": "\\frac {1}{\\max \\left(L _ {1} , L _ {2}\\right) / s} \\sum_ {l = 0} ^ {\\max \\left(L _ {1}, L _ {2}\\right) - 1} | \\mathbf {O} (\\tilde {\\boldsymbol {y}} _ {l}) - \\operatorname {O n e H o t E n c} (\\tilde {\\boldsymbol {y}} _ {l}) |, \\tag {4}", + "image_path": "e030e6fd114c0cd24c655fe74696d4ea9482904cc836404d1129e859e85b6a53.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": "where OneHotEncoding " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "(\\tilde{\\boldsymbol{x}}_l)" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": " and OneHotEncoding " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "(\\tilde{\\boldsymbol{y}}_l)" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": " denote the one-hot vector determined by " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{x}}_l" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{y}}_l" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": " represents the sampling step. It is worth noting that the dot coordinates " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\boldsymbol{y}_i" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": " are decimal numbers. Therefore, to ensure that the network O can accurately handle different coordinate values, it is necessary to densely sample the interval " + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "inline_equation", + "content": "[0, \\max(L_1, L_2) - 1]" + }, + { + "bbox": [ + 46, + 396, + 287, + 503 + ], + "type": "text", + "content": ". In our experiments, we use a sampling step of 0.01 for this interval. The architecture of O-Net is illustrated in Figure 4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 505, + 242, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 505, + 242, + 517 + ], + "spans": [ + { + "bbox": [ + 59, + 505, + 242, + 517 + ], + "type": "text", + "content": "The precision " + }, + { + "bbox": [ + 59, + 505, + 242, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\mathbf{O})" + }, + { + "bbox": [ + 59, + 505, + 242, + 517 + ], + "type": "text", + "content": " is calculated as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 287, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {P} (\\mathbf {O}) = \\frac {1}{\\max (L _ {1} , L _ {2}) / s} \\sum_ {l = 0} ^ {\\max (L _ {1}, L _ {2}) - 1} \\mathbb {1} \\left\\{\\arg \\max (\\mathbf {O} (\\tilde {\\boldsymbol {x}} _ {l})) \\right.,", + "image_path": "48857e38d9dad0360fef274f989df67e68f32728d2c2dbad8f1b17cf26ea62bc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 84, + 565, + 235, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 565, + 235, + 578 + ], + "spans": [ + { + "bbox": [ + 84, + 565, + 235, + 578 + ], + "type": "inline_equation", + "content": "\\arg \\max (\\mathrm{OneHotEncoding}(\\tilde{\\boldsymbol{x}}_l))\\} +" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 83, + 581, + 287, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 581, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 83, + 581, + 287, + 614 + ], + "type": "interline_equation", + "content": "\\frac {1}{\\max \\left(L _ {1} , L _ {2}\\right) / s} \\sum_ {l = 0} ^ {\\max \\left(L _ {1}, L _ {2}\\right) - 1} \\mathbb {1} \\left\\{\\arg \\max \\left(\\mathbf {O} \\left(\\tilde {\\boldsymbol {y}} _ {l}\\right)\\right), \\right.", + "image_path": "f00c8d0dd0442d54bbde5154cd3a1ffb35bc4b9d13dd6e283220829f1a499c5d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 84, + 616, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 616, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 84, + 616, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\arg \\max (\\mathrm{OneHotEncoding}(\\tilde{\\mathbf{y}}_l)))\\}" + }, + { + "bbox": [ + 84, + 616, + 287, + 640 + ], + "type": "text", + "content": " (5)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathbb{1}\\{a,b\\}" + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "text", + "content": " is 1 when " + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 640, + 287, + 677 + ], + "type": "text", + "content": " are equal, and 0 otherwise. In the experiments, O-Net is first trained to convergence and its parameters are fixed during halftone generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Discussion. We eschew the use of embedding matrix lookups to establish the mapping between dot coordinates and one-hot encodings due to their non-differentiability." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 547, + 174 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 547, + 174 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 547, + 174 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 547, + 174 + ], + "type": "image", + "image_path": "9d95e883099e2e704951724a1dc8c41abee4199183350e7376b9bf91ed4f8a51.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 182, + 547, + 214 + ], + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 214 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 214 + ], + "type": "text", + "content": "Figure 4. Illustration of O-Net for differentiable transformation from discrete dots to continuous vector-based halftone representations." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 225, + 545, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 225, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 225, + 545, + 250 + ], + "type": "text", + "content": "This characteristic disrupts gradients and impedes the process of backpropagation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 257, + 488, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 488, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 488, + 269 + ], + "type": "text", + "content": "3.2. P-Net: Ink Dot Motion Prediction" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "text", + "content": "A primary contribution of this work is the achievement of dot controllable halftones, with the prediction of the ink dot motion playing a crucial role in this realization. While some deep learning methods have introduced techniques for point motion control and prediction, exemplified in point cloud generation [1, 4, 24, 28, 33, 36], applying these methods directly to halftoning is not feasible for the following reasons: (1) Point clouds typically consist of a small number of points, for instance, the 2,048 points utilized in [24] to generate point clouds of various shapes. In contrast, halftones comprise a substantial number of ink dots, with " + }, + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "inline_equation", + "content": "20,000 \\sim 30,000" + }, + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "text", + "content": " ink dots in a " + }, + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 275, + 545, + 502 + ], + "type": "text", + "content": " resolution image. As the dot count escalates, optimizing the model becomes progressively more challenging. (2) Point cloud generation methods are primarily employed to create point cloud shapes with a coarse level of detail. In contrast, halftones incorporate intricate details and textures, demanding precise and meticulous control over the movement of each ink dot to achieve a fine-grained result." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "content": "To tackle the aforementioned challenges, we propose P-Net, a network that employs image gray levels as guidance to achieve ink dot motion prediction, as shown in Figure 5. Inspired by recent diffusion generative models [9, 29-31], we explore the efficacy of simple and lightweight convolutional blocks for dot motion prediction. P-Net takes the halftone " + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "content": " formed by ink dots (Equation 2) and the continuous tone image " + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "content": " as input. Each element in the matrix " + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "content": " represents the gray level of the image at the corresponding position. The approach employed by P-Net to integrate information from " + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 503, + 545, + 657 + ], + "type": "text", + "content": " is relatively straightforward, involving concatenation of the two matrices along the channel dimension:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 373, + 658, + 545, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 658, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 373, + 658, + 545, + 672 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {\\text {i n}} = \\operatorname {C o n v 2 D} (\\mathbf {H} | | \\mathbf {C}), \\tag {6}", + "image_path": "bd43487f120b848827a29731110c22ac33092ccaabaec5c4080fee9e1ad33f0b.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "where Conv2D means two-dimensional convolution, " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "||" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " means the concatenation operation. While alternative approaches, including post-smooth concatenation and density-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27531" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 275, + 84 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 275, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 275, + 84 + ], + "type": "text", + "content": "Algorithm 1 Algorithm for Dot Controllable Halftoning" + } + ] + } + ], + "index": 0, + "type": "text" + }, + { + "bbox": [ + 50, + 88, + 80, + 99 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 88, + 80, + 99 + ], + "spans": [ + { + "bbox": [ + 50, + 88, + 80, + 99 + ], + "type": "text", + "content": "Input:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 65, + 99, + 261, + 111 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 99, + 261, + 111 + ], + "spans": [ + { + "bbox": [ + 65, + 99, + 261, + 111 + ], + "type": "text", + "content": "The set of random dots, " + }, + { + "bbox": [ + 65, + 99, + 261, + 111 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = \\{\\pmb {q}_0,\\pmb {q}_1,\\dots ,\\pmb {q}_{k - 1}\\}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 65, + 112, + 208, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 112, + 208, + 122 + ], + "spans": [ + { + "bbox": [ + 65, + 112, + 208, + 122 + ], + "type": "text", + "content": "The number of dots in the set " + }, + { + "bbox": [ + 65, + 112, + 208, + 122 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}, k" + }, + { + "bbox": [ + 65, + 112, + 208, + 122 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 65, + 124, + 176, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 124, + 176, + 135 + ], + "spans": [ + { + "bbox": [ + 65, + 124, + 176, + 135 + ], + "type": "text", + "content": "Continuous tone image, C;" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 65, + 136, + 179, + 146 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 136, + 179, + 146 + ], + "spans": [ + { + "bbox": [ + 65, + 136, + 179, + 146 + ], + "type": "text", + "content": "The number of iterations, " + }, + { + "bbox": [ + 65, + 136, + 179, + 146 + ], + "type": "inline_equation", + "content": "\\tau" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 148, + 86, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 148, + 86, + 158 + ], + "spans": [ + { + "bbox": [ + 51, + 148, + 86, + 158 + ], + "type": "text", + "content": "Output:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 159, + 287, + 352 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 65, + 159, + 171, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 159, + 171, + 171 + ], + "spans": [ + { + "bbox": [ + 65, + 159, + 171, + 171 + ], + "type": "text", + "content": "Generated halftone, " + }, + { + "bbox": [ + 65, + 159, + 171, + 171 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathrm{out}}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "spans": [ + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "type": "text", + "content": "1: Transform the dots in the set " + }, + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "type": "text", + "content": " into halftone " + }, + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{(0)}" + }, + { + "bbox": [ + 53, + 171, + 287, + 195 + ], + "type": "text", + "content": " using O-Net; /* Equation 2 */" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "spans": [ + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "type": "text", + "content": "2: for " + }, + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "type": "inline_equation", + "content": "i = 0" + }, + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "type": "inline_equation", + "content": "\\tau - 1" + }, + { + "bbox": [ + 53, + 196, + 152, + 205 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "spans": [ + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "type": "text", + "content": "3: Feed " + }, + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{(i)}" + }, + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 53, + 206, + 287, + 231 + ], + "type": "text", + "content": " into P-Net as input; /* Equation 6*/" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "spans": [ + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "type": "text", + "content": "4: Obtain motion predictions of each dot in " + }, + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{out}}^{(i)} \\gets \\mathbb{P} - \\mathrm{Net}(\\mathbf{H}^{(i)}, \\mathbf{C})" + }, + { + "bbox": [ + 53, + 232, + 286, + 256 + ], + "type": "text", + "content": "; /* Equation 8 */" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "spans": [ + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "type": "text", + "content": "5: Update the position of ink dot " + }, + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{q}_i \\in \\mathcal{Q}" + }, + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "type": "text", + "content": ", and update the set " + }, + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 53, + 257, + 286, + 280 + ], + "type": "text", + "content": "; /* Equation 9*/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "spans": [ + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "type": "text", + "content": "6: Transform the dots in the set " + }, + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "type": "text", + "content": " into halftone " + }, + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{(i + 1)}" + }, + { + "bbox": [ + 53, + 281, + 285, + 304 + ], + "type": "text", + "content": " using O-Net; /* Equation 2 */" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 53, + 305, + 287, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 305, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 53, + 305, + 287, + 328 + ], + "type": "text", + "content": "7: Calculate " + }, + { + "bbox": [ + 53, + 305, + 287, + 328 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{P}}" + }, + { + "bbox": [ + 53, + 305, + 287, + 328 + ], + "type": "text", + "content": " and update the model parameters of P-Net; 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P-Net utilizes a sequence of convolution modules to acquire the fusion representation of matrices " + }, + { + "bbox": [ + 46, + 374, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 374, + 287, + 447 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 374, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 374, + 287, + 447 + ], + "type": "text", + "content": ", followed by several downsampling modules to reduce the image resolution:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 75, + 453, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 453, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 75, + 453, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {P}} = \\operatorname {D o w n S a m p l e} (\\operatorname {S t a c k e d C o n v 2 D} \\left(\\mathbf {P} _ {\\text {i n}}\\right)), \\tag {7}", + "image_path": "081e288841d6cc2421ecf3ea6a87d2286f71cf08b3d154f91f525a5224b085f9.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{P}}" + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "content": " represents the feature matrix of high-level gray scale information, which coarsely expresses the overall movement trend of the ink dots within adjacent image blocks. Next, a prediction head composed of convolutions is used on the upsampled " + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{P}}" + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "content": " matrix to make the output dot motion " + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "content": " consistent with the resolutions of the halftone matrix " + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 79, + 567, + 287, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 567, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 79, + 567, + 287, + 581 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {\\text {o u t}} = \\operatorname {S t a c k e d C o n v 2 D} (\\operatorname {U p S a m p l e} (\\tilde {\\mathbf {P}})). \\tag {8}", + "image_path": "93e9b886ed9e212afe0cb3d40a3b05ebd9adf76605e562590fdd86bb4ff7f235.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "text", + "content": "Each element in " + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "text", + "content": " represents the displacement vector of the ink dot at the corresponding position, and it has two channels representing the motion prediction along " + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "text", + "content": " directions, respectively. For " + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\forall \\pmb {q}_i\\in \\mathcal{Q},\\pmb {q}_i = \\{\\pmb {x}_i,\\pmb {y}_i\\}" + }, + { + "bbox": [ + 46, + 588, + 287, + 647 + ], + "type": "text", + "content": ", its new position can be derived as:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 85, + 655, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 655, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 85, + 655, + 287, + 670 + ], + "type": "interline_equation", + "content": "\\left(\\hat {\\boldsymbol {x}} _ {i}, \\hat {\\boldsymbol {y}} _ {i}\\right) = \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {y} _ {i}\\right) + \\mathbf {P} _ {\\text {o u t}} \\left[ \\left\\lfloor \\boldsymbol {x} _ {i} \\right\\rfloor , \\left\\lfloor \\boldsymbol {y} _ {i} \\right\\rfloor \\right]. \\tag {9}", + "image_path": "1c55752b8ca4071201029ef3dcec06583aa6cc6c0f4a23b0535fb0b6c9c75ae6.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "type": "text", + "content": "The ink dot coordinates " + }, + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{q}}_i = \\{\\hat{x}_i,\\hat{y}_i\\}" + }, + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "type": "text", + "content": " after the motion can be differentiated to form a new halftone matrix " + }, + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{H}}" + }, + { + "bbox": [ + 46, + 676, + 287, + 713 + ], + "type": "text", + "content": " through O-Net, and the iteration is completed." + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 310, + 73, + 545, + 152 + ], + "blocks": [ + { + "bbox": [ + 310, + 73, + 545, + 152 + ], + "lines": [ + { + "bbox": [ + 310, + 73, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 310, + 73, + 545, + 152 + ], + "type": "image", + "image_path": "39cb4c56660063f093c69c8d449f644835a7f4db7d67434b0d033c723188dd9e.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 164, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 305, + 164, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 305, + 164, + 545, + 186 + ], + "type": "text", + "content": "Figure 5. Schematic diagram of the proposed P-Net, which is used to predict the motion of each ink dot." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 194, + 508, + 208 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 194, + 508, + 208 + ], + "spans": [ + { + "bbox": [ + 306, + 194, + 508, + 208 + ], + "type": "text", + "content": "3.3. Training Scheduling and Optimization" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": "To optimize our model, following [27, 35], we use the tone loss " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_T" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": ", which computes the dissimilarity between halftone predictions " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathrm{out}}" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": " and continuous tone images " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 311, + 256, + 545, + 280 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 256, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 311, + 256, + 545, + 280 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {T} = \\mathbb {E} _ {\\mathbf {H}} \\| \\text {G a u S m o o t h} (\\mathbf {H} _ {\\text {o u t}}) - \\text {G a u S m o o t h} (\\mathbf {C}) \\| _ {2}, \\tag {10}", + "image_path": "55aa7d84f8f2138a6c01bfee7496eee6680404212aa8a01cd42da2a880de164c.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _2" + }, + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "type": "text", + "content": " represents the L2 norm. To improve the structural similarity of the generated halftones, the structural loss " + }, + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 305, + 281, + 545, + 317 + ], + "type": "text", + "content": " is employed:" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 340, + 324, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 324, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 340, + 324, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S} = \\mathbb {E} _ {\\mathbf {H}} \\| \\operatorname {S t r u c} \\text {- M e a s u r e} (\\mathbf {H} _ {\\text {o u t}}, \\mathbf {C}) \\| _ {1}. \\tag {11}", + "image_path": "479d9dfbf4206bf01d74828eed65fe14accd0151504fd75dd00d0feb690feee0.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 345, + 545, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 345, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 545, + 381 + ], + "type": "text", + "content": "Additionally, the pixel loss " + }, + { + "bbox": [ + 305, + 345, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_R" + }, + { + "bbox": [ + 305, + 345, + 545, + 381 + ], + "type": "text", + "content": " is adopted to measure the difference between the generated halftone after inverse halftoning transformation and the continuous tone image:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 364, + 389, + 545, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 389, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 364, + 389, + 545, + 403 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R} = \\mathbb {E} _ {\\mathbf {H}} \\| \\mathcal {R} \\left(\\mathbf {H} _ {\\text {o u t}}\\right) - \\mathbf {C} \\| _ {2}, \\tag {12}", + "image_path": "276788330446b109d23a599ddf7e1c70b166416a080aa71e1305c4bdc510d867.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "type": "text", + "content": " represents the frozen inverse halftoning network [35]. The total loss " + }, + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_P" + }, + { + "bbox": [ + 305, + 410, + 545, + 434 + ], + "type": "text", + "content": " is as follows:" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 366, + 441, + 545, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 441, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 366, + 441, + 545, + 454 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {P} = \\mathcal {L} _ {T} + \\gamma_ {S} \\mathcal {L} _ {S} + \\gamma_ {R} \\mathcal {L} _ {R}, \\tag {13}", + "image_path": "a20175593899ef6ea1ffdc3b9dbcbc6157b67e43eb41eaf55df4ac3f715dbc4e.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\gamma_{S}" + }, + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\gamma_{R}" + }, + { + "bbox": [ + 305, + 462, + 545, + 486 + ], + "type": "text", + "content": " are hyperparameters to trade-off each loss term. We detail the training process in Algorithm 1." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 496, + 387, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 496, + 387, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 387, + 510 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 515, + 539, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 539, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 539, + 528 + ], + "type": "text", + "content": "4.1. Datasets, Baselines, and Evaluation Protocols" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 305, + 533, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 533, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 533, + 545, + 713 + ], + "type": "text", + "content": "Datasets and Baselines. Following previous research [13, 35], we curate a halftoning dataset by selecting images from UTKFace [37] and DIV2K [2]. The dataset comprises 4000, 1000, and 400 images in the training, validation, and test sets, respectively. We select baseline models from two categories: traditional halftoning methods [12, 21, 26] and deep learning-based halftoning methods [35]. The traditional methods include amplitude modulation techniques (such as Ordered Dithering), frequency modulation techniques (such as Floyd-Steinberg Error Diffusion, Simpler Floyd-Steinberg Error Diffusion, Jarvis, Judice, and Ninke Dithering, Stucki Dithering, Atkinson Dithering, Burkes Dithering, Sierra Dithering, Two Row Sierra Dithering, and Sierra Lite Dithering), and improvements of Floyd-Steinberg error diffusion algorithm (such as Ostromoukhov's Method)." + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27532" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 170, + 155 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 170, + 155 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 170, + 155 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 170, + 155 + ], + "type": "image", + "image_path": "6c0a68b7369da5cd36fd6ef1804600b8a292ff020e9ef4b9f7fbacb0193d36d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 157, + 160, + 166 + ], + "lines": [ + { + "bbox": [ + 72, + 157, + 160, + 166 + ], + "spans": [ + { + "bbox": [ + 72, + 157, + 160, + 166 + ], + "type": "text", + "content": "(a) training iteration " + }, + { + "bbox": [ + 72, + 157, + 160, + 166 + ], + "type": "inline_equation", + "content": "= 1000" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 72, + 291, + 155 + ], + "blocks": [ + { + "bbox": [ + 175, + 72, + 291, + 155 + ], + "lines": [ + { + "bbox": [ + 175, + 72, + 291, + 155 + ], + "spans": [ + { + "bbox": [ + 175, + 72, + 291, + 155 + ], + "type": "image", + "image_path": "29effad5bb89312958b237c71e72bcdff28d64750b75faa016047a33ab25dc7c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 192, + 157, + 280, + 166 + ], + "lines": [ + { + "bbox": [ + 192, + 157, + 280, + 166 + ], + "spans": [ + { + "bbox": [ + 192, + 157, + 280, + 166 + ], + "type": "text", + "content": "(b) training iteration " + }, + { + "bbox": [ + 192, + 157, + 280, + 166 + ], + "type": "inline_equation", + "content": "= 3000" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "type": "text", + "content": "Figure 6. O-Net robustness test experiment. The figure shows the variation trend of the halftone quality obtained by O-Net with the noise intensity. a, b, c, and d represent 1000, 3000, 6000, and 9000 model iterations " + }, + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "type": "inline_equation", + "content": "(\\times 10^{4})" + }, + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 295, + 72, + 410, + 154 + ], + "blocks": [ + { + "bbox": [ + 295, + 72, + 410, + 154 + ], + "lines": [ + { + "bbox": [ + 295, + 72, + 410, + 154 + ], + "spans": [ + { + "bbox": [ + 295, + 72, + 410, + 154 + ], + "type": "image", + "image_path": "80e942c4c366fd9384bec6463e3e1910f7933283037a06b8d387338946e7f7a3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 157, + 399, + 166 + ], + "lines": [ + { + "bbox": [ + 312, + 157, + 399, + 166 + ], + "spans": [ + { + "bbox": [ + 312, + 157, + 399, + 166 + ], + "type": "text", + "content": "(c) training iteration " + }, + { + "bbox": [ + 312, + 157, + 399, + 166 + ], + "type": "inline_equation", + "content": "= 6000" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 415, + 72, + 530, + 155 + ], + "blocks": [ + { + "bbox": [ + 415, + 72, + 530, + 155 + ], + "lines": [ + { + "bbox": [ + 415, + 72, + 530, + 155 + ], + "spans": [ + { + "bbox": [ + 415, + 72, + 530, + 155 + ], + "type": "image", + "image_path": "2bd068e964e91eb7c905938d2ef23eedd8b19e2edb31b84c5e7823a10b4cb410.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 430, + 157, + 518, + 166 + ], + "lines": [ + { + "bbox": [ + 430, + 157, + 518, + 166 + ], + "spans": [ + { + "bbox": [ + 430, + 157, + 518, + 166 + ], + "type": "text", + "content": "(d) training iteration " + }, + { + "bbox": [ + 430, + 157, + 518, + 166 + ], + "type": "inline_equation", + "content": "= 9000" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 52, + 227, + 282, + 393 + ], + "blocks": [ + { + "bbox": [ + 47, + 201, + 286, + 223 + ], + "lines": [ + { + "bbox": [ + 47, + 201, + 286, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 286, + 223 + ], + "type": "text", + "content": "Table 1. Performance comparison of different halftoning methods on test images in terms of peak signal to noise ratio." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 227, + 282, + 393 + ], + "lines": [ + { + "bbox": [ + 52, + 227, + 282, + 393 + ], + "spans": [ + { + "bbox": [ + 52, + 227, + 282, + 393 + ], + "type": "table", + "html": "
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]29.6936.491.1433.04
Floyd-S. [12]35.3144.401.7239.52
Simpler Floyd-S. [21]32.5241.611.6436.81
Jarvis, J., and N. [21]27.7038.291.8532.67
Stucki [21]28.5739.101.8533.40
Atkinson [21]21.7831.771.8226.36
Burkes [21]31.7441.581.7535.62
Sierra [21]28.2338.511.8733.25
Two Row Sierra [21]30.8241.211.7334.86
Sierra Lite [21]35.9545.581.6540.90
Ostromoukhov [26]36.0445.901.7641.18
Xia's Method [35]29.8935.940.8133.83
Our Proposed Method34.7446.642.1843.04
", + "image_path": "3413eff1b5d0b910578bfdb03bb22f880462836d801564f9d576ce6a61935391.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "content": "Regarding deep learning methods, we select [35] as the baseline, which is a recently proposed deep learning-based halftoning approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "content": "Evaluation Protocols and Implementation Details. Following previous work [35], we use Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) to measure the quality of the generated halftones. Before computing PSNR, we first smooth both the halftone and continuous tone image with an " + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "inline_equation", + "content": "11 \\times 11" + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "content": " Gaussian filter, and then use the smoothed images to calculate the metrics. In addition, we also use qualitative experiments to evaluate the performance of different methods. The quantity of initial dots " + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "content": " is determined through a linear transformation based on the grayscale of the continuous tone. In P-Net, the number of channels is 64, the convolution kernel size is set to " + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "content": ". O-Net consists of 4 fully connected layers, and the activation function between layers is ReLU. " + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\gamma_{S}" + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\gamma_{R}" + }, + { + "bbox": [ + 46, + 437, + 287, + 628 + ], + "type": "text", + "content": " are set to 0.04 and 0.08 respectively. Adam optimizer [19] is used to optimize the model, and the learning rate is set to 0.0001." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 635, + 190, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 190, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 190, + 647 + ], + "type": "text", + "content": "4.2. Performance Comparison" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "We conduct quantitative experiments on images with " + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": " resolutions, and the experimental results are shown in Table 1. It can be observed that our proposed method achieves superior performance than previous methods. Traditional methods (e.g., Ordered Dithering, Floyd-Steinberg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 202, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 545, + 346 + ], + "type": "text", + "content": "Error Diffusion, Ostromoukhov's Method) usually predefine some dithering matrices or diffusion coefficients, which achieve relatively good results. However, these traditional methods apply a hand-crafted halftoning criterion to all images indiscriminately, and thus have limited flexibility compared to data-driven approaches like [35]. Besides, previous methods perform halftone generation on the global image and cannot adaptively control the motion of each ink dot, which makes it difficult to flexibly remove some undesired artifacts in the generated halftones. In contrast, our method can flexibly control the motion of each ink dot on the halftone, thus achieving better experimental results." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 357, + 494, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 494, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 494, + 369 + ], + "type": "text", + "content": "4.3. Study on the Effectiveness of O-Net" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "type": "text", + "content": "A well-performing O-Net should be able to handle various coordinate values produced by model predictions. Although we sample the " + }, + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "type": "inline_equation", + "content": "[0, \\max(L_1, L_2) - 1]" + }, + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "type": "text", + "content": " interval as densely as possible during training, it is still not enough to cover various float coordinate values that may be encountered during model training. In light of this, we design some experiments to verify the robustness of O-Net to numerical noise of float numbers, as shown in Figure 6. The main process of the experiment is that we randomly add noises of different intensities to the correct coordinates of ink dots, and observe the prediction precision of O-Net after adding noises. The magnitude of the noise is constrained between " + }, + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "type": "inline_equation", + "content": "[0, 1]" + }, + { + "bbox": [ + 304, + 377, + 545, + 628 + ], + "type": "text", + "content": ", which is to ensure that the original position of the ink dot will not be changed when the noise is added to the coordinates. The intensity of the noise is defined by its coverage percentage of the coordinate value. As illustrated in Figure 6, during the initial stages of training, noise interference adversely impacts the quality of the halftones generated by the model. However, as training advances towards convergence, the model becomes less sensitive to noise interference, affirming the robustness of O-Net." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "In addition, we visualize the heat maps of O-Net prediction results at different stages of training, as shown in Figure 7. We first randomly initialize 64 ink dot coordinates on a " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " resolution image, then feed these 64 dot coordinates into O-Net, and visualize the model prediction results. As depicted in Figure 7, prior to the convergence of O-Net, the predicted image exhibits numerous non-binarized gray" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27533" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 151, + 173 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 151, + 173 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 151, + 173 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 151, + 173 + ], + "type": "image", + "image_path": "0c6ab0862b593f66381d8106f81554a3e3bdd75c1ec4a42d415faef347b8459a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 175, + 150, + 184 + ], + "lines": [ + { + "bbox": [ + 80, + 175, + 150, + 184 + ], + "spans": [ + { + "bbox": [ + 80, + 175, + 150, + 184 + ], + "type": "text", + "content": "(a) random initialized" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 156, + 72, + 279, + 173 + ], + "blocks": [ + { + "bbox": [ + 156, + 72, + 279, + 173 + ], + "lines": [ + { + "bbox": [ + 156, + 72, + 279, + 173 + ], + "spans": [ + { + "bbox": [ + 156, + 72, + 279, + 173 + ], + "type": "image", + "image_path": "aa74e95b3353ca56192e7d99303c808726c9f06a1e817351955f7ccfe26a31b7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 200, + 175, + 279, + 184 + ], + "lines": [ + { + "bbox": [ + 200, + 175, + 279, + 184 + ], + "spans": [ + { + "bbox": [ + 200, + 175, + 279, + 184 + ], + "type": "text", + "content": "(b) training iteration " + }, + { + "bbox": [ + 200, + 175, + 279, + 184 + ], + "type": "inline_equation", + "content": "= 10" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 284, + 72, + 402, + 172 + ], + "blocks": [ + { + "bbox": [ + 284, + 72, + 402, + 172 + ], + "lines": [ + { + "bbox": [ + 284, + 72, + 402, + 172 + ], + "spans": [ + { + "bbox": [ + 284, + 72, + 402, + 172 + ], + "type": "image", + "image_path": "0f9670b92e8c8f79181a3ee931bcacf559461b0b305f7409b663515e0cee65bf.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 175, + 404, + 185 + ], + "lines": [ + { + "bbox": [ + 317, + 175, + 404, + 185 + ], + "spans": [ + { + "bbox": [ + 317, + 175, + 404, + 185 + ], + "type": "text", + "content": "(c) training iteration=6000" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 406, + 72, + 524, + 172 + ], + "blocks": [ + { + "bbox": [ + 406, + 72, + 524, + 172 + ], + "lines": [ + { + "bbox": [ + 406, + 72, + 524, + 172 + ], + "spans": [ + { + "bbox": [ + 406, + 72, + 524, + 172 + ], + "type": "image", + "image_path": "24b19fe4754260c45de449713cfe095c7ff843f564b1788efdd7ed47597d923b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 175, + 525, + 185 + ], + "lines": [ + { + "bbox": [ + 438, + 175, + 525, + 185 + ], + "spans": [ + { + "bbox": [ + 438, + 175, + 525, + 185 + ], + "type": "text", + "content": "(d) training iteration " + }, + { + "bbox": [ + 438, + 175, + 525, + 185 + ], + "type": "inline_equation", + "content": "= 9000" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 527, + 72, + 542, + 168 + ], + "blocks": [ + { + "bbox": [ + 527, + 72, + 542, + 168 + ], + "lines": [ + { + "bbox": [ + 527, + 72, + 542, + 168 + ], + "spans": [ + { + "bbox": [ + 527, + 72, + 542, + 168 + ], + "type": "image", + "image_path": "b51b5cade0ed58a2221b0c8f61b6225c307ce09ecee050df234454f4e8ea7c92.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 53, + 222, + 134, + 305 + ], + "blocks": [ + { + "bbox": [ + 46, + 194, + 545, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 545, + 217 + ], + "type": "text", + "content": "Figure 7. Visualization of model predictions at different stages of O-Net training. a, b, c, and d represent 0, 10, 6000, and 9000 model iterations " + }, + { + "bbox": [ + 46, + 194, + 545, + 217 + ], + "type": "inline_equation", + "content": "(\\times 10^{4})" + }, + { + "bbox": [ + 46, + 194, + 545, + 217 + ], + "type": "text", + "content": ", respectively. The effectiveness of O-Net increases as the image transitions towards a binary representation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 222, + 134, + 305 + ], + "lines": [ + { + "bbox": [ + 53, + 222, + 134, + 305 + ], + "spans": [ + { + "bbox": [ + 53, + 222, + 134, + 305 + ], + "type": "image", + "image_path": "901009823ea8982d69bee154005d70284a288e823a12e79081e0d12c92c9dead.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 306, + 125, + 314 + ], + "lines": [ + { + "bbox": [ + 62, + 306, + 125, + 314 + ], + "spans": [ + { + "bbox": [ + 62, + 306, + 125, + 314 + ], + "type": "text", + "content": "(a) continuous tone" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 135, + 222, + 217, + 304 + ], + "blocks": [ + { + "bbox": [ + 135, + 222, + 217, + 304 + ], + "lines": [ + { + "bbox": [ + 135, + 222, + 217, + 304 + ], + "spans": [ + { + "bbox": [ + 135, + 222, + 217, + 304 + ], + "type": "image", + "image_path": "ba615fafe11f44aaff548626466567280301643e32f90ff69c9378736cbe2c93.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 161, + 306, + 209, + 314 + ], + "lines": [ + { + "bbox": [ + 161, + 306, + 209, + 314 + ], + "spans": [ + { + "bbox": [ + 161, + 306, + 209, + 314 + ], + "type": "text", + "content": "(b) iteration #1" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 221, + 222, + 317, + 304 + ], + "blocks": [ + { + "bbox": [ + 221, + 222, + 317, + 304 + ], + "lines": [ + { + "bbox": [ + 221, + 222, + 317, + 304 + ], + "spans": [ + { + "bbox": [ + 221, + 222, + 317, + 304 + ], + "type": "image", + "image_path": "e3636afd32fd7572cc9918d3ddadc6b10f68fb6653911dc34282d038c644f5b8.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 262, + 306, + 312, + 314 + ], + "lines": [ + { + "bbox": [ + 262, + 306, + 312, + 314 + ], + "spans": [ + { + "bbox": [ + 262, + 306, + 312, + 314 + ], + "type": "text", + "content": "(c) iteration #2" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 321, + 223, + 418, + 304 + ], + "blocks": [ + { + "bbox": [ + 321, + 223, + 418, + 304 + ], + "lines": [ + { + "bbox": [ + 321, + 223, + 418, + 304 + ], + "spans": [ + { + "bbox": [ + 321, + 223, + 418, + 304 + ], + "type": "image", + "image_path": "86146f3eb8ad72546c80e0c6d8d3b4f54df843b0dad1ba313ce706a1b94ea322.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 364, + 306, + 413, + 314 + ], + "lines": [ + { + "bbox": [ + 364, + 306, + 413, + 314 + ], + "spans": [ + { + "bbox": [ + 364, + 306, + 413, + 314 + ], + "type": "text", + "content": "(d) iteration #3" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 422, + 223, + 521, + 304 + ], + "blocks": [ + { + "bbox": [ + 422, + 223, + 521, + 304 + ], + "lines": [ + { + "bbox": [ + 422, + 223, + 521, + 304 + ], + "spans": [ + { + "bbox": [ + 422, + 223, + 521, + 304 + ], + "type": "image", + "image_path": "f5e29f41d2dfdd799ef56eabefe4c0f28fe39f5ac256a8aa98ce33ed558a7cf1.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 466, + 306, + 514, + 314 + ], + "lines": [ + { + "bbox": [ + 466, + 306, + 514, + 314 + ], + "spans": [ + { + "bbox": [ + 466, + 306, + 514, + 314 + ], + "type": "text", + "content": "(e) iteration #4" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 54, + 344, + 129, + 419 + ], + "blocks": [ + { + "bbox": [ + 46, + 325, + 545, + 336 + ], + "lines": [ + { + "bbox": [ + 46, + 325, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 545, + 336 + ], + "type": "text", + "content": "Figure 8. Visualization of ink dot motion predictions over several iterations. Here we visualize the motions on x-axis, normalized to 0 to 1." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 344, + 129, + 419 + ], + "lines": [ + { + "bbox": [ + 54, + 344, + 129, + 419 + ], + "spans": [ + { + "bbox": [ + 54, + 344, + 129, + 419 + ], + "type": "image", + "image_path": "7cf657eda71856b3bbf7cf171394f4a9373709fb02a099565f288fa62f8f2b91.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 421, + 121, + 430 + ], + "lines": [ + { + "bbox": [ + 61, + 421, + 121, + 430 + ], + "spans": [ + { + "bbox": [ + 61, + 421, + 121, + 430 + ], + "type": "text", + "content": "(a) quantity level 1" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 441, + 287, + 474 + ], + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 474 + ], + "type": "text", + "content": "Figure 9. Illustration of the resulting halftones with different numbers of ink dots. Number of ink dots: (a): 10K; (b): 14K; (c): 18K. More ink dots enrich the texture details of the image." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 130, + 344, + 205, + 419 + ], + "blocks": [ + { + "bbox": [ + 130, + 344, + 205, + 419 + ], + "lines": [ + { + "bbox": [ + 130, + 344, + 205, + 419 + ], + "spans": [ + { + "bbox": [ + 130, + 344, + 205, + 419 + ], + "type": "image", + "image_path": "fbe7e7a46e5f5095d46781a043d12a320879d216955d94801bfd8851abc2869e.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 137, + 421, + 199, + 430 + ], + "lines": [ + { + "bbox": [ + 137, + 421, + 199, + 430 + ], + "spans": [ + { + "bbox": [ + 137, + 421, + 199, + 430 + ], + "type": "text", + "content": "(b) quantity level 2" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 205, + 344, + 281, + 419 + ], + "blocks": [ + { + "bbox": [ + 205, + 344, + 281, + 419 + ], + "lines": [ + { + "bbox": [ + 205, + 344, + 281, + 419 + ], + "spans": [ + { + "bbox": [ + 205, + 344, + 281, + 419 + ], + "type": "image", + "image_path": "92ed0c7984f06810b1a5113b7b7521d633645fe91dc600b207a04fb3b02db18d.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 212, + 422, + 274, + 431 + ], + "lines": [ + { + "bbox": [ + 212, + 422, + 274, + 431 + ], + "spans": [ + { + "bbox": [ + 212, + 422, + 274, + 431 + ], + "type": "text", + "content": "(c) quantity level 3" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 491, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 550 + ], + "type": "text", + "content": "pixels, indicating that the one-hot encoding at this stage is not fully optimized. In contrast, upon O-Net convergence, the generated halftone comprises solely black and white pixels, affirming the capability of O-Net in producing binary halftones." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 47, + 559, + 229, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 229, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 229, + 572 + ], + "type": "text", + "content": "4.4. Comparison of Structural Quality" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 578, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 649 + ], + "type": "text", + "content": "The structural quality of halftones is also an important indicator for evaluating the performance of an algorithm. We compare the structural similarity with methods that generate halftones with higher PSNR, as shown in Table 2. It can be observed that our proposed method achieves better structural similarity than the baseline methods." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 658, + 235, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 235, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 235, + 670 + ], + "type": "text", + "content": "4.5. Visualization of Motion Predictions" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "We depict the dot motion predictions generated by P-Net across multiple iterations, as illustrated in Figure 8. Notably, the model rapidly shifts the ink dots from regions with" + } + ] + } + ], + "index": 32 + }, + { + "type": "table", + "bbox": [ + 307, + 376, + 545, + 466 + ], + "blocks": [ + { + "bbox": [ + 305, + 344, + 545, + 367 + ], + "lines": [ + { + "bbox": [ + 305, + 344, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 305, + 344, + 545, + 367 + ], + "type": "text", + "content": "Table 2. Performance comparison of different halftoning methods on test images in terms of structural similarity." + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 376, + 545, + 466 + ], + "lines": [ + { + "bbox": [ + 307, + 376, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 307, + 376, + 545, + 466 + ], + "type": "table", + "html": "
MethodMin.Max.Std. Dev.Avg.
Ordered Dithering [21]0.02540.30700.04860.1384
Floyd-S. [12]0.02960.43350.06040.1687
Simpler Floyd.-S. [21]0.02950.46100.06290.1664
Sierra Lite [21]0.02840.41100.05960.1660
Ostromoukhov [26]0.02650.41850.05900.1628
Our Proposed Method0.03050.41590.06280.1709
", + "image_path": "1666227016905ebad5fc68cf364a8cf1fb1643b8b05ebdfccaab9aa1916b86b4.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_body" + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 478, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 478, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 545, + 561 + ], + "type": "text", + "content": "elevated grayscale to those with lower grayscale in the initial stage. This observation substantiates that the motion predictions of P-Net are grounded in a keen awareness of image grayscale. With the progression of iterations, the motions converge towards zero across the majority of the image, leading the model to confine ink dot movements to a limited local area." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 574, + 443, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 443, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 443, + 586 + ], + "type": "text", + "content": "4.6. Qualitative Experiments" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Figure 10 presents qualitative experimental results of different halftone methods, which focus on generating halftones on flat textures with subtle variations in image tone (e.g., light and shadow on clouds). Earlier efforts yield halftones with either undesirable white holes or repetitive streaks of ink dots, compromising the overall quality of the output. Additionally, deep learning methods (Figure " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ") introduce visual artifacts and struggle to faithfully reproduce subtle variations in light and shade. In contrast, our method better preserves tonal details in flat regions and achieves su" + } + ] + } + ], + "index": 37 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "27534" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 120, + 140 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 120, + 140 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 120, + 140 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 120, + 140 + ], + "type": "image", + "image_path": "1f9f2f3e70313faf8a44ae248cf9749b82ee19396631c0611a44570019411a83.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 142, + 104, + 151 + ], + "lines": [ + { + "bbox": [ + 64, + 142, + 104, + 151 + ], + "spans": [ + { + "bbox": [ + 64, + 142, + 104, + 151 + ], + "type": "text", + "content": "(a) Contone" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 121, + 70, + 191, + 140 + ], + "blocks": [ + { + "bbox": [ + 121, + 70, + 191, + 140 + ], + "lines": [ + { + "bbox": [ + 121, + 70, + 191, + 140 + ], + "spans": [ + { + "bbox": [ + 121, + 70, + 191, + 140 + ], + "type": "image", + "image_path": "19ce8d847670b691e2ed68075e98c887199b832a771fb6be1658d39e2b44c26b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 128, + 142, + 181, + 151 + ], + "lines": [ + { + "bbox": [ + 128, + 142, + 181, + 151 + ], + "spans": [ + { + "bbox": [ + 128, + 142, + 181, + 151 + ], + "type": "text", + "content": "(b) Simpler F.-S." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 192, + 70, + 260, + 140 + ], + "blocks": [ + { + "bbox": [ + 192, + 70, + 260, + 140 + ], + "lines": [ + { + "bbox": [ + 192, + 70, + 260, + 140 + ], + "spans": [ + { + "bbox": [ + 192, + 70, + 260, + 140 + ], + "type": "image", + "image_path": "5958c5bdc2effc542b658f99fe0e1ac351abf2809bb8d428db042cb5c395394b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 196, + 142, + 257, + 151 + ], + "lines": [ + { + "bbox": [ + 196, + 142, + 257, + 151 + ], + "spans": [ + { + "bbox": [ + 196, + 142, + 257, + 151 + ], + "type": "text", + "content": "(c) J. 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Qualitative experimental results. Baseline methods yields halftones with some imperfections, including holes (e, m), striped dot distribution (b, f, g, h, l), or other regular visual artifacts (c, d, i, j, k). Images are from the DIV2K dataset [2]." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 52, + 273, + 164, + 386 + ], + "lines": [ + { + "bbox": [ + 52, + 273, + 164, + 386 + ], + "spans": [ + { + "bbox": [ + 52, + 273, + 164, + 386 + ], + "type": "image", + "image_path": "8bc396ace471dca3950f7a9898e1afd0fa9a8f05333fa1739a6b617bae0e223a.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 387, + 140, + 396 + ], + "lines": [ + { + "bbox": [ + 77, + 387, + 140, + 396 + ], + "spans": [ + { + "bbox": [ + 77, + 387, + 140, + 396 + ], + "type": "text", + "content": "(a) continuous tone" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 406, + 287, + 450 + ], + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 450 + ], + "type": "text", + "content": "Figure 11. Experimental results of refining areas with artifacts in generated halftones by manipulating local ink dots. PSNR: (c): 37.24; (d): 44.10; (e): 44.43. 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Statistical results of collisions during ink dot movement." + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 476, + 278, + 512 + ], + "lines": [ + { + "bbox": [ + 52, + 476, + 278, + 512 + ], + "spans": [ + { + "bbox": [ + 52, + 476, + 278, + 512 + ], + "type": "table", + "html": "
Iteration (τ)48121620
Reduction Ratio0.03140.02490.02960.03160.0287
", + "image_path": "216232aabd7f738fc907fe2a6d9ca8003284fbd3a18d88f6c66b57baf7c39990.jpg" + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "table_body" + } + ], + "index": 41 + }, + { + "bbox": [ + 46, + 520, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 556 + ], + "type": "text", + "content": "perior visual results. Additional qualitative experimental results, encompassing high-resolution and color images, are presented in the supplementary material." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 563, + 253, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 253, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 253, + 575 + ], + "type": "text", + "content": "4.7. Study on the Collision Rate of Ink Dots" + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "Ink dots may experience collisions during their movement. We compute the reduction ratio in the number of ink dots resulting from these collisions and overlaps, as outlined in Table 3. It can be observed that the reduction in the number of ink dots due to collisions is minimal, constituting approximately " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " of the total ink dot count. This observation suggests that collisions have a negligible impact on both the overall quantity of ink dots and the dithering process in halftones. We will investigate methods to further minimize ink dot collisions and develop strategies for managing colliding ink dots in our future work." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 306, + 274, + 528, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 528, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 528, + 288 + ], + "type": "text", + "content": "4.8. Dot Control Helps Remove Local Artifacts" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 295, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 545, + 415 + ], + "type": "text", + "content": "We explore an advantage of controllable ink dots: the capability to enhance specific areas within generated halftones through precise manipulation of the ink dots. As illustrated in Figure 11, the initially generated halftone may exhibit artifacts in local regions (Figure 11c). To address this, we refine the halftone by readjusting the ink dots in these areas, resulting in a further enhancement of the generated halftone's quality and the elimination of artifacts (Figure 11d, 11e). This process serves as validation for the efficacy of our proposed concept of controllable ink dots." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 305, + 426, + 493, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 493, + 440 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 493, + 440 + ], + "type": "text", + "content": "4.9. Study on Ink Dot Quantity Control" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 447, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 567 + ], + "type": "text", + "content": "We investigate another advantage of dot control: the capacity to regulate the quantity of ink dots. In Figure 9, we present some examples of halftones with a gradual increase in the quantity of ink dots, from level 1 (Figure 9a) to level 3 (Figure 9c). Notably, even with a smaller number of ink dots, the halftones still maintain visually pleasing levels of detail. The experimental results verify that the proposed method can control the number of ink dots and generate visually pleasing halftones, making it more flexibly applicable to halftone prints of different consumable levels." + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 306, + 582, + 378, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 378, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 378, + 594 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "content": "We introduce ink dot-oriented neural halftoning in this work. O-Net propagates dense gradients to sparse halftone dots, and completes the differentiable transformation between dot coordinates and halftone matrices. P-Net achieves direct control of halftone dots through dot motion predictions. Extensive quantitative and qualitative experiments verify the effectiveness of our proposed method." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement: This work is supported by National Key R&D Program of China (2022ZD0160300)." + } + ] + } + ], + "index": 51 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27535" + } + ] + } + ], + "index": 52 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In Proceedings of the International MultiConference of Engineers and Computer Scientists, 2008. 2" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "27537" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_content_list.json b/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5297f360f2b78ffcaf64cdf35d1ae0df864998a8 --- /dev/null +++ b/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_content_list.json @@ -0,0 +1,1679 @@ +[ + { + "type": "text", + "text": "Inlier Confidence Calibration for Point Cloud Registration", + "text_level": 1, + "bbox": [ + 189, + 130, + 782, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yongzhe Yuan $^{1,2}$ Yue Wu $^{1,2*}$ Xiaolong Fan $^{1,3}$ Maoguo Gong $^{1,3}$ Qiguang Miao $^{1,2}$ Wenping Ma $^{4}$", + "bbox": [ + 98, + 178, + 870, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ MoE Key Lab of Collaborative Intelligence Systems, Xidian University", + "bbox": [ + 197, + 198, + 769, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Computer Science and Technology, Xidian University", + "bbox": [ + 227, + 215, + 741, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ School of Electronic Engineering, Xidian University", + "bbox": [ + 274, + 233, + 694, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ School of Artificial Intelligence, Xidian University", + "bbox": [ + 277, + 251, + 689, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yyz@stu.xidian.edu.cn, {ywu, qgmiao}@xidian.edu.cn,", + "bbox": [ + 256, + 271, + 707, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "xiaolongfan@outlook.com, gong@ieee.org, wpma@mail.xidian.edu.cn", + "bbox": [ + 199, + 290, + 759, + 304 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 339, + 313, + 356 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inliers estimation constitutes a pivotal step in partially overlapping point cloud registration. Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration performance. In this paper, we explore to extend a new definition called inlier confidence calibration (ICC) to alleviate the above issues. Firstly, we provide finely initial correspondences for ICC in order to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy. Finally, transformation is further calculated by the weighted SVD algorithm with the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on synthetic and real-world datasets illustrate the effectiveness of the proposed method.", + "bbox": [ + 75, + 371, + 473, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 806, + 209, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid development of 3D data acquisition technology, point cloud data collected by LiDAR [45], Structured Light Sensors [30], and Stereo Cameras [9] has become", + "bbox": [ + 75, + 832, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5c62cc448034e57fa575244f7733f4424694409f48c961bb17e5546ef21be8b2.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 526, + 340, + 870, + 503 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a0dd6e5c6fa1805b735b46ce8e094eb65343ffc54896fe8fa40bc03503bf2d8a.jpg", + "image_caption": [ + "(b)", + "Figure 1. A toy example of proposed geometric constraints for inlier confidence calibration. The indicative center points pair is inlier pair in reality. (a) shows the situation without constraints. (b) demonstrates the situation with reliable geometric constraints. The experimental results are derived from ablation study." + ], + "image_footnote": [], + "bbox": [ + 522, + 522, + 883, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ubiquitous in various 3D computer vision and robotics applications [6, 20], such as autopilot [15], surgical navigation [23], and simultaneous localization and mapping [11]. In such applications, rigid body point cloud registration plays an essential role, which aims to find a rigid transformation to align one point cloud to another.", + "bbox": [ + 496, + 792, + 892, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The recent advances have been dominated by learning-", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5312", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "based methods. Most of these methods focus on solving the point cloud registration task in a supervised manner [16, 21, 27, 33, 38-41]. They require labeled data as the supervision signal to learn effective representations. In addition, obtaining labeled data is cumbersome and time-consuming, which may hinder applications in real world. To overcome this limitation, unsupervised point cloud registration is gradually garnering the interest of researchers [17, 24, 32]. However, in partially overlapping scenarios, learning-based methods must achieve robust inlier estimation, as inlier estimation serves as a fundamental source for identifying overlapping regions and predicting transformation. Existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context. Meanwhile, the current guiding principle is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate present among point clouds pose a considerable challenge in differentiating inliers, thereby elevating the risk of misinterpretation. Thus, a crucial question remains to be addressed in order to make point cloud registration a success: How to alleviate the bias in inlier confidence caused by massive coordinate differences?", + "bbox": [ + 76, + 90, + 472, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We provide answer to this question in Figure 1. Our key insight is that simple coordinates cannot provide strong evidence for scoring inlier confidence. In Figure 1a, the indicative center points pair is very difficult to distinguish because of coordinate differences, which diminish the confidence of this points pair and further classify it as an outlier pair. To alleviate this issue, we construct transformation-invariant geometric constraints for center points pair in Figure 1b. This strategy is based on two intuitive observations: (i) a rigorously defined property of rigid transformation, i.e., it does not change the length of a vector and an angle between two vectors (isometric isomorphism). (ii) the neighborhood patch fromed by inlier and its neighborhood should have consistency. Under strict constraints, the inlier confidence in Figure 1a can be effectively calibrate.", + "bbox": [ + 76, + 473, + 472, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the discussion above, in this paper, we explore to extend a new definition called inlier confidence calibration (ICC) for point cloud registration. Note that our method adheres to the pipeline of \"pseudo correspondences-to-inlier estimation\" [32, 38], which encompasses critical task reference point cloud copy generation and scoring inlier confidence, respectively. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn [25]. This the", + "bbox": [ + 76, + 704, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "orem is founded on the unique properties of the Gaussian distribution and cancels independent row and column normalization iteratively, along with the extra dustbin parameters in Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy. Finally, transformation are further calculated by the weighted SVD algorithm with the estimated correspondences and the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on the synthetic datasets ModelNet40 [35], Augmented ICL-NUIM [7] and real-world dataset 7Scenes [43] demonstrate our model achieves competitive performance.", + "bbox": [ + 496, + 90, + 893, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions are as follows:", + "bbox": [ + 517, + 363, + 834, + 377 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An effective ICC method for point cloud registration by constructing transformation-invariant geometric constraints.", + "- A soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn, which can provide finely initial correspondences for ICC in order to generate the reference point cloud copy corresponding to the source point cloud.", + "- Under the unsupervised setting, the constructed geometric constraints provide self-supervised signal and optimization objective for model training." + ], + "bbox": [ + 500, + 378, + 890, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 558, + 650, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional point cloud registration methods. Most traditional methods require a good initial transformation and converge to the local minima near the initialization point. One of the most profound methods is the Iterative Closest Point (ICP) algorithm [4], which begins with an initial transformation and iteratively alternates between solving two trivial subproblems: finding the closest points as correspondence under current transformation, and computing optimal transformation by SVD [19] based on identified correspondences. Though ICP can complete a high-precision registration, it is susceptible to the initial perturbation. In recent years, variants of ICP have been proposed [5, 14, 28, 31], and they can improve the defects of ICP and enhance the registration accuracy [3]. However, these methods retain a few essential drawbacks. Firstly, they depend strongly on the initialization. Secondly, it is difficult to integrate them into the deep learning pipeline as they lack differentiability. Thirdly, explicit estimation of corresponding points leads to quadratic complexity scaling with the number of points [29], which can introduce significant computational challenges.", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5313", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning-based registration methods. At present, most learning-based methods are based on supervision [12, 27, 33, 40]. PointnetLK [1] is a classical correspondence-free method, which calculates global feature descriptors through PointNet and iteratively uses the Inverse Compositional formulation and Lucas & Kanade algorithm [22, 37] to minimize distance between the descriptors to achieve registration. RPM-Net [38] utilizes the differentiable Sinkhorn layer and annealing to get soft assignments of point correspondences from hybrid features learned from both spatial coordinates and local geometry.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, unsupervised point cloud registration has gained increasing attention due to its applicability in scenarios where labeled training data is scarce or unavailable. Some methods have been proposed to address this challenge and achieved promising results [2, 8, 10, 17, 18]. Feature-metric point cloud registration framework (FMR) [16] enforces the optimisation of registration by minimising a feature-metric projection error with a autoencoder-based network. CEMNet [17] treats the point cloud registration as a reinforcement learning task. However, the current methods lack a concept of calibrating inlier confidence, which poses a potential challenge for partially overlapping point cloud registration. In comparison, our method provides a reliable ICC by constructing strict constraints.", + "bbox": [ + 75, + 257, + 472, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 479, + 169, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given two point clouds: source point cloud $\\mathcal{P} = \\{\\mathbf{p}_i\\in$ $\\mathbb{R}^3\\mid i = 1,\\dots ,N\\}$ and reference point cloud $\\mathcal{Q} = \\{\\mathbf{q}_j\\in$ $\\mathbb{R}^3\\mid j = 1,\\dots ,M\\}$ , where each point is represented as a vector of $(x,y,z)$ coordinates. Our goal is to estimate a rigid transformation $\\{\\mathbf{R},\\mathbf{t}\\}$ which accurately aligns $\\mathcal{P}$ and $\\mathcal{Q}$ , with a 3D rotation $\\mathbf{R}\\in SO(3)$ and a 3D translation $\\mathbf{t}\\in \\mathbb{R}^3$ .", + "bbox": [ + 75, + 506, + 468, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, our method adheres to the pipeline of \"pseudo correspondences-to-inlier estimation\" [32, 38], which encompasses two critical tasks: reference point cloud copy generation and scoring inlier confidence. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud (Section 3.1). In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy (Section 3.2). The pipeline is illustrated in Figure 2.", + "bbox": [ + 75, + 613, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Finely Initial Correspondences", + "text_level": 1, + "bbox": [ + 498, + 90, + 772, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To generate high quality reference point cloud copy corresponding to the source point cloud, constructing the matching map between $\\mathcal{P}$ and $\\mathcal{Q}$ to refine the initial correspondences is an essential prerequisite. Different from previous work [32, 38], the model input is expanded into four point clouds through a 1-NN strategy, a methodology whose advantages have been substantiated in [42].", + "bbox": [ + 496, + 113, + 890, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let 1-NN point cloud $\\widehat{\\mathcal{P}}$ and $\\widehat{\\mathcal{Q}}$ as the closest point for each point in $\\mathcal{P}$ and $\\mathcal{Q}$ , respectively. Next, we construct a local patch $\\mathcal{N}_{\\circ}$ with $K$ -nearest neighborhood for each point and extract local features with Dynamic Graph CNN [34] for input point cloud and 1-NN point cloud. Associated learned features are denoted as $\\mathcal{F}_{\\mathcal{P}}, \\mathcal{F}_{\\widehat{\\mathcal{P}}}, \\mathcal{F}_{\\mathcal{Q}}$ and $\\mathcal{F}_{\\widehat{\\mathcal{Q}}}$ , respectively. Then, we aim to learn a soft assignment matrix $\\mathbf{M}(\\widehat{\\mathbf{M}})$ to explicitly indicate the matching between any two points of $\\mathcal{P}(\\widehat{\\mathcal{P}})$ and $\\mathcal{Q}(\\widehat{\\mathcal{Q}})$ . Ideally, there is only a single prominent element dominating each row and column. To further enhance $\\mathbf{M}(\\widehat{\\mathbf{M}})$ , the widely adopted method is Sinkhorn [25], which performs the softmax operation on column-wise and row-wise iteratively and alternatively. However, the efficiency of Sinkhorn is limited by iterative strategy and extra dustbin parameters. To tackle this issue, we develop a soft assignment matrix optimization theorem to improve $\\mathbf{M}(\\widehat{\\mathbf{M}})$ based on the following unique properties of the Gaussian distribution, which is a promotion for [44].", + "bbox": [ + 496, + 219, + 892, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1. (Three-sigma rule). The variation or dispersion of data can be measured by the three-sigma rule, which is based on the properties of the normal distribution curve, indicating that within a dataset $99.7\\%$ of data values fall within the range of three standard deviation from the mean.", + "bbox": [ + 496, + 518, + 893, + 597 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recalling definitions of three-sigma rule, we have the following Theorem for $\\mathbf{M} \\in \\mathbb{R}^{N \\times M}$ (maybe a non-square matrix), and $\\widehat{\\mathbf{M}}$ follows the same principles.", + "bbox": [ + 496, + 608, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1. Suppose the $\\mathbf{M}_{i,j}$ obeys a series of Gaussian distributions, $\\exists$ two constants $\\epsilon, \\xi$ , such that there is only a single prominent element dominating each row by three-sigma rule.", + "bbox": [ + 496, + 664, + 890, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proof. Given $\\mu_{i}$ and $\\sigma_{i}$ are the mean and standard deviation of the $i$ -th row of $\\mathbf{M}$ . $\\mathbf{M}_{i,j}$ is normalized in row-wise and the normalized elements follow a standard normal distribution, i.e.:", + "bbox": [ + 496, + 733, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {i, j} = \\frac {\\mathbf {M} _ {i , j} - \\mu_ {i}}{\\sigma_ {i}} \\sim \\mathcal {N} (0, 1), j = 1, \\dots , M. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 801, + 890, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on above setting, we set tuning constants $\\epsilon$ and $\\xi$ to $h_{i,j}$ and obtain", + "bbox": [ + 496, + 842, + 890, + 873 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {h} _ {i, j} = \\epsilon \\cdot h _ {i, j} + \\xi \\sim \\mathcal {N} (\\xi , \\epsilon^ {2} \\mathbb {I}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 882, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5314", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/973d0dd2328b0e4f860dfbf00a64b2858c9e0fe06886759ca619475a9d991843.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 97, + 890, + 234 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c8f72432aca7dcc797ff63a72bccfcdce52dee70ab6fc357223f1443aef2dd3e.jpg", + "image_caption": [ + "Figure 2. The pipeline of the proposed method. We first extract local features of input point cloud and 1-NN point cloud with DGCNN. Then, we construct matching map to generate high quality reference point cloud copy $\\mathcal{Q}$ for fining initial correspondences. Based on the observation that the neighborhood graph formed by inlier and its neighborhood should have geometric structure consistency between $\\mathcal{P}$ and $\\tilde{\\mathcal{Q}}$ , we construct transformation-invariant geometric structure constraints (edge and included angle) and captures their consistency to score and calibrate the inlier confidence for each estimated correspondences between $\\mathcal{P}$ and $\\tilde{\\mathcal{Q}}$ . Finally, the transformation is estimated with SVD method via the calibrated inlier confidence." + ], + "image_footnote": [], + "bbox": [ + 89, + 236, + 883, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For $i$ -th row of $\\mathbf{H} \\in \\mathbb{R}^{N \\times M}(\\widetilde{h}_{i,j} \\subset \\mathbf{H})$ , the number of elements whose values are not less than a threshold $\\Delta$ is calculated:", + "bbox": [ + 75, + 473, + 470, + 518 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nb _ {i} = \\left| \\left\\{\\widetilde {h} _ {i, j} \\mid \\widetilde {h} _ {i, j} \\geq \\Delta , j = 1, 2, \\dots , M \\right\\} \\right|. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 529, + 468, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to prompt $b_{i}$ closer to 1, which means that in each row there is only a single element dominates the row. In addition, the $N$ rows of $\\mathbf{H}$ can be regarded as $N$ independent and identically distributed events, thus the set $\\{b_{1}, b_{2}, \\ldots, b_{N}\\}$ also follows a Gaussian distribution with the expectation $\\mu_{b}$ and variance $\\sigma_{b}$ depending on the tuning constants $\\epsilon, \\xi$ . Hence, by the Definition 1, we can select suitable values of $\\epsilon, \\xi$ to control the bound $[\\mu_{b} - 3\\sigma_{b}, \\mu_{b} + 3\\sigma_{b}]$ , which is centered around 1, such that the expectation of only a single element dominates the row can be implemented.", + "bbox": [ + 75, + 560, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 tells us that column-wise and row-wise iteratively and alternatively may be not essential. Operating solely on the rows can achieve the objective with higher efficiency and accuracy (Please refer to Section 4.4).", + "bbox": [ + 75, + 729, + 468, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the scores in soft assignment matrix $\\mathbf{H}$ and $\\widehat{\\mathbf{H}}$ , we construct dual neighborhood matching map by fusing and averaging matching scores of each $\\mathcal{N}_{\\circ}$ :", + "bbox": [ + 75, + 789, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} _ {i, j} = \\frac {1}{K} \\sum_ {\\mathbf {p} _ {i ^ {\\prime}} \\in \\mathcal {N} _ {\\mathbf {p} _ {i}}} \\sum_ {\\mathbf {q} _ {j ^ {\\prime}} \\in \\mathcal {N} _ {\\mathbf {q} _ {j}}} \\mathbf {H} _ {i ^ {\\prime}, j ^ {\\prime}} + \\frac {1}{K} \\sum_ {\\widehat {\\mathbf {p}} _ {i ^ {\\prime}} \\in \\mathcal {N} _ {\\widehat {\\mathbf {p}} _ {i}}} \\sum_ {\\widehat {\\mathbf {q}} _ {j ^ {\\prime}} \\in \\mathcal {N} _ {\\widehat {\\mathbf {q}} _ {j}}} \\widehat {\\mathbf {H}} _ {i ^ {\\prime}, j ^ {\\prime}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 845, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we formulate the final matching map as:", + "bbox": [ + 500, + 474, + 821, + 491 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {i, j} = \\operatorname {s o f t m a x} \\left(- \\mathbf {D} _ {i, 1} ^ {\\prime}, - \\mathbf {D} _ {i, 2} ^ {\\prime}, \\dots , - \\mathbf {D} _ {i, M} ^ {\\prime}\\right) _ {j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 494, + 888, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D} _ {i, j} ^ {\\prime} = \\exp (\\alpha - \\mathbf {G} _ {i, j}) * \\left(\\mathbf {D} _ {i, j} + \\widehat {\\mathbf {D}} _ {i, j}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 516, + 810, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{D}_{i,j} = \\| \\mathcal{F}_{\\mathbf{p}_i} - \\mathcal{F}_{\\mathbf{q}_j}\\| _2$ and $\\widehat{\\mathbf{D}}_{i,j} = \\| \\mathcal{F}_{\\widehat{\\mathbf{p}}_i} - \\mathcal{F}_{\\widehat{\\mathbf{q}}_j}\\| _2$ denote the Euclidean distance between learned local features, $\\mathbf{D}_{i,j}^{\\prime}$ is negatively related to the matching score $\\mathbf{G}_{i,j}$ . We utilize the exponential strategy to control the changing ratio, along with a hyper-parameter $\\alpha$ to control the influence of the dual neighborhood matching [32].", + "bbox": [ + 496, + 551, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the high quality matching map $\\mathbf{F} \\in \\mathbb{R}^{N \\times M}$ , we generate the reference point cloud copy $\\widetilde{\\mathcal{Q}} \\in \\mathbb{R}^{N \\times 3}$ including finely initial correspondences for each point $\\mathbf{p}_i$ in source point cloud $\\mathcal{P}$ :", + "bbox": [ + 496, + 643, + 890, + 704 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} ^ {\\prime} = \\left\\{\\left(\\mathbf {p} _ {i}, \\widetilde {\\mathbf {q}} _ {i}\\right) \\mid i = 1, \\dots , N, \\widetilde {\\mathbf {q}} _ {i} \\in \\widetilde {\\mathcal {Q}} \\right\\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 710, + 890, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 742, + 544, + 753 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {q}} _ {i} = \\sum_ {j = 1} ^ {M} \\mathbf {F} _ {i, j} \\cdot \\mathbf {q} _ {j}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 752, + 890, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Inlier Confidence Calibration", + "text_level": 1, + "bbox": [ + 500, + 801, + 763, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After generating reference copy $\\widetilde{\\mathcal{Q}}$ , we score inlier confidence for each point pair in $\\mathcal{C}'$ . However, existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context, and the current guiding principle", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5315", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate pose a challenge in differentiating inliers, thereby elevating the risk of misinterpretation.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we explore to extend a new definition called ICC to alleviate the above issues. Benefiting from the high quality matching map $\\mathbf{F}$ in Section 3.1, we argue that the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy, i.e., if $\\mathbf{p}_i$ is an inlier, its neighborhood points also tend to be the inliers and $\\widetilde{\\mathbf{q}}_i$ have geometric structure neighborhood consistency in the reference copy. Conversely, if $\\mathbf{p}_i$ is an outlier, its neighborhood may also be the outliers and spatial structure is prone to be significantly different from the reference copy neighborhood. Based on this observation, we construct transformation-invariant geometric constraints and formulate geometric structure consistency between $\\mathcal{N}_{\\mathbf{p}_i}$ and $\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}$ to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy.", + "bbox": [ + 75, + 167, + 470, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first construct a learnable neighborhood graph by transformation-invariant geometric structure constraints of $\\mathcal{N}_{\\mathbf{p}_i}$ and $\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}$ , which consists of edge representation and angle representation:", + "bbox": [ + 76, + 407, + 470, + 468 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {i, k} ^ {\\mathbf {p}} = \\mathbf {p} _ {i} - \\mathbf {p} _ {k}, \\mathbf {a} _ {r, s} ^ {\\mathbf {p}} = \\angle (\\mathbf {e} _ {i, r} ^ {\\mathbf {p}}, \\mathbf {e} _ {i, s} ^ {\\mathbf {p}}),\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 473, + 393, + 494 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {i, k} ^ {\\widetilde {\\mathbf {q}}} = \\widetilde {\\mathbf {q}} _ {i} - \\widetilde {\\mathbf {q}} _ {k}, \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}} = \\angle \\left(\\mathbf {e} _ {i, r} ^ {\\widetilde {\\mathbf {q}}}, \\mathbf {e} _ {i, s} ^ {\\widetilde {\\mathbf {q}}}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 496, + 468, + 521 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ni \\neq k, k = 1, \\dots , K r, s \\in \\{1, \\dots , K \\}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 523, + 411, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{p}_k$ and $\\widetilde{\\mathbf{q}}_k$ are the points in $\\mathcal{N}_{\\mathbf{p}_i}$ and $\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}$ . Moreover, these representations express sensitive and discriminative geometric structure in the point cloud, and provide adequate geometric cues for subsequent pipeline.", + "bbox": [ + 75, + 547, + 468, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to better capture the neighborhood relevance and promote contextual message propagation, we utilize Multi-layer Perceptron (MLP) $f_{\\theta}$ with parameters $\\theta$ to fuse representations and characterize the consistency between the neighborhoods by the subtraction of the fused geometric representations:", + "bbox": [ + 75, + 607, + 468, + 698 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {i, k} = f _ {\\theta} \\left(\\operatorname {c o n c a t} \\left(\\mathbf {e} _ {i, k} ^ {\\mathbf {p}}, \\mathbf {a} _ {r, s} ^ {\\mathbf {p}}\\right)\\right) - f _ {\\theta} \\left(\\operatorname {c o n c a t} \\left(\\mathbf {e} _ {i, k} ^ {\\widetilde {\\mathbf {q}}}, \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}}\\right)\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 703, + 470, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, the model further adaptively learns the attention coefficients $\\delta_{i,k}$ of each geometric structure consistency:", + "bbox": [ + 76, + 742, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {i, k} = \\operatorname {s o f t m a x} \\left(f _ {\\mu} \\left(\\mathbf {d} _ {i, 1}\\right), f _ {\\mu} \\left(\\mathbf {d} _ {i, 2}\\right), \\dots , f _ {\\mu} \\left(\\mathbf {d} _ {i, K}\\right)\\right) _ {k}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 779, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{\\mu}$ is another MLP with parameters $\\mu$ . Then, inlier confidence $\\mathbf{w}_i$ of correspondence $(\\mathbf{p}_i, \\widetilde{\\mathbf{q}}_i)$ is calculated by aggregating the geometric structure consistency weighted:", + "bbox": [ + 76, + 810, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} _ {i} = 1 - \\operatorname {T a n h} \\left(\\left| l \\left(\\sum_ {k = 1} ^ {K} \\delta_ {i, k} * \\mathbf {d} _ {i, k}\\right) \\right|\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 861, + 468, + 905 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $l$ is a linear function. Through strict geometric constraints, the scored inlier confidence can be effectively calibrated, ensuring the sustained high credibility of $\\mathbf{w}_i$ . However, some potential repetitive structures, textureless structures and other uncertain factors may still exist. In order to enhance the robustness of the proposed method and reduce the bias caused by the above issues, we select inlier correspondences from $\\mathcal{C}'$ with the largest $N_c$ inlier confidence:", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {h} = \\left\\{\\left(\\mathbf {p} _ {h}, \\widetilde {\\mathbf {q}} _ {h}\\right) \\mid h \\in \\operatorname {T o p k} \\left(\\mathbf {w} _ {i}\\right), i = 1, \\dots , N _ {c} \\right\\}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 218, + 890, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, transformation $\\{\\mathbf{R}_{est},\\mathbf{t}_{est}\\}$ can be solved in closed form using weighted SVD, which has been shown to be differentiable in [26]:", + "bbox": [ + 496, + 239, + 890, + 286 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} _ {e s t}, \\mathbf {t} _ {e s t} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\sum_ {\\left(\\mathbf {p} _ {i}, \\widetilde {\\mathbf {q}} _ {i}\\right) \\in \\mathcal {C} _ {h}} \\mathbf {w} _ {i} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {i} + \\mathbf {t} - \\widetilde {\\mathbf {q}} _ {i} \\| _ {2} ^ {2}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 291, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides, ICC provides useful byproduct for unsupervised learning, which can be reliable self-supervised signal. More details can be seen in the following section.", + "bbox": [ + 496, + 330, + 890, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Optimization", + "text_level": 1, + "bbox": [ + 500, + 383, + 638, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we conduct four loss functions for model optimization. Moreover, the proposed model is trained in an unsupervised manner instead of using the ground-truth transformations.", + "bbox": [ + 496, + 406, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Global Consistency Loss. We investigate the global consistency loss between the final transformed source point cloud $\\mathcal{P}'$ and the reference point cloud $\\mathcal{Q}$ . Specifically, the Huber function is utilized to assemble the global consistency loss, which is defined as follow:", + "bbox": [ + 496, + 467, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {g c} = \\sum_ {\\mathbf {p} ^ {\\prime} \\in \\mathcal {P} ^ {\\prime}} H _ {\\beta} \\left(\\min _ {\\mathbf {q} \\in \\mathcal {Q}} \\| \\mathbf {p} ^ {\\prime} - \\mathbf {q} \\| _ {2} ^ {2}\\right) \\tag {14} \\\\ + \\sum_ {\\mathbf {q} \\in \\mathcal {Q}} H _ {\\beta} \\left(\\min _ {\\mathbf {p} ^ {\\prime} \\in \\mathcal {P} ^ {\\prime}} \\| \\mathbf {q} - \\mathbf {p} ^ {\\prime} \\| _ {2} ^ {2}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 547, + 890, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, relying solely on global consistency loss is detrimental to the accuracy and reliability of our model. Since the model may still potentially converge to sub-optimization due to the existing outliers, leading massive potential information of point cloud is wasted. Hence, it is critical to mine the potential self-supervised signals in the point cloud and construct loss functions based on other existing elements.", + "bbox": [ + 496, + 633, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dual Neighborhood Consistency Loss. Based on reliable inlier correspondences in Equation 12, we denote the inliers set of the source and its reference point cloud copy as $\\mathbf{X} \\in \\mathbb{R}^{N_c \\times 3}$ and $\\mathbf{Y} \\in \\mathbb{R}^{N_c \\times 3}$ , respectively. We utilize the neighborhood between the inliers to construct consistency objective, which aims to minimize the registration error between each neighborhood $\\mathcal{N}_{\\mathbf{x}_i}$ and $\\mathcal{N}_{\\mathbf{y}_i}$ :", + "bbox": [ + 496, + 738, + 890, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i n} = \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {R} _ {e s t} \\mathbf {p} _ {j} + \\mathbf {t} _ {e s t} - \\widetilde {\\mathbf {q}} _ {j} \\right\\| _ {2}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 851, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5316", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_{\\mathbf{x}_i}$ is transformed by $\\mathcal{N}_{\\mathbf{y}_i}$ .", + "bbox": [ + 76, + 90, + 303, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Geometric Structure Consistency Loss. The geometric signal buried in point cloud is readily ignored, which hinders ICC. To address this issue, we design a geometric neighborhood loss with the reliable geometric self-supervised signal proposed in Section 3.2:", + "bbox": [ + 75, + 107, + 467, + 181 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {g s} = \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {e} _ {i, j} ^ {\\mathbf {p}} - \\mathbf {e} _ {i, j} ^ {\\widetilde {\\mathbf {q}}} \\right\\| _ {2} + \\\\ \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {a} _ {r, s} ^ {\\mathbf {p}} - \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}} \\right\\| _ {2}, \\tag {16} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 189, + 467, + 267 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{a}_{r,s}^{\\mathbf{p}}$ and $\\mathbf{a}_{r,s}^{\\widetilde{\\mathbf{q}}}$ is calculated by $\\mathbf{e}_{i,j}^{\\mathbf{p}}$ and $\\mathbf{e}_{i,j}^{\\widetilde{\\mathbf{q}}}$ shown in Equation 8.", + "bbox": [ + 76, + 277, + 467, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Spatial Consistency Loss. We further explore to eliminate the spatial difference between the estimated correspondence and the real correspondence for each selected inlier $\\mathbf{x}_i$ and utilize spatial consistency loss with cross-entropy to sharpen matching map $\\mathbf{G}$ :", + "bbox": [ + 76, + 311, + 467, + 386 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s c} = - \\frac {1}{| \\mathbf {X} |} \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}} \\sum_ {j = 1} ^ {M} [ [ j = \\arg \\max _ {j ^ {\\prime}} \\mathbf {G} _ {i, j ^ {\\prime}} ] ] \\log \\mathbf {G} _ {i, j}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 395, + 467, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\llbracket \\cdot \\rrbracket$ is the Iverson bracket. Spatial consistency loss encourages to improve the matching probability and thus the estimated correspondence point in reference copy tends to have an stable position.", + "bbox": [ + 76, + 446, + 467, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall Loss. Since our work utilizes an iterative scheme, we compute the loss at each iteration $N_{l}$ and have the weighted sum loss:", + "bbox": [ + 76, + 507, + 467, + 551 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {l = 1} ^ {N _ {l}} \\left(\\mathcal {L} _ {g c} ^ {l} + \\gamma \\mathcal {L} _ {i n} ^ {l} + \\rho \\mathcal {L} _ {g s} ^ {l} + \\lambda \\mathcal {L} _ {s c} ^ {l}\\right), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 561, + 467, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\gamma$ , $\\rho$ and $\\lambda$ are trade-off parameters to control corresponding loss function.", + "bbox": [ + 76, + 611, + 467, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 654, + 207, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 679, + 264, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method to traditional methods and recent state of the arts learning-based methods. The traditional methods include ICP [4], FGR [16] and FPFH + RANSAC [13]. The recent learning based methods include IDAM [21], FMR [16], RPMNet [38], CEMNet [17], REGTR [39], GeoTransformer [27] and RIE [32]. For consistency with previous work, we measure Mean Isotropic Error (MIE) and Mean Absolute Error (MAE).", + "bbox": [ + 76, + 702, + 467, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. ModelNet40 Dataset and Evaluation", + "text_level": 1, + "bbox": [ + 76, + 830, + 390, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Noted that, to simulate partial-to-partial registration, the reference point cloud $\\mathcal{Q}$ and the source point cloud $\\mathcal{P}$ are cropped respectively, and retain $70\\%$ of the points.", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2066246c6ba72d48b59d862c491538e166157c077841839ad9d4f1711e19176d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
ICP [4] (○)3.43390.01146.77060.0227
FGR [16] (○)0.59720.00211.15630.0041
FPFH+RANSAC [13] (○)0.70310.00251.27720.0050
IDAM [21] (▲)0.42430.00200.81700.0040
RPMNet [38] (▲)0.00510.00000.02010.0000
FMR [16] (▲)3.64970.01017.28100.0200
REGTR [39] (▲)0.18940.00150.34930.0030
GeoTransformer [27] (▲)0.59700.00570.90100.0102
CEMNet [17] (△)0.13850.00010.24890.0002
RIE [32] (△)0.00330.00000.02100.0000
Ours (△)0.00120.00000.01920.0000
", + "bbox": [ + 501, + 90, + 895, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. $(\\bigcirc)$ , $(\\triangle)$ and $(\\triangle)$ denote the traditional, supervised and unsupervised methods, respectively.", + "bbox": [ + 498, + 282, + 890, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unseen Objects. Our models are trained and tested on datasets comprising of samples belonging to the same categories, and both the training and test sets are obtained without any preprocessing or manipulation. We apply a random transformation on the reference point cloud $\\mathcal{Q}$ to generate corresponding source point cloud $\\mathcal{P}$ . Table 1 shows quantitative results of the various algorithms under current experimental settings. The proposed method substantially outperforms all baseline in all metrics. We can observe our method can even outperform the supervised IDAM, RPMNet, FMR, REGTR and GeoTransformer by a large margin. Benefiting from ICC, our method attains highly accurate registration and improves the registration accuracy by an order of magnitude. In order to show the effect of our proposed approach clearly, a qualitative comparison of the registration results can be found in Figure 3. Our method ensures minimal impact on changing of the shape, and achieves the best performance even on asymmetric shape.", + "bbox": [ + 496, + 354, + 890, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unseen Categories. To verify the generalization ability on categories, we train the models on the first 20 categories and test on the remaining unseen categories. The results are summarized in Table 2. We can observe that the majority of baseline consistently exhibit lower performance on the unseen categories, especially learning-based methods. In contrast, traditional algorithms are less susceptible to this issue due to the insensitivity of handcrafted methods to shape variance [36]. Our registration process remains highly precise, achieving the lowest error across all metrics, while also maintaining acceptable levels of fluctuation.", + "bbox": [ + 496, + 627, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Gaussian Noise. In order to assess performance in the presence of noise, which is commonly encountered in real-world point clouds, we train our model on noise-free data and then evaluate all baselines using a test set featuring Gaussian noise. We randomly and independently generate noisy points to introduce noise into in source point cloud and reference point cloud by sampling from $\\mathcal{N}(0,0.5)$ and", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5317", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/968c03ec93627a35b7b0d1c652cc6a1ad892e8cf95a62a97aa3ef3052beddb23.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison of the registration results on unseen objects data (blue: source point cloud, yellow: reference point cloud, green: transformed source point cloud)." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 888, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "clipped to $[-1.0, 1.0]$ . This experiment is significantly challenging, as constructing matching map and ICC become much more difficult. As shown in Table 2, our method outperforms other baselines. The experimental results demonstrate that our method is robust to the noise. In addition, experimental results indirectly confirms the generality and high adaptability of ICC in point cloud registration with partially overlapping.", + "bbox": [ + 75, + 351, + 473, + 474 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/98673382517542eddcaf353d006eedc9e6e91f116a962105cb8514c29206af33.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Unseen Categories
ICP [4] (○)3.60990.01167.05560.0228
FGR [16] (○)0.45790.00160.84420.0032
FPFH+RANSAC [13] (○)0.44270.00210.94470.0043
IDAM [21] (▲)0.48090.00280.91570.0055
RPMNet [38] (▲)0.00640.00010.02070.0001
FMR [16] (▲)3.85940.01147.64500.0225
CEMNet[17] (△)0.08040.00020.14050.0003
RIE [32] (△)0.00590.00000.02280.0001
Ours (△)0.00220.00000.01890.0000
Gaussian Noise
ICP [4] (○)4.64410.01679.21940.0333
FGR [16] (○)1.06760.00362.00380.0072
FPFH+RANSAC [13] (○)1.43160.00612.53450.0120
IDAM [21] (▲)2.30760.01244.53320.0246
RPMNet [38] (▲)1.58900.01752.98300.0378
FMR [16] (▲)18.03550.053635.79860.1063
CEMNet[17] (△)10.70260.039321.18360.0781
RIE [32] (△)0.04310.00040.07760.0008
Ours (△)0.00880.00010.02450.0002
", + "bbox": [ + 78, + 491, + 475, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. $(\\bigcirc)$ , $(\\triangle)$ and $(\\bigtriangleup)$ denote the traditional, supervised and unsupervised methods, respectively.", + "bbox": [ + 75, + 837, + 470, + 893 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Other Datasets and Evaluation", + "text_level": 1, + "bbox": [ + 498, + 351, + 772, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further conduct comparison evaluation on other datasets: 7Scenes and Augmented ICL-NUIM. We sample the reference point clouds to 2,048 points and randomly sample three Euler angle rotations within $[0^{\\circ}, 45^{\\circ}]$ and translations within $[-0.5, 0.5]$ on each axis as the rigid transformation to obtain source point clouds, then down-sample the point clouds to 1,536 points to generate the partial data. As demonstrated in Table 4, our method exhibits extremely higher registration precision on all criteria on Augmneted ICL-NUIM and 7Scenes, especially the rotation error. We can summarize our method has best performance and is comfortable with real-world dataset.", + "bbox": [ + 496, + 376, + 890, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study and Analysis", + "text_level": 1, + "bbox": [ + 498, + 571, + 756, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Soft Assignment Matrix Optimization Theorem. We compare the developed theorem with the Sinkhorn, and evaluate precision and efficiency against Sinkhorn, which iterate 1 (Sinkhorn-1) and 5 (Sinkhorn-5) times. As shown in Figure 4, we can observe that under the same tolerant error, the developed theorem demonstrates superior performance, especially the optimization for rotation. Additionally, the proposed theorem improves the efficiency up to nearly $2 \\times$ compared to Sinkhorn-1 and nearly up to $5 \\times$ compared to Sinkhorn-5. It needs to be emphasized once again that the proposed theorem has a smaller computational complexity than Sinkhorn as shown in Table 5, since this theorem does not normalize the rows and columns repeatedly, and only operates on the rows.", + "bbox": [ + 496, + 595, + 890, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Geometric Constraints. To investigate whether geometric constraints are meaningful to ICC, we conduct an experiment to verify our motivation. Experimental results are shown in the first row of Table 3. Compared to constraints-free, which score inlier confidence by simple coordinates, geometric constraints effectively generate more convincing", + "bbox": [ + 496, + 810, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5318", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/87bc78e8479d0f2d079c9bb571f87df84c45ec87e6aeeea8efe3108204426488.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
GeometricConstraints\\( \\mathcal{L}_{gc} \\)\\( \\mathcal{L}_{in} \\)\\( \\mathcal{L}_{gs} \\)\\( \\mathcal{L}_{sc} \\)ModelNet407Scenes
MAE(R)MAE(t)MIE(R)MIE(R)MAE(R)MAE(t)MIE(R)MIE(R)
✓✓N/A✓1.01230.01611.83980.03502.22380.01484.36980.0286
✓✓✓✓0.39980.00610.76650.01290.00420.00000.02170.0001
✓✓✓✓22.51990.134042.44280.27103.30870.03405.87700.0657
✓✓✓✓0.00700.00010.02350.00020.00370.00000.01860.0001
✓✓✓✓0.11250.00140.018620.00300.01420.00010.03450.0003
✓✓✓✓✓0.00120.00000.01920.00000.00330.00000.01810.0001
", + "bbox": [ + 102, + 88, + 870, + 227 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a2a9aa35e46aefe9ad9b69698b3abed124ca2492a042264d7945014bb399668b.jpg", + "table_caption": [ + "Table 3. Ablation study of different components. ${\\mathcal{L}}_{gc},{\\mathcal{L}}_{in},{\\mathcal{L}}_{gs}$ and ${\\mathcal{L}}_{sc}$ : Each Loss Function in Equation 18." + ], + "table_footnote": [], + "table_body": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Augmented ICL-NUIM
ICP [4] (○)2.40220.06994.48320.1410
FGR [16] (○)2.24770.08084.18500.1573
FPFH+RANSAC [13] (○)1.23490.04292.31670.0839
IDAM [21] (▲)4.41530.13858.61780.2756
RPMNet [38] (▲)0.32670.01250.62770.0246
FMR [16] (▲)1.10850.03982.13230.0786
CEMNet[17] (△)0.23740.00050.39870.0010
RIE [32] (△)0.04920.00230.08970.0049
Ours (△)0.00480.00020.01990.0003
7Scenes
ICP [4] (○)6.00910.013013.04840.0260
FGR [16] (○)0.09190.00040.17050.0008
FPFH+RANSAC [13] (○)1.23250.00622.18750.0124
IDAM [21] (▲)5.67270.030311.59490.0629
RPMNet [38] (▲)0.38850.00210.76490.0042
FMR [16] (▲)2.54380.00724.90890.0150
CEMNet[17] (△)0.05590.00010.07720.0003
RIE [32] (△)0.01210.00010.02990.0001
Ours (△)0.00330.00000.01810.0001
", + "bbox": [ + 78, + 261, + 475, + 603 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/98eb6c06e5bc59ca7484fa8c7d204fb1fb50d4af13da78e0cc20f52fb11a475c.jpg", + "table_caption": [ + "Table 4. Evaluation results on Augmented ICL-NUIM and 7Scenes. Bold indicates the best performance and underline indicates the second-best performance. $(\\bigcirc)$ , $(\\triangle)$ and $(\\bigtriangleup)$ denote the traditional, supervised and unsupervised methods, respectively." + ], + "table_footnote": [], + "table_body": "
Complexity
Sinkhorn with dustbin parametersO((N+1) × (M+1))
Sinkhorn with iterate G timesO(G × (N × M))
Proposed theoremO(N)
", + "bbox": [ + 78, + 684, + 470, + 761 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Computational complexity of Sinkhorn and the proposed theorem comparison.", + "bbox": [ + 75, + 768, + 468, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "scoring mechanism. Noted that geometric constraints provide a self-supervised signal for our model, and $\\mathcal{L}_{gs}$ is designed based on this signal. Therefore, when geometric constraints is deleted, the loss function $\\mathcal{L}_{gs}$ should not participate in optimization.", + "bbox": [ + 75, + 809, + 468, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Loss Function. We evaluate the performance of the model", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3bb17ae991e3f7f89580c394126b39631bfc60df0b93db26e064b66c74347dc5.jpg", + "image_caption": [ + "Figure 4. Comparisons between the proposed theorem and the Sinkhorn in terms of precision and efficiency." + ], + "image_footnote": [], + "bbox": [ + 500, + 263, + 898, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "with different loss functions. Comprehensively, lacking any part of $\\mathcal{L}$ will degrade the performance of the model. Comparing $2\\sim 5$ rows in Table 3, the error observed in the third row is extremely large, primarily due to the absence of any optimization objective related to transformation in the loss function. This significantly reduces the registration performance of the model. In particular, this ablation study confirms the byproduct of ICC $\\mathcal{L}_{gs}$ can provide reliable and effective self-supervised signal for model optimization.", + "bbox": [ + 496, + 407, + 890, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 558, + 617, + 573 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we explore to extend a new definition called inlier confidence calibration (ICC). Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration accuracy. Thus, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed methods. In the future, we would like to extend our method to crossmodality (e.g., 2D-3D) registration with richer applications.", + "bbox": [ + 496, + 583, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by the National Natural Science Foundation of China (62036006, 62276200), the CAAI-Huawei MINDSPORE Academic Open Fund, the Key Research and Development Project of Shaanxi Province (2022QCY-LL-35), the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5319", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yasuhiro Aoki, Hunter Goforth, Rangaprasad Arun Srivatsan, and Simon Lucey. Pointnetlk: Robust & efficient point cloud registration using pointnet. 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IEEE Transactions on Robotics, 37(2):314-333, 2021. 3", + "[38] Zi Jian Yew and Gim Hee Lee. RPM-net: Robust point matching using learned features. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11824-11833, 2020. 2, 3, 6, 7, 8", + "[39] Zi Jian Yew and Gim Hee Lee. Regtr: End-to-end point cloud correspondences with transformers. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6677-6686, 2022. 6", + "[40] Wentao Yuan, Benjamin Eckart, Kihwan Kim, Varun Jampani, Dieter Fox, and Jan Kautz. Deepgmr: Learning latent gaussian mixture models for registration. In European Conference on Computer Vision, pages 733-750, 2020. 3" + ], + "bbox": [ + 78, + 90, + 470, + 900 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[41] Yongzhe Yuan, Yue Wu, Xiaolong Fan, Maoguo Gong, Wenping Ma, and Qiguang Miao. Egst: Enhanced geometric structure transformer for point cloud registration. IEEE Transactions on Visualization and Computer Graphics, pages 1-13, 2023. 2", + "[42] Yongzhe Yuan, Yue Wu, Maoguo Gong, Qiguang Miao, and AK Qin. One-nearest neighborhood guides inlier estimation for unsupervised point cloud registration. arXiv preprint arXiv:2307.14019, 2023. 3", + "[43] Andy Zeng, Shuran Song, Matthias Nießner, Matthew Fisher, Jianxiong Xiao, and Thomas Funkhouser. 3dmatch: Learning local geometric descriptors from rgb-d reconstructions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1802-1811, 2017. 2", + "[44] Yiming Zeng, Yue Qian, Zhiyu Zhu, Junhui Hou, Hui Yuan, and Ying He. Corrnet3d: Unsupervised end-to-end learning of dense correspondence for 3d point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6052-6061, 2021. 3", + "[45] Ji Zhang and Sanjiv Singh. Loam: Lidar odometry and mapping in real-time. In Robotics: Science and Systems, 2014. 1" + ], + "bbox": [ + 501, + 92, + 890, + 412 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5321", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_model.json b/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_model.json new file mode 100644 index 0000000000000000000000000000000000000000..af837556e4691fb4d9cf2575b4b489802c237ac6 --- /dev/null +++ b/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.19, + 0.131, + 0.783, + 0.154 + ], + "angle": 0, + "content": "Inlier Confidence Calibration for Point Cloud Registration" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.179, + 0.871, + 0.199 + ], + "angle": 0, + "content": "Yongzhe Yuan\\(^{1,2}\\) Yue Wu\\(^{1,2*}\\) Xiaolong Fan\\(^{1,3}\\) Maoguo Gong\\(^{1,3}\\) Qiguang Miao\\(^{1,2}\\) Wenping Ma\\(^{4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.199, + 0.77, + 0.218 + ], + "angle": 0, + "content": "\\(^{1}\\)MoE Key Lab of Collaborative Intelligence Systems, Xidian University" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.217, + 0.742, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Computer Science and Technology, Xidian University" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.234, + 0.695, + 0.252 + ], + "angle": 0, + "content": "\\(^{3}\\)School of Electronic Engineering, Xidian University" + }, + { + "type": "text", + "bbox": [ + 0.279, + 0.252, + 0.69, + 0.27 + ], + "angle": 0, + "content": "\\(^{4}\\)School of Artificial Intelligence, Xidian University" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.272, + 0.708, + 0.288 + ], + "angle": 0, + "content": "yyz@stu.xidian.edu.cn, {ywu, qgmiao}@xidian.edu.cn," + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.291, + 0.76, + 0.305 + ], + "angle": 0, + "content": "xiaolongfan@outlook.com, gong@ieee.org, wpma@mail.xidian.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.34, + 0.314, + 0.357 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.474, + 0.78 + ], + "angle": 0, + "content": "Inliers estimation constitutes a pivotal step in partially overlapping point cloud registration. Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration performance. In this paper, we explore to extend a new definition called inlier confidence calibration (ICC) to alleviate the above issues. Firstly, we provide finely initial correspondences for ICC in order to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy. Finally, transformation is further calculated by the weighted SVD algorithm with the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on synthetic and real-world datasets illustrate the effectiveness of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.808, + 0.21, + 0.823 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.833, + 0.47, + 0.879 + ], + "angle": 0, + "content": "With the rapid development of 3D data acquisition technology, point cloud data collected by LiDAR [45], Structured Light Sensors [30], and Stereo Cameras [9] has become" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.342, + 0.871, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.509, + 0.706, + 0.52 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.523, + 0.885, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.686, + 0.706, + 0.697 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.71, + 0.894, + 0.781 + ], + "angle": 0, + "content": "Figure 1. A toy example of proposed geometric constraints for inlier confidence calibration. The indicative center points pair is inlier pair in reality. (a) shows the situation without constraints. (b) demonstrates the situation with reliable geometric constraints. The experimental results are derived from ablation study." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.794, + 0.893, + 0.884 + ], + "angle": 0, + "content": "ubiquitous in various 3D computer vision and robotics applications [6, 20], such as autopilot [15], surgical navigation [23], and simultaneous localization and mapping [11]. In such applications, rigid body point cloud registration plays an essential role, which aims to find a rigid transformation to align one point cloud to another." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The recent advances have been dominated by learning-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5312" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.469 + ], + "angle": 0, + "content": "based methods. Most of these methods focus on solving the point cloud registration task in a supervised manner [16, 21, 27, 33, 38-41]. They require labeled data as the supervision signal to learn effective representations. In addition, obtaining labeled data is cumbersome and time-consuming, which may hinder applications in real world. To overcome this limitation, unsupervised point cloud registration is gradually garnering the interest of researchers [17, 24, 32]. However, in partially overlapping scenarios, learning-based methods must achieve robust inlier estimation, as inlier estimation serves as a fundamental source for identifying overlapping regions and predicting transformation. Existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context. Meanwhile, the current guiding principle is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate present among point clouds pose a considerable challenge in differentiating inliers, thereby elevating the risk of misinterpretation. Thus, a crucial question remains to be addressed in order to make point cloud registration a success: How to alleviate the bias in inlier confidence caused by massive coordinate differences?" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.473, + 0.701 + ], + "angle": 0, + "content": "We provide answer to this question in Figure 1. Our key insight is that simple coordinates cannot provide strong evidence for scoring inlier confidence. In Figure 1a, the indicative center points pair is very difficult to distinguish because of coordinate differences, which diminish the confidence of this points pair and further classify it as an outlier pair. To alleviate this issue, we construct transformation-invariant geometric constraints for center points pair in Figure 1b. This strategy is based on two intuitive observations: (i) a rigorously defined property of rigid transformation, i.e., it does not change the length of a vector and an angle between two vectors (isometric isomorphism). (ii) the neighborhood patch fromed by inlier and its neighborhood should have consistency. Under strict constraints, the inlier confidence in Figure 1a can be effectively calibrate." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Motivated by the discussion above, in this paper, we explore to extend a new definition called inlier confidence calibration (ICC) for point cloud registration. Note that our method adheres to the pipeline of \"pseudo correspondences-to-inlier estimation\" [32, 38], which encompasses critical task reference point cloud copy generation and scoring inlier confidence, respectively. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn [25]. This the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.363 + ], + "angle": 0, + "content": "orem is founded on the unique properties of the Gaussian distribution and cancels independent row and column normalization iteratively, along with the extra dustbin parameters in Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy. Finally, transformation are further calculated by the weighted SVD algorithm with the estimated correspondences and the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on the synthetic datasets ModelNet40 [35], Augmented ICL-NUIM [7] and real-world dataset 7Scenes [43] demonstrate our model achieves competitive performance." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.364, + 0.835, + 0.378 + ], + "angle": 0, + "content": "To summarize, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.379, + 0.891, + 0.422 + ], + "angle": 0, + "content": "- An effective ICC method for point cloud registration by constructing transformation-invariant geometric constraints." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.424, + 0.892, + 0.499 + ], + "angle": 0, + "content": "- A soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn, which can provide finely initial correspondences for ICC in order to generate the reference point cloud copy corresponding to the source point cloud." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.5, + 0.891, + 0.545 + ], + "angle": 0, + "content": "- Under the unsupervised setting, the constructed geometric constraints provide self-supervised signal and optimization objective for model training." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.379, + 0.892, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.559, + 0.651, + 0.575 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Traditional point cloud registration methods. Most traditional methods require a good initial transformation and converge to the local minima near the initialization point. One of the most profound methods is the Iterative Closest Point (ICP) algorithm [4], which begins with an initial transformation and iteratively alternates between solving two trivial subproblems: finding the closest points as correspondence under current transformation, and computing optimal transformation by SVD [19] based on identified correspondences. Though ICP can complete a high-precision registration, it is susceptible to the initial perturbation. In recent years, variants of ICP have been proposed [5, 14, 28, 31], and they can improve the defects of ICP and enhance the registration accuracy [3]. However, these methods retain a few essential drawbacks. Firstly, they depend strongly on the initialization. Secondly, it is difficult to integrate them into the deep learning pipeline as they lack differentiability. Thirdly, explicit estimation of corresponding points leads to quadratic complexity scaling with the number of points [29], which can introduce significant computational challenges." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5313" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "Learning-based registration methods. At present, most learning-based methods are based on supervision [12, 27, 33, 40]. PointnetLK [1] is a classical correspondence-free method, which calculates global feature descriptors through PointNet and iteratively uses the Inverse Compositional formulation and Lucas & Kanade algorithm [22, 37] to minimize distance between the descriptors to achieve registration. RPM-Net [38] utilizes the differentiable Sinkhorn layer and annealing to get soft assignments of point correspondences from hybrid features learned from both spatial coordinates and local geometry." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.471 + ], + "angle": 0, + "content": "Recently, unsupervised point cloud registration has gained increasing attention due to its applicability in scenarios where labeled training data is scarce or unavailable. Some methods have been proposed to address this challenge and achieved promising results [2, 8, 10, 17, 18]. Feature-metric point cloud registration framework (FMR) [16] enforces the optimisation of registration by minimising a feature-metric projection error with a autoencoder-based network. CEMNet [17] treats the point cloud registration as a reinforcement learning task. However, the current methods lack a concept of calibrating inlier confidence, which poses a potential challenge for partially overlapping point cloud registration. In comparison, our method provides a reliable ICC by constructing strict constraints." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.481, + 0.17, + 0.497 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Given two point clouds: source point cloud \\(\\mathcal{P} = \\{\\mathbf{p}_i\\in\\) \\(\\mathbb{R}^3\\mid i = 1,\\dots ,N\\}\\) and reference point cloud \\(\\mathcal{Q} = \\{\\mathbf{q}_j\\in\\) \\(\\mathbb{R}^3\\mid j = 1,\\dots ,M\\}\\), where each point is represented as a vector of \\((x,y,z)\\) coordinates. Our goal is to estimate a rigid transformation \\(\\{\\mathbf{R},\\mathbf{t}\\}\\) which accurately aligns \\(\\mathcal{P}\\) and \\(\\mathcal{Q}\\), with a 3D rotation \\(\\mathbf{R}\\in SO(3)\\) and a 3D translation \\(\\mathbf{t}\\in \\mathbb{R}^3\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, our method adheres to the pipeline of \"pseudo correspondences-to-inlier estimation\" [32, 38], which encompasses two critical tasks: reference point cloud copy generation and scoring inlier confidence. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud (Section 3.1). In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy (Section 3.2). The pipeline is illustrated in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.773, + 0.108 + ], + "angle": 0, + "content": "3.1. Finely Initial Correspondences" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.22 + ], + "angle": 0, + "content": "To generate high quality reference point cloud copy corresponding to the source point cloud, constructing the matching map between \\(\\mathcal{P}\\) and \\(\\mathcal{Q}\\) to refine the initial correspondences is an essential prerequisite. Different from previous work [32, 38], the model input is expanded into four point clouds through a 1-NN strategy, a methodology whose advantages have been substantiated in [42]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.893, + 0.512 + ], + "angle": 0, + "content": "Let 1-NN point cloud \\(\\widehat{\\mathcal{P}}\\) and \\(\\widehat{\\mathcal{Q}}\\) as the closest point for each point in \\(\\mathcal{P}\\) and \\(\\mathcal{Q}\\), respectively. Next, we construct a local patch \\(\\mathcal{N}_{\\circ}\\) with \\(K\\)-nearest neighborhood for each point and extract local features with Dynamic Graph CNN [34] for input point cloud and 1-NN point cloud. Associated learned features are denoted as \\(\\mathcal{F}_{\\mathcal{P}}, \\mathcal{F}_{\\widehat{\\mathcal{P}}}, \\mathcal{F}_{\\mathcal{Q}}\\) and \\(\\mathcal{F}_{\\widehat{\\mathcal{Q}}}\\), respectively. Then, we aim to learn a soft assignment matrix \\(\\mathbf{M}(\\widehat{\\mathbf{M}})\\) to explicitly indicate the matching between any two points of \\(\\mathcal{P}(\\widehat{\\mathcal{P}})\\) and \\(\\mathcal{Q}(\\widehat{\\mathcal{Q}})\\). Ideally, there is only a single prominent element dominating each row and column. To further enhance \\(\\mathbf{M}(\\widehat{\\mathbf{M}})\\), the widely adopted method is Sinkhorn [25], which performs the softmax operation on column-wise and row-wise iteratively and alternatively. However, the efficiency of Sinkhorn is limited by iterative strategy and extra dustbin parameters. To tackle this issue, we develop a soft assignment matrix optimization theorem to improve \\(\\mathbf{M}(\\widehat{\\mathbf{M}})\\) based on the following unique properties of the Gaussian distribution, which is a promotion for [44]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.894, + 0.598 + ], + "angle": 0, + "content": "Definition 1. (Three-sigma rule). The variation or dispersion of data can be measured by the three-sigma rule, which is based on the properties of the normal distribution curve, indicating that within a dataset \\(99.7\\%\\) of data values fall within the range of three standard deviation from the mean." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Recalling definitions of three-sigma rule, we have the following Theorem for \\(\\mathbf{M} \\in \\mathbb{R}^{N \\times M}\\) (maybe a non-square matrix), and \\(\\widehat{\\mathbf{M}}\\) follows the same principles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.665, + 0.892, + 0.726 + ], + "angle": 0, + "content": "Theorem 1. Suppose the \\(\\mathbf{M}_{i,j}\\) obeys a series of Gaussian distributions, \\(\\exists\\) two constants \\(\\epsilon, \\xi\\), such that there is only a single prominent element dominating each row by three-sigma rule." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Proof. Given \\(\\mu_{i}\\) and \\(\\sigma_{i}\\) are the mean and standard deviation of the \\(i\\)-th row of \\(\\mathbf{M}\\). \\(\\mathbf{M}_{i,j}\\) is normalized in row-wise and the normalized elements follow a standard normal distribution, i.e.:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.802, + 0.892, + 0.835 + ], + "angle": 0, + "content": "\\[\nh _ {i, j} = \\frac {\\mathbf {M} _ {i , j} - \\mu_ {i}}{\\sigma_ {i}} \\sim \\mathcal {N} (0, 1), j = 1, \\dots , M. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.843, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Based on above setting, we set tuning constants \\(\\epsilon\\) and \\(\\xi\\) to \\(h_{i,j}\\) and obtain" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.883, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\widetilde {h} _ {i, j} = \\epsilon \\cdot h _ {i, j} + \\xi \\sim \\mathcal {N} (\\xi , \\epsilon^ {2} \\mathbb {I}). \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5314" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.098, + 0.892, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.237, + 0.885, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.893, + 0.466 + ], + "angle": 0, + "content": "Figure 2. The pipeline of the proposed method. We first extract local features of input point cloud and 1-NN point cloud with DGCNN. Then, we construct matching map to generate high quality reference point cloud copy \\(\\mathcal{Q}\\) for fining initial correspondences. Based on the observation that the neighborhood graph formed by inlier and its neighborhood should have geometric structure consistency between \\(\\mathcal{P}\\) and \\(\\tilde{\\mathcal{Q}}\\), we construct transformation-invariant geometric structure constraints (edge and included angle) and captures their consistency to score and calibrate the inlier confidence for each estimated correspondences between \\(\\mathcal{P}\\) and \\(\\tilde{\\mathcal{Q}}\\). Finally, the transformation is estimated with SVD method via the calibrated inlier confidence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.471, + 0.52 + ], + "angle": 0, + "content": "For \\(i\\)-th row of \\(\\mathbf{H} \\in \\mathbb{R}^{N \\times M}(\\widetilde{h}_{i,j} \\subset \\mathbf{H})\\), the number of elements whose values are not less than a threshold \\(\\Delta\\) is calculated:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.53, + 0.47, + 0.55 + ], + "angle": 0, + "content": "\\[\nb _ {i} = \\left| \\left\\{\\widetilde {h} _ {i, j} \\mid \\widetilde {h} _ {i, j} \\geq \\Delta , j = 1, 2, \\dots , M \\right\\} \\right|. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.726 + ], + "angle": 0, + "content": "We aim to prompt \\( b_{i} \\) closer to 1, which means that in each row there is only a single element dominates the row. In addition, the \\( N \\) rows of \\( \\mathbf{H} \\) can be regarded as \\( N \\) independent and identically distributed events, thus the set \\( \\{b_{1}, b_{2}, \\ldots, b_{N}\\} \\) also follows a Gaussian distribution with the expectation \\( \\mu_{b} \\) and variance \\( \\sigma_{b} \\) depending on the tuning constants \\( \\epsilon, \\xi \\). Hence, by the Definition 1, we can select suitable values of \\( \\epsilon, \\xi \\) to control the bound \\( [\\mu_{b} - 3\\sigma_{b}, \\mu_{b} + 3\\sigma_{b}] \\), which is centered around 1, such that the expectation of only a single element dominates the row can be implemented." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Theorem 1 tells us that column-wise and row-wise iteratively and alternatively may be not essential. Operating solely on the rows can achieve the objective with higher efficiency and accuracy (Please refer to Section 4.4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.79, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Based on the scores in soft assignment matrix \\(\\mathbf{H}\\) and \\(\\widehat{\\mathbf{H}}\\), we construct dual neighborhood matching map by fusing and averaging matching scores of each \\(\\mathcal{N}_{\\circ}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.846, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} _ {i, j} = \\frac {1}{K} \\sum_ {\\mathbf {p} _ {i ^ {\\prime}} \\in \\mathcal {N} _ {\\mathbf {p} _ {i}}} \\sum_ {\\mathbf {q} _ {j ^ {\\prime}} \\in \\mathcal {N} _ {\\mathbf {q} _ {j}}} \\mathbf {H} _ {i ^ {\\prime}, j ^ {\\prime}} + \\frac {1}{K} \\sum_ {\\widehat {\\mathbf {p}} _ {i ^ {\\prime}} \\in \\mathcal {N} _ {\\widehat {\\mathbf {p}} _ {i}}} \\sum_ {\\widehat {\\mathbf {q}} _ {j ^ {\\prime}} \\in \\mathcal {N} _ {\\widehat {\\mathbf {q}} _ {j}}} \\widehat {\\mathbf {H}} _ {i ^ {\\prime}, j ^ {\\prime}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.476, + 0.822, + 0.492 + ], + "angle": 0, + "content": "Finally, we formulate the final matching map as:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.496, + 0.89, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {i, j} = \\operatorname {s o f t m a x} \\left(- \\mathbf {D} _ {i, 1} ^ {\\prime}, - \\mathbf {D} _ {i, 2} ^ {\\prime}, \\dots , - \\mathbf {D} _ {i, M} ^ {\\prime}\\right) _ {j}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.517, + 0.812, + 0.546 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D} _ {i, j} ^ {\\prime} = \\exp (\\alpha - \\mathbf {G} _ {i, j}) * \\left(\\mathbf {D} _ {i, j} + \\widehat {\\mathbf {D}} _ {i, j}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.644 + ], + "angle": 0, + "content": "where \\(\\mathbf{D}_{i,j} = \\| \\mathcal{F}_{\\mathbf{p}_i} - \\mathcal{F}_{\\mathbf{q}_j}\\| _2\\) and \\(\\widehat{\\mathbf{D}}_{i,j} = \\| \\mathcal{F}_{\\widehat{\\mathbf{p}}_i} - \\mathcal{F}_{\\widehat{\\mathbf{q}}_j}\\| _2\\) denote the Euclidean distance between learned local features, \\(\\mathbf{D}_{i,j}^{\\prime}\\) is negatively related to the matching score \\(\\mathbf{G}_{i,j}\\). We utilize the exponential strategy to control the changing ratio, along with a hyper-parameter \\(\\alpha\\) to control the influence of the dual neighborhood matching [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.705 + ], + "angle": 0, + "content": "Based on the high quality matching map \\(\\mathbf{F} \\in \\mathbb{R}^{N \\times M}\\), we generate the reference point cloud copy \\(\\widetilde{\\mathcal{Q}} \\in \\mathbb{R}^{N \\times 3}\\) including finely initial correspondences for each point \\(\\mathbf{p}_i\\) in source point cloud \\(\\mathcal{P}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.711, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} ^ {\\prime} = \\left\\{\\left(\\mathbf {p} _ {i}, \\widetilde {\\mathbf {q}} _ {i}\\right) \\mid i = 1, \\dots , N, \\widetilde {\\mathbf {q}} _ {i} \\in \\widetilde {\\mathcal {Q}} \\right\\}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.743, + 0.545, + 0.755 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.753, + 0.892, + 0.796 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {q}} _ {i} = \\sum_ {j = 1} ^ {M} \\mathbf {F} _ {i, j} \\cdot \\mathbf {q} _ {j}. \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.764, + 0.816 + ], + "angle": 0, + "content": "3.2. Inlier Confidence Calibration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "After generating reference copy \\(\\widetilde{\\mathcal{Q}}\\), we score inlier confidence for each point pair in \\(\\mathcal{C}'\\). However, existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context, and the current guiding principle" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5315" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate pose a challenge in differentiating inliers, thereby elevating the risk of misinterpretation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.408 + ], + "angle": 0, + "content": "In this section, we explore to extend a new definition called ICC to alleviate the above issues. Benefiting from the high quality matching map \\(\\mathbf{F}\\) in Section 3.1, we argue that the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy, i.e., if \\(\\mathbf{p}_i\\) is an inlier, its neighborhood points also tend to be the inliers and \\(\\widetilde{\\mathbf{q}}_i\\) have geometric structure neighborhood consistency in the reference copy. Conversely, if \\(\\mathbf{p}_i\\) is an outlier, its neighborhood may also be the outliers and spatial structure is prone to be significantly different from the reference copy neighborhood. Based on this observation, we construct transformation-invariant geometric constraints and formulate geometric structure consistency between \\(\\mathcal{N}_{\\mathbf{p}_i}\\) and \\(\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}\\) to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.472, + 0.469 + ], + "angle": 0, + "content": "We first construct a learnable neighborhood graph by transformation-invariant geometric structure constraints of \\(\\mathcal{N}_{\\mathbf{p}_i}\\) and \\(\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}\\), which consists of edge representation and angle representation:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.474, + 0.395, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {i, k} ^ {\\mathbf {p}} = \\mathbf {p} _ {i} - \\mathbf {p} _ {k}, \\mathbf {a} _ {r, s} ^ {\\mathbf {p}} = \\angle (\\mathbf {e} _ {i, r} ^ {\\mathbf {p}}, \\mathbf {e} _ {i, s} ^ {\\mathbf {p}}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.497, + 0.47, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {i, k} ^ {\\widetilde {\\mathbf {q}}} = \\widetilde {\\mathbf {q}} _ {i} - \\widetilde {\\mathbf {q}} _ {k}, \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}} = \\angle \\left(\\mathbf {e} _ {i, r} ^ {\\widetilde {\\mathbf {q}}}, \\mathbf {e} _ {i, s} ^ {\\widetilde {\\mathbf {q}}}\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.525, + 0.412, + 0.541 + ], + "angle": 0, + "content": "\\[\ni \\neq k, k = 1, \\dots , K r, s \\in \\{1, \\dots , K \\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.608 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}_k\\) and \\(\\widetilde{\\mathbf{q}}_k\\) are the points in \\(\\mathcal{N}_{\\mathbf{p}_i}\\) and \\(\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}\\). Moreover, these representations express sensitive and discriminative geometric structure in the point cloud, and provide adequate geometric cues for subsequent pipeline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.699 + ], + "angle": 0, + "content": "In order to better capture the neighborhood relevance and promote contextual message propagation, we utilize Multi-layer Perceptron (MLP) \\( f_{\\theta} \\) with parameters \\( \\theta \\) to fuse representations and characterize the consistency between the neighborhoods by the subtraction of the fused geometric representations:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.704, + 0.472, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {i, k} = f _ {\\theta} \\left(\\operatorname {c o n c a t} \\left(\\mathbf {e} _ {i, k} ^ {\\mathbf {p}}, \\mathbf {a} _ {r, s} ^ {\\mathbf {p}}\\right)\\right) - f _ {\\theta} \\left(\\operatorname {c o n c a t} \\left(\\mathbf {e} _ {i, k} ^ {\\widetilde {\\mathbf {q}}}, \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}}\\right)\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.743, + 0.469, + 0.773 + ], + "angle": 0, + "content": "Next, the model further adaptively learns the attention coefficients \\(\\delta_{i,k}\\) of each geometric structure consistency:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.78, + 0.469, + 0.81 + ], + "angle": 0, + "content": "\\[\n\\delta_ {i, k} = \\operatorname {s o f t m a x} \\left(f _ {\\mu} \\left(\\mathbf {d} _ {i, 1}\\right), f _ {\\mu} \\left(\\mathbf {d} _ {i, 2}\\right), \\dots , f _ {\\mu} \\left(\\mathbf {d} _ {i, K}\\right)\\right) _ {k}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.47, + 0.857 + ], + "angle": 0, + "content": "where \\(f_{\\mu}\\) is another MLP with parameters \\(\\mu\\). Then, inlier confidence \\(\\mathbf{w}_i\\) of correspondence \\((\\mathbf{p}_i, \\widetilde{\\mathbf{q}}_i)\\) is calculated by aggregating the geometric structure consistency weighted:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.862, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} _ {i} = 1 - \\operatorname {T a n h} \\left(\\left| l \\left(\\sum_ {k = 1} ^ {K} \\delta_ {i, k} * \\mathbf {d} _ {i, k}\\right) \\right|\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "where \\( l \\) is a linear function. Through strict geometric constraints, the scored inlier confidence can be effectively calibrated, ensuring the sustained high credibility of \\( \\mathbf{w}_i \\). However, some potential repetitive structures, textureless structures and other uncertain factors may still exist. In order to enhance the robustness of the proposed method and reduce the bias caused by the above issues, we select inlier correspondences from \\( \\mathcal{C}' \\) with the largest \\( N_c \\) inlier confidence:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.219, + 0.892, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {h} = \\left\\{\\left(\\mathbf {p} _ {h}, \\widetilde {\\mathbf {q}} _ {h}\\right) \\mid h \\in \\operatorname {T o p k} \\left(\\mathbf {w} _ {i}\\right), i = 1, \\dots , N _ {c} \\right\\}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.241, + 0.892, + 0.287 + ], + "angle": 0, + "content": "Finally, transformation \\(\\{\\mathbf{R}_{est},\\mathbf{t}_{est}\\}\\) can be solved in closed form using weighted SVD, which has been shown to be differentiable in [26]:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.292, + 0.892, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} _ {e s t}, \\mathbf {t} _ {e s t} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\sum_ {\\left(\\mathbf {p} _ {i}, \\widetilde {\\mathbf {q}} _ {i}\\right) \\in \\mathcal {C} _ {h}} \\mathbf {w} _ {i} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {i} + \\mathbf {t} - \\widetilde {\\mathbf {q}} _ {i} \\| _ {2} ^ {2}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.378 + ], + "angle": 0, + "content": "Besides, ICC provides useful byproduct for unsupervised learning, which can be reliable self-supervised signal. More details can be seen in the following section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.384, + 0.64, + 0.401 + ], + "angle": 0, + "content": "3.3. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.892, + 0.466 + ], + "angle": 0, + "content": "In this section, we conduct four loss functions for model optimization. Moreover, the proposed model is trained in an unsupervised manner instead of using the ground-truth transformations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Global Consistency Loss. We investigate the global consistency loss between the final transformed source point cloud \\(\\mathcal{P}'\\) and the reference point cloud \\(\\mathcal{Q}\\). Specifically, the Huber function is utilized to assemble the global consistency loss, which is defined as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.548, + 0.892, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {g c} = \\sum_ {\\mathbf {p} ^ {\\prime} \\in \\mathcal {P} ^ {\\prime}} H _ {\\beta} \\left(\\min _ {\\mathbf {q} \\in \\mathcal {Q}} \\| \\mathbf {p} ^ {\\prime} - \\mathbf {q} \\| _ {2} ^ {2}\\right) \\tag {14} \\\\ + \\sum_ {\\mathbf {q} \\in \\mathcal {Q}} H _ {\\beta} \\left(\\min _ {\\mathbf {p} ^ {\\prime} \\in \\mathcal {P} ^ {\\prime}} \\| \\mathbf {q} - \\mathbf {p} ^ {\\prime} \\| _ {2} ^ {2}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.739 + ], + "angle": 0, + "content": "However, relying solely on global consistency loss is detrimental to the accuracy and reliability of our model. Since the model may still potentially converge to sub-optimization due to the existing outliers, leading massive potential information of point cloud is wasted. Hence, it is critical to mine the potential self-supervised signals in the point cloud and construct loss functions based on other existing elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.739, + 0.892, + 0.847 + ], + "angle": 0, + "content": "Dual Neighborhood Consistency Loss. Based on reliable inlier correspondences in Equation 12, we denote the inliers set of the source and its reference point cloud copy as \\(\\mathbf{X} \\in \\mathbb{R}^{N_c \\times 3}\\) and \\(\\mathbf{Y} \\in \\mathbb{R}^{N_c \\times 3}\\), respectively. We utilize the neighborhood between the inliers to construct consistency objective, which aims to minimize the registration error between each neighborhood \\(\\mathcal{N}_{\\mathbf{x}_i}\\) and \\(\\mathcal{N}_{\\mathbf{y}_i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.852, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i n} = \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {R} _ {e s t} \\mathbf {p} _ {j} + \\mathbf {t} _ {e s t} - \\widetilde {\\mathbf {q}} _ {j} \\right\\| _ {2}, \\tag {15}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5316" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.304, + 0.108 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_{\\mathbf{x}_i}\\) is transformed by \\(\\mathcal{N}_{\\mathbf{y}_i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.468, + 0.182 + ], + "angle": 0, + "content": "Geometric Structure Consistency Loss. The geometric signal buried in point cloud is readily ignored, which hinders ICC. To address this issue, we design a geometric neighborhood loss with the reliable geometric self-supervised signal proposed in Section 3.2:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.19, + 0.468, + 0.268 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {g s} = \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {e} _ {i, j} ^ {\\mathbf {p}} - \\mathbf {e} _ {i, j} ^ {\\widetilde {\\mathbf {q}}} \\right\\| _ {2} + \\\\ \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {a} _ {r, s} ^ {\\mathbf {p}} - \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}} \\right\\| _ {2}, \\tag {16} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.279, + 0.468, + 0.311 + ], + "angle": 0, + "content": "where \\(\\mathbf{a}_{r,s}^{\\mathbf{p}}\\) and \\(\\mathbf{a}_{r,s}^{\\widetilde{\\mathbf{q}}}\\) is calculated by \\(\\mathbf{e}_{i,j}^{\\mathbf{p}}\\) and \\(\\mathbf{e}_{i,j}^{\\widetilde{\\mathbf{q}}}\\) shown in Equation 8." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.312, + 0.468, + 0.387 + ], + "angle": 0, + "content": "Spatial Consistency Loss. We further explore to eliminate the spatial difference between the estimated correspondence and the real correspondence for each selected inlier \\(\\mathbf{x}_i\\) and utilize spatial consistency loss with cross-entropy to sharpen matching map \\(\\mathbf{G}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.396, + 0.468, + 0.438 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s c} = - \\frac {1}{| \\mathbf {X} |} \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}} \\sum_ {j = 1} ^ {M} [ [ j = \\arg \\max _ {j ^ {\\prime}} \\mathbf {G} _ {i, j ^ {\\prime}} ] ] \\log \\mathbf {G} _ {i, j}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.447, + 0.468, + 0.507 + ], + "angle": 0, + "content": "where \\(\\llbracket \\cdot \\rrbracket\\) is the Iverson bracket. Spatial consistency loss encourages to improve the matching probability and thus the estimated correspondence point in reference copy tends to have an stable position." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.508, + 0.468, + 0.553 + ], + "angle": 0, + "content": "Overall Loss. Since our work utilizes an iterative scheme, we compute the loss at each iteration \\( N_{l} \\) and have the weighted sum loss:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.562, + 0.468, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {l = 1} ^ {N _ {l}} \\left(\\mathcal {L} _ {g c} ^ {l} + \\gamma \\mathcal {L} _ {i n} ^ {l} + \\rho \\mathcal {L} _ {g s} ^ {l} + \\lambda \\mathcal {L} _ {s c} ^ {l}\\right), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.612, + 0.468, + 0.643 + ], + "angle": 0, + "content": "where \\(\\gamma\\), \\(\\rho\\) and \\(\\lambda\\) are trade-off parameters to control corresponding loss function." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.655, + 0.209, + 0.672 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.68, + 0.266, + 0.696 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.703, + 0.468, + 0.822 + ], + "angle": 0, + "content": "We compare our method to traditional methods and recent state of the arts learning-based methods. The traditional methods include ICP [4], FGR [16] and FPFH + RANSAC [13]. The recent learning based methods include IDAM [21], FMR [16], RPMNet [38], CEMNet [17], REGTR [39], GeoTransformer [27] and RIE [32]. For consistency with previous work, we measure Mean Isotropic Error (MIE) and Mean Absolute Error (MAE)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.391, + 0.848 + ], + "angle": 0, + "content": "4.2. ModelNet40 Dataset and Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Noted that, to simulate partial-to-partial registration, the reference point cloud \\(\\mathcal{Q}\\) and the source point cloud \\(\\mathcal{P}\\) are cropped respectively, and retain \\(70\\%\\) of the points." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.091, + 0.897, + 0.279 + ], + "angle": 0, + "content": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
ICP [4] (○)3.43390.01146.77060.0227
FGR [16] (○)0.59720.00211.15630.0041
FPFH+RANSAC [13] (○)0.70310.00251.27720.0050
IDAM [21] (▲)0.42430.00200.81700.0040
RPMNet [38] (▲)0.00510.00000.02010.0000
FMR [16] (▲)3.64970.01017.28100.0200
REGTR [39] (▲)0.18940.00150.34930.0030
GeoTransformer [27] (▲)0.59700.00570.90100.0102
CEMNet [17] (△)0.13850.00010.24890.0002
RIE [32] (△)0.00330.00000.02100.0000
Ours (△)0.00120.00000.01920.0000
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.284, + 0.892, + 0.34 + ], + "angle": 0, + "content": "Table 1. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. \\((\\bigcirc)\\), \\((\\triangle)\\) and \\((\\triangle)\\) denote the traditional, supervised and unsupervised methods, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Unseen Objects. Our models are trained and tested on datasets comprising of samples belonging to the same categories, and both the training and test sets are obtained without any preprocessing or manipulation. We apply a random transformation on the reference point cloud \\(\\mathcal{Q}\\) to generate corresponding source point cloud \\(\\mathcal{P}\\). Table 1 shows quantitative results of the various algorithms under current experimental settings. The proposed method substantially outperforms all baseline in all metrics. We can observe our method can even outperform the supervised IDAM, RPMNet, FMR, REGTR and GeoTransformer by a large margin. Benefiting from ICC, our method attains highly accurate registration and improves the registration accuracy by an order of magnitude. In order to show the effect of our proposed approach clearly, a qualitative comparison of the registration results can be found in Figure 3. Our method ensures minimal impact on changing of the shape, and achieves the best performance even on asymmetric shape." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Unseen Categories. To verify the generalization ability on categories, we train the models on the first 20 categories and test on the remaining unseen categories. The results are summarized in Table 2. We can observe that the majority of baseline consistently exhibit lower performance on the unseen categories, especially learning-based methods. In contrast, traditional algorithms are less susceptible to this issue due to the insensitivity of handcrafted methods to shape variance [36]. Our registration process remains highly precise, achieving the lowest error across all metrics, while also maintaining acceptable levels of fluctuation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Gaussian Noise. In order to assess performance in the presence of noise, which is commonly encountered in real-world point clouds, we train our model on noise-free data and then evaluate all baselines using a test set featuring Gaussian noise. We randomly and independently generate noisy points to introduce noise into in source point cloud and reference point cloud by sampling from \\(\\mathcal{N}(0,0.5)\\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5317" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.889, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.893, + 0.34 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison of the registration results on unseen objects data (blue: source point cloud, yellow: reference point cloud, green: transformed source point cloud)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.475, + 0.475 + ], + "angle": 0, + "content": "clipped to \\([-1.0, 1.0]\\). This experiment is significantly challenging, as constructing matching map and ICC become much more difficult. As shown in Table 2, our method outperforms other baselines. The experimental results demonstrate that our method is robust to the noise. In addition, experimental results indirectly confirms the generality and high adaptability of ICC in point cloud registration with partially overlapping." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.492, + 0.477, + 0.833 + ], + "angle": 0, + "content": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Unseen Categories
ICP [4] (○)3.60990.01167.05560.0228
FGR [16] (○)0.45790.00160.84420.0032
FPFH+RANSAC [13] (○)0.44270.00210.94470.0043
IDAM [21] (▲)0.48090.00280.91570.0055
RPMNet [38] (▲)0.00640.00010.02070.0001
FMR [16] (▲)3.85940.01147.64500.0225
CEMNet[17] (△)0.08040.00020.14050.0003
RIE [32] (△)0.00590.00000.02280.0001
Ours (△)0.00220.00000.01890.0000
Gaussian Noise
ICP [4] (○)4.64410.01679.21940.0333
FGR [16] (○)1.06760.00362.00380.0072
FPFH+RANSAC [13] (○)1.43160.00612.53450.0120
IDAM [21] (▲)2.30760.01244.53320.0246
RPMNet [38] (▲)1.58900.01752.98300.0378
FMR [16] (▲)18.03550.053635.79860.1063
CEMNet[17] (△)10.70260.039321.18360.0781
RIE [32] (△)0.04310.00040.07760.0008
Ours (△)0.00880.00010.02450.0002
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.838, + 0.471, + 0.895 + ], + "angle": 0, + "content": "Table 2. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. \\((\\bigcirc)\\), \\((\\triangle)\\) and \\((\\bigtriangleup)\\) denote the traditional, supervised and unsupervised methods, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.352, + 0.774, + 0.368 + ], + "angle": 0, + "content": "4.3. Other Datasets and Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.892, + 0.558 + ], + "angle": 0, + "content": "We further conduct comparison evaluation on other datasets: 7Scenes and Augmented ICL-NUIM. We sample the reference point clouds to 2,048 points and randomly sample three Euler angle rotations within \\([0^{\\circ}, 45^{\\circ}]\\) and translations within \\([-0.5, 0.5]\\) on each axis as the rigid transformation to obtain source point clouds, then down-sample the point clouds to 1,536 points to generate the partial data. As demonstrated in Table 4, our method exhibits extremely higher registration precision on all criteria on Augmneted ICL-NUIM and 7Scenes, especially the rotation error. We can summarize our method has best performance and is comfortable with real-world dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.572, + 0.757, + 0.589 + ], + "angle": 0, + "content": "4.4. Ablation Study and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Soft Assignment Matrix Optimization Theorem. We compare the developed theorem with the Sinkhorn, and evaluate precision and efficiency against Sinkhorn, which iterate 1 (Sinkhorn-1) and 5 (Sinkhorn-5) times. As shown in Figure 4, we can observe that under the same tolerant error, the developed theorem demonstrates superior performance, especially the optimization for rotation. Additionally, the proposed theorem improves the efficiency up to nearly \\(2 \\times\\) compared to Sinkhorn-1 and nearly up to \\(5 \\times\\) compared to Sinkhorn-5. It needs to be emphasized once again that the proposed theorem has a smaller computational complexity than Sinkhorn as shown in Table 5, since this theorem does not normalize the rows and columns repeatedly, and only operates on the rows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Geometric Constraints. To investigate whether geometric constraints are meaningful to ICC, we conduct an experiment to verify our motivation. Experimental results are shown in the first row of Table 3. Compared to constraints-free, which score inlier confidence by simple coordinates, geometric constraints effectively generate more convincing" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5318" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.104, + 0.089, + 0.872, + 0.228 + ], + "angle": 0, + "content": "
GeometricConstraints\\( \\mathcal{L}_{gc} \\)\\( \\mathcal{L}_{in} \\)\\( \\mathcal{L}_{gs} \\)\\( \\mathcal{L}_{sc} \\)ModelNet407Scenes
MAE(R)MAE(t)MIE(R)MIE(R)MAE(R)MAE(t)MIE(R)MIE(R)
✓✓N/A✓1.01230.01611.83980.03502.22380.01484.36980.0286
✓✓✓✓0.39980.00610.76650.01290.00420.00000.02170.0001
✓✓✓✓22.51990.134042.44280.27103.30870.03405.87700.0657
✓✓✓✓0.00700.00010.02350.00020.00370.00000.01860.0001
✓✓✓✓0.11250.00140.018620.00300.01420.00010.03450.0003
✓✓✓✓✓0.00120.00000.01920.00000.00330.00000.01810.0001
" + }, + { + "type": "table_caption", + "bbox": [ + 0.16, + 0.236, + 0.808, + 0.252 + ], + "angle": 0, + "content": "Table 3. Ablation study of different components. \\( {\\mathcal{L}}_{gc},{\\mathcal{L}}_{in},{\\mathcal{L}}_{gs} \\) and \\( {\\mathcal{L}}_{sc} \\) : Each Loss Function in Equation 18." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.262, + 0.477, + 0.604 + ], + "angle": 0, + "content": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Augmented ICL-NUIM
ICP [4] (○)2.40220.06994.48320.1410
FGR [16] (○)2.24770.08084.18500.1573
FPFH+RANSAC [13] (○)1.23490.04292.31670.0839
IDAM [21] (▲)4.41530.13858.61780.2756
RPMNet [38] (▲)0.32670.01250.62770.0246
FMR [16] (▲)1.10850.03982.13230.0786
CEMNet[17] (△)0.23740.00050.39870.0010
RIE [32] (△)0.04920.00230.08970.0049
Ours (△)0.00480.00020.01990.0003
7Scenes
ICP [4] (○)6.00910.013013.04840.0260
FGR [16] (○)0.09190.00040.17050.0008
FPFH+RANSAC [13] (○)1.23250.00622.18750.0124
IDAM [21] (▲)5.67270.030311.59490.0629
RPMNet [38] (▲)0.38850.00210.76490.0042
FMR [16] (▲)2.54380.00724.90890.0150
CEMNet[17] (△)0.05590.00010.07720.0003
RIE [32] (△)0.01210.00010.02990.0001
Ours (△)0.00330.00000.01810.0001
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.611, + 0.471, + 0.669 + ], + "angle": 0, + "content": "Table 4. Evaluation results on Augmented ICL-NUIM and 7Scenes. Bold indicates the best performance and underline indicates the second-best performance. \\((\\bigcirc)\\), \\((\\triangle)\\) and \\((\\bigtriangleup)\\) denote the traditional, supervised and unsupervised methods, respectively." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.685, + 0.472, + 0.762 + ], + "angle": 0, + "content": "
Complexity
Sinkhorn with dustbin parametersO((N+1) × (M+1))
Sinkhorn with iterate G timesO(G × (N × M))
Proposed theoremO(N)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.8 + ], + "angle": 0, + "content": "Table 5. Computational complexity of Sinkhorn and the proposed theorem comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.884 + ], + "angle": 0, + "content": "scoring mechanism. Noted that geometric constraints provide a self-supervised signal for our model, and \\(\\mathcal{L}_{gs}\\) is designed based on this signal. Therefore, when geometric constraints is deleted, the loss function \\(\\mathcal{L}_{gs}\\) should not participate in optimization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Loss Function. We evaluate the performance of the model" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.265, + 0.9, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.375, + 0.892, + 0.403 + ], + "angle": 0, + "content": "Figure 4. Comparisons between the proposed theorem and the Sinkhorn in terms of precision and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.545 + ], + "angle": 0, + "content": "with different loss functions. Comprehensively, lacking any part of \\(\\mathcal{L}\\) will degrade the performance of the model. Comparing \\(2\\sim 5\\) rows in Table 3, the error observed in the third row is extremely large, primarily due to the absence of any optimization objective related to transformation in the loss function. This significantly reduces the registration performance of the model. In particular, this ablation study confirms the byproduct of ICC \\(\\mathcal{L}_{gs}\\) can provide reliable and effective self-supervised signal for model optimization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.619, + 0.574 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.794 + ], + "angle": 0, + "content": "In this paper, we explore to extend a new definition called inlier confidence calibration (ICC). Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration accuracy. Thus, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed methods. In the future, we would like to extend our method to crossmodality (e.g., 2D-3D) registration with richer applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by the National Natural Science Foundation of China (62036006, 62276200), the CAAI-Huawei MINDSPORE Academic Open Fund, the Key Research and Development Project of Shaanxi Province (2022QCY-LL-35), the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5319" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.473, + 0.185 + ], + "angle": 0, + "content": "[1] Yasuhiro Aoki, Hunter Goforth, Rangaprasad Arun Srivatsan, and Simon Lucey. Pointnetlk: Robust & efficient point cloud registration using pointnet. 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In Robotics: Science and Systems, 2014. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5321" + } + ] +] \ No newline at end of file diff --git a/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_origin.pdf b/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..201af83b3ec31391049ceac291afe45573e6d238 --- /dev/null +++ b/2024/Inlier Confidence Calibration for Point Cloud Registration/55d4a26e-41c5-4e7c-ab72-057a3c3654dd_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d89dcba3b9c725f741d7995f407ad2c199aa96f179ba67fd868031538744d3b2 +size 2040964 diff --git a/2024/Inlier Confidence Calibration for Point Cloud Registration/full.md b/2024/Inlier Confidence Calibration for Point Cloud Registration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7c5522bccf9189e1a9c7bb397c6ab3df4df5b3d4 --- /dev/null +++ b/2024/Inlier Confidence Calibration for Point Cloud Registration/full.md @@ -0,0 +1,349 @@ +# Inlier Confidence Calibration for Point Cloud Registration + +Yongzhe Yuan $^{1,2}$ Yue Wu $^{1,2*}$ Xiaolong Fan $^{1,3}$ Maoguo Gong $^{1,3}$ Qiguang Miao $^{1,2}$ Wenping Ma $^{4}$ + +$^{1}$ MoE Key Lab of Collaborative Intelligence Systems, Xidian University + +$^{2}$ School of Computer Science and Technology, Xidian University + +$^{3}$ School of Electronic Engineering, Xidian University + +$^{4}$ School of Artificial Intelligence, Xidian University + +yyz@stu.xidian.edu.cn, {ywu, qgmiao}@xidian.edu.cn, + +xiaolongfan@outlook.com, gong@ieee.org, wpma@mail.xidian.edu.cn + +# Abstract + +Inliers estimation constitutes a pivotal step in partially overlapping point cloud registration. Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration performance. In this paper, we explore to extend a new definition called inlier confidence calibration (ICC) to alleviate the above issues. Firstly, we provide finely initial correspondences for ICC in order to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy. Finally, transformation is further calculated by the weighted SVD algorithm with the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on synthetic and real-world datasets illustrate the effectiveness of the proposed method. + +# 1. Introduction + +With the rapid development of 3D data acquisition technology, point cloud data collected by LiDAR [45], Structured Light Sensors [30], and Stereo Cameras [9] has become + +![](images/5c62cc448034e57fa575244f7733f4424694409f48c961bb17e5546ef21be8b2.jpg) +(a) + +![](images/a0dd6e5c6fa1805b735b46ce8e094eb65343ffc54896fe8fa40bc03503bf2d8a.jpg) +(b) +Figure 1. A toy example of proposed geometric constraints for inlier confidence calibration. The indicative center points pair is inlier pair in reality. (a) shows the situation without constraints. (b) demonstrates the situation with reliable geometric constraints. The experimental results are derived from ablation study. + +ubiquitous in various 3D computer vision and robotics applications [6, 20], such as autopilot [15], surgical navigation [23], and simultaneous localization and mapping [11]. In such applications, rigid body point cloud registration plays an essential role, which aims to find a rigid transformation to align one point cloud to another. + +The recent advances have been dominated by learning- + +based methods. Most of these methods focus on solving the point cloud registration task in a supervised manner [16, 21, 27, 33, 38-41]. They require labeled data as the supervision signal to learn effective representations. In addition, obtaining labeled data is cumbersome and time-consuming, which may hinder applications in real world. To overcome this limitation, unsupervised point cloud registration is gradually garnering the interest of researchers [17, 24, 32]. However, in partially overlapping scenarios, learning-based methods must achieve robust inlier estimation, as inlier estimation serves as a fundamental source for identifying overlapping regions and predicting transformation. Existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context. Meanwhile, the current guiding principle is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate present among point clouds pose a considerable challenge in differentiating inliers, thereby elevating the risk of misinterpretation. Thus, a crucial question remains to be addressed in order to make point cloud registration a success: How to alleviate the bias in inlier confidence caused by massive coordinate differences? + +We provide answer to this question in Figure 1. Our key insight is that simple coordinates cannot provide strong evidence for scoring inlier confidence. In Figure 1a, the indicative center points pair is very difficult to distinguish because of coordinate differences, which diminish the confidence of this points pair and further classify it as an outlier pair. To alleviate this issue, we construct transformation-invariant geometric constraints for center points pair in Figure 1b. This strategy is based on two intuitive observations: (i) a rigorously defined property of rigid transformation, i.e., it does not change the length of a vector and an angle between two vectors (isometric isomorphism). (ii) the neighborhood patch fromed by inlier and its neighborhood should have consistency. Under strict constraints, the inlier confidence in Figure 1a can be effectively calibrate. + +Motivated by the discussion above, in this paper, we explore to extend a new definition called inlier confidence calibration (ICC) for point cloud registration. Note that our method adheres to the pipeline of "pseudo correspondences-to-inlier estimation" [32, 38], which encompasses critical task reference point cloud copy generation and scoring inlier confidence, respectively. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn [25]. This the + +orem is founded on the unique properties of the Gaussian distribution and cancels independent row and column normalization iteratively, along with the extra dustbin parameters in Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy. Finally, transformation are further calculated by the weighted SVD algorithm with the estimated correspondences and the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on the synthetic datasets ModelNet40 [35], Augmented ICL-NUIM [7] and real-world dataset 7Scenes [43] demonstrate our model achieves competitive performance. + +To summarize, our contributions are as follows: + +- An effective ICC method for point cloud registration by constructing transformation-invariant geometric constraints. +- A soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn, which can provide finely initial correspondences for ICC in order to generate the reference point cloud copy corresponding to the source point cloud. +- Under the unsupervised setting, the constructed geometric constraints provide self-supervised signal and optimization objective for model training. + +# 2. Related Works + +Traditional point cloud registration methods. Most traditional methods require a good initial transformation and converge to the local minima near the initialization point. One of the most profound methods is the Iterative Closest Point (ICP) algorithm [4], which begins with an initial transformation and iteratively alternates between solving two trivial subproblems: finding the closest points as correspondence under current transformation, and computing optimal transformation by SVD [19] based on identified correspondences. Though ICP can complete a high-precision registration, it is susceptible to the initial perturbation. In recent years, variants of ICP have been proposed [5, 14, 28, 31], and they can improve the defects of ICP and enhance the registration accuracy [3]. However, these methods retain a few essential drawbacks. Firstly, they depend strongly on the initialization. Secondly, it is difficult to integrate them into the deep learning pipeline as they lack differentiability. Thirdly, explicit estimation of corresponding points leads to quadratic complexity scaling with the number of points [29], which can introduce significant computational challenges. + +Learning-based registration methods. At present, most learning-based methods are based on supervision [12, 27, 33, 40]. PointnetLK [1] is a classical correspondence-free method, which calculates global feature descriptors through PointNet and iteratively uses the Inverse Compositional formulation and Lucas & Kanade algorithm [22, 37] to minimize distance between the descriptors to achieve registration. RPM-Net [38] utilizes the differentiable Sinkhorn layer and annealing to get soft assignments of point correspondences from hybrid features learned from both spatial coordinates and local geometry. + +Recently, unsupervised point cloud registration has gained increasing attention due to its applicability in scenarios where labeled training data is scarce or unavailable. Some methods have been proposed to address this challenge and achieved promising results [2, 8, 10, 17, 18]. Feature-metric point cloud registration framework (FMR) [16] enforces the optimisation of registration by minimising a feature-metric projection error with a autoencoder-based network. CEMNet [17] treats the point cloud registration as a reinforcement learning task. However, the current methods lack a concept of calibrating inlier confidence, which poses a potential challenge for partially overlapping point cloud registration. In comparison, our method provides a reliable ICC by constructing strict constraints. + +# 3. Method + +Given two point clouds: source point cloud $\mathcal{P} = \{\mathbf{p}_i\in$ $\mathbb{R}^3\mid i = 1,\dots ,N\}$ and reference point cloud $\mathcal{Q} = \{\mathbf{q}_j\in$ $\mathbb{R}^3\mid j = 1,\dots ,M\}$ , where each point is represented as a vector of $(x,y,z)$ coordinates. Our goal is to estimate a rigid transformation $\{\mathbf{R},\mathbf{t}\}$ which accurately aligns $\mathcal{P}$ and $\mathcal{Q}$ , with a 3D rotation $\mathbf{R}\in SO(3)$ and a 3D translation $\mathbf{t}\in \mathbb{R}^3$ . + +In this paper, our method adheres to the pipeline of "pseudo correspondences-to-inlier estimation" [32, 38], which encompasses two critical tasks: reference point cloud copy generation and scoring inlier confidence. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud (Section 3.1). In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy (Section 3.2). The pipeline is illustrated in Figure 2. + +# 3.1. Finely Initial Correspondences + +To generate high quality reference point cloud copy corresponding to the source point cloud, constructing the matching map between $\mathcal{P}$ and $\mathcal{Q}$ to refine the initial correspondences is an essential prerequisite. Different from previous work [32, 38], the model input is expanded into four point clouds through a 1-NN strategy, a methodology whose advantages have been substantiated in [42]. + +Let 1-NN point cloud $\widehat{\mathcal{P}}$ and $\widehat{\mathcal{Q}}$ as the closest point for each point in $\mathcal{P}$ and $\mathcal{Q}$ , respectively. Next, we construct a local patch $\mathcal{N}_{\circ}$ with $K$ -nearest neighborhood for each point and extract local features with Dynamic Graph CNN [34] for input point cloud and 1-NN point cloud. Associated learned features are denoted as $\mathcal{F}_{\mathcal{P}}, \mathcal{F}_{\widehat{\mathcal{P}}}, \mathcal{F}_{\mathcal{Q}}$ and $\mathcal{F}_{\widehat{\mathcal{Q}}}$ , respectively. Then, we aim to learn a soft assignment matrix $\mathbf{M}(\widehat{\mathbf{M}})$ to explicitly indicate the matching between any two points of $\mathcal{P}(\widehat{\mathcal{P}})$ and $\mathcal{Q}(\widehat{\mathcal{Q}})$ . Ideally, there is only a single prominent element dominating each row and column. To further enhance $\mathbf{M}(\widehat{\mathbf{M}})$ , the widely adopted method is Sinkhorn [25], which performs the softmax operation on column-wise and row-wise iteratively and alternatively. However, the efficiency of Sinkhorn is limited by iterative strategy and extra dustbin parameters. To tackle this issue, we develop a soft assignment matrix optimization theorem to improve $\mathbf{M}(\widehat{\mathbf{M}})$ based on the following unique properties of the Gaussian distribution, which is a promotion for [44]. + +Definition 1. (Three-sigma rule). The variation or dispersion of data can be measured by the three-sigma rule, which is based on the properties of the normal distribution curve, indicating that within a dataset $99.7\%$ of data values fall within the range of three standard deviation from the mean. + +Recalling definitions of three-sigma rule, we have the following Theorem for $\mathbf{M} \in \mathbb{R}^{N \times M}$ (maybe a non-square matrix), and $\widehat{\mathbf{M}}$ follows the same principles. + +Theorem 1. Suppose the $\mathbf{M}_{i,j}$ obeys a series of Gaussian distributions, $\exists$ two constants $\epsilon, \xi$ , such that there is only a single prominent element dominating each row by three-sigma rule. + +Proof. Given $\mu_{i}$ and $\sigma_{i}$ are the mean and standard deviation of the $i$ -th row of $\mathbf{M}$ . $\mathbf{M}_{i,j}$ is normalized in row-wise and the normalized elements follow a standard normal distribution, i.e.: + +$$ +h _ {i, j} = \frac {\mathbf {M} _ {i , j} - \mu_ {i}}{\sigma_ {i}} \sim \mathcal {N} (0, 1), j = 1, \dots , M. \tag {1} +$$ + +Based on above setting, we set tuning constants $\epsilon$ and $\xi$ to $h_{i,j}$ and obtain + +$$ +\widetilde {h} _ {i, j} = \epsilon \cdot h _ {i, j} + \xi \sim \mathcal {N} (\xi , \epsilon^ {2} \mathbb {I}). \tag {2} +$$ + +![](images/973d0dd2328b0e4f860dfbf00a64b2858c9e0fe06886759ca619475a9d991843.jpg) + +![](images/c8f72432aca7dcc797ff63a72bccfcdce52dee70ab6fc357223f1443aef2dd3e.jpg) +Figure 2. The pipeline of the proposed method. We first extract local features of input point cloud and 1-NN point cloud with DGCNN. Then, we construct matching map to generate high quality reference point cloud copy $\mathcal{Q}$ for fining initial correspondences. Based on the observation that the neighborhood graph formed by inlier and its neighborhood should have geometric structure consistency between $\mathcal{P}$ and $\tilde{\mathcal{Q}}$ , we construct transformation-invariant geometric structure constraints (edge and included angle) and captures their consistency to score and calibrate the inlier confidence for each estimated correspondences between $\mathcal{P}$ and $\tilde{\mathcal{Q}}$ . Finally, the transformation is estimated with SVD method via the calibrated inlier confidence. + +For $i$ -th row of $\mathbf{H} \in \mathbb{R}^{N \times M}(\widetilde{h}_{i,j} \subset \mathbf{H})$ , the number of elements whose values are not less than a threshold $\Delta$ is calculated: + +$$ +b _ {i} = \left| \left\{\widetilde {h} _ {i, j} \mid \widetilde {h} _ {i, j} \geq \Delta , j = 1, 2, \dots , M \right\} \right|. \tag {3} +$$ + +We aim to prompt $b_{i}$ closer to 1, which means that in each row there is only a single element dominates the row. In addition, the $N$ rows of $\mathbf{H}$ can be regarded as $N$ independent and identically distributed events, thus the set $\{b_{1}, b_{2}, \ldots, b_{N}\}$ also follows a Gaussian distribution with the expectation $\mu_{b}$ and variance $\sigma_{b}$ depending on the tuning constants $\epsilon, \xi$ . Hence, by the Definition 1, we can select suitable values of $\epsilon, \xi$ to control the bound $[\mu_{b} - 3\sigma_{b}, \mu_{b} + 3\sigma_{b}]$ , which is centered around 1, such that the expectation of only a single element dominates the row can be implemented. + +Theorem 1 tells us that column-wise and row-wise iteratively and alternatively may be not essential. Operating solely on the rows can achieve the objective with higher efficiency and accuracy (Please refer to Section 4.4). + +Based on the scores in soft assignment matrix $\mathbf{H}$ and $\widehat{\mathbf{H}}$ , we construct dual neighborhood matching map by fusing and averaging matching scores of each $\mathcal{N}_{\circ}$ : + +$$ +\mathbf {G} _ {i, j} = \frac {1}{K} \sum_ {\mathbf {p} _ {i ^ {\prime}} \in \mathcal {N} _ {\mathbf {p} _ {i}}} \sum_ {\mathbf {q} _ {j ^ {\prime}} \in \mathcal {N} _ {\mathbf {q} _ {j}}} \mathbf {H} _ {i ^ {\prime}, j ^ {\prime}} + \frac {1}{K} \sum_ {\widehat {\mathbf {p}} _ {i ^ {\prime}} \in \mathcal {N} _ {\widehat {\mathbf {p}} _ {i}}} \sum_ {\widehat {\mathbf {q}} _ {j ^ {\prime}} \in \mathcal {N} _ {\widehat {\mathbf {q}} _ {j}}} \widehat {\mathbf {H}} _ {i ^ {\prime}, j ^ {\prime}}. \tag {4} +$$ + +Finally, we formulate the final matching map as: + +$$ +\mathbf {F} _ {i, j} = \operatorname {s o f t m a x} \left(- \mathbf {D} _ {i, 1} ^ {\prime}, - \mathbf {D} _ {i, 2} ^ {\prime}, \dots , - \mathbf {D} _ {i, M} ^ {\prime}\right) _ {j}, \tag {5} +$$ + +$$ +\mathbf {D} _ {i, j} ^ {\prime} = \exp (\alpha - \mathbf {G} _ {i, j}) * \left(\mathbf {D} _ {i, j} + \widehat {\mathbf {D}} _ {i, j}\right), +$$ + +where $\mathbf{D}_{i,j} = \| \mathcal{F}_{\mathbf{p}_i} - \mathcal{F}_{\mathbf{q}_j}\| _2$ and $\widehat{\mathbf{D}}_{i,j} = \| \mathcal{F}_{\widehat{\mathbf{p}}_i} - \mathcal{F}_{\widehat{\mathbf{q}}_j}\| _2$ denote the Euclidean distance between learned local features, $\mathbf{D}_{i,j}^{\prime}$ is negatively related to the matching score $\mathbf{G}_{i,j}$ . We utilize the exponential strategy to control the changing ratio, along with a hyper-parameter $\alpha$ to control the influence of the dual neighborhood matching [32]. + +Based on the high quality matching map $\mathbf{F} \in \mathbb{R}^{N \times M}$ , we generate the reference point cloud copy $\widetilde{\mathcal{Q}} \in \mathbb{R}^{N \times 3}$ including finely initial correspondences for each point $\mathbf{p}_i$ in source point cloud $\mathcal{P}$ : + +$$ +\mathcal {C} ^ {\prime} = \left\{\left(\mathbf {p} _ {i}, \widetilde {\mathbf {q}} _ {i}\right) \mid i = 1, \dots , N, \widetilde {\mathbf {q}} _ {i} \in \widetilde {\mathcal {Q}} \right\}, \tag {6} +$$ + +where + +$$ +\widetilde {\mathbf {q}} _ {i} = \sum_ {j = 1} ^ {M} \mathbf {F} _ {i, j} \cdot \mathbf {q} _ {j}. \tag {7} +$$ + +# 3.2. Inlier Confidence Calibration + +After generating reference copy $\widetilde{\mathcal{Q}}$ , we score inlier confidence for each point pair in $\mathcal{C}'$ . However, existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context, and the current guiding principle + +is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate pose a challenge in differentiating inliers, thereby elevating the risk of misinterpretation. + +In this section, we explore to extend a new definition called ICC to alleviate the above issues. Benefiting from the high quality matching map $\mathbf{F}$ in Section 3.1, we argue that the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy, i.e., if $\mathbf{p}_i$ is an inlier, its neighborhood points also tend to be the inliers and $\widetilde{\mathbf{q}}_i$ have geometric structure neighborhood consistency in the reference copy. Conversely, if $\mathbf{p}_i$ is an outlier, its neighborhood may also be the outliers and spatial structure is prone to be significantly different from the reference copy neighborhood. Based on this observation, we construct transformation-invariant geometric constraints and formulate geometric structure consistency between $\mathcal{N}_{\mathbf{p}_i}$ and $\mathcal{N}_{\widetilde{\mathbf{q}}_i}$ to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy. + +We first construct a learnable neighborhood graph by transformation-invariant geometric structure constraints of $\mathcal{N}_{\mathbf{p}_i}$ and $\mathcal{N}_{\widetilde{\mathbf{q}}_i}$ , which consists of edge representation and angle representation: + +$$ +\mathbf {e} _ {i, k} ^ {\mathbf {p}} = \mathbf {p} _ {i} - \mathbf {p} _ {k}, \mathbf {a} _ {r, s} ^ {\mathbf {p}} = \angle (\mathbf {e} _ {i, r} ^ {\mathbf {p}}, \mathbf {e} _ {i, s} ^ {\mathbf {p}}), +$$ + +$$ +\mathbf {e} _ {i, k} ^ {\widetilde {\mathbf {q}}} = \widetilde {\mathbf {q}} _ {i} - \widetilde {\mathbf {q}} _ {k}, \mathbf {a} _ {r, s} ^ {\widetilde {\mathbf {q}}} = \angle \left(\mathbf {e} _ {i, r} ^ {\widetilde {\mathbf {q}}}, \mathbf {e} _ {i, s} ^ {\widetilde {\mathbf {q}}}\right), \tag {8} +$$ + +$$ +i \neq k, k = 1, \dots , K r, s \in \{1, \dots , K \} +$$ + +where $\mathbf{p}_k$ and $\widetilde{\mathbf{q}}_k$ are the points in $\mathcal{N}_{\mathbf{p}_i}$ and $\mathcal{N}_{\widetilde{\mathbf{q}}_i}$ . Moreover, these representations express sensitive and discriminative geometric structure in the point cloud, and provide adequate geometric cues for subsequent pipeline. + +In order to better capture the neighborhood relevance and promote contextual message propagation, we utilize Multi-layer Perceptron (MLP) $f_{\theta}$ with parameters $\theta$ to fuse representations and characterize the consistency between the neighborhoods by the subtraction of the fused geometric representations: + +$$ +\mathbf {d} _ {i, k} = f _ {\theta} \left(\operatorname {c o n c a t} \left(\mathbf {e} _ {i, k} ^ {\mathbf {p}}, \mathbf {a} _ {r, s} ^ {\mathbf {p}}\right)\right) - f _ {\theta} \left(\operatorname {c o n c a t} \left(\mathbf {e} _ {i, k} ^ {\widetilde {\mathbf {q}}}, \mathbf {a} _ {r, s} ^ {\widetilde {\mathbf {q}}}\right)\right). \tag {9} +$$ + +Next, the model further adaptively learns the attention coefficients $\delta_{i,k}$ of each geometric structure consistency: + +$$ +\delta_ {i, k} = \operatorname {s o f t m a x} \left(f _ {\mu} \left(\mathbf {d} _ {i, 1}\right), f _ {\mu} \left(\mathbf {d} _ {i, 2}\right), \dots , f _ {\mu} \left(\mathbf {d} _ {i, K}\right)\right) _ {k}, \tag {10} +$$ + +where $f_{\mu}$ is another MLP with parameters $\mu$ . Then, inlier confidence $\mathbf{w}_i$ of correspondence $(\mathbf{p}_i, \widetilde{\mathbf{q}}_i)$ is calculated by aggregating the geometric structure consistency weighted: + +$$ +\mathbf {w} _ {i} = 1 - \operatorname {T a n h} \left(\left| l \left(\sum_ {k = 1} ^ {K} \delta_ {i, k} * \mathbf {d} _ {i, k}\right) \right|\right), \tag {11} +$$ + +where $l$ is a linear function. Through strict geometric constraints, the scored inlier confidence can be effectively calibrated, ensuring the sustained high credibility of $\mathbf{w}_i$ . However, some potential repetitive structures, textureless structures and other uncertain factors may still exist. In order to enhance the robustness of the proposed method and reduce the bias caused by the above issues, we select inlier correspondences from $\mathcal{C}'$ with the largest $N_c$ inlier confidence: + +$$ +\mathcal {C} _ {h} = \left\{\left(\mathbf {p} _ {h}, \widetilde {\mathbf {q}} _ {h}\right) \mid h \in \operatorname {T o p k} \left(\mathbf {w} _ {i}\right), i = 1, \dots , N _ {c} \right\}. \tag {12} +$$ + +Finally, transformation $\{\mathbf{R}_{est},\mathbf{t}_{est}\}$ can be solved in closed form using weighted SVD, which has been shown to be differentiable in [26]: + +$$ +\mathbf {R} _ {e s t}, \mathbf {t} _ {e s t} = \min _ {\mathbf {R}, \mathbf {t}} \sum_ {\left(\mathbf {p} _ {i}, \widetilde {\mathbf {q}} _ {i}\right) \in \mathcal {C} _ {h}} \mathbf {w} _ {i} \| \mathbf {R} \cdot \mathbf {p} _ {i} + \mathbf {t} - \widetilde {\mathbf {q}} _ {i} \| _ {2} ^ {2}. \tag {13} +$$ + +Besides, ICC provides useful byproduct for unsupervised learning, which can be reliable self-supervised signal. More details can be seen in the following section. + +# 3.3. Optimization + +In this section, we conduct four loss functions for model optimization. Moreover, the proposed model is trained in an unsupervised manner instead of using the ground-truth transformations. + +Global Consistency Loss. We investigate the global consistency loss between the final transformed source point cloud $\mathcal{P}'$ and the reference point cloud $\mathcal{Q}$ . Specifically, the Huber function is utilized to assemble the global consistency loss, which is defined as follow: + +$$ +\begin{array}{l} \mathcal {L} _ {g c} = \sum_ {\mathbf {p} ^ {\prime} \in \mathcal {P} ^ {\prime}} H _ {\beta} \left(\min _ {\mathbf {q} \in \mathcal {Q}} \| \mathbf {p} ^ {\prime} - \mathbf {q} \| _ {2} ^ {2}\right) \tag {14} \\ + \sum_ {\mathbf {q} \in \mathcal {Q}} H _ {\beta} \left(\min _ {\mathbf {p} ^ {\prime} \in \mathcal {P} ^ {\prime}} \| \mathbf {q} - \mathbf {p} ^ {\prime} \| _ {2} ^ {2}\right). \\ \end{array} +$$ + +However, relying solely on global consistency loss is detrimental to the accuracy and reliability of our model. Since the model may still potentially converge to sub-optimization due to the existing outliers, leading massive potential information of point cloud is wasted. Hence, it is critical to mine the potential self-supervised signals in the point cloud and construct loss functions based on other existing elements. + +Dual Neighborhood Consistency Loss. Based on reliable inlier correspondences in Equation 12, we denote the inliers set of the source and its reference point cloud copy as $\mathbf{X} \in \mathbb{R}^{N_c \times 3}$ and $\mathbf{Y} \in \mathbb{R}^{N_c \times 3}$ , respectively. We utilize the neighborhood between the inliers to construct consistency objective, which aims to minimize the registration error between each neighborhood $\mathcal{N}_{\mathbf{x}_i}$ and $\mathcal{N}_{\mathbf{y}_i}$ : + +$$ +\mathcal {L} _ {i n} = \sum_ {\mathbf {x} _ {i} \in \mathbf {X}, \mathbf {y} _ {i} \in \mathbf {Y}} \sum_ {\mathbf {p} _ {j} \in \mathcal {N} _ {\mathbf {x} _ {i}}, \widetilde {\mathbf {q}} _ {j} \in \mathcal {N} _ {\mathbf {y} _ {i}}} \left\| \mathbf {R} _ {e s t} \mathbf {p} _ {j} + \mathbf {t} _ {e s t} - \widetilde {\mathbf {q}} _ {j} \right\| _ {2}, \tag {15} +$$ + +where $\mathcal{N}_{\mathbf{x}_i}$ is transformed by $\mathcal{N}_{\mathbf{y}_i}$ . + +Geometric Structure Consistency Loss. The geometric signal buried in point cloud is readily ignored, which hinders ICC. To address this issue, we design a geometric neighborhood loss with the reliable geometric self-supervised signal proposed in Section 3.2: + +$$ +\begin{array}{l} \mathcal {L} _ {g s} = \sum_ {\mathbf {x} _ {i} \in \mathbf {X}, \mathbf {y} _ {i} \in \mathbf {Y}} \sum_ {\mathbf {p} _ {j} \in \mathcal {N} _ {\mathbf {x} _ {i}}, \widetilde {\mathbf {q}} _ {j} \in \mathcal {N} _ {\mathbf {y} _ {i}}} \left\| \mathbf {e} _ {i, j} ^ {\mathbf {p}} - \mathbf {e} _ {i, j} ^ {\widetilde {\mathbf {q}}} \right\| _ {2} + \\ \sum_ {\mathbf {x} _ {i} \in \mathbf {X}, \mathbf {y} _ {i} \in \mathbf {Y}} \sum_ {\mathbf {p} _ {j} \in \mathcal {N} _ {\mathbf {x} _ {i}}, \widetilde {\mathbf {q}} _ {j} \in \mathcal {N} _ {\mathbf {y} _ {i}}} \left\| \mathbf {a} _ {r, s} ^ {\mathbf {p}} - \mathbf {a} _ {r, s} ^ {\widetilde {\mathbf {q}}} \right\| _ {2}, \tag {16} \\ \end{array} +$$ + +where $\mathbf{a}_{r,s}^{\mathbf{p}}$ and $\mathbf{a}_{r,s}^{\widetilde{\mathbf{q}}}$ is calculated by $\mathbf{e}_{i,j}^{\mathbf{p}}$ and $\mathbf{e}_{i,j}^{\widetilde{\mathbf{q}}}$ shown in Equation 8. + +Spatial Consistency Loss. We further explore to eliminate the spatial difference between the estimated correspondence and the real correspondence for each selected inlier $\mathbf{x}_i$ and utilize spatial consistency loss with cross-entropy to sharpen matching map $\mathbf{G}$ : + +$$ +\mathcal {L} _ {s c} = - \frac {1}{| \mathbf {X} |} \sum_ {\mathbf {x} _ {i} \in \mathbf {X}} \sum_ {j = 1} ^ {M} [ [ j = \arg \max _ {j ^ {\prime}} \mathbf {G} _ {i, j ^ {\prime}} ] ] \log \mathbf {G} _ {i, j}, \tag {17} +$$ + +where $\llbracket \cdot \rrbracket$ is the Iverson bracket. Spatial consistency loss encourages to improve the matching probability and thus the estimated correspondence point in reference copy tends to have an stable position. + +Overall Loss. Since our work utilizes an iterative scheme, we compute the loss at each iteration $N_{l}$ and have the weighted sum loss: + +$$ +\mathcal {L} = \sum_ {l = 1} ^ {N _ {l}} \left(\mathcal {L} _ {g c} ^ {l} + \gamma \mathcal {L} _ {i n} ^ {l} + \rho \mathcal {L} _ {g s} ^ {l} + \lambda \mathcal {L} _ {s c} ^ {l}\right), \tag {18} +$$ + +where $\gamma$ , $\rho$ and $\lambda$ are trade-off parameters to control corresponding loss function. + +# 4. Experiments + +# 4.1. Experimental Setup + +We compare our method to traditional methods and recent state of the arts learning-based methods. The traditional methods include ICP [4], FGR [16] and FPFH + RANSAC [13]. The recent learning based methods include IDAM [21], FMR [16], RPMNet [38], CEMNet [17], REGTR [39], GeoTransformer [27] and RIE [32]. For consistency with previous work, we measure Mean Isotropic Error (MIE) and Mean Absolute Error (MAE). + +# 4.2. ModelNet40 Dataset and Evaluation + +Noted that, to simulate partial-to-partial registration, the reference point cloud $\mathcal{Q}$ and the source point cloud $\mathcal{P}$ are cropped respectively, and retain $70\%$ of the points. + +
MethodMAE(R)MAE(t)MIE(R)MIE(t)
ICP [4] (○)3.43390.01146.77060.0227
FGR [16] (○)0.59720.00211.15630.0041
FPFH+RANSAC [13] (○)0.70310.00251.27720.0050
IDAM [21] (▲)0.42430.00200.81700.0040
RPMNet [38] (▲)0.00510.00000.02010.0000
FMR [16] (▲)3.64970.01017.28100.0200
REGTR [39] (▲)0.18940.00150.34930.0030
GeoTransformer [27] (▲)0.59700.00570.90100.0102
CEMNet [17] (△)0.13850.00010.24890.0002
RIE [32] (△)0.00330.00000.02100.0000
Ours (△)0.00120.00000.01920.0000
+ +Table 1. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. $(\bigcirc)$ , $(\triangle)$ and $(\triangle)$ denote the traditional, supervised and unsupervised methods, respectively. + +Unseen Objects. Our models are trained and tested on datasets comprising of samples belonging to the same categories, and both the training and test sets are obtained without any preprocessing or manipulation. We apply a random transformation on the reference point cloud $\mathcal{Q}$ to generate corresponding source point cloud $\mathcal{P}$ . Table 1 shows quantitative results of the various algorithms under current experimental settings. The proposed method substantially outperforms all baseline in all metrics. We can observe our method can even outperform the supervised IDAM, RPMNet, FMR, REGTR and GeoTransformer by a large margin. Benefiting from ICC, our method attains highly accurate registration and improves the registration accuracy by an order of magnitude. In order to show the effect of our proposed approach clearly, a qualitative comparison of the registration results can be found in Figure 3. Our method ensures minimal impact on changing of the shape, and achieves the best performance even on asymmetric shape. + +Unseen Categories. To verify the generalization ability on categories, we train the models on the first 20 categories and test on the remaining unseen categories. The results are summarized in Table 2. We can observe that the majority of baseline consistently exhibit lower performance on the unseen categories, especially learning-based methods. In contrast, traditional algorithms are less susceptible to this issue due to the insensitivity of handcrafted methods to shape variance [36]. Our registration process remains highly precise, achieving the lowest error across all metrics, while also maintaining acceptable levels of fluctuation. + +Gaussian Noise. In order to assess performance in the presence of noise, which is commonly encountered in real-world point clouds, we train our model on noise-free data and then evaluate all baselines using a test set featuring Gaussian noise. We randomly and independently generate noisy points to introduce noise into in source point cloud and reference point cloud by sampling from $\mathcal{N}(0,0.5)$ and + +![](images/968c03ec93627a35b7b0d1c652cc6a1ad892e8cf95a62a97aa3ef3052beddb23.jpg) +Figure 3. Qualitative comparison of the registration results on unseen objects data (blue: source point cloud, yellow: reference point cloud, green: transformed source point cloud). + +clipped to $[-1.0, 1.0]$ . This experiment is significantly challenging, as constructing matching map and ICC become much more difficult. As shown in Table 2, our method outperforms other baselines. The experimental results demonstrate that our method is robust to the noise. In addition, experimental results indirectly confirms the generality and high adaptability of ICC in point cloud registration with partially overlapping. + +
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Unseen Categories
ICP [4] (○)3.60990.01167.05560.0228
FGR [16] (○)0.45790.00160.84420.0032
FPFH+RANSAC [13] (○)0.44270.00210.94470.0043
IDAM [21] (▲)0.48090.00280.91570.0055
RPMNet [38] (▲)0.00640.00010.02070.0001
FMR [16] (▲)3.85940.01147.64500.0225
CEMNet[17] (△)0.08040.00020.14050.0003
RIE [32] (△)0.00590.00000.02280.0001
Ours (△)0.00220.00000.01890.0000
Gaussian Noise
ICP [4] (○)4.64410.01679.21940.0333
FGR [16] (○)1.06760.00362.00380.0072
FPFH+RANSAC [13] (○)1.43160.00612.53450.0120
IDAM [21] (▲)2.30760.01244.53320.0246
RPMNet [38] (▲)1.58900.01752.98300.0378
FMR [16] (▲)18.03550.053635.79860.1063
CEMNet[17] (△)10.70260.039321.18360.0781
RIE [32] (△)0.04310.00040.07760.0008
Ours (△)0.00880.00010.02450.0002
+ +Table 2. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. $(\bigcirc)$ , $(\triangle)$ and $(\bigtriangleup)$ denote the traditional, supervised and unsupervised methods, respectively. + +# 4.3. Other Datasets and Evaluation + +We further conduct comparison evaluation on other datasets: 7Scenes and Augmented ICL-NUIM. We sample the reference point clouds to 2,048 points and randomly sample three Euler angle rotations within $[0^{\circ}, 45^{\circ}]$ and translations within $[-0.5, 0.5]$ on each axis as the rigid transformation to obtain source point clouds, then down-sample the point clouds to 1,536 points to generate the partial data. As demonstrated in Table 4, our method exhibits extremely higher registration precision on all criteria on Augmneted ICL-NUIM and 7Scenes, especially the rotation error. We can summarize our method has best performance and is comfortable with real-world dataset. + +# 4.4. Ablation Study and Analysis + +Soft Assignment Matrix Optimization Theorem. We compare the developed theorem with the Sinkhorn, and evaluate precision and efficiency against Sinkhorn, which iterate 1 (Sinkhorn-1) and 5 (Sinkhorn-5) times. As shown in Figure 4, we can observe that under the same tolerant error, the developed theorem demonstrates superior performance, especially the optimization for rotation. Additionally, the proposed theorem improves the efficiency up to nearly $2 \times$ compared to Sinkhorn-1 and nearly up to $5 \times$ compared to Sinkhorn-5. It needs to be emphasized once again that the proposed theorem has a smaller computational complexity than Sinkhorn as shown in Table 5, since this theorem does not normalize the rows and columns repeatedly, and only operates on the rows. + +Geometric Constraints. To investigate whether geometric constraints are meaningful to ICC, we conduct an experiment to verify our motivation. Experimental results are shown in the first row of Table 3. Compared to constraints-free, which score inlier confidence by simple coordinates, geometric constraints effectively generate more convincing + +
GeometricConstraints\( \mathcal{L}_{gc} \)\( \mathcal{L}_{in} \)\( \mathcal{L}_{gs} \)\( \mathcal{L}_{sc} \)ModelNet407Scenes
MAE(R)MAE(t)MIE(R)MIE(R)MAE(R)MAE(t)MIE(R)MIE(R)
✓✓N/A✓1.01230.01611.83980.03502.22380.01484.36980.0286
✓✓✓✓0.39980.00610.76650.01290.00420.00000.02170.0001
✓✓✓✓22.51990.134042.44280.27103.30870.03405.87700.0657
✓✓✓✓0.00700.00010.02350.00020.00370.00000.01860.0001
✓✓✓✓0.11250.00140.018620.00300.01420.00010.03450.0003
✓✓✓✓✓0.00120.00000.01920.00000.00330.00000.01810.0001
+ +Table 3. Ablation study of different components. ${\mathcal{L}}_{gc},{\mathcal{L}}_{in},{\mathcal{L}}_{gs}$ and ${\mathcal{L}}_{sc}$ : Each Loss Function in Equation 18. + +
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Augmented ICL-NUIM
ICP [4] (○)2.40220.06994.48320.1410
FGR [16] (○)2.24770.08084.18500.1573
FPFH+RANSAC [13] (○)1.23490.04292.31670.0839
IDAM [21] (▲)4.41530.13858.61780.2756
RPMNet [38] (▲)0.32670.01250.62770.0246
FMR [16] (▲)1.10850.03982.13230.0786
CEMNet[17] (△)0.23740.00050.39870.0010
RIE [32] (△)0.04920.00230.08970.0049
Ours (△)0.00480.00020.01990.0003
7Scenes
ICP [4] (○)6.00910.013013.04840.0260
FGR [16] (○)0.09190.00040.17050.0008
FPFH+RANSAC [13] (○)1.23250.00622.18750.0124
IDAM [21] (▲)5.67270.030311.59490.0629
RPMNet [38] (▲)0.38850.00210.76490.0042
FMR [16] (▲)2.54380.00724.90890.0150
CEMNet[17] (△)0.05590.00010.07720.0003
RIE [32] (△)0.01210.00010.02990.0001
Ours (△)0.00330.00000.01810.0001
+ +Table 4. Evaluation results on Augmented ICL-NUIM and 7Scenes. Bold indicates the best performance and underline indicates the second-best performance. $(\bigcirc)$ , $(\triangle)$ and $(\bigtriangleup)$ denote the traditional, supervised and unsupervised methods, respectively. + +
Complexity
Sinkhorn with dustbin parametersO((N+1) × (M+1))
Sinkhorn with iterate G timesO(G × (N × M))
Proposed theoremO(N)
+ +Table 5. Computational complexity of Sinkhorn and the proposed theorem comparison. + +scoring mechanism. Noted that geometric constraints provide a self-supervised signal for our model, and $\mathcal{L}_{gs}$ is designed based on this signal. Therefore, when geometric constraints is deleted, the loss function $\mathcal{L}_{gs}$ should not participate in optimization. + +Loss Function. We evaluate the performance of the model + +![](images/3bb17ae991e3f7f89580c394126b39631bfc60df0b93db26e064b66c74347dc5.jpg) +Figure 4. Comparisons between the proposed theorem and the Sinkhorn in terms of precision and efficiency. + +with different loss functions. Comprehensively, lacking any part of $\mathcal{L}$ will degrade the performance of the model. Comparing $2\sim 5$ rows in Table 3, the error observed in the third row is extremely large, primarily due to the absence of any optimization objective related to transformation in the loss function. This significantly reduces the registration performance of the model. In particular, this ablation study confirms the byproduct of ICC $\mathcal{L}_{gs}$ can provide reliable and effective self-supervised signal for model optimization. + +# 5. Conclusion + +In this paper, we explore to extend a new definition called inlier confidence calibration (ICC). Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration accuracy. Thus, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed methods. In the future, we would like to extend our method to crossmodality (e.g., 2D-3D) registration with richer applications. + +Acknowledgement. This work is supported by the National Natural Science Foundation of China (62036006, 62276200), the CAAI-Huawei MINDSPORE Academic Open Fund, the Key Research and Development Project of Shaanxi Province (2022QCY-LL-35), the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University. + +# References + +[1] Yasuhiro Aoki, Hunter Goforth, Rangaprasad Arun Srivatsan, and Simon Lucey. Pointnetlk: Robust & efficient point cloud registration using pointnet. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7163-7172, 2019. 3 +[2] Dominik Bauer, Timothy Patten, and Markus Vincze. Reagent: Point cloud registration using imitation and reinforcement learning. 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Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration performance. In this paper, we explore to extend a new definition called inlier confidence calibration (ICC) to alleviate the above issues. Firstly, we provide finely initial correspondences for ICC in order to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. 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Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 659, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 659, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 659, + 287, + 696 + ], + "type": "text", + "content": "With the rapid development of 3D data acquisition technology, point cloud data collected by LiDAR [45], Structured Light Sensors [30], and Stereo Cameras [9] has become" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 322, + 270, + 533, + 399 + ], + "blocks": [ + { + "bbox": [ + 322, + 270, + 533, + 399 + ], + "lines": [ + { + "bbox": [ + 322, + 270, + 533, + 399 + ], + "spans": [ + { + "bbox": [ + 322, + 270, + 533, + 399 + ], + "type": "image", + "image_path": "5c62cc448034e57fa575244f7733f4424694409f48c961bb17e5546ef21be8b2.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 420, + 403, + 432, + 411 + ], + "lines": [ + { + "bbox": [ + 420, + 403, + 432, + 411 + ], + "spans": [ + { + "bbox": [ + 420, + 403, + 432, + 411 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 320, + 414, + 541, + 540 + ], + "blocks": [ + { + "bbox": [ + 320, + 414, + 541, + 540 + ], + "lines": [ + { + "bbox": [ + 320, + 414, + 541, + 540 + ], + "spans": [ + { + "bbox": [ + 320, + 414, + 541, + 540 + ], + "type": "image", + "image_path": "a0dd6e5c6fa1805b735b46ce8e094eb65343ffc54896fe8fa40bc03503bf2d8a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 543, + 432, + 552 + ], + "lines": [ + { + "bbox": [ + 421, + 543, + 432, + 552 + ], + "spans": [ + { + "bbox": [ + 421, + 543, + 432, + 552 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 562, + 547, + 618 + ], + "lines": [ + { + "bbox": [ + 305, + 562, + 547, + 618 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 547, + 618 + ], + "type": "text", + "content": "Figure 1. A toy example of proposed geometric constraints for inlier confidence calibration. The indicative center points pair is inlier pair in reality. (a) shows the situation without constraints. (b) demonstrates the situation with reliable geometric constraints. The experimental results are derived from ablation study." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 628, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 628, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 628, + 546, + 700 + ], + "type": "text", + "content": "ubiquitous in various 3D computer vision and robotics applications [6, 20], such as autopilot [15], surgical navigation [23], and simultaneous localization and mapping [11]. In such applications, rigid body point cloud registration plays an essential role, which aims to find a rigid transformation to align one point cloud to another." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "The recent advances have been dominated by learning-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5312" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 371 + ], + "type": "text", + "content": "based methods. Most of these methods focus on solving the point cloud registration task in a supervised manner [16, 21, 27, 33, 38-41]. They require labeled data as the supervision signal to learn effective representations. In addition, obtaining labeled data is cumbersome and time-consuming, which may hinder applications in real world. To overcome this limitation, unsupervised point cloud registration is gradually garnering the interest of researchers [17, 24, 32]. However, in partially overlapping scenarios, learning-based methods must achieve robust inlier estimation, as inlier estimation serves as a fundamental source for identifying overlapping regions and predicting transformation. Existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context. Meanwhile, the current guiding principle is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate present among point clouds pose a considerable challenge in differentiating inliers, thereby elevating the risk of misinterpretation. Thus, a crucial question remains to be addressed in order to make point cloud registration a success: How to alleviate the bias in inlier confidence caused by massive coordinate differences?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 375, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 289, + 555 + ], + "type": "text", + "content": "We provide answer to this question in Figure 1. Our key insight is that simple coordinates cannot provide strong evidence for scoring inlier confidence. In Figure 1a, the indicative center points pair is very difficult to distinguish because of coordinate differences, which diminish the confidence of this points pair and further classify it as an outlier pair. To alleviate this issue, we construct transformation-invariant geometric constraints for center points pair in Figure 1b. This strategy is based on two intuitive observations: (i) a rigorously defined property of rigid transformation, i.e., it does not change the length of a vector and an angle between two vectors (isometric isomorphism). (ii) the neighborhood patch fromed by inlier and its neighborhood should have consistency. Under strict constraints, the inlier confidence in Figure 1a can be effectively calibrate." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "type": "text", + "content": "Motivated by the discussion above, in this paper, we explore to extend a new definition called inlier confidence calibration (ICC) for point cloud registration. Note that our method adheres to the pipeline of \"pseudo correspondences-to-inlier estimation\" [32, 38], which encompasses critical task reference point cloud copy generation and scoring inlier confidence, respectively. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud. In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn [25]. This the" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 287 + ], + "type": "text", + "content": "orem is founded on the unique properties of the Gaussian distribution and cancels independent row and column normalization iteratively, along with the extra dustbin parameters in Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy. Finally, transformation are further calculated by the weighted SVD algorithm with the estimated correspondences and the calibrated inlier confidence. Our model is trained in an unsupervised manner, and extensive experiments on the synthetic datasets ModelNet40 [35], Augmented ICL-NUIM [7] and real-world dataset 7Scenes [43] demonstrate our model achieves competitive performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 288, + 511, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 288, + 511, + 299 + ], + "spans": [ + { + "bbox": [ + 317, + 288, + 511, + 299 + ], + "type": "text", + "content": "To summarize, our contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 300, + 545, + 431 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 300, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 300, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 545, + 334 + ], + "type": "text", + "content": "- An effective ICC method for point cloud registration by constructing transformation-invariant geometric constraints." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 335, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 545, + 395 + ], + "type": "text", + "content": "- A soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn, which can provide finely initial correspondences for ICC in order to generate the reference point cloud copy corresponding to the source point cloud." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 396, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 431 + ], + "type": "text", + "content": "- Under the unsupervised setting, the constructed geometric constraints provide self-supervised signal and optimization objective for model training." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 442, + 398, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 398, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 398, + 455 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "Traditional point cloud registration methods. Most traditional methods require a good initial transformation and converge to the local minima near the initialization point. One of the most profound methods is the Iterative Closest Point (ICP) algorithm [4], which begins with an initial transformation and iteratively alternates between solving two trivial subproblems: finding the closest points as correspondence under current transformation, and computing optimal transformation by SVD [19] based on identified correspondences. Though ICP can complete a high-precision registration, it is susceptible to the initial perturbation. In recent years, variants of ICP have been proposed [5, 14, 28, 31], and they can improve the defects of ICP and enhance the registration accuracy [3]. However, these methods retain a few essential drawbacks. Firstly, they depend strongly on the initialization. Secondly, it is difficult to integrate them into the deep learning pipeline as they lack differentiability. Thirdly, explicit estimation of corresponding points leads to quadratic complexity scaling with the number of points [29], which can introduce significant computational challenges." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5313" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "Learning-based registration methods. At present, most learning-based methods are based on supervision [12, 27, 33, 40]. PointnetLK [1] is a classical correspondence-free method, which calculates global feature descriptors through PointNet and iteratively uses the Inverse Compositional formulation and Lucas & Kanade algorithm [22, 37] to minimize distance between the descriptors to achieve registration. RPM-Net [38] utilizes the differentiable Sinkhorn layer and annealing to get soft assignments of point correspondences from hybrid features learned from both spatial coordinates and local geometry." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 373 + ], + "type": "text", + "content": "Recently, unsupervised point cloud registration has gained increasing attention due to its applicability in scenarios where labeled training data is scarce or unavailable. Some methods have been proposed to address this challenge and achieved promising results [2, 8, 10, 17, 18]. Feature-metric point cloud registration framework (FMR) [16] enforces the optimisation of registration by minimising a feature-metric projection error with a autoencoder-based network. CEMNet [17] treats the point cloud registration as a reinforcement learning task. However, the current methods lack a concept of calibrating inlier confidence, which poses a potential challenge for partially overlapping point cloud registration. In comparison, our method provides a reliable ICC by constructing strict constraints." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 380, + 104, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 104, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 104, + 393 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": "Given two point clouds: source point cloud " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{\\mathbf{p}_i\\in" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3\\mid i = 1,\\dots ,N\\}" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": " and reference point cloud " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = \\{\\mathbf{q}_j\\in" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3\\mid j = 1,\\dots ,M\\}" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": ", where each point is represented as a vector of " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": " coordinates. Our goal is to estimate a rigid transformation " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R},\\mathbf{t}\\}" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": " which accurately aligns " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": ", with a 3D rotation " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{R}\\in SO(3)" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": " and a 3D translation " + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{t}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": "In this paper, our method adheres to the pipeline of \"pseudo correspondences-to-inlier estimation\" [32, 38], which encompasses two critical tasks: reference point cloud copy generation and scoring inlier confidence. A prerequisite for the success of ICC is the provision of high quality reference copy. Firstly, we provide finely initial correspondences to generate high quality reference point cloud copy corresponding to the source point cloud (Section 3.1). In particular, we develop a soft assignment matrix optimization theorem that offers faster speed and greater precision compared to Sinkhorn. Benefiting from the high quality reference copy, we argue the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy. Based on this insight, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence for each point pair between source point cloud and its reference copy (Section 3.2). The pipeline is illustrated in Figure 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 473, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 473, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 473, + 85 + ], + "type": "text", + "content": "3.1. Finely Initial Correspondences" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "type": "text", + "content": "To generate high quality reference point cloud copy corresponding to the source point cloud, constructing the matching map between " + }, + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 90, + 545, + 174 + ], + "type": "text", + "content": " to refine the initial correspondences is an essential prerequisite. Different from previous work [32, 38], the model input is expanded into four point clouds through a 1-NN strategy, a methodology whose advantages have been substantiated in [42]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": "Let 1-NN point cloud " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{Q}}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " as the closest point for each point in " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": ", respectively. Next, we construct a local patch " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\circ}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": "-nearest neighborhood for each point and extract local features with Dynamic Graph CNN [34] for input point cloud and 1-NN point cloud. Associated learned features are denoted as " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathcal{P}}, \\mathcal{F}_{\\widehat{\\mathcal{P}}}, \\mathcal{F}_{\\mathcal{Q}}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\widehat{\\mathcal{Q}}}" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": ", respectively. Then, we aim to learn a soft assignment matrix " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{M}(\\widehat{\\mathbf{M}})" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " to explicitly indicate the matching between any two points of " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathcal{P}})" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(\\widehat{\\mathcal{Q}})" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": ". Ideally, there is only a single prominent element dominating each row and column. To further enhance " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{M}(\\widehat{\\mathbf{M}})" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": ", the widely adopted method is Sinkhorn [25], which performs the softmax operation on column-wise and row-wise iteratively and alternatively. However, the efficiency of Sinkhorn is limited by iterative strategy and extra dustbin parameters. To tackle this issue, we develop a soft assignment matrix optimization theorem to improve " + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{M}(\\widehat{\\mathbf{M}})" + }, + { + "bbox": [ + 304, + 174, + 546, + 405 + ], + "type": "text", + "content": " based on the following unique properties of the Gaussian distribution, which is a promotion for [44]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 411, + 547, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 473 + ], + "type": "text", + "content": "Definition 1. (Three-sigma rule). The variation or dispersion of data can be measured by the three-sigma rule, which is based on the properties of the normal distribution curve, indicating that within a dataset " + }, + { + "bbox": [ + 304, + 411, + 547, + 473 + ], + "type": "inline_equation", + "content": "99.7\\%" + }, + { + "bbox": [ + 304, + 411, + 547, + 473 + ], + "type": "text", + "content": " of data values fall within the range of three standard deviation from the mean." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "type": "text", + "content": "Recalling definitions of three-sigma rule, we have the following Theorem for " + }, + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{N \\times M}" + }, + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "type": "text", + "content": " (maybe a non-square matrix), and " + }, + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 482, + 545, + 520 + ], + "type": "text", + "content": " follows the same principles." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "text", + "content": "Theorem 1. Suppose the " + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{i,j}" + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "text", + "content": " obeys a series of Gaussian distributions, " + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\exists" + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "text", + "content": " two constants " + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\epsilon, \\xi" + }, + { + "bbox": [ + 304, + 526, + 545, + 574 + ], + "type": "text", + "content": ", such that there is only a single prominent element dominating each row by three-sigma rule." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "content": "Proof. Given " + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "content": " are the mean and standard deviation of the " + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "content": "-th row of " + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{i,j}" + }, + { + "bbox": [ + 304, + 581, + 545, + 628 + ], + "type": "text", + "content": " is normalized in row-wise and the normalized elements follow a standard normal distribution, i.e.:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 332, + 635, + 545, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 635, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 332, + 635, + 545, + 661 + ], + "type": "interline_equation", + "content": "h _ {i, j} = \\frac {\\mathbf {M} _ {i , j} - \\mu_ {i}}{\\sigma_ {i}} \\sim \\mathcal {N} (0, 1), j = 1, \\dots , M. \\tag {1}", + "image_path": "2561f4b75739e2b35b15ea6cd866613e7d8b2cfc56e7a75655d3c5eb51e02925.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "text", + "content": "Based on above setting, we set tuning constants " + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "inline_equation", + "content": "h_{i,j}" + }, + { + "bbox": [ + 304, + 667, + 545, + 692 + ], + "type": "text", + "content": " and obtain" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 699, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 699, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 359, + 699, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\widetilde {h} _ {i, j} = \\epsilon \\cdot h _ {i, j} + \\xi \\sim \\mathcal {N} (\\xi , \\epsilon^ {2} \\mathbb {I}). \\tag {2}", + "image_path": "d9787be4d7c08efcd1f9f46ddc73e9d3b93784e2d32424b00ced2912ffc62fbc.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5314" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 77, + 545, + 186 + ], + "blocks": [ + { + "bbox": [ + 55, + 77, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 55, + 77, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 55, + 77, + 545, + 186 + ], + "type": "image", + "image_path": "973d0dd2328b0e4f860dfbf00a64b2858c9e0fe06886759ca619475a9d991843.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 187, + 541, + 293 + ], + "blocks": [ + { + "bbox": [ + 55, + 187, + 541, + 293 + ], + "lines": [ + { + "bbox": [ + 55, + 187, + 541, + 293 + ], + "spans": [ + { + "bbox": [ + 55, + 187, + 541, + 293 + ], + "type": "image", + "image_path": "c8f72432aca7dcc797ff63a72bccfcdce52dee70ab6fc357223f1443aef2dd3e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "text", + "content": "Figure 2. The pipeline of the proposed method. We first extract local features of input point cloud and 1-NN point cloud with DGCNN. Then, we construct matching map to generate high quality reference point cloud copy " + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "text", + "content": " for fining initial correspondences. Based on the observation that the neighborhood graph formed by inlier and its neighborhood should have geometric structure consistency between " + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{Q}}" + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "text", + "content": ", we construct transformation-invariant geometric structure constraints (edge and included angle) and captures their consistency to score and calibrate the inlier confidence for each estimated correspondences between " + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{Q}}" + }, + { + "bbox": [ + 46, + 303, + 546, + 369 + ], + "type": "text", + "content": ". Finally, the transformation is estimated with SVD method via the calibrated inlier confidence." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "text", + "content": "-th row of " + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{H} \\in \\mathbb{R}^{N \\times M}(\\widetilde{h}_{i,j} \\subset \\mathbf{H})" + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "text", + "content": ", the number of elements whose values are not less than a threshold " + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 46, + 375, + 288, + 411 + ], + "type": "text", + "content": " is calculated:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 80, + 419, + 287, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 419, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 80, + 419, + 287, + 435 + ], + "type": "interline_equation", + "content": "b _ {i} = \\left| \\left\\{\\widetilde {h} _ {i, j} \\mid \\widetilde {h} _ {i, j} \\geq \\Delta , j = 1, 2, \\dots , M \\right\\} \\right|. \\tag {3}", + "image_path": "d59c517ea71486500ae9a04ff2a8bdbcbb499d0a1fba02fa2a0c7e5f66ba65f4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": "We aim to prompt " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " closer to 1, which means that in each row there is only a single element dominates the row. In addition, the " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " rows of " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " can be regarded as " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " independent and identically distributed events, thus the set " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\{b_{1}, b_{2}, \\ldots, b_{N}\\}" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " also follows a Gaussian distribution with the expectation " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mu_{b}" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\sigma_{b}" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " depending on the tuning constants " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\epsilon, \\xi" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": ". Hence, by the Definition 1, we can select suitable values of " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\epsilon, \\xi" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": " to control the bound " + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "inline_equation", + "content": "[\\mu_{b} - 3\\sigma_{b}, \\mu_{b} + 3\\sigma_{b}]" + }, + { + "bbox": [ + 46, + 444, + 287, + 574 + ], + "type": "text", + "content": ", which is centered around 1, such that the expectation of only a single element dominates the row can be implemented." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 578, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 625 + ], + "type": "text", + "content": "Theorem 1 tells us that column-wise and row-wise iteratively and alternatively may be not essential. Operating solely on the rows can achieve the objective with higher efficiency and accuracy (Please refer to Section 4.4)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "text", + "content": "Based on the scores in soft assignment matrix " + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{H}}" + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "text", + "content": ", we construct dual neighborhood matching map by fusing and averaging matching scores of each " + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\circ}" + }, + { + "bbox": [ + 46, + 625, + 287, + 662 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 670, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathbf {G} _ {i, j} = \\frac {1}{K} \\sum_ {\\mathbf {p} _ {i ^ {\\prime}} \\in \\mathcal {N} _ {\\mathbf {p} _ {i}}} \\sum_ {\\mathbf {q} _ {j ^ {\\prime}} \\in \\mathcal {N} _ {\\mathbf {q} _ {j}}} \\mathbf {H} _ {i ^ {\\prime}, j ^ {\\prime}} + \\frac {1}{K} \\sum_ {\\widehat {\\mathbf {p}} _ {i ^ {\\prime}} \\in \\mathcal {N} _ {\\widehat {\\mathbf {p}} _ {i}}} \\sum_ {\\widehat {\\mathbf {q}} _ {j ^ {\\prime}} \\in \\mathcal {N} _ {\\widehat {\\mathbf {q}} _ {j}}} \\widehat {\\mathbf {H}} _ {i ^ {\\prime}, j ^ {\\prime}}. \\tag {4}", + "image_path": "def14f0cff1a59702a2ef3d0be3f7634af3832a2259d14fe71b4639e9e351fa6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 376, + 503, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 503, + 389 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 503, + 389 + ], + "type": "text", + "content": "Finally, we formulate the final matching map as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 330, + 392, + 544, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 392, + 544, + 417 + ], + "spans": [ + { + "bbox": [ + 330, + 392, + 544, + 417 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {i, j} = \\operatorname {s o f t m a x} \\left(- \\mathbf {D} _ {i, 1} ^ {\\prime}, - \\mathbf {D} _ {i, 2} ^ {\\prime}, \\dots , - \\mathbf {D} _ {i, M} ^ {\\prime}\\right) _ {j}, \\tag {5}", + "image_path": "4a9095f7f4d2ce4b14b128b60fac8adc090cc36f1cd489183b3125e8dc2e5cbb.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 330, + 409, + 496, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 409, + 496, + 432 + ], + "spans": [ + { + "bbox": [ + 330, + 409, + 496, + 432 + ], + "type": "interline_equation", + "content": "\\mathbf {D} _ {i, j} ^ {\\prime} = \\exp (\\alpha - \\mathbf {G} _ {i, j}) * \\left(\\mathbf {D} _ {i, j} + \\widehat {\\mathbf {D}} _ {i, j}\\right),", + "image_path": "7d35d0f76ee93c45cbae83ef3f2abae1ffa5b461344b4b118f9d6a37630fd0b0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{i,j} = \\| \\mathcal{F}_{\\mathbf{p}_i} - \\mathcal{F}_{\\mathbf{q}_j}\\| _2" + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{D}}_{i,j} = \\| \\mathcal{F}_{\\widehat{\\mathbf{p}}_i} - \\mathcal{F}_{\\widehat{\\mathbf{q}}_j}\\| _2" + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": " denote the Euclidean distance between learned local features, " + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_{i,j}^{\\prime}" + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": " is negatively related to the matching score " + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{i,j}" + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": ". We utilize the exponential strategy to control the changing ratio, along with a hyper-parameter " + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": " to control the influence of the dual neighborhood matching [32]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "text", + "content": "Based on the high quality matching map " + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{N \\times M}" + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "text", + "content": ", we generate the reference point cloud copy " + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{Q}} \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "text", + "content": " including finely initial correspondences for each point " + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "text", + "content": " in source point cloud " + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 510, + 545, + 558 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 341, + 563, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 563, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 341, + 563, + 545, + 583 + ], + "type": "interline_equation", + "content": "\\mathcal {C} ^ {\\prime} = \\left\\{\\left(\\mathbf {p} _ {i}, \\widetilde {\\mathbf {q}} _ {i}\\right) \\mid i = 1, \\dots , N, \\widetilde {\\mathbf {q}} _ {i} \\in \\widetilde {\\mathcal {Q}} \\right\\}, \\tag {6}", + "image_path": "ac3a132fec70158a51307393cc13b992ea9cf4252dd9edef15a5384a44d28bff.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 588, + 333, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 588, + 333, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 588, + 333, + 597 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 386, + 596, + 545, + 630 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 596, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 386, + 596, + 545, + 630 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {q}} _ {i} = \\sum_ {j = 1} ^ {M} \\mathbf {F} _ {i, j} \\cdot \\mathbf {q} _ {j}. \\tag {7}", + "image_path": "7b260fa03328e715d384bbd36d15b11ba1969b2b1feb06d932d3f64a23c6e64d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 635, + 467, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 467, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 467, + 646 + ], + "type": "text", + "content": "3.2. Inlier Confidence Calibration" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "After generating reference copy " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{Q}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ", we score inlier confidence for each point pair in " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ". However, existing methods broadly obey coordinate-based scheme, where inlier confidence are scored through simply capturing coordinate differences in the context, and the current guiding principle" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5315" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "is that the reduced confidence of points pair indicates to the diminished probability that they represent inliers. But this assertion is not universally valid. The significant differences in coordinate pose a challenge in differentiating inliers, thereby elevating the risk of misinterpretation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": "In this section, we explore to extend a new definition called ICC to alleviate the above issues. Benefiting from the high quality matching map " + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": " in Section 3.1, we argue that the neighborhood patch formed by inlier and its neighborhood should have consistency between source point cloud and its reference copy, i.e., if " + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": " is an inlier, its neighborhood points also tend to be the inliers and " + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{q}}_i" + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": " have geometric structure neighborhood consistency in the reference copy. Conversely, if " + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": " is an outlier, its neighborhood may also be the outliers and spatial structure is prone to be significantly different from the reference copy neighborhood. Based on this observation, we construct transformation-invariant geometric constraints and formulate geometric structure consistency between " + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{p}_i}" + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}" + }, + { + "bbox": [ + 46, + 133, + 288, + 323 + ], + "type": "text", + "content": " to calibrate inlier confidence for estimated correspondences between source point cloud and its reference copy." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "type": "text", + "content": "We first construct a learnable neighborhood graph by transformation-invariant geometric structure constraints of " + }, + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{p}_i}" + }, + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}" + }, + { + "bbox": [ + 47, + 323, + 288, + 371 + ], + "type": "text", + "content": ", which consists of edge representation and angle representation:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 375, + 241, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 375, + 241, + 392 + ], + "spans": [ + { + "bbox": [ + 82, + 375, + 241, + 392 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {i, k} ^ {\\mathbf {p}} = \\mathbf {p} _ {i} - \\mathbf {p} _ {k}, \\mathbf {a} _ {r, s} ^ {\\mathbf {p}} = \\angle (\\mathbf {e} _ {i, r} ^ {\\mathbf {p}}, \\mathbf {e} _ {i, s} ^ {\\mathbf {p}}),", + "image_path": "11ef553a00ad132e616d78ad7ea5e0b4e037dcb4f12bfc958e697ee9568a974a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 82, + 393, + 287, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 393, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 82, + 393, + 287, + 413 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {i, k} ^ {\\widetilde {\\mathbf {q}}} = \\widetilde {\\mathbf {q}} _ {i} - \\widetilde {\\mathbf {q}} _ {k}, \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}} = \\angle \\left(\\mathbf {e} _ {i, r} ^ {\\widetilde {\\mathbf {q}}}, \\mathbf {e} _ {i, s} ^ {\\widetilde {\\mathbf {q}}}\\right), \\tag {8}", + "image_path": "c8e2bad2a758c83b7e2eb6c3154817d57d6c489617c959b3b128b659bbd4aa0c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 82, + 415, + 252, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 415, + 252, + 428 + ], + "spans": [ + { + "bbox": [ + 82, + 415, + 252, + 428 + ], + "type": "interline_equation", + "content": "i \\neq k, k = 1, \\dots , K r, s \\in \\{1, \\dots , K \\}", + "image_path": "02bafb02d8fbb1f8d67731b676b981c5661f6329419fe4e7282667bfdcd676cd.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_k" + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{q}}_k" + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "text", + "content": " are the points in " + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{p}_i}" + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\widetilde{\\mathbf{q}}_i}" + }, + { + "bbox": [ + 46, + 434, + 287, + 481 + ], + "type": "text", + "content": ". Moreover, these representations express sensitive and discriminative geometric structure in the point cloud, and provide adequate geometric cues for subsequent pipeline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "type": "text", + "content": "In order to better capture the neighborhood relevance and promote contextual message propagation, we utilize Multi-layer Perceptron (MLP) " + }, + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 481, + 287, + 553 + ], + "type": "text", + "content": " to fuse representations and characterize the consistency between the neighborhoods by the subtraction of the fused geometric representations:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 557, + 288, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 288, + 587 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 288, + 587 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {i, k} = f _ {\\theta} \\left(\\operatorname {c o n c a t} \\left(\\mathbf {e} _ {i, k} ^ {\\mathbf {p}}, \\mathbf {a} _ {r, s} ^ {\\mathbf {p}}\\right)\\right) - f _ {\\theta} \\left(\\operatorname {c o n c a t} \\left(\\mathbf {e} _ {i, k} ^ {\\widetilde {\\mathbf {q}}}, \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}}\\right)\\right). \\tag {9}", + "image_path": "264ac187449c9239d0a9e5f9ed3b806c322202ccfcff737725cea12f2b4c7fcb.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 588, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 287, + 612 + ], + "type": "text", + "content": "Next, the model further adaptively learns the attention coefficients " + }, + { + "bbox": [ + 47, + 588, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\delta_{i,k}" + }, + { + "bbox": [ + 47, + 588, + 287, + 612 + ], + "type": "text", + "content": " of each geometric structure consistency:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 617, + 287, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 617, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 55, + 617, + 287, + 641 + ], + "type": "interline_equation", + "content": "\\delta_ {i, k} = \\operatorname {s o f t m a x} \\left(f _ {\\mu} \\left(\\mathbf {d} _ {i, 1}\\right), f _ {\\mu} \\left(\\mathbf {d} _ {i, 2}\\right), \\dots , f _ {\\mu} \\left(\\mathbf {d} _ {i, K}\\right)\\right) _ {k}, \\tag {10}", + "image_path": "44d1f3dc84ecd2ea02e3a9cd0ecd46a3d4b7337735a4d286d7b352db46ce9f23.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "inline_equation", + "content": "f_{\\mu}" + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "text", + "content": " is another MLP with parameters " + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "text", + "content": ". Then, inlier confidence " + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "text", + "content": " of correspondence " + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}_i, \\widetilde{\\mathbf{q}}_i)" + }, + { + "bbox": [ + 47, + 642, + 287, + 678 + ], + "type": "text", + "content": " is calculated by aggregating the geometric structure consistency weighted:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 70, + 682, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 682, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 70, + 682, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {w} _ {i} = 1 - \\operatorname {T a n h} \\left(\\left| l \\left(\\sum_ {k = 1} ^ {K} \\delta_ {i, k} * \\mathbf {d} _ {i, k}\\right) \\right|\\right), \\tag {11}", + "image_path": "7cdb2a7e9b6d2f33cf04c1d5ebbb9566b6506f357502129f31a369c9e9100960.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " is a linear function. Through strict geometric constraints, the scored inlier confidence can be effectively calibrated, ensuring the sustained high credibility of " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ". However, some potential repetitive structures, textureless structures and other uncertain factors may still exist. In order to enhance the robustness of the proposed method and reduce the bias caused by the above issues, we select inlier correspondences from " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{C}'" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " with the largest " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " inlier confidence:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 173, + 545, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 173, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 314, + 173, + 545, + 186 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {h} = \\left\\{\\left(\\mathbf {p} _ {h}, \\widetilde {\\mathbf {q}} _ {h}\\right) \\mid h \\in \\operatorname {T o p k} \\left(\\mathbf {w} _ {i}\\right), i = 1, \\dots , N _ {c} \\right\\}. \\tag {12}", + "image_path": "a2528099ba8498c377e6200846ef824206aa28e2e2197cc601a1f0e402ef375c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 190, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 190, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 190, + 545, + 227 + ], + "type": "text", + "content": "Finally, transformation " + }, + { + "bbox": [ + 304, + 190, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R}_{est},\\mathbf{t}_{est}\\}" + }, + { + "bbox": [ + 304, + 190, + 545, + 227 + ], + "type": "text", + "content": " can be solved in closed form using weighted SVD, which has been shown to be differentiable in [26]:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 231, + 545, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 231, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 317, + 231, + 545, + 258 + ], + "type": "interline_equation", + "content": "\\mathbf {R} _ {e s t}, \\mathbf {t} _ {e s t} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\sum_ {\\left(\\mathbf {p} _ {i}, \\widetilde {\\mathbf {q}} _ {i}\\right) \\in \\mathcal {C} _ {h}} \\mathbf {w} _ {i} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {i} + \\mathbf {t} - \\widetilde {\\mathbf {q}} _ {i} \\| _ {2} ^ {2}. \\tag {13}", + "image_path": "94aa964dc58c386f1b556835299eda26b27d122c71951018059f05aa45021c1d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 262, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 299 + ], + "type": "text", + "content": "Besides, ICC provides useful byproduct for unsupervised learning, which can be reliable self-supervised signal. More details can be seen in the following section." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 304, + 391, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 391, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 391, + 317 + ], + "type": "text", + "content": "3.3. Optimization" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 322, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 545, + 369 + ], + "type": "text", + "content": "In this section, we conduct four loss functions for model optimization. Moreover, the proposed model is trained in an unsupervised manner instead of using the ground-truth transformations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "type": "text", + "content": "Global Consistency Loss. We investigate the global consistency loss between the final transformed source point cloud " + }, + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "type": "text", + "content": " and the reference point cloud " + }, + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 370, + 545, + 430 + ], + "type": "text", + "content": ". Specifically, the Huber function is utilized to assemble the global consistency loss, which is defined as follow:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 327, + 434, + 545, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 434, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 327, + 434, + 545, + 497 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {g c} = \\sum_ {\\mathbf {p} ^ {\\prime} \\in \\mathcal {P} ^ {\\prime}} H _ {\\beta} \\left(\\min _ {\\mathbf {q} \\in \\mathcal {Q}} \\| \\mathbf {p} ^ {\\prime} - \\mathbf {q} \\| _ {2} ^ {2}\\right) \\tag {14} \\\\ + \\sum_ {\\mathbf {q} \\in \\mathcal {Q}} H _ {\\beta} \\left(\\min _ {\\mathbf {p} ^ {\\prime} \\in \\mathcal {P} ^ {\\prime}} \\| \\mathbf {q} - \\mathbf {p} ^ {\\prime} \\| _ {2} ^ {2}\\right). \\\\ \\end{array}", + "image_path": "311c3a9fd108fe644e0b7eb5fa9d8c0a236496251fa40dc4bcc39ff399009e62.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 502, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 585 + ], + "type": "text", + "content": "However, relying solely on global consistency loss is detrimental to the accuracy and reliability of our model. Since the model may still potentially converge to sub-optimization due to the existing outliers, leading massive potential information of point cloud is wasted. Hence, it is critical to mine the potential self-supervised signals in the point cloud and construct loss functions based on other existing elements." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "text", + "content": "Dual Neighborhood Consistency Loss. Based on reliable inlier correspondences in Equation 12, we denote the inliers set of the source and its reference point cloud copy as " + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N_c \\times 3}" + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\mathbb{R}^{N_c \\times 3}" + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "text", + "content": ", respectively. We utilize the neighborhood between the inliers to construct consistency objective, which aims to minimize the registration error between each neighborhood " + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{x}_i}" + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 304, + 585, + 545, + 670 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 315, + 674, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 674, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 674, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i n} = \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {R} _ {e s t} \\mathbf {p} _ {j} + \\mathbf {t} _ {e s t} - \\widetilde {\\mathbf {q}} _ {j} \\right\\| _ {2}, \\tag {15}", + "image_path": "bad8c8ab7a68c22d6831d7929090c5be9296badf774f03972873ea3de6855d4b.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5316" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{x}_i}" + }, + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "type": "text", + "content": " is transformed by " + }, + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 47, + 72, + 186, + 85 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 286, + 144 + ], + "type": "text", + "content": "Geometric Structure Consistency Loss. The geometric signal buried in point cloud is readily ignored, which hinders ICC. To address this issue, we design a geometric neighborhood loss with the reliable geometric self-supervised signal proposed in Section 3.2:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 150, + 286, + 212 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 150, + 286, + 212 + ], + "spans": [ + { + "bbox": [ + 63, + 150, + 286, + 212 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {g s} = \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {e} _ {i, j} ^ {\\mathbf {p}} - \\mathbf {e} _ {i, j} ^ {\\widetilde {\\mathbf {q}}} \\right\\| _ {2} + \\\\ \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}, \\mathbf {y} _ {i} \\in \\mathbf {Y}} \\sum_ {\\mathbf {p} _ {j} \\in \\mathcal {N} _ {\\mathbf {x} _ {i}}, \\widetilde {\\mathbf {q}} _ {j} \\in \\mathcal {N} _ {\\mathbf {y} _ {i}}} \\left\\| \\mathbf {a} _ {r, s} ^ {\\mathbf {p}} - \\mathbf {a} _ {r, s} ^ {\\widetilde {\\mathbf {q}}} \\right\\| _ {2}, \\tag {16} \\\\ \\end{array}", + "image_path": "27c526f0492689726d141555f6fc2e68455f19b5d09829375ac75d26a4fbab92.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{r,s}^{\\mathbf{p}}" + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{r,s}^{\\widetilde{\\mathbf{q}}}" + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "text", + "content": " is calculated by " + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{i,j}^{\\mathbf{p}}" + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{i,j}^{\\widetilde{\\mathbf{q}}}" + }, + { + "bbox": [ + 47, + 220, + 286, + 246 + ], + "type": "text", + "content": " shown in Equation 8." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "type": "text", + "content": "Spatial Consistency Loss. We further explore to eliminate the spatial difference between the estimated correspondence and the real correspondence for each selected inlier " + }, + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "type": "text", + "content": " and utilize spatial consistency loss with cross-entropy to sharpen matching map " + }, + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 47, + 247, + 286, + 306 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 313, + 286, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 313, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 53, + 313, + 286, + 346 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s c} = - \\frac {1}{| \\mathbf {X} |} \\sum_ {\\mathbf {x} _ {i} \\in \\mathbf {X}} \\sum_ {j = 1} ^ {M} [ [ j = \\arg \\max _ {j ^ {\\prime}} \\mathbf {G} _ {i, j ^ {\\prime}} ] ] \\log \\mathbf {G} _ {i, j}, \\tag {17}", + "image_path": "39b3d85db8311efa71cf7e9633d4b4b2302fb86b954fdbe712489ca341bd1ef6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 354, + 286, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 286, + 401 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 286, + 401 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 354, + 286, + 401 + ], + "type": "inline_equation", + "content": "\\llbracket \\cdot \\rrbracket" + }, + { + "bbox": [ + 47, + 354, + 286, + 401 + ], + "type": "text", + "content": " is the Iverson bracket. Spatial consistency loss encourages to improve the matching probability and thus the estimated correspondence point in reference copy tends to have an stable position." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 402, + 286, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 402, + 286, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 402, + 286, + 437 + ], + "type": "text", + "content": "Overall Loss. Since our work utilizes an iterative scheme, we compute the loss at each iteration " + }, + { + "bbox": [ + 47, + 402, + 286, + 437 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 47, + 402, + 286, + 437 + ], + "type": "text", + "content": " and have the weighted sum loss:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 445, + 286, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 445, + 286, + 478 + ], + "spans": [ + { + "bbox": [ + 83, + 445, + 286, + 478 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {l = 1} ^ {N _ {l}} \\left(\\mathcal {L} _ {g c} ^ {l} + \\gamma \\mathcal {L} _ {i n} ^ {l} + \\rho \\mathcal {L} _ {g s} ^ {l} + \\lambda \\mathcal {L} _ {s c} ^ {l}\\right), \\tag {18}", + "image_path": "a7d01c679dffb714f28bfe1209335dcf7bf62597d1a4115d14d574ba7d890ae0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 484, + 286, + 509 + ], + "type": "text", + "content": " are trade-off parameters to control corresponding loss function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 518, + 127, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 127, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 127, + 532 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 538, + 162, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 162, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 162, + 551 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 556, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 556, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 556, + 286, + 651 + ], + "type": "text", + "content": "We compare our method to traditional methods and recent state of the arts learning-based methods. The traditional methods include ICP [4], FGR [16] and FPFH + RANSAC [13]. The recent learning based methods include IDAM [21], FMR [16], RPMNet [38], CEMNet [17], REGTR [39], GeoTransformer [27] and RIE [32]. For consistency with previous work, we measure Mean Isotropic Error (MIE) and Mean Absolute Error (MAE)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 658, + 239, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 239, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 239, + 671 + ], + "type": "text", + "content": "4.2. ModelNet40 Dataset and Evaluation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Noted that, to simulate partial-to-partial registration, the reference point cloud " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " and the source point cloud " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " are cropped respectively, and retain " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " of the points." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 72, + 548, + 220 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 548, + 220 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 548, + 220 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 548, + 220 + ], + "type": "table", + "html": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
ICP [4] (○)3.43390.01146.77060.0227
FGR [16] (○)0.59720.00211.15630.0041
FPFH+RANSAC [13] (○)0.70310.00251.27720.0050
IDAM [21] (▲)0.42430.00200.81700.0040
RPMNet [38] (▲)0.00510.00000.02010.0000
FMR [16] (▲)3.64970.01017.28100.0200
REGTR [39] (▲)0.18940.00150.34930.0030
GeoTransformer [27] (▲)0.59700.00570.90100.0102
CEMNet [17] (△)0.13850.00010.24890.0002
RIE [32] (△)0.00330.00000.02100.0000
Ours (△)0.00120.00000.01920.0000
", + "image_path": "2066246c6ba72d48b59d862c491538e166157c077841839ad9d4f1711e19176d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "text", + "content": "Table 1. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. " + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "inline_equation", + "content": "(\\bigcirc)" + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "inline_equation", + "content": "(\\triangle)" + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "inline_equation", + "content": "(\\triangle)" + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "text", + "content": " denote the traditional, supervised and unsupervised methods, respectively." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "type": "text", + "content": "Unseen Objects. Our models are trained and tested on datasets comprising of samples belonging to the same categories, and both the training and test sets are obtained without any preprocessing or manipulation. We apply a random transformation on the reference point cloud " + }, + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "type": "text", + "content": " to generate corresponding source point cloud " + }, + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 281, + 545, + 496 + ], + "type": "text", + "content": ". Table 1 shows quantitative results of the various algorithms under current experimental settings. The proposed method substantially outperforms all baseline in all metrics. We can observe our method can even outperform the supervised IDAM, RPMNet, FMR, REGTR and GeoTransformer by a large margin. Benefiting from ICC, our method attains highly accurate registration and improves the registration accuracy by an order of magnitude. In order to show the effect of our proposed approach clearly, a qualitative comparison of the registration results can be found in Figure 3. Our method ensures minimal impact on changing of the shape, and achieves the best performance even on asymmetric shape." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "type": "text", + "content": "Unseen Categories. To verify the generalization ability on categories, we train the models on the first 20 categories and test on the remaining unseen categories. The results are summarized in Table 2. We can observe that the majority of baseline consistently exhibit lower performance on the unseen categories, especially learning-based methods. In contrast, traditional algorithms are less susceptible to this issue due to the insensitivity of handcrafted methods to shape variance [36]. Our registration process remains highly precise, achieving the lowest error across all metrics, while also maintaining acceptable levels of fluctuation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Gaussian Noise. In order to assess performance in the presence of noise, which is commonly encountered in real-world point clouds, we train our model on noise-free data and then evaluate all baselines using a test set featuring Gaussian noise. We randomly and independently generate noisy points to introduce noise into in source point cloud and reference point cloud by sampling from " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,0.5)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5317" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 544, + 237 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 544, + 237 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 544, + 237 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 544, + 237 + ], + "type": "image", + "image_path": "968c03ec93627a35b7b0d1c652cc6a1ad892e8cf95a62a97aa3ef3052beddb23.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 546, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 546, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 546, + 269 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison of the registration results on unseen objects data (blue: source point cloud, yellow: reference point cloud, green: transformed source point cloud)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 278, + 290, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 290, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 290, + 376 + ], + "type": "text", + "content": "clipped to " + }, + { + "bbox": [ + 46, + 278, + 290, + 376 + ], + "type": "inline_equation", + "content": "[-1.0, 1.0]" + }, + { + "bbox": [ + 46, + 278, + 290, + 376 + ], + "type": "text", + "content": ". This experiment is significantly challenging, as constructing matching map and ICC become much more difficult. As shown in Table 2, our method outperforms other baselines. The experimental results demonstrate that our method is robust to the noise. In addition, experimental results indirectly confirms the generality and high adaptability of ICC in point cloud registration with partially overlapping." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 389, + 291, + 659 + ], + "blocks": [ + { + "bbox": [ + 48, + 389, + 291, + 659 + ], + "lines": [ + { + "bbox": [ + 48, + 389, + 291, + 659 + ], + "spans": [ + { + "bbox": [ + 48, + 389, + 291, + 659 + ], + "type": "table", + "html": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Unseen Categories
ICP [4] (○)3.60990.01167.05560.0228
FGR [16] (○)0.45790.00160.84420.0032
FPFH+RANSAC [13] (○)0.44270.00210.94470.0043
IDAM [21] (▲)0.48090.00280.91570.0055
RPMNet [38] (▲)0.00640.00010.02070.0001
FMR [16] (▲)3.85940.01147.64500.0225
CEMNet[17] (△)0.08040.00020.14050.0003
RIE [32] (△)0.00590.00000.02280.0001
Ours (△)0.00220.00000.01890.0000
Gaussian Noise
ICP [4] (○)4.64410.01679.21940.0333
FGR [16] (○)1.06760.00362.00380.0072
FPFH+RANSAC [13] (○)1.43160.00612.53450.0120
IDAM [21] (▲)2.30760.01244.53320.0246
RPMNet [38] (▲)1.58900.01752.98300.0378
FMR [16] (▲)18.03550.053635.79860.1063
CEMNet[17] (△)10.70260.039321.18360.0781
RIE [32] (△)0.04310.00040.07760.0008
Ours (△)0.00880.00010.02450.0002
", + "image_path": "98673382517542eddcaf353d006eedc9e6e91f116a962105cb8514c29206af33.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "lines": [ + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "text", + "content": "Table 2. Evaluation results on ModelNet40. Bold indicates the best performance and underline indicates the second-best performance. " + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "inline_equation", + "content": "(\\bigcirc)" + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "inline_equation", + "content": "(\\triangle)" + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "inline_equation", + "content": "(\\bigtriangleup)" + }, + { + "bbox": [ + 46, + 663, + 288, + 708 + ], + "type": "text", + "content": " denote the traditional, supervised and unsupervised methods, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 278, + 473, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 473, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 473, + 291 + ], + "type": "text", + "content": "4.3. Other Datasets and Evaluation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "type": "text", + "content": "We further conduct comparison evaluation on other datasets: 7Scenes and Augmented ICL-NUIM. We sample the reference point clouds to 2,048 points and randomly sample three Euler angle rotations within " + }, + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "type": "inline_equation", + "content": "[0^{\\circ}, 45^{\\circ}]" + }, + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "type": "text", + "content": " and translations within " + }, + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "type": "inline_equation", + "content": "[-0.5, 0.5]" + }, + { + "bbox": [ + 304, + 298, + 545, + 441 + ], + "type": "text", + "content": " on each axis as the rigid transformation to obtain source point clouds, then down-sample the point clouds to 1,536 points to generate the partial data. As demonstrated in Table 4, our method exhibits extremely higher registration precision on all criteria on Augmneted ICL-NUIM and 7Scenes, especially the rotation error. We can summarize our method has best performance and is comfortable with real-world dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 453, + 463, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 463, + 466 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 463, + 466 + ], + "type": "text", + "content": "4.4. Ablation Study and Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": "Soft Assignment Matrix Optimization Theorem. We compare the developed theorem with the Sinkhorn, and evaluate precision and efficiency against Sinkhorn, which iterate 1 (Sinkhorn-1) and 5 (Sinkhorn-5) times. As shown in Figure 4, we can observe that under the same tolerant error, the developed theorem demonstrates superior performance, especially the optimization for rotation. Additionally, the proposed theorem improves the efficiency up to nearly " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " compared to Sinkhorn-1 and nearly up to " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " compared to Sinkhorn-5. It needs to be emphasized once again that the proposed theorem has a smaller computational complexity than Sinkhorn as shown in Table 5, since this theorem does not normalize the rows and columns repeatedly, and only operates on the rows." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "type": "text", + "content": "Geometric Constraints. To investigate whether geometric constraints are meaningful to ICC, we conduct an experiment to verify our motivation. Experimental results are shown in the first row of Table 3. Compared to constraints-free, which score inlier confidence by simple coordinates, geometric constraints effectively generate more convincing" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5318" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 70, + 533, + 180 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 533, + 180 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 533, + 180 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 533, + 180 + ], + "type": "table", + "html": "
GeometricConstraints\\( \\mathcal{L}_{gc} \\)\\( \\mathcal{L}_{in} \\)\\( \\mathcal{L}_{gs} \\)\\( \\mathcal{L}_{sc} \\)ModelNet407Scenes
MAE(R)MAE(t)MIE(R)MIE(R)MAE(R)MAE(t)MIE(R)MIE(R)
✓✓N/A✓1.01230.01611.83980.03502.22380.01484.36980.0286
✓✓✓✓0.39980.00610.76650.01290.00420.00000.02170.0001
✓✓✓✓22.51990.134042.44280.27103.30870.03405.87700.0657
✓✓✓✓0.00700.00010.02350.00020.00370.00000.01860.0001
✓✓✓✓0.11250.00140.018620.00300.01420.00010.03450.0003
✓✓✓✓✓0.00120.00000.01920.00000.00330.00000.01810.0001
", + "image_path": "87bc78e8479d0f2d079c9bb571f87df84c45ec87e6aeeea8efe3108204426488.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 207, + 291, + 478 + ], + "blocks": [ + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "lines": [ + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "spans": [ + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "type": "text", + "content": "Table 3. Ablation study of different components. " + }, + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{gc},{\\mathcal{L}}_{in},{\\mathcal{L}}_{gs}" + }, + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{sc}" + }, + { + "bbox": [ + 97, + 186, + 494, + 199 + ], + "type": "text", + "content": " : Each Loss Function in Equation 18." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 207, + 291, + 478 + ], + "lines": [ + { + "bbox": [ + 48, + 207, + 291, + 478 + ], + "spans": [ + { + "bbox": [ + 48, + 207, + 291, + 478 + ], + "type": "table", + "html": "
MethodMAE(R)MAE(t)MIE(R)MIE(t)
Augmented ICL-NUIM
ICP [4] (○)2.40220.06994.48320.1410
FGR [16] (○)2.24770.08084.18500.1573
FPFH+RANSAC [13] (○)1.23490.04292.31670.0839
IDAM [21] (▲)4.41530.13858.61780.2756
RPMNet [38] (▲)0.32670.01250.62770.0246
FMR [16] (▲)1.10850.03982.13230.0786
CEMNet[17] (△)0.23740.00050.39870.0010
RIE [32] (△)0.04920.00230.08970.0049
Ours (△)0.00480.00020.01990.0003
7Scenes
ICP [4] (○)6.00910.013013.04840.0260
FGR [16] (○)0.09190.00040.17050.0008
FPFH+RANSAC [13] (○)1.23250.00622.18750.0124
IDAM [21] (▲)5.67270.030311.59490.0629
RPMNet [38] (▲)0.38850.00210.76490.0042
FMR [16] (▲)2.54380.00724.90890.0150
CEMNet[17] (△)0.05590.00010.07720.0003
RIE [32] (△)0.01210.00010.02990.0001
Ours (△)0.00330.00000.01810.0001
", + "image_path": "a2a9aa35e46aefe9ad9b69698b3abed124ca2492a042264d7945014bb399668b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 542, + 288, + 603 + ], + "blocks": [ + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "lines": [ + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "text", + "content": "Table 4. Evaluation results on Augmented ICL-NUIM and 7Scenes. Bold indicates the best performance and underline indicates the second-best performance. " + }, + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "inline_equation", + "content": "(\\bigcirc)" + }, + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "inline_equation", + "content": "(\\triangle)" + }, + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "inline_equation", + "content": "(\\bigtriangleup)" + }, + { + "bbox": [ + 46, + 483, + 288, + 529 + ], + "type": "text", + "content": " denote the traditional, supervised and unsupervised methods, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 542, + 288, + 603 + ], + "lines": [ + { + "bbox": [ + 48, + 542, + 288, + 603 + ], + "spans": [ + { + "bbox": [ + 48, + 542, + 288, + 603 + ], + "type": "table", + "html": "
Complexity
Sinkhorn with dustbin parametersO((N+1) × (M+1))
Sinkhorn with iterate G timesO(G × (N × M))
Proposed theoremO(N)
", + "image_path": "98eb6c06e5bc59ca7484fa8c7d204fb1fb50d4af13da78e0cc20f52fb11a475c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 609, + 287, + 633 + ], + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 633 + ], + "type": "text", + "content": "Table 5. Computational complexity of Sinkhorn and the proposed theorem comparison." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "type": "text", + "content": "scoring mechanism. Noted that geometric constraints provide a self-supervised signal for our model, and " + }, + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gs}" + }, + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "type": "text", + "content": " is designed based on this signal. Therefore, when geometric constraints is deleted, the loss function " + }, + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gs}" + }, + { + "bbox": [ + 46, + 641, + 287, + 700 + ], + "type": "text", + "content": " should not participate in optimization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "Loss Function. We evaluate the performance of the model" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 209, + 550, + 289 + ], + "blocks": [ + { + "bbox": [ + 306, + 209, + 550, + 289 + ], + "lines": [ + { + "bbox": [ + 306, + 209, + 550, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 550, + 289 + ], + "type": "image", + "image_path": "3bb17ae991e3f7f89580c394126b39631bfc60df0b93db26e064b66c74347dc5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "type": "text", + "content": "Figure 4. Comparisons between the proposed theorem and the Sinkhorn in terms of precision and efficiency." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "text", + "content": "with different loss functions. Comprehensively, lacking any part of " + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "text", + "content": " will degrade the performance of the model. Comparing " + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "inline_equation", + "content": "2\\sim 5" + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "text", + "content": " rows in Table 3, the error observed in the third row is extremely large, primarily due to the absence of any optimization objective related to transformation in the loss function. This significantly reduces the registration performance of the model. In particular, this ablation study confirms the byproduct of ICC " + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gs}" + }, + { + "bbox": [ + 304, + 323, + 545, + 431 + ], + "type": "text", + "content": " can provide reliable and effective self-supervised signal for model optimization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 442, + 378, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 378, + 454 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 378, + 454 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 628 + ], + "type": "text", + "content": "In this paper, we explore to extend a new definition called inlier confidence calibration (ICC). Existing methods broadly obey coordinate-based scheme, where inlier confidence is scored through simply capturing coordinate differences in the context. However, this scheme results in massive inlier misinterpretation readily, consequently affecting the registration accuracy. Thus, we construct transformation-invariant geometric constraints and capture geometric structure consistency to calibrate inlier confidence. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed methods. In the future, we would like to extend our method to crossmodality (e.g., 2D-3D) registration with richer applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work is supported by the National Natural Science Foundation of China (62036006, 62276200), the CAAI-Huawei MINDSPORE Academic Open Fund, the Key Research and Development Project of Shaanxi Province (2022QCY-LL-35), the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5319" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 289, + 715 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 289, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 289, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 289, + 146 + ], + "type": "text", + "content": "[1] Yasuhiro Aoki, Hunter Goforth, Rangaprasad Arun Srivatsan, and Simon Lucey. 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Loam: Lidar odometry and mapping in real-time. In Robotics: Science and Systems, 2014. 1" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5321" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Insect-Foundation_ A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding/15f153cc-fc03-4374-8076-9262f9d4ae0f_content_list.json b/2024/Insect-Foundation_ A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding/15f153cc-fc03-4374-8076-9262f9d4ae0f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4956eedd53264787fca285488f25cc958046fded --- /dev/null +++ b/2024/Insect-Foundation_ A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding/15f153cc-fc03-4374-8076-9262f9d4ae0f_content_list.json @@ -0,0 +1,1699 @@ +[ + { + "type": "text", + "text": "Insect-Foundation: A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding", + "text_level": 1, + "bbox": [ + 119, + 130, + 849, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hoang-Quan Nguyen $^{1*}$ , Thanh-Dat Truong $^{1*}$ , Xuan Bac Nguyen $^{1}$ , Ashley Dowling $^{2}$ , Xin Li $^{3}$ , Khoa Luu $^{1}$ $^{1}$ Department of Electrical Engineering and Computer Science, University of Arkansas, AR \n $^{2}$ Department of Entomology and Plant Pathology, University of Arkansas, AR \n $^{3}$ Department of Computer Science, SUNY Albany, NY", + "bbox": [ + 86, + 202, + 911, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hn016, tt032, xnguyen, adowling, khoaluu}@uark.edu, xli48@albany.edu", + "bbox": [ + 196, + 276, + 803, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://uark-cviu.github.io/projects/insect_foundation.html", + "bbox": [ + 233, + 295, + 756, + 308 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 312, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In precision agriculture, the detection and recognition of insects play an essential role in the ability of crops to grow healthy and produce a high-quality yield. The current machine vision model requires a large volume of data to achieve high performance. However, there are approximately 5.5 million different insect species in the world. None of the existing insect datasets can cover even a fraction of them due to varying geographic locations and acquisition costs. In this paper, we introduce a novel \"Insect-1M\" dataset, a game-changing resource poised to revolutionize insect-related foundation model training. Covering a vast spectrum of insect species, our dataset, including 1 million images with dense identification labels of taxonomy hierarchy and insect descriptions, offers a panoramic view of entomology, enabling foundation models to comprehend visual and semantic information about insects like never before. Then, to efficiently establish an Insect Foundation Model, we develop a micro-feature self-supervised learning method with a Patch-wise Relevant Attention mechanism capable of discerning the subtle differences among insect images. In addition, we introduce Description Consistency loss to improve micro-feature modeling via insect descriptions. Through our experiments, we illustrate the effectiveness of our proposed approach in insect modeling and achieve State-of-the-Art performance on standard benchmarks of insect-related tasks. Our Insect Foundation Model and Dataset promise to empower the next generation of insect-related vision models, bringing them closer to the ultimate goal of precision agriculture.", + "bbox": [ + 76, + 376, + 473, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 821, + 207, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Insects are the most diverse and abundant eukaryotic organisms on the planet. They inhabit all terrestrial and aquatic", + "bbox": [ + 76, + 847, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3b1c15557806e533d6862da19719bf6e911a7d4c7cb5362b37e470bb381d3ce8.jpg", + "image_caption": [ + "Masked Monarch" + ], + "image_footnote": [], + "bbox": [ + 513, + 345, + 596, + 411 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d426c76f6c2d3908193e5385bbfec00c72e0914992c581275b8cb8aac5ac035.jpg", + "image_caption": [ + "Patch-wise Relevant" + ], + "image_footnote": [], + "bbox": [ + 609, + 348, + 720, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b303a242aa5b2686a1148796ac9611eca7f5cac51e35d8746c9a94bbc0676aac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 345, + 779, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5afd677a309d2591aa88863f76575800246d2fa68b058030fd78c0582a143532.jpg", + "image_caption": [ + "Completed Monarch" + ], + "image_footnote": [], + "bbox": [ + 785, + 347, + 870, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7ba4cc60bc0971429f56f7ee7066f7afac7404e899e4bbdf2ec5971985566a8e.jpg", + "image_caption": [ + "Which patches belong to the Monarch/Euryurus?", + "Masked Euryurus" + ], + "image_footnote": [], + "bbox": [ + 513, + 440, + 596, + 505 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7437a64b24665e5fce8f26c05c1c285c4bea813ae51a3ee495476aaa8da03448.jpg", + "image_caption": [ + "Figure 1. Our Proposed Patch-wise Relevant Attention. Given masked insect images and separated image patches, our model can discriminate these patches that have small differences via relevant scores computed between masked images and image patches." + ], + "image_footnote": [], + "bbox": [ + 756, + 440, + 779, + 507 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8c90ab060363e0b61bf14013002ff2b8d851cd2cba921485f2683599520b4c20.jpg", + "image_caption": [ + "Completed Euryurus" + ], + "image_footnote": [], + "bbox": [ + 787, + 440, + 870, + 506 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "habitats and play a significant role within their community, habitat, and ecosystem as contributors to nutrient cycling, maintenance of plant and animal communities, disease cycling, and overall ecosystem health. Therefore, in the agricultural revolution, the detection and identification of insects plays a key role in ensuring healthy crop growth and high-quality production. Prior methods [2, 3, 6, 32, 55, 66] often fine-tuned the pre-trained ImageNet models on insect data for specific insect-related tasks, e.g., Insect Classification [2, 6, 13, 66], Insect Detection [66]. However, these methods remained limited since the models pre-trained on ImageNet [12, 15, 16, 20, 50, 52] could not model the micro features of insects, e.g., tiny texture and details of insects, as ImageNet [12] is the generic object dataset.", + "bbox": [ + 496, + 579, + 890, + 790 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent foundation models [7-9, 17-19, 40, 43, 69, 70] pre-trained on large-scale datasets have revolutionized vision models with solid performance on downstream applications. These models are designed to model general or specific properties of images or videos that can later be generalized to downstream tasks and unseen data. The capability of the foundation model is often implemented with", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Co-first authors", + "bbox": [ + 101, + 887, + 192, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21945", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/f66e1202693f4d18c4aabbfffb8bf0bedae6983ea9065c701c74d941574d905e.jpg", + "table_caption": [ + "Table 1. Comparison with existing datasets related to insects. Our proposed dataset has hierarchical labels with 6 main hierarchical levels, i.e., Subphylum, Class, Order, Family, Genus, and Species, and large numbers of species and samples. Moreover, the proposed dataset contains hierarchical descriptions for each insect and auxiliary taxonomic level, i.e., Subclass, Suborder, Subfamily, etc." + ], + "table_footnote": [], + "table_body": "
DatasetYearSpeciesHierarchical \nLabelsHierarchical \nLevelsInsect \nDescriptionAuxiliary \nTaxonomic LevelNumber of \nSamples
Samanta et al. [48]20128X1XX609
Wang et al. [61]2012221✓3XX225
Venugoban et al. [60]201420X1XX200
Xie et al. [67]201524X1XX1,440
Liu et al. [28]201612X1XX5,136
Xie et al. [68]201840X1XX4,500
Deng et al. [13]201810X1XX563
Alfarisy et al. [1]201813X1XX4,511
PestNet [25]201916X1XX88,670
IP102 [66]2019102✓3XX75,222
AgriPest [63]202114✓2XX49,707
INSECT [4]20211,213X1XX21,212
iNat-2021 [59]20212,752✓5XX723,816
Our Insect-1M202334,212✓6✓✓1,017,036
", + "bbox": [ + 120, + 132, + 848, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "self-supervised or prompt-engineering training on large-scale datasets [12, 19, 49, 71]. However, the current insect datasets [1, 2, 6, 13, 28, 48, 60, 61, 66-68] are insufficient to establish the foundation model of insects due to their scale and diversity. Indeed, the most recent work presents an insect recognition dataset containing over 75,000 images of 102 species [66]. Although the dataset includes many species, compared to the species of insects in the natural environment with over 5.5 million species [45, 51], the current work needs to have the diversity of insects. Furthermore, to our knowledge, the current insect dataset [66] does not provide the corresponding insect descriptions, limiting the ability to learn the foundation models.", + "bbox": [ + 73, + 349, + 470, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although the dataset is an important factor in developing an insect foundation model, the learning approach of the foundation model plays a significant role in performance. There is significant progress in developing vision foundation models. Common approaches learned alignment between vision and language, for example, CLIP [43], ALIGN [19], CoCa [70], to model visual concepts and data distributions. Meanwhile, self-supervised contrastive or distillation learning approaches, e.g., MoCo [9, 10, 17], DINO [7, 40], MAE [18], etc., learned the vision model by various pretext tasks and have shown its scaling ability and generalizes well to various downstream tasks. However, most of these previous foundation models represent the general information of natural images without specific knowledge. When deploying in the insect domains, they cannot capture the micro-features of insects, i.e., key features or appearance to distinguish the species, since the texture and details of insects are often small and diverse compared to generic objects. Meanwhile, fine-grained discrimination between insect images is crucial in insect foundation models due to the high diversity of species. Therefore, to successfully develop the insect foundation model, the learning approach needs to understand and be able to model the micro-features of in", + "bbox": [ + 75, + 551, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sects. Based on this observation, we present a novel pre-text task to enhance the recognition ability of the model between small features of the insect, as illustrated in Fig. 1.", + "bbox": [ + 496, + 349, + 890, + 395 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions of this Work: To contribute to the development of the Insect Foundation Model in precision agriculture, we introduce a novel large-scale insect dataset, i.e., Insect-1M, and a new Insect Foundation Model, i.e., Insect-Foundation, that can transfer to various downstream insect-related applications, e.g., insect detection, insect classification, insect vision-language understanding. Our contributions can be summarized as follows. First, we present a new rich and large-volume insect dataset, i.e., Insect-1M, that consists of 1 million images of insects with dense identifications of taxonomy hierarchy from the abstract level of taxonomy, e.g., Class, Order, to the detailed level of taxonomy, e.g., Genus, Species. In addition, each insect contains a detailed description that describes the details and features of insects. To the best of our knowledge, our proposed Insect-1M dataset is $13 \\times$ larger than the prior published IP102 dataset [66]. Second, to model the micro features of insects, we introduce a new self-supervised contrastive learning paradigm with a novel Patch-wise Relevant Attention mechanism to model the feature correlations of insect details. Third, to increase the modeling capability of the Insect Foundation Model in learning insect details, we introduce a new Description Consistency loss to learn the detailed features of insects via the textual description. Finally, through our intensive experiments on the Insect Classification and Insect Detection benchmarks [66], we show the effectiveness of our approach in insect modeling and our superior performance compared to the prior methods.", + "bbox": [ + 496, + 396, + 892, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 829, + 640, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Insect Datasets. There are prior studies releasing insect datasets on a small scale for recognition problems. [60] presented a dataset consisting of 20 species with 10 samples", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21946", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7d86b46415b9e3383fb4bf0a357e6aedbbb06693aa1e598426876d8ab0278e36.jpg", + "image_caption": [ + "Figure 2. Examples of Our Insect-1M Dataset. The left figure illustrates the samples of the four Subphylums, including Chelicerata, Crustacea, Hexapoda, and Myriapoda. The right figure shows an example of hierarchical descriptions of the Aurantia Species." + ], + "image_footnote": [], + "bbox": [ + 158, + 89, + 803, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for each species. Then, [67] introduced an insect dataset including 1,440 samples of 24 species. Several subsequent studies have larger datasets for deep learning, e.g., [68] proposed an insect dataset of 4,500 images with 40 different species for insect classification, and [28] proposed an insect dataset with over 5,000 samples for insect recognition and localization. PestNet [25] and AgriPest [63] were introduced for the small pest detection task. Recently, [66] has presented IP102 as a large-scale dataset containing over $75K$ samples of insects with 102 species for classification and detection tasks. Meanwhile, [59] proposed a large-scale dataset including over $723K$ samples of Arthropoda phylum with 2,752 species. Although prior efforts promoted the development of vision and machine intelligence in precision agriculture, no dataset has a large volume of samples and diverse species for insect-related foundation model training. Therefore, this work introduces a novel dataset that not only contains a large number of samples, i.e. 1M images, but also has hierarchical labels from the high to the low taxonomy level, including class, order, family, genus, and species. Table 1 compares our proposed dataset with the prior ones. In comparison with prior datasets, the number of images in our proposed Insect-1M dataset is $13\\times$ higher than the prior IP102 dataset, and the number of species is $335\\times$ higher than IP102 [66]. To preserve the rights of datasets and authors of images, instead of publishing images, we only provide labels and links to download images.", + "bbox": [ + 75, + 324, + 472, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-supervised Pre-training. Self-supervised pre-training has become a popular strategy for solving visual recognition problems, including classification, localization, segmentation, video recognition, tracking, and many other problems [18, 33-38, 53, 54, 56-58]. SimCLR [8] learned the visual representation of images via a contrastive learning framework using different data augmentation operations. MoCo [17] introduced momentum updating for the encoder while learning the image representation via contrastive learning. The MoCo framework was later used to improve the SimCLR approach without requiring a large training batch size", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[9]. MoCo-V3 [10] improved prior Momentum Contrastive frameworks by eliminating the memory queue to stabilize the training when the batch size is large. DINO [7] proposed a self-supervised learning approach using knowledge distillation with no labels. Later, it was extended to DINO-V2 [40] by stabilizing self-supervised learning when scaling the size of models and data. BEiT [5] proposed a masked image modeling task and used discrete visual tokens from the original image as prediction targets. MAE [18] and SimMIM [69] directly used a decoder to reconstruct pixel values from masked regions. Jigsaw-ViT [11] presented a pre-training task for transformer models by solving the shuffled patches of images. This learning strategy was also applied on the temporal dimension to improve the robustness of video modeling [54]. Micron-BERT [36] studied the micro-changing in facial videos by learning to detect the minor differences in an image that has swapping regions between two frames.", + "bbox": [ + 496, + 324, + 893, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Joint Vision-Language Pre-training. Recent work introduced joint vision-language pre-training. CLIP [43], and ALIGN [19] addressed that dual-encoder models pretrained on image-text pairs in contrastive objectives can learn strong representations of image and text for cross-modal alignment and zero-shot image recognition problems. LiT [72] and BASIC [42] proposed zero-shot transfer learning approaches by teaching the text model to learn the representation of the pre-trained image model via contrastive losses with large-scale data. SimVLM [65], OFA [62], and BLIP [22] trained an encoder-decoder model with language generative losses and achieved high performance in the vision-language benchmarks. CoCa [70] utilized contrastive learning and generative image captioning for global representation learning and fine-grained image-text alignment. Later work [73] used sigmoid loss to compute the image-text similarity for batch size scaling. LexLIP [31] projected images into a lexicon space for image-text sparse matching. Meanwhile, EQSIM [64] computed the similarity by the image-text equivariant changing.", + "bbox": [ + 496, + 598, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21947", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/06daa06c74ccd557973d43c1fe3491f4b93d37481b091872dc27b381125c674e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 161, + 88, + 464, + 280 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c0148a2debcd1348e61db86f23f5ebfb392200ef781fd28b71089a86304e9f63.jpg", + "image_caption": [ + "Figure 3. The Distribution of Subphylum and Its Classes (Left) and The Distribution of Class and Its Orders (Right). Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 464, + 88, + 810, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. The Proposed Insect 1M Dataset", + "text_level": 1, + "bbox": [ + 76, + 306, + 374, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To contribute to establishing the insect foundation model, the large-scale dataset of insects with diverse species is essential. Therefore, we collect a new insect dataset with dense labels of a hierarchical taxonomy. In particular, our Insect-1M dataset contains 1 million insect images with dense hierarchical labels with six main taxonomies, i.e., Subphylum, Class*, Order, Family, Genus, and Species. The samples are in the Phylum Arthropoda and can be divided into 4 Subphylums, which are Chelicerata, Crustacea, Hexapoda, and Myriapoda as shown in Fig. 2. Compared to prior datasets, our Insect-1M has more hierarchical levels with large numbers of species and samples as in Table 1.", + "bbox": [ + 75, + 332, + 473, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Data Collection Protocol", + "text_level": 1, + "bbox": [ + 76, + 526, + 302, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We utilize insect information containing insect data with images and taxonomies collected by naturalists and entomologists. Each insect sample has a corresponding image and its taxonomic label. From the taxonomic label, we crawl the identification description of the corresponding taxonomy. Notice that the taxonomic labels are hierarchical. The description is written from high-level descriptions, e.g., Subphylum and Class, to low-level descriptions, e.g., Species. Fig. 2 shows an example of an insect description.", + "bbox": [ + 75, + 550, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Data Preprocessing and Statistic", + "text_level": 1, + "bbox": [ + 76, + 699, + 362, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data Preprocessing. The raw data is stored in over 1 million HTML files with predefined HTML structures. Then, we parse the data structures to collect the insect images and their labels. More than 2 million raw images and their corresponding labels have been collected. However, the raw data collected consists of a lot of noise, e.g., incorrect identification of insects, corrupted images, and non-insect images. Therefore, to filter these outliers, our entomology experts must verify the images and their labels, i.e., insect identification. Finally, our collected Insect-1M dataset consists of", + "bbox": [ + 75, + 722, + 470, + 875 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1,017,036 clean images with dense labels of 34,212 different insect species.", + "bbox": [ + 500, + 306, + 890, + 337 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data Statistic Fig. 3 shows the sample distributions of the Subphylums and their Classes. It is shown that the Class Insecta has the majority of samples. Fig. 3 also illustrates the distribution of the Orders in the major Classes. For each major Class, the data distribution of Orders is well-balanced.", + "bbox": [ + 496, + 338, + 890, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. The Proposed Insect Foundation Model", + "text_level": 1, + "bbox": [ + 498, + 426, + 854, + 443 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Limitations of Prior Foundation Training Approaches", + "text_level": 1, + "bbox": [ + 498, + 450, + 890, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Limitations One of the issues in the visual insect understanding problem is the visual representation and discrimination of the small and undistinguished features of the insects. While MAE [18] reconstructs an image from a masked image for visual representation learning, it focuses", + "bbox": [ + 496, + 489, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cc30fdf6b1dc6d41449fbfe704560a3ca745d687b3671bdef5e502e546c0e2eb.jpg", + "image_caption": [ + "Figure 4. Comparisons of Self-supervised Methods. MAE [18] fails to reconstruct the details of the insect since it learns general information about the image. Micron-BERT [36] hardly distinguishes the insect and background. Jigsaw-ViT [11] cannot correct shuffled patches due to confusion between the background and the object. Meanwhile, our approach can find separated patches belonging to the insect by scoring each patch. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 517, + 570, + 874, + 799 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "*In this paper, we use the term \"Class\" as a biological taxonomic level.", + "bbox": [ + 99, + 887, + 467, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21948", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/20cc3161fbaa9ff89e008ecc322ba72e6bb398a764e73717a8ad38f39de8e147.jpg", + "image_caption": [ + "Figure 5. The Overview Framework of Our Proposed Approach to Insect Foundation Model." + ], + "image_footnote": [], + "bbox": [ + 122, + 92, + 848, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "on the context inside the image individually without realizing the small details to discriminate between the insects. Meanwhile, Jigsaw solving methods [11, 39] correct the position of image patches to enhance the model robustness to the image structure. This strategy needs more mechanisms to focus on the small details of the image. Micron-BERT [36] highlights the small changes in the image by swapping the regions between two images with similar contexts. However, the small changes in the insect image still preserve the signature features representing the insect. Thus, it makes the model collapse in detecting the small features of insects. Therefore, to address these limitations, we introduce a new approach that learns to recognize the tiny features in the insect images. These features are distinguished from the background by discriminating the minor differences between patches of images individually. Fig. 4 compares prior self-supervised methods [11, 18, 36] with our approach.", + "bbox": [ + 75, + 356, + 472, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 5 illustrates our insect foundation model. The model is designed to capture the small differences in insect features, i.e., textures or limbs, via our new self-supervised pre-text task. Moreover, the model is pre-trained to learn the fine-grained alignment between the insect description and its visual features. Formally, given an input image $I$ , we divide $I$ into non-overlapping patches. Then, a subset of patches $P_{s}$ is sampled, and the remaining patches are put into a pool of image patches $P_{\\mathrm{pool}}$ . The sampling is processed randomly in a uniform distribution. An image encoder is used to map $I_{p}$ into latent vectors. Given an insect description $T$ of the image, a text encoder is presented to extract information from $T$ . A text decoder and joint image-text contrastive learning module are introduced to map the description into the image. Finally, a Patch-wise Relevant Attention module is proposed for self-supervised learning to enhance the discrimination robustness of the model.", + "bbox": [ + 75, + 643, + 472, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Input Modeling", + "text_level": 1, + "bbox": [ + 498, + 356, + 658, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "An input image $I \\in \\mathbb{R}^{H \\times W \\times 3}$ is divided into non-overlapping patches $P = \\{p_s^i\\}_{i=1}^{N_P}$ where $H, W$ are the height and width of the input image, $N_P = HW / (s_p)^2$ is the number of patches. Each patch $p_s^i$ has a resolution of $s_p \\times s_p$ . The non-overlapping patches $P$ are then randomly sampled into a subset of patches $P_s \\subset P$ and put the other patches into a pool of image patches $P_{\\mathrm{pool}}$ . Note that $P_{\\mathrm{pool}}$ contains patches from multiple images in the training set.", + "bbox": [ + 496, + 377, + 890, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Image Encoder", + "text_level": 1, + "bbox": [ + 500, + 508, + 653, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each patch $p_s^i \\in P_s$ is projected into a latent vector $\\mathbf{x}_s^i \\in \\mathbb{R}^d$ where $d$ is the dimension of the latent vectors. A subset patches $P_s$ can be represented as follows:", + "bbox": [ + 496, + 531, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {s} = \\operatorname {c o n c a t} \\left[ \\mathbf {x} _ {s} ^ {i} \\right] _ {i = 1} ^ {N P _ {s}} \\in \\mathbb {R} ^ {N P _ {s} \\times d}, \\quad \\mathbf {x} _ {s} ^ {i} = \\alpha_ {p} \\left(p _ {s} ^ {i}\\right) + \\mathbf {e} _ {p} (i) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 579, + 890, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{p}$ and $\\mathbf{e}_p$ are the projection embedding and position embedding.", + "bbox": [ + 496, + 599, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let an image encoder $E_{\\mathrm{image}}(\\mathbf{X}_s)$ be a stack of $L_{e}$ transformer blocks where each block contains multi-head self-attention (MSA) and multi-layer perceptron (MLP).", + "bbox": [ + 496, + 630, + 890, + 675 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {X} _ {l} ^ {\\prime} = \\mathbf {X} _ {l - 1} + \\operatorname {M S A} (\\ln (\\mathbf {X} _ {l - 1})) \\\\ \\mathbf {X} _ {l} = \\mathbf {X} _ {l} ^ {\\prime} + \\operatorname {M L P} \\left(\\ln \\left(\\mathbf {X} _ {l} ^ {\\prime}\\right)\\right) \\tag {2} \\\\ \\mathbf {X} _ {0} = \\mathbf {X} _ {s}, 1 \\leq l \\leq L _ {e} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 676, + 890, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where LN is the layer normalization. Then, given $\\mathbf{X}_s$ , the output latent vector $\\mathbf{Z}_s$ is represented as follows:", + "bbox": [ + 496, + 729, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} _ {s} = E _ {\\text {i m a g e}} \\left(\\mathbf {X} _ {s}\\right), \\quad \\mathbf {Z} _ {s} \\in \\mathbb {R} ^ {N _ {P _ {s}} \\times d} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 760, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Insect Micro-feature Self-supervised Learning", + "text_level": 1, + "bbox": [ + 498, + 787, + 888, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The recognition of insects relies on the insect texture, eyes, or limbs that are tiny to detect. To make the model robust to the small features of insect images, we propose a self-supervised learning strategy to spot these small features via the small differences in the images. Notice that the insects can be distinguished by detecting and discriminating the", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21949", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "critical features in each part of those insects. To enhance this ability for the model, a pre-text task is presented. In particular, after extracting global information from a masked image of the insect, the vision model learns to find the remaining patches of the image by comparing image patches of different insect species. Thanks to our learning mechanism, the model learns the key features representing each insect and discriminates the small features between different species. As illustrated in Fig. 6, given a subset of patches $P_{s}$ from the image $I$ and a pool of image patches $P_{\\mathrm{pool}}$ , we train the model to find the patches $p_t \\in P_{\\mathrm{pool}}$ that originally belong to the image $I$ . Then, given latent vectors $\\mathbf{Z}_s$ of $P_{s}$ , a patch-wise relevant attention score (PRS) is computed between $\\mathbf{Z}_s$ and each patch $p \\in P_{\\mathrm{pool}}$ . The score can be defined as:", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P R S} = f \\left(\\mathbf {Z} _ {s}, p\\right) \\in [ 0, 1 ] \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 321, + 468, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The higher the score is, the more possibility that $p \\in P$ .", + "bbox": [ + 75, + 340, + 444, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Attention Pooling To compute the relevance between latent vectors $\\mathbf{Z}_s$ from the image $I$ and the patch $p\\in P_{\\mathrm{pool}}$ , the latent vectors $\\mathbf{Z}_s$ should be aggregated to represent the holistic information of $I$ . Inspired by [70], we compute the global information of $I$ via attention pooling. Given a placeholder contextual token $\\mathbf{z}_{ct}^{\\prime}$ as a query $\\mathbf{Q}_{ct}$ and latent vectors $\\mathbf{Z}_s$ as a key $\\mathbf{K}_Z$ and a value $\\mathbf{V}_Z$ , we compute an attention map between $\\mathbf{Q}_{ct}$ and $\\mathbf{K}_Z$ . Then, a contextual token $\\mathbf{z}_{ct}$ representing the global information of $I$ is computed via the attention map and the value $\\mathbf{V}_Z$ . The attention pooling (Fig. 7) can be formulated as Eqn. (5).", + "bbox": [ + 75, + 356, + 468, + 521 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {c t} = \\operatorname {L i n e a r} \\left(\\mathbf {z} _ {c t} ^ {\\prime}\\right) \\quad \\mathbf {K} _ {Z} = \\operatorname {L i n e a r} \\left(\\mathbf {Z} _ {s}\\right) \\quad \\mathbf {V} _ {Z} = \\operatorname {L i n e a r} \\left(\\mathbf {Z} _ {s}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 527, + 455, + 544 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {c t} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {c t} \\mathbf {K} _ {Z} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V} _ {Z} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 547, + 468, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Patch-wise Relevant Attention Given $\\mathbf{z}_{ct}$ as a contextual token representing the information of $I$ , we compute the relevance between $\\mathbf{z}_{ct}$ and $p \\in P_{\\mathrm{pool}}$ . From Eqn. (4), we expand the attention score function $f$ as in Eqn. (6).", + "bbox": [ + 75, + 595, + 468, + 656 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P R S} = f \\left(\\mathbf {Z} _ {s}, p\\right) = H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 660, + 468, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_p = E_{\\mathrm{image}}(\\alpha_p(p))$ is a latent vector representing the patch $p$ , $H$ is a similarity function between two latent", + "bbox": [ + 75, + 678, + 468, + 709 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bdf928a9da0d6066052047a8511a2b9f24dd8acfd9213bde54e8690134def5a8.jpg", + "image_caption": [ + "Figure 6. Pool of Image Patches. A subset of patches of an image is sampled for image encoding while the remaining patches are placed into a pool of patches for the self-supervised pre-text task." + ], + "image_footnote": [], + "bbox": [ + 109, + 729, + 437, + 851 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "vectors. From Eqn. (6), we expand the score function into a self-supervised loss function $\\mathcal{L}_{\\mathrm{PRS}}$ as follow:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e l}} = - y \\log \\left(H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right)\\right) - (1 - y) \\log \\left(1 - H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right)\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 127, + 890, + 143 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $y = 1$ if $p\\in P$ and $y = 0$ otherwise.", + "bbox": [ + 500, + 150, + 787, + 165 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Fine-grained Insect Image-Text Alignment", + "text_level": 1, + "bbox": [ + 498, + 175, + 861, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Each species has an individual definition and description that can be aligned to parts of the insect image. We adopt a text decoder to generate the species descriptions from insect images. Moreover, to capture the general information of species, we utilize contrastive learning between global features of the insect images and description. As a result, the model can learn specific information from insect images via insect descriptions.", + "bbox": [ + 496, + 199, + 890, + 319 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Formally, an insect description text is tokenized into $T = \\{t_i\\}_{i=1}^{N_T}$ where $N_T$ is the number of tokens of the description. Each token $t_i \\in T$ is embedded into a latent vector $\\mathbf{w}_i \\in \\mathbb{R}^d$ . The description can be represented as:", + "bbox": [ + 498, + 319, + 890, + 380 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} = \\operatorname {c o n c a t} \\left[ \\mathbf {w} _ {i} \\right] _ {i = 1} ^ {N _ {T}} \\in \\mathbb {R} ^ {N _ {T} \\times d}, \\quad \\mathbf {w} _ {i} = \\alpha_ {w} + \\mathbf {e} _ {w} (i) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 385, + 890, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha_w$ and $\\mathbf{e}_w$ are the projection embedding and position embedding.", + "bbox": [ + 498, + 409, + 890, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similar to the image encoder, let the text encoder $E_{\\mathrm{text}}(\\mathbf{W})$ be a stack of $L_e'$ transformer blocks containing multi-head self-attention and multi-layer perceptron. The output latent vector $\\mathbf{Z}'$ of the description is computed as", + "bbox": [ + 498, + 439, + 890, + 500 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} ^ {\\prime} = E _ {\\text {t e x t}} (\\mathbf {W}), \\quad \\mathbf {Z} ^ {\\prime} \\in \\mathbb {R} ^ {N _ {T} \\times d} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 503, + 890, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then use the latent vector $\\mathbf{Z}_s$ of the insect image and $\\mathbf{W}'$ of the description text for image-text contrastive learning and multi-modal image description decoding.", + "bbox": [ + 496, + 529, + 890, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image-text Contrastive Learning. Inspired by the prior language model frameworks [14, 21, 27, 44], a contextual token $\\mathbf{w}_{ct}$ representing the semantic information of the description is added at the beginning of $\\mathbf{W}$ as in Eqn. 8. Then the two encoders $E_{\\mathrm{image}}$ and $E_{\\mathrm{text}}$ can be jointly optimized via contrastive learning as follow:", + "bbox": [ + 496, + 574, + 890, + 664 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n}} = \\frac {- 1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {T} \\mathbf {w} _ {i}\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\mathbf {z} _ {i} ^ {T} \\mathbf {w} _ {j}\\right)} + \\log \\frac {\\exp \\left(\\mathbf {w} _ {i} ^ {T} \\mathbf {z} _ {i}\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\mathbf {w} _ {i} ^ {T} \\mathbf {z} _ {j}\\right)} \\right] \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 667, + 890, + 714 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3b125a3998166813f7ef7a0902320f8b897438cecb35cb6396300e90809fc2f2.jpg", + "image_caption": [ + "Figure 7. Attention Pooling Module. The contextual token $\\mathbf{z}_{ct}$ represents the global information of the image $I$ ." + ], + "image_footnote": [], + "bbox": [ + 531, + 738, + 861, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21950", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/adacfdca71c17c3470354757a50c30fb1b4b26d8592aa81b8e73624d42c4d593.jpg", + "table_caption": [ + "Table 2. Effectiveness of our method on the IP102 Classification. We evaluate approach with three different vision transformer backbones, i.e., ViT-small/16, ViT-base/16, and ViT-large/16, without or with Attention Pooling (Attn Pool), and three different losses, i.e. Patch-wise Relevant Loss $(\\mathcal{L}_{\\mathrm{rel}})$ , Image-Text Contrastive Loss $(\\mathcal{L}_{\\mathrm{con}})$ , and Description Loss $(\\mathcal{L}_{\\mathrm{desc}})$ ." + ], + "table_footnote": [], + "table_body": "
BackboneLrelAttn PoolLconLdescAcc@1 (%)Acc@5 (%)
ViT-small/16✓68.988.8
✓✓69.589.7
✓✓✓70.789.9
✓✓✓✓71.587.7
ViT-base/16✓72.491.0
✓✓73.391.6
✓✓✓74.291.9
✓✓✓✓75.892.1
ViT-large/16✓73.890.9
✓✓74.691.6
✓✓✓75.991.4
✓✓✓✓76.992.7
", + "bbox": [ + 106, + 174, + 433, + 349 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_i$ and $\\mathbf{w}_i$ is the contextual token of the $i$ -th insect image and description.", + "bbox": [ + 76, + 354, + 468, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multi-modal Image Description Decoding. While image-text contrastive learning represents the global semantic information between the image and description, the multi-model image description decoding aims for the fine-grained details by predicting the tokenized texts of $T$ in an autoregressive manner, as shown in Eqn. (11).", + "bbox": [ + 75, + 385, + 468, + 476 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e s c}} = - \\sum_ {t = 1} ^ {N _ {T}} \\log D _ {\\text {m u l t i}} \\left(\\mathbf {w} _ {t} \\mid \\mathbf {W} _ {0: t - 1}, \\mathbf {Z} _ {s}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 486, + 468, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $D_{\\mathrm{multi}}$ is an autoregressive multi-modal text decoder.", + "bbox": [ + 76, + 530, + 467, + 546 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 560, + 282, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Foundation Model Pre-training", + "text_level": 1, + "bbox": [ + 76, + 585, + 354, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our experiments use ViT-Base (ViT-B/16) [15] as the backbone. The images are resized and cropped randomly into the resolution of $224 \\times 224$ . Then, each image is divided into patches of $16 \\times 16$ , creating $N_P = 196$ patches. The patch sampling ratio is selected as $50\\%$ , and the remaining patches are put into the pool of image patches. Each patch is projected to latent space of $d = 768$ dimensions. The text encoder and multi-modal text decoder are adopted from the pre-trained BERT model [14]. The model is implemented in PyTorch [41] and trained by $16 \\times \\mathrm{A}100$ GPUs. The learning rate is initially set to $1.5 \\times 10^{-4}$ with the Consine learning rate scheduler [29]. The model is optimized by AdamW [30] with 200 epochs and a batch size of 64 per GPU.", + "bbox": [ + 75, + 608, + 468, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Datasets and Benchmarks", + "text_level": 1, + "bbox": [ + 76, + 816, + 313, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "IP102 Classification [66] provides 102 species of insects and contains 45,095 training samples, 7,508 validation samples, and 22,619 testing samples. For each species, an image might contain a single insect, multiple insects, or even a", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/edf3dd6da9bed99a83cd07b9beb609ea3899199b730e558d1a02e9fbe04564c1.jpg", + "table_caption": [ + "Table 3. Classification results on IP102 Classification benchmark. Both proposed models pre-trained with and without the insect descriptions outperform prior methods by a large margin." + ], + "table_footnote": [], + "table_body": "
MethodDescriptionPre-train DataAcc@1 (%)Acc@5 (%)
ResNet [66]XImageNet1K49.4-
EfficientNet [6]XImageNet1K60.7-
DenseNet [32]XImageNet1K61.9-
GAEnsemble [3]XImageNet1K67.1-
ViT [15]XImageNet1K71.687.7
MoCo [17]X1M-Insect70.688.4
DINO [7]X1M-Insect71.591.4
MAE [18]X1M-Insect72.091.5
CoCa [70]✓1M-Insect72.891.1
Insect-FoundationX1M-Insect73.391.6
Insect-Foundation✓1M-Insect75.892.1
", + "bbox": [ + 532, + 132, + 856, + 265 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "diseased crop caused by the species. The insects are in different forms for each class, e.g., egg, larva, pupa, and adult. The performance of insect classification is evaluated by the accuracy of Top 1 (Acc@1) and Top 5 (Acc@5).", + "bbox": [ + 496, + 270, + 890, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "IP102 Detection [66] includes 15,178 training images and 3,798 testing images of 102 different species. Following the COCO benchmark [23], the insect detection performance is measured by the Average Precision (AP) and Average Precision at IoU thresholds of 0.5 (AP $^{50}$ ) and 0.75 (AP $^{75}$ ).", + "bbox": [ + 496, + 330, + 890, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 419, + 663, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our ablation experiments study the effectiveness of our proposed model and hyper-parameters on the IP102 Classification Benchmark as shown in Table 2.", + "bbox": [ + 496, + 443, + 890, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Network Backbones Table 2 studies the impact of different Vision Transformer backbone sizes, including ViT-small/16, ViT-base/16, and ViT-large/16. As shown in our results, the powerful backbone carries more improvement. In particular, when changing the Transformer backbone size from small to base, the accuracy score increases by a large margin of $4.3\\%$ while the large Transformer backbone improves the accuracy score by $1.1\\%$ .", + "bbox": [ + 496, + 489, + 890, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Attention Pooling We evaluate the impact of the attention pooling in the visual representation of the insect images. As shown in Table 2, the Attention Pooling has better representation than the standard classification token computed through transformer layers. In particular, the top-1 accuracies for the three backbones, i.e., small, base, and large, have been increased from $68.9\\%$ to $69.5\\%$ , from $72.4\\%$ to $73.3\\%$ , and from $73.8\\%$ to $74.6\\%$ .", + "bbox": [ + 496, + 611, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Image-Text Contrastive Loss As reported in Table 2, the model can understand the insect images better when the model learns to match the images and their descriptions. In detail, the accuracy scores have been increased by $0.8\\%$ , $0.9\\%$ , and $1.3\\%$ for the three backbones when applying the Image-Text Contrastive Loss.", + "bbox": [ + 496, + 733, + 890, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Description Loss The full configuration in Table 2 shows the experimental results of our model using the Description Loss. As shown in Table 2, the Description Loss helps the model to well-align the information between images and the details of descriptions. Hence, the model", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21951", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6fd20269ab7c086a5d012da4231972dc298fa232ae1c6cb10e4ed8d7befb1139.jpg", + "image_caption": [ + "Figure 8. Attention Visualization. Compared to MAE [18], our model is robust to small details of insect images. The model can focus on the small textures of the insect, even if the texture is the same as the background (bottom images). Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 109, + 89, + 436, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "can represent the fine-grained features of the insects better. In particular, the accuracy scores have been improved from $70.7\\%$ to $71.5\\%$ , from $74.2\\%$ to $75.8\\%$ , and from $75.9\\%$ to $76.9\\%$ for ViT-small/16, ViT-base/16, and ViT-large/16.", + "bbox": [ + 76, + 329, + 467, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Comparisons with Prior SOTA Methods", + "text_level": 1, + "bbox": [ + 76, + 398, + 421, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Insect Classification Tasks. We fine-tune the linear layer with our pre-trained model on the IP102 dataset [66] for the classification task. As shown in Table 3, our model outperforms deep learning models [15, 16, 20, 50, 52] pre-trained on ImageNet [12] by a large margin. Compared to other pre-training methods [7, 17, 18, 70] on the proposed 1M-Insect dataset, our model shows better performance for both training without and with insect descriptions of $73.3\\%$ and $75.8\\%$ , respectively. It is shown that the proposed approach has a better visual representation of insect images than the prior pre-training methods on the same dataset.", + "bbox": [ + 75, + 421, + 467, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization Results Fig. 8 visualizes the attention maps of our model compared to MAE [18] pre-trained on the proposed dataset. Since the textures are similar to the background, it is hard for MAE to focus on the small details of the insect. On the contrary, our model can detect the key features, i.e., the textures and the limbs, of the insects.", + "bbox": [ + 75, + 587, + 467, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Zero-shot Insect Classification. We evaluate the performance of our model on the IP102 dataset [66] in a zero-shot manner. In detail, a description corresponds to each species to make the text encoder extract more semantic information about each species. Then, for each insect image, we use the image encoder to extract global features and compare them to each description feature to predict the insect Table 4. Zero-shot classification results on IP102 Classification benchmark. The proposed model outperforms prior vision-language pretraining methods.", + "bbox": [ + 75, + 678, + 467, + 825 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c61d226177e3b245d206c27ca99b22b4fa8c10cc9c9e38c149d7311bb5badbf0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPretrain DataAccuracy (%)
CLIP [43]1M-Insect41.1
LiT [72]1M-Insect43.6
CoCa [70]1M-Insect45.3
Insect-Foundation1M-Insect49.9
", + "bbox": [ + 117, + 828, + 423, + 897 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ca9505deb18b437f3a03e3ac36119f4e7ea85b25b8e75c140cb8fb30fa2ec376.jpg", + "table_caption": [ + "Table 5. Detection results on IP102 Detection benchmark. The proposed model outperforms prior pre-training methods." + ], + "table_footnote": [], + "table_body": "
MethodBackbonePre-train DataAP (%)\\( AP^{50} \\)(%)\\( AP^{75} \\)(%)
FRCNN [47]VGG-16 [50]ImageNet1K21.147.915.2
FPN [24]ResNet-50 [16]ImageNet1K28.154.923.3
SSD300 [26]VGG-16 [50]ImageNet1K21.547.216.6
RefineDet [74]VGG-16 [50]ImageNet1K22.849.016.8
YOLOv3 [46]DarkNet-53 [46]ImageNet1K25.750.621.8
FPN [24]ViT [15]ImageNet1K32.854.735.0
FPN [24]MoCo [17]1M-Insect33.656.135.3
FPN [24]DINO [7]1M-Insect34.055.837.1
FPN [24]MAE [18]1M-Insect34.758.437.8
FPN [24]Insect-Foundation1M-Insect36.659.140.3
", + "bbox": [ + 531, + 117, + 854, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "species. Table 4 reports the results of zero-shot classification on the IP102 Classification benchmark. Our model outperforms prior image-text pre-training methods [43, 70, 72] at an accuracy of $49.9\\%$ . It shows that our model has well-alignment between the insect image and its description.", + "bbox": [ + 496, + 251, + 890, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Insect Detection Tasks. As shown in Table 5, we train a Faster R-CNN model [47] on the IP102 Detection dataset with the ViT backbone adapted for FPN [24]. Compared to models pre-trained on ImageNet [12], our model achieves SOTA results with an average precision of $36.6\\%$ and $\\mathrm{AP}^{50}$ of $59.1\\%$ higher than the same backbone pre-trained on ImageNet [12] having AP of $32.8\\%$ and $\\mathrm{AP}^{50}$ of $54.7\\%$ . Compared to other self-supervised methods [7, 17, 18], our model achieves higher precision. Thus, our model focuses on the features of insects better than prior methods.", + "bbox": [ + 496, + 327, + 890, + 478 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 494, + 625, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper has introduced a new large-scale Insect-1M dataset that supports the development of the Insect Foundation Model in precision agriculture. Our proposed dataset includes a large diversity of insect species and multi-level labels of taxonomy. In addition, Insect-1M consists of detailed descriptions of insects that support vision-language insect model training. Then, to improve the micro-feature modeling of our insect foundation model, we introduce a new Patch-wise Relevant Attention mechanism and Description Consistency loss to learn the details of insects. Our experimental results have illustrated the effectiveness and significance of our Insect-1M and Insect Foundation Model. Limitations This study used a specific network design and learning hyper-parameter to support our hypothesis. However, our approach potentially consists of several limitations related to the design of our Patch-wise Relevant Attention mechanism, where the patches of background and foreground are equally treated. It could result in difficulty in learning the different features of insects. This limitation will further motivate future research to improve the Insect Foundation Model and Micro-feature Modeling.", + "bbox": [ + 496, + 520, + 890, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work is partly supported by NSF DART, NSF SBIR Phase 2, and JBHunt Company. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4203-4212, 2018. 8" + ], + "bbox": [ + 501, + 92, + 890, + 795 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21955", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Insect-Foundation_ A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding/15f153cc-fc03-4374-8076-9262f9d4ae0f_model.json b/2024/Insect-Foundation_ A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding/15f153cc-fc03-4374-8076-9262f9d4ae0f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ed5a650ba7f8a3e84c2d2849adc21f358676d1ce --- /dev/null +++ b/2024/Insect-Foundation_ A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding/15f153cc-fc03-4374-8076-9262f9d4ae0f_model.json @@ -0,0 +1,2565 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.12, + 0.131, + 0.85, + 0.175 + ], + "angle": 0, + "content": "Insect-Foundation: A Foundation Model and Large-scale 1M Dataset for Visual Insect Understanding" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.203, + 0.912, + 0.275 + ], + "angle": 0, + "content": "Hoang-Quan Nguyen\\(^{1*}\\), Thanh-Dat Truong\\(^{1*}\\), Xuan Bac Nguyen\\(^{1}\\), Ashley Dowling\\(^{2}\\), Xin Li\\(^{3}\\), Khoa Luu\\(^{1}\\) \n\\(^{1}\\)Department of Electrical Engineering and Computer Science, University of Arkansas, AR \n\\(^{2}\\)Department of Entomology and Plant Pathology, University of Arkansas, AR \n\\(^{3}\\)Department of Computer Science, SUNY Albany, NY" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.277, + 0.804, + 0.293 + ], + "angle": 0, + "content": "{hn016, tt032, xnguyen, adowling, khoaluu}@uark.edu, xli48@albany.edu" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.296, + 0.757, + 0.309 + ], + "angle": 0, + "content": "https://uark-cviu.github.io/projects/insect_foundation.html" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.313, + 0.36 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.474, + 0.816 + ], + "angle": 0, + "content": "In precision agriculture, the detection and recognition of insects play an essential role in the ability of crops to grow healthy and produce a high-quality yield. The current machine vision model requires a large volume of data to achieve high performance. However, there are approximately 5.5 million different insect species in the world. None of the existing insect datasets can cover even a fraction of them due to varying geographic locations and acquisition costs. In this paper, we introduce a novel \"Insect-1M\" dataset, a game-changing resource poised to revolutionize insect-related foundation model training. Covering a vast spectrum of insect species, our dataset, including 1 million images with dense identification labels of taxonomy hierarchy and insect descriptions, offers a panoramic view of entomology, enabling foundation models to comprehend visual and semantic information about insects like never before. Then, to efficiently establish an Insect Foundation Model, we develop a micro-feature self-supervised learning method with a Patch-wise Relevant Attention mechanism capable of discerning the subtle differences among insect images. In addition, we introduce Description Consistency loss to improve micro-feature modeling via insect descriptions. Through our experiments, we illustrate the effectiveness of our proposed approach in insect modeling and achieve State-of-the-Art performance on standard benchmarks of insect-related tasks. Our Insect Foundation Model and Dataset promise to empower the next generation of insect-related vision models, bringing them closer to the ultimate goal of precision agriculture." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.208, + 0.837 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.848, + 0.469, + 0.878 + ], + "angle": 0, + "content": "Insects are the most diverse and abundant eukaryotic organisms on the planet. They inhabit all terrestrial and aquatic" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.347, + 0.598, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.414, + 0.595, + 0.422 + ], + "angle": 0, + "content": "Masked Monarch" + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.349, + 0.721, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.465, + 0.701, + 0.495 + ], + "angle": 0, + "content": "Which patches belong to the Monarch/Euryurus?" + }, + { + "type": "image_caption", + "bbox": [ + 0.727, + 0.408, + 0.747, + 0.484 + ], + "angle": 270, + "content": "Patch-wise Relevant" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.346, + 0.78, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.348, + 0.872, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.414, + 0.875, + 0.423 + ], + "angle": 0, + "content": "Completed Monarch" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.441, + 0.598, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.507, + 0.595, + 0.515 + ], + "angle": 0, + "content": "Masked Euryurus" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.441, + 0.78, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.441, + 0.872, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.507, + 0.875, + 0.515 + ], + "angle": 0, + "content": "Completed Euryurus" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.517, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Figure 1. Our Proposed Patch-wise Relevant Attention. Given masked insect images and separated image patches, our model can discriminate these patches that have small differences via relevant scores computed between masked images and image patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.791 + ], + "angle": 0, + "content": "habitats and play a significant role within their community, habitat, and ecosystem as contributors to nutrient cycling, maintenance of plant and animal communities, disease cycling, and overall ecosystem health. Therefore, in the agricultural revolution, the detection and identification of insects plays a key role in ensuring healthy crop growth and high-quality production. Prior methods [2, 3, 6, 32, 55, 66] often fine-tuned the pre-trained ImageNet models on insect data for specific insect-related tasks, e.g., Insect Classification [2, 6, 13, 66], Insect Detection [66]. However, these methods remained limited since the models pre-trained on ImageNet [12, 15, 16, 20, 50, 52] could not model the micro features of insects, e.g., tiny texture and details of insects, as ImageNet [12] is the generic object dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recent foundation models [7-9, 17-19, 40, 43, 69, 70] pre-trained on large-scale datasets have revolutionized vision models with solid performance on downstream applications. These models are designed to model general or specific properties of images or videos that can later be generalized to downstream tasks and unseen data. The capability of the foundation model is often implemented with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.193, + 0.899 + ], + "angle": 0, + "content": "*Co-first authors" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21945" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.894, + 0.131 + ], + "angle": 0, + "content": "Table 1. Comparison with existing datasets related to insects. Our proposed dataset has hierarchical labels with 6 main hierarchical levels, i.e., Subphylum, Class, Order, Family, Genus, and Species, and large numbers of species and samples. Moreover, the proposed dataset contains hierarchical descriptions for each insect and auxiliary taxonomic level, i.e., Subclass, Suborder, Subfamily, etc." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.133, + 0.849, + 0.348 + ], + "angle": 0, + "content": "
DatasetYearSpeciesHierarchical \nLabelsHierarchical \nLevelsInsect \nDescriptionAuxiliary \nTaxonomic LevelNumber of \nSamples
Samanta et al. [48]20128X1XX609
Wang et al. [61]2012221✓3XX225
Venugoban et al. [60]201420X1XX200
Xie et al. [67]201524X1XX1,440
Liu et al. [28]201612X1XX5,136
Xie et al. [68]201840X1XX4,500
Deng et al. [13]201810X1XX563
Alfarisy et al. [1]201813X1XX4,511
PestNet [25]201916X1XX88,670
IP102 [66]2019102✓3XX75,222
AgriPest [63]202114✓2XX49,707
INSECT [4]20211,213X1XX21,212
iNat-2021 [59]20212,752✓5XX723,816
Our Insect-1M202334,212✓6✓✓1,017,036
" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.351, + 0.472, + 0.548 + ], + "angle": 0, + "content": "self-supervised or prompt-engineering training on large-scale datasets [12, 19, 49, 71]. However, the current insect datasets [1, 2, 6, 13, 28, 48, 60, 61, 66-68] are insufficient to establish the foundation model of insects due to their scale and diversity. Indeed, the most recent work presents an insect recognition dataset containing over 75,000 images of 102 species [66]. Although the dataset includes many species, compared to the species of insects in the natural environment with over 5.5 million species [45, 51], the current work needs to have the diversity of insects. Furthermore, to our knowledge, the current insect dataset [66] does not provide the corresponding insect descriptions, limiting the ability to learn the foundation models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Although the dataset is an important factor in developing an insect foundation model, the learning approach of the foundation model plays a significant role in performance. There is significant progress in developing vision foundation models. Common approaches learned alignment between vision and language, for example, CLIP [43], ALIGN [19], CoCa [70], to model visual concepts and data distributions. Meanwhile, self-supervised contrastive or distillation learning approaches, e.g., MoCo [9, 10, 17], DINO [7, 40], MAE [18], etc., learned the vision model by various pretext tasks and have shown its scaling ability and generalizes well to various downstream tasks. However, most of these previous foundation models represent the general information of natural images without specific knowledge. When deploying in the insect domains, they cannot capture the micro-features of insects, i.e., key features or appearance to distinguish the species, since the texture and details of insects are often small and diverse compared to generic objects. Meanwhile, fine-grained discrimination between insect images is crucial in insect foundation models due to the high diversity of species. Therefore, to successfully develop the insect foundation model, the learning approach needs to understand and be able to model the micro-features of in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.396 + ], + "angle": 0, + "content": "sects. Based on this observation, we present a novel pre-text task to enhance the recognition ability of the model between small features of the insect, as illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.893, + 0.82 + ], + "angle": 0, + "content": "Contributions of this Work: To contribute to the development of the Insect Foundation Model in precision agriculture, we introduce a novel large-scale insect dataset, i.e., Insect-1M, and a new Insect Foundation Model, i.e., Insect-Foundation, that can transfer to various downstream insect-related applications, e.g., insect detection, insect classification, insect vision-language understanding. Our contributions can be summarized as follows. First, we present a new rich and large-volume insect dataset, i.e., Insect-1M, that consists of 1 million images of insects with dense identifications of taxonomy hierarchy from the abstract level of taxonomy, e.g., Class, Order, to the detailed level of taxonomy, e.g., Genus, Species. In addition, each insect contains a detailed description that describes the details and features of insects. To the best of our knowledge, our proposed Insect-1M dataset is \\(13 \\times\\) larger than the prior published IP102 dataset [66]. Second, to model the micro features of insects, we introduce a new self-supervised contrastive learning paradigm with a novel Patch-wise Relevant Attention mechanism to model the feature correlations of insect details. Third, to increase the modeling capability of the Insect Foundation Model in learning insect details, we introduce a new Description Consistency loss to learn the detailed features of insects via the textual description. Finally, through our intensive experiments on the Insect Classification and Insect Detection benchmarks [66], we show the effectiveness of our approach in insect modeling and our superior performance compared to the prior methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.642, + 0.846 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Insect Datasets. There are prior studies releasing insect datasets on a small scale for recognition problems. [60] presented a dataset consisting of 20 species with 10 samples" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21946" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.09, + 0.805, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.89, + 0.32 + ], + "angle": 0, + "content": "Figure 2. Examples of Our Insect-1M Dataset. The left figure illustrates the samples of the four Subphylums, including Chelicerata, Crustacea, Hexapoda, and Myriapoda. The right figure shows an example of hierarchical descriptions of the Aurantia Species." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.473, + 0.734 + ], + "angle": 0, + "content": "for each species. Then, [67] introduced an insect dataset including 1,440 samples of 24 species. Several subsequent studies have larger datasets for deep learning, e.g., [68] proposed an insect dataset of 4,500 images with 40 different species for insect classification, and [28] proposed an insect dataset with over 5,000 samples for insect recognition and localization. PestNet [25] and AgriPest [63] were introduced for the small pest detection task. Recently, [66] has presented IP102 as a large-scale dataset containing over \\(75K\\) samples of insects with 102 species for classification and detection tasks. Meanwhile, [59] proposed a large-scale dataset including over \\(723K\\) samples of Arthropoda phylum with 2,752 species. Although prior efforts promoted the development of vision and machine intelligence in precision agriculture, no dataset has a large volume of samples and diverse species for insect-related foundation model training. Therefore, this work introduces a novel dataset that not only contains a large number of samples, i.e. 1M images, but also has hierarchical labels from the high to the low taxonomy level, including class, order, family, genus, and species. Table 1 compares our proposed dataset with the prior ones. In comparison with prior datasets, the number of images in our proposed Insect-1M dataset is \\(13\\times\\) higher than the prior IP102 dataset, and the number of species is \\(335\\times\\) higher than IP102 [66]. To preserve the rights of datasets and authors of images, instead of publishing images, we only provide labels and links to download images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Self-supervised Pre-training. Self-supervised pre-training has become a popular strategy for solving visual recognition problems, including classification, localization, segmentation, video recognition, tracking, and many other problems [18, 33-38, 53, 54, 56-58]. SimCLR [8] learned the visual representation of images via a contrastive learning framework using different data augmentation operations. MoCo [17] introduced momentum updating for the encoder while learning the image representation via contrastive learning. The MoCo framework was later used to improve the SimCLR approach without requiring a large training batch size" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.596 + ], + "angle": 0, + "content": "[9]. MoCo-V3 [10] improved prior Momentum Contrastive frameworks by eliminating the memory queue to stabilize the training when the batch size is large. DINO [7] proposed a self-supervised learning approach using knowledge distillation with no labels. Later, it was extended to DINO-V2 [40] by stabilizing self-supervised learning when scaling the size of models and data. BEiT [5] proposed a masked image modeling task and used discrete visual tokens from the original image as prediction targets. MAE [18] and SimMIM [69] directly used a decoder to reconstruct pixel values from masked regions. Jigsaw-ViT [11] presented a pre-training task for transformer models by solving the shuffled patches of images. This learning strategy was also applied on the temporal dimension to improve the robustness of video modeling [54]. Micron-BERT [36] studied the micro-changing in facial videos by learning to detect the minor differences in an image that has swapping regions between two frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Joint Vision-Language Pre-training. Recent work introduced joint vision-language pre-training. CLIP [43], and ALIGN [19] addressed that dual-encoder models pretrained on image-text pairs in contrastive objectives can learn strong representations of image and text for cross-modal alignment and zero-shot image recognition problems. LiT [72] and BASIC [42] proposed zero-shot transfer learning approaches by teaching the text model to learn the representation of the pre-trained image model via contrastive losses with large-scale data. SimVLM [65], OFA [62], and BLIP [22] trained an encoder-decoder model with language generative losses and achieved high performance in the vision-language benchmarks. CoCa [70] utilized contrastive learning and generative image captioning for global representation learning and fine-grained image-text alignment. Later work [73] used sigmoid loss to compute the image-text similarity for batch size scaling. LexLIP [31] projected images into a lexicon space for image-text sparse matching. Meanwhile, EQSIM [64] computed the similarity by the image-text equivariant changing." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21947" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.163, + 0.089, + 0.465, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.089, + 0.811, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.289, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Figure 3. The Distribution of Subphylum and Its Classes (Left) and The Distribution of Class and Its Orders (Right). Best viewed in color." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.307, + 0.375, + 0.323 + ], + "angle": 0, + "content": "3. The Proposed Insect 1M Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.474, + 0.516 + ], + "angle": 0, + "content": "To contribute to establishing the insect foundation model, the large-scale dataset of insects with diverse species is essential. Therefore, we collect a new insect dataset with dense labels of a hierarchical taxonomy. In particular, our Insect-1M dataset contains 1 million insect images with dense hierarchical labels with six main taxonomies, i.e., Subphylum, Class*, Order, Family, Genus, and Species. The samples are in the Phylum Arthropoda and can be divided into 4 Subphylums, which are Chelicerata, Crustacea, Hexapoda, and Myriapoda as shown in Fig. 2. Compared to prior datasets, our Insect-1M has more hierarchical levels with large numbers of species and samples as in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.527, + 0.303, + 0.541 + ], + "angle": 0, + "content": "3.1. Data Collection Protocol" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.688 + ], + "angle": 0, + "content": "We utilize insect information containing insect data with images and taxonomies collected by naturalists and entomologists. Each insect sample has a corresponding image and its taxonomic label. From the taxonomic label, we crawl the identification description of the corresponding taxonomy. Notice that the taxonomic labels are hierarchical. The description is written from high-level descriptions, e.g., Subphylum and Class, to low-level descriptions, e.g., Species. Fig. 2 shows an example of an insect description." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.7, + 0.363, + 0.716 + ], + "angle": 0, + "content": "3.2. Data Preprocessing and Statistic" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Data Preprocessing. The raw data is stored in over 1 million HTML files with predefined HTML structures. Then, we parse the data structures to collect the insect images and their labels. More than 2 million raw images and their corresponding labels have been collected. However, the raw data collected consists of a lot of noise, e.g., incorrect identification of insects, corrupted images, and non-insect images. Therefore, to filter these outliers, our entomology experts must verify the images and their labels, i.e., insect identification. Finally, our collected Insect-1M dataset consists of" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.308, + 0.891, + 0.338 + ], + "angle": 0, + "content": "1,017,036 clean images with dense labels of 34,212 different insect species." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.415 + ], + "angle": 0, + "content": "Data Statistic Fig. 3 shows the sample distributions of the Subphylums and their Classes. It is shown that the Class Insecta has the majority of samples. Fig. 3 also illustrates the distribution of the Orders in the major Classes. For each major Class, the data distribution of Orders is well-balanced." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.428, + 0.855, + 0.444 + ], + "angle": 0, + "content": "4. The Proposed Insect Foundation Model" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.452, + 0.892, + 0.483 + ], + "angle": 0, + "content": "4.1. Limitations of Prior Foundation Training Approaches" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Limitations One of the issues in the visual insect understanding problem is the visual representation and discrimination of the small and undistinguished features of the insects. While MAE [18] reconstructs an image from a masked image for visual representation learning, it focuses" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.571, + 0.875, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.8, + 0.892, + 0.897 + ], + "angle": 0, + "content": "Figure 4. Comparisons of Self-supervised Methods. MAE [18] fails to reconstruct the details of the insect since it learns general information about the image. Micron-BERT [36] hardly distinguishes the insect and background. Jigsaw-ViT [11] cannot correct shuffled patches due to confusion between the background and the object. Meanwhile, our approach can find separated patches belonging to the insect by scoring each patch. Best viewed in color." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.888, + 0.468, + 0.9 + ], + "angle": 0, + "content": "*In this paper, we use the term \"Class\" as a biological taxonomic level." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21948" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.093, + 0.849, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.209, + 0.337, + 0.759, + 0.352 + ], + "angle": 0, + "content": "Figure 5. The Overview Framework of Our Proposed Approach to Insect Foundation Model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.473, + 0.63 + ], + "angle": 0, + "content": "on the context inside the image individually without realizing the small details to discriminate between the insects. Meanwhile, Jigsaw solving methods [11, 39] correct the position of image patches to enhance the model robustness to the image structure. This strategy needs more mechanisms to focus on the small details of the image. Micron-BERT [36] highlights the small changes in the image by swapping the regions between two images with similar contexts. However, the small changes in the insect image still preserve the signature features representing the insect. Thus, it makes the model collapse in detecting the small features of insects. Therefore, to address these limitations, we introduce a new approach that learns to recognize the tiny features in the insect images. These features are distinguished from the background by discriminating the minor differences between patches of images individually. Fig. 4 compares prior self-supervised methods [11, 18, 36] with our approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Fig. 5 illustrates our insect foundation model. The model is designed to capture the small differences in insect features, i.e., textures or limbs, via our new self-supervised pre-text task. Moreover, the model is pre-trained to learn the fine-grained alignment between the insect description and its visual features. Formally, given an input image \\(I\\), we divide \\(I\\) into non-overlapping patches. Then, a subset of patches \\(P_{s}\\) is sampled, and the remaining patches are put into a pool of image patches \\(P_{\\mathrm{pool}}\\). The sampling is processed randomly in a uniform distribution. An image encoder is used to map \\(I_{p}\\) into latent vectors. Given an insect description \\(T\\) of the image, a text encoder is presented to extract information from \\(T\\). A text decoder and joint image-text contrastive learning module are introduced to map the description into the image. Finally, a Patch-wise Relevant Attention module is proposed for self-supervised learning to enhance the discrimination robustness of the model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.357, + 0.66, + 0.373 + ], + "angle": 0, + "content": "4.2. Input Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.892, + 0.501 + ], + "angle": 0, + "content": "An input image \\( I \\in \\mathbb{R}^{H \\times W \\times 3} \\) is divided into non-overlapping patches \\( P = \\{p_s^i\\}_{i=1}^{N_P} \\) where \\( H, W \\) are the height and width of the input image, \\( N_P = HW / (s_p)^2 \\) is the number of patches. Each patch \\( p_s^i \\) has a resolution of \\( s_p \\times s_p \\). The non-overlapping patches \\( P \\) are then randomly sampled into a subset of patches \\( P_s \\subset P \\) and put the other patches into a pool of image patches \\( P_{\\mathrm{pool}} \\). Note that \\( P_{\\mathrm{pool}} \\) contains patches from multiple images in the training set." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.655, + 0.526 + ], + "angle": 0, + "content": "4.3. Image Encoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Each patch \\( p_s^i \\in P_s \\) is projected into a latent vector \\( \\mathbf{x}_s^i \\in \\mathbb{R}^d \\) where \\( d \\) is the dimension of the latent vectors. A subset patches \\( P_s \\) can be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.58, + 0.891, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {s} = \\operatorname {c o n c a t} \\left[ \\mathbf {x} _ {s} ^ {i} \\right] _ {i = 1} ^ {N P _ {s}} \\in \\mathbb {R} ^ {N P _ {s} \\times d}, \\quad \\mathbf {x} _ {s} ^ {i} = \\alpha_ {p} \\left(p _ {s} ^ {i}\\right) + \\mathbf {e} _ {p} (i) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.891, + 0.63 + ], + "angle": 0, + "content": "where \\(\\alpha_{p}\\) and \\(\\mathbf{e}_p\\) are the projection embedding and position embedding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.676 + ], + "angle": 0, + "content": "Let an image encoder \\( E_{\\mathrm{image}}(\\mathbf{X}_s) \\) be a stack of \\( L_{e} \\) transformer blocks where each block contains multi-head self-attention (MSA) and multi-layer perceptron (MLP)." + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.678, + 0.891, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {X} _ {l} ^ {\\prime} = \\mathbf {X} _ {l - 1} + \\operatorname {M S A} (\\ln (\\mathbf {X} _ {l - 1})) \\\\ \\mathbf {X} _ {l} = \\mathbf {X} _ {l} ^ {\\prime} + \\operatorname {M L P} \\left(\\ln \\left(\\mathbf {X} _ {l} ^ {\\prime}\\right)\\right) \\tag {2} \\\\ \\mathbf {X} _ {0} = \\mathbf {X} _ {s}, 1 \\leq l \\leq L _ {e} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.891, + 0.76 + ], + "angle": 0, + "content": "where LN is the layer normalization. Then, given \\(\\mathbf{X}_s\\), the output latent vector \\(\\mathbf{Z}_s\\) is represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.761, + 0.891, + 0.779 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} _ {s} = E _ {\\text {i m a g e}} \\left(\\mathbf {X} _ {s}\\right), \\quad \\mathbf {Z} _ {s} \\in \\mathbb {R} ^ {N _ {P _ {s}} \\times d} \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.788, + 0.89, + 0.803 + ], + "angle": 0, + "content": "4.4. Insect Micro-feature Self-supervised Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The recognition of insects relies on the insect texture, eyes, or limbs that are tiny to detect. To make the model robust to the small features of insect images, we propose a self-supervised learning strategy to spot these small features via the small differences in the images. Notice that the insects can be distinguished by detecting and discriminating the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21949" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "critical features in each part of those insects. To enhance this ability for the model, a pre-text task is presented. In particular, after extracting global information from a masked image of the insect, the vision model learns to find the remaining patches of the image by comparing image patches of different insect species. Thanks to our learning mechanism, the model learns the key features representing each insect and discriminates the small features between different species. As illustrated in Fig. 6, given a subset of patches \\( P_{s} \\) from the image \\( I \\) and a pool of image patches \\( P_{\\mathrm{pool}} \\), we train the model to find the patches \\( p_t \\in P_{\\mathrm{pool}} \\) that originally belong to the image \\( I \\). Then, given latent vectors \\( \\mathbf{Z}_s \\) of \\( P_{s} \\), a patch-wise relevant attention score (PRS) is computed between \\( \\mathbf{Z}_s \\) and each patch \\( p \\in P_{\\mathrm{pool}} \\). The score can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.322, + 0.469, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P R S} = f \\left(\\mathbf {Z} _ {s}, p\\right) \\in [ 0, 1 ] \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.445, + 0.356 + ], + "angle": 0, + "content": "The higher the score is, the more possibility that \\( p \\in P \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.522 + ], + "angle": 0, + "content": "Attention Pooling To compute the relevance between latent vectors \\(\\mathbf{Z}_s\\) from the image \\(I\\) and the patch \\(p\\in P_{\\mathrm{pool}}\\), the latent vectors \\(\\mathbf{Z}_s\\) should be aggregated to represent the holistic information of \\(I\\). Inspired by [70], we compute the global information of \\(I\\) via attention pooling. Given a placeholder contextual token \\(\\mathbf{z}_{ct}^{\\prime}\\) as a query \\(\\mathbf{Q}_{ct}\\) and latent vectors \\(\\mathbf{Z}_s\\) as a key \\(\\mathbf{K}_Z\\) and a value \\(\\mathbf{V}_Z\\), we compute an attention map between \\(\\mathbf{Q}_{ct}\\) and \\(\\mathbf{K}_Z\\). Then, a contextual token \\(\\mathbf{z}_{ct}\\) representing the global information of \\(I\\) is computed via the attention map and the value \\(\\mathbf{V}_Z\\). The attention pooling (Fig. 7) can be formulated as Eqn. (5)." + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.529, + 0.457, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {c t} = \\operatorname {L i n e a r} \\left(\\mathbf {z} _ {c t} ^ {\\prime}\\right) \\quad \\mathbf {K} _ {Z} = \\operatorname {L i n e a r} \\left(\\mathbf {Z} _ {s}\\right) \\quad \\mathbf {V} _ {Z} = \\operatorname {L i n e a r} \\left(\\mathbf {Z} _ {s}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.548, + 0.469, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {c t} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {c t} \\mathbf {K} _ {Z} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V} _ {Z} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.657 + ], + "angle": 0, + "content": "Patch-wise Relevant Attention Given \\(\\mathbf{z}_{ct}\\) as a contextual token representing the information of \\(I\\), we compute the relevance between \\(\\mathbf{z}_{ct}\\) and \\(p \\in P_{\\mathrm{pool}}\\). From Eqn. (4), we expand the attention score function \\(f\\) as in Eqn. (6)." + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.661, + 0.469, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P R S} = f \\left(\\mathbf {Z} _ {s}, p\\right) = H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.47, + 0.71 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_p = E_{\\mathrm{image}}(\\alpha_p(p))\\) is a latent vector representing the patch \\(p\\), \\(H\\) is a similarity function between two latent" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.73, + 0.439, + 0.852 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.855, + 0.469, + 0.897 + ], + "angle": 0, + "content": "Figure 6. Pool of Image Patches. A subset of patches of an image is sampled for image encoding while the remaining patches are placed into a pool of patches for the self-supervised pre-text task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "vectors. From Eqn. (6), we expand the score function into a self-supervised loss function \\(\\mathcal{L}_{\\mathrm{PRS}}\\) as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.128, + 0.892, + 0.144 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e l}} = - y \\log \\left(H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right)\\right) - (1 - y) \\log \\left(1 - H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right)\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.151, + 0.788, + 0.166 + ], + "angle": 0, + "content": "where \\(y = 1\\) if \\(p\\in P\\) and \\(y = 0\\) otherwise." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.176, + 0.862, + 0.192 + ], + "angle": 0, + "content": "4.5. Fine-grained Insect Image-Text Alignment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.892, + 0.32 + ], + "angle": 0, + "content": "Each species has an individual definition and description that can be aligned to parts of the insect image. We adopt a text decoder to generate the species descriptions from insect images. Moreover, to capture the general information of species, we utilize contrastive learning between global features of the insect images and description. As a result, the model can learn specific information from insect images via insect descriptions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.32, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Formally, an insect description text is tokenized into \\( T = \\{t_i\\}_{i=1}^{N_T} \\) where \\( N_T \\) is the number of tokens of the description. Each token \\( t_i \\in T \\) is embedded into a latent vector \\( \\mathbf{w}_i \\in \\mathbb{R}^d \\). The description can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.386, + 0.892, + 0.403 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} = \\operatorname {c o n c a t} \\left[ \\mathbf {w} _ {i} \\right] _ {i = 1} ^ {N _ {T}} \\in \\mathbb {R} ^ {N _ {T} \\times d}, \\quad \\mathbf {w} _ {i} = \\alpha_ {w} + \\mathbf {e} _ {w} (i) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.41, + 0.892, + 0.439 + ], + "angle": 0, + "content": "where \\(\\alpha_w\\) and \\(\\mathbf{e}_w\\) are the projection embedding and position embedding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.44, + 0.892, + 0.501 + ], + "angle": 0, + "content": "Similar to the image encoder, let the text encoder \\( E_{\\mathrm{text}}(\\mathbf{W}) \\) be a stack of \\( L_e' \\) transformer blocks containing multi-head self-attention and multi-layer perceptron. The output latent vector \\( \\mathbf{Z}' \\) of the description is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.505, + 0.892, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} ^ {\\prime} = E _ {\\text {t e x t}} (\\mathbf {W}), \\quad \\mathbf {Z} ^ {\\prime} \\in \\mathbb {R} ^ {N _ {T} \\times d} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.892, + 0.575 + ], + "angle": 0, + "content": "We then use the latent vector \\(\\mathbf{Z}_s\\) of the insect image and \\(\\mathbf{W}'\\) of the description text for image-text contrastive learning and multi-modal image description decoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Image-text Contrastive Learning. Inspired by the prior language model frameworks [14, 21, 27, 44], a contextual token \\(\\mathbf{w}_{ct}\\) representing the semantic information of the description is added at the beginning of \\(\\mathbf{W}\\) as in Eqn. 8. Then the two encoders \\(E_{\\mathrm{image}}\\) and \\(E_{\\mathrm{text}}\\) can be jointly optimized via contrastive learning as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.503, + 0.669, + 0.892, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n}} = \\frac {- 1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {T} \\mathbf {w} _ {i}\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\mathbf {z} _ {i} ^ {T} \\mathbf {w} _ {j}\\right)} + \\log \\frac {\\exp \\left(\\mathbf {w} _ {i} ^ {T} \\mathbf {z} _ {i}\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\mathbf {w} _ {i} ^ {T} \\mathbf {z} _ {j}\\right)} \\right] \\tag {10}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.739, + 0.862, + 0.865 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.869, + 0.89, + 0.897 + ], + "angle": 0, + "content": "Figure 7. Attention Pooling Module. The contextual token \\(\\mathbf{z}_{ct}\\) represents the global information of the image \\(I\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21950" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.173 + ], + "angle": 0, + "content": "Table 2. Effectiveness of our method on the IP102 Classification. We evaluate approach with three different vision transformer backbones, i.e., ViT-small/16, ViT-base/16, and ViT-large/16, without or with Attention Pooling (Attn Pool), and three different losses, i.e. Patch-wise Relevant Loss \\((\\mathcal{L}_{\\mathrm{rel}})\\), Image-Text Contrastive Loss \\((\\mathcal{L}_{\\mathrm{con}})\\), and Description Loss \\((\\mathcal{L}_{\\mathrm{desc}})\\)." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.175, + 0.434, + 0.351 + ], + "angle": 0, + "content": "
BackboneLrelAttn PoolLconLdescAcc@1 (%)Acc@5 (%)
ViT-small/16✓68.988.8
✓✓69.589.7
✓✓✓70.789.9
✓✓✓✓71.587.7
ViT-base/16✓72.491.0
✓✓73.391.6
✓✓✓74.291.9
✓✓✓✓75.892.1
ViT-large/16✓73.890.9
✓✓74.691.6
✓✓✓75.991.4
✓✓✓✓76.992.7
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.356, + 0.47, + 0.387 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_i\\) and \\(\\mathbf{w}_i\\) is the contextual token of the \\(i\\)-th insect image and description." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.469, + 0.477 + ], + "angle": 0, + "content": "Multi-modal Image Description Decoding. While image-text contrastive learning represents the global semantic information between the image and description, the multi-model image description decoding aims for the fine-grained details by predicting the tokenized texts of \\( T \\) in an autoregressive manner, as shown in Eqn. (11)." + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.487, + 0.469, + 0.525 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e s c}} = - \\sum_ {t = 1} ^ {N _ {T}} \\log D _ {\\text {m u l t i}} \\left(\\mathbf {w} _ {t} \\mid \\mathbf {W} _ {0: t - 1}, \\mathbf {Z} _ {s}\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.531, + 0.468, + 0.547 + ], + "angle": 0, + "content": "where \\(D_{\\mathrm{multi}}\\) is an autoregressive multi-modal text decoder." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.561, + 0.283, + 0.579 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.355, + 0.603 + ], + "angle": 0, + "content": "5.1. Foundation Model Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Our experiments use ViT-Base (ViT-B/16) [15] as the backbone. The images are resized and cropped randomly into the resolution of \\(224 \\times 224\\). Then, each image is divided into patches of \\(16 \\times 16\\), creating \\(N_P = 196\\) patches. The patch sampling ratio is selected as \\(50\\%\\), and the remaining patches are put into the pool of image patches. Each patch is projected to latent space of \\(d = 768\\) dimensions. The text encoder and multi-modal text decoder are adopted from the pre-trained BERT model [14]. The model is implemented in PyTorch [41] and trained by \\(16 \\times \\mathrm{A}100\\) GPUs. The learning rate is initially set to \\(1.5 \\times 10^{-4}\\) with the Consine learning rate scheduler [29]. The model is optimized by AdamW [30] with 200 epochs and a batch size of 64 per GPU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.314, + 0.832 + ], + "angle": 0, + "content": "5.2. Datasets and Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "IP102 Classification [66] provides 102 species of insects and contains 45,095 training samples, 7,508 validation samples, and 22,619 testing samples. For each species, an image might contain a single insect, multiple insects, or even a" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 3. Classification results on IP102 Classification benchmark. Both proposed models pre-trained with and without the insect descriptions outperform prior methods by a large margin." + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.133, + 0.857, + 0.266 + ], + "angle": 0, + "content": "
MethodDescriptionPre-train DataAcc@1 (%)Acc@5 (%)
ResNet [66]XImageNet1K49.4-
EfficientNet [6]XImageNet1K60.7-
DenseNet [32]XImageNet1K61.9-
GAEnsemble [3]XImageNet1K67.1-
ViT [15]XImageNet1K71.687.7
MoCo [17]X1M-Insect70.688.4
DINO [7]X1M-Insect71.591.4
MAE [18]X1M-Insect72.091.5
CoCa [70]✓1M-Insect72.891.1
Insect-FoundationX1M-Insect73.391.6
Insect-Foundation✓1M-Insect75.892.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.271, + 0.892, + 0.331 + ], + "angle": 0, + "content": "diseased crop caused by the species. The insects are in different forms for each class, e.g., egg, larva, pupa, and adult. The performance of insect classification is evaluated by the accuracy of Top 1 (Acc@1) and Top 5 (Acc@5)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.407 + ], + "angle": 0, + "content": "IP102 Detection [66] includes 15,178 training images and 3,798 testing images of 102 different species. Following the COCO benchmark [23], the insect detection performance is measured by the Average Precision (AP) and Average Precision at IoU thresholds of 0.5 (AP\\(^{50}\\)) and 0.75 (AP\\(^{75}\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.42, + 0.665, + 0.435 + ], + "angle": 0, + "content": "5.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Our ablation experiments study the effectiveness of our proposed model and hyper-parameters on the IP102 Classification Benchmark as shown in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.612 + ], + "angle": 0, + "content": "Effectiveness of Network Backbones Table 2 studies the impact of different Vision Transformer backbone sizes, including ViT-small/16, ViT-base/16, and ViT-large/16. As shown in our results, the powerful backbone carries more improvement. In particular, when changing the Transformer backbone size from small to base, the accuracy score increases by a large margin of \\(4.3\\%\\) while the large Transformer backbone improves the accuracy score by \\(1.1\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Effectiveness of Attention Pooling We evaluate the impact of the attention pooling in the visual representation of the insect images. As shown in Table 2, the Attention Pooling has better representation than the standard classification token computed through transformer layers. In particular, the top-1 accuracies for the three backbones, i.e., small, base, and large, have been increased from \\(68.9\\%\\) to \\(69.5\\%\\), from \\(72.4\\%\\) to \\(73.3\\%\\), and from \\(73.8\\%\\) to \\(74.6\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Effectiveness of Image-Text Contrastive Loss As reported in Table 2, the model can understand the insect images better when the model learns to match the images and their descriptions. In detail, the accuracy scores have been increased by \\(0.8\\%\\), \\(0.9\\%\\), and \\(1.3\\%\\) for the three backbones when applying the Image-Text Contrastive Loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of Description Loss The full configuration in Table 2 shows the experimental results of our model using the Description Loss. As shown in Table 2, the Description Loss helps the model to well-align the information between images and the details of descriptions. Hence, the model" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21951" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.09, + 0.437, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.47, + 0.327 + ], + "angle": 0, + "content": "Figure 8. Attention Visualization. Compared to MAE [18], our model is robust to small details of insect images. The model can focus on the small textures of the insect, even if the texture is the same as the background (bottom images). Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.33, + 0.468, + 0.389 + ], + "angle": 0, + "content": "can represent the fine-grained features of the insects better. In particular, the accuracy scores have been improved from \\(70.7\\%\\) to \\(71.5\\%\\), from \\(74.2\\%\\) to \\(75.8\\%\\), and from \\(75.9\\%\\) to \\(76.9\\%\\) for ViT-small/16, ViT-base/16, and ViT-large/16." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.422, + 0.415 + ], + "angle": 0, + "content": "5.4. Comparisons with Prior SOTA Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.468, + 0.587 + ], + "angle": 0, + "content": "Insect Classification Tasks. We fine-tune the linear layer with our pre-trained model on the IP102 dataset [66] for the classification task. As shown in Table 3, our model outperforms deep learning models [15, 16, 20, 50, 52] pre-trained on ImageNet [12] by a large margin. Compared to other pre-training methods [7, 17, 18, 70] on the proposed 1M-Insect dataset, our model shows better performance for both training without and with insect descriptions of \\(73.3\\%\\) and \\(75.8\\%\\), respectively. It is shown that the proposed approach has a better visual representation of insect images than the prior pre-training methods on the same dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.468, + 0.678 + ], + "angle": 0, + "content": "Visualization Results Fig. 8 visualizes the attention maps of our model compared to MAE [18] pre-trained on the proposed dataset. Since the textures are similar to the background, it is hard for MAE to focus on the small details of the insect. On the contrary, our model can detect the key features, i.e., the textures and the limbs, of the insects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.468, + 0.827 + ], + "angle": 0, + "content": "Zero-shot Insect Classification. We evaluate the performance of our model on the IP102 dataset [66] in a zero-shot manner. In detail, a description corresponds to each species to make the text encoder extract more semantic information about each species. Then, for each insect image, we use the image encoder to extract global features and compare them to each description feature to predict the insect Table 4. Zero-shot classification results on IP102 Classification benchmark. The proposed model outperforms prior vision-language pretraining methods." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.829, + 0.424, + 0.898 + ], + "angle": 0, + "content": "
MethodPretrain DataAccuracy (%)
CLIP [43]1M-Insect41.1
LiT [72]1M-Insect43.6
CoCa [70]1M-Insect45.3
Insect-Foundation1M-Insect49.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 5. Detection results on IP102 Detection benchmark. The proposed model outperforms prior pre-training methods." + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.118, + 0.855, + 0.248 + ], + "angle": 0, + "content": "
MethodBackbonePre-train DataAP (%)\\( AP^{50} \\)(%)\\( AP^{75} \\)(%)
FRCNN [47]VGG-16 [50]ImageNet1K21.147.915.2
FPN [24]ResNet-50 [16]ImageNet1K28.154.923.3
SSD300 [26]VGG-16 [50]ImageNet1K21.547.216.6
RefineDet [74]VGG-16 [50]ImageNet1K22.849.016.8
YOLOv3 [46]DarkNet-53 [46]ImageNet1K25.750.621.8
FPN [24]ViT [15]ImageNet1K32.854.735.0
FPN [24]MoCo [17]1M-Insect33.656.135.3
FPN [24]DINO [7]1M-Insect34.055.837.1
FPN [24]MAE [18]1M-Insect34.758.437.8
FPN [24]Insect-Foundation1M-Insect36.659.140.3
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.892, + 0.327 + ], + "angle": 0, + "content": "species. Table 4 reports the results of zero-shot classification on the IP102 Classification benchmark. Our model outperforms prior image-text pre-training methods [43, 70, 72] at an accuracy of \\(49.9\\%\\). It shows that our model has well-alignment between the insect image and its description." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.479 + ], + "angle": 0, + "content": "Insect Detection Tasks. As shown in Table 5, we train a Faster R-CNN model [47] on the IP102 Detection dataset with the ViT backbone adapted for FPN [24]. Compared to models pre-trained on ImageNet [12], our model achieves SOTA results with an average precision of \\(36.6\\%\\) and \\(\\mathrm{AP}^{50}\\) of \\(59.1\\%\\) higher than the same backbone pre-trained on ImageNet [12] having AP of \\(32.8\\%\\) and \\(\\mathrm{AP}^{50}\\) of \\(54.7\\%\\). Compared to other self-supervised methods [7, 17, 18], our model achieves higher precision. Thus, our model focuses on the features of insects better than prior methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.495, + 0.627, + 0.51 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.839 + ], + "angle": 0, + "content": "This paper has introduced a new large-scale Insect-1M dataset that supports the development of the Insect Foundation Model in precision agriculture. Our proposed dataset includes a large diversity of insect species and multi-level labels of taxonomy. In addition, Insect-1M consists of detailed descriptions of insects that support vision-language insect model training. Then, to improve the micro-feature modeling of our insect foundation model, we introduce a new Patch-wise Relevant Attention mechanism and Description Consistency loss to learn the details of insects. Our experimental results have illustrated the effectiveness and significance of our Insect-1M and Insect Foundation Model. Limitations This study used a specific network design and learning hyper-parameter to support our hypothesis. However, our approach potentially consists of several limitations related to the design of our Patch-wise Relevant Attention mechanism, where the patches of background and foreground are equally treated. It could result in difficulty in learning the different features of insects. This limitation will further motivate future research to improve the Insect Foundation Model and Micro-feature Modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.899 + ], + "angle": 0, + "content": "Acknowledgment. This work is partly supported by NSF DART, NSF SBIR Phase 2, and JBHunt Company. We also acknowledge the Arkansas High-Performance Computing Center for GPU servers and Jesse Ford for dataset tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21952" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Ahmad Arib Alfarisy, Quan Chen, and Minyi Guo. Deep learning based classification for paddy pests & diseases recognition. In Proceedings of 2018 international conference on mathematics and artificial intelligence, pages 21-25, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Adão Nunes Alves, Witenberg SR Souza, and Díbio Leandro Borges. Cotton pests classification in field-based images using deep residual networks. 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The current machine vision model requires a large volume of data to achieve high performance. However, there are approximately 5.5 million different insect species in the world. None of the existing insect datasets can cover even a fraction of them due to varying geographic locations and acquisition costs. In this paper, we introduce a novel "Insect-1M" dataset, a game-changing resource poised to revolutionize insect-related foundation model training. Covering a vast spectrum of insect species, our dataset, including 1 million images with dense identification labels of taxonomy hierarchy and insect descriptions, offers a panoramic view of entomology, enabling foundation models to comprehend visual and semantic information about insects like never before. Then, to efficiently establish an Insect Foundation Model, we develop a micro-feature self-supervised learning method with a Patch-wise Relevant Attention mechanism capable of discerning the subtle differences among insect images. In addition, we introduce Description Consistency loss to improve micro-feature modeling via insect descriptions. Through our experiments, we illustrate the effectiveness of our proposed approach in insect modeling and achieve State-of-the-Art performance on standard benchmarks of insect-related tasks. Our Insect Foundation Model and Dataset promise to empower the next generation of insect-related vision models, bringing them closer to the ultimate goal of precision agriculture. + +# 1. Introduction + +Insects are the most diverse and abundant eukaryotic organisms on the planet. They inhabit all terrestrial and aquatic + +![](images/3b1c15557806e533d6862da19719bf6e911a7d4c7cb5362b37e470bb381d3ce8.jpg) +Masked Monarch + +![](images/8d426c76f6c2d3908193e5385bbfec00c72e0914992c581275b8cb8aac5ac035.jpg) +Patch-wise Relevant + +![](images/b303a242aa5b2686a1148796ac9611eca7f5cac51e35d8746c9a94bbc0676aac.jpg) + +![](images/5afd677a309d2591aa88863f76575800246d2fa68b058030fd78c0582a143532.jpg) +Completed Monarch + +![](images/7ba4cc60bc0971429f56f7ee7066f7afac7404e899e4bbdf2ec5971985566a8e.jpg) +Which patches belong to the Monarch/Euryurus? +Masked Euryurus + +![](images/7437a64b24665e5fce8f26c05c1c285c4bea813ae51a3ee495476aaa8da03448.jpg) +Figure 1. Our Proposed Patch-wise Relevant Attention. Given masked insect images and separated image patches, our model can discriminate these patches that have small differences via relevant scores computed between masked images and image patches. + +![](images/8c90ab060363e0b61bf14013002ff2b8d851cd2cba921485f2683599520b4c20.jpg) +Completed Euryurus + +habitats and play a significant role within their community, habitat, and ecosystem as contributors to nutrient cycling, maintenance of plant and animal communities, disease cycling, and overall ecosystem health. Therefore, in the agricultural revolution, the detection and identification of insects plays a key role in ensuring healthy crop growth and high-quality production. Prior methods [2, 3, 6, 32, 55, 66] often fine-tuned the pre-trained ImageNet models on insect data for specific insect-related tasks, e.g., Insect Classification [2, 6, 13, 66], Insect Detection [66]. However, these methods remained limited since the models pre-trained on ImageNet [12, 15, 16, 20, 50, 52] could not model the micro features of insects, e.g., tiny texture and details of insects, as ImageNet [12] is the generic object dataset. + +Recent foundation models [7-9, 17-19, 40, 43, 69, 70] pre-trained on large-scale datasets have revolutionized vision models with solid performance on downstream applications. These models are designed to model general or specific properties of images or videos that can later be generalized to downstream tasks and unseen data. The capability of the foundation model is often implemented with + +Table 1. Comparison with existing datasets related to insects. Our proposed dataset has hierarchical labels with 6 main hierarchical levels, i.e., Subphylum, Class, Order, Family, Genus, and Species, and large numbers of species and samples. Moreover, the proposed dataset contains hierarchical descriptions for each insect and auxiliary taxonomic level, i.e., Subclass, Suborder, Subfamily, etc. + +
DatasetYearSpeciesHierarchical +LabelsHierarchical +LevelsInsect +DescriptionAuxiliary +Taxonomic LevelNumber of +Samples
Samanta et al. [48]20128X1XX609
Wang et al. [61]2012221✓3XX225
Venugoban et al. [60]201420X1XX200
Xie et al. [67]201524X1XX1,440
Liu et al. [28]201612X1XX5,136
Xie et al. [68]201840X1XX4,500
Deng et al. [13]201810X1XX563
Alfarisy et al. [1]201813X1XX4,511
PestNet [25]201916X1XX88,670
IP102 [66]2019102✓3XX75,222
AgriPest [63]202114✓2XX49,707
INSECT [4]20211,213X1XX21,212
iNat-2021 [59]20212,752✓5XX723,816
Our Insect-1M202334,212✓6✓✓1,017,036
+ +self-supervised or prompt-engineering training on large-scale datasets [12, 19, 49, 71]. However, the current insect datasets [1, 2, 6, 13, 28, 48, 60, 61, 66-68] are insufficient to establish the foundation model of insects due to their scale and diversity. Indeed, the most recent work presents an insect recognition dataset containing over 75,000 images of 102 species [66]. Although the dataset includes many species, compared to the species of insects in the natural environment with over 5.5 million species [45, 51], the current work needs to have the diversity of insects. Furthermore, to our knowledge, the current insect dataset [66] does not provide the corresponding insect descriptions, limiting the ability to learn the foundation models. + +Although the dataset is an important factor in developing an insect foundation model, the learning approach of the foundation model plays a significant role in performance. There is significant progress in developing vision foundation models. Common approaches learned alignment between vision and language, for example, CLIP [43], ALIGN [19], CoCa [70], to model visual concepts and data distributions. Meanwhile, self-supervised contrastive or distillation learning approaches, e.g., MoCo [9, 10, 17], DINO [7, 40], MAE [18], etc., learned the vision model by various pretext tasks and have shown its scaling ability and generalizes well to various downstream tasks. However, most of these previous foundation models represent the general information of natural images without specific knowledge. When deploying in the insect domains, they cannot capture the micro-features of insects, i.e., key features or appearance to distinguish the species, since the texture and details of insects are often small and diverse compared to generic objects. Meanwhile, fine-grained discrimination between insect images is crucial in insect foundation models due to the high diversity of species. Therefore, to successfully develop the insect foundation model, the learning approach needs to understand and be able to model the micro-features of in + +sects. Based on this observation, we present a novel pre-text task to enhance the recognition ability of the model between small features of the insect, as illustrated in Fig. 1. + +Contributions of this Work: To contribute to the development of the Insect Foundation Model in precision agriculture, we introduce a novel large-scale insect dataset, i.e., Insect-1M, and a new Insect Foundation Model, i.e., Insect-Foundation, that can transfer to various downstream insect-related applications, e.g., insect detection, insect classification, insect vision-language understanding. Our contributions can be summarized as follows. First, we present a new rich and large-volume insect dataset, i.e., Insect-1M, that consists of 1 million images of insects with dense identifications of taxonomy hierarchy from the abstract level of taxonomy, e.g., Class, Order, to the detailed level of taxonomy, e.g., Genus, Species. In addition, each insect contains a detailed description that describes the details and features of insects. To the best of our knowledge, our proposed Insect-1M dataset is $13 \times$ larger than the prior published IP102 dataset [66]. Second, to model the micro features of insects, we introduce a new self-supervised contrastive learning paradigm with a novel Patch-wise Relevant Attention mechanism to model the feature correlations of insect details. Third, to increase the modeling capability of the Insect Foundation Model in learning insect details, we introduce a new Description Consistency loss to learn the detailed features of insects via the textual description. Finally, through our intensive experiments on the Insect Classification and Insect Detection benchmarks [66], we show the effectiveness of our approach in insect modeling and our superior performance compared to the prior methods. + +# 2. Related Work + +Insect Datasets. There are prior studies releasing insect datasets on a small scale for recognition problems. [60] presented a dataset consisting of 20 species with 10 samples + +![](images/7d86b46415b9e3383fb4bf0a357e6aedbbb06693aa1e598426876d8ab0278e36.jpg) +Figure 2. Examples of Our Insect-1M Dataset. The left figure illustrates the samples of the four Subphylums, including Chelicerata, Crustacea, Hexapoda, and Myriapoda. The right figure shows an example of hierarchical descriptions of the Aurantia Species. + +for each species. Then, [67] introduced an insect dataset including 1,440 samples of 24 species. Several subsequent studies have larger datasets for deep learning, e.g., [68] proposed an insect dataset of 4,500 images with 40 different species for insect classification, and [28] proposed an insect dataset with over 5,000 samples for insect recognition and localization. PestNet [25] and AgriPest [63] were introduced for the small pest detection task. Recently, [66] has presented IP102 as a large-scale dataset containing over $75K$ samples of insects with 102 species for classification and detection tasks. Meanwhile, [59] proposed a large-scale dataset including over $723K$ samples of Arthropoda phylum with 2,752 species. Although prior efforts promoted the development of vision and machine intelligence in precision agriculture, no dataset has a large volume of samples and diverse species for insect-related foundation model training. Therefore, this work introduces a novel dataset that not only contains a large number of samples, i.e. 1M images, but also has hierarchical labels from the high to the low taxonomy level, including class, order, family, genus, and species. Table 1 compares our proposed dataset with the prior ones. In comparison with prior datasets, the number of images in our proposed Insect-1M dataset is $13\times$ higher than the prior IP102 dataset, and the number of species is $335\times$ higher than IP102 [66]. To preserve the rights of datasets and authors of images, instead of publishing images, we only provide labels and links to download images. + +Self-supervised Pre-training. Self-supervised pre-training has become a popular strategy for solving visual recognition problems, including classification, localization, segmentation, video recognition, tracking, and many other problems [18, 33-38, 53, 54, 56-58]. SimCLR [8] learned the visual representation of images via a contrastive learning framework using different data augmentation operations. MoCo [17] introduced momentum updating for the encoder while learning the image representation via contrastive learning. The MoCo framework was later used to improve the SimCLR approach without requiring a large training batch size + +[9]. MoCo-V3 [10] improved prior Momentum Contrastive frameworks by eliminating the memory queue to stabilize the training when the batch size is large. DINO [7] proposed a self-supervised learning approach using knowledge distillation with no labels. Later, it was extended to DINO-V2 [40] by stabilizing self-supervised learning when scaling the size of models and data. BEiT [5] proposed a masked image modeling task and used discrete visual tokens from the original image as prediction targets. MAE [18] and SimMIM [69] directly used a decoder to reconstruct pixel values from masked regions. Jigsaw-ViT [11] presented a pre-training task for transformer models by solving the shuffled patches of images. This learning strategy was also applied on the temporal dimension to improve the robustness of video modeling [54]. Micron-BERT [36] studied the micro-changing in facial videos by learning to detect the minor differences in an image that has swapping regions between two frames. + +Joint Vision-Language Pre-training. Recent work introduced joint vision-language pre-training. CLIP [43], and ALIGN [19] addressed that dual-encoder models pretrained on image-text pairs in contrastive objectives can learn strong representations of image and text for cross-modal alignment and zero-shot image recognition problems. LiT [72] and BASIC [42] proposed zero-shot transfer learning approaches by teaching the text model to learn the representation of the pre-trained image model via contrastive losses with large-scale data. SimVLM [65], OFA [62], and BLIP [22] trained an encoder-decoder model with language generative losses and achieved high performance in the vision-language benchmarks. CoCa [70] utilized contrastive learning and generative image captioning for global representation learning and fine-grained image-text alignment. Later work [73] used sigmoid loss to compute the image-text similarity for batch size scaling. LexLIP [31] projected images into a lexicon space for image-text sparse matching. Meanwhile, EQSIM [64] computed the similarity by the image-text equivariant changing. + +![](images/06daa06c74ccd557973d43c1fe3491f4b93d37481b091872dc27b381125c674e.jpg) + +![](images/c0148a2debcd1348e61db86f23f5ebfb392200ef781fd28b71089a86304e9f63.jpg) +Figure 3. The Distribution of Subphylum and Its Classes (Left) and The Distribution of Class and Its Orders (Right). Best viewed in color. + +# 3. The Proposed Insect 1M Dataset + +To contribute to establishing the insect foundation model, the large-scale dataset of insects with diverse species is essential. Therefore, we collect a new insect dataset with dense labels of a hierarchical taxonomy. In particular, our Insect-1M dataset contains 1 million insect images with dense hierarchical labels with six main taxonomies, i.e., Subphylum, Class*, Order, Family, Genus, and Species. The samples are in the Phylum Arthropoda and can be divided into 4 Subphylums, which are Chelicerata, Crustacea, Hexapoda, and Myriapoda as shown in Fig. 2. Compared to prior datasets, our Insect-1M has more hierarchical levels with large numbers of species and samples as in Table 1. + +# 3.1. Data Collection Protocol + +We utilize insect information containing insect data with images and taxonomies collected by naturalists and entomologists. Each insect sample has a corresponding image and its taxonomic label. From the taxonomic label, we crawl the identification description of the corresponding taxonomy. Notice that the taxonomic labels are hierarchical. The description is written from high-level descriptions, e.g., Subphylum and Class, to low-level descriptions, e.g., Species. Fig. 2 shows an example of an insect description. + +# 3.2. Data Preprocessing and Statistic + +Data Preprocessing. The raw data is stored in over 1 million HTML files with predefined HTML structures. Then, we parse the data structures to collect the insect images and their labels. More than 2 million raw images and their corresponding labels have been collected. However, the raw data collected consists of a lot of noise, e.g., incorrect identification of insects, corrupted images, and non-insect images. Therefore, to filter these outliers, our entomology experts must verify the images and their labels, i.e., insect identification. Finally, our collected Insect-1M dataset consists of + +1,017,036 clean images with dense labels of 34,212 different insect species. + +Data Statistic Fig. 3 shows the sample distributions of the Subphylums and their Classes. It is shown that the Class Insecta has the majority of samples. Fig. 3 also illustrates the distribution of the Orders in the major Classes. For each major Class, the data distribution of Orders is well-balanced. + +# 4. The Proposed Insect Foundation Model + +# 4.1. Limitations of Prior Foundation Training Approaches + +Limitations One of the issues in the visual insect understanding problem is the visual representation and discrimination of the small and undistinguished features of the insects. While MAE [18] reconstructs an image from a masked image for visual representation learning, it focuses + +![](images/cc30fdf6b1dc6d41449fbfe704560a3ca745d687b3671bdef5e502e546c0e2eb.jpg) +Figure 4. Comparisons of Self-supervised Methods. MAE [18] fails to reconstruct the details of the insect since it learns general information about the image. Micron-BERT [36] hardly distinguishes the insect and background. Jigsaw-ViT [11] cannot correct shuffled patches due to confusion between the background and the object. Meanwhile, our approach can find separated patches belonging to the insect by scoring each patch. Best viewed in color. + +![](images/20cc3161fbaa9ff89e008ecc322ba72e6bb398a764e73717a8ad38f39de8e147.jpg) +Figure 5. The Overview Framework of Our Proposed Approach to Insect Foundation Model. + +on the context inside the image individually without realizing the small details to discriminate between the insects. Meanwhile, Jigsaw solving methods [11, 39] correct the position of image patches to enhance the model robustness to the image structure. This strategy needs more mechanisms to focus on the small details of the image. Micron-BERT [36] highlights the small changes in the image by swapping the regions between two images with similar contexts. However, the small changes in the insect image still preserve the signature features representing the insect. Thus, it makes the model collapse in detecting the small features of insects. Therefore, to address these limitations, we introduce a new approach that learns to recognize the tiny features in the insect images. These features are distinguished from the background by discriminating the minor differences between patches of images individually. Fig. 4 compares prior self-supervised methods [11, 18, 36] with our approach. + +Fig. 5 illustrates our insect foundation model. The model is designed to capture the small differences in insect features, i.e., textures or limbs, via our new self-supervised pre-text task. Moreover, the model is pre-trained to learn the fine-grained alignment between the insect description and its visual features. Formally, given an input image $I$ , we divide $I$ into non-overlapping patches. Then, a subset of patches $P_{s}$ is sampled, and the remaining patches are put into a pool of image patches $P_{\mathrm{pool}}$ . The sampling is processed randomly in a uniform distribution. An image encoder is used to map $I_{p}$ into latent vectors. Given an insect description $T$ of the image, a text encoder is presented to extract information from $T$ . A text decoder and joint image-text contrastive learning module are introduced to map the description into the image. Finally, a Patch-wise Relevant Attention module is proposed for self-supervised learning to enhance the discrimination robustness of the model. + +# 4.2. Input Modeling + +An input image $I \in \mathbb{R}^{H \times W \times 3}$ is divided into non-overlapping patches $P = \{p_s^i\}_{i=1}^{N_P}$ where $H, W$ are the height and width of the input image, $N_P = HW / (s_p)^2$ is the number of patches. Each patch $p_s^i$ has a resolution of $s_p \times s_p$ . The non-overlapping patches $P$ are then randomly sampled into a subset of patches $P_s \subset P$ and put the other patches into a pool of image patches $P_{\mathrm{pool}}$ . Note that $P_{\mathrm{pool}}$ contains patches from multiple images in the training set. + +# 4.3. Image Encoder + +Each patch $p_s^i \in P_s$ is projected into a latent vector $\mathbf{x}_s^i \in \mathbb{R}^d$ where $d$ is the dimension of the latent vectors. A subset patches $P_s$ can be represented as follows: + +$$ +\mathbf {X} _ {s} = \operatorname {c o n c a t} \left[ \mathbf {x} _ {s} ^ {i} \right] _ {i = 1} ^ {N P _ {s}} \in \mathbb {R} ^ {N P _ {s} \times d}, \quad \mathbf {x} _ {s} ^ {i} = \alpha_ {p} \left(p _ {s} ^ {i}\right) + \mathbf {e} _ {p} (i) \tag {1} +$$ + +where $\alpha_{p}$ and $\mathbf{e}_p$ are the projection embedding and position embedding. + +Let an image encoder $E_{\mathrm{image}}(\mathbf{X}_s)$ be a stack of $L_{e}$ transformer blocks where each block contains multi-head self-attention (MSA) and multi-layer perceptron (MLP). + +$$ +\begin{array}{l} \mathbf {X} _ {l} ^ {\prime} = \mathbf {X} _ {l - 1} + \operatorname {M S A} (\ln (\mathbf {X} _ {l - 1})) \\ \mathbf {X} _ {l} = \mathbf {X} _ {l} ^ {\prime} + \operatorname {M L P} \left(\ln \left(\mathbf {X} _ {l} ^ {\prime}\right)\right) \tag {2} \\ \mathbf {X} _ {0} = \mathbf {X} _ {s}, 1 \leq l \leq L _ {e} \\ \end{array} +$$ + +where LN is the layer normalization. Then, given $\mathbf{X}_s$ , the output latent vector $\mathbf{Z}_s$ is represented as follows: + +$$ +\mathbf {Z} _ {s} = E _ {\text {i m a g e}} \left(\mathbf {X} _ {s}\right), \quad \mathbf {Z} _ {s} \in \mathbb {R} ^ {N _ {P _ {s}} \times d} \tag {3} +$$ + +# 4.4. Insect Micro-feature Self-supervised Learning + +The recognition of insects relies on the insect texture, eyes, or limbs that are tiny to detect. To make the model robust to the small features of insect images, we propose a self-supervised learning strategy to spot these small features via the small differences in the images. Notice that the insects can be distinguished by detecting and discriminating the + +critical features in each part of those insects. To enhance this ability for the model, a pre-text task is presented. In particular, after extracting global information from a masked image of the insect, the vision model learns to find the remaining patches of the image by comparing image patches of different insect species. Thanks to our learning mechanism, the model learns the key features representing each insect and discriminates the small features between different species. As illustrated in Fig. 6, given a subset of patches $P_{s}$ from the image $I$ and a pool of image patches $P_{\mathrm{pool}}$ , we train the model to find the patches $p_t \in P_{\mathrm{pool}}$ that originally belong to the image $I$ . Then, given latent vectors $\mathbf{Z}_s$ of $P_{s}$ , a patch-wise relevant attention score (PRS) is computed between $\mathbf{Z}_s$ and each patch $p \in P_{\mathrm{pool}}$ . The score can be defined as: + +$$ +\operatorname {P R S} = f \left(\mathbf {Z} _ {s}, p\right) \in [ 0, 1 ] \tag {4} +$$ + +The higher the score is, the more possibility that $p \in P$ . + +Attention Pooling To compute the relevance between latent vectors $\mathbf{Z}_s$ from the image $I$ and the patch $p\in P_{\mathrm{pool}}$ , the latent vectors $\mathbf{Z}_s$ should be aggregated to represent the holistic information of $I$ . Inspired by [70], we compute the global information of $I$ via attention pooling. Given a placeholder contextual token $\mathbf{z}_{ct}^{\prime}$ as a query $\mathbf{Q}_{ct}$ and latent vectors $\mathbf{Z}_s$ as a key $\mathbf{K}_Z$ and a value $\mathbf{V}_Z$ , we compute an attention map between $\mathbf{Q}_{ct}$ and $\mathbf{K}_Z$ . Then, a contextual token $\mathbf{z}_{ct}$ representing the global information of $I$ is computed via the attention map and the value $\mathbf{V}_Z$ . The attention pooling (Fig. 7) can be formulated as Eqn. (5). + +$$ +\mathbf {Q} _ {c t} = \operatorname {L i n e a r} \left(\mathbf {z} _ {c t} ^ {\prime}\right) \quad \mathbf {K} _ {Z} = \operatorname {L i n e a r} \left(\mathbf {Z} _ {s}\right) \quad \mathbf {V} _ {Z} = \operatorname {L i n e a r} \left(\mathbf {Z} _ {s}\right) +$$ + +$$ +\mathbf {z} _ {c t} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {c t} \mathbf {K} _ {Z} ^ {T}}{\sqrt {d}}\right) \mathbf {V} _ {Z} \tag {5} +$$ + +Patch-wise Relevant Attention Given $\mathbf{z}_{ct}$ as a contextual token representing the information of $I$ , we compute the relevance between $\mathbf{z}_{ct}$ and $p \in P_{\mathrm{pool}}$ . From Eqn. (4), we expand the attention score function $f$ as in Eqn. (6). + +$$ +\operatorname {P R S} = f \left(\mathbf {Z} _ {s}, p\right) = H \left(\mathbf {z} _ {c t}, \mathbf {z} _ {p}\right) \tag {6} +$$ + +where $\mathbf{z}_p = E_{\mathrm{image}}(\alpha_p(p))$ is a latent vector representing the patch $p$ , $H$ is a similarity function between two latent + +![](images/bdf928a9da0d6066052047a8511a2b9f24dd8acfd9213bde54e8690134def5a8.jpg) +Figure 6. Pool of Image Patches. A subset of patches of an image is sampled for image encoding while the remaining patches are placed into a pool of patches for the self-supervised pre-text task. + +vectors. From Eqn. (6), we expand the score function into a self-supervised loss function $\mathcal{L}_{\mathrm{PRS}}$ as follow: + +$$ +\mathcal {L} _ {\text {r e l}} = - y \log \left(H \left(\mathbf {z} _ {c t}, \mathbf {z} _ {p}\right)\right) - (1 - y) \log \left(1 - H \left(\mathbf {z} _ {c t}, \mathbf {z} _ {p}\right)\right) \tag {7} +$$ + +where $y = 1$ if $p\in P$ and $y = 0$ otherwise. + +# 4.5. Fine-grained Insect Image-Text Alignment + +Each species has an individual definition and description that can be aligned to parts of the insect image. We adopt a text decoder to generate the species descriptions from insect images. Moreover, to capture the general information of species, we utilize contrastive learning between global features of the insect images and description. As a result, the model can learn specific information from insect images via insect descriptions. + +Formally, an insect description text is tokenized into $T = \{t_i\}_{i=1}^{N_T}$ where $N_T$ is the number of tokens of the description. Each token $t_i \in T$ is embedded into a latent vector $\mathbf{w}_i \in \mathbb{R}^d$ . The description can be represented as: + +$$ +\mathbf {W} = \operatorname {c o n c a t} \left[ \mathbf {w} _ {i} \right] _ {i = 1} ^ {N _ {T}} \in \mathbb {R} ^ {N _ {T} \times d}, \quad \mathbf {w} _ {i} = \alpha_ {w} + \mathbf {e} _ {w} (i) \tag {8} +$$ + +where $\alpha_w$ and $\mathbf{e}_w$ are the projection embedding and position embedding. + +Similar to the image encoder, let the text encoder $E_{\mathrm{text}}(\mathbf{W})$ be a stack of $L_e'$ transformer blocks containing multi-head self-attention and multi-layer perceptron. The output latent vector $\mathbf{Z}'$ of the description is computed as + +$$ +\mathbf {W} ^ {\prime} = E _ {\text {t e x t}} (\mathbf {W}), \quad \mathbf {Z} ^ {\prime} \in \mathbb {R} ^ {N _ {T} \times d} \tag {9} +$$ + +We then use the latent vector $\mathbf{Z}_s$ of the insect image and $\mathbf{W}'$ of the description text for image-text contrastive learning and multi-modal image description decoding. + +Image-text Contrastive Learning. Inspired by the prior language model frameworks [14, 21, 27, 44], a contextual token $\mathbf{w}_{ct}$ representing the semantic information of the description is added at the beginning of $\mathbf{W}$ as in Eqn. 8. Then the two encoders $E_{\mathrm{image}}$ and $E_{\mathrm{text}}$ can be jointly optimized via contrastive learning as follow: + +$$ +\mathcal {L} _ {\text {c o n}} = \frac {- 1}{N} \sum_ {i = 1} ^ {N} \left[ \log \frac {\exp \left(\mathbf {z} _ {i} ^ {T} \mathbf {w} _ {i}\right)}{\sum_ {j = 1} ^ {N} \exp \left(\mathbf {z} _ {i} ^ {T} \mathbf {w} _ {j}\right)} + \log \frac {\exp \left(\mathbf {w} _ {i} ^ {T} \mathbf {z} _ {i}\right)}{\sum_ {j = 1} ^ {N} \exp \left(\mathbf {w} _ {i} ^ {T} \mathbf {z} _ {j}\right)} \right] \tag {10} +$$ + +![](images/3b125a3998166813f7ef7a0902320f8b897438cecb35cb6396300e90809fc2f2.jpg) +Figure 7. Attention Pooling Module. The contextual token $\mathbf{z}_{ct}$ represents the global information of the image $I$ . + +Table 2. Effectiveness of our method on the IP102 Classification. We evaluate approach with three different vision transformer backbones, i.e., ViT-small/16, ViT-base/16, and ViT-large/16, without or with Attention Pooling (Attn Pool), and three different losses, i.e. Patch-wise Relevant Loss $(\mathcal{L}_{\mathrm{rel}})$ , Image-Text Contrastive Loss $(\mathcal{L}_{\mathrm{con}})$ , and Description Loss $(\mathcal{L}_{\mathrm{desc}})$ . + +
BackboneLrelAttn PoolLconLdescAcc@1 (%)Acc@5 (%)
ViT-small/16✓68.988.8
✓✓69.589.7
✓✓✓70.789.9
✓✓✓✓71.587.7
ViT-base/16✓72.491.0
✓✓73.391.6
✓✓✓74.291.9
✓✓✓✓75.892.1
ViT-large/16✓73.890.9
✓✓74.691.6
✓✓✓75.991.4
✓✓✓✓76.992.7
+ +where $\mathbf{z}_i$ and $\mathbf{w}_i$ is the contextual token of the $i$ -th insect image and description. + +Multi-modal Image Description Decoding. While image-text contrastive learning represents the global semantic information between the image and description, the multi-model image description decoding aims for the fine-grained details by predicting the tokenized texts of $T$ in an autoregressive manner, as shown in Eqn. (11). + +$$ +\mathcal {L} _ {\text {d e s c}} = - \sum_ {t = 1} ^ {N _ {T}} \log D _ {\text {m u l t i}} \left(\mathbf {w} _ {t} \mid \mathbf {W} _ {0: t - 1}, \mathbf {Z} _ {s}\right) \tag {11} +$$ + +where $D_{\mathrm{multi}}$ is an autoregressive multi-modal text decoder. + +# 5. Experimental Results + +# 5.1. Foundation Model Pre-training + +Our experiments use ViT-Base (ViT-B/16) [15] as the backbone. The images are resized and cropped randomly into the resolution of $224 \times 224$ . Then, each image is divided into patches of $16 \times 16$ , creating $N_P = 196$ patches. The patch sampling ratio is selected as $50\%$ , and the remaining patches are put into the pool of image patches. Each patch is projected to latent space of $d = 768$ dimensions. The text encoder and multi-modal text decoder are adopted from the pre-trained BERT model [14]. The model is implemented in PyTorch [41] and trained by $16 \times \mathrm{A}100$ GPUs. The learning rate is initially set to $1.5 \times 10^{-4}$ with the Consine learning rate scheduler [29]. The model is optimized by AdamW [30] with 200 epochs and a batch size of 64 per GPU. + +# 5.2. Datasets and Benchmarks + +IP102 Classification [66] provides 102 species of insects and contains 45,095 training samples, 7,508 validation samples, and 22,619 testing samples. For each species, an image might contain a single insect, multiple insects, or even a + +Table 3. Classification results on IP102 Classification benchmark. Both proposed models pre-trained with and without the insect descriptions outperform prior methods by a large margin. + +
MethodDescriptionPre-train DataAcc@1 (%)Acc@5 (%)
ResNet [66]XImageNet1K49.4-
EfficientNet [6]XImageNet1K60.7-
DenseNet [32]XImageNet1K61.9-
GAEnsemble [3]XImageNet1K67.1-
ViT [15]XImageNet1K71.687.7
MoCo [17]X1M-Insect70.688.4
DINO [7]X1M-Insect71.591.4
MAE [18]X1M-Insect72.091.5
CoCa [70]✓1M-Insect72.891.1
Insect-FoundationX1M-Insect73.391.6
Insect-Foundation✓1M-Insect75.892.1
+ +diseased crop caused by the species. The insects are in different forms for each class, e.g., egg, larva, pupa, and adult. The performance of insect classification is evaluated by the accuracy of Top 1 (Acc@1) and Top 5 (Acc@5). + +IP102 Detection [66] includes 15,178 training images and 3,798 testing images of 102 different species. Following the COCO benchmark [23], the insect detection performance is measured by the Average Precision (AP) and Average Precision at IoU thresholds of 0.5 (AP $^{50}$ ) and 0.75 (AP $^{75}$ ). + +# 5.3. Ablation Studies + +Our ablation experiments study the effectiveness of our proposed model and hyper-parameters on the IP102 Classification Benchmark as shown in Table 2. + +Effectiveness of Network Backbones Table 2 studies the impact of different Vision Transformer backbone sizes, including ViT-small/16, ViT-base/16, and ViT-large/16. As shown in our results, the powerful backbone carries more improvement. In particular, when changing the Transformer backbone size from small to base, the accuracy score increases by a large margin of $4.3\%$ while the large Transformer backbone improves the accuracy score by $1.1\%$ . + +Effectiveness of Attention Pooling We evaluate the impact of the attention pooling in the visual representation of the insect images. As shown in Table 2, the Attention Pooling has better representation than the standard classification token computed through transformer layers. In particular, the top-1 accuracies for the three backbones, i.e., small, base, and large, have been increased from $68.9\%$ to $69.5\%$ , from $72.4\%$ to $73.3\%$ , and from $73.8\%$ to $74.6\%$ . + +Effectiveness of Image-Text Contrastive Loss As reported in Table 2, the model can understand the insect images better when the model learns to match the images and their descriptions. In detail, the accuracy scores have been increased by $0.8\%$ , $0.9\%$ , and $1.3\%$ for the three backbones when applying the Image-Text Contrastive Loss. + +Effectiveness of Description Loss The full configuration in Table 2 shows the experimental results of our model using the Description Loss. As shown in Table 2, the Description Loss helps the model to well-align the information between images and the details of descriptions. Hence, the model + +![](images/6fd20269ab7c086a5d012da4231972dc298fa232ae1c6cb10e4ed8d7befb1139.jpg) +Figure 8. Attention Visualization. Compared to MAE [18], our model is robust to small details of insect images. The model can focus on the small textures of the insect, even if the texture is the same as the background (bottom images). Best viewed in color. + +can represent the fine-grained features of the insects better. In particular, the accuracy scores have been improved from $70.7\%$ to $71.5\%$ , from $74.2\%$ to $75.8\%$ , and from $75.9\%$ to $76.9\%$ for ViT-small/16, ViT-base/16, and ViT-large/16. + +# 5.4. Comparisons with Prior SOTA Methods + +Insect Classification Tasks. We fine-tune the linear layer with our pre-trained model on the IP102 dataset [66] for the classification task. As shown in Table 3, our model outperforms deep learning models [15, 16, 20, 50, 52] pre-trained on ImageNet [12] by a large margin. Compared to other pre-training methods [7, 17, 18, 70] on the proposed 1M-Insect dataset, our model shows better performance for both training without and with insect descriptions of $73.3\%$ and $75.8\%$ , respectively. It is shown that the proposed approach has a better visual representation of insect images than the prior pre-training methods on the same dataset. + +Visualization Results Fig. 8 visualizes the attention maps of our model compared to MAE [18] pre-trained on the proposed dataset. Since the textures are similar to the background, it is hard for MAE to focus on the small details of the insect. On the contrary, our model can detect the key features, i.e., the textures and the limbs, of the insects. + +Zero-shot Insect Classification. We evaluate the performance of our model on the IP102 dataset [66] in a zero-shot manner. In detail, a description corresponds to each species to make the text encoder extract more semantic information about each species. Then, for each insect image, we use the image encoder to extract global features and compare them to each description feature to predict the insect Table 4. Zero-shot classification results on IP102 Classification benchmark. The proposed model outperforms prior vision-language pretraining methods. + +
MethodPretrain DataAccuracy (%)
CLIP [43]1M-Insect41.1
LiT [72]1M-Insect43.6
CoCa [70]1M-Insect45.3
Insect-Foundation1M-Insect49.9
+ +Table 5. Detection results on IP102 Detection benchmark. The proposed model outperforms prior pre-training methods. + +
MethodBackbonePre-train DataAP (%)\( AP^{50} \)(%)\( AP^{75} \)(%)
FRCNN [47]VGG-16 [50]ImageNet1K21.147.915.2
FPN [24]ResNet-50 [16]ImageNet1K28.154.923.3
SSD300 [26]VGG-16 [50]ImageNet1K21.547.216.6
RefineDet [74]VGG-16 [50]ImageNet1K22.849.016.8
YOLOv3 [46]DarkNet-53 [46]ImageNet1K25.750.621.8
FPN [24]ViT [15]ImageNet1K32.854.735.0
FPN [24]MoCo [17]1M-Insect33.656.135.3
FPN [24]DINO [7]1M-Insect34.055.837.1
FPN [24]MAE [18]1M-Insect34.758.437.8
FPN [24]Insect-Foundation1M-Insect36.659.140.3
+ +species. Table 4 reports the results of zero-shot classification on the IP102 Classification benchmark. Our model outperforms prior image-text pre-training methods [43, 70, 72] at an accuracy of $49.9\%$ . It shows that our model has well-alignment between the insect image and its description. + +Insect Detection Tasks. As shown in Table 5, we train a Faster R-CNN model [47] on the IP102 Detection dataset with the ViT backbone adapted for FPN [24]. Compared to models pre-trained on ImageNet [12], our model achieves SOTA results with an average precision of $36.6\%$ and $\mathrm{AP}^{50}$ of $59.1\%$ higher than the same backbone pre-trained on ImageNet [12] having AP of $32.8\%$ and $\mathrm{AP}^{50}$ of $54.7\%$ . Compared to other self-supervised methods [7, 17, 18], our model achieves higher precision. Thus, our model focuses on the features of insects better than prior methods. + +# 6. Conclusions + +This paper has introduced a new large-scale Insect-1M dataset that supports the development of the Insect Foundation Model in precision agriculture. Our proposed dataset includes a large diversity of insect species and multi-level labels of taxonomy. In addition, Insect-1M consists of detailed descriptions of insects that support vision-language insect model training. Then, to improve the micro-feature modeling of our insect foundation model, we introduce a new Patch-wise Relevant Attention mechanism and Description Consistency loss to learn the details of insects. Our experimental results have illustrated the effectiveness and significance of our Insect-1M and Insect Foundation Model. Limitations This study used a specific network design and learning hyper-parameter to support our hypothesis. However, our approach potentially consists of several limitations related to the design of our Patch-wise Relevant Attention mechanism, where the patches of background and foreground are equally treated. It could result in difficulty in learning the different features of insects. This limitation will further motivate future research to improve the Insect Foundation Model and Micro-feature Modeling. + +Acknowledgment. This work is partly supported by NSF DART, NSF SBIR Phase 2, and JBHunt Company. We also acknowledge the Arkansas High-Performance Computing Center for GPU servers and Jesse Ford for dataset tasks. + +# References + +[1] Ahmad Arib Alfarisy, Quan Chen, and Minyi Guo. Deep learning based classification for paddy pests & diseases recognition. In Proceedings of 2018 international conference on mathematics and artificial intelligence, pages 21-25, 2018. 2 +[2] Adão Nunes Alves, Witenberg SR Souza, and Díbio Leandro Borges. 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+ ], + "type": "text", + "content": "In precision agriculture, the detection and recognition of insects play an essential role in the ability of crops to grow healthy and produce a high-quality yield. The current machine vision model requires a large volume of data to achieve high performance. However, there are approximately 5.5 million different insect species in the world. None of the existing insect datasets can cover even a fraction of them due to varying geographic locations and acquisition costs. In this paper, we introduce a novel \"Insect-1M\" dataset, a game-changing resource poised to revolutionize insect-related foundation model training. Covering a vast spectrum of insect species, our dataset, including 1 million images with dense identification labels of taxonomy hierarchy and insect descriptions, offers a panoramic view of entomology, enabling foundation models to comprehend visual and semantic information about insects like never before. Then, to efficiently establish an Insect Foundation Model, we develop a micro-feature self-supervised learning method with a Patch-wise Relevant Attention mechanism capable of discerning the subtle differences among insect images. In addition, we introduce Description Consistency loss to improve micro-feature modeling via insect descriptions. Through our experiments, we illustrate the effectiveness of our proposed approach in insect modeling and achieve State-of-the-Art performance on standard benchmarks of insect-related tasks. Our Insect Foundation Model and Dataset promise to empower the next generation of insect-related vision models, bringing them closer to the ultimate goal of precision agriculture." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 651, + 127, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 127, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 127, + 662 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "type": "text", + "content": "Insects are the most diverse and abundant eukaryotic organisms on the planet. 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Our Proposed Patch-wise Relevant Attention. Given masked insect images and separated image patches, our model can discriminate these patches that have small differences via relevant scores computed between masked images and image patches." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 482, + 349, + 533, + 401 + ], + "blocks": [ + { + "bbox": [ + 482, + 349, + 533, + 401 + ], + "lines": [ + { + "bbox": [ + 482, + 349, + 533, + 401 + ], + "spans": [ + { + "bbox": [ + 482, + 349, + 533, + 401 + ], + "type": "image", + "image_path": "8c90ab060363e0b61bf14013002ff2b8d851cd2cba921485f2683599520b4c20.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 401, + 535, + 407 + ], + "lines": [ + { + "bbox": [ + 481, + 401, + 535, + 407 + ], + "spans": [ + { + "bbox": [ + 481, + 401, + 535, + 407 + ], + "type": "text", + "content": "Completed Euryurus" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 459, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 626 + ], + "type": "text", + "content": "habitats and play a significant role within their community, habitat, and ecosystem as contributors to nutrient cycling, maintenance of plant and animal communities, disease cycling, and overall ecosystem health. Therefore, in the agricultural revolution, the detection and identification of insects plays a key role in ensuring healthy crop growth and high-quality production. Prior methods [2, 3, 6, 32, 55, 66] often fine-tuned the pre-trained ImageNet models on insect data for specific insect-related tasks, e.g., Insect Classification [2, 6, 13, 66], Insect Detection [66]. However, these methods remained limited since the models pre-trained on ImageNet [12, 15, 16, 20, 50, 52] could not model the micro features of insects, e.g., tiny texture and details of insects, as ImageNet [12] is the generic object dataset." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Recent foundation models [7-9, 17-19, 40, 43, 69, 70] pre-trained on large-scale datasets have revolutionized vision models with solid performance on downstream applications. These models are designed to model general or specific properties of images or videos that can later be generalized to downstream tasks and unseen data. The capability of the foundation model is often implemented with" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 118, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 118, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 118, + 712 + ], + "type": "text", + "content": "*Co-first authors" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21945" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 105, + 519, + 275 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 103 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 103 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 103 + ], + "type": "text", + "content": "Table 1. Comparison with existing datasets related to insects. Our proposed dataset has hierarchical labels with 6 main hierarchical levels, i.e., Subphylum, Class, Order, Family, Genus, and Species, and large numbers of species and samples. Moreover, the proposed dataset contains hierarchical descriptions for each insect and auxiliary taxonomic level, i.e., Subclass, Suborder, Subfamily, etc." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 105, + 519, + 275 + ], + "lines": [ + { + "bbox": [ + 74, + 105, + 519, + 275 + ], + "spans": [ + { + "bbox": [ + 74, + 105, + 519, + 275 + ], + "type": "table", + "html": "
DatasetYearSpeciesHierarchical \nLabelsHierarchical \nLevelsInsect \nDescriptionAuxiliary \nTaxonomic LevelNumber of \nSamples
Samanta et al. [48]20128X1XX609
Wang et al. [61]2012221✓3XX225
Venugoban et al. [60]201420X1XX200
Xie et al. [67]201524X1XX1,440
Liu et al. [28]201612X1XX5,136
Xie et al. [68]201840X1XX4,500
Deng et al. [13]201810X1XX563
Alfarisy et al. [1]201813X1XX4,511
PestNet [25]201916X1XX88,670
IP102 [66]2019102✓3XX75,222
AgriPest [63]202114✓2XX49,707
INSECT [4]20211,213X1XX21,212
iNat-2021 [59]20212,752✓5XX723,816
Our Insect-1M202334,212✓6✓✓1,017,036
", + "image_path": "f66e1202693f4d18c4aabbfffb8bf0bedae6983ea9065c701c74d941574d905e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 277, + 288, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 277, + 288, + 434 + ], + "spans": [ + { + "bbox": [ + 45, + 277, + 288, + 434 + ], + "type": "text", + "content": "self-supervised or prompt-engineering training on large-scale datasets [12, 19, 49, 71]. However, the current insect datasets [1, 2, 6, 13, 28, 48, 60, 61, 66-68] are insufficient to establish the foundation model of insects due to their scale and diversity. Indeed, the most recent work presents an insect recognition dataset containing over 75,000 images of 102 species [66]. Although the dataset includes many species, compared to the species of insects in the natural environment with over 5.5 million species [45, 51], the current work needs to have the diversity of insects. Furthermore, to our knowledge, the current insect dataset [66] does not provide the corresponding insect descriptions, limiting the ability to learn the foundation models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "content": "Although the dataset is an important factor in developing an insect foundation model, the learning approach of the foundation model plays a significant role in performance. There is significant progress in developing vision foundation models. Common approaches learned alignment between vision and language, for example, CLIP [43], ALIGN [19], CoCa [70], to model visual concepts and data distributions. Meanwhile, self-supervised contrastive or distillation learning approaches, e.g., MoCo [9, 10, 17], DINO [7, 40], MAE [18], etc., learned the vision model by various pretext tasks and have shown its scaling ability and generalizes well to various downstream tasks. However, most of these previous foundation models represent the general information of natural images without specific knowledge. When deploying in the insect domains, they cannot capture the micro-features of insects, i.e., key features or appearance to distinguish the species, since the texture and details of insects are often small and diverse compared to generic objects. Meanwhile, fine-grained discrimination between insect images is crucial in insect foundation models due to the high diversity of species. Therefore, to successfully develop the insect foundation model, the learning approach needs to understand and be able to model the micro-features of in" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 277, + 545, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 313 + ], + "type": "text", + "content": "sects. Based on this observation, we present a novel pre-text task to enhance the recognition ability of the model between small features of the insect, as illustrated in Fig. 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 314, + 546, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 546, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 546, + 649 + ], + "type": "text", + "content": "Contributions of this Work: To contribute to the development of the Insect Foundation Model in precision agriculture, we introduce a novel large-scale insect dataset, i.e., Insect-1M, and a new Insect Foundation Model, i.e., Insect-Foundation, that can transfer to various downstream insect-related applications, e.g., insect detection, insect classification, insect vision-language understanding. Our contributions can be summarized as follows. First, we present a new rich and large-volume insect dataset, i.e., Insect-1M, that consists of 1 million images of insects with dense identifications of taxonomy hierarchy from the abstract level of taxonomy, e.g., Class, Order, to the detailed level of taxonomy, e.g., Genus, Species. In addition, each insect contains a detailed description that describes the details and features of insects. To the best of our knowledge, our proposed Insect-1M dataset is " + }, + { + "bbox": [ + 304, + 314, + 546, + 649 + ], + "type": "inline_equation", + "content": "13 \\times" + }, + { + "bbox": [ + 304, + 314, + 546, + 649 + ], + "type": "text", + "content": " larger than the prior published IP102 dataset [66]. Second, to model the micro features of insects, we introduce a new self-supervised contrastive learning paradigm with a novel Patch-wise Relevant Attention mechanism to model the feature correlations of insect details. Third, to increase the modeling capability of the Insect Foundation Model in learning insect details, we introduce a new Description Consistency loss to learn the detailed features of insects via the textual description. Finally, through our intensive experiments on the Insect Classification and Insect Detection benchmarks [66], we show the effectiveness of our approach in insect modeling and our superior performance compared to the prior methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 657, + 392, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 392, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 392, + 670 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Insect Datasets. There are prior studies releasing insect datasets on a small scale for recognition problems. [60] presented a dataset consisting of 20 species with 10 samples" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "21946" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 71, + 492, + 227 + ], + "blocks": [ + { + "bbox": [ + 97, + 71, + 492, + 227 + ], + "lines": [ + { + "bbox": [ + 97, + 71, + 492, + 227 + ], + "spans": [ + { + "bbox": [ + 97, + 71, + 492, + 227 + ], + "type": "image", + "image_path": "7d86b46415b9e3383fb4bf0a357e6aedbbb06693aa1e598426876d8ab0278e36.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 230, + 544, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 230, + 544, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 544, + 253 + ], + "type": "text", + "content": "Figure 2. Examples of Our Insect-1M Dataset. The left figure illustrates the samples of the four Subphylums, including Chelicerata, Crustacea, Hexapoda, and Myriapoda. The right figure shows an example of hierarchical descriptions of the Aurantia Species." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "text", + "content": "for each species. Then, [67] introduced an insect dataset including 1,440 samples of 24 species. Several subsequent studies have larger datasets for deep learning, e.g., [68] proposed an insect dataset of 4,500 images with 40 different species for insect classification, and [28] proposed an insect dataset with over 5,000 samples for insect recognition and localization. PestNet [25] and AgriPest [63] were introduced for the small pest detection task. Recently, [66] has presented IP102 as a large-scale dataset containing over " + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "inline_equation", + "content": "75K" + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "text", + "content": " samples of insects with 102 species for classification and detection tasks. Meanwhile, [59] proposed a large-scale dataset including over " + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "inline_equation", + "content": "723K" + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "text", + "content": " samples of Arthropoda phylum with 2,752 species. Although prior efforts promoted the development of vision and machine intelligence in precision agriculture, no dataset has a large volume of samples and diverse species for insect-related foundation model training. Therefore, this work introduces a novel dataset that not only contains a large number of samples, i.e. 1M images, but also has hierarchical labels from the high to the low taxonomy level, including class, order, family, genus, and species. Table 1 compares our proposed dataset with the prior ones. In comparison with prior datasets, the number of images in our proposed Insect-1M dataset is " + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "inline_equation", + "content": "13\\times" + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "text", + "content": " higher than the prior IP102 dataset, and the number of species is " + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "inline_equation", + "content": "335\\times" + }, + { + "bbox": [ + 46, + 257, + 289, + 581 + ], + "type": "text", + "content": " higher than IP102 [66]. To preserve the rights of datasets and authors of images, instead of publishing images, we only provide labels and links to download images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Self-supervised Pre-training. Self-supervised pre-training has become a popular strategy for solving visual recognition problems, including classification, localization, segmentation, video recognition, tracking, and many other problems [18, 33-38, 53, 54, 56-58]. SimCLR [8] learned the visual representation of images via a contrastive learning framework using different data augmentation operations. MoCo [17] introduced momentum updating for the encoder while learning the image representation via contrastive learning. The MoCo framework was later used to improve the SimCLR approach without requiring a large training batch size" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 257, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 472 + ], + "type": "text", + "content": "[9]. MoCo-V3 [10] improved prior Momentum Contrastive frameworks by eliminating the memory queue to stabilize the training when the batch size is large. DINO [7] proposed a self-supervised learning approach using knowledge distillation with no labels. Later, it was extended to DINO-V2 [40] by stabilizing self-supervised learning when scaling the size of models and data. BEiT [5] proposed a masked image modeling task and used discrete visual tokens from the original image as prediction targets. MAE [18] and SimMIM [69] directly used a decoder to reconstruct pixel values from masked regions. Jigsaw-ViT [11] presented a pre-training task for transformer models by solving the shuffled patches of images. This learning strategy was also applied on the temporal dimension to improve the robustness of video modeling [54]. Micron-BERT [36] studied the micro-changing in facial videos by learning to detect the minor differences in an image that has swapping regions between two frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": "Joint Vision-Language Pre-training. Recent work introduced joint vision-language pre-training. CLIP [43], and ALIGN [19] addressed that dual-encoder models pretrained on image-text pairs in contrastive objectives can learn strong representations of image and text for cross-modal alignment and zero-shot image recognition problems. LiT [72] and BASIC [42] proposed zero-shot transfer learning approaches by teaching the text model to learn the representation of the pre-trained image model via contrastive losses with large-scale data. SimVLM [65], OFA [62], and BLIP [22] trained an encoder-decoder model with language generative losses and achieved high performance in the vision-language benchmarks. CoCa [70] utilized contrastive learning and generative image captioning for global representation learning and fine-grained image-text alignment. Later work [73] used sigmoid loss to compute the image-text similarity for batch size scaling. LexLIP [31] projected images into a lexicon space for image-text sparse matching. Meanwhile, EQSIM [64] computed the similarity by the image-text equivariant changing." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21947" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 99, + 70, + 284, + 222 + ], + "blocks": [ + { + "bbox": [ + 99, + 70, + 284, + 222 + ], + "lines": [ + { + "bbox": [ + 99, + 70, + 284, + 222 + ], + "spans": [ + { + "bbox": [ + 99, + 70, + 284, + 222 + ], + "type": "image", + "image_path": "06daa06c74ccd557973d43c1fe3491f4b93d37481b091872dc27b381125c674e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 284, + 70, + 496, + 227 + ], + "blocks": [ + { + "bbox": [ + 284, + 70, + 496, + 227 + ], + "lines": [ + { + "bbox": [ + 284, + 70, + 496, + 227 + ], + "spans": [ + { + "bbox": [ + 284, + 70, + 496, + 227 + ], + "type": "image", + "image_path": "c0148a2debcd1348e61db86f23f5ebfb392200ef781fd28b71089a86304e9f63.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 228, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 47, + 228, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 545, + 239 + ], + "type": "text", + "content": "Figure 3. The Distribution of Subphylum and Its Classes (Left) and The Distribution of Class and Its Orders (Right). Best viewed in color." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 243, + 229, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 229, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 229, + 255 + ], + "type": "text", + "content": "3. The Proposed Insect 1M Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 263, + 290, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 290, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 290, + 408 + ], + "type": "text", + "content": "To contribute to establishing the insect foundation model, the large-scale dataset of insects with diverse species is essential. Therefore, we collect a new insect dataset with dense labels of a hierarchical taxonomy. In particular, our Insect-1M dataset contains 1 million insect images with dense hierarchical labels with six main taxonomies, i.e., Subphylum, Class*, Order, Family, Genus, and Species. The samples are in the Phylum Arthropoda and can be divided into 4 Subphylums, which are Chelicerata, Crustacea, Hexapoda, and Myriapoda as shown in Fig. 2. Compared to prior datasets, our Insect-1M has more hierarchical levels with large numbers of species and samples as in Table 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 417, + 185, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 417, + 185, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 417, + 185, + 428 + ], + "type": "text", + "content": "3.1. Data Collection Protocol" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 436, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 544 + ], + "type": "text", + "content": "We utilize insect information containing insect data with images and taxonomies collected by naturalists and entomologists. Each insect sample has a corresponding image and its taxonomic label. From the taxonomic label, we crawl the identification description of the corresponding taxonomy. Notice that the taxonomic labels are hierarchical. The description is written from high-level descriptions, e.g., Subphylum and Class, to low-level descriptions, e.g., Species. Fig. 2 shows an example of an insect description." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 554, + 222, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 222, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 222, + 567 + ], + "type": "text", + "content": "3.2. Data Preprocessing and Statistic" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 572, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 288, + 693 + ], + "type": "text", + "content": "Data Preprocessing. The raw data is stored in over 1 million HTML files with predefined HTML structures. Then, we parse the data structures to collect the insect images and their labels. More than 2 million raw images and their corresponding labels have been collected. However, the raw data collected consists of a lot of noise, e.g., incorrect identification of insects, corrupted images, and non-insect images. Therefore, to filter these outliers, our entomology experts must verify the images and their labels, i.e., insect identification. Finally, our collected Insect-1M dataset consists of" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 243, + 545, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 243, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 306, + 243, + 545, + 267 + ], + "type": "text", + "content": "1,017,036 clean images with dense labels of 34,212 different insect species." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 268, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 328 + ], + "type": "text", + "content": "Data Statistic Fig. 3 shows the sample distributions of the Subphylums and their Classes. It is shown that the Class Insecta has the majority of samples. Fig. 3 also illustrates the distribution of the Orders in the major Classes. For each major Class, the data distribution of Orders is well-balanced." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 338, + 523, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 523, + 351 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 523, + 351 + ], + "type": "text", + "content": "4. The Proposed Insect Foundation Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 357, + 545, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 382 + ], + "type": "text", + "content": "4.1. Limitations of Prior Foundation Training Approaches" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 388, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 449 + ], + "type": "text", + "content": "Limitations One of the issues in the visual insect understanding problem is the visual representation and discrimination of the small and undistinguished features of the insects. While MAE [18] reconstructs an image from a masked image for visual representation learning, it focuses" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 317, + 452, + 535, + 633 + ], + "blocks": [ + { + "bbox": [ + 317, + 452, + 535, + 633 + ], + "lines": [ + { + "bbox": [ + 317, + 452, + 535, + 633 + ], + "spans": [ + { + "bbox": [ + 317, + 452, + 535, + 633 + ], + "type": "image", + "image_path": "cc30fdf6b1dc6d41449fbfe704560a3ca745d687b3671bdef5e502e546c0e2eb.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 633, + 545, + 710 + ], + "lines": [ + { + "bbox": [ + 304, + 633, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 545, + 710 + ], + "type": "text", + "content": "Figure 4. Comparisons of Self-supervised Methods. MAE [18] fails to reconstruct the details of the insect since it learns general information about the image. Micron-BERT [36] hardly distinguishes the insect and background. Jigsaw-ViT [11] cannot correct shuffled patches due to confusion between the background and the object. Meanwhile, our approach can find separated patches belonging to the insect by scoring each patch. Best viewed in color." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 61, + 703, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 286, + 712 + ], + "type": "text", + "content": "*In this paper, we use the term \"Class\" as a biological taxonomic level." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21948" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 73, + 519, + 263 + ], + "blocks": [ + { + "bbox": [ + 75, + 73, + 519, + 263 + ], + "lines": [ + { + "bbox": [ + 75, + 73, + 519, + 263 + ], + "spans": [ + { + "bbox": [ + 75, + 73, + 519, + 263 + ], + "type": "image", + "image_path": "20cc3161fbaa9ff89e008ecc322ba72e6bb398a764e73717a8ad38f39de8e147.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 127, + 266, + 464, + 278 + ], + "lines": [ + { + "bbox": [ + 127, + 266, + 464, + 278 + ], + "spans": [ + { + "bbox": [ + 127, + 266, + 464, + 278 + ], + "type": "text", + "content": "Figure 5. The Overview Framework of Our Proposed Approach to Insect Foundation Model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 289, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 289, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 289, + 498 + ], + "type": "text", + "content": "on the context inside the image individually without realizing the small details to discriminate between the insects. Meanwhile, Jigsaw solving methods [11, 39] correct the position of image patches to enhance the model robustness to the image structure. This strategy needs more mechanisms to focus on the small details of the image. Micron-BERT [36] highlights the small changes in the image by swapping the regions between two images with similar contexts. However, the small changes in the insect image still preserve the signature features representing the insect. Thus, it makes the model collapse in detecting the small features of insects. Therefore, to address these limitations, we introduce a new approach that learns to recognize the tiny features in the insect images. These features are distinguished from the background by discriminating the minor differences between patches of images individually. Fig. 4 compares prior self-supervised methods [11, 18, 36] with our approach." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": "Fig. 5 illustrates our insect foundation model. The model is designed to capture the small differences in insect features, i.e., textures or limbs, via our new self-supervised pre-text task. Moreover, the model is pre-trained to learn the fine-grained alignment between the insect description and its visual features. Formally, given an input image " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": ", we divide " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": " into non-overlapping patches. Then, a subset of patches " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": " is sampled, and the remaining patches are put into a pool of image patches " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": ". The sampling is processed randomly in a uniform distribution. An image encoder is used to map " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "I_{p}" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": " into latent vectors. Given an insect description " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": " of the image, a text encoder is presented to extract information from " + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": ". A text decoder and joint image-text contrastive learning module are introduced to map the description into the image. Finally, a Patch-wise Relevant Attention module is proposed for self-supervised learning to enhance the discrimination robustness of the model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 282, + 403, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 282, + 403, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 403, + 295 + ], + "type": "text", + "content": "4.2. Input Modeling" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": "An input image " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " is divided into non-overlapping patches " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "P = \\{p_s^i\\}_{i=1}^{N_P}" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " are the height and width of the input image, " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "N_P = HW / (s_p)^2" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " is the number of patches. Each patch " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "p_s^i" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " has a resolution of " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "s_p \\times s_p" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": ". The non-overlapping patches " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " are then randomly sampled into a subset of patches " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "P_s \\subset P" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " and put the other patches into a pool of image patches " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 304, + 299, + 545, + 396 + ], + "type": "text", + "content": " contains patches from multiple images in the training set." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 403, + 400, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 400, + 416 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 400, + 416 + ], + "type": "text", + "content": "4.3. Image Encoder" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "text", + "content": "Each patch " + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "inline_equation", + "content": "p_s^i \\in P_s" + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "text", + "content": " is projected into a latent vector " + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s^i \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "text", + "content": " is the dimension of the latent vectors. A subset patches " + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "inline_equation", + "content": "P_s" + }, + { + "bbox": [ + 304, + 421, + 545, + 457 + ], + "type": "text", + "content": " can be represented as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 459, + 545, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 459, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 312, + 459, + 545, + 473 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {s} = \\operatorname {c o n c a t} \\left[ \\mathbf {x} _ {s} ^ {i} \\right] _ {i = 1} ^ {N P _ {s}} \\in \\mathbb {R} ^ {N P _ {s} \\times d}, \\quad \\mathbf {x} _ {s} ^ {i} = \\alpha_ {p} \\left(p _ {s} ^ {i}\\right) + \\mathbf {e} _ {p} (i) \\tag {1}", + "image_path": "160bd5b3debd83482d5008db80341d9814cf8918cd944e23c090fac377eb5b1c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\alpha_{p}" + }, + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_p" + }, + { + "bbox": [ + 304, + 475, + 545, + 498 + ], + "type": "text", + "content": " are the projection embedding and position embedding." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "type": "text", + "content": "Let an image encoder " + }, + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{image}}(\\mathbf{X}_s)" + }, + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "type": "text", + "content": " be a stack of " + }, + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "type": "inline_equation", + "content": "L_{e}" + }, + { + "bbox": [ + 304, + 499, + 545, + 535 + ], + "type": "text", + "content": " transformer blocks where each block contains multi-head self-attention (MSA) and multi-layer perceptron (MLP)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 536, + 545, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 536, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 364, + 536, + 545, + 575 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {X} _ {l} ^ {\\prime} = \\mathbf {X} _ {l - 1} + \\operatorname {M S A} (\\ln (\\mathbf {X} _ {l - 1})) \\\\ \\mathbf {X} _ {l} = \\mathbf {X} _ {l} ^ {\\prime} + \\operatorname {M L P} \\left(\\ln \\left(\\mathbf {X} _ {l} ^ {\\prime}\\right)\\right) \\tag {2} \\\\ \\mathbf {X} _ {0} = \\mathbf {X} _ {s}, 1 \\leq l \\leq L _ {e} \\\\ \\end{array}", + "image_path": "42c75881e353cb3053a73be6e754acadd04358fdfb31ecd2ce54a29f8982a3d5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "type": "text", + "content": "where LN is the layer normalization. Then, given " + }, + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_s" + }, + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "type": "text", + "content": ", the output latent vector " + }, + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 304, + 578, + 545, + 601 + ], + "type": "text", + "content": " is represented as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 358, + 602, + 545, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 602, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 358, + 602, + 545, + 616 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} _ {s} = E _ {\\text {i m a g e}} \\left(\\mathbf {X} _ {s}\\right), \\quad \\mathbf {Z} _ {s} \\in \\mathbb {R} ^ {N _ {P _ {s}} \\times d} \\tag {3}", + "image_path": "3c765c018f9ee4bb93fe4d3ff6e984e0c309af31dc92095252f32b86a0cbd2dc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 624, + 544, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 624, + 544, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 624, + 544, + 635 + ], + "type": "text", + "content": "4.4. Insect Micro-feature Self-supervised Learning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "The recognition of insects relies on the insect texture, eyes, or limbs that are tiny to detect. To make the model robust to the small features of insect images, we propose a self-supervised learning strategy to spot these small features via the small differences in the images. Notice that the insects can be distinguished by detecting and discriminating the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21949" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "critical features in each part of those insects. To enhance this ability for the model, a pre-text task is presented. In particular, after extracting global information from a masked image of the insect, the vision model learns to find the remaining patches of the image by comparing image patches of different insect species. Thanks to our learning mechanism, the model learns the key features representing each insect and discriminates the small features between different species. As illustrated in Fig. 6, given a subset of patches " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " from the image " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and a pool of image patches " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ", we train the model to find the patches " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "p_t \\in P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " that originally belong to the image " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ". Then, given latent vectors " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ", a patch-wise relevant attention score (PRS) is computed between " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and each patch " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "p \\in P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ". The score can be defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 120, + 255, + 287, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 255, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 120, + 255, + 287, + 266 + ], + "type": "interline_equation", + "content": "\\operatorname {P R S} = f \\left(\\mathbf {Z} _ {s}, p\\right) \\in [ 0, 1 ] \\tag {4}", + "image_path": "c7a199c879fd6f341694cef00b6b9e80e30120addae47cda03109017aacfba5a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 270, + 272, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 272, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 272, + 281 + ], + "type": "text", + "content": "The higher the score is, the more possibility that " + }, + { + "bbox": [ + 46, + 270, + 272, + 281 + ], + "type": "inline_equation", + "content": "p \\in P" + }, + { + "bbox": [ + 46, + 270, + 272, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": "Attention Pooling To compute the relevance between latent vectors " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " from the image " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " and the patch " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "p\\in P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": ", the latent vectors " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " should be aggregated to represent the holistic information of " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": ". Inspired by [70], we compute the global information of " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " via attention pooling. Given a placeholder contextual token " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{ct}^{\\prime}" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " as a query " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ct}" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " and latent vectors " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " as a key " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_Z" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " and a value " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_Z" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": ", we compute an attention map between " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ct}" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_Z" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": ". Then, a contextual token " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{ct}" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " representing the global information of " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": " is computed via the attention map and the value " + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_Z" + }, + { + "bbox": [ + 46, + 282, + 287, + 413 + ], + "type": "text", + "content": ". The attention pooling (Fig. 7) can be formulated as Eqn. (5)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 418, + 279, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 418, + 279, + 431 + ], + "spans": [ + { + "bbox": [ + 54, + 418, + 279, + 431 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {c t} = \\operatorname {L i n e a r} \\left(\\mathbf {z} _ {c t} ^ {\\prime}\\right) \\quad \\mathbf {K} _ {Z} = \\operatorname {L i n e a r} \\left(\\mathbf {Z} _ {s}\\right) \\quad \\mathbf {V} _ {Z} = \\operatorname {L i n e a r} \\left(\\mathbf {Z} _ {s}\\right)", + "image_path": "fea9857c4bd5fb57348e8fc7d51169f8fc93d1226605df4f251c9309cdbb1e71.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 434, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 434, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 58, + 434, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {c t} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {c t} \\mathbf {K} _ {Z} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V} _ {Z} \\tag {5}", + "image_path": "cf8a5d6eda7c2aec530b9d2bbfcb0223b33a0f2b2df10480d5efb2ee1affc17e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": "Patch-wise Relevant Attention Given " + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{ct}" + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": " as a contextual token representing the information of " + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": ", we compute the relevance between " + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{ct}" + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "inline_equation", + "content": "p \\in P_{\\mathrm{pool}}" + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": ". From Eqn. (4), we expand the attention score function " + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": " as in Eqn. (6)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 108, + 523, + 287, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 523, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 108, + 523, + 287, + 534 + ], + "type": "interline_equation", + "content": "\\operatorname {P R S} = f \\left(\\mathbf {Z} _ {s}, p\\right) = H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right) \\tag {6}", + "image_path": "615e4aa14797921e11ddf54dc5b12f60bca5002a45d52f470fe4b66fa12bfae1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_p = E_{\\mathrm{image}}(\\alpha_p(p))" + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "text", + "content": " is a latent vector representing the patch " + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 537, + 287, + 562 + ], + "type": "text", + "content": " is a similarity function between two latent" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 67, + 578, + 268, + 674 + ], + "blocks": [ + { + "bbox": [ + 67, + 578, + 268, + 674 + ], + "lines": [ + { + "bbox": [ + 67, + 578, + 268, + 674 + ], + "spans": [ + { + "bbox": [ + 67, + 578, + 268, + 674 + ], + "type": "image", + "image_path": "bdf928a9da0d6066052047a8511a2b9f24dd8acfd9213bde54e8690134def5a8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "type": "text", + "content": "Figure 6. Pool of Image Patches. A subset of patches of an image is sampled for image encoding while the remaining patches are placed into a pool of patches for the self-supervised pre-text task." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "vectors. From Eqn. (6), we expand the score function into a self-supervised loss function " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{PRS}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " as follow:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 310, + 101, + 545, + 114 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 101, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 310, + 101, + 545, + 114 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e l}} = - y \\log \\left(H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right)\\right) - (1 - y) \\log \\left(1 - H \\left(\\mathbf {z} _ {c t}, \\mathbf {z} _ {p}\\right)\\right) \\tag {7}", + "image_path": "410b9389179e9f6c699f8a61d440ef56e119e2b4aca0dcb9074a4418efc26001.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "spans": [ + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "inline_equation", + "content": "y = 1" + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "inline_equation", + "content": "p\\in P" + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "inline_equation", + "content": "y = 0" + }, + { + "bbox": [ + 306, + 119, + 482, + 131 + ], + "type": "text", + "content": " otherwise." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 139, + 527, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 139, + 527, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 139, + 527, + 152 + ], + "type": "text", + "content": "4.5. Fine-grained Insect Image-Text Alignment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 158, + 545, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 545, + 253 + ], + "type": "text", + "content": "Each species has an individual definition and description that can be aligned to parts of the insect image. We adopt a text decoder to generate the species descriptions from insect images. Moreover, to capture the general information of species, we utilize contrastive learning between global features of the insect images and description. As a result, the model can learn specific information from insect images via insect descriptions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "text", + "content": "Formally, an insect description text is tokenized into " + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "inline_equation", + "content": "T = \\{t_i\\}_{i=1}^{N_T}" + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "inline_equation", + "content": "N_T" + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "text", + "content": " is the number of tokens of the description. Each token " + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "inline_equation", + "content": "t_i \\in T" + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "text", + "content": " is embedded into a latent vector " + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 253, + 545, + 301 + ], + "type": "text", + "content": ". The description can be represented as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 321, + 305, + 545, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 305, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 321, + 305, + 545, + 319 + ], + "type": "interline_equation", + "content": "\\mathbf {W} = \\operatorname {c o n c a t} \\left[ \\mathbf {w} _ {i} \\right] _ {i = 1} ^ {N _ {T}} \\in \\mathbb {R} ^ {N _ {T} \\times d}, \\quad \\mathbf {w} _ {i} = \\alpha_ {w} + \\mathbf {e} _ {w} (i) \\tag {8}", + "image_path": "fa1cdc002e7f2bc6b440896de46ac1f2f25c8a4343eebd1eb5eb0e788497e55d.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "type": "inline_equation", + "content": "\\alpha_w" + }, + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_w" + }, + { + "bbox": [ + 305, + 324, + 545, + 347 + ], + "type": "text", + "content": " are the projection embedding and position embedding." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "text", + "content": "Similar to the image encoder, let the text encoder " + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{text}}(\\mathbf{W})" + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "text", + "content": " be a stack of " + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "L_e'" + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "text", + "content": " transformer blocks containing multi-head self-attention and multi-layer perceptron. The output latent vector " + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}'" + }, + { + "bbox": [ + 305, + 348, + 545, + 396 + ], + "type": "text", + "content": " of the description is computed as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 361, + 399, + 545, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 399, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 361, + 399, + 545, + 413 + ], + "type": "interline_equation", + "content": "\\mathbf {W} ^ {\\prime} = E _ {\\text {t e x t}} (\\mathbf {W}), \\quad \\mathbf {Z} ^ {\\prime} \\in \\mathbb {R} ^ {N _ {T} \\times d} \\tag {9}", + "image_path": "070a5078213b2200d9447112a950d0ac3bf6630c6d34ab77604cae77ad960d73.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "type": "text", + "content": "We then use the latent vector " + }, + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_s" + }, + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "type": "text", + "content": " of the insect image and " + }, + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{W}'" + }, + { + "bbox": [ + 304, + 419, + 545, + 455 + ], + "type": "text", + "content": " of the description text for image-text contrastive learning and multi-modal image description decoding." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "text", + "content": "Image-text Contrastive Learning. Inspired by the prior language model frameworks [14, 21, 27, 44], a contextual token " + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{ct}" + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "text", + "content": " representing the semantic information of the description is added at the beginning of " + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "text", + "content": " as in Eqn. 8. Then the two encoders " + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{image}}" + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{text}}" + }, + { + "bbox": [ + 304, + 455, + 545, + 526 + ], + "type": "text", + "content": " can be jointly optimized via contrastive learning as follow:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 307, + 529, + 545, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 529, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 307, + 529, + 545, + 566 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n}} = \\frac {- 1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {T} \\mathbf {w} _ {i}\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\mathbf {z} _ {i} ^ {T} \\mathbf {w} _ {j}\\right)} + \\log \\frac {\\exp \\left(\\mathbf {w} _ {i} ^ {T} \\mathbf {z} _ {i}\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\mathbf {w} _ {i} ^ {T} \\mathbf {z} _ {j}\\right)} \\right] \\tag {10}", + "image_path": "5860866d40f9c339b0b184c2bac1a909e6c4d1a2883cd0b4f770c0b03b7c3cd1.jpg" + } + ] + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 325, + 585, + 527, + 685 + ], + "blocks": [ + { + "bbox": [ + 325, + 585, + 527, + 685 + ], + "lines": [ + { + "bbox": [ + 325, + 585, + 527, + 685 + ], + "spans": [ + { + "bbox": [ + 325, + 585, + 527, + 685 + ], + "type": "image", + "image_path": "3b125a3998166813f7ef7a0902320f8b897438cecb35cb6396300e90809fc2f2.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "lines": [ + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "spans": [ + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "type": "text", + "content": "Figure 7. Attention Pooling Module. The contextual token " + }, + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{ct}" + }, + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "type": "text", + "content": " represents the global information of the image " + }, + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 688, + 544, + 710 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21950" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 138, + 265, + 277 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "text", + "content": "Table 2. Effectiveness of our method on the IP102 Classification. We evaluate approach with three different vision transformer backbones, i.e., ViT-small/16, ViT-base/16, and ViT-large/16, without or with Attention Pooling (Attn Pool), and three different losses, i.e. Patch-wise Relevant Loss " + }, + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{rel}})" + }, + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "text", + "content": ", Image-Text Contrastive Loss " + }, + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{con}})" + }, + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "text", + "content": ", and Description Loss " + }, + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{desc}})" + }, + { + "bbox": [ + 47, + 70, + 287, + 137 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 138, + 265, + 277 + ], + "lines": [ + { + "bbox": [ + 65, + 138, + 265, + 277 + ], + "spans": [ + { + "bbox": [ + 65, + 138, + 265, + 277 + ], + "type": "table", + "html": "
BackboneLrelAttn PoolLconLdescAcc@1 (%)Acc@5 (%)
ViT-small/16✓68.988.8
✓✓69.589.7
✓✓✓70.789.9
✓✓✓✓71.587.7
ViT-base/16✓72.491.0
✓✓73.391.6
✓✓✓74.291.9
✓✓✓✓75.892.1
ViT-large/16✓73.890.9
✓✓74.691.6
✓✓✓75.991.4
✓✓✓✓76.992.7
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While image-text contrastive learning represents the global semantic information between the image and description, the multi-model image description decoding aims for the fine-grained details by predicting the tokenized texts of " + }, + { + "bbox": [ + 46, + 305, + 287, + 377 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 305, + 287, + 377 + ], + "type": "text", + "content": " in an autoregressive manner, as shown in Eqn. (11)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 385, + 287, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 385, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 86, + 385, + 287, + 415 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e s c}} = - \\sum_ {t = 1} ^ {N _ {T}} \\log D _ {\\text {m u l t i}} \\left(\\mathbf {w} _ {t} \\mid \\mathbf {W} _ {0: t - 1}, \\mathbf {Z} _ {s}\\right) \\tag {11}", + "image_path": "0f24060b3722431aa5f2ffcde242a95a37e70b2e3739310a417959b0d6a383d4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 420, + 286, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 286, + 433 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 286, + 433 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 420, + 286, + 433 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{multi}}" + }, + { + "bbox": [ + 47, + 420, + 286, + 433 + ], + "type": "text", + "content": " is an autoregressive multi-modal text decoder." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 444, + 173, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 173, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 173, + 458 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 464, + 217, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 217, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 217, + 477 + ], + "type": "text", + "content": "5.1. Foundation Model Pre-training" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": "Our experiments use ViT-Base (ViT-B/16) [15] as the backbone. The images are resized and cropped randomly into the resolution of " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": ". Then, each image is divided into patches of " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": ", creating " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "N_P = 196" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": " patches. The patch sampling ratio is selected as " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": ", and the remaining patches are put into the pool of image patches. Each patch is projected to latent space of " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "d = 768" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": " dimensions. The text encoder and multi-modal text decoder are adopted from the pre-trained BERT model [14]. The model is implemented in PyTorch [41] and trained by " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "16 \\times \\mathrm{A}100" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": " GPUs. The learning rate is initially set to " + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "inline_equation", + "content": "1.5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 482, + 287, + 639 + ], + "type": "text", + "content": " with the Consine learning rate scheduler [29]. The model is optimized by AdamW [30] with 200 epochs and a batch size of 64 per GPU." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 647, + 192, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 192, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 192, + 658 + ], + "type": "text", + "content": "5.2. Datasets and Benchmarks" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "IP102 Classification [66] provides 102 species of insects and contains 45,095 training samples, 7,508 validation samples, and 22,619 testing samples. For each species, an image might contain a single insect, multiple insects, or even a" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 326, + 105, + 524, + 210 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "type": "text", + "content": "Table 3. Classification results on IP102 Classification benchmark. Both proposed models pre-trained with and without the insect descriptions outperform prior methods by a large margin." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 105, + 524, + 210 + ], + "lines": [ + { + "bbox": [ + 326, + 105, + 524, + 210 + ], + "spans": [ + { + "bbox": [ + 326, + 105, + 524, + 210 + ], + "type": "table", + "html": "
MethodDescriptionPre-train DataAcc@1 (%)Acc@5 (%)
ResNet [66]XImageNet1K49.4-
EfficientNet [6]XImageNet1K60.7-
DenseNet [32]XImageNet1K61.9-
GAEnsemble [3]XImageNet1K67.1-
ViT [15]XImageNet1K71.687.7
MoCo [17]X1M-Insect70.688.4
DINO [7]X1M-Insect71.591.4
MAE [18]X1M-Insect72.091.5
CoCa [70]✓1M-Insect72.891.1
Insect-FoundationX1M-Insect73.391.6
Insect-Foundation✓1M-Insect75.892.1
", + "image_path": "edf3dd6da9bed99a83cd07b9beb609ea3899199b730e558d1a02e9fbe04564c1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 214, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 214, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 214, + 545, + 262 + ], + "type": "text", + "content": "diseased crop caused by the species. The insects are in different forms for each class, e.g., egg, larva, pupa, and adult. The performance of insect classification is evaluated by the accuracy of Top 1 (Acc@1) and Top 5 (Acc@5)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "type": "text", + "content": "IP102 Detection [66] includes 15,178 training images and 3,798 testing images of 102 different species. Following the COCO benchmark [23], the insect detection performance is measured by the Average Precision (AP) and Average Precision at IoU thresholds of 0.5 (AP" + }, + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "type": "inline_equation", + "content": "^{50}" + }, + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "type": "text", + "content": ") and 0.75 (AP" + }, + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "type": "inline_equation", + "content": "^{75}" + }, + { + "bbox": [ + 304, + 262, + 545, + 322 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 332, + 406, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 332, + 406, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 332, + 406, + 344 + ], + "type": "text", + "content": "5.3. Ablation Studies" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 351, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 387 + ], + "type": "text", + "content": "Our ablation experiments study the effectiveness of our proposed model and hyper-parameters on the IP102 Classification Benchmark as shown in Table 2." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "type": "text", + "content": "Effectiveness of Network Backbones Table 2 studies the impact of different Vision Transformer backbone sizes, including ViT-small/16, ViT-base/16, and ViT-large/16. As shown in our results, the powerful backbone carries more improvement. In particular, when changing the Transformer backbone size from small to base, the accuracy score increases by a large margin of " + }, + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "type": "inline_equation", + "content": "4.3\\%" + }, + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "type": "text", + "content": " while the large Transformer backbone improves the accuracy score by " + }, + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 388, + 545, + 484 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": "Effectiveness of Attention Pooling We evaluate the impact of the attention pooling in the visual representation of the insect images. As shown in Table 2, the Attention Pooling has better representation than the standard classification token computed through transformer layers. In particular, the top-1 accuracies for the three backbones, i.e., small, base, and large, have been increased from " + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "inline_equation", + "content": "68.9\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "inline_equation", + "content": "69.5\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": ", from " + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "inline_equation", + "content": "72.4\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "inline_equation", + "content": "73.3\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": ", and from " + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "inline_equation", + "content": "73.8\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "inline_equation", + "content": "74.6\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 579 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "text", + "content": "Effectiveness of Image-Text Contrastive Loss As reported in Table 2, the model can understand the insect images better when the model learns to match the images and their descriptions. In detail, the accuracy scores have been increased by " + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 304, + 581, + 545, + 653 + ], + "type": "text", + "content": " for the three backbones when applying the Image-Text Contrastive Loss." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of Description Loss The full configuration in Table 2 shows the experimental results of our model using the Description Loss. As shown in Table 2, the Description Loss helps the model to well-align the information between images and the details of descriptions. Hence, the model" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21951" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 71, + 267, + 213 + ], + "blocks": [ + { + "bbox": [ + 67, + 71, + 267, + 213 + ], + "lines": [ + { + "bbox": [ + 67, + 71, + 267, + 213 + ], + "spans": [ + { + "bbox": [ + 67, + 71, + 267, + 213 + ], + "type": "image", + "image_path": "6fd20269ab7c086a5d012da4231972dc298fa232ae1c6cb10e4ed8d7befb1139.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 287, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 287, + 258 + ], + "type": "text", + "content": "Figure 8. Attention Visualization. Compared to MAE [18], our model is robust to small details of insect images. The model can focus on the small textures of the insect, even if the texture is the same as the background (bottom images). Best viewed in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": "can represent the fine-grained features of the insects better. In particular, the accuracy scores have been improved from " + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "inline_equation", + "content": "70.7\\%" + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "inline_equation", + "content": "71.5\\%" + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": ", from " + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "inline_equation", + "content": "74.2\\%" + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "inline_equation", + "content": "75.8\\%" + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": ", and from " + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "inline_equation", + "content": "75.9\\%" + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "inline_equation", + "content": "76.9\\%" + }, + { + "bbox": [ + 47, + 261, + 286, + 308 + ], + "type": "text", + "content": " for ViT-small/16, ViT-base/16, and ViT-large/16." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 258, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 258, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 258, + 328 + ], + "type": "text", + "content": "5.4. Comparisons with Prior SOTA Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "type": "text", + "content": "Insect Classification Tasks. We fine-tune the linear layer with our pre-trained model on the IP102 dataset [66] for the classification task. As shown in Table 3, our model outperforms deep learning models [15, 16, 20, 50, 52] pre-trained on ImageNet [12] by a large margin. Compared to other pre-training methods [7, 17, 18, 70] on the proposed 1M-Insect dataset, our model shows better performance for both training without and with insect descriptions of " + }, + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "type": "inline_equation", + "content": "73.3\\%" + }, + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "type": "inline_equation", + "content": "75.8\\%" + }, + { + "bbox": [ + 46, + 334, + 286, + 464 + ], + "type": "text", + "content": ", respectively. It is shown that the proposed approach has a better visual representation of insect images than the prior pre-training methods on the same dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 465, + 286, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 286, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 286, + 536 + ], + "type": "text", + "content": "Visualization Results Fig. 8 visualizes the attention maps of our model compared to MAE [18] pre-trained on the proposed dataset. Since the textures are similar to the background, it is hard for MAE to focus on the small details of the insect. On the contrary, our model can detect the key features, i.e., the textures and the limbs, of the insects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 537, + 286, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 286, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 286, + 654 + ], + "type": "text", + "content": "Zero-shot Insect Classification. We evaluate the performance of our model on the IP102 dataset [66] in a zero-shot manner. In detail, a description corresponds to each species to make the text encoder extract more semantic information about each species. Then, for each insect image, we use the image encoder to extract global features and compare them to each description feature to predict the insect Table 4. Zero-shot classification results on IP102 Classification benchmark. The proposed model outperforms prior vision-language pretraining methods." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 72, + 656, + 259, + 711 + ], + "blocks": [ + { + "bbox": [ + 72, + 656, + 259, + 711 + ], + "lines": [ + { + "bbox": [ + 72, + 656, + 259, + 711 + ], + "spans": [ + { + "bbox": [ + 72, + 656, + 259, + 711 + ], + "type": "table", + "html": "
MethodPretrain DataAccuracy (%)
CLIP [43]1M-Insect41.1
LiT [72]1M-Insect43.6
CoCa [70]1M-Insect45.3
Insect-Foundation1M-Insect49.9
", + "image_path": "c61d226177e3b245d206c27ca99b22b4fa8c10cc9c9e38c149d7311bb5badbf0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 325, + 93, + 523, + 196 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 5. Detection results on IP102 Detection benchmark. The proposed model outperforms prior pre-training methods." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 325, + 93, + 523, + 196 + ], + "lines": [ + { + "bbox": [ + 325, + 93, + 523, + 196 + ], + "spans": [ + { + "bbox": [ + 325, + 93, + 523, + 196 + ], + "type": "table", + "html": "
MethodBackbonePre-train DataAP (%)\\( AP^{50} \\)(%)\\( AP^{75} \\)(%)
FRCNN [47]VGG-16 [50]ImageNet1K21.147.915.2
FPN [24]ResNet-50 [16]ImageNet1K28.154.923.3
SSD300 [26]VGG-16 [50]ImageNet1K21.547.216.6
RefineDet [74]VGG-16 [50]ImageNet1K22.849.016.8
YOLOv3 [46]DarkNet-53 [46]ImageNet1K25.750.621.8
FPN [24]ViT [15]ImageNet1K32.854.735.0
FPN [24]MoCo [17]1M-Insect33.656.135.3
FPN [24]DINO [7]1M-Insect34.055.837.1
FPN [24]MAE [18]1M-Insect34.758.437.8
FPN [24]Insect-Foundation1M-Insect36.659.140.3
", + "image_path": "ca9505deb18b437f3a03e3ac36119f4e7ea85b25b8e75c140cb8fb30fa2ec376.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 199, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 545, + 258 + ], + "type": "text", + "content": "species. Table 4 reports the results of zero-shot classification on the IP102 Classification benchmark. Our model outperforms prior image-text pre-training methods [43, 70, 72] at an accuracy of " + }, + { + "bbox": [ + 304, + 199, + 545, + 258 + ], + "type": "inline_equation", + "content": "49.9\\%" + }, + { + "bbox": [ + 304, + 199, + 545, + 258 + ], + "type": "text", + "content": ". It shows that our model has well-alignment between the insect image and its description." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": "Insect Detection Tasks. As shown in Table 5, we train a Faster R-CNN model [47] on the IP102 Detection dataset with the ViT backbone adapted for FPN [24]. Compared to models pre-trained on ImageNet [12], our model achieves SOTA results with an average precision of " + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "inline_equation", + "content": "36.6\\%" + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}^{50}" + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "inline_equation", + "content": "59.1\\%" + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": " higher than the same backbone pre-trained on ImageNet [12] having AP of " + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "inline_equation", + "content": "32.8\\%" + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}^{50}" + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "inline_equation", + "content": "54.7\\%" + }, + { + "bbox": [ + 304, + 259, + 545, + 379 + ], + "type": "text", + "content": ". Compared to other self-supervised methods [7, 17, 18], our model achieves higher precision. Thus, our model focuses on the features of insects better than prior methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 392, + 383, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 383, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 383, + 403 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 412, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 664 + ], + "type": "text", + "content": "This paper has introduced a new large-scale Insect-1M dataset that supports the development of the Insect Foundation Model in precision agriculture. Our proposed dataset includes a large diversity of insect species and multi-level labels of taxonomy. In addition, Insect-1M consists of detailed descriptions of insects that support vision-language insect model training. Then, to improve the micro-feature modeling of our insect foundation model, we introduce a new Patch-wise Relevant Attention mechanism and Description Consistency loss to learn the details of insects. Our experimental results have illustrated the effectiveness and significance of our Insect-1M and Insect Foundation Model. Limitations This study used a specific network design and learning hyper-parameter to support our hypothesis. However, our approach potentially consists of several limitations related to the design of our Patch-wise Relevant Attention mechanism, where the patches of background and foreground are equally treated. It could result in difficulty in learning the different features of insects. This limitation will further motivate future research to improve the Insect Foundation Model and Micro-feature Modeling." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgment. This work is partly supported by NSF DART, NSF SBIR Phase 2, and JBHunt Company. 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Stephen McGough $^{1}$", + "bbox": [ + 84, + 179, + 888, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Newcastle University, UK — 2Durham University, UK — 3The Alan Turing Institute, UK", + "bbox": [ + 125, + 222, + 844, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rob@geada.net, amir.atapour-abarghouei@durham.ac.uk {d.towers2, matthew.forshaw, stephen.mcgough}@ncl.ac.uk", + "bbox": [ + 241, + 244, + 727, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 311, + 313, + 328 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The boundless possibility of neural networks which can be used to solve a problem - each with different performance - leads to a situation where a Deep Learning expert is required to identify the best neural network. This goes against the hope of removing the need for experts. Neural Architecture Search (NAS) offers a solution to this by automatically identifying the best architecture. However, to date, NAS work has focused on a small set of datasets which we argue are not representative of real-world problems. We introduce eight new datasets created for a series of NAS Challenges: AddNIST, Language, MultNIST, CIFAR-Tile, Gutenberg, Isabella, GeoClassing, and Chesseract. These datasets and challenges are developed to direct attention to issues in NAS development and to encourage authors to consider how their models will perform on datasets unknown to them at development time. We present experimentation using standard Deep Learning methods as well as the best results from challenge participants.", + "bbox": [ + 76, + 342, + 473, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 625, + 209, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the main appeals of Deep Learning (DL) was its ability to democratise Machine Learning. No longer would you require a domain expert to develop an optimal solution to a given problem since DL models are capable of learning the required patterns and features from the data themselves and would not need the domain expert to identify and extract the required features. Unfortunately, rather than removing the need for an expert, the new paradigm has just shifted where the expert is required. These experts now spend their time identifying the most optimal neural network architecture for a given problem. Those who are not that proficient would select between pre-existing off-the-shelf networks such as ResNet [10], VGG [23] or Inception [25]. However, to get the best results for a particular problem, one should search across all possible solutions,", + "bbox": [ + 76, + 651, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "not just those which may have shown good results in other problem domains, as no network is optimal for all problems. This idea of the 'no free lunch' [34] is backed up by our findings here, with some networks giving far poorer performance than what would be expected.", + "bbox": [ + 500, + 311, + 890, + 388 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A DL problem can be seen as the combination of a particular task – such as classification – one wishes to apply in a particular data domain. The data domain is normally realised as a dataset for training the DL network.", + "bbox": [ + 498, + 391, + 890, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural Architecture Search (NAS) is a fast-developing field of DL – which can be seen from the increase of published papers in the domain over the last few years [3]. The aim of NAS is to remove the need for an expert's time and knowledge to generate state-of-the-art competitive Neural Networks from a particular dataset [40]. NAS methods search through millions (if not billions) of candidate architectures from a pre-defined search space to find optimum networks. These search spaces comprise not only different network topologies but also the types of nodes which make up these networks – such as fully connected layers, convolutions and pooling. Although NAS can be applied to any data modality, the majority of work to date has focused on image-based datasets, with modern NAS methods achieving this feat in a few GPU hours [19, 37]. In addition to a predefined search space, a NAS approach will have a search strategy. In terms of the task, the majority of work in NAS has focused on classification problems.", + "bbox": [ + 496, + 455, + 892, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "NAS techniques are often evaluated by their ability to find networks that perform well on benchmark datasets, such as CIFAR-10 [12] and ImageNet [5]. These datasets, combined with standard search spaces such as NAS-Bench [6], fill an important role, allowing a direct comparison between NAS methods. While there is a clear benefit in using common benchmark datasets, we argue this is against the ethos of NAS - removing the need for domain experts, required to develop optimal architectures for a given problem.", + "bbox": [ + 496, + 729, + 890, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Developing against common datasets can be seen as over-engineering a process to reach a solution we already", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors performed equal contribution.", + "bbox": [ + 94, + 886, + 336, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22541", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "know. For example, for datasets such as CIFAR-10, extensive experimentation with various neural network architectures has led to extremely high levels of accuracy [1,8,20], rendering this dataset easily solvable. In essence, since we already know what achieves high performance, NAS strategies may be optimised to reach these solutions, which may not generalise to other datasets. Prior work [18] has found that just because NAS methods perform well on benchmarks such as NAS-Bench-101 [38], this does not mean they will match other benchmarks.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "If NAS is to truly replace architecture design experts, it must be able to find optimal networks for datasets that it has never seen before – the unseen data challenge. There is a dichotomy here in that proposing a new 'unseen' dataset for NAS may lead to that dataset being adopted as one of the core datasets for NAS. We, therefore, see our work as having two values. In the first case, we are diluting the effect of overfitting to the core datasets – having more core datasets is less likely to create a NAS approach, which can overfit to all of them. For the second case, we see this as a 'call to arms' to encourage the development and use of more datasets for NAS, which we will continue to do ourselves.", + "bbox": [ + 75, + 242, + 472, + 421 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present eight new datasets created and used for unseen dataset NAS challenges. We define how these datasets were constructed and illustrate benchmark performance metrics that have been achieved, with the intention of encouraging others in the NAS community to develop approaches that will work on more general datasets.", + "bbox": [ + 75, + 422, + 472, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Motivation", + "text_level": 1, + "bbox": [ + 76, + 526, + 194, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To understand how well NAS methods might generalise to novel datasets and drive the direction of NAS research towards more impactful real-world applications, we organised a challenge tasking participants with creating NAS methods that perform well on unknown datasets. Participants were provided with a small number of \"development\" datasets to develop and test their NAS algorithm(s). After development, the algorithms were submitted to the competition servers, where the algorithms would be run over novel \"evaluation\" datasets. The datasets were created bespoke for the challenge and withheld from the participants throughout its duration, such that no participant could gain an advantage by knowing or guessing the evaluation datasets. As such, the participants are encouraged to create NAS approaches that generalise well to multiple problems rather than ones specifically targeted at one dataset.", + "bbox": [ + 75, + 551, + 472, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These unseen datasets explore one of two concepts:", + "bbox": [ + 96, + 794, + 437, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Type-1: A problem an expert could solve themselves or create a program, which may include basic DL, that can outperform a naive DL approach on the raw datasets. An example of this type of data is the AddNIST dataset Sec. 4.1, one of the datasets outlined later in this paper, which consists of images with three", + "bbox": [ + 94, + 810, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "channels, with each channel being an image from the MNIST dataset [14] having the class label as the sum (the numbers are chosen so the sum is less than twenty) of the individual MNIST digits. With prior knowledge of this dataset, a solution that attains the highest accuracy is splitting the colour channels into three separate images, using a model trained on MNIST to identify the individual numbers, and then hardcoding in the necessary arithmetic to get the final answer.", + "bbox": [ + 529, + 90, + 890, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Type-2: A problem that would be almost impossible for a human to solve or create a program without task-specific tools. An example is the Language dataset Sec. 4.2, which encodes words from ten languages into an image. The models needs to identify which letter frequency is attributed to the correct language. Without prior knowledge of what is encoded within the images and which language is represented by each class label, correctly labelling each image to the correct language would be nearly impossible. The motivation for using a type 2 dataset is to see if bespoke models can perform better than random guesswork over datasets that appear human-impossible at face value.", + "bbox": [ + 517, + 233, + 890, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We believe that both types of tasks are essential for NAS algorithms to make a meaningful impact in real-world applications. First, if NAS remains incapable of solving problems that are effortlessly solvable by humans, it would be premature to assert that NAS can remove the requirement for expert knowledge. The second type relates to how machine learning is often deployed to find solutions to problems humans find complicated. Essentially, NAS methods should be able to perform at a level at least commensurate with other conventional machine learning techniques to effectively supplant manually designed models.", + "bbox": [ + 496, + 435, + 890, + 601 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further obfuscate the true nature of the datasets from the challenge participants, within our datasets, data shapes were deliberately chosen that appeared to correlate to normal images or well-known datasets, such as $3 \\times 64 \\times 64$ , and data split sizes to align with well-known benchmark datasets, such as 50,000 training images to align with CIFAR. We also asked participants for their guesses as to what each development dataset was: most participants correctly described the Type-1 datasets. In contrast, none of the Type-2 datasets have been correctly identified.", + "bbox": [ + 496, + 602, + 890, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Related Work", + "text_level": 1, + "bbox": [ + 500, + 762, + 640, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We consider related work within the NAS literature and the datasets commonly used in NAS research.", + "bbox": [ + 498, + 787, + 890, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Neural Architecture Search", + "text_level": 1, + "bbox": [ + 500, + 830, + 748, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NAS aims to automate the process of neural network architecture design. Traditional network design requires extensive human expertise and significant time investment.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22542", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NAS seeks to streamline this process by employing algorithms that efficiently identify architectures tailored to specific tasks and datasets from a vast search space.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Initially, the work by Zoph and Le [40] applied NAS using reinforcement learning to CIFAR-10, achieving an architecture slightly outperforming manually designed models. NASNet [41] addressed the challenge of learning architectures directly on large datasets by transferring a building block designed for a small dataset to a larger one using ImageNet. ENAS [21] focused on computational efficiency by learning to search for an optimal sub-graph within a large graph, thus reducing computational resources. Evolutionary algorithms [22] have emerged, providing comparable results but with a distinct evolutionary overview. Weight-sharing methods [15] define over-parameterised super-networks (one-shot models), reducing computational costs, allowing the training of one super-network encompassing many different sub-architectures rather than training numerous networks independently.", + "bbox": [ + 75, + 137, + 468, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Differentiable NAS [9, 16] marks another significant advancement, allowing gradient-based optimisation methods to explore the neural architecture search space efficiently. Each of these developments in NAS represents a significant stride towards the more efficient, automated and effective design of neural network architectures; however, the effectiveness of these approaches is often only tested on common benchmark datasets, some of which we will briefly cover in the following sections. The real-world applicability of these approaches needs to be tested on \"unseen\" datasets, which better simulate what is needed of NAS in practice.", + "bbox": [ + 75, + 378, + 468, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Common NAS datasets", + "text_level": 1, + "bbox": [ + 76, + 556, + 290, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although any dataset can be used to evaluate NAS methods, CIFAR-10 [12], and ImageNet [5] are highly popular.", + "bbox": [ + 75, + 580, + 468, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CIFAR-10 [12] comprises 60,000 images from ten classes evenly distributed in training and testing sets. Accuracy on CIFAR-10 is often used to evaluate performance, and it is also used in NAS, with the very first NAS algorithm [40] highlighting the potential power of NAS by demonstrating its ability to achieve better CIFAR-10 performance than human-designed models. While CIFAR-10 is a good dataset for comparing performance, it is an easy problem, with modern architectures and NAS methods easily achieving accuracies over $90\\%$ . Furthermore, since CIFAR-10 is used as a standard benchmark, new methods are encouraged to focus on this dataset, which may come at a cost of generalisability across other datasets.", + "bbox": [ + 75, + 613, + 468, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ImageNet [5] is another popular dataset for evaluation and benchmarking. It contains 1,000 classes and presents a more challenging problem, with the results often presented in tandem with CIFAR-10 results to demonstrate model performance. ImageNet poses similar issues to CIFAR-10 due to its similar prevalence in benchmarking DL methods.", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While including ImageNet and CIFAR-10 as datasets for NAS comparison demonstrates that the NAS approach is not overfitting to just one dataset, it does not solve the problem of generalisation. We argue that both more datasets and datasets that the developers are unaware of are needed.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. NAS Benchmark Suites", + "text_level": 1, + "bbox": [ + 500, + 179, + 718, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To make NAS development more comparable and easier, benchmark suites such as NAS-Bench-101 [38], NAS-Bench-201 [7], and NATS-Bench [6] have been developed. In these benchmarks, the performance achieved for each network in the search space has been pre-computed, thus removing the model training step in NAS approaches.", + "bbox": [ + 496, + 203, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Benchmark suites allow developers to focus on the development of search strategies and allow for easy comparison between different approaches as they work directly on the same search space. Thus, performance gains over other methods cannot be attributed to different search spaces.", + "bbox": [ + 496, + 294, + 890, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These benchmark suites suffer from the same issues of reliance on CIFAR-10 and ImageNet. The search spaces used by these benchmarking tools have been fully explored on CIFAR-10 and ImageNet. These results are stored so a NAS method can look up an architecture's final result without having to retrain fully. These lookup tables do not exist for other datasets, meaning that NAS methods developed using these tools can quickly generate results for CIFAR-10 and ImageNet but not easily for other datasets.", + "bbox": [ + 496, + 371, + 892, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Dataset Descriptions", + "text_level": 1, + "bbox": [ + 500, + 523, + 696, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The code to generate our datasets is available at our GitHub page1. Each dataset comprises six NumPy files, X (images) and Y (labels) files for the training, validation, and testing sets, and a metadata file. This metadata file includes the shape of the training data, the ResNet-18 [10] benchmark result, and the number of classes in the data. Further details and examples are provided in the Appendices.", + "bbox": [ + 496, + 549, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1.AddNIST", + "text_level": 1, + "bbox": [ + 500, + 667, + 611, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "AddNIST [27], is a Type-1 dataset of 70,000 images with an image shape of $3 \\times 28 \\times 28$ (channels first). The training, validation, and testing split is 45,000, 15,000, and 10,000, respectively. Each colour channel is an image from MNIST [14]. An example AddNIST image is depicted in Fig. 1 (left), the larger image, shows the image as is, with the three channels laid on top of each other, and three images to the right show each channel more clearly.", + "bbox": [ + 496, + 691, + 890, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "AddNIST has twenty classes (0 - 19), with the class derived from the MNIST label of each channel, such that $l = (r + g + b) - 1$ , where $l$ is the image label and $r, g$ , and $b$ are the respective MNIST labels of each colour channel.", + "bbox": [ + 496, + 813, + 890, + 873 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "$^{1}$ github.com/Towers-D/NAS-Unseen-Datasets", + "bbox": [ + 517, + 886, + 763, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22543", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1fa374d918eb0cc1e4a36f427b81b47af6af3340f9299329329fe048ad89f246.jpg", + "image_caption": [ + "Figure 1. Left: AddNIST image - the sum of the channels adds up to 15 $(\\mathrm{r} = 2, \\mathrm{g} = 9, \\mathrm{b} = 4)$ , implying a label of 14. Middle MultNIST image - the product of the channels equals 35 $(\\mathrm{r} = 5, \\mathrm{g} = 7, \\mathrm{b} = 1)$ , which implies a label of 5 $(35\\%10 = 5)$ . Right CIFARTile image - two deer, one aeroplane, and one horse, meaning there are three unique labels among the sub-images, which equates to a final label of 2" + ], + "image_footnote": [], + "bbox": [ + 189, + 90, + 781, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "AddNIST adds complexity to the MNIST data. In MNIST, the goal is to identify what numerical digit is seen within the image, while in AddNIST, not only does the model have to identify the digit in each channel, but it must also learn to sum up these values in a specific manner to identify the class correctly. In this manner, AddNIST was designed around the research question of whether NAS could \"figure out\" a calculation was required and apply it.", + "bbox": [ + 75, + 277, + 468, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the task this dataset puts forward is still rather simple, which is expected for a Type 1 dataset, it requires high-level inference capabilities within the model, which would mean the NAS algorithm searching for the optimal architecture would have to consider the capacity of the model to encompass the required function.", + "bbox": [ + 75, + 398, + 470, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Language", + "text_level": 1, + "bbox": [ + 76, + 500, + 191, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the open-source, public spell checker ASPELL, which can be found at aspell.net, we created Language [32], a Type-2 dataset.", + "bbox": [ + 75, + 522, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using dictionaries from 10 languages that use the Latin alphabet (English, Dutch, German, Spanish, French, Portuguese, Swedish, Zulu, Swahili, and Finnish), all six-letter words within each language are extracted, and any words with letters that use diacritics (such as é or ii) or include 'y' or 'z' are subsequently removed.", + "bbox": [ + 75, + 568, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each image is generated by first selecting one of the ten languages. We then randomly select four words that we filter from the selected dictionary and concatenate them into a 24-character string. Since we eliminated letters with diacritics and y and z, we have a remaining alphabet of twenty-four letters. This allows for a $24 \\times 24$ -grid encoding the string as a $1 \\times 24 \\times 24$ image. Using the $y$ -axis to denote the index of the string and the $x$ -axis to denote the character, we construct the image so each black pixel denotes the letter used in that position. See Fig. 2 (top) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively.", + "bbox": [ + 75, + 657, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Language research question pertained to whether a linguistic character encoding contained enough information for DL to correctly identify the original language, requiring the model to perform linguistic analysis. To ensure no leak-", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9fe09169410b6442fea7cd2f5ce3ca73060231657523c07e8745b5286091334e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 277, + 795, + 436 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2cbabe158acb5a2427bb0d6e4e2f0616ad72cf5cd1e19619ef587d9332ded1a2.jpg", + "image_caption": [ + "Figure 2. Top: An example of a Language image with a readable axis included. The right-hand axis contains the four six-letter words \"Uvulas\", \"Minted\", \"Suckle\", and \"Debits\", which are all English words given the label 0. Bottom: An example Gutenberg image, the words \"their\", \"spring\", and \"their\" have been encoded from one of Shakespeare's works which give the label 4" + ], + "image_footnote": [], + "bbox": [ + 601, + 440, + 792, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "age between the training and testing data, when selecting a word for the training data, we ensure that this word does not appear in the validation or testing data and vice versa.", + "bbox": [ + 498, + 768, + 890, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. MultNIST", + "text_level": 1, + "bbox": [ + 500, + 829, + 617, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "MultNIST [33] is a Type-1 dataset similar in concept to AddNIST (Sec. 4.1), originating from the same research question. Like AddNIST, MultNIST images have a", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22544", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ceb4abaceaf59e86c38d15e52f2bc3d8995a7aedcfa315dc51dd760c76adae38.jpg", + "image_caption": [ + "Figure 3. Left: An example of an Isabella generated using a piece of music labelled as “20th Century”(0). Middle An example of the GeoClassing dataset showing a photo taken over Portugal (9). Right: An example rendering of a board position in the Chesseract dataset wherein white goes on to eventually win and is thus given a label of White Wins (0)" + ], + "image_footnote": [], + "bbox": [ + 187, + 88, + 480, + 203 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e0d03ac3240cda94b3c7247a0c2b7c327fa91e5f9ce31421942b319a5f0aba71.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 630, + 203 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cfe23c1796bd32982c3a632b09fa252369a1ebcca2a92a88cb605a3b69fac1c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 88, + 781, + 203 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$3 \\times 28 \\times 28$ channel first shape, and each channel is an image from the MNIST dataset [14]. See Fig. 1 (middle) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively.", + "bbox": [ + 76, + 272, + 468, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MultNIST has only ten classes (0 - 9). The label of each MultNIST image is calculated such that $l = (r*g*b) \\mod 10$ where $l$ is the image label and $r, g$ , and $b$ are the respective MNIST labels of each colour channel.", + "bbox": [ + 76, + 333, + 468, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In AddNIST, the class was directly affected by how large the numbers were in each channel. The only way for an image to have a label of 0 was if one colour channel contained an MNIST with label 1 and the remaining channels contained MNIST images for 0. MultNIST introduces the additional complexity over MNIST by retaining a calculation but removes the bias of larger numbers to higher classes.", + "bbox": [ + 75, + 393, + 468, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4.CIFARTile", + "text_level": 1, + "bbox": [ + 76, + 512, + 199, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CIFARTile is a Type-1 dataset where each image in the CIFARTile [29] dataset is a compilation of four CIFAR-10 [12] images tiled together in a grid resulting in images which are of size $3 \\times 64 \\times 64$ . See Fig. 1 (right) for an example. The training, validation, and testing split is 45,000, 15,000, and 10,000 images, respectively.", + "bbox": [ + 76, + 537, + 468, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "There are four classes (0 - 3), which represent the number of CIFAR-10 classes in each grid minus one. For example, a grid consisting of CIFAR-10 images with labels [horse, horse, frog, car] has three distinct classes, and thus a label of $3 - 1 = 2$ . As such, CIFARTile is a Type-1 dataset; any human should be able to identify and solve this task.", + "bbox": [ + 76, + 628, + 468, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CIFARTile requires a model to identify multiple CIFAR-10 classes simultaneously and determine which are similar and which differ. Whether models could adequately do this is the driving research question behind this dataset.", + "bbox": [ + 76, + 719, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Gutenberg", + "text_level": 1, + "bbox": [ + 76, + 785, + 196, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gutenberg [31] is a Type-2 dataset named after the source of the data, Project Gutenberg, found at www.gutenberg.org, which provides free eBooks of literary works that are no longer under US copyright protection. We selected six authors (Thomas Aquinas, Confucius, Hawthorne, Plato, Shakespeare, and Tolstoy) and down", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "loaded several books from each author - see the Appendices for further details and examples.", + "bbox": [ + 498, + 272, + 890, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The selected works are English translations that represent a variety of cultures and time periods. We perform basic text preprocessing, including removing punctuation, converting letters with diacritics to the base letter, and removing \"structure\" words (e.g., 'Chapter', 'Scene', 'Prologue'). We then extracted consecutive sequences of three words between 3 and 6 letters long. In each sequence, the three words were padded up to 6 characters with spaces. Then, the three words were concatenated together to produce an 18-character string. These strings were used as the base for image creation. Training, test, and validation sequences were chosen such that there was no overlap between any sequence across any data split.", + "bbox": [ + 496, + 301, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to the Language dataset (Sec. 4.2), we converted these strings into images. On a $27 \\times 18$ grid, we created a mapping of each character in the string. See Fig. 2 (bottom) for an example. The $x$ -axis represents the position in the string, and the $y$ -axis represents the alphabetical letter (or space) located at that position. This results in the shape being $1 \\times 27 \\times 18$ . The task is then to predict which of the original six authors the original word sequence came from. The training, validation, and testing split is 45,000, 15,000, and 6,000, respectively, to prevent participants from exploiting the standard distribution we used for the other datasets.", + "bbox": [ + 496, + 500, + 890, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The research question behind this dataset was whether specific spatial patterns of letters were sufficient information for a neural network to identify the authors from which they originated, which seems impossible from face value.", + "bbox": [ + 496, + 665, + 890, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.6. Isabella", + "text_level": 1, + "bbox": [ + 500, + 734, + 596, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Isabella2 is a Type-2 dataset that uses musical recordings from the Isabella Stewart Gardner Museum, Boston.", + "bbox": [ + 498, + 758, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The four classes of this dataset refer to the era of composition (Baroque, Classical, Romantic, and 20th Century) attributed by the museum. The recordings are split into five-second snippets converted into 64-band spectrograms, creating a dataset of $1 \\times 64 \\times 128$ shaped images. See Fig. 3", + "bbox": [ + 496, + 789, + 890, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$^{2}$ Code to generate Isabella is available at github.com/Towers-D/NAS-Unseen-Datasets.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22545", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4832ef2af80dc1880e43e5a0c9ee76620f2ee909e9069f794eeb256234feaf51.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetResNet-18AlexNetVGG16ConvNextMNASNetDenseNetResNeXtRandom
AddNIST92.08%94.87%92.06%38.06%90.51%93.52%91.42%5%
Language87.00%85.71%84.54%83.40%84.63%84.57%93.97%10%
MultNIST91.55%94.01%90.43%64.20%87.70%92.81%90.57%10%
CIFARTile45.56%48.88%24.43%31.06%48.49%51.28%46.23%25%
Gutenberg40.98%45.53%44.00%31.93%38.00%43.28%40.30%16.6%
Isabella62.02%61.37%58.13%57.18%60.69%63.27%60.46%25%
GeoClassing80.33%92.49%83.67%72.76%86.00%94.21%89.99%10%
Chesseract57.83%57.45%55.69%52.74%56.26%59.60%55.15%33.3%
", + "bbox": [ + 99, + 87, + 869, + 228 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Experiments on commonly-used CNN-based classification models [10,11,13,17,23,26,35] using the presented datasets.", + "bbox": [ + 99, + 238, + 866, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(left) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively.", + "bbox": [ + 75, + 262, + 468, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The task for the models is to predict the era of composition from the spectrogram. No recording used in a training snippet appeared in the validation or test sets. The research question behind this dataset was to explore whether era-defining characteristics appear at the spectrogram level and whether CNNs could reliably identify such patterns.", + "bbox": [ + 75, + 292, + 468, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.7. GeoClassing", + "text_level": 1, + "bbox": [ + 76, + 397, + 210, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GeoClassing [30], known as Sadie in the competition, is a Type-2 dataset that takes advantage of the BigEarthNet dataset [24] as a foundation. The BigEarthNet dataset, as originally published, consists of satellite photography with ground-cover classification labels, i.e., \"airports\" or \"vineyards\". An example image is shown in Fig. 3 (middle).", + "bbox": [ + 75, + 421, + 468, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The GeoClassing dataset uses these images, but instead of using the given ground-cover labels, we identified the European Space Agency Sentinel patch from which the BigEarthNet image was sourced. We cross-referenced the coordinates of that patch within a map of Europe to identify the corresponding country depicted in the image. This gave us ten classes (Austria, Belgium, Finland, Ireland, Kosovo, Lithuania, Luxembourg, Portugal, Serbia, and Switzerland).", + "bbox": [ + 75, + 513, + 468, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Each image has a shape of $3 \\times 60 \\times 60$ , and the training, validation, and testing split contains 43,821, 8,758, and 8,751 images, respectively. The research question is whether NAS can find models that identify countries from differences in topology and ground coverage, which, without specific knowledge of geography and vegetation type, would be extremely difficult for a human to do manually.", + "bbox": [ + 75, + 636, + 468, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.8. Chesseract", + "text_level": 1, + "bbox": [ + 76, + 755, + 197, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Chesseract [28], a Type-1 dataset wherein we accessed public chess games from eight grandmasters (Bobby Fischer, Garry Kasparov, Magnus Carlsen, Viswanathan Anand, Hikaru Nakamura, Anatoly Karpov, Fabiano Caruana, and Mikhail Tal) extracting the final $15\\%$ of board states. These positions were then one-hot encoded by piece type and colour, creating a $12 \\times 8 \\times 8$ image. As a 12-channel image is hard to render, we provided a flattened 2D image", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of one of the chess boards we used Fig. 3 (right). A 3D visualisation can be seen in the Appendices.", + "bbox": [ + 496, + 262, + 890, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The training, validation, and testing split is 49,998, 9,999, and 9,999 images, respectively. Each image in the Chesseract dataset is one of three classes (White wins, Draw, Black wins). No individual positions from the same game appeared across the data splits. This dataset requires the model to identify the game's final result from the position. Chesseract presented a problem for some participants of the challenge. This was because Chesseract uses twelve instead of the usual 1 or 3 channels applied for image datasets, which often caused errors for hardcoded algorithms that only accepted 1 or 3 channel dimensions.", + "bbox": [ + 496, + 292, + 890, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Machine learning is already prominent in chess, with competing learning-based chess engines that beat grandmaster players, such as AlphaZero [4]. Our research question for this dataset was based on the understanding that any position can be analysed to show whether black or white has the advantage. Is NAS able to develop a DL network to identify this from just an encoding of the board position?", + "bbox": [ + 496, + 459, + 890, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Baseline Experimentation", + "text_level": 1, + "bbox": [ + 500, + 580, + 740, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, we provide some baseline results for our datasets to motivate future NAS experimentation. We provide a set of baseline results across several well-known CNNs and three NAS methods across two search spaces.", + "bbox": [ + 496, + 607, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. CNN Experiments", + "text_level": 1, + "bbox": [ + 500, + 679, + 678, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To generate baseline results of our datasets for future work comparison, we have performed experiments using commonly used off-the-shelf CNNs, which can be seen in Tab. 1. In all our CNN experiments, we have followed a similar experimental setup. We use stochastic gradient descent as our optimiser with an initial learning rate of 0.01, momentum of 0.9, and a weight decay of $3 \\times 10^{-4}$ . We have used a Cosine Annealing Learning rate with the max number of iterations equaling 64, the number of epochs. Cross Entropy is used as the Loss function.", + "bbox": [ + 496, + 703, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ResNet-18 is used as the baseline throughout our competition, and any NAS method would be expected to easily outperform this architecture. As you can see in Tab. 1,", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22546", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d1c29422377dea0adba1f3a2d6cd8578622797c51359232f0170534a7b1ba007.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetPC-DARTSDrNASBonsai-NetRandom Search
DARTSBonsaiRandom
Addnist96.60%97.06%97.91%97.07%34.17%5%
Language90.12%88.55%87.65%90.12%76.83%10%
MultNIST96.68%98.10%97.17%96.55%39.76%10%
CIFARTile92.28%81.08%91.47%90.74%24.76%25%
Gutenberg49.12%46.62%48.57%47.72%29.00%16.6%
Isabella65.77%64.53%64.08%66.35%58.53%25%
GeoClassing94.61%96.03%95.66%95.54%63.56%10%
Chesseract57.20%58.24%60.76%59.16%68.83%33.3%
", + "bbox": [ + 186, + 89, + 782, + 244 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Experimental results on PC-DARTS [36], DrNAS [2], Bonsai-Net [9] as well as random search.", + "bbox": [ + 174, + 253, + 792, + 268 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ResNet-18 produces competitive results across our datasets, though it does not excel on any particular dataset. ResNet-18 particularly struggles with the GeoClassing dataset compared to the others, only beating ConvNext in our trials.", + "bbox": [ + 75, + 277, + 468, + 337 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AlexNet [13] shows decent performance across all datasets, achieving the highest accuracy on three of the eight datasets (AddNIST, MultNIST, and Gutenberg). AddNIST and MultNIST are similar, both being derived from MNIST. This may suggest that AlexNet is particularly good at working with MNIST Images. AlexNet captures spatial hierarchies in images well and is thus suitable for the clear, structured layouts of MNIST digits. VGG16 [23], on the other hand, does not achieve particularly impressive levels of accuracy on any of the datasets, though it does not perform badly, either. The only exception is the CIFARTile dataset, where VGG suffers and only achieves roughly the same accuracy as random chance, as seen in Tab. 1.", + "bbox": [ + 75, + 338, + 468, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ConvNext [17] performs poorly across our datasets, most likely since our datasets may not exhibit the specific spatial complexity that ConvNext is optimised for. However, it is important to note that for purposes of generating our CNN baselines, we have kept the experimental setup the same across CNNs. Thus, hyperparameter tuning may be beneficial to ConvNext. We have used the base version of ConvNext in our experiments.", + "bbox": [ + 75, + 536, + 468, + 656 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also perform the same experiments on MnasNet [26] using a depth multiplier of 1.0. Despite being a lightweight architecture designed for mobile efficiency, MnasNet achieves competitive results across our datasets. It has strong generalisation capabilities since it uses a reinforcement learning approach to automate architecture design, thus performing well on unseen datasets [26].", + "bbox": [ + 75, + 657, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DenseNet [11] performs significantly well on the latter three datasets (Isabella, GeoClassing, and Chesseract) as well as CIFARTile, achieving the highest accuracy of the CNNs over these datasets. With the exception of Chesseract, the datasets that DenseNet excels on are the most memory-intensive datasets. This is due to the DenseNet mechanism allowing efficient re-use of features through dense connectivity and ensuring maximal information flow between layers in the network [11]. For memory-intensive", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "datasets, which often contain complex and rich information, this feature reuse allows DenseNet to exploit the data more thoroughly and efficiently, leading to better performance. The DenseNet-161 architecture is used in our experiments.", + "bbox": [ + 496, + 277, + 890, + 337 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, ResNeXt [35] performs fairly well across our datasets, but especially well on the Language Dataset, scoring almost $7\\%$ higher than the other methods. The particular version of ResNeXt we used is ResNeXt-50 (32 x 4d), which has a high level of cardinality (the size of the set of transformations) [35]. This high cardinality allows ResNeXt to learn more complex and diverse representations, which is crucial for distinguishing subtle patterns in the Language Dataset, such as the frequency and arrangement of characters encoded in images.", + "bbox": [ + 496, + 338, + 890, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our analysis across these CNN architectures reveals distinct performance trends tied to the nature of each dataset. ResNet-18 serves as a versatile baseline, while AlexNet is especially capable of handling structured patterns. VGG16's mixed results and ConvNext's overall underperformance emphasise the need within conventional deep learning for matching architectural strengths to dataset characteristics, which is not desirable for evaluating generalisation capabilities in general and NAS algorithms in particular. DenseNet and ResNeXt are good at handling memory-intensive datasets and those with nuanced patterns, respectively. These insights confirm that the effectiveness of a CNN architecture is highly contingent on the specific demands of the dataset, which underscores the need for unseen datasets for effective evaluation of NAS methods.", + "bbox": [ + 496, + 489, + 890, + 714 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. NAS Experiments", + "text_level": 1, + "bbox": [ + 500, + 724, + 671, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to the experiments performed on the CNNs, we have also applied the NAS methods of PC-DARTS [36], DrNAS [2] (DARTS-space), and Bonsai-Net [9] to our datasets. Furthermore, as a baseline of comparison, we perform a random search in both the DARTS and Bonsai search spaces, using the provided methods from PC-DARTS and Bonsai-NET. These results can be found in Tab. 2.", + "bbox": [ + 496, + 750, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "During our random search experiments using the DARTS search space, it is noted that random search often outperforms either PC-DARTS or DrNAS and outper", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22547", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3a08fb6e6165457e64c0a7b33fd3815013597f96483b1fac710d8e230c20381e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCNNNASCompetition
AddNIST94.87%97.91%95.06%
Language93.97%90.12%89.71%
MultNIST94.01%98.10%95.45%
CIFARTile51.28%92.28%73.08%
Gutenberg45.53%49.12%50.85%
Isabella63.27%65.77%61.42%
GeoClassing94.21%96.03%96.08%
Chesseract59.60%60.76%62.98%
", + "bbox": [ + 81, + 88, + 433, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Results on each dataset from our CNN and NAS experiments, and Competition Submissions", + "bbox": [ + 76, + 238, + 468, + 265 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "forms both models on AddNIST, Chesseract and Isabella, tying PC-DARTS on Language while outperforming DrNAS. These results support findings by Yu et al. [39] that searches using these search spaces often do not significantly outperform random search.", + "bbox": [ + 75, + 268, + 468, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We can see in Tab. 2 that PC-DARTS [36] performs well, scoring the highest accuracies over four of the eight datasets and gives competitive results over the others. DrNAS [2], however, scores the highest on two of the eight datasets but struggles with CIFARTile, where it scores $10\\%$ lower than the other methods. We used the DARTS search space during our DrNAS experiments; while DrNAS is also available to work on the NAS-Bench-201 [7] search space, it employs the NAS-Bench API to look at the performance of architectures fully trained on CIFAR-10, which would not reflect the performance these architectures found on our datasets. In most cases, Bonsai-Net [9] outperforms random search, with the exception of Chesseract. It returns the best results on AddNIST and Chesseract (though it is significantly beaten by random search on the latter dataset).", + "bbox": [ + 75, + 345, + 468, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The varied performance of these NAS methods across our datasets highlights their ability to challenge and assess the adaptability and effectiveness of different architecture search strategies. This underscores the strengths of our datasets in providing a comprehensive benchmark for evaluating NAS methods' capability to generalise across a diverse range of tasks and complexities.", + "bbox": [ + 75, + 571, + 468, + 678 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 691, + 191, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 shows the best-reported performance of the CNN and NAS experiments on each dataset, as well as the best result found by competition participants; for further information, see the Appendices. From these results, we can see that NAS found the best model for seven datasets, supporting the usage of NAS methods in finding good models for given datasets. Three of these architectures were found by competition submissions, NAS methods designed for unseen data; given the competition's time restrictions this may suggest that methods designed in this way can generalise to other datasets better.", + "bbox": [ + 75, + 718, + 468, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "It is important to mention that we did not test the deepest", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "versions of these CNN architectures or perform hyperparameter optimisation. Similarly, while we allowed the traditional NAS methods to run in their preset configuration, the competition participants were only given twenty-four hours to evaluate across three datasets. However, even with these limitations, CNNs and NAS architectures from the competition outperformed traditional NAS methods across several datasets, reinforcing our belief that current NAS methods do not necessarily generalise properly to unseen datasets.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Rights and Reproduction", + "text_level": 1, + "bbox": [ + 498, + 241, + 736, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "These datasets have been created under the licence agreements of the original data. Where available, we have made the datasets publicly accessible under an CC BY 4.0 Licence. The Isabella dataset uses data from the Isabella Stewart Gardner Museum, which withdraws the right to share modifications to the music they have made available. Instead of providing the dataset, we provide a Python script to convert music files obtained from the Museum into the format of the competition dataset on our GitHub4.", + "bbox": [ + 496, + 266, + 890, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 416, + 619, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Machine learning is a valuable and fast-growing tool that is quickly becoming part of the tools we use daily. For small businesses to stay competitive, they need to be able to easily include machine learning techniques in their products or business strategy. NAS promises to be a tool that removes the cost of an expert's time and knowledge to create bespoke neural networks while remaining competitive. NAS is currently evaluated primarily on a few benchmark datasets and developed based on these datasets as well. This does not reveal how generalisable NAS methods are when given a dataset, especially when the problem is distinctly different.", + "bbox": [ + 496, + 441, + 890, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces eight new datasets to be used when testing NAS methods. These datasets represent problems that are either simple or difficult for humans to solve and provide difficulty outside of normal image classification. While we believe using these datasets will improve the generalisability of NAS methods, the problem of not knowing whether NAS is good in general or only good on benchmark datasets is a rolling problem. Simply including these datasets for upcoming NAS works will mean they become part of the datasets developed in mind. To solve this problem, more datasets will be continually needed.", + "bbox": [ + 496, + 608, + 890, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the future, we seek to develop further datasets to enable people to work on 'unseen' data for NAS. We will also evaluate these datasets against pre-existing, and NAS approaches we are developing.", + "bbox": [ + 496, + 773, + 890, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For a video overview of the paper, please follow this link: youtu.be/YdYHdxNZUIw", + "bbox": [ + 496, + 835, + 890, + 864 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "3Available here https://www.gardnermuseum.org/experience/music", + "bbox": [ + 514, + 875, + 872, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "github.com/Towers-D/NAS-Unseen-Datasets", + "bbox": [ + 514, + 887, + 764, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22548", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Andrea Gesmundo and J. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 303 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22550", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/0098ce82-8d53-4ba3-8f97-4927160fad84_model.json b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/0098ce82-8d53-4ba3-8f97-4927160fad84_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b5680169ba598f660328689087216b64ce8d175e --- /dev/null +++ b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/0098ce82-8d53-4ba3-8f97-4927160fad84_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.89, + 0.153 + ], + "angle": 0, + "content": "Insights from the Use of Previously Unseen Neural Architecture Search Datasets" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.18, + 0.89, + 0.201 + ], + "angle": 0, + "content": "Rob Geada* David Towers*,1 Matthew Forshaw\\(^{1,3}\\) Amir Atapour-Abarghouei\\(^{2}\\) A. Stephen McGough\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.223, + 0.845, + 0.242 + ], + "angle": 0, + "content": "1Newcastle University, UK — 2Durham University, UK — 3The Alan Turing Institute, UK" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.245, + 0.728, + 0.277 + ], + "angle": 0, + "content": "rob@geada.net, amir.atapour-abarghouei@durham.ac.uk {d.towers2, matthew.forshaw, stephen.mcgough}@ncl.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.312, + 0.314, + 0.329 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.474, + 0.617 + ], + "angle": 0, + "content": "The boundless possibility of neural networks which can be used to solve a problem - each with different performance - leads to a situation where a Deep Learning expert is required to identify the best neural network. This goes against the hope of removing the need for experts. Neural Architecture Search (NAS) offers a solution to this by automatically identifying the best architecture. However, to date, NAS work has focused on a small set of datasets which we argue are not representative of real-world problems. We introduce eight new datasets created for a series of NAS Challenges: AddNIST, Language, MultNIST, CIFAR-Tile, Gutenberg, Isabella, GeoClassing, and Chesseract. These datasets and challenges are developed to direct attention to issues in NAS development and to encourage authors to consider how their models will perform on datasets unknown to them at development time. We present experimentation using standard Deep Learning methods as well as the best results from challenge participants." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.626, + 0.21, + 0.643 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.652, + 0.471, + 0.879 + ], + "angle": 0, + "content": "One of the main appeals of Deep Learning (DL) was its ability to democratise Machine Learning. No longer would you require a domain expert to develop an optimal solution to a given problem since DL models are capable of learning the required patterns and features from the data themselves and would not need the domain expert to identify and extract the required features. Unfortunately, rather than removing the need for an expert, the new paradigm has just shifted where the expert is required. These experts now spend their time identifying the most optimal neural network architecture for a given problem. Those who are not that proficient would select between pre-existing off-the-shelf networks such as ResNet [10], VGG [23] or Inception [25]. However, to get the best results for a particular problem, one should search across all possible solutions," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.313, + 0.892, + 0.389 + ], + "angle": 0, + "content": "not just those which may have shown good results in other problem domains, as no network is optimal for all problems. This idea of the 'no free lunch' [34] is backed up by our findings here, with some networks giving far poorer performance than what would be expected." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.392, + 0.892, + 0.453 + ], + "angle": 0, + "content": "A DL problem can be seen as the combination of a particular task – such as classification – one wishes to apply in a particular data domain. The data domain is normally realised as a dataset for training the DL network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.893, + 0.729 + ], + "angle": 0, + "content": "Neural Architecture Search (NAS) is a fast-developing field of DL – which can be seen from the increase of published papers in the domain over the last few years [3]. The aim of NAS is to remove the need for an expert's time and knowledge to generate state-of-the-art competitive Neural Networks from a particular dataset [40]. NAS methods search through millions (if not billions) of candidate architectures from a pre-defined search space to find optimum networks. These search spaces comprise not only different network topologies but also the types of nodes which make up these networks – such as fully connected layers, convolutions and pooling. Although NAS can be applied to any data modality, the majority of work to date has focused on image-based datasets, with modern NAS methods achieving this feat in a few GPU hours [19, 37]. In addition to a predefined search space, a NAS approach will have a search strategy. In terms of the task, the majority of work in NAS has focused on classification problems." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.868 + ], + "angle": 0, + "content": "NAS techniques are often evaluated by their ability to find networks that perform well on benchmark datasets, such as CIFAR-10 [12] and ImageNet [5]. These datasets, combined with standard search spaces such as NAS-Bench [6], fill an important role, allowing a direct comparison between NAS methods. While there is a clear benefit in using common benchmark datasets, we argue this is against the ethos of NAS - removing the need for domain experts, required to develop optimal architectures for a given problem." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Developing against common datasets can be seen as over-engineering a process to reach a solution we already" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.338, + 0.901 + ], + "angle": 0, + "content": "*These authors performed equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22541" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "know. For example, for datasets such as CIFAR-10, extensive experimentation with various neural network architectures has led to extremely high levels of accuracy [1,8,20], rendering this dataset easily solvable. In essence, since we already know what achieves high performance, NAS strategies may be optimised to reach these solutions, which may not generalise to other datasets. Prior work [18] has found that just because NAS methods perform well on benchmarks such as NAS-Bench-101 [38], this does not mean they will match other benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.422 + ], + "angle": 0, + "content": "If NAS is to truly replace architecture design experts, it must be able to find optimal networks for datasets that it has never seen before – the unseen data challenge. There is a dichotomy here in that proposing a new 'unseen' dataset for NAS may lead to that dataset being adopted as one of the core datasets for NAS. We, therefore, see our work as having two values. In the first case, we are diluting the effect of overfitting to the core datasets – having more core datasets is less likely to create a NAS approach, which can overfit to all of them. For the second case, we see this as a 'call to arms' to encourage the development and use of more datasets for NAS, which we will continue to do ourselves." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.473, + 0.515 + ], + "angle": 0, + "content": "In this work, we present eight new datasets created and used for unseen dataset NAS challenges. We define how these datasets were constructed and illustrate benchmark performance metrics that have been achieved, with the intention of encouraging others in the NAS community to develop approaches that will work on more general datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.527, + 0.195, + 0.543 + ], + "angle": 0, + "content": "2. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.473, + 0.794 + ], + "angle": 0, + "content": "To understand how well NAS methods might generalise to novel datasets and drive the direction of NAS research towards more impactful real-world applications, we organised a challenge tasking participants with creating NAS methods that perform well on unknown datasets. Participants were provided with a small number of \"development\" datasets to develop and test their NAS algorithm(s). After development, the algorithms were submitted to the competition servers, where the algorithms would be run over novel \"evaluation\" datasets. The datasets were created bespoke for the challenge and withheld from the participants throughout its duration, such that no participant could gain an advantage by knowing or guessing the evaluation datasets. As such, the participants are encouraged to create NAS approaches that generalise well to multiple problems rather than ones specifically targeted at one dataset." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.795, + 0.439, + 0.809 + ], + "angle": 0, + "content": "These unseen datasets explore one of two concepts:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- Type-1: A problem an expert could solve themselves or create a program, which may include basic DL, that can outperform a naive DL approach on the raw datasets. An example of this type of data is the AddNIST dataset Sec. 4.1, one of the datasets outlined later in this paper, which consists of images with three" + }, + { + "type": "text", + "bbox": [ + 0.53, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "channels, with each channel being an image from the MNIST dataset [14] having the class label as the sum (the numbers are chosen so the sum is less than twenty) of the individual MNIST digits. With prior knowledge of this dataset, a solution that attains the highest accuracy is splitting the colour channels into three separate images, using a model trained on MNIST to identify the individual numbers, and then hardcoding in the necessary arithmetic to get the final answer." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.234, + 0.892, + 0.43 + ], + "angle": 0, + "content": "- Type-2: A problem that would be almost impossible for a human to solve or create a program without task-specific tools. An example is the Language dataset Sec. 4.2, which encodes words from ten languages into an image. The models needs to identify which letter frequency is attributed to the correct language. Without prior knowledge of what is encoded within the images and which language is represented by each class label, correctly labelling each image to the correct language would be nearly impossible. The motivation for using a type 2 dataset is to see if bespoke models can perform better than random guesswork over datasets that appear human-impossible at face value." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.602 + ], + "angle": 0, + "content": "We believe that both types of tasks are essential for NAS algorithms to make a meaningful impact in real-world applications. First, if NAS remains incapable of solving problems that are effortlessly solvable by humans, it would be premature to assert that NAS can remove the requirement for expert knowledge. The second type relates to how machine learning is often deployed to find solutions to problems humans find complicated. Essentially, NAS methods should be able to perform at a level at least commensurate with other conventional machine learning techniques to effectively supplant manually designed models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.754 + ], + "angle": 0, + "content": "To further obfuscate the true nature of the datasets from the challenge participants, within our datasets, data shapes were deliberately chosen that appeared to correlate to normal images or well-known datasets, such as \\(3 \\times 64 \\times 64\\), and data split sizes to align with well-known benchmark datasets, such as 50,000 training images to align with CIFAR. We also asked participants for their guesses as to what each development dataset was: most participants correctly described the Type-1 datasets. In contrast, none of the Type-2 datasets have been correctly identified." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.642, + 0.779 + ], + "angle": 0, + "content": "3. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.789, + 0.892, + 0.819 + ], + "angle": 0, + "content": "We consider related work within the NAS literature and the datasets commonly used in NAS research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.749, + 0.846 + ], + "angle": 0, + "content": "3.1. Neural Architecture Search" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "NAS aims to automate the process of neural network architecture design. Traditional network design requires extensive human expertise and significant time investment." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22542" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "NAS seeks to streamline this process by employing algorithms that efficiently identify architectures tailored to specific tasks and datasets from a vast search space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.379 + ], + "angle": 0, + "content": "Initially, the work by Zoph and Le [40] applied NAS using reinforcement learning to CIFAR-10, achieving an architecture slightly outperforming manually designed models. NASNet [41] addressed the challenge of learning architectures directly on large datasets by transferring a building block designed for a small dataset to a larger one using ImageNet. ENAS [21] focused on computational efficiency by learning to search for an optimal sub-graph within a large graph, thus reducing computational resources. Evolutionary algorithms [22] have emerged, providing comparable results but with a distinct evolutionary overview. Weight-sharing methods [15] define over-parameterised super-networks (one-shot models), reducing computational costs, allowing the training of one super-network encompassing many different sub-architectures rather than training numerous networks independently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.546 + ], + "angle": 0, + "content": "Differentiable NAS [9, 16] marks another significant advancement, allowing gradient-based optimisation methods to explore the neural architecture search space efficiently. Each of these developments in NAS represents a significant stride towards the more efficient, automated and effective design of neural network architectures; however, the effectiveness of these approaches is often only tested on common benchmark datasets, some of which we will briefly cover in the following sections. The real-world applicability of these approaches needs to be tested on \"unseen\" datasets, which better simulate what is needed of NAS in practice." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.292, + 0.573 + ], + "angle": 0, + "content": "3.2. Common NAS datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.469, + 0.613 + ], + "angle": 0, + "content": "Although any dataset can be used to evaluate NAS methods, CIFAR-10 [12], and ImageNet [5] are highly popular." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.809 + ], + "angle": 0, + "content": "CIFAR-10 [12] comprises 60,000 images from ten classes evenly distributed in training and testing sets. Accuracy on CIFAR-10 is often used to evaluate performance, and it is also used in NAS, with the very first NAS algorithm [40] highlighting the potential power of NAS by demonstrating its ability to achieve better CIFAR-10 performance than human-designed models. While CIFAR-10 is a good dataset for comparing performance, it is an easy problem, with modern architectures and NAS methods easily achieving accuracies over \\(90\\%\\). Furthermore, since CIFAR-10 is used as a standard benchmark, new methods are encouraged to focus on this dataset, which may come at a cost of generalisability across other datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "ImageNet [5] is another popular dataset for evaluation and benchmarking. It contains 1,000 classes and presents a more challenging problem, with the results often presented in tandem with CIFAR-10 results to demonstrate model performance. ImageNet poses similar issues to CIFAR-10 due to its similar prevalence in benchmarking DL methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "While including ImageNet and CIFAR-10 as datasets for NAS comparison demonstrates that the NAS approach is not overfitting to just one dataset, it does not solve the problem of generalisation. We argue that both more datasets and datasets that the developers are unaware of are needed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.18, + 0.719, + 0.194 + ], + "angle": 0, + "content": "3.3. NAS Benchmark Suites" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.204, + 0.892, + 0.294 + ], + "angle": 0, + "content": "To make NAS development more comparable and easier, benchmark suites such as NAS-Bench-101 [38], NAS-Bench-201 [7], and NATS-Bench [6] have been developed. In these benchmarks, the performance achieved for each network in the search space has been pre-computed, thus removing the model training step in NAS approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.37 + ], + "angle": 0, + "content": "Benchmark suites allow developers to focus on the development of search strategies and allow for easy comparison between different approaches as they work directly on the same search space. Thus, performance gains over other methods cannot be attributed to different search spaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.893, + 0.508 + ], + "angle": 0, + "content": "These benchmark suites suffer from the same issues of reliance on CIFAR-10 and ImageNet. The search spaces used by these benchmarking tools have been fully explored on CIFAR-10 and ImageNet. These results are stored so a NAS method can look up an architecture's final result without having to retrain fully. These lookup tables do not exist for other datasets, meaning that NAS methods developed using these tools can quickly generate results for CIFAR-10 and ImageNet but not easily for other datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.524, + 0.697, + 0.541 + ], + "angle": 0, + "content": "4. Dataset Descriptions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.657 + ], + "angle": 0, + "content": "The code to generate our datasets is available at our GitHub page1. Each dataset comprises six NumPy files, X (images) and Y (labels) files for the training, validation, and testing sets, and a metadata file. This metadata file includes the shape of the training data, the ResNet-18 [10] benchmark result, and the number of classes in the data. Further details and examples are provided in the Appendices." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.668, + 0.612, + 0.683 + ], + "angle": 0, + "content": "4.1.AddNIST" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.692, + 0.892, + 0.812 + ], + "angle": 0, + "content": "AddNIST [27], is a Type-1 dataset of 70,000 images with an image shape of \\(3 \\times 28 \\times 28\\) (channels first). The training, validation, and testing split is 45,000, 15,000, and 10,000, respectively. Each colour channel is an image from MNIST [14]. An example AddNIST image is depicted in Fig. 1 (left), the larger image, shows the image as is, with the three channels laid on top of each other, and three images to the right show each channel more clearly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.814, + 0.892, + 0.874 + ], + "angle": 0, + "content": "AddNIST has twenty classes (0 - 19), with the class derived from the MNIST label of each channel, such that \\( l = (r + g + b) - 1 \\), where \\( l \\) is the image label and \\( r, g \\), and \\( b \\) are the respective MNIST labels of each colour channel." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.764, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)github.com/Towers-D/NAS-Unseen-Datasets" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22543" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.191, + 0.092, + 0.782, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.895, + 0.27 + ], + "angle": 0, + "content": "Figure 1. Left: AddNIST image - the sum of the channels adds up to 15 \\((\\mathrm{r} = 2, \\mathrm{g} = 9, \\mathrm{b} = 4)\\), implying a label of 14. Middle MultNIST image - the product of the channels equals 35 \\((\\mathrm{r} = 5, \\mathrm{g} = 7, \\mathrm{b} = 1)\\), which implies a label of 5 \\((35\\%10 = 5)\\). Right CIFARTile image - two deer, one aeroplane, and one horse, meaning there are three unique labels among the sub-images, which equates to a final label of 2" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.47, + 0.399 + ], + "angle": 0, + "content": "AddNIST adds complexity to the MNIST data. In MNIST, the goal is to identify what numerical digit is seen within the image, while in AddNIST, not only does the model have to identify the digit in each channel, but it must also learn to sum up these values in a specific manner to identify the class correctly. In this manner, AddNIST was designed around the research question of whether NAS could \"figure out\" a calculation was required and apply it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.471, + 0.49 + ], + "angle": 0, + "content": "While the task this dataset puts forward is still rather simple, which is expected for a Type 1 dataset, it requires high-level inference capabilities within the model, which would mean the NAS algorithm searching for the optimal architecture would have to consider the capacity of the model to encompass the required function." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.192, + 0.515 + ], + "angle": 0, + "content": "4.2. Language" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.469, + 0.568 + ], + "angle": 0, + "content": "Using the open-source, public spell checker ASPELL, which can be found at aspell.net, we created Language [32], a Type-2 dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.659 + ], + "angle": 0, + "content": "Using dictionaries from 10 languages that use the Latin alphabet (English, Dutch, German, Spanish, French, Portuguese, Swedish, Zulu, Swahili, and Finnish), all six-letter words within each language are extracted, and any words with letters that use diacritics (such as é or ii) or include 'y' or 'z' are subsequently removed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Each image is generated by first selecting one of the ten languages. We then randomly select four words that we filter from the selected dictionary and concatenate them into a 24-character string. Since we eliminated letters with diacritics and y and z, we have a remaining alphabet of twenty-four letters. This allows for a \\(24 \\times 24\\) -grid encoding the string as a \\(1 \\times 24 \\times 24\\) image. Using the \\(y\\)-axis to denote the index of the string and the \\(x\\)-axis to denote the character, we construct the image so each black pixel denotes the letter used in that position. See Fig. 2 (top) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The Language research question pertained to whether a linguistic character encoding contained enough information for DL to correctly identify the original language, requiring the model to perform linguistic analysis. To ensure no leak-" + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.279, + 0.797, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.441, + 0.794, + 0.66 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.673, + 0.892, + 0.756 + ], + "angle": 0, + "content": "Figure 2. Top: An example of a Language image with a readable axis included. The right-hand axis contains the four six-letter words \"Uvulas\", \"Minted\", \"Suckle\", and \"Debits\", which are all English words given the label 0. Bottom: An example Gutenberg image, the words \"their\", \"spring\", and \"their\" have been encoded from one of Shakespeare's works which give the label 4" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.77, + 0.892, + 0.815 + ], + "angle": 0, + "content": "age between the training and testing data, when selecting a word for the training data, we ensure that this word does not appear in the validation or testing data and vice versa." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.618, + 0.845 + ], + "angle": 0, + "content": "4.3. MultNIST" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "MultNIST [33] is a Type-1 dataset similar in concept to AddNIST (Sec. 4.1), originating from the same research question. Like AddNIST, MultNIST images have a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22544" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.189, + 0.089, + 0.481, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.631, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.089, + 0.782, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.214, + 0.895, + 0.258 + ], + "angle": 0, + "content": "Figure 3. Left: An example of an Isabella generated using a piece of music labelled as “20th Century”(0). Middle An example of the GeoClassing dataset showing a photo taken over Portugal (9). Right: An example rendering of a board position in the Chesseract dataset wherein white goes on to eventually win and is thus given a label of White Wins (0)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.469, + 0.334 + ], + "angle": 0, + "content": "\\(3 \\times 28 \\times 28\\) channel first shape, and each channel is an image from the MNIST dataset [14]. See Fig. 1 (middle) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.469, + 0.395 + ], + "angle": 0, + "content": "MultNIST has only ten classes (0 - 9). The label of each MultNIST image is calculated such that \\( l = (r*g*b) \\mod 10 \\) where \\( l \\) is the image label and \\( r, g \\), and \\( b \\) are the respective MNIST labels of each colour channel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.469, + 0.502 + ], + "angle": 0, + "content": "In AddNIST, the class was directly affected by how large the numbers were in each channel. The only way for an image to have a label of 0 was if one colour channel contained an MNIST with label 1 and the remaining channels contained MNIST images for 0. MultNIST introduces the additional complexity over MNIST by retaining a calculation but removes the bias of larger numbers to higher classes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.2, + 0.529 + ], + "angle": 0, + "content": "4.4.CIFARTile" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.538, + 0.469, + 0.629 + ], + "angle": 0, + "content": "CIFARTile is a Type-1 dataset where each image in the CIFARTile [29] dataset is a compilation of four CIFAR-10 [12] images tiled together in a grid resulting in images which are of size \\(3 \\times 64 \\times 64\\). See Fig. 1 (right) for an example. The training, validation, and testing split is 45,000, 15,000, and 10,000 images, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.469, + 0.719 + ], + "angle": 0, + "content": "There are four classes (0 - 3), which represent the number of CIFAR-10 classes in each grid minus one. For example, a grid consisting of CIFAR-10 images with labels [horse, horse, frog, car] has three distinct classes, and thus a label of \\(3 - 1 = 2\\). As such, CIFARTile is a Type-1 dataset; any human should be able to identify and solve this task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.469, + 0.782 + ], + "angle": 0, + "content": "CIFARTile requires a model to identify multiple CIFAR-10 classes simultaneously and determine which are similar and which differ. Whether models could adequately do this is the driving research question behind this dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.197, + 0.803 + ], + "angle": 0, + "content": "4.5. Gutenberg" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Gutenberg [31] is a Type-2 dataset named after the source of the data, Project Gutenberg, found at www.gutenberg.org, which provides free eBooks of literary works that are no longer under US copyright protection. We selected six authors (Thomas Aquinas, Confucius, Hawthorne, Plato, Shakespeare, and Tolstoy) and down" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.273, + 0.891, + 0.302 + ], + "angle": 0, + "content": "loaded several books from each author - see the Appendices for further details and examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.499 + ], + "angle": 0, + "content": "The selected works are English translations that represent a variety of cultures and time periods. We perform basic text preprocessing, including removing punctuation, converting letters with diacritics to the base letter, and removing \"structure\" words (e.g., 'Chapter', 'Scene', 'Prologue'). We then extracted consecutive sequences of three words between 3 and 6 letters long. In each sequence, the three words were padded up to 6 characters with spaces. Then, the three words were concatenated together to produce an 18-character string. These strings were used as the base for image creation. Training, test, and validation sequences were chosen such that there was no overlap between any sequence across any data split." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Similar to the Language dataset (Sec. 4.2), we converted these strings into images. On a \\(27 \\times 18\\) grid, we created a mapping of each character in the string. See Fig. 2 (bottom) for an example. The \\(x\\)-axis represents the position in the string, and the \\(y\\)-axis represents the alphabetical letter (or space) located at that position. This results in the shape being \\(1 \\times 27 \\times 18\\). The task is then to predict which of the original six authors the original word sequence came from. The training, validation, and testing split is 45,000, 15,000, and 6,000, respectively, to prevent participants from exploiting the standard distribution we used for the other datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.892, + 0.727 + ], + "angle": 0, + "content": "The research question behind this dataset was whether specific spatial patterns of letters were sufficient information for a neural network to identify the authors from which they originated, which seems impossible from face value." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.736, + 0.597, + 0.751 + ], + "angle": 0, + "content": "4.6. Isabella" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.759, + 0.891, + 0.789 + ], + "angle": 0, + "content": "Isabella2 is a Type-2 dataset that uses musical recordings from the Isabella Stewart Gardner Museum, Boston." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.892, + 0.866 + ], + "angle": 0, + "content": "The four classes of this dataset refer to the era of composition (Baroque, Classical, Romantic, and 20th Century) attributed by the museum. The recordings are split into five-second snippets converted into 64-band spectrograms, creating a dataset of \\(1 \\times 64 \\times 128\\) shaped images. See Fig. 3" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)Code to generate Isabella is available at github.com/Towers-D/NAS-Unseen-Datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22545" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.088, + 0.87, + 0.229 + ], + "angle": 0, + "content": "
DatasetResNet-18AlexNetVGG16ConvNextMNASNetDenseNetResNeXtRandom
AddNIST92.08%94.87%92.06%38.06%90.51%93.52%91.42%5%
Language87.00%85.71%84.54%83.40%84.63%84.57%93.97%10%
MultNIST91.55%94.01%90.43%64.20%87.70%92.81%90.57%10%
CIFARTile45.56%48.88%24.43%31.06%48.49%51.28%46.23%25%
Gutenberg40.98%45.53%44.00%31.93%38.00%43.28%40.30%16.6%
Isabella62.02%61.37%58.13%57.18%60.69%63.27%60.46%25%
GeoClassing80.33%92.49%83.67%72.76%86.00%94.21%89.99%10%
Chesseract57.83%57.45%55.69%52.74%56.26%59.60%55.15%33.3%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.239, + 0.867, + 0.254 + ], + "angle": 0, + "content": "Table 1. Experiments on commonly-used CNN-based classification models [10,11,13,17,23,26,35] using the presented datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.263, + 0.469, + 0.293 + ], + "angle": 0, + "content": "(left) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.294, + 0.469, + 0.384 + ], + "angle": 0, + "content": "The task for the models is to predict the era of composition from the spectrogram. No recording used in a training snippet appeared in the validation or test sets. The research question behind this dataset was to explore whether era-defining characteristics appear at the spectrogram level and whether CNNs could reliably identify such patterns." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.398, + 0.212, + 0.415 + ], + "angle": 0, + "content": "4.7. GeoClassing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.469, + 0.514 + ], + "angle": 0, + "content": "GeoClassing [30], known as Sadie in the competition, is a Type-2 dataset that takes advantage of the BigEarthNet dataset [24] as a foundation. The BigEarthNet dataset, as originally published, consists of satellite photography with ground-cover classification labels, i.e., \"airports\" or \"vineyards\". An example image is shown in Fig. 3 (middle)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.469, + 0.636 + ], + "angle": 0, + "content": "The GeoClassing dataset uses these images, but instead of using the given ground-cover labels, we identified the European Space Agency Sentinel patch from which the BigEarthNet image was sourced. We cross-referenced the coordinates of that patch within a map of Europe to identify the corresponding country depicted in the image. This gave us ten classes (Austria, Belgium, Finland, Ireland, Kosovo, Lithuania, Luxembourg, Portugal, Serbia, and Switzerland)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.469, + 0.743 + ], + "angle": 0, + "content": "Each image has a shape of \\(3 \\times 60 \\times 60\\), and the training, validation, and testing split contains 43,821, 8,758, and 8,751 images, respectively. The research question is whether NAS can find models that identify countries from differences in topology and ground coverage, which, without specific knowledge of geography and vegetation type, would be extremely difficult for a human to do manually." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.199, + 0.77 + ], + "angle": 0, + "content": "4.8. Chesseract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Chesseract [28], a Type-1 dataset wherein we accessed public chess games from eight grandmasters (Bobby Fischer, Garry Kasparov, Magnus Carlsen, Viswanathan Anand, Hikaru Nakamura, Anatoly Karpov, Fabiano Caruana, and Mikhail Tal) extracting the final \\(15\\%\\) of board states. These positions were then one-hot encoded by piece type and colour, creating a \\(12 \\times 8 \\times 8\\) image. As a 12-channel image is hard to render, we provided a flattened 2D image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.263, + 0.892, + 0.293 + ], + "angle": 0, + "content": "of one of the chess boards we used Fig. 3 (right). A 3D visualisation can be seen in the Appendices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.892, + 0.459 + ], + "angle": 0, + "content": "The training, validation, and testing split is 49,998, 9,999, and 9,999 images, respectively. Each image in the Chesseract dataset is one of three classes (White wins, Draw, Black wins). No individual positions from the same game appeared across the data splits. This dataset requires the model to identify the game's final result from the position. Chesseract presented a problem for some participants of the challenge. This was because Chesseract uses twelve instead of the usual 1 or 3 channels applied for image datasets, which often caused errors for hardcoded algorithms that only accepted 1 or 3 channel dimensions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Machine learning is already prominent in chess, with competing learning-based chess engines that beat grandmaster players, such as AlphaZero [4]. Our research question for this dataset was based on the understanding that any position can be analysed to show whether black or white has the advantage. Is NAS able to develop a DL network to identify this from just an encoding of the board position?" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.582, + 0.741, + 0.599 + ], + "angle": 0, + "content": "5. Baseline Experimentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Here, we provide some baseline results for our datasets to motivate future NAS experimentation. We provide a set of baseline results across several well-known CNNs and three NAS methods across two search spaces." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.679, + 0.696 + ], + "angle": 0, + "content": "5.1. CNN Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.854 + ], + "angle": 0, + "content": "To generate baseline results of our datasets for future work comparison, we have performed experiments using commonly used off-the-shelf CNNs, which can be seen in Tab. 1. In all our CNN experiments, we have followed a similar experimental setup. We use stochastic gradient descent as our optimiser with an initial learning rate of 0.01, momentum of 0.9, and a weight decay of \\(3 \\times 10^{-4}\\). We have used a Cosine Annealing Learning rate with the max number of iterations equaling 64, the number of epochs. Cross Entropy is used as the Loss function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ResNet-18 is used as the baseline throughout our competition, and any NAS method would be expected to easily outperform this architecture. As you can see in Tab. 1," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22546" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.187, + 0.09, + 0.784, + 0.245 + ], + "angle": 0, + "content": "
DatasetPC-DARTSDrNASBonsai-NetRandom Search
DARTSBonsaiRandom
Addnist96.60%97.06%97.91%97.07%34.17%5%
Language90.12%88.55%87.65%90.12%76.83%10%
MultNIST96.68%98.10%97.17%96.55%39.76%10%
CIFARTile92.28%81.08%91.47%90.74%24.76%25%
Gutenberg49.12%46.62%48.57%47.72%29.00%16.6%
Isabella65.77%64.53%64.08%66.35%58.53%25%
GeoClassing94.61%96.03%95.66%95.54%63.56%10%
Chesseract57.20%58.24%60.76%59.16%68.83%33.3%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.176, + 0.254, + 0.793, + 0.269 + ], + "angle": 0, + "content": "Table 2. Experimental results on PC-DARTS [36], DrNAS [2], Bonsai-Net [9] as well as random search." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.469, + 0.338 + ], + "angle": 0, + "content": "ResNet-18 produces competitive results across our datasets, though it does not excel on any particular dataset. ResNet-18 particularly struggles with the GeoClassing dataset compared to the others, only beating ConvNext in our trials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.469, + 0.534 + ], + "angle": 0, + "content": "AlexNet [13] shows decent performance across all datasets, achieving the highest accuracy on three of the eight datasets (AddNIST, MultNIST, and Gutenberg). AddNIST and MultNIST are similar, both being derived from MNIST. This may suggest that AlexNet is particularly good at working with MNIST Images. AlexNet captures spatial hierarchies in images well and is thus suitable for the clear, structured layouts of MNIST digits. VGG16 [23], on the other hand, does not achieve particularly impressive levels of accuracy on any of the datasets, though it does not perform badly, either. The only exception is the CIFARTile dataset, where VGG suffers and only achieves roughly the same accuracy as random chance, as seen in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.469, + 0.657 + ], + "angle": 0, + "content": "ConvNext [17] performs poorly across our datasets, most likely since our datasets may not exhibit the specific spatial complexity that ConvNext is optimised for. However, it is important to note that for purposes of generating our CNN baselines, we have kept the experimental setup the same across CNNs. Thus, hyperparameter tuning may be beneficial to ConvNext. We have used the base version of ConvNext in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.764 + ], + "angle": 0, + "content": "We also perform the same experiments on MnasNet [26] using a depth multiplier of 1.0. Despite being a lightweight architecture designed for mobile efficiency, MnasNet achieves competitive results across our datasets. It has strong generalisation capabilities since it uses a reinforcement learning approach to automate architecture design, thus performing well on unseen datasets [26]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "DenseNet [11] performs significantly well on the latter three datasets (Isabella, GeoClassing, and Chesseract) as well as CIFARTile, achieving the highest accuracy of the CNNs over these datasets. With the exception of Chesseract, the datasets that DenseNet excels on are the most memory-intensive datasets. This is due to the DenseNet mechanism allowing efficient re-use of features through dense connectivity and ensuring maximal information flow between layers in the network [11]. For memory-intensive" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.338 + ], + "angle": 0, + "content": "datasets, which often contain complex and rich information, this feature reuse allows DenseNet to exploit the data more thoroughly and efficiently, leading to better performance. The DenseNet-161 architecture is used in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Finally, ResNeXt [35] performs fairly well across our datasets, but especially well on the Language Dataset, scoring almost \\(7\\%\\) higher than the other methods. The particular version of ResNeXt we used is ResNeXt-50 (32 x 4d), which has a high level of cardinality (the size of the set of transformations) [35]. This high cardinality allows ResNeXt to learn more complex and diverse representations, which is crucial for distinguishing subtle patterns in the Language Dataset, such as the frequency and arrangement of characters encoded in images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.715 + ], + "angle": 0, + "content": "Our analysis across these CNN architectures reveals distinct performance trends tied to the nature of each dataset. ResNet-18 serves as a versatile baseline, while AlexNet is especially capable of handling structured patterns. VGG16's mixed results and ConvNext's overall underperformance emphasise the need within conventional deep learning for matching architectural strengths to dataset characteristics, which is not desirable for evaluating generalisation capabilities in general and NAS algorithms in particular. DenseNet and ResNeXt are good at handling memory-intensive datasets and those with nuanced patterns, respectively. These insights confirm that the effectiveness of a CNN architecture is highly contingent on the specific demands of the dataset, which underscores the need for unseen datasets for effective evaluation of NAS methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.673, + 0.741 + ], + "angle": 0, + "content": "5.2. NAS Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.854 + ], + "angle": 0, + "content": "In addition to the experiments performed on the CNNs, we have also applied the NAS methods of PC-DARTS [36], DrNAS [2] (DARTS-space), and Bonsai-Net [9] to our datasets. Furthermore, as a baseline of comparison, we perform a random search in both the DARTS and Bonsai search spaces, using the provided methods from PC-DARTS and Bonsai-NET. These results can be found in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "During our random search experiments using the DARTS search space, it is noted that random search often outperforms either PC-DARTS or DrNAS and outper" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22547" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.434, + 0.228 + ], + "angle": 0, + "content": "
DatasetCNNNASCompetition
AddNIST94.87%97.91%95.06%
Language93.97%90.12%89.71%
MultNIST94.01%98.10%95.45%
CIFARTile51.28%92.28%73.08%
Gutenberg45.53%49.12%50.85%
Isabella63.27%65.77%61.42%
GeoClassing94.21%96.03%96.08%
Chesseract59.60%60.76%62.98%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.239, + 0.47, + 0.266 + ], + "angle": 0, + "content": "Table 3. Results on each dataset from our CNN and NAS experiments, and Competition Submissions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.269, + 0.469, + 0.344 + ], + "angle": 0, + "content": "forms both models on AddNIST, Chesseract and Isabella, tying PC-DARTS on Language while outperforming DrNAS. These results support findings by Yu et al. [39] that searches using these search spaces often do not significantly outperform random search." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.346, + 0.47, + 0.571 + ], + "angle": 0, + "content": "We can see in Tab. 2 that PC-DARTS [36] performs well, scoring the highest accuracies over four of the eight datasets and gives competitive results over the others. DrNAS [2], however, scores the highest on two of the eight datasets but struggles with CIFARTile, where it scores \\(10\\%\\) lower than the other methods. We used the DARTS search space during our DrNAS experiments; while DrNAS is also available to work on the NAS-Bench-201 [7] search space, it employs the NAS-Bench API to look at the performance of architectures fully trained on CIFAR-10, which would not reflect the performance these architectures found on our datasets. In most cases, Bonsai-Net [9] outperforms random search, with the exception of Chesseract. It returns the best results on AddNIST and Chesseract (though it is significantly beaten by random search on the latter dataset)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.47, + 0.679 + ], + "angle": 0, + "content": "The varied performance of these NAS methods across our datasets highlights their ability to challenge and assess the adaptability and effectiveness of different architecture search strategies. This underscores the strengths of our datasets in providing a comprehensive benchmark for evaluating NAS methods' capability to generalise across a diverse range of tasks and complexities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.693, + 0.192, + 0.71 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Tab. 3 shows the best-reported performance of the CNN and NAS experiments on each dataset, as well as the best result found by competition participants; for further information, see the Appendices. From these results, we can see that NAS found the best model for seven datasets, supporting the usage of NAS methods in finding good models for given datasets. Three of these architectures were found by competition submissions, NAS methods designed for unseen data; given the competition's time restrictions this may suggest that methods designed in this way can generalise to other datasets better." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "It is important to mention that we did not test the deepest" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "versions of these CNN architectures or perform hyperparameter optimisation. Similarly, while we allowed the traditional NAS methods to run in their preset configuration, the competition participants were only given twenty-four hours to evaluate across three datasets. However, even with these limitations, CNNs and NAS architectures from the competition outperformed traditional NAS methods across several datasets, reinforcing our belief that current NAS methods do not necessarily generalise properly to unseen datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.242, + 0.738, + 0.26 + ], + "angle": 0, + "content": "7. Rights and Reproduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.403 + ], + "angle": 0, + "content": "These datasets have been created under the licence agreements of the original data. Where available, we have made the datasets publicly accessible under an CC BY 4.0 Licence. The Isabella dataset uses data from the Isabella Stewart Gardner Museum, which withdraws the right to share modifications to the music they have made available. Instead of providing the dataset, we provide a Python script to convert music files obtained from the Museum into the format of the competition dataset on our GitHub4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.417, + 0.62, + 0.433 + ], + "angle": 0, + "content": "8. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.608 + ], + "angle": 0, + "content": "Machine learning is a valuable and fast-growing tool that is quickly becoming part of the tools we use daily. For small businesses to stay competitive, they need to be able to easily include machine learning techniques in their products or business strategy. NAS promises to be a tool that removes the cost of an expert's time and knowledge to create bespoke neural networks while remaining competitive. NAS is currently evaluated primarily on a few benchmark datasets and developed based on these datasets as well. This does not reveal how generalisable NAS methods are when given a dataset, especially when the problem is distinctly different." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.774 + ], + "angle": 0, + "content": "This paper introduces eight new datasets to be used when testing NAS methods. These datasets represent problems that are either simple or difficult for humans to solve and provide difficulty outside of normal image classification. While we believe using these datasets will improve the generalisability of NAS methods, the problem of not knowing whether NAS is good in general or only good on benchmark datasets is a rolling problem. Simply including these datasets for upcoming NAS works will mean they become part of the datasets developed in mind. To solve this problem, more datasets will be continually needed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.892, + 0.835 + ], + "angle": 0, + "content": "In the future, we seek to develop further datasets to enable people to work on 'unseen' data for NAS. We will also evaluate these datasets against pre-existing, and NAS approaches we are developing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.836, + 0.892, + 0.865 + ], + "angle": 0, + "content": "For a video overview of the paper, please follow this link: youtu.be/YdYHdxNZUIw" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.875, + 0.874, + 0.888 + ], + "angle": 0, + "content": "3Available here https://www.gardnermuseum.org/experience/music" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.888, + 0.765, + 0.901 + ], + "angle": 0, + "content": "github.com/Towers-D/NAS-Unseen-Datasets" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.875, + 0.874, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22548" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Andrea Gesmundo and J. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22550" + } + ] +] \ No newline at end of file diff --git a/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/0098ce82-8d53-4ba3-8f97-4927160fad84_origin.pdf b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/0098ce82-8d53-4ba3-8f97-4927160fad84_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..008b218458103d3d929c5ccaf7299880129c4001 --- /dev/null +++ b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/0098ce82-8d53-4ba3-8f97-4927160fad84_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ab80ed1b0f6327aee2ebd2fb8e5afe96730dabf0267705d3e0fce381150b351d +size 501025 diff --git a/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/full.md b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2544f974d41dca9b377c41455ddea91cf98c03fb --- /dev/null +++ b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/full.md @@ -0,0 +1,300 @@ +# Insights from the Use of Previously Unseen Neural Architecture Search Datasets + +Rob Geada* David Towers*,1 Matthew Forshaw $^{1,3}$ Amir Atapour-Abarghouei $^{2}$ A. Stephen McGough $^{1}$ + +1Newcastle University, UK — 2Durham University, UK — 3The Alan Turing Institute, UK + +rob@geada.net, amir.atapour-abarghouei@durham.ac.uk {d.towers2, matthew.forshaw, stephen.mcgough}@ncl.ac.uk + +# Abstract + +The boundless possibility of neural networks which can be used to solve a problem - each with different performance - leads to a situation where a Deep Learning expert is required to identify the best neural network. This goes against the hope of removing the need for experts. Neural Architecture Search (NAS) offers a solution to this by automatically identifying the best architecture. However, to date, NAS work has focused on a small set of datasets which we argue are not representative of real-world problems. We introduce eight new datasets created for a series of NAS Challenges: AddNIST, Language, MultNIST, CIFAR-Tile, Gutenberg, Isabella, GeoClassing, and Chesseract. These datasets and challenges are developed to direct attention to issues in NAS development and to encourage authors to consider how their models will perform on datasets unknown to them at development time. We present experimentation using standard Deep Learning methods as well as the best results from challenge participants. + +# 1. Introduction + +One of the main appeals of Deep Learning (DL) was its ability to democratise Machine Learning. No longer would you require a domain expert to develop an optimal solution to a given problem since DL models are capable of learning the required patterns and features from the data themselves and would not need the domain expert to identify and extract the required features. Unfortunately, rather than removing the need for an expert, the new paradigm has just shifted where the expert is required. These experts now spend their time identifying the most optimal neural network architecture for a given problem. Those who are not that proficient would select between pre-existing off-the-shelf networks such as ResNet [10], VGG [23] or Inception [25]. However, to get the best results for a particular problem, one should search across all possible solutions, + +not just those which may have shown good results in other problem domains, as no network is optimal for all problems. This idea of the 'no free lunch' [34] is backed up by our findings here, with some networks giving far poorer performance than what would be expected. + +A DL problem can be seen as the combination of a particular task – such as classification – one wishes to apply in a particular data domain. The data domain is normally realised as a dataset for training the DL network. + +Neural Architecture Search (NAS) is a fast-developing field of DL – which can be seen from the increase of published papers in the domain over the last few years [3]. The aim of NAS is to remove the need for an expert's time and knowledge to generate state-of-the-art competitive Neural Networks from a particular dataset [40]. NAS methods search through millions (if not billions) of candidate architectures from a pre-defined search space to find optimum networks. These search spaces comprise not only different network topologies but also the types of nodes which make up these networks – such as fully connected layers, convolutions and pooling. Although NAS can be applied to any data modality, the majority of work to date has focused on image-based datasets, with modern NAS methods achieving this feat in a few GPU hours [19, 37]. In addition to a predefined search space, a NAS approach will have a search strategy. In terms of the task, the majority of work in NAS has focused on classification problems. + +NAS techniques are often evaluated by their ability to find networks that perform well on benchmark datasets, such as CIFAR-10 [12] and ImageNet [5]. These datasets, combined with standard search spaces such as NAS-Bench [6], fill an important role, allowing a direct comparison between NAS methods. While there is a clear benefit in using common benchmark datasets, we argue this is against the ethos of NAS - removing the need for domain experts, required to develop optimal architectures for a given problem. + +Developing against common datasets can be seen as over-engineering a process to reach a solution we already + +know. For example, for datasets such as CIFAR-10, extensive experimentation with various neural network architectures has led to extremely high levels of accuracy [1,8,20], rendering this dataset easily solvable. In essence, since we already know what achieves high performance, NAS strategies may be optimised to reach these solutions, which may not generalise to other datasets. Prior work [18] has found that just because NAS methods perform well on benchmarks such as NAS-Bench-101 [38], this does not mean they will match other benchmarks. + +If NAS is to truly replace architecture design experts, it must be able to find optimal networks for datasets that it has never seen before – the unseen data challenge. There is a dichotomy here in that proposing a new 'unseen' dataset for NAS may lead to that dataset being adopted as one of the core datasets for NAS. We, therefore, see our work as having two values. In the first case, we are diluting the effect of overfitting to the core datasets – having more core datasets is less likely to create a NAS approach, which can overfit to all of them. For the second case, we see this as a 'call to arms' to encourage the development and use of more datasets for NAS, which we will continue to do ourselves. + +In this work, we present eight new datasets created and used for unseen dataset NAS challenges. We define how these datasets were constructed and illustrate benchmark performance metrics that have been achieved, with the intention of encouraging others in the NAS community to develop approaches that will work on more general datasets. + +# 2. Motivation + +To understand how well NAS methods might generalise to novel datasets and drive the direction of NAS research towards more impactful real-world applications, we organised a challenge tasking participants with creating NAS methods that perform well on unknown datasets. Participants were provided with a small number of "development" datasets to develop and test their NAS algorithm(s). After development, the algorithms were submitted to the competition servers, where the algorithms would be run over novel "evaluation" datasets. The datasets were created bespoke for the challenge and withheld from the participants throughout its duration, such that no participant could gain an advantage by knowing or guessing the evaluation datasets. As such, the participants are encouraged to create NAS approaches that generalise well to multiple problems rather than ones specifically targeted at one dataset. + +These unseen datasets explore one of two concepts: + +- Type-1: A problem an expert could solve themselves or create a program, which may include basic DL, that can outperform a naive DL approach on the raw datasets. An example of this type of data is the AddNIST dataset Sec. 4.1, one of the datasets outlined later in this paper, which consists of images with three + +channels, with each channel being an image from the MNIST dataset [14] having the class label as the sum (the numbers are chosen so the sum is less than twenty) of the individual MNIST digits. With prior knowledge of this dataset, a solution that attains the highest accuracy is splitting the colour channels into three separate images, using a model trained on MNIST to identify the individual numbers, and then hardcoding in the necessary arithmetic to get the final answer. + +- Type-2: A problem that would be almost impossible for a human to solve or create a program without task-specific tools. An example is the Language dataset Sec. 4.2, which encodes words from ten languages into an image. The models needs to identify which letter frequency is attributed to the correct language. Without prior knowledge of what is encoded within the images and which language is represented by each class label, correctly labelling each image to the correct language would be nearly impossible. The motivation for using a type 2 dataset is to see if bespoke models can perform better than random guesswork over datasets that appear human-impossible at face value. + +We believe that both types of tasks are essential for NAS algorithms to make a meaningful impact in real-world applications. First, if NAS remains incapable of solving problems that are effortlessly solvable by humans, it would be premature to assert that NAS can remove the requirement for expert knowledge. The second type relates to how machine learning is often deployed to find solutions to problems humans find complicated. Essentially, NAS methods should be able to perform at a level at least commensurate with other conventional machine learning techniques to effectively supplant manually designed models. + +To further obfuscate the true nature of the datasets from the challenge participants, within our datasets, data shapes were deliberately chosen that appeared to correlate to normal images or well-known datasets, such as $3 \times 64 \times 64$ , and data split sizes to align with well-known benchmark datasets, such as 50,000 training images to align with CIFAR. We also asked participants for their guesses as to what each development dataset was: most participants correctly described the Type-1 datasets. In contrast, none of the Type-2 datasets have been correctly identified. + +# 3. Related Work + +We consider related work within the NAS literature and the datasets commonly used in NAS research. + +# 3.1. Neural Architecture Search + +NAS aims to automate the process of neural network architecture design. Traditional network design requires extensive human expertise and significant time investment. + +NAS seeks to streamline this process by employing algorithms that efficiently identify architectures tailored to specific tasks and datasets from a vast search space. + +Initially, the work by Zoph and Le [40] applied NAS using reinforcement learning to CIFAR-10, achieving an architecture slightly outperforming manually designed models. NASNet [41] addressed the challenge of learning architectures directly on large datasets by transferring a building block designed for a small dataset to a larger one using ImageNet. ENAS [21] focused on computational efficiency by learning to search for an optimal sub-graph within a large graph, thus reducing computational resources. Evolutionary algorithms [22] have emerged, providing comparable results but with a distinct evolutionary overview. Weight-sharing methods [15] define over-parameterised super-networks (one-shot models), reducing computational costs, allowing the training of one super-network encompassing many different sub-architectures rather than training numerous networks independently. + +Differentiable NAS [9, 16] marks another significant advancement, allowing gradient-based optimisation methods to explore the neural architecture search space efficiently. Each of these developments in NAS represents a significant stride towards the more efficient, automated and effective design of neural network architectures; however, the effectiveness of these approaches is often only tested on common benchmark datasets, some of which we will briefly cover in the following sections. The real-world applicability of these approaches needs to be tested on "unseen" datasets, which better simulate what is needed of NAS in practice. + +# 3.2. Common NAS datasets + +Although any dataset can be used to evaluate NAS methods, CIFAR-10 [12], and ImageNet [5] are highly popular. + +CIFAR-10 [12] comprises 60,000 images from ten classes evenly distributed in training and testing sets. Accuracy on CIFAR-10 is often used to evaluate performance, and it is also used in NAS, with the very first NAS algorithm [40] highlighting the potential power of NAS by demonstrating its ability to achieve better CIFAR-10 performance than human-designed models. While CIFAR-10 is a good dataset for comparing performance, it is an easy problem, with modern architectures and NAS methods easily achieving accuracies over $90\%$ . Furthermore, since CIFAR-10 is used as a standard benchmark, new methods are encouraged to focus on this dataset, which may come at a cost of generalisability across other datasets. + +ImageNet [5] is another popular dataset for evaluation and benchmarking. It contains 1,000 classes and presents a more challenging problem, with the results often presented in tandem with CIFAR-10 results to demonstrate model performance. ImageNet poses similar issues to CIFAR-10 due to its similar prevalence in benchmarking DL methods. + +While including ImageNet and CIFAR-10 as datasets for NAS comparison demonstrates that the NAS approach is not overfitting to just one dataset, it does not solve the problem of generalisation. We argue that both more datasets and datasets that the developers are unaware of are needed. + +# 3.3. NAS Benchmark Suites + +To make NAS development more comparable and easier, benchmark suites such as NAS-Bench-101 [38], NAS-Bench-201 [7], and NATS-Bench [6] have been developed. In these benchmarks, the performance achieved for each network in the search space has been pre-computed, thus removing the model training step in NAS approaches. + +Benchmark suites allow developers to focus on the development of search strategies and allow for easy comparison between different approaches as they work directly on the same search space. Thus, performance gains over other methods cannot be attributed to different search spaces. + +These benchmark suites suffer from the same issues of reliance on CIFAR-10 and ImageNet. The search spaces used by these benchmarking tools have been fully explored on CIFAR-10 and ImageNet. These results are stored so a NAS method can look up an architecture's final result without having to retrain fully. These lookup tables do not exist for other datasets, meaning that NAS methods developed using these tools can quickly generate results for CIFAR-10 and ImageNet but not easily for other datasets. + +# 4. Dataset Descriptions + +The code to generate our datasets is available at our GitHub page1. Each dataset comprises six NumPy files, X (images) and Y (labels) files for the training, validation, and testing sets, and a metadata file. This metadata file includes the shape of the training data, the ResNet-18 [10] benchmark result, and the number of classes in the data. Further details and examples are provided in the Appendices. + +# 4.1.AddNIST + +AddNIST [27], is a Type-1 dataset of 70,000 images with an image shape of $3 \times 28 \times 28$ (channels first). The training, validation, and testing split is 45,000, 15,000, and 10,000, respectively. Each colour channel is an image from MNIST [14]. An example AddNIST image is depicted in Fig. 1 (left), the larger image, shows the image as is, with the three channels laid on top of each other, and three images to the right show each channel more clearly. + +AddNIST has twenty classes (0 - 19), with the class derived from the MNIST label of each channel, such that $l = (r + g + b) - 1$ , where $l$ is the image label and $r, g$ , and $b$ are the respective MNIST labels of each colour channel. + +![](images/1fa374d918eb0cc1e4a36f427b81b47af6af3340f9299329329fe048ad89f246.jpg) +Figure 1. Left: AddNIST image - the sum of the channels adds up to 15 $(\mathrm{r} = 2, \mathrm{g} = 9, \mathrm{b} = 4)$ , implying a label of 14. Middle MultNIST image - the product of the channels equals 35 $(\mathrm{r} = 5, \mathrm{g} = 7, \mathrm{b} = 1)$ , which implies a label of 5 $(35\%10 = 5)$ . Right CIFARTile image - two deer, one aeroplane, and one horse, meaning there are three unique labels among the sub-images, which equates to a final label of 2 + +AddNIST adds complexity to the MNIST data. In MNIST, the goal is to identify what numerical digit is seen within the image, while in AddNIST, not only does the model have to identify the digit in each channel, but it must also learn to sum up these values in a specific manner to identify the class correctly. In this manner, AddNIST was designed around the research question of whether NAS could "figure out" a calculation was required and apply it. + +While the task this dataset puts forward is still rather simple, which is expected for a Type 1 dataset, it requires high-level inference capabilities within the model, which would mean the NAS algorithm searching for the optimal architecture would have to consider the capacity of the model to encompass the required function. + +# 4.2. Language + +Using the open-source, public spell checker ASPELL, which can be found at aspell.net, we created Language [32], a Type-2 dataset. + +Using dictionaries from 10 languages that use the Latin alphabet (English, Dutch, German, Spanish, French, Portuguese, Swedish, Zulu, Swahili, and Finnish), all six-letter words within each language are extracted, and any words with letters that use diacritics (such as é or ii) or include 'y' or 'z' are subsequently removed. + +Each image is generated by first selecting one of the ten languages. We then randomly select four words that we filter from the selected dictionary and concatenate them into a 24-character string. Since we eliminated letters with diacritics and y and z, we have a remaining alphabet of twenty-four letters. This allows for a $24 \times 24$ -grid encoding the string as a $1 \times 24 \times 24$ image. Using the $y$ -axis to denote the index of the string and the $x$ -axis to denote the character, we construct the image so each black pixel denotes the letter used in that position. See Fig. 2 (top) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively. + +The Language research question pertained to whether a linguistic character encoding contained enough information for DL to correctly identify the original language, requiring the model to perform linguistic analysis. To ensure no leak- + +![](images/9fe09169410b6442fea7cd2f5ce3ca73060231657523c07e8745b5286091334e.jpg) + +![](images/2cbabe158acb5a2427bb0d6e4e2f0616ad72cf5cd1e19619ef587d9332ded1a2.jpg) +Figure 2. Top: An example of a Language image with a readable axis included. The right-hand axis contains the four six-letter words "Uvulas", "Minted", "Suckle", and "Debits", which are all English words given the label 0. Bottom: An example Gutenberg image, the words "their", "spring", and "their" have been encoded from one of Shakespeare's works which give the label 4 + +age between the training and testing data, when selecting a word for the training data, we ensure that this word does not appear in the validation or testing data and vice versa. + +# 4.3. MultNIST + +MultNIST [33] is a Type-1 dataset similar in concept to AddNIST (Sec. 4.1), originating from the same research question. Like AddNIST, MultNIST images have a + +![](images/ceb4abaceaf59e86c38d15e52f2bc3d8995a7aedcfa315dc51dd760c76adae38.jpg) +Figure 3. Left: An example of an Isabella generated using a piece of music labelled as “20th Century”(0). Middle An example of the GeoClassing dataset showing a photo taken over Portugal (9). Right: An example rendering of a board position in the Chesseract dataset wherein white goes on to eventually win and is thus given a label of White Wins (0) + +![](images/e0d03ac3240cda94b3c7247a0c2b7c327fa91e5f9ce31421942b319a5f0aba71.jpg) + +![](images/cfe23c1796bd32982c3a632b09fa252369a1ebcca2a92a88cb605a3b69fac1c2.jpg) + +$3 \times 28 \times 28$ channel first shape, and each channel is an image from the MNIST dataset [14]. See Fig. 1 (middle) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively. + +MultNIST has only ten classes (0 - 9). The label of each MultNIST image is calculated such that $l = (r*g*b) \mod 10$ where $l$ is the image label and $r, g$ , and $b$ are the respective MNIST labels of each colour channel. + +In AddNIST, the class was directly affected by how large the numbers were in each channel. The only way for an image to have a label of 0 was if one colour channel contained an MNIST with label 1 and the remaining channels contained MNIST images for 0. MultNIST introduces the additional complexity over MNIST by retaining a calculation but removes the bias of larger numbers to higher classes. + +# 4.4.CIFARTile + +CIFARTile is a Type-1 dataset where each image in the CIFARTile [29] dataset is a compilation of four CIFAR-10 [12] images tiled together in a grid resulting in images which are of size $3 \times 64 \times 64$ . See Fig. 1 (right) for an example. The training, validation, and testing split is 45,000, 15,000, and 10,000 images, respectively. + +There are four classes (0 - 3), which represent the number of CIFAR-10 classes in each grid minus one. For example, a grid consisting of CIFAR-10 images with labels [horse, horse, frog, car] has three distinct classes, and thus a label of $3 - 1 = 2$ . As such, CIFARTile is a Type-1 dataset; any human should be able to identify and solve this task. + +CIFARTile requires a model to identify multiple CIFAR-10 classes simultaneously and determine which are similar and which differ. Whether models could adequately do this is the driving research question behind this dataset. + +# 4.5. Gutenberg + +Gutenberg [31] is a Type-2 dataset named after the source of the data, Project Gutenberg, found at www.gutenberg.org, which provides free eBooks of literary works that are no longer under US copyright protection. We selected six authors (Thomas Aquinas, Confucius, Hawthorne, Plato, Shakespeare, and Tolstoy) and down + +loaded several books from each author - see the Appendices for further details and examples. + +The selected works are English translations that represent a variety of cultures and time periods. We perform basic text preprocessing, including removing punctuation, converting letters with diacritics to the base letter, and removing "structure" words (e.g., 'Chapter', 'Scene', 'Prologue'). We then extracted consecutive sequences of three words between 3 and 6 letters long. In each sequence, the three words were padded up to 6 characters with spaces. Then, the three words were concatenated together to produce an 18-character string. These strings were used as the base for image creation. Training, test, and validation sequences were chosen such that there was no overlap between any sequence across any data split. + +Similar to the Language dataset (Sec. 4.2), we converted these strings into images. On a $27 \times 18$ grid, we created a mapping of each character in the string. See Fig. 2 (bottom) for an example. The $x$ -axis represents the position in the string, and the $y$ -axis represents the alphabetical letter (or space) located at that position. This results in the shape being $1 \times 27 \times 18$ . The task is then to predict which of the original six authors the original word sequence came from. The training, validation, and testing split is 45,000, 15,000, and 6,000, respectively, to prevent participants from exploiting the standard distribution we used for the other datasets. + +The research question behind this dataset was whether specific spatial patterns of letters were sufficient information for a neural network to identify the authors from which they originated, which seems impossible from face value. + +# 4.6. Isabella + +Isabella2 is a Type-2 dataset that uses musical recordings from the Isabella Stewart Gardner Museum, Boston. + +The four classes of this dataset refer to the era of composition (Baroque, Classical, Romantic, and 20th Century) attributed by the museum. The recordings are split into five-second snippets converted into 64-band spectrograms, creating a dataset of $1 \times 64 \times 128$ shaped images. See Fig. 3 + +
DatasetResNet-18AlexNetVGG16ConvNextMNASNetDenseNetResNeXtRandom
AddNIST92.08%94.87%92.06%38.06%90.51%93.52%91.42%5%
Language87.00%85.71%84.54%83.40%84.63%84.57%93.97%10%
MultNIST91.55%94.01%90.43%64.20%87.70%92.81%90.57%10%
CIFARTile45.56%48.88%24.43%31.06%48.49%51.28%46.23%25%
Gutenberg40.98%45.53%44.00%31.93%38.00%43.28%40.30%16.6%
Isabella62.02%61.37%58.13%57.18%60.69%63.27%60.46%25%
GeoClassing80.33%92.49%83.67%72.76%86.00%94.21%89.99%10%
Chesseract57.83%57.45%55.69%52.74%56.26%59.60%55.15%33.3%
+ +Table 1. Experiments on commonly-used CNN-based classification models [10,11,13,17,23,26,35] using the presented datasets. + +(left) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively. + +The task for the models is to predict the era of composition from the spectrogram. No recording used in a training snippet appeared in the validation or test sets. The research question behind this dataset was to explore whether era-defining characteristics appear at the spectrogram level and whether CNNs could reliably identify such patterns. + +# 4.7. GeoClassing + +GeoClassing [30], known as Sadie in the competition, is a Type-2 dataset that takes advantage of the BigEarthNet dataset [24] as a foundation. The BigEarthNet dataset, as originally published, consists of satellite photography with ground-cover classification labels, i.e., "airports" or "vineyards". An example image is shown in Fig. 3 (middle). + +The GeoClassing dataset uses these images, but instead of using the given ground-cover labels, we identified the European Space Agency Sentinel patch from which the BigEarthNet image was sourced. We cross-referenced the coordinates of that patch within a map of Europe to identify the corresponding country depicted in the image. This gave us ten classes (Austria, Belgium, Finland, Ireland, Kosovo, Lithuania, Luxembourg, Portugal, Serbia, and Switzerland). + +Each image has a shape of $3 \times 60 \times 60$ , and the training, validation, and testing split contains 43,821, 8,758, and 8,751 images, respectively. The research question is whether NAS can find models that identify countries from differences in topology and ground coverage, which, without specific knowledge of geography and vegetation type, would be extremely difficult for a human to do manually. + +# 4.8. Chesseract + +Chesseract [28], a Type-1 dataset wherein we accessed public chess games from eight grandmasters (Bobby Fischer, Garry Kasparov, Magnus Carlsen, Viswanathan Anand, Hikaru Nakamura, Anatoly Karpov, Fabiano Caruana, and Mikhail Tal) extracting the final $15\%$ of board states. These positions were then one-hot encoded by piece type and colour, creating a $12 \times 8 \times 8$ image. As a 12-channel image is hard to render, we provided a flattened 2D image + +of one of the chess boards we used Fig. 3 (right). A 3D visualisation can be seen in the Appendices. + +The training, validation, and testing split is 49,998, 9,999, and 9,999 images, respectively. Each image in the Chesseract dataset is one of three classes (White wins, Draw, Black wins). No individual positions from the same game appeared across the data splits. This dataset requires the model to identify the game's final result from the position. Chesseract presented a problem for some participants of the challenge. This was because Chesseract uses twelve instead of the usual 1 or 3 channels applied for image datasets, which often caused errors for hardcoded algorithms that only accepted 1 or 3 channel dimensions. + +Machine learning is already prominent in chess, with competing learning-based chess engines that beat grandmaster players, such as AlphaZero [4]. Our research question for this dataset was based on the understanding that any position can be analysed to show whether black or white has the advantage. Is NAS able to develop a DL network to identify this from just an encoding of the board position? + +# 5. Baseline Experimentation + +Here, we provide some baseline results for our datasets to motivate future NAS experimentation. We provide a set of baseline results across several well-known CNNs and three NAS methods across two search spaces. + +# 5.1. CNN Experiments + +To generate baseline results of our datasets for future work comparison, we have performed experiments using commonly used off-the-shelf CNNs, which can be seen in Tab. 1. In all our CNN experiments, we have followed a similar experimental setup. We use stochastic gradient descent as our optimiser with an initial learning rate of 0.01, momentum of 0.9, and a weight decay of $3 \times 10^{-4}$ . We have used a Cosine Annealing Learning rate with the max number of iterations equaling 64, the number of epochs. Cross Entropy is used as the Loss function. + +ResNet-18 is used as the baseline throughout our competition, and any NAS method would be expected to easily outperform this architecture. As you can see in Tab. 1, + +
DatasetPC-DARTSDrNASBonsai-NetRandom Search
DARTSBonsaiRandom
Addnist96.60%97.06%97.91%97.07%34.17%5%
Language90.12%88.55%87.65%90.12%76.83%10%
MultNIST96.68%98.10%97.17%96.55%39.76%10%
CIFARTile92.28%81.08%91.47%90.74%24.76%25%
Gutenberg49.12%46.62%48.57%47.72%29.00%16.6%
Isabella65.77%64.53%64.08%66.35%58.53%25%
GeoClassing94.61%96.03%95.66%95.54%63.56%10%
Chesseract57.20%58.24%60.76%59.16%68.83%33.3%
+ +Table 2. Experimental results on PC-DARTS [36], DrNAS [2], Bonsai-Net [9] as well as random search. + +ResNet-18 produces competitive results across our datasets, though it does not excel on any particular dataset. ResNet-18 particularly struggles with the GeoClassing dataset compared to the others, only beating ConvNext in our trials. + +AlexNet [13] shows decent performance across all datasets, achieving the highest accuracy on three of the eight datasets (AddNIST, MultNIST, and Gutenberg). AddNIST and MultNIST are similar, both being derived from MNIST. This may suggest that AlexNet is particularly good at working with MNIST Images. AlexNet captures spatial hierarchies in images well and is thus suitable for the clear, structured layouts of MNIST digits. VGG16 [23], on the other hand, does not achieve particularly impressive levels of accuracy on any of the datasets, though it does not perform badly, either. The only exception is the CIFARTile dataset, where VGG suffers and only achieves roughly the same accuracy as random chance, as seen in Tab. 1. + +ConvNext [17] performs poorly across our datasets, most likely since our datasets may not exhibit the specific spatial complexity that ConvNext is optimised for. However, it is important to note that for purposes of generating our CNN baselines, we have kept the experimental setup the same across CNNs. Thus, hyperparameter tuning may be beneficial to ConvNext. We have used the base version of ConvNext in our experiments. + +We also perform the same experiments on MnasNet [26] using a depth multiplier of 1.0. Despite being a lightweight architecture designed for mobile efficiency, MnasNet achieves competitive results across our datasets. It has strong generalisation capabilities since it uses a reinforcement learning approach to automate architecture design, thus performing well on unseen datasets [26]. + +DenseNet [11] performs significantly well on the latter three datasets (Isabella, GeoClassing, and Chesseract) as well as CIFARTile, achieving the highest accuracy of the CNNs over these datasets. With the exception of Chesseract, the datasets that DenseNet excels on are the most memory-intensive datasets. This is due to the DenseNet mechanism allowing efficient re-use of features through dense connectivity and ensuring maximal information flow between layers in the network [11]. For memory-intensive + +datasets, which often contain complex and rich information, this feature reuse allows DenseNet to exploit the data more thoroughly and efficiently, leading to better performance. The DenseNet-161 architecture is used in our experiments. + +Finally, ResNeXt [35] performs fairly well across our datasets, but especially well on the Language Dataset, scoring almost $7\%$ higher than the other methods. The particular version of ResNeXt we used is ResNeXt-50 (32 x 4d), which has a high level of cardinality (the size of the set of transformations) [35]. This high cardinality allows ResNeXt to learn more complex and diverse representations, which is crucial for distinguishing subtle patterns in the Language Dataset, such as the frequency and arrangement of characters encoded in images. + +Our analysis across these CNN architectures reveals distinct performance trends tied to the nature of each dataset. ResNet-18 serves as a versatile baseline, while AlexNet is especially capable of handling structured patterns. VGG16's mixed results and ConvNext's overall underperformance emphasise the need within conventional deep learning for matching architectural strengths to dataset characteristics, which is not desirable for evaluating generalisation capabilities in general and NAS algorithms in particular. DenseNet and ResNeXt are good at handling memory-intensive datasets and those with nuanced patterns, respectively. These insights confirm that the effectiveness of a CNN architecture is highly contingent on the specific demands of the dataset, which underscores the need for unseen datasets for effective evaluation of NAS methods. + +# 5.2. NAS Experiments + +In addition to the experiments performed on the CNNs, we have also applied the NAS methods of PC-DARTS [36], DrNAS [2] (DARTS-space), and Bonsai-Net [9] to our datasets. Furthermore, as a baseline of comparison, we perform a random search in both the DARTS and Bonsai search spaces, using the provided methods from PC-DARTS and Bonsai-NET. These results can be found in Tab. 2. + +During our random search experiments using the DARTS search space, it is noted that random search often outperforms either PC-DARTS or DrNAS and outper + +
DatasetCNNNASCompetition
AddNIST94.87%97.91%95.06%
Language93.97%90.12%89.71%
MultNIST94.01%98.10%95.45%
CIFARTile51.28%92.28%73.08%
Gutenberg45.53%49.12%50.85%
Isabella63.27%65.77%61.42%
GeoClassing94.21%96.03%96.08%
Chesseract59.60%60.76%62.98%
+ +Table 3. Results on each dataset from our CNN and NAS experiments, and Competition Submissions + +forms both models on AddNIST, Chesseract and Isabella, tying PC-DARTS on Language while outperforming DrNAS. These results support findings by Yu et al. [39] that searches using these search spaces often do not significantly outperform random search. + +We can see in Tab. 2 that PC-DARTS [36] performs well, scoring the highest accuracies over four of the eight datasets and gives competitive results over the others. DrNAS [2], however, scores the highest on two of the eight datasets but struggles with CIFARTile, where it scores $10\%$ lower than the other methods. We used the DARTS search space during our DrNAS experiments; while DrNAS is also available to work on the NAS-Bench-201 [7] search space, it employs the NAS-Bench API to look at the performance of architectures fully trained on CIFAR-10, which would not reflect the performance these architectures found on our datasets. In most cases, Bonsai-Net [9] outperforms random search, with the exception of Chesseract. It returns the best results on AddNIST and Chesseract (though it is significantly beaten by random search on the latter dataset). + +The varied performance of these NAS methods across our datasets highlights their ability to challenge and assess the adaptability and effectiveness of different architecture search strategies. This underscores the strengths of our datasets in providing a comprehensive benchmark for evaluating NAS methods' capability to generalise across a diverse range of tasks and complexities. + +# 6. Discussion + +Tab. 3 shows the best-reported performance of the CNN and NAS experiments on each dataset, as well as the best result found by competition participants; for further information, see the Appendices. From these results, we can see that NAS found the best model for seven datasets, supporting the usage of NAS methods in finding good models for given datasets. Three of these architectures were found by competition submissions, NAS methods designed for unseen data; given the competition's time restrictions this may suggest that methods designed in this way can generalise to other datasets better. + +It is important to mention that we did not test the deepest + +versions of these CNN architectures or perform hyperparameter optimisation. Similarly, while we allowed the traditional NAS methods to run in their preset configuration, the competition participants were only given twenty-four hours to evaluate across three datasets. However, even with these limitations, CNNs and NAS architectures from the competition outperformed traditional NAS methods across several datasets, reinforcing our belief that current NAS methods do not necessarily generalise properly to unseen datasets. + +# 7. Rights and Reproduction + +These datasets have been created under the licence agreements of the original data. Where available, we have made the datasets publicly accessible under an CC BY 4.0 Licence. The Isabella dataset uses data from the Isabella Stewart Gardner Museum, which withdraws the right to share modifications to the music they have made available. Instead of providing the dataset, we provide a Python script to convert music files obtained from the Museum into the format of the competition dataset on our GitHub4. + +# 8. Conclusion + +Machine learning is a valuable and fast-growing tool that is quickly becoming part of the tools we use daily. For small businesses to stay competitive, they need to be able to easily include machine learning techniques in their products or business strategy. NAS promises to be a tool that removes the cost of an expert's time and knowledge to create bespoke neural networks while remaining competitive. NAS is currently evaluated primarily on a few benchmark datasets and developed based on these datasets as well. This does not reveal how generalisable NAS methods are when given a dataset, especially when the problem is distinctly different. + +This paper introduces eight new datasets to be used when testing NAS methods. These datasets represent problems that are either simple or difficult for humans to solve and provide difficulty outside of normal image classification. While we believe using these datasets will improve the generalisability of NAS methods, the problem of not knowing whether NAS is good in general or only good on benchmark datasets is a rolling problem. Simply including these datasets for upcoming NAS works will mean they become part of the datasets developed in mind. To solve this problem, more datasets will be continually needed. + +In the future, we seek to develop further datasets to enable people to work on 'unseen' data for NAS. 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Language Dataset, 2023. https://data.ncl.ac.uk/articles/dataset/Language_Dataset/245_74729/1.4 +[33] David Towers, Rob Geada, Amir Atapour-Abarghouei, and Andrew Stephen McGough. MultNIST Dataset, 2023. https://data.ncl.ac.uk/articles/dataset/MultNIST_Dataset/24574678/1.4 +[34] D.H. Wolpert and W.G. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1):67-82, 1997. 1 +[35] Saining Xie, Ross Girshick, Piotr Dollar, Zhuowen Tu, and Kaiming He. Aggregated residual transformations for deep neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. 6, 7 +[36] Yuhui Xu, Lingxi Xie, Xiaopeng Zhang, Xin Chen, Guo-Jun Qi, Qi Tian, and Hongkai Xiong. PC-DARTS: Partial Channel Connections for Memory-Efficient Architecture Search. In International Conference on Learning Representations, 2020. 7, 8 +[37] Peng Ye, Baopu Li, Yikang Li, Tao Chen, Jiayuan Fan, and Wanli Ouyang. b-darts: Beta-decay regularization for differentiable architecture search. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10874-10883, 2022. 1 +[38] Chris Ying, Aaron Klein, Eric Christiansen, Esteban Real, Kevin Murphy, and Frank Hutter. NAS-bench-101: Towards reproducible neural architecture search. In Kamalika + +Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 7105-7114. PMLR, 2019. 2, 3 +[39] Kaicheng Yu, Christian Sciuto, Martin Jaggi, Claudi Musat, and Mathieu Salzmann. Evaluating the search phase of neural architecture search. In International Conference on Learning Representations, 2020. 8 +[40] Barret Zoph and Quoc Le. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 3 \ No newline at end of file diff --git a/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/images.zip b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ccba3f8ff81fce370891436ca96ab6e41899ca6e --- /dev/null +++ b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3c1b50fb21b92b99bf1a85f009a7a87f876cc6cd44001783d556e19411c2e830 +size 294855 diff --git a/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/layout.json b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..0b5215e76e620276a2168bb5a57107eb8a32819e --- /dev/null +++ b/2024/Insights from the Use of Previously Unseen Neural Architecture Search Datasets/layout.json @@ -0,0 +1,7220 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 50, + 103, + 544, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 103, + 544, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 103, + 544, + 121 + ], + "type": "text", + "content": "Insights from the Use of Previously Unseen Neural Architecture Search Datasets" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "spans": [ + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "type": "text", + "content": "Rob Geada* David Towers*,1 Matthew Forshaw" + }, + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "type": "text", + "content": " Amir Atapour-Abarghouei" + }, + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 52, + 142, + 544, + 159 + ], + "type": "text", + "content": " A. 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This goes against the hope of removing the need for experts. Neural Architecture Search (NAS) offers a solution to this by automatically identifying the best architecture. However, to date, NAS work has focused on a small set of datasets which we argue are not representative of real-world problems. We introduce eight new datasets created for a series of NAS Challenges: AddNIST, Language, MultNIST, CIFAR-Tile, Gutenberg, Isabella, GeoClassing, and Chesseract. These datasets and challenges are developed to direct attention to issues in NAS development and to encourage authors to consider how their models will perform on datasets unknown to them at development time. 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No longer would you require a domain expert to develop an optimal solution to a given problem since DL models are capable of learning the required patterns and features from the data themselves and would not need the domain expert to identify and extract the required features. Unfortunately, rather than removing the need for an expert, the new paradigm has just shifted where the expert is required. These experts now spend their time identifying the most optimal neural network architecture for a given problem. Those who are not that proficient would select between pre-existing off-the-shelf networks such as ResNet [10], VGG [23] or Inception [25]. However, to get the best results for a particular problem, one should search across all possible solutions," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 247, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 545, + 308 + ], + "type": "text", + "content": "not just those which may have shown good results in other problem domains, as no network is optimal for all problems. This idea of the 'no free lunch' [34] is backed up by our findings here, with some networks giving far poorer performance than what would be expected." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 310, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 310, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 310, + 545, + 358 + ], + "type": "text", + "content": "A DL problem can be seen as the combination of a particular task – such as classification – one wishes to apply in a particular data domain. The data domain is normally realised as a dataset for training the DL network." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 361, + 546, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 546, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 546, + 577 + ], + "type": "text", + "content": "Neural Architecture Search (NAS) is a fast-developing field of DL – which can be seen from the increase of published papers in the domain over the last few years [3]. The aim of NAS is to remove the need for an expert's time and knowledge to generate state-of-the-art competitive Neural Networks from a particular dataset [40]. NAS methods search through millions (if not billions) of candidate architectures from a pre-defined search space to find optimum networks. These search spaces comprise not only different network topologies but also the types of nodes which make up these networks – such as fully connected layers, convolutions and pooling. Although NAS can be applied to any data modality, the majority of work to date has focused on image-based datasets, with modern NAS methods achieving this feat in a few GPU hours [19, 37]. In addition to a predefined search space, a NAS approach will have a search strategy. In terms of the task, the majority of work in NAS has focused on classification problems." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 578, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 687 + ], + "type": "text", + "content": "NAS techniques are often evaluated by their ability to find networks that perform well on benchmark datasets, such as CIFAR-10 [12] and ImageNet [5]. These datasets, combined with standard search spaces such as NAS-Bench [6], fill an important role, allowing a direct comparison between NAS methods. While there is a clear benefit in using common benchmark datasets, we argue this is against the ethos of NAS - removing the need for domain experts, required to develop optimal architectures for a given problem." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Developing against common datasets can be seen as over-engineering a process to reach a solution we already" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 206, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 206, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 206, + 713 + ], + "type": "text", + "content": "*These authors performed equal contribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22541" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "know. For example, for datasets such as CIFAR-10, extensive experimentation with various neural network architectures has led to extremely high levels of accuracy [1,8,20], rendering this dataset easily solvable. In essence, since we already know what achieves high performance, NAS strategies may be optimised to reach these solutions, which may not generalise to other datasets. Prior work [18] has found that just because NAS methods perform well on benchmarks such as NAS-Bench-101 [38], this does not mean they will match other benchmarks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 334 + ], + "type": "text", + "content": "If NAS is to truly replace architecture design experts, it must be able to find optimal networks for datasets that it has never seen before – the unseen data challenge. There is a dichotomy here in that proposing a new 'unseen' dataset for NAS may lead to that dataset being adopted as one of the core datasets for NAS. We, therefore, see our work as having two values. In the first case, we are diluting the effect of overfitting to the core datasets – having more core datasets is less likely to create a NAS approach, which can overfit to all of them. For the second case, we see this as a 'call to arms' to encourage the development and use of more datasets for NAS, which we will continue to do ourselves." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 407 + ], + "type": "text", + "content": "In this work, we present eight new datasets created and used for unseen dataset NAS challenges. We define how these datasets were constructed and illustrate benchmark performance metrics that have been achieved, with the intention of encouraging others in the NAS community to develop approaches that will work on more general datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 417, + 119, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 417, + 119, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 417, + 119, + 430 + ], + "type": "text", + "content": "2. Motivation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 289, + 628 + ], + "type": "text", + "content": "To understand how well NAS methods might generalise to novel datasets and drive the direction of NAS research towards more impactful real-world applications, we organised a challenge tasking participants with creating NAS methods that perform well on unknown datasets. Participants were provided with a small number of \"development\" datasets to develop and test their NAS algorithm(s). After development, the algorithms were submitted to the competition servers, where the algorithms would be run over novel \"evaluation\" datasets. The datasets were created bespoke for the challenge and withheld from the participants throughout its duration, such that no participant could gain an advantage by knowing or guessing the evaluation datasets. As such, the participants are encouraged to create NAS approaches that generalise well to multiple problems rather than ones specifically targeted at one dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 629, + 268, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 629, + 268, + 640 + ], + "spans": [ + { + "bbox": [ + 59, + 629, + 268, + 640 + ], + "type": "text", + "content": "These unseen datasets explore one of two concepts:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 642, + 287, + 714 + ], + "type": "text", + "content": "- Type-1: A problem an expert could solve themselves or create a program, which may include basic DL, that can outperform a naive DL approach on the raw datasets. An example of this type of data is the AddNIST dataset Sec. 4.1, one of the datasets outlined later in this paper, which consists of images with three" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 324, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 180 + ], + "type": "text", + "content": "channels, with each channel being an image from the MNIST dataset [14] having the class label as the sum (the numbers are chosen so the sum is less than twenty) of the individual MNIST digits. With prior knowledge of this dataset, a solution that attains the highest accuracy is splitting the colour channels into three separate images, using a model trained on MNIST to identify the individual numbers, and then hardcoding in the necessary arithmetic to get the final answer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 185, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 185, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 317, + 185, + 545, + 340 + ], + "type": "text", + "content": "- Type-2: A problem that would be almost impossible for a human to solve or create a program without task-specific tools. An example is the Language dataset Sec. 4.2, which encodes words from ten languages into an image. The models needs to identify which letter frequency is attributed to the correct language. Without prior knowledge of what is encoded within the images and which language is represented by each class label, correctly labelling each image to the correct language would be nearly impossible. The motivation for using a type 2 dataset is to see if bespoke models can perform better than random guesswork over datasets that appear human-impossible at face value." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 345, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 476 + ], + "type": "text", + "content": "We believe that both types of tasks are essential for NAS algorithms to make a meaningful impact in real-world applications. First, if NAS remains incapable of solving problems that are effortlessly solvable by humans, it would be premature to assert that NAS can remove the requirement for expert knowledge. The second type relates to how machine learning is often deployed to find solutions to problems humans find complicated. Essentially, NAS methods should be able to perform at a level at least commensurate with other conventional machine learning techniques to effectively supplant manually designed models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 477, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 597 + ], + "type": "text", + "content": "To further obfuscate the true nature of the datasets from the challenge participants, within our datasets, data shapes were deliberately chosen that appeared to correlate to normal images or well-known datasets, such as " + }, + { + "bbox": [ + 304, + 477, + 545, + 597 + ], + "type": "inline_equation", + "content": "3 \\times 64 \\times 64" + }, + { + "bbox": [ + 304, + 477, + 545, + 597 + ], + "type": "text", + "content": ", and data split sizes to align with well-known benchmark datasets, such as 50,000 training images to align with CIFAR. We also asked participants for their guesses as to what each development dataset was: most participants correctly described the Type-1 datasets. In contrast, none of the Type-2 datasets have been correctly identified." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 604, + 392, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 392, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 392, + 616 + ], + "type": "text", + "content": "3. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 624, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 624, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 305, + 624, + 545, + 648 + ], + "type": "text", + "content": "We consider related work within the NAS literature and the datasets commonly used in NAS research." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 658, + 458, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 458, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 458, + 670 + ], + "type": "text", + "content": "3.1. Neural Architecture Search" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "NAS aims to automate the process of neural network architecture design. Traditional network design requires extensive human expertise and significant time investment." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22542" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "NAS seeks to streamline this process by employing algorithms that efficiently identify architectures tailored to specific tasks and datasets from a vast search space." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 300 + ], + "type": "text", + "content": "Initially, the work by Zoph and Le [40] applied NAS using reinforcement learning to CIFAR-10, achieving an architecture slightly outperforming manually designed models. NASNet [41] addressed the challenge of learning architectures directly on large datasets by transferring a building block designed for a small dataset to a larger one using ImageNet. ENAS [21] focused on computational efficiency by learning to search for an optimal sub-graph within a large graph, thus reducing computational resources. Evolutionary algorithms [22] have emerged, providing comparable results but with a distinct evolutionary overview. Weight-sharing methods [15] define over-parameterised super-networks (one-shot models), reducing computational costs, allowing the training of one super-network encompassing many different sub-architectures rather than training numerous networks independently." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 432 + ], + "type": "text", + "content": "Differentiable NAS [9, 16] marks another significant advancement, allowing gradient-based optimisation methods to explore the neural architecture search space efficiently. Each of these developments in NAS represents a significant stride towards the more efficient, automated and effective design of neural network architectures; however, the effectiveness of these approaches is often only tested on common benchmark datasets, some of which we will briefly cover in the following sections. The real-world applicability of these approaches needs to be tested on \"unseen\" datasets, which better simulate what is needed of NAS in practice." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 178, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 178, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 178, + 453 + ], + "type": "text", + "content": "3.2. Common NAS datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 485 + ], + "type": "text", + "content": "Although any dataset can be used to evaluate NAS methods, CIFAR-10 [12], and ImageNet [5] are highly popular." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "type": "text", + "content": "CIFAR-10 [12] comprises 60,000 images from ten classes evenly distributed in training and testing sets. Accuracy on CIFAR-10 is often used to evaluate performance, and it is also used in NAS, with the very first NAS algorithm [40] highlighting the potential power of NAS by demonstrating its ability to achieve better CIFAR-10 performance than human-designed models. While CIFAR-10 is a good dataset for comparing performance, it is an easy problem, with modern architectures and NAS methods easily achieving accuracies over " + }, + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "type": "text", + "content": ". Furthermore, since CIFAR-10 is used as a standard benchmark, new methods are encouraged to focus on this dataset, which may come at a cost of generalisability across other datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "ImageNet [5] is another popular dataset for evaluation and benchmarking. It contains 1,000 classes and presents a more challenging problem, with the results often presented in tandem with CIFAR-10 results to demonstrate model performance. ImageNet poses similar issues to CIFAR-10 due to its similar prevalence in benchmarking DL methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "While including ImageNet and CIFAR-10 as datasets for NAS comparison demonstrates that the NAS approach is not overfitting to just one dataset, it does not solve the problem of generalisation. We argue that both more datasets and datasets that the developers are unaware of are needed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 142, + 440, + 153 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 142, + 440, + 153 + ], + "spans": [ + { + "bbox": [ + 306, + 142, + 440, + 153 + ], + "type": "text", + "content": "3.3. NAS Benchmark Suites" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 161, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 161, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 161, + 545, + 232 + ], + "type": "text", + "content": "To make NAS development more comparable and easier, benchmark suites such as NAS-Bench-101 [38], NAS-Bench-201 [7], and NATS-Bench [6] have been developed. In these benchmarks, the performance achieved for each network in the search space has been pre-computed, thus removing the model training step in NAS approaches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 233, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 293 + ], + "type": "text", + "content": "Benchmark suites allow developers to focus on the development of search strategies and allow for easy comparison between different approaches as they work directly on the same search space. Thus, performance gains over other methods cannot be attributed to different search spaces." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 294, + 546, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 546, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 546, + 402 + ], + "type": "text", + "content": "These benchmark suites suffer from the same issues of reliance on CIFAR-10 and ImageNet. The search spaces used by these benchmarking tools have been fully explored on CIFAR-10 and ImageNet. These results are stored so a NAS method can look up an architecture's final result without having to retrain fully. These lookup tables do not exist for other datasets, meaning that NAS methods developed using these tools can quickly generate results for CIFAR-10 and ImageNet but not easily for other datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 415, + 426, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 426, + 428 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 426, + 428 + ], + "type": "text", + "content": "4. Dataset Descriptions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 435, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 520 + ], + "type": "text", + "content": "The code to generate our datasets is available at our GitHub page1. Each dataset comprises six NumPy files, X (images) and Y (labels) files for the training, validation, and testing sets, and a metadata file. This metadata file includes the shape of the training data, the ResNet-18 [10] benchmark result, and the number of classes in the data. Further details and examples are provided in the Appendices." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 529, + 374, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 374, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 374, + 540 + ], + "type": "text", + "content": "4.1.AddNIST" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 548, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 545, + 643 + ], + "type": "text", + "content": "AddNIST [27], is a Type-1 dataset of 70,000 images with an image shape of " + }, + { + "bbox": [ + 304, + 548, + 545, + 643 + ], + "type": "inline_equation", + "content": "3 \\times 28 \\times 28" + }, + { + "bbox": [ + 304, + 548, + 545, + 643 + ], + "type": "text", + "content": " (channels first). The training, validation, and testing split is 45,000, 15,000, and 10,000, respectively. Each colour channel is an image from MNIST [14]. An example AddNIST image is depicted in Fig. 1 (left), the larger image, shows the image as is, with the three channels laid on top of each other, and three images to the right show each channel more clearly." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "content": "AddNIST has twenty classes (0 - 19), with the class derived from the MNIST label of each channel, such that " + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "inline_equation", + "content": "l = (r + g + b) - 1" + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "content": " is the image label and " + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "inline_equation", + "content": "r, g" + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "content": " are the respective MNIST labels of each colour channel." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 467, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 467, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 467, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 317, + 702, + 467, + 712 + ], + "type": "text", + "content": "github.com/Towers-D/NAS-Unseen-Datasets" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22543" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 116, + 72, + 478, + 171 + ], + "blocks": [ + { + "bbox": [ + 116, + 72, + 478, + 171 + ], + "lines": [ + { + "bbox": [ + 116, + 72, + 478, + 171 + ], + "spans": [ + { + "bbox": [ + 116, + 72, + 478, + 171 + ], + "type": "image", + "image_path": "1fa374d918eb0cc1e4a36f427b81b47af6af3340f9299329329fe048ad89f246.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "text", + "content": "Figure 1. Left: AddNIST image - the sum of the channels adds up to 15 " + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "inline_equation", + "content": "(\\mathrm{r} = 2, \\mathrm{g} = 9, \\mathrm{b} = 4)" + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "text", + "content": ", implying a label of 14. Middle MultNIST image - the product of the channels equals 35 " + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "inline_equation", + "content": "(\\mathrm{r} = 5, \\mathrm{g} = 7, \\mathrm{b} = 1)" + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "text", + "content": ", which implies a label of 5 " + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "inline_equation", + "content": "(35\\%10 = 5)" + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "text", + "content": ". Right CIFARTile image - two deer, one aeroplane, and one horse, meaning there are three unique labels among the sub-images, which equates to a final label of 2" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 220, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 316 + ], + "type": "text", + "content": "AddNIST adds complexity to the MNIST data. In MNIST, the goal is to identify what numerical digit is seen within the image, while in AddNIST, not only does the model have to identify the digit in each channel, but it must also learn to sum up these values in a specific manner to identify the class correctly. In this manner, AddNIST was designed around the research question of whether NAS could \"figure out\" a calculation was required and apply it." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 288, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 388 + ], + "type": "text", + "content": "While the task this dataset puts forward is still rather simple, which is expected for a Type 1 dataset, it requires high-level inference capabilities within the model, which would mean the NAS algorithm searching for the optimal architecture would have to consider the capacity of the model to encompass the required function." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 396, + 117, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 117, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 117, + 407 + ], + "type": "text", + "content": "4.2. Language" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 414, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 449 + ], + "type": "text", + "content": "Using the open-source, public spell checker ASPELL, which can be found at aspell.net, we created Language [32], a Type-2 dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 521 + ], + "type": "text", + "content": "Using dictionaries from 10 languages that use the Latin alphabet (English, Dutch, German, Spanish, French, Portuguese, Swedish, Zulu, Swahili, and Finnish), all six-letter words within each language are extracted, and any words with letters that use diacritics (such as é or ii) or include 'y' or 'z' are subsequently removed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": "Each image is generated by first selecting one of the ten languages. We then randomly select four words that we filter from the selected dictionary and concatenate them into a 24-character string. Since we eliminated letters with diacritics and y and z, we have a remaining alphabet of twenty-four letters. This allows for a " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "24 \\times 24" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": " -grid encoding the string as a " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "1 \\times 24 \\times 24" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": " image. Using the " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": "-axis to denote the index of the string and the " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": "-axis to denote the character, we construct the image so each black pixel denotes the letter used in that position. See Fig. 2 (top) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "The Language research question pertained to whether a linguistic character encoding contained enough information for DL to correctly identify the original language, requiring the model to perform linguistic analysis. To ensure no leak-" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 364, + 220, + 487, + 346 + ], + "blocks": [ + { + "bbox": [ + 364, + 220, + 487, + 346 + ], + "lines": [ + { + "bbox": [ + 364, + 220, + 487, + 346 + ], + "spans": [ + { + "bbox": [ + 364, + 220, + 487, + 346 + ], + "type": "image", + "image_path": "9fe09169410b6442fea7cd2f5ce3ca73060231657523c07e8745b5286091334e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 368, + 349, + 485, + 522 + ], + "blocks": [ + { + "bbox": [ + 368, + 349, + 485, + 522 + ], + "lines": [ + { + "bbox": [ + 368, + 349, + 485, + 522 + ], + "spans": [ + { + "bbox": [ + 368, + 349, + 485, + 522 + ], + "type": "image", + "image_path": "2cbabe158acb5a2427bb0d6e4e2f0616ad72cf5cd1e19619ef587d9332ded1a2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 533, + 545, + 598 + ], + "lines": [ + { + "bbox": [ + 305, + 533, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 533, + 545, + 598 + ], + "type": "text", + "content": "Figure 2. Top: An example of a Language image with a readable axis included. The right-hand axis contains the four six-letter words \"Uvulas\", \"Minted\", \"Suckle\", and \"Debits\", which are all English words given the label 0. Bottom: An example Gutenberg image, the words \"their\", \"spring\", and \"their\" have been encoded from one of Shakespeare's works which give the label 4" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 609, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 645 + ], + "type": "text", + "content": "age between the training and testing data, when selecting a word for the training data, we ensure that this word does not appear in the validation or testing data and vice versa." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 657, + 378, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 378, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 378, + 669 + ], + "type": "text", + "content": "4.3. MultNIST" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "MultNIST [33] is a Type-1 dataset similar in concept to AddNIST (Sec. 4.1), originating from the same research question. Like AddNIST, MultNIST images have a" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22544" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 70, + 294, + 161 + ], + "blocks": [ + { + "bbox": [ + 115, + 70, + 294, + 161 + ], + "lines": [ + { + "bbox": [ + 115, + 70, + 294, + 161 + ], + "spans": [ + { + "bbox": [ + 115, + 70, + 294, + 161 + ], + "type": "image", + "image_path": "ceb4abaceaf59e86c38d15e52f2bc3d8995a7aedcfa315dc51dd760c76adae38.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 169, + 547, + 204 + ], + "lines": [ + { + "bbox": [ + 46, + 169, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 547, + 204 + ], + "type": "text", + "content": "Figure 3. Left: An example of an Isabella generated using a piece of music labelled as “20th Century”(0). Middle An example of the GeoClassing dataset showing a photo taken over Portugal (9). Right: An example rendering of a board position in the Chesseract dataset wherein white goes on to eventually win and is thus given a label of White Wins (0)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 386, + 161 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 386, + 161 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 386, + 161 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 386, + 161 + ], + "type": "image", + "image_path": "e0d03ac3240cda94b3c7247a0c2b7c327fa91e5f9ce31421942b319a5f0aba71.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 387, + 70, + 478, + 161 + ], + "blocks": [ + { + "bbox": [ + 387, + 70, + 478, + 161 + ], + "lines": [ + { + "bbox": [ + 387, + 70, + 478, + 161 + ], + "spans": [ + { + "bbox": [ + 387, + 70, + 478, + 161 + ], + "type": "image", + "image_path": "cfe23c1796bd32982c3a632b09fa252369a1ebcca2a92a88cb605a3b69fac1c2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 216, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 264 + ], + "type": "inline_equation", + "content": "3 \\times 28 \\times 28" + }, + { + "bbox": [ + 47, + 216, + 287, + 264 + ], + "type": "text", + "content": " channel first shape, and each channel is an image from the MNIST dataset [14]. See Fig. 1 (middle) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "text", + "content": "MultNIST has only ten classes (0 - 9). The label of each MultNIST image is calculated such that " + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "inline_equation", + "content": "l = (r*g*b) \\mod 10" + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "text", + "content": " is the image label and " + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "inline_equation", + "content": "r, g" + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 47, + 264, + 287, + 312 + ], + "type": "text", + "content": " are the respective MNIST labels of each colour channel." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 312, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 397 + ], + "type": "text", + "content": "In AddNIST, the class was directly affected by how large the numbers were in each channel. The only way for an image to have a label of 0 was if one colour channel contained an MNIST with label 1 and the remaining channels contained MNIST images for 0. MultNIST introduces the additional complexity over MNIST by retaining a calculation but removes the bias of larger numbers to higher classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 406, + 122, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 122, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 122, + 418 + ], + "type": "text", + "content": "4.4.CIFARTile" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 426, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 498 + ], + "type": "text", + "content": "CIFARTile is a Type-1 dataset where each image in the CIFARTile [29] dataset is a compilation of four CIFAR-10 [12] images tiled together in a grid resulting in images which are of size " + }, + { + "bbox": [ + 47, + 426, + 287, + 498 + ], + "type": "inline_equation", + "content": "3 \\times 64 \\times 64" + }, + { + "bbox": [ + 47, + 426, + 287, + 498 + ], + "type": "text", + "content": ". See Fig. 1 (right) for an example. The training, validation, and testing split is 45,000, 15,000, and 10,000 images, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 498, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 569 + ], + "type": "text", + "content": "There are four classes (0 - 3), which represent the number of CIFAR-10 classes in each grid minus one. For example, a grid consisting of CIFAR-10 images with labels [horse, horse, frog, car] has three distinct classes, and thus a label of " + }, + { + "bbox": [ + 47, + 498, + 287, + 569 + ], + "type": "inline_equation", + "content": "3 - 1 = 2" + }, + { + "bbox": [ + 47, + 498, + 287, + 569 + ], + "type": "text", + "content": ". As such, CIFARTile is a Type-1 dataset; any human should be able to identify and solve this task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 570, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 619 + ], + "type": "text", + "content": "CIFARTile requires a model to identify multiple CIFAR-10 classes simultaneously and determine which are similar and which differ. Whether models could adequately do this is the driving research question behind this dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 622, + 120, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 120, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 120, + 635 + ], + "type": "text", + "content": "4.5. Gutenberg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Gutenberg [31] is a Type-2 dataset named after the source of the data, Project Gutenberg, found at www.gutenberg.org, which provides free eBooks of literary works that are no longer under US copyright protection. We selected six authors (Thomas Aquinas, Confucius, Hawthorne, Plato, Shakespeare, and Tolstoy) and down" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 216, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 216, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 216, + 545, + 239 + ], + "type": "text", + "content": "loaded several books from each author - see the Appendices for further details and examples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 239, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 395 + ], + "type": "text", + "content": "The selected works are English translations that represent a variety of cultures and time periods. We perform basic text preprocessing, including removing punctuation, converting letters with diacritics to the base letter, and removing \"structure\" words (e.g., 'Chapter', 'Scene', 'Prologue'). We then extracted consecutive sequences of three words between 3 and 6 letters long. In each sequence, the three words were padded up to 6 characters with spaces. Then, the three words were concatenated together to produce an 18-character string. These strings were used as the base for image creation. Training, test, and validation sequences were chosen such that there was no overlap between any sequence across any data split." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "text", + "content": "Similar to the Language dataset (Sec. 4.2), we converted these strings into images. On a " + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "inline_equation", + "content": "27 \\times 18" + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "text", + "content": " grid, we created a mapping of each character in the string. See Fig. 2 (bottom) for an example. The " + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "text", + "content": "-axis represents the position in the string, and the " + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "text", + "content": "-axis represents the alphabetical letter (or space) located at that position. This results in the shape being " + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "inline_equation", + "content": "1 \\times 27 \\times 18" + }, + { + "bbox": [ + 304, + 396, + 545, + 526 + ], + "type": "text", + "content": ". The task is then to predict which of the original six authors the original word sequence came from. The training, validation, and testing split is 45,000, 15,000, and 6,000, respectively, to prevent participants from exploiting the standard distribution we used for the other datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 527, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 545, + 575 + ], + "type": "text", + "content": "The research question behind this dataset was whether specific spatial patterns of letters were sufficient information for a neural network to identify the authors from which they originated, which seems impossible from face value." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 582, + 365, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 365, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 365, + 594 + ], + "type": "text", + "content": "4.6. Isabella" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 601, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 601, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 601, + 545, + 624 + ], + "type": "text", + "content": "Isabella2 is a Type-2 dataset that uses musical recordings from the Isabella Stewart Gardner Museum, Boston." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "type": "text", + "content": "The four classes of this dataset refer to the era of composition (Baroque, Classical, Romantic, and 20th Century) attributed by the museum. The recordings are split into five-second snippets converted into 64-band spectrograms, creating a dataset of " + }, + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "type": "inline_equation", + "content": "1 \\times 64 \\times 128" + }, + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "type": "text", + "content": " shaped images. See Fig. 3" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "Code to generate Isabella is available at github.com/Towers-D/NAS-Unseen-Datasets." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22545" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 69, + 532, + 181 + ], + "blocks": [ + { + "bbox": [ + 61, + 69, + 532, + 181 + ], + "lines": [ + { + "bbox": [ + 61, + 69, + 532, + 181 + ], + "spans": [ + { + "bbox": [ + 61, + 69, + 532, + 181 + ], + "type": "table", + "html": "
DatasetResNet-18AlexNetVGG16ConvNextMNASNetDenseNetResNeXtRandom
AddNIST92.08%94.87%92.06%38.06%90.51%93.52%91.42%5%
Language87.00%85.71%84.54%83.40%84.63%84.57%93.97%10%
MultNIST91.55%94.01%90.43%64.20%87.70%92.81%90.57%10%
CIFARTile45.56%48.88%24.43%31.06%48.49%51.28%46.23%25%
Gutenberg40.98%45.53%44.00%31.93%38.00%43.28%40.30%16.6%
Isabella62.02%61.37%58.13%57.18%60.69%63.27%60.46%25%
GeoClassing80.33%92.49%83.67%72.76%86.00%94.21%89.99%10%
Chesseract57.83%57.45%55.69%52.74%56.26%59.60%55.15%33.3%
", + "image_path": "4832ef2af80dc1880e43e5a0c9ee76620f2ee909e9069f794eeb256234feaf51.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 189, + 530, + 201 + ], + "lines": [ + { + "bbox": [ + 61, + 189, + 530, + 201 + ], + "spans": [ + { + "bbox": [ + 61, + 189, + 530, + 201 + ], + "type": "text", + "content": "Table 1. Experiments on commonly-used CNN-based classification models [10,11,13,17,23,26,35] using the presented datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "type": "text", + "content": "(left) for an example. The training, validation, and testing split is 50,000, 10,000, and 10,000 images, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "text", + "content": "The task for the models is to predict the era of composition from the spectrogram. No recording used in a training snippet appeared in the validation or test sets. The research question behind this dataset was to explore whether era-defining characteristics appear at the spectrogram level and whether CNNs could reliably identify such patterns." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 315, + 129, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 129, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 129, + 328 + ], + "type": "text", + "content": "4.7. GeoClassing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 334, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 287, + 407 + ], + "type": "text", + "content": "GeoClassing [30], known as Sadie in the competition, is a Type-2 dataset that takes advantage of the BigEarthNet dataset [24] as a foundation. The BigEarthNet dataset, as originally published, consists of satellite photography with ground-cover classification labels, i.e., \"airports\" or \"vineyards\". An example image is shown in Fig. 3 (middle)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 407, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 503 + ], + "type": "text", + "content": "The GeoClassing dataset uses these images, but instead of using the given ground-cover labels, we identified the European Space Agency Sentinel patch from which the BigEarthNet image was sourced. We cross-referenced the coordinates of that patch within a map of Europe to identify the corresponding country depicted in the image. This gave us ten classes (Austria, Belgium, Finland, Ireland, Kosovo, Lithuania, Luxembourg, Portugal, Serbia, and Switzerland)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 504, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 287, + 588 + ], + "type": "text", + "content": "Each image has a shape of " + }, + { + "bbox": [ + 46, + 504, + 287, + 588 + ], + "type": "inline_equation", + "content": "3 \\times 60 \\times 60" + }, + { + "bbox": [ + 46, + 504, + 287, + 588 + ], + "type": "text", + "content": ", and the training, validation, and testing split contains 43,821, 8,758, and 8,751 images, respectively. The research question is whether NAS can find models that identify countries from differences in topology and ground coverage, which, without specific knowledge of geography and vegetation type, would be extremely difficult for a human to do manually." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 598, + 121, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 121, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 121, + 609 + ], + "type": "text", + "content": "4.8. Chesseract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Chesseract [28], a Type-1 dataset wherein we accessed public chess games from eight grandmasters (Bobby Fischer, Garry Kasparov, Magnus Carlsen, Viswanathan Anand, Hikaru Nakamura, Anatoly Karpov, Fabiano Caruana, and Mikhail Tal) extracting the final " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " of board states. These positions were then one-hot encoded by piece type and colour, creating a " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "12 \\times 8 \\times 8" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " image. As a 12-channel image is hard to render, we provided a flattened 2D image" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 208, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 208, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 208, + 545, + 232 + ], + "type": "text", + "content": "of one of the chess boards we used Fig. 3 (right). A 3D visualisation can be seen in the Appendices." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 232, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 363 + ], + "type": "text", + "content": "The training, validation, and testing split is 49,998, 9,999, and 9,999 images, respectively. Each image in the Chesseract dataset is one of three classes (White wins, Draw, Black wins). No individual positions from the same game appeared across the data splits. This dataset requires the model to identify the game's final result from the position. Chesseract presented a problem for some participants of the challenge. This was because Chesseract uses twelve instead of the usual 1 or 3 channels applied for image datasets, which often caused errors for hardcoded algorithms that only accepted 1 or 3 channel dimensions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 364, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 449 + ], + "type": "text", + "content": "Machine learning is already prominent in chess, with competing learning-based chess engines that beat grandmaster players, such as AlphaZero [4]. Our research question for this dataset was based on the understanding that any position can be analysed to show whether black or white has the advantage. Is NAS able to develop a DL network to identify this from just an encoding of the board position?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 460, + 453, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 453, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 453, + 474 + ], + "type": "text", + "content": "5. Baseline Experimentation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 481, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 529 + ], + "type": "text", + "content": "Here, we provide some baseline results for our datasets to motivate future NAS experimentation. We provide a set of baseline results across several well-known CNNs and three NAS methods across two search spaces." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 538, + 415, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 415, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 415, + 551 + ], + "type": "text", + "content": "5.1. CNN Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": "To generate baseline results of our datasets for future work comparison, we have performed experiments using commonly used off-the-shelf CNNs, which can be seen in Tab. 1. In all our CNN experiments, we have followed a similar experimental setup. We use stochastic gradient descent as our optimiser with an initial learning rate of 0.01, momentum of 0.9, and a weight decay of " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "3 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": ". We have used a Cosine Annealing Learning rate with the max number of iterations equaling 64, the number of epochs. Cross Entropy is used as the Loss function." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "ResNet-18 is used as the baseline throughout our competition, and any NAS method would be expected to easily outperform this architecture. As you can see in Tab. 1," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22546" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 114, + 71, + 479, + 194 + ], + "blocks": [ + { + "bbox": [ + 114, + 71, + 479, + 194 + ], + "lines": [ + { + "bbox": [ + 114, + 71, + 479, + 194 + ], + "spans": [ + { + "bbox": [ + 114, + 71, + 479, + 194 + ], + "type": "table", + "html": "
DatasetPC-DARTSDrNASBonsai-NetRandom Search
DARTSBonsaiRandom
Addnist96.60%97.06%97.91%97.07%34.17%5%
Language90.12%88.55%87.65%90.12%76.83%10%
MultNIST96.68%98.10%97.17%96.55%39.76%10%
CIFARTile92.28%81.08%91.47%90.74%24.76%25%
Gutenberg49.12%46.62%48.57%47.72%29.00%16.6%
Isabella65.77%64.53%64.08%66.35%58.53%25%
GeoClassing94.61%96.03%95.66%95.54%63.56%10%
Chesseract57.20%58.24%60.76%59.16%68.83%33.3%
", + "image_path": "d1c29422377dea0adba1f3a2d6cd8578622797c51359232f0170534a7b1ba007.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 201, + 485, + 213 + ], + "lines": [ + { + "bbox": [ + 107, + 201, + 485, + 213 + ], + "spans": [ + { + "bbox": [ + 107, + 201, + 485, + 213 + ], + "type": "text", + "content": "Table 2. Experimental results on PC-DARTS [36], DrNAS [2], Bonsai-Net [9] as well as random search." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 220, + 287, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 267 + ], + "type": "text", + "content": "ResNet-18 produces competitive results across our datasets, though it does not excel on any particular dataset. ResNet-18 particularly struggles with the GeoClassing dataset compared to the others, only beating ConvNext in our trials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 268, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 287, + 422 + ], + "type": "text", + "content": "AlexNet [13] shows decent performance across all datasets, achieving the highest accuracy on three of the eight datasets (AddNIST, MultNIST, and Gutenberg). AddNIST and MultNIST are similar, both being derived from MNIST. This may suggest that AlexNet is particularly good at working with MNIST Images. AlexNet captures spatial hierarchies in images well and is thus suitable for the clear, structured layouts of MNIST digits. VGG16 [23], on the other hand, does not achieve particularly impressive levels of accuracy on any of the datasets, though it does not perform badly, either. The only exception is the CIFARTile dataset, where VGG suffers and only achieves roughly the same accuracy as random chance, as seen in Tab. 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 520 + ], + "type": "text", + "content": "ConvNext [17] performs poorly across our datasets, most likely since our datasets may not exhibit the specific spatial complexity that ConvNext is optimised for. However, it is important to note that for purposes of generating our CNN baselines, we have kept the experimental setup the same across CNNs. Thus, hyperparameter tuning may be beneficial to ConvNext. We have used the base version of ConvNext in our experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": "We also perform the same experiments on MnasNet [26] using a depth multiplier of 1.0. Despite being a lightweight architecture designed for mobile efficiency, MnasNet achieves competitive results across our datasets. It has strong generalisation capabilities since it uses a reinforcement learning approach to automate architecture design, thus performing well on unseen datasets [26]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "DenseNet [11] performs significantly well on the latter three datasets (Isabella, GeoClassing, and Chesseract) as well as CIFARTile, achieving the highest accuracy of the CNNs over these datasets. With the exception of Chesseract, the datasets that DenseNet excels on are the most memory-intensive datasets. This is due to the DenseNet mechanism allowing efficient re-use of features through dense connectivity and ensuring maximal information flow between layers in the network [11]. For memory-intensive" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 220, + 545, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 267 + ], + "type": "text", + "content": "datasets, which often contain complex and rich information, this feature reuse allows DenseNet to exploit the data more thoroughly and efficiently, leading to better performance. The DenseNet-161 architecture is used in our experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 268, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 387 + ], + "type": "text", + "content": "Finally, ResNeXt [35] performs fairly well across our datasets, but especially well on the Language Dataset, scoring almost " + }, + { + "bbox": [ + 304, + 268, + 545, + 387 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 304, + 268, + 545, + 387 + ], + "type": "text", + "content": " higher than the other methods. The particular version of ResNeXt we used is ResNeXt-50 (32 x 4d), which has a high level of cardinality (the size of the set of transformations) [35]. This high cardinality allows ResNeXt to learn more complex and diverse representations, which is crucial for distinguishing subtle patterns in the Language Dataset, such as the frequency and arrangement of characters encoded in images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 388, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 566 + ], + "type": "text", + "content": "Our analysis across these CNN architectures reveals distinct performance trends tied to the nature of each dataset. ResNet-18 serves as a versatile baseline, while AlexNet is especially capable of handling structured patterns. VGG16's mixed results and ConvNext's overall underperformance emphasise the need within conventional deep learning for matching architectural strengths to dataset characteristics, which is not desirable for evaluating generalisation capabilities in general and NAS algorithms in particular. DenseNet and ResNeXt are good at handling memory-intensive datasets and those with nuanced patterns, respectively. These insights confirm that the effectiveness of a CNN architecture is highly contingent on the specific demands of the dataset, which underscores the need for unseen datasets for effective evaluation of NAS methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 574, + 411, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 411, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 411, + 586 + ], + "type": "text", + "content": "5.2. NAS Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 676 + ], + "type": "text", + "content": "In addition to the experiments performed on the CNNs, we have also applied the NAS methods of PC-DARTS [36], DrNAS [2] (DARTS-space), and Bonsai-Net [9] to our datasets. Furthermore, as a baseline of comparison, we perform a random search in both the DARTS and Bonsai search spaces, using the provided methods from PC-DARTS and Bonsai-NET. These results can be found in Tab. 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "During our random search experiments using the DARTS search space, it is noted that random search often outperforms either PC-DARTS or DrNAS and outper" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22547" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 265, + 180 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 265, + 180 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 265, + 180 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 265, + 180 + ], + "type": "table", + "html": "
DatasetCNNNASCompetition
AddNIST94.87%97.91%95.06%
Language93.97%90.12%89.71%
MultNIST94.01%98.10%95.45%
CIFARTile51.28%92.28%73.08%
Gutenberg45.53%49.12%50.85%
Isabella63.27%65.77%61.42%
GeoClassing94.21%96.03%96.08%
Chesseract59.60%60.76%62.98%
", + "image_path": "3a08fb6e6165457e64c0a7b33fd3815013597f96483b1fac710d8e230c20381e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 189, + 287, + 210 + ], + "lines": [ + { + "bbox": [ + 47, + 189, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 189, + 287, + 210 + ], + "type": "text", + "content": "Table 3. Results on each dataset from our CNN and NAS experiments, and Competition Submissions" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 213, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 272 + ], + "type": "text", + "content": "forms both models on AddNIST, Chesseract and Isabella, tying PC-DARTS on Language while outperforming DrNAS. These results support findings by Yu et al. [39] that searches using these search spaces often do not significantly outperform random search." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 274, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 452 + ], + "type": "text", + "content": "We can see in Tab. 2 that PC-DARTS [36] performs well, scoring the highest accuracies over four of the eight datasets and gives competitive results over the others. DrNAS [2], however, scores the highest on two of the eight datasets but struggles with CIFARTile, where it scores " + }, + { + "bbox": [ + 46, + 274, + 287, + 452 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 274, + 287, + 452 + ], + "type": "text", + "content": " lower than the other methods. We used the DARTS search space during our DrNAS experiments; while DrNAS is also available to work on the NAS-Bench-201 [7] search space, it employs the NAS-Bench API to look at the performance of architectures fully trained on CIFAR-10, which would not reflect the performance these architectures found on our datasets. In most cases, Bonsai-Net [9] outperforms random search, with the exception of Chesseract. It returns the best results on AddNIST and Chesseract (though it is significantly beaten by random search on the latter dataset)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 453, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 537 + ], + "type": "text", + "content": "The varied performance of these NAS methods across our datasets highlights their ability to challenge and assess the adaptability and effectiveness of different architecture search strategies. This underscores the strengths of our datasets in providing a comprehensive benchmark for evaluating NAS methods' capability to generalise across a diverse range of tasks and complexities." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 548, + 117, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 117, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 117, + 562 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 569, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 700 + ], + "type": "text", + "content": "Tab. 3 shows the best-reported performance of the CNN and NAS experiments on each dataset, as well as the best result found by competition participants; for further information, see the Appendices. From these results, we can see that NAS found the best model for seven datasets, supporting the usage of NAS methods in finding good models for given datasets. Three of these architectures were found by competition submissions, NAS methods designed for unseen data; given the competition's time restrictions this may suggest that methods designed in this way can generalise to other datasets better." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "It is important to mention that we did not test the deepest" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "versions of these CNN architectures or perform hyperparameter optimisation. Similarly, while we allowed the traditional NAS methods to run in their preset configuration, the competition participants were only given twenty-four hours to evaluate across three datasets. However, even with these limitations, CNNs and NAS architectures from the competition outperformed traditional NAS methods across several datasets, reinforcing our belief that current NAS methods do not necessarily generalise properly to unseen datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 191, + 451, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 451, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 451, + 205 + ], + "type": "text", + "content": "7. Rights and Reproduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "content": "These datasets have been created under the licence agreements of the original data. Where available, we have made the datasets publicly accessible under an CC BY 4.0 Licence. The Isabella dataset uses data from the Isabella Stewart Gardner Museum, which withdraws the right to share modifications to the music they have made available. Instead of providing the dataset, we provide a Python script to convert music files obtained from the Museum into the format of the competition dataset on our GitHub4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 330, + 379, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 330, + 379, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 330, + 379, + 342 + ], + "type": "text", + "content": "8. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 350, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 481 + ], + "type": "text", + "content": "Machine learning is a valuable and fast-growing tool that is quickly becoming part of the tools we use daily. For small businesses to stay competitive, they need to be able to easily include machine learning techniques in their products or business strategy. NAS promises to be a tool that removes the cost of an expert's time and knowledge to create bespoke neural networks while remaining competitive. NAS is currently evaluated primarily on a few benchmark datasets and developed based on these datasets as well. This does not reveal how generalisable NAS methods are when given a dataset, especially when the problem is distinctly different." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 482, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 613 + ], + "type": "text", + "content": "This paper introduces eight new datasets to be used when testing NAS methods. These datasets represent problems that are either simple or difficult for humans to solve and provide difficulty outside of normal image classification. While we believe using these datasets will improve the generalisability of NAS methods, the problem of not knowing whether NAS is good in general or only good on benchmark datasets is a rolling problem. Simply including these datasets for upcoming NAS works will mean they become part of the datasets developed in mind. To solve this problem, more datasets will be continually needed." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 613, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 661 + ], + "type": "text", + "content": "In the future, we seek to develop further datasets to enable people to work on 'unseen' data for NAS. We will also evaluate these datasets against pre-existing, and NAS approaches we are developing." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 662, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 662, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 545, + 685 + ], + "type": "text", + "content": "For a video overview of the paper, please follow this link: youtu.be/YdYHdxNZUIw" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 693, + 534, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 693, + 534, + 703 + ], + "spans": [ + { + "bbox": [ + 315, + 693, + 534, + 703 + ], + "type": "text", + "content": "3Available here https://www.gardnermuseum.org/experience/music" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 703, + 468, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 703, + 468, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 703, + 468, + 713 + ], + "type": "text", + "content": "github.com/Towers-D/NAS-Unseen-Datasets" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22548" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Andrea Gesmundo and J. 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(a) The synthetic images generated from Stable Diffusion and our proposed InstaGen, which can serve as a dataset synthesizer for sourcing photo-realistic images and instance bounding boxes at scale. (b) On open-vocabulary detection, training on synthetic images demonstrates significant improvement over CLIP-based methods on novel categories. (c) Training on the synthetic images generated from InstaGen also enhances the detection performance in close-set scenarios, particularly in data-sparse circumstances." + ], + "image_footnote": [], + "bbox": [ + 441, + 243, + 678, + 372 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ad8e4cfd2fb59d2e55678ba9d7646f55738abdcb5f1ed2ef9a728cda20199984.jpg", + "image_caption": [ + "(c) The detection AP with respect to the portion $(\\%)$ of real data (COCO) usage." + ], + "image_footnote": [], + "bbox": [ + 684, + 243, + 887, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 474, + 313, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present a novel paradigm to enhance the ability of object detector, e.g., expanding categories or improving detection performance, by training on synthetic dataset generated from diffusion models. Specifically, we integrate an instance-level grounding head into a pretrained, generative diffusion model, to augment it with the ability of localising instances in the generated images. The grounding head is trained to align the text embedding of category names with the regional visual feature of the diffusion model, using supervision from an off-the-shelf object detector, and a novel self-training scheme on (novel) categories not covered by the detector. We conduct thorough experiments to show that, this enhanced version of diffusion model, termed as InstaGen, can serve as a data synthesizer, to enhance object detectors by training on its generated samples, demonstrating superior performance over existing state-of-the-art methods in open-vocabulary (+4.5 AP) and data-sparse (+1.2 ~ 5.2 AP) scenarios.", + "bbox": [ + 73, + 500, + 473, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 789, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Object detection has been extensively studied in the field of computer vision, focusing on the localization and categorization of objects within images [3, 5, 12, 26, 27]. The common practise is to train the detectors on large-scale im", + "bbox": [ + 75, + 814, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "age datasets, such as MS-COCO [20] and Object365 [30], where objects are exhaustively annotated with bounding boxes and corresponding category labels. However, the procedure for collecting images and annotations is often laborious and time-consuming, limiting the datasets' scalability.", + "bbox": [ + 496, + 470, + 890, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the recent literature, text-to-image diffusion models have demonstrated remarkable success in generating high-quality images [28, 29], that unlocks the possibility of training vision systems with synthetic images. In general, existing text-to-image diffusion models are capable of synthesizing images based on some free-form text prompt, as shown in the first row of Figure 1a. Despite being photorealistic, such synthesized images can not support training sophisticated systems, that normally requires the inclusion of instance-level annotations, e.g., bounding boxes for object detection in our case. In this paper, we investigate a novel paradigm of dataset synthesis for training object detector, i.e., augmenting the text-to-image diffusion model to generate instance-level bounding boxes along with images.", + "bbox": [ + 496, + 549, + 892, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To begin with, we build an image synthesizer by fine-tuning the diffusion model on existing detection dataset. This is driven by the observation that off-the-shelf diffusion models often generate images with only one or two objects on simplistic background, training detectors on such images may thus lead to reduced robustness in complex real-world scenarios. Specifically, we exploit the existing detection dataset, and subsequently fine-tune the diffusion model with the image-caption pairs, constructed by taking", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†: corresponding author.", + "bbox": [ + 76, + 887, + 210, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14121", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "random image crops, and composing the category name of the objects in the crop. As illustrated in the second row of the Figure 1a, once finetuned, the image synthesizer now enables to produce images with multiple objects and intricate contexts, thereby providing a more accurate simulation of real-world detection scenarios.", + "bbox": [ + 75, + 90, + 470, + 180 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To generate bounding boxes for objects within synthetic images, we propose an instance grounding module that establishes the correlation between the regional visual features from diffusion model and the text embedding of category names, and infers the coordinates for the objects' bounding boxes. Specifically, we adopt a two-step training strategies, firstly, we train the grounding module on synthetic images, with the supervision from an off-the-shelf object detector, which has been trained on a set of base categories; secondly, we utilize the trained grounding head to generate pseudo labels for a larger set of categories, including those not seen in existing detection dataset, and selftrain the grounding module. Once finished training, the grounding module will be able to identify the objects of arbitrary category and their bounding boxes in the synthetic image, by simply providing the name in free-form language.", + "bbox": [ + 75, + 181, + 468, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we explore a novel approach to enhance object detection capabilities, such as expanding detectable categories and improving overall detection performance, by training on synthetic dataset generated from diffusion model. We make the following contribution: (i) We develop an image synthesizer by fine-tuning the diffusion model, with image-caption pairs derived from existing object detection datasets, our synthesizer can generate images with multiple objects and complex contexts, offering a more realistic simulation for real-world detection scenarios. (ii) We introduce a data synthesis framework for detection, termed as InstaGen. This is achieved through a novel grounding module that enables to generate labels and bounding boxes for objects in synthetic images. (iii) We train standard object detectors on the combination of real and synthetic dataset, and demonstrate superior performance over existing state-of-the-art detectors across various benchmarks, including open-vocabulary detection (increasing Average Precision [AP] by +4.5), data-sparse detection (enhancing AP by +1.2 to +5.2), and cross-dataset transfer (boosting AP by +0.5 to +1.1).", + "bbox": [ + 75, + 424, + 470, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 753, + 218, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object Detection. Object detection aims to simultaneously predict the category and corresponding bounding box for the objects in the images. Generally, object detectors [3, 4, 6, 26, 27] are trained on a substantial amount of training data with bounding box annotations and can only recognize a predetermined set of categories present in the training data. In the recent literature, to further expand the ability of object detector, open-vocabulary object detec", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion (OVD) has been widely researched, for example, OVR-CNN [37] introduces the concept of OVD and pre-trains a vision-language model with image-caption pairs. The subsequent works make use of the robust multi-modal representation of CLIP [24], and transfer its knowledge to object detectors through knowledge distillation [9, 36], exploiting extra data [5, 41] and text prompt tuning [2, 5]. In this paper, we propose to expand the ability of object detectors, e.g., expanding categories or improving detection performance, by training on synthetic dataset.", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generative Models. Image generation has been considered as a task of interest in computer vision for decades. In the recent literature, significant progress has been made, for example, the generative adversarial networks (GANs) [8], variational autoencoders (VAEs) [15], flow-based models [14], and autoregressive models (ARMs) [32]. More recently, there has been a growing research interest in diffusion probabilistic models (DPMs), which have shown great promise in generating high-quality images across diverse datasets. For examples, GLIDE [23] utilizes a pre-trained language model and a cascaded diffusion structure for text-to-image generation. DALL-E 2 [25] is trained to generate images by inverting the CLIP image space, while Imagegen [29] explores the advantages of using pre-trained language models. Stable Diffusion [28] proposes the diffusion process in VAE latent spaces rather than pixel spaces, effectively reducing resource consumption. In general, the rapid development of generative models opens the possibility for training large models with synthetic dataset.", + "bbox": [ + 496, + 246, + 892, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 549, + 633, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we present details for constructing a dataset synthesizer, that enables to generate photo-realistic images with bounding boxes for each object instance, and train an object detector on the combined real and synthetic datasets.", + "bbox": [ + 496, + 575, + 890, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 648, + 702, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a detection dataset of real images with manual annotations, i.e., $\\mathcal{D}_{\\mathrm{real}} = \\{(x_1,\\mathcal{B}_1,\\mathcal{Y}_1),\\ldots ,(x_N,\\mathcal{B}_N,\\mathcal{Y}_N)\\}$ where $\\mathcal{B}_i = \\{b_1,\\dots ,b_m|b_j\\in \\mathbb{R}^{2\\times 2}\\}$ denotes the set of box coordinates for the annotated instances in one image, and $\\mathcal{V}_i = \\{y_1,\\dots ,y_m|y_j\\in \\mathcal{R}^{\\mathcal{C}_{\\mathrm{base}}}\\}$ refers to the categories of the instances. Our goal is thus to exploit the given real dataset $(\\mathcal{D}_{\\mathrm{real}})$ , to steer a generative diffusion model into dataset synthesizer, that enables to augment the existing detection dataset, i.e., $\\mathcal{D}_{\\mathrm{final}} = \\mathcal{D}_{\\mathrm{real}} + \\mathcal{D}_{\\mathrm{syn}}$ . As a result, detectors trained on the combined dataset demonstrate enhanced ability, i.e., extending the detection categories or improving the detection performance.", + "bbox": [ + 496, + 672, + 890, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the following sections, we first describe the procedure for constructing an image synthesizer, that can generate images suitable for training object detector (Section 3.2). To", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14122", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/55deda742119a4332e8facb3114600260cdc94ddd588d874ed54c91430dc8e87.jpg", + "image_caption": [ + "(a) Fine-tuning diffusion model on detection dataset." + ], + "image_footnote": [], + "bbox": [ + 83, + 97, + 467, + 256 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/78726df096b1a2fb19481af1d6124e7e5487c72fc63153b7c53e93174c36f7c3.jpg", + "image_caption": [ + "(b) Supervised training and self-training for grounding head (i.e. student).", + "Figure 2. Illustration of the process for finetuning diffusion model and training the grounding head: (a) stable diffusion model is fine-tuned on the detection dataset on base categories. (b) The grounding head is trained on synthetic images, with supervised learning on base categories and self-training on novel categories." + ], + "image_footnote": [], + "bbox": [ + 498, + 89, + 883, + 261 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "simultaneously generate the images and object bounding boxes, we propose a novel instance-level grounding module, which aligns the text embedding of category name with the regional visual features from image synthesizer, and infers the coordinates for the objects in synthetic images. To further improve the alignment towards objects of arbitrary category, we adopt self-training to tune the grounding module on object categories not existing in $\\mathcal{D}_{\\mathrm{real}}$ (Section 3.3). As a result, the proposed model, termed as InstaGen, can automatically generate images along with bounding boxes for object instances, and construct synthetic dataset $(\\mathcal{D}_{\\mathrm{syn}})$ at scale, leading to improved ability when training detectors on it (Section 3.4).", + "bbox": [ + 75, + 335, + 472, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Image Synthesizer for Object Detection", + "text_level": 1, + "bbox": [ + 76, + 541, + 415, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we build our image synthesizer based on an off-the-shelf stable diffusion model (SDM [28]). Despite of its impressive ability in generating photo-realistic images, it often outputs images with only one or two objects on simplistic background with the text prompts, for example, 'a photograph of a [category1 name] and a [category2 name]' as demonstrated in Figure 4b. As a result, object detectors trained on such images may exhibit reduced robustness when dealing with complex real-world scenarios. To bridge such domain gap, we propose to construct the image synthesizer by fine-tuning the SDM with an existing real-world detection dataset $(\\mathcal{D}_{\\mathrm{real}})$ .", + "bbox": [ + 75, + 564, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fine-tuning procedure. To fine-tune the stable diffusion model (SDM), one approach is to naively use the sample from detection dataset, for example, randomly pick an image and construct the text prompt with all categories in the image. However, as the image often contains multiple objects, such approach renders significant difficulty for fine-tuning the SDM, especially for small or occluded objects. We adopt a mild strategy by taking random crops from the images, and construct the text prompt with categories in the image crops, as shown in Figure 2a. If an image crop con", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tains multiple objects of the same category, we only use this category name once in the text prompt.", + "bbox": [ + 496, + 335, + 890, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fine-tuning loss. We use the sampled image crop and constructed text prompt to fine-tune SDM with a squared error loss on the predicted noise term as follows:", + "bbox": [ + 496, + 369, + 892, + 415 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f i n e - t u n e}} = \\mathbb {E} _ {z, \\epsilon \\sim \\mathcal {N} (0, 1), t, y} \\left[ | | \\epsilon - \\epsilon_ {\\theta} \\left(z ^ {t}, t, y\\right) | | _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 415, + 890, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $z$ denotes a latent vector mapped from the input image with VAE, $t$ denotes the denoising step, uniformly sampled from $\\{1,\\dots ,T\\}$ , $T$ refers to the length of the diffusion Markov chain, and $\\epsilon_{\\theta}$ refers to the estimated noise from SDM with parameters $\\theta$ being updated. We have experimentally verified the necessity of this fine-tuning step, as shown in Table 4.", + "bbox": [ + 496, + 450, + 892, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Dataset Synthesizer for Object Detection", + "text_level": 1, + "bbox": [ + 498, + 564, + 848, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present details for steering the image synthesizer into dataset synthesizer for object detection, which enables to simultaneously generate images and object bounding boxes. Specifically, we propose an instance-level grounding module that aligns the text embedding of object category, with the regional visual feature of the diffusion model, and infers the coordinates for bounding boxes, effectively augmenting the image synthesizer with instance grounding, as shown in Figure 3. To further improve the alignment in large visual diversity, we propose a self-training scheme that enables the grounding module to generalise towards arbitrary categories, including those not exist in real detection dataset $(\\mathcal{D}_{\\mathrm{real}})$ . As a result, our data synthesizer, termed as InstaGen, can be used to construct synthetic dataset for training object detectors.", + "bbox": [ + 496, + 588, + 892, + 815 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3.1 Instance Grounding on Base Categories", + "text_level": 1, + "bbox": [ + 498, + 821, + 830, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To localise the object instances in synthetic images, we introduce an open-vocabulary grounding module, that aims to simultaneously generate image $(x)$ and the corresponding instance-level bounding boxes $(\\mathcal{B})$ based on a set of", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14123", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bccb423f8f5aad018cd1d7c9571f9ee6743743209874d0f42abc938ab9cb5069.jpg", + "image_caption": [ + "Figure 3. Illustration of the dataset generation process in InstaGen. The data generation process consists of two steps: (i) Image collection: given a text prompt, SDM generates images with the objects described in the text prompt; (ii) Annotation generation: the instance-level grounding head aligns the category embedding with the visual feature region of SDM, generating the corresponding object bounding-boxes." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "categories $(\\mathcal{V})$ , i.e., $\\{x, \\mathcal{B}, \\mathcal{Y}\\} = \\Phi_{\\mathrm{InstaGen}}(\\epsilon, \\mathcal{Y})$ , where $\\epsilon \\sim \\mathcal{N}(0, I)$ denotes the sampled noise.", + "bbox": [ + 75, + 402, + 468, + 433 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we propose an instance grounding head, as shown in Figure 3, it takes the intermediate representation from image synthesizer and the text embedding of category as inputs, then predicts the corresponding object bounding boxes, i.e., $\\{\\mathcal{B}_i,\\mathcal{Y}_i\\} = \\Phi_{\\mathrm{g - head}}(\\mathcal{F}_i,\\Phi_{\\mathrm{t - enc}}(g(\\mathcal{Y}_i)))$ , where $\\mathcal{F}_i = \\{f_i^1,\\dots ,f_i^n\\}$ refers to the multi-scale dense features from the image synthesizer at time step $t = 1$ $g(\\cdot)$ denotes a template that decorates each of the visual categories in the text prompt, e.g., 'a photograph of [category1 name] and [category2 name], $\\Phi_{\\mathrm{t - enc}}(\\cdot)$ denotes the text encoder.", + "bbox": [ + 75, + 439, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by GroundingDINO [22], our grounding head $\\Phi_{\\mathrm{g - head}}(\\cdot)$ mainly contains four components: (i) a channel-compression layer, implemented with a $3\\times 3$ convolution, for reducing the dimensionality of the visual features; (ii) a feature enhancer, consisting of six feature enhancer layers, to fuse the visual and text features. Each layer employs a deformable self-attention to enhance image features, a vanilla self-attention for text feature enhancers, an image-to-text cross-attention and a text-to-image cross-attention for feature fusion; (iii) a language-guided query selection module for query initialization. This module predicts top- $N$ anchor boxes based on the similarity between text features and image features. Following DINO [38], it adopts a mixed query selection where the positional queries are initialized with the anchor boxes and the content queries remain learnable; (iv) a cross-modality decoder for classification and box refinement. It comprises six decoder layers, with each layer utilizing a self-attention mechanism for query interaction, an image cross-attention layer for combining image features, and a text cross-attention layer for combining text", + "bbox": [ + 75, + 598, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "features. Finally, we apply the dot product between each query and the text features, followed by a Sigmoid function to predict the classification score $\\hat{s}$ for each category. Additionally, the object queries are passed through a Multi-Layer Perceptron (MLP) to predict the object bounding boxes $\\hat{b}$ , as shown in Figure 3. We train the grounding head by aligning the category embedding with the regional visual features from diffusion model, as detailed below. Once trained, the grounding head is open-vocabulary, i.e., given any categories (even beyond the training categories), the grounding head can generate the corresponding bounding-boxes for the object instances.", + "bbox": [ + 496, + 402, + 892, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training triplets of base categories. Following [18], we apply an automatic pipeline to construct the $\\{$ visual feature, bounding-box, text prompt\\} triplets, with an object detector trained on base categories from a given dataset $(D_{\\mathrm{real}})$ . In specific, assuming there exists a set of base categories $\\{c_{\\mathrm{base}}^{1},\\ldots ,c_{\\mathrm{base}}^{N}\\}$ , e.g., the classes in MS-COCO [20]. We first select a random number of base categories to construct a text prompt, e.g., 'a photograph of [base category1] and [base category2]' and generate both the visual features and images with our image synthesizer. Then we take an off-the-shelf object detector, for example, pre-trained Mask R-CNN [12], to run the inference procedure on the synthetic images, and infer the bounding boxes of the selected categories. To acquire the confident bounding-boxes for training, we use a score threshold $\\alpha$ to filter out the bounding-boxes with low confidence (an ablation study on the selection of the score threshold has been conducted in Section 4.5). As a result, an infinite number of training triplets for the given base categories can be constructed by repeating the above operation.", + "bbox": [ + 496, + 598, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14124", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7ea2c8d082a4325287778db1498f4094d90ddbec49a9345045a2f32109f27c98.jpg", + "image_caption": [ + "(a) Stable Diffusion $^+$ Grounding head w/ Supervised training." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 161, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/18578e5af17a8eaf7f6b1e5f8dbd8ef7289313346dcaad9ba62ac788e215dd7a.jpg", + "image_caption": [ + "Figure 4. Visualization of the synthetic images and bounding-boxes generated from different models. The bounding-boxes with green denote the objects from base categories, while the ones with red denote the objects from novel categories." + ], + "image_footnote": [], + "bbox": [ + 165, + 88, + 248, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/589961f3dce58985693b59a078cf68aacebb20e2113507e81ab8a6d271094ff6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 89, + 334, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4a32387c50e652d3e70db3d2fa251aace6053703da1a85d9272824bf1cb80884.jpg", + "image_caption": [ + "(b) Stable Diffusion + Grounding head w/ Supervised- and Self-training." + ], + "image_footnote": [], + "bbox": [ + 354, + 90, + 437, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e182df7a10d9dacd84a46b12268e5ba42ef6b8e81a0a3a3be42ccfe46ca6c296.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 90, + 524, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f92f9e7dd2d7b2e309f8b3e68fc666d8f30aa71d9f27603d5ac9c53827c12c42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 90, + 609, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3341a9bb888d21634ab254ebbf93daa0ecabc73dac0075e7272fdb4efb082360.jpg", + "image_caption": [ + "(c) Stable Diffusion w/ Fine-tuning + Grounding head w/ Supervised- and Self-training." + ], + "image_footnote": [], + "bbox": [ + 630, + 90, + 712, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/10e097f2ad4820ec6212695681030377cdeefdf84f54eb4c4f803c96a02c4534.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 715, + 90, + 797, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cf0bfba5805d764f34b1f2b60c3b1cdb9465d0a016e78b919111b642d841836b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 802, + 90, + 883, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training loss. We use the constructed training triplets to train the grounding head:", + "bbox": [ + 75, + 300, + 467, + 330 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b a s e}} = \\sum_ {i = 1} ^ {N} \\left[ \\mathcal {L} _ {\\operatorname {c l s}} \\left(\\hat {s} _ {i}, c _ {i}\\right) + \\mathbb {1} _ {\\{c _ {i} \\neq \\emptyset \\}} \\mathcal {L} _ {\\text {b o x}} \\left(\\hat {b} _ {i}, b _ {i}\\right) \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 335, + 468, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $i$ th prediction $(\\hat{s}_i, \\hat{b}_i)$ from the $N$ object queries is assigned to a ground-truth $(c_i, b_i)$ or $\\varnothing$ (no object) with bipartite matching. $\\mathcal{L}_{\\mathrm{cls}}$ and $\\mathcal{L}_{\\mathrm{box}}$ denote the classification loss (e.g. Focal loss) and box regression loss (e.g. L1 loss and GIoU loss), respectively.", + "bbox": [ + 75, + 386, + 468, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Instance Grounding on Novel Categories", + "text_level": 1, + "bbox": [ + 76, + 479, + 413, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Till here, we have obtained a diffusion model with open-vocabulary grounding, which has been only trained with base categories. In this section, we propose to further leverage the synthetic training triplets from a wider range of categories to enhance the alignment for novel/unseen categories. Specifically, as shown in Figure 2b, we describe a framework that generates the training triplets for novel categories using the grounded diffusion model, and then selftrain the grounding head.", + "bbox": [ + 75, + 503, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training triplets of novel categories. We design the text prompts of novel categories, e.g., 'a photograph of [novel category1] and [novel category2], and pass them through our proposed image synthesizer, to generate the visual features. To acquire the corresponding bounding-boxes for novel categories, we propose a self-training scheme that takes the above grounding head as the student, and apply a mean teacher (an exponential moving average (EMA) of the student model) to create pseudo labels for update. In contrast to the widely adopted self-training scheme that takes the image as input, the student and teacher in our case only take the visual features as input, thus cannot apply data augmentation as for images. Instead, we insert dropout module within each feature enhancer layer and decoder layer in the student. During training, we run inference (without dropout module) with teacher model on the visual features to produce bounding boxes, and then use a score threshold $\\beta$ to", + "bbox": [ + 75, + 643, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "filter out those with low confidence, and use the remaining training triplets $(\\mathcal{F}_i,\\hat{b}_i,y_i^{\\mathrm{novel}})$ to train the student, i.e., grounding head.", + "bbox": [ + 498, + 300, + 890, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training loss. Now, we can also train the grounding head on the mined triplets of novel categories (that are unseen in the existing real dataset) with the training loss $\\mathcal{L}_{\\mathrm{novel}}$ defined similar to Eq. 2. Thus, the total training loss for training the grounding head can be: $\\mathcal{L}_{\\mathrm{grounding}} = \\mathcal{L}_{\\mathrm{base}} + \\mathcal{L}_{\\mathrm{novel}}$ .", + "bbox": [ + 498, + 349, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Detector with Synthetic Dataset", + "text_level": 1, + "bbox": [ + 500, + 440, + 849, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we augment the real dataset $(\\mathcal{D}_{\\mathrm{real}})$ , with synthetic dataset $(\\mathcal{D}_{\\mathrm{syn}})$ , and train popular object detectors, for example, Faster R-CNN [27] with the standard training loss:", + "bbox": [ + 498, + 464, + 890, + 510 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\det } = \\mathcal {L} _ {\\text {r p n ＿ c l s}} + \\mathcal {L} _ {\\text {r p n ＿ b o x}} + \\mathcal {L} _ {\\det ＿ c l s} + \\mathcal {L} _ {\\det ＿ \\text {b o x}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 520, + 890, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{rpn\\_cls}}$ , $\\mathcal{L}_{\\mathrm{rpn\\_box}}$ are the classification and box regression losses of region proposal network, and $\\mathcal{L}_{\\mathrm{det\\_cls}}$ , $\\mathcal{L}_{\\mathrm{det\\_box}}$ are the classification and box regression losses of the detection head. Generally speaking, the synthetic dataset enables to improve the detector's ability from two aspects: (i) expanding the original data with more categories, (ii) improving the detection performance by increasing data diversity.", + "bbox": [ + 496, + 544, + 890, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Expanding detection categories. The grounding head is designed to be open-vocabulary, that enables to generate object bounding boxes for novel categories, even though it is trained with a specific set of base categories. This feature enables InstaGen to construct a detection dataset for any category. Figure 4 demonstrates several synthetic images and object bounding boxes for novel categories, i.e., the object with red bounding box. We evaluate the effectiveness of training on synthetic dataset through experiments on open-vocabulary detection benchmark. For more details, please refer to Figure 1b and Section 4.2.", + "bbox": [ + 496, + 654, + 890, + 820 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Increasing data diversity. The base diffusion model is trained on a large corpus of image-caption pairs, that enables to generate diverse images. Taking advantage of such capabilities, InstaGen is capable of generating dataset with diverse images and box annotations, which can expand the", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14125", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3f34f8509f35c3a708dc9f9fec3a199d3943b43058d2d8c4d8d3a4f344c55ea9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSupervisionDetectorBackbone\\(AP50_{all}^{box}\\)\\(AP50_{base}^{box}\\)\\(AP50_{novel}^{box}\\)
Detic [41]CLIPFaster R-CNNR5045.047.127.8
PromptDet [5]CLIPFaster R-CNNR50-50.626.6
BARON [34]CLIPFaster R-CNNR5053.560.434.0
OADP [33]CLIPFaster R-CNNR5047.253.330.0
ViLD [9]CLIPMask R-CNNR5051.359.527.6
F-VLM [16]CLIPMask R-CNNR5039.6-28.0
RO-ViT [13]CLIPMask R-CNNViT-B [1]41.5-30.2
VLDet [19]CLIPCenterNet2 [40]R5045.850.632.0
CxORA [35]CLIPDAB-DETR [21]R5035.435.535.1
DK-DETR [17]CLIPDeformable DETR [42]R50-61.132.3
EdaDet [31]CLIPDeformable DETR [42]R5052.557.737.8
InstaGenStable DiffusionFaster R-CNNR5052.355.842.3
", + "bbox": [ + 140, + 88, + 823, + 290 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Results on open-vocabulary COCO benchmark. $\\mathrm{AP50}_{\\text {novel }}^{\\text {box }}$ is the main metric for evaluation. Our detector, trained on synthetic dataset from InstaGen, significantly outperforms state-of-the-art CLIP-based approaches on novel categories.", + "bbox": [ + 75, + 294, + 892, + 324 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "original dataset, i.e., increase the data diversity and improve detection performance, particularly in data-sparse scenarios. We conducted experiments with varying proportions of COCO [20] images as available real data, and show the effectiveness of training on synthetic dataset when the number of real-world images is limited. We refer the readers for more details in Section 4.3, and results in Figure 1c.", + "bbox": [ + 75, + 335, + 470, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 448, + 202, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we use the proposed InstaGen to construct synthetic dataset for training object detectors, i.e., generating images with the corresponding bounding boxes. Specifically, we present the implementation details in Section 4.1. To evaluate the effectiveness of the synthetic dataset for training object detector, we consider three protocols: open-vocabulary object detection (Section 4.2), data-sparse object detection (Section 4.3) and cross-dataset object detection (Section 4.4). Lastly, we conduct ablation studies on the effectiveness of the proposed components and the selection of hyper-parameters (Section 4.5).", + "bbox": [ + 75, + 474, + 468, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 647, + 290, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Network architecture. We build image synthesizer from the pre-trained Stable Diffusion v1.4 [28], and use the CLIP text encoder [24] to get text embedding for the category name. The channel compression layer maps the dimension of visual features to 256, which is implemented with a $3 \\times 3$ convolution. For simplicity, the feature enhancer, language-guided query selection module and cross-modality decoder are designed to the same structure as the ones in [22]. The number of the object queries is set to 900.", + "bbox": [ + 75, + 670, + 468, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Constructing image synthesizer. In our experiments, we first fine-tune the stable diffusion model on a real detection dataset, e.g., the images of base categories. During training, the text encoder of CLIP is kept frozen, while the remaining components are trained for 6 epochs with a batch size of 16 and a learning rate of 1e-4.", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Instance grounding module. We start by constructing the training triplets using base categories i.e., the categories present in the existing dataset. The text prompt for each triplet is constructed by randomly selecting one or two categories. The regional visual features are taken from the image synthesizer time step $t = 1$ , and the oracle ground-truth bounding boxes are obtained using a Mask R-CNN model trained on base categories, as explained in Section 3.3.1.", + "bbox": [ + 496, + 335, + 890, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Subsequently, we train the instance grounding module with these training triplets for 6 epochs, with a batch size of 32. In the 6th epoch, we transfer the weights from the student model to the teacher model, and proceed to train the student for an additional 6 epochs. During this training, the student receives supervised training on the base categories and engages in self-training on novel categories, and the teacher model is updated using exponential moving average (EMA) with a momentum of 0.999. The initial learning rate is set to 1e-4 and is subsequently reduced by a factor of 10 at the 11th epoch, and the score thresholds $\\alpha$ and $\\beta$ are set to 0.8 and 0.4, respectively.", + "bbox": [ + 496, + 455, + 892, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training object detector on combined dataset. In our experiment, we train an object detector (Faster R-CNN [27]) with ResNet-50 [11] as backbone, on a combination of the existing real dataset and the synthetic dataset. Specifically, for synthetic dataset, we randomly select one or two categories at each iteration, construct the text prompts, and feed them as input to generate images along with the corresponding bounding boxes with $\\beta$ of 0.4. Following the standard implementation [27], the detector is trained for 12 epochs ( $1\\times$ learning schedule) unless specified. The initial learning rate is set to 0.01 and then reduced by a factor of 10 at the 8th and the 11th epochs.", + "bbox": [ + 496, + 641, + 893, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Open-vocabulary object detection", + "text_level": 1, + "bbox": [ + 500, + 832, + 795, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental setup. Following the previous works [5, 39], we conduct experiments on the open-vocabulary COCO benchmark, where 48 classes are treated as base categories,", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14126", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bb73ab333d022f716aa7c96c94c8997f470b58f1c7762a8c24bccce5b36123e8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
InstaGen10%25%50%75%100%
X23.329.534.136.137.5
✓28.532.635.837.338.5
", + "bbox": [ + 78, + 89, + 341, + 145 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/69c38325dd2000d73f8c12da3ea304b716e6b8f8dc8d7464215cce3e779d4ce7.jpg", + "table_caption": [ + "Table 2. Results on data-sparse object detection. We employ Faster R-CNN with the ResNet-50 backbone as the default object detector and evaluate its performance using the AP metric on MS COCO benchmark. Please refer to the text for more details." + ], + "table_footnote": [], + "table_body": "
MethodSupervisionDetectorExtra DataObject365LVIS
Gao et al. [7]CLIPCenterNet2✓6.98.0
VL-PLM [39]CLIPMask R-CNN✓10.922.2
InstaGenStable DiffusionFaster R-CNN✗11.423.3
", + "bbox": [ + 364, + 88, + 874, + 166 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c8f1929aee34bca9b3f4200320368aa4157df46290f6b6b13edea82850ec7d48.jpg", + "table_caption": [ + "Table 3. Results on generalizing COCO-base to Object365 and LVIS. All detectors utilize the ResNet-50 backbone. The evaluation protocol follows [7] and reports AP50. Extra data refers to an additional dataset that encompasses objects from the categories within the target dataset. In both experiments, the extra data consists of all the images from COCO, which has covered the majority of categories in Object365 and LVIS." + ], + "table_footnote": [], + "table_body": "
G-headSTFT\\( AP50_{all}^{box} \\)\\( AP50_{base}^{box} \\)\\( AP50_{novel}^{box} \\)
✓50.655.337.1
✓✓51.155.040.3
✓✓✓52.355.842.3
", + "bbox": [ + 93, + 252, + 447, + 323 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. The effectiveness of the proposed components. G-head, ST and FT refer to the grounding head, self-training the grounding head and fine-tuning SDM, respectively.", + "bbox": [ + 75, + 327, + 468, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and 17 classes as the novel categories. More results for LVIS can be found in the supplementary material. To train the grounding head, we employ 1250 synthetic images per category per training epoch. While for training the object detector, we use 3000 synthetic images per category, along with the original real dataset for base categories. The object detector is trained with input size of $800 \\times 800$ and scale jitter. The performance is measured by COCO Average Precision at an Intersection over Union of 0.5 (AP50).", + "bbox": [ + 73, + 388, + 468, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to SOTA. As shown in Table 1, we evaluate the performance by comparing with existing CLIP-based open-vocabulary object detectors. It is clear that our detector trained on synthetic dataset from InstaGen outperforms existing state-of-the-art approaches significantly, i.e., around $+5\\mathrm{AP}$ improvement over the second best. In essence, through the utilization of our proposed open-vocabulary grounding head, InstaGen is able to generate detection data for novel categories, enabling the detector to attain exceptional performance. To the best of our knowledge, this is the first work that applies generative diffusion model for dataset synthesis, to tackle open-vocabulary object detection, and showcase its superiority in this task.", + "bbox": [ + 73, + 529, + 468, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Data-sparse object detection", + "text_level": 1, + "bbox": [ + 75, + 739, + 331, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental setup. Here, we evaluate the effectiveness of synthetic dataset in data-spare scenario, by varying the amount of real data. We randomly select subsets comprising $10\\%$ , $25\\%$ , $50\\%$ , $75\\%$ and $100\\%$ of the COCO training set, this covers all COCO categories. These subsets are used to fine-tune stable diffusion model for constructing image synthesizer, and train a Mask R-CNN for generating oracle ground-truth bounding boxes in synthetic images. We employ 1250 synthetic images per category to train a Faster R-", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CNN in conjunction with the corresponding COCO subset. The performance is measured by Average Precision [20].", + "bbox": [ + 498, + 255, + 888, + 286 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to baseline. As shown in Table 2, the Faster R-CNN trained with synthetic images achieves consistent improvement across various real training data budgets. Notably, as the availability of real data becomes sparse, synthetic dataset plays even more important role for performance improvement, for instance, it improves the detector by $+5.2$ AP $(23.3\\rightarrow 28.5$ AP) when only $10\\%$ real COCO training subset is available.", + "bbox": [ + 498, + 291, + 890, + 412 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Cross-dataset object detection", + "text_level": 1, + "bbox": [ + 500, + 430, + 764, + 446 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental setup. In this section, we assess the effectiveness of synthetic data on a more challenging task, namely cross-dataset object detection. Following [39], we evaluate the COCO-trained model on two unseen datasets: Object365 [30] and LVIS [10]. Specifically, we consider the 48 classes in the open-vocabulary COCO benchmark as the source dataset, while Object365 (with 365 classes) and LVIS (with 1203 classes) serve as the target dataset. When training the instance grounding module, we acquire 1250 synthetic images for base categories from the source dataset, and 100 synthetic images for the category from the target dataset at each training iteration. In the case of training the object detector, we employ 500 synthetic images per category from the target dataset for each training iteration. The detector is trained with input size of $1024 \\times 1024$ and scale jitter [39].", + "bbox": [ + 496, + 455, + 890, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to SOTA. The results presented in Table 3 demonstrate that the proposed InstaGen achieves superior performance in generalization from COCO-base to Object365 and LVIS, when compared to CLIP-based methods such as [7, 39]. It is worth noting that CLIP-based methods require the generation of pseudo-labels for the categories from the target dataset on COCO images, and subsequently train the detector using these images. These methods necessitate a dataset that includes objects belonging to the categories of the target dataset. In contrast, InstaGen possesses the ability to generate images featuring objects of any category without the need for additional datasets, thereby enhancing its versatility across various scenarios.", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14127", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5de6f0f9e9afebf92ea8f9844251a4b0409390ae722aadd3d27459d13aa295b5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
#ImagesAP50boxallAP50boxbaseAP50boxnovel
100051.655.939.7
200051.755.441.1
300052.355.842.3
", + "bbox": [ + 83, + 88, + 333, + 160 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/620c8b3087d3576742b934eec78b2a05aeb5142d535fb0388c255e929e649df1.jpg", + "table_caption": [ + "Table 5. Number of generated images." + ], + "table_footnote": [], + "table_body": "
αAP50boxallAP50boxbaseAP50boxnovel
0.751.355.140.6
0.852.355.842.3
0.951.855.641.1
", + "bbox": [ + 375, + 88, + 602, + 160 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3b4204242bc21184ad9d727dc228e72096802302c6aac6610fda2e2fba08c273.jpg", + "table_caption": [ + "Table 6. $\\alpha$ for bounding-box filtration." + ], + "table_footnote": [], + "table_body": "
βAP50boxallAP50boxbaseAP50boxnovel
0.346.453.326.9
0.452.355.842.3
0.551.255.439.2
", + "bbox": [ + 650, + 88, + 875, + 160 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. $\\beta$ for bounding-box filtration.", + "bbox": [ + 648, + 164, + 877, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 186, + 225, + 203 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To understand the effectiveness of the proposed components, we perform thorough ablation studies on the open-vocabulary COCO benchmark [20], investigating the effect of fine-tuning stable diffusion model, training instance grounding module, self-training on novel categories. Additionally, we investigate other hyper-parameters by comparing the effectiveness of synthetic images and different score thresholds for base and novel categories.", + "bbox": [ + 75, + 212, + 467, + 332 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fine-tuning diffusion model. We assess the effectiveness of fine-tuning stable diffusion model, and its impact for synthesizing images for training object detector. Figure 4c illustrates that InstaGen is capable of generating images with more intricate contexts, featuring multiple objects, small objects, and occluded objects. Subsequently, we employed these generated images to train Faster R-CNN for object detection. The results are presented in Table 4, showing that image synthesizer from fine-tuning stable diffusion model delivers improvement detection performance by 2.0 AP (from 40.3 to 42.3 AP).", + "bbox": [ + 75, + 338, + 467, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Instance grounding module. To demonstrate the effectiveness of the grounding head in open-vocabulary scenario, we exclusively train it on base categories. Visualization examples of the generated images are presented in Figure 4a. These examples demonstrate that the trained grounding head is also capable of predicting bounding boxes for instances from novel categories. Leveraging these generated images to train the object detector leads to a 37.1 AP on novel categories, surpassing or rivaling all existing state-of-the-art methods, as shown in Table 1 and Table 4.", + "bbox": [ + 75, + 510, + 467, + 661 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Self-training scheme. We evaluate the performance after self-training the grounding head with novel categories. As shown in Table 4, training Faster R-CNN with the generated images of novel categories, leads to a noticeable enhancement in detection performance, increasing from 37.1 to 40.3 AP. Qualitatively, it also demonstrates enhanced recall for novel objects after self-training, as shown in Figure 4b.", + "bbox": [ + 75, + 667, + 467, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of synthetic images. We investigate the performance variation while increasing the number of the generated images per category for detector training. As shown in Table 5, when increasing the number of generated images from 1000 to 3000, the detector's performance tends to be increasing monotonically, from 39.7 to 42.3 AP on novel categories, showing the scalability of the proposed training mechanism.", + "bbox": [ + 75, + 779, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Score thresholds for bounding box filtration. We compare the performance with different score thresholds $\\alpha$ and $\\beta$ for filtering bounding boxes on base categories and novel categories, respectively. From the experiment results in Table 6, we observe that the performance is not sensitive to the value of $\\alpha$ , and $\\alpha = 0.8$ yields the best performance. The experimental results using different $\\beta$ are presented in Table 7. With a low score threshold ( $\\alpha = 0.3$ ), there are still numerous inaccurate bounding boxes remaining, resulting in an AP of 26.9 for novel categories. by increasing $\\beta$ to 0.4, numerous inaccurate bounding boxes are filtered out, resulting in optimal performance. Hence, we set $\\alpha = 0.8$ and $\\beta = 0.4$ in our experiments.", + "bbox": [ + 496, + 186, + 890, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation", + "text_level": 1, + "bbox": [ + 500, + 398, + 612, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using synthetic or artificially generated data in training AI algorithms is a burgeoning practice with significant potential. It can address data scarcity, privacy, and bias issues. However, there remains two limitations for training object detectors with synthetic data, (i) synthetic datasets commonly focus on clean, isolated object instances, which limits the exposure of the detector to the complexities and contextual diversity of real-world scenes, such as occlusions, clutter, varied environmental factors, deformation, therefore, models trained on synthetic data struggle to adapt to real-world conditions, affecting their overall robustness and accuracy, (ii) existing diffusion-based generative model also suffers from long-tail issue, that means the generative model struggles to generate images for objects of rare categories, resulting in imbalanced class representation during training and reduced detector performance for less common objects.", + "bbox": [ + 496, + 422, + 890, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 681, + 617, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes a dataset synthesis pipeline, termed as InstaGen, that enables to generate images with object bounding boxes for arbitrary categories, acting as an annotation-free approach for constructing large-scale synthetic dataset to train object detector. We have conducted thorough experiments to show the effectiveness of training on synthetic data, on improving detection performance, or expanding the number of detection categories. Significant improvements have been shown in various detection scenarios, including open-vocabulary $(+4.5\\mathrm{AP})$ and datasparse $(+1.2\\sim 5.2\\mathrm{AP})$ detection.", + "bbox": [ + 496, + 705, + 890, + 871 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. WX is supported by National Key R&D Program of China (No. 2022ZD0161400).", + "bbox": [ + 500, + 872, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14128", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020. 6", + "[2] Yu Du, Fangyun Wei, Zihe Zhang, Miaojing Shi, Yue Gao, and Guoqi Li. Learning to prompt for open-vocabulary object detection with vision-language model. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 6" + ], + "bbox": [ + 78, + 90, + 468, + 742 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14130", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/InstaGen_ Enhancing Object Detection by Training on Synthetic Dataset/44612d68-2249-4388-abaf-3d6e6fc8d9fa_model.json b/2024/InstaGen_ Enhancing Object Detection by Training on Synthetic Dataset/44612d68-2249-4388-abaf-3d6e6fc8d9fa_model.json new file mode 100644 index 0000000000000000000000000000000000000000..930bb555c4de99fb1c743c8901e7b0410291e4fc --- /dev/null +++ b/2024/InstaGen_ Enhancing Object Detection by Training on Synthetic Dataset/44612d68-2249-4388-abaf-3d6e6fc8d9fa_model.json @@ -0,0 +1,2090 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.12, + 0.131, + 0.851, + 0.153 + ], + "angle": 0, + "content": "InstaGen: Enhancing Object Detection by Training on Synthetic Dataset" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.17, + 0.782, + 0.227 + ], + "angle": 0, + "content": "Chengjian Feng1 Yujie Zhong1 Zequn Jie1,† Weidi Xie2,† Lin Ma1 \n1 Meituan Inc. 2 CMIC, Shanghai Jiao Tong University \nhttps://fcjian.github.io/InstaGen" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.241, + 0.271, + 0.25 + ], + "angle": 0, + "content": "Stable Diffusion: Image synthesis (collection)" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.251, + 0.432, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.307, + 0.345, + 0.316 + ], + "angle": 0, + "content": "InstaGen: Image synthesis (collection) & Annotation generation" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.317, + 0.432, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.376, + 0.43, + 0.397 + ], + "angle": 0, + "content": "(a) Demonstration of the synthetic images generated from Stable Diffusion and InstaGen with text prompt: 'a photograph of [base category] and [novel category]." + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.244, + 0.679, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.376, + 0.676, + 0.397 + ], + "angle": 0, + "content": "(b) The detection AP of novel categories of different paradigms on COCO-OVD benchmarks." + }, + { + "type": "image", + "bbox": [ + 0.686, + 0.244, + 0.888, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.697, + 0.376, + 0.888, + 0.397 + ], + "angle": 0, + "content": "(c) The detection AP with respect to the portion \\((\\%)\\) of real data (COCO) usage." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.405, + 0.894, + 0.462 + ], + "angle": 0, + "content": "Figure 1. (a) The synthetic images generated from Stable Diffusion and our proposed InstaGen, which can serve as a dataset synthesizer for sourcing photo-realistic images and instance bounding boxes at scale. (b) On open-vocabulary detection, training on synthetic images demonstrates significant improvement over CLIP-based methods on novel categories. (c) Training on the synthetic images generated from InstaGen also enhances the detection performance in close-set scenarios, particularly in data-sparse circumstances." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.475, + 0.314, + 0.491 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.501, + 0.474, + 0.775 + ], + "angle": 0, + "content": "In this paper, we present a novel paradigm to enhance the ability of object detector, e.g., expanding categories or improving detection performance, by training on synthetic dataset generated from diffusion models. Specifically, we integrate an instance-level grounding head into a pretrained, generative diffusion model, to augment it with the ability of localising instances in the generated images. The grounding head is trained to align the text embedding of category names with the regional visual feature of the diffusion model, using supervision from an off-the-shelf object detector, and a novel self-training scheme on (novel) categories not covered by the detector. We conduct thorough experiments to show that, this enhanced version of diffusion model, termed as InstaGen, can serve as a data synthesizer, to enhance object detectors by training on its generated samples, demonstrating superior performance over existing state-of-the-art methods in open-vocabulary (+4.5 AP) and data-sparse (+1.2 ~ 5.2 AP) scenarios." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.79, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.47, + 0.878 + ], + "angle": 0, + "content": "Object detection has been extensively studied in the field of computer vision, focusing on the localization and categorization of objects within images [3, 5, 12, 26, 27]. The common practise is to train the detectors on large-scale im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.548 + ], + "angle": 0, + "content": "age datasets, such as MS-COCO [20] and Object365 [30], where objects are exhaustively annotated with bounding boxes and corresponding category labels. However, the procedure for collecting images and annotations is often laborious and time-consuming, limiting the datasets' scalability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.893, + 0.763 + ], + "angle": 0, + "content": "In the recent literature, text-to-image diffusion models have demonstrated remarkable success in generating high-quality images [28, 29], that unlocks the possibility of training vision systems with synthetic images. In general, existing text-to-image diffusion models are capable of synthesizing images based on some free-form text prompt, as shown in the first row of Figure 1a. Despite being photorealistic, such synthesized images can not support training sophisticated systems, that normally requires the inclusion of instance-level annotations, e.g., bounding boxes for object detection in our case. In this paper, we investigate a novel paradigm of dataset synthesis for training object detector, i.e., augmenting the text-to-image diffusion model to generate instance-level bounding boxes along with images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To begin with, we build an image synthesizer by fine-tuning the diffusion model on existing detection dataset. This is driven by the observation that off-the-shelf diffusion models often generate images with only one or two objects on simplistic background, training detectors on such images may thus lead to reduced robustness in complex real-world scenarios. Specifically, we exploit the existing detection dataset, and subsequently fine-tune the diffusion model with the image-caption pairs, constructed by taking" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.888, + 0.212, + 0.901 + ], + "angle": 0, + "content": "†: corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "14121" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.181 + ], + "angle": 0, + "content": "random image crops, and composing the category name of the objects in the crop. As illustrated in the second row of the Figure 1a, once finetuned, the image synthesizer now enables to produce images with multiple objects and intricate contexts, thereby providing a more accurate simulation of real-world detection scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.47, + 0.424 + ], + "angle": 0, + "content": "To generate bounding boxes for objects within synthetic images, we propose an instance grounding module that establishes the correlation between the regional visual features from diffusion model and the text embedding of category names, and infers the coordinates for the objects' bounding boxes. Specifically, we adopt a two-step training strategies, firstly, we train the grounding module on synthetic images, with the supervision from an off-the-shelf object detector, which has been trained on a set of base categories; secondly, we utilize the trained grounding head to generate pseudo labels for a larger set of categories, including those not seen in existing detection dataset, and selftrain the grounding module. Once finished training, the grounding module will be able to identify the objects of arbitrary category and their bounding boxes in the synthetic image, by simply providing the name in free-form language." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.471, + 0.742 + ], + "angle": 0, + "content": "To summarize, we explore a novel approach to enhance object detection capabilities, such as expanding detectable categories and improving overall detection performance, by training on synthetic dataset generated from diffusion model. We make the following contribution: (i) We develop an image synthesizer by fine-tuning the diffusion model, with image-caption pairs derived from existing object detection datasets, our synthesizer can generate images with multiple objects and complex contexts, offering a more realistic simulation for real-world detection scenarios. (ii) We introduce a data synthesis framework for detection, termed as InstaGen. This is achieved through a novel grounding module that enables to generate labels and bounding boxes for objects in synthetic images. (iii) We train standard object detectors on the combination of real and synthetic dataset, and demonstrate superior performance over existing state-of-the-art detectors across various benchmarks, including open-vocabulary detection (increasing Average Precision [AP] by +4.5), data-sparse detection (enhancing AP by +1.2 to +5.2), and cross-dataset transfer (boosting AP by +0.5 to +1.1)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.22, + 0.77 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Object Detection. Object detection aims to simultaneously predict the category and corresponding bounding box for the objects in the images. Generally, object detectors [3, 4, 6, 26, 27] are trained on a substantial amount of training data with bounding box annotations and can only recognize a predetermined set of categories present in the training data. In the recent literature, to further expand the ability of object detector, open-vocabulary object detec" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "tion (OVD) has been widely researched, for example, OVR-CNN [37] introduces the concept of OVD and pre-trains a vision-language model with image-caption pairs. The subsequent works make use of the robust multi-modal representation of CLIP [24], and transfer its knowledge to object detectors through knowledge distillation [9, 36], exploiting extra data [5, 41] and text prompt tuning [2, 5]. In this paper, we propose to expand the ability of object detectors, e.g., expanding categories or improving detection performance, by training on synthetic dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.893, + 0.535 + ], + "angle": 0, + "content": "Generative Models. Image generation has been considered as a task of interest in computer vision for decades. In the recent literature, significant progress has been made, for example, the generative adversarial networks (GANs) [8], variational autoencoders (VAEs) [15], flow-based models [14], and autoregressive models (ARMs) [32]. More recently, there has been a growing research interest in diffusion probabilistic models (DPMs), which have shown great promise in generating high-quality images across diverse datasets. For examples, GLIDE [23] utilizes a pre-trained language model and a cascaded diffusion structure for text-to-image generation. DALL-E 2 [25] is trained to generate images by inverting the CLIP image space, while Imagegen [29] explores the advantages of using pre-trained language models. Stable Diffusion [28] proposes the diffusion process in VAE latent spaces rather than pixel spaces, effectively reducing resource consumption. In general, the rapid development of generative models opens the possibility for training large models with synthetic dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.634, + 0.568 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.639 + ], + "angle": 0, + "content": "In this section, we present details for constructing a dataset synthesizer, that enables to generate photo-realistic images with bounding boxes for each object instance, and train an object detector on the combined real and synthetic datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.704, + 0.665 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Given a detection dataset of real images with manual annotations, i.e., \\(\\mathcal{D}_{\\mathrm{real}} = \\{(x_1,\\mathcal{B}_1,\\mathcal{Y}_1),\\ldots ,(x_N,\\mathcal{B}_N,\\mathcal{Y}_N)\\}\\) where \\(\\mathcal{B}_i = \\{b_1,\\dots ,b_m|b_j\\in \\mathbb{R}^{2\\times 2}\\}\\) denotes the set of box coordinates for the annotated instances in one image, and \\(\\mathcal{V}_i = \\{y_1,\\dots ,y_m|y_j\\in \\mathcal{R}^{\\mathcal{C}_{\\mathrm{base}}}\\}\\) refers to the categories of the instances. Our goal is thus to exploit the given real dataset \\((\\mathcal{D}_{\\mathrm{real}})\\), to steer a generative diffusion model into dataset synthesizer, that enables to augment the existing detection dataset, i.e., \\(\\mathcal{D}_{\\mathrm{final}} = \\mathcal{D}_{\\mathrm{real}} + \\mathcal{D}_{\\mathrm{syn}}\\). As a result, detectors trained on the combined dataset demonstrate enhanced ability, i.e., extending the detection categories or improving the detection performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the following sections, we first describe the procedure for constructing an image synthesizer, that can generate images suitable for training object detector (Section 3.2). To" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14122" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.098, + 0.468, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.265, + 0.414, + 0.278 + ], + "angle": 0, + "content": "(a) Fine-tuning diffusion model on detection dataset." + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.09, + 0.885, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.265, + 0.885, + 0.278 + ], + "angle": 0, + "content": "(b) Supervised training and self-training for grounding head (i.e. student)." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.283, + 0.893, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Illustration of the process for finetuning diffusion model and training the grounding head: (a) stable diffusion model is fine-tuned on the detection dataset on base categories. (b) The grounding head is trained on synthetic images, with supervised learning on base categories and self-training on novel categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.534 + ], + "angle": 0, + "content": "simultaneously generate the images and object bounding boxes, we propose a novel instance-level grounding module, which aligns the text embedding of category name with the regional visual features from image synthesizer, and infers the coordinates for the objects in synthetic images. To further improve the alignment towards objects of arbitrary category, we adopt self-training to tune the grounding module on object categories not existing in \\(\\mathcal{D}_{\\mathrm{real}}\\) (Section 3.3). As a result, the proposed model, termed as InstaGen, can automatically generate images along with bounding boxes for object instances, and construct synthetic dataset \\((\\mathcal{D}_{\\mathrm{syn}})\\) at scale, leading to improved ability when training detectors on it (Section 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.542, + 0.416, + 0.558 + ], + "angle": 0, + "content": "3.2. Image Synthesizer for Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Here, we build our image synthesizer based on an off-the-shelf stable diffusion model (SDM [28]). Despite of its impressive ability in generating photo-realistic images, it often outputs images with only one or two objects on simplistic background with the text prompts, for example, 'a photograph of a [category1 name] and a [category2 name]' as demonstrated in Figure 4b. As a result, object detectors trained on such images may exhibit reduced robustness when dealing with complex real-world scenarios. To bridge such domain gap, we propose to construct the image synthesizer by fine-tuning the SDM with an existing real-world detection dataset \\((\\mathcal{D}_{\\mathrm{real}})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Fine-tuning procedure. To fine-tune the stable diffusion model (SDM), one approach is to naively use the sample from detection dataset, for example, randomly pick an image and construct the text prompt with all categories in the image. However, as the image often contains multiple objects, such approach renders significant difficulty for fine-tuning the SDM, especially for small or occluded objects. We adopt a mild strategy by taking random crops from the images, and construct the text prompt with categories in the image crops, as shown in Figure 2a. If an image crop con" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.368 + ], + "angle": 0, + "content": "tains multiple objects of the same category, we only use this category name once in the text prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.893, + 0.416 + ], + "angle": 0, + "content": "Fine-tuning loss. We use the sampled image crop and constructed text prompt to fine-tune SDM with a squared error loss on the predicted noise term as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.416, + 0.892, + 0.443 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f i n e - t u n e}} = \\mathbb {E} _ {z, \\epsilon \\sim \\mathcal {N} (0, 1), t, y} \\left[ | | \\epsilon - \\epsilon_ {\\theta} \\left(z ^ {t}, t, y\\right) | | _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.893, + 0.555 + ], + "angle": 0, + "content": "where \\(z\\) denotes a latent vector mapped from the input image with VAE, \\(t\\) denotes the denoising step, uniformly sampled from \\(\\{1,\\dots ,T\\}\\), \\(T\\) refers to the length of the diffusion Markov chain, and \\(\\epsilon_{\\theta}\\) refers to the estimated noise from SDM with parameters \\(\\theta\\) being updated. We have experimentally verified the necessity of this fine-tuning step, as shown in Table 4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.565, + 0.849, + 0.581 + ], + "angle": 0, + "content": "3.3. Dataset Synthesizer for Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.893, + 0.816 + ], + "angle": 0, + "content": "In this section, we present details for steering the image synthesizer into dataset synthesizer for object detection, which enables to simultaneously generate images and object bounding boxes. Specifically, we propose an instance-level grounding module that aligns the text embedding of object category, with the regional visual feature of the diffusion model, and infers the coordinates for bounding boxes, effectively augmenting the image synthesizer with instance grounding, as shown in Figure 3. To further improve the alignment in large visual diversity, we propose a self-training scheme that enables the grounding module to generalise towards arbitrary categories, including those not exist in real detection dataset \\((\\mathcal{D}_{\\mathrm{real}})\\). As a result, our data synthesizer, termed as InstaGen, can be used to construct synthetic dataset for training object detectors." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.823, + 0.831, + 0.838 + ], + "angle": 0, + "content": "3.3.1 Instance Grounding on Base Categories" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To localise the object instances in synthetic images, we introduce an open-vocabulary grounding module, that aims to simultaneously generate image \\((x)\\) and the corresponding instance-level bounding boxes \\((\\mathcal{B})\\) based on a set of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14123" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.891, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.893, + 0.388 + ], + "angle": 0, + "content": "Figure 3. Illustration of the dataset generation process in InstaGen. The data generation process consists of two steps: (i) Image collection: given a text prompt, SDM generates images with the objects described in the text prompt; (ii) Annotation generation: the instance-level grounding head aligns the category embedding with the visual feature region of SDM, generating the corresponding object bounding-boxes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.47, + 0.434 + ], + "angle": 0, + "content": "categories \\((\\mathcal{V})\\), i.e., \\(\\{x, \\mathcal{B}, \\mathcal{Y}\\} = \\Phi_{\\mathrm{InstaGen}}(\\epsilon, \\mathcal{Y})\\), where \\(\\epsilon \\sim \\mathcal{N}(0, I)\\) denotes the sampled noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.593 + ], + "angle": 0, + "content": "To this end, we propose an instance grounding head, as shown in Figure 3, it takes the intermediate representation from image synthesizer and the text embedding of category as inputs, then predicts the corresponding object bounding boxes, i.e., \\(\\{\\mathcal{B}_i,\\mathcal{Y}_i\\} = \\Phi_{\\mathrm{g - head}}(\\mathcal{F}_i,\\Phi_{\\mathrm{t - enc}}(g(\\mathcal{Y}_i)))\\) , where \\(\\mathcal{F}_i = \\{f_i^1,\\dots ,f_i^n\\}\\) refers to the multi-scale dense features from the image synthesizer at time step \\(t = 1\\) \\(g(\\cdot)\\) denotes a template that decorates each of the visual categories in the text prompt, e.g., 'a photograph of [category1 name] and [category2 name], \\(\\Phi_{\\mathrm{t - enc}}(\\cdot)\\) denotes the text encoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Inspired by GroundingDINO [22], our grounding head \\(\\Phi_{\\mathrm{g - head}}(\\cdot)\\) mainly contains four components: (i) a channel-compression layer, implemented with a \\(3\\times 3\\) convolution, for reducing the dimensionality of the visual features; (ii) a feature enhancer, consisting of six feature enhancer layers, to fuse the visual and text features. Each layer employs a deformable self-attention to enhance image features, a vanilla self-attention for text feature enhancers, an image-to-text cross-attention and a text-to-image cross-attention for feature fusion; (iii) a language-guided query selection module for query initialization. This module predicts top-\\(N\\) anchor boxes based on the similarity between text features and image features. Following DINO [38], it adopts a mixed query selection where the positional queries are initialized with the anchor boxes and the content queries remain learnable; (iv) a cross-modality decoder for classification and box refinement. It comprises six decoder layers, with each layer utilizing a self-attention mechanism for query interaction, an image cross-attention layer for combining image features, and a text cross-attention layer for combining text" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.893, + 0.584 + ], + "angle": 0, + "content": "features. Finally, we apply the dot product between each query and the text features, followed by a Sigmoid function to predict the classification score \\(\\hat{s}\\) for each category. Additionally, the object queries are passed through a Multi-Layer Perceptron (MLP) to predict the object bounding boxes \\(\\hat{b}\\), as shown in Figure 3. We train the grounding head by aligning the category embedding with the regional visual features from diffusion model, as detailed below. Once trained, the grounding head is open-vocabulary, i.e., given any categories (even beyond the training categories), the grounding head can generate the corresponding bounding-boxes for the object instances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Training triplets of base categories. Following [18], we apply an automatic pipeline to construct the \\(\\{\\) visual feature, bounding-box, text prompt\\} triplets, with an object detector trained on base categories from a given dataset \\((D_{\\mathrm{real}})\\). In specific, assuming there exists a set of base categories \\(\\{c_{\\mathrm{base}}^{1},\\ldots ,c_{\\mathrm{base}}^{N}\\}\\), e.g., the classes in MS-COCO [20]. We first select a random number of base categories to construct a text prompt, e.g., 'a photograph of [base category1] and [base category2]' and generate both the visual features and images with our image synthesizer. Then we take an off-the-shelf object detector, for example, pre-trained Mask R-CNN [12], to run the inference procedure on the synthetic images, and infer the bounding boxes of the selected categories. To acquire the confident bounding-boxes for training, we use a score threshold \\(\\alpha\\) to filter out the bounding-boxes with low confidence (an ablation study on the selection of the score threshold has been conducted in Section 4.5). As a result, an infinite number of training triplets for the given base categories can be constructed by repeating the above operation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14124" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.163, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.166, + 0.089, + 0.249, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.09, + 0.335, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.224, + 0.337, + 0.249 + ], + "angle": 0, + "content": "(a) Stable Diffusion \\(^+\\) Grounding head w/ Supervised training." + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.091, + 0.439, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.091, + 0.525, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.091, + 0.611, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.224, + 0.612, + 0.248 + ], + "angle": 0, + "content": "(b) Stable Diffusion + Grounding head w/ Supervised- and Self-training." + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.091, + 0.713, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.717, + 0.091, + 0.799, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.803, + 0.091, + 0.885, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.224, + 0.887, + 0.248 + ], + "angle": 0, + "content": "(c) Stable Diffusion w/ Fine-tuning + Grounding head w/ Supervised- and Self-training." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.254, + 0.892, + 0.281 + ], + "angle": 0, + "content": "Figure 4. Visualization of the synthetic images and bounding-boxes generated from different models. The bounding-boxes with green denote the objects from base categories, while the ones with red denote the objects from novel categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.468, + 0.331 + ], + "angle": 0, + "content": "Training loss. We use the constructed training triplets to train the grounding head:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.336, + 0.469, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b a s e}} = \\sum_ {i = 1} ^ {N} \\left[ \\mathcal {L} _ {\\operatorname {c l s}} \\left(\\hat {s} _ {i}, c _ {i}\\right) + \\mathbb {1} _ {\\{c _ {i} \\neq \\emptyset \\}} \\mathcal {L} _ {\\text {b o x}} \\left(\\hat {b} _ {i}, b _ {i}\\right) \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.469, + 0.463 + ], + "angle": 0, + "content": "where the \\(i\\)th prediction \\((\\hat{s}_i, \\hat{b}_i)\\) from the \\(N\\) object queries is assigned to a ground-truth \\((c_i, b_i)\\) or \\(\\varnothing\\) (no object) with bipartite matching. \\(\\mathcal{L}_{\\mathrm{cls}}\\) and \\(\\mathcal{L}_{\\mathrm{box}}\\) denote the classification loss (e.g. Focal loss) and box regression loss (e.g. L1 loss and GIoU loss), respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.481, + 0.414, + 0.496 + ], + "angle": 0, + "content": "3.3.2 Instance Grounding on Novel Categories" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.469, + 0.64 + ], + "angle": 0, + "content": "Till here, we have obtained a diffusion model with open-vocabulary grounding, which has been only trained with base categories. In this section, we propose to further leverage the synthetic training triplets from a wider range of categories to enhance the alignment for novel/unseen categories. Specifically, as shown in Figure 2b, we describe a framework that generates the training triplets for novel categories using the grounded diffusion model, and then selftrain the grounding head." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Training triplets of novel categories. We design the text prompts of novel categories, e.g., 'a photograph of [novel category1] and [novel category2], and pass them through our proposed image synthesizer, to generate the visual features. To acquire the corresponding bounding-boxes for novel categories, we propose a self-training scheme that takes the above grounding head as the student, and apply a mean teacher (an exponential moving average (EMA) of the student model) to create pseudo labels for update. In contrast to the widely adopted self-training scheme that takes the image as input, the student and teacher in our case only take the visual features as input, thus cannot apply data augmentation as for images. Instead, we insert dropout module within each feature enhancer layer and decoder layer in the student. During training, we run inference (without dropout module) with teacher model on the visual features to produce bounding boxes, and then use a score threshold \\(\\beta\\) to" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.301, + 0.891, + 0.347 + ], + "angle": 0, + "content": "filter out those with low confidence, and use the remaining training triplets \\((\\mathcal{F}_i,\\hat{b}_i,y_i^{\\mathrm{novel}})\\) to train the student, i.e., grounding head." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.351, + 0.892, + 0.428 + ], + "angle": 0, + "content": "Training loss. Now, we can also train the grounding head on the mined triplets of novel categories (that are unseen in the existing real dataset) with the training loss \\(\\mathcal{L}_{\\mathrm{novel}}\\) defined similar to Eq. 2. Thus, the total training loss for training the grounding head can be: \\(\\mathcal{L}_{\\mathrm{grounding}} = \\mathcal{L}_{\\mathrm{base}} + \\mathcal{L}_{\\mathrm{novel}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.441, + 0.85, + 0.457 + ], + "angle": 0, + "content": "3.4. Training Detector with Synthetic Dataset" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.465, + 0.892, + 0.511 + ], + "angle": 0, + "content": "In this section, we augment the real dataset \\((\\mathcal{D}_{\\mathrm{real}})\\), with synthetic dataset \\((\\mathcal{D}_{\\mathrm{syn}})\\), and train popular object detectors, for example, Faster R-CNN [27] with the standard training loss:" + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.521, + 0.891, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\det } = \\mathcal {L} _ {\\text {r p n ＿ c l s}} + \\mathcal {L} _ {\\text {r p n ＿ b o x}} + \\mathcal {L} _ {\\det ＿ c l s} + \\mathcal {L} _ {\\det ＿ \\text {b o x}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.652 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{rpn\\_cls}}\\), \\(\\mathcal{L}_{\\mathrm{rpn\\_box}}\\) are the classification and box regression losses of region proposal network, and \\(\\mathcal{L}_{\\mathrm{det\\_cls}}\\), \\(\\mathcal{L}_{\\mathrm{det\\_box}}\\) are the classification and box regression losses of the detection head. Generally speaking, the synthetic dataset enables to improve the detector's ability from two aspects: (i) expanding the original data with more categories, (ii) improving the detection performance by increasing data diversity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.821 + ], + "angle": 0, + "content": "Expanding detection categories. The grounding head is designed to be open-vocabulary, that enables to generate object bounding boxes for novel categories, even though it is trained with a specific set of base categories. This feature enables InstaGen to construct a detection dataset for any category. Figure 4 demonstrates several synthetic images and object bounding boxes for novel categories, i.e., the object with red bounding box. We evaluate the effectiveness of training on synthetic dataset through experiments on open-vocabulary detection benchmark. For more details, please refer to Figure 1b and Section 4.2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Increasing data diversity. The base diffusion model is trained on a large corpus of image-caption pairs, that enables to generate diverse images. Taking advantage of such capabilities, InstaGen is capable of generating dataset with diverse images and box annotations, which can expand the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14125" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.141, + 0.089, + 0.825, + 0.291 + ], + "angle": 0, + "content": "
MethodSupervisionDetectorBackbone\\(AP50_{all}^{box}\\)\\(AP50_{base}^{box}\\)\\(AP50_{novel}^{box}\\)
Detic [41]CLIPFaster R-CNNR5045.047.127.8
PromptDet [5]CLIPFaster R-CNNR50-50.626.6
BARON [34]CLIPFaster R-CNNR5053.560.434.0
OADP [33]CLIPFaster R-CNNR5047.253.330.0
ViLD [9]CLIPMask R-CNNR5051.359.527.6
F-VLM [16]CLIPMask R-CNNR5039.6-28.0
RO-ViT [13]CLIPMask R-CNNViT-B [1]41.5-30.2
VLDet [19]CLIPCenterNet2 [40]R5045.850.632.0
CxORA [35]CLIPDAB-DETR [21]R5035.435.535.1
DK-DETR [17]CLIPDeformable DETR [42]R50-61.132.3
EdaDet [31]CLIPDeformable DETR [42]R5052.557.737.8
InstaGenStable DiffusionFaster R-CNNR5052.355.842.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.295, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Table 1. Results on open-vocabulary COCO benchmark. \\( \\mathrm{AP50}_{\\text {novel }}^{\\text {box }} \\) is the main metric for evaluation. Our detector, trained on synthetic dataset from InstaGen, significantly outperforms state-of-the-art CLIP-based approaches on novel categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.471, + 0.442 + ], + "angle": 0, + "content": "original dataset, i.e., increase the data diversity and improve detection performance, particularly in data-sparse scenarios. We conducted experiments with varying proportions of COCO [20] images as available real data, and show the effectiveness of training on synthetic dataset when the number of real-world images is limited. We refer the readers for more details in Section 4.3, and results in Figure 1c." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.449, + 0.203, + 0.466 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.47, + 0.641 + ], + "angle": 0, + "content": "In this section, we use the proposed InstaGen to construct synthetic dataset for training object detectors, i.e., generating images with the corresponding bounding boxes. Specifically, we present the implementation details in Section 4.1. To evaluate the effectiveness of the synthetic dataset for training object detector, we consider three protocols: open-vocabulary object detection (Section 4.2), data-sparse object detection (Section 4.3) and cross-dataset object detection (Section 4.4). Lastly, we conduct ablation studies on the effectiveness of the proposed components and the selection of hyper-parameters (Section 4.5)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.648, + 0.292, + 0.664 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.47, + 0.806 + ], + "angle": 0, + "content": "Network architecture. We build image synthesizer from the pre-trained Stable Diffusion v1.4 [28], and use the CLIP text encoder [24] to get text embedding for the category name. The channel compression layer maps the dimension of visual features to 256, which is implemented with a \\(3 \\times 3\\) convolution. For simplicity, the feature enhancer, language-guided query selection module and cross-modality decoder are designed to the same structure as the ones in [22]. The number of the object queries is set to 900." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Constructing image synthesizer. In our experiments, we first fine-tune the stable diffusion model on a real detection dataset, e.g., the images of base categories. During training, the text encoder of CLIP is kept frozen, while the remaining components are trained for 6 epochs with a batch size of 16 and a learning rate of 1e-4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Instance grounding module. We start by constructing the training triplets using base categories i.e., the categories present in the existing dataset. The text prompt for each triplet is constructed by randomly selecting one or two categories. The regional visual features are taken from the image synthesizer time step \\( t = 1 \\), and the oracle ground-truth bounding boxes are obtained using a Mask R-CNN model trained on base categories, as explained in Section 3.3.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.893, + 0.638 + ], + "angle": 0, + "content": "Subsequently, we train the instance grounding module with these training triplets for 6 epochs, with a batch size of 32. In the 6th epoch, we transfer the weights from the student model to the teacher model, and proceed to train the student for an additional 6 epochs. During this training, the student receives supervised training on the base categories and engages in self-training on novel categories, and the teacher model is updated using exponential moving average (EMA) with a momentum of 0.999. The initial learning rate is set to 1e-4 and is subsequently reduced by a factor of 10 at the 11th epoch, and the score thresholds \\(\\alpha\\) and \\(\\beta\\) are set to 0.8 and 0.4, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.894, + 0.823 + ], + "angle": 0, + "content": "Training object detector on combined dataset. In our experiment, we train an object detector (Faster R-CNN [27]) with ResNet-50 [11] as backbone, on a combination of the existing real dataset and the synthetic dataset. Specifically, for synthetic dataset, we randomly select one or two categories at each iteration, construct the text prompts, and feed them as input to generate images along with the corresponding bounding boxes with \\(\\beta\\) of 0.4. Following the standard implementation [27], the detector is trained for 12 epochs (\\(1\\times\\) learning schedule) unless specified. The initial learning rate is set to 0.01 and then reduced by a factor of 10 at the 8th and the 11th epochs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.796, + 0.849 + ], + "angle": 0, + "content": "4.2. Open-vocabulary object detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Experimental setup. Following the previous works [5, 39], we conduct experiments on the open-vocabulary COCO benchmark, where 48 classes are treated as base categories," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14126" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.342, + 0.146 + ], + "angle": 0, + "content": "
InstaGen10%25%50%75%100%
X23.329.534.136.137.5
✓28.532.635.837.338.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.155, + 0.342, + 0.238 + ], + "angle": 0, + "content": "Table 2. Results on data-sparse object detection. We employ Faster R-CNN with the ResNet-50 backbone as the default object detector and evaluate its performance using the AP metric on MS COCO benchmark. Please refer to the text for more details." + }, + { + "type": "table", + "bbox": [ + 0.365, + 0.089, + 0.875, + 0.167 + ], + "angle": 0, + "content": "
MethodSupervisionDetectorExtra DataObject365LVIS
Gao et al. [7]CLIPCenterNet2✓6.98.0
VL-PLM [39]CLIPMask R-CNN✓10.922.2
InstaGenStable DiffusionFaster R-CNN✗11.423.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.356, + 0.17, + 0.888, + 0.24 + ], + "angle": 0, + "content": "Table 3. Results on generalizing COCO-base to Object365 and LVIS. All detectors utilize the ResNet-50 backbone. The evaluation protocol follows [7] and reports AP50. Extra data refers to an additional dataset that encompasses objects from the categories within the target dataset. In both experiments, the extra data consists of all the images from COCO, which has covered the majority of categories in Object365 and LVIS." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.253, + 0.449, + 0.324 + ], + "angle": 0, + "content": "
G-headSTFT\\( AP50_{all}^{box} \\)\\( AP50_{base}^{box} \\)\\( AP50_{novel}^{box} \\)
✓50.655.337.1
✓✓51.155.040.3
✓✓✓52.355.842.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.328, + 0.47, + 0.371 + ], + "angle": 0, + "content": "Table 4. The effectiveness of the proposed components. G-head, ST and FT refer to the grounding head, self-training the grounding head and fine-tuning SDM, respectively." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.389, + 0.469, + 0.526 + ], + "angle": 0, + "content": "and 17 classes as the novel categories. More results for LVIS can be found in the supplementary material. To train the grounding head, we employ 1250 synthetic images per category per training epoch. While for training the object detector, we use 3000 synthetic images per category, along with the original real dataset for base categories. The object detector is trained with input size of \\(800 \\times 800\\) and scale jitter. The performance is measured by COCO Average Precision at an Intersection over Union of 0.5 (AP50)." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.53, + 0.469, + 0.727 + ], + "angle": 0, + "content": "Comparison to SOTA. As shown in Table 1, we evaluate the performance by comparing with existing CLIP-based open-vocabulary object detectors. It is clear that our detector trained on synthetic dataset from InstaGen outperforms existing state-of-the-art approaches significantly, i.e., around \\(+5\\mathrm{AP}\\) improvement over the second best. In essence, through the utilization of our proposed open-vocabulary grounding head, InstaGen is able to generate detection data for novel categories, enabling the detector to attain exceptional performance. To the best of our knowledge, this is the first work that applies generative diffusion model for dataset synthesis, to tackle open-vocabulary object detection, and showcase its superiority in this task." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.74, + 0.332, + 0.757 + ], + "angle": 0, + "content": "4.3. Data-sparse object detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Experimental setup. Here, we evaluate the effectiveness of synthetic dataset in data-spare scenario, by varying the amount of real data. We randomly select subsets comprising \\(10\\%\\), \\(25\\%\\), \\(50\\%\\), \\(75\\%\\) and \\(100\\%\\) of the COCO training set, this covers all COCO categories. These subsets are used to fine-tune stable diffusion model for constructing image synthesizer, and train a Mask R-CNN for generating oracle ground-truth bounding boxes in synthetic images. We employ 1250 synthetic images per category to train a Faster R-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.256, + 0.89, + 0.287 + ], + "angle": 0, + "content": "CNN in conjunction with the corresponding COCO subset. The performance is measured by Average Precision [20]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.292, + 0.892, + 0.413 + ], + "angle": 0, + "content": "Comparison to baseline. As shown in Table 2, the Faster R-CNN trained with synthetic images achieves consistent improvement across various real training data budgets. Notably, as the availability of real data becomes sparse, synthetic dataset plays even more important role for performance improvement, for instance, it improves the detector by \\(+5.2\\) AP \\((23.3\\rightarrow 28.5\\) AP) when only \\(10\\%\\) real COCO training subset is available." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.431, + 0.766, + 0.447 + ], + "angle": 0, + "content": "4.4. Cross-dataset object detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.699 + ], + "angle": 0, + "content": "Experimental setup. In this section, we assess the effectiveness of synthetic data on a more challenging task, namely cross-dataset object detection. Following [39], we evaluate the COCO-trained model on two unseen datasets: Object365 [30] and LVIS [10]. Specifically, we consider the 48 classes in the open-vocabulary COCO benchmark as the source dataset, while Object365 (with 365 classes) and LVIS (with 1203 classes) serve as the target dataset. When training the instance grounding module, we acquire 1250 synthetic images for base categories from the source dataset, and 100 synthetic images for the category from the target dataset at each training iteration. In the case of training the object detector, we employ 500 synthetic images per category from the target dataset for each training iteration. The detector is trained with input size of \\(1024 \\times 1024\\) and scale jitter [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison to SOTA. The results presented in Table 3 demonstrate that the proposed InstaGen achieves superior performance in generalization from COCO-base to Object365 and LVIS, when compared to CLIP-based methods such as [7, 39]. It is worth noting that CLIP-based methods require the generation of pseudo-labels for the categories from the target dataset on COCO images, and subsequently train the detector using these images. These methods necessitate a dataset that includes objects belonging to the categories of the target dataset. In contrast, InstaGen possesses the ability to generate images featuring objects of any category without the need for additional datasets, thereby enhancing its versatility across various scenarios." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14127" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.334, + 0.161 + ], + "angle": 0, + "content": "
#ImagesAP50boxallAP50boxbaseAP50boxnovel
100051.655.939.7
200051.755.441.1
300052.355.842.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.095, + 0.165, + 0.324, + 0.179 + ], + "angle": 0, + "content": "Table 5. Number of generated images." + }, + { + "type": "table", + "bbox": [ + 0.377, + 0.089, + 0.603, + 0.161 + ], + "angle": 0, + "content": "
αAP50boxallAP50boxbaseAP50boxnovel
0.751.355.140.6
0.852.355.842.3
0.951.855.641.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.377, + 0.165, + 0.605, + 0.178 + ], + "angle": 0, + "content": "Table 6. \\( \\alpha \\) for bounding-box filtration." + }, + { + "type": "table", + "bbox": [ + 0.651, + 0.089, + 0.876, + 0.161 + ], + "angle": 0, + "content": "
βAP50boxallAP50boxbaseAP50boxnovel
0.346.453.326.9
0.452.355.842.3
0.551.255.439.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.65, + 0.165, + 0.878, + 0.178 + ], + "angle": 0, + "content": "Table 7. \\( \\beta \\) for bounding-box filtration." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.187, + 0.227, + 0.204 + ], + "angle": 0, + "content": "4.5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.468, + 0.333 + ], + "angle": 0, + "content": "To understand the effectiveness of the proposed components, we perform thorough ablation studies on the open-vocabulary COCO benchmark [20], investigating the effect of fine-tuning stable diffusion model, training instance grounding module, self-training on novel categories. Additionally, we investigate other hyper-parameters by comparing the effectiveness of synthetic images and different score thresholds for base and novel categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.468, + 0.505 + ], + "angle": 0, + "content": "Fine-tuning diffusion model. We assess the effectiveness of fine-tuning stable diffusion model, and its impact for synthesizing images for training object detector. Figure 4c illustrates that InstaGen is capable of generating images with more intricate contexts, featuring multiple objects, small objects, and occluded objects. Subsequently, we employed these generated images to train Faster R-CNN for object detection. The results are presented in Table 4, showing that image synthesizer from fine-tuning stable diffusion model delivers improvement detection performance by 2.0 AP (from 40.3 to 42.3 AP)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.511, + 0.468, + 0.662 + ], + "angle": 0, + "content": "Instance grounding module. To demonstrate the effectiveness of the grounding head in open-vocabulary scenario, we exclusively train it on base categories. Visualization examples of the generated images are presented in Figure 4a. These examples demonstrate that the trained grounding head is also capable of predicting bounding boxes for instances from novel categories. Leveraging these generated images to train the object detector leads to a 37.1 AP on novel categories, surpassing or rivaling all existing state-of-the-art methods, as shown in Table 1 and Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.468, + 0.774 + ], + "angle": 0, + "content": "Self-training scheme. We evaluate the performance after self-training the grounding head with novel categories. As shown in Table 4, training Faster R-CNN with the generated images of novel categories, leads to a noticeable enhancement in detection performance, increasing from 37.1 to 40.3 AP. Qualitatively, it also demonstrates enhanced recall for novel objects after self-training, as shown in Figure 4b." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Number of synthetic images. We investigate the performance variation while increasing the number of the generated images per category for detector training. As shown in Table 5, when increasing the number of generated images from 1000 to 3000, the detector's performance tends to be increasing monotonically, from 39.7 to 42.3 AP on novel categories, showing the scalability of the proposed training mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.187, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Score thresholds for bounding box filtration. We compare the performance with different score thresholds \\(\\alpha\\) and \\(\\beta\\) for filtering bounding boxes on base categories and novel categories, respectively. From the experiment results in Table 6, we observe that the performance is not sensitive to the value of \\(\\alpha\\), and \\(\\alpha = 0.8\\) yields the best performance. The experimental results using different \\(\\beta\\) are presented in Table 7. With a low score threshold (\\(\\alpha = 0.3\\)), there are still numerous inaccurate bounding boxes remaining, resulting in an AP of 26.9 for novel categories. by increasing \\(\\beta\\) to 0.4, numerous inaccurate bounding boxes are filtered out, resulting in optimal performance. Hence, we set \\(\\alpha = 0.8\\) and \\(\\beta = 0.4\\) in our experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.614, + 0.415 + ], + "angle": 0, + "content": "5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.667 + ], + "angle": 0, + "content": "Using synthetic or artificially generated data in training AI algorithms is a burgeoning practice with significant potential. It can address data scarcity, privacy, and bias issues. However, there remains two limitations for training object detectors with synthetic data, (i) synthetic datasets commonly focus on clean, isolated object instances, which limits the exposure of the detector to the complexities and contextual diversity of real-world scenes, such as occlusions, clutter, varied environmental factors, deformation, therefore, models trained on synthetic data struggle to adapt to real-world conditions, affecting their overall robustness and accuracy, (ii) existing diffusion-based generative model also suffers from long-tail issue, that means the generative model struggles to generate images for objects of rare categories, resulting in imbalanced class representation during training and reduced detector performance for less common objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.619, + 0.697 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.872 + ], + "angle": 0, + "content": "This paper proposes a dataset synthesis pipeline, termed as InstaGen, that enables to generate images with object bounding boxes for arbitrary categories, acting as an annotation-free approach for constructing large-scale synthetic dataset to train object detector. We have conducted thorough experiments to show the effectiveness of training on synthetic data, on improving detection performance, or expanding the number of detection categories. Significant improvements have been shown in various detection scenarios, including open-vocabulary \\((+4.5\\mathrm{AP})\\) and datasparse \\((+1.2\\sim 5.2\\mathrm{AP})\\) detection." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.873, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. WX is supported by National Key R&D Program of China (No. 2022ZD0161400)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14128" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.2, + 0.472, + 0.255 + ], + "angle": 0, + "content": "[2] Yu Du, Fangyun Wei, Zihe Zhang, Miaojing Shi, Yue Gao, and Guoqi Li. 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(a) The synthetic images generated from Stable Diffusion and our proposed InstaGen, which can serve as a dataset synthesizer for sourcing photo-realistic images and instance bounding boxes at scale. (b) On open-vocabulary detection, training on synthetic images demonstrates significant improvement over CLIP-based methods on novel categories. (c) Training on the synthetic images generated from InstaGen also enhances the detection performance in close-set scenarios, particularly in data-sparse circumstances. + +![](images/ad8e4cfd2fb59d2e55678ba9d7646f55738abdcb5f1ed2ef9a728cda20199984.jpg) +(c) The detection AP with respect to the portion $(\%)$ of real data (COCO) usage. + +# Abstract + +In this paper, we present a novel paradigm to enhance the ability of object detector, e.g., expanding categories or improving detection performance, by training on synthetic dataset generated from diffusion models. Specifically, we integrate an instance-level grounding head into a pretrained, generative diffusion model, to augment it with the ability of localising instances in the generated images. The grounding head is trained to align the text embedding of category names with the regional visual feature of the diffusion model, using supervision from an off-the-shelf object detector, and a novel self-training scheme on (novel) categories not covered by the detector. We conduct thorough experiments to show that, this enhanced version of diffusion model, termed as InstaGen, can serve as a data synthesizer, to enhance object detectors by training on its generated samples, demonstrating superior performance over existing state-of-the-art methods in open-vocabulary (+4.5 AP) and data-sparse (+1.2 ~ 5.2 AP) scenarios. + +# 1. Introduction + +Object detection has been extensively studied in the field of computer vision, focusing on the localization and categorization of objects within images [3, 5, 12, 26, 27]. The common practise is to train the detectors on large-scale im + +age datasets, such as MS-COCO [20] and Object365 [30], where objects are exhaustively annotated with bounding boxes and corresponding category labels. However, the procedure for collecting images and annotations is often laborious and time-consuming, limiting the datasets' scalability. + +In the recent literature, text-to-image diffusion models have demonstrated remarkable success in generating high-quality images [28, 29], that unlocks the possibility of training vision systems with synthetic images. In general, existing text-to-image diffusion models are capable of synthesizing images based on some free-form text prompt, as shown in the first row of Figure 1a. Despite being photorealistic, such synthesized images can not support training sophisticated systems, that normally requires the inclusion of instance-level annotations, e.g., bounding boxes for object detection in our case. In this paper, we investigate a novel paradigm of dataset synthesis for training object detector, i.e., augmenting the text-to-image diffusion model to generate instance-level bounding boxes along with images. + +To begin with, we build an image synthesizer by fine-tuning the diffusion model on existing detection dataset. This is driven by the observation that off-the-shelf diffusion models often generate images with only one or two objects on simplistic background, training detectors on such images may thus lead to reduced robustness in complex real-world scenarios. Specifically, we exploit the existing detection dataset, and subsequently fine-tune the diffusion model with the image-caption pairs, constructed by taking + +random image crops, and composing the category name of the objects in the crop. As illustrated in the second row of the Figure 1a, once finetuned, the image synthesizer now enables to produce images with multiple objects and intricate contexts, thereby providing a more accurate simulation of real-world detection scenarios. + +To generate bounding boxes for objects within synthetic images, we propose an instance grounding module that establishes the correlation between the regional visual features from diffusion model and the text embedding of category names, and infers the coordinates for the objects' bounding boxes. Specifically, we adopt a two-step training strategies, firstly, we train the grounding module on synthetic images, with the supervision from an off-the-shelf object detector, which has been trained on a set of base categories; secondly, we utilize the trained grounding head to generate pseudo labels for a larger set of categories, including those not seen in existing detection dataset, and selftrain the grounding module. Once finished training, the grounding module will be able to identify the objects of arbitrary category and their bounding boxes in the synthetic image, by simply providing the name in free-form language. + +To summarize, we explore a novel approach to enhance object detection capabilities, such as expanding detectable categories and improving overall detection performance, by training on synthetic dataset generated from diffusion model. We make the following contribution: (i) We develop an image synthesizer by fine-tuning the diffusion model, with image-caption pairs derived from existing object detection datasets, our synthesizer can generate images with multiple objects and complex contexts, offering a more realistic simulation for real-world detection scenarios. (ii) We introduce a data synthesis framework for detection, termed as InstaGen. This is achieved through a novel grounding module that enables to generate labels and bounding boxes for objects in synthetic images. (iii) We train standard object detectors on the combination of real and synthetic dataset, and demonstrate superior performance over existing state-of-the-art detectors across various benchmarks, including open-vocabulary detection (increasing Average Precision [AP] by +4.5), data-sparse detection (enhancing AP by +1.2 to +5.2), and cross-dataset transfer (boosting AP by +0.5 to +1.1). + +# 2. Related Work + +Object Detection. Object detection aims to simultaneously predict the category and corresponding bounding box for the objects in the images. Generally, object detectors [3, 4, 6, 26, 27] are trained on a substantial amount of training data with bounding box annotations and can only recognize a predetermined set of categories present in the training data. In the recent literature, to further expand the ability of object detector, open-vocabulary object detec + +tion (OVD) has been widely researched, for example, OVR-CNN [37] introduces the concept of OVD and pre-trains a vision-language model with image-caption pairs. The subsequent works make use of the robust multi-modal representation of CLIP [24], and transfer its knowledge to object detectors through knowledge distillation [9, 36], exploiting extra data [5, 41] and text prompt tuning [2, 5]. In this paper, we propose to expand the ability of object detectors, e.g., expanding categories or improving detection performance, by training on synthetic dataset. + +Generative Models. Image generation has been considered as a task of interest in computer vision for decades. In the recent literature, significant progress has been made, for example, the generative adversarial networks (GANs) [8], variational autoencoders (VAEs) [15], flow-based models [14], and autoregressive models (ARMs) [32]. More recently, there has been a growing research interest in diffusion probabilistic models (DPMs), which have shown great promise in generating high-quality images across diverse datasets. For examples, GLIDE [23] utilizes a pre-trained language model and a cascaded diffusion structure for text-to-image generation. DALL-E 2 [25] is trained to generate images by inverting the CLIP image space, while Imagegen [29] explores the advantages of using pre-trained language models. Stable Diffusion [28] proposes the diffusion process in VAE latent spaces rather than pixel spaces, effectively reducing resource consumption. In general, the rapid development of generative models opens the possibility for training large models with synthetic dataset. + +# 3. Methodology + +In this section, we present details for constructing a dataset synthesizer, that enables to generate photo-realistic images with bounding boxes for each object instance, and train an object detector on the combined real and synthetic datasets. + +# 3.1. Problem Formulation + +Given a detection dataset of real images with manual annotations, i.e., $\mathcal{D}_{\mathrm{real}} = \{(x_1,\mathcal{B}_1,\mathcal{Y}_1),\ldots ,(x_N,\mathcal{B}_N,\mathcal{Y}_N)\}$ where $\mathcal{B}_i = \{b_1,\dots ,b_m|b_j\in \mathbb{R}^{2\times 2}\}$ denotes the set of box coordinates for the annotated instances in one image, and $\mathcal{V}_i = \{y_1,\dots ,y_m|y_j\in \mathcal{R}^{\mathcal{C}_{\mathrm{base}}}\}$ refers to the categories of the instances. Our goal is thus to exploit the given real dataset $(\mathcal{D}_{\mathrm{real}})$ , to steer a generative diffusion model into dataset synthesizer, that enables to augment the existing detection dataset, i.e., $\mathcal{D}_{\mathrm{final}} = \mathcal{D}_{\mathrm{real}} + \mathcal{D}_{\mathrm{syn}}$ . As a result, detectors trained on the combined dataset demonstrate enhanced ability, i.e., extending the detection categories or improving the detection performance. + +In the following sections, we first describe the procedure for constructing an image synthesizer, that can generate images suitable for training object detector (Section 3.2). To + +![](images/55deda742119a4332e8facb3114600260cdc94ddd588d874ed54c91430dc8e87.jpg) +(a) Fine-tuning diffusion model on detection dataset. + +![](images/78726df096b1a2fb19481af1d6124e7e5487c72fc63153b7c53e93174c36f7c3.jpg) +(b) Supervised training and self-training for grounding head (i.e. student). +Figure 2. Illustration of the process for finetuning diffusion model and training the grounding head: (a) stable diffusion model is fine-tuned on the detection dataset on base categories. (b) The grounding head is trained on synthetic images, with supervised learning on base categories and self-training on novel categories. + +simultaneously generate the images and object bounding boxes, we propose a novel instance-level grounding module, which aligns the text embedding of category name with the regional visual features from image synthesizer, and infers the coordinates for the objects in synthetic images. To further improve the alignment towards objects of arbitrary category, we adopt self-training to tune the grounding module on object categories not existing in $\mathcal{D}_{\mathrm{real}}$ (Section 3.3). As a result, the proposed model, termed as InstaGen, can automatically generate images along with bounding boxes for object instances, and construct synthetic dataset $(\mathcal{D}_{\mathrm{syn}})$ at scale, leading to improved ability when training detectors on it (Section 3.4). + +# 3.2. Image Synthesizer for Object Detection + +Here, we build our image synthesizer based on an off-the-shelf stable diffusion model (SDM [28]). Despite of its impressive ability in generating photo-realistic images, it often outputs images with only one or two objects on simplistic background with the text prompts, for example, 'a photograph of a [category1 name] and a [category2 name]' as demonstrated in Figure 4b. As a result, object detectors trained on such images may exhibit reduced robustness when dealing with complex real-world scenarios. To bridge such domain gap, we propose to construct the image synthesizer by fine-tuning the SDM with an existing real-world detection dataset $(\mathcal{D}_{\mathrm{real}})$ . + +Fine-tuning procedure. To fine-tune the stable diffusion model (SDM), one approach is to naively use the sample from detection dataset, for example, randomly pick an image and construct the text prompt with all categories in the image. However, as the image often contains multiple objects, such approach renders significant difficulty for fine-tuning the SDM, especially for small or occluded objects. We adopt a mild strategy by taking random crops from the images, and construct the text prompt with categories in the image crops, as shown in Figure 2a. If an image crop con + +tains multiple objects of the same category, we only use this category name once in the text prompt. + +Fine-tuning loss. We use the sampled image crop and constructed text prompt to fine-tune SDM with a squared error loss on the predicted noise term as follows: + +$$ +\mathcal {L} _ {\text {f i n e - t u n e}} = \mathbb {E} _ {z, \epsilon \sim \mathcal {N} (0, 1), t, y} \left[ | | \epsilon - \epsilon_ {\theta} \left(z ^ {t}, t, y\right) | | _ {2} ^ {2} \right], \tag {1} +$$ + +where $z$ denotes a latent vector mapped from the input image with VAE, $t$ denotes the denoising step, uniformly sampled from $\{1,\dots ,T\}$ , $T$ refers to the length of the diffusion Markov chain, and $\epsilon_{\theta}$ refers to the estimated noise from SDM with parameters $\theta$ being updated. We have experimentally verified the necessity of this fine-tuning step, as shown in Table 4. + +# 3.3. Dataset Synthesizer for Object Detection + +In this section, we present details for steering the image synthesizer into dataset synthesizer for object detection, which enables to simultaneously generate images and object bounding boxes. Specifically, we propose an instance-level grounding module that aligns the text embedding of object category, with the regional visual feature of the diffusion model, and infers the coordinates for bounding boxes, effectively augmenting the image synthesizer with instance grounding, as shown in Figure 3. To further improve the alignment in large visual diversity, we propose a self-training scheme that enables the grounding module to generalise towards arbitrary categories, including those not exist in real detection dataset $(\mathcal{D}_{\mathrm{real}})$ . As a result, our data synthesizer, termed as InstaGen, can be used to construct synthetic dataset for training object detectors. + +# 3.3.1 Instance Grounding on Base Categories + +To localise the object instances in synthetic images, we introduce an open-vocabulary grounding module, that aims to simultaneously generate image $(x)$ and the corresponding instance-level bounding boxes $(\mathcal{B})$ based on a set of + +![](images/bccb423f8f5aad018cd1d7c9571f9ee6743743209874d0f42abc938ab9cb5069.jpg) +Figure 3. Illustration of the dataset generation process in InstaGen. The data generation process consists of two steps: (i) Image collection: given a text prompt, SDM generates images with the objects described in the text prompt; (ii) Annotation generation: the instance-level grounding head aligns the category embedding with the visual feature region of SDM, generating the corresponding object bounding-boxes. + +categories $(\mathcal{V})$ , i.e., $\{x, \mathcal{B}, \mathcal{Y}\} = \Phi_{\mathrm{InstaGen}}(\epsilon, \mathcal{Y})$ , where $\epsilon \sim \mathcal{N}(0, I)$ denotes the sampled noise. + +To this end, we propose an instance grounding head, as shown in Figure 3, it takes the intermediate representation from image synthesizer and the text embedding of category as inputs, then predicts the corresponding object bounding boxes, i.e., $\{\mathcal{B}_i,\mathcal{Y}_i\} = \Phi_{\mathrm{g - head}}(\mathcal{F}_i,\Phi_{\mathrm{t - enc}}(g(\mathcal{Y}_i)))$ , where $\mathcal{F}_i = \{f_i^1,\dots ,f_i^n\}$ refers to the multi-scale dense features from the image synthesizer at time step $t = 1$ $g(\cdot)$ denotes a template that decorates each of the visual categories in the text prompt, e.g., 'a photograph of [category1 name] and [category2 name], $\Phi_{\mathrm{t - enc}}(\cdot)$ denotes the text encoder. + +Inspired by GroundingDINO [22], our grounding head $\Phi_{\mathrm{g - head}}(\cdot)$ mainly contains four components: (i) a channel-compression layer, implemented with a $3\times 3$ convolution, for reducing the dimensionality of the visual features; (ii) a feature enhancer, consisting of six feature enhancer layers, to fuse the visual and text features. Each layer employs a deformable self-attention to enhance image features, a vanilla self-attention for text feature enhancers, an image-to-text cross-attention and a text-to-image cross-attention for feature fusion; (iii) a language-guided query selection module for query initialization. This module predicts top- $N$ anchor boxes based on the similarity between text features and image features. Following DINO [38], it adopts a mixed query selection where the positional queries are initialized with the anchor boxes and the content queries remain learnable; (iv) a cross-modality decoder for classification and box refinement. It comprises six decoder layers, with each layer utilizing a self-attention mechanism for query interaction, an image cross-attention layer for combining image features, and a text cross-attention layer for combining text + +features. Finally, we apply the dot product between each query and the text features, followed by a Sigmoid function to predict the classification score $\hat{s}$ for each category. Additionally, the object queries are passed through a Multi-Layer Perceptron (MLP) to predict the object bounding boxes $\hat{b}$ , as shown in Figure 3. We train the grounding head by aligning the category embedding with the regional visual features from diffusion model, as detailed below. Once trained, the grounding head is open-vocabulary, i.e., given any categories (even beyond the training categories), the grounding head can generate the corresponding bounding-boxes for the object instances. + +Training triplets of base categories. Following [18], we apply an automatic pipeline to construct the $\{$ visual feature, bounding-box, text prompt\} triplets, with an object detector trained on base categories from a given dataset $(D_{\mathrm{real}})$ . In specific, assuming there exists a set of base categories $\{c_{\mathrm{base}}^{1},\ldots ,c_{\mathrm{base}}^{N}\}$ , e.g., the classes in MS-COCO [20]. We first select a random number of base categories to construct a text prompt, e.g., 'a photograph of [base category1] and [base category2]' and generate both the visual features and images with our image synthesizer. Then we take an off-the-shelf object detector, for example, pre-trained Mask R-CNN [12], to run the inference procedure on the synthetic images, and infer the bounding boxes of the selected categories. To acquire the confident bounding-boxes for training, we use a score threshold $\alpha$ to filter out the bounding-boxes with low confidence (an ablation study on the selection of the score threshold has been conducted in Section 4.5). As a result, an infinite number of training triplets for the given base categories can be constructed by repeating the above operation. + +![](images/7ea2c8d082a4325287778db1498f4094d90ddbec49a9345045a2f32109f27c98.jpg) +(a) Stable Diffusion $^+$ Grounding head w/ Supervised training. + +![](images/18578e5af17a8eaf7f6b1e5f8dbd8ef7289313346dcaad9ba62ac788e215dd7a.jpg) +Figure 4. Visualization of the synthetic images and bounding-boxes generated from different models. The bounding-boxes with green denote the objects from base categories, while the ones with red denote the objects from novel categories. + +![](images/589961f3dce58985693b59a078cf68aacebb20e2113507e81ab8a6d271094ff6.jpg) + +![](images/4a32387c50e652d3e70db3d2fa251aace6053703da1a85d9272824bf1cb80884.jpg) +(b) Stable Diffusion + Grounding head w/ Supervised- and Self-training. + +![](images/e182df7a10d9dacd84a46b12268e5ba42ef6b8e81a0a3a3be42ccfe46ca6c296.jpg) + +![](images/f92f9e7dd2d7b2e309f8b3e68fc666d8f30aa71d9f27603d5ac9c53827c12c42.jpg) + +![](images/3341a9bb888d21634ab254ebbf93daa0ecabc73dac0075e7272fdb4efb082360.jpg) +(c) Stable Diffusion w/ Fine-tuning + Grounding head w/ Supervised- and Self-training. + +![](images/10e097f2ad4820ec6212695681030377cdeefdf84f54eb4c4f803c96a02c4534.jpg) + +![](images/cf0bfba5805d764f34b1f2b60c3b1cdb9465d0a016e78b919111b642d841836b.jpg) + +Training loss. We use the constructed training triplets to train the grounding head: + +$$ +\mathcal {L} _ {\text {b a s e}} = \sum_ {i = 1} ^ {N} \left[ \mathcal {L} _ {\operatorname {c l s}} \left(\hat {s} _ {i}, c _ {i}\right) + \mathbb {1} _ {\{c _ {i} \neq \emptyset \}} \mathcal {L} _ {\text {b o x}} \left(\hat {b} _ {i}, b _ {i}\right) \right], \tag {2} +$$ + +where the $i$ th prediction $(\hat{s}_i, \hat{b}_i)$ from the $N$ object queries is assigned to a ground-truth $(c_i, b_i)$ or $\varnothing$ (no object) with bipartite matching. $\mathcal{L}_{\mathrm{cls}}$ and $\mathcal{L}_{\mathrm{box}}$ denote the classification loss (e.g. Focal loss) and box regression loss (e.g. L1 loss and GIoU loss), respectively. + +# 3.3.2 Instance Grounding on Novel Categories + +Till here, we have obtained a diffusion model with open-vocabulary grounding, which has been only trained with base categories. In this section, we propose to further leverage the synthetic training triplets from a wider range of categories to enhance the alignment for novel/unseen categories. Specifically, as shown in Figure 2b, we describe a framework that generates the training triplets for novel categories using the grounded diffusion model, and then selftrain the grounding head. + +Training triplets of novel categories. We design the text prompts of novel categories, e.g., 'a photograph of [novel category1] and [novel category2], and pass them through our proposed image synthesizer, to generate the visual features. To acquire the corresponding bounding-boxes for novel categories, we propose a self-training scheme that takes the above grounding head as the student, and apply a mean teacher (an exponential moving average (EMA) of the student model) to create pseudo labels for update. In contrast to the widely adopted self-training scheme that takes the image as input, the student and teacher in our case only take the visual features as input, thus cannot apply data augmentation as for images. Instead, we insert dropout module within each feature enhancer layer and decoder layer in the student. During training, we run inference (without dropout module) with teacher model on the visual features to produce bounding boxes, and then use a score threshold $\beta$ to + +filter out those with low confidence, and use the remaining training triplets $(\mathcal{F}_i,\hat{b}_i,y_i^{\mathrm{novel}})$ to train the student, i.e., grounding head. + +Training loss. Now, we can also train the grounding head on the mined triplets of novel categories (that are unseen in the existing real dataset) with the training loss $\mathcal{L}_{\mathrm{novel}}$ defined similar to Eq. 2. Thus, the total training loss for training the grounding head can be: $\mathcal{L}_{\mathrm{grounding}} = \mathcal{L}_{\mathrm{base}} + \mathcal{L}_{\mathrm{novel}}$ . + +# 3.4. Training Detector with Synthetic Dataset + +In this section, we augment the real dataset $(\mathcal{D}_{\mathrm{real}})$ , with synthetic dataset $(\mathcal{D}_{\mathrm{syn}})$ , and train popular object detectors, for example, Faster R-CNN [27] with the standard training loss: + +$$ +\mathcal {L} _ {\det } = \mathcal {L} _ {\text {r p n ＿ c l s}} + \mathcal {L} _ {\text {r p n ＿ b o x}} + \mathcal {L} _ {\det ＿ c l s} + \mathcal {L} _ {\det ＿ \text {b o x}}, \tag {3} +$$ + +where $\mathcal{L}_{\mathrm{rpn\_cls}}$ , $\mathcal{L}_{\mathrm{rpn\_box}}$ are the classification and box regression losses of region proposal network, and $\mathcal{L}_{\mathrm{det\_cls}}$ , $\mathcal{L}_{\mathrm{det\_box}}$ are the classification and box regression losses of the detection head. Generally speaking, the synthetic dataset enables to improve the detector's ability from two aspects: (i) expanding the original data with more categories, (ii) improving the detection performance by increasing data diversity. + +Expanding detection categories. The grounding head is designed to be open-vocabulary, that enables to generate object bounding boxes for novel categories, even though it is trained with a specific set of base categories. This feature enables InstaGen to construct a detection dataset for any category. Figure 4 demonstrates several synthetic images and object bounding boxes for novel categories, i.e., the object with red bounding box. We evaluate the effectiveness of training on synthetic dataset through experiments on open-vocabulary detection benchmark. For more details, please refer to Figure 1b and Section 4.2. + +Increasing data diversity. The base diffusion model is trained on a large corpus of image-caption pairs, that enables to generate diverse images. Taking advantage of such capabilities, InstaGen is capable of generating dataset with diverse images and box annotations, which can expand the + +
MethodSupervisionDetectorBackbone\(AP50_{all}^{box}\)\(AP50_{base}^{box}\)\(AP50_{novel}^{box}\)
Detic [41]CLIPFaster R-CNNR5045.047.127.8
PromptDet [5]CLIPFaster R-CNNR50-50.626.6
BARON [34]CLIPFaster R-CNNR5053.560.434.0
OADP [33]CLIPFaster R-CNNR5047.253.330.0
ViLD [9]CLIPMask R-CNNR5051.359.527.6
F-VLM [16]CLIPMask R-CNNR5039.6-28.0
RO-ViT [13]CLIPMask R-CNNViT-B [1]41.5-30.2
VLDet [19]CLIPCenterNet2 [40]R5045.850.632.0
CxORA [35]CLIPDAB-DETR [21]R5035.435.535.1
DK-DETR [17]CLIPDeformable DETR [42]R50-61.132.3
EdaDet [31]CLIPDeformable DETR [42]R5052.557.737.8
InstaGenStable DiffusionFaster R-CNNR5052.355.842.3
+ +Table 1. Results on open-vocabulary COCO benchmark. $\mathrm{AP50}_{\text {novel }}^{\text {box }}$ is the main metric for evaluation. Our detector, trained on synthetic dataset from InstaGen, significantly outperforms state-of-the-art CLIP-based approaches on novel categories. + +original dataset, i.e., increase the data diversity and improve detection performance, particularly in data-sparse scenarios. We conducted experiments with varying proportions of COCO [20] images as available real data, and show the effectiveness of training on synthetic dataset when the number of real-world images is limited. We refer the readers for more details in Section 4.3, and results in Figure 1c. + +# 4. Experiment + +In this section, we use the proposed InstaGen to construct synthetic dataset for training object detectors, i.e., generating images with the corresponding bounding boxes. Specifically, we present the implementation details in Section 4.1. To evaluate the effectiveness of the synthetic dataset for training object detector, we consider three protocols: open-vocabulary object detection (Section 4.2), data-sparse object detection (Section 4.3) and cross-dataset object detection (Section 4.4). Lastly, we conduct ablation studies on the effectiveness of the proposed components and the selection of hyper-parameters (Section 4.5). + +# 4.1. Implementation details + +Network architecture. We build image synthesizer from the pre-trained Stable Diffusion v1.4 [28], and use the CLIP text encoder [24] to get text embedding for the category name. The channel compression layer maps the dimension of visual features to 256, which is implemented with a $3 \times 3$ convolution. For simplicity, the feature enhancer, language-guided query selection module and cross-modality decoder are designed to the same structure as the ones in [22]. The number of the object queries is set to 900. + +Constructing image synthesizer. In our experiments, we first fine-tune the stable diffusion model on a real detection dataset, e.g., the images of base categories. During training, the text encoder of CLIP is kept frozen, while the remaining components are trained for 6 epochs with a batch size of 16 and a learning rate of 1e-4. + +Instance grounding module. We start by constructing the training triplets using base categories i.e., the categories present in the existing dataset. The text prompt for each triplet is constructed by randomly selecting one or two categories. The regional visual features are taken from the image synthesizer time step $t = 1$ , and the oracle ground-truth bounding boxes are obtained using a Mask R-CNN model trained on base categories, as explained in Section 3.3.1. + +Subsequently, we train the instance grounding module with these training triplets for 6 epochs, with a batch size of 32. In the 6th epoch, we transfer the weights from the student model to the teacher model, and proceed to train the student for an additional 6 epochs. During this training, the student receives supervised training on the base categories and engages in self-training on novel categories, and the teacher model is updated using exponential moving average (EMA) with a momentum of 0.999. The initial learning rate is set to 1e-4 and is subsequently reduced by a factor of 10 at the 11th epoch, and the score thresholds $\alpha$ and $\beta$ are set to 0.8 and 0.4, respectively. + +Training object detector on combined dataset. In our experiment, we train an object detector (Faster R-CNN [27]) with ResNet-50 [11] as backbone, on a combination of the existing real dataset and the synthetic dataset. Specifically, for synthetic dataset, we randomly select one or two categories at each iteration, construct the text prompts, and feed them as input to generate images along with the corresponding bounding boxes with $\beta$ of 0.4. Following the standard implementation [27], the detector is trained for 12 epochs ( $1\times$ learning schedule) unless specified. The initial learning rate is set to 0.01 and then reduced by a factor of 10 at the 8th and the 11th epochs. + +# 4.2. Open-vocabulary object detection + +Experimental setup. Following the previous works [5, 39], we conduct experiments on the open-vocabulary COCO benchmark, where 48 classes are treated as base categories, + +
InstaGen10%25%50%75%100%
X23.329.534.136.137.5
✓28.532.635.837.338.5
+ +Table 2. Results on data-sparse object detection. We employ Faster R-CNN with the ResNet-50 backbone as the default object detector and evaluate its performance using the AP metric on MS COCO benchmark. Please refer to the text for more details. + +
MethodSupervisionDetectorExtra DataObject365LVIS
Gao et al. [7]CLIPCenterNet2✓6.98.0
VL-PLM [39]CLIPMask R-CNN✓10.922.2
InstaGenStable DiffusionFaster R-CNN✗11.423.3
+ +Table 3. Results on generalizing COCO-base to Object365 and LVIS. All detectors utilize the ResNet-50 backbone. The evaluation protocol follows [7] and reports AP50. Extra data refers to an additional dataset that encompasses objects from the categories within the target dataset. In both experiments, the extra data consists of all the images from COCO, which has covered the majority of categories in Object365 and LVIS. + +
G-headSTFT\( AP50_{all}^{box} \)\( AP50_{base}^{box} \)\( AP50_{novel}^{box} \)
✓50.655.337.1
✓✓51.155.040.3
✓✓✓52.355.842.3
+ +Table 4. The effectiveness of the proposed components. G-head, ST and FT refer to the grounding head, self-training the grounding head and fine-tuning SDM, respectively. + +and 17 classes as the novel categories. More results for LVIS can be found in the supplementary material. To train the grounding head, we employ 1250 synthetic images per category per training epoch. While for training the object detector, we use 3000 synthetic images per category, along with the original real dataset for base categories. The object detector is trained with input size of $800 \times 800$ and scale jitter. The performance is measured by COCO Average Precision at an Intersection over Union of 0.5 (AP50). + +Comparison to SOTA. As shown in Table 1, we evaluate the performance by comparing with existing CLIP-based open-vocabulary object detectors. It is clear that our detector trained on synthetic dataset from InstaGen outperforms existing state-of-the-art approaches significantly, i.e., around $+5\mathrm{AP}$ improvement over the second best. In essence, through the utilization of our proposed open-vocabulary grounding head, InstaGen is able to generate detection data for novel categories, enabling the detector to attain exceptional performance. To the best of our knowledge, this is the first work that applies generative diffusion model for dataset synthesis, to tackle open-vocabulary object detection, and showcase its superiority in this task. + +# 4.3. Data-sparse object detection + +Experimental setup. Here, we evaluate the effectiveness of synthetic dataset in data-spare scenario, by varying the amount of real data. We randomly select subsets comprising $10\%$ , $25\%$ , $50\%$ , $75\%$ and $100\%$ of the COCO training set, this covers all COCO categories. These subsets are used to fine-tune stable diffusion model for constructing image synthesizer, and train a Mask R-CNN for generating oracle ground-truth bounding boxes in synthetic images. We employ 1250 synthetic images per category to train a Faster R- + +CNN in conjunction with the corresponding COCO subset. The performance is measured by Average Precision [20]. + +Comparison to baseline. As shown in Table 2, the Faster R-CNN trained with synthetic images achieves consistent improvement across various real training data budgets. Notably, as the availability of real data becomes sparse, synthetic dataset plays even more important role for performance improvement, for instance, it improves the detector by $+5.2$ AP $(23.3\rightarrow 28.5$ AP) when only $10\%$ real COCO training subset is available. + +# 4.4. Cross-dataset object detection + +Experimental setup. In this section, we assess the effectiveness of synthetic data on a more challenging task, namely cross-dataset object detection. Following [39], we evaluate the COCO-trained model on two unseen datasets: Object365 [30] and LVIS [10]. Specifically, we consider the 48 classes in the open-vocabulary COCO benchmark as the source dataset, while Object365 (with 365 classes) and LVIS (with 1203 classes) serve as the target dataset. When training the instance grounding module, we acquire 1250 synthetic images for base categories from the source dataset, and 100 synthetic images for the category from the target dataset at each training iteration. In the case of training the object detector, we employ 500 synthetic images per category from the target dataset for each training iteration. The detector is trained with input size of $1024 \times 1024$ and scale jitter [39]. + +Comparison to SOTA. The results presented in Table 3 demonstrate that the proposed InstaGen achieves superior performance in generalization from COCO-base to Object365 and LVIS, when compared to CLIP-based methods such as [7, 39]. It is worth noting that CLIP-based methods require the generation of pseudo-labels for the categories from the target dataset on COCO images, and subsequently train the detector using these images. These methods necessitate a dataset that includes objects belonging to the categories of the target dataset. In contrast, InstaGen possesses the ability to generate images featuring objects of any category without the need for additional datasets, thereby enhancing its versatility across various scenarios. + +
#ImagesAP50boxallAP50boxbaseAP50boxnovel
100051.655.939.7
200051.755.441.1
300052.355.842.3
+ +Table 5. Number of generated images. + +
αAP50boxallAP50boxbaseAP50boxnovel
0.751.355.140.6
0.852.355.842.3
0.951.855.641.1
+ +Table 6. $\alpha$ for bounding-box filtration. + +
βAP50boxallAP50boxbaseAP50boxnovel
0.346.453.326.9
0.452.355.842.3
0.551.255.439.2
+ +Table 7. $\beta$ for bounding-box filtration. + +# 4.5. Ablation study + +To understand the effectiveness of the proposed components, we perform thorough ablation studies on the open-vocabulary COCO benchmark [20], investigating the effect of fine-tuning stable diffusion model, training instance grounding module, self-training on novel categories. Additionally, we investigate other hyper-parameters by comparing the effectiveness of synthetic images and different score thresholds for base and novel categories. + +Fine-tuning diffusion model. We assess the effectiveness of fine-tuning stable diffusion model, and its impact for synthesizing images for training object detector. Figure 4c illustrates that InstaGen is capable of generating images with more intricate contexts, featuring multiple objects, small objects, and occluded objects. Subsequently, we employed these generated images to train Faster R-CNN for object detection. The results are presented in Table 4, showing that image synthesizer from fine-tuning stable diffusion model delivers improvement detection performance by 2.0 AP (from 40.3 to 42.3 AP). + +Instance grounding module. To demonstrate the effectiveness of the grounding head in open-vocabulary scenario, we exclusively train it on base categories. Visualization examples of the generated images are presented in Figure 4a. These examples demonstrate that the trained grounding head is also capable of predicting bounding boxes for instances from novel categories. Leveraging these generated images to train the object detector leads to a 37.1 AP on novel categories, surpassing or rivaling all existing state-of-the-art methods, as shown in Table 1 and Table 4. + +Self-training scheme. We evaluate the performance after self-training the grounding head with novel categories. As shown in Table 4, training Faster R-CNN with the generated images of novel categories, leads to a noticeable enhancement in detection performance, increasing from 37.1 to 40.3 AP. Qualitatively, it also demonstrates enhanced recall for novel objects after self-training, as shown in Figure 4b. + +Number of synthetic images. We investigate the performance variation while increasing the number of the generated images per category for detector training. As shown in Table 5, when increasing the number of generated images from 1000 to 3000, the detector's performance tends to be increasing monotonically, from 39.7 to 42.3 AP on novel categories, showing the scalability of the proposed training mechanism. + +Score thresholds for bounding box filtration. We compare the performance with different score thresholds $\alpha$ and $\beta$ for filtering bounding boxes on base categories and novel categories, respectively. From the experiment results in Table 6, we observe that the performance is not sensitive to the value of $\alpha$ , and $\alpha = 0.8$ yields the best performance. The experimental results using different $\beta$ are presented in Table 7. With a low score threshold ( $\alpha = 0.3$ ), there are still numerous inaccurate bounding boxes remaining, resulting in an AP of 26.9 for novel categories. by increasing $\beta$ to 0.4, numerous inaccurate bounding boxes are filtered out, resulting in optimal performance. Hence, we set $\alpha = 0.8$ and $\beta = 0.4$ in our experiments. + +# 5. Limitation + +Using synthetic or artificially generated data in training AI algorithms is a burgeoning practice with significant potential. It can address data scarcity, privacy, and bias issues. However, there remains two limitations for training object detectors with synthetic data, (i) synthetic datasets commonly focus on clean, isolated object instances, which limits the exposure of the detector to the complexities and contextual diversity of real-world scenes, such as occlusions, clutter, varied environmental factors, deformation, therefore, models trained on synthetic data struggle to adapt to real-world conditions, affecting their overall robustness and accuracy, (ii) existing diffusion-based generative model also suffers from long-tail issue, that means the generative model struggles to generate images for objects of rare categories, resulting in imbalanced class representation during training and reduced detector performance for less common objects. + +# 6. Conclusion + +This paper proposes a dataset synthesis pipeline, termed as InstaGen, that enables to generate images with object bounding boxes for arbitrary categories, acting as an annotation-free approach for constructing large-scale synthetic dataset to train object detector. We have conducted thorough experiments to show the effectiveness of training on synthetic data, on improving detection performance, or expanding the number of detection categories. Significant improvements have been shown in various detection scenarios, including open-vocabulary $(+4.5\mathrm{AP})$ and datasparse $(+1.2\sim 5.2\mathrm{AP})$ detection. + +Acknowledgement. WX is supported by National Key R&D Program of China (No. 2022ZD0161400). + +# References + +[1] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. 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Specifically, we integrate an instance-level grounding head into a pretrained, generative diffusion model, to augment it with the ability of localising instances in the generated images. The grounding head is trained to align the text embedding of category names with the regional visual feature of the diffusion model, using supervision from an off-the-shelf object detector, and a novel self-training scheme on (novel) categories not covered by the detector. We conduct thorough experiments to show that, this enhanced version of diffusion model, termed as InstaGen, can serve as a data synthesizer, to enhance object detectors by training on its generated samples, demonstrating superior performance over existing state-of-the-art methods in open-vocabulary (+4.5 AP) and data-sparse (+1.2 ~ 5.2 AP) scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 625, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 645, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 287, + 695 + ], + "type": "text", + "content": "Object detection has been extensively studied in the field of computer vision, focusing on the localization and categorization of objects within images [3, 5, 12, 26, 27]. The common practise is to train the detectors on large-scale im" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 373, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 434 + ], + "type": "text", + "content": "age datasets, such as MS-COCO [20] and Object365 [30], where objects are exhaustively annotated with bounding boxes and corresponding category labels. However, the procedure for collecting images and annotations is often laborious and time-consuming, limiting the datasets' scalability." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 435, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 546, + 604 + ], + "type": "text", + "content": "In the recent literature, text-to-image diffusion models have demonstrated remarkable success in generating high-quality images [28, 29], that unlocks the possibility of training vision systems with synthetic images. In general, existing text-to-image diffusion models are capable of synthesizing images based on some free-form text prompt, as shown in the first row of Figure 1a. Despite being photorealistic, such synthesized images can not support training sophisticated systems, that normally requires the inclusion of instance-level annotations, e.g., bounding boxes for object detection in our case. In this paper, we investigate a novel paradigm of dataset synthesis for training object detector, i.e., augmenting the text-to-image diffusion model to generate instance-level bounding boxes along with images." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "To begin with, we build an image synthesizer by fine-tuning the diffusion model on existing detection dataset. This is driven by the observation that off-the-shelf diffusion models often generate images with only one or two objects on simplistic background, training detectors on such images may thus lead to reduced robustness in complex real-world scenarios. Specifically, we exploit the existing detection dataset, and subsequently fine-tune the diffusion model with the image-caption pairs, constructed by taking" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 703, + 129, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 703, + 129, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 703, + 129, + 713 + ], + "type": "text", + "content": "†: corresponding author." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "14121" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 143 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 143 + ], + "type": "text", + "content": "random image crops, and composing the category name of the objects in the crop. As illustrated in the second row of the Figure 1a, once finetuned, the image synthesizer now enables to produce images with multiple objects and intricate contexts, thereby providing a more accurate simulation of real-world detection scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 287, + 335 + ], + "type": "text", + "content": "To generate bounding boxes for objects within synthetic images, we propose an instance grounding module that establishes the correlation between the regional visual features from diffusion model and the text embedding of category names, and infers the coordinates for the objects' bounding boxes. Specifically, we adopt a two-step training strategies, firstly, we train the grounding module on synthetic images, with the supervision from an off-the-shelf object detector, which has been trained on a set of base categories; secondly, we utilize the trained grounding head to generate pseudo labels for a larger set of categories, including those not seen in existing detection dataset, and selftrain the grounding module. Once finished training, the grounding module will be able to identify the objects of arbitrary category and their bounding boxes in the synthetic image, by simply providing the name in free-form language." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 336, + 288, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 288, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 288, + 587 + ], + "type": "text", + "content": "To summarize, we explore a novel approach to enhance object detection capabilities, such as expanding detectable categories and improving overall detection performance, by training on synthetic dataset generated from diffusion model. We make the following contribution: (i) We develop an image synthesizer by fine-tuning the diffusion model, with image-caption pairs derived from existing object detection datasets, our synthesizer can generate images with multiple objects and complex contexts, offering a more realistic simulation for real-world detection scenarios. (ii) We introduce a data synthesis framework for detection, termed as InstaGen. This is achieved through a novel grounding module that enables to generate labels and bounding boxes for objects in synthetic images. (iii) We train standard object detectors on the combination of real and synthetic dataset, and demonstrate superior performance over existing state-of-the-art detectors across various benchmarks, including open-vocabulary detection (increasing Average Precision [AP] by +4.5), data-sparse detection (enhancing AP by +1.2 to +5.2), and cross-dataset transfer (boosting AP by +0.5 to +1.1)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Object Detection. Object detection aims to simultaneously predict the category and corresponding bounding box for the objects in the images. Generally, object detectors [3, 4, 6, 26, 27] are trained on a substantial amount of training data with bounding box annotations and can only recognize a predetermined set of categories present in the training data. In the recent literature, to further expand the ability of object detector, open-vocabulary object detec" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "tion (OVD) has been widely researched, for example, OVR-CNN [37] introduces the concept of OVD and pre-trains a vision-language model with image-caption pairs. The subsequent works make use of the robust multi-modal representation of CLIP [24], and transfer its knowledge to object detectors through knowledge distillation [9, 36], exploiting extra data [5, 41] and text prompt tuning [2, 5]. In this paper, we propose to expand the ability of object detectors, e.g., expanding categories or improving detection performance, by training on synthetic dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 195, + 546, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 546, + 423 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 546, + 423 + ], + "type": "text", + "content": "Generative Models. Image generation has been considered as a task of interest in computer vision for decades. In the recent literature, significant progress has been made, for example, the generative adversarial networks (GANs) [8], variational autoencoders (VAEs) [15], flow-based models [14], and autoregressive models (ARMs) [32]. More recently, there has been a growing research interest in diffusion probabilistic models (DPMs), which have shown great promise in generating high-quality images across diverse datasets. For examples, GLIDE [23] utilizes a pre-trained language model and a cascaded diffusion structure for text-to-image generation. DALL-E 2 [25] is trained to generate images by inverting the CLIP image space, while Imagegen [29] explores the advantages of using pre-trained language models. Stable Diffusion [28] proposes the diffusion process in VAE latent spaces rather than pixel spaces, effectively reducing resource consumption. In general, the rapid development of generative models opens the possibility for training large models with synthetic dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 435, + 388, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 388, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 388, + 449 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 456, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 506 + ], + "type": "text", + "content": "In this section, we present details for constructing a dataset synthesizer, that enables to generate photo-realistic images with bounding boxes for each object instance, and train an object detector on the combined real and synthetic datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 514, + 430, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 430, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 430, + 526 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": "Given a detection dataset of real images with manual annotations, i.e., " + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{real}} = \\{(x_1,\\mathcal{B}_1,\\mathcal{Y}_1),\\ldots ,(x_N,\\mathcal{B}_N,\\mathcal{Y}_N)\\}" + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_i = \\{b_1,\\dots ,b_m|b_j\\in \\mathbb{R}^{2\\times 2}\\}" + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": " denotes the set of box coordinates for the annotated instances in one image, and " + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i = \\{y_1,\\dots ,y_m|y_j\\in \\mathcal{R}^{\\mathcal{C}_{\\mathrm{base}}}\\}" + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": " refers to the categories of the instances. Our goal is thus to exploit the given real dataset " + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{real}})" + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": ", to steer a generative diffusion model into dataset synthesizer, that enables to augment the existing detection dataset, i.e., " + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{final}} = \\mathcal{D}_{\\mathrm{real}} + \\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": ". As a result, detectors trained on the combined dataset demonstrate enhanced ability, i.e., extending the detection categories or improving the detection performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In the following sections, we first describe the procedure for constructing an image synthesizer, that can generate images suitable for training object detector (Section 3.2). To" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14122" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 77, + 286, + 203 + ], + "blocks": [ + { + "bbox": [ + 51, + 77, + 286, + 203 + ], + "lines": [ + { + "bbox": [ + 51, + 77, + 286, + 203 + ], + "spans": [ + { + "bbox": [ + 51, + 77, + 286, + 203 + ], + "type": "image", + "image_path": "55deda742119a4332e8facb3114600260cdc94ddd588d874ed54c91430dc8e87.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 209, + 253, + 220 + ], + "lines": [ + { + "bbox": [ + 83, + 209, + 253, + 220 + ], + "spans": [ + { + "bbox": [ + 83, + 209, + 253, + 220 + ], + "type": "text", + "content": "(a) Fine-tuning diffusion model on detection dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 305, + 71, + 541, + 207 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 541, + 207 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 541, + 207 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 541, + 207 + ], + "type": "image", + "image_path": "78726df096b1a2fb19481af1d6124e7e5487c72fc63153b7c53e93174c36f7c3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 209, + 541, + 220 + ], + "lines": [ + { + "bbox": [ + 304, + 209, + 541, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 541, + 220 + ], + "type": "text", + "content": "(b) Supervised training and self-training for grounding head (i.e. student)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 224, + 546, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 224, + 546, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 546, + 258 + ], + "type": "text", + "content": "Figure 2. Illustration of the process for finetuning diffusion model and training the grounding head: (a) stable diffusion model is fine-tuned on the detection dataset on base categories. (b) The grounding head is trained on synthetic images, with supervised learning on base categories and self-training on novel categories." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": "simultaneously generate the images and object bounding boxes, we propose a novel instance-level grounding module, which aligns the text embedding of category name with the regional visual features from image synthesizer, and infers the coordinates for the objects in synthetic images. To further improve the alignment towards objects of arbitrary category, we adopt self-training to tune the grounding module on object categories not existing in " + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{real}}" + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": " (Section 3.3). As a result, the proposed model, termed as InstaGen, can automatically generate images along with bounding boxes for object instances, and construct synthetic dataset " + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{syn}})" + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": " at scale, leading to improved ability when training detectors on it (Section 3.4)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 429, + 254, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 254, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 254, + 441 + ], + "type": "text", + "content": "3.2. Image Synthesizer for Object Detection" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 447, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 590 + ], + "type": "text", + "content": "Here, we build our image synthesizer based on an off-the-shelf stable diffusion model (SDM [28]). Despite of its impressive ability in generating photo-realistic images, it often outputs images with only one or two objects on simplistic background with the text prompts, for example, 'a photograph of a [category1 name] and a [category2 name]' as demonstrated in Figure 4b. As a result, object detectors trained on such images may exhibit reduced robustness when dealing with complex real-world scenarios. To bridge such domain gap, we propose to construct the image synthesizer by fine-tuning the SDM with an existing real-world detection dataset " + }, + { + "bbox": [ + 46, + 447, + 287, + 590 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{real}})" + }, + { + "bbox": [ + 46, + 447, + 287, + 590 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Fine-tuning procedure. To fine-tune the stable diffusion model (SDM), one approach is to naively use the sample from detection dataset, for example, randomly pick an image and construct the text prompt with all categories in the image. However, as the image often contains multiple objects, such approach renders significant difficulty for fine-tuning the SDM, especially for small or occluded objects. We adopt a mild strategy by taking random crops from the images, and construct the text prompt with categories in the image crops, as shown in Figure 2a. If an image crop con" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 266, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 291 + ], + "type": "text", + "content": "tains multiple objects of the same category, we only use this category name once in the text prompt." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 293, + 546, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 546, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 546, + 329 + ], + "type": "text", + "content": "Fine-tuning loss. We use the sampled image crop and constructed text prompt to fine-tune SDM with a squared error loss on the predicted noise term as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 322, + 329, + 545, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 329, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 322, + 329, + 545, + 350 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f i n e - t u n e}} = \\mathbb {E} _ {z, \\epsilon \\sim \\mathcal {N} (0, 1), t, y} \\left[ | | \\epsilon - \\epsilon_ {\\theta} \\left(z ^ {t}, t, y\\right) | | _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "8f19a7f13df34d4571f3eec4a8cb8cd97e4892777d89805baca19b015bcdf309.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": " denotes a latent vector mapped from the input image with VAE, " + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": " denotes the denoising step, uniformly sampled from " + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "inline_equation", + "content": "\\{1,\\dots ,T\\}" + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": " refers to the length of the diffusion Markov chain, and " + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": " refers to the estimated noise from SDM with parameters " + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 357, + 546, + 439 + ], + "type": "text", + "content": " being updated. We have experimentally verified the necessity of this fine-tuning step, as shown in Table 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 447, + 519, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 519, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 519, + 460 + ], + "type": "text", + "content": "3.3. Dataset Synthesizer for Object Detection" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 466, + 546, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 546, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 546, + 646 + ], + "type": "text", + "content": "In this section, we present details for steering the image synthesizer into dataset synthesizer for object detection, which enables to simultaneously generate images and object bounding boxes. Specifically, we propose an instance-level grounding module that aligns the text embedding of object category, with the regional visual feature of the diffusion model, and infers the coordinates for bounding boxes, effectively augmenting the image synthesizer with instance grounding, as shown in Figure 3. To further improve the alignment in large visual diversity, we propose a self-training scheme that enables the grounding module to generalise towards arbitrary categories, including those not exist in real detection dataset " + }, + { + "bbox": [ + 304, + 466, + 546, + 646 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{real}})" + }, + { + "bbox": [ + 304, + 466, + 546, + 646 + ], + "type": "text", + "content": ". As a result, our data synthesizer, termed as InstaGen, can be used to construct synthetic dataset for training object detectors." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 651, + 508, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 651, + 508, + 663 + ], + "spans": [ + { + "bbox": [ + 305, + 651, + 508, + 663 + ], + "type": "text", + "content": "3.3.1 Instance Grounding on Base Categories" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "To localise the object instances in synthetic images, we introduce an open-vocabulary grounding module, that aims to simultaneously generate image " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "(x)" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " and the corresponding instance-level bounding boxes " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "(\\mathcal{B})" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " based on a set of" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14123" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 268 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 268 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 268 + ], + "type": "image", + "image_path": "bccb423f8f5aad018cd1d7c9571f9ee6743743209874d0f42abc938ab9cb5069.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 273, + 546, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 546, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 546, + 307 + ], + "type": "text", + "content": "Figure 3. Illustration of the dataset generation process in InstaGen. The data generation process consists of two steps: (i) Image collection: given a text prompt, SDM generates images with the objects described in the text prompt; (ii) Annotation generation: the instance-level grounding head aligns the category embedding with the visual feature region of SDM, generating the corresponding object bounding-boxes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "text", + "content": "categories " + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "inline_equation", + "content": "(\\mathcal{V})" + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "inline_equation", + "content": "\\{x, \\mathcal{B}, \\mathcal{Y}\\} = \\Phi_{\\mathrm{InstaGen}}(\\epsilon, \\mathcal{Y})" + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 46, + 319, + 287, + 343 + ], + "type": "text", + "content": " denotes the sampled noise." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "text", + "content": "To this end, we propose an instance grounding head, as shown in Figure 3, it takes the intermediate representation from image synthesizer and the text embedding of category as inputs, then predicts the corresponding object bounding boxes, i.e., " + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{B}_i,\\mathcal{Y}_i\\} = \\Phi_{\\mathrm{g - head}}(\\mathcal{F}_i,\\Phi_{\\mathrm{t - enc}}(g(\\mathcal{Y}_i)))" + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i = \\{f_i^1,\\dots ,f_i^n\\}" + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "text", + "content": " refers to the multi-scale dense features from the image synthesizer at time step " + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "text", + "content": " denotes a template that decorates each of the visual categories in the text prompt, e.g., 'a photograph of [category1 name] and [category2 name], " + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathrm{t - enc}}(\\cdot)" + }, + { + "bbox": [ + 46, + 348, + 287, + 469 + ], + "type": "text", + "content": " denotes the text encoder." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": "Inspired by GroundingDINO [22], our grounding head " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathrm{g - head}}(\\cdot)" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " mainly contains four components: (i) a channel-compression layer, implemented with a " + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " convolution, for reducing the dimensionality of the visual features; (ii) a feature enhancer, consisting of six feature enhancer layers, to fuse the visual and text features. Each layer employs a deformable self-attention to enhance image features, a vanilla self-attention for text feature enhancers, an image-to-text cross-attention and a text-to-image cross-attention for feature fusion; (iii) a language-guided query selection module for query initialization. This module predicts top-" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": " anchor boxes based on the similarity between text features and image features. Following DINO [38], it adopts a mixed query selection where the positional queries are initialized with the anchor boxes and the content queries remain learnable; (iv) a cross-modality decoder for classification and box refinement. It comprises six decoder layers, with each layer utilizing a self-attention mechanism for query interaction, an image cross-attention layer for combining image features, and a text cross-attention layer for combining text" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "type": "text", + "content": "features. Finally, we apply the dot product between each query and the text features, followed by a Sigmoid function to predict the classification score " + }, + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "type": "inline_equation", + "content": "\\hat{s}" + }, + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "type": "text", + "content": " for each category. Additionally, the object queries are passed through a Multi-Layer Perceptron (MLP) to predict the object bounding boxes " + }, + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "type": "inline_equation", + "content": "\\hat{b}" + }, + { + "bbox": [ + 304, + 319, + 546, + 462 + ], + "type": "text", + "content": ", as shown in Figure 3. We train the grounding head by aligning the category embedding with the regional visual features from diffusion model, as detailed below. Once trained, the grounding head is open-vocabulary, i.e., given any categories (even beyond the training categories), the grounding head can generate the corresponding bounding-boxes for the object instances." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": "Training triplets of base categories. Following [18], we apply an automatic pipeline to construct the " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\{" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": " visual feature, bounding-box, text prompt\\} triplets, with an object detector trained on base categories from a given dataset " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "(D_{\\mathrm{real}})" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": ". In specific, assuming there exists a set of base categories " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\{c_{\\mathrm{base}}^{1},\\ldots ,c_{\\mathrm{base}}^{N}\\}" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": ", e.g., the classes in MS-COCO [20]. We first select a random number of base categories to construct a text prompt, e.g., 'a photograph of [base category1] and [base category2]' and generate both the visual features and images with our image synthesizer. Then we take an off-the-shelf object detector, for example, pre-trained Mask R-CNN [12], to run the inference procedure on the synthetic images, and infer the bounding boxes of the selected categories. To acquire the confident bounding-boxes for training, we use a score threshold " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": " to filter out the bounding-boxes with low confidence (an ablation study on the selection of the score threshold has been conducted in Section 4.5). As a result, an infinite number of training triplets for the given base categories can be constructed by repeating the above operation." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14124" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 99, + 175 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 99, + 175 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 99, + 175 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 99, + 175 + ], + "type": "image", + "image_path": "7ea2c8d082a4325287778db1498f4094d90ddbec49a9345045a2f32109f27c98.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 177, + 206, + 197 + ], + "lines": [ + { + "bbox": [ + 48, + 177, + 206, + 197 + ], + "spans": [ + { + "bbox": [ + 48, + 177, + 206, + 197 + ], + "type": "text", + "content": "(a) Stable Diffusion " + }, + { + "bbox": [ + 48, + 177, + 206, + 197 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 48, + 177, + 206, + 197 + ], + "type": "text", + "content": " Grounding head w/ Supervised training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 101, + 70, + 152, + 175 + ], + "blocks": [ + { + "bbox": [ + 101, + 70, + 152, + 175 + ], + "lines": [ + { + "bbox": [ + 101, + 70, + 152, + 175 + ], + "spans": [ + { + "bbox": [ + 101, + 70, + 152, + 175 + ], + "type": "image", + "image_path": "18578e5af17a8eaf7f6b1e5f8dbd8ef7289313346dcaad9ba62ac788e215dd7a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 545, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 545, + 222 + ], + "type": "text", + "content": "Figure 4. Visualization of the synthetic images and bounding-boxes generated from different models. 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We use the constructed training triplets to train the grounding head:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 64, + 266, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 266, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 64, + 266, + 287, + 298 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {b a s e}} = \\sum_ {i = 1} ^ {N} \\left[ \\mathcal {L} _ {\\operatorname {c l s}} \\left(\\hat {s} _ {i}, c _ {i}\\right) + \\mathbb {1} _ {\\{c _ {i} \\neq \\emptyset \\}} \\mathcal {L} _ {\\text {b o x}} \\left(\\hat {b} _ {i}, b _ {i}\\right) \\right], \\tag {2}", + "image_path": "715ef42e8a61bad1631358e361e322fcecf7835b738cc081166018831854a2e0.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": "th prediction " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "(\\hat{s}_i, \\hat{b}_i)" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": " object queries is assigned to a ground-truth " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "(c_i, b_i)" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\varnothing" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": " (no object) with bipartite matching. " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{box}}" + }, + { + "bbox": [ + 46, + 306, + 287, + 366 + ], + "type": "text", + "content": " denote the classification loss (e.g. Focal loss) and box regression loss (e.g. L1 loss and GIoU loss), respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 380, + 253, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 253, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 253, + 392 + ], + "type": "text", + "content": "3.3.2 Instance Grounding on Novel Categories" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "content": "Till here, we have obtained a diffusion model with open-vocabulary grounding, which has been only trained with base categories. In this section, we propose to further leverage the synthetic training triplets from a wider range of categories to enhance the alignment for novel/unseen categories. Specifically, as shown in Figure 2b, we describe a framework that generates the training triplets for novel categories using the grounded diffusion model, and then selftrain the grounding head." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": "Training triplets of novel categories. We design the text prompts of novel categories, e.g., 'a photograph of [novel category1] and [novel category2], and pass them through our proposed image synthesizer, to generate the visual features. To acquire the corresponding bounding-boxes for novel categories, we propose a self-training scheme that takes the above grounding head as the student, and apply a mean teacher (an exponential moving average (EMA) of the student model) to create pseudo labels for update. In contrast to the widely adopted self-training scheme that takes the image as input, the student and teacher in our case only take the visual features as input, thus cannot apply data augmentation as for images. Instead, we insert dropout module within each feature enhancer layer and decoder layer in the student. During training, we run inference (without dropout module) with teacher model on the visual features to produce bounding boxes, and then use a score threshold " + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": " to" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 238, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 238, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 238, + 545, + 274 + ], + "type": "text", + "content": "filter out those with low confidence, and use the remaining training triplets " + }, + { + "bbox": [ + 305, + 238, + 545, + 274 + ], + "type": "inline_equation", + "content": "(\\mathcal{F}_i,\\hat{b}_i,y_i^{\\mathrm{novel}})" + }, + { + "bbox": [ + 305, + 238, + 545, + 274 + ], + "type": "text", + "content": " to train the student, i.e., grounding head." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "content": "Training loss. Now, we can also train the grounding head on the mined triplets of novel categories (that are unseen in the existing real dataset) with the training loss " + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{novel}}" + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "content": " defined similar to Eq. 2. Thus, the total training loss for training the grounding head can be: " + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{grounding}} = \\mathcal{L}_{\\mathrm{base}} + \\mathcal{L}_{\\mathrm{novel}}" + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 349, + 520, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 520, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 520, + 361 + ], + "type": "text", + "content": "3.4. Training Detector with Synthetic Dataset" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "type": "text", + "content": "In this section, we augment the real dataset " + }, + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{real}})" + }, + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "type": "text", + "content": ", with synthetic dataset " + }, + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{syn}})" + }, + { + "bbox": [ + 305, + 368, + 545, + 404 + ], + "type": "text", + "content": ", and train popular object detectors, for example, Faster R-CNN [27] with the standard training loss:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 334, + 412, + 545, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 412, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 334, + 412, + 545, + 425 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\det } = \\mathcal {L} _ {\\text {r p n ＿ c l s}} + \\mathcal {L} _ {\\text {r p n ＿ b o x}} + \\mathcal {L} _ {\\det ＿ c l s} + \\mathcal {L} _ {\\det ＿ \\text {b o x}}, \\tag {3}", + "image_path": "668e26bf0ca301db90e69a10b4416ac6953988acf0de3f1054bbd6728beeef8e.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rpn\\_cls}}" + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rpn\\_box}}" + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "text", + "content": " are the classification and box regression losses of region proposal network, and " + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{det\\_cls}}" + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{det\\_box}}" + }, + { + "bbox": [ + 304, + 431, + 545, + 516 + ], + "type": "text", + "content": " are the classification and box regression losses of the detection head. Generally speaking, the synthetic dataset enables to improve the detector's ability from two aspects: (i) expanding the original data with more categories, (ii) improving the detection performance by increasing data diversity." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 518, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 650 + ], + "type": "text", + "content": "Expanding detection categories. The grounding head is designed to be open-vocabulary, that enables to generate object bounding boxes for novel categories, even though it is trained with a specific set of base categories. This feature enables InstaGen to construct a detection dataset for any category. Figure 4 demonstrates several synthetic images and object bounding boxes for novel categories, i.e., the object with red bounding box. We evaluate the effectiveness of training on synthetic dataset through experiments on open-vocabulary detection benchmark. For more details, please refer to Figure 1b and Section 4.2." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Increasing data diversity. The base diffusion model is trained on a large corpus of image-caption pairs, that enables to generate diverse images. Taking advantage of such capabilities, InstaGen is capable of generating dataset with diverse images and box annotations, which can expand the" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14125" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 70, + 504, + 230 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 504, + 230 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 504, + 230 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 504, + 230 + ], + "type": "table", + "html": "
MethodSupervisionDetectorBackbone\\(AP50_{all}^{box}\\)\\(AP50_{base}^{box}\\)\\(AP50_{novel}^{box}\\)
Detic [41]CLIPFaster R-CNNR5045.047.127.8
PromptDet [5]CLIPFaster R-CNNR50-50.626.6
BARON [34]CLIPFaster R-CNNR5053.560.434.0
OADP [33]CLIPFaster R-CNNR5047.253.330.0
ViLD [9]CLIPMask R-CNNR5051.359.527.6
F-VLM [16]CLIPMask R-CNNR5039.6-28.0
RO-ViT [13]CLIPMask R-CNNViT-B [1]41.5-30.2
VLDet [19]CLIPCenterNet2 [40]R5045.850.632.0
CxORA [35]CLIPDAB-DETR [21]R5035.435.535.1
DK-DETR [17]CLIPDeformable DETR [42]R50-61.132.3
EdaDet [31]CLIPDeformable DETR [42]R5052.557.737.8
InstaGenStable DiffusionFaster R-CNNR5052.355.842.3
", + "image_path": "3f34f8509f35c3a708dc9f9fec3a199d3943b43058d2d8c4d8d3a4f344c55ea9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "type": "text", + "content": "Table 1. Results on open-vocabulary COCO benchmark. " + }, + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "type": "inline_equation", + "content": "\\mathrm{AP50}_{\\text {novel }}^{\\text {box }}" + }, + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "type": "text", + "content": " is the main metric for evaluation. Our detector, trained on synthetic dataset from InstaGen, significantly outperforms state-of-the-art CLIP-based approaches on novel categories." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 266, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 288, + 350 + ], + "type": "text", + "content": "original dataset, i.e., increase the data diversity and improve detection performance, particularly in data-sparse scenarios. We conducted experiments with varying proportions of COCO [20] images as available real data, and show the effectiveness of training on synthetic dataset when the number of real-world images is limited. We refer the readers for more details in Section 4.3, and results in Figure 1c." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 355, + 124, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 355, + 124, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 124, + 369 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 507 + ], + "type": "text", + "content": "In this section, we use the proposed InstaGen to construct synthetic dataset for training object detectors, i.e., generating images with the corresponding bounding boxes. Specifically, we present the implementation details in Section 4.1. To evaluate the effectiveness of the synthetic dataset for training object detector, we consider three protocols: open-vocabulary object detection (Section 4.2), data-sparse object detection (Section 4.3) and cross-dataset object detection (Section 4.4). Lastly, we conduct ablation studies on the effectiveness of the proposed components and the selection of hyper-parameters (Section 4.5)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 513, + 178, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 178, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 178, + 525 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 531, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 638 + ], + "type": "text", + "content": "Network architecture. We build image synthesizer from the pre-trained Stable Diffusion v1.4 [28], and use the CLIP text encoder [24] to get text embedding for the category name. The channel compression layer maps the dimension of visual features to 256, which is implemented with a " + }, + { + "bbox": [ + 46, + 531, + 287, + 638 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 531, + 287, + 638 + ], + "type": "text", + "content": " convolution. For simplicity, the feature enhancer, language-guided query selection module and cross-modality decoder are designed to the same structure as the ones in [22]. The number of the object queries is set to 900." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Constructing image synthesizer. In our experiments, we first fine-tune the stable diffusion model on a real detection dataset, e.g., the images of base categories. During training, the text encoder of CLIP is kept frozen, while the remaining components are trained for 6 epochs with a batch size of 16 and a learning rate of 1e-4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 266, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 361 + ], + "type": "text", + "content": "Instance grounding module. We start by constructing the training triplets using base categories i.e., the categories present in the existing dataset. The text prompt for each triplet is constructed by randomly selecting one or two categories. The regional visual features are taken from the image synthesizer time step " + }, + { + "bbox": [ + 304, + 266, + 545, + 361 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 304, + 266, + 545, + 361 + ], + "type": "text", + "content": ", and the oracle ground-truth bounding boxes are obtained using a Mask R-CNN model trained on base categories, as explained in Section 3.3.1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "type": "text", + "content": "Subsequently, we train the instance grounding module with these training triplets for 6 epochs, with a batch size of 32. In the 6th epoch, we transfer the weights from the student model to the teacher model, and proceed to train the student for an additional 6 epochs. During this training, the student receives supervised training on the base categories and engages in self-training on novel categories, and the teacher model is updated using exponential moving average (EMA) with a momentum of 0.999. The initial learning rate is set to 1e-4 and is subsequently reduced by a factor of 10 at the 11th epoch, and the score thresholds " + }, + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 361, + 546, + 505 + ], + "type": "text", + "content": " are set to 0.8 and 0.4, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "type": "text", + "content": "Training object detector on combined dataset. In our experiment, we train an object detector (Faster R-CNN [27]) with ResNet-50 [11] as backbone, on a combination of the existing real dataset and the synthetic dataset. Specifically, for synthetic dataset, we randomly select one or two categories at each iteration, construct the text prompts, and feed them as input to generate images along with the corresponding bounding boxes with " + }, + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "type": "text", + "content": " of 0.4. Following the standard implementation [27], the detector is trained for 12 epochs (" + }, + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "type": "inline_equation", + "content": "1\\times" + }, + { + "bbox": [ + 304, + 508, + 547, + 651 + ], + "type": "text", + "content": " learning schedule) unless specified. The initial learning rate is set to 0.01 and then reduced by a factor of 10 at the 8th and the 11th epochs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 659, + 487, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 487, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 487, + 672 + ], + "type": "text", + "content": "4.2. Open-vocabulary object detection" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Experimental setup. Following the previous works [5, 39], we conduct experiments on the open-vocabulary COCO benchmark, where 48 classes are treated as base categories," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14126" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 209, + 115 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 209, + 115 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 209, + 115 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 209, + 115 + ], + "type": "table", + "html": "
InstaGen10%25%50%75%100%
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✓28.532.635.837.338.5
", + "image_path": "bb73ab333d022f716aa7c96c94c8997f470b58f1c7762a8c24bccce5b36123e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 223, + 70, + 535, + 132 + ], + "blocks": [ + { + "bbox": [ + 47, + 122, + 209, + 188 + ], + "lines": [ + { + "bbox": [ + 47, + 122, + 209, + 188 + ], + "spans": [ + { + "bbox": [ + 47, + 122, + 209, + 188 + ], + "type": "text", + "content": "Table 2. Results on data-sparse object detection. We employ Faster R-CNN with the ResNet-50 backbone as the default object detector and evaluate its performance using the AP metric on MS COCO benchmark. Please refer to the text for more details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 223, + 70, + 535, + 132 + ], + "lines": [ + { + "bbox": [ + 223, + 70, + 535, + 132 + ], + "spans": [ + { + "bbox": [ + 223, + 70, + 535, + 132 + ], + "type": "table", + "html": "
MethodSupervisionDetectorExtra DataObject365LVIS
Gao et al. [7]CLIPCenterNet2✓6.98.0
VL-PLM [39]CLIPMask R-CNN✓10.922.2
InstaGenStable DiffusionFaster R-CNN✗11.423.3
", + "image_path": "69c38325dd2000d73f8c12da3ea304b716e6b8f8dc8d7464215cce3e779d4ce7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 57, + 200, + 274, + 256 + ], + "blocks": [ + { + "bbox": [ + 217, + 134, + 543, + 190 + ], + "lines": [ + { + "bbox": [ + 217, + 134, + 543, + 190 + ], + "spans": [ + { + "bbox": [ + 217, + 134, + 543, + 190 + ], + "type": "text", + "content": "Table 3. Results on generalizing COCO-base to Object365 and LVIS. All detectors utilize the ResNet-50 backbone. The evaluation protocol follows [7] and reports AP50. Extra data refers to an additional dataset that encompasses objects from the categories within the target dataset. In both experiments, the extra data consists of all the images from COCO, which has covered the majority of categories in Object365 and LVIS." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 200, + 274, + 256 + ], + "lines": [ + { + "bbox": [ + 57, + 200, + 274, + 256 + ], + "spans": [ + { + "bbox": [ + 57, + 200, + 274, + 256 + ], + "type": "table", + "html": "
G-headSTFT\\( AP50_{all}^{box} \\)\\( AP50_{base}^{box} \\)\\( AP50_{novel}^{box} \\)
✓50.655.337.1
✓✓51.155.040.3
✓✓✓52.355.842.3
", + "image_path": "c8f1929aee34bca9b3f4200320368aa4157df46290f6b6b13edea82850ec7d48.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 259, + 287, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 287, + 293 + ], + "type": "text", + "content": "Table 4. The effectiveness of the proposed components. G-head, ST and FT refer to the grounding head, self-training the grounding head and fine-tuning SDM, respectively." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 308, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 308, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 45, + 308, + 287, + 416 + ], + "type": "text", + "content": "and 17 classes as the novel categories. More results for LVIS can be found in the supplementary material. To train the grounding head, we employ 1250 synthetic images per category per training epoch. While for training the object detector, we use 3000 synthetic images per category, along with the original real dataset for base categories. The object detector is trained with input size of " + }, + { + "bbox": [ + 45, + 308, + 287, + 416 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 45, + 308, + 287, + 416 + ], + "type": "text", + "content": " and scale jitter. The performance is measured by COCO Average Precision at an Intersection over Union of 0.5 (AP50)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 419, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 419, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 45, + 419, + 287, + 575 + ], + "type": "text", + "content": "Comparison to SOTA. As shown in Table 1, we evaluate the performance by comparing with existing CLIP-based open-vocabulary object detectors. It is clear that our detector trained on synthetic dataset from InstaGen outperforms existing state-of-the-art approaches significantly, i.e., around " + }, + { + "bbox": [ + 45, + 419, + 287, + 575 + ], + "type": "inline_equation", + "content": "+5\\mathrm{AP}" + }, + { + "bbox": [ + 45, + 419, + 287, + 575 + ], + "type": "text", + "content": " improvement over the second best. In essence, through the utilization of our proposed open-vocabulary grounding head, InstaGen is able to generate detection data for novel categories, enabling the detector to attain exceptional performance. To the best of our knowledge, this is the first work that applies generative diffusion model for dataset synthesis, to tackle open-vocabulary object detection, and showcase its superiority in this task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 586, + 203, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 203, + 599 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 203, + 599 + ], + "type": "text", + "content": "4.3. Data-sparse object detection" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Experimental setup. Here, we evaluate the effectiveness of synthetic dataset in data-spare scenario, by varying the amount of real data. We randomly select subsets comprising " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " of the COCO training set, this covers all COCO categories. These subsets are used to fine-tune stable diffusion model for constructing image synthesizer, and train a Mask R-CNN for generating oracle ground-truth bounding boxes in synthetic images. We employ 1250 synthetic images per category to train a Faster R-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 202, + 544, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 202, + 544, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 202, + 544, + 227 + ], + "type": "text", + "content": "CNN in conjunction with the corresponding COCO subset. The performance is measured by Average Precision [20]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "text", + "content": "Comparison to baseline. As shown in Table 2, the Faster R-CNN trained with synthetic images achieves consistent improvement across various real training data budgets. Notably, as the availability of real data becomes sparse, synthetic dataset plays even more important role for performance improvement, for instance, it improves the detector by " + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "inline_equation", + "content": "+5.2" + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "text", + "content": " AP " + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "inline_equation", + "content": "(23.3\\rightarrow 28.5" + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "text", + "content": " AP) when only " + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 231, + 545, + 327 + ], + "type": "text", + "content": " real COCO training subset is available." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 341, + 468, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 341, + 468, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 341, + 468, + 354 + ], + "type": "text", + "content": "4.4. Cross-dataset object detection" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 361, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 553 + ], + "type": "text", + "content": "Experimental setup. In this section, we assess the effectiveness of synthetic data on a more challenging task, namely cross-dataset object detection. Following [39], we evaluate the COCO-trained model on two unseen datasets: Object365 [30] and LVIS [10]. Specifically, we consider the 48 classes in the open-vocabulary COCO benchmark as the source dataset, while Object365 (with 365 classes) and LVIS (with 1203 classes) serve as the target dataset. When training the instance grounding module, we acquire 1250 synthetic images for base categories from the source dataset, and 100 synthetic images for the category from the target dataset at each training iteration. In the case of training the object detector, we employ 500 synthetic images per category from the target dataset for each training iteration. The detector is trained with input size of " + }, + { + "bbox": [ + 304, + 361, + 545, + 553 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 361, + 545, + 553 + ], + "type": "text", + "content": " and scale jitter [39]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Comparison to SOTA. The results presented in Table 3 demonstrate that the proposed InstaGen achieves superior performance in generalization from COCO-base to Object365 and LVIS, when compared to CLIP-based methods such as [7, 39]. It is worth noting that CLIP-based methods require the generation of pseudo-labels for the categories from the target dataset on COCO images, and subsequently train the detector using these images. These methods necessitate a dataset that includes objects belonging to the categories of the target dataset. In contrast, InstaGen possesses the ability to generate images featuring objects of any category without the need for additional datasets, thereby enhancing its versatility across various scenarios." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14127" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 204, + 127 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 204, + 127 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 204, + 127 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 204, + 127 + ], + "type": "table", + "html": "
#ImagesAP50boxallAP50boxbaseAP50boxnovel
100051.655.939.7
200051.755.441.1
300052.355.842.3
", + "image_path": "5de6f0f9e9afebf92ea8f9844251a4b0409390ae722aadd3d27459d13aa295b5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 230, + 70, + 369, + 127 + ], + "blocks": [ + { + "bbox": [ + 58, + 130, + 198, + 141 + ], + "lines": [ + { + "bbox": [ + 58, + 130, + 198, + 141 + ], + "spans": [ + { + "bbox": [ + 58, + 130, + 198, + 141 + ], + "type": "text", + "content": "Table 5. Number of generated images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 230, + 70, + 369, + 127 + ], + "lines": [ + { + "bbox": [ + 230, + 70, + 369, + 127 + ], + "spans": [ + { + "bbox": [ + 230, + 70, + 369, + 127 + ], + "type": "table", + "html": "
αAP50boxallAP50boxbaseAP50boxnovel
0.751.355.140.6
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", + "image_path": "3b4204242bc21184ad9d727dc228e72096802302c6aac6610fda2e2fba08c273.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 397, + 130, + 537, + 140 + ], + "lines": [ + { + "bbox": [ + 397, + 130, + 537, + 140 + ], + "spans": [ + { + "bbox": [ + 397, + 130, + 537, + 140 + ], + "type": "text", + "content": "Table 7. " + }, + { + "bbox": [ + 397, + 130, + 537, + 140 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 397, + 130, + 537, + 140 + ], + "type": "text", + "content": " for bounding-box filtration." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 148, + 138, + 161 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 138, + 161 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 138, + 161 + ], + "type": "text", + "content": "4.5. Ablation study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "type": "text", + "content": "To understand the effectiveness of the proposed components, we perform thorough ablation studies on the open-vocabulary COCO benchmark [20], investigating the effect of fine-tuning stable diffusion model, training instance grounding module, self-training on novel categories. Additionally, we investigate other hyper-parameters by comparing the effectiveness of synthetic images and different score thresholds for base and novel categories." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 268, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 286, + 399 + ], + "type": "text", + "content": "Fine-tuning diffusion model. We assess the effectiveness of fine-tuning stable diffusion model, and its impact for synthesizing images for training object detector. Figure 4c illustrates that InstaGen is capable of generating images with more intricate contexts, featuring multiple objects, small objects, and occluded objects. Subsequently, we employed these generated images to train Faster R-CNN for object detection. The results are presented in Table 4, showing that image synthesizer from fine-tuning stable diffusion model delivers improvement detection performance by 2.0 AP (from 40.3 to 42.3 AP)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 404, + 286, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 404, + 286, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 286, + 524 + ], + "type": "text", + "content": "Instance grounding module. To demonstrate the effectiveness of the grounding head in open-vocabulary scenario, we exclusively train it on base categories. Visualization examples of the generated images are presented in Figure 4a. These examples demonstrate that the trained grounding head is also capable of predicting bounding boxes for instances from novel categories. Leveraging these generated images to train the object detector leads to a 37.1 AP on novel categories, surpassing or rivaling all existing state-of-the-art methods, as shown in Table 1 and Table 4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 529, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 286, + 613 + ], + "type": "text", + "content": "Self-training scheme. We evaluate the performance after self-training the grounding head with novel categories. As shown in Table 4, training Faster R-CNN with the generated images of novel categories, leads to a noticeable enhancement in detection performance, increasing from 37.1 to 40.3 AP. Qualitatively, it also demonstrates enhanced recall for novel objects after self-training, as shown in Figure 4b." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 712 + ], + "type": "text", + "content": "Number of synthetic images. We investigate the performance variation while increasing the number of the generated images per category for detector training. As shown in Table 5, when increasing the number of generated images from 1000 to 3000, the detector's performance tends to be increasing monotonically, from 39.7 to 42.3 AP on novel categories, showing the scalability of the proposed training mechanism." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": "Score thresholds for bounding box filtration. We compare the performance with different score thresholds " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " for filtering bounding boxes on base categories and novel categories, respectively. From the experiment results in Table 6, we observe that the performance is not sensitive to the value of " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\alpha = 0.8" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " yields the best performance. The experimental results using different " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " are presented in Table 7. With a low score threshold (" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\alpha = 0.3" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": "), there are still numerous inaccurate bounding boxes remaining, resulting in an AP of 26.9 for novel categories. by increasing " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " to 0.4, numerous inaccurate bounding boxes are filtered out, resulting in optimal performance. Hence, we set " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\alpha = 0.8" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\beta = 0.4" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " in our experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 316, + 375, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 375, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 375, + 328 + ], + "type": "text", + "content": "5. Limitation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 335, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 528 + ], + "type": "text", + "content": "Using synthetic or artificially generated data in training AI algorithms is a burgeoning practice with significant potential. It can address data scarcity, privacy, and bias issues. However, there remains two limitations for training object detectors with synthetic data, (i) synthetic datasets commonly focus on clean, isolated object instances, which limits the exposure of the detector to the complexities and contextual diversity of real-world scenes, such as occlusions, clutter, varied environmental factors, deformation, therefore, models trained on synthetic data struggle to adapt to real-world conditions, affecting their overall robustness and accuracy, (ii) existing diffusion-based generative model also suffers from long-tail issue, that means the generative model struggles to generate images for objects of rare categories, resulting in imbalanced class representation during training and reduced detector performance for less common objects." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 540, + 378, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 378, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 378, + 552 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "type": "text", + "content": "This paper proposes a dataset synthesis pipeline, termed as InstaGen, that enables to generate images with object bounding boxes for arbitrary categories, acting as an annotation-free approach for constructing large-scale synthetic dataset to train object detector. We have conducted thorough experiments to show the effectiveness of training on synthetic data, on improving detection performance, or expanding the number of detection categories. Significant improvements have been shown in various detection scenarios, including open-vocabulary " + }, + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "type": "inline_equation", + "content": "(+4.5\\mathrm{AP})" + }, + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "type": "text", + "content": " and datasparse " + }, + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "type": "inline_equation", + "content": "(+1.2\\sim 5.2\\mathrm{AP})" + }, + { + "bbox": [ + 304, + 559, + 545, + 690 + ], + "type": "text", + "content": " detection." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. WX is supported by National Key R&D Program of China (No. 2022ZD0161400)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14128" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. 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This capability requires instance tracking in real-world 3D scenes from egocentric videos (IT3DEgo). We explore this problem by first introducing a new benchmark dataset, consisting of RGB and depth videos, per-frame camera pose, and instance-level annotations in both 2D camera and 3D world coordinates. We present an evaluation protocol which evaluates tracking performance in 3D coordinates with two settings for enrolling instances to track: (1) single-view online enrollment where an instance is specified on-the-fly based on the human wearer's interactions, and (2) multi-view pre-enrollment where images of an instance to be tracked are stored in memory ahead of time. To address IT3DEgo, we first repurpose methods from relevant areas, e.g., single object tracking (SOT) — running SOT methods to track instances in 2D frames and lifting them to 3D using camera pose and depth. We also present a simple method that leverages pretrained segmentation and detection models to generate proposals from RGB frames and match proposals with enrolled instance images. Our experiments show that our method (with no finetuning) significantly outperforms SOT-based approaches in the egocentric setting. We conclude by arguing that the problem of egocentric instance tracking is made easier by leveraging camera pose and using a 3D allocentric (world) coordinate representation. Dataset and open-source code: https://github.com/IT3DEgo/IT3DEgo.", + "bbox": [ + 76, + 292, + 473, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Egocentric video obtained from AR/VR devices provides a unique perspective that captures the interaction between the human wearer and the surrounding 3D environment. With the rapid development of AR/VR hardware, there is increasing interest in building assistive agents [41, 57, 59, 68], that track the user's environment and provide contextual guidance on the location of objects of interest (illustrated in Figure 1). We argue that developing such an agent requires solving the", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "largely unexplored problem of tracking object instances in $3D$ from egocentric video.", + "bbox": [ + 496, + 263, + 890, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Why this problem? First, tracking in egocentric video is a novel and underexplored problem, compared to the well-studied tracking from fixed, third-person viewpoints. More broadly, egocentric visual understanding tasks, such as human pose estimation and trajectory prediction [4, 15, 64] are a growing area of interest. Second, tracking in 3D scenes is essential in robotics, autonomous driving, and AR/VR applications. Compared to the 2D counterpart, tracking objects in 3D is crucial for an agent to not only understand the surrounding 3D environment but also to determine precise locations for planning and navigation. Combining the two perspectives above, there is a broader question of what information processing constraints govern how the human visual system integrates egocentric sensory data into a seemingly allocentric perception of the world around us.", + "bbox": [ + 496, + 292, + 893, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Challenges and new opportunities. (1) Egocentric video often features motion blur, hand occlusions, and frequent object disappearances and reappearance which make the 2D tracking problem very challenging from pure visual signals [15, 60]. Tracking in 3D offers an opportunity to fuse additional sensor streams, such as depth and camera pose, to improve accuracy. Unlike 2D tracking with a moving camera, 3D tracking in world coordinates allows the model to leverage the unique prior information – an object should remain still unless being interacted with the human operator. (2) For the downstream application of task guidance, we propose exploring novel approaches to identify or enroll object instances to be tracked. One approach is automatically enrolling objects with which the user interacts or identifies via hand gestures such as pointing. Alternatively, object instances relevant to a particular task could be pre-enrolled based on a collection of images that specify the visual appearance of the object in advance.", + "bbox": [ + 496, + 518, + 895, + 790 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contribution 1: Dataset collection. To our best knowledge, no existing dataset supports exploring the problem of IT3DEgo (c.f. Table 1). The recent Ego4D dataset [23] highlights some of these challenges. However, the Ego4D dataset only provides RGB frames1 and sparse annotations (may", + "bbox": [ + 496, + 791, + 893, + 867 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Ego4D does provide a sparse set of camera poses (less than $15\\%$ of frames) estimated with COLMAP and predicted depth maps using monocu", + "bbox": [ + 500, + 875, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21933", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67cb49cfc42ccaf2d076ade462e6735c1482b41882bda493b7ed8627ad15b281.jpg", + "image_caption": [ + "Figure 1. Motivation for the proposed IT3DEgo benchmark task. We envision the real-world application of an assistive agent that continuously tracks enrolled object instances in 3D and can provide navigation guidance to users to retrieve object instances at any time. Tracked objects are either enrolled online (first row in the library) where objects of interest are identified automatically based on user interactions or pre-enrolled (bottom four rows in the library), where task-relevant objects are modeled from a collection of photos taken from different views. The former setup comes with additional in-context sensor information, such as camera pose and depth while the latter features richer visual information." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 885, + 265 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "miss potential object location changes), making it unsuitable to fully explore the problem. We collect a new benchmark dataset with HoloLens2, including an RGB camera, a depth sensor, four grayscale cameras, per-frame camera pose and coarse scene geometry as a mesh. We describe the details of dataset statistics, capture procedures, and annotations in Section 3.2.", + "bbox": [ + 75, + 369, + 470, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contribution 2: Benchmarking protocol. We propose a new IT3DEgo Benchmark for studying instance tracking in 3D scenes from egocentric videos with two settings for how objects are selected for tracking. (1) Tracking with single-view online enrollment (SVOE) studies the scenario where object instances of interest are defined on-the-fly, i.e., objects are specified with a 2D bounding box in the frame where they first become fully visible to the user. (2) Tracking with multiview pre-enrollment (MVPE) assumes objects of interest are specified by multiple photos of the object of interest from different viewpoints before the tracking system starts. As detailed in Section 3.1, we evaluate performance with standard precision/recall metrics as well as geometric L2 and angular errors used in the Ego4D VQ3D evaluation [23].", + "bbox": [ + 75, + 477, + 470, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contribution 3: Technical explorations. Since our benchmark task is novel and underexplored in the literature, it is natural to re-purpose and evaluate existing approaches (e.g., SOT methods). We also explore an alternative piecewise constant velocity method that utilizes the Kalman filter [26] with instance proposals from SAM [29] and encoded by DINOv2 [43], resulting in drastic performance improvement over state-of-the-art SOT methods. Section 4 and 5 provide details regarding baselines and benchmark results, respectively. From the experimental results, we provide the following insights: Tracking object instances in egocentric videos is easier in 3D scenes leveraging camera poses and", + "bbox": [ + 75, + 690, + 470, + 872 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "depth maps. Intuitively, an object not being interacted with has the same 3D position in a predefined world coordinate but the positions in 2D frames can change drastically due to the head motion. As a result, existing state-of-the-art 2D SOT approaches perform poorly on egocentric data. Future work should address the problem of re-identifying objects by leveraging the camera poses and accurately identifying and updating object motion changes.", + "bbox": [ + 496, + 369, + 893, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 508, + 640, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Egocentric video datasets have been developed to study different problems over the last decade [10, 17, 23, 32, 46, 58]. Traditionally, egocentric video understanding has focused on tasks such as activity recognition [27, 47, 48, 54], human-object interactions [9, 36, 37], and inferring the camera wearer's body pose [25, 40, 52, 64]. Recently, more tasks have emerged due to the increasing interest in egocentric videos, such as action anticipation [18, 19, 51], privacy protection [13, 53, 61], and estimating social interactions [33, 42, 74]. However, object tracking in egocentric videos is largely underexplored in the literature until the introduction of recent datasets [15, 60]. These existing tracking datasets only support 2D tracking, which motivates us to collect and setup a new benchmark to evaluate real-world 3D instance tracking.", + "bbox": [ + 496, + 536, + 893, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Tracking in 3D scenes aims to identify objects of interest in 3D space from a sequence of frames. The prediction output format depends on the downstream tasks, including 3D bounding boxes [28, 67], 3D object centers [73, 79], or 6DOF poses [2, 20]. State-of-the-art 3D tracking models [6, 38, 78] have focused on well-established third-person perspective benchmark datasets [5, 8, 21]. The recent largescale Ego4D dataset starts to address the problem of querying the 3D positions of objects from a first-person perspective.", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "lar depth estimation.", + "bbox": [ + 76, + 887, + 187, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21934", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/461df97ea062571b4d2ece5744e429658cc4cf20f5f6da062e72ee833282b21d.jpg", + "table_caption": [ + "Table 1. Comparisons of egocentric datasets that explore tracking-related problem. Existing egocentric datasets only explore the tracking problem in 2D or predicting discrete 3D locations. Some mention the tracking problem in 3D but only consider limited sensor data (RGB) or synthetic environments. Our benchmark dataset supports the study of instance tracking in 3D real-world scenarios (RWS in the table) from egocentric videos." + ], + "table_footnote": [], + "table_body": "
DatasetModalityDeviceAvg. LengthAnnot. FPSRWSCamera Trajectory3D TrackingYear
TREK-150 [14]RGBGoPro10s60✓Natural✗2021
EK-VISOR [10]RGBGoPro12s0.9✓Natural✗2022
Ego4D-VQ3D [23]RGBGoPro--✓Natural✗2022
EMQA [12]RGB-D+IMU---✗Simulated✗2022
EgoPAT3D [35]RGB-D+IMUKinect4min30✗Object-Centric✗2022
DigitalTwin [44]RGB-D+IMUAria2min-✗Natural✓2022
EgoTrack [60]RGBGoPro6min5✓Natural✗2022
OursRGB-D+IMUHoloLens>5min6✓Natural✓2023
", + "bbox": [ + 81, + 146, + 879, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, the raw sensor data in Ego4D only includes RGB images and no other 3D information, such as depth and camera poses [75, 76]. However, contemporary AR/VR headsets come with additional cameras, depth, and IMU sensors that allow for richer geometric reasoning [44, 62]. Therefore, we believe it is realistic to leverage diverse sensor streams and explore the egocentric tracking problem in 3D. Our benchmark dataset thus includes multiple raw sensors and derived data streams to support the study tracking in 3D scenes with modern hardware platforms.", + "bbox": [ + 75, + 292, + 472, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object instance detection and tracking is a long-standing problem in computer vision and robotics [16, 22, 24, 56, 63]. Instead of predicting labels from a predefined set of object categories, instance-level predictions treat every object instance as a separate category. Instance-level tracking aims to locate given object instances in a sequence of frames, commonly using a tracking-by-detection paradigm. One common formulation is person re-identification [71, 77], which aims to track and associate individual people as they enter and leave multiple cameras' fields of view. Our setting is closely related but is dominated by the motion of the (egocentric) camera rather than the dynamics of object motion.", + "bbox": [ + 75, + 445, + 473, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. IT3DEgo: Protocol and Dataset", + "text_level": 1, + "bbox": [ + 76, + 657, + 366, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The problem of IT3DEgo is motivated by real-world assistive agents running on AR/VR devices. Given an object instance specified by the end user, developed models are required to track it in the 3D environment, i.e., recording its 3D location over time (cf. Fig. 2). In this section, we introduce our benchmarking protocol and dataset.", + "bbox": [ + 75, + 683, + 470, + 776 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Benchmarking Protocol", + "text_level": 1, + "bbox": [ + 76, + 785, + 295, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Because object instances of interest are naturally diverse and may fall outside of the vocabulary of existing detectors, we set up a benchmarking protocol that focuses on evaluation without a separate training set. In other words, models should be pretrained on other data sources and cannot see objects in our dataset. This aligns with the contemporary foun", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dation models (e.g., CLIP [49] and SAM [29]) pretrained on open-world data.", + "bbox": [ + 496, + 292, + 890, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instances enrollment. We consider two distinct setups to specify object instances of interest. The first is single-view online enrollment (SVOE), similar to single object tracking (SOT) where an object is specified on-the-fly by the end users. For example, the user can specify an object of interest by interacting or pointing to it, after which the system should track it in the 3D world. The second is multi-view pre-enrollment (MVPE), which defines (or pre-enrolls) concerned objects with a set of object-centric images captured from multiple angles. The two setups present different challenges. SVOE provides a bounding box of the object (similar to specifying an object in SOT), but the visual quality is generally lower in resolution as the objects can be far from the camera. MVPE provides 25 high-resolution $(2124\\times 2832)$ object-centric images of the instances captured from different angles. However, the object instance is captured under different lighting conditions than the tracking environment, and can be posed differently (e.g., keys can be deformed over time).", + "bbox": [ + 496, + 323, + 893, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Evaluation protocols. Following the literature on object tracking and detection, we use the metrics below in our benchmarking protocol.", + "bbox": [ + 496, + 611, + 893, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- Precision and recall at different L2 distance thresholds. Given $N$ specific thresholds $\\tau_{i}$ with $i\\in \\{1,2,\\dots N\\}$ , specifically 0.25, 0.5, 0.75, 1.0, and 1.5 meters, a ground-truth object location $\\mathbf{o}_{\\mathrm{gt}}\\in \\mathbb{R}^3$ and a predicted location $\\mathbf{o}_{\\mathrm{pred}}\\in \\mathbb{R}^3$ , we count a true positive $(\\mathrm{TP}_i)$ when $||\\mathbf{o}_{\\mathrm{gt}} - \\mathbf{o}_{\\mathrm{pred}}||_2\\leq \\tau_i$ . At each timestamp, each ground-truth is matched to the prediction with the smallest L2 distance below the threshold. Unmatched predictions and ground-truth at threshold $\\tau_{i}$ are counted as false positives $(\\mathrm{FP}_i)$ and false negatives $(\\mathrm{FN}_i)$ , respectively. $\\mathrm{TP}_i$ , $\\mathrm{FP}_i$ , and $\\mathrm{FN}_i$ are computed over all object instances in every frame. The precision and recall at threshold $\\tau_{i}$ is computed as $\\sum \\mathrm{TP}_i / (\\sum \\mathrm{TP}_i + \\sum \\mathrm{FP}_i)$ and $\\sum \\mathrm{TP}_i / (\\sum \\mathrm{TP}_i + \\sum \\mathrm{FN}_i)$ , respectively [50, 72].", + "bbox": [ + 500, + 657, + 893, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- L2 and angular error. Following VQ3D in Ego4D [23], we also compute the L2 distance between the ground-truth", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21935", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e1cb59c4bab8a8277df27bc4491190694c0db709d35277fa4999c691565405a8.jpg", + "image_caption": [ + "Figure 2. Illustration of input and output of our benchmark task. Given a raw RGB-D video sequence with camera poses and object instances of interest, i.e., either by online enrollment (SVOE) or pre-enrollment (MVPE), the goal of our benchmark task is to output the object instance 3D centers in a predefined world coordinate at each timestamp. Please check Section 3.1 for more details." + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 558, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e17cc6ff4d2cec06b0d793d19da5a0cf2d466b1fe99f80aab6075d80efc61b2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 85, + 883, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and predictions in the world coordinates in meters. We also report the angular error in radians in the current camera coordinate system. Unlike threshold-aware 3D precision and recall, these metrics are computed only on frames where both ground-truth and prediction of the object instance location are available.", + "bbox": [ + 89, + 318, + 470, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To make 3D annotation tractable, we only evaluate predictions during time intervals when target objects are stationary (i.e., not being handled by the camera wearer).", + "bbox": [ + 76, + 411, + 470, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dataset", + "text_level": 1, + "bbox": [ + 76, + 468, + 171, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Raw video collection. The raw IT3DEgo data was recorded by three individuals in ten diverse indoor scenes, e.g., kitchen, garage, office, labs, etc. The participants perform naturalistic tasks with different object instances in the scene, e.g., cooking, repairing, writing, etc. The raw data includes 50 recordings in total. Each recording contains five or more object instances, each of which appears at three different 3D locations on average. The average length of each recording is $10\\mathrm{K}$ frames or $>5\\mathrm{min}$ . We capture the raw data with HoloLens2 (see Suppl.) which includes an RGB camera, a depth sensor, and four grayscale cameras with the resolution of $720\\times 1280$ , $480\\times 640$ , $512\\times 512$ , respectively. Raw sensors operate at different frequencies, we sync all other sensors to the frequency of the RGB camera (30 fps). We also provide a coarse resolution scene mesh of each environment reconstructed by the Hololense OS. Additional details of the video sequences are described in the supplementary material.", + "bbox": [ + 75, + 491, + 470, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object instance collection. To support the SVOE setup, annotators identify the first RGB frame where a given object is fully visible and close enough to specify a 2D bounding box which is at least 500 pixels in area. For MVPE, we collected 25 high-resolution images of each object instance using iPhone 13 Pro. Each object was placed on a rotary table with QR codes. We took 12 photos of each object evenly from $360^{\\circ}$ while keeping the camera at about $30^{\\circ}$ elevation, 12 more at $60^{\\circ}$ elevation and 1 top-down view.", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We provide additional details and visualizations of object instances in the supplementary material.", + "bbox": [ + 498, + 318, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Annotations. Our dataset includes three types of manual annotations: (1) Object instance 3D centers describe the 3D positions of each object instance center in a world coordinate frame. We annotate the 3D center by first averaging 3D points computed from camera poses and depth maps of different views of the object instance. Annotators then examine and adjust computed 3D points by visualizing them together with the coarse mesh of the scene. (2) 2D bounding box annotations are axis-aligned 2D bounding boxes of the instance every five frames starting from the beginning of the video. Specifically, we ask annotators to draw amodal bounding boxes of each object instance. We do not annotate the object instances with heavy occlusions (i.e., when less than $25\\%$ of the object is visible). (3) Object motion state annotations are a per-frame annotation of whether the object is stationary or dynamic. For the data we collected, dynamic implies the camera wearer is interacting with the object.", + "bbox": [ + 496, + 349, + 892, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 500, + 623, + 635, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Baseline: Re-purposed SOT Trackers", + "text_level": 1, + "bbox": [ + 500, + 648, + 823, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To approach the problem of IT3DEgo, we first explore a simple unified pipeline as the baseline approach based on single object tracking (SOT). It allows instance-level 2D tracking by providing the visual appearance of object instances to track [3, 11, 70], which enables us to re-purpose them for our benchmark task. In the unified pipeline, we first compute the 2D trajectories of each object instance with SOT. The final 3D trajectories are computed by lifting the center of 2D bounding boxes with depth maps and camera poses. Lastly, we adopt a simple memory mechanism that stores the previous locations of each object instance to handle the case where the instance moves out of sight, i.e., frames without valid predictions.", + "bbox": [ + 496, + 672, + 893, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lifting 2D trajectories to 3D. With the 2D trajectory predicted from SOT, each valid 2D detection is then lifted", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21936", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "into 3D space with the equation: $\\mathbf{o}_t^i = \\mathbf{T}_tz\\mathbf{K}^{-1}\\mathbf{c}_t^i$ , where $\\mathbf{c}_t^i$ is the 2D coordinate of the center of the bounding box of instance $i$ at timestamp $t$ , $\\mathbf{o}_t^i$ is the 3D position of instance $i$ at timestamp $t$ in world coordinate. $z$ is the corresponding depth value of $\\mathbf{c}_t^i$ on the depth map. $\\mathbf{T}_t$ is the camera pose at timestamp $t$ that specifies the camera rotation and translation w.r.t to a predefined world coordinate. $\\mathbf{K}$ is the intrinsic matrix. A frame may lack a valid 3D prediction because either there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map is missing the depth value at $\\mathbf{c}_t^i$ .", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Completing 3D trajectories with memory. Any given frame may lack a valid 3D prediction, either because there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map has missing depth values at $\\mathbf{c}_t^i$ . To address this we implement a simple memory mechanism that stores only the most recent 3D location for each tracked instance (memory size=1). We update the memory whenever there is a new valid prediction. We note that this heuristic is a good match for the prior that object locations change only when they are being interacted with, in which case they should also be visible to the camera.", + "bbox": [ + 75, + 258, + 472, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Improved Baseline", + "text_level": 1, + "bbox": [ + 76, + 436, + 256, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also explore the approach that leverages the recent foundation model SAM [29] and state-of-the-art feature encoder DINOv2 [43] for IT3DEgo. Following a tracking-by-detection pipeline, we first compute the per-frame 2D detections of each object instance by comparing the cosine similarity of DINOv2 encoded features between candidate proposals from SAM and a visual feature template. Together with the depth and camera pose information, we convert the 2D detection of each object into a 3D point in a predefined world coordinate. A simple memory with size 1 is also adopted to handle the frames without valid predictions.", + "bbox": [ + 75, + 460, + 472, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Exploring motion prior with Kalman filters. Currently, the naive update mechanism, i.e., always updating the memory for all incoming predictions, does not exploit the temporal information in video sequences. Inspired by the Kalman filter [45, 66, 67] that is widely adopted in the tracking literature, we simply model the stationary position of each object instance as piecewise constant velocity motion, leveraging the prior information that an object without being interacted with has the same 3D coordinate. Mathematically, the motion update with Kalman filter in each stationary position: $\\hat{\\mathbf{x}}_{t + 1} = \\hat{\\mathbf{x}}_t + \\mathbf{K}_t(\\mathbf{z_t} - \\mathbf{H}\\hat{\\mathbf{x}}_{\\mathbf{t}})$ , where $\\hat{\\mathbf{x}}_t$ is a 6DOF estimated state vector including position and velocity at time step $t$ , $\\mathbf{K}_t$ is the Kalman gain, $\\mathbf{z}_{\\mathrm{t}}$ is a 3DOF the measurement vector, $\\mathbf{H}$ is the observation matrix. Please refer to Kalman [26] for more details. Moving from one stationary position to the next one, we introduce an L2 distance heuristic to model the period where objects are being interacted. Specifically, we compute the L2 distance between incoming 3D positions", + "bbox": [ + 75, + 628, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and the state predictions from the Kalman filter. If the L2 distance is above the threshold, we reset the Kalman filter with the current 3D predictions as the initialization.", + "bbox": [ + 496, + 90, + 893, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 146, + 633, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first describe the implementation details of benchmark results. Then, we show the quantitative results of both setups and the visualizations of tracking results. Lastly, we demonstrate the importance of exploiting camera pose for tracking in 3D and perform ablation studies of the trackers. Note that we split our benchmark dataset into validation and test sets. All experiments are conducted on the validation set; the test set is used for future work.", + "bbox": [ + 496, + 172, + 893, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baseline SOT trackers. We choose top-ranked trackers from well-established SOT literature and VOT challenges with open-source code for both tracking setups. Specifically, we benchmark three short-term trackers ToMP [39], MixFormer [7], and ARTrack [65]; and three top-performing trackers from VOT long-term tracking challenges 2021 [30] and 2022 [31], mixLT, mlpLT and VITKT_M. We also evaluate trackers that utilize additional depth information as part of the input, including SAMF and MixForRGBD from VOT RGB-D tracking challenge 2022 [31], and ViPT [80]. Lastly, we benchmark the recent egocentric specific finetuned trackers, EgoSTARK [60]. Note that SOT trackers require initial bounding boxes to track, which are not available in MVPE. When re-purposing to MVPE setup, we explore two different initializations: (1) detection-based initialization: use multiview pre-enrollment images to search for the initial bounding boxes where object instances first appear in the video and initialize SOT trackers with the predicted 2D boxes. (2) template-based initialization: directly adopt multi-view pre-enrollment images as visual templates in the tracker and set the initial tracking search region to the entire frame.", + "bbox": [ + 496, + 295, + 895, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. The cosine similarity threshold in the SAM+DINOv2 approach is 0.6, i.e., the object is considered not visible if the cosine similarity is smaller than the threshold. For a fair comparison, we add additional 2D prediction filtering when re-purposing SOT trackers. We discard 2D predictions from SOT trackers whose prediction scores are lower than $75\\%$ of the maximum prediction score. When tracking with MVPE, we first preprocess the captured multi-view images by segmenting and cropping the foreground object using [34]. Many transformer-based SOT trackers only encode a limited number of templates, therefore, we choose 5 images from $0^{\\circ}$ , $90^{\\circ}$ , $180^{\\circ}$ , $270^{\\circ}$ and top-down for all models in MVPE experiments. We include an ablation study exploring the relationship between tracking results and the number of views used in the supplementary material. To keep the comparison fair, all detection-based trackers in MVPE use SAM+DINOv2 with the same cosine thresholds to locate the initial bounding boxes. In terms of benchmarking RGB-D trackers in MVPE, we utilize the", + "bbox": [ + 496, + 613, + 895, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21937", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b9529dda03dbccdf893a86dcdf31b7aa3eea91fafdbf14a7cc9a7a64f4eb6a5d.jpg", + "image_caption": [ + "Figure 3. Qualitative visualizations of tracking with SVOE in both 3D space (left) and projected 2D view (right). We visualize three top-performing trackers from different categories, i.e., EgoSTARK, VITKT_M, and SAM+DINOv2. For projected 2D visualization, we compare the projected 3D points of each model w.r.t to the ground-truth annotated 2D bounding boxes. In the 3D view, we show 3 concentric circles at each ground-truth position representing 0.25, 0.5 and 0.75 meter thresholds. In both 2D and 3D visualizations, we find SAM+DINOv2 outperforms others as the predictions are closer to the center of object instances." + ], + "image_footnote": [], + "bbox": [ + 94, + 116, + 401, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/06513af8d920b71d82d735596f4ce56f5e19ca28d86f49d1bd178080b11f0a52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 405, + 116, + 883, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "estimated sparse depth maps using COLMAP [55]. The L2 distance threshold of resetting Kalman filters is $0.15\\mathrm{m}$ . All experiments are implemented with PyTorch and run on Nvidia 2080Ti GPUs.", + "bbox": [ + 75, + 367, + 470, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Benchmark Results", + "text_level": 1, + "bbox": [ + 76, + 438, + 264, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tracking with SVOE. From the results shown in Table 2, we have the following salient insights: (1) Re-identifying object instances is important. Trackers designed with strong re-identify ability, i.e., long-term and egocentric specific types, outperform short-term trackers. Similar findings are shown in recent 2D egocentric tracking work [15, 60]. Surprisingly, SAM+DINOv2, the non-learned approach which does not exploit temporal information beyond the memory heuristic, performs the best among all baselines. We believe the exhaustive proposals on every frame and high quality features provide the model strong, generic re-identification ability. (2) Depth information is not fully leveraged. Current RGB-D trackers show similar or slightly worse performance compared to RGB-ST trackers (c.f. MixFormer and MixforRGBD). The main reason is that RGB-D trackers only encode depth maps as auxiliary visual features, which cannot fully exploit the geometric information from depth maps. Additionally, the depth maps are sparse and not always perfectly aligned with RGB images due to camera distortions. (3) Simple Kalman filter brings marginal benefits. The Kalman filter does not improve over the simple \"most recent\" memory heuristic for stationary objects. The naive filter is also not sufficient for modeling the switching between stationary and dynamic motions needed to capture user-object interactions.", + "bbox": [ + 75, + 462, + 470, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tracking with MVPE. We benchmark top-performing trackers in each category in Table 2 for MVPE setup. From the results shown in Table 3, we find: (1) SOT trackers cannot fully exploit pre-enrollment information. SOT methods", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rely on the initial position defined by 2D boxes on the frame to perform well. Comparing detection-based initializations and SVOE results, e.g., $\\mathrm{ARTrack}^{\\mathrm{D}}$ and ARTrack in Table 2, the model performance drops since the initial boxes are not as accurate as ground-truth initialization. VITKT_M adopts many complicated modules that all rely on the initial bounding boxes and degrades more significantly, compared to other types of trackers. (2) Encoding rich visual information generally helps. From the results of template-based initializations, VITKT_M for the same reason mentioned before, we find trackers benefit from the high-resolution multi-view images. SAM+DINOv2 shows a significant performance boost because it is more robust to inaccurate initialization without relying on temporal information.", + "bbox": [ + 496, + 367, + 893, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results. Figure 3 shows predictions of top-performing trackers from three different categories, i.e., best tracker in long-term and egocentric specific, and SAM+DINOv2. Clearly, SAM+DINOv2 predictions are closer to the object center in both 3D and projected 2D space.", + "bbox": [ + 496, + 579, + 893, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Further Analysis and Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 680, + 820, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further compare tracking object instances in both 2D and 3D settings, demonstrating tracking object instances is much easier in 3D space. We also include an ablation study regarding the cosine similarity thresholds. All studies shown in this section are using SAM+DINOv2 unless otherwise specified. More quantitative and qualitative results are shown in the supplementary materials.", + "bbox": [ + 496, + 704, + 890, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tracking in 2D with 3D guidance. We experimentally demonstrate the importance of leveraging 3D information in egocentric instance tracking by comparing 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D tracking results are computed with predicted 3D trajectories as the guidance. For each object instance, the per-frame", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21938", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e693609a9746589ba7885a1a8c0348305c2e2c2fb73f09de20409e255cc7a9f.jpg", + "table_caption": [ + "Table 2. Benchmark results of tracking with SVOE. From the results, we draw three salient conclusions: (1) The ability of re-identifying object instances after they disappear is important, as long-term and egocentric specific trackers outperform short-term trackers, i.e., RGB-ST and RGB-D. (2) Currently, encoding depth maps as auxiliary information cannot improve performance since depth maps are sparse and not always perfectly aligned with RGB frames due to distortions. (3) The Kalman filter smoothing yields marginal improvements over the simple memory heuristic. The method with KF subscript indicates it applies the Kalman filter." + ], + "table_footnote": [], + "table_body": "
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
ToMPRGB-ST5.610.117.225.339.06.111.018.827.742.62.111.32
MixFormerRGB-ST8.312.218.727.043.09.013.420.429.547.01.971.15
ARTrackRGB-ST9.113.921.530.345.110.115.323.732.447.21.921.10
SAMFRGB-D7.011.515.724.040.87.712.517.226.344.71.901.00
MixForRGBDRGB-D7.512.116.825.341.08.313.420.128.545.02.111.32
ViPTRGB-D8.913.620.628.141.49.714.922.530.745.32.021.21
mixLTRGB-LT14.417.523.931.847.215.819.226.134.851.61.851.02
mlpLTRGB-LT16.020.025.535.248.216.720.826.536.750.11.770.97
VITKT_MRGB-LT21.524.229.737.550.623.025.931.840.254.21.550.83
EgoSTARKRGB-Ego17.521.226.836.349.117.622.027.438.051.21.700.91
SAM + DINOv2RGB23.326.433.143.359.424.928.135.346.363.41.350.81
SAM + DINOv2KFRGB23.727.133.944.561.225.529.036.848.064.91.320.79
", + "bbox": [ + 80, + 159, + 888, + 364 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/de8825be45c13fa00fd509a2cce121c98bc785ca7218e0b7cd38bf51860e8274.jpg", + "table_caption": [ + "Table 3. Benchmark results of tracking with MVPE. We evaluate top-performing trackers in each category in Table 2 for MVPE setup. From the results, we have the following summaries: (1) SOT trackers cannot fully exploit pre-enrollment information. Detection-initialized versions perform less well compared to SVOE due to the inaccurate estimated initial bounding boxes. VITKT_M, which uses many modules that rely heavily on the initialization, degrades more significantly. (2) Encoding rich visual information generally helps. SAM+DINOv2 shows an even larger performance boost because it is more robust to the inaccurate initialization. The D and T superscripts indicate the detection- and template-based initializations, respectively." + ], + "table_footnote": [], + "table_body": "
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
\\( ARTrack^D \\)RGB-ST6.812.118.525.841.07.112.318.826.842.11.981.16
\\( ARTrack^T \\)RGB-ST11.218.125.228.738.512.720.928.533.045.11.911.07
\\( ViPT^D \\)RGB-D6.311.717.924.940.26.911.817.925.941.02.011.21
\\( ViPT^T \\)RGB-D10.517.424.027.136.311.920.127.131.344.01.931.10
\\( VITKT_M^D \\)RGB-LT13.818.025.033.046.614.318.625.834.148.21.770.98
\\( VITKT_M^T \\)RGB-LT9.212.820.728.544.09.714.222.431.346.51.951.08
\\( EgoSTARK^D \\)RGB-Ego13.217.023.130.547.014.718.525.934.449.71.821.01
\\( EgoSTARK^T \\)RGB-Ego18.923.128.337.149.619.123.129.339.152.91.670.88
SAM + DINOv2RGB56.059.061.867.574.350.052.755.260.366.40.670.40
SAM + DINOv2_KFRGB56.259.462.268.174.850.353.155.761.167.10.650.39
", + "bbox": [ + 80, + 455, + 890, + 638 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b243618e58df93377c32f299d7d00d451df41d7a95720615bad0650572669f13.jpg", + "table_caption": [ + "Table 4. Quantitative comparisons of 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D results are computed by finding the bounding box proposal with the smallest L2 distance from projected 3D trajectories. Without 3D guidance means proposals are selected purely based on the visual feature cosine similarity. Please refer to Section 5.2 for more details. From the results, we find the tracking results are significantly improved with the 3D guidance, indicating that tracking in 3D in egocentric videos is much easier than in 2D by leveraging camera pose and depth sensors." + ], + "table_footnote": [], + "table_body": "
3D Guid.AUC(%)↑N. Prec.(%)↑Prec.(%)↑
SVOEX20.714.98.9
✓27.621.711.5
MVPEX14.17.43.0
✓39.135.218.7
", + "bbox": [ + 84, + 795, + 459, + 873 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "2D detection results are computed by selecting the (above threshold) proposal with the smallest L2 distance between projected 3D points and the center of bounding boxes proposals. Without 3D guidance means the 2D tracking results are produced by selecting the proposal with the highest cosine feature similarity. To keep a fair comparison, the cosine similarity threshold is the same when computing the 3D and 2D trajectories. We evaluate the 2D tracking performance using widely adopted precision, normalized precision metrics and AUC in SOT literature [69]. As shown in Table 4, the model with 3D guidance performs significantly better in both SVOE and MVPE, demonstrating that leveraging the 3D information, such as camera pose and depth map, makes the tracking problem much easier.", + "bbox": [ + 496, + 654, + 893, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance w.r.t cosine similarity thresholds. Feature cosine similarity threshold is adopted to determine whether", + "bbox": [ + 500, + 869, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21939", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/19d022e3941fe38a206a8267ac85d18c86a3fef8507c39084977a0f5631dd1a1.jpg", + "image_caption": [ + "Figure 4. Performance comparisons of SAM+DINOv2 with different cosine thresholds. By increasing the threshold, we find the model performance first improves and then gradually decreases. Intuitively, increasing the threshold will initially filter noisy predictions but when the threshold is too large the model will miss correct object 3D location updates." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 888, + 210 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the object instance is present in the current frame, which is crucial for the memory updating mechanism. To characterize the relationship between tracking performance and cosine similarity thresholds, we run the experiment with different cosine similarity thresholds but keep everything else the same. As shown in Figure 4, both models show improved performance at first and then a gradual decrease. Higher cosine thresholds result in fewer predictions so the model must increasingly rely on previous confident predictions stored in the memory. Models with large cosine similarity thresholds have a higher chance of missing valid location updates, which leads to a drop in both precision and recall.", + "bbox": [ + 75, + 267, + 472, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 465, + 191, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. We point out that the current benchmark dataset has limited geographic and demographic diversity and captures only a small range of objects and activities. As such it is not appropriate for training large models and only serves as a diagnostic test to identify some limitations of existing approaches. Our hope is that it serves as a starting point for the research community to explore and eventually grow into a more comprehensive challenge. Currently, the studied baseline approaches follow the same paradigm, i.e., lifting predicted 2D trajectories into 3D space. We found empirically that the simplest memory mechanism performed best but it seems very likely there are more nuanced state-update models which can integrate multiple observations effectively.", + "bbox": [ + 75, + 491, + 470, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we highlight two opportunities for future work. First, advanced models to detect object 3D motion changes. Our experiments demonstrate that tracking in 3D world coordinates effectively narrows the problem to that of accurately predicting the object motion status, i.e., finding all stationary periods for each object instance. However, accurately predicting object state changes is still a non-trivial problem to solve. Second, better utilization of object instance information. Currently, the object instances enrollments, i.e., SVOE and MVPE are naively encoded as visual features. Future work should explore the approaches of fusing the additional scene 3D information with object instances for better tracking performance.", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Broader impact. We believe the broader impact of our work is two-fold. First, we hope our benchmark brings more attention to the problem of tracking object instances in 3D from the egocentric perspective and contributes towards building future task-aware assistive agents. Second, our multi-modal benchmark dataset is beneficial to the study of other 3D scene understanding related problems from the egocentric perspective, such as SLAM, camera localization, 3D reconstruction, and depth estimation.", + "bbox": [ + 496, + 267, + 893, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Potential negative impacts. Tracking in 3D from egocentric videos requires the geometric data of surrounding environments and the sensor streams that continuously capture their workplace or daily lives. There are obvious privacy concerns when deploying such hardware and algorithms. Similar to other apps running on personal devices, the simple solution is to keep all user data locally or (in the context of research) develop techniques for anonymizing video [61].", + "bbox": [ + 496, + 406, + 895, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 550, + 619, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce a new IT3DEgo benchmark that allows us to study the problem of tracking object instances in 3D from egocentric videos. The object instances to be tracked are either determined in advance or enrolled online during user interactions with the environment. To support the study, we collect and annotate a new dataset that features RGB-D videos and per-frame camera poses, along with instance-level annotations in both 2D camera and 3D world coordinate frames. We re-purpose and evaluate state-of-the-art single object trackers and develop a strong baseline using large pretrained recognition models and Kalman filtering. We hope our benchmark brings more attention to this challenge and contributes to the development of perceptually-aware assistive agents.", + "bbox": [ + 496, + 579, + 893, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was partially supported by the DARPA Perceptually enabled Task Guidance (PTG) Program (HR00112220005). Shu Kong was partially supported by the University of Macau (SRG2023-00044-FST). We thank Juan Carlos Dibene for the help of using hl2ss [1]; An Dang for the help with the initial development of the data capture; Yi-Ling Lin for the help of partial data annotations.", + "bbox": [ + 496, + 795, + 895, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21940", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hololens 2 sensor streaming. https://github.com/jdibenes/hl2ss, 2023.8", + "[2] Adel Ahmadyan, Liangkai Zhang, Artsiom Ablavatski, Jianing Wei, and Matthias Grundmann. Objectron: A large scale dataset of object-centric videos in the wild with pose annotations. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9516-9526, 2023. 5" + ], + "bbox": [ + 78, + 90, + 470, + 388 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "21944", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/Instance Tracking in 3D Scenes from Egocentric Videos/7d6af3cb-cad2-4fee-942f-c5f4b1f4a49b_model.json b/2024/Instance Tracking in 3D Scenes from Egocentric Videos/7d6af3cb-cad2-4fee-942f-c5f4b1f4a49b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e711fb4cfb4d1df790fcc0a30b93cfa4449b247f --- /dev/null +++ b/2024/Instance Tracking in 3D Scenes from Egocentric Videos/7d6af3cb-cad2-4fee-942f-c5f4b1f4a49b_model.json @@ -0,0 +1,2182 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.131, + 0.768, + 0.154 + ], + "angle": 0, + "content": "Instance Tracking in 3D Scenes from Egocentric Videos" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.18, + 0.905, + 0.234 + ], + "angle": 0, + "content": "Yunhan Zhao\\(^{1}\\) Haoyu Ma\\(^{1}\\) Shu Kong\\(^{2,3,4}\\) Charless Fowlkes\\(^{1}\\) \n\\(^{1}\\)UC Irvine \\(^{2}\\)Texas A&M University \\(^{3}\\)Institute of Collaborative Innovation \\(^{4}\\)University of Macau \n{yunhaz5, haoyum3, fowlkes}@ics.uci.edu skong@um.edu.mo" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.262, + 0.314, + 0.279 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.294, + 0.474, + 0.732 + ], + "angle": 0, + "content": "Egocentric sensors such as AR/VR devices capture human-object interactions and offer the potential to provide task-assistance by recalling 3D locations of objects of interest in the surrounding environment. This capability requires instance tracking in real-world 3D scenes from egocentric videos (IT3DEgo). We explore this problem by first introducing a new benchmark dataset, consisting of RGB and depth videos, per-frame camera pose, and instance-level annotations in both 2D camera and 3D world coordinates. We present an evaluation protocol which evaluates tracking performance in 3D coordinates with two settings for enrolling instances to track: (1) single-view online enrollment where an instance is specified on-the-fly based on the human wearer's interactions, and (2) multi-view pre-enrollment where images of an instance to be tracked are stored in memory ahead of time. To address IT3DEgo, we first repurpose methods from relevant areas, e.g., single object tracking (SOT) — running SOT methods to track instances in 2D frames and lifting them to 3D using camera pose and depth. We also present a simple method that leverages pretrained segmentation and detection models to generate proposals from RGB frames and match proposals with enrolled instance images. Our experiments show that our method (with no finetuning) significantly outperforms SOT-based approaches in the egocentric setting. We conclude by arguing that the problem of egocentric instance tracking is made easier by leveraging camera pose and using a 3D allocentric (world) coordinate representation. Dataset and open-source code: https://github.com/IT3DEgo/IT3DEgo." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Egocentric video obtained from AR/VR devices provides a unique perspective that captures the interaction between the human wearer and the surrounding 3D environment. With the rapid development of AR/VR hardware, there is increasing interest in building assistive agents [41, 57, 59, 68], that track the user's environment and provide contextual guidance on the location of objects of interest (illustrated in Figure 1). We argue that developing such an agent requires solving the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.293 + ], + "angle": 0, + "content": "largely unexplored problem of tracking object instances in \\(3D\\) from egocentric video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.895, + 0.52 + ], + "angle": 0, + "content": "Why this problem? First, tracking in egocentric video is a novel and underexplored problem, compared to the well-studied tracking from fixed, third-person viewpoints. More broadly, egocentric visual understanding tasks, such as human pose estimation and trajectory prediction [4, 15, 64] are a growing area of interest. Second, tracking in 3D scenes is essential in robotics, autonomous driving, and AR/VR applications. Compared to the 2D counterpart, tracking objects in 3D is crucial for an agent to not only understand the surrounding 3D environment but also to determine precise locations for planning and navigation. Combining the two perspectives above, there is a broader question of what information processing constraints govern how the human visual system integrates egocentric sensory data into a seemingly allocentric perception of the world around us." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.896, + 0.791 + ], + "angle": 0, + "content": "Challenges and new opportunities. (1) Egocentric video often features motion blur, hand occlusions, and frequent object disappearances and reappearance which make the 2D tracking problem very challenging from pure visual signals [15, 60]. Tracking in 3D offers an opportunity to fuse additional sensor streams, such as depth and camera pose, to improve accuracy. Unlike 2D tracking with a moving camera, 3D tracking in world coordinates allows the model to leverage the unique prior information – an object should remain still unless being interacted with the human operator. (2) For the downstream application of task guidance, we propose exploring novel approaches to identify or enroll object instances to be tracked. One approach is automatically enrolling objects with which the user interacts or identifies via hand gestures such as pointing. Alternatively, object instances relevant to a particular task could be pre-enrolled based on a collection of images that specify the visual appearance of the object in advance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Contribution 1: Dataset collection. To our best knowledge, no existing dataset supports exploring the problem of IT3DEgo (c.f. Table 1). The recent Ego4D dataset [23] highlights some of these challenges. However, the Ego4D dataset only provides RGB frames1 and sparse annotations (may" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.895, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)Ego4D does provide a sparse set of camera poses (less than \\(15\\%\\) of frames) estimated with COLMAP and predicted depth maps using monocu" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21933" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.887, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.896, + 0.355 + ], + "angle": 0, + "content": "Figure 1. Motivation for the proposed IT3DEgo benchmark task. We envision the real-world application of an assistive agent that continuously tracks enrolled object instances in 3D and can provide navigation guidance to users to retrieve object instances at any time. Tracked objects are either enrolled online (first row in the library) where objects of interest are identified automatically based on user interactions or pre-enrolled (bottom four rows in the library), where task-relevant objects are modeled from a collection of photos taken from different views. The former setup comes with additional in-context sensor information, such as camera pose and depth while the latter features richer visual information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.471, + 0.476 + ], + "angle": 0, + "content": "miss potential object location changes), making it unsuitable to fully explore the problem. We collect a new benchmark dataset with HoloLens2, including an RGB camera, a depth sensor, four grayscale cameras, per-frame camera pose and coarse scene geometry as a mesh. We describe the details of dataset statistics, capture procedures, and annotations in Section 3.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.471, + 0.689 + ], + "angle": 0, + "content": "Contribution 2: Benchmarking protocol. We propose a new IT3DEgo Benchmark for studying instance tracking in 3D scenes from egocentric videos with two settings for how objects are selected for tracking. (1) Tracking with single-view online enrollment (SVOE) studies the scenario where object instances of interest are defined on-the-fly, i.e., objects are specified with a 2D bounding box in the frame where they first become fully visible to the user. (2) Tracking with multiview pre-enrollment (MVPE) assumes objects of interest are specified by multiple photos of the object of interest from different viewpoints before the tracking system starts. As detailed in Section 3.1, we evaluate performance with standard precision/recall metrics as well as geometric L2 and angular errors used in the Ego4D VQ3D evaluation [23]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.471, + 0.873 + ], + "angle": 0, + "content": "Contribution 3: Technical explorations. Since our benchmark task is novel and underexplored in the literature, it is natural to re-purpose and evaluate existing approaches (e.g., SOT methods). We also explore an alternative piecewise constant velocity method that utilizes the Kalman filter [26] with instance proposals from SAM [29] and encoded by DINOv2 [43], resulting in drastic performance improvement over state-of-the-art SOT methods. Section 4 and 5 provide details regarding baselines and benchmark results, respectively. From the experimental results, we provide the following insights: Tracking object instances in egocentric videos is easier in 3D scenes leveraging camera poses and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.895, + 0.492 + ], + "angle": 0, + "content": "depth maps. Intuitively, an object not being interacted with has the same 3D position in a predefined world coordinate but the positions in 2D frames can change drastically due to the head motion. As a result, existing state-of-the-art 2D SOT approaches perform poorly on egocentric data. Future work should address the problem of re-identifying objects by leveraging the camera poses and accurately identifying and updating object motion changes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.642, + 0.525 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.895, + 0.764 + ], + "angle": 0, + "content": "Egocentric video datasets have been developed to study different problems over the last decade [10, 17, 23, 32, 46, 58]. Traditionally, egocentric video understanding has focused on tasks such as activity recognition [27, 47, 48, 54], human-object interactions [9, 36, 37], and inferring the camera wearer's body pose [25, 40, 52, 64]. Recently, more tasks have emerged due to the increasing interest in egocentric videos, such as action anticipation [18, 19, 51], privacy protection [13, 53, 61], and estimating social interactions [33, 42, 74]. However, object tracking in egocentric videos is largely underexplored in the literature until the introduction of recent datasets [15, 60]. These existing tracking datasets only support 2D tracking, which motivates us to collect and setup a new benchmark to evaluate real-world 3D instance tracking." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Tracking in 3D scenes aims to identify objects of interest in 3D space from a sequence of frames. The prediction output format depends on the downstream tasks, including 3D bounding boxes [28, 67], 3D object centers [73, 79], or 6DOF poses [2, 20]. State-of-the-art 3D tracking models [6, 38, 78] have focused on well-established third-person perspective benchmark datasets [5, 8, 21]. The recent largescale Ego4D dataset starts to address the problem of querying the 3D positions of objects from a first-person perspective." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.888, + 0.189, + 0.9 + ], + "angle": 0, + "content": "lar depth estimation." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21934" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.146 + ], + "angle": 0, + "content": "Table 1. Comparisons of egocentric datasets that explore tracking-related problem. Existing egocentric datasets only explore the tracking problem in 2D or predicting discrete 3D locations. Some mention the tracking problem in 3D but only consider limited sensor data (RGB) or synthetic environments. Our benchmark dataset supports the study of instance tracking in 3D real-world scenarios (RWS in the table) from egocentric videos." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.147, + 0.88, + 0.281 + ], + "angle": 0, + "content": "
DatasetModalityDeviceAvg. LengthAnnot. FPSRWSCamera Trajectory3D TrackingYear
TREK-150 [14]RGBGoPro10s60✓Natural✗2021
EK-VISOR [10]RGBGoPro12s0.9✓Natural✗2022
Ego4D-VQ3D [23]RGBGoPro--✓Natural✗2022
EMQA [12]RGB-D+IMU---✗Simulated✗2022
EgoPAT3D [35]RGB-D+IMUKinect4min30✗Object-Centric✗2022
DigitalTwin [44]RGB-D+IMUAria2min-✗Natural✓2022
EgoTrack [60]RGBGoPro6min5✓Natural✗2022
OursRGB-D+IMUHoloLens>5min6✓Natural✓2023
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.473, + 0.446 + ], + "angle": 0, + "content": "However, the raw sensor data in Ego4D only includes RGB images and no other 3D information, such as depth and camera poses [75, 76]. However, contemporary AR/VR headsets come with additional cameras, depth, and IMU sensors that allow for richer geometric reasoning [44, 62]. Therefore, we believe it is realistic to leverage diverse sensor streams and explore the egocentric tracking problem in 3D. Our benchmark dataset thus includes multiple raw sensors and derived data streams to support the study tracking in 3D scenes with modern hardware platforms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.474, + 0.642 + ], + "angle": 0, + "content": "Object instance detection and tracking is a long-standing problem in computer vision and robotics [16, 22, 24, 56, 63]. Instead of predicting labels from a predefined set of object categories, instance-level predictions treat every object instance as a separate category. Instance-level tracking aims to locate given object instances in a sequence of frames, commonly using a tracking-by-detection paradigm. One common formulation is person re-identification [71, 77], which aims to track and associate individual people as they enter and leave multiple cameras' fields of view. Our setting is closely related but is dominated by the motion of the (egocentric) camera rather than the dynamics of object motion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.658, + 0.367, + 0.675 + ], + "angle": 0, + "content": "3. IT3DEgo: Protocol and Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.471, + 0.777 + ], + "angle": 0, + "content": "The problem of IT3DEgo is motivated by real-world assistive agents running on AR/VR devices. Given an object instance specified by the end user, developed models are required to track it in the 3D environment, i.e., recording its 3D location over time (cf. Fig. 2). In this section, we introduce our benchmarking protocol and dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.296, + 0.803 + ], + "angle": 0, + "content": "3.1. Benchmarking Protocol" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Because object instances of interest are naturally diverse and may fall outside of the vocabulary of existing detectors, we set up a benchmarking protocol that focuses on evaluation without a separate training set. In other words, models should be pretrained on other data sources and cannot see objects in our dataset. This aligns with the contemporary foun" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.892, + 0.323 + ], + "angle": 0, + "content": "dation models (e.g., CLIP [49] and SAM [29]) pretrained on open-world data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Instances enrollment. We consider two distinct setups to specify object instances of interest. The first is single-view online enrollment (SVOE), similar to single object tracking (SOT) where an object is specified on-the-fly by the end users. For example, the user can specify an object of interest by interacting or pointing to it, after which the system should track it in the 3D world. The second is multi-view pre-enrollment (MVPE), which defines (or pre-enrolls) concerned objects with a set of object-centric images captured from multiple angles. The two setups present different challenges. SVOE provides a bounding box of the object (similar to specifying an object in SOT), but the visual quality is generally lower in resolution as the objects can be far from the camera. MVPE provides 25 high-resolution \\((2124\\times 2832)\\) object-centric images of the instances captured from different angles. However, the object instance is captured under different lighting conditions than the tracking environment, and can be posed differently (e.g., keys can be deformed over time)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.895, + 0.657 + ], + "angle": 0, + "content": "Evaluation protocols. Following the literature on object tracking and detection, we use the metrics below in our benchmarking protocol." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.659, + 0.895, + 0.87 + ], + "angle": 0, + "content": "- Precision and recall at different L2 distance thresholds. Given \\(N\\) specific thresholds \\(\\tau_{i}\\) with \\(i\\in \\{1,2,\\dots N\\}\\), specifically 0.25, 0.5, 0.75, 1.0, and 1.5 meters, a ground-truth object location \\(\\mathbf{o}_{\\mathrm{gt}}\\in \\mathbb{R}^3\\) and a predicted location \\(\\mathbf{o}_{\\mathrm{pred}}\\in \\mathbb{R}^3\\), we count a true positive \\((\\mathrm{TP}_i)\\) when \\(||\\mathbf{o}_{\\mathrm{gt}} - \\mathbf{o}_{\\mathrm{pred}}||_2\\leq \\tau_i\\). At each timestamp, each ground-truth is matched to the prediction with the smallest L2 distance below the threshold. Unmatched predictions and ground-truth at threshold \\(\\tau_{i}\\) are counted as false positives \\((\\mathrm{FP}_i)\\) and false negatives \\((\\mathrm{FN}_i)\\), respectively. \\(\\mathrm{TP}_i\\), \\(\\mathrm{FP}_i\\), and \\(\\mathrm{FN}_i\\) are computed over all object instances in every frame. The precision and recall at threshold \\(\\tau_{i}\\) is computed as \\(\\sum \\mathrm{TP}_i / (\\sum \\mathrm{TP}_i + \\sum \\mathrm{FP}_i)\\) and \\(\\sum \\mathrm{TP}_i / (\\sum \\mathrm{TP}_i + \\sum \\mathrm{FN}_i)\\), respectively [50, 72]." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "- L2 and angular error. Following VQ3D in Ego4D [23], we also compute the L2 distance between the ground-truth" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21935" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.56, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.087, + 0.885, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.262, + 0.895, + 0.306 + ], + "angle": 0, + "content": "Figure 2. Illustration of input and output of our benchmark task. Given a raw RGB-D video sequence with camera poses and object instances of interest, i.e., either by online enrollment (SVOE) or pre-enrollment (MVPE), the goal of our benchmark task is to output the object instance 3D centers in a predefined world coordinate at each timestamp. Please check Section 3.1 for more details." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.319, + 0.471, + 0.409 + ], + "angle": 0, + "content": "and predictions in the world coordinates in meters. We also report the angular error in radians in the current camera coordinate system. Unlike threshold-aware 3D precision and recall, these metrics are computed only on frames where both ground-truth and prediction of the object instance location are available." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.472, + 0.457 + ], + "angle": 0, + "content": "To make 3D annotation tractable, we only evaluate predictions during time intervals when target objects are stationary (i.e., not being handled by the camera wearer)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.469, + 0.173, + 0.484 + ], + "angle": 0, + "content": "3.2. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.471, + 0.764 + ], + "angle": 0, + "content": "Raw video collection. The raw IT3DEgo data was recorded by three individuals in ten diverse indoor scenes, e.g., kitchen, garage, office, labs, etc. The participants perform naturalistic tasks with different object instances in the scene, e.g., cooking, repairing, writing, etc. The raw data includes 50 recordings in total. Each recording contains five or more object instances, each of which appears at three different 3D locations on average. The average length of each recording is \\(10\\mathrm{K}\\) frames or \\(>5\\mathrm{min}\\). We capture the raw data with HoloLens2 (see Suppl.) which includes an RGB camera, a depth sensor, and four grayscale cameras with the resolution of \\(720\\times 1280\\), \\(480\\times 640\\), \\(512\\times 512\\), respectively. Raw sensors operate at different frequencies, we sync all other sensors to the frequency of the RGB camera (30 fps). We also provide a coarse resolution scene mesh of each environment reconstructed by the Hololense OS. Additional details of the video sequences are described in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Object instance collection. To support the SVOE setup, annotators identify the first RGB frame where a given object is fully visible and close enough to specify a 2D bounding box which is at least 500 pixels in area. For MVPE, we collected 25 high-resolution images of each object instance using iPhone 13 Pro. Each object was placed on a rotary table with QR codes. We took 12 photos of each object evenly from \\(360^{\\circ}\\) while keeping the camera at about \\(30^{\\circ}\\) elevation, 12 more at \\(60^{\\circ}\\) elevation and 1 top-down view." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.319, + 0.892, + 0.35 + ], + "angle": 0, + "content": "We provide additional details and visualizations of object instances in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.893, + 0.609 + ], + "angle": 0, + "content": "Annotations. Our dataset includes three types of manual annotations: (1) Object instance 3D centers describe the 3D positions of each object instance center in a world coordinate frame. We annotate the 3D center by first averaging 3D points computed from camera poses and depth maps of different views of the object instance. Annotators then examine and adjust computed 3D points by visualizing them together with the coarse mesh of the scene. (2) 2D bounding box annotations are axis-aligned 2D bounding boxes of the instance every five frames starting from the beginning of the video. Specifically, we ask annotators to draw amodal bounding boxes of each object instance. We do not annotate the object instances with heavy occlusions (i.e., when less than \\(25\\%\\) of the object is visible). (3) Object motion state annotations are a per-frame annotation of whether the object is stationary or dynamic. For the data we collected, dynamic implies the camera wearer is interacting with the object." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.637, + 0.641 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.825, + 0.667 + ], + "angle": 0, + "content": "4.1. Baseline: Re-purposed SOT Trackers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.895, + 0.869 + ], + "angle": 0, + "content": "To approach the problem of IT3DEgo, we first explore a simple unified pipeline as the baseline approach based on single object tracking (SOT). It allows instance-level 2D tracking by providing the visual appearance of object instances to track [3, 11, 70], which enables us to re-purpose them for our benchmark task. In the unified pipeline, we first compute the 2D trajectories of each object instance with SOT. The final 3D trajectories are computed by lifting the center of 2D bounding boxes with depth maps and camera poses. Lastly, we adopt a simple memory mechanism that stores the previous locations of each object instance to handle the case where the instance moves out of sight, i.e., frames without valid predictions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Lifting 2D trajectories to 3D. With the 2D trajectory predicted from SOT, each valid 2D detection is then lifted" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21936" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.258 + ], + "angle": 0, + "content": "into 3D space with the equation: \\(\\mathbf{o}_t^i = \\mathbf{T}_tz\\mathbf{K}^{-1}\\mathbf{c}_t^i\\), where \\(\\mathbf{c}_t^i\\) is the 2D coordinate of the center of the bounding box of instance \\(i\\) at timestamp \\(t\\), \\(\\mathbf{o}_t^i\\) is the 3D position of instance \\(i\\) at timestamp \\(t\\) in world coordinate. \\(z\\) is the corresponding depth value of \\(\\mathbf{c}_t^i\\) on the depth map. \\(\\mathbf{T}_t\\) is the camera pose at timestamp \\(t\\) that specifies the camera rotation and translation w.r.t to a predefined world coordinate. \\(\\mathbf{K}\\) is the intrinsic matrix. A frame may lack a valid 3D prediction because either there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map is missing the depth value at \\(\\mathbf{c}_t^i\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.259, + 0.473, + 0.426 + ], + "angle": 0, + "content": "Completing 3D trajectories with memory. Any given frame may lack a valid 3D prediction, either because there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map has missing depth values at \\(\\mathbf{c}_t^i\\). To address this we implement a simple memory mechanism that stores only the most recent 3D location for each tracked instance (memory size=1). We update the memory whenever there is a new valid prediction. We note that this heuristic is a good match for the prior that object locations change only when they are being interacted with, in which case they should also be visible to the camera." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.438, + 0.258, + 0.453 + ], + "angle": 0, + "content": "4.2. Improved Baseline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.473, + 0.628 + ], + "angle": 0, + "content": "We also explore the approach that leverages the recent foundation model SAM [29] and state-of-the-art feature encoder DINOv2 [43] for IT3DEgo. Following a tracking-by-detection pipeline, we first compute the per-frame 2D detections of each object instance by comparing the cosine similarity of DINOv2 encoded features between candidate proposals from SAM and a visual feature template. Together with the depth and camera pose information, we convert the 2D detection of each object into a 3D point in a predefined world coordinate. A simple memory with size 1 is also adopted to handle the frames without valid predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Exploring motion prior with Kalman filters. Currently, the naive update mechanism, i.e., always updating the memory for all incoming predictions, does not exploit the temporal information in video sequences. Inspired by the Kalman filter [45, 66, 67] that is widely adopted in the tracking literature, we simply model the stationary position of each object instance as piecewise constant velocity motion, leveraging the prior information that an object without being interacted with has the same 3D coordinate. Mathematically, the motion update with Kalman filter in each stationary position: \\(\\hat{\\mathbf{x}}_{t + 1} = \\hat{\\mathbf{x}}_t + \\mathbf{K}_t(\\mathbf{z_t} - \\mathbf{H}\\hat{\\mathbf{x}}_{\\mathbf{t}})\\), where \\(\\hat{\\mathbf{x}}_t\\) is a 6DOF estimated state vector including position and velocity at time step \\(t\\), \\(\\mathbf{K}_t\\) is the Kalman gain, \\(\\mathbf{z}_{\\mathrm{t}}\\) is a 3DOF the measurement vector, \\(\\mathbf{H}\\) is the observation matrix. Please refer to Kalman [26] for more details. Moving from one stationary position to the next one, we introduce an L2 distance heuristic to model the period where objects are being interacted. Specifically, we compute the L2 distance between incoming 3D positions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.138 + ], + "angle": 0, + "content": "and the state predictions from the Kalman filter. If the L2 distance is above the threshold, we reset the Kalman filter with the current 3D predictions as the initialization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.147, + 0.634, + 0.164 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.174, + 0.895, + 0.295 + ], + "angle": 0, + "content": "In this section, we first describe the implementation details of benchmark results. Then, we show the quantitative results of both setups and the visualizations of tracking results. Lastly, we demonstrate the importance of exploiting camera pose for tracking in 3D and perform ablation studies of the trackers. Note that we split our benchmark dataset into validation and test sets. All experiments are conducted on the validation set; the test set is used for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.897, + 0.612 + ], + "angle": 0, + "content": "Baseline SOT trackers. We choose top-ranked trackers from well-established SOT literature and VOT challenges with open-source code for both tracking setups. Specifically, we benchmark three short-term trackers ToMP [39], MixFormer [7], and ARTrack [65]; and three top-performing trackers from VOT long-term tracking challenges 2021 [30] and 2022 [31], mixLT, mlpLT and VITKT_M. We also evaluate trackers that utilize additional depth information as part of the input, including SAMF and MixForRGBD from VOT RGB-D tracking challenge 2022 [31], and ViPT [80]. Lastly, we benchmark the recent egocentric specific finetuned trackers, EgoSTARK [60]. Note that SOT trackers require initial bounding boxes to track, which are not available in MVPE. When re-purposing to MVPE setup, we explore two different initializations: (1) detection-based initialization: use multiview pre-enrollment images to search for the initial bounding boxes where object instances first appear in the video and initialize SOT trackers with the predicted 2D boxes. (2) template-based initialization: directly adopt multi-view pre-enrollment images as visual templates in the tracker and set the initial tracking search region to the entire frame." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Implementation details. The cosine similarity threshold in the SAM+DINOv2 approach is 0.6, i.e., the object is considered not visible if the cosine similarity is smaller than the threshold. For a fair comparison, we add additional 2D prediction filtering when re-purposing SOT trackers. We discard 2D predictions from SOT trackers whose prediction scores are lower than \\(75\\%\\) of the maximum prediction score. When tracking with MVPE, we first preprocess the captured multi-view images by segmenting and cropping the foreground object using [34]. Many transformer-based SOT trackers only encode a limited number of templates, therefore, we choose 5 images from \\(0^{\\circ}\\), \\(90^{\\circ}\\), \\(180^{\\circ}\\), \\(270^{\\circ}\\) and top-down for all models in MVPE experiments. We include an ablation study exploring the relationship between tracking results and the number of views used in the supplementary material. To keep the comparison fair, all detection-based trackers in MVPE use SAM+DINOv2 with the same cosine thresholds to locate the initial bounding boxes. In terms of benchmarking RGB-D trackers in MVPE, we utilize the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21937" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.117, + 0.402, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.117, + 0.885, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.894, + 0.352 + ], + "angle": 0, + "content": "Figure 3. Qualitative visualizations of tracking with SVOE in both 3D space (left) and projected 2D view (right). We visualize three top-performing trackers from different categories, i.e., EgoSTARK, VITKT_M, and SAM+DINOv2. For projected 2D visualization, we compare the projected 3D points of each model w.r.t to the ground-truth annotated 2D bounding boxes. In the 3D view, we show 3 concentric circles at each ground-truth position representing 0.25, 0.5 and 0.75 meter thresholds. In both 2D and 3D visualizations, we find SAM+DINOv2 outperforms others as the predictions are closer to the center of object instances." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.429 + ], + "angle": 0, + "content": "estimated sparse depth maps using COLMAP [55]. The L2 distance threshold of resetting Kalman filters is \\(0.15\\mathrm{m}\\). All experiments are implemented with PyTorch and run on Nvidia 2080Ti GPUs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.439, + 0.265, + 0.453 + ], + "angle": 0, + "content": "5.1. Benchmark Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Tracking with SVOE. From the results shown in Table 2, we have the following salient insights: (1) Re-identifying object instances is important. Trackers designed with strong re-identify ability, i.e., long-term and egocentric specific types, outperform short-term trackers. Similar findings are shown in recent 2D egocentric tracking work [15, 60]. Surprisingly, SAM+DINOv2, the non-learned approach which does not exploit temporal information beyond the memory heuristic, performs the best among all baselines. We believe the exhaustive proposals on every frame and high quality features provide the model strong, generic re-identification ability. (2) Depth information is not fully leveraged. Current RGB-D trackers show similar or slightly worse performance compared to RGB-ST trackers (c.f. MixFormer and MixforRGBD). The main reason is that RGB-D trackers only encode depth maps as auxiliary visual features, which cannot fully exploit the geometric information from depth maps. Additionally, the depth maps are sparse and not always perfectly aligned with RGB images due to camera distortions. (3) Simple Kalman filter brings marginal benefits. The Kalman filter does not improve over the simple \"most recent\" memory heuristic for stationary objects. The naive filter is also not sufficient for modeling the switching between stationary and dynamic motions needed to capture user-object interactions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Tracking with MVPE. We benchmark top-performing trackers in each category in Table 2 for MVPE setup. From the results shown in Table 3, we find: (1) SOT trackers cannot fully exploit pre-enrollment information. SOT methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.895, + 0.579 + ], + "angle": 0, + "content": "rely on the initial position defined by 2D boxes on the frame to perform well. Comparing detection-based initializations and SVOE results, e.g., \\(\\mathrm{ARTrack}^{\\mathrm{D}}\\) and ARTrack in Table 2, the model performance drops since the initial boxes are not as accurate as ground-truth initialization. VITKT_M adopts many complicated modules that all rely on the initial bounding boxes and degrades more significantly, compared to other types of trackers. (2) Encoding rich visual information generally helps. From the results of template-based initializations, VITKT_M for the same reason mentioned before, we find trackers benefit from the high-resolution multi-view images. SAM+DINOv2 shows a significant performance boost because it is more robust to inaccurate initialization without relying on temporal information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.894, + 0.671 + ], + "angle": 0, + "content": "Qualitative results. Figure 3 shows predictions of top-performing trackers from three different categories, i.e., best tracker in long-term and egocentric specific, and SAM+DINOv2. Clearly, SAM+DINOv2 predictions are closer to the object center in both 3D and projected 2D space." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.821, + 0.697 + ], + "angle": 0, + "content": "5.2. Further Analysis and Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.81 + ], + "angle": 0, + "content": "We further compare tracking object instances in both 2D and 3D settings, demonstrating tracking object instances is much easier in 3D space. We also include an ablation study regarding the cosine similarity thresholds. All studies shown in this section are using SAM+DINOv2 unless otherwise specified. More quantitative and qualitative results are shown in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Tracking in 2D with 3D guidance. We experimentally demonstrate the importance of leveraging 3D information in egocentric instance tracking by comparing 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D tracking results are computed with predicted 3D trajectories as the guidance. For each object instance, the per-frame" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21938" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.16 + ], + "angle": 0, + "content": "Table 2. Benchmark results of tracking with SVOE. From the results, we draw three salient conclusions: (1) The ability of re-identifying object instances after they disappear is important, as long-term and egocentric specific trackers outperform short-term trackers, i.e., RGB-ST and RGB-D. (2) Currently, encoding depth maps as auxiliary information cannot improve performance since depth maps are sparse and not always perfectly aligned with RGB frames due to distortions. (3) The Kalman filter smoothing yields marginal improvements over the simple memory heuristic. The method with KF subscript indicates it applies the Kalman filter." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.16, + 0.89, + 0.365 + ], + "angle": 0, + "content": "
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
ToMPRGB-ST5.610.117.225.339.06.111.018.827.742.62.111.32
MixFormerRGB-ST8.312.218.727.043.09.013.420.429.547.01.971.15
ARTrackRGB-ST9.113.921.530.345.110.115.323.732.447.21.921.10
SAMFRGB-D7.011.515.724.040.87.712.517.226.344.71.901.00
MixForRGBDRGB-D7.512.116.825.341.08.313.420.128.545.02.111.32
ViPTRGB-D8.913.620.628.141.49.714.922.530.745.32.021.21
mixLTRGB-LT14.417.523.931.847.215.819.226.134.851.61.851.02
mlpLTRGB-LT16.020.025.535.248.216.720.826.536.750.11.770.97
VITKT_MRGB-LT21.524.229.737.550.623.025.931.840.254.21.550.83
EgoSTARKRGB-Ego17.521.226.836.349.117.622.027.438.051.21.700.91
SAM + DINOv2RGB23.326.433.143.359.424.928.135.346.363.41.350.81
SAM + DINOv2KFRGB23.727.133.944.561.225.529.036.848.064.91.320.79
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.372, + 0.895, + 0.457 + ], + "angle": 0, + "content": "Table 3. Benchmark results of tracking with MVPE. We evaluate top-performing trackers in each category in Table 2 for MVPE setup. From the results, we have the following summaries: (1) SOT trackers cannot fully exploit pre-enrollment information. Detection-initialized versions perform less well compared to SVOE due to the inaccurate estimated initial bounding boxes. VITKT_M, which uses many modules that rely heavily on the initialization, degrades more significantly. (2) Encoding rich visual information generally helps. SAM+DINOv2 shows an even larger performance boost because it is more robust to the inaccurate initialization. The D and T superscripts indicate the detection- and template-based initializations, respectively." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.457, + 0.892, + 0.64 + ], + "angle": 0, + "content": "
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
\\( ARTrack^D \\)RGB-ST6.812.118.525.841.07.112.318.826.842.11.981.16
\\( ARTrack^T \\)RGB-ST11.218.125.228.738.512.720.928.533.045.11.911.07
\\( ViPT^D \\)RGB-D6.311.717.924.940.26.911.817.925.941.02.011.21
\\( ViPT^T \\)RGB-D10.517.424.027.136.311.920.127.131.344.01.931.10
\\( VITKT_M^D \\)RGB-LT13.818.025.033.046.614.318.625.834.148.21.770.98
\\( VITKT_M^T \\)RGB-LT9.212.820.728.544.09.714.222.431.346.51.951.08
\\( EgoSTARK^D \\)RGB-Ego13.217.023.130.547.014.718.525.934.449.71.821.01
\\( EgoSTARK^T \\)RGB-Ego18.923.128.337.149.619.123.129.339.152.91.670.88
SAM + DINOv2RGB56.059.061.867.574.350.052.755.260.366.40.670.40
SAM + DINOv2_KFRGB56.259.462.268.174.850.353.155.761.167.10.650.39
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.653, + 0.472, + 0.791 + ], + "angle": 0, + "content": "Table 4. Quantitative comparisons of 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D results are computed by finding the bounding box proposal with the smallest L2 distance from projected 3D trajectories. Without 3D guidance means proposals are selected purely based on the visual feature cosine similarity. Please refer to Section 5.2 for more details. From the results, we find the tracking results are significantly improved with the 3D guidance, indicating that tracking in 3D in egocentric videos is much easier than in 2D by leveraging camera pose and depth sensors." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.796, + 0.46, + 0.874 + ], + "angle": 0, + "content": "
3D Guid.AUC(%)↑N. Prec.(%)↑Prec.(%)↑
SVOEX20.714.98.9
✓27.621.711.5
MVPEX14.17.43.0
✓39.135.218.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.895, + 0.867 + ], + "angle": 0, + "content": "2D detection results are computed by selecting the (above threshold) proposal with the smallest L2 distance between projected 3D points and the center of bounding boxes proposals. Without 3D guidance means the 2D tracking results are produced by selecting the proposal with the highest cosine feature similarity. To keep a fair comparison, the cosine similarity threshold is the same when computing the 3D and 2D trajectories. We evaluate the 2D tracking performance using widely adopted precision, normalized precision metrics and AUC in SOT literature [69]. As shown in Table 4, the model with 3D guidance performs significantly better in both SVOE and MVPE, demonstrating that leveraging the 3D information, such as camera pose and depth map, makes the tracking problem much easier." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Performance w.r.t cosine similarity thresholds. Feature cosine similarity threshold is adopted to determine whether" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21939" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.889, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.894, + 0.257 + ], + "angle": 0, + "content": "Figure 4. Performance comparisons of SAM+DINOv2 with different cosine thresholds. By increasing the threshold, we find the model performance first improves and then gradually decreases. Intuitively, increasing the threshold will initially filter noisy predictions but when the threshold is too large the model will miss correct object 3D location updates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.268, + 0.473, + 0.451 + ], + "angle": 0, + "content": "the object instance is present in the current frame, which is crucial for the memory updating mechanism. To characterize the relationship between tracking performance and cosine similarity thresholds, we run the experiment with different cosine similarity thresholds but keep everything else the same. As shown in Figure 4, both models show improved performance at first and then a gradual decrease. Higher cosine thresholds result in fewer predictions so the model must increasingly rely on previous confident predictions stored in the memory. Models with large cosine similarity thresholds have a higher chance of missing valid location updates, which leads to a drop in both precision and recall." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.466, + 0.192, + 0.481 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.471, + 0.703 + ], + "angle": 0, + "content": "Limitations and future work. We point out that the current benchmark dataset has limited geographic and demographic diversity and captures only a small range of objects and activities. As such it is not appropriate for training large models and only serves as a diagnostic test to identify some limitations of existing approaches. Our hope is that it serves as a starting point for the research community to explore and eventually grow into a more comprehensive challenge. Currently, the studied baseline approaches follow the same paradigm, i.e., lifting predicted 2D trajectories into 3D space. We found empirically that the simplest memory mechanism performed best but it seems very likely there are more nuanced state-update models which can integrate multiple observations effectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Finally, we highlight two opportunities for future work. First, advanced models to detect object 3D motion changes. Our experiments demonstrate that tracking in 3D world coordinates effectively narrows the problem to that of accurately predicting the object motion status, i.e., finding all stationary periods for each object instance. However, accurately predicting object state changes is still a non-trivial problem to solve. Second, better utilization of object instance information. Currently, the object instances enrollments, i.e., SVOE and MVPE are naively encoded as visual features. Future work should explore the approaches of fusing the additional scene 3D information with object instances for better tracking performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Broader impact. We believe the broader impact of our work is two-fold. First, we hope our benchmark brings more attention to the problem of tracking object instances in 3D from the egocentric perspective and contributes towards building future task-aware assistive agents. Second, our multi-modal benchmark dataset is beneficial to the study of other 3D scene understanding related problems from the egocentric perspective, such as SLAM, camera localization, 3D reconstruction, and depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.897, + 0.529 + ], + "angle": 0, + "content": "Potential negative impacts. Tracking in 3D from egocentric videos requires the geometric data of surrounding environments and the sensor streams that continuously capture their workplace or daily lives. There are obvious privacy concerns when deploying such hardware and algorithms. Similar to other apps running on personal devices, the simple solution is to keep all user data locally or (in the context of research) develop techniques for anonymizing video [61]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.62, + 0.567 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.793 + ], + "angle": 0, + "content": "We introduce a new IT3DEgo benchmark that allows us to study the problem of tracking object instances in 3D from egocentric videos. The object instances to be tracked are either determined in advance or enrolled online during user interactions with the environment. To support the study, we collect and annotate a new dataset that features RGB-D videos and per-frame camera poses, along with instance-level annotations in both 2D camera and 3D world coordinate frames. We re-purpose and evaluate state-of-the-art single object trackers and develop a strong baseline using large pretrained recognition models and Kalman filtering. We hope our benchmark brings more attention to this challenge and contributes to the development of perceptually-aware assistive agents." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This work was partially supported by the DARPA Perceptually enabled Task Guidance (PTG) Program (HR00112220005). Shu Kong was partially supported by the University of Macau (SRG2023-00044-FST). We thank Juan Carlos Dibene for the help of using hl2ss [1]; An Dang for the help with the initial development of the data capture; Yi-Ling Lin for the help of partial data annotations." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21940" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.142 + ], + "angle": 0, + "content": "[1] Hololens 2 sensor streaming. https://github.com/jdibenes/hl2ss, 2023.8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.472, + 0.225 + ], + "angle": 0, + "content": "[2] Adel Ahmadyan, Liangkai Zhang, Artsiom Ablavatski, Jianing Wei, and Matthias Grundmann. Objectron: A large scale dataset of object-centric videos in the wild with pose annotations. 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This capability requires instance tracking in real-world 3D scenes from egocentric videos (IT3DEgo). We explore this problem by first introducing a new benchmark dataset, consisting of RGB and depth videos, per-frame camera pose, and instance-level annotations in both 2D camera and 3D world coordinates. We present an evaluation protocol which evaluates tracking performance in 3D coordinates with two settings for enrolling instances to track: (1) single-view online enrollment where an instance is specified on-the-fly based on the human wearer's interactions, and (2) multi-view pre-enrollment where images of an instance to be tracked are stored in memory ahead of time. To address IT3DEgo, we first repurpose methods from relevant areas, e.g., single object tracking (SOT) — running SOT methods to track instances in 2D frames and lifting them to 3D using camera pose and depth. We also present a simple method that leverages pretrained segmentation and detection models to generate proposals from RGB frames and match proposals with enrolled instance images. Our experiments show that our method (with no finetuning) significantly outperforms SOT-based approaches in the egocentric setting. We conclude by arguing that the problem of egocentric instance tracking is made easier by leveraging camera pose and using a 3D allocentric (world) coordinate representation. Dataset and open-source code: https://github.com/IT3DEgo/IT3DEgo. + +# 1. Introduction + +Egocentric video obtained from AR/VR devices provides a unique perspective that captures the interaction between the human wearer and the surrounding 3D environment. With the rapid development of AR/VR hardware, there is increasing interest in building assistive agents [41, 57, 59, 68], that track the user's environment and provide contextual guidance on the location of objects of interest (illustrated in Figure 1). We argue that developing such an agent requires solving the + +largely unexplored problem of tracking object instances in $3D$ from egocentric video. + +Why this problem? First, tracking in egocentric video is a novel and underexplored problem, compared to the well-studied tracking from fixed, third-person viewpoints. More broadly, egocentric visual understanding tasks, such as human pose estimation and trajectory prediction [4, 15, 64] are a growing area of interest. Second, tracking in 3D scenes is essential in robotics, autonomous driving, and AR/VR applications. Compared to the 2D counterpart, tracking objects in 3D is crucial for an agent to not only understand the surrounding 3D environment but also to determine precise locations for planning and navigation. Combining the two perspectives above, there is a broader question of what information processing constraints govern how the human visual system integrates egocentric sensory data into a seemingly allocentric perception of the world around us. + +Challenges and new opportunities. (1) Egocentric video often features motion blur, hand occlusions, and frequent object disappearances and reappearance which make the 2D tracking problem very challenging from pure visual signals [15, 60]. Tracking in 3D offers an opportunity to fuse additional sensor streams, such as depth and camera pose, to improve accuracy. Unlike 2D tracking with a moving camera, 3D tracking in world coordinates allows the model to leverage the unique prior information – an object should remain still unless being interacted with the human operator. (2) For the downstream application of task guidance, we propose exploring novel approaches to identify or enroll object instances to be tracked. One approach is automatically enrolling objects with which the user interacts or identifies via hand gestures such as pointing. Alternatively, object instances relevant to a particular task could be pre-enrolled based on a collection of images that specify the visual appearance of the object in advance. + +Contribution 1: Dataset collection. To our best knowledge, no existing dataset supports exploring the problem of IT3DEgo (c.f. Table 1). The recent Ego4D dataset [23] highlights some of these challenges. However, the Ego4D dataset only provides RGB frames1 and sparse annotations (may + +![](images/67cb49cfc42ccaf2d076ade462e6735c1482b41882bda493b7ed8627ad15b281.jpg) +Figure 1. Motivation for the proposed IT3DEgo benchmark task. We envision the real-world application of an assistive agent that continuously tracks enrolled object instances in 3D and can provide navigation guidance to users to retrieve object instances at any time. Tracked objects are either enrolled online (first row in the library) where objects of interest are identified automatically based on user interactions or pre-enrolled (bottom four rows in the library), where task-relevant objects are modeled from a collection of photos taken from different views. The former setup comes with additional in-context sensor information, such as camera pose and depth while the latter features richer visual information. + +miss potential object location changes), making it unsuitable to fully explore the problem. We collect a new benchmark dataset with HoloLens2, including an RGB camera, a depth sensor, four grayscale cameras, per-frame camera pose and coarse scene geometry as a mesh. We describe the details of dataset statistics, capture procedures, and annotations in Section 3.2. + +Contribution 2: Benchmarking protocol. We propose a new IT3DEgo Benchmark for studying instance tracking in 3D scenes from egocentric videos with two settings for how objects are selected for tracking. (1) Tracking with single-view online enrollment (SVOE) studies the scenario where object instances of interest are defined on-the-fly, i.e., objects are specified with a 2D bounding box in the frame where they first become fully visible to the user. (2) Tracking with multiview pre-enrollment (MVPE) assumes objects of interest are specified by multiple photos of the object of interest from different viewpoints before the tracking system starts. As detailed in Section 3.1, we evaluate performance with standard precision/recall metrics as well as geometric L2 and angular errors used in the Ego4D VQ3D evaluation [23]. + +Contribution 3: Technical explorations. Since our benchmark task is novel and underexplored in the literature, it is natural to re-purpose and evaluate existing approaches (e.g., SOT methods). We also explore an alternative piecewise constant velocity method that utilizes the Kalman filter [26] with instance proposals from SAM [29] and encoded by DINOv2 [43], resulting in drastic performance improvement over state-of-the-art SOT methods. Section 4 and 5 provide details regarding baselines and benchmark results, respectively. From the experimental results, we provide the following insights: Tracking object instances in egocentric videos is easier in 3D scenes leveraging camera poses and + +depth maps. Intuitively, an object not being interacted with has the same 3D position in a predefined world coordinate but the positions in 2D frames can change drastically due to the head motion. As a result, existing state-of-the-art 2D SOT approaches perform poorly on egocentric data. Future work should address the problem of re-identifying objects by leveraging the camera poses and accurately identifying and updating object motion changes. + +# 2. Related Work + +Egocentric video datasets have been developed to study different problems over the last decade [10, 17, 23, 32, 46, 58]. Traditionally, egocentric video understanding has focused on tasks such as activity recognition [27, 47, 48, 54], human-object interactions [9, 36, 37], and inferring the camera wearer's body pose [25, 40, 52, 64]. Recently, more tasks have emerged due to the increasing interest in egocentric videos, such as action anticipation [18, 19, 51], privacy protection [13, 53, 61], and estimating social interactions [33, 42, 74]. However, object tracking in egocentric videos is largely underexplored in the literature until the introduction of recent datasets [15, 60]. These existing tracking datasets only support 2D tracking, which motivates us to collect and setup a new benchmark to evaluate real-world 3D instance tracking. + +Tracking in 3D scenes aims to identify objects of interest in 3D space from a sequence of frames. The prediction output format depends on the downstream tasks, including 3D bounding boxes [28, 67], 3D object centers [73, 79], or 6DOF poses [2, 20]. State-of-the-art 3D tracking models [6, 38, 78] have focused on well-established third-person perspective benchmark datasets [5, 8, 21]. The recent largescale Ego4D dataset starts to address the problem of querying the 3D positions of objects from a first-person perspective. + +Table 1. Comparisons of egocentric datasets that explore tracking-related problem. Existing egocentric datasets only explore the tracking problem in 2D or predicting discrete 3D locations. Some mention the tracking problem in 3D but only consider limited sensor data (RGB) or synthetic environments. Our benchmark dataset supports the study of instance tracking in 3D real-world scenarios (RWS in the table) from egocentric videos. + +
DatasetModalityDeviceAvg. LengthAnnot. FPSRWSCamera Trajectory3D TrackingYear
TREK-150 [14]RGBGoPro10s60✓Natural✗2021
EK-VISOR [10]RGBGoPro12s0.9✓Natural✗2022
Ego4D-VQ3D [23]RGBGoPro--✓Natural✗2022
EMQA [12]RGB-D+IMU---✗Simulated✗2022
EgoPAT3D [35]RGB-D+IMUKinect4min30✗Object-Centric✗2022
DigitalTwin [44]RGB-D+IMUAria2min-✗Natural✓2022
EgoTrack [60]RGBGoPro6min5✓Natural✗2022
OursRGB-D+IMUHoloLens>5min6✓Natural✓2023
+ +However, the raw sensor data in Ego4D only includes RGB images and no other 3D information, such as depth and camera poses [75, 76]. However, contemporary AR/VR headsets come with additional cameras, depth, and IMU sensors that allow for richer geometric reasoning [44, 62]. Therefore, we believe it is realistic to leverage diverse sensor streams and explore the egocentric tracking problem in 3D. Our benchmark dataset thus includes multiple raw sensors and derived data streams to support the study tracking in 3D scenes with modern hardware platforms. + +Object instance detection and tracking is a long-standing problem in computer vision and robotics [16, 22, 24, 56, 63]. Instead of predicting labels from a predefined set of object categories, instance-level predictions treat every object instance as a separate category. Instance-level tracking aims to locate given object instances in a sequence of frames, commonly using a tracking-by-detection paradigm. One common formulation is person re-identification [71, 77], which aims to track and associate individual people as they enter and leave multiple cameras' fields of view. Our setting is closely related but is dominated by the motion of the (egocentric) camera rather than the dynamics of object motion. + +# 3. IT3DEgo: Protocol and Dataset + +The problem of IT3DEgo is motivated by real-world assistive agents running on AR/VR devices. Given an object instance specified by the end user, developed models are required to track it in the 3D environment, i.e., recording its 3D location over time (cf. Fig. 2). In this section, we introduce our benchmarking protocol and dataset. + +# 3.1. Benchmarking Protocol + +Because object instances of interest are naturally diverse and may fall outside of the vocabulary of existing detectors, we set up a benchmarking protocol that focuses on evaluation without a separate training set. In other words, models should be pretrained on other data sources and cannot see objects in our dataset. This aligns with the contemporary foun + +dation models (e.g., CLIP [49] and SAM [29]) pretrained on open-world data. + +Instances enrollment. We consider two distinct setups to specify object instances of interest. The first is single-view online enrollment (SVOE), similar to single object tracking (SOT) where an object is specified on-the-fly by the end users. For example, the user can specify an object of interest by interacting or pointing to it, after which the system should track it in the 3D world. The second is multi-view pre-enrollment (MVPE), which defines (or pre-enrolls) concerned objects with a set of object-centric images captured from multiple angles. The two setups present different challenges. SVOE provides a bounding box of the object (similar to specifying an object in SOT), but the visual quality is generally lower in resolution as the objects can be far from the camera. MVPE provides 25 high-resolution $(2124\times 2832)$ object-centric images of the instances captured from different angles. However, the object instance is captured under different lighting conditions than the tracking environment, and can be posed differently (e.g., keys can be deformed over time). + +Evaluation protocols. Following the literature on object tracking and detection, we use the metrics below in our benchmarking protocol. + +- Precision and recall at different L2 distance thresholds. Given $N$ specific thresholds $\tau_{i}$ with $i\in \{1,2,\dots N\}$ , specifically 0.25, 0.5, 0.75, 1.0, and 1.5 meters, a ground-truth object location $\mathbf{o}_{\mathrm{gt}}\in \mathbb{R}^3$ and a predicted location $\mathbf{o}_{\mathrm{pred}}\in \mathbb{R}^3$ , we count a true positive $(\mathrm{TP}_i)$ when $||\mathbf{o}_{\mathrm{gt}} - \mathbf{o}_{\mathrm{pred}}||_2\leq \tau_i$ . At each timestamp, each ground-truth is matched to the prediction with the smallest L2 distance below the threshold. Unmatched predictions and ground-truth at threshold $\tau_{i}$ are counted as false positives $(\mathrm{FP}_i)$ and false negatives $(\mathrm{FN}_i)$ , respectively. $\mathrm{TP}_i$ , $\mathrm{FP}_i$ , and $\mathrm{FN}_i$ are computed over all object instances in every frame. The precision and recall at threshold $\tau_{i}$ is computed as $\sum \mathrm{TP}_i / (\sum \mathrm{TP}_i + \sum \mathrm{FP}_i)$ and $\sum \mathrm{TP}_i / (\sum \mathrm{TP}_i + \sum \mathrm{FN}_i)$ , respectively [50, 72]. + +- L2 and angular error. Following VQ3D in Ego4D [23], we also compute the L2 distance between the ground-truth + +![](images/e1cb59c4bab8a8277df27bc4491190694c0db709d35277fa4999c691565405a8.jpg) +Figure 2. Illustration of input and output of our benchmark task. Given a raw RGB-D video sequence with camera poses and object instances of interest, i.e., either by online enrollment (SVOE) or pre-enrollment (MVPE), the goal of our benchmark task is to output the object instance 3D centers in a predefined world coordinate at each timestamp. Please check Section 3.1 for more details. + +![](images/e17cc6ff4d2cec06b0d793d19da5a0cf2d466b1fe99f80aab6075d80efc61b2f.jpg) + +and predictions in the world coordinates in meters. We also report the angular error in radians in the current camera coordinate system. Unlike threshold-aware 3D precision and recall, these metrics are computed only on frames where both ground-truth and prediction of the object instance location are available. + +To make 3D annotation tractable, we only evaluate predictions during time intervals when target objects are stationary (i.e., not being handled by the camera wearer). + +# 3.2. Dataset + +Raw video collection. The raw IT3DEgo data was recorded by three individuals in ten diverse indoor scenes, e.g., kitchen, garage, office, labs, etc. The participants perform naturalistic tasks with different object instances in the scene, e.g., cooking, repairing, writing, etc. The raw data includes 50 recordings in total. Each recording contains five or more object instances, each of which appears at three different 3D locations on average. The average length of each recording is $10\mathrm{K}$ frames or $>5\mathrm{min}$ . We capture the raw data with HoloLens2 (see Suppl.) which includes an RGB camera, a depth sensor, and four grayscale cameras with the resolution of $720\times 1280$ , $480\times 640$ , $512\times 512$ , respectively. Raw sensors operate at different frequencies, we sync all other sensors to the frequency of the RGB camera (30 fps). We also provide a coarse resolution scene mesh of each environment reconstructed by the Hololense OS. Additional details of the video sequences are described in the supplementary material. + +Object instance collection. To support the SVOE setup, annotators identify the first RGB frame where a given object is fully visible and close enough to specify a 2D bounding box which is at least 500 pixels in area. For MVPE, we collected 25 high-resolution images of each object instance using iPhone 13 Pro. Each object was placed on a rotary table with QR codes. We took 12 photos of each object evenly from $360^{\circ}$ while keeping the camera at about $30^{\circ}$ elevation, 12 more at $60^{\circ}$ elevation and 1 top-down view. + +We provide additional details and visualizations of object instances in the supplementary material. + +Annotations. Our dataset includes three types of manual annotations: (1) Object instance 3D centers describe the 3D positions of each object instance center in a world coordinate frame. We annotate the 3D center by first averaging 3D points computed from camera poses and depth maps of different views of the object instance. Annotators then examine and adjust computed 3D points by visualizing them together with the coarse mesh of the scene. (2) 2D bounding box annotations are axis-aligned 2D bounding boxes of the instance every five frames starting from the beginning of the video. Specifically, we ask annotators to draw amodal bounding boxes of each object instance. We do not annotate the object instances with heavy occlusions (i.e., when less than $25\%$ of the object is visible). (3) Object motion state annotations are a per-frame annotation of whether the object is stationary or dynamic. For the data we collected, dynamic implies the camera wearer is interacting with the object. + +# 4. Methodology + +# 4.1. Baseline: Re-purposed SOT Trackers + +To approach the problem of IT3DEgo, we first explore a simple unified pipeline as the baseline approach based on single object tracking (SOT). It allows instance-level 2D tracking by providing the visual appearance of object instances to track [3, 11, 70], which enables us to re-purpose them for our benchmark task. In the unified pipeline, we first compute the 2D trajectories of each object instance with SOT. The final 3D trajectories are computed by lifting the center of 2D bounding boxes with depth maps and camera poses. Lastly, we adopt a simple memory mechanism that stores the previous locations of each object instance to handle the case where the instance moves out of sight, i.e., frames without valid predictions. + +Lifting 2D trajectories to 3D. With the 2D trajectory predicted from SOT, each valid 2D detection is then lifted + +into 3D space with the equation: $\mathbf{o}_t^i = \mathbf{T}_tz\mathbf{K}^{-1}\mathbf{c}_t^i$ , where $\mathbf{c}_t^i$ is the 2D coordinate of the center of the bounding box of instance $i$ at timestamp $t$ , $\mathbf{o}_t^i$ is the 3D position of instance $i$ at timestamp $t$ in world coordinate. $z$ is the corresponding depth value of $\mathbf{c}_t^i$ on the depth map. $\mathbf{T}_t$ is the camera pose at timestamp $t$ that specifies the camera rotation and translation w.r.t to a predefined world coordinate. $\mathbf{K}$ is the intrinsic matrix. A frame may lack a valid 3D prediction because either there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map is missing the depth value at $\mathbf{c}_t^i$ . + +Completing 3D trajectories with memory. Any given frame may lack a valid 3D prediction, either because there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map has missing depth values at $\mathbf{c}_t^i$ . To address this we implement a simple memory mechanism that stores only the most recent 3D location for each tracked instance (memory size=1). We update the memory whenever there is a new valid prediction. We note that this heuristic is a good match for the prior that object locations change only when they are being interacted with, in which case they should also be visible to the camera. + +# 4.2. Improved Baseline + +We also explore the approach that leverages the recent foundation model SAM [29] and state-of-the-art feature encoder DINOv2 [43] for IT3DEgo. Following a tracking-by-detection pipeline, we first compute the per-frame 2D detections of each object instance by comparing the cosine similarity of DINOv2 encoded features between candidate proposals from SAM and a visual feature template. Together with the depth and camera pose information, we convert the 2D detection of each object into a 3D point in a predefined world coordinate. A simple memory with size 1 is also adopted to handle the frames without valid predictions. + +Exploring motion prior with Kalman filters. Currently, the naive update mechanism, i.e., always updating the memory for all incoming predictions, does not exploit the temporal information in video sequences. Inspired by the Kalman filter [45, 66, 67] that is widely adopted in the tracking literature, we simply model the stationary position of each object instance as piecewise constant velocity motion, leveraging the prior information that an object without being interacted with has the same 3D coordinate. Mathematically, the motion update with Kalman filter in each stationary position: $\hat{\mathbf{x}}_{t + 1} = \hat{\mathbf{x}}_t + \mathbf{K}_t(\mathbf{z_t} - \mathbf{H}\hat{\mathbf{x}}_{\mathbf{t}})$ , where $\hat{\mathbf{x}}_t$ is a 6DOF estimated state vector including position and velocity at time step $t$ , $\mathbf{K}_t$ is the Kalman gain, $\mathbf{z}_{\mathrm{t}}$ is a 3DOF the measurement vector, $\mathbf{H}$ is the observation matrix. Please refer to Kalman [26] for more details. Moving from one stationary position to the next one, we introduce an L2 distance heuristic to model the period where objects are being interacted. Specifically, we compute the L2 distance between incoming 3D positions + +and the state predictions from the Kalman filter. If the L2 distance is above the threshold, we reset the Kalman filter with the current 3D predictions as the initialization. + +# 5. Experiments + +In this section, we first describe the implementation details of benchmark results. Then, we show the quantitative results of both setups and the visualizations of tracking results. Lastly, we demonstrate the importance of exploiting camera pose for tracking in 3D and perform ablation studies of the trackers. Note that we split our benchmark dataset into validation and test sets. All experiments are conducted on the validation set; the test set is used for future work. + +Baseline SOT trackers. We choose top-ranked trackers from well-established SOT literature and VOT challenges with open-source code for both tracking setups. Specifically, we benchmark three short-term trackers ToMP [39], MixFormer [7], and ARTrack [65]; and three top-performing trackers from VOT long-term tracking challenges 2021 [30] and 2022 [31], mixLT, mlpLT and VITKT_M. We also evaluate trackers that utilize additional depth information as part of the input, including SAMF and MixForRGBD from VOT RGB-D tracking challenge 2022 [31], and ViPT [80]. Lastly, we benchmark the recent egocentric specific finetuned trackers, EgoSTARK [60]. Note that SOT trackers require initial bounding boxes to track, which are not available in MVPE. When re-purposing to MVPE setup, we explore two different initializations: (1) detection-based initialization: use multiview pre-enrollment images to search for the initial bounding boxes where object instances first appear in the video and initialize SOT trackers with the predicted 2D boxes. (2) template-based initialization: directly adopt multi-view pre-enrollment images as visual templates in the tracker and set the initial tracking search region to the entire frame. + +Implementation details. The cosine similarity threshold in the SAM+DINOv2 approach is 0.6, i.e., the object is considered not visible if the cosine similarity is smaller than the threshold. For a fair comparison, we add additional 2D prediction filtering when re-purposing SOT trackers. We discard 2D predictions from SOT trackers whose prediction scores are lower than $75\%$ of the maximum prediction score. When tracking with MVPE, we first preprocess the captured multi-view images by segmenting and cropping the foreground object using [34]. Many transformer-based SOT trackers only encode a limited number of templates, therefore, we choose 5 images from $0^{\circ}$ , $90^{\circ}$ , $180^{\circ}$ , $270^{\circ}$ and top-down for all models in MVPE experiments. We include an ablation study exploring the relationship between tracking results and the number of views used in the supplementary material. To keep the comparison fair, all detection-based trackers in MVPE use SAM+DINOv2 with the same cosine thresholds to locate the initial bounding boxes. In terms of benchmarking RGB-D trackers in MVPE, we utilize the + +![](images/b9529dda03dbccdf893a86dcdf31b7aa3eea91fafdbf14a7cc9a7a64f4eb6a5d.jpg) +Figure 3. Qualitative visualizations of tracking with SVOE in both 3D space (left) and projected 2D view (right). We visualize three top-performing trackers from different categories, i.e., EgoSTARK, VITKT_M, and SAM+DINOv2. For projected 2D visualization, we compare the projected 3D points of each model w.r.t to the ground-truth annotated 2D bounding boxes. In the 3D view, we show 3 concentric circles at each ground-truth position representing 0.25, 0.5 and 0.75 meter thresholds. In both 2D and 3D visualizations, we find SAM+DINOv2 outperforms others as the predictions are closer to the center of object instances. + +![](images/06513af8d920b71d82d735596f4ce56f5e19ca28d86f49d1bd178080b11f0a52.jpg) + +estimated sparse depth maps using COLMAP [55]. The L2 distance threshold of resetting Kalman filters is $0.15\mathrm{m}$ . All experiments are implemented with PyTorch and run on Nvidia 2080Ti GPUs. + +# 5.1. Benchmark Results + +Tracking with SVOE. From the results shown in Table 2, we have the following salient insights: (1) Re-identifying object instances is important. Trackers designed with strong re-identify ability, i.e., long-term and egocentric specific types, outperform short-term trackers. Similar findings are shown in recent 2D egocentric tracking work [15, 60]. Surprisingly, SAM+DINOv2, the non-learned approach which does not exploit temporal information beyond the memory heuristic, performs the best among all baselines. We believe the exhaustive proposals on every frame and high quality features provide the model strong, generic re-identification ability. (2) Depth information is not fully leveraged. Current RGB-D trackers show similar or slightly worse performance compared to RGB-ST trackers (c.f. MixFormer and MixforRGBD). The main reason is that RGB-D trackers only encode depth maps as auxiliary visual features, which cannot fully exploit the geometric information from depth maps. Additionally, the depth maps are sparse and not always perfectly aligned with RGB images due to camera distortions. (3) Simple Kalman filter brings marginal benefits. The Kalman filter does not improve over the simple "most recent" memory heuristic for stationary objects. The naive filter is also not sufficient for modeling the switching between stationary and dynamic motions needed to capture user-object interactions. + +Tracking with MVPE. We benchmark top-performing trackers in each category in Table 2 for MVPE setup. From the results shown in Table 3, we find: (1) SOT trackers cannot fully exploit pre-enrollment information. SOT methods + +rely on the initial position defined by 2D boxes on the frame to perform well. Comparing detection-based initializations and SVOE results, e.g., $\mathrm{ARTrack}^{\mathrm{D}}$ and ARTrack in Table 2, the model performance drops since the initial boxes are not as accurate as ground-truth initialization. VITKT_M adopts many complicated modules that all rely on the initial bounding boxes and degrades more significantly, compared to other types of trackers. (2) Encoding rich visual information generally helps. From the results of template-based initializations, VITKT_M for the same reason mentioned before, we find trackers benefit from the high-resolution multi-view images. SAM+DINOv2 shows a significant performance boost because it is more robust to inaccurate initialization without relying on temporal information. + +Qualitative results. Figure 3 shows predictions of top-performing trackers from three different categories, i.e., best tracker in long-term and egocentric specific, and SAM+DINOv2. Clearly, SAM+DINOv2 predictions are closer to the object center in both 3D and projected 2D space. + +# 5.2. Further Analysis and Ablation Study + +We further compare tracking object instances in both 2D and 3D settings, demonstrating tracking object instances is much easier in 3D space. We also include an ablation study regarding the cosine similarity thresholds. All studies shown in this section are using SAM+DINOv2 unless otherwise specified. More quantitative and qualitative results are shown in the supplementary materials. + +Tracking in 2D with 3D guidance. We experimentally demonstrate the importance of leveraging 3D information in egocentric instance tracking by comparing 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D tracking results are computed with predicted 3D trajectories as the guidance. For each object instance, the per-frame + +Table 2. Benchmark results of tracking with SVOE. From the results, we draw three salient conclusions: (1) The ability of re-identifying object instances after they disappear is important, as long-term and egocentric specific trackers outperform short-term trackers, i.e., RGB-ST and RGB-D. (2) Currently, encoding depth maps as auxiliary information cannot improve performance since depth maps are sparse and not always perfectly aligned with RGB frames due to distortions. (3) The Kalman filter smoothing yields marginal improvements over the simple memory heuristic. The method with KF subscript indicates it applies the Kalman filter. + +
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
ToMPRGB-ST5.610.117.225.339.06.111.018.827.742.62.111.32
MixFormerRGB-ST8.312.218.727.043.09.013.420.429.547.01.971.15
ARTrackRGB-ST9.113.921.530.345.110.115.323.732.447.21.921.10
SAMFRGB-D7.011.515.724.040.87.712.517.226.344.71.901.00
MixForRGBDRGB-D7.512.116.825.341.08.313.420.128.545.02.111.32
ViPTRGB-D8.913.620.628.141.49.714.922.530.745.32.021.21
mixLTRGB-LT14.417.523.931.847.215.819.226.134.851.61.851.02
mlpLTRGB-LT16.020.025.535.248.216.720.826.536.750.11.770.97
VITKT_MRGB-LT21.524.229.737.550.623.025.931.840.254.21.550.83
EgoSTARKRGB-Ego17.521.226.836.349.117.622.027.438.051.21.700.91
SAM + DINOv2RGB23.326.433.143.359.424.928.135.346.363.41.350.81
SAM + DINOv2KFRGB23.727.133.944.561.225.529.036.848.064.91.320.79
+ +Table 3. Benchmark results of tracking with MVPE. We evaluate top-performing trackers in each category in Table 2 for MVPE setup. From the results, we have the following summaries: (1) SOT trackers cannot fully exploit pre-enrollment information. Detection-initialized versions perform less well compared to SVOE due to the inaccurate estimated initial bounding boxes. VITKT_M, which uses many modules that rely heavily on the initialization, degrades more significantly. (2) Encoding rich visual information generally helps. SAM+DINOv2 shows an even larger performance boost because it is more robust to the inaccurate initialization. The D and T superscripts indicate the detection- and template-based initializations, respectively. + +
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
\( ARTrack^D \)RGB-ST6.812.118.525.841.07.112.318.826.842.11.981.16
\( ARTrack^T \)RGB-ST11.218.125.228.738.512.720.928.533.045.11.911.07
\( ViPT^D \)RGB-D6.311.717.924.940.26.911.817.925.941.02.011.21
\( ViPT^T \)RGB-D10.517.424.027.136.311.920.127.131.344.01.931.10
\( VITKT_M^D \)RGB-LT13.818.025.033.046.614.318.625.834.148.21.770.98
\( VITKT_M^T \)RGB-LT9.212.820.728.544.09.714.222.431.346.51.951.08
\( EgoSTARK^D \)RGB-Ego13.217.023.130.547.014.718.525.934.449.71.821.01
\( EgoSTARK^T \)RGB-Ego18.923.128.337.149.619.123.129.339.152.91.670.88
SAM + DINOv2RGB56.059.061.867.574.350.052.755.260.366.40.670.40
SAM + DINOv2_KFRGB56.259.462.268.174.850.353.155.761.167.10.650.39
+ +Table 4. Quantitative comparisons of 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D results are computed by finding the bounding box proposal with the smallest L2 distance from projected 3D trajectories. Without 3D guidance means proposals are selected purely based on the visual feature cosine similarity. Please refer to Section 5.2 for more details. From the results, we find the tracking results are significantly improved with the 3D guidance, indicating that tracking in 3D in egocentric videos is much easier than in 2D by leveraging camera pose and depth sensors. + +
3D Guid.AUC(%)↑N. Prec.(%)↑Prec.(%)↑
SVOEX20.714.98.9
✓27.621.711.5
MVPEX14.17.43.0
✓39.135.218.7
+ +2D detection results are computed by selecting the (above threshold) proposal with the smallest L2 distance between projected 3D points and the center of bounding boxes proposals. Without 3D guidance means the 2D tracking results are produced by selecting the proposal with the highest cosine feature similarity. To keep a fair comparison, the cosine similarity threshold is the same when computing the 3D and 2D trajectories. We evaluate the 2D tracking performance using widely adopted precision, normalized precision metrics and AUC in SOT literature [69]. As shown in Table 4, the model with 3D guidance performs significantly better in both SVOE and MVPE, demonstrating that leveraging the 3D information, such as camera pose and depth map, makes the tracking problem much easier. + +Performance w.r.t cosine similarity thresholds. Feature cosine similarity threshold is adopted to determine whether + +![](images/19d022e3941fe38a206a8267ac85d18c86a3fef8507c39084977a0f5631dd1a1.jpg) +Figure 4. Performance comparisons of SAM+DINOv2 with different cosine thresholds. By increasing the threshold, we find the model performance first improves and then gradually decreases. Intuitively, increasing the threshold will initially filter noisy predictions but when the threshold is too large the model will miss correct object 3D location updates. + +the object instance is present in the current frame, which is crucial for the memory updating mechanism. To characterize the relationship between tracking performance and cosine similarity thresholds, we run the experiment with different cosine similarity thresholds but keep everything else the same. As shown in Figure 4, both models show improved performance at first and then a gradual decrease. Higher cosine thresholds result in fewer predictions so the model must increasingly rely on previous confident predictions stored in the memory. Models with large cosine similarity thresholds have a higher chance of missing valid location updates, which leads to a drop in both precision and recall. + +# 6. Discussion + +Limitations and future work. We point out that the current benchmark dataset has limited geographic and demographic diversity and captures only a small range of objects and activities. As such it is not appropriate for training large models and only serves as a diagnostic test to identify some limitations of existing approaches. Our hope is that it serves as a starting point for the research community to explore and eventually grow into a more comprehensive challenge. Currently, the studied baseline approaches follow the same paradigm, i.e., lifting predicted 2D trajectories into 3D space. We found empirically that the simplest memory mechanism performed best but it seems very likely there are more nuanced state-update models which can integrate multiple observations effectively. + +Finally, we highlight two opportunities for future work. First, advanced models to detect object 3D motion changes. Our experiments demonstrate that tracking in 3D world coordinates effectively narrows the problem to that of accurately predicting the object motion status, i.e., finding all stationary periods for each object instance. However, accurately predicting object state changes is still a non-trivial problem to solve. Second, better utilization of object instance information. Currently, the object instances enrollments, i.e., SVOE and MVPE are naively encoded as visual features. Future work should explore the approaches of fusing the additional scene 3D information with object instances for better tracking performance. + +Broader impact. We believe the broader impact of our work is two-fold. First, we hope our benchmark brings more attention to the problem of tracking object instances in 3D from the egocentric perspective and contributes towards building future task-aware assistive agents. Second, our multi-modal benchmark dataset is beneficial to the study of other 3D scene understanding related problems from the egocentric perspective, such as SLAM, camera localization, 3D reconstruction, and depth estimation. + +Potential negative impacts. Tracking in 3D from egocentric videos requires the geometric data of surrounding environments and the sensor streams that continuously capture their workplace or daily lives. There are obvious privacy concerns when deploying such hardware and algorithms. Similar to other apps running on personal devices, the simple solution is to keep all user data locally or (in the context of research) develop techniques for anonymizing video [61]. + +# 7. Conclusion + +We introduce a new IT3DEgo benchmark that allows us to study the problem of tracking object instances in 3D from egocentric videos. The object instances to be tracked are either determined in advance or enrolled online during user interactions with the environment. To support the study, we collect and annotate a new dataset that features RGB-D videos and per-frame camera poses, along with instance-level annotations in both 2D camera and 3D world coordinate frames. We re-purpose and evaluate state-of-the-art single object trackers and develop a strong baseline using large pretrained recognition models and Kalman filtering. We hope our benchmark brings more attention to this challenge and contributes to the development of perceptually-aware assistive agents. + +Acknowledgements. This work was partially supported by the DARPA Perceptually enabled Task Guidance (PTG) Program (HR00112220005). Shu Kong was partially supported by the University of Macau (SRG2023-00044-FST). We thank Juan Carlos Dibene for the help of using hl2ss [1]; An Dang for the help with the initial development of the data capture; Yi-Ling Lin for the help of partial data annotations. + +# References + +[1] Hololens 2 sensor streaming. https://github.com/jdibenes/hl2ss, 2023.8 +[2] Adel Ahmadyan, Liangkai Zhang, Artsiom Ablavatski, Jianing Wei, and Matthias Grundmann. Objectron: A large scale dataset of object-centric videos in the wild with pose annotations. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 7822-7831, 2021. 2 +[3] Goutam Bhat, Martin Danelljan, Luc Van Gool, and Radu Timofte. Learning discriminative model prediction for tracking. In Proceedings of the IEEE/CVF international conference on computer vision, pages 6182-6191, 2019. 4 +[4] Huikun Bi, Ruisi Zhang, Tianlu Mao, Zhigang Deng, and Zhaoqi Wang. How can i see my future? fvtraj: Using first-person view for pedestrian trajectory prediction. 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This capability requires instance tracking in real-world 3D scenes from egocentric videos (IT3DEgo). We explore this problem by first introducing a new benchmark dataset, consisting of RGB and depth videos, per-frame camera pose, and instance-level annotations in both 2D camera and 3D world coordinates. We present an evaluation protocol which evaluates tracking performance in 3D coordinates with two settings for enrolling instances to track: (1) single-view online enrollment where an instance is specified on-the-fly based on the human wearer's interactions, and (2) multi-view pre-enrollment where images of an instance to be tracked are stored in memory ahead of time. To address IT3DEgo, we first repurpose methods from relevant areas, e.g., single object tracking (SOT) — running SOT methods to track instances in 2D frames and lifting them to 3D using camera pose and depth. We also present a simple method that leverages pretrained segmentation and detection models to generate proposals from RGB frames and match proposals with enrolled instance images. Our experiments show that our method (with no finetuning) significantly outperforms SOT-based approaches in the egocentric setting. We conclude by arguing that the problem of egocentric instance tracking is made easier by leveraging camera pose and using a 3D allocentric (world) coordinate representation. Dataset and open-source code: https://github.com/IT3DEgo/IT3DEgo." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Egocentric video obtained from AR/VR devices provides a unique perspective that captures the interaction between the human wearer and the surrounding 3D environment. With the rapid development of AR/VR hardware, there is increasing interest in building assistive agents [41, 57, 59, 68], that track the user's environment and provide contextual guidance on the location of objects of interest (illustrated in Figure 1). We argue that developing such an agent requires solving the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "type": "text", + "content": "largely unexplored problem of tracking object instances in " + }, + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "type": "inline_equation", + "content": "3D" + }, + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "type": "text", + "content": " from egocentric video." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 232, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 411 + ], + "type": "text", + "content": "Why this problem? First, tracking in egocentric video is a novel and underexplored problem, compared to the well-studied tracking from fixed, third-person viewpoints. More broadly, egocentric visual understanding tasks, such as human pose estimation and trajectory prediction [4, 15, 64] are a growing area of interest. Second, tracking in 3D scenes is essential in robotics, autonomous driving, and AR/VR applications. Compared to the 2D counterpart, tracking objects in 3D is crucial for an agent to not only understand the surrounding 3D environment but also to determine precise locations for planning and navigation. Combining the two perspectives above, there is a broader question of what information processing constraints govern how the human visual system integrates egocentric sensory data into a seemingly allocentric perception of the world around us." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 411, + 548, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 548, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 548, + 626 + ], + "type": "text", + "content": "Challenges and new opportunities. (1) Egocentric video often features motion blur, hand occlusions, and frequent object disappearances and reappearance which make the 2D tracking problem very challenging from pure visual signals [15, 60]. Tracking in 3D offers an opportunity to fuse additional sensor streams, such as depth and camera pose, to improve accuracy. Unlike 2D tracking with a moving camera, 3D tracking in world coordinates allows the model to leverage the unique prior information – an object should remain still unless being interacted with the human operator. (2) For the downstream application of task guidance, we propose exploring novel approaches to identify or enroll object instances to be tracked. One approach is automatically enrolling objects with which the user interacts or identifies via hand gestures such as pointing. Alternatively, object instances relevant to a particular task could be pre-enrolled based on a collection of images that specify the visual appearance of the object in advance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 627, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 547, + 687 + ], + "type": "text", + "content": "Contribution 1: Dataset collection. To our best knowledge, no existing dataset supports exploring the problem of IT3DEgo (c.f. Table 1). The recent Ego4D dataset [23] highlights some of these challenges. However, the Ego4D dataset only provides RGB frames1 and sparse annotations (may" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "text", + "content": "Ego4D does provide a sparse set of camera poses (less than " + }, + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "text", + "content": " of frames) estimated with COLMAP and predicted depth maps using monocu" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21933" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 542, + 210 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 542, + 210 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 542, + 210 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 542, + 210 + ], + "type": "image", + "image_path": "67cb49cfc42ccaf2d076ade462e6735c1482b41882bda493b7ed8627ad15b281.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 548, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 548, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 548, + 281 + ], + "type": "text", + "content": "Figure 1. Motivation for the proposed IT3DEgo benchmark task. We envision the real-world application of an assistive agent that continuously tracks enrolled object instances in 3D and can provide navigation guidance to users to retrieve object instances at any time. Tracked objects are either enrolled online (first row in the library) where objects of interest are identified automatically based on user interactions or pre-enrolled (bottom four rows in the library), where task-relevant objects are modeled from a collection of photos taken from different views. The former setup comes with additional in-context sensor information, such as camera pose and depth while the latter features richer visual information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 293, + 288, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 288, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 288, + 376 + ], + "type": "text", + "content": "miss potential object location changes), making it unsuitable to fully explore the problem. We collect a new benchmark dataset with HoloLens2, including an RGB camera, a depth sensor, four grayscale cameras, per-frame camera pose and coarse scene geometry as a mesh. We describe the details of dataset statistics, capture procedures, and annotations in Section 3.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 378, + 288, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 288, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 288, + 545 + ], + "type": "text", + "content": "Contribution 2: Benchmarking protocol. We propose a new IT3DEgo Benchmark for studying instance tracking in 3D scenes from egocentric videos with two settings for how objects are selected for tracking. (1) Tracking with single-view online enrollment (SVOE) studies the scenario where object instances of interest are defined on-the-fly, i.e., objects are specified with a 2D bounding box in the frame where they first become fully visible to the user. (2) Tracking with multiview pre-enrollment (MVPE) assumes objects of interest are specified by multiple photos of the object of interest from different viewpoints before the tracking system starts. As detailed in Section 3.1, we evaluate performance with standard precision/recall metrics as well as geometric L2 and angular errors used in the Ego4D VQ3D evaluation [23]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 547, + 288, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 547, + 288, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 547, + 288, + 691 + ], + "type": "text", + "content": "Contribution 3: Technical explorations. Since our benchmark task is novel and underexplored in the literature, it is natural to re-purpose and evaluate existing approaches (e.g., SOT methods). We also explore an alternative piecewise constant velocity method that utilizes the Kalman filter [26] with instance proposals from SAM [29] and encoded by DINOv2 [43], resulting in drastic performance improvement over state-of-the-art SOT methods. Section 4 and 5 provide details regarding baselines and benchmark results, respectively. From the experimental results, we provide the following insights: Tracking object instances in egocentric videos is easier in 3D scenes leveraging camera poses and" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 293, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 389 + ], + "type": "text", + "content": "depth maps. Intuitively, an object not being interacted with has the same 3D position in a predefined world coordinate but the positions in 2D frames can change drastically due to the head motion. As a result, existing state-of-the-art 2D SOT approaches perform poorly on egocentric data. Future work should address the problem of re-identifying objects by leveraging the camera poses and accurately identifying and updating object motion changes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 403, + 392, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 392, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 392, + 415 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 425, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 547, + 605 + ], + "type": "text", + "content": "Egocentric video datasets have been developed to study different problems over the last decade [10, 17, 23, 32, 46, 58]. Traditionally, egocentric video understanding has focused on tasks such as activity recognition [27, 47, 48, 54], human-object interactions [9, 36, 37], and inferring the camera wearer's body pose [25, 40, 52, 64]. Recently, more tasks have emerged due to the increasing interest in egocentric videos, such as action anticipation [18, 19, 51], privacy protection [13, 53, 61], and estimating social interactions [33, 42, 74]. However, object tracking in egocentric videos is largely underexplored in the literature until the introduction of recent datasets [15, 60]. These existing tracking datasets only support 2D tracking, which motivates us to collect and setup a new benchmark to evaluate real-world 3D instance tracking." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "Tracking in 3D scenes aims to identify objects of interest in 3D space from a sequence of frames. The prediction output format depends on the downstream tasks, including 3D bounding boxes [28, 67], 3D object centers [73, 79], or 6DOF poses [2, 20]. State-of-the-art 3D tracking models [6, 38, 78] have focused on well-established third-person perspective benchmark datasets [5, 8, 21]. The recent largescale Ego4D dataset starts to address the problem of querying the 3D positions of objects from a first-person perspective." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 703, + 115, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 703, + 115, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 703, + 115, + 712 + ], + "type": "text", + "content": "lar depth estimation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21934" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 116, + 538, + 222 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "text", + "content": "Table 1. Comparisons of egocentric datasets that explore tracking-related problem. Existing egocentric datasets only explore the tracking problem in 2D or predicting discrete 3D locations. Some mention the tracking problem in 3D but only consider limited sensor data (RGB) or synthetic environments. Our benchmark dataset supports the study of instance tracking in 3D real-world scenarios (RWS in the table) from egocentric videos." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 116, + 538, + 222 + ], + "lines": [ + { + "bbox": [ + 50, + 116, + 538, + 222 + ], + "spans": [ + { + "bbox": [ + 50, + 116, + 538, + 222 + ], + "type": "table", + "html": "
DatasetModalityDeviceAvg. LengthAnnot. FPSRWSCamera Trajectory3D TrackingYear
TREK-150 [14]RGBGoPro10s60✓Natural✗2021
EK-VISOR [10]RGBGoPro12s0.9✓Natural✗2022
Ego4D-VQ3D [23]RGBGoPro--✓Natural✗2022
EMQA [12]RGB-D+IMU---✗Simulated✗2022
EgoPAT3D [35]RGB-D+IMUKinect4min30✗Object-Centric✗2022
DigitalTwin [44]RGB-D+IMUAria2min-✗Natural✓2022
EgoTrack [60]RGBGoPro6min5✓Natural✗2022
OursRGB-D+IMUHoloLens>5min6✓Natural✓2023
", + "image_path": "461df97ea062571b4d2ece5744e429658cc4cf20f5f6da062e72ee833282b21d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 232, + 289, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 289, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 289, + 353 + ], + "type": "text", + "content": "However, the raw sensor data in Ego4D only includes RGB images and no other 3D information, such as depth and camera poses [75, 76]. However, contemporary AR/VR headsets come with additional cameras, depth, and IMU sensors that allow for richer geometric reasoning [44, 62]. Therefore, we believe it is realistic to leverage diverse sensor streams and explore the egocentric tracking problem in 3D. Our benchmark dataset thus includes multiple raw sensors and derived data streams to support the study tracking in 3D scenes with modern hardware platforms." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 353, + 290, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 290, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 290, + 508 + ], + "type": "text", + "content": "Object instance detection and tracking is a long-standing problem in computer vision and robotics [16, 22, 24, 56, 63]. Instead of predicting labels from a predefined set of object categories, instance-level predictions treat every object instance as a separate category. Instance-level tracking aims to locate given object instances in a sequence of frames, commonly using a tracking-by-detection paradigm. One common formulation is person re-identification [71, 77], which aims to track and associate individual people as they enter and leave multiple cameras' fields of view. Our setting is closely related but is dominated by the motion of the (egocentric) camera rather than the dynamics of object motion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 521, + 224, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 224, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 224, + 534 + ], + "type": "text", + "content": "3. IT3DEgo: Protocol and Dataset" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 541, + 288, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 288, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 288, + 615 + ], + "type": "text", + "content": "The problem of IT3DEgo is motivated by real-world assistive agents running on AR/VR devices. Given an object instance specified by the end user, developed models are required to track it in the 3D environment, i.e., recording its 3D location over time (cf. Fig. 2). In this section, we introduce our benchmarking protocol and dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 622, + 181, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 181, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 181, + 635 + ], + "type": "text", + "content": "3.1. Benchmarking Protocol" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Because object instances of interest are naturally diverse and may fall outside of the vocabulary of existing detectors, we set up a benchmarking protocol that focuses on evaluation without a separate training set. In other words, models should be pretrained on other data sources and cannot see objects in our dataset. This aligns with the contemporary foun" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 232, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 255 + ], + "type": "text", + "content": "dation models (e.g., CLIP [49] and SAM [29]) pretrained on open-world data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 256, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 547, + 483 + ], + "type": "text", + "content": "Instances enrollment. We consider two distinct setups to specify object instances of interest. The first is single-view online enrollment (SVOE), similar to single object tracking (SOT) where an object is specified on-the-fly by the end users. For example, the user can specify an object of interest by interacting or pointing to it, after which the system should track it in the 3D world. The second is multi-view pre-enrollment (MVPE), which defines (or pre-enrolls) concerned objects with a set of object-centric images captured from multiple angles. The two setups present different challenges. SVOE provides a bounding box of the object (similar to specifying an object in SOT), but the visual quality is generally lower in resolution as the objects can be far from the camera. MVPE provides 25 high-resolution " + }, + { + "bbox": [ + 304, + 256, + 547, + 483 + ], + "type": "inline_equation", + "content": "(2124\\times 2832)" + }, + { + "bbox": [ + 304, + 256, + 547, + 483 + ], + "type": "text", + "content": " object-centric images of the instances captured from different angles. However, the object instance is captured under different lighting conditions than the tracking environment, and can be posed differently (e.g., keys can be deformed over time)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 520 + ], + "type": "text", + "content": "Evaluation protocols. Following the literature on object tracking and detection, we use the metrics below in our benchmarking protocol." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": "- Precision and recall at different L2 distance thresholds. Given " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " specific thresholds " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\tau_{i}" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "i\\in \\{1,2,\\dots N\\}" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ", specifically 0.25, 0.5, 0.75, 1.0, and 1.5 meters, a ground-truth object location " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_{\\mathrm{gt}}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " and a predicted location " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_{\\mathrm{pred}}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ", we count a true positive " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "(\\mathrm{TP}_i)" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "||\\mathbf{o}_{\\mathrm{gt}} - \\mathbf{o}_{\\mathrm{pred}}||_2\\leq \\tau_i" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ". At each timestamp, each ground-truth is matched to the prediction with the smallest L2 distance below the threshold. Unmatched predictions and ground-truth at threshold " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\tau_{i}" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " are counted as false positives " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "(\\mathrm{FP}_i)" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " and false negatives " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "(\\mathrm{FN}_i)" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{TP}_i" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{FP}_i" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{FN}_i" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " are computed over all object instances in every frame. The precision and recall at threshold " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\tau_{i}" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " is computed as " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\sum \\mathrm{TP}_i / (\\sum \\mathrm{TP}_i + \\sum \\mathrm{FP}_i)" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\sum \\mathrm{TP}_i / (\\sum \\mathrm{TP}_i + \\sum \\mathrm{FN}_i)" + }, + { + "bbox": [ + 306, + 521, + 547, + 689 + ], + "type": "text", + "content": ", respectively [50, 72]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "- L2 and angular error. Following VQ3D in Ego4D [23], we also compute the L2 distance between the ground-truth" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21935" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 342, + 205 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 342, + 205 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 342, + 205 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 342, + 205 + ], + "type": "image", + "image_path": "e1cb59c4bab8a8277df27bc4491190694c0db709d35277fa4999c691565405a8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 207, + 547, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 207, + 547, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 547, + 242 + ], + "type": "text", + "content": "Figure 2. Illustration of input and output of our benchmark task. Given a raw RGB-D video sequence with camera poses and object instances of interest, i.e., either by online enrollment (SVOE) or pre-enrollment (MVPE), the goal of our benchmark task is to output the object instance 3D centers in a predefined world coordinate at each timestamp. Please check Section 3.1 for more details." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 344, + 68, + 541, + 204 + ], + "blocks": [ + { + "bbox": [ + 344, + 68, + 541, + 204 + ], + "lines": [ + { + "bbox": [ + 344, + 68, + 541, + 204 + ], + "spans": [ + { + "bbox": [ + 344, + 68, + 541, + 204 + ], + "type": "image", + "image_path": "e17cc6ff4d2cec06b0d793d19da5a0cf2d466b1fe99f80aab6075d80efc61b2f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 252, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 252, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 252, + 288, + 323 + ], + "type": "text", + "content": "and predictions in the world coordinates in meters. We also report the angular error in radians in the current camera coordinate system. Unlike threshold-aware 3D precision and recall, these metrics are computed only on frames where both ground-truth and prediction of the object instance location are available." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 326, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 288, + 361 + ], + "type": "text", + "content": "To make 3D annotation tractable, we only evaluate predictions during time intervals when target objects are stationary (i.e., not being handled by the camera wearer)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 371, + 105, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 105, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 105, + 383 + ], + "type": "text", + "content": "3.2. Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "content": "Raw video collection. The raw IT3DEgo data was recorded by three individuals in ten diverse indoor scenes, e.g., kitchen, garage, office, labs, etc. The participants perform naturalistic tasks with different object instances in the scene, e.g., cooking, repairing, writing, etc. The raw data includes 50 recordings in total. Each recording contains five or more object instances, each of which appears at three different 3D locations on average. The average length of each recording is " + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "inline_equation", + "content": "10\\mathrm{K}" + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "content": " frames or " + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "inline_equation", + "content": ">5\\mathrm{min}" + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "content": ". We capture the raw data with HoloLens2 (see Suppl.) which includes an RGB camera, a depth sensor, and four grayscale cameras with the resolution of " + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "inline_equation", + "content": "720\\times 1280" + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "inline_equation", + "content": "480\\times 640" + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "inline_equation", + "content": "512\\times 512" + }, + { + "bbox": [ + 46, + 389, + 288, + 605 + ], + "type": "text", + "content": ", respectively. Raw sensors operate at different frequencies, we sync all other sensors to the frequency of the RGB camera (30 fps). We also provide a coarse resolution scene mesh of each environment reconstructed by the Hololense OS. Additional details of the video sequences are described in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Object instance collection. To support the SVOE setup, annotators identify the first RGB frame where a given object is fully visible and close enough to specify a 2D bounding box which is at least 500 pixels in area. For MVPE, we collected 25 high-resolution images of each object instance using iPhone 13 Pro. Each object was placed on a rotary table with QR codes. We took 12 photos of each object evenly from " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " while keeping the camera at about " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "30^{\\circ}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " elevation, 12 more at " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "60^{\\circ}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " elevation and 1 top-down view." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 252, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 252, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 252, + 545, + 277 + ], + "type": "text", + "content": "We provide additional details and visualizations of object instances in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 546, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 546, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 546, + 482 + ], + "type": "text", + "content": "Annotations. Our dataset includes three types of manual annotations: (1) Object instance 3D centers describe the 3D positions of each object instance center in a world coordinate frame. We annotate the 3D center by first averaging 3D points computed from camera poses and depth maps of different views of the object instance. Annotators then examine and adjust computed 3D points by visualizing them together with the coarse mesh of the scene. (2) 2D bounding box annotations are axis-aligned 2D bounding boxes of the instance every five frames starting from the beginning of the video. Specifically, we ask annotators to draw amodal bounding boxes of each object instance. We do not annotate the object instances with heavy occlusions (i.e., when less than " + }, + { + "bbox": [ + 304, + 277, + 546, + 482 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 277, + 546, + 482 + ], + "type": "text", + "content": " of the object is visible). (3) Object motion state annotations are a per-frame annotation of whether the object is stationary or dynamic. For the data we collected, dynamic implies the camera wearer is interacting with the object." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 494, + 389, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 389, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 389, + 507 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 514, + 504, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 504, + 528 + ], + "type": "text", + "content": "4.1. Baseline: Re-purposed SOT Trackers" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 688 + ], + "type": "text", + "content": "To approach the problem of IT3DEgo, we first explore a simple unified pipeline as the baseline approach based on single object tracking (SOT). It allows instance-level 2D tracking by providing the visual appearance of object instances to track [3, 11, 70], which enables us to re-purpose them for our benchmark task. In the unified pipeline, we first compute the 2D trajectories of each object instance with SOT. The final 3D trajectories are computed by lifting the center of 2D bounding boxes with depth maps and camera poses. Lastly, we adopt a simple memory mechanism that stores the previous locations of each object instance to handle the case where the instance moves out of sight, i.e., frames without valid predictions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Lifting 2D trajectories to 3D. With the 2D trajectory predicted from SOT, each valid 2D detection is then lifted" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21936" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "into 3D space with the equation: " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_t^i = \\mathbf{T}_tz\\mathbf{K}^{-1}\\mathbf{c}_t^i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_t^i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the 2D coordinate of the center of the bounding box of instance " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " at timestamp " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_t^i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the 3D position of instance " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " at timestamp " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " in world coordinate. " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the corresponding depth value of " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_t^i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " on the depth map. " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_t" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the camera pose at timestamp " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " that specifies the camera rotation and translation w.r.t to a predefined world coordinate. " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the intrinsic matrix. A frame may lack a valid 3D prediction because either there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map is missing the depth value at " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_t^i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 205, + 289, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 289, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 289, + 337 + ], + "type": "text", + "content": "Completing 3D trajectories with memory. Any given frame may lack a valid 3D prediction, either because there is no 2D location from SOT (e.g., the object is outside the field-of-view) or the depth map has missing depth values at " + }, + { + "bbox": [ + 46, + 205, + 289, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_t^i" + }, + { + "bbox": [ + 46, + 205, + 289, + 337 + ], + "type": "text", + "content": ". To address this we implement a simple memory mechanism that stores only the most recent 3D location for each tracked instance (memory size=1). We update the memory whenever there is a new valid prediction. We note that this heuristic is a good match for the prior that object locations change only when they are being interacted with, in which case they should also be visible to the camera." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 346, + 157, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 157, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 157, + 358 + ], + "type": "text", + "content": "4.2. Improved Baseline" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 289, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 497 + ], + "type": "text", + "content": "We also explore the approach that leverages the recent foundation model SAM [29] and state-of-the-art feature encoder DINOv2 [43] for IT3DEgo. Following a tracking-by-detection pipeline, we first compute the per-frame 2D detections of each object instance by comparing the cosine similarity of DINOv2 encoded features between candidate proposals from SAM and a visual feature template. Together with the depth and camera pose information, we convert the 2D detection of each object into a 3D point in a predefined world coordinate. A simple memory with size 1 is also adopted to handle the frames without valid predictions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": "Exploring motion prior with Kalman filters. Currently, the naive update mechanism, i.e., always updating the memory for all incoming predictions, does not exploit the temporal information in video sequences. Inspired by the Kalman filter [45, 66, 67] that is widely adopted in the tracking literature, we simply model the stationary position of each object instance as piecewise constant velocity motion, leveraging the prior information that an object without being interacted with has the same 3D coordinate. Mathematically, the motion update with Kalman filter in each stationary position: " + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_{t + 1} = \\hat{\\mathbf{x}}_t + \\mathbf{K}_t(\\mathbf{z_t} - \\mathbf{H}\\hat{\\mathbf{x}}_{\\mathbf{t}})" + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_t" + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": " is a 6DOF estimated state vector including position and velocity at time step " + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_t" + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": " is the Kalman gain, " + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{t}}" + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": " is a 3DOF the measurement vector, " + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": " is the observation matrix. Please refer to Kalman [26] for more details. Moving from one stationary position to the next one, we introduce an L2 distance heuristic to model the period where objects are being interacted. Specifically, we compute the L2 distance between incoming 3D positions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "content": "and the state predictions from the Kalman filter. If the L2 distance is above the threshold, we reset the Kalman filter with the current 3D predictions as the initialization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 116, + 388, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 116, + 388, + 129 + ], + "spans": [ + { + "bbox": [ + 306, + 116, + 388, + 129 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 137, + 547, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 547, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 547, + 233 + ], + "type": "text", + "content": "In this section, we first describe the implementation details of benchmark results. Then, we show the quantitative results of both setups and the visualizations of tracking results. Lastly, we demonstrate the importance of exploiting camera pose for tracking in 3D and perform ablation studies of the trackers. Note that we split our benchmark dataset into validation and test sets. All experiments are conducted on the validation set; the test set is used for future work." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 234, + 548, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 548, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 548, + 484 + ], + "type": "text", + "content": "Baseline SOT trackers. We choose top-ranked trackers from well-established SOT literature and VOT challenges with open-source code for both tracking setups. Specifically, we benchmark three short-term trackers ToMP [39], MixFormer [7], and ARTrack [65]; and three top-performing trackers from VOT long-term tracking challenges 2021 [30] and 2022 [31], mixLT, mlpLT and VITKT_M. We also evaluate trackers that utilize additional depth information as part of the input, including SAMF and MixForRGBD from VOT RGB-D tracking challenge 2022 [31], and ViPT [80]. Lastly, we benchmark the recent egocentric specific finetuned trackers, EgoSTARK [60]. Note that SOT trackers require initial bounding boxes to track, which are not available in MVPE. When re-purposing to MVPE setup, we explore two different initializations: (1) detection-based initialization: use multiview pre-enrollment images to search for the initial bounding boxes where object instances first appear in the video and initialize SOT trackers with the predicted 2D boxes. (2) template-based initialization: directly adopt multi-view pre-enrollment images as visual templates in the tracker and set the initial tracking search region to the entire frame." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "content": "Implementation details. The cosine similarity threshold in the SAM+DINOv2 approach is 0.6, i.e., the object is considered not visible if the cosine similarity is smaller than the threshold. For a fair comparison, we add additional 2D prediction filtering when re-purposing SOT trackers. We discard 2D predictions from SOT trackers whose prediction scores are lower than " + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "content": " of the maximum prediction score. When tracking with MVPE, we first preprocess the captured multi-view images by segmenting and cropping the foreground object using [34]. Many transformer-based SOT trackers only encode a limited number of templates, therefore, we choose 5 images from " + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "inline_equation", + "content": "270^{\\circ}" + }, + { + "bbox": [ + 304, + 486, + 548, + 713 + ], + "type": "text", + "content": " and top-down for all models in MVPE experiments. We include an ablation study exploring the relationship between tracking results and the number of views used in the supplementary material. To keep the comparison fair, all detection-based trackers in MVPE use SAM+DINOv2 with the same cosine thresholds to locate the initial bounding boxes. In terms of benchmarking RGB-D trackers in MVPE, we utilize the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21937" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 92, + 246, + 218 + ], + "blocks": [ + { + "bbox": [ + 58, + 92, + 246, + 218 + ], + "lines": [ + { + "bbox": [ + 58, + 92, + 246, + 218 + ], + "spans": [ + { + "bbox": [ + 58, + 92, + 246, + 218 + ], + "type": "image", + "image_path": "b9529dda03dbccdf893a86dcdf31b7aa3eea91fafdbf14a7cc9a7a64f4eb6a5d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 223, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 223, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 547, + 278 + ], + "type": "text", + "content": "Figure 3. Qualitative visualizations of tracking with SVOE in both 3D space (left) and projected 2D view (right). We visualize three top-performing trackers from different categories, i.e., EgoSTARK, VITKT_M, and SAM+DINOv2. For projected 2D visualization, we compare the projected 3D points of each model w.r.t to the ground-truth annotated 2D bounding boxes. In the 3D view, we show 3 concentric circles at each ground-truth position representing 0.25, 0.5 and 0.75 meter thresholds. In both 2D and 3D visualizations, we find SAM+DINOv2 outperforms others as the predictions are closer to the center of object instances." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 248, + 92, + 541, + 217 + ], + "blocks": [ + { + "bbox": [ + 248, + 92, + 541, + 217 + ], + "lines": [ + { + "bbox": [ + 248, + 92, + 541, + 217 + ], + "spans": [ + { + "bbox": [ + 248, + 92, + 541, + 217 + ], + "type": "image", + "image_path": "06513af8d920b71d82d735596f4ce56f5e19ca28d86f49d1bd178080b11f0a52.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 291, + 288, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 339 + ], + "type": "text", + "content": "estimated sparse depth maps using COLMAP [55]. The L2 distance threshold of resetting Kalman filters is " + }, + { + "bbox": [ + 46, + 291, + 288, + 339 + ], + "type": "inline_equation", + "content": "0.15\\mathrm{m}" + }, + { + "bbox": [ + 46, + 291, + 288, + 339 + ], + "type": "text", + "content": ". All experiments are implemented with PyTorch and run on Nvidia 2080Ti GPUs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 347, + 162, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 162, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 162, + 358 + ], + "type": "text", + "content": "5.1. Benchmark Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 366, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 288, + 664 + ], + "type": "text", + "content": "Tracking with SVOE. From the results shown in Table 2, we have the following salient insights: (1) Re-identifying object instances is important. Trackers designed with strong re-identify ability, i.e., long-term and egocentric specific types, outperform short-term trackers. Similar findings are shown in recent 2D egocentric tracking work [15, 60]. Surprisingly, SAM+DINOv2, the non-learned approach which does not exploit temporal information beyond the memory heuristic, performs the best among all baselines. We believe the exhaustive proposals on every frame and high quality features provide the model strong, generic re-identification ability. (2) Depth information is not fully leveraged. Current RGB-D trackers show similar or slightly worse performance compared to RGB-ST trackers (c.f. MixFormer and MixforRGBD). The main reason is that RGB-D trackers only encode depth maps as auxiliary visual features, which cannot fully exploit the geometric information from depth maps. Additionally, the depth maps are sparse and not always perfectly aligned with RGB images due to camera distortions. (3) Simple Kalman filter brings marginal benefits. The Kalman filter does not improve over the simple \"most recent\" memory heuristic for stationary objects. The naive filter is also not sufficient for modeling the switching between stationary and dynamic motions needed to capture user-object interactions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Tracking with MVPE. We benchmark top-performing trackers in each category in Table 2 for MVPE setup. From the results shown in Table 3, we find: (1) SOT trackers cannot fully exploit pre-enrollment information. SOT methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 291, + 547, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 547, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 547, + 458 + ], + "type": "text", + "content": "rely on the initial position defined by 2D boxes on the frame to perform well. Comparing detection-based initializations and SVOE results, e.g., " + }, + { + "bbox": [ + 304, + 291, + 547, + 458 + ], + "type": "inline_equation", + "content": "\\mathrm{ARTrack}^{\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 291, + 547, + 458 + ], + "type": "text", + "content": " and ARTrack in Table 2, the model performance drops since the initial boxes are not as accurate as ground-truth initialization. VITKT_M adopts many complicated modules that all rely on the initial bounding boxes and degrades more significantly, compared to other types of trackers. (2) Encoding rich visual information generally helps. From the results of template-based initializations, VITKT_M for the same reason mentioned before, we find trackers benefit from the high-resolution multi-view images. SAM+DINOv2 shows a significant performance boost because it is more robust to inaccurate initialization without relying on temporal information." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 459, + 547, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 531 + ], + "type": "text", + "content": "Qualitative results. Figure 3 shows predictions of top-performing trackers from three different categories, i.e., best tracker in long-term and egocentric specific, and SAM+DINOv2. Clearly, SAM+DINOv2 predictions are closer to the object center in both 3D and projected 2D space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 539, + 502, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 502, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 502, + 552 + ], + "type": "text", + "content": "5.2. Further Analysis and Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "content": "We further compare tracking object instances in both 2D and 3D settings, demonstrating tracking object instances is much easier in 3D space. We also include an ablation study regarding the cosine similarity thresholds. All studies shown in this section are using SAM+DINOv2 unless otherwise specified. More quantitative and qualitative results are shown in the supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "Tracking in 2D with 3D guidance. We experimentally demonstrate the importance of leveraging 3D information in egocentric instance tracking by comparing 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D tracking results are computed with predicted 3D trajectories as the guidance. For each object instance, the per-frame" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21938" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 126, + 544, + 289 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 126 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 126 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 126 + ], + "type": "text", + "content": "Table 2. Benchmark results of tracking with SVOE. From the results, we draw three salient conclusions: (1) The ability of re-identifying object instances after they disappear is important, as long-term and egocentric specific trackers outperform short-term trackers, i.e., RGB-ST and RGB-D. (2) Currently, encoding depth maps as auxiliary information cannot improve performance since depth maps are sparse and not always perfectly aligned with RGB frames due to distortions. (3) The Kalman filter smoothing yields marginal improvements over the simple memory heuristic. The method with KF subscript indicates it applies the Kalman filter." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 126, + 544, + 289 + ], + "lines": [ + { + "bbox": [ + 49, + 126, + 544, + 289 + ], + "spans": [ + { + "bbox": [ + 49, + 126, + 544, + 289 + ], + "type": "table", + "html": "
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
ToMPRGB-ST5.610.117.225.339.06.111.018.827.742.62.111.32
MixFormerRGB-ST8.312.218.727.043.09.013.420.429.547.01.971.15
ARTrackRGB-ST9.113.921.530.345.110.115.323.732.447.21.921.10
SAMFRGB-D7.011.515.724.040.87.712.517.226.344.71.901.00
MixForRGBDRGB-D7.512.116.825.341.08.313.420.128.545.02.111.32
ViPTRGB-D8.913.620.628.141.49.714.922.530.745.32.021.21
mixLTRGB-LT14.417.523.931.847.215.819.226.134.851.61.851.02
mlpLTRGB-LT16.020.025.535.248.216.720.826.536.750.11.770.97
VITKT_MRGB-LT21.524.229.737.550.623.025.931.840.254.21.550.83
EgoSTARKRGB-Ego17.521.226.836.349.117.622.027.438.051.21.700.91
SAM + DINOv2RGB23.326.433.143.359.424.928.135.346.363.41.350.81
SAM + DINOv2KFRGB23.727.133.944.561.225.529.036.848.064.91.320.79
", + "image_path": "1e693609a9746589ba7885a1a8c0348305c2e2c2fb73f09de20409e255cc7a9f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 361, + 545, + 506 + ], + "blocks": [ + { + "bbox": [ + 46, + 294, + 547, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 547, + 361 + ], + "type": "text", + "content": "Table 3. Benchmark results of tracking with MVPE. We evaluate top-performing trackers in each category in Table 2 for MVPE setup. From the results, we have the following summaries: (1) SOT trackers cannot fully exploit pre-enrollment information. Detection-initialized versions perform less well compared to SVOE due to the inaccurate estimated initial bounding boxes. VITKT_M, which uses many modules that rely heavily on the initialization, degrades more significantly. (2) Encoding rich visual information generally helps. SAM+DINOv2 shows an even larger performance boost because it is more robust to the inaccurate initialization. The D and T superscripts indicate the detection- and template-based initializations, respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 361, + 545, + 506 + ], + "lines": [ + { + "bbox": [ + 49, + 361, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 49, + 361, + 545, + 506 + ], + "type": "table", + "html": "
ModelModalityPrecision(%)↑Recall(%)↑L2↓ (m)Angle↓ (rad)
0.250.50.751.01.50.250.50.751.01.5
\\( ARTrack^D \\)RGB-ST6.812.118.525.841.07.112.318.826.842.11.981.16
\\( ARTrack^T \\)RGB-ST11.218.125.228.738.512.720.928.533.045.11.911.07
\\( ViPT^D \\)RGB-D6.311.717.924.940.26.911.817.925.941.02.011.21
\\( ViPT^T \\)RGB-D10.517.424.027.136.311.920.127.131.344.01.931.10
\\( VITKT_M^D \\)RGB-LT13.818.025.033.046.614.318.625.834.148.21.770.98
\\( VITKT_M^T \\)RGB-LT9.212.820.728.544.09.714.222.431.346.51.951.08
\\( EgoSTARK^D \\)RGB-Ego13.217.023.130.547.014.718.525.934.449.71.821.01
\\( EgoSTARK^T \\)RGB-Ego18.923.128.337.149.619.123.129.339.152.91.670.88
SAM + DINOv2RGB56.059.061.867.574.350.052.755.260.366.40.670.40
SAM + DINOv2_KFRGB56.259.462.268.174.850.353.155.761.167.10.650.39
", + "image_path": "de8825be45c13fa00fd509a2cce121c98bc785ca7218e0b7cd38bf51860e8274.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 52, + 630, + 281, + 692 + ], + "blocks": [ + { + "bbox": [ + 46, + 517, + 288, + 626 + ], + "lines": [ + { + "bbox": [ + 46, + 517, + 288, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 288, + 626 + ], + "type": "text", + "content": "Table 4. Quantitative comparisons of 2D tracking results w/ and w/o 3D guidance. With 3D guidance means the 2D results are computed by finding the bounding box proposal with the smallest L2 distance from projected 3D trajectories. Without 3D guidance means proposals are selected purely based on the visual feature cosine similarity. Please refer to Section 5.2 for more details. From the results, we find the tracking results are significantly improved with the 3D guidance, indicating that tracking in 3D in egocentric videos is much easier than in 2D by leveraging camera pose and depth sensors." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 630, + 281, + 692 + ], + "lines": [ + { + "bbox": [ + 52, + 630, + 281, + 692 + ], + "spans": [ + { + "bbox": [ + 52, + 630, + 281, + 692 + ], + "type": "table", + "html": "
3D Guid.AUC(%)↑N. Prec.(%)↑Prec.(%)↑
SVOEX20.714.98.9
✓27.621.711.5
MVPEX14.17.43.0
✓39.135.218.7
", + "image_path": "b243618e58df93377c32f299d7d00d451df41d7a95720615bad0650572669f13.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 518, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 547, + 686 + ], + "type": "text", + "content": "2D detection results are computed by selecting the (above threshold) proposal with the smallest L2 distance between projected 3D points and the center of bounding boxes proposals. Without 3D guidance means the 2D tracking results are produced by selecting the proposal with the highest cosine feature similarity. To keep a fair comparison, the cosine similarity threshold is the same when computing the 3D and 2D trajectories. We evaluate the 2D tracking performance using widely adopted precision, normalized precision metrics and AUC in SOT literature [69]. As shown in Table 4, the model with 3D guidance performs significantly better in both SVOE and MVPE, demonstrating that leveraging the 3D information, such as camera pose and depth map, makes the tracking problem much easier." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "content": "Performance w.r.t cosine similarity thresholds. Feature cosine similarity threshold is adopted to determine whether" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21939" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 544, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 544, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 544, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 544, + 167 + ], + "type": "image", + "image_path": "19d022e3941fe38a206a8267ac85d18c86a3fef8507c39084977a0f5631dd1a1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 168, + 547, + 203 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 547, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 547, + 203 + ], + "type": "text", + "content": "Figure 4. Performance comparisons of SAM+DINOv2 with different cosine thresholds. By increasing the threshold, we find the model performance first improves and then gradually decreases. Intuitively, increasing the threshold will initially filter noisy predictions but when the threshold is too large the model will miss correct object 3D location updates." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 212, + 289, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 212, + 289, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 289, + 357 + ], + "type": "text", + "content": "the object instance is present in the current frame, which is crucial for the memory updating mechanism. To characterize the relationship between tracking performance and cosine similarity thresholds, we run the experiment with different cosine similarity thresholds but keep everything else the same. As shown in Figure 4, both models show improved performance at first and then a gradual decrease. Higher cosine thresholds result in fewer predictions so the model must increasingly rely on previous confident predictions stored in the memory. Models with large cosine similarity thresholds have a higher chance of missing valid location updates, which leads to a drop in both precision and recall." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 369, + 117, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 117, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 117, + 380 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 288, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 288, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 288, + 556 + ], + "type": "text", + "content": "Limitations and future work. We point out that the current benchmark dataset has limited geographic and demographic diversity and captures only a small range of objects and activities. As such it is not appropriate for training large models and only serves as a diagnostic test to identify some limitations of existing approaches. Our hope is that it serves as a starting point for the research community to explore and eventually grow into a more comprehensive challenge. Currently, the studied baseline approaches follow the same paradigm, i.e., lifting predicted 2D trajectories into 3D space. We found empirically that the simplest memory mechanism performed best but it seems very likely there are more nuanced state-update models which can integrate multiple observations effectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Finally, we highlight two opportunities for future work. First, advanced models to detect object 3D motion changes. Our experiments demonstrate that tracking in 3D world coordinates effectively narrows the problem to that of accurately predicting the object motion status, i.e., finding all stationary periods for each object instance. However, accurately predicting object state changes is still a non-trivial problem to solve. Second, better utilization of object instance information. Currently, the object instances enrollments, i.e., SVOE and MVPE are naively encoded as visual features. Future work should explore the approaches of fusing the additional scene 3D information with object instances for better tracking performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 212, + 547, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 547, + 319 + ], + "type": "text", + "content": "Broader impact. We believe the broader impact of our work is two-fold. First, we hope our benchmark brings more attention to the problem of tracking object instances in 3D from the egocentric perspective and contributes towards building future task-aware assistive agents. Second, our multi-modal benchmark dataset is beneficial to the study of other 3D scene understanding related problems from the egocentric perspective, such as SLAM, camera localization, 3D reconstruction, and depth estimation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 322, + 548, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 548, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 548, + 418 + ], + "type": "text", + "content": "Potential negative impacts. Tracking in 3D from egocentric videos requires the geometric data of surrounding environments and the sensor streams that continuously capture their workplace or daily lives. There are obvious privacy concerns when deploying such hardware and algorithms. Similar to other apps running on personal devices, the simple solution is to keep all user data locally or (in the context of research) develop techniques for anonymizing video [61]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 436, + 379, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 379, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 379, + 449 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "We introduce a new IT3DEgo benchmark that allows us to study the problem of tracking object instances in 3D from egocentric videos. The object instances to be tracked are either determined in advance or enrolled online during user interactions with the environment. To support the study, we collect and annotate a new dataset that features RGB-D videos and per-frame camera poses, along with instance-level annotations in both 2D camera and 3D world coordinate frames. We re-purpose and evaluate state-of-the-art single object trackers and develop a strong baseline using large pretrained recognition models and Kalman filtering. We hope our benchmark brings more attention to this challenge and contributes to the development of perceptually-aware assistive agents." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "type": "text", + "content": "Acknowledgements. This work was partially supported by the DARPA Perceptually enabled Task Guidance (PTG) Program (HR00112220005). Shu Kong was partially supported by the University of Macau (SRG2023-00044-FST). We thank Juan Carlos Dibene for the help of using hl2ss [1]; An Dang for the help with the initial development of the data capture; Yi-Ling Lin for the help of partial data annotations." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21940" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "type": "text", + "content": "[1] Hololens 2 sensor streaming. https://github.com/jdibenes/hl2ss, 2023.8" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 288, + 178 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 288, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 288, + 178 + ], + "type": "text", + "content": "[2] Adel Ahmadyan, Liangkai Zhang, Artsiom Ablavatski, Jianing Wei, and Matthias Grundmann. 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In this area, dense correspondence-based methods have achieved leading performance. However, they do not explicitly consider the local and global geometric information of different instances, resulting in poor generalization ability to unseen instances with significant shape variations. To deal with this problem, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose), which includes two key designs: (1) The first design is an Instance-Adaptive Keypoint Detection module, which can adaptively detect a set of sparse keypoints for various instances to represent their geometric structures. (2) The second design is a Geometric-Aware Feature Aggregation module, which can efficiently integrate the local and global geometric information into keypoint features. These two modules can work together to establish robust keypoint-level correspondences for unseen instances, thus enhancing the generalization ability of the model. Experimental results on CAMERA25 and REAL275 datasets show that the proposed AG-Pose outperforms state-of-the-art methods by a large margin without category-specific shape priors.", + "bbox": [ + 75, + 328, + 473, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 717, + 209, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The 6D object pose estimation task aims to predict the rotation, translation and size of objects with 2D/3D observations. Due to its great potential in many real-world applications such as robotic manipulation [25, 38, 39], augmented reality [1, 23] and autonomous driving [3, 7, 22], this task has been attracting increasing attention in the research community. While many previous methods [10, 11, 19, 27, 34, 41] have achieved significant performance on instance-level 6D object pose estimation, their reliance on instance-level", + "bbox": [ + 75, + 742, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fee0a8f388f67550c7a9cb11aee471b240b69241e96d1da148993cd54deb9013.jpg", + "image_caption": [ + "a) Existing dense correspondence-based method DPDN" + ], + "image_footnote": [], + "bbox": [ + 527, + 297, + 588, + 373 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b5bab674c4fc4d7eba58ffa11bbe8372d794a324d7295f9c131341765fead2d.jpg", + "image_caption": [ + "Dense Correspondence Prediction", + "Correspondence Error Map" + ], + "image_footnote": [], + "bbox": [ + 683, + 301, + 767, + 359 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/086da8447efdc80ae16cbac70ea7254e83228d18686aeaff3d53f0a87b336fb4.jpg", + "image_caption": [ + "Pose Estimation" + ], + "image_footnote": [], + "bbox": [ + 776, + 301, + 862, + 358 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/575d2bc59998b6f5a7dea0a895be42695911f4b0de5bfa1e8777f824edd82fe4.jpg", + "image_caption": [ + "b) Local Geometric Information" + ], + "image_footnote": [], + "bbox": [ + 501, + 388, + 686, + 511 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8bdbde412b0b1c6497b2a89a5bf9a84c8e54bd19bf695a06ec4a9060b43bb5ea.jpg", + "image_caption": [ + "c) Global Geometric Information", + "Figure 1. a) The visualization for the correspondence error map and final pose estimation of the dense correspondence-based method, DPDN [17]. Green/red indicates small/large errors and GT/predicted bounding box. b) Points belonging to different parts of the same instance may exhibit similar visual features. Thus, the local geometric information is essential to distinguish them from each other. c) Points belonging to different instances may exhibit similar local geometric structures. Therefore, the global geometric information is crucial for correctly mapping them to the corresponding NOCS coordinates." + ], + "image_footnote": [], + "bbox": [ + 702, + 388, + 880, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CAD models hinders their generalization to novel instances. To deal with this problem, category-level 6D object pose estimation has been introduced in [35], which aims to estimate the poses of unseen instances within specific categories without using their CAD models.", + "bbox": [ + 496, + 686, + 890, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the category-level 6D object pose estimation task, networks are trained with numerous CAD models of different instances and required to estimate the 6D poses of unseen instances which belong to the same category but have different 3D shapes. Consequently, the main challenge of this task lies in the significant intra-category shape variation. Most of the existing category-level methods aim to establish dense correspondences between observed image points (RGB or RGB-D) and the Normalized Object Coor", + "bbox": [ + 496, + 763, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21040", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dinate Space (NOCS) [35]. They can be categorized into two groups, i.e., the direct dense prediction methods and the two-stage deform-and-match methods. The direct dense prediction methods train their networks to directly map observed image points into the NOCS to obtain dense correspondences [13, 14, 16, 18, 35]. On the other hand, the two-stage methods predict deformation fields on a categorical shape prior [30] to reconstruct instance models first, and then establish dense correspondences between observed points and reconstructed models. With point-level dense correspondences, the final pose and size can be retrieved via Umeyama algorithm [31] or regression networks. Although dense correspondence-based methods have made significant progress, they tend to generate numerous incorrect correspondences for instances with large shape variations (Figure 1 (a)). We owe this problem to that these methods do not explicitly consider the geometric information of different instances, which is of significant importance for generalization to unseen instances. As shown in Figure 1 (b), the three points corresponding to different parts of the camera have similar visual features but distinct local structures. Thus, incorporating local geometric information is crucial to effectively distinguish them from each other. On the other hand, as illustrated in Figure 1 (c), the three points on different cameras exhibit similar local structures but correspond to different NOCS coordinates due to the large shape variations on the camera lenses. These points can be effectively discriminated by taking the global geometric information into account.", + "bbox": [ + 76, + 90, + 472, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To facilitate each point with geometric information in dense correspondence-based methods, an intuitive way is to employ vanilla attention mechanism [32] to aggregate features from all other points. However, it will greatly increase the computational overhead due to the vast number of points. Different from existing methods, we aim to utilize a set of sparse keypoints to represent the shapes of different instances and extract geometric-aware keypoint features to establish robust keypoint-level correspondences for 6D pose estimation. Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Nevertheless, it's non-trivial because of following challenges: 1) The shapes of different instances vary significantly. Thus, the model needs to adaptively detect representative keypoints for different instances to comprehensively represent their shapes. 2) The local and global geometric information are indispensable. How to efficiently encode such geometric information into keypoint features needs to be carefully considered to achieve better generalization on unseen instances.", + "bbox": [ + 76, + 532, + 472, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the above discussions, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning method for category-level 6D object pose estimation (AG-Pose). The framework is shown in Figure 2 (a). The proposed method has two key designs: the Instance-Adaptive Keypoint Detection (IAKD) module and the Geometric-Aware Feature Aggregation (GAFA) module. The IAKD is designed to adaptively detect keypoints for various instances. Specifically, we initialize a set of category-shared learnable queries as keypoint detectors. We first convert them to instance-adaptive detectors by aggregating the object features into learnable queries via attention mechanism [32]. Subsequently, the heatmap of keypoints is obtained by calculating similarities between instance-adaptive detectors and object features. However, the IAKD alone can not guarantee the detected keypoints to focus on different local parts to fully represent the shapes of different instances. Thus, we further design a diversity loss and an object-aware chamfer distance loss to constrain the distribution of keypoints, yielding dispersed and object-focused keypoints. The GAFA module is designed to efficiently extract the local and global geometric information for detected keypoints. In particular, to incorporate local geometric information, GAFA selects the spatially nearest K points for each keypoint and incorporate their relative positions to aggregate features from its neighbors. To incorporate global geometric information, we further integrate global feature and relative positional embeddings into keypoint features. By combining these two modules together, the proposed method can efficiently learn instance-adaptive and geometric-aware keypoints to establish robust keypoint-level correspondences for pose estimation.", + "bbox": [ + 496, + 90, + 893, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 517, + 545, + 820, + 559 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel instance-adaptive and geometric-aware keypoint learning method for category-level 6D object pose estimation, which can better generalize to unseen instances with large shape variations. To the best of our knowledge, this is the first adaptive keypoint-based method for category-level 6D object pose estimation.", + "- We evaluate our framework on widely adopted CAMERA25 and REAL275 datasets, and results demonstrate that the proposed method sets a new state-of-the-art performance without using categorical shape priors." + ], + "bbox": [ + 500, + 561, + 890, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 729, + 650, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Instance-level 6D object pose estimation", + "text_level": 1, + "bbox": [ + 500, + 755, + 841, + 771 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instance-level 6D object pose estimation aims to estimate the pose of a known object given its CAD model. In recent years, numerous methods based on direct regression [4, 24, 33, 42], fixed keypoint detection [6, 27, 40, 41], and dense 2D-3D correspondences [26, 43] have been proposed. Direct regression-based methods take the observation image (RGB or RGBD) as input and directly predict the 3D rotation and translation via regression networks. The ad", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21041", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "vantage of these methods lies in end-to-end pose estimation without extra post-processing. On the other hand, methods based on fixed keypoint detection usually predefine a set of keypoints on the object CAD model and detect their corresponding positions in the input image. Subsequently, pose estimation is achieved through Perspectiveen-Point (PnP) algorithms. For example, [10, 11, 27, 41] utilize a dense voting strategy to detect keypoints and achieve state-of-the-art performance. Dense 2D-3D correspondence-based methods aim to predict the corresponding position on the object CAD model for every point [19, 34], which are more robust to occlusion. Among them, the approaches based on fixed keypoints are most related to our method. However, they adopt fixed keypoints on a given CAD model while our method aims to adaptively detect keypoints for different instances because the CAD models are not accessible during inference in category-level task.", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Category-level 6D object pose estimation", + "text_level": 1, + "bbox": [ + 76, + 358, + 426, + 375 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To improve the generalization ability on unseen instances, the category-level 6D object pose estimation is introduced, which aims to estimate the poses of all instances belonging to a specific category without using their CAD models. NOCS [35] proposes to use a shared canonical representation called Normalized Object Coordinate Space (NOCS) to represent the shapes of all instances. They first predict the NOCS coordinates of observed points and then apply Umeyama [31] algorithm to recover the pose and size. To handle the intra-category shape variation, SPD [30] proposes a deformation and matching strategy. They first reconstruct instance models by deforming a categorical shape prior and then match observations to the reconstructed models. Inspired by SPD, multiple works [2, 17, 36, 44] have been proposed to improve the processes of shape prior deformation, correspondence matching and et al., continuously improving the pose estimation performance. However, the above methods have not explicitly taken the local and global geometric information of different instances into consideration, which results in poor generalization ability to unseen instances with significant shape variations.", + "bbox": [ + 75, + 383, + 472, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 715, + 210, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 739, + 187, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a RGB-D image, we first employ a segmentation model such as [20, 21] to obtain the segmentation mask and category label for each object. Following previous works [17, 46], here we employ an off-the-shelf MaskRCNN [9]. For each segmented object, we use the segmentation mask to get the cropped RGB image $\\mathbf{I}_{obj} \\in \\mathbb{R}^{H \\times W \\times 3}$ and the point cloud $\\mathbf{P}_{obj} \\in \\mathbb{R}^{N \\times 3}$ , where $N$ is the number of points and $\\mathbf{P}_{obj}$ is acquired by back-projecting the cropped depth image using camera intrinsics followed by a downsampling", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "process. By taking $\\mathbf{I}_{obj}$ and $\\mathbf{P}_{obj}$ as input, the proposed method aims to estimate the 3D rotation $\\mathbf{R} \\in SO(3)$ , the 3D translation $\\pmb{t} \\in \\mathbb{R}^3$ and the size $s \\in \\mathbb{R}^3$ of the target object.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The framework of proposed AG-Pose is shown in Figure 2 (a). Our method consists of four main components: Feature Extractor (Sec. 3.2), Instance-Adaptive Keypoint Detector (Sec. 3.3), Geometric-Aware Feature Aggregator (Sec. 3.4) and Pose&Size Estimator (Sec. 3.5). Details about each component are as follows.", + "bbox": [ + 496, + 152, + 893, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Feature Extractor", + "text_level": 1, + "bbox": [ + 498, + 255, + 676, + 270 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the input point cloud $\\mathbf{P}_{obj}$ , we utilize the PointNet++ [28] to extract point features $\\mathbf{F}_P \\in \\mathbb{R}^{N \\times C_1}$ . For the RGB image $\\mathbf{I}_{obj}$ , following [33], a PSP network [45] with ResNet-18 [8] is applied to extract pixel-wise appearance features from $\\mathbf{I}_{obj}$ . We then choose those pixel features corresponding to $\\mathbf{P}_{obj}$ to obtain the RGB features $\\mathbf{F}_I \\in \\mathbb{R}^{N \\times C_2}$ . Lastly, we concatenate $\\mathbf{F}_I$ and $\\mathbf{F}_P$ to form $\\mathbf{F}_{obj} \\in \\mathbb{R}^{N \\times C}$ as the input for the subsequent networks.", + "bbox": [ + 496, + 279, + 890, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Instance-Adaptive Keypoint Detector", + "text_level": 1, + "bbox": [ + 498, + 412, + 821, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As introduced in Section 1, the geometric information is indispensable to establish robust correspondences. An intuitive idea to facilitate each point with geometric information is to employ the vanilla attention mechanism [32] to aggregate features from all other points. But it is computationally expensive due to the large number of points. Instead, we aim to utilize a set of sparse keypoints to represent the shapes of different instances for pose estimation. However, since the shapes vary across different instances and the instance models are not accessible during inference, fixed keypoint detection methods like [10, 11, 27, 41] are not applicable. Besides, methods like Farest Point Sampling are not end-to-end trainable, which may detect keypoints on outlier points caused by the noisy segmentation mask, the incorrect depth values and et al. Consequently, we design an Instance-Adaptive Keypoint Detection module to adaptively detect keypoints for instances with different shapes which can efficiently represent the object and avoid focusing on outlier points.", + "bbox": [ + 496, + 436, + 890, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The pipeline of IAKD is illustrated in Figure 2 (b). Specifically, we initialize a set of category-shared learnable queries $\\mathbf{Q}_{cat} \\in \\mathbb{R}^{N_{kpt} \\times C}$ and each of them represents a keypoint detector. We first inject the object features $\\mathbf{F}_{obj}$ into learnable queries via Transformer Layers [32]. This process converts the category-shared detectors $\\mathbf{Q}_{cat}$ into instance-adaptive detectors $\\mathbf{Q}_{ins} \\in \\mathbb{R}^{N_{kpt} \\times C}$ conditioned on object features $\\mathbf{F}_{obj}$ . In detail,", + "bbox": [ + 496, + 724, + 890, + 847 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {Q} _ {\\text {c a t}} \\mathbf {W} ^ {q}, \\mathbf {K} = \\mathbf {F} _ {\\text {o b j}} \\mathbf {W} ^ {k}, \\mathbf {V} = \\mathbf {F} _ {\\text {o b j}} \\mathbf {W} ^ {v}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 858, + 890, + 876 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {i n s} = \\operatorname {N o r m} \\left(\\mathbf {Q} _ {c a t} + \\operatorname {s o f t m a x} \\left(\\mathbf {Q K} ^ {T}\\right) \\mathbf {V}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 878, + 890, + 897 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21042", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d0f2a0c0aed6bae1d3176d7d7f52410e42eb74e21d4dd924345f7643bb71be1e.jpg", + "image_caption": [ + "Feature Extractor & Instance-Adaptive Keypoint Detector", + "Geometric-Aware Feature Aggregator & Pose Estimator", + "(a) Framework Overview" + ], + "image_footnote": [], + "bbox": [ + 76, + 102, + 893, + 243 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/720c937e430941d84101838b4e77364accdc02cbd3f9cb634a347601612c800e.jpg", + "image_caption": [ + "Figure 2. a) Overview of the proposed AG-Pose. b) Illustration of the IAKD module. We initialize a set of category-shared learnable queries and convert them into instance-adaptive detectors by integrating the object features. The instance-adaptive detectors are then used to detect keypoints for the object. To guide the learning of the IAKD module, we further design the $L_{div}$ and $L_{ocd}$ to constrain the distribution of keypoints. c) Illustration of the GAFA module. Our GAFA can efficiently integrate the geometric information into keypoint features through a two-stage feature aggregation process." + ], + "image_footnote": [], + "bbox": [ + 83, + 258, + 885, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then we calculate the cosine similarities between the instance-adaptive detectors $\\mathbf{Q}_{ins}$ and the object features $\\mathbf{F}_{obj}$ to generate keypoint heatmap $\\mathbf{H} \\in \\mathbb{R}^{N_{kpt} \\times N}$ . Subsequently, the 3D coordinates of keypoints $\\mathbf{P}_{kpt} \\in \\mathbb{R}^{N_{kpt} \\times 3}$ and their corresponding features $\\mathbf{F}_{kpt} \\in \\mathbb{R}^{N_{kpt} \\times C}$ under camera space are obtained by weighted sum as:", + "bbox": [ + 75, + 590, + 468, + 680 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {k p t} = \\operatorname {s o f t m a x} (\\mathbf {H}) \\times \\mathbf {P} _ {o b j}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 712, + 468, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {k p t} = \\operatorname {s o f t m a x} (\\mathbf {H}) \\times \\mathbf {F} _ {o b j}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 732, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since our target is to utilize a set of sparse keypoints to represent the geometric information of the object, the detected keypoints should be well distributed on the surface of the object. However, we find that the keypoints tend to cluster in small regions and often focus on non-surface or outlier points without explicit supervision. To encourage the keypoints to focus on different parts, we further design a diversity loss $L_{div}$ to force the detected keypoints to be away", + "bbox": [ + 75, + 780, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from each other. In detail,", + "bbox": [ + 500, + 590, + 673, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d i v} = \\sum_ {i = 1} ^ {N _ {k p t}} \\sum_ {j = 1, j \\neq i} ^ {N _ {k p t}} \\mathbf {d} \\left(\\mathbf {P} _ {k p t} ^ {(i)}, \\mathbf {P} _ {k p t} ^ {(j)}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 613, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} \\left(\\mathbf {P} _ {k p t} ^ {(i)}, \\mathbf {P} _ {k p t} ^ {(j)}\\right) = \\max \\left\\{t h _ {1} - \\left\\| \\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k p t} ^ {(j)} \\right\\| _ {2}, 0 \\right\\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 659, + 890, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $th_{1}$ is a hyperparameter and $\\mathbf{P}_{kpt}^{(i)}$ stands for the $i$ -th keypoint. To encourage the keypoints to locate on the surface of the object and exclude outliers simultaneously, we design an object-aware chamfer distance loss $L_{ocd}$ to constrain the distribution of $\\mathbf{P}_{kpt}$ . Formally, we first utilize the ground truth pose and size $\\mathbf{R}_{gt}, \\mathbf{t}_{gt}, \\mathbf{s}_{gt}$ to transform $\\mathbf{P}_{obj}$ to the NOCS and remove outlier points based on instance model $\\mathbf{M}_{obj} \\in \\mathbb{R}^{M \\times 3}$ to produce $\\mathbf{P}_{obj}^{\\star}$ . In formula,", + "bbox": [ + 496, + 691, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {o b j} ^ {\\star} = \\left\\{x _ {i} \\mid x _ {i} \\in \\mathbf {P} _ {o b j} \\quad a n d \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 825, + 794, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {y _ {j} \\in \\mathbf {M} _ {o b j}} \\| \\frac {1}{\\| \\mathbf {s} _ {g t} \\| _ {2}} \\mathbf {R} _ {g t} \\left(x _ {i} - \\mathbf {t} _ {g t}\\right) - y _ {j} \\| _ {2} < t h _ {2} \\}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 845, + 890, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The outlier filter process is also illustrated in Figure 3. Then", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21043", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/758ec3373b217130b52dfd34d09a31ecd3ac9953e51591a841b04629faea0560.jpg", + "image_caption": [ + "Figure 3. Illustration of the outlier filter process." + ], + "image_footnote": [], + "bbox": [ + 106, + 82, + 433, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the $L_{ocd}$ is calculated as follows,", + "bbox": [ + 76, + 208, + 297, + 223 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {o c d} = \\frac {1}{| \\mathbf {P} _ {k p t} |} \\sum_ {x _ {i} \\in \\mathbf {P} _ {k p t}} \\min _ {y _ {j} \\in \\mathbf {P} _ {o b j} ^ {\\star}} \\| x _ {i} - y _ {j} \\| _ {2}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 229, + 468, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By constraining keypoints to be close to $\\mathbf{P}_{obj}^{\\star}$ , the IAKD module can automatically learn to filter out outlier points during inference.", + "bbox": [ + 76, + 273, + 468, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Geometric-Aware Feature Aggregator", + "text_level": 1, + "bbox": [ + 76, + 327, + 403, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the detected keypoints for each object, a straightforward way is to predict the NOCS coordinates for these keypoints to establish keypoint-level correspondences. However, the keypoint features are lack of geometric information, which can result in numerous incorrect correspondences on unseen instances. Thus, we propose a Geometric-Aware Feature Aggregation module to efficiently incorporate geometric information into keypoint features.", + "bbox": [ + 75, + 349, + 468, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The GAFA adopts a two-stage pipeline for geometric feature aggregation, as illustrated in Figure 2 (c). We first select the nearest $K$ neighbors in $\\mathbf{P}_{obj}$ and their corresponding features in $\\mathbf{F}_{obj}$ for each keypoint to obtain $\\mathbf{P}_{knn} \\in \\mathbb{R}^{N_{kpt} \\times K \\times 3}$ and $\\mathbf{F}_{knn} \\in \\mathbb{R}^{N_{kpt} \\times K \\times C}$ . Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Thus, we utilize the relative positional embeddings $\\alpha$ and $\\beta$ between keypoints and their neighbors to represent the local geometric features $f_l$ and global geometric features $f_g$ , respectively. In detail,", + "bbox": [ + 75, + 472, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i, j} = M L P \\left(\\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k n n} ^ {(i, j)}\\right), f _ {l} ^ {(i)} = \\operatorname {A v g P o o l} \\left(\\alpha_ {i,:}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 674, + 468, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\beta_ {i, j} = M L P \\left(\\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k p t} ^ {(j)}\\right), f _ {g} ^ {(i)} = \\operatorname {A v g P o o l} \\left(\\beta_ {i,:}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 698, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{l}^{(i)}, f_{g}^{(i)} \\in \\mathbb{R}^{1 \\times C}$ and $\\mathbf{P}_{knn}^{(i,j)}$ is the $j$ -th neighboring point of $\\mathbf{P}_{kpt}^{(i)}$ . To incorporate local geometric information into keypoints, we combine the keypoint features $\\mathbf{Q}_{ins}$ with $f_{l}$ and calculate local correlation scores $\\mathbf{A}$ between keypoints and neighboring points, which is then used to aggregate features from neighbors. The local feature aggregation process for $i$ -th keypoint feature $\\mathbf{Q}_{ins}^{(i)}$ is as follows,", + "bbox": [ + 76, + 727, + 468, + 843 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} = \\operatorname {s i m} \\left(M L P \\left(\\operatorname {c a t} \\left[ \\mathbf {Q} _ {\\text {i n s}} ^ {(i)}, f _ {l} ^ {(i)} \\right]\\right), \\mathbf {F} _ {\\text {k n n}} ^ {(i)}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 848, + 468, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {i n s} ^ {(i)} = M L P \\left(\\operatorname {s o f t m a x} (\\mathbf {A}) \\times \\mathbf {F} _ {k n n} ^ {(i)} + \\mathbf {Q} _ {i n s} ^ {(i)}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 876, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above process is executed for all keypoints in parallel to extract representative local geometric features. However, as shown in Figure 1 (c), the local geometric information alone is insufficient to handle significant shape variation across different instances. Therefore, we further inject the global geometric feature into $\\mathbf{Q}_{ins}$ by leveraging all keypoint features and the global geometric features $f_{g}$ . In formula,", + "bbox": [ + 496, + 90, + 890, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {\\text {i n s}} ^ {\\text {g l o b a l}} = \\operatorname {A v g P o o l} \\left(\\mathbf {Q} _ {\\text {i n s}}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 204, + 890, + 224 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {i n s} ^ {(i)} = M L P \\left(\\text {c o n c a t} \\left[ \\mathbf {Q} _ {i n s} ^ {(i)}, \\mathbf {Q} _ {i n s} ^ {\\text {g l o b a l}}, f _ {g} ^ {(i)} \\right]\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 227, + 890, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{Q}_{ins}^{global}\\in \\mathbb{R}^{1\\times C}$ is the global feature of $\\mathbf{Q}_{ins}$ .", + "bbox": [ + 498, + 260, + 849, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above two-stage aggregation allows keypoints to adaptively aggregate local geometric features from neighbors and global geometric information from other keypoints. It's worth noting that since the number of keypoints is small, the above process is computationally efficient.", + "bbox": [ + 496, + 277, + 890, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Pose&Size Estimator", + "text_level": 1, + "bbox": [ + 500, + 361, + 697, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining geometric-aware keypoint features, following previous work [17], we use MLP to predict the NOCS coordinates of keypoints $\\mathbf{P}_{kpt}^{nocs} \\in \\mathbb{R}^{N_{kpt} \\times 3}$ from $\\mathbf{Q}_{ins}$ and regress the final pose and size $\\mathbf{R}, \\mathbf{t}, \\mathbf{s}$ via this set of keypoint-level correspondences. In formula,", + "bbox": [ + 496, + 383, + 890, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {k p t} ^ {\\text {n o c s}} = M L P \\left(\\mathbf {Q} _ {\\text {i n s}}\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 468, + 890, + 486 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\text {p o s e}} = \\operatorname {c o n c a t} \\left[ \\mathbf {P} _ {\\text {k p t}}, \\mathbf {F} _ {\\text {k p t}}, \\mathbf {P} _ {\\text {k p t}} ^ {\\text {n o c s}}, \\mathbf {Q} _ {\\text {i n s}} \\right], \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 488, + 890, + 507 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R}, \\mathbf {t}, \\mathbf {s} = M L P _ {R} (\\mathbf {f} _ {\\text {p o s e}}), M L P _ {t} (\\mathbf {f} _ {\\text {p o s e}}), M L P _ {s} (\\mathbf {f} _ {\\text {p o s e}}). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 508, + 890, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For more details please refer to [17]. We use the 6D representation [47] for the rotation $\\mathbf{R}$ . And for the translation $\\mathbf{t}$ we follow [46] to predict the residual translation between the ground truth and the mean value of the point cloud.", + "bbox": [ + 496, + 549, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Overall Loss Function", + "text_level": 1, + "bbox": [ + 500, + 617, + 707, + 631 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function is as follows:", + "bbox": [ + 500, + 640, + 756, + 654 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a l l} = \\lambda_ {1} L _ {o c d} + \\lambda_ {2} L _ {d i v} + \\lambda_ {3} L _ {n o c s} + \\lambda_ {4} L _ {p o s e}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 664, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4$ are hyperparameters to balance the contribution of each term. For $L_{\\text{pose}}$ , we simply use $L_1$ loss as follows,", + "bbox": [ + 496, + 688, + 890, + 733 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {p o s e} = \\left\\| \\mathbf {R} _ {g t} - \\mathbf {R} \\right\\| _ {2} + \\left\\| \\mathbf {t} _ {g t} - \\mathbf {t} \\right\\| _ {2} + \\left\\| \\mathbf {s} _ {g t} - \\mathbf {s} \\right\\| _ {2}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 742, + 890, + 760 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We generate ground truth NOCS coordinates of keypoints $\\mathbf{P}_{kpt}^{gt}$ by projecting their coordinates under camera space $\\mathbf{P}_{kpt}$ into NOCS using the ground-truth $\\mathbf{R}_{gt},\\mathbf{t}_{gt},\\mathbf{s}_{gt}$ . For $L_{nocs}$ , we use the Smooth $L_{1}$ loss [17]. In formula,", + "bbox": [ + 500, + 767, + 890, + 828 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {k p t} ^ {g t} = \\frac {1}{\\| \\mathbf {s} _ {g t} \\| _ {2}} \\mathbf {R} _ {g t} \\left(\\mathbf {P} _ {k p t} - \\mathbf {t} _ {g t}\\right), \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 834, + 890, + 867 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {n o c s} = \\operatorname {S m o o t h} L _ {1} \\left(\\mathbf {P} _ {k p t} ^ {g t}, \\mathbf {P} _ {k p t} ^ {n o c s}\\right). \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 869, + 890, + 888 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21044", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a54796a86a01e864e0d622295b53201058fa660f9c49543ac4e898cc59c06eb6.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons with state-of-the-art methods on the REAL275 dataset." + ], + "table_footnote": [], + "table_body": "
MethodUse of Shape Priors\\( IoU_{50} \\)\\( IoU_{75} \\)\\( 5^{\\circ}2\\mathbf{cm} \\)\\( 5^{\\circ}5\\mathbf{cm} \\)\\( 10^{\\circ}2\\mathbf{cm} \\)\\( 10^{\\circ}5\\mathbf{cm} \\)
NOCS [35]X7830.17.21013.825.2
DualPoseNet [16]X79.862.229.335.95066.8
GPV-Pose [5]X—64.43242.9—73.3
IST-Net [18]X82.576.647.553.472.180.5
Query6DoF [37]X82.576.14958.968.783
SPD [30]✓77.353.219.321.443.254.1
SGPA [2]✓80.161.935.939.661.370.7
SAR-Net [15]✓79.362.431.642.350.368.3
RBP-Pose [44]✓—67.838.248.163.179.2
DPDN [17]✓83.4764650.770.478.4
AG-PoseX83.779.554.761.774.783.1
", + "bbox": [ + 127, + 113, + 843, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 324, + 209, + 342 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Following previous works [17, 18, 37], we conduct experiments on CAMERA25 and REAL275 [35], the most widely adopted datasets for category-level object pose estimation. CAMERA25 is a synthetic RGB-D dataset that contains 300K synthetic images of 1,085 instances from 6 different categories. In this dataset, 25,000 images of 184 instances are used for evaluation and the others are used for training. REAL275 dataset is a more challenging real-world dataset which shares the same categories with CAMERA25. It comprises 7K images from 13 different scenes. 2,750 images of 6 scenes are left for validation, including 3 unseen instances per category.", + "bbox": [ + 75, + 352, + 470, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. For a fair comparison, we use the same segmentation masks as SPD [30] and DPDN [17] from MaskRCNN [9]. For the data preprocessing, images are cropped and resized to $192 \\times 192$ before feature extraction, and the number of points $N$ in point cloud is set as 1024. For model parameters, the number of keypoints is set as $N_{kpt} = 96$ , and the local range for each keypoint in GAFA is set as $K = 16$ . The feature dimensions are set as $C_1 = 128$ , $C_2 = 128$ and $C = 256$ , respectively. For the hyper-parameters in the loss functions, the two thresholds in LQKD are set as $th_1 = 0.01$ and $th_2 = 0.1$ , and $\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4$ are 1.0, 5.0, 1.0, 0.3, respectively. For model optimizing, we train our model on both synthetic and real datasets for evaluation on REAL275 while only on synthetic dataset for evaluation on CAMERA25. Following previous work [17], we use random translation $\\Delta t \\sim U(-0.02, 0.02)$ and scaling $\\Delta s \\sim U(-0.8, 1.2)$ for data augmentation and apply random rotation for each axis with rotation degree sampled from $U(0, 20)$ . We train our network using the ADAM [12] optimizer and employ the triangular2 cyclical learning rate schedule [29] ranging from 2e-5 to 5e-4. All experiments are conducted on a single RTX3090Ti GPU with a batch size of 24.", + "bbox": [ + 75, + 536, + 470, + 882 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Following previous works [30, 35],", + "bbox": [ + 96, + 885, + 467, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we evaluate the model performance with two metrics.", + "bbox": [ + 498, + 325, + 852, + 340 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- 3D IoU. We report the mean precision of Intersection-over-Union (IoU) for 3D bounding boxes with thresholds of $50\\%$ and $75\\%$ . This metric incorporates both the pose and size of the object.", + "- $n^{\\circ} m \\, \\text{cm}$ is used for direct evaluation of the rotation and translation errors. Only predictions with rotation error less than $n^{\\circ}$ and translation error less than $m \\, \\text{cm}$ are considered correct." + ], + "bbox": [ + 500, + 340, + 890, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 498, + 469, + 867, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on REAL275 dataset. The comparisons between our AG-Pose and existing state-of-the-art methods on the challenging REAL275 dataset are shown in Table 1. As demonstrated by the results, our AG-Pose outperforms all previous methods in all metrics on REAL275 dataset. It should be noted that our method does not require the use of shape priors. In detail, on the most rigorous metric of $5^{\\circ}2\\mathrm{cm}$ , AG-Pose achieves the precision of $54.7\\%$ , surpassing the current state-of-the-art shape prior-based method DPDN [17] with a large margin by $8.7\\%$ . As for prior-free methods, our method surpasses Query6DoF [37], IST-Net [18] and GPV-Pose [5] by $5.7\\%$ , $7.2\\%$ , and $22.7\\%$ , respectively. It should be noted that Query6DoF aims to learn a set of sparse queries as implicit shape priors, and the query features are used to update the point features to establish better dense correspondences. Different from it, the proposed AG-Pose aims to use a sparse set of keypoints to explicitly model the geometric information of objects to establish robust keypoint-level correspondences for pose estimation. The superior performance of our method indicates the importance of geometric information in category-level 6D object pose estimation.", + "bbox": [ + 496, + 492, + 890, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on CAMERA25 dataset. Table 2 shows the quantitative results of the proposed AG-Pose on CAMERA25 dataset. Our method achieves the best performance under most of metrics. In detail, the proposed AG-Pose outperforms the state-of-the-art method Query6DoF [37]", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21045", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/17b872c82776d84f57bb1db9ad617e0838ebbc5b1b2263f3660ba0ac2f11edc3.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons with state-of-the-art methods on the CAMERA25 dataset." + ], + "table_footnote": [], + "table_body": "
MethodUse of Shape Prior\\( IoU_{50} \\)\\( IoU_{75} \\)\\( 5^{\\circ}2\\mathbf{cm} \\)\\( 5^{\\circ}5\\mathbf{cm} \\)\\( 10^{\\circ}2\\mathbf{cm} \\)\\( 10^{\\circ}5\\mathbf{cm} \\)
NOCS [35]X83.969.532.340.948.264.4
DualPoseNet [16]X92.486.464.770.777.284.7
GPV-Pose [5]X93.488.372.179.1—89
Query6DoF [37]X91.988.17883.183.990
SPD [30]✓93.283.154.35973.381.5
SGPA [2]✓93.288.170.774.582.788.4
SAR-Net [15]✓86.87966.770.975.380.3
RBP-Pose [44]✓93.18973.579.682.189.5
AG-PoseX93.891.377.882.885.591.6
", + "bbox": [ + 133, + 113, + 836, + 272 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/326e535f6b348bba722cabbd83ed65221e6cb4a0d03af458ea653d4ccb21ffd0.jpg", + "table_caption": [ + "Table 3. Comparisons between the IAKD and FPS." + ], + "table_footnote": [], + "table_body": "
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
FPS46.255.567.080.2
IAKD54.761.774.783.1
", + "bbox": [ + 91, + 319, + 455, + 369 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/92bffc11aa296d28fc396bc0990ffccded22be92a3e96e7608caea61b7ea94b9.jpg", + "table_caption": [ + "Table 4. Ablation studies on the number of keypoints." + ], + "table_footnote": [], + "table_body": "
Nkpt5° 2 cm5° 5 cm10° 2 cm10° 5 cm
1647.955.168.879.8
3248.855.773.182.9
645157.272.882
9654.761.774.783.1
12852.859.974.383.7
", + "bbox": [ + 96, + 409, + 450, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "by $1.9\\%$ on $I_oU_{50}$ , $3.2\\%$ on $I_oU_{75}$ , $1.6\\%$ on $10^{\\circ}2\\mathbf{cm}$ and $1.6\\%$ on $10^{\\circ}5\\mathbf{cm}$ , respectively. Our method achieves comparable performance with Query6DoF on $5^{\\circ}2\\mathbf{cm}$ and $5^{\\circ}5\\mathbf{cm}$ (lower by $0.2\\%$ and $0.3\\%$ , respectively).", + "bbox": [ + 75, + 530, + 468, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results of correspondence errors. To validate that the keypoint-level correspondences of AG-Pose are more accurate than point-level correspondences, we calculate the NOCS error distributions of DPDN [17], ISTNet [18] and our method on the REAL275 validation set. As shown in Figure 4, the NOCS error of our keypoint-level correspondences is concentrated more on the interval from 0 to 0.1, while errors of dense correspondence-based methods are concentrated more on the interval from 0.15 to 0.5. It proves that the keypoint-level correspondences produced by AG-Pose exhibit better generalizability on unseen instances.", + "bbox": [ + 75, + 592, + 468, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 770, + 240, + 784 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation experiments to demonstrate the effectiveness of the proposed method on the REAL275 dataset.", + "bbox": [ + 75, + 794, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effects of the IAKD module. To evaluate the effectiveness of the proposed Instance-Adaptive Keypoint Detection module, we first replace the IAKD with the most widely adopted Farest Point Sampling (FPS) strategy. Specifically,", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ad3fed26233823ea7648404419b691dc509bfa546cce823785fc71c758d13431.jpg", + "table_caption": [ + "Table 5. Ablation studies on the proposed loss functions." + ], + "table_footnote": [], + "table_body": "
Loss5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Ldiv+Locd54.761.774.783.1
Ldiv+Lucd49.857.374.482.0
Ldiv46.4537181.3
Locd3036.155.068.6
None29.335.656.469.6
", + "bbox": [ + 501, + 319, + 890, + 415 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5495f5d2c3d63234c85342241dcd814fa734d9fd4d09f5f9974782848e91b72.jpg", + "image_caption": [ + "Figure 4. Comparisons of NOCS error distributions." + ], + "image_footnote": [], + "bbox": [ + 517, + 433, + 854, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we use FPS to sample the same number of keypoints and use their corresponding features in $\\mathbf{F}_{obj}$ as $\\mathbf{Q}_{ins}$ . For a fair comparison, we add extra MLPs to ensure that the number of parameters remain unchanged. As shown in Table 3, the proposed IAKD outperforms FPS on all metrics. We owe the advantage to the end-to-end trainable property of IAKD and the optimized distribution of keypoints brought by the proposed losses.", + "bbox": [ + 496, + 613, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effects of different keypoint numbers. In Table 4, we show the impact of different keypoint numbers $N_{kpt}$ . Surprisingly, the result shows that our method can achieve comparable performance (47.9% on $5^{\\circ}2\\mathbf{cm}$ ) with the SOTA methods by using only a very small number ( $N_{kpt} = 16$ ) of keypoints, which demonstrates the superiority of proposed AG-Pose. And as the number of keypoints ( $N_{kpt}$ ) increases, the performance of our method continues to improve. We choose $N_{kpt} = 96$ in our method for the balance between efficiency and accuracy.", + "bbox": [ + 496, + 734, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effects of the $L_{div}$ and the $L_{ocd}$ . In our method, we", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21046", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c2783aef8452f564b2ec1028f00a4a2eaea7061980fd5d41be278701e2a281ef.jpg", + "table_caption": [ + "Table 6. Ablation study on two-stage feature aggregation." + ], + "table_footnote": [], + "table_body": "
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Full54.761.774.783.1
w/o GAFA47.155.370.280.9
w/o Local4957.871.282.2
w/o Global50.155.874.582.7
w/ vanilla attn536172.282.1
", + "bbox": [ + 78, + 108, + 490, + 204 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/248a07e44703f91e1e1e79a160727250c6670ee0a120ccfbbfd60b035b6c60cd.jpg", + "table_caption": [ + "Table 7. Ablation study on proposed GAFA." + ], + "table_footnote": [], + "table_body": "
5° 2 cm5° 5 cm10° 2 cm10° 5 cm
K=849.957.673.182.5
K=1654.761.774.783.1
K=2454.161.173.783.2
K=3252.759.973.682.8
", + "bbox": [ + 93, + 237, + 449, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "utilize the proposed $L_{div}$ and $L_{ocd}$ to encourage the keypoints to be well distributed on the surface of the object. To verify the effectiveness of them, we conduct ablation experiments on these losses and the results are shown in Table 5. By replacing the proposed $L_{ocd}$ with the normal chamfer distance loss $L_{ucd}$ , the performance of our model drops by $4.5\\%$ on $5^{\\circ}2\\mathrm{cm}$ . The reason is that our object-aware chamfer distance loss can prevent the model from being affected by outliers, thereby improving the performance. The accuracy of the model further declines by $8.3\\%$ after we remove the $L_{ocd}$ . It is because $L_{ocd}$ encourages keypoints to distribute on the surface of objects, which can better represent the shapes of objects. Without $L_{div}$ , the model performance declines significantly by $24.7\\%$ , since $L_{div}$ is indispensable for keypoints to focus on distinct regions of objects. The excessive clustering of keypoints can result in a degradation in model performance.", + "bbox": [ + 75, + 325, + 468, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of the GAFA module. Here we conduct ablation studies on the Geometric-Aware Feature Aggregation module. For a fair comparison, we replace the GAFA with MLPs that have the same number of parameters. The results are shown in Table 6. In particular, we observe that performance drops by $7.6\\%$ , $4.6\\%$ and $5.7\\%$ on $5^{\\circ}2\\mathrm{cm}$ when removing the whole GAFA, the global feature aggregation and the local feature aggregation, respectively. As discussed in section 1, both local and global geometric information play crucial roles in establishing accurate correspondences on unseen objects. Our GAFA can effectively encode such geometric information into keypoint features, thus achieving better accuracy. Furthermore, we replace the geometric-aware feature aggregation operation with vanilla attention mechanism (w/ vanilla attn) in the GAFA. The experimental result shows that the proposed geometric-aware feature aggregation achieve better performance because the geometric information is indispensable in category-level 6D object pose estimation. Last, we explore the influence of the local aggregation range $K$ on the accuracy of our model in Table 7. The results demonstrate that $K = 16$ yields the most", + "bbox": [ + 75, + 583, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a7872242879de6756e4794ce594528d011fa994d242b383ea5fa8673572e3298.jpg", + "image_caption": [ + "Figure 5. Qualitative comparisons between our method and DPDN [17] on REAL275 dataset. We visualize the correspondence error maps and pose estimation results of our AG-Pose and DPDN. Red/green indicates large/small errors and predicted/gt bounding boxes." + ], + "image_footnote": [], + "bbox": [ + 501, + 82, + 890, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "significant performance gains.", + "bbox": [ + 500, + 321, + 699, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Visualization", + "text_level": 1, + "bbox": [ + 500, + 345, + 635, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results. The qualitative results of DPDN [17] and proposed AG-Pose are shown in Figure 5. Specifically, we visualize the NOCS prediction errors and the final pose predictions for both methods, in which green/red indicate small/large errors and gt/predicted results. The visualization results show that dense correspondence-based methods such as DPDN generate larger numbers of incorrect correspondences on novel instances with significant shape variations (e.g., cameras) as well as on outlier points (e.g., edge of objects), which severely degrade the performance of pose estimation. In contrast, our AG-Pose can perform instance-adaptive keypoint detection and extract geometric-aware features to establish accurate keypoint-level correspondences, leading to better pose estimation performance.", + "bbox": [ + 496, + 368, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 593, + 617, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In summary, we present a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose). Specifically, we propose a Instance-Adaptive Keypoint Detection module represent the geometric information of different instances through a set of sparse keypoints. Furthermore, we propose a Geometric-Aware Feature Aggregation module to effectively incorporate local and global geometric information into keypoints to establish robust keypoint-level correspondences. We conduct comprehensive experiments and the experimental results verify the effectiveness of our method.", + "bbox": [ + 496, + 619, + 890, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 799, + 686, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by the National Nature Science Foundation of China (Grant 62306294), Dreams Foundation of Jianghuai Advance Technology Center (NO.Q/JH-063-2023-T02A/0) and Anhui Provincial Natural Science Foundation (Grant 2308085QF222).", + "bbox": [ + 496, + 824, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21047", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ronald T Azuma. A survey of augmented reality. Presence: teleoperators & virtual environments, 6(4):355-385, 1997. 1", + "[2] Kai Chen and Qi Dou. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5745-5753, 2019. 5" + ], + "bbox": [ + 501, + 92, + 890, + 709 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21049", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Instance-Adaptive and Geometric-Aware Keypoint Learning for Category-Level 6D Object Pose Estimation/2e346385-1067-495a-b77c-624a4cea3be4_model.json b/2024/Instance-Adaptive and Geometric-Aware Keypoint Learning for Category-Level 6D Object Pose Estimation/2e346385-1067-495a-b77c-624a4cea3be4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..09f956d4b27c95c4f4d9f976700e482cae636b68 --- /dev/null +++ b/2024/Instance-Adaptive and Geometric-Aware Keypoint Learning for Category-Level 6D Object Pose Estimation/2e346385-1067-495a-b77c-624a4cea3be4_model.json @@ -0,0 +1,2321 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.118, + 0.79, + 0.164 + ], + "angle": 0, + "content": "Instance-Adaptive and Geometric-Aware Keypoint Learning for Category-Level 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.19, + 0.747, + 0.21 + ], + "angle": 0, + "content": "Xiao Lin\\(^{1}\\) Wenfei Yang\\(^{1,2}\\) Yuan Gao\\(^{1}\\) Tianzhu Zhang\\(^{1,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.209, + 0.677, + 0.227 + ], + "angle": 0, + "content": "1University of Science and Technology of China" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.227, + 0.732, + 0.246 + ], + "angle": 0, + "content": "\\(^{2}\\)Jianghuai Advance Technology Center, Hefei, 230000, China" + }, + { + "type": "text", + "bbox": [ + 0.195, + 0.246, + 0.761, + 0.263 + ], + "angle": 0, + "content": "{llinxiao,wazs98}@mail.ustc.edu.cn {yangwf,tzzhang}@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.297, + 0.313, + 0.312 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.474, + 0.692 + ], + "angle": 0, + "content": "Category-level 6D object pose estimation aims to estimate the rotation, translation and size of unseen instances within specific categories. In this area, dense correspondence-based methods have achieved leading performance. However, they do not explicitly consider the local and global geometric information of different instances, resulting in poor generalization ability to unseen instances with significant shape variations. To deal with this problem, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose), which includes two key designs: (1) The first design is an Instance-Adaptive Keypoint Detection module, which can adaptively detect a set of sparse keypoints for various instances to represent their geometric structures. (2) The second design is a Geometric-Aware Feature Aggregation module, which can efficiently integrate the local and global geometric information into keypoint features. These two modules can work together to establish robust keypoint-level correspondences for unseen instances, thus enhancing the generalization ability of the model. Experimental results on CAMERA25 and REAL275 datasets show that the proposed AG-Pose outperforms state-of-the-art methods by a large margin without category-specific shape priors." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.718, + 0.21, + 0.734 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.47, + 0.88 + ], + "angle": 0, + "content": "The 6D object pose estimation task aims to predict the rotation, translation and size of objects with 2D/3D observations. Due to its great potential in many real-world applications such as robotic manipulation [25, 38, 39], augmented reality [1, 23] and autonomous driving [3, 7, 22], this task has been attracting increasing attention in the research community. While many previous methods [10, 11, 19, 27, 34, 41] have achieved significant performance on instance-level 6D object pose estimation, their reliance on instance-level" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.298, + 0.589, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.328, + 0.678, + 0.343 + ], + "angle": 0, + "content": "Dense Correspondence Prediction" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.302, + 0.769, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.361, + 0.774, + 0.369 + ], + "angle": 0, + "content": "Correspondence Error Map" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.302, + 0.864, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.361, + 0.853, + 0.369 + ], + "angle": 0, + "content": "Pose Estimation" + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.376, + 0.832, + 0.386 + ], + "angle": 0, + "content": "a) Existing dense correspondence-based method DPDN" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.389, + 0.687, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.515, + 0.678, + 0.526 + ], + "angle": 0, + "content": "b) Local Geometric Information" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.389, + 0.881, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.516, + 0.869, + 0.526 + ], + "angle": 0, + "content": "c) Global Geometric Information" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.671 + ], + "angle": 0, + "content": "Figure 1. a) The visualization for the correspondence error map and final pose estimation of the dense correspondence-based method, DPDN [17]. Green/red indicates small/large errors and GT/predicted bounding box. b) Points belonging to different parts of the same instance may exhibit similar visual features. Thus, the local geometric information is essential to distinguish them from each other. c) Points belonging to different instances may exhibit similar local geometric structures. Therefore, the global geometric information is crucial for correctly mapping them to the corresponding NOCS coordinates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.891, + 0.764 + ], + "angle": 0, + "content": "CAD models hinders their generalization to novel instances. To deal with this problem, category-level 6D object pose estimation has been introduced in [35], which aims to estimate the poses of unseen instances within specific categories without using their CAD models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.893, + 0.902 + ], + "angle": 0, + "content": "In the category-level 6D object pose estimation task, networks are trained with numerous CAD models of different instances and required to estimate the 6D poses of unseen instances which belong to the same category but have different 3D shapes. Consequently, the main challenge of this task lies in the significant intra-category shape variation. Most of the existing category-level methods aim to establish dense correspondences between observed image points (RGB or RGB-D) and the Normalized Object Coor" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21040" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.53 + ], + "angle": 0, + "content": "dinate Space (NOCS) [35]. They can be categorized into two groups, i.e., the direct dense prediction methods and the two-stage deform-and-match methods. The direct dense prediction methods train their networks to directly map observed image points into the NOCS to obtain dense correspondences [13, 14, 16, 18, 35]. On the other hand, the two-stage methods predict deformation fields on a categorical shape prior [30] to reconstruct instance models first, and then establish dense correspondences between observed points and reconstructed models. With point-level dense correspondences, the final pose and size can be retrieved via Umeyama algorithm [31] or regression networks. Although dense correspondence-based methods have made significant progress, they tend to generate numerous incorrect correspondences for instances with large shape variations (Figure 1 (a)). We owe this problem to that these methods do not explicitly consider the geometric information of different instances, which is of significant importance for generalization to unseen instances. As shown in Figure 1 (b), the three points corresponding to different parts of the camera have similar visual features but distinct local structures. Thus, incorporating local geometric information is crucial to effectively distinguish them from each other. On the other hand, as illustrated in Figure 1 (c), the three points on different cameras exhibit similar local structures but correspond to different NOCS coordinates due to the large shape variations on the camera lenses. These points can be effectively discriminated by taking the global geometric information into account." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.534, + 0.473, + 0.866 + ], + "angle": 0, + "content": "To facilitate each point with geometric information in dense correspondence-based methods, an intuitive way is to employ vanilla attention mechanism [32] to aggregate features from all other points. However, it will greatly increase the computational overhead due to the vast number of points. Different from existing methods, we aim to utilize a set of sparse keypoints to represent the shapes of different instances and extract geometric-aware keypoint features to establish robust keypoint-level correspondences for 6D pose estimation. Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Nevertheless, it's non-trivial because of following challenges: 1) The shapes of different instances vary significantly. Thus, the model needs to adaptively detect representative keypoints for different instances to comprehensively represent their shapes. 2) The local and global geometric information are indispensable. How to efficiently encode such geometric information into keypoint features needs to be carefully considered to achieve better generalization on unseen instances." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Motivated by the above discussions, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.544 + ], + "angle": 0, + "content": "Learning method for category-level 6D object pose estimation (AG-Pose). The framework is shown in Figure 2 (a). The proposed method has two key designs: the Instance-Adaptive Keypoint Detection (IAKD) module and the Geometric-Aware Feature Aggregation (GAFA) module. The IAKD is designed to adaptively detect keypoints for various instances. Specifically, we initialize a set of category-shared learnable queries as keypoint detectors. We first convert them to instance-adaptive detectors by aggregating the object features into learnable queries via attention mechanism [32]. Subsequently, the heatmap of keypoints is obtained by calculating similarities between instance-adaptive detectors and object features. However, the IAKD alone can not guarantee the detected keypoints to focus on different local parts to fully represent the shapes of different instances. Thus, we further design a diversity loss and an object-aware chamfer distance loss to constrain the distribution of keypoints, yielding dispersed and object-focused keypoints. The GAFA module is designed to efficiently extract the local and global geometric information for detected keypoints. In particular, to incorporate local geometric information, GAFA selects the spatially nearest K points for each keypoint and incorporate their relative positions to aggregate features from its neighbors. To incorporate global geometric information, we further integrate global feature and relative positional embeddings into keypoint features. By combining these two modules together, the proposed method can efficiently learn instance-adaptive and geometric-aware keypoints to establish robust keypoint-level correspondences for pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.546, + 0.821, + 0.56 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.562, + 0.892, + 0.652 + ], + "angle": 0, + "content": "- We propose a novel instance-adaptive and geometric-aware keypoint learning method for category-level 6D object pose estimation, which can better generalize to unseen instances with large shape variations. To the best of our knowledge, this is the first adaptive keypoint-based method for category-level 6D object pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.653, + 0.892, + 0.713 + ], + "angle": 0, + "content": "- We evaluate our framework on widely adopted CAMERA25 and REAL275 datasets, and results demonstrate that the proposed method sets a new state-of-the-art performance without using categorical shape priors." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.562, + 0.892, + 0.713 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.73, + 0.651, + 0.745 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.842, + 0.772 + ], + "angle": 0, + "content": "2.1. Instance-level 6D object pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Instance-level 6D object pose estimation aims to estimate the pose of a known object given its CAD model. In recent years, numerous methods based on direct regression [4, 24, 33, 42], fixed keypoint detection [6, 27, 40, 41], and dense 2D-3D correspondences [26, 43] have been proposed. Direct regression-based methods take the observation image (RGB or RGBD) as input and directly predict the 3D rotation and translation via regression networks. The ad" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21041" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.35 + ], + "angle": 0, + "content": "vantage of these methods lies in end-to-end pose estimation without extra post-processing. On the other hand, methods based on fixed keypoint detection usually predefine a set of keypoints on the object CAD model and detect their corresponding positions in the input image. Subsequently, pose estimation is achieved through Perspectiveen-Point (PnP) algorithms. For example, [10, 11, 27, 41] utilize a dense voting strategy to detect keypoints and achieve state-of-the-art performance. Dense 2D-3D correspondence-based methods aim to predict the corresponding position on the object CAD model for every point [19, 34], which are more robust to occlusion. Among them, the approaches based on fixed keypoints are most related to our method. However, they adopt fixed keypoints on a given CAD model while our method aims to adaptively detect keypoints for different instances because the CAD models are not accessible during inference in category-level task." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.359, + 0.427, + 0.376 + ], + "angle": 0, + "content": "2.2. Category-level 6D object pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.473, + 0.701 + ], + "angle": 0, + "content": "To improve the generalization ability on unseen instances, the category-level 6D object pose estimation is introduced, which aims to estimate the poses of all instances belonging to a specific category without using their CAD models. NOCS [35] proposes to use a shared canonical representation called Normalized Object Coordinate Space (NOCS) to represent the shapes of all instances. They first predict the NOCS coordinates of observed points and then apply Umeyama [31] algorithm to recover the pose and size. To handle the intra-category shape variation, SPD [30] proposes a deformation and matching strategy. They first reconstruct instance models by deforming a categorical shape prior and then match observations to the reconstructed models. Inspired by SPD, multiple works [2, 17, 36, 44] have been proposed to improve the processes of shape prior deformation, correspondence matching and et al., continuously improving the pose estimation performance. However, the above methods have not explicitly taken the local and global geometric information of different instances into consideration, which results in poor generalization ability to unseen instances with significant shape variations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.716, + 0.212, + 0.733 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.188, + 0.756 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Given a RGB-D image, we first employ a segmentation model such as [20, 21] to obtain the segmentation mask and category label for each object. Following previous works [17, 46], here we employ an off-the-shelf MaskRCNN [9]. For each segmented object, we use the segmentation mask to get the cropped RGB image \\(\\mathbf{I}_{obj} \\in \\mathbb{R}^{H \\times W \\times 3}\\) and the point cloud \\(\\mathbf{P}_{obj} \\in \\mathbb{R}^{N \\times 3}\\), where \\(N\\) is the number of points and \\(\\mathbf{P}_{obj}\\) is acquired by back-projecting the cropped depth image using camera intrinsics followed by a downsampling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "process. By taking \\(\\mathbf{I}_{obj}\\) and \\(\\mathbf{P}_{obj}\\) as input, the proposed method aims to estimate the 3D rotation \\(\\mathbf{R} \\in SO(3)\\), the 3D translation \\(\\pmb{t} \\in \\mathbb{R}^3\\) and the size \\(s \\in \\mathbb{R}^3\\) of the target object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.894, + 0.244 + ], + "angle": 0, + "content": "The framework of proposed AG-Pose is shown in Figure 2 (a). Our method consists of four main components: Feature Extractor (Sec. 3.2), Instance-Adaptive Keypoint Detector (Sec. 3.3), Geometric-Aware Feature Aggregator (Sec. 3.4) and Pose&Size Estimator (Sec. 3.5). Details about each component are as follows." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.256, + 0.677, + 0.271 + ], + "angle": 0, + "content": "3.2. Feature Extractor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.402 + ], + "angle": 0, + "content": "For the input point cloud \\(\\mathbf{P}_{obj}\\), we utilize the PointNet++ [28] to extract point features \\(\\mathbf{F}_P \\in \\mathbb{R}^{N \\times C_1}\\). For the RGB image \\(\\mathbf{I}_{obj}\\), following [33], a PSP network [45] with ResNet-18 [8] is applied to extract pixel-wise appearance features from \\(\\mathbf{I}_{obj}\\). We then choose those pixel features corresponding to \\(\\mathbf{P}_{obj}\\) to obtain the RGB features \\(\\mathbf{F}_I \\in \\mathbb{R}^{N \\times C_2}\\). Lastly, we concatenate \\(\\mathbf{F}_I\\) and \\(\\mathbf{F}_P\\) to form \\(\\mathbf{F}_{obj} \\in \\mathbb{R}^{N \\times C}\\) as the input for the subsequent networks." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.414, + 0.822, + 0.43 + ], + "angle": 0, + "content": "3.3. Instance-Adaptive Keypoint Detector" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.892, + 0.724 + ], + "angle": 0, + "content": "As introduced in Section 1, the geometric information is indispensable to establish robust correspondences. An intuitive idea to facilitate each point with geometric information is to employ the vanilla attention mechanism [32] to aggregate features from all other points. But it is computationally expensive due to the large number of points. Instead, we aim to utilize a set of sparse keypoints to represent the shapes of different instances for pose estimation. However, since the shapes vary across different instances and the instance models are not accessible during inference, fixed keypoint detection methods like [10, 11, 27, 41] are not applicable. Besides, methods like Farest Point Sampling are not end-to-end trainable, which may detect keypoints on outlier points caused by the noisy segmentation mask, the incorrect depth values and et al. Consequently, we design an Instance-Adaptive Keypoint Detection module to adaptively detect keypoints for instances with different shapes which can efficiently represent the object and avoid focusing on outlier points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.848 + ], + "angle": 0, + "content": "The pipeline of IAKD is illustrated in Figure 2 (b). Specifically, we initialize a set of category-shared learnable queries \\(\\mathbf{Q}_{cat} \\in \\mathbb{R}^{N_{kpt} \\times C}\\) and each of them represents a keypoint detector. We first inject the object features \\(\\mathbf{F}_{obj}\\) into learnable queries via Transformer Layers [32]. This process converts the category-shared detectors \\(\\mathbf{Q}_{cat}\\) into instance-adaptive detectors \\(\\mathbf{Q}_{ins} \\in \\mathbb{R}^{N_{kpt} \\times C}\\) conditioned on object features \\(\\mathbf{F}_{obj}\\). In detail," + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.859, + 0.892, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {Q} _ {\\text {c a t}} \\mathbf {W} ^ {q}, \\mathbf {K} = \\mathbf {F} _ {\\text {o b j}} \\mathbf {W} ^ {k}, \\mathbf {V} = \\mathbf {F} _ {\\text {o b j}} \\mathbf {W} ^ {v}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.88, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {i n s} = \\operatorname {N o r m} \\left(\\mathbf {Q} _ {c a t} + \\operatorname {s o f t m a x} \\left(\\mathbf {Q K} ^ {T}\\right) \\mathbf {V}\\right). \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21042" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.083, + 0.45, + 0.097 + ], + "angle": 0, + "content": "Feature Extractor & Instance-Adaptive Keypoint Detector" + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.084, + 0.877, + 0.097 + ], + "angle": 0, + "content": "Geometric-Aware Feature Aggregator & Pose Estimator" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.103, + 0.895, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.244, + 0.574, + 0.258 + ], + "angle": 0, + "content": "(a) Framework Overview" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.259, + 0.887, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.504, + 0.893, + 0.575 + ], + "angle": 0, + "content": "Figure 2. a) Overview of the proposed AG-Pose. b) Illustration of the IAKD module. We initialize a set of category-shared learnable queries and convert them into instance-adaptive detectors by integrating the object features. The instance-adaptive detectors are then used to detect keypoints for the object. To guide the learning of the IAKD module, we further design the \\( L_{div} \\) and \\( L_{ocd} \\) to constrain the distribution of keypoints. c) Illustration of the GAFA module. Our GAFA can efficiently integrate the geometric information into keypoint features through a two-stage feature aggregation process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.47, + 0.681 + ], + "angle": 0, + "content": "Then we calculate the cosine similarities between the instance-adaptive detectors \\(\\mathbf{Q}_{ins}\\) and the object features \\(\\mathbf{F}_{obj}\\) to generate keypoint heatmap \\(\\mathbf{H} \\in \\mathbb{R}^{N_{kpt} \\times N}\\). Subsequently, the 3D coordinates of keypoints \\(\\mathbf{P}_{kpt} \\in \\mathbb{R}^{N_{kpt} \\times 3}\\) and their corresponding features \\(\\mathbf{F}_{kpt} \\in \\mathbb{R}^{N_{kpt} \\times C}\\) under camera space are obtained by weighted sum as:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.713, + 0.469, + 0.73 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {k p t} = \\operatorname {s o f t m a x} (\\mathbf {H}) \\times \\mathbf {P} _ {o b j}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.733, + 0.469, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {k p t} = \\operatorname {s o f t m a x} (\\mathbf {H}) \\times \\mathbf {F} _ {o b j}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Since our target is to utilize a set of sparse keypoints to represent the geometric information of the object, the detected keypoints should be well distributed on the surface of the object. However, we find that the keypoints tend to cluster in small regions and often focus on non-surface or outlier points without explicit supervision. To encourage the keypoints to focus on different parts, we further design a diversity loss \\( L_{div} \\) to force the detected keypoints to be away" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.591, + 0.674, + 0.605 + ], + "angle": 0, + "content": "from each other. In detail," + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.614, + 0.892, + 0.658 + ], + "angle": 0, + "content": "\\[\nL _ {d i v} = \\sum_ {i = 1} ^ {N _ {k p t}} \\sum_ {j = 1, j \\neq i} ^ {N _ {k p t}} \\mathbf {d} \\left(\\mathbf {P} _ {k p t} ^ {(i)}, \\mathbf {P} _ {k p t} ^ {(j)}\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.66, + 0.891, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} \\left(\\mathbf {P} _ {k p t} ^ {(i)}, \\mathbf {P} _ {k p t} ^ {(j)}\\right) = \\max \\left\\{t h _ {1} - \\left\\| \\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k p t} ^ {(j)} \\right\\| _ {2}, 0 \\right\\}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.693, + 0.892, + 0.818 + ], + "angle": 0, + "content": "where \\( th_{1} \\) is a hyperparameter and \\( \\mathbf{P}_{kpt}^{(i)} \\) stands for the \\( i \\)-th keypoint. To encourage the keypoints to locate on the surface of the object and exclude outliers simultaneously, we design an object-aware chamfer distance loss \\( L_{ocd} \\) to constrain the distribution of \\( \\mathbf{P}_{kpt} \\). Formally, we first utilize the ground truth pose and size \\( \\mathbf{R}_{gt}, \\mathbf{t}_{gt}, \\mathbf{s}_{gt} \\) to transform \\( \\mathbf{P}_{obj} \\) to the NOCS and remove outlier points based on instance model \\( \\mathbf{M}_{obj} \\in \\mathbb{R}^{M \\times 3} \\) to produce \\( \\mathbf{P}_{obj}^{\\star} \\). In formula," + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.827, + 0.795, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {o b j} ^ {\\star} = \\left\\{x _ {i} \\mid x _ {i} \\in \\mathbf {P} _ {o b j} \\quad a n d \\right.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.846, + 0.892, + 0.879 + ], + "angle": 0, + "content": "\\[\n\\min _ {y _ {j} \\in \\mathbf {M} _ {o b j}} \\| \\frac {1}{\\| \\mathbf {s} _ {g t} \\| _ {2}} \\mathbf {R} _ {g t} \\left(x _ {i} - \\mathbf {t} _ {g t}\\right) - y _ {j} \\| _ {2} < t h _ {2} \\}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The outlier filter process is also illustrated in Figure 3. Then" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21043" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.083, + 0.434, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.182, + 0.418, + 0.195 + ], + "angle": 0, + "content": "Figure 3. Illustration of the outlier filter process." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.209, + 0.299, + 0.224 + ], + "angle": 0, + "content": "the \\(L_{ocd}\\) is calculated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.23, + 0.47, + 0.269 + ], + "angle": 0, + "content": "\\[\nL _ {o c d} = \\frac {1}{| \\mathbf {P} _ {k p t} |} \\sum_ {x _ {i} \\in \\mathbf {P} _ {k p t}} \\min _ {y _ {j} \\in \\mathbf {P} _ {o b j} ^ {\\star}} \\| x _ {i} - y _ {j} \\| _ {2}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.275, + 0.47, + 0.32 + ], + "angle": 0, + "content": "By constraining keypoints to be close to \\(\\mathbf{P}_{obj}^{\\star}\\), the IAKD module can automatically learn to filter out outlier points during inference." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.328, + 0.405, + 0.344 + ], + "angle": 0, + "content": "3.4. Geometric-Aware Feature Aggregator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.469, + 0.472 + ], + "angle": 0, + "content": "With the detected keypoints for each object, a straightforward way is to predict the NOCS coordinates for these keypoints to establish keypoint-level correspondences. However, the keypoint features are lack of geometric information, which can result in numerous incorrect correspondences on unseen instances. Thus, we propose a Geometric-Aware Feature Aggregation module to efficiently incorporate geometric information into keypoint features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.669 + ], + "angle": 0, + "content": "The GAFA adopts a two-stage pipeline for geometric feature aggregation, as illustrated in Figure 2 (c). We first select the nearest \\(K\\) neighbors in \\(\\mathbf{P}_{obj}\\) and their corresponding features in \\(\\mathbf{F}_{obj}\\) for each keypoint to obtain \\(\\mathbf{P}_{knn} \\in \\mathbb{R}^{N_{kpt} \\times K \\times 3}\\) and \\(\\mathbf{F}_{knn} \\in \\mathbb{R}^{N_{kpt} \\times K \\times C}\\). Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Thus, we utilize the relative positional embeddings \\(\\alpha\\) and \\(\\beta\\) between keypoints and their neighbors to represent the local geometric features \\(f_l\\) and global geometric features \\(f_g\\), respectively. In detail," + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.675, + 0.47, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i, j} = M L P \\left(\\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k n n} ^ {(i, j)}\\right), f _ {l} ^ {(i)} = \\operatorname {A v g P o o l} \\left(\\alpha_ {i,:}\\right), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.699, + 0.47, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\beta_ {i, j} = M L P \\left(\\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k p t} ^ {(j)}\\right), f _ {g} ^ {(i)} = \\operatorname {A v g P o o l} \\left(\\beta_ {i,:}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.728, + 0.47, + 0.844 + ], + "angle": 0, + "content": "where \\(f_{l}^{(i)}, f_{g}^{(i)} \\in \\mathbb{R}^{1 \\times C}\\) and \\(\\mathbf{P}_{knn}^{(i,j)}\\) is the \\(j\\)-th neighboring point of \\(\\mathbf{P}_{kpt}^{(i)}\\). To incorporate local geometric information into keypoints, we combine the keypoint features \\(\\mathbf{Q}_{ins}\\) with \\(f_{l}\\) and calculate local correlation scores \\(\\mathbf{A}\\) between keypoints and neighboring points, which is then used to aggregate features from neighbors. The local feature aggregation process for \\(i\\)-th keypoint feature \\(\\mathbf{Q}_{ins}^{(i)}\\) is as follows," + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.849, + 0.469, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} = \\operatorname {s i m} \\left(M L P \\left(\\operatorname {c a t} \\left[ \\mathbf {Q} _ {\\text {i n s}} ^ {(i)}, f _ {l} ^ {(i)} \\right]\\right), \\mathbf {F} _ {\\text {k n n}} ^ {(i)}\\right), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.877, + 0.47, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {i n s} ^ {(i)} = M L P \\left(\\operatorname {s o f t m a x} (\\mathbf {A}) \\times \\mathbf {F} _ {k n n} ^ {(i)} + \\mathbf {Q} _ {i n s} ^ {(i)}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.199 + ], + "angle": 0, + "content": "The above process is executed for all keypoints in parallel to extract representative local geometric features. However, as shown in Figure 1 (c), the local geometric information alone is insufficient to handle significant shape variation across different instances. Therefore, we further inject the global geometric feature into \\(\\mathbf{Q}_{ins}\\) by leveraging all keypoint features and the global geometric features \\(f_{g}\\). In formula," + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.205, + 0.892, + 0.225 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {\\text {i n s}} ^ {\\text {g l o b a l}} = \\operatorname {A v g P o o l} \\left(\\mathbf {Q} _ {\\text {i n s}}\\right), \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.228, + 0.892, + 0.254 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {i n s} ^ {(i)} = M L P \\left(\\text {c o n c a t} \\left[ \\mathbf {Q} _ {i n s} ^ {(i)}, \\mathbf {Q} _ {i n s} ^ {\\text {g l o b a l}}, f _ {g} ^ {(i)} \\right]\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.261, + 0.85, + 0.279 + ], + "angle": 0, + "content": "where \\(\\mathbf{Q}_{ins}^{global}\\in \\mathbb{R}^{1\\times C}\\) is the global feature of \\(\\mathbf{Q}_{ins}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.279, + 0.892, + 0.354 + ], + "angle": 0, + "content": "The above two-stage aggregation allows keypoints to adaptively aggregate local geometric features from neighbors and global geometric information from other keypoints. It's worth noting that since the number of keypoints is small, the above process is computationally efficient." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.362, + 0.698, + 0.376 + ], + "angle": 0, + "content": "3.5. Pose&Size Estimator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.461 + ], + "angle": 0, + "content": "After obtaining geometric-aware keypoint features, following previous work [17], we use MLP to predict the NOCS coordinates of keypoints \\(\\mathbf{P}_{kpt}^{nocs} \\in \\mathbb{R}^{N_{kpt} \\times 3}\\) from \\(\\mathbf{Q}_{ins}\\) and regress the final pose and size \\(\\mathbf{R}, \\mathbf{t}, \\mathbf{s}\\) via this set of keypoint-level correspondences. In formula," + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.469, + 0.891, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {k p t} ^ {\\text {n o c s}} = M L P \\left(\\mathbf {Q} _ {\\text {i n s}}\\right), \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.489, + 0.891, + 0.508 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\text {p o s e}} = \\operatorname {c o n c a t} \\left[ \\mathbf {P} _ {\\text {k p t}}, \\mathbf {F} _ {\\text {k p t}}, \\mathbf {P} _ {\\text {k p t}} ^ {\\text {n o c s}}, \\mathbf {Q} _ {\\text {i n s}} \\right], \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.51, + 0.891, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R}, \\mathbf {t}, \\mathbf {s} = M L P _ {R} (\\mathbf {f} _ {\\text {p o s e}}), M L P _ {t} (\\mathbf {f} _ {\\text {p o s e}}), M L P _ {s} (\\mathbf {f} _ {\\text {p o s e}}). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.61 + ], + "angle": 0, + "content": "For more details please refer to [17]. We use the 6D representation [47] for the rotation \\(\\mathbf{R}\\). And for the translation \\(\\mathbf{t}\\) we follow [46] to predict the residual translation between the ground truth and the mean value of the point cloud." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.708, + 0.632 + ], + "angle": 0, + "content": "3.6. Overall Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.641, + 0.757, + 0.655 + ], + "angle": 0, + "content": "The overall loss function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.665, + 0.891, + 0.682 + ], + "angle": 0, + "content": "\\[\nL _ {a l l} = \\lambda_ {1} L _ {o c d} + \\lambda_ {2} L _ {d i v} + \\lambda_ {3} L _ {n o c s} + \\lambda_ {4} L _ {p o s e}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.891, + 0.734 + ], + "angle": 0, + "content": "where \\(\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4\\) are hyperparameters to balance the contribution of each term. For \\(L_{\\text{pose}}\\), we simply use \\(L_1\\) loss as follows," + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.743, + 0.891, + 0.761 + ], + "angle": 0, + "content": "\\[\nL _ {p o s e} = \\left\\| \\mathbf {R} _ {g t} - \\mathbf {R} \\right\\| _ {2} + \\left\\| \\mathbf {t} _ {g t} - \\mathbf {t} \\right\\| _ {2} + \\left\\| \\mathbf {s} _ {g t} - \\mathbf {s} \\right\\| _ {2}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.768, + 0.892, + 0.829 + ], + "angle": 0, + "content": "We generate ground truth NOCS coordinates of keypoints \\(\\mathbf{P}_{kpt}^{gt}\\) by projecting their coordinates under camera space \\(\\mathbf{P}_{kpt}\\) into NOCS using the ground-truth \\(\\mathbf{R}_{gt},\\mathbf{t}_{gt},\\mathbf{s}_{gt}\\). For \\(L_{nocs}\\), we use the Smooth \\(L_{1}\\) loss [17]. In formula," + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.835, + 0.891, + 0.868 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {k p t} ^ {g t} = \\frac {1}{\\| \\mathbf {s} _ {g t} \\| _ {2}} \\mathbf {R} _ {g t} \\left(\\mathbf {P} _ {k p t} - \\mathbf {t} _ {g t}\\right), \\tag {20}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.87, + 0.891, + 0.89 + ], + "angle": 0, + "content": "\\[\nL _ {n o c s} = \\operatorname {S m o o t h} L _ {1} \\left(\\mathbf {P} _ {k p t} ^ {g t}, \\mathbf {P} _ {k p t} ^ {n o c s}\\right). \\tag {21}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21044" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.2, + 0.089, + 0.768, + 0.104 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons with state-of-the-art methods on the REAL275 dataset." + }, + { + "type": "table", + "bbox": [ + 0.129, + 0.114, + 0.844, + 0.303 + ], + "angle": 0, + "content": "
MethodUse of Shape Priors\\( IoU_{50} \\)\\( IoU_{75} \\)\\( 5^{\\circ}2\\mathbf{cm} \\)\\( 5^{\\circ}5\\mathbf{cm} \\)\\( 10^{\\circ}2\\mathbf{cm} \\)\\( 10^{\\circ}5\\mathbf{cm} \\)
NOCS [35]X7830.17.21013.825.2
DualPoseNet [16]X79.862.229.335.95066.8
GPV-Pose [5]X—64.43242.9—73.3
IST-Net [18]X82.576.647.553.472.180.5
Query6DoF [37]X82.576.14958.968.783
SPD [30]✓77.353.219.321.443.254.1
SGPA [2]✓80.161.935.939.661.370.7
SAR-Net [15]✓79.362.431.642.350.368.3
RBP-Pose [44]✓—67.838.248.163.179.2
DPDN [17]✓83.4764650.770.478.4
AG-PoseX83.779.554.761.774.783.1
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.325, + 0.21, + 0.343 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.471, + 0.534 + ], + "angle": 0, + "content": "Datasets. Following previous works [17, 18, 37], we conduct experiments on CAMERA25 and REAL275 [35], the most widely adopted datasets for category-level object pose estimation. CAMERA25 is a synthetic RGB-D dataset that contains 300K synthetic images of 1,085 instances from 6 different categories. In this dataset, 25,000 images of 184 instances are used for evaluation and the others are used for training. REAL275 dataset is a more challenging real-world dataset which shares the same categories with CAMERA25. It comprises 7K images from 13 different scenes. 2,750 images of 6 scenes are left for validation, including 3 unseen instances per category." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.471, + 0.883 + ], + "angle": 0, + "content": "Implementation details. For a fair comparison, we use the same segmentation masks as SPD [30] and DPDN [17] from MaskRCNN [9]. For the data preprocessing, images are cropped and resized to \\( 192 \\times 192 \\) before feature extraction, and the number of points \\( N \\) in point cloud is set as 1024. For model parameters, the number of keypoints is set as \\( N_{kpt} = 96 \\), and the local range for each keypoint in GAFA is set as \\( K = 16 \\). The feature dimensions are set as \\( C_1 = 128 \\), \\( C_2 = 128 \\) and \\( C = 256 \\), respectively. For the hyper-parameters in the loss functions, the two thresholds in LQKD are set as \\( th_1 = 0.01 \\) and \\( th_2 = 0.1 \\), and \\( \\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4 \\) are 1.0, 5.0, 1.0, 0.3, respectively. For model optimizing, we train our model on both synthetic and real datasets for evaluation on REAL275 while only on synthetic dataset for evaluation on CAMERA25. Following previous work [17], we use random translation \\( \\Delta t \\sim U(-0.02, 0.02) \\) and scaling \\( \\Delta s \\sim U(-0.8, 1.2) \\) for data augmentation and apply random rotation for each axis with rotation degree sampled from \\( U(0, 20) \\). We train our network using the ADAM [12] optimizer and employ the triangular2 cyclical learning rate schedule [29] ranging from 2e-5 to 5e-4. All experiments are conducted on a single RTX3090Ti GPU with a batch size of 24." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Evaluation metrics. Following previous works [30, 35]," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.327, + 0.854, + 0.341 + ], + "angle": 0, + "content": "we evaluate the model performance with two metrics." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.342, + 0.891, + 0.401 + ], + "angle": 0, + "content": "- 3D IoU. We report the mean precision of Intersection-over-Union (IoU) for 3D bounding boxes with thresholds of \\(50\\%\\) and \\(75\\%\\). This metric incorporates both the pose and size of the object." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.402, + 0.891, + 0.461 + ], + "angle": 0, + "content": "- \\(n^{\\circ} m \\, \\text{cm}\\) is used for direct evaluation of the rotation and translation errors. Only predictions with rotation error less than \\(n^{\\circ}\\) and translation error less than \\(m \\, \\text{cm}\\) are considered correct." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.342, + 0.891, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.47, + 0.868, + 0.485 + ], + "angle": 0, + "content": "4.1. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Results on REAL275 dataset. The comparisons between our AG-Pose and existing state-of-the-art methods on the challenging REAL275 dataset are shown in Table 1. As demonstrated by the results, our AG-Pose outperforms all previous methods in all metrics on REAL275 dataset. It should be noted that our method does not require the use of shape priors. In detail, on the most rigorous metric of \\(5^{\\circ}2\\mathrm{cm}\\), AG-Pose achieves the precision of \\(54.7\\%\\), surpassing the current state-of-the-art shape prior-based method DPDN [17] with a large margin by \\(8.7\\%\\). As for prior-free methods, our method surpasses Query6DoF [37], IST-Net [18] and GPV-Pose [5] by \\(5.7\\%\\), \\(7.2\\%\\), and \\(22.7\\%\\), respectively. It should be noted that Query6DoF aims to learn a set of sparse queries as implicit shape priors, and the query features are used to update the point features to establish better dense correspondences. Different from it, the proposed AG-Pose aims to use a sparse set of keypoints to explicitly model the geometric information of objects to establish robust keypoint-level correspondences for pose estimation. The superior performance of our method indicates the importance of geometric information in category-level 6D object pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on CAMERA25 dataset. Table 2 shows the quantitative results of the proposed AG-Pose on CAMERA25 dataset. Our method achieves the best performance under most of metrics. In detail, the proposed AG-Pose outperforms the state-of-the-art method Query6DoF [37]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21045" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.191, + 0.089, + 0.777, + 0.104 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons with state-of-the-art methods on the CAMERA25 dataset." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.114, + 0.837, + 0.273 + ], + "angle": 0, + "content": "
MethodUse of Shape Prior\\( IoU_{50} \\)\\( IoU_{75} \\)\\( 5^{\\circ}2\\mathbf{cm} \\)\\( 5^{\\circ}5\\mathbf{cm} \\)\\( 10^{\\circ}2\\mathbf{cm} \\)\\( 10^{\\circ}5\\mathbf{cm} \\)
NOCS [35]X83.969.532.340.948.264.4
DualPoseNet [16]X92.486.464.770.777.284.7
GPV-Pose [5]X93.488.372.179.1—89
Query6DoF [37]X91.988.17883.183.990
SPD [30]✓93.283.154.35973.381.5
SGPA [2]✓93.288.170.774.582.788.4
SAR-Net [15]✓86.87966.770.975.380.3
RBP-Pose [44]✓93.18973.579.682.189.5
AG-PoseX93.891.377.882.885.591.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.111, + 0.294, + 0.435, + 0.309 + ], + "angle": 0, + "content": "Table 3. Comparisons between the IAKD and FPS." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.32, + 0.457, + 0.371 + ], + "angle": 0, + "content": "
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
FPS46.255.567.080.2
IAKD54.761.774.783.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.385, + 0.443, + 0.399 + ], + "angle": 0, + "content": "Table 4. Ablation studies on the number of keypoints." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.41, + 0.451, + 0.505 + ], + "angle": 0, + "content": "
Nkpt5° 2 cm5° 5 cm10° 2 cm10° 5 cm
1647.955.168.879.8
3248.855.773.182.9
645157.272.882
9654.761.774.783.1
12852.859.974.383.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.47, + 0.592 + ], + "angle": 0, + "content": "by \\(1.9\\%\\) on \\(I_oU_{50}\\), \\(3.2\\%\\) on \\(I_oU_{75}\\), \\(1.6\\%\\) on \\(10^{\\circ}2\\mathbf{cm}\\) and \\(1.6\\%\\) on \\(10^{\\circ}5\\mathbf{cm}\\), respectively. Our method achieves comparable performance with Query6DoF on \\(5^{\\circ}2\\mathbf{cm}\\) and \\(5^{\\circ}5\\mathbf{cm}\\) (lower by \\(0.2\\%\\) and \\(0.3\\%\\), respectively)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Results of correspondence errors. To validate that the keypoint-level correspondences of AG-Pose are more accurate than point-level correspondences, we calculate the NOCS error distributions of DPDN [17], ISTNet [18] and our method on the REAL275 validation set. As shown in Figure 4, the NOCS error of our keypoint-level correspondences is concentrated more on the interval from 0 to 0.1, while errors of dense correspondence-based methods are concentrated more on the interval from 0.15 to 0.5. It proves that the keypoint-level correspondences produced by AG-Pose exhibit better generalizability on unseen instances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.241, + 0.785 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.839 + ], + "angle": 0, + "content": "In this section, we conduct ablation experiments to demonstrate the effectiveness of the proposed method on the REAL275 dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Effects of the IAKD module. To evaluate the effectiveness of the proposed Instance-Adaptive Keypoint Detection module, we first replace the IAKD with the most widely adopted Farest Point Sampling (FPS) strategy. Specifically," + }, + { + "type": "table_caption", + "bbox": [ + 0.517, + 0.294, + 0.874, + 0.309 + ], + "angle": 0, + "content": "Table 5. Ablation studies on the proposed loss functions." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.32, + 0.892, + 0.416 + ], + "angle": 0, + "content": "
Loss5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Ldiv+Locd54.761.774.783.1
Ldiv+Lucd49.857.374.482.0
Ldiv46.4537181.3
Locd3036.155.068.6
None29.335.656.469.6
" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.434, + 0.855, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.583, + 0.86, + 0.597 + ], + "angle": 0, + "content": "Figure 4. Comparisons of NOCS error distributions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.734 + ], + "angle": 0, + "content": "we use FPS to sample the same number of keypoints and use their corresponding features in \\(\\mathbf{F}_{obj}\\) as \\(\\mathbf{Q}_{ins}\\). For a fair comparison, we add extra MLPs to ensure that the number of parameters remain unchanged. As shown in Table 3, the proposed IAKD outperforms FPS on all metrics. We owe the advantage to the end-to-end trainable property of IAKD and the optimized distribution of keypoints brought by the proposed losses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Effects of different keypoint numbers. In Table 4, we show the impact of different keypoint numbers \\( N_{kpt} \\). Surprisingly, the result shows that our method can achieve comparable performance (47.9% on \\( 5^{\\circ}2\\mathbf{cm} \\)) with the SOTA methods by using only a very small number (\\( N_{kpt} = 16 \\)) of keypoints, which demonstrates the superiority of proposed AG-Pose. And as the number of keypoints (\\( N_{kpt} \\)) increases, the performance of our method continues to improve. We choose \\( N_{kpt} = 96 \\) in our method for the balance between efficiency and accuracy." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effects of the \\(L_{div}\\) and the \\(L_{ocd}\\). In our method, we" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21046" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.455, + 0.104 + ], + "angle": 0, + "content": "Table 6. Ablation study on two-stage feature aggregation." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.109, + 0.491, + 0.205 + ], + "angle": 0, + "content": "
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Full54.761.774.783.1
w/o GAFA47.155.370.280.9
w/o Local4957.871.282.2
w/o Global50.155.874.582.7
w/ vanilla attn536172.282.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.133, + 0.219, + 0.414, + 0.234 + ], + "angle": 0, + "content": "Table 7. Ablation study on proposed GAFA." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.238, + 0.45, + 0.318 + ], + "angle": 0, + "content": "
5° 2 cm5° 5 cm10° 2 cm10° 5 cm
K=849.957.673.182.5
K=1654.761.774.783.1
K=2454.161.173.783.2
K=3252.759.973.682.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.47, + 0.583 + ], + "angle": 0, + "content": "utilize the proposed \\( L_{div} \\) and \\( L_{ocd} \\) to encourage the keypoints to be well distributed on the surface of the object. To verify the effectiveness of them, we conduct ablation experiments on these losses and the results are shown in Table 5. By replacing the proposed \\( L_{ocd} \\) with the normal chamfer distance loss \\( L_{ucd} \\), the performance of our model drops by \\( 4.5\\% \\) on \\( 5^{\\circ}2\\mathrm{cm} \\). The reason is that our object-aware chamfer distance loss can prevent the model from being affected by outliers, thereby improving the performance. The accuracy of the model further declines by \\( 8.3\\% \\) after we remove the \\( L_{ocd} \\). It is because \\( L_{ocd} \\) encourages keypoints to distribute on the surface of objects, which can better represent the shapes of objects. Without \\( L_{div} \\), the model performance declines significantly by \\( 24.7\\% \\), since \\( L_{div} \\) is indispensable for keypoints to focus on distinct regions of objects. The excessive clustering of keypoints can result in a degradation in model performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Effects of the GAFA module. Here we conduct ablation studies on the Geometric-Aware Feature Aggregation module. For a fair comparison, we replace the GAFA with MLPs that have the same number of parameters. The results are shown in Table 6. In particular, we observe that performance drops by \\(7.6\\%\\), \\(4.6\\%\\) and \\(5.7\\%\\) on \\(5^{\\circ}2\\mathrm{cm}\\) when removing the whole GAFA, the global feature aggregation and the local feature aggregation, respectively. As discussed in section 1, both local and global geometric information play crucial roles in establishing accurate correspondences on unseen objects. Our GAFA can effectively encode such geometric information into keypoint features, thus achieving better accuracy. Furthermore, we replace the geometric-aware feature aggregation operation with vanilla attention mechanism (w/ vanilla attn) in the GAFA. The experimental result shows that the proposed geometric-aware feature aggregation achieve better performance because the geometric information is indispensable in category-level 6D object pose estimation. Last, we explore the influence of the local aggregation range \\(K\\) on the accuracy of our model in Table 7. The results demonstrate that \\(K = 16\\) yields the most" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.083, + 0.892, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.314 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons between our method and DPDN [17] on REAL275 dataset. We visualize the correspondence error maps and pose estimation results of our AG-Pose and DPDN. Red/green indicates large/small errors and predicted/gt bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.322, + 0.7, + 0.337 + ], + "angle": 0, + "content": "significant performance gains." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.346, + 0.637, + 0.361 + ], + "angle": 0, + "content": "4.3. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Qualitative Results. The qualitative results of DPDN [17] and proposed AG-Pose are shown in Figure 5. Specifically, we visualize the NOCS prediction errors and the final pose predictions for both methods, in which green/red indicate small/large errors and gt/predicted results. The visualization results show that dense correspondence-based methods such as DPDN generate larger numbers of incorrect correspondences on novel instances with significant shape variations (e.g., cameras) as well as on outlier points (e.g., edge of objects), which severely degrade the performance of pose estimation. In contrast, our AG-Pose can perform instance-adaptive keypoint detection and extract geometric-aware features to establish accurate keypoint-level correspondences, leading to better pose estimation performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.594, + 0.618, + 0.61 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.786 + ], + "angle": 0, + "content": "In summary, we present a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose). Specifically, we propose a Instance-Adaptive Keypoint Detection module represent the geometric information of different instances through a set of sparse keypoints. Furthermore, we propose a Geometric-Aware Feature Aggregation module to effectively incorporate local and global geometric information into keypoints to establish robust keypoint-level correspondences. We conduct comprehensive experiments and the experimental results verify the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.687, + 0.816 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62306294), Dreams Foundation of Jianghuai Advance Technology Center (NO.Q/JH-063-2023-T02A/0) and Anhui Provincial Natural Science Foundation (Grant 2308085QF222)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21047" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.143 + ], + "angle": 0, + "content": "[1] Ronald T Azuma. A survey of augmented reality. Presence: teleoperators & virtual environments, 6(4):355-385, 1997. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[2] Kai Chen and Qi Dou. 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In this area, dense correspondence-based methods have achieved leading performance. However, they do not explicitly consider the local and global geometric information of different instances, resulting in poor generalization ability to unseen instances with significant shape variations. To deal with this problem, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose), which includes two key designs: (1) The first design is an Instance-Adaptive Keypoint Detection module, which can adaptively detect a set of sparse keypoints for various instances to represent their geometric structures. (2) The second design is a Geometric-Aware Feature Aggregation module, which can efficiently integrate the local and global geometric information into keypoint features. These two modules can work together to establish robust keypoint-level correspondences for unseen instances, thus enhancing the generalization ability of the model. Experimental results on CAMERA25 and REAL275 datasets show that the proposed AG-Pose outperforms state-of-the-art methods by a large margin without category-specific shape priors. + +# 1. Introduction + +The 6D object pose estimation task aims to predict the rotation, translation and size of objects with 2D/3D observations. Due to its great potential in many real-world applications such as robotic manipulation [25, 38, 39], augmented reality [1, 23] and autonomous driving [3, 7, 22], this task has been attracting increasing attention in the research community. While many previous methods [10, 11, 19, 27, 34, 41] have achieved significant performance on instance-level 6D object pose estimation, their reliance on instance-level + +![](images/fee0a8f388f67550c7a9cb11aee471b240b69241e96d1da148993cd54deb9013.jpg) +a) Existing dense correspondence-based method DPDN + +![](images/0b5bab674c4fc4d7eba58ffa11bbe8372d794a324d7295f9c131341765fead2d.jpg) +Dense Correspondence Prediction +Correspondence Error Map + +![](images/086da8447efdc80ae16cbac70ea7254e83228d18686aeaff3d53f0a87b336fb4.jpg) +Pose Estimation + +![](images/575d2bc59998b6f5a7dea0a895be42695911f4b0de5bfa1e8777f824edd82fe4.jpg) +b) Local Geometric Information + +![](images/8bdbde412b0b1c6497b2a89a5bf9a84c8e54bd19bf695a06ec4a9060b43bb5ea.jpg) +c) Global Geometric Information +Figure 1. a) The visualization for the correspondence error map and final pose estimation of the dense correspondence-based method, DPDN [17]. Green/red indicates small/large errors and GT/predicted bounding box. b) Points belonging to different parts of the same instance may exhibit similar visual features. Thus, the local geometric information is essential to distinguish them from each other. c) Points belonging to different instances may exhibit similar local geometric structures. Therefore, the global geometric information is crucial for correctly mapping them to the corresponding NOCS coordinates. + +CAD models hinders their generalization to novel instances. To deal with this problem, category-level 6D object pose estimation has been introduced in [35], which aims to estimate the poses of unseen instances within specific categories without using their CAD models. + +In the category-level 6D object pose estimation task, networks are trained with numerous CAD models of different instances and required to estimate the 6D poses of unseen instances which belong to the same category but have different 3D shapes. Consequently, the main challenge of this task lies in the significant intra-category shape variation. Most of the existing category-level methods aim to establish dense correspondences between observed image points (RGB or RGB-D) and the Normalized Object Coor + +dinate Space (NOCS) [35]. They can be categorized into two groups, i.e., the direct dense prediction methods and the two-stage deform-and-match methods. The direct dense prediction methods train their networks to directly map observed image points into the NOCS to obtain dense correspondences [13, 14, 16, 18, 35]. On the other hand, the two-stage methods predict deformation fields on a categorical shape prior [30] to reconstruct instance models first, and then establish dense correspondences between observed points and reconstructed models. With point-level dense correspondences, the final pose and size can be retrieved via Umeyama algorithm [31] or regression networks. Although dense correspondence-based methods have made significant progress, they tend to generate numerous incorrect correspondences for instances with large shape variations (Figure 1 (a)). We owe this problem to that these methods do not explicitly consider the geometric information of different instances, which is of significant importance for generalization to unseen instances. As shown in Figure 1 (b), the three points corresponding to different parts of the camera have similar visual features but distinct local structures. Thus, incorporating local geometric information is crucial to effectively distinguish them from each other. On the other hand, as illustrated in Figure 1 (c), the three points on different cameras exhibit similar local structures but correspond to different NOCS coordinates due to the large shape variations on the camera lenses. These points can be effectively discriminated by taking the global geometric information into account. + +To facilitate each point with geometric information in dense correspondence-based methods, an intuitive way is to employ vanilla attention mechanism [32] to aggregate features from all other points. However, it will greatly increase the computational overhead due to the vast number of points. Different from existing methods, we aim to utilize a set of sparse keypoints to represent the shapes of different instances and extract geometric-aware keypoint features to establish robust keypoint-level correspondences for 6D pose estimation. Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Nevertheless, it's non-trivial because of following challenges: 1) The shapes of different instances vary significantly. Thus, the model needs to adaptively detect representative keypoints for different instances to comprehensively represent their shapes. 2) The local and global geometric information are indispensable. How to efficiently encode such geometric information into keypoint features needs to be carefully considered to achieve better generalization on unseen instances. + +Motivated by the above discussions, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint + +Learning method for category-level 6D object pose estimation (AG-Pose). The framework is shown in Figure 2 (a). The proposed method has two key designs: the Instance-Adaptive Keypoint Detection (IAKD) module and the Geometric-Aware Feature Aggregation (GAFA) module. The IAKD is designed to adaptively detect keypoints for various instances. Specifically, we initialize a set of category-shared learnable queries as keypoint detectors. We first convert them to instance-adaptive detectors by aggregating the object features into learnable queries via attention mechanism [32]. Subsequently, the heatmap of keypoints is obtained by calculating similarities between instance-adaptive detectors and object features. However, the IAKD alone can not guarantee the detected keypoints to focus on different local parts to fully represent the shapes of different instances. Thus, we further design a diversity loss and an object-aware chamfer distance loss to constrain the distribution of keypoints, yielding dispersed and object-focused keypoints. The GAFA module is designed to efficiently extract the local and global geometric information for detected keypoints. In particular, to incorporate local geometric information, GAFA selects the spatially nearest K points for each keypoint and incorporate their relative positions to aggregate features from its neighbors. To incorporate global geometric information, we further integrate global feature and relative positional embeddings into keypoint features. By combining these two modules together, the proposed method can efficiently learn instance-adaptive and geometric-aware keypoints to establish robust keypoint-level correspondences for pose estimation. + +In summary, our contributions are as follows: + +- We propose a novel instance-adaptive and geometric-aware keypoint learning method for category-level 6D object pose estimation, which can better generalize to unseen instances with large shape variations. To the best of our knowledge, this is the first adaptive keypoint-based method for category-level 6D object pose estimation. +- We evaluate our framework on widely adopted CAMERA25 and REAL275 datasets, and results demonstrate that the proposed method sets a new state-of-the-art performance without using categorical shape priors. + +# 2. Related Works + +# 2.1. Instance-level 6D object pose estimation + +Instance-level 6D object pose estimation aims to estimate the pose of a known object given its CAD model. In recent years, numerous methods based on direct regression [4, 24, 33, 42], fixed keypoint detection [6, 27, 40, 41], and dense 2D-3D correspondences [26, 43] have been proposed. Direct regression-based methods take the observation image (RGB or RGBD) as input and directly predict the 3D rotation and translation via regression networks. The ad + +vantage of these methods lies in end-to-end pose estimation without extra post-processing. On the other hand, methods based on fixed keypoint detection usually predefine a set of keypoints on the object CAD model and detect their corresponding positions in the input image. Subsequently, pose estimation is achieved through Perspectiveen-Point (PnP) algorithms. For example, [10, 11, 27, 41] utilize a dense voting strategy to detect keypoints and achieve state-of-the-art performance. Dense 2D-3D correspondence-based methods aim to predict the corresponding position on the object CAD model for every point [19, 34], which are more robust to occlusion. Among them, the approaches based on fixed keypoints are most related to our method. However, they adopt fixed keypoints on a given CAD model while our method aims to adaptively detect keypoints for different instances because the CAD models are not accessible during inference in category-level task. + +# 2.2. Category-level 6D object pose estimation + +To improve the generalization ability on unseen instances, the category-level 6D object pose estimation is introduced, which aims to estimate the poses of all instances belonging to a specific category without using their CAD models. NOCS [35] proposes to use a shared canonical representation called Normalized Object Coordinate Space (NOCS) to represent the shapes of all instances. They first predict the NOCS coordinates of observed points and then apply Umeyama [31] algorithm to recover the pose and size. To handle the intra-category shape variation, SPD [30] proposes a deformation and matching strategy. They first reconstruct instance models by deforming a categorical shape prior and then match observations to the reconstructed models. Inspired by SPD, multiple works [2, 17, 36, 44] have been proposed to improve the processes of shape prior deformation, correspondence matching and et al., continuously improving the pose estimation performance. However, the above methods have not explicitly taken the local and global geometric information of different instances into consideration, which results in poor generalization ability to unseen instances with significant shape variations. + +# 3. Methodology + +# 3.1. Overview + +Given a RGB-D image, we first employ a segmentation model such as [20, 21] to obtain the segmentation mask and category label for each object. Following previous works [17, 46], here we employ an off-the-shelf MaskRCNN [9]. For each segmented object, we use the segmentation mask to get the cropped RGB image $\mathbf{I}_{obj} \in \mathbb{R}^{H \times W \times 3}$ and the point cloud $\mathbf{P}_{obj} \in \mathbb{R}^{N \times 3}$ , where $N$ is the number of points and $\mathbf{P}_{obj}$ is acquired by back-projecting the cropped depth image using camera intrinsics followed by a downsampling + +process. By taking $\mathbf{I}_{obj}$ and $\mathbf{P}_{obj}$ as input, the proposed method aims to estimate the 3D rotation $\mathbf{R} \in SO(3)$ , the 3D translation $\pmb{t} \in \mathbb{R}^3$ and the size $s \in \mathbb{R}^3$ of the target object. + +The framework of proposed AG-Pose is shown in Figure 2 (a). Our method consists of four main components: Feature Extractor (Sec. 3.2), Instance-Adaptive Keypoint Detector (Sec. 3.3), Geometric-Aware Feature Aggregator (Sec. 3.4) and Pose&Size Estimator (Sec. 3.5). Details about each component are as follows. + +# 3.2. Feature Extractor + +For the input point cloud $\mathbf{P}_{obj}$ , we utilize the PointNet++ [28] to extract point features $\mathbf{F}_P \in \mathbb{R}^{N \times C_1}$ . For the RGB image $\mathbf{I}_{obj}$ , following [33], a PSP network [45] with ResNet-18 [8] is applied to extract pixel-wise appearance features from $\mathbf{I}_{obj}$ . We then choose those pixel features corresponding to $\mathbf{P}_{obj}$ to obtain the RGB features $\mathbf{F}_I \in \mathbb{R}^{N \times C_2}$ . Lastly, we concatenate $\mathbf{F}_I$ and $\mathbf{F}_P$ to form $\mathbf{F}_{obj} \in \mathbb{R}^{N \times C}$ as the input for the subsequent networks. + +# 3.3. Instance-Adaptive Keypoint Detector + +As introduced in Section 1, the geometric information is indispensable to establish robust correspondences. An intuitive idea to facilitate each point with geometric information is to employ the vanilla attention mechanism [32] to aggregate features from all other points. But it is computationally expensive due to the large number of points. Instead, we aim to utilize a set of sparse keypoints to represent the shapes of different instances for pose estimation. However, since the shapes vary across different instances and the instance models are not accessible during inference, fixed keypoint detection methods like [10, 11, 27, 41] are not applicable. Besides, methods like Farest Point Sampling are not end-to-end trainable, which may detect keypoints on outlier points caused by the noisy segmentation mask, the incorrect depth values and et al. Consequently, we design an Instance-Adaptive Keypoint Detection module to adaptively detect keypoints for instances with different shapes which can efficiently represent the object and avoid focusing on outlier points. + +The pipeline of IAKD is illustrated in Figure 2 (b). Specifically, we initialize a set of category-shared learnable queries $\mathbf{Q}_{cat} \in \mathbb{R}^{N_{kpt} \times C}$ and each of them represents a keypoint detector. We first inject the object features $\mathbf{F}_{obj}$ into learnable queries via Transformer Layers [32]. This process converts the category-shared detectors $\mathbf{Q}_{cat}$ into instance-adaptive detectors $\mathbf{Q}_{ins} \in \mathbb{R}^{N_{kpt} \times C}$ conditioned on object features $\mathbf{F}_{obj}$ . In detail, + +$$ +\mathbf {Q} = \mathbf {Q} _ {\text {c a t}} \mathbf {W} ^ {q}, \mathbf {K} = \mathbf {F} _ {\text {o b j}} \mathbf {W} ^ {k}, \mathbf {V} = \mathbf {F} _ {\text {o b j}} \mathbf {W} ^ {v}, \tag {1} +$$ + +$$ +\mathbf {Q} _ {i n s} = \operatorname {N o r m} \left(\mathbf {Q} _ {c a t} + \operatorname {s o f t m a x} \left(\mathbf {Q K} ^ {T}\right) \mathbf {V}\right). \tag {2} +$$ + +![](images/d0f2a0c0aed6bae1d3176d7d7f52410e42eb74e21d4dd924345f7643bb71be1e.jpg) +Feature Extractor & Instance-Adaptive Keypoint Detector +Geometric-Aware Feature Aggregator & Pose Estimator +(a) Framework Overview + +![](images/720c937e430941d84101838b4e77364accdc02cbd3f9cb634a347601612c800e.jpg) +Figure 2. a) Overview of the proposed AG-Pose. b) Illustration of the IAKD module. We initialize a set of category-shared learnable queries and convert them into instance-adaptive detectors by integrating the object features. The instance-adaptive detectors are then used to detect keypoints for the object. To guide the learning of the IAKD module, we further design the $L_{div}$ and $L_{ocd}$ to constrain the distribution of keypoints. c) Illustration of the GAFA module. Our GAFA can efficiently integrate the geometric information into keypoint features through a two-stage feature aggregation process. + +Then we calculate the cosine similarities between the instance-adaptive detectors $\mathbf{Q}_{ins}$ and the object features $\mathbf{F}_{obj}$ to generate keypoint heatmap $\mathbf{H} \in \mathbb{R}^{N_{kpt} \times N}$ . Subsequently, the 3D coordinates of keypoints $\mathbf{P}_{kpt} \in \mathbb{R}^{N_{kpt} \times 3}$ and their corresponding features $\mathbf{F}_{kpt} \in \mathbb{R}^{N_{kpt} \times C}$ under camera space are obtained by weighted sum as: + +$$ +\mathbf {P} _ {k p t} = \operatorname {s o f t m a x} (\mathbf {H}) \times \mathbf {P} _ {o b j}, \tag {3} +$$ + +$$ +\mathbf {F} _ {k p t} = \operatorname {s o f t m a x} (\mathbf {H}) \times \mathbf {F} _ {o b j}. \tag {4} +$$ + +Since our target is to utilize a set of sparse keypoints to represent the geometric information of the object, the detected keypoints should be well distributed on the surface of the object. However, we find that the keypoints tend to cluster in small regions and often focus on non-surface or outlier points without explicit supervision. To encourage the keypoints to focus on different parts, we further design a diversity loss $L_{div}$ to force the detected keypoints to be away + +from each other. In detail, + +$$ +L _ {d i v} = \sum_ {i = 1} ^ {N _ {k p t}} \sum_ {j = 1, j \neq i} ^ {N _ {k p t}} \mathbf {d} \left(\mathbf {P} _ {k p t} ^ {(i)}, \mathbf {P} _ {k p t} ^ {(j)}\right), \tag {5} +$$ + +$$ +\mathbf {d} \left(\mathbf {P} _ {k p t} ^ {(i)}, \mathbf {P} _ {k p t} ^ {(j)}\right) = \max \left\{t h _ {1} - \left\| \mathbf {P} _ {k p t} ^ {(i)} - \mathbf {P} _ {k p t} ^ {(j)} \right\| _ {2}, 0 \right\}, \tag {6} +$$ + +where $th_{1}$ is a hyperparameter and $\mathbf{P}_{kpt}^{(i)}$ stands for the $i$ -th keypoint. To encourage the keypoints to locate on the surface of the object and exclude outliers simultaneously, we design an object-aware chamfer distance loss $L_{ocd}$ to constrain the distribution of $\mathbf{P}_{kpt}$ . Formally, we first utilize the ground truth pose and size $\mathbf{R}_{gt}, \mathbf{t}_{gt}, \mathbf{s}_{gt}$ to transform $\mathbf{P}_{obj}$ to the NOCS and remove outlier points based on instance model $\mathbf{M}_{obj} \in \mathbb{R}^{M \times 3}$ to produce $\mathbf{P}_{obj}^{\star}$ . In formula, + +$$ +\mathbf {P} _ {o b j} ^ {\star} = \left\{x _ {i} \mid x _ {i} \in \mathbf {P} _ {o b j} \quad a n d \right. +$$ + +$$ +\min _ {y _ {j} \in \mathbf {M} _ {o b j}} \| \frac {1}{\| \mathbf {s} _ {g t} \| _ {2}} \mathbf {R} _ {g t} \left(x _ {i} - \mathbf {t} _ {g t}\right) - y _ {j} \| _ {2} < t h _ {2} \}. \tag {7} +$$ + +The outlier filter process is also illustrated in Figure 3. Then + +![](images/758ec3373b217130b52dfd34d09a31ecd3ac9953e51591a841b04629faea0560.jpg) +Figure 3. Illustration of the outlier filter process. + +the $L_{ocd}$ is calculated as follows, + +$$ +L _ {o c d} = \frac {1}{| \mathbf {P} _ {k p t} |} \sum_ {x _ {i} \in \mathbf {P} _ {k p t}} \min _ {y _ {j} \in \mathbf {P} _ {o b j} ^ {\star}} \| x _ {i} - y _ {j} \| _ {2}. \tag {8} +$$ + +By constraining keypoints to be close to $\mathbf{P}_{obj}^{\star}$ , the IAKD module can automatically learn to filter out outlier points during inference. + +# 3.4. Geometric-Aware Feature Aggregator + +With the detected keypoints for each object, a straightforward way is to predict the NOCS coordinates for these keypoints to establish keypoint-level correspondences. However, the keypoint features are lack of geometric information, which can result in numerous incorrect correspondences on unseen instances. Thus, we propose a Geometric-Aware Feature Aggregation module to efficiently incorporate geometric information into keypoint features. + +The GAFA adopts a two-stage pipeline for geometric feature aggregation, as illustrated in Figure 2 (c). We first select the nearest $K$ neighbors in $\mathbf{P}_{obj}$ and their corresponding features in $\mathbf{F}_{obj}$ for each keypoint to obtain $\mathbf{P}_{knn} \in \mathbb{R}^{N_{kpt} \times K \times 3}$ and $\mathbf{F}_{knn} \in \mathbb{R}^{N_{kpt} \times K \times C}$ . Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Thus, we utilize the relative positional embeddings $\alpha$ and $\beta$ between keypoints and their neighbors to represent the local geometric features $f_l$ and global geometric features $f_g$ , respectively. In detail, + +$$ +\alpha_ {i, j} = M L P \left(\mathbf {P} _ {k p t} ^ {(i)} - \mathbf {P} _ {k n n} ^ {(i, j)}\right), f _ {l} ^ {(i)} = \operatorname {A v g P o o l} \left(\alpha_ {i,:}\right), \tag {9} +$$ + +$$ +\beta_ {i, j} = M L P \left(\mathbf {P} _ {k p t} ^ {(i)} - \mathbf {P} _ {k p t} ^ {(j)}\right), f _ {g} ^ {(i)} = \operatorname {A v g P o o l} \left(\beta_ {i,:}\right), \tag {10} +$$ + +where $f_{l}^{(i)}, f_{g}^{(i)} \in \mathbb{R}^{1 \times C}$ and $\mathbf{P}_{knn}^{(i,j)}$ is the $j$ -th neighboring point of $\mathbf{P}_{kpt}^{(i)}$ . To incorporate local geometric information into keypoints, we combine the keypoint features $\mathbf{Q}_{ins}$ with $f_{l}$ and calculate local correlation scores $\mathbf{A}$ between keypoints and neighboring points, which is then used to aggregate features from neighbors. The local feature aggregation process for $i$ -th keypoint feature $\mathbf{Q}_{ins}^{(i)}$ is as follows, + +$$ +\mathbf {A} = \operatorname {s i m} \left(M L P \left(\operatorname {c a t} \left[ \mathbf {Q} _ {\text {i n s}} ^ {(i)}, f _ {l} ^ {(i)} \right]\right), \mathbf {F} _ {\text {k n n}} ^ {(i)}\right), \tag {11} +$$ + +$$ +\mathbf {Q} _ {i n s} ^ {(i)} = M L P \left(\operatorname {s o f t m a x} (\mathbf {A}) \times \mathbf {F} _ {k n n} ^ {(i)} + \mathbf {Q} _ {i n s} ^ {(i)}\right). \tag {12} +$$ + +The above process is executed for all keypoints in parallel to extract representative local geometric features. However, as shown in Figure 1 (c), the local geometric information alone is insufficient to handle significant shape variation across different instances. Therefore, we further inject the global geometric feature into $\mathbf{Q}_{ins}$ by leveraging all keypoint features and the global geometric features $f_{g}$ . In formula, + +$$ +\mathbf {Q} _ {\text {i n s}} ^ {\text {g l o b a l}} = \operatorname {A v g P o o l} \left(\mathbf {Q} _ {\text {i n s}}\right), \tag {13} +$$ + +$$ +\mathbf {Q} _ {i n s} ^ {(i)} = M L P \left(\text {c o n c a t} \left[ \mathbf {Q} _ {i n s} ^ {(i)}, \mathbf {Q} _ {i n s} ^ {\text {g l o b a l}}, f _ {g} ^ {(i)} \right]\right), \tag {14} +$$ + +where $\mathbf{Q}_{ins}^{global}\in \mathbb{R}^{1\times C}$ is the global feature of $\mathbf{Q}_{ins}$ . + +The above two-stage aggregation allows keypoints to adaptively aggregate local geometric features from neighbors and global geometric information from other keypoints. It's worth noting that since the number of keypoints is small, the above process is computationally efficient. + +# 3.5. Pose&Size Estimator + +After obtaining geometric-aware keypoint features, following previous work [17], we use MLP to predict the NOCS coordinates of keypoints $\mathbf{P}_{kpt}^{nocs} \in \mathbb{R}^{N_{kpt} \times 3}$ from $\mathbf{Q}_{ins}$ and regress the final pose and size $\mathbf{R}, \mathbf{t}, \mathbf{s}$ via this set of keypoint-level correspondences. In formula, + +$$ +\mathbf {P} _ {k p t} ^ {\text {n o c s}} = M L P \left(\mathbf {Q} _ {\text {i n s}}\right), \tag {15} +$$ + +$$ +\mathbf {f} _ {\text {p o s e}} = \operatorname {c o n c a t} \left[ \mathbf {P} _ {\text {k p t}}, \mathbf {F} _ {\text {k p t}}, \mathbf {P} _ {\text {k p t}} ^ {\text {n o c s}}, \mathbf {Q} _ {\text {i n s}} \right], \tag {16} +$$ + +$$ +\mathbf {R}, \mathbf {t}, \mathbf {s} = M L P _ {R} (\mathbf {f} _ {\text {p o s e}}), M L P _ {t} (\mathbf {f} _ {\text {p o s e}}), M L P _ {s} (\mathbf {f} _ {\text {p o s e}}). \tag {17} +$$ + +For more details please refer to [17]. We use the 6D representation [47] for the rotation $\mathbf{R}$ . And for the translation $\mathbf{t}$ we follow [46] to predict the residual translation between the ground truth and the mean value of the point cloud. + +# 3.6. Overall Loss Function + +The overall loss function is as follows: + +$$ +L _ {a l l} = \lambda_ {1} L _ {o c d} + \lambda_ {2} L _ {d i v} + \lambda_ {3} L _ {n o c s} + \lambda_ {4} L _ {p o s e}, \tag {18} +$$ + +where $\lambda_1, \lambda_2, \lambda_3, \lambda_4$ are hyperparameters to balance the contribution of each term. For $L_{\text{pose}}$ , we simply use $L_1$ loss as follows, + +$$ +L _ {p o s e} = \left\| \mathbf {R} _ {g t} - \mathbf {R} \right\| _ {2} + \left\| \mathbf {t} _ {g t} - \mathbf {t} \right\| _ {2} + \left\| \mathbf {s} _ {g t} - \mathbf {s} \right\| _ {2}. \tag {19} +$$ + +We generate ground truth NOCS coordinates of keypoints $\mathbf{P}_{kpt}^{gt}$ by projecting their coordinates under camera space $\mathbf{P}_{kpt}$ into NOCS using the ground-truth $\mathbf{R}_{gt},\mathbf{t}_{gt},\mathbf{s}_{gt}$ . For $L_{nocs}$ , we use the Smooth $L_{1}$ loss [17]. In formula, + +$$ +\mathbf {P} _ {k p t} ^ {g t} = \frac {1}{\| \mathbf {s} _ {g t} \| _ {2}} \mathbf {R} _ {g t} \left(\mathbf {P} _ {k p t} - \mathbf {t} _ {g t}\right), \tag {20} +$$ + +$$ +L _ {n o c s} = \operatorname {S m o o t h} L _ {1} \left(\mathbf {P} _ {k p t} ^ {g t}, \mathbf {P} _ {k p t} ^ {n o c s}\right). \tag {21} +$$ + +Table 1. Quantitative comparisons with state-of-the-art methods on the REAL275 dataset. + +
MethodUse of Shape Priors\( IoU_{50} \)\( IoU_{75} \)\( 5^{\circ}2\mathbf{cm} \)\( 5^{\circ}5\mathbf{cm} \)\( 10^{\circ}2\mathbf{cm} \)\( 10^{\circ}5\mathbf{cm} \)
NOCS [35]X7830.17.21013.825.2
DualPoseNet [16]X79.862.229.335.95066.8
GPV-Pose [5]X—64.43242.9—73.3
IST-Net [18]X82.576.647.553.472.180.5
Query6DoF [37]X82.576.14958.968.783
SPD [30]✓77.353.219.321.443.254.1
SGPA [2]✓80.161.935.939.661.370.7
SAR-Net [15]✓79.362.431.642.350.368.3
RBP-Pose [44]✓—67.838.248.163.179.2
DPDN [17]✓83.4764650.770.478.4
AG-PoseX83.779.554.761.774.783.1
+ +# 4. Experiments + +Datasets. Following previous works [17, 18, 37], we conduct experiments on CAMERA25 and REAL275 [35], the most widely adopted datasets for category-level object pose estimation. CAMERA25 is a synthetic RGB-D dataset that contains 300K synthetic images of 1,085 instances from 6 different categories. In this dataset, 25,000 images of 184 instances are used for evaluation and the others are used for training. REAL275 dataset is a more challenging real-world dataset which shares the same categories with CAMERA25. It comprises 7K images from 13 different scenes. 2,750 images of 6 scenes are left for validation, including 3 unseen instances per category. + +Implementation details. For a fair comparison, we use the same segmentation masks as SPD [30] and DPDN [17] from MaskRCNN [9]. For the data preprocessing, images are cropped and resized to $192 \times 192$ before feature extraction, and the number of points $N$ in point cloud is set as 1024. For model parameters, the number of keypoints is set as $N_{kpt} = 96$ , and the local range for each keypoint in GAFA is set as $K = 16$ . The feature dimensions are set as $C_1 = 128$ , $C_2 = 128$ and $C = 256$ , respectively. For the hyper-parameters in the loss functions, the two thresholds in LQKD are set as $th_1 = 0.01$ and $th_2 = 0.1$ , and $\lambda_1, \lambda_2, \lambda_3, \lambda_4$ are 1.0, 5.0, 1.0, 0.3, respectively. For model optimizing, we train our model on both synthetic and real datasets for evaluation on REAL275 while only on synthetic dataset for evaluation on CAMERA25. Following previous work [17], we use random translation $\Delta t \sim U(-0.02, 0.02)$ and scaling $\Delta s \sim U(-0.8, 1.2)$ for data augmentation and apply random rotation for each axis with rotation degree sampled from $U(0, 20)$ . We train our network using the ADAM [12] optimizer and employ the triangular2 cyclical learning rate schedule [29] ranging from 2e-5 to 5e-4. All experiments are conducted on a single RTX3090Ti GPU with a batch size of 24. + +Evaluation metrics. Following previous works [30, 35], + +we evaluate the model performance with two metrics. + +- 3D IoU. We report the mean precision of Intersection-over-Union (IoU) for 3D bounding boxes with thresholds of $50\%$ and $75\%$ . This metric incorporates both the pose and size of the object. +- $n^{\circ} m \, \text{cm}$ is used for direct evaluation of the rotation and translation errors. Only predictions with rotation error less than $n^{\circ}$ and translation error less than $m \, \text{cm}$ are considered correct. + +# 4.1. Comparison with State-of-the-Art Methods + +Results on REAL275 dataset. The comparisons between our AG-Pose and existing state-of-the-art methods on the challenging REAL275 dataset are shown in Table 1. As demonstrated by the results, our AG-Pose outperforms all previous methods in all metrics on REAL275 dataset. It should be noted that our method does not require the use of shape priors. In detail, on the most rigorous metric of $5^{\circ}2\mathrm{cm}$ , AG-Pose achieves the precision of $54.7\%$ , surpassing the current state-of-the-art shape prior-based method DPDN [17] with a large margin by $8.7\%$ . As for prior-free methods, our method surpasses Query6DoF [37], IST-Net [18] and GPV-Pose [5] by $5.7\%$ , $7.2\%$ , and $22.7\%$ , respectively. It should be noted that Query6DoF aims to learn a set of sparse queries as implicit shape priors, and the query features are used to update the point features to establish better dense correspondences. Different from it, the proposed AG-Pose aims to use a sparse set of keypoints to explicitly model the geometric information of objects to establish robust keypoint-level correspondences for pose estimation. The superior performance of our method indicates the importance of geometric information in category-level 6D object pose estimation. + +Results on CAMERA25 dataset. Table 2 shows the quantitative results of the proposed AG-Pose on CAMERA25 dataset. Our method achieves the best performance under most of metrics. In detail, the proposed AG-Pose outperforms the state-of-the-art method Query6DoF [37] + +Table 2. Quantitative comparisons with state-of-the-art methods on the CAMERA25 dataset. + +
MethodUse of Shape Prior\( IoU_{50} \)\( IoU_{75} \)\( 5^{\circ}2\mathbf{cm} \)\( 5^{\circ}5\mathbf{cm} \)\( 10^{\circ}2\mathbf{cm} \)\( 10^{\circ}5\mathbf{cm} \)
NOCS [35]X83.969.532.340.948.264.4
DualPoseNet [16]X92.486.464.770.777.284.7
GPV-Pose [5]X93.488.372.179.1—89
Query6DoF [37]X91.988.17883.183.990
SPD [30]✓93.283.154.35973.381.5
SGPA [2]✓93.288.170.774.582.788.4
SAR-Net [15]✓86.87966.770.975.380.3
RBP-Pose [44]✓93.18973.579.682.189.5
AG-PoseX93.891.377.882.885.591.6
+ +Table 3. Comparisons between the IAKD and FPS. + +
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
FPS46.255.567.080.2
IAKD54.761.774.783.1
+ +Table 4. Ablation studies on the number of keypoints. + +
Nkpt5° 2 cm5° 5 cm10° 2 cm10° 5 cm
1647.955.168.879.8
3248.855.773.182.9
645157.272.882
9654.761.774.783.1
12852.859.974.383.7
+ +by $1.9\%$ on $I_oU_{50}$ , $3.2\%$ on $I_oU_{75}$ , $1.6\%$ on $10^{\circ}2\mathbf{cm}$ and $1.6\%$ on $10^{\circ}5\mathbf{cm}$ , respectively. Our method achieves comparable performance with Query6DoF on $5^{\circ}2\mathbf{cm}$ and $5^{\circ}5\mathbf{cm}$ (lower by $0.2\%$ and $0.3\%$ , respectively). + +Results of correspondence errors. To validate that the keypoint-level correspondences of AG-Pose are more accurate than point-level correspondences, we calculate the NOCS error distributions of DPDN [17], ISTNet [18] and our method on the REAL275 validation set. As shown in Figure 4, the NOCS error of our keypoint-level correspondences is concentrated more on the interval from 0 to 0.1, while errors of dense correspondence-based methods are concentrated more on the interval from 0.15 to 0.5. It proves that the keypoint-level correspondences produced by AG-Pose exhibit better generalizability on unseen instances. + +# 4.2. Ablation Studies + +In this section, we conduct ablation experiments to demonstrate the effectiveness of the proposed method on the REAL275 dataset. + +Effects of the IAKD module. To evaluate the effectiveness of the proposed Instance-Adaptive Keypoint Detection module, we first replace the IAKD with the most widely adopted Farest Point Sampling (FPS) strategy. Specifically, + +Table 5. Ablation studies on the proposed loss functions. + +
Loss5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Ldiv+Locd54.761.774.783.1
Ldiv+Lucd49.857.374.482.0
Ldiv46.4537181.3
Locd3036.155.068.6
None29.335.656.469.6
+ +![](images/a5495f5d2c3d63234c85342241dcd814fa734d9fd4d09f5f9974782848e91b72.jpg) +Figure 4. Comparisons of NOCS error distributions. + +we use FPS to sample the same number of keypoints and use their corresponding features in $\mathbf{F}_{obj}$ as $\mathbf{Q}_{ins}$ . For a fair comparison, we add extra MLPs to ensure that the number of parameters remain unchanged. As shown in Table 3, the proposed IAKD outperforms FPS on all metrics. We owe the advantage to the end-to-end trainable property of IAKD and the optimized distribution of keypoints brought by the proposed losses. + +Effects of different keypoint numbers. In Table 4, we show the impact of different keypoint numbers $N_{kpt}$ . Surprisingly, the result shows that our method can achieve comparable performance (47.9% on $5^{\circ}2\mathbf{cm}$ ) with the SOTA methods by using only a very small number ( $N_{kpt} = 16$ ) of keypoints, which demonstrates the superiority of proposed AG-Pose. And as the number of keypoints ( $N_{kpt}$ ) increases, the performance of our method continues to improve. We choose $N_{kpt} = 96$ in our method for the balance between efficiency and accuracy. + +Effects of the $L_{div}$ and the $L_{ocd}$ . In our method, we + +Table 6. Ablation study on two-stage feature aggregation. + +
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Full54.761.774.783.1
w/o GAFA47.155.370.280.9
w/o Local4957.871.282.2
w/o Global50.155.874.582.7
w/ vanilla attn536172.282.1
+ +Table 7. Ablation study on proposed GAFA. + +
5° 2 cm5° 5 cm10° 2 cm10° 5 cm
K=849.957.673.182.5
K=1654.761.774.783.1
K=2454.161.173.783.2
K=3252.759.973.682.8
+ +utilize the proposed $L_{div}$ and $L_{ocd}$ to encourage the keypoints to be well distributed on the surface of the object. To verify the effectiveness of them, we conduct ablation experiments on these losses and the results are shown in Table 5. By replacing the proposed $L_{ocd}$ with the normal chamfer distance loss $L_{ucd}$ , the performance of our model drops by $4.5\%$ on $5^{\circ}2\mathrm{cm}$ . The reason is that our object-aware chamfer distance loss can prevent the model from being affected by outliers, thereby improving the performance. The accuracy of the model further declines by $8.3\%$ after we remove the $L_{ocd}$ . It is because $L_{ocd}$ encourages keypoints to distribute on the surface of objects, which can better represent the shapes of objects. Without $L_{div}$ , the model performance declines significantly by $24.7\%$ , since $L_{div}$ is indispensable for keypoints to focus on distinct regions of objects. The excessive clustering of keypoints can result in a degradation in model performance. + +Effects of the GAFA module. Here we conduct ablation studies on the Geometric-Aware Feature Aggregation module. For a fair comparison, we replace the GAFA with MLPs that have the same number of parameters. The results are shown in Table 6. In particular, we observe that performance drops by $7.6\%$ , $4.6\%$ and $5.7\%$ on $5^{\circ}2\mathrm{cm}$ when removing the whole GAFA, the global feature aggregation and the local feature aggregation, respectively. As discussed in section 1, both local and global geometric information play crucial roles in establishing accurate correspondences on unseen objects. Our GAFA can effectively encode such geometric information into keypoint features, thus achieving better accuracy. Furthermore, we replace the geometric-aware feature aggregation operation with vanilla attention mechanism (w/ vanilla attn) in the GAFA. The experimental result shows that the proposed geometric-aware feature aggregation achieve better performance because the geometric information is indispensable in category-level 6D object pose estimation. Last, we explore the influence of the local aggregation range $K$ on the accuracy of our model in Table 7. The results demonstrate that $K = 16$ yields the most + +![](images/a7872242879de6756e4794ce594528d011fa994d242b383ea5fa8673572e3298.jpg) +Figure 5. Qualitative comparisons between our method and DPDN [17] on REAL275 dataset. We visualize the correspondence error maps and pose estimation results of our AG-Pose and DPDN. Red/green indicates large/small errors and predicted/gt bounding boxes. + +significant performance gains. + +# 4.3. Visualization + +Qualitative Results. The qualitative results of DPDN [17] and proposed AG-Pose are shown in Figure 5. Specifically, we visualize the NOCS prediction errors and the final pose predictions for both methods, in which green/red indicate small/large errors and gt/predicted results. The visualization results show that dense correspondence-based methods such as DPDN generate larger numbers of incorrect correspondences on novel instances with significant shape variations (e.g., cameras) as well as on outlier points (e.g., edge of objects), which severely degrade the performance of pose estimation. In contrast, our AG-Pose can perform instance-adaptive keypoint detection and extract geometric-aware features to establish accurate keypoint-level correspondences, leading to better pose estimation performance. + +# 5. Conclusion + +In summary, we present a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose). Specifically, we propose a Instance-Adaptive Keypoint Detection module represent the geometric information of different instances through a set of sparse keypoints. Furthermore, we propose a Geometric-Aware Feature Aggregation module to effectively incorporate local and global geometric information into keypoints to establish robust keypoint-level correspondences. We conduct comprehensive experiments and the experimental results verify the effectiveness of our method. + +# 6. Acknowledgements + +This work was partially supported by the National Nature Science Foundation of China (Grant 62306294), Dreams Foundation of Jianghuai Advance Technology Center (NO.Q/JH-063-2023-T02A/0) and Anhui Provincial Natural Science Foundation (Grant 2308085QF222). + +# References + +[1] Ronald T Azuma. A survey of augmented reality. Presence: teleoperators & virtual environments, 6(4):355-385, 1997. 1 +[2] Kai Chen and Qi Dou. 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In this area, dense correspondence-based methods have achieved leading performance. However, they do not explicitly consider the local and global geometric information of different instances, resulting in poor generalization ability to unseen instances with significant shape variations. To deal with this problem, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose), which includes two key designs: (1) The first design is an Instance-Adaptive Keypoint Detection module, which can adaptively detect a set of sparse keypoints for various instances to represent their geometric structures. (2) The second design is a Geometric-Aware Feature Aggregation module, which can efficiently integrate the local and global geometric information into keypoint features. These two modules can work together to establish robust keypoint-level correspondences for unseen instances, thus enhancing the generalization ability of the model. Experimental results on CAMERA25 and REAL275 datasets show that the proposed AG-Pose outperforms state-of-the-art methods by a large margin without category-specific shape priors." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 588, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 588, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 588, + 287, + 696 + ], + "type": "text", + "content": "The 6D object pose estimation task aims to predict the rotation, translation and size of objects with 2D/3D observations. Due to its great potential in many real-world applications such as robotic manipulation [25, 38, 39], augmented reality [1, 23] and autonomous driving [3, 7, 22], this task has been attracting increasing attention in the research community. While many previous methods [10, 11, 19, 27, 34, 41] have achieved significant performance on instance-level 6D object pose estimation, their reliance on instance-level" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 323, + 236, + 360, + 296 + ], + "blocks": [ + { + "bbox": [ + 323, + 236, + 360, + 296 + ], + "lines": [ + { + "bbox": [ + 323, + 236, + 360, + 296 + ], + "spans": [ + { + "bbox": [ + 323, + 236, + 360, + 296 + ], + "type": "image", + "image_path": "fee0a8f388f67550c7a9cb11aee471b240b69241e96d1da148993cd54deb9013.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 359, + 297, + 509, + 305 + ], + "lines": [ + { + "bbox": [ + 359, + 297, + 509, + 305 + ], + "spans": [ + { + "bbox": [ + 359, + 297, + 509, + 305 + ], + "type": "text", + "content": "a) Existing dense correspondence-based method DPDN" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 418, + 239, + 470, + 285 + ], + "blocks": [ + { + "bbox": [ + 362, + 259, + 414, + 271 + ], + "lines": [ + { + "bbox": [ + 362, + 259, + 414, + 271 + ], + "spans": [ + { + "bbox": [ + 362, + 259, + 414, + 271 + ], + "type": "text", + "content": "Dense Correspondence Prediction" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 418, + 239, + 470, + 285 + ], + "lines": [ + { + "bbox": [ + 418, + 239, + 470, + 285 + ], + "spans": [ + { + "bbox": [ + 418, + 239, + 470, + 285 + ], + "type": "image", + "image_path": "0b5bab674c4fc4d7eba58ffa11bbe8372d794a324d7295f9c131341765fead2d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 414, + 285, + 473, + 292 + ], + "lines": [ + { + "bbox": [ + 414, + 285, + 473, + 292 + ], + "spans": [ + { + "bbox": [ + 414, + 285, + 473, + 292 + ], + "type": "text", + "content": "Correspondence Error Map" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 475, + 239, + 528, + 284 + ], + "blocks": [ + { + "bbox": [ + 475, + 239, + 528, + 284 + ], + "lines": [ + { + "bbox": [ + 475, + 239, + 528, + 284 + ], + "spans": [ + { + "bbox": [ + 475, + 239, + 528, + 284 + ], + "type": "image", + "image_path": "086da8447efdc80ae16cbac70ea7254e83228d18686aeaff3d53f0a87b336fb4.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 485, + 285, + 522, + 292 + ], + "lines": [ + { + "bbox": [ + 485, + 285, + 522, + 292 + ], + "spans": [ + { + "bbox": [ + 485, + 285, + 522, + 292 + ], + "type": "text", + "content": "Pose Estimation" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 307, + 308, + 420, + 405 + ], + "blocks": [ + { + "bbox": [ + 307, + 308, + 420, + 405 + ], + "lines": [ + { + "bbox": [ + 307, + 308, + 420, + 405 + ], + "spans": [ + { + "bbox": [ + 307, + 308, + 420, + 405 + ], + "type": "image", + "image_path": "575d2bc59998b6f5a7dea0a895be42695911f4b0de5bfa1e8777f824edd82fe4.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 407, + 414, + 416 + ], + "lines": [ + { + "bbox": [ + 328, + 407, + 414, + 416 + ], + "spans": [ + { + "bbox": [ + 328, + 407, + 414, + 416 + ], + "type": "text", + "content": "b) Local Geometric Information" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 430, + 308, + 539, + 407 + ], + "blocks": [ + { + "bbox": [ + 430, + 308, + 539, + 407 + ], + "lines": [ + { + "bbox": [ + 430, + 308, + 539, + 407 + ], + "spans": [ + { + "bbox": [ + 430, + 308, + 539, + 407 + ], + "type": "image", + "image_path": "8bdbde412b0b1c6497b2a89a5bf9a84c8e54bd19bf695a06ec4a9060b43bb5ea.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 408, + 531, + 416 + ], + "lines": [ + { + "bbox": [ + 443, + 408, + 531, + 416 + ], + "spans": [ + { + "bbox": [ + 443, + 408, + 531, + 416 + ], + "type": "text", + "content": "c) Global Geometric Information" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 421, + 545, + 531 + ], + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 531 + ], + "type": "text", + "content": "Figure 1. a) The visualization for the correspondence error map and final pose estimation of the dense correspondence-based method, DPDN [17]. Green/red indicates small/large errors and GT/predicted bounding box. b) Points belonging to different parts of the same instance may exhibit similar visual features. Thus, the local geometric information is essential to distinguish them from each other. c) Points belonging to different instances may exhibit similar local geometric structures. Therefore, the global geometric information is crucial for correctly mapping them to the corresponding NOCS coordinates." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": "CAD models hinders their generalization to novel instances. To deal with this problem, category-level 6D object pose estimation has been introduced in [35], which aims to estimate the poses of unseen instances within specific categories without using their CAD models." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 605, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 546, + 714 + ], + "type": "text", + "content": "In the category-level 6D object pose estimation task, networks are trained with numerous CAD models of different instances and required to estimate the 6D poses of unseen instances which belong to the same category but have different 3D shapes. Consequently, the main challenge of this task lies in the significant intra-category shape variation. Most of the existing category-level methods aim to establish dense correspondences between observed image points (RGB or RGB-D) and the Normalized Object Coor" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21040" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 419 + ], + "type": "text", + "content": "dinate Space (NOCS) [35]. They can be categorized into two groups, i.e., the direct dense prediction methods and the two-stage deform-and-match methods. The direct dense prediction methods train their networks to directly map observed image points into the NOCS to obtain dense correspondences [13, 14, 16, 18, 35]. On the other hand, the two-stage methods predict deformation fields on a categorical shape prior [30] to reconstruct instance models first, and then establish dense correspondences between observed points and reconstructed models. With point-level dense correspondences, the final pose and size can be retrieved via Umeyama algorithm [31] or regression networks. Although dense correspondence-based methods have made significant progress, they tend to generate numerous incorrect correspondences for instances with large shape variations (Figure 1 (a)). We owe this problem to that these methods do not explicitly consider the geometric information of different instances, which is of significant importance for generalization to unseen instances. As shown in Figure 1 (b), the three points corresponding to different parts of the camera have similar visual features but distinct local structures. Thus, incorporating local geometric information is crucial to effectively distinguish them from each other. On the other hand, as illustrated in Figure 1 (c), the three points on different cameras exhibit similar local structures but correspond to different NOCS coordinates due to the large shape variations on the camera lenses. These points can be effectively discriminated by taking the global geometric information into account." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 422, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 289, + 685 + ], + "type": "text", + "content": "To facilitate each point with geometric information in dense correspondence-based methods, an intuitive way is to employ vanilla attention mechanism [32] to aggregate features from all other points. However, it will greatly increase the computational overhead due to the vast number of points. Different from existing methods, we aim to utilize a set of sparse keypoints to represent the shapes of different instances and extract geometric-aware keypoint features to establish robust keypoint-level correspondences for 6D pose estimation. Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Nevertheless, it's non-trivial because of following challenges: 1) The shapes of different instances vary significantly. Thus, the model needs to adaptively detect representative keypoints for different instances to comprehensively represent their shapes. 2) The local and global geometric information are indispensable. How to efficiently encode such geometric information into keypoint features needs to be carefully considered to achieve better generalization on unseen instances." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Motivated by the above discussions, we propose a novel Instance-Adaptive and Geometric-Aware Keypoint" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 430 + ], + "type": "text", + "content": "Learning method for category-level 6D object pose estimation (AG-Pose). The framework is shown in Figure 2 (a). The proposed method has two key designs: the Instance-Adaptive Keypoint Detection (IAKD) module and the Geometric-Aware Feature Aggregation (GAFA) module. The IAKD is designed to adaptively detect keypoints for various instances. Specifically, we initialize a set of category-shared learnable queries as keypoint detectors. We first convert them to instance-adaptive detectors by aggregating the object features into learnable queries via attention mechanism [32]. Subsequently, the heatmap of keypoints is obtained by calculating similarities between instance-adaptive detectors and object features. However, the IAKD alone can not guarantee the detected keypoints to focus on different local parts to fully represent the shapes of different instances. Thus, we further design a diversity loss and an object-aware chamfer distance loss to constrain the distribution of keypoints, yielding dispersed and object-focused keypoints. The GAFA module is designed to efficiently extract the local and global geometric information for detected keypoints. In particular, to incorporate local geometric information, GAFA selects the spatially nearest K points for each keypoint and incorporate their relative positions to aggregate features from its neighbors. To incorporate global geometric information, we further integrate global feature and relative positional embeddings into keypoint features. By combining these two modules together, the proposed method can efficiently learn instance-adaptive and geometric-aware keypoints to establish robust keypoint-level correspondences for pose estimation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 432, + 502, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 432, + 502, + 443 + ], + "spans": [ + { + "bbox": [ + 317, + 432, + 502, + 443 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 445, + 545, + 564 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 306, + 445, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 545, + 516 + ], + "type": "text", + "content": "- We propose a novel instance-adaptive and geometric-aware keypoint learning method for category-level 6D object pose estimation, which can better generalize to unseen instances with large shape variations. To the best of our knowledge, this is the first adaptive keypoint-based method for category-level 6D object pose estimation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 517, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 545, + 564 + ], + "type": "text", + "content": "- We evaluate our framework on widely adopted CAMERA25 and REAL275 datasets, and results demonstrate that the proposed method sets a new state-of-the-art performance without using categorical shape priors." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 578, + 398, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 398, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 398, + 590 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 598, + 515, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 515, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 515, + 611 + ], + "type": "text", + "content": "2.1. Instance-level 6D object pose estimation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Instance-level 6D object pose estimation aims to estimate the pose of a known object given its CAD model. In recent years, numerous methods based on direct regression [4, 24, 33, 42], fixed keypoint detection [6, 27, 40, 41], and dense 2D-3D correspondences [26, 43] have been proposed. Direct regression-based methods take the observation image (RGB or RGBD) as input and directly predict the 3D rotation and translation via regression networks. The ad" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21041" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "vantage of these methods lies in end-to-end pose estimation without extra post-processing. On the other hand, methods based on fixed keypoint detection usually predefine a set of keypoints on the object CAD model and detect their corresponding positions in the input image. Subsequently, pose estimation is achieved through Perspectiveen-Point (PnP) algorithms. For example, [10, 11, 27, 41] utilize a dense voting strategy to detect keypoints and achieve state-of-the-art performance. Dense 2D-3D correspondence-based methods aim to predict the corresponding position on the object CAD model for every point [19, 34], which are more robust to occlusion. Among them, the approaches based on fixed keypoints are most related to our method. However, they adopt fixed keypoints on a given CAD model while our method aims to adaptively detect keypoints for different instances because the CAD models are not accessible during inference in category-level task." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 284, + 261, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 284, + 261, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 284, + 261, + 297 + ], + "type": "text", + "content": "2.2. Category-level 6D object pose estimation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "content": "To improve the generalization ability on unseen instances, the category-level 6D object pose estimation is introduced, which aims to estimate the poses of all instances belonging to a specific category without using their CAD models. NOCS [35] proposes to use a shared canonical representation called Normalized Object Coordinate Space (NOCS) to represent the shapes of all instances. They first predict the NOCS coordinates of observed points and then apply Umeyama [31] algorithm to recover the pose and size. To handle the intra-category shape variation, SPD [30] proposes a deformation and matching strategy. They first reconstruct instance models by deforming a categorical shape prior and then match observations to the reconstructed models. Inspired by SPD, multiple works [2, 17, 36, 44] have been proposed to improve the processes of shape prior deformation, correspondence matching and et al., continuously improving the pose estimation performance. However, the above methods have not explicitly taken the local and global geometric information of different instances into consideration, which results in poor generalization ability to unseen instances with significant shape variations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 567, + 129, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 129, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 129, + 580 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 115, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 115, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 115, + 598 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Given a RGB-D image, we first employ a segmentation model such as [20, 21] to obtain the segmentation mask and category label for each object. Following previous works [17, 46], here we employ an off-the-shelf MaskRCNN [9]. For each segmented object, we use the segmentation mask to get the cropped RGB image " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{obj} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " and the point cloud " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj} \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " is the number of points and " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " is acquired by back-projecting the cropped depth image using camera intrinsics followed by a downsampling" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "process. By taking " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{obj}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " as input, the proposed method aims to estimate the 3D rotation " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in SO(3)" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ", the 3D translation " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\pmb{t} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " and the size " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " of the target object." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 121, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 193 + ], + "type": "text", + "content": "The framework of proposed AG-Pose is shown in Figure 2 (a). Our method consists of four main components: Feature Extractor (Sec. 3.2), Instance-Adaptive Keypoint Detector (Sec. 3.3), Geometric-Aware Feature Aggregator (Sec. 3.4) and Pose&Size Estimator (Sec. 3.5). Details about each component are as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 202, + 414, + 214 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 202, + 414, + 214 + ], + "spans": [ + { + "bbox": [ + 305, + 202, + 414, + 214 + ], + "type": "text", + "content": "3.2. Feature Extractor" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": "For the input point cloud " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": ", we utilize the PointNet++ [28] to extract point features " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_P \\in \\mathbb{R}^{N \\times C_1}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": ". For the RGB image " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{obj}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": ", following [33], a PSP network [45] with ResNet-18 [8] is applied to extract pixel-wise appearance features from " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{obj}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": ". We then choose those pixel features corresponding to " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": " to obtain the RGB features " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_I \\in \\mathbb{R}^{N \\times C_2}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": ". Lastly, we concatenate " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_I" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_P" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": " to form " + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{obj} \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 304, + 221, + 545, + 318 + ], + "type": "text", + "content": " as the input for the subsequent networks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 327, + 503, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 503, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 503, + 340 + ], + "type": "text", + "content": "3.3. Instance-Adaptive Keypoint Detector" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 346, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 573 + ], + "type": "text", + "content": "As introduced in Section 1, the geometric information is indispensable to establish robust correspondences. An intuitive idea to facilitate each point with geometric information is to employ the vanilla attention mechanism [32] to aggregate features from all other points. But it is computationally expensive due to the large number of points. Instead, we aim to utilize a set of sparse keypoints to represent the shapes of different instances for pose estimation. However, since the shapes vary across different instances and the instance models are not accessible during inference, fixed keypoint detection methods like [10, 11, 27, 41] are not applicable. Besides, methods like Farest Point Sampling are not end-to-end trainable, which may detect keypoints on outlier points caused by the noisy segmentation mask, the incorrect depth values and et al. Consequently, we design an Instance-Adaptive Keypoint Detection module to adaptively detect keypoints for instances with different shapes which can efficiently represent the object and avoid focusing on outlier points." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": "The pipeline of IAKD is illustrated in Figure 2 (b). Specifically, we initialize a set of category-shared learnable queries " + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{cat} \\in \\mathbb{R}^{N_{kpt} \\times C}" + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": " and each of them represents a keypoint detector. We first inject the object features " + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{obj}" + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": " into learnable queries via Transformer Layers [32]. This process converts the category-shared detectors " + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{cat}" + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": " into instance-adaptive detectors " + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins} \\in \\mathbb{R}^{N_{kpt} \\times C}" + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": " conditioned on object features " + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{obj}" + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": ". In detail," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 331, + 680, + 545, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 680, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 331, + 680, + 545, + 694 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {Q} _ {\\text {c a t}} \\mathbf {W} ^ {q}, \\mathbf {K} = \\mathbf {F} _ {\\text {o b j}} \\mathbf {W} ^ {k}, \\mathbf {V} = \\mathbf {F} _ {\\text {o b j}} \\mathbf {W} ^ {v}, \\tag {1}", + "image_path": "a18356d08dd5238366faac974a908b2737595da7e137ba024a6b23bdf312ec45.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 339, + 696, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 696, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 339, + 696, + 545, + 711 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {i n s} = \\operatorname {N o r m} \\left(\\mathbf {Q} _ {c a t} + \\operatorname {s o f t m a x} \\left(\\mathbf {Q K} ^ {T}\\right) \\mathbf {V}\\right). \\tag {2}", + "image_path": "c45cea007769252948c6d752774b0c231f3159b014d430f4954a38652b222e66.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21042" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 81, + 547, + 193 + ], + "blocks": [ + { + "bbox": [ + 51, + 65, + 275, + 76 + ], + "lines": [ + { + "bbox": [ + 51, + 65, + 275, + 76 + ], + "spans": [ + { + "bbox": [ + 51, + 65, + 275, + 76 + ], + "type": "text", + "content": "Feature Extractor & Instance-Adaptive Keypoint Detector" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 320, + 66, + 536, + 76 + ], + "lines": [ + { + "bbox": [ + 320, + 66, + 536, + 76 + ], + "spans": [ + { + "bbox": [ + 320, + 66, + 536, + 76 + ], + "type": "text", + "content": "Geometric-Aware Feature Aggregator & Pose Estimator" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 81, + 547, + 193 + ], + "lines": [ + { + "bbox": [ + 47, + 81, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 81, + 547, + 193 + ], + "type": "image", + "image_path": "d0f2a0c0aed6bae1d3176d7d7f52410e42eb74e21d4dd924345f7643bb71be1e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 247, + 193, + 351, + 204 + ], + "lines": [ + { + "bbox": [ + 247, + 193, + 351, + 204 + ], + "spans": [ + { + "bbox": [ + 247, + 193, + 351, + 204 + ], + "type": "text", + "content": "(a) Framework Overview" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 51, + 205, + 542, + 388 + ], + "blocks": [ + { + "bbox": [ + 51, + 205, + 542, + 388 + ], + "lines": [ + { + "bbox": [ + 51, + 205, + 542, + 388 + ], + "spans": [ + { + "bbox": [ + 51, + 205, + 542, + 388 + ], + "type": "image", + "image_path": "720c937e430941d84101838b4e77364accdc02cbd3f9cb634a347601612c800e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "lines": [ + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "type": "text", + "content": "Figure 2. a) Overview of the proposed AG-Pose. b) Illustration of the IAKD module. We initialize a set of category-shared learnable queries and convert them into instance-adaptive detectors by integrating the object features. The instance-adaptive detectors are then used to detect keypoints for the object. To guide the learning of the IAKD module, we further design the " + }, + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 46, + 399, + 546, + 455 + ], + "type": "text", + "content": " to constrain the distribution of keypoints. c) Illustration of the GAFA module. Our GAFA can efficiently integrate the geometric information into keypoint features through a two-stage feature aggregation process." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "content": "Then we calculate the cosine similarities between the instance-adaptive detectors " + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}" + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "content": " and the object features " + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{obj}" + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "content": " to generate keypoint heatmap " + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathbf{H} \\in \\mathbb{R}^{N_{kpt} \\times N}" + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "content": ". Subsequently, the 3D coordinates of keypoints " + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt} \\in \\mathbb{R}^{N_{kpt} \\times 3}" + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "content": " and their corresponding features " + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{kpt} \\in \\mathbb{R}^{N_{kpt} \\times C}" + }, + { + "bbox": [ + 46, + 468, + 287, + 539 + ], + "type": "text", + "content": " under camera space are obtained by weighted sum as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 564, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 564, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 107, + 564, + 287, + 578 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {k p t} = \\operatorname {s o f t m a x} (\\mathbf {H}) \\times \\mathbf {P} _ {o b j}, \\tag {3}", + "image_path": "0126448c14ef03772b2bbb41fac92332e6d131a1643071fda275aa5b28595056.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 108, + 580, + 287, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 580, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 108, + 580, + 287, + 594 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {k p t} = \\operatorname {s o f t m a x} (\\mathbf {H}) \\times \\mathbf {F} _ {o b j}. \\tag {4}", + "image_path": "9e91eb8f9160917b0f5ee0fdb35626141813ec229ac42ae2b73fa035791368f1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "content": "Since our target is to utilize a set of sparse keypoints to represent the geometric information of the object, the detected keypoints should be well distributed on the surface of the object. However, we find that the keypoints tend to cluster in small regions and often focus on non-surface or outlier points without explicit supervision. To encourage the keypoints to focus on different parts, we further design a diversity loss " + }, + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "content": " to force the detected keypoints to be away" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 468, + 412, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 412, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 412, + 479 + ], + "type": "text", + "content": "from each other. In detail," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 353, + 486, + 545, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 486, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 353, + 486, + 545, + 521 + ], + "type": "interline_equation", + "content": "L _ {d i v} = \\sum_ {i = 1} ^ {N _ {k p t}} \\sum_ {j = 1, j \\neq i} ^ {N _ {k p t}} \\mathbf {d} \\left(\\mathbf {P} _ {k p t} ^ {(i)}, \\mathbf {P} _ {k p t} ^ {(j)}\\right), \\tag {5}", + "image_path": "5785f0b96ca0e15963051e604886e8cf168562c57b78f5835a936e04757bff96.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 522, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 522, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 315, + 522, + 545, + 541 + ], + "type": "interline_equation", + "content": "\\mathbf {d} \\left(\\mathbf {P} _ {k p t} ^ {(i)}, \\mathbf {P} _ {k p t} ^ {(j)}\\right) = \\max \\left\\{t h _ {1} - \\left\\| \\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k p t} ^ {(j)} \\right\\| _ {2}, 0 \\right\\}, \\tag {6}", + "image_path": "5d3c00df74e701c3adacbf8dfa546954ef39694c51812c6ecdde7c90f8165832.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "th_{1}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": " is a hyperparameter and " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt}^{(i)}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": " stands for the " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": "-th keypoint. To encourage the keypoints to locate on the surface of the object and exclude outliers simultaneously, we design an object-aware chamfer distance loss " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": " to constrain the distribution of " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": ". Formally, we first utilize the ground truth pose and size " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{gt}, \\mathbf{t}_{gt}, \\mathbf{s}_{gt}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": " to transform " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": " to the NOCS and remove outlier points based on instance model " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{obj} \\in \\mathbb{R}^{M \\times 3}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": " to produce " + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}^{\\star}" + }, + { + "bbox": [ + 304, + 548, + 545, + 647 + ], + "type": "text", + "content": ". In formula," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 365, + 654, + 486, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 654, + 486, + 669 + ], + "spans": [ + { + "bbox": [ + 365, + 654, + 486, + 669 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {o b j} ^ {\\star} = \\left\\{x _ {i} \\mid x _ {i} \\in \\mathbf {P} _ {o b j} \\quad a n d \\right.", + "image_path": "28fd1a3ce63c6cfd2aed9b1ecedb4a3d0675a57a424842b21e6aa7f84af4110f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 323, + 670, + 545, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 670, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 323, + 670, + 545, + 696 + ], + "type": "interline_equation", + "content": "\\min _ {y _ {j} \\in \\mathbf {M} _ {o b j}} \\| \\frac {1}{\\| \\mathbf {s} _ {g t} \\| _ {2}} \\mathbf {R} _ {g t} \\left(x _ {i} - \\mathbf {t} _ {g t}\\right) - y _ {j} \\| _ {2} < t h _ {2} \\}. \\tag {7}", + "image_path": "bf92a55e8dac6c7ff8ff4559e7207c9bbb7e7de57ed103cf3ed4b5b435bbde54.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "The outlier filter process is also illustrated in Figure 3. Then" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21043" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 65, + 265, + 140 + ], + "blocks": [ + { + "bbox": [ + 65, + 65, + 265, + 140 + ], + "lines": [ + { + "bbox": [ + 65, + 65, + 265, + 140 + ], + "spans": [ + { + "bbox": [ + 65, + 65, + 265, + 140 + ], + "type": "image", + "image_path": "758ec3373b217130b52dfd34d09a31ecd3ac9953e51591a841b04629faea0560.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 144, + 255, + 154 + ], + "lines": [ + { + "bbox": [ + 78, + 144, + 255, + 154 + ], + "spans": [ + { + "bbox": [ + 78, + 144, + 255, + 154 + ], + "type": "text", + "content": "Figure 3. Illustration of the outlier filter process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 165, + 182, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 165, + 182, + 177 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 182, + 177 + ], + "type": "text", + "content": "the " + }, + { + "bbox": [ + 47, + 165, + 182, + 177 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 47, + 165, + 182, + 177 + ], + "type": "text", + "content": " is calculated as follows," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 79, + 182, + 287, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 182, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 79, + 182, + 287, + 213 + ], + "type": "interline_equation", + "content": "L _ {o c d} = \\frac {1}{| \\mathbf {P} _ {k p t} |} \\sum_ {x _ {i} \\in \\mathbf {P} _ {k p t}} \\min _ {y _ {j} \\in \\mathbf {P} _ {o b j} ^ {\\star}} \\| x _ {i} - y _ {j} \\| _ {2}. \\tag {8}", + "image_path": "22c85ff51fa2e5d99a67e3be0f37cbbe0bec9e82b80fa04ba80d21092571e473.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 217, + 287, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 287, + 253 + ], + "type": "text", + "content": "By constraining keypoints to be close to " + }, + { + "bbox": [ + 47, + 217, + 287, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}^{\\star}" + }, + { + "bbox": [ + 47, + 217, + 287, + 253 + ], + "type": "text", + "content": ", the IAKD module can automatically learn to filter out outlier points during inference." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 259, + 247, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 247, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 247, + 272 + ], + "type": "text", + "content": "3.4. Geometric-Aware Feature Aggregator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 277, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 373 + ], + "type": "text", + "content": "With the detected keypoints for each object, a straightforward way is to predict the NOCS coordinates for these keypoints to establish keypoint-level correspondences. However, the keypoint features are lack of geometric information, which can result in numerous incorrect correspondences on unseen instances. Thus, we propose a Geometric-Aware Feature Aggregation module to efficiently incorporate geometric information into keypoint features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": "The GAFA adopts a two-stage pipeline for geometric feature aggregation, as illustrated in Figure 2 (c). We first select the nearest " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " neighbors in " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{obj}" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " and their corresponding features in " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{obj}" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " for each keypoint to obtain " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{knn} \\in \\mathbb{R}^{N_{kpt} \\times K \\times 3}" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{knn} \\in \\mathbb{R}^{N_{kpt} \\times K \\times C}" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": ". Essentially, the global geometric information can be represented by the relative positions among keypoints, and the local geometric information can be represented by the relative positions between keypoints and their neighboring points. Thus, we utilize the relative positional embeddings " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " between keypoints and their neighbors to represent the local geometric features " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "f_l" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": " and global geometric features " + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "inline_equation", + "content": "f_g" + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": ", respectively. In detail," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 534, + 287, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 287, + 552 + ], + "type": "interline_equation", + "content": "\\alpha_ {i, j} = M L P \\left(\\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k n n} ^ {(i, j)}\\right), f _ {l} ^ {(i)} = \\operatorname {A v g P o o l} \\left(\\alpha_ {i,:}\\right), \\tag {9}", + "image_path": "8f7a655e608273731af4ab2cc91ce646675a6cc38f060bfa544fc9a1a1a8f1c4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 553, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 553, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 55, + 553, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\beta_ {i, j} = M L P \\left(\\mathbf {P} _ {k p t} ^ {(i)} - \\mathbf {P} _ {k p t} ^ {(j)}\\right), f _ {g} ^ {(i)} = \\operatorname {A v g P o o l} \\left(\\beta_ {i,:}\\right), \\tag {10}", + "image_path": "39466f5cfbbcd39784724e38c85075beebaff3cb6c681bae4814292b8cf94f50.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "f_{l}^{(i)}, f_{g}^{(i)} \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{knn}^{(i,j)}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": "-th neighboring point of " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt}^{(i)}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": ". To incorporate local geometric information into keypoints, we combine the keypoint features " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "f_{l}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": " and calculate local correlation scores " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": " between keypoints and neighboring points, which is then used to aggregate features from neighbors. The local feature aggregation process for " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": "-th keypoint feature " + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}^{(i)}" + }, + { + "bbox": [ + 47, + 576, + 287, + 668 + ], + "type": "text", + "content": " is as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 70, + 672, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 672, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 70, + 672, + 287, + 693 + ], + "type": "interline_equation", + "content": "\\mathbf {A} = \\operatorname {s i m} \\left(M L P \\left(\\operatorname {c a t} \\left[ \\mathbf {Q} _ {\\text {i n s}} ^ {(i)}, f _ {l} ^ {(i)} \\right]\\right), \\mathbf {F} _ {\\text {k n n}} ^ {(i)}\\right), \\tag {11}", + "image_path": "49475f755f7813c643b0c142d72c79246de0025db4669af62cb9391da038edc9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 61, + 694, + 287, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 694, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 694, + 287, + 712 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {i n s} ^ {(i)} = M L P \\left(\\operatorname {s o f t m a x} (\\mathbf {A}) \\times \\mathbf {F} _ {k n n} ^ {(i)} + \\mathbf {Q} _ {i n s} ^ {(i)}\\right). \\tag {12}", + "image_path": "1e4c34d9b08fd4503b687a532b6551709cbb4cd6199b2fef8237764907c3ebc6.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": "The above process is executed for all keypoints in parallel to extract representative local geometric features. However, as shown in Figure 1 (c), the local geometric information alone is insufficient to handle significant shape variation across different instances. Therefore, we further inject the global geometric feature into " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": " by leveraging all keypoint features and the global geometric features " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "f_{g}" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": ". In formula," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 370, + 162, + 545, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 162, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 370, + 162, + 545, + 178 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {\\text {i n s}} ^ {\\text {g l o b a l}} = \\operatorname {A v g P o o l} \\left(\\mathbf {Q} _ {\\text {i n s}}\\right), \\tag {13}", + "image_path": "f553bde7d9bd48922ea2e677a1f5196cbf803f21eade1e28e81abef6d123f385.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 324, + 180, + 545, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 180, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 324, + 180, + 545, + 201 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {i n s} ^ {(i)} = M L P \\left(\\text {c o n c a t} \\left[ \\mathbf {Q} _ {i n s} ^ {(i)}, \\mathbf {Q} _ {i n s} ^ {\\text {g l o b a l}}, f _ {g} ^ {(i)} \\right]\\right), \\tag {14}", + "image_path": "0bd35ec0470a6acea48c56fd6c870f3b84fd0bb5fece0f3b5dc8e407fee8755a.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}^{global}\\in \\mathbb{R}^{1\\times C}" + }, + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "type": "text", + "content": " is the global feature of " + }, + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}" + }, + { + "bbox": [ + 305, + 206, + 520, + 220 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 220, + 545, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 280 + ], + "type": "text", + "content": "The above two-stage aggregation allows keypoints to adaptively aggregate local geometric features from neighbors and global geometric information from other keypoints. It's worth noting that since the number of keypoints is small, the above process is computationally efficient." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 286, + 427, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 286, + 427, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 286, + 427, + 297 + ], + "type": "text", + "content": "3.5. Pose&Size Estimator" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "text", + "content": "After obtaining geometric-aware keypoint features, following previous work [17], we use MLP to predict the NOCS coordinates of keypoints " + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt}^{nocs} \\in \\mathbb{R}^{N_{kpt} \\times 3}" + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}" + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "text", + "content": " and regress the final pose and size " + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{R}, \\mathbf{t}, \\mathbf{s}" + }, + { + "bbox": [ + 304, + 304, + 545, + 365 + ], + "type": "text", + "content": " via this set of keypoint-level correspondences. In formula," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 376, + 371, + 545, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 371, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 376, + 371, + 545, + 385 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {k p t} ^ {\\text {n o c s}} = M L P \\left(\\mathbf {Q} _ {\\text {i n s}}\\right), \\tag {15}", + "image_path": "11771889ba93eb12e50a25a4e64ecc4a3a712b4bf9bf6c41663d3bc347b0ccba.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 330, + 387, + 545, + 402 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 387, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 330, + 387, + 545, + 402 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\text {p o s e}} = \\operatorname {c o n c a t} \\left[ \\mathbf {P} _ {\\text {k p t}}, \\mathbf {F} _ {\\text {k p t}}, \\mathbf {P} _ {\\text {k p t}} ^ {\\text {n o c s}}, \\mathbf {Q} _ {\\text {i n s}} \\right], \\tag {16}", + "image_path": "239b71c1395b57d877ee84dec361cdb9e06e289f391e2f3e279f1858de763c7d.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 315, + 403, + 545, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 403, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 315, + 403, + 545, + 428 + ], + "type": "interline_equation", + "content": "\\mathbf {R}, \\mathbf {t}, \\mathbf {s} = M L P _ {R} (\\mathbf {f} _ {\\text {p o s e}}), M L P _ {t} (\\mathbf {f} _ {\\text {p o s e}}), M L P _ {s} (\\mathbf {f} _ {\\text {p o s e}}). \\tag {17}", + "image_path": "1724f0d22843ffd77db4ea9108aca58874400dcd543883f82dde57c8002b456c.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "type": "text", + "content": "For more details please refer to [17]. We use the 6D representation [47] for the rotation " + }, + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "type": "text", + "content": ". And for the translation " + }, + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 304, + 435, + 545, + 483 + ], + "type": "text", + "content": " we follow [46] to predict the residual translation between the ground truth and the mean value of the point cloud." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 489, + 433, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 433, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 433, + 500 + ], + "type": "text", + "content": "3.6. Overall Loss Function" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 507, + 463, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 507, + 463, + 518 + ], + "spans": [ + { + "bbox": [ + 306, + 507, + 463, + 518 + ], + "type": "text", + "content": "The overall loss function is as follows:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 318, + 526, + 545, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 526, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 318, + 526, + 545, + 540 + ], + "type": "interline_equation", + "content": "L _ {a l l} = \\lambda_ {1} L _ {o c d} + \\lambda_ {2} L _ {d i v} + \\lambda_ {3} L _ {n o c s} + \\lambda_ {4} L _ {p o s e}, \\tag {18}", + "image_path": "7f89c66d5e94d4c2faca86741beacab7b9eb1beb30d9e89cc4794cc8650809f9.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": " are hyperparameters to balance the contribution of each term. For " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "L_{\\text{pose}}" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": ", we simply use " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "L_1" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": " loss as follows," + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 315, + 588, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 588, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 315, + 588, + 545, + 602 + ], + "type": "interline_equation", + "content": "L _ {p o s e} = \\left\\| \\mathbf {R} _ {g t} - \\mathbf {R} \\right\\| _ {2} + \\left\\| \\mathbf {t} _ {g t} - \\mathbf {t} \\right\\| _ {2} + \\left\\| \\mathbf {s} _ {g t} - \\mathbf {s} \\right\\| _ {2}. \\tag {19}", + "image_path": "5af2644216af4bd1a47186449b475567147a2f785cb6461d648f10dd9a8ecbd1.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "content": "We generate ground truth NOCS coordinates of keypoints " + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt}^{gt}" + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "content": " by projecting their coordinates under camera space " + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{kpt}" + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "content": " into NOCS using the ground-truth " + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{gt},\\mathbf{t}_{gt},\\mathbf{s}_{gt}" + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "L_{nocs}" + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "content": ", we use the Smooth " + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 306, + 608, + 545, + 656 + ], + "type": "text", + "content": " loss [17]. In formula," + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 357, + 661, + 545, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 661, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 357, + 661, + 545, + 687 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {k p t} ^ {g t} = \\frac {1}{\\| \\mathbf {s} _ {g t} \\| _ {2}} \\mathbf {R} _ {g t} \\left(\\mathbf {P} _ {k p t} - \\mathbf {t} _ {g t}\\right), \\tag {20}", + "image_path": "fe6e9e1890b50239f3e85d6c1969a5d07a3c8eb5d30bb48214ffbbd057b9df29.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 353, + 689, + 545, + 704 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 689, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 353, + 689, + 545, + 704 + ], + "type": "interline_equation", + "content": "L _ {n o c s} = \\operatorname {S m o o t h} L _ {1} \\left(\\mathbf {P} _ {k p t} ^ {g t}, \\mathbf {P} _ {k p t} ^ {n o c s}\\right). \\tag {21}", + "image_path": "68f14039465e43c5149d2f5cfb4d00c9fa375b81497b860fa04075aca0689218.jpg" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21044" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 78, + 90, + 516, + 239 + ], + "blocks": [ + { + "bbox": [ + 122, + 70, + 470, + 82 + ], + "lines": [ + { + "bbox": [ + 122, + 70, + 470, + 82 + ], + "spans": [ + { + "bbox": [ + 122, + 70, + 470, + 82 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons with state-of-the-art methods on the REAL275 dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 90, + 516, + 239 + ], + "lines": [ + { + "bbox": [ + 78, + 90, + 516, + 239 + ], + "spans": [ + { + "bbox": [ + 78, + 90, + 516, + 239 + ], + "type": "table", + "html": "
MethodUse of Shape Priors\\( IoU_{50} \\)\\( IoU_{75} \\)\\( 5^{\\circ}2\\mathbf{cm} \\)\\( 5^{\\circ}5\\mathbf{cm} \\)\\( 10^{\\circ}2\\mathbf{cm} \\)\\( 10^{\\circ}5\\mathbf{cm} \\)
NOCS [35]X7830.17.21013.825.2
DualPoseNet [16]X79.862.229.335.95066.8
GPV-Pose [5]X—64.43242.9—73.3
IST-Net [18]X82.576.647.553.472.180.5
Query6DoF [37]X82.576.14958.968.783
SPD [30]✓77.353.219.321.443.254.1
SGPA [2]✓80.161.935.939.661.370.7
SAR-Net [15]✓79.362.431.642.350.368.3
RBP-Pose [44]✓—67.838.248.163.179.2
DPDN [17]✓83.4764650.770.478.4
AG-PoseX83.779.554.761.774.783.1
", + "image_path": "a54796a86a01e864e0d622295b53201058fa660f9c49543ac4e898cc59c06eb6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 257, + 128, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 128, + 271 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 128, + 271 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 279, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 288, + 422 + ], + "type": "text", + "content": "Datasets. Following previous works [17, 18, 37], we conduct experiments on CAMERA25 and REAL275 [35], the most widely adopted datasets for category-level object pose estimation. CAMERA25 is a synthetic RGB-D dataset that contains 300K synthetic images of 1,085 instances from 6 different categories. In this dataset, 25,000 images of 184 instances are used for evaluation and the others are used for training. REAL275 dataset is a more challenging real-world dataset which shares the same categories with CAMERA25. It comprises 7K images from 13 different scenes. 2,750 images of 6 scenes are left for validation, including 3 unseen instances per category." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": "Implementation details. For a fair comparison, we use the same segmentation masks as SPD [30] and DPDN [17] from MaskRCNN [9]. For the data preprocessing, images are cropped and resized to " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "192 \\times 192" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " before feature extraction, and the number of points " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " in point cloud is set as 1024. For model parameters, the number of keypoints is set as " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "N_{kpt} = 96" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": ", and the local range for each keypoint in GAFA is set as " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": ". The feature dimensions are set as " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "C_1 = 128" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "C_2 = 128" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "C = 256" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": ", respectively. For the hyper-parameters in the loss functions, the two thresholds in LQKD are set as " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "th_1 = 0.01" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "th_2 = 0.1" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " are 1.0, 5.0, 1.0, 0.3, respectively. For model optimizing, we train our model on both synthetic and real datasets for evaluation on REAL275 while only on synthetic dataset for evaluation on CAMERA25. Following previous work [17], we use random translation " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "\\Delta t \\sim U(-0.02, 0.02)" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " and scaling " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "\\Delta s \\sim U(-0.8, 1.2)" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": " for data augmentation and apply random rotation for each axis with rotation degree sampled from " + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "inline_equation", + "content": "U(0, 20)" + }, + { + "bbox": [ + 46, + 425, + 288, + 699 + ], + "type": "text", + "content": ". We train our network using the ADAM [12] optimizer and employ the triangular2 cyclical learning rate schedule [29] ranging from 2e-5 to 5e-4. All experiments are conducted on a single RTX3090Ti GPU with a batch size of 24." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 714 + ], + "type": "text", + "content": "Evaluation metrics. Following previous works [30, 35]," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 258, + 522, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 522, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 522, + 270 + ], + "type": "text", + "content": "we evaluate the model performance with two metrics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 270, + 545, + 365 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "type": "text", + "content": "- 3D IoU. We report the mean precision of Intersection-over-Union (IoU) for 3D bounding boxes with thresholds of " + }, + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 306, + 270, + 545, + 317 + ], + "type": "text", + "content": ". This metric incorporates both the pose and size of the object." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "inline_equation", + "content": "n^{\\circ} m \\, \\text{cm}" + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "text", + "content": " is used for direct evaluation of the rotation and translation errors. Only predictions with rotation error less than " + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "inline_equation", + "content": "n^{\\circ}" + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "text", + "content": " and translation error less than " + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "inline_equation", + "content": "m \\, \\text{cm}" + }, + { + "bbox": [ + 306, + 318, + 545, + 365 + ], + "type": "text", + "content": " are considered correct." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 372, + 531, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 531, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 531, + 384 + ], + "type": "text", + "content": "4.1. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": "Results on REAL275 dataset. The comparisons between our AG-Pose and existing state-of-the-art methods on the challenging REAL275 dataset are shown in Table 1. As demonstrated by the results, our AG-Pose outperforms all previous methods in all metrics on REAL275 dataset. It should be noted that our method does not require the use of shape priors. In detail, on the most rigorous metric of " + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "inline_equation", + "content": "5^{\\circ}2\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": ", AG-Pose achieves the precision of " + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "inline_equation", + "content": "54.7\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": ", surpassing the current state-of-the-art shape prior-based method DPDN [17] with a large margin by " + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "inline_equation", + "content": "8.7\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": ". As for prior-free methods, our method surpasses Query6DoF [37], IST-Net [18] and GPV-Pose [5] by " + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "inline_equation", + "content": "7.2\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "inline_equation", + "content": "22.7\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": ", respectively. It should be noted that Query6DoF aims to learn a set of sparse queries as implicit shape priors, and the query features are used to update the point features to establish better dense correspondences. Different from it, the proposed AG-Pose aims to use a sparse set of keypoints to explicitly model the geometric information of objects to establish robust keypoint-level correspondences for pose estimation. The superior performance of our method indicates the importance of geometric information in category-level 6D object pose estimation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Results on CAMERA25 dataset. Table 2 shows the quantitative results of the proposed AG-Pose on CAMERA25 dataset. Our method achieves the best performance under most of metrics. In detail, the proposed AG-Pose outperforms the state-of-the-art method Query6DoF [37]" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21045" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 82, + 90, + 512, + 216 + ], + "blocks": [ + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "lines": [ + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "spans": [ + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons with state-of-the-art methods on the CAMERA25 dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 82, + 90, + 512, + 216 + ], + "lines": [ + { + "bbox": [ + 82, + 90, + 512, + 216 + ], + "spans": [ + { + "bbox": [ + 82, + 90, + 512, + 216 + ], + "type": "table", + "html": "
MethodUse of Shape Prior\\( IoU_{50} \\)\\( IoU_{75} \\)\\( 5^{\\circ}2\\mathbf{cm} \\)\\( 5^{\\circ}5\\mathbf{cm} \\)\\( 10^{\\circ}2\\mathbf{cm} \\)\\( 10^{\\circ}5\\mathbf{cm} \\)
NOCS [35]X83.969.532.340.948.264.4
DualPoseNet [16]X92.486.464.770.777.284.7
GPV-Pose [5]X93.488.372.179.1—89
Query6DoF [37]X91.988.17883.183.990
SPD [30]✓93.283.154.35973.381.5
SGPA [2]✓93.288.170.774.582.788.4
SAR-Net [15]✓86.87966.770.975.380.3
RBP-Pose [44]✓93.18973.579.682.189.5
AG-PoseX93.891.377.882.885.591.6
", + "image_path": "17b872c82776d84f57bb1db9ad617e0838ebbc5b1b2263f3660ba0ac2f11edc3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 253, + 279, + 293 + ], + "blocks": [ + { + "bbox": [ + 67, + 232, + 266, + 244 + ], + "lines": [ + { + "bbox": [ + 67, + 232, + 266, + 244 + ], + "spans": [ + { + "bbox": [ + 67, + 232, + 266, + 244 + ], + "type": "text", + "content": "Table 3. Comparisons between the IAKD and FPS." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 253, + 279, + 293 + ], + "lines": [ + { + "bbox": [ + 56, + 253, + 279, + 293 + ], + "spans": [ + { + "bbox": [ + 56, + 253, + 279, + 293 + ], + "type": "table", + "html": "
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
FPS46.255.567.080.2
IAKD54.761.774.783.1
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Nkpt5° 2 cm5° 5 cm10° 2 cm10° 5 cm
1647.955.168.879.8
3248.855.773.182.9
645157.272.882
9654.761.774.783.1
12852.859.974.383.7
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Our method achieves comparable performance with Query6DoF on " + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "inline_equation", + "content": "5^{\\circ}2\\mathbf{cm}" + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "inline_equation", + "content": "5^{\\circ}5\\mathbf{cm}" + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "text", + "content": " (lower by " + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 46, + 420, + 287, + 468 + ], + "type": "text", + "content": ", respectively)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 469, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 601 + ], + "type": "text", + "content": "Results of correspondence errors. To validate that the keypoint-level correspondences of AG-Pose are more accurate than point-level correspondences, we calculate the NOCS error distributions of DPDN [17], ISTNet [18] and our method on the REAL275 validation set. As shown in Figure 4, the NOCS error of our keypoint-level correspondences is concentrated more on the interval from 0 to 0.1, while errors of dense correspondence-based methods are concentrated more on the interval from 0.15 to 0.5. It proves that the keypoint-level correspondences produced by AG-Pose exhibit better generalizability on unseen instances." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 610, + 147, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 147, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 147, + 621 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 664 + ], + "type": "text", + "content": "In this section, we conduct ablation experiments to demonstrate the effectiveness of the proposed method on the REAL275 dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Effects of the IAKD module. To evaluate the effectiveness of the proposed Instance-Adaptive Keypoint Detection module, we first replace the IAKD with the most widely adopted Farest Point Sampling (FPS) strategy. Specifically," + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 253, + 545, + 329 + ], + "blocks": [ + { + "bbox": [ + 316, + 232, + 534, + 244 + ], + "lines": [ + { + "bbox": [ + 316, + 232, + 534, + 244 + ], + "spans": [ + { + "bbox": [ + 316, + 232, + 534, + 244 + ], + "type": "text", + "content": "Table 5. Ablation studies on the proposed loss functions." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 253, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 307, + 253, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 307, + 253, + 545, + 329 + ], + "type": "table", + "html": "
Loss5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Ldiv+Locd54.761.774.783.1
Ldiv+Lucd49.857.374.482.0
Ldiv46.4537181.3
Locd3036.155.068.6
None29.335.656.469.6
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Comparisons of NOCS error distributions." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "type": "text", + "content": "we use FPS to sample the same number of keypoints and use their corresponding features in " + }, + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{obj}" + }, + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{ins}" + }, + { + "bbox": [ + 304, + 486, + 545, + 581 + ], + "type": "text", + "content": ". For a fair comparison, we add extra MLPs to ensure that the number of parameters remain unchanged. As shown in Table 3, the proposed IAKD outperforms FPS on all metrics. We owe the advantage to the end-to-end trainable property of IAKD and the optimized distribution of keypoints brought by the proposed losses." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": "Effects of different keypoint numbers. In Table 4, we show the impact of different keypoint numbers " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{kpt}" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": ". Surprisingly, the result shows that our method can achieve comparable performance (47.9% on " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "5^{\\circ}2\\mathbf{cm}" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": ") with the SOTA methods by using only a very small number (" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{kpt} = 16" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": ") of keypoints, which demonstrates the superiority of proposed AG-Pose. And as the number of keypoints (" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{kpt}" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": ") increases, the performance of our method continues to improve. We choose " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{kpt} = 96" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " in our method for the balance between efficiency and accuracy." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Effects of the " + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": ". In our method, we" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21046" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 86, + 300, + 162 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 278, + 82 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 278, + 82 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 278, + 82 + ], + "type": "text", + "content": "Table 6. Ablation study on two-stage feature aggregation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 86, + 300, + 162 + ], + "lines": [ + { + "bbox": [ + 48, + 86, + 300, + 162 + ], + "spans": [ + { + "bbox": [ + 48, + 86, + 300, + 162 + ], + "type": "table", + "html": "
Setting5° 2 cm5° 5 cm10° 2 cm10° 5 cm
Full54.761.774.783.1
w/o GAFA47.155.370.280.9
w/o Local4957.871.282.2
w/o Global50.155.874.582.7
w/ vanilla attn536172.282.1
", + "image_path": "c2783aef8452f564b2ec1028f00a4a2eaea7061980fd5d41be278701e2a281ef.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 57, + 188, + 275, + 251 + ], + "blocks": [ + { + "bbox": [ + 81, + 173, + 253, + 185 + ], + "lines": [ + { + "bbox": [ + 81, + 173, + 253, + 185 + ], + "spans": [ + { + "bbox": [ + 81, + 173, + 253, + 185 + ], + "type": "text", + "content": "Table 7. Ablation study on proposed GAFA." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 188, + 275, + 251 + ], + "lines": [ + { + "bbox": [ + 57, + 188, + 275, + 251 + ], + "spans": [ + { + "bbox": [ + 57, + 188, + 275, + 251 + ], + "type": "table", + "html": "
5° 2 cm5° 5 cm10° 2 cm10° 5 cm
K=849.957.673.182.5
K=1654.761.774.783.1
K=2454.161.173.783.2
K=3252.759.973.682.8
", + "image_path": "248a07e44703f91e1e1e79a160727250c6670ee0a120ccfbbfd60b035b6c60cd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": "utilize the proposed " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " to encourage the keypoints to be well distributed on the surface of the object. To verify the effectiveness of them, we conduct ablation experiments on these losses and the results are shown in Table 5. By replacing the proposed " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " with the normal chamfer distance loss " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{ucd}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": ", the performance of our model drops by " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "4.5\\%" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "5^{\\circ}2\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": ". The reason is that our object-aware chamfer distance loss can prevent the model from being affected by outliers, thereby improving the performance. The accuracy of the model further declines by " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "8.3\\%" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " after we remove the " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": ". It is because " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{ocd}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " encourages keypoints to distribute on the surface of objects, which can better represent the shapes of objects. Without " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": ", the model performance declines significantly by " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "24.7\\%" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": ", since " + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 258, + 287, + 461 + ], + "type": "text", + "content": " is indispensable for keypoints to focus on distinct regions of objects. The excessive clustering of keypoints can result in a degradation in model performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": "Effects of the GAFA module. Here we conduct ablation studies on the Geometric-Aware Feature Aggregation module. For a fair comparison, we replace the GAFA with MLPs that have the same number of parameters. The results are shown in Table 6. In particular, we observe that performance drops by " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "7.6\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "4.6\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "5^{\\circ}2\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " when removing the whole GAFA, the global feature aggregation and the local feature aggregation, respectively. As discussed in section 1, both local and global geometric information play crucial roles in establishing accurate correspondences on unseen objects. Our GAFA can effectively encode such geometric information into keypoint features, thus achieving better accuracy. Furthermore, we replace the geometric-aware feature aggregation operation with vanilla attention mechanism (w/ vanilla attn) in the GAFA. The experimental result shows that the proposed geometric-aware feature aggregation achieve better performance because the geometric information is indispensable in category-level 6D object pose estimation. Last, we explore the influence of the local aggregation range " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " on the accuracy of our model in Table 7. The results demonstrate that " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " yields the most" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 65, + 545, + 178 + ], + "blocks": [ + { + "bbox": [ + 307, + 65, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 307, + 65, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 307, + 65, + 545, + 178 + ], + "type": "image", + "image_path": "a7872242879de6756e4794ce594528d011fa994d242b383ea5fa8673572e3298.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 193, + 545, + 248 + ], + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 248 + ], + "type": "text", + "content": "Figure 5. Qualitative comparisons between our method and DPDN [17] on REAL275 dataset. We visualize the correspondence error maps and pose estimation results of our AG-Pose and DPDN. Red/green indicates large/small errors and predicted/gt bounding boxes." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 255, + 428, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 255, + 428, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 255, + 428, + 266 + ], + "type": "text", + "content": "significant performance gains." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 274, + 389, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 389, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 389, + 285 + ], + "type": "text", + "content": "4.3. Visualization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 292, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 460 + ], + "type": "text", + "content": "Qualitative Results. The qualitative results of DPDN [17] and proposed AG-Pose are shown in Figure 5. Specifically, we visualize the NOCS prediction errors and the final pose predictions for both methods, in which green/red indicate small/large errors and gt/predicted results. The visualization results show that dense correspondence-based methods such as DPDN generate larger numbers of incorrect correspondences on novel instances with significant shape variations (e.g., cameras) as well as on outlier points (e.g., edge of objects), which severely degrade the performance of pose estimation. In contrast, our AG-Pose can perform instance-adaptive keypoint detection and extract geometric-aware features to establish accurate keypoint-level correspondences, leading to better pose estimation performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 470, + 378, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 470, + 378, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 470, + 378, + 483 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 491, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 622 + ], + "type": "text", + "content": "In summary, we present a novel Instance-Adaptive and Geometric-Aware Keypoint Learning method for category-level 6D object pose estimation (AG-Pose). Specifically, we propose a Instance-Adaptive Keypoint Detection module represent the geometric information of different instances through a set of sparse keypoints. Furthermore, we propose a Geometric-Aware Feature Aggregation module to effectively incorporate local and global geometric information into keypoints to establish robust keypoint-level correspondences. We conduct comprehensive experiments and the experimental results verify the effectiveness of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 633, + 420, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 420, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 420, + 646 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62306294), Dreams Foundation of Jianghuai Advance Technology Center (NO.Q/JH-063-2023-T02A/0) and Anhui Provincial Natural Science Foundation (Grant 2308085QF222)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21047" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 113 + ], + "type": "text", + "content": "[1] Ronald T Azuma. 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PTQ methods for convolutional neural networks (CNNs) provide quantization results comparable to full-precision counterparts. Directly applying them to vision transformers (ViTs), however, incurs severe performance degradation, mainly due to the differences in architectures between CNNs and ViTs. In particular, the distribution of activations for each channel varies drastically according to input instances, making PTQ methods for CNNs inappropriate for ViTs. To address this, we introduce instance-aware group quantization for ViTs (IGQ-ViT). To this end, we propose to split the channels of activation maps into multiple groups dynamically for each input instance, such that activations within each group share similar statistical properties. We also extend our scheme to quantize softmax attention across tokens. In addition, the number of groups for each layer is adjusted to minimize the discrepancies between predictions from quantized and full-precision models, under a bit-operation (BOP) constraint. We show extensive experimental results on image classification, object detection, and instance segmentation, with various transformer architectures, demonstrating the effectiveness of our approach.", + "bbox": [ + 75, + 305, + 473, + 683 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 699, + 209, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transformers [34] can capture long-range dependencies across sequential inputs, which is of central importance in natural language processing, aggregating contextual information and providing discriminative feature representations. Recently, vision transformers (ViTs) [10] has demonstrated the effectiveness of transformers for images, providing state-of-the-art results on various visual recognition tasks, including image classification [24, 33], object detection [24, 40], and semantic segmentation [24, 32, 38]. However, a series of fully-connected (FC) and self-attention lay", + "bbox": [ + 75, + 724, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3299d2112c8003088c3ed8b624ede52ebb49e311577409deeb7739a7dac5be89.jpg", + "image_caption": [ + "(a) Group quantization" + ], + "image_footnote": [], + "bbox": [ + 514, + 273, + 684, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/447db164dc1a83dbe4434ba4df05629ee2adb069e536154f6243217825c29bc2.jpg", + "image_caption": [ + "(b) IGQ-ViT", + "Figure 1. Visual comparison of group quantization and IGQ-ViT. (a) Conventional group quantization techniques [7, 31] divide consecutive channels uniformly into a number of groups without considering their dynamic ranges. The distribution of activations in each group varies significantly for individual input instances. (b) To alleviate this problem, IGQ-ViT proposes an instance-aware grouping technique that splits the channels of activation maps and softmax attentions across tokens dynamically for each input instance at runtime." + ], + "image_footnote": [], + "bbox": [ + 702, + 273, + 890, + 391 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ers in ViTs requires a substantial amount of memory and computational cost, making it challenging to deploy them on devices with limited resources (e.g., drones and mobile phones). The growing demand for ViTs to operate on the resource-constrained devices has led to increased interest in developing network quantization techniques for ViTs.", + "bbox": [ + 496, + 564, + 893, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Network quantization generally reduces bit-widths of weights and activations of a model for an efficient inference process, which can be categorized into two groups: Quantization-aware training (QAT) and post-training quantization (PTQ). QAT methods [11, 41, 42] train full-precision models, while simulating the quantization process by inserting discretizers into networks to quantize, such that the discrepancy between the full-precision and quantized models is minimized in terms of accuracy. This suggests that QAT methods require entire training samples, and they are computationally expensive, making them impractical for the prompt deployment of neural networks. PTQ methods [19, 26, 36], on the other hand, calibrate quantization parameters (e.g., quantization intervals, zero-points) from pretrained full-precision models, enabling faster quantization of networks compared to QAT methods with only a", + "bbox": [ + 496, + 657, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16132", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "limited number of training samples (usually less than 1k).", + "bbox": [ + 76, + 90, + 460, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several PTQ methods for transformers [9, 25, 39] apply layer-wise quantization techniques, where a single quantizer is applied to all activation values for efficiency. These methods, however, are not directly applicable for quantizing models using extremely low bit-widths (e.g., 4-bit), due to the significant scale variation on the activations for each channel. Exploiting channel-wise quantizers (i.e., applying different quantizers for each channel) could be a potential solution, but at the expense of computational overheads, due to floating-point summations of channel-wise outputs for matrix multiplication. Group quantization techniques [7, 31] could be an alternative to address this problem, where they divide consecutive channels uniformly into multiple groups, and apply a single quantizer for each group (Fig. 1a). However, we have observed that the channel-wise distributions of activation values vary largely among different samples, making conventional approaches inappropriate for ViTs.", + "bbox": [ + 75, + 109, + 468, + 380 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present instance-aware group quantization for ViTs (IGQ-ViT), that effectively and efficiently addresses the variations of channel-wise distributions across different input instances (Fig. 1b). Specifically, we split the channels of activation maps into multiple groups dynamically, such that the activation values within each group share similar statistical properties, and then quantize the activations within the group using identical quantization parameters. We also propose to use the instance-aware grouping technique to softmax attentions, since the distributions of attention values vary significantly according to tokens. In addition, we present a simple yet effective method to optimize the number of groups for individual layers, under a bit-operation (BOP) constraint. IGQ-ViT can be applied to various components in ViTs, including input activations of FC layers and softmax attentions, unlike previous methods [20, 22, 25, 39] that are limited to specific parts of transformer architectures. We demonstrate the effectiveness and efficiency of IGQ-ViT for various transformers, including ViT [10] and its variants [24, 33], and show that IGQ-ViT achieves state-of-the-art results on standard benchmarks. We summarize the main contributions of our work as follows:", + "bbox": [ + 75, + 383, + 472, + 731 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a novel PTQ method for ViTs, dubbed IGQ-ViT, that splits channels of activation maps into a number of groups dynamically according to input instances. We also propose to use the instance-aware grouping technique to split softmax attentions across tokens.", + "- We present a group size allocation technique searching for an optimal number of groups for each layer given a BOP constraint.", + "- We set a new state of the art on image classification [8], object detection, and instance segmentation [21], with various ViT architectures [10, 24, 33]." + ], + "bbox": [ + 73, + 734, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 89, + 637, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Network quantization. Network quantization aims at reducing bit-widths of weights and activations of neural networks. QAT methods simulate the quantization process by applying a round function to weights and activations of the network. Since derivatives of the round function is either zero or infinite, they approximate the gradients (e.g., using the straight-through estimator [3]) to train the network with backpropagation. These methods also adjust the derivatives of the round function [17, 18] or train quantization parameters jointly with network weights based on task losses [11, 16]. For better convergence of the training process, many heuristics have been introduced, e.g., progressively shrinking bit-widths [42] or freezing parts of the network weights [28, 41]. Quantized networks using QAT show performance comparable to or even better than full-precision counterparts. However, the quantization process is computationally demanding, requiring a significant amount of training time. PTQ offers an alternative approach to quantizing neural networks. Instead of training full-precision models and simulating the quantization process at training time, PTQ methods calibrate quantization parameters (e.g., quantization intervals) using a subset of training samples. Early efforts focus on optimizing the quantization parameters to minimize the difference between floating-point and quantized values [2, 27]. Another line of research proposes to consider distributions of weights and/or activations to design quantizers. For instance, the work of [12] has observed that network weights follow a bell-shaped distribution. Based on this, it introduces piecewise linear quantizers that assign different quantization intervals according to the magnitudes of activations, performing better compared to uniform quantizers. Recent PTQ methods learn to either round up or down network weights by using a reconstruction error of layer outputs [26] or exploiting the Hessian of training losses [19], and they have proven the effectiveness on CNN architectures (e.g., ResNet [13], MobileNetV2 [30]).", + "bbox": [ + 496, + 114, + 893, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformer quantization. While ViTs [10] and the variants [24, 33] have become increasingly popular in computer vision, the unique structure and characteristics of ViT architectures makes network quantization challenging. For example, PTQ methods for CNNs [2, 19, 26, 27] do not perform well on quantizing softmax attentions and GELU activations in transformers, suggesting that directly applying them for ViT quantization results in significant performance degradation [25]. To date, only a limited number of PTQ methods have been developed for ViTs. The work of [25] estimates quantization parameters that maximize similarities between full-precision and quantized outputs of linear operations, and proposes to preserve a relative order of attention values after quantization. APQ-ViT [9] introduces a calibration metric to minimize the discrepancies", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16133", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "between full-precision and quantized outputs, while maintaining the power-law distribution of softmax attentions. PTQ4ViT [39] introduces twin uniform quantizers to handle asymmetric distributions in softmax attentions and GELU activations effectively. Most PTQ methods for ViTs exploit a single quantizer for all channels, suggesting that they do not consider the distributions of activation values across channels, typically having extreme scale variations. Recent works [20, 22] attempt to alleviate the scale variation problem efficiently. FQ-ViT [22] proposes to consider inter-channel scale variations for LayerNorm [1], and exploits channel-wise quantizers with the constraint of the ratio of quantization intervals being power-of-two values. This enables using bit-shift operations, calculating mean and variance of LayerNorm in an integer level. The scale reparameterization technique, introduced by RepQ-ViT [20], allows to use layer-wise quantizers, instead of adopting channelwise ones, by adjusting the affine factors of LayerNorm and the weights of FC layers. However, this technique applies to the activations for LayerNorm only, and does not fully address the inter-channel scale variations for other layers in transformers.", + "bbox": [ + 76, + 90, + 472, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similar to ours, the works of [4, 7, 31, 35] adopt group quantization techniques for transformers. For instance, Qbert [31] and VS-quant [7] divide consecutive channels uniformly into a number of groups without considering the dynamic range of each channel, and thus the channels assigned to each group do not follow similar distributions. PEG [4] alleviates this issue by sorting the activations across channels w.r.t. the dynamic ranges during calibration, before grouping the channels. Quantformer [35] proposes to use a differentiable search [6, 23] for QAT in order to group channels of activation maps. The channels assigned to particular groups are however fixed after calibrating pretrained networks for PTQ in the group quantization techniques [4, 7, 31], which makes them inappropriate for ViTs having diverse channel distributions according to input instances. In contrast, our approach apply group quantization along channels of activation maps and tokens of softmax attentions dynamically at runtime for each input instance, without additional parameters for PTQ.", + "bbox": [ + 76, + 422, + 472, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 719, + 169, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we provide a brief description of uniform quantizer (Sec. 3.1). We then present our approach in detail, including IGQ-ViT (Sec. 3.2) and a group size allocation technique (Sec. 3.3).", + "bbox": [ + 76, + 744, + 468, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Uniform quantizer", + "text_level": 1, + "bbox": [ + 76, + 816, + 256, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a floating-point value $x$ and the quantization bitwidth $b$ , uniform quantizers discretize the inputs into a finite set of values with equally spaced intervals. To this end, it normalizes the floating-point value $x$ using a scale param", + "bbox": [ + 76, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e1e417b0529afc47b8a0dd7d2bbb304cbb6023043b9425b0a0ea413617ad8071.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 633, + 172 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/82293fe0e4edef98ec7d48642753494d0bdd6d4199c0caee841ecea36a3e22fe.jpg", + "image_caption": [ + "(b)", + "Figure 2. (a) Plots of standard deviations of activations across channels for DeiT-S [33]; (b-c) Boxplots of activation values across different input instances for a particular channel of ResNet-50 [13] and DeiT-S, respectively. We use ImageNet [8] for the visualizations. We have observed that there is a significant scale variation across channels, and the activation ranges for each channel change drastically among different samples for ViTs, in contrast to CNNs." + ], + "image_footnote": [], + "bbox": [ + 638, + 89, + 761, + 172 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0c437cdcdad15ce15a7cbf9e20ce3efe2e1c5dadff6b9b939e625b8bbf18dd18.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 764, + 89, + 888, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "eter $s$ , calibrate the normalized value with a zero-point $z$ , and clip the output as follows:", + "bbox": [ + 498, + 319, + 890, + 349 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = \\operatorname {c l i p} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z, 0, 2 ^ {b} - 1\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 361, + 890, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the scale parameter $s$ and zero-point $z$ are defined as:", + "bbox": [ + 500, + 398, + 890, + 412 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns = \\frac {u - l}{2 ^ {b} - 1}, \\quad z = \\operatorname {c l i p} \\left(\\left\\lfloor - \\frac {l}{s} \\right\\rfloor , 0, 2 ^ {b} - 1\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 422, + 890, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote by $u$ and $l$ upper and lower bounds of the quantizer, respectively. $\\lfloor .\\rfloor$ is a rounding function, and $\\operatorname{clip}(.,m,n)$ restricts an input to the range with lower and upper bounds of $m$ and $n$ , respectively. The quantized output is then obtained as follows:", + "bbox": [ + 496, + 460, + 890, + 535 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nQ (x; s, z) = s (\\hat {x} - z). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 547, + 890, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. IGQ-ViT", + "text_level": 1, + "bbox": [ + 500, + 580, + 606, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following the work of [25], we quantize all network weights except for the positional embedding. We also quantize input activations of FC layers in the multi-layer perceptron (MLP) block, and the activations for the multi-head self-attention (MSA) block, including queries, keys, values, and softmax attentions. We exploit uniform quantizers for all weights and activations in ViTs.", + "bbox": [ + 496, + 604, + 890, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 IGQ for linear operations", + "text_level": 1, + "bbox": [ + 500, + 719, + 733, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we first provide empirical observations on input activations of FC layers, and explain the details of our IGQ framework for linear operations.", + "bbox": [ + 496, + 743, + 890, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Distributions of activations across channels. Most quantization frameworks [2, 19, 25, 26] exploit layer-wise quantizers for activations, applying a single quantization parameter for all channels for efficient inference. However, we have observed that the input activations of FC layers have significant scale variations across channels (Fig. 2(a)). Similar findings can be found in [20, 22]. This suggests", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16134", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that layer-wise quantizers degrade the quantization performance significantly, as they cannot handle scale variations across different channels. Although adopting separate quantizers for individual channels could be an effective strategy for overcoming the scale variation problem, this requires a summation of a floating-point output for every channel, which is computationally expensive. We have also found that the ranges of these activations for each channel vary drastically among different input instances (Fig. 2(b, c)), since ViTs do not have preceding BatchNorm [15] layers in contrast to state-of-the-art CNNs (e.g., ResNet [13], MobileNetV2 [30]). Conventional approaches (e.g., [4, 7, 31, 35]) exploit a fixed quantization interval (i.e., from lower to upper bounds of the quantizer) for every input instance, thus cannot adapt to such diverse distributions across different samples.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instance-aware grouping across channels. We introduce an instance-aware group quantization framework for linear operations that alleviates the scale variation problem, while maintaining efficiency. We split the channels of activation maps into $G_{1}$ groups based on statistical properties, where activation values within each group are quantized with identical quantization parameters. We assign the channels of activations to appropriate groups, and optimize the scale parameter $s_i$ and the zero-point $z_{i}$ for the $i$ -th group. Specifically, given floating-point activations of $\\mathbf{X}\\in \\mathbb{R}^{N\\times C}$ and a set of candidate quantizers $\\{Q_i\\}_{i = 1}^{G_1}$ , where we denote by $N$ and $C$ as the number of tokens and channels, respectively, we define a distance metric between the $c$ -th channel of the activations $\\mathbf{X}$ , denoted by $\\mathbf{X}_c$ , and the quantizer $Q_{i}$ as follows:", + "bbox": [ + 75, + 335, + 472, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd \\left(\\mathbf {X} _ {c}, Q _ {i}\\right) = \\left(\\min \\left(\\mathbf {X} _ {c}\\right) - u _ {i}\\right) ^ {2} + \\left(\\max \\left(\\mathbf {X} _ {c}\\right) - l _ {i}\\right) ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 574, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $u_{i}$ and $l_{i}$ are upper and lower bounds of the quantizer $Q_{i}$ , respectively. We then assign each channel of the activation $\\mathbf{X}$ to one of candidate quantizers with the minimum distance as follows:", + "bbox": [ + 76, + 603, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\pi (c) = \\underset {i} {\\arg \\min } d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 676, + 468, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we denote by $\\pi (c)$ a group index assigned to the $c$ -th channel. The upper and lower bounds of quantizers are then optimized by minimizing the distances as follows:", + "bbox": [ + 76, + 710, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nu _ {i} ^ {*}, l _ {i} ^ {*} = \\underset {u _ {i}, l _ {i}} {\\arg \\min } \\sum_ {\\pi (c) = i} d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 768, + 468, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We optimize $u_{i}$ and $l_{i}$ by solving Eq. (5) and Eq. (6) alternately similar to the expectation-maximization (EM) algorithm, which guarantees the convergence [37]. Finally, we obtain quantization parameters of each group (i.e., s and z) using Eq. (2). At test time, we fix the quantization parameters, and assign the channels to appropriate groups using Eq. (5).", + "bbox": [ + 75, + 813, + 470, + 919 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Comparison of BOPs for a 4-bit DeiT-B [33] model using various quantization strategies. We denote by 'Model' the required BOP for layer-wise quantization. In contrast to layer-wise quantization, IGQ-ViT involves additional computations, including (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the outputs of each group in a floating-point format. The corresponding BOPs for these steps are denoted by 'Minmax', 'Assign', and 'FP sum', respectively.", + "bbox": [ + 496, + 88, + 890, + 214 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/0075318197229051c2f02ebbdeb189ca51a3b75cf50df74a041c4155868340e5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsModel Minmax Assign FP sumTotal
Layer-wise340.3G---340.3G
IGQ-ViT(#groups=4)340.3G0.99G0.57G1.57G343.4G
IGQ-ViT(#groups=8)340.3G0.99G1.14G3.66G346.1G
IGQ-ViT(#groups=16)340.3G0.99G2.28G7.84G351.4G
", + "bbox": [ + 504, + 217, + 885, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Computational overhead. Compared to layer-wise quantization, our approach requires (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the floating-point outputs of each group. Specifically, consider a matrix multiplication between a quantized activation $Q(\\mathbf{X})$ and the quantized weight $Q(\\mathbf{W})$ with a group size of $G_{1}$ . The quantized activation $Q(\\mathbf{X})$ is obtained by partitioning $\\mathbf{X}$ into a number of groups across channels using Eq. (5), i.e. $\\mathbf{X} = [\\mathbf{X}_1, \\dots, \\mathbf{X}_{G_1}]$ , followed by quantizing $\\mathbf{X}_i$ with a scale parameter of $s_i$ , where $i \\in \\{1, \\dots, G_1\\}$ . The matrix multiplication between $Q(\\mathbf{X})$ and $Q(\\mathbf{W})$ can then be represented as follows:", + "bbox": [ + 496, + 308, + 890, + 505 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ (\\mathbf {X}) Q (\\mathbf {W}) = s ^ {w} \\cdot \\left(\\sum_ {i = 1} ^ {G _ {1}} s _ {i} \\cdot \\hat {\\mathbf {X}} _ {i} \\hat {\\mathbf {W}} _ {i}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 513, + 890, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that we omit zero-points for clarity. We denote by $s^w$ the scale parameter for $\\mathbf{W}$ . $\\hat{\\mathbf{X}}_i$ and $\\hat{\\mathbf{W}}_i$ are obtained by applying Eq. (1) to $\\mathbf{X}_i$ and $\\mathbf{W}_i$ , the channels and rows of $\\mathbf{X}$ and $\\mathbf{W}$ associated with group $i$ , respectively. Computing Eq. (7) requires the summation of floating-point matrices for each group (i.e., $s_i \\cdot \\hat{\\mathbf{X}}_i\\hat{\\mathbf{W}}_i$ ), which can be reduced with sufficiently small values of $G_1$ . As the values of $G_1$ , we use no more than 16 in our experiments, which is extremely small compared to the number of channels, usually scaling up to over a thousand. We show in Table 1 BOPs of IGQ-ViT for DeiT-B [33] quantized with 4-bit. We can see that IGQ-ViT introduces only $3.3\\%$ additional BOPs for a group size of 16, compared to layer-wise quantization.", + "bbox": [ + 496, + 564, + 890, + 761 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 IGQ for softmax attentions", + "text_level": 1, + "bbox": [ + 500, + 767, + 743, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we present our observation for the distribution of softmax attentions, and present the details of IGQ for softmax attentions.", + "bbox": [ + 496, + 791, + 890, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Distributions of softmax attentions. ViTs capture correlations between tokens through softmax attentions. The distribution of attention values varies drastically across different tokens (Fig. 3). Therefore, using a single quantization", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16135", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8d69f8e5a5949ce8ca4c844ff4bf832dfff5ffc5669c66bf85803e31a786215f.jpg", + "image_caption": [ + "Figure 3. Distributions of softmax attentions across tokens. We can see that the distributions are different significantly across tokens. Our approach can handle this issue by splitting the rows of softmax attentions into several groups and applying separate quantizers for each group, such that the attentions assigned to each group share similar statistical properties." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 449, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/73b50d009c4796d34b5b8f9a75f3f0283e767588cc035d5a325398cb19eb621d.jpg", + "image_caption": [ + "Figure 4. Comparisons for dynamic ranges of activation values across channels, chosen from different layers of ViT-S [10]. $\\sigma_{range}$ is the standard deviation of the dynamic ranges of channels for each layer. We can see that the degree of scale variations across channels varies according to the layer, suggesting that the number of groups for each layer would be adjusted." + ], + "image_footnote": [], + "bbox": [ + 83, + 314, + 267, + 441 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fb66275e92b7578f58e998e09504c1861764725f9dd46057fc4ac53dc385d836.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 314, + 455, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "parameter to quantize softmax attentions degrades quantization performance severely. Separate quantizers might be exploited for individual tokens to handle the attention values, but this requires a large number of quantizers, and needs to adjust the quantization parameters for each instance.", + "bbox": [ + 75, + 542, + 468, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instance-aware grouping across tokens. We extend our approach in order to quantize softmax attentions across tokens. We split softmax attentions for tokens (i.e., the rows of the softmax attentions) into $G_{2}$ groups, according to the distribution of attention values. Specifically, given softmax attentions $\\mathbf{A} \\in \\mathbb{R}^{H \\times N \\times N}$ and a set of quantizers $\\{Q_{j}\\}_{j=1}^{G_{2}}$ , where we denote by $H$ the number of heads, we define the distance between each row of softmax attentions and a quantizer $Q_{j}$ as follows:", + "bbox": [ + 75, + 637, + 468, + 773 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd \\left(\\mathbf {A} _ {n}, Q _ {j}\\right) = \\left(\\max \\left(\\mathbf {A} _ {n}\\right) - v _ {j}\\right) ^ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 789, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we denote by $\\mathbf{A}_n$ and $v_{j}$ the $n$ -th row of $\\mathbf{A}$ and the upper bound of the quantizer $Q_{j}$ , respectively. Note that we set lower bounds to 0, as all attention values are positive. We then optimize $v_{j}$ with the EM algorithm and set the quantization parameters for quantizer $Q_{j}$ using Eq. (2).", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 IGQ-ViT", + "text_level": 1, + "bbox": [ + 501, + 104, + 653, + 119 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Hyperparameter: Number of iterations $N_{\\mathrm{iter}}$ ; update period of group size $T$ .", + "Input: Pre-trained model; calibration set; target BOPs $N_{bop}$", + "2: For inputs of FC layers and softmax attentions, compute the distance between their channels/rows and quantizers using Eq. (4) or Eq. (8).", + "3: for $k = 1, \\dots, N_{\\mathrm{iter}}$ do", + "4: Update the parameters for each group using Eq. (5) and Eq. (6).", + "5: if $k\\% T == 0$ then", + "6: Update the group size for each layer using Eq. (10).", + "7: end if", + "8: end for", + "9: Obtain quantization parameters $\\mathbf{s}$ , $\\mathbf{z}$ using Eq. (2).", + "10: Output: Quantized model" + ], + "bbox": [ + 504, + 125, + 890, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Group size allocation", + "text_level": 1, + "bbox": [ + 500, + 351, + 697, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We observe that activations and softmax attentions in different layers show different amount of scale variations across channels and tokens, respectively, indicating that using the same number of groups for different layers might be suboptimal (Fig. 4). To address this, we search for the optimal group size for each layer that minimizes the discrepancy between the predictions from quantized and full-precision models, under a BOP constraint. However, the search space for finding the optimal group sizes is exponential w.r.t. the number of layers $L$ , which is intractable for a large model. We propose a group size allocation technique that efficiently optimizes the group size for each layer within such a large search space. Concretely, we define a perturbation metric for a particular layer $\\psi(.)$ as the Kullback-Leibler (KL) divergence between predictions of the model before and after quantization as follows:", + "bbox": [ + 496, + 375, + 890, + 617 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\psi (g, l) = D _ {\\mathrm {K L}} \\left(y _ {l} \\| y _ {l} ^ {g}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 628, + 890, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we denote by $y_{l}$ and $y_{l}^{g}$ the predictions of the model before and after quantizing $l$ -th layer with a group size of $g$ , respectively. Note that we quantize all other layers except for the $l$ -th layer for computing the predictions of $y_{l}$ and $y_{l}^{g}$ , to account for the effects of quantization on different layers. For a target BOP $N_{bop}$ , we formulate the group size allocation as a integer linear programming (ILP) problem, and search for the optimal group size for each layer, such that an overall perturbation of the model is minimized as follows:", + "bbox": [ + 496, + 656, + 890, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {g} ^ {*} = \\arg \\min _ {\\mathbf {g}} \\sum_ {l = 1} ^ {L} \\psi (g _ {l}, l) \\text {s . t .} B (\\mathbf {g}) \\leq N _ {b o p}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 816, + 890, + 858 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{g} = \\{g_l\\}_{l=1}^L$ , and $g_l$ is the group size assigned to $l$ -th layer. We denote by $B(\\mathbf{g})$ the BOP of the model with the", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16136", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/27bb43af26d7ef08589bb43f2cf02526e45cb321c61353d6bef39becd801e5d0.jpg", + "table_caption": [ + "Table 2. Quantitative results of quantizing ViT architectures on ImageNet [8]. W/A represents the bit-width of weights (W) and activations (A), respectively. We report the top-1 validation accuracy $(\\%)$ with different group sizes for comparison. The numbers of other quantization methods are taken from [9, 20]. $\\dagger$ : Results without using a group size allocation (i.e., a fixed group size for all layers)." + ], + "table_footnote": [], + "table_body": "
Method#bits(W/A)ViT-TViT-SViT-BDeiT-TDeiT-SDeiT-BSwin-TSwin-SSwin-B
Full-precision32/3275.4781.3984.5472.2179.8581.8081.3983.2385.27
PTQ4ViT [39]4/417.4542.5730.6936.9634.0864.39-76.0974.02
APQ-ViT [9]4/417.5647.9541.4147.9443.5567.48-77.1576.48
RepQ-ViT [20]4/4-65.0568.4857.4369.0375.61-79.4578.32
IGQ-ViT† (#groups=8)4/454.4672.9977.9161.9474.0178.8576.9180.5482.88
IGQ-ViT† (#groups=12)4/455.6673.4679.1362.2874.5279.2177.5380.7983.08
IGQ-ViT (#groups=8)4/455.2973.1878.2862.2574.2379.0477.1980.6683.02
IGQ-ViT (#groups=12)4/456.0173.6179.3262.4574.6679.2377.7780.9883.14
IGQ-ViT (upper bound)4/457.5974.7379.8862.5575.0879.7478.5881.4883.53
PTQ4ViT [39]6/664.4678.6381.6569.6876.2880.25-82.3884.01
APQ-ViT [9]6/669.5579.1082.2170.4977.7680.42-82.6784.18
RepQ-ViT [20]6/6-80.4383.6270.7678.9081.27-82.7984.57
IGQ-ViT† (#groups=8)6/672.9080.0783.1170.7178.9281.3480.2382.5584.43
IGQ-ViT† (#groups=12)6/673.6380.6683.6371.0279.1781.4880.5982.6684.70
IGQ-ViT (#groups=8)6/673.1980.4883.4670.9279.0481.4480.4882.6584.62
IGQ-ViT (#groups=12)6/673.7780.7683.7771.1579.2881.7180.8982.8684.82
IGQ-ViT (upper bound)6/674.6180.9984.2771.4279.4281.7581.2083.0885.06
", + "bbox": [ + 140, + 133, + 826, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "group sizes of $\\mathbf{g}$ . We solve Eq. (10) with the PULP [29] library, using group size for each layer within the set of $\\{4,6,8,10,12,16\\}$ . We allocate the group sizes for every $T$ alternating steps of Eq. (5) and Eq. (6), where $T$ is a hyperparameter. We show in Algorithm 1 an overall quantization process of our approach.", + "bbox": [ + 75, + 446, + 470, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 551, + 209, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we describe our experimental settings (Sec. 4.1), and evaluate IGQ-ViT on image classification, object detection and semantic segmentation (Sec. 4.2). We then present a detailed analysis of our approach (Sec. 4.3).", + "bbox": [ + 75, + 579, + 468, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 650, + 290, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our IGQ-ViT framework on the tasks of image classification, object detection, and instance segmentation. We use the ImageNet [8] dataset for image classification, which contains approximately 1.2M images for training, and 50K for validation. We use COCO [21] for object detection and instance segmentation, which includes 118K training, 5K validation, and 20K test images. We adopt various transformer architectures, including ViT [10], DeiT [33], and Swin transformer [24], for image classification. For the tasks of object detection and instance segmentation, we use Mask R-CNN [14] and Cascade Mask R-CNN [5] with Swin transformers as the backbone. Following [9, 20], we randomly sample 32 images from the ImageNet [8] dataset for image classification, and a single image from COCO [21] for object detection and instance", + "bbox": [ + 75, + 674, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "segmentation to calibrate the quantization parameters. We apply our instance-aware grouping technique for all input activations of FC layers, and softmax attentions. More detailed settings are available in the supplement.", + "bbox": [ + 496, + 446, + 890, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 500, + 515, + 591, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on ImageNet. We show in Table 2 the top-1 accuracy $(\\%)$ on the validation split of ImageNet [8] with various ViT architectures. We report the accuracy with an average group size of 8 and 12. We summarize our findings as follows: (1) Our IGQ-ViT framework with 8 groups already outperforms the state of the art except for ViT-B [10] and Swin-S [24] under 6/6-bit setting, while using more groups further boosts the performance. (2) Our approach under 4/4-bit setting consistently outperforms RepQ-ViT [20] by a large margin. Similar to ours, RepQ-ViT also addresses the scale variations between channels, but it can be applied to the activations with preceding LayerNorm only. In contrast, our method handles the scale variations on all input activations of FC layers and softmax attentions, providing better results. (3) Our group size allocation technique boosts the quantization performance for all models, indicating that using the same number of groups for all layers is suboptimal. (4) Exploiting 12 groups for our approach incurs less than $0.9\\%$ accuracy drop, compared to the upper bound under the 6/6-bit setting. Note that the results of upper bound are obtained by using a separate quantizer for each channel of activations and each row of softmax attentions.", + "bbox": [ + 496, + 537, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on COCO. We show in Table 3 the quantization results for object detection and instance segmentation on", + "bbox": [ + 498, + 869, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16137", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cbe1fb20f81c3aac5fc88ba5833c968f8f41586ccaaf6512468615ee5d575c2c.jpg", + "table_caption": [ + "Table 3. Quantitative results of quantizing Mask R-CNN [14] and Cascade Mask R-CNN [5] using Swin transformers [24] on COCO [21]. We report the box average precision $\\mathrm{AP^{box}}$ for object detection and the mask average precision $\\mathrm{AP^{mask}}$ for instance segmentation." + ], + "table_footnote": [], + "table_body": "
Method#bits(W/A)Mask R-CNNCascade Mask R-CNN
Swin-TSwin-SSwin-TSwin-SSwin-B
APboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmask
Full-precision32/3246.041.648.543.350.443.751.945.051.945.0
PTQ4ViT [39]4/46.97.026.726.614.713.50.50.510.69.3
APQ-ViT [9]4/423.722.644.740.127.224.447.741.147.641.5
RepQ-ViT [20]4/436.136.044.240.247.041.449.343.1--
IGQ-ViT (#groups=8)4/440.538.544.741.348.442.350.544.050.444.0
IGQ-ViT (#groups=12)4/441.038.844.841.348.542.450.544.050.544.0
PTQ4ViT [39]6/65.86.86.56.614.713.612.510.814.212.9
APQ-ViT [9]6/645.441.247.942.948.642.550.543.950.143.7
RepQ-ViT [20]6/645.141.247.843.050.043.551.444.6--
IGQ-ViT (#groups=8)6/645.441.548.243.150.443.751.944.951.945.0
IGQ-ViT (#groups=12)6/645.541.548.243.250.443.851.945.051.945.0
", + "bbox": [ + 142, + 119, + 823, + 359 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/412c057ce4f9599d5328d9d3917ab59bd40bf0e3c013fcc91f72d7d940140e39.jpg", + "table_caption": [ + "Table 4. Quantitative comparison of our instance-aware group quantization technique with various configurations under a 4/4-bit setting. We denote by 'Linear' and 'Attention' the quantization method for linear operations and softmax attentions, respectively. For applying our method, we use a group size of 8 for all layers." + ], + "table_footnote": [], + "table_body": "
LinearAttentionViT-SDeiT-BSwin-T
Layer-wiseLayer-wise42.8262.2355.51
Layer-wiseOurs53.6965.0562.27
OursLayer-wise57.3275.5172.89
OursOurs72.9978.8576.91
OursRow-wise73.2278.8877.19
Channel-wiseOurs74.5679.6978.39
Channel-wiseRow-wise74.7379.7478.58
", + "bbox": [ + 112, + 440, + 431, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "COCO [21]. We quantize the backbones of Swin transformers [24] and the convolutional layers in the neck and head of Mask R-CNN [14] and Cascade Mask R-CNN [5]. We observe that PTQ4ViT [39] and APQ-ViT [9], that use layerwise quantizers for activations, do not perform well. In contrast, IGQ-ViT outperforms the state of the art with 8 groups only, and the quantization performance further boosts by exploiting more groups. In particular, it provides the results nearly the same as the full-precision ones for the 6/6-bit setting. This suggests that scale variations across different channels or tokens are much more critical for object detection and instance segmentation.", + "bbox": [ + 75, + 566, + 468, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Discussion", + "text_level": 1, + "bbox": [ + 76, + 756, + 194, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with different quantizers. We compare in Table 4 the results of the variants of our method adopting different types of quantizers on input activations of FC layers and softmax attentions. From the first four rows, we can see that our approach outperforms layer-wise quantization by a large margin, both for linear operations and softmax attentions. This indicates that adopting a single quantization parameter for all channels and rows without considering", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/61275b130005c3aaef16649ad573d930d6e0d56f75e69736b501f1e68e070097.jpg", + "table_caption": [ + "Table 5. Quantitative comparison of quantizing transformer architectures using various group quantization techniques under a 4/4-bit setting, with a group size of 8 for all linear operations. Note that we use layer-wise quantization for softmax attentions for a fair comparison." + ], + "table_footnote": [], + "table_body": "
Grouping methodsViT-SDeiT-BSwin-T
No grouping (#groups=1)42.8262.2355.51
Grouping consecutive channels [7, 31]41.0465.5070.39
Sorting before grouping channels [4]41.2662.6156.04
Ours57.3275.5172.89
", + "bbox": [ + 501, + 444, + 890, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "their individual distributions can severely limit the quantization performance. The last three rows compare the results of our approach with channel/row-wise quantization. We observe that the difference in performance between our approach and channel/row-wise quantization is less than $1.8\\%$ for three different models. With a small group size, our framework can achieve comparable performance to the upper bound, while maintaining efficiency.", + "bbox": [ + 496, + 539, + 890, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5 shows the results of quantizing ViT architectures using various group quantization techniques, including [4, 7, 31], and ours. While the works of [7, 31] divide consecutive channels uniformly into a number of groups, the method of [4] first sorts channels w.r.t. the dynamic ranges before partitioning them into groups. In contrast, we dynamically assign channels to groups according to the statistical properties of the channels. We find that our approach outperforms other methods by a large margin, indicating that fixing the channels assigned to each group can degrade the quantization performance significantly. We also observe that sorting the channels w.r.t. their dynamic ranges during calibration does not boost the quantization performance for DeiT-B [33] and Swin-T [24], suggesting that the dynamic range of each channel vary drastically across different input instances.", + "bbox": [ + 496, + 670, + 890, + 912 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16138", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5514b5d87b22119b31a6723e59d44fc9a270688ea1e21cb9da2d4b262470921.jpg", + "image_caption": [ + "Figure 5. Top-1 validation accuracies on ImageNet [8] w.r.t. group sizes for linear operations ( $G_{1}$ , left) and that for softmax attentions ( $G_{2}$ , right). We set either $G_{1}$ or $G_{2}$ to 8, while varying the other to compute the accuracies. We report the quantization results of ViT-S [10], Swin-T [24], and DeiT-B [33] under a 4/4-bit setting, with a fixed group size across different layers. We visualize the upper bounds with horizontal stripes of corresponding colors." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 269, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8266ec5bb5e81b24f73aca7f8f533efd086f741a8c633fc1d41f48408e02b850.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 90, + 462, + 198 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/de6994070c5fe31ce1a0b1d0400ec57c4858234ee72b2364f67ae8ff34c16bcc.jpg", + "table_caption": [ + "Table 6. Quantitative comparison of ViT architectures with and without a group size allocation technique under the 4/4-bit setting." + ], + "table_footnote": [], + "table_body": "
#groupsGroup size allocationViT-SDeiT-BSwin-T
6✓71.4478.4476.31
71.8078.5776.99
8✓72.9978.8576.91
73.1879.0477.19
10✓73.3479.0077.21
73.5179.1977.64
", + "bbox": [ + 107, + 354, + 436, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on group size. We show in Fig. 5 the results of IGQ-ViT according to the group size for linear operations (left) and softmax attentions (right). We can see that the quantization performance improves as the group size increases, for both linear operations and softmax attentions, demonstrating that using more groups better addresses the scale variation problem for channels and tokens. We also observe that the performance of our approach reaches near the upper bound with a small group size. This suggests that IGQ-ViT can effectively address the variations with a small amount of additional computations.", + "bbox": [ + 75, + 492, + 468, + 659 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Convergence analysis. We compare in Fig. 6(top) distances between channels of activation and quantizers in Eq. (4) (rows of softmax attention and quantizers in Eq. (8)) over optimization steps. It shows that our algorithm converges quickly within a small number of optimization steps. We show in Fig. 6(bottom) the dynamic ranges of activations and attentions in a particular layer, along with their assigned groups after convergence. We can see that activations/attentions in each group share similar statistical properties, demonstrating that they can be effectively quantized with a single quantization parameter.", + "bbox": [ + 75, + 661, + 467, + 827 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Group size allocation. We compare in Table 6 the results of our approach with/without the group size allocation technique. We can see that the group size allocation improves the quantization performance consistently, suggesting that assigning the same group size for all layers is suboptimal.", + "bbox": [ + 75, + 829, + 467, + 905 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b17e847c276b60c2d5b2b0009a694d5d446a3643a3dd023132fa5103c4908023.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 90, + 692, + 222 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bb9483e1aa3b2ea1ceec35d4f59181b5bfe537602ed3b0378ee86e7df391b3b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 90, + 882, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2a2b587bd3f02daf335a7da6dc387fb60ba56787b1dc9bfb6ecd2f37ac39548c.jpg", + "image_caption": [ + "Figure 6. (Top) Distances between channels of activations/rows of softmax attentions and quantizers in a particular layer of DeiT-S [33], that is, the distances as in Eq. (4) and Eq. (8), respectively; (Bottom) Dynamic ranges of activations and attentions in a specific layer of DeiT-S w.r.t. the assigned group of the same color. Note that we sort the activations and attentions based on the group indices for the purpose of the visualization only." + ], + "image_footnote": [], + "bbox": [ + 506, + 224, + 691, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0b65bd812c2837a8f9dced58fc5e2d4cfb7b772f92ee0031fbf556977e1b5a56.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 226, + 880, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 472, + 617, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have observed that activations and softmax attentions in ViTs have significant scale variations for individual channels and tokens, respectively, across different input instances. Based on this, we have introduced a instance-aware group quantization framework for ViTs, IGQ-ViT, that alleviates the scale variation problem across channels and tokens. Specifically, our approach splits the activations and softmax attentions dynamically into multiple groups along the channels and tokens, such that each group shares similar statistical properties. It then applies separate quantizers for individual groups. Additionally, we have present a simple yet effective method to assign a group size for each layer adaptively. We have shown that IGQ-ViT outperforms the state of the art, using a small number of groups, with various ViT-based architectures. We have also demonstrated the effectiveness of IGQ-ViT compared with its variants, including layer-wise quantizers, channel/row-wise quantizers, and state-of-the-art group quantizers, with a detailed analysis.", + "bbox": [ + 496, + 502, + 890, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.RS-2022-00143524, Development of Fundamental Technology and Integrated Solution for Next-Generation Automatic Artificial Intelligence System, and No.2021-0-02068, Artificial Intelligence Innovation Hub).", + "bbox": [ + 496, + 794, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16139", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv, 2016. 3", + "[2] Ron Banner, Yury Nahshan, and Daniel Soudry. Post training 4-bit quantization of convolutional networks for rapid-deployment. 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In CVPR, 2018. 1, 2" + ], + "bbox": [ + 78, + 90, + 467, + 445 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16141", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Instance-Aware Group Quantization for Vision Transformers/ecc41151-6303-4521-9423-fe8c05533db0_model.json b/2024/Instance-Aware Group Quantization for Vision Transformers/ecc41151-6303-4521-9423-fe8c05533db0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6c0abcd8d9e5d10decf01375c88fd691158c3f --- /dev/null +++ b/2024/Instance-Aware Group Quantization for Vision Transformers/ecc41151-6303-4521-9423-fe8c05533db0_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.177, + 0.131, + 0.795, + 0.154 + ], + "angle": 0, + "content": "Instance-Aware Group Quantization for Vision Transformers" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.18, + 0.281, + 0.2 + ], + "angle": 0, + "content": "Jaehyeon Moon\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.339, + 0.181, + 0.463, + 0.199 + ], + "angle": 0, + "content": "Dohyung Kim" + }, + { + "type": "text", + "bbox": [ + 0.344, + 0.2, + 0.495, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Yonsei University" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.181, + 0.657, + 0.199 + ], + "angle": 0, + "content": "Junyong Cheon" + }, + { + "type": "text", + "bbox": [ + 0.549, + 0.2, + 0.627, + 0.216 + ], + "angle": 0, + "content": "2Articron" + }, + { + "type": "text", + "bbox": [ + 0.718, + 0.181, + 0.843, + 0.198 + ], + "angle": 0, + "content": "Bumsub \\(\\mathrm{Ham}^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.218, + 0.742, + 0.235 + ], + "angle": 0, + "content": "https://cvlab.yonsei.ac.kr/projects/IGQ-ViT/" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.474, + 0.684 + ], + "angle": 0, + "content": "Post-training quantization (PTQ) is an efficient model compression technique that quantizes a pretrained full-precision model using only a small calibration set of unlabeled samples without retraining. PTQ methods for convolutional neural networks (CNNs) provide quantization results comparable to full-precision counterparts. Directly applying them to vision transformers (ViTs), however, incurs severe performance degradation, mainly due to the differences in architectures between CNNs and ViTs. In particular, the distribution of activations for each channel varies drastically according to input instances, making PTQ methods for CNNs inappropriate for ViTs. To address this, we introduce instance-aware group quantization for ViTs (IGQ-ViT). To this end, we propose to split the channels of activation maps into multiple groups dynamically for each input instance, such that activations within each group share similar statistical properties. We also extend our scheme to quantize softmax attention across tokens. In addition, the number of groups for each layer is adjusted to minimize the discrepancies between predictions from quantized and full-precision models, under a bit-operation (BOP) constraint. We show extensive experimental results on image classification, object detection, and instance segmentation, with various transformer architectures, demonstrating the effectiveness of our approach." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.7, + 0.21, + 0.715 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Transformers [34] can capture long-range dependencies across sequential inputs, which is of central importance in natural language processing, aggregating contextual information and providing discriminative feature representations. Recently, vision transformers (ViTs) [10] has demonstrated the effectiveness of transformers for images, providing state-of-the-art results on various visual recognition tasks, including image classification [24, 33], object detection [24, 40], and semantic segmentation [24, 32, 38]. However, a series of fully-connected (FC) and self-attention lay" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.275, + 0.685, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.537, + 0.397, + 0.66, + 0.41 + ], + "angle": 0, + "content": "(a) Group quantization" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.275, + 0.891, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.397, + 0.831, + 0.41 + ], + "angle": 0, + "content": "(b) IGQ-ViT" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.419, + 0.895, + 0.543 + ], + "angle": 0, + "content": "Figure 1. Visual comparison of group quantization and IGQ-ViT. (a) Conventional group quantization techniques [7, 31] divide consecutive channels uniformly into a number of groups without considering their dynamic ranges. The distribution of activations in each group varies significantly for individual input instances. (b) To alleviate this problem, IGQ-ViT proposes an instance-aware grouping technique that splits the channels of activation maps and softmax attentions across tokens dynamically for each input instance at runtime." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.894, + 0.656 + ], + "angle": 0, + "content": "ers in ViTs requires a substantial amount of memory and computational cost, making it challenging to deploy them on devices with limited resources (e.g., drones and mobile phones). The growing demand for ViTs to operate on the resource-constrained devices has led to increased interest in developing network quantization techniques for ViTs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Network quantization generally reduces bit-widths of weights and activations of a model for an efficient inference process, which can be categorized into two groups: Quantization-aware training (QAT) and post-training quantization (PTQ). QAT methods [11, 41, 42] train full-precision models, while simulating the quantization process by inserting discretizers into networks to quantize, such that the discrepancy between the full-precision and quantized models is minimized in terms of accuracy. This suggests that QAT methods require entire training samples, and they are computationally expensive, making them impractical for the prompt deployment of neural networks. PTQ methods [19, 26, 36], on the other hand, calibrate quantization parameters (e.g., quantization intervals, zero-points) from pretrained full-precision models, enabling faster quantization of networks compared to QAT methods with only a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16132" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.462, + 0.108 + ], + "angle": 0, + "content": "limited number of training samples (usually less than 1k)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.11, + 0.47, + 0.381 + ], + "angle": 0, + "content": "Several PTQ methods for transformers [9, 25, 39] apply layer-wise quantization techniques, where a single quantizer is applied to all activation values for efficiency. These methods, however, are not directly applicable for quantizing models using extremely low bit-widths (e.g., 4-bit), due to the significant scale variation on the activations for each channel. Exploiting channel-wise quantizers (i.e., applying different quantizers for each channel) could be a potential solution, but at the expense of computational overheads, due to floating-point summations of channel-wise outputs for matrix multiplication. Group quantization techniques [7, 31] could be an alternative to address this problem, where they divide consecutive channels uniformly into multiple groups, and apply a single quantizer for each group (Fig. 1a). However, we have observed that the channel-wise distributions of activation values vary largely among different samples, making conventional approaches inappropriate for ViTs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.473, + 0.732 + ], + "angle": 0, + "content": "In this paper, we present instance-aware group quantization for ViTs (IGQ-ViT), that effectively and efficiently addresses the variations of channel-wise distributions across different input instances (Fig. 1b). Specifically, we split the channels of activation maps into multiple groups dynamically, such that the activation values within each group share similar statistical properties, and then quantize the activations within the group using identical quantization parameters. We also propose to use the instance-aware grouping technique to softmax attentions, since the distributions of attention values vary significantly according to tokens. In addition, we present a simple yet effective method to optimize the number of groups for individual layers, under a bit-operation (BOP) constraint. IGQ-ViT can be applied to various components in ViTs, including input activations of FC layers and softmax attentions, unlike previous methods [20, 22, 25, 39] that are limited to specific parts of transformer architectures. We demonstrate the effectiveness and efficiency of IGQ-ViT for various transformers, including ViT [10] and its variants [24, 33], and show that IGQ-ViT achieves state-of-the-art results on standard benchmarks. We summarize the main contributions of our work as follows:" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.735, + 0.469, + 0.81 + ], + "angle": 0, + "content": "- We introduce a novel PTQ method for ViTs, dubbed IGQ-ViT, that splits channels of activation maps into a number of groups dynamically according to input instances. We also propose to use the instance-aware grouping technique to split softmax attentions across tokens." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.811, + 0.469, + 0.855 + ], + "angle": 0, + "content": "- We present a group size allocation technique searching for an optimal number of groups for each layer given a BOP constraint." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- We set a new state of the art on image classification [8], object detection, and instance segmentation [21], with various ViT architectures [10, 24, 33]." + }, + { + "type": "list", + "bbox": [ + 0.075, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.638, + 0.106 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.674 + ], + "angle": 0, + "content": "Network quantization. Network quantization aims at reducing bit-widths of weights and activations of neural networks. QAT methods simulate the quantization process by applying a round function to weights and activations of the network. Since derivatives of the round function is either zero or infinite, they approximate the gradients (e.g., using the straight-through estimator [3]) to train the network with backpropagation. These methods also adjust the derivatives of the round function [17, 18] or train quantization parameters jointly with network weights based on task losses [11, 16]. For better convergence of the training process, many heuristics have been introduced, e.g., progressively shrinking bit-widths [42] or freezing parts of the network weights [28, 41]. Quantized networks using QAT show performance comparable to or even better than full-precision counterparts. However, the quantization process is computationally demanding, requiring a significant amount of training time. PTQ offers an alternative approach to quantizing neural networks. Instead of training full-precision models and simulating the quantization process at training time, PTQ methods calibrate quantization parameters (e.g., quantization intervals) using a subset of training samples. Early efforts focus on optimizing the quantization parameters to minimize the difference between floating-point and quantized values [2, 27]. Another line of research proposes to consider distributions of weights and/or activations to design quantizers. For instance, the work of [12] has observed that network weights follow a bell-shaped distribution. Based on this, it introduces piecewise linear quantizers that assign different quantization intervals according to the magnitudes of activations, performing better compared to uniform quantizers. Recent PTQ methods learn to either round up or down network weights by using a reconstruction error of layer outputs [26] or exploiting the Hessian of training losses [19], and they have proven the effectiveness on CNN architectures (e.g., ResNet [13], MobileNetV2 [30])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Transformer quantization. While ViTs [10] and the variants [24, 33] have become increasingly popular in computer vision, the unique structure and characteristics of ViT architectures makes network quantization challenging. For example, PTQ methods for CNNs [2, 19, 26, 27] do not perform well on quantizing softmax attentions and GELU activations in transformers, suggesting that directly applying them for ViT quantization results in significant performance degradation [25]. To date, only a limited number of PTQ methods have been developed for ViTs. The work of [25] estimates quantization parameters that maximize similarities between full-precision and quantized outputs of linear operations, and proposes to preserve a relative order of attention values after quantization. APQ-ViT [9] introduces a calibration metric to minimize the discrepancies" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16133" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.422 + ], + "angle": 0, + "content": "between full-precision and quantized outputs, while maintaining the power-law distribution of softmax attentions. PTQ4ViT [39] introduces twin uniform quantizers to handle asymmetric distributions in softmax attentions and GELU activations effectively. Most PTQ methods for ViTs exploit a single quantizer for all channels, suggesting that they do not consider the distributions of activation values across channels, typically having extreme scale variations. Recent works [20, 22] attempt to alleviate the scale variation problem efficiently. FQ-ViT [22] proposes to consider inter-channel scale variations for LayerNorm [1], and exploits channel-wise quantizers with the constraint of the ratio of quantization intervals being power-of-two values. This enables using bit-shift operations, calculating mean and variance of LayerNorm in an integer level. The scale reparameterization technique, introduced by RepQ-ViT [20], allows to use layer-wise quantizers, instead of adopting channelwise ones, by adjusting the affine factors of LayerNorm and the weights of FC layers. However, this technique applies to the activations for LayerNorm only, and does not fully address the inter-channel scale variations for other layers in transformers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.473, + 0.712 + ], + "angle": 0, + "content": "Similar to ours, the works of [4, 7, 31, 35] adopt group quantization techniques for transformers. For instance, Qbert [31] and VS-quant [7] divide consecutive channels uniformly into a number of groups without considering the dynamic range of each channel, and thus the channels assigned to each group do not follow similar distributions. PEG [4] alleviates this issue by sorting the activations across channels w.r.t. the dynamic ranges during calibration, before grouping the channels. Quantformer [35] proposes to use a differentiable search [6, 23] for QAT in order to group channels of activation maps. The channels assigned to particular groups are however fixed after calibrating pretrained networks for PTQ in the group quantization techniques [4, 7, 31], which makes them inappropriate for ViTs having diverse channel distributions according to input instances. In contrast, our approach apply group quantization along channels of activation maps and tokens of softmax attentions dynamically at runtime for each input instance, without additional parameters for PTQ." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.72, + 0.17, + 0.735 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.745, + 0.47, + 0.806 + ], + "angle": 0, + "content": "In this section, we provide a brief description of uniform quantizer (Sec. 3.1). We then present our approach in detail, including IGQ-ViT (Sec. 3.2) and a group size allocation technique (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.258, + 0.833 + ], + "angle": 0, + "content": "3.1. Uniform quantizer" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Given a floating-point value \\( x \\) and the quantization bitwidth \\( b \\), uniform quantizers discretize the inputs into a finite set of values with equally spaced intervals. To this end, it normalizes the floating-point value \\( x \\) using a scale param" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.635, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.178, + 0.58, + 0.191 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.09, + 0.763, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.178, + 0.71, + 0.19 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.09, + 0.89, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.178, + 0.838, + 0.19 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.308 + ], + "angle": 0, + "content": "Figure 2. (a) Plots of standard deviations of activations across channels for DeiT-S [33]; (b-c) Boxplots of activation values across different input instances for a particular channel of ResNet-50 [13] and DeiT-S, respectively. We use ImageNet [8] for the visualizations. We have observed that there is a significant scale variation across channels, and the activation ranges for each channel change drastically among different samples for ViTs, in contrast to CNNs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.32, + 0.892, + 0.351 + ], + "angle": 0, + "content": "eter \\(s\\), calibrate the normalized value with a zero-point \\(z\\), and clip the output as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.362, + 0.892, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = \\operatorname {c l i p} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z, 0, 2 ^ {b} - 1\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.399, + 0.892, + 0.414 + ], + "angle": 0, + "content": "where the scale parameter \\(s\\) and zero-point \\(z\\) are defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.424, + 0.892, + 0.455 + ], + "angle": 0, + "content": "\\[\ns = \\frac {u - l}{2 ^ {b} - 1}, \\quad z = \\operatorname {c l i p} \\left(\\left\\lfloor - \\frac {l}{s} \\right\\rfloor , 0, 2 ^ {b} - 1\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.536 + ], + "angle": 0, + "content": "We denote by \\( u \\) and \\( l \\) upper and lower bounds of the quantizer, respectively. \\( \\lfloor .\\rfloor \\) is a rounding function, and \\( \\operatorname{clip}(.,m,n) \\) restricts an input to the range with lower and upper bounds of \\( m \\) and \\( n \\), respectively. The quantized output is then obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.549, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\nQ (x; s, z) = s (\\hat {x} - z). \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.607, + 0.597 + ], + "angle": 0, + "content": "3.2. IGQ-ViT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Following the work of [25], we quantize all network weights except for the positional embedding. We also quantize input activations of FC layers in the multi-layer perceptron (MLP) block, and the activations for the multi-head self-attention (MSA) block, including queries, keys, values, and softmax attentions. We exploit uniform quantizers for all weights and activations in ViTs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.72, + 0.734, + 0.735 + ], + "angle": 0, + "content": "3.2.1 IGQ for linear operations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.744, + 0.892, + 0.79 + ], + "angle": 0, + "content": "In the following, we first provide empirical observations on input activations of FC layers, and explain the details of our IGQ framework for linear operations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Distributions of activations across channels. Most quantization frameworks [2, 19, 25, 26] exploit layer-wise quantizers for activations, applying a single quantization parameter for all channels for efficient inference. However, we have observed that the input activations of FC layers have significant scale variations across channels (Fig. 2(a)). Similar findings can be found in [20, 22]. This suggests" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16134" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "that layer-wise quantizers degrade the quantization performance significantly, as they cannot handle scale variations across different channels. Although adopting separate quantizers for individual channels could be an effective strategy for overcoming the scale variation problem, this requires a summation of a floating-point output for every channel, which is computationally expensive. We have also found that the ranges of these activations for each channel vary drastically among different input instances (Fig. 2(b, c)), since ViTs do not have preceding BatchNorm [15] layers in contrast to state-of-the-art CNNs (e.g., ResNet [13], MobileNetV2 [30]). Conventional approaches (e.g., [4, 7, 31, 35]) exploit a fixed quantization interval (i.e., from lower to upper bounds of the quantizer) for every input instance, thus cannot adapt to such diverse distributions across different samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.563 + ], + "angle": 0, + "content": "Instance-aware grouping across channels. We introduce an instance-aware group quantization framework for linear operations that alleviates the scale variation problem, while maintaining efficiency. We split the channels of activation maps into \\( G_{1} \\) groups based on statistical properties, where activation values within each group are quantized with identical quantization parameters. We assign the channels of activations to appropriate groups, and optimize the scale parameter \\( s_i \\) and the zero-point \\( z_{i} \\) for the \\( i \\)-th group. Specifically, given floating-point activations of \\( \\mathbf{X}\\in \\mathbb{R}^{N\\times C} \\) and a set of candidate quantizers \\( \\{Q_i\\}_{i = 1}^{G_1} \\), where we denote by \\( N \\) and \\( C \\) as the number of tokens and channels, respectively, we define a distance metric between the \\( c \\)-th channel of the activations \\( \\mathbf{X} \\), denoted by \\( \\mathbf{X}_c \\), and the quantizer \\( Q_{i} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.575, + 0.47, + 0.593 + ], + "angle": 0, + "content": "\\[\nd \\left(\\mathbf {X} _ {c}, Q _ {i}\\right) = \\left(\\min \\left(\\mathbf {X} _ {c}\\right) - u _ {i}\\right) ^ {2} + \\left(\\max \\left(\\mathbf {X} _ {c}\\right) - l _ {i}\\right) ^ {2} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.604, + 0.47, + 0.664 + ], + "angle": 0, + "content": "where \\( u_{i} \\) and \\( l_{i} \\) are upper and lower bounds of the quantizer \\( Q_{i} \\), respectively. We then assign each channel of the activation \\( \\mathbf{X} \\) to one of candidate quantizers with the minimum distance as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.677, + 0.47, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\pi (c) = \\underset {i} {\\arg \\min } d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.712, + 0.47, + 0.759 + ], + "angle": 0, + "content": "where we denote by \\(\\pi (c)\\) a group index assigned to the \\(c\\)-th channel. The upper and lower bounds of quantizers are then optimized by minimizing the distances as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.77, + 0.47, + 0.803 + ], + "angle": 0, + "content": "\\[\nu _ {i} ^ {*}, l _ {i} ^ {*} = \\underset {u _ {i}, l _ {i}} {\\arg \\min } \\sum_ {\\pi (c) = i} d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.471, + 0.92 + ], + "angle": 0, + "content": "We optimize \\( u_{i} \\) and \\( l_{i} \\) by solving Eq. (5) and Eq. (6) alternately similar to the expectation-maximization (EM) algorithm, which guarantees the convergence [37]. Finally, we obtain quantization parameters of each group (i.e., s and z) using Eq. (2). At test time, we fix the quantization parameters, and assign the channels to appropriate groups using Eq. (5)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.215 + ], + "angle": 0, + "content": "Table 1. Comparison of BOPs for a 4-bit DeiT-B [33] model using various quantization strategies. We denote by 'Model' the required BOP for layer-wise quantization. In contrast to layer-wise quantization, IGQ-ViT involves additional computations, including (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the outputs of each group in a floating-point format. The corresponding BOPs for these steps are denoted by 'Minmax', 'Assign', and 'FP sum', respectively." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.218, + 0.887, + 0.294 + ], + "angle": 0, + "content": "
MethodsModel Minmax Assign FP sumTotal
Layer-wise340.3G---340.3G
IGQ-ViT(#groups=4)340.3G0.99G0.57G1.57G343.4G
IGQ-ViT(#groups=8)340.3G0.99G1.14G3.66G346.1G
IGQ-ViT(#groups=16)340.3G0.99G2.28G7.84G351.4G
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Computational overhead. Compared to layer-wise quantization, our approach requires (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the floating-point outputs of each group. Specifically, consider a matrix multiplication between a quantized activation \\( Q(\\mathbf{X}) \\) and the quantized weight \\( Q(\\mathbf{W}) \\) with a group size of \\( G_{1} \\). The quantized activation \\( Q(\\mathbf{X}) \\) is obtained by partitioning \\( \\mathbf{X} \\) into a number of groups across channels using Eq. (5), i.e. \\( \\mathbf{X} = [\\mathbf{X}_1, \\dots, \\mathbf{X}_{G_1}] \\), followed by quantizing \\( \\mathbf{X}_i \\) with a scale parameter of \\( s_i \\), where \\( i \\in \\{1, \\dots, G_1\\} \\). The matrix multiplication between \\( Q(\\mathbf{X}) \\) and \\( Q(\\mathbf{W}) \\) can then be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.515, + 0.892, + 0.556 + ], + "angle": 0, + "content": "\\[\nQ (\\mathbf {X}) Q (\\mathbf {W}) = s ^ {w} \\cdot \\left(\\sum_ {i = 1} ^ {G _ {1}} s _ {i} \\cdot \\hat {\\mathbf {X}} _ {i} \\hat {\\mathbf {W}} _ {i}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.762 + ], + "angle": 0, + "content": "Note that we omit zero-points for clarity. We denote by \\( s^w \\) the scale parameter for \\( \\mathbf{W} \\). \\( \\hat{\\mathbf{X}}_i \\) and \\( \\hat{\\mathbf{W}}_i \\) are obtained by applying Eq. (1) to \\( \\mathbf{X}_i \\) and \\( \\mathbf{W}_i \\), the channels and rows of \\( \\mathbf{X} \\) and \\( \\mathbf{W} \\) associated with group \\( i \\), respectively. Computing Eq. (7) requires the summation of floating-point matrices for each group (i.e., \\( s_i \\cdot \\hat{\\mathbf{X}}_i\\hat{\\mathbf{W}}_i \\)), which can be reduced with sufficiently small values of \\( G_1 \\). As the values of \\( G_1 \\), we use no more than 16 in our experiments, which is extremely small compared to the number of channels, usually scaling up to over a thousand. We show in Table 1 BOPs of IGQ-ViT for DeiT-B [33] quantized with 4-bit. We can see that IGQ-ViT introduces only \\( 3.3\\% \\) additional BOPs for a group size of 16, compared to layer-wise quantization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.744, + 0.783 + ], + "angle": 0, + "content": "3.2.2 IGQ for softmax attentions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.892, + 0.836 + ], + "angle": 0, + "content": "Here, we present our observation for the distribution of softmax attentions, and present the details of IGQ for softmax attentions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Distributions of softmax attentions. ViTs capture correlations between tokens through softmax attentions. The distribution of attention values varies drastically across different tokens (Fig. 3). Therefore, using a single quantization" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16135" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.092, + 0.45, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.221, + 0.473, + 0.306 + ], + "angle": 0, + "content": "Figure 3. Distributions of softmax attentions across tokens. We can see that the distributions are different significantly across tokens. Our approach can handle this issue by splitting the rows of softmax attentions into several groups and applying separate quantizers for each group, such that the attentions assigned to each group share similar statistical properties." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.315, + 0.268, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.315, + 0.457, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.527 + ], + "angle": 0, + "content": "Figure 4. Comparisons for dynamic ranges of activation values across channels, chosen from different layers of ViT-S [10]. \\(\\sigma_{range}\\) is the standard deviation of the dynamic ranges of channels for each layer. We can see that the degree of scale variations across channels varies according to the layer, suggesting that the number of groups for each layer would be adjusted." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.618 + ], + "angle": 0, + "content": "parameter to quantize softmax attentions degrades quantization performance severely. Separate quantizers might be exploited for individual tokens to handle the attention values, but this requires a large number of quantizers, and needs to adjust the quantization parameters for each instance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Instance-aware grouping across tokens. We extend our approach in order to quantize softmax attentions across tokens. We split softmax attentions for tokens (i.e., the rows of the softmax attentions) into \\( G_{2} \\) groups, according to the distribution of attention values. Specifically, given softmax attentions \\( \\mathbf{A} \\in \\mathbb{R}^{H \\times N \\times N} \\) and a set of quantizers \\( \\{Q_{j}\\}_{j=1}^{G_{2}} \\), where we denote by \\( H \\) the number of heads, we define the distance between each row of softmax attentions and a quantizer \\( Q_{j} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.79, + 0.469, + 0.81 + ], + "angle": 0, + "content": "\\[\nd \\left(\\mathbf {A} _ {n}, Q _ {j}\\right) = \\left(\\max \\left(\\mathbf {A} _ {n}\\right) - v _ {j}\\right) ^ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where we denote by \\(\\mathbf{A}_n\\) and \\(v_{j}\\) the \\(n\\)-th row of \\(\\mathbf{A}\\) and the upper bound of the quantizer \\(Q_{j}\\), respectively. Note that we set lower bounds to 0, as all attention values are positive. We then optimize \\(v_{j}\\) with the EM algorithm and set the quantization parameters for quantizer \\(Q_{j}\\) using Eq. (2)." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.106, + 0.655, + 0.121 + ], + "angle": 0, + "content": "Algorithm 1 IGQ-ViT" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.126, + 0.892, + 0.153 + ], + "angle": 0, + "content": "1: Hyperparameter: Number of iterations \\( N_{\\mathrm{iter}} \\); update period of group size \\( T \\)." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.154, + 0.885, + 0.167 + ], + "angle": 0, + "content": "Input: Pre-trained model; calibration set; target BOPs \\(N_{bop}\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.167, + 0.892, + 0.209 + ], + "angle": 0, + "content": "2: For inputs of FC layers and softmax attentions, compute the distance between their channels/rows and quantizers using Eq. (4) or Eq. (8)." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.209, + 0.66, + 0.222 + ], + "angle": 0, + "content": "3: for \\( k = 1, \\dots, N_{\\mathrm{iter}} \\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.222, + 0.892, + 0.25 + ], + "angle": 0, + "content": "4: Update the parameters for each group using Eq. (5) and Eq. (6)." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.251, + 0.669, + 0.263 + ], + "angle": 0, + "content": "5: if \\( k\\% T == 0 \\) then" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.264, + 0.866, + 0.278 + ], + "angle": 0, + "content": "6: Update the group size for each layer using Eq. (10)." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.279, + 0.583, + 0.29 + ], + "angle": 0, + "content": "7: end if" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.292, + 0.575, + 0.304 + ], + "angle": 0, + "content": "8: end for" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.305, + 0.822, + 0.32 + ], + "angle": 0, + "content": "9: Obtain quantization parameters \\(\\mathbf{s}\\), \\(\\mathbf{z}\\) using Eq. (2)." + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.32, + 0.685, + 0.333 + ], + "angle": 0, + "content": "10: Output: Quantized model" + }, + { + "type": "list", + "bbox": [ + 0.505, + 0.126, + 0.892, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.352, + 0.699, + 0.369 + ], + "angle": 0, + "content": "3.3. Group size allocation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.892, + 0.618 + ], + "angle": 0, + "content": "We observe that activations and softmax attentions in different layers show different amount of scale variations across channels and tokens, respectively, indicating that using the same number of groups for different layers might be suboptimal (Fig. 4). To address this, we search for the optimal group size for each layer that minimizes the discrepancy between the predictions from quantized and full-precision models, under a BOP constraint. However, the search space for finding the optimal group sizes is exponential w.r.t. the number of layers \\( L \\), which is intractable for a large model. We propose a group size allocation technique that efficiently optimizes the group size for each layer within such a large search space. Concretely, we define a perturbation metric for a particular layer \\( \\psi(.) \\) as the Kullback-Leibler (KL) divergence between predictions of the model before and after quantization as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.629, + 0.892, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\psi (g, l) = D _ {\\mathrm {K L}} \\left(y _ {l} \\| y _ {l} ^ {g}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.807 + ], + "angle": 0, + "content": "where we denote by \\( y_{l} \\) and \\( y_{l}^{g} \\) the predictions of the model before and after quantizing \\( l \\)-th layer with a group size of \\( g \\), respectively. Note that we quantize all other layers except for the \\( l \\)-th layer for computing the predictions of \\( y_{l} \\) and \\( y_{l}^{g} \\), to account for the effects of quantization on different layers. For a target BOP \\( N_{bop} \\), we formulate the group size allocation as a integer linear programming (ILP) problem, and search for the optimal group size for each layer, such that an overall perturbation of the model is minimized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.817, + 0.892, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\mathbf {g} ^ {*} = \\arg \\min _ {\\mathbf {g}} \\sum_ {l = 1} ^ {L} \\psi (g _ {l}, l) \\text {s . t .} B (\\mathbf {g}) \\leq N _ {b o p}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{g} = \\{g_l\\}_{l=1}^L\\), and \\(g_l\\) is the group size assigned to \\(l\\)-th layer. We denote by \\(B(\\mathbf{g})\\) the BOP of the model with the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16136" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 2. Quantitative results of quantizing ViT architectures on ImageNet [8]. W/A represents the bit-width of weights (W) and activations (A), respectively. We report the top-1 validation accuracy \\((\\%)\\) with different group sizes for comparison. The numbers of other quantization methods are taken from [9, 20]. \\(\\dagger\\): Results without using a group size allocation (i.e., a fixed group size for all layers)." + }, + { + "type": "table", + "bbox": [ + 0.142, + 0.135, + 0.827, + 0.44 + ], + "angle": 0, + "content": "
Method#bits(W/A)ViT-TViT-SViT-BDeiT-TDeiT-SDeiT-BSwin-TSwin-SSwin-B
Full-precision32/3275.4781.3984.5472.2179.8581.8081.3983.2385.27
PTQ4ViT [39]4/417.4542.5730.6936.9634.0864.39-76.0974.02
APQ-ViT [9]4/417.5647.9541.4147.9443.5567.48-77.1576.48
RepQ-ViT [20]4/4-65.0568.4857.4369.0375.61-79.4578.32
IGQ-ViT† (#groups=8)4/454.4672.9977.9161.9474.0178.8576.9180.5482.88
IGQ-ViT† (#groups=12)4/455.6673.4679.1362.2874.5279.2177.5380.7983.08
IGQ-ViT (#groups=8)4/455.2973.1878.2862.2574.2379.0477.1980.6683.02
IGQ-ViT (#groups=12)4/456.0173.6179.3262.4574.6679.2377.7780.9883.14
IGQ-ViT (upper bound)4/457.5974.7379.8862.5575.0879.7478.5881.4883.53
PTQ4ViT [39]6/664.4678.6381.6569.6876.2880.25-82.3884.01
APQ-ViT [9]6/669.5579.1082.2170.4977.7680.42-82.6784.18
RepQ-ViT [20]6/6-80.4383.6270.7678.9081.27-82.7984.57
IGQ-ViT† (#groups=8)6/672.9080.0783.1170.7178.9281.3480.2382.5584.43
IGQ-ViT† (#groups=12)6/673.6380.6683.6371.0279.1781.4880.5982.6684.70
IGQ-ViT (#groups=8)6/673.1980.4883.4670.9279.0481.4480.4882.6584.62
IGQ-ViT (#groups=12)6/673.7780.7683.7771.1579.2881.7180.8982.8684.82
IGQ-ViT (upper bound)6/674.6180.9984.2771.4279.4281.7581.2083.0885.06
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.472, + 0.542 + ], + "angle": 0, + "content": "group sizes of \\(\\mathbf{g}\\). We solve Eq. (10) with the PULP [29] library, using group size for each layer within the set of \\(\\{4,6,8,10,12,16\\}\\). We allocate the group sizes for every \\(T\\) alternating steps of Eq. (5) and Eq. (6), where \\(T\\) is a hyperparameter. We show in Algorithm 1 an overall quantization process of our approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.553, + 0.21, + 0.571 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.643 + ], + "angle": 0, + "content": "In this section, we describe our experimental settings (Sec. 4.1), and evaluate IGQ-ViT on image classification, object detection and semantic segmentation (Sec. 4.2). We then present a detailed analysis of our approach (Sec. 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.292, + 0.667 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We evaluate our IGQ-ViT framework on the tasks of image classification, object detection, and instance segmentation. We use the ImageNet [8] dataset for image classification, which contains approximately 1.2M images for training, and 50K for validation. We use COCO [21] for object detection and instance segmentation, which includes 118K training, 5K validation, and 20K test images. We adopt various transformer architectures, including ViT [10], DeiT [33], and Swin transformer [24], for image classification. For the tasks of object detection and instance segmentation, we use Mask R-CNN [14] and Cascade Mask R-CNN [5] with Swin transformers as the backbone. Following [9, 20], we randomly sample 32 images from the ImageNet [8] dataset for image classification, and a single image from COCO [21] for object detection and instance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.51 + ], + "angle": 0, + "content": "segmentation to calibrate the quantization parameters. We apply our instance-aware grouping technique for all input activations of FC layers, and softmax attentions. More detailed settings are available in the supplement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.516, + 0.593, + 0.53 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Results on ImageNet. We show in Table 2 the top-1 accuracy \\((\\%)\\) on the validation split of ImageNet [8] with various ViT architectures. We report the accuracy with an average group size of 8 and 12. We summarize our findings as follows: (1) Our IGQ-ViT framework with 8 groups already outperforms the state of the art except for ViT-B [10] and Swin-S [24] under 6/6-bit setting, while using more groups further boosts the performance. (2) Our approach under 4/4-bit setting consistently outperforms RepQ-ViT [20] by a large margin. Similar to ours, RepQ-ViT also addresses the scale variations between channels, but it can be applied to the activations with preceding LayerNorm only. In contrast, our method handles the scale variations on all input activations of FC layers and softmax attentions, providing better results. (3) Our group size allocation technique boosts the quantization performance for all models, indicating that using the same number of groups for all layers is suboptimal. (4) Exploiting 12 groups for our approach incurs less than \\(0.9\\%\\) accuracy drop, compared to the upper bound under the 6/6-bit setting. Note that the results of upper bound are obtained by using a separate quantizer for each channel of activations and each row of softmax attentions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Results on COCO. We show in Table 3 the quantization results for object detection and instance segmentation on" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16137" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.891, + 0.118 + ], + "angle": 0, + "content": "Table 3. Quantitative results of quantizing Mask R-CNN [14] and Cascade Mask R-CNN [5] using Swin transformers [24] on COCO [21]. We report the box average precision \\(\\mathrm{AP^{box}}\\) for object detection and the mask average precision \\(\\mathrm{AP^{mask}}\\) for instance segmentation." + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.121, + 0.825, + 0.36 + ], + "angle": 0, + "content": "
Method#bits(W/A)Mask R-CNNCascade Mask R-CNN
Swin-TSwin-SSwin-TSwin-SSwin-B
APboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmask
Full-precision32/3246.041.648.543.350.443.751.945.051.945.0
PTQ4ViT [39]4/46.97.026.726.614.713.50.50.510.69.3
APQ-ViT [9]4/423.722.644.740.127.224.447.741.147.641.5
RepQ-ViT [20]4/436.136.044.240.247.041.449.343.1--
IGQ-ViT (#groups=8)4/440.538.544.741.348.442.350.544.050.444.0
IGQ-ViT (#groups=12)4/441.038.844.841.348.542.450.544.050.544.0
PTQ4ViT [39]6/65.86.86.56.614.713.612.510.814.212.9
APQ-ViT [9]6/645.441.247.942.948.642.550.543.950.143.7
RepQ-ViT [20]6/645.141.247.843.050.043.551.444.6--
IGQ-ViT (#groups=8)6/645.441.548.243.150.443.751.944.951.945.0
IGQ-ViT (#groups=12)6/645.541.548.243.250.443.851.945.051.945.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.364, + 0.47, + 0.435 + ], + "angle": 0, + "content": "Table 4. Quantitative comparison of our instance-aware group quantization technique with various configurations under a 4/4-bit setting. We denote by 'Linear' and 'Attention' the quantization method for linear operations and softmax attentions, respectively. For applying our method, we use a group size of 8 for all layers." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.441, + 0.432, + 0.557 + ], + "angle": 0, + "content": "
LinearAttentionViT-SDeiT-BSwin-T
Layer-wiseLayer-wise42.8262.2355.51
Layer-wiseOurs53.6965.0562.27
OursLayer-wise57.3275.5172.89
OursOurs72.9978.8576.91
OursRow-wise73.2278.8877.19
Channel-wiseOurs74.5679.6978.39
Channel-wiseRow-wise74.7379.7478.58
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.749 + ], + "angle": 0, + "content": "COCO [21]. We quantize the backbones of Swin transformers [24] and the convolutional layers in the neck and head of Mask R-CNN [14] and Cascade Mask R-CNN [5]. We observe that PTQ4ViT [39] and APQ-ViT [9], that use layerwise quantizers for activations, do not perform well. In contrast, IGQ-ViT outperforms the state of the art with 8 groups only, and the quantization performance further boosts by exploiting more groups. In particular, it provides the results nearly the same as the full-precision ones for the 6/6-bit setting. This suggests that scale variations across different channels or tokens are much more critical for object detection and instance segmentation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.195, + 0.772 + ], + "angle": 0, + "content": "4.3. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Comparison with different quantizers. We compare in Table 4 the results of the variants of our method adopting different types of quantizers on input activations of FC layers and softmax attentions. From the first four rows, we can see that our approach outperforms layer-wise quantization by a large margin, both for linear operations and softmax attentions. This indicates that adopting a single quantization parameter for all channels and rows without considering" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Table 5. Quantitative comparison of quantizing transformer architectures using various group quantization techniques under a 4/4-bit setting, with a group size of 8 for all linear operations. Note that we use layer-wise quantization for softmax attentions for a fair comparison." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.445, + 0.892, + 0.521 + ], + "angle": 0, + "content": "
Grouping methodsViT-SDeiT-BSwin-T
No grouping (#groups=1)42.8262.2355.51
Grouping consecutive channels [7, 31]41.0465.5070.39
Sorting before grouping channels [4]41.2662.6156.04
Ours57.3275.5172.89
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.892, + 0.663 + ], + "angle": 0, + "content": "their individual distributions can severely limit the quantization performance. The last three rows compare the results of our approach with channel/row-wise quantization. We observe that the difference in performance between our approach and channel/row-wise quantization is less than \\(1.8\\%\\) for three different models. With a small group size, our framework can achieve comparable performance to the upper bound, while maintaining efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.913 + ], + "angle": 0, + "content": "Table 5 shows the results of quantizing ViT architectures using various group quantization techniques, including [4, 7, 31], and ours. While the works of [7, 31] divide consecutive channels uniformly into a number of groups, the method of [4] first sorts channels w.r.t. the dynamic ranges before partitioning them into groups. In contrast, we dynamically assign channels to groups according to the statistical properties of the channels. We find that our approach outperforms other methods by a large margin, indicating that fixing the channels assigned to each group can degrade the quantization performance significantly. We also observe that sorting the channels w.r.t. their dynamic ranges during calibration does not boost the quantization performance for DeiT-B [33] and Swin-T [24], suggesting that the dynamic range of each channel vary drastically across different input instances." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16138" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.27, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.091, + 0.464, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.209, + 0.47, + 0.306 + ], + "angle": 0, + "content": "Figure 5. Top-1 validation accuracies on ImageNet [8] w.r.t. group sizes for linear operations (\\(G_{1}\\), left) and that for softmax attentions (\\(G_{2}\\), right). We set either \\(G_{1}\\) or \\(G_{2}\\) to 8, while varying the other to compute the accuracies. We report the quantization results of ViT-S [10], Swin-T [24], and DeiT-B [33] under a 4/4-bit setting, with a fixed group size across different layers. We visualize the upper bounds with horizontal stripes of corresponding colors." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.323, + 0.47, + 0.351 + ], + "angle": 0, + "content": "Table 6. Quantitative comparison of ViT architectures with and without a group size allocation technique under the 4/4-bit setting." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.355, + 0.437, + 0.482 + ], + "angle": 0, + "content": "
#groupsGroup size allocationViT-SDeiT-BSwin-T
6✓71.4478.4476.31
71.8078.5776.99
8✓72.9978.8576.91
73.1879.0477.19
10✓73.3479.0077.21
73.5179.1977.64
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.66 + ], + "angle": 0, + "content": "Analysis on group size. We show in Fig. 5 the results of IGQ-ViT according to the group size for linear operations (left) and softmax attentions (right). We can see that the quantization performance improves as the group size increases, for both linear operations and softmax attentions, demonstrating that using more groups better addresses the scale variation problem for channels and tokens. We also observe that the performance of our approach reaches near the upper bound with a small group size. This suggests that IGQ-ViT can effectively address the variations with a small amount of additional computations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.468, + 0.828 + ], + "angle": 0, + "content": "Convergence analysis. We compare in Fig. 6(top) distances between channels of activation and quantizers in Eq. (4) (rows of softmax attention and quantizers in Eq. (8)) over optimization steps. It shows that our algorithm converges quickly within a small number of optimization steps. We show in Fig. 6(bottom) the dynamic ranges of activations and attentions in a particular layer, along with their assigned groups after convergence. We can see that activations/attentions in each group share similar statistical properties, demonstrating that they can be effectively quantized with a single quantization parameter." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.83, + 0.468, + 0.906 + ], + "angle": 0, + "content": "Group size allocation. We compare in Table 6 the results of our approach with/without the group size allocation technique. We can see that the group size allocation improves the quantization performance consistently, suggesting that assigning the same group size for all layers is suboptimal." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.091, + 0.693, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.091, + 0.883, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.226, + 0.692, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.227, + 0.882, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.358, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Figure 6. (Top) Distances between channels of activations/rows of softmax attentions and quantizers in a particular layer of DeiT-S [33], that is, the distances as in Eq. (4) and Eq. (8), respectively; (Bottom) Dynamic ranges of activations and attentions in a specific layer of DeiT-S w.r.t. the assigned group of the same color. Note that we sort the activations and attentions based on the group indices for the purpose of the visualization only." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.473, + 0.619, + 0.489 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.775 + ], + "angle": 0, + "content": "We have observed that activations and softmax attentions in ViTs have significant scale variations for individual channels and tokens, respectively, across different input instances. Based on this, we have introduced a instance-aware group quantization framework for ViTs, IGQ-ViT, that alleviates the scale variation problem across channels and tokens. Specifically, our approach splits the activations and softmax attentions dynamically into multiple groups along the channels and tokens, such that each group shares similar statistical properties. It then applies separate quantizers for individual groups. Additionally, we have present a simple yet effective method to assign a group size for each layer adaptively. We have shown that IGQ-ViT outperforms the state of the art, using a small number of groups, with various ViT-based architectures. We have also demonstrated the effectiveness of IGQ-ViT compared with its variants, including layer-wise quantizers, channel/row-wise quantizers, and state-of-the-art group quantizers, with a detailed analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.RS-2022-00143524, Development of Fundamental Technology and Integrated Solution for Next-Generation Automatic Artificial Intelligence System, and No.2021-0-02068, Artificial Intelligence Innovation Hub)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16139" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv, 2016. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.469, + 0.186 + ], + "angle": 0, + "content": "[2] Ron Banner, Yury Nahshan, and Daniel Soudry. 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PTQ methods for convolutional neural networks (CNNs) provide quantization results comparable to full-precision counterparts. Directly applying them to vision transformers (ViTs), however, incurs severe performance degradation, mainly due to the differences in architectures between CNNs and ViTs. In particular, the distribution of activations for each channel varies drastically according to input instances, making PTQ methods for CNNs inappropriate for ViTs. To address this, we introduce instance-aware group quantization for ViTs (IGQ-ViT). To this end, we propose to split the channels of activation maps into multiple groups dynamically for each input instance, such that activations within each group share similar statistical properties. We also extend our scheme to quantize softmax attention across tokens. In addition, the number of groups for each layer is adjusted to minimize the discrepancies between predictions from quantized and full-precision models, under a bit-operation (BOP) constraint. We show extensive experimental results on image classification, object detection, and instance segmentation, with various transformer architectures, demonstrating the effectiveness of our approach. + +# 1. Introduction + +Transformers [34] can capture long-range dependencies across sequential inputs, which is of central importance in natural language processing, aggregating contextual information and providing discriminative feature representations. Recently, vision transformers (ViTs) [10] has demonstrated the effectiveness of transformers for images, providing state-of-the-art results on various visual recognition tasks, including image classification [24, 33], object detection [24, 40], and semantic segmentation [24, 32, 38]. However, a series of fully-connected (FC) and self-attention lay + +![](images/3299d2112c8003088c3ed8b624ede52ebb49e311577409deeb7739a7dac5be89.jpg) +(a) Group quantization + +![](images/447db164dc1a83dbe4434ba4df05629ee2adb069e536154f6243217825c29bc2.jpg) +(b) IGQ-ViT +Figure 1. Visual comparison of group quantization and IGQ-ViT. (a) Conventional group quantization techniques [7, 31] divide consecutive channels uniformly into a number of groups without considering their dynamic ranges. The distribution of activations in each group varies significantly for individual input instances. (b) To alleviate this problem, IGQ-ViT proposes an instance-aware grouping technique that splits the channels of activation maps and softmax attentions across tokens dynamically for each input instance at runtime. + +ers in ViTs requires a substantial amount of memory and computational cost, making it challenging to deploy them on devices with limited resources (e.g., drones and mobile phones). The growing demand for ViTs to operate on the resource-constrained devices has led to increased interest in developing network quantization techniques for ViTs. + +Network quantization generally reduces bit-widths of weights and activations of a model for an efficient inference process, which can be categorized into two groups: Quantization-aware training (QAT) and post-training quantization (PTQ). QAT methods [11, 41, 42] train full-precision models, while simulating the quantization process by inserting discretizers into networks to quantize, such that the discrepancy between the full-precision and quantized models is minimized in terms of accuracy. This suggests that QAT methods require entire training samples, and they are computationally expensive, making them impractical for the prompt deployment of neural networks. PTQ methods [19, 26, 36], on the other hand, calibrate quantization parameters (e.g., quantization intervals, zero-points) from pretrained full-precision models, enabling faster quantization of networks compared to QAT methods with only a + +limited number of training samples (usually less than 1k). + +Several PTQ methods for transformers [9, 25, 39] apply layer-wise quantization techniques, where a single quantizer is applied to all activation values for efficiency. These methods, however, are not directly applicable for quantizing models using extremely low bit-widths (e.g., 4-bit), due to the significant scale variation on the activations for each channel. Exploiting channel-wise quantizers (i.e., applying different quantizers for each channel) could be a potential solution, but at the expense of computational overheads, due to floating-point summations of channel-wise outputs for matrix multiplication. Group quantization techniques [7, 31] could be an alternative to address this problem, where they divide consecutive channels uniformly into multiple groups, and apply a single quantizer for each group (Fig. 1a). However, we have observed that the channel-wise distributions of activation values vary largely among different samples, making conventional approaches inappropriate for ViTs. + +In this paper, we present instance-aware group quantization for ViTs (IGQ-ViT), that effectively and efficiently addresses the variations of channel-wise distributions across different input instances (Fig. 1b). Specifically, we split the channels of activation maps into multiple groups dynamically, such that the activation values within each group share similar statistical properties, and then quantize the activations within the group using identical quantization parameters. We also propose to use the instance-aware grouping technique to softmax attentions, since the distributions of attention values vary significantly according to tokens. In addition, we present a simple yet effective method to optimize the number of groups for individual layers, under a bit-operation (BOP) constraint. IGQ-ViT can be applied to various components in ViTs, including input activations of FC layers and softmax attentions, unlike previous methods [20, 22, 25, 39] that are limited to specific parts of transformer architectures. We demonstrate the effectiveness and efficiency of IGQ-ViT for various transformers, including ViT [10] and its variants [24, 33], and show that IGQ-ViT achieves state-of-the-art results on standard benchmarks. We summarize the main contributions of our work as follows: + +- We introduce a novel PTQ method for ViTs, dubbed IGQ-ViT, that splits channels of activation maps into a number of groups dynamically according to input instances. We also propose to use the instance-aware grouping technique to split softmax attentions across tokens. +- We present a group size allocation technique searching for an optimal number of groups for each layer given a BOP constraint. +- We set a new state of the art on image classification [8], object detection, and instance segmentation [21], with various ViT architectures [10, 24, 33]. + +# 2. Related work + +Network quantization. Network quantization aims at reducing bit-widths of weights and activations of neural networks. QAT methods simulate the quantization process by applying a round function to weights and activations of the network. Since derivatives of the round function is either zero or infinite, they approximate the gradients (e.g., using the straight-through estimator [3]) to train the network with backpropagation. These methods also adjust the derivatives of the round function [17, 18] or train quantization parameters jointly with network weights based on task losses [11, 16]. For better convergence of the training process, many heuristics have been introduced, e.g., progressively shrinking bit-widths [42] or freezing parts of the network weights [28, 41]. Quantized networks using QAT show performance comparable to or even better than full-precision counterparts. However, the quantization process is computationally demanding, requiring a significant amount of training time. PTQ offers an alternative approach to quantizing neural networks. Instead of training full-precision models and simulating the quantization process at training time, PTQ methods calibrate quantization parameters (e.g., quantization intervals) using a subset of training samples. Early efforts focus on optimizing the quantization parameters to minimize the difference between floating-point and quantized values [2, 27]. Another line of research proposes to consider distributions of weights and/or activations to design quantizers. For instance, the work of [12] has observed that network weights follow a bell-shaped distribution. Based on this, it introduces piecewise linear quantizers that assign different quantization intervals according to the magnitudes of activations, performing better compared to uniform quantizers. Recent PTQ methods learn to either round up or down network weights by using a reconstruction error of layer outputs [26] or exploiting the Hessian of training losses [19], and they have proven the effectiveness on CNN architectures (e.g., ResNet [13], MobileNetV2 [30]). + +Transformer quantization. While ViTs [10] and the variants [24, 33] have become increasingly popular in computer vision, the unique structure and characteristics of ViT architectures makes network quantization challenging. For example, PTQ methods for CNNs [2, 19, 26, 27] do not perform well on quantizing softmax attentions and GELU activations in transformers, suggesting that directly applying them for ViT quantization results in significant performance degradation [25]. To date, only a limited number of PTQ methods have been developed for ViTs. The work of [25] estimates quantization parameters that maximize similarities between full-precision and quantized outputs of linear operations, and proposes to preserve a relative order of attention values after quantization. APQ-ViT [9] introduces a calibration metric to minimize the discrepancies + +between full-precision and quantized outputs, while maintaining the power-law distribution of softmax attentions. PTQ4ViT [39] introduces twin uniform quantizers to handle asymmetric distributions in softmax attentions and GELU activations effectively. Most PTQ methods for ViTs exploit a single quantizer for all channels, suggesting that they do not consider the distributions of activation values across channels, typically having extreme scale variations. Recent works [20, 22] attempt to alleviate the scale variation problem efficiently. FQ-ViT [22] proposes to consider inter-channel scale variations for LayerNorm [1], and exploits channel-wise quantizers with the constraint of the ratio of quantization intervals being power-of-two values. This enables using bit-shift operations, calculating mean and variance of LayerNorm in an integer level. The scale reparameterization technique, introduced by RepQ-ViT [20], allows to use layer-wise quantizers, instead of adopting channelwise ones, by adjusting the affine factors of LayerNorm and the weights of FC layers. However, this technique applies to the activations for LayerNorm only, and does not fully address the inter-channel scale variations for other layers in transformers. + +Similar to ours, the works of [4, 7, 31, 35] adopt group quantization techniques for transformers. For instance, Qbert [31] and VS-quant [7] divide consecutive channels uniformly into a number of groups without considering the dynamic range of each channel, and thus the channels assigned to each group do not follow similar distributions. PEG [4] alleviates this issue by sorting the activations across channels w.r.t. the dynamic ranges during calibration, before grouping the channels. Quantformer [35] proposes to use a differentiable search [6, 23] for QAT in order to group channels of activation maps. The channels assigned to particular groups are however fixed after calibrating pretrained networks for PTQ in the group quantization techniques [4, 7, 31], which makes them inappropriate for ViTs having diverse channel distributions according to input instances. In contrast, our approach apply group quantization along channels of activation maps and tokens of softmax attentions dynamically at runtime for each input instance, without additional parameters for PTQ. + +# 3. Method + +In this section, we provide a brief description of uniform quantizer (Sec. 3.1). We then present our approach in detail, including IGQ-ViT (Sec. 3.2) and a group size allocation technique (Sec. 3.3). + +# 3.1. Uniform quantizer + +Given a floating-point value $x$ and the quantization bitwidth $b$ , uniform quantizers discretize the inputs into a finite set of values with equally spaced intervals. To this end, it normalizes the floating-point value $x$ using a scale param + +![](images/e1e417b0529afc47b8a0dd7d2bbb304cbb6023043b9425b0a0ea413617ad8071.jpg) +(a) + +![](images/82293fe0e4edef98ec7d48642753494d0bdd6d4199c0caee841ecea36a3e22fe.jpg) +(b) +Figure 2. (a) Plots of standard deviations of activations across channels for DeiT-S [33]; (b-c) Boxplots of activation values across different input instances for a particular channel of ResNet-50 [13] and DeiT-S, respectively. We use ImageNet [8] for the visualizations. We have observed that there is a significant scale variation across channels, and the activation ranges for each channel change drastically among different samples for ViTs, in contrast to CNNs. + +![](images/0c437cdcdad15ce15a7cbf9e20ce3efe2e1c5dadff6b9b939e625b8bbf18dd18.jpg) +(c) + +eter $s$ , calibrate the normalized value with a zero-point $z$ , and clip the output as follows: + +$$ +\hat {x} = \operatorname {c l i p} \left(\left\lfloor \frac {x}{s} \right\rceil + z, 0, 2 ^ {b} - 1\right), \tag {1} +$$ + +where the scale parameter $s$ and zero-point $z$ are defined as: + +$$ +s = \frac {u - l}{2 ^ {b} - 1}, \quad z = \operatorname {c l i p} \left(\left\lfloor - \frac {l}{s} \right\rfloor , 0, 2 ^ {b} - 1\right). \tag {2} +$$ + +We denote by $u$ and $l$ upper and lower bounds of the quantizer, respectively. $\lfloor .\rfloor$ is a rounding function, and $\operatorname{clip}(.,m,n)$ restricts an input to the range with lower and upper bounds of $m$ and $n$ , respectively. The quantized output is then obtained as follows: + +$$ +Q (x; s, z) = s (\hat {x} - z). \tag {3} +$$ + +# 3.2. IGQ-ViT + +Following the work of [25], we quantize all network weights except for the positional embedding. We also quantize input activations of FC layers in the multi-layer perceptron (MLP) block, and the activations for the multi-head self-attention (MSA) block, including queries, keys, values, and softmax attentions. We exploit uniform quantizers for all weights and activations in ViTs. + +# 3.2.1 IGQ for linear operations + +In the following, we first provide empirical observations on input activations of FC layers, and explain the details of our IGQ framework for linear operations. + +Distributions of activations across channels. Most quantization frameworks [2, 19, 25, 26] exploit layer-wise quantizers for activations, applying a single quantization parameter for all channels for efficient inference. However, we have observed that the input activations of FC layers have significant scale variations across channels (Fig. 2(a)). Similar findings can be found in [20, 22]. This suggests + +that layer-wise quantizers degrade the quantization performance significantly, as they cannot handle scale variations across different channels. Although adopting separate quantizers for individual channels could be an effective strategy for overcoming the scale variation problem, this requires a summation of a floating-point output for every channel, which is computationally expensive. We have also found that the ranges of these activations for each channel vary drastically among different input instances (Fig. 2(b, c)), since ViTs do not have preceding BatchNorm [15] layers in contrast to state-of-the-art CNNs (e.g., ResNet [13], MobileNetV2 [30]). Conventional approaches (e.g., [4, 7, 31, 35]) exploit a fixed quantization interval (i.e., from lower to upper bounds of the quantizer) for every input instance, thus cannot adapt to such diverse distributions across different samples. + +Instance-aware grouping across channels. We introduce an instance-aware group quantization framework for linear operations that alleviates the scale variation problem, while maintaining efficiency. We split the channels of activation maps into $G_{1}$ groups based on statistical properties, where activation values within each group are quantized with identical quantization parameters. We assign the channels of activations to appropriate groups, and optimize the scale parameter $s_i$ and the zero-point $z_{i}$ for the $i$ -th group. Specifically, given floating-point activations of $\mathbf{X}\in \mathbb{R}^{N\times C}$ and a set of candidate quantizers $\{Q_i\}_{i = 1}^{G_1}$ , where we denote by $N$ and $C$ as the number of tokens and channels, respectively, we define a distance metric between the $c$ -th channel of the activations $\mathbf{X}$ , denoted by $\mathbf{X}_c$ , and the quantizer $Q_{i}$ as follows: + +$$ +d \left(\mathbf {X} _ {c}, Q _ {i}\right) = \left(\min \left(\mathbf {X} _ {c}\right) - u _ {i}\right) ^ {2} + \left(\max \left(\mathbf {X} _ {c}\right) - l _ {i}\right) ^ {2} \tag {4} +$$ + +where $u_{i}$ and $l_{i}$ are upper and lower bounds of the quantizer $Q_{i}$ , respectively. We then assign each channel of the activation $\mathbf{X}$ to one of candidate quantizers with the minimum distance as follows: + +$$ +\pi (c) = \underset {i} {\arg \min } d \left(\mathbf {X} _ {c}, Q _ {i}\right) \tag {5} +$$ + +where we denote by $\pi (c)$ a group index assigned to the $c$ -th channel. The upper and lower bounds of quantizers are then optimized by minimizing the distances as follows: + +$$ +u _ {i} ^ {*}, l _ {i} ^ {*} = \underset {u _ {i}, l _ {i}} {\arg \min } \sum_ {\pi (c) = i} d \left(\mathbf {X} _ {c}, Q _ {i}\right). \tag {6} +$$ + +We optimize $u_{i}$ and $l_{i}$ by solving Eq. (5) and Eq. (6) alternately similar to the expectation-maximization (EM) algorithm, which guarantees the convergence [37]. Finally, we obtain quantization parameters of each group (i.e., s and z) using Eq. (2). At test time, we fix the quantization parameters, and assign the channels to appropriate groups using Eq. (5). + +Table 1. Comparison of BOPs for a 4-bit DeiT-B [33] model using various quantization strategies. We denote by 'Model' the required BOP for layer-wise quantization. In contrast to layer-wise quantization, IGQ-ViT involves additional computations, including (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the outputs of each group in a floating-point format. The corresponding BOPs for these steps are denoted by 'Minmax', 'Assign', and 'FP sum', respectively. + +
MethodsModel Minmax Assign FP sumTotal
Layer-wise340.3G---340.3G
IGQ-ViT(#groups=4)340.3G0.99G0.57G1.57G343.4G
IGQ-ViT(#groups=8)340.3G0.99G1.14G3.66G346.1G
IGQ-ViT(#groups=16)340.3G0.99G2.28G7.84G351.4G
+ +Computational overhead. Compared to layer-wise quantization, our approach requires (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the floating-point outputs of each group. Specifically, consider a matrix multiplication between a quantized activation $Q(\mathbf{X})$ and the quantized weight $Q(\mathbf{W})$ with a group size of $G_{1}$ . The quantized activation $Q(\mathbf{X})$ is obtained by partitioning $\mathbf{X}$ into a number of groups across channels using Eq. (5), i.e. $\mathbf{X} = [\mathbf{X}_1, \dots, \mathbf{X}_{G_1}]$ , followed by quantizing $\mathbf{X}_i$ with a scale parameter of $s_i$ , where $i \in \{1, \dots, G_1\}$ . The matrix multiplication between $Q(\mathbf{X})$ and $Q(\mathbf{W})$ can then be represented as follows: + +$$ +Q (\mathbf {X}) Q (\mathbf {W}) = s ^ {w} \cdot \left(\sum_ {i = 1} ^ {G _ {1}} s _ {i} \cdot \hat {\mathbf {X}} _ {i} \hat {\mathbf {W}} _ {i}\right). \tag {7} +$$ + +Note that we omit zero-points for clarity. We denote by $s^w$ the scale parameter for $\mathbf{W}$ . $\hat{\mathbf{X}}_i$ and $\hat{\mathbf{W}}_i$ are obtained by applying Eq. (1) to $\mathbf{X}_i$ and $\mathbf{W}_i$ , the channels and rows of $\mathbf{X}$ and $\mathbf{W}$ associated with group $i$ , respectively. Computing Eq. (7) requires the summation of floating-point matrices for each group (i.e., $s_i \cdot \hat{\mathbf{X}}_i\hat{\mathbf{W}}_i$ ), which can be reduced with sufficiently small values of $G_1$ . As the values of $G_1$ , we use no more than 16 in our experiments, which is extremely small compared to the number of channels, usually scaling up to over a thousand. We show in Table 1 BOPs of IGQ-ViT for DeiT-B [33] quantized with 4-bit. We can see that IGQ-ViT introduces only $3.3\%$ additional BOPs for a group size of 16, compared to layer-wise quantization. + +# 3.2.2 IGQ for softmax attentions + +Here, we present our observation for the distribution of softmax attentions, and present the details of IGQ for softmax attentions. + +Distributions of softmax attentions. ViTs capture correlations between tokens through softmax attentions. The distribution of attention values varies drastically across different tokens (Fig. 3). Therefore, using a single quantization + +![](images/8d69f8e5a5949ce8ca4c844ff4bf832dfff5ffc5669c66bf85803e31a786215f.jpg) +Figure 3. Distributions of softmax attentions across tokens. We can see that the distributions are different significantly across tokens. Our approach can handle this issue by splitting the rows of softmax attentions into several groups and applying separate quantizers for each group, such that the attentions assigned to each group share similar statistical properties. + +![](images/73b50d009c4796d34b5b8f9a75f3f0283e767588cc035d5a325398cb19eb621d.jpg) +Figure 4. Comparisons for dynamic ranges of activation values across channels, chosen from different layers of ViT-S [10]. $\sigma_{range}$ is the standard deviation of the dynamic ranges of channels for each layer. We can see that the degree of scale variations across channels varies according to the layer, suggesting that the number of groups for each layer would be adjusted. + +![](images/fb66275e92b7578f58e998e09504c1861764725f9dd46057fc4ac53dc385d836.jpg) + +parameter to quantize softmax attentions degrades quantization performance severely. Separate quantizers might be exploited for individual tokens to handle the attention values, but this requires a large number of quantizers, and needs to adjust the quantization parameters for each instance. + +Instance-aware grouping across tokens. We extend our approach in order to quantize softmax attentions across tokens. We split softmax attentions for tokens (i.e., the rows of the softmax attentions) into $G_{2}$ groups, according to the distribution of attention values. Specifically, given softmax attentions $\mathbf{A} \in \mathbb{R}^{H \times N \times N}$ and a set of quantizers $\{Q_{j}\}_{j=1}^{G_{2}}$ , where we denote by $H$ the number of heads, we define the distance between each row of softmax attentions and a quantizer $Q_{j}$ as follows: + +$$ +d \left(\mathbf {A} _ {n}, Q _ {j}\right) = \left(\max \left(\mathbf {A} _ {n}\right) - v _ {j}\right) ^ {2} \tag {8} +$$ + +where we denote by $\mathbf{A}_n$ and $v_{j}$ the $n$ -th row of $\mathbf{A}$ and the upper bound of the quantizer $Q_{j}$ , respectively. Note that we set lower bounds to 0, as all attention values are positive. We then optimize $v_{j}$ with the EM algorithm and set the quantization parameters for quantizer $Q_{j}$ using Eq. (2). + +# Algorithm 1 IGQ-ViT + +1: Hyperparameter: Number of iterations $N_{\mathrm{iter}}$ ; update period of group size $T$ . +Input: Pre-trained model; calibration set; target BOPs $N_{bop}$ +2: For inputs of FC layers and softmax attentions, compute the distance between their channels/rows and quantizers using Eq. (4) or Eq. (8). +3: for $k = 1, \dots, N_{\mathrm{iter}}$ do +4: Update the parameters for each group using Eq. (5) and Eq. (6). +5: if $k\% T == 0$ then +6: Update the group size for each layer using Eq. (10). +7: end if +8: end for +9: Obtain quantization parameters $\mathbf{s}$ , $\mathbf{z}$ using Eq. (2). +10: Output: Quantized model + +# 3.3. Group size allocation + +We observe that activations and softmax attentions in different layers show different amount of scale variations across channels and tokens, respectively, indicating that using the same number of groups for different layers might be suboptimal (Fig. 4). To address this, we search for the optimal group size for each layer that minimizes the discrepancy between the predictions from quantized and full-precision models, under a BOP constraint. However, the search space for finding the optimal group sizes is exponential w.r.t. the number of layers $L$ , which is intractable for a large model. We propose a group size allocation technique that efficiently optimizes the group size for each layer within such a large search space. Concretely, we define a perturbation metric for a particular layer $\psi(.)$ as the Kullback-Leibler (KL) divergence between predictions of the model before and after quantization as follows: + +$$ +\psi (g, l) = D _ {\mathrm {K L}} \left(y _ {l} \| y _ {l} ^ {g}\right), \tag {9} +$$ + +where we denote by $y_{l}$ and $y_{l}^{g}$ the predictions of the model before and after quantizing $l$ -th layer with a group size of $g$ , respectively. Note that we quantize all other layers except for the $l$ -th layer for computing the predictions of $y_{l}$ and $y_{l}^{g}$ , to account for the effects of quantization on different layers. For a target BOP $N_{bop}$ , we formulate the group size allocation as a integer linear programming (ILP) problem, and search for the optimal group size for each layer, such that an overall perturbation of the model is minimized as follows: + +$$ +\mathbf {g} ^ {*} = \arg \min _ {\mathbf {g}} \sum_ {l = 1} ^ {L} \psi (g _ {l}, l) \text {s . t .} B (\mathbf {g}) \leq N _ {b o p}, \tag {10} +$$ + +where $\mathbf{g} = \{g_l\}_{l=1}^L$ , and $g_l$ is the group size assigned to $l$ -th layer. We denote by $B(\mathbf{g})$ the BOP of the model with the + +Table 2. Quantitative results of quantizing ViT architectures on ImageNet [8]. W/A represents the bit-width of weights (W) and activations (A), respectively. We report the top-1 validation accuracy $(\%)$ with different group sizes for comparison. The numbers of other quantization methods are taken from [9, 20]. $\dagger$ : Results without using a group size allocation (i.e., a fixed group size for all layers). + +
Method#bits(W/A)ViT-TViT-SViT-BDeiT-TDeiT-SDeiT-BSwin-TSwin-SSwin-B
Full-precision32/3275.4781.3984.5472.2179.8581.8081.3983.2385.27
PTQ4ViT [39]4/417.4542.5730.6936.9634.0864.39-76.0974.02
APQ-ViT [9]4/417.5647.9541.4147.9443.5567.48-77.1576.48
RepQ-ViT [20]4/4-65.0568.4857.4369.0375.61-79.4578.32
IGQ-ViT† (#groups=8)4/454.4672.9977.9161.9474.0178.8576.9180.5482.88
IGQ-ViT† (#groups=12)4/455.6673.4679.1362.2874.5279.2177.5380.7983.08
IGQ-ViT (#groups=8)4/455.2973.1878.2862.2574.2379.0477.1980.6683.02
IGQ-ViT (#groups=12)4/456.0173.6179.3262.4574.6679.2377.7780.9883.14
IGQ-ViT (upper bound)4/457.5974.7379.8862.5575.0879.7478.5881.4883.53
PTQ4ViT [39]6/664.4678.6381.6569.6876.2880.25-82.3884.01
APQ-ViT [9]6/669.5579.1082.2170.4977.7680.42-82.6784.18
RepQ-ViT [20]6/6-80.4383.6270.7678.9081.27-82.7984.57
IGQ-ViT† (#groups=8)6/672.9080.0783.1170.7178.9281.3480.2382.5584.43
IGQ-ViT† (#groups=12)6/673.6380.6683.6371.0279.1781.4880.5982.6684.70
IGQ-ViT (#groups=8)6/673.1980.4883.4670.9279.0481.4480.4882.6584.62
IGQ-ViT (#groups=12)6/673.7780.7683.7771.1579.2881.7180.8982.8684.82
IGQ-ViT (upper bound)6/674.6180.9984.2771.4279.4281.7581.2083.0885.06
+ +group sizes of $\mathbf{g}$ . We solve Eq. (10) with the PULP [29] library, using group size for each layer within the set of $\{4,6,8,10,12,16\}$ . We allocate the group sizes for every $T$ alternating steps of Eq. (5) and Eq. (6), where $T$ is a hyperparameter. We show in Algorithm 1 an overall quantization process of our approach. + +# 4. Experiments + +In this section, we describe our experimental settings (Sec. 4.1), and evaluate IGQ-ViT on image classification, object detection and semantic segmentation (Sec. 4.2). We then present a detailed analysis of our approach (Sec. 4.3). + +# 4.1. Implementation details + +We evaluate our IGQ-ViT framework on the tasks of image classification, object detection, and instance segmentation. We use the ImageNet [8] dataset for image classification, which contains approximately 1.2M images for training, and 50K for validation. We use COCO [21] for object detection and instance segmentation, which includes 118K training, 5K validation, and 20K test images. We adopt various transformer architectures, including ViT [10], DeiT [33], and Swin transformer [24], for image classification. For the tasks of object detection and instance segmentation, we use Mask R-CNN [14] and Cascade Mask R-CNN [5] with Swin transformers as the backbone. Following [9, 20], we randomly sample 32 images from the ImageNet [8] dataset for image classification, and a single image from COCO [21] for object detection and instance + +segmentation to calibrate the quantization parameters. We apply our instance-aware grouping technique for all input activations of FC layers, and softmax attentions. More detailed settings are available in the supplement. + +# 4.2. Results + +Results on ImageNet. We show in Table 2 the top-1 accuracy $(\%)$ on the validation split of ImageNet [8] with various ViT architectures. We report the accuracy with an average group size of 8 and 12. We summarize our findings as follows: (1) Our IGQ-ViT framework with 8 groups already outperforms the state of the art except for ViT-B [10] and Swin-S [24] under 6/6-bit setting, while using more groups further boosts the performance. (2) Our approach under 4/4-bit setting consistently outperforms RepQ-ViT [20] by a large margin. Similar to ours, RepQ-ViT also addresses the scale variations between channels, but it can be applied to the activations with preceding LayerNorm only. In contrast, our method handles the scale variations on all input activations of FC layers and softmax attentions, providing better results. (3) Our group size allocation technique boosts the quantization performance for all models, indicating that using the same number of groups for all layers is suboptimal. (4) Exploiting 12 groups for our approach incurs less than $0.9\%$ accuracy drop, compared to the upper bound under the 6/6-bit setting. Note that the results of upper bound are obtained by using a separate quantizer for each channel of activations and each row of softmax attentions. + +Results on COCO. We show in Table 3 the quantization results for object detection and instance segmentation on + +Table 3. Quantitative results of quantizing Mask R-CNN [14] and Cascade Mask R-CNN [5] using Swin transformers [24] on COCO [21]. We report the box average precision $\mathrm{AP^{box}}$ for object detection and the mask average precision $\mathrm{AP^{mask}}$ for instance segmentation. + +
Method#bits(W/A)Mask R-CNNCascade Mask R-CNN
Swin-TSwin-SSwin-TSwin-SSwin-B
APboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmask
Full-precision32/3246.041.648.543.350.443.751.945.051.945.0
PTQ4ViT [39]4/46.97.026.726.614.713.50.50.510.69.3
APQ-ViT [9]4/423.722.644.740.127.224.447.741.147.641.5
RepQ-ViT [20]4/436.136.044.240.247.041.449.343.1--
IGQ-ViT (#groups=8)4/440.538.544.741.348.442.350.544.050.444.0
IGQ-ViT (#groups=12)4/441.038.844.841.348.542.450.544.050.544.0
PTQ4ViT [39]6/65.86.86.56.614.713.612.510.814.212.9
APQ-ViT [9]6/645.441.247.942.948.642.550.543.950.143.7
RepQ-ViT [20]6/645.141.247.843.050.043.551.444.6--
IGQ-ViT (#groups=8)6/645.441.548.243.150.443.751.944.951.945.0
IGQ-ViT (#groups=12)6/645.541.548.243.250.443.851.945.051.945.0
+ +Table 4. Quantitative comparison of our instance-aware group quantization technique with various configurations under a 4/4-bit setting. We denote by 'Linear' and 'Attention' the quantization method for linear operations and softmax attentions, respectively. For applying our method, we use a group size of 8 for all layers. + +
LinearAttentionViT-SDeiT-BSwin-T
Layer-wiseLayer-wise42.8262.2355.51
Layer-wiseOurs53.6965.0562.27
OursLayer-wise57.3275.5172.89
OursOurs72.9978.8576.91
OursRow-wise73.2278.8877.19
Channel-wiseOurs74.5679.6978.39
Channel-wiseRow-wise74.7379.7478.58
+ +COCO [21]. We quantize the backbones of Swin transformers [24] and the convolutional layers in the neck and head of Mask R-CNN [14] and Cascade Mask R-CNN [5]. We observe that PTQ4ViT [39] and APQ-ViT [9], that use layerwise quantizers for activations, do not perform well. In contrast, IGQ-ViT outperforms the state of the art with 8 groups only, and the quantization performance further boosts by exploiting more groups. In particular, it provides the results nearly the same as the full-precision ones for the 6/6-bit setting. This suggests that scale variations across different channels or tokens are much more critical for object detection and instance segmentation. + +# 4.3. Discussion + +Comparison with different quantizers. We compare in Table 4 the results of the variants of our method adopting different types of quantizers on input activations of FC layers and softmax attentions. From the first four rows, we can see that our approach outperforms layer-wise quantization by a large margin, both for linear operations and softmax attentions. This indicates that adopting a single quantization parameter for all channels and rows without considering + +Table 5. Quantitative comparison of quantizing transformer architectures using various group quantization techniques under a 4/4-bit setting, with a group size of 8 for all linear operations. Note that we use layer-wise quantization for softmax attentions for a fair comparison. + +
Grouping methodsViT-SDeiT-BSwin-T
No grouping (#groups=1)42.8262.2355.51
Grouping consecutive channels [7, 31]41.0465.5070.39
Sorting before grouping channels [4]41.2662.6156.04
Ours57.3275.5172.89
+ +their individual distributions can severely limit the quantization performance. The last three rows compare the results of our approach with channel/row-wise quantization. We observe that the difference in performance between our approach and channel/row-wise quantization is less than $1.8\%$ for three different models. With a small group size, our framework can achieve comparable performance to the upper bound, while maintaining efficiency. + +Table 5 shows the results of quantizing ViT architectures using various group quantization techniques, including [4, 7, 31], and ours. While the works of [7, 31] divide consecutive channels uniformly into a number of groups, the method of [4] first sorts channels w.r.t. the dynamic ranges before partitioning them into groups. In contrast, we dynamically assign channels to groups according to the statistical properties of the channels. We find that our approach outperforms other methods by a large margin, indicating that fixing the channels assigned to each group can degrade the quantization performance significantly. We also observe that sorting the channels w.r.t. their dynamic ranges during calibration does not boost the quantization performance for DeiT-B [33] and Swin-T [24], suggesting that the dynamic range of each channel vary drastically across different input instances. + +![](images/a5514b5d87b22119b31a6723e59d44fc9a270688ea1e21cb9da2d4b262470921.jpg) +Figure 5. Top-1 validation accuracies on ImageNet [8] w.r.t. group sizes for linear operations ( $G_{1}$ , left) and that for softmax attentions ( $G_{2}$ , right). We set either $G_{1}$ or $G_{2}$ to 8, while varying the other to compute the accuracies. We report the quantization results of ViT-S [10], Swin-T [24], and DeiT-B [33] under a 4/4-bit setting, with a fixed group size across different layers. We visualize the upper bounds with horizontal stripes of corresponding colors. + +![](images/8266ec5bb5e81b24f73aca7f8f533efd086f741a8c633fc1d41f48408e02b850.jpg) + +Table 6. Quantitative comparison of ViT architectures with and without a group size allocation technique under the 4/4-bit setting. + +
#groupsGroup size allocationViT-SDeiT-BSwin-T
6✓71.4478.4476.31
71.8078.5776.99
8✓72.9978.8576.91
73.1879.0477.19
10✓73.3479.0077.21
73.5179.1977.64
+ +Analysis on group size. We show in Fig. 5 the results of IGQ-ViT according to the group size for linear operations (left) and softmax attentions (right). We can see that the quantization performance improves as the group size increases, for both linear operations and softmax attentions, demonstrating that using more groups better addresses the scale variation problem for channels and tokens. We also observe that the performance of our approach reaches near the upper bound with a small group size. This suggests that IGQ-ViT can effectively address the variations with a small amount of additional computations. + +Convergence analysis. We compare in Fig. 6(top) distances between channels of activation and quantizers in Eq. (4) (rows of softmax attention and quantizers in Eq. (8)) over optimization steps. It shows that our algorithm converges quickly within a small number of optimization steps. We show in Fig. 6(bottom) the dynamic ranges of activations and attentions in a particular layer, along with their assigned groups after convergence. We can see that activations/attentions in each group share similar statistical properties, demonstrating that they can be effectively quantized with a single quantization parameter. + +Group size allocation. We compare in Table 6 the results of our approach with/without the group size allocation technique. We can see that the group size allocation improves the quantization performance consistently, suggesting that assigning the same group size for all layers is suboptimal. + +![](images/b17e847c276b60c2d5b2b0009a694d5d446a3643a3dd023132fa5103c4908023.jpg) + +![](images/bb9483e1aa3b2ea1ceec35d4f59181b5bfe537602ed3b0378ee86e7df391b3b4.jpg) + +![](images/2a2b587bd3f02daf335a7da6dc387fb60ba56787b1dc9bfb6ecd2f37ac39548c.jpg) +Figure 6. (Top) Distances between channels of activations/rows of softmax attentions and quantizers in a particular layer of DeiT-S [33], that is, the distances as in Eq. (4) and Eq. (8), respectively; (Bottom) Dynamic ranges of activations and attentions in a specific layer of DeiT-S w.r.t. the assigned group of the same color. Note that we sort the activations and attentions based on the group indices for the purpose of the visualization only. + +![](images/0b65bd812c2837a8f9dced58fc5e2d4cfb7b772f92ee0031fbf556977e1b5a56.jpg) + +# 5. Conclusion + +We have observed that activations and softmax attentions in ViTs have significant scale variations for individual channels and tokens, respectively, across different input instances. Based on this, we have introduced a instance-aware group quantization framework for ViTs, IGQ-ViT, that alleviates the scale variation problem across channels and tokens. Specifically, our approach splits the activations and softmax attentions dynamically into multiple groups along the channels and tokens, such that each group shares similar statistical properties. It then applies separate quantizers for individual groups. Additionally, we have present a simple yet effective method to assign a group size for each layer adaptively. We have shown that IGQ-ViT outperforms the state of the art, using a small number of groups, with various ViT-based architectures. We have also demonstrated the effectiveness of IGQ-ViT compared with its variants, including layer-wise quantizers, channel/row-wise quantizers, and state-of-the-art group quantizers, with a detailed analysis. + +Acknowledgements. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.RS-2022-00143524, Development of Fundamental Technology and Integrated Solution for Next-Generation Automatic Artificial Intelligence System, and No.2021-0-02068, Artificial Intelligence Innovation Hub). + +# References + +[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv, 2016. 3 +[2] Ron Banner, Yury Nahshan, and Daniel Soudry. Post training 4-bit quantization of convolutional networks for rapid-deployment. In NeurIPS, 2019. 2, 3 +[3] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv, 2013. 2 +[4] Yelysei Bondarenko, Markus Nagel, and Tijmen Blankevoort. Understanding and overcoming the challenges of efficient transformer quantization. EMNLP, 2021. 3, 4, 7 +[5] Zhaowei Cai and Nuno Vasconcelos. 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In ECCV, 2022. 2, 3, 6, 7 +[40] Zixiao Zhang, Xiaoqiang Lu, Guojin Cao, Yuting Yang, Licheng Jiao, and Fang Liu. Vit-yolo: Transformer-based yolo for object detection. In ICCV, 2021. 1 +[41] Aojun Zhou, Anbang Yao, Yiwen Guo, Lin Xu, and Yurong Chen. Incremental network quantization: Towards lossless cnns with low-precision weights. In ICLR, 2017. 1, 2 +[42] Bohan Zhuang, Chunhua Shen, Mingkui Tan, Lingqiao Liu, and Ian Reid. Towards effective low-bitwidth convolutional neural networks. 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PTQ methods for convolutional neural networks (CNNs) provide quantization results comparable to full-precision counterparts. Directly applying them to vision transformers (ViTs), however, incurs severe performance degradation, mainly due to the differences in architectures between CNNs and ViTs. In particular, the distribution of activations for each channel varies drastically according to input instances, making PTQ methods for CNNs inappropriate for ViTs. To address this, we introduce instance-aware group quantization for ViTs (IGQ-ViT). To this end, we propose to split the channels of activation maps into multiple groups dynamically for each input instance, such that activations within each group share similar statistical properties. We also extend our scheme to quantize softmax attention across tokens. In addition, the number of groups for each layer is adjusted to minimize the discrepancies between predictions from quantized and full-precision models, under a bit-operation (BOP) constraint. We show extensive experimental results on image classification, object detection, and instance segmentation, with various transformer architectures, demonstrating the effectiveness of our approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 554, + 128, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 128, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 128, + 566 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": "Transformers [34] can capture long-range dependencies across sequential inputs, which is of central importance in natural language processing, aggregating contextual information and providing discriminative feature representations. Recently, vision transformers (ViTs) [10] has demonstrated the effectiveness of transformers for images, providing state-of-the-art results on various visual recognition tasks, including image classification [24, 33], object detection [24, 40], and semantic segmentation [24, 32, 38]. However, a series of fully-connected (FC) and self-attention lay" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 315, + 217, + 419, + 306 + ], + "blocks": [ + { + "bbox": [ + 315, + 217, + 419, + 306 + ], + "lines": [ + { + "bbox": [ + 315, + 217, + 419, + 306 + ], + "spans": [ + { + "bbox": [ + 315, + 217, + 419, + 306 + ], + "type": "image", + "image_path": "3299d2112c8003088c3ed8b624ede52ebb49e311577409deeb7739a7dac5be89.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 314, + 403, + 324 + ], + "lines": [ + { + "bbox": [ + 328, + 314, + 403, + 324 + ], + "spans": [ + { + "bbox": [ + 328, + 314, + 403, + 324 + ], + "type": "text", + "content": "(a) Group quantization" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 430, + 217, + 545, + 310 + ], + "blocks": [ + { + "bbox": [ + 430, + 217, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 430, + 217, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 430, + 217, + 545, + 310 + ], + "type": "image", + "image_path": "447db164dc1a83dbe4434ba4df05629ee2adb069e536154f6243217825c29bc2.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 465, + 314, + 508, + 324 + ], + "lines": [ + { + "bbox": [ + 465, + 314, + 508, + 324 + ], + "spans": [ + { + "bbox": [ + 465, + 314, + 508, + 324 + ], + "type": "text", + "content": "(b) IGQ-ViT" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 331, + 547, + 430 + ], + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 430 + ], + "type": "text", + "content": "Figure 1. Visual comparison of group quantization and IGQ-ViT. (a) Conventional group quantization techniques [7, 31] divide consecutive channels uniformly into a number of groups without considering their dynamic ranges. The distribution of activations in each group varies significantly for individual input instances. (b) To alleviate this problem, IGQ-ViT proposes an instance-aware grouping technique that splits the channels of activation maps and softmax attentions across tokens dynamically for each input instance at runtime." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 447, + 547, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 547, + 519 + ], + "type": "text", + "content": "ers in ViTs requires a substantial amount of memory and computational cost, making it challenging to deploy them on devices with limited resources (e.g., drones and mobile phones). The growing demand for ViTs to operate on the resource-constrained devices has led to increased interest in developing network quantization techniques for ViTs." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": "Network quantization generally reduces bit-widths of weights and activations of a model for an efficient inference process, which can be categorized into two groups: Quantization-aware training (QAT) and post-training quantization (PTQ). QAT methods [11, 41, 42] train full-precision models, while simulating the quantization process by inserting discretizers into networks to quantize, such that the discrepancy between the full-precision and quantized models is minimized in terms of accuracy. This suggests that QAT methods require entire training samples, and they are computationally expensive, making them impractical for the prompt deployment of neural networks. PTQ methods [19, 26, 36], on the other hand, calibrate quantization parameters (e.g., quantization intervals, zero-points) from pretrained full-precision models, enabling faster quantization of networks compared to QAT methods with only a" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16132" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 282, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 282, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 282, + 85 + ], + "type": "text", + "content": "limited number of training samples (usually less than 1k)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 287, + 301 + ], + "type": "text", + "content": "Several PTQ methods for transformers [9, 25, 39] apply layer-wise quantization techniques, where a single quantizer is applied to all activation values for efficiency. These methods, however, are not directly applicable for quantizing models using extremely low bit-widths (e.g., 4-bit), due to the significant scale variation on the activations for each channel. Exploiting channel-wise quantizers (i.e., applying different quantizers for each channel) could be a potential solution, but at the expense of computational overheads, due to floating-point summations of channel-wise outputs for matrix multiplication. Group quantization techniques [7, 31] could be an alternative to address this problem, where they divide consecutive channels uniformly into multiple groups, and apply a single quantizer for each group (Fig. 1a). However, we have observed that the channel-wise distributions of activation values vary largely among different samples, making conventional approaches inappropriate for ViTs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 304, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 289, + 579 + ], + "type": "text", + "content": "In this paper, we present instance-aware group quantization for ViTs (IGQ-ViT), that effectively and efficiently addresses the variations of channel-wise distributions across different input instances (Fig. 1b). Specifically, we split the channels of activation maps into multiple groups dynamically, such that the activation values within each group share similar statistical properties, and then quantize the activations within the group using identical quantization parameters. We also propose to use the instance-aware grouping technique to softmax attentions, since the distributions of attention values vary significantly according to tokens. In addition, we present a simple yet effective method to optimize the number of groups for individual layers, under a bit-operation (BOP) constraint. IGQ-ViT can be applied to various components in ViTs, including input activations of FC layers and softmax attentions, unlike previous methods [20, 22, 25, 39] that are limited to specific parts of transformer architectures. We demonstrate the effectiveness and efficiency of IGQ-ViT for various transformers, including ViT [10] and its variants [24, 33], and show that IGQ-ViT achieves state-of-the-art results on standard benchmarks. We summarize the main contributions of our work as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 582, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 45, + 582, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 582, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 45, + 582, + 287, + 641 + ], + "type": "text", + "content": "- We introduce a novel PTQ method for ViTs, dubbed IGQ-ViT, that splits channels of activation maps into a number of groups dynamically according to input instances. We also propose to use the instance-aware grouping technique to split softmax attentions across tokens." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 642, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 642, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 45, + 642, + 287, + 677 + ], + "type": "text", + "content": "- We present a group size allocation technique searching for an optimal number of groups for each layer given a BOP constraint." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 45, + 677, + 287, + 713 + ], + "type": "text", + "content": "- We set a new state of the art on image classification [8], object detection, and instance segmentation [21], with various ViT architectures [10, 24, 33]." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 390, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 390, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 390, + 83 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 533 + ], + "type": "text", + "content": "Network quantization. Network quantization aims at reducing bit-widths of weights and activations of neural networks. QAT methods simulate the quantization process by applying a round function to weights and activations of the network. Since derivatives of the round function is either zero or infinite, they approximate the gradients (e.g., using the straight-through estimator [3]) to train the network with backpropagation. These methods also adjust the derivatives of the round function [17, 18] or train quantization parameters jointly with network weights based on task losses [11, 16]. For better convergence of the training process, many heuristics have been introduced, e.g., progressively shrinking bit-widths [42] or freezing parts of the network weights [28, 41]. Quantized networks using QAT show performance comparable to or even better than full-precision counterparts. However, the quantization process is computationally demanding, requiring a significant amount of training time. PTQ offers an alternative approach to quantizing neural networks. Instead of training full-precision models and simulating the quantization process at training time, PTQ methods calibrate quantization parameters (e.g., quantization intervals) using a subset of training samples. Early efforts focus on optimizing the quantization parameters to minimize the difference between floating-point and quantized values [2, 27]. Another line of research proposes to consider distributions of weights and/or activations to design quantizers. For instance, the work of [12] has observed that network weights follow a bell-shaped distribution. Based on this, it introduces piecewise linear quantizers that assign different quantization intervals according to the magnitudes of activations, performing better compared to uniform quantizers. Recent PTQ methods learn to either round up or down network weights by using a reconstruction error of layer outputs [26] or exploiting the Hessian of training losses [19], and they have proven the effectiveness on CNN architectures (e.g., ResNet [13], MobileNetV2 [30])." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "Transformer quantization. While ViTs [10] and the variants [24, 33] have become increasingly popular in computer vision, the unique structure and characteristics of ViT architectures makes network quantization challenging. For example, PTQ methods for CNNs [2, 19, 26, 27] do not perform well on quantizing softmax attentions and GELU activations in transformers, suggesting that directly applying them for ViT quantization results in significant performance degradation [25]. To date, only a limited number of PTQ methods have been developed for ViTs. The work of [25] estimates quantization parameters that maximize similarities between full-precision and quantized outputs of linear operations, and proposes to preserve a relative order of attention values after quantization. APQ-ViT [9] introduces a calibration metric to minimize the discrepancies" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16133" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 334 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 334 + ], + "type": "text", + "content": "between full-precision and quantized outputs, while maintaining the power-law distribution of softmax attentions. PTQ4ViT [39] introduces twin uniform quantizers to handle asymmetric distributions in softmax attentions and GELU activations effectively. Most PTQ methods for ViTs exploit a single quantizer for all channels, suggesting that they do not consider the distributions of activation values across channels, typically having extreme scale variations. Recent works [20, 22] attempt to alleviate the scale variation problem efficiently. FQ-ViT [22] proposes to consider inter-channel scale variations for LayerNorm [1], and exploits channel-wise quantizers with the constraint of the ratio of quantization intervals being power-of-two values. This enables using bit-shift operations, calculating mean and variance of LayerNorm in an integer level. The scale reparameterization technique, introduced by RepQ-ViT [20], allows to use layer-wise quantizers, instead of adopting channelwise ones, by adjusting the affine factors of LayerNorm and the weights of FC layers. However, this technique applies to the activations for LayerNorm only, and does not fully address the inter-channel scale variations for other layers in transformers." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 335, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 289, + 563 + ], + "type": "text", + "content": "Similar to ours, the works of [4, 7, 31, 35] adopt group quantization techniques for transformers. For instance, Qbert [31] and VS-quant [7] divide consecutive channels uniformly into a number of groups without considering the dynamic range of each channel, and thus the channels assigned to each group do not follow similar distributions. PEG [4] alleviates this issue by sorting the activations across channels w.r.t. the dynamic ranges during calibration, before grouping the channels. Quantformer [35] proposes to use a differentiable search [6, 23] for QAT in order to group channels of activation maps. The channels assigned to particular groups are however fixed after calibrating pretrained networks for PTQ in the group quantization techniques [4, 7, 31], which makes them inappropriate for ViTs having diverse channel distributions according to input instances. In contrast, our approach apply group quantization along channels of activation maps and tokens of softmax attentions dynamically at runtime for each input instance, without additional parameters for PTQ." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 570, + 104, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 104, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 104, + 582 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 590, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 287, + 638 + ], + "type": "text", + "content": "In this section, we provide a brief description of uniform quantizer (Sec. 3.1). We then present our approach in detail, including IGQ-ViT (Sec. 3.2) and a group size allocation technique (Sec. 3.3)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 647, + 157, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 157, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 157, + 659 + ], + "type": "text", + "content": "3.1. Uniform quantizer" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": "Given a floating-point value " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " and the quantization bitwidth " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": ", uniform quantizers discretize the inputs into a finite set of values with equally spaced intervals. To this end, it normalizes the floating-point value " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " using a scale param" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 388, + 137 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 388, + 137 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 388, + 137 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 388, + 137 + ], + "type": "image", + "image_path": "e1e417b0529afc47b8a0dd7d2bbb304cbb6023043b9425b0a0ea413617ad8071.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 140, + 354, + 151 + ], + "lines": [ + { + "bbox": [ + 343, + 140, + 354, + 151 + ], + "spans": [ + { + "bbox": [ + 343, + 140, + 354, + 151 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 391, + 71, + 466, + 137 + ], + "blocks": [ + { + "bbox": [ + 391, + 71, + 466, + 137 + ], + "lines": [ + { + "bbox": [ + 391, + 71, + 466, + 137 + ], + "spans": [ + { + "bbox": [ + 391, + 71, + 466, + 137 + ], + "type": "image", + "image_path": "82293fe0e4edef98ec7d48642753494d0bdd6d4199c0caee841ecea36a3e22fe.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 140, + 434, + 150 + ], + "lines": [ + { + "bbox": [ + 422, + 140, + 434, + 150 + ], + "spans": [ + { + "bbox": [ + 422, + 140, + 434, + 150 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 156, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 243 + ], + "type": "text", + "content": "Figure 2. (a) Plots of standard deviations of activations across channels for DeiT-S [33]; (b-c) Boxplots of activation values across different input instances for a particular channel of ResNet-50 [13] and DeiT-S, respectively. We use ImageNet [8] for the visualizations. We have observed that there is a significant scale variation across channels, and the activation ranges for each channel change drastically among different samples for ViTs, in contrast to CNNs." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 468, + 71, + 544, + 137 + ], + "blocks": [ + { + "bbox": [ + 468, + 71, + 544, + 137 + ], + "lines": [ + { + "bbox": [ + 468, + 71, + 544, + 137 + ], + "spans": [ + { + "bbox": [ + 468, + 71, + 544, + 137 + ], + "type": "image", + "image_path": "0c437cdcdad15ce15a7cbf9e20ce3efe2e1c5dadff6b9b939e625b8bbf18dd18.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 140, + 512, + 150 + ], + "lines": [ + { + "bbox": [ + 501, + 140, + 512, + 150 + ], + "spans": [ + { + "bbox": [ + 501, + 140, + 512, + 150 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "type": "text", + "content": "eter " + }, + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "type": "text", + "content": ", calibrate the normalized value with a zero-point " + }, + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 253, + 545, + 277 + ], + "type": "text", + "content": ", and clip the output as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 364, + 286, + 545, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 286, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 364, + 286, + 545, + 306 + ], + "type": "interline_equation", + "content": "\\hat {x} = \\operatorname {c l i p} \\left(\\left\\lfloor \\frac {x}{s} \\right\\rceil + z, 0, 2 ^ {b} - 1\\right), \\tag {1}", + "image_path": "65ef683a501c93b61d9496c4fe61af6a6800bb1c06b977f1c0d6157d222e1eaf.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "text", + "content": "where the scale parameter " + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "text", + "content": " and zero-point " + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "text", + "content": " are defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 339, + 335, + 545, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 335, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 339, + 335, + 545, + 360 + ], + "type": "interline_equation", + "content": "s = \\frac {u - l}{2 ^ {b} - 1}, \\quad z = \\operatorname {c l i p} \\left(\\left\\lfloor - \\frac {l}{s} \\right\\rfloor , 0, 2 ^ {b} - 1\\right). \\tag {2}", + "image_path": "b95d702703255484c2b887e058602f16ac194469760a9f0c5abd4b3be25a2e8b.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": "We denote by " + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": " upper and lower bounds of the quantizer, respectively. " + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\lfloor .\\rfloor" + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": " is a rounding function, and " + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\operatorname{clip}(.,m,n)" + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": " restricts an input to the range with lower and upper bounds of " + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": ", respectively. The quantized output is then obtained as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 378, + 434, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 434, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 378, + 434, + 545, + 447 + ], + "type": "interline_equation", + "content": "Q (x; s, z) = s (\\hat {x} - z). \\tag {3}", + "image_path": "3948c878c461bf1d436d28fdf5c72690e9774c264ab0a07d791b0de9a38ff673.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 460, + 371, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 371, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 371, + 472 + ], + "type": "text", + "content": "3.2. IGQ-ViT" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 479, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 562 + ], + "type": "text", + "content": "Following the work of [25], we quantize all network weights except for the positional embedding. We also quantize input activations of FC layers in the multi-layer perceptron (MLP) block, and the activations for the multi-head self-attention (MSA) block, including queries, keys, values, and softmax attentions. We exploit uniform quantizers for all weights and activations in ViTs." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 570, + 449, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 570, + 449, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 570, + 449, + 582 + ], + "type": "text", + "content": "3.2.1 IGQ for linear operations" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 589, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 589, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 589, + 545, + 625 + ], + "type": "text", + "content": "In the following, we first provide empirical observations on input activations of FC layers, and explain the details of our IGQ framework for linear operations." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Distributions of activations across channels. Most quantization frameworks [2, 19, 25, 26] exploit layer-wise quantizers for activations, applying a single quantization parameter for all channels for efficient inference. However, we have observed that the input activations of FC layers have significant scale variations across channels (Fig. 2(a)). Similar findings can be found in [20, 22]. This suggests" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16134" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "that layer-wise quantizers degrade the quantization performance significantly, as they cannot handle scale variations across different channels. Although adopting separate quantizers for individual channels could be an effective strategy for overcoming the scale variation problem, this requires a summation of a floating-point output for every channel, which is computationally expensive. We have also found that the ranges of these activations for each channel vary drastically among different input instances (Fig. 2(b, c)), since ViTs do not have preceding BatchNorm [15] layers in contrast to state-of-the-art CNNs (e.g., ResNet [13], MobileNetV2 [30]). Conventional approaches (e.g., [4, 7, 31, 35]) exploit a fixed quantization interval (i.e., from lower to upper bounds of the quantizer) for every input instance, thus cannot adapt to such diverse distributions across different samples." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": "Instance-aware grouping across channels. We introduce an instance-aware group quantization framework for linear operations that alleviates the scale variation problem, while maintaining efficiency. We split the channels of activation maps into " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "G_{1}" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " groups based on statistical properties, where activation values within each group are quantized with identical quantization parameters. We assign the channels of activations to appropriate groups, and optimize the scale parameter " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " and the zero-point " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": "-th group. Specifically, given floating-point activations of " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\in \\mathbb{R}^{N\\times C}" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " and a set of candidate quantizers " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\{Q_i\\}_{i = 1}^{G_1}" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": ", where we denote by " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " as the number of tokens and channels, respectively, we define a distance metric between the " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": "-th channel of the activations " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_c" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": ", and the quantizer " + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 46, + 266, + 289, + 445 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 455, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 455, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 455, + 287, + 469 + ], + "type": "interline_equation", + "content": "d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right) = \\left(\\min \\left(\\mathbf {X} _ {c}\\right) - u _ {i}\\right) ^ {2} + \\left(\\max \\left(\\mathbf {X} _ {c}\\right) - l _ {i}\\right) ^ {2} \\tag {4}", + "image_path": "15f64138aab83d147320d754682016c62bda7495c3bf60a000ebe26e085cb263.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "inline_equation", + "content": "u_{i}" + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": " are upper and lower bounds of the quantizer " + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": ", respectively. We then assign each channel of the activation " + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": " to one of candidate quantizers with the minimum distance as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 536, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 536, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 111, + 536, + 287, + 554 + ], + "type": "interline_equation", + "content": "\\pi (c) = \\underset {i} {\\arg \\min } d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right) \\tag {5}", + "image_path": "1d75baedf5f9018b0e2187fdfbca79d7a2187a9d8a2eef2181855eaac6c9e00c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "type": "text", + "content": "where we denote by " + }, + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\pi (c)" + }, + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "type": "text", + "content": " a group index assigned to the " + }, + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 563, + 287, + 601 + ], + "type": "text", + "content": "-th channel. The upper and lower bounds of quantizers are then optimized by minimizing the distances as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 95, + 609, + 287, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 609, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 95, + 609, + 287, + 635 + ], + "type": "interline_equation", + "content": "u _ {i} ^ {*}, l _ {i} ^ {*} = \\underset {u _ {i}, l _ {i}} {\\arg \\min } \\sum_ {\\pi (c) = i} d \\left(\\mathbf {X} _ {c}, Q _ {i}\\right). \\tag {6}", + "image_path": "d179465d9f902cb4f0baf74773ade7b29d810891b76147286dc88bd52f1f2307.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "type": "text", + "content": "We optimize " + }, + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "type": "inline_equation", + "content": "u_{i}" + }, + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 46, + 644, + 288, + 728 + ], + "type": "text", + "content": " by solving Eq. (5) and Eq. (6) alternately similar to the expectation-maximization (EM) algorithm, which guarantees the convergence [37]. Finally, we obtain quantization parameters of each group (i.e., s and z) using Eq. (2). At test time, we fix the quantization parameters, and assign the channels to appropriate groups using Eq. (5)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "content": "Table 1. Comparison of BOPs for a 4-bit DeiT-B [33] model using various quantization strategies. We denote by 'Model' the required BOP for layer-wise quantization. In contrast to layer-wise quantization, IGQ-ViT involves additional computations, including (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the outputs of each group in a floating-point format. The corresponding BOPs for these steps are denoted by 'Minmax', 'Assign', and 'FP sum', respectively." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 172, + 542, + 232 + ], + "blocks": [ + { + "bbox": [ + 309, + 172, + 542, + 232 + ], + "lines": [ + { + "bbox": [ + 309, + 172, + 542, + 232 + ], + "spans": [ + { + "bbox": [ + 309, + 172, + 542, + 232 + ], + "type": "table", + "html": "
MethodsModel Minmax Assign FP sumTotal
Layer-wise340.3G---340.3G
IGQ-ViT(#groups=4)340.3G0.99G0.57G1.57G343.4G
IGQ-ViT(#groups=8)340.3G0.99G1.14G3.66G346.1G
IGQ-ViT(#groups=16)340.3G0.99G2.28G7.84G351.4G
", + "image_path": "0075318197229051c2f02ebbdeb189ca51a3b75cf50df74a041c4155868340e5.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": "Computational overhead. Compared to layer-wise quantization, our approach requires (1) computing the min/max values of each channel, (2) assigning channels to quantizers with the minimum distance, and (3) summing the floating-point outputs of each group. Specifically, consider a matrix multiplication between a quantized activation " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "Q(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " and the quantized weight " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "Q(\\mathbf{W})" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " with a group size of " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "G_{1}" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": ". The quantized activation " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "Q(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " is obtained by partitioning " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " into a number of groups across channels using Eq. (5), i.e. " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = [\\mathbf{X}_1, \\dots, \\mathbf{X}_{G_1}]" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": ", followed by quantizing " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " with a scale parameter of " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "i \\in \\{1, \\dots, G_1\\}" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": ". The matrix multiplication between " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "Q(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "inline_equation", + "content": "Q(\\mathbf{W})" + }, + { + "bbox": [ + 304, + 244, + 545, + 400 + ], + "type": "text", + "content": " can then be represented as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 407, + 545, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 407, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 347, + 407, + 545, + 440 + ], + "type": "interline_equation", + "content": "Q (\\mathbf {X}) Q (\\mathbf {W}) = s ^ {w} \\cdot \\left(\\sum_ {i = 1} ^ {G _ {1}} s _ {i} \\cdot \\hat {\\mathbf {X}} _ {i} \\hat {\\mathbf {W}} _ {i}\\right). \\tag {7}", + "image_path": "4d66747083fa5e0eabe3aebc851faeca7dcdfdd322979169d30d811bba4ea218.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": "Note that we omit zero-points for clarity. We denote by " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "s^w" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " the scale parameter for " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}}_i" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}_i" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " are obtained by applying Eq. (1) to " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_i" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": ", the channels and rows of " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " associated with group " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": ", respectively. Computing Eq. (7) requires the summation of floating-point matrices for each group (i.e., " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "s_i \\cdot \\hat{\\mathbf{X}}_i\\hat{\\mathbf{W}}_i" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": "), which can be reduced with sufficiently small values of " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "G_1" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": ". As the values of " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "G_1" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": ", we use no more than 16 in our experiments, which is extremely small compared to the number of channels, usually scaling up to over a thousand. We show in Table 1 BOPs of IGQ-ViT for DeiT-B [33] quantized with 4-bit. We can see that IGQ-ViT introduces only " + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 304, + 447, + 545, + 603 + ], + "type": "text", + "content": " additional BOPs for a group size of 16, compared to layer-wise quantization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 608, + 455, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 455, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 455, + 620 + ], + "type": "text", + "content": "3.2.2 IGQ for softmax attentions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 627, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 545, + 662 + ], + "type": "text", + "content": "Here, we present our observation for the distribution of softmax attentions, and present the details of IGQ for softmax attentions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Distributions of softmax attentions. ViTs capture correlations between tokens through softmax attentions. The distribution of attention values varies drastically across different tokens (Fig. 3). Therefore, using a single quantization" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16135" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 275, + 167 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 275, + 167 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 275, + 167 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 275, + 167 + ], + "type": "image", + "image_path": "8d69f8e5a5949ce8ca4c844ff4bf832dfff5ffc5669c66bf85803e31a786215f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 175, + 289, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 289, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 289, + 242 + ], + "type": "text", + "content": "Figure 3. Distributions of softmax attentions across tokens. We can see that the distributions are different significantly across tokens. Our approach can handle this issue by splitting the rows of softmax attentions into several groups and applying separate quantizers for each group, such that the attentions assigned to each group share similar statistical properties." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 249, + 164, + 350 + ], + "blocks": [ + { + "bbox": [ + 51, + 249, + 164, + 350 + ], + "lines": [ + { + "bbox": [ + 51, + 249, + 164, + 350 + ], + "spans": [ + { + "bbox": [ + 51, + 249, + 164, + 350 + ], + "type": "image", + "image_path": "73b50d009c4796d34b5b8f9a75f3f0283e767588cc035d5a325398cb19eb621d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 350, + 287, + 417 + ], + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 417 + ], + "type": "text", + "content": "Figure 4. Comparisons for dynamic ranges of activation values across channels, chosen from different layers of ViT-S [10]. " + }, + { + "bbox": [ + 46, + 350, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\sigma_{range}" + }, + { + "bbox": [ + 46, + 350, + 287, + 417 + ], + "type": "text", + "content": " is the standard deviation of the dynamic ranges of channels for each layer. We can see that the degree of scale variations across channels varies according to the layer, suggesting that the number of groups for each layer would be adjusted." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 249, + 279, + 350 + ], + "blocks": [ + { + "bbox": [ + 167, + 249, + 279, + 350 + ], + "lines": [ + { + "bbox": [ + 167, + 249, + 279, + 350 + ], + "spans": [ + { + "bbox": [ + 167, + 249, + 279, + 350 + ], + "type": "image", + "image_path": "fb66275e92b7578f58e998e09504c1861764725f9dd46057fc4ac53dc385d836.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 430, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 489 + ], + "type": "text", + "content": "parameter to quantize softmax attentions degrades quantization performance severely. Separate quantizers might be exploited for individual tokens to handle the attention values, but this requires a large number of quantizers, and needs to adjust the quantization parameters for each instance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": "Instance-aware grouping across tokens. We extend our approach in order to quantize softmax attentions across tokens. We split softmax attentions for tokens (i.e., the rows of the softmax attentions) into " + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "inline_equation", + "content": "G_{2}" + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": " groups, according to the distribution of attention values. Specifically, given softmax attentions " + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{H \\times N \\times N}" + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": " and a set of quantizers " + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\{Q_{j}\\}_{j=1}^{G_{2}}" + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": ", where we denote by " + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": " the number of heads, we define the distance between each row of softmax attentions and a quantizer " + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "inline_equation", + "content": "Q_{j}" + }, + { + "bbox": [ + 46, + 505, + 287, + 613 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 99, + 625, + 287, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 625, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 99, + 625, + 287, + 641 + ], + "type": "interline_equation", + "content": "d \\left(\\mathbf {A} _ {n}, Q _ {j}\\right) = \\left(\\max \\left(\\mathbf {A} _ {n}\\right) - v _ {j}\\right) ^ {2} \\tag {8}", + "image_path": "1b94ebbf63a67c3b750c23d72e3a89583ca9e0d0e3c81875c49c02d3a0c70aba.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "where we denote by " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_n" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "v_{j}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " the " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "-th row of " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " and the upper bound of the quantizer " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "Q_{j}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": ", respectively. Note that we set lower bounds to 0, as all attention values are positive. We then optimize " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "v_{j}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " with the EM algorithm and set the quantization parameters for quantizer " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "Q_{j}" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " using Eq. (2)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 83, + 400, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 83, + 400, + 95 + ], + "spans": [ + { + "bbox": [ + 307, + 83, + 400, + 95 + ], + "type": "text", + "content": "Algorithm 1 IGQ-ViT" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 309, + 99, + 545, + 263 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "type": "text", + "content": "1: Hyperparameter: Number of iterations " + }, + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{iter}}" + }, + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "type": "text", + "content": "; update period of group size " + }, + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 311, + 99, + 545, + 121 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 121, + 541, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 121, + 541, + 132 + ], + "spans": [ + { + "bbox": [ + 321, + 121, + 541, + 132 + ], + "type": "text", + "content": "Input: Pre-trained model; calibration set; target BOPs " + }, + { + "bbox": [ + 321, + 121, + 541, + 132 + ], + "type": "inline_equation", + "content": "N_{bop}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 311, + 132, + 545, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 132, + 545, + 165 + ], + "spans": [ + { + "bbox": [ + 311, + 132, + 545, + 165 + ], + "type": "text", + "content": "2: For inputs of FC layers and softmax attentions, compute the distance between their channels/rows and quantizers using Eq. (4) or Eq. (8)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 165, + 403, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 165, + 403, + 175 + ], + "spans": [ + { + "bbox": [ + 311, + 165, + 403, + 175 + ], + "type": "text", + "content": "3: for " + }, + { + "bbox": [ + 311, + 165, + 403, + 175 + ], + "type": "inline_equation", + "content": "k = 1, \\dots, N_{\\mathrm{iter}}" + }, + { + "bbox": [ + 311, + 165, + 403, + 175 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 311, + 175, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 175, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 311, + 175, + 545, + 198 + ], + "type": "text", + "content": "4: Update the parameters for each group using Eq. (5) and Eq. (6)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 311, + 198, + 409, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 198, + 409, + 208 + ], + "spans": [ + { + "bbox": [ + 311, + 198, + 409, + 208 + ], + "type": "text", + "content": "5: if " + }, + { + "bbox": [ + 311, + 198, + 409, + 208 + ], + "type": "inline_equation", + "content": "k\\% T == 0" + }, + { + "bbox": [ + 311, + 198, + 409, + 208 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 209, + 529, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 209, + 529, + 220 + ], + "spans": [ + { + "bbox": [ + 310, + 209, + 529, + 220 + ], + "type": "text", + "content": "6: Update the group size for each layer using Eq. (10)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 311, + 220, + 356, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 220, + 356, + 229 + ], + "spans": [ + { + "bbox": [ + 311, + 220, + 356, + 229 + ], + "type": "text", + "content": "7: end if" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 311, + 231, + 351, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 231, + 351, + 240 + ], + "spans": [ + { + "bbox": [ + 311, + 231, + 351, + 240 + ], + "type": "text", + "content": "8: end for" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "spans": [ + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "type": "text", + "content": "9: Obtain quantization parameters " + }, + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 311, + 241, + 503, + 253 + ], + "type": "text", + "content": " using Eq. (2)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 309, + 253, + 419, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 253, + 419, + 263 + ], + "spans": [ + { + "bbox": [ + 309, + 253, + 419, + 263 + ], + "type": "text", + "content": "10: Output: Quantized model" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 278, + 427, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 278, + 427, + 292 + ], + "spans": [ + { + "bbox": [ + 306, + 278, + 427, + 292 + ], + "type": "text", + "content": "3.3. Group size allocation" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "type": "text", + "content": "We observe that activations and softmax attentions in different layers show different amount of scale variations across channels and tokens, respectively, indicating that using the same number of groups for different layers might be suboptimal (Fig. 4). To address this, we search for the optimal group size for each layer that minimizes the discrepancy between the predictions from quantized and full-precision models, under a BOP constraint. However, the search space for finding the optimal group sizes is exponential w.r.t. the number of layers " + }, + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "type": "text", + "content": ", which is intractable for a large model. We propose a group size allocation technique that efficiently optimizes the group size for each layer within such a large search space. Concretely, we define a perturbation metric for a particular layer " + }, + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "type": "inline_equation", + "content": "\\psi(.)" + }, + { + "bbox": [ + 304, + 297, + 545, + 489 + ], + "type": "text", + "content": " as the Kullback-Leibler (KL) divergence between predictions of the model before and after quantization as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 378, + 498, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 498, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 378, + 498, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\psi (g, l) = D _ {\\mathrm {K L}} \\left(y _ {l} \\| y _ {l} ^ {g}\\right), \\tag {9}", + "image_path": "6537106e8188957c2f1307c0c0d4f15639e25ead6ca03ff64882a8ed57c5e253.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": "where we denote by " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "y_{l}" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "y_{l}^{g}" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": " the predictions of the model before and after quantizing " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": "-th layer with a group size of " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": ", respectively. Note that we quantize all other layers except for the " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": "-th layer for computing the predictions of " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "y_{l}" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "y_{l}^{g}" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": ", to account for the effects of quantization on different layers. For a target BOP " + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "inline_equation", + "content": "N_{bop}" + }, + { + "bbox": [ + 304, + 520, + 545, + 639 + ], + "type": "text", + "content": ", we formulate the group size allocation as a integer linear programming (ILP) problem, and search for the optimal group size for each layer, such that an overall perturbation of the model is minimized as follows:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 326, + 647, + 545, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 647, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 326, + 647, + 545, + 680 + ], + "type": "interline_equation", + "content": "\\mathbf {g} ^ {*} = \\arg \\min _ {\\mathbf {g}} \\sum_ {l = 1} ^ {L} \\psi (g _ {l}, l) \\text {s . t .} B (\\mathbf {g}) \\leq N _ {b o p}, \\tag {10}", + "image_path": "c6579086c6717794694af471b4c19bd723ff1e14dd7ed7827e2e7146154a0fab.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g} = \\{g_l\\}_{l=1}^L" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "g_l" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the group size assigned to " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "-th layer. We denote by " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "B(\\mathbf{g})" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " the BOP of the model with the" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16136" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 106, + 506, + 348 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 2. Quantitative results of quantizing ViT architectures on ImageNet [8]. W/A represents the bit-width of weights (W) and activations (A), respectively. We report the top-1 validation accuracy " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " with different group sizes for comparison. The numbers of other quantization methods are taken from [9, 20]. " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ": Results without using a group size allocation (i.e., a fixed group size for all layers)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 106, + 506, + 348 + ], + "lines": [ + { + "bbox": [ + 86, + 106, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 86, + 106, + 506, + 348 + ], + "type": "table", + "html": "
Method#bits(W/A)ViT-TViT-SViT-BDeiT-TDeiT-SDeiT-BSwin-TSwin-SSwin-B
Full-precision32/3275.4781.3984.5472.2179.8581.8081.3983.2385.27
PTQ4ViT [39]4/417.4542.5730.6936.9634.0864.39-76.0974.02
APQ-ViT [9]4/417.5647.9541.4147.9443.5567.48-77.1576.48
RepQ-ViT [20]4/4-65.0568.4857.4369.0375.61-79.4578.32
IGQ-ViT† (#groups=8)4/454.4672.9977.9161.9474.0178.8576.9180.5482.88
IGQ-ViT† (#groups=12)4/455.6673.4679.1362.2874.5279.2177.5380.7983.08
IGQ-ViT (#groups=8)4/455.2973.1878.2862.2574.2379.0477.1980.6683.02
IGQ-ViT (#groups=12)4/456.0173.6179.3262.4574.6679.2377.7780.9883.14
IGQ-ViT (upper bound)4/457.5974.7379.8862.5575.0879.7478.5881.4883.53
PTQ4ViT [39]6/664.4678.6381.6569.6876.2880.25-82.3884.01
APQ-ViT [9]6/669.5579.1082.2170.4977.7680.42-82.6784.18
RepQ-ViT [20]6/6-80.4383.6270.7678.9081.27-82.7984.57
IGQ-ViT† (#groups=8)6/672.9080.0783.1170.7178.9281.3480.2382.5584.43
IGQ-ViT† (#groups=12)6/673.6380.6683.6371.0279.1781.4880.5982.6684.70
IGQ-ViT (#groups=8)6/673.1980.4883.4670.9279.0481.4480.4882.6584.62
IGQ-ViT (#groups=12)6/673.7780.7683.7771.1579.2881.7180.8982.8684.82
IGQ-ViT (upper bound)6/674.6180.9984.2771.4279.4281.7581.2083.0885.06
", + "image_path": "27bb43af26d7ef08589bb43f2cf02526e45cb321c61353d6bef39becd801e5d0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "text", + "content": "group sizes of " + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "text", + "content": ". We solve Eq. (10) with the PULP [29] library, using group size for each layer within the set of " + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "inline_equation", + "content": "\\{4,6,8,10,12,16\\}" + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "text", + "content": ". We allocate the group sizes for every " + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "text", + "content": " alternating steps of Eq. (5) and Eq. (6), where " + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 354, + 288, + 429 + ], + "type": "text", + "content": " is a hyperparameter. We show in Algorithm 1 an overall quantization process of our approach." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 437, + 128, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 128, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 128, + 452 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 509 + ], + "type": "text", + "content": "In this section, we describe our experimental settings (Sec. 4.1), and evaluate IGQ-ViT on image classification, object detection and semantic segmentation (Sec. 4.2). We then present a detailed analysis of our approach (Sec. 4.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 515, + 178, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 178, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 178, + 528 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 715 + ], + "type": "text", + "content": "We evaluate our IGQ-ViT framework on the tasks of image classification, object detection, and instance segmentation. We use the ImageNet [8] dataset for image classification, which contains approximately 1.2M images for training, and 50K for validation. We use COCO [21] for object detection and instance segmentation, which includes 118K training, 5K validation, and 20K test images. We adopt various transformer architectures, including ViT [10], DeiT [33], and Swin transformer [24], for image classification. For the tasks of object detection and instance segmentation, we use Mask R-CNN [14] and Cascade Mask R-CNN [5] with Swin transformers as the backbone. Following [9, 20], we randomly sample 32 images from the ImageNet [8] dataset for image classification, and a single image from COCO [21] for object detection and instance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 354, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 403 + ], + "type": "text", + "content": "segmentation to calibrate the quantization parameters. We apply our instance-aware grouping technique for all input activations of FC layers, and softmax attentions. More detailed settings are available in the supplement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 408, + 362, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 408, + 362, + 419 + ], + "spans": [ + { + "bbox": [ + 306, + 408, + 362, + 419 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "type": "text", + "content": "Results on ImageNet. We show in Table 2 the top-1 accuracy " + }, + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "type": "text", + "content": " on the validation split of ImageNet [8] with various ViT architectures. We report the accuracy with an average group size of 8 and 12. We summarize our findings as follows: (1) Our IGQ-ViT framework with 8 groups already outperforms the state of the art except for ViT-B [10] and Swin-S [24] under 6/6-bit setting, while using more groups further boosts the performance. (2) Our approach under 4/4-bit setting consistently outperforms RepQ-ViT [20] by a large margin. Similar to ours, RepQ-ViT also addresses the scale variations between channels, but it can be applied to the activations with preceding LayerNorm only. In contrast, our method handles the scale variations on all input activations of FC layers and softmax attentions, providing better results. (3) Our group size allocation technique boosts the quantization performance for all models, indicating that using the same number of groups for all layers is suboptimal. (4) Exploiting 12 groups for our approach incurs less than " + }, + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 689 + ], + "type": "text", + "content": " accuracy drop, compared to the upper bound under the 6/6-bit setting. Note that the results of upper bound are obtained by using a separate quantizer for each channel of activations and each row of softmax attentions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "content": "Results on COCO. We show in Table 3 the quantization results for object detection and instance segmentation on" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16137" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 87, + 95, + 504, + 285 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 3. Quantitative results of quantizing Mask R-CNN [14] and Cascade Mask R-CNN [5] using Swin transformers [24] on COCO [21]. We report the box average precision " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{box}}" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": " for object detection and the mask average precision " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{mask}}" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": " for instance segmentation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 87, + 95, + 504, + 285 + ], + "lines": [ + { + "bbox": [ + 87, + 95, + 504, + 285 + ], + "spans": [ + { + "bbox": [ + 87, + 95, + 504, + 285 + ], + "type": "table", + "html": "
Method#bits(W/A)Mask R-CNNCascade Mask R-CNN
Swin-TSwin-SSwin-TSwin-SSwin-B
APboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmaskAPboxAPmask
Full-precision32/3246.041.648.543.350.443.751.945.051.945.0
PTQ4ViT [39]4/46.97.026.726.614.713.50.50.510.69.3
APQ-ViT [9]4/423.722.644.740.127.224.447.741.147.641.5
RepQ-ViT [20]4/436.136.044.240.247.041.449.343.1--
IGQ-ViT (#groups=8)4/440.538.544.741.348.442.350.544.050.444.0
IGQ-ViT (#groups=12)4/441.038.844.841.348.542.450.544.050.544.0
PTQ4ViT [39]6/65.86.86.56.614.713.612.510.814.212.9
APQ-ViT [9]6/645.441.247.942.948.642.550.543.950.143.7
RepQ-ViT [20]6/645.141.247.843.050.043.551.444.6--
IGQ-ViT (#groups=8)6/645.441.548.243.150.443.751.944.951.945.0
IGQ-ViT (#groups=12)6/645.541.548.243.250.443.851.945.051.945.0
", + "image_path": "cbe1fb20f81c3aac5fc88ba5833c968f8f41586ccaaf6512468615ee5d575c2c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 69, + 349, + 264, + 441 + ], + "blocks": [ + { + "bbox": [ + 46, + 288, + 287, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 288, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 287, + 344 + ], + "type": "text", + "content": "Table 4. Quantitative comparison of our instance-aware group quantization technique with various configurations under a 4/4-bit setting. We denote by 'Linear' and 'Attention' the quantization method for linear operations and softmax attentions, respectively. For applying our method, we use a group size of 8 for all layers." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 349, + 264, + 441 + ], + "lines": [ + { + "bbox": [ + 69, + 349, + 264, + 441 + ], + "spans": [ + { + "bbox": [ + 69, + 349, + 264, + 441 + ], + "type": "table", + "html": "
LinearAttentionViT-SDeiT-BSwin-T
Layer-wiseLayer-wise42.8262.2355.51
Layer-wiseOurs53.6965.0562.27
OursLayer-wise57.3275.5172.89
OursOurs72.9978.8576.91
OursRow-wise73.2278.8877.19
Channel-wiseOurs74.5679.6978.39
Channel-wiseRow-wise74.7379.7478.58
", + "image_path": "412c057ce4f9599d5328d9d3917ab59bd40bf0e3c013fcc91f72d7d940140e39.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 593 + ], + "type": "text", + "content": "COCO [21]. We quantize the backbones of Swin transformers [24] and the convolutional layers in the neck and head of Mask R-CNN [14] and Cascade Mask R-CNN [5]. We observe that PTQ4ViT [39] and APQ-ViT [9], that use layerwise quantizers for activations, do not perform well. In contrast, IGQ-ViT outperforms the state of the art with 8 groups only, and the quantization performance further boosts by exploiting more groups. In particular, it provides the results nearly the same as the full-precision ones for the 6/6-bit setting. This suggests that scale variations across different channels or tokens are much more critical for object detection and instance segmentation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 599, + 119, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 119, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 119, + 611 + ], + "type": "text", + "content": "4.3. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Comparison with different quantizers. We compare in Table 4 the results of the variants of our method adopting different types of quantizers on input activations of FC layers and softmax attentions. From the first four rows, we can see that our approach outperforms layer-wise quantization by a large margin, both for linear operations and softmax attentions. This indicates that adopting a single quantization parameter for all channels and rows without considering" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 352, + 545, + 412 + ], + "blocks": [ + { + "bbox": [ + 304, + 288, + 545, + 344 + ], + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 344 + ], + "type": "text", + "content": "Table 5. Quantitative comparison of quantizing transformer architectures using various group quantization techniques under a 4/4-bit setting, with a group size of 8 for all linear operations. Note that we use layer-wise quantization for softmax attentions for a fair comparison." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 352, + 545, + 412 + ], + "lines": [ + { + "bbox": [ + 307, + 352, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 307, + 352, + 545, + 412 + ], + "type": "table", + "html": "
Grouping methodsViT-SDeiT-BSwin-T
No grouping (#groups=1)42.8262.2355.51
Grouping consecutive channels [7, 31]41.0465.5070.39
Sorting before grouping channels [4]41.2662.6156.04
Ours57.3275.5172.89
", + "image_path": "61275b130005c3aaef16649ad573d930d6e0d56f75e69736b501f1e68e070097.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 427, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 545, + 525 + ], + "type": "text", + "content": "their individual distributions can severely limit the quantization performance. The last three rows compare the results of our approach with channel/row-wise quantization. We observe that the difference in performance between our approach and channel/row-wise quantization is less than " + }, + { + "bbox": [ + 304, + 427, + 545, + 525 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 304, + 427, + 545, + 525 + ], + "type": "text", + "content": " for three different models. With a small group size, our framework can achieve comparable performance to the upper bound, while maintaining efficiency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 531, + 545, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 723 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 723 + ], + "type": "text", + "content": "Table 5 shows the results of quantizing ViT architectures using various group quantization techniques, including [4, 7, 31], and ours. While the works of [7, 31] divide consecutive channels uniformly into a number of groups, the method of [4] first sorts channels w.r.t. the dynamic ranges before partitioning them into groups. In contrast, we dynamically assign channels to groups according to the statistical properties of the channels. We find that our approach outperforms other methods by a large margin, indicating that fixing the channels assigned to each group can degrade the quantization performance significantly. We also observe that sorting the channels w.r.t. their dynamic ranges during calibration does not boost the quantization performance for DeiT-B [33] and Swin-T [24], suggesting that the dynamic range of each channel vary drastically across different input instances." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16138" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 165, + 157 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 165, + 157 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 165, + 157 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 165, + 157 + ], + "type": "image", + "image_path": "a5514b5d87b22119b31a6723e59d44fc9a270688ea1e21cb9da2d4b262470921.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "text", + "content": "Figure 5. Top-1 validation accuracies on ImageNet [8] w.r.t. group sizes for linear operations (" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "inline_equation", + "content": "G_{1}" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "text", + "content": ", left) and that for softmax attentions (" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "inline_equation", + "content": "G_{2}" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "text", + "content": ", right). We set either " + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "inline_equation", + "content": "G_{1}" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "inline_equation", + "content": "G_{2}" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "text", + "content": " to 8, while varying the other to compute the accuracies. We report the quantization results of ViT-S [10], Swin-T [24], and DeiT-B [33] under a 4/4-bit setting, with a fixed group size across different layers. We visualize the upper bounds with horizontal stripes of corresponding colors." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 72, + 283, + 157 + ], + "blocks": [ + { + "bbox": [ + 167, + 72, + 283, + 157 + ], + "lines": [ + { + "bbox": [ + 167, + 72, + 283, + 157 + ], + "spans": [ + { + "bbox": [ + 167, + 72, + 283, + 157 + ], + "type": "image", + "image_path": "8266ec5bb5e81b24f73aca7f8f533efd086f741a8c633fc1d41f48408e02b850.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 66, + 281, + 267, + 381 + ], + "blocks": [ + { + "bbox": [ + 47, + 255, + 287, + 277 + ], + "lines": [ + { + "bbox": [ + 47, + 255, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 287, + 277 + ], + "type": "text", + "content": "Table 6. Quantitative comparison of ViT architectures with and without a group size allocation technique under the 4/4-bit setting." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 281, + 267, + 381 + ], + "lines": [ + { + "bbox": [ + 66, + 281, + 267, + 381 + ], + "spans": [ + { + "bbox": [ + 66, + 281, + 267, + 381 + ], + "type": "table", + "html": "
#groupsGroup size allocationViT-SDeiT-BSwin-T
6✓71.4478.4476.31
71.8078.5776.99
8✓72.9978.8576.91
73.1879.0477.19
10✓73.3479.0077.21
73.5179.1977.64
", + "image_path": "de6994070c5fe31ce1a0b1d0400ec57c4858234ee72b2364f67ae8ff34c16bcc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 390, + 287, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 522 + ], + "type": "text", + "content": "Analysis on group size. We show in Fig. 5 the results of IGQ-ViT according to the group size for linear operations (left) and softmax attentions (right). We can see that the quantization performance improves as the group size increases, for both linear operations and softmax attentions, demonstrating that using more groups better addresses the scale variation problem for channels and tokens. We also observe that the performance of our approach reaches near the upper bound with a small group size. This suggests that IGQ-ViT can effectively address the variations with a small amount of additional computations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 524, + 286, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 286, + 655 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 286, + 655 + ], + "type": "text", + "content": "Convergence analysis. We compare in Fig. 6(top) distances between channels of activation and quantizers in Eq. (4) (rows of softmax attention and quantizers in Eq. (8)) over optimization steps. It shows that our algorithm converges quickly within a small number of optimization steps. We show in Fig. 6(bottom) the dynamic ranges of activations and attentions in a particular layer, along with their assigned groups after convergence. We can see that activations/attentions in each group share similar statistical properties, demonstrating that they can be effectively quantized with a single quantization parameter." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 657, + 286, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 657, + 286, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 657, + 286, + 717 + ], + "type": "text", + "content": "Group size allocation. We compare in Table 6 the results of our approach with/without the group size allocation technique. We can see that the group size allocation improves the quantization performance consistently, suggesting that assigning the same group size for all layers is suboptimal." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 424, + 176 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 424, + 176 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 424, + 176 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 424, + 176 + ], + "type": "image", + "image_path": "b17e847c276b60c2d5b2b0009a694d5d446a3643a3dd023132fa5103c4908023.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 427, + 72, + 540, + 175 + ], + "blocks": [ + { + "bbox": [ + 427, + 72, + 540, + 175 + ], + "lines": [ + { + "bbox": [ + 427, + 72, + 540, + 175 + ], + "spans": [ + { + "bbox": [ + 427, + 72, + 540, + 175 + ], + "type": "image", + "image_path": "bb9483e1aa3b2ea1ceec35d4f59181b5bfe537602ed3b0378ee86e7df391b3b4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 178, + 423, + 277 + ], + "blocks": [ + { + "bbox": [ + 310, + 178, + 423, + 277 + ], + "lines": [ + { + "bbox": [ + 310, + 178, + 423, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 178, + 423, + 277 + ], + "type": "image", + "image_path": "2a2b587bd3f02daf335a7da6dc387fb60ba56787b1dc9bfb6ecd2f37ac39548c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 283, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 283, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 545, + 361 + ], + "type": "text", + "content": "Figure 6. (Top) Distances between channels of activations/rows of softmax attentions and quantizers in a particular layer of DeiT-S [33], that is, the distances as in Eq. (4) and Eq. (8), respectively; (Bottom) Dynamic ranges of activations and attentions in a specific layer of DeiT-S w.r.t. the assigned group of the same color. Note that we sort the activations and attentions based on the group indices for the purpose of the visualization only." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 426, + 179, + 539, + 277 + ], + "blocks": [ + { + "bbox": [ + 426, + 179, + 539, + 277 + ], + "lines": [ + { + "bbox": [ + 426, + 179, + 539, + 277 + ], + "spans": [ + { + "bbox": [ + 426, + 179, + 539, + 277 + ], + "type": "image", + "image_path": "0b65bd812c2837a8f9dced58fc5e2d4cfb7b772f92ee0031fbf556977e1b5a56.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 374, + 378, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 374, + 378, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 374, + 378, + 387 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 398, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 613 + ], + "type": "text", + "content": "We have observed that activations and softmax attentions in ViTs have significant scale variations for individual channels and tokens, respectively, across different input instances. Based on this, we have introduced a instance-aware group quantization framework for ViTs, IGQ-ViT, that alleviates the scale variation problem across channels and tokens. Specifically, our approach splits the activations and softmax attentions dynamically into multiple groups along the channels and tokens, such that each group shares similar statistical properties. It then applies separate quantizers for individual groups. Additionally, we have present a simple yet effective method to assign a group size for each layer adaptively. We have shown that IGQ-ViT outperforms the state of the art, using a small number of groups, with various ViT-based architectures. We have also demonstrated the effectiveness of IGQ-ViT compared with its variants, including layer-wise quantizers, channel/row-wise quantizers, and state-of-the-art group quantizers, with a detailed analysis." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.RS-2022-00143524, Development of Fundamental Technology and Integrated Solution for Next-Generation Automatic Artificial Intelligence System, and No.2021-0-02068, Artificial Intelligence Innovation Hub)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16139" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. 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Although many recent studies have shown the remarkable improvement in human mesh reconstruction, it is still difficult to generate accurate meshes when person-to-person occlusion occurs due to the ambiguity of who a body part belongs to. To address this problem, we propose an instance-aware contrastive learning scheme. Specifically, joint features belonging to the target human are trained to be proximate with the center feature (i.e., feature extracted from the body center position). On the other hand, center features of different human instances are forced to be far apart so that joint features of each person can be clearly distinguished from others. By interpreting the joint possession based on such contrastive learning scheme, the proposed method easily understands the spatial occupancy of body parts for each person in a given image, thus can reconstruct reliable human meshes even with severely overlapped cases between multiple persons. Experimental results on benchmark datasets demonstrate the robustness of the proposed method compared to previous approaches under person-to-person occlusions. The code and model are publicly available at: https://github.com/DCVL-3D/InstanceHMR_release.", + "bbox": [ + 75, + 300, + 473, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 209, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, 3D human mesh reconstruction has become a major research topic with the increasing demand in entertainment areas such as AR/VR and sports broadcasting. In line with this trend, considerable efforts have been made to predict reliable meshes from a single image by using deep learning techniques. Specifically, model-based methods, which aim to reconstruct human poses and shapes by estimating parameters of the skinned multi-person linear (SMPL) model [32], have been introduced. Since the problem of inferring a large number of vertices is simplified to the problem of estimating a few parameters through various network architectures, model-based approaches have been", + "bbox": [ + 75, + 696, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "actively explored while bringing the significant progress in human mesh reconstruction [2, 4, 15, 18, 19, 21, 24, 25, 37, 46]. On the other hand, model-free approaches also have drawn a lot of attentions due to their ability to express local details of mesh surfaces by directly regressing every vertex without any constraint of the parameter space. In particular, the transformer architecture has been widely adopted to reconstruct accurate meshes by considering the relationship between vertices in a global manner [5, 17, 27, 28, 44, 45, 50, 51].", + "bbox": [ + 500, + 268, + 893, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite meaningful advances in the field of 3D human mesh reconstruction, person-to-person occlusions frequently occurring in crowd scenes still remain a challenging issue due to ambiguities of possession for body parts. To resolve this issue, several approaches have recently begun to be introduced. For example, there have been attempts to estimate discriminative locations of each person in the 2D space and utilize them to extract features for individual mesh regression [7, 16, 38]. Reasoning the depth order of multiple people also has been considered to understand the relationship between overlapped subjects in a given image [11, 39, 47]. Some methods first predict the occlusion-robust 3D skeletons, which form reliable poses even for invisible body parts, and then lift them to mesh structures [31]. Even though considerable efforts have been consistently devoted to this task, attempts to exploit contextual cues of the occluded area, which is occupied by each person, are still insufficient.", + "bbox": [ + 496, + 426, + 893, + 699 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, a new perspective for effectively handling person-to-person occlusions is presented. In the scene where people are overlapped, one of the biggest obstacles is the uncertainty about the ownership of a body part. While it is relatively easy to semantically understand which area in a given image corresponds to which type of body part (e.g., hand or foot), it can be challenging to determine who owns that body part. This makes the model confused and eventually yields unnatural reconstruction results. To deal with this problem, we propose to guide the network to learn discriminative representations of body parts for each person by our instance-aware contrastive learning scheme. Specifically, two novel feature maps, i.e., center-aligned instance", + "bbox": [ + 496, + 704, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "\\*corresponding author", + "bbox": [ + 94, + 887, + 217, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10553", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e75e118b01d61be156737621e758895f2ac5aa9f2df5be4c80d173aa91a95582.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 71, + 256, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/16871440777b88972a5ac055ee350c78e7b918362e4f850f4375d8593ffe8aea.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 276, + 71, + 468, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7fb235781eca841b8e175c8afdb5d43dd9648e713220c5131fe763c564d749ef.jpg", + "image_caption": [ + "(c)", + "Figure 1. (a) An example of person-to-person occlusion. (b), (c), and (d) Visualizations of the information adopted to guide the feature encoding for human mesh reconstruction in OCHMR [16], 3DCrowdNet [7], and the proposed method, respectively. For better visibility, all joints are represented in a single image at the 2D pose heatmap of (c) and the joint heatmap of (d), and only a few of joint features (e.g., right hand, left elbow, and right foot) are shown in the joint-aligned instance map of (d)." + ], + "image_footnote": [], + "bbox": [ + 478, + 71, + 697, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/75c3d38cb65a14c1e30f788fcbddc4c534549d279dbcf9e8926a133656e9d6a3.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 709, + 71, + 890, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "map and joint-aligned instance map, are encoded in the proposed architecture, which can describe the possession relationship between all human instances and their visible body joints. These maps learn to represent the identity information of each human instance by forcing the center feature to pull joint features of the same person while pushing out center features of non-target persons in the latent space. Note that center features and joint features are sampled at the body center position and joint locations in the center-aligned instance map and the joint-aligned instance map, respectively, as shown in Fig. 1(d). Such identity representations make it easy to distinguish which instance each joint belongs to, thus the model can better understand the occluded context and determine the area of the image to focus on for occluded human mesh reconstruction. A comparison between previous approaches and the proposed method for handling person-to-person occlusions is illustrated in Fig. 1. In [16], relative positions of multiple persons are given to the model in the form of global and local center maps as shown in Fig. 1(b). However, since the center position is an extremely small amount of information compared to the complex body structure, the model may hardly figure out details of body part regions in occlusion situations. On the other hand, the spatial guidance of the body region for the target person is provided to the network based on the 2D pose heatmap in [7]. However, features of nontarget person areas also can be unnecessarily fused into features for target mesh reconstruction (see the bottom part of Fig. 1(c)). Unlike such previous approaches, the proposed method clearly indicates the possession of all body parts by expressing the identity information at joint locations as well as body center positions via the instance-aware contrastive learning scheme as shown in Fig. 1(d). Moreover, meshes for every person can be reliably reconstructed in a single stream (i.e., without using the bounding box) by considering the mutual relationship among the spatial occupancy of each person's body part. The main contributions of this paper are summarized as follows:", + "bbox": [ + 76, + 318, + 472, + 892 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to indicate the spatial occupancy of body parts corresponding to each human instance for occlusion-robust 3D human mesh reconstruction. With the awareness of the body part possession of every person, the model can easily understand the person-to-person occlusion and successfully generate human meshes with natural poses.", + "- We represent the relationship between human instances and their spatial keypoints (i.e., body centers and joints) at the feature level via the proposed instance-aware contrastive learning scheme. Specifically, by guiding the center feature of the target person to push out that of non-target persons and pull corresponding joint features in the latent space, identities of different persons can be distinctively embedded into center and joint features." + ], + "bbox": [ + 517, + 318, + 892, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 571, + 648, + 587 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this Section, we present a systematic review of previous methods for monocular 3D human mesh reconstruction and explore various approaches for handling person-to-person occlusions.", + "bbox": [ + 498, + 597, + 890, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. 3D Human Mesh Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 665, + 787, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep learning-based methods for 3D human mesh reconstruction can be divided into two main groups, i.e., model-based and model-free methods. The former aims to estimate pose and shape parameters of the SMPL [2] model. In the early stage, Kanazawa et al. [15] proposed to regress SMPL parameters by using the end-to-end convolutional neural network and devised the adversarial loss for plausible mesh generation. Kolotouros et al. [19] designed the optimization loop that can be combined with end-to-end regression frameworks such as [15], to further refine reconstruction results. Moreover, Zhang et al. [46] tried to rectify meshes by iteratively feeding pyramidal mesh-aligned features into the mesh regression network. A bottom-up framework, which predicts meshes of multiple persons in a given image dur", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10554", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing a single inference, was introduced by Sun et al. [38] for the first time. Specifically, they proposed to extract SMPL parameters by the sampling process based on body center positions. Li et al. [26] incorporated the bounding box location into the network for accurately estimating the global orientation. To reconstruct the human mesh that is aligned well to the image pixel, Shetty et al. [37] proposed to first predict vertices on the input image plane, and then compute SMPL parameters by comparing them with the template mesh part by part based on inverse kinematics. Cho et al. [4] attempted to learn the consistency of human pose and shape in arbitrary view directions by using neural feature fields. In contrast to such model-based approaches, modelfree methods directly estimate 3D coordinates of mesh vertices. As a pioneer, Kolotouros et al. [20] adopted the graph convolutional neural network (GraphCNN) to effectively transform image features into vertex coordinates. Choi et al. [6] also utilized GraphCNN to lift estimated 2D and 3D poses to the 3D mesh. Meanwhile, Lin et al. [27] presented a new direction in model-free approaches, by employing the transformer encoder with the dimension reduction technique for mesh regression. They further improved the performance by incorporating GraphCNN into the transformer encoder block [28]. To alleviate the computational burden of the transformer-based architecture, Cho et al. [5] proposed to disentangle image features and geometric parameters of the human body based on the cross-attention module. Kim et al. [17] designed a point-guided feature sampling scheme to effectively extract vertex-relevant features for the transformer-based mesh regressor. More recently, Foo et al. [8] adopted the diffusion model for the human mesh reconstruction by leveraging the pose heatmap in the diffusion process to enable the mesh estimation conditioned on the input image.", + "bbox": [ + 76, + 90, + 472, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Handling Person-to-Person Occlusions", + "text_level": 1, + "bbox": [ + 76, + 619, + 410, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Even though many studies mentioned above have brought significant advances for monocular 3D human mesh reconstruction, they still suffer from ambiguities driven by person-to-person occlusions, which often occur in real-world environments. To cope with this problem, there have been various technical attempts. For example, Jiang et al. [11] introduced a new loss function that minimizes the discrepancy between the human segmentation masks and projected meshes to arrange the depth order of the people. In a similar vein, Zhang et al. [47] tried to learn the ordinal relation by supervising the difference between depth values of multiple persons. Instead of simply guiding the network via loss functions, Sun et al. [39] incorporated the bird's-eye-view body center heatmap into the pipeline of mesh estimation to consider the depth cue. Yang et al. [43] adopted to synthesize the other people to the input data for consideration of more variants from person-to-person occlusions.", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2a75a9087a078c4adfcb7b70c4dba081fa8a02e257e5c94de27ddc41fdc80bae.jpg", + "image_caption": [ + "Figure 2. The detailed process of the instance-aware contrastive learning scheme. Note that the ground truth of body center and joint positions is used for the feature sampling." + ], + "image_footnote": [], + "bbox": [ + 498, + 85, + 895, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To specify the position of the target person, Khirodkar et al. [16] introduced the context normalization block, which fuses global and local center heatmaps with corresponding features. Choi et al. [7] utilized the 2D pose heatmap to focus on the feature belonging to the area of the target person in crowded scenes. Cha et al. [3] attempted to refine multiple human meshes based on inter-person relations that are computed by the transformer architecture. Liu et al. [31] proposed to apply the knowledge transfer technique to the 3D keypoint detection [49] for successfully reasoning invisible body parts under occlusions. Li et al. [22] proposed a body center attention mechanism to consider spatial-temporal relations of multiple persons at the pixel level. To complement the lack of the training data under multi-person scenes, Sun et al. [40] tried to synthesize plausible crowded examples by putting human samples at appropriate places of the given image with a reasonable scale according to the scene context. Moreover, they also proposed to learn the consistency between features extracted from the same human sample with and without occlusions.", + "bbox": [ + 496, + 299, + 893, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 614, + 671, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed method aims to learn the spatial occupancy of body parts for each person by using the instance-aware contrastive learning scheme as shown in Fig. 2. By incorporating the identity information into encoded features, the proposed method can achieve the robust performance against person-to-person occlusions. The overall architecture of the proposed method is illustrated in Fig. 3.", + "bbox": [ + 496, + 641, + 893, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Instance-aware Contrastive Learning", + "text_level": 1, + "bbox": [ + 500, + 756, + 823, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the bottom-up approach for human mesh reconstruction, it is important to grasp the individual cue between multiple persons. To this end, we guide the process of mesh estimation based on the regional distinction of each human area, i.e., 24 body joints defined by the SMPL model [2]. Specifically, the backbone feature is encoded into two different feature maps, i.e., center-aligned instance map and joint-aligned instance map, through the corresponding network", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10555", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6b917a70c60b3b8e9f20880b69e4bf624606191be5ecedd96fc93ff3afe4aff1.jpg", + "image_caption": [ + "Figure 3. The overall architecture of the proposed method for occluded human mesh reconstruction. $h$ and $w$ are set to 64. $\\theta$ and $\\beta$ denote pose and shape parameters of the SMPL model. Note that instance-aware contrastive learning is conducted only in the training phase." + ], + "image_footnote": [], + "bbox": [ + 81, + 68, + 888, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "branch as shown in Fig. 3. Note that the predicted center heatmap $H_{C}$ and joint heatmap $H_{J}$ are adopted in this encoding process to provide the spatial information of body centers and joints. In addition, the positional encoding is also applied to the center-aligned instance map to prevent ambiguous representations between different people who have similar appearances. After that, center features and joint features are sampled at body center locations and visible joint positions of the center-aligned instance map and the joint-aligned instance map, respectively. These sampled features are subsequently projected into the latent space by using the nonlinear projector, which consists of fully connected layers and ReLUs (see $P_{C}$ and $P_{J}$ in Fig. 3).", + "bbox": [ + 75, + 404, + 472, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now, such projected features are fed into our instance-aware contrastive learning scheme. The detailed process is shown in Fig. 2. First, the center feature of the target person (i.e., anchor) is forced to push out those of other persons. By placing different human instances far apart from each other in the latent space, center features can implicitly represent the identity information for each person in a discriminative way. Second, the center feature pulls joint features belonging to the same person to a close distance. This facilitates the joint feature to express the human instance to which it belongs, by embedding the target identity information. To this end, two loss functions are designed based on the cosine similarity, which is suitable for measuring the directional coherence between embedding vectors, as follows:", + "bbox": [ + 75, + 604, + 470, + 815 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p u s h}} (a, b) = 1 + \\frac {a \\cdot b}{\\| a \\| \\| b \\|}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 830, + 468, + 871 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p u l l} (a, b) = 1 - \\frac {a \\cdot b}{| | a | | | | b | |}.\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 867, + 362, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, $\\mathcal{L}_{push}$ is used to maximize the distance between center features of different people and $\\mathcal{L}_{pull}$ is used to minimize the distance between the center feature and the joint feature of the same person in the latent space. By considering every possible center-to-center and center-to-joint combination, the proposed contrastive loss is defined as follows:", + "bbox": [ + 498, + 404, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o n t}} = \\frac {2}{N (N - 1)} \\sum_ {i \\neq j} ^ {N} \\mathcal {L} _ {\\text {p u s h}} \\left(u _ {i}, u _ {j}\\right) \\tag {2} \\\\ + \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {1}{K _ {i}} \\sum_ {k = 1} ^ {K _ {i}} \\mathcal {L} _ {p u l l} (u _ {i}, v _ {i} ^ {k}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 517, + 890, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $u$ and $v$ indicate the center feature and the joint feature, respectively. $N$ and $K_{i}$ denote the number of people and the number of visible joints belonging to the $i$ -th person in the input image, respectively. The effect of the proposed instance-aware contrastive learning scheme is shown in Fig. 4. As can be seen, the identity information is embedded into latent features during our instance-aware contrastive learning. Consequently, it is thought that both center-aligned instance map and joint-aligned instance map play an important role to describe the possession relationship between human instances and their visible joints. Note that the instance-aware contrastive learning part is conducted only in the training phase.", + "bbox": [ + 496, + 613, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to utilize this possession cue in the process of mesh regression, we incorporate the center-aligned instance map and the joint-aligned instance map into the network branch for estimating the SMPL parameter map (see the second branch from bottom in Fig. 3). To accurately indicate valid locations, the center heatmap and the joint", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10556", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/60c82af62a3fcfe4859fa73aa61b496f32dbcfacb678c1011bd9f57e7e8c6463.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 78, + 285, + 170 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/40898637b1082da41ccc76ee6b712cdec6ba59f538e77ee5b5c17208387c44f2.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 295, + 71, + 477, + 174 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/21e2a0c947a523e7e966972a0e05024aa1bfa3e73d516a753c6b55cfa6cbdadf.jpg", + "image_caption": [ + "(c)", + "Figure 4. A visualization example of center features and joint features in the latent space. The feature dimension is reduced from 64 to 3 by using [33] for the visualization. (a) Input image with marks for positions of body centers (dark) and joints (bright). Note that points belonging to the same person are represented as the same color attribute. The effect of the proposed instance-aware contrastive learning scheme is shown sequentially, i.e., (b) before training, (c) middle of training, and (d) after training." + ], + "image_footnote": [], + "bbox": [ + 478, + 71, + 679, + 175 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0c6e9be33d7ec5c45443e4a641ccad1f92da287066a97f9bc8e603b426be7372.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 702, + 71, + 887, + 174 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "heatmap are also employed for this concatenation process. Finally, pose and shape parameters of each person are sampled from the SMPL parameter map according to the predicted center position in a similar way of [38]. It is noteworthy that the model can precisely consider the occupancy of each human instance via such identity representation in the feature space, which leads to generation of reliable human meshes even with various person-to-person occlusions. An example of occluded human mesh reconstruction is shown in the bottom right of Fig. 3.", + "bbox": [ + 75, + 271, + 468, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Loss functions", + "text_level": 1, + "bbox": [ + 76, + 431, + 225, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed method is trained based on nine loss terms, i.e., contrastive loss $\\mathcal{L}_{cont}$ (which is explained in subsection 3.1), body center heatmap loss $\\mathcal{L}_{center}$ , joint heatmap loss $\\mathcal{L}_{joint}$ , pose loss $\\mathcal{L}_{pose}$ , shape loss $\\mathcal{L}_{shape}$ , Mixture Gaussian prior loss $\\mathcal{L}_{prior}$ , 3D joint loss $\\mathcal{L}_{3d}$ , Procrustes-aligned 3D joint loss $\\mathcal{L}_{pa3d}$ , and 2D joint loss $\\mathcal{L}_{2d}$ . First, the focal loss [30, 38] is adopted to train the body center heatmap $H_{C}$ and the joint heatmap $H_{J}$ , which is defined as follows:", + "bbox": [ + 75, + 455, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {f o c a l} (H, \\tilde {H}, \\tilde {H} ^ {\\prime}) = - \\frac {\\mathcal {L} _ {p o s} (H , \\tilde {H} ^ {\\prime}) + \\mathcal {L} _ {n e g} (H , \\tilde {H} , \\tilde {H} ^ {\\prime})}{\\sum \\tilde {H} ^ {\\prime}}, \\\\ \\mathcal {L} _ {n e g} (H, \\tilde {H}, \\tilde {H} ^ {\\prime}) = \\log (1 - H) H ^ {2} (1 - \\tilde {H}) ^ {4} (1 - \\tilde {H} ^ {\\prime}), \\\\ \\mathcal {L} _ {\\text {p o s}} \\left(H, \\tilde {H} ^ {\\prime}\\right) = \\log (H) \\left(1 - H\\right) ^ {2} \\tilde {H} ^ {\\prime}, \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 599, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H$ and $\\tilde{H}$ denote a single heatmap and the corresponding ground truth, respectively. $\\tilde{H}^{\\prime}$ indicates the binary map that is marked on the location of the positive class in $\\tilde{H}$ . By using the focal loss, $\\mathcal{L}_{center}$ and $\\mathcal{L}_{joint}$ are formulated as follows:", + "bbox": [ + 76, + 709, + 468, + 784 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {c e n t e r} = \\mathcal {L} _ {f o c a l} (H _ {C}, \\tilde {H} _ {C}, \\tilde {H} _ {C} ^ {\\prime}), \\\\ \\mathcal {L} _ {\\text {j o i n t}} = \\frac {1}{\\mathcal {J}} \\sum_ {j = 1} ^ {\\mathcal {J}} \\mathcal {L} _ {\\text {f o c a l}} \\left(H _ {J} ^ {j}, \\tilde {H} _ {J} ^ {j}, \\tilde {H} _ {J} ^ {' j}\\right), \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 792, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{J}$ is the number of joint heatmaps which is set to 24 according to the SMPL model. The remaining loss terms", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are used to directly supervise the process of human mesh reconstruction. In particular, $\\mathcal{L}_{\\text {pose }}$ and $\\mathcal{L}_{\\text {shape }}$ compute the difference between predicted pose and shape parameters and the corresponding ground truth based on $L_{2}$ loss, respectively [15, 20]. Mixture Gaussian prior loss $\\mathcal{L}_{\\text {prior }}$ is employed to attain the naturalness of body meshes as introduced in [2]. In our work, Euclidean distance is utilized to calculate the spatial gap in the coordinate system for following three loss terms. The distance between estimated 3D joints and the corresponding ground truth is computed by $\\mathcal{L}_{3d}$ [15, 20]. $\\mathcal{L}_{pa3d}$ indicates $\\mathcal{L}_{3d}$ after Procrustes alignment is conducted to the reconstructed mesh [38]. The coordinates of joints projected onto the 2D space are used to measure $\\mathcal{L}_{2d}$ [15, 20]. Finally, the total loss function is defined by using the weighted sum of all the aforementioned loss terms as follows:", + "bbox": [ + 496, + 271, + 890, + 512 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {\\text {c o n t}} \\mathcal {L} _ {\\text {c o n t}} + \\lambda_ {\\text {c e n t e r}} \\mathcal {L} _ {\\text {c e n t e r}} + \\lambda_ {\\text {j o i n t}} \\mathcal {L} _ {\\text {j o i n t}} \\\\ + \\lambda_ {p o s e} \\mathcal {L} _ {p o s e} + \\lambda_ {s h a p e} \\mathcal {L} _ {s h a p e} + \\lambda_ {p r i o r} \\mathcal {L} _ {p r i o r} \\\\ + \\lambda_ {3 d} \\mathcal {L} _ {3 d} + \\lambda_ {p a 3 d} \\mathcal {L} _ {p a 3 d} + \\lambda_ {2 d} \\mathcal {L} _ {2 d}, \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 517, + 890, + 584 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{cont}$ , $\\lambda_{center}$ , $\\lambda_{joint}$ , $\\lambda_{pose}$ , $\\lambda_{shape}$ , $\\lambda_{prior}$ , $\\lambda_{3d}$ , $\\lambda_{pa3d}$ , and $\\lambda_{2d}$ are the balancing factor for each loss term, which are set to 50, 160, 50, 80, 6, 1.6, 200, 360, and 400, respectively.", + "bbox": [ + 500, + 585, + 890, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 657, + 705, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 681, + 715, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed method is implemented on the PyTorch framework with an Intel E5-1650@3.60GHz CPU and two NVIDIA GeForce RTX 3090 GPUs. All the parameters of the proposed network are updated by the Adam optimizer, where momentum factors are set to 0.9 and 0.999, respectively. We use the batch size of 64 and the learning rate is set to $5 \\times 10^{-6}$ during 30 training epochs. Input images are randomly cropped and rotated before they are resized to the resolution of $512 \\times 512$ pixels by using zero padding.", + "bbox": [ + 496, + 705, + 890, + 842 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Benchmark Datasets", + "text_level": 1, + "bbox": [ + 500, + 848, + 694, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed method is trained by using three 3D human pose datasets (i.e., Human3.6M [10], MPI-INF-3DHP [34],", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10557", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c952188275138a0e0c317a3b8a9cb44112489eb5b3b18546db0a0ae7fd852c7b.jpg", + "image_caption": [ + "Figure 5. Results of 3D human mesh reconstruction on the CrowdPose [23] dataset. From top to bottom: input images, results by ROMP [38], 3DCrowdNet [7], and the proposed method." + ], + "image_footnote": [], + "bbox": [ + 76, + 75, + 893, + 373 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/613888b8fb9ae2baabeecb40701d56ca23cdb6ef29aac42027cf7cc956542cc2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods3DPW-PCOCHumanCrowdPose
MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)AP(↑)\\( AP^{50}(↑) \\)\\( AP^{75}(↑) \\)\\( AP^M(↑) \\)\\( AP^L(↑) \\)\\( AP(↑) \\)\\( AP^{50}(↑) \\)\\( AP^{75}(↑) \\)
SPIN* [19]129.682.6157.612.746.819.417.826.216.440.110.6
PyMAF* [46]126.781.3154.314.348.721.518.028.717.442.713.0
ROMP* [38]119.779.7152.815.655.023.618.730.018.944.613.8
ROMP [38]115.675.8147.519.856.225.019.332.928.558.824.7
OCHMR* [16]117.577.1149.624.860.728.622.334.221.448.316.5
CLIFF* [26]---23.249.820.4--27.451.525.9
HMDiff* [8]114.273.5143.1--------
CoordFormer* [22]101.579.3---------
Ours*99.976.3126.430.575.817.335.130.528.561.623.2
Ours102.077.2131.034.980.024.027.135.031.665.726.7
", + "bbox": [ + 78, + 428, + 895, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance comparison of occluded human mesh reconstruction based on 3DPW-PC, OCHuman, and CrowdPose datasets (best results and second results are shown in bold and underlined, respectively). Note that * denotes the performance without using the CrowdPose dataset for training.", + "bbox": [ + 75, + 636, + 892, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and MuCo-3DHP [35]) and four 2D human pose datasets (i.e., MPII [1], LSP [12], COCO [29], and CrowdPose [23]). In particular, only 2D pose labels are used for [23] while pseudo mesh labels, which are generated by [14], are employed to utilize other 2D human pose datasets [1, 12, 29] for training.", + "bbox": [ + 75, + 705, + 468, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the performance evaluation of the proposed method, four person-to-person occlusion datasets (i.e., 3DPW-PC [41], OCHuman [48], CrowdPose [23], and CMU-Panoptic [13]) are adopted. Specifically, the 3DPW-PC dataset is a subset of the 3DPW dataset where images taken under person-to-person occlusions are collected ac", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cording to [38]. The OCHuman dataset consists of severe occlusion cases between multiple persons while the CrowdPose dataset contains various person-to-person occlusions occurring in crowded scenes. Moreover, the CMU-Panoptic dataset includes multi-person sequences with diverse inter-person interactions. Based on such occlusion-oriented benchmark datasets, the performance of the proposed method will be evaluated and analyzed in-depth in the following subsection.", + "bbox": [ + 496, + 705, + 893, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Performance Evaluation", + "text_level": 1, + "bbox": [ + 498, + 848, + 723, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Evaluation. To show the effectiveness of the proposed method, we compare ours with previous meth-", + "bbox": [ + 496, + 869, + 892, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10558", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c6ad056a2dc827e8a7cdbfb6ce262158e4f2e3502ff9accb43394d2b28cef213.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 74, + 197, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/875d2a8a7cf7f8299b06ec969044c6addd02bdff9bf5093d701587c5f93dae72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 199, + 74, + 297, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05abd969148a7c3478b89837d54b4eca58552aac0037b4172cb33e4b988a9f59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 74, + 408, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/53da101d757856d6ca98c5b860d0c81f396a7775d42ac25db3460c65e78f9e46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 74, + 516, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c0d56390c2f07ab8c4501947517a4c2097c61aa5cd88b6336ffe54b52ce042f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 74, + 617, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/49fbadafe65103e7b6b683ce71da8372fe5f5c2d76f48843d1ce1fd3955be598.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 74, + 718, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2dd82cf77a3ecb50cdc45fd95a6e684b219062a97b8742063b3c3fd30741c71d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 74, + 789, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc005b9173a5a976d60b0f3fcdf6c9a3362278203b02a74b1db22bd6bff7c2cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 74, + 890, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf4d62d0525d537ebdcd17148caf07841467cd9c86400d2ee5c21c155ef964c3.jpg", + "image_caption": [ + "Figure 6. More results of 3D human mesh reconstruction by the proposed method on 3DPW-PC [41] (1st row) and OCHuman [48] (2nd row) datasets." + ], + "image_footnote": [], + "bbox": [ + 80, + 161, + 158, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3cfab3697e6199b14bbba3eab4dfc1c2ddd827bab112c6d5b4e2dee50fe4269e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 161, + 161, + 279, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/15c110ced19d9fe5e30b9d628b61240e99094978bd9cf5daaff0d0093433a15c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 161, + 375, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86e875228e12af3217561233a517cd9b4895c2e7a9f9187049dedad0a389f17c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 161, + 457, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5eef3872593dc598fffed0eb2da83e0bdd6f4fde3ec796dc8467b8c525a40ef7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 459, + 161, + 535, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/968454e7772b5fb51673a7442018324923adec459c91ca912c9c9dee0bbe25e9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 161, + 669, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5f95b6139acb27b2918bd7467ef3d79b304bc92883bcf152fc38f7564d92712a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 161, + 743, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/456e54ad7d4351caa95d940c43cd5d873142e235b06a10591eae7cb97ff86774.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 161, + 890, + 247 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/941311720fac82805014f234ef4dcd1369c9a3302b2358268ab3b5f7833f82ba.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsHaggl.MafiaUtim.PizzaMean
SPIN [19]124.3132.4150.4153.5133.1
CRMH [11]129.6133.5153.0156.7143.2
BMP [47]120.4132.7140.9147.5135.4
PARE [18]143.1193.1219.8190.4186.6
ROMP [38]111.8129.0148.5149.1134.6
OCHMR [16]115.5123.7142.6150.6133.1
3DCrowdNet [7]109.6135.9129.8135.6127.6
Ours109.1122.5137.8135.0126.1
", + "bbox": [ + 86, + 311, + 460, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ods for 3D human mesh reconstruction, i.e., SPIN [19], CRMH [11], BMP [47], PyMAF [46], PARE [18], ROMP [38], OCHMR [16], 3DCrowdNet [7], HMDiff [8], and Coordinate [22], based on person-to-person occlusion benchmarks. To evaluate the proposed method on 3D human mesh datasets, three metrics are adopted, i.e., mean per joint position error (MPJPE) [10], Procrustes-aligned mean per joint position error (PA-MPJPE) [52], and mean per vertex position error (MPVPE) [36]. Specifically, MPJPE indicates the average value of the Euclidean distance between the predicted 3D joint and the corresponding ground truth. PA-MPJPE means MPJPE that is calculated after applying the Procrustes analysis to the estimated body mesh. MPVPE is computed by averaging the Euclidean distance between the predicted vertex and the corresponding ground truth. For 2D human pose datasets, the performance is evaluated by using the average precision (AP), which is calculated based on the object keypoint similarity (OKS) [29]. In addition, AP according to different threshold values (i.e., $\\mathrm{AP^{50}}$ and $\\mathrm{AP^{75}}$ ) and scales of the human object (i.e., $\\mathrm{AP^M}$ and $\\mathrm{AP^L}$ ) is also adopted for the performance comparison. Note that ResNet-50 [9] is employed as the backbone network of the proposed method, which is the default setting for the performance report in this subsection.", + "bbox": [ + 75, + 537, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b2291a1d9cab5da70d92a785d8e2c9dfe8b084a33acd2adf8632323fc0e86f76.jpg", + "table_caption": [ + "Table 2. Performance comparison by MPJPE based on the CMU-Panoptic dataset (best results and second results are shown in bold and underlined, respectively)." + ], + "table_footnote": [], + "table_body": "
MethodsMPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
METRO [27]77.147.988.2
PARE [18]74.546.588.6
ROMP [38]76.747.393.4
MeshGraphormer [28]74.745.687.7
FastMETRO [5]73.544.684.1
CLIFF [26]72.045.785.3
PointHMR [17]73.944.985.5
ImpHMR [4]74.345.487.1
HMDiff [8]72.744.582.4
CoordFormer [22]79.446.594.4
Ours (ResNet-50)78.047.885.6
Ours (HRNet-32)73.244.380.3
", + "bbox": [ + 503, + 310, + 890, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Performance comparison based on the 3DPW dataset by following the protocol 3, i.e., fine-tuned on 3DPW (best results and second results are shown in bold and underlined, respectively).", + "bbox": [ + 498, + 523, + 892, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "First of all, the performance comparison based on 3DPW-PC, OCHuman, and CrowdPose datasets is shown in Table 1. As can be seen, the proposed method shows the meaningful performance improvement compared to previous approaches. Specifically, MPJPE and MPVPE on the 3DPW-PC dataset prove that our model can successfully estimate both pose and shape for occluded human mesh reconstruction. Moreover, the proposed method outperforms all state-of-the-art methods in terms of AP and $\\mathrm{AP^{50}}$ with the significant performance gain on OCHuman and CrowdPose datasets. In Table 2, MPJPE of the proposed method on the CMU-Panoptic dataset is compared with others. We can see that the proposed method yields the reliable performance in most sequences while achieving the best result in the average MPJPE (see the rightmost column of Table 2). From the result reported in Tables 1 and 2, we could confirm that the proposed instance-aware contrastive learning scheme is effective to reconstruct human meshes under various person-to-person occlusions. Furthermore, we also evaluate the proposed method on the entire test set of 3DPW", + "bbox": [ + 496, + 598, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10559", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d70be056808bab7c68d2207b7c580fb1497e52069f76ddd0ba4d55cd0b81eb70.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsMPJPE(↓)PA-MPJPE(↓)
Baseline (i.e., w/o center and joint features)104.280.2
Ours†102.278.2
Ours102.077.2
", + "bbox": [ + 78, + 88, + 467, + 170 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/78389bf544cf1d48dda62b5541c36e4cb51f8f9c0a9a80bb39ed10a948b3be3a.jpg", + "table_caption": [ + "Table 4. Performance analysis according to the change of the network architecture. $\\dagger$ denotes the performance without applying positional encoding to the center-aligned instance map." + ], + "table_footnote": [], + "table_body": "
Feature DimensionMPJPE(↓)PA-MPJPE(↓)
32103.578.3
64102.077.2
128103.178.0
256104.278.6
", + "bbox": [ + 112, + 243, + 433, + 329 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance variations according to the change of the feature dimension for the center-aligned instance map and the joint-aligned instance map.", + "bbox": [ + 75, + 340, + 468, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "by following the protocol 3 [41]. In particular, we conduct the experiment by using two different backbone networks, i.e., ResNet-50 [9] and HRNet-32 [42], and the corresponding results are shown in Table 3. As can be seen, the proposed method performs robustly in a variety of real-world environments, not just for occlusion cases.", + "bbox": [ + 75, + 411, + 467, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Evaluation. The qualitative comparison of the proposed method with ROMP [38] and 3DCrowdNet [7] based on the CrowdPose dataset is shown in Fig. 5. As can be seen, the proposed method can successfully reconstruct multiple human meshes in complicated person-to-person occlusions. Specifically, the reconstructed mesh is well aligned to the target person without confusion with other persons (see the left two examples in Fig. 5). This is because the proposed method is able to effectively utilize the identity information of each person in the feature space. The fourth and fifth columns of Fig. 5 show the robustness of our method in crowded scenes. Furthermore, the proposed method works reliably even under severe occlusions between multiple persons as shown in the rightmost three examples in Fig. 5. More reconstruction results by the proposed method on 3DPW-PC and OCHuman datasets are also shown in Fig. 6. Based on this, it is thought that our instance-aware contrastive learning scheme is greatly helpful in understanding the occlusion context by overlapped persons and generating the plausible human mesh.", + "bbox": [ + 75, + 503, + 467, + 804 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 816, + 228, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, several comparative experiments are conducted to demonstrate the effectiveness of the proposed method. The performance for all the experiments in this subsection is evaluated on the 3DPW-PC [41] dataset. First", + "bbox": [ + 75, + 839, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7258e91c36869dce4b91dc8ec6268d67449ba71a1c45c1636c22325fd7239a1c.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 629, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0fdb233cda4d9d4f315a29130e33ff5e2a1d46fab10abce77de34fc3173e845c.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 632, + 88, + 758, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f333580801e9ec988eca831d330e51ea247529c90ba4b0b2dca7b1a86e665e0f.jpg", + "image_caption": [ + "(c)", + "Figure 7. (a) Input image. (b) Reconstruction result by baseline. (c) Reconstruction result by the proposed method." + ], + "image_footnote": [], + "bbox": [ + 761, + 88, + 888, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of all, the effect of our instance-aware contrastive learning scheme is analyzed and the corresponding result is shown in Table 4. As can be seen in Table 4, the performance for occluded human mesh reconstruction is significantly improved by leveraging the identity information into latent features for centers and their related joints. Furthermore, we can see that applying positional encoding to the center-aligned instance map is also useful for the model to discriminatively represent each center feature under severe occlusion cases. The effect of our instance-aware learning scheme is shown in Fig. 7. In the following, we check the performance variation by the change of the feature dimension for both center-aligned and joint-aligned instance maps is shown in Table 5. The best performance is achieved when the feature dimension is set to 64, thus this setting has been used as default for the performance evaluation of the proposed method. Note that the performance in all the settings is better than our baseline (i.e., the first row of Table 4). Based on ablation studies, we can conclude that the proposed instance-aware contrastive learning scheme is effective for occluded human mesh reconstruction under various real-world environments.", + "bbox": [ + 496, + 287, + 890, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 635, + 625, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a simple yet powerful method for occluded human mesh reconstruction, especially focusing on person-to-person occlusions. The core of the proposed method is to embed the identity information into latent features for body centers and joints of each person. To do this, we propose a novel instance-aware contrastive learning scheme. Experimental results on benchmark datasets show that the proposed method works reliably even under various person-to-person occlusions occurring in real-world environment.", + "bbox": [ + 496, + 661, + 890, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by Institute of Information Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00207, Immersive Media Research Laboratory).", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10560", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. In Proc. IEEE Conf. Comput. Vis. Pattern Recog., pages 3686-3693, 2014. 6", + "[2] Federica Bogo, Angjoo Kanazawa, Christoph Lassner, Peter Gehler, Javier Romero, and Michael J Black. Keep it SMPL: Automatic estimation of 3D human pose and shape from a single image. 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Intell., 41(4):901-914, 2018. 7" + ], + "bbox": [ + 501, + 92, + 893, + 839 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10562", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Instance-aware Contrastive Learning for Occluded Human Mesh Reconstruction/fc45c75f-97ff-434b-b185-fb7682fd134e_model.json b/2024/Instance-aware Contrastive Learning for Occluded Human Mesh Reconstruction/fc45c75f-97ff-434b-b185-fb7682fd134e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..771268f156546488c48e902fb3e49eba6d9523e8 --- /dev/null +++ b/2024/Instance-aware Contrastive Learning for Occluded Human Mesh Reconstruction/fc45c75f-97ff-434b-b185-fb7682fd134e_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.131, + 0.895, + 0.152 + ], + "angle": 0, + "content": "Instance-aware Contrastive Learning for Occluded Human Mesh Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.18, + 0.799, + 0.216 + ], + "angle": 0, + "content": "Mi-Gyeong Gwon1 Gi-Mun Um2 Won-Sik Cheong2 Wonjun Kim1* \n1Konkuk University 2Electronics and Telecommunications Research Institute" + }, + { + "type": "text", + "bbox": [ + 0.225, + 0.219, + 0.742, + 0.235 + ], + "angle": 0, + "content": "{kmk3942,wonjkim}@konkuk.ac.kr {gmum,wscheong}@etri.re.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.664 + ], + "angle": 0, + "content": "A simple yet effective method for occlusion-robust 3D human mesh reconstruction from a single image is presented in this paper. Although many recent studies have shown the remarkable improvement in human mesh reconstruction, it is still difficult to generate accurate meshes when person-to-person occlusion occurs due to the ambiguity of who a body part belongs to. To address this problem, we propose an instance-aware contrastive learning scheme. Specifically, joint features belonging to the target human are trained to be proximate with the center feature (i.e., feature extracted from the body center position). On the other hand, center features of different human instances are forced to be far apart so that joint features of each person can be clearly distinguished from others. By interpreting the joint possession based on such contrastive learning scheme, the proposed method easily understands the spatial occupancy of body parts for each person in a given image, thus can reconstruct reliable human meshes even with severely overlapped cases between multiple persons. Experimental results on benchmark datasets demonstrate the robustness of the proposed method compared to previous approaches under person-to-person occlusions. The code and model are publicly available at: https://github.com/DCVL-3D/InstanceHMR_release." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.677, + 0.21, + 0.692 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.471, + 0.88 + ], + "angle": 0, + "content": "Recently, 3D human mesh reconstruction has become a major research topic with the increasing demand in entertainment areas such as AR/VR and sports broadcasting. In line with this trend, considerable efforts have been made to predict reliable meshes from a single image by using deep learning techniques. Specifically, model-based methods, which aim to reconstruct human poses and shapes by estimating parameters of the skinned multi-person linear (SMPL) model [32], have been introduced. Since the problem of inferring a large number of vertices is simplified to the problem of estimating a few parameters through various network architectures, model-based approaches have been" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.27, + 0.895, + 0.422 + ], + "angle": 0, + "content": "actively explored while bringing the significant progress in human mesh reconstruction [2, 4, 15, 18, 19, 21, 24, 25, 37, 46]. On the other hand, model-free approaches also have drawn a lot of attentions due to their ability to express local details of mesh surfaces by directly regressing every vertex without any constraint of the parameter space. In particular, the transformer architecture has been widely adopted to reconstruct accurate meshes by considering the relationship between vertices in a global manner [5, 17, 27, 28, 44, 45, 50, 51]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.895, + 0.7 + ], + "angle": 0, + "content": "Despite meaningful advances in the field of 3D human mesh reconstruction, person-to-person occlusions frequently occurring in crowd scenes still remain a challenging issue due to ambiguities of possession for body parts. To resolve this issue, several approaches have recently begun to be introduced. For example, there have been attempts to estimate discriminative locations of each person in the 2D space and utilize them to extract features for individual mesh regression [7, 16, 38]. Reasoning the depth order of multiple people also has been considered to understand the relationship between overlapped subjects in a given image [11, 39, 47]. Some methods first predict the occlusion-robust 3D skeletons, which form reliable poses even for invisible body parts, and then lift them to mesh structures [31]. Even though considerable efforts have been consistently devoted to this task, attempts to exploit contextual cues of the occluded area, which is occupied by each person, are still insufficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.896, + 0.903 + ], + "angle": 0, + "content": "In this paper, a new perspective for effectively handling person-to-person occlusions is presented. In the scene where people are overlapped, one of the biggest obstacles is the uncertainty about the ownership of a body part. While it is relatively easy to semantically understand which area in a given image corresponds to which type of body part (e.g., hand or foot), it can be challenging to determine who owns that body part. This makes the model confused and eventually yields unnatural reconstruction results. To deal with this problem, we propose to guide the network to learn discriminative representations of body parts for each person by our instance-aware contrastive learning scheme. Specifically, two novel feature maps, i.e., center-aligned instance" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.218, + 0.9 + ], + "angle": 0, + "content": "\\*corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10553" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.073, + 0.258, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.23, + 0.176, + 0.242 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.073, + 0.47, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.229, + 0.378, + 0.242 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.48, + 0.073, + 0.699, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.583, + 0.23, + 0.598, + 0.242 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.073, + 0.891, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.23, + 0.81, + 0.242 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.247, + 0.894, + 0.304 + ], + "angle": 0, + "content": "Figure 1. (a) An example of person-to-person occlusion. (b), (c), and (d) Visualizations of the information adopted to guide the feature encoding for human mesh reconstruction in OCHMR [16], 3DCrowdNet [7], and the proposed method, respectively. For better visibility, all joints are represented in a single image at the 2D pose heatmap of (c) and the joint heatmap of (d), and only a few of joint features (e.g., right hand, left elbow, and right foot) are shown in the joint-aligned instance map of (d)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.473, + 0.893 + ], + "angle": 0, + "content": "map and joint-aligned instance map, are encoded in the proposed architecture, which can describe the possession relationship between all human instances and their visible body joints. These maps learn to represent the identity information of each human instance by forcing the center feature to pull joint features of the same person while pushing out center features of non-target persons in the latent space. Note that center features and joint features are sampled at the body center position and joint locations in the center-aligned instance map and the joint-aligned instance map, respectively, as shown in Fig. 1(d). Such identity representations make it easy to distinguish which instance each joint belongs to, thus the model can better understand the occluded context and determine the area of the image to focus on for occluded human mesh reconstruction. A comparison between previous approaches and the proposed method for handling person-to-person occlusions is illustrated in Fig. 1. In [16], relative positions of multiple persons are given to the model in the form of global and local center maps as shown in Fig. 1(b). However, since the center position is an extremely small amount of information compared to the complex body structure, the model may hardly figure out details of body part regions in occlusion situations. On the other hand, the spatial guidance of the body region for the target person is provided to the network based on the 2D pose heatmap in [7]. However, features of nontarget person areas also can be unnecessarily fused into features for target mesh reconstruction (see the bottom part of Fig. 1(c)). Unlike such previous approaches, the proposed method clearly indicates the possession of all body parts by expressing the identity information at joint locations as well as body center positions via the instance-aware contrastive learning scheme as shown in Fig. 1(d). Moreover, meshes for every person can be reliably reconstructed in a single stream (i.e., without using the bounding box) by considering the mutual relationship among the spatial occupancy of each person's body part. The main contributions of this paper are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.319, + 0.892, + 0.425 + ], + "angle": 0, + "content": "- We propose to indicate the spatial occupancy of body parts corresponding to each human instance for occlusion-robust 3D human mesh reconstruction. With the awareness of the body part possession of every person, the model can easily understand the person-to-person occlusion and successfully generate human meshes with natural poses." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.425, + 0.893, + 0.561 + ], + "angle": 0, + "content": "- We represent the relationship between human instances and their spatial keypoints (i.e., body centers and joints) at the feature level via the proposed instance-aware contrastive learning scheme. Specifically, by guiding the center feature of the target person to push out that of non-target persons and pull corresponding joint features in the latent space, identities of different persons can be distinctively embedded into center and joint features." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.319, + 0.893, + 0.561 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.573, + 0.65, + 0.588 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.892, + 0.658 + ], + "angle": 0, + "content": "In this Section, we present a systematic review of previous methods for monocular 3D human mesh reconstruction and explore various approaches for handling person-to-person occlusions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.788, + 0.681 + ], + "angle": 0, + "content": "2.1. 3D Human Mesh Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Deep learning-based methods for 3D human mesh reconstruction can be divided into two main groups, i.e., model-based and model-free methods. The former aims to estimate pose and shape parameters of the SMPL [2] model. In the early stage, Kanazawa et al. [15] proposed to regress SMPL parameters by using the end-to-end convolutional neural network and devised the adversarial loss for plausible mesh generation. Kolotouros et al. [19] designed the optimization loop that can be combined with end-to-end regression frameworks such as [15], to further refine reconstruction results. Moreover, Zhang et al. [46] tried to rectify meshes by iteratively feeding pyramidal mesh-aligned features into the mesh regression network. A bottom-up framework, which predicts meshes of multiple persons in a given image dur" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10554" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.606 + ], + "angle": 0, + "content": "ing a single inference, was introduced by Sun et al. [38] for the first time. Specifically, they proposed to extract SMPL parameters by the sampling process based on body center positions. Li et al. [26] incorporated the bounding box location into the network for accurately estimating the global orientation. To reconstruct the human mesh that is aligned well to the image pixel, Shetty et al. [37] proposed to first predict vertices on the input image plane, and then compute SMPL parameters by comparing them with the template mesh part by part based on inverse kinematics. Cho et al. [4] attempted to learn the consistency of human pose and shape in arbitrary view directions by using neural feature fields. In contrast to such model-based approaches, modelfree methods directly estimate 3D coordinates of mesh vertices. As a pioneer, Kolotouros et al. [20] adopted the graph convolutional neural network (GraphCNN) to effectively transform image features into vertex coordinates. Choi et al. [6] also utilized GraphCNN to lift estimated 2D and 3D poses to the 3D mesh. Meanwhile, Lin et al. [27] presented a new direction in model-free approaches, by employing the transformer encoder with the dimension reduction technique for mesh regression. They further improved the performance by incorporating GraphCNN into the transformer encoder block [28]. To alleviate the computational burden of the transformer-based architecture, Cho et al. [5] proposed to disentangle image features and geometric parameters of the human body based on the cross-attention module. Kim et al. [17] designed a point-guided feature sampling scheme to effectively extract vertex-relevant features for the transformer-based mesh regressor. More recently, Foo et al. [8] adopted the diffusion model for the human mesh reconstruction by leveraging the pose heatmap in the diffusion process to enable the mesh estimation conditioned on the input image." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.62, + 0.411, + 0.636 + ], + "angle": 0, + "content": "2.2. Handling Person-to-Person Occlusions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Even though many studies mentioned above have brought significant advances for monocular 3D human mesh reconstruction, they still suffer from ambiguities driven by person-to-person occlusions, which often occur in real-world environments. To cope with this problem, there have been various technical attempts. For example, Jiang et al. [11] introduced a new loss function that minimizes the discrepancy between the human segmentation masks and projected meshes to arrange the depth order of the people. In a similar vein, Zhang et al. [47] tried to learn the ordinal relation by supervising the difference between depth values of multiple persons. Instead of simply guiding the network via loss functions, Sun et al. [39] incorporated the bird's-eye-view body center heatmap into the pipeline of mesh estimation to consider the depth cue. Yang et al. [43] adopted to synthesize the other people to the input data for consideration of more variants from person-to-person occlusions." + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.087, + 0.897, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.243, + 0.895, + 0.286 + ], + "angle": 0, + "content": "Figure 2. The detailed process of the instance-aware contrastive learning scheme. Note that the ground truth of body center and joint positions is used for the feature sampling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.3, + 0.895, + 0.603 + ], + "angle": 0, + "content": "To specify the position of the target person, Khirodkar et al. [16] introduced the context normalization block, which fuses global and local center heatmaps with corresponding features. Choi et al. [7] utilized the 2D pose heatmap to focus on the feature belonging to the area of the target person in crowded scenes. Cha et al. [3] attempted to refine multiple human meshes based on inter-person relations that are computed by the transformer architecture. Liu et al. [31] proposed to apply the knowledge transfer technique to the 3D keypoint detection [49] for successfully reasoning invisible body parts under occlusions. Li et al. [22] proposed a body center attention mechanism to consider spatial-temporal relations of multiple persons at the pixel level. To complement the lack of the training data under multi-person scenes, Sun et al. [40] tried to synthesize plausible crowded examples by putting human samples at appropriate places of the given image with a reasonable scale according to the scene context. Moreover, they also proposed to learn the consistency between features extracted from the same human sample with and without occlusions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.673, + 0.634 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.895, + 0.749 + ], + "angle": 0, + "content": "The proposed method aims to learn the spatial occupancy of body parts for each person by using the instance-aware contrastive learning scheme as shown in Fig. 2. By incorporating the identity information into encoded features, the proposed method can achieve the robust performance against person-to-person occlusions. The overall architecture of the proposed method is illustrated in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.824, + 0.774 + ], + "angle": 0, + "content": "3.1. Instance-aware Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In the bottom-up approach for human mesh reconstruction, it is important to grasp the individual cue between multiple persons. To this end, we guide the process of mesh estimation based on the regional distinction of each human area, i.e., 24 body joints defined by the SMPL model [2]. Specifically, the backbone feature is encoded into two different feature maps, i.e., center-aligned instance map and joint-aligned instance map, through the corresponding network" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10555" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.069, + 0.889, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.361, + 0.893, + 0.391 + ], + "angle": 0, + "content": "Figure 3. The overall architecture of the proposed method for occluded human mesh reconstruction. \\( h \\) and \\( w \\) are set to 64. \\( \\theta \\) and \\( \\beta \\) denote pose and shape parameters of the SMPL model. Note that instance-aware contrastive learning is conducted only in the training phase." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.473, + 0.603 + ], + "angle": 0, + "content": "branch as shown in Fig. 3. Note that the predicted center heatmap \\( H_{C} \\) and joint heatmap \\( H_{J} \\) are adopted in this encoding process to provide the spatial information of body centers and joints. In addition, the positional encoding is also applied to the center-aligned instance map to prevent ambiguous representations between different people who have similar appearances. After that, center features and joint features are sampled at body center locations and visible joint positions of the center-aligned instance map and the joint-aligned instance map, respectively. These sampled features are subsequently projected into the latent space by using the nonlinear projector, which consists of fully connected layers and ReLUs (see \\( P_{C} \\) and \\( P_{J} \\) in Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.472, + 0.816 + ], + "angle": 0, + "content": "Now, such projected features are fed into our instance-aware contrastive learning scheme. The detailed process is shown in Fig. 2. First, the center feature of the target person (i.e., anchor) is forced to push out those of other persons. By placing different human instances far apart from each other in the latent space, center features can implicitly represent the identity information for each person in a discriminative way. Second, the center feature pulls joint features belonging to the same person to a close distance. This facilitates the joint feature to express the human instance to which it belongs, by embedding the target identity information. To this end, two loss functions are designed based on the cosine similarity, which is suitable for measuring the directional coherence between embedding vectors, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.832, + 0.47, + 0.872 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p u s h}} (a, b) = 1 + \\frac {a \\cdot b}{\\| a \\| \\| b \\|}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.868, + 0.363, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p u l l} (a, b) = 1 - \\frac {a \\cdot b}{| | a | | | | b | |}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.405, + 0.892, + 0.51 + ], + "angle": 0, + "content": "Specifically, \\(\\mathcal{L}_{push}\\) is used to maximize the distance between center features of different people and \\(\\mathcal{L}_{pull}\\) is used to minimize the distance between the center feature and the joint feature of the same person in the latent space. By considering every possible center-to-center and center-to-joint combination, the proposed contrastive loss is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.518, + 0.892, + 0.606 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o n t}} = \\frac {2}{N (N - 1)} \\sum_ {i \\neq j} ^ {N} \\mathcal {L} _ {\\text {p u s h}} \\left(u _ {i}, u _ {j}\\right) \\tag {2} \\\\ + \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {1}{K _ {i}} \\sum_ {k = 1} ^ {K _ {i}} \\mathcal {L} _ {p u l l} (u _ {i}, v _ {i} ^ {k}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.81 + ], + "angle": 0, + "content": "where \\( u \\) and \\( v \\) indicate the center feature and the joint feature, respectively. \\( N \\) and \\( K_{i} \\) denote the number of people and the number of visible joints belonging to the \\( i \\)-th person in the input image, respectively. The effect of the proposed instance-aware contrastive learning scheme is shown in Fig. 4. As can be seen, the identity information is embedded into latent features during our instance-aware contrastive learning. Consequently, it is thought that both center-aligned instance map and joint-aligned instance map play an important role to describe the possession relationship between human instances and their visible joints. Note that the instance-aware contrastive learning part is conducted only in the training phase." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In order to utilize this possession cue in the process of mesh regression, we incorporate the center-aligned instance map and the joint-aligned instance map into the network branch for estimating the SMPL parameter map (see the second branch from bottom in Fig. 3). To accurately indicate valid locations, the center heatmap and the joint" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10556" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.079, + 0.287, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.181, + 0.192, + 0.193 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.072, + 0.478, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.377, + 0.181, + 0.395, + 0.193 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.48, + 0.073, + 0.681, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.582, + 0.182, + 0.599, + 0.194 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.073, + 0.888, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.181, + 0.804, + 0.194 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.2, + 0.894, + 0.256 + ], + "angle": 0, + "content": "Figure 4. A visualization example of center features and joint features in the latent space. The feature dimension is reduced from 64 to 3 by using [33] for the visualization. (a) Input image with marks for positions of body centers (dark) and joints (bright). Note that points belonging to the same person are represented as the same color attribute. The effect of the proposed instance-aware contrastive learning scheme is shown sequentially, i.e., (b) before training, (c) middle of training, and (d) after training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.47, + 0.424 + ], + "angle": 0, + "content": "heatmap are also employed for this concatenation process. Finally, pose and shape parameters of each person are sampled from the SMPL parameter map according to the predicted center position in a similar way of [38]. It is noteworthy that the model can precisely consider the occupancy of each human instance via such identity representation in the feature space, which leads to generation of reliable human meshes even with various person-to-person occlusions. An example of occluded human mesh reconstruction is shown in the bottom right of Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.433, + 0.226, + 0.447 + ], + "angle": 0, + "content": "3.2. Loss functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.47, + 0.59 + ], + "angle": 0, + "content": "The proposed method is trained based on nine loss terms, i.e., contrastive loss \\(\\mathcal{L}_{cont}\\) (which is explained in subsection 3.1), body center heatmap loss \\(\\mathcal{L}_{center}\\), joint heatmap loss \\(\\mathcal{L}_{joint}\\), pose loss \\(\\mathcal{L}_{pose}\\), shape loss \\(\\mathcal{L}_{shape}\\), Mixture Gaussian prior loss \\(\\mathcal{L}_{prior}\\), 3D joint loss \\(\\mathcal{L}_{3d}\\), Procrustes-aligned 3D joint loss \\(\\mathcal{L}_{pa3d}\\), and 2D joint loss \\(\\mathcal{L}_{2d}\\). First, the focal loss [30, 38] is adopted to train the body center heatmap \\(H_{C}\\) and the joint heatmap \\(H_{J}\\), which is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.6, + 0.469, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {f o c a l} (H, \\tilde {H}, \\tilde {H} ^ {\\prime}) = - \\frac {\\mathcal {L} _ {p o s} (H , \\tilde {H} ^ {\\prime}) + \\mathcal {L} _ {n e g} (H , \\tilde {H} , \\tilde {H} ^ {\\prime})}{\\sum \\tilde {H} ^ {\\prime}}, \\\\ \\mathcal {L} _ {n e g} (H, \\tilde {H}, \\tilde {H} ^ {\\prime}) = \\log (1 - H) H ^ {2} (1 - \\tilde {H}) ^ {4} (1 - \\tilde {H} ^ {\\prime}), \\\\ \\mathcal {L} _ {\\text {p o s}} \\left(H, \\tilde {H} ^ {\\prime}\\right) = \\log (H) \\left(1 - H\\right) ^ {2} \\tilde {H} ^ {\\prime}, \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.71, + 0.469, + 0.785 + ], + "angle": 0, + "content": "where \\(H\\) and \\(\\tilde{H}\\) denote a single heatmap and the corresponding ground truth, respectively. \\(\\tilde{H}^{\\prime}\\) indicates the binary map that is marked on the location of the positive class in \\(\\tilde{H}\\). By using the focal loss, \\(\\mathcal{L}_{center}\\) and \\(\\mathcal{L}_{joint}\\) are formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.794, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {c e n t e r} = \\mathcal {L} _ {f o c a l} (H _ {C}, \\tilde {H} _ {C}, \\tilde {H} _ {C} ^ {\\prime}), \\\\ \\mathcal {L} _ {\\text {j o i n t}} = \\frac {1}{\\mathcal {J}} \\sum_ {j = 1} ^ {\\mathcal {J}} \\mathcal {L} _ {\\text {f o c a l}} \\left(H _ {J} ^ {j}, \\tilde {H} _ {J} ^ {j}, \\tilde {H} _ {J} ^ {' j}\\right), \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{J}\\) is the number of joint heatmaps which is set to 24 according to the SMPL model. The remaining loss terms" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.892, + 0.513 + ], + "angle": 0, + "content": "are used to directly supervise the process of human mesh reconstruction. In particular, \\(\\mathcal{L}_{\\text {pose }}\\) and \\(\\mathcal{L}_{\\text {shape }}\\) compute the difference between predicted pose and shape parameters and the corresponding ground truth based on \\(L_{2}\\) loss, respectively [15, 20]. Mixture Gaussian prior loss \\(\\mathcal{L}_{\\text {prior }}\\) is employed to attain the naturalness of body meshes as introduced in [2]. In our work, Euclidean distance is utilized to calculate the spatial gap in the coordinate system for following three loss terms. The distance between estimated 3D joints and the corresponding ground truth is computed by \\(\\mathcal{L}_{3d}\\) [15, 20]. \\(\\mathcal{L}_{pa3d}\\) indicates \\(\\mathcal{L}_{3d}\\) after Procrustes alignment is conducted to the reconstructed mesh [38]. The coordinates of joints projected onto the 2D space are used to measure \\(\\mathcal{L}_{2d}\\) [15, 20]. Finally, the total loss function is defined by using the weighted sum of all the aforementioned loss terms as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.518, + 0.891, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {\\text {c o n t}} \\mathcal {L} _ {\\text {c o n t}} + \\lambda_ {\\text {c e n t e r}} \\mathcal {L} _ {\\text {c e n t e r}} + \\lambda_ {\\text {j o i n t}} \\mathcal {L} _ {\\text {j o i n t}} \\\\ + \\lambda_ {p o s e} \\mathcal {L} _ {p o s e} + \\lambda_ {s h a p e} \\mathcal {L} _ {s h a p e} + \\lambda_ {p r i o r} \\mathcal {L} _ {p r i o r} \\\\ + \\lambda_ {3 d} \\mathcal {L} _ {3 d} + \\lambda_ {p a 3 d} \\mathcal {L} _ {p a 3 d} + \\lambda_ {2 d} \\mathcal {L} _ {2 d}, \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.586, + 0.891, + 0.647 + ], + "angle": 0, + "content": "where \\(\\lambda_{cont}\\), \\(\\lambda_{center}\\), \\(\\lambda_{joint}\\), \\(\\lambda_{pose}\\), \\(\\lambda_{shape}\\), \\(\\lambda_{prior}\\), \\(\\lambda_{3d}\\), \\(\\lambda_{pa3d}\\), and \\(\\lambda_{2d}\\) are the balancing factor for each loss term, which are set to 50, 160, 50, 80, 6, 1.6, 200, 360, and 400, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.658, + 0.706, + 0.674 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.683, + 0.716, + 0.699 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.892, + 0.843 + ], + "angle": 0, + "content": "The proposed method is implemented on the PyTorch framework with an Intel E5-1650@3.60GHz CPU and two NVIDIA GeForce RTX 3090 GPUs. All the parameters of the proposed network are updated by the Adam optimizer, where momentum factors are set to 0.9 and 0.999, respectively. We use the batch size of 64 and the learning rate is set to \\(5 \\times 10^{-6}\\) during 30 training epochs. Input images are randomly cropped and rotated before they are resized to the resolution of \\(512 \\times 512\\) pixels by using zero padding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.849, + 0.696, + 0.864 + ], + "angle": 0, + "content": "4.2. Benchmark Datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The proposed method is trained by using three 3D human pose datasets (i.e., Human3.6M [10], MPI-INF-3DHP [34]," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10557" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.077, + 0.895, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.382, + 0.893, + 0.41 + ], + "angle": 0, + "content": "Figure 5. Results of 3D human mesh reconstruction on the CrowdPose [23] dataset. From top to bottom: input images, results by ROMP [38], 3DCrowdNet [7], and the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.429, + 0.896, + 0.626 + ], + "angle": 0, + "content": "
Methods3DPW-PCOCHumanCrowdPose
MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)AP(↑)\\( AP^{50}(↑) \\)\\( AP^{75}(↑) \\)\\( AP^M(↑) \\)\\( AP^L(↑) \\)\\( AP(↑) \\)\\( AP^{50}(↑) \\)\\( AP^{75}(↑) \\)
SPIN* [19]129.682.6157.612.746.819.417.826.216.440.110.6
PyMAF* [46]126.781.3154.314.348.721.518.028.717.442.713.0
ROMP* [38]119.779.7152.815.655.023.618.730.018.944.613.8
ROMP [38]115.675.8147.519.856.225.019.332.928.558.824.7
OCHMR* [16]117.577.1149.624.860.728.622.334.221.448.316.5
CLIFF* [26]---23.249.820.4--27.451.525.9
HMDiff* [8]114.273.5143.1--------
CoordFormer* [22]101.579.3---------
Ours*99.976.3126.430.575.817.335.130.528.561.623.2
Ours102.077.2131.034.980.024.027.135.031.665.726.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.637, + 0.893, + 0.679 + ], + "angle": 0, + "content": "Table 1. Performance comparison of occluded human mesh reconstruction based on 3DPW-PC, OCHuman, and CrowdPose datasets (best results and second results are shown in bold and underlined, respectively). Note that * denotes the performance without using the CrowdPose dataset for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.706, + 0.47, + 0.797 + ], + "angle": 0, + "content": "and MuCo-3DHP [35]) and four 2D human pose datasets (i.e., MPII [1], LSP [12], COCO [29], and CrowdPose [23]). In particular, only 2D pose labels are used for [23] while pseudo mesh labels, which are generated by [14], are employed to utilize other 2D human pose datasets [1, 12, 29] for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "For the performance evaluation of the proposed method, four person-to-person occlusion datasets (i.e., 3DPW-PC [41], OCHuman [48], CrowdPose [23], and CMU-Panoptic [13]) are adopted. Specifically, the 3DPW-PC dataset is a subset of the 3DPW dataset where images taken under person-to-person occlusions are collected ac" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.895, + 0.842 + ], + "angle": 0, + "content": "cording to [38]. The OCHuman dataset consists of severe occlusion cases between multiple persons while the CrowdPose dataset contains various person-to-person occlusions occurring in crowded scenes. Moreover, the CMU-Panoptic dataset includes multi-person sequences with diverse inter-person interactions. Based on such occlusion-oriented benchmark datasets, the performance of the proposed method will be evaluated and analyzed in-depth in the following subsection." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.849, + 0.725, + 0.864 + ], + "angle": 0, + "content": "4.3. Performance Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Quantitative Evaluation. To show the effectiveness of the proposed method, we compare ours with previous meth-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10558" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.075, + 0.198, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.2, + 0.075, + 0.298, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.075, + 0.409, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.075, + 0.517, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.075, + 0.619, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.075, + 0.719, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.075, + 0.79, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.793, + 0.075, + 0.891, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.162, + 0.16, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.163, + 0.162, + 0.281, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.162, + 0.377, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.162, + 0.458, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.46, + 0.162, + 0.536, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.538, + 0.162, + 0.671, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.673, + 0.162, + 0.745, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.162, + 0.891, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.259, + 0.893, + 0.287 + ], + "angle": 0, + "content": "Figure 6. More results of 3D human mesh reconstruction by the proposed method on 3DPW-PC [41] (1st row) and OCHuman [48] (2nd row) datasets." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.312, + 0.462, + 0.459 + ], + "angle": 0, + "content": "
MethodsHaggl.MafiaUtim.PizzaMean
SPIN [19]124.3132.4150.4153.5133.1
CRMH [11]129.6133.5153.0156.7143.2
BMP [47]120.4132.7140.9147.5135.4
PARE [18]143.1193.1219.8190.4186.6
ROMP [38]111.8129.0148.5149.1134.6
OCHMR [16]115.5123.7142.6150.6133.1
3DCrowdNet [7]109.6135.9129.8135.6127.6
Ours109.1122.5137.8135.0126.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.512 + ], + "angle": 0, + "content": "Table 2. Performance comparison by MPJPE based on the CMU-Panoptic dataset (best results and second results are shown in bold and underlined, respectively)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.901 + ], + "angle": 0, + "content": "ods for 3D human mesh reconstruction, i.e., SPIN [19], CRMH [11], BMP [47], PyMAF [46], PARE [18], ROMP [38], OCHMR [16], 3DCrowdNet [7], HMDiff [8], and Coordinate [22], based on person-to-person occlusion benchmarks. To evaluate the proposed method on 3D human mesh datasets, three metrics are adopted, i.e., mean per joint position error (MPJPE) [10], Procrustes-aligned mean per joint position error (PA-MPJPE) [52], and mean per vertex position error (MPVPE) [36]. Specifically, MPJPE indicates the average value of the Euclidean distance between the predicted 3D joint and the corresponding ground truth. PA-MPJPE means MPJPE that is calculated after applying the Procrustes analysis to the estimated body mesh. MPVPE is computed by averaging the Euclidean distance between the predicted vertex and the corresponding ground truth. For 2D human pose datasets, the performance is evaluated by using the average precision (AP), which is calculated based on the object keypoint similarity (OKS) [29]. In addition, AP according to different threshold values (i.e., \\(\\mathrm{AP^{50}}\\) and \\(\\mathrm{AP^{75}}\\)) and scales of the human object (i.e., \\(\\mathrm{AP^M}\\) and \\(\\mathrm{AP^L}\\)) is also adopted for the performance comparison. Note that ResNet-50 [9] is employed as the backbone network of the proposed method, which is the default setting for the performance report in this subsection." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.311, + 0.891, + 0.515 + ], + "angle": 0, + "content": "
MethodsMPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
METRO [27]77.147.988.2
PARE [18]74.546.588.6
ROMP [38]76.747.393.4
MeshGraphormer [28]74.745.687.7
FastMETRO [5]73.544.684.1
CLIFF [26]72.045.785.3
PointHMR [17]73.944.985.5
ImpHMR [4]74.345.487.1
HMDiff [8]72.744.582.4
CoordFormer [22]79.446.594.4
Ours (ResNet-50)78.047.885.6
Ours (HRNet-32)73.244.380.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.524, + 0.893, + 0.568 + ], + "angle": 0, + "content": "Table 3. Performance comparison based on the 3DPW dataset by following the protocol 3, i.e., fine-tuned on 3DPW (best results and second results are shown in bold and underlined, respectively)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.901 + ], + "angle": 0, + "content": "First of all, the performance comparison based on 3DPW-PC, OCHuman, and CrowdPose datasets is shown in Table 1. As can be seen, the proposed method shows the meaningful performance improvement compared to previous approaches. Specifically, MPJPE and MPVPE on the 3DPW-PC dataset prove that our model can successfully estimate both pose and shape for occluded human mesh reconstruction. Moreover, the proposed method outperforms all state-of-the-art methods in terms of AP and \\(\\mathrm{AP^{50}}\\) with the significant performance gain on OCHuman and CrowdPose datasets. In Table 2, MPJPE of the proposed method on the CMU-Panoptic dataset is compared with others. We can see that the proposed method yields the reliable performance in most sequences while achieving the best result in the average MPJPE (see the rightmost column of Table 2). From the result reported in Tables 1 and 2, we could confirm that the proposed instance-aware contrastive learning scheme is effective to reconstruct human meshes under various person-to-person occlusions. Furthermore, we also evaluate the proposed method on the entire test set of 3DPW" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10559" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.171 + ], + "angle": 0, + "content": "
MethodsMPJPE(↓)PA-MPJPE(↓)
Baseline (i.e., w/o center and joint features)104.280.2
Ours†102.278.2
Ours102.077.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.182, + 0.47, + 0.224 + ], + "angle": 0, + "content": "Table 4. Performance analysis according to the change of the network architecture. \\( \\dagger \\) denotes the performance without applying positional encoding to the center-aligned instance map." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.244, + 0.434, + 0.33 + ], + "angle": 0, + "content": "
Feature DimensionMPJPE(↓)PA-MPJPE(↓)
32103.578.3
64102.077.2
128103.178.0
256104.278.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.341, + 0.47, + 0.382 + ], + "angle": 0, + "content": "Table 5. Performance variations according to the change of the feature dimension for the center-aligned instance map and the joint-aligned instance map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.468, + 0.501 + ], + "angle": 0, + "content": "by following the protocol 3 [41]. In particular, we conduct the experiment by using two different backbone networks, i.e., ResNet-50 [9] and HRNet-32 [42], and the corresponding results are shown in Table 3. As can be seen, the proposed method performs robustly in a variety of real-world environments, not just for occlusion cases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.468, + 0.805 + ], + "angle": 0, + "content": "Qualitative Evaluation. The qualitative comparison of the proposed method with ROMP [38] and 3DCrowdNet [7] based on the CrowdPose dataset is shown in Fig. 5. As can be seen, the proposed method can successfully reconstruct multiple human meshes in complicated person-to-person occlusions. Specifically, the reconstructed mesh is well aligned to the target person without confusion with other persons (see the left two examples in Fig. 5). This is because the proposed method is able to effectively utilize the identity information of each person in the feature space. The fourth and fifth columns of Fig. 5 show the robustness of our method in crowded scenes. Furthermore, the proposed method works reliably even under severe occlusions between multiple persons as shown in the rightmost three examples in Fig. 5. More reconstruction results by the proposed method on 3DPW-PC and OCHuman datasets are also shown in Fig. 6. Based on this, it is thought that our instance-aware contrastive learning scheme is greatly helpful in understanding the occlusion context by overlapped persons and generating the plausible human mesh." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.229, + 0.833 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In this subsection, several comparative experiments are conducted to demonstrate the effectiveness of the proposed method. The performance for all the experiments in this subsection is evaluated on the 3DPW-PC [41] dataset. First" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.63, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.559, + 0.219, + 0.574, + 0.231 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.089, + 0.759, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.689, + 0.219, + 0.704, + 0.23 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.089, + 0.89, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.219, + 0.834, + 0.23 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.24, + 0.89, + 0.268 + ], + "angle": 0, + "content": "Figure 7. (a) Input image. (b) Reconstruction result by baseline. (c) Reconstruction result by the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.62 + ], + "angle": 0, + "content": "of all, the effect of our instance-aware contrastive learning scheme is analyzed and the corresponding result is shown in Table 4. As can be seen in Table 4, the performance for occluded human mesh reconstruction is significantly improved by leveraging the identity information into latent features for centers and their related joints. Furthermore, we can see that applying positional encoding to the center-aligned instance map is also useful for the model to discriminatively represent each center feature under severe occlusion cases. The effect of our instance-aware learning scheme is shown in Fig. 7. In the following, we check the performance variation by the change of the feature dimension for both center-aligned and joint-aligned instance maps is shown in Table 5. The best performance is achieved when the feature dimension is set to 64, thus this setting has been used as default for the performance evaluation of the proposed method. Note that the performance in all the settings is better than our baseline (i.e., the first row of Table 4). Based on ablation studies, we can conclude that the proposed instance-aware contrastive learning scheme is effective for occluded human mesh reconstruction under various real-world environments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.627, + 0.651 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.811 + ], + "angle": 0, + "content": "In this paper, we present a simple yet powerful method for occluded human mesh reconstruction, especially focusing on person-to-person occlusions. The core of the proposed method is to embed the identity information into latent features for body centers and joints of each person. To do this, we propose a novel instance-aware contrastive learning scheme. Experimental results on benchmark datasets show that the proposed method works reliably even under various person-to-person occlusions occurring in real-world environment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by Institute of Information Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00207, Immersive Media Research Laboratory)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10560" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. In Proc. IEEE Conf. Comput. Vis. 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Although many recent studies have shown the remarkable improvement in human mesh reconstruction, it is still difficult to generate accurate meshes when person-to-person occlusion occurs due to the ambiguity of who a body part belongs to. To address this problem, we propose an instance-aware contrastive learning scheme. Specifically, joint features belonging to the target human are trained to be proximate with the center feature (i.e., feature extracted from the body center position). On the other hand, center features of different human instances are forced to be far apart so that joint features of each person can be clearly distinguished from others. By interpreting the joint possession based on such contrastive learning scheme, the proposed method easily understands the spatial occupancy of body parts for each person in a given image, thus can reconstruct reliable human meshes even with severely overlapped cases between multiple persons. Experimental results on benchmark datasets demonstrate the robustness of the proposed method compared to previous approaches under person-to-person occlusions. The code and model are publicly available at: https://github.com/DCVL-3D/InstanceHMR_release. + +# 1. Introduction + +Recently, 3D human mesh reconstruction has become a major research topic with the increasing demand in entertainment areas such as AR/VR and sports broadcasting. In line with this trend, considerable efforts have been made to predict reliable meshes from a single image by using deep learning techniques. Specifically, model-based methods, which aim to reconstruct human poses and shapes by estimating parameters of the skinned multi-person linear (SMPL) model [32], have been introduced. Since the problem of inferring a large number of vertices is simplified to the problem of estimating a few parameters through various network architectures, model-based approaches have been + +actively explored while bringing the significant progress in human mesh reconstruction [2, 4, 15, 18, 19, 21, 24, 25, 37, 46]. On the other hand, model-free approaches also have drawn a lot of attentions due to their ability to express local details of mesh surfaces by directly regressing every vertex without any constraint of the parameter space. In particular, the transformer architecture has been widely adopted to reconstruct accurate meshes by considering the relationship between vertices in a global manner [5, 17, 27, 28, 44, 45, 50, 51]. + +Despite meaningful advances in the field of 3D human mesh reconstruction, person-to-person occlusions frequently occurring in crowd scenes still remain a challenging issue due to ambiguities of possession for body parts. To resolve this issue, several approaches have recently begun to be introduced. For example, there have been attempts to estimate discriminative locations of each person in the 2D space and utilize them to extract features for individual mesh regression [7, 16, 38]. Reasoning the depth order of multiple people also has been considered to understand the relationship between overlapped subjects in a given image [11, 39, 47]. Some methods first predict the occlusion-robust 3D skeletons, which form reliable poses even for invisible body parts, and then lift them to mesh structures [31]. Even though considerable efforts have been consistently devoted to this task, attempts to exploit contextual cues of the occluded area, which is occupied by each person, are still insufficient. + +In this paper, a new perspective for effectively handling person-to-person occlusions is presented. In the scene where people are overlapped, one of the biggest obstacles is the uncertainty about the ownership of a body part. While it is relatively easy to semantically understand which area in a given image corresponds to which type of body part (e.g., hand or foot), it can be challenging to determine who owns that body part. This makes the model confused and eventually yields unnatural reconstruction results. To deal with this problem, we propose to guide the network to learn discriminative representations of body parts for each person by our instance-aware contrastive learning scheme. Specifically, two novel feature maps, i.e., center-aligned instance + +![](images/e75e118b01d61be156737621e758895f2ac5aa9f2df5be4c80d173aa91a95582.jpg) +(a) + +![](images/16871440777b88972a5ac055ee350c78e7b918362e4f850f4375d8593ffe8aea.jpg) +(b) + +![](images/7fb235781eca841b8e175c8afdb5d43dd9648e713220c5131fe763c564d749ef.jpg) +(c) +Figure 1. (a) An example of person-to-person occlusion. (b), (c), and (d) Visualizations of the information adopted to guide the feature encoding for human mesh reconstruction in OCHMR [16], 3DCrowdNet [7], and the proposed method, respectively. For better visibility, all joints are represented in a single image at the 2D pose heatmap of (c) and the joint heatmap of (d), and only a few of joint features (e.g., right hand, left elbow, and right foot) are shown in the joint-aligned instance map of (d). + +![](images/75c3d38cb65a14c1e30f788fcbddc4c534549d279dbcf9e8926a133656e9d6a3.jpg) +(d) + +map and joint-aligned instance map, are encoded in the proposed architecture, which can describe the possession relationship between all human instances and their visible body joints. These maps learn to represent the identity information of each human instance by forcing the center feature to pull joint features of the same person while pushing out center features of non-target persons in the latent space. Note that center features and joint features are sampled at the body center position and joint locations in the center-aligned instance map and the joint-aligned instance map, respectively, as shown in Fig. 1(d). Such identity representations make it easy to distinguish which instance each joint belongs to, thus the model can better understand the occluded context and determine the area of the image to focus on for occluded human mesh reconstruction. A comparison between previous approaches and the proposed method for handling person-to-person occlusions is illustrated in Fig. 1. In [16], relative positions of multiple persons are given to the model in the form of global and local center maps as shown in Fig. 1(b). However, since the center position is an extremely small amount of information compared to the complex body structure, the model may hardly figure out details of body part regions in occlusion situations. On the other hand, the spatial guidance of the body region for the target person is provided to the network based on the 2D pose heatmap in [7]. However, features of nontarget person areas also can be unnecessarily fused into features for target mesh reconstruction (see the bottom part of Fig. 1(c)). Unlike such previous approaches, the proposed method clearly indicates the possession of all body parts by expressing the identity information at joint locations as well as body center positions via the instance-aware contrastive learning scheme as shown in Fig. 1(d). Moreover, meshes for every person can be reliably reconstructed in a single stream (i.e., without using the bounding box) by considering the mutual relationship among the spatial occupancy of each person's body part. The main contributions of this paper are summarized as follows: + +- We propose to indicate the spatial occupancy of body parts corresponding to each human instance for occlusion-robust 3D human mesh reconstruction. With the awareness of the body part possession of every person, the model can easily understand the person-to-person occlusion and successfully generate human meshes with natural poses. +- We represent the relationship between human instances and their spatial keypoints (i.e., body centers and joints) at the feature level via the proposed instance-aware contrastive learning scheme. Specifically, by guiding the center feature of the target person to push out that of non-target persons and pull corresponding joint features in the latent space, identities of different persons can be distinctively embedded into center and joint features. + +# 2. Related Works + +In this Section, we present a systematic review of previous methods for monocular 3D human mesh reconstruction and explore various approaches for handling person-to-person occlusions. + +# 2.1. 3D Human Mesh Reconstruction + +Deep learning-based methods for 3D human mesh reconstruction can be divided into two main groups, i.e., model-based and model-free methods. The former aims to estimate pose and shape parameters of the SMPL [2] model. In the early stage, Kanazawa et al. [15] proposed to regress SMPL parameters by using the end-to-end convolutional neural network and devised the adversarial loss for plausible mesh generation. Kolotouros et al. [19] designed the optimization loop that can be combined with end-to-end regression frameworks such as [15], to further refine reconstruction results. Moreover, Zhang et al. [46] tried to rectify meshes by iteratively feeding pyramidal mesh-aligned features into the mesh regression network. A bottom-up framework, which predicts meshes of multiple persons in a given image dur + +ing a single inference, was introduced by Sun et al. [38] for the first time. Specifically, they proposed to extract SMPL parameters by the sampling process based on body center positions. Li et al. [26] incorporated the bounding box location into the network for accurately estimating the global orientation. To reconstruct the human mesh that is aligned well to the image pixel, Shetty et al. [37] proposed to first predict vertices on the input image plane, and then compute SMPL parameters by comparing them with the template mesh part by part based on inverse kinematics. Cho et al. [4] attempted to learn the consistency of human pose and shape in arbitrary view directions by using neural feature fields. In contrast to such model-based approaches, modelfree methods directly estimate 3D coordinates of mesh vertices. As a pioneer, Kolotouros et al. [20] adopted the graph convolutional neural network (GraphCNN) to effectively transform image features into vertex coordinates. Choi et al. [6] also utilized GraphCNN to lift estimated 2D and 3D poses to the 3D mesh. Meanwhile, Lin et al. [27] presented a new direction in model-free approaches, by employing the transformer encoder with the dimension reduction technique for mesh regression. They further improved the performance by incorporating GraphCNN into the transformer encoder block [28]. To alleviate the computational burden of the transformer-based architecture, Cho et al. [5] proposed to disentangle image features and geometric parameters of the human body based on the cross-attention module. Kim et al. [17] designed a point-guided feature sampling scheme to effectively extract vertex-relevant features for the transformer-based mesh regressor. More recently, Foo et al. [8] adopted the diffusion model for the human mesh reconstruction by leveraging the pose heatmap in the diffusion process to enable the mesh estimation conditioned on the input image. + +# 2.2. Handling Person-to-Person Occlusions + +Even though many studies mentioned above have brought significant advances for monocular 3D human mesh reconstruction, they still suffer from ambiguities driven by person-to-person occlusions, which often occur in real-world environments. To cope with this problem, there have been various technical attempts. For example, Jiang et al. [11] introduced a new loss function that minimizes the discrepancy between the human segmentation masks and projected meshes to arrange the depth order of the people. In a similar vein, Zhang et al. [47] tried to learn the ordinal relation by supervising the difference between depth values of multiple persons. Instead of simply guiding the network via loss functions, Sun et al. [39] incorporated the bird's-eye-view body center heatmap into the pipeline of mesh estimation to consider the depth cue. Yang et al. [43] adopted to synthesize the other people to the input data for consideration of more variants from person-to-person occlusions. + +![](images/2a75a9087a078c4adfcb7b70c4dba081fa8a02e257e5c94de27ddc41fdc80bae.jpg) +Figure 2. The detailed process of the instance-aware contrastive learning scheme. Note that the ground truth of body center and joint positions is used for the feature sampling. + +To specify the position of the target person, Khirodkar et al. [16] introduced the context normalization block, which fuses global and local center heatmaps with corresponding features. Choi et al. [7] utilized the 2D pose heatmap to focus on the feature belonging to the area of the target person in crowded scenes. Cha et al. [3] attempted to refine multiple human meshes based on inter-person relations that are computed by the transformer architecture. Liu et al. [31] proposed to apply the knowledge transfer technique to the 3D keypoint detection [49] for successfully reasoning invisible body parts under occlusions. Li et al. [22] proposed a body center attention mechanism to consider spatial-temporal relations of multiple persons at the pixel level. To complement the lack of the training data under multi-person scenes, Sun et al. [40] tried to synthesize plausible crowded examples by putting human samples at appropriate places of the given image with a reasonable scale according to the scene context. Moreover, they also proposed to learn the consistency between features extracted from the same human sample with and without occlusions. + +# 3. Proposed Method + +The proposed method aims to learn the spatial occupancy of body parts for each person by using the instance-aware contrastive learning scheme as shown in Fig. 2. By incorporating the identity information into encoded features, the proposed method can achieve the robust performance against person-to-person occlusions. The overall architecture of the proposed method is illustrated in Fig. 3. + +# 3.1. Instance-aware Contrastive Learning + +In the bottom-up approach for human mesh reconstruction, it is important to grasp the individual cue between multiple persons. To this end, we guide the process of mesh estimation based on the regional distinction of each human area, i.e., 24 body joints defined by the SMPL model [2]. Specifically, the backbone feature is encoded into two different feature maps, i.e., center-aligned instance map and joint-aligned instance map, through the corresponding network + +![](images/6b917a70c60b3b8e9f20880b69e4bf624606191be5ecedd96fc93ff3afe4aff1.jpg) +Figure 3. The overall architecture of the proposed method for occluded human mesh reconstruction. $h$ and $w$ are set to 64. $\theta$ and $\beta$ denote pose and shape parameters of the SMPL model. Note that instance-aware contrastive learning is conducted only in the training phase. + +branch as shown in Fig. 3. Note that the predicted center heatmap $H_{C}$ and joint heatmap $H_{J}$ are adopted in this encoding process to provide the spatial information of body centers and joints. In addition, the positional encoding is also applied to the center-aligned instance map to prevent ambiguous representations between different people who have similar appearances. After that, center features and joint features are sampled at body center locations and visible joint positions of the center-aligned instance map and the joint-aligned instance map, respectively. These sampled features are subsequently projected into the latent space by using the nonlinear projector, which consists of fully connected layers and ReLUs (see $P_{C}$ and $P_{J}$ in Fig. 3). + +Now, such projected features are fed into our instance-aware contrastive learning scheme. The detailed process is shown in Fig. 2. First, the center feature of the target person (i.e., anchor) is forced to push out those of other persons. By placing different human instances far apart from each other in the latent space, center features can implicitly represent the identity information for each person in a discriminative way. Second, the center feature pulls joint features belonging to the same person to a close distance. This facilitates the joint feature to express the human instance to which it belongs, by embedding the target identity information. To this end, two loss functions are designed based on the cosine similarity, which is suitable for measuring the directional coherence between embedding vectors, as follows: + +$$ +\mathcal {L} _ {\text {p u s h}} (a, b) = 1 + \frac {a \cdot b}{\| a \| \| b \|}, \tag {1} +$$ + +$$ +\mathcal {L} _ {p u l l} (a, b) = 1 - \frac {a \cdot b}{| | a | | | | b | |}. +$$ + +Specifically, $\mathcal{L}_{push}$ is used to maximize the distance between center features of different people and $\mathcal{L}_{pull}$ is used to minimize the distance between the center feature and the joint feature of the same person in the latent space. By considering every possible center-to-center and center-to-joint combination, the proposed contrastive loss is defined as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {c o n t}} = \frac {2}{N (N - 1)} \sum_ {i \neq j} ^ {N} \mathcal {L} _ {\text {p u s h}} \left(u _ {i}, u _ {j}\right) \tag {2} \\ + \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {1}{K _ {i}} \sum_ {k = 1} ^ {K _ {i}} \mathcal {L} _ {p u l l} (u _ {i}, v _ {i} ^ {k}), \\ \end{array} +$$ + +where $u$ and $v$ indicate the center feature and the joint feature, respectively. $N$ and $K_{i}$ denote the number of people and the number of visible joints belonging to the $i$ -th person in the input image, respectively. The effect of the proposed instance-aware contrastive learning scheme is shown in Fig. 4. As can be seen, the identity information is embedded into latent features during our instance-aware contrastive learning. Consequently, it is thought that both center-aligned instance map and joint-aligned instance map play an important role to describe the possession relationship between human instances and their visible joints. Note that the instance-aware contrastive learning part is conducted only in the training phase. + +In order to utilize this possession cue in the process of mesh regression, we incorporate the center-aligned instance map and the joint-aligned instance map into the network branch for estimating the SMPL parameter map (see the second branch from bottom in Fig. 3). To accurately indicate valid locations, the center heatmap and the joint + +![](images/60c82af62a3fcfe4859fa73aa61b496f32dbcfacb678c1011bd9f57e7e8c6463.jpg) +(a) + +![](images/40898637b1082da41ccc76ee6b712cdec6ba59f538e77ee5b5c17208387c44f2.jpg) +(b) + +![](images/21e2a0c947a523e7e966972a0e05024aa1bfa3e73d516a753c6b55cfa6cbdadf.jpg) +(c) +Figure 4. A visualization example of center features and joint features in the latent space. The feature dimension is reduced from 64 to 3 by using [33] for the visualization. (a) Input image with marks for positions of body centers (dark) and joints (bright). Note that points belonging to the same person are represented as the same color attribute. The effect of the proposed instance-aware contrastive learning scheme is shown sequentially, i.e., (b) before training, (c) middle of training, and (d) after training. + +![](images/0c6e9be33d7ec5c45443e4a641ccad1f92da287066a97f9bc8e603b426be7372.jpg) +(d) + +heatmap are also employed for this concatenation process. Finally, pose and shape parameters of each person are sampled from the SMPL parameter map according to the predicted center position in a similar way of [38]. It is noteworthy that the model can precisely consider the occupancy of each human instance via such identity representation in the feature space, which leads to generation of reliable human meshes even with various person-to-person occlusions. An example of occluded human mesh reconstruction is shown in the bottom right of Fig. 3. + +# 3.2. Loss functions + +The proposed method is trained based on nine loss terms, i.e., contrastive loss $\mathcal{L}_{cont}$ (which is explained in subsection 3.1), body center heatmap loss $\mathcal{L}_{center}$ , joint heatmap loss $\mathcal{L}_{joint}$ , pose loss $\mathcal{L}_{pose}$ , shape loss $\mathcal{L}_{shape}$ , Mixture Gaussian prior loss $\mathcal{L}_{prior}$ , 3D joint loss $\mathcal{L}_{3d}$ , Procrustes-aligned 3D joint loss $\mathcal{L}_{pa3d}$ , and 2D joint loss $\mathcal{L}_{2d}$ . First, the focal loss [30, 38] is adopted to train the body center heatmap $H_{C}$ and the joint heatmap $H_{J}$ , which is defined as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {f o c a l} (H, \tilde {H}, \tilde {H} ^ {\prime}) = - \frac {\mathcal {L} _ {p o s} (H , \tilde {H} ^ {\prime}) + \mathcal {L} _ {n e g} (H , \tilde {H} , \tilde {H} ^ {\prime})}{\sum \tilde {H} ^ {\prime}}, \\ \mathcal {L} _ {n e g} (H, \tilde {H}, \tilde {H} ^ {\prime}) = \log (1 - H) H ^ {2} (1 - \tilde {H}) ^ {4} (1 - \tilde {H} ^ {\prime}), \\ \mathcal {L} _ {\text {p o s}} \left(H, \tilde {H} ^ {\prime}\right) = \log (H) \left(1 - H\right) ^ {2} \tilde {H} ^ {\prime}, \tag {3} \\ \end{array} +$$ + +where $H$ and $\tilde{H}$ denote a single heatmap and the corresponding ground truth, respectively. $\tilde{H}^{\prime}$ indicates the binary map that is marked on the location of the positive class in $\tilde{H}$ . By using the focal loss, $\mathcal{L}_{center}$ and $\mathcal{L}_{joint}$ are formulated as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {c e n t e r} = \mathcal {L} _ {f o c a l} (H _ {C}, \tilde {H} _ {C}, \tilde {H} _ {C} ^ {\prime}), \\ \mathcal {L} _ {\text {j o i n t}} = \frac {1}{\mathcal {J}} \sum_ {j = 1} ^ {\mathcal {J}} \mathcal {L} _ {\text {f o c a l}} \left(H _ {J} ^ {j}, \tilde {H} _ {J} ^ {j}, \tilde {H} _ {J} ^ {' j}\right), \tag {4} \\ \end{array} +$$ + +where $\mathcal{J}$ is the number of joint heatmaps which is set to 24 according to the SMPL model. The remaining loss terms + +are used to directly supervise the process of human mesh reconstruction. In particular, $\mathcal{L}_{\text {pose }}$ and $\mathcal{L}_{\text {shape }}$ compute the difference between predicted pose and shape parameters and the corresponding ground truth based on $L_{2}$ loss, respectively [15, 20]. Mixture Gaussian prior loss $\mathcal{L}_{\text {prior }}$ is employed to attain the naturalness of body meshes as introduced in [2]. In our work, Euclidean distance is utilized to calculate the spatial gap in the coordinate system for following three loss terms. The distance between estimated 3D joints and the corresponding ground truth is computed by $\mathcal{L}_{3d}$ [15, 20]. $\mathcal{L}_{pa3d}$ indicates $\mathcal{L}_{3d}$ after Procrustes alignment is conducted to the reconstructed mesh [38]. The coordinates of joints projected onto the 2D space are used to measure $\mathcal{L}_{2d}$ [15, 20]. Finally, the total loss function is defined by using the weighted sum of all the aforementioned loss terms as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \lambda_ {\text {c o n t}} \mathcal {L} _ {\text {c o n t}} + \lambda_ {\text {c e n t e r}} \mathcal {L} _ {\text {c e n t e r}} + \lambda_ {\text {j o i n t}} \mathcal {L} _ {\text {j o i n t}} \\ + \lambda_ {p o s e} \mathcal {L} _ {p o s e} + \lambda_ {s h a p e} \mathcal {L} _ {s h a p e} + \lambda_ {p r i o r} \mathcal {L} _ {p r i o r} \\ + \lambda_ {3 d} \mathcal {L} _ {3 d} + \lambda_ {p a 3 d} \mathcal {L} _ {p a 3 d} + \lambda_ {2 d} \mathcal {L} _ {2 d}, \tag {5} \\ \end{array} +$$ + +where $\lambda_{cont}$ , $\lambda_{center}$ , $\lambda_{joint}$ , $\lambda_{pose}$ , $\lambda_{shape}$ , $\lambda_{prior}$ , $\lambda_{3d}$ , $\lambda_{pa3d}$ , and $\lambda_{2d}$ are the balancing factor for each loss term, which are set to 50, 160, 50, 80, 6, 1.6, 200, 360, and 400, respectively. + +# 4. Experimental Results + +# 4.1. Implementation Details + +The proposed method is implemented on the PyTorch framework with an Intel E5-1650@3.60GHz CPU and two NVIDIA GeForce RTX 3090 GPUs. All the parameters of the proposed network are updated by the Adam optimizer, where momentum factors are set to 0.9 and 0.999, respectively. We use the batch size of 64 and the learning rate is set to $5 \times 10^{-6}$ during 30 training epochs. Input images are randomly cropped and rotated before they are resized to the resolution of $512 \times 512$ pixels by using zero padding. + +# 4.2. Benchmark Datasets + +The proposed method is trained by using three 3D human pose datasets (i.e., Human3.6M [10], MPI-INF-3DHP [34], + +![](images/c952188275138a0e0c317a3b8a9cb44112489eb5b3b18546db0a0ae7fd852c7b.jpg) +Figure 5. Results of 3D human mesh reconstruction on the CrowdPose [23] dataset. From top to bottom: input images, results by ROMP [38], 3DCrowdNet [7], and the proposed method. + +
Methods3DPW-PCOCHumanCrowdPose
MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)AP(↑)\( AP^{50}(↑) \)\( AP^{75}(↑) \)\( AP^M(↑) \)\( AP^L(↑) \)\( AP(↑) \)\( AP^{50}(↑) \)\( AP^{75}(↑) \)
SPIN* [19]129.682.6157.612.746.819.417.826.216.440.110.6
PyMAF* [46]126.781.3154.314.348.721.518.028.717.442.713.0
ROMP* [38]119.779.7152.815.655.023.618.730.018.944.613.8
ROMP [38]115.675.8147.519.856.225.019.332.928.558.824.7
OCHMR* [16]117.577.1149.624.860.728.622.334.221.448.316.5
CLIFF* [26]---23.249.820.4--27.451.525.9
HMDiff* [8]114.273.5143.1--------
CoordFormer* [22]101.579.3---------
Ours*99.976.3126.430.575.817.335.130.528.561.623.2
Ours102.077.2131.034.980.024.027.135.031.665.726.7
+ +Table 1. Performance comparison of occluded human mesh reconstruction based on 3DPW-PC, OCHuman, and CrowdPose datasets (best results and second results are shown in bold and underlined, respectively). Note that * denotes the performance without using the CrowdPose dataset for training. + +and MuCo-3DHP [35]) and four 2D human pose datasets (i.e., MPII [1], LSP [12], COCO [29], and CrowdPose [23]). In particular, only 2D pose labels are used for [23] while pseudo mesh labels, which are generated by [14], are employed to utilize other 2D human pose datasets [1, 12, 29] for training. + +For the performance evaluation of the proposed method, four person-to-person occlusion datasets (i.e., 3DPW-PC [41], OCHuman [48], CrowdPose [23], and CMU-Panoptic [13]) are adopted. Specifically, the 3DPW-PC dataset is a subset of the 3DPW dataset where images taken under person-to-person occlusions are collected ac + +cording to [38]. The OCHuman dataset consists of severe occlusion cases between multiple persons while the CrowdPose dataset contains various person-to-person occlusions occurring in crowded scenes. Moreover, the CMU-Panoptic dataset includes multi-person sequences with diverse inter-person interactions. Based on such occlusion-oriented benchmark datasets, the performance of the proposed method will be evaluated and analyzed in-depth in the following subsection. + +# 4.3. Performance Evaluation + +Quantitative Evaluation. To show the effectiveness of the proposed method, we compare ours with previous meth- + +![](images/c6ad056a2dc827e8a7cdbfb6ce262158e4f2e3502ff9accb43394d2b28cef213.jpg) + +![](images/875d2a8a7cf7f8299b06ec969044c6addd02bdff9bf5093d701587c5f93dae72.jpg) + +![](images/05abd969148a7c3478b89837d54b4eca58552aac0037b4172cb33e4b988a9f59.jpg) + +![](images/53da101d757856d6ca98c5b860d0c81f396a7775d42ac25db3460c65e78f9e46.jpg) + +![](images/c0d56390c2f07ab8c4501947517a4c2097c61aa5cd88b6336ffe54b52ce042f4.jpg) + +![](images/49fbadafe65103e7b6b683ce71da8372fe5f5c2d76f48843d1ce1fd3955be598.jpg) + +![](images/2dd82cf77a3ecb50cdc45fd95a6e684b219062a97b8742063b3c3fd30741c71d.jpg) + +![](images/bc005b9173a5a976d60b0f3fcdf6c9a3362278203b02a74b1db22bd6bff7c2cd.jpg) + +![](images/bf4d62d0525d537ebdcd17148caf07841467cd9c86400d2ee5c21c155ef964c3.jpg) +Figure 6. More results of 3D human mesh reconstruction by the proposed method on 3DPW-PC [41] (1st row) and OCHuman [48] (2nd row) datasets. + +![](images/3cfab3697e6199b14bbba3eab4dfc1c2ddd827bab112c6d5b4e2dee50fe4269e.jpg) + +![](images/15c110ced19d9fe5e30b9d628b61240e99094978bd9cf5daaff0d0093433a15c.jpg) + +![](images/86e875228e12af3217561233a517cd9b4895c2e7a9f9187049dedad0a389f17c.jpg) + +![](images/5eef3872593dc598fffed0eb2da83e0bdd6f4fde3ec796dc8467b8c525a40ef7.jpg) + +![](images/968454e7772b5fb51673a7442018324923adec459c91ca912c9c9dee0bbe25e9.jpg) + +![](images/5f95b6139acb27b2918bd7467ef3d79b304bc92883bcf152fc38f7564d92712a.jpg) + +![](images/456e54ad7d4351caa95d940c43cd5d873142e235b06a10591eae7cb97ff86774.jpg) + +
MethodsHaggl.MafiaUtim.PizzaMean
SPIN [19]124.3132.4150.4153.5133.1
CRMH [11]129.6133.5153.0156.7143.2
BMP [47]120.4132.7140.9147.5135.4
PARE [18]143.1193.1219.8190.4186.6
ROMP [38]111.8129.0148.5149.1134.6
OCHMR [16]115.5123.7142.6150.6133.1
3DCrowdNet [7]109.6135.9129.8135.6127.6
Ours109.1122.5137.8135.0126.1
+ +ods for 3D human mesh reconstruction, i.e., SPIN [19], CRMH [11], BMP [47], PyMAF [46], PARE [18], ROMP [38], OCHMR [16], 3DCrowdNet [7], HMDiff [8], and Coordinate [22], based on person-to-person occlusion benchmarks. To evaluate the proposed method on 3D human mesh datasets, three metrics are adopted, i.e., mean per joint position error (MPJPE) [10], Procrustes-aligned mean per joint position error (PA-MPJPE) [52], and mean per vertex position error (MPVPE) [36]. Specifically, MPJPE indicates the average value of the Euclidean distance between the predicted 3D joint and the corresponding ground truth. PA-MPJPE means MPJPE that is calculated after applying the Procrustes analysis to the estimated body mesh. MPVPE is computed by averaging the Euclidean distance between the predicted vertex and the corresponding ground truth. For 2D human pose datasets, the performance is evaluated by using the average precision (AP), which is calculated based on the object keypoint similarity (OKS) [29]. In addition, AP according to different threshold values (i.e., $\mathrm{AP^{50}}$ and $\mathrm{AP^{75}}$ ) and scales of the human object (i.e., $\mathrm{AP^M}$ and $\mathrm{AP^L}$ ) is also adopted for the performance comparison. Note that ResNet-50 [9] is employed as the backbone network of the proposed method, which is the default setting for the performance report in this subsection. + +Table 2. Performance comparison by MPJPE based on the CMU-Panoptic dataset (best results and second results are shown in bold and underlined, respectively). + +
MethodsMPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
METRO [27]77.147.988.2
PARE [18]74.546.588.6
ROMP [38]76.747.393.4
MeshGraphormer [28]74.745.687.7
FastMETRO [5]73.544.684.1
CLIFF [26]72.045.785.3
PointHMR [17]73.944.985.5
ImpHMR [4]74.345.487.1
HMDiff [8]72.744.582.4
CoordFormer [22]79.446.594.4
Ours (ResNet-50)78.047.885.6
Ours (HRNet-32)73.244.380.3
+ +Table 3. Performance comparison based on the 3DPW dataset by following the protocol 3, i.e., fine-tuned on 3DPW (best results and second results are shown in bold and underlined, respectively). + +First of all, the performance comparison based on 3DPW-PC, OCHuman, and CrowdPose datasets is shown in Table 1. As can be seen, the proposed method shows the meaningful performance improvement compared to previous approaches. Specifically, MPJPE and MPVPE on the 3DPW-PC dataset prove that our model can successfully estimate both pose and shape for occluded human mesh reconstruction. Moreover, the proposed method outperforms all state-of-the-art methods in terms of AP and $\mathrm{AP^{50}}$ with the significant performance gain on OCHuman and CrowdPose datasets. In Table 2, MPJPE of the proposed method on the CMU-Panoptic dataset is compared with others. We can see that the proposed method yields the reliable performance in most sequences while achieving the best result in the average MPJPE (see the rightmost column of Table 2). From the result reported in Tables 1 and 2, we could confirm that the proposed instance-aware contrastive learning scheme is effective to reconstruct human meshes under various person-to-person occlusions. Furthermore, we also evaluate the proposed method on the entire test set of 3DPW + +
MethodsMPJPE(↓)PA-MPJPE(↓)
Baseline (i.e., w/o center and joint features)104.280.2
Ours†102.278.2
Ours102.077.2
+ +Table 4. Performance analysis according to the change of the network architecture. $\dagger$ denotes the performance without applying positional encoding to the center-aligned instance map. + +
Feature DimensionMPJPE(↓)PA-MPJPE(↓)
32103.578.3
64102.077.2
128103.178.0
256104.278.6
+ +Table 5. Performance variations according to the change of the feature dimension for the center-aligned instance map and the joint-aligned instance map. + +by following the protocol 3 [41]. In particular, we conduct the experiment by using two different backbone networks, i.e., ResNet-50 [9] and HRNet-32 [42], and the corresponding results are shown in Table 3. As can be seen, the proposed method performs robustly in a variety of real-world environments, not just for occlusion cases. + +Qualitative Evaluation. The qualitative comparison of the proposed method with ROMP [38] and 3DCrowdNet [7] based on the CrowdPose dataset is shown in Fig. 5. As can be seen, the proposed method can successfully reconstruct multiple human meshes in complicated person-to-person occlusions. Specifically, the reconstructed mesh is well aligned to the target person without confusion with other persons (see the left two examples in Fig. 5). This is because the proposed method is able to effectively utilize the identity information of each person in the feature space. The fourth and fifth columns of Fig. 5 show the robustness of our method in crowded scenes. Furthermore, the proposed method works reliably even under severe occlusions between multiple persons as shown in the rightmost three examples in Fig. 5. More reconstruction results by the proposed method on 3DPW-PC and OCHuman datasets are also shown in Fig. 6. Based on this, it is thought that our instance-aware contrastive learning scheme is greatly helpful in understanding the occlusion context by overlapped persons and generating the plausible human mesh. + +# 4.4. Ablation Study + +In this subsection, several comparative experiments are conducted to demonstrate the effectiveness of the proposed method. The performance for all the experiments in this subsection is evaluated on the 3DPW-PC [41] dataset. First + +![](images/7258e91c36869dce4b91dc8ec6268d67449ba71a1c45c1636c22325fd7239a1c.jpg) +(a) + +![](images/0fdb233cda4d9d4f315a29130e33ff5e2a1d46fab10abce77de34fc3173e845c.jpg) +(b) + +![](images/f333580801e9ec988eca831d330e51ea247529c90ba4b0b2dca7b1a86e665e0f.jpg) +(c) +Figure 7. (a) Input image. (b) Reconstruction result by baseline. (c) Reconstruction result by the proposed method. + +of all, the effect of our instance-aware contrastive learning scheme is analyzed and the corresponding result is shown in Table 4. As can be seen in Table 4, the performance for occluded human mesh reconstruction is significantly improved by leveraging the identity information into latent features for centers and their related joints. Furthermore, we can see that applying positional encoding to the center-aligned instance map is also useful for the model to discriminatively represent each center feature under severe occlusion cases. The effect of our instance-aware learning scheme is shown in Fig. 7. In the following, we check the performance variation by the change of the feature dimension for both center-aligned and joint-aligned instance maps is shown in Table 5. The best performance is achieved when the feature dimension is set to 64, thus this setting has been used as default for the performance evaluation of the proposed method. Note that the performance in all the settings is better than our baseline (i.e., the first row of Table 4). Based on ablation studies, we can conclude that the proposed instance-aware contrastive learning scheme is effective for occluded human mesh reconstruction under various real-world environments. + +# 5. Conclusions + +In this paper, we present a simple yet powerful method for occluded human mesh reconstruction, especially focusing on person-to-person occlusions. The core of the proposed method is to embed the identity information into latent features for body centers and joints of each person. To do this, we propose a novel instance-aware contrastive learning scheme. Experimental results on benchmark datasets show that the proposed method works reliably even under various person-to-person occlusions occurring in real-world environment. + +Acknowledgments. This work was supported by Institute of Information Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00207, Immersive Media Research Laboratory). + +# References + +[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. In Proc. IEEE Conf. Comput. Vis. Pattern Recog., pages 3686-3693, 2014. 6 +[2] Federica Bogo, Angjoo Kanazawa, Christoph Lassner, Peter Gehler, Javier Romero, and Michael J Black. 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Although many recent studies have shown the remarkable improvement in human mesh reconstruction, it is still difficult to generate accurate meshes when person-to-person occlusion occurs due to the ambiguity of who a body part belongs to. To address this problem, we propose an instance-aware contrastive learning scheme. Specifically, joint features belonging to the target human are trained to be proximate with the center feature (i.e., feature extracted from the body center position). On the other hand, center features of different human instances are forced to be far apart so that joint features of each person can be clearly distinguished from others. By interpreting the joint possession based on such contrastive learning scheme, the proposed method easily understands the spatial occupancy of body parts for each person in a given image, thus can reconstruct reliable human meshes even with severely overlapped cases between multiple persons. Experimental results on benchmark datasets demonstrate the robustness of the proposed method compared to previous approaches under person-to-person occlusions. The code and model are publicly available at: https://github.com/DCVL-3D/InstanceHMR_release." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 552, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 696 + ], + "type": "text", + "content": "Recently, 3D human mesh reconstruction has become a major research topic with the increasing demand in entertainment areas such as AR/VR and sports broadcasting. In line with this trend, considerable efforts have been made to predict reliable meshes from a single image by using deep learning techniques. Specifically, model-based methods, which aim to reconstruct human poses and shapes by estimating parameters of the skinned multi-person linear (SMPL) model [32], have been introduced. Since the problem of inferring a large number of vertices is simplified to the problem of estimating a few parameters through various network architectures, model-based approaches have been" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 213, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 547, + 334 + ], + "type": "text", + "content": "actively explored while bringing the significant progress in human mesh reconstruction [2, 4, 15, 18, 19, 21, 24, 25, 37, 46]. On the other hand, model-free approaches also have drawn a lot of attentions due to their ability to express local details of mesh surfaces by directly regressing every vertex without any constraint of the parameter space. In particular, the transformer architecture has been widely adopted to reconstruct accurate meshes by considering the relationship between vertices in a global manner [5, 17, 27, 28, 44, 45, 50, 51]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 338, + 547, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 547, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 547, + 554 + ], + "type": "text", + "content": "Despite meaningful advances in the field of 3D human mesh reconstruction, person-to-person occlusions frequently occurring in crowd scenes still remain a challenging issue due to ambiguities of possession for body parts. To resolve this issue, several approaches have recently begun to be introduced. For example, there have been attempts to estimate discriminative locations of each person in the 2D space and utilize them to extract features for individual mesh regression [7, 16, 38]. Reasoning the depth order of multiple people also has been considered to understand the relationship between overlapped subjects in a given image [11, 39, 47]. Some methods first predict the occlusion-robust 3D skeletons, which form reliable poses even for invisible body parts, and then lift them to mesh structures [31]. Even though considerable efforts have been consistently devoted to this task, attempts to exploit contextual cues of the occluded area, which is occupied by each person, are still insufficient." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "type": "text", + "content": "In this paper, a new perspective for effectively handling person-to-person occlusions is presented. In the scene where people are overlapped, one of the biggest obstacles is the uncertainty about the ownership of a body part. While it is relatively easy to semantically understand which area in a given image corresponds to which type of body part (e.g., hand or foot), it can be challenging to determine who owns that body part. This makes the model confused and eventually yields unnatural reconstruction results. To deal with this problem, we propose to guide the network to learn discriminative representations of body parts for each person by our instance-aware contrastive learning scheme. Specifically, two novel feature maps, i.e., center-aligned instance" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 133, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 133, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 133, + 712 + ], + "type": "text", + "content": "\\*corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10553" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 57, + 157, + 178 + ], + "blocks": [ + { + "bbox": [ + 49, + 57, + 157, + 178 + ], + "lines": [ + { + "bbox": [ + 49, + 57, + 157, + 178 + ], + "spans": [ + { + "bbox": [ + 49, + 57, + 157, + 178 + ], + "type": "image", + "image_path": "e75e118b01d61be156737621e758895f2ac5aa9f2df5be4c80d173aa91a95582.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 182, + 107, + 191 + ], + "lines": [ + { + "bbox": [ + 97, + 182, + 107, + 191 + ], + "spans": [ + { + "bbox": [ + 97, + 182, + 107, + 191 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 169, + 57, + 287, + 178 + ], + "blocks": [ + { + "bbox": [ + 169, + 57, + 287, + 178 + ], + "lines": [ + { + "bbox": [ + 169, + 57, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 169, + 57, + 287, + 178 + ], + "type": "image", + "image_path": "16871440777b88972a5ac055ee350c78e7b918362e4f850f4375d8593ffe8aea.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 181, + 231, + 191 + ], + "lines": [ + { + "bbox": [ + 220, + 181, + 231, + 191 + ], + "spans": [ + { + "bbox": [ + 220, + 181, + 231, + 191 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 293, + 57, + 427, + 178 + ], + "blocks": [ + { + "bbox": [ + 293, + 57, + 427, + 178 + ], + "lines": [ + { + "bbox": [ + 293, + 57, + 427, + 178 + ], + "spans": [ + { + "bbox": [ + 293, + 57, + 427, + 178 + ], + "type": "image", + "image_path": "7fb235781eca841b8e175c8afdb5d43dd9648e713220c5131fe763c564d749ef.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 356, + 182, + 365, + 191 + ], + "lines": [ + { + "bbox": [ + 356, + 182, + 365, + 191 + ], + "spans": [ + { + "bbox": [ + 356, + 182, + 365, + 191 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 195, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 195, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 547, + 240 + ], + "type": "text", + "content": "Figure 1. (a) An example of person-to-person occlusion. (b), (c), and (d) Visualizations of the information adopted to guide the feature encoding for human mesh reconstruction in OCHMR [16], 3DCrowdNet [7], and the proposed method, respectively. For better visibility, all joints are represented in a single image at the 2D pose heatmap of (c) and the joint heatmap of (d), and only a few of joint features (e.g., right hand, left elbow, and right foot) are shown in the joint-aligned instance map of (d)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 434, + 57, + 545, + 178 + ], + "blocks": [ + { + "bbox": [ + 434, + 57, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 434, + 57, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 434, + 57, + 545, + 178 + ], + "type": "image", + "image_path": "75c3d38cb65a14c1e30f788fcbddc4c534549d279dbcf9e8926a133656e9d6a3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 485, + 182, + 495, + 191 + ], + "lines": [ + { + "bbox": [ + 485, + 182, + 495, + 191 + ], + "spans": [ + { + "bbox": [ + 485, + 182, + 495, + 191 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 252, + 289, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 289, + 707 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 289, + 707 + ], + "type": "text", + "content": "map and joint-aligned instance map, are encoded in the proposed architecture, which can describe the possession relationship between all human instances and their visible body joints. These maps learn to represent the identity information of each human instance by forcing the center feature to pull joint features of the same person while pushing out center features of non-target persons in the latent space. Note that center features and joint features are sampled at the body center position and joint locations in the center-aligned instance map and the joint-aligned instance map, respectively, as shown in Fig. 1(d). Such identity representations make it easy to distinguish which instance each joint belongs to, thus the model can better understand the occluded context and determine the area of the image to focus on for occluded human mesh reconstruction. A comparison between previous approaches and the proposed method for handling person-to-person occlusions is illustrated in Fig. 1. In [16], relative positions of multiple persons are given to the model in the form of global and local center maps as shown in Fig. 1(b). However, since the center position is an extremely small amount of information compared to the complex body structure, the model may hardly figure out details of body part regions in occlusion situations. On the other hand, the spatial guidance of the body region for the target person is provided to the network based on the 2D pose heatmap in [7]. However, features of nontarget person areas also can be unnecessarily fused into features for target mesh reconstruction (see the bottom part of Fig. 1(c)). Unlike such previous approaches, the proposed method clearly indicates the possession of all body parts by expressing the identity information at joint locations as well as body center positions via the instance-aware contrastive learning scheme as shown in Fig. 1(d). Moreover, meshes for every person can be reliably reconstructed in a single stream (i.e., without using the bounding box) by considering the mutual relationship among the spatial occupancy of each person's body part. The main contributions of this paper are summarized as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 252, + 546, + 444 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 317, + 252, + 545, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 252, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 317, + 252, + 545, + 336 + ], + "type": "text", + "content": "- We propose to indicate the spatial occupancy of body parts corresponding to each human instance for occlusion-robust 3D human mesh reconstruction. With the awareness of the body part possession of every person, the model can easily understand the person-to-person occlusion and successfully generate human meshes with natural poses." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 336, + 546, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 336, + 546, + 444 + ], + "spans": [ + { + "bbox": [ + 317, + 336, + 546, + 444 + ], + "type": "text", + "content": "- We represent the relationship between human instances and their spatial keypoints (i.e., body centers and joints) at the feature level via the proposed instance-aware contrastive learning scheme. Specifically, by guiding the center feature of the target person to push out that of non-target persons and pull corresponding joint features in the latent space, identities of different persons can be distinctively embedded into center and joint features." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 453, + 397, + 465 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 453, + 397, + 465 + ], + "spans": [ + { + "bbox": [ + 306, + 453, + 397, + 465 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 473, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 521 + ], + "type": "text", + "content": "In this Section, we present a systematic review of previous methods for monocular 3D human mesh reconstruction and explore various approaches for handling person-to-person occlusions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 527, + 482, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 482, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 482, + 539 + ], + "type": "text", + "content": "2.1. 3D Human Mesh Reconstruction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Deep learning-based methods for 3D human mesh reconstruction can be divided into two main groups, i.e., model-based and model-free methods. The former aims to estimate pose and shape parameters of the SMPL [2] model. In the early stage, Kanazawa et al. [15] proposed to regress SMPL parameters by using the end-to-end convolutional neural network and devised the adversarial loss for plausible mesh generation. Kolotouros et al. [19] designed the optimization loop that can be combined with end-to-end regression frameworks such as [15], to further refine reconstruction results. Moreover, Zhang et al. [46] tried to rectify meshes by iteratively feeding pyramidal mesh-aligned features into the mesh regression network. A bottom-up framework, which predicts meshes of multiple persons in a given image dur" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10554" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 479 + ], + "type": "text", + "content": "ing a single inference, was introduced by Sun et al. [38] for the first time. Specifically, they proposed to extract SMPL parameters by the sampling process based on body center positions. Li et al. [26] incorporated the bounding box location into the network for accurately estimating the global orientation. To reconstruct the human mesh that is aligned well to the image pixel, Shetty et al. [37] proposed to first predict vertices on the input image plane, and then compute SMPL parameters by comparing them with the template mesh part by part based on inverse kinematics. Cho et al. [4] attempted to learn the consistency of human pose and shape in arbitrary view directions by using neural feature fields. In contrast to such model-based approaches, modelfree methods directly estimate 3D coordinates of mesh vertices. As a pioneer, Kolotouros et al. [20] adopted the graph convolutional neural network (GraphCNN) to effectively transform image features into vertex coordinates. Choi et al. [6] also utilized GraphCNN to lift estimated 2D and 3D poses to the 3D mesh. Meanwhile, Lin et al. [27] presented a new direction in model-free approaches, by employing the transformer encoder with the dimension reduction technique for mesh regression. They further improved the performance by incorporating GraphCNN into the transformer encoder block [28]. To alleviate the computational burden of the transformer-based architecture, Cho et al. [5] proposed to disentangle image features and geometric parameters of the human body based on the cross-attention module. Kim et al. [17] designed a point-guided feature sampling scheme to effectively extract vertex-relevant features for the transformer-based mesh regressor. More recently, Foo et al. [8] adopted the diffusion model for the human mesh reconstruction by leveraging the pose heatmap in the diffusion process to enable the mesh estimation conditioned on the input image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 491, + 251, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 251, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 251, + 503 + ], + "type": "text", + "content": "2.2. Handling Person-to-Person Occlusions" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Even though many studies mentioned above have brought significant advances for monocular 3D human mesh reconstruction, they still suffer from ambiguities driven by person-to-person occlusions, which often occur in real-world environments. To cope with this problem, there have been various technical attempts. For example, Jiang et al. [11] introduced a new loss function that minimizes the discrepancy between the human segmentation masks and projected meshes to arrange the depth order of the people. In a similar vein, Zhang et al. [47] tried to learn the ordinal relation by supervising the difference between depth values of multiple persons. Instead of simply guiding the network via loss functions, Sun et al. [39] incorporated the bird's-eye-view body center heatmap into the pipeline of mesh estimation to consider the depth cue. Yang et al. [43] adopted to synthesize the other people to the input data for consideration of more variants from person-to-person occlusions." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 305, + 68, + 548, + 190 + ], + "blocks": [ + { + "bbox": [ + 305, + 68, + 548, + 190 + ], + "lines": [ + { + "bbox": [ + 305, + 68, + 548, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 68, + 548, + 190 + ], + "type": "image", + "image_path": "2a75a9087a078c4adfcb7b70c4dba081fa8a02e257e5c94de27ddc41fdc80bae.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 192, + 547, + 226 + ], + "lines": [ + { + "bbox": [ + 304, + 192, + 547, + 226 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 547, + 226 + ], + "type": "text", + "content": "Figure 2. The detailed process of the instance-aware contrastive learning scheme. Note that the ground truth of body center and joint positions is used for the feature sampling." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 237, + 547, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 237, + 547, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 237, + 547, + 477 + ], + "type": "text", + "content": "To specify the position of the target person, Khirodkar et al. [16] introduced the context normalization block, which fuses global and local center heatmaps with corresponding features. Choi et al. [7] utilized the 2D pose heatmap to focus on the feature belonging to the area of the target person in crowded scenes. Cha et al. [3] attempted to refine multiple human meshes based on inter-person relations that are computed by the transformer architecture. Liu et al. [31] proposed to apply the knowledge transfer technique to the 3D keypoint detection [49] for successfully reasoning invisible body parts under occlusions. Li et al. [22] proposed a body center attention mechanism to consider spatial-temporal relations of multiple persons at the pixel level. To complement the lack of the training data under multi-person scenes, Sun et al. [40] tried to synthesize plausible crowded examples by putting human samples at appropriate places of the given image with a reasonable scale according to the scene context. Moreover, they also proposed to learn the consistency between features extracted from the same human sample with and without occlusions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 487, + 411, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 411, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 411, + 502 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "content": "The proposed method aims to learn the spatial occupancy of body parts for each person by using the instance-aware contrastive learning scheme as shown in Fig. 2. By incorporating the identity information into encoded features, the proposed method can achieve the robust performance against person-to-person occlusions. The overall architecture of the proposed method is illustrated in Fig. 3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 599, + 504, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 504, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 504, + 613 + ], + "type": "text", + "content": "3.1. Instance-aware Contrastive Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "In the bottom-up approach for human mesh reconstruction, it is important to grasp the individual cue between multiple persons. To this end, we guide the process of mesh estimation based on the regional distinction of each human area, i.e., 24 body joints defined by the SMPL model [2]. Specifically, the backbone feature is encoded into two different feature maps, i.e., center-aligned instance map and joint-aligned instance map, through the corresponding network" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10555" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 54, + 544, + 277 + ], + "blocks": [ + { + "bbox": [ + 50, + 54, + 544, + 277 + ], + "lines": [ + { + "bbox": [ + 50, + 54, + 544, + 277 + ], + "spans": [ + { + "bbox": [ + 50, + 54, + 544, + 277 + ], + "type": "image", + "image_path": "6b917a70c60b3b8e9f20880b69e4bf624606191be5ecedd96fc93ff3afe4aff1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "text", + "content": "Figure 3. The overall architecture of the proposed method for occluded human mesh reconstruction. " + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "text", + "content": " are set to 64. " + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "text", + "content": " denote pose and shape parameters of the SMPL model. Note that instance-aware contrastive learning is conducted only in the training phase." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "text", + "content": "branch as shown in Fig. 3. Note that the predicted center heatmap " + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "inline_equation", + "content": "H_{C}" + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "text", + "content": " and joint heatmap " + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "inline_equation", + "content": "H_{J}" + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "text", + "content": " are adopted in this encoding process to provide the spatial information of body centers and joints. In addition, the positional encoding is also applied to the center-aligned instance map to prevent ambiguous representations between different people who have similar appearances. After that, center features and joint features are sampled at body center locations and visible joint positions of the center-aligned instance map and the joint-aligned instance map, respectively. These sampled features are subsequently projected into the latent space by using the nonlinear projector, which consists of fully connected layers and ReLUs (see " + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "inline_equation", + "content": "P_{C}" + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "inline_equation", + "content": "P_{J}" + }, + { + "bbox": [ + 46, + 320, + 289, + 477 + ], + "type": "text", + "content": " in Fig. 3)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 288, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 646 + ], + "type": "text", + "content": "Now, such projected features are fed into our instance-aware contrastive learning scheme. The detailed process is shown in Fig. 2. First, the center feature of the target person (i.e., anchor) is forced to push out those of other persons. By placing different human instances far apart from each other in the latent space, center features can implicitly represent the identity information for each person in a discriminative way. Second, the center feature pulls joint features belonging to the same person to a close distance. This facilitates the joint feature to express the human instance to which it belongs, by embedding the target identity information. To this end, two loss functions are designed based on the cosine similarity, which is suitable for measuring the directional coherence between embedding vectors, as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 658, + 287, + 690 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 658, + 287, + 690 + ], + "spans": [ + { + "bbox": [ + 110, + 658, + 287, + 690 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p u s h}} (a, b) = 1 + \\frac {a \\cdot b}{\\| a \\| \\| b \\|}, \\tag {1}", + "image_path": "6bf54d64e0c34a41d493e5cc4353da4c41fff1caa29a255ec46f1b1eb8bdae80.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 111, + 687, + 222, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 687, + 222, + 712 + ], + "spans": [ + { + "bbox": [ + 111, + 687, + 222, + 712 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p u l l} (a, b) = 1 - \\frac {a \\cdot b}{| | a | | | | b | |}.", + "image_path": "8438a80dc92dae114c9f43b802dfca0e4f968191e4fa982f06f5b3bdfb7398a6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "type": "text", + "content": "Specifically, " + }, + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{push}" + }, + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "type": "text", + "content": " is used to maximize the distance between center features of different people and " + }, + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pull}" + }, + { + "bbox": [ + 305, + 320, + 545, + 403 + ], + "type": "text", + "content": " is used to minimize the distance between the center feature and the joint feature of the same person in the latent space. By considering every possible center-to-center and center-to-joint combination, the proposed contrastive loss is defined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 341, + 410, + 545, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 410, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 341, + 410, + 545, + 479 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {c o n t}} = \\frac {2}{N (N - 1)} \\sum_ {i \\neq j} ^ {N} \\mathcal {L} _ {\\text {p u s h}} \\left(u _ {i}, u _ {j}\\right) \\tag {2} \\\\ + \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {1}{K _ {i}} \\sum_ {k = 1} ^ {K _ {i}} \\mathcal {L} _ {p u l l} (u _ {i}, v _ {i} ^ {k}), \\\\ \\end{array}", + "image_path": "bcefcd4969523ae32775c71300a546fb3b51183b2dfdf7280f1c0d98652945e9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " indicate the center feature and the joint feature, respectively. " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "K_{i}" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " denote the number of people and the number of visible joints belonging to the " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": "-th person in the input image, respectively. The effect of the proposed instance-aware contrastive learning scheme is shown in Fig. 4. As can be seen, the identity information is embedded into latent features during our instance-aware contrastive learning. Consequently, it is thought that both center-aligned instance map and joint-aligned instance map play an important role to describe the possession relationship between human instances and their visible joints. Note that the instance-aware contrastive learning part is conducted only in the training phase." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "In order to utilize this possession cue in the process of mesh regression, we incorporate the center-aligned instance map and the joint-aligned instance map into the network branch for estimating the SMPL parameter map (see the second branch from bottom in Fig. 3). To accurately indicate valid locations, the center heatmap and the joint" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10556" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 62, + 175, + 135 + ], + "blocks": [ + { + "bbox": [ + 49, + 62, + 175, + 135 + ], + "lines": [ + { + "bbox": [ + 49, + 62, + 175, + 135 + ], + "spans": [ + { + "bbox": [ + 49, + 62, + 175, + 135 + ], + "type": "image", + "image_path": "60c82af62a3fcfe4859fa73aa61b496f32dbcfacb678c1011bd9f57e7e8c6463.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 143, + 117, + 152 + ], + "lines": [ + { + "bbox": [ + 107, + 143, + 117, + 152 + ], + "spans": [ + { + "bbox": [ + 107, + 143, + 117, + 152 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 181, + 57, + 292, + 138 + ], + "blocks": [ + { + "bbox": [ + 181, + 57, + 292, + 138 + ], + "lines": [ + { + "bbox": [ + 181, + 57, + 292, + 138 + ], + "spans": [ + { + "bbox": [ + 181, + 57, + 292, + 138 + ], + "type": "image", + "image_path": "40898637b1082da41ccc76ee6b712cdec6ba59f538e77ee5b5c17208387c44f2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 230, + 143, + 241, + 152 + ], + "lines": [ + { + "bbox": [ + 230, + 143, + 241, + 152 + ], + "spans": [ + { + "bbox": [ + 230, + 143, + 241, + 152 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 293, + 57, + 416, + 139 + ], + "blocks": [ + { + "bbox": [ + 293, + 57, + 416, + 139 + ], + "lines": [ + { + "bbox": [ + 293, + 57, + 416, + 139 + ], + "spans": [ + { + "bbox": [ + 293, + 57, + 416, + 139 + ], + "type": "image", + "image_path": "21e2a0c947a523e7e966972a0e05024aa1bfa3e73d516a753c6b55cfa6cbdadf.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 356, + 144, + 366, + 153 + ], + "lines": [ + { + "bbox": [ + 356, + 144, + 366, + 153 + ], + "spans": [ + { + "bbox": [ + 356, + 144, + 366, + 153 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 158, + 547, + 202 + ], + "lines": [ + { + "bbox": [ + 46, + 158, + 547, + 202 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 547, + 202 + ], + "type": "text", + "content": "Figure 4. A visualization example of center features and joint features in the latent space. The feature dimension is reduced from 64 to 3 by using [33] for the visualization. (a) Input image with marks for positions of body centers (dark) and joints (bright). Note that points belonging to the same person are represented as the same color attribute. The effect of the proposed instance-aware contrastive learning scheme is shown sequentially, i.e., (b) before training, (c) middle of training, and (d) after training." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 430, + 57, + 543, + 138 + ], + "blocks": [ + { + "bbox": [ + 430, + 57, + 543, + 138 + ], + "lines": [ + { + "bbox": [ + 430, + 57, + 543, + 138 + ], + "spans": [ + { + "bbox": [ + 430, + 57, + 543, + 138 + ], + "type": "image", + "image_path": "0c6e9be33d7ec5c45443e4a641ccad1f92da287066a97f9bc8e603b426be7372.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 143, + 492, + 153 + ], + "lines": [ + { + "bbox": [ + 481, + 143, + 492, + 153 + ], + "spans": [ + { + "bbox": [ + 481, + 143, + 492, + 153 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 215, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 287, + 335 + ], + "type": "text", + "content": "heatmap are also employed for this concatenation process. Finally, pose and shape parameters of each person are sampled from the SMPL parameter map according to the predicted center position in a similar way of [38]. It is noteworthy that the model can precisely consider the occupancy of each human instance via such identity representation in the feature space, which leads to generation of reliable human meshes even with various person-to-person occlusions. An example of occluded human mesh reconstruction is shown in the bottom right of Fig. 3." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 342, + 138, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 138, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 138, + 354 + ], + "type": "text", + "content": "3.2. Loss functions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": "The proposed method is trained based on nine loss terms, i.e., contrastive loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cont}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": " (which is explained in subsection 3.1), body center heatmap loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{center}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", joint heatmap loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{joint}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", pose loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pose}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", shape loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{shape}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", Mixture Gaussian prior loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{prior}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", 3D joint loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{3d}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", Procrustes-aligned 3D joint loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pa3d}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", and 2D joint loss " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{2d}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ". First, the focal loss [30, 38] is adopted to train the body center heatmap " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "H_{C}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": " and the joint heatmap " + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "inline_equation", + "content": "H_{J}" + }, + { + "bbox": [ + 46, + 361, + 287, + 467 + ], + "type": "text", + "content": ", which is defined as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 50, + 475, + 287, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 475, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 50, + 475, + 287, + 550 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {f o c a l} (H, \\tilde {H}, \\tilde {H} ^ {\\prime}) = - \\frac {\\mathcal {L} _ {p o s} (H , \\tilde {H} ^ {\\prime}) + \\mathcal {L} _ {n e g} (H , \\tilde {H} , \\tilde {H} ^ {\\prime})}{\\sum \\tilde {H} ^ {\\prime}}, \\\\ \\mathcal {L} _ {n e g} (H, \\tilde {H}, \\tilde {H} ^ {\\prime}) = \\log (1 - H) H ^ {2} (1 - \\tilde {H}) ^ {4} (1 - \\tilde {H} ^ {\\prime}), \\\\ \\mathcal {L} _ {\\text {p o s}} \\left(H, \\tilde {H} ^ {\\prime}\\right) = \\log (H) \\left(1 - H\\right) ^ {2} \\tilde {H} ^ {\\prime}, \\tag {3} \\\\ \\end{array}", + "image_path": "6865261703d6af6af0dfc85ad99e52229741a8f793c578ce4ca06cacebada76f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\tilde{H}" + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": " denote a single heatmap and the corresponding ground truth, respectively. " + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\tilde{H}^{\\prime}" + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": " indicates the binary map that is marked on the location of the positive class in " + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\tilde{H}" + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": ". By using the focal loss, " + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{center}" + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{joint}" + }, + { + "bbox": [ + 47, + 562, + 287, + 621 + ], + "type": "text", + "content": " are formulated as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 85, + 628, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 628, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 85, + 628, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {c e n t e r} = \\mathcal {L} _ {f o c a l} (H _ {C}, \\tilde {H} _ {C}, \\tilde {H} _ {C} ^ {\\prime}), \\\\ \\mathcal {L} _ {\\text {j o i n t}} = \\frac {1}{\\mathcal {J}} \\sum_ {j = 1} ^ {\\mathcal {J}} \\mathcal {L} _ {\\text {f o c a l}} \\left(H _ {J} ^ {j}, \\tilde {H} _ {J} ^ {j}, \\tilde {H} _ {J} ^ {' j}\\right), \\tag {4} \\\\ \\end{array}", + "image_path": "152a4f544fe95c9659ae18430c4a294eced7f8453236f791c74ce38950d27b59.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{J}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " is the number of joint heatmaps which is set to 24 according to the SMPL model. The remaining loss terms" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": "are used to directly supervise the process of human mesh reconstruction. In particular, " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {pose }}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {shape }}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " compute the difference between predicted pose and shape parameters and the corresponding ground truth based on " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " loss, respectively [15, 20]. Mixture Gaussian prior loss " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {prior }}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " is employed to attain the naturalness of body meshes as introduced in [2]. In our work, Euclidean distance is utilized to calculate the spatial gap in the coordinate system for following three loss terms. The distance between estimated 3D joints and the corresponding ground truth is computed by " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{3d}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " [15, 20]. " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pa3d}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " indicates " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{3d}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " after Procrustes alignment is conducted to the reconstructed mesh [38]. The coordinates of joints projected onto the 2D space are used to measure " + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{2d}" + }, + { + "bbox": [ + 304, + 215, + 545, + 406 + ], + "type": "text", + "content": " [15, 20]. Finally, the total loss function is defined by using the weighted sum of all the aforementioned loss terms as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 410, + 545, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 410, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 312, + 410, + 545, + 463 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {\\text {c o n t}} \\mathcal {L} _ {\\text {c o n t}} + \\lambda_ {\\text {c e n t e r}} \\mathcal {L} _ {\\text {c e n t e r}} + \\lambda_ {\\text {j o i n t}} \\mathcal {L} _ {\\text {j o i n t}} \\\\ + \\lambda_ {p o s e} \\mathcal {L} _ {p o s e} + \\lambda_ {s h a p e} \\mathcal {L} _ {s h a p e} + \\lambda_ {p r i o r} \\mathcal {L} _ {p r i o r} \\\\ + \\lambda_ {3 d} \\mathcal {L} _ {3 d} + \\lambda_ {p a 3 d} \\mathcal {L} _ {p a 3 d} + \\lambda_ {2 d} \\mathcal {L} _ {2 d}, \\tag {5} \\\\ \\end{array}", + "image_path": "96b0aeae90d999786eeb1955507d3a215f7d1c38abf8a9c83bbe34e6268f1b02.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{cont}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{center}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{joint}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{pose}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{shape}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{prior}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{3d}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{pa3d}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\lambda_{2d}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": " are the balancing factor for each loss term, which are set to 50, 160, 50, 80, 6, 1.6, 200, 360, and 400, respectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 521, + 432, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 432, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 432, + 533 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 540, + 438, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 438, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 438, + 553 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "type": "text", + "content": "The proposed method is implemented on the PyTorch framework with an Intel E5-1650@3.60GHz CPU and two NVIDIA GeForce RTX 3090 GPUs. All the parameters of the proposed network are updated by the Adam optimizer, where momentum factors are set to 0.9 and 0.999, respectively. We use the batch size of 64 and the learning rate is set to " + }, + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-6}" + }, + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "type": "text", + "content": " during 30 training epochs. Input images are randomly cropped and rotated before they are resized to the resolution of " + }, + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 559, + 545, + 667 + ], + "type": "text", + "content": " pixels by using zero padding." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 672, + 425, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 672, + 425, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 672, + 425, + 684 + ], + "type": "text", + "content": "4.2. Benchmark Datasets" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "The proposed method is trained by using three 3D human pose datasets (i.e., Human3.6M [10], MPI-INF-3DHP [34]," + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10557" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 60, + 547, + 296 + ], + "blocks": [ + { + "bbox": [ + 47, + 60, + 547, + 296 + ], + "lines": [ + { + "bbox": [ + 47, + 60, + 547, + 296 + ], + "spans": [ + { + "bbox": [ + 47, + 60, + 547, + 296 + ], + "type": "image", + "image_path": "c952188275138a0e0c317a3b8a9cb44112489eb5b3b18546db0a0ae7fd852c7b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 302, + 546, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 302, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 546, + 324 + ], + "type": "text", + "content": "Figure 5. Results of 3D human mesh reconstruction on the CrowdPose [23] dataset. From top to bottom: input images, results by ROMP [38], 3DCrowdNet [7], and the proposed method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 339, + 548, + 495 + ], + "blocks": [ + { + "bbox": [ + 48, + 339, + 548, + 495 + ], + "lines": [ + { + "bbox": [ + 48, + 339, + 548, + 495 + ], + "spans": [ + { + "bbox": [ + 48, + 339, + 548, + 495 + ], + "type": "table", + "html": "
Methods3DPW-PCOCHumanCrowdPose
MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)AP(↑)\\( AP^{50}(↑) \\)\\( AP^{75}(↑) \\)\\( AP^M(↑) \\)\\( AP^L(↑) \\)\\( AP(↑) \\)\\( AP^{50}(↑) \\)\\( AP^{75}(↑) \\)
SPIN* [19]129.682.6157.612.746.819.417.826.216.440.110.6
PyMAF* [46]126.781.3154.314.348.721.518.028.717.442.713.0
ROMP* [38]119.779.7152.815.655.023.618.730.018.944.613.8
ROMP [38]115.675.8147.519.856.225.019.332.928.558.824.7
OCHMR* [16]117.577.1149.624.860.728.622.334.221.448.316.5
CLIFF* [26]---23.249.820.4--27.451.525.9
HMDiff* [8]114.273.5143.1--------
CoordFormer* [22]101.579.3---------
Ours*99.976.3126.430.575.817.335.130.528.561.623.2
Ours102.077.2131.034.980.024.027.135.031.665.726.7
", + "image_path": "613888b8fb9ae2baabeecb40701d56ca23cdb6ef29aac42027cf7cc956542cc2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 504, + 546, + 537 + ], + "lines": [ + { + "bbox": [ + 46, + 504, + 546, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 546, + 537 + ], + "type": "text", + "content": "Table 1. Performance comparison of occluded human mesh reconstruction based on 3DPW-PC, OCHuman, and CrowdPose datasets (best results and second results are shown in bold and underlined, respectively). Note that * denotes the performance without using the CrowdPose dataset for training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 559, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 559, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 559, + 287, + 631 + ], + "type": "text", + "content": "and MuCo-3DHP [35]) and four 2D human pose datasets (i.e., MPII [1], LSP [12], COCO [29], and CrowdPose [23]). In particular, only 2D pose labels are used for [23] while pseudo mesh labels, which are generated by [14], are employed to utilize other 2D human pose datasets [1, 12, 29] for training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "For the performance evaluation of the proposed method, four person-to-person occlusion datasets (i.e., 3DPW-PC [41], OCHuman [48], CrowdPose [23], and CMU-Panoptic [13]) are adopted. Specifically, the 3DPW-PC dataset is a subset of the 3DPW dataset where images taken under person-to-person occlusions are collected ac" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 559, + 547, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 547, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 547, + 666 + ], + "type": "text", + "content": "cording to [38]. The OCHuman dataset consists of severe occlusion cases between multiple persons while the CrowdPose dataset contains various person-to-person occlusions occurring in crowded scenes. Moreover, the CMU-Panoptic dataset includes multi-person sequences with diverse inter-person interactions. Based on such occlusion-oriented benchmark datasets, the performance of the proposed method will be evaluated and analyzed in-depth in the following subsection." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 672, + 443, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 672, + 443, + 684 + ], + "spans": [ + { + "bbox": [ + 305, + 672, + 443, + 684 + ], + "type": "text", + "content": "4.3. Performance Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 546, + 714 + ], + "type": "text", + "content": "Quantitative Evaluation. To show the effectiveness of the proposed method, we compare ours with previous meth-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10558" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 59, + 121, + 126 + ], + "blocks": [ + { + "bbox": [ + 49, + 59, + 121, + 126 + ], + "lines": [ + { + "bbox": [ + 49, + 59, + 121, + 126 + ], + "spans": [ + { + "bbox": [ + 49, + 59, + 121, + 126 + ], + "type": "image", + "image_path": "c6ad056a2dc827e8a7cdbfb6ce262158e4f2e3502ff9accb43394d2b28cef213.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 122, + 59, + 182, + 126 + ], + "blocks": [ + { + "bbox": [ + 122, + 59, + 182, + 126 + ], + "lines": [ + { + "bbox": [ + 122, + 59, + 182, + 126 + ], + "spans": [ + { + "bbox": [ + 122, + 59, + 182, + 126 + ], + "type": "image", + "image_path": "875d2a8a7cf7f8299b06ec969044c6addd02bdff9bf5093d701587c5f93dae72.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 184, + 59, + 250, + 126 + ], + "blocks": [ + { + "bbox": [ + 184, + 59, + 250, + 126 + ], + "lines": [ + { + "bbox": [ + 184, + 59, + 250, + 126 + ], + "spans": [ + { + "bbox": [ + 184, + 59, + 250, + 126 + ], + "type": "image", + "image_path": "05abd969148a7c3478b89837d54b4eca58552aac0037b4172cb33e4b988a9f59.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 251, + 59, + 316, + 126 + ], + "blocks": [ + { + "bbox": [ + 251, + 59, + 316, + 126 + ], + "lines": [ + { + "bbox": [ + 251, + 59, + 316, + 126 + ], + "spans": [ + { + "bbox": [ + 251, + 59, + 316, + 126 + ], + "type": "image", + "image_path": "53da101d757856d6ca98c5b860d0c81f396a7775d42ac25db3460c65e78f9e46.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 317, + 59, + 378, + 126 + ], + "blocks": [ + { + "bbox": [ + 317, + 59, + 378, + 126 + ], + "lines": [ + { + "bbox": [ + 317, + 59, + 378, + 126 + ], + "spans": [ + { + "bbox": [ + 317, + 59, + 378, + 126 + ], + "type": "image", + "image_path": "c0d56390c2f07ab8c4501947517a4c2097c61aa5cd88b6336ffe54b52ce042f4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 380, + 59, + 440, + 126 + ], + "blocks": [ + { + "bbox": [ + 380, + 59, + 440, + 126 + ], + "lines": [ + { + "bbox": [ + 380, + 59, + 440, + 126 + ], + "spans": [ + { + "bbox": [ + 380, + 59, + 440, + 126 + ], + "type": "image", + "image_path": "49fbadafe65103e7b6b683ce71da8372fe5f5c2d76f48843d1ce1fd3955be598.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 441, + 59, + 483, + 126 + ], + "blocks": [ + { + "bbox": [ + 441, + 59, + 483, + 126 + ], + "lines": [ + { + "bbox": [ + 441, + 59, + 483, + 126 + ], + "spans": [ + { + "bbox": [ + 441, + 59, + 483, + 126 + ], + "type": "image", + "image_path": "2dd82cf77a3ecb50cdc45fd95a6e684b219062a97b8742063b3c3fd30741c71d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 485, + 59, + 545, + 126 + ], + "blocks": [ + { + "bbox": [ + 485, + 59, + 545, + 126 + ], + "lines": [ + { + "bbox": [ + 485, + 59, + 545, + 126 + ], + "spans": [ + { + "bbox": [ + 485, + 59, + 545, + 126 + ], + "type": "image", + "image_path": "bc005b9173a5a976d60b0f3fcdf6c9a3362278203b02a74b1db22bd6bff7c2cd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 49, + 128, + 97, + 196 + ], + "blocks": [ + { + "bbox": [ + 49, + 128, + 97, + 196 + ], + "lines": [ + { + "bbox": [ + 49, + 128, + 97, + 196 + ], + "spans": [ + { + "bbox": [ + 49, + 128, + 97, + 196 + ], + "type": "image", + "image_path": "bf4d62d0525d537ebdcd17148caf07841467cd9c86400d2ee5c21c155ef964c3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 546, + 227 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 546, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 546, + 227 + ], + "type": "text", + "content": "Figure 6. More results of 3D human mesh reconstruction by the proposed method on 3DPW-PC [41] (1st row) and OCHuman [48] (2nd row) datasets." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 99, + 128, + 171, + 196 + ], + "blocks": [ + { + "bbox": [ + 99, + 128, + 171, + 196 + ], + "lines": [ + { + "bbox": [ + 99, + 128, + 171, + 196 + ], + "spans": [ + { + "bbox": [ + 99, + 128, + 171, + 196 + ], + "type": "image", + "image_path": "3cfab3697e6199b14bbba3eab4dfc1c2ddd827bab112c6d5b4e2dee50fe4269e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 173, + 128, + 230, + 196 + ], + "blocks": [ + { + "bbox": [ + 173, + 128, + 230, + 196 + ], + "lines": [ + { + "bbox": [ + 173, + 128, + 230, + 196 + ], + "spans": [ + { + "bbox": [ + 173, + 128, + 230, + 196 + ], + "type": "image", + "image_path": "15c110ced19d9fe5e30b9d628b61240e99094978bd9cf5daaff0d0093433a15c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 231, + 128, + 280, + 196 + ], + "blocks": [ + { + "bbox": [ + 231, + 128, + 280, + 196 + ], + "lines": [ + { + "bbox": [ + 231, + 128, + 280, + 196 + ], + "spans": [ + { + "bbox": [ + 231, + 128, + 280, + 196 + ], + "type": "image", + "image_path": "86e875228e12af3217561233a517cd9b4895c2e7a9f9187049dedad0a389f17c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 281, + 128, + 328, + 196 + ], + "blocks": [ + { + "bbox": [ + 281, + 128, + 328, + 196 + ], + "lines": [ + { + "bbox": [ + 281, + 128, + 328, + 196 + ], + "spans": [ + { + "bbox": [ + 281, + 128, + 328, + 196 + ], + "type": "image", + "image_path": "5eef3872593dc598fffed0eb2da83e0bdd6f4fde3ec796dc8467b8c525a40ef7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 329, + 128, + 410, + 196 + ], + "blocks": [ + { + "bbox": [ + 329, + 128, + 410, + 196 + ], + "lines": [ + { + "bbox": [ + 329, + 128, + 410, + 196 + ], + "spans": [ + { + "bbox": [ + 329, + 128, + 410, + 196 + ], + "type": "image", + "image_path": "968454e7772b5fb51673a7442018324923adec459c91ca912c9c9dee0bbe25e9.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 411, + 128, + 455, + 196 + ], + "blocks": [ + { + "bbox": [ + 411, + 128, + 455, + 196 + ], + "lines": [ + { + "bbox": [ + 411, + 128, + 455, + 196 + ], + "spans": [ + { + "bbox": [ + 411, + 128, + 455, + 196 + ], + "type": "image", + "image_path": "5f95b6139acb27b2918bd7467ef3d79b304bc92883bcf152fc38f7564d92712a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 457, + 128, + 545, + 196 + ], + "blocks": [ + { + "bbox": [ + 457, + 128, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 457, + 128, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 457, + 128, + 545, + 196 + ], + "type": "image", + "image_path": "456e54ad7d4351caa95d940c43cd5d873142e235b06a10591eae7cb97ff86774.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 53, + 247, + 282, + 363 + ], + "blocks": [ + { + "bbox": [ + 53, + 247, + 282, + 363 + ], + "lines": [ + { + "bbox": [ + 53, + 247, + 282, + 363 + ], + "spans": [ + { + "bbox": [ + 53, + 247, + 282, + 363 + ], + "type": "table", + "html": "
MethodsHaggl.MafiaUtim.PizzaMean
SPIN [19]124.3132.4150.4153.5133.1
CRMH [11]129.6133.5153.0156.7143.2
BMP [47]120.4132.7140.9147.5135.4
PARE [18]143.1193.1219.8190.4186.6
ROMP [38]111.8129.0148.5149.1134.6
OCHMR [16]115.5123.7142.6150.6133.1
3DCrowdNet [7]109.6135.9129.8135.6127.6
Ours109.1122.5137.8135.0126.1
", + "image_path": "941311720fac82805014f234ef4dcd1369c9a3302b2358268ab3b5f7833f82ba.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "content": "ods for 3D human mesh reconstruction, i.e., SPIN [19], CRMH [11], BMP [47], PyMAF [46], PARE [18], ROMP [38], OCHMR [16], 3DCrowdNet [7], HMDiff [8], and Coordinate [22], based on person-to-person occlusion benchmarks. To evaluate the proposed method on 3D human mesh datasets, three metrics are adopted, i.e., mean per joint position error (MPJPE) [10], Procrustes-aligned mean per joint position error (PA-MPJPE) [52], and mean per vertex position error (MPVPE) [36]. Specifically, MPJPE indicates the average value of the Euclidean distance between the predicted 3D joint and the corresponding ground truth. PA-MPJPE means MPJPE that is calculated after applying the Procrustes analysis to the estimated body mesh. MPVPE is computed by averaging the Euclidean distance between the predicted vertex and the corresponding ground truth. For 2D human pose datasets, the performance is evaluated by using the average precision (AP), which is calculated based on the object keypoint similarity (OKS) [29]. In addition, AP according to different threshold values (i.e., " + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{50}}" + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{75}}" + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "content": ") and scales of the human object (i.e., " + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^M}" + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^L}" + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "content": ") is also adopted for the performance comparison. Note that ResNet-50 [9] is employed as the backbone network of the proposed method, which is the default setting for the performance report in this subsection." + } + ] + } + ], + "index": 19 + }, + { + "type": "table", + "bbox": [ + 308, + 246, + 545, + 407 + ], + "blocks": [ + { + "bbox": [ + 46, + 371, + 287, + 405 + ], + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 405 + ], + "type": "text", + "content": "Table 2. Performance comparison by MPJPE based on the CMU-Panoptic dataset (best results and second results are shown in bold and underlined, respectively)." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 246, + 545, + 407 + ], + "lines": [ + { + "bbox": [ + 308, + 246, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 308, + 246, + 545, + 407 + ], + "type": "table", + "html": "
MethodsMPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
METRO [27]77.147.988.2
PARE [18]74.546.588.6
ROMP [38]76.747.393.4
MeshGraphormer [28]74.745.687.7
FastMETRO [5]73.544.684.1
CLIFF [26]72.045.785.3
PointHMR [17]73.944.985.5
ImpHMR [4]74.345.487.1
HMDiff [8]72.744.582.4
CoordFormer [22]79.446.594.4
Ours (ResNet-50)78.047.885.6
Ours (HRNet-32)73.244.380.3
", + "image_path": "b2291a1d9cab5da70d92a785d8e2c9dfe8b084a33acd2adf8632323fc0e86f76.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 415, + 546, + 449 + ], + "lines": [ + { + "bbox": [ + 305, + 415, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 546, + 449 + ], + "type": "text", + "content": "Table 3. Performance comparison based on the 3DPW dataset by following the protocol 3, i.e., fine-tuned on 3DPW (best results and second results are shown in bold and underlined, respectively)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": "First of all, the performance comparison based on 3DPW-PC, OCHuman, and CrowdPose datasets is shown in Table 1. As can be seen, the proposed method shows the meaningful performance improvement compared to previous approaches. Specifically, MPJPE and MPVPE on the 3DPW-PC dataset prove that our model can successfully estimate both pose and shape for occluded human mesh reconstruction. Moreover, the proposed method outperforms all state-of-the-art methods in terms of AP and " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP^{50}}" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": " with the significant performance gain on OCHuman and CrowdPose datasets. In Table 2, MPJPE of the proposed method on the CMU-Panoptic dataset is compared with others. We can see that the proposed method yields the reliable performance in most sequences while achieving the best result in the average MPJPE (see the rightmost column of Table 2). From the result reported in Tables 1 and 2, we could confirm that the proposed instance-aware contrastive learning scheme is effective to reconstruct human meshes under various person-to-person occlusions. Furthermore, we also evaluate the proposed method on the entire test set of 3DPW" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10559" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 286, + 135 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 135 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 135 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 135 + ], + "type": "table", + "html": "
MethodsMPJPE(↓)PA-MPJPE(↓)
Baseline (i.e., w/o center and joint features)104.280.2
Ours†102.278.2
Ours102.077.2
", + "image_path": "d70be056808bab7c68d2207b7c580fb1497e52069f76ddd0ba4d55cd0b81eb70.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 69, + 193, + 265, + 261 + ], + "blocks": [ + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "lines": [ + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "type": "text", + "content": "Table 4. Performance analysis according to the change of the network architecture. " + }, + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "type": "text", + "content": " denotes the performance without applying positional encoding to the center-aligned instance map." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 193, + 265, + 261 + ], + "lines": [ + { + "bbox": [ + 69, + 193, + 265, + 261 + ], + "spans": [ + { + "bbox": [ + 69, + 193, + 265, + 261 + ], + "type": "table", + "html": "
Feature DimensionMPJPE(↓)PA-MPJPE(↓)
32103.578.3
64102.077.2
128103.178.0
256104.278.6
", + "image_path": "78389bf544cf1d48dda62b5541c36e4cb51f8f9c0a9a80bb39ed10a948b3be3a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 287, + 302 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 302 + ], + "type": "text", + "content": "Table 5. Performance variations according to the change of the feature dimension for the center-aligned instance map and the joint-aligned instance map." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 326, + 286, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 286, + 396 + ], + "type": "text", + "content": "by following the protocol 3 [41]. In particular, we conduct the experiment by using two different backbone networks, i.e., ResNet-50 [9] and HRNet-32 [42], and the corresponding results are shown in Table 3. As can be seen, the proposed method performs robustly in a variety of real-world environments, not just for occlusion cases." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 286, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 286, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 286, + 637 + ], + "type": "text", + "content": "Qualitative Evaluation. The qualitative comparison of the proposed method with ROMP [38] and 3DCrowdNet [7] based on the CrowdPose dataset is shown in Fig. 5. As can be seen, the proposed method can successfully reconstruct multiple human meshes in complicated person-to-person occlusions. Specifically, the reconstructed mesh is well aligned to the target person without confusion with other persons (see the left two examples in Fig. 5). This is because the proposed method is able to effectively utilize the identity information of each person in the feature space. The fourth and fifth columns of Fig. 5 show the robustness of our method in crowded scenes. Furthermore, the proposed method works reliably even under severe occlusions between multiple persons as shown in the rightmost three examples in Fig. 5. More reconstruction results by the proposed method on 3DPW-PC and OCHuman datasets are also shown in Fig. 6. Based on this, it is thought that our instance-aware contrastive learning scheme is greatly helpful in understanding the occlusion context by overlapped persons and generating the plausible human mesh." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 647, + 140, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 140, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 140, + 659 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "type": "text", + "content": "In this subsection, several comparative experiments are conducted to demonstrate the effectiveness of the proposed method. The performance for all the experiments in this subsection is evaluated on the 3DPW-PC [41] dataset. First" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 385, + 171 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 385, + 171 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 385, + 171 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 385, + 171 + ], + "type": "image", + "image_path": "7258e91c36869dce4b91dc8ec6268d67449ba71a1c45c1636c22325fd7239a1c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 342, + 173, + 351, + 182 + ], + "lines": [ + { + "bbox": [ + 342, + 173, + 351, + 182 + ], + "spans": [ + { + "bbox": [ + 342, + 173, + 351, + 182 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 387, + 70, + 464, + 171 + ], + "blocks": [ + { + "bbox": [ + 387, + 70, + 464, + 171 + ], + "lines": [ + { + "bbox": [ + 387, + 70, + 464, + 171 + ], + "spans": [ + { + "bbox": [ + 387, + 70, + 464, + 171 + ], + "type": "image", + "image_path": "0fdb233cda4d9d4f315a29130e33ff5e2a1d46fab10abce77de34fc3173e845c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 173, + 430, + 182 + ], + "lines": [ + { + "bbox": [ + 421, + 173, + 430, + 182 + ], + "spans": [ + { + "bbox": [ + 421, + 173, + 430, + 182 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 466, + 70, + 544, + 171 + ], + "blocks": [ + { + "bbox": [ + 466, + 70, + 544, + 171 + ], + "lines": [ + { + "bbox": [ + 466, + 70, + 544, + 171 + ], + "spans": [ + { + "bbox": [ + 466, + 70, + 544, + 171 + ], + "type": "image", + "image_path": "f333580801e9ec988eca831d330e51ea247529c90ba4b0b2dca7b1a86e665e0f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 173, + 510, + 182 + ], + "lines": [ + { + "bbox": [ + 501, + 173, + 510, + 182 + ], + "spans": [ + { + "bbox": [ + 501, + 173, + 510, + 182 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 190, + 544, + 212 + ], + "lines": [ + { + "bbox": [ + 306, + 190, + 544, + 212 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 544, + 212 + ], + "type": "text", + "content": "Figure 7. (a) Input image. (b) Reconstruction result by baseline. (c) Reconstruction result by the proposed method." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 228, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 491 + ], + "type": "text", + "content": "of all, the effect of our instance-aware contrastive learning scheme is analyzed and the corresponding result is shown in Table 4. As can be seen in Table 4, the performance for occluded human mesh reconstruction is significantly improved by leveraging the identity information into latent features for centers and their related joints. Furthermore, we can see that applying positional encoding to the center-aligned instance map is also useful for the model to discriminatively represent each center feature under severe occlusion cases. The effect of our instance-aware learning scheme is shown in Fig. 7. In the following, we check the performance variation by the change of the feature dimension for both center-aligned and joint-aligned instance maps is shown in Table 5. The best performance is achieved when the feature dimension is set to 64, thus this setting has been used as default for the performance evaluation of the proposed method. Note that the performance in all the settings is better than our baseline (i.e., the first row of Table 4). Based on ablation studies, we can conclude that the proposed instance-aware contrastive learning scheme is effective for occluded human mesh reconstruction under various real-world environments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 503, + 383, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 383, + 515 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 383, + 515 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 524, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 642 + ], + "type": "text", + "content": "In this paper, we present a simple yet powerful method for occluded human mesh reconstruction, especially focusing on person-to-person occlusions. The core of the proposed method is to embed the identity information into latent features for body centers and joints of each person. To do this, we propose a novel instance-aware contrastive learning scheme. Experimental results on benchmark datasets show that the proposed method works reliably even under various person-to-person occlusions occurring in real-world environment." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by Institute of Information Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00207, Immersive Media Research Laboratory)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10560" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. 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The main challenge of this task lies in identifying the target object from different viewpoints while rejecting similar distractors. Existing ImageGoal Navigation methods usually adopt the simple Exploration-Exploitation framework and ignore the identification of specific instance during navigation. In this work, we propose to imitate the human behaviour of \"getting closer to confirm\" when distinguishing objects from a distance. Specifically, we design a new modular navigation framework named Instance-aware Exploration-Verification-Exploitation (IEVE) for instance-level image goal navigation. Our method allows for active switching among the exploration, verification, and exploitation actions, thereby facilitating the agent in making reasonable decisions under different situations. On the challenging HabitatMatterport 3D semantic (HM3DSEM) dataset, our method surpasses previous state-of-the-art work, with a classical segmentation model (0.684 vs. 0.561 success) or a robust model (0.702 vs. 0.561 success). Our code will be made publicly available at https://github.com/XiaohanLei/IEVE.", + "bbox": [ + 76, + 340, + 473, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 703, + 209, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Embodied navigation is an emerging computer vision task, where an agent utilizes visual sensing to actively interact with its surroundings and execute navigation tasks [2, 4]. Over the past decade, substantial advancements have been witnessed in the field of embodied visual navigation, driven by the emergence of large-scale photorealistic 3D scene", + "bbox": [ + 75, + 728, + 468, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China under Contract 62102128 and 62021001, and in part by the Fundamental Research Funds for the Central Universities under contract WK3490000007. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution of USTC. Corresponding authors: Min Wang and Wengang Zhou.", + "bbox": [ + 75, + 827, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bdf81e7ef1ccbe524f0b348a08bd736448b6e3ae2902ed835be614eb031ad289.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 311, + 880, + 563 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef5f96049ab6350e7d27596995c6245b3a7fd6f10de265339a80c3e8268835bb.jpg", + "image_caption": [ + "Figure 1. Instance ImageGoal Navigation tasks an agent with navigating to a particular object instance described by the goal image. The agent is initially in an unexplored environment at $t_1$ . While exploring the environment, it encounters a \"bed\" similar to the target at $t_2$ and discerns their differences. Eventually, at $t_3$ , agent finds the \"bed\" described in the goal image." + ], + "image_footnote": [], + "bbox": [ + 513, + 566, + 598, + 665 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8c305c445374725622e2ac9aada2509e258a9e5a7737eac37a162acb8fc7e933.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 566, + 689, + 665 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/30f9c2d769c9ee22dc720c3c369c4812db8d40a2f8997526144f66b0461aa3f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 566, + 781, + 665 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/92630ff627a7de7241dc4f539250101676c3777ee4604ebafadd396d2eae3f66.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 575, + 879, + 660 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "datasets [6, 41, 48, 53, 57], the implementation of advanced simulators [24, 46, 49, 53], the development of deep learning algorithms [5, 19, 38, 47], and so on.", + "bbox": [ + 496, + 762, + 890, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ability for an agent to navigate its environment and accomplish tasks without human intervention is essential for the advancement of embodied visual navigation. One common setting for tasking an agent is to give it natural language instructions, such as \"check if my laptop is on the chair.\" However, this setting becomes confusing when", + "bbox": [ + 496, + 810, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16329", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "there are multiple chairs in the house. To overcome this challenge, Krantz et al. [26] propose the Instance Image-Goal Navigation task (IIN), which involves providing the agent with an image captured from goal camera that depicts a specific instance. The agent is then required to navigate to the location of the instance depicted in the image, as shown in Fig. 1. By utilizing the visual information, the agent is expected to avoid confusion caused by multiple similar distractors of the same class.", + "bbox": [ + 75, + 90, + 470, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The most relevant task with IIN is ImageGoal Navigation [1, 9, 17, 33, 35, 56, 63], which has been a popular topic in embodied visual navigation research. The difference between IIN and ImageGoal Navigation lies in their requirements for navigation success. In other words, IIN demands that the agent has the ability to recognize the same object from different viewpoints, while ImageGoal Navigation requires maximizing the similarity between the agent's observations and the goal image. Previous ImageGoal navigation requires targeting random goal images captured by cameras that share the same parameters like height, look-at-angle, and field-of-view as the agent camera. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation. They typically expect the agent to accurately determine whether the current observation matches the goal image. However, it is extremely challenging to enable the agent to correctly identify the target object from a considerable distance. In addition, they treat the decision-making process as a one-shot task, perceiving it as a match between the current observation and the target, while overlooking the judgment process across the temporal dimension.", + "bbox": [ + 75, + 226, + 470, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above limitations, we propose a novel IIN framework, i.e., Instance-aware Exploration-Verification-Exploitation (IEVE), for Instance ImageGoal Navigation. Inspired by the human behavior of \"getting closer to confirm\" when recognizing distant objects, we formulate the task of determining whether an object matches the one in the goal image as a sequential decision problem. In addition, we design a novel matching function that relies not only on the current observation and goal image but also on the Euclidean distance between the agent and the potential target. We categorize the targets into confirmed target, potential target, and no-target (exploration), and allow the agent to actively choose among these three targets. After an efficient training process of our framework, our result on the IIN task outperforms previous state-of-the-art methods, achieving 0.684 Success with a classical instance segmentation model [18], and 0.702 with a robust model [51].", + "bbox": [ + 75, + 559, + 468, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 830, + 218, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, there has been great research interest in the field of embodied vision and active agents. Embodied agents are required to effectively and creatively resolve", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "complex tasks and interact with the physical environment. Notably, the navigation task plays a pivotal role in embodied vision. Numerous researchers have devoted their efforts to exploring different forms of navigation problems, encompassing various task goals and input formats. Specifically, there are five main categories of visual navigation problems: Point Goal Navigation [2, 8, 45], Object Goal Navigation [4, 14, 15, 45, 61], Visual Language Navigation [3, 16, 20-22, 25, 27, 30, 30, 59], ImageGoal Navigation [1, 9, 17, 29, 33, 35, 56, 63], and Instance ImageGoal Navigation [28]. According to the learning framework design, existing visual navigation methods are typically divided into two categories: modular and end-to-end approaches.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "End-to-end navigation policies are commonly optimized with improved visual representations [37, 58], auxiliary tasks [60], carefully reward-shaping [34] and data augmentation techniques [34]. Visual representations can be improved with fine-tuned segmentation model [37] and object relation graphs [12, 13, 36, 39, 62]. Prior works also learn fine-tuning visual encoder with Self-Supervised Learning (SSL) [40, 55], while some researchers employ imitation learning approaches, such as Ramrakhya et al. [43], gathering data from large-scale human annotations. Although achieving promising navigation success in simulator, end-to-end methods often suffer high computation complexity in training and generalizability, which may degrade the success of navigation in diverse environments.", + "bbox": [ + 496, + 289, + 892, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, modular methods have been proposed to solve navigation tasks with separate modules, including perception, mapping, path planning, etc. Chaplot et al. [7] address the Object Goal Navigation problem using semantic mapping and exploration. Majumdar et al. [33] adopt the zero-shot learning and inference approach with the use of CLIP. Rmakrishnan et al. [42] propose a potential field function to tackle the exploration problem in Object Goal Navigation. Mezghan et al. [35] and Savinov et al. [44] construct augmented memory mechanisms in ImageGoal Navigation. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation for ImageGoal Navigation. In general, modular-based methods typically exhibit excellent scalability with lower training cost.", + "bbox": [ + 496, + 505, + 890, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we focus on IIN task, which is a newly formulated but more real navigation task. It is relevant with the classical ImageGoal Navigation task. ImageGoal Navigation is commonly studied in a previous-unseen environment where goal images are randomly sampled sharing the same parameter with the agent's camera [63]. Many approaches study the ImageGoal Navigation task with RL to learn policies that directly map observations to action [1, 10, 55, 56]. Yadav et al. [55] postulate that SSL for visual representation greatly contributes to the success of the end-to-end navigation policy training. Choi et al. [10] attribute the success", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16330", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/de581b6c3349e32279e4bf33b93762870e738a12359ea54357689746ea5c6c8c.jpg", + "image_caption": [ + "Figure 2. Framework Overview. Our model consists of five main components. Instance Classification $f_{class}$ predicts the object's class in goal image $n$ . Online Mapping $f_{SLAM}$ uses RGB-D and sensor pose reading $\\mathcal{P}(t)$ to construct a semantic map $\\mathcal{M}(t)$ of the environment. The Switch Policy $\\pi_S$ and Goal Mapping Policy $\\pi_{GM}$ are interconnected. The Switch Policy $\\pi_S$ determines the output of the Goal Mapping Policy's goal map $\\mathcal{M}_g(t)$ based on its input judgments (whether a potential target exists and whether the potential target is confirmed). Once the goal map $\\mathcal{M}_g(t)$ is determined, the Local Policy $\\pi_l$ is used to determine the action $a(t)$ taken by the agent at the current timestep." + ], + "image_footnote": [], + "bbox": [ + 122, + 92, + 848, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of RL training to the carefully reward shaping. Chaplot et al. [9] propose a topological mapping system to address the ImageGoal navigation problem, as well as Kim et al. [23]. Kwon et al. [29] propose a novel type of map for ImageGoal Navigation, a renderable neural radiance map.", + "bbox": [ + 75, + 378, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike ImageGoal Navigation, IIN [26] focuses on distinguishing different similar instances and being able to identify the object in the goal image at different viewpoints. On the other hand, ImageGoal Navigation pays more attention to maximizing the similarity between observations and the goal image within an episode. To be more specific, the goal camera in IIN task is disentangled from the agent's camera on the sampled parameters such as height, look-at-angle, and field-of-view reflect the realistic use case of a user-supplied goal image. Additionally, previous state-of-the-art work employs the confidence score for object re-identification. Differently, we propose a new switchable strategy to meticulously examine a currently visible object. Our key insight lies in treating the subtask of target confirmation as a sequential decision problem and designing a new matching function, which enables the agent to more accurately distinguish target objects from misleading ones.", + "bbox": [ + 75, + 460, + 468, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 748, + 166, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We devise a new framework, Instance-aware Exploration-Verification-Exploitation (IEVE) for Instance ImageGoal Navigation, which consists of five key modules, including Instance Classification, Online Mapping, Switch Policy, Goal Mapping Policy and Local Policy, as depicted in Fig. 2. In the following subsections, we will first introduce the preliminaries in Sec. 3.1, and sequentially elaborate the five modules of our framework.", + "bbox": [ + 75, + 780, + 467, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 378, + 638, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We follow the embodiment setting of Hello Robot Stretch. The agent in the simulation environment is a rigid-body, zero-turn-radius cylinder of height $1.41\\mathrm{m}$ and radius $0.17\\mathrm{m}$ . The forward-facing RGB-D camera is mounted at a height of $1.31\\mathrm{m}$ . At each timestep $t$ , the agent's observation $\\mathcal{O}_t$ consists of an egocentric RGB image $\\mathcal{I}_t$ , depth image $\\mathcal{D}(t)$ , goal image $\\mathcal{I}_g$ and sensor pose reading $\\mathcal{P}(t)$ . Camera parameters of $\\mathcal{I}_t$ and $\\mathcal{I}_g$ like height, look-at-angle and field-of-view are not the same. Specifically, $\\mathcal{I}_t$ is a $640\\times 480$ image while $\\mathcal{I}_g$ is a $512\\times 512$ image.", + "bbox": [ + 496, + 401, + 890, + 553 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Instance Classification", + "text_level": 1, + "bbox": [ + 500, + 559, + 707, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At the onset of each episode, the Instance Classification model will first process $\\mathcal{I}_g$ and output an object class label $n$ . We adopt two different types of models to achieve instance classification, including 1) classification model: we use the goal images on the train split of HM3D-SEM [57] to finetune the image classification model, i.e., Swin Transformer [32], pretrained on ImageNet [11]. It may face the inherent semantic ambiguity of Ground Truth labels in the HM3D-SEM, such as the difficulties in distinguishing between the class \"sofa\" and \"chair\". 2) instance segmentation model: we use the semantic label of the most central segmented instance in the goal image as the classification result. This approach can maintain semantic consistency without being affected by Ground Truth labels.", + "bbox": [ + 496, + 583, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Online Mapping", + "text_level": 1, + "bbox": [ + 500, + 801, + 661, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At each time step $t$ , the agent will utilize the egocentric view to construct the current semantic map $\\hat{m}(t)$ within its local coordinate system. The RGB frame $\\mathcal{I}(t)$ is first processed through instance segmentation (Mask RCNN [18]), yielding the output $\\mathcal{I}_{seg}(t)$ with dimensions of $(B, N +$", + "bbox": [ + 496, + 825, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16331", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/edaa1a16fcc256d0832b992a92e740006de527c5563175d56096f3352955c50c.jpg", + "image_caption": [ + "Figure 3. Switch Policy and Goal Mapping Policy. The Goal Map Selection module $f_{\\text{switch}}$ receives two inputs: the shortest Euclidean distance between the agent and the potential target (or non-existence), and the number of matched keypoints. These inputs are mapped to a selection signal using Goal Map Selection function $f_{\\text{switch}}$ . At each timestep, the Switch Policy $\\pi_S$ will choose one and only one of the three parallel modules of Goal Mapping Policy $\\pi_{GM}$ ." + ], + "image_footnote": [], + "bbox": [ + 130, + 93, + 836, + 284 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3, $H,W$ ), denoting batch size, the number of classes $N$ plus RGB channels of $\\mathcal{I}(t)$ , frame height, and frame width. Simultaneously, the depth image $\\mathcal{D}(t)$ is transformed into a pointcloud $P_{c}(t)$ using the camera's intrinsic matrix $\\pmb{T}_{int}$ , followed by the voxelization of the pointcloud. Subsequently, the feature points of $\\mathcal{I}_{seg}(t)$ are scattered into the voxels, resulting in the overall local map construction process being formulated as:", + "bbox": [ + 75, + 368, + 472, + 489 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {m} (t) = \\operatorname {S c a t t e r} (\\operatorname {V o x e l} \\left(\\boldsymbol {T} _ {\\text {i n t}} \\mathcal {D} (t)\\right), \\mathcal {I} _ {\\text {s e g}} (t)). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 498, + 468, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the constructed semantic map $\\hat{m}(t)$ within local coordinate system, agent will subsequently conduct max pooling with the previous global semantic map to obtain the global semantic map $\\mathcal{M}(t)$ at timestep $t$ as follows:", + "bbox": [ + 75, + 523, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} (t) = \\operatorname {M a x P o o l i n g} (\\mathcal {M} (t - 1), T _ {l g} \\hat {m} (t)), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 592, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T_{lg}$ denotes the transformation matrix from the agent's local frame to the world's global coordinate system. The size of $\\mathcal{M}(t)$ is specified as $(B, 2 + N, H_m, W_m)$ , where the first channel represents the explored area of the entire environment, the second channel defines the nontraversable area, and the last $N$ channels signify the location of each object class.", + "bbox": [ + 75, + 618, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Switch Policy", + "text_level": 1, + "bbox": [ + 76, + 731, + 217, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At each time step $t$ , Switch Policy actively selects the functional goal map from the three parallel sub-modules in Goal Mapping Policy. We summarize the switch process as a function with segmented depth image $\\mathcal{I}_{seg}(t,n) \\cdot \\mathcal{D}(t)$ , the number of matched keypoints $\\omega$ using local feature matching algorithm and the minimum Euclidean distance $d$ between the current position of the agent and the potential target (if exists). This can be described as follows:", + "bbox": [ + 75, + 755, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = f _ {s w i t c h} \\left(\\mathcal {I} _ {s e g} (t, n) \\cdot \\mathcal {D} (t), \\omega , d\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $S$ indicates which goal mapping policy to be selected, depicted in Fig. 3. To obtain the specific expression of $f_{\\text{switch}}$ , we construct an Instance Re-Identification dataset as depicted in Fig. 6 to illuminate the influence of distance $d$ and the number of matched keypoints $w$ on the goal object's re-identification.", + "bbox": [ + 496, + 368, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Goal Map Selection function $f_{\\text{switch}}$ aligns with human experience in object verification. $f_{\\text{switch}}$ sets objects of the same category as potential targets. At a larger distance to make accurate decisions, a higher threshold on number of matched keypoints is set to convert a potential target into a determined target as depicted in Fig. 4. As the distance decreases, the upper threshold also degrades continuously. At closer distance, the agent's judgment of the object becomes more reliable, so when the number of matched keypoints falls below the lower threshold, it can be very reliably determined that the potential target is not the goal target, thereby switching to the Exploration Policy.", + "bbox": [ + 496, + 460, + 892, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local Feature Matching. We employ a keypoint-based re-identification method to help in the selection of goal mapping policy in Eq. (3). Conditioned on the goal image $\\mathcal{I}_g$ and egocentric image $\\mathcal{I}(t)$ , we extract the pixel-wise $(x,y)$ coordinates of the keypoints $K_{t}\\in \\mathbb{R}^{n\\times 2}$ and their associated feature descriptors $V_{t}\\in \\mathbb{R}^{n\\times 256}$ . These features are extracted utilizing DISK [50], an end-to-end local feature learning algorithm that utilizes policy gradient. Likewise, the same process is repeated with the goal image, resulting in $K_{g}\\in \\mathbb{R}^{m\\times 2}$ and $V_{g}\\in \\mathbb{R}^{m\\times 256}$ . The feature extraction processes are formulated as follows:", + "bbox": [ + 496, + 643, + 893, + 809 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(K _ {t}, V _ {t}\\right) = \\operatorname {D I S K} (\\mathcal {I} (t)), \\quad \\left(K _ {g}, V _ {g}\\right) = \\operatorname {D I S K} (\\mathcal {I} _ {g}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 821, + 890, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, the matched pairs $(\\hat{K}_t,\\hat{K}_g)\\in \\mathbb{R}^{\\omega \\times 2}$ are computed using LightGlue [31], a deep neural network that matches sparse local features across image pairs. The fea", + "bbox": [ + 496, + 853, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16332", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ture matching process is formulated as follows:", + "bbox": [ + 76, + 90, + 392, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\hat {K} _ {t}, \\hat {K} _ {g}\\right) = \\operatorname {L i g h t G l u e} \\left(\\left(K _ {t}, V _ {t}\\right), \\left(K _ {g}, V _ {g}\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 116, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, the number of matched points $\\omega$ is utilized as an adaptive threshold for the verification and exploitation goal selection.", + "bbox": [ + 75, + 146, + 468, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Goal Mapping Policy", + "text_level": 1, + "bbox": [ + 76, + 200, + 274, + 217 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depicted in Fig. 3, Goal Mapping Policy module is divided into three parallel sub-modules, which will function at different timesteps. In other words, at each timestep, only one sub-module will function. More specifically, given the predicted goal object's class $n$ and segmented vision $\\mathcal{I}_{seg}(t)$ , if the mask $\\mathcal{I}_{seg}(t,n)$ has any value greater than zero, then the Exploitation or Verification Policy is activated. They project the masked depth image $\\mathcal{I}_{seg}(t,n)\\cdot \\mathcal{D}(t)$ to current semantic map. Similar to previous Online Mapping module, the two goal mapping policies in local coordinate system can be summarized as follows:", + "bbox": [ + 75, + 223, + 470, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {m} _ {g} (t) = \\operatorname {V o x e l} \\left(\\boldsymbol {T} _ {\\text {i n t}} \\mathcal {I} _ {\\text {s e g}} (t, n) \\cdot \\mathcal {D} (t)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 401, + 468, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{m}_g(t)$ indicates the goal map in the local coordinate system. Then we transform $\\hat{m}_g(t)$ into the global coordinate system, $\\mathcal{M}_g(t) = T_{lg}\\hat{m}_g(t)$ . Although with the same goal map formulas, Exploitation and Verification policy represent the targets with different confidence. Specifically, Exploitation policy refers to the confirmed target, which will be kept and used for the rest navigation process. In contrast, Verification policy represents potential target, which will be further checked by local feature matching in the Switch policy module.", + "bbox": [ + 75, + 429, + 468, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Exploration Policy use a convolutional neural network to predict a waypoint $g_{rl}(t) = \\pi_{rl}(\\mathcal{M}(t)|\\theta_{rl})$ , where $\\theta_{rl}$ are parameters of Exploration Policy. We train it with RL to maximize coverage of the environment while also successfully employing the stop action upon encountering a correct oracle facing the goal object. The goal map $\\mathcal{M}_g(t)$ is constructed with the value at position $g_{rl}(t)$ set as 1.", + "bbox": [ + 75, + 580, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Local Policy", + "text_level": 1, + "bbox": [ + 76, + 696, + 207, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When Switch Policy selects one of three goal mapping policies, agent adopts Local Policy to infer next action in accordance with the semantic map $\\mathcal{M}(t)$ , and the goal map, $\\mathcal{M}_g(t)$ . Specifically, Fast Matching Method (FMM) is employed to generate a distance field, which establishes the shortest distance between a traversible point and the selected goal map. A subset of the distance field is chosen within the agent's feasible range, and a waypoint is selected, ensuring that it does not intersect with existing obstacles and maintains the local minimum within the subset. With the selected waypoint, the agent can readily calculate an action based on the angle and distance from its current state.", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dbacca8315c95a9e2a90586dfa175bd8c9118e85739e24f41bd00510fc6468f0.jpg", + "image_caption": [ + "Figure 4. Goal Map Selection function $f_{switch}$ with respect to the Euclidean distance from agent to the potential target and the number of matched keypoints. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 540, + 90, + 846, + 273 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/265fce2862f2b54a8111b99b66b3acb292c2b2ea65b328782a039b98e8fe2189.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelValidation
Success ↑SPL ↑
RL Baseline [26]0.0830.035
OVRL-v2 ImageNav [55]0.0060.002
OVRL-v2 IIN [55]*0.2480.118
Mod-IIN [28]0.5610.233
IEVE Mask RCNN (ours)0.6840.241
IEVE InternImage (ours)0.7020.252
", + "bbox": [ + 552, + 325, + 841, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Comparison between our IEVE and prior methods on IIN task. “*” means we finetune OVRL-v2 [55] on the IIN task. IEVE outperforms the baseline model (row 1) with up to $8.75\\mathrm{x}$ increase in Success and outperforms a state-of-the-art model [28] (Mod-IIN, row 4) from 0.561 to 0.684 with a lightweight segmentation model (Mask RCNN) on Success, and higher Success of 0.702 with a strong backbone (InternImage [51]).", + "bbox": [ + 498, + 462, + 890, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also add a visited trajectory mechanism for the agent to avoid been stuck by invisible obstacles, which will be discussed in the supplementary materials. In our framework, only Instance Classification and Exploration Policy require few training, underscoring the computation efficiency of our design.", + "bbox": [ + 498, + 573, + 890, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 678, + 624, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 500, + 703, + 674, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. For our experiment, we employ the Habitat [49] simulator to conduct our experiments. The definition of the Instance ImageGoal Navigation [26] task utilized in the Habitat Navigation Challenge $2023^{1}$ serves as our primary reference point. The episode dataset proposed by Krantz et al. [28] for Instance ImageGoal Navigation serves as our key data source. The scene dataset utilized in this study stems from the Habitat-Matterport3D with semantic annotations (HM3D-SEM) [54], which encompasses a total of 216 scenes. These scenes are split into three distinct sub", + "bbox": [ + 498, + 726, + 890, + 877 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1https://aihabitat.org/challenge/2023/", + "bbox": [ + 517, + 886, + 816, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16333", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sets for training, validation, and testing purposes, consisting of 145/36/35 scenes, respectively. Additionally, the episode dataset has been partitioned into four subsets for training, validation, testing, and testing under a modified challenge regime, comprising 7,056K/1K/1K/1K episodes respectively. We train our agent on the train split and evaluate it on validation split. The object depicted by the goal image belongs to the following six categories: {chair, couch, plant, bed, toilet, television}. On the validation subset, a total of 795 unique object instances have been observed.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Action Space. Adhering to the task setting of the Habitat Navigation Challenge 2023, we employ the continuous action space. The action space encompasses four actions: linear velocity, angular velocity, camera pitch velocity, velocity stop, each of which accepts values ranging between $-1$ and $1$ and is appropriately scaled according to the respective configurations. Our linear speed is capped at a maximum of $35cm/frame$ and angular velocity at $60^{\\circ}/frame$ .", + "bbox": [ + 75, + 242, + 472, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We evaluate our model with both success and efficiency. We report Success Rate (Success), Success rate weighted by normalized inverse Path Length (SPL). Success is True if the agent calls velocity stop action within $1.0m$ Euclidean distance of the goal object and the object is oracle-visible by turning or looking up and down. SPL is an efficiency measure defined in [2].", + "bbox": [ + 75, + 364, + 472, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 481, + 441, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We undertake a comprehensive evaluation of our proposed model against various baselines and the SOTA work.", + "bbox": [ + 76, + 505, + 468, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "End-to-End RL Agent. The baseline model for the IIN task is trained in a fully-fledged end-to-end fashion. This involves inputting both an egocentric rgb and depth image as well as a pose into the model, which is then processed by a visual encoder and a recurrent neural network. The network output directly determines the agent's action. The agent is trained from scratch utilizing Proximal Policy Optimization (PPO) [47]. Our method exhibits 8.24x higher Success in Val (row 5 vs. row 1 in Tab. 1). Although it takes a staggering 3.5 billion steps for RL agent model to achieve convergence, the generalization capability of the agent remains unsatisfactory.", + "bbox": [ + 75, + 536, + 472, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "OVRL-v2. Offline Visual Representation Learning v2 (OVRL-v2 [55]) was proposed by Karmesh et al., who introduced a novel model-free, end-to-end navigation policy that emphasizes the significance of self-supervised pretraining of visual encoders and introduces the concept of Compression Layer (CL). Employing a ViT + LSTM backbone, this policy exhibits state-of-the-art performance in ImageGoal Navigation and approaches the state-of-the-art in ObjectGoal Navigation. Due to the task disparity between ImageGoal Navigation and Instance ImageGoal Navigation, we fine-tune the pretrained policy for our specific task.", + "bbox": [ + 75, + 718, + 472, + 885 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The original OVRL-v2 is trained under the setting of the", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f5280a6a062504dc3a036d1d439485f449be6141dcd56371486361c1cb7479d4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Model VariationValidation
ClassificationPerceptionSwitchExplorationSuccess ↑SPL ↑
Mask RCNNMask RCNNEVERL0.6660.235
Mask RCNNMask RCNNEVEFrontier0.6760.182
Mask RCNNMask RCNNEVERandom0.6540.233
Mask RCNNMask RCNNEERL0.5900.221
InternImageInternImageEVERL0.7020.252
SwinTransMask RCNNEVERL0.6840.241
SwinTransMask RCNNEVEFrontier0.6280.180
SwinTransMask RCNNEVERandom0.6360.236
SwinTransMask RCNNEERL0.6200.216
SwinTransInternImageEVERL0.6760.238
GroundTruthMask RCNNEVERL0.6820.238
GroundTruthOracle-RL0.8500.399
", + "bbox": [ + 504, + 88, + 890, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Variants of our method with different settings of instance classification, perception, switch policy and exploration policy. Perception means the Instance Segmentation model variations in Online Mapping module. \"EE\" refers to the exploration-exploitation policy, which establishes a fixed threshold for decision-making. \"EVE\" represents our Exploration-Verification-Exploitation Switch policy. The last row gives the upper bound of our method, where with ground truth instance segmented observations, the agent can identify the specified object instance as soon as the object becomes visible.", + "bbox": [ + 496, + 275, + 893, + 415 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ImageGoal Navigation task. Evaluating OVRL-v2's performance without finetuning for Instance ImageGoal Navigation reveals suboptimal results (0.006 Success row 2 in Tab. 1). Several factors impact the performance: a shift in scene datasets (Gibson [53] vs. HM3D-SEM [57]), changes in embodiment (Locobot vs. Stretch), and disparity in goal destinations (image source vs. image subject). When specifically finetuned for Instance ImageGoal Navigation (row 3 in Tab. 1) on HM3D-SEM, OVRL-v2 yields improved performance rates at 0.248 Success. Our approach with Mask RCNN exhibits 0.436 higher Success in Val (row 5 vs. row 3 in Tab. 1), and 0.454 higher Success with InternImage (row 6 vs. row 3 in Tab. 1).", + "bbox": [ + 496, + 428, + 893, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mod-IIN. Mod-IIN [28] decomposes Instance ImageGoal Navigation task into exploration, goal re-identification, goal localization and local navigation. It outperforms previous state-of-the-art end-to-end learned policies without fine-tuning. Mod-IIN achieves 0.561 Success and 0.233 SPL (row 4 in Tab. 1), and we surpass their results in Success with a substantial margin of 0.123 by attaining 0.684 Success and a marginal improvement in SPL with the help of a classical visual backbone trained with Mask RCNN [18] (row 5 in Tab. 1). Additionally, with the current state-of-the-art Semantic Segmentation model InternImage [51], our results (row 6 in Tab. 1) are notably superior with an impressive score of 0.702 Success and 0.252 SPL.", + "bbox": [ + 496, + 625, + 895, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 830, + 653, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Instance Classification. Our instance classification method falls into two categories. One is to fine-tune the pretrained SwinTransformer [32] on the goal images of the HM3D-", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16334", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/de8b1d97ed7cdd7c4a8a2bf232de5fe87f36d9f9e6e1bc853816fad7e3128a2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 133, + 210, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/532167c380b4371d8d3e6dbcc1df7ca9691b059fa2831d8d88c5a24d9aa4b321.jpg", + "image_caption": [ + "T=1" + ], + "image_footnote": [], + "bbox": [ + 228, + 97, + 343, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/751d8d754291ac44a92d61bd55ef172c1e706ace7b9361f70d932d64aff02649.jpg", + "image_caption": [ + "T=5" + ], + "image_footnote": [], + "bbox": [ + 359, + 98, + 473, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44b2ae5e72c294425b50718eff5a2fb767b6d293c5b8e6e6cb9d4d3700b5149b.jpg", + "image_caption": [ + "T=12" + ], + "image_footnote": [], + "bbox": [ + 491, + 98, + 606, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61fbb2d9c7ad03fd3814e23d588a2cf8e545b3d711abc51bd46afbe9c103650c.jpg", + "image_caption": [ + "T=70" + ], + "image_footnote": [], + "bbox": [ + 622, + 98, + 738, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cb68f28e29704657fc41932fd25dcbb5603a232936f758b2d3131ae69f5244fd.jpg", + "image_caption": [ + "T=95" + ], + "image_footnote": [], + "bbox": [ + 753, + 98, + 869, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f6f24d1a06447b243f709e5e71deccff7b92f54f71cb339d2e552f0a09756e9f.jpg", + "image_caption": [ + "Figure 5. Qualitative example of our IVE agent performing the Instance ImageGoal Navigation task in the Habitat simulator. Agent is initialized at $T = 1$ , and finds a potential target at $T = 5$ . After carefully evaluating the potential target from $T = 5$ to $T = 12$ , the agent proceeds with its exploration. Finally, agents identify the goal bed instance at $T = 95$ .", + "Figure 6. Instance Re-Identification Dataset. Based on the object depicted in the goal image, we sample positive and negative samples with varying Euclidean distance which represents the difficulty level of instance re-identification. For each difficulty level, the left side shows the ground truth segmentation results and the right side shows the RGB images." + ], + "image_footnote": [], + "bbox": [ + 86, + 366, + 467, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SEM training set. The other method is to obtain the semantic category of the most central segmentation result of the goal image using the segmentation model. Ablation experiments conducted on these two methods demonstrate that SwinTrans is helpful for Mask RCNN (row 6 vs. row 1 in Tab. 2), but it actually suppresses the performance of InternImage (row 10 vs. row 5 in Tab. 2). We believe this is because the InternImage segmentation model has a larger parameter size, better zero-shot capabilities on this dataset, and stronger semantic labeling capabilities.", + "bbox": [ + 75, + 612, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Exploration Policy. To scrutinize the extent to which exploration policy exerts a meaningful influence on final outcomes, we separately train our framework with three different exploration policies: a random exploration policy, an RL exploration policy, and a frontier exploration policy. Each of these three policies generates an exploration goal map every ten local steps. The first random policy involves taking the semantic map as input and randomly generating a goal map. The second policy, trained through Reinforce-", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ment Learning, seeks to maximize coverage of the environment while also encouraging the velocity stop action upon encountering a correct oracle facing the goal object. The frontier exploration policy, in contrast, endeavors to delineate the boundaries of the currently explored and free regions of the map, thereby constructing a goal map that encourages exploration. The implementation details of exploration policy are discussed in the supplementary materials.", + "bbox": [ + 496, + 364, + 892, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Tab. 2, the performance of RL (row 1 and row 6 in Tab. 2) and random (row 3 and row 8 in Tab. 2) exploration policy on the SPL significantly exceeds that of Frontier exploration policy (row 2 and row 7 in Tab. 2). This disparity in performance is due to the fact that Frontier Exploration requires exploring every corner of a given environment, which is time-consuming and unnecessary in most cases. Specifically, the agent should focus on gaining a comprehensive understanding of the most salient aspects of a small room, which facilitates the identification of the target object.", + "bbox": [ + 496, + 488, + 892, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Instance Segmentation. Initially, we employ the Mask RCNN instance segmentation model on the Online Mapping module. In order to explore the influence of the visual model on the framework, we have employed the current state-of-the-art semantic segmentation approach: InternImage [51] finetuned on the COCO dataset. Furthermore, in order to ascertain the upper bound of our method, we have employed the ground truth labeled instance class and the ground truth instance segmentation to conduct comprehensive evaluations of the Success and SPL rates. This entails the use of a local policy for the purpose of goal map-to-action, where the agent is directly capable of ascertaining whether the goal object is present in the current view while exploring the environment.", + "bbox": [ + 496, + 656, + 892, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Tab. 2, we can observe that state-of-the-art semantic segmentation model InternImage (row 5 in Tab. 2)", + "bbox": [ + 498, + 869, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16335", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/daf8e31b3e4ede18a2a348225cbdcc5e2b1bc067adf1151a9d2faec670023e15.jpg", + "image_caption": [ + "Figure 7. The TP, TN, FN and FP rates vary with changes in the threshold and difficulty levels (representing the closest Euclidean distance between the agent and the potential target). Threshold represents the threshold for the number of matched keypoints that determines whether two images are considered to be the same instance. TP decays rapidly as the difficulty increases, indicating that it becomes increasingly challenging for the agent to make correct judgments at a larger distance." + ], + "image_footnote": [], + "bbox": [ + 86, + 66, + 282, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db600c397733e889ac7d0d0471b44131cfaec5336b0e27e9e00ec6c4c3c341a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 66, + 480, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea10c4b69f13b992207e912f6a18a2694b0a86e94d4993057549c5ffb68ac60c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 66, + 681, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c1900638ca7ce7987fba56c7442968424affc922cc3cb423ddd901ae28098a3d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 683, + 66, + 880, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "indeed benefits navigation, and the ground truth segmented observation (last row in Tab. 2) gives the upper bound of navigation. Specifically, more precisely segmented observation from InternImage gives higher metrics both in Success and SPL. This is due to the more precise goal localization and less wrong segmentation results.", + "bbox": [ + 75, + 301, + 470, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Switch Policy. We conduct a comparative analysis of Switch policy. We innovatively incorporate a verification policy into the decision-making process of the agent, and through ablation experiments (row 1 vs. row 4 and row 6 vs. row 9 in Tab. 2), we demonstrate its effectiveness and significance. The implementation details of the Exploration-Exploitation Policy will be presented in supplementary materials. As depicted in Tab. 2, our EVE policy (row 1, row 6 in Tab. 2) outperforms Exploration-Exploitation (EE) Policy (row 4, row 9 in Tab. 2) by a substantial margin both on Success and SPL. This suggests that the EVE policy provides the agent with greater opportunities to discern the current observation from the goal image, rather than arbitrarily assigning a false label to the current observed object in the EE policy. Depicted in Fig. 5, agent finds the potential target at $T = 5$ and employ verification policy. After carefully examining the similar object, the agent determines that the object is not the target and actively switches back to Exploration Policy.", + "bbox": [ + 75, + 395, + 470, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Instance Re-Identification. To assess our Switch module and identify optimal hyperparameters of the Goal Map Selection module $f_{\\text{switch}}$ , we have constructed a comprehensive dataset, as depicted in Fig. 6. This dataset is created based on the HM3D-SEM train/val split. Anchor images are defined as goal images that depict specific object instances, which do not share the same parameters as agent's camera.", + "bbox": [ + 75, + 685, + 468, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For each anchor goal image, we sample 10 positive and negative images using the agent's camera. Positive images are defined as observations where the target instance is visible to the oracle, while negative images are randomly sampled from the same scene and do not contain the specified goal instance. We have divided the dataset into three distinct difficulty levels: easy, medium, hard, as shown in Fig. 6.", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different difficulty levels represent different Euclidean distances from the target to current viewpoint. The further implementation details will be discussed in the supplementary materials. To demonstrate the capabilities of our Switch module, we employ the train split to determine hyperparameters and subsequently evaluate performance on the val split. Notably, the train and val splits are two distinct sets, which ensure that the agent has never encountered any scene or object instance present in the train split.", + "bbox": [ + 496, + 301, + 893, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As depicted in Fig. 7, it is evident that with a fixed threshold of 60, the TP values for the difficulty level decrease significantly. It becomes more evident in the hard level with a threshold of 100 that yields TP rate close to 0. This highlights the importance of careful examination and decision-making based on the utilization of local matching feature algorithms to differentiate between similar objects. By meticulously examining the possible object instance, the agent is able to confidently arrive at a decision. We believe this explains why our model significantly surpasses previous state-of-the-art research in terms of Success.", + "bbox": [ + 496, + 439, + 893, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 625, + 619, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose an innovative framework of Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation. We rethink previous work that decouple the decision-making process into an Exploration-Exploitation paradigm. By considering human behavior in the \"approach-verify\" phase of identifying potential targets, we propose a new decision-making paradigm: Exploration-Verification-Exploitation. Our experimental results demonstrate that the Exploration-Verification-Exploitation paradigm effectively aids agents in their planning and decision-making process. Our proposed model significantly outperforms existing methods on the Instance ImageGoal Navigation task (0.684 vs. 0.561 Success) with a lightweight instance segmentation model. In the future, we will focus on enhancing the context of visual reasoning for more efficient exploration, and extend the application of the three-stage planning and decision-making paradigm to a broader range of tasks of embodied vision.", + "bbox": [ + 496, + 648, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16336", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 174, + 107 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ziad Al-Halah, Santhosh Kumar Ramakrishnan, and Kristen Grauman. Zero experience required: Plug & play modular transfer learning for semantic visual navigation. 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In Proceedings of the IEEE international conference on robotics and automation (ICRA), pages 3357–3364, 2017. 2" + ], + "bbox": [ + 501, + 92, + 890, + 455 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16339", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation/22b62f8c-49cb-4dc8-b958-1da0c2cefd6e_model.json b/2024/Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation/22b62f8c-49cb-4dc8-b958-1da0c2cefd6e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7f5757f7c23e1137aec8bdc24d5b9d82d1a954ad --- /dev/null +++ b/2024/Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation/22b62f8c-49cb-4dc8-b958-1da0c2cefd6e_model.json @@ -0,0 +1,2268 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.217, + 0.131, + 0.756, + 0.177 + ], + "angle": 0, + "content": "Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation" + }, + { + "type": "text", + "bbox": [ + 0.196, + 0.203, + 0.804, + 0.223 + ], + "angle": 0, + "content": "Xiaohan Lei1 Min Wang2 Wengang Zhou1,2 Li Li1 Houqiang Li1,2" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.223, + 0.92, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\)MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China" + }, + { + "type": "text", + "bbox": [ + 0.234, + 0.24, + 0.774, + 0.256 + ], + "angle": 0, + "content": "\\(^{2}\\)Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.26, + 0.842, + 0.275 + ], + "angle": 0, + "content": "leixh@mail.ustc.edu.cn, wangmin@iai.ustc.edu.cn, {zhwg,lill,lihq}@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.341, + 0.474, + 0.689 + ], + "angle": 0, + "content": "As a new embodied vision task, Instance ImageGoal Navigation (IIN) aims to navigate to a specified object depicted by a goal image in an unexplored environment. The main challenge of this task lies in identifying the target object from different viewpoints while rejecting similar distractors. Existing ImageGoal Navigation methods usually adopt the simple Exploration-Exploitation framework and ignore the identification of specific instance during navigation. In this work, we propose to imitate the human behaviour of \"getting closer to confirm\" when distinguishing objects from a distance. Specifically, we design a new modular navigation framework named Instance-aware Exploration-Verification-Exploitation (IEVE) for instance-level image goal navigation. Our method allows for active switching among the exploration, verification, and exploitation actions, thereby facilitating the agent in making reasonable decisions under different situations. On the challenging HabitatMatterport 3D semantic (HM3DSEM) dataset, our method surpasses previous state-of-the-art work, with a classical segmentation model (0.684 vs. 0.561 success) or a robust model (0.702 vs. 0.561 success). Our code will be made publicly available at https://github.com/XiaohanLei/IEVE." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.704, + 0.21, + 0.719 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Embodied navigation is an emerging computer vision task, where an agent utilizes visual sensing to actively interact with its surroundings and execute navigation tasks [2, 4]. Over the past decade, substantial advancements have been witnessed in the field of embodied visual navigation, driven by the emergence of large-scale photorealistic 3D scene" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.828, + 0.47, + 0.902 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China under Contract 62102128 and 62021001, and in part by the Fundamental Research Funds for the Central Universities under contract WK3490000007. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution of USTC. Corresponding authors: Min Wang and Wengang Zhou." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.312, + 0.882, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.568, + 0.599, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.568, + 0.69, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.568, + 0.782, + 0.666 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.577, + 0.88, + 0.661 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.759 + ], + "angle": 0, + "content": "Figure 1. Instance ImageGoal Navigation tasks an agent with navigating to a particular object instance described by the goal image. The agent is initially in an unexplored environment at \\( t_1 \\). While exploring the environment, it encounters a \"bed\" similar to the target at \\( t_2 \\) and discerns their differences. Eventually, at \\( t_3 \\), agent finds the \"bed\" described in the goal image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.809 + ], + "angle": 0, + "content": "datasets [6, 41, 48, 53, 57], the implementation of advanced simulators [24, 46, 49, 53], the development of deep learning algorithms [5, 19, 38, 47], and so on." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The ability for an agent to navigate its environment and accomplish tasks without human intervention is essential for the advancement of embodied visual navigation. One common setting for tasking an agent is to give it natural language instructions, such as \"check if my laptop is on the chair.\" However, this setting becomes confusing when" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16329" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.226 + ], + "angle": 0, + "content": "there are multiple chairs in the house. To overcome this challenge, Krantz et al. [26] propose the Instance Image-Goal Navigation task (IIN), which involves providing the agent with an image captured from goal camera that depicts a specific instance. The agent is then required to navigate to the location of the instance depicted in the image, as shown in Fig. 1. By utilizing the visual information, the agent is expected to avoid confusion caused by multiple similar distractors of the same class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.227, + 0.471, + 0.56 + ], + "angle": 0, + "content": "The most relevant task with IIN is ImageGoal Navigation [1, 9, 17, 33, 35, 56, 63], which has been a popular topic in embodied visual navigation research. The difference between IIN and ImageGoal Navigation lies in their requirements for navigation success. In other words, IIN demands that the agent has the ability to recognize the same object from different viewpoints, while ImageGoal Navigation requires maximizing the similarity between the agent's observations and the goal image. Previous ImageGoal navigation requires targeting random goal images captured by cameras that share the same parameters like height, look-at-angle, and field-of-view as the agent camera. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation. They typically expect the agent to accurately determine whether the current observation matches the goal image. However, it is extremely challenging to enable the agent to correctly identify the target object from a considerable distance. In addition, they treat the decision-making process as a one-shot task, perceiving it as a match between the current observation and the target, while overlooking the judgment process across the temporal dimension." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.47, + 0.817 + ], + "angle": 0, + "content": "To address the above limitations, we propose a novel IIN framework, i.e., Instance-aware Exploration-Verification-Exploitation (IEVE), for Instance ImageGoal Navigation. Inspired by the human behavior of \"getting closer to confirm\" when recognizing distant objects, we formulate the task of determining whether an object matches the one in the goal image as a sequential decision problem. In addition, we design a novel matching function that relies not only on the current observation and goal image but also on the Euclidean distance between the agent and the potential target. We categorize the targets into confirmed target, potential target, and no-target (exploration), and allow the agent to actively choose among these three targets. After an efficient training process of our framework, our result on the IIN task outperforms previous state-of-the-art methods, achieving 0.684 Success with a classical instance segmentation model [18], and 0.702 with a robust model [51]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.831, + 0.22, + 0.845 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In recent years, there has been great research interest in the field of embodied vision and active agents. Embodied agents are required to effectively and creatively resolve" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "complex tasks and interact with the physical environment. Notably, the navigation task plays a pivotal role in embodied vision. Numerous researchers have devoted their efforts to exploring different forms of navigation problems, encompassing various task goals and input formats. Specifically, there are five main categories of visual navigation problems: Point Goal Navigation [2, 8, 45], Object Goal Navigation [4, 14, 15, 45, 61], Visual Language Navigation [3, 16, 20-22, 25, 27, 30, 30, 59], ImageGoal Navigation [1, 9, 17, 29, 33, 35, 56, 63], and Instance ImageGoal Navigation [28]. According to the learning framework design, existing visual navigation methods are typically divided into two categories: modular and end-to-end approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.893, + 0.502 + ], + "angle": 0, + "content": "End-to-end navigation policies are commonly optimized with improved visual representations [37, 58], auxiliary tasks [60], carefully reward-shaping [34] and data augmentation techniques [34]. Visual representations can be improved with fine-tuned segmentation model [37] and object relation graphs [12, 13, 36, 39, 62]. Prior works also learn fine-tuning visual encoder with Self-Supervised Learning (SSL) [40, 55], while some researchers employ imitation learning approaches, such as Ramrakhya et al. [43], gathering data from large-scale human annotations. Although achieving promising navigation success in simulator, end-to-end methods often suffer high computation complexity in training and generalizability, which may degrade the success of navigation in diverse environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.732 + ], + "angle": 0, + "content": "To address these challenges, modular methods have been proposed to solve navigation tasks with separate modules, including perception, mapping, path planning, etc. Chaplot et al. [7] address the Object Goal Navigation problem using semantic mapping and exploration. Majumdar et al. [33] adopt the zero-shot learning and inference approach with the use of CLIP. Rmakrishnan et al. [42] propose a potential field function to tackle the exploration problem in Object Goal Navigation. Mezghan et al. [35] and Savinov et al. [44] construct augmented memory mechanisms in ImageGoal Navigation. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation for ImageGoal Navigation. In general, modular-based methods typically exhibit excellent scalability with lower training cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we focus on IIN task, which is a newly formulated but more real navigation task. It is relevant with the classical ImageGoal Navigation task. ImageGoal Navigation is commonly studied in a previous-unseen environment where goal images are randomly sampled sharing the same parameter with the agent's camera [63]. Many approaches study the ImageGoal Navigation task with RL to learn policies that directly map observations to action [1, 10, 55, 56]. Yadav et al. [55] postulate that SSL for visual representation greatly contributes to the success of the end-to-end navigation policy training. Choi et al. [10] attribute the success" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16330" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.093, + 0.849, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.892, + 0.366 + ], + "angle": 0, + "content": "Figure 2. Framework Overview. Our model consists of five main components. Instance Classification \\( f_{class} \\) predicts the object's class in goal image \\( n \\). Online Mapping \\( f_{SLAM} \\) uses RGB-D and sensor pose reading \\( \\mathcal{P}(t) \\) to construct a semantic map \\( \\mathcal{M}(t) \\) of the environment. The Switch Policy \\( \\pi_S \\) and Goal Mapping Policy \\( \\pi_{GM} \\) are interconnected. The Switch Policy \\( \\pi_S \\) determines the output of the Goal Mapping Policy's goal map \\( \\mathcal{M}_g(t) \\) based on its input judgments (whether a potential target exists and whether the potential target is confirmed). Once the goal map \\( \\mathcal{M}_g(t) \\) is determined, the Local Policy \\( \\pi_l \\) is used to determine the action \\( a(t) \\) taken by the agent at the current timestep." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.456 + ], + "angle": 0, + "content": "of RL training to the carefully reward shaping. Chaplot et al. [9] propose a topological mapping system to address the ImageGoal navigation problem, as well as Kim et al. [23]. Kwon et al. [29] propose a novel type of map for ImageGoal Navigation, a renderable neural radiance map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.718 + ], + "angle": 0, + "content": "Unlike ImageGoal Navigation, IIN [26] focuses on distinguishing different similar instances and being able to identify the object in the goal image at different viewpoints. On the other hand, ImageGoal Navigation pays more attention to maximizing the similarity between observations and the goal image within an episode. To be more specific, the goal camera in IIN task is disentangled from the agent's camera on the sampled parameters such as height, look-at-angle, and field-of-view reflect the realistic use case of a user-supplied goal image. Additionally, previous state-of-the-art work employs the confidence score for object re-identification. Differently, we propose a new switchable strategy to meticulously examine a currently visible object. Our key insight lies in treating the subtask of target confirmation as a sequential decision problem and designing a new matching function, which enables the agent to more accurately distinguish target objects from misleading ones." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.749, + 0.168, + 0.765 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.468, + 0.9 + ], + "angle": 0, + "content": "We devise a new framework, Instance-aware Exploration-Verification-Exploitation (IEVE) for Instance ImageGoal Navigation, which consists of five key modules, including Instance Classification, Online Mapping, Switch Policy, Goal Mapping Policy and Local Policy, as depicted in Fig. 2. In the following subsections, we will first introduce the preliminaries in Sec. 3.1, and sequentially elaborate the five modules of our framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.379, + 0.64, + 0.394 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.892, + 0.554 + ], + "angle": 0, + "content": "We follow the embodiment setting of Hello Robot Stretch. The agent in the simulation environment is a rigid-body, zero-turn-radius cylinder of height \\(1.41\\mathrm{m}\\) and radius \\(0.17\\mathrm{m}\\). The forward-facing RGB-D camera is mounted at a height of \\(1.31\\mathrm{m}\\). At each timestep \\(t\\), the agent's observation \\(\\mathcal{O}_t\\) consists of an egocentric RGB image \\(\\mathcal{I}_t\\), depth image \\(\\mathcal{D}(t)\\), goal image \\(\\mathcal{I}_g\\) and sensor pose reading \\(\\mathcal{P}(t)\\). Camera parameters of \\(\\mathcal{I}_t\\) and \\(\\mathcal{I}_g\\) like height, look-at-angle and field-of-view are not the same. Specifically, \\(\\mathcal{I}_t\\) is a \\(640\\times 480\\) image while \\(\\mathcal{I}_g\\) is a \\(512\\times 512\\) image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.56, + 0.708, + 0.575 + ], + "angle": 0, + "content": "3.2. Instance Classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.795 + ], + "angle": 0, + "content": "At the onset of each episode, the Instance Classification model will first process \\(\\mathcal{I}_g\\) and output an object class label \\(n\\). We adopt two different types of models to achieve instance classification, including 1) classification model: we use the goal images on the train split of HM3D-SEM [57] to finetune the image classification model, i.e., Swin Transformer [32], pretrained on ImageNet [11]. It may face the inherent semantic ambiguity of Ground Truth labels in the HM3D-SEM, such as the difficulties in distinguishing between the class \"sofa\" and \"chair\". 2) instance segmentation model: we use the semantic label of the most central segmented instance in the goal image as the classification result. This approach can maintain semantic consistency without being affected by Ground Truth labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.663, + 0.818 + ], + "angle": 0, + "content": "3.3. Online Mapping" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.903 + ], + "angle": 0, + "content": "At each time step \\(t\\), the agent will utilize the egocentric view to construct the current semantic map \\(\\hat{m}(t)\\) within its local coordinate system. The RGB frame \\(\\mathcal{I}(t)\\) is first processed through instance segmentation (Mask RCNN [18]), yielding the output \\(\\mathcal{I}_{seg}(t)\\) with dimensions of \\((B, N +\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16331" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.094, + 0.837, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.895, + 0.356 + ], + "angle": 0, + "content": "Figure 3. Switch Policy and Goal Mapping Policy. The Goal Map Selection module \\( f_{\\text{switch}} \\) receives two inputs: the shortest Euclidean distance between the agent and the potential target (or non-existence), and the number of matched keypoints. These inputs are mapped to a selection signal using Goal Map Selection function \\( f_{\\text{switch}} \\). At each timestep, the Switch Policy \\( \\pi_S \\) will choose one and only one of the three parallel modules of Goal Mapping Policy \\( \\pi_{GM} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.473, + 0.491 + ], + "angle": 0, + "content": "3, \\(H,W\\)), denoting batch size, the number of classes \\(N\\) plus RGB channels of \\(\\mathcal{I}(t)\\), frame height, and frame width. Simultaneously, the depth image \\(\\mathcal{D}(t)\\) is transformed into a pointcloud \\(P_{c}(t)\\) using the camera's intrinsic matrix \\(\\pmb{T}_{int}\\), followed by the voxelization of the pointcloud. Subsequently, the feature points of \\(\\mathcal{I}_{seg}(t)\\) are scattered into the voxels, resulting in the overall local map construction process being formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.499, + 0.47, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\hat {m} (t) = \\operatorname {S c a t t e r} (\\operatorname {V o x e l} \\left(\\boldsymbol {T} _ {\\text {i n t}} \\mathcal {D} (t)\\right), \\mathcal {I} _ {\\text {s e g}} (t)). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.586 + ], + "angle": 0, + "content": "With the constructed semantic map \\(\\hat{m}(t)\\) within local coordinate system, agent will subsequently conduct max pooling with the previous global semantic map to obtain the global semantic map \\(\\mathcal{M}(t)\\) at timestep \\(t\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.593, + 0.47, + 0.611 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} (t) = \\operatorname {M a x P o o l i n g} (\\mathcal {M} (t - 1), T _ {l g} \\hat {m} (t)), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.725 + ], + "angle": 0, + "content": "where \\( T_{lg} \\) denotes the transformation matrix from the agent's local frame to the world's global coordinate system. The size of \\( \\mathcal{M}(t) \\) is specified as \\( (B, 2 + N, H_m, W_m) \\), where the first channel represents the explored area of the entire environment, the second channel defines the nontraversable area, and the last \\( N \\) channels signify the location of each object class." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.732, + 0.218, + 0.749 + ], + "angle": 0, + "content": "3.4. Switch Policy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.877 + ], + "angle": 0, + "content": "At each time step \\( t \\), Switch Policy actively selects the functional goal map from the three parallel sub-modules in Goal Mapping Policy. We summarize the switch process as a function with segmented depth image \\( \\mathcal{I}_{seg}(t,n) \\cdot \\mathcal{D}(t) \\), the number of matched keypoints \\( \\omega \\) using local feature matching algorithm and the minimum Euclidean distance \\( d \\) between the current position of the agent and the potential target (if exists). This can be described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.885, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\nS = f _ {s w i t c h} \\left(\\mathcal {I} _ {s e g} (t, n) \\cdot \\mathcal {D} (t), \\omega , d\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.459 + ], + "angle": 0, + "content": "where \\( S \\) indicates which goal mapping policy to be selected, depicted in Fig. 3. To obtain the specific expression of \\( f_{\\text{switch}} \\), we construct an Instance Re-Identification dataset as depicted in Fig. 6 to illuminate the influence of distance \\( d \\) and the number of matched keypoints \\( w \\) on the goal object's re-identification." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.893, + 0.643 + ], + "angle": 0, + "content": "The Goal Map Selection function \\( f_{\\text{switch}} \\) aligns with human experience in object verification. \\( f_{\\text{switch}} \\) sets objects of the same category as potential targets. At a larger distance to make accurate decisions, a higher threshold on number of matched keypoints is set to convert a potential target into a determined target as depicted in Fig. 4. As the distance decreases, the upper threshold also degrades continuously. At closer distance, the agent's judgment of the object becomes more reliable, so when the number of matched keypoints falls below the lower threshold, it can be very reliably determined that the potential target is not the goal target, thereby switching to the Exploration Policy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.81 + ], + "angle": 0, + "content": "Local Feature Matching. We employ a keypoint-based re-identification method to help in the selection of goal mapping policy in Eq. (3). Conditioned on the goal image \\(\\mathcal{I}_g\\) and egocentric image \\(\\mathcal{I}(t)\\), we extract the pixel-wise \\((x,y)\\) coordinates of the keypoints \\(K_{t}\\in \\mathbb{R}^{n\\times 2}\\) and their associated feature descriptors \\(V_{t}\\in \\mathbb{R}^{n\\times 256}\\). These features are extracted utilizing DISK [50], an end-to-end local feature learning algorithm that utilizes policy gradient. Likewise, the same process is repeated with the goal image, resulting in \\(K_{g}\\in \\mathbb{R}^{m\\times 2}\\) and \\(V_{g}\\in \\mathbb{R}^{m\\times 256}\\). The feature extraction processes are formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.823, + 0.892, + 0.842 + ], + "angle": 0, + "content": "\\[\n\\left(K _ {t}, V _ {t}\\right) = \\operatorname {D I S K} (\\mathcal {I} (t)), \\quad \\left(K _ {g}, V _ {g}\\right) = \\operatorname {D I S K} (\\mathcal {I} _ {g}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.854, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Subsequently, the matched pairs \\((\\hat{K}_t,\\hat{K}_g)\\in \\mathbb{R}^{\\omega \\times 2}\\) are computed using LightGlue [31], a deep neural network that matches sparse local features across image pairs. The fea" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16332" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.393, + 0.107 + ], + "angle": 0, + "content": "ture matching process is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.117, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\left(\\hat {K} _ {t}, \\hat {K} _ {g}\\right) = \\operatorname {L i g h t G l u e} \\left(\\left(K _ {t}, V _ {t}\\right), \\left(K _ {g}, V _ {g}\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.147, + 0.47, + 0.193 + ], + "angle": 0, + "content": "Subsequently, the number of matched points \\(\\omega\\) is utilized as an adaptive threshold for the verification and exploitation goal selection." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.201, + 0.276, + 0.218 + ], + "angle": 0, + "content": "3.5. Goal Mapping Policy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.224, + 0.471, + 0.39 + ], + "angle": 0, + "content": "Depicted in Fig. 3, Goal Mapping Policy module is divided into three parallel sub-modules, which will function at different timesteps. In other words, at each timestep, only one sub-module will function. More specifically, given the predicted goal object's class \\( n \\) and segmented vision \\( \\mathcal{I}_{seg}(t) \\), if the mask \\( \\mathcal{I}_{seg}(t,n) \\) has any value greater than zero, then the Exploitation or Verification Policy is activated. They project the masked depth image \\( \\mathcal{I}_{seg}(t,n)\\cdot \\mathcal{D}(t) \\) to current semantic map. Similar to previous Online Mapping module, the two goal mapping policies in local coordinate system can be summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.402, + 0.469, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\hat {m} _ {g} (t) = \\operatorname {V o x e l} \\left(\\boldsymbol {T} _ {\\text {i n t}} \\mathcal {I} _ {\\text {s e g}} (t, n) \\cdot \\mathcal {D} (t)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.581 + ], + "angle": 0, + "content": "where \\(\\hat{m}_g(t)\\) indicates the goal map in the local coordinate system. Then we transform \\(\\hat{m}_g(t)\\) into the global coordinate system, \\(\\mathcal{M}_g(t) = T_{lg}\\hat{m}_g(t)\\). Although with the same goal map formulas, Exploitation and Verification policy represent the targets with different confidence. Specifically, Exploitation policy refers to the confirmed target, which will be kept and used for the rest navigation process. In contrast, Verification policy represents potential target, which will be further checked by local feature matching in the Switch policy module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.689 + ], + "angle": 0, + "content": "The Exploration Policy use a convolutional neural network to predict a waypoint \\( g_{rl}(t) = \\pi_{rl}(\\mathcal{M}(t)|\\theta_{rl}) \\), where \\( \\theta_{rl} \\) are parameters of Exploration Policy. We train it with RL to maximize coverage of the environment while also successfully employing the stop action upon encountering a correct oracle facing the goal object. The goal map \\( \\mathcal{M}_g(t) \\) is constructed with the value at position \\( g_{rl}(t) \\) set as 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.208, + 0.713 + ], + "angle": 0, + "content": "3.6. Local Policy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "When Switch Policy selects one of three goal mapping policies, agent adopts Local Policy to infer next action in accordance with the semantic map \\(\\mathcal{M}(t)\\), and the goal map, \\(\\mathcal{M}_g(t)\\). Specifically, Fast Matching Method (FMM) is employed to generate a distance field, which establishes the shortest distance between a traversible point and the selected goal map. A subset of the distance field is chosen within the agent's feasible range, and a waypoint is selected, ensuring that it does not intersect with existing obstacles and maintains the local minimum within the subset. With the selected waypoint, the agent can readily calculate an action based on the angle and distance from its current state." + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.091, + 0.848, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.279, + 0.892, + 0.321 + ], + "angle": 0, + "content": "Figure 4. Goal Map Selection function \\( f_{switch} \\) with respect to the Euclidean distance from agent to the potential target and the number of matched keypoints. Best viewed in color." + }, + { + "type": "table", + "bbox": [ + 0.553, + 0.327, + 0.842, + 0.453 + ], + "angle": 0, + "content": "
ModelValidation
Success ↑SPL ↑
RL Baseline [26]0.0830.035
OVRL-v2 ImageNav [55]0.0060.002
OVRL-v2 IIN [55]*0.2480.118
Mod-IIN [28]0.5610.233
IEVE Mask RCNN (ours)0.6840.241
IEVE InternImage (ours)0.7020.252
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.463, + 0.892, + 0.561 + ], + "angle": 0, + "content": "Table 1. Comparison between our IEVE and prior methods on IIN task. “*” means we finetune OVRL-v2 [55] on the IIN task. IEVE outperforms the baseline model (row 1) with up to \\(8.75\\mathrm{x}\\) increase in Success and outperforms a state-of-the-art model [28] (Mod-IIN, row 4) from 0.561 to 0.684 with a lightweight segmentation model (Mask RCNN) on Success, and higher Success of 0.702 with a strong backbone (InternImage [51])." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.574, + 0.892, + 0.666 + ], + "angle": 0, + "content": "We also add a visited trajectory mechanism for the agent to avoid been stuck by invisible obstacles, which will be discussed in the supplementary materials. In our framework, only Instance Classification and Exploration Policy require few training, underscoring the computation efficiency of our design." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.625, + 0.696 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.704, + 0.676, + 0.72 + ], + "angle": 0, + "content": "4.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.727, + 0.892, + 0.878 + ], + "angle": 0, + "content": "Dataset. For our experiment, we employ the Habitat [49] simulator to conduct our experiments. The definition of the Instance ImageGoal Navigation [26] task utilized in the Habitat Navigation Challenge \\(2023^{1}\\) serves as our primary reference point. The episode dataset proposed by Krantz et al. [28] for Instance ImageGoal Navigation serves as our key data source. The scene dataset utilized in this study stems from the Habitat-Matterport3D with semantic annotations (HM3D-SEM) [54], which encompasses a total of 216 scenes. These scenes are split into three distinct sub" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.818, + 0.9 + ], + "angle": 0, + "content": "1https://aihabitat.org/challenge/2023/" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16333" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "sets for training, validation, and testing purposes, consisting of 145/36/35 scenes, respectively. Additionally, the episode dataset has been partitioned into four subsets for training, validation, testing, and testing under a modified challenge regime, comprising 7,056K/1K/1K/1K episodes respectively. We train our agent on the train split and evaluate it on validation split. The object depicted by the goal image belongs to the following six categories: {chair, couch, plant, bed, toilet, television}. On the validation subset, a total of 795 unique object instances have been observed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.365 + ], + "angle": 0, + "content": "Action Space. Adhering to the task setting of the Habitat Navigation Challenge 2023, we employ the continuous action space. The action space encompasses four actions: linear velocity, angular velocity, camera pitch velocity, velocity stop, each of which accepts values ranging between \\(-1\\) and \\(1\\) and is appropriately scaled according to the respective configurations. Our linear speed is capped at a maximum of \\(35cm/frame\\) and angular velocity at \\(60^{\\circ}/frame\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Metrics. We evaluate our model with both success and efficiency. We report Success Rate (Success), Success rate weighted by normalized inverse Path Length (SPL). Success is True if the agent calls velocity stop action within \\(1.0m\\) Euclidean distance of the goal object and the object is oracle-visible by turning or looking up and down. SPL is an efficiency measure defined in [2]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.442, + 0.499 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.506, + 0.47, + 0.537 + ], + "angle": 0, + "content": "We undertake a comprehensive evaluation of our proposed model against various baselines and the SOTA work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.718 + ], + "angle": 0, + "content": "End-to-End RL Agent. The baseline model for the IIN task is trained in a fully-fledged end-to-end fashion. This involves inputting both an egocentric rgb and depth image as well as a pose into the model, which is then processed by a visual encoder and a recurrent neural network. The network output directly determines the agent's action. The agent is trained from scratch utilizing Proximal Policy Optimization (PPO) [47]. Our method exhibits 8.24x higher Success in Val (row 5 vs. row 1 in Tab. 1). Although it takes a staggering 3.5 billion steps for RL agent model to achieve convergence, the generalization capability of the agent remains unsatisfactory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.473, + 0.886 + ], + "angle": 0, + "content": "OVRL-v2. Offline Visual Representation Learning v2 (OVRL-v2 [55]) was proposed by Karmesh et al., who introduced a novel model-free, end-to-end navigation policy that emphasizes the significance of self-supervised pretraining of visual encoders and introduces the concept of Compression Layer (CL). Employing a ViT + LSTM backbone, this policy exhibits state-of-the-art performance in ImageGoal Navigation and approaches the state-of-the-art in ObjectGoal Navigation. Due to the task disparity between ImageGoal Navigation and Instance ImageGoal Navigation, we fine-tune the pretrained policy for our specific task." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The original OVRL-v2 is trained under the setting of the" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.892, + 0.272 + ], + "angle": 0, + "content": "
Model VariationValidation
ClassificationPerceptionSwitchExplorationSuccess ↑SPL ↑
Mask RCNNMask RCNNEVERL0.6660.235
Mask RCNNMask RCNNEVEFrontier0.6760.182
Mask RCNNMask RCNNEVERandom0.6540.233
Mask RCNNMask RCNNEERL0.5900.221
InternImageInternImageEVERL0.7020.252
SwinTransMask RCNNEVERL0.6840.241
SwinTransMask RCNNEVEFrontier0.6280.180
SwinTransMask RCNNEVERandom0.6360.236
SwinTransMask RCNNEERL0.6200.216
SwinTransInternImageEVERL0.6760.238
GroundTruthMask RCNNEVERL0.6820.238
GroundTruthOracle-RL0.8500.399
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.276, + 0.895, + 0.416 + ], + "angle": 0, + "content": "Table 2. Variants of our method with different settings of instance classification, perception, switch policy and exploration policy. Perception means the Instance Segmentation model variations in Online Mapping module. \"EE\" refers to the exploration-exploitation policy, which establishes a fixed threshold for decision-making. \"EVE\" represents our Exploration-Verification-Exploitation Switch policy. The last row gives the upper bound of our method, where with ground truth instance segmented observations, the agent can identify the specified object instance as soon as the object becomes visible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.895, + 0.626 + ], + "angle": 0, + "content": "ImageGoal Navigation task. Evaluating OVRL-v2's performance without finetuning for Instance ImageGoal Navigation reveals suboptimal results (0.006 Success row 2 in Tab. 1). Several factors impact the performance: a shift in scene datasets (Gibson [53] vs. HM3D-SEM [57]), changes in embodiment (Locobot vs. Stretch), and disparity in goal destinations (image source vs. image subject). When specifically finetuned for Instance ImageGoal Navigation (row 3 in Tab. 1) on HM3D-SEM, OVRL-v2 yields improved performance rates at 0.248 Success. Our approach with Mask RCNN exhibits 0.436 higher Success in Val (row 5 vs. row 3 in Tab. 1), and 0.454 higher Success with InternImage (row 6 vs. row 3 in Tab. 1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.896, + 0.822 + ], + "angle": 0, + "content": "Mod-IIN. Mod-IIN [28] decomposes Instance ImageGoal Navigation task into exploration, goal re-identification, goal localization and local navigation. It outperforms previous state-of-the-art end-to-end learned policies without fine-tuning. Mod-IIN achieves 0.561 Success and 0.233 SPL (row 4 in Tab. 1), and we surpass their results in Success with a substantial margin of 0.123 by attaining 0.684 Success and a marginal improvement in SPL with the help of a classical visual backbone trained with Mask RCNN [18] (row 5 in Tab. 1). Additionally, with the current state-of-the-art Semantic Segmentation model InternImage [51], our results (row 6 in Tab. 1) are notably superior with an impressive score of 0.702 Success and 0.252 SPL." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.655, + 0.849 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Instance Classification. Our instance classification method falls into two categories. One is to fine-tune the pretrained SwinTransformer [32] on the goal images of the HM3D-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16334" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.135, + 0.212, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.229, + 0.098, + 0.344, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.279, + 0.296, + 0.287 + ], + "angle": 0, + "content": "T=1" + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.099, + 0.475, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.408, + 0.279, + 0.427, + 0.287 + ], + "angle": 0, + "content": "T=5" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.099, + 0.607, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.279, + 0.561, + 0.287 + ], + "angle": 0, + "content": "T=12" + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.099, + 0.739, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.279, + 0.692, + 0.287 + ], + "angle": 0, + "content": "T=70" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.099, + 0.87, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.279, + 0.824, + 0.287 + ], + "angle": 0, + "content": "T=95" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.309, + 0.894, + 0.352 + ], + "angle": 0, + "content": "Figure 5. Qualitative example of our IVE agent performing the Instance ImageGoal Navigation task in the Habitat simulator. Agent is initialized at \\( T = 1 \\), and finds a potential target at \\( T = 5 \\). After carefully evaluating the potential target from \\( T = 5 \\) to \\( T = 12 \\), the agent proceeds with its exploration. Finally, agents identify the goal bed instance at \\( T = 95 \\)." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.367, + 0.468, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.521, + 0.471, + 0.605 + ], + "angle": 0, + "content": "Figure 6. Instance Re-Identification Dataset. Based on the object depicted in the goal image, we sample positive and negative samples with varying Euclidean distance which represents the difficulty level of instance re-identification. For each difficulty level, the left side shows the ground truth segmentation results and the right side shows the RGB images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.764 + ], + "angle": 0, + "content": "SEM training set. The other method is to obtain the semantic category of the most central segmentation result of the goal image using the segmentation model. Ablation experiments conducted on these two methods demonstrate that SwinTrans is helpful for Mask RCNN (row 6 vs. row 1 in Tab. 2), but it actually suppresses the performance of InternImage (row 10 vs. row 5 in Tab. 2). We believe this is because the InternImage segmentation model has a larger parameter size, better zero-shot capabilities on this dataset, and stronger semantic labeling capabilities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Exploration Policy. To scrutinize the extent to which exploration policy exerts a meaningful influence on final outcomes, we separately train our framework with three different exploration policies: a random exploration policy, an RL exploration policy, and a frontier exploration policy. Each of these three policies generates an exploration goal map every ten local steps. The first random policy involves taking the semantic map as input and randomly generating a goal map. The second policy, trained through Reinforce-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.893, + 0.487 + ], + "angle": 0, + "content": "ment Learning, seeks to maximize coverage of the environment while also encouraging the velocity stop action upon encountering a correct oracle facing the goal object. The frontier exploration policy, in contrast, endeavors to delineate the boundaries of the currently explored and free regions of the map, thereby constructing a goal map that encourages exploration. The implementation details of exploration policy are discussed in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.893, + 0.655 + ], + "angle": 0, + "content": "From Tab. 2, the performance of RL (row 1 and row 6 in Tab. 2) and random (row 3 and row 8 in Tab. 2) exploration policy on the SPL significantly exceeds that of Frontier exploration policy (row 2 and row 7 in Tab. 2). This disparity in performance is due to the fact that Frontier Exploration requires exploring every corner of a given environment, which is time-consuming and unnecessary in most cases. Specifically, the agent should focus on gaining a comprehensive understanding of the most salient aspects of a small room, which facilitates the identification of the target object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.893, + 0.869 + ], + "angle": 0, + "content": "Instance Segmentation. Initially, we employ the Mask RCNN instance segmentation model on the Online Mapping module. In order to explore the influence of the visual model on the framework, we have employed the current state-of-the-art semantic segmentation approach: InternImage [51] finetuned on the COCO dataset. Furthermore, in order to ascertain the upper bound of our method, we have employed the ground truth labeled instance class and the ground truth instance segmentation to conduct comprehensive evaluations of the Success and SPL rates. This entails the use of a local policy for the purpose of goal map-to-action, where the agent is directly capable of ascertaining whether the goal object is present in the current view while exploring the environment." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "From Tab. 2, we can observe that state-of-the-art semantic segmentation model InternImage (row 5 in Tab. 2)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16335" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.068, + 0.283, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.067, + 0.482, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.067, + 0.682, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.067, + 0.882, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.231, + 0.895, + 0.288 + ], + "angle": 0, + "content": "Figure 7. The TP, TN, FN and FP rates vary with changes in the threshold and difficulty levels (representing the closest Euclidean distance between the agent and the potential target). Threshold represents the threshold for the number of matched keypoints that determines whether two images are considered to be the same instance. TP decays rapidly as the difficulty increases, indicating that it becomes increasingly challenging for the agent to make correct judgments at a larger distance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.471, + 0.392 + ], + "angle": 0, + "content": "indeed benefits navigation, and the ground truth segmented observation (last row in Tab. 2) gives the upper bound of navigation. Specifically, more precisely segmented observation from InternImage gives higher metrics both in Success and SPL. This is due to the more precise goal localization and less wrong segmentation results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.471, + 0.683 + ], + "angle": 0, + "content": "Switch Policy. We conduct a comparative analysis of Switch policy. We innovatively incorporate a verification policy into the decision-making process of the agent, and through ablation experiments (row 1 vs. row 4 and row 6 vs. row 9 in Tab. 2), we demonstrate its effectiveness and significance. The implementation details of the Exploration-Exploitation Policy will be presented in supplementary materials. As depicted in Tab. 2, our EVE policy (row 1, row 6 in Tab. 2) outperforms Exploration-Exploitation (EE) Policy (row 4, row 9 in Tab. 2) by a substantial margin both on Success and SPL. This suggests that the EVE policy provides the agent with greater opportunities to discern the current observation from the goal image, rather than arbitrarily assigning a false label to the current observed object in the EE policy. Depicted in Fig. 5, agent finds the potential target at \\( T = 5 \\) and employ verification policy. After carefully examining the similar object, the agent determines that the object is not the target and actively switches back to Exploration Policy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Instance Re-Identification. To assess our Switch module and identify optimal hyperparameters of the Goal Map Selection module \\( f_{\\text{switch}} \\), we have constructed a comprehensive dataset, as depicted in Fig. 6. This dataset is created based on the HM3D-SEM train/val split. Anchor images are defined as goal images that depict specific object instances, which do not share the same parameters as agent's camera." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "For each anchor goal image, we sample 10 positive and negative images using the agent's camera. Positive images are defined as observations where the target instance is visible to the oracle, while negative images are randomly sampled from the same scene and do not contain the specified goal instance. We have divided the dataset into three distinct difficulty levels: easy, medium, hard, as shown in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.895, + 0.438 + ], + "angle": 0, + "content": "Different difficulty levels represent different Euclidean distances from the target to current viewpoint. The further implementation details will be discussed in the supplementary materials. To demonstrate the capabilities of our Switch module, we employ the train split to determine hyperparameters and subsequently evaluate performance on the val split. Notably, the train and val splits are two distinct sets, which ensure that the agent has never encountered any scene or object instance present in the train split." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.895, + 0.606 + ], + "angle": 0, + "content": "As depicted in Fig. 7, it is evident that with a fixed threshold of 60, the TP values for the difficulty level decrease significantly. It becomes more evident in the hard level with a threshold of 100 that yields TP rate close to 0. This highlights the importance of careful examination and decision-making based on the utilization of local matching feature algorithms to differentiate between similar objects. By meticulously examining the possible object instance, the agent is able to confidently arrive at a decision. We believe this explains why our model significantly surpasses previous state-of-the-art research in terms of Success." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.62, + 0.641 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We propose an innovative framework of Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation. We rethink previous work that decouple the decision-making process into an Exploration-Exploitation paradigm. By considering human behavior in the \"approach-verify\" phase of identifying potential targets, we propose a new decision-making paradigm: Exploration-Verification-Exploitation. Our experimental results demonstrate that the Exploration-Verification-Exploitation paradigm effectively aids agents in their planning and decision-making process. Our proposed model significantly outperforms existing methods on the Instance ImageGoal Navigation task (0.684 vs. 0.561 Success) with a lightweight instance segmentation model. In the future, we will focus on enhancing the context of visual reasoning for more efficient exploration, and extend the application of the three-stage planning and decision-making paradigm to a broader range of tasks of embodied vision." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "16336" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.092, + 0.176, + 0.108 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.187 + ], + "angle": 0, + "content": "[1] Ziad Al-Halah, Santhosh Kumar Ramakrishnan, and Kristen Grauman. Zero experience required: Plug & play modular transfer learning for semantic visual navigation. 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The main challenge of this task lies in identifying the target object from different viewpoints while rejecting similar distractors. Existing ImageGoal Navigation methods usually adopt the simple Exploration-Exploitation framework and ignore the identification of specific instance during navigation. In this work, we propose to imitate the human behaviour of "getting closer to confirm" when distinguishing objects from a distance. Specifically, we design a new modular navigation framework named Instance-aware Exploration-Verification-Exploitation (IEVE) for instance-level image goal navigation. Our method allows for active switching among the exploration, verification, and exploitation actions, thereby facilitating the agent in making reasonable decisions under different situations. On the challenging HabitatMatterport 3D semantic (HM3DSEM) dataset, our method surpasses previous state-of-the-art work, with a classical segmentation model (0.684 vs. 0.561 success) or a robust model (0.702 vs. 0.561 success). Our code will be made publicly available at https://github.com/XiaohanLei/IEVE. + +# 1. Introduction + +Embodied navigation is an emerging computer vision task, where an agent utilizes visual sensing to actively interact with its surroundings and execute navigation tasks [2, 4]. Over the past decade, substantial advancements have been witnessed in the field of embodied visual navigation, driven by the emergence of large-scale photorealistic 3D scene + +This work was supported in part by the National Natural Science Foundation of China under Contract 62102128 and 62021001, and in part by the Fundamental Research Funds for the Central Universities under contract WK3490000007. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution of USTC. Corresponding authors: Min Wang and Wengang Zhou. + +![](images/bdf81e7ef1ccbe524f0b348a08bd736448b6e3ae2902ed835be614eb031ad289.jpg) + +![](images/ef5f96049ab6350e7d27596995c6245b3a7fd6f10de265339a80c3e8268835bb.jpg) +Figure 1. Instance ImageGoal Navigation tasks an agent with navigating to a particular object instance described by the goal image. The agent is initially in an unexplored environment at $t_1$ . While exploring the environment, it encounters a "bed" similar to the target at $t_2$ and discerns their differences. Eventually, at $t_3$ , agent finds the "bed" described in the goal image. + +![](images/8c305c445374725622e2ac9aada2509e258a9e5a7737eac37a162acb8fc7e933.jpg) + +![](images/30f9c2d769c9ee22dc720c3c369c4812db8d40a2f8997526144f66b0461aa3f5.jpg) + +![](images/92630ff627a7de7241dc4f539250101676c3777ee4604ebafadd396d2eae3f66.jpg) + +datasets [6, 41, 48, 53, 57], the implementation of advanced simulators [24, 46, 49, 53], the development of deep learning algorithms [5, 19, 38, 47], and so on. + +The ability for an agent to navigate its environment and accomplish tasks without human intervention is essential for the advancement of embodied visual navigation. One common setting for tasking an agent is to give it natural language instructions, such as "check if my laptop is on the chair." However, this setting becomes confusing when + +there are multiple chairs in the house. To overcome this challenge, Krantz et al. [26] propose the Instance Image-Goal Navigation task (IIN), which involves providing the agent with an image captured from goal camera that depicts a specific instance. The agent is then required to navigate to the location of the instance depicted in the image, as shown in Fig. 1. By utilizing the visual information, the agent is expected to avoid confusion caused by multiple similar distractors of the same class. + +The most relevant task with IIN is ImageGoal Navigation [1, 9, 17, 33, 35, 56, 63], which has been a popular topic in embodied visual navigation research. The difference between IIN and ImageGoal Navigation lies in their requirements for navigation success. In other words, IIN demands that the agent has the ability to recognize the same object from different viewpoints, while ImageGoal Navigation requires maximizing the similarity between the agent's observations and the goal image. Previous ImageGoal navigation requires targeting random goal images captured by cameras that share the same parameters like height, look-at-angle, and field-of-view as the agent camera. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation. They typically expect the agent to accurately determine whether the current observation matches the goal image. However, it is extremely challenging to enable the agent to correctly identify the target object from a considerable distance. In addition, they treat the decision-making process as a one-shot task, perceiving it as a match between the current observation and the target, while overlooking the judgment process across the temporal dimension. + +To address the above limitations, we propose a novel IIN framework, i.e., Instance-aware Exploration-Verification-Exploitation (IEVE), for Instance ImageGoal Navigation. Inspired by the human behavior of "getting closer to confirm" when recognizing distant objects, we formulate the task of determining whether an object matches the one in the goal image as a sequential decision problem. In addition, we design a novel matching function that relies not only on the current observation and goal image but also on the Euclidean distance between the agent and the potential target. We categorize the targets into confirmed target, potential target, and no-target (exploration), and allow the agent to actively choose among these three targets. After an efficient training process of our framework, our result on the IIN task outperforms previous state-of-the-art methods, achieving 0.684 Success with a classical instance segmentation model [18], and 0.702 with a robust model [51]. + +# 2. Related Work + +In recent years, there has been great research interest in the field of embodied vision and active agents. Embodied agents are required to effectively and creatively resolve + +complex tasks and interact with the physical environment. Notably, the navigation task plays a pivotal role in embodied vision. Numerous researchers have devoted their efforts to exploring different forms of navigation problems, encompassing various task goals and input formats. Specifically, there are five main categories of visual navigation problems: Point Goal Navigation [2, 8, 45], Object Goal Navigation [4, 14, 15, 45, 61], Visual Language Navigation [3, 16, 20-22, 25, 27, 30, 30, 59], ImageGoal Navigation [1, 9, 17, 29, 33, 35, 56, 63], and Instance ImageGoal Navigation [28]. According to the learning framework design, existing visual navigation methods are typically divided into two categories: modular and end-to-end approaches. + +End-to-end navigation policies are commonly optimized with improved visual representations [37, 58], auxiliary tasks [60], carefully reward-shaping [34] and data augmentation techniques [34]. Visual representations can be improved with fine-tuned segmentation model [37] and object relation graphs [12, 13, 36, 39, 62]. Prior works also learn fine-tuning visual encoder with Self-Supervised Learning (SSL) [40, 55], while some researchers employ imitation learning approaches, such as Ramrakhya et al. [43], gathering data from large-scale human annotations. Although achieving promising navigation success in simulator, end-to-end methods often suffer high computation complexity in training and generalizability, which may degrade the success of navigation in diverse environments. + +To address these challenges, modular methods have been proposed to solve navigation tasks with separate modules, including perception, mapping, path planning, etc. Chaplot et al. [7] address the Object Goal Navigation problem using semantic mapping and exploration. Majumdar et al. [33] adopt the zero-shot learning and inference approach with the use of CLIP. Rmakrishnan et al. [42] propose a potential field function to tackle the exploration problem in Object Goal Navigation. Mezghan et al. [35] and Savinov et al. [44] construct augmented memory mechanisms in ImageGoal Navigation. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation for ImageGoal Navigation. In general, modular-based methods typically exhibit excellent scalability with lower training cost. + +In this work, we focus on IIN task, which is a newly formulated but more real navigation task. It is relevant with the classical ImageGoal Navigation task. ImageGoal Navigation is commonly studied in a previous-unseen environment where goal images are randomly sampled sharing the same parameter with the agent's camera [63]. Many approaches study the ImageGoal Navigation task with RL to learn policies that directly map observations to action [1, 10, 55, 56]. Yadav et al. [55] postulate that SSL for visual representation greatly contributes to the success of the end-to-end navigation policy training. Choi et al. [10] attribute the success + +![](images/de581b6c3349e32279e4bf33b93762870e738a12359ea54357689746ea5c6c8c.jpg) +Figure 2. Framework Overview. Our model consists of five main components. Instance Classification $f_{class}$ predicts the object's class in goal image $n$ . Online Mapping $f_{SLAM}$ uses RGB-D and sensor pose reading $\mathcal{P}(t)$ to construct a semantic map $\mathcal{M}(t)$ of the environment. The Switch Policy $\pi_S$ and Goal Mapping Policy $\pi_{GM}$ are interconnected. The Switch Policy $\pi_S$ determines the output of the Goal Mapping Policy's goal map $\mathcal{M}_g(t)$ based on its input judgments (whether a potential target exists and whether the potential target is confirmed). Once the goal map $\mathcal{M}_g(t)$ is determined, the Local Policy $\pi_l$ is used to determine the action $a(t)$ taken by the agent at the current timestep. + +of RL training to the carefully reward shaping. Chaplot et al. [9] propose a topological mapping system to address the ImageGoal navigation problem, as well as Kim et al. [23]. Kwon et al. [29] propose a novel type of map for ImageGoal Navigation, a renderable neural radiance map. + +Unlike ImageGoal Navigation, IIN [26] focuses on distinguishing different similar instances and being able to identify the object in the goal image at different viewpoints. On the other hand, ImageGoal Navigation pays more attention to maximizing the similarity between observations and the goal image within an episode. To be more specific, the goal camera in IIN task is disentangled from the agent's camera on the sampled parameters such as height, look-at-angle, and field-of-view reflect the realistic use case of a user-supplied goal image. Additionally, previous state-of-the-art work employs the confidence score for object re-identification. Differently, we propose a new switchable strategy to meticulously examine a currently visible object. Our key insight lies in treating the subtask of target confirmation as a sequential decision problem and designing a new matching function, which enables the agent to more accurately distinguish target objects from misleading ones. + +# 3. Method + +We devise a new framework, Instance-aware Exploration-Verification-Exploitation (IEVE) for Instance ImageGoal Navigation, which consists of five key modules, including Instance Classification, Online Mapping, Switch Policy, Goal Mapping Policy and Local Policy, as depicted in Fig. 2. In the following subsections, we will first introduce the preliminaries in Sec. 3.1, and sequentially elaborate the five modules of our framework. + +# 3.1. Preliminaries + +We follow the embodiment setting of Hello Robot Stretch. The agent in the simulation environment is a rigid-body, zero-turn-radius cylinder of height $1.41\mathrm{m}$ and radius $0.17\mathrm{m}$ . The forward-facing RGB-D camera is mounted at a height of $1.31\mathrm{m}$ . At each timestep $t$ , the agent's observation $\mathcal{O}_t$ consists of an egocentric RGB image $\mathcal{I}_t$ , depth image $\mathcal{D}(t)$ , goal image $\mathcal{I}_g$ and sensor pose reading $\mathcal{P}(t)$ . Camera parameters of $\mathcal{I}_t$ and $\mathcal{I}_g$ like height, look-at-angle and field-of-view are not the same. Specifically, $\mathcal{I}_t$ is a $640\times 480$ image while $\mathcal{I}_g$ is a $512\times 512$ image. + +# 3.2. Instance Classification + +At the onset of each episode, the Instance Classification model will first process $\mathcal{I}_g$ and output an object class label $n$ . We adopt two different types of models to achieve instance classification, including 1) classification model: we use the goal images on the train split of HM3D-SEM [57] to finetune the image classification model, i.e., Swin Transformer [32], pretrained on ImageNet [11]. It may face the inherent semantic ambiguity of Ground Truth labels in the HM3D-SEM, such as the difficulties in distinguishing between the class "sofa" and "chair". 2) instance segmentation model: we use the semantic label of the most central segmented instance in the goal image as the classification result. This approach can maintain semantic consistency without being affected by Ground Truth labels. + +# 3.3. Online Mapping + +At each time step $t$ , the agent will utilize the egocentric view to construct the current semantic map $\hat{m}(t)$ within its local coordinate system. The RGB frame $\mathcal{I}(t)$ is first processed through instance segmentation (Mask RCNN [18]), yielding the output $\mathcal{I}_{seg}(t)$ with dimensions of $(B, N +$ + +![](images/edaa1a16fcc256d0832b992a92e740006de527c5563175d56096f3352955c50c.jpg) +Figure 3. Switch Policy and Goal Mapping Policy. The Goal Map Selection module $f_{\text{switch}}$ receives two inputs: the shortest Euclidean distance between the agent and the potential target (or non-existence), and the number of matched keypoints. These inputs are mapped to a selection signal using Goal Map Selection function $f_{\text{switch}}$ . At each timestep, the Switch Policy $\pi_S$ will choose one and only one of the three parallel modules of Goal Mapping Policy $\pi_{GM}$ . + +3, $H,W$ ), denoting batch size, the number of classes $N$ plus RGB channels of $\mathcal{I}(t)$ , frame height, and frame width. Simultaneously, the depth image $\mathcal{D}(t)$ is transformed into a pointcloud $P_{c}(t)$ using the camera's intrinsic matrix $\pmb{T}_{int}$ , followed by the voxelization of the pointcloud. Subsequently, the feature points of $\mathcal{I}_{seg}(t)$ are scattered into the voxels, resulting in the overall local map construction process being formulated as: + +$$ +\hat {m} (t) = \operatorname {S c a t t e r} (\operatorname {V o x e l} \left(\boldsymbol {T} _ {\text {i n t}} \mathcal {D} (t)\right), \mathcal {I} _ {\text {s e g}} (t)). \tag {1} +$$ + +With the constructed semantic map $\hat{m}(t)$ within local coordinate system, agent will subsequently conduct max pooling with the previous global semantic map to obtain the global semantic map $\mathcal{M}(t)$ at timestep $t$ as follows: + +$$ +\mathcal {M} (t) = \operatorname {M a x P o o l i n g} (\mathcal {M} (t - 1), T _ {l g} \hat {m} (t)), \tag {2} +$$ + +where $T_{lg}$ denotes the transformation matrix from the agent's local frame to the world's global coordinate system. The size of $\mathcal{M}(t)$ is specified as $(B, 2 + N, H_m, W_m)$ , where the first channel represents the explored area of the entire environment, the second channel defines the nontraversable area, and the last $N$ channels signify the location of each object class. + +# 3.4. Switch Policy + +At each time step $t$ , Switch Policy actively selects the functional goal map from the three parallel sub-modules in Goal Mapping Policy. We summarize the switch process as a function with segmented depth image $\mathcal{I}_{seg}(t,n) \cdot \mathcal{D}(t)$ , the number of matched keypoints $\omega$ using local feature matching algorithm and the minimum Euclidean distance $d$ between the current position of the agent and the potential target (if exists). This can be described as follows: + +$$ +S = f _ {s w i t c h} \left(\mathcal {I} _ {s e g} (t, n) \cdot \mathcal {D} (t), \omega , d\right), \tag {3} +$$ + +where $S$ indicates which goal mapping policy to be selected, depicted in Fig. 3. To obtain the specific expression of $f_{\text{switch}}$ , we construct an Instance Re-Identification dataset as depicted in Fig. 6 to illuminate the influence of distance $d$ and the number of matched keypoints $w$ on the goal object's re-identification. + +The Goal Map Selection function $f_{\text{switch}}$ aligns with human experience in object verification. $f_{\text{switch}}$ sets objects of the same category as potential targets. At a larger distance to make accurate decisions, a higher threshold on number of matched keypoints is set to convert a potential target into a determined target as depicted in Fig. 4. As the distance decreases, the upper threshold also degrades continuously. At closer distance, the agent's judgment of the object becomes more reliable, so when the number of matched keypoints falls below the lower threshold, it can be very reliably determined that the potential target is not the goal target, thereby switching to the Exploration Policy. + +Local Feature Matching. We employ a keypoint-based re-identification method to help in the selection of goal mapping policy in Eq. (3). Conditioned on the goal image $\mathcal{I}_g$ and egocentric image $\mathcal{I}(t)$ , we extract the pixel-wise $(x,y)$ coordinates of the keypoints $K_{t}\in \mathbb{R}^{n\times 2}$ and their associated feature descriptors $V_{t}\in \mathbb{R}^{n\times 256}$ . These features are extracted utilizing DISK [50], an end-to-end local feature learning algorithm that utilizes policy gradient. Likewise, the same process is repeated with the goal image, resulting in $K_{g}\in \mathbb{R}^{m\times 2}$ and $V_{g}\in \mathbb{R}^{m\times 256}$ . The feature extraction processes are formulated as follows: + +$$ +\left(K _ {t}, V _ {t}\right) = \operatorname {D I S K} (\mathcal {I} (t)), \quad \left(K _ {g}, V _ {g}\right) = \operatorname {D I S K} (\mathcal {I} _ {g}). \tag {4} +$$ + +Subsequently, the matched pairs $(\hat{K}_t,\hat{K}_g)\in \mathbb{R}^{\omega \times 2}$ are computed using LightGlue [31], a deep neural network that matches sparse local features across image pairs. The fea + +ture matching process is formulated as follows: + +$$ +\left(\hat {K} _ {t}, \hat {K} _ {g}\right) = \operatorname {L i g h t G l u e} \left(\left(K _ {t}, V _ {t}\right), \left(K _ {g}, V _ {g}\right)\right). \tag {5} +$$ + +Subsequently, the number of matched points $\omega$ is utilized as an adaptive threshold for the verification and exploitation goal selection. + +# 3.5. Goal Mapping Policy + +Depicted in Fig. 3, Goal Mapping Policy module is divided into three parallel sub-modules, which will function at different timesteps. In other words, at each timestep, only one sub-module will function. More specifically, given the predicted goal object's class $n$ and segmented vision $\mathcal{I}_{seg}(t)$ , if the mask $\mathcal{I}_{seg}(t,n)$ has any value greater than zero, then the Exploitation or Verification Policy is activated. They project the masked depth image $\mathcal{I}_{seg}(t,n)\cdot \mathcal{D}(t)$ to current semantic map. Similar to previous Online Mapping module, the two goal mapping policies in local coordinate system can be summarized as follows: + +$$ +\hat {m} _ {g} (t) = \operatorname {V o x e l} \left(\boldsymbol {T} _ {\text {i n t}} \mathcal {I} _ {\text {s e g}} (t, n) \cdot \mathcal {D} (t)\right), \tag {6} +$$ + +where $\hat{m}_g(t)$ indicates the goal map in the local coordinate system. Then we transform $\hat{m}_g(t)$ into the global coordinate system, $\mathcal{M}_g(t) = T_{lg}\hat{m}_g(t)$ . Although with the same goal map formulas, Exploitation and Verification policy represent the targets with different confidence. Specifically, Exploitation policy refers to the confirmed target, which will be kept and used for the rest navigation process. In contrast, Verification policy represents potential target, which will be further checked by local feature matching in the Switch policy module. + +The Exploration Policy use a convolutional neural network to predict a waypoint $g_{rl}(t) = \pi_{rl}(\mathcal{M}(t)|\theta_{rl})$ , where $\theta_{rl}$ are parameters of Exploration Policy. We train it with RL to maximize coverage of the environment while also successfully employing the stop action upon encountering a correct oracle facing the goal object. The goal map $\mathcal{M}_g(t)$ is constructed with the value at position $g_{rl}(t)$ set as 1. + +# 3.6. Local Policy + +When Switch Policy selects one of three goal mapping policies, agent adopts Local Policy to infer next action in accordance with the semantic map $\mathcal{M}(t)$ , and the goal map, $\mathcal{M}_g(t)$ . Specifically, Fast Matching Method (FMM) is employed to generate a distance field, which establishes the shortest distance between a traversible point and the selected goal map. A subset of the distance field is chosen within the agent's feasible range, and a waypoint is selected, ensuring that it does not intersect with existing obstacles and maintains the local minimum within the subset. With the selected waypoint, the agent can readily calculate an action based on the angle and distance from its current state. + +![](images/dbacca8315c95a9e2a90586dfa175bd8c9118e85739e24f41bd00510fc6468f0.jpg) +Figure 4. Goal Map Selection function $f_{switch}$ with respect to the Euclidean distance from agent to the potential target and the number of matched keypoints. Best viewed in color. + +
ModelValidation
Success ↑SPL ↑
RL Baseline [26]0.0830.035
OVRL-v2 ImageNav [55]0.0060.002
OVRL-v2 IIN [55]*0.2480.118
Mod-IIN [28]0.5610.233
IEVE Mask RCNN (ours)0.6840.241
IEVE InternImage (ours)0.7020.252
+ +Table 1. Comparison between our IEVE and prior methods on IIN task. “*” means we finetune OVRL-v2 [55] on the IIN task. IEVE outperforms the baseline model (row 1) with up to $8.75\mathrm{x}$ increase in Success and outperforms a state-of-the-art model [28] (Mod-IIN, row 4) from 0.561 to 0.684 with a lightweight segmentation model (Mask RCNN) on Success, and higher Success of 0.702 with a strong backbone (InternImage [51]). + +We also add a visited trajectory mechanism for the agent to avoid been stuck by invisible obstacles, which will be discussed in the supplementary materials. In our framework, only Instance Classification and Exploration Policy require few training, underscoring the computation efficiency of our design. + +# 4. Experiment + +# 4.1. Experiment Setup + +Dataset. For our experiment, we employ the Habitat [49] simulator to conduct our experiments. The definition of the Instance ImageGoal Navigation [26] task utilized in the Habitat Navigation Challenge $2023^{1}$ serves as our primary reference point. The episode dataset proposed by Krantz et al. [28] for Instance ImageGoal Navigation serves as our key data source. The scene dataset utilized in this study stems from the Habitat-Matterport3D with semantic annotations (HM3D-SEM) [54], which encompasses a total of 216 scenes. These scenes are split into three distinct sub + +sets for training, validation, and testing purposes, consisting of 145/36/35 scenes, respectively. Additionally, the episode dataset has been partitioned into four subsets for training, validation, testing, and testing under a modified challenge regime, comprising 7,056K/1K/1K/1K episodes respectively. We train our agent on the train split and evaluate it on validation split. The object depicted by the goal image belongs to the following six categories: {chair, couch, plant, bed, toilet, television}. On the validation subset, a total of 795 unique object instances have been observed. + +Action Space. Adhering to the task setting of the Habitat Navigation Challenge 2023, we employ the continuous action space. The action space encompasses four actions: linear velocity, angular velocity, camera pitch velocity, velocity stop, each of which accepts values ranging between $-1$ and $1$ and is appropriately scaled according to the respective configurations. Our linear speed is capped at a maximum of $35cm/frame$ and angular velocity at $60^{\circ}/frame$ . + +Metrics. We evaluate our model with both success and efficiency. We report Success Rate (Success), Success rate weighted by normalized inverse Path Length (SPL). Success is True if the agent calls velocity stop action within $1.0m$ Euclidean distance of the goal object and the object is oracle-visible by turning or looking up and down. SPL is an efficiency measure defined in [2]. + +# 4.2. Comparison with State-of-the-art Methods + +We undertake a comprehensive evaluation of our proposed model against various baselines and the SOTA work. + +End-to-End RL Agent. The baseline model for the IIN task is trained in a fully-fledged end-to-end fashion. This involves inputting both an egocentric rgb and depth image as well as a pose into the model, which is then processed by a visual encoder and a recurrent neural network. The network output directly determines the agent's action. The agent is trained from scratch utilizing Proximal Policy Optimization (PPO) [47]. Our method exhibits 8.24x higher Success in Val (row 5 vs. row 1 in Tab. 1). Although it takes a staggering 3.5 billion steps for RL agent model to achieve convergence, the generalization capability of the agent remains unsatisfactory. + +OVRL-v2. Offline Visual Representation Learning v2 (OVRL-v2 [55]) was proposed by Karmesh et al., who introduced a novel model-free, end-to-end navigation policy that emphasizes the significance of self-supervised pretraining of visual encoders and introduces the concept of Compression Layer (CL). Employing a ViT + LSTM backbone, this policy exhibits state-of-the-art performance in ImageGoal Navigation and approaches the state-of-the-art in ObjectGoal Navigation. Due to the task disparity between ImageGoal Navigation and Instance ImageGoal Navigation, we fine-tune the pretrained policy for our specific task. + +The original OVRL-v2 is trained under the setting of the + +
Model VariationValidation
ClassificationPerceptionSwitchExplorationSuccess ↑SPL ↑
Mask RCNNMask RCNNEVERL0.6660.235
Mask RCNNMask RCNNEVEFrontier0.6760.182
Mask RCNNMask RCNNEVERandom0.6540.233
Mask RCNNMask RCNNEERL0.5900.221
InternImageInternImageEVERL0.7020.252
SwinTransMask RCNNEVERL0.6840.241
SwinTransMask RCNNEVEFrontier0.6280.180
SwinTransMask RCNNEVERandom0.6360.236
SwinTransMask RCNNEERL0.6200.216
SwinTransInternImageEVERL0.6760.238
GroundTruthMask RCNNEVERL0.6820.238
GroundTruthOracle-RL0.8500.399
+ +Table 2. Variants of our method with different settings of instance classification, perception, switch policy and exploration policy. Perception means the Instance Segmentation model variations in Online Mapping module. "EE" refers to the exploration-exploitation policy, which establishes a fixed threshold for decision-making. "EVE" represents our Exploration-Verification-Exploitation Switch policy. The last row gives the upper bound of our method, where with ground truth instance segmented observations, the agent can identify the specified object instance as soon as the object becomes visible. + +ImageGoal Navigation task. Evaluating OVRL-v2's performance without finetuning for Instance ImageGoal Navigation reveals suboptimal results (0.006 Success row 2 in Tab. 1). Several factors impact the performance: a shift in scene datasets (Gibson [53] vs. HM3D-SEM [57]), changes in embodiment (Locobot vs. Stretch), and disparity in goal destinations (image source vs. image subject). When specifically finetuned for Instance ImageGoal Navigation (row 3 in Tab. 1) on HM3D-SEM, OVRL-v2 yields improved performance rates at 0.248 Success. Our approach with Mask RCNN exhibits 0.436 higher Success in Val (row 5 vs. row 3 in Tab. 1), and 0.454 higher Success with InternImage (row 6 vs. row 3 in Tab. 1). + +Mod-IIN. Mod-IIN [28] decomposes Instance ImageGoal Navigation task into exploration, goal re-identification, goal localization and local navigation. It outperforms previous state-of-the-art end-to-end learned policies without fine-tuning. Mod-IIN achieves 0.561 Success and 0.233 SPL (row 4 in Tab. 1), and we surpass their results in Success with a substantial margin of 0.123 by attaining 0.684 Success and a marginal improvement in SPL with the help of a classical visual backbone trained with Mask RCNN [18] (row 5 in Tab. 1). Additionally, with the current state-of-the-art Semantic Segmentation model InternImage [51], our results (row 6 in Tab. 1) are notably superior with an impressive score of 0.702 Success and 0.252 SPL. + +# 4.3. Ablation Study + +Instance Classification. Our instance classification method falls into two categories. One is to fine-tune the pretrained SwinTransformer [32] on the goal images of the HM3D- + +![](images/de8b1d97ed7cdd7c4a8a2bf232de5fe87f36d9f9e6e1bc853816fad7e3128a2f.jpg) + +![](images/532167c380b4371d8d3e6dbcc1df7ca9691b059fa2831d8d88c5a24d9aa4b321.jpg) +T=1 + +![](images/751d8d754291ac44a92d61bd55ef172c1e706ace7b9361f70d932d64aff02649.jpg) +T=5 + +![](images/44b2ae5e72c294425b50718eff5a2fb767b6d293c5b8e6e6cb9d4d3700b5149b.jpg) +T=12 + +![](images/61fbb2d9c7ad03fd3814e23d588a2cf8e545b3d711abc51bd46afbe9c103650c.jpg) +T=70 + +![](images/cb68f28e29704657fc41932fd25dcbb5603a232936f758b2d3131ae69f5244fd.jpg) +T=95 + +![](images/f6f24d1a06447b243f709e5e71deccff7b92f54f71cb339d2e552f0a09756e9f.jpg) +Figure 5. Qualitative example of our IVE agent performing the Instance ImageGoal Navigation task in the Habitat simulator. Agent is initialized at $T = 1$ , and finds a potential target at $T = 5$ . After carefully evaluating the potential target from $T = 5$ to $T = 12$ , the agent proceeds with its exploration. Finally, agents identify the goal bed instance at $T = 95$ . +Figure 6. Instance Re-Identification Dataset. Based on the object depicted in the goal image, we sample positive and negative samples with varying Euclidean distance which represents the difficulty level of instance re-identification. For each difficulty level, the left side shows the ground truth segmentation results and the right side shows the RGB images. + +SEM training set. The other method is to obtain the semantic category of the most central segmentation result of the goal image using the segmentation model. Ablation experiments conducted on these two methods demonstrate that SwinTrans is helpful for Mask RCNN (row 6 vs. row 1 in Tab. 2), but it actually suppresses the performance of InternImage (row 10 vs. row 5 in Tab. 2). We believe this is because the InternImage segmentation model has a larger parameter size, better zero-shot capabilities on this dataset, and stronger semantic labeling capabilities. + +Exploration Policy. To scrutinize the extent to which exploration policy exerts a meaningful influence on final outcomes, we separately train our framework with three different exploration policies: a random exploration policy, an RL exploration policy, and a frontier exploration policy. Each of these three policies generates an exploration goal map every ten local steps. The first random policy involves taking the semantic map as input and randomly generating a goal map. The second policy, trained through Reinforce- + +ment Learning, seeks to maximize coverage of the environment while also encouraging the velocity stop action upon encountering a correct oracle facing the goal object. The frontier exploration policy, in contrast, endeavors to delineate the boundaries of the currently explored and free regions of the map, thereby constructing a goal map that encourages exploration. The implementation details of exploration policy are discussed in the supplementary materials. + +From Tab. 2, the performance of RL (row 1 and row 6 in Tab. 2) and random (row 3 and row 8 in Tab. 2) exploration policy on the SPL significantly exceeds that of Frontier exploration policy (row 2 and row 7 in Tab. 2). This disparity in performance is due to the fact that Frontier Exploration requires exploring every corner of a given environment, which is time-consuming and unnecessary in most cases. Specifically, the agent should focus on gaining a comprehensive understanding of the most salient aspects of a small room, which facilitates the identification of the target object. + +Instance Segmentation. Initially, we employ the Mask RCNN instance segmentation model on the Online Mapping module. In order to explore the influence of the visual model on the framework, we have employed the current state-of-the-art semantic segmentation approach: InternImage [51] finetuned on the COCO dataset. Furthermore, in order to ascertain the upper bound of our method, we have employed the ground truth labeled instance class and the ground truth instance segmentation to conduct comprehensive evaluations of the Success and SPL rates. This entails the use of a local policy for the purpose of goal map-to-action, where the agent is directly capable of ascertaining whether the goal object is present in the current view while exploring the environment. + +From Tab. 2, we can observe that state-of-the-art semantic segmentation model InternImage (row 5 in Tab. 2) + +![](images/daf8e31b3e4ede18a2a348225cbdcc5e2b1bc067adf1151a9d2faec670023e15.jpg) +Figure 7. The TP, TN, FN and FP rates vary with changes in the threshold and difficulty levels (representing the closest Euclidean distance between the agent and the potential target). Threshold represents the threshold for the number of matched keypoints that determines whether two images are considered to be the same instance. TP decays rapidly as the difficulty increases, indicating that it becomes increasingly challenging for the agent to make correct judgments at a larger distance. + +![](images/db600c397733e889ac7d0d0471b44131cfaec5336b0e27e9e00ec6c4c3c341a1.jpg) + +![](images/ea10c4b69f13b992207e912f6a18a2694b0a86e94d4993057549c5ffb68ac60c.jpg) + +![](images/c1900638ca7ce7987fba56c7442968424affc922cc3cb423ddd901ae28098a3d.jpg) + +indeed benefits navigation, and the ground truth segmented observation (last row in Tab. 2) gives the upper bound of navigation. Specifically, more precisely segmented observation from InternImage gives higher metrics both in Success and SPL. This is due to the more precise goal localization and less wrong segmentation results. + +Switch Policy. We conduct a comparative analysis of Switch policy. We innovatively incorporate a verification policy into the decision-making process of the agent, and through ablation experiments (row 1 vs. row 4 and row 6 vs. row 9 in Tab. 2), we demonstrate its effectiveness and significance. The implementation details of the Exploration-Exploitation Policy will be presented in supplementary materials. As depicted in Tab. 2, our EVE policy (row 1, row 6 in Tab. 2) outperforms Exploration-Exploitation (EE) Policy (row 4, row 9 in Tab. 2) by a substantial margin both on Success and SPL. This suggests that the EVE policy provides the agent with greater opportunities to discern the current observation from the goal image, rather than arbitrarily assigning a false label to the current observed object in the EE policy. Depicted in Fig. 5, agent finds the potential target at $T = 5$ and employ verification policy. After carefully examining the similar object, the agent determines that the object is not the target and actively switches back to Exploration Policy. + +Instance Re-Identification. To assess our Switch module and identify optimal hyperparameters of the Goal Map Selection module $f_{\text{switch}}$ , we have constructed a comprehensive dataset, as depicted in Fig. 6. This dataset is created based on the HM3D-SEM train/val split. Anchor images are defined as goal images that depict specific object instances, which do not share the same parameters as agent's camera. + +For each anchor goal image, we sample 10 positive and negative images using the agent's camera. Positive images are defined as observations where the target instance is visible to the oracle, while negative images are randomly sampled from the same scene and do not contain the specified goal instance. We have divided the dataset into three distinct difficulty levels: easy, medium, hard, as shown in Fig. 6. + +Different difficulty levels represent different Euclidean distances from the target to current viewpoint. The further implementation details will be discussed in the supplementary materials. To demonstrate the capabilities of our Switch module, we employ the train split to determine hyperparameters and subsequently evaluate performance on the val split. Notably, the train and val splits are two distinct sets, which ensure that the agent has never encountered any scene or object instance present in the train split. + +As depicted in Fig. 7, it is evident that with a fixed threshold of 60, the TP values for the difficulty level decrease significantly. It becomes more evident in the hard level with a threshold of 100 that yields TP rate close to 0. This highlights the importance of careful examination and decision-making based on the utilization of local matching feature algorithms to differentiate between similar objects. By meticulously examining the possible object instance, the agent is able to confidently arrive at a decision. We believe this explains why our model significantly surpasses previous state-of-the-art research in terms of Success. + +# 5. Conclusion + +We propose an innovative framework of Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation. We rethink previous work that decouple the decision-making process into an Exploration-Exploitation paradigm. By considering human behavior in the "approach-verify" phase of identifying potential targets, we propose a new decision-making paradigm: Exploration-Verification-Exploitation. Our experimental results demonstrate that the Exploration-Verification-Exploitation paradigm effectively aids agents in their planning and decision-making process. Our proposed model significantly outperforms existing methods on the Instance ImageGoal Navigation task (0.684 vs. 0.561 Success) with a lightweight instance segmentation model. In the future, we will focus on enhancing the context of visual reasoning for more efficient exploration, and extend the application of the three-stage planning and decision-making paradigm to a broader range of tasks of embodied vision. + +# References + +[1] Ziad Al-Halah, Santhosh Kumar Ramakrishnan, and Kristen Grauman. Zero experience required: Plug & play modular transfer learning for semantic visual navigation. 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The main challenge of this task lies in identifying the target object from different viewpoints while rejecting similar distractors. Existing ImageGoal Navigation methods usually adopt the simple Exploration-Exploitation framework and ignore the identification of specific instance during navigation. In this work, we propose to imitate the human behaviour of \"getting closer to confirm\" when distinguishing objects from a distance. Specifically, we design a new modular navigation framework named Instance-aware Exploration-Verification-Exploitation (IEVE) for instance-level image goal navigation. Our method allows for active switching among the exploration, verification, and exploitation actions, thereby facilitating the agent in making reasonable decisions under different situations. On the challenging HabitatMatterport 3D semantic (HM3DSEM) dataset, our method surpasses previous state-of-the-art work, with a classical segmentation model (0.684 vs. 0.561 success) or a robust model (0.702 vs. 0.561 success). Our code will be made publicly available at https://github.com/XiaohanLei/IEVE." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 557, + 128, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 128, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 128, + 569 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 577, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 577, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 577, + 287, + 649 + ], + "type": "text", + "content": "Embodied navigation is an emerging computer vision task, where an agent utilizes visual sensing to actively interact with its surroundings and execute navigation tasks [2, 4]. Over the past decade, substantial advancements have been witnessed in the field of embodied visual navigation, driven by the emergence of large-scale photorealistic 3D scene" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 655, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 655, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 655, + 287, + 714 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China under Contract 62102128 and 62021001, and in part by the Fundamental Research Funds for the Central Universities under contract WK3490000007. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution of USTC. Corresponding authors: Min Wang and Wengang Zhou." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 319, + 247, + 539, + 446 + ], + "blocks": [ + { + "bbox": [ + 319, + 247, + 539, + 446 + ], + "lines": [ + { + "bbox": [ + 319, + 247, + 539, + 446 + ], + "spans": [ + { + "bbox": [ + 319, + 247, + 539, + 446 + ], + "type": "image", + "image_path": "bdf81e7ef1ccbe524f0b348a08bd736448b6e3ae2902ed835be614eb031ad289.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 314, + 449, + 366, + 527 + ], + "blocks": [ + { + "bbox": [ + 314, + 449, + 366, + 527 + ], + "lines": [ + { + "bbox": [ + 314, + 449, + 366, + 527 + ], + "spans": [ + { + "bbox": [ + 314, + 449, + 366, + 527 + ], + "type": "image", + "image_path": "ef5f96049ab6350e7d27596995c6245b3a7fd6f10de265339a80c3e8268835bb.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "text", + "content": "Figure 1. Instance ImageGoal Navigation tasks an agent with navigating to a particular object instance described by the goal image. The agent is initially in an unexplored environment at " + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "text", + "content": ". While exploring the environment, it encounters a \"bed\" similar to the target at " + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "text", + "content": " and discerns their differences. Eventually, at " + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "inline_equation", + "content": "t_3" + }, + { + "bbox": [ + 304, + 534, + 545, + 601 + ], + "type": "text", + "content": ", agent finds the \"bed\" described in the goal image." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 370, + 449, + 422, + 527 + ], + "blocks": [ + { + "bbox": [ + 370, + 449, + 422, + 527 + ], + "lines": [ + { + "bbox": [ + 370, + 449, + 422, + 527 + ], + "spans": [ + { + "bbox": [ + 370, + 449, + 422, + 527 + ], + "type": "image", + "image_path": "8c305c445374725622e2ac9aada2509e258a9e5a7737eac37a162acb8fc7e933.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 425, + 449, + 478, + 527 + ], + "blocks": [ + { + "bbox": [ + 425, + 449, + 478, + 527 + ], + "lines": [ + { + "bbox": [ + 425, + 449, + 478, + 527 + ], + "spans": [ + { + "bbox": [ + 425, + 449, + 478, + 527 + ], + "type": "image", + "image_path": "30f9c2d769c9ee22dc720c3c369c4812db8d40a2f8997526144f66b0461aa3f5.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 482, + 456, + 538, + 523 + ], + "blocks": [ + { + "bbox": [ + 482, + 456, + 538, + 523 + ], + "lines": [ + { + "bbox": [ + 482, + 456, + 538, + 523 + ], + "spans": [ + { + "bbox": [ + 482, + 456, + 538, + 523 + ], + "type": "image", + "image_path": "92630ff627a7de7241dc4f539250101676c3777ee4604ebafadd396d2eae3f66.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 604, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 640 + ], + "type": "text", + "content": "datasets [6, 41, 48, 53, 57], the implementation of advanced simulators [24, 46, 49, 53], the development of deep learning algorithms [5, 19, 38, 47], and so on." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": "The ability for an agent to navigate its environment and accomplish tasks without human intervention is essential for the advancement of embodied visual navigation. One common setting for tasking an agent is to give it natural language instructions, such as \"check if my laptop is on the chair.\" However, this setting becomes confusing when" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16329" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 178 + ], + "type": "text", + "content": "there are multiple chairs in the house. To overcome this challenge, Krantz et al. [26] propose the Instance Image-Goal Navigation task (IIN), which involves providing the agent with an image captured from goal camera that depicts a specific instance. The agent is then required to navigate to the location of the instance depicted in the image, as shown in Fig. 1. By utilizing the visual information, the agent is expected to avoid confusion caused by multiple similar distractors of the same class." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 179, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 179, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 288, + 443 + ], + "type": "text", + "content": "The most relevant task with IIN is ImageGoal Navigation [1, 9, 17, 33, 35, 56, 63], which has been a popular topic in embodied visual navigation research. The difference between IIN and ImageGoal Navigation lies in their requirements for navigation success. In other words, IIN demands that the agent has the ability to recognize the same object from different viewpoints, while ImageGoal Navigation requires maximizing the similarity between the agent's observations and the goal image. Previous ImageGoal navigation requires targeting random goal images captured by cameras that share the same parameters like height, look-at-angle, and field-of-view as the agent camera. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation. They typically expect the agent to accurately determine whether the current observation matches the goal image. However, it is extremely challenging to enable the agent to correctly identify the target object from a considerable distance. In addition, they treat the decision-making process as a one-shot task, perceiving it as a match between the current observation and the target, while overlooking the judgment process across the temporal dimension." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 443, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 647 + ], + "type": "text", + "content": "To address the above limitations, we propose a novel IIN framework, i.e., Instance-aware Exploration-Verification-Exploitation (IEVE), for Instance ImageGoal Navigation. Inspired by the human behavior of \"getting closer to confirm\" when recognizing distant objects, we formulate the task of determining whether an object matches the one in the goal image as a sequential decision problem. In addition, we design a novel matching function that relies not only on the current observation and goal image but also on the Euclidean distance between the agent and the potential target. We categorize the targets into confirmed target, potential target, and no-target (exploration), and allow the agent to actively choose among these three targets. After an efficient training process of our framework, our result on the IIN task outperforms previous state-of-the-art methods, achieving 0.684 Success with a classical instance segmentation model [18], and 0.702 with a robust model [51]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 658, + 134, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 134, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 134, + 669 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "In recent years, there has been great research interest in the field of embodied vision and active agents. Embodied agents are required to effectively and creatively resolve" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "complex tasks and interact with the physical environment. Notably, the navigation task plays a pivotal role in embodied vision. Numerous researchers have devoted their efforts to exploring different forms of navigation problems, encompassing various task goals and input formats. Specifically, there are five main categories of visual navigation problems: Point Goal Navigation [2, 8, 45], Object Goal Navigation [4, 14, 15, 45, 61], Visual Language Navigation [3, 16, 20-22, 25, 27, 30, 30, 59], ImageGoal Navigation [1, 9, 17, 29, 33, 35, 56, 63], and Instance ImageGoal Navigation [28]. According to the learning framework design, existing visual navigation methods are typically divided into two categories: modular and end-to-end approaches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 229, + 546, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 546, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 546, + 397 + ], + "type": "text", + "content": "End-to-end navigation policies are commonly optimized with improved visual representations [37, 58], auxiliary tasks [60], carefully reward-shaping [34] and data augmentation techniques [34]. Visual representations can be improved with fine-tuned segmentation model [37] and object relation graphs [12, 13, 36, 39, 62]. Prior works also learn fine-tuning visual encoder with Self-Supervised Learning (SSL) [40, 55], while some researchers employ imitation learning approaches, such as Ramrakhya et al. [43], gathering data from large-scale human annotations. Although achieving promising navigation success in simulator, end-to-end methods often suffer high computation complexity in training and generalizability, which may degrade the success of navigation in diverse environments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 400, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 579 + ], + "type": "text", + "content": "To address these challenges, modular methods have been proposed to solve navigation tasks with separate modules, including perception, mapping, path planning, etc. Chaplot et al. [7] address the Object Goal Navigation problem using semantic mapping and exploration. Majumdar et al. [33] adopt the zero-shot learning and inference approach with the use of CLIP. Rmakrishnan et al. [42] propose a potential field function to tackle the exploration problem in Object Goal Navigation. Mezghan et al. [35] and Savinov et al. [44] construct augmented memory mechanisms in ImageGoal Navigation. Some approaches [28, 52] employ local feature matching algorithms and make binary decisions based on the current observation for ImageGoal Navigation. In general, modular-based methods typically exhibit excellent scalability with lower training cost." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "In this work, we focus on IIN task, which is a newly formulated but more real navigation task. It is relevant with the classical ImageGoal Navigation task. ImageGoal Navigation is commonly studied in a previous-unseen environment where goal images are randomly sampled sharing the same parameter with the agent's camera [63]. Many approaches study the ImageGoal Navigation task with RL to learn policies that directly map observations to action [1, 10, 55, 56]. Yadav et al. [55] postulate that SSL for visual representation greatly contributes to the success of the end-to-end navigation policy training. Choi et al. [10] attribute the success" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16330" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 73, + 519, + 224 + ], + "blocks": [ + { + "bbox": [ + 75, + 73, + 519, + 224 + ], + "lines": [ + { + "bbox": [ + 75, + 73, + 519, + 224 + ], + "spans": [ + { + "bbox": [ + 75, + 73, + 519, + 224 + ], + "type": "image", + "image_path": "de581b6c3349e32279e4bf33b93762870e738a12359ea54357689746ea5c6c8c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": "Figure 2. Framework Overview. Our model consists of five main components. Instance Classification " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "f_{class}" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " predicts the object's class in goal image " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": ". Online Mapping " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "f_{SLAM}" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " uses RGB-D and sensor pose reading " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(t)" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " to construct a semantic map " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(t)" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " of the environment. The Switch Policy " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pi_S" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " and Goal Mapping Policy " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pi_{GM}" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " are interconnected. The Switch Policy " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pi_S" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " determines the output of the Goal Mapping Policy's goal map " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_g(t)" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " based on its input judgments (whether a potential target exists and whether the potential target is confirmed). Once the goal map " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_g(t)" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " is determined, the Local Policy " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pi_l" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " is used to determine the action " + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "inline_equation", + "content": "a(t)" + }, + { + "bbox": [ + 46, + 234, + 545, + 289 + ], + "type": "text", + "content": " taken by the agent at the current timestep." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "content": "of RL training to the carefully reward shaping. Chaplot et al. [9] propose a topological mapping system to address the ImageGoal navigation problem, as well as Kim et al. [23]. Kwon et al. [29] propose a novel type of map for ImageGoal Navigation, a renderable neural radiance map." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 568 + ], + "type": "text", + "content": "Unlike ImageGoal Navigation, IIN [26] focuses on distinguishing different similar instances and being able to identify the object in the goal image at different viewpoints. On the other hand, ImageGoal Navigation pays more attention to maximizing the similarity between observations and the goal image within an episode. To be more specific, the goal camera in IIN task is disentangled from the agent's camera on the sampled parameters such as height, look-at-angle, and field-of-view reflect the realistic use case of a user-supplied goal image. Additionally, previous state-of-the-art work employs the confidence score for object re-identification. Differently, we propose a new switchable strategy to meticulously examine a currently visible object. Our key insight lies in treating the subtask of target confirmation as a sequential decision problem and designing a new matching function, which enables the agent to more accurately distinguish target objects from misleading ones." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 593, + 102, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 593, + 102, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 593, + 102, + 605 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "text", + "content": "We devise a new framework, Instance-aware Exploration-Verification-Exploitation (IEVE) for Instance ImageGoal Navigation, which consists of five key modules, including Instance Classification, Online Mapping, Switch Policy, Goal Mapping Policy and Local Policy, as depicted in Fig. 2. In the following subsections, we will first introduce the preliminaries in Sec. 3.1, and sequentially elaborate the five modules of our framework." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 300, + 391, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 300, + 391, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 391, + 312 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": "We follow the embodiment setting of Hello Robot Stretch. The agent in the simulation environment is a rigid-body, zero-turn-radius cylinder of height " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "1.41\\mathrm{m}" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " and radius " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "0.17\\mathrm{m}" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": ". The forward-facing RGB-D camera is mounted at a height of " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "1.31\\mathrm{m}" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": ". At each timestep " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": ", the agent's observation " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_t" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " consists of an egocentric RGB image " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_t" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": ", depth image " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(t)" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": ", goal image " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_g" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " and sensor pose reading " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(t)" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": ". Camera parameters of " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_t" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_g" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " like height, look-at-angle and field-of-view are not the same. Specifically, " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_t" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "640\\times 480" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " image while " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_g" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "inline_equation", + "content": "512\\times 512" + }, + { + "bbox": [ + 304, + 318, + 545, + 438 + ], + "type": "text", + "content": " image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 443, + 433, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 443, + 433, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 433, + 455 + ], + "type": "text", + "content": "3.2. Instance Classification" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "type": "text", + "content": "At the onset of each episode, the Instance Classification model will first process " + }, + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_g" + }, + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "type": "text", + "content": " and output an object class label " + }, + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 462, + 545, + 629 + ], + "type": "text", + "content": ". We adopt two different types of models to achieve instance classification, including 1) classification model: we use the goal images on the train split of HM3D-SEM [57] to finetune the image classification model, i.e., Swin Transformer [32], pretrained on ImageNet [11]. It may face the inherent semantic ambiguity of Ground Truth labels in the HM3D-SEM, such as the difficulties in distinguishing between the class \"sofa\" and \"chair\". 2) instance segmentation model: we use the semantic label of the most central segmented instance in the goal image as the classification result. This approach can maintain semantic consistency without being affected by Ground Truth labels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 635, + 405, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 405, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 405, + 647 + ], + "type": "text", + "content": "3.3. 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Switch Policy and Goal Mapping Policy. The Goal Map Selection module " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "f_{\\text{switch}}" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": " receives two inputs: the shortest Euclidean distance between the agent and the potential target (or non-existence), and the number of matched keypoints. These inputs are mapped to a selection signal using Goal Map Selection function " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "f_{\\text{switch}}" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": ". 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Simultaneously, the depth image " + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(t)" + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "text", + "content": " is transformed into a pointcloud " + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "inline_equation", + "content": "P_{c}(t)" + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "text", + "content": " using the camera's intrinsic matrix " + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "inline_equation", + "content": "\\pmb{T}_{int}" + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "text", + "content": ", followed by the voxelization of the pointcloud. Subsequently, the feature points of " + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{seg}(t)" + }, + { + "bbox": [ + 46, + 292, + 289, + 388 + ], + "type": "text", + "content": " are scattered into the voxels, resulting in the overall local map construction process being formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 395, + 287, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 395, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 78, + 395, + 287, + 409 + ], + "type": "interline_equation", + "content": "\\hat {m} (t) = \\operatorname {S c a t t e r} (\\operatorname {V o x e l} \\left(\\boldsymbol {T} _ {\\text {i n t}} \\mathcal {D} (t)\\right), \\mathcal {I} _ {\\text {s e g}} (t)). \\tag {1}", + "image_path": "ac165a7c392530728c7a0f9c6697e7790af50654b0f1a95fa7dfbab8faa9e354.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "text", + "content": "With the constructed semantic map " + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\hat{m}(t)" + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "text", + "content": " within local coordinate system, agent will subsequently conduct max pooling with the previous global semantic map to obtain the global semantic map " + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(t)" + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 415, + 287, + 464 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 77, + 469, + 287, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 469, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 77, + 469, + 287, + 483 + ], + "type": "interline_equation", + "content": "\\mathcal {M} (t) = \\operatorname {M a x P o o l i n g} (\\mathcal {M} (t - 1), T _ {l g} \\hat {m} (t)), \\tag {2}", + "image_path": "f6ebadc97df87329664b97282864a487eb6397572b96e7c3b85c95a3bb734b57.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "inline_equation", + "content": "T_{lg}" + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "text", + "content": " denotes the transformation matrix from the agent's local frame to the world's global coordinate system. The size of " + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(t)" + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "text", + "content": " is specified as " + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "inline_equation", + "content": "(B, 2 + N, H_m, W_m)" + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "text", + "content": ", where the first channel represents the explored area of the entire environment, the second channel defines the nontraversable area, and the last " + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 490, + 287, + 574 + ], + "type": "text", + "content": " channels signify the location of each object class." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 579, + 133, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 133, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 133, + 593 + ], + "type": "text", + "content": "3.4. Switch Policy" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "text", + "content": "At each time step " + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "text", + "content": ", Switch Policy actively selects the functional goal map from the three parallel sub-modules in Goal Mapping Policy. We summarize the switch process as a function with segmented depth image " + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{seg}(t,n) \\cdot \\mathcal{D}(t)" + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "text", + "content": ", the number of matched keypoints " + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "text", + "content": " using local feature matching algorithm and the minimum Euclidean distance " + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 598, + 287, + 694 + ], + "type": "text", + "content": " between the current position of the agent and the potential target (if exists). This can be described as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 91, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 91, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "S = f _ {s w i t c h} \\left(\\mathcal {I} _ {s e g} (t, n) \\cdot \\mathcal {D} (t), \\omega , d\\right), \\tag {3}", + "image_path": "3cc46b4e0bff818f55128335e22f1a1c14b0e03bc84638f204c87a34f347bad9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "text", + "content": " indicates which goal mapping policy to be selected, depicted in Fig. 3. To obtain the specific expression of " + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "inline_equation", + "content": "f_{\\text{switch}}" + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "text", + "content": ", we construct an Instance Re-Identification dataset as depicted in Fig. 6 to illuminate the influence of distance " + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "text", + "content": " and the number of matched keypoints " + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 292, + 545, + 363 + ], + "type": "text", + "content": " on the goal object's re-identification." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "type": "text", + "content": "The Goal Map Selection function " + }, + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "type": "inline_equation", + "content": "f_{\\text{switch}}" + }, + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "type": "text", + "content": " aligns with human experience in object verification. " + }, + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "type": "inline_equation", + "content": "f_{\\text{switch}}" + }, + { + "bbox": [ + 304, + 365, + 546, + 509 + ], + "type": "text", + "content": " sets objects of the same category as potential targets. At a larger distance to make accurate decisions, a higher threshold on number of matched keypoints is set to convert a potential target into a determined target as depicted in Fig. 4. As the distance decreases, the upper threshold also degrades continuously. At closer distance, the agent's judgment of the object becomes more reliable, so when the number of matched keypoints falls below the lower threshold, it can be very reliably determined that the potential target is not the goal target, thereby switching to the Exploration Policy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": "Local Feature Matching. We employ a keypoint-based re-identification method to help in the selection of goal mapping policy in Eq. (3). Conditioned on the goal image " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_g" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": " and egocentric image " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(t)" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": ", we extract the pixel-wise " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": " coordinates of the keypoints " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "K_{t}\\in \\mathbb{R}^{n\\times 2}" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": " and their associated feature descriptors " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "V_{t}\\in \\mathbb{R}^{n\\times 256}" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": ". These features are extracted utilizing DISK [50], an end-to-end local feature learning algorithm that utilizes policy gradient. Likewise, the same process is repeated with the goal image, resulting in " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "K_{g}\\in \\mathbb{R}^{m\\times 2}" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "V_{g}\\in \\mathbb{R}^{m\\times 256}" + }, + { + "bbox": [ + 304, + 510, + 547, + 641 + ], + "type": "text", + "content": ". The feature extraction processes are formulated as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 651, + 545, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 651, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 317, + 651, + 545, + 666 + ], + "type": "interline_equation", + "content": "\\left(K _ {t}, V _ {t}\\right) = \\operatorname {D I S K} (\\mathcal {I} (t)), \\quad \\left(K _ {g}, V _ {g}\\right) = \\operatorname {D I S K} (\\mathcal {I} _ {g}). \\tag {4}", + "image_path": "f60e36a7102be665fb264dab58023e94b01d2242be0c223d87833c01ffa55905.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 676, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 676, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 676, + 547, + 714 + ], + "type": "text", + "content": "Subsequently, the matched pairs " + }, + { + "bbox": [ + 304, + 676, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\hat{K}_t,\\hat{K}_g)\\in \\mathbb{R}^{\\omega \\times 2}" + }, + { + "bbox": [ + 304, + 676, + 547, + 714 + ], + "type": "text", + "content": " are computed using LightGlue [31], a deep neural network that matches sparse local features across image pairs. The fea" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "16332" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 240, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 240, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 240, + 84 + ], + "type": "text", + "content": "ture matching process is formulated as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 78, + 92, + 287, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 92, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 78, + 92, + 287, + 107 + ], + "type": "interline_equation", + "content": "\\left(\\hat {K} _ {t}, \\hat {K} _ {g}\\right) = \\operatorname {L i g h t G l u e} \\left(\\left(K _ {t}, V _ {t}\\right), \\left(K _ {g}, V _ {g}\\right)\\right). \\tag {5}", + "image_path": "d36871308a9ed95d1b59602f064d9206b043b49657607e0726104e9ccbaeec3a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 116, + 287, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 116, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 46, + 116, + 287, + 152 + ], + "type": "text", + "content": "Subsequently, the number of matched points " + }, + { + "bbox": [ + 46, + 116, + 287, + 152 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 116, + 287, + 152 + ], + "type": "text", + "content": " is utilized as an adaptive threshold for the verification and exploitation goal selection." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 159, + 168, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 159, + 168, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 168, + 172 + ], + "type": "text", + "content": "3.5. Goal Mapping Policy" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "text", + "content": "Depicted in Fig. 3, Goal Mapping Policy module is divided into three parallel sub-modules, which will function at different timesteps. In other words, at each timestep, only one sub-module will function. More specifically, given the predicted goal object's class " + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "text", + "content": " and segmented vision " + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{seg}(t)" + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "text", + "content": ", if the mask " + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{seg}(t,n)" + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "text", + "content": " has any value greater than zero, then the Exploitation or Verification Policy is activated. They project the masked depth image " + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{seg}(t,n)\\cdot \\mathcal{D}(t)" + }, + { + "bbox": [ + 46, + 177, + 288, + 308 + ], + "type": "text", + "content": " to current semantic map. Similar to previous Online Mapping module, the two goal mapping policies in local coordinate system can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 318, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 318, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 86, + 318, + 287, + 332 + ], + "type": "interline_equation", + "content": "\\hat {m} _ {g} (t) = \\operatorname {V o x e l} \\left(\\boldsymbol {T} _ {\\text {i n t}} \\mathcal {I} _ {\\text {s e g}} (t, n) \\cdot \\mathcal {D} (t)\\right), \\tag {6}", + "image_path": "e43b2ab320b8f7ad4afb4e202a78db9814eaa7dd1b928e085ae9efabb704f327.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\hat{m}_g(t)" + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "text", + "content": " indicates the goal map in the local coordinate system. Then we transform " + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\hat{m}_g(t)" + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "text", + "content": " into the global coordinate system, " + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_g(t) = T_{lg}\\hat{m}_g(t)" + }, + { + "bbox": [ + 46, + 340, + 287, + 460 + ], + "type": "text", + "content": ". Although with the same goal map formulas, Exploitation and Verification policy represent the targets with different confidence. Specifically, Exploitation policy refers to the confirmed target, which will be kept and used for the rest navigation process. In contrast, Verification policy represents potential target, which will be further checked by local feature matching in the Switch policy module." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "text", + "content": "The Exploration Policy use a convolutional neural network to predict a waypoint " + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "inline_equation", + "content": "g_{rl}(t) = \\pi_{rl}(\\mathcal{M}(t)|\\theta_{rl})" + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\theta_{rl}" + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "text", + "content": " are parameters of Exploration Policy. We train it with RL to maximize coverage of the environment while also successfully employing the stop action upon encountering a correct oracle facing the goal object. The goal map " + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_g(t)" + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "text", + "content": " is constructed with the value at position " + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "inline_equation", + "content": "g_{rl}(t)" + }, + { + "bbox": [ + 46, + 460, + 287, + 545 + ], + "type": "text", + "content": " set as 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 127, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 127, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 127, + 564 + ], + "type": "text", + "content": "3.6. Local Policy" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "When Switch Policy selects one of three goal mapping policies, agent adopts Local Policy to infer next action in accordance with the semantic map " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(t)" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": ", and the goal map, " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_g(t)" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": ". Specifically, Fast Matching Method (FMM) is employed to generate a distance field, which establishes the shortest distance between a traversible point and the selected goal map. A subset of the distance field is chosen within the agent's feasible range, and a waypoint is selected, ensuring that it does not intersect with existing obstacles and maintains the local minimum within the subset. With the selected waypoint, the agent can readily calculate an action based on the angle and distance from its current state." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 331, + 72, + 518, + 217 + ], + "blocks": [ + { + "bbox": [ + 331, + 72, + 518, + 217 + ], + "lines": [ + { + "bbox": [ + 331, + 72, + 518, + 217 + ], + "spans": [ + { + "bbox": [ + 331, + 72, + 518, + 217 + ], + "type": "image", + "image_path": "dbacca8315c95a9e2a90586dfa175bd8c9118e85739e24f41bd00510fc6468f0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "type": "text", + "content": "Figure 4. Goal Map Selection function " + }, + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "type": "inline_equation", + "content": "f_{switch}" + }, + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "type": "text", + "content": " with respect to the Euclidean distance from agent to the potential target and the number of matched keypoints. Best viewed in color." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 338, + 258, + 515, + 358 + ], + "blocks": [ + { + "bbox": [ + 338, + 258, + 515, + 358 + ], + "lines": [ + { + "bbox": [ + 338, + 258, + 515, + 358 + ], + "spans": [ + { + "bbox": [ + 338, + 258, + 515, + 358 + ], + "type": "table", + "html": "
ModelValidation
Success ↑SPL ↑
RL Baseline [26]0.0830.035
OVRL-v2 ImageNav [55]0.0060.002
OVRL-v2 IIN [55]*0.2480.118
Mod-IIN [28]0.5610.233
IEVE Mask RCNN (ours)0.6840.241
IEVE InternImage (ours)0.7020.252
", + "image_path": "265fce2862f2b54a8111b99b66b3acb292c2b2ea65b328782a039b98e8fe2189.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 366, + 545, + 444 + ], + "lines": [ + { + "bbox": [ + 305, + 366, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 545, + 444 + ], + "type": "text", + "content": "Table 1. Comparison between our IEVE and prior methods on IIN task. “*” means we finetune OVRL-v2 [55] on the IIN task. IEVE outperforms the baseline model (row 1) with up to " + }, + { + "bbox": [ + 305, + 366, + 545, + 444 + ], + "type": "inline_equation", + "content": "8.75\\mathrm{x}" + }, + { + "bbox": [ + 305, + 366, + 545, + 444 + ], + "type": "text", + "content": " increase in Success and outperforms a state-of-the-art model [28] (Mod-IIN, row 4) from 0.561 to 0.684 with a lightweight segmentation model (Mask RCNN) on Success, and higher Success of 0.702 with a strong backbone (InternImage [51])." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 454, + 545, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 454, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 305, + 454, + 545, + 527 + ], + "type": "text", + "content": "We also add a visited trajectory mechanism for the agent to avoid been stuck by invisible obstacles, which will be discussed in the supplementary materials. In our framework, only Instance Classification and Exploration Policy require few training, underscoring the computation efficiency of our design." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 537, + 382, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 382, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 382, + 551 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 557, + 413, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 557, + 413, + 570 + ], + "spans": [ + { + "bbox": [ + 306, + 557, + 413, + 570 + ], + "type": "text", + "content": "4.1. Experiment Setup" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 575, + 545, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 575, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 305, + 575, + 545, + 695 + ], + "type": "text", + "content": "Dataset. For our experiment, we employ the Habitat [49] simulator to conduct our experiments. The definition of the Instance ImageGoal Navigation [26] task utilized in the Habitat Navigation Challenge " + }, + { + "bbox": [ + 305, + 575, + 545, + 695 + ], + "type": "inline_equation", + "content": "2023^{1}" + }, + { + "bbox": [ + 305, + 575, + 545, + 695 + ], + "type": "text", + "content": " serves as our primary reference point. The episode dataset proposed by Krantz et al. [28] for Instance ImageGoal Navigation serves as our key data source. The scene dataset utilized in this study stems from the Habitat-Matterport3D with semantic annotations (HM3D-SEM) [54], which encompasses a total of 216 scenes. These scenes are split into three distinct sub" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 500, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 500, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 500, + 712 + ], + "type": "text", + "content": "1https://aihabitat.org/challenge/2023/" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16333" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "sets for training, validation, and testing purposes, consisting of 145/36/35 scenes, respectively. Additionally, the episode dataset has been partitioned into four subsets for training, validation, testing, and testing under a modified challenge regime, comprising 7,056K/1K/1K/1K episodes respectively. We train our agent on the train split and evaluate it on validation split. The object depicted by the goal image belongs to the following six categories: {chair, couch, plant, bed, toilet, television}. On the validation subset, a total of 795 unique object instances have been observed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "text", + "content": "Action Space. Adhering to the task setting of the Habitat Navigation Challenge 2023, we employ the continuous action space. The action space encompasses four actions: linear velocity, angular velocity, camera pitch velocity, velocity stop, each of which accepts values ranging between " + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "inline_equation", + "content": "1" + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "text", + "content": " and is appropriately scaled according to the respective configurations. Our linear speed is capped at a maximum of " + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "inline_equation", + "content": "35cm/frame" + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "text", + "content": " and angular velocity at " + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "inline_equation", + "content": "60^{\\circ}/frame" + }, + { + "bbox": [ + 46, + 192, + 289, + 289 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 289, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 373 + ], + "type": "text", + "content": "Metrics. We evaluate our model with both success and efficiency. We report Success Rate (Success), Success rate weighted by normalized inverse Path Length (SPL). Success is True if the agent calls velocity stop action within " + }, + { + "bbox": [ + 46, + 289, + 289, + 373 + ], + "type": "inline_equation", + "content": "1.0m" + }, + { + "bbox": [ + 46, + 289, + 289, + 373 + ], + "type": "text", + "content": " Euclidean distance of the goal object and the object is oracle-visible by turning or looking up and down. SPL is an efficiency measure defined in [2]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 381, + 270, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 270, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 270, + 395 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "content": "We undertake a comprehensive evaluation of our proposed model against various baselines and the SOTA work." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 425, + 289, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 568 + ], + "type": "text", + "content": "End-to-End RL Agent. The baseline model for the IIN task is trained in a fully-fledged end-to-end fashion. This involves inputting both an egocentric rgb and depth image as well as a pose into the model, which is then processed by a visual encoder and a recurrent neural network. The network output directly determines the agent's action. The agent is trained from scratch utilizing Proximal Policy Optimization (PPO) [47]. Our method exhibits 8.24x higher Success in Val (row 5 vs. row 1 in Tab. 1). Although it takes a staggering 3.5 billion steps for RL agent model to achieve convergence, the generalization capability of the agent remains unsatisfactory." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 569, + 289, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 289, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 289, + 701 + ], + "type": "text", + "content": "OVRL-v2. Offline Visual Representation Learning v2 (OVRL-v2 [55]) was proposed by Karmesh et al., who introduced a novel model-free, end-to-end navigation policy that emphasizes the significance of self-supervised pretraining of visual encoders and introduces the concept of Compression Layer (CL). Employing a ViT + LSTM backbone, this policy exhibits state-of-the-art performance in ImageGoal Navigation and approaches the state-of-the-art in ObjectGoal Navigation. Due to the task disparity between ImageGoal Navigation and Instance ImageGoal Navigation, we fine-tune the pretrained policy for our specific task." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "The original OVRL-v2 is trained under the setting of the" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 215 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 215 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 215 + ], + "type": "table", + "html": "
Model VariationValidation
ClassificationPerceptionSwitchExplorationSuccess ↑SPL ↑
Mask RCNNMask RCNNEVERL0.6660.235
Mask RCNNMask RCNNEVEFrontier0.6760.182
Mask RCNNMask RCNNEVERandom0.6540.233
Mask RCNNMask RCNNEERL0.5900.221
InternImageInternImageEVERL0.7020.252
SwinTransMask RCNNEVERL0.6840.241
SwinTransMask RCNNEVEFrontier0.6280.180
SwinTransMask RCNNEVERandom0.6360.236
SwinTransMask RCNNEERL0.6200.216
SwinTransInternImageEVERL0.6760.238
GroundTruthMask RCNNEVERL0.6820.238
GroundTruthOracle-RL0.8500.399
", + "image_path": "f5280a6a062504dc3a036d1d439485f449be6141dcd56371486361c1cb7479d4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 218, + 547, + 329 + ], + "lines": [ + { + "bbox": [ + 304, + 218, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 547, + 329 + ], + "type": "text", + "content": "Table 2. Variants of our method with different settings of instance classification, perception, switch policy and exploration policy. Perception means the Instance Segmentation model variations in Online Mapping module. \"EE\" refers to the exploration-exploitation policy, which establishes a fixed threshold for decision-making. \"EVE\" represents our Exploration-Verification-Exploitation Switch policy. The last row gives the upper bound of our method, where with ground truth instance segmented observations, the agent can identify the specified object instance as soon as the object becomes visible." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 339, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 547, + 495 + ], + "type": "text", + "content": "ImageGoal Navigation task. Evaluating OVRL-v2's performance without finetuning for Instance ImageGoal Navigation reveals suboptimal results (0.006 Success row 2 in Tab. 1). Several factors impact the performance: a shift in scene datasets (Gibson [53] vs. HM3D-SEM [57]), changes in embodiment (Locobot vs. Stretch), and disparity in goal destinations (image source vs. image subject). When specifically finetuned for Instance ImageGoal Navigation (row 3 in Tab. 1) on HM3D-SEM, OVRL-v2 yields improved performance rates at 0.248 Success. Our approach with Mask RCNN exhibits 0.436 higher Success in Val (row 5 vs. row 3 in Tab. 1), and 0.454 higher Success with InternImage (row 6 vs. row 3 in Tab. 1)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 495, + 548, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 548, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 548, + 651 + ], + "type": "text", + "content": "Mod-IIN. Mod-IIN [28] decomposes Instance ImageGoal Navigation task into exploration, goal re-identification, goal localization and local navigation. It outperforms previous state-of-the-art end-to-end learned policies without fine-tuning. Mod-IIN achieves 0.561 Success and 0.233 SPL (row 4 in Tab. 1), and we surpass their results in Success with a substantial margin of 0.123 by attaining 0.684 Success and a marginal improvement in SPL with the help of a classical visual backbone trained with Mask RCNN [18] (row 5 in Tab. 1). Additionally, with the current state-of-the-art Semantic Segmentation model InternImage [51], our results (row 6 in Tab. 1) are notably superior with an impressive score of 0.702 Success and 0.252 SPL." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 658, + 400, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 400, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 400, + 672 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Instance Classification. Our instance classification method falls into two categories. One is to fine-tune the pretrained SwinTransformer [32] on the goal images of the HM3D-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16334" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 106, + 129, + 190 + ], + "blocks": [ + { + "bbox": [ + 53, + 106, + 129, + 190 + ], + "lines": [ + { + "bbox": [ + 53, + 106, + 129, + 190 + ], + "spans": [ + { + "bbox": [ + 53, + 106, + 129, + 190 + ], + "type": "image", + "image_path": "de8b1d97ed7cdd7c4a8a2bf232de5fe87f36d9f9e6e1bc853816fad7e3128a2f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 140, + 77, + 210, + 219 + ], + "blocks": [ + { + "bbox": [ + 140, + 77, + 210, + 219 + ], + "lines": [ + { + "bbox": [ + 140, + 77, + 210, + 219 + ], + "spans": [ + { + "bbox": [ + 140, + 77, + 210, + 219 + ], + "type": "image", + "image_path": "532167c380b4371d8d3e6dbcc1df7ca9691b059fa2831d8d88c5a24d9aa4b321.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 169, + 220, + 181, + 227 + ], + "lines": [ + { + "bbox": [ + 169, + 220, + 181, + 227 + ], + "spans": [ + { + "bbox": [ + 169, + 220, + 181, + 227 + ], + "type": "text", + "content": "T=1" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 220, + 78, + 290, + 218 + ], + "blocks": [ + { + "bbox": [ + 220, + 78, + 290, + 218 + ], + "lines": [ + { + "bbox": [ + 220, + 78, + 290, + 218 + ], + "spans": [ + { + "bbox": [ + 220, + 78, + 290, + 218 + ], + "type": "image", + "image_path": "751d8d754291ac44a92d61bd55ef172c1e706ace7b9361f70d932d64aff02649.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 249, + 220, + 261, + 227 + ], + "lines": [ + { + "bbox": [ + 249, + 220, + 261, + 227 + ], + "spans": [ + { + "bbox": [ + 249, + 220, + 261, + 227 + ], + "type": "text", + "content": "T=5" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 301, + 78, + 371, + 219 + ], + "blocks": [ + { + "bbox": [ + 301, + 78, + 371, + 219 + ], + "lines": [ + { + "bbox": [ + 301, + 78, + 371, + 219 + ], + "spans": [ + { + "bbox": [ + 301, + 78, + 371, + 219 + ], + "type": "image", + "image_path": "44b2ae5e72c294425b50718eff5a2fb767b6d293c5b8e6e6cb9d4d3700b5149b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 220, + 343, + 227 + ], + "lines": [ + { + "bbox": [ + 329, + 220, + 343, + 227 + ], + "spans": [ + { + "bbox": [ + 329, + 220, + 343, + 227 + ], + "type": "text", + "content": "T=12" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 381, + 78, + 452, + 219 + ], + "blocks": [ + { + "bbox": [ + 381, + 78, + 452, + 219 + ], + "lines": [ + { + "bbox": [ + 381, + 78, + 452, + 219 + ], + "spans": [ + { + "bbox": [ + 381, + 78, + 452, + 219 + ], + "type": "image", + "image_path": "61fbb2d9c7ad03fd3814e23d588a2cf8e545b3d711abc51bd46afbe9c103650c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 409, + 220, + 423, + 227 + ], + "lines": [ + { + "bbox": [ + 409, + 220, + 423, + 227 + ], + "spans": [ + { + "bbox": [ + 409, + 220, + 423, + 227 + ], + "type": "text", + "content": "T=70" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 461, + 78, + 532, + 219 + ], + "blocks": [ + { + "bbox": [ + 461, + 78, + 532, + 219 + ], + "lines": [ + { + "bbox": [ + 461, + 78, + 532, + 219 + ], + "spans": [ + { + "bbox": [ + 461, + 78, + 532, + 219 + ], + "type": "image", + "image_path": "cb68f28e29704657fc41932fd25dcbb5603a232936f758b2d3131ae69f5244fd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 490, + 220, + 504, + 227 + ], + "lines": [ + { + "bbox": [ + 490, + 220, + 504, + 227 + ], + "spans": [ + { + "bbox": [ + 490, + 220, + 504, + 227 + ], + "type": "text", + "content": "T=95" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 53, + 290, + 286, + 401 + ], + "blocks": [ + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "text", + "content": "Figure 5. Qualitative example of our IVE agent performing the Instance ImageGoal Navigation task in the Habitat simulator. Agent is initialized at " + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "inline_equation", + "content": "T = 1" + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "text", + "content": ", and finds a potential target at " + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "inline_equation", + "content": "T = 5" + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "text", + "content": ". After carefully evaluating the potential target from " + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "inline_equation", + "content": "T = 5" + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "inline_equation", + "content": "T = 12" + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "text", + "content": ", the agent proceeds with its exploration. Finally, agents identify the goal bed instance at " + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "inline_equation", + "content": "T = 95" + }, + { + "bbox": [ + 46, + 244, + 547, + 278 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 290, + 286, + 401 + ], + "lines": [ + { + "bbox": [ + 53, + 290, + 286, + 401 + ], + "spans": [ + { + "bbox": [ + 53, + 290, + 286, + 401 + ], + "type": "image", + "image_path": "f6f24d1a06447b243f709e5e71deccff7b92f54f71cb339d2e552f0a09756e9f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 412, + 288, + 479 + ], + "lines": [ + { + "bbox": [ + 46, + 412, + 288, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 288, + 479 + ], + "type": "text", + "content": "Figure 6. Instance Re-Identification Dataset. Based on the object depicted in the goal image, we sample positive and negative samples with varying Euclidean distance which represents the difficulty level of instance re-identification. For each difficulty level, the left side shows the ground truth segmentation results and the right side shows the RGB images." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 485, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 605 + ], + "type": "text", + "content": "SEM training set. The other method is to obtain the semantic category of the most central segmentation result of the goal image using the segmentation model. Ablation experiments conducted on these two methods demonstrate that SwinTrans is helpful for Mask RCNN (row 6 vs. row 1 in Tab. 2), but it actually suppresses the performance of InternImage (row 10 vs. row 5 in Tab. 2). We believe this is because the InternImage segmentation model has a larger parameter size, better zero-shot capabilities on this dataset, and stronger semantic labeling capabilities." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Exploration Policy. To scrutinize the extent to which exploration policy exerts a meaningful influence on final outcomes, we separately train our framework with three different exploration policies: a random exploration policy, an RL exploration policy, and a frontier exploration policy. Each of these three policies generates an exploration goal map every ten local steps. The first random policy involves taking the semantic map as input and randomly generating a goal map. The second policy, trained through Reinforce-" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 289, + 546, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 546, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 546, + 385 + ], + "type": "text", + "content": "ment Learning, seeks to maximize coverage of the environment while also encouraging the velocity stop action upon encountering a correct oracle facing the goal object. The frontier exploration policy, in contrast, endeavors to delineate the boundaries of the currently explored and free regions of the map, thereby constructing a goal map that encourages exploration. The implementation details of exploration policy are discussed in the supplementary materials." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 387, + 546, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 546, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 546, + 518 + ], + "type": "text", + "content": "From Tab. 2, the performance of RL (row 1 and row 6 in Tab. 2) and random (row 3 and row 8 in Tab. 2) exploration policy on the SPL significantly exceeds that of Frontier exploration policy (row 2 and row 7 in Tab. 2). This disparity in performance is due to the fact that Frontier Exploration requires exploring every corner of a given environment, which is time-consuming and unnecessary in most cases. Specifically, the agent should focus on gaining a comprehensive understanding of the most salient aspects of a small room, which facilitates the identification of the target object." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 520, + 546, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 546, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 546, + 688 + ], + "type": "text", + "content": "Instance Segmentation. Initially, we employ the Mask RCNN instance segmentation model on the Online Mapping module. In order to explore the influence of the visual model on the framework, we have employed the current state-of-the-art semantic segmentation approach: InternImage [51] finetuned on the COCO dataset. Furthermore, in order to ascertain the upper bound of our method, we have employed the ground truth labeled instance class and the ground truth instance segmentation to conduct comprehensive evaluations of the Success and SPL rates. This entails the use of a local policy for the purpose of goal map-to-action, where the agent is directly capable of ascertaining whether the goal object is present in the current view while exploring the environment." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "From Tab. 2, we can observe that state-of-the-art semantic segmentation model InternImage (row 5 in Tab. 2)" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16335" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 53, + 173, + 171 + ], + "blocks": [ + { + "bbox": [ + 53, + 53, + 173, + 171 + ], + "lines": [ + { + "bbox": [ + 53, + 53, + 173, + 171 + ], + "spans": [ + { + "bbox": [ + 53, + 53, + 173, + 171 + ], + "type": "image", + "image_path": "daf8e31b3e4ede18a2a348225cbdcc5e2b1bc067adf1151a9d2faec670023e15.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "text", + "content": "Figure 7. The TP, TN, FN and FP rates vary with changes in the threshold and difficulty levels (representing the closest Euclidean distance between the agent and the potential target). Threshold represents the threshold for the number of matched keypoints that determines whether two images are considered to be the same instance. TP decays rapidly as the difficulty increases, indicating that it becomes increasingly challenging for the agent to make correct judgments at a larger distance." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 53, + 294, + 171 + ], + "blocks": [ + { + "bbox": [ + 173, + 53, + 294, + 171 + ], + "lines": [ + { + "bbox": [ + 173, + 53, + 294, + 171 + ], + "spans": [ + { + "bbox": [ + 173, + 53, + 294, + 171 + ], + "type": "image", + "image_path": "db600c397733e889ac7d0d0471b44131cfaec5336b0e27e9e00ec6c4c3c341a1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 298, + 53, + 417, + 171 + ], + "blocks": [ + { + "bbox": [ + 298, + 53, + 417, + 171 + ], + "lines": [ + { + "bbox": [ + 298, + 53, + 417, + 171 + ], + "spans": [ + { + "bbox": [ + 298, + 53, + 417, + 171 + ], + "type": "image", + "image_path": "ea10c4b69f13b992207e912f6a18a2694b0a86e94d4993057549c5ffb68ac60c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 418, + 53, + 539, + 171 + ], + "blocks": [ + { + "bbox": [ + 418, + 53, + 539, + 171 + ], + "lines": [ + { + "bbox": [ + 418, + 53, + 539, + 171 + ], + "spans": [ + { + "bbox": [ + 418, + 53, + 539, + 171 + ], + "type": "image", + "image_path": "c1900638ca7ce7987fba56c7442968424affc922cc3cb423ddd901ae28098a3d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 239, + 288, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 310 + ], + "type": "text", + "content": "indeed benefits navigation, and the ground truth segmented observation (last row in Tab. 2) gives the upper bound of navigation. Specifically, more precisely segmented observation from InternImage gives higher metrics both in Success and SPL. This is due to the more precise goal localization and less wrong segmentation results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 313, + 288, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 540 + ], + "type": "text", + "content": "Switch Policy. We conduct a comparative analysis of Switch policy. We innovatively incorporate a verification policy into the decision-making process of the agent, and through ablation experiments (row 1 vs. row 4 and row 6 vs. row 9 in Tab. 2), we demonstrate its effectiveness and significance. The implementation details of the Exploration-Exploitation Policy will be presented in supplementary materials. As depicted in Tab. 2, our EVE policy (row 1, row 6 in Tab. 2) outperforms Exploration-Exploitation (EE) Policy (row 4, row 9 in Tab. 2) by a substantial margin both on Success and SPL. This suggests that the EVE policy provides the agent with greater opportunities to discern the current observation from the goal image, rather than arbitrarily assigning a false label to the current observed object in the EE policy. Depicted in Fig. 5, agent finds the potential target at " + }, + { + "bbox": [ + 46, + 313, + 288, + 540 + ], + "type": "inline_equation", + "content": "T = 5" + }, + { + "bbox": [ + 46, + 313, + 288, + 540 + ], + "type": "text", + "content": " and employ verification policy. After carefully examining the similar object, the agent determines that the object is not the target and actively switches back to Exploration Policy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 543, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 628 + ], + "type": "text", + "content": "Instance Re-Identification. To assess our Switch module and identify optimal hyperparameters of the Goal Map Selection module " + }, + { + "bbox": [ + 46, + 543, + 287, + 628 + ], + "type": "inline_equation", + "content": "f_{\\text{switch}}" + }, + { + "bbox": [ + 46, + 543, + 287, + 628 + ], + "type": "text", + "content": ", we have constructed a comprehensive dataset, as depicted in Fig. 6. This dataset is created based on the HM3D-SEM train/val split. Anchor images are defined as goal images that depict specific object instances, which do not share the same parameters as agent's camera." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "For each anchor goal image, we sample 10 positive and negative images using the agent's camera. Positive images are defined as observations where the target instance is visible to the oracle, while negative images are randomly sampled from the same scene and do not contain the specified goal instance. We have divided the dataset into three distinct difficulty levels: easy, medium, hard, as shown in Fig. 6." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 239, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 547, + 346 + ], + "type": "text", + "content": "Different difficulty levels represent different Euclidean distances from the target to current viewpoint. The further implementation details will be discussed in the supplementary materials. To demonstrate the capabilities of our Switch module, we employ the train split to determine hyperparameters and subsequently evaluate performance on the val split. Notably, the train and val splits are two distinct sets, which ensure that the agent has never encountered any scene or object instance present in the train split." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 348, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 547, + 479 + ], + "type": "text", + "content": "As depicted in Fig. 7, it is evident that with a fixed threshold of 60, the TP values for the difficulty level decrease significantly. It becomes more evident in the hard level with a threshold of 100 that yields TP rate close to 0. This highlights the importance of careful examination and decision-making based on the utilization of local matching feature algorithms to differentiate between similar objects. By meticulously examining the possible object instance, the agent is able to confidently arrive at a decision. We believe this explains why our model significantly surpasses previous state-of-the-art research in terms of Success." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 495, + 379, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 379, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 379, + 507 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 514, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 715 + ], + "type": "text", + "content": "We propose an innovative framework of Instance-aware Exploration-Verification-Exploitation for Instance ImageGoal Navigation. We rethink previous work that decouple the decision-making process into an Exploration-Exploitation paradigm. By considering human behavior in the \"approach-verify\" phase of identifying potential targets, we propose a new decision-making paradigm: Exploration-Verification-Exploitation. Our experimental results demonstrate that the Exploration-Verification-Exploitation paradigm effectively aids agents in their planning and decision-making process. Our proposed model significantly outperforms existing methods on the Instance ImageGoal Navigation task (0.684 vs. 0.561 Success) with a lightweight instance segmentation model. In the future, we will focus on enhancing the context of visual reasoning for more efficient exploration, and extend the application of the three-stage planning and decision-making paradigm to a broader range of tasks of embodied vision." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16336" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 107, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 107, + 85 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 107, + 85 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 148 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 148 + ], + "type": "text", + "content": "[1] Ziad Al-Halah, Santhosh Kumar Ramakrishnan, and Kristen Grauman. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 15130-15140, 2021. 2" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 307, + 297, + 545, + 361 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 297, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 307, + 297, + 545, + 361 + ], + "type": "text", + "content": "[63] Yuke Zhu, Roozbeh Mottaghi, Eric Kolve, Joseph J Lim, Abhinav Gupta, Li Fei-Fei, and Ali Farhadi. Target-driven visual navigation in indoor scenes using deep reinforcement learning. In Proceedings of the IEEE international conference on robotics and automation (ICRA), pages 3357–3364, 2017. 2" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16339" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_content_list.json b/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0bd16d6e2c5b349db0bca63a3ee68b564a5ce97a --- /dev/null +++ b/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_content_list.json @@ -0,0 +1,1658 @@ +[ + { + "type": "text", + "text": "Instance-based Max-margin for Practical Few-shot Recognition", + "text_level": 1, + "bbox": [ + 165, + 130, + 805, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Minghao Fu Ke Zhu\\* National Key Laboratory for Novel Software Technology, Nanjing University, China School of Artificial Intelligence, Nanjing University, China", + "bbox": [ + 151, + 180, + 816, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fumh@lamda.nju.edu.cn, zhuk@lamda.nju.edu.cn", + "bbox": [ + 287, + 237, + 676, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 285, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In order to mimic the human few-shot learning (FSL) ability better and to make FSL closer to real-world applications, this paper proposes a practical FSL (pFSL) setting. pFSL is based on unsupervised pre-trained models (analogous to human prior knowledge) and recognizes many novel classes simultaneously. Compared to traditional FSL, pFSL is simpler in its formulation, easier to evaluate, more challenging and more practical. To cope with the rarity of training examples, this paper proposes IbM2, an instance-based max-margin method not only for the new pFSL setting, but also works well in traditional FSL scenarios. Based on the Gaussian Annulus Theorem, IbM2 converts random noise applied to the instances into a mechanism to achieve maximum margin in the many-way pFSL (or traditional FSL) recognition task. Experiments with various self-supervised pre-training methods and diverse many- or few-way FSL tasks show that IbM2 almost always leads to improvements compared to its respective baseline methods, and in most cases the improvements are significant. With both the new pFSL setting and novel IbM2 method, this paper shows that practical few-shot learning is both viable and promising.", + "bbox": [ + 75, + 318, + 473, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 666, + 207, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We human have the ability to learn new concepts based on a few exemplars, thanks to both our ability to learn and the previously accumulated knowledge. As a stark contrast, learning machines (especially deep learning models) mostly require plentiful training examples to learn just few (e.g., 5) concepts. Both the vision and learning community are fully aware of this shortcoming, and few-shot learning (FSL) is our community's effort to counter this weakness, which has been studied for a long time [39].", + "bbox": [ + 75, + 691, + 468, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "FSL relies on prior knowledge, too. Currently, the setting is to set aside a collection of object categories (known as the base set), with many training examples in every base", + "bbox": [ + 76, + 829, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5e0878b4d1552db5a5882964b262b35758656d28cb75f934f29ab4bccf97a450.jpg", + "image_caption": [ + "Figure 1. Instance-based max-margin. We create a hypersphere (large dashed circles) centered at every example (solid shapes), sample many virtual examples (hollow shapes) around the hypersphere, and require the decision boundary to classify all virtual samples correctly. Then we in effect achieve instance-based maxmargin. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 573, + 285, + 816, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "set category. A model is first pre-trained on the base set, which naturally encodes prior knowledge. Then, few novel object categories (most commonly 5) are to be recognized based on the pre-trained model given few training examples from these new concepts (e.g., 1 or 5 per category). Note that the base and novel training sets are semantically closely related (e.g., both contain different kinds of birds).", + "bbox": [ + 496, + 566, + 890, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There is a clear mismatch between the human ability and this FSL setting. We human can learn many instead of few novel concepts; and, the human prior knowledge include those accumulated as both common-sense and domain knowledge from many diverse domains rather than a limited set of concepts closely related to a specific task.", + "bbox": [ + 496, + 672, + 890, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although this FSL setting has served our community well and has pushed the technical frontier for years, with the immense advances in deep learning and emerging practical needs for real-world FSL applications, it is time that we need a better, simpler, and more practical FSL setting.", + "bbox": [ + 496, + 763, + 890, + 840 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hence we advocate a practical few-shot learning (or pFSL) setting: based on an unsupervised model pre-trained from a large number of concepts (e.g., ImageNet [30]), simultaneously learn many new concepts (e.g., 200) with few", + "bbox": [ + 496, + 840, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^*$ K. Zhu is the corresponding author.", + "bbox": [ + 94, + 886, + 290, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28674", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "examples (e.g., 1 or 5 per category).", + "bbox": [ + 76, + 90, + 316, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An ImageNet pre-trained model is more analogous to human knowledge than those learned from a base set in traditional FSL, and learning many new concepts makes it more practical in applications. Without the base set, the learning phase of pFSL is simple, too. More importantly, evaluation of algorithms is difficult, complicated, and very time consuming in the current FSL setting [16], but as will be discussed later, pFSL does not suffer from this drawback.", + "bbox": [ + 75, + 112, + 467, + 232 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although an ImageNet pre-trained model undoubtedly contains more prior knowledge than a base-set trained one, simultaneously learning many new concepts will inevitably make pFSL much more difficult than traditional FSL. We believe that a more challenging task will help technology advancement, too—the traditional FSL setting is already saturated to certain extent (cf. results in [22, 41]).", + "bbox": [ + 75, + 239, + 467, + 344 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hence, we propose a novel approach for pFSL: Instance-based Max-margin (IbM2), which is effective in traditional FSL, too. The max-margin idea has been shown to be effective in improving generalization. Classic methods like SVM [7] build max-margin decision boundaries with only a very small portion of the training examples (i.e., support vectors). This idea is problematic when we have both very few training examples and a very high dimensionality. Intuitively, the support vectors chosen by SVM are highly likely wrong or misleading, because a small training set leads to excessively unstable estimation [16].", + "bbox": [ + 75, + 349, + 467, + 515 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the proposed IbM2, we achieve max-margin at the instance level, instead of at the class level as in SVM. As illustrated in Fig. 1, we create a hypersphere for every training example, with the example being the center of the hypersphere. Then, we can sample as many virtual samples as we want around this hypersphere, and assign the label of the center (original training example) to all its associated virtual examples. By finding a properly maximized radius for the hypersphere and requiring a classifier to correctly classify the virtual examples, we in effect achieve max-margin. Another benefit of IbM2 is that we do not need any special handling for multi-class recognition, while vanilla SVM is for binary classification only. In short, the contributions of this paper are twofold:", + "bbox": [ + 75, + 522, + 467, + 733 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a practical few-shot learning setting (pFSL): many-way (e.g., 200-way) recognition, uses an unsupervised pre-trained model, and has no base set.", + "- We propose IbM2, an instance-based max-margin algorithm, which suits few-shot, high dimensionality, and multi-class naturally." + ], + "bbox": [ + 80, + 739, + 467, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As will be shown by extensive experiments, IbM2 consistently improves both traditional FSL and the proposed pFSL. The benefits of pFSL against traditional FSL will be verified by both analyses and experiments, too.", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-shot learning aims at recognizing novel categories with the help of prior knowledge. Given the base set as prior knowledge, few-shot learning methods can be roughly divided into two types: those based on meta-learning or transfer-learning.", + "bbox": [ + 496, + 114, + 890, + 190 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Meta-learning based FSL. Meta-learning [21] learns a model through a large quantity of episodes consisting of different training and evaluation sets. Given a new task during evaluation, the model performs what it does in training to predict. In FSL, the training episodes are randomly sampled from the base set. One line of work [14, 15, 25, 31] focuses on learning general initial weights for fast adapting the model to unseen categories with a few steps of optimization. For example, [14] explicitly trains the classifier in a model-agnostic way. [25] extends meta-learning with linear predictors as a differentiable convex problem. [15] learns the task distribution from a probabilistic perspective. Another line of work [1, 11, 32, 33, 37, 42, 43] boosts meta-learning by exploring different distance metrics. For example, [32] aggregates training features to generate prototypes for different classes as the classification head. [43] leverages the Earth Mover's Distance to calculate the structural distance for classification. [1] extracts sets of features from each image to build a set-based matching schema.", + "bbox": [ + 496, + 191, + 890, + 478 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transfer-learning based FSL. This line of attack [9, 12, 27, 35, 40] leverages the idea of standard transfer learning, which first pre-trains a model on base classes and then finetunes the model weights with limited training samples from novel classes. [9] normalizes the features and classification weights and calculates their cosine distances as the logits. [27] pre-trains with manifold mixup [36] to improve robustness. [12] introduces a baseline for effectively and transductively finetuning. [40] calibrates the training distribution of a few-shot task using statistics from the base set. [35] explores learning a general representation of base classes in supervised or self-supervised ways with self-distillation.", + "bbox": [ + 496, + 479, + 890, + 660 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised learning. We stress that in pFSL the pre-trained model is unsupervised, for which the reason is to be explained in Sec. 3. Self-supervised learning (SSL) is the mainstream approach to train a deep net in the unsupervised manner. Popular SSL methods, whether applied to traditional ResNet [18] models (e.g., BYOL [17], MoCo [19] and SwAV [5]) or Vision Transformers (ViT) [13] (e.g., MSN [2], DINO [6] and MoCov3 [10]), all produce pretrained models based on large-scale datasets. In this paper, we utilize such models as our prior knowledge in FSL.", + "bbox": [ + 496, + 662, + 890, + 811 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. pFSL: Practical Few-Shot Learning", + "text_level": 1, + "bbox": [ + 500, + 828, + 823, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In traditional FSL, the training dataset is split into 1) the base set with $N_{b}$ labeled images, denoted as $D_{b} = \\{(x_{i}^{b},y_{i}^{b})\\}_{i = 1}^{N_{b}}$ where $y_{i}^{b}\\in \\mathcal{V}_{b}$ is the label of instance $x_{i}^{b}$ and", + "bbox": [ + 500, + 854, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28675", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "$\\mathcal{V}_b$ is the label space of $D_{b}$ 2) the novel set with $N_{n}$ labeled images, denoted as $D_{n} = \\{(x_{j}^{n},y_{j}^{n})\\}_{j = 1}^{N_{n}}$ where $y_{j}^{n}\\in \\mathcal{V}_{n}$ is the label of $x_{j}^{n}$ and $\\mathcal{V}_n$ is the label space of $D_{n}$ . Note that although $\\mathcal{V}_b\\cap \\mathcal{V}_n = \\emptyset$ , the concepts in $\\mathcal{V}_b$ and $\\mathcal{V}_n$ are semantically similar to each other. Then, the task is to learn a recognizer generalizing well on unknown samples from $\\mathcal{V}_n$ . By letting $N_{n}\\ll N_{b}$ , the training samples in $D_{n}$ are few-shot (i.e., few training examples per class). In traditional FSL, $|\\mathcal{V}_b|$ is relatively large but $|\\mathcal{V}_n|$ is small. For example, in most cases $|\\mathcal{V}_n| = 5$ , which is called a 5-way FSL. The evaluation of traditional FSL is a rather complicated task.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The pFSL Formulation", + "text_level": 1, + "bbox": [ + 76, + 266, + 292, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To make FSL simpler, more practical, and closer to human's few-shot learning capability, we propose a new practical few-shot learning (pFSL) paradigm, which is characterized by the following properties:", + "bbox": [ + 75, + 287, + 468, + 349 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Removing the base set. The prior knowledge obtained through pre-training on the base set is limited, as the base set only contains limited number of concepts. In some applications, collecting data sharing similar concepts with the novel set may be as difficult as collecting more samples for the novel set itself.", + "- Pre-trained model based on big data. A model pretrained on a large training set containing a wide variety of concepts is analogous to the common-sense and domain knowledge our brains encode, which will be useful for few-shot learning in diverse domains.", + "- Many-way FSL. In a $N$ -way $k$ -shot FSL, we seek $N$ to be large and $k$ to be small, e.g., using all the CUB [38] categories ( $N = 200$ categories and $k$ is 1 or 5). This makes pFSL much closer to real-world applications than traditional FSL.", + "- Unsupervised pre-training. In pFSL, we require the pre-training to be unsupervised. Since a large scale dataset (e.g., ImageNet) may contain the concept in few-shot learning (e.g., those birds in CUB), avoiding using the labels during pre-training is necessary to make the evaluation of FSL algorithm fairer." + ], + "bbox": [ + 80, + 351, + 468, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These properties distinguish pFSL from traditional FSL and some recent variants of it [9, 12, 22, 23, 27].", + "bbox": [ + 75, + 686, + 468, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Simplicity and Better Evaluation", + "text_level": 1, + "bbox": [ + 76, + 726, + 366, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The pFSL framework is clearly simpler than traditional FSL, and it leads to not only benefits in the training phase, but more importantly better evaluation of FSL algorithms.", + "bbox": [ + 75, + 750, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traditional $N$ -way $k$ -shot FSL typical use $N = 5$ and $k = 1, 5$ , which inevitably leads to unreliable estimation of the test accuracy. Hence, the common practice is to sample a large number of $n$ episodes ( $n \\geq 500$ ), find the accuracy in each episode, and report the average accuracy $\\mu$ along with its $95\\%$ confidence interval $Z_{95\\%}$ . Note that with $n$ episodes, the standard deviation $\\sigma$ of the accuracy within", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the $n$ episodes is $\\sigma = 0.51\\sqrt{n} Z_{95\\%}$ . For example, a typical result is: average accuracy $64.93\\%$ , $95\\%$ confidence interval $0.18\\%$ , but the standard deviation of accuracy is $9.18\\%$ [16] (in which $n = 10000$ ). In short, one single evaluation of traditional FSL requires training and testing for $n$ times ( $n \\geq 500$ ) and the evaluation results are still unreliable. Because of the complicated setup, both learning and evaluation of traditional FSL algorithms are not only costly, but often carried out in slightly different ways, which renders the fair comparison even more difficult.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As a stark contrast, pFSL is much simpler and as the experimental results will show in Table 1, the estimate of average accuracy is reliable. The standard deviation is small (mostly $< 1.0\\%$ ). This reliable estimation comes from the fact that pSFL is many-way (i.e., $N$ is large). Hence, instead of running $n$ episodes, few episodes (e.g., 3) is enough to evaluate pFSL, which not only means savings in computation, but also more reliable evaluation of algorithms.", + "bbox": [ + 496, + 242, + 890, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. IbM2: Instance-based Max-margin", + "text_level": 1, + "bbox": [ + 498, + 375, + 818, + 392 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In pFSL, we have a pre-trained model $\\mathcal{M}$ (unsupervised trained on a large set) and a novel set. There is no base set $D_{b}$ any more, hence we will simply denote the novel set as $D = \\{x_{i},y_{i}\\}_{i = 1}^{M}$ (that is, ignoring the subscript $^b$ ). The label set of $D$ is $\\mathcal{V}$ . In an $N$ -way $k$ -shot pFSL task, we have $|\\mathcal{V}| = N$ and there will be $k$ training examples in each of the $N$ novel classes, hence $M = kN$ . Note that we expect $|\\mathcal{V}| = N$ to be large (i.e., many-way FSL) and $k$ to be small (e.g., 1 or 5).", + "bbox": [ + 496, + 400, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Generating Virtual Samples", + "text_level": 1, + "bbox": [ + 498, + 545, + 751, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since $k$ (the number of training images in each class) is still small but the number of classes ( $N$ ) becomes much larger (e.g., from 5 in traditional FSL to 200 in pFSL), we expect that the challenge in learning a pFSL model is greater than that in traditional FSL. This is verified by our experiments (cf. the results in Table 1 vs. those in Table 3).", + "bbox": [ + 496, + 568, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Virtual examples, or examples that are sampled based on the original training examples, have been repeatedly proven useful when the number of training examples is small, e.g., in traditional few-shot learning [40] or long-tailed recognition (where the tail classes have few training images) [20].", + "bbox": [ + 496, + 659, + 890, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The common idea in generating virtual samples is to make the virtual samples follow the underlying distributions of the classes. However, in few-shot learning this requirement is very difficult to entertain even with the help of techniques such as distribution calibration (DC) in [40], because there is only 1 or 5 examples per class.", + "bbox": [ + 496, + 734, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast, we do not try to sample from any underlying distribution, but try to achieve max-margin of the decision boundary, as illustrated in Fig. 1. Specifically, for every training instance $x_{i}$ , we i.i.d. generate $R$ virtual samples $x_{i,r}$ ( $1 \\leq r \\leq R$ ) which distribute around the shell of the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28676", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "hypersphere centered at $x_{i}$ and whose radius is controlled by a parameter $\\epsilon$ . Note that the same $\\epsilon$ is shared by all training examples $x_{i}$ ( $1 \\leq i \\leq kN$ ).", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Technically, let $z_{i}$ be the feature vector produced by the pre-trained model $\\mathcal{M}$ : $z_{i} = \\mathcal{M}(x_{i})$ from a forward calculation. Then, a noise vector $\\delta_{i,r}$ is randomly sampled from the standard multi-dimensional normal distribution $N(0, I_d)$ , where $d$ is the length of $z_{i}$ and $I_{d}$ is a $d \\times d$ identity matrix. By adding a scaled version of the noise vector to the $i$ -th training example, we obtain $z_{i,r}$ (the $r$ -th virtual example for $x_{i}$ ):", + "bbox": [ + 75, + 136, + 467, + 256 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {i, r} = z _ {i} + \\epsilon \\delta_ {i, r}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 257, + 467, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Its label $y_{i,r}$ is $y_{i}$ (the label of $x_{i}$ ) and $\\epsilon$ is a positive number. Interesting properties exist in our virtual examples:", + "bbox": [ + 76, + 279, + 467, + 310 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Hypersphere for different training examples can overlap, so long as they belong to the same class (cf. Fig. 1).", + "- We require the virtual examples to be correctly classified, or, the original training examples are discarded.", + "- The virtual examples lie around the shell, not the interior of the hypersphere. According to the Gaussian Annulus Theorem [4], almost all the probability of a high-dimensional spherical Gaussian with unit variance is concentrated in a thin annulus of width $O(1)$ with radius $\\sqrt{d}$ when $d$ is large. Since $d$ is indeed large (e.g., $d = 2048$ ), the virtual examples reside around the shell. Hence, if we maximize the radius parameter $\\epsilon$ but require that the virtual examples are correctly classified, as Fig. 1 shows, we in essence achieve margin maximization in an instance-based manner." + ], + "bbox": [ + 80, + 311, + 467, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, the proposed method is named Instance-based Max-margin, abbreviated as IbM2.", + "bbox": [ + 76, + 541, + 467, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Ellipsoidal Noise Generation", + "text_level": 1, + "bbox": [ + 76, + 580, + 333, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One issue with the above isotropic noise sampling is that it ignores the structural property of the training examples. For instance, if the ranges for two feature dimensions are $[-1, 1]$ and $[-100, 100]$ , respectively, isotropic sampling is clearly unsuitable.", + "bbox": [ + 76, + 604, + 467, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To overcome this drawback, we calculate a range vector $s = (s_1, s_2, \\ldots, s_d)$ using all the original training examples regardless of the class label, where $s_i$ is the sample standard deviation for the $i$ -th dimension. Then, the IbM2 virtual examples are generated as (replacing Eq. 1)", + "bbox": [ + 76, + 680, + 467, + 755 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {i, r} = z _ {i} + \\epsilon (s \\odot \\delta_ {i, r}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 767, + 467, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ is element-wise multiplication. The final virtual example generation process is illustrated in Fig. 2. Note that estimating $s$ is dramatically easier than estimating the underlying distribution of every novel class.", + "bbox": [ + 76, + 794, + 467, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is worth noting that this ellipsoidal noise generation is unsupervised, which distinguishes itself from Distribution calibration (DC) [40]. DC samples virtual examples based", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/712447196ab4e0ccd9fc2fb06b741943edec2ae3728db5f0a05caa24af42252c.jpg", + "image_caption": [ + "Figure 2. Virtual example generation. Original input images pass through the pre-trained model $\\mathcal{M}$ to get feature vectors (solid rectangles). Then, every feature vector i.i.d. samples $R$ virtual examples ( $R = 2$ here) using Eq. 2." + ], + "image_footnote": [], + "bbox": [ + 535, + 99, + 859, + 261 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on an estimated covariance structure, which is estimated from the few novel class training examples in a sample-wise manner and calibrated using the base set. As aforementioned, we argue that it makes sense to get rid of the dependency on a base set, then DC is not applicable.", + "bbox": [ + 496, + 364, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More importantly, the reliability of this estimation of a dense covariance matrix is understandably much lower than our estimation of the range indicator vector $s$ — we estimate $d$ values using $k \\times N$ examples, while DC estimates $d \\times d$ values using only 1 example and the base set. The base set calibration will help DC, but clearly its estimation is still unreliable, as shown by experiments in [40, 44]", + "bbox": [ + 496, + 439, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Binary Search to Find the Largest Possible $\\epsilon$", + "text_level": 1, + "bbox": [ + 498, + 556, + 872, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Obviously we want $\\epsilon$ to be as large as possible to achieve max-margin, under the condition that virtual examples are classified correctly. Hence, we design a simple binary search to find the optimal value for $\\epsilon$ .", + "bbox": [ + 496, + 579, + 890, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For any given $\\epsilon$ value, we can generate $kNR$ virtual examples $(x_{i,r},y_{i,r})$ $(1\\leq i\\leq kN,1\\leq r\\leq R)$ using Eq. 2. We denote the virtual training set for this particular value of $\\epsilon$ as $D^{\\epsilon}$ . Then, we train a linear classifier with parameters $W$ to classify $D^{\\epsilon}$ and obtain the training accuracy. If the training accuracy is too high (larger than a threshold $T$ ), $\\epsilon$ is enlarged; otherwise $\\epsilon$ is shrunk. The binary search maintains a search range, when the search range is tight enough (when the range is less than 0.05 in Algorithm 1), the search terminates, and we have found the optimal value $\\hat{\\epsilon}$ .", + "bbox": [ + 496, + 638, + 890, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We have a few notes for finding $\\hat{\\epsilon}$ :", + "bbox": [ + 517, + 791, + 746, + 805 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Unlike DC [40], we do not need a validation set.", + "- The threshold $T$ does not need to be 1 (100%). In SVM learning, the slack variable trick allows some support vectors not to have max-margin. Similarly, we just need $T$ to be close to 1 (0.9 in our experiments).", + "- Different from classic augmentation techniques [26, 28]," + ], + "bbox": [ + 503, + 806, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28677", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [ + "Algorithm 1 Pseudo code for searching $\\epsilon$" + ], + "code_body": "Inputs: \nx : training features of a few-shot task \ny : training labels of a few-shot task \nR : sampling times for an instance \nT : accuracy threshold for searching \nOutputs: \neps : epsilon for sampling \nleft = 0.0 \nright = a large value \neps = right / 2 \nW = initclassifier \nwhile True: \n acc = train_and.eval(W, x, y, eps, R) \n if acc > T: \n left = eps # increase epsilon \n else: \n right = eps # decrease epsilon \n eps = (left + right) / 2.0 \n if right - left < 0.05: \n break", + "guess_lang": "python", + "bbox": [ + 76, + 116, + 450, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which introduce minor disturbance into input features, the distribution of $D^{\\hat{\\epsilon}}$ is drastically different from $D$ because of a large $\\hat{\\epsilon}$ (empirically 1.24 on average).", + "bbox": [ + 94, + 375, + 467, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the IbM2 pipeline is simple: First, use Algorithm 1 to find $\\hat{\\epsilon}$ . Second, generate the virtual dataset $D^{\\hat{\\epsilon}}$ . And third, learn a linear classifier $W$ . Note that the pretrained model $\\mathcal{M}$ is frozen and will not be updated.", + "bbox": [ + 76, + 421, + 467, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 494, + 281, + 510 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our IbM2 method on both setups: the proposed pFSL in many-way few-shot scenario, and also comparing IbM2 under the traditional FSL few-way setting with state-of-the-art FSL methods to further validate its effectiveness.", + "bbox": [ + 76, + 518, + 467, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 589, + 292, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For both the searching and training stages of IbM2, all features extracted by the backbone $\\mathcal{M}$ were $L2$ -normalized first. When learning the classification head (both during the binary search and after $\\hat{\\epsilon}$ was determined), we used Adam as the optimizer and the label smoothed cross-entropy loss [34] as the learning objective. The pre-trained model was trained using various self-supervised learning methods on the ImageNet-1K [30] training set.", + "bbox": [ + 75, + 611, + 467, + 732 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the binary search, for all the experiments we will report, we always set $R$ as 200, $T$ as 0.9 in pFSL and 0.999 in the traditional FSL setting, except when we carried out ablation experiments on these hyperparameters.", + "bbox": [ + 76, + 732, + 467, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Full implementation details are included in the appendix.", + "bbox": [ + 94, + 792, + 467, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Experiments in the pFSL Setting", + "text_level": 1, + "bbox": [ + 76, + 816, + 364, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Evaluation Setup. We explored two common many-way classification datasets, ImageNet-1K [30] and CUB-200-2011 (CUB) [38]. ImageNet-1K contains about 1.28 million training images from 1,000 classes and", + "bbox": [ + 76, + 839, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "50,000 images for evaluation. CUB is a fine-grained recognition dataset composed of 11,788 images belonging to 200 classes of birds, 5,994 for training and 5,794 for evaluation.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For both datasets, we randomly sampled the training sets for pFSL by selecting $k$ images from every class (i.e., $k$ -shot) and using all the classes (1000 and 200, respectively) to form the novel set. $k$ is chosen from $\\{1, 2, 3, 4, 5, 8, 16\\}$ . The evaluation was carried out on the full validation (for ImageNet) or test (for CUB) set.", + "bbox": [ + 498, + 137, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Utilizing various self-supervised backbone network $\\mathcal{M}$ pre-trained on ImageNet, we compare two sets of results: one in which the linear classifier was obtained by using the original training set, the other by using IbM2's virtual examples. We report the top-1 accuracy and its standard deviation computed over 3 randomly sampled novel sets.", + "bbox": [ + 496, + 228, + 890, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Main Results. As the results in Table 1 suggest, we evaluated on two types of backbones: Vision Transformer (ViT) [13] and ResNet50 [18]. The pre-training methods included DINO [6], MoCov3 [10], MSN [2], SimCLR [8] and BYOL [17]. Table 1 shows that in almost all cases, IbM2 benefited the few-shot learning process and improved the top-1 accuracy.", + "bbox": [ + 496, + 319, + 890, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When the number of shots $(k)$ is very small $(\\leq 2)$ , the improvement of IbM2 over the baseline is roughly $1\\%$ on average. However, as the number of training shots goes larger, it is clear that the level of accuracy improvement increases gradually from $\\sim 1\\%$ to $\\sim 2\\%$ , even $>3\\%$ in some cases.", + "bbox": [ + 496, + 426, + 890, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A useful observation from these results is that in pFSL, both the baseline and IbM2 have small standard deviations, that is, more robust in evaluation. Hence, we do not need 500 episodes in pFSL any longer—3 is enough.", + "bbox": [ + 498, + 517, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semi-supervised learning. In the self-supervised learning literature, it is a common practice to use ImageNet-1K training images to learn a backbone in the unsupervised manner, then use a small portion (e.g., $1\\%$ ) of the training data now with labels to train a classifier. This semi-supervised learning task can also be viewed as our pFSL setting. Hence, we also report the $1\\%$ ImageNet-1K semi-supervised learning (on average 12 labeled training images per class) results in Table 2. IbM2 consistently improved various self-supervised models and backbone architectures in all cases, with $0.8\\%$ to $2.9\\%$ top-1 accuracy increase.", + "bbox": [ + 496, + 578, + 890, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Experiments in the Traditional FSL Setting", + "text_level": 1, + "bbox": [ + 500, + 755, + 867, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Evaluation Setup. We evaluated IbM2 in the traditional FSL setup, too. We conducted experiments on two standard benchmark datasets, mini-ImageNet [37] and CIFAR-FS [3]. mini-ImageNet consists of 100 categories selected from ImageNet-1K, which are further split into 64 base, 16 val and 20 novel categories according to [29]. CIFAR-FS is created by randomly shuffling the 100 categories of CIFAR-100 [24] into 64 base, 16 val, 20 novel", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28678", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4a7e434bbbf813df594e06937efd54181e9cb8c15869f5665f0de17fca1cea00.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetPre-training MethodBackboneIbM2Shot per Class
12345816
ImageNet-1KDINOViT-S/16✓39.2 ± 0.349.2 ± 0.254.1 ± 0.456.7 ± 0.258.0 ± 0.160.4 ± 0.162.7 ± 0.1
39.2 ± 0.349.4 ± 0.354.6 ± 0.457.6 ± 0.159.3 ± 0.162.4 ± 0.265.8 ± 0.1
MoCov3ViT-S/16✓32.7 ± 0.642.0 ± 0.246.9 ± 0.349.6 ± 0.451.0 ± 0.153.8 ± 0.156.6 ± 0.2
33.9 ± 0.643.2 ± 0.248.4 ± 0.351.3 ± 0.352.8 ± 0.256.1 ± 0.159.8 ± 0.2
MSNViT-S/16✓47.9 ± 0.156.2 ± 0.459.8 ± 0.361.6 ± 0.162.4 ± 0.264.4 ± 0.366.1 ± 0.1
47.8 ± 0.256.4 ± 0.460.5 ± 0.262.5 ± 0.263.6 ± 0.266.0 ± 0.268.4 ± 0.0
ViT-B/4✓53.2 ± 0.264.5 ± 0.468.9 ± 0.270.9 ± 0.272.0 ± 0.373.8 ± 0.175.0 ± 0.2
54.0 ± 0.164.9 ± 0.569.4 ± 0.271.4 ± 0.172.7 ± 0.474.7 ± 0.076.4 ± 0.2
ViT-L/7✓57.3 ± 0.466.5 ± 0.469.8 ± 0.571.6 ± 0.472.2 ± 0.273.8 ± 0.175.1 ± 0.1
57.7 ± 0.466.6 ± 0.570.1 ± 0.671.8 ± 0.472.6 ± 0.274.3 ± 0.176.0 ± 0.0
SimCLRResNet50✓21.4 ± 0.430.3 ± 0.136.1 ± 0.339.8 ± 0.242.0 ± 0.146.8 ± 0.151.9 ± 0.0
23.6 ± 0.433.4 ± 0.239.0 ± 0.442.0 ± 0.344.2 ± 0.148.0 ± 0.052.7 ± 0.0
BYOLResNet50✓26.5 ± 0.335.7 ± 0.241.5 ± 0.445.1 ± 0.247.2 ± 0.151.8 ± 0.157.1 ± 0.1
27.5 ± 0.337.5 ± 0.143.3 ± 0.446.8 ± 0.249.1 ± 0.153.2 ± 0.158.0 ± 0.1
CUBDINOViT-S/16✓35.4 ± 1.249.0 ± 0.556.8 ± 0.860.8 ± 0.765.2 ± 0.970.6 ± 0.975.9 ± 0.3
36.2 ± 1.449.6 ± 0.657.4 ± 1.062.0 ± 0.666.4 ± 0.872.5 ± 0.879.0 ± 0.2
MSNViT-S/16✓32.1 ± 1.645.0 ± 0.653.1 ± 0.656.7 ± 0.161.4 ± 0.567.3 ± 0.073.6 ± 0.4
33.0 ± 1.445.8 ± 0.753.2 ± 0.957.1 ± 0.462.0 ± 1.068.4 ± 0.175.7 ± 0.2
ViT-L/7✓34.9 ± 1.349.4 ± 0.458.8 ± 0.862.7 ± 0.967.2 ± 0.373.8 ± 0.880.4 ± 0.2
37.5 ± 1.250.1 ± 0.559.0 ± 0.862.6 ± 0.567.5 ± 0.673.9 ± 0.481.0 ± 0.1
", + "bbox": [ + 140, + 87, + 831, + 363 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bf4058dbff62a46f46c03869804b761720262bb2e83ac4a5e9dbf1eff34b95be.jpg", + "table_caption": [ + "Table 1. Average of top-1 accuracy (%) with standard deviation across 3 random subsets on ImageNet-1K and CUB. A √ in the column IbM2 denotes the proposed IbM2 method, or the baseline method if it is blank. Those IbM2 results that are at least 0.5% higher than the baseline are shown in boldface." + ], + "table_footnote": [], + "table_body": "
Pre-training MethodBackboneIbM2Top 1
DINOViT-S/16✓62.5
65.0
MoCov3ViT-S/16✓56.0
58.9
MSNViT-S/16✓65.9
67.9
ViT-B/4✓74.9
76.1
ViT-L/7✓74.8
75.6
SimCLRResNet50✓50.5
51.3
BYOLResNet50✓55.7
56.8
", + "bbox": [ + 135, + 436, + 415, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Top-1 accuracy (\\%) of $1\\%$ ImageNet-1K semi-supervised learning. The training set contains on average 12 labeled training samples per category.", + "bbox": [ + 75, + 686, + 470, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "categories. Note that in order to perform traditional few-shot learning, only the novel split of these two datasets is required to sample many 5-way 1/5-shot episodes. We report the metrics mentioned in [16]: the average $(\\mathrm{ACC}_m)$ , worst-case $(\\mathrm{ACC}_1)$ , average of worst 10 $(\\mathrm{ACC}_{10})$ , average of worst 100 $(\\mathrm{ACC}_{100})$ episodes' accuracy, and the standard deviation $(\\sigma)$ over 500 episodes for comprehensive evaluation. To make the results more reliable, we average the value of each metric from 5 runs with different", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "random seeds. We adopted PMF [22], $S2M2_{R}$ [27] and Meta-Baseline [11] as the pre-training or meta-training approaches to obtain the backbone weights out of the base set.", + "bbox": [ + 496, + 440, + 890, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main Results. As shown in Table 3, by plugging IbM2 in during classifier learning, the proposed IbM2 improved the average accuracy $\\mathrm{ACC}_m$ in all cases except only 1 result. And, the standard deviation $\\sigma$ was reduced by IbM2 or remain unchanged in all cases. As [16] advocated, smaller $\\sigma$ means the learning process is more stable.", + "bbox": [ + 496, + 484, + 892, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[16] also advocates the worst-case episode's accuracy is more important than the average accuracy among all episodes. Table 3 shows that IbM2 almost always leads to higher worst-case $(\\mathrm{ACC}_1)$ or near-worst-case $(\\mathrm{ACC}_{10},$ $\\mathrm{ACC}_{100})$ accuracy. Furthermore, the average gain of $\\mathrm{ACC}_m$ is $0.4\\%$ , which is far less than that of $\\mathrm{ACC}_1$ $(1.3\\%)$ .As for $\\mathrm{ACC}_{10}$ and $\\mathrm{ACC}_{100}$ , their gains are very similar, both around $0.5\\%$ . These observations demonstrate that IbM2 can boost the recognition accuracy of few-shot learning in almost every scenario, especially the worst case one.", + "bbox": [ + 496, + 577, + 893, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "At last, by comparing the numbers in Tables 1 and 3, pFSL is more challenging than traditional FSL, which leads to more open questions to solve.", + "bbox": [ + 496, + 729, + 893, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 785, + 665, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We performed ablation studies for IbM2 in the pFSL setting on ImageNet-1K.", + "bbox": [ + 496, + 809, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Instance-based vs. class-based max-margin. IbM2 seeks max-margin through an instance-based manner. In this study, we compare this instance-based max-margin with the well-known support vector machine (SVM), which", + "bbox": [ + 496, + 840, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28679", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9a64f718319518e02c57030c5d203ef3fd47780a923afe879b9e2040a2d35723.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetPre-training & Meta-trainingBackboneIbM21-shot5-shot
ACCmσACC1ACC10ACC100ACCmσACC1ACC10ACC100
mini-ImageNetPMFViT-S/16✓93.46.161.372.483.498.41.887.791.495.6
94.45.663.274.785.198.61.886.191.395.9
ViT-B/16✓94.95.466.975.586.098.81.689.192.996.3
95.65.169.677.687.198.91.689.393.096.3
ResNet50✓94.95.367.275.286.398.51.789.391.995.8
95.35.266.174.686.998.81.689.392.796.3
S2M2RWRN-28-10✓65.410.032.039.350.782.37.152.062.571.8
65.810.032.540.551.182.97.053.363.372.3
Meta-BaselineResNet12✓62.910.426.734.347.479.07.554.758.067.9
63.010.232.335.647.979.57.354.958.568.7
CIFAR-FSPMFViT-S/16✓87.98.351.761.774.895.54.274.781.888.5
89.08.159.264.175.995.74.273.381.788.7
ViT-B/16✓89.88.155.264.876.896.04.173.182.289.2
90.38.058.965.577.496.04.174.181.889.2
ResNet50✓81.710.435.251.665.891.35.571.275.182.7
82.310.336.351.166.591.65.373.376.083.2
S2M2RWRN-28-10✓75.210.844.046.759.287.77.154.767.976.8
75.510.842.445.559.287.77.054.968.177.0
Meta-BaselineResNet12✓72.711.632.042.956.184.87.554.765.173.6
72.311.532.842.355.785.17.556.365.474.1
", + "bbox": [ + 138, + 87, + 831, + 361 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "achieves max-margin in a class-based manner. We experimented with SVM using the linear kernel function in the LIBSVM [7] software package. By iterating the value of SVM's regularization hyperparameter $C$ from the set $\\{0.1, 1, 10, 100, 1000\\}$ , we found the best accuracy among them to compare with our IbM2 method.", + "bbox": [ + 75, + 426, + 468, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 4, the proposed IbM2 method outperforms SVM with the best $C$ by a significant margin in all cases. Specifically, the recognition accuracy improves $\\sim 2\\%$ on average, and even up to $\\sim 4\\%$ in the extremely scarce 1-shot case. These results demonstrate that our instance-based margin generated by IbM2 helps more to learn a robust classification boundary, especially when the training distribution is drastically shifted.", + "bbox": [ + 75, + 518, + 468, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sensitivity of $R$ . As described in Sec. 4, one original training example is turned into $R$ virtual examples to form the training set $D^{\\hat{\\epsilon}}$ . In this part, we study the effect of the hyperparameter $R$ . As shown in Table 5, when the training shots are highly limited, increasing $R$ significantly improves recognition accuracy. As the number of training shots gets larger, the accuracy difference between a large $R$ ( $R = 400$ ) and a small one ( $R = 1$ ) gradually decreases from $1.6\\%$ to $0.2\\%$ .", + "bbox": [ + 75, + 641, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "When training samples are extremely scarce, it is difficult to model the correct Gaussian distribution with a few samples in a high-dimensional space. Therefore, increasing $R$ is necessary for a good estimation. When more training shots are available, the need for a large value of sampling times is reduced, hence the accuracy difference between different $R$ becomes smaller, too. Based on these results, we let $R = 200$ in all our experiments.", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e9892f2ebb7e676f9097e5070b4781911490d89360b61d3dbd0fc0ffcc5140b1.jpg", + "table_caption": [ + "Table 3. Results of 5-way classification on mini-ImageNet and CIFAR-FS in the traditional few-shot learning setting. For the baseline methods, we obtain the results from their respective official implementations." + ], + "table_footnote": [], + "table_body": "
MethodShot per Class
12345816
SVM54.864.868.270.070.872.874.7
IbM258.266.970.271.972.774.376.1
", + "bbox": [ + 503, + 422, + 888, + 484 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/90f01a545b47ef078a4cb74b56fa6a19aaf3d08d5e8935c96f4eaa6b9e6eac94.jpg", + "table_caption": [ + "Table 4. Top-1 accuracy $(\\%)$ with different margin-based methods on ImageNet-1K classification with ViT-L/7 from MSN as the pretrained backbone." + ], + "table_footnote": [], + "table_body": "
RShot per Class
12345816
132.942.747.850.852.555.960.1
1033.743.648.551.452.956.260.3
5033.843.748.651.553.056.260.3
20034.443.848.751.553.056.260.3
40034.543.848.651.553.056.260.3
", + "bbox": [ + 514, + 549, + 877, + 652 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9faa6ef010c33c561d21df73961e02f0702ec572bfda0bad7476b29389a8b7a8.jpg", + "table_caption": [ + "Table 5. Top-1 accuracy $(\\%)$ of classification with different $R$ on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone." + ], + "table_footnote": [], + "table_body": "
Sampling SchemaShot per Class
12345816
-33.142.447.249.851.655.259.2
Spherical33.042.147.150.251.855.359.8
Ellipsoidal34.443.848.751.553.056.260.3
", + "bbox": [ + 506, + 717, + 885, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Top-1 accuracy (\\%) of classification with different sampling schemas on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone. '-' denotes the simple baseline using only the original training examples.", + "bbox": [ + 498, + 801, + 890, + 859 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28680", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ellipsoidal vs. isotropic sampling. We have described two noise sampling strategies to generate virtual examples. The ellipsoidal one is preferred over the isotropic one, and is used in IbM2. In this part, we evaluate the effectiveness of this sampling schema by experimentally comparing these two sampling strategies. The isotropic sampling strategy is denoted as Spherical in Table 6.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 6, the accuracy in the ellipsoidal sampling schema is consistently better than its spherical counterpart or the baseline. Moreover, in low-shot cases $(\\leq 3)$ , sampling with spherical Gaussian slightly degraded the recognition accuracy. The reason may be that the standard deviation of different channels calculated from training features varied a lot, thus simply regarding all channels as independent and identically distributed might make the sampled points significantly shifted from the underlying distribution. However, as the number of training samples increases, both isotropic and ellipsoidal sampling outperformed the baseline.", + "bbox": [ + 75, + 196, + 467, + 376 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Based on these observations, we chose to adopt the ellipsoidal noise sampling (Eq. 2) in IbM2.", + "bbox": [ + 76, + 378, + 467, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On what classes can IbM2 help? Finally, we study what classes will benefit from IbM2—will most or only a small portion of classes be improved by IbM2? After the training of the baseline and IbM2 finished, we calculated the class-wise validation accuracy for every class on ImageNet-1K, as", + "bbox": [ + 76, + 407, + 467, + 496 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {A C C} ^ {k} = \\frac {N _ {c o r} ^ {k}}{N _ {c l s} ^ {k}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 496, + 467, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\mathrm{ACC}^k$ is the per-class accuracy (i.e., recall) of the $k$ -th class, $N_{cls}^k$ is the number of test samples class $k$ contains ( $N_{cls}^k = 50$ in ImageNet-1K) and $N_{cor}^k$ is the number of correctly classified samples of class $k$ . For every class, we obtain the difference of per-class accuracy (that of IbM2 minus that of the baseline). A positive difference is an accuracy gain and a negative gain is in fact an accuracy loss.", + "bbox": [ + 75, + 537, + 467, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We then sort the baseline's per-class accuracy in the ascending order. Following this order, we rearrange the per-class accuracy gains. The 1000 accuracy gains are divided into 10 histogram bins in the rearranged order, and inside each bin the 100 per-class accuracy gains are averaged to obtain the accuracy gain of that bin. Fig. 3 plots the average accuracy gain in each bin.", + "bbox": [ + 75, + 643, + 467, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We find that IbM2 improves average per-class accuracy in almost every histogram bin (i.e., is above the \"0.0\" horizon in the $y$ -axis). More detailed numbers reveal that the recognition accuracy of more than $65\\%$ categories out of 1000 is improved in all shots. Furthermore, Fig. 3 shows a trend: the more accurate a class is, the higher gains IbM2 can achieve over the baseline. That is, when the task is too difficult for the baseline, IbM2 can help but its usefulness is restricted. But, when the baseline is already accurate enough (categorical subset 9 and later), the room for IbM2's", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/02cd9849b59af841bb571db21f0955ff5801327a920237f0a8f470a67f08f3ad.jpg", + "image_caption": [ + "Figure 3. Categorical accuracy gain $(\\%)$ of IbM2 compared to baseline with ViT-S/16 pre-trained by MoCov3 [10] as the backbone." + ], + "image_footnote": [], + "bbox": [ + 504, + 94, + 885, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "- further improvement is small again. It is the middle range that IbM2 is the most useful.", + "bbox": [ + 498, + 337, + 888, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions and Limitations", + "text_level": 1, + "bbox": [ + 500, + 381, + 764, + 397 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we advocated pFSL, a new practical few-shot learning setting. We also proposed IbM2, an instance-based max-margin method to improve few-shot learning. With the technological advancements, it is time to upgrade the traditional FSL settings. We need a simpler, easier-to-evaluate, more challenging and more practical FSL setting, and the proposed pFSL task satisfies these requirements.", + "bbox": [ + 498, + 407, + 890, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To address the challenges associated with the scarcity of training examples, we introduced IbM2. Instead of maximizing the class-level margin, IbM2 is instance-based margin maximization. It achieved significant improvements in both pFSL and the traditional FSL settings consistently. IbM2 is simple and reliable. It introduces only 2 hyperparameters, and the default values of them worked well in experiments across different architectures and tasks.", + "bbox": [ + 498, + 513, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As the experiments indicated, IbM2 works the best for the middle range in terms of task difficulty. In a $k$ -shot task when $k$ is extremely small, there is still considerable room for improvement in the pFSL setting. Furthermore, IbM2 freezes the backbone and only learns the linear classifier. In the future, we plan to improve the very small shot cases (e.g., $k = 1$ ) and better tune the backbone in few-shot learning to push the current limits further.", + "bbox": [ + 498, + 633, + 890, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 768, + 678, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research received substantial support from Jianxin Wu, who wrote IbM2's first working code and whose generous assistance and invaluable guidance were sincerely appreciated throughout our research process. Additionally, we acknowledge the funding provided by the National Natural Science Foundation of China under Grant 62276123 and Grant 61921006.", + "bbox": [ + 498, + 794, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28681", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Arman Afrasiyabi, Hugo Larochelle, Jean-François Lalonde, and Christian Gagné. 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In ACM International Conference on Multimedia, page 6831-6839, 2022." + ], + "bbox": [ + 501, + 92, + 890, + 316 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "28683", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_model.json b/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_model.json new file mode 100644 index 0000000000000000000000000000000000000000..29c387c5e085d4d76eebe4fe9cc1b4d05a41905e --- /dev/null +++ b/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_model.json @@ -0,0 +1,2255 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.131, + 0.806, + 0.154 + ], + "angle": 0, + "content": "Instance-based Max-margin for Practical Few-shot Recognition" + }, + { + "type": "text", + "bbox": [ + 0.152, + 0.181, + 0.817, + 0.234 + ], + "angle": 0, + "content": "Minghao Fu Ke Zhu\\* National Key Laboratory for Novel Software Technology, Nanjing University, China School of Artificial Intelligence, Nanjing University, China" + }, + { + "type": "text", + "bbox": [ + 0.288, + 0.238, + 0.678, + 0.251 + ], + "angle": 0, + "content": "fumh@lamda.nju.edu.cn, zhuk@lamda.nju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.286, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.637 + ], + "angle": 0, + "content": "In order to mimic the human few-shot learning (FSL) ability better and to make FSL closer to real-world applications, this paper proposes a practical FSL (pFSL) setting. pFSL is based on unsupervised pre-trained models (analogous to human prior knowledge) and recognizes many novel classes simultaneously. Compared to traditional FSL, pFSL is simpler in its formulation, easier to evaluate, more challenging and more practical. To cope with the rarity of training examples, this paper proposes IbM2, an instance-based max-margin method not only for the new pFSL setting, but also works well in traditional FSL scenarios. Based on the Gaussian Annulus Theorem, IbM2 converts random noise applied to the instances into a mechanism to achieve maximum margin in the many-way pFSL (or traditional FSL) recognition task. Experiments with various self-supervised pre-training methods and diverse many- or few-way FSL tasks show that IbM2 almost always leads to improvements compared to its respective baseline methods, and in most cases the improvements are significant. With both the new pFSL setting and novel IbM2 method, this paper shows that practical few-shot learning is both viable and promising." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.667, + 0.208, + 0.683 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.47, + 0.829 + ], + "angle": 0, + "content": "We human have the ability to learn new concepts based on a few exemplars, thanks to both our ability to learn and the previously accumulated knowledge. As a stark contrast, learning machines (especially deep learning models) mostly require plentiful training examples to learn just few (e.g., 5) concepts. Both the vision and learning community are fully aware of this shortcoming, and few-shot learning (FSL) is our community's effort to counter this weakness, which has been studied for a long time [39]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.47, + 0.876 + ], + "angle": 0, + "content": "FSL relies on prior knowledge, too. Currently, the setting is to set aside a collection of object categories (known as the base set), with many training examples in every base" + }, + { + "type": "image", + "bbox": [ + 0.574, + 0.286, + 0.817, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.457, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Figure 1. Instance-based max-margin. We create a hypersphere (large dashed circles) centered at every example (solid shapes), sample many virtual examples (hollow shapes) around the hypersphere, and require the decision boundary to classify all virtual samples correctly. Then we in effect achieve instance-based maxmargin. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.674 + ], + "angle": 0, + "content": "set category. A model is first pre-trained on the base set, which naturally encodes prior knowledge. Then, few novel object categories (most commonly 5) are to be recognized based on the pre-trained model given few training examples from these new concepts (e.g., 1 or 5 per category). Note that the base and novel training sets are semantically closely related (e.g., both contain different kinds of birds)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.765 + ], + "angle": 0, + "content": "There is a clear mismatch between the human ability and this FSL setting. We human can learn many instead of few novel concepts; and, the human prior knowledge include those accumulated as both common-sense and domain knowledge from many diverse domains rather than a limited set of concepts closely related to a specific task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.841 + ], + "angle": 0, + "content": "Although this FSL setting has served our community well and has pushed the technical frontier for years, with the immense advances in deep learning and emerging practical needs for real-world FSL applications, it is time that we need a better, simpler, and more practical FSL setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Hence we advocate a practical few-shot learning (or pFSL) setting: based on an unsupervised model pre-trained from a large number of concepts (e.g., ImageNet [30]), simultaneously learn many new concepts (e.g., 200) with few" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.291, + 0.901 + ], + "angle": 0, + "content": "\\(^*\\) K. Zhu is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28674" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.317, + 0.108 + ], + "angle": 0, + "content": "examples (e.g., 1 or 5 per category)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.468, + 0.233 + ], + "angle": 0, + "content": "An ImageNet pre-trained model is more analogous to human knowledge than those learned from a base set in traditional FSL, and learning many new concepts makes it more practical in applications. Without the base set, the learning phase of pFSL is simple, too. More importantly, evaluation of algorithms is difficult, complicated, and very time consuming in the current FSL setting [16], but as will be discussed later, pFSL does not suffer from this drawback." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.24, + 0.468, + 0.345 + ], + "angle": 0, + "content": "Although an ImageNet pre-trained model undoubtedly contains more prior knowledge than a base-set trained one, simultaneously learning many new concepts will inevitably make pFSL much more difficult than traditional FSL. We believe that a more challenging task will help technology advancement, too—the traditional FSL setting is already saturated to certain extent (cf. results in [22, 41])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.468, + 0.516 + ], + "angle": 0, + "content": "Hence, we propose a novel approach for pFSL: Instance-based Max-margin (IbM2), which is effective in traditional FSL, too. The max-margin idea has been shown to be effective in improving generalization. Classic methods like SVM [7] build max-margin decision boundaries with only a very small portion of the training examples (i.e., support vectors). This idea is problematic when we have both very few training examples and a very high dimensionality. Intuitively, the support vectors chosen by SVM are highly likely wrong or misleading, because a small training set leads to excessively unstable estimation [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.734 + ], + "angle": 0, + "content": "In the proposed IbM2, we achieve max-margin at the instance level, instead of at the class level as in SVM. As illustrated in Fig. 1, we create a hypersphere for every training example, with the example being the center of the hypersphere. Then, we can sample as many virtual samples as we want around this hypersphere, and assign the label of the center (original training example) to all its associated virtual examples. By finding a properly maximized radius for the hypersphere and requiring a classifier to correctly classify the virtual examples, we in effect achieve max-margin. Another benefit of IbM2 is that we do not need any special handling for multi-class recognition, while vanilla SVM is for binary classification only. In short, the contributions of this paper are twofold:" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.741, + 0.466, + 0.784 + ], + "angle": 0, + "content": "- We propose a practical few-shot learning setting (pFSL): many-way (e.g., 200-way) recognition, uses an unsupervised pre-trained model, and has no base set." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.788, + 0.468, + 0.832 + ], + "angle": 0, + "content": "- We propose IbM2, an instance-based max-margin algorithm, which suits few-shot, high dimensionality, and multi-class naturally." + }, + { + "type": "list", + "bbox": [ + 0.081, + 0.741, + 0.468, + 0.832 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "As will be shown by extensive experiments, IbM2 consistently improves both traditional FSL and the proposed pFSL. The benefits of pFSL against traditional FSL will be verified by both analyses and experiments, too." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.191 + ], + "angle": 0, + "content": "Few-shot learning aims at recognizing novel categories with the help of prior knowledge. Given the base set as prior knowledge, few-shot learning methods can be roughly divided into two types: those based on meta-learning or transfer-learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.193, + 0.892, + 0.479 + ], + "angle": 0, + "content": "Meta-learning based FSL. Meta-learning [21] learns a model through a large quantity of episodes consisting of different training and evaluation sets. Given a new task during evaluation, the model performs what it does in training to predict. In FSL, the training episodes are randomly sampled from the base set. One line of work [14, 15, 25, 31] focuses on learning general initial weights for fast adapting the model to unseen categories with a few steps of optimization. For example, [14] explicitly trains the classifier in a model-agnostic way. [25] extends meta-learning with linear predictors as a differentiable convex problem. [15] learns the task distribution from a probabilistic perspective. Another line of work [1, 11, 32, 33, 37, 42, 43] boosts meta-learning by exploring different distance metrics. For example, [32] aggregates training features to generate prototypes for different classes as the classification head. [43] leverages the Earth Mover's Distance to calculate the structural distance for classification. [1] extracts sets of features from each image to build a set-based matching schema." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Transfer-learning based FSL. This line of attack [9, 12, 27, 35, 40] leverages the idea of standard transfer learning, which first pre-trains a model on base classes and then finetunes the model weights with limited training samples from novel classes. [9] normalizes the features and classification weights and calculates their cosine distances as the logits. [27] pre-trains with manifold mixup [36] to improve robustness. [12] introduces a baseline for effectively and transductively finetuning. [40] calibrates the training distribution of a few-shot task using statistics from the base set. [35] explores learning a general representation of base classes in supervised or self-supervised ways with self-distillation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.892, + 0.813 + ], + "angle": 0, + "content": "Self-supervised learning. We stress that in pFSL the pre-trained model is unsupervised, for which the reason is to be explained in Sec. 3. Self-supervised learning (SSL) is the mainstream approach to train a deep net in the unsupervised manner. Popular SSL methods, whether applied to traditional ResNet [18] models (e.g., BYOL [17], MoCo [19] and SwAV [5]) or Vision Transformers (ViT) [13] (e.g., MSN [2], DINO [6] and MoCov3 [10]), all produce pretrained models based on large-scale datasets. In this paper, we utilize such models as our prior knowledge in FSL." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.829, + 0.825, + 0.846 + ], + "angle": 0, + "content": "3. pFSL: Practical Few-Shot Learning" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In traditional FSL, the training dataset is split into 1) the base set with \\(N_{b}\\) labeled images, denoted as \\(D_{b} = \\{(x_{i}^{b},y_{i}^{b})\\}_{i = 1}^{N_{b}}\\) where \\(y_{i}^{b}\\in \\mathcal{V}_{b}\\) is the label of instance \\(x_{i}^{b}\\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28675" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.258 + ], + "angle": 0, + "content": "\\(\\mathcal{V}_b\\) is the label space of \\(D_{b}\\) 2) the novel set with \\(N_{n}\\) labeled images, denoted as \\(D_{n} = \\{(x_{j}^{n},y_{j}^{n})\\}_{j = 1}^{N_{n}}\\) where \\(y_{j}^{n}\\in \\mathcal{V}_{n}\\) is the label of \\(x_{j}^{n}\\) and \\(\\mathcal{V}_n\\) is the label space of \\(D_{n}\\). Note that although \\(\\mathcal{V}_b\\cap \\mathcal{V}_n = \\emptyset\\), the concepts in \\(\\mathcal{V}_b\\) and \\(\\mathcal{V}_n\\) are semantically similar to each other. Then, the task is to learn a recognizer generalizing well on unknown samples from \\(\\mathcal{V}_n\\). By letting \\(N_{n}\\ll N_{b}\\), the training samples in \\(D_{n}\\) are few-shot (i.e., few training examples per class). In traditional FSL, \\(|\\mathcal{V}_b|\\) is relatively large but \\(|\\mathcal{V}_n|\\) is small. For example, in most cases \\(|\\mathcal{V}_n| = 5\\), which is called a 5-way FSL. The evaluation of traditional FSL is a rather complicated task." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.267, + 0.293, + 0.282 + ], + "angle": 0, + "content": "3.1. The pFSL Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.47, + 0.35 + ], + "angle": 0, + "content": "To make FSL simpler, more practical, and closer to human's few-shot learning capability, we propose a new practical few-shot learning (pFSL) paradigm, which is characterized by the following properties:" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.352, + 0.47, + 0.44 + ], + "angle": 0, + "content": "- Removing the base set. The prior knowledge obtained through pre-training on the base set is limited, as the base set only contains limited number of concepts. In some applications, collecting data sharing similar concepts with the novel set may be as difficult as collecting more samples for the novel set itself." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.443, + 0.469, + 0.517 + ], + "angle": 0, + "content": "- Pre-trained model based on big data. A model pretrained on a large training set containing a wide variety of concepts is analogous to the common-sense and domain knowledge our brains encode, which will be useful for few-shot learning in diverse domains." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.52, + 0.469, + 0.594 + ], + "angle": 0, + "content": "- Many-way FSL. In a \\(N\\)-way \\(k\\)-shot FSL, we seek \\(N\\) to be large and \\(k\\) to be small, e.g., using all the CUB [38] categories (\\(N = 200\\) categories and \\(k\\) is 1 or 5). This makes pFSL much closer to real-world applications than traditional FSL." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.597, + 0.469, + 0.686 + ], + "angle": 0, + "content": "- Unsupervised pre-training. In pFSL, we require the pre-training to be unsupervised. Since a large scale dataset (e.g., ImageNet) may contain the concept in few-shot learning (e.g., those birds in CUB), avoiding using the labels during pre-training is necessary to make the evaluation of FSL algorithm fairer." + }, + { + "type": "list", + "bbox": [ + 0.081, + 0.352, + 0.47, + 0.686 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.718 + ], + "angle": 0, + "content": "These properties distinguish pFSL from traditional FSL and some recent variants of it [9, 12, 22, 23, 27]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.367, + 0.743 + ], + "angle": 0, + "content": "3.2. Simplicity and Better Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.795 + ], + "angle": 0, + "content": "The pFSL framework is clearly simpler than traditional FSL, and it leads to not only benefits in the training phase, but more importantly better evaluation of FSL algorithms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Traditional \\(N\\)-way \\(k\\)-shot FSL typical use \\(N = 5\\) and \\(k = 1, 5\\), which inevitably leads to unreliable estimation of the test accuracy. Hence, the common practice is to sample a large number of \\(n\\) episodes (\\(n \\geq 500\\)), find the accuracy in each episode, and report the average accuracy \\(\\mu\\) along with its \\(95\\%\\) confidence interval \\(Z_{95\\%}\\). Note that with \\(n\\) episodes, the standard deviation \\(\\sigma\\) of the accuracy within" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "the \\( n \\) episodes is \\( \\sigma = 0.51\\sqrt{n} Z_{95\\%} \\). For example, a typical result is: average accuracy \\( 64.93\\% \\), \\( 95\\% \\) confidence interval \\( 0.18\\% \\), but the standard deviation of accuracy is \\( 9.18\\% \\) [16] (in which \\( n = 10000 \\)). In short, one single evaluation of traditional FSL requires training and testing for \\( n \\) times (\\( n \\geq 500 \\)) and the evaluation results are still unreliable. Because of the complicated setup, both learning and evaluation of traditional FSL algorithms are not only costly, but often carried out in slightly different ways, which renders the fair comparison even more difficult." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.364 + ], + "angle": 0, + "content": "As a stark contrast, pFSL is much simpler and as the experimental results will show in Table 1, the estimate of average accuracy is reliable. The standard deviation is small (mostly \\(< 1.0\\%\\)). This reliable estimation comes from the fact that pSFL is many-way (i.e., \\(N\\) is large). Hence, instead of running \\(n\\) episodes, few episodes (e.g., 3) is enough to evaluate pFSL, which not only means savings in computation, but also more reliable evaluation of algorithms." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.376, + 0.82, + 0.393 + ], + "angle": 0, + "content": "4. IbM2: Instance-based Max-margin" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.537 + ], + "angle": 0, + "content": "In pFSL, we have a pre-trained model \\(\\mathcal{M}\\) (unsupervised trained on a large set) and a novel set. There is no base set \\(D_{b}\\) any more, hence we will simply denote the novel set as \\(D = \\{x_{i},y_{i}\\}_{i = 1}^{M}\\) (that is, ignoring the subscript \\(^b\\)). The label set of \\(D\\) is \\(\\mathcal{V}\\). In an \\(N\\)-way \\(k\\)-shot pFSL task, we have \\(|\\mathcal{V}| = N\\) and there will be \\(k\\) training examples in each of the \\(N\\) novel classes, hence \\(M = kN\\). Note that we expect \\(|\\mathcal{V}| = N\\) to be large (i.e., many-way FSL) and \\(k\\) to be small (e.g., 1 or 5)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.546, + 0.753, + 0.563 + ], + "angle": 0, + "content": "4.1. Generating Virtual Samples" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.659 + ], + "angle": 0, + "content": "Since \\( k \\) (the number of training images in each class) is still small but the number of classes (\\( N \\)) becomes much larger (e.g., from 5 in traditional FSL to 200 in pFSL), we expect that the challenge in learning a pFSL model is greater than that in traditional FSL. This is verified by our experiments (cf. the results in Table 1 vs. those in Table 3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Virtual examples, or examples that are sampled based on the original training examples, have been repeatedly proven useful when the number of training examples is small, e.g., in traditional few-shot learning [40] or long-tailed recognition (where the tail classes have few training images) [20]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.736, + 0.892, + 0.825 + ], + "angle": 0, + "content": "The common idea in generating virtual samples is to make the virtual samples follow the underlying distributions of the classes. However, in few-shot learning this requirement is very difficult to entertain even with the help of techniques such as distribution calibration (DC) in [40], because there is only 1 or 5 examples per class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In contrast, we do not try to sample from any underlying distribution, but try to achieve max-margin of the decision boundary, as illustrated in Fig. 1. Specifically, for every training instance \\( x_{i} \\), we i.i.d. generate \\( R \\) virtual samples \\( x_{i,r} \\) (\\( 1 \\leq r \\leq R \\)) which distribute around the shell of the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28676" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "hypersphere centered at \\( x_{i} \\) and whose radius is controlled by a parameter \\( \\epsilon \\). Note that the same \\( \\epsilon \\) is shared by all training examples \\( x_{i} \\) (\\( 1 \\leq i \\leq kN \\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.468, + 0.257 + ], + "angle": 0, + "content": "Technically, let \\( z_{i} \\) be the feature vector produced by the pre-trained model \\( \\mathcal{M} \\): \\( z_{i} = \\mathcal{M}(x_{i}) \\) from a forward calculation. Then, a noise vector \\( \\delta_{i,r} \\) is randomly sampled from the standard multi-dimensional normal distribution \\( N(0, I_d) \\), where \\( d \\) is the length of \\( z_{i} \\) and \\( I_{d} \\) is a \\( d \\times d \\) identity matrix. By adding a scaled version of the noise vector to the \\( i \\)-th training example, we obtain \\( z_{i,r} \\) (the \\( r \\)-th virtual example for \\( x_{i} \\)):" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.258, + 0.468, + 0.273 + ], + "angle": 0, + "content": "\\[\nz _ {i, r} = z _ {i} + \\epsilon \\delta_ {i, r}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.28, + 0.468, + 0.311 + ], + "angle": 0, + "content": "Its label \\( y_{i,r} \\) is \\( y_{i} \\) (the label of \\( x_{i} \\)) and \\( \\epsilon \\) is a positive number. Interesting properties exist in our virtual examples:" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.312, + 0.468, + 0.342 + ], + "angle": 0, + "content": "- Hypersphere for different training examples can overlap, so long as they belong to the same class (cf. Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.343, + 0.468, + 0.373 + ], + "angle": 0, + "content": "- We require the virtual examples to be correctly classified, or, the original training examples are discarded." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.375, + 0.468, + 0.539 + ], + "angle": 0, + "content": "- The virtual examples lie around the shell, not the interior of the hypersphere. According to the Gaussian Annulus Theorem [4], almost all the probability of a high-dimensional spherical Gaussian with unit variance is concentrated in a thin annulus of width \\(O(1)\\) with radius \\(\\sqrt{d}\\) when \\(d\\) is large. Since \\(d\\) is indeed large (e.g., \\(d = 2048\\)), the virtual examples reside around the shell. Hence, if we maximize the radius parameter \\(\\epsilon\\) but require that the virtual examples are correctly classified, as Fig. 1 shows, we in essence achieve margin maximization in an instance-based manner." + }, + { + "type": "list", + "bbox": [ + 0.081, + 0.312, + 0.468, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.542, + 0.468, + 0.572 + ], + "angle": 0, + "content": "Hence, the proposed method is named Instance-based Max-margin, abbreviated as IbM2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.334, + 0.597 + ], + "angle": 0, + "content": "4.2. Ellipsoidal Noise Generation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.605, + 0.468, + 0.679 + ], + "angle": 0, + "content": "One issue with the above isotropic noise sampling is that it ignores the structural property of the training examples. For instance, if the ranges for two feature dimensions are \\([-1, 1]\\) and \\([-100, 100]\\), respectively, isotropic sampling is clearly unsuitable." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.681, + 0.468, + 0.756 + ], + "angle": 0, + "content": "To overcome this drawback, we calculate a range vector \\( s = (s_1, s_2, \\ldots, s_d) \\) using all the original training examples regardless of the class label, where \\( s_i \\) is the sample standard deviation for the \\( i \\)-th dimension. Then, the IbM2 virtual examples are generated as (replacing Eq. 1)" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.768, + 0.468, + 0.784 + ], + "angle": 0, + "content": "\\[\nz _ {i, r} = z _ {i} + \\epsilon (s \\odot \\delta_ {i, r}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.468, + 0.855 + ], + "angle": 0, + "content": "where \\( \\odot \\) is element-wise multiplication. The final virtual example generation process is illustrated in Fig. 2. Note that estimating \\( s \\) is dramatically easier than estimating the underlying distribution of every novel class." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "It is worth noting that this ellipsoidal noise generation is unsupervised, which distinguishes itself from Distribution calibration (DC) [40]. DC samples virtual examples based" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.1, + 0.86, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.281, + 0.892, + 0.338 + ], + "angle": 0, + "content": "Figure 2. Virtual example generation. Original input images pass through the pre-trained model \\(\\mathcal{M}\\) to get feature vectors (solid rectangles). Then, every feature vector i.i.d. samples \\(R\\) virtual examples (\\(R = 2\\) here) using Eq. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.892, + 0.44 + ], + "angle": 0, + "content": "on an estimated covariance structure, which is estimated from the few novel class training examples in a sample-wise manner and calibrated using the base set. As aforementioned, we argue that it makes sense to get rid of the dependency on a base set, then DC is not applicable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.546 + ], + "angle": 0, + "content": "More importantly, the reliability of this estimation of a dense covariance matrix is understandably much lower than our estimation of the range indicator vector \\( s \\) — we estimate \\( d \\) values using \\( k \\times N \\) examples, while DC estimates \\( d \\times d \\) values using only 1 example and the base set. The base set calibration will help DC, but clearly its estimation is still unreliable, as shown by experiments in [40, 44]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.557, + 0.874, + 0.573 + ], + "angle": 0, + "content": "4.3. Binary Search to Find the Largest Possible \\(\\epsilon\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.891, + 0.639 + ], + "angle": 0, + "content": "Obviously we want \\(\\epsilon\\) to be as large as possible to achieve max-margin, under the condition that virtual examples are classified correctly. Hence, we design a simple binary search to find the optimal value for \\(\\epsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.79 + ], + "angle": 0, + "content": "For any given \\(\\epsilon\\) value, we can generate \\(kNR\\) virtual examples \\((x_{i,r},y_{i,r})\\) \\((1\\leq i\\leq kN,1\\leq r\\leq R)\\) using Eq. 2. We denote the virtual training set for this particular value of \\(\\epsilon\\) as \\(D^{\\epsilon}\\). Then, we train a linear classifier with parameters \\(W\\) to classify \\(D^{\\epsilon}\\) and obtain the training accuracy. If the training accuracy is too high (larger than a threshold \\(T\\)), \\(\\epsilon\\) is enlarged; otherwise \\(\\epsilon\\) is shrunk. The binary search maintains a search range, when the search range is tight enough (when the range is less than 0.05 in Algorithm 1), the search terminates, and we have found the optimal value \\(\\hat{\\epsilon}\\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.792, + 0.747, + 0.806 + ], + "angle": 0, + "content": "We have a few notes for finding \\(\\hat{\\epsilon}\\):" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.808, + 0.84, + 0.822 + ], + "angle": 0, + "content": "- Unlike DC [40], we do not need a validation set." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.824, + 0.892, + 0.884 + ], + "angle": 0, + "content": "- The threshold \\( T \\) does not need to be 1 (100%). In SVM learning, the slack variable trick allows some support vectors not to have max-margin. Similarly, we just need \\( T \\) to be close to 1 (0.9 in our experiments)." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "- Different from classic augmentation techniques [26, 28]," + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.808, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28677" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.081, + 0.092, + 0.353, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Pseudo code for searching \\(\\epsilon\\)" + }, + { + "type": "code", + "bbox": [ + 0.078, + 0.117, + 0.452, + 0.341 + ], + "angle": 0, + "content": "Inputs: \nx : training features of a few-shot task \ny : training labels of a few-shot task \nR : sampling times for an instance \nT : accuracy threshold for searching \nOutputs: \neps : epsilon for sampling \nleft = 0.0 \nright = a large value \neps = right / 2 \nW = initclassifier \nwhile True: \n acc = train_and.eval(W, x, y, eps, R) \n if acc > T: \n left = eps # increase epsilon \n else: \n right = eps # decrease epsilon \n eps = (left + right) / 2.0 \n if right - left < 0.05: \n break" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.375, + 0.468, + 0.42 + ], + "angle": 0, + "content": "which introduce minor disturbance into input features, the distribution of \\( D^{\\hat{\\epsilon}} \\) is drastically different from \\( D \\) because of a large \\( \\hat{\\epsilon} \\) (empirically 1.24 on average)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.422, + 0.468, + 0.482 + ], + "angle": 0, + "content": "Finally, the IbM2 pipeline is simple: First, use Algorithm 1 to find \\(\\hat{\\epsilon}\\). Second, generate the virtual dataset \\(D^{\\hat{\\epsilon}}\\). And third, learn a linear classifier \\(W\\). Note that the pretrained model \\(\\mathcal{M}\\) is frozen and will not be updated." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.495, + 0.282, + 0.511 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.52, + 0.468, + 0.58 + ], + "angle": 0, + "content": "We evaluate our IbM2 method on both setups: the proposed pFSL in many-way few-shot scenario, and also comparing IbM2 under the traditional FSL few-way setting with state-of-the-art FSL methods to further validate its effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.59, + 0.294, + 0.605 + ], + "angle": 0, + "content": "5.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.733 + ], + "angle": 0, + "content": "For both the searching and training stages of IbM2, all features extracted by the backbone \\(\\mathcal{M}\\) were \\(L2\\)-normalized first. When learning the classification head (both during the binary search and after \\(\\hat{\\epsilon}\\) was determined), we used Adam as the optimizer and the label smoothed cross-entropy loss [34] as the learning objective. The pre-trained model was trained using various self-supervised learning methods on the ImageNet-1K [30] training set." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.733, + 0.468, + 0.793 + ], + "angle": 0, + "content": "During the binary search, for all the experiments we will report, we always set \\( R \\) as 200, \\( T \\) as 0.9 in pFSL and 0.999 in the traditional FSL setting, except when we carried out ablation experiments on these hyperparameters." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.794, + 0.468, + 0.809 + ], + "angle": 0, + "content": "Full implementation details are included in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.818, + 0.365, + 0.833 + ], + "angle": 0, + "content": "5.2. Experiments in the pFSL Setting" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Datasets and Evaluation Setup. We explored two common many-way classification datasets, ImageNet-1K [30] and CUB-200-2011 (CUB) [38]. ImageNet-1K contains about 1.28 million training images from 1,000 classes and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "50,000 images for evaluation. CUB is a fine-grained recognition dataset composed of 11,788 images belonging to 200 classes of birds, 5,994 for training and 5,794 for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.138, + 0.892, + 0.228 + ], + "angle": 0, + "content": "For both datasets, we randomly sampled the training sets for pFSL by selecting \\( k \\) images from every class (i.e., \\( k \\)-shot) and using all the classes (1000 and 200, respectively) to form the novel set. \\( k \\) is chosen from \\( \\{1, 2, 3, 4, 5, 8, 16\\} \\). The evaluation was carried out on the full validation (for ImageNet) or test (for CUB) set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Utilizing various self-supervised backbone network \\(\\mathcal{M}\\) pre-trained on ImageNet, we compare two sets of results: one in which the linear classifier was obtained by using the original training set, the other by using IbM2's virtual examples. We report the top-1 accuracy and its standard deviation computed over 3 randomly sampled novel sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Main Results. As the results in Table 1 suggest, we evaluated on two types of backbones: Vision Transformer (ViT) [13] and ResNet50 [18]. The pre-training methods included DINO [6], MoCov3 [10], MSN [2], SimCLR [8] and BYOL [17]. Table 1 shows that in almost all cases, IbM2 benefited the few-shot learning process and improved the top-1 accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.516 + ], + "angle": 0, + "content": "When the number of shots \\((k)\\) is very small \\((\\leq 2)\\), the improvement of IbM2 over the baseline is roughly \\(1\\%\\) on average. However, as the number of training shots goes larger, it is clear that the level of accuracy improvement increases gradually from \\(\\sim 1\\%\\) to \\(\\sim 2\\%\\), even \\(>3\\%\\) in some cases." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.518, + 0.892, + 0.578 + ], + "angle": 0, + "content": "A useful observation from these results is that in pFSL, both the baseline and IbM2 have small standard deviations, that is, more robust in evaluation. Hence, we do not need 500 episodes in pFSL any longer—3 is enough." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.745 + ], + "angle": 0, + "content": "Semi-supervised learning. In the self-supervised learning literature, it is a common practice to use ImageNet-1K training images to learn a backbone in the unsupervised manner, then use a small portion (e.g., \\(1\\%\\)) of the training data now with labels to train a classifier. This semi-supervised learning task can also be viewed as our pFSL setting. Hence, we also report the \\(1\\%\\) ImageNet-1K semi-supervised learning (on average 12 labeled training images per class) results in Table 2. IbM2 consistently improved various self-supervised models and backbone architectures in all cases, with \\(0.8\\%\\) to \\(2.9\\%\\) top-1 accuracy increase." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.869, + 0.772 + ], + "angle": 0, + "content": "5.3. Experiments in the Traditional FSL Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets and Evaluation Setup. We evaluated IbM2 in the traditional FSL setup, too. We conducted experiments on two standard benchmark datasets, mini-ImageNet [37] and CIFAR-FS [3]. mini-ImageNet consists of 100 categories selected from ImageNet-1K, which are further split into 64 base, 16 val and 20 novel categories according to [29]. CIFAR-FS is created by randomly shuffling the 100 categories of CIFAR-100 [24] into 64 base, 16 val, 20 novel" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28678" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.142, + 0.088, + 0.832, + 0.364 + ], + "angle": 0, + "content": "
DatasetPre-training MethodBackboneIbM2Shot per Class
12345816
ImageNet-1KDINOViT-S/16✓39.2 ± 0.349.2 ± 0.254.1 ± 0.456.7 ± 0.258.0 ± 0.160.4 ± 0.162.7 ± 0.1
39.2 ± 0.349.4 ± 0.354.6 ± 0.457.6 ± 0.159.3 ± 0.162.4 ± 0.265.8 ± 0.1
MoCov3ViT-S/16✓32.7 ± 0.642.0 ± 0.246.9 ± 0.349.6 ± 0.451.0 ± 0.153.8 ± 0.156.6 ± 0.2
33.9 ± 0.643.2 ± 0.248.4 ± 0.351.3 ± 0.352.8 ± 0.256.1 ± 0.159.8 ± 0.2
MSNViT-S/16✓47.9 ± 0.156.2 ± 0.459.8 ± 0.361.6 ± 0.162.4 ± 0.264.4 ± 0.366.1 ± 0.1
47.8 ± 0.256.4 ± 0.460.5 ± 0.262.5 ± 0.263.6 ± 0.266.0 ± 0.268.4 ± 0.0
ViT-B/4✓53.2 ± 0.264.5 ± 0.468.9 ± 0.270.9 ± 0.272.0 ± 0.373.8 ± 0.175.0 ± 0.2
54.0 ± 0.164.9 ± 0.569.4 ± 0.271.4 ± 0.172.7 ± 0.474.7 ± 0.076.4 ± 0.2
ViT-L/7✓57.3 ± 0.466.5 ± 0.469.8 ± 0.571.6 ± 0.472.2 ± 0.273.8 ± 0.175.1 ± 0.1
57.7 ± 0.466.6 ± 0.570.1 ± 0.671.8 ± 0.472.6 ± 0.274.3 ± 0.176.0 ± 0.0
SimCLRResNet50✓21.4 ± 0.430.3 ± 0.136.1 ± 0.339.8 ± 0.242.0 ± 0.146.8 ± 0.151.9 ± 0.0
23.6 ± 0.433.4 ± 0.239.0 ± 0.442.0 ± 0.344.2 ± 0.148.0 ± 0.052.7 ± 0.0
BYOLResNet50✓26.5 ± 0.335.7 ± 0.241.5 ± 0.445.1 ± 0.247.2 ± 0.151.8 ± 0.157.1 ± 0.1
27.5 ± 0.337.5 ± 0.143.3 ± 0.446.8 ± 0.249.1 ± 0.153.2 ± 0.158.0 ± 0.1
CUBDINOViT-S/16✓35.4 ± 1.249.0 ± 0.556.8 ± 0.860.8 ± 0.765.2 ± 0.970.6 ± 0.975.9 ± 0.3
36.2 ± 1.449.6 ± 0.657.4 ± 1.062.0 ± 0.666.4 ± 0.872.5 ± 0.879.0 ± 0.2
MSNViT-S/16✓32.1 ± 1.645.0 ± 0.653.1 ± 0.656.7 ± 0.161.4 ± 0.567.3 ± 0.073.6 ± 0.4
33.0 ± 1.445.8 ± 0.753.2 ± 0.957.1 ± 0.462.0 ± 1.068.4 ± 0.175.7 ± 0.2
ViT-L/7✓34.9 ± 1.349.4 ± 0.458.8 ± 0.862.7 ± 0.967.2 ± 0.373.8 ± 0.880.4 ± 0.2
37.5 ± 1.250.1 ± 0.559.0 ± 0.862.6 ± 0.567.5 ± 0.673.9 ± 0.481.0 ± 0.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.372, + 0.895, + 0.415 + ], + "angle": 0, + "content": "Table 1. Average of top-1 accuracy (%) with standard deviation across 3 random subsets on ImageNet-1K and CUB. A √ in the column IbM2 denotes the proposed IbM2 method, or the baseline method if it is blank. Those IbM2 results that are at least 0.5% higher than the baseline are shown in boldface." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.438, + 0.416, + 0.678 + ], + "angle": 0, + "content": "
Pre-training MethodBackboneIbM2Top 1
DINOViT-S/16✓62.5
65.0
MoCov3ViT-S/16✓56.0
58.9
MSNViT-S/16✓65.9
67.9
ViT-B/4✓74.9
76.1
ViT-L/7✓74.8
75.6
SimCLRResNet50✓50.5
51.3
BYOLResNet50✓55.7
56.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.688, + 0.472, + 0.732 + ], + "angle": 0, + "content": "Table 2. Top-1 accuracy (\\%) of \\(1\\%\\) ImageNet-1K semi-supervised learning. The training set contains on average 12 labeled training samples per category." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "categories. Note that in order to perform traditional few-shot learning, only the novel split of these two datasets is required to sample many 5-way 1/5-shot episodes. We report the metrics mentioned in [16]: the average \\((\\mathrm{ACC}_m)\\), worst-case \\((\\mathrm{ACC}_1)\\), average of worst 10 \\((\\mathrm{ACC}_{10})\\), average of worst 100 \\((\\mathrm{ACC}_{100})\\) episodes' accuracy, and the standard deviation \\((\\sigma)\\) over 500 episodes for comprehensive evaluation. To make the results more reliable, we average the value of each metric from 5 runs with different" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.486 + ], + "angle": 0, + "content": "random seeds. We adopted PMF [22], \\( S2M2_{R} \\) [27] and Meta-Baseline [11] as the pre-training or meta-training approaches to obtain the backbone weights out of the base set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.893, + 0.577 + ], + "angle": 0, + "content": "Main Results. As shown in Table 3, by plugging IbM2 in during classifier learning, the proposed IbM2 improved the average accuracy \\(\\mathrm{ACC}_m\\) in all cases except only 1 result. And, the standard deviation \\(\\sigma\\) was reduced by IbM2 or remain unchanged in all cases. As [16] advocated, smaller \\(\\sigma\\) means the learning process is more stable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.895, + 0.729 + ], + "angle": 0, + "content": "[16] also advocates the worst-case episode's accuracy is more important than the average accuracy among all episodes. Table 3 shows that IbM2 almost always leads to higher worst-case \\((\\mathrm{ACC}_1)\\) or near-worst-case \\((\\mathrm{ACC}_{10},\\) \\(\\mathrm{ACC}_{100})\\) accuracy. Furthermore, the average gain of \\(\\mathrm{ACC}_m\\) is \\(0.4\\%\\) , which is far less than that of \\(\\mathrm{ACC}_1\\) \\((1.3\\%)\\) .As for \\(\\mathrm{ACC}_{10}\\) and \\(\\mathrm{ACC}_{100}\\) , their gains are very similar, both around \\(0.5\\%\\) . These observations demonstrate that IbM2 can boost the recognition accuracy of few-shot learning in almost every scenario, especially the worst case one." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.895, + 0.775 + ], + "angle": 0, + "content": "At last, by comparing the numbers in Tables 1 and 3, pFSL is more challenging than traditional FSL, which leads to more open questions to solve." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.666, + 0.801 + ], + "angle": 0, + "content": "5.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We performed ablation studies for IbM2 in the pFSL setting on ImageNet-1K." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Instance-based vs. class-based max-margin. IbM2 seeks max-margin through an instance-based manner. In this study, we compare this instance-based max-margin with the well-known support vector machine (SVM), which" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28679" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.139, + 0.088, + 0.833, + 0.362 + ], + "angle": 0, + "content": "
DatasetPre-training & Meta-trainingBackboneIbM21-shot5-shot
ACCmσACC1ACC10ACC100ACCmσACC1ACC10ACC100
mini-ImageNetPMFViT-S/16✓93.46.161.372.483.498.41.887.791.495.6
94.45.663.274.785.198.61.886.191.395.9
ViT-B/16✓94.95.466.975.586.098.81.689.192.996.3
95.65.169.677.687.198.91.689.393.096.3
ResNet50✓94.95.367.275.286.398.51.789.391.995.8
95.35.266.174.686.998.81.689.392.796.3
S2M2RWRN-28-10✓65.410.032.039.350.782.37.152.062.571.8
65.810.032.540.551.182.97.053.363.372.3
Meta-BaselineResNet12✓62.910.426.734.347.479.07.554.758.067.9
63.010.232.335.647.979.57.354.958.568.7
CIFAR-FSPMFViT-S/16✓87.98.351.761.774.895.54.274.781.888.5
89.08.159.264.175.995.74.273.381.788.7
ViT-B/16✓89.88.155.264.876.896.04.173.182.289.2
90.38.058.965.577.496.04.174.181.889.2
ResNet50✓81.710.435.251.665.891.35.571.275.182.7
82.310.336.351.166.591.65.373.376.083.2
S2M2RWRN-28-10✓75.210.844.046.759.287.77.154.767.976.8
75.510.842.445.559.287.77.054.968.177.0
Meta-BaselineResNet12✓72.711.632.042.956.184.87.554.765.173.6
72.311.532.842.355.785.17.556.365.474.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.372, + 0.892, + 0.401 + ], + "angle": 0, + "content": "Table 3. Results of 5-way classification on mini-ImageNet and CIFAR-FS in the traditional few-shot learning setting. For the baseline methods, we obtain the results from their respective official implementations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.469, + 0.518 + ], + "angle": 0, + "content": "achieves max-margin in a class-based manner. We experimented with SVM using the linear kernel function in the LIBSVM [7] software package. By iterating the value of SVM's regularization hyperparameter \\( C \\) from the set \\( \\{0.1, 1, 10, 100, 1000\\} \\), we found the best accuracy among them to compare with our IbM2 method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.469, + 0.641 + ], + "angle": 0, + "content": "As shown in Table 4, the proposed IbM2 method outperforms SVM with the best \\( C \\) by a significant margin in all cases. Specifically, the recognition accuracy improves \\( \\sim 2\\% \\) on average, and even up to \\( \\sim 4\\% \\) in the extremely scarce 1-shot case. These results demonstrate that our instance-based margin generated by IbM2 helps more to learn a robust classification boundary, especially when the training distribution is drastically shifted." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.469, + 0.779 + ], + "angle": 0, + "content": "Sensitivity of \\( R \\). As described in Sec. 4, one original training example is turned into \\( R \\) virtual examples to form the training set \\( D^{\\hat{\\epsilon}} \\). In this part, we study the effect of the hyperparameter \\( R \\). As shown in Table 5, when the training shots are highly limited, increasing \\( R \\) significantly improves recognition accuracy. As the number of training shots gets larger, the accuracy difference between a large \\( R \\) (\\( R = 400 \\)) and a small one (\\( R = 1 \\)) gradually decreases from \\( 1.6\\% \\) to \\( 0.2\\% \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.903 + ], + "angle": 0, + "content": "When training samples are extremely scarce, it is difficult to model the correct Gaussian distribution with a few samples in a high-dimensional space. Therefore, increasing \\( R \\) is necessary for a good estimation. When more training shots are available, the need for a large value of sampling times is reduced, hence the accuracy difference between different \\( R \\) becomes smaller, too. Based on these results, we let \\( R = 200 \\) in all our experiments." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.424, + 0.89, + 0.485 + ], + "angle": 0, + "content": "
MethodShot per Class
12345816
SVM54.864.868.270.070.872.874.7
IbM258.266.970.271.972.774.376.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.494, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Table 4. Top-1 accuracy \\((\\%)\\) with different margin-based methods on ImageNet-1K classification with ViT-L/7 from MSN as the pretrained backbone." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.55, + 0.878, + 0.653 + ], + "angle": 0, + "content": "
RShot per Class
12345816
132.942.747.850.852.555.960.1
1033.743.648.551.452.956.260.3
5033.843.748.651.553.056.260.3
20034.443.848.751.553.056.260.3
40034.543.848.651.553.056.260.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.663, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Table 5. Top-1 accuracy \\((\\%)\\) of classification with different \\(R\\) on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.718, + 0.886, + 0.793 + ], + "angle": 0, + "content": "
Sampling SchemaShot per Class
12345816
-33.142.447.249.851.655.259.2
Spherical33.042.147.150.251.855.359.8
Ellipsoidal34.443.848.751.553.056.260.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.803, + 0.892, + 0.86 + ], + "angle": 0, + "content": "Table 6. Top-1 accuracy (\\%) of classification with different sampling schemas on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone. '-' denotes the simple baseline using only the original training examples." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28680" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.197 + ], + "angle": 0, + "content": "Ellipsoidal vs. isotropic sampling. We have described two noise sampling strategies to generate virtual examples. The ellipsoidal one is preferred over the isotropic one, and is used in IbM2. In this part, we evaluate the effectiveness of this sampling schema by experimentally comparing these two sampling strategies. The isotropic sampling strategy is denoted as Spherical in Table 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.468, + 0.377 + ], + "angle": 0, + "content": "As shown in Table 6, the accuracy in the ellipsoidal sampling schema is consistently better than its spherical counterpart or the baseline. Moreover, in low-shot cases \\((\\leq 3)\\), sampling with spherical Gaussian slightly degraded the recognition accuracy. The reason may be that the standard deviation of different channels calculated from training features varied a lot, thus simply regarding all channels as independent and identically distributed might make the sampled points significantly shifted from the underlying distribution. However, as the number of training samples increases, both isotropic and ellipsoidal sampling outperformed the baseline." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.468, + 0.409 + ], + "angle": 0, + "content": "Based on these observations, we chose to adopt the ellipsoidal noise sampling (Eq. 2) in IbM2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.468, + 0.497 + ], + "angle": 0, + "content": "On what classes can IbM2 help? Finally, we study what classes will benefit from IbM2—will most or only a small portion of classes be improved by IbM2? After the training of the baseline and IbM2 finished, we calculated the class-wise validation accuracy for every class on ImageNet-1K, as" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.497, + 0.468, + 0.532 + ], + "angle": 0, + "content": "\\[\n\\mathrm {A C C} ^ {k} = \\frac {N _ {c o r} ^ {k}}{N _ {c l s} ^ {k}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.468, + 0.645 + ], + "angle": 0, + "content": "where \\(\\mathrm{ACC}^k\\) is the per-class accuracy (i.e., recall) of the \\(k\\)-th class, \\(N_{cls}^k\\) is the number of test samples class \\(k\\) contains (\\(N_{cls}^k = 50\\) in ImageNet-1K) and \\(N_{cor}^k\\) is the number of correctly classified samples of class \\(k\\). For every class, we obtain the difference of per-class accuracy (that of IbM2 minus that of the baseline). A positive difference is an accuracy gain and a negative gain is in fact an accuracy loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.468, + 0.75 + ], + "angle": 0, + "content": "We then sort the baseline's per-class accuracy in the ascending order. Following this order, we rearrange the per-class accuracy gains. The 1000 accuracy gains are divided into 10 histogram bins in the rearranged order, and inside each bin the 100 per-class accuracy gains are averaged to obtain the accuracy gain of that bin. Fig. 3 plots the average accuracy gain in each bin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We find that IbM2 improves average per-class accuracy in almost every histogram bin (i.e., is above the \"0.0\" horizon in the \\(y\\)-axis). More detailed numbers reveal that the recognition accuracy of more than \\(65\\%\\) categories out of 1000 is improved in all shots. Furthermore, Fig. 3 shows a trend: the more accurate a class is, the higher gains IbM2 can achieve over the baseline. That is, when the task is too difficult for the baseline, IbM2 can help but its usefulness is restricted. But, when the baseline is already accurate enough (categorical subset 9 and later), the room for IbM2's" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.095, + 0.887, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.268, + 0.892, + 0.308 + ], + "angle": 0, + "content": "Figure 3. Categorical accuracy gain \\((\\%)\\) of IbM2 compared to baseline with ViT-S/16 pre-trained by MoCov3 [10] as the backbone." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.338, + 0.89, + 0.367 + ], + "angle": 0, + "content": "- further improvement is small again. It is the middle range that IbM2 is the most useful." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.382, + 0.765, + 0.398 + ], + "angle": 0, + "content": "6. Conclusions and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.408, + 0.891, + 0.514 + ], + "angle": 0, + "content": "In this paper, we advocated pFSL, a new practical few-shot learning setting. We also proposed IbM2, an instance-based max-margin method to improve few-shot learning. With the technological advancements, it is time to upgrade the traditional FSL settings. We need a simpler, easier-to-evaluate, more challenging and more practical FSL setting, and the proposed pFSL task satisfies these requirements." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.514, + 0.892, + 0.634 + ], + "angle": 0, + "content": "To address the challenges associated with the scarcity of training examples, we introduced IbM2. Instead of maximizing the class-level margin, IbM2 is instance-based margin maximization. It achieved significant improvements in both pFSL and the traditional FSL settings consistently. IbM2 is simple and reliable. It introduces only 2 hyperparameters, and the default values of them worked well in experiments across different architectures and tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.635, + 0.892, + 0.756 + ], + "angle": 0, + "content": "As the experiments indicated, IbM2 works the best for the middle range in terms of task difficulty. In a \\( k \\)-shot task when \\( k \\) is extremely small, there is still considerable room for improvement in the pFSL setting. Furthermore, IbM2 freezes the backbone and only learns the linear classifier. In the future, we plan to improve the very small shot cases (e.g., \\( k = 1 \\)) and better tune the backbone in few-shot learning to push the current limits further." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.679, + 0.788 + ], + "angle": 0, + "content": "7. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This research received substantial support from Jianxin Wu, who wrote IbM2's first working code and whose generous assistance and invaluable guidance were sincerely appreciated throughout our research process. Additionally, we acknowledge the funding provided by the National Natural Science Foundation of China under Grant 62276123 and Grant 61921006." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28681" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Arman Afrasiyabi, Hugo Larochelle, Jean-François Lalonde, and Christian Gagné. Matching feature sets for few-shot image classification. 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In ACM International Conference on Multimedia, page 6831-6839, 2022." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "28683" + } + ] +] \ No newline at end of file diff --git a/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_origin.pdf b/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..07fa101bc6dad1f5fce89a793e340d66d6c1a450 --- /dev/null +++ b/2024/Instance-based Max-margin for Practical Few-shot Recognition/661d9576-3318-460a-b4ae-7562837e1a63_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:96ea1c4d57c15fd83f173e874a27add64008657109d80d42fda34abc71949e7a +size 460827 diff --git a/2024/Instance-based Max-margin for Practical Few-shot Recognition/full.md b/2024/Instance-based Max-margin for Practical Few-shot Recognition/full.md new file mode 100644 index 0000000000000000000000000000000000000000..6fddd1560ede413e742c2ab9ff6d2f0bfbc9b35d --- /dev/null +++ b/2024/Instance-based Max-margin for Practical Few-shot Recognition/full.md @@ -0,0 +1,337 @@ +# Instance-based Max-margin for Practical Few-shot Recognition + +Minghao Fu Ke Zhu\* National Key Laboratory for Novel Software Technology, Nanjing University, China School of Artificial Intelligence, Nanjing University, China + +fumh@lamda.nju.edu.cn, zhuk@lamda.nju.edu.cn + +# Abstract + +In order to mimic the human few-shot learning (FSL) ability better and to make FSL closer to real-world applications, this paper proposes a practical FSL (pFSL) setting. pFSL is based on unsupervised pre-trained models (analogous to human prior knowledge) and recognizes many novel classes simultaneously. Compared to traditional FSL, pFSL is simpler in its formulation, easier to evaluate, more challenging and more practical. To cope with the rarity of training examples, this paper proposes IbM2, an instance-based max-margin method not only for the new pFSL setting, but also works well in traditional FSL scenarios. Based on the Gaussian Annulus Theorem, IbM2 converts random noise applied to the instances into a mechanism to achieve maximum margin in the many-way pFSL (or traditional FSL) recognition task. Experiments with various self-supervised pre-training methods and diverse many- or few-way FSL tasks show that IbM2 almost always leads to improvements compared to its respective baseline methods, and in most cases the improvements are significant. With both the new pFSL setting and novel IbM2 method, this paper shows that practical few-shot learning is both viable and promising. + +# 1. Introduction + +We human have the ability to learn new concepts based on a few exemplars, thanks to both our ability to learn and the previously accumulated knowledge. As a stark contrast, learning machines (especially deep learning models) mostly require plentiful training examples to learn just few (e.g., 5) concepts. Both the vision and learning community are fully aware of this shortcoming, and few-shot learning (FSL) is our community's effort to counter this weakness, which has been studied for a long time [39]. + +FSL relies on prior knowledge, too. Currently, the setting is to set aside a collection of object categories (known as the base set), with many training examples in every base + +![](images/5e0878b4d1552db5a5882964b262b35758656d28cb75f934f29ab4bccf97a450.jpg) +Figure 1. Instance-based max-margin. We create a hypersphere (large dashed circles) centered at every example (solid shapes), sample many virtual examples (hollow shapes) around the hypersphere, and require the decision boundary to classify all virtual samples correctly. Then we in effect achieve instance-based maxmargin. Best viewed in color. + +set category. A model is first pre-trained on the base set, which naturally encodes prior knowledge. Then, few novel object categories (most commonly 5) are to be recognized based on the pre-trained model given few training examples from these new concepts (e.g., 1 or 5 per category). Note that the base and novel training sets are semantically closely related (e.g., both contain different kinds of birds). + +There is a clear mismatch between the human ability and this FSL setting. We human can learn many instead of few novel concepts; and, the human prior knowledge include those accumulated as both common-sense and domain knowledge from many diverse domains rather than a limited set of concepts closely related to a specific task. + +Although this FSL setting has served our community well and has pushed the technical frontier for years, with the immense advances in deep learning and emerging practical needs for real-world FSL applications, it is time that we need a better, simpler, and more practical FSL setting. + +Hence we advocate a practical few-shot learning (or pFSL) setting: based on an unsupervised model pre-trained from a large number of concepts (e.g., ImageNet [30]), simultaneously learn many new concepts (e.g., 200) with few + +examples (e.g., 1 or 5 per category). + +An ImageNet pre-trained model is more analogous to human knowledge than those learned from a base set in traditional FSL, and learning many new concepts makes it more practical in applications. Without the base set, the learning phase of pFSL is simple, too. More importantly, evaluation of algorithms is difficult, complicated, and very time consuming in the current FSL setting [16], but as will be discussed later, pFSL does not suffer from this drawback. + +Although an ImageNet pre-trained model undoubtedly contains more prior knowledge than a base-set trained one, simultaneously learning many new concepts will inevitably make pFSL much more difficult than traditional FSL. We believe that a more challenging task will help technology advancement, too—the traditional FSL setting is already saturated to certain extent (cf. results in [22, 41]). + +Hence, we propose a novel approach for pFSL: Instance-based Max-margin (IbM2), which is effective in traditional FSL, too. The max-margin idea has been shown to be effective in improving generalization. Classic methods like SVM [7] build max-margin decision boundaries with only a very small portion of the training examples (i.e., support vectors). This idea is problematic when we have both very few training examples and a very high dimensionality. Intuitively, the support vectors chosen by SVM are highly likely wrong or misleading, because a small training set leads to excessively unstable estimation [16]. + +In the proposed IbM2, we achieve max-margin at the instance level, instead of at the class level as in SVM. As illustrated in Fig. 1, we create a hypersphere for every training example, with the example being the center of the hypersphere. Then, we can sample as many virtual samples as we want around this hypersphere, and assign the label of the center (original training example) to all its associated virtual examples. By finding a properly maximized radius for the hypersphere and requiring a classifier to correctly classify the virtual examples, we in effect achieve max-margin. Another benefit of IbM2 is that we do not need any special handling for multi-class recognition, while vanilla SVM is for binary classification only. In short, the contributions of this paper are twofold: + +- We propose a practical few-shot learning setting (pFSL): many-way (e.g., 200-way) recognition, uses an unsupervised pre-trained model, and has no base set. +- We propose IbM2, an instance-based max-margin algorithm, which suits few-shot, high dimensionality, and multi-class naturally. + +As will be shown by extensive experiments, IbM2 consistently improves both traditional FSL and the proposed pFSL. The benefits of pFSL against traditional FSL will be verified by both analyses and experiments, too. + +# 2. Related Work + +Few-shot learning aims at recognizing novel categories with the help of prior knowledge. Given the base set as prior knowledge, few-shot learning methods can be roughly divided into two types: those based on meta-learning or transfer-learning. + +Meta-learning based FSL. Meta-learning [21] learns a model through a large quantity of episodes consisting of different training and evaluation sets. Given a new task during evaluation, the model performs what it does in training to predict. In FSL, the training episodes are randomly sampled from the base set. One line of work [14, 15, 25, 31] focuses on learning general initial weights for fast adapting the model to unseen categories with a few steps of optimization. For example, [14] explicitly trains the classifier in a model-agnostic way. [25] extends meta-learning with linear predictors as a differentiable convex problem. [15] learns the task distribution from a probabilistic perspective. Another line of work [1, 11, 32, 33, 37, 42, 43] boosts meta-learning by exploring different distance metrics. For example, [32] aggregates training features to generate prototypes for different classes as the classification head. [43] leverages the Earth Mover's Distance to calculate the structural distance for classification. [1] extracts sets of features from each image to build a set-based matching schema. + +Transfer-learning based FSL. This line of attack [9, 12, 27, 35, 40] leverages the idea of standard transfer learning, which first pre-trains a model on base classes and then finetunes the model weights with limited training samples from novel classes. [9] normalizes the features and classification weights and calculates their cosine distances as the logits. [27] pre-trains with manifold mixup [36] to improve robustness. [12] introduces a baseline for effectively and transductively finetuning. [40] calibrates the training distribution of a few-shot task using statistics from the base set. [35] explores learning a general representation of base classes in supervised or self-supervised ways with self-distillation. + +Self-supervised learning. We stress that in pFSL the pre-trained model is unsupervised, for which the reason is to be explained in Sec. 3. Self-supervised learning (SSL) is the mainstream approach to train a deep net in the unsupervised manner. Popular SSL methods, whether applied to traditional ResNet [18] models (e.g., BYOL [17], MoCo [19] and SwAV [5]) or Vision Transformers (ViT) [13] (e.g., MSN [2], DINO [6] and MoCov3 [10]), all produce pretrained models based on large-scale datasets. In this paper, we utilize such models as our prior knowledge in FSL. + +# 3. pFSL: Practical Few-Shot Learning + +In traditional FSL, the training dataset is split into 1) the base set with $N_{b}$ labeled images, denoted as $D_{b} = \{(x_{i}^{b},y_{i}^{b})\}_{i = 1}^{N_{b}}$ where $y_{i}^{b}\in \mathcal{V}_{b}$ is the label of instance $x_{i}^{b}$ and + +$\mathcal{V}_b$ is the label space of $D_{b}$ 2) the novel set with $N_{n}$ labeled images, denoted as $D_{n} = \{(x_{j}^{n},y_{j}^{n})\}_{j = 1}^{N_{n}}$ where $y_{j}^{n}\in \mathcal{V}_{n}$ is the label of $x_{j}^{n}$ and $\mathcal{V}_n$ is the label space of $D_{n}$ . Note that although $\mathcal{V}_b\cap \mathcal{V}_n = \emptyset$ , the concepts in $\mathcal{V}_b$ and $\mathcal{V}_n$ are semantically similar to each other. Then, the task is to learn a recognizer generalizing well on unknown samples from $\mathcal{V}_n$ . By letting $N_{n}\ll N_{b}$ , the training samples in $D_{n}$ are few-shot (i.e., few training examples per class). In traditional FSL, $|\mathcal{V}_b|$ is relatively large but $|\mathcal{V}_n|$ is small. For example, in most cases $|\mathcal{V}_n| = 5$ , which is called a 5-way FSL. The evaluation of traditional FSL is a rather complicated task. + +# 3.1. The pFSL Formulation + +To make FSL simpler, more practical, and closer to human's few-shot learning capability, we propose a new practical few-shot learning (pFSL) paradigm, which is characterized by the following properties: + +- Removing the base set. The prior knowledge obtained through pre-training on the base set is limited, as the base set only contains limited number of concepts. In some applications, collecting data sharing similar concepts with the novel set may be as difficult as collecting more samples for the novel set itself. +- Pre-trained model based on big data. A model pretrained on a large training set containing a wide variety of concepts is analogous to the common-sense and domain knowledge our brains encode, which will be useful for few-shot learning in diverse domains. +- Many-way FSL. In a $N$ -way $k$ -shot FSL, we seek $N$ to be large and $k$ to be small, e.g., using all the CUB [38] categories ( $N = 200$ categories and $k$ is 1 or 5). This makes pFSL much closer to real-world applications than traditional FSL. +- Unsupervised pre-training. In pFSL, we require the pre-training to be unsupervised. Since a large scale dataset (e.g., ImageNet) may contain the concept in few-shot learning (e.g., those birds in CUB), avoiding using the labels during pre-training is necessary to make the evaluation of FSL algorithm fairer. + +These properties distinguish pFSL from traditional FSL and some recent variants of it [9, 12, 22, 23, 27]. + +# 3.2. Simplicity and Better Evaluation + +The pFSL framework is clearly simpler than traditional FSL, and it leads to not only benefits in the training phase, but more importantly better evaluation of FSL algorithms. + +Traditional $N$ -way $k$ -shot FSL typical use $N = 5$ and $k = 1, 5$ , which inevitably leads to unreliable estimation of the test accuracy. Hence, the common practice is to sample a large number of $n$ episodes ( $n \geq 500$ ), find the accuracy in each episode, and report the average accuracy $\mu$ along with its $95\%$ confidence interval $Z_{95\%}$ . Note that with $n$ episodes, the standard deviation $\sigma$ of the accuracy within + +the $n$ episodes is $\sigma = 0.51\sqrt{n} Z_{95\%}$ . For example, a typical result is: average accuracy $64.93\%$ , $95\%$ confidence interval $0.18\%$ , but the standard deviation of accuracy is $9.18\%$ [16] (in which $n = 10000$ ). In short, one single evaluation of traditional FSL requires training and testing for $n$ times ( $n \geq 500$ ) and the evaluation results are still unreliable. Because of the complicated setup, both learning and evaluation of traditional FSL algorithms are not only costly, but often carried out in slightly different ways, which renders the fair comparison even more difficult. + +As a stark contrast, pFSL is much simpler and as the experimental results will show in Table 1, the estimate of average accuracy is reliable. The standard deviation is small (mostly $< 1.0\%$ ). This reliable estimation comes from the fact that pSFL is many-way (i.e., $N$ is large). Hence, instead of running $n$ episodes, few episodes (e.g., 3) is enough to evaluate pFSL, which not only means savings in computation, but also more reliable evaluation of algorithms. + +# 4. IbM2: Instance-based Max-margin + +In pFSL, we have a pre-trained model $\mathcal{M}$ (unsupervised trained on a large set) and a novel set. There is no base set $D_{b}$ any more, hence we will simply denote the novel set as $D = \{x_{i},y_{i}\}_{i = 1}^{M}$ (that is, ignoring the subscript $^b$ ). The label set of $D$ is $\mathcal{V}$ . In an $N$ -way $k$ -shot pFSL task, we have $|\mathcal{V}| = N$ and there will be $k$ training examples in each of the $N$ novel classes, hence $M = kN$ . Note that we expect $|\mathcal{V}| = N$ to be large (i.e., many-way FSL) and $k$ to be small (e.g., 1 or 5). + +# 4.1. Generating Virtual Samples + +Since $k$ (the number of training images in each class) is still small but the number of classes ( $N$ ) becomes much larger (e.g., from 5 in traditional FSL to 200 in pFSL), we expect that the challenge in learning a pFSL model is greater than that in traditional FSL. This is verified by our experiments (cf. the results in Table 1 vs. those in Table 3). + +Virtual examples, or examples that are sampled based on the original training examples, have been repeatedly proven useful when the number of training examples is small, e.g., in traditional few-shot learning [40] or long-tailed recognition (where the tail classes have few training images) [20]. + +The common idea in generating virtual samples is to make the virtual samples follow the underlying distributions of the classes. However, in few-shot learning this requirement is very difficult to entertain even with the help of techniques such as distribution calibration (DC) in [40], because there is only 1 or 5 examples per class. + +In contrast, we do not try to sample from any underlying distribution, but try to achieve max-margin of the decision boundary, as illustrated in Fig. 1. Specifically, for every training instance $x_{i}$ , we i.i.d. generate $R$ virtual samples $x_{i,r}$ ( $1 \leq r \leq R$ ) which distribute around the shell of the + +hypersphere centered at $x_{i}$ and whose radius is controlled by a parameter $\epsilon$ . Note that the same $\epsilon$ is shared by all training examples $x_{i}$ ( $1 \leq i \leq kN$ ). + +Technically, let $z_{i}$ be the feature vector produced by the pre-trained model $\mathcal{M}$ : $z_{i} = \mathcal{M}(x_{i})$ from a forward calculation. Then, a noise vector $\delta_{i,r}$ is randomly sampled from the standard multi-dimensional normal distribution $N(0, I_d)$ , where $d$ is the length of $z_{i}$ and $I_{d}$ is a $d \times d$ identity matrix. By adding a scaled version of the noise vector to the $i$ -th training example, we obtain $z_{i,r}$ (the $r$ -th virtual example for $x_{i}$ ): + +$$ +z _ {i, r} = z _ {i} + \epsilon \delta_ {i, r}. \tag {1} +$$ + +Its label $y_{i,r}$ is $y_{i}$ (the label of $x_{i}$ ) and $\epsilon$ is a positive number. Interesting properties exist in our virtual examples: + +- Hypersphere for different training examples can overlap, so long as they belong to the same class (cf. Fig. 1). +- We require the virtual examples to be correctly classified, or, the original training examples are discarded. +- The virtual examples lie around the shell, not the interior of the hypersphere. According to the Gaussian Annulus Theorem [4], almost all the probability of a high-dimensional spherical Gaussian with unit variance is concentrated in a thin annulus of width $O(1)$ with radius $\sqrt{d}$ when $d$ is large. Since $d$ is indeed large (e.g., $d = 2048$ ), the virtual examples reside around the shell. Hence, if we maximize the radius parameter $\epsilon$ but require that the virtual examples are correctly classified, as Fig. 1 shows, we in essence achieve margin maximization in an instance-based manner. + +Hence, the proposed method is named Instance-based Max-margin, abbreviated as IbM2. + +# 4.2. Ellipsoidal Noise Generation + +One issue with the above isotropic noise sampling is that it ignores the structural property of the training examples. For instance, if the ranges for two feature dimensions are $[-1, 1]$ and $[-100, 100]$ , respectively, isotropic sampling is clearly unsuitable. + +To overcome this drawback, we calculate a range vector $s = (s_1, s_2, \ldots, s_d)$ using all the original training examples regardless of the class label, where $s_i$ is the sample standard deviation for the $i$ -th dimension. Then, the IbM2 virtual examples are generated as (replacing Eq. 1) + +$$ +z _ {i, r} = z _ {i} + \epsilon (s \odot \delta_ {i, r}), \tag {2} +$$ + +where $\odot$ is element-wise multiplication. The final virtual example generation process is illustrated in Fig. 2. Note that estimating $s$ is dramatically easier than estimating the underlying distribution of every novel class. + +It is worth noting that this ellipsoidal noise generation is unsupervised, which distinguishes itself from Distribution calibration (DC) [40]. DC samples virtual examples based + +![](images/712447196ab4e0ccd9fc2fb06b741943edec2ae3728db5f0a05caa24af42252c.jpg) +Figure 2. Virtual example generation. Original input images pass through the pre-trained model $\mathcal{M}$ to get feature vectors (solid rectangles). Then, every feature vector i.i.d. samples $R$ virtual examples ( $R = 2$ here) using Eq. 2. + +on an estimated covariance structure, which is estimated from the few novel class training examples in a sample-wise manner and calibrated using the base set. As aforementioned, we argue that it makes sense to get rid of the dependency on a base set, then DC is not applicable. + +More importantly, the reliability of this estimation of a dense covariance matrix is understandably much lower than our estimation of the range indicator vector $s$ — we estimate $d$ values using $k \times N$ examples, while DC estimates $d \times d$ values using only 1 example and the base set. The base set calibration will help DC, but clearly its estimation is still unreliable, as shown by experiments in [40, 44] + +# 4.3. Binary Search to Find the Largest Possible $\epsilon$ + +Obviously we want $\epsilon$ to be as large as possible to achieve max-margin, under the condition that virtual examples are classified correctly. Hence, we design a simple binary search to find the optimal value for $\epsilon$ . + +For any given $\epsilon$ value, we can generate $kNR$ virtual examples $(x_{i,r},y_{i,r})$ $(1\leq i\leq kN,1\leq r\leq R)$ using Eq. 2. We denote the virtual training set for this particular value of $\epsilon$ as $D^{\epsilon}$ . Then, we train a linear classifier with parameters $W$ to classify $D^{\epsilon}$ and obtain the training accuracy. If the training accuracy is too high (larger than a threshold $T$ ), $\epsilon$ is enlarged; otherwise $\epsilon$ is shrunk. The binary search maintains a search range, when the search range is tight enough (when the range is less than 0.05 in Algorithm 1), the search terminates, and we have found the optimal value $\hat{\epsilon}$ . + +We have a few notes for finding $\hat{\epsilon}$ : + +- Unlike DC [40], we do not need a validation set. +- The threshold $T$ does not need to be 1 (100%). In SVM learning, the slack variable trick allows some support vectors not to have max-margin. Similarly, we just need $T$ to be close to 1 (0.9 in our experiments). +- Different from classic augmentation techniques [26, 28], + +Algorithm 1 Pseudo code for searching $\epsilon$ +```python +Inputs: +x : training features of a few-shot task +y : training labels of a few-shot task +R : sampling times for an instance +T : accuracy threshold for searching +Outputs: +eps : epsilon for sampling +left = 0.0 +right = a large value +eps = right / 2 +W = initclassifier +while True: + acc = train_and.eval(W, x, y, eps, R) + if acc > T: + left = eps # increase epsilon + else: + right = eps # decrease epsilon + eps = (left + right) / 2.0 + if right - left < 0.05: + break +``` + +which introduce minor disturbance into input features, the distribution of $D^{\hat{\epsilon}}$ is drastically different from $D$ because of a large $\hat{\epsilon}$ (empirically 1.24 on average). + +Finally, the IbM2 pipeline is simple: First, use Algorithm 1 to find $\hat{\epsilon}$ . Second, generate the virtual dataset $D^{\hat{\epsilon}}$ . And third, learn a linear classifier $W$ . Note that the pretrained model $\mathcal{M}$ is frozen and will not be updated. + +# 5. Experimental Results + +We evaluate our IbM2 method on both setups: the proposed pFSL in many-way few-shot scenario, and also comparing IbM2 under the traditional FSL few-way setting with state-of-the-art FSL methods to further validate its effectiveness. + +# 5.1. Implementation Details + +For both the searching and training stages of IbM2, all features extracted by the backbone $\mathcal{M}$ were $L2$ -normalized first. When learning the classification head (both during the binary search and after $\hat{\epsilon}$ was determined), we used Adam as the optimizer and the label smoothed cross-entropy loss [34] as the learning objective. The pre-trained model was trained using various self-supervised learning methods on the ImageNet-1K [30] training set. + +During the binary search, for all the experiments we will report, we always set $R$ as 200, $T$ as 0.9 in pFSL and 0.999 in the traditional FSL setting, except when we carried out ablation experiments on these hyperparameters. + +Full implementation details are included in the appendix. + +# 5.2. Experiments in the pFSL Setting + +Datasets and Evaluation Setup. We explored two common many-way classification datasets, ImageNet-1K [30] and CUB-200-2011 (CUB) [38]. ImageNet-1K contains about 1.28 million training images from 1,000 classes and + +50,000 images for evaluation. CUB is a fine-grained recognition dataset composed of 11,788 images belonging to 200 classes of birds, 5,994 for training and 5,794 for evaluation. + +For both datasets, we randomly sampled the training sets for pFSL by selecting $k$ images from every class (i.e., $k$ -shot) and using all the classes (1000 and 200, respectively) to form the novel set. $k$ is chosen from $\{1, 2, 3, 4, 5, 8, 16\}$ . The evaluation was carried out on the full validation (for ImageNet) or test (for CUB) set. + +Utilizing various self-supervised backbone network $\mathcal{M}$ pre-trained on ImageNet, we compare two sets of results: one in which the linear classifier was obtained by using the original training set, the other by using IbM2's virtual examples. We report the top-1 accuracy and its standard deviation computed over 3 randomly sampled novel sets. + +Main Results. As the results in Table 1 suggest, we evaluated on two types of backbones: Vision Transformer (ViT) [13] and ResNet50 [18]. The pre-training methods included DINO [6], MoCov3 [10], MSN [2], SimCLR [8] and BYOL [17]. Table 1 shows that in almost all cases, IbM2 benefited the few-shot learning process and improved the top-1 accuracy. + +When the number of shots $(k)$ is very small $(\leq 2)$ , the improvement of IbM2 over the baseline is roughly $1\%$ on average. However, as the number of training shots goes larger, it is clear that the level of accuracy improvement increases gradually from $\sim 1\%$ to $\sim 2\%$ , even $>3\%$ in some cases. + +A useful observation from these results is that in pFSL, both the baseline and IbM2 have small standard deviations, that is, more robust in evaluation. Hence, we do not need 500 episodes in pFSL any longer—3 is enough. + +Semi-supervised learning. In the self-supervised learning literature, it is a common practice to use ImageNet-1K training images to learn a backbone in the unsupervised manner, then use a small portion (e.g., $1\%$ ) of the training data now with labels to train a classifier. This semi-supervised learning task can also be viewed as our pFSL setting. Hence, we also report the $1\%$ ImageNet-1K semi-supervised learning (on average 12 labeled training images per class) results in Table 2. IbM2 consistently improved various self-supervised models and backbone architectures in all cases, with $0.8\%$ to $2.9\%$ top-1 accuracy increase. + +# 5.3. Experiments in the Traditional FSL Setting + +Datasets and Evaluation Setup. We evaluated IbM2 in the traditional FSL setup, too. We conducted experiments on two standard benchmark datasets, mini-ImageNet [37] and CIFAR-FS [3]. mini-ImageNet consists of 100 categories selected from ImageNet-1K, which are further split into 64 base, 16 val and 20 novel categories according to [29]. CIFAR-FS is created by randomly shuffling the 100 categories of CIFAR-100 [24] into 64 base, 16 val, 20 novel + +
DatasetPre-training MethodBackboneIbM2Shot per Class
12345816
ImageNet-1KDINOViT-S/16✓39.2 ± 0.349.2 ± 0.254.1 ± 0.456.7 ± 0.258.0 ± 0.160.4 ± 0.162.7 ± 0.1
39.2 ± 0.349.4 ± 0.354.6 ± 0.457.6 ± 0.159.3 ± 0.162.4 ± 0.265.8 ± 0.1
MoCov3ViT-S/16✓32.7 ± 0.642.0 ± 0.246.9 ± 0.349.6 ± 0.451.0 ± 0.153.8 ± 0.156.6 ± 0.2
33.9 ± 0.643.2 ± 0.248.4 ± 0.351.3 ± 0.352.8 ± 0.256.1 ± 0.159.8 ± 0.2
MSNViT-S/16✓47.9 ± 0.156.2 ± 0.459.8 ± 0.361.6 ± 0.162.4 ± 0.264.4 ± 0.366.1 ± 0.1
47.8 ± 0.256.4 ± 0.460.5 ± 0.262.5 ± 0.263.6 ± 0.266.0 ± 0.268.4 ± 0.0
ViT-B/4✓53.2 ± 0.264.5 ± 0.468.9 ± 0.270.9 ± 0.272.0 ± 0.373.8 ± 0.175.0 ± 0.2
54.0 ± 0.164.9 ± 0.569.4 ± 0.271.4 ± 0.172.7 ± 0.474.7 ± 0.076.4 ± 0.2
ViT-L/7✓57.3 ± 0.466.5 ± 0.469.8 ± 0.571.6 ± 0.472.2 ± 0.273.8 ± 0.175.1 ± 0.1
57.7 ± 0.466.6 ± 0.570.1 ± 0.671.8 ± 0.472.6 ± 0.274.3 ± 0.176.0 ± 0.0
SimCLRResNet50✓21.4 ± 0.430.3 ± 0.136.1 ± 0.339.8 ± 0.242.0 ± 0.146.8 ± 0.151.9 ± 0.0
23.6 ± 0.433.4 ± 0.239.0 ± 0.442.0 ± 0.344.2 ± 0.148.0 ± 0.052.7 ± 0.0
BYOLResNet50✓26.5 ± 0.335.7 ± 0.241.5 ± 0.445.1 ± 0.247.2 ± 0.151.8 ± 0.157.1 ± 0.1
27.5 ± 0.337.5 ± 0.143.3 ± 0.446.8 ± 0.249.1 ± 0.153.2 ± 0.158.0 ± 0.1
CUBDINOViT-S/16✓35.4 ± 1.249.0 ± 0.556.8 ± 0.860.8 ± 0.765.2 ± 0.970.6 ± 0.975.9 ± 0.3
36.2 ± 1.449.6 ± 0.657.4 ± 1.062.0 ± 0.666.4 ± 0.872.5 ± 0.879.0 ± 0.2
MSNViT-S/16✓32.1 ± 1.645.0 ± 0.653.1 ± 0.656.7 ± 0.161.4 ± 0.567.3 ± 0.073.6 ± 0.4
33.0 ± 1.445.8 ± 0.753.2 ± 0.957.1 ± 0.462.0 ± 1.068.4 ± 0.175.7 ± 0.2
ViT-L/7✓34.9 ± 1.349.4 ± 0.458.8 ± 0.862.7 ± 0.967.2 ± 0.373.8 ± 0.880.4 ± 0.2
37.5 ± 1.250.1 ± 0.559.0 ± 0.862.6 ± 0.567.5 ± 0.673.9 ± 0.481.0 ± 0.1
+ +Table 1. Average of top-1 accuracy (%) with standard deviation across 3 random subsets on ImageNet-1K and CUB. A √ in the column IbM2 denotes the proposed IbM2 method, or the baseline method if it is blank. Those IbM2 results that are at least 0.5% higher than the baseline are shown in boldface. + +
Pre-training MethodBackboneIbM2Top 1
DINOViT-S/16✓62.5
65.0
MoCov3ViT-S/16✓56.0
58.9
MSNViT-S/16✓65.9
67.9
ViT-B/4✓74.9
76.1
ViT-L/7✓74.8
75.6
SimCLRResNet50✓50.5
51.3
BYOLResNet50✓55.7
56.8
+ +Table 2. Top-1 accuracy (\%) of $1\%$ ImageNet-1K semi-supervised learning. The training set contains on average 12 labeled training samples per category. + +categories. Note that in order to perform traditional few-shot learning, only the novel split of these two datasets is required to sample many 5-way 1/5-shot episodes. We report the metrics mentioned in [16]: the average $(\mathrm{ACC}_m)$ , worst-case $(\mathrm{ACC}_1)$ , average of worst 10 $(\mathrm{ACC}_{10})$ , average of worst 100 $(\mathrm{ACC}_{100})$ episodes' accuracy, and the standard deviation $(\sigma)$ over 500 episodes for comprehensive evaluation. To make the results more reliable, we average the value of each metric from 5 runs with different + +random seeds. We adopted PMF [22], $S2M2_{R}$ [27] and Meta-Baseline [11] as the pre-training or meta-training approaches to obtain the backbone weights out of the base set. + +Main Results. As shown in Table 3, by plugging IbM2 in during classifier learning, the proposed IbM2 improved the average accuracy $\mathrm{ACC}_m$ in all cases except only 1 result. And, the standard deviation $\sigma$ was reduced by IbM2 or remain unchanged in all cases. As [16] advocated, smaller $\sigma$ means the learning process is more stable. + +[16] also advocates the worst-case episode's accuracy is more important than the average accuracy among all episodes. Table 3 shows that IbM2 almost always leads to higher worst-case $(\mathrm{ACC}_1)$ or near-worst-case $(\mathrm{ACC}_{10},$ $\mathrm{ACC}_{100})$ accuracy. Furthermore, the average gain of $\mathrm{ACC}_m$ is $0.4\%$ , which is far less than that of $\mathrm{ACC}_1$ $(1.3\%)$ .As for $\mathrm{ACC}_{10}$ and $\mathrm{ACC}_{100}$ , their gains are very similar, both around $0.5\%$ . These observations demonstrate that IbM2 can boost the recognition accuracy of few-shot learning in almost every scenario, especially the worst case one. + +At last, by comparing the numbers in Tables 1 and 3, pFSL is more challenging than traditional FSL, which leads to more open questions to solve. + +# 5.4. Ablation Studies + +We performed ablation studies for IbM2 in the pFSL setting on ImageNet-1K. + +Instance-based vs. class-based max-margin. IbM2 seeks max-margin through an instance-based manner. In this study, we compare this instance-based max-margin with the well-known support vector machine (SVM), which + +
DatasetPre-training & Meta-trainingBackboneIbM21-shot5-shot
ACCmσACC1ACC10ACC100ACCmσACC1ACC10ACC100
mini-ImageNetPMFViT-S/16✓93.46.161.372.483.498.41.887.791.495.6
94.45.663.274.785.198.61.886.191.395.9
ViT-B/16✓94.95.466.975.586.098.81.689.192.996.3
95.65.169.677.687.198.91.689.393.096.3
ResNet50✓94.95.367.275.286.398.51.789.391.995.8
95.35.266.174.686.998.81.689.392.796.3
S2M2RWRN-28-10✓65.410.032.039.350.782.37.152.062.571.8
65.810.032.540.551.182.97.053.363.372.3
Meta-BaselineResNet12✓62.910.426.734.347.479.07.554.758.067.9
63.010.232.335.647.979.57.354.958.568.7
CIFAR-FSPMFViT-S/16✓87.98.351.761.774.895.54.274.781.888.5
89.08.159.264.175.995.74.273.381.788.7
ViT-B/16✓89.88.155.264.876.896.04.173.182.289.2
90.38.058.965.577.496.04.174.181.889.2
ResNet50✓81.710.435.251.665.891.35.571.275.182.7
82.310.336.351.166.591.65.373.376.083.2
S2M2RWRN-28-10✓75.210.844.046.759.287.77.154.767.976.8
75.510.842.445.559.287.77.054.968.177.0
Meta-BaselineResNet12✓72.711.632.042.956.184.87.554.765.173.6
72.311.532.842.355.785.17.556.365.474.1
+ +achieves max-margin in a class-based manner. We experimented with SVM using the linear kernel function in the LIBSVM [7] software package. By iterating the value of SVM's regularization hyperparameter $C$ from the set $\{0.1, 1, 10, 100, 1000\}$ , we found the best accuracy among them to compare with our IbM2 method. + +As shown in Table 4, the proposed IbM2 method outperforms SVM with the best $C$ by a significant margin in all cases. Specifically, the recognition accuracy improves $\sim 2\%$ on average, and even up to $\sim 4\%$ in the extremely scarce 1-shot case. These results demonstrate that our instance-based margin generated by IbM2 helps more to learn a robust classification boundary, especially when the training distribution is drastically shifted. + +Sensitivity of $R$ . As described in Sec. 4, one original training example is turned into $R$ virtual examples to form the training set $D^{\hat{\epsilon}}$ . In this part, we study the effect of the hyperparameter $R$ . As shown in Table 5, when the training shots are highly limited, increasing $R$ significantly improves recognition accuracy. As the number of training shots gets larger, the accuracy difference between a large $R$ ( $R = 400$ ) and a small one ( $R = 1$ ) gradually decreases from $1.6\%$ to $0.2\%$ . + +When training samples are extremely scarce, it is difficult to model the correct Gaussian distribution with a few samples in a high-dimensional space. Therefore, increasing $R$ is necessary for a good estimation. When more training shots are available, the need for a large value of sampling times is reduced, hence the accuracy difference between different $R$ becomes smaller, too. Based on these results, we let $R = 200$ in all our experiments. + +Table 3. Results of 5-way classification on mini-ImageNet and CIFAR-FS in the traditional few-shot learning setting. For the baseline methods, we obtain the results from their respective official implementations. + +
MethodShot per Class
12345816
SVM54.864.868.270.070.872.874.7
IbM258.266.970.271.972.774.376.1
+ +Table 4. Top-1 accuracy $(\%)$ with different margin-based methods on ImageNet-1K classification with ViT-L/7 from MSN as the pretrained backbone. + +
RShot per Class
12345816
132.942.747.850.852.555.960.1
1033.743.648.551.452.956.260.3
5033.843.748.651.553.056.260.3
20034.443.848.751.553.056.260.3
40034.543.848.651.553.056.260.3
+ +Table 5. Top-1 accuracy $(\%)$ of classification with different $R$ on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone. + +
Sampling SchemaShot per Class
12345816
-33.142.447.249.851.655.259.2
Spherical33.042.147.150.251.855.359.8
Ellipsoidal34.443.848.751.553.056.260.3
+ +Table 6. Top-1 accuracy (\%) of classification with different sampling schemas on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone. '-' denotes the simple baseline using only the original training examples. + +Ellipsoidal vs. isotropic sampling. We have described two noise sampling strategies to generate virtual examples. The ellipsoidal one is preferred over the isotropic one, and is used in IbM2. In this part, we evaluate the effectiveness of this sampling schema by experimentally comparing these two sampling strategies. The isotropic sampling strategy is denoted as Spherical in Table 6. + +As shown in Table 6, the accuracy in the ellipsoidal sampling schema is consistently better than its spherical counterpart or the baseline. Moreover, in low-shot cases $(\leq 3)$ , sampling with spherical Gaussian slightly degraded the recognition accuracy. The reason may be that the standard deviation of different channels calculated from training features varied a lot, thus simply regarding all channels as independent and identically distributed might make the sampled points significantly shifted from the underlying distribution. However, as the number of training samples increases, both isotropic and ellipsoidal sampling outperformed the baseline. + +Based on these observations, we chose to adopt the ellipsoidal noise sampling (Eq. 2) in IbM2. + +On what classes can IbM2 help? Finally, we study what classes will benefit from IbM2—will most or only a small portion of classes be improved by IbM2? After the training of the baseline and IbM2 finished, we calculated the class-wise validation accuracy for every class on ImageNet-1K, as + +$$ +\mathrm {A C C} ^ {k} = \frac {N _ {c o r} ^ {k}}{N _ {c l s} ^ {k}}, \tag {3} +$$ + +where $\mathrm{ACC}^k$ is the per-class accuracy (i.e., recall) of the $k$ -th class, $N_{cls}^k$ is the number of test samples class $k$ contains ( $N_{cls}^k = 50$ in ImageNet-1K) and $N_{cor}^k$ is the number of correctly classified samples of class $k$ . For every class, we obtain the difference of per-class accuracy (that of IbM2 minus that of the baseline). A positive difference is an accuracy gain and a negative gain is in fact an accuracy loss. + +We then sort the baseline's per-class accuracy in the ascending order. Following this order, we rearrange the per-class accuracy gains. The 1000 accuracy gains are divided into 10 histogram bins in the rearranged order, and inside each bin the 100 per-class accuracy gains are averaged to obtain the accuracy gain of that bin. Fig. 3 plots the average accuracy gain in each bin. + +We find that IbM2 improves average per-class accuracy in almost every histogram bin (i.e., is above the "0.0" horizon in the $y$ -axis). More detailed numbers reveal that the recognition accuracy of more than $65\%$ categories out of 1000 is improved in all shots. Furthermore, Fig. 3 shows a trend: the more accurate a class is, the higher gains IbM2 can achieve over the baseline. That is, when the task is too difficult for the baseline, IbM2 can help but its usefulness is restricted. But, when the baseline is already accurate enough (categorical subset 9 and later), the room for IbM2's + +![](images/02cd9849b59af841bb571db21f0955ff5801327a920237f0a8f470a67f08f3ad.jpg) +Figure 3. Categorical accuracy gain $(\%)$ of IbM2 compared to baseline with ViT-S/16 pre-trained by MoCov3 [10] as the backbone. + +- further improvement is small again. It is the middle range that IbM2 is the most useful. + +# 6. Conclusions and Limitations + +In this paper, we advocated pFSL, a new practical few-shot learning setting. We also proposed IbM2, an instance-based max-margin method to improve few-shot learning. With the technological advancements, it is time to upgrade the traditional FSL settings. We need a simpler, easier-to-evaluate, more challenging and more practical FSL setting, and the proposed pFSL task satisfies these requirements. + +To address the challenges associated with the scarcity of training examples, we introduced IbM2. Instead of maximizing the class-level margin, IbM2 is instance-based margin maximization. It achieved significant improvements in both pFSL and the traditional FSL settings consistently. IbM2 is simple and reliable. It introduces only 2 hyperparameters, and the default values of them worked well in experiments across different architectures and tasks. + +As the experiments indicated, IbM2 works the best for the middle range in terms of task difficulty. In a $k$ -shot task when $k$ is extremely small, there is still considerable room for improvement in the pFSL setting. Furthermore, IbM2 freezes the backbone and only learns the linear classifier. In the future, we plan to improve the very small shot cases (e.g., $k = 1$ ) and better tune the backbone in few-shot learning to push the current limits further. + +# 7. Acknowledgments + +This research received substantial support from Jianxin Wu, who wrote IbM2's first working code and whose generous assistance and invaluable guidance were sincerely appreciated throughout our research process. 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Compared to traditional FSL, pFSL is simpler in its formulation, easier to evaluate, more challenging and more practical. To cope with the rarity of training examples, this paper proposes IbM2, an instance-based max-margin method not only for the new pFSL setting, but also works well in traditional FSL scenarios. Based on the Gaussian Annulus Theorem, IbM2 converts random noise applied to the instances into a mechanism to achieve maximum margin in the many-way pFSL (or traditional FSL) recognition task. Experiments with various self-supervised pre-training methods and diverse many- or few-way FSL tasks show that IbM2 almost always leads to improvements compared to its respective baseline methods, and in most cases the improvements are significant. With both the new pFSL setting and novel IbM2 method, this paper shows that practical few-shot learning is both viable and promising." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 127, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 127, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 127, + 540 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 656 + ], + "type": "text", + "content": "We human have the ability to learn new concepts based on a few exemplars, thanks to both our ability to learn and the previously accumulated knowledge. As a stark contrast, learning machines (especially deep learning models) mostly require plentiful training examples to learn just few (e.g., 5) concepts. Both the vision and learning community are fully aware of this shortcoming, and few-shot learning (FSL) is our community's effort to counter this weakness, which has been studied for a long time [39]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "content": "FSL relies on prior knowledge, too. Currently, the setting is to set aside a collection of object categories (known as the base set), with many training examples in every base" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 351, + 226, + 500, + 353 + ], + "blocks": [ + { + "bbox": [ + 351, + 226, + 500, + 353 + ], + "lines": [ + { + "bbox": [ + 351, + 226, + 500, + 353 + ], + "spans": [ + { + "bbox": [ + 351, + 226, + 500, + 353 + ], + "type": "image", + "image_path": "5e0878b4d1552db5a5882964b262b35758656d28cb75f934f29ab4bccf97a450.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 361, + 545, + 428 + ], + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 428 + ], + "type": "text", + "content": "Figure 1. Instance-based max-margin. We create a hypersphere (large dashed circles) centered at every example (solid shapes), sample many virtual examples (hollow shapes) around the hypersphere, and require the decision boundary to classify all virtual samples correctly. Then we in effect achieve instance-based maxmargin. Best viewed in color." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "type": "text", + "content": "set category. A model is first pre-trained on the base set, which naturally encodes prior knowledge. Then, few novel object categories (most commonly 5) are to be recognized based on the pre-trained model given few training examples from these new concepts (e.g., 1 or 5 per category). Note that the base and novel training sets are semantically closely related (e.g., both contain different kinds of birds)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 605 + ], + "type": "text", + "content": "There is a clear mismatch between the human ability and this FSL setting. We human can learn many instead of few novel concepts; and, the human prior knowledge include those accumulated as both common-sense and domain knowledge from many diverse domains rather than a limited set of concepts closely related to a specific task." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 666 + ], + "type": "text", + "content": "Although this FSL setting has served our community well and has pushed the technical frontier for years, with the immense advances in deep learning and emerging practical needs for real-world FSL applications, it is time that we need a better, simpler, and more practical FSL setting." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": "Hence we advocate a practical few-shot learning (or pFSL) setting: based on an unsupervised model pre-trained from a large number of concepts (e.g., ImageNet [30]), simultaneously learn many new concepts (e.g., 200) with few" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "type": "inline_equation", + "content": "^*" + }, + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "type": "text", + "content": " K. Zhu is the corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28674" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 194, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 194, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 194, + 85 + ], + "type": "text", + "content": "examples (e.g., 1 or 5 per category)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 286, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 286, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 286, + 184 + ], + "type": "text", + "content": "An ImageNet pre-trained model is more analogous to human knowledge than those learned from a base set in traditional FSL, and learning many new concepts makes it more practical in applications. Without the base set, the learning phase of pFSL is simple, too. More importantly, evaluation of algorithms is difficult, complicated, and very time consuming in the current FSL setting [16], but as will be discussed later, pFSL does not suffer from this drawback." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 190, + 286, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 190, + 286, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 286, + 273 + ], + "type": "text", + "content": "Although an ImageNet pre-trained model undoubtedly contains more prior knowledge than a base-set trained one, simultaneously learning many new concepts will inevitably make pFSL much more difficult than traditional FSL. We believe that a more challenging task will help technology advancement, too—the traditional FSL setting is already saturated to certain extent (cf. results in [22, 41])." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 286, + 408 + ], + "type": "text", + "content": "Hence, we propose a novel approach for pFSL: Instance-based Max-margin (IbM2), which is effective in traditional FSL, too. The max-margin idea has been shown to be effective in improving generalization. Classic methods like SVM [7] build max-margin decision boundaries with only a very small portion of the training examples (i.e., support vectors). This idea is problematic when we have both very few training examples and a very high dimensionality. Intuitively, the support vectors chosen by SVM are highly likely wrong or misleading, because a small training set leads to excessively unstable estimation [16]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 414, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 581 + ], + "type": "text", + "content": "In the proposed IbM2, we achieve max-margin at the instance level, instead of at the class level as in SVM. As illustrated in Fig. 1, we create a hypersphere for every training example, with the example being the center of the hypersphere. Then, we can sample as many virtual samples as we want around this hypersphere, and assign the label of the center (original training example) to all its associated virtual examples. By finding a properly maximized radius for the hypersphere and requiring a classifier to correctly classify the virtual examples, we in effect achieve max-margin. Another benefit of IbM2 is that we do not need any special handling for multi-class recognition, while vanilla SVM is for binary classification only. In short, the contributions of this paper are twofold:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 586, + 286, + 658 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 49, + 586, + 285, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 586, + 285, + 620 + ], + "spans": [ + { + "bbox": [ + 49, + 586, + 285, + 620 + ], + "type": "text", + "content": "- We propose a practical few-shot learning setting (pFSL): many-way (e.g., 200-way) recognition, uses an unsupervised pre-trained model, and has no base set." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 49, + 624, + 286, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 624, + 286, + 658 + ], + "spans": [ + { + "bbox": [ + 49, + 624, + 286, + 658 + ], + "type": "text", + "content": "- We propose IbM2, an instance-based max-margin algorithm, which suits few-shot, high dimensionality, and multi-class naturally." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "As will be shown by extensive experiments, IbM2 consistently improves both traditional FSL and the proposed pFSL. The benefits of pFSL against traditional FSL will be verified by both analyses and experiments, too." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "text", + "content": "Few-shot learning aims at recognizing novel categories with the help of prior knowledge. Given the base set as prior knowledge, few-shot learning methods can be roughly divided into two types: those based on meta-learning or transfer-learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 152, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 152, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 304, + 152, + 545, + 379 + ], + "type": "text", + "content": "Meta-learning based FSL. Meta-learning [21] learns a model through a large quantity of episodes consisting of different training and evaluation sets. Given a new task during evaluation, the model performs what it does in training to predict. In FSL, the training episodes are randomly sampled from the base set. One line of work [14, 15, 25, 31] focuses on learning general initial weights for fast adapting the model to unseen categories with a few steps of optimization. For example, [14] explicitly trains the classifier in a model-agnostic way. [25] extends meta-learning with linear predictors as a differentiable convex problem. [15] learns the task distribution from a probabilistic perspective. Another line of work [1, 11, 32, 33, 37, 42, 43] boosts meta-learning by exploring different distance metrics. For example, [32] aggregates training features to generate prototypes for different classes as the classification head. [43] leverages the Earth Mover's Distance to calculate the structural distance for classification. [1] extracts sets of features from each image to build a set-based matching schema." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 380, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 523 + ], + "type": "text", + "content": "Transfer-learning based FSL. This line of attack [9, 12, 27, 35, 40] leverages the idea of standard transfer learning, which first pre-trains a model on base classes and then finetunes the model weights with limited training samples from novel classes. [9] normalizes the features and classification weights and calculates their cosine distances as the logits. [27] pre-trains with manifold mixup [36] to improve robustness. [12] introduces a baseline for effectively and transductively finetuning. [40] calibrates the training distribution of a few-shot task using statistics from the base set. [35] explores learning a general representation of base classes in supervised or self-supervised ways with self-distillation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 525, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 643 + ], + "type": "text", + "content": "Self-supervised learning. We stress that in pFSL the pre-trained model is unsupervised, for which the reason is to be explained in Sec. 3. Self-supervised learning (SSL) is the mainstream approach to train a deep net in the unsupervised manner. Popular SSL methods, whether applied to traditional ResNet [18] models (e.g., BYOL [17], MoCo [19] and SwAV [5]) or Vision Transformers (ViT) [13] (e.g., MSN [2], DINO [6] and MoCov3 [10]), all produce pretrained models based on large-scale datasets. In this paper, we utilize such models as our prior knowledge in FSL." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 656, + 504, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 656, + 504, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 656, + 504, + 670 + ], + "type": "text", + "content": "3. pFSL: Practical Few-Shot Learning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "text", + "content": "In traditional FSL, the training dataset is split into 1) the base set with " + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "N_{b}" + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "text", + "content": " labeled images, denoted as " + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "D_{b} = \\{(x_{i}^{b},y_{i}^{b})\\}_{i = 1}^{N_{b}}" + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "y_{i}^{b}\\in \\mathcal{V}_{b}" + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "text", + "content": " is the label of instance " + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "x_{i}^{b}" + }, + { + "bbox": [ + 306, + 677, + 545, + 715 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28675" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_b" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the label space of " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "D_{b}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " 2) the novel set with " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "N_{n}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " labeled images, denoted as " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "D_{n} = \\{(x_{j}^{n},y_{j}^{n})\\}_{j = 1}^{N_{n}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "y_{j}^{n}\\in \\mathcal{V}_{n}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the label of " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "x_{j}^{n}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_n" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the label space of " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "D_{n}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ". Note that although " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_b\\cap \\mathcal{V}_n = \\emptyset" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", the concepts in " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_b" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_n" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " are semantically similar to each other. Then, the task is to learn a recognizer generalizing well on unknown samples from " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_n" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ". By letting " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "N_{n}\\ll N_{b}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", the training samples in " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "D_{n}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " are few-shot (i.e., few training examples per class). In traditional FSL, " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}_b|" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is relatively large but " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}_n|" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is small. For example, in most cases " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}_n| = 5" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", which is called a 5-way FSL. The evaluation of traditional FSL is a rather complicated task." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 211, + 179, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 211, + 179, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 211, + 179, + 223 + ], + "type": "text", + "content": "3.1. The pFSL Formulation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 228, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 277 + ], + "type": "text", + "content": "To make FSL simpler, more practical, and closer to human's few-shot learning capability, we propose a new practical few-shot learning (pFSL) paradigm, which is characterized by the following properties:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 278, + 287, + 543 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 49, + 278, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 278, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 49, + 278, + 287, + 348 + ], + "type": "text", + "content": "- Removing the base set. The prior knowledge obtained through pre-training on the base set is limited, as the base set only contains limited number of concepts. In some applications, collecting data sharing similar concepts with the novel set may be as difficult as collecting more samples for the novel set itself." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 350, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 350, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 49, + 350, + 287, + 409 + ], + "type": "text", + "content": "- Pre-trained model based on big data. A model pretrained on a large training set containing a wide variety of concepts is analogous to the common-sense and domain knowledge our brains encode, which will be useful for few-shot learning in diverse domains." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": "- Many-way FSL. In a " + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": "-shot FSL, we seek " + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": " to be large and " + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": " to be small, e.g., using all the CUB [38] categories (" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "N = 200" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": " categories and " + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 49, + 411, + 287, + 470 + ], + "type": "text", + "content": " is 1 or 5). This makes pFSL much closer to real-world applications than traditional FSL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 49, + 472, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 472, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 49, + 472, + 287, + 543 + ], + "type": "text", + "content": "- Unsupervised pre-training. In pFSL, we require the pre-training to be unsupervised. Since a large scale dataset (e.g., ImageNet) may contain the concept in few-shot learning (e.g., those birds in CUB), avoiding using the labels during pre-training is necessary to make the evaluation of FSL algorithm fairer." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 544, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 568 + ], + "type": "text", + "content": "These properties distinguish pFSL from traditional FSL and some recent variants of it [9, 12, 22, 23, 27]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 575, + 224, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 224, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 224, + 588 + ], + "type": "text", + "content": "3.2. Simplicity and Better Evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 629 + ], + "type": "text", + "content": "The pFSL framework is clearly simpler than traditional FSL, and it leads to not only benefits in the training phase, but more importantly better evaluation of FSL algorithms." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Traditional " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "-shot FSL typical use " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "k = 1, 5" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": ", which inevitably leads to unreliable estimation of the test accuracy. Hence, the common practice is to sample a large number of " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " episodes (" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "n \\geq 500" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "), find the accuracy in each episode, and report the average accuracy " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " along with its " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " confidence interval " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "Z_{95\\%}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": ". Note that with " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " episodes, the standard deviation " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " of the accuracy within" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "the " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " episodes is " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "\\sigma = 0.51\\sqrt{n} Z_{95\\%}" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": ". For example, a typical result is: average accuracy " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "64.93\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " confidence interval " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "0.18\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": ", but the standard deviation of accuracy is " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "9.18\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " [16] (in which " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "n = 10000" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "). In short, one single evaluation of traditional FSL requires training and testing for " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " times (" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "n \\geq 500" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": ") and the evaluation results are still unreliable. Because of the complicated setup, both learning and evaluation of traditional FSL algorithms are not only costly, but often carried out in slightly different ways, which renders the fair comparison even more difficult." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "text", + "content": "As a stark contrast, pFSL is much simpler and as the experimental results will show in Table 1, the estimate of average accuracy is reliable. The standard deviation is small (mostly " + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "inline_equation", + "content": "< 1.0\\%" + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "text", + "content": "). This reliable estimation comes from the fact that pSFL is many-way (i.e., " + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "text", + "content": " is large). Hence, instead of running " + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 192, + 545, + 288 + ], + "type": "text", + "content": " episodes, few episodes (e.g., 3) is enough to evaluate pFSL, which not only means savings in computation, but also more reliable evaluation of algorithms." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 297, + 501, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 501, + 311 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 501, + 311 + ], + "type": "text", + "content": "4. IbM2: Instance-based Max-margin" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": "In pFSL, we have a pre-trained model " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " (unsupervised trained on a large set) and a novel set. There is no base set " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "D_{b}" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " any more, hence we will simply denote the novel set as " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "D = \\{x_{i},y_{i}\\}_{i = 1}^{M}" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " (that is, ignoring the subscript " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "^b" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": "). The label set of " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": ". In an " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": "-shot pFSL task, we have " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}| = N" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " and there will be " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " training examples in each of the " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " novel classes, hence " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "M = kN" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": ". Note that we expect " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}| = N" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " to be large (i.e., many-way FSL) and " + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": " to be small (e.g., 1 or 5)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 432, + 460, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 432, + 460, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 432, + 460, + 445 + ], + "type": "text", + "content": "4.1. Generating Virtual Samples" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": " (the number of training images in each class) is still small but the number of classes (" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 450, + 545, + 521 + ], + "type": "text", + "content": ") becomes much larger (e.g., from 5 in traditional FSL to 200 in pFSL), we expect that the challenge in learning a pFSL model is greater than that in traditional FSL. This is verified by our experiments (cf. the results in Table 1 vs. those in Table 3)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 522, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 582 + ], + "type": "text", + "content": "Virtual examples, or examples that are sampled based on the original training examples, have been repeatedly proven useful when the number of training examples is small, e.g., in traditional few-shot learning [40] or long-tailed recognition (where the tail classes have few training images) [20]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "content": "The common idea in generating virtual samples is to make the virtual samples follow the underlying distributions of the classes. However, in few-shot learning this requirement is very difficult to entertain even with the help of techniques such as distribution calibration (DC) in [40], because there is only 1 or 5 examples per class." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "In contrast, we do not try to sample from any underlying distribution, but try to achieve max-margin of the decision boundary, as illustrated in Fig. 1. Specifically, for every training instance " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ", we i.i.d. generate " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " virtual samples " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "x_{i,r}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\leq r \\leq R" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ") which distribute around the shell of the" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "28676" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "hypersphere centered at " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " and whose radius is controlled by a parameter " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": ". Note that the same " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " is shared by all training examples " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "1 \\leq i \\leq kN" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": "Technically, let " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " be the feature vector produced by the pre-trained model " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "z_{i} = \\mathcal{M}(x_{i})" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " from a forward calculation. Then, a noise vector " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "\\delta_{i,r}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " is randomly sampled from the standard multi-dimensional normal distribution " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "N(0, I_d)" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " is the length of " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "I_{d}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "d \\times d" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " identity matrix. By adding a scaled version of the noise vector to the " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": "-th training example, we obtain " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "z_{i,r}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": " (the " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": "-th virtual example for " + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 108, + 286, + 203 + ], + "type": "text", + "content": "):" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 130, + 204, + 286, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 204, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 130, + 204, + 286, + 216 + ], + "type": "interline_equation", + "content": "z _ {i, r} = z _ {i} + \\epsilon \\delta_ {i, r}. \\tag {1}", + "image_path": "010f71de7703ada38101c46a1871006df299010a5f1e51b4317228348f693796.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "text", + "content": "Its label " + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "inline_equation", + "content": "y_{i,r}" + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "text", + "content": " (the label of " + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 221, + 286, + 246 + ], + "type": "text", + "content": " is a positive number. Interesting properties exist in our virtual examples:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 247, + 286, + 426 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 49, + 247, + 286, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 247, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 49, + 247, + 286, + 270 + ], + "type": "text", + "content": "- Hypersphere for different training examples can overlap, so long as they belong to the same class (cf. Fig. 1)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 271, + 286, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 271, + 286, + 295 + ], + "spans": [ + { + "bbox": [ + 49, + 271, + 286, + 295 + ], + "type": "text", + "content": "- We require the virtual examples to be correctly classified, or, the original training examples are discarded." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "spans": [ + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": "- The virtual examples lie around the shell, not the interior of the hypersphere. According to the Gaussian Annulus Theorem [4], almost all the probability of a high-dimensional spherical Gaussian with unit variance is concentrated in a thin annulus of width " + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "inline_equation", + "content": "O(1)" + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": " with radius " + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "inline_equation", + "content": "\\sqrt{d}" + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": " is large. Since " + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": " is indeed large (e.g., " + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "inline_equation", + "content": "d = 2048" + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": "), the virtual examples reside around the shell. Hence, if we maximize the radius parameter " + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 49, + 297, + 286, + 426 + ], + "type": "text", + "content": " but require that the virtual examples are correctly classified, as Fig. 1 shows, we in essence achieve margin maximization in an instance-based manner." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 429, + 286, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 286, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 286, + 453 + ], + "type": "text", + "content": "Hence, the proposed method is named Instance-based Max-margin, abbreviated as IbM2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 460, + 204, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 204, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 204, + 472 + ], + "type": "text", + "content": "4.2. Ellipsoidal Noise Generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "type": "text", + "content": "One issue with the above isotropic noise sampling is that it ignores the structural property of the training examples. For instance, if the ranges for two feature dimensions are " + }, + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "type": "inline_equation", + "content": "[-100, 100]" + }, + { + "bbox": [ + 47, + 479, + 286, + 537 + ], + "type": "text", + "content": ", respectively, isotropic sampling is clearly unsuitable." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "text", + "content": "To overcome this drawback, we calculate a range vector " + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "inline_equation", + "content": "s = (s_1, s_2, \\ldots, s_d)" + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "text", + "content": " using all the original training examples regardless of the class label, where " + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "text", + "content": " is the sample standard deviation for the " + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 539, + 286, + 598 + ], + "type": "text", + "content": "-th dimension. Then, the IbM2 virtual examples are generated as (replacing Eq. 1)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 118, + 608, + 286, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 608, + 286, + 620 + ], + "spans": [ + { + "bbox": [ + 118, + 608, + 286, + 620 + ], + "type": "interline_equation", + "content": "z _ {i, r} = z _ {i} + \\epsilon (s \\odot \\delta_ {i, r}), \\tag {2}", + "image_path": "83f84a1a0bd6b7b5a0d2b3a33efbd3063ec67c1ea626859cd9d6374af5c9cf62.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "type": "text", + "content": " is element-wise multiplication. The final virtual example generation process is illustrated in Fig. 2. Note that estimating " + }, + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 47, + 629, + 286, + 677 + ], + "type": "text", + "content": " is dramatically easier than estimating the underlying distribution of every novel class." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "It is worth noting that this ellipsoidal noise generation is unsupervised, which distinguishes itself from Distribution calibration (DC) [40]. DC samples virtual examples based" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 328, + 79, + 526, + 207 + ], + "blocks": [ + { + "bbox": [ + 328, + 79, + 526, + 207 + ], + "lines": [ + { + "bbox": [ + 328, + 79, + 526, + 207 + ], + "spans": [ + { + "bbox": [ + 328, + 79, + 526, + 207 + ], + "type": "image", + "image_path": "712447196ab4e0ccd9fc2fb06b741943edec2ae3728db5f0a05caa24af42252c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "lines": [ + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "text", + "content": "Figure 2. Virtual example generation. Original input images pass through the pre-trained model " + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "text", + "content": " to get feature vectors (solid rectangles). Then, every feature vector i.i.d. samples " + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "text", + "content": " virtual examples (" + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "inline_equation", + "content": "R = 2" + }, + { + "bbox": [ + 305, + 222, + 545, + 267 + ], + "type": "text", + "content": " here) using Eq. 2." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 289, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 348 + ], + "type": "text", + "content": "on an estimated covariance structure, which is estimated from the few novel class training examples in a sample-wise manner and calibrated using the base set. As aforementioned, we argue that it makes sense to get rid of the dependency on a base set, then DC is not applicable." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "content": "More importantly, the reliability of this estimation of a dense covariance matrix is understandably much lower than our estimation of the range indicator vector " + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "content": " — we estimate " + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "content": " values using " + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "inline_equation", + "content": "k \\times N" + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "content": " examples, while DC estimates " + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "inline_equation", + "content": "d \\times d" + }, + { + "bbox": [ + 304, + 348, + 545, + 432 + ], + "type": "text", + "content": " values using only 1 example and the base set. The base set calibration will help DC, but clearly its estimation is still unreliable, as shown by experiments in [40, 44]" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 441, + 534, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 534, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 534, + 453 + ], + "type": "text", + "content": "4.3. Binary Search to Find the Largest Possible " + }, + { + "bbox": [ + 305, + 441, + 534, + 453 + ], + "type": "inline_equation", + "content": "\\epsilon" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "type": "text", + "content": "Obviously we want " + }, + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "type": "text", + "content": " to be as large as possible to achieve max-margin, under the condition that virtual examples are classified correctly. Hence, we design a simple binary search to find the optimal value for " + }, + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 459, + 545, + 506 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": "For any given " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " value, we can generate " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "kNR" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " virtual examples " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "(x_{i,r},y_{i,r})" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "(1\\leq i\\leq kN,1\\leq r\\leq R)" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " using Eq. 2. We denote the virtual training set for this particular value of " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "D^{\\epsilon}" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": ". Then, we train a linear classifier with parameters " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " to classify " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "D^{\\epsilon}" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " and obtain the training accuracy. If the training accuracy is too high (larger than a threshold " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " is enlarged; otherwise " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": " is shrunk. The binary search maintains a search range, when the search range is tight enough (when the range is less than 0.05 in Algorithm 1), the search terminates, and we have found the optimal value " + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 304, + 506, + 545, + 625 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 627, + 457, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 627, + 457, + 638 + ], + "spans": [ + { + "bbox": [ + 317, + 627, + 457, + 638 + ], + "type": "text", + "content": "We have a few notes for finding " + }, + { + "bbox": [ + 317, + 627, + 457, + 638 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 317, + 627, + 457, + 638 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 308, + 639, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 26, + "blocks": [ + { + "bbox": [ + 308, + 639, + 514, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 639, + 514, + 651 + ], + "spans": [ + { + "bbox": [ + 308, + 639, + 514, + 651 + ], + "type": "text", + "content": "- Unlike DC [40], we do not need a validation set." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "type": "text", + "content": "- The threshold " + }, + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "type": "text", + "content": " does not need to be 1 (100%). In SVM learning, the slack variable trick allows some support vectors not to have max-margin. Similarly, we just need " + }, + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 308, + 652, + 545, + 700 + ], + "type": "text", + "content": " to be close to 1 (0.9 in our experiments)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 308, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 308, + 701, + 545, + 713 + ], + "type": "text", + "content": "- Different from classic augmentation techniques [26, 28]," + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28677" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 92, + 276, + 270 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 216, + 83 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 216, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 216, + 83 + ], + "type": "text", + "content": "Algorithm 1 Pseudo code for searching " + }, + { + "bbox": [ + 49, + 72, + 216, + 83 + ], + "type": "inline_equation", + "content": "\\epsilon" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 92, + 276, + 270 + ], + "lines": [ + { + "bbox": [ + 47, + 92, + 276, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 276, + 270 + ], + "type": "text", + "content": "Inputs: \nx : training features of a few-shot task \ny : training labels of a few-shot task \nR : sampling times for an instance \nT : accuracy threshold for searching \nOutputs: \neps : epsilon for sampling \nleft = 0.0 \nright = a large value \neps = right / 2 \nW = initclassifier \nwhile True: \n acc = train_and.eval(W, x, y, eps, R) \n if acc > T: \n left = eps # increase epsilon \n else: \n right = eps # decrease epsilon \n eps = (left + right) / 2.0 \n if right - left < 0.05: \n break" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "code", + "guess_lang": "python" + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "spans": [ + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "text", + "content": "which introduce minor disturbance into input features, the distribution of " + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "inline_equation", + "content": "D^{\\hat{\\epsilon}}" + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "text", + "content": " is drastically different from " + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "text", + "content": " because of a large " + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 58, + 297, + 286, + 332 + ], + "type": "text", + "content": " (empirically 1.24 on average)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "text", + "content": "Finally, the IbM2 pipeline is simple: First, use Algorithm 1 to find " + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "text", + "content": ". Second, generate the virtual dataset " + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "inline_equation", + "content": "D^{\\hat{\\epsilon}}" + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "text", + "content": ". And third, learn a linear classifier " + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "text", + "content": ". Note that the pretrained model " + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 334, + 286, + 381 + ], + "type": "text", + "content": " is frozen and will not be updated." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 392, + 172, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 172, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 172, + 404 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 411, + 286, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 286, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 286, + 459 + ], + "type": "text", + "content": "We evaluate our IbM2 method on both setups: the proposed pFSL in many-way few-shot scenario, and also comparing IbM2 under the traditional FSL few-way setting with state-of-the-art FSL methods to further validate its effectiveness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 467, + 179, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 179, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 179, + 479 + ], + "type": "text", + "content": "5.1. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "text", + "content": "For both the searching and training stages of IbM2, all features extracted by the backbone " + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "text", + "content": " were " + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "text", + "content": "-normalized first. When learning the classification head (both during the binary search and after " + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 46, + 484, + 286, + 580 + ], + "type": "text", + "content": " was determined), we used Adam as the optimizer and the label smoothed cross-entropy loss [34] as the learning objective. The pre-trained model was trained using various self-supervised learning methods on the ImageNet-1K [30] training set." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "type": "text", + "content": "During the binary search, for all the experiments we will report, we always set " + }, + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "type": "text", + "content": " as 200, " + }, + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 580, + 286, + 628 + ], + "type": "text", + "content": " as 0.9 in pFSL and 0.999 in the traditional FSL setting, except when we carried out ablation experiments on these hyperparameters." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 628, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 628, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 58, + 628, + 286, + 640 + ], + "type": "text", + "content": "Full implementation details are included in the appendix." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 223, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 223, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 223, + 659 + ], + "type": "text", + "content": "5.2. Experiments in the pFSL Setting" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": "Datasets and Evaluation Setup. We explored two common many-way classification datasets, ImageNet-1K [30] and CUB-200-2011 (CUB) [38]. ImageNet-1K contains about 1.28 million training images from 1,000 classes and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "50,000 images for evaluation. CUB is a fine-grained recognition dataset composed of 11,788 images belonging to 200 classes of birds, 5,994 for training and 5,794 for evaluation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "text", + "content": "For both datasets, we randomly sampled the training sets for pFSL by selecting " + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "text", + "content": " images from every class (i.e., " + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "text", + "content": "-shot) and using all the classes (1000 and 200, respectively) to form the novel set. " + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "text", + "content": " is chosen from " + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\{1, 2, 3, 4, 5, 8, 16\\}" + }, + { + "bbox": [ + 305, + 109, + 545, + 180 + ], + "type": "text", + "content": ". The evaluation was carried out on the full validation (for ImageNet) or test (for CUB) set." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 181, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 545, + 252 + ], + "type": "text", + "content": "Utilizing various self-supervised backbone network " + }, + { + "bbox": [ + 304, + 181, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 181, + 545, + 252 + ], + "type": "text", + "content": " pre-trained on ImageNet, we compare two sets of results: one in which the linear classifier was obtained by using the original training set, the other by using IbM2's virtual examples. We report the top-1 accuracy and its standard deviation computed over 3 randomly sampled novel sets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 253, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 337 + ], + "type": "text", + "content": "Main Results. As the results in Table 1 suggest, we evaluated on two types of backbones: Vision Transformer (ViT) [13] and ResNet50 [18]. The pre-training methods included DINO [6], MoCov3 [10], MSN [2], SimCLR [8] and BYOL [17]. Table 1 shows that in almost all cases, IbM2 benefited the few-shot learning process and improved the top-1 accuracy." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": "When the number of shots " + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "inline_equation", + "content": "(k)" + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": " is very small " + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "inline_equation", + "content": "(\\leq 2)" + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": ", the improvement of IbM2 over the baseline is roughly " + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": " on average. However, as the number of training shots goes larger, it is clear that the level of accuracy improvement increases gradually from " + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "inline_equation", + "content": "\\sim 1\\%" + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "inline_equation", + "content": "\\sim 2\\%" + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": ", even " + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "inline_equation", + "content": ">3\\%" + }, + { + "bbox": [ + 304, + 338, + 545, + 408 + ], + "type": "text", + "content": " in some cases." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 410, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 545, + 457 + ], + "type": "text", + "content": "A useful observation from these results is that in pFSL, both the baseline and IbM2 have small standard deviations, that is, more robust in evaluation. Hence, we do not need 500 episodes in pFSL any longer—3 is enough." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "text", + "content": "Semi-supervised learning. In the self-supervised learning literature, it is a common practice to use ImageNet-1K training images to learn a backbone in the unsupervised manner, then use a small portion (e.g., " + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "text", + "content": ") of the training data now with labels to train a classifier. This semi-supervised learning task can also be viewed as our pFSL setting. Hence, we also report the " + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "text", + "content": " ImageNet-1K semi-supervised learning (on average 12 labeled training images per class) results in Table 2. IbM2 consistently improved various self-supervised models and backbone architectures in all cases, with " + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 304, + 458, + 545, + 590 + ], + "type": "text", + "content": " top-1 accuracy increase." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 598, + 531, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 531, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 531, + 611 + ], + "type": "text", + "content": "5.3. Experiments in the Traditional FSL Setting" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Datasets and Evaluation Setup. We evaluated IbM2 in the traditional FSL setup, too. We conducted experiments on two standard benchmark datasets, mini-ImageNet [37] and CIFAR-FS [3]. mini-ImageNet consists of 100 categories selected from ImageNet-1K, which are further split into 64 base, 16 val and 20 novel categories according to [29]. CIFAR-FS is created by randomly shuffling the 100 categories of CIFAR-100 [24] into 64 base, 16 val, 20 novel" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28678" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 69, + 509, + 288 + ], + "blocks": [ + { + "bbox": [ + 86, + 69, + 509, + 288 + ], + "lines": [ + { + "bbox": [ + 86, + 69, + 509, + 288 + ], + "spans": [ + { + "bbox": [ + 86, + 69, + 509, + 288 + ], + "type": "table", + "html": "
DatasetPre-training MethodBackboneIbM2Shot per Class
12345816
ImageNet-1KDINOViT-S/16✓39.2 ± 0.349.2 ± 0.254.1 ± 0.456.7 ± 0.258.0 ± 0.160.4 ± 0.162.7 ± 0.1
39.2 ± 0.349.4 ± 0.354.6 ± 0.457.6 ± 0.159.3 ± 0.162.4 ± 0.265.8 ± 0.1
MoCov3ViT-S/16✓32.7 ± 0.642.0 ± 0.246.9 ± 0.349.6 ± 0.451.0 ± 0.153.8 ± 0.156.6 ± 0.2
33.9 ± 0.643.2 ± 0.248.4 ± 0.351.3 ± 0.352.8 ± 0.256.1 ± 0.159.8 ± 0.2
MSNViT-S/16✓47.9 ± 0.156.2 ± 0.459.8 ± 0.361.6 ± 0.162.4 ± 0.264.4 ± 0.366.1 ± 0.1
47.8 ± 0.256.4 ± 0.460.5 ± 0.262.5 ± 0.263.6 ± 0.266.0 ± 0.268.4 ± 0.0
ViT-B/4✓53.2 ± 0.264.5 ± 0.468.9 ± 0.270.9 ± 0.272.0 ± 0.373.8 ± 0.175.0 ± 0.2
54.0 ± 0.164.9 ± 0.569.4 ± 0.271.4 ± 0.172.7 ± 0.474.7 ± 0.076.4 ± 0.2
ViT-L/7✓57.3 ± 0.466.5 ± 0.469.8 ± 0.571.6 ± 0.472.2 ± 0.273.8 ± 0.175.1 ± 0.1
57.7 ± 0.466.6 ± 0.570.1 ± 0.671.8 ± 0.472.6 ± 0.274.3 ± 0.176.0 ± 0.0
SimCLRResNet50✓21.4 ± 0.430.3 ± 0.136.1 ± 0.339.8 ± 0.242.0 ± 0.146.8 ± 0.151.9 ± 0.0
23.6 ± 0.433.4 ± 0.239.0 ± 0.442.0 ± 0.344.2 ± 0.148.0 ± 0.052.7 ± 0.0
BYOLResNet50✓26.5 ± 0.335.7 ± 0.241.5 ± 0.445.1 ± 0.247.2 ± 0.151.8 ± 0.157.1 ± 0.1
27.5 ± 0.337.5 ± 0.143.3 ± 0.446.8 ± 0.249.1 ± 0.153.2 ± 0.158.0 ± 0.1
CUBDINOViT-S/16✓35.4 ± 1.249.0 ± 0.556.8 ± 0.860.8 ± 0.765.2 ± 0.970.6 ± 0.975.9 ± 0.3
36.2 ± 1.449.6 ± 0.657.4 ± 1.062.0 ± 0.666.4 ± 0.872.5 ± 0.879.0 ± 0.2
MSNViT-S/16✓32.1 ± 1.645.0 ± 0.653.1 ± 0.656.7 ± 0.161.4 ± 0.567.3 ± 0.073.6 ± 0.4
33.0 ± 1.445.8 ± 0.753.2 ± 0.957.1 ± 0.462.0 ± 1.068.4 ± 0.175.7 ± 0.2
ViT-L/7✓34.9 ± 1.349.4 ± 0.458.8 ± 0.862.7 ± 0.967.2 ± 0.373.8 ± 0.880.4 ± 0.2
37.5 ± 1.250.1 ± 0.559.0 ± 0.862.6 ± 0.567.5 ± 0.673.9 ± 0.481.0 ± 0.1
", + "image_path": "4a7e434bbbf813df594e06937efd54181e9cb8c15869f5665f0de17fca1cea00.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 83, + 346, + 254, + 536 + ], + "blocks": [ + { + "bbox": [ + 46, + 294, + 547, + 328 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 547, + 328 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 547, + 328 + ], + "type": "text", + "content": "Table 1. Average of top-1 accuracy (%) with standard deviation across 3 random subsets on ImageNet-1K and CUB. A √ in the column IbM2 denotes the proposed IbM2 method, or the baseline method if it is blank. Those IbM2 results that are at least 0.5% higher than the baseline are shown in boldface." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 346, + 254, + 536 + ], + "lines": [ + { + "bbox": [ + 83, + 346, + 254, + 536 + ], + "spans": [ + { + "bbox": [ + 83, + 346, + 254, + 536 + ], + "type": "table", + "html": "
Pre-training MethodBackboneIbM2Top 1
DINOViT-S/16✓62.5
65.0
MoCov3ViT-S/16✓56.0
58.9
MSNViT-S/16✓65.9
67.9
ViT-B/4✓74.9
76.1
ViT-L/7✓74.8
75.6
SimCLRResNet50✓50.5
51.3
BYOLResNet50✓55.7
56.8
", + "image_path": "bf4058dbff62a46f46c03869804b761720262bb2e83ac4a5e9dbf1eff34b95be.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 544, + 288, + 579 + ], + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 579 + ], + "type": "text", + "content": "Table 2. Top-1 accuracy (\\%) of " + }, + { + "bbox": [ + 46, + 544, + 288, + 579 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 544, + 288, + 579 + ], + "type": "text", + "content": " ImageNet-1K semi-supervised learning. The training set contains on average 12 labeled training samples per category." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "categories. Note that in order to perform traditional few-shot learning, only the novel split of these two datasets is required to sample many 5-way 1/5-shot episodes. We report the metrics mentioned in [16]: the average " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{ACC}_m)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", worst-case " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{ACC}_1)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", average of worst 10 " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{ACC}_{10})" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", average of worst 100 " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{ACC}_{100})" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " episodes' accuracy, and the standard deviation " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\sigma)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " over 500 episodes for comprehensive evaluation. To make the results more reliable, we average the value of each metric from 5 runs with different" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 349, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 384 + ], + "type": "text", + "content": "random seeds. We adopted PMF [22], " + }, + { + "bbox": [ + 304, + 349, + 545, + 384 + ], + "type": "inline_equation", + "content": "S2M2_{R}" + }, + { + "bbox": [ + 304, + 349, + 545, + 384 + ], + "type": "text", + "content": " [27] and Meta-Baseline [11] as the pre-training or meta-training approaches to obtain the backbone weights out of the base set." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "text", + "content": "Main Results. As shown in Table 3, by plugging IbM2 in during classifier learning, the proposed IbM2 improved the average accuracy " + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_m" + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "text", + "content": " in all cases except only 1 result. And, the standard deviation " + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "text", + "content": " was reduced by IbM2 or remain unchanged in all cases. As [16] advocated, smaller " + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 384, + 546, + 456 + ], + "type": "text", + "content": " means the learning process is more stable." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": "[16] also advocates the worst-case episode's accuracy is more important than the average accuracy among all episodes. Table 3 shows that IbM2 almost always leads to higher worst-case " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "(\\mathrm{ACC}_1)" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " or near-worst-case " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "(\\mathrm{ACC}_{10}," + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_{100})" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " accuracy. Furthermore, the average gain of " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_m" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " , which is far less than that of " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_1" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "(1.3\\%)" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " .As for " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_{10}" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_{100}" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " , their gains are very similar, both around " + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 457, + 547, + 577 + ], + "type": "text", + "content": " . These observations demonstrate that IbM2 can boost the recognition accuracy of few-shot learning in almost every scenario, especially the worst case one." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 578, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 547, + 613 + ], + "type": "text", + "content": "At last, by comparing the numbers in Tables 1 and 3, pFSL is more challenging than traditional FSL, which leads to more open questions to solve." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 622, + 407, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 407, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 407, + 634 + ], + "type": "text", + "content": "5.4. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 665 + ], + "type": "text", + "content": "We performed ablation studies for IbM2 in the pFSL setting on ImageNet-1K." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": "Instance-based vs. class-based max-margin. IbM2 seeks max-margin through an instance-based manner. In this study, we compare this instance-based max-margin with the well-known support vector machine (SVM), which" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28679" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 69, + 509, + 286 + ], + "blocks": [ + { + "bbox": [ + 85, + 69, + 509, + 286 + ], + "lines": [ + { + "bbox": [ + 85, + 69, + 509, + 286 + ], + "spans": [ + { + "bbox": [ + 85, + 69, + 509, + 286 + ], + "type": "table", + "html": "
DatasetPre-training & Meta-trainingBackboneIbM21-shot5-shot
ACCmσACC1ACC10ACC100ACCmσACC1ACC10ACC100
mini-ImageNetPMFViT-S/16✓93.46.161.372.483.498.41.887.791.495.6
94.45.663.274.785.198.61.886.191.395.9
ViT-B/16✓94.95.466.975.586.098.81.689.192.996.3
95.65.169.677.687.198.91.689.393.096.3
ResNet50✓94.95.367.275.286.398.51.789.391.995.8
95.35.266.174.686.998.81.689.392.796.3
S2M2RWRN-28-10✓65.410.032.039.350.782.37.152.062.571.8
65.810.032.540.551.182.97.053.363.372.3
Meta-BaselineResNet12✓62.910.426.734.347.479.07.554.758.067.9
63.010.232.335.647.979.57.354.958.568.7
CIFAR-FSPMFViT-S/16✓87.98.351.761.774.895.54.274.781.888.5
89.08.159.264.175.995.74.273.381.788.7
ViT-B/16✓89.88.155.264.876.896.04.173.182.289.2
90.38.058.965.577.496.04.174.181.889.2
ResNet50✓81.710.435.251.665.891.35.571.275.182.7
82.310.336.351.166.591.65.373.376.083.2
S2M2RWRN-28-10✓75.210.844.046.759.287.77.154.767.976.8
75.510.842.445.559.287.77.054.968.177.0
Meta-BaselineResNet12✓72.711.632.042.956.184.87.554.765.173.6
72.311.532.842.355.785.17.556.365.474.1
", + "image_path": "9a64f718319518e02c57030c5d203ef3fd47780a923afe879b9e2040a2d35723.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "type": "text", + "content": "achieves max-margin in a class-based manner. We experimented with SVM using the linear kernel function in the LIBSVM [7] software package. By iterating the value of SVM's regularization hyperparameter " + }, + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "type": "text", + "content": " from the set " + }, + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\{0.1, 1, 10, 100, 1000\\}" + }, + { + "bbox": [ + 46, + 338, + 287, + 410 + ], + "type": "text", + "content": ", we found the best accuracy among them to compare with our IbM2 method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "content": "As shown in Table 4, the proposed IbM2 method outperforms SVM with the best " + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "content": " by a significant margin in all cases. Specifically, the recognition accuracy improves " + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "inline_equation", + "content": "\\sim 2\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "content": " on average, and even up to " + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "inline_equation", + "content": "\\sim 4\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "content": " in the extremely scarce 1-shot case. These results demonstrate that our instance-based margin generated by IbM2 helps more to learn a robust classification boundary, especially when the training distribution is drastically shifted." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": "Sensitivity of " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ". As described in Sec. 4, one original training example is turned into " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": " virtual examples to form the training set " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "D^{\\hat{\\epsilon}}" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ". In this part, we study the effect of the hyperparameter " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ". As shown in Table 5, when the training shots are highly limited, increasing " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": " significantly improves recognition accuracy. As the number of training shots gets larger, the accuracy difference between a large " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R = 400" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ") and a small one (" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "R = 1" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ") gradually decreases from " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "When training samples are extremely scarce, it is difficult to model the correct Gaussian distribution with a few samples in a high-dimensional space. Therefore, increasing " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " is necessary for a good estimation. When more training shots are available, the need for a large value of sampling times is reduced, hence the accuracy difference between different " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " becomes smaller, too. Based on these results, we let " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "R = 200" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " in all our experiments." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 335, + 544, + 384 + ], + "blocks": [ + { + "bbox": [ + 46, + 294, + 545, + 317 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 545, + 317 + ], + "type": "text", + "content": "Table 3. Results of 5-way classification on mini-ImageNet and CIFAR-FS in the traditional few-shot learning setting. For the baseline methods, we obtain the results from their respective official implementations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 335, + 544, + 384 + ], + "lines": [ + { + "bbox": [ + 308, + 335, + 544, + 384 + ], + "spans": [ + { + "bbox": [ + 308, + 335, + 544, + 384 + ], + "type": "table", + "html": "
MethodShot per Class
12345816
SVM54.864.868.270.070.872.874.7
IbM258.266.970.271.972.774.376.1
", + "image_path": "e9892f2ebb7e676f9097e5070b4781911490d89360b61d3dbd0fc0ffcc5140b1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 315, + 435, + 537, + 517 + ], + "blocks": [ + { + "bbox": [ + 305, + 391, + 545, + 424 + ], + "lines": [ + { + "bbox": [ + 305, + 391, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 545, + 424 + ], + "type": "text", + "content": "Table 4. Top-1 accuracy " + }, + { + "bbox": [ + 305, + 391, + 545, + 424 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 391, + 545, + 424 + ], + "type": "text", + "content": " with different margin-based methods on ImageNet-1K classification with ViT-L/7 from MSN as the pretrained backbone." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 435, + 537, + 517 + ], + "lines": [ + { + "bbox": [ + 315, + 435, + 537, + 517 + ], + "spans": [ + { + "bbox": [ + 315, + 435, + 537, + 517 + ], + "type": "table", + "html": "
RShot per Class
12345816
132.942.747.850.852.555.960.1
1033.743.648.551.452.956.260.3
5033.843.748.651.553.056.260.3
20034.443.848.751.553.056.260.3
40034.543.848.651.553.056.260.3
", + "image_path": "90f01a545b47ef078a4cb74b56fa6a19aaf3d08d5e8935c96f4eaa6b9e6eac94.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 568, + 542, + 628 + ], + "blocks": [ + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "lines": [ + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "type": "text", + "content": "Table 5. Top-1 accuracy " + }, + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "type": "text", + "content": " of classification with different " + }, + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 525, + 545, + 556 + ], + "type": "text", + "content": " on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 568, + 542, + 628 + ], + "lines": [ + { + "bbox": [ + 310, + 568, + 542, + 628 + ], + "spans": [ + { + "bbox": [ + 310, + 568, + 542, + 628 + ], + "type": "table", + "html": "
Sampling SchemaShot per Class
12345816
-33.142.447.249.851.655.259.2
Spherical33.042.147.150.251.855.359.8
Ellipsoidal34.443.848.751.553.056.260.3
", + "image_path": "9faa6ef010c33c561d21df73961e02f0702ec572bfda0bad7476b29389a8b7a8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 635, + 545, + 681 + ], + "lines": [ + { + "bbox": [ + 305, + 635, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 305, + 635, + 545, + 681 + ], + "type": "text", + "content": "Table 6. Top-1 accuracy (\\%) of classification with different sampling schemas on ImageNet-1K with ViT-S/16 from MoCov3 as the pre-trained backbone. '-' denotes the simple baseline using only the original training examples." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28680" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "Ellipsoidal vs. isotropic sampling. We have described two noise sampling strategies to generate virtual examples. The ellipsoidal one is preferred over the isotropic one, and is used in IbM2. In this part, we evaluate the effectiveness of this sampling schema by experimentally comparing these two sampling strategies. The isotropic sampling strategy is denoted as Spherical in Table 6." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 286, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 286, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 286, + 298 + ], + "type": "text", + "content": "As shown in Table 6, the accuracy in the ellipsoidal sampling schema is consistently better than its spherical counterpart or the baseline. Moreover, in low-shot cases " + }, + { + "bbox": [ + 46, + 156, + 286, + 298 + ], + "type": "inline_equation", + "content": "(\\leq 3)" + }, + { + "bbox": [ + 46, + 156, + 286, + 298 + ], + "type": "text", + "content": ", sampling with spherical Gaussian slightly degraded the recognition accuracy. The reason may be that the standard deviation of different channels calculated from training features varied a lot, thus simply regarding all channels as independent and identically distributed might make the sampled points significantly shifted from the underlying distribution. However, as the number of training samples increases, both isotropic and ellipsoidal sampling outperformed the baseline." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 300, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 286, + 323 + ], + "type": "text", + "content": "Based on these observations, we chose to adopt the ellipsoidal noise sampling (Eq. 2) in IbM2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 286, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 286, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 286, + 393 + ], + "type": "text", + "content": "On what classes can IbM2 help? Finally, we study what classes will benefit from IbM2—will most or only a small portion of classes be improved by IbM2? After the training of the baseline and IbM2 finished, we calculated the class-wise validation accuracy for every class on ImageNet-1K, as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 393, + 286, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 393, + 286, + 421 + ], + "spans": [ + { + "bbox": [ + 132, + 393, + 286, + 421 + ], + "type": "interline_equation", + "content": "\\mathrm {A C C} ^ {k} = \\frac {N _ {c o r} ^ {k}}{N _ {c l s} ^ {k}}, \\tag {3}", + "image_path": "bf375abb91f237a908bdd02d9efc30d2fc781f3c4c7bea7c02591e2e296e8e63.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}^k" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": " is the per-class accuracy (i.e., recall) of the " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": "-th class, " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "N_{cls}^k" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": " is the number of test samples class " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": " contains (" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "N_{cls}^k = 50" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": " in ImageNet-1K) and " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "N_{cor}^k" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": " is the number of correctly classified samples of class " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": ". For every class, we obtain the difference of per-class accuracy (that of IbM2 minus that of the baseline). A positive difference is an accuracy gain and a negative gain is in fact an accuracy loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "type": "text", + "content": "We then sort the baseline's per-class accuracy in the ascending order. Following this order, we rearrange the per-class accuracy gains. The 1000 accuracy gains are divided into 10 histogram bins in the rearranged order, and inside each bin the 100 per-class accuracy gains are averaged to obtain the accuracy gain of that bin. Fig. 3 plots the average accuracy gain in each bin." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "We find that IbM2 improves average per-class accuracy in almost every histogram bin (i.e., is above the \"0.0\" horizon in the " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "-axis). More detailed numbers reveal that the recognition accuracy of more than " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "65\\%" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " categories out of 1000 is improved in all shots. Furthermore, Fig. 3 shows a trend: the more accurate a class is, the higher gains IbM2 can achieve over the baseline. That is, when the task is too difficult for the baseline, IbM2 can help but its usefulness is restricted. But, when the baseline is already accurate enough (categorical subset 9 and later), the room for IbM2's" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 75, + 542, + 198 + ], + "blocks": [ + { + "bbox": [ + 309, + 75, + 542, + 198 + ], + "lines": [ + { + "bbox": [ + 309, + 75, + 542, + 198 + ], + "spans": [ + { + "bbox": [ + 309, + 75, + 542, + 198 + ], + "type": "image", + "image_path": "02cd9849b59af841bb571db21f0955ff5801327a920237f0a8f470a67f08f3ad.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 212, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 305, + 212, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 545, + 243 + ], + "type": "text", + "content": "Figure 3. Categorical accuracy gain " + }, + { + "bbox": [ + 305, + 212, + 545, + 243 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 212, + 545, + 243 + ], + "type": "text", + "content": " of IbM2 compared to baseline with ViT-S/16 pre-trained by MoCov3 [10] as the backbone." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 267, + 544, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 544, + 290 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 544, + 290 + ], + "type": "text", + "content": "- further improvement is small again. It is the middle range that IbM2 is the most useful." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 302, + 468, + 315 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 302, + 468, + 315 + ], + "spans": [ + { + "bbox": [ + 306, + 302, + 468, + 315 + ], + "type": "text", + "content": "6. Conclusions and Limitations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 323, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 323, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 545, + 407 + ], + "type": "text", + "content": "In this paper, we advocated pFSL, a new practical few-shot learning setting. We also proposed IbM2, an instance-based max-margin method to improve few-shot learning. With the technological advancements, it is time to upgrade the traditional FSL settings. We need a simpler, easier-to-evaluate, more challenging and more practical FSL setting, and the proposed pFSL task satisfies these requirements." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 407, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 545, + 502 + ], + "type": "text", + "content": "To address the challenges associated with the scarcity of training examples, we introduced IbM2. Instead of maximizing the class-level margin, IbM2 is instance-based margin maximization. It achieved significant improvements in both pFSL and the traditional FSL settings consistently. IbM2 is simple and reliable. It introduces only 2 hyperparameters, and the default values of them worked well in experiments across different architectures and tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "content": "As the experiments indicated, IbM2 works the best for the middle range in terms of task difficulty. In a " + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "content": "-shot task when " + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "content": " is extremely small, there is still considerable room for improvement in the pFSL setting. Furthermore, IbM2 freezes the backbone and only learns the linear classifier. In the future, we plan to improve the very small shot cases (e.g., " + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 305, + 502, + 545, + 598 + ], + "type": "text", + "content": ") and better tune the backbone in few-shot learning to push the current limits further." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 609, + 415, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 415, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 415, + 624 + ], + "type": "text", + "content": "7. Acknowledgments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 629, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 712 + ], + "type": "text", + "content": "This research received substantial support from Jianxin Wu, who wrote IbM2's first working code and whose generous assistance and invaluable guidance were sincerely appreciated throughout our research process. Additionally, we acknowledge the funding provided by the National Natural Science Foundation of China under Grant 62276123 and Grant 61921006." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28681" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Arman Afrasiyabi, Hugo Larochelle, Jean-François Lalonde, and Christian Gagné. 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In ACM International Conference on Multimedia, page 6831-6839, 2022." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28683" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Instance-level Expert Knowledge and Aggregate Discriminative Attention for Radiology Report Generation/67919adf-151b-4ec6-a2cc-6cf5e3e354ee_content_list.json b/2024/Instance-level Expert Knowledge and Aggregate Discriminative Attention for Radiology Report Generation/67919adf-151b-4ec6-a2cc-6cf5e3e354ee_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ab4949644df7b923377ef773d821e0f7dc4132aa --- /dev/null +++ b/2024/Instance-level Expert Knowledge and Aggregate Discriminative Attention for Radiology Report Generation/67919adf-151b-4ec6-a2cc-6cf5e3e354ee_content_list.json @@ -0,0 +1,1753 @@ +[ + { + "type": "text", + "text": "Instance-level Expert Knowledge and Aggregate Discriminative Attention for Radiology Report Generation", + "text_level": 1, + "bbox": [ + 98, + 130, + 872, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shenshen Bu, Taiji Li, Yuedong Yang,*Zhiming Dai * \nSchool of Computer Science and Engineering, Sun Yat-sen University, China \n{bushh, litj5}@mail2.sysu.edu.cn, {yangyd25, daizhim}@mail.sysu.edu.cn", + "bbox": [ + 173, + 203, + 795, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic radiology report generation can provide substantial advantages to clinical physicians by effectively reducing their workload and improving efficiency. Despite the promising potential of current methods, challenges persist in effectively extracting and preventing degradation of prominent features, as well as enhancing attention on pivotal regions. In this paper, we propose an Instance-level Expert Knowledge and Aggregate Discriminative Attention framework (EKAGen1) for radiology report generation. We convert expert reports into an embedding space and generate comprehensive representations for each disease, which serve as Preliminary Knowledge Support (PKS). To prevent feature disruption, we select the representations in the embedding space with the smallest distances to PKS as Rectified Knowledge Support (RKS). Then, EKAGen diagnoses the diseases and retrieves knowledge from RKS, creating Instance-level Expert Knowledge (IEK) for each query image, boosting generation. Additionally, we introduce Aggregate Discriminative Attention Map (ADM), which uses weak supervision to create maps of discriminative regions that highlight pivotal regions. For training, we propose a Global Information Self-Distillation (GID) strategy, using an iteratively optimized model to distill global knowledge into EKAGen. Extensive experiments and analyses on IU X-Ray and MIMIC-CXR datasets demonstrate that EKAGen outperforms previous state-of-the-art methods.", + "bbox": [ + 75, + 324, + 473, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 746, + 209, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Radiology reports play a crucial role in the medical diagnosis and treatment process. However, interpreting radiology image can be extremely time-consuming, even for experienced radiologists. Hence, the automatic report generation [25, 29, 44, 47, 55] has emerged as a prominent research area within the medical imaging community. In", + "bbox": [ + 75, + 772, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6117816f5361dc6781376bf5d648266d936d771534e106af8cd4703e9011778e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 290, + 890, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eb02dce2227d9141d87781fb6c35650166d95e8a77e67f6a21747a5ff9703d0d.jpg", + "image_caption": [ + "Figure 1. (a) displays the feature degradation caused by the distinction between vanilla methods' prior knowledge and LGM's embedding networks. (b) demonstrates our method that unifies the embedding network to prevent feature degradation and generates instance-level expert knowledge based on diseases." + ], + "image_footnote": [], + "bbox": [ + 504, + 390, + 890, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "recent years, significant strides have been made in the automatic generation of radiology reports, benefiting from the development of image captioning [2, 7, 14, 16, 21].", + "bbox": [ + 496, + 580, + 890, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In addition to the inherent challenges of natural image captioning, radiology report generation suffers three additional bottlenecks [27, 31, 47]. Firstly, radiology images often lack discriminative features, which results in a scarcity of reference information for the report generation models. Secondly, abnormal lesions in medical images may not always have obvious appearances, making them challenging even for experienced radiologists to identify. Thirdly, there is significant data deviation in these datasets due to the rarity of certain diseases, making it challenging to collect positive samples. In recent years, several methods, including the template retrieval structure [8, 31], memory driven network [5, 6], and knowledge aware module [27, 34, 49], were developed to address these challenges and have shown promising results in report generation. For instance, R2GenCMN [6] leveraged a shared memory to capture the alignment between images and texts. GSKET [49] proposed a multi-head attention mechanism that enhances", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors. \n1https://github.com/hnjzbss/EKAGen", + "bbox": [ + 94, + 875, + 362, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14194", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "generation by combining visual features and knowledge.", + "bbox": [ + 76, + 90, + 450, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, as shown in Figure 1, (a) depicts that vanilla methods use separate embedding networks such as BERT [9, 48, 49] and Graph [15, 26, 54] to encode prior knowledge. This inconsistency between the embedding network for prior knowledge and the Language Generation Model (LGM) results in feature degradation, which causes prediction shifts when mapping word vectors back to the word space. As depicted in Figure 1 (b), our approach unifies the embedding network for prior knowledge and the Language Generation Model, and assigns instance-level prior knowledge to each instance based on the disease category, which differs to previous methods [15, 27, 49] incorporating general knowledge for every case, effectively resolving this issue. Additionally, previous methods [6, 18, 29, 31] fail to enhance attention on pivotal regions of the radiology image, thereby presenting certain limitations.", + "bbox": [ + 75, + 108, + 468, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method is based on two implicit and valuable priors: (i) Diseases with the same label should have similar representations in the feature space, and vice versa; and (ii) Features from pivotal regions offer richer and more meaningful semantic references. Guided by these priors, we propose an Instance-level Expert Knowledge and Aggregate Discriminative Attention framework (EKAGen) for radiology report generation. We use an embedding network that shares parameters with LGM to map the expert report set into an embedding space as support set. From this, we calculate the Preliminary Knowledge Support (PKS) for each disease by taking the mean of its support set in the embedding space. Then, we compute the distances between the representations of each disease in PKS and all representations of corresponding disease in embedding space and select the representations with the smallest distances as the Rectified Knowledge Support (RKS). For a query image, we utilize a DiagnosisBot to identify diseases and retrieve their corresponding representations from RKS. These representations are then combined to create Instance-level Expert Knowledge (IEK), which facilitates report generation during the decoding process. In addition, identifying abnormal regions in images is crucial for report generation. However, obtaining pixel-level annotations for these regions is laborious and expensive. To tackle this challenge, we propose the Aggregate Discriminative Attention Map (ADM), which can generate discriminative regions of multiple diseases in a radiology image and integrate them to enhance attention on pivotal regions, thereby boosting generation.", + "bbox": [ + 75, + 351, + 472, + 789 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 94, + 792, + 423, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We develop comprehensive embedding representations for each disease. By diagnosing the health conditions of different cases, we create Instance-level Expert Knowledge to provide our EKAGen with expert insights during the decoding process, addressing the issues of complex knowledge extraction and prominent feature degradation.", + "bbox": [ + 76, + 810, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To highlight pivotal regions, we employ weak supervision to generate activation maps, which are then used to create Aggregate Discriminative Attention Map (ADM). The ADM prioritizes key regions for each disease, reducing background noise and enhancing generation.", + "- To prevent potential feature erosion and provide more soft supervision, we propose a Global Information Self-Distillation (GID) strategy which utilizes an iteratively optimized model to distill global knowledge into our EK-AGen, enhancing generation without additional labels." + ], + "bbox": [ + 500, + 90, + 893, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 257, + 642, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Captioning", + "text_level": 1, + "bbox": [ + 500, + 282, + 674, + 299 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional image captioning methods typically rely on curated image-caption pairs to train an encoder-decoder model for generating text descriptions from input images. Early approaches [10, 12, 43] in this field employed a CNN-based encoder to extract visual features and an RNN/LSTM-based decoder for generating output sentences. To enhance visual comprehension, certain methods [2, 7, 17, 39] incorporated an object detector to identify and extract salient image regions. To foster greater interaction between the two modalities, attention mechanisms [7, 35, 36, 53] and graph neural networks [50, 51] gained widespread adoption. Recently, several impressive large-scale visual-language pre-training models [1, 16, 23, 24, 52] emerged, demonstrating outstanding performance in image captioning task. Natural scene image description focuses on generating concise sentences, while medical report generation requires detailed descriptions of medical images. Therefore, these approaches may not be suitable for the field of medical report generation.", + "bbox": [ + 496, + 306, + 893, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Medical Report Generation", + "text_level": 1, + "bbox": [ + 500, + 589, + 750, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Medical report generation, as an extension of image captioning, presents greater challenges with higher requirements for text description length and accuracy. Extensive research [4, 22, 42, 46] has yielded significant advancements in this task. PPKED [32] presented an approach that explored and distilled posterior and prior knowledge in radiology to mitigate data bias issues in report generation. Clinical-BERT [48] proposed a visual-language pretraining model that learned medical domain knowledge to enhance the performance of report generation. DCL [26] extracted specific knowledge from retrieved reports to modify the graph structure and integrated image features with updated graphs to improve textual representation. ME-Transformer [47] introduced learnable \"expert\" tokens in the encoder and decoder, allowing them to interact with vision tokens and enabling the model to focus on different regions, while an orthogonal loss minimizes overlap to capture distinct information. However, these methods have drawbacks such as complex prior knowledge extraction,", + "bbox": [ + 496, + 613, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14195", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ee928dc2411e8b458c5e185fbb761b3dce5195dbbd5107dd394e3a62a7cb0fdb.jpg", + "image_caption": [ + "Figure 2. EKAGen consists of four components: Instance-level Expert Knowledge (IEK), Aggregate Discriminative Attention Map (ADM), Global Information Self-Distillation (GID), and Language Generation Model (LGM). EKAGen utilizes IEK to address the problem of feature degradation, employs ADM to prioritize pivotal regions, and incorporates GID to distill global knowledge." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 890, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "prominent feature degradation, and inability to enhance attention on pivotal regions, resulting in certain limitations.", + "bbox": [ + 75, + 476, + 470, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 518, + 168, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present a comprehensive analysis of the generation process for Instance-level Expert Knowledge and Aggregate Discriminative Attention Map. Additionally, we describe the structure of our Language Generation Model and elaborate on the Global Information Self-Distillation strategy. Figure 2 shows our EKAGen structure.", + "bbox": [ + 75, + 544, + 468, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Instance-level Expert Knowledge", + "text_level": 1, + "bbox": [ + 76, + 642, + 369, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to address the problem of feature degradation of prior knowledge during the embedding process and the sparsity of features in radiology images, we propose the Instance-level Expert Knowledge (IEK) to boost generation.", + "bbox": [ + 75, + 665, + 468, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminary Theory of Knowledge Support Given an expert report set $\\mathcal{X} = \\{x_1, \\dots, x_N\\}$ with $C$ types of diseases, we compute the average similarity between $x_i$ belonging to class $c$ with the remaining cases within that class, and take the average as the panoptic score for $x_i$ . The case with the highest panoptic score is selected as the Knowledge Support. This process formulated as follows:", + "bbox": [ + 75, + 726, + 468, + 832 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} _ {c} = \\underset {\\mathcal {F} (x _ {i})} {\\arg \\max } \\frac {1}{| \\mathcal {X} _ {c} |} \\sum_ {x _ {j} \\in \\mathcal {X} _ {c}} S (\\mathcal {F} (x _ {i}), \\mathcal {F} (x _ {j})), x _ {i} \\in \\mathcal {X} _ {c} (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 839, + 468, + 878 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $S(\\cdot)$ is similarity metric, and $\\mathcal{F}(\\cdot)$ is the embedding", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "network that shares parameters with LGM, used to map reports to embedding space. $\\mathcal{X}_c\\subseteq \\mathcal{X}$ is all cases in class $c$", + "bbox": [ + 498, + 476, + 890, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminary Knowledge Support (PKS) The computational complexity of Equation 1 is $O\\left(\\sum_{c} N_{c}^{2}\\right)$ , which incurs high time cost. Inspired by the prototype [28, 41] paradigm, we first calculate the mean of all cases in class $c$ as the PKS, serving as a compressed representation for each disease:", + "bbox": [ + 498, + 506, + 890, + 580 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {c} = \\frac {1}{| \\mathcal {X} _ {c} |} \\sum_ {x _ {i} \\in \\mathcal {X} _ {c}} \\mathcal {F} \\left(x _ {i}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 589, + 890, + 627 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rectified Knowledge Support (RKS) As shown in Figure 1 (b), Formula 2 directly operates on the embedding features, potentially causing disruption to the original word features and leading to catastrophic forgetting. To tackle this issue, we compute the cosine similarity between $\\mathcal{P}_c$ and all cases in class $c$ . The cases with the highest similarity are considered as the Rectified knowledge Support $\\mathcal{K}$ :", + "bbox": [ + 496, + 633, + 893, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} _ {c} = \\underset {\\mathcal {F} \\left(x _ {i}\\right)} {\\arg \\max } \\frac {\\mathcal {P} _ {c} ^ {T} \\mathcal {F} \\left(x _ {i}\\right)}{\\left| \\left| \\mathcal {P} _ {c} \\right| \\right| \\cdot \\left| \\left| \\mathcal {F} \\left(x _ {i}\\right) \\right| \\right|}, x _ {i} \\in \\mathcal {X} _ {c} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 748, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{K}_c\\in \\mathbb{R}^{l_c\\times d}$ , $l_{c}$ is the number of tokens and $d$ is the embedding dimension. The combined computational complexities of Equation 2 and Equation 3 is $O(\\sum_{c}N_{c})$ , significantly lower than that of Equation 1.", + "bbox": [ + 496, + 794, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Expert Knowledge Navigator (EKN) In order to obtain the instance level expert knowledge, we utilize a multiclassification method as DiagnosisBot to detect diseases for", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14196", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a given image $I$ . By applying a threshold operation, we derive the category matrix $\\mathcal{C}_i$ for the $i$ -th disease:", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl o g i t = \\text {D i a g n o s i s B o t} (I) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 132, + 468, + 148 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {i} = \\left\\{ \\begin{array}{l l} \\mathbf {E}, & \\text {i f} \\sigma (\\operatorname {l o g i t} _ {i}) > \\text {t h r e} _ {i} \\\\ \\mathbf {0}, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 152, + 468, + 191 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{E} \\in \\mathbb{R}^{d \\times d}$ represents the identity matrix and $\\mathbf{0} \\in \\mathbb{R}^{d \\times d}$ represents the zero matrix. We conduct matrix multiplication between the $\\kappa_{i}$ and $\\mathcal{C}_i$ , followed by concatenation to generate Instance-level Expert Knowledge $\\kappa^I$ :", + "bbox": [ + 76, + 202, + 468, + 263 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} ^ {I} = \\operatorname {c o n c a t} \\left(\\mathcal {K} _ {1} \\mathcal {C} _ {1}, \\dots , \\mathcal {K} _ {i} \\mathcal {C} _ {i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 273, + 468, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Aggregate Discriminative Attention Map", + "text_level": 1, + "bbox": [ + 76, + 301, + 426, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The radiology image differs from natural scene images in that it contains more noise and the discriminative areas are often blurry. Inspired by Grad CAM [40], we introduce the Aggregate Discriminative Attention Map (ADM), which leverages weak supervision signal to generate discriminative regions while attenuating the background.", + "bbox": [ + 75, + 324, + 468, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gradient-weighted Class Activation Mapping To obtain the class discrimination localization map $L_{GradCAM}^{c}$ , Grad-CAM initially calculates the gradient of $y^{c}$ with respect to the feature maps $A$ . These gradients utilize GAP to calculate the weight $\\alpha_{k}^{c}$ for $k$ -th feature map and $c$ -th class:", + "bbox": [ + 75, + 415, + 468, + 489 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {k} ^ {c} = \\frac {1}{Z} \\sum_ {i} \\sum_ {j} \\frac {\\partial y ^ {c}}{\\partial A _ {i j} ^ {k}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 500, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Z$ are the number of pixels, $y^c$ is activation class score for the $c$ -th class, and $A_{ij}^{k}$ is activation of cell at spatial location i, j for $k$ -th feature map. Then, a weighted combination is performed followed by ReLU activation:", + "bbox": [ + 75, + 542, + 468, + 603 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {G r a d C A M} ^ {c} = R e L U \\sum_ {k} \\alpha_ {k} ^ {c} A _ {i j} ^ {k} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 617, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-diseases Aggregate Attention We utilize Grad-CAM to generate activation maps highlighting the salient regions. Specifically, a multi-classification method is used as Anomaly Locator, which produces logit scores, with the scores exceeding the threshold considered valid. For image $I$ with $K$ valid classes, we combine the activation maps and apply thresholding to identify regions with strong signals:", + "bbox": [ + 75, + 659, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {I} = \\sum_ {c = 1} ^ {K} R e L U \\sum_ {k} \\alpha_ {k} ^ {c} A _ {i j} ^ {k} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 775, + 468, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {i, j} ^ {I} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} M _ {i, j} > \\theta \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 820, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During visual analysis, we notice multiple gaps in $\\mathcal{M}^I$ . Therefore, we fill these gaps using morphological dilation", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to generate Aggregate Discriminative Attention Map $\\mathcal{A}^I$ :", + "bbox": [ + 500, + 90, + 877, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} _ {i j} ^ {I} = \\max _ {\\left(i ^ {\\prime}, j ^ {\\prime}\\right) \\in S} \\mathcal {M} _ {i + i ^ {\\prime}, j + j ^ {\\prime}} ^ {I} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 116, + 890, + 143 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $S$ defines the neighborhood range, we can then use $\\mathcal{A}^I$ as the foreground mask to diminish the background thereby boosting the discriminative regions in the image $I$ :", + "bbox": [ + 500, + 155, + 890, + 200 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI m g _ {a u g} = \\mathcal {A} ^ {I} \\odot I + \\gamma (1 - \\mathcal {A} ^ {I}) \\odot I \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 212, + 890, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma$ represents the scaling factor for the background, and $\\odot$ denotes the Hadamard Product operation.", + "bbox": [ + 498, + 242, + 890, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Language Generation Model", + "text_level": 1, + "bbox": [ + 500, + 282, + 756, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-modal Aligner We leverage linear layers to process the expert knowledge $\\mathcal{K}^I$ for image $I$ and the hidden features $\\mathcal{H}^{i - 1}\\in \\mathbb{R}^{n\\times d}$ from the previous (i-1)-th decoder output. These features are then concatenated and projected to generate the multi-modal feature $\\mathcal{M}^i\\in \\mathbb{R}^{n\\times d}$ :", + "bbox": [ + 498, + 306, + 890, + 381 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} _ {p} ^ {I}, \\mathcal {H} _ {p} ^ {i - 1} = \\mathcal {K} ^ {I} W _ {1} ^ {i} + b _ {1} ^ {i}, \\mathcal {H} ^ {i - 1} W _ {2} ^ {i} + b _ {2} ^ {i} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 392, + 890, + 417 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} ^ {i} = c o n c a t \\left(\\mathcal {K} _ {p} ^ {I}, \\mathcal {H} _ {p} ^ {i - 1}\\right) W _ {3} ^ {i} + b _ {3} ^ {i}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 415, + 810, + 433 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_1^i, W_2^i \\in \\mathbb{R}^{d \\times d}$ , $W_3^i \\in \\mathbb{R}^{2d \\times d}$ and $\\text{concat}(\\cdot)$ is concatenation operation in the embedding dimension.", + "bbox": [ + 500, + 444, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Encoder-Decoder We use encoder-decoder structure as Language Generation Model based on the Pre-Norm Transformer [45]. Specifically, the encoder is formulated as:", + "bbox": [ + 498, + 476, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} ^ {I} = \\operatorname {E n c o d e r} (\\mathcal {V} ^ {\\mathcal {I}}) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 532, + 890, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{V}^{\\mathcal{I}}\\in \\mathbb{R}^{m\\times d}$ is the visual features extracted by the Visual Extractor (e.g., ResNet [13], ViT [11]), $S^I\\in \\mathbb{R}^{m\\times d}$ , with $m$ patches and embedding dimension $d$ . The decoding process of predicting the current word is:", + "bbox": [ + 498, + 561, + 890, + 623 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH _ {t} ^ {i} = \\left\\{ \\begin{array}{l l} D e c o d e r \\left(Y _ {< t}, \\mathcal {S} ^ {I}\\right), & \\text {i f} i = 1 \\\\ D e c o d e r \\left(\\mathcal {M} _ {< t} ^ {i}, \\mathcal {S} ^ {I}\\right), & \\text {i f} i \\geqslant 2 \\end{array} \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 633, + 890, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Y_{